LMFDB - Embedded newform 13.7.f.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,7,Mod(2,13)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("13.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99070308706$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	13.7
Dual form			13.7.f.a.2.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.5088 - 3.35172i) q^{2} +(-1.31220 + 2.27280i) q^{3} +(89.8106 - 51.8522i) q^{4} +(24.9454 + 24.9454i) q^{5} +(-8.79628 + 32.8282i) q^{6} +(-400.516 - 107.318i) q^{7} +(363.576 - 363.576i) q^{8} +(361.056 + 625.368i) q^{9} +O(q^{10})$	\(q+(12.5088 - 3.35172i) q^{2} +(-1.31220 + 2.27280i) q^{3} +(89.8106 - 51.8522i) q^{4} +(24.9454 + 24.9454i) q^{5} +(-8.79628 + 32.8282i) q^{6} +(-400.516 - 107.318i) q^{7} +(363.576 - 363.576i) q^{8} +(361.056 + 625.368i) q^{9} +(395.648 + 228.427i) q^{10} +(-169.267 - 631.712i) q^{11} +272.162i q^{12} +(-1807.65 + 1248.68i) q^{13} -5369.68 q^{14} +(-89.4294 + 23.9625i) q^{15} +(10.7557 - 18.6295i) q^{16} +(4044.24 - 2334.94i) q^{17} +(6612.44 + 6612.44i) q^{18} +(2588.98 - 9662.21i) q^{19} +(3533.84 + 946.889i) q^{20} +(769.471 - 769.471i) q^{21} +(-4234.65 - 7334.63i) q^{22} +(13824.2 + 7981.38i) q^{23} +(349.251 + 1303.42i) q^{24} -14380.5i q^{25} +(-18426.3 + 21678.3i) q^{26} -3808.31 q^{27} +(-41535.3 + 11129.3i) q^{28} +(6616.02 - 11459.3i) q^{29} +(-1038.34 + 599.486i) q^{30} +(-6057.12 - 6057.12i) q^{31} +(-8444.89 + 31516.8i) q^{32} +(1657.87 + 444.225i) q^{33} +(42762.5 - 42762.5i) q^{34} +(-7313.95 - 12668.1i) q^{35} +(64853.3 + 37443.1i) q^{36} +(21020.2 + 78448.4i) q^{37} -129540. i q^{38} +(-466.005 - 5746.96i) q^{39} +18139.1 q^{40} +(-114237. + 30609.7i) q^{41} +(7046.11 - 12204.2i) q^{42} +(-38616.8 + 22295.4i) q^{43} +(-47957.6 - 47957.6i) q^{44} +(-6593.36 + 24606.8i) q^{45} +(199675. + 53502.8i) q^{46} +(34061.0 - 34061.0i) q^{47} +(28.2274 + 48.8913i) q^{48} +(47009.1 + 27140.7i) q^{49} +(-48199.3 - 179882. i) q^{50} +12255.7i q^{51} +(-97599.2 + 205876. i) q^{52} -14637.4 q^{53} +(-47637.4 + 12764.4i) q^{54} +(11535.9 - 19980.8i) q^{55} +(-184636. + 106600. i) q^{56} +(18563.0 + 18563.0i) q^{57} +(44350.1 - 165517. i) q^{58} +(-101893. - 27302.2i) q^{59} +(-6789.20 + 6789.20i) q^{60} +(107360. + 185953. i) q^{61} +(-96069.2 - 55465.6i) q^{62} +(-77495.7 - 289218. i) q^{63} +423919. i q^{64} +(-76241.5 - 13943.7i) q^{65} +22226.9 q^{66} +(470454. - 126058. i) q^{67} +(242144. - 419405. i) q^{68} +(-36280.2 + 20946.4i) q^{69} +(-133949. - 133949. i) q^{70} +(4932.21 - 18407.2i) q^{71} +(358640. + 96097.3i) q^{72} +(158416. - 158416. i) q^{73} +(525875. + 910842. i) q^{74} +(32683.9 + 18870.1i) q^{75} +(-268489. - 1.00201e6i) q^{76} +271176. i q^{77} +(-25091.4 - 70325.6i) q^{78} -280091. q^{79} +(733.027 - 196.414i) q^{80} +(-258213. + 447238. i) q^{81} +(-1.32637e6 + 765781. i) q^{82} +(-662356. - 662356. i) q^{83} +(29207.9 - 109005. i) q^{84} +(159131. + 42639.1i) q^{85} +(-408322. + 408322. i) q^{86} +(17363.1 + 30073.8i) q^{87} +(-291217. - 168134. i) q^{88} +(-4803.85 - 17928.2i) q^{89} +329900. i q^{90} +(858000. - 306124. i) q^{91} +1.65541e6 q^{92} +(21714.8 - 5818.47i) q^{93} +(311899. - 540225. i) q^{94} +(305611. - 176445. i) q^{95} +(-60549.9 - 60549.9i) q^{96} +(-295344. + 1.10224e6i) q^{97} +(678996. + 181936. i) q^{98} +(333938. - 333938. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9} + 4674 q^{10} + 228 q^{11} - 1552 q^{13} - 14616 q^{14} + 7486 q^{15} - 2138 q^{16} + 20898 q^{17} - 5630 q^{18} - 14036 q^{19} - 14634 q^{20} - 314 q^{21} + 37852 q^{22} + 29634 q^{23} + 47154 q^{24} + 510 q^{26} - 107060 q^{27} - 40572 q^{28} + 1026 q^{29} - 247734 q^{30} - 118116 q^{31} + 180876 q^{32} + 306046 q^{33} + 101898 q^{34} + 104862 q^{35} + 105066 q^{36} - 31470 q^{37} + 28510 q^{39} - 275328 q^{40} - 357216 q^{41} - 25636 q^{42} - 480486 q^{43} - 797712 q^{44} + 464248 q^{45} + 1012050 q^{46} + 140028 q^{47} + 676102 q^{48} + 854562 q^{49} + 756714 q^{50} - 771704 q^{52} - 1397076 q^{53} - 1271048 q^{54} - 205490 q^{55} - 1461108 q^{56} - 1483394 q^{57} + 1133806 q^{58} + 1568052 q^{59} + 886808 q^{60} + 768676 q^{61} + 3741966 q^{62} + 1336264 q^{63} - 946968 q^{65} - 5076928 q^{66} - 1489892 q^{67} - 569052 q^{68} - 1475766 q^{69} - 2626556 q^{70} + 2136948 q^{71} + 4787052 q^{72} + 326326 q^{73} + 2159718 q^{74} + 3466008 q^{75} + 1522158 q^{76} - 1573544 q^{78} - 1734344 q^{79} - 5214300 q^{80} - 773072 q^{81} - 3540426 q^{82} - 3642132 q^{83} + 2952364 q^{84} + 3509916 q^{85} - 132324 q^{86} + 531698 q^{87} + 4478052 q^{88} + 632754 q^{89} - 2946788 q^{91} - 1656060 q^{92} - 295514 q^{93} + 1552210 q^{94} - 2753718 q^{95} - 3979208 q^{96} + 2258214 q^{97} + 4984308 q^{98} + 4336480 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9 + 4674 * q^10 + 228 * q^11 - 1552 * q^13 - 14616 * q^14 + 7486 * q^15 - 2138 * q^16 + 20898 * q^17 - 5630 * q^18 - 14036 * q^19 - 14634 * q^20 - 314 * q^21 + 37852 * q^22 + 29634 * q^23 + 47154 * q^24 + 510 * q^26 - 107060 * q^27 - 40572 * q^28 + 1026 * q^29 - 247734 * q^30 - 118116 * q^31 + 180876 * q^32 + 306046 * q^33 + 101898 * q^34 + 104862 * q^35 + 105066 * q^36 - 31470 * q^37 + 28510 * q^39 - 275328 * q^40 - 357216 * q^41 - 25636 * q^42 - 480486 * q^43 - 797712 * q^44 + 464248 * q^45 + 1012050 * q^46 + 140028 * q^47 + 676102 * q^48 + 854562 * q^49 + 756714 * q^50 - 771704 * q^52 - 1397076 * q^53 - 1271048 * q^54 - 205490 * q^55 - 1461108 * q^56 - 1483394 * q^57 + 1133806 * q^58 + 1568052 * q^59 + 886808 * q^60 + 768676 * q^61 + 3741966 * q^62 + 1336264 * q^63 - 946968 * q^65 - 5076928 * q^66 - 1489892 * q^67 - 569052 * q^68 - 1475766 * q^69 - 2626556 * q^70 + 2136948 * q^71 + 4787052 * q^72 + 326326 * q^73 + 2159718 * q^74 + 3466008 * q^75 + 1522158 * q^76 - 1573544 * q^78 - 1734344 * q^79 - 5214300 * q^80 - 773072 * q^81 - 3540426 * q^82 - 3642132 * q^83 + 2952364 * q^84 + 3509916 * q^85 - 132324 * q^86 + 531698 * q^87 + 4478052 * q^88 + 632754 * q^89 - 2946788 * q^91 - 1656060 * q^92 - 295514 * q^93 + 1552210 * q^94 - 2753718 * q^95 - 3979208 * q^96 + 2258214 * q^97 + 4984308 * q^98 + 4336480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	12.5088	−	3.35172i	1.56360	−	0.418966i	0.629800	−	0.776758i	$-0.283137\pi$
$2$	12.5088	−	3.35172i	1.56360	−	0.418966i	0.933801	+	0.357792i	$0.116470\pi$
$3$	−1.31220	+	2.27280i	−0.0486001	+	0.0841778i	−0.889302	−	0.457320i	$-0.848809\pi$
$3$	−1.31220	+	2.27280i	−0.0486001	+	0.0841778i	0.840702	+	0.541498i	$0.182143\pi$
$4$	89.8106	−	51.8522i	1.40329	−	0.810190i
$5$	24.9454	+	24.9454i	0.199563	+	0.199563i	0.799813	−	0.600249i	$-0.204932\pi$
$5$	24.9454	+	24.9454i	0.199563	+	0.199563i	−0.600249	+	0.799813i	$0.704932\pi$
$6$	−8.79628	+	32.8282i	−0.0407235	+	0.151982i
$7$	−400.516	−	107.318i	−1.16769	−	0.312880i	−0.377654	−	0.925947i	$-0.623269\pi$
$7$	−400.516	−	107.318i	−1.16769	−	0.312880i	−0.790032	+	0.613066i	$0.789936\pi$
$8$	363.576	−	363.576i	0.710109	−	0.710109i
$9$	361.056	+	625.368i	0.495276	+	0.857843i
$10$	395.648	+	228.427i	0.395648	+	0.228427i
$11$	−169.267	−	631.712i	−0.127173	−	0.474615i	0.872735	−	0.488194i	$-0.162344\pi$
$11$	−169.267	−	631.712i	−0.127173	−	0.474615i	−0.999908	+	0.0135791i	$0.995677\pi$
$12$			272.162i			0.157501i
$13$	−1807.65	+	1248.68i	−0.822781	+	0.568358i
$13$	−1807.65	+	1248.68i	−0.822781	+	0.568358i
$14$	−5369.68			−1.95688
$15$	−89.4294	+	23.9625i	−0.0264976	+	0.00710001i
$16$	10.7557	−	18.6295i	0.00262591	−	0.00454822i
$17$	4044.24	−	2334.94i	0.823171	−	0.475258i	−0.0283376	−	0.999598i	$-0.509021\pi$
$17$	4044.24	−	2334.94i	0.823171	−	0.475258i	0.851509	+	0.524340i	$0.175688\pi$
$18$	6612.44	+	6612.44i	1.13382	+	1.13382i
$19$	2588.98	−	9662.21i	0.377458	−	1.40869i	−0.472263	−	0.881458i	$-0.656563\pi$
$19$	2588.98	−	9662.21i	0.377458	−	1.40869i	0.849721	−	0.527233i	$-0.176771\pi$
$20$	3533.84	+	946.889i	0.441730	+	0.118361i
$21$	769.471	−	769.471i	0.0830872	−	0.0830872i
$22$	−4234.65	−	7334.63i	−0.397695	−	0.688827i
$23$	13824.2	+	7981.38i	1.13620	+	0.655986i	0.945487	−	0.325660i	$-0.105586\pi$
$23$	13824.2	+	7981.38i	1.13620	+	0.655986i	0.190714	+	0.981646i	$0.438920\pi$
$24$	349.251	+	1303.42i	0.0252641	+	0.0942868i
$25$		−	14380.5i		−	0.920349i
$26$	−18426.3	+	21678.3i	−1.04838	+	1.23340i
$27$	−3808.31			−0.193482
$28$	−41535.3	+	11129.3i	−1.89210	+	0.506985i
$29$	6616.02	−	11459.3i	0.271271	−	0.469854i	−0.697917	−	0.716179i	$-0.745890\pi$
$29$	6616.02	−	11459.3i	0.271271	−	0.469854i	0.969187	+	0.246324i	$0.0792229\pi$
$30$	−1038.34	+	599.486i	−0.0384570	+	0.0222032i
$31$	−6057.12	−	6057.12i	−0.203321	−	0.203321i	0.598100	−	0.801421i	$-0.295922\pi$
$31$	−6057.12	−	6057.12i	−0.203321	−	0.203321i	−0.801421	+	0.598100i	$0.795922\pi$
$32$	−8444.89	+	31516.8i	−0.257718	+	0.961815i
$33$	1657.87	+	444.225i	0.0461327	+	0.0123612i
$34$	42762.5	−	42762.5i	1.08799	−	1.08799i
$35$	−7313.95	−	12668.1i	−0.170588	−	0.295467i
$36$	64853.3	+	37443.1i	1.39003	+	0.802536i
$37$	21020.2	+	78448.4i	0.414984	+	1.54874i	0.784868	+	0.619663i	$0.212731\pi$
$37$	21020.2	+	78448.4i	0.414984	+	1.54874i	−0.369884	+	0.929078i	$0.620603\pi$
$38$		−	129540.i		−	2.36077i
$39$	−466.005	−	5746.96i	−0.00785591	−	0.0968822i
$40$	18139.1			0.283424
$41$	−114237.	+	30609.7i	−1.65750	+	0.444127i	−0.961700	−	0.274105i	$-0.911618\pi$
$41$	−114237.	+	30609.7i	−1.65750	+	0.444127i	−0.695804	+	0.718232i	$0.744952\pi$
$42$	7046.11	−	12204.2i	0.0951046	−	0.164726i
$43$	−38616.8	+	22295.4i	−0.485703	+	0.280421i	−0.722790	−	0.691068i	$-0.757141\pi$
$43$	−38616.8	+	22295.4i	−0.485703	+	0.280421i	0.237087	+	0.971488i	$0.423807\pi$
$44$	−47957.6	−	47957.6i	−0.562988	−	0.562988i
$45$	−6593.36	+	24606.8i	−0.0723551	+	0.270033i
$46$	199675.	+	53502.8i	2.05140	+	0.549671i
$47$	34061.0	−	34061.0i	0.328068	−	0.328068i	−0.523784	−	0.851851i	$-0.675480\pi$
$47$	34061.0	−	34061.0i	0.328068	−	0.328068i	0.851851	+	0.523784i	$0.175480\pi$
$48$	28.2274	+	48.8913i	0.000255239	+	0.000442087i
$49$	47009.1	+	27140.7i	0.399571	+	0.230692i
