LMFDB - Embedded newform 980.2.s.g.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(19,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("980.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	980.19
Dual form			980.2.s.g.619.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.01395 + 0.985849i) q^{2} +(0.366665 - 0.211694i) q^{3} +(0.0562045 - 1.99921i) q^{4} +(2.08328 - 0.812373i) q^{5} +(-0.163083 + 0.576124i) q^{6} +(1.91393 + 2.08252i) q^{8} +(-1.41037 + 2.44283i) q^{9} +(-1.31147 + 2.87751i) q^{10} +(-4.23964 + 2.44776i) q^{11} +(-0.402613 - 0.744938i) q^{12} -2.54664 q^{13} +(0.591890 - 0.738886i) q^{15} +(-3.99368 - 0.224729i) q^{16} +(-2.55715 - 4.42911i) q^{17} +(-0.978214 - 3.86733i) q^{18} +(-3.13300 + 5.42652i) q^{19} +(-1.50701 - 4.21057i) q^{20} +(1.88568 - 6.66155i) q^{22} +(-2.31555 + 4.01064i) q^{23} +(1.14263 + 0.358418i) q^{24} +(3.68010 - 3.38480i) q^{25} +(2.58218 - 2.51060i) q^{26} +2.46443i q^{27} -1.88958 q^{29} +(0.128280 + 1.33271i) q^{30} +(0.738782 + 1.27961i) q^{31} +(4.27096 - 3.70930i) q^{32} +(-1.03635 + 1.79501i) q^{33} +(6.95926 + 1.96995i) q^{34} +(4.80447 + 2.95693i) q^{36} +(-2.04313 - 1.17960i) q^{37} +(-2.17301 - 8.59091i) q^{38} +(-0.933764 + 0.539109i) q^{39} +(5.67903 + 2.78364i) q^{40} +7.05393i q^{41} -10.7790 q^{43} +(4.65529 + 8.61350i) q^{44} +(-0.953704 + 6.23485i) q^{45} +(-1.60603 - 6.34939i) q^{46} +(10.5781 + 6.10725i) q^{47} +(-1.51192 + 0.763038i) q^{48} +(-0.394553 + 7.06005i) q^{50} +(-1.87523 - 1.08267i) q^{51} +(-0.143133 + 5.09127i) q^{52} +(1.93661 - 1.11810i) q^{53} +(-2.42956 - 2.49882i) q^{54} +(-6.84386 + 8.54352i) q^{55} +2.65295i q^{57} +(1.91594 - 1.86284i) q^{58} +(2.84500 + 4.92768i) q^{59} +(-1.44392 - 1.22484i) q^{60} +(3.35156 + 1.93502i) q^{61} +(-2.01059 - 0.569136i) q^{62} +(-0.673743 + 7.97158i) q^{64} +(-5.30536 + 2.06882i) q^{65} +(-0.718799 - 2.84174i) q^{66} +(-0.444655 - 0.770165i) q^{67} +(-8.99844 + 4.86334i) q^{68} +1.96075i q^{69} -14.3310i q^{71} +(-7.78659 + 1.73829i) q^{72} +(-3.93594 - 6.81724i) q^{73} +(3.23454 - 0.818154i) q^{74} +(0.632822 - 2.02014i) q^{75} +(10.6727 + 6.56853i) q^{76} +(0.415314 - 1.46718i) q^{78} +(4.01812 + 2.31987i) q^{79} +(-8.50252 + 2.77619i) q^{80} +(-3.70941 - 6.42488i) q^{81} +(-6.95411 - 7.15236i) q^{82} +4.32876i q^{83} +(-8.92534 - 7.14971i) q^{85} +(10.9294 - 10.6264i) q^{86} +(-0.692841 + 0.400012i) q^{87} +(-13.2119 - 4.14428i) q^{88} +(-1.89013 - 1.09127i) q^{89} +(-5.17961 - 7.26206i) q^{90} +(7.88798 + 4.85468i) q^{92} +(0.541770 + 0.312791i) q^{93} +(-16.7465 + 4.23590i) q^{94} +(-2.11856 + 13.8501i) q^{95} +(0.780773 - 2.26421i) q^{96} -3.42330 q^{97} -13.8090i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 16 q^{4} + 64 q^{9} - 16 q^{16} + 16 q^{25} - 96 q^{29} + 8 q^{30} + 352 q^{36} + 48 q^{44} + 32 q^{46} + 64 q^{50} - 24 q^{60} - 160 q^{64} + 16 q^{65} + 112 q^{74} + 48 q^{81} - 128 q^{85} + 112 q^{86}+O(q^{100}) $ 96 * q - 16 * q^4 + 64 * q^9 - 16 * q^16 + 16 * q^25 - 96 * q^29 + 8 * q^30 + 352 * q^36 + 48 * q^44 + 32 * q^46 + 64 * q^50 - 24 * q^60 - 160 * q^64 + 16 * q^65 + 112 * q^74 + 48 * q^81 - 128 * q^85 + 112 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−1.01395	+	0.985849i	−0.716974	+	0.697100i
$2$	−1.01395	+	0.985849i	−0.716974	+	0.697100i
$3$	0.366665	−	0.211694i	0.211694	−	0.122222i	−0.390404	−	0.920643i	$-0.627665\pi$
$3$	0.366665	−	0.211694i	0.211694	−	0.122222i	0.602098	+	0.798422i	$0.294331\pi$
$4$	0.0562045	−	1.99921i	0.0281022	−	0.999605i
$5$	2.08328	−	0.812373i	0.931671	−	0.363304i
$5$	2.08328	−	0.812373i	0.931671	−	0.363304i
$6$	−0.163083	+	0.576124i	−0.0665783	+	0.235202i
$7$		0			0
$7$		0			0
$8$	1.91393	+	2.08252i	0.676676	+	0.736280i
$9$	−1.41037	+	2.44283i	−0.470124	+	0.814278i
$10$	−1.31147	+	2.87751i	−0.414724	+	0.909947i
$11$	−4.23964	+	2.44776i	−1.27830	+	0.738026i	−0.976535	−	0.215357i	$-0.930909\pi$
$11$	−4.23964	+	2.44776i	−1.27830	+	0.738026i	−0.301763	+	0.953383i	$0.597575\pi$
$12$	−0.402613	−	0.744938i	−0.116224	−	0.215045i
$13$	−2.54664			−0.706311			−0.353156	−	0.935565i	$-0.614891\pi$
$13$	−2.54664			−0.706311			−0.353156	+	0.935565i	$0.614891\pi$
$14$		0			0
$15$	0.591890	−	0.738886i	0.152825	−	0.190780i
$16$	−3.99368	−	0.224729i	−0.998421	−	0.0561823i
$17$	−2.55715	−	4.42911i	−0.620199	−	1.07422i	−0.989448	−	0.144886i	$-0.953718\pi$
$17$	−2.55715	−	4.42911i	−0.620199	−	1.07422i	0.369249	−	0.929330i	$-0.379615\pi$
$18$	−0.978214	−	3.86733i	−0.230567	−	0.911539i
$19$	−3.13300	+	5.42652i	−0.718760	+	1.24493i	0.242731	+	0.970094i	$0.421957\pi$
