LMFDB - Embedded newform 72.7.p.b.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(43,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("72.43");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.p (of order $6$, degree $2$, 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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	72.43
Dual form			72.7.p.b.67.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.70909 + 2.13776i) q^{2} +(-20.4110 + 17.6746i) q^{3} +(54.8600 - 32.9603i) q^{4} +(-67.6940 + 39.0831i) q^{5} +(119.566 - 179.888i) q^{6} +(139.025 + 80.2661i) q^{7} +(-352.459 + 371.371i) q^{8} +(104.220 - 721.512i) q^{9} +O(q^{10})$	\(q+(-7.70909 + 2.13776i) q^{2} +(-20.4110 + 17.6746i) q^{3} +(54.8600 - 32.9603i) q^{4} +(-67.6940 + 39.0831i) q^{5} +(119.566 - 179.888i) q^{6} +(139.025 + 80.2661i) q^{7} +(-352.459 + 371.371i) q^{8} +(104.220 - 721.512i) q^{9} +(438.308 - 446.009i) q^{10} +(703.041 - 1217.70i) q^{11} +(-537.190 + 1642.38i) q^{12} +(1657.51 - 956.964i) q^{13} +(-1243.35 - 321.577i) q^{14} +(690.927 - 1994.19i) q^{15} +(1923.24 - 3616.40i) q^{16} -2071.65 q^{17} +(738.973 + 5784.99i) q^{18} +7230.73 q^{19} +(-2425.50 + 4375.32i) q^{20} +(-4256.31 + 818.891i) q^{21} +(-2816.65 + 10890.3i) q^{22} +(-13079.0 + 7551.16i) q^{23} +(630.239 - 13809.6i) q^{24} +(-4757.52 + 8240.26i) q^{25} +(-10732.1 + 10920.7i) q^{26} +(10625.2 + 16568.8i) q^{27} +(10272.5 - 178.907i) q^{28} +(21851.0 + 12615.7i) q^{29} +(-1063.33 + 16850.4i) q^{30} +(-1188.04 + 685.913i) q^{31} +(-7095.41 + 31990.6i) q^{32} +(7172.56 + 37280.5i) q^{33} +(15970.5 - 4428.68i) q^{34} -12548.2 q^{35} +(-18063.7 - 43017.3i) q^{36} +74749.2i q^{37} +(-55742.3 + 15457.5i) q^{38} +(-16917.6 + 48828.4i) q^{39} +(9345.03 - 38914.8i) q^{40} +(11098.3 + 19222.8i) q^{41} +(31061.7 - 15411.9i) q^{42} +(46620.4 - 80748.9i) q^{43} +(-1567.02 - 89975.6i) q^{44} +(21143.9 + 52915.3i) q^{45} +(84684.5 - 86172.2i) q^{46} +(-28284.3 - 16329.9i) q^{47} +(24663.1 + 107807. i) q^{48} +(-45939.2 - 79569.0i) q^{49} +(19060.4 - 73695.3i) q^{50} +(42284.5 - 36615.4i) q^{51} +(59389.2 - 107131. i) q^{52} +197801. i q^{53} +(-117330. - 105017. i) q^{54} +109908. i q^{55} +(-78809.2 + 23339.3i) q^{56} +(-147587. + 127800. i) q^{57} +(-195420. - 50543.2i) q^{58} +(-18443.5 - 31945.0i) q^{59} +(-27824.8 - 132174. i) q^{60} +(252653. + 145869. i) q^{61} +(7692.36 - 7827.49i) q^{62} +(72402.2 - 91942.8i) q^{63} +(-13688.9 - 261786. i) q^{64} +(-74802.3 + 129561. i) q^{65} +(-134991. - 272065. i) q^{66} +(-137226. - 237682. i) q^{67} +(-113651. + 68282.1i) q^{68} +(133492. - 385292. i) q^{69} +(96735.2 - 26825.0i) q^{70} +31817.8i q^{71} +(231215. + 293008. i) q^{72} +499108. q^{73} +(-159796. - 576248. i) q^{74} +(-48537.1 - 252279. i) q^{75} +(396678. - 238327. i) q^{76} +(195481. - 112861. i) q^{77} +(26035.9 - 412588. i) q^{78} +(452567. + 261290. i) q^{79} +(11148.8 + 319975. i) q^{80} +(-509717. - 150392. i) q^{81} +(-126652. - 124465. i) q^{82} +(-313892. + 543676. i) q^{83} +(-206510. + 185214. i) q^{84} +(140238. - 80966.5i) q^{85} +(-186779. + 722163. i) q^{86} +(-668978. + 128708. i) q^{87} +(204426. + 690280. i) q^{88} +499277. q^{89} +(-276120. - 362728. i) q^{90} +307247. q^{91} +(-468625. + 845344. i) q^{92} +(12125.8 - 34998.2i) q^{93} +(252955. + 65424.0i) q^{94} +(-489477. + 282600. i) q^{95} +(-420595. - 778369. i) q^{96} +(-573043. + 992540. i) q^{97} +(524248. + 515198. i) q^{98} +(-805315. - 634161. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) $ 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−7.70909	+	2.13776i	−0.963636	+	0.267220i
$2$	−7.70909	+	2.13776i	−0.963636	+	0.267220i
$3$	−20.4110	+	17.6746i	−0.755964	+	0.654613i
$3$	−20.4110	+	17.6746i	−0.755964	+	0.654613i
$4$	54.8600	−	32.9603i	0.857187	−	0.515005i
$5$	−67.6940	+	39.0831i	−0.541552	+	0.312665i	−0.745708	−	0.666273i	$-0.767888\pi$
$5$	−67.6940	+	39.0831i	−0.541552	+	0.312665i	0.204156	+	0.978938i	$0.434555\pi$
$6$	119.566	−	179.888i	0.553548	−	0.832817i
$7$	139.025	+	80.2661i	0.405321	+	0.234012i	0.688777	−	0.724973i	$-0.258148\pi$
$7$	139.025	+	80.2661i	0.405321	+	0.234012i	−0.283456	+	0.958985i	$0.591481\pi$
$8$	−352.459	+	371.371i	−0.688397	+	0.725334i
$9$	104.220	−	721.512i	0.142963	−	0.989728i
$10$	438.308	−	446.009i	0.438308	−	0.446009i
$11$	703.041	−	1217.70i	0.528205	−	0.914878i	−0.471254	−	0.881997i	$-0.656199\pi$
$11$	703.041	−	1217.70i	0.528205	−	0.914878i	0.999459	−	0.0328805i	$-0.0104681\pi$
$12$	−537.190	+	1642.38i	−0.310874	+	0.950451i
$13$	1657.51	−	956.964i	0.754443	−	0.435578i	−0.0728542	−	0.997343i	$-0.523211\pi$
$13$	1657.51	−	956.964i	0.754443	−	0.435578i	0.827297	+	0.561765i	$0.189877\pi$
$14$	−1243.35	−	321.577i	−0.453114	−	0.117193i
$15$	690.927	−	1994.19i	0.204719	−	0.590871i
$16$	1923.24	−	3616.40i	0.469540	−	0.882911i
$17$	−2071.65			−0.421666			−0.210833	−	0.977522i	$-0.567618\pi$
$17$	−2071.65			−0.421666			−0.210833	+	0.977522i	$0.567618\pi$
$18$	738.973	+	5784.99i	0.126710	+	0.991940i
$19$	7230.73			1.05420			0.527098	−	0.849805i	$-0.323280\pi$
$19$	7230.73			1.05420			0.527098	+	0.849805i	$0.323280\pi$
$20$	−2425.50	+	4375.32i	−0.303187	+	0.546914i
$21$	−4256.31	+	818.891i	−0.459595	+	0.0884236i
$22$	−2816.65	+	10890.3i	−0.264524	+	1.02276i
$23$	−13079.0	+	7551.16i	−1.07496	+	0.620626i	−0.929531	−	0.368743i	$-0.879788\pi$
$23$	−13079.0	+	7551.16i	−1.07496	+	0.620626i	−0.145425	+	0.989369i	$0.546455\pi$
$24$	630.239	−	13809.6i	0.0455902	−	0.998960i
$25$	−4757.52	+	8240.26i	−0.304481	+	0.527377i
$26$	−10732.1	+	10920.7i	−0.610613	+	0.621340i
$27$	10625.2	+	16568.8i	0.539814	+	0.841784i
$28$	10272.5	−	178.907i	0.467953	−	0.00814990i
$29$	21851.0	+	12615.7i	0.895937	+	0.517269i	0.875880	−	0.482530i	$-0.160282\pi$
$29$	21851.0	+	12615.7i	0.895937	+	0.517269i	0.0200570	+	0.999799i	$0.493615\pi$
$30$	−1063.33	+	16850.4i	−0.0393824	+	0.624089i
$31$	−1188.04	+	685.913i	−0.0398790	+	0.0230242i	−0.519807	−	0.854284i	$-0.673996\pi$
$31$	−1188.04	+	685.913i	−0.0398790	+	0.0230242i	0.479928	+	0.877308i	$0.340663\pi$
$32$	−7095.41	+	31990.6i	−0.216535	+	0.976275i
$33$	7172.56	+	37280.5i	0.199587	+	1.03738i
$34$	15970.5	−	4428.68i	0.406333	−	0.112678i
$35$	−12548.2			−0.292670
$36$	−18063.7	−	43017.3i	−0.387168	−	0.922009i
$37$			74749.2i			1.47571i	0.674959	+	0.737855i	$0.264161\pi$
$37$			74749.2i			1.47571i	−0.674959	+	0.737855i	$0.735839\pi$
$38$	−55742.3	+	15457.5i	−1.01586	+	0.281702i
$39$	−16917.6	+	48828.4i	−0.285197	+	0.823149i
$40$	9345.03	−	38914.8i	0.146016	−	0.608044i
$41$	11098.3	+	19222.8i	0.161030	+	0.278911i	0.935238	−	0.354019i	$-0.115185\pi$
$41$	11098.3	+	19222.8i	0.161030	+	0.278911i	−0.774209	+	0.632930i	$0.781852\pi$
$42$	31061.7	−	15411.9i	0.419254	−	0.208021i
$43$	46620.4	−	80748.9i	0.586368	−	1.01562i	−0.408335	−	0.912832i	$-0.633890\pi$
$43$	46620.4	−	80748.9i	0.586368	−	1.01562i	0.994703	−	0.102788i	$-0.0327763\pi$
$44$	−1567.02	−	89975.6i	−0.0183957	−	1.05625i
$45$	21143.9	+	52915.3i	0.232031	+	0.580689i
$46$	84684.5	−	86172.2i	0.870023	−	0.885307i
$47$	−28284.3	−	16329.9i	−0.272428	−	0.157286i	0.357563	−	0.933889i	$-0.383608\pi$
$47$	−28284.3	−	16329.9i	−0.272428	−	0.157286i	−0.629991	+	0.776603i	$0.716941\pi$
$48$	24663.1	+	107807.i	0.223009	+	0.974816i
$49$	−45939.2	−	79569.0i	−0.390477	−	0.676326i
$50$	19060.4	−	73695.3i	0.152483	−	0.589562i
$51$	42284.5	−	36615.4i	0.318765	−	0.276028i
$52$	59389.2	−	107131.i	0.422374	−	0.761913i
$53$			197801.i			1.32862i	0.747457	+	0.664311i	$0.231275\pi$
$53$			197801.i			1.32862i	−0.747457	+	0.664311i	$0.768725\pi$
$54$	−117330.	−	105017.i	−0.745125	−	0.666925i
$55$			109908.i			0.660605i
$56$	−78809.2	+	23339.3i	−0.448758	+	0.132900i
$57$	−147587.	+	127800.i	−0.796934	+	0.690090i
$58$	−195420.	−	50543.2i	−1.00158	−	0.259047i
$59$	−18443.5	−	31945.0i	−0.0898021	−	0.155542i	0.817625	−	0.575751i	$-0.195290\pi$
$59$	−18443.5	−	31945.0i	−0.0898021	−	0.155542i	−0.907427	+	0.420209i	$0.861957\pi$
$60$	−27824.8	−	132174.i	−0.128818	−	0.611918i
$61$	252653.	+	145869.i	1.11310	+	0.642649i	0.939631	−	0.342190i	$-0.111169\pi$
$61$	252653.	+	145869.i	1.11310	+	0.642649i	0.173470	+	0.984839i	$0.444502\pi$
$62$	7692.36	−	7827.49i	0.0322763	−	0.0328434i
$63$	72402.2	−	91942.8i	0.289554	−	0.367702i
$64$	−13688.9	−	261786.i	−0.0522192	−	0.998636i
$65$	−74802.3	+	129561.i	−0.272380	+	0.471776i
$66$	−134991.	−	272065.i	−0.469539	−	0.946327i
$67$	−137226.	−	237682.i	−0.456259	−	0.790263i	0.542501	−	0.840055i	$-0.317477\pi$
$67$	−137226.	−	237682.i	−0.456259	−	0.790263i	−0.998760	+	0.0497920i	$0.984144\pi$
$68$	−113651.	+	68282.1i	−0.361447	+	0.217160i
$69$	133492.	−	385292.i	0.406358	−	1.17285i
$70$	96735.2	−	26825.0i	0.282027	−	0.0782071i
$71$			31817.8i			0.0888985i	0.999012	+	0.0444493i	$0.0141533\pi$
$71$			31817.8i			0.0888985i	−0.999012	+	0.0444493i	$0.985847\pi$
$72$	231215.	+	293008.i	0.619468	+	0.785022i
$73$	499108.			1.28300			0.641499	−	0.767124i	$-0.278313\pi$
$73$	499108.			1.28300			0.641499	+	0.767124i	$0.278313\pi$
$74$	−159796.	−	576248.i	−0.394339	−	1.42205i
$75$	−48537.1	−	252279.i	−0.115051	−	0.597995i
$76$	396678.	−	238327.i	0.903643	−	0.542916i
$77$	195481.	−	112861.i	0.428185	−	0.247213i
$78$	26035.9	−	412588.i	0.0548641	−	0.869426i
$79$	452567.	+	261290.i	0.917914	+	0.529958i	0.882969	−	0.469431i	$-0.155541\pi$
$79$	452567.	+	261290.i	0.917914	+	0.529958i	0.0349451	+	0.999389i	$0.488874\pi$