$50$	−48199.3	−	179882.i	−0.385595	−	1.43906i
$51$			12255.7i			0.0923904i
$52$	−97599.2	+	205876.i	−0.694123	+	1.46418i
$53$	−14637.4			−0.0983186			−0.0491593	−	0.998791i	$-0.515654\pi$
$53$	−14637.4			−0.0983186			−0.0491593	+	0.998791i	$0.515654\pi$
$54$	−47637.4	+	12764.4i	−0.302529	+	0.0810623i
$55$	11535.9	−	19980.8i	0.0693367	−	0.120095i
$56$	−184636.	+	106600.i	−1.05136	+	0.607005i
$57$	18563.0	+	18563.0i	0.100236	+	0.100236i
$58$	44350.1	−	165517.i	0.227306	−	0.848318i
$59$	−101893.	−	27302.2i	−0.496124	−	0.132936i	0.00207678	−	0.999998i	$-0.499339\pi$
$59$	−101893.	−	27302.2i	−0.496124	−	0.132936i	−0.498200	+	0.867062i	$0.666006\pi$
$60$	−6789.20	+	6789.20i	−0.0314315	+	0.0314315i
$61$	107360.	+	185953.i	0.472991	+	0.819245i	0.999522	−	0.0309113i	$-0.00984093\pi$
$61$	107360.	+	185953.i	0.472991	+	0.819245i	−0.526531	+	0.850156i	$0.676508\pi$
$62$	−96069.2	−	55465.6i	−0.403097	−	0.232728i
$63$	−77495.7	−	289218.i	−0.309924	−	1.15665i
$64$			423919.i			1.61712i
$65$	−76241.5	−	13943.7i	−0.277620	−	0.0507735i
$66$	22226.9			0.0773120
$67$	470454.	−	126058.i	1.56420	−	0.419126i	0.630210	−	0.776425i	$-0.282969\pi$
$67$	470454.	−	126058.i	1.56420	−	0.419126i	0.933990	+	0.357299i	$0.116302\pi$
$68$	242144.	−	419405.i	0.770099	−	1.33385i
$69$	−36280.2	+	20946.4i	−0.110439	+	0.0637620i
$70$	−133949.	−	133949.i	−0.390522	−	0.390522i
$71$	4932.21	−	18407.2i	0.0137805	−	0.0514297i	−0.958693	−	0.284442i	$-0.908192\pi$
$71$	4932.21	−	18407.2i	0.0137805	−	0.0514297i	0.972474	+	0.233012i	$0.0748583\pi$
$72$	358640.	+	96097.3i	0.960862	+	0.257462i
$73$	158416.	−	158416.i	0.407222	−	0.407222i	−0.473547	−	0.880769i	$-0.657027\pi$
$73$	158416.	−	158416.i	0.407222	−	0.407222i	0.880769	+	0.473547i	$0.157027\pi$
$74$	525875.	+	910842.i	1.29774	+	2.24775i
$75$	32683.9	+	18870.1i	0.0774730	+	0.0447290i
$76$	−268489.	−	1.00201e6i	−0.611625	−	2.28262i
$77$			271176.i			0.593991i
$78$	−25091.4	−	70325.6i	−0.0528738	−	0.148194i
$79$	−280091.			−0.568091			−0.284046	−	0.958811i	$-0.591677\pi$
$79$	−280091.			−0.568091			−0.284046	+	0.958811i	$0.591677\pi$
$80$	733.027	−	196.414i	0.00143169	−	0.000383621i
$81$	−258213.	+	447238.i	−0.485873	+	0.841556i
$82$	−1.32637e6	+	765781.i	−2.40560	+	1.38887i
$83$	−662356.	−	662356.i	−1.15840	−	1.15840i	−0.984820	−	0.173576i	$-0.944468\pi$
$83$	−662356.	−	662356.i	−1.15840	−	1.15840i	−0.173576	−	0.984820i	$-0.555532\pi$
$84$	29207.9	−	109005.i	0.0492791	−	0.183912i
$85$	159131.	+	42639.1i	0.259119	+	0.0694307i
$86$	−408322.	+	408322.i	−0.641959	+	0.641959i
$87$	17363.1	+	30073.8i	0.0263675	+	0.0456699i
$88$	−291217.	−	168134.i	−0.427335	−	0.246722i
$89$	−4803.85	−	17928.2i	−0.00681427	−	0.0254312i	0.962435	−	0.271512i	$-0.0875237\pi$
$89$	−4803.85	−	17928.2i	−0.00681427	−	0.0254312i	−0.969249	+	0.246081i	$0.920857\pi$
$90$			329900.i			0.452538i
$91$	858000.	−	306124.i	1.13858	−	0.406232i
$92$	1.65541e6			2.12589
$93$	21714.8	−	5818.47i	0.0269965	−	0.00723369i
$94$	311899.	−	540225.i	0.375518	−	0.650416i
$95$	305611.	−	176445.i	0.356450	−	0.205796i
$96$	−60549.9	−	60549.9i	−0.0684384	−	0.0684384i
$97$	−295344.	+	1.10224e6i	−0.323603	+	1.20770i	0.592106	+	0.805860i	$0.298297\pi$
$97$	−295344.	+	1.10224e6i	−0.323603	+	1.20770i	−0.915709	+	0.401843i	$0.868370\pi$
$98$	678996.	+	181936.i	0.721421	+	0.193304i
$99$	333938.	−	333938.i	0.344160	−	0.344160i
$100$	−745658.	−	1.29152e6i	−0.745658	−	1.29152i
$101$	−197622.	−	114097.i	−0.191810	−	0.110742i	0.401019	−	0.916070i	$-0.368656\pi$
$101$	−197622.	−	114097.i	−0.191810	−	0.110742i	−0.592830	+	0.805328i	$0.701989\pi$
$102$	41077.6	+	153304.i	0.0387084	+	0.144462i
$103$		−	844428.i		−	0.772772i	−0.922337	−	0.386386i	$-0.873723\pi$
$103$		−	844428.i		−	0.772772i	0.922337	−	0.386386i	$-0.126277\pi$
$104$	−203227.	+	1.11121e6i	−0.180668	+	0.987861i
$105$	38389.6			0.0331623
$106$	−183096.	+	49060.4i	−0.153731	+	0.0411921i
$107$	183259.	−	317414.i	0.149594	−	0.259104i	−0.781484	−	0.623926i	$-0.785537\pi$
$107$	183259.	−	317414.i	0.149594	−	0.259104i	0.931077	+	0.364822i	$0.118870\pi$
$108$	−342026.	+	197469.i	−0.271511	+	0.156757i
$109$	−239407.	−	239407.i	−0.184866	−	0.184866i	0.608606	−	0.793473i	$-0.291729\pi$
$109$	−239407.	−	239407.i	−0.184866	−	0.184866i	−0.793473	+	0.608606i	$0.791729\pi$
$110$	77330.3	−	288601.i	0.0580994	−	0.216830i
$111$	−205880.	−	55165.5i	−0.150538	−	0.0403365i
$112$	−6307.13	+	6307.13i	−0.00448929	+	0.00448929i
$113$	1.14875e6	+	1.98970e6i	0.796145	+	1.37896i	0.922110	+	0.386928i	$0.126464\pi$
$113$	1.14875e6	+	1.98970e6i	0.796145	+	1.37896i	−0.125965	+	0.992035i	$0.540203\pi$
$114$	294419.	+	169983.i	0.198725	+	0.114734i
$115$	145751.	+	543948.i	0.0958333	+	0.357655i
$116$		−	1.37222e6i		−	0.879123i
$117$	−1.43355e6	−	679602.i	−0.895066	−	0.424323i
$118$	−1.36607e6			−0.831435
$119$	−1.87037e6	+	501163.i	−1.10990	+	0.297398i
$120$	−23802.2	+	41226.6i	−0.0137744	+	0.0238580i
$121$	1.16381e6	−	671925.i	0.656939	−	0.379284i
$122$	1.96621e6	+	1.96621e6i	1.08280	+	1.08280i
$123$	80332.1	−	299804.i	0.0431692	−	0.161110i
$124$	−858069.	−	229919.i	−0.450046	−	0.120590i
$125$	748499.	−	748499.i	0.383231	−	0.383231i
$126$	−1.93876e6	−	3.35803e6i	−0.969196	−	1.67870i
$127$	2.93309e6	+	1.69342e6i	1.43191	+	0.826712i	0.997266	−	0.0738916i	$-0.0235419\pi$
$127$	2.93309e6	+	1.69342e6i	1.43191	+	0.826712i	0.434641	+	0.900604i	$0.356875\pi$
$128$	880386.	+	3.28565e6i	0.419801	+	1.56672i
$129$		−	117024.i		−	0.0545139i
$130$	−1.00043e6	+	81121.8i	−0.455360	+	0.0369239i
$131$	−4.30851e6			−1.91652			−0.958259	−	0.285900i	$-0.907707\pi$
$131$	−4.30851e6			−1.91652			−0.958259	+	0.285900i	$0.907707\pi$
$132$	171928.	−	46068.0i	0.0747524	−	0.0200299i
$133$	−2.07386e6	+	3.59203e6i	−0.881504	+	1.52681i
$134$	5.46230e6	−	3.15366e6i	2.27019	−	1.31069i
$135$	−94999.8	−	94999.8i	−0.0386119	−	0.0386119i
$136$	621459.	−	2.31932e6i	0.247056	−	0.922027i
$137$	−2.56532e6	−	687375.i	−0.997654	−	0.267321i	−0.277192	−	0.960815i	$-0.589404\pi$
$137$	−2.56532e6	−	687375.i	−0.997654	−	0.267321i	−0.720462	+	0.693494i	$0.756070\pi$
$138$	−383615.	+	383615.i	−0.145968	+	0.145968i
$139$	63545.5	+	110064.i	0.0236614	+	0.0409827i	0.877614	−	0.479369i	$-0.159134\pi$
$139$	63545.5	+	110064.i	0.0236614	+	0.0409827i	−0.853952	+	0.520351i	$0.825801\pi$
$140$	−1.31374e6	−	758489.i	−0.478769	−	0.276417i
$141$	32718.9	+	122109.i	0.0116719	+	0.0435601i
$142$		−	246784.i		−	0.0861890i
$143$	1.09478e6	+	930555.i	0.374387	+	0.318225i
$144$	15533.7			0.00520221
$145$	450896.	−	120817.i	0.147901	−	0.0396301i
$146$	1.45063e6	−	2.51256e6i	0.466120	−	0.807344i
$147$	−123371.	+	71228.2i	−0.0388383	+	0.0224233i
$148$	5.95555e6	+	5.95555e6i	1.83712	+	1.83712i
$149$	720669.	−	2.68957e6i	0.217860	−	0.813064i	−0.767280	−	0.641312i	$-0.778391\pi$
$149$	720669.	−	2.68957e6i	0.217860	−	0.813064i	0.985140	−	0.171752i	$-0.0549428\pi$
$150$	472084.	+	126495.i	0.139877	+	0.0374799i
$151$	2.69616e6	−	2.69616e6i	0.783097	−	0.783097i	−0.197255	−	0.980352i	$-0.563203\pi$
$151$	2.69616e6	−	2.69616e6i	0.783097	−	0.783097i	0.980352	+	0.197255i	$0.0632027\pi$
$152$	−2.57166e6	−	4.45424e6i	−0.732288	−	1.26836i
$153$	2.92040e6	+	1.68609e6i	0.815394	+	0.470768i
$154$	908909.	+	3.39209e6i	0.248862	+	0.928765i
$155$		−	302195.i		−	0.0811507i
$156$	−339844.	−	491974.i	−0.0895171	−	0.129589i
$157$	4.22843e6			1.09265			0.546325	−	0.837574i	$-0.316027\pi$
$157$	4.22843e6			1.09265			0.546325	+	0.837574i	$0.316027\pi$
$158$	−3.50361e6	+	938789.i	−0.888268	+	0.238011i
$159$	19207.2	−	33267.8i	0.00477829	−	0.00827624i
$160$	−996860.	+	575538.i	−0.243374	+	0.140512i
$161$	−4.68025e6	−	4.68025e6i	−1.12148	−	1.12148i
$162$	−1.73092e6	+	6.45987e6i	−0.407128	+	1.51942i
$163$	−4.39530e6	−	1.17772e6i	−1.01491	−	0.271943i	−0.287228	−	0.957862i	$-0.592734\pi$
$163$	−4.39530e6	−	1.17772e6i	−1.01491	−	0.271943i	−0.727678	+	0.685919i	$0.759400\pi$
$164$	−8.67250e6	+	8.67250e6i	−1.96613	+	1.96613i
$165$	30274.9	+	52437.6i	0.00673954	+	0.0116732i
$166$	−1.05053e7	−	6.06525e6i	−2.29660	−	1.32594i
$167$	817591.	+	3.05129e6i	0.175544	+	0.655140i	0.996458	+	0.0840883i	$0.0267978\pi$
$167$	817591.	+	3.05129e6i	0.175544	+	0.655140i	−0.820914	+	0.571052i	$0.806536\pi$
$168$		−	559522.i		−	0.118002i
$169$	1.70839e6	−	4.51436e6i	0.353938	−	0.935269i
$170$	2.13346e6			0.434248
$171$	6.97720e6	−	1.86954e6i	1.39538	−	0.373891i
$172$	−2.31213e6	+	4.00473e6i	−0.454388	+	0.787023i
$173$	3.36007e6	−	1.93994e6i	0.648948	−	0.374671i	−0.139105	−	0.990278i	$-0.544422\pi$
$173$	3.36007e6	−	1.93994e6i	0.648948	−	0.374671i	0.788053	+	0.615607i	$0.211089\pi$
$174$	317991.	+	317991.i	0.0603625	+	0.0603625i
$175$	−1.54328e6	+	5.75960e6i	−0.287959	+	1.07468i
$176$	−13589.1	−	3641.18i	−0.00249260	−	0.000667889i
$177$	195757.	−	195757.i	0.0353019	−	0.0353019i
$178$	−120181.	−	208159.i	−0.0213096	−	0.0369093i
$179$	877019.	+	506347.i	0.152915	+	0.0882854i	0.574505	−	0.818501i	$-0.305195\pi$
$179$	877019.	+	506347.i	0.152915	+	0.0882854i	−0.421590	+	0.906786i	$0.638528\pi$
$180$	683760.	+	2.55183e6i	0.117243	+	0.437556i
$181$		−	3.85774e6i		−	0.650574i	−0.945615	−	0.325287i	$-0.894539\pi$
$181$		−	3.85774e6i		−	0.650574i	0.945615	−	0.325287i	$-0.105461\pi$
$182$	9.70651e6	−	6.70503e6i	1.61009	−	1.11221i
$183$	−563512.			−0.0919496
$184$	7.92797e6	−	2.12429e6i	1.27265	−	0.341005i
$185$	−1.43257e6	+	2.48129e6i	−0.226256	+	0.391888i
$186$	252125.	−	145564.i	0.0391811	−	0.0226212i
$187$	−2.15957e6	−	2.15957e6i	−0.330249	−	0.330249i
$188$	1.29290e6	−	4.82517e6i	0.194577	−	0.726171i
$189$	1.52529e6	+	408700.i	0.225926	+	0.0605368i
$190$	3.23144e6	−	3.23144e6i	0.471124	−	0.471124i
$191$	2.86422e6	+	4.96098e6i	0.411061	+	0.711979i	0.995006	−	0.0998143i	$-0.0318249\pi$
$191$	2.86422e6	+	4.96098e6i	0.411061	+	0.711979i	−0.583945	+	0.811793i	$0.698492\pi$
$192$	−963483.	−	556267.i	−0.136126	−	0.0785923i
$193$	−1.95867e6	−	7.30986e6i	−0.272452	−	1.01680i	−0.957530	−	0.288334i	$-0.906899\pi$
$193$	−1.95867e6	−	7.30986e6i	−0.272452	−	1.01680i	0.685078	−	0.728470i	$-0.259768\pi$
$194$			1.47776e7i			2.02394i
