LMFDB - Embedded newform 348.2.t.a.35.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			35.17
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.845038 - 1.13398i) q^{2} +(1.72591 - 0.145741i) q^{3} +(-0.571822 + 1.91651i) q^{4} +(-1.76879 - 1.41056i) q^{5} +(-1.62373 - 1.83399i) q^{6} +(-4.04660 - 0.923610i) q^{7} +(2.65650 - 0.971091i) q^{8} +(2.95752 - 0.503073i) q^{9} +O(q^{10})$	\(q+(-0.845038 - 1.13398i) q^{2} +(1.72591 - 0.145741i) q^{3} +(-0.571822 + 1.91651i) q^{4} +(-1.76879 - 1.41056i) q^{5} +(-1.62373 - 1.83399i) q^{6} +(-4.04660 - 0.923610i) q^{7} +(2.65650 - 0.971091i) q^{8} +(2.95752 - 0.503073i) q^{9} +(-0.104856 + 3.19775i) q^{10} +(-1.83496 - 3.81034i) q^{11} +(-0.707597 + 3.39106i) q^{12} +(-3.43689 + 1.65512i) q^{13} +(2.37217 + 5.36925i) q^{14} +(-3.25835 - 2.17672i) q^{15} +(-3.34604 - 2.19181i) q^{16} +1.04033 q^{17} +(-3.06969 - 2.92865i) q^{18} +(0.177666 + 0.778407i) q^{19} +(3.71479 - 2.58332i) q^{20} +(-7.11866 - 1.00431i) q^{21} +(-2.77023 + 5.30069i) q^{22} +(-3.60359 - 4.51876i) q^{23} +(4.44334 - 2.06318i) q^{24} +(0.0263246 + 0.115336i) q^{25} +(4.78118 + 2.49873i) q^{26} +(5.03109 - 1.29929i) q^{27} +(4.08404 - 7.22721i) q^{28} +(4.22559 - 3.33832i) q^{29} +(0.285073 + 5.53431i) q^{30} +(-1.40533 + 1.76223i) q^{31} +(0.342064 + 5.64650i) q^{32} +(-3.72230 - 6.30886i) q^{33} +(-0.879122 - 1.17972i) q^{34} +(5.85477 + 7.34165i) q^{35} +(-0.727029 + 5.95579i) q^{36} +(2.75551 - 5.72187i) q^{37} +(0.732563 - 0.859253i) q^{38} +(-5.69054 + 3.35748i) q^{39} +(-6.06857 - 2.02950i) q^{40} -6.16205 q^{41} +(4.87668 + 8.92110i) q^{42} +(5.16346 + 6.47477i) q^{43} +(8.35183 - 1.33789i) q^{44} +(-5.94084 - 3.28194i) q^{45} +(-2.07901 + 7.90493i) q^{46} +(3.12260 + 6.48414i) q^{47} +(-6.09439 - 3.29520i) q^{48} +(9.21512 + 4.43777i) q^{49} +(0.108543 - 0.127315i) q^{50} +(1.79552 - 0.151620i) q^{51} +(-1.20677 - 7.53328i) q^{52} +(-5.00979 - 3.99517i) q^{53} +(-5.72483 - 4.60720i) q^{54} +(-2.12906 + 9.32801i) q^{55} +(-11.6467 + 1.47605i) q^{56} +(0.420082 + 1.31757i) q^{57} +(-7.35637 - 1.97074i) q^{58} -7.80721 q^{59} +(6.03490 - 4.99997i) q^{60} +(5.36844 + 1.22531i) q^{61} +(3.18590 + 0.104467i) q^{62} +(-12.4325 - 0.695860i) q^{63} +(6.11396 - 5.15940i) q^{64} +(8.41379 + 1.92039i) q^{65} +(-4.00864 + 9.55224i) q^{66} +(3.34418 - 6.94426i) q^{67} +(-0.594886 + 1.99381i) q^{68} +(-6.87804 - 7.27378i) q^{69} +(3.37778 - 12.8432i) q^{70} +(7.49248 - 3.60819i) q^{71} +(7.36811 - 4.20843i) q^{72} +(3.17787 - 2.53427i) q^{73} +(-8.81699 + 1.71051i) q^{74} +(0.0622431 + 0.195222i) q^{75} +(-1.59342 - 0.104610i) q^{76} +(3.90609 + 17.1137i) q^{77} +(8.61605 + 3.61576i) q^{78} +(15.4626 + 7.44641i) q^{79} +(2.82676 + 8.59664i) q^{80} +(8.49384 - 2.97569i) q^{81} +(5.20717 + 6.98764i) q^{82} +(-0.454596 - 1.99171i) q^{83} +(5.99538 - 13.0687i) q^{84} +(-1.84013 - 1.46746i) q^{85} +(2.97894 - 11.3267i) q^{86} +(6.80646 - 6.37747i) q^{87} +(-8.57476 - 8.34024i) q^{88} +(5.31062 - 6.65930i) q^{89} +(1.29859 + 9.51016i) q^{90} +(15.4364 - 3.52326i) q^{91} +(10.7209 - 4.32240i) q^{92} +(-2.16865 + 3.24627i) q^{93} +(4.71417 - 9.02031i) q^{94} +(0.783737 - 1.62745i) q^{95} +(1.41330 + 9.69549i) q^{96} +(-13.8570 + 3.16276i) q^{97} +(-2.75478 - 14.1998i) q^{98} +(-7.34381 - 10.3460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$	$-1$

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 $

$2$	−0.845038	−	1.13398i	−0.597532	−	0.801845i
$2$	−0.845038	−	1.13398i	−0.597532	−	0.801845i
$3$	1.72591	−	0.145741i	0.996454	−	0.0841439i
$3$	1.72591	−	0.145741i	0.996454	−	0.0841439i
$4$	−0.571822	+	1.91651i	−0.285911	+	0.958256i
$5$	−1.76879	−	1.41056i	−0.791027	−	0.630823i	0.142311	−	0.989822i	$-0.454547\pi$
$5$	−1.76879	−	1.41056i	−0.791027	−	0.630823i	−0.933338	+	0.358999i	$0.883118\pi$
$6$	−1.62373	−	1.83399i	−0.662883	−	0.748723i
$7$	−4.04660	−	0.923610i	−1.52947	−	0.349092i	−0.626716	−	0.779248i	$-0.715601\pi$
$7$	−4.04660	−	0.923610i	−1.52947	−	0.349092i	−0.902754	+	0.430156i	$0.858458\pi$
$8$	2.65650	−	0.971091i	0.939214	−	0.343333i
$9$	2.95752	−	0.503073i	0.985840	−	0.167691i
$10$	−0.104856	+	3.19775i	−0.0331583	+	1.01122i
$11$	−1.83496	−	3.81034i	−0.553262	−	1.14886i	−0.970731	−	0.240169i	$-0.922797\pi$
$11$	−1.83496	−	3.81034i	−0.553262	−	1.14886i	0.417469	−	0.908691i	$-0.362917\pi$
$12$	−0.707597	+	3.39106i	−0.204266	+	0.978916i
$13$	−3.43689	+	1.65512i	−0.953223	+	0.459048i	−0.844815	−	0.535059i	$-0.820290\pi$
$13$	−3.43689	+	1.65512i	−0.953223	+	0.459048i	−0.108408	+	0.994107i	$0.534575\pi$
$14$	2.37217	+	5.36925i	0.633990	+	1.43499i
$15$	−3.25835	−	2.17672i	−0.841301	−	0.562026i
$16$	−3.34604	−	2.19181i	−0.836510	−	0.547952i
$17$	1.04033			0.252318			0.126159	−	0.992010i	$-0.459735\pi$
$17$	1.04033			0.252318			0.126159	+	0.992010i	$0.459735\pi$
$18$	−3.06969	−	2.92865i	−0.723533	−	0.690290i
$19$	0.177666	+	0.778407i	0.0407594	+	0.178579i	0.991210	−	0.132296i	$-0.0422351\pi$
$19$	0.177666	+	0.778407i	0.0407594	+	0.178579i	−0.950451	+	0.310875i	$0.899378\pi$
$20$	3.71479	−	2.58332i	0.830653	−	0.577647i
$21$	−7.11866	−	1.00431i	−1.55342	−	0.219158i
$22$	−2.77023	+	5.30069i	−0.590616	+	1.13011i
$23$	−3.60359	−	4.51876i	−0.751401	−	0.942227i	0.248248	−	0.968696i	$-0.420145\pi$
$23$	−3.60359	−	4.51876i	−0.751401	−	0.942227i	−0.999650	+	0.0264690i	$0.991574\pi$
$24$	4.44334	−	2.06318i	0.906994	−	0.421144i
$25$	0.0263246	+	0.115336i	0.00526493	+	0.0230672i
$26$	4.78118	+	2.49873i	0.937666	+	0.490041i
$27$	5.03109	−	1.29929i	0.968233	−	0.250049i
$28$	4.08404	−	7.22721i	0.771811	−	1.36582i
$29$	4.22559	−	3.33832i	0.784673	−	0.619910i
$29$	4.22559	−	3.33832i	0.784673	−	0.619910i
$30$	0.285073	+	5.53431i	0.0520470	+	1.01042i
$31$	−1.40533	+	1.76223i	−0.252405	+	0.316506i	−0.891850	−	0.452331i	$-0.850593\pi$
$31$	−1.40533	+	1.76223i	−0.252405	+	0.316506i	0.639445	+	0.768837i	$0.279164\pi$
$32$	0.342064	+	5.64650i	0.0604690	+	0.998170i
$33$	−3.72230	−	6.30886i	−0.647969	−	1.09823i
$34$	−0.879122	−	1.17972i	−0.150768	−	0.202320i
$35$	5.85477	+	7.34165i	0.989637	+	1.24097i
$36$	−0.727029	+	5.95579i	−0.121171	+	0.992632i
$37$	2.75551	−	5.72187i	0.453003	−	0.940670i	−0.541958	−	0.840405i	$-0.682317\pi$
$37$	2.75551	−	5.72187i	0.453003	−	0.940670i	0.994961	−	0.100264i	$-0.0319688\pi$
$38$	0.732563	−	0.859253i	0.118837	−	0.139389i
$39$	−5.69054	+	3.35748i	−0.911216	+	0.537628i
$40$	−6.06857	−	2.02950i	−0.959525	−	0.320892i
$41$	−6.16205			−0.962351			−0.481175	−	0.876624i	$-0.659790\pi$
$41$	−6.16205			−0.962351			−0.481175	+	0.876624i	$0.659790\pi$
$42$	4.87668	+	8.92110i	0.752487	+	1.37656i
$43$	5.16346	+	6.47477i	0.787420	+	0.987393i	0.999948	+	0.0102380i	$0.00325890\pi$
$43$	5.16346	+	6.47477i	0.787420	+	0.987393i	−0.212528	+	0.977155i	$0.568170\pi$
$44$	8.35183	−	1.33789i	1.25909	−	0.201695i
$45$	−5.94084	−	3.28194i	−0.885609	−	0.489242i
$46$	−2.07901	+	7.90493i	−0.306534	+	1.16552i
$47$	3.12260	+	6.48414i	0.455478	+	0.945809i	0.994620	+	0.103594i	$0.0330344\pi$
$47$	3.12260	+	6.48414i	0.455478	+	0.945809i	−0.539142	+	0.842215i	$0.681251\pi$
$48$	−6.09439	−	3.29520i	−0.879650	−	0.475621i
$49$	9.21512	+	4.43777i	1.31645	+	0.633967i
$50$	0.108543	−	0.127315i	0.0153503	−	0.0180050i
$51$	1.79552	−	0.151620i	0.251423	−	0.0212310i
$52$	−1.20677	−	7.53328i	−0.167349	−	1.04468i
$53$	−5.00979	−	3.99517i	−0.688148	−	0.548779i	0.215792	−	0.976439i	$-0.430767\pi$
$53$	−5.00979	−	3.99517i	−0.688148	−	0.548779i	−0.903940	+	0.427660i	$0.859338\pi$
$54$	−5.72483	−	4.60720i	−0.779051	−	0.626961i
$55$	−2.12906	+	9.32801i	−0.287082	+	1.25779i
$56$	−11.6467	+	1.47605i	−1.55635	+	0.197245i
$57$	0.420082	+	1.31757i	0.0556412	+	0.174516i
$58$	−7.35637	−	1.97074i	−0.965939	−	0.258771i
$59$	−7.80721			−1.01641			−0.508206	−	0.861235i	$-0.669691\pi$
$59$	−7.80721			−1.01641			−0.508206	+	0.861235i	$0.669691\pi$
$60$	6.03490	−	4.99997i	0.779102	−	0.645493i
$61$	5.36844	+	1.22531i	0.687358	+	0.156885i	0.551915	−	0.833900i	$-0.313897\pi$
$61$	5.36844	+	1.22531i	0.687358	+	0.156885i	0.135443	+	0.990785i	$0.456754\pi$
$62$	3.18590	+	0.104467i	0.404609	+	0.0132673i
$63$	−12.4325	−	0.695860i	−1.56635	−	0.0876701i
$64$	6.11396	−	5.15940i	0.764246	−	0.644925i
$65$	8.41379	+	1.92039i	1.04360	+	0.238195i
$66$	−4.00864	+	9.55224i	−0.493430	+	1.17580i
$67$	3.34418	−	6.94426i	0.408556	−	0.848376i	−0.590586	−	0.806974i	$-0.701103\pi$
$67$	3.34418	−	6.94426i	0.408556	−	0.848376i	0.999143	−	0.0414014i	$-0.0131822\pi$
$68$	−0.594886	+	1.99381i	−0.0721405	+	0.241785i
$69$	−6.87804	−	7.27378i	−0.828019	−	0.875660i
$70$	3.37778	−	12.8432i	0.403722	−	1.53505i
$71$	7.49248	−	3.60819i	0.889194	−	0.428213i	0.0672201	−	0.997738i	$-0.478587\pi$
$71$	7.49248	−	3.60819i	0.889194	−	0.428213i	0.821974	+	0.569525i	$0.192873\pi$
$72$	7.36811	−	4.20843i	0.868341	−	0.495968i
$73$	3.17787	−	2.53427i	0.371942	−	0.296614i	−0.419624	−	0.907698i	$-0.637838\pi$
$73$	3.17787	−	2.53427i	0.371942	−	0.296614i	0.791565	+	0.611085i	$0.209266\pi$
$74$	−8.81699	+	1.71051i	−1.02495	+	0.198842i
$75$	0.0622431	+	0.195222i	0.00718722	+	0.0225423i
$76$	−1.59342	−	0.104610i	−0.182778	−	0.0119996i
$77$	3.90609	+	17.1137i	0.445140	+	1.95029i
$78$	8.61605	+	3.61576i	0.975575	+	0.409404i