$19$	−3.13300	+	5.42652i	−0.718760	+	1.24493i	−0.961491	+	0.274836i	$0.911377\pi$
$20$	−1.50701	−	4.21057i	−0.336979	−	0.941512i
$21$		0			0
$22$	1.88568	−	6.66155i	0.402028	−	1.42025i
$23$	−2.31555	+	4.01064i	−0.482825	+	0.836277i	−0.999806	−	0.0197200i	$-0.993723\pi$
$23$	−2.31555	+	4.01064i	−0.482825	+	0.836277i	0.516981	+	0.855997i	$0.327056\pi$
$24$	1.14263	+	0.358418i	0.233238	+	0.0731617i
$25$	3.68010	−	3.38480i	0.736020	−	0.676960i
$26$	2.58218	−	2.51060i	0.506407	−	0.492370i
$27$			2.46443i			0.474280i
$28$		0			0
$29$	−1.88958			−0.350886			−0.175443	−	0.984490i	$-0.556136\pi$
$29$	−1.88958			−0.350886			−0.175443	+	0.984490i	$0.556136\pi$
$30$	0.128280	+	1.33271i	0.0234207	+	0.243319i
$31$	0.738782	+	1.27961i	0.132689	+	0.229824i	0.924712	−	0.380667i	$-0.124305\pi$
$31$	0.738782	+	1.27961i	0.132689	+	0.229824i	−0.792023	+	0.610491i	$0.790972\pi$
$32$	4.27096	−	3.70930i	0.755006	−	0.655718i
$33$	−1.03635	+	1.79501i	−0.180405	+	0.312471i
$34$	6.95926	+	1.96995i	1.19350	+	0.337844i
$35$		0			0
$36$	4.80447	+	2.95693i	0.800745	+	0.492821i
$37$	−2.04313	−	1.17960i	−0.335888	−	0.193925i	0.322564	−	0.946548i	$-0.395455\pi$
$37$	−2.04313	−	1.17960i	−0.335888	−	0.193925i	−0.658452	+	0.752623i	$0.728789\pi$
$38$	−2.17301	−	8.59091i	−0.352509	−	1.39363i
$39$	−0.933764	+	0.539109i	−0.149522	+	0.0863265i
$40$	5.67903	+	2.78364i	0.897933	+	0.440131i
$41$			7.05393i			1.10164i	0.834624	+	0.550819i	$0.185685\pi$
$41$			7.05393i			1.10164i	−0.834624	+	0.550819i	$0.814315\pi$
$42$		0			0
$43$	−10.7790			−1.64378			−0.821890	−	0.569646i	$-0.807080\pi$
$43$	−10.7790			−1.64378			−0.821890	+	0.569646i	$0.807080\pi$
$44$	4.65529	+	8.61350i	0.701812	+	1.29853i
$45$	−0.953704	+	6.23485i	−0.142170	+	0.929437i
$46$	−1.60603	−	6.34939i	−0.236796	−	0.936166i
$47$	10.5781	+	6.10725i	1.54297	+	0.890834i	0.998649	+	0.0519561i	$0.0165456\pi$
$47$	10.5781	+	6.10725i	1.54297	+	0.890834i	0.544320	+	0.838878i	$0.316788\pi$
$48$	−1.51192	+	0.763038i	−0.218226	+	0.110135i
$49$		0			0
$50$	−0.394553	+	7.06005i	−0.0557982	+	0.998442i
$51$	−1.87523	−	1.08267i	−0.262585	−	0.151603i
$52$	−0.143133	+	5.09127i	−0.0198489	+	0.706032i
$53$	1.93661	−	1.11810i	0.266014	−	0.153583i	−0.361061	−	0.932542i	$-0.617585\pi$
$53$	1.93661	−	1.11810i	0.266014	−	0.153583i	0.627075	+	0.778959i	$0.284252\pi$
$54$	−2.42956	−	2.49882i	−0.330621	−	0.340046i
$55$	−6.84386	+	8.54352i	−0.922825	+	1.15201i
$56$		0			0
$57$			2.65295i			0.351392i
$58$	1.91594	−	1.86284i	0.251576	−	0.244602i
$59$	2.84500	+	4.92768i	0.370387	+	0.641529i	0.989625	−	0.143674i	$-0.0458917\pi$
$59$	2.84500	+	4.92768i	0.370387	+	0.641529i	−0.619238	+	0.785203i	$0.712558\pi$
$60$	−1.44392	−	1.22484i	−0.186410	−	0.158126i
$61$	3.35156	+	1.93502i	0.429123	+	0.247754i	0.698973	−	0.715148i	$-0.253641\pi$
$61$	3.35156	+	1.93502i	0.429123	+	0.247754i	−0.269850	+	0.962902i	$0.586974\pi$
$62$	−2.01059	−	0.569136i	−0.255345	−	0.0722803i
$63$		0			0
$64$	−0.673743	+	7.97158i	−0.0842179	+	0.996447i
$65$	−5.30536	+	2.06882i	−0.658049	+	0.256606i
$66$	−0.718799	−	2.84174i	−0.0884780	−	0.349794i
$67$	−0.444655	−	0.770165i	−0.0543232	−	0.0940906i	0.837585	−	0.546307i	$-0.183967\pi$
$67$	−0.444655	−	0.770165i	−0.0543232	−	0.0940906i	−0.891908	+	0.452216i	$0.850633\pi$
$68$	−8.99844	+	4.86334i	−1.09122	+	0.589766i
$69$			1.96075i			0.236046i
$70$		0			0
$71$		−	14.3310i		−	1.70078i	−0.526152	−	0.850391i	$-0.676366\pi$
$71$		−	14.3310i		−	1.70078i	0.526152	−	0.850391i	$-0.323634\pi$
$72$	−7.78659	+	1.73829i	−0.917659	+	0.204860i
$73$	−3.93594	−	6.81724i	−0.460667	−	0.797898i	0.538328	−	0.842736i	$-0.319056\pi$
$73$	−3.93594	−	6.81724i	−0.460667	−	0.797898i	−0.998994	+	0.0448377i	$0.985723\pi$
$74$	3.23454	−	0.818154i	0.376008	−	0.0951085i
$75$	0.632822	−	2.02014i	0.0730720	−	0.233266i
$76$	10.6727	+	6.56853i	1.22424	+	0.753462i
$77$		0			0
$78$	0.415314	−	1.46718i	0.0470250	−	0.166126i
$79$	4.01812	+	2.31987i	0.452074	+	0.261005i	0.708706	−	0.705504i	$-0.249279\pi$
$79$	4.01812	+	2.31987i	0.452074	+	0.261005i	−0.256632	+	0.966509i	$0.582613\pi$
$80$	−8.50252	+	2.77619i	−0.950610	+	0.310387i
$81$	−3.70941	−	6.42488i	−0.412156	−	0.713876i
$82$	−6.95411	−	7.15236i	−0.767953	−	0.789846i
$83$			4.32876i			0.475143i	0.971370	+	0.237571i	$0.0763514\pi$
$83$			4.32876i			0.475143i	−0.971370	+	0.237571i	$0.923649\pi$
$84$		0			0
$85$	−8.92534	−	7.14971i	−0.968089	−	0.775495i
$86$	10.9294	−	10.6264i	1.17855	−	1.14588i
$87$	−0.692841	+	0.400012i	−0.0742804	+	0.0428858i
$88$	−13.2119	−	4.14428i	−1.40839	−	0.441782i
$89$	−1.89013	−	1.09127i	−0.200354	−	0.115674i	0.396467	−	0.918049i	$-0.370236\pi$
