LMFDB - Embedded newform 627.2.bo.b.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(4,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([0, 18, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("627.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.bo (of order $45$, degree $24$, 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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$20$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	627.4
Dual form			627.2.bo.b.157.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35368 - 2.00692i) q^{2} +(0.990268 + 0.139173i) q^{3} +(-1.44604 + 3.57908i) q^{4} +(-0.344111 + 1.38016i) q^{5} +(-1.06120 - 2.17578i) q^{6} +(0.142915 + 0.0303776i) q^{7} +(4.40463 - 0.936234i) q^{8} +(0.961262 + 0.275637i) q^{9} +(3.23567 - 1.17769i) q^{10} +(1.85052 - 2.75238i) q^{11} +(-1.93008 + 3.34300i) q^{12} +(-3.90816 + 3.77406i) q^{13} +(-0.132496 - 0.327940i) q^{14} +(-0.532843 + 1.31883i) q^{15} +(-2.28788 - 2.20938i) q^{16} +(-4.54624 + 1.30361i) q^{17} +(-0.748061 - 2.30230i) q^{18} +(-1.74467 + 3.99451i) q^{19} +(-4.44209 - 3.22737i) q^{20} +(0.137297 + 0.0499719i) q^{21} +(-8.02880 + 0.0120100i) q^{22} +(3.30947 + 2.77698i) q^{23} +(4.49207 - 0.314116i) q^{24} +(2.62832 + 1.39750i) q^{25} +(12.8646 + 2.73446i) q^{26} +(0.913545 + 0.406737i) q^{27} +(-0.315385 + 0.467578i) q^{28} +(1.68590 + 2.15785i) q^{29} +(3.36809 - 0.715909i) q^{30} +(-0.681549 + 0.303445i) q^{31} +(0.226912 - 1.28688i) q^{32} +(2.21557 - 2.46805i) q^{33} +(8.77040 + 7.35924i) q^{34} +(-0.0911046 + 0.186792i) q^{35} +(-2.37655 + 3.04185i) q^{36} +(3.49952 + 10.7704i) q^{37} +(10.3784 - 1.90590i) q^{38} +(-4.39537 + 3.19342i) q^{39} +(-0.223537 + 6.40125i) q^{40} +(4.81834 + 0.677174i) q^{41} +(-0.0855666 - 0.343189i) q^{42} +(-2.87533 + 2.41269i) q^{43} +(7.17505 + 10.6032i) q^{44} +(-0.711204 + 1.23184i) q^{45} +(1.09319 - 10.4010i) q^{46} +(-0.350869 - 10.0476i) q^{47} +(-1.95813 - 2.50629i) q^{48} +(-6.37532 - 2.83847i) q^{49} +(-0.753239 - 7.16659i) q^{50} +(-4.68342 + 0.658212i) q^{51} +(-7.85631 - 19.4451i) q^{52} +(3.24252 + 13.0050i) q^{53} +(-0.420364 - 2.38400i) q^{54} +(3.16193 + 3.50113i) q^{55} +0.657930 q^{56} +(-2.28362 + 3.71283i) q^{57} +(2.04845 - 6.30449i) q^{58} +(-0.241031 + 6.90224i) q^{59} +(-3.94970 - 3.81418i) q^{60} +(-0.0187411 - 0.00131050i) q^{61} +(1.53159 + 0.957043i) q^{62} +(0.129006 + 0.0685936i) q^{63} +(-8.70093 + 3.87390i) q^{64} +(-3.86395 - 6.69256i) q^{65} +(-7.95234 - 1.10550i) q^{66} +(7.70784 - 2.80543i) q^{67} +(1.90832 - 18.1564i) q^{68} +(2.89078 + 3.21054i) q^{69} +(0.498202 - 0.0700178i) q^{70} +(2.48030 - 9.94794i) q^{71} +(4.49207 + 0.314116i) q^{72} +(-9.21169 + 4.89794i) q^{73} +(16.8781 - 21.6029i) q^{74} +(2.40825 + 1.74969i) q^{75} +(-11.7738 - 12.0205i) q^{76} +(0.348078 - 0.337142i) q^{77} +(12.3589 + 4.49826i) q^{78} +(0.473880 - 0.971598i) q^{79} +(3.83657 - 2.39736i) q^{80} +(0.848048 + 0.529919i) q^{81} +(-5.16347 - 10.5867i) q^{82} +(-0.697777 - 6.63890i) q^{83} +(-0.377390 + 0.419134i) q^{84} +(-0.234776 - 6.72311i) q^{85} +(8.73436 + 2.50454i) q^{86} +(1.36917 + 2.37148i) q^{87} +(5.57399 - 13.8557i) q^{88} +(-0.0203437 + 0.115375i) q^{89} +(3.43494 - 0.240195i) q^{90} +(-0.673182 + 0.420651i) q^{91} +(-14.7247 + 7.82924i) q^{92} +(-0.717147 + 0.205639i) q^{93} +(-19.6897 + 14.3054i) q^{94} +(-4.91269 - 3.78247i) q^{95} +(0.403802 - 1.24278i) q^{96} +(1.40334 + 2.08054i) q^{97} +(2.93357 + 16.6371i) q^{98} +(2.53749 - 2.13568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 18 q^{5} + 3 q^{7} + 12 q^{10} + 3 q^{11} - 240 q^{12} + 42 q^{14} - 12 q^{15} + 72 q^{16} - 18 q^{17} - 102 q^{20} + 24 q^{22} + 54 q^{23} - 18 q^{25} - 12 q^{26} + 60 q^{27} + 36 q^{29} + 12 q^{30}+ \cdots - 6 q^{99}+O(q^{100}) $ 480 * q + 18 * q^5 + 3 * q^7 + 12 * q^10 + 3 * q^11 - 240 * q^12 + 42 * q^14 - 12 * q^15 + 72 * q^16 - 18 * q^17 - 102 * q^20 + 24 * q^22 + 54 * q^23 - 18 * q^25 - 12 * q^26 + 60 * q^27 + 36 * q^29 + 12 * q^30 + 60 * q^31 - 30 * q^32 - 21 * q^33 - 84 * q^34 + 12 * q^35 + 36 * q^37 - 90 * q^38 - 12 * q^39 + 300 * q^40 - 63 * q^41 - 18 * q^42 - 24 * q^43 - 15 * q^44 + 6 * q^45 - 6 * q^46 + 24 * q^48 + 39 * q^49 + 12 * q^51 - 21 * q^52 + 9 * q^53 + 45 * q^55 + 156 * q^56 + 30 * q^57 + 12 * q^58 - 69 * q^59 - 36 * q^60 + 12 * q^61 - 90 * q^62 + 60 * q^64 - 66 * q^65 + 30 * q^66 + 72 * q^67 + 24 * q^68 + 18 * q^69 - 96 * q^70 + 72 * q^71 + 18 * q^73 + 57 * q^74 - 102 * q^75 + 48 * q^76 - 114 * q^77 - 216 * q^78 - 24 * q^79 - 30 * q^80 - 24 * q^82 + 78 * q^83 - 36 * q^84 - 36 * q^85 - 189 * q^86 - 24 * q^87 + 120 * q^88 - 318 * q^89 - 18 * q^90 - 48 * q^91 + 354 * q^92 + 12 * q^93 - 282 * q^94 + 6 * q^95 + 60 * q^96 + 120 * q^97 - 96 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−1.35368	−	2.00692i	−0.957197	−	1.41910i	−0.907364	−	0.420346i	$-0.861909\pi$
$2$	−1.35368	−	2.00692i	−0.957197	−	1.41910i	−0.0498333	−	0.998758i	$-0.515869\pi$
$3$	0.990268	+	0.139173i	0.571732	+	0.0803516i
$3$	0.990268	+	0.139173i	0.571732	+	0.0803516i
$4$	−1.44604	+	3.57908i	−0.723021	+	1.78954i
$5$	−0.344111	+	1.38016i	−0.153891	+	0.617224i	0.842963	+	0.537971i	$0.180809\pi$
$5$	−0.344111	+	1.38016i	−0.153891	+	0.617224i	−0.996855	+	0.0792532i	$0.974746\pi$
$6$	−1.06120	−	2.17578i	−0.433233	−	0.888258i
$7$	0.142915	+	0.0303776i	0.0540169	+	0.0114816i	0.234841	−	0.972034i	$-0.424543\pi$
$7$	0.142915	+	0.0303776i	0.0540169	+	0.0114816i	−0.180824	+	0.983515i	$0.557876\pi$
$8$	4.40463	−	0.936234i	1.55727	−	0.331009i
$9$	0.961262	+	0.275637i	0.320421	+	0.0918791i
$10$	3.23567	−	1.17769i	1.02321	−	0.372418i
$11$	1.85052	−	2.75238i	0.557952	−	0.829873i
$11$	1.85052	−	2.75238i	0.557952	−	0.829873i
$12$	−1.93008	+	3.34300i	−0.557166	+	0.965040i
$13$	−3.90816	+	3.77406i	−1.08393	+	1.04674i	−0.0851970	+	0.996364i	$0.527152\pi$
$13$	−3.90816	+	3.77406i	−1.08393	+	1.04674i	−0.998731	+	0.0503725i	$0.983959\pi$
$14$	−0.132496	−	0.327940i	−0.0354112	−	0.0876457i
$15$	−0.532843	+	1.31883i	−0.137580	+	0.340521i
$16$	−2.28788	−	2.20938i	−0.571970	−	0.552345i
$17$	−4.54624	+	1.30361i	−1.10262	+	0.316173i	−0.777110	−	0.629364i	$-0.783315\pi$
$17$	−4.54624	+	1.30361i	−1.10262	+	0.316173i	−0.325515	+	0.945537i	$0.605538\pi$
$18$	−0.748061	−	2.30230i	−0.176320	−	0.542656i
$19$	−1.74467	+	3.99451i	−0.400254	+	0.916404i
$19$	−1.74467	+	3.99451i	−0.400254	+	0.916404i
$20$	−4.44209	−	3.22737i	−0.993281	−	0.721661i
$21$	0.137297	+	0.0499719i	0.0299606	+	0.0109048i
$22$	−8.02880	+	0.0120100i	−1.71175	+	0.00256054i
$23$	3.30947	+	2.77698i	0.690072	+	0.579039i	0.918930	−	0.394420i	$-0.129055\pi$
$23$	3.30947	+	2.77698i	0.690072	+	0.579039i	−0.228858	+	0.973460i	$0.573499\pi$
$24$	4.49207	−	0.314116i	0.916939	−	0.0641187i
$25$	2.62832	+	1.39750i	0.525664	+	0.279501i
$26$	12.8646	+	2.73446i	2.52296	+	0.536272i
$27$	0.913545	+	0.406737i	0.175812	+	0.0782765i
$28$	−0.315385	+	0.467578i	−0.0596022	+	0.0883639i
$29$	1.68590	+	2.15785i	0.313063	+	0.400702i	0.918647	−	0.395079i	$-0.129283\pi$
$29$	1.68590	+	2.15785i	0.313063	+	0.400702i	−0.605584	+	0.795781i	$0.707061\pi$
$30$	3.36809	−	0.715909i	0.614926	−	0.130706i
$31$	−0.681549	+	0.303445i	−0.122410	+	0.0545004i	−0.467028	−	0.884243i	$-0.654675\pi$
$31$	−0.681549	+	0.303445i	−0.122410	+	0.0545004i	0.344618	+	0.938743i	$0.388008\pi$
$32$	0.226912	−	1.28688i	0.0401127	−	0.227490i
$33$	2.21557	−	2.46805i	0.385680	−	0.429632i
$34$	8.77040	+	7.35924i	1.50411	+	1.26210i
$35$	−0.0911046	+	0.186792i	−0.0153995	+	0.0315736i
$36$	−2.37655	+	3.04185i	−0.396092	+	0.506975i
$37$	3.49952	+	10.7704i	0.575317	+	1.77064i	0.635097	+	0.772432i	$0.280960\pi$
$37$	3.49952	+	10.7704i	0.575317	+	1.77064i	−0.0597800	+	0.998212i	$0.519040\pi$
$38$	10.3784	−	1.90590i	1.68359	−	0.309179i
$39$	−4.39537	+	3.19342i	−0.703823	+	0.511357i
$40$	−0.223537	+	6.40125i	−0.0353442	+	1.01213i
$41$	4.81834	+	0.677174i	0.752499	+	0.105757i	0.504986	−	0.863128i	$-0.331498\pi$
$41$	4.81834	+	0.677174i	0.752499	+	0.105757i	0.247513	+	0.968885i	$0.420387\pi$
$42$	−0.0855666	−	0.343189i	−0.0132032	−	0.0529552i
$43$	−2.87533	+	2.41269i	−0.438484	+	0.367932i	−0.835142	−	0.550035i	$-0.814615\pi$
$43$	−2.87533	+	2.41269i	−0.438484	+	0.367932i	0.396657	+	0.917967i	$0.370170\pi$
$44$	7.17505	+	10.6032i	1.08168	+	1.59849i
$45$	−0.711204	+	1.23184i	−0.106020	+	0.183632i
$46$	1.09319	−	10.4010i	0.161181	−	1.53354i
$47$	−0.350869	−	10.0476i	−0.0511795	−	1.46559i	−0.705144	−	0.709064i	$-0.749118\pi$
$47$	−0.350869	−	10.0476i	−0.0511795	−	1.46559i	0.653964	−	0.756525i	$-0.273105\pi$
$48$	−1.95813	−	2.50629i	−0.282631	−	0.361751i
$49$	−6.37532	−	2.83847i	−0.910759	−	0.405496i
$50$	−0.753239	−	7.16659i	−0.106524	−	1.01351i
$51$	−4.68342	+	0.658212i	−0.655810	+	0.0921681i
$52$	−7.85631	−	19.4451i	−1.08947	−	2.69654i
$53$	3.24252	+	13.0050i	0.445394	+	1.78638i	0.601758	+	0.798679i	$0.294467\pi$
$53$	3.24252	+	13.0050i	0.445394	+	1.78638i	−0.156364	+	0.987700i	$0.549977\pi$
$54$	−0.420364	−	2.38400i	−0.0572042	−	0.324421i
$55$	3.16193	+	3.50113i	0.426354	+	0.472092i
$56$	0.657930			0.0879196
$57$	−2.28362	+	3.71283i	−0.302472	+	0.491776i
$58$	2.04845	−	6.30449i	0.268975	−	0.827820i
$59$	−0.241031	+	6.90224i	−0.0313796	+	0.898595i	0.877011	+	0.480471i	$0.159534\pi$
$59$	−0.241031	+	6.90224i	−0.0313796	+	0.898595i	−0.908390	+	0.418124i	$0.862688\pi$
$60$	−3.94970	−	3.81418i	−0.509903	−	0.492408i
$61$	−0.0187411	−	0.00131050i	−0.00239955	−	0.000167793i	0.0685566	−	0.997647i	$-0.478161\pi$
$61$	−0.0187411	−	0.00131050i	−0.00239955	−	0.000167793i	−0.0709562	+	0.997479i	$0.522605\pi$
$62$	1.53159	+	0.957043i	0.194512	+	0.121545i
$63$	0.129006	+	0.0685936i	0.0162532	+	0.00864198i