$79$	15.4626	+	7.44641i	1.73968	+	0.837787i	0.982905	+	0.184114i	$0.0589417\pi$
$79$	15.4626	+	7.44641i	1.73968	+	0.837787i	0.756778	+	0.653673i	$0.226773\pi$
$80$	2.82676	+	8.59664i	0.316041	+	0.961134i
$81$	8.49384	−	2.97569i	0.943760	−	0.330633i
$82$	5.20717	+	6.98764i	0.575035	+	0.771656i
$83$	−0.454596	−	1.99171i	−0.0498984	−	0.218619i	0.943831	−	0.330427i	$-0.107193\pi$
$83$	−0.454596	−	1.99171i	−0.0498984	−	0.218619i	−0.993730	+	0.111808i	$0.964336\pi$
$84$	5.99538	−	13.0687i	0.654149	−	1.42591i
$85$	−1.84013	−	1.46746i	−0.199590	−	0.159168i
$86$	2.97894	−	11.3267i	0.321228	−	1.22139i
$87$	6.80646	−	6.37747i	0.729729	−	0.683737i
$88$	−8.57476	−	8.34024i	−0.914072	−	0.889072i
$89$	5.31062	−	6.65930i	0.562924	−	0.705885i	−0.416171	−	0.909286i	$-0.636628\pi$
$89$	5.31062	−	6.65930i	0.562924	−	0.705885i	0.979095	+	0.203401i	$0.0651997\pi$
$90$	1.29859	+	9.51016i	0.136883	+	1.00246i
$91$	15.4364	−	3.52326i	1.61818	−	0.369338i
$92$	10.7209	−	4.32240i	1.11773	−	0.450642i
$93$	−2.16865	+	3.24627i	−0.224878	+	0.336622i
$94$	4.71417	−	9.02031i	0.486230	−	0.930374i
$95$	0.783737	−	1.62745i	0.0804097	−	0.166973i
$96$	1.41330	+	9.69549i	0.144244	+	0.989542i
$97$	−13.8570	+	3.16276i	−1.40696	+	0.321130i	−0.857540	−	0.514417i	$-0.828009\pi$
$97$	−13.8570	+	3.16276i	−1.40696	+	0.321130i	−0.549420	+	0.835546i	$0.685151\pi$
$98$	−2.75478	−	14.1998i	−0.278275	−	1.43440i
$99$	−7.34381	−	10.3460i	−0.738081	−	1.03981i
$100$	−0.236095	−	0.0155000i	−0.0236095	−	0.00155000i
$101$	3.01088	+	3.77553i	0.299594	+	0.375679i	0.908728	−	0.417388i	$-0.137054\pi$
$101$	3.01088	+	3.77553i	0.299594	+	0.375679i	−0.609134	+	0.793067i	$0.708483\pi$
$102$	−1.68922	−	1.90796i	−0.167257	−	0.188916i
$103$	−4.70985	−	9.78011i	−0.464075	−	0.963662i	−0.993342	−	0.115207i	$-0.963247\pi$
$103$	−4.70985	−	9.78011i	−0.464075	−	0.963662i	0.529266	−	0.848456i	$-0.322467\pi$
$104$	−7.52283	+	7.73436i	−0.737674	+	0.758417i
$105$	11.1748	+	11.8177i	1.09055	+	1.15329i
$106$	−0.296986	+	9.05708i	−0.0288458	+	0.879701i
$107$	−4.41349	−	2.12543i	−0.426669	−	0.205473i	0.208211	−	0.978084i	$-0.433236\pi$
$107$	−4.41349	−	2.12543i	−0.426669	−	0.205473i	−0.634879	+	0.772611i	$0.718950\pi$
$108$	−0.386780	+	10.3851i	−0.0372179	+	0.999307i
$109$	3.05263	−	13.3745i	0.292389	−	1.28104i	−0.588801	−	0.808278i	$-0.700400\pi$
$109$	3.05263	−	13.3745i	0.292389	−	1.28104i	0.881190	−	0.472763i	$-0.156743\pi$
$110$	12.3769	−	5.46821i	1.18009	−	0.521374i
$111$	3.92184	−	10.2770i	0.372244	−	0.975451i
$112$	11.5157	+	11.9598i	1.08813	+	1.13009i
$113$	2.74217	−	12.0142i	0.257962	−	1.13020i	−0.665465	−	0.746429i	$-0.731767\pi$
$113$	2.74217	−	12.0142i	0.257962	−	1.13020i	0.923427	−	0.383775i	$-0.125376\pi$
$114$	1.13911	−	1.58976i	0.106687	−	0.148894i
$115$			13.0758i			1.21933i
$116$	3.98164	+	10.0073i	0.369686	+	0.929157i
$117$	−9.33203	+	6.62406i	−0.862747	+	0.612394i
$118$	6.59739	+	8.85323i	0.607339	+	0.815005i
$119$	−4.20981	−	0.960862i	−0.385913	−	0.0880821i
$120$	−10.7696	−	2.61829i	−0.983123	−	0.239016i
$121$	−4.29320	+	5.38350i	−0.390291	+	0.489409i
$122$	−3.14706	−	7.12314i	−0.284921	−	0.644899i
$123$	−10.6351	+	0.898066i	−0.958938	+	0.0809759i
$124$	−2.57374	−	3.70102i	−0.231129	−	0.332362i
$125$	−4.79189	+	9.95047i	−0.428600	+	0.889997i
$126$	9.71687	+	14.6863i	0.865648	+	1.30836i
$127$	−18.3158	+	8.82041i	−1.62526	+	0.782685i	−0.625265	+	0.780412i	$0.715009\pi$
$127$	−18.3158	+	8.82041i	−1.62526	+	0.782685i	−0.999997	+	0.00227273i	$0.999277\pi$
$128$	−11.0172	−	2.57322i	−0.973791	−	0.227443i
$129$	9.85529	+	10.4223i	0.867710	+	0.917635i
$130$	−4.93229	−	11.1639i	−0.432590	−	0.979137i
$131$	11.2647	−	8.98329i	0.984201	−	0.784874i	0.00760790	−	0.999971i	$-0.497578\pi$
$131$	11.2647	−	8.98329i	0.984201	−	0.784874i	0.976593	+	0.215097i	$0.0690069\pi$
$132$	14.2195	−	3.52629i	1.23765	−	0.306924i
$133$		−	3.31399i		−	0.287360i
$134$	−10.7006	+	2.07593i	−0.924391	+	0.179333i
$135$	−10.7317	−	4.79849i	−0.923635	−	0.412988i
$136$	2.76365	−	1.01026i	0.236981	−	0.0866290i
$137$	−13.2621	−	6.38671i	−1.13306	−	0.545654i	−0.229157	−	0.973389i	$-0.573597\pi$
$137$	−13.2621	−	6.38671i	−1.13306	−	0.545654i	−0.903904	+	0.427736i	$0.859311\pi$
$138$	−2.43611	+	13.9462i	−0.207376	+	1.18718i
$139$	−0.857287	+	0.683663i	−0.0727141	+	0.0579876i	−0.659172	−	0.751992i	$-0.729093\pi$
$139$	−0.857287	+	0.683663i	−0.0727141	+	0.0579876i	0.586458	+	0.809979i	$0.300522\pi$
$140$	−17.4182	+	7.02262i	−1.47211	+	0.593520i
$141$	6.33433	+	10.7359i	0.533447	+	0.904130i
$142$	−10.4230	−	5.44727i	−0.874683	−	0.457125i
$143$	12.6131	+	10.0586i	1.05476	+	0.841146i
$144$	−10.9986	−	4.79901i	−0.916551	−	0.399918i
$145$	−12.1831	−	0.0556889i	−1.01175	−	0.00462471i
$146$	−5.55923	−	1.46209i	−0.460085	−	0.121004i
$147$	16.5512	+	6.31615i	1.36512	+	0.520947i
$148$	9.39037	+	8.55285i	0.771884	+	0.703040i
$149$	9.92052	−	2.26429i	0.812721	−	0.185498i	0.204090	−	0.978952i	$-0.434576\pi$
$149$	9.92052	−	2.26429i	0.812721	−	0.185498i	0.608630	+	0.793454i	$0.291719\pi$
$150$	0.168781	−	0.235553i	0.0137809	−	0.0192328i
$151$	−13.3320	+	10.6319i	−1.08494	+	0.865211i	−0.991460	−	0.130411i	$-0.958370\pi$
$151$	−13.3320	+	10.6319i	−1.08494	+	0.865211i	−0.0934797	+	0.995621i	$0.529799\pi$
$152$	1.22787	+	1.89531i	0.0995937	+	0.153730i
$153$	3.07681	−	0.523364i	0.248745	−	0.0423114i
$154$	16.1058	−	18.8911i	1.29784	−	1.52229i
$155$	4.97148	−	1.13471i	0.399319	−	0.0911419i
$156$	−3.18068	−	12.8259i	−0.254658	−	1.02689i
$157$			13.1723i			1.05126i	0.850712	+	0.525631i	$0.176171\pi$
$157$			13.1723i			1.05126i	−0.850712	+	0.525631i	$0.823829\pi$
$158$	−4.62243	−	23.8268i	−0.367741	−	1.89556i
$159$	−9.22870	−	6.16517i	−0.731884	−	0.488930i
$160$	7.35970	−	10.4700i	0.581836	−	0.827724i
$161$	10.4087	+	21.6139i	0.820322	+	1.70342i
$162$	−10.5520	−	7.11727i	−0.829043	−	0.559185i
$163$	12.5753	−	6.05592i	0.984970	−	0.474336i	0.129158	−	0.991624i	$-0.458773\pi$
$163$	12.5753	−	6.05592i	0.984970	−	0.474336i	0.855812	+	0.517288i	$0.173058\pi$
$164$	3.52360	−	11.8096i	0.275147	−	0.922178i
$165$	−2.31508	+	16.4096i	−0.180229	+	1.27748i
$166$	−1.87441	+	2.19858i	−0.145483	+	0.170643i
$167$	−0.268463	+	1.17621i	−0.0207743	+	0.0910182i	−0.984252	−	0.176769i	$-0.943435\pi$
$167$	−0.268463	+	1.17621i	−0.0207743	+	0.0910182i	0.963478	+	0.267787i	$0.0862925\pi$
$168$	−19.8860	+	4.24493i	−1.53424	+	0.327503i
$169$	0.967445	−	1.21314i	0.0744189	−	0.0933183i
$170$	−0.109085	+	3.32673i	−0.00836643	+	0.255148i
$171$	0.917046	+	2.21277i	0.0701283	+	0.169215i
$172$	−15.3616	+	6.19341i	−1.17131	+	0.472243i
$173$		−	1.17630i		−	0.0894326i	−0.999000	−	0.0447163i	$-0.985762\pi$
$173$		−	1.17630i		−	0.0894326i	0.999000	−	0.0447163i	$-0.0142384\pi$
$174$	−12.9836	−	2.32918i	−0.984287	−	0.176575i
$175$		−	0.491031i		−	0.0371185i
$176$	−2.21167	+	16.7714i	−0.166711	+	1.26419i
$177$	−13.4745	+	1.13783i	−1.01281	+	0.0855249i
$178$	−12.0392	−	0.394771i	−0.902376	−	0.0295893i
$179$	−9.77664	+	12.2595i	−0.730741	+	0.916320i	−0.998892	−	0.0470569i	$-0.985016\pi$
$179$	−9.77664	+	12.2595i	−0.730741	+	0.916320i	0.268151	+	0.963377i	$0.413587\pi$
$180$	9.68697	−	9.50902i	0.722024	−	0.708760i
$181$	4.79430	−	21.0052i	0.356358	−	1.56130i	−0.405830	−	0.913949i	$-0.633018\pi$
$181$	4.79430	−	21.0052i	0.356358	−	1.56130i	0.762188	−	0.647356i	$-0.224125\pi$
$182$	−17.0397	−	14.5273i	−1.26306	−	1.07683i
$183$	9.44401	+	1.33237i	0.698122	+	0.0984917i
$184$	−13.9611	−	8.50467i	−1.02922	−	0.626973i
$185$	−12.9450	+	6.23397i	−0.951733	+	0.458330i
$186$	5.51379	−	0.284017i	0.404291	−	0.0208251i
$187$	−1.90897	−	3.96402i	−0.139598	−	0.289878i
$188$	−14.2125	+	2.27672i	−1.03655	+	0.166047i
$189$	−21.5588	+	0.610945i	−1.56817	+	0.0444397i
$190$	−2.50778	+	0.486512i	−0.181933	+	0.0352953i
$191$		−	13.5175i		−	0.978091i	−0.872258	−	0.489046i	$-0.837345\pi$
$191$		−	13.5175i		−	0.978091i	0.872258	−	0.489046i	$-0.162655\pi$
$192$	9.80020	−	9.79571i	0.707269	−	0.706945i
$193$	−14.5266	+	3.31560i	−1.04565	+	0.238662i	−0.710642	−	0.703554i	$-0.751595\pi$
$193$	−14.5266	+	3.31560i	−1.04565	+	0.238662i	−0.335005	+	0.942216i	$0.608738\pi$
$194$	15.2962	+	13.0409i	1.09820	+	0.936279i
$195$	14.8013	+	2.08818i	1.05994	+	0.149538i
$196$	−13.7744	+	15.1233i	−0.983888	+	1.08023i
$197$	2.05722	−	1.64058i	0.146571	−	0.116886i	−0.547459	−	0.836832i	$-0.684405\pi$
$197$	2.05722	−	1.64058i	0.146571	−	0.116886i	0.694030	+	0.719946i	$0.255833\pi$
$198$	−5.52639	+	17.0705i	−0.392743	+	1.21315i
$199$	−8.10543	+	1.85001i	−0.574578	+	0.131144i	−0.499930	−	0.866066i	$-0.666641\pi$
$199$	−8.10543	+	1.85001i	−0.574578	+	0.131144i	−0.0746489	+	0.997210i	$0.523784\pi$
$200$	0.181933	+	0.280826i	0.0128646	+	0.0198574i
$201$	4.75968	−	12.4725i	0.335722	−	0.879745i
$202$	1.73706	−	6.60474i	0.122219	−	0.464708i
$203$	−20.1826	+	9.60602i	−1.41654	+	0.674210i
$204$	−0.736137	+	3.52784i	−0.0515399	+	0.246998i
$205$	10.8994	+	8.69196i	0.761245	+	0.607073i
$206$	−7.11044	+	13.6054i	−0.495408	+	0.947936i
$207$	−12.9310	−	11.5515i	−0.898764	−	0.802882i
$208$	15.1277	+	1.99491i	1.04892	+	0.138322i
$209$	2.63998	−	2.10531i	0.182611	−	0.145628i
$210$	3.95796	−	22.6584i	0.273125	−	1.56358i
$211$	7.64241	+	3.68039i	0.526126	+	0.253369i	0.678040	−	0.735025i	$-0.262830\pi$
