LMFDB - Embedded newform 690.2.x.a.77.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.19
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(1.03732 - 1.38707i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.58434 + 1.57793i) q^{5} +(-1.73205 + 0.000829396i) q^{6} +(-0.607715 - 2.79362i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.847954 - 2.87767i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(1.03732 - 1.38707i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.58434 + 1.57793i) q^{5} +(-1.73205 + 0.000829396i) q^{6} +(-0.607715 - 2.79362i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.847954 - 2.87767i) q^{9} +(0.313734 - 2.21395i) q^{10} +(3.33383 - 0.479333i) q^{11} +(1.03864 + 1.38608i) q^{12} +(-0.0676390 + 0.310931i) q^{13} +(-1.87222 + 2.16066i) q^{14} +(3.83217 - 0.560795i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-3.04731 + 5.58073i) q^{17} +(-1.79553 + 2.40334i) q^{18} +(1.98866 - 6.77276i) q^{19} +(-1.96037 + 1.07561i) q^{20} +(-4.50535 - 2.05492i) q^{21} +(-2.38162 - 2.38162i) q^{22} +(3.22028 - 3.55384i) q^{23} +(0.487179 - 1.66212i) q^{24} +(0.0202902 + 4.99996i) q^{25} +(0.289448 - 0.132186i) q^{26} +(-4.87114 - 1.80887i) q^{27} +(2.85167 + 0.203956i) q^{28} +(3.49752 - 1.02696i) q^{29} +(-2.74547 - 2.73174i) q^{30} +(0.852554 - 1.86683i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(2.79337 - 5.12150i) q^{33} +(6.29379 - 0.904911i) q^{34} +(3.44530 - 5.38499i) q^{35} +(3.00000 - 0.00287311i) q^{36} +(-9.10836 + 0.651443i) q^{37} +(-6.61363 + 2.46676i) q^{38} +(0.361122 + 0.416354i) q^{39} +(2.03588 + 0.924767i) q^{40} +(8.79895 - 7.62433i) q^{41} +(1.05491 + 4.83819i) q^{42} +(1.60290 + 0.597850i) q^{43} +(-0.479333 + 3.33383i) q^{44} +(3.19730 - 5.89723i) q^{45} +(-4.77484 - 0.448234i) q^{46} +(-0.972081 + 0.972081i) q^{47} +(-1.62255 + 0.606067i) q^{48} +(-1.06758 + 0.487546i) q^{49} +(3.99051 - 3.01261i) q^{50} +(4.57987 + 10.0158i) q^{51} +(-0.279280 - 0.152499i) q^{52} +(1.65874 + 7.62509i) q^{53} +(1.47109 + 4.98356i) q^{54} +(6.03829 + 4.50112i) q^{55} +(-1.54567 - 2.40511i) q^{56} +(-7.33145 - 9.78390i) q^{57} +(-2.91811 - 2.18447i) q^{58} +(-8.44559 + 5.42765i) q^{59} +(-0.541567 + 3.83493i) q^{60} +(4.32476 - 9.46990i) q^{61} +(-2.00539 + 0.436247i) q^{62} +(-7.52380 + 4.11766i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-0.597791 + 0.385893i) q^{65} +(-5.77397 + 0.832994i) q^{66} +(-4.29708 + 3.21675i) q^{67} +(-4.49615 - 4.49615i) q^{68} +(-1.58899 - 8.15323i) q^{69} +(-6.37560 + 0.468996i) q^{70} +(-10.2965 - 1.48042i) q^{71} +(-1.80013 - 2.39990i) q^{72} +(-11.4377 + 6.24546i) q^{73} +(5.97994 + 6.90122i) q^{74} +(6.95637 + 5.15839i) q^{75} +(5.93814 + 3.81621i) q^{76} +(-3.36509 - 9.02217i) q^{77} +(0.116896 - 0.538605i) q^{78} +(-2.99854 - 4.66582i) q^{79} +(-0.479743 - 2.18400i) q^{80} +(-7.56195 + 4.88026i) q^{81} +(-11.3766 - 2.47483i) q^{82} +(11.3910 - 0.814697i) q^{83} +(3.24099 - 3.74392i) q^{84} +(-13.6340 + 4.03337i) q^{85} +(-0.481977 - 1.64146i) q^{86} +(2.20355 - 5.91661i) q^{87} +(2.95612 - 1.61417i) q^{88} +(2.61445 + 5.72485i) q^{89} +(-6.63704 + 0.974504i) q^{90} +0.909730 q^{91} +(2.50262 + 4.09107i) q^{92} +(-1.70507 - 3.11905i) q^{93} +(1.36074 + 0.195644i) q^{94} +(13.8376 - 7.59241i) q^{95} +(1.45754 + 0.935720i) q^{96} +(-0.565057 + 7.90053i) q^{97} +(1.03007 + 0.562463i) q^{98} +(-4.20630 - 9.18721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	1.03732	−	1.38707i	0.598894	−	0.800828i
$3$	1.03732	−	1.38707i	0.598894	−	0.800828i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	1.58434	+	1.57793i	0.708540	+	0.705671i
$5$	1.58434	+	1.57793i	0.708540	+	0.705671i
$6$	−1.73205		0.000829396i	−0.707107		0.000338599i
$7$	−0.607715	−	2.79362i	−0.229695	−	1.05589i	−0.937094	−	0.349076i	$-0.886496\pi$
$7$	−0.607715	−	2.79362i	−0.229695	−	1.05589i	0.707400	−	0.706814i	$-0.249868\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	−0.847954	−	2.87767i	−0.282651	−	0.959223i
$10$	0.313734	−	2.21395i	0.0992114	−	0.700112i
$11$	3.33383	−	0.479333i	1.00519	−	0.144524i	0.379990	−	0.924990i	$-0.375927\pi$
$11$	3.33383	−	0.479333i	1.00519	−	0.144524i	0.625198	+	0.780466i	$0.285018\pi$
$12$	1.03864	+	1.38608i	0.299830	+	0.400127i
$13$	−0.0676390	+	0.310931i	−0.0187597	+	0.0862369i	−0.985575	−	0.169240i	$-0.945869\pi$
$13$	−0.0676390	+	0.310931i	−0.0187597	+	0.0862369i	0.966815	+	0.255477i	$0.0822324\pi$
$14$	−1.87222	+	2.16066i	−0.500371	+	0.577459i
$15$	3.83217	−	0.560795i	0.989461	−	0.144797i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	−3.04731	+	5.58073i	−0.739082	+	1.35353i	0.189308	+	0.981918i	$0.439376\pi$
$17$	−3.04731	+	5.58073i	−0.739082	+	1.35353i	−0.928389	+	0.371609i	$0.878806\pi$
$18$	−1.79553	+	2.40334i	−0.423211	+	0.566474i
$19$	1.98866	−	6.77276i	0.456230	−	1.55378i	−0.334976	−	0.942227i	$-0.608728\pi$
$19$	1.98866	−	6.77276i	0.456230	−	1.55378i	0.791206	−	0.611550i	$-0.209454\pi$
$20$	−1.96037	+	1.07561i	−0.438352	+	0.240514i
$21$	−4.50535	−	2.05492i	−0.983149	−	0.448420i
$22$	−2.38162	−	2.38162i	−0.507763	−	0.507763i
$23$	3.22028	−	3.55384i	0.671476	−	0.741027i
$23$	3.22028	−	3.55384i	0.671476	−	0.741027i
$24$	0.487179	−	1.66212i	0.0994450	−	0.339280i
$25$	0.0202902	+	4.99996i	0.00405803	+	0.999992i
$26$	0.289448	−	0.132186i	0.0567654	−	0.0259239i
$27$	−4.87114	−	1.80887i	−0.937451	−	0.348118i
$28$	2.85167	+	0.203956i	0.538915	+	0.0385440i
$29$	3.49752	−	1.02696i	0.649473	−	0.190703i	0.0596302	−	0.998221i	$-0.481008\pi$
$29$	3.49752	−	1.02696i	0.649473	−	0.190703i	0.589843	+	0.807518i	$0.299190\pi$
$30$	−2.74547	−	2.73174i	−0.501252	−	0.498744i
$31$	0.852554	−	1.86683i	0.153123	−	0.335293i	−0.817488	−	0.575945i	$-0.804634\pi$
$31$	0.852554	−	1.86683i	0.153123	−	0.335293i	0.970611	+	0.240652i	$0.0773614\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	2.79337	−	5.12150i	0.486263	−	0.891538i
$34$	6.29379	−	0.904911i	1.07938	−	0.155191i
$35$	3.44530	−	5.38499i	0.582362	−	0.910229i
$36$	3.00000	−	0.00287311i	0.500000	−	0.000478852i
$37$	−9.10836	+	0.651443i	−1.49741	+	0.107097i	−0.795839	−	0.605508i	$-0.792970\pi$
$37$	−9.10836	+	0.651443i	−1.49741	+	0.107097i	−0.701566	+	0.712604i	$0.747516\pi$
$38$	−6.61363	+	2.46676i	−1.07287	+	0.400161i
$39$	0.361122	+	0.416354i	0.0578258	+	0.0666701i
$40$	2.03588	+	0.924767i	0.321901	+	0.146219i
$41$	8.79895	−	7.62433i	1.37416	−	1.19072i	0.414339	−	0.910123i	$-0.364013\pi$
$41$	8.79895	−	7.62433i	1.37416	−	1.19072i	0.959825	−	0.280598i	$-0.0905327\pi$
$42$	1.05491	+	4.83819i	0.162776	+	0.746549i
$43$	1.60290	+	0.597850i	0.244440	+	0.0911713i	0.468698	−	0.883358i	$-0.344723\pi$
$43$	1.60290	+	0.597850i	0.244440	+	0.0911713i	−0.224258	+	0.974530i	$0.571996\pi$
$44$	−0.479333	+	3.33383i	−0.0722621	+	0.502594i
$45$	3.19730	−	5.89723i	0.476625	−	0.879106i
$46$	−4.77484	−	0.448234i	−0.704012	−	0.0660885i
$47$	−0.972081	+	0.972081i	−0.141793	+	0.141793i	−0.774440	−	0.632647i	$-0.781968\pi$
$47$	−0.972081	+	0.972081i	−0.141793	+	0.141793i	0.632647	+	0.774440i	$0.281968\pi$
$48$	−1.62255	+	0.606067i	−0.234196	+	0.0874782i
$49$	−1.06758	+	0.487546i	−0.152511	+	0.0696494i
$50$	3.99051	−	3.01261i	0.564344	−	0.426047i
$51$	4.57987	+	10.0158i	0.641311	+	1.40250i
$52$	−0.279280	−	0.152499i	−0.0387292	−	0.0211478i
$53$	1.65874	+	7.62509i	0.227845	+	1.04739i	0.938884	+	0.344234i	$0.111861\pi$
$53$	1.65874	+	7.62509i	0.227845	+	1.04739i	−0.711039	+	0.703153i	$0.751775\pi$
$54$	1.47109	+	4.98356i	0.200189	+	0.678177i
$55$	6.03829	+	4.50112i	0.814203	+	0.606931i
$56$	−1.54567	−	2.40511i	−0.206549	−	0.321396i
$57$	−7.33145	−	9.78390i	−0.971075	−	1.29591i
$58$	−2.91811	−	2.18447i	−0.383167	−	0.286835i
$59$	−8.44559	+	5.42765i	−1.09952	+	0.706620i	−0.958985	−	0.283455i	$-0.908519\pi$
$59$	−8.44559	+	5.42765i	−1.09952	+	0.706620i	−0.140537	+	0.990075i	$0.544883\pi$
$60$	−0.541567	+	3.83493i	−0.0699160	+	0.495088i
$61$	4.32476	−	9.46990i	0.553728	−	1.21250i	−0.401291	−	0.915951i	$-0.631438\pi$
$61$	4.32476	−	9.46990i	0.553728	−	1.21250i	0.955019	−	0.296545i	$-0.0958345\pi$
$62$	−2.00539	+	0.436247i	−0.254685	+	0.0554034i
$63$	−7.52380	+	4.11766i	−0.947910	+	0.518777i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	−0.597791	+	0.385893i	−0.0741468	+	0.0478641i
$66$	−5.77397	+	0.832994i	−0.710727	+	0.102534i
$67$	−4.29708	+	3.21675i	−0.524972	+	0.392989i	−0.828634	−	0.559791i	$-0.810881\pi$
$67$	−4.29708	+	3.21675i	−0.524972	+	0.392989i	0.303662	+	0.952780i	$0.401791\pi$
$68$	−4.49615	−	4.49615i	−0.545238	−	0.545238i
$69$	−1.58899	−	8.15323i	−0.191292	−	0.981533i
$70$	−6.37560	+	0.468996i	−0.762029	+	0.0560557i
$71$	−10.2965	−	1.48042i	−1.22197	−	0.175693i	−0.499020	−	0.866590i	$-0.666307\pi$
$71$	−10.2965	−	1.48042i	−1.22197	−	0.175693i	−0.722953	+	0.690897i	$0.757216\pi$
$72$	−1.80013	−	2.39990i	−0.212148	−	0.282831i
$73$	−11.4377	+	6.24546i	−1.33868	+	0.730975i	−0.979338	−	0.202230i	$-0.935181\pi$
$73$	−11.4377	+	6.24546i	−1.33868	+	0.730975i	−0.359343	+	0.933205i	$0.616999\pi$
$74$	5.97994	+	6.90122i	0.695154	+	0.802251i
$75$	6.95637	+	5.15839i	0.803252	+	0.595640i
$76$	5.93814	+	3.81621i	0.681151	+	0.437749i
$77$	−3.36509	−	9.02217i	−0.383488	−	1.02817i
$78$	0.116896	−	0.538605i	0.0132359	−	0.0609850i
$79$	−2.99854	−	4.66582i	−0.337362	−	0.524946i	0.630578	−	0.776126i	$-0.282818\pi$
$79$	−2.99854	−	4.66582i	−0.337362	−	0.524946i	−0.967940	+	0.251180i	$0.919181\pi$
