LMFDB - Embedded newform 13.7.f.a.7.5

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			7.5
Character	$\chi$	$=$	13.7
Dual form			13.7.f.a.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.89025 - 1.57829i) q^{2} +(20.5701 - 35.6285i) q^{3} +(-23.2216 + 13.4070i) q^{4} +(-37.1940 - 37.1940i) q^{5} +(64.9312 - 242.326i) q^{6} +(588.562 + 157.705i) q^{7} +(-391.586 + 391.586i) q^{8} +(-481.762 - 834.436i) q^{9} +O(q^{10})$	\(q+(5.89025 - 1.57829i) q^{2} +(20.5701 - 35.6285i) q^{3} +(-23.2216 + 13.4070i) q^{4} +(-37.1940 - 37.1940i) q^{5} +(64.9312 - 242.326i) q^{6} +(588.562 + 157.705i) q^{7} +(-391.586 + 391.586i) q^{8} +(-481.762 - 834.436i) q^{9} +(-277.785 - 160.379i) q^{10} +(357.486 + 1334.15i) q^{11} +1103.14i q^{12} +(-2195.96 + 67.7273i) q^{13} +3715.68 q^{14} +(-2090.25 + 560.082i) q^{15} +(-830.455 + 1438.39i) q^{16} +(542.831 - 313.404i) q^{17} +(-4154.67 - 4154.67i) q^{18} +(493.874 - 1843.16i) q^{19} +(1362.37 + 365.045i) q^{20} +(17725.6 - 17725.6i) q^{21} +(4211.36 + 7294.28i) q^{22} +(-8024.91 - 4633.18i) q^{23} +(5896.66 + 22006.6i) q^{24} -12858.2i q^{25} +(-12827.8 + 3864.78i) q^{26} -9648.36 q^{27} +(-15781.7 + 4228.70i) q^{28} +(-15187.1 + 26304.9i) q^{29} +(-11428.1 + 6598.04i) q^{30} +(10734.1 + 10734.1i) q^{31} +(6551.76 - 24451.5i) q^{32} +(54887.5 + 14707.1i) q^{33} +(2702.77 - 2702.77i) q^{34} +(-16025.3 - 27756.7i) q^{35} +(22374.6 + 12918.0i) q^{36} +(-15082.9 - 56290.2i) q^{37} -11636.2i q^{38} +(-42758.1 + 79631.8i) q^{39} +29129.3 q^{40} +(-51334.8 + 13755.1i) q^{41} +(76432.1 - 132384. i) q^{42} +(22415.5 - 12941.6i) q^{43} +(-26188.4 - 26188.4i) q^{44} +(-13117.4 + 48954.7i) q^{45} +(-54581.2 - 14625.0i) q^{46} +(-21563.6 + 21563.6i) q^{47} +(34165.2 + 59175.8i) q^{48} +(219648. + 126814. i) q^{49} +(-20293.9 - 75738.0i) q^{50} -25787.0i q^{51} +(50085.6 - 31013.9i) q^{52} -219021. q^{53} +(-56831.2 + 15227.9i) q^{54} +(36326.2 - 62918.9i) q^{55} +(-292228. + 168718. i) q^{56} +(-55510.2 - 55510.2i) q^{57} +(-47939.3 + 178912. i) q^{58} +(156719. + 41992.7i) q^{59} +(41030.1 - 41030.1i) q^{60} +(201313. + 348684. i) q^{61} +(80167.7 + 46284.8i) q^{62} +(-151952. - 567093. i) q^{63} -260664. i q^{64} +(84195.5 + 79157.4i) q^{65} +346513. q^{66} +(-14911.4 + 3995.51i) q^{67} +(-8403.61 + 14555.5i) q^{68} +(-330147. + 190611. i) q^{69} +(-138201. - 138201. i) q^{70} +(136535. - 509556. i) q^{71} +(515405. + 138102. i) q^{72} +(121026. - 121026. i) q^{73} +(-177684. - 307758. i) q^{74} +(-458119. - 264495. i) q^{75} +(13242.8 + 49422.6i) q^{76} +841610. i q^{77} +(-126174. + 536536. i) q^{78} +326385. q^{79} +(84387.5 - 22611.6i) q^{80} +(152736. - 264547. i) q^{81} +(-280665. + 162042. i) q^{82} +(-342983. - 342983. i) q^{83} +(-173970. + 649264. i) q^{84} +(-31846.8 - 8533.32i) q^{85} +(111607. - 111607. i) q^{86} +(624804. + 1.08219e6i) q^{87} +(-662423. - 382450. i) q^{88} +(-56310.2 - 210152. i) q^{89} +309058. i q^{90} +(-1.30314e6 - 306451. i) q^{91} +248469. q^{92} +(603240. - 161638. i) q^{93} +(-92981.5 + 161049. i) q^{94} +(-86923.8 + 50185.5i) q^{95} +(-736401. - 736401. i) q^{96} +(281554. - 1.05078e6i) q^{97} +(1.49393e6 + 400296. i) q^{98} +(941043. - 941043. 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 $

$2$	5.89025	−	1.57829i	0.736281	−	0.197286i	0.128856	−	0.991663i	$-0.458869\pi$
$2$	5.89025	−	1.57829i	0.736281	−	0.197286i	0.607424	+	0.794377i	$0.292203\pi$
$3$	20.5701	−	35.6285i	0.761857	−	1.31958i	−0.180035	−	0.983660i	$-0.557621\pi$
$3$	20.5701	−	35.6285i	0.761857	−	1.31958i	0.941892	−	0.335915i	$-0.109046\pi$
$4$	−23.2216	+	13.4070i	−0.362838	+	0.209485i
$5$	−37.1940	−	37.1940i	−0.297552	−	0.297552i	0.542502	−	0.840054i	$-0.317477\pi$
$5$	−37.1940	−	37.1940i	−0.297552	−	0.297552i	−0.840054	+	0.542502i	$0.817477\pi$
$6$	64.9312	−	242.326i	0.300607	−	1.12188i
$7$	588.562	+	157.705i	1.71592	+	0.459781i	0.976865	−	0.213859i	$-0.0686032\pi$
$7$	588.562	+	157.705i	1.71592	+	0.459781i	0.739060	+	0.673639i	$0.235270\pi$
$8$	−391.586	+	391.586i	−0.764817	+	0.764817i
$9$	−481.762	−	834.436i	−0.660853	−	1.14463i
$10$	−277.785	−	160.379i	−0.277785	−	0.160379i
$11$	357.486	+	1334.15i	0.268584	+	1.00237i	0.960020	+	0.279932i	$0.0903119\pi$
$11$	357.486	+	1334.15i	0.268584	+	1.00237i	−0.691436	+	0.722438i	$0.743021\pi$
$12$			1103.14i			0.638389i
$13$	−2195.96	+	67.7273i	−0.999525	+	0.0308272i
$13$	−2195.96	+	67.7273i	−0.999525	+	0.0308272i
$14$	3715.68			1.35411
$15$	−2090.25	+	560.082i	−0.619335	+	0.165950i
$16$	−830.455	+	1438.39i	−0.202748	+	0.351170i
$17$	542.831	−	313.404i	0.110489	−	0.0637907i	−0.443737	−	0.896157i	$-0.646348\pi$
$17$	542.831	−	313.404i	0.110489	−	0.0637907i	0.554226	+	0.832366i	$0.313014\pi$
$18$	−4154.67	−	4154.67i	−0.712392	−	0.712392i
$19$	493.874	−	1843.16i	0.0720038	−	0.268722i	−0.920533	−	0.390664i	$-0.872245\pi$
$19$	493.874	−	1843.16i	0.0720038	−	0.268722i	0.992537	+	0.121942i	$0.0389122\pi$
$20$	1362.37	+	365.045i	0.170296	+	0.0456306i
$21$	17725.6	−	17725.6i	1.91400	−	1.91400i
$22$	4211.36	+	7294.28i	0.395507	+	0.685038i
$23$	−8024.91	−	4633.18i	−0.659564	−	0.380799i	0.132547	−	0.991177i	$-0.457684\pi$
$23$	−8024.91	−	4633.18i	−0.659564	−	0.380799i	−0.792111	+	0.610378i	$0.791018\pi$
$24$	5896.66	+	22006.6i	0.426552	+	1.59192i
$25$		−	12858.2i		−	0.822926i
$26$	−12827.8	+	3864.78i	−0.729849	+	0.219889i
$27$	−9648.36			−0.490187
$28$	−15781.7	+	4228.70i	−0.718919	+	0.192634i
$29$	−15187.1	+	26304.9i	−0.622705	+	1.07856i	0.366275	+	0.930507i	$0.380633\pi$
$29$	−15187.1	+	26304.9i	−0.622705	+	1.07856i	−0.988980	+	0.148050i	$0.952700\pi$
$30$	−11428.1	+	6598.04i	−0.423264	+	0.244372i
$31$	10734.1	+	10734.1i	0.360312	+	0.360312i	0.863928	−	0.503616i	$-0.167997\pi$
$31$	10734.1	+	10734.1i	0.360312	+	0.360312i	−0.503616	+	0.863928i	$0.667997\pi$
$32$	6551.76	−	24451.5i	0.199944	−	0.746201i
$33$	54887.5	+	14707.1i	1.52733	+	0.409246i
$34$	2702.77	−	2702.77i	0.0687657	−	0.0687657i
$35$	−16025.3	−	27756.7i	−0.373768	−	0.647386i
$36$	22374.6	+	12918.0i	0.479565	+	0.276877i
$37$	−15082.9	−	56290.2i	−0.297770	−	1.11129i	−0.938993	−	0.343937i	$-0.888239\pi$
$37$	−15082.9	−	56290.2i	−0.297770	−	1.11129i	0.641223	−	0.767354i	$-0.278427\pi$
$38$		−	11636.2i		−	0.212060i
$39$	−42758.1	+	79631.8i	−0.720816	+	1.34243i
$40$	29129.3			0.455146
$41$	−51334.8	+	13755.1i	−0.744835	+	0.199578i	−0.611226	−	0.791456i	$-0.709323\pi$
$41$	−51334.8	+	13755.1i	−0.744835	+	0.199578i	−0.133609	+	0.991034i	$0.542657\pi$
$42$	76432.1	−	132384.i	1.03164	−	1.78685i
$43$	22415.5	−	12941.6i	0.281931	−	0.162773i	−0.352366	−	0.935862i	$-0.614623\pi$
$43$	22415.5	−	12941.6i	0.281931	−	0.162773i	0.634297	+	0.773089i	$0.281290\pi$
$44$	−26188.4	−	26188.4i	−0.307434	−	0.307434i
$45$	−13117.4	+	48954.7i	−0.143949	+	0.537225i
$46$	−54581.2	−	14625.0i	−0.560750	−	0.150253i
$47$	−21563.6	+	21563.6i	−0.207696	+	0.207696i	−0.803288	−	0.595591i	$-0.796918\pi$
$47$	−21563.6	+	21563.6i	−0.207696	+	0.207696i	0.595591	+	0.803288i	$0.296918\pi$
$48$	34165.2	+	59175.8i	0.308930	+	0.535082i
$49$	219648.	+	126814.i	1.86697	+	1.07790i
$50$	−20293.9	−	75738.0i	−0.162352	−	0.605904i
$51$		−	25787.0i		−	0.194398i
$52$	50085.6	−	31013.9i	0.356208	−	0.220570i
$53$	−219021.			−1.47115			−0.735576	−	0.677443i	$-0.763088\pi$
$53$	−219021.			−1.47115			−0.735576	+	0.677443i	$0.763088\pi$
$54$	−56831.2	+	15227.9i	−0.360915	+	0.0967070i
$55$	36326.2	−	62918.9i	0.218340	−	0.378175i
$56$	−292228.	+	168718.i	−1.66402	+	0.960720i
$57$	−55510.2	−	55510.2i	−0.299742	−	0.299742i
$58$	−47939.3	+	178912.i	−0.245702	+	0.916971i
$59$	156719.	+	41992.7i	0.763072	+	0.204465i	0.619309	−	0.785148i	$-0.287413\pi$
$59$	156719.	+	41992.7i	0.763072	+	0.204465i	0.143763	+	0.989612i	$0.454080\pi$
$60$	41030.1	−	41030.1i	0.189954	−	0.189954i
$61$	201313.	+	348684.i	0.886915	+	1.53618i	0.843503	+	0.537124i	$0.180489\pi$
$61$	201313.	+	348684.i	0.886915	+	1.53618i	0.0434114	+	0.999057i	$0.486177\pi$
$62$	80167.7	+	46284.8i	0.336375	+	0.194206i
$63$	−151952.	−	567093.i	−0.607695	−	2.26795i
$64$		−	260664.i		−	0.994355i
$65$	84195.5	+	79157.4i	0.306583	+	0.288238i
$66$	346513.			1.20528
$67$	−14911.4	+	3995.51i	−0.0495787	+	0.0132846i	−0.283523	−	0.958965i	$-0.591503\pi$
$67$	−14911.4	+	3995.51i	−0.0495787	+	0.0132846i	0.233944	+	0.972250i	$0.424837\pi$
$68$	−8403.61	+	14555.5i	−0.0267263	+	0.0462914i
$69$	−330147.	+	190611.i	−1.00499	+	0.580229i
$70$	−138201.	−	138201.i	−0.402918	−	0.402918i
$71$	136535.	−	509556.i	0.381477	−	1.42369i	−0.462168	−	0.886792i	$-0.652928\pi$
$71$	136535.	−	509556.i	0.381477	−	1.42369i	0.843645	−	0.536901i	$-0.180405\pi$
$72$	515405.	+	138102.i	1.38086	+	0.370001i
$73$	121026.	−	121026.i	0.311106	−	0.311106i	−0.534232	−	0.845338i	$-0.679399\pi$
$73$	121026.	−	121026.i	0.311106	−	0.311106i	0.845338	+	0.534232i	$0.179399\pi$
$74$	−177684.	−	307758.i	−0.438484	−	0.759477i
$75$	−458119.	−	264495.i	−1.08591	−	0.626952i
$76$	13242.8	+	49422.6i	0.0301674	+	0.112586i
$77$			841610.i			1.84348i
$78$	−126174.	+	536536.i	−0.265880	+	1.13062i
$79$	326385.			0.661986			0.330993	−	0.943633i	$-0.392616\pi$
$79$	326385.			0.661986			0.330993	+	0.943633i	$0.392616\pi$
$80$	84387.5	−	22611.6i	0.164819	−	0.0441632i
$81$	152736.	−	264547.i	0.287400	−	0.497791i
$82$	−280665.	+	162042.i	−0.509034	+	0.293891i