$64$	−8.70093	+	3.87390i	−1.08762	+	0.484238i
$65$	−3.86395	−	6.69256i	−0.479264	−	0.830110i
$66$	−7.95234	−	1.10550i	−0.978865	−	0.136078i
$67$	7.70784	−	2.80543i	0.941663	−	0.342737i	0.174841	−	0.984597i	$-0.444059\pi$
$67$	7.70784	−	2.80543i	0.941663	−	0.342737i	0.766822	+	0.641859i	$0.221837\pi$
$68$	1.90832	−	18.1564i	0.231418	−	2.20179i
$69$	2.89078	+	3.21054i	0.348009	+	0.386504i
$70$	0.498202	−	0.0700178i	0.0595466	−	0.00836872i
$71$	2.48030	−	9.94794i	0.294358	−	1.18060i	−0.622898	−	0.782303i	$-0.714045\pi$
$71$	2.48030	−	9.94794i	0.294358	−	1.18060i	0.917255	−	0.398300i	$-0.130400\pi$
$72$	4.49207	+	0.314116i	0.529395	+	0.0370189i
$73$	−9.21169	+	4.89794i	−1.07815	+	0.573261i	−0.910889	−	0.412653i	$-0.864602\pi$
$73$	−9.21169	+	4.89794i	−1.07815	+	0.573261i	−0.167258	+	0.985913i	$0.553491\pi$
$74$	16.8781	−	21.6029i	1.96203	−	2.51129i
$75$	2.40825	+	1.74969i	0.278080	+	0.202037i
$76$	−11.7738	−	12.0205i	−1.35055	−	1.37885i
$77$	0.348078	−	0.337142i	0.0396671	−	0.0384210i
$78$	12.3589	+	4.49826i	1.39937	+	0.509327i
$79$	0.473880	−	0.971598i	0.0533157	−	0.109313i	−0.870473	−	0.492216i	$-0.836187\pi$
$79$	0.473880	−	0.971598i	0.0533157	−	0.109313i	0.923788	+	0.382903i	$0.125076\pi$
$80$	3.83657	−	2.39736i	0.428942	−	0.268033i
$81$	0.848048	+	0.529919i	0.0942276	+	0.0588799i
$82$	−5.16347	−	10.5867i	−0.570210	−	1.16910i
$83$	−0.697777	−	6.63890i	−0.0765910	−	0.728714i	−0.963670	−	0.267096i	$-0.913936\pi$
$83$	−0.697777	−	6.63890i	−0.0765910	−	0.728714i	0.887079	−	0.461618i	$-0.152731\pi$
$84$	−0.377390	+	0.419134i	−0.0411766	+	0.0457313i
$85$	−0.234776	−	6.72311i	−0.0254650	−	0.729223i
$86$	8.73436	+	2.50454i	0.941850	+	0.270071i
$87$	1.36917	+	2.37148i	0.146791	+	0.254249i
$88$	5.57399	−	13.8557i	0.594189	−	1.47703i
$89$	−0.0203437	+	0.115375i	−0.00215642	+	0.0122297i	−0.985867	−	0.167530i	$-0.946421\pi$
$89$	−0.0203437	+	0.115375i	−0.00215642	+	0.0122297i	0.983711	+	0.179760i	$0.0575320\pi$
$90$	3.43494	−	0.240195i	0.362075	−	0.0253187i
$91$	−0.673182	+	0.420651i	−0.0705686	+	0.0440962i
$92$	−14.7247	+	7.82924i	−1.53515	+	0.816254i
$93$	−0.717147	+	0.205639i	−0.0743647	+	0.0213237i
$94$	−19.6897	+	14.3054i	−2.03083	+	1.47549i
$95$	−4.91269	−	3.78247i	−0.504032	−	0.388073i
$96$	0.403802	−	1.24278i	0.0412129	−	0.126840i
$97$	1.40334	+	2.08054i	0.142488	+	0.211247i	0.893526	−	0.449012i	$-0.148224\pi$
$97$	1.40334	+	2.08054i	0.142488	+	0.211247i	−0.751038	+	0.660260i	$0.770446\pi$
$98$	2.93357	+	16.6371i	0.296335	+	1.68060i
$99$	2.53749	−	2.13568i	0.255027	−	0.214644i
$100$	−8.80244	+	7.38612i	−0.880244	+	0.738612i
$101$	0.580765	−	0.560839i	0.0577883	−	0.0558055i	−0.665204	−	0.746662i	$-0.731655\pi$
$101$	0.580765	−	0.560839i	0.0577883	−	0.0558055i	0.722992	+	0.690857i	$0.242766\pi$
$102$	7.66084	+	8.50822i	0.758536	+	0.842440i
$103$	3.34500	−	3.71499i	0.329592	−	0.366049i	−0.555458	−	0.831545i	$-0.687457\pi$
$103$	3.34500	−	3.71499i	0.329592	−	0.366049i	0.885050	+	0.465495i	$0.154124\pi$
$104$	−13.6806	+	20.2823i	−1.34149	+	1.98884i
$105$	−0.116214	+	0.172295i	−0.0113414	+	0.0168143i
$106$	21.7107	−	24.1121i	2.10873	−	2.34198i
$107$	0.836331	+	0.928840i	0.0808512	+	0.0897943i	0.782213	−	0.623011i	$-0.214091\pi$
$107$	0.836331	+	0.928840i	0.0808512	+	0.0897943i	−0.701362	+	0.712805i	$0.747424\pi$
$108$	−2.77677	+	2.68149i	−0.267195	+	0.258027i
$109$	11.5292	−	9.67414i	1.10430	−	0.926614i	0.106589	−	0.994303i	$-0.466007\pi$
$109$	11.5292	−	9.67414i	1.10430	−	0.926614i	0.997706	+	0.0676889i	$0.0215625\pi$
$110$	2.74623	−	11.0851i	0.261842	−	1.05693i
$111$	1.96651	+	11.1526i	0.186653	+	1.05856i
$112$	−0.259857	−	0.385254i	−0.0245542	−	0.0364031i
$113$	−0.587609	+	1.80847i	−0.0552776	+	0.170127i	−0.974884	−	0.222715i	$-0.928508\pi$
$113$	−0.587609	+	1.80847i	−0.0552776	+	0.170127i	0.919606	+	0.392842i	$0.128508\pi$
$114$	10.5426	−	0.442966i	0.987407	−	0.0414876i
$115$	−4.97149	+	3.61200i	−0.463593	+	0.336820i
$116$	−10.1610	+	2.91362i	−0.943424	+	0.270522i
$117$	−4.79703	+	2.55063i	−0.443486	+	0.235806i
$118$	14.1785	−	8.85970i	1.30524	−	0.815602i
$119$	−0.689327	+	0.0482025i	−0.0631905	+	0.00441871i
$120$	−1.11224	+	6.30784i	−0.101533	+	0.575825i
$121$	−4.15117	−	10.1866i	−0.377379	−	0.926059i
$122$	0.0227394	+	0.0393857i	0.00205873	+	0.00356582i
$123$	4.67721	+	1.34117i	0.421729	+	0.120929i
$124$	−0.100506	−	2.87811i	−0.00902570	−	0.258462i
$125$	−7.59209	+	8.43187i	−0.679057	+	0.754169i
$126$	−0.0369712	−	0.351757i	−0.00329366	−	0.0313370i
$127$	7.89434	+	16.1858i	0.700509	+	1.43626i	0.890738	+	0.454517i	$0.150188\pi$
$127$	7.89434	+	16.1858i	0.700509	+	1.43626i	−0.190229	+	0.981740i	$0.560923\pi$
$128$	17.3365	+	10.8331i	1.53235	+	0.957518i
$129$	−3.18313	+	1.98904i	−0.280259	+	0.175125i
$130$	−8.20084	+	16.8142i	−0.719262	+	1.47470i
$131$	−15.8377	−	5.76444i	−1.38374	−	0.503641i	−0.460432	−	0.887695i	$-0.652305\pi$
$131$	−15.8377	−	5.76444i	−1.38374	−	0.503641i	−0.923311	+	0.384054i	$0.874528\pi$
$132$	5.62954	+	11.4986i	0.489989	+	1.00082i
$133$	−0.370683	+	0.517878i	−0.0321423	+	0.0449057i
$134$	−16.0642	−	11.6713i	−1.38774	−	1.00825i
$135$	−0.875721	+	1.12087i	−0.0753701	+	0.0964693i
$136$	−18.8040	+	9.99828i	−1.61243	+	0.857346i
$137$	−21.4148	−	1.49747i	−1.82959	−	0.127937i	−0.886975	−	0.461817i	$-0.847198\pi$
$137$	−21.4148	−	1.49747i	−1.82959	−	0.127937i	−0.942616	+	0.333880i	$0.891642\pi$
$138$	2.53008	−	10.1476i	0.215375	−	0.863821i
$139$	17.9330	−	2.52031i	1.52105	−	0.213770i	0.671393	−	0.741101i	$-0.265696\pi$
$139$	17.9330	−	2.52031i	1.52105	−	0.213770i	0.849660	+	0.527331i	$0.176807\pi$
$140$	−0.536802	−	0.596180i	−0.0453681	−	0.0503864i
$141$	1.05090	−	9.99862i	0.0885016	−	0.842036i
$142$	−23.3222	+	8.48859i	−1.95716	+	0.712347i
$143$	3.15553	+	17.7407i	0.263879	+	1.48355i
$144$	−1.59026	−	2.75442i	−0.132522	−	0.229535i
$145$	−3.55830	+	1.58426i	−0.295501	+	0.131566i
$146$	22.2994	+	11.8568i	1.84551	+	0.981278i
$147$	−5.91823	−	3.69812i	−0.488128	−	0.305016i
$148$	−43.6086	−	3.04941i	−3.58460	−	0.250660i
$149$	−11.2133	−	10.8286i	−0.918630	−	0.887111i	0.0752960	−	0.997161i	$-0.476010\pi$
$149$	−11.2133	−	10.8286i	−0.918630	−	0.887111i	−0.993926	+	0.110051i	$0.964899\pi$
$150$	0.251488	−	7.20168i	0.0205339	−	0.588014i
$151$	−2.43888	+	7.50609i	−0.198473	+	0.610837i	0.801445	+	0.598068i	$0.204065\pi$
$151$	−2.43888	+	7.50609i	−0.198473	+	0.610837i	−0.999918	+	0.0127692i	$0.995935\pi$
$152$	−3.94481	+	19.2278i	−0.319967	+	1.55958i
$153$	−4.72945			−0.382353
$154$	−1.14780	−	0.242179i	−0.0924926	−	0.0195153i
$155$	−0.184273	−	1.04506i	−0.0148011	−	0.0839414i
$156$	−5.07363	−	20.3492i	−0.406215	−	1.62924i
$157$	1.60655	+	3.97635i	0.128217	+	0.317347i	0.977614	−	0.210407i	$-0.0674788\pi$
$157$	1.60655	+	3.97635i	0.128217	+	0.317347i	−0.849397	+	0.527754i	$0.823034\pi$
$158$	−2.59140	+	0.364197i	−0.206160	+	0.0289740i
$159$	1.40101	+	13.3297i	0.111107	+	1.05712i
$160$	1.69801	+	0.756004i	0.134240	+	0.0597673i
$161$	0.388616	+	0.497406i	0.0306272	+	0.0392011i
$162$	−0.0844839	−	2.41930i	−0.00663768	−	0.190078i
$163$	0.584115	−	5.55749i	0.0457514	−	0.435296i	−0.947538	−	0.319643i	$-0.896437\pi$
$163$	0.584115	−	5.55749i	0.0457514	−	0.435296i	0.993290	−	0.115653i	$-0.0368962\pi$
$164$	−9.39118	+	16.2660i	−0.733328	+	1.27016i
$165$	2.64389	+	3.90711i	0.205827	+	0.304168i
$166$	−12.3791	+	10.3873i	−0.960808	+	0.806214i
$167$	5.19799	+	20.8480i	0.402233	+	1.61327i	0.740390	+	0.672177i	$0.234641\pi$
$167$	5.19799	+	20.8480i	0.402233	+	1.61327i	−0.338158	+	0.941089i	$0.609804\pi$
$168$	0.651527	+	0.0915661i	0.0502664	+	0.00706448i
$169$	0.576443	−	16.5072i	0.0443418	−	1.26978i
$170$	−13.1749	+	9.57212i	−1.01047	+	0.734148i
$171$	−2.77812	+	3.35888i	−0.212448	+	0.256860i
$172$	−4.47736	−	13.7799i	−0.341396	−	1.05071i
$173$	0.585547	−	0.749466i	0.0445183	−	0.0569808i	−0.765236	−	0.643749i	$-0.777378\pi$
$173$	0.585547	−	0.749466i	0.0445183	−	0.0569808i	0.809755	+	0.586769i	$0.199600\pi$
$174$	2.90593	−	5.95804i	0.220298	−	0.451678i
$175$	0.333174	+	0.279566i	0.0251856	+	0.0211332i
$176$	−10.3148	+	2.20861i	−0.777508	+	0.166480i
$177$	−1.19929	+	6.80152i	−0.0901443	+	0.511234i
$178$	0.259086	−	0.115352i	0.0194193	−	0.00864603i
$179$	−14.4149	+	3.06399i	−1.07742	+	0.229013i	−0.712249	−	0.701927i	$-0.752323\pi$
$179$	−14.4149	+	3.06399i	−1.07742	+	0.229013i	−0.365173	+	0.930940i	$0.618990\pi$
$180$	−3.38043	−	4.32675i	−0.251962	−	0.322497i
$181$	7.92880	−	11.7549i	0.589343	−	0.873737i	−0.409920	−	0.912122i	$-0.634443\pi$
$181$	7.92880	−	11.7549i	0.589343	−	0.873737i	0.999263	+	0.0383844i	$0.0122211\pi$
$182$	1.75548	+	0.781592i	0.130125	+	0.0579354i
$183$	−0.0183763	−	0.00390600i	−0.00135842	−	0.000288740i
$184$	17.1769	+	9.13312i	1.26630	+	0.673303i
$185$	−16.0691	+	1.12366i	−1.18142	+	0.0826130i
$186$	1.38349	+	1.16088i	0.101442	+	0.0851202i
$187$	−4.82486	+	14.9253i	−0.352829	+	1.09145i
$188$	36.4684	+	13.2734i	2.65973	+	0.968064i
$189$	0.118204	+	0.0858802i	0.00859807	+	0.00624686i
$190$	−0.940872	+	14.9796i	−0.0682580	+	1.08674i
$191$	−5.38329	−	16.5681i	−0.389521	−	1.19882i	−0.933147	−	0.359495i	$-0.882949\pi$
$191$	−5.38329	−	16.5681i	−0.389521	−	1.19882i	0.543626	−	0.839328i	$-0.317051\pi$
$192$	−9.15540	+	2.62527i	−0.660734	+	0.189462i
$193$	10.6197	+	10.2553i	0.764420	+	0.738192i	0.970698	−	0.240301i	$-0.0772463\pi$
$193$	10.6197	+	10.2553i	0.764420	+	0.738192i	−0.206278	+	0.978493i	$0.566135\pi$
$194$	2.27579	−	5.63279i	0.163392	−	0.404411i
$195$	−2.89492	−	7.16519i	−0.207310	−	0.513110i
$196$	19.3781	−	18.7132i	1.38415	−	1.33666i
$197$	−0.659041	+	1.14149i	−0.0469547	+	0.0813279i	−0.888548	−	0.458785i	$-0.848285\pi$
$197$	−0.659041	+	1.14149i	−0.0469547	+	0.0813279i	0.841593	+	0.540112i	$0.181618\pi$