$80$	−0.479743	−	2.18400i	−0.0536369	−	0.244178i
$81$	−7.56195	+	4.88026i	−0.840216	+	0.542251i
$82$	−11.3766	−	2.47483i	−1.25634	−	0.273299i
$83$	11.3910	−	0.814697i	1.25032	−	0.0894246i	0.569571	−	0.821942i	$-0.307109\pi$
$83$	11.3910	−	0.814697i	1.25032	−	0.0894246i	0.680748	+	0.732517i	$0.261655\pi$
$84$	3.24099	−	3.74392i	0.353620	−	0.408495i
$85$	−13.6340	+	4.03337i	−1.47881	+	0.437480i
$86$	−0.481977	−	1.64146i	−0.0519729	−	0.177004i
$87$	2.20355	−	5.91661i	0.236246	−	0.634327i
$88$	2.95612	−	1.61417i	0.315124	−	0.172071i
$89$	2.61445	+	5.72485i	0.277131	+	0.606833i	0.996102	−	0.0882072i	$-0.0281138\pi$
$89$	2.61445	+	5.72485i	0.277131	+	0.606833i	−0.718971	+	0.695040i	$0.755386\pi$
$90$	−6.63704	+	0.974504i	−0.699606	+	0.102722i
$91$	0.909730			0.0953656
$92$	2.50262	+	4.09107i	0.260917	+	0.426524i
$93$	−1.70507	−	3.11905i	−0.176808	−	0.323430i
$94$	1.36074	+	0.195644i	0.140349	+	0.0201792i
$95$	13.8376	−	7.59241i	1.41971	−	0.778965i
$96$	1.45754	+	0.935720i	0.148760	+	0.0955015i
$97$	−0.565057	+	7.90053i	−0.0573729	+	0.802178i	0.884571	+	0.466406i	$0.154451\pi$
$97$	−0.565057	+	7.90053i	−0.0573729	+	0.802178i	−0.941944	+	0.335771i	$0.891003\pi$
$98$	1.03007	+	0.562463i	0.104053	+	0.0568174i
$99$	−4.20630	−	9.18721i	−0.422749	−	0.923350i
$100$	−4.80314	−	1.38918i	−0.480314	−	0.138918i
$101$	2.25874	+	1.95721i	0.224753	+	0.194749i	0.759957	−	0.649973i	$-0.225220\pi$
$101$	2.25874	+	1.95721i	0.224753	+	0.194749i	−0.535204	+	0.844723i	$0.679765\pi$
$102$	5.27347	−	9.66864i	0.522151	−	0.957338i
$103$	9.60719	+	7.19185i	0.946624	+	0.708634i	0.956627	−	0.291316i	$-0.0940931\pi$
$103$	9.60719	+	7.19185i	0.946624	+	0.708634i	−0.0100026	+	0.999950i	$0.503184\pi$
$104$	0.0452851	+	0.314965i	0.00444057	+	0.0308848i
$105$	−3.89552	−	10.3648i	−0.380163	−	1.01150i
$106$	5.11015	−	5.89743i	0.496342	−	0.572809i
$107$	3.46965	+	9.30250i	0.335424	+	0.899306i	0.989714	+	0.143062i	$0.0456950\pi$
$107$	3.46965	+	9.30250i	0.335424	+	0.899306i	−0.654290	+	0.756244i	$0.727032\pi$
$108$	3.10796	−	4.16420i	0.299064	−	0.400701i
$109$	2.52846	+	8.61114i	0.242182	+	0.824798i	0.987436	+	0.158017i	$0.0505100\pi$
$109$	2.52846	+	8.61114i	0.242182	+	0.824798i	−0.745254	+	0.666781i	$0.767672\pi$
$110$	−0.0152812	−	7.53132i	−0.00145701	−	0.718083i
$111$	−8.54464	+	13.3097i	−0.811022	+	1.26330i
$112$	−0.999103	+	2.67870i	−0.0944064	+	0.253113i
$113$	9.82285	−	7.35330i	0.924056	−	0.691740i	−0.0273670	−	0.999625i	$-0.508712\pi$
$113$	9.82285	−	7.35330i	0.924056	−	0.691740i	0.951423	+	0.307885i	$0.0996214\pi$
$114$	−3.43884	+	11.7324i	−0.322077	+	1.09884i
$115$	10.7097	−	0.549128i	0.998688	−	0.0512065i
$116$			3.64517i			0.338446i
$117$	0.952112	−	0.0690130i	0.0880228	−	0.00638025i
$118$	9.40632	+	3.50837i	0.865922	+	0.322972i
$119$	17.4424	+	5.12154i	1.59894	+	0.469491i
$120$	3.39457	−	1.86464i	0.309880	−	0.170218i
$121$	0.330261	−	0.0969733i	0.0300237	−	0.00881575i
$122$	−10.1728	+	2.21295i	−0.920999	+	0.200351i
$123$	−1.44824	−	20.1136i	−0.130583	−	1.81359i
$124$	1.55102	+	1.34397i	0.139286	+	0.120692i
$125$	−7.85743	+	7.95367i	−0.702790	+	0.711398i
$126$	7.80520	+	3.55549i	0.695343	+	0.316748i
$127$	1.05262	−	1.40614i	0.0934051	−	0.124775i	−0.751404	−	0.659842i	$-0.770623\pi$
$127$	1.05262	−	1.40614i	0.0934051	−	0.124775i	0.844809	+	0.535068i	$0.179714\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	2.49197	−	1.60318i	0.219406	−	0.141152i
$130$	0.667166	+	0.247299i	0.0585143	+	0.0216896i
$131$	−8.61038	+	13.3980i	−0.752292	+	1.17059i	0.228120	+	0.973633i	$0.426742\pi$
$131$	−8.61038	+	13.3980i	−0.752292	+	1.17059i	−0.980412	+	0.196956i	$0.936894\pi$
$132$	4.12706	+	4.12311i	0.359214	+	0.358870i
$133$	−20.1290	−	1.43966i	−1.74541	−	0.124834i
$134$	5.15029	+	1.51226i	0.444917	+	0.130639i
$135$	−4.86328	−	10.5522i	−0.418565	−	0.908187i
$136$	−0.904911	+	6.29379i	−0.0775955	+	0.539688i
$137$	11.9291	−	11.9291i	1.01918	−	1.01918i	0.0193635	−	0.999813i	$-0.493836\pi$
$137$	11.9291	−	11.9291i	1.01918	−	1.01918i	0.999813	−	0.0193635i	$-0.00616397\pi$
$138$	−5.57475	+	6.15810i	−0.474554	+	0.524212i
$139$			15.3405i			1.30116i	0.759437	+	0.650581i	$0.225475\pi$
$139$			15.3405i			1.30116i	−0.759437	+	0.650581i	$0.774525\pi$
$140$	4.19620	+	4.82287i	0.354644	+	0.407607i
$141$	0.339995	+	2.35670i	0.0286327	+	0.198470i
$142$	4.98535	+	9.12998i	0.418361	+	0.766171i
$143$	−0.0764575	+	1.06902i	−0.00639370	+	0.0893955i
$144$	−0.842441	+	2.87929i	−0.0702034	+	0.239941i
$145$	7.16175	+	3.89177i	0.594751	+	0.323194i
$146$	11.8541	+	5.41359i	0.981053	+	0.448032i
$147$	−0.431150	+	1.98655i	−0.0355607	+	0.163848i
$148$	1.94107	−	8.92294i	0.159555	−	0.733461i
$149$	1.25312	+	8.71564i	0.102660	+	0.714013i	0.974527	+	0.224271i	$0.0720001\pi$
$149$	1.25312	+	8.71564i	0.102660	+	0.714013i	−0.871867	+	0.489742i	$0.837091\pi$
$150$	−0.0392905	−	8.66016i	−0.00320806	−	0.707100i
$151$	13.6439	−	8.76842i	1.11033	−	0.713564i	0.148962	−	0.988843i	$-0.452407\pi$
$151$	13.6439	−	8.76842i	1.11033	−	0.713564i	0.961364	+	0.275279i	$0.0887703\pi$
$152$	−0.503561	−	7.04070i	−0.0408442	−	0.571076i
$153$	18.6435	+	4.03695i	1.50724	+	0.326368i
$154$	−5.20599	+	8.10068i	−0.419511	+	0.652771i
$155$	4.29647	−	1.61244i	0.345100	−	0.129514i
$156$	−0.501229	+	0.229194i	−0.0401304	+	0.0183502i
$157$	−3.40609	−	6.23779i	−0.271836	−	0.497830i	0.705725	−	0.708486i	$-0.250622\pi$
$157$	−3.40609	−	6.23779i	−0.271836	−	0.497830i	−0.977560	+	0.210657i	$0.932440\pi$
$158$	−1.93822	+	5.19657i	−0.154197	+	0.413417i
$159$	12.2972	+	5.60883i	0.975232	+	0.444809i
$160$	−1.46088	+	1.69288i	−0.115493	+	0.133834i
$161$	−11.8851	−	6.83653i	−0.936677	−	0.538794i
$162$	8.43856	+	3.12902i	0.662996	+	0.245839i
$163$	−6.82133	−	9.11223i	−0.534288	−	0.713725i	0.449456	−	0.893303i	$-0.351618\pi$
$163$	−6.82133	−	9.11223i	−0.534288	−	0.713725i	−0.983744	+	0.179577i	$0.942527\pi$
$164$	4.83654	+	10.5905i	0.377670	+	0.826983i
$165$	12.5070	−	3.70648i	0.973669	−	0.288549i
$166$	−7.47854	−	8.63070i	−0.580448	−	0.669872i
$167$	−2.96817	+	5.43579i	−0.229684	+	0.420634i	−0.966949	−	0.254969i	$-0.917935\pi$
$167$	−2.96817	+	5.43579i	−0.229684	+	0.420634i	0.737266	+	0.675603i	$0.236117\pi$
$168$	−4.93941	−	0.350896i	−0.381084	−	0.0270722i
$169$	11.7331	+	5.35833i	0.902547	+	0.412179i
$170$	11.3994	+	8.49746i	0.874295	+	0.651725i
$171$	−21.1760	+	0.0202804i	−1.61937	+	0.00155088i
$172$	−1.02522	+	1.36954i	−0.0781724	+	0.104426i
$173$	−6.30426	+	8.42151i	−0.479304	+	0.640275i	−0.973395	−	0.229135i	$-0.926410\pi$
$173$	−6.30426	+	8.42151i	−0.479304	+	0.640275i	0.494090	+	0.869411i	$0.335501\pi$
$174$	−6.05703	+	1.78166i	−0.459182	+	0.135067i
$175$	13.9557	−	3.09523i	1.05495	−	0.233978i
$176$	−3.06375	−	1.39917i	−0.230939	−	0.105466i
$177$	−1.23218	+	17.3449i	−0.0926164	+	1.30372i
$178$	3.01620	−	5.52375i	0.226074	−	0.414023i
$179$	7.52027	+	8.67885i	0.562091	+	0.648688i	0.963657	−	0.267142i	$-0.0860794\pi$
$179$	7.52027	+	8.67885i	0.562091	+	0.648688i	−0.401566	+	0.915830i	$0.631534\pi$
$180$	4.75756	+	4.72923i	0.354608	+	0.352496i
$181$	3.19588	+	6.99801i	0.237548	+	0.520158i	0.990433	−	0.137994i	$-0.0440656\pi$
$181$	3.19588	+	6.99801i	0.237548	+	0.520158i	−0.752885	+	0.658152i	$0.771338\pi$
$182$	−0.545181	−	0.728276i	−0.0404115	−	0.0539834i
$183$	−8.64932	−	15.8220i	−0.639376	−	1.16960i
$184$	1.77530	−	4.45514i	0.130877	−	0.328437i
$185$	−15.4587	−	13.3402i	−1.13655	−	0.980793i
$186$	−1.47512	+	3.23416i	−0.108161	+	0.237140i
$187$	−7.48420	+	20.0659i	−0.547299	+	1.46737i
$188$	−0.658838	−	1.20657i	−0.0480507	−	0.0879982i
$189$	−2.09304	+	14.7074i	−0.152246	+	1.06981i
$190$	−14.3706	−	6.52764i	−1.04255	−	0.473565i
$191$	−0.160444	+	0.249656i	−0.0116093	+	0.0180645i	−0.847010	−	0.531577i	$-0.821599\pi$
$191$	−0.160444	+	0.249656i	−0.0116093	+	0.0180645i	0.835400	+	0.549642i	$0.185236\pi$
$192$	−0.124390	−	1.72758i	−0.00897710	−	0.124677i
$193$	0.338118	+	4.72750i	0.0243382	+	0.340293i	0.995002	+	0.0998530i	$0.0318372\pi$
$193$	0.338118	+	4.72750i	0.0243382	+	0.340293i	−0.970664	+	0.240440i	$0.922708\pi$
$194$	6.66333	−	4.28226i	0.478399	−	0.307448i
$195$	−0.0848351	+	1.22947i	−0.00607517	+	0.0880444i
$196$	−0.167026	−	1.16169i	−0.0119304	−	0.0829778i
$197$	−3.08475	+	14.1804i	−0.219780	+	1.01031i	0.726552	+	0.687112i	$0.241122\pi$
$197$	−3.08475	+	14.1804i	−0.219780	+	1.01031i	−0.946331	+	0.323199i	$0.895242\pi$
$198$	−4.83400	+	8.87301i	−0.343538	+	0.630577i
$199$	−9.14267	−	4.17532i	−0.648106	−	0.295980i	0.0641072	−	0.997943i	$-0.479580\pi$
$199$	−9.14267	−	4.17532i	−0.648106	−	0.295980i	−0.712214	+	0.701963i	$0.752307\pi$
$200$	1.76632	+	4.67762i	0.124897	+	0.330758i
$201$	0.00445196	+	9.29716i	0.000314017	+	0.655771i
$202$	0.213214	−	2.98112i	0.0150017	−	0.209751i
$203$	−4.99444	−	9.14664i	−0.350541	−	0.641968i
$204$	−10.9004	+	1.57257i	−0.763182	+	0.110102i
$205$	25.9712	+	1.80454i	1.81391	+	0.126034i
$206$		−	12.0009i		−	0.836140i
$207$	−12.9574	−	6.25342i	−0.900603	−	0.434642i
$208$	0.225004	−	0.225004i	0.0156012	−	0.0156012i
$209$	3.38346	−	23.5325i	0.234039	−	1.62777i
$210$	−5.96297	+	9.32993i	−0.411484	+	0.643826i
$211$	12.5508	+	3.68524i	0.864031	+	0.253702i	0.683575	−	0.729881i	$-0.260424\pi$
$211$	12.5508	+	3.68524i	0.864031	+	0.253702i	0.180456	+	0.983583i	$0.442243\pi$
$212$	−7.78354	−	0.556690i	−0.534576	−	0.0382336i