$83$	−342983.	−	342983.i	−0.599844	−	0.599844i	0.340427	−	0.940271i	$-0.389428\pi$
$83$	−342983.	−	342983.i	−0.599844	−	0.599844i	−0.940271	+	0.340427i	$0.889428\pi$
$84$	−173970.	+	649264.i	−0.293519	+	1.09543i
$85$	−31846.8	−	8533.32i	−0.0518572	−	0.0138951i
$86$	111607.	−	111607.i	0.175467	−	0.175467i
$87$	624804.	+	1.08219e6i	0.948824	+	1.64341i
$88$	−662423.	−	382450.i	−0.972048	−	0.561212i
$89$	−56310.2	−	210152.i	−0.0798761	−	0.298102i	0.914419	−	0.404770i	$-0.132648\pi$
$89$	−56310.2	−	210152.i	−0.0798761	−	0.298102i	−0.994295	+	0.106668i	$0.965982\pi$
$90$			309058.i			0.423948i
$91$	−1.30314e6	−	306451.i	−1.72928	−	0.406665i
$92$	248469.			0.319086
$93$	603240.	−	161638.i	0.749965	−	0.200953i
$94$	−92981.5	+	161049.i	−0.111947	+	0.193898i
$95$	−86923.8	+	50185.5i	−0.101384	+	0.0585339i
$96$	−736401.	−	736401.i	−0.832339	−	0.832339i
$97$	281554.	−	1.05078e6i	0.308494	−	1.15132i	−0.621401	−	0.783493i	$-0.713436\pi$
$97$	281554.	−	1.05078e6i	0.308494	−	1.15132i	0.929895	−	0.367824i	$-0.119897\pi$
$98$	1.49393e6	+	400296.i	1.58727	+	0.425308i
$99$	941043.	−	941043.i	0.969849	−	0.969849i
$100$	172390.	+	298589.i	0.172390	+	0.298589i
$101$	1.32885e6	+	767214.i	1.28977	+	0.744651i	0.978614	−	0.205707i	$-0.0659495\pi$
$101$	1.32885e6	+	767214.i	1.28977	+	0.744651i	0.311159	+	0.950358i	$0.399283\pi$
$102$	−40699.3	−	151892.i	−0.0383519	−	0.143131i
$103$		−	338349.i		−	0.309637i	−0.987943	−	0.154818i	$-0.950521\pi$
$103$		−	338349.i		−	0.309637i	0.987943	−	0.154818i	$-0.0494793\pi$
$104$	833385.	−	886427.i	0.740876	−	0.788031i
$105$	−1.31857e6			−1.13903
$106$	−1.29009e6	+	345677.i	−1.08318	+	0.290237i
$107$	−442472.	+	766384.i	−0.361189	+	0.625597i	−0.988157	−	0.153448i	$-0.950962\pi$
$107$	−442472.	+	766384.i	−0.361189	+	0.625597i	0.626968	+	0.779045i	$0.284296\pi$
$108$	224050.	−	129356.i	0.177859	−	0.102687i
$109$	789617.	+	789617.i	0.609729	+	0.609729i	0.942875	−	0.333146i	$-0.108110\pi$
$109$	789617.	+	789617.i	0.609729	+	0.609729i	−0.333146	+	0.942875i	$0.608110\pi$
$110$	114666.	−	427941.i	0.0861506	−	0.321518i
$111$	−2.31580e6	−	620516.i	−1.69329	−	0.453716i
$112$	−715616.	+	715616.i	−0.509361	+	0.509361i
$113$	−311238.	−	539079.i	−0.215703	−	0.373609i	0.737787	−	0.675034i	$-0.235871\pi$
$113$	−311238.	−	539079.i	−0.215703	−	0.373609i	−0.953490	+	0.301425i	$0.902538\pi$
$114$	−414579.	−	239357.i	−0.279829	−	0.161559i
$115$	126152.	+	470805.i	0.0829469	+	0.309562i
$116$		−	814457.i		−	0.521788i
$117$	1.11444e6	+	1.79976e6i	0.695824	+	1.12371i
$118$	989390.			0.602173
$119$	368915.	−	98850.5i	0.218920	−	0.0586594i
$120$	599195.	−	1.03784e6i	0.346756	−	0.600599i
$121$	−117956.	+	68102.0i	−0.0665831	+	0.0384418i
$122$	1.73610e6	+	1.73610e6i	0.956085	+	0.956085i
$123$	−565890.	+	2.11193e6i	−0.304100	+	1.13492i
$124$	−393174.	−	105351.i	−0.206215	−	0.0552551i
$125$	−1.05940e6	+	1.05940e6i	−0.542415	+	0.542415i
$126$	−1.79007e6	−	3.10050e6i	−0.894868	−	1.54996i
$127$	1.44203e6	+	832554.i	0.703982	+	0.406444i	0.808829	−	0.588044i	$-0.200102\pi$
$127$	1.44203e6	+	832554.i	0.703982	+	0.406444i	−0.104847	+	0.994488i	$0.533435\pi$
$128$	7909.89	+	29520.1i	0.00377173	+	0.0140763i
$129$		−	1.06484e6i		−	0.496039i
$130$	620865.	+	333372.i	0.282597	+	0.151740i
$131$	−1.50567e6			−0.669753			−0.334877	−	0.942262i	$-0.608695\pi$
$131$	−1.50567e6			−0.669753			−0.334877	+	0.942262i	$0.608695\pi$
$132$	−1.47175e6	+	394356.i	−0.639902	+	0.171461i
$133$	581351.	−	1.00693e6i	0.247106	−	0.428001i
$134$	−81526.0	+	47069.0i	−0.0338830	+	0.0195623i
$135$	358861.	+	358861.i	0.145856	+	0.145856i
$136$	−89840.6	+	335290.i	−0.0357154	+	0.133292i
$137$	−387164.	−	103740.i	−0.150568	−	0.0403446i	0.182748	−	0.983160i	$-0.441501\pi$
$137$	−387164.	−	103740.i	−0.150568	−	0.0403446i	−0.333316	+	0.942815i	$0.608168\pi$
$138$	−1.64381e6	+	1.64381e6i	−0.625481	+	0.625481i
$139$	−349527.	−	605399.i	−0.130148	−	0.225422i	0.793586	−	0.608459i	$-0.208212\pi$
$139$	−349527.	−	605399.i	−0.130148	−	0.225422i	−0.923733	+	0.383036i	$0.874878\pi$
$140$	744268.	+	429703.i	0.271235	+	0.156597i
$141$	324714.	+	1.21185e6i	0.115836	+	0.432305i
$142$		−	3.21690e6i		−	1.12350i
$143$	−875381.	−	2.90553e6i	−0.299357	−	0.993614i
$144$	1.60033e6			0.535946
$145$	1.54326e6	−	413514.i	0.506214	−	0.135640i
$146$	521857.	−	903883.i	0.167685	−	0.290438i
$147$	9.03637e6	−	5.21715e6i	2.84474	−	1.64241i
$148$	1.10493e6	+	1.10493e6i	0.340840	+	0.340840i
$149$	−598758.	+	2.23460e6i	−0.181006	+	0.675523i	0.814444	+	0.580242i	$0.197042\pi$
$149$	−598758.	+	2.23460e6i	−0.181006	+	0.675523i	−0.995450	+	0.0952818i	$0.969625\pi$
$150$	−3.11588e6	−	834899.i	−0.923225	−	0.247377i
$151$	−376032.	+	376032.i	−0.109218	+	0.109218i	−0.759604	−	0.650386i	$-0.774607\pi$
$151$	−376032.	+	376032.i	−0.109218	+	0.109218i	0.650386	+	0.759604i	$0.274607\pi$
$152$	528363.	+	915152.i	0.150453	+	0.260593i
$153$	−523030.	−	301972.i	−0.146034	−	0.0843125i
$154$	1.32830e6	+	4.95729e6i	0.363693	+	1.35732i
$155$		−	798485.i		−	0.214423i
$156$	−74712.4	−	2.42244e6i	−0.0196797	−	0.638086i
$157$	−5.94555e6			−1.53636			−0.768181	−	0.640233i	$-0.778838\pi$
$157$	−5.94555e6			−1.53636			−0.768181	+	0.640233i	$0.778838\pi$
$158$	1.92249e6	−	515129.i	0.487408	−	0.130600i
$159$	−4.50529e6	+	7.80338e6i	−1.12081	+	1.94130i
$160$	−1.15314e6	+	665763.i	−0.281527	+	0.162540i
$161$	−3.99248e6	−	3.99248e6i	−0.956677	−	0.956677i
$162$	482123.	−	1.79931e6i	0.113400	−	0.423214i
$163$	544880.	+	146000.i	0.125817	+	0.0337124i	0.321178	−	0.947019i	$-0.395921\pi$
$163$	544880.	+	146000.i	0.125817	+	0.0337124i	−0.195361	+	0.980731i	$0.562588\pi$
$164$	1.00766e6	−	1.00766e6i	0.228446	−	0.228446i
$165$	−1.49447e6	−	2.58850e6i	−0.332687	−	0.576231i
$166$	−2.56158e6	−	1.47893e6i	−0.559994	−	0.323313i
$167$	1.07668e6	+	4.01821e6i	0.231172	+	0.862746i	0.979837	+	0.199797i	$0.0640284\pi$
$167$	1.07668e6	+	4.01821e6i	0.231172	+	0.862746i	−0.748665	+	0.662948i	$0.769305\pi$
$168$			1.38822e7i			2.92773i
$169$	4.81764e6	−	297452.i	0.998099	−	0.0616250i
$170$	−201053.			−0.0409228
$171$	−1.77593e6	+	475859.i	−0.355171	+	0.0951678i
$172$	−347016.	+	601049.i	−0.0681968	+	0.118120i
$173$	−2.75990e6	+	1.59343e6i	−0.533034	+	0.307748i	−0.742251	−	0.670122i	$-0.766242\pi$
$173$	−2.75990e6	+	1.59343e6i	−0.533034	+	0.307748i	0.209217	+	0.977869i	$0.432909\pi$
$174$	5.38825e6	+	5.38825e6i	1.02282	+	1.02282i
$175$	2.02780e6	−	7.56786e6i	0.378365	−	1.41208i
$176$	−2.21591e6	−	593752.i	−0.406457	−	0.108910i
$177$	4.71987e6	−	4.71987e6i	0.851158	−	0.851158i
$178$	−663361.	−	1.14898e6i	−0.117622	−	0.203728i
$179$	−6.65010e6	−	3.83944e6i	−1.15950	−	0.669435i	−0.208313	−	0.978062i	$-0.566797\pi$
$179$	−6.65010e6	−	3.83944e6i	−1.15950	−	0.669435i	−0.951183	+	0.308627i	$0.900130\pi$
$180$	−351729.	−	1.31267e6i	−0.0603102	−	0.225081i
$181$		−	3.22097e6i		−	0.543188i	−0.962412	−	0.271594i	$-0.912449\pi$
$181$		−	3.22097e6i		−	0.543188i	0.962412	−	0.271594i	$-0.0875508\pi$
$182$	−8.15947e6	+	251653.i	−1.35347	+	0.0417434i
$183$	1.65641e7			2.70281
$184$	4.95674e6	−	1.32815e6i	0.795687	−	0.213204i
$185$	−1.53267e6	+	2.65465e6i	−0.242065	+	0.419269i
$186$	3.29812e6	−	1.90417e6i	0.512540	−	0.295915i
$187$	612183.	+	612183.i	0.0936174	+	0.0936174i
$188$	211639.	−	789846.i	0.0318509	−	0.118869i
$189$	−5.67866e6	−	1.52159e6i	−0.841124	−	0.225379i
$190$	−432795.	+	432795.i	−0.0630989	+	0.0630989i
$191$	901256.	+	1.56102e6i	0.129344	+	0.224031i	0.923423	−	0.383784i	$-0.125379\pi$
$191$	901256.	+	1.56102e6i	0.129344	+	0.224031i	−0.794078	+	0.607815i	$0.792046\pi$
$192$	−9.28708e6	−	5.36190e6i	−1.31213	−	0.757557i
$193$	795631.	+	2.96934e6i	0.110673	+	0.413035i	0.998927	−	0.0463166i	$-0.0147483\pi$
$193$	795631.	+	2.96934e6i	0.110673	+	0.413035i	−0.888254	+	0.459352i	$0.848082\pi$
$194$		−	6.63370e6i		−	0.908554i
$195$	4.55217e6	−	1.37148e6i	0.613924	−	0.184964i
$196$	−6.80077e6			−0.903212
$197$	9.54013e6	−	2.55627e6i	1.24783	−	0.334355i	0.426332	−	0.904567i	$-0.359805\pi$
$197$	9.54013e6	−	2.55627e6i	1.24783	−	0.334355i	0.821498	+	0.570212i	$0.193139\pi$
$198$	4.05774e6	−	7.02821e6i	0.522744	−	0.905418i
$199$	−4.83432e6	+	2.79110e6i	−0.613446	+	0.354173i	−0.774313	−	0.632803i	$-0.781904\pi$
$199$	−4.83432e6	+	2.79110e6i	−0.613446	+	0.354173i	0.160867	+	0.986976i	$0.448571\pi$
$200$	5.03510e6	+	5.03510e6i	0.629387	+	0.629387i
$201$	−164376.	+	613461.i	−0.0202419	+	0.0755438i
$202$	9.03816e6	+	2.42177e6i	1.09654	+	0.293818i
$203$	−1.30870e7	+	1.30870e7i	−1.56441	+	1.56441i
$204$	345727.	+	598817.i	0.0407233	+	0.0705348i
$205$	2.42096e6	+	1.39774e6i	0.281012	+	0.162242i
$206$	−534011.	−	1.99296e6i	−0.0610870	−	0.227980i
$207$			8.92836e6i			1.00661i
$208$	1.72623e6	−	3.21489e6i	0.191826	−	0.357253i
$209$	2.63562e6			0.288698
$210$	−7.76671e6	+	2.08108e6i	−0.838647	+	0.224715i
$211$	−5.39915e6	+	9.35160e6i	−0.574749	+	0.995494i	0.421320	+	0.906912i	$0.361567\pi$
$211$	−5.39915e6	+	9.35160e6i	−0.574749	+	0.995494i	−0.996069	+	0.0885821i	$0.971766\pi$
$212$	5.08601e6	−	2.93641e6i	0.533789	−	0.308183i
$213$	−1.53462e7	−	1.53462e7i	−1.58804	−	1.58804i
$214$	−1.39669e6	+	5.21253e6i	−0.142515	+	0.531873i
$215$	−1.31507e6	−	352372.i	−0.132323	−	0.0354557i
$216$	3.77816e6	−	3.77816e6i	0.374904	−	0.374904i
$217$	4.62485e6	+	8.01047e6i	0.452604	+	0.783933i
$218$	5.89728e6	+	3.40480e6i	0.569223	+	0.328641i