$195$	131736.	−	154985.i	0.0177664	−	0.0209019i
$196$	5.62922e6			0.747618
$197$	−173531.	+	46497.5i	−0.0226975	+	0.00608178i	−0.270150	−	0.962818i	$-0.587073\pi$
$197$	−173531.	+	46497.5i	−0.0226975	+	0.00608178i	0.247452	+	0.968900i	$0.420407\pi$
$198$	3.05790e6	−	5.29643e6i	0.393937	−	0.682319i
$199$	−7.25547e6	+	4.18895e6i	−0.920675	+	0.531552i	−0.883850	−	0.467770i	$-0.845058\pi$
$199$	−7.25547e6	+	4.18895e6i	−0.920675	+	0.531552i	−0.0368244	+	0.999322i	$0.511724\pi$
$200$	−5.22839e6	−	5.22839e6i	−0.653548	−	0.653548i
$201$	−330826.	+	1.23466e6i	−0.0407391	+	0.152041i
$202$	−2.85444e6	−	764845.i	−0.346312	−	0.0927939i
$203$	−3.87961e6	+	3.87961e6i	−0.463767	+	0.463767i
$204$	635483.	+	1.10069e6i	0.0748538	+	0.129651i
$205$	−3.61326e6	−	2.08611e6i	−0.419409	−	0.242146i
$206$	−2.83029e6	−	1.05628e7i	−0.323765	−	1.20831i
$207$			1.15269e7i			1.29958i
$208$	3819.71	+	47106.1i	0.000424463	+	0.00523465i
$209$	−6.54197e6			−0.716588
$210$	480208.	−	128671.i	0.0518527	−	0.0138939i
$211$	−4.52220e6	+	7.83268e6i	−0.481396	+	0.833802i	−0.999772	−	0.0213508i	$-0.993203\pi$
$211$	−4.52220e6	+	7.83268e6i	−0.481396	+	0.833802i	0.518376	+	0.855153i	$0.326537\pi$
$212$	−1.31459e6	+	758979.i	−0.137969	+	0.0796567i
$213$	35364.0	+	35364.0i	0.00365950	+	0.00365950i
$214$	1.22847e6	−	4.58470e6i	0.125349	−	0.467810i
$215$	−1.51948e6	−	407143.i	−0.152890	−	0.0409668i
$216$	−1.38461e6	+	1.38461e6i	−0.137393	+	0.137393i
$217$	1.77594e6	+	3.07602e6i	0.173800	+	0.301030i
$218$	−3.79713e6	−	2.19227e6i	−0.366510	−	0.211605i
$219$	152174.	+	567922.i	0.0144880	+	0.0540700i
$220$		−	2.39265e6i		−	0.224704i
$221$	−4.39497e6	+	9.27074e6i	−0.407173	+	0.858890i
$222$	−2.76022e6			−0.252281
$223$	9.34354e6	−	2.50359e6i	0.842553	−	0.225761i	0.188370	−	0.982098i	$-0.439680\pi$
$223$	9.34354e6	−	2.50359e6i	0.842553	−	0.225761i	0.654182	+	0.756337i	$0.273013\pi$
$224$	6.76463e6	−	1.17167e7i	0.601867	−	1.04246i
$225$	8.99307e6	−	5.19215e6i	0.789515	−	0.455827i
$226$	2.10385e7	+	2.10385e7i	1.82259	+	1.82259i
$227$	2.93077e6	−	1.09378e7i	0.250556	−	0.935087i	−0.719953	−	0.694023i	$-0.755837\pi$
$227$	2.93077e6	−	1.09378e7i	0.250556	−	0.935087i	0.970509	−	0.241065i	$-0.0774965\pi$
$228$	2.62969e6	+	704623.i	0.221871	+	0.0594501i
$229$	−1.76098e6	+	1.76098e6i	−0.146639	+	0.146639i	−0.776615	−	0.629976i	$-0.783065\pi$
$229$	−1.76098e6	+	1.76098e6i	−0.146639	+	0.146639i	0.629976	+	0.776615i	$0.283065\pi$
$230$	3.64633e6	+	6.31563e6i	0.299690	+	0.519079i
$231$	−616330.	−	355838.i	−0.0500009	−	0.0288680i
$232$	−1.76089e6	−	6.57174e6i	−0.141016	−	0.526280i
$233$		−	6.96111e6i		−	0.550314i	−0.961399	−	0.275157i	$-0.911270\pi$
$233$		−	6.96111e6i		−	0.550314i	0.961399	−	0.275157i	$-0.0887299\pi$
$234$	−2.02098e7	−	3.69614e6i	−1.57730	−	0.288470i
$235$	1.69933e6			0.130941
$236$	−1.05668e7	+	2.83136e6i	−0.803909	+	0.215407i
$237$	367536.	−	636592.i	0.0276093	−	0.0478207i
$238$	−2.17163e7	+	1.25379e7i	−1.61085	+	0.930024i
$239$	−8.08660e6	−	8.08660e6i	−0.592341	−	0.592341i	0.345922	−	0.938263i	$-0.387566\pi$
$239$	−8.08660e6	−	8.08660e6i	−0.592341	−	0.592341i	−0.938263	+	0.345922i	$0.887566\pi$
$240$	−515.470	+	1923.76i	−3.72881e−5	+	0.000139161i
$241$	−2.82455e6	−	756837.i	−0.201790	−	0.0540694i	0.156508	−	0.987677i	$-0.449976\pi$
$241$	−2.82455e6	−	756837.i	−0.201790	−	0.0540694i	−0.358298	+	0.933607i	$0.616643\pi$
$242$	1.23057e7	−	1.23057e7i	0.868284	−	0.868284i
$243$	−2.06578e6	−	3.57804e6i	−0.143968	−	0.249360i
$244$	1.92841e7	+	1.11337e7i	1.32749	+	0.766425i
$245$	495625.	+	1.84970e6i	0.0337020	+	0.125777i
$246$		−	4.01944e6i		−	0.269998i
$247$	7.38506e6	+	2.06987e7i	0.490076	+	1.37358i
$248$	−4.40445e6			−0.288760
$249$	2.37455e6	−	636258.i	0.153809	−	0.0412131i
$250$	6.85406e6	−	1.18716e7i	0.438660	−	0.759782i
$251$	5.83721e6	−	3.37012e6i	0.369134	−	0.213120i	−0.303946	−	0.952689i	$-0.598304\pi$
$251$	5.83721e6	−	3.37012e6i	0.369134	−	0.213120i	0.673080	+	0.739569i	$0.264971\pi$
$252$	−2.19565e7	−	2.19565e7i	−1.37202	−	1.37202i
$253$	2.70197e6	−	1.00839e7i	0.166847	−	0.622681i
$254$	4.23654e7	+	1.13518e7i	2.58530	+	0.692728i
$255$	−305723.	+	305723.i	−0.0184377	+	0.0184377i
$256$	8.45976e6	+	1.46527e7i	0.504241	+	0.873371i
$257$	2.33937e7	+	1.35064e7i	1.37816	+	0.795682i	0.991938	−	0.126723i	$-0.0404460\pi$
$257$	2.33937e7	+	1.35064e7i	1.37816	+	0.795682i	0.386224	+	0.922405i	$0.373779\pi$
$258$	−392233.	−	1.46383e6i	−0.0228394	−	0.0852379i
$259$		−	3.36757e7i		−	1.93828i
$260$	−7.57031e6	+	2.70100e6i	−0.430718	+	0.153675i
$261$	9.55502e6			0.537415
$262$	−5.38943e7	+	1.44409e7i	−2.99667	+	0.802956i
$263$	−5.21923e6	+	9.03997e6i	−0.286906	+	0.496935i	−0.973070	−	0.230512i	$-0.925960\pi$
$263$	−5.21923e6	+	9.03997e6i	−0.286906	+	0.496935i	0.686164	+	0.727447i	$0.259293\pi$
$264$	764271.	−	441252.i	0.0415370	−	0.0239814i
$265$	−365135.	−	365135.i	−0.0196208	−	0.0196208i
$266$	−1.39020e7	+	5.18830e7i	−0.738640	+	2.75664i
$267$	47050.9	+	12607.2i	0.00247192	+	0.000662348i
$268$	3.57153e7	−	3.57153e7i	1.85546	−	1.85546i
$269$	−1.53380e7	−	2.65662e7i	−0.787973	−	1.36481i	−0.927207	−	0.374550i	$-0.877797\pi$
$269$	−1.53380e7	−	2.65662e7i	−0.787973	−	1.36481i	0.139233	−	0.990260i	$-0.455536\pi$
$270$	−1.50675e6	−	869921.i	−0.0765507	−	0.0441966i
$271$	2.31549e6	+	8.64151e6i	0.116341	+	0.434192i	0.999384	−	0.0351012i	$-0.0111754\pi$
$271$	2.31549e6	+	8.64151e6i	0.116341	+	0.434192i	−0.883042	+	0.469293i	$0.844509\pi$
$272$		−	100456.i		−	0.00499195i
$273$	−430109.	+	2.35176e6i	−0.0211393	+	0.115586i
$274$	−3.43930e7			−1.67193
$275$	−9.08431e6	+	2.43413e6i	−0.436811	+	0.117043i
$276$	−2.17223e6	+	3.76241e6i	−0.103319	+	0.178953i
$277$	−1.90907e7	+	1.10220e7i	−0.898218	+	0.518587i	−0.876622	−	0.481180i	$-0.840208\pi$
$277$	−1.90907e7	+	1.10220e7i	−0.898218	+	0.518587i	−0.0215966	+	0.999767i	$0.506875\pi$
$278$	1.16378e6	+	1.16378e6i	0.0541673	+	0.0541673i
$279$	1.60097e6	−	5.97489e6i	0.0737174	−	0.275117i
$280$	−7.26501e6	−	1.94665e6i	−0.330950	−	0.0886777i
$281$	−1.70282e7	+	1.70282e7i	−0.767449	+	0.767449i	−0.977657	−	0.210208i	$-0.932586\pi$
$281$	−1.70282e7	+	1.70282e7i	−0.767449	+	0.767449i	0.210208	+	0.977657i	$0.432586\pi$
$282$	818549.	+	1.41777e6i	0.0365004	+	0.0632205i
$283$	−8.32872e6	−	4.80859e6i	−0.367467	−	0.212157i	0.304884	−	0.952389i	$-0.401382\pi$
$283$	−8.32872e6	−	4.80859e6i	−0.367467	−	0.212157i	−0.672351	+	0.740232i	$0.734716\pi$
$284$	−511491.	−	1.90891e6i	−0.0223297	−	0.0833356i
$285$			926125.i			0.0400069i
$286$	1.68134e7	+	7.97072e6i	0.718716	+	0.340721i
$287$	4.90387e7			2.07440
$288$	−2.27587e7	+	6.09816e6i	−0.952728	+	0.255283i
$289$	−1.16486e6	+	2.01760e6i	−0.0482594	+	0.0835877i
$290$	5.23522e6	−	3.02256e6i	0.214655	−	0.123931i
$291$	−2.11762e6	−	2.11762e6i	−0.0859347	−	0.0859347i
$292$	6.01323e6	−	2.24417e7i	0.241523	−	0.901377i
$293$	1.15240e6	+	308784.i	0.0458141	+	0.0122758i	0.281653	−	0.959516i	$-0.409117\pi$
$293$	1.15240e6	+	308784.i	0.0458141	+	0.0122758i	−0.235839	+	0.971792i	$0.575784\pi$
$294$	−1.30449e6	+	1.30449e6i	−0.0513331	+	0.0513331i
$295$	−1.86071e6	−	3.22284e6i	−0.0724790	−	0.125537i
$296$	3.61644e7	+	2.08795e7i	1.39446	+	0.805091i
$297$	644620.	+	2.40575e6i	0.0246056	+	0.0918295i
$298$		−	3.60588e7i		−	1.36258i
$299$	−3.49555e7	+	2.83444e6i	−1.30768	+	0.106036i
$300$	3.91381e6			0.144956
$301$	1.78593e7	−	4.78540e6i	0.654886	−	0.175476i
$302$	2.46890e7	−	4.27626e7i	0.896361	−	1.55254i
$303$	518641.	−	299437.i	0.0186440	−	0.0107641i
$304$	−152156.	−	152156.i	−0.00541586	−	0.00541586i
$305$	−1.96053e6	+	7.31682e6i	−0.0690995	+	0.257883i
$306$	4.21820e7	+	1.13026e7i	1.47219	+	0.394471i
$307$	4.80186e6	−	4.80186e6i	0.165956	−	0.165956i	−0.619243	−	0.785199i	$-0.712560\pi$
$307$	4.80186e6	−	4.80186e6i	0.165956	−	0.165956i	0.785199	+	0.619243i	$0.212560\pi$
$308$	1.40611e7	+	2.43545e7i	0.481246	+	0.833542i
$309$	1.91922e6	+	1.10806e6i	0.0650502	+	0.0375568i
$310$	−1.01287e6	−	3.78010e6i	−0.0339994	−	0.126887i
$311$			6.99673e6i			0.232602i	0.993214	+	0.116301i	$0.0371038\pi$
$311$			6.99673e6i			0.232602i	−0.993214	+	0.116301i	$0.962896\pi$
$312$	−2.25888e6	−	1.92003e6i	−0.0743755	−	0.0632184i
$313$	4.60593e6			0.150205			0.0751025	−	0.997176i	$-0.476072\pi$
$313$	4.60593e6			0.150205			0.0751025	+	0.997176i	$0.476072\pi$
$314$	5.28927e7	−	1.41726e7i	1.70847	−	0.457782i
$315$	5.28150e6	−	9.14782e6i	0.168976	−	0.292675i
$316$	−2.51552e7	+	1.45233e7i	−0.797197	+	0.460262i
$317$	1.11600e7	+	1.11600e7i	0.350337	+	0.350337i	0.860235	−	0.509898i	$-0.170317\pi$
$317$	1.11600e7	+	1.11600e7i	0.350337	+	0.350337i	−0.509898	+	0.860235i	$0.670317\pi$
$318$	128754.	−	480518.i	0.00400388	−	0.0149427i
$319$	−8.35884e6	−	2.23974e6i	−0.257498	−	0.0689964i
$320$	−1.05748e7	+	1.05748e7i	−0.322718	+	0.322718i
$321$	480946.	+	833022.i	0.0145405	+	0.0251850i
$322$	−7.42313e7	−	4.28575e7i	−2.22341	−	1.28369i
$323$	−1.20903e7	−	4.51214e7i	−0.358780	−	1.33898i
$324$			5.35556e7i			1.57460i
$325$	1.79566e7	+	2.59948e7i	0.523088	+	0.757246i
$326$	−5.89273e7			−1.70084
$327$	858277.	−	229975.i	0.0245462	−	0.00657713i
$328$	−3.04048e7	+	5.26627e7i	−0.861630	+	1.49239i
$329$	−1.72973e7	+	9.98661e6i	−0.485726	+	0.280434i
$330$	554459.	+	554459.i	0.0154286	+	0.0154286i
$331$	1.63243e7	−	6.09232e7i	0.450144	−	1.67996i	−0.251842	−	0.967768i	$-0.581036\pi$
$331$	1.63243e7	−	6.09232e7i	0.450144	−	1.67996i	0.701986	−	0.712191i	$-0.252297\pi$
$332$	−9.38312e7	−	2.51420e7i	−2.56409	−	0.687045i
$333$	−4.14696e7	+	4.14696e7i	−1.12305	+	1.12305i
$334$	2.04542e7	+	3.54277e7i	0.548962	+	0.950831i
$335$	1.48802e7	+	8.59110e6i	0.395799	+	0.228515i
$336$	−6058.62	−	22611.1i	−0.000159719	−	0.000596079i
$337$			4.12078e7i			1.07669i	0.842725	+	0.538344i	$0.180950\pi$
$337$			4.12078e7i			1.07669i	−0.842725	+	0.538344i	$0.819050\pi$
$338$	6.23903e6	−	6.21954e7i	0.161572	−	1.61068i
$339$	−6.02959e6			−0.154771
$340$	1.65026e7	−	4.42186e6i	0.419871	−	0.112504i
$341$	−2.80109e6	+	4.85163e6i	−0.0706422	+	0.122356i
$342$	8.10103e7	−	4.67713e7i	2.02517	−	1.16923i
$343$	1.85793e7	+	1.85793e7i	0.460411	+	0.460411i