$198$	−7.72109	−	2.20149i	−0.548714	−	0.156453i
$199$	−0.946257	+	0.344409i	−0.0670784	+	0.0244145i	−0.375341	−	0.926887i	$-0.622475\pi$
$199$	−0.946257	+	0.344409i	−0.0670784	+	0.0244145i	0.308263	+	0.951301i	$0.400252\pi$
$200$	12.8852	+	3.69477i	0.911120	+	0.261259i
$201$	8.02327	−	1.70540i	0.565918	−	0.120290i
$202$	−1.91173	−	0.406350i	−0.134509	−	0.0285907i
$203$	0.175390	+	0.359603i	0.0123100	+	0.0252392i
$204$	4.41663	−	17.7141i	0.309226	−	1.24024i
$205$	−2.59265	+	6.41704i	−0.181079	+	0.448185i
$206$	−11.9837	−	1.68420i	−0.834947	−	0.117344i
$207$	2.41583	+	3.58161i	0.167912	+	0.248939i
$208$	17.2797			1.19813
$209$	7.76588	+	12.1939i	0.537177	+	0.843470i
$210$	0.503098			0.0347171
$211$	−4.53134	−	6.71799i	−0.311950	−	0.462485i	0.640159	−	0.768242i	$-0.278868\pi$
$211$	−4.53134	−	6.71799i	−0.311950	−	0.462485i	−0.952110	+	0.305757i	$0.901091\pi$
$212$	−51.2349	−	7.20059i	−3.51882	−	0.494538i
$213$	3.84065	−	9.50594i	0.263157	−	0.651336i
$214$	0.731977	−	2.93580i	0.0500369	−	0.200687i
$215$	−2.34046	−	4.79865i	−0.159618	−	0.327265i
$216$	4.40463	+	0.936234i	0.299697	+	0.0637027i
$217$	−0.106622	+	0.0226631i	−0.00723795	+	0.00153847i
$218$	−35.0220	−	10.0424i	−2.37199	−	0.680157i
$219$	−9.80370	+	3.56826i	−0.662473	+	0.241120i
$220$	−17.1031	+	6.25401i	−1.15309	+	0.421645i
$221$	12.8475	−	22.2525i	0.864216	−	1.49687i
$222$	19.7204	−	19.0437i	1.32354	−	1.27813i
$223$	−3.18163	−	7.87481i	−0.213058	−	0.527336i	0.782374	−	0.622808i	$-0.214008\pi$
$223$	−3.18163	−	7.87481i	−0.213058	−	0.527336i	−0.995432	+	0.0954721i	$0.969564\pi$
$224$	0.0715214	−	0.177022i	0.00477873	−	0.0118278i
$225$	2.14130	+	2.06783i	0.142753	+	0.137855i
$226$	4.42489	−	1.26882i	0.294339	−	0.0844004i
$227$	−2.26704	−	6.97722i	−0.150468	−	0.463094i	0.847205	−	0.531266i	$-0.178283\pi$
$227$	−2.26704	−	6.97722i	−0.150468	−	0.463094i	−0.997674	+	0.0681716i	$0.978283\pi$
$228$	−9.98631	−	13.5421i	−0.661359	−	0.896851i
$229$	9.36206	+	6.80193i	0.618662	+	0.449484i	0.852454	−	0.522802i	$-0.175113\pi$
$229$	9.36206	+	6.80193i	0.618662	+	0.449484i	−0.233792	+	0.972287i	$0.575113\pi$
$230$	13.9788	+	5.08786i	0.921733	+	0.335483i
$231$	0.391611	−	0.285418i	0.0257661	−	0.0187792i
$232$	9.44601	+	7.92614i	0.620161	+	0.520377i
$233$	7.35635	−	0.514406i	0.481931	−	0.0336999i	0.173275	−	0.984874i	$-0.444565\pi$
$233$	7.35635	−	0.514406i	0.481931	−	0.0336999i	0.308656	+	0.951174i	$0.400121\pi$
$234$	11.6125	+	6.17450i	0.759136	+	0.403640i
$235$	13.9880	+	2.97323i	0.912474	+	0.193952i
$236$	−24.3551	−	10.8436i	−1.58538	−	0.705858i
$237$	0.604488	−	0.896191i	0.0392657	−	0.0582139i
$238$	1.02987	+	1.31817i	0.0667564	+	0.0854443i
$239$	23.2681	−	4.94578i	1.50509	−	0.319916i	0.619724	−	0.784819i	$-0.287244\pi$
$239$	23.2681	−	4.94578i	1.50509	−	0.319916i	0.885361	+	0.464904i	$0.153911\pi$
$240$	4.13288	−	1.84008i	0.266776	−	0.118776i
$241$	3.38223	−	19.1816i	0.217868	−	1.23559i	−0.657990	−	0.753026i	$-0.728593\pi$
$241$	3.38223	−	19.1816i	0.217868	−	1.23559i	0.875859	−	0.482567i	$-0.160296\pi$
$242$	−14.8244	+	22.1205i	−0.952947	+	1.42196i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	0.0317908	−	0.0651807i	0.00203520	−	0.00417277i
$245$	6.11136	−	7.82218i	0.390440	−	0.499741i
$246$	−3.63984	−	11.2023i	−0.232068	−	0.714231i
$247$	−8.25712	−	22.1957i	−0.525388	−	1.41228i
$248$	−2.71788	+	1.97465i	−0.172585	+	0.125391i
$249$	0.232971	−	6.67141i	0.0147639	−	0.422783i
$250$	27.1993	+	3.82261i	1.72024	+	0.241763i
$251$	3.02888	+	12.1482i	0.191181	+	0.766787i	0.986929	+	0.161158i	$0.0515228\pi$
$251$	3.02888	+	12.1482i	0.191181	+	0.766787i	−0.795747	+	0.605629i	$0.792922\pi$
$252$	−0.432050	+	0.362533i	−0.0272166	+	0.0228374i
$253$	13.7675	−	3.97007i	0.865557	−	0.249596i
$254$	21.7971	−	37.7537i	1.36767	−	2.36888i
$255$	0.703184	−	6.69035i	0.0440351	−	0.418966i
$256$	−1.06230	−	30.4204i	−0.0663940	−	1.90127i
$257$	−4.40889	−	5.64312i	−0.275019	−	0.352008i	0.630594	−	0.776113i	$-0.282811\pi$
$257$	−4.40889	−	5.64312i	−0.275019	−	0.352008i	−0.905613	+	0.424104i	$0.860589\pi$
$258$	8.30079	+	3.69575i	0.516785	+	0.230087i
$259$	0.172956	+	1.64556i	0.0107469	+	0.102250i
$260$	29.5407	−	4.15167i	1.83203	−	0.257476i
$261$	1.02580	+	2.53895i	0.0634956	+	0.157157i
$262$	9.87041	+	39.5880i	0.609796	+	2.44576i
$263$	−1.37488	−	7.79733i	−0.0847787	−	0.480804i	−0.997404	−	0.0720072i	$-0.977060\pi$
$263$	−1.37488	−	7.79733i	−0.0847787	−	0.480804i	0.912625	−	0.408797i	$-0.134052\pi$
$264$	7.44809	−	12.9451i	0.458398	−	0.796719i
$265$	−19.0648			−1.17114
$266$	1.54112	+	0.0428870i	0.0944924	+	0.00262957i
$267$	−0.0362027	+	0.111420i	−0.00221557	+	0.00681882i
$268$	−1.10502	+	31.6438i	−0.0675001	+	1.93295i
$269$	−13.0999	−	12.6504i	−0.798714	−	0.771309i	0.178415	−	0.983955i	$-0.442903\pi$
$269$	−13.0999	−	12.6504i	−0.798714	−	0.771309i	−0.977129	+	0.212646i	$0.931792\pi$
$270$	3.43494	+	0.240195i	0.209044	+	0.0146178i
$271$	−9.21218	−	5.75641i	−0.559600	−	0.349677i	0.220446	−	0.975399i	$-0.429249\pi$
$271$	−9.21218	−	5.75641i	−0.559600	−	0.349677i	−0.780046	+	0.625722i	$0.784804\pi$
$272$	13.2814	+	7.06185i	0.805304	+	0.428188i
$273$	−0.725174	+	0.322868i	−0.0438895	+	0.0195409i
$274$	25.9835	+	45.0048i	1.56972	+	2.71884i
$275$	8.71021	−	4.64803i	0.525245	−	0.280287i
$276$	−15.6710	+	5.70377i	−0.943282	+	0.343326i
$277$	0.0698204	−	0.664297i	0.00419510	−	0.0399137i	−0.992224	−	0.124464i	$-0.960279\pi$
$277$	0.0698204	−	0.664297i	0.00419510	−	0.0399137i	0.996419	+	0.0845506i	$0.0269454\pi$
$278$	−29.3336	−	32.5782i	−1.75931	−	1.95391i
$279$	−0.738788	+	0.103830i	−0.0442301	+	0.00621613i
$280$	−0.226401	+	0.908046i	−0.0135301	+	0.0542661i
$281$	4.95567	+	0.346534i	0.295630	+	0.0206725i	0.216802	−	0.976216i	$-0.430438\pi$
$281$	4.95567	+	0.346534i	0.295630	+	0.0206725i	0.0788287	+	0.996888i	$0.474882\pi$
$282$	−21.4890	+	11.4259i	−1.27965	+	0.680402i
$283$	−18.5021	+	23.6816i	−1.09983	+	1.40772i	−0.195602	+	0.980683i	$0.562666\pi$
$283$	−18.5021	+	23.6816i	−1.09983	+	1.40772i	−0.904233	+	0.427040i	$0.859556\pi$
$284$	32.0179	+	23.2623i	1.89991	+	1.38037i
$285$	−4.33846	−	4.42937i	−0.256988	−	0.262373i
$286$	31.3325	−	30.3481i	1.85273	−	1.79452i
$287$	0.668044	+	0.243148i	0.0394334	+	0.0143526i
$288$	0.572834	−	1.17448i	0.0337545	−	0.0692071i
$289$	4.55207	−	2.84445i	0.267769	−	0.167320i
$290$	7.99628	+	4.99663i	0.469558	+	0.293412i
$291$	1.10013	+	2.25560i	0.0644909	+	0.132226i
$292$	−4.20963	−	40.0520i	−0.246350	−	2.34387i
$293$	6.31358	−	7.01194i	0.368843	−	0.409642i	−0.529940	−	0.848035i	$-0.677786\pi$
$293$	6.31358	−	7.01194i	0.368843	−	0.409642i	0.898783	+	0.438393i	$0.144452\pi$
$294$	0.589584	+	16.8835i	0.0343852	+	0.984664i
$295$	−9.44322	−	2.70780i	−0.549806	−	0.157654i
$296$	25.4977	+	44.1633i	1.48202	+	2.56694i
$297$	2.81003	−	1.76175i	0.163054	−	0.102227i
$298$	−6.55277	+	37.1626i	−0.379592	+	2.15277i
$299$	−23.4144	+	1.63729i	−1.35409	+	0.0946872i
$300$	−9.74472	+	6.08918i	−0.562612	+	0.351559i
$301$	−0.484221	+	0.257465i	−0.0279100	+	0.0148400i
$302$	18.3655	−	5.26624i	1.05682	−	0.303038i
$303$	0.653167	−	0.474554i	0.0375235	−	0.0272624i
$304$	12.8170	−	5.28434i	0.735104	−	0.303077i
$305$	0.00825772	−	0.0254146i	0.000472835	−	0.00145524i
$306$	6.40217	+	9.49160i	0.365988	+	0.542599i
$307$	−2.31351	−	13.1206i	−0.132039	−	0.748830i	−0.976876	−	0.213807i	$-0.931414\pi$
$307$	−2.31351	−	13.1206i	−0.132039	−	0.748830i	0.844837	−	0.535024i	$-0.179697\pi$
$308$	0.703325	+	1.73332i	0.0400756	+	0.0987651i
$309$	3.82947	−	3.21331i	0.217851	−	0.182799i
$310$	−1.84791	+	1.78450i	−0.104954	+	0.101353i
$311$	19.9935	+	22.2050i	1.13373	+	1.25913i	0.961720	+	0.274034i	$0.0883581\pi$
$311$	19.9935	+	22.2050i	1.13373	+	1.25913i	0.172006	+	0.985096i	$0.444975\pi$
$312$	−16.3702	+	18.1810i	−0.926781	+	1.02929i
$313$	3.43594	−	5.09399i	0.194211	−	0.287929i	−0.719337	−	0.694662i	$-0.755554\pi$
$313$	3.43594	−	5.09399i	0.194211	−	0.287929i	0.913547	+	0.406733i	$0.133332\pi$
$314$	5.80544	−	8.60691i	0.327620	−	0.485716i
$315$	−0.139062	+	0.154444i	−0.00783527	+	0.00870194i
$316$	2.79218	+	3.10103i	0.157072	+	0.174446i
$317$	−6.62044	+	6.39328i	−0.371841	+	0.359082i	−0.856976	−	0.515357i	$-0.827659\pi$
$317$	−6.62044	+	6.39328i	−0.371841	+	0.359082i	0.485135	+	0.874439i	$0.338770\pi$
$318$	24.8551	−	20.8559i	1.39381	−	1.16954i
$319$	9.05899	−	0.647085i	0.507206	−	0.0362298i
$320$	−2.35250	−	13.3417i	−0.131509	−	0.745824i
$321$	0.698922	+	1.03620i	0.0390100	+	0.0578348i
$322$	0.472189	−	1.45325i	0.0263141	−	0.0809864i
$323$	2.72436	−	20.4344i	0.151588	−	1.13700i
$324$	−3.12294	+	2.26895i	−0.173496	+	0.126053i
$325$	−15.5462	+	4.45779i	−0.862345	+	0.247274i
$326$	−11.9441	+	6.35079i	−0.661523	+	0.351738i
$327$	12.7634	−	7.97544i	0.705816	−	0.441043i
$328$	21.8570	−	1.52839i	1.20685	−	0.0843914i
$329$	0.255076	−	1.44661i	0.0140628	−	0.0797542i
$330$	4.26225	−	10.5950i	0.234629	−	0.583238i
$331$	16.9943	+	29.4350i	0.934092	+	1.61790i	0.776244	+	0.630432i	$0.217122\pi$
$331$	16.9943	+	29.4350i	0.934092	+	1.61790i	0.157848	+	0.987463i	$0.449544\pi$
$332$	24.7702	+	7.10273i	1.35944	+	0.389813i
$333$	0.395225	+	11.3178i	0.0216582	+	0.620210i
$334$	34.8037	−	38.6535i	1.90438	−	2.11502i
$335$	1.21957	+	11.6034i	0.0666321	+	0.633962i
$336$	−0.203711	−	0.417670i	−0.0111134	−	0.0227858i
$337$	−2.43664	−	1.52258i	−0.132732	−	0.0829404i	0.461928	−	0.886917i	$-0.347158\pi$
$337$	−2.43664	−	1.52258i	−0.132732	−	0.0829404i	−0.594660	+	0.803977i	$0.702713\pi$
$338$	−33.9088	+	21.1886i	−1.84440	+	1.15251i
$339$	−0.833581	+	1.70909i	−0.0452739	+	0.0928253i
$340$	24.4020	+	8.88161i	1.32339	+	0.481673i
$341$	−0.426023	+	2.43741i	−0.0230704	+	0.131993i