$80$	11148.8	+	319975.i	0.0217750	+	0.624951i
$81$	−509717.	−	150392.i	−0.959123	−	0.282990i
$82$	−126652.	−	124465.i	−0.229704	−	0.225739i
$83$	−313892.	+	543676.i	−0.548966	+	0.950837i	0.449380	+	0.893341i	$0.351645\pi$
$83$	−313892.	+	543676.i	−0.548966	+	0.950837i	−0.998346	+	0.0574963i	$0.981688\pi$
$84$	−206510.	+	185214.i	−0.348421	+	0.312489i
$85$	140238.	−	80966.5i	0.228354	−	0.131840i
$86$	−186779.	+	722163.i	−0.293652	+	1.13538i
$87$	−668978.	+	128708.i	−1.01591	+	0.195455i
$88$	204426.	+	690280.i	0.299977	+	1.01292i
$89$	499277.			0.708226			0.354113	−	0.935203i	$-0.384783\pi$
$89$	499277.			0.708226			0.354113	+	0.935203i	$0.384783\pi$
$90$	−276120.	−	362728.i	−0.378765	−	0.497569i
$91$	307247.			0.407722
$92$	−468625.	+	845344.i	−0.601814	+	1.08560i
$93$	12125.8	−	34998.2i	0.0150752	−	0.0435108i
$94$	252955.	+	65424.0i	0.304551	+	0.0787687i
$95$	−489477.	+	282600.i	−0.570902	+	0.329610i
$96$	−420595.	−	778369.i	−0.475390	−	0.879775i
$97$	−573043.	+	992540.i	−0.627874	+	1.08751i	0.360104	+	0.932912i	$0.382741\pi$
$97$	−573043.	+	992540.i	−0.627874	+	1.08751i	−0.987978	+	0.154597i	$0.950592\pi$
$98$	524248.	+	515198.i	0.557005	+	0.547388i
$99$	−805315.	−	634161.i	−0.829966	−	0.653573i
$100$	10604.1	+	608870.i	0.0106041	+	0.608870i
$101$	470072.	+	271396.i	0.456247	+	0.263414i	0.710465	−	0.703733i	$-0.248485\pi$
$101$	470072.	+	271396.i	0.456247	+	0.263414i	−0.254218	+	0.967147i	$0.581818\pi$
$102$	−247700.	+	372665.i	−0.233413	+	0.351171i
$103$	−687099.	+	396697.i	−0.628793	+	0.363034i	−0.780284	−	0.625425i	$-0.784926\pi$
$103$	−687099.	+	396697.i	−0.628793	+	0.363034i	0.151492	+	0.988459i	$0.451592\pi$
$104$	−228816.	+	952842.i	−0.203417	+	0.847073i
$105$	256122.	−	221784.i	0.221248	−	0.191585i
$106$	−422851.	−	1.52487e6i	−0.355034	−	1.28031i
$107$	2.16883e6			1.77041			0.885204	−	0.465203i	$-0.154019\pi$
$107$	2.16883e6			1.77041			0.885204	+	0.465203i	$0.154019\pi$
$108$	1.12901e6	+	558758.i	0.896244	+	0.443560i
$109$			2.07739e6i			1.60413i	0.597237	+	0.802065i	$0.296265\pi$
$109$			2.07739e6i			1.60413i	−0.597237	+	0.802065i	$0.703735\pi$
$110$	−234957.	−	847292.i	−0.176527	−	0.636583i
$111$	−1.32116e6	−	1.52571e6i	−0.966020	−	1.11558i
$112$	557653.	−	348400.i	0.396926	−	0.247984i
$113$	606809.	+	1.05102e6i	0.420549	+	0.728412i	0.995993	−	0.0894289i	$-0.0285042\pi$
$113$	606809.	+	1.05102e6i	0.420549	+	0.728412i	−0.575444	+	0.817841i	$0.695171\pi$
$114$	864553.	−	1.30072e6i	0.583548	−	0.877952i
$115$	590246.	−	1.02234e6i	0.388096	−	0.672203i
$116$	1.61456e6	−	28119.3i	1.03438	−	0.0180149i
$117$	−517715.	−	1.29565e6i	−0.323246	−	0.808965i
$118$	210473.	+	206839.i	0.128100	+	0.125889i
$119$	−288011.	−	166283.i	−0.170910	−	0.0986750i
$120$	497060.	+	959460.i	0.287651	+	0.555243i
$121$	−102752.	−	177972.i	−0.0580010	−	0.100461i
$122$	−2.25955e6	−	584407.i	−1.24435	−	0.321837i
$123$	−566283.	−	196200.i	−0.304312	−	0.105435i
$124$	−42567.8	+	76787.2i	−0.0223262	+	0.0402739i
$125$		−	1.96510e6i		−	1.00613i
$126$	−361603.	+	863573.i	−0.180768	+	0.431705i
$127$			104112.i			0.0508262i	0.999677	+	0.0254131i	$0.00809012\pi$
$127$			104112.i			0.0508262i	−0.999677	+	0.0254131i	$0.991910\pi$
$128$	665165.	+	1.98887e6i	0.317175	+	0.948367i
$129$	475630.	+	2.47216e6i	0.221565	+	1.15162i
$130$	299687.	−	1.15871e6i	0.136407	−	0.527405i
$131$	−1.47683e6	−	2.55794e6i	−0.656925	−	1.13783i	−0.981408	−	0.191935i	$-0.938524\pi$
$131$	−1.47683e6	−	2.55794e6i	−0.656925	−	1.13783i	0.324483	−	0.945892i	$-0.394810\pi$
$132$	1.62226e6	+	1.80880e6i	0.705341	+	0.786445i
$133$	1.00525e6	+	580383.i	0.427287	+	0.246694i
$134$	1.56599e6	+	1.53896e6i	0.650841	+	0.639605i
$135$	−1.36682e6	−	706347.i	−0.555534	−	0.287089i
$136$	730171.	−	769350.i	0.290274	−	0.305849i
$137$	−751401.	+	1.30147e6i	−0.292220	+	0.506140i	−0.974334	−	0.225105i	$-0.927727\pi$
$137$	−751401.	+	1.30147e6i	−0.292220	+	0.506140i	0.682114	+	0.731246i	$0.261061\pi$
$138$	−205442.	+	3.25563e6i	−0.0781723	+	1.23879i
$139$	−697668.	−	1.20840e6i	−0.259779	−	0.449951i	0.706404	−	0.707809i	$-0.250316\pi$
$139$	−697668.	−	1.20840e6i	−0.259779	−	0.449951i	−0.966183	+	0.257859i	$0.916983\pi$
$140$	−688395.	+	413593.i	−0.250873	+	0.150726i
$141$	865936.	−	166601.i	0.308907	−	0.0594321i
$142$	−68018.6	−	245286.i	−0.0237554	−	0.0856658i
$143$		−	2.69114e6i		−	0.920297i
$144$	−2.40884e6	−	1.76454e6i	−0.806715	−	0.590941i
$145$	−1.97224e6			−0.646928
$146$	−3.84766e6	+	1.06697e6i	−1.23634	+	0.342842i
$147$	2.34401e6	+	812131.i	0.737918	+	0.255667i
$148$	2.46376e6	+	4.10074e6i	0.759998	+	1.26496i
$149$	3.25675e6	−	1.88028e6i	0.984522	−	0.568414i	0.0808898	−	0.996723i	$-0.474224\pi$
$149$	3.25675e6	−	1.88028e6i	0.984522	−	0.568414i	0.903632	+	0.428309i	$0.140890\pi$
$150$	913488.	+	1.84108e6i	0.270663	+	0.545505i
$151$	−3.29574e6	−	1.90280e6i	−0.957244	−	0.552665i	−0.0619200	−	0.998081i	$-0.519722\pi$
$151$	−3.29574e6	−	1.90280e6i	−0.957244	−	0.552665i	−0.895324	+	0.445416i	$0.853056\pi$
$152$	−2.54854e6	+	2.68528e6i	−0.725705	+	0.764644i
$153$	−215908.	+	1.49472e6i	−0.0602828	+	0.417335i
$154$	−1.26571e6	+	1.28794e6i	−0.346554	+	0.352642i
$155$	53615.3	−	92864.4i	0.0143977	−	0.0249376i
$156$	681300.	+	3.23633e6i	0.179459	+	0.852471i
$157$	2.02753e6	−	1.17059e6i	0.523924	−	0.302488i	−0.214615	−	0.976699i	$-0.568850\pi$
$157$	2.02753e6	−	1.17059e6i	0.523924	−	0.302488i	0.738539	+	0.674211i	$0.235516\pi$
$158$	−4.04746e6	−	1.04683e6i	−1.02615	−	0.265402i
$159$	−3.49605e6	−	4.03732e6i	−0.869733	−	1.00439i
$160$	−769976.	−	2.44288e6i	−0.187982	−	0.596406i
$161$	−2.42441e6			−0.580936
$162$	4.25096e6	+	69735.6i	0.999865	+	0.0164025i
$163$	3.75178e6			0.866312			0.433156	−	0.901319i	$-0.357400\pi$
$163$	3.75178e6			0.866312			0.433156	+	0.901319i	$0.357400\pi$
$164$	1.24244e6	+	688761.i	0.281673	+	0.156148i
$165$	−1.94258e6	−	2.24334e6i	−0.432441	−	0.499394i
$166$	1.25757e6	−	4.86227e6i	0.274921	−	1.06296i
$167$	7.68380e6	−	4.43624e6i	1.64978	−	0.952502i	0.672626	−	0.739983i	$-0.265166\pi$
$167$	7.68380e6	−	4.43624e6i	1.64978	−	0.952502i	0.977157	−	0.212520i	$-0.0681670\pi$
$168$	1.19606e6	−	1.86930e6i	0.252247	−	0.394231i
$169$	−581843.	+	1.00778e6i	−0.120544	+	0.208788i
$170$	−908021.	+	923972.i	−0.184820	+	0.188067i
$171$	753588.	−	5.21705e6i	0.150711	−	1.04337i
$172$	−103913.	−	5.96651e6i	−0.0204214	−	1.17256i
$173$	2.07837e6	+	1.19995e6i	0.401407	+	0.231752i	0.687091	−	0.726572i	$-0.258887\pi$
$173$	2.07837e6	+	1.19995e6i	0.401407	+	0.231752i	−0.285684	+	0.958324i	$0.592221\pi$
$174$	4.88206e6	−	2.42233e6i	0.926735	−	0.459818i
$175$	−1.32283e6	+	763735.i	−0.246825	+	0.142504i
$176$	−3.05159e6	−	4.88441e6i	−0.559742	−	0.895930i
$177$	941064.	+	326051.i	0.169707	+	0.0587984i
$178$	−3.84897e6	+	1.06733e6i	−0.682472	+	0.189252i
$179$	−5.12211e6			−0.893079			−0.446539	−	0.894764i	$-0.647344\pi$
$179$	−5.12211e6			−0.893079			−0.446539	+	0.894764i	$0.647344\pi$
$180$	2.90405e6	+	2.20602e6i	0.497952	+	0.378262i
$181$			8.90152e6i			1.50116i	0.660777	+	0.750582i	$0.270227\pi$
$181$			8.90152e6i			1.50116i	−0.660777	+	0.750582i	$0.729773\pi$
$182$	−2.36860e6	+	656820.i	−0.392895	+	0.108951i
$183$	−7.73507e6	+	1.48819e6i	−1.26215	+	0.242831i
$184$	1.80553e6	−	7.51864e6i	0.289835	−	1.20694i
$185$	−2.92143e6	−	5.06007e6i	−0.461403	−	0.799174i
$186$	−18661.5	+	295726.i	−0.00290006	+	0.0459569i
$187$	−1.45645e6	+	2.52265e6i	−0.222726	+	0.385773i
$188$	−2.08992e6	+	36398.1i	−0.314525	+	0.00547779i
$189$	147245.	+	3.15632e6i	0.0218100	+	0.467516i
$190$	3.16929e6	−	3.22497e6i	0.462063	−	0.470180i
$191$	8.41372e6	+	4.85767e6i	1.20750	+	0.697152i	0.962213	−	0.272298i	$-0.0877835\pi$
$191$	8.41372e6	+	4.85767e6i	1.20750	+	0.697152i	0.245290	+	0.969450i	$0.421117\pi$
$192$	4.90636e6	+	5.10138e6i	0.693196	+	0.720749i
$193$	−1.88304e6	−	3.26151e6i	−0.261931	−	0.453678i	0.704824	−	0.709382i	$-0.251026\pi$
$193$	−1.88304e6	−	3.26151e6i	−0.261931	−	0.453678i	−0.966755	+	0.255704i	$0.917693\pi$
$194$	2.29583e6	−	8.87661e6i	0.314438	−	1.21574i
$195$	−763148.	−	3.96658e6i	−0.102921	−	0.534949i
$196$	−5.14284e6	−	2.85099e6i	−0.683023	−	0.378640i
$197$		−	7.76461e6i		−	1.01560i	−0.861476	−	0.507798i	$-0.830460\pi$
$197$		−	7.76461e6i		−	1.01560i	0.861476	−	0.507798i	$-0.169540\pi$
$198$	7.56393e6	+	3.16724e6i	0.974433	+	0.408023i
$199$			1.23922e7i			1.57249i	0.617915	+	0.786245i	$0.287977\pi$
$199$			1.23922e7i			1.57249i	−0.617915	+	0.786245i	$0.712023\pi$
$200$	−1.38336e6	−	4.67116e6i	−0.172920	−	0.583895i
$201$	7.00184e6	+	2.42593e6i	0.862232	+	0.298738i
$202$	−4.20400e6	−	1.08732e6i	−0.510045	−	0.131917i
$203$	2.02522e6	+	3.50779e6i	0.242094	+	0.419320i
$204$	1.11287e6	−	3.40243e6i	0.131085	−	0.400773i
$205$	−1.50258e6	−	867514.i	−0.174412	−	0.100697i
$206$	4.44886e6	−	4.52702e6i	0.508918	−	0.517858i
$207$	4.08515e6	+	1.02236e7i	0.460572	+	1.15264i
$208$	−272982.	−	7.83470e6i	−0.0303350	−	0.870627i
$209$	5.08350e6	−	8.80487e6i	0.556831	−	0.964460i
$210$	−1.50035e6	+	2.25728e6i	−0.162007	+	0.243740i
$211$	4.26832e6	+	7.39295e6i	0.454370	+	0.786992i	0.998652	−	0.0519106i	$-0.0165311\pi$
$211$	4.26832e6	+	7.39295e6i	0.454370	+	0.786992i	−0.544282	+	0.838902i	$0.683198\pi$
$212$	6.51958e6	+	1.08514e7i	0.684246	+	1.13888i
$213$	−562365.	−	649433.i	−0.0581941	−	0.0672041i
$214$	−1.67197e7	+	4.63642e6i	−1.70603	+	0.473088i
$215$			7.28829e6i			0.733348i
$216$	−9.89812e6	−	1.89397e6i	−0.982181	−	0.187937i