$213$	−12.7342	+	12.7464i	−0.872533	+	0.873369i
$214$	5.36775	−	8.35238i	0.366932	−	0.570957i
$215$	1.59618	+	3.47646i	0.108858	+	0.237092i
$216$	−5.19615	+	0.00746456i	−0.353553	+	0.000507899i
$217$	−5.73333	−	1.24721i	−0.389204	−	0.0846661i
$218$	5.37832	−	7.18460i	0.364266	−	0.486602i
$219$	−3.20158	+	22.3435i	−0.216343	+	1.50983i
$220$	−6.01997	+	4.52559i	−0.405867	+	0.305115i
$221$	−1.52911	−	1.32498i	−0.102859	−	0.0891278i
$222$	15.7756	−	1.13589i	1.05879	−	0.0762357i
$223$	5.28253	−	1.14914i	0.353745	−	0.0769524i	−0.0321817	−	0.999482i	$-0.510246\pi$
$223$	5.28253	−	1.14914i	0.353745	−	0.0769524i	0.385926	+	0.922530i	$0.373882\pi$
$224$	2.74315	−	0.805461i	0.183284	−	0.0538171i
$225$	14.3710	−	4.29812i	0.958068	−	0.286542i
$226$	−11.7732	−	3.45693i	−0.783144	−	0.229952i
$227$	12.1930	+	4.54776i	0.809279	+	0.301846i	0.719834	−	0.694146i	$-0.244218\pi$
$227$	12.1930	+	4.54776i	0.809279	+	0.301846i	0.0894452	+	0.995992i	$0.471491\pi$
$228$	11.4531	−	4.27803i	0.758500	−	0.283320i
$229$		−	15.8876i		−	1.04989i	−0.851138	−	0.524943i	$-0.824087\pi$
$229$		−	15.8876i		−	1.04989i	0.851138	−	0.524943i	$-0.175913\pi$
$230$	−6.85771	−	8.24451i	−0.452184	−	0.543627i
$231$	−16.0051	−	4.69119i	−1.05306	−	0.308658i
$232$	2.91811	−	2.18447i	0.191583	−	0.143418i
$233$	1.22809	−	3.29264i	0.0804548	−	0.215708i	−0.890494	−	0.454995i	$-0.849641\pi$
$233$	1.22809	−	3.29264i	0.0804548	−	0.215708i	0.970949	+	0.239287i	$0.0769138\pi$
$234$	−0.625827	−	0.720847i	−0.0409116	−	0.0471233i
$235$	−3.07398	+	0.00623718i	−0.200524	+	0.000406869i
$236$	−2.82840	−	9.63263i	−0.184113	−	0.627031i
$237$	−9.58227	−	0.680726i	−0.622435	−	0.0442179i
$238$	−6.35281	−	17.0325i	−0.411792	−	1.10406i
$239$	−16.2920	+	18.8019i	−1.05384	+	1.21620i	−0.0781717	+	0.996940i	$0.524908\pi$
$239$	−16.2920	+	18.8019i	−1.05384	+	1.21620i	−0.975668	+	0.219255i	$0.929637\pi$
$240$	−3.52701	−	1.60006i	−0.227668	−	0.103283i
$241$	2.94544	+	20.4860i	0.189733	+	1.31962i	0.832699	+	0.553725i	$0.186794\pi$
$241$	2.94544	+	20.4860i	0.189733	+	1.31962i	−0.642967	+	0.765894i	$0.722297\pi$
$242$	−0.275549	−	0.206273i	−0.0177130	−	0.0132598i
$243$	−1.07484	+	15.5514i	−0.0689508	+	0.997620i
$244$	7.86787	+	6.81755i	0.503689	+	0.436449i
$245$	−2.46072	−	0.912117i	−0.157210	−	0.0582730i
$246$	−15.2339	+	13.2130i	−0.971278	+	0.842432i
$247$	1.97135	+	1.07644i	0.125434	+	0.0684922i
$248$	0.146409	−	2.04707i	0.00929698	−	0.129989i
$249$	10.6860	−	16.6452i	0.677196	−	1.05485i
$250$	11.0760	+	1.52374i	0.700509	+	0.0963696i
$251$	−2.00766	−	0.288658i	−0.126722	−	0.0182199i	0.0786618	−	0.996901i	$-0.474935\pi$
$251$	−2.00766	−	0.288658i	−0.126722	−	0.0182199i	−0.205384	+	0.978681i	$0.565844\pi$
$252$	−1.83117	−	8.37911i	−0.115353	−	0.527834i
$253$	9.03242	−	13.3915i	0.567863	−	0.841916i
$254$	−1.75648			−0.110212
$255$	−8.54816	+	23.0952i	−0.535306	+	1.44628i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	18.6557	−	10.1868i	1.16371	−	0.635436i	0.223060	−	0.974805i	$-0.428395\pi$
$257$	18.6557	−	10.1868i	1.16371	−	0.635436i	0.940653	+	0.339369i	$0.110214\pi$
$258$	−2.77680	−	1.03418i	−0.172876	−	0.0643850i
$259$	7.35517	+	25.0494i	0.457028	+	1.55650i
$260$	−0.201844	−	0.682295i	−0.0125179	−	0.0423141i
$261$	−5.92100	−	9.19388i	−0.366501	−	0.569087i
$262$	15.8857	−	1.13617i	0.981420	−	0.0701925i
$263$	−20.7996	−	4.52468i	−1.28256	−	0.279004i	−0.480896	−	0.876778i	$-0.659688\pi$
$263$	−20.7996	−	4.52468i	−1.28256	−	0.279004i	−0.801665	+	0.597774i	$0.796052\pi$
$264$	0.827464	−	5.77477i	0.0509269	−	0.355412i
$265$	−9.40383	+	14.6981i	−0.577673	+	0.902899i
$266$	10.9104	+	16.9769i	0.668959	+	1.04092i
$267$	10.6528	+	2.31204i	0.651942	+	0.141494i
$268$	−1.87583	−	5.02928i	−0.114584	−	0.307212i
$269$	−10.9090	−	7.01081i	−0.665135	−	0.427457i	0.164033	−	0.986455i	$-0.447550\pi$
$269$	−10.9090	−	7.01081i	−0.665135	−	0.427457i	−0.829169	+	0.558998i	$0.811186\pi$
$270$	−5.53300	+	10.2169i	−0.336727	+	0.621783i
$271$	−4.61355	−	5.32432i	−0.280253	−	0.323430i	0.598118	−	0.801408i	$-0.295915\pi$
$271$	−4.61355	−	5.32432i	−0.280253	−	0.323430i	−0.878372	+	0.477978i	$0.841370\pi$
$272$	5.58073	−	3.04731i	0.338382	−	0.184770i
$273$	0.943677	−	1.26186i	0.0571139	−	0.0763715i
$274$	−16.6986	−	2.40090i	−1.00880	−	0.145044i
$275$	2.46429	+	16.6593i	0.148602	+	1.00459i
$276$	8.27063	+	0.772403i	0.497834	+	0.0464932i
$277$	5.70677	+	5.70677i	0.342886	+	0.342886i	0.857451	−	0.514565i	$-0.172047\pi$
$277$	5.70677	+	5.70677i	0.342886	+	0.342886i	−0.514565	+	0.857451i	$0.672047\pi$
$278$	12.2807	−	9.19321i	0.736547	−	0.551372i
$279$	−6.09505	−	0.870379i	−0.364901	−	0.0521082i
$280$	1.34621	−	6.24947i	0.0804517	−	0.373477i
$281$	−9.79632	+	8.48856i	−0.584400	+	0.506385i	−0.896134	−	0.443784i	$-0.853636\pi$
$281$	−9.79632	+	8.48856i	−0.584400	+	0.506385i	0.311734	+	0.950169i	$0.399090\pi$
$282$	1.68289	−	1.68450i	0.100214	−	0.100310i
$283$	12.9823	−	2.82413i	0.771718	−	0.167877i	0.190569	−	0.981674i	$-0.438967\pi$
$283$	12.9823	−	2.82413i	0.771718	−	0.167877i	0.581150	+	0.813797i	$0.302603\pi$
$284$	4.32132	−	9.46237i	0.256423	−	0.561488i
$285$	3.82275	−	27.0696i	0.226440	−	1.60346i
$286$	0.901610	−	0.579430i	0.0533133	−	0.0342624i
$287$	−26.6467	−	19.9475i	−1.57291	−	1.17746i
$288$	2.80984	−	1.05108i	0.165572	−	0.0619357i
$289$	−12.6676	−	19.7112i	−0.745153	−	1.15948i
$290$	−1.17636	−	8.06552i	−0.0690780	−	0.473624i
$291$	10.3725	+	8.97912i	0.608046	+	0.526365i
$292$	−2.77010	−	12.7339i	−0.162108	−	0.745198i
$293$	−21.3810	−	11.6749i	−1.24909	−	0.682055i	−0.287826	−	0.957683i	$-0.592933\pi$
$293$	−21.3810	−	11.6749i	−1.24909	−	0.682055i	−0.961265	+	0.275628i	$0.911114\pi$
$294$	1.84869	−	0.845339i	0.107818	−	0.0493012i
$295$	−21.9452	−	4.72726i	−1.27770	−	0.275232i
$296$	−8.30642	+	3.79342i	−0.482801	+	0.220488i
$297$	−17.1066	−	3.69559i	−0.992626	−	0.214440i
$298$	6.22627	−	6.22627i	0.360678	−	0.360678i
$299$	0.887184	+	1.24167i	0.0513072	+	0.0718074i
$300$	−6.90927	+	5.22130i	−0.398907	+	0.301452i
$301$	0.696061	−	4.84121i	0.0401203	−	0.279043i
$302$	−15.1960	−	5.66781i	−0.874430	−	0.326146i
$303$	5.05781	−	1.10280i	0.290564	−	0.0633540i
$304$	−5.33460	+	4.62245i	−0.305960	+	0.265116i
$305$	21.7947	−	8.17942i	1.24796	−	0.468352i
$306$	−7.94088	−	17.3441i	−0.453950	−	0.991498i
$307$	2.10272	−	0.784274i	0.120009	−	0.0447609i	−0.288742	−	0.957407i	$-0.593237\pi$
$307$	2.10272	−	0.784274i	0.120009	−	0.0447609i	0.408751	+	0.912646i	$0.365964\pi$
$308$	9.60476	−	0.686946i	0.547282	−	0.0391424i
$309$	19.9413	−	5.86567i	1.13442	−	0.333686i
$310$	−3.86560	−	2.47320i	−0.219551	−	0.140468i
$311$	24.0246	−	3.45422i	1.36231	−	0.195871i	0.577898	−	0.816109i	$-0.303873\pi$
$311$	24.0246	−	3.45422i	1.36231	−	0.195871i	0.784414	+	0.620238i	$0.212964\pi$
$312$	0.483854	+	0.263904i	0.0273929	+	0.0149406i
$313$	1.73306	+	24.2314i	0.0979584	+	1.36964i	0.774192	+	0.632950i	$0.218156\pi$
$313$	1.73306	+	24.2314i	0.0979584	+	1.36964i	−0.676234	+	0.736687i	$0.736389\pi$
$314$	−2.95241	+	6.46488i	−0.166614	+	0.364834i
$315$	−18.4177	−	5.34821i	−1.03772	−	0.301338i
$316$	5.32161	−	1.56256i	0.299364	−	0.0879011i
$317$	−20.1121	−	1.43845i	−1.12961	−	0.0807913i	−0.506005	−	0.862531i	$-0.668878\pi$
$317$	−20.1121	−	1.43845i	−1.12961	−	0.0807913i	−0.623605	+	0.781739i	$0.714333\pi$
$318$	−2.87934	−	13.2057i	−0.161465	−	0.740537i
$319$	11.1679	−	5.10020i	0.625282	−	0.285557i
$320$	2.23069	+	0.154993i	0.124699	+	0.00866440i
$321$	16.5024	+	4.83696i	0.921073	+	0.269973i
$322$	1.64955	+	13.6115i	0.0919256	+	0.758539i
$323$	31.7369	+	31.7369i	1.76589	+	1.76589i
$324$	−2.55213	−	8.63056i	−0.141785	−	0.479476i
$325$	−1.55602	−	0.331883i	−0.0863123	−	0.0184096i
$326$	−3.20685	+	10.9215i	−0.177611	+	0.604887i
$327$	14.5671	+	5.42530i	0.805563	+	0.300020i
$328$	5.57974	−	10.2185i	0.308090	−	0.564224i
$329$	3.30637	+	2.12488i	0.182286	+	0.117148i
$330$	−10.4624	−	7.79116i	−0.575934	−	0.428889i
$331$	−0.959124	+	1.10689i	−0.0527182	+	0.0608401i	−0.781496	−	0.623910i	$-0.785543\pi$
$331$	−0.959124	+	1.10689i	−0.0527182	+	0.0608401i	0.728778	+	0.684750i	$0.240089\pi$
$332$	−2.42751	+	11.1591i	−0.133227	+	0.612433i
$333$	9.59811	+	25.6585i	0.525973	+	1.40607i
$334$	6.13033	−	0.881408i	0.335437	−	0.0482285i
$335$	−11.8839	−	1.68404i	−0.649284	−	0.0920087i
$336$	2.67917	+	4.16449i	0.146161	+	0.227191i
$337$	18.9612	−	7.07214i	1.03288	−	0.385244i	0.224855	−	0.974392i	$-0.427809\pi$
$337$	18.9612	−	7.07214i	1.03288	−	0.385244i	0.808025	+	0.589148i	$0.200537\pi$
$338$	−2.74183	−	12.6040i	−0.149136	−	0.685566i
$339$	−0.0101769	−	21.2527i	−0.000552734	−	1.15429i
$340$	−0.0288488	−	14.2180i	−0.00156454	−	0.771082i
$341$	1.94744	−	6.63237i	0.105460	−	0.359163i
$342$	12.7066	+	16.9401i	0.687092	+	0.916018i
$343$	−9.98236	−	13.3349i	−0.538997	−	0.720016i
$344$	1.71076			0.0922381
$345$	10.3477	−	15.4248i	0.557101	−	0.830445i
$346$	10.5198			0.565546
$347$	1.20354	+	1.60774i	0.0646093	+	0.0863080i	0.831682	−	0.555252i	$-0.187378\pi$
$347$	1.20354	+	1.60774i	0.0646093	+	0.0863080i	−0.767073	+	0.641560i	$0.778287\pi$
$348$	5.05613	+	3.78120i	0.271037	+	0.202693i
$349$	2.85713	−	9.73050i	0.152939	−	0.520862i	−0.847004	−	0.531587i	$-0.821596\pi$
$349$	2.85713	−	9.73050i	0.152939	−	0.520862i	0.999942	+	0.0107253i	$0.00341403\pi$
$350$	−10.8412	−	9.31718i	−0.579485	−	0.498024i
$351$	0.891915	−	1.39224i	0.0476069	−	0.0743122i
$352$	0.715944	+	3.29114i	0.0381600	+	0.175419i