$89$	−1.89013	−	1.09127i	−0.200354	−	0.115674i	−0.596820	+	0.802375i	$0.703570\pi$
$90$	−5.17961	−	7.26206i	−0.545979	−	0.765488i
$91$		0			0
$92$	7.88798	+	4.85468i	0.822378	+	0.506135i
$93$	0.541770	+	0.312791i	0.0561790	+	0.0324349i
$94$	−16.7465	+	4.23590i	−1.72727	+	0.436900i
$95$	−2.11856	+	13.8501i	−0.217360	+	1.42099i
$96$	0.780773	−	2.26421i	0.0796873	−	0.231090i
$97$	−3.42330			−0.347584			−0.173792	−	0.984782i	$-0.555602\pi$
$97$	−3.42330			−0.347584			−0.173792	+	0.984782i	$0.555602\pi$
$98$		0			0
$99$		−	13.8090i		−	1.38785i
$100$	−6.56008	−	7.54754i	−0.656008	−	0.754754i
$101$	6.32803	−	3.65349i	0.629663	−	0.363536i	−0.150959	−	0.988540i	$-0.548236\pi$
$101$	6.32803	−	3.65349i	0.629663	−	0.363536i	0.780621	+	0.625004i	$0.214903\pi$
$102$	2.96874	−	0.750922i	0.293949	−	0.0743524i
$103$	−5.84630	−	3.37536i	−0.576053	−	0.332584i	0.183510	−	0.983018i	$-0.441254\pi$
$103$	−5.84630	−	3.37536i	−0.576053	−	0.332584i	−0.759563	+	0.650434i	$0.774587\pi$
$104$	−4.87409	−	5.30342i	−0.477944	−	0.520043i
$105$		0			0
$106$	−0.861354	+	3.04291i	−0.0836621	+	0.295554i
$107$	4.91497	−	8.51298i	0.475148	−	0.822980i	−0.524447	−	0.851443i	$-0.675728\pi$
$107$	4.91497	−	8.51298i	0.475148	−	0.822980i	0.999595	+	0.0284627i	$0.00906119\pi$
$108$	4.92692	+	0.138512i	0.474093	+	0.0133283i
$109$	4.70610	+	8.15121i	0.450763	+	0.780744i	0.998434	−	0.0559497i	$-0.0178186\pi$
$109$	4.70610	+	8.15121i	0.450763	+	0.780744i	−0.547671	+	0.836694i	$0.684485\pi$
$110$	−1.48327	−	15.4097i	−0.141424	−	1.46926i
$111$	−0.998857			−0.0948073
$112$		0			0
$113$			15.9261i			1.49820i	0.662455	+	0.749102i	$0.269515\pi$
$113$			15.9261i			1.49820i	−0.662455	+	0.749102i	$0.730485\pi$
$114$	−2.61541	−	2.68997i	−0.244956	−	0.251939i
$115$	−1.56579	+	10.2364i	−0.146011	+	0.954547i
$116$	−0.106203	+	3.77766i	−0.00986067	+	0.350747i
$117$	3.59171	−	6.22102i	0.332054	−	0.575134i
$118$	−7.74264	−	2.19170i	−0.712768	−	0.201763i
$119$		0			0
$120$	2.67158	−	0.181555i	0.243881	−	0.0165736i
$121$	6.48302	−	11.2289i	0.589365	−	1.02081i
$122$	−5.30597	+	1.34211i	−0.480380	+	0.121509i
$123$	1.49327	+	2.58643i	0.134644	+	0.233210i
$124$	2.59973	−	1.40506i	0.233462	−	0.126178i
$125$	4.91696	−	10.0411i	0.439786	−	0.898103i
$126$		0			0
$127$	−12.2192			−1.08428			−0.542138	−	0.840290i	$-0.682385\pi$
$127$	−12.2192			−1.08428			−0.542138	+	0.840290i	$0.682385\pi$
$128$	−7.17563	−	8.74702i	−0.634242	−	0.773135i
$129$	−3.95227	+	2.28185i	−0.347978	+	0.200905i
$130$	3.33985	−	7.32798i	0.292924	−	0.642706i
$131$	−4.92530	+	8.53087i	−0.430325	+	0.745345i	−0.996901	−	0.0786642i	$-0.974935\pi$
$131$	−4.92530	+	8.53087i	−0.430325	+	0.745345i	0.566576	+	0.824010i	$0.308268\pi$
$132$	3.53036	+	2.17277i	0.307278	+	0.189115i
$133$		0			0
$134$	1.21013	+	0.342549i	0.104539	+	0.0295917i
$135$	2.00204	+	5.13410i	0.172308	+	0.441873i
$136$	4.32949	−	13.8023i	0.371250	−	1.18354i
$137$	4.06585	−	2.34742i	0.347369	−	0.200554i	−0.316157	−	0.948707i	$-0.602393\pi$
$137$	4.06585	−	2.34742i	0.347369	−	0.200554i	0.663526	+	0.748153i	$0.269059\pi$
$138$	−1.93300	−	1.98811i	−0.164548	−	0.169239i
$139$	−13.8745			−1.17682			−0.588409	−	0.808564i	$-0.700245\pi$
$139$	−13.8745			−1.17682			−0.588409	+	0.808564i	$0.700245\pi$
$140$		0			0
$141$	5.17147			0.435516
$142$	14.1282	+	14.5310i	1.18562	+	1.21942i
$143$	10.7968	−	6.23356i	0.902877	−	0.521276i
$144$	6.18155	−	9.43895i	0.515129	−	0.786579i
$145$	−3.93652	+	1.53504i	−0.326910	+	0.127478i
$146$	10.7116	+	3.03213i	0.886501	+	0.250941i
$147$		0			0
$148$	−2.47310	+	4.01834i	−0.203288	+	0.330306i
$149$	2.73179	−	4.73161i	0.223797	−	0.387628i	−0.732161	−	0.681132i	$-0.761488\pi$
$149$	2.73179	−	4.73161i	0.223797	−	0.387628i	0.955958	+	0.293504i	$0.0948213\pi$
$150$	1.34990	+	2.67220i	0.110219	+	0.218184i
$151$	−1.29567	+	0.748053i	−0.105440	+	0.0608757i	−0.551793	−	0.833981i	$-0.686056\pi$
$151$	−1.29567	+	0.748053i	−0.105440	+	0.0608757i	0.446353	+	0.894857i	$0.352723\pi$
$152$	−17.2972	+	3.86145i	−1.40299	+	0.313205i
$153$	14.4261			1.16628
$154$		0			0
$155$	2.57861	+	2.06561i	0.207119	+	0.165914i
$156$	1.02531	+	1.89709i	0.0820905	+	0.151889i
$157$	11.4517	+	19.8350i	0.913948	+	1.58300i	0.808434	+	0.588587i	$0.200316\pi$
$157$	11.4517	+	19.8350i	0.913948	+	1.58300i	0.105515	+	0.994418i	$0.466351\pi$
$158$	−6.36123	+	1.60903i	−0.506072	+	0.128007i
$159$	0.473392	−	0.819938i	0.0375424	−	0.0650253i
$160$	5.88426	−	11.1971i	0.465192	−	0.885210i
$161$		0			0
$162$	10.0951	+	2.85762i	0.793148	+	0.224516i
$163$	−0.965256	+	1.67187i	−0.0756047	+	0.130951i	−0.901349	−	0.433093i	$-0.857422\pi$