$344$	−5.93406e6	+	2.21462e7i	−0.145773	+	0.544031i
$345$	−1.42754e6	−	382508.i	−0.0347641	−	0.00931502i
$346$	3.55283e7	−	3.55283e7i	0.857722	−	0.857722i
$347$	−2.18829e7	−	3.79023e7i	−0.523741	−	0.907146i	−0.999618	−	0.0276341i	$-0.991203\pi$
$347$	−2.18829e7	−	3.79023e7i	−0.523741	−	0.907146i	0.475877	−	0.879512i	$-0.342131\pi$
$348$	3.11878e6	+	1.80063e6i	0.0740026	+	0.0427254i
$349$	7.45551e6	+	2.78243e7i	0.175389	+	0.654559i	0.996485	+	0.0837696i	$0.0266960\pi$
$349$	7.45551e6	+	2.78243e7i	0.175389	+	0.654559i	−0.821097	+	0.570789i	$0.806637\pi$
$350$			7.72184e7i			1.80101i
$351$	6.88409e6	−	4.75537e6i	0.159193	−	0.109967i
$352$	2.13390e7			0.489267
$353$	6.61158e7	−	1.77157e7i	1.50308	−	0.402748i	0.588947	−	0.808172i	$-0.299543\pi$
$353$	6.61158e7	−	1.77157e7i	1.50308	−	0.402748i	0.914129	+	0.405423i	$0.132876\pi$
$354$	1.79257e6	−	3.10482e6i	0.0404078	−	0.0699884i
$355$	582212.	−	336141.i	0.0130136	−	0.00751339i
$356$	−1.36105e6	−	1.36105e6i	−0.0301665	−	0.0301665i
$357$	1.31525e6	−	4.90860e6i	0.0289071	−	0.107883i
$358$	1.26676e7	+	3.39427e6i	0.276086	+	0.0739771i
$359$	−2.63511e7	+	2.63511e7i	−0.569529	+	0.569529i	−0.931997	−	0.362467i	$-0.881934\pi$
$359$	−2.63511e7	+	2.63511e7i	−0.569529	+	0.569529i	0.362467	+	0.931997i	$0.381934\pi$
$360$	6.54924e6	+	1.13436e7i	0.140373	+	0.243133i
$361$	−4.59126e7	−	2.65076e7i	−0.975911	−	0.563442i
$362$	−1.29301e7	−	4.82557e7i	−0.272568	−	1.01724i
$363$			3.52680e6i			0.0737329i
$364$	6.11842e7	−	7.19823e7i	1.26863	−	1.49253i
$365$	7.90351e6			0.162533
$366$	−7.04887e6	+	1.88874e6i	−0.143773	+	0.0385237i
$367$	−2.68381e7	+	4.64849e7i	−0.542942	+	0.940403i	0.455791	+	0.890087i	$0.349356\pi$
$367$	−2.68381e7	+	4.64849e7i	−0.542942	+	0.940403i	−0.998733	+	0.0503164i	$0.983977\pi$
$368$	297378.	−	171691.i	0.00596713	−	0.00344513i
$369$	−6.03882e7	−	6.03882e7i	−1.20191	−	1.20191i
$370$	−9.60317e6	+	3.58395e7i	−0.189587	+	0.707549i
$371$	5.86251e6	+	1.57085e6i	0.114805	+	0.0307620i
$372$	1.64852e6	−	1.64852e6i	0.0320233	−	0.0320233i
$373$	2.29187e7	+	3.96963e7i	0.441634	+	0.764933i	0.997811	−	0.0661312i	$-0.0210656\pi$
$373$	2.29187e7	+	3.96963e7i	0.441634	+	0.764933i	−0.556177	+	0.831064i	$0.687732\pi$
$374$	−3.42519e7	−	1.97753e7i	−0.654742	−	0.378015i
$375$	719007.	+	2.68337e6i	0.0136345	+	0.0508847i
$376$		−	2.47675e7i		−	0.465928i
$377$	2.34956e6	+	2.89757e7i	0.0438492	+	0.540766i
$378$	2.04494e7			0.378621
$379$	2.24848e7	−	6.02479e6i	0.413021	−	0.110669i	−0.0463244	−	0.998926i	$-0.514751\pi$
$379$	2.24848e7	−	6.02479e6i	0.413021	−	0.110669i	0.459345	+	0.888258i	$0.348084\pi$
$380$	1.82981e7	−	3.16932e7i	0.333468	−	0.577584i
$381$	−7.69763e6	+	4.44423e6i	−0.139182	+	0.0803566i
$382$	5.24558e7	+	5.24558e7i	0.941031	+	0.941031i
$383$	−1.88742e7	+	7.04396e7i	−0.335949	+	1.25378i	0.566888	+	0.823795i	$0.308147\pi$
$383$	−1.88742e7	+	7.04396e7i	−0.335949	+	1.25378i	−0.902837	+	0.429983i	$0.858520\pi$
$384$	−8.62287e6	−	2.31049e6i	−0.152285	−	0.0408047i
$385$	−6.76461e6	+	6.76461e6i	−0.118539	+	0.118539i
$386$	−4.90013e7	−	8.48727e7i	−0.852011	−	1.47573i
$387$	−2.78857e7	−	1.60998e7i	−0.481114	−	0.277771i
$388$	3.06284e7	+	1.14307e8i	0.524360	+	1.95694i
$389$		−	1.07448e8i		−	1.82537i	−0.408666	−	0.912684i	$-0.634006\pi$
$389$		−	1.07448e8i		−	1.82537i	0.408666	−	0.912684i	$-0.365994\pi$
$390$	1.12839e6	−	2.38022e6i	0.0190224	−	0.0401257i
$391$	7.45443e7			1.24705
$392$	2.69591e7	−	7.22366e6i	0.447556	−	0.119922i
$393$	5.65364e6	−	9.79238e6i	0.0931430	−	0.161328i
$394$	−2.01482e6	+	1.16326e6i	−0.0329418	+	0.0190189i
$395$	−6.98699e6	−	6.98699e6i	−0.113370	−	0.113370i
$396$	1.26757e7	−	4.73065e7i	0.204121	−	0.761791i
$397$	−4.47372e7	−	1.19873e7i	−0.714986	−	0.191580i	−0.117052	−	0.993126i	$-0.537345\pi$
$397$	−4.47372e7	−	1.19873e7i	−0.714986	−	0.191580i	−0.597933	+	0.801546i	$0.704011\pi$
$398$	−7.67170e7	+	7.67170e7i	−1.21687	+	1.21687i
$399$	−5.44265e6	−	9.42694e6i	−0.0856823	−	0.148406i
$400$	−267901.	−	154672.i	−0.00418595	−	0.00241676i
$401$	1.44648e7	+	5.39833e7i	0.224325	+	0.837194i	0.982674	+	0.185344i	$0.0593400\pi$
$401$	1.44648e7	+	5.39833e7i	0.224325	+	0.837194i	−0.758348	+	0.651850i	$0.773993\pi$
$402$			1.65530e7i			0.254799i
$403$	1.85126e7	+	3.38574e6i	0.282847	+	0.0517295i
$404$	−2.36648e7			−0.358887
$405$	−1.75978e7	+	4.71530e6i	−0.264906	+	0.0709814i
$406$	−3.55259e7	+	6.15327e7i	−0.530844	+	0.919449i
$407$	4.59988e7	−	2.65574e7i	0.682281	−	0.393915i
$408$	4.45587e6	+	4.45587e6i	0.0656072	+	0.0656072i
$409$	1.01992e7	−	3.80638e7i	0.149072	−	0.556343i	−0.850469	−	0.526026i	$-0.823682\pi$
$409$	1.01992e7	−	3.80638e7i	0.149072	−	0.556343i	0.999540	−	0.0303171i	$-0.00965171\pi$
$410$	−5.21896e7	−	1.39842e7i	−0.757238	−	0.202901i
$411$	4.92849e6	−	4.92849e6i	0.0709885	−	0.0709885i
$412$	−4.37854e7	−	7.58386e7i	−0.626092	−	1.08442i
$413$	3.78799e7	+	2.18700e7i	0.537723	+	0.310455i
$414$	3.86350e7	+	1.44188e8i	0.544478	+	2.03202i
$415$		−	3.30455e7i		−	0.462347i
$416$	−2.40890e7	−	6.75163e7i	−0.334610	−	0.937840i
$417$	−333538.			−0.00459978
$418$	−8.18322e7	+	2.19269e7i	−1.12046	+	0.300226i
$419$	1.16420e7	−	2.01646e7i	0.158266	−	0.274124i	−0.775978	−	0.630760i	$-0.782743\pi$
$419$	1.16420e7	−	2.01646e7i	0.158266	−	0.274124i	0.934243	+	0.356636i	$0.116076\pi$
$420$	3.44779e6	−	1.99058e6i	0.0465364	−	0.0268678i
$421$	3.75681e7	+	3.75681e7i	0.503469	+	0.503469i	0.912514	−	0.409045i	$-0.134138\pi$
$421$	3.75681e7	+	3.75681e7i	0.503469	+	0.503469i	−0.409045	+	0.912514i	$0.634138\pi$
$422$	−3.03143e7	+	1.13135e8i	−0.403376	+	1.50542i
$423$	3.35986e7	+	9.00270e6i	0.443915	+	0.118947i
$424$	−5.32180e6	+	5.32180e6i	−0.0698169	+	0.0698169i
$425$	−3.35775e7	−	5.81580e7i	−0.437403	−	0.757605i
$426$	560891.	+	323831.i	0.00725521	+	0.00418880i
$427$	−2.30433e7	−	8.59988e7i	−0.295979	−	1.10461i
$428$		−	3.80095e7i		−	0.484798i
$429$	−3.55154e6	+	1.26715e6i	−0.0449827	+	0.0160493i
$430$	−2.03715e7			−0.256223
$431$	−8.54875e7	+	2.29063e7i	−1.06775	+	0.286104i	−0.749570	−	0.661926i	$-0.769739\pi$
$431$	−8.54875e7	+	2.29063e7i	−1.06775	+	0.286104i	−0.318183	+	0.948029i	$0.603073\pi$
$432$	−40961.2	+	70946.8i	−0.000508067	+	0.000879998i
$433$	5.45440e7	−	3.14910e7i	0.671867	−	0.387903i	−0.124917	−	0.992167i	$-0.539866\pi$
$433$	5.45440e7	−	3.14910e7i	0.671867	−	0.387903i	0.796784	+	0.604265i	$0.206533\pi$
$434$	3.25248e7	+	3.25248e7i	0.397874	+	0.397874i
$435$	−317073.	+	1.18333e6i	−0.00385205	+	0.0143760i
$436$	−3.39151e7	−	9.08753e6i	−0.409198	−	0.109644i
$437$	1.12908e8	−	1.12908e8i	1.35295	−	1.35295i
$438$	3.80704e6	+	6.59399e6i	0.0453070	+	0.0784740i
$439$	4.53364e7	+	2.61750e7i	0.535862	+	0.309380i	0.743400	−	0.668847i	$-0.233212\pi$
$439$	4.53364e7	+	2.61750e7i	0.535862	+	0.309380i	−0.207538	+	0.978227i	$0.566545\pi$
$440$	−3.07035e6	−	1.14587e7i	−0.0360437	−	0.134517i
$441$			3.91973e7i			0.457025i
$442$	−2.39029e7	+	1.30697e8i	−0.276811	+	1.51355i
$443$	−1.06292e8			−1.22261			−0.611306	−	0.791395i	$-0.709355\pi$
$443$	−1.06292e8			−1.22261			−0.611306	+	0.791395i	$0.709355\pi$
$444$	−2.13507e7	+	5.72090e6i	−0.243929	+	0.0653605i
$445$	327393.	−	567061.i	0.00371526	−	0.00643501i
$446$	1.08485e8	−	6.26340e7i	1.22283	−	0.706001i
$447$	5.16720e6	+	5.16720e6i	0.0578539	+	0.0578539i
$448$	4.54941e7	−	1.69786e8i	0.505966	−	1.88829i
$449$	8.62989e7	+	2.31237e7i	0.953380	+	0.255457i	0.701796	−	0.712378i	$-0.252382\pi$
$449$	8.62989e7	+	2.31237e7i	0.953380	+	0.255457i	0.251584	+	0.967835i	$0.419048\pi$
$450$	9.50899e7	−	9.50899e7i	1.04351	−	1.04351i
$451$	3.86730e7	+	6.69836e7i	0.421578	+	0.730195i
$452$	2.06341e8	+	1.19131e8i	2.23444	+	1.29006i
$453$	2.58993e6	+	9.66576e6i	0.0278608	+	0.103978i
$454$		−	1.46642e8i		−	1.56708i
$455$	2.90396e7	+	1.37668e7i	0.308287	+	0.146150i
$456$	1.34981e7			0.142357
$457$	−2.83776e7	+	7.60377e6i	−0.297323	+	0.0796673i	−0.404397	−	0.914584i	$-0.632518\pi$
$457$	−2.83776e7	+	7.60377e6i	−0.297323	+	0.0796673i	0.107074	+	0.994251i	$0.465852\pi$
$458$	−1.61255e7	+	2.79301e7i	−0.167848	+	0.290721i
$459$	−1.54017e7	+	8.89218e6i	−0.159269	+	0.0919539i
$460$	4.12948e7	+	4.12948e7i	0.424251	+	0.424251i
$461$	1.04941e7	−	3.91645e7i	0.107113	−	0.399751i	−0.891463	−	0.453093i	$-0.850321\pi$
$461$	1.04941e7	−	3.91645e7i	0.107113	−	0.399751i	0.998576	+	0.0533418i	$0.0169873\pi$
$462$	−8.90223e6	−	2.38535e6i	−0.0902761	−	0.0241894i
$463$	−7.77336e6	+	7.77336e6i	−0.0783188	+	0.0783188i	−0.745181	−	0.666862i	$-0.767637\pi$
$463$	−7.77336e6	+	7.77336e6i	−0.0783188	+	0.0783188i	0.666862	+	0.745181i	$0.267637\pi$
$464$	−142320.	−	246506.i	−0.00142467	−	0.00246759i
$465$	686829.	+	396541.i	0.00683109	+	0.00394393i
$466$	−2.33317e7	−	8.70752e7i	−0.230563	−	0.860472i
$467$			1.44943e8i			1.42314i	0.702615	+	0.711570i	$0.252016\pi$
$467$			1.44943e8i			1.42314i	−0.702615	+	0.711570i	$0.747984\pi$
$468$	−1.63987e8	+	1.32972e7i	−1.59982	+	0.129725i
$469$	−2.01953e8			−1.95763
$470$	2.12566e7	−	5.69569e6i	0.204739	−	0.0548596i
$471$	−5.54856e6	+	9.61039e6i	−0.0531028	+	0.0919768i
$472$	−4.69724e7	+	2.71195e7i	−0.446701	+	0.257903i
$473$	2.06208e7	+	2.06208e7i	0.194860	+	0.194860i
$474$	2.46376e6	−	9.19488e6i	0.0231347	−	0.0863398i
$475$	−1.38947e8	−	3.72307e7i	−1.29649	−	0.347393i
$476$	−1.41992e8	+	1.41992e8i	−1.31657	+	1.31657i
$477$	−5.28491e6	−	9.15374e6i	−0.0486948	−	0.0843419i
$478$	−1.28258e8	−	7.40496e7i	−1.17436	−	0.678015i
$479$	3.29660e7	+	1.23031e8i	0.299958	+	1.11946i	0.937200	+	0.348793i	$0.113408\pi$
$479$	3.29660e7	+	1.23031e8i	0.299958	+	1.11946i	−0.637242	+	0.770664i	$0.719925\pi$
$480$		−	3.02089e6i		−	0.0273156i
$481$	−1.35954e8	−	1.15560e8i	−1.22168	−	1.03842i
$482$	−3.78685e7			−0.338172
$483$	1.67787e7	−	4.49585e6i	0.148908	−	0.0398997i
$484$	6.96815e7	−	1.20692e8i	0.614584	−	1.06449i
$485$	−3.48633e7	+	2.01283e7i	−0.305593	+	0.176434i
$486$	−3.78331e7	−	3.78331e7i	−0.329582	−	0.329582i
$487$	−3.76889e7	+	1.40657e8i	−0.326307	+	1.21779i	0.586685	+	0.809815i	$0.300433\pi$
$487$	−3.76889e7	+	1.40657e8i	−0.326307	+	1.21779i	−0.912992	+	0.407978i	$0.866234\pi$