$353$	−22.4457	+	8.37183i	−1.19467	+	0.445588i	−0.866570	−	0.499056i	$-0.833680\pi$
$353$	−22.4457	+	8.37183i	−1.19467	+	0.445588i	−0.328097	+	0.944644i	$0.606407\pi$
$354$	14.6237	−	9.40797i	0.777241	−	0.500028i
$355$	−13.9773	−	18.5927i	−0.741836	−	0.986797i
$356$	−6.22953	+	0.895672i	−0.330165	+	0.0474705i
$357$	25.1972	−	18.8812i	1.33358	−	0.999299i
$358$	2.44105	−	11.2213i	0.129014	−	0.593066i
$359$	−8.30632	+	9.58601i	−0.438391	+	0.505930i	−0.931351	−	0.364122i	$-0.881369\pi$
$359$	−8.30632	+	9.58601i	−0.438391	+	0.505930i	0.492960	+	0.870052i	$0.335915\pi$
$360$	0.934841	−	6.64275i	0.0492705	−	0.350103i
$361$	−25.9316	−	16.6652i	−1.36482	−	0.877118i
$362$	3.68697	−	6.75219i	0.193783	−	0.354887i
$363$	0.208075	−	0.558688i	0.0109211	−	0.0293235i
$364$	−0.256301	+	0.872879i	−0.0134338	+	0.0457513i
$365$	−27.9761	−	8.15291i	−1.46434	−	0.426743i
$366$	−7.48284	+	16.4059i	−0.391134	+	0.857551i
$367$	−13.3069	−	13.3069i	−0.694613	−	0.694613i	0.268631	−	0.963243i	$-0.413429\pi$
$367$	−13.3069	−	13.3069i	−0.694613	−	0.694613i	−0.963243	+	0.268631i	$0.913429\pi$
$368$	−4.63043	+	1.24866i	−0.241378	+	0.0650910i
$369$	−29.4014	−	18.8554i	−1.53058	−	0.981571i
$370$	−1.41534	+	20.3698i	−0.0735802	+	1.05898i
$371$	20.2936	−	9.26776i	1.05359	−	0.481158i
$372$	3.47308	−	0.757264i	0.180071	−	0.0392623i
$373$	4.82479	+	0.345076i	0.249818	+	0.0178673i	0.195687	−	0.980666i	$-0.437306\pi$
$373$	4.82479	+	0.345076i	0.249818	+	0.0178673i	0.0541315	+	0.998534i	$0.482761\pi$
$374$	20.5487	−	6.03364i	1.06255	−	0.311992i
$375$	2.88171	+	19.1493i	0.148811	+	0.988866i
$376$	−0.571083	+	1.25050i	−0.0294514	+	0.0644895i
$377$	0.0827468	+	1.15695i	0.00426168	+	0.0595860i
$378$	13.0282	−	7.13824i	0.670098	−	0.367152i
$379$	−6.15621	+	0.885130i	−0.316223	+	0.0454661i	−0.298599	−	0.954379i	$-0.596519\pi$
$379$	−6.15621	+	0.885130i	−0.316223	+	0.0454661i	−0.0176242	+	0.999845i	$0.505610\pi$
$380$	3.38635	+	15.4161i	0.173716	+	0.790832i
$381$	−0.858518	−	2.91867i	−0.0439832	−	0.149528i
$382$	0.296011	−	0.0211711i	0.0151452	−	0.00108321i
$383$	3.12500	−	1.16556i	0.159680	−	0.0595576i	−0.268353	−	0.963321i	$-0.586479\pi$
$383$	3.12500	−	1.16556i	0.159680	−	0.0595576i	0.428033	+	0.903763i	$0.359207\pi$
$384$	−1.30845	+	1.13488i	−0.0667717	+	0.0579140i
$385$	8.90486	−	19.6041i	0.453834	−	0.999117i
$386$	3.58194	−	3.10376i	0.182316	−	0.157977i
$387$	0.361230	−	5.11956i	0.0183624	−	0.260242i
$388$	−7.42131	−	2.76801i	−0.376760	−	0.140524i
$389$	2.62353	−	18.2470i	0.133018	−	0.925162i	−0.808571	−	0.588399i	$-0.799759\pi$
$389$	2.62353	−	18.2470i	0.133018	−	0.925162i	0.941589	−	0.336763i	$-0.109332\pi$
$390$	1.03508	−	0.668882i	0.0524135	−	0.0338701i
$391$	10.0198	+	28.8012i	0.506724	+	1.45654i
$392$	−0.829885	+	0.829885i	−0.0419155	+	0.0419155i
$393$	9.65237	+	25.8412i	0.486898	+	1.30352i
$394$	13.2006	−	6.02851i	0.665037	−	0.303712i
$395$	2.61161	−	12.1237i	0.131404	−	0.610011i
$396$	10.0001	−	1.44758i	0.502525	−	0.0727434i
$397$	−21.1270	−	11.5362i	−1.06033	−	0.578986i	−0.148233	−	0.988952i	$-0.547359\pi$
$397$	−21.1270	−	11.5362i	−1.06033	−	0.578986i	−0.912101	+	0.409966i	$0.865540\pi$
$398$	2.13648	+	9.82126i	0.107092	+	0.492295i
$399$	−22.8771	+	26.4271i	−1.14529	+	1.32301i
$400$	2.68611	−	4.21720i	0.134306	−	0.210860i
$401$	−13.4077	−	20.8628i	−0.669549	−	1.04184i	−0.995343	−	0.0963983i	$-0.969268\pi$
$401$	−13.4077	−	20.8628i	−0.669549	−	1.04184i	0.325793	−	0.945441i	$-0.394369\pi$
$402$	7.44009	−	5.57514i	0.371078	−	0.278063i
$403$	0.522791	+	0.391357i	0.0260421	+	0.0194949i
$404$	−2.51429	+	1.61583i	−0.125090	+	0.0803907i
$405$	−19.6814	−	4.20019i	−0.977978	−	0.208709i
$406$	−4.32921	+	9.47964i	−0.214855	+	0.470466i
$407$	−30.0535	+	6.53774i	−1.48970	+	0.324064i
$408$	7.79129	+	7.78383i	0.385726	+	0.385357i
$409$	−7.23517	+	6.26931i	−0.357756	+	0.309998i	−0.815131	−	0.579276i	$-0.803335\pi$
$409$	−7.23517	+	6.26931i	−0.357756	+	0.309998i	0.457375	+	0.889274i	$0.348790\pi$
$410$	−14.1193	−	21.8724i	−0.697305	−	1.08020i
$411$	−4.17234	−	28.9209i	−0.205806	−	1.42656i
$412$	−9.60719	+	7.19185i	−0.473312	+	0.354317i
$413$	20.2953	+	20.2953i	0.998667	+	0.998667i
$414$	2.75898	+	14.1205i	0.135596	+	0.693984i
$415$	19.3327	+	16.6833i	0.949006	+	0.818953i
$416$	−0.314965	−	0.0452851i	−0.0154424	−	0.00222028i
$417$	21.2784	+	15.9129i	1.04201	+	0.779259i
$418$	−20.8663	+	11.3939i	−1.02061	+	0.557293i
$419$	−18.5984	−	21.4637i	−0.908589	−	1.04857i	−0.998614	−	0.0526284i	$-0.983240\pi$
$419$	−18.5984	−	21.4637i	−0.908589	−	1.04857i	0.0900249	−	0.995940i	$-0.471305\pi$
$420$	11.0425	−	0.817612i	0.538817	−	0.0398954i
$421$	−33.2147	−	21.3458i	−1.61879	−	1.04033i	−0.956771	−	0.290842i	$-0.906065\pi$
$421$	−33.2147	−	21.3458i	−1.61879	−	1.04033i	−0.662016	−	0.749490i	$-0.730299\pi$
$422$	−4.57121	−	12.2559i	−0.222523	−	0.596608i
$423$	3.62160	+	1.97305i	0.176088	+	0.0959328i
$424$	4.21885	+	6.56466i	0.204885	+	0.318808i
$425$	−27.9653	−	15.1232i	−1.35652	−	0.733583i
$426$	17.8353	+	2.55562i	0.864125	+	0.123820i
$427$	−29.0835	−	6.32673i	−1.40745	−	0.306172i
$428$	−9.90320	+	0.708291i	−0.478689	+	0.0342365i
$429$	1.40349	+	1.21496i	0.0677613	+	0.0586587i
$430$	1.82649	−	3.36117i	0.0880813	−	0.162090i
$431$	−0.0366827	−	0.124930i	−0.00176694	−	0.00601766i	0.958605	−	0.284740i	$-0.0919073\pi$
$431$	−0.0366827	−	0.124930i	−0.00176694	−	0.00601766i	−0.960372	+	0.278722i	$0.910089\pi$
$432$	3.11991	+	4.15526i	0.150107	+	0.199920i
$433$	−11.2217	+	6.12752i	−0.539281	+	0.294470i	−0.725712	−	0.687998i	$-0.758490\pi$
$433$	−11.2217	+	6.12752i	−0.539281	+	0.294470i	0.186431	+	0.982468i	$0.440308\pi$
$434$	2.43742	+	5.33719i	0.117000	+	0.256194i
$435$	12.8272	−	5.89689i	0.615015	−	0.282734i
$436$	−8.97468			−0.429809
$437$	−17.6652	−	28.8776i	−0.845043	−	1.38140i
$438$	19.8055	−	10.8269i	0.946343	−	0.517331i
$439$	22.5510	+	3.24235i	1.07630	+	0.154749i	0.657594	−	0.753373i	$-0.271574\pi$
$439$	22.5510	+	3.24235i	1.07630	+	0.154749i	0.418707	+	0.908121i	$0.362483\pi$
$440$	7.23055	+	2.10716i	0.344703	+	0.100455i
$441$	2.30825	+	2.65871i	0.109917	+	0.126605i
$442$	−0.144341	+	2.01815i	−0.00686558	+	0.0959934i
$443$	−0.0822227	−	0.0448970i	−0.00390652	−	0.00213312i	0.477295	−	0.878743i	$-0.341617\pi$
$443$	−0.0822227	−	0.0448970i	−0.00390652	−	0.00213312i	−0.481201	+	0.876610i	$0.659799\pi$
$444$	−10.3633	−	11.9483i	−0.491820	−	0.567042i
$445$	−4.89121	+	13.1956i	−0.231866	+	0.625529i
$446$	−4.08564	−	3.54023i	−0.193461	−	0.167635i
$447$	13.3891	+	7.30270i	0.633284	+	0.345406i
$448$	−2.28871	−	1.71331i	−0.108132	−	0.0809462i
$449$	2.37419	+	16.5129i	0.112045	+	0.779290i	0.965925	+	0.258821i	$0.0833339\pi$
$449$	2.37419	+	16.5129i	0.112045	+	0.779290i	−0.853880	+	0.520469i	$0.825757\pi$
$450$	−12.0531	−	8.92882i	−0.568186	−	0.420909i
$451$	25.6796	−	29.6359i	1.20921	−	1.39550i
$452$	4.28802	+	11.4966i	0.201691	+	0.540756i
$453$	1.99060	−	28.0208i	0.0935264	−	1.31653i
$454$	−3.66633	−	12.4864i	−0.172070	−	0.586015i
$455$	1.44132	+	1.43549i	0.0675704	+	0.0672967i
$456$	−10.2883	−	6.60495i	−0.481795	−	0.309305i
$457$	6.06927	−	16.2724i	0.283909	−	0.761189i	−0.714213	−	0.699928i	$-0.753215\pi$
$457$	6.06927	−	16.2724i	0.283909	−	0.761189i	0.998122	−	0.0612604i	$-0.0195120\pi$
$458$	−12.7187	+	9.52111i	−0.594307	+	0.444892i
$459$	24.9387	−	21.6723i	1.16404	−	1.01158i
$460$	−2.49040	+	10.4306i	−0.116115	+	0.486330i
$461$			32.8838i			1.53155i	0.643107	+	0.765777i	$0.277645\pi$
$461$			32.8838i			1.53155i	−0.643107	+	0.765777i	$0.722355\pi$
$462$	5.83600	+	15.6241i	0.271515	+	0.726897i
$463$	−24.0702	−	8.97771i	−1.11864	−	0.417230i	−0.278952	−	0.960305i	$-0.589987\pi$
$463$	−24.0702	−	8.97771i	−1.11864	−	0.417230i	−0.839684	+	0.543075i	$0.817260\pi$
$464$	−3.49752	−	1.02696i	−0.162368	−	0.0476756i
$465$	2.22022	−	7.63212i	0.102960	−	0.353931i
$466$	−3.37186	+	0.990067i	−0.156198	+	0.0458640i
$467$	−1.40569	+	0.305790i	−0.0650478	+	0.0141503i	−0.244971	−	0.969530i	$-0.578779\pi$
$467$	−1.40569	+	0.305790i	−0.0650478	+	0.0141503i	0.179924	+	0.983681i	$0.442415\pi$
$468$	−0.202024	+	0.932988i	−0.00933854	+	0.0431274i
$469$	11.5978	+	10.0495i	0.535536	+	0.464045i
$470$	1.84716	+	2.45711i	0.0852032	+	0.113338i
$471$	−12.1855	−	1.74605i	−0.561477	−	0.0804538i
$472$	−6.01633	+	8.03687i	−0.276924	+	0.369927i
$473$	5.63036	+	1.22481i	0.258884	+	0.0563168i
$474$	5.19749	+	8.07895i	0.238729	+	0.371078i
$475$	33.9038	+	9.80580i	1.55562	+	0.449921i
$476$	−9.82816	+	15.2929i	−0.450473	+	0.700949i
$477$	20.5359	−	11.2390i	0.940276	−	0.514599i
$478$	24.8151	+	1.77481i	1.13502	+	0.0811780i
$479$	4.22322	+	1.24005i	0.192964	+	0.0566593i	0.376787	−	0.926300i	$-0.377029\pi$
$479$	4.22322	+	1.24005i	0.192964	+	0.0566593i	−0.183823	+	0.982959i	$0.558847\pi$
$480$	0.832750	+	3.78240i	0.0380097	+	0.172642i
$481$	0.413526	−	2.87614i	0.0188552	−	0.131141i
$482$	14.6348	−	14.6348i	0.666595	−	0.666595i
$483$	−21.8114	+	9.39388i	−0.992452	+	0.427436i
$484$			0.344203i			0.0156456i
$485$	−13.3617	+	11.6255i	−0.606724	+	0.527889i
$486$	13.0936	−	8.45913i	0.593939	−	0.383714i
$487$	−3.44571	−	6.31035i	−0.156140	−	0.285949i	0.787885	−	0.615822i	$-0.211176\pi$
$487$	−3.44571	−	6.31035i	−0.156140	−	0.285949i	−0.944025	+	0.329873i	$0.892994\pi$
$488$	0.742690	−	10.3842i	0.0336200	−	0.470069i
$489$	−19.7152	+	0.00944067i	−0.891553	+	0.000426922i
$490$	0.744466	+	2.51652i	0.0336315	+	0.113685i