$163$	−0.965256	+	1.67187i	−0.0756047	+	0.130951i	0.825744	+	0.564045i	$0.190755\pi$
$164$	14.1023	+	0.396462i	1.10120	+	0.0309585i
$165$	−0.700788	+	4.58141i	−0.0545563	+	0.356663i
$166$	−4.26750	−	4.38916i	−0.331222	−	0.340665i
$167$		−	16.9677i		−	1.31300i	−0.754327	−	0.656499i	$-0.772037\pi$
$167$		−	16.9677i		−	1.31300i	0.754327	−	0.656499i	$-0.227963\pi$
$168$		0			0
$169$	−6.51462			−0.501124
$170$	16.0984	−	1.54956i	1.23469	−	0.118846i
$171$	−8.83740	−	15.3068i	−0.675813	−	1.17054i
$172$	−0.605827	+	21.5495i	−0.0461939	+	1.64313i
$173$	−5.01816	+	8.69171i	−0.381524	+	0.660818i	−0.991280	−	0.131770i	$-0.957934\pi$
$173$	−5.01816	+	8.69171i	−0.381524	+	0.660818i	0.609757	+	0.792589i	$0.291267\pi$
$174$	0.308158	−	1.08863i	0.0233614	−	0.0825289i
$175$		0			0
$176$	17.4818	−	8.82279i	1.31774	−	0.665043i
$177$	2.08632	+	1.20454i	0.156818	+	0.0905386i
$178$	2.99233	−	0.756890i	0.224285	−	0.0567313i
$179$	−3.07683	+	1.77641i	−0.229973	+	0.132775i	−0.610560	−	0.791970i	$-0.709056\pi$
$179$	−3.07683	+	1.77641i	−0.229973	+	0.132775i	0.380586	+	0.924745i	$0.375722\pi$
$180$	12.4112	+	2.25708i	0.925075	+	0.168233i
$181$			22.2716i			1.65543i	0.561148	+	0.827716i	$0.310360\pi$
$181$			22.2716i			1.65543i	−0.561148	+	0.827716i	$0.689640\pi$
$182$		0			0
$183$	1.63853			0.121124
$184$	−12.7840	+	2.85393i	−0.942451	+	0.210395i
$185$	−5.21468	−	0.797654i	−0.383391	−	0.0586447i
$186$	−0.857695	+	0.216948i	−0.0628893	+	0.0159074i
$187$	21.6828	+	12.5185i	1.58560	+	0.915447i
$188$	12.8042	−	20.8045i	0.933843	−	1.51733i
$189$		0			0
$190$	−11.5060	−	16.1320i	−0.834733	−	1.17034i
$191$	−15.4551	−	8.92302i	−1.11829	−	0.645647i	−0.177328	−	0.984152i	$-0.556746\pi$
$191$	−15.4551	−	8.92302i	−1.11829	−	0.645647i	−0.940965	+	0.338505i	$0.890079\pi$
$192$	1.44050	+	3.06552i	0.103959	+	0.221235i
$193$	−15.7903	+	9.11654i	−1.13661	+	0.656223i	−0.945589	−	0.325363i	$-0.894513\pi$
$193$	−15.7903	+	9.11654i	−1.13661	+	0.656223i	−0.191022	+	0.981586i	$0.561180\pi$
$194$	3.47107	−	3.37486i	0.249208	−	0.242301i
$195$	−1.50733	+	1.88168i	−0.107942	+	0.134750i
$196$		0			0
$197$		−	11.3569i		−	0.809148i	−0.914505	−	0.404574i	$-0.867420\pi$
$197$		−	11.3569i		−	0.809148i	0.914505	−	0.404574i	$-0.132580\pi$
$198$	13.6136	+	14.0017i	0.967474	+	0.995055i
$199$	−4.51414	−	7.81873i	−0.319999	−	0.554255i	0.660488	−	0.750836i	$-0.270349\pi$
$199$	−4.51414	−	7.81873i	−0.319999	−	0.554255i	−0.980487	+	0.196581i	$0.937016\pi$
$200$	14.0924	+	1.18560i	0.996480	+	0.0838346i
$201$	−0.326079	−	0.188262i	−0.0229998	−	0.0132789i
$202$	−2.81454	+	9.94295i	−0.198030	+	0.699584i
$203$		0			0
$204$	−2.26987	+	3.68813i	−0.158923	+	0.258221i
$205$	5.73042	+	14.6953i	0.400230	+	1.02636i
$206$	9.25547	−	2.34110i	0.644859	−	0.163112i
$207$	−6.53156	−	11.3130i	−0.453975	−	0.786307i
$208$	10.1705	+	0.572304i	0.705196	+	0.0396822i
$209$		−	30.6753i		−	2.12186i
$210$		0			0
$211$			4.40164i			0.303021i	0.988456	+	0.151511i	$0.0484138\pi$
$211$			4.40164i			0.303021i	−0.988456	+	0.151511i	$0.951586\pi$
$212$	−2.12648	−	3.93454i	−0.146047	−	0.270225i
$213$	−3.03379	−	5.25469i	−0.207872	−	0.360045i
$214$	3.40896	+	13.4772i	0.233031	+	0.921281i
$215$	−22.4556	+	8.75655i	−1.53146	+	0.597192i
$216$	−5.13222	+	4.71675i	−0.349203	+	0.320934i
$217$		0			0
$218$	−12.8076	−	3.62544i	−0.867442	−	0.245546i
$219$	−2.88634	−	1.66643i	−0.195041	−	0.112607i
$220$	16.6956	+	14.1625i	1.12562	+	0.954835i
$221$	6.51214	+	11.2794i	0.438054	+	0.758731i
$222$	1.01279	−	0.984722i	0.0679743	−	0.0660902i
$223$			14.1103i			0.944899i	0.881358	+	0.472449i	$0.156630\pi$
$223$			14.1103i			0.944899i	−0.881358	+	0.472449i	$0.843370\pi$
$224$		0			0
$225$	3.07819	+	13.7637i	0.205213	+	0.917580i
$226$	−15.7008	−	16.1484i	−1.04440	−	1.07417i
$227$	9.52419	−	5.49880i	0.632143	−	0.364968i	−0.149439	−	0.988771i	$-0.547747\pi$
$227$	9.52419	−	5.49880i	0.632143	−	0.364968i	0.781582	+	0.623803i	$0.214413\pi$
$228$	5.30381	+	0.149108i	0.351253	+	0.00987490i
$229$	7.02292	+	4.05469i	0.464088	+	0.267941i	0.713762	−	0.700389i	$-0.246990\pi$
$229$	7.02292	+	4.05469i	0.464088	+	0.267941i	−0.249674	+	0.968330i	$0.580323\pi$
$230$	−8.50388	−	11.9228i	−0.560729	−	0.786169i
$231$		0			0
$232$	−3.61652	−	3.93507i	−0.237436	−	0.258350i
$233$	13.7475	+	7.93710i	0.900626	+	0.519977i	0.877403	−	0.479754i	$-0.159274\pi$
$233$	13.7475	+	7.93710i	0.900626	+	0.519977i	0.0232229	+	0.999730i	$0.492607\pi$
$234$	2.49116	+	9.84871i	0.162852	+	0.643831i
$235$	26.9984	+	4.12977i	1.76118	+	0.269396i
$236$	10.0114	−	5.41079i	0.651685	−	0.352213i
$237$	1.96441			0.127602
$238$		0			0