$488$	1.06642e8	+	2.85745e7i	0.917628	+	0.245878i
$489$	8.44424e6	−	8.44424e6i	0.0722161	−	0.0722161i
$490$	1.23994e7	+	2.14763e7i	0.105393	+	0.182546i
$491$	9.25186e7	+	5.34156e7i	0.781600	+	0.451257i	0.836997	−	0.547208i	$-0.184309\pi$
$491$	9.25186e7	+	5.34156e7i	0.781600	+	0.451257i	−0.0553972	+	0.998464i	$0.517643\pi$
$492$	−8.33079e6	−	3.10909e7i	−0.0699505	−	0.261059i
$493$		−	6.17921e7i		−	0.515694i
$494$	1.61755e8	+	2.34164e8i	1.34176	+	1.94240i
$495$	1.66604e7			0.137363
$496$	−177990.	+	47692.3i	−0.00145865	+	0.000390844i
$497$	−3.95086e6	+	6.84309e6i	−0.0321827	+	0.0557420i
$498$	2.75702e7	−	1.59177e7i	0.223230	−	0.128882i
$499$	−5.23268e7	−	5.23268e7i	−0.421136	−	0.421136i	0.464459	−	0.885595i	$-0.346249\pi$
$499$	−5.23268e7	−	5.23268e7i	−0.421136	−	0.421136i	−0.885595	+	0.464459i	$0.846249\pi$
$500$	2.84118e7	−	1.06034e8i	0.227295	−	0.848275i
$501$	−8.00782e6	−	2.14569e6i	−0.0636797	−	0.0170629i
$502$	6.17209e7	−	6.17209e7i	0.487889	−	0.487889i
$503$	5.19728e7	+	9.00196e7i	0.408388	+	0.707348i	0.994709	−	0.102730i	$-0.0327579\pi$
$503$	5.19728e7	+	9.00196e7i	0.408388	+	0.707348i	−0.586322	+	0.810078i	$0.699425\pi$
$504$	−1.33328e8	−	7.69771e7i	−1.04143	−	0.601270i
$505$	−2.08357e6	−	7.77598e6i	−0.0161783	−	0.0603783i
$506$		−	1.35194e8i		−	1.04353i
$507$	8.01850e6	+	9.80659e6i	0.0615275	+	0.0752479i
$508$	3.51231e8			2.67918
$509$	−6.66679e6	+	1.78636e6i	−0.0505549	+	0.0135462i	−0.284008	−	0.958822i	$-0.591664\pi$
$509$	−6.66679e6	+	1.78636e6i	−0.0505549	+	0.0135462i	0.233453	+	0.972368i	$0.424998\pi$
$510$	−2.79953e6	+	4.84893e6i	−0.0211045	+	0.0365540i
$511$	−8.04491e7	+	4.64473e7i	−0.602919	+	0.348095i
$512$	996858.	+	996858.i	0.00742717	+	0.00742717i
$513$	−9.85964e6	+	3.67967e7i	−0.0730313	+	0.272556i
$514$	3.37897e8	+	9.05393e7i	2.48826	+	0.666727i
$515$	2.10646e7	−	2.10646e7i	0.154217	−	0.154217i
$516$	−6.06796e6	−	1.05100e7i	−0.0441666	−	0.0764988i
$517$	−2.72821e7	−	1.57513e7i	−0.197427	−	0.113985i
$518$	−1.12872e8	−	4.21243e8i	−0.812074	−	3.03070i
$519$			1.01824e7i			0.0728361i
$520$	−3.27892e7	+	2.26500e7i	−0.233196	+	0.161086i
$521$	1.25619e8			0.888264			0.444132	−	0.895961i	$-0.353512\pi$
$521$	1.25619e8			0.888264			0.444132	+	0.895961i	$0.353512\pi$
$522$	1.19522e8	−	3.20258e7i	0.840303	−	0.225158i
$523$	1.38607e7	−	2.40074e7i	0.0968903	−	0.167819i	−0.813506	−	0.581557i	$-0.802444\pi$
$523$	1.38607e7	−	2.40074e7i	0.0968903	−	0.167819i	0.910396	+	0.413738i	$0.135777\pi$
$524$	−3.86950e8	+	2.23406e8i	−2.68943	+	1.55274i
$525$	−1.10653e7	−	1.10653e7i	−0.0764693	−	0.0764693i
$526$	−3.49868e7	+	1.30573e8i	−0.240407	+	0.897212i
$527$	−3.86395e7	−	1.03534e7i	−0.263997	−	0.0707379i
$528$	26107.3	−	26107.3i	0.000177362	−	0.000177362i
$529$	5.33870e7	+	9.24689e7i	0.360635	+	0.624639i
$530$	−5.79124e6	−	3.34358e6i	−0.0388995	−	0.0224586i
$531$	−1.97153e7	−	7.35785e7i	−0.131680	−	0.491436i
$532$			4.30136e8i			2.85674i
$533$	1.68278e8	−	1.97977e8i	1.11134	−	1.30747i
$534$	630806.			0.00414259
$535$	1.24895e7	−	3.34655e6i	0.0815612	−	0.0218542i
$536$	1.25214e8	−	2.16877e8i	0.813128	−	1.40838i
$537$	−2.30165e6	+	1.32886e6i	−0.0148634	+	0.00858136i
$538$	−2.80902e8	−	2.80902e8i	−1.80388	−	1.80388i
$539$	9.18805e6	−	3.42903e7i	0.0586755	−	0.218980i
$540$	−1.34579e7	−	3.60604e6i	−0.0854668	−	0.0229007i
$541$	8.17036e7	−	8.17036e7i	0.516000	−	0.516000i	−0.400359	−	0.916359i	$-0.631114\pi$
$541$	8.17036e7	−	8.17036e7i	0.516000	−	0.516000i	0.916359	+	0.400359i	$0.131114\pi$
$542$	5.79280e7	+	1.00334e8i	0.363823	+	0.630160i
$543$	8.76787e6	+	5.06213e6i	0.0547639	+	0.0316180i
$544$	3.94367e7	+	1.47180e8i	0.244965	+	0.914221i
$545$		−	1.19442e7i		−	0.0737852i
$546$	2.50230e6	+	3.08593e7i	0.0153731	+	0.189587i
$547$	3.62271e7			0.221346			0.110673	−	0.993857i	$-0.464699\pi$
$547$	3.62271e7			0.221346			0.110673	+	0.993857i	$0.464699\pi$
$548$	−2.66035e8	+	7.12838e7i	−1.61658	+	0.433161i
$549$	−7.75260e7	+	1.34279e8i	−0.468522	+	0.811505i
$550$	−1.05475e8	+	6.08962e7i	−0.633961	+	0.366018i
$551$	−9.35932e7	−	9.35932e7i	−0.559487	−	0.559487i
$552$	−5.57500e6	+	2.08062e7i	−0.0331458	+	0.123702i
$553$	1.12181e8	+	3.00588e7i	0.663352	+	0.177745i
$554$	−2.01859e8	+	2.01859e8i	−1.18719	+	1.18719i
$555$	−3.75965e6	−	6.51190e6i	−0.0219922	−	0.0380915i
$556$	1.14141e7	+	6.58994e6i	0.0664076	+	0.0383404i
$557$	−4.42041e7	−	1.64972e8i	−0.255798	−	0.954652i	−0.967645	−	0.252317i	$-0.918808\pi$
$557$	−4.42041e7	−	1.64972e8i	−0.255798	−	0.954652i	0.711847	−	0.702335i	$-0.247859\pi$
$558$		−	8.01048e7i		−	0.461058i
$559$	4.19657e7	−	8.85224e7i	0.240248	−	0.506778i
$560$	−314668.			−0.00179180
$561$	7.74206e6	−	2.07448e6i	0.0438498	−	0.0117495i
$562$	−1.55928e8	+	2.70076e8i	−0.878449	+	1.52152i
$563$	1.47839e8	−	8.53549e7i	0.828445	−	0.478303i	−0.0248749	−	0.999691i	$-0.507919\pi$
$563$	1.47839e8	−	8.53549e7i	0.828445	−	0.478303i	0.853320	+	0.521388i	$0.174585\pi$
$564$	9.27011e6	+	9.27011e6i	0.0516711	+	0.0516711i
$565$	−2.09778e7	+	7.82901e7i	−0.116309	+	0.434072i
$566$	−1.20299e8	−	3.22341e7i	−0.663459	−	0.177773i
$567$	1.51415e8	−	1.51415e8i	0.830653	−	0.830653i
$568$	−4.89920e6	−	8.48566e6i	−0.0267350	−	0.0463064i
$569$	−1.04701e8	−	6.04490e7i	−0.568347	−	0.328135i	0.188142	−	0.982142i	$-0.439753\pi$
$569$	−1.04701e8	−	6.04490e7i	−0.568347	−	0.328135i	−0.756489	+	0.654007i	$0.773087\pi$
$570$	3.10412e6	+	1.15847e7i	0.0167615	+	0.0625548i
$571$			1.76317e8i			0.947080i	0.880772	+	0.473540i	$0.157024\pi$
$571$			1.76317e8i			0.947080i	−0.880772	+	0.473540i	$0.842976\pi$
$572$	1.46574e8	+	2.68068e7i	0.783195	+	0.143237i
$573$	−1.50338e7			−0.0799105
$574$	6.13415e8	−	1.64364e8i	3.24354	−	0.869103i
$575$	1.14776e8	−	1.98798e8i	0.603736	−	1.04570i
$576$	−2.65105e8	+	1.53059e8i	−1.38724	+	0.800922i
$577$	−5.78495e7	−	5.78495e7i	−0.301142	−	0.301142i	0.540318	−	0.841461i	$-0.318304\pi$
$577$	−5.78495e7	−	5.78495e7i	−0.301142	−	0.301142i	−0.841461	+	0.540318i	$0.818304\pi$
$578$	−7.80861e6	+	2.91421e7i	−0.0404380	+	0.150917i
$579$	1.91840e7	+	5.14035e6i	0.0988335	+	0.0264824i
$580$	3.42306e7	−	3.42306e7i	0.175441	−	0.175441i
$581$	1.94202e8	+	3.36367e8i	0.990204	+	1.71508i
$582$	−3.35865e7	−	1.93912e7i	−0.170371	−	0.0983639i
$583$	2.47762e6	+	9.24661e6i	0.0125034	+	0.0466634i
$584$		−	1.15193e8i		−	0.578343i
$585$	−1.88076e7	−	5.27134e7i	−0.0939430	−	0.263302i
$586$	1.54501e7			0.0767781
$587$	−1.68309e8	+	4.50984e7i	−0.832135	+	0.222970i	−0.649645	−	0.760238i	$-0.725082\pi$
$587$	−1.68309e8	+	4.50984e7i	−0.832135	+	0.222970i	−0.182490	+	0.983208i	$0.558416\pi$
$588$	−7.38668e6	+	1.27941e7i	−0.0363343	+	0.0629329i
$589$	−7.42070e7	+	4.28434e7i	−0.363161	+	0.209671i
$590$	−3.40773e7	−	3.40773e7i	−0.165924	−	0.165924i
$591$	122028.	−	455415.i	0.000591150	−	0.00220620i
$592$	1.68754e6	+	452175.i	0.00813372	+	0.00217942i
$593$	−2.18905e8	+	2.18905e8i	−1.04977	+	1.04977i	−0.0510709	+	0.998695i	$0.516263\pi$
$593$	−2.18905e8	+	2.18905e8i	−1.04977	+	1.04977i	−0.998695	+	0.0510709i	$0.983737\pi$
$594$	1.61269e7	+	2.79325e7i	0.0769468	+	0.133276i
$595$	−5.91588e7	−	3.41553e7i	−0.280846	−	0.162147i
$596$	−7.47365e7	−	2.78920e8i	−0.353016	−	1.31747i
$597$		−	2.19870e7i		−	0.103334i
$598$	−4.27751e8	+	1.52617e8i	−2.00026	+	0.713671i
$599$	−3.89795e8			−1.81366			−0.906829	−	0.421499i	$-0.861504\pi$
$599$	−3.89795e8			−1.81366			−0.906829	+	0.421499i	$0.861504\pi$
$600$	1.87438e7	−	5.02238e6i	0.0867768	−	0.0232518i
$601$	1.20190e8	−	2.08175e8i	0.553662	−	0.958971i	−0.444344	−	0.895856i	$-0.646563\pi$
$601$	1.20190e8	−	2.08175e8i	0.553662	−	0.958971i	0.998006	−	0.0631150i	$-0.0201035\pi$
$602$	2.07360e8	−	1.19719e8i	0.950462	−	0.548750i
$603$	2.48693e8	+	2.48693e8i	1.13426	+	1.13426i
$604$	1.02342e8	−	3.81946e8i	0.464455	−	1.73337i
$605$	4.57931e7	+	1.22702e7i	0.206792	+	0.0554098i
$606$	5.48395e6	−	5.48395e6i	0.0246420	−	0.0246420i
$607$	−7.71816e7	−	1.33682e8i	−0.345102	−	0.597735i	0.640270	−	0.768150i	$-0.278822\pi$
$607$	−7.71816e7	−	1.33682e8i	−0.345102	−	0.597735i	−0.985372	+	0.170415i	$0.945489\pi$
$608$	2.82658e8	+	1.63193e8i	1.25762	+	0.726089i
$609$	−3.72675e6	−	1.39084e7i	−0.0164998	−	0.0615780i
$610$			9.80958e7i			0.432176i
$611$	−1.90390e7	+	1.04102e8i	−0.0834680	+	0.456388i
$612$	3.49710e8			1.52565
$613$	−1.48913e8	+	3.99012e7i	−0.646475	+	0.173222i	−0.567135	−	0.823625i	$-0.691948\pi$
$613$	−1.48913e8	+	3.99012e7i	−0.646475	+	0.173222i	−0.0793403	+	0.996848i	$0.525281\pi$
$614$	4.39710e7	−	7.61600e7i	0.189960	−	0.329020i
$615$	9.48265e6	−	5.47481e6i	0.0407666	−	0.0235366i
$616$	9.85932e7	+	9.85932e7i	0.421798	+	0.421798i
$617$	6.25487e6	−	2.33435e7i	0.0266295	−	0.0993825i	−0.951332	−	0.308168i	$-0.900284\pi$
$617$	6.25487e6	−	2.33435e7i	0.0266295	−	0.0993825i	0.977962	+	0.208785i	$0.0669509\pi$
$618$	2.77210e7	+	7.42783e6i	0.117448	+	0.0314700i
$619$	2.54367e8	−	2.54367e8i	1.07248	−	1.07248i	0.0753200	−	0.997159i	$-0.476002\pi$
$619$	2.54367e8	−	2.54367e8i	1.07248	−	1.07248i	0.997159	−	0.0753200i	$-0.0239978\pi$
$620$	−1.56695e7	−	2.71403e7i	−0.0657475	−	0.113878i
$621$	−5.26466e7	−	3.03956e7i	−0.219834	−	0.126922i
$622$	2.34511e7	+	8.75208e7i	0.0974524	+	0.363697i
$623$			7.69608e6i			0.0318277i
$624$	−112075.	−	53131.3i	−0.000461270	−	0.000218674i
$625$	−1.87351e8			−0.767391
$626$	5.76147e7	−	1.54378e7i	0.234861	−	0.0629308i
$627$	8.58439e6	−	1.48686e7i	0.0348262	−	0.0603208i
$628$	3.79758e8	−	2.19254e8i	1.53330	−	0.885253i
$629$	2.68183e8	+	2.68183e8i	1.07765	+	1.07765i
$630$	3.54043e7	−	1.32130e8i	0.141590	−	0.528423i
$631$	5.46658e7	+	1.46477e7i	0.217584	+	0.0583015i	0.365964	−	0.930629i	$-0.380739\pi$
$631$	5.46658e7	+	1.46477e7i	0.217584	+	0.0583015i	−0.148380	+	0.988930i	$0.547406\pi$
$632$	−1.01834e8	+	1.01834e8i	−0.403407	+	0.403407i
$633$	−1.18681e7	−	2.05561e7i	−0.0467917	−	0.0810457i
$634$	1.77003e8	+	1.02193e8i	0.694566	+	0.401008i
$635$	3.09241e7	+	1.15410e8i	0.120775	+	0.450738i
$636$		−	3.98374e6i		−	0.0154853i
$637$	−1.18866e8	+	9.63853e6i	−0.459875	+	0.0372900i
$638$	−1.12066e8			−0.431531
$639$	1.32921e7	−	3.56161e6i	0.0509438	−	0.0136503i