$211$	7.64241	+	3.68039i	0.526126	+	0.253369i	−0.151915	+	0.988394i	$0.548544\pi$
$212$	10.5215	−	7.31680i	0.722620	−	0.502520i
$213$	12.4055	−	7.31937i	0.850009	−	0.501515i
$214$	1.31938	+	6.80088i	0.0901908	+	0.464899i
$215$		−	18.7359i		−	1.27778i
$216$	12.1033	−	8.33721i	0.823528	−	0.567275i
$217$	7.31443	−	5.83307i	0.496536	−	0.395974i
$218$	−17.7460	+	7.84030i	−1.20191	+	0.531012i
$219$	5.11537	−	4.83706i	0.345665	−	0.326858i
$220$	−16.6598	−	9.41433i	−1.12320	−	0.634714i
$221$	−3.57552	+	1.72188i	−0.240515	+	0.115826i
$222$	−14.9680	+	4.23718i	−1.00459	+	0.284381i
$223$	4.21686	−	8.75640i	0.282382	−	0.586372i	−0.710740	−	0.703454i	$-0.751640\pi$
$223$	4.21686	−	8.75640i	0.282382	−	0.586372i	0.993122	+	0.117083i	$0.0373542\pi$
$224$	3.83097	−	23.1651i	0.255967	−	1.54778i
$225$	0.135878	+	0.327865i	0.00905853	+	0.0218576i
$226$	−15.9411	+	7.04292i	−1.06039	+	0.468488i
$227$	−13.7970	+	17.3009i	−0.915737	+	1.14830i	0.0728040	+	0.997346i	$0.476805\pi$
$227$	−13.7970	+	17.3009i	−0.915737	+	1.14830i	−0.988541	+	0.150952i	$0.951766\pi$
$228$	−2.76534	+	0.0516793i	−0.183139	+	0.00342255i
$229$	19.5316	+	4.45796i	1.29068	+	0.294590i	0.812134	−	0.583470i	$-0.198306\pi$
$229$	19.5316	+	4.45796i	1.29068	+	0.294590i	0.478549	+	0.878061i	$0.341163\pi$
$230$	14.8277	−	11.0496i	0.977712	−	0.728587i
$231$	9.23572	+	28.9674i	0.607666	+	1.90591i
$232$	7.98348	−	12.9717i	0.524141	−	0.851632i
$233$			8.34823i			0.546911i	0.961885	+	0.273455i	$0.0881666\pi$
$233$			8.34823i			0.546911i	−0.961885	+	0.273455i	$0.911833\pi$
$234$	15.3975	+	4.98476i	1.00656	+	0.325864i
$235$	3.62307	−	15.8737i	0.236343	−	1.03549i
$236$	4.46434	−	14.9626i	0.290603	−	0.973984i
$237$	27.7723	+	10.5983i	1.80401	+	0.688432i
$238$	2.46785	+	5.58581i	0.159967	+	0.362074i
$239$	1.47053	−	6.44282i	0.0951208	−	0.416751i	−0.904839	−	0.425755i	$-0.860009\pi$
$239$	1.47053	−	6.44282i	0.0951208	−	0.416751i	0.999959	+	0.00900317i	$0.00286584\pi$
$240$	6.13161	+	14.4250i	0.395794	+	0.931132i
$241$	17.0794	+	8.22500i	1.10018	+	0.529819i	0.893715	−	0.448635i	$-0.148090\pi$
$241$	17.0794	+	8.22500i	1.10018	+	0.529819i	0.206465	+	0.978454i	$0.433804\pi$
$242$	9.73270	+	0.319140i	0.625641	+	0.0205151i
$243$	14.2259	−	6.37368i	0.912592	−	0.408872i
$244$	−5.41812	+	9.58802i	−0.346859	+	0.613810i
$245$	−10.0399	−	20.8480i	−0.641423	−	1.33193i
$246$	10.0055	+	11.3011i	0.637926	+	0.720534i
$247$	−1.89898	−	2.38124i	−0.120829	−	0.151515i
$248$	−2.02198	+	6.04607i	−0.128396	+	0.383926i
$249$	−1.07487	−	3.37126i	−0.0681169	−	0.213645i
$250$	15.3330	−	2.97461i	0.969742	−	0.188131i
$251$	−8.46412	+	1.93188i	−0.534250	+	0.121939i	−0.481130	−	0.876649i	$-0.659774\pi$
$251$	−8.46412	+	1.93188i	−0.534250	+	0.121939i	−0.0531198	+	0.998588i	$0.516917\pi$
$252$	8.44282	−	23.4292i	0.531847	−	1.47590i
$253$	−10.6056	+	22.0227i	−0.666766	+	1.38455i
$254$	25.4797	+	13.3161i	1.59874	+	0.835529i
$255$	−3.38977	−	2.26451i	−0.212276	−	0.141809i
$256$	6.39196	+	14.6677i	0.399498	+	0.916734i
$257$	−18.3586	+	4.19023i	−1.14518	+	0.261380i	−0.752689	−	0.658377i	$-0.771243\pi$
$257$	−18.3586	+	4.19023i	−1.14518	+	0.261380i	−0.392490	+	0.919756i	$0.628386\pi$
$258$	3.49062	−	19.9830i	0.217316	−	1.24409i
$259$	−16.4352	+	20.6091i	−1.02123	+	1.28059i
$260$	−8.49165	+	15.0270i	−0.526630	+	0.931936i
$261$	10.8179	−	11.9989i	0.669609	−	0.742714i
$262$	−19.7060	−	5.18271i	−1.21744	−	0.320189i
$263$	−9.10035	−	7.25728i	−0.561151	−	0.447503i	0.301382	−	0.953504i	$-0.402552\pi$
$263$	−9.10035	−	7.25728i	−0.561151	−	0.447503i	−0.862533	+	0.506000i	$0.831124\pi$
$264$	−16.0148	−	13.1448i	−0.985640	−	0.809006i
$265$	3.22582	+	14.1332i	0.198161	+	0.868198i
$266$	−3.75800	+	2.80045i	−0.230418	+	0.171707i
$267$	8.19510	−	12.2673i	0.501532	−	0.750748i
$268$	11.3965	+	10.3800i	0.696151	+	0.634062i
$269$	9.98929	+	4.81059i	0.609058	+	0.293307i	0.712877	−	0.701289i	$-0.247392\pi$
$269$	9.98929	+	4.81059i	0.609058	+	0.293307i	−0.103819	+	0.994596i	$0.533106\pi$
$270$	3.62727	+	16.2244i	0.220749	+	0.987386i
$271$	−2.21329	−	9.69704i	−0.134448	−	0.589053i	−0.996599	−	0.0824028i	$-0.973741\pi$
$271$	−2.21329	−	9.69704i	−0.134448	−	0.589053i	0.862152	−	0.506650i	$-0.169117\pi$
$272$	−3.48100	−	2.28021i	−0.211067	−	0.138258i
$273$	26.1283	−	8.33055i	1.58136	−	0.504188i
$274$	3.96461	+	20.4360i	0.239511	+	1.23458i
$275$	0.391164	−	0.311942i	0.0235880	−	0.0188108i
$276$	17.8733	−	9.02255i	1.07585	−	0.543094i
$277$	−14.9940	+	7.22073i	−0.900902	+	0.433852i	−0.826215	−	0.563355i	$-0.809510\pi$
$277$	−14.9940	+	7.22073i	−0.900902	+	0.433852i	−0.0746873	+	0.997207i	$0.523796\pi$
$278$	1.49970	+	0.394425i	0.0899460	+	0.0236560i
$279$	−3.26977	+	5.91882i	−0.195756	+	0.354350i
$280$	22.6826	+	13.8176i	1.35554	+	0.825757i
$281$	−4.54433	+	9.43639i	−0.271092	+	0.562928i	−0.991421	−	0.130704i	$-0.958276\pi$
$281$	−4.54433	+	9.43639i	−0.271092	+	0.562928i	0.720330	+	0.693632i	$0.243991\pi$
$282$	6.82160	−	16.2553i	0.406220	−	0.967988i
$283$	−0.704214	−	0.160732i	−0.0418612	−	0.00955454i	0.201539	−	0.979480i	$-0.435406\pi$
$283$	−0.704214	−	0.160732i	−0.0418612	−	0.00955454i	−0.243400	+	0.969926i	$0.578263\pi$
$284$	2.63078	+	16.4227i	0.156108	+	0.974507i
$285$	1.11547	−	2.92305i	0.0660749	−	0.173146i
$286$	0.747720	−	22.8030i	0.0442136	−	1.34837i
$287$	24.9353	+	5.69133i	1.47189	+	0.335948i
$288$	3.85226	+	16.5276i	0.226997	+	0.973896i
$289$	−15.9177			−0.936336
$290$	10.2320	+	13.8624i	0.600845	+	0.814030i
$291$	−23.4549	+	7.47817i	−1.37495	+	0.438378i
$292$	3.03978	+	7.53958i	0.177890	+	0.441221i
$293$	6.03249	−	26.4301i	0.352422	−	1.54406i	−0.419149	−	0.907917i	$-0.637672\pi$
$293$	6.03249	−	26.4301i	0.352422	−	1.54406i	0.771571	−	0.636143i	$-0.219471\pi$
$294$	−6.82401	−	24.1061i	−0.397984	−	1.40590i
$295$	13.8093	+	11.0126i	0.804009	+	0.641176i
$296$	1.76354	−	17.8760i	0.102504	−	1.03902i
$297$	−14.1826	−	16.7860i	−0.822957	−	0.974022i
$298$	−10.9509	−	9.33626i	−0.634367	−	0.540835i
$299$	19.8643	+	9.56613i	1.14878	+	0.553223i
$300$	−0.409738	+	0.00765727i	−0.0236562	+	0.000442093i
$301$	−14.9143	−	30.9698i	−0.859644	−	1.78507i
$302$	23.3224	+	6.13383i	1.34205	+	0.352963i
$303$	5.74676	+	6.07740i	0.330142	+	0.349138i
$304$	1.11164	−	2.99399i	0.0637569	−	0.171717i
$305$	−7.76726	−	9.73984i	−0.444752	−	0.557701i
$306$	−3.19350	−	3.04678i	−0.182560	−	0.174173i
$307$	21.4155			1.22225			0.611124	−	0.791535i	$-0.290718\pi$
$307$	21.4155			1.22225			0.611124	+	0.791535i	$0.290718\pi$
$308$	−35.0322	−	2.29992i	−1.99614	−	0.131050i
$309$	−9.55414	−	16.1931i	−0.543516	−	0.921196i
$310$	−5.48782	−	4.67869i	−0.311687	−	0.265731i
$311$	−8.16273	+	16.9501i	−0.462866	+	0.961151i	0.530664	+	0.847582i	$0.321943\pi$
$311$	−8.16273	+	16.9501i	−0.462866	+	0.961151i	−0.993530	+	0.113569i	$0.963772\pi$
$312$	−11.8565	+	14.4452i	−0.671242	+	0.817798i
$313$	1.77869	+	2.23041i	0.100538	+	0.126070i	0.829555	−	0.558425i	$-0.188594\pi$
$313$	1.77869	+	2.23041i	0.100538	+	0.126070i	−0.729017	+	0.684495i	$0.760023\pi$
$314$	14.9371	−	11.1311i	0.842950	−	0.628163i
$315$	21.0090	+	18.7677i	1.18372	+	1.05744i
$316$	−23.1130	+	25.3763i	−1.30021	+	1.42753i
$317$	4.11743	−	5.16309i	0.231258	−	0.289988i	−0.652640	−	0.757668i	$-0.726339\pi$
$317$	4.11743	−	5.16309i	0.231258	−	0.289988i	0.883898	+	0.467680i	$0.154910\pi$
$318$	0.807421	+	15.6750i	0.0452779	+	0.879009i
$319$	−20.4739	−	9.97526i	−1.14632	−	0.558507i
$320$	−18.0920	+	0.501769i	−1.01137	+	0.0280497i
$321$	−7.92705	−	3.02506i	−0.442445	−	0.168843i
$322$	15.7140	−	30.0679i	0.875707	−	1.67562i
$323$	0.184832	+	0.809803i	0.0102843	+	0.0450586i
$324$	0.845993	+	17.9801i	0.0469996	+	0.998895i
$325$	−0.281370	−	0.352826i	−0.0156076	−	0.0195713i
$326$	−17.4939	−	9.14260i	−0.968895	−	0.506362i
$327$	3.31935	−	23.5280i	0.183561	−	1.30110i
$328$	−16.3695	+	5.98391i	−0.903853	+	0.330406i
$329$	−6.64708	−	29.1228i	−0.366466	−	1.60559i
$330$	20.5645	−	11.2415i	1.13204	−	0.618822i
$331$	8.91501			0.490013			0.245007	−	0.969521i	$-0.421210\pi$
$331$	8.91501			0.490013			0.245007	+	0.969521i	$0.421210\pi$
$332$	4.07709	+	0.267667i	0.223760	+	0.0146902i
$333$	5.27095	−	18.3088i	0.288846	−	1.00331i
$334$	1.56067	−	0.689514i	0.0853958	−	0.0377285i
$335$	−15.7105	+	7.56575i	−0.858354	+	0.413361i
$336$	21.6181	+	18.9632i	1.17936	+	1.03453i
$337$	−4.64237	−	9.63998i	−0.252886	−	0.525123i	0.735419	−	0.677613i	$-0.236985\pi$
$337$	−4.64237	−	9.63998i	−0.252886	−	0.525123i	−0.988305	+	0.152489i	$0.951271\pi$
$338$	−2.19320	−	0.0719161i	−0.119294	−	0.00391172i
$339$	2.98176	−	21.1351i	0.161947	−	1.14790i
$340$	3.86463	−	2.68751i	0.209589	−	0.145751i
$341$	9.29343	+	2.12117i	0.503268	+	0.114868i
$342$	1.73430	−	2.90979i	0.0937803	−	0.157343i
$343$	−10.4753	−	8.35375i	−0.565611	−	0.451060i
$344$	20.0043	+	12.1860i	1.07856	+	0.657026i
$345$	1.90569	+	22.5677i	0.102599	+	1.21500i
$346$	−1.33390	+	0.994020i	−0.0717111	+	0.0534388i
$347$	27.1398			1.45694			0.728471	−	0.685077i	$-0.240231\pi$
$347$	27.1398			1.45694			0.728471	+	0.685077i	$0.240231\pi$
$348$	8.33042	+	16.6914i	0.446557	+	0.894755i
$349$	19.2422			1.03001			0.515007	−	0.857186i	$-0.327789\pi$
$349$	19.2422			1.03001			0.515007	+	0.857186i	$0.327789\pi$
$350$	−0.556820	+	0.414940i	−0.0297633	+	0.0221795i