$239$			24.4934i			1.58435i	0.610295	+	0.792174i	$0.291051\pi$
$239$			24.4934i			1.58435i	−0.610295	+	0.792174i	$0.708949\pi$
$240$	−2.52987	+	2.81786i	−0.163303	+	0.181892i
$241$	16.6157	−	9.59308i	1.07031	−	0.617945i	0.142045	−	0.989860i	$-0.454632\pi$
$241$	16.6157	−	9.59308i	1.07031	−	0.617945i	0.928267	+	0.371916i	$0.121299\pi$
$242$	4.49653	+	17.7769i	0.289048	+	1.14274i
$243$	−9.12300	−	5.26717i	−0.585241	−	0.337889i
$244$	4.05689	−	6.59171i	0.259716	−	0.421991i
$245$		0			0
$246$	−4.06394	−	1.15038i	−0.259107	−	0.0733452i
$247$	7.97864	−	13.8194i	0.507668	−	0.879308i
$248$	−1.25083	+	3.98760i	−0.0794275	+	0.253213i
$249$	0.916372	+	1.58720i	0.0580727	+	0.100585i
$250$	4.91343	+	15.0286i	0.310753	+	0.950491i
$251$	21.1323			1.33386			0.666929	−	0.745121i	$-0.267608\pi$
$251$	21.1323			1.33386			0.666929	+	0.745121i	$0.267608\pi$
$252$		0			0
$253$		−	22.6716i		−	1.42535i
$254$	12.3897	−	12.0462i	0.777397	−	0.755848i
$255$	−4.78616	−	0.732107i	−0.299721	−	0.0458463i
$256$	15.8990	+	1.79499i	0.993687	+	0.112187i
$257$	12.8260	−	22.2153i	0.800064	−	1.38575i	−0.119509	−	0.992833i	$-0.538132\pi$
$257$	12.8260	−	22.2153i	0.800064	−	1.38575i	0.919573	−	0.392918i	$-0.128534\pi$
$258$	1.75787	−	6.21003i	0.109440	−	0.386620i
$259$		0			0
$260$	3.83783	+	10.7228i	0.238012	+	0.665001i
$261$	2.66501	−	4.61592i	0.164960	−	0.285719i
$262$	−3.41612	−	13.5055i	−0.211049	−	0.834373i
$263$	5.00988	+	8.67737i	0.308922	+	0.535069i	0.978127	−	0.208009i	$-0.0666983\pi$
$263$	5.00988	+	8.67737i	0.308922	+	0.535069i	−0.669204	+	0.743078i	$0.733365\pi$
$264$	−5.72164	+	1.27731i	−0.352143	+	0.0786130i
$265$	3.12619	−	3.90257i	0.192040	−	0.239733i
$266$		0			0
$267$	−0.924061			−0.0565516
$268$	−1.56471	+	0.845672i	−0.0955801	+	0.0516576i
$269$	11.8597	−	6.84723i	0.723102	−	0.417483i	−0.0927916	−	0.995686i	$-0.529579\pi$
$269$	11.8597	−	6.84723i	0.723102	−	0.417483i	0.815893	+	0.578203i	$0.196246\pi$
$270$	−7.09142	−	3.23203i	−0.431570	−	0.196695i
$271$	7.68044	−	13.3029i	0.466554	−	0.808095i	−0.532716	−	0.846294i	$-0.678829\pi$
$271$	7.68044	−	13.3029i	0.466554	−	0.808095i	0.999270	+	0.0381991i	$0.0121621\pi$
$272$	9.21708	+	18.2631i	0.558868	+	1.10736i
$273$		0			0
$274$	−1.80838	+	6.38849i	−0.109249	+	0.385943i
$275$	−7.31713	+	23.3583i	−0.441240	+	1.40856i
$276$	3.91995	+	0.110203i	0.235953	+	0.00663343i
$277$	−15.4230	+	8.90447i	−0.926678	+	0.535018i	−0.885759	−	0.464145i	$-0.846362\pi$
$277$	−15.4230	+	8.90447i	−0.926678	+	0.535018i	−0.0409188	+	0.999162i	$0.513028\pi$
$278$	14.0681	−	13.6781i	0.843747	−	0.820360i
$279$	−4.16783			−0.249521
$280$		0			0
$281$	29.6169			1.76680			0.883398	−	0.468624i	$-0.155250\pi$
$281$	29.6169			1.76680			0.883398	+	0.468624i	$0.155250\pi$
$282$	−5.24363	+	5.09829i	−0.312254	+	0.303599i
$283$	3.09887	−	1.78914i	0.184209	−	0.106353i	−0.405060	−	0.914290i	$-0.632749\pi$
$283$	3.09887	−	1.78914i	0.184209	−	0.106353i	0.589269	+	0.807937i	$0.299416\pi$
$284$	−28.6508	−	0.805468i	−1.70011	−	0.0477957i
$285$	2.15519	+	5.52684i	0.127662	+	0.327382i
$286$	−4.80215	+	16.9646i	−0.283957	+	1.00314i
$287$		0			0
$288$	3.03757	+	15.6647i	0.178991	+	0.923053i
$289$	−4.57800	+	7.92933i	−0.269294	+	0.466431i
$290$	2.47813	−	5.43727i	0.145521	−	0.319287i
$291$	−1.25520	+	0.724692i	−0.0735814	+	0.0424822i
$292$	−13.8503	+	7.48560i	−0.810528	+	0.438062i
$293$	−17.7739			−1.03836			−0.519180	−	0.854665i	$-0.673763\pi$
$293$	−17.7739			−1.03836			−0.519180	+	0.854665i	$0.673763\pi$
$294$		0			0
$295$	9.93004	+	7.95453i	0.578149	+	0.463131i
$296$	−1.45387	−	6.51252i	−0.0845043	−	0.378532i
$297$	−6.03233	−	10.4483i	−0.350031	−	0.606272i
$298$	1.89474	+	7.49077i	0.109759	+	0.433928i
$299$	5.89687	−	10.2137i	0.341025	−	0.590672i
$300$	−4.00312	−	1.37868i	−0.231120	−	0.0795984i
$301$		0			0
$302$	0.576278	−	2.03582i	0.0331611	−	0.117148i
$303$	1.54684	−	2.67921i	0.0888639	−	0.153917i
$304$	13.7317	−	20.9677i	0.787568	−	1.20258i
$305$	8.55419	+	1.30848i	0.489812	+	0.0749232i
$306$	−14.6274	+	14.2220i	−0.836193	+	0.813015i
$307$		−	32.8923i		−	1.87726i	−0.344923	−	0.938631i	$-0.612095\pi$
$307$		−	32.8923i		−	1.87726i	0.344923	−	0.938631i	$-0.387905\pi$
$308$		0			0
$309$	−2.85818			−0.162596
$310$	−4.65097	+	0.447680i	−0.264157	+	0.0254265i
$311$	9.93741	+	17.2121i	0.563499	+	0.976009i	0.997188	+	0.0749459i	$0.0238784\pi$
$311$	9.93741	+	17.2121i	0.563499	+	0.976009i	−0.433689	+	0.901063i	$0.642788\pi$
$312$	−2.90986	−	0.912761i	−0.164738	−	0.0516749i
$313$	3.18572	−	5.51783i	0.180068	−	0.311886i	−0.761836	−	0.647770i	$-0.775702\pi$