$640$	−6.00002e7	+	1.03923e8i	−0.228883	+	0.396437i
$641$	1.29789e8	−	7.49340e7i	0.492794	−	0.284515i	−0.232939	−	0.972491i	$-0.574834\pi$
$641$	1.29789e8	−	7.49340e7i	0.492794	−	0.284515i	0.725733	+	0.687977i	$0.241501\pi$
$642$	8.80812e6	+	8.80812e6i	0.0332873	+	0.0332873i
$643$	−7.50428e7	+	2.80064e8i	−0.282277	+	1.05347i	0.668528	+	0.743687i	$0.266925\pi$
$643$	−7.50428e7	+	2.80064e8i	−0.282277	+	1.05347i	−0.950806	+	0.309787i	$0.899742\pi$
$644$	−6.63018e8	−	1.77655e8i	−2.48238	−	0.665151i
$645$	2.91922e6	−	2.91922e6i	0.0108790	−	0.0108790i
$646$	−3.02469e8	−	5.23892e8i	−1.12198	−	1.94332i
$647$	−3.12630e8	−	1.80497e8i	−1.15430	−	0.666435i	−0.204368	−	0.978894i	$-0.565514\pi$
$647$	−3.12630e8	−	1.80497e8i	−1.15430	−	0.666435i	−0.949931	+	0.312459i	$0.898847\pi$
$648$	6.87249e7	+	2.56485e8i	0.252574	+	0.942620i
$649$			6.89887e7i			0.252373i
$650$	3.11743e8	+	2.64979e8i	1.13516	+	0.964875i
$651$	−9.32156e6			−0.0337867
$652$	−4.55812e8	+	1.22134e8i	−1.64453	+	0.440651i
$653$	−1.36881e8	+	2.37084e8i	−0.491589	+	0.851457i	−0.999953	−	0.00968495i	$-0.996917\pi$
$653$	−1.36881e8	+	2.37084e8i	−0.491589	+	0.851457i	0.508364	+	0.861142i	$0.330250\pi$
$654$	9.96521e6	−	5.75341e6i	0.0356248	−	0.0205680i
$655$	−1.07478e8	−	1.07478e8i	−0.382467	−	0.382467i
$656$	−658459.	+	2.45740e6i	−0.00233248	+	0.00870492i
$657$	1.56265e8	+	4.18712e7i	0.551019	+	0.147645i
$658$	−1.82897e8	+	1.82897e8i	−0.641989	+	0.641989i
$659$	−1.69995e8	−	2.94439e8i	−0.593990	−	1.02882i	−0.993689	−	0.112174i	$-0.964218\pi$
$659$	−1.69995e8	−	2.94439e8i	−0.593990	−	1.02882i	0.399698	−	0.916647i	$-0.369115\pi$
$660$	5.43801e6	+	3.13964e6i	0.0189151	+	0.0109206i
$661$	6.71663e7	+	2.50668e8i	0.232566	+	0.867950i	0.979231	+	0.202749i	$0.0649875\pi$
$661$	6.71663e7	+	2.50668e8i	0.232566	+	0.867950i	−0.746664	+	0.665201i	$0.768346\pi$
$662$		−	8.16791e8i		−	2.81538i
$663$	−1.53034e7	−	2.21540e7i	−0.0525108	−	0.0760171i
$664$	−4.81633e8			−1.64518
$665$	−1.41338e8	+	3.78714e7i	−0.480611	+	0.128779i
$666$	−3.79741e8	+	6.57730e8i	−1.28548	+	2.22651i
$667$	1.82922e8	−	1.05610e8i	0.616436	−	0.355899i
$668$	2.31644e8	+	2.31644e8i	0.777127	+	0.777127i
$669$	−6.57045e6	+	2.45212e7i	−0.0219440	+	0.0818963i
$670$	2.14929e8	+	5.75900e7i	0.714612	+	0.191480i
$671$	9.92963e7	−	9.92963e7i	0.328674	−	0.328674i
$672$	1.77531e7	+	3.07493e7i	0.0585015	+	0.101328i
$673$	3.56842e8	+	2.06023e8i	1.17066	+	0.675881i	0.953836	−	0.300329i	$-0.0970965\pi$
$673$	3.56842e8	+	2.06023e8i	1.17066	+	0.675881i	0.216825	+	0.976210i	$0.430430\pi$
$674$	1.38117e8	+	5.15461e8i	0.451096	+	1.68351i
$675$			5.47652e7i			0.178071i
$676$	−8.06479e7	−	4.94021e8i	−0.261068	−	1.59921i
$677$	7.49337e7			0.241497			0.120748	−	0.992683i	$-0.461471\pi$
$677$	7.49337e7			0.241497			0.120748	+	0.992683i	$0.461471\pi$
$678$	−7.54230e7	+	2.02095e7i	−0.242000	+	0.0648436i
$679$	2.36580e8	−	4.09768e8i	0.755733	−	1.30897i
$680$	7.33589e7	−	4.23538e7i	0.233306	−	0.134699i
$681$	2.10137e7	+	2.10137e7i	0.0665366	+	0.0665366i
$682$	−1.87770e7	+	7.00766e7i	−0.0591933	+	0.220912i
$683$	−1.53175e8	−	4.10431e7i	−0.480756	−	0.128818i	0.0102984	−	0.999947i	$-0.496722\pi$
$683$	−1.53175e8	−	4.10431e7i	−0.480756	−	0.128818i	−0.491055	+	0.871129i	$0.663389\pi$
$684$	5.29687e8	−	5.29687e8i	1.65520	−	1.65520i
$685$	−4.68461e7	−	8.11399e7i	−0.145748	−	0.252443i
$686$	2.94677e8	+	1.70132e8i	0.912796	+	0.527003i
$687$	−1.69160e6	−	6.31313e6i	−0.00521707	−	0.0194704i
$688$			959215.i			0.00294544i
$689$	2.64593e7	−	1.82774e7i	0.0808947	−	0.0558802i
$690$	−1.91389e7			−0.0582599
$691$	−1.22148e8	+	3.27294e7i	−0.370212	+	0.0991981i	−0.439128	−	0.898424i	$-0.644713\pi$
$691$	−1.22148e8	+	3.27294e7i	−0.370212	+	0.0991981i	0.0689160	+	0.997622i	$0.478046\pi$
$692$	2.01180e8	−	3.48454e8i	0.607109	−	1.05154i
$693$	−1.69585e8	+	9.79100e7i	−0.509551	+	0.294189i
$694$	−4.00767e8	−	4.00767e8i	−1.19898	−	1.19898i
$695$	−1.16042e6	+	4.33076e6i	−0.00345670	+	0.0129006i
$696$	1.72469e7	+	4.62130e6i	0.0511545	+	0.0137068i
$697$	−3.90529e8	+	3.90529e8i	−1.15333	+	1.15333i
$698$	1.86519e8	+	3.23061e8i	0.548475	+	0.949987i
$699$	1.58212e7	+	9.13439e6i	0.0463243	+	0.0267453i
$700$	1.60045e8	+	5.97296e8i	0.466603	+	1.74139i
$701$		−	4.53196e8i		−	1.31562i	−0.753182	−	0.657812i	$-0.771482\pi$
$701$		−	4.53196e8i		−	1.31562i	0.753182	−	0.657812i	$-0.228518\pi$
$702$	7.01730e7	−	8.25575e7i	0.202843	−	0.238641i
$703$	8.12406e8			2.33834
$704$	2.67795e8	−	7.17554e7i	0.767510	−	0.205654i
$705$	−2.22987e6	+	3.86224e6i	−0.00636372	+	0.0110223i
$706$	7.67651e8	−	4.43204e8i	2.18147	−	1.25947i
$707$	6.69062e7	+	6.69062e7i	0.189325	+	0.189325i
$708$	7.43064e6	−	2.77315e7i	0.0209376	−	0.0781401i
$709$	1.76984e8	+	4.74227e7i	0.496587	+	0.133060i	0.498416	−	0.866938i	$-0.333915\pi$
$709$	1.76984e8	+	4.74227e7i	0.496587	+	0.133060i	−0.00182856	+	0.999998i	$0.500582\pi$
$710$	6.15613e6	−	6.15613e6i	0.0172002	−	0.0172002i
$711$	−1.01129e8	−	1.75160e8i	−0.281362	−	0.487333i
$712$	−8.26483e6	−	4.77170e6i	−0.0228978	−	0.0132201i
$713$	−3.53904e7	−	1.32079e8i	−0.0976376	−	0.364389i
$714$		−	6.58091e7i		−	0.180797i
$715$	4.09676e6	+	5.05229e7i	0.0112079	+	0.138220i
$716$	1.05021e8			0.286112
$717$	2.89905e7	−	7.76797e6i	0.0786498	−	0.0210742i
$718$	−2.41300e8	+	4.17943e8i	−0.651903	+	1.12913i
$719$	−4.25042e8	+	2.45398e8i	−1.14352	+	0.660213i	−0.947301	−	0.320346i	$-0.896201\pi$
$719$	−4.25042e8	+	2.45398e8i	−1.14352	+	0.660213i	−0.196223	+	0.980559i	$0.562868\pi$
$720$	387495.	+	387495.i	0.00103817	+	0.00103817i
$721$	−9.06224e7	+	3.38207e8i	−0.241785	+	0.902354i
$722$	−6.63158e8	−	1.77693e8i	−1.76200	−	0.472126i
$723$	5.42653e6	−	5.42653e6i	0.0143584	−	0.0143584i
$724$	−2.00032e8	−	3.46466e8i	−0.527089	−	0.912945i
$725$	−1.64790e8	−	9.51413e7i	−0.432430	−	0.249664i
$726$	1.18209e7	+	4.41161e7i	0.0308916	+	0.115289i
$727$			5.71482e7i			0.148730i	0.997231	+	0.0743651i	$0.0236930\pi$
$727$			5.71482e7i			0.148730i	−0.997231	+	0.0743651i	$0.976307\pi$
$728$	2.00649e8	−	4.23247e8i	0.520046	−	1.09698i
$729$	−3.65631e8			−0.943758
$730$	9.88635e7	−	2.64904e7i	0.254137	−	0.0680958i
$731$	−1.04117e8	+	1.80336e8i	−0.266544	+	0.461668i
$732$	−5.06094e7	+	2.92193e7i	−0.129032	+	0.0744967i
$733$	2.08775e8	+	2.08775e8i	0.530112	+	0.530112i	0.920606	−	0.390494i	$-0.127696\pi$
$733$	2.08775e8	+	2.08775e8i	0.530112	+	0.530112i	−0.390494	+	0.920606i	$0.627696\pi$
$734$	−1.79908e8	+	6.71425e8i	−0.454948	+	1.69789i
$735$	−4.85436e6	−	1.30072e6i	−0.0122256	−	0.00327584i
$736$	−3.68291e8	+	3.68291e8i	−0.923756	+	0.923756i
$737$	−1.59264e8	−	2.75854e8i	−0.397847	−	0.689091i
$738$	−9.57789e8	−	5.52980e8i	−2.38287	−	1.37575i
$739$	5.73400e7	+	2.13996e8i	0.142077	+	0.530239i	0.999868	+	0.0162405i	$0.00516974\pi$
$739$	5.73400e7	+	2.13996e8i	0.142077	+	0.530239i	−0.857791	+	0.513999i	$0.828164\pi$
$740$			2.97128e8i			0.733243i
$741$	−5.67348e7	−	1.03761e7i	−0.139442	−	0.0255024i
$742$	7.85980e7			0.192398
$743$	−1.76192e8	+	4.72106e7i	−0.429557	+	0.115099i	−0.467118	−	0.884195i	$-0.654708\pi$
$743$	−1.76192e8	+	4.72106e7i	−0.429557	+	0.115099i	0.0375612	+	0.999294i	$0.488041\pi$
$744$	5.77953e6	−	1.00104e7i	0.0140337	−	0.0243072i
$745$	8.50700e7	−	4.91152e7i	0.205735	−	0.118781i
$746$	4.19736e8	+	4.19736e8i	1.01102	+	1.01102i
$747$	1.75068e8	−	6.53364e8i	0.419997	−	1.56745i
$748$	−3.05930e8	−	8.19738e7i	−0.731001	−	0.195871i
$749$	−1.07462e8	+	1.07462e8i	−0.255747	+	0.255747i
$750$	1.79878e7	+	3.11559e7i	0.0426378	+	0.0738509i
$751$	−3.85818e8	−	2.22752e8i	−0.910882	−	0.525898i	−0.0301672	−	0.999545i	$-0.509604\pi$
$751$	−3.85818e8	−	2.22752e8i	−0.910882	−	0.525898i	−0.880715	+	0.473647i	$0.842937\pi$
$752$	−268188.	−	1.00089e6i	−0.000630645	−	0.00235360i
$753$			1.76891e7i			0.0414306i
$754$	1.26509e8	+	3.54576e8i	0.295125	+	0.827171i
$755$	1.34514e8			0.312555
$756$	1.58179e8	−	4.23840e7i	0.366086	−	0.0980926i
$757$	2.61550e8	−	4.53018e8i	0.602930	−	1.04431i	−0.389445	−	0.921050i	$-0.627333\pi$
$757$	2.61550e8	−	4.53018e8i	0.602930	−	1.04431i	0.992375	−	0.123255i	$-0.0393334\pi$
$758$	2.61065e8	−	1.50726e8i	0.599433	−	0.346083i
$759$	1.93731e7	+	1.93731e7i	0.0443072	+	0.0443072i
$760$	4.69618e7	−	1.75264e8i	0.106980	−	0.399256i
$761$	3.46101e8	+	9.27376e7i	0.785325	+	0.210427i	0.629131	−	0.777299i	$-0.283411\pi$
$761$	3.46101e8	+	9.27376e7i	0.785325	+	0.210427i	0.156194	+	0.987726i	$0.450078\pi$
$762$	−8.13923e7	+	8.13923e7i	−0.183958	+	0.183958i
$763$	7.01938e7	+	1.21579e8i	0.158025	+	0.273707i
$764$	5.14475e8	+	2.97032e8i	1.15368	+	0.666076i
$765$	3.07903e7	+	1.14911e8i	0.0687747	+	0.256671i
$766$			9.44377e8i			2.10116i
$767$	2.18279e8	−	7.78796e7i	0.483756	−	0.172599i
$768$	−4.44037e7			−0.0980247
$769$	5.81914e8	−	1.55924e8i	1.27962	−	0.342872i	0.445909	−	0.895078i	$-0.352880\pi$
$769$	5.81914e8	−	1.55924e8i	1.27962	−	0.342872i	0.833708	+	0.552206i	$0.186214\pi$
$770$	−6.19441e7	+	1.07290e8i	−0.135684	+	0.235011i
$771$	−6.13946e7	+	3.54462e7i	−0.133958	+	0.0773404i
$772$	−5.54941e8	−	5.54941e8i	−1.20613	−	1.20613i
$773$	1.65831e8	−	6.18891e8i	0.359028	−	1.33991i	−0.516312	−	0.856401i	$-0.672695\pi$
$773$	1.65831e8	−	6.18891e8i	0.359028	−	1.33991i	0.875339	−	0.483509i	$-0.160638\pi$
$774$	−4.02778e8	−	1.07924e8i	−0.868647	−	0.232753i
$775$	−8.71042e7	+	8.71042e7i	−0.187126	+	0.187126i
$776$	2.93367e8	+	5.08127e8i	0.627807	+	1.08739i
$777$	7.65382e7	+	4.41893e7i	0.163160	+	0.0942007i
$778$	−3.60137e8	−	1.34405e9i	−0.764766	−	2.85415i
$779$			1.18303e9i			2.50255i
$780$	3.79494e6	−	2.07501e7i	0.00799690	−	0.0437256i
$781$	−1.24629e7			−0.0261618
$782$	9.32460e8	−	2.49852e8i	1.94989	−	0.522471i
$783$	−2.51958e7	+	4.36404e7i	−0.0524860	+	0.0909084i
$784$	1.01124e6	−	583837.i	0.00209848	−	0.00121156i
$785$	1.05480e8	+	1.05480e8i	0.218053	+	0.218053i
$786$	3.78989e7	−	1.41440e8i	0.0780474	−	0.291277i
$787$	1.35170e8	+	3.62188e7i	0.277305	+	0.0743035i	0.394791	−	0.918771i	$-0.370817\pi$
$787$	1.35170e8	+	3.62188e7i	0.277305	+	0.0743035i	−0.117486	+	0.993074i	$0.537484\pi$
$788$	−1.31739e7	+	1.31739e7i	−0.0269238	+	0.0269238i