$342$	10.5017	+	1.02859i	0.567865	+	0.0556200i
$343$	−1.65233	−	1.20049i	−0.0892175	−	0.0648203i
$344$	−10.4060	+	13.3190i	−0.561051	+	0.718113i
$345$	−5.42580	+	2.88495i	−0.292115	+	0.155320i
$346$	−2.29676	−	0.160605i	−0.123475	−	0.00863418i
$347$	2.61663	−	10.4947i	0.140468	−	0.563386i	−0.858272	−	0.513195i	$-0.828462\pi$
$347$	2.61663	−	10.4947i	0.140468	−	0.563386i	0.998740	−	0.0501903i	$-0.0159828\pi$
$348$	−10.4676	+	1.47112i	−0.561122	+	0.0788606i
$349$	10.4028	+	11.5535i	0.556850	+	0.618444i	0.954181	−	0.299231i	$-0.0967302\pi$
$349$	10.4028	+	11.5535i	0.556850	+	0.618444i	−0.397331	+	0.917675i	$0.630064\pi$
$350$	0.110054	−	1.04710i	0.00588265	−	0.0559697i
$351$	−5.10533	+	1.85819i	−0.272502	+	0.0991827i
$352$	−3.12208	−	3.00594i	−0.166407	−	0.160217i
$353$	−0.603946	−	1.04606i	−0.0321448	−	0.0556764i	0.849505	−	0.527580i	$-0.176900\pi$
$353$	−0.603946	−	1.04606i	−0.0321448	−	0.0556764i	−0.881650	+	0.471903i	$0.843567\pi$
$354$	15.2735	−	6.80022i	0.811779	−	0.361427i
$355$	12.8762	+	6.84640i	0.683398	+	0.363369i
$356$	−0.383517	−	0.239648i	−0.0203264	−	0.0127013i
$357$	−0.689327	−	0.0482025i	−0.0364831	−	0.00255115i
$358$	25.6624	+	24.7819i	1.35630	+	1.30976i
$359$	0.461696	−	13.2213i	0.0243674	−	0.697791i	−0.924328	−	0.381599i	$-0.875373\pi$
$359$	0.461696	−	13.2213i	0.0243674	−	0.697791i	0.948695	−	0.316192i	$-0.102404\pi$
$360$	−1.97930	+	6.09166i	−0.104318	+	0.321059i
$361$	−12.9123	−	13.9382i	−0.679594	−	0.733588i
$362$	−34.3242			−1.80404
$363$	−2.69306	−	10.6652i	−0.141349	−	0.559780i
$364$	−0.532093	−	3.01765i	−0.0278893	−	0.158168i
$365$	−3.59007	−	14.3990i	−0.187913	−	0.753678i
$366$	0.0170366	+	0.0421672i	0.000890519	+	0.00220411i
$367$	−2.04302	+	0.287127i	−0.106645	+	0.0149879i	−0.192293	−	0.981337i	$-0.561593\pi$
$367$	−2.04302	+	0.287127i	−0.106645	+	0.0149879i	0.0856489	+	0.996325i	$0.472704\pi$
$368$	−1.43628	−	13.6653i	−0.0748711	−	0.712351i
$369$	4.44503	+	1.97906i	0.231399	+	0.103026i
$370$	24.0075	+	30.7282i	1.24809	+	1.59748i
$371$	0.0683440	+	1.95712i	0.00354824	+	0.101608i
$372$	0.301028	−	2.86409i	0.0156076	−	0.148496i
$373$	8.08317	−	14.0005i	0.418531	−	0.724916i	−0.577261	−	0.816560i	$-0.695879\pi$
$373$	8.08317	−	14.0005i	0.418531	−	0.724916i	0.995792	+	0.0916432i	$0.0292119\pi$
$374$	36.4852	−	10.5210i	1.88660	−	0.544031i
$375$	−8.69169	+	7.29320i	−0.448837	+	0.376619i
$376$	−10.9523	−	43.9274i	−0.564823	−	2.26538i
$377$	−14.7326	−	2.07053i	−0.758767	−	0.106638i
$378$	0.0123438	−	0.353480i	0.000634895	−	0.0181810i
$379$	18.3513	−	13.3330i	0.942641	−	0.684869i	−0.00641407	−	0.999979i	$-0.502042\pi$
$379$	18.3513	−	13.3330i	0.942641	−	0.684869i	0.949055	+	0.315111i	$0.102042\pi$
$380$	20.6417	−	12.1133i	1.05890	−	0.621400i
$381$	5.56488	+	17.1269i	0.285098	+	0.877440i
$382$	−25.9634	+	33.2317i	−1.32840	+	1.70028i
$383$	0.0103797	−	0.0212816i	0.000530378	−	0.00108744i	−0.898529	−	0.438915i	$-0.855363\pi$
$383$	0.0103797	−	0.0212816i	0.000530378	−	0.00108744i	0.899059	+	0.437827i	$0.144252\pi$
$384$	15.6602	+	13.1404i	0.799154	+	0.670570i
$385$	0.345532	+	0.596416i	0.0176099	+	0.0303962i
$386$	6.20586	−	35.1952i	0.315870	−	1.79139i
$387$	−3.42898	+	1.52668i	−0.174305	+	0.0776055i
$388$	−9.47573	+	2.01413i	−0.481057	+	0.102252i
$389$	3.72275	+	4.76491i	0.188751	+	0.241590i	0.873073	−	0.487590i	$-0.162124\pi$
$389$	3.72275	+	4.76491i	0.188751	+	0.241590i	−0.684322	+	0.729180i	$0.739902\pi$
$390$	−10.4611	+	15.5093i	−0.529719	+	0.785341i
$391$	−18.6657	−	8.31053i	−0.943967	−	0.420281i
$392$	−30.7384	−	6.53365i	−1.55252	−	0.329999i
$393$	−14.8813	−	7.91251i	−0.750661	−	0.399133i
$394$	3.18301	−	0.222578i	0.160358	−	0.0112133i
$395$	1.17789	+	0.988366i	0.0592660	+	0.0497301i
$396$	3.97446	+	12.1702i	0.199724	+	0.611574i
$397$	−20.0868	−	7.31101i	−1.00813	−	0.366929i	−0.215416	−	0.976522i	$-0.569111\pi$
$397$	−20.0868	−	7.31101i	−1.00813	−	0.366929i	−0.792714	+	0.609593i	$0.791333\pi$
$398$	1.97213	+	1.43284i	0.0988540	+	0.0718216i
$399$	−0.439150	+	0.461249i	−0.0219850	+	0.0230913i
$400$	−2.92566	−	9.00427i	−0.146283	−	0.450214i
$401$	−22.8085	+	6.54023i	−1.13900	+	0.326603i	−0.791556	−	0.611097i	$-0.790729\pi$
$401$	−22.8085	+	6.54023i	−1.13900	+	0.326603i	−0.347446	+	0.937700i	$0.612951\pi$
$402$	−14.2835	−	13.7935i	−0.712399	−	0.687955i
$403$	1.51838	−	3.75812i	0.0756358	−	0.187205i
$404$	1.16747	+	2.88960i	0.0580840	+	0.143763i
$405$	−1.02319	+	0.988087i	−0.0508429	+	0.0490984i
$406$	0.484270	−	0.838780i	0.0240339	−	0.0416280i
$407$	36.1201	+	10.2988i	1.79041	+	0.510494i
$408$	−20.0125	+	7.28396i	−0.990768	+	0.360610i
$409$	−14.7749	−	4.23665i	−0.730574	−	0.209489i	−0.110327	−	0.993895i	$-0.535190\pi$
$409$	−14.7749	−	4.23665i	−0.730574	−	0.209489i	−0.620247	+	0.784407i	$0.712968\pi$
$410$	16.3881	−	3.48339i	0.809350	−	0.172033i
$411$	−20.9980	−	4.46326i	−1.03575	−	0.220156i
$412$	8.45926	+	17.3440i	0.416758	+	0.854480i
$413$	−0.244120	+	0.979113i	−0.0120124	+	0.0481790i
$414$	3.91773	−	9.69673i	0.192546	−	0.476568i
$415$	9.40283	+	1.32148i	0.461567	+	0.0648690i
$416$	3.96996	+	5.88571i	0.194643	+	0.288570i
$417$	18.1092			0.886811
$418$	13.9596	−	32.0921i	0.682786	−	1.56968i
$419$	−24.3169			−1.18796			−0.593980	−	0.804480i	$-0.702444\pi$
$419$	−24.3169			−1.18796			−0.593980	+	0.804480i	$0.702444\pi$
$420$	−0.448606	−	0.665086i	−0.0218897	−	0.0324529i
$421$	11.7715	+	1.65438i	0.573710	+	0.0806297i	0.420061	−	0.907496i	$-0.362009\pi$
$421$	11.7715	+	1.65438i	0.573710	+	0.0806297i	0.153649	+	0.988126i	$0.450898\pi$
$422$	−7.34844	+	18.1880i	−0.357716	+	0.885379i
$423$	2.43221	−	9.75506i	0.118258	−	0.474307i
$424$	26.4579	+	54.2466i	1.28491	+	2.63445i
$425$	−13.7708	−	2.92707i	−0.667981	−	0.141984i
$426$	−24.2766	+	5.16016i	−1.17621	+	0.250010i
$427$	−0.00263857		0.000756599i	−0.000127690		3.66144e-5i
$428$	−4.53376	+	1.65015i	−0.219148	+	0.0797632i
$429$	0.655796	+	18.0072i	0.0316621	+	0.869396i
$430$	−6.46224	+	11.1929i	−0.311637	+	0.539771i
$431$	7.46785	−	7.21162i	0.359713	−	0.347371i	−0.492738	−	0.870178i	$-0.664004\pi$
$431$	7.46785	−	7.21162i	0.359713	−	0.347371i	0.852451	+	0.522806i	$0.175115\pi$
$432$	−1.19145	−	2.94893i	−0.0573235	−	0.141881i
$433$	15.3831	−	38.0746i	0.739265	−	1.82975i	0.219044	−	0.975715i	$-0.429706\pi$
$433$	15.3831	−	38.0746i	0.739265	−	1.82975i	0.520222	−	0.854031i	$-0.325849\pi$
$434$	0.189815	+	0.183302i	0.00911140	+	0.00879877i
$435$	−3.74416	+	1.07362i	−0.179519	+	0.0514762i
$436$	17.9528	+	55.2531i	0.859784	+	2.64614i
$437$	−16.8666	+	8.37483i	−0.806838	+	0.400623i
$438$	20.4323	+	14.8449i	0.976292	+	0.709318i
$439$	16.9396	+	6.16550i	0.808481	+	0.294263i	0.712996	−	0.701168i	$-0.247338\pi$
$439$	16.9396	+	6.16550i	0.808481	+	0.294263i	0.0954849	+	0.995431i	$0.469560\pi$
$440$	17.2050	+	12.4609i	0.820216	+	0.594049i
$441$	−5.34596	−	4.48579i	−0.254569	−	0.213609i
$442$	−62.0503	+	4.33898i	−2.95143	+	0.206384i
$443$	6.61641	+	3.51801i	0.314355	+	0.167146i	0.619151	−	0.785272i	$-0.287477\pi$
$443$	6.61641	+	3.51801i	0.314355	+	0.167146i	−0.304796	+	0.952418i	$0.598588\pi$
$444$	−42.7598	−	9.08888i	−2.02929	−	0.431339i
$445$	−0.152234	−	0.0677791i	−0.00721660	−	0.00321304i
$446$	−11.4972	+	17.0452i	−0.544406	+	0.807116i
$447$	−9.59714	−	12.2838i	−0.453929	−	0.581003i
$448$	−1.36118	+	0.289327i	−0.0643095	+	0.0136694i
$449$	28.3876	−	12.6390i	1.33969	−	0.596470i	0.393277	−	0.919420i	$-0.371341\pi$
$449$	28.3876	−	12.6390i	1.33969	−	0.596470i	0.946416	+	0.322950i	$0.104675\pi$
$450$	1.25132	−	7.09659i	0.0589878	−	0.334536i
$451$	10.7803	−	12.0088i	0.507623	−	0.565471i
$452$	−5.62296	−	4.71823i	−0.264482	−	0.221927i
$453$	−3.45979	+	7.09362i	−0.162555	+	0.333287i
$454$	−10.9338	+	13.9947i	−0.513151	+	0.656803i
$455$	−0.348914	−	1.07385i	−0.0163573	−	0.0503427i
$456$	−6.58241	+	18.4917i	−0.308250	+	0.865951i
$457$	7.76614	−	5.64243i	0.363285	−	0.263942i	−0.391136	−	0.920333i	$-0.627918\pi$
$457$	7.76614	−	5.64243i	0.363285	−	0.263942i	0.754421	+	0.656391i	$0.227918\pi$
$458$	0.977659	−	27.9965i	0.0456830	−	1.30819i
$459$	−4.68342	−	0.658212i	−0.218603	−	0.0307227i
$460$	−5.73864	−	23.0164i	−0.267566	−	1.07315i
$461$	27.5392	−	23.1081i	1.28263	−	1.07625i	0.289752	−	0.957102i	$-0.406427\pi$
$461$	27.5392	−	23.1081i	1.28263	−	1.07625i	0.992876	−	0.119151i	$-0.0380173\pi$
$462$	−1.10293	−	0.399565i	−0.0513128	−	0.0185895i
$463$	−13.8341	+	23.9614i	−0.642927	+	1.11358i	0.341849	+	0.939755i	$0.388947\pi$
$463$	−13.8341	+	23.9614i	−0.642927	+	1.11358i	−0.984776	+	0.173827i	$0.944386\pi$
$464$	0.910379	−	8.66167i	0.0422633	−	0.402108i
$465$	−0.0370348	−	1.06054i	−0.00171745	−	0.0491813i
$466$	−10.9905	−	14.0672i	−0.509126	−	0.651652i
$467$	33.5161	+	14.9223i	1.55094	+	0.690524i	0.990480	−	0.137657i	$-0.0439571\pi$
$467$	33.5161	+	14.9223i	1.55094	+	0.690524i	0.560462	+	0.828180i	$0.310624\pi$
$468$	−2.19219	−	20.8573i	−0.101334	−	0.964128i
$469$	1.18679	−	0.166793i	0.0548009	−	0.00770176i
$470$	−12.9682	−	32.0974i	−0.598179	−	1.48054i
$471$	1.03751	+	4.16124i	0.0478061	+	0.191740i
$472$	5.40045	+	30.6275i	0.248576	+	1.40974i
$473$	1.31978	+	12.3787i	0.0606837	+	0.569175i
$474$	−2.61686			−0.120197
$475$	−10.1679	+	8.06069i	−0.466535	+	0.369850i
$476$	0.824276	−	2.53686i	0.0377806	−	0.116277i
$477$	−0.467764	+	13.3950i	−0.0214174	+	0.613315i
$478$	−41.4233	−	40.0020i	−1.89466	−	1.82965i
$479$	6.63320	+	0.463839i	0.303079	+	0.0211933i	0.220486	−	0.975390i	$-0.429236\pi$
$479$	6.63320	+	0.463839i	0.303079	+	0.0211933i	0.0825924	+	0.996583i	$0.473680\pi$
$480$	1.57627	+	0.984964i	0.0719466	+	0.0449572i
$481$	−54.3248	−	28.8850i	−2.47700	−	1.31704i
$482$	−43.0742	+	19.1779i	−1.96198	+	0.873529i
$483$	0.315609	+	0.546650i	0.0143607	+	0.0248734i