$313$	3.18572	−	5.51783i	0.180068	−	0.311886i	0.941903	+	0.335884i	$0.109035\pi$
$314$	−31.1658	−	8.82208i	−1.75879	−	0.497859i
$315$		0			0
$316$	4.86373	−	7.90269i	0.273606	−	0.444561i
$317$	−14.7244	−	8.50113i	−0.827004	−	0.477471i	0.0258220	−	0.999667i	$-0.491780\pi$
$317$	−14.7244	−	8.50113i	−0.827004	−	0.477471i	−0.852826	+	0.522196i	$0.825113\pi$
$318$	0.328338	+	1.29807i	0.0184123	+	0.0727923i
$319$	8.01112	−	4.62522i	0.448537	−	0.258963i
$320$	5.07230	+	17.1544i	0.283550	+	0.958957i
$321$		−	4.16188i		−	0.232293i
$322$		0			0
$323$	32.0462			1.78310
$324$	−13.0532	+	7.05478i	−0.725177	+	0.391932i
$325$	−9.37190	+	8.61987i	−0.519859	+	0.478144i
$326$	−0.669488	−	2.64680i	−0.0370795	−	0.146593i
$327$	3.45112	+	1.99251i	0.190848	+	0.110186i
$328$	−14.6899	+	13.5007i	−0.811115	+	0.745453i
$329$		0			0
$330$	−3.80601	−	5.33621i	−0.209514	−	0.293749i
$331$	12.6971	+	7.33065i	0.697893	+	0.402929i	0.806562	−	0.591149i	$-0.201326\pi$
$331$	12.6971	+	7.33065i	0.697893	+	0.402929i	−0.108669	+	0.994078i	$0.534659\pi$
$332$	8.65409	+	0.243295i	0.474955	+	0.0133526i
$333$	5.76313	−	3.32735i	0.315818	−	0.182338i
$334$	16.7276	+	17.2044i	0.915291	+	0.941385i
$335$	−1.55200	−	1.24324i	−0.0847949	−	0.0679256i
$336$		0			0
$337$			15.2435i			0.830368i	0.909738	+	0.415184i	$0.136283\pi$
$337$			15.2435i			0.830368i	−0.909738	+	0.415184i	$0.863717\pi$
$338$	6.60552	−	6.42243i	0.359293	−	0.349334i
$339$	3.37147	+	5.83955i	0.183113	+	0.317161i
$340$	−14.7954	+	17.4418i	−0.802394	+	0.945913i
$341$	−6.26433	−	3.61671i	−0.339233	−	0.195856i
$342$	24.0509	+	6.80807i	1.30052	+	0.368138i
$343$		0			0
$344$	−20.6302	−	22.4474i	−1.11231	−	1.21028i
$345$	1.59286	+	4.08479i	0.0857567	+	0.219918i
$346$	−3.48053	−	13.7601i	−0.187114	−	0.739750i
$347$	−16.7097	−	28.9420i	−0.897024	−	1.55369i	−0.831280	−	0.555854i	$-0.812391\pi$
$347$	−16.7097	−	28.9420i	−0.897024	−	1.55369i	−0.0657437	−	0.997837i	$-0.520942\pi$
$348$	0.760768	+	1.40762i	0.0407814	+	0.0754562i
$349$			16.1586i			0.864951i	0.901646	+	0.432476i	$0.142360\pi$
$349$			16.1586i			0.864951i	−0.901646	+	0.432476i	$0.857640\pi$
$350$		0			0
$351$		−	6.27603i		−	0.334990i
$352$	−9.02785	+	26.1804i	−0.481186	+	1.39542i
$353$	11.3427	+	19.6461i	0.603711	+	1.04566i	0.992254	+	0.124228i	$0.0396453\pi$
$353$	11.3427	+	19.6461i	0.603711	+	1.04566i	−0.388543	+	0.921431i	$0.627021\pi$
$354$	−3.30293	+	0.835451i	−0.175549	+	0.0444037i
$355$	−11.6421	−	29.8555i	−0.617901	−	1.58457i
$356$	−2.28791	+	3.71744i	−0.121259	+	0.197024i
$357$		0			0
$358$	1.36850	−	4.83449i	0.0723272	−	0.255511i
$359$	−14.5214	−	8.38391i	−0.766408	−	0.442486i	0.0651839	−	0.997873i	$-0.479237\pi$
$359$	−14.5214	−	8.38391i	−0.766408	−	0.442486i	−0.831592	+	0.555388i	$0.812570\pi$
$360$	−14.8095	+	9.94697i	−0.780529	+	0.524251i
$361$	−10.1314	−	17.5481i	−0.533233	−	0.923586i
$362$	−21.9564	−	22.5823i	−1.15400	−	1.18690i
$363$		−	5.48966i		−	0.288133i
$364$		0			0
$365$	−13.7378	−	11.0048i	−0.719069	−	0.576016i
$366$	−1.66139	+	1.61534i	−0.0868425	+	0.0844354i
$367$	−13.5474	+	7.82159i	−0.707168	+	0.408284i	−0.810012	−	0.586414i	$-0.800539\pi$
$367$	−13.5474	+	7.82159i	−0.707168	+	0.408284i	0.102844	+	0.994698i	$0.467206\pi$
$368$	10.1489	−	15.4969i	0.529046	−	0.807830i
$369$	−17.2316	−	9.94866i	−0.897041	−	0.517907i
$370$	6.07381	−	4.33210i	0.315762	−	0.225215i
$371$		0			0
$372$	0.655785	−	1.06553i	0.0340009	−	0.0552453i
$373$	−14.8129	−	8.55225i	−0.766985	−	0.442819i	0.0648133	−	0.997897i	$-0.479355\pi$
$373$	−14.8129	−	8.55225i	−0.766985	−	0.442819i	−0.831798	+	0.555079i	$0.812688\pi$
$374$	−34.3267	+	8.68269i	−1.77499	+	0.448971i
$375$	−0.322764	−	4.72261i	−0.0166675	−	0.243874i
$376$	7.52724	+	33.7178i	0.388188	+	1.73886i
$377$	4.81207			0.247834
$378$		0			0
$379$			10.3762i			0.532990i	0.963836	+	0.266495i	$0.0858655\pi$
$379$			10.3762i			0.532990i	−0.963836	+	0.266495i	$0.914134\pi$
$380$	27.5702	+	5.01389i	1.41432	+	0.257207i
$381$	−4.48034	+	2.58672i	−0.229535	+	0.132522i
$382$	24.4675	−	6.18888i	1.25187	−	0.316651i
$383$	−8.00016	−	4.61890i	−0.408789	−	0.236015i	0.281480	−	0.959567i	$-0.409175\pi$
$383$	−8.00016	−	4.61890i	−0.408789	−	0.236015i	−0.690269	+	0.723552i	$0.742508\pi$
$384$	−4.48274	−	1.68819i	−0.228759	−	0.0861500i
$385$		0			0
$386$	7.02311	−	24.8106i	0.357467	−	1.26283i
$387$	15.2024	−	26.3313i	0.772780	−	1.33849i
$388$	−0.192405	+	6.84390i	−0.00976787	+	0.347446i
$389$	−8.54214	−	14.7954i	−0.433104	−	0.750158i	0.564035	−	0.825751i	$-0.309248\pi$
$389$	−8.54214	−	14.7954i	−0.433104	−	0.750158i	−0.997139	+	0.0755930i	$0.975915\pi$
$390$	−0.326684	−	3.39394i	−0.0165423	−	0.171859i