$217$	−220222.			−0.0215517
$218$	−4.44096e6	−	1.60148e7i	−0.428655	−	1.54580i
$219$	−1.01873e7	+	8.82151e6i	−0.969900	+	0.839867i
$220$	3.62261e6	+	6.02956e6i	0.340215	+	0.566262i
$221$	−3.43378e6	+	1.98249e6i	−0.318123	+	0.183669i
$222$	1.34465e7	+	8.93750e6i	1.22900	+	0.816878i
$223$	1.77684e6	+	1.02586e6i	0.160226	+	0.0925065i	0.577969	−	0.816059i	$-0.303845\pi$
$223$	1.77684e6	+	1.02586e6i	0.160226	+	0.0925065i	−0.417743	+	0.908565i	$0.637179\pi$
$224$	−3.55420e6	+	3.87797e6i	−0.316226	+	0.345033i
$225$	5.44961e6	+	4.29141e6i	0.478430	+	0.376749i
$226$	−6.92477e6	−	6.80522e6i	−0.599902	−	0.589545i
$227$	−5.85784e6	+	1.01461e7i	−0.500795	+	0.867402i	0.499205	+	0.866484i	$0.333626\pi$
$227$	−5.85784e6	+	1.01461e7i	−0.500795	+	0.867402i	−1.00000		0.000918181i	$0.999708\pi$
$228$	−3.88428e6	+	1.18756e7i	−0.327722	+	1.00196i
$229$	−1.72644e7	+	9.96762e6i	−1.43762	+	0.830013i	−0.997684	−	0.0680138i	$-0.978334\pi$
$229$	−1.72644e7	+	9.96762e6i	−1.43762	+	0.830013i	−0.439940	+	0.898027i	$0.645000\pi$
$230$	−2.36475e6	+	9.14308e6i	−0.194358	+	0.751466i
$231$	−1.99520e6	+	5.75864e6i	−0.161864	+	0.467179i
$232$	−1.23867e7	+	3.66832e6i	−0.991953	+	0.293767i
$233$	1.42369e7			1.12551			0.562754	−	0.826625i	$-0.309742\pi$
$233$	1.42369e7			1.12551			0.562754	+	0.826625i	$0.309742\pi$
$234$	6.76089e6	+	8.88152e6i	0.527662	+	0.693170i
$235$	2.55290e6			0.196712
$236$	−2.06473e6	−	1.14460e6i	−0.157082	−	0.0870800i
$237$	−1.38555e7	+	2.66573e6i	−1.04083	+	0.200249i
$238$	2.57577e6	+	666194.i	0.191063	+	0.0494162i
$239$	1.38963e7	−	8.02305e6i	1.01790	−	0.587686i	0.104407	−	0.994535i	$-0.466706\pi$
$239$	1.38963e7	−	8.02305e6i	1.01790	−	0.587686i	0.913496	+	0.406848i	$0.133372\pi$
$240$	−5.88297e6	−	6.33397e6i	−0.425562	−	0.458186i
$241$	−7.56621e6	+	1.31051e7i	−0.540539	+	0.936241i	0.458334	+	0.888780i	$0.348446\pi$
$241$	−7.56621e6	+	1.31051e7i	−0.540539	+	0.936241i	−0.998873	+	0.0474611i	$0.984887\pi$
$242$	1.17259e6	+	1.15234e6i	0.0827369	+	0.0813085i
$243$	1.30620e7	−	5.93936e6i	0.910311	−	0.413924i
$244$	1.86684e7	−	325130.i	1.28510	−	0.0223814i
$245$	6.21962e6	+	3.59090e6i	0.422927	+	0.244177i
$246$	4.78496e6	+	301949.i	0.321420	+	0.0202828i
$247$	1.19850e7	−	6.91955e6i	0.795330	−	0.459184i
$248$	164006.	−	682959.i	0.0107524	−	0.0447754i
$249$	−3.20238e6	−	1.66449e7i	−0.207432	−	1.07816i
$250$	4.20091e6	+	1.51491e7i	0.268858	+	0.969545i
$251$	−2.14043e6			−0.135357			−0.0676783	−	0.997707i	$-0.521559\pi$
$251$	−2.14043e6			−0.135357			−0.0676783	+	0.997707i	$0.521559\pi$
$252$	941520.	−	7.43038e6i	0.0588340	−	0.464311i
$253$			2.12351e7i			1.31127i
$254$	−222565.	−	802605.i	−0.0135818	−	0.0489780i
$255$	−1.43136e6	+	4.13125e6i	−0.0863232	+	0.249150i
$256$	−9.37953e6	−	1.39104e7i	−0.559064	−	0.829125i
$257$	−1.55017e6	−	2.68498e6i	−0.0913231	−	0.158176i	0.816745	−	0.576999i	$-0.195776\pi$
$257$	−1.55017e6	−	2.68498e6i	−0.0913231	−	0.158176i	−0.908068	+	0.418823i	$0.862443\pi$
$258$	−8.95156e6	−	1.80413e7i	−0.521242	−	1.05053i
$259$	−5.99983e6	+	1.03920e7i	−0.345334	+	0.598136i
$260$	166728.	+	9.57325e6i	0.00948614	+	0.544677i
$261$	1.13797e7	−	1.44509e7i	0.640042	−	0.812783i
$262$	1.68532e7	+	1.65623e7i	0.937086	+	0.920907i
$263$	1.55649e7	+	8.98640e6i	0.855617	+	0.493991i	0.862542	−	0.505986i	$-0.168871\pi$
$263$	1.55649e7	+	8.98640e6i	0.855617	+	0.493991i	−0.00692532	+	0.999976i	$0.502204\pi$
$264$	−1.63729e7	−	1.04762e7i	−0.889846	−	0.569365i
$265$	−7.73069e6	−	1.33899e7i	−0.415414	−	0.719517i
$266$	−8.99029e6	−	2.32523e6i	−0.477671	−	0.123544i
$267$	−1.01908e7	+	8.82451e6i	−0.535393	+	0.463614i
$268$	−1.53623e7	−	8.51623e6i	−0.798088	−	0.442428i
$269$		−	2.55398e7i		−	1.31208i	−0.754727	−	0.656039i	$-0.772230\pi$
$269$		−	2.55398e7i		−	1.31208i	0.754727	−	0.656039i	$-0.227770\pi$
$270$	1.20469e7	+	2.52336e6i	0.612048	+	0.128200i
$271$		−	2.65318e7i		−	1.33309i	−0.745466	−	0.666544i	$-0.767773\pi$
$271$		−	2.65318e7i		−	1.33309i	0.745466	−	0.666544i	$-0.232227\pi$
$272$	−3.98427e6	+	7.49191e6i	−0.197989	+	0.372294i
$273$	−6.27123e6	+	5.43046e6i	−0.308223	+	0.266900i
$274$	3.01040e6	−	1.16394e7i	0.146343	−	0.565822i
$275$	6.68946e6	+	1.15865e7i	0.321657	+	0.557126i
$276$	−5.37596e6	−	2.55371e7i	−0.255699	−	1.21463i
$277$	1.27358e6	+	735300.i	0.0599219	+	0.0345959i	0.529662	−	0.848209i	$-0.322319\pi$
$277$	1.27358e6	+	735300.i	0.0599219	+	0.0345959i	−0.469740	+	0.882805i	$0.655652\pi$
$278$	7.96164e6	+	7.82418e6i	0.370568	+	0.364170i
$279$	371077.	+	928668.i	0.0170864	+	0.0427610i
$280$	4.42273e6	−	4.66004e6i	0.201473	−	0.212283i
$281$	1.99229e7	−	3.45074e7i	0.897910	−	1.55523i	0.0677488	−	0.997702i	$-0.478418\pi$
$281$	1.99229e7	−	3.45074e7i	0.897910	−	1.55523i	0.830161	−	0.557523i	$-0.188248\pi$
$282$	−6.31942e6	+	3.13550e6i	−0.281793	+	0.139817i
$283$	−4.80160e6	−	8.31662e6i	−0.211849	−	0.366934i	0.740444	−	0.672118i	$-0.234615\pi$
$283$	−4.80160e6	−	8.31662e6i	−0.211849	−	0.366934i	−0.952293	+	0.305184i	$0.901282\pi$
$284$	1.04872e6	+	1.74552e6i	0.0457832	+	0.0762027i
$285$	4.99590e6	−	1.44194e7i	0.215814	−	0.622893i
$286$	5.75300e6	+	2.07462e7i	0.245921	+	0.886831i
$287$			3.56328e6i			0.150731i
$288$	2.23421e7	+	8.45349e6i	0.935290	+	0.353882i
$289$	−1.98458e7			−0.822197
$290$	1.52042e7	−	4.21617e6i	0.623403	−	0.172872i
$291$	−5.84630e6	−	3.03871e7i	−0.237248	−	1.23313i
$292$	2.73810e7	−	1.64507e7i	1.09977	−	0.660749i
$293$	−3.77936e7	+	2.18201e7i	−1.50250	+	0.867470i	−0.502506	+	0.864574i	$0.667589\pi$
$293$	−3.77936e7	+	2.18201e7i	−1.50250	+	0.867470i	−0.999996	+	0.00289638i	$0.999078\pi$
$294$	−1.98063e7	−	1.24986e6i	−0.779403	−	0.0491833i
$295$	2.49702e6	+	1.44166e6i	0.0972650	+	0.0561560i
$296$	−2.77597e7	−	2.63460e7i	−1.07038	−	1.01587i
$297$	2.76458e7	−	1.28970e6i	1.05526	−	0.0492289i
$298$	−2.10870e7	+	2.14574e7i	−0.796829	+	0.810828i
$299$	−1.44524e7	+	2.50323e7i	−0.540662	+	0.936454i
$300$	−1.09779e7	−	1.22402e7i	−0.406590	−	0.453342i
$301$	1.29628e7	−	7.48408e6i	0.475335	−	0.274435i
$302$	2.94749e7	+	7.62334e6i	1.07012	+	0.276773i
$303$	−1.43914e7	+	2.76884e6i	−0.517341	+	0.0995335i
$304$	1.39064e7	−	2.61492e7i	0.494987	−	0.930761i
$305$	−2.28041e7			−0.803736
$306$	−1.53089e6	−	1.19845e7i	−0.0534294	−	0.418268i
$307$	4.73530e7			1.63656			0.818280	−	0.574819i	$-0.194928\pi$
$307$	4.73530e7			1.63656			0.818280	+	0.574819i	$0.194928\pi$
$308$	7.00414e6	−	1.26346e7i	0.239719	−	0.432425i
$309$	7.01296e6	−	2.02412e7i	0.237698	−	0.686057i
$310$	−214803.	+	830516.i	−0.00721034	+	0.0278781i
$311$	−1.81208e7	+	1.04621e7i	−0.602416	+	0.347805i	−0.769991	−	0.638054i	$-0.779740\pi$
$311$	−1.81208e7	+	1.04621e7i	−0.602416	+	0.347805i	0.167575	+	0.985859i	$0.446406\pi$
$312$	−1.21707e7	−	2.34927e7i	−0.400730	−	0.773516i
$313$	1.03860e7	−	1.79891e7i	0.338700	−	0.586646i	−0.645488	−	0.763770i	$-0.723346\pi$
$313$	1.03860e7	−	1.79891e7i	0.338700	−	0.586646i	0.984188	+	0.177124i	$0.0566795\pi$
$314$	−1.31280e7	+	1.33586e7i	−0.424041	+	0.431491i
$315$	−1.30778e6	+	9.05368e6i	−0.0418410	+	0.289663i
$316$	3.34400e7	−	582394.i	1.05976	−	0.0184568i
$317$	−4.18063e7	−	2.41369e7i	−1.31239	−	0.757710i	−0.329901	−	0.944016i	$-0.607015\pi$
$317$	−4.18063e7	−	2.41369e7i	−1.31239	−	0.757710i	−0.982492	+	0.186305i	$0.940349\pi$
$318$	3.55821e7	+	2.36504e7i	1.10650	+	0.735456i
$319$	3.07243e7	−	1.77387e7i	0.946476	−	0.546448i
$320$	1.11581e7	+	1.71864e7i	0.340518	+	0.524486i
$321$	−4.42680e7	+	3.83330e7i	−1.33836	+	1.15893i
$322$	1.86900e7	−	5.18280e6i	0.559811	−	0.155238i
$323$	−1.49795e7			−0.444519
$324$	−3.29201e7	+	8.54991e6i	−0.967889	+	0.251378i
$325$			1.82111e7i			0.530501i
$326$	−2.89228e7	+	8.02039e6i	−0.834809	+	0.231496i
$327$	−3.67170e7	−	4.24018e7i	−1.05008	−	1.21266i
$328$	−1.10505e7	−	2.65368e6i	−0.313156	−	0.0752015i
$329$	−2.62148e6	−	4.54054e6i	−0.0736138	−	0.127503i
$330$	1.97712e7	+	1.31413e7i	0.550163	+	0.365677i
$331$	1.55954e7	−	2.70121e7i	0.430044	−	0.744859i	−0.566832	−	0.823833i	$-0.691831\pi$
$331$	1.55954e7	−	2.70121e7i	0.430044	−	0.744859i	0.996877	+	0.0789745i	$0.0251646\pi$
$332$	699639.	+	4.01720e7i	0.0191188	+	1.09777i
$333$	5.39324e7	+	7.79038e6i	1.46055	+	0.210973i
$334$	−4.97515e7	+	5.06255e7i	−1.33526	+	1.35872i
$335$	1.85787e7	+	1.07264e7i	0.494176	+	0.285312i
$336$	−5.22446e6	+	1.69675e7i	−0.137728	+	0.447300i
$337$	−7.84409e6	−	1.35864e7i	−0.204952	−	0.354988i	0.745165	−	0.666880i	$-0.232371\pi$
$337$	−7.84409e6	−	1.35864e7i	−0.204952	−	0.354988i	−0.950118	+	0.311892i	$0.899037\pi$
$338$	2.33109e6	−	9.01292e6i	0.0603682	−	0.233408i
$339$	−3.09620e7	−	1.07274e7i	−0.794748	−	0.275357i
$340$	5.02478e6	−	9.06411e6i	0.127844	−	0.230615i
$341$			1.92890e6i			0.0486459i
$342$	5.34332e6	+	4.18297e7i	0.133577	+	1.04570i
$343$		−	3.36359e7i		−	0.833529i
$344$	1.35560e7	+	4.57742e7i	0.333010	+	1.12446i
$345$	6.02181e6	+	3.12993e7i	0.146646	+	0.762214i
$346$	−1.85875e7	−	4.80745e6i	−0.448739	−	0.116061i
$347$	2.49660e7	+	4.32423e7i	0.597530	+	1.03495i	0.993184	+	0.116553i	$0.0371846\pi$
$347$	2.49660e7	+	4.32423e7i	0.597530	+	1.03495i	−0.395654	+	0.918400i	$0.629482\pi$
$348$	−3.24579e7	+	2.91106e7i	−0.770163	+	0.690738i
$349$	−3.99473e7	−	2.30636e7i	−0.939747	−	0.542563i	−0.0498662	−	0.998756i	$-0.515879\pi$
$349$	−3.99473e7	−	2.30636e7i	−0.939747	−	0.542563i	−0.889881	+	0.456193i	$0.849213\pi$
$350$	8.56511e6	−	8.71558e6i	0.199769	−	0.203279i
$351$	3.34671e7	+	1.72951e7i	0.773921	+	0.399947i