$484$	42.4616	−	0.127034i	1.93007	−	0.00577426i
$485$	−3.35438	+	1.22090i	−0.152315	+	0.0554380i
$486$	0.253040	−	2.40752i	0.0114781	−	0.109207i
$487$	−6.46206	−	7.17684i	−0.292824	−	0.325214i	0.578725	−	0.815523i	$-0.303551\pi$
$487$	−6.46206	−	7.17684i	−0.292824	−	0.325214i	−0.871549	+	0.490309i	$0.836884\pi$
$488$	−0.0837745	+	0.0117737i	−0.00379229	+	0.000532972i
$489$	1.35188	−	5.42211i	0.0611343	−	0.245196i
$490$	−23.9713	−	1.67623i	−1.08291	−	0.0757246i
$491$	−13.6244	+	7.24424i	−0.614862	+	0.326928i	−0.747525	−	0.664233i	$-0.768758\pi$
$491$	−13.6244	+	7.24424i	−0.614862	+	0.326928i	0.132663	+	0.991161i	$0.457647\pi$
$492$	−11.5636	+	14.8007i	−0.521326	+	0.667267i
$493$	−10.4775	−	7.61234i	−0.471882	−	0.342842i
$494$	−33.3673	+	46.6172i	−1.50127	+	2.09741i
$495$	2.07440	+	4.23704i	0.0932372	+	0.190441i
$496$	2.22973	+	0.811554i	0.100118	+	0.0364398i
$497$	0.656667	−	1.34637i	0.0294555	−	0.0603928i
$498$	−13.7043	+	8.56341i	−0.614105	+	0.383735i
$499$	35.1131	+	21.9411i	1.57188	+	0.982218i	0.985002	+	0.172541i	$0.0551978\pi$
$499$	35.1131	+	21.9411i	1.57188	+	0.982218i	0.586876	+	0.809677i	$0.300358\pi$
$500$	−19.1998	−	39.3655i	−0.858643	−	1.76048i
$501$	2.24592	+	21.3685i	0.100340	+	0.954675i
$502$	20.2802	−	22.5235i	0.905151	−	1.00527i
$503$	−0.0839762	−	2.40476i	−0.00374432	−	0.107223i	−0.999824	−	0.0187623i	$-0.994027\pi$
$503$	−0.0839762	−	2.40476i	−0.00374432	−	0.107223i	0.996080	−	0.0884608i	$-0.0281948\pi$
$504$	0.632443	+	0.181350i	0.0281712	+	0.00807797i
$505$	0.574197	+	0.994538i	0.0255514	+	0.0442563i
$506$	−26.6044	−	22.2560i	−1.18271	−	0.989401i
$507$	2.86819	−	16.2663i	0.127381	−	0.722412i
$508$	−69.3458	+	4.84913i	−3.07672	+	0.215145i
$509$	24.3780	−	15.2331i	1.08054	−	0.675195i	0.131806	−	0.991276i	$-0.457923\pi$
$509$	24.3780	−	15.2331i	1.08054	−	0.675195i	0.948732	+	0.316080i	$0.102367\pi$
$510$	−14.3789	+	7.64537i	−0.636706	+	0.338543i
$511$	−1.46528	+	0.420162i	−0.0648201	+	0.0185869i
$512$	−26.5359	+	19.2794i	−1.17273	+	0.852039i
$513$	−3.21855	+	2.93955i	−0.142102	+	0.129784i
$514$	−5.35704	+	16.4873i	−0.236289	+	0.727222i
$515$	3.97622	+	5.89499i	0.175213	+	0.259764i
$516$	−2.51600	−	14.2689i	−0.110761	−	0.628155i
$517$	−28.3040	−	17.6275i	−1.24481	−	0.775256i
$518$	3.06838	−	2.57467i	0.134817	−	0.113125i
$519$	0.684154	−	0.660680i	0.0300310	−	0.0290006i
$520$	−23.2851	−	25.8607i	−1.02112	−	1.13407i
$521$	−16.7853	+	18.6419i	−0.735376	+	0.816718i	−0.988580	−	0.150695i	$-0.951849\pi$
$521$	−16.7853	+	18.6419i	−0.735376	+	0.816718i	0.253204	+	0.967413i	$0.418516\pi$
$522$	3.70685	−	5.49563i	0.162244	−	0.240537i
$523$	2.67418	−	3.96463i	0.116934	−	0.173361i	−0.766027	−	0.642809i	$-0.777769\pi$
$523$	2.67418	−	3.96463i	0.116934	−	0.173361i	0.882960	+	0.469447i	$0.155547\pi$
$524$	43.5333	−	48.3486i	1.90176	−	2.11212i
$525$	0.291024	+	0.323215i	0.0127013	+	0.0141062i
$526$	−13.7874	+	13.3144i	−0.601161	+	0.580534i
$527$	2.70291	−	2.26801i	0.117741	−	0.0987961i
$528$	−10.5218	+	0.751574i	−0.457903	+	0.0327080i
$529$	−0.752906	−	4.26994i	−0.0327350	−	0.185650i
$530$	25.8076	+	38.2613i	1.12101	+	1.66197i
$531$	−2.13421	+	6.56842i	−0.0926168	+	0.285045i
$532$	−1.31750	−	2.07558i	−0.0571211	−	0.0899877i
$533$	−21.3865	+	15.5382i	−0.926353	+	0.673035i
$534$	0.272618	−	0.0781721i	0.0117974	−	0.00338284i
$535$	−1.56973	+	0.834643i	−0.0678655	+	0.0360847i
$536$	31.3237	−	19.5732i	1.35298	−	0.845434i
$537$	−14.7011	+	1.02800i	−0.634398	+	0.0443614i
$538$	−7.65523	+	43.4150i	−0.330040	+	1.87175i
$539$	−19.6102	+	12.2946i	−0.844671	+	0.529567i
$540$	−2.74536	−	4.75510i	−0.118142	−	0.204627i
$541$	28.8824	+	8.28190i	1.24175	+	0.356067i	0.831305	−	0.555817i	$-0.187595\pi$
$541$	28.8824	+	8.28190i	1.24175	+	0.356067i	0.410448	+	0.911884i	$0.365372\pi$
$542$	0.917732	+	26.2804i	0.0394200	+	1.12884i
$543$	9.48761	−	10.5371i	0.407152	−	0.452188i
$544$	0.645999	+	6.14627i	0.0276970	+	0.263519i
$545$	9.38449	+	19.2411i	0.401987	+	0.824196i
$546$	1.62962	+	1.01830i	0.0697414	+	0.0435793i
$547$	6.22103	−	3.88733i	0.265992	−	0.166210i	−0.390366	−	0.920660i	$-0.627652\pi$
$547$	6.22103	−	3.88733i	0.265992	−	0.166210i	0.656358	+	0.754449i	$0.272096\pi$
$548$	36.3263	−	74.4799i	1.55178	−	3.18162i
$549$	−0.0176539	−	0.00642548i	−0.000753448	−	0.000274233i
$550$	−21.1190	−	11.1887i	−0.900519	−	0.477088i
$551$	−11.5609	+	2.96961i	−0.492510	+	0.126510i
$552$	15.7387	+	11.4348i	0.669882	+	0.486698i
$553$	0.0972394	−	0.124461i	0.00413504	−	0.00529261i
$554$	−1.42770	+	0.759123i	−0.0606572	+	0.0322520i
$555$	−16.0691	−	1.12366i	−0.682094	−	0.0476966i
$556$	−16.9114	+	67.8279i	−0.717203	+	2.87655i
$557$	23.4105	−	3.29013i	0.991934	−	0.139407i	0.375507	−	0.926819i	$-0.377468\pi$
$557$	23.4105	−	3.29013i	0.991934	−	0.139407i	0.616427	+	0.787412i	$0.288580\pi$
$558$	1.20846	+	1.34213i	0.0511582	+	0.0568170i
$559$	2.13161	−	20.2809i	0.0901573	−	0.857790i
$560$	0.621130	−	0.226073i	0.0262475	−	0.00955333i
$561$	−6.85511	+	14.1086i	−0.289423	+	0.595665i
$562$	−6.01293	−	10.4147i	−0.253640	−	0.439318i
$563$	−28.9211	+	12.8765i	−1.21888	+	0.542679i	−0.912440	−	0.409211i	$-0.865804\pi$
$563$	−28.9211	+	12.8765i	−1.21888	+	0.542679i	−0.306438	+	0.951891i	$0.599137\pi$
$564$	34.2662	+	18.2197i	1.44287	+	0.767187i
$565$	−2.29377	−	1.43331i	−0.0964997	−	0.0602997i
$566$	72.5728	+	5.07479i	3.05046	+	0.213309i
$567$	0.105101	+	0.101495i	0.00441384	+	0.00426240i
$568$	1.61122	−	46.1392i	0.0676051	−	1.93596i
$569$	−10.3522	+	31.8609i	−0.433988	+	1.33568i	0.460132	+	0.887850i	$0.347802\pi$
$569$	−10.3522	+	31.8609i	−0.433988	+	1.33568i	−0.894120	+	0.447827i	$0.852198\pi$
$570$	−3.01647	+	14.7029i	−0.126346	+	0.615836i
$571$	5.86574			0.245473			0.122737	−	0.992439i	$-0.460833\pi$
$571$	5.86574			0.245473			0.122737	+	0.992439i	$0.460833\pi$
$572$	−68.0584	−	14.3599i	−2.84566	−	0.600417i
$573$	−3.02507	−	17.1560i	−0.126374	−	0.716703i
$574$	−0.416341	−	1.66985i	−0.0173777	−	0.0696983i
$575$	4.81752	+	11.9238i	0.200904	+	0.497256i
$576$	−9.43167	+	1.32553i	−0.392986	+	0.0552306i
$577$	−2.87011	−	27.3073i	−0.119484	−	1.13682i	−0.875821	−	0.482636i	$-0.839679\pi$
$577$	−2.87011	−	27.3073i	−0.119484	−	1.13682i	0.756337	−	0.654183i	$-0.226987\pi$
$578$	−11.8706	−	5.28514i	−0.493752	−	0.219833i
$579$	9.08906	+	11.6335i	0.377728	+	0.483470i
$580$	−0.524732	−	15.0264i	−0.0217883	−	0.623935i
$581$	0.101951	−	0.969997i	0.00422963	−	0.0402423i
$582$	3.03758	−	5.26124i	0.125912	−	0.218085i
$583$	41.7951	+	15.1414i	1.73098	+	0.627093i
$584$	−35.9885	+	30.1979i	−1.48921	+	1.24960i
$585$	−1.86955	−	7.49835i	−0.0772964	−	0.310019i
$586$	−22.6190	−	3.17889i	−0.934380	−	0.131319i
$587$	−0.188159	+	5.38817i	−0.00776616	+	0.222394i	0.989302	+	0.145880i	$0.0466012\pi$
$587$	−0.188159	+	5.38817i	−0.00776616	+	0.222394i	−0.997069	+	0.0765140i	$0.975621\pi$
$588$	21.7939	−	15.8342i	0.898765	−	0.652991i
$589$	−0.0230412	−	3.25187i	−0.000949395	−	0.133991i
$590$	7.34879	+	22.6172i	0.302545	+	0.931137i
$591$	−0.811492	+	1.03866i	−0.0333803	+	0.0427248i
$592$	15.7894	−	32.3731i	0.648942	−	1.33053i
$593$	18.7438	+	15.7279i	0.769715	+	0.645867i	0.940636	−	0.339417i	$-0.110230\pi$
$593$	18.7438	+	15.7279i	0.769715	+	0.645867i	−0.170921	+	0.985285i	$0.554674\pi$
$594$	−7.33956	−	3.25464i	−0.301146	−	0.133539i
$595$	0.170679	−	0.967966i	0.00699714	−	0.0396827i
$596$	54.9712	−	24.4748i	2.25171	−	1.00253i
$597$	−0.984981	+	0.209364i	−0.0403126	+	0.00856870i
$598$	34.9816	+	44.7744i	1.43050	+	1.83096i
$599$	−4.60791	+	6.83151i	−0.188274	+	0.279128i	−0.911343	−	0.411648i	$-0.864953\pi$
$599$	−4.60791	+	6.83151i	−0.188274	+	0.279128i	0.723069	+	0.690776i	$0.242731\pi$
$600$	12.2456	+	5.45208i	0.499923	+	0.222580i
$601$	−31.0424	−	6.59826i	−1.26624	−	0.269148i	−0.474638	−	0.880181i	$-0.657421\pi$
$601$	−31.0424	−	6.59826i	−1.26624	−	0.269148i	−0.791606	+	0.611032i	$0.790754\pi$
$602$	1.17219	+	0.623265i	0.0477749	+	0.0254024i
$603$	8.18254	−	0.572179i	0.333219	−	0.0233009i
$604$	−23.3382	−	19.5831i	−0.949617	−	0.796823i
$605$	15.4876	−	2.22391i	0.629662	−	0.0904150i
$606$	−1.83657	−	0.668456i	−0.0746055	−	0.0271542i
$607$	39.2163	+	28.4923i	1.59174	+	1.15647i	0.901405	+	0.432976i	$0.142537\pi$
$607$	39.2163	+	28.4923i	1.59174	+	1.15647i	0.690334	+	0.723490i	$0.257463\pi$
$608$	4.74457	+	3.15158i	0.192418	+	0.127813i
$609$	0.123636	+	0.380513i	0.00500999	+	0.0154192i
$610$	−0.0621833	+	0.0178308i	−0.00251773	+	0.000721947i
$611$	39.2914	+	37.9433i	1.58956	+	1.53502i
$612$	6.83898	−	16.9271i	0.276450	−	0.684237i
$613$	11.1063	+	27.4890i	0.448578	+	1.11027i	0.966916	+	0.255094i	$0.0821063\pi$
$613$	11.1063	+	27.4890i	0.448578	+	1.11027i	−0.518338	+	0.855176i	$0.673449\pi$
$614$	−23.2001	+	22.4041i	−0.936280	+	0.904155i
$615$	−3.46050	+	5.99376i	−0.139541	+	0.241692i
$616$	1.21751	−	1.81087i	0.0490549	−	0.0729621i
$617$	36.7502	−	13.3760i	1.47951	−	0.538496i	0.528842	−	0.848720i	$-0.322626\pi$
$617$	36.7502	−	13.3760i	1.47951	−	0.538496i	0.950663	+	0.310224i	$0.100404\pi$
$618$	−11.6327	−	3.33563i	−0.467937	−	0.134179i
$619$	9.62843	−	2.04659i	0.386999	−	0.0822593i	−0.0103032	−	0.999947i	$-0.503280\pi$
$619$	9.62843	−	2.04659i	0.386999	−	0.0822593i	0.397303	+	0.917688i	$0.369946\pi$
$620$	4.00683	+	0.851678i	0.160918	+	0.0342042i
$621$	1.89385	+	3.88298i	0.0759977	+	0.155818i
$622$	17.4988	−	70.1837i	0.701636	−	2.81411i
$623$	−0.00641222	+	0.0158708i	−0.000256900	+	0.000635850i
$624$	17.1116	+	2.40487i	0.685010	+	0.0962719i
$625$	−0.701859	−	1.04055i	−0.0280744	−	0.0416220i
$626$	−14.8744			−0.594499
$627$	5.99324	+	13.1560i	0.239347	+	0.525401i
$628$	−16.5548			−0.660608
$629$	−29.9501	−	44.4028i	−1.19419	−	1.77046i
$630$	0.498202	+	0.0700178i	0.0198489	+	0.00278957i