$789$	−1.36974e7	−	2.37245e7i	−0.0278873	−	0.0483022i
$790$	−1.10817e8	−	6.39805e7i	−0.224764	−	0.129768i
$791$	−2.46564e8	−	9.20190e8i	−0.498196	−	1.85929i
$792$		−	2.42823e8i		−	0.488782i
$793$	−4.26266e8	−	2.02079e8i	−0.854793	−	0.405231i
$794$	−5.99787e8			−1.19822
$795$	1.30901e6	−	350749.i	0.00260521	−	0.000698063i
$796$	−4.34412e8	+	7.52423e8i	−0.861316	+	1.49184i
$797$	−6.95299e8	+	4.01431e8i	−1.37340	+	0.792932i	−0.991354	−	0.131212i	$-0.958113\pi$
$797$	−6.95299e8	+	4.01431e8i	−1.37340	+	0.792932i	−0.382044	+	0.924144i	$0.624780\pi$
$798$	−9.96775e7	−	9.96775e7i	−0.196150	−	0.196150i
$799$	5.82203e7	−	2.17281e8i	0.114139	−	0.425973i
$800$	4.53225e8	+	1.21441e8i	0.885206	+	0.237190i
$801$	9.47726e6	−	9.47726e6i	0.0184410	−	0.0184410i
$802$	3.61874e8	+	6.26784e8i	0.701511	+	1.21505i
$803$	−1.26888e8	−	7.32588e7i	−0.245061	−	0.141486i
$804$	3.43081e7	+	1.28040e8i	0.0660129	+	0.246363i
$805$		−	2.33502e8i		−	0.447613i
$806$	2.42918e8	−	1.96976e7i	0.463933	−	0.0376191i
$807$	8.05062e7			0.153182
$808$	−1.13334e8	+	3.03677e7i	−0.214845	+	0.0575675i
$809$	4.03049e8	−	6.98102e8i	0.761224	−	1.31848i	−0.180996	−	0.983484i	$-0.557932\pi$
$809$	4.03049e8	−	6.98102e8i	0.761224	−	1.31848i	0.942220	−	0.334995i	$-0.108735\pi$
$810$	−2.04323e8	+	1.17966e8i	−0.384469	+	0.221973i
$811$	3.56371e8	+	3.56371e8i	0.668098	+	0.668098i	0.957275	−	0.289178i	$-0.0933818\pi$
$811$	3.56371e8	+	3.56371e8i	0.668098	+	0.668098i	−0.289178	+	0.957275i	$0.593382\pi$
$812$	−1.47264e8	+	5.49596e8i	−0.275060	+	1.02654i
$813$	−2.26788e7	−	6.07677e6i	−0.0422036	−	0.0113084i
$814$	4.86377e8	−	4.86377e8i	0.901778	−	0.901778i
$815$	−8.02640e7	−	1.39021e8i	−0.148268	−	0.256808i
$816$	228317.	+	131819.i	0.000420211	+	0.000242609i
$817$	1.15445e8	+	4.30846e8i	0.211694	+	0.790052i
$818$		−	5.10318e8i		−	0.932354i
$819$	5.01226e8	+	4.26037e8i	0.912394	+	0.775525i
$820$	−4.32678e8			−0.784736
$821$	4.65527e8	−	1.24737e8i	0.841230	−	0.225407i	0.187623	−	0.982241i	$-0.439922\pi$
$821$	4.65527e8	−	1.24737e8i	0.841230	−	0.225407i	0.653607	+	0.756834i	$0.273255\pi$
$822$	4.51306e7	−	7.81684e7i	0.0812560	−	0.140739i
$823$	8.02665e8	−	4.63419e8i	1.43991	−	0.831331i	0.442065	−	0.896983i	$-0.354246\pi$
$823$	8.02665e8	−	4.63419e8i	1.43991	−	0.831331i	0.997843	+	0.0656521i	$0.0209128\pi$
$824$	−3.07014e8	−	3.07014e8i	−0.548752	−	0.548752i
$825$	6.38815e6	−	2.38409e7i	0.0113766	−	0.0424581i
$826$	5.47135e8	+	1.46604e8i	0.970855	+	0.260140i
$827$	−3.00632e8	+	3.00632e8i	−0.531519	+	0.531519i	−0.921024	−	0.389505i	$-0.872646\pi$
$827$	−3.00632e8	+	3.00632e8i	−0.531519	+	0.531519i	0.389505	+	0.921024i	$0.372646\pi$
$828$	5.97695e8	+	1.03524e9i	1.05290	+	1.82368i
$829$	−7.50796e8	−	4.33472e8i	−1.31783	−	0.760847i	−0.334448	−	0.942414i	$-0.608550\pi$
$829$	−7.50796e8	−	4.33472e8i	−1.31783	−	0.760847i	−0.983379	+	0.181567i	$0.941883\pi$
$830$	−1.10759e8	−	4.13360e8i	−0.193708	−	0.722926i
$831$		−	5.78524e7i		−	0.100813i
$832$	−5.29340e8	−	7.66297e8i	−0.919105	−	1.33054i
$833$	2.53488e8			0.438554
$834$	−4.17216e6	+	1.11793e6i	−0.00719222	+	0.00192715i
$835$	−5.57206e7	+	9.65109e7i	−0.0957098	+	0.165774i
$836$	−5.87538e8	+	3.39215e8i	−1.00558	+	0.580573i
$837$	2.30674e7	+	2.30674e7i	0.0393389	+	0.0393389i
$838$	7.80418e7	−	2.91256e8i	0.132616	−	0.494929i
$839$	−8.54335e8	−	2.28918e8i	−1.44658	−	0.387610i	−0.551747	−	0.834011i	$-0.686039\pi$
$839$	−8.54335e8	−	2.28918e8i	−1.44658	−	0.387610i	−0.894833	+	0.446401i	$0.852705\pi$
$840$	1.39575e7	−	1.39575e7i	0.0235489	−	0.0235489i
$841$	2.09868e8	+	3.63503e8i	0.352825	+	0.611110i
$842$	5.95850e8	+	3.44014e8i	0.998161	+	0.576288i
$843$	−1.63573e7	−	6.10461e7i	−0.0273041	−	0.101900i
$844$			9.37943e8i			1.56009i
$845$	1.55229e8	−	6.99962e7i	0.257279	−	0.116012i
$846$	4.50452e8			0.743940
$847$	−5.38233e8	+	1.44219e8i	−0.885769	+	0.237341i
$848$	−157436.	+	272687.i	−0.000258176	+	0.000447174i
$849$	2.18579e7	−	1.26197e7i	0.0357179	−	0.0206217i
$850$	−6.14945e8	−	6.14945e8i	−1.00133	−	1.00133i
$851$	−3.35540e8	+	1.25225e9i	−0.544447	+	2.03190i
$852$	5.00976e6	+	1.34236e6i	0.00810024	+	0.00217045i
$853$	−3.73539e8	+	3.73539e8i	−0.601851	+	0.601851i	−0.940804	−	0.338952i	$-0.889927\pi$
$853$	−3.73539e8	+	3.73539e8i	−0.601851	+	0.601851i	0.338952	+	0.940804i	$0.389927\pi$
$854$	−5.76489e8	−	9.98508e8i	−0.925587	−	1.60316i
$855$	2.20686e8	+	1.27413e8i	0.353082	+	0.203852i
$856$	−4.87755e7	−	1.82032e8i	−0.0777643	−	0.290220i
$857$		−	4.41628e8i		−	0.701639i	−0.936443	−	0.350820i	$-0.885903\pi$
$857$		−	4.41628e8i		−	0.701639i	0.936443	−	0.350820i	$-0.114097\pi$
$858$	−4.01784e7	+	2.77543e7i	−0.0636109	+	0.0439409i
$859$	6.30993e8			0.995508			0.497754	−	0.867318i	$-0.334158\pi$
$859$	6.30993e8			0.995508			0.497754	+	0.867318i	$0.334158\pi$
$860$	−1.57577e8	+	4.22225e7i	−0.247740	+	0.0663818i
$861$	−6.43487e7	+	1.11455e8i	−0.100816	+	0.174619i
$862$	−9.92571e8	+	5.73061e8i	−1.54967	+	0.894704i
$863$	−2.45901e7	−	2.45901e7i	−0.0382585	−	0.0382585i	0.687719	−	0.725977i	$-0.258612\pi$
$863$	−2.45901e7	−	2.45901e7i	−0.0382585	−	0.0382585i	−0.725977	+	0.687719i	$0.758612\pi$
$864$	3.21607e7	−	1.20026e8i	0.0498637	−	0.186094i
$865$	1.32211e8	+	3.54258e7i	0.204277	+	0.0547358i
$866$	5.76731e8	−	5.76731e8i	0.888014	−	0.888014i
$867$	−3.05707e6	−	5.29501e6i	−0.00469082	−	0.00812474i
$868$	3.18996e8	+	1.84172e8i	0.487783	+	0.281621i
$869$	4.74102e7	+	1.76937e8i	0.0722457	+	0.269625i
$870$			1.58648e7i			0.0240923i
$871$	−6.93010e8	+	8.15315e8i	−1.04878	+	1.23388i
$872$	−1.74086e8			−0.262551
$873$	−7.95940e8	+	2.13271e8i	−1.19629	+	0.320546i
$874$	1.03391e9	−	1.79079e9i	1.54863	−	2.68231i
$875$	−3.80113e8	+	2.19459e8i	−0.567399	+	0.327588i
$876$	4.31149e7	+	4.31149e7i	0.0641379	+	0.0641379i
$877$	7.59185e7	−	2.83332e8i	0.112551	−	0.420045i	−0.886541	−	0.462650i	$-0.846899\pi$
$877$	7.59185e7	−	2.83332e8i	0.112551	−	0.420045i	0.999092	+	0.0426043i	$0.0135655\pi$
$878$	6.54835e8	+	1.75462e8i	0.967494	+	0.259239i
$879$	−2.21398e6	+	2.21398e6i	−0.00325992	+	0.00325992i
$880$	−248154.	−	429816.i	−0.000364145	−	0.000630717i
$881$	3.03371e8	+	1.75152e8i	0.443656	+	0.256145i	0.705147	−	0.709061i	$-0.250881\pi$
$881$	3.03371e8	+	1.75152e8i	0.443656	+	0.256145i	−0.261491	+	0.965206i	$0.584214\pi$
$882$	1.31379e8	+	4.90311e8i	0.191478	+	0.714605i
$883$		−	4.75275e8i		−	0.690340i	−0.938540	−	0.345170i	$-0.887821\pi$
$883$		−	4.75275e8i		−	0.690340i	0.938540	−	0.345170i	$-0.112179\pi$
$884$	8.59929e7	+	1.06050e9i	0.124482	+	1.53516i
$885$	9.76650e6			0.0140899
$886$	−1.32958e9	+	3.56261e8i	−1.91168	+	0.512232i
$887$	−6.27037e8	+	1.08606e9i	−0.898509	+	1.55626i	−0.0691083	+	0.997609i	$0.522015\pi$
$887$	−6.27037e8	+	1.08606e9i	−0.898509	+	1.55626i	−0.829401	+	0.558654i	$0.811318\pi$
$888$	−9.49099e7	+	5.47963e7i	−0.135542	+	0.0782550i
$889$	−9.93017e8	−	9.93017e8i	−1.41336	−	1.41336i
$890$	2.19466e6	−	8.19058e6i	0.00311313	−	0.0116184i
$891$	3.26232e8	+	8.74137e7i	0.461205	+	0.123579i
$892$	7.09332e8	−	7.09332e8i	0.999436	−	0.999436i
$893$	−2.40921e8	−	4.17287e8i	−0.338314	−	0.585978i
$894$	8.19546e7	+	4.73165e7i	0.114699	+	0.0662217i
$895$	9.24656e6	+	3.45086e7i	0.0128977	+	0.0481348i
$896$		−	1.41044e9i		−	1.96078i
$897$	3.94265e7	−	8.31662e7i	0.0546275	−	0.115231i
$898$	1.15700e9			1.59773
$899$	−1.09484e8	+	2.93362e7i	−0.150686	+	0.0403762i
$900$	5.38449e8	−	9.32620e8i	0.738613	−	1.27931i
$901$	−5.91970e7	+	3.41774e7i	−0.0809330	+	0.0467267i
$902$	7.08264e8	+	7.08264e8i	0.965107	+	0.965107i
$903$	−1.25588e7	+	4.68701e7i	−0.0170563	+	0.0636551i
$904$	1.14107e9	+	3.05748e8i	1.54456	+	0.413865i
$905$	9.62329e7	−	9.62329e7i	0.129831	−	0.129831i
$906$	6.47939e7	+	1.12226e8i	0.0871264	+	0.150907i
$907$	6.78874e8	+	3.91948e8i	0.909844	+	0.525299i	0.880381	−	0.474267i	$-0.157287\pi$
$907$	6.78874e8	+	3.91948e8i	0.909844	+	0.525299i	0.0294634	+	0.999566i	$0.490620\pi$
$908$	−3.03934e8	−	1.13430e9i	−0.405996	−	1.51520i
$909$		−	1.64782e8i		−	0.219391i
$910$	4.09393e8	+	7.48731e7i	0.543270	+	0.0993578i
$911$	3.07792e8			0.407101			0.203551	−	0.979064i	$-0.434752\pi$
$911$	3.07792e8			0.407101			0.203551	+	0.979064i	$0.434752\pi$
$912$	545479.	−	146161.i	0.000719107	−	0.000192684i
$913$	−3.06304e8	+	5.30533e8i	−0.402476	+	0.697109i
$914$	−3.29485e8	+	1.90228e8i	−0.431516	+	0.249136i
$915$	−1.40571e7	−	1.40571e7i	−0.0183498	−	0.0183498i
$916$	−6.68441e7	+	2.49466e8i	−0.0869714	+	0.324582i
$917$	1.72563e9	+	4.62381e8i	2.23789	+	0.599641i
$918$	−1.62853e8	+	1.62853e8i	−0.210507	+	0.210507i
$919$	−1.81018e8	−	3.13532e8i	−0.233225	−	0.403957i	0.725530	−	0.688190i	$-0.241594\pi$
$919$	−1.81018e8	−	3.13532e8i	−0.233225	−	0.403957i	−0.958755	+	0.284233i	$0.908261\pi$
$920$	2.50758e8	+	1.44775e8i	0.322026	+	0.185922i
$921$	4.61266e6	+	1.72147e7i	0.00590435	+	0.0220354i
$922$		−	5.25074e8i		−	0.669928i
$923$	1.40691e7	+	3.94326e7i	0.0178921	+	0.0501476i
$924$	−7.38040e7			−0.0935543
$925$	1.12812e9	−	3.02280e8i	1.42538	−	0.381930i
$926$	−7.11813e7	+	1.23290e8i	−0.0896465	+	0.155272i
$927$	5.28078e8	−	3.04886e8i	0.662917	−	0.382735i
$928$	3.05288e8	+	3.05288e8i	0.382002	+	0.382002i
$929$	1.64325e8	−	6.13269e8i	0.204954	−	0.764899i	−0.784510	−	0.620117i	$-0.787085\pi$
$929$	1.64325e8	−	6.13269e8i	0.204954	−	0.764899i	0.989464	−	0.144782i	$-0.0462481\pi$
$930$	9.92051e6	+	2.65819e6i	0.0123335	+	0.00330474i
$931$	3.83945e8	−	3.83945e8i	0.475795	−	0.475795i
$932$	−3.60949e8	−	6.25182e8i	−0.445859	−	0.772251i
$933$	−1.59022e7	−	9.18113e6i	−0.0195800	−	0.0113045i
$934$	4.85811e8	+	1.81307e9i	0.596247	+	2.22522i
$935$		−	1.07743e8i		−	0.131811i
$936$	−7.68291e8	+	2.74117e8i	−0.936910	+	0.334279i
$937$	−1.43436e9			−1.74357			−0.871786	−	0.489887i	$-0.837038\pi$
$937$	−1.43436e9			−1.74357			−0.871786	+	0.489887i	$0.837038\pi$
$938$	−2.52619e9	+	6.76889e8i	−3.06095	+	0.820180i
$939$	−6.04392e6	+	1.04684e7i	−0.00729998	+	0.0126439i
$940$	1.52618e8	−	8.81140e7i	0.183748	−	0.106087i
$941$	−2.80616e8	−	2.80616e8i	−0.336778	−	0.336778i	0.518376	−	0.855153i	$-0.326537\pi$