$351$	−15.1408	+	12.7926i	−0.808158	+	0.682817i
$352$	20.8874	−	11.6645i	1.11330	−	0.621720i
$353$	−27.4366	−	21.8800i	−1.46030	−	1.16455i	−0.953072	−	0.302745i	$-0.902097\pi$
$353$	−27.4366	−	21.8800i	−1.46030	−	1.16455i	−0.507233	−	0.861809i	$-0.669332\pi$
$354$	12.6768	+	14.3183i	0.673763	+	0.761011i
$355$	−18.3422	−	4.18649i	−0.973503	−	0.222196i
$356$	9.72591	+	13.9858i	0.515472	+	0.741246i
$357$	−7.40579	−	1.04482i	−0.391956	−	0.0552975i
$358$	22.1637	+	0.726758i	1.17139	+	0.0384103i
$359$	−8.13539	−	16.8933i	−0.429370	−	0.891595i	−0.997634	−	0.0687490i	$-0.978099\pi$
$359$	−8.13539	−	16.8933i	−0.429370	−	0.891595i	0.568264	−	0.822846i	$-0.307615\pi$
$360$	−18.9689	−	2.94936i	−0.999749	−	0.155445i
$361$	16.5441	−	7.96720i	0.870740	−	0.419326i
$362$	−27.8709	+	12.3136i	−1.46486	+	0.647186i
$363$	−6.62507	+	9.91712i	−0.347726	+	0.520514i
$364$	−2.07451	+	31.5987i	−0.108734	+	1.65622i
$365$	−9.19573			−0.481327
$366$	−6.46967	−	11.8352i	−0.338175	−	0.618637i
$367$	−2.48003	−	10.8657i	−0.129456	−	0.567185i	−0.997498	−	0.0706939i	$-0.977479\pi$
$367$	−2.48003	−	10.8657i	−0.129456	−	0.567185i	0.868042	−	0.496491i	$-0.165378\pi$
$368$	2.15351	+	23.0183i	0.112259	+	1.19991i
$369$	−18.2244	+	3.09996i	−0.948723	+	0.161377i
$370$	18.0082	+	9.41139i	0.936201	+	0.489275i
$371$	16.5826	+	20.7940i	0.860927	+	1.07957i
$372$	−4.98143	−	6.01252i	−0.258275	−	0.311735i
$373$	6.71625	+	29.4258i	0.347754	+	1.52361i	0.782266	+	0.622945i	$0.214064\pi$
$373$	6.71625	+	29.4258i	0.347754	+	1.52361i	−0.434512	+	0.900666i	$0.643079\pi$
$374$	−2.88197	+	5.51449i	−0.149023	+	0.285147i
$375$	−6.82017	+	17.8720i	−0.352192	+	0.922905i
$376$	14.5919	+	14.1928i	0.752518	+	0.731937i
$377$	−8.99760	+	18.4673i	−0.463400	+	0.951115i
$378$	18.9108	+	23.9310i	0.972668	+	1.23088i
$379$	12.3209	−	15.4499i	0.632882	−	0.793609i	−0.357211	−	0.934024i	$-0.616272\pi$
$379$	12.3209	−	15.4499i	0.632882	−	0.793609i	0.990093	+	0.140415i	$0.0448436\pi$
$380$	2.67086	+	2.43265i	0.137012	+	0.124792i
$381$	−30.3259	+	17.8926i	−1.55364	+	0.916665i
$382$	−15.3286	+	11.4228i	−0.784278	+	0.584441i
$383$	0.946432	+	1.18679i	0.0483604	+	0.0606420i	0.805424	−	0.592700i	$-0.201938\pi$
$383$	0.946432	+	1.18679i	0.0483604	+	0.0606420i	−0.757063	+	0.653342i	$0.773366\pi$
$384$	−19.3897	−	2.83549i	−0.989476	−	0.144698i
$385$	17.2309	−	35.7803i	0.878167	−	1.82353i
$386$	16.0353	+	13.6711i	0.816178	+	0.695839i
$387$	18.5283	+	16.5517i	0.941846	+	0.841368i
$388$	1.86224	−	28.3656i	0.0945410	−	1.44004i
$389$	−13.7097			−0.695111			−0.347555	−	0.937659i	$-0.612988\pi$
$389$	−13.7097			−0.695111			−0.347555	+	0.937659i	$0.612988\pi$
$390$	−10.1397	−	18.5490i	−0.513444	−	0.939265i
$391$	−3.74894	−	4.70102i	−0.189592	−	0.237741i
$392$	28.7894	+	2.84020i	1.45408	+	0.143452i
$393$	18.1326	−	17.1461i	0.914668	−	0.864905i
$394$	−3.59881	−	0.946496i	−0.181306	−	0.0476838i
$395$	−16.8465	−	34.9821i	−0.847640	−	1.76014i
$396$	24.0276	−	8.15842i	1.20743	−	0.409976i
$397$	−16.7409	−	8.06197i	−0.840200	−	0.404619i	−0.0362692	−	0.999342i	$-0.511547\pi$
$397$	−16.7409	−	8.06197i	−0.840200	−	0.404619i	−0.803931	+	0.594723i	$0.797262\pi$
$398$	8.94727	+	7.62806i	0.448486	+	0.382360i
$399$	−0.482986	−	5.71965i	−0.0241795	−	0.286341i
$400$	0.164711	−	0.443617i	0.00823553	−	0.0221808i
$401$	11.5463	+	9.20790i	0.576597	+	0.459820i	0.867851	−	0.496825i	$-0.165501\pi$
$401$	11.5463	+	9.20790i	0.576597	+	0.459820i	−0.291254	+	0.956646i	$0.594072\pi$
$402$	−18.1657	+	5.14238i	−0.906023	+	0.256479i
$403$	1.91327	−	8.38260i	0.0953070	−	0.417567i
$404$	−8.95753	+	3.61146i	−0.445654	+	0.179677i
$405$	−19.2212	−	6.71771i	−0.955109	−	0.333806i
$406$	27.9481	+	14.7692i	1.38704	+	0.732983i
$407$	−26.8585			−1.33133
$408$	4.62256	−	2.14639i	0.228851	−	0.106262i
$409$	−15.0521	−	3.43553i	−0.744276	−	0.169876i	−0.166466	−	0.986047i	$-0.553236\pi$
$409$	−15.0521	−	3.43553i	−0.744276	−	0.169876i	−0.577810	+	0.816171i	$0.696093\pi$
$410$	0.646126	−	19.7047i	0.0319099	−	0.973146i
$411$	−23.8200	−	9.09003i	−1.17496	−	0.448378i
$412$	21.4369	−	3.43401i	1.05612	−	0.169181i
$413$	31.5927	+	7.21082i	1.55457	+	0.354821i
$414$	−2.17197	+	24.4249i	−0.106747	+	1.20042i
$415$	−2.00535	+	4.16416i	−0.0984389	+	0.204411i
$416$	−10.5213	−	18.8403i	−0.515848	−	0.923720i
$417$	−1.37996	+	1.30488i	−0.0675769	+	0.0639004i
$418$	−4.61827	−	1.21462i	−0.225887	−	0.0594088i
$419$	−2.82330	+	1.35963i	−0.137927	+	0.0664223i	−0.501574	−	0.865114i	$-0.667246\pi$
$419$	−2.82330	+	1.35963i	−0.137927	+	0.0664223i	0.363647	+	0.931537i	$0.381531\pi$
$420$	−29.0388	+	14.6590i	−1.41695	+	0.715284i
$421$	14.1184	−	11.2591i	0.688090	−	0.548734i	−0.215832	−	0.976430i	$-0.569246\pi$
$421$	14.1184	−	11.2591i	0.688090	−	0.548734i	0.903922	+	0.427697i	$0.140675\pi$
$422$	−2.28464	−	11.7764i	−0.111214	−	0.573267i
$423$	12.4971	+	17.6061i	0.607632	+	0.856037i
$424$	−17.1882	−	5.74821i	−0.834732	−	0.279158i
$425$	0.0273864	+	0.119988i	0.00132844	+	0.00582026i
$426$	−18.7831	−	7.88242i	−0.910045	−	0.381904i
$427$	−20.5922	−	9.91668i	−0.996527	−	0.479902i
$428$	6.59714	−	7.24315i	0.318885	−	0.350111i
$429$	23.2351	+	15.5220i	1.12180	+	0.749411i
$430$	−21.2461	+	15.8325i	−1.02458	+	0.763512i
$431$	6.58581	+	28.8543i	0.317227	+	1.38986i	0.842393	+	0.538863i	$0.181146\pi$
$431$	6.58581	+	28.8543i	0.317227	+	1.38986i	−0.525166	+	0.851000i	$0.675997\pi$
$432$	−19.6820	−	6.67970i	−0.946951	−	0.321377i
$433$	5.90071	+	4.70566i	0.283570	+	0.226140i	0.754937	−	0.655798i	$-0.227668\pi$
$433$	5.90071	+	4.70566i	0.283570	+	0.226140i	−0.471366	+	0.881937i	$0.656239\pi$
$434$	−12.7956	−	3.36526i	−0.614206	−	0.161538i
$435$	−21.0350	+	1.67947i	−1.00855	+	0.0805243i
$436$	23.8868	+	13.4982i	1.14397	+	0.646447i
$437$	2.87720	−	3.60789i	0.137635	−	0.172589i
$438$	−9.80781	−	1.71322i	−0.468635	−	0.0818610i
$439$	9.09095	−	2.07495i	0.433888	−	0.0990320i	2.03377e−6	−	1.00000i	$-0.499999\pi$
$439$	9.09095	−	2.07495i	0.433888	−	0.0990320i	0.433886	+	0.900968i	$0.357142\pi$
$440$	3.40251	+	26.8474i	0.162208	+	1.27990i
$441$	29.4864	+	8.48890i	1.40411	+	0.404233i
$442$	4.97402	+	2.59951i	0.236590	+	0.123646i
$443$	7.81371	−	16.2253i	0.371240	−	0.770889i	−0.628737	−	0.777618i	$-0.716428\pi$
$443$	7.81371	−	16.2253i	0.371240	−	0.770889i	0.999977	+	0.00672946i	$0.00214207\pi$
$444$	17.4534	+	13.3929i	0.828303	+	0.635598i
$445$	−18.7867	+	4.28795i	−0.890576	+	0.203268i
$446$	−13.4930	+	2.61765i	−0.638912	+	0.123950i
$447$	16.7919	−	5.35379i	0.794230	−	0.253226i
$448$	−29.5060	+	15.2311i	−1.39403	+	0.719602i
$449$	10.2009	+	12.7915i	0.481409	+	0.603668i	0.961923	−	0.273319i	$-0.0881215\pi$
$449$	10.2009	+	12.7915i	0.481409	+	0.603668i	−0.480515	+	0.876987i	$0.659550\pi$
$450$	0.256970	−	0.431141i	0.0121137	−	0.0203242i
$451$	11.3071	+	23.4795i	0.532432	+	1.10561i
$452$	21.4574	+	12.1254i	1.00927	+	0.570331i
$453$	−21.4602	+	20.2927i	−1.00829	+	0.953433i
$454$	31.2778	+	1.02561i	1.46794	+	0.0481344i
$455$	−32.2735	−	15.5421i	−1.51301	−	0.728626i
$456$	2.39542	+	3.09217i	0.112176	+	0.144804i
$457$	2.41706	−	10.5898i	0.113065	−	0.495372i	−0.886407	−	0.462906i	$-0.846807\pi$
$457$	2.41706	−	10.5898i	0.113065	−	0.495372i	0.999473	−	0.0324659i	$-0.0103360\pi$
$458$	−11.4497	−	25.9156i	−0.535009	−	1.21096i
$459$	5.23401	−	1.35170i	0.244303	−	0.0630918i
$460$	−25.0600	−	7.47705i	−1.16843	−	0.348619i
$461$	2.44175	−	10.6980i	0.113724	−	0.498256i	−0.885698	−	0.464261i	$-0.846320\pi$
$461$	2.44175	−	10.6980i	0.113724	−	0.498256i	0.999422	−	0.0339947i	$-0.0108229\pi$
$462$	25.0439	−	34.9517i	1.16515	−	1.62610i
$463$		−	25.8090i		−	1.19945i	−0.800208	−	0.599723i	$-0.795278\pi$
$463$		−	25.8090i		−	1.19945i	0.800208	−	0.599723i	$-0.204722\pi$
$464$	−21.4560	+	1.90845i	−0.996068	+	0.0885973i
$465$	8.41494	−	2.68295i	0.390233	−	0.124419i
$466$	9.46673	−	7.05457i	0.438538	−	0.326797i
$467$	25.0620	+	5.72024i	1.15973	+	0.264701i	0.758748	−	0.651384i	$-0.225811\pi$
$467$	25.0620	+	5.72024i	1.15973	+	0.264701i	0.400984	+	0.916085i	$0.368668\pi$
$468$	−7.35883	−	21.6727i	−0.340162	−	1.00182i
$469$	−19.9463	+	25.0119i	−0.921035	+	1.15494i
$470$	−21.0621	+	9.30539i	−0.971522	+	0.429226i
$471$	1.91975	+	22.7342i	0.0884573	+	1.04753i
$472$	−20.7398	+	7.58152i	−0.954629	+	0.348968i
$473$	15.1963	−	31.5555i	0.698727	−	1.45092i
$474$	−11.4504	−	40.4492i	−0.525936	−	1.85789i
$475$	−0.0851011	+	0.0409826i	−0.00390471	+	0.00188041i
$476$	4.24877	−	7.51872i	0.194742	−	0.344620i
$477$	−16.8264	−	9.29552i	−0.770429	−	0.425612i
$478$	−8.54869	+	3.77687i	−0.391008	+	0.172750i
$479$	5.47609	−	4.36704i	0.250209	−	0.199535i	−0.490351	−	0.871525i	$-0.663132\pi$
$479$	5.47609	−	4.36704i	0.250209	−	0.199535i	0.740560	+	0.671990i	$0.234560\pi$
$480$	11.1763	−	19.1428i	0.510124	−	0.873747i
$481$			24.2262i			1.10462i
$482$	−5.10574	−	26.3181i	−0.232560	−	1.19876i
$483$	21.1145	+	35.7867i	0.960745	+	1.62835i
$484$	−7.86260	−	11.3064i	−0.357391	−	0.513926i
$485$	28.9713	+	13.9518i	1.31552	+	0.633521i
$486$	−19.2490	−	10.7459i	−0.873155	−	0.487443i
$487$	8.57136	−	6.83543i	0.388405	−	0.309743i	−0.409746	−	0.912200i	$-0.634383\pi$
$487$	8.57136	−	6.83543i	0.388405	−	0.309743i	0.798152	+	0.602457i	$0.205811\pi$
$488$	15.4511	−	1.95821i	0.699440	−	0.0886438i
$489$	20.8211	−	12.2847i	0.941564	−	0.555533i