$491$	−13.5792	−	6.20140i	−0.612820	−	0.279865i	0.0847275	−	0.996404i	$-0.472998\pi$
$491$	−13.5792	−	6.20140i	−0.612820	−	0.279865i	−0.697547	+	0.716539i	$0.745725\pi$
$492$	19.7069	+	4.27709i	0.888456	+	0.192826i
$493$	−4.92682	+	22.6482i	−0.221893	+	1.02002i
$494$	−0.319653	−	2.22323i	−0.0143819	−	0.100028i
$495$	7.83253	−	21.1929i	0.352046	−	0.952552i
$496$	−1.72650	+	1.10955i	−0.0775221	+	0.0498205i
$497$	2.12163	+	29.6643i	0.0951682	+	1.33062i
$498$	−19.7290	+	1.42054i	−0.884079	+	0.0636561i
$499$	−5.80370	+	9.03073i	−0.259809	+	0.404271i	−0.946513	−	0.322667i	$-0.895421\pi$
$499$	−5.80370	+	9.03073i	−0.259809	+	0.404271i	0.686703	+	0.726938i	$0.259057\pi$
$500$	−5.41780	−	9.77995i	−0.242291	−	0.437373i
$501$	4.46092	+	9.75569i	0.199299	+	0.435852i
$502$	0.972063	+	1.78020i	0.0433853	+	0.0794542i
$503$	−10.0676	+	26.9924i	−0.448894	+	1.20353i	0.493712	+	0.869625i	$0.335640\pi$
$503$	−10.0676	+	26.9924i	−0.448894	+	1.20353i	−0.942606	+	0.333906i	$0.891633\pi$
$504$	−5.61045	+	6.48734i	−0.249909	+	0.288969i
$505$	0.490286	+	6.66501i	0.0218174	+	0.296589i
$506$	−16.1334	+	0.794400i	−0.717216	+	0.0353154i
$507$	19.6033	−	10.7164i	0.870615	−	0.475933i
$508$	1.05262	+	1.40614i	0.0467025	+	0.0623873i
$509$	3.46176	+	7.58019i	0.153440	+	0.335986i	0.970705	−	0.240276i	$-0.0772380\pi$
$509$	3.46176	+	7.58019i	0.153440	+	0.335986i	−0.817265	+	0.576262i	$0.804511\pi$
$510$	23.6114	−	6.99730i	1.04553	−	0.309846i
$511$	24.3983	+	28.1571i	1.07932	+	1.24560i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	−21.9381	+	29.3938i	−0.968591	+	1.29777i
$514$	−19.3349	−	8.82997i	−0.852827	−	0.389473i
$515$	3.87287	+	26.5538i	0.170659	+	1.17010i
$516$	0.836170	+	2.84270i	0.0368104	+	0.125143i
$517$	−2.77480	+	3.70670i	−0.122036	+	0.163021i
$518$	15.6453	−	20.8997i	0.687415	−	0.918279i
$519$	5.14176	+	17.4802i	0.225698	+	0.767298i
$520$	−0.425244	+	0.570469i	−0.0186482	+	0.0250167i
$521$	24.0938	+	11.0033i	1.05557	+	0.482061i	0.866123	−	0.499830i	$-0.166604\pi$
$521$	24.0938	+	11.0033i	1.05557	+	0.482061i	0.189444	+	0.981892i	$0.439332\pi$
$522$	−3.81176	+	10.2497i	−0.166836	+	0.448617i
$523$	11.2445	−	20.5928i	0.491689	−	0.900461i	−0.507557	−	0.861618i	$-0.669451\pi$
$523$	11.2445	−	20.5928i	0.491689	−	0.900461i	0.999245	−	0.0388424i	$-0.0123670\pi$
$524$	−10.4295	−	12.0363i	−0.455614	−	0.525806i
$525$	10.1831	−	22.5683i	0.444427	−	0.984960i
$526$	8.84256	+	19.3625i	0.385554	+	0.844246i
$527$	7.82030	+	10.4467i	0.340658	+	0.455065i
$528$	−5.11882	+	2.79827i	−0.222768	+	0.121779i
$529$	−2.25954	−	22.8887i	−0.0982410	−	0.995163i
$530$	17.4020	−	1.28011i	0.755893	−	0.0556043i
$531$	22.7805	+	19.7012i	0.988588	+	0.854960i
$532$	7.05235	−	18.9081i	0.305758	−	0.819769i
$533$	1.77549	+	3.25157i	0.0769051	+	0.140841i
$534$	−4.53311	−	9.91357i	−0.196167	−	0.429002i
$535$	−9.18154	+	20.2132i	−0.396953	+	0.873893i
$536$	−2.90201	+	4.51561i	−0.125348	+	0.195045i
$537$	19.8391	−	1.42847i	0.856121	−	0.0616430i
$538$	0.925097	+	12.9346i	0.0398838	+	0.557648i
$539$	−3.32542	+	2.13712i	−0.143236	+	0.0920523i
$540$	11.4949	−	1.69340i	0.494661	−	0.0728721i
$541$	0.113749	+	0.791143i	0.00489046	+	0.0340139i	0.992121	−	0.125287i	$-0.0399851\pi$
$541$	0.113749	+	0.791143i	0.00489046	+	0.0340139i	−0.987230	+	0.159301i	$0.949076\pi$
$542$	−1.49754	+	6.88409i	−0.0643249	+	0.295697i
$543$	13.0219	+	2.82621i	0.558823	+	0.121284i
$544$	−5.78391	−	2.64142i	−0.247983	−	0.113250i
$545$	−9.58180	+	17.6327i	−0.410439	+	0.755303i
$546$	−1.57570		0.000754526i	−0.0674337		3.22907e-5i
$547$	−1.59711	+	22.3305i	−0.0682873	+	0.954782i	0.841647	+	0.540029i	$0.181587\pi$
$547$	−1.59711	+	22.3305i	−0.0682873	+	0.954782i	−0.909934	+	0.414753i	$0.863868\pi$
$548$	8.08510	+	14.8068i	0.345379	+	0.632514i
$549$	−30.9184	−	4.41518i	−1.31957	−	0.188435i
$550$	11.8597	−	11.9563i	0.505698	−	0.509819i
$551$		−	25.7301i		−	1.09614i
$552$	−4.33807	−	7.08387i	−0.184640	−	0.301509i
$553$	−11.2123	+	11.2123i	−0.476794	+	0.476794i
$554$	1.14856	−	7.98844i	0.0487978	−	0.339396i
$555$	−34.5394	+	7.60437i	−1.46612	+	0.322787i
$556$	−14.7191	−	4.32191i	−0.624228	−	0.183290i
$557$	37.8188	+	2.70486i	1.60244	+	0.114608i	0.843709	−	0.536801i	$-0.180367\pi$
$557$	37.8188	+	2.70486i	1.60244	+	0.114608i	0.758726	+	0.651409i	$0.225822\pi$
$558$	2.95585	+	5.40094i	0.125131	+	0.228640i
$559$	−0.294309	+	0.457953i	−0.0124479	+	0.0193694i
$560$	−5.80972	+	2.66747i	−0.245505	+	0.112721i
$561$	20.0695	+	31.1958i	0.847333	+	1.31709i
$562$	12.6662	+	2.75535i	0.534290	+	0.116228i
$563$	9.19806	−	12.2872i	0.387652	−	0.517842i	−0.563687	−	0.825988i	$-0.690618\pi$
$563$	9.19806	−	12.2872i	0.387652	−	0.517842i	0.951339	+	0.308146i	$0.0997085\pi$
$564$	−2.35703	−	0.337737i	−0.0992487	−	0.0142213i
$565$	27.1657	+	3.84960i	1.14287	+	0.161954i
$566$	−10.0408	−	8.70044i	−0.422048	−	0.365707i
$567$	18.2291	+	18.1594i	0.765551	+	0.762623i
$568$	−10.1647	+	2.21119i	−0.426501	+	0.0927796i
$569$	−23.5042	+	6.90144i	−0.985345	+	0.289323i	−0.734429	−	0.678685i	$-0.762550\pi$
$569$	−23.5042	+	6.90144i	−0.985345	+	0.289323i	−0.250916	+	0.968009i	$0.580732\pi$
$570$	−23.9612	+	13.1619i	−1.00362	+	0.551292i
$571$	−17.2577	−	5.06732i	−0.722212	−	0.212061i	−0.100087	−	0.994979i	$-0.531912\pi$
$571$	−17.2577	−	5.06732i	−0.722212	−	0.212061i	−0.622125	+	0.782918i	$0.713730\pi$
$572$	−1.00417	−	0.374537i	−0.0419865	−	0.0156602i
$573$	0.179861	+	0.481521i	0.00751378	+	0.0201158i
$574$			33.2859i			1.38933i
$575$	17.8344	+	16.0292i	0.743745	+	0.668463i
$576$	−2.52531	−	1.61950i	−0.105221	−	0.0674794i
$577$	−0.671961	+	0.503024i	−0.0279741	+	0.0209412i	−0.613173	−	0.789948i	$-0.710107\pi$
$577$	−0.671961	+	0.503024i	−0.0279741	+	0.0209412i	0.585199	+	0.810890i	$0.301016\pi$
$578$	−8.18819	+	21.9534i	−0.340584	+	0.913141i
$579$	6.90814	+	4.43492i	0.287092	+	0.184309i
$580$	−5.75182	+	5.77521i	−0.238831	+	0.239803i
$581$	−9.19841	−	31.3269i	−0.381614	−	1.29966i
$582$	0.972155	−	13.6846i	0.0402971	−	0.567245i
$583$	9.18491	+	24.6257i	0.380400	+	1.01989i
$584$	−8.53399	+	9.84875i	−0.353139	+	0.407544i
$585$	1.61737	+	1.39302i	0.0668701	+	0.0575945i
$586$	3.46691	+	24.1129i	0.143217	+	0.996094i
$587$	14.1235	+	10.5727i	0.582939	+	0.436382i	0.849615	−	0.527404i	$-0.176835\pi$
$587$	14.1235	+	10.5727i	0.582939	+	0.436382i	−0.266676	+	0.963786i	$0.585925\pi$
$588$	−1.78461	−	0.973361i	−0.0735960	−	0.0401407i
$589$	−10.9482	−	9.48664i	−0.451111	−	0.390890i
$590$	9.36688	+	20.4010i	0.385628	+	0.839894i
$591$	16.4694	+	18.9883i	0.677460	+	0.781075i
$592$	8.01464	+	4.37632i	0.329400	+	0.179866i
$593$	−0.279307	+	3.90522i	−0.0114698	+	0.160368i	0.988489	+	0.151292i	$0.0483435\pi$
$593$	−0.279307	+	3.90522i	−0.0114698	+	0.160368i	−0.999959	+	0.00907588i	$0.997111\pi$
$594$	7.29314	+	15.9092i	0.299241	+	0.652764i
$595$	19.5533	+	35.6370i	0.801606	+	1.46098i
$596$	−8.71564	−	1.25312i	−0.357007	−	0.0513298i
$597$	−15.2753	+	8.35045i	−0.625177	+	0.341761i
$598$	0.462335	−	1.45433i	0.0189063	−	0.0594720i
$599$	−5.80707			−0.237270			−0.118635	−	0.992938i	$-0.537852\pi$
$599$	−5.80707			−0.237270			−0.118635	+	0.992938i	$0.537852\pi$
$600$	8.32044	+	2.40215i	0.339680	+	0.0980674i
$601$	−5.20007	−	11.3866i	−0.212115	−	0.464468i	0.773430	−	0.633882i	$-0.218540\pi$
$601$	−5.20007	−	11.3866i	−0.212115	−	0.464468i	−0.985545	+	0.169414i	$0.945812\pi$
$602$	−4.29272	+	2.34400i	−0.174958	+	0.0955345i
$603$	12.9005	+	9.63791i	0.525348	+	0.392486i
$604$	4.56930	+	15.5616i	0.185922	+	0.633192i
$605$	0.676263	+	0.367488i	0.0274940	+	0.0149405i
$606$	−3.91387	−	3.38811i	−0.158990	−	0.137632i
$607$	−28.8821	+	2.06569i	−1.17229	+	0.0838439i	−0.643867	−	0.765137i	$-0.722671\pi$
$607$	−28.8821	+	2.06569i	−1.17229	+	0.0838439i	−0.528423	+	0.848981i	$0.677217\pi$
$608$	6.89737	+	1.50043i	0.279725	+	0.0608505i
$609$	−17.8679	−	2.56028i	−0.724044	−	0.103748i
$610$	−19.6090	−	12.5458i	−0.793947	−	0.507965i
$611$	−0.236500	−	0.368001i	−0.00956776	−	0.0148877i
$612$	−9.12590	+	16.7510i	−0.368893	+	0.677117i
$613$	−12.1757	−	32.6443i	−0.491772	−	1.31849i	−0.911671	−	0.410920i	$-0.865207\pi$
$613$	−12.1757	−	32.6443i	−0.491772	−	1.31849i	0.419900	−	0.907571i	$-0.362065\pi$
$614$	−1.88796	−	1.21332i	−0.0761918	−	0.0489655i
$615$	29.4433	−	34.1521i	1.18727	−	1.37715i
$616$	−6.30585	−	7.27734i	−0.254070	−	0.293212i
$617$	5.57266	−	3.04290i	0.224347	−	0.122503i	−0.363145	−	0.931733i	$-0.618297\pi$
$617$	5.57266	−	3.04290i	0.224347	−	0.122503i	0.587492	+	0.809230i	$0.300115\pi$
$618$	−16.6461	−	12.4487i	−0.669604	−	0.500759i
$619$	−4.52123	−	0.650055i	−0.181724	−	0.0261279i	0.0508521	−	0.998706i	$-0.483806\pi$
$619$	−4.52123	−	0.650055i	−0.181724	−	0.0261279i	−0.232576	+	0.972578i	$0.574715\pi$
$620$	0.336667	+	4.57670i	0.0135209	+	0.183805i
$621$	−22.1149	+	11.4862i	−0.887440	+	0.460923i
$622$	−17.1627	−	17.1627i	−0.688160	−	0.688160i
$623$	14.4042	−	10.7829i	0.577093	−	0.432007i
$624$	−0.0786973	−	0.545497i	−0.00315041	−	0.0218374i
$625$	−24.9992	+	0.202900i	−0.999967	+	0.00811600i
$626$	18.3596	−	15.9087i	0.733798	−	0.635839i
$627$	−29.1316	−	29.1037i	−1.16340	−	1.16229i
$628$	6.94472	−	1.51073i	0.277125	−	0.0602847i
$629$	24.1205	−	52.8165i	0.961747	−	2.10593i
$630$	6.75583	+	17.9492i	0.269159	+	0.715112i
$631$	29.9099	−	19.2219i	1.19069	−	0.765212i	0.213372	−	0.976971i	$-0.431555\pi$
$631$	29.9099	−	19.2219i	1.19069	−	0.765212i	0.977322	+	0.211759i	$0.0679191\pi$