$219$	−1.82245e6	−	6.80147e6i	−0.173509	−	0.647546i
$220$			1.94811e6i			0.182955i
$221$	−1.17081e6	+	724985.i	−0.108470	+	0.0671664i
$222$	−1.46200e7			−1.33625
$223$	838627.	−	224709.i	0.0756230	−	0.0202631i	−0.220809	−	0.975317i	$-0.570870\pi$
$223$	838627.	−	224709.i	0.0756230	−	0.0202631i	0.296432	+	0.955054i	$0.404203\pi$
$224$	7.71224e6	−	1.33580e7i	0.686177	−	1.18849i
$225$	−1.07294e7	+	6.19459e6i	−0.941946	+	0.543833i
$226$	−2.68409e6	−	2.68409e6i	−0.232526	−	0.232526i
$227$	−5.26126e6	+	1.96353e7i	−0.449792	+	1.67865i	0.253172	+	0.967421i	$0.418526\pi$
$227$	−5.26126e6	+	1.96353e7i	−0.449792	+	1.67865i	−0.702964	+	0.711226i	$0.748140\pi$
$228$	2.03326e6	+	544811.i	0.171549	+	0.0459665i
$229$	6.16858e6	−	6.16858e6i	0.513664	−	0.513664i	−0.401983	−	0.915647i	$-0.631679\pi$
$229$	6.16858e6	−	6.16858e6i	0.513664	−	0.513664i	0.915647	+	0.401983i	$0.131679\pi$
$230$	1.48613e6	+	2.57405e6i	0.122144	+	0.211560i
$231$	2.99853e7	+	1.73120e7i	2.43261	+	1.40447i
$232$	−4.35356e6	−	1.62477e7i	−0.348643	−	1.30115i
$233$		−	1.35981e7i		−	1.07500i	−0.843263	−	0.537502i	$-0.819368\pi$
$233$		−	1.35981e7i		−	1.07500i	0.843263	−	0.537502i	$-0.180632\pi$
$234$	9.40486e6	+	8.84209e6i	0.734015	+	0.690093i
$235$	1.60408e6			0.123601
$236$	−4.20227e6	+	1.12599e6i	−0.319704	+	0.0856643i
$237$	6.71379e6	−	1.16286e7i	0.504339	−	0.873541i
$238$	2.01699e6	−	1.16451e6i	0.149614	−	0.0863796i
$239$	−875426.	−	875426.i	−0.0641248	−	0.0641248i	0.674317	−	0.738442i	$-0.264438\pi$
$239$	−875426.	−	875426.i	−0.0641248	−	0.0641248i	−0.738442	+	0.674317i	$0.764438\pi$
$240$	930246.	−	3.47173e6i	0.0672921	−	0.251138i
$241$	3.66411e6	+	981795.i	0.261768	+	0.0701407i	0.387316	−	0.921947i	$-0.373402\pi$
$241$	3.66411e6	+	981795.i	0.261768	+	0.0701407i	−0.125548	+	0.992088i	$0.540069\pi$
$242$	−587306.	+	587306.i	−0.0414398	+	0.0414398i
$243$	−9.80044e6	−	1.69749e7i	−0.683009	−	1.18301i
$244$	−9.34962e6	−	5.39801e6i	−0.643612	−	0.371590i
$245$	−3.45287e6	−	1.28863e7i	−0.234791	−	0.876253i
$246$			1.33329e7i			0.895612i
$247$	−959693.	+	4.08095e6i	−0.0636857	+	0.270814i
$248$	−8.40662e6			−0.551146
$249$	−1.92752e7	+	5.16477e6i	−1.24854	+	0.334544i
$250$	−4.56811e6	+	7.91220e6i	−0.292359	+	0.506381i
$251$	2.41782e6	−	1.39593e6i	0.152898	−	0.0882757i	−0.421599	−	0.906782i	$-0.638531\pi$
$251$	2.41782e6	−	1.39593e6i	0.152898	−	0.0882757i	0.574497	+	0.818507i	$0.305198\pi$
$252$	1.11316e7	+	1.11316e7i	0.695594	+	0.695594i
$253$	3.31259e6	−	1.23628e7i	0.204553	−	0.763404i
$254$	9.80789e6	+	2.62802e6i	0.598514	+	0.160371i
$255$	−959123.	+	959123.i	−0.0578434	+	0.0578434i
$256$	8.43444e6	+	1.46089e7i	0.502732	+	0.870757i
$257$	8.55478e6	+	4.93910e6i	0.503975	+	0.290970i	0.730354	−	0.683069i	$-0.239355\pi$
$257$	8.55478e6	+	4.93910e6i	0.503975	+	0.290970i	−0.226378	+	0.974039i	$0.572689\pi$
$258$	−1.68062e6	−	6.27217e6i	−0.0978614	−	0.365224i
$259$		−	3.55090e7i		−	2.04380i
$260$	−3.01642e6	−	709353.i	−0.171621	−	0.0403592i
$261$	2.92663e7			1.64606
$262$	−8.86875e6	+	2.37637e6i	−0.493126	+	0.132133i
$263$	7.81292e6	−	1.35324e7i	0.429483	−	0.743887i	−0.567344	−	0.823481i	$-0.692029\pi$
$263$	7.81292e6	−	1.35324e7i	0.429483	−	0.743887i	0.996827	+	0.0795938i	$0.0253623\pi$
$264$	−2.72523e7	+	1.57341e7i	−1.48112	+	0.855127i
$265$	8.14625e6	+	8.14625e6i	0.437744	+	0.437744i
$266$	1.83508e6	−	6.84860e6i	0.0975011	−	0.363879i
$267$	−8.64573e6	−	2.31662e6i	−0.454222	−	0.121708i
$268$	292700.	−	292700.i	0.0152061	−	0.0152061i
$269$	8.28748e6	+	1.43543e7i	0.425761	+	0.737439i	0.996491	−	0.0836985i	$-0.0266733\pi$
$269$	8.28748e6	+	1.43543e7i	0.425761	+	0.737439i	−0.570731	+	0.821137i	$0.693340\pi$
$270$	2.68017e6	+	1.54739e6i	0.136167	+	0.0786158i
$271$	4.29602e6	+	1.60330e7i	0.215853	+	0.805574i	0.985865	+	0.167544i	$0.0535837\pi$
$271$	4.29602e6	+	1.60330e7i	0.215853	+	0.805574i	−0.770012	+	0.638030i	$0.779750\pi$
$272$			1.04107e6i			0.0517337i
$273$	−3.77241e7	+	4.01251e7i	−1.85409	+	1.97210i
$274$	−2.44422e6			−0.118820
$275$	1.71548e7	−	4.59663e6i	0.824876	−	0.221025i
$276$	5.11103e6	−	8.85257e6i	0.243098	−	0.421058i
$277$	−2.90678e7	+	1.67823e7i	−1.36764	+	0.789610i	−0.990627	−	0.136597i	$-0.956384\pi$
$277$	−2.90678e7	+	1.67823e7i	−1.36764	+	0.789610i	−0.377017	+	0.926206i	$0.623050\pi$
$278$	−3.01429e6	−	3.01429e6i	−0.140298	−	0.140298i
$279$	3.78562e6	−	1.41281e7i	0.174311	−	0.650538i
$280$	1.71444e7	+	4.59383e6i	0.780996	+	0.209267i
$281$	4.20270e6	−	4.20270e6i	0.189413	−	0.189413i	−0.606029	−	0.795442i	$-0.707239\pi$
$281$	4.20270e6	−	4.20270e6i	0.189413	−	0.189413i	0.795442	+	0.606029i	$0.207239\pi$
$282$	3.82529e6	+	6.62559e6i	0.170575	+	0.295445i
$283$	−2.31934e7	−	1.33907e7i	−1.02330	−	0.590805i	−0.108245	−	0.994124i	$-0.534523\pi$
$283$	−2.31934e7	−	1.33907e7i	−1.02330	−	0.590805i	−0.915059	+	0.403319i	$0.867856\pi$
$284$	3.66105e6	+	1.36632e7i	0.159827	+	0.596483i
$285$			4.12929e6i			0.178378i
$286$	−9.74198e6	−	1.57327e7i	−0.416437	−	0.672520i
$287$	−3.23830e7			−1.36984
$288$	−2.35596e7	+	6.31277e6i	−0.986258	+	0.264267i
$289$	−1.18723e7	+	2.05635e7i	−0.491861	+	0.851929i
$290$	8.43751e6	−	4.87140e6i	0.345956	−	0.199738i
$291$	−3.16460e7	−	3.16460e7i	−1.28422	−	1.28422i
$292$	−1.18782e6	+	4.43300e6i	−0.0477091	+	0.178053i
$293$	4.37798e7	+	1.17307e7i	1.74049	+	0.466362i	0.982555	−	0.185973i	$-0.0595438\pi$
$293$	4.37798e7	+	1.17307e7i	1.74049	+	0.466362i	0.757931	+	0.652335i	$0.226210\pi$
$294$	4.49923e7	−	4.49923e7i	1.77050	−	1.77050i
$295$	−4.26713e6	−	7.39088e6i	−0.166215	−	0.287892i
$296$	2.79488e7	+	1.61362e7i	1.07767	+	0.622195i
$297$	−3.44915e6	−	1.28724e7i	−0.131657	−	0.491349i
$298$			1.41073e7i			0.533085i
$299$	1.79361e7	+	9.63076e6i	0.670989	+	0.360286i
$300$	1.41844e7			0.525347
$301$	1.52339e7	−	4.08190e6i	0.558612	−	0.149680i
$302$	−1.62143e6	+	2.80840e6i	−0.0588679	+	0.101962i
$303$	5.46694e7	−	3.15634e7i	1.96525	−	1.13463i
$304$	2.24105e6	+	2.24105e6i	0.0797684	+	0.0797684i
$305$	5.48133e6	−	2.04566e7i	0.193191	−	0.720997i
$306$	−3.55737e6	−	953196.i	−0.124155	−	0.0332673i
$307$	9.50157e6	−	9.50157e6i	0.328383	−	0.328383i	−0.523589	−	0.851971i	$-0.675407\pi$
$307$	9.50157e6	−	9.50157e6i	0.328383	−	0.328383i	0.851971	+	0.523589i	$0.175407\pi$
$308$	−1.12835e7	−	1.95436e7i	−0.386181	−	0.668885i
$309$	−1.20549e7	−	6.95988e6i	−0.408589	−	0.235899i
$310$	−1.26024e6	−	4.70327e6i	−0.0423027	−	0.157876i
$311$			3.62353e7i			1.20462i	0.798262	+	0.602311i	$0.205753\pi$
$311$			3.62353e7i			1.20462i	−0.798262	+	0.602311i	$0.794247\pi$
$312$	−1.44393e7	−	4.79262e7i	−0.475424	−	1.57801i
$313$	2.57794e7			0.840698			0.420349	−	0.907363i	$-0.361908\pi$
$313$	2.57794e7			0.840698			0.420349	+	0.907363i	$0.361908\pi$
$314$	−3.50208e7	+	9.38379e6i	−1.13119	+	0.303102i
$315$	−1.54408e7	+	2.67442e7i	−0.494012	+	0.855653i
$316$	−7.57919e6	+	4.37585e6i	−0.240194	+	0.138676i
$317$	−1.85929e7	−	1.85929e7i	−0.583674	−	0.583674i	0.352237	−	0.935911i	$-0.385421\pi$
$317$	−1.85929e7	−	1.85929e7i	−0.583674	−	0.583674i	−0.935911	+	0.352237i	$0.885421\pi$
$318$	−1.42213e7	+	5.30745e7i	−0.442239	+	1.65046i
$319$	−4.05240e7	−	1.08584e7i	−1.24836	−	0.334497i
$320$	−9.69515e6	+	9.69515e6i	−0.295872	+	0.295872i
$321$	1.82034e7	+	3.15292e7i	0.550349	+	0.953232i
$322$	−2.98180e7	−	1.72154e7i	−0.893122	−	0.515644i
$323$	−309564.	−	1.15531e6i	−0.00918635	−	0.0342839i
$324$			8.19094e6i			0.240823i
$325$	870852.	+	2.82361e7i	0.0253685	+	0.822534i
$326$	3.43990e6			0.0992873
$327$	4.43754e7	−	1.18904e7i	1.26911	−	0.340057i
$328$	1.47157e7	−	2.54883e7i	0.417022	−	0.722304i
$329$	−1.60922e7	+	9.29085e6i	−0.451885	+	0.260896i
$330$	−1.28882e7	−	1.28882e7i	−0.358633	−	0.358633i
$331$	5.15160e6	−	1.92260e7i	0.142056	−	0.530159i	−0.857813	−	0.513961i	$-0.828177\pi$
$331$	5.15160e6	−	1.92260e7i	0.142056	−	0.530159i	0.999869	−	0.0161971i	$-0.00515592\pi$
$332$	1.25630e7	+	3.36625e6i	0.343304	+	0.0919881i
$333$	−3.97042e7	+	3.97042e7i	−1.07524	+	1.07524i
$334$	1.26838e7	+	2.19689e7i	0.340415	+	0.589616i
$335$	703225.	+	406007.i	0.0187051	+	0.0107994i
$336$	1.07760e7	+	4.02167e7i	0.284080	+	1.06020i
$337$		−	1.74513e7i		−	0.455972i	−0.973664	−	0.227986i	$-0.926786\pi$
$337$		−	1.74513e7i		−	0.455972i	0.973664	−	0.227986i	$-0.0732140\pi$
$338$	2.79076e7	−	9.35568e6i	0.722724	−	0.242284i
$339$	−2.56088e7			−0.657340
$340$	853941.	−	228813.i	0.0217266	−	0.00582161i
$341$	−1.04836e7	+	1.81582e7i	−0.264392	+	0.457940i
$342$	−9.70963e6	+	5.60586e6i	−0.242730	+	0.140140i
$343$	5.85872e7	+	5.85872e7i	1.45185	+	1.45185i
$344$	−3.70985e6	+	1.38453e7i	−0.0911341	+	0.340117i
$345$	1.93691e7	+	5.18992e6i	0.471684	+	0.126387i
$346$	−1.37416e7	+	1.37416e7i	−0.331749	+	0.331749i
$347$	−2.82107e7	−	4.88624e7i	−0.675190	−	1.16946i	−0.976413	−	0.215910i	$-0.930728\pi$
$347$	−2.82107e7	−	4.88624e7i	−0.675190	−	1.16946i	0.301223	−	0.953554i	$-0.402605\pi$
$348$	−2.90179e7	−	1.67535e7i	−0.688539	−	0.397528i
$349$	−1.25014e7	−	4.66558e7i	−0.294091	−	1.09756i	−0.941937	−	0.335791i	$-0.890997\pi$
$349$	−1.25014e7	−	4.66558e7i	−0.294091	−	1.09756i	0.647846	−	0.761772i	$-0.275670\pi$
$350$		−	4.77770e7i		−	1.11433i
$351$	2.11874e7	−	653457.i	0.489954	−	0.0151111i
$352$	3.49643e7			0.801671
$353$	9.02976e6	−	2.41952e6i	0.205283	−	0.0550053i	−0.154712	−	0.987960i	$-0.549445\pi$