$490$	−15.1571	+	29.0023i	−0.684729	+	1.31019i
$491$	1.95381	+	1.55811i	0.0881743	+	0.0703166i	0.666585	−	0.745429i	$-0.267755\pi$
$491$	1.95381	+	1.55811i	0.0881743	+	0.0703166i	−0.578411	+	0.815746i	$0.696327\pi$
$492$	4.36025	−	20.8959i	0.196575	−	0.942060i
$493$	4.39603	−	3.47296i	0.197987	−	0.156414i
$494$	−1.09557	+	4.16564i	−0.0492922	+	0.187421i
$495$	−1.60406	+	28.6588i	−0.0720972	+	1.28812i
$496$	8.56477	−	2.81628i	0.384570	−	0.126455i
$497$	−33.6516	+	7.68076i	−1.50948	+	0.344529i
$498$	−2.91464	+	4.06772i	−0.130608	+	0.182279i
$499$	−6.63744	+	5.29318i	−0.297133	+	0.236955i	−0.760696	−	0.649108i	$-0.775142\pi$
$499$	−6.63744	+	5.29318i	−0.297133	+	0.236955i	0.463563	+	0.886064i	$0.346571\pi$
$500$	−16.3301	−	14.8736i	−0.730304	−	0.665169i
$501$	−0.291920	+	2.06916i	−0.0130420	+	0.0924435i
$502$	9.34321	+	7.96563i	0.417008	+	0.355523i
$503$	30.7886	−	7.02730i	1.37280	−	0.313332i	0.528375	−	0.849011i	$-0.322802\pi$
$503$	30.7886	−	7.02730i	1.37280	−	0.313332i	0.844421	+	0.535679i	$0.179944\pi$
$504$	−33.7027	+	10.2246i	−1.50124	+	0.455439i
$505$		−	10.9251i		−	0.486163i
$506$	33.9354	−	6.58350i	1.50861	−	0.292672i
$507$	1.49292	−	2.23476i	0.0663028	−	0.0992492i
$508$	−6.43107	−	40.1461i	−0.285333	−	1.78120i
$509$	11.9568	+	24.8285i	0.529975	+	1.10050i	0.978407	+	0.206687i	$0.0662683\pi$
$509$	11.9568	+	24.8285i	0.529975	+	1.10050i	−0.448432	+	0.893817i	$0.648017\pi$
$510$	0.296572	+	5.75753i	0.0131324	+	0.254948i
$511$	−15.2002	+	7.32005i	−0.672419	+	0.323820i
$512$	11.2315	−	19.6432i	0.496366	−	0.868113i
$513$	1.90523	+	3.68539i	0.0841180	+	0.162714i
$514$	20.2654	+	17.2774i	0.893867	+	0.762073i
$515$	−5.46472	+	23.9425i	−0.240804	+	1.05503i
$516$	−25.6100	+	12.9281i	−1.12742	+	0.569127i
$517$	18.9769	−	23.7963i	0.834604	−	1.04656i
$518$	37.2587	+	1.22173i	1.63705	+	0.0536797i
$519$	−0.171436	−	2.03019i	−0.00752520	−	0.0891154i
$520$	24.2161	−	3.06904i	1.06195	−	0.134586i
$521$		−	6.75573i		−	0.295974i	−0.988989	−	0.147987i	$-0.952721\pi$
$521$		−	6.75573i		−	0.295974i	0.988989	−	0.147987i	$-0.0472794\pi$
$522$	−22.7480	−	2.12770i	−0.995654	−	0.0931271i
$523$		−	39.0473i		−	1.70742i	−0.520748	−	0.853711i	$-0.674347\pi$
$523$		−	39.0473i		−	1.70742i	0.520748	−	0.853711i	$-0.325653\pi$
$524$	10.7752	+	26.7258i	0.470716	+	1.16752i
$525$	−0.0715636	−	0.847475i	−0.00312329	−	0.0369868i
$526$	−0.539478	+	16.4523i	−0.0235224	+	0.717354i
$527$	−1.46202	+	1.83331i	−0.0636864	+	0.0798602i
$528$	−1.37285	+	29.2683i	−0.0597456	+	1.27374i
$529$	−2.31536	+	10.1442i	−0.100668	+	0.441054i
$530$	13.3009	−	15.6011i	0.577753	−	0.677670i
$531$	−23.0900	+	3.92760i	−1.00202	+	0.170443i
$532$	6.35131	+	1.89501i	0.275364	+	0.0821593i
$533$	21.1783	−	10.1989i	0.917335	−	0.441765i
$534$	−20.8361	+	1.07327i	−0.901665	+	0.0464450i
$535$	4.80849	+	9.98494i	0.207889	+	0.431687i
$536$	2.14030	−	21.6949i	0.0924467	−	0.937077i
$537$	−15.0869	+	22.5837i	−0.651047	+	0.974558i
$538$	−2.98622	−	15.3928i	−0.128745	−	0.663630i
$539$		−	43.2558i		−	1.86316i
$540$	15.3330	−	17.8235i	0.659826	−	0.767001i
$541$	−22.5147	+	5.13882i	−0.967980	+	0.220935i	−0.677155	−	0.735841i	$-0.736787\pi$
$541$	−22.5147	+	5.13882i	−0.967980	+	0.220935i	−0.290826	+	0.956776i	$0.593930\pi$
$542$	−9.12594	+	10.7042i	−0.391993	+	0.459784i
$543$	5.21320	−	36.9518i	0.223720	−	1.58575i
$544$	0.355861	+	5.87425i	0.0152574	+	0.251856i
$545$	−24.2650	+	19.3507i	−1.03940	+	0.828892i
$546$	−31.5261	−	22.5894i	−1.34919	−	0.966737i
$547$	0.468541	−	0.106941i	0.0200334	−	0.00457248i	−0.212493	−	0.977163i	$-0.568158\pi$
$547$	0.468541	−	0.106941i	0.0200334	−	0.00457248i	0.232526	+	0.972590i	$0.425301\pi$
$548$	19.8238	−	21.7650i	0.846830	−	0.929755i
$549$	16.4937	+	0.923166i	0.703933	+	0.0393998i
$550$	−0.684285	−	0.179968i	−0.0291780	−	0.00767388i
$551$	3.34931	+	2.69613i	0.142686	+	0.114859i
$552$	−25.3350	−	12.6436i	−1.07833	−	0.538146i
$553$	−55.6935	−	44.4141i	−2.36833	−	1.88868i
$554$	20.8587	+	10.9011i	0.886199	+	0.463144i
$555$	−21.4333	+	12.6459i	−0.909792	+	0.536787i
$556$	−0.820034	−	2.03393i	−0.0347772	−	0.0862580i
$557$	−1.65510	+	1.31990i	−0.0701287	+	0.0559258i	−0.657927	−	0.753082i	$-0.728566\pi$
$557$	−1.65510	+	1.31990i	−0.0701287	+	0.0559258i	0.587798	+	0.809008i	$0.299995\pi$
$558$	9.47490	−	1.29377i	0.401105	−	0.0547698i
$559$	−28.4628	−	13.7069i	−1.20385	−	0.579742i
$560$	−3.49881	−	37.3980i	−0.147852	−	1.58035i
$561$	−3.87244	−	6.56333i	−0.163494	−	0.277104i
$562$	14.5408	−	2.82093i	0.613367	−	0.118994i
$563$		−	2.09901i		−	0.0884628i	−0.999021	−	0.0442314i	$-0.985916\pi$
$563$		−	2.09901i		−	0.0884628i	0.999021	−	0.0442314i	$-0.0140839\pi$
$564$	−24.1977	+	6.00077i	−1.01891	+	0.252678i
$565$	−21.7972	+	17.3826i	−0.917013	+	0.731293i
$566$	0.412820	+	0.934390i	0.0173521	+	0.0392753i
$567$	−37.1195	+	4.19645i	−1.55887	+	0.176234i
$568$	16.3999	−	16.8610i	0.688124	−	0.707473i
$569$	−4.11046	+	1.97949i	−0.172319	+	0.0829846i	−0.518055	−	0.855347i	$-0.673344\pi$
$569$	−4.11046	+	1.97949i	−0.172319	+	0.0829846i	0.345736	+	0.938332i	$0.387629\pi$
$570$	−4.25729	+	1.20516i	−0.178318	+	0.0504787i
$571$	12.0139	−	24.9472i	0.502767	−	1.04401i	−0.482958	−	0.875643i	$-0.660438\pi$
$571$	12.0139	−	24.9472i	0.502767	−	1.04401i	0.985725	−	0.168363i	$-0.0538481\pi$
$572$	−26.4900	+	18.4215i	−1.10760	+	0.770241i
$573$	−1.97006	−	23.3299i	−0.0823004	−	0.974623i
$574$	−14.6175	−	33.0856i	−0.610121	−	1.38096i
$575$	0.426312	−	0.534578i	0.0177784	−	0.0222934i
$576$	15.4866	−	18.3348i	0.645275	−	0.763950i
$577$	44.0575	+	10.0558i	1.83414	+	0.418630i	0.992585	−	0.121548i	$-0.0387860\pi$
$577$	44.0575	+	10.0558i	1.83414	+	0.418630i	0.841551	+	0.540178i	$0.181643\pi$
$578$	13.4511	+	18.0504i	0.559491	+	0.750796i
$579$	−24.5883	+	7.83955i	−1.02186	+	0.325800i
$580$	7.07328	−	23.3172i	0.293702	−	0.968194i
$581$			8.47954i			0.351790i
$582$	28.3004	+	20.2780i	1.17309	+	0.840552i
$583$	−6.03019	+	26.4200i	−0.249745	+	1.09420i
$584$	5.98101	−	9.81828i	0.247496	−	0.406283i
$585$	25.8500	+	1.44685i	1.06877	+	0.0598199i
$586$	−35.0688	+	15.4937i	−1.44868	+	0.640038i
$587$	0.0128961	−	0.0565013i	0.000532277	−	0.00233206i	−0.974661	−	0.223687i	$-0.928191\pi$
$587$	0.0128961	−	0.0565013i	0.000532277	−	0.00233206i	0.975193	+	0.221355i	$0.0710479\pi$
$588$	−21.5693	+	28.1089i	−0.889504	+	1.15919i
$589$	−1.62141	−	0.780832i	−0.0668092	−	0.0321736i
$590$	0.818631	−	24.9655i	0.0337025	−	1.02781i
$591$	3.31147	−	3.13131i	0.136216	−	0.128805i
$592$	−21.7613	+	13.1061i	−0.894383	+	0.538656i
$593$	13.8589	+	28.7784i	0.569119	+	1.18179i	0.964699	+	0.263356i	$0.0848293\pi$
$593$	13.8589	+	28.7784i	0.569119	+	1.18179i	−0.395580	+	0.918432i	$0.629456\pi$
$594$	−7.05016	+	30.2676i	−0.289272	+	1.24189i
$595$	6.09092	+	7.63777i	0.249703	+	0.313118i
$596$	−1.33322	+	20.3076i	−0.0546109	+	0.831830i
$597$	−13.7196	+	4.37425i	−0.561506	+	0.179026i
$598$	−5.93826	−	30.6094i	−0.242834	−	1.25171i
$599$	−0.959699	+	0.219045i	−0.0392123	+	0.00894994i	−0.242082	−	0.970256i	$-0.577830\pi$
$599$	−0.959699	+	0.219045i	−0.0392123	+	0.00894994i	0.202870	+	0.979206i	$0.434973\pi$
$600$	0.354927	+	0.458164i	0.0144899	+	0.0187045i
$601$	−1.58046	+	3.28185i	−0.0644682	+	0.133870i	−0.930713	−	0.365750i	$-0.880813\pi$
$601$	−1.58046	+	3.28185i	−0.0644682	+	0.133870i	0.866245	+	0.499620i	$0.166527\pi$
$602$	−22.5160	+	43.0831i	−0.917684	+	1.75594i
$603$	6.39700	−	22.2201i	0.260506	−	0.904874i
$604$	−12.7526	−	31.6304i	−0.518897	−	1.28702i
$605$	15.1875	−	3.46645i	0.617461	−	0.140931i
$606$	2.03543	−	11.6523i	0.0826835	−	0.473344i
$607$	10.7282	−	13.4527i	0.435444	−	0.546029i	−0.514892	−	0.857255i	$-0.672168\pi$
$607$	10.7282	−	13.4527i	0.435444	−	0.546029i	0.950336	+	0.311226i	$0.100740\pi$
$608$	−4.33450	+	1.26946i	−0.175787	+	0.0514833i
$609$	−33.4333	+	19.5205i	−1.35479	+	0.791012i
$610$	−4.48115	+	17.0385i	−0.181437	+	0.689867i
$611$	−21.4641	−	17.1170i	−0.868344	−	0.692481i
$612$	−0.756353	+	6.19601i	−0.0305738	+	0.250459i
$613$	5.90990	+	25.8930i	0.238699	+	1.04581i	0.942184	+	0.335097i	$0.108769\pi$
$613$	5.90990	+	25.8930i	0.238699	+	1.04581i	−0.703485	+	0.710710i	$0.748374\pi$
$614$	−18.0969	−	24.2848i	−0.730332	−	0.980053i
$615$	20.0781	+	13.4130i	0.809627	+	0.540866i
$616$	26.9955	+	41.6693i	1.08768	+	1.67890i
$617$	−13.2172	−	6.36506i	−0.532104	−	0.256248i	0.148483	−	0.988915i	$-0.452561\pi$
$617$	−13.2172	−	6.36506i	−0.532104	−	0.256248i	−0.680587	+	0.732667i	$0.738275\pi$
$618$	−10.2891	+	24.5180i	−0.413888	+	0.986260i
$619$	7.00771	+	30.7028i	0.281664	+	1.23405i	0.895660	+	0.444740i	$0.146704\pi$
$619$	7.00771	+	30.7028i	0.281664	+	1.23405i	−0.613996	+	0.789309i	$0.710439\pi$
$620$	−0.668119	+	10.1767i	−0.0268323	+	0.408708i
$621$	−24.0012	−	18.0522i	−0.963134	−	0.724409i
$622$	26.1189	−	5.06709i	1.04727	−	0.203172i
$623$	−27.6405	+	22.0426i	−1.10739	+	0.883118i
$624$	26.3997	+	1.23830i	1.05684	+	0.0495716i
$625$	23.0445	−	11.0977i	0.921782	−	0.443907i
$626$	1.02618	−	3.90179i	0.0410144	−	0.155947i
$627$	4.24953	−	4.01834i	0.169710	−	0.160477i
$628$	−25.2448	−	7.53220i	−1.00738	−	0.300567i
$629$	2.86665	−	5.95266i	0.114301	−	0.237348i
$630$	3.52881	−	39.6832i	0.140591	−	1.58102i
$631$	2.03856	+	0.465288i	0.0811538	+	0.0185228i	0.262905	−	0.964822i	$-0.415319\pi$