$352$	3.39666e7	+	3.11308e7i	0.778798	+	0.713776i
$353$	2.73045e6	−	4.72929e6i	0.0620742	−	0.107516i	−0.833318	−	0.552794i	$-0.813562\pi$
$353$	2.73045e6	−	4.72929e6i	0.0620742	−	0.107516i	0.895392	+	0.445278i	$0.146895\pi$
$354$	−7.95176e6	−	501787.i	−0.179248	−	0.0113112i
$355$	−1.24354e6	−	2.15387e6i	−0.0277955	−	0.0481432i
$356$	2.73904e7	−	1.64563e7i	0.607082	−	0.364740i
$357$	8.81758e6	−	1.69645e6i	0.193796	−	0.0372853i
$358$	3.94868e7	−	1.09498e7i	0.860602	−	0.238648i
$359$		−	3.35404e7i		−	0.724911i	−0.932001	−	0.362455i	$-0.881938\pi$
$359$		−	3.35404e7i		−	0.724911i	0.932001	−	0.362455i	$-0.118062\pi$
$360$	−2.71035e7	−	1.07983e7i	−0.580923	−	0.231444i
$361$	5.23754e6			0.111328
$362$	−1.90293e7	−	6.86226e7i	−0.401141	−	1.44658i
$363$	5.24286e6	+	1.81650e6i	0.109610	+	0.0379765i
$364$	1.68556e7	−	1.01270e7i	0.349494	−	0.209979i
$365$	−3.37866e7	+	1.95067e7i	−0.694810	+	0.401148i
$366$	5.64490e7	−	2.80083e7i	1.15136	−	0.571272i
$367$	−5.71302e7	−	3.29841e7i	−1.15576	−	0.667278i	−0.205475	−	0.978662i	$-0.565874\pi$
$367$	−5.71302e7	−	3.29841e7i	−1.15576	−	0.667278i	−0.950284	+	0.311384i	$0.899207\pi$
$368$	2.15403e6	+	6.18216e7i	0.0432224	+	1.24050i
$369$	1.50262e7	−	6.00415e6i	0.299068	−	0.119501i
$370$	3.33388e7	+	3.27632e7i	0.658180	+	0.646817i
$371$	−1.58767e7	+	2.74993e7i	−0.310913	+	0.538518i
$372$	−488328.	−	2.31967e6i	−0.00948599	−	0.0450607i
$373$	4.37355e7	−	2.52507e7i	0.842768	−	0.486572i	−0.0154365	−	0.999881i	$-0.504914\pi$
$373$	4.37355e7	−	2.52507e7i	0.842768	−	0.486572i	0.858204	+	0.513309i	$0.171580\pi$
$374$	5.83511e6	−	2.25609e7i	0.111541	−	0.431262i
$375$	3.47323e7	+	4.01098e7i	0.658628	+	0.760600i
$376$	1.60335e7	−	4.74833e6i	0.301624	−	0.0893258i
$377$	4.82910e7			0.901244
$378$	−7.88258e6	−	2.40176e7i	−0.145946	−	0.444687i
$379$	6.30244e7			1.15769			0.578844	−	0.815439i	$-0.303504\pi$
$379$	6.30244e7			1.15769			0.578844	+	0.815439i	$0.303504\pi$
$380$	−1.75381e7	+	3.16367e7i	−0.319619	+	0.576555i
$381$	−1.84013e6	−	2.12502e6i	−0.0332715	−	0.0384228i
$382$	−7.52466e7	−	1.94617e7i	−1.34989	−	0.349132i
$383$	−9.28798e7	+	5.36242e7i	−1.65320	+	0.954475i	−0.677454	+	0.735565i	$0.736917\pi$
$383$	−9.28798e7	+	5.36242e7i	−1.65320	+	0.954475i	−0.975745	+	0.218909i	$0.929750\pi$
$384$	−4.87291e7	−	2.88384e7i	−0.860587	−	0.509304i
$385$	−8.82190e6	+	1.52800e7i	−0.154590	+	0.267757i
$386$	2.14888e7	+	2.11178e7i	0.373638	+	0.367187i
$387$	−5.34025e7	−	4.20528e7i	−0.921358	−	0.725542i
$388$	1.27727e6	+	7.33384e7i	0.0218669	+	1.25556i
$389$	−6.15051e7	−	3.55100e7i	−1.04487	−	0.603256i	−0.123661	−	0.992324i	$-0.539464\pi$
$389$	−6.15051e7	−	3.55100e7i	−1.04487	−	0.603256i	−0.921209	+	0.389068i	$0.872797\pi$
$390$	1.43628e7	+	2.89473e7i	0.242127	+	0.487994i
$391$	2.70951e7	−	1.56433e7i	0.453273	−	0.261697i
$392$	4.57413e7	+	1.09844e7i	0.759365	+	0.182354i
$393$	7.53540e7	+	2.61079e7i	1.24145	+	0.430125i
$394$	1.65988e7	+	5.98580e7i	0.271387	+	0.978665i
$395$	−4.08481e7			−0.662797
$396$	−6.50818e7	−	8.24666e6i	−1.04803	−	0.132798i
$397$			1.08942e7i			0.174111i	0.996203	+	0.0870554i	$0.0277457\pi$
$397$			1.08942e7i			0.174111i	−0.996203	+	0.0870554i	$0.972254\pi$
$398$	−2.64914e7	−	9.55322e7i	−0.420200	−	1.51531i
$399$	−3.07762e7	+	5.92118e6i	−0.484503	+	0.0932157i
$400$	2.06503e7	+	3.30531e7i	0.322660	+	0.516454i
$401$	2.28119e7	+	3.95113e7i	0.353776	+	0.612758i	0.986908	−	0.161286i	$-0.0515643\pi$
$401$	2.28119e7	+	3.95113e7i	0.353776	+	0.612758i	−0.633132	+	0.774044i	$0.718231\pi$
$402$	−5.91638e7	−	3.73347e6i	−0.910706	−	0.0574690i
$403$	−1.31279e6	+	2.27382e6i	−0.0200576	+	0.0347408i
$404$	3.47334e7	−	604920.i	0.526749	−	0.00917389i
$405$	4.03826e7	−	9.74070e6i	0.607896	−	0.146631i
$406$	−2.31114e7	−	2.27124e7i	−0.345341	−	0.339379i
$407$	9.10223e7	+	5.25517e7i	1.35010	+	0.779478i
$408$	−1.30563e6	+	2.86087e7i	−0.0192238	+	0.421228i
$409$	−2.10230e7	−	3.64130e7i	−0.307274	−	0.532214i	0.670491	−	0.741917i	$-0.266083\pi$
$409$	−2.10230e7	−	3.64130e7i	−0.307274	−	0.532214i	−0.977765	+	0.209704i	$0.932750\pi$
$410$	1.34380e7	+	3.47559e6i	0.194977	+	0.0504287i
$411$	−7.66594e6	−	3.98449e7i	−0.110418	−	0.573915i
$412$	−2.46190e7	+	4.44098e7i	−0.352029	+	0.635019i
$413$		−	5.92154e6i		−	0.0840591i
$414$	−5.33484e7	−	7.00818e7i	−0.751832	−	0.987652i
$415$		−	4.90715e7i		−	0.686570i
$416$	1.88531e7	+	5.98148e7i	0.261881	+	0.830861i
$417$	3.55980e7	+	1.23336e7i	0.490927	+	0.170092i
$418$	−2.03664e7	+	7.87448e7i	−0.278860	+	1.07818i
$419$	−3.78520e7	−	6.55615e7i	−0.514572	−	0.891265i	−0.999857	−	0.0169089i	$-0.994617\pi$
$419$	−3.78520e7	−	6.55615e7i	−0.514572	−	0.891265i	0.485285	−	0.874356i	$-0.338716\pi$
$420$	6.74078e6	−	2.06089e7i	0.0909834	−	0.278168i
$421$	1.07698e8	+	6.21795e7i	1.44332	+	0.833299i	0.998069	−	0.0621085i	$-0.0197825\pi$
$421$	1.07698e8	+	6.21795e7i	1.44332	+	0.833299i	0.445247	+	0.895408i	$0.353116\pi$
$422$	−4.87092e7	−	4.78682e7i	−0.648147	−	0.636957i
$423$	−1.47300e7	+	1.87055e7i	−0.194618	+	0.247143i
$424$	−7.34576e7	−	6.97168e7i	−0.963694	−	0.914619i
$425$	9.85589e6	−	1.70709e7i	0.128389	−	0.222377i
$426$	5.72365e6	+	3.80434e6i	0.0740362	+	0.0492096i
$427$	2.34167e7	+	4.05589e7i	0.300775	+	0.520958i
$428$	1.18982e8	−	7.14852e7i	1.51757	−	0.911768i
$429$	4.75647e7	+	5.49289e7i	0.602439	+	0.695712i
$430$	−1.55806e7	−	5.61860e7i	−0.195965	−	0.706680i
$431$			8.10455e7i			1.01227i	0.862454	+	0.506136i	$0.168926\pi$
$431$			8.10455e7i			1.01227i	−0.862454	+	0.506136i	$0.831074\pi$
$432$	8.03543e7	−	6.55902e6i	0.996685	−	0.0813557i
$433$	−1.35272e8			−1.66627			−0.833133	−	0.553073i	$-0.813455\pi$
$433$	−1.35272e8			−1.66627			−0.833133	+	0.553073i	$0.813455\pi$
$434$	1.69771e6	−	470782.i	0.0207680	−	0.00575904i
$435$	4.02555e7	−	3.48585e7i	0.489055	−	0.423488i
$436$	6.84715e7	+	1.13966e8i	0.826134	+	1.37504i
$437$	−9.45706e7	+	5.46004e7i	−1.13321	+	0.654261i
$438$	5.96765e7	−	8.97837e7i	0.710201	−	1.06850i
$439$	−6.85787e7	−	3.95939e7i	−0.810580	−	0.467989i	0.0365773	−	0.999331i	$-0.488354\pi$
$439$	−6.85787e7	−	3.95939e7i	−0.810580	−	0.467989i	−0.847157	+	0.531342i	$0.821688\pi$
$440$	−4.08167e7	−	3.87382e7i	−0.479159	−	0.454759i
$441$	−6.21978e7	+	2.48530e7i	−0.725202	+	0.289776i
$442$	2.22332e7	−	2.26238e7i	0.257475	−	0.261998i
$443$	1.48886e7	−	2.57879e7i	0.171255	−	0.296622i	−0.767604	−	0.640925i	$-0.778551\pi$
$443$	1.48886e7	−	2.57879e7i	0.171255	−	0.296622i	0.938859	+	0.344302i	$0.111884\pi$
$444$	−1.22767e8	−	4.01545e7i	−1.40259	−	0.458760i
$445$	−3.37981e7	+	1.95133e7i	−0.383541	+	0.221438i
$446$	−1.58908e7	−	4.10997e6i	−0.179119	−	0.0463270i
$447$	−3.32404e7	+	9.59401e7i	−0.372172	+	1.07418i
$448$	1.91095e7	−	3.74936e7i	0.212527	−	0.416988i
$449$	1.56701e7			0.173114			0.0865570	−	0.996247i	$-0.472414\pi$
$449$	1.56701e7			0.173114			0.0865570	+	0.996247i	$0.472414\pi$
$450$	−5.11855e7	−	2.14329e7i	−0.561707	−	0.235203i
$451$	3.12103e7			0.340226
$452$	6.79316e7	+	3.76585e7i	0.735625	+	0.407801i
$453$	1.00901e8	−	1.94127e7i	1.08542	−	0.208829i
$454$	2.34687e7	−	9.07396e7i	0.250797	−	0.969682i
$455$	−2.07988e7	+	1.20082e7i	−0.220802	+	0.127480i
$456$	4.55708e6	−	9.98536e7i	0.0480610	−	1.05310i
$457$	−6.17820e7	+	1.07010e8i	−0.647311	+	1.12118i	0.336451	+	0.941701i	$0.390773\pi$
$457$	−6.17820e7	+	1.07010e8i	−0.647311	+	1.12118i	−0.983763	+	0.179475i	$0.942560\pi$
$458$	1.11785e8	−	1.13748e8i	1.16355	−	1.18399i
$459$	−2.20116e7	−	3.43248e7i	−0.227621	−	0.354952i
$460$	−1.31561e6	−	7.55401e7i	−0.0135162	−	0.776075i
$461$	1.48809e8	+	8.59150e7i	1.51889	+	0.876933i	0.999753	+	0.0222438i	$0.00708100\pi$
$461$	1.48809e8	+	8.59150e7i	1.51889	+	0.876933i	0.519140	+	0.854689i	$0.326252\pi$
$462$	3.07057e6	−	4.86591e7i	0.0311382	−	0.493444i
$463$	−2.55791e7	+	1.47681e7i	−0.257717	+	0.148793i	−0.623293	−	0.781989i	$-0.714205\pi$
$463$	−2.55791e7	+	1.47681e7i	−0.257717	+	0.148793i	0.365576	+	0.930782i	$0.380872\pi$
$464$	8.76481e7	−	5.47591e7i	0.877381	−	0.548154i
$465$	546994.	+	2.84308e6i	0.00544031	+	0.0282768i
$466$	−1.09754e8	+	3.04351e7i	−1.08458	+	0.300758i
$467$	7.62044e7			0.748220			0.374110	−	0.927384i	$-0.377948\pi$
$467$	7.62044e7			0.748220			0.374110	+	0.927384i	$0.377948\pi$
$468$	−7.11068e7	−	5.40152e7i	−0.693703	−	0.526961i
$469$		−	4.40583e7i		−	0.427080i
$470$	−1.96805e7	+	5.45748e6i	−0.189559	+	0.0525653i
$471$	−2.06942e7	+	5.97287e7i	−0.198055	+	0.571637i
$472$	1.83640e7	+	4.40995e6i	0.174639	+	0.0419380i
$473$	−6.55521e7	−	1.13540e8i	−0.619446	−	1.07291i
$474$	1.01115e8	−	5.01701e7i	0.949468	−	0.471097i
$475$	−3.44003e7	+	5.95831e7i	−0.320983	+	0.555958i
$476$	−2.12810e7	+	370632.i	−0.197320	+	0.00343654i
$477$	1.42716e8	+	2.06149e7i	1.31497	+	0.189944i
$478$	−8.99766e7	+	9.15573e7i	−0.823846	+	0.838319i
$479$	−2.84114e7	−	1.64033e7i	−0.258515	−	0.149254i	0.365142	−	0.930952i	$-0.381020\pi$
$479$	−2.84114e7	−	1.64033e7i	−0.258515	−	0.149254i	−0.623657	+	0.781698i	$0.714354\pi$
$480$	5.88928e7	+	3.62527e7i	0.532523	+	0.327806i
$481$	7.15323e7	+	1.23898e8i	0.642787	+	1.11334i
$482$	3.03131e7	−	1.17203e8i	0.270701	−	1.04664i
$483$	4.94847e7	−	4.28504e7i	0.439167	−	0.380288i
$484$	−1.15030e7	−	6.37681e6i	−0.101456	−	0.0562429i
$485$		−	8.95854e7i		−	0.785257i
$486$	−8.79989e7	+	7.37104e7i	−0.766600	+	0.642125i
$487$		−	1.43724e8i		−	1.24435i	−0.782877	−	0.622177i	$-0.786249\pi$
$487$		−	1.43724e8i		−	1.24435i	0.782877	−	0.622177i	$-0.213751\pi$