$353$	9.02976e6	−	2.41952e6i	0.205283	−	0.0550053i	0.359995	+	0.932954i	$0.382778\pi$
$354$	2.03519e7	−	3.52505e7i	0.458770	−	0.794613i
$355$	−2.40307e7	+	1.38741e7i	−0.537132	+	0.310113i
$356$	4.12513e6	+	4.12513e6i	0.0914297	+	0.0914297i
$357$	4.06674e6	−	1.51773e7i	0.0893802	−	0.333572i
$358$	−4.52305e7	−	1.21195e7i	−0.985784	−	0.264140i
$359$	−5.67389e7	+	5.67389e7i	−1.22630	+	1.22630i	−0.260949	+	0.965353i	$0.584036\pi$
$359$	−5.67389e7	+	5.67389e7i	−1.22630	+	1.22630i	−0.965353	+	0.260949i	$0.915964\pi$
$360$	−1.40334e7	−	2.43066e7i	−0.300784	−	0.520974i
$361$	3.75896e7	+	2.17024e7i	0.798998	+	0.461302i
$362$	−5.08361e6	−	1.89723e7i	−0.107163	−	0.399939i
$363$			5.60347e6i			0.117149i
$364$	3.43696e7	−	1.03549e7i	0.712639	−	0.214705i
$365$	−9.00285e6			−0.185140
$366$	9.75668e7	−	2.61429e7i	1.99003	−	0.533226i
$367$	8.54109e6	−	1.47936e7i	0.172789	−	0.299279i	−0.766605	−	0.642119i	$-0.778056\pi$
$367$	8.54109e6	−	1.47936e7i	0.172789	−	0.299279i	0.939394	+	0.342840i	$0.111389\pi$
$368$	1.33287e7	−	7.69531e6i	0.267450	−	0.154412i
$369$	3.62089e7	+	3.62089e7i	0.720670	+	0.720670i
$370$	−4.83797e6	+	1.80555e7i	−0.0955120	+	0.356456i
$371$	−1.28907e8	−	3.45406e7i	−2.52438	−	0.676407i
$372$	−1.18411e7	+	1.18411e7i	−0.230019	+	0.230019i
$373$	−3.59883e6	−	6.23336e6i	−0.0693482	−	0.120115i	0.829266	−	0.558854i	$-0.188759\pi$
$373$	−3.59883e6	−	6.23336e6i	−0.0693482	−	0.120115i	−0.898615	+	0.438739i	$0.855425\pi$
$374$	4.57211e6	+	2.63971e6i	0.0873981	+	0.0504593i
$375$	1.59529e7	+	5.95372e7i	0.302515	+	1.12900i
$376$		−	1.68880e7i		−	0.317699i
$377$	3.15687e7	−	5.87930e7i	0.589160	−	1.09724i
$378$	−3.58502e7			−0.663768
$379$	3.06199e7	−	8.20458e6i	0.562453	−	0.150709i	0.0336201	−	0.999435i	$-0.489296\pi$
$379$	3.06199e7	−	8.20458e6i	0.562453	−	0.150709i	0.528833	+	0.848726i	$0.322630\pi$
$380$	1.34567e6	−	2.33078e6i	0.0245239	−	0.0424766i
$381$	5.93253e7	−	3.42515e7i	1.07267	−	0.619305i
$382$	7.77235e6	+	7.77235e6i	0.139432	+	0.139432i
$383$	5.39463e6	−	2.01330e7i	0.0960207	−	0.358354i	−0.901151	−	0.433504i	$-0.857277\pi$
$383$	5.39463e6	−	2.01330e7i	0.0960207	−	0.358354i	0.997172	+	0.0751500i	$0.0239436\pi$
$384$	1.21447e6	+	325415.i	0.0214482	+	0.00574704i
$385$	3.13029e7	−	3.13029e7i	0.548532	−	0.548532i
$386$	9.37292e6	+	1.62344e7i	0.162972	+	0.282276i
$387$	−2.15978e7	−	1.24695e7i	−0.372630	−	0.215138i
$388$	7.54961e6	+	2.81755e7i	0.129250	+	0.482366i
$389$			1.01669e8i			1.72719i	0.504184	+	0.863596i	$0.331793\pi$
$389$			1.01669e8i			1.72719i	−0.504184	+	0.863596i	$0.668207\pi$
$390$	2.46488e7	−	1.52630e7i	0.415530	−	0.257304i
$391$	−5.80823e6			−0.0971658
$392$	−1.35669e8	+	3.63525e7i	−2.25229	+	0.603499i
$393$	−3.09718e7	+	5.36447e7i	−0.510256	+	0.883790i
$394$	5.21592e7	−	3.01141e7i	0.852790	−	0.492358i
$395$	−1.21396e7	−	1.21396e7i	−0.196975	−	0.196975i
$396$	−9.23598e6	+	3.44691e7i	−0.148730	+	0.555066i
$397$	8.39118e6	+	2.24841e6i	0.134107	+	0.0359339i	0.325248	−	0.945629i	$-0.394552\pi$
$397$	8.39118e6	+	2.24841e6i	0.134107	+	0.0359339i	−0.191141	+	0.981563i	$0.561219\pi$
$398$	−2.40702e7	+	2.40702e7i	−0.381795	+	0.381795i
$399$	−2.39170e7	−	4.14254e7i	−0.376519	−	0.652151i
$400$	1.84951e7	+	1.06782e7i	0.288987	+	0.166846i
$401$	−2.75003e7	−	1.02633e8i	−0.426486	−	1.59167i	−0.760656	−	0.649155i	$-0.775122\pi$
$401$	−2.75003e7	−	1.02633e8i	−0.426486	−	1.59167i	0.334169	−	0.942513i	$-0.391544\pi$
$402$			3.87287e6i			0.0596148i
$403$	−2.42985e7	−	2.28445e7i	−0.371248	−	0.349033i
$404$	−4.11442e7			−0.623971
$405$	−1.55204e7	+	4.15869e6i	−0.233635	+	0.0626024i
$406$	−5.64306e7	+	9.77406e7i	−0.843211	+	1.46048i
$407$	6.97080e7	−	4.02459e7i	1.03395	−	0.596951i
$408$	1.00978e7	+	1.00978e7i	0.148679	+	0.148679i
$409$	3.85040e6	−	1.43699e7i	0.0562776	−	0.210031i	−0.932061	−	0.362300i	$-0.881991\pi$
$409$	3.85040e6	−	1.43699e7i	0.0562776	−	0.210031i	0.988339	+	0.152269i	$0.0486581\pi$
$410$	1.64661e7	+	4.41207e6i	0.238912	+	0.0640163i
$411$	−1.16601e7	+	1.16601e7i	−0.167949	+	0.167949i
$412$	4.53624e6	+	7.85700e6i	0.0648642	+	0.112348i
$413$	8.56164e7	+	4.94307e7i	1.21537	+	0.701691i
$414$	1.40915e7	+	5.25902e7i	0.198590	+	0.741147i
$415$			2.55138e7i			0.356970i
$416$	−1.27313e7	+	5.41382e7i	−0.176846	+	0.752010i
$417$	−2.87593e7			−0.396616
$418$	1.55244e7	−	4.15976e6i	0.212563	−	0.0569560i
$419$	3.40038e7	−	5.88963e7i	0.462259	−	0.800655i	−0.536815	−	0.843700i	$-0.680373\pi$
$419$	3.40038e7	−	5.88963e7i	0.462259	−	0.800655i	0.999073	+	0.0430449i	$0.0137058\pi$
$420$	3.06194e7	−	1.76781e7i	0.413284	−	0.238610i
$421$	−6.87030e7	−	6.87030e7i	−0.920724	−	0.920724i	0.0763570	−	0.997081i	$-0.475671\pi$
$421$	−6.87030e7	−	6.87030e7i	−0.920724	−	0.920724i	−0.997081	+	0.0763570i	$0.975671\pi$
$422$	−1.70428e7	+	6.36046e7i	−0.226780	+	0.846353i
$423$	2.83820e7	+	7.60493e6i	0.374992	+	0.100479i
$424$	8.57655e7	−	8.57655e7i	1.12516	−	1.12516i
$425$	−4.02981e6	−	6.97984e6i	−0.0524950	−	0.0909240i
$426$	−1.14613e8	−	6.61721e7i	−1.48254	−	0.855945i
$427$	6.34960e7	+	2.36970e8i	0.815572	+	3.04376i
$428$		−	2.37289e7i		−	0.302654i
$429$	−1.21527e8	−	2.85787e7i	−1.53922	−	0.361968i
$430$	−8.30223e6			−0.104421
$431$	9.70536e7	−	2.60054e7i	1.21222	−	0.324812i	0.404584	−	0.914501i	$-0.367416\pi$
$431$	9.70536e7	−	2.60054e7i	1.21222	−	0.324812i	0.807631	+	0.589689i	$0.200750\pi$
$432$	8.01253e6	−	1.38781e7i	0.0993845	−	0.172139i
$433$	−4.15723e7	+	2.40018e7i	−0.512083	+	0.295651i	−0.733689	−	0.679485i	$-0.762203\pi$
$433$	−4.15723e7	+	2.40018e7i	−0.512083	+	0.295651i	0.221607	+	0.975136i	$0.428870\pi$
$434$	3.98843e7	+	3.98843e7i	0.487902	+	0.487902i
$435$	1.70121e7	−	6.34900e7i	0.206676	−	0.771325i
$436$	−2.89226e7	−	7.74979e6i	−0.348962	−	0.0935040i
$437$	−1.25030e7	+	1.25030e7i	−0.149820	+	0.149820i
$438$	−2.14694e7	−	3.71860e7i	−0.255503	−	0.442545i
$439$	−9.78649e7	−	5.65023e7i	−1.15673	−	0.667840i	−0.206215	−	0.978507i	$-0.566114\pi$
$439$	−9.78649e7	−	5.65023e7i	−1.15673	−	0.667840i	−0.950519	+	0.310666i	$0.899448\pi$
$440$	1.04133e7	+	3.88630e7i	0.122245	+	0.456225i
$441$		−	2.44376e8i		−	2.84933i
$442$	−5.75211e6	+	6.11821e6i	−0.0666132	+	0.0708529i
$443$	1.35440e8			1.55788			0.778941	−	0.627097i	$-0.215757\pi$
$443$	1.35440e8			1.55788			0.778941	+	0.627097i	$0.215757\pi$
$444$	6.20958e7	−	1.66385e7i	0.709436	−	0.190093i
$445$	−5.72201e6	+	9.91081e6i	−0.0649334	+	0.112468i
$446$	4.58506e6	−	2.64719e6i	0.0516822	−	0.0298387i
$447$	6.72989e7	+	6.72989e7i	0.753503	+	0.753503i
$448$	4.11080e7	−	1.53417e8i	0.457185	−	1.70624i
$449$	−1.84343e7	−	4.93946e6i	−0.203652	−	0.0545683i	0.155551	−	0.987828i	$-0.450285\pi$
$449$	−1.84343e7	−	4.93946e6i	−0.203652	−	0.0545683i	−0.359203	+	0.933260i	$0.616951\pi$
$450$	−5.34217e7	+	5.34217e7i	−0.586246	+	0.586246i
$451$	−3.67029e7	−	6.35713e7i	−0.400102	−	0.692997i
$452$	1.44549e7	+	8.34553e6i	0.156531	+	0.0903730i
$453$	5.66243e6	+	2.11325e7i	0.0609128	+	0.227330i
$454$			1.23960e8i			1.32469i
$455$	3.70708e7	+	5.98670e7i	0.393548	+	0.635556i
$456$	4.34740e7			0.458496
$457$	−1.59389e8	+	4.27082e7i	−1.66998	+	0.447469i	−0.965105	−	0.261864i	$-0.915663\pi$
$457$	−1.59389e8	+	4.27082e7i	−1.66998	+	0.447469i	−0.704873	+	0.709334i	$0.748996\pi$
$458$	2.65987e7	−	4.60703e7i	0.276862	−	0.479539i
$459$	−5.23743e6	+	3.02383e6i	−0.0541602	+	0.0312694i
$460$	−9.24154e6	−	9.24154e6i	−0.0949447	−	0.0949447i
$461$	−2.58912e7	+	9.66273e7i	−0.264271	+	0.986273i	0.698424	+	0.715684i	$0.253885\pi$
$461$	−2.58912e7	+	9.66273e7i	−0.264271	+	0.986273i	−0.962695	+	0.270589i	$0.912782\pi$
$462$	2.03944e8	+	5.46467e7i	2.06817	+	0.554164i
$463$	1.37158e8	−	1.37158e8i	1.38190	−	1.38190i	0.540667	−	0.841236i	$-0.318172\pi$
$463$	1.37158e8	−	1.37158e8i	1.38190	−	1.38190i	0.841236	−	0.540667i	$-0.181828\pi$
$464$	−2.52245e7	−	4.36901e7i	−0.252504	−	0.437350i
$465$	−2.84489e7	−	1.64250e7i	−0.282948	−	0.163360i
$466$	−2.14617e7	−	8.00960e7i	−0.212083	−	0.791504i
$467$		−	3.37853e7i		−	0.331725i	−0.986149	−	0.165862i	$-0.946959\pi$
$467$		−	3.37853e7i		−	0.331725i	0.986149	−	0.165862i	$-0.0530407\pi$
$468$	−5.00085e7	−	2.68519e7i	−0.487872	−	0.261962i
$469$	−9.40642e6			−0.0911813
$470$	9.44840e6	−	2.53169e6i	0.0910049	−	0.0243847i
$471$	−1.22301e8	+	2.11831e8i	−1.17049	+	2.02734i
$472$	−7.78128e7	+	4.49252e7i	−0.739988	+	0.427233i
$473$	2.52793e7	+	2.52793e7i	0.238881	+	0.238881i
$474$	2.11926e7	−	7.90917e7i	0.198998	−	0.742670i
$475$	−2.36998e7	−	6.35034e6i	−0.221138	−	0.0592538i
$476$	−7.24152e6	+	7.24152e6i	−0.0671442	+	0.0671442i
$477$	1.05516e8	+	1.82759e8i	0.972214	+	1.68392i
$478$	−6.53815e6	−	3.77480e6i	−0.0598648	−	0.0345629i
$479$	−1.19218e7	−	4.44927e7i	−0.108476	−	0.404839i	0.890240	−	0.455492i	$-0.150537\pi$
$479$	−1.19218e7	−	4.44927e7i	−0.108476	−	0.404839i	−0.998716	+	0.0506525i	$0.983870\pi$
$480$			5.47794e7i			0.495329i
$481$	3.69338e7	+	1.22589e8i	0.331886	+	1.10158i
$482$	2.31321e7			0.206573
$483$	−2.24372e8	+	6.01204e7i	−1.99126	+	0.533556i
$484$	1.82609e6	−	3.16288e6i	0.0161059	−	0.0278963i
$485$	−4.95547e7	+	2.86104e7i	−0.434370	+	0.250783i
$486$	−8.45182e7	−	8.45182e7i	−0.736277	−	0.736277i
$487$	−4.13444e7	+	1.54299e8i	−0.357956	+	1.33591i	0.518767	+	0.854915i	$0.326391\pi$
$487$	−4.13444e7	+	1.54299e8i	−0.357956	+	1.33591i	−0.876723	+	0.480995i	$0.840276\pi$
$488$	−2.15371e8	−	5.77085e7i	−1.85323	−	0.496570i
$489$	1.64100e7	−	1.64100e7i	0.140340	−	0.140340i