$631$	2.03856	+	0.465288i	0.0811538	+	0.0185228i	−0.181751	+	0.983345i	$0.558177\pi$
$632$	48.3076	+	4.76575i	1.92157	+	0.189572i
$633$	13.7265	+	5.23820i	0.545579	+	0.208200i
$634$	−9.33422	−	0.306073i	−0.370709	−	0.0121557i
$635$	44.8385	+	10.2341i	1.77936	+	0.406128i
$636$	17.0928	−	14.1615i	0.677774	−	0.561542i
$637$	−39.0164			−1.54589
$638$	5.98948	+	31.6465i	0.237126	+	1.25290i
$639$	20.3440	−	14.4406i	0.804796	−	0.571260i
$640$	15.8574	+	20.0919i	0.626819	+	0.794203i
$641$	−4.27510	+	18.7304i	−0.168856	+	0.739808i	0.817600	+	0.575786i	$0.195304\pi$
$641$	−4.27510	+	18.7304i	−0.168856	+	0.739808i	−0.986457	+	0.164022i	$0.947553\pi$
$642$	3.26830	+	11.5454i	0.128989	+	0.455661i
$643$	−0.0842578	−	0.0671933i	−0.00332280	−	0.00264985i	0.621827	−	0.783155i	$-0.286391\pi$
$643$	−0.0842578	−	0.0671933i	−0.00332280	−	0.00264985i	−0.625150	+	0.780505i	$0.714962\pi$
$644$	−47.3753	+	7.58912i	−1.86685	+	0.299053i
$645$	−2.73059	−	32.3364i	−0.107517	−	1.27324i
$646$	0.762110	−	0.893910i	0.0299848	−	0.0351704i
$647$	4.06401	+	1.95713i	0.159773	+	0.0769425i	0.512061	−	0.858949i	$-0.328882\pi$
$647$	4.06401	+	1.95713i	0.159773	+	0.0769425i	−0.352288	+	0.935891i	$0.614596\pi$
$648$	19.6742	−	16.1532i	0.772875	−	0.634558i
$649$	14.3259	+	29.7481i	0.562342	+	1.16772i
$650$	−0.162330	+	0.617219i	−0.00636711	+	0.0242093i
$651$	11.7739	−	11.1334i	0.461456	−	0.436350i
$652$	4.41545	+	27.5635i	0.172922	+	1.07947i
$653$	13.4375	+	16.8501i	0.525850	+	0.659395i	0.971840	−	0.235643i	$-0.0757196\pi$
$653$	13.4375	+	16.8501i	0.525850	+	0.659395i	−0.445990	+	0.895038i	$0.647148\pi$
$654$	−29.4852	+	16.1180i	−1.15296	+	0.630262i
$655$	−32.5964			−1.27364
$656$	20.6185	+	13.5060i	0.805016	+	0.527322i
$657$	8.12370	−	9.09385i	0.316936	−	0.354785i
$658$	−27.4076	+	32.1475i	−1.06846	+	1.25324i
$659$	2.45496	−	5.09779i	0.0956318	−	0.198582i	−0.847665	−	0.530532i	$-0.821992\pi$
$659$	2.45496	−	5.09779i	0.0956318	−	0.198582i	0.943297	+	0.331950i	$0.107707\pi$
$660$	−30.1254	−	13.8202i	−1.17263	−	0.537952i
$661$	21.4973	+	26.9567i	0.836147	+	1.04850i	0.998095	+	0.0616960i	$0.0196509\pi$
$661$	21.4973	+	26.9567i	0.836147	+	1.04850i	−0.161948	+	0.986799i	$0.551778\pi$
$662$	−7.53352	−	10.1094i	−0.292799	−	0.392915i
$663$	−5.92007	+	3.49291i	−0.229916	+	0.135653i
$664$	−3.14177	−	4.84953i	−0.121924	−	0.188198i
$665$	−4.67459	+	5.86176i	−0.181273	+	0.227309i
$666$	−25.2159	+	9.49444i	−0.977097	+	0.367902i
$667$	−30.3124	−	7.06453i	−1.17370	−	0.273540i
$668$	−2.10072	−	1.18710i	−0.0812792	−	0.0459302i
$669$	6.00174	−	15.7273i	0.232041	−	0.608053i
$670$	21.8553	+	11.4220i	0.844346	+	0.441270i
$671$	−5.18203	−	22.7040i	−0.200050	−	0.876477i
$672$	3.23579	−	40.5391i	0.124823	−	1.56383i
$673$	−8.96706	−	11.2443i	−0.345655	−	0.433438i	0.578367	−	0.815777i	$-0.303690\pi$
$673$	−8.96706	−	11.2443i	−0.345655	−	0.433438i	−0.924022	+	0.382339i	$0.875119\pi$
$674$	−7.00857	+	13.4105i	−0.269960	+	0.516553i
$675$	0.282296	+	0.546061i	0.0108656	+	0.0210179i
$676$	1.77179	+	2.54782i	0.0681457	+	0.0979930i
$677$	8.96200	+	39.2651i	0.344438	+	1.50908i	0.789596	+	0.613628i	$0.210290\pi$
$677$	8.96200	+	39.2651i	0.344438	+	1.50908i	−0.445158	+	0.895452i	$0.646852\pi$
$678$	−26.4865	+	14.4787i	−1.01721	+	0.556052i
$679$	58.9947			2.26401
$680$	−6.31334	−	2.11136i	−0.242106	−	0.0809669i
$681$	−21.2909	+	31.8705i	−0.815867	+	1.22128i
$682$	−5.44794	−	12.3310i	−0.208613	−	0.472180i
$683$	−1.56961	+	0.755883i	−0.0600594	+	0.0289231i	−0.463672	−	0.886007i	$-0.653469\pi$
$683$	−1.56961	+	0.755883i	−0.0600594	+	0.0289231i	0.403613	+	0.914930i	$0.367754\pi$
$684$	−4.76520	+	0.492219i	−0.182202	+	0.0188205i
$685$	14.4491	+	30.0038i	0.552071	+	1.14639i
$686$	−0.620985	+	18.9380i	−0.0237093	+	0.723055i
$687$	34.3594	+	4.84746i	1.31089	+	0.184942i
$688$	−3.08568	−	32.9821i	−0.117641	−	1.25743i
$689$	23.8306	+	5.43918i	0.907874	+	0.207216i
$690$	23.9809	−	21.2316i	0.912939	−	0.808272i
$691$	7.58622	+	6.04981i	0.288594	+	0.230146i	0.757075	−	0.653327i	$-0.226627\pi$
$691$	7.58622	+	6.04981i	0.288594	+	0.230146i	−0.468482	+	0.883473i	$0.655199\pi$
$692$	2.25440	+	0.672635i	0.0856993	+	0.0255697i
$693$	20.1618	+	48.6490i	0.765882	+	1.84802i
$694$	−22.9342	−	30.7760i	−0.870570	−	1.16824i
$695$	2.48071			0.0940987
$696$	11.8882	−	23.5514i	0.450623	−	0.892715i
$697$	−6.41059			−0.242818
$698$	−16.2604	−	21.8203i	−0.615466	−	0.825911i
$699$	1.21668	+	14.4083i	0.0460192	+	0.544971i
$700$	0.941067	+	0.280782i	0.0355690	+	0.0106126i
$701$	4.08783	+	3.25993i	0.154395	+	0.123126i	0.697641	−	0.716448i	$-0.254233\pi$
$701$	4.08783	+	3.25993i	0.154395	+	0.123126i	−0.543245	+	0.839574i	$0.682805\pi$
$702$	27.3011	+	6.35919i	1.03041	+	0.240012i
$703$	4.94350	+	1.12832i	0.186448	+	0.0425555i
$704$	−30.8780	−	13.8290i	−1.16376	−	0.521199i
$705$	3.93963	−	27.9246i	0.148375	−	1.05170i
$706$	−1.62647	+	49.6020i	−0.0612131	+	1.86680i
$707$	−8.69671	−	18.0589i	−0.327074	−	0.679175i
$708$	5.52436	−	26.4748i	0.207618	−	0.994982i
$709$	39.8284	−	19.1804i	1.49579	−	0.720334i	0.505954	−	0.862560i	$-0.331140\pi$
$709$	39.8284	−	19.1804i	1.49579	−	0.720334i	0.989834	+	0.142227i	$0.0454262\pi$
$710$	10.7525	+	24.3374i	0.403533	+	0.913368i
$711$	49.4771	+	14.2441i	1.85554	+	0.534195i
$712$	7.64086	−	22.8475i	0.286353	−	0.856247i
$713$	13.0274			0.487879
$714$	5.07337	+	9.28093i	0.189866	+	0.347330i
$715$	−8.12164	−	35.5832i	−0.303732	−	1.33074i
$716$	−17.9050	−	25.7473i	−0.669142	−	0.962223i
$717$	1.59902	−	11.3340i	0.0597164	−	0.423277i
$718$	−12.2820	+	23.5009i	−0.458359	+	0.877044i
$719$	−9.21344	−	11.5533i	−0.343604	−	0.430865i	0.579763	−	0.814785i	$-0.303145\pi$
$719$	−9.21344	−	11.5533i	−0.343604	−	0.430865i	−0.923366	+	0.383920i	$0.874574\pi$
$720$	12.6849	+	24.0027i	0.472739	+	0.894527i
$721$	10.0259	+	43.9262i	0.373383	+	1.63590i
$722$	−23.0150	−	12.0280i	−0.856530	−	0.447638i
$723$	30.6762	+	11.7064i	1.14086	+	0.435366i
$724$	37.5153	+	21.1996i	1.39424	+	0.787876i
$725$	0.496264	+	0.399482i	0.0184308	+	0.0148364i
$726$	16.8443	−	0.867652i	0.625149	−	0.0322016i
$727$	−21.8270	+	27.3702i	−0.809520	+	1.01511i	0.189925	+	0.981799i	$0.439175\pi$
$727$	−21.8270	+	27.3702i	−0.809520	+	1.01511i	−0.999445	+	0.0333073i	$0.989396\pi$
$728$	37.5854	−	24.3497i	1.39301	−	0.902460i
$729$	23.6237	−	13.0737i	0.874951	−	0.484211i
$730$	7.77074	+	10.4278i	0.287608	+	0.385949i
$731$	5.37172	+	6.73592i	0.198680	+	0.249137i
$732$	−7.95380	+	17.3377i	−0.293981	+	0.640819i
$733$	13.5899	−	28.2197i	0.501953	−	1.04232i	−0.483965	−	0.875087i	$-0.660804\pi$
$733$	13.5899	−	28.2197i	0.501953	−	1.04232i	0.985918	−	0.167229i	$-0.0534820\pi$
$734$	−10.2258	+	11.9942i	−0.377440	+	0.442715i
$735$	−20.3663	−	34.5185i	−0.751221	−	1.27323i
$736$	24.2826	−	21.8934i	0.895067	−	0.807002i
$737$	−32.5964			−1.20070
$738$	18.9156	+	18.0465i	0.696292	+	0.664301i
$739$	5.60113	+	7.02359i	0.206041	+	0.258367i	0.874105	−	0.485736i	$-0.161448\pi$
$739$	5.60113	+	7.02359i	0.206041	+	0.258367i	−0.668065	+	0.744103i	$0.732877\pi$
$740$	−4.54526	−	28.3739i	−0.167087	−	1.04305i
$741$	−3.62451	−	3.83305i	−0.133150	−	0.140810i
$742$	9.56698	−	36.3761i	0.351215	−	1.33541i
$743$	5.74348	+	11.9265i	0.210708	+	0.437539i	0.979359	−	0.202129i	$-0.0647861\pi$
$743$	5.74348	+	11.9265i	0.210708	+	0.437539i	−0.768651	+	0.639668i	$0.779072\pi$
$744$	−2.60858	+	10.7297i	−0.0956353	+	0.393368i
$745$	−20.7412	−	9.98845i	−0.759900	−	0.365949i
$746$	27.6928	−	32.4820i	1.01391	−	1.18925i
$747$	−2.34645	−	5.66184i	−0.0858522	−	0.207156i
$748$	8.68869	−	1.39186i	0.317690	−	0.0508913i
$749$	15.8966	+	12.6771i	0.580848	+	0.463211i
$750$	26.0298	−	7.36856i	0.950473	−	0.269062i
$751$	7.70916	−	33.7760i	0.281311	−	1.23250i	−0.614803	−	0.788681i	$-0.710765\pi$
$751$	7.70916	−	33.7760i	0.281311	−	1.23250i	0.896114	−	0.443824i	$-0.146378\pi$
$752$	3.76365	−	28.5403i	0.137246	−	1.04076i
$753$	−14.3267	+	4.56782i	−0.522095	+	0.166461i
$754$	28.5449	−	5.40247i	1.03954	−	0.196746i
$755$	38.5784			1.40401
$756$	11.1569	−	41.6671i	0.405773	−	1.51542i
$757$	0.913918	+	0.208596i	0.0332169	+	0.00758154i	0.239097	−	0.970996i	$-0.423149\pi$
$757$	0.913918	+	0.208596i	0.0332169	+	0.00758154i	−0.205880	+	0.978577i	$0.566006\pi$
$758$	−27.9315	−	0.915888i	−1.01452	−	0.0332665i
$759$	−15.0946	+	39.5548i	−0.547899	+	1.43575i
$760$	0.501597	−	5.08439i	0.0181948	−	0.184430i
$761$	4.24898	+	0.969802i	0.154025	+	0.0351553i	0.298838	−	0.954304i	$-0.403401\pi$
$761$	4.24898	+	0.969802i	0.154025	+	0.0351553i	−0.144813	+	0.989459i	$0.546258\pi$
$762$	45.9163	+	19.2690i	1.66337	+	0.698042i
$763$	−24.7056	+	51.3016i	−0.894401	+	1.85724i
$764$	25.9064	+	7.72960i	0.937262	+	0.279647i
$765$	−6.18046	−	3.41431i	−0.223455	−	0.123445i
$766$	0.546023	−	2.07612i	0.0197286	−	0.0750131i
$767$	26.8326	−	12.9219i	0.968868	−	0.466582i
$768$	13.1696	+	24.3836i	0.475218	+	0.879868i
$769$	−30.2990	+	24.1627i	−1.09261	+	0.871328i	−0.992328	−	0.123631i	$-0.960546\pi$
$769$	−30.2990	+	24.1627i	−1.09261	+	0.871328i	−0.100283	+	0.994959i	$0.531975\pi$
$770$	−55.1349	+	10.6962i	−1.98692	+	0.385465i
$771$	−31.0746	+	9.90757i	−1.11912	+	0.356812i
$772$	1.95223	−	29.7363i	0.0702625	−	1.07023i