$632$	−4.44002	−	3.32375i	−0.176614	−	0.132212i
$633$	18.1308	−	13.5861i	0.720635	−	0.539999i
$634$	10.9012	+	16.9626i	0.432943	+	0.673672i
$635$	3.88650	−	0.566845i	0.154231	−	0.0224946i
$636$	−8.84615	+	10.2189i	−0.350773	+	0.405205i
$637$	−0.0793835	−	0.364920i	−0.00314529	−	0.0144587i
$638$	−10.7756	−	5.88392i	−0.426610	−	0.232947i
$639$	4.47084	+	30.8853i	0.176864	+	1.22180i
$640$	−1.21272	−	1.87864i	−0.0479371	−	0.0742599i
$641$	23.0908	−	10.5452i	0.912033	−	0.416511i	0.0965736	−	0.995326i	$-0.469212\pi$
$641$	23.0908	−	10.5452i	0.912033	−	0.416511i	0.815459	+	0.578814i	$0.196484\pi$
$642$	−6.01733	−	16.1095i	−0.237485	−	0.635792i
$643$	15.3204	−	15.3204i	0.604178	−	0.604178i	−0.337240	−	0.941419i	$-0.609494\pi$
$643$	15.3204	−	15.3204i	0.604178	−	0.604178i	0.941419	+	0.337240i	$0.109494\pi$
$644$	9.90802	−	9.47759i	0.390431	−	0.373469i
$645$	6.47784	+	1.39216i	0.255065	+	0.0548164i
$646$	6.38748	−	44.4259i	0.251312	−	1.74791i
$647$	−12.5694	−	4.68815i	−0.494155	−	0.184310i	0.0900170	−	0.995940i	$-0.471308\pi$
$647$	−12.5694	−	4.68815i	−0.494155	−	0.184310i	−0.584172	+	0.811630i	$0.698581\pi$
$648$	−5.37969	+	7.21519i	−0.211334	+	0.283439i
$649$	−25.5545	+	22.1431i	−1.00310	+	0.869194i
$650$	0.666800	+	1.44455i	0.0261540	+	0.0566598i
$651$	−7.67725	+	6.65881i	−0.300895	+	0.260979i
$652$	10.6649	−	3.97781i	0.417670	−	0.155783i
$653$	14.3817	−	1.02860i	0.562798	−	0.0402521i	0.212958	−	0.977061i	$-0.431690\pi$
$653$	14.3817	−	1.02860i	0.562798	−	0.0402521i	0.349841	+	0.936809i	$0.386236\pi$
$654$	−4.38656	−	14.9128i	−0.171528	−	0.583138i
$655$	−34.7829	+	7.64050i	−1.35908	+	0.298539i
$656$	−11.5242	+	1.65693i	−0.449943	+	0.0646921i
$657$	27.6710	+	27.6180i	1.07955	+	1.07748i
$658$	−0.280384	−	3.92028i	−0.0109305	−	0.152828i
$659$	14.6033	−	31.9769i	0.568865	−	1.24564i	−0.378534	−	0.925587i	$-0.623572\pi$
$659$	14.6033	−	31.9769i	0.568865	−	1.24564i	0.947399	−	0.320054i	$-0.103701\pi$
$660$	0.0327143	+	13.0446i	0.00127340	+	0.507761i
$661$	7.77523	−	2.28301i	0.302421	−	0.0887989i	−0.127001	−	0.991903i	$-0.540535\pi$
$661$	7.77523	−	2.28301i	0.302421	−	0.0887989i	0.429423	+	0.903104i	$0.358717\pi$
$662$	1.46089	+	0.104485i	0.0567792	+	0.00406093i
$663$	−3.42402	+	0.746566i	−0.132978	+	0.0289942i
$664$	10.3880	−	4.74406i	0.403134	−	0.184105i
$665$	−29.6197	−	34.0431i	−1.14860	−	1.32013i
$666$	14.7887	−	23.0602i	0.573051	−	0.893565i
$667$	7.61334	−	15.7367i	0.294790	−	0.609329i
$668$	−4.37937	−	4.37937i	−0.169443	−	0.169443i
$669$	3.88570	−	8.51930i	0.150230	−	0.329375i
$670$	5.77359	+	10.5227i	0.223053	+	0.406528i
$671$	9.87878	−	33.6440i	0.381366	−	1.29881i
$672$	1.72828	−	4.64047i	0.0666697	−	0.179010i
$673$	3.55281	−	6.50648i	0.136951	−	0.250806i	−0.800199	−	0.599735i	$-0.795273\pi$
$673$	3.55281	−	6.50648i	0.136951	−	0.250806i	0.937149	+	0.348929i	$0.113454\pi$
$674$	−17.0245	−	10.9410i	−0.655761	−	0.421432i
$675$	8.94546	−	24.3922i	0.344311	−	0.938856i
$676$	−8.44688	+	9.74822i	−0.324880	+	0.374932i
$677$	6.96797	−	32.0313i	0.267801	−	1.23106i	−0.625005	−	0.780620i	$-0.714903\pi$
$677$	6.96797	−	32.0313i	0.267801	−	1.23106i	0.892806	−	0.450441i	$-0.148733\pi$
$678$	−17.0076	+	12.7444i	−0.653172	+	0.489447i
$679$	22.4145	−	3.22272i	0.860189	−	0.123677i
$680$	−11.3648	+	8.54365i	−0.435822	+	0.327634i
$681$	18.9561	−	12.1952i	0.726399	−	0.467320i
$682$	−6.47654	+	2.41562i	−0.247999	+	0.0924990i
$683$	0.410102	+	1.88521i	0.0156921	+	0.0721355i	0.984327	−	0.176353i	$-0.0564299\pi$
$683$	0.410102	+	1.88521i	0.0156921	+	0.0721355i	−0.968635	+	0.248488i	$0.920066\pi$
$684$	5.94652	−	20.3240i	0.227371	−	0.777106i
$685$	37.7232	−	0.0765413i	1.44133	−	0.00292449i
$686$	−4.69291	+	15.9826i	−0.179176	+	0.610218i
$687$	−22.0374	−	16.4805i	−0.840778	−	0.628770i
$688$	−1.02522	−	1.36954i	−0.0390862	−	0.0522130i
$689$	−2.48308			−0.0945976
$690$	−18.5494	+	0.960000i	−0.706162	+	0.0365466i
$691$	1.44798			0.0550839			0.0275419	−	0.999621i	$-0.491232\pi$
$691$	1.44798			0.0550839			0.0275419	+	0.999621i	$0.491232\pi$
$692$	−6.30426	−	8.42151i	−0.239652	−	0.320138i
$693$	−23.1094	+	17.3340i	−0.877852	+	0.658465i
$694$	0.565808	−	1.92696i	0.0214778	−	0.0731466i
$695$	−24.2062	+	24.3046i	−0.918192	+	0.921926i
$696$	−0.00302329	−	6.31363i	−0.000114598	−	0.239317i
$697$	15.7362	+	72.3383i	0.596052	+	2.74001i
$698$	−9.50188	+	3.54402i	−0.359652	+	0.134143i
$699$	−3.29322	−	5.11895i	−0.124561	−	0.193617i
$700$	−0.961909	+	14.2624i	−0.0363567	+	0.539067i
$701$	48.5915	−	6.98641i	1.83528	−	0.263873i	0.864288	−	0.502997i	$-0.167769\pi$
$701$	48.5915	−	6.98641i	1.83528	−	0.263873i	0.970989	+	0.239124i	$0.0768603\pi$
$702$	−1.64905	+	0.120324i	−0.0622394	+	0.00454132i
$703$	−13.7014	+	62.9842i	−0.516757	+	2.37549i
$704$	2.20565	−	2.54545i	0.0831284	−	0.0959353i
$705$	−3.18004	+	4.27031i	−0.119767	+	0.160829i
$706$	20.1532	+	12.9517i	0.758477	+	0.487444i
$707$	4.09502	−	7.49948i	0.154009	−	0.282047i
$708$	−16.2951	−	6.06888i	−0.612408	−	0.228082i
$709$	6.91937	−	23.5652i	0.259862	−	0.885010i	−0.721430	−	0.692487i	$-0.756515\pi$
$709$	6.91937	−	23.5652i	0.259862	−	0.885010i	0.981293	−	0.192523i	$-0.0616669\pi$
$710$	−6.50794	+	22.3315i	−0.244239	+	0.838088i
$711$	−10.8841	+	12.5852i	−0.408184	+	0.471982i
$712$	4.45024	+	4.45024i	0.166780	+	0.166780i
$713$	−3.88896	−	9.04157i	−0.145643	−	0.338610i
$714$	−30.2153	−	8.85630i	−1.13078	−	0.331439i
$715$	−1.80796	+	1.57304i	−0.0676140	+	0.0588285i
$716$	−10.4460	+	4.77053i	−0.390385	+	0.178283i
$717$	9.17978	+	42.1017i	0.342825	+	1.57232i
$718$	12.6518	+	0.904874i	0.472161	+	0.0337696i
$719$	−44.4756	+	13.0592i	−1.65866	+	0.487026i	−0.971014	−	0.239021i	$-0.923173\pi$
$719$	−44.4756	+	13.0592i	−1.65866	+	0.487026i	−0.687645	+	0.726047i	$0.741355\pi$
$720$	−5.87802	+	3.23247i	−0.219061	+	0.120467i
$721$	14.2529	−	31.2094i	0.530805	−	1.16230i
$722$	2.19903	+	30.7464i	0.0818394	+	1.14426i
$723$	31.4710	+	17.1649i	1.17042	+	0.638369i
$724$	−7.61492	+	1.09486i	−0.283006	+	0.0406902i
$725$	5.20574	+	17.4666i	0.193337	+	0.648694i
$726$	−0.571948	+	0.168237i	−0.0212270	+	0.00624385i
$727$	−32.4997	+	2.32443i	−1.20535	+	0.0862082i	−0.659519	−	0.751688i	$-0.729240\pi$
$727$	−32.4997	+	2.32443i	−1.20535	+	0.0862082i	−0.545829	+	0.837896i	$0.683785\pi$
$728$	0.852371	−	0.317918i	0.0315910	−	0.0117828i
$729$	20.4560	+	17.6225i	0.757628	+	0.652687i
$730$	10.2387	+	27.2819i	0.378952	+	1.00975i
$731$	−8.22097	+	7.12351i	−0.304064	+	0.263473i
$732$	17.6179	−	3.84138i	0.651177	−	0.141982i
$733$	−19.2378	−	7.17532i	−0.710563	−	0.265026i	−0.0319158	−	0.999491i	$-0.510161\pi$
$733$	−19.2378	−	7.17532i	−0.710563	−	0.265026i	−0.678648	+	0.734464i	$0.737434\pi$
$734$	−2.67819	+	18.6272i	−0.0988537	+	0.687543i
$735$	−3.81772	+	2.46705i	−0.140819	+	0.0909984i
$736$	3.77452	+	2.95855i	0.139131	+	0.109054i
$737$	−12.7839	+	12.7839i	−0.470899	+	0.470899i
$738$	2.52510	+	34.8366i	0.0929503	+	1.28235i
$739$	17.9311	−	8.18886i	0.659606	−	0.301232i	−0.0573459	−	0.998354i	$-0.518264\pi$
$739$	17.9311	−	8.18886i	0.659606	−	0.301232i	0.716952	+	0.697122i	$0.245537\pi$
$740$	17.1551	−	11.0741i	0.630633	−	0.407094i
$741$	3.53802	−	1.61781i	0.129972	−	0.0594316i
$742$	−19.5807	−	10.6919i	−0.718830	−	0.392511i
$743$	−1.18077	−	5.42792i	−0.0433183	−	0.199131i	0.950402	−	0.311025i	$-0.100672\pi$
$743$	−1.18077	−	5.42792i	−0.0433183	−	0.199131i	−0.993720	+	0.111893i	$0.964308\pi$
$744$	−2.68756	−	2.32653i	−0.0985308	−	0.0852948i
$745$	−11.7673	+	15.7859i	−0.431120	+	0.578351i
$746$	−2.61514	−	4.06924i	−0.0957471	−	0.148985i
$747$	−12.0034	−	32.0886i	−0.439183	−	1.17406i
$748$	−17.1446	−	12.8343i	−0.626867	−	0.469267i
$749$	23.8791	−	15.3462i	0.872523	−	0.560737i
$750$	13.6029	−	13.7827i	0.496706	−	0.503272i
$751$	10.9802	−	24.0433i	0.400673	−	0.877352i	−0.596528	−	0.802592i	$-0.703454\pi$
$751$	10.9802	−	24.0433i	0.400673	−	0.877352i	0.997202	−	0.0747600i	$-0.0238191\pi$
$752$	1.34331	−	0.292220i	0.0489856	−	0.0106562i
$753$	−2.48297	+	2.48535i	−0.0904843	+	0.0905710i
$754$	0.876599	−	0.759578i	0.0319239	−	0.0276622i
$755$	35.4526	+	7.63693i	1.29025	+	0.277936i
$756$	−13.5220	−	6.15181i	−0.491789	−	0.223739i
$757$	−23.4640	+	17.5649i	−0.852812	+	0.638407i	−0.933597	−	0.358325i	$-0.883348\pi$
$757$	−23.4640	+	17.5649i	−0.852812	+	0.638407i	0.0807853	+	0.996732i	$0.474257\pi$
$758$	4.39786	+	4.39786i	0.159738	+	0.159738i
$759$	−9.20554	−	26.4198i	−0.334140	−	0.958980i
$760$	10.3119	−	11.9495i	0.374052	−	0.433453i
$761$	36.3790	+	5.23052i	1.31874	+	0.189606i	0.765510	−	0.643423i	$-0.222487\pi$
$761$	36.3790	+	5.23052i	1.31874	+	0.189606i	0.553229	+	0.833030i	$0.313396\pi$
$762$	−1.82203	+	2.43638i	−0.0660051	+	0.0882606i
$763$	22.5197	−	12.2967i	0.815267	−	0.445169i
$764$	−0.194341	−	0.224282i	−0.00703101	−	0.00811422i
$765$	23.1677	+	35.8140i	0.837629	+	1.29486i
$766$	−2.80583	−	1.80319i	−0.101379	−	0.0651521i
$767$	−1.11638	−	2.99312i	−0.0403100	−	0.108075i
$768$	1.69264	+	0.367363i	0.0610780	+	0.0132561i
$769$	−0.409481	−	0.637165i	−0.0147663	−	0.0229767i	0.833792	−	0.552079i	$-0.186165\pi$
$769$	−0.409481	−	0.637165i	−0.0147663	−	0.0229767i	−0.848558	+	0.529102i	$0.822529\pi$
$770$	−21.0304	+	4.61959i	−0.757882	+	0.166478i
$771$	5.22202	−	36.4438i	0.188067	−	1.31249i
$772$	−4.63127	−	1.00747i	−0.166683	−	0.0362596i
$773$	13.6639	−	0.977260i	0.491456	−	0.0351496i	0.176587	−	0.984285i	$-0.443494\pi$