$488$	−1.43221e8	+	4.24150e7i	−1.23239	+	0.364972i
$489$	−7.65776e7	+	6.63110e7i	−0.654901	+	0.567099i
$490$	−5.56240e7	−	1.43865e7i	−0.472796	−	0.122283i
$491$	9.80279e6	+	1.69789e7i	0.0828143	+	0.143439i	0.904458	−	0.426563i	$-0.140276\pi$
$491$	9.80279e6	+	1.69789e7i	0.0828143	+	0.143439i	−0.821643	+	0.570002i	$0.806943\pi$
$492$	−3.75331e7	+	7.90132e6i	−0.315151	+	0.0663444i
$493$	−4.52676e7	−	2.61352e7i	−0.377786	−	0.218115i
$494$	−7.76011e7	+	7.89644e7i	−0.643706	+	0.655014i
$495$	7.93000e7	+	1.14547e7i	0.653819	+	0.0944423i
$496$	195662.	+	5.61559e6i	0.00160348	+	0.0460204i
$497$	−2.55389e6	+	4.42346e6i	−0.0208033	+	0.0360324i
$498$	6.02702e7	+	1.21471e8i	0.487994	+	0.983523i
$499$	−8.15420e7	−	1.41235e8i	−0.656265	−	1.13668i	−0.981575	−	0.191077i	$-0.938802\pi$
$499$	−8.15420e7	−	1.41235e8i	−0.656265	−	1.13668i	0.325310	−	0.945608i	$-0.394531\pi$
$500$	−6.47704e7	−	1.07806e8i	−0.518163	−	0.862444i
$501$	−7.84257e7	+	2.26356e8i	−0.623656	+	1.80003i
$502$	1.65007e7	−	4.57571e6i	0.130434	−	0.0361699i
$503$		−	1.56926e8i		−	1.23308i	−0.787325	−	0.616538i	$-0.788535\pi$
$503$		−	1.56926e8i		−	1.23308i	0.787325	−	0.616538i	$-0.211465\pi$
$504$	8.62608e6	+	5.92942e7i	0.0673786	+	0.463149i
$505$	−4.24280e7			−0.329442
$506$	−4.53955e7	−	1.63703e8i	−0.350397	−	1.26359i
$507$	−5.93608e6	−	3.08537e7i	−0.0455487	−	0.236746i
$508$	3.43155e6	+	5.71156e6i	0.0261757	+	0.0435676i
$509$	4.46217e7	−	2.57623e7i	0.338371	−	0.195358i	−0.321181	−	0.947018i	$-0.604080\pi$
$509$	4.46217e7	−	2.57623e7i	0.338371	−	0.195358i	0.659551	+	0.751660i	$0.270746\pi$
$510$	2.20283e6	−	3.49081e7i	0.0166062	−	0.263157i
$511$	6.93885e7	+	4.00614e7i	0.520025	+	0.300237i
$512$	1.02045e8	+	8.71853e7i	0.760292	+	0.649581i
$513$	7.68276e7	+	1.19805e8i	0.569069	+	0.887405i
$514$	1.76902e7	+	1.73848e7i	0.130270	+	0.128021i
$515$	3.10083e7	−	5.37080e7i	0.227016	−	0.393203i
$516$	1.07576e8	+	1.19946e8i	0.783010	+	0.873044i
$517$	−3.97700e7	+	2.29612e7i	−0.287796	+	0.166159i
$518$	2.40376e7	−	9.29390e7i	0.172943	−	0.668665i
$519$	−6.36302e7	+	1.22421e7i	−0.455157	+	0.0875697i
$520$	−2.17506e7	−	7.34446e7i	−0.154690	−	0.522336i
$521$	4.07682e7			0.288276			0.144138	−	0.989558i	$-0.453959\pi$
$521$	4.07682e7			0.288276			0.144138	+	0.989558i	$0.453959\pi$
$522$	−5.68343e7	+	1.35731e8i	−0.399576	+	0.954259i
$523$	−2.71760e7			−0.189968			−0.0949840	−	0.995479i	$-0.530280\pi$
$523$	−2.71760e7			−0.189968			−0.0949840	+	0.995479i	$0.530280\pi$
$524$	−1.65329e8	−	9.16518e7i	−1.14909	−	0.637012i
$525$	1.35016e7	−	3.89690e7i	0.0933055	−	0.269303i
$526$	−1.39202e8	−	3.60030e7i	−0.956507	−	0.247389i
$527$	2.46119e6	−	1.42097e6i	0.0168156	−	0.00970852i
$528$	1.48616e8	+	4.57604e7i	1.00963	+	0.310876i
$529$	4.00221e7	−	6.93203e7i	0.270354	−	0.468267i
$530$	8.82210e7	+	8.66979e7i	0.592576	+	0.582346i
$531$	−2.49709e7	+	9.97786e6i	−0.166782	+	0.0666429i
$532$	7.42777e7	−	1.29363e6i	0.493314	−	0.00859159i
$533$	3.67912e7	+	2.12414e7i	0.242975	+	0.140282i
$534$	5.96968e7	−	8.98143e7i	0.392037	−	0.589823i
$535$	−1.46816e8	+	8.47645e7i	−0.958768	+	0.553545i
$536$	1.36635e8	+	3.28115e7i	0.887292	+	0.213075i
$537$	1.04548e8	−	9.05310e7i	0.675135	−	0.584621i
$538$	5.45978e7	+	1.96888e8i	0.350613	+	1.26437i
$539$	−1.29189e8			−0.825007
$540$	−9.82652e7	+	6.30067e6i	−0.624049	+	0.0400134i
$541$			8.11890e7i			0.512750i	0.966577	+	0.256375i	$0.0825281\pi$
$541$			8.11890e7i			0.512750i	−0.966577	+	0.256375i	$0.917472\pi$
$542$	5.67185e7	+	2.04536e8i	0.356227	+	1.28461i
$543$	−1.57330e8	−	1.81689e8i	−0.982682	−	1.13483i
$544$	1.46992e7	−	6.62732e7i	0.0913054	−	0.411662i
$545$	−8.11911e7	−	1.40627e8i	−0.501555	−	0.868719i
$546$	3.67365e7	−	5.52702e7i	0.225694	−	0.339558i
$547$	1.15588e8	−	2.00205e8i	0.706239	−	1.22324i	−0.260003	−	0.965608i	$-0.583724\pi$
$547$	1.15588e8	−	2.00205e8i	0.706239	−	1.22324i	0.966242	−	0.257635i	$-0.0829431\pi$
$548$	1.67481e6	+	9.61648e7i	0.0101771	+	0.584352i
$549$	1.31578e8	−	1.67089e8i	0.795180	−	1.00979i
$550$	−7.63387e7	−	7.50207e7i	−0.458835	−	0.450913i
$551$	1.57999e8	+	9.12205e7i	0.944492	+	0.545303i
$552$	9.60358e7	+	1.85375e8i	0.570974	+	1.10213i
$553$	4.19455e7	+	7.26517e7i	0.248033	+	0.429606i
$554$	−1.13900e7	−	2.94589e6i	−0.0669876	−	0.0173256i
$555$	1.49064e8	+	5.16462e7i	0.871954	+	0.302106i
$556$	−7.81031e7	−	4.32973e7i	−0.454406	−	0.251905i
$557$		−	1.14597e8i		−	0.663145i	−0.943430	−	0.331572i	$-0.892421\pi$
$557$		−	1.14597e8i		−	0.663145i	0.943430	−	0.331572i	$-0.107579\pi$
$558$	−4.84593e6	−	6.36591e6i	−0.0278917	−	0.0366402i
$559$		−	1.78456e8i		−	1.02164i
$560$	−2.41332e7	+	4.53794e7i	−0.137420	+	0.258401i
$561$	−1.48590e7	−	7.72320e7i	−0.0841592	−	0.437430i
$562$	−7.98186e7	+	3.08611e8i	−0.449671	+	1.73861i
$563$	1.64021e7	+	2.84093e7i	0.0919124	+	0.159197i	0.908316	−	0.418285i	$-0.137369\pi$
$563$	1.64021e7	+	2.84093e7i	0.0919124	+	0.159197i	−0.816403	+	0.577482i	$0.804035\pi$
$564$	4.20140e7	−	3.76813e7i	0.234184	−	0.210033i
$565$	−8.21546e7	−	4.74320e7i	−0.455498	−	0.262982i
$566$	5.47949e7	+	5.38489e7i	0.302197	+	0.296980i
$567$	−5.87920e7	−	6.18213e7i	−0.322529	−	0.339148i
$568$	−1.18162e7	−	1.12145e7i	−0.0644811	−	0.0611975i
$569$	−1.27637e8	+	2.21074e8i	−0.692852	+	1.20005i	0.278048	+	0.960567i	$0.410313\pi$
$569$	−1.27637e8	+	2.21074e8i	−0.692852	+	1.20005i	−0.970900	+	0.239487i	$0.923021\pi$
$570$	−7.68861e6	+	1.21841e8i	−0.0415168	+	0.657912i
$571$	1.15763e8	+	2.00507e8i	0.621814	+	1.07701i	0.989148	+	0.146924i	$0.0469372\pi$
$571$	1.15763e8	+	2.00507e8i	0.621814	+	1.07701i	−0.367334	+	0.930089i	$0.619729\pi$
$572$	−8.87008e7	−	1.47636e8i	−0.473957	−	0.788867i
$573$	−2.57590e8	+	4.95589e7i	−1.36919	+	0.263425i
$574$	−7.61742e6	−	2.74696e7i	−0.0402784	−	0.145250i
$575$		−	1.43699e8i		−	0.755876i
$576$	−1.90309e8	−	1.74067e7i	−0.995843	−	0.0910855i
$577$	1.04705e7			0.0545057			0.0272529	−	0.999629i	$-0.491324\pi$
$577$	1.04705e7			0.0545057			0.0272529	+	0.999629i	$0.491324\pi$
$578$	1.52993e8	−	4.24256e7i	0.792299	−	0.219707i
$579$	9.60805e7	+	3.32890e7i	0.494994	+	0.171501i
$580$	−1.08197e8	+	6.50057e7i	−0.554539	+	0.333171i
$581$	−8.72776e7	+	5.03897e7i	−0.445015	+	0.256929i
$582$	1.10030e8	+	2.21758e8i	0.558138	+	1.12489i
$583$	2.40863e8	+	1.39062e8i	1.21553	+	0.701784i
$584$	−1.75915e8	+	1.85354e8i	−0.883211	+	0.930602i
$585$	8.56842e7	+	6.74737e7i	0.427989	+	0.337029i
$586$	2.44708e8	−	2.49007e8i	1.21606	−	1.23742i
$587$	−1.60407e8	+	2.77833e8i	−0.793064	+	1.37363i	0.130997	+	0.991383i	$0.458182\pi$
$587$	−1.60407e8	+	2.77833e8i	−0.793064	+	1.37363i	−0.924061	+	0.382245i	$0.875151\pi$
$588$	1.55361e8	−	3.27059e7i	0.764203	−	0.160877i
$589$	−8.59037e6	+	4.95965e6i	−0.0420403	+	0.0242720i
$590$	−2.23317e7	−	5.77583e6i	−0.108734	−	0.0281228i
$591$	1.37236e8	+	1.58484e8i	0.664822	+	0.767754i
$592$	2.70323e8	+	1.43760e8i	1.30292	+	0.692906i
$593$	1.25750e8			0.603035			0.301517	−	0.953461i	$-0.402507\pi$
$593$	1.25750e8			0.603035			0.301517	+	0.953461i	$0.402507\pi$
$594$	−2.10367e8	+	6.90425e7i	−1.00373	+	0.329425i
$595$	2.59955e7			0.123409
$596$	1.16690e8	−	2.10496e8i	0.551184	−	0.994271i
$597$	−2.19026e8	−	2.52937e8i	−1.02937	−	1.18875i
$598$	5.79018e7	−	2.23871e8i	0.270762	−	1.04688i
$599$	−1.69748e8	+	9.80043e7i	−0.789815	+	0.456000i	−0.839897	−	0.542745i	$-0.817385\pi$
$599$	−1.69748e8	+	9.80043e7i	−0.789815	+	0.456000i	0.0500826	+	0.998745i	$0.484052\pi$
$600$	1.10797e8	+	7.08928e7i	0.512947	+	0.328208i
$601$	1.32545e8	−	2.29575e8i	0.610577	−	1.05755i	−0.380566	−	0.924754i	$-0.624271\pi$
$601$	1.32545e8	−	2.29575e8i	0.610577	−	1.05755i	0.991143	−	0.132797i	$-0.0423958\pi$
$602$	−8.39322e7	+	8.54067e7i	−0.384715	+	0.391474i
$603$	−1.85792e8	+	7.42387e7i	−0.847374	+	0.338593i
$604$	−2.43521e8	+	4.24118e6i	−1.10516	+	0.0192476i
$605$	1.39114e7	+	8.03177e6i	0.0628211	+	0.0362698i
$606$	1.05026e8	−	5.21106e7i	0.471931	−	0.234158i
$607$	−6.59619e7	+	3.80831e7i	−0.294936	+	0.170281i	−0.640166	−	0.768237i	$-0.721134\pi$
$607$	−6.59619e7	+	3.80831e7i	−0.294936	+	0.170281i	0.345230	+	0.938518i	$0.387801\pi$
$608$	−5.13050e7	+	2.31315e8i	−0.228270	+	1.02918i
$609$	−1.03336e8	−	3.58027e7i	−0.457507	−	0.158513i
$610$	1.75799e8	−	4.87496e7i	0.774508	−	0.214774i
$611$	−6.25087e7			−0.274042
$612$	3.74216e7	+	8.91166e7i	0.163256	+	0.388780i
$613$			1.61761e8i			0.702250i	0.936329	+	0.351125i	$0.114201\pi$
$613$			1.61761e8i			0.702250i	−0.936329	+	0.351125i	$0.885799\pi$
$614$	−3.65048e8	+	1.01229e8i	−1.57705	+	0.437321i
$615$	4.60021e7	−	8.85055e6i	0.197766	−	0.0380491i
$616$	−2.69857e7	+	1.12375e8i	−0.115449	+	0.480758i
$617$	3.32428e7	+	5.75782e7i	0.141528	+	0.245133i	0.928072	−	0.372400i	$-0.121465\pi$
$617$	3.32428e7	+	5.75782e7i	0.141528	+	0.245133i	−0.786544	+	0.617534i	$0.788132\pi$
$618$	−1.07928e7	+	1.71033e8i	−0.0457267	+	0.724626i
$619$	−1.48153e8	+	2.56608e8i	−0.624652	+	1.08193i	0.363956	+	0.931416i	$0.381426\pi$
$619$	−1.48153e8	+	2.56608e8i	−0.624652	+	1.08193i	−0.988608	+	0.150512i	$0.951908\pi$
$620$	−119504.	−	6.86171e6i	−0.000501427	−	0.0287911i
$621$	−2.64080e8	−	1.36472e8i	−1.10271	−	0.569859i
$622$	1.17330e8	−	1.19391e8i	0.487569	−	0.496135i
$623$	6.94121e7	+	4.00751e7i	0.287059	+	0.165733i
$624$	1.44047e8	+	1.55089e8i	0.592856	+	0.638305i
$625$	2.46622e6	+	4.27162e6i	0.0101016	+	0.0174965i
$626$	−4.16103e7	+	1.60882e8i	−0.169620	+	0.655820i
$627$	5.18628e7	+	2.69565e8i	0.210404	+	1.09361i
$628$	7.26471e7	−	1.31047e8i	0.293318	−	0.529112i