$773$	−6.92394	−	30.3358i	−0.249037	−	1.09110i	−0.932515	−	0.361131i	$-0.882391\pi$
$773$	−6.92394	−	30.3358i	−0.249037	−	1.09110i	0.683478	−	0.729971i	$-0.260466\pi$
$774$	3.11214	−	34.9975i	0.111863	−	1.25796i
$775$	−0.240243	−	0.115695i	−0.00862979	−	0.00415589i
$776$	−33.7396	+	21.8582i	−1.21118	+	0.784665i
$777$	−25.3621	+	37.9647i	−0.909859	+	1.36198i
$778$	11.5852	+	15.5466i	0.415351	+	0.557371i
$779$	−1.09479	−	4.79658i	−0.0392249	−	0.171855i
$780$	−12.4657	+	27.1728i	−0.446345	+	0.972943i
$781$	−27.4968	−	21.9280i	−0.983914	−	0.784646i
$782$	−2.16287	+	8.22377i	−0.0773441	+	0.294081i
$783$	16.9219	−	22.2856i	0.604739	−	0.796423i
$784$	−21.1074	−	35.0467i	−0.753836	−	1.25167i
$785$	18.5803	−	23.2990i	0.663160	−	0.831577i
$786$	−34.7660	−	6.07291i	−1.24006	−	0.216614i
$787$	28.9831	−	6.61521i	1.03314	−	0.235807i	0.327851	−	0.944729i	$-0.393676\pi$
$787$	28.9831	−	6.61521i	1.03314	−	0.235807i	0.705286	+	0.708922i	$0.250818\pi$
$788$	1.96783	+	4.88081i	0.0701009	+	0.173872i
$789$	−16.7641	−	11.1991i	−0.596816	−	0.398699i
$790$	−25.4331	+	48.6649i	−0.904870	+	1.73142i
$791$	−22.1929	+	46.0841i	−0.789090	+	1.63856i
$792$	−29.5558	−	20.3527i	−1.05022	−	0.723201i
$793$	−20.4788	+	4.67415i	−0.727223	+	0.165984i
$794$	5.00454	+	25.7965i	0.177605	+	0.915483i
$795$	7.62727	+	23.9225i	0.270511	+	0.848445i
$796$	1.08929	−	16.5920i	0.0386089	−	0.588089i
$797$	23.0573	+	28.9129i	0.816731	+	1.02415i	0.999162	+	0.0409298i	$0.0130320\pi$
$797$	23.0573	+	28.9129i	0.816731	+	1.02415i	−0.182431	+	0.983219i	$0.558397\pi$
$798$	−6.07783	+	5.38102i	−0.215153	+	0.190486i
$799$	3.24855	+	6.74568i	0.114925	+	0.238645i
$800$	−0.642239	+	0.188094i	−0.0227066	+	0.00665014i
$801$	12.3561	−	22.3666i	0.436583	−	0.790287i
$802$	0.684479	−	20.8743i	0.0241698	−	0.737098i
$803$	−15.4877	−	7.45848i	−0.546549	−	0.263204i
$804$	21.1821	+	16.2540i	0.747034	+	0.573236i
$805$	12.0770	−	52.9126i	0.425657	−	1.86493i
$806$	−11.1225	+	4.91400i	−0.391773	+	0.173088i
$807$	17.9417	+	6.84678i	0.631578	+	0.241018i
$808$	11.6648	+	7.10584i	0.410366	+	0.249982i
$809$	7.91929	−	34.6967i	0.278427	−	1.21987i	−0.621354	−	0.783530i	$-0.713417\pi$
$809$	7.91929	−	34.6967i	0.278427	−	1.21987i	0.899782	−	0.436340i	$-0.143726\pi$
$810$	8.62490	+	27.4732i	0.303048	+	0.965309i
$811$		−	13.4746i		−	0.473158i	−0.971612	−	0.236579i	$-0.923974\pi$
$811$		−	13.4746i		−	0.473158i	0.971612	−	0.236579i	$-0.0760263\pi$
$812$	−6.86921	−	44.1731i	−0.241062	−	1.55017i
$813$	−5.23319	−	16.4136i	−0.183536	−	0.575651i
$814$	22.6965	+	30.4570i	0.795510	+	1.06752i
$815$	−30.7852	−	7.02653i	−1.07836	−	0.246129i
$816$	−6.34021	−	3.42811i	−0.221952	−	0.120008i
$817$	−4.12263	+	5.16962i	−0.144233	+	0.180862i
$818$	8.82373	+	19.9719i	0.308514	+	0.698301i
$819$	43.8810	−	18.1857i	1.53333	−	0.635461i
$820$	−22.8907	+	15.9185i	−0.799379	+	0.555899i
$821$	−5.80776	+	12.0599i	−0.202692	+	0.420895i	−0.977392	−	0.211434i	$-0.932187\pi$
$821$	−5.80776	+	12.0599i	−0.202692	+	0.420895i	0.774700	+	0.632329i	$0.217901\pi$
$822$	9.82093	+	34.6929i	0.342544	+	1.21005i
$823$	−7.30807	+	3.51938i	−0.254743	+	0.122678i	−0.556898	−	0.830581i	$-0.688008\pi$
$823$	−7.30807	+	3.51938i	−0.254743	+	0.122678i	0.302154	+	0.953259i	$0.402294\pi$
$824$	−22.0091	−	21.4071i	−0.766723	−	0.745753i
$825$	0.629649	−	0.595393i	0.0219216	−	0.0207289i
$826$	−18.5201	−	41.9189i	−0.644396	−	1.45854i
$827$	−18.4777	+	14.7355i	−0.642534	+	0.512404i	−0.889686	−	0.456573i	$-0.849077\pi$
$827$	−18.4777	+	14.7355i	−0.642534	+	0.512404i	0.247152	+	0.968977i	$0.420505\pi$
$828$	29.5327	−	18.1770i	1.02633	−	0.631694i
$829$		−	44.5437i		−	1.54707i	−0.633756	−	0.773533i	$-0.718488\pi$
$829$		−	44.5437i		−	1.54707i	0.633756	−	0.773533i	$-0.281512\pi$
$830$	6.41667	−	1.24484i	0.222726	−	0.0432091i
$831$	−24.8259	+	14.6476i	−0.861201	+	0.508118i
$832$	−12.4736	+	27.8517i	−0.432445	+	0.965583i
$833$	9.58680	+	4.61676i	0.332163	+	0.159961i
$834$	2.64583	+	0.462172i	0.0916176	+	0.0160037i
$835$	2.13398	−	1.70179i	0.0738494	−	0.0588929i
$836$	2.52526	+	6.26342i	0.0873381	+	0.216625i
$837$	−4.78070	+	10.6919i	−0.165245	+	0.369565i
$838$	3.92759	+	2.05263i	0.135676	+	0.0709069i
$839$	3.54921	+	2.83040i	0.122532	+	0.0977164i	0.682839	−	0.730569i	$-0.260745\pi$
$839$	3.54921	+	2.83040i	0.122532	+	0.0977164i	−0.560306	+	0.828285i	$0.689317\pi$
$840$	41.1619	+	20.5421i	1.42022	+	0.708768i
$841$	6.71130	−	28.2127i	0.231424	−	0.972853i
$842$	−24.6982	−	6.49567i	−0.851155	−	0.223856i
$843$	−6.46782	+	16.9486i	−0.222763	+	0.583742i
$844$	−11.4236	+	12.5423i	−0.393217	+	0.431722i
$845$	−3.42241	+	0.781143i	−0.117735	+	0.0268722i
$846$	9.40439	−	29.0493i	0.323330	−	0.998736i
$847$	22.3451	−	17.8196i	0.767787	−	0.612289i
$848$	8.00630	+	24.3485i	0.274938	+	0.836131i
$849$	−1.23883	−	0.174776i	−0.0425167	−	0.00599830i
$850$	0.112921	−	0.132450i	0.00387316	−	0.00454299i
$851$	−35.7855	+	8.16781i	−1.22671	+	0.279989i
$852$	6.93394	+	27.9606i	0.237553	+	0.957915i
$853$			41.5741i			1.42347i	0.702449	+	0.711735i	$0.252090\pi$
$853$			41.5741i			1.42347i	−0.702449	+	0.711735i	$0.747910\pi$
$854$	6.15587	+	31.7311i	0.210650	+	1.08582i
$855$	1.49919	−	5.20748i	0.0512713	−	0.178092i
$856$	−13.7884	−	1.36029i	−0.471279	−	0.0464937i
$857$	−22.0032	−	45.6902i	−0.751616	−	1.56075i	−0.826099	−	0.563525i	$-0.809445\pi$
$857$	−22.0032	−	45.6902i	−0.751616	−	1.56075i	0.0744830	−	0.997222i	$-0.476269\pi$
$858$	−2.03284	−	39.4648i	−0.0694001	−	1.34731i
$859$	−0.876605	+	0.422151i	−0.0299094	+	0.0144036i	−0.448779	−	0.893643i	$-0.648141\pi$
$859$	−0.876605	+	0.422151i	−0.0299094	+	0.0144036i	0.418869	+	0.908047i	$0.362427\pi$
$860$	35.9075	+	10.7136i	1.22444	+	0.365330i
$861$	43.8656	+	6.18860i	1.49493	+	0.210907i
$862$	27.1550	−	31.8512i	0.924901	−	1.08485i
$863$	5.34315	−	23.4099i	0.181883	−	0.796881i	−0.798850	−	0.601530i	$-0.794558\pi$
$863$	5.34315	−	23.4099i	0.181883	−	0.796881i	0.980733	−	0.195352i	$-0.0625848\pi$
$864$	9.05740	+	27.9636i	0.308139	+	0.951341i
$865$	−1.65925	+	2.08063i	−0.0564161	+	0.0707435i
$866$	0.349800	−	10.6678i	0.0118867	−	0.362505i
$867$	−27.4725	+	2.31987i	−0.933015	+	0.0787869i
$868$	6.99659	+	17.3537i	0.237480	+	0.589022i
$869$		−	72.5817i		−	2.46217i
$870$	19.6799	+	22.4341i	0.667210	+	0.760586i
$871$			29.4017i			0.996238i
$872$	−4.87850	−	38.4936i	−0.165207	−	1.30356i
$873$	−39.3911	+	16.3250i	−1.33319	+	0.552517i
$874$	−6.52262	−	0.213880i	−0.220631	−	0.00723459i
$875$	28.5812	−	35.8397i	0.966222	−	1.21160i
$876$	6.34521	+	12.5696i	0.214385	+	0.424688i
$877$	−2.93790	+	12.8718i	−0.0992057	+	0.434649i	0.900794	+	0.434246i	$0.142985\pi$
$877$	−2.93790	+	12.8718i	−0.0992057	+	0.434649i	−1.00000		0.000402428i	$0.999872\pi$
$878$	−10.0352	−	8.55555i	−0.338670	−	0.288736i
$879$	6.55957	−	46.4950i	0.221249	−	1.56824i
$880$	27.5691	−	26.5454i	0.929355	−	0.894846i
$881$	−12.5531	+	6.04527i	−0.422926	+	0.203670i	−0.633227	−	0.773966i	$-0.718270\pi$
$881$	−12.5531	+	6.04527i	−0.422926	+	0.203670i	0.210301	+	0.977637i	$0.432556\pi$
$882$	−15.2909	−	40.6104i	−0.514871	−	1.36742i
$883$	1.26562	+	2.62808i	0.0425914	+	0.0884420i	0.921179	−	0.389140i	$-0.127228\pi$
$883$	1.26562	+	2.62808i	0.0425914	+	0.0884420i	−0.878587	+	0.477582i	$0.841513\pi$
$884$	−1.25544	−	7.83713i	−0.0422251	−	0.263591i
$885$	25.4386	+	16.9941i	0.855109	+	0.571250i
$886$	−25.0021	+	4.85043i	−0.839961	+	0.162953i
$887$			28.9169i			0.970936i	0.874255	+	0.485468i	$0.161351\pi$
$887$			28.9169i			0.970936i	−0.874255	+	0.485468i	$0.838649\pi$
$888$	0.438443	−	31.1093i	0.0147132	−	1.04396i
$889$	82.2632	−	18.7760i	2.75902	−	0.629728i
$890$	20.7379	+	17.6803i	0.695138	+	0.592645i
$891$	−26.9243	−	26.9041i	−0.901997	−	0.901321i
$892$	14.3705	+	13.0888i	0.481158	+	0.438244i
$893$	−4.49252	+	3.58267i	−0.150336	+	0.119889i
$894$	−20.2609	−	14.5175i	−0.677626	−	0.485539i
$895$	34.5856	−	7.89395i	1.15607	−	0.263866i
$896$	42.2055	+	20.5884i	1.40999	+	0.687810i
$897$	35.6781	+	13.6152i	1.19126	+	0.454599i
$898$	5.88517	−	22.3769i	0.196391	−	0.746726i
$899$	−0.0554824	+	12.1379i	−0.00185044	+	0.404822i
$900$	−0.706054	+	0.0729316i	−0.0235351	+	0.00243105i
$901$	−5.21186	−	4.15632i	−0.173632	−	0.138467i
$902$	17.0703	−	32.6631i	0.568380	−	1.08756i
$903$	−30.2542	−	51.2774i	−1.00680	−	1.70641i
$904$	−4.38234	−	34.5787i	−0.145755	−	1.15007i
$905$	−38.1093	+	30.3911i	−1.26679	+	1.01024i
$906$	41.1462	+	7.18740i	1.36699	+	0.238785i
$907$	11.8083	+	5.68656i	0.392087	+	0.188819i	0.619531	−	0.784972i	$-0.287323\pi$
$907$	11.8083	+	5.68656i	0.392087	+	0.188819i	−0.227444	+	0.973791i	$0.573037\pi$
$908$	−25.2679	−	36.3351i	−0.838544	−	1.20582i
$909$	10.8041	+	9.65150i	0.358349	+	0.320120i
$910$	9.64791	+	49.7312i	0.319825	+	1.64857i
$911$		−	4.50902i		−	0.149390i	−0.997206	−	0.0746952i	$-0.976202\pi$
$911$		−	4.50902i		−	0.149390i	0.997206	−	0.0746952i	$-0.0237984\pi$
$912$	1.48224	−	5.32936i	0.0490818	−	0.176473i
$913$	−6.75494	+	5.38688i	−0.223556	+	0.178280i
$914$	−14.0512	+	6.20792i	−0.464772	+	0.205340i
$915$	−14.8251	−	15.6781i	−0.490102	−	0.518300i
$916$	−19.7123	+	34.8834i	−0.651313	+	1.15258i
$917$	−53.8807	+	25.9476i	−1.77930	+	0.856865i
$918$	−5.95574	−	4.79303i	−0.196569	−	0.158194i
$919$	−23.4577	+	48.7104i	−0.773798	+	1.60681i	0.0208833	+	0.999782i	$0.493352\pi$