$490$	−4.06765e7	−	7.04538e7i	−0.345744	−	0.598847i
$491$	1.04150e8	+	6.01311e7i	0.879863	+	0.507989i	0.870613	−	0.491968i	$-0.163722\pi$
$491$	1.04150e8	+	6.01311e7i	0.879863	+	0.507989i	0.00924998	+	0.999957i	$0.497056\pi$
$492$	−1.51738e7	−	5.66293e7i	−0.127408	−	0.475495i
$493$			1.90388e7i			0.158891i
$494$	788086.	+	2.55525e7i	0.00653721	+	0.211959i
$495$	−7.00024e7			−0.577161
$496$	−2.43539e7	+	6.52562e6i	−0.199583	+	0.0534782i
$497$	1.60719e8	−	2.78373e8i	1.30917	−	2.26755i
$498$	−1.05384e8	+	6.08436e7i	−0.853272	+	0.492637i
$499$	−6.47841e7	−	6.47841e7i	−0.521395	−	0.521395i	0.396597	−	0.917993i	$-0.370191\pi$
$499$	−6.47841e7	−	6.47841e7i	−0.521395	−	0.521395i	−0.917993	+	0.396597i	$0.870191\pi$
$500$	1.03976e7	−	3.88046e7i	0.0831812	−	0.310436i
$501$	1.65310e8	+	4.42947e7i	1.31458	+	0.352240i
$502$	1.20384e7	−	1.20384e7i	0.0951603	−	0.0951603i
$503$	8.90246e7	+	1.54195e8i	0.699530	+	1.21162i	0.968630	+	0.248509i	$0.0799405\pi$
$503$	8.90246e7	+	1.54195e8i	0.699530	+	1.21162i	−0.269100	+	0.963112i	$0.586726\pi$
$504$	2.81568e8	+	1.62564e8i	2.19934	+	1.26979i
$505$	−2.08896e7	−	7.79612e7i	−0.162202	−	0.605347i
$506$		−	7.80480e7i		−	0.602435i
$507$	8.85017e7	−	1.77764e8i	0.679090	−	1.36402i
$508$	−4.46482e7			−0.340575
$509$	1.21969e8	−	3.26816e7i	0.924905	−	0.247827i	0.235224	−	0.971941i	$-0.424418\pi$
$509$	1.21969e8	−	3.26816e7i	0.924905	−	0.247827i	0.689681	+	0.724114i	$0.257751\pi$
$510$	−4.13570e6	+	7.16324e6i	−0.0311773	+	0.0540007i
$511$	9.03174e7	−	5.21447e7i	0.676875	−	0.390794i
$512$	7.13548e7	+	7.13548e7i	0.531635	+	0.531635i
$513$	−4.76507e6	+	1.77835e7i	−0.0352954	+	0.131724i
$514$	5.81850e7	+	1.55906e7i	0.428472	+	0.114809i
$515$	−1.25845e7	+	1.25845e7i	−0.0921331	+	0.0921331i
$516$	1.42763e7	+	2.47273e7i	0.103912	+	0.179982i
$517$	−3.64779e7	−	2.10605e7i	−0.263972	−	0.152404i
$518$	−5.60433e7	−	2.09156e8i	−0.403213	−	1.50481i
$519$			1.31108e8i			0.937839i
$520$	−6.39667e7	+	1.97285e6i	−0.454929	+	0.0140309i
$521$	−1.31649e8			−0.930905			−0.465453	−	0.885073i	$-0.654108\pi$
$521$	−1.31649e8			−0.930905			−0.465453	+	0.885073i	$0.654108\pi$
$522$	1.72386e8	−	4.61907e7i	1.21197	−	0.324745i
$523$	7.27598e6	−	1.26024e7i	0.0508612	−	0.0880941i	−0.839474	−	0.543400i	$-0.817137\pi$
$523$	7.27598e6	−	1.26024e7i	0.0508612	−	0.0880941i	0.890335	+	0.455306i	$0.150470\pi$
$524$	3.49640e7	−	2.01865e7i	0.243012	−	0.140303i
$525$	−2.27919e8	−	2.27919e8i	−1.57508	−	1.57508i
$526$	2.46621e7	−	9.20401e7i	0.169462	−	0.632441i
$527$	9.19087e6	+	2.46269e6i	0.0627950	+	0.0168259i
$528$	−6.67361e7	+	6.67361e7i	−0.453377	+	0.453377i
$529$	−3.10852e7	−	5.38411e7i	−0.209984	−	0.363703i
$530$	6.08406e7	+	3.51263e7i	0.408663	+	0.235942i
$531$	−4.04610e7	−	1.51002e8i	−0.270242	−	1.00856i
$532$			3.11767e7i			0.207060i
$533$	1.11797e8	−	3.36824e7i	0.738329	−	0.222444i
$534$	−5.45817e7			−0.358446
$535$	4.49622e7	−	1.20476e7i	0.293620	−	0.0786753i
$536$	4.27453e6	−	7.40370e6i	0.0277584	−	0.0480789i
$537$	−2.73587e8	+	1.57956e8i	−1.76674	+	1.02003i
$538$	7.14705e7	+	7.14705e7i	0.458966	+	0.458966i
$539$	−9.06681e7	+	3.38378e8i	−0.579013	+	2.16091i
$540$	−1.31446e7	−	3.52208e6i	−0.0834768	−	0.0223675i
$541$	−1.29901e8	+	1.29901e8i	−0.820392	+	0.820392i	−0.986164	−	0.165772i	$-0.946988\pi$
$541$	−1.29901e8	+	1.29901e8i	−0.820392	+	0.820392i	0.165772	+	0.986164i	$0.446988\pi$
$542$	5.06092e7	+	8.76577e7i	0.317857	+	0.550544i
$543$	−1.14758e8	−	6.62557e7i	−0.716778	−	0.413832i
$544$	−4.10669e6	−	1.53264e7i	−0.0255091	−	0.0952013i
$545$		−	5.87381e7i		−	0.362852i
$546$	−1.58875e8	+	2.95886e8i	−0.976065	+	1.81780i
$547$	1.40207e8			0.856656			0.428328	−	0.903623i	$-0.359103\pi$
$547$	1.40207e8			0.856656			0.428328	+	0.903623i	$0.359103\pi$
$548$	1.03814e7	−	2.78170e6i	0.0630835	−	0.0169032i
$549$	1.93970e8	−	3.35965e8i	1.17224	−	2.03038i
$550$	9.37914e7	−	5.41505e7i	0.563735	−	0.325473i
$551$	4.09837e7	+	4.09837e7i	0.244995	+	0.244995i
$552$	5.46406e7	−	2.03922e8i	0.324862	−	1.21240i
$553$	1.92098e8	+	5.14725e7i	1.13592	+	0.304368i
$554$	−1.44729e8	+	1.44729e8i	−0.851191	+	0.851191i
$555$	6.30543e7	+	1.09213e8i	0.368838	+	0.638846i
$556$	1.62332e7	+	9.37223e6i	0.0944450	+	0.0545279i
$557$	−3.91711e7	−	1.46189e8i	−0.226673	−	0.845956i	−0.981727	−	0.190293i	$-0.939056\pi$
$557$	−3.91711e7	−	1.46189e8i	−0.226673	−	0.845956i	0.755054	−	0.655662i	$-0.227611\pi$
$558$		−	8.91930e7i		−	0.513367i
$559$	−4.83469e7	+	2.99373e7i	−0.276779	+	0.171387i
$560$	5.32332e7			0.303123
$561$	3.44039e7	−	9.21849e6i	0.194858	−	0.0522121i
$562$	1.81219e7	−	3.13880e7i	0.102092	−	0.176829i
$563$	−1.30583e8	+	7.53920e7i	−0.731746	+	0.422474i	−0.819061	−	0.573707i	$-0.805505\pi$
$563$	−1.30583e8	+	7.53920e7i	−0.731746	+	0.422474i	0.0873144	+	0.996181i	$0.472172\pi$
$564$	−2.37876e7	−	2.37876e7i	−0.132591	−	0.132591i
$565$	−8.47435e6	+	3.16267e7i	−0.0469852	+	0.175351i
$566$	−1.57749e8	−	4.22687e7i	−0.869996	−	0.233115i
$567$	1.31615e8	−	1.31615e8i	0.722032	−	0.722032i
$568$	1.46070e8	+	2.53000e8i	0.797104	+	1.38063i
$569$	−384148.	−	221788.i	−0.00208527	−	0.00120393i	0.498957	−	0.866627i	$-0.333717\pi$
$569$	−384148.	−	221788.i	−0.00208527	−	0.00120393i	−0.501042	+	0.865423i	$0.667050\pi$
$570$	6.51720e6	+	2.43225e7i	0.0351914	+	0.131336i
$571$			7.75206e7i			0.416398i	0.978086	+	0.208199i	$0.0667602\pi$
$571$			7.75206e7i			0.416398i	−0.978086	+	0.208199i	$0.933240\pi$
$572$	5.92823e7	+	5.57350e7i	0.316765	+	0.297810i
$573$	7.41558e7			0.394168
$574$	−1.90744e8	+	5.11096e7i	−1.00859	+	0.270251i
$575$	−5.95745e7	+	1.03186e8i	−0.313369	+	0.542772i
$576$	−2.17508e8	+	1.25578e8i	−1.13817	+	0.657122i
$577$	1.09012e8	+	1.09012e8i	0.567477	+	0.567477i	0.931421	−	0.363944i	$-0.118570\pi$
$577$	1.09012e8	+	1.09012e8i	0.567477	+	0.567477i	−0.363944	+	0.931421i	$0.618570\pi$
$578$	−3.74759e7	+	1.39862e8i	−0.194075	+	0.724296i
$579$	1.22159e8	+	3.27325e7i	0.629348	+	0.168633i
$580$	−3.02929e7	+	3.02929e7i	−0.155259	+	0.155259i
$581$	−1.47777e8	−	2.55957e8i	−0.753491	−	1.30508i
$582$	−2.36349e8	−	1.36456e8i	−1.19890	−	0.692188i
$583$	−7.82967e7	−	2.92207e8i	−0.395128	−	1.47464i
$584$			9.47839e7i			0.475878i
$585$	2.54896e7	−	1.08391e8i	0.127320	−	0.541408i
$586$	2.76388e8			1.37349
$587$	−2.70549e8	+	7.24933e7i	−1.33762	+	0.358413i	−0.855549	−	0.517722i	$-0.826780\pi$
$587$	−2.70549e8	+	7.24933e7i	−1.33762	+	0.358413i	−0.482066	+	0.876135i	$0.660114\pi$
$588$	−1.39893e8	+	2.42301e8i	−0.688118	+	1.19186i
$589$	2.50859e7	−	1.44834e7i	0.122768	−	0.0708799i
$590$	−3.67994e7	−	3.67994e7i	−0.179178	−	0.179178i
$591$	1.05166e8	−	3.92484e8i	0.509462	−	1.90134i
$592$	9.34931e7	+	2.50514e7i	0.450624	+	0.120744i
$593$	2.24720e8	−	2.24720e8i	1.07765	−	1.07765i	0.0809317	−	0.996720i	$-0.474210\pi$
$593$	2.24720e8	−	2.24720e8i	1.07765	−	1.07765i	0.996720	−	0.0809317i	$-0.0257896\pi$
$594$	−4.06327e7	−	7.03779e7i	−0.193872	−	0.335797i
$595$	−1.73981e7	−	1.00448e7i	−0.0825943	−	0.0476859i
$596$	−1.60551e7	−	5.99185e7i	−0.0758359	−	0.283023i
$597$			2.29653e8i			1.07932i
$598$	1.20848e8	+	2.84192e7i	0.565116	+	0.132895i
$599$	−1.89014e8			−0.879457			−0.439728	−	0.898131i	$-0.644925\pi$
$599$	−1.89014e8			−0.879457			−0.439728	+	0.898131i	$0.644925\pi$
$600$	2.82966e8	−	7.58205e7i	1.31003	−	0.351021i
$601$	−1.60503e8	+	2.78000e8i	−0.739368	+	1.28062i	0.213413	+	0.976962i	$0.431542\pi$
$601$	−1.60503e8	+	2.78000e8i	−0.739368	+	1.28062i	−0.952780	+	0.303660i	$0.901791\pi$
$602$	8.32887e7	−	4.80868e7i	0.381765	−	0.220412i
$603$	1.05178e7	+	1.05178e7i	0.0479701	+	0.0479701i
$604$	3.69061e6	−	1.37735e7i	0.0167489	−	0.0625078i
$605$	6.92024e6	+	1.85427e6i	0.0312504	+	0.00837351i
$606$	2.72200e8	−	2.72200e8i	1.22312	−	1.22312i
$607$	−6.47784e7	−	1.12199e8i	−0.289644	−	0.501677i	0.684081	−	0.729406i	$-0.260203\pi$
$607$	−6.47784e7	−	1.12199e8i	−0.289644	−	0.501677i	−0.973725	+	0.227729i	$0.926870\pi$
$608$	−4.18324e7	−	2.41519e7i	−0.186124	−	0.107459i
$609$	1.97069e8	+	7.35472e8i	0.872502	+	3.25622i
$610$		−	1.29145e8i		−	0.568970i
$611$	4.58923e7	−	4.88132e7i	0.201195	−	0.214000i
$612$	1.61942e7			0.0706487
$613$	1.68194e8	−	4.50675e7i	0.730180	−	0.195651i	0.125470	−	0.992097i	$-0.459956\pi$
$613$	1.68194e8	−	4.50675e7i	0.730180	−	0.195651i	0.604709	+	0.796446i	$0.293289\pi$
$614$	4.09704e7	−	7.09628e7i	0.176997	−	0.306567i
$615$	9.95988e7	−	5.75034e7i	0.428182	−	0.247211i
$616$	−3.29563e8	−	3.29563e8i	−1.40993	−	1.40993i
$617$	8.12698e6	−	3.03303e7i	0.0345998	−	0.129128i	−0.946466	−	0.322804i	$-0.895374\pi$
$617$	8.12698e6	−	3.03303e7i	0.0345998	−	0.129128i	0.981066	+	0.193676i	$0.0620411\pi$
$618$	−8.19908e7	−	2.19694e7i	−0.347376	−	0.0930791i
$619$	1.32206e8	−	1.32206e8i	0.557414	−	0.557414i	−0.371156	−	0.928570i	$-0.621039\pi$
$619$	1.32206e8	−	1.32206e8i	0.557414	−	0.557414i	0.928570	+	0.371156i	$0.121039\pi$
$620$	1.07053e7	+	1.85421e7i	0.0449184	+	0.0778009i
$621$	7.74272e7	+	4.47026e7i	0.323310	+	0.186663i
$622$	5.71897e7	+	2.13435e8i	0.237655	+	0.886939i
$623$		−	1.32568e8i		−	0.548245i
$624$	−7.90330e7	−	1.27634e8i	−0.325278	−	0.525305i
$625$	−1.22103e8			−0.500132
$626$	1.51847e8	−	4.06873e7i	0.618989	−	0.165858i
$627$	5.42150e7	−	9.39032e7i	0.219947	−	0.380959i
$628$	1.38065e8	−	7.97121e7i	0.557450	−	0.321844i
$629$	−2.58290e7	−	2.58290e7i	−0.103790	−	0.103790i