$773$	13.6639	−	0.977260i	0.491456	−	0.0351496i	0.314868	+	0.949135i	$0.398040\pi$
$774$	−4.31489	+	2.77886i	−0.155096	+	0.0998839i
$775$	9.35139	+	4.22486i	0.335912	+	0.151761i
$776$	2.23152	+	7.59987i	0.0801070	+	0.272819i
$777$	42.3751	+	15.7820i	1.52020	+	0.566175i
$778$	−16.1797	+	8.83480i	−0.580072	+	0.316743i
$779$	−34.1396	−	74.7553i	−1.22318	−	2.67839i
$780$	−1.15577	−	0.427781i	−0.0413832	−	0.0153170i
$781$	−35.0365			−1.25371
$782$	17.0519	−	25.2812i	0.609775	−	0.904054i
$783$	−18.8945	−	1.32409i	−0.675236	−	0.0473190i
$784$	1.16169	+	0.167026i	0.0414889	+	0.00596520i
$785$	4.44636	−	15.2574i	0.158697	−	0.544559i
$786$	14.9025	−	23.2132i	0.531554	−	0.827986i
$787$	2.78732	−	38.9719i	0.0993573	−	1.38920i	−0.666173	−	0.745797i	$-0.732069\pi$
$787$	2.78732	−	38.9719i	0.0993573	−	1.38920i	0.765530	−	0.643400i	$-0.222477\pi$
$788$	−12.7369	−	6.95488i	−0.453733	−	0.247757i
$789$	−27.8519	+	24.1571i	−0.991552	+	0.860017i
$790$	−11.2706	+	5.17479i	−0.400991	+	0.184111i
$791$	−26.5118	−	22.9726i	−0.942652	−	0.816812i
$792$	−7.15169	−	7.13801i	−0.254124	−	0.253638i
$793$	2.65197	+	1.98524i	0.0941741	+	0.0704978i
$794$	3.42572	+	23.8264i	0.121574	+	0.845568i
$795$	10.6327	+	28.2904i	0.377102	+	1.00336i
$796$	6.58197	−	7.59600i	0.233292	−	0.269233i
$797$	18.3059	+	49.0799i	0.648427	+	1.73850i	0.673899	+	0.738824i	$0.264618\pi$
$797$	18.3059	+	49.0799i	0.648427	+	1.73850i	−0.0254722	+	0.999676i	$0.508109\pi$
$798$	34.8657	+	2.47687i	1.23423	+	0.0876801i
$799$	−2.46269	−	8.38716i	−0.0871238	−	0.296716i
$800$	−4.98577	+	0.376931i	−0.176274	+	0.0133265i
$801$	14.2573	−	12.3779i	0.503757	−	0.437353i
$802$	−8.66660	+	23.2360i	−0.306028	+	0.820493i
$803$	−35.1377	+	26.3038i	−1.23998	+	0.928240i
$804$	−8.92181	−	2.61504i	−0.314648	−	0.0922254i
$805$	−8.04252	−	29.5852i	−0.283462	−	1.04274i
$806$		−	0.653047i		−	0.0230026i
$807$	−21.0406	+	7.85923i	−0.740665	+	0.276658i
$808$	2.80030	+	1.04446i	0.0985141	+	0.0367438i
$809$	−3.83069	−	1.12479i	−0.134680	−	0.0395456i	0.213698	−	0.976900i	$-0.431449\pi$
$809$	−3.83069	−	1.12479i	−0.134680	−	0.0395456i	−0.348378	+	0.937354i	$0.613267\pi$
$810$	8.43221	+	18.2729i	0.296278	+	0.642043i
$811$	49.7525	−	14.6087i	1.74705	−	0.512980i	0.756964	−	0.653456i	$-0.226682\pi$
$811$	49.7525	−	14.6087i	1.74705	−	0.512980i	0.990084	+	0.140477i	$0.0448636\pi$
$812$	10.1832	−	2.21523i	0.357362	−	0.0777392i
$813$	−12.1709	+	0.876341i	−0.426854	+	0.0307346i
$814$	23.2441	+	20.1411i	0.814706	+	0.705947i
$815$	3.57111	−	25.2005i	0.125090	−	0.882734i
$816$	1.56213	−	10.9019i	0.0546855	−	0.381644i
$817$	7.23671	−	9.66711i	0.253180	−	0.338210i
$818$	9.35472	+	2.03500i	0.327080	+	0.0711519i
$819$	−0.771409	−	2.61790i	−0.0269552	−	0.0914769i
$820$	−9.04837	+	24.4108i	−0.315983	+	0.852461i
$821$	−15.2127	+	23.6715i	−0.530928	+	0.826139i	−0.998322	−	0.0579096i	$-0.981556\pi$
$821$	−15.2127	+	23.6715i	−0.530928	+	0.826139i	0.467394	+	0.884049i	$0.345193\pi$
$822$	−20.6520	+	20.6718i	−0.720321	+	0.721011i
$823$	−22.0376	−	1.57616i	−0.768184	−	0.0549416i	−0.318254	−	0.948006i	$-0.603096\pi$
$823$	−22.0376	−	1.57616i	−0.768184	−	0.0549416i	−0.449930	+	0.893064i	$0.648551\pi$
$824$	11.5147	+	3.38103i	0.401135	+	0.117784i
$825$	25.6639	+	13.8628i	0.893504	+	0.482641i
$826$	4.08471	−	28.4098i	0.142125	−	0.988502i
$827$	34.8550	−	34.8550i	1.21203	−	1.21203i	0.241670	−	0.970358i	$-0.422305\pi$
$827$	34.8550	−	34.8550i	1.21203	−	1.21203i	0.970358	−	0.241670i	$-0.0776953\pi$
$828$	9.65064	−	10.6708i	0.335383	−	0.370835i
$829$			24.5921i			0.854119i	0.904224	+	0.427060i	$0.140451\pi$
$829$			24.5921i			0.854119i	−0.904224	+	0.427060i	$0.859549\pi$
$830$	1.77003	−	25.4746i	0.0614388	−	0.884236i
$831$	13.8354	−	1.99600i	0.479946	−	0.0692404i
$832$	0.152499	+	0.279280i	0.00528694	+	0.00968231i
$833$	0.532374	−	7.44356i	0.0184457	−	0.257904i
$834$	−0.0127233	−	26.5705i	−0.000440573	−	0.920061i
$835$	−13.2799	+	3.92861i	−0.459569	+	0.135955i
$836$	21.6260	+	9.87627i	0.747951	+	0.341578i
$837$	−7.52977	+	7.55144i	−0.260267	+	0.261016i
$838$	−6.03696	+	27.7514i	−0.208543	+	0.958658i
$839$	−2.47593	−	17.2205i	−0.0854786	−	0.594517i	−0.986871	−	0.161513i	$-0.948363\pi$
$839$	−2.47593	−	17.2205i	−0.0854786	−	0.594517i	0.901392	−	0.433004i	$-0.142546\pi$
$840$	−7.27204	−	8.34997i	−0.250909	−	0.288101i
$841$	−13.2184	+	8.49493i	−0.455806	+	0.292929i
$842$	2.81664	+	39.3818i	0.0970680	+	1.35719i
$843$	1.61240	+	22.3935i	0.0555339	+	0.771275i
$844$	−7.07192	+	11.0041i	−0.243426	+	0.378778i
$845$	10.1342	+	27.0034i	0.348628	+	0.928947i
$846$	−0.590842	−	4.08165i	−0.0203136	−	0.140330i
$847$	−0.471611	−	0.863691i	−0.0162047	−	0.0296768i
$848$	2.72702	−	7.31141i	0.0936461	−	0.251075i
$849$	9.54947	−	20.9370i	0.327737	−	0.718554i
$850$	4.65222	+	31.4504i	0.159570	+	1.07874i
$851$	−27.0164	+	34.4675i	−0.926110	+	1.18153i
$852$	−8.64245	−	15.8095i	−0.296085	−	0.541623i
$853$	−15.0882	−	20.1554i	−0.516609	−	0.690109i	0.464055	−	0.885806i	$-0.346394\pi$
$853$	−15.0882	−	20.1554i	−0.516609	−	0.690109i	−0.980664	+	0.195698i	$0.937303\pi$
$854$	12.3643	+	27.0740i	0.423097	+	0.926454i
$855$	−33.5821	−	33.3821i	−1.14848	−	1.14164i
$856$	6.50178	+	7.50345i	0.222226	+	0.256463i
$857$	15.4584	−	28.3100i	0.528050	−	0.967052i	−0.468452	−	0.883489i	$-0.655188\pi$
$857$	15.4584	−	28.3100i	0.528050	−	0.967052i	0.996502	−	0.0835632i	$-0.0266301\pi$
$858$	0.131542	−	1.85165i	0.00449076	−	0.0632144i
$859$	13.1747	+	6.01670i	0.449516	+	0.205287i	0.627293	−	0.778784i	$-0.284163\pi$
$859$	13.1747	+	6.01670i	0.449516	+	0.205287i	−0.177776	+	0.984071i	$0.556890\pi$
$860$	−3.78533	+	0.552090i	−0.129079	+	0.0188261i
$861$	−55.3097	+	16.2692i	−1.88495	+	0.554452i
$862$	−0.0780284	+	0.104234i	−0.00265766	+	0.00355022i
$863$	−9.81927	+	13.1170i	−0.334252	+	0.446508i	−0.935907	−	0.352248i	$-0.885417\pi$
$863$	−9.81927	+	13.1170i	−0.334252	+	0.446508i	0.601655	+	0.798756i	$0.294508\pi$
$864$	1.45676	−	4.98777i	0.0495600	−	0.169687i
$865$	−23.2766	+	3.39490i	−0.791430	+	0.115430i
$866$	11.6303	+	5.31136i	0.395212	+	0.180487i
$867$	−40.4812	−	2.87579i	−1.37481	−	0.0976668i
$868$	2.81196	−	5.14971i	0.0954440	−	0.174793i
$869$	−12.2331	−	14.1178i	−0.414980	−	0.478912i
$870$	−12.4077	−	6.73480i	−0.420662	−	0.228331i
$871$	−0.709540	−	1.55368i	−0.0240418	−	0.0526443i
$872$	5.37832	+	7.18460i	0.182133	+	0.243301i
$873$	23.2143	−	5.07324i	0.785683	−	0.171703i
$874$	−12.5313	+	31.4474i	−0.423878	+	1.06373i
$875$	26.9946	+	17.1171i	0.912584	+	0.578664i
$876$	−20.5364	−	9.36678i	−0.693861	−	0.316474i
$877$	12.6567	−	33.9339i	0.427386	−	1.14587i	−0.527672	−	0.849448i	$-0.676935\pi$
$877$	12.6567	−	33.9339i	0.427386	−	1.14587i	0.955058	−	0.296418i	$-0.0957923\pi$
$878$	−10.9187	−	19.9961i	−0.368488	−	0.674835i
$879$	−38.3728	+	17.5465i	−1.29428	+	0.591828i
$880$	−2.64624	−	7.05113i	−0.0892049	−	0.237693i
$881$	−4.26709	+	6.63972i	−0.143762	+	0.223698i	−0.905666	−	0.423992i	$-0.860628\pi$
$881$	−4.26709	+	6.63972i	−0.143762	+	0.223698i	0.761904	+	0.647690i	$0.224265\pi$
$882$	0.745127	−	3.44116i	0.0250897	−	0.115870i
$883$	−1.42109	−	19.8694i	−0.0478234	−	0.668658i	−0.963664	−	0.267117i	$-0.913929\pi$
$883$	−1.42109	−	19.8694i	−0.0478234	−	0.668658i	0.915841	−	0.401541i	$-0.131525\pi$
$884$	1.70211	−	1.09388i	0.0572481	−	0.0367911i
$885$	−29.3211	+	25.5359i	−0.985619	+	0.858381i
$886$	0.0133323	+	0.0927284i	0.000447908	+	0.00311527i
$887$	−7.88929	+	36.2665i	−0.264896	+	1.21771i	0.631824	+	0.775112i	$0.282307\pi$
$887$	−7.88929	+	36.2665i	−0.264896	+	1.21771i	−0.896720	+	0.442597i	$0.854057\pi$
$888$	−3.35463	+	15.4566i	−0.112574	+	0.518689i
$889$	−4.56791	−	2.08610i	−0.153203	−	0.0699654i
$890$	13.4948	−	3.99218i	0.452346	−	0.133818i
$891$	−22.8710	+	19.8947i	−0.766207	+	0.666496i
$892$	−0.385665	+	5.39231i	−0.0129130	+	0.180548i
$893$	4.65053	+	8.51680i	0.155624	+	0.285004i
$894$	−2.17770	−	15.0949i	−0.0728331	−	0.504849i
$895$	−1.77991	+	25.6167i	−0.0594958	+	0.856273i
$896$			2.85896i			0.0955110i
$897$	2.64257	+	0.0574087i	0.0882329	+	0.00191682i
$898$	11.7964	−	11.7964i	0.393652	−	0.393652i
$899$	1.06465	−	7.40483i	0.0355082	−	0.246965i
$900$	0.0752359	+	14.9998i	0.00250786	+	0.499994i
$901$	−47.6083	−	13.9791i	−1.58606	−	0.465710i
$902$	−39.1140	−	2.79749i	−1.30235	−	0.0931461i
$903$	−5.99309	−	5.98735i	−0.199437	−	0.199247i
$904$	6.63381	−	10.3224i	0.220637	−	0.343318i
$905$	−5.97897	+	16.1301i	−0.198748	+	0.536183i
$906$	−23.6247	+	15.1987i	−0.784878	+	0.504942i
$907$	−20.1391	−	4.38100i	−0.668709	−	0.145469i	−0.134621	−	0.990897i	$-0.542982\pi$
$907$	−20.1391	−	4.38100i	−0.668709	−	0.145469i	−0.534089	+	0.845428i	$0.679345\pi$
$908$	−7.79872	+	10.4179i	−0.258809	+	0.345729i
$909$	3.71689	−	8.15952i	0.123281	−	0.270634i
$910$	0.285413	−	2.01410i	0.00946136	−	0.0667666i
$911$	34.9623	+	30.2950i	1.15835	+	1.00372i	0.999866	+	0.0163579i	$0.00520711\pi$
$911$	34.9623	+	30.2950i	1.15835	+	1.00372i	0.158487	+	0.987361i	$0.449338\pi$
$912$	0.878032	+	12.1944i	0.0290745	+	0.403798i
$913$	37.5850	−	8.17612i	1.24388	−	0.270590i
$914$	−16.6639	+	4.89295i	−0.551192	+	0.161845i
$915$	11.2625	−	38.7155i	0.372327	−	1.27990i
$916$	15.2441	+	4.47607i	0.503679	+	0.147893i
$917$	42.6616	+	15.9120i	1.40881	+	0.525459i
$918$	−32.2948	−	6.97673i	−1.06589	−	0.230266i
$919$			36.4264i			1.20160i	0.799400	+	0.600799i	$0.205151\pi$