$629$		−	1.54854e8i		−	0.622258i
$630$	−9.27279e6	−	7.25913e7i	−0.0370842	−	0.290311i
$631$			2.25516e8i			0.897612i	0.893629	+	0.448806i	$0.148151\pi$
$631$			2.25516e8i			0.897612i	−0.893629	+	0.448806i	$0.851849\pi$
$632$	−2.56547e8	+	7.59764e7i	−1.01629	+	0.300973i
$633$	−2.17788e8	−	7.54570e7i	−0.858663	−	0.297501i
$634$	3.73887e8	+	9.67015e7i	1.46714	+	0.379460i
$635$	−4.06901e6	−	7.04773e6i	−0.0158916	−	0.0275250i
$636$	−3.24865e8	−	1.06257e8i	−1.26279	−	0.413034i
$637$	−1.52289e8	−	8.79243e7i	−0.589185	−	0.340166i
$638$	−1.98935e8	+	2.02430e8i	−0.766037	+	0.779494i
$639$	2.29569e7	+	3.31606e6i	0.0879854	+	0.0127092i
$640$	−1.22759e8	−	1.08638e8i	−0.468288	−	0.414420i
$641$	1.44649e8	−	2.50539e8i	0.549214	−	0.951266i	−0.449115	−	0.893474i	$-0.648261\pi$
$641$	1.44649e8	−	2.50539e8i	0.549214	−	0.951266i	0.998329	−	0.0577920i	$-0.0184060\pi$
$642$	2.59319e8	−	3.90147e8i	0.980007	−	1.47443i
$643$	−5.23228e7	−	9.06258e7i	−0.196815	−	0.340894i	0.750679	−	0.660667i	$-0.229727\pi$
$643$	−5.23228e7	−	9.06258e7i	−0.196815	−	0.340894i	−0.947494	+	0.319773i	$0.896393\pi$
$644$	−1.33003e8	+	7.99093e7i	−0.497971	+	0.299185i
$645$	−1.28817e8	−	1.48761e8i	−0.480059	−	0.554385i
$646$	1.15478e8	−	3.20226e7i	0.428354	−	0.118784i
$647$		−	2.62016e8i		−	0.967418i	−0.875229	−	0.483709i	$-0.839289\pi$
$647$		−	2.62016e8i		−	0.967418i	0.875229	−	0.483709i	$-0.160711\pi$
$648$	2.35506e8	−	1.36287e8i	0.865519	−	0.500875i
$649$	−5.18660e7			−0.189736
$650$	−3.89309e7	−	1.40391e8i	−0.141760	−	0.511209i
$651$	4.49496e6	−	3.89233e6i	0.0162923	−	0.0141080i
$652$	2.05823e8	−	1.23660e8i	0.742592	−	0.446155i
$653$	1.21515e8	−	7.01566e7i	0.436405	−	0.251958i	−0.265667	−	0.964065i	$-0.585592\pi$
$653$	1.21515e8	−	7.01566e7i	0.436405	−	0.251958i	0.702071	+	0.712106i	$0.252259\pi$
$654$	3.73699e8	+	2.48387e8i	1.33595	+	0.887963i
$655$	1.99945e8	+	1.15438e8i	0.711518	+	0.410795i
$656$	9.08623e7	−	3.16589e6i	0.321864	−	0.0112146i
$657$	5.20171e7	−	3.60112e8i	0.183422	−	1.26982i
$658$	2.99158e7	+	2.93993e7i	0.105008	+	0.103195i
$659$	2.15784e8	−	3.73750e8i	0.753987	−	1.30594i	−0.191889	−	0.981417i	$-0.561461\pi$
$659$	2.15784e8	−	3.73750e8i	0.753987	−	1.30594i	0.945876	−	0.324527i	$-0.105205\pi$
$660$	−1.80511e8	−	5.90416e7i	−0.627873	−	0.205365i
$661$	1.94576e8	−	1.12339e8i	0.673730	−	0.388978i	−0.123759	−	0.992312i	$-0.539495\pi$
$661$	1.94576e8	−	1.12339e8i	0.673730	−	0.388978i	0.797488	+	0.603334i	$0.206161\pi$
$662$	−6.24812e7	+	2.41578e8i	−0.215365	+	0.832689i
$663$	3.50473e7	−	1.01155e8i	0.120258	−	0.347094i
$664$	−9.12716e7	−	3.08194e8i	−0.311768	−	1.05274i
$665$	−9.07327e7			−0.308531
$666$	−4.32424e8	+	5.52377e7i	−1.46382	+	0.186988i
$667$	−3.81052e8			−1.28412
$668$	2.75313e8	−	4.96633e8i	0.923630	−	1.66612i
$669$	−5.43986e7	+	1.04660e7i	−0.181681	+	0.0349544i
$670$	−1.66155e8	−	4.29742e7i	−0.552446	−	0.142884i
$671$	3.55250e8	−	2.05104e8i	1.17589	−	0.678901i
$672$	4.00350e6	−	1.41972e8i	0.0131926	−	0.467838i
$673$	2.78173e8	−	4.81809e8i	0.912576	−	1.58063i	0.102165	−	0.994767i	$-0.467423\pi$
$673$	2.78173e8	−	4.81809e8i	0.912576	−	1.58063i	0.810411	−	0.585861i	$-0.199244\pi$
$674$	8.95151e7	+	8.79697e7i	0.292359	+	0.287312i
$675$	−1.87081e8	+	8.72749e6i	−0.608300	+	0.0283777i
$676$	1.29688e6	+	7.44646e7i	0.00419817	+	0.241052i
$677$	1.82930e8	+	1.05615e8i	0.589547	+	0.340375i	0.764918	−	0.644127i	$-0.222779\pi$
$677$	1.82930e8	+	1.05615e8i	0.589547	+	0.340375i	−0.175371	+	0.984502i	$0.556113\pi$
$678$	2.61621e8	+	1.65093e7i	0.839428	+	0.0529711i
$679$	−1.59335e8	+	9.19920e7i	−0.508981	+	0.293860i
$680$	−1.93596e7	+	8.06178e7i	−0.0615701	+	0.256392i
$681$	−5.97628e7	−	3.10627e8i	−0.189230	−	0.983552i
$682$	−4.12352e6	−	1.48701e7i	−0.0129991	−	0.0468769i
$683$	3.55446e8			1.11561			0.557804	−	0.829973i	$-0.311644\pi$
$683$	3.55446e8			1.11561			0.557804	+	0.829973i	$0.311644\pi$
$684$	−1.30614e8	−	3.11046e8i	−0.408151	−	0.971978i
$685$		−	1.17468e8i		−	0.365468i
$686$	7.19054e7	+	2.59302e8i	0.222735	+	0.803218i
$687$	1.76211e8	−	5.08590e8i	0.543455	−	1.56855i
$688$	−2.02358e8	−	3.23897e8i	−0.621378	−	0.994586i
$689$	1.89289e8	+	3.27858e8i	0.578718	+	1.00237i
$690$	−1.13333e8	−	2.28416e8i	−0.344992	−	0.695310i
$691$	3.17323e7	−	5.49620e7i	0.0961762	−	0.166582i	−0.813923	−	0.580973i	$-0.802672\pi$
$691$	3.17323e7	−	5.49620e7i	0.0961762	−	0.166582i	0.910099	+	0.414391i	$0.136005\pi$
$692$	1.53570e8	−	2.67459e6i	0.463434	−	0.00807120i
$693$	−6.10573e7	−	1.52804e8i	−0.183459	−	0.459129i
$694$	−2.84906e8	−	2.79988e8i	−0.852361	−	0.837646i
$695$	9.44558e7	+	5.45341e7i	0.281368	+	0.162448i
$696$	1.87989e8	−	2.93803e8i	0.557577	−	0.871423i
$697$	−2.29918e7	−	3.98230e7i	−0.0679008	−	0.117608i
$698$	3.57261e8	+	9.24015e7i	1.05056	+	0.271714i
$699$	−2.90590e8	+	2.51631e8i	−0.850843	+	0.736772i
$700$	−4.73974e7	+	8.54993e7i	−0.138185	+	0.249269i
$701$		−	1.09484e8i		−	0.317832i	−0.987292	−	0.158916i	$-0.949200\pi$
$701$		−	1.09484e8i		−	0.317832i	0.987292	−	0.158916i	$-0.0508000\pi$
$702$	−2.94974e8	−	6.17852e7i	−0.852652	−	0.178597i
$703$			5.40491e8i			1.55569i
$704$	−3.28402e8	−	1.67377e8i	−0.941212	−	0.479710i
$705$	−5.21074e7	+	4.51214e7i	−0.148707	+	0.128770i
$706$	−1.09392e7	+	4.22955e7i	−0.0310866	+	0.120193i
$707$	4.35678e7	+	7.54617e7i	0.123284	+	0.213535i
$708$	6.23735e7	−	1.31306e7i	0.175752	−	0.0369986i
$709$	2.01762e8	+	1.16487e8i	0.566110	+	0.326843i	0.755594	−	0.655040i	$-0.227348\pi$
$709$	2.01762e8	+	1.16487e8i	0.566110	+	0.326843i	−0.189484	+	0.981884i	$0.560682\pi$
$710$	1.41910e7	+	1.39460e7i	0.0396495	+	0.0389650i
$711$	2.35690e8	−	2.99301e8i	0.655742	−	0.832721i
$712$	−1.75975e8	+	1.85417e8i	−0.487541	+	0.513701i
$713$	1.03589e7	−	1.79421e7i	0.0285788	−	0.0495000i
$714$	−6.43488e7	+	3.19279e7i	−0.176785	+	0.0877155i
$715$	1.05178e8	+	1.82174e8i	0.287745	+	0.498389i
$716$	−2.80999e8	+	1.68826e8i	−0.765536	+	0.459940i
$717$	−1.41835e8	+	4.09370e8i	−0.384791	+	1.11060i
$718$	7.17012e7	+	2.58566e8i	0.193710	+	0.698550i
$719$			2.67884e6i			0.00720710i	0.999994	+	0.00360355i	$0.00114705\pi$
$719$			2.67884e6i			0.00720710i	−0.999994	+	0.00360355i	$0.998853\pi$
$720$	2.32028e8	+	2.53039e7i	0.621645	+	0.0677938i
$721$	−1.27365e8			−0.339817
$722$	−4.03766e7	+	1.11966e7i	−0.107280	+	0.0297491i
$723$	−7.71919e7	−	4.01217e8i	−0.204248	−	1.06161i
$724$	2.93397e8	+	4.88337e8i	0.773107	+	1.28678i
$725$	−2.07913e8	+	1.20039e8i	−0.545591	+	0.314997i
$726$	−4.43009e7	−	2.79556e6i	−0.115772	−	0.00730565i
$727$	5.76106e8	+	3.32615e8i	1.49934	+	0.865643i	1.00000		0.000764805i	$-0.000243445\pi$
$727$	5.76106e8	+	3.32615e8i	1.49934	+	0.865643i	0.499338	+	0.866408i	$0.333577\pi$
$728$	−1.08292e8	+	1.14103e8i	−0.280674	+	0.295734i
$729$	−1.61633e8	+	3.52093e8i	−0.417202	+	0.908814i
$730$	2.18763e8	−	2.22606e8i	0.562349	−	0.572228i
$731$	−9.65810e7	+	1.67283e8i	−0.247252	+	0.428253i
$732$	−3.75295e8	+	3.36592e8i	−0.956841	+	0.858165i
$733$	−1.10429e8	+	6.37562e7i	−0.280396	+	0.161886i	−0.633602	−	0.773659i	$-0.718424\pi$
$733$	−1.10429e8	+	6.37562e7i	−0.280396	+	0.161886i	0.353207	+	0.935545i	$0.385091\pi$
$734$	5.10934e8	+	1.32147e8i	1.29204	+	0.334171i
$735$	−1.90416e8	+	3.66350e7i	−0.479559	+	0.0922645i
$736$	−1.48765e8	−	4.71983e8i	−0.373136	−	1.18384i
$737$	−3.85901e8			−0.963992
$738$	−1.03003e8	+	7.84089e7i	−0.256259	+	0.195072i
$739$	−1.06875e8			−0.264816			−0.132408	−	0.991195i	$-0.542271\pi$
$739$	−1.06875e8			−0.264816			−0.132408	+	0.991195i	$0.542271\pi$
$740$	−3.27051e8	−	1.81304e8i	−0.807088	−	0.447417i
$741$	−1.22326e8	+	3.53065e8i	−0.300653	+	0.867760i
$742$	6.36083e7	−	2.45935e8i	0.155705	−	0.602017i
$743$	−2.53231e8	+	1.46203e8i	−0.617377	+	0.356443i	−0.775847	−	0.630921i	$-0.782677\pi$
$743$	−2.53231e8	+	1.46203e8i	−0.617377	+	0.356443i	0.158470	+	0.987364i	$0.449344\pi$
$744$	8.72346e6	+	1.68386e7i	0.0211821	+	0.0408872i
$745$	−1.46975e8	+	2.54568e8i	−0.355447	+	0.615652i
$746$	−2.83181e8	+	2.88156e8i	−0.682099	+	0.694082i
$747$	3.59555e8	+	2.83139e8i	0.862588	+	0.679262i
$748$	3.24631e6	+	1.86398e8i	0.00775686	+	0.445385i
$749$	3.01521e8	+	1.74083e8i	0.717583	+	0.414297i
$750$	−3.53499e8	−	2.34960e8i	−0.837924	−	0.556943i
$751$	−2.76321e8	+	1.59534e8i	−0.652369	+	0.376646i	−0.789363	−	0.613926i	$-0.789589\pi$
$751$	−2.76321e8	+	1.59534e8i	−0.652369	+	0.376646i	0.136994	+	0.990572i	$0.456256\pi$
$752$	−1.13453e8	+	7.08810e7i	−0.266786	+	0.166677i
$753$	4.36883e7	−	3.78311e7i	0.102325	−	0.0886062i
$754$	−3.72280e8	+	1.03234e8i	−0.868471	+	0.240830i
$755$	2.97469e8			0.691196
$756$	1.12111e8	+	1.68303e8i	0.259468	+	0.389516i
$757$			3.86913e8i			0.891919i	0.895053	+	0.445960i	$0.147137\pi$
$757$			3.86913e8i			0.891919i	−0.895053	+	0.445960i	$0.852863\pi$
$758$	−4.85861e8	+	1.34731e8i	−1.11559	+	0.309357i
$759$	−3.75321e8	−	4.33430e8i	−0.858376	−	0.991274i
$760$	6.75713e7	−	2.81382e8i	0.153929	−	0.640997i
$761$	2.24204e8	+	3.88333e8i	0.508733	+	0.881152i	0.999949	+	0.0101139i	$0.00321940\pi$
$761$	2.24204e8	+	3.88333e8i	0.508733	+	0.881152i	−0.491216	+	0.871038i	$0.663447\pi$
$762$	1.87285e7	+	1.24483e7i	0.0423289	+	0.0281348i
$763$	−1.66744e8	+	2.88810e8i	−0.375386	+	0.650187i
$764$	6.21687e8	−	1.08273e7i	1.39409	−	0.0242796i
$765$	−4.38026e7	−	1.09622e8i	−0.0978398	−	0.244857i
$766$	6.01383e8	−	6.11948e8i	1.33803	−	1.36153i
$767$	−6.11405e7	−	3.52995e7i	−0.135501	−	0.0782316i
$768$	4.37306e8	+	1.18147e8i	0.965388	+	0.260818i