$631$	−16.8227	+	41.6377i	−0.669702	+	1.65757i	0.0808215	+	0.996729i	$0.474246\pi$
$631$	−16.8227	+	41.6377i	−0.669702	+	1.65757i	−0.750524	+	0.660843i	$0.770199\pi$
$632$	1.17762	−	4.72320i	0.0468434	−	0.187879i
$633$	−3.55228	−	7.28325i	−0.141190	−	0.289483i
$634$	21.7927	+	4.63219i	0.865500	+	0.183968i
$635$	−25.0554	+	5.32570i	−0.994295	+	0.211344i
$636$	−49.7341	−	14.2610i	−1.97209	−	0.565487i
$637$	35.6283	−	12.9676i	1.41164	−	0.513797i
$638$	−13.5616	−	17.3047i	−0.536910	−	0.685099i
$639$	5.12624	−	8.87891i	0.202791	−	0.351244i
$640$	−20.9170	+	20.1993i	−0.826818	+	0.798449i
$641$	1.26519	+	3.13146i	0.0499721	+	0.123685i	0.950105	−	0.311930i	$-0.100975\pi$
$641$	1.26519	+	3.13146i	0.0499721	+	0.123685i	−0.900133	+	0.435615i	$0.856531\pi$
$642$	1.13344	−	2.80536i	0.0447332	−	0.110719i
$643$	23.0110	+	22.2215i	0.907466	+	0.876329i	0.992771	−	0.120025i	$-0.0382976\pi$
$643$	23.0110	+	22.2215i	0.907466	+	0.876329i	−0.0853051	+	0.996355i	$0.527186\pi$
$644$	−2.34221	+	0.671618i	−0.0922960	+	0.0264655i
$645$	−1.64984	−	5.07767i	−0.0649622	−	0.199933i
$646$	−44.6980	+	22.1941i	−1.75862	+	0.873214i
$647$	−14.6849	−	10.6692i	−0.577324	−	0.419450i	0.260434	−	0.965492i	$-0.416134\pi$
$647$	−14.6849	−	10.6692i	−0.577324	−	0.419450i	−0.837758	+	0.546041i	$0.816134\pi$
$648$	4.23147	+	1.54013i	0.166228	+	0.0605020i
$649$	18.5515	+	13.4361i	0.728211	+	0.527414i
$650$	29.9909	+	25.1654i	1.17634	+	0.987068i
$651$	−0.108738	+	0.00760371i	−0.00426178	+	0.000298013i
$652$	19.0460	+	10.1270i	0.745900	+	0.396602i
$653$	18.9621	+	4.03053i	0.742046	+	0.157727i	0.563397	−	0.826186i	$-0.309494\pi$
$653$	18.9621	+	4.03053i	0.742046	+	0.157727i	0.178649	+	0.983913i	$0.442827\pi$
$654$	−33.2836	−	14.8188i	−1.30149	−	0.579461i
$655$	13.4057	−	19.8748i	0.523806	−	0.776574i
$656$	−9.52765	−	12.1948i	−0.371992	−	0.476128i
$657$	−10.2049	+	2.16912i	−0.398131	+	0.0846254i
$658$	−3.24852	+	1.44633i	−0.126640	+	0.0563839i
$659$	8.09495	−	45.9087i	0.315334	−	1.78835i	−0.255003	−	0.966940i	$-0.582077\pi$
$659$	8.09495	−	45.9087i	0.315334	−	1.78835i	0.570338	−	0.821410i	$-0.306812\pi$
$660$	−17.8070	+	3.81285i	−0.693138	+	0.148415i
$661$	17.4700	+	14.6591i	0.679506	+	0.570173i	0.915862	−	0.401493i	$-0.131509\pi$
$661$	17.4700	+	14.6591i	0.679506	+	0.570173i	−0.236356	+	0.971667i	$0.575953\pi$
$662$	36.0687	−	73.9518i	1.40185	−	2.87422i
$663$	15.8194	−	20.2479i	0.614375	−	0.786364i
$664$	−9.28902	−	28.5887i	−0.360484	−	1.10946i
$665$	−0.587196	−	0.689808i	−0.0227705	−	0.0267496i
$666$	22.1788	−	16.1138i	0.859411	−	0.624399i
$667$	−0.412869	+	11.8230i	−0.0159864	+	0.457789i
$668$	−82.1332	−	11.5431i	−3.17783	−	0.446614i
$669$	−2.05470	−	8.24097i	−0.0794395	−	0.318614i
$670$	21.6361	−	18.1549i	0.835877	−	0.701384i
$671$	−0.0382877	+	0.0491574i	−0.00147808	+	0.00189770i
$672$	0.0954620	−	0.165345i	0.00368253	−	0.00637833i
$673$	−2.49159	+	23.7059i	−0.0960439	+	0.913796i	0.835334	+	0.549743i	$0.185274\pi$
$673$	−2.49159	+	23.7059i	−0.0960439	+	0.913796i	−0.931378	+	0.364054i	$0.881392\pi$
$674$	0.242742	+	6.95123i	0.00935008	+	0.267751i
$675$	1.83267	+	2.34572i	0.0705397	+	0.0902867i
$676$	58.2469	+	25.9332i	2.24027	+	0.997431i
$677$	2.91949	+	27.7771i	0.112205	+	1.06756i	0.895240	+	0.445584i	$0.147004\pi$
$677$	2.91949	+	27.7771i	0.112205	+	1.06756i	−0.783035	+	0.621978i	$0.786329\pi$
$678$	4.55841	−	0.640643i	0.175065	−	0.0246037i
$679$	0.137357	+	0.339972i	0.00527130	+	0.0130469i
$680$	−7.32850	−	29.3930i	−0.281035	−	1.12717i
$681$	−1.27393	−	7.22483i	−0.0488172	−	0.276856i
$682$	5.46838	−	2.44449i	0.209395	−	0.0936042i
$683$	−0.747492			−0.0286020			−0.0143010	−	0.999898i	$-0.504552\pi$
$683$	−0.747492			−0.0286020			−0.0143010	+	0.999898i	$0.504552\pi$
$684$	−8.00442	−	14.8002i	−0.306057	−	0.565899i
$685$	9.43582	−	29.0405i	0.360524	−	1.10958i
$686$	−0.172549	+	4.94117i	−0.00658797	+	0.188655i
$687$	8.32430	+	8.03868i	0.317592	+	0.306695i
$688$	11.9090	+	0.832756i	0.454025	+	0.0317485i
$689$	−61.7541	−	38.5882i	−2.35264	−	1.47009i
$690$	13.1346	+	6.98381i	0.500027	+	0.265869i
$691$	7.99512	−	3.55966i	0.304149	−	0.135416i	−0.248987	−	0.968507i	$-0.580098\pi$
$691$	7.99512	−	3.55966i	0.304149	−	0.135416i	0.553136	+	0.833091i	$0.313431\pi$
$692$	1.83567	+	3.17948i	0.0697818	+	0.120866i
$693$	0.427523	−	0.228139i	0.0162403	−	0.00866628i
$694$	−24.6041	+	8.95515i	−0.933958	+	0.339933i
$695$	−2.69251	+	25.6175i	−0.102133	+	0.971728i
$696$	8.25097	+	9.16363i	0.312752	+	0.347347i
$697$	−22.7881	+	3.20266i	−0.863161	+	0.121309i
$698$	9.10478	−	36.5173i	0.344621	−	1.38220i
$699$	7.35635	+	0.514406i	0.278243	+	0.0194566i
$700$	−1.48237	+	0.788193i	−0.0560285	+	0.0297909i
$701$	18.7346	−	23.9792i	0.707598	−	0.905684i	−0.291101	−	0.956692i	$-0.594021\pi$
$701$	18.7346	−	23.9792i	0.707598	−	0.905684i	0.998698	+	0.0510088i	$0.0162437\pi$
$702$	10.6402	+	7.73057i	0.401589	+	0.291771i
$703$	−49.1280	−	4.81188i	−1.85290	−	0.181484i
$704$	−5.43878	+	31.1170i	−0.204982	+	1.17277i
$705$	13.4380	+	4.89104i	0.506106	+	0.184207i
$706$	−1.28181	+	2.62811i	−0.0482417	+	0.0989101i
$707$	0.100037	−	0.0625101i	0.00376228	−	0.00235094i
$708$	−22.6090	−	14.1276i	−0.849697	−	0.530949i
$709$	−15.8298	−	32.4558i	−0.594500	−	1.21890i	−0.957854	−	0.287254i	$-0.907258\pi$
$709$	−15.8298	−	32.4558i	−0.594500	−	1.21890i	0.363355	−	0.931651i	$-0.381631\pi$
$710$	−3.69014	−	35.1093i	−0.138488	−	1.31763i
$711$	0.723331	−	0.803341i	0.0271270	−	0.0301276i
$712$	0.0184113	+	0.527229i	0.000689991	+	0.0197588i
$713$	−3.09823	−	0.888402i	−0.116029	−	0.0332709i
$714$	0.836391	+	1.44867i	0.0313012	+	0.0542152i
$715$	−25.5708	−	1.74965i	−0.956293	−	0.0654332i
$716$	9.87833	−	56.0228i	0.369171	−	2.09367i
$717$	23.7299	−	1.65936i	0.886211	−	0.0619699i
$718$	−27.1589	+	16.9708i	−1.01356	+	0.633344i
$719$	20.5892	−	10.9475i	0.767846	−	0.408271i	−0.0388441	−	0.999245i	$-0.512368\pi$
$719$	20.5892	−	10.9475i	0.767846	−	0.408271i	0.806691	+	0.590974i	$0.201256\pi$
$720$	4.34875	−	1.24698i	0.162068	−	0.0464723i
$721$	0.590903	−	0.429317i	0.0220064	−	0.0159886i
$722$	−10.4936	+	44.7817i	−0.390532	+	1.66660i
$723$	6.01887	−	18.5242i	0.223844	−	0.688922i
$724$	30.6065	+	45.3759i	1.13748	+	1.68638i
$725$	1.41548	+	8.02756i	0.0525694	+	0.298136i
$726$	−17.7587	+	19.8421i	−0.659087	+	0.736409i
$727$	20.9690	−	17.5950i	0.777696	−	0.652564i	−0.164971	−	0.986298i	$-0.552753\pi$
$727$	20.9690	−	17.5950i	0.777696	−	0.652564i	0.942667	+	0.333734i	$0.108309\pi$
$728$	−2.57129	+	2.48307i	−0.0952985	+	0.0920286i
$729$	0.669131	+	0.743145i	0.0247826	+	0.0275239i
$730$	−24.0378	+	26.6966i	−0.889677	+	0.988087i
$731$	9.92674	−	14.7170i	0.367154	−	0.544328i
$732$	0.0405528	−	0.0601220i	0.00149887	−	0.00222217i
$733$	−9.79196	+	10.8751i	−0.361674	+	0.401680i	−0.896328	−	0.443391i	$-0.853775\pi$
$733$	−9.79196	+	10.8751i	−0.361674	+	0.401680i	0.534654	+	0.845071i	$0.320442\pi$
$734$	3.34183	+	3.71148i	0.123349	+	0.136993i
$735$	7.14052	−	6.89552i	0.263382	−	0.254345i
$736$	4.32459	−	3.62876i	0.159407	−	0.133758i
$737$	6.54191	−	26.4064i	0.240974	−	0.972692i
$738$	−2.04536	−	11.5998i	−0.0752908	−	0.426995i
$739$	19.6630	+	29.1516i	0.723315	+	1.07236i	0.993967	+	0.109681i	$0.0349829\pi$
$739$	19.6630	+	29.1516i	0.723315	+	1.07236i	−0.270652	+	0.962677i	$0.587239\pi$
$740$	19.2149	−	59.1373i	0.706353	−	2.17393i
$741$	−5.08773	−	23.1288i	−0.186902	−	0.849659i
$742$	3.83525	−	2.78647i	0.140797	−	0.102295i
$743$	4.12706	−	1.18342i	0.151407	−	0.0434153i	−0.199078	−	0.979984i	$-0.563795\pi$
$743$	4.12706	−	1.18342i	0.151407	−	0.0434153i	0.350485	+	0.936568i	$0.386017\pi$
$744$	−2.96625	+	1.57718i	−0.108748	+	0.0578223i
$745$	18.8037	−	11.7499i	0.688916	−	0.430482i
$746$	−39.0398	+	2.72993i	−1.42935	+	0.0999497i
$747$	1.15918	−	6.57406i	0.0424123	−	0.240532i
$748$	−46.4420	−	38.8512i	−1.69809	−	1.42054i
$749$	0.0913086	+	0.158151i	0.00333634	+	0.00577871i
$750$	26.4026	+	7.57083i	0.964087	+	0.276447i
$751$	1.57452	+	45.0884i	0.0574551	+	1.64530i	0.596204	+	0.802833i	$0.296675\pi$
$751$	1.57452	+	45.0884i	0.0574551	+	1.64530i	−0.538749	+	0.842466i	$0.681103\pi$
$752$	−21.3961	+	23.7628i	−0.780237	+	0.866541i
$753$	1.30871	+	12.4515i	0.0476919	+	0.453758i
$754$	15.7879	+	32.3699i	0.574960	+	1.17884i
$755$	−9.52033	−	5.94896i	−0.346480	−	0.216505i
$756$	−0.478300	+	0.298875i	−0.0173956	+	0.0108700i
$757$	20.1717	−	41.3581i	0.733152	−	1.50318i	−0.126313	−	0.991990i	$-0.540314\pi$
$757$	20.1717	−	41.3581i	0.733152	−	1.50318i	0.859465	−	0.511194i	$-0.170797\pi$
$758$	−51.5999	−	18.7808i	−1.87419	−	0.682150i
$759$	14.1861	−	2.01537i	0.514921	−	0.0731531i
$760$	−25.1799	−	12.0610i	−0.913371	−	0.437497i
$761$	25.4970	+	18.5247i	0.924265	+	0.671518i	0.944582	−	0.328275i	$-0.106467\pi$
$761$	25.4970	+	18.5247i	0.924265	+	0.671518i	−0.0203166	+	0.999794i	$0.506467\pi$
$762$	26.8393	−	34.3527i	0.972283	−	1.24447i
$763$	1.94157	−	1.03235i	0.0702897	−	0.0373737i
$764$	67.0828	+	4.69089i	2.42697	+	0.169710i
$765$	1.62746	−	6.52738i	0.0588409	−	0.235998i
$766$	−0.0567611	+	0.00797725i	−0.00205086	+	0.000288230i
$767$	−25.1075	−	27.8847i	−0.906579	−	1.00686i
$768$	3.18174	−	30.2722i	0.114811	−	1.09235i
$769$	26.8877	−	9.78631i	0.969594	−	0.352904i	0.191808	−	0.981432i	$-0.438565\pi$
$769$	26.8877	−	9.78631i	0.969594	−	0.352904i	0.777786	+	0.628529i	$0.216343\pi$
$770$	0.729217	−	1.50081i	0.0262792	−	0.0540854i
$771$	−3.58061	−	6.20180i	−0.128953	−	0.223353i
$772$	−52.0610	+	23.1790i	−1.87372	+	0.834232i
$773$	−25.1889	−	13.3932i	−0.905981	−	0.481718i	−0.0500134	−	0.998749i	$-0.515926\pi$
$773$	−25.1889	−	13.3932i	−0.905981	−	0.481718i	−0.855967	+	0.517030i	$0.827038\pi$
$774$	7.70566	+	4.81503i	0.276974	+	0.173073i