$919$			36.4264i			1.20160i	−0.799400	+	0.600799i	$0.794849\pi$
$920$	9.84258	−	4.25717i	0.324500	−	0.140355i
$921$	1.09334	−	3.73017i	0.0360267	−	0.122913i
$922$	26.3249	−	19.7066i	0.866964	−	0.649001i
$923$	1.15676	−	3.10138i	0.0380751	−	0.102083i
$924$	9.01032	−	14.0351i	0.296418	−	0.461721i
$925$	−3.44200	−	45.5282i	−0.113172	−	1.49696i
$926$	7.23769	+	24.6493i	0.237845	+	0.810027i
$927$	12.5493	−	33.7447i	0.412173	−	1.10832i
$928$	1.27386	+	3.41535i	0.0418164	+	0.112114i
$929$	−38.4073	+	44.3244i	−1.26010	+	1.45424i	−0.424005	+	0.905660i	$0.639376\pi$
$929$	−38.4073	+	44.3244i	−1.26010	+	1.45424i	−0.836100	+	0.548578i	$0.815169\pi$
$930$	−7.44036	+	2.79639i	−0.243979	+	0.0916971i
$931$	1.17898	+	8.19999i	0.0386395	+	0.268744i
$932$	2.81327	+	2.10599i	0.0921517	+	0.0689839i
$933$	20.1299	−	36.9071i	0.659022	−	1.20828i
$934$	1.08720	+	0.942063i	0.0355742	+	0.0308253i
$935$	−43.5201	+	19.9818i	−1.42326	+	0.653474i
$936$	0.867964	−	0.397391i	0.0283703	−	0.0129891i
$937$	−1.03478	−	0.565031i	−0.0338047	−	0.0184588i	0.462258	−	0.886746i	$-0.347039\pi$
$937$	−1.03478	−	0.565031i	−0.0338047	−	0.0184588i	−0.496062	+	0.868287i	$0.665221\pi$
$938$	1.09478	−	15.3070i	0.0357457	−	0.499790i
$939$	35.4084	+	22.7317i	1.15551	+	0.741820i
$940$	0.860056	−	2.95122i	0.0280519	−	0.0962582i
$941$	18.3827	+	2.64304i	0.599260	+	0.0861606i	0.435268	−	0.900301i	$-0.356654\pi$
$941$	18.3827	+	2.64304i	0.599260	+	0.0861606i	0.163992	+	0.986462i	$0.447563\pi$
$942$	5.90469	+	10.8013i	0.192385	+	0.351927i
$943$	1.23946	−	55.8225i	0.0403625	−	1.81783i
$944$	10.0393			0.326751
$945$	−26.5233	+	19.9989i	−0.862803	+	0.650564i
$946$	−2.39364	−	5.24134i	−0.0778239	−	0.170411i
$947$	24.2936	−	13.2653i	0.789437	−	0.431065i	−0.0333295	−	0.999444i	$-0.510611\pi$
$947$	24.2936	−	13.2653i	0.789437	−	0.431065i	0.822767	+	0.568379i	$0.192429\pi$
$948$	3.35279	−	9.00234i	0.108894	−	0.292382i
$949$	−1.16827	−	3.97878i	−0.0379238	−	0.129157i
$950$	−12.4679	−	33.0178i	−0.404511	−	1.07124i
$951$	−22.8579	+	26.4049i	−0.741217	+	0.856238i
$952$	18.1324	−	1.29686i	0.587675	−	0.0420313i
$953$	−34.1856	−	7.43661i	−1.10738	−	0.240896i	−0.378543	−	0.925584i	$-0.623575\pi$
$953$	−34.1856	−	7.43661i	−1.10738	−	0.240896i	−0.728836	+	0.684688i	$0.759938\pi$
$954$	−21.3040	−	9.70458i	−0.689743	−	0.314197i
$955$	−0.648138	+	0.142372i	−0.0209733	+	0.00460704i
$956$	−13.4503	−	20.9291i	−0.435015	−	0.676897i
$957$	4.51026	−	20.7812i	0.145796	−	0.671761i
$958$	−1.53817	−	4.12400i	−0.0496961	−	0.133240i
$959$	−40.5750	−	26.0760i	−1.31024	−	0.842038i
$960$	2.52892	−	2.93336i	0.0816204	−	0.0946737i
$961$	17.5425	+	20.2451i	0.565886	+	0.653067i
$962$	−2.55029	+	1.39256i	−0.0822245	+	0.0448980i
$963$	23.8274	−	17.8726i	0.767827	−	0.575936i
$964$	−20.4860	−	2.94544i	−0.659810	−	0.0948663i
$965$	−6.92396	+	8.02352i	−0.222890	+	0.258286i
$966$	20.5913	+	11.8314i	0.662513	+	0.380668i
$967$	−16.3332	−	16.3332i	−0.525242	−	0.525242i	0.393908	−	0.919150i	$-0.371123\pi$
$967$	−16.3332	−	16.3332i	−0.525242	−	0.525242i	−0.919150	+	0.393908i	$0.871123\pi$
$968$	0.275549	−	0.206273i	0.00885648	−	0.00662988i
$969$	76.9426	−	11.1003i	2.47175	−	0.356592i
$970$	17.3141	+	3.72967i	0.555922	+	0.119753i
$971$	−30.0556	+	26.0433i	−0.964529	+	0.835769i	−0.986462	−	0.163990i	$-0.947563\pi$
$971$	−30.0556	+	26.0433i	−0.964529	+	0.835769i	0.0219328	+	0.999759i	$0.493018\pi$
$972$	−14.6186	−	5.41262i	−0.468892	−	0.173610i
$973$	42.8555	−	9.32264i	1.37388	−	0.298870i
$974$	−2.98676	+	6.54008i	−0.0957018	+	0.209558i
$975$	−2.07443	+	1.81404i	−0.0664348	+	0.0580959i
$976$	−8.75803	+	5.62844i	−0.280338	+	0.180162i
$977$	−7.80938	−	5.84603i	−0.249844	−	0.187031i	0.467014	−	0.884250i	$-0.345330\pi$
$977$	−7.80938	−	5.84603i	−0.249844	−	0.187031i	−0.716858	+	0.697219i	$0.754421\pi$
$978$	11.8225	+	15.7772i	0.378040	+	0.504499i
$979$	11.4603	+	17.8325i	0.366271	+	0.569930i
$980$	1.56843	−	2.10407i	0.0501018	−	0.0672120i
$981$	22.6360	−	14.5779i	0.722711	−	0.465437i
$982$	3.17322	+	14.5871i	0.101262	+	0.465492i
$983$	−31.8947	−	17.4158i	−1.01728	−	0.555479i	−0.118077	−	0.993004i	$-0.537673\pi$
$983$	−31.8947	−	17.4158i	−1.01728	−	0.555479i	−0.899206	+	0.437526i	$0.855855\pi$
$984$	−8.38592	−	18.3394i	−0.267333	−	0.584637i
$985$	−27.2629	+	17.5991i	−0.868669	+	0.560753i
$986$	21.0834	−	9.62845i	0.671431	−	0.306632i
$987$	6.37711	−	2.38202i	0.202986	−	0.0758205i
$988$	−1.58823	+	1.58823i	−0.0505283	+	0.0505283i
$989$	7.28645	−	3.77119i	0.231696	−	0.119917i
$990$	−21.6597	+	6.43019i	−0.688390	+	0.204365i
$991$	0.896667	−	6.23646i	0.0284836	−	0.198108i	−0.970611	−	0.240654i	$-0.922638\pi$
$991$	0.896667	−	6.23646i	0.0284836	−	0.198108i	0.999094	+	0.0425466i	$0.0135471\pi$
$992$	1.92290	+	0.717203i	0.0610520	+	0.0227712i
$993$	0.540423	+	2.47857i	0.0171498	+	0.0786550i
$994$	22.4760	−	19.4756i	0.712897	−	0.617728i
$995$	−7.89678	−	21.0416i	−0.250345	−	0.667064i
$996$	12.9604	+	14.9426i	0.410665	+	0.473475i
$997$	8.32317	−	3.10438i	0.263598	−	0.0983168i	−0.214191	−	0.976792i	$-0.568711\pi$
$997$	8.32317	−	3.10438i	0.263598	−	0.0983168i	0.477788	+	0.878475i	$0.341439\pi$
$998$	10.7075	−	0.765816i	0.338940	−	0.0242415i
$999$	45.5465	+	13.3026i	1.44103	+	0.420876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.19	✓	960
3.2	odd	2	inner	690.2.x.a.77.36	yes	960
5.3	odd	4	inner	690.2.x.a.353.19	yes	960
15.8	even	4	inner	690.2.x.a.353.26	yes	960
23.3	even	11	inner	690.2.x.a.647.26	yes	960
69.26	odd	22	inner	690.2.x.a.647.19	yes	960
115.3	odd	44	inner	690.2.x.a.233.36	yes	960
345.233	even	44	inner	690.2.x.a.233.19	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.19	✓	960	1.1	even	1	trivial
690.2.x.a.77.36	yes	960	3.2	odd	2	inner
690.2.x.a.233.19	yes	960	345.233	even	44	inner
690.2.x.a.233.36	yes	960	115.3	odd	44	inner
690.2.x.a.353.19	yes	960	5.3	odd	4	inner
690.2.x.a.353.26	yes	960	15.8	even	4	inner
690.2.x.a.647.19	yes	960	69.26	odd	22	inner
690.2.x.a.647.26	yes	960	23.3	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(1.03732 - 1.38707i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.58434 + 1.57793i) q^{5} +(-1.73205 + 0.000829396i) q^{6} +(-0.607715 - 2.79362i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.847954 - 2.87767i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(1.03732 - 1.38707i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.58434 + 1.57793i) q^{5} +(-1.73205 + 0.000829396i) q^{6} +(-0.607715 - 2.79362i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.847954 - 2.87767i) q^{9} +(0.313734 - 2.21395i) q^{10} +(3.33383 - 0.479333i) q^{11} +(1.03864 + 1.38608i) q^{12} +(-0.0676390 + 0.310931i) q^{13} +(-1.87222 + 2.16066i) q^{14} +(3.83217 - 0.560795i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-3.04731 + 5.58073i) q^{17} +(-1.79553 + 2.40334i) q^{18} +(1.98866 - 6.77276i) q^{19} +(-1.96037 + 1.07561i) q^{20} +(-4.50535 - 2.05492i) q^{21} +(-2.38162 - 2.38162i) q^{22} +(3.22028 - 3.55384i) q^{23} +(0.487179 - 1.66212i) q^{24} +(0.0202902 + 4.99996i) q^{25} +(0.289448 - 0.132186i) q^{26} +(-4.87114 - 1.80887i) q^{27} +(2.85167 + 0.203956i) q^{28} +(3.49752 - 1.02696i) q^{29} +(-2.74547 - 2.73174i) q^{30} +(0.852554 - 1.86683i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(2.79337 - 5.12150i) q^{33} +(6.29379 - 0.904911i) q^{34} +(3.44530 - 5.38499i) q^{35} +(3.00000 - 0.00287311i) q^{36} +(-9.10836 + 0.651443i) q^{37} +(-6.61363 + 2.46676i) q^{38} +(0.361122 + 0.416354i) q^{39} +(2.03588 + 0.924767i) q^{40} +(8.79895 - 7.62433i) q^{41} +(1.05491 + 4.83819i) q^{42} +(1.60290 + 0.597850i) q^{43} +(-0.479333 + 3.33383i) q^{44} +(3.19730 - 5.89723i) q^{45} +(-4.77484 - 0.448234i) q^{46} +(-0.972081 + 0.972081i) q^{47} +(-1.62255 + 0.606067i) q^{48} +(-1.06758 + 0.487546i) q^{49} +(3.99051 - 3.01261i) q^{50} +(4.57987 + 10.0158i) q^{51} +(-0.279280 - 0.152499i) q^{52} +(1.65874 + 7.62509i) q^{53} +(1.47109 + 4.98356i) q^{54} +(6.03829 + 4.50112i) q^{55} +(-1.54567 - 2.40511i) q^{56} +(-7.33145 - 9.78390i) q^{57} +(-2.91811 - 2.18447i) q^{58} +(-8.44559 + 5.42765i) q^{59} +(-0.541567 + 3.83493i) q^{60} +(4.32476 - 9.46990i) q^{61} +(-2.00539 + 0.436247i) q^{62} +(-7.52380 + 4.11766i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-0.597791 + 0.385893i) q^{65} +(-5.77397 + 0.832994i) q^{66} +(-4.29708 + 3.21675i) q^{67} +(-4.49615 - 4.49615i) q^{68} +(-1.58899 - 8.15323i) q^{69} +(-6.37560 + 0.468996i) q^{70} +(-10.2965 - 1.48042i) q^{71} +(-1.80013 - 2.39990i) q^{72} +(-11.4377 + 6.24546i) q^{73} +(5.97994 + 6.90122i) q^{74} +(6.95637 + 5.15839i) q^{75} +(5.93814 + 3.81621i) q^{76} +(-3.36509 - 9.02217i) q^{77} +(0.116896 - 0.538605i) q^{78} +(-2.99854 - 4.66582i) q^{79} +(-0.479743 - 2.18400i) q^{80} +(-7.56195 + 4.88026i) q^{81} +(-11.3766 - 2.47483i) q^{82} +(11.3910 - 0.814697i) q^{83} +(3.24099 - 3.74392i) q^{84} +(-13.6340 + 4.03337i) q^{85} +(-0.481977 - 1.64146i) q^{86} +(2.20355 - 5.91661i) q^{87} +(2.95612 - 1.61417i) q^{88} +(2.61445 + 5.72485i) q^{89} +(-6.63704 + 0.974504i) q^{90} +0.909730 q^{91} +(2.50262 + 4.09107i) q^{92} +(-1.70507 - 3.11905i) q^{93} +(1.36074 + 0.195644i) q^{94} +(13.8376 - 7.59241i) q^{95} +(1.45754 + 0.935720i) q^{96} +(-0.565057 + 7.90053i) q^{97} +(1.03007 + 0.562463i) q^{98} +(-4.20630 - 9.18721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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