$391$	23.6848			1.19779
$392$		0			0
$393$			4.17063i			0.210380i
$394$	11.1962	+	11.5154i	0.564057	+	0.580138i
$395$	10.2555	+	1.56871i	0.516009	+	0.0789304i
$396$	−27.6071	−	0.776126i	−1.38731	−	0.0390018i
$397$	−16.7682	+	29.0434i	−0.841573	+	1.45765i	0.0469909	+	0.998895i	$0.485037\pi$
$397$	−16.7682	+	29.0434i	−0.841573	+	1.45765i	−0.888564	+	0.458752i	$0.848297\pi$
$398$	12.2852	+	3.47756i	0.615802	+	0.174315i
$399$		0			0
$400$	−15.4578	+	12.6908i	−0.772891	+	0.634539i
$401$	6.41428	−	11.1099i	0.320314	−	0.554800i	−0.660239	−	0.751056i	$-0.729545\pi$
$401$	6.41428	−	11.1099i	0.320314	−	0.554800i	0.980553	+	0.196256i	$0.0628784\pi$
$402$	0.516226	−	0.130576i	0.0257470	−	0.00651252i
$403$	−1.88141	−	3.25870i	−0.0937198	−	0.162327i
$404$	−6.94843	−	12.8564i	−0.345697	−	0.639630i
$405$	−12.9471	−	10.3714i	−0.643348	−	0.515359i
$406$		0			0
$407$	11.5495			0.572487
$408$	−1.33439	−	5.97734i	−0.0660624	−	0.295923i
$409$	−18.7038	+	10.7986i	−0.924841	+	0.533957i	−0.885176	−	0.465256i	$-0.845962\pi$
$409$	−18.7038	+	10.7986i	−0.924841	+	0.533957i	−0.0396649	+	0.999213i	$0.512629\pi$
$410$	−20.2977	−	9.25103i	−1.00243	−	0.456876i
$411$	0.993870	−	1.72143i	0.0490240	−	0.0849121i
$412$	−7.07664	+	11.4983i	−0.348641	+	0.566479i
$413$		0			0
$414$	17.7756	+	5.03172i	0.873623	+	0.247296i
$415$	3.51656	+	9.01801i	0.172621	+	0.442677i
$416$	−10.8766	+	9.44626i	−0.533269	+	0.463141i
$417$	−5.08728	+	2.93714i	−0.249125	+	0.143833i
$418$	30.2412	+	31.1033i	1.47915	+	1.52131i
$419$	18.7281			0.914929			0.457464	−	0.889228i	$-0.348758\pi$
$419$	18.7281			0.914929			0.457464	+	0.889228i	$0.348758\pi$
$420$		0			0
$421$	−18.9665			−0.924371			−0.462186	−	0.886783i	$-0.652935\pi$
$421$	−18.9665			−0.924371			−0.462186	+	0.886783i	$0.652935\pi$
$422$	−4.33935	−	4.46306i	−0.211236	−	0.217258i
$423$	−29.8380	+	17.2270i	−1.45077	+	0.837604i
$424$	6.03501	+	1.89305i	0.293086	+	0.0919348i
$425$	−24.4022	−	7.64414i	−1.18368	−	0.370795i
$426$	8.25645	+	2.33715i	0.400026	+	0.113235i
$427$		0			0
$428$	−16.7430	−	10.3045i	−0.809303	−	0.498088i
$429$	2.63921	−	4.57125i	0.127422	−	0.220702i
$430$	14.1363	−	31.0166i	0.681714	−	1.49575i
$431$	23.4036	−	13.5121i	1.12731	−	0.650854i	0.184055	−	0.982916i	$-0.441077\pi$
$431$	23.4036	−	13.5121i	1.12731	−	0.650854i	0.943258	+	0.332061i	$0.107744\pi$
$432$	0.553830	−	9.84216i	0.0266461	−	0.473531i
$433$	15.0015			0.720928			0.360464	−	0.932773i	$-0.382618\pi$
$433$	15.0015			0.720928			0.360464	+	0.932773i	$0.382618\pi$
$434$		0			0
$435$	−1.11842	+	1.39618i	−0.0536243	+	0.0669418i
$436$	16.5605	−	8.95036i	0.793103	−	0.428644i
$437$	−14.5092	−	25.1307i	−0.694071	−	1.20217i
$438$	4.56946	−	1.15581i	0.218337	−	0.0552268i
$439$	9.21899	−	15.9678i	0.439998	−	0.762099i	−0.557690	−	0.830049i	$-0.688312\pi$
$439$	9.21899	−	15.9678i	0.439998	−	0.762099i	0.997689	+	0.0679495i	$0.0216457\pi$
$440$	−30.8907	+	2.09927i	−1.47266	+	0.100079i
$441$		0			0
$442$	−17.7227	−	5.01676i	−0.842985	−	0.238623i
$443$	−10.4298	+	18.0649i	−0.495533	+	0.858289i	−0.999987	−	0.00514984i	$-0.998361\pi$
$443$	−10.4298	+	18.0649i	−0.495533	+	0.858289i	0.504453	+	0.863439i	$0.331694\pi$
$444$	−0.0561402	+	1.99692i	−0.00266430	+	0.0947699i
$445$	−4.82419	−	0.737925i	−0.228689	−	0.0349810i
$446$	−13.9107	−	14.3072i	−0.658689	−	0.677467i
$447$		−	2.31322i		−	0.109411i
$448$		0			0
$449$	14.6483			0.691298			0.345649	−	0.938364i	$-0.387659\pi$
$449$	14.6483			0.691298			0.345649	+	0.938364i	$0.387659\pi$
$450$	−16.6901	−	10.9211i	−0.786778	−	0.514827i
$451$	−17.2663	−	29.9061i	−0.813038	−	1.40822i
$452$	31.8397	+	0.895119i	1.49761	+	0.0421029i
$453$	−0.316717	+	0.548569i	−0.0148806	+	0.0257740i
$454$	−4.23611	+	14.9649i	−0.198811	+	0.702339i
$455$		0			0
$456$	−5.52481	+	5.07756i	−0.258723	+	0.237779i
$457$	−1.03058	−	0.595004i	−0.0482084	−	0.0278331i	0.475702	−	0.879606i	$-0.342194\pi$
$457$	−1.03058	−	0.595004i	−0.0482084	−	0.0278331i	−0.523910	+	0.851773i	$0.675527\pi$
$458$	−11.1182	+	2.81228i	−0.519521	+	0.131409i
$459$	10.9152	−	6.30192i	0.509480	−	0.294148i
$460$	20.3767	+	3.70567i	0.950067	+	0.172778i
$461$			14.5645i			0.678336i	0.940726	+	0.339168i	$0.110146\pi$
$461$			14.5645i			0.678336i	−0.940726	+	0.339168i	$0.889854\pi$
$462$		0			0
$463$	4.69391			0.218145			0.109072	−	0.994034i	$-0.465212\pi$
$463$	4.69391			0.218145			0.109072	+	0.994034i	$0.465212\pi$
$464$	7.54637	+	0.424643i	0.350331	+	0.0197136i
$465$	1.38276	+	0.211512i	0.0641241	+	0.00980863i
$466$	−21.7641	+	5.50506i	−1.00820	+	0.255017i
$467$	21.8947	+	12.6409i	1.01317	+	0.584952i	0.912117	−	0.409929i	$-0.134447\pi$