$775$	−2.21539	−	0.154915i	−0.0795793	−	0.00556473i
$776$	8.12910	+	7.85018i	0.291818	+	0.281805i
$777$	−0.0577456	+	1.65362i	−0.00207161	+	0.0593232i
$778$	4.52334	−	13.9214i	0.162170	−	0.499107i
$779$	−11.1114	+	18.0655i	−0.398106	+	0.647264i
$780$	29.8310			1.06812
$781$	−22.7907	−	25.2356i	−0.815514	−	0.903000i
$782$	8.58895	+	48.7104i	0.307140	+	1.74188i
$783$	0.662466	+	2.65701i	0.0236746	+	0.0949537i
$784$	8.31468	+	20.5796i	0.296953	+	0.734985i
$785$	−6.04081	+	0.848981i	−0.215606	+	0.0303014i
$786$	4.26476	+	40.5765i	0.152119	+	1.44731i
$787$	0.494241	+	0.220050i	0.0176178	+	0.00784395i	0.415527	−	0.909581i	$-0.363597\pi$
$787$	0.494241	+	0.220050i	0.0176178	+	0.00784395i	−0.397909	+	0.917425i	$0.630264\pi$
$788$	−3.13249	−	4.00940i	−0.111590	−	0.142829i
$789$	−0.276321	−	7.91279i	−0.00983728	−	0.281703i
$790$	0.389081	−	3.70186i	0.0138429	−	0.131706i
$791$	−0.138915	+	0.240608i	−0.00493926	+	0.00855505i
$792$	9.17722	−	11.7826i	0.326098	−	0.418676i
$793$	0.0781890	−	0.0656083i	0.00277657	−	0.00232982i
$794$	12.5186	+	50.2094i	0.444269	+	1.78186i
$795$	−18.8792	−	2.65330i	−0.669577	−	0.0941029i
$796$	0.135659	−	3.88476i	0.00480830	−	0.137692i
$797$	−38.8843	+	28.2511i	−1.37735	+	1.00070i	−0.380229	+	0.924892i	$0.624155\pi$
$797$	−38.8843	+	28.2511i	−1.37735	+	1.00070i	−0.997122	+	0.0758121i	$0.975845\pi$
$798$	1.52016	+	0.256953i	0.0538130	+	0.00909602i
$799$	14.6933	+	45.2213i	0.519811	+	1.59981i
$800$	2.39481	−	3.06522i	0.0846695	−	0.108372i
$801$	−0.0513571	+	0.105298i	−0.00181461	+	0.00372051i
$802$	44.0011	+	36.9213i	1.55373	+	1.30374i
$803$	−3.56541	+	34.4178i	−0.125821	+	1.21458i
$804$	−5.49823	+	31.1820i	−0.193908	+	1.09970i
$805$	−0.820225	+	0.365188i	−0.0289091	+	0.0128712i
$806$	−9.59763	+	2.04004i	−0.338062	+	0.0718573i
$807$	−11.2118	−	14.3504i	−0.394674	−	0.505160i
$808$	2.03298	−	3.01402i	0.0715201	−	0.106033i
$809$	24.2369	+	10.7910i	0.852124	+	0.379390i	0.785854	−	0.618412i	$-0.212224\pi$
$809$	24.2369	+	10.7910i	0.852124	+	0.379390i	0.0662695	+	0.997802i	$0.478890\pi$
$810$	3.36809	+	0.715909i	0.118342	+	0.0251545i
$811$	9.16143	+	4.87122i	0.321701	+	0.171052i	0.622466	−	0.782647i	$-0.286131\pi$
$811$	9.16143	+	4.87122i	0.321701	+	0.171052i	−0.300765	+	0.953698i	$0.597242\pi$
$812$	−1.54067	+	0.107734i	−0.0540669	+	0.00378072i
$813$	−8.32139	−	6.98248i	−0.291844	−	0.244886i
$814$	−28.2263	−	86.4314i	−0.989331	−	3.02942i
$815$	7.46919	+	2.71856i	0.261634	+	0.0952272i
$816$	12.1693	+	8.84154i	0.426012	+	0.309516i
$817$	−4.62104	−	15.6949i	−0.161670	−	0.549095i
$818$	11.4980	+	35.3871i	0.402017	+	1.23728i
$819$	−0.763051	+	0.218801i	−0.0266632	+	0.00764554i
$820$	−19.2180	−	18.5586i	−0.671122	−	0.648095i
$821$	−14.3292	+	35.4660i	−0.500093	+	1.23777i	0.440352	+	0.897825i	$0.354854\pi$
$821$	−14.3292	+	35.4660i	−0.500093	+	1.23777i	−0.940444	+	0.339947i	$0.889591\pi$
$822$	19.4672	+	48.1830i	0.678997	+	1.68058i
$823$	−9.19273	+	8.87731i	−0.320438	+	0.309444i	−0.837428	−	0.546548i	$-0.815942\pi$
$823$	−9.19273	+	8.87731i	−0.320438	+	0.309444i	0.516989	+	0.855992i	$0.327053\pi$
$824$	11.2554	−	19.4949i	0.392100	−	0.679137i
$825$	9.27232	−	3.39057i	0.322821	−	0.118044i
$826$	2.29546	−	0.835478i	0.0798692	−	0.0290700i
$827$	−2.72603	−	0.781676i	−0.0947933	−	0.0271815i	0.227905	−	0.973683i	$-0.426812\pi$
$827$	−2.72603	−	0.781676i	−0.0947933	−	0.0271815i	−0.322699	+	0.946502i	$0.604590\pi$
$828$	−16.3123	+	3.46728i	−0.566891	+	0.120496i
$829$	3.39134	+	0.720851i	0.117786	+	0.0250362i	0.266427	−	0.963855i	$-0.414157\pi$
$829$	3.39134	+	0.720851i	0.117786	+	0.0250362i	−0.148641	+	0.988891i	$0.547490\pi$
$830$	−10.0763	−	20.6596i	−0.349755	−	0.717104i
$831$	0.161593	−	0.648115i	0.00560561	−	0.0224829i
$832$	19.3842	−	47.9777i	0.672028	−	1.66333i
$833$	32.6840	+	4.59343i	1.13243	+	0.159153i
$834$	−24.5141	−	36.3436i	−0.848853	−	1.25848i
$835$	−30.5622			−1.05765
$836$	−54.8727	+	10.1618i	−1.89781	+	0.351453i
$837$	−0.746048			−0.0257872
$838$	32.9174	+	48.8020i	1.13711	+	1.68584i
$839$	51.4772	+	7.23465i	1.77719	+	0.249768i	0.950021	−	0.312185i	$-0.101061\pi$
$839$	51.4772	+	7.23465i	1.77719	+	0.249768i	0.827170	+	0.561952i	$0.189950\pi$
$840$	−0.350573	+	0.867700i	−0.0120959	+	0.0299385i
$841$	5.20167	−	20.8628i	0.179368	−	0.719406i
$842$	−12.6147	−	25.8640i	−0.434732	−	0.891332i
$843$	4.85921	+	1.03286i	0.167360	+	0.0355735i
$844$	30.5967	−	6.50353i	1.05318	−	0.223861i
$845$	22.5841	+	6.47589i	0.776917	+	0.222777i
$846$	−22.8700	+	8.32401i	−0.786287	+	0.286185i
$847$	−0.283819	−	1.58193i	−0.00975215	−	0.0543557i
$848$	21.3145	−	36.9179i	0.731944	−	1.26776i
$849$	−21.6179	+	20.8761i	−0.741923	+	0.716467i
$850$	12.7669	+	31.5991i	0.437900	+	1.08384i
$851$	−18.3276	+	45.3624i	−0.628262	+	1.55500i
$852$	28.4688	+	27.4920i	0.975324	+	0.941860i
$853$	4.59905	−	1.31876i	0.157468	−	0.0451533i	−0.195977	−	0.980608i	$-0.562788\pi$
$853$	4.59905	−	1.31876i	0.157468	−	0.0451533i	0.353445	+	0.935455i	$0.385010\pi$
$854$	0.00205336	+	0.00631959i	7.02645e−5	+	0.000216252i
$855$	−3.67979	−	4.99006i	−0.125846	−	0.170657i
$856$	4.55334	+	3.30820i	0.155630	+	0.113072i
$857$	−37.4619	−	13.6350i	−1.27967	−	0.465763i	−0.389350	−	0.921090i	$-0.627300\pi$
$857$	−37.4619	−	13.6350i	−1.27967	−	0.465763i	−0.890324	+	0.455327i	$0.849522\pi$
$858$	35.2512	−	25.6921i	1.20346	−	0.877115i
$859$	−21.7472	−	18.2480i	−0.742004	−	0.622615i	0.191371	−	0.981518i	$-0.438707\pi$
$859$	−21.7472	−	18.2480i	−0.742004	−	0.622615i	−0.933375	+	0.358902i	$0.883151\pi$
$860$	20.5591	−	1.43763i	0.701061	−	0.0490229i
$861$	0.627703	+	0.333755i	0.0213920	+	0.0113744i
$862$	−24.5822	−	5.22510i	−0.837273	−	0.177968i
$863$	−3.90423	−	1.73828i	−0.132902	−	0.0591716i	0.339208	−	0.940711i	$-0.389841\pi$
$863$	−3.90423	−	1.73828i	−0.132902	−	0.0591716i	−0.472110	+	0.881540i	$0.656508\pi$
$864$	0.730715	−	1.08333i	0.0248594	−	0.0368556i
$865$	0.832886	+	1.06605i	0.0283190	+	0.0362466i
$866$	−97.2362	+	20.6682i	−3.30422	+	0.702334i
$867$	4.90364	−	2.18324i	0.166536	−	0.0741467i
$868$	0.0730662	−	0.414379i	0.00248003	−	0.0140649i
$869$	−1.79728	−	3.10226i	−0.0609686	−	0.105237i
$870$	7.22306	+	6.06087i	0.244885	+	0.205483i
$871$	−19.5356	+	40.0539i	−0.661939	+	1.35718i
$872$	41.7246	−	53.4051i	1.41297	−	1.80852i
$873$	0.775506	+	2.38676i	0.0262469	+	0.0807796i
$874$	39.6396	+	22.5130i	1.34083	+	0.761512i
$875$	−1.34116	+	0.974413i	−0.0453396	+	0.0329412i
$876$	1.40549	−	40.2481i	0.0474872	−	1.35986i
$877$	9.91378	+	1.39329i	0.334765	+	0.0470481i	0.304553	−	0.952495i	$-0.401493\pi$
$877$	9.91378	+	1.39329i	0.334765	+	0.0470481i	0.0302117	+	0.999544i	$0.490382\pi$
$878$	−10.5571	−	42.3424i	−0.356286	−	1.42899i
$879$	7.22801	−	6.06502i	0.243795	−	0.204568i
$880$	0.501215	−	14.9960i	0.0168960	−	0.505516i
$881$	−20.9857	+	36.3483i	−0.707026	+	1.22461i	0.258929	+	0.965896i	$0.416630\pi$
$881$	−20.9857	+	36.3483i	−0.707026	+	1.22461i	−0.965955	+	0.258709i	$0.916703\pi$
$882$	−1.76588	+	16.8012i	−0.0594602	+	0.565726i
$883$	0.466885	+	13.3698i	0.0157119	+	0.449931i	0.981597	+	0.190962i	$0.0611606\pi$
$883$	0.466885	+	13.3698i	0.0157119	+	0.449931i	−0.965886	+	0.258969i	$0.916617\pi$
$884$	61.0655	+	78.1603i	2.05386	+	2.62881i
$885$	−8.97447	−	3.99569i	−0.301673	−	0.134314i
$886$	−1.89617	−	18.0408i	−0.0637030	−	0.606094i
$887$	−27.7847	+	3.90488i	−0.932919	+	0.131113i	−0.589225	−	0.807969i	$-0.700567\pi$
$887$	−27.7847	+	3.90488i	−0.932919	+	0.131113i	−0.343693	+	0.939082i	$0.611678\pi$
$888$	19.1032	+	47.2821i	0.641062	+	1.58668i
$889$	0.636536	+	2.55301i	0.0213487	+	0.0856251i
$890$	0.0700499	+	0.397273i	0.00234808	+	0.0133166i
$891$	3.02787	−	1.35352i	0.101437	−	0.0453447i
$892$	32.7853			1.09773
$893$	40.7473	+	16.1281i	1.36356	+	0.539706i
$894$	−11.6610	+	35.8890i	−0.390003	+	1.20031i
$895$	0.731562	−	20.9492i	0.0244534	−	0.700254i
$896$	2.14857	+	2.07485i	0.0717788	+	0.0693160i
$897$	−23.4144	−	1.63729i	−0.781784	−	0.0546677i
$898$	−63.7931	−	39.8623i	−2.12880	−	1.33022i
$899$	−1.80381	−	0.959102i	−0.0601604	−	0.0319878i
$900$	−10.4973	+	4.67372i	−0.349911	+	0.155791i
$901$	−31.6948	−	54.8970i	−1.05591	−	1.82888i
$902$	−38.6936	−	5.37903i	−1.28836	−	0.179102i
$903$	−0.515341	+	0.187569i	−0.0171495	+	0.00624189i
$904$	−0.895047	+	8.51580i	−0.0297688	+	0.283231i
$905$	13.4952	+	14.9880i	0.448597	+	0.498218i
$906$	18.9197	−	2.65900i	0.628566	−	0.0883392i
$907$	6.47380	−	25.9650i	0.214959	−	0.862154i	−0.761800	−	0.647813i	$-0.775684\pi$
$907$	6.47380	−	25.9650i	0.214959	−	0.862154i	0.976759	−	0.214341i	$-0.0687605\pi$
$908$	28.2503	+	1.97545i	0.937518	+	0.0655576i
$909$	0.712855	−	0.379032i	0.0236439	−	0.0125717i
$910$	−1.68280	+	2.15389i	−0.0557843	+	0.0714007i
$911$	29.1721	+	21.1947i	0.966514	+	0.702213i	0.954654	−	0.297716i	$-0.0962250\pi$
$911$	29.1721	+	21.1947i	0.966514	+	0.702213i	0.0118592	+	0.999930i	$0.496225\pi$
$912$	13.4277	−	3.44913i	0.444635	−	0.114212i
$913$	−19.5640	−	10.3649i	−0.647475	−	0.343027i
$914$	−21.8368	−	7.94794i	−0.722296	−	0.262894i
$915$	0.0117144	−	0.0240181i	0.000387266	−	0.000794012i
$916$	−37.8826	+	23.6717i	−1.25168	+	0.782134i
$917$	−2.08833	−	1.30494i	−0.0689628	−	0.0430928i
$918$	5.01889	+	10.2902i	0.165648	+	0.339629i
$919$	−1.89948	−	18.0724i	−0.0626582	−	0.596153i	−0.980131	−	0.198354i	$-0.936441\pi$
$919$	−1.89948	−	18.0724i	−0.0626582	−	0.596153i	0.917472	−	0.397800i	$-0.130226\pi$
$920$	−18.5159	+	20.5640i	−0.610451	+	0.677975i
$921$	−0.464965	−	13.3149i	−0.0153211	−	0.438740i
$922$	−83.6554	−	23.9878i	−2.75504	−	0.789996i
$923$	27.8508	+	48.2389i	0.916719	+	1.58780i
$924$	0.455248	+	1.81434i	0.0149766	+	0.0596873i
$925$	−5.85382	+	33.1987i	−0.192472	+	1.09157i
$926$	66.8156	−	4.67220i	2.19570	−	0.153538i