$769$	3.49633e8	+	6.05582e8i	0.768835	+	1.33166i	0.938195	+	0.346107i	$0.112497\pi$
$769$	3.49633e8	+	6.05582e8i	0.768835	+	1.33166i	−0.169360	+	0.985554i	$0.554170\pi$
$770$	3.53439e7	−	1.36654e8i	0.0774181	−	0.299330i
$771$	7.90964e7	+	2.74046e7i	0.172581	+	0.0597943i
$772$	−2.10804e8	−	1.16861e8i	−0.458170	−	0.253991i
$773$			4.62316e8i			1.00092i	0.865759	+	0.500461i	$0.166836\pi$
$773$			4.62316e8i			1.00092i	−0.865759	+	0.500461i	$0.833164\pi$
$774$	5.01583e8	+	2.10027e8i	1.08173	+	0.452953i
$775$		−	1.30530e7i		−	0.0280417i
$776$	−1.66626e8	−	5.62642e8i	−0.356581	−	1.20406i
$777$	−6.12114e7	−	3.18156e8i	−0.130488	−	0.678230i
$778$	5.50060e8	+	1.42267e8i	1.16808	+	0.302109i
$779$	8.02489e7	+	1.38995e8i	0.169757	+	0.294027i
$780$	−1.72606e8	−	1.92453e8i	−0.363724	−	0.405547i
$781$	3.87446e7	+	2.23692e7i	0.0813313	+	0.0469566i
$782$	−1.75436e8	+	1.78518e8i	−0.366859	+	0.373304i
$783$	2.31430e7	+	4.96089e8i	0.0482097	+	1.03341i
$784$	−3.76106e8	+	1.31045e7i	−0.780480	+	0.0271940i
$785$	−9.15010e7	+	1.58484e8i	−0.189155	+	0.327626i
$786$	−6.36723e8	−	4.01796e7i	−1.31124	−	0.0827444i
$787$	−4.14144e8	−	7.17318e8i	−0.849624	−	1.47159i	−0.881544	−	0.472101i	$-0.843496\pi$
$787$	−4.14144e8	−	7.17318e8i	−0.849624	−	1.47159i	0.0319202	−	0.999490i	$-0.489838\pi$
$788$	−2.55924e8	−	4.25966e8i	−0.523037	−	0.870556i
$789$	−4.76526e8	+	9.16810e7i	−0.970188	+	0.186659i
$790$	3.14902e8	−	8.73234e7i	0.638695	−	0.177112i
$791$			1.94825e8i			0.393654i
$792$	5.19350e8	−	7.55548e7i	1.04541	−	0.152085i
$793$	5.58366e8			1.11969
$794$	−2.32892e7	−	8.39846e7i	−0.0465258	−	0.167779i
$795$	3.94453e8	+	1.36666e8i	0.785043	+	0.271994i
$796$	4.08449e8	+	6.79834e8i	0.809839	+	1.34792i
$797$	1.44267e8	−	8.32928e7i	0.284966	−	0.164525i	−0.350703	−	0.936487i	$-0.614057\pi$
$797$	1.44267e8	−	8.32928e7i	0.284966	−	0.164525i	0.635670	+	0.771961i	$0.280724\pi$
$798$	2.24599e8	−	1.11439e8i	0.441976	−	0.219295i
$799$	5.85951e7	+	3.38299e7i	0.114874	+	0.0663224i
$800$	−2.29854e8	−	2.10664e8i	−0.448934	−	0.411453i
$801$	5.20348e7	−	3.60235e8i	0.101250	−	0.700951i
$802$	−2.60324e8	−	2.55830e8i	−0.504652	−	0.495939i
$803$	3.50893e8	−	6.07765e8i	0.677685	−	1.17379i
$804$	4.64080e8	−	9.76963e7i	0.892946	−	0.187979i
$805$	1.64118e8	−	9.47536e7i	0.314607	−	0.181638i
$806$	5.25953e6	−	2.03355e7i	0.0100448	−	0.0388373i
$807$	4.51404e8	+	5.21293e8i	0.858904	+	0.991885i
$808$	−2.66470e8	+	7.89150e7i	−0.505142	+	0.149598i
$809$	−9.68443e8			−1.82906			−0.914531	−	0.404516i	$-0.867440\pi$
$809$	−9.68443e8			−1.82906			−0.914531	+	0.404516i	$0.867440\pi$
$810$	−2.90490e8	+	1.61420e8i	−0.546608	+	0.303740i
$811$	8.25101e8			1.54684			0.773418	−	0.633896i	$-0.218545\pi$
$811$	8.25101e8			1.54684			0.773418	+	0.633896i	$0.218545\pi$
$812$	2.26722e8	+	1.25685e8i	0.423472	+	0.234756i
$813$	4.68937e8	+	5.41541e8i	0.872656	+	1.00777i
$814$	−8.14041e8	−	2.10542e8i	−1.50929	−	0.390361i
$815$	−2.53973e8	+	1.46631e8i	−0.469153	+	0.270866i
$816$	−5.10932e7	−	2.23338e8i	−0.0940356	−	0.411047i
$817$	3.37099e8	−	5.83873e8i	0.618147	−	1.07066i
$818$	2.39910e8	+	2.35768e8i	0.438318	+	0.430751i
$819$	3.20214e7	−	2.21683e8i	0.0582893	−	0.403534i
$820$	−1.11025e8	+	1.93362e6i	−0.201363	+	0.00350695i
$821$	6.56033e8	+	3.78761e8i	1.18548	+	0.684440i	0.957277	−	0.289172i	$-0.0933801\pi$
$821$	6.56033e8	+	3.78761e8i	1.18548	+	0.684440i	0.228208	+	0.973612i	$0.426713\pi$
$822$	1.44276e8	+	2.90780e8i	0.259764	+	0.523539i
$823$	−5.66543e8	+	3.27094e8i	−1.01633	+	0.586776i	−0.913038	−	0.407875i	$-0.866270\pi$
$823$	−5.66543e8	+	3.27094e8i	−1.01633	+	0.586776i	−0.103288	+	0.994651i	$0.532936\pi$
$824$	9.48527e7	−	3.94988e8i	0.169538	−	0.705996i
$825$	−3.41324e8	−	1.18259e8i	−0.607863	−	0.210606i
$826$	1.26588e7	+	4.56497e7i	0.0224622	+	0.0810023i
$827$	−4.41065e8			−0.779806			−0.389903	−	0.920856i	$-0.627491\pi$
$827$	−4.41065e8			−0.779806			−0.389903	+	0.920856i	$0.627491\pi$
$828$	5.61085e8	+	4.26220e8i	0.988412	+	0.750833i
$829$		−	4.70596e8i		−	0.826009i	−0.910729	−	0.413004i	$-0.864479\pi$
$829$		−	4.70596e8i		−	0.826009i	0.910729	−	0.413004i	$-0.135521\pi$
$830$	1.04903e8	+	3.78296e8i	0.183465	+	0.661604i
$831$	−3.89911e7	+	7.50167e6i	−0.0679458	+	0.0130724i
$832$	−2.73210e8	−	4.20814e8i	−0.474380	−	0.730668i
$833$	9.51698e7	+	1.64839e8i	0.164651	+	0.285184i
$834$	−3.00794e8	−	1.89813e7i	−0.518527	−	0.0327210i
$835$	−3.46765e8	+	6.00614e8i	−0.595629	+	1.03166i
$836$	−1.13307e7	−	6.50589e8i	−0.0193927	−	1.11349i
$837$	−2.39879e7	−	1.23965e7i	−0.0409086	−	0.0211408i
$838$	4.31958e8	+	4.24501e8i	0.734023	+	0.721351i
$839$	−4.91025e8	−	2.83494e8i	−0.831416	−	0.480018i	0.0229215	−	0.999737i	$-0.492703\pi$
$839$	−4.91025e8	−	2.83494e8i	−0.831416	−	0.480018i	−0.854337	+	0.519719i	$0.826037\pi$
$840$	−7.90837e6	+	1.73286e8i	−0.0133429	+	0.292365i
$841$	2.08991e7	+	3.61984e7i	0.0351350	+	0.0608557i
$842$	−9.63178e8	−	2.49115e8i	−1.61351	−	0.417314i
$843$	2.03257e8	+	1.05646e9i	0.339283	+	1.76348i
$844$	4.77834e8	+	2.64892e8i	0.794785	+	0.440597i
$845$		−	9.09610e7i		−	0.150760i
$846$	7.35673e7	−	1.75692e8i	0.121499	−	0.290162i
$847$		−	3.29901e7i		−	0.0542918i
$848$	7.15329e8	+	3.80419e8i	1.17305	+	0.623841i
$849$	2.44998e8	+	8.48846e7i	0.400350	+	0.138709i
$850$	−3.94865e7	+	1.52671e8i	−0.0642971	+	0.248599i
$851$	−5.64443e8	−	9.77644e8i	−0.915865	−	1.58632i
$852$	−5.22568e7	−	1.70922e7i	−0.0844937	−	0.0276362i
$853$	−7.42258e8	−	4.28543e8i	−1.19593	−	0.690473i	−0.236289	−	0.971683i	$-0.575931\pi$
$853$	−7.42258e8	−	4.28543e8i	−1.19593	−	0.690473i	−0.959646	+	0.281210i	$0.909264\pi$
$854$	−2.67226e8	−	2.62613e8i	−0.429048	−	0.421641i
$855$	1.52885e8	+	3.82616e8i	0.244606	+	0.612160i
$856$	−7.64423e8	+	8.05439e8i	−1.21874	+	1.28414i
$857$	−3.41231e8	+	5.91030e8i	−0.542133	+	0.939003i	0.456648	+	0.889648i	$0.349050\pi$
$857$	−3.41231e8	+	5.91030e8i	−0.542133	+	0.939003i	−0.998781	+	0.0493552i	$0.984283\pi$
$858$	−4.84105e8	−	3.21770e8i	−0.766439	−	0.509429i
$859$	−5.60807e8	−	9.71347e8i	−0.884778	−	1.53248i	−0.845968	−	0.533233i	$-0.820977\pi$
$859$	−5.60807e8	−	9.71347e8i	−0.884778	−	1.53248i	−0.0388096	−	0.999247i	$-0.512357\pi$
$860$	2.40224e8	+	3.99835e8i	0.377678	+	0.628617i
$861$	−6.29793e7	−	7.27301e7i	−0.0986707	−	0.113948i
$862$	−1.73255e8	−	6.24786e8i	−0.270499	−	0.975461i
$863$		−	6.02013e8i		−	0.936642i	−0.883558	−	0.468321i	$-0.844859\pi$
$863$		−	6.02013e8i		−	0.936642i	0.883558	−	0.468321i	$-0.155141\pi$
$864$	−6.05437e8	+	2.22342e8i	−0.938702	+	0.344731i
$865$	−1.87591e8			−0.289843
$866$	1.04282e9	−	2.89179e8i	1.60567	−	0.445259i
$867$	4.05074e8	−	3.50766e8i	0.621552	−	0.538221i
$868$	−1.20814e7	+	7.25859e6i	−0.0184739	+	0.0110992i
$869$	6.36347e8	−	3.67395e8i	0.969694	−	0.559853i
$870$	−2.35814e8	+	3.54784e8i	−0.358106	+	0.538773i
$871$	−4.54906e8	−	2.62640e8i	−0.688442	−	0.397472i
$872$	−7.71484e8	−	7.32197e8i	−1.16353	−	1.10428i
$873$	6.56407e8	+	5.16900e8i	0.986575	+	0.776898i
$874$	6.12331e8	−	6.23088e8i	0.917174	−	0.933287i
$875$	1.57731e8	−	2.73198e8i	0.235447	−	0.407806i
$876$	−2.68116e8	+	8.19724e8i	−0.398851	+	1.21943i
$877$	6.39359e8	−	3.69134e8i	0.947864	−	0.547250i	0.0554475	−	0.998462i	$-0.482341\pi$
$877$	6.39359e8	−	3.69134e8i	0.947864	−	0.547250i	0.892417	+	0.451212i	$0.149008\pi$
$878$	6.13321e8	+	1.58628e8i	0.906159	+	0.234368i
$879$	3.85745e8	−	1.11336e9i	0.567980	−	1.63933i
$880$	3.97472e8	+	2.11380e8i	0.583256	+	0.310181i
$881$	7.77090e8			1.13643			0.568216	−	0.822879i	$-0.307634\pi$
$881$	7.77090e8			1.13643			0.568216	+	0.822879i	$0.307634\pi$
$882$	4.26358e8	−	3.24557e8i	0.621397	−	0.473027i
$883$	1.80566e8			0.262273			0.131136	−	0.991364i	$-0.458137\pi$
$883$	1.80566e8			0.262273			0.131136	+	0.991364i	$0.458137\pi$
$884$	−1.23033e8	+	2.21938e8i	−0.178101	+	0.321273i
$885$	−7.64475e7	+	1.47081e7i	−0.110289	+	0.0212190i
$886$	−5.96495e7	+	2.30629e8i	−0.0857641	+	0.331599i
$887$	−9.72882e7	+	5.61694e7i	−0.139408	+	0.0804875i	−0.568082	−	0.822972i	$-0.692314\pi$
$887$	−9.72882e7	+	5.61694e7i	−0.139408	+	0.0804875i	0.428674	+	0.903459i	$0.358981\pi$
$888$	1.03226e9	+	4.71098e7i	1.47418	+	0.0672779i
$889$	−8.35663e6	+	1.44741e7i	−0.0118939	+	0.0206009i
$890$	2.18838e8	−	2.22682e8i	0.310422	−	0.315875i
$891$	−5.41485e8	+	5.14952e8i	−0.765515	+	0.728004i
$892$	1.31290e8	−	2.28655e6i	0.184985	−	0.00322171i
$893$	−2.04516e8	−	1.18077e8i	−0.287192	−	0.165811i
$894$	5.11564e7	−	8.10671e8i	0.0715958	−	1.13457i
$895$	3.46736e8	−	2.00188e8i	0.483648	−	0.279235i
$896$	−6.71643e7	+	3.29893e8i	−0.0933716	+	0.458616i
$897$	−1.47446e8	−	7.66374e8i	−0.204294	−	1.06185i
$898$	−1.20802e8	+	3.34988e7i	−0.166819	+	0.0462595i
$899$	−3.46130e7			−0.0476388
$900$	4.40412e8	+	5.58056e7i	0.604131	+	0.0765509i
$901$		−	4.09774e8i		−	0.560235i
$902$	−2.40603e8	+	6.67200e7i	−0.327854	+	0.0909152i
$903$	−1.32306e8	+	3.81870e8i	−0.179687	+	0.518623i
$904$	−6.04195e8	−	1.45092e8i	−0.817847	−	0.196398i
$905$	−3.47899e8	−	6.02579e8i	−0.469362	−	0.812959i
$906$	−7.36352e8	+	3.65355e8i	−0.990149	+	0.491282i
$907$	−5.13022e8	+	8.88580e8i	−0.687566	+	1.19090i	0.285057	+	0.958511i	$0.407987\pi$
$907$	−5.13022e8	+	8.88580e8i	−0.687566	+	1.19090i	−0.972623	+	0.232388i	$0.925346\pi$
$908$	1.30566e7	+	7.49690e8i	0.0174411	+	1.00144i
$909$	2.44806e8	−	3.10877e8i	0.325935	−	0.413902i
$910$	1.34669e8	−	1.37035e8i	0.178708	−	0.181847i
$911$	−7.17736e8	−	4.14385e8i	−0.949314	−	0.548087i	−0.0564462	−	0.998406i	$-0.517977\pi$