$941$	−2.80616e8	−	2.80616e8i	−0.336778	−	0.336778i	−0.855153	+	0.518376i	$0.826537\pi$
$942$	−3.71945e7	+	1.38812e8i	−0.0444965	+	0.166063i
$943$	−1.82354e9	−	4.88615e8i	−2.17460	−	0.582682i
$944$	−1.60457e6	+	1.60457e6i	−0.00190740	+	0.00190740i
$945$	2.78538e7	+	4.82442e7i	0.0330057	+	0.0571675i
$946$	3.27057e8	+	1.88827e8i	0.386323	+	0.223044i
$947$	−1.24965e8	−	4.66375e8i	−0.147142	−	0.549143i	−0.999651	−	0.0264291i	$-0.991586\pi$
$947$	−1.24965e8	−	4.66375e8i	−0.147142	−	0.549143i	0.852508	−	0.522714i	$-0.175080\pi$
$948$		−	7.62302e7i		−	0.0894751i
$949$	−8.85495e7	+	4.84172e8i	−0.103607	+	0.566502i
$950$	−1.86285e9			−2.17273
$951$	−4.00086e7	+	1.07203e7i	−0.0465170	+	0.0124642i
$952$	−4.97809e8	+	8.62231e8i	−0.576968	+	0.999338i
$953$	3.91070e8	−	2.25784e8i	0.451830	−	0.260864i	−0.256772	−	0.966472i	$-0.582659\pi$
$953$	3.91070e8	−	2.25784e8i	0.451830	−	0.260864i	0.708603	+	0.705607i	$0.249326\pi$
$954$	−9.67888e7	−	9.67888e7i	−0.111476	−	0.111476i
$955$	−5.23045e7	+	1.95203e8i	−0.0600522	+	0.224118i
$956$	−1.14557e9	−	3.06954e8i	−1.31114	−	0.351318i
$957$	1.60590e7	−	1.60590e7i	0.0183224	−	0.0183224i
$958$	8.24731e8	+	1.42848e9i	0.938028	+	1.62471i
$959$	9.53685e8	+	5.50610e8i	1.08131	+	0.624293i
$960$	−1.01582e7	−	3.79108e7i	−0.0114816	−	0.0428499i
$961$		−	8.14126e8i		−	0.917321i
$962$	−2.08795e9	−	9.89833e8i	−2.34528	−	1.11183i
$963$	2.64667e8			0.296361
$964$	−2.92919e8	+	7.84873e7i	−0.326976	+	0.0876129i
$965$	1.33488e8	−	2.31207e8i	0.148545	−	0.257288i
$966$	1.94813e8	−	1.12475e8i	0.216116	−	0.124775i
$967$	7.56435e8	+	7.56435e8i	0.836550	+	0.836550i	0.988403	−	0.151853i	$-0.0485240\pi$
$967$	7.56435e8	+	7.56435e8i	0.836550	+	0.836550i	−0.151853	+	0.988403i	$0.548524\pi$
$968$	1.78837e8	−	6.67428e8i	0.197165	−	0.735831i
$969$	1.18417e8	+	3.17297e7i	0.130149	+	0.0348734i
$970$	−3.68633e8	+	3.68633e8i	−0.403905	+	0.403905i
$971$	−7.51609e7	−	1.30182e8i	−0.0820983	−	0.142198i	0.822053	−	0.569411i	$-0.192829\pi$
$971$	−7.51609e7	−	1.30182e8i	−0.0820983	−	0.142198i	−0.904151	+	0.427213i	$0.859495\pi$
$972$	−3.71058e8	−	2.14231e8i	−0.404058	−	0.233283i
$973$	−1.36391e7	−	5.09020e7i	−0.0148064	−	0.0552581i
$974$			1.88577e9i			2.04085i
$975$	−8.26438e7	+	6.70136e6i	−0.0891654	+	0.00723018i
$976$	4.61895e6			0.00496814
$977$	1.35012e9	−	3.61763e8i	1.44773	−	0.387918i	0.552497	−	0.833515i	$-0.313675\pi$
$977$	1.35012e9	−	3.61763e8i	1.44773	−	0.387918i	0.895234	+	0.445597i	$0.147008\pi$
$978$	7.73246e7	−	1.33930e8i	0.0826611	−	0.143173i
$979$	−1.05123e7	+	6.06930e6i	−0.0112034	+	0.00646831i
$980$	1.40423e8	+	1.40423e8i	0.149197	+	0.149197i
$981$	6.32781e7	−	2.36157e8i	0.0670265	−	0.250146i
$982$	1.33633e9	+	3.58069e8i	1.41117	+	0.378122i
$983$	1.07866e9	−	1.07866e9i	1.13559	−	1.13559i	0.146362	−	0.989231i	$-0.453244\pi$
$983$	1.07866e9	−	1.07866e9i	1.13559	−	1.13559i	0.989231	−	0.146362i	$-0.0467563\pi$
$984$	−7.97945e7	−	1.38208e8i	−0.0837506	−	0.145060i
$985$	−5.48870e6	−	3.16890e6i	−0.00574329	−	0.00331589i
$986$	−2.07110e8	−	7.72945e8i	−0.216058	−	0.806340i
$987$		−	5.24178e7i		−	0.0545165i
$988$	1.73653e9	+	1.47603e9i	1.80058	+	1.53047i
$989$	−7.11792e8			−0.735808
$990$	2.08402e8	−	5.58412e7i	0.214781	−	0.0575505i
$991$	7.41446e8	−	1.28422e9i	0.761830	−	1.31953i	−0.180076	−	0.983653i	$-0.557634\pi$
$991$	7.41446e8	−	1.28422e9i	0.761830	−	1.31953i	0.941906	−	0.335876i	$-0.109032\pi$
$992$	2.42053e8	−	1.39749e8i	0.247956	−	0.143158i
$993$	1.17046e8	+	1.17046e8i	0.119538	+	0.119538i
$994$	−2.64844e7	+	9.88410e7i	−0.0269669	+	0.100642i
$995$	−2.85486e8	−	7.64957e7i	−0.289811	−	0.0776547i
$996$	1.80268e8	−	1.80268e8i	0.182449	−	0.182449i
$997$	7.97273e8	+	1.38092e9i	0.804492	+	1.39342i	0.916633	+	0.399729i	$0.130896\pi$
$997$	7.97273e8	+	1.38092e9i	0.804492	+	1.39342i	−0.112141	+	0.993692i	$0.535771\pi$
$998$	−8.29931e8	−	4.79161e8i	−0.834931	−	0.482048i
$999$	−8.00513e7	−	2.98755e8i	−0.0802919	−	0.299654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.f.a.7.6	yes	24
13.2	odd	12	inner	13.7.f.a.2.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.f.a.2.6	✓	24	13.2	odd	12	inner
13.7.f.a.7.6	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(12.5088 - 3.35172i) q^{2} +(-1.31220 + 2.27280i) q^{3} +(89.8106 - 51.8522i) q^{4} +(24.9454 + 24.9454i) q^{5} +(-8.79628 + 32.8282i) q^{6} +(-400.516 - 107.318i) q^{7} +(363.576 - 363.576i) q^{8} +(361.056 + 625.368i) q^{9} +O(q^{10})\)	\(q+(12.5088 - 3.35172i) q^{2} +(-1.31220 + 2.27280i) q^{3} +(89.8106 - 51.8522i) q^{4} +(24.9454 + 24.9454i) q^{5} +(-8.79628 + 32.8282i) q^{6} +(-400.516 - 107.318i) q^{7} +(363.576 - 363.576i) q^{8} +(361.056 + 625.368i) q^{9} +(395.648 + 228.427i) q^{10} +(-169.267 - 631.712i) q^{11} +272.162i q^{12} +(-1807.65 + 1248.68i) q^{13} -5369.68 q^{14} +(-89.4294 + 23.9625i) q^{15} +(10.7557 - 18.6295i) q^{16} +(4044.24 - 2334.94i) q^{17} +(6612.44 + 6612.44i) q^{18} +(2588.98 - 9662.21i) q^{19} +(3533.84 + 946.889i) q^{20} +(769.471 - 769.471i) q^{21} +(-4234.65 - 7334.63i) q^{22} +(13824.2 + 7981.38i) q^{23} +(349.251 + 1303.42i) q^{24} -14380.5i q^{25} +(-18426.3 + 21678.3i) q^{26} -3808.31 q^{27} +(-41535.3 + 11129.3i) q^{28} +(6616.02 - 11459.3i) q^{29} +(-1038.34 + 599.486i) q^{30} +(-6057.12 - 6057.12i) q^{31} +(-8444.89 + 31516.8i) q^{32} +(1657.87 + 444.225i) q^{33} +(42762.5 - 42762.5i) q^{34} +(-7313.95 - 12668.1i) q^{35} +(64853.3 + 37443.1i) q^{36} +(21020.2 + 78448.4i) q^{37} -129540. i q^{38} +(-466.005 - 5746.96i) q^{39} +18139.1 q^{40} +(-114237. + 30609.7i) q^{41} +(7046.11 - 12204.2i) q^{42} +(-38616.8 + 22295.4i) q^{43} +(-47957.6 - 47957.6i) q^{44} +(-6593.36 + 24606.8i) q^{45} +(199675. + 53502.8i) q^{46} +(34061.0 - 34061.0i) q^{47} +(28.2274 + 48.8913i) q^{48} +(47009.1 + 27140.7i) q^{49} +(-48199.3 - 179882. i) q^{50} +12255.7i q^{51} +(-97599.2 + 205876. i) q^{52} -14637.4 q^{53} +(-47637.4 + 12764.4i) q^{54} +(11535.9 - 19980.8i) q^{55} +(-184636. + 106600. i) q^{56} +(18563.0 + 18563.0i) q^{57} +(44350.1 - 165517. i) q^{58} +(-101893. - 27302.2i) q^{59} +(-6789.20 + 6789.20i) q^{60} +(107360. + 185953. i) q^{61} +(-96069.2 - 55465.6i) q^{62} +(-77495.7 - 289218. i) q^{63} +423919. i q^{64} +(-76241.5 - 13943.7i) q^{65} +22226.9 q^{66} +(470454. - 126058. i) q^{67} +(242144. - 419405. i) q^{68} +(-36280.2 + 20946.4i) q^{69} +(-133949. - 133949. i) q^{70} +(4932.21 - 18407.2i) q^{71} +(358640. + 96097.3i) q^{72} +(158416. - 158416. i) q^{73} +(525875. + 910842. i) q^{74} +(32683.9 + 18870.1i) q^{75} +(-268489. - 1.00201e6i) q^{76} +271176. i q^{77} +(-25091.4 - 70325.6i) q^{78} -280091. q^{79} +(733.027 - 196.414i) q^{80} +(-258213. + 447238. i) q^{81} +(-1.32637e6 + 765781. i) q^{82} +(-662356. - 662356. i) q^{83} +(29207.9 - 109005. i) q^{84} +(159131. + 42639.1i) q^{85} +(-408322. + 408322. i) q^{86} +(17363.1 + 30073.8i) q^{87} +(-291217. - 168134. i) q^{88} +(-4803.85 - 17928.2i) q^{89} +329900. i q^{90} +(858000. - 306124. i) q^{91} +1.65541e6 q^{92} +(21714.8 - 5818.47i) q^{93} +(311899. - 540225. i) q^{94} +(305611. - 176445. i) q^{95} +(-60549.9 - 60549.9i) q^{96} +(-295344. + 1.10224e6i) q^{97} +(678996. + 181936. i) q^{98} +(333938. - 333938. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9} + 4674 q^{10} + 228 q^{11} - 1552 q^{13} - 14616 q^{14} + 7486 q^{15} - 2138 q^{16} + 20898 q^{17} - 5630 q^{18} - 14036 q^{19} - 14634 q^{20} - 314 q^{21} + 37852 q^{22} + 29634 q^{23} + 47154 q^{24} + 510 q^{26} - 107060 q^{27} - 40572 q^{28} + 1026 q^{29} - 247734 q^{30} - 118116 q^{31} + 180876 q^{32} + 306046 q^{33} + 101898 q^{34} + 104862 q^{35} + 105066 q^{36} - 31470 q^{37} + 28510 q^{39} - 275328 q^{40} - 357216 q^{41} - 25636 q^{42} - 480486 q^{43} - 797712 q^{44} + 464248 q^{45} + 1012050 q^{46} + 140028 q^{47} + 676102 q^{48} + 854562 q^{49} + 756714 q^{50} - 771704 q^{52} - 1397076 q^{53} - 1271048 q^{54} - 205490 q^{55} - 1461108 q^{56} - 1483394 q^{57} + 1133806 q^{58} + 1568052 q^{59} + 886808 q^{60} + 768676 q^{61} + 3741966 q^{62} + 1336264 q^{63} - 946968 q^{65} - 5076928 q^{66} - 1489892 q^{67} - 569052 q^{68} - 1475766 q^{69} - 2626556 q^{70} + 2136948 q^{71} + 4787052 q^{72} + 326326 q^{73} + 2159718 q^{74} + 3466008 q^{75} + 1522158 q^{76} - 1573544 q^{78} - 1734344 q^{79} - 5214300 q^{80} - 773072 q^{81} - 3540426 q^{82} - 3642132 q^{83} + 2952364 q^{84} + 3509916 q^{85} - 132324 q^{86} + 531698 q^{87} + 4478052 q^{88} + 632754 q^{89} - 2946788 q^{91} - 1656060 q^{92} - 295514 q^{93} + 1552210 q^{94} - 2753718 q^{95} - 3979208 q^{96} + 2258214 q^{97} + 4984308 q^{98} + 4336480 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9 + 4674 * q^10 + 228 * q^11 - 1552 * q^13 - 14616 * q^14 + 7486 * q^15 - 2138 * q^16 + 20898 * q^17 - 5630 * q^18 - 14036 * q^19 - 14634 * q^20 - 314 * q^21 + 37852 * q^22 + 29634 * q^23 + 47154 * q^24 + 510 * q^26 - 107060 * q^27 - 40572 * q^28 + 1026 * q^29 - 247734 * q^30 - 118116 * q^31 + 180876 * q^32 + 306046 * q^33 + 101898 * q^34 + 104862 * q^35 + 105066 * q^36 - 31470 * q^37 + 28510 * q^39 - 275328 * q^40 - 357216 * q^41 - 25636 * q^42 - 480486 * q^43 - 797712 * q^44 + 464248 * q^45 + 1012050 * q^46 + 140028 * q^47 + 676102 * q^48 + 854562 * q^49 + 756714 * q^50 - 771704 * q^52 - 1397076 * q^53 - 1271048 * q^54 - 205490 * q^55 - 1461108 * q^56 - 1483394 * q^57 + 1133806 * q^58 + 1568052 * q^59 + 886808 * q^60 + 768676 * q^61 + 3741966 * q^62 + 1336264 * q^63 - 946968 * q^65 - 5076928 * q^66 - 1489892 * q^67 - 569052 * q^68 - 1475766 * q^69 - 2626556 * q^70 + 2136948 * q^71 + 4787052 * q^72 + 326326 * q^73 + 2159718 * q^74 + 3466008 * q^75 + 1522158 * q^76 - 1573544 * q^78 - 1734344 * q^79 - 5214300 * q^80 - 773072 * q^81 - 3540426 * q^82 - 3642132 * q^83 + 2952364 * q^84 + 3509916 * q^85 - 132324 * q^86 + 531698 * q^87 + 4478052 * q^88 + 632754 * q^89 - 2946788 * q^91 - 1656060 * q^92 - 295514 * q^93 + 1552210 * q^94 - 2753718 * q^95 - 3979208 * q^96 + 2258214 * q^97 + 4984308 * q^98 + 4336480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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