$927$	4.23941	−	2.64908i	0.139240	−	0.0870071i
$928$	3.15944	−	1.67990i	0.103714	−	0.0551456i
$929$	17.7500	−	5.08973i	0.582359	−	0.166989i	0.0284921	−	0.999594i	$-0.490929\pi$
$929$	17.7500	−	5.08973i	0.582359	−	0.166989i	0.553867	+	0.832605i	$0.313152\pi$
$930$	−2.07828	+	1.50996i	−0.0681494	+	0.0495134i
$931$	22.4611	−	20.5141i	0.736133	−	0.672323i
$932$	−8.79650	+	27.0728i	−0.288139	+	0.886800i
$933$	16.7086	+	24.7715i	0.547014	+	0.810981i
$934$	−15.4223	−	87.4641i	−0.504633	−	2.86191i
$935$	−18.9390	−	11.7950i	−0.619371	−	0.385739i
$936$	−18.7412	+	15.7257i	−0.612575	+	0.514012i
$937$	12.0870	−	11.6723i	0.394866	−	0.381317i	−0.470549	−	0.882374i	$-0.655944\pi$
$937$	12.0870	−	11.6723i	0.394866	−	0.381317i	0.865414	+	0.501057i	$0.167055\pi$
$938$	−1.94127	−	2.15600i	−0.0633849	−	0.0703960i
$939$	4.11144	−	4.56622i	0.134172	−	0.149013i
$940$	−30.8686	+	45.7646i	−1.00682	+	1.49268i
$941$	2.96747	−	4.39946i	0.0967369	−	0.143418i	−0.777562	−	0.628806i	$-0.783544\pi$
$941$	2.96747	−	4.39946i	0.0967369	−	0.143418i	0.874299	+	0.485388i	$0.161322\pi$
$942$	6.94679	−	7.71519i	0.226339	−	0.251375i
$943$	14.0657	+	15.6215i	0.458041	+	0.508706i
$944$	15.8011	−	15.2589i	0.514282	−	0.496636i
$945$	−0.159203	+	0.133587i	−0.00517888	+	0.00434560i
$946$	23.0565	−	19.4056i	0.749632	−	0.630929i
$947$	−6.94230	−	39.3718i	−0.225595	−	1.27941i	−0.861545	−	0.507681i	$-0.830503\pi$
$947$	−6.94230	−	39.3718i	−0.225595	−	1.27941i	0.635951	−	0.771730i	$-0.280608\pi$
$948$	2.33342	+	3.45944i	0.0757861	+	0.112357i
$949$	17.5156	−	53.9074i	0.568580	−	1.74991i
$950$	29.9412	+	9.49448i	0.971421	+	0.308042i
$951$	−7.44578	+	5.40968i	−0.241446	+	0.175421i
$952$	−2.99111	+	0.857686i	−0.0969423	+	0.0277978i
$953$	−16.2771	+	8.65467i	−0.527266	+	0.280352i	−0.711689	−	0.702495i	$-0.752070\pi$
$953$	−16.2771	+	8.65467i	−0.527266	+	0.280352i	0.184423	+	0.982847i	$0.440958\pi$
$954$	27.5158	−	17.1938i	0.890858	−	0.556670i
$955$	24.7189	−	1.72852i	0.799886	−	0.0559335i
$956$	−15.9453	+	90.4300i	−0.515706	+	2.92472i
$957$	9.06089	+	0.619980i	0.292897	+	0.0200411i
$958$	−8.04836	−	13.9402i	−0.260031	−	0.450386i
$959$	−3.01501	−	0.864541i	−0.0973599	−	0.0279175i
$960$	−0.472801	−	13.5393i	−0.0152596	−	0.436978i
$961$	−20.3706	+	22.6239i	−0.657117	+	0.729802i
$962$	15.5687	+	148.126i	0.501956	+	4.77579i
$963$	0.547910	+	1.12338i	0.0176562	+	0.0362005i
$964$	63.7615	+	39.8426i	2.05362	+	1.28324i
$965$	−17.8082	+	11.1278i	−0.573268	+	0.358217i
$966$	0.669847	−	1.37339i	0.0215520	−	0.0441881i
$967$	−38.6010	−	14.0496i	−1.24132	−	0.451805i	−0.363862	−	0.931453i	$-0.618542\pi$
$967$	−38.6010	−	14.0496i	−1.24132	−	0.451805i	−0.877461	+	0.479648i	$0.840764\pi$
$968$	−27.8215	−	40.9820i	−0.894216	−	1.31721i
$969$	5.54177	−	19.8564i	0.178027	−	0.637878i
$970$	6.99100	+	5.07926i	0.224467	+	0.163085i
$971$	10.7076	−	13.7051i	0.343623	−	0.439817i	−0.584893	−	0.811111i	$-0.698863\pi$
$971$	10.7076	−	13.7051i	0.343623	−	0.439817i	0.928516	+	0.371293i	$0.121086\pi$
$972$	−3.40832	+	1.81224i	−0.109322	+	0.0581275i
$973$	2.63945	+	0.184569i	0.0846170	+	0.00591700i
$974$	−5.65575	+	22.6840i	−0.181222	+	0.726841i
$975$	−16.0153	+	2.25080i	−0.512899	+	0.0720832i
$976$	0.0399819	+	0.0444044i	0.00127979	+	0.00142135i
$977$	1.93045	−	18.3670i	0.0617605	−	0.587612i	−0.919252	−	0.393669i	$-0.871206\pi$
$977$	1.93045	−	18.3670i	0.0617605	−	0.587612i	0.981013	−	0.193943i	$-0.0621278\pi$
$978$	−12.7117	+	4.62669i	−0.406476	+	0.147945i
$979$	0.279908	+	0.269496i	0.00894590	+	0.00861314i
$980$	19.1589	+	33.1842i	0.612009	+	1.06003i
$981$	13.7491	−	6.12150i	0.438976	−	0.195445i
$982$	32.9817	+	17.5367i	1.05249	+	0.559618i
$983$	0.541867	+	0.338596i	0.0172829	+	0.0107995i	0.538533	−	0.842604i	$-0.318979\pi$
$983$	0.541867	+	0.338596i	0.0172829	+	0.0107995i	−0.521250	+	0.853404i	$0.674534\pi$
$984$	21.8570	+	1.52839i	0.696777	+	0.0487234i
$985$	−1.34865	−	1.30238i	−0.0429717	−	0.0414972i
$986$	−1.09414	+	31.3321i	−0.0348446	+	0.997817i
$987$	0.453923	−	1.39703i	0.0144485	−	0.0444680i
$988$	91.3802	+	2.54296i	2.90719	+	0.0809024i
$989$	−16.2158			−0.515633
$990$	5.69532	−	9.89875i	0.181009	−	0.314603i
$991$	−3.33238	−	18.8989i	−0.105857	−	0.600343i	−0.990875	−	0.134786i	$-0.956965\pi$
$991$	−3.33238	−	18.8989i	−0.105857	−	0.600343i	0.885018	−	0.465557i	$-0.154146\pi$
$992$	0.235846	+	0.945927i	0.00748812	+	0.0300332i
$993$	12.7324	+	31.5137i	0.404050	+	1.00006i
$994$	−3.59096	+	0.504677i	−0.113898	+	0.0160074i
$995$	−0.149721	−	1.42450i	−0.00474647	−	0.0451596i
$996$	23.5406	+	10.4810i	0.745913	+	0.332102i
$997$	−3.63134	−	4.64790i	−0.115006	−	0.147200i	0.727063	−	0.686570i	$-0.240885\pi$
$997$	−3.63134	−	4.64790i	−0.115006	−	0.147200i	−0.842069	+	0.539370i	$0.818662\pi$
$998$	−3.49802	−	100.170i	−0.110728	−	3.17083i
$999$	−1.18375	+	11.2626i	−0.0374522	+	0.356334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.bo.b.4.3	✓	480
11.3	even	5	inner	627.2.bo.b.289.3	yes	480
19.5	even	9	inner	627.2.bo.b.499.3	yes	480
209.157	even	45	inner	627.2.bo.b.157.3	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.bo.b.4.3	✓	480	1.1	even	1	trivial
627.2.bo.b.157.3	yes	480	209.157	even	45	inner
627.2.bo.b.289.3	yes	480	11.3	even	5	inner
627.2.bo.b.499.3	yes	480	19.5	even	9	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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.bo (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35368 - 2.00692i) q^{2} +(0.990268 + 0.139173i) q^{3} +(-1.44604 + 3.57908i) q^{4} +(-0.344111 + 1.38016i) q^{5} +(-1.06120 - 2.17578i) q^{6} +(0.142915 + 0.0303776i) q^{7} +(4.40463 - 0.936234i) q^{8} +(0.961262 + 0.275637i) q^{9} +(3.23567 - 1.17769i) q^{10} +(1.85052 - 2.75238i) q^{11} +(-1.93008 + 3.34300i) q^{12} +(-3.90816 + 3.77406i) q^{13} +(-0.132496 - 0.327940i) q^{14} +(-0.532843 + 1.31883i) q^{15} +(-2.28788 - 2.20938i) q^{16} +(-4.54624 + 1.30361i) q^{17} +(-0.748061 - 2.30230i) q^{18} +(-1.74467 + 3.99451i) q^{19} +(-4.44209 - 3.22737i) q^{20} +(0.137297 + 0.0499719i) q^{21} +(-8.02880 + 0.0120100i) q^{22} +(3.30947 + 2.77698i) q^{23} +(4.49207 - 0.314116i) q^{24} +(2.62832 + 1.39750i) q^{25} +(12.8646 + 2.73446i) q^{26} +(0.913545 + 0.406737i) q^{27} +(-0.315385 + 0.467578i) q^{28} +(1.68590 + 2.15785i) q^{29} +(3.36809 - 0.715909i) q^{30} +(-0.681549 + 0.303445i) q^{31} +(0.226912 - 1.28688i) q^{32} +(2.21557 - 2.46805i) q^{33} +(8.77040 + 7.35924i) q^{34} +(-0.0911046 + 0.186792i) q^{35} +(-2.37655 + 3.04185i) q^{36} +(3.49952 + 10.7704i) q^{37} +(10.3784 - 1.90590i) q^{38} +(-4.39537 + 3.19342i) q^{39} +(-0.223537 + 6.40125i) q^{40} +(4.81834 + 0.677174i) q^{41} +(-0.0855666 - 0.343189i) q^{42} +(-2.87533 + 2.41269i) q^{43} +(7.17505 + 10.6032i) q^{44} +(-0.711204 + 1.23184i) q^{45} +(1.09319 - 10.4010i) q^{46} +(-0.350869 - 10.0476i) q^{47} +(-1.95813 - 2.50629i) q^{48} +(-6.37532 - 2.83847i) q^{49} +(-0.753239 - 7.16659i) q^{50} +(-4.68342 + 0.658212i) q^{51} +(-7.85631 - 19.4451i) q^{52} +(3.24252 + 13.0050i) q^{53} +(-0.420364 - 2.38400i) q^{54} +(3.16193 + 3.50113i) q^{55} +0.657930 q^{56} +(-2.28362 + 3.71283i) q^{57} +(2.04845 - 6.30449i) q^{58} +(-0.241031 + 6.90224i) q^{59} +(-3.94970 - 3.81418i) q^{60} +(-0.0187411 - 0.00131050i) q^{61} +(1.53159 + 0.957043i) q^{62} +(0.129006 + 0.0685936i) q^{63} +(-8.70093 + 3.87390i) q^{64} +(-3.86395 - 6.69256i) q^{65} +(-7.95234 - 1.10550i) q^{66} +(7.70784 - 2.80543i) q^{67} +(1.90832 - 18.1564i) q^{68} +(2.89078 + 3.21054i) q^{69} +(0.498202 - 0.0700178i) q^{70} +(2.48030 - 9.94794i) q^{71} +(4.49207 + 0.314116i) q^{72} +(-9.21169 + 4.89794i) q^{73} +(16.8781 - 21.6029i) q^{74} +(2.40825 + 1.74969i) q^{75} +(-11.7738 - 12.0205i) q^{76} +(0.348078 - 0.337142i) q^{77} +(12.3589 + 4.49826i) q^{78} +(0.473880 - 0.971598i) q^{79} +(3.83657 - 2.39736i) q^{80} +(0.848048 + 0.529919i) q^{81} +(-5.16347 - 10.5867i) q^{82} +(-0.697777 - 6.63890i) q^{83} +(-0.377390 + 0.419134i) q^{84} +(-0.234776 - 6.72311i) q^{85} +(8.73436 + 2.50454i) q^{86} +(1.36917 + 2.37148i) q^{87} +(5.57399 - 13.8557i) q^{88} +(-0.0203437 + 0.115375i) q^{89} +(3.43494 - 0.240195i) q^{90} +(-0.673182 + 0.420651i) q^{91} +(-14.7247 + 7.82924i) q^{92} +(-0.717147 + 0.205639i) q^{93} +(-19.6897 + 14.3054i) q^{94} +(-4.91269 - 3.78247i) q^{95} +(0.403802 - 1.24278i) q^{96} +(1.40334 + 2.08054i) q^{97} +(2.93357 + 16.6371i) q^{98} +(2.53749 - 2.13568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 18 q^{5} + 3 q^{7} + 12 q^{10} + 3 q^{11} - 240 q^{12} + 42 q^{14} - 12 q^{15} + 72 q^{16} - 18 q^{17} - 102 q^{20} + 24 q^{22} + 54 q^{23} - 18 q^{25} - 12 q^{26} + 60 q^{27} + 36 q^{29} + 12 q^{30}+ \cdots - 6 q^{99}+O(q^{100}) \) 480 * q + 18 * q^5 + 3 * q^7 + 12 * q^10 + 3 * q^11 - 240 * q^12 + 42 * q^14 - 12 * q^15 + 72 * q^16 - 18 * q^17 - 102 * q^20 + 24 * q^22 + 54 * q^23 - 18 * q^25 - 12 * q^26 + 60 * q^27 + 36 * q^29 + 12 * q^30 + 60 * q^31 - 30 * q^32 - 21 * q^33 - 84 * q^34 + 12 * q^35 + 36 * q^37 - 90 * q^38 - 12 * q^39 + 300 * q^40 - 63 * q^41 - 18 * q^42 - 24 * q^43 - 15 * q^44 + 6 * q^45 - 6 * q^46 + 24 * q^48 + 39 * q^49 + 12 * q^51 - 21 * q^52 + 9 * q^53 + 45 * q^55 + 156 * q^56 + 30 * q^57 + 12 * q^58 - 69 * q^59 - 36 * q^60 + 12 * q^61 - 90 * q^62 + 60 * q^64 - 66 * q^65 + 30 * q^66 + 72 * q^67 + 24 * q^68 + 18 * q^69 - 96 * q^70 + 72 * q^71 + 18 * q^73 + 57 * q^74 - 102 * q^75 + 48 * q^76 - 114 * q^77 - 216 * q^78 - 24 * q^79 - 30 * q^80 - 24 * q^82 + 78 * q^83 - 36 * q^84 - 36 * q^85 - 189 * q^86 - 24 * q^87 + 120 * q^88 - 318 * q^89 - 18 * q^90 - 48 * q^91 + 354 * q^92 + 12 * q^93 - 282 * q^94 + 6 * q^95 + 60 * q^96 + 120 * q^97 - 96 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more