$919$	−23.4577	+	48.7104i	−0.773798	+	1.60681i	−0.794681	+	0.607027i	$0.792362\pi$
$920$	12.6978	+	34.7359i	0.418635	+	1.14521i
$921$	36.9612	−	3.12113i	1.21791	−	0.102845i
$922$	−14.1947	+	6.27132i	−0.467477	+	0.206535i
$923$	−19.7789	+	24.8019i	−0.651030	+	0.816366i
$924$	−60.7975	+	1.13620i	−2.00009	+	0.0373782i
$925$	0.732474	+	0.167182i	0.0240836	+	0.00549692i
$926$	−29.2669	+	21.8096i	−0.961769	+	0.716707i
$927$	−18.8496	−	26.5555i	−0.619101	−	0.872195i
$928$	20.2952	+	22.7179i	0.666224	+	0.745752i
$929$			27.3832i			0.898415i	0.893427	+	0.449208i	$0.148294\pi$
$929$			27.3832i			0.898415i	−0.893427	+	0.449208i	$0.851706\pi$
$930$	−10.1534	−	7.27518i	−0.332942	−	0.238563i
$931$	−1.81717	+	7.96155i	−0.0595554	+	0.260929i
$932$	−15.9995	−	4.77370i	−0.524081	−	0.156368i
$933$	−11.6178	+	30.4439i	−0.380349	+	0.996690i
$934$	−14.6917	−	33.2536i	−0.480728	−	1.08809i
$935$	−2.21493	+	9.70425i	−0.0724360	+	0.317363i
$936$	−18.3580	+	26.6590i	−0.600049	+	0.871378i
$937$	−40.5949	−	19.5495i	−1.32618	−	0.638653i	−0.369344	−	0.929293i	$-0.620418\pi$
$937$	−40.5949	−	19.5495i	−1.32618	−	0.638653i	−0.956833	+	0.290640i	$0.906132\pi$
$938$	45.2184	+	1.48273i	1.47643	+	0.0484129i
$939$	3.39493	+	3.59026i	0.110789	+	0.117164i
$940$	28.3504	+	16.0206i	0.924688	+	0.522534i
$941$	−20.4429	−	42.4501i	−0.666420	−	1.38383i	−0.910267	−	0.414021i	$-0.864124\pi$
$941$	−20.4429	−	42.4501i	−0.666420	−	1.38383i	0.243848	−	0.969814i	$-0.421590\pi$
$942$	24.1578	−	21.3882i	0.787104	−	0.696865i
$943$	22.2055	+	27.8449i	0.723111	+	0.906753i
$944$	26.1232	+	17.1119i	0.850239	+	0.556945i
$945$	38.9948	+	29.3294i	1.26850	+	0.954087i
$946$	−48.6247	+	9.43325i	−1.58093	+	0.306701i
$947$	−16.4833	+	3.76220i	−0.535634	+	0.122255i	−0.481777	−	0.876294i	$-0.660009\pi$
$947$	−16.4833	+	3.76220i	−0.535634	+	0.122255i	−0.0538569	+	0.998549i	$0.517151\pi$
$948$	−36.1926	+	47.1657i	−1.17548	+	1.53187i
$949$	−6.72749	+	13.9698i	−0.218384	+	0.453478i
$950$	0.118387	+	0.0618712i	0.00384098	+	0.00200737i
$951$	6.35383	−	9.51110i	0.206037	−	0.308419i
$952$	−12.1164	+	1.53558i	−0.392696	+	0.0497685i
$953$	−16.5325	+	3.77343i	−0.535539	+	0.122233i	−0.481733	−	0.876318i	$-0.659992\pi$
$953$	−16.5325	+	3.77343i	−0.535539	+	0.122233i	−0.0538062	+	0.998551i	$0.517135\pi$
$954$	3.67803	+	26.9359i	0.119081	+	0.872081i
$955$	−19.0673	+	23.9096i	−0.617002	+	0.773696i
$956$	11.5069	+	6.50244i	0.372159	+	0.210304i
$957$	−36.7899	−	14.2325i	−1.18925	−	0.460071i
$958$	−9.57964	−	2.51947i	−0.309504	−	0.0814003i
$959$	47.7677	+	38.0935i	1.54250	+	1.23010i
$960$	−31.1520	+	3.50276i	−1.00543	+	0.113051i
$961$	5.76765	+	25.2697i	0.186053	+	0.815152i
$962$	27.4720	−	20.4720i	0.885732	−	0.660044i
$963$	−14.1222	−	4.06568i	−0.455083	−	0.131015i
$964$	−25.5297	+	28.0296i	−0.822255	+	0.902773i
$965$	30.3713	+	14.6261i	0.977688	+	0.470830i
$966$	22.7388	−	54.1846i	0.731609	−	1.74336i
$967$	5.98044	+	26.2020i	0.192318	+	0.842600i	0.975358	+	0.220629i	$0.0708108\pi$
$967$	5.98044	+	26.2020i	0.192318	+	0.842600i	−0.783040	+	0.621971i	$0.786332\pi$
$968$	−6.17700	+	18.4703i	−0.198536	+	0.593659i
$969$	0.437025	+	1.37071i	0.0140393	+	0.0440335i
$970$	−8.66074	−	44.6427i	−0.278079	−	1.43339i
$971$	−12.8497	+	10.2473i	−0.412366	+	0.328851i	−0.807601	−	0.589729i	$-0.799234\pi$
$971$	−12.8497	+	10.2473i	−0.412366	+	0.328851i	0.395235	+	0.918580i	$0.370663\pi$
$972$	4.08055	+	30.9087i	0.130884	+	0.991398i
$973$	4.10053	−	1.97471i	0.131457	−	0.0633064i
$974$	−14.9944	−	3.94355i	−0.480451	−	0.126360i
$975$	−0.537040	−	0.567939i	−0.0171990	−	0.0181886i
$976$	−15.2774	−	15.8665i	−0.489017	−	0.507875i
$977$	10.9848	−	22.8103i	0.351436	−	0.729765i	−0.648057	−	0.761592i	$-0.724418\pi$
$977$	10.9848	−	22.8103i	0.351436	−	0.729765i	0.999493	+	0.0318270i	$0.0101326\pi$
$978$	−31.5253	−	13.2297i	−1.00807	−	0.423040i
$979$	−35.1190	−	8.01568i	−1.12241	−	0.256182i
$980$	45.6964	−	7.32018i	1.45972	−	0.233835i
$981$	2.29989	−	41.0909i	0.0734300	−	1.31193i
$982$	0.115824	−	3.53225i	0.00369609	−	0.112719i
$983$	21.7345	+	4.96077i	0.693224	+	0.158224i	0.554595	−	0.832120i	$-0.312873\pi$
$983$	21.7345	+	4.96077i	0.693224	+	0.158224i	0.138629	+	0.990344i	$0.455730\pi$
$984$	−27.3801	+	12.7134i	−0.872846	+	0.405288i
$985$	−5.95293			−0.189676
$986$	−7.65308	−	2.05023i	−0.243724	−	0.0652925i
$987$	−15.7167	−	49.2945i	−0.500267	−	1.56906i
$988$	5.64956	−	2.27777i	0.179736	−	0.0724654i
$989$	10.6510	−	46.6649i	0.338681	−	1.48386i
$990$	33.8540	−	22.3988i	1.07595	−	0.711882i
$991$	−2.18652	−	1.74369i	−0.0694570	−	0.0553901i	0.588146	−	0.808755i	$-0.299858\pi$
$991$	−2.18652	−	1.74369i	−0.0694570	−	0.0553901i	−0.657603	+	0.753365i	$0.728430\pi$
$992$	−10.4312	−	7.33242i	−0.331190	−	0.232805i
$993$	15.3865	−	1.29929i	0.488276	−	0.0412316i
$994$	37.1467	+	31.6697i	1.17822	+	1.00450i
$995$	16.9463	+	8.16093i	0.537235	+	0.258719i
$996$	7.07570	−	0.132232i	0.224202	−	0.00418994i
$997$	−7.22103	−	14.9946i	−0.228692	−	0.474885i	0.754772	−	0.655987i	$-0.227748\pi$
$997$	−7.22103	−	14.9946i	−0.228692	−	0.474885i	−0.983464	+	0.181103i	$0.942033\pi$
$998$	11.6113	+	3.05379i	0.367548	+	0.0966659i
$999$	6.42883	−	32.3674i	0.203399	−	1.02406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.17	yes	336
3.2	odd	2	inner	348.2.t.a.35.40	yes	336
4.3	odd	2	inner	348.2.t.a.35.50	yes	336
12.11	even	2	inner	348.2.t.a.35.7	✓	336
29.5	even	14	inner	348.2.t.a.179.7	yes	336
87.5	odd	14	inner	348.2.t.a.179.50	yes	336
116.63	odd	14	inner	348.2.t.a.179.40	yes	336
348.179	even	14	inner	348.2.t.a.179.17	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.7	✓	336	12.11	even	2	inner
348.2.t.a.35.17	yes	336	1.1	even	1	trivial
348.2.t.a.35.40	yes	336	3.2	odd	2	inner
348.2.t.a.35.50	yes	336	4.3	odd	2	inner
348.2.t.a.179.7	yes	336	29.5	even	14	inner
348.2.t.a.179.17	yes	336	348.179	even	14	inner
348.2.t.a.179.40	yes	336	116.63	odd	14	inner
348.2.t.a.179.50	yes	336	87.5	odd	14	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:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.845038 - 1.13398i) q^{2} +(1.72591 - 0.145741i) q^{3} +(-0.571822 + 1.91651i) q^{4} +(-1.76879 - 1.41056i) q^{5} +(-1.62373 - 1.83399i) q^{6} +(-4.04660 - 0.923610i) q^{7} +(2.65650 - 0.971091i) q^{8} +(2.95752 - 0.503073i) q^{9} +O(q^{10})\)	\(q+(-0.845038 - 1.13398i) q^{2} +(1.72591 - 0.145741i) q^{3} +(-0.571822 + 1.91651i) q^{4} +(-1.76879 - 1.41056i) q^{5} +(-1.62373 - 1.83399i) q^{6} +(-4.04660 - 0.923610i) q^{7} +(2.65650 - 0.971091i) q^{8} +(2.95752 - 0.503073i) q^{9} +(-0.104856 + 3.19775i) q^{10} +(-1.83496 - 3.81034i) q^{11} +(-0.707597 + 3.39106i) q^{12} +(-3.43689 + 1.65512i) q^{13} +(2.37217 + 5.36925i) q^{14} +(-3.25835 - 2.17672i) q^{15} +(-3.34604 - 2.19181i) q^{16} +1.04033 q^{17} +(-3.06969 - 2.92865i) q^{18} +(0.177666 + 0.778407i) q^{19} +(3.71479 - 2.58332i) q^{20} +(-7.11866 - 1.00431i) q^{21} +(-2.77023 + 5.30069i) q^{22} +(-3.60359 - 4.51876i) q^{23} +(4.44334 - 2.06318i) q^{24} +(0.0263246 + 0.115336i) q^{25} +(4.78118 + 2.49873i) q^{26} +(5.03109 - 1.29929i) q^{27} +(4.08404 - 7.22721i) q^{28} +(4.22559 - 3.33832i) q^{29} +(0.285073 + 5.53431i) q^{30} +(-1.40533 + 1.76223i) q^{31} +(0.342064 + 5.64650i) q^{32} +(-3.72230 - 6.30886i) q^{33} +(-0.879122 - 1.17972i) q^{34} +(5.85477 + 7.34165i) q^{35} +(-0.727029 + 5.95579i) q^{36} +(2.75551 - 5.72187i) q^{37} +(0.732563 - 0.859253i) q^{38} +(-5.69054 + 3.35748i) q^{39} +(-6.06857 - 2.02950i) q^{40} -6.16205 q^{41} +(4.87668 + 8.92110i) q^{42} +(5.16346 + 6.47477i) q^{43} +(8.35183 - 1.33789i) q^{44} +(-5.94084 - 3.28194i) q^{45} +(-2.07901 + 7.90493i) q^{46} +(3.12260 + 6.48414i) q^{47} +(-6.09439 - 3.29520i) q^{48} +(9.21512 + 4.43777i) q^{49} +(0.108543 - 0.127315i) q^{50} +(1.79552 - 0.151620i) q^{51} +(-1.20677 - 7.53328i) q^{52} +(-5.00979 - 3.99517i) q^{53} +(-5.72483 - 4.60720i) q^{54} +(-2.12906 + 9.32801i) q^{55} +(-11.6467 + 1.47605i) q^{56} +(0.420082 + 1.31757i) q^{57} +(-7.35637 - 1.97074i) q^{58} -7.80721 q^{59} +(6.03490 - 4.99997i) q^{60} +(5.36844 + 1.22531i) q^{61} +(3.18590 + 0.104467i) q^{62} +(-12.4325 - 0.695860i) q^{63} +(6.11396 - 5.15940i) q^{64} +(8.41379 + 1.92039i) q^{65} +(-4.00864 + 9.55224i) q^{66} +(3.34418 - 6.94426i) q^{67} +(-0.594886 + 1.99381i) q^{68} +(-6.87804 - 7.27378i) q^{69} +(3.37778 - 12.8432i) q^{70} +(7.49248 - 3.60819i) q^{71} +(7.36811 - 4.20843i) q^{72} +(3.17787 - 2.53427i) q^{73} +(-8.81699 + 1.71051i) q^{74} +(0.0622431 + 0.195222i) q^{75} +(-1.59342 - 0.104610i) q^{76} +(3.90609 + 17.1137i) q^{77} +(8.61605 + 3.61576i) q^{78} +(15.4626 + 7.44641i) q^{79} +(2.82676 + 8.59664i) q^{80} +(8.49384 - 2.97569i) q^{81} +(5.20717 + 6.98764i) q^{82} +(-0.454596 - 1.99171i) q^{83} +(5.99538 - 13.0687i) q^{84} +(-1.84013 - 1.46746i) q^{85} +(2.97894 - 11.3267i) q^{86} +(6.80646 - 6.37747i) q^{87} +(-8.57476 - 8.34024i) q^{88} +(5.31062 - 6.65930i) q^{89} +(1.29859 + 9.51016i) q^{90} +(15.4364 - 3.52326i) q^{91} +(10.7209 - 4.32240i) q^{92} +(-2.16865 + 3.24627i) q^{93} +(4.71417 - 9.02031i) q^{94} +(0.783737 - 1.62745i) q^{95} +(1.41330 + 9.69549i) q^{96} +(-13.8570 + 3.16276i) q^{97} +(-2.75478 - 14.1998i) q^{98} +(-7.34381 - 10.3460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more