$630$	−4.87399e7	+	1.81900e8i	−0.194923	+	0.727462i
$631$	−4.57632e7	−	1.22622e7i	−0.182150	−	0.0488068i	0.166591	−	0.986026i	$-0.446724\pi$
$631$	−4.57632e7	−	1.22622e7i	−0.182150	−	0.0488068i	−0.348741	+	0.937219i	$0.613391\pi$
$632$	−1.27808e8	+	1.27808e8i	−0.506298	+	0.506298i
$633$	2.22123e8	+	3.84728e8i	0.875753	+	1.51685i
$634$	−1.38862e8	−	8.01719e7i	−0.544898	−	0.314597i
$635$	−2.26687e7	−	8.46007e7i	−0.0885330	−	0.330410i
$636$		−	2.41610e8i		−	0.939167i
$637$	−4.90925e8	−	2.63601e8i	−1.89932	−	1.01983i
$638$	−2.55834e8			−0.985136
$639$	−4.90969e8	+	1.31555e8i	−1.88170	+	0.504201i
$640$	803771.	−	1.39217e6i	0.00306614	−	0.00531072i
$641$	−1.55805e8	+	8.99538e7i	−0.591570	+	0.341543i	−0.765718	−	0.643176i	$-0.777616\pi$
$641$	−1.55805e8	+	8.99538e7i	−0.591570	+	0.341543i	0.174148	+	0.984719i	$0.444283\pi$
$642$	1.56985e8	+	1.56985e8i	0.593270	+	0.593270i
$643$	−551397.	+	2.05784e6i	−0.00207411	+	0.00774068i	−0.966955	−	0.254947i	$-0.917942\pi$
$643$	−551397.	+	2.05784e6i	−0.00207411	+	0.00774068i	0.964881	+	0.262687i	$0.0846088\pi$
$644$	1.46239e8	+	3.91847e7i	0.547528	+	0.146710i
$645$	−3.96057e7	+	3.96057e7i	−0.147597	+	0.147597i
$646$	−3.64681e6	−	6.31647e6i	−0.0135275	−	0.0234302i
$647$	2.57470e8	+	1.48650e8i	0.950634	+	0.548849i	0.893278	−	0.449505i	$-0.148400\pi$
$647$	2.57470e8	+	1.48650e8i	0.950634	+	0.548849i	0.0573560	+	0.998354i	$0.481733\pi$
$648$	4.37835e7	+	1.63402e8i	0.160911	+	0.600528i
$649$			2.24099e8i			0.819797i
$650$	4.96941e7	+	1.64943e8i	0.180953	+	0.600611i
$651$	3.80535e8			1.37928
$652$	−1.46104e7	+	3.91485e6i	−0.0527132	+	0.0141245i
$653$	−8.83620e7	+	1.53047e8i	−0.317341	+	0.549651i	−0.979932	−	0.199330i	$-0.936123\pi$
$653$	−8.83620e7	+	1.53047e8i	−0.317341	+	0.549651i	0.662591	+	0.748981i	$0.269457\pi$
$654$	2.42616e8	−	1.40074e8i	0.867333	−	0.500755i
$655$	5.60018e7	+	5.60018e7i	0.199287	+	0.199287i
$656$	2.28460e7	−	8.52625e7i	0.0809281	−	0.302028i
$657$	−1.59293e8	−	4.26826e7i	−0.561697	−	0.150506i
$658$	−8.01235e7	+	8.01235e7i	−0.281243	+	0.281243i
$659$	−1.57139e8	−	2.72172e8i	−0.549069	−	0.951015i	−0.998339	−	0.0576191i	$-0.981649\pi$
$659$	−1.57139e8	−	2.72172e8i	−0.549069	−	0.951015i	0.449270	−	0.893396i	$-0.351684\pi$
$660$	6.94081e7	+	4.00728e7i	0.241423	+	0.139386i
$661$	1.31352e8	+	4.90212e8i	0.454812	+	1.69738i	0.688640	+	0.725103i	$0.258208\pi$
$661$	1.31352e8	+	4.90212e8i	0.454812	+	1.69738i	−0.233829	+	0.972278i	$0.575125\pi$
$662$		−	1.21377e8i		−	0.418371i
$663$	1.74649e6	+	5.66272e7i	0.00599273	+	0.194305i
$664$	2.68615e8			0.917542
$665$	−5.90746e7	+	1.58290e7i	−0.200879	+	0.0538255i
$666$	−1.71203e8	+	2.96532e8i	−0.579547	+	1.00380i
$667$	2.43751e8	−	1.40730e8i	0.821427	−	0.474251i
$668$	−7.88743e7	−	7.88743e7i	−0.264610	−	0.264610i
$669$	9.24461e6	−	3.45013e7i	0.0308752	−	0.115228i
$670$	4.78296e6	+	1.28159e6i	0.0159028	+	0.00426113i
$671$	−3.93232e8	+	3.93232e8i	−1.30161	+	1.30161i
$672$	−3.17284e8	−	5.49551e8i	−1.04554	−	1.81093i
$673$	−3.50156e8	−	2.02162e8i	−1.14872	−	0.663216i	−0.200148	−	0.979766i	$-0.564142\pi$
$673$	−3.50156e8	−	2.02162e8i	−1.14872	−	0.663216i	−0.948576	+	0.316549i	$0.897476\pi$
$674$	−2.75432e7	−	1.02792e8i	−0.0899568	−	0.335723i
$675$			1.24061e8i			0.403388i
$676$	−1.07885e8	+	7.14974e7i	−0.349239	+	0.231446i
$677$	−5.26969e8			−1.69832			−0.849160	−	0.528136i	$-0.822891\pi$
$677$	−5.26969e8			−1.69832			−0.849160	+	0.528136i	$0.822891\pi$
$678$	−1.50842e8	+	4.04180e7i	−0.483987	+	0.129684i
$679$	3.31425e8	−	5.74044e8i	1.05871	−	1.83373i
$680$	1.58123e7	−	9.12924e6i	0.0502885	−	0.0290341i
$681$	5.91351e8	+	5.91351e8i	1.87242	+	1.87242i
$682$	−3.30923e7	+	1.23502e8i	−0.104322	+	0.389333i
$683$	−1.82383e8	−	4.88693e7i	−0.572429	−	0.153382i	−0.0390189	−	0.999238i	$-0.512423\pi$
$683$	−1.82383e8	−	4.88693e7i	−0.572429	−	0.153382i	−0.533411	+	0.845856i	$0.679090\pi$
$684$	3.48601e7	−	3.48601e7i	0.108933	−	0.108933i
$685$	1.05417e7	+	1.82587e7i	0.0327973	+	0.0568065i
$686$	4.37561e8	+	2.52626e8i	1.35540	+	0.782538i
$687$	−9.28889e7	−	3.46666e8i	−0.286480	−	1.06916i
$688$			4.29896e7i			0.132007i
$689$	4.80960e8	−	1.48337e7i	1.47045	−	0.0453514i
$690$	1.22280e8			0.372226
$691$	3.63265e8	−	9.73365e7i	1.10101	−	0.295013i	0.337831	−	0.941207i	$-0.390307\pi$
$691$	3.63265e8	−	9.73365e7i	1.10101	−	0.295013i	0.763174	+	0.646193i	$0.223640\pi$
$692$	4.27263e7	−	7.40041e7i	0.128937	−	0.223325i
$693$	7.02270e8	−	4.05456e8i	2.11011	−	1.21827i
$694$	−2.43287e8	−	2.43287e8i	−0.727848	−	0.727848i
$695$	−9.51689e6	+	3.55175e7i	−0.0283492	+	0.105801i
$696$	−6.68436e8	−	1.79107e8i	−1.98259	−	0.531232i
$697$	−2.35552e7	+	2.35552e7i	−0.0695647	+	0.0695647i
$698$	−1.47272e8	−	2.55083e8i	−0.433067	−	0.750094i
$699$	−4.84480e8	−	2.79714e8i	−1.41855	−	0.818999i
$700$	5.43735e7	+	2.02925e8i	0.158523	+	0.591617i
$701$		−	4.53376e8i		−	1.31615i	−0.752954	−	0.658073i	$-0.771372\pi$
$701$		−	4.53376e8i		−	1.31615i	0.752954	−	0.658073i	$-0.228628\pi$
$702$	1.23767e8	−	3.72888e7i	0.357763	−	0.107787i
$703$	−1.11201e8			−0.320069
$704$	3.47766e8	−	9.31837e7i	0.996712	−	0.267068i
$705$	3.29961e7	−	5.71509e7i	0.0941662	−	0.163101i
$706$	4.93688e7	−	2.85031e7i	0.140294	−	0.0809987i
$707$	6.61120e8	+	6.61120e8i	1.87078	+	1.87078i
$708$	−4.63237e7	+	1.72882e8i	−0.130528	+	0.487137i
$709$	5.22169e7	+	1.39915e7i	0.146512	+	0.0392577i	0.331330	−	0.943515i	$-0.392503\pi$
$709$	5.22169e7	+	1.39915e7i	0.146512	+	0.0392577i	−0.184818	+	0.982773i	$0.559169\pi$
$710$	−1.19649e8	+	1.19649e8i	−0.334299	+	0.334299i
$711$	−1.57240e8	−	2.72347e8i	−0.437475	−	0.757730i
$712$	1.04343e8	+	6.02425e7i	0.289084	+	0.166903i
$713$	−3.64070e7	−	1.35873e8i	−0.100442	−	0.374855i
$714$		−	9.58163e7i		−	0.263236i
$715$	−7.55095e7	+	1.40627e8i	−0.206578	+	0.384726i
$716$	2.05902e8			0.560945
$717$	−4.91978e7	+	1.31825e7i	−0.133471	+	0.0357636i
$718$	−2.44656e8	+	4.23756e8i	−0.660970	+	1.14483i
$719$	−2.73888e8	+	1.58129e8i	−0.736861	+	0.425427i	−0.820927	−	0.571033i	$-0.806543\pi$
$719$	−2.73888e8	+	1.58129e8i	−0.736861	+	0.425427i	0.0840657	+	0.996460i	$0.473209\pi$
$720$	−5.95226e7	−	5.95226e7i	−0.159472	−	0.159472i
$721$	5.33592e7	−	1.99139e8i	0.142365	−	0.531314i
$722$	2.55664e8	+	6.85051e7i	0.679295	+	0.182017i
$723$	1.10351e8	−	1.10351e8i	0.291986	−	0.291986i
$724$	4.31835e7	+	7.47961e7i	0.113790	+	0.197089i
$725$	3.38234e8	+	1.95280e8i	0.887572	+	0.512440i
$726$	8.84388e6	+	3.30058e7i	0.0231118	+	0.0862542i
$727$			2.63153e8i			0.684866i	0.939542	+	0.342433i	$0.111251\pi$
$727$			2.63153e8i			0.684866i	−0.939542	+	0.342433i	$0.888749\pi$
$728$	6.30293e8	−	3.90289e8i	1.63361	−	1.01156i
$729$	−5.83696e8			−1.50662
$730$	−5.30290e7	+	1.42091e7i	−0.136315	+	0.0365256i
$731$	8.11188e6	−	1.40502e7i	0.0207668	−	0.0359691i
$732$	−3.84646e8	+	2.22075e8i	−0.980682	+	0.566197i
$733$	−4.60409e7	−	4.60409e7i	−0.116905	−	0.116905i	0.646234	−	0.763139i	$-0.276343\pi$
$733$	−4.60409e7	−	4.60409e7i	−0.116905	−	0.116905i	−0.763139	+	0.646234i	$0.776343\pi$
$734$	2.69606e7	−	1.00618e8i	0.0681775	−	0.254442i
$735$	−5.30145e8	−	1.42052e8i	−1.33516	−	0.357755i
$736$	−1.65866e8	+	1.65866e8i	−0.416028	+	0.416028i
$737$	−1.06612e7	−	1.84658e7i	−0.0266321	−	0.0461282i
$738$	2.70427e8	+	1.56131e8i	0.672793	+	0.388437i
$739$	−9.27244e6	−	3.46052e7i	−0.0229753	−	0.0857449i	0.953486	−	0.301436i	$-0.0974661\pi$
$739$	−9.27244e6	−	3.46052e7i	−0.0229753	−	0.0857449i	−0.976462	+	0.215692i	$0.930799\pi$
$740$		−	8.21938e7i		−	0.202836i
$741$	1.25657e8	+	1.18138e8i	0.308840	+	0.290360i
$742$	−8.13810e8			−1.99210
$743$	−4.50262e8	+	1.20647e8i	−1.09774	+	0.294138i	−0.761843	−	0.647762i	$-0.775705\pi$
$743$	−4.50262e8	+	1.20647e8i	−1.09774	+	0.294138i	−0.335894	+	0.941900i	$0.609039\pi$
$744$	−1.72925e8	+	2.99516e8i	−0.419894	+	0.727278i
$745$	1.05384e8	−	6.08434e7i	0.254862	−	0.147145i
$746$	−3.10360e7	−	3.10360e7i	−0.0747566	−	0.0747566i
$747$	−1.20961e8	+	4.51433e8i	−0.290191	+	1.08301i
$748$	−2.24234e7	−	6.00834e6i	−0.0535793	−	0.0143565i
$749$	−3.81284e8	+	3.81284e8i	−0.907410	+	0.907410i
$750$	1.87933e8	+	3.25510e8i	0.445472	+	0.771580i
$751$	1.83433e8	+	1.05905e8i	0.433069	+	0.250032i	0.700653	−	0.713502i	$-0.252892\pi$
$751$	1.83433e8	+	1.05905e8i	0.433069	+	0.250032i	−0.267584	+	0.963534i	$0.586225\pi$
$752$	−1.31093e7	−	4.89246e7i	−0.0308266	−	0.115047i
$753$		−	1.14858e8i		−	0.269014i
$754$	9.31554e7	−	3.96130e8i	0.217317	−	0.924109i
$755$	2.79722e7			0.0649960
$756$	1.52268e8	−	4.08000e7i	0.352405	−	0.0944267i
$757$	−6.25279e7	+	1.08301e8i	−0.144141	+	0.249659i	−0.929052	−	0.369949i	$-0.879375\pi$
$757$	−6.25279e7	+	1.08301e8i	−0.144141	+	0.249659i	0.784911	+	0.619608i	$0.212708\pi$
$758$	1.67410e8	−	9.66540e7i	0.384391	−	0.221928i
$759$	−3.72327e8	−	3.72327e8i	−0.851528	−	0.851528i
$760$	1.43862e7	−	5.36901e7i	0.0327722	−	0.122308i
$761$	1.03565e8	+	2.77502e7i	0.234996	+	0.0629670i	0.374395	−	0.927269i	$-0.377850\pi$
$761$	1.03565e8	+	2.77502e7i	0.234996	+	0.0629670i	−0.139399	+	0.990236i	$0.544517\pi$
$762$	2.95382e8	−	2.95382e8i	0.667604	−	0.667604i
$763$	3.40212e8	+	5.89265e8i	0.765908	+	1.32659i
$764$	−4.18572e7	−	2.41663e7i	−0.0938622	−	0.0541913i
$765$	8.22206e6	+	3.06851e7i	0.0183652	+	0.0685399i
$766$		−	1.27103e8i		−	0.282793i
$767$	−3.46992e8	−	8.16000e7i	−0.769012	−	0.180844i
$768$	6.93990e8			1.53204