$911$	−7.17736e8	−	4.14385e8i	−0.949314	−	0.548087i	−0.892868	+	0.450319i	$0.851310\pi$
$912$	1.78332e8	+	7.79522e8i	0.235096	+	1.02765i
$913$	4.41357e8	+	7.64453e8i	0.579933	+	1.00447i
$914$	2.47522e8	−	9.57020e8i	0.324172	−	1.25338i
$915$	4.65455e8	−	4.03052e8i	0.607595	−	0.526136i
$916$	−6.18590e8	+	1.11586e9i	−0.804853	+	1.45186i
$917$		−	4.74157e8i		−	0.614913i
$918$	2.43067e8	+	2.17557e8i	0.314194	+	0.281220i
$919$		−	1.20934e9i		−	1.55813i	−0.626943	−	0.779065i	$-0.715694\pi$
$919$		−	1.20934e9i		−	1.55813i	0.626943	−	0.779065i	$-0.284306\pi$
$920$	1.71628e8	+	5.79532e8i	0.220407	+	0.744242i
$921$	−9.66523e8	+	8.36943e8i	−1.23718	+	1.07131i
$922$	−1.33085e9	−	3.44208e8i	−1.69799	−	0.439166i
$923$	3.04485e7	+	5.27383e7i	0.0387222	+	0.0670688i
$924$	8.03499e7	+	3.81681e8i	0.101852	+	0.483821i
$925$	−6.15953e8	−	3.55620e8i	−0.778255	−	0.449326i
$926$	1.65621e8	−	1.68531e8i	0.208585	−	0.212249i
$927$	2.14612e8	+	5.37094e8i	0.269410	+	0.674234i
$928$	−5.58625e8	+	6.09513e8i	−0.698998	+	0.762674i
$929$	−1.10930e8	+	1.92137e8i	−0.138358	+	0.239643i	−0.926875	−	0.375370i	$-0.877516\pi$
$929$	−1.10930e8	+	1.92137e8i	−0.138358	+	0.239643i	0.788517	+	0.615012i	$0.210849\pi$
$930$	−1.02946e7	−	2.07482e7i	−0.0127986	−	0.0257948i
$931$	−3.32174e8	−	5.75342e8i	−0.411639	−	0.712979i
$932$	7.81037e8	−	4.69253e8i	0.964771	−	0.579641i
$933$	1.84952e8	−	5.33819e8i	0.227727	−	0.657278i
$934$	−5.87466e8	+	1.62907e8i	−0.721012	+	0.199939i
$935$		−	2.27691e8i		−	0.278555i
$936$	6.63640e8	+	2.64399e8i	0.809291	+	0.322428i
$937$	−5.18244e8			−0.629963			−0.314982	−	0.949098i	$-0.601998\pi$
$937$	−5.18244e8			−0.629963			−0.314982	+	0.949098i	$0.601998\pi$
$938$	9.41860e7	+	3.39649e8i	0.114124	+	0.411550i
$939$	1.05960e8	+	5.50744e8i	0.127981	+	0.665201i
$940$	1.40052e8	−	8.41444e7i	0.168619	−	0.101308i
$941$	3.60001e7	−	2.07847e7i	0.0432051	−	0.0249445i	−0.478242	−	0.878228i	$-0.658726\pi$
$941$	3.60001e7	−	2.07847e7i	0.0432051	−	0.0249445i	0.521447	+	0.853284i	$0.325392\pi$
$942$	3.18481e7	−	5.04693e8i	0.0381005	−	0.603774i
$943$	−2.90310e8	−	1.67610e8i	−0.346199	−	0.199878i
$944$	−1.50997e8	+	5.26115e6i	−0.179495	+	0.00625410i
$945$	−1.33327e8	−	2.07909e8i	−0.157987	−	0.246365i
$946$	7.48067e8	+	7.35152e8i	0.883623	+	0.868367i
$947$	7.82993e7	−	1.35618e8i	0.0921951	−	0.159687i	−0.816239	−	0.577714i	$-0.803945\pi$
$947$	7.82993e7	−	1.35618e8i	0.0921951	−	0.159687i	0.908435	+	0.418027i	$0.137278\pi$
$948$	−6.72252e8	+	6.02925e8i	−0.789055	+	0.707682i
$949$	8.27276e8	−	4.77628e8i	0.967948	−	0.558845i
$950$	1.37821e8	−	5.32870e8i	0.160747	−	0.621514i
$951$	1.27992e9	−	2.46249e8i	1.48813	−	0.286308i
$952$	1.63265e8	−	4.83509e7i	0.189226	−	0.0560394i
$953$	4.05094e8			0.468034			0.234017	−	0.972233i	$-0.424813\pi$
$953$	4.05094e8			0.468034			0.234017	+	0.972233i	$0.424813\pi$
$954$	−1.14428e9	+	1.46170e8i	−1.31791	+	0.168350i
$955$	−7.59411e8			−0.871901
$956$	4.97910e8	−	8.98171e8i	0.569872	−	1.02798i
$957$	−3.13591e8	+	9.05103e8i	−0.357790	+	1.03267i
$958$	2.54092e8	+	6.57179e7i	0.288998	+	0.0747459i
$959$	−2.08927e8	+	1.20624e8i	−0.236886	+	0.136766i
$960$	−5.31509e8	−	1.53577e8i	−0.600755	−	0.173585i
$961$	−4.42811e8	+	7.66971e8i	−0.498940	+	0.864189i
$962$	−8.16311e8	−	8.02218e8i	−0.916918	−	0.901088i
$963$	2.26036e8	−	1.56483e9i	0.253103	−	1.75222i
$964$	1.68645e7	+	9.68328e8i	0.0188253	+	1.08091i
$965$	2.54941e8	+	1.47190e8i	0.283698	+	0.163793i
$966$	−2.89878e8	+	4.36123e8i	−0.321576	+	0.483813i
$967$	2.30564e7	−	1.33116e7i	0.0254983	−	0.0147215i	−0.487197	−	0.873292i	$-0.661981\pi$
$967$	2.30564e7	−	1.33116e7i	0.0254983	−	0.0147215i	0.512695	+	0.858571i	$0.328647\pi$
$968$	1.02310e8	+	2.45687e7i	0.112795	+	0.0270867i
$969$	3.05747e8	−	2.64756e8i	0.336040	−	0.290988i
$970$	1.91512e8	+	6.90621e8i	0.209836	+	0.756702i
$971$	7.61206e8			0.831466			0.415733	−	0.909487i	$-0.363525\pi$
$971$	7.61206e8			0.831466			0.415733	+	0.909487i	$0.363525\pi$
$972$	5.20816e8	−	7.56360e8i	0.567134	−	0.823625i
$973$		−	2.23996e8i		−	0.243166i
$974$	3.07248e8	+	1.10798e9i	0.332516	+	1.19910i
$975$	−3.21873e8	−	3.71707e8i	−0.347273	−	0.401039i
$976$	1.01343e9	−	6.33153e8i	1.09005	−	0.681019i
$977$	−2.17518e8	−	3.76752e8i	−0.233245	−	0.403992i	0.725516	−	0.688205i	$-0.241601\pi$
$977$	−2.17518e8	−	3.76752e8i	−0.233245	−	0.403992i	−0.958761	+	0.284213i	$0.908268\pi$
$978$	4.48587e8	−	6.74902e8i	0.479546	−	0.721479i
$979$	3.51012e8	−	6.07971e8i	0.374089	−	0.647940i
$980$	4.59565e8	−	8.00382e6i	0.488280	−	0.00850391i
$981$	1.49886e9	+	2.16507e8i	1.58765	+	0.229332i
$982$	−1.11867e8	−	1.09936e8i	−0.118132	−	0.116093i
$983$	−1.15418e9	−	6.66368e8i	−1.21511	−	0.701542i	−0.251239	−	0.967925i	$-0.580838\pi$
$983$	−1.15418e9	−	6.66368e8i	−1.21511	−	0.701542i	−0.963867	+	0.266384i	$0.914171\pi$
$984$	2.72455e8	−	1.41149e8i	0.285963	−	0.148146i
$985$	3.03465e8	+	5.25617e8i	0.317541	+	0.549998i
$986$	4.04842e8	+	1.04708e8i	0.422333	+	0.109232i
$987$	1.33759e8	+	4.63436e7i	0.139114	+	0.0481990i
$988$	4.29427e8	−	7.74636e8i	0.445265	−	0.803206i
$989$			1.40815e9i			1.45566i
$990$	−6.35818e8	+	8.12192e7i	−0.655281	+	0.0837054i
$991$			1.48888e8i			0.152982i	0.997070	+	0.0764909i	$0.0243716\pi$
$991$			1.48888e8i			0.152982i	−0.997070	+	0.0764909i	$0.975628\pi$
$992$	−1.35131e7	−	4.28728e7i	−0.0138427	−	0.0439184i
$993$	1.59108e8	+	8.26986e8i	0.162496	+	0.844599i
$994$	1.02319e7	−	3.95605e7i	0.0104183	−	0.0402812i
$995$	−4.84324e8	−	8.38875e8i	−0.491663	−	0.851585i
$996$	−7.24303e8	−	8.07587e8i	−0.733065	−	0.817356i
$997$	−1.59219e9	−	9.19252e8i	−1.60661	−	0.927575i	−0.990122	−	0.140208i	$-0.955223\pi$
$997$	−1.59219e9	−	9.19252e8i	−1.60661	−	0.927575i	−0.616485	−	0.787367i	$-0.711444\pi$
$998$	9.30540e8	+	9.14474e8i	0.936145	+	0.919983i
$999$	−1.23851e9	+	7.94222e8i	−1.24223	+	0.796609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.p.b.43.7	✓	136
8.3	odd	2	inner	72.7.p.b.43.41	yes	136
9.4	even	3	inner	72.7.p.b.67.41	yes	136
72.67	odd	6	inner	72.7.p.b.67.7	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.p.b.43.7	✓	136	1.1	even	1	trivial
72.7.p.b.43.41	yes	136	8.3	odd	2	inner
72.7.p.b.67.7	yes	136	72.67	odd	6	inner
72.7.p.b.67.41	yes	136	9.4	even	3	inner

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.70909 + 2.13776i) q^{2} +(-20.4110 + 17.6746i) q^{3} +(54.8600 - 32.9603i) q^{4} +(-67.6940 + 39.0831i) q^{5} +(119.566 - 179.888i) q^{6} +(139.025 + 80.2661i) q^{7} +(-352.459 + 371.371i) q^{8} +(104.220 - 721.512i) q^{9} +O(q^{10})\)	\(q+(-7.70909 + 2.13776i) q^{2} +(-20.4110 + 17.6746i) q^{3} +(54.8600 - 32.9603i) q^{4} +(-67.6940 + 39.0831i) q^{5} +(119.566 - 179.888i) q^{6} +(139.025 + 80.2661i) q^{7} +(-352.459 + 371.371i) q^{8} +(104.220 - 721.512i) q^{9} +(438.308 - 446.009i) q^{10} +(703.041 - 1217.70i) q^{11} +(-537.190 + 1642.38i) q^{12} +(1657.51 - 956.964i) q^{13} +(-1243.35 - 321.577i) q^{14} +(690.927 - 1994.19i) q^{15} +(1923.24 - 3616.40i) q^{16} -2071.65 q^{17} +(738.973 + 5784.99i) q^{18} +7230.73 q^{19} +(-2425.50 + 4375.32i) q^{20} +(-4256.31 + 818.891i) q^{21} +(-2816.65 + 10890.3i) q^{22} +(-13079.0 + 7551.16i) q^{23} +(630.239 - 13809.6i) q^{24} +(-4757.52 + 8240.26i) q^{25} +(-10732.1 + 10920.7i) q^{26} +(10625.2 + 16568.8i) q^{27} +(10272.5 - 178.907i) q^{28} +(21851.0 + 12615.7i) q^{29} +(-1063.33 + 16850.4i) q^{30} +(-1188.04 + 685.913i) q^{31} +(-7095.41 + 31990.6i) q^{32} +(7172.56 + 37280.5i) q^{33} +(15970.5 - 4428.68i) q^{34} -12548.2 q^{35} +(-18063.7 - 43017.3i) q^{36} +74749.2i q^{37} +(-55742.3 + 15457.5i) q^{38} +(-16917.6 + 48828.4i) q^{39} +(9345.03 - 38914.8i) q^{40} +(11098.3 + 19222.8i) q^{41} +(31061.7 - 15411.9i) q^{42} +(46620.4 - 80748.9i) q^{43} +(-1567.02 - 89975.6i) q^{44} +(21143.9 + 52915.3i) q^{45} +(84684.5 - 86172.2i) q^{46} +(-28284.3 - 16329.9i) q^{47} +(24663.1 + 107807. i) q^{48} +(-45939.2 - 79569.0i) q^{49} +(19060.4 - 73695.3i) q^{50} +(42284.5 - 36615.4i) q^{51} +(59389.2 - 107131. i) q^{52} +197801. i q^{53} +(-117330. - 105017. i) q^{54} +109908. i q^{55} +(-78809.2 + 23339.3i) q^{56} +(-147587. + 127800. i) q^{57} +(-195420. - 50543.2i) q^{58} +(-18443.5 - 31945.0i) q^{59} +(-27824.8 - 132174. i) q^{60} +(252653. + 145869. i) q^{61} +(7692.36 - 7827.49i) q^{62} +(72402.2 - 91942.8i) q^{63} +(-13688.9 - 261786. i) q^{64} +(-74802.3 + 129561. i) q^{65} +(-134991. - 272065. i) q^{66} +(-137226. - 237682. i) q^{67} +(-113651. + 68282.1i) q^{68} +(133492. - 385292. i) q^{69} +(96735.2 - 26825.0i) q^{70} +31817.8i q^{71} +(231215. + 293008. i) q^{72} +499108. q^{73} +(-159796. - 576248. i) q^{74} +(-48537.1 - 252279. i) q^{75} +(396678. - 238327. i) q^{76} +(195481. - 112861. i) q^{77} +(26035.9 - 412588. i) q^{78} +(452567. + 261290. i) q^{79} +(11148.8 + 319975. i) q^{80} +(-509717. - 150392. i) q^{81} +(-126652. - 124465. i) q^{82} +(-313892. + 543676. i) q^{83} +(-206510. + 185214. i) q^{84} +(140238. - 80966.5i) q^{85} +(-186779. + 722163. i) q^{86} +(-668978. + 128708. i) q^{87} +(204426. + 690280. i) q^{88} +499277. q^{89} +(-276120. - 362728. i) q^{90} +307247. q^{91} +(-468625. + 845344. i) q^{92} +(12125.8 - 34998.2i) q^{93} +(252955. + 65424.0i) q^{94} +(-489477. + 282600. i) q^{95} +(-420595. - 778369. i) q^{96} +(-573043. + 992540. i) q^{97} +(524248. + 515198. i) q^{98} +(-805315. - 634161. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more