$769$	7.39073e8	−	1.98034e8i	1.62521	−	0.435473i	0.672681	−	0.739932i	$-0.265143\pi$
$769$	7.39073e8	−	1.98034e8i	1.62521	−	0.435473i	0.952525	+	0.304460i	$0.0984758\pi$
$770$	1.34977e8	−	2.33786e8i	0.295656	−	0.512091i
$771$	3.51946e8	−	2.03196e8i	0.767914	−	0.443356i
$772$	−5.82857e7	−	5.82857e7i	−0.126681	−	0.126681i
$773$	2.59877e7	−	9.69875e7i	0.0562639	−	0.209980i	−0.932071	−	0.362275i	$-0.882000\pi$
$773$	2.59877e7	−	9.69875e7i	0.0562639	−	0.209980i	0.988335	+	0.152296i	$0.0486666\pi$
$774$	−1.46897e8	−	3.93609e7i	−0.316804	−	0.0848873i
$775$	1.38021e8	−	1.38021e8i	0.296510	−	0.296510i
$776$	3.01216e8	+	5.21722e8i	0.644605	+	1.11649i
$777$	−1.26513e9	−	7.30424e8i	−2.69695	−	1.55708i
$778$	1.60463e8	+	5.98857e8i	0.340751	+	1.27170i
$779$			1.01412e8i			0.214524i
$780$	−8.73214e7	+	9.28791e7i	−0.184008	+	0.195719i
$781$	7.28635e8			1.52953
$782$	−3.42119e7	+	9.16705e6i	−0.0715413	+	0.0191694i
$783$	1.46531e8	−	2.53799e8i	0.305242	−	0.528695i
$784$	−3.64815e8	+	2.10626e8i	−0.757050	+	0.437083i
$785$	2.21139e8	+	2.21139e8i	0.457147	+	0.457147i
$786$	−9.77647e7	+	3.64863e8i	−0.201333	+	0.751384i
$787$	1.55032e8	+	4.15408e7i	0.318052	+	0.0852218i	0.414313	−	0.910134i	$-0.364022\pi$
$787$	1.55032e8	+	4.15408e7i	0.318052	+	0.0852218i	−0.0962614	+	0.995356i	$0.530688\pi$
$788$	−1.87265e8	+	1.87265e8i	−0.382718	+	0.382718i
$789$	−3.21426e8	−	5.56726e8i	−0.654410	−	1.13347i
$790$	−9.06647e7	−	5.23453e7i	−0.183890	−	0.106169i
$791$	−9.81673e7	−	3.66365e8i	−0.198352	−	0.740261i
$792$			7.36999e8i			1.48351i
$793$	−4.65689e8	−	7.52060e8i	−0.933849	−	1.50811i
$794$	5.29747e7			0.105830
$795$	4.57809e8	−	1.22669e8i	0.911135	−	0.244138i
$796$	7.48405e7	−	1.29628e8i	0.148388	−	0.257015i
$797$	3.02592e8	−	1.74702e8i	0.597699	−	0.345082i	−0.170437	−	0.985369i	$-0.554518\pi$
$797$	3.02592e8	−	1.74702e8i	0.597699	−	0.345082i	0.768136	+	0.640287i	$0.221185\pi$
$798$	−2.06258e8	−	2.06258e8i	−0.405884	−	0.405884i
$799$	−4.94729e6	+	1.84635e7i	−0.00969900	+	0.0361971i
$800$	−3.14403e8	−	8.42439e7i	−0.614068	−	0.164539i
$801$	−1.48231e8	+	1.48231e8i	−0.288430	+	0.288430i
$802$	−3.23968e8	−	5.61128e8i	−0.628027	−	1.08778i
$803$	2.04732e8	+	1.18202e8i	0.395402	+	0.228285i
$804$	−4.40759e6	−	1.64493e7i	−0.00848073	−	0.0316505i
$805$			2.96993e8i			0.569323i
$806$	−1.79179e8	−	9.62099e7i	−0.342202	−	0.183745i
$807$	6.81898e8			1.29747
$808$	−8.20792e8	+	2.19930e8i	−1.55596	+	0.416919i
$809$	−9.69278e7	+	1.67884e8i	−0.183064	+	0.317076i	−0.942922	−	0.333012i	$-0.891935\pi$
$809$	−9.69278e7	+	1.67884e8i	−0.183064	+	0.317076i	0.759858	+	0.650089i	$0.225268\pi$
$810$	−8.48555e7	+	4.89914e7i	−0.159671	+	0.0921859i
$811$	−5.91708e8	−	5.91708e8i	−1.10929	−	1.10929i	−0.993244	−	0.116045i	$-0.962978\pi$
$811$	−5.91708e8	−	5.91708e8i	−1.10929	−	1.10929i	−0.116045	−	0.993244i	$-0.537022\pi$
$812$	1.28444e8	−	4.79359e8i	0.239908	−	0.895349i
$813$	6.59600e8	+	1.76739e8i	1.22747	+	0.328898i
$814$	3.47077e8	−	3.47077e8i	0.643507	−	0.643507i
$815$	−1.48359e7	−	2.56966e7i	−0.0274058	−	0.0474682i
$816$	3.70918e7	+	2.14150e7i	0.0682665	+	0.0394137i
$817$	−1.27830e7	−	4.77069e7i	−0.0234405	−	0.0874813i
$818$		−	9.07192e7i		−	0.165745i
$819$	3.72088e8	+	1.23502e9i	0.677320	+	2.24814i
$820$	−7.49580e7			−0.135949
$821$	4.08162e8	−	1.09367e8i	0.737569	−	0.197631i	0.129572	−	0.991570i	$-0.458640\pi$
$821$	4.08162e8	−	1.09367e8i	0.737569	−	0.197631i	0.607997	+	0.793939i	$0.291973\pi$
$822$	−5.02780e7	+	8.70841e7i	−0.0905238	+	0.156792i
$823$	−7.73729e8	+	4.46713e8i	−1.38800	+	0.801362i	−0.993090	−	0.117358i	$-0.962558\pi$
$823$	−7.73729e8	+	4.46713e8i	−1.38800	+	0.801362i	−0.394910	+	0.918720i	$0.629224\pi$
$824$	1.32493e8	+	1.32493e8i	0.236816	+	0.236816i
$825$	1.89107e8	−	7.05755e8i	0.336779	−	1.25688i
$826$	5.82317e8	+	1.56031e8i	1.03328	+	0.276868i
$827$	3.91052e8	−	3.91052e8i	0.691382	−	0.691382i	−0.271154	−	0.962536i	$-0.587405\pi$
$827$	3.91052e8	−	3.91052e8i	0.691382	−	0.691382i	0.962536	+	0.271154i	$0.0874053\pi$
$828$	−1.19703e8	−	2.07331e8i	−0.210869	−	0.365236i
$829$	−8.33349e7	−	4.81135e7i	−0.146273	−	0.0844506i	0.425077	−	0.905157i	$-0.360247\pi$
$829$	−8.33349e7	−	4.81135e7i	−0.146273	−	0.0844506i	−0.571350	+	0.820706i	$0.693580\pi$
$830$	4.02681e7	+	1.50283e8i	0.0704251	+	0.262830i
$831$			1.38086e9i			2.40628i
$832$	1.76541e7	+	5.72407e8i	0.0306532	+	0.993883i
$833$	1.58975e8			0.275039
$834$	−1.69399e8	+	4.53904e7i	−0.292021	+	0.0782467i
$835$	1.09407e8	−	1.89499e8i	0.187926	−	0.325497i
$836$	−6.12033e7	+	3.53358e7i	−0.104751	+	0.0604777i
$837$	−1.03566e8	−	1.03566e8i	−0.176620	−	0.176620i
$838$	1.07335e8	−	4.00581e8i	0.182394	−	0.680704i
$839$	3.49673e8	+	9.36947e7i	0.592075	+	0.158646i	0.542401	−	0.840120i	$-0.317515\pi$
$839$	3.49673e8	+	9.36947e7i	0.592075	+	0.158646i	0.0496735	+	0.998766i	$0.484182\pi$
$840$	5.16335e8	−	5.16335e8i	0.871151	−	0.871151i
$841$	−1.63887e8	−	2.83861e8i	−0.275523	−	0.477219i
$842$	−5.13110e8	−	2.96244e8i	−0.859557	−	0.496265i
$843$	−6.32858e7	−	2.36186e8i	−0.105639	−	0.394250i
$844$		−	2.89546e8i		−	0.481604i
$845$	−1.90251e8	−	1.68124e8i	−0.315323	−	0.278650i
$846$	1.79180e8			0.295922
$847$	−8.01645e7	+	2.14800e7i	−0.131926	+	0.0353496i
$848$	1.81887e8	−	3.15037e8i	0.298273	−	0.516624i
$849$	−9.54182e8	+	5.50897e8i	−1.55922	+	0.900218i
$850$	−3.47528e7	−	3.47528e7i	−0.0565891	−	0.0565891i
$851$	−1.39764e8	+	5.21606e8i	−0.226781	+	0.846358i
$852$	5.62109e8	+	1.50617e8i	0.908870	+	0.243531i
$853$	−7.85405e8	+	7.85405e8i	−1.26546	+	1.26546i	−0.317044	+	0.948411i	$0.602690\pi$
$853$	−7.85405e8	+	7.85405e8i	−1.26546	+	1.26546i	−0.948411	+	0.317044i	$0.897310\pi$
$854$	7.48014e8	+	1.29560e9i	1.20098	+	2.08016i
$855$	8.37531e7	+	4.83549e7i	0.133999	+	0.0773645i
$856$	−1.26839e8	−	4.73371e8i	−0.202224	−	0.754711i
$857$		−	1.14238e9i		−	1.81496i	−0.420092	−	0.907482i	$-0.638002\pi$
$857$		−	1.14238e9i		−	1.81496i	0.420092	−	0.907482i	$-0.361998\pi$
$858$	−7.60927e8	+	2.34684e7i	−1.20471	+	0.0371553i
$859$	−5.62443e8			−0.887359			−0.443679	−	0.896186i	$-0.646327\pi$
$859$	−5.62443e8			−0.887359			−0.443679	+	0.896186i	$0.646327\pi$
$860$	3.52623e7	−	9.44851e6i	0.0554390	−	0.0148548i
$861$	−6.66122e8	+	1.15376e9i	−1.04363	+	1.80761i
$862$	5.30625e8	−	3.06357e8i	0.828450	−	0.478306i
$863$	−2.31354e8	−	2.31354e8i	−0.359952	−	0.359952i	0.503843	−	0.863795i	$-0.331919\pi$
$863$	−2.31354e8	−	2.31354e8i	−0.359952	−	0.359952i	−0.863795	+	0.503843i	$0.831919\pi$
$864$	−6.32137e7	+	2.35917e8i	−0.0980100	+	0.365778i
$865$	1.61918e8	+	4.33858e7i	0.250176	+	0.0670346i
$866$	−2.06989e8	+	2.06989e8i	−0.318709	+	0.318709i
$867$	4.88432e8	+	8.45988e8i	0.749456	+	1.29810i
$868$	−2.14793e8	−	1.24011e8i	−0.328444	−	0.189627i
$869$	1.16678e8	+	4.35448e8i	0.177799	+	0.663555i
$870$		−	4.00822e8i		−	0.608686i
$871$	3.24742e7	−	9.78387e6i	0.0491456	−	0.0148066i
$872$	−6.18407e8			−0.932663
$873$	−1.01245e9	+	2.71284e8i	−1.52170	+	0.407739i
$874$	−5.39125e7	+	9.33791e7i	−0.0807523	+	0.139867i
$875$	−7.90599e8	+	4.56452e8i	−1.18014	+	0.681352i
$876$	1.33508e8	+	1.33508e8i	0.198607	+	0.198607i
$877$	−7.34972e6	+	2.74295e7i	−0.0108961	+	0.0406649i	−0.971160	−	0.238429i	$-0.923367\pi$
$877$	−7.34972e6	+	2.74295e7i	−0.0108961	+	0.0406649i	0.960264	+	0.279094i	$0.0900342\pi$
$878$	−6.65625e8	−	1.78354e8i	−0.983436	−	0.263511i
$879$	1.31851e9	−	1.31851e9i	1.94140	−	1.94140i
$880$	6.03346e7	+	1.04503e8i	0.0885358	+	0.153348i
$881$	6.05572e8	+	3.49627e8i	0.885601	+	0.511302i	0.872501	−	0.488612i	$-0.162497\pi$
$881$	6.05572e8	+	3.49627e8i	0.885601	+	0.511302i	0.0130999	+	0.999914i	$0.495830\pi$
$882$	−3.85695e8	−	1.43943e9i	−0.562132	−	2.09790i
$883$		−	1.03923e8i		−	0.150949i	−0.997148	−	0.0754746i	$-0.975953\pi$
$883$		−	1.03923e8i		−	0.150949i	0.997148	−	0.0754746i	$-0.0240472\pi$
$884$	1.74682e7	−	3.25324e7i	0.0252866	−	0.0470932i
$885$	−3.51102e8			−0.506528
$886$	7.97773e8	−	2.13763e8i	1.14704	−	0.307348i
$887$	2.07203e8	−	3.58887e8i	0.296911	−	0.514265i	−0.678517	−	0.734585i	$-0.737377\pi$
$887$	2.07203e8	−	3.58887e8i	0.296911	−	0.514265i	0.975428	+	0.220320i	$0.0707103\pi$
$888$	1.14982e9	−	6.63849e8i	1.64207	−	0.948048i
$889$	7.17424e8	+	7.17424e8i	1.02111	+	1.02111i
$890$	−1.80619e7	+	6.74081e7i	−0.0256209	+	0.0956185i
$891$	4.07547e8	+	1.09202e8i	0.576162	+	0.154382i
$892$	−1.64616e7	+	1.64616e7i	−0.0231941	+	0.0231941i
$893$	2.90956e7	+	5.03950e7i	0.0408576	+	0.0707674i
$894$	5.02624e8	+	2.90190e8i	0.703445	+	0.406134i
$895$	1.04540e8	+	3.90148e8i	0.145819	+	0.544202i
$896$			1.86219e7i			0.0258880i
$897$	7.12079e8	−	4.40932e8i	0.986622	−	0.610934i
$898$	−1.16379e8			−0.160710
$899$	−4.45378e8	+	1.19339e8i	−0.612985	+	0.164249i
$900$	1.66102e8	−	2.87697e8i	0.227849	−	0.394646i
$901$	−1.18891e8	+	6.86419e7i	−0.162546	+	0.0938458i
$902$	−3.16523e8	−	3.16523e8i	−0.431306	−	0.431306i
$903$	1.67930e8	−	6.26725e8i	0.228069	−	0.851165i
$904$	3.32973e8	+	8.92197e7i	0.450716	+	0.120769i
$905$	−1.19801e8	+	1.19801e8i	−0.161627	+	0.161627i
$906$	6.67062e7	+	1.15539e8i	0.0896978	+	0.155361i
$907$	1.22234e9	+	7.05716e8i	1.63821	+	0.945819i	0.981450	+	0.191716i	$0.0614053\pi$
$907$	1.22234e9	+	7.05716e8i	1.63821	+	0.945819i	0.656756	+	0.754103i	$0.271928\pi$
$908$	−1.41075e8	−	5.26501e8i	−0.188449	−	0.703301i
$909$		−	1.47846e9i		−	1.96842i
$910$	3.12843e8	+	2.94123e8i	0.415148	+	0.390306i
$911$	1.21681e8			0.160941			0.0804706	−	0.996757i	$-0.474358\pi$
$911$	1.21681e8			0.160941			0.0804706	+	0.996757i	$0.474358\pi$
$912$	1.25944e8	−	3.37466e7i	0.166032	−	0.0444883i
$913$	3.34981e8	−	5.80204e8i	0.440157	−	0.762375i
$914$	−8.71436e8	+	5.03124e8i	−1.14129	+	0.658926i
$915$	−6.16086e8	−	6.16086e8i	−0.804227	−	0.804227i
$916$	−6.05423e7	+	2.25947e8i	−0.0787721	+	0.293981i
$917$	−8.86178e8	−	2.37451e8i	−1.14925	−	0.307940i
$918$	−2.60773e7	+	2.60773e7i	−0.0337081	+	0.0337081i
$919$	−4.14575e8	−	7.18065e8i	−0.534142	−	0.925161i	−0.999204	−	0.0398833i	$-0.987301\pi$
$919$	−4.14575e8	−	7.18065e8i	−0.534142	−	0.925161i	0.465062	−	0.885278i	$-0.346032\pi$
$920$	−2.33760e8	−	1.34962e8i	−0.300198	−	0.173319i
$921$	−1.43078e8	−	5.33976e8i	−0.183145	−	0.683506i
$922$			6.10022e8i			0.778311i
$923$	−2.65314e8	+	1.12821e9i	−0.337408	+	1.43478i
$924$	−9.28411e8			−1.17686
$925$	−7.23792e8	+	1.93939e8i	−0.914510	+	0.245042i
$926$	5.91419e8	−	1.02437e9i	0.744839	−	1.29010i
$927$	−2.82330e8	+	1.63003e8i	−0.354420	+	0.204624i
$928$	5.43692e8	+	5.43692e8i	0.680314	+	0.680314i
$929$	−2.06537e8	+	7.70807e8i	−0.257603	+	0.961387i	0.709021	+	0.705188i	$0.249137\pi$
$929$	−2.06537e8	+	7.70807e8i	−0.257603	+	0.961387i	−0.966624	+	0.256200i	$0.917529\pi$
$930$	−1.93494e8	−	5.18466e7i	−0.240557	−	0.0644572i
$931$	3.42217e8	−	3.42217e8i	0.424084	−	0.424084i
$932$	1.82310e8	+	3.15769e8i	0.225197	+	0.390052i
$933$	1.29101e9	+	7.45365e8i	1.58959	+	0.917749i
$934$	−5.33229e7	−	1.99004e8i	−0.0654445	−	0.244242i
$935$		−	4.55391e7i		−	0.0557121i
$936$	−1.14116e9	−	2.68360e8i	−1.39161	−	0.327258i
$937$	8.99243e8			1.09310			0.546548	−	0.837428i	$-0.315942\pi$
$937$	8.99243e8			1.09310			0.546548	+	0.837428i	$0.315942\pi$
$938$	−5.54061e7	+	1.48460e7i	−0.0671350	+	0.0179888i
$939$	5.30286e8	−	9.18482e8i	0.640492	−	1.10936i
$940$	−3.72492e7	+	2.15059e7i	−0.0448470	+	0.0258925i
$941$	−5.00314e8	−	5.00314e8i	−0.600446	−	0.600446i	0.339985	−	0.940431i	$-0.389578\pi$
$941$	−5.00314e8	−	5.00314e8i	−0.600446	−	0.600446i	−0.940431	+	0.339985i	$0.889578\pi$
$942$	−3.86052e8	+	1.44076e9i	−0.461841	+	1.72361i
$943$	4.75687e8	+	1.27460e8i	0.567265	+	0.151998i
$944$	−1.90550e8	+	1.90550e8i	−0.226513	+	0.226513i
$945$	1.54618e8	+	2.67806e8i	0.183216	+	0.317340i
$946$	1.88799e8	+	1.09003e8i	0.223011	+	0.128756i
$947$	−1.43680e7	−	5.36222e7i	−0.0169179	−	0.0631386i	0.956951	−	0.290250i	$-0.0937385\pi$
$947$	−1.43680e7	−	5.36222e7i	−0.0169179	−	0.0631386i	−0.973869	+	0.227111i	$0.927072\pi$
$948$			3.60047e8i			0.422605i
$949$	−2.57570e8	+	2.73963e8i	−0.301368	+	0.320549i
$950$	−1.49620e8			−0.174510
$951$	−1.04490e9	+	2.79980e8i	−1.21488	+	0.325525i
$952$	−1.05754e8	+	1.83171e8i	−0.122570	+	0.212298i
$953$	9.82546e8	−	5.67273e8i	1.13520	−	0.655411i	0.189966	−	0.981791i	$-0.439162\pi$
$953$	9.82546e8	−	5.67273e8i	1.13520	−	0.655411i	0.945239	+	0.326380i	$0.105829\pi$
$954$	9.09959e8	+	9.09959e8i	1.04804	+	1.04804i
$955$	2.45393e7	−	9.15819e7i	0.0281742	−	0.105148i
$956$	3.20657e7	+	8.59197e6i	0.0367001	+	0.00983375i
$957$	−1.22045e9	+	1.22045e9i	−1.39247	+	1.39247i
$958$	−1.40445e8	−	2.43257e8i	−0.159738	−	0.276674i
$959$	−2.11510e8	−	1.22115e8i	−0.239814	−	0.138457i
$960$	1.45993e8	+	5.44854e8i	0.165013	+	0.615839i
$961$		−	6.57064e8i		−	0.740350i
$962$	4.11030e8	+	6.63789e8i	0.461688	+	0.745598i
$963$	8.52664e8			0.954770
$964$	−9.82495e7	+	2.63259e7i	−0.109673	+	0.0293868i
$965$	8.08488e7	−	1.40034e8i	0.0899687	−	0.155830i
$966$	−1.22672e9	+	7.08247e8i	−1.36086	+	0.785694i
$967$	−8.67817e8	−	8.67817e8i	−0.959730	−	0.959730i	0.0394902	−	0.999220i	$-0.487427\pi$
$967$	−8.67817e8	−	8.67817e8i	−0.959730	−	0.959730i	−0.999220	+	0.0394902i	$0.987427\pi$
$968$	1.95222e7	−	7.28578e7i	0.0215230	−	0.0803248i
$969$	−4.75297e7	−	1.27355e7i	−0.0522389	−	0.0139974i
$970$	−2.46734e8	+	2.46734e8i	−0.270342	+	0.270342i
$971$	−8.16768e8	−	1.41468e9i	−0.892156	−	1.54526i	−0.837285	−	0.546767i	$-0.815858\pi$
$971$	−8.16768e8	−	1.41468e9i	−0.892156	−	1.54526i	−0.0548713	−	0.998493i	$-0.517475\pi$
$972$	4.55164e8	+	2.62789e8i	0.495643	+	0.286160i
$973$	−1.10244e8	−	4.11437e8i	−0.119679	−	0.446647i
$974$			9.74115e8i			1.05422i
$975$	1.02392e9	+	5.49793e8i	1.10472	+	0.593178i
$976$	−6.68725e8			−0.719280
$977$	8.63792e8	−	2.31452e8i	0.926244	−	0.248186i	0.235992	−	0.971755i	$-0.424166\pi$
$977$	8.63792e8	−	2.31452e8i	0.926244	−	0.248186i	0.690252	+	0.723569i	$0.257500\pi$
$978$	7.07593e7	−	1.22559e8i	0.0756427	−	0.131017i
$979$	2.60246e8	−	1.50253e8i	0.277355	−	0.160131i
$980$	2.52948e8	+	2.52948e8i	0.268753	+	0.268753i
$981$	2.78477e8	−	1.03929e9i	0.294974	−	1.10086i
$982$	7.08374e8	+	1.89808e8i	0.748045	+	0.200438i
$983$	−7.86290e8	+	7.86290e8i	−0.827793	+	0.827793i	−0.987211	−	0.159418i	$-0.949038\pi$
$983$	−7.86290e8	+	7.86290e8i	−0.827793	+	0.827793i	0.159418	+	0.987211i	$0.449038\pi$
$984$	−6.05408e8	−	1.04860e9i	−0.635423	−	1.10058i
$985$	−4.49913e8	−	2.59758e8i	−0.470782	−	0.271806i
$986$	3.00487e7	+	1.12143e8i	0.0313470	+	0.116988i
$987$			7.64456e8i			0.795063i
$988$	−3.24278e7	−	1.07633e8i	−0.0336237	−	0.111603i
$989$	−2.39843e8			−0.247935
$990$	−4.12331e8	+	1.10484e8i	−0.424953	+	0.113866i
$991$	−8.74680e8	+	1.51499e9i	−0.898728	+	1.55664i	−0.0696065	+	0.997575i	$0.522174\pi$
$991$	−8.74680e8	+	1.51499e9i	−0.898728	+	1.55664i	−0.829122	+	0.559068i	$0.811159\pi$
$992$	3.32791e8	−	1.92137e8i	0.340907	−	0.196823i
$993$	−5.79026e8	−	5.79026e8i	−0.591358	−	0.591358i
$994$	5.07320e8	−	1.89334e9i	0.516563	−	1.92784i
$995$	2.83620e8	+	7.59957e7i	0.287917	+	0.0771471i
$996$	3.78357e8	−	3.78357e8i	0.382934	−	0.382934i
$997$	6.46846e8	+	1.12037e9i	0.652703	+	1.13051i	0.982464	+	0.186450i	$0.0596983\pi$
$997$	6.46846e8	+	1.12037e9i	0.652703	+	1.13051i	−0.329762	+	0.944064i	$0.606968\pi$
$998$	−4.83842e8	−	2.79347e8i	−0.486757	−	0.281029i
$999$	1.45525e8	+	5.43108e8i	0.145963	+	0.544741i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.f.a.7.5	yes	24
13.2	odd	12	inner	13.7.f.a.2.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.f.a.2.5	✓	24	13.2	odd	12	inner
13.7.f.a.7.5	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)

\(f(q)\)	\(=\)	\(q+(5.89025 - 1.57829i) q^{2} +(20.5701 - 35.6285i) q^{3} +(-23.2216 + 13.4070i) q^{4} +(-37.1940 - 37.1940i) q^{5} +(64.9312 - 242.326i) q^{6} +(588.562 + 157.705i) q^{7} +(-391.586 + 391.586i) q^{8} +(-481.762 - 834.436i) q^{9} +O(q^{10})\)	\(q+(5.89025 - 1.57829i) q^{2} +(20.5701 - 35.6285i) q^{3} +(-23.2216 + 13.4070i) q^{4} +(-37.1940 - 37.1940i) q^{5} +(64.9312 - 242.326i) q^{6} +(588.562 + 157.705i) q^{7} +(-391.586 + 391.586i) q^{8} +(-481.762 - 834.436i) q^{9} +(-277.785 - 160.379i) q^{10} +(357.486 + 1334.15i) q^{11} +1103.14i q^{12} +(-2195.96 + 67.7273i) q^{13} +3715.68 q^{14} +(-2090.25 + 560.082i) q^{15} +(-830.455 + 1438.39i) q^{16} +(542.831 - 313.404i) q^{17} +(-4154.67 - 4154.67i) q^{18} +(493.874 - 1843.16i) q^{19} +(1362.37 + 365.045i) q^{20} +(17725.6 - 17725.6i) q^{21} +(4211.36 + 7294.28i) q^{22} +(-8024.91 - 4633.18i) q^{23} +(5896.66 + 22006.6i) q^{24} -12858.2i q^{25} +(-12827.8 + 3864.78i) q^{26} -9648.36 q^{27} +(-15781.7 + 4228.70i) q^{28} +(-15187.1 + 26304.9i) q^{29} +(-11428.1 + 6598.04i) q^{30} +(10734.1 + 10734.1i) q^{31} +(6551.76 - 24451.5i) q^{32} +(54887.5 + 14707.1i) q^{33} +(2702.77 - 2702.77i) q^{34} +(-16025.3 - 27756.7i) q^{35} +(22374.6 + 12918.0i) q^{36} +(-15082.9 - 56290.2i) q^{37} -11636.2i q^{38} +(-42758.1 + 79631.8i) q^{39} +29129.3 q^{40} +(-51334.8 + 13755.1i) q^{41} +(76432.1 - 132384. i) q^{42} +(22415.5 - 12941.6i) q^{43} +(-26188.4 - 26188.4i) q^{44} +(-13117.4 + 48954.7i) q^{45} +(-54581.2 - 14625.0i) q^{46} +(-21563.6 + 21563.6i) q^{47} +(34165.2 + 59175.8i) q^{48} +(219648. + 126814. i) q^{49} +(-20293.9 - 75738.0i) q^{50} -25787.0i q^{51} +(50085.6 - 31013.9i) q^{52} -219021. q^{53} +(-56831.2 + 15227.9i) q^{54} +(36326.2 - 62918.9i) q^{55} +(-292228. + 168718. i) q^{56} +(-55510.2 - 55510.2i) q^{57} +(-47939.3 + 178912. i) q^{58} +(156719. + 41992.7i) q^{59} +(41030.1 - 41030.1i) q^{60} +(201313. + 348684. i) q^{61} +(80167.7 + 46284.8i) q^{62} +(-151952. - 567093. i) q^{63} -260664. i q^{64} +(84195.5 + 79157.4i) q^{65} +346513. q^{66} +(-14911.4 + 3995.51i) q^{67} +(-8403.61 + 14555.5i) q^{68} +(-330147. + 190611. i) q^{69} +(-138201. - 138201. i) q^{70} +(136535. - 509556. i) q^{71} +(515405. + 138102. i) q^{72} +(121026. - 121026. i) q^{73} +(-177684. - 307758. i) q^{74} +(-458119. - 264495. i) q^{75} +(13242.8 + 49422.6i) q^{76} +841610. i q^{77} +(-126174. + 536536. i) q^{78} +326385. q^{79} +(84387.5 - 22611.6i) q^{80} +(152736. - 264547. i) q^{81} +(-280665. + 162042. i) q^{82} +(-342983. - 342983. i) q^{83} +(-173970. + 649264. i) q^{84} +(-31846.8 - 8533.32i) q^{85} +(111607. - 111607. i) q^{86} +(624804. + 1.08219e6i) q^{87} +(-662423. - 382450. i) q^{88} +(-56310.2 - 210152. i) q^{89} +309058. i q^{90} +(-1.30314e6 - 306451. i) q^{91} +248469. q^{92} +(603240. - 161638. i) q^{93} +(-92981.5 + 161049. i) q^{94} +(-86923.8 + 50185.5i) q^{95} +(-736401. - 736401. i) q^{96} +(281554. - 1.05078e6i) q^{97} +(1.49393e6 + 400296. i) q^{98} +(941043. - 941043. 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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