$467$	21.8947	+	12.6409i	1.01317	+	0.584952i	0.101050	+	0.994881i	$0.467780\pi$
$468$	−12.2353	−	7.53023i	−0.565575	−	0.348085i
$469$		0			0
$470$	−31.4465	+	22.4290i	−1.45052	+	1.03457i
$471$	8.39790	+	4.84853i	0.386955	+	0.223408i
$472$	−4.81685	+	15.3560i	−0.221713	+	0.706817i
$473$	45.6990	−	26.3843i	2.10124	−	1.21315i
$474$	−1.99182	+	1.93661i	−0.0914872	+	0.0889513i
$475$	6.83791	+	30.5747i	0.313745	+	1.40286i
$476$		0			0
$477$			6.30776i			0.288813i
$478$	−24.1468	−	24.8352i	−1.10445	−	1.13594i
$479$	2.05143	+	3.55318i	0.0937322	+	0.162349i	0.909079	−	0.416624i	$-0.136787\pi$
$479$	2.05143	+	3.55318i	0.0937322	+	0.162349i	−0.815347	+	0.578973i	$0.803454\pi$
$480$	−0.212812	−	5.35125i	−0.00971351	−	0.244250i
$481$	5.20311	+	3.00402i	0.237241	+	0.136971i
$482$	−7.39023	+	26.1075i	−0.336616	+	1.18916i
$483$		0			0
$484$	−22.0846	−	13.5920i	−1.00385	−	0.617820i
$485$	−7.13169	+	2.78100i	−0.323833	+	0.126279i
$486$	14.4429	−	3.65324i	0.655145	−	0.165714i
$487$	−16.9058	−	29.2816i	−0.766073	−	1.32688i	−0.939678	−	0.342062i	$-0.888875\pi$
$487$	−16.9058	−	29.2816i	−0.766073	−	1.32688i	0.173605	−	0.984815i	$-0.444458\pi$
$488$	2.38493	+	10.6832i	0.107961	+	0.483604i
$489$			0.817356i			0.0369621i
$490$		0			0
$491$			25.9116i			1.16937i	0.811259	+	0.584686i	$0.198782\pi$
$491$			25.9116i			1.16937i	−0.811259	+	0.584686i	$0.801218\pi$
$492$	5.25474	−	2.84000i	0.236902	−	0.128037i
$493$	4.83193	+	8.36914i	0.217619	+	0.376927i
$494$	5.53387	+	21.8780i	0.248981	+	0.984336i
$495$	−11.2180	−	28.7680i	−0.504213	−	1.29302i
$496$	−2.66289	−	5.27637i	−0.119567	−	0.236916i
$497$		0			0
$498$	−2.49390	−	0.705946i	−0.111754	−	0.0316342i
$499$	21.0465	+	12.1512i	0.942170	+	0.543962i	0.890640	−	0.454709i	$-0.150257\pi$
$499$	21.0465	+	12.1512i	0.942170	+	0.543962i	0.0515304	+	0.998671i	$0.483590\pi$
$500$	−19.7979	−	10.3944i	−0.885389	−	0.464851i
$501$	−3.59195	−	6.22145i	−0.160477	−	0.277954i
$502$	−21.4272	+	20.8332i	−0.956341	+	0.929833i
$503$		−	11.5222i		−	0.513750i	−0.966445	−	0.256875i	$-0.917307\pi$
$503$		−	11.5222i		−	0.513750i	0.966445	−	0.256875i	$-0.0826928\pi$
$504$		0			0
$505$	10.2151	−	12.7520i	0.454564	−	0.567455i
$506$	22.3507	+	22.9879i	0.993612	+	1.02194i
$507$	−2.38868	+	1.37911i	−0.106085	+	0.0612482i
$508$	−0.686771	+	24.4287i	−0.0304705	+	1.08385i
$509$	23.4965	+	13.5657i	1.04147	+	0.601290i	0.920248	−	0.391336i	$-0.127987\pi$
$509$	23.4965	+	13.5657i	1.04147	+	0.601290i	0.121218	+	0.992626i	$0.461320\pi$
$510$	5.57469	−	3.97611i	0.246851	−	0.176065i
$511$		0			0
$512$	−17.8904	+	13.8540i	−0.790653	+	0.612264i
$513$	−13.3733	−	7.72108i	−0.590445	−	0.340894i
$514$	8.89594	+	35.1698i	0.392383	+	1.55127i
$515$	−14.9215	−	2.28245i	−0.657521	−	0.100577i
$516$	4.33976	+	8.02968i	0.191047	+	0.353487i
$517$	−59.7962			−2.62983
$518$		0			0
$519$			4.24926i			0.186522i
$520$	−14.4625	−	7.08892i	−0.634220	−	0.310870i
$521$	−14.9657	+	8.64045i	−0.655659	+	0.378545i	−0.790621	−	0.612306i	$-0.790242\pi$
$521$	−14.9657	+	8.64045i	−0.655659	+	0.378545i	0.134962	+	0.990851i	$0.456909\pi$
$522$	1.84841	+	7.30763i	0.0809028	+	0.319846i
$523$	−16.4944	−	9.52305i	−0.721250	−	0.416414i	0.0939627	−	0.995576i	$-0.470047\pi$
$523$	−16.4944	−	9.52305i	−0.721250	−	0.416414i	−0.815213	+	0.579162i	$0.803380\pi$
$524$	16.7782	+	10.3262i	0.732958	+	0.451101i
$525$		0			0
$526$	−13.6344	−	3.85946i	−0.594486	−	0.168281i
$527$	3.77835	−	6.54429i	0.164587	−	0.285074i
$528$	4.54225	−	6.93581i	0.197676	−	0.301842i
$529$	0.776490	+	1.34492i	0.0337605	+	0.0584748i
$530$	0.677538	+	7.03897i	0.0294304	+	0.305753i
$531$	−16.0500			−0.696511
$532$		0			0
$533$		−	17.9638i		−	0.778100i
$534$	0.936955	−	0.910984i	0.0405460	−	0.0394221i
$535$	3.32354	−	21.7277i	0.143689	−	0.939370i
$536$	0.752842	−	2.40004i	0.0325178	−	0.103666i
$537$	−0.752111	+	1.30269i	−0.0324560	+	0.0562154i
$538$	−5.27490	+	18.6347i	−0.227417	+	0.803399i
$539$		0			0
$540$	10.3767	−	3.71394i	0.446541	−	0.159822i
$541$	−9.19403	+	15.9245i	−0.395282	+	0.684649i	−0.993137	−	0.116955i	$-0.962687\pi$
$541$	−9.19403	+	15.9245i	−0.395282	+	0.684649i	0.597855	+	0.801604i	$0.296020\pi$
$542$	5.32705	+	21.0603i	0.228816	+	0.904617i
$543$	4.71475	+	8.16619i	0.202329	+	0.350445i
$544$	−27.3504	−	9.43131i	−1.17264	−	0.404364i
$545$	16.4259	+	13.1581i	0.703610	+	0.563632i
$546$		0			0
$547$	−18.9519			−0.810323			−0.405161	−	0.914245i	$-0.632785\pi$
$547$	−18.9519			−0.810323			−0.405161	+	0.914245i	$0.632785\pi$
$548$	−4.46447	−	8.26043i	−0.190713	−	0.352868i
$549$	−9.45388	+	5.45820i	−0.403482	+	0.232950i
$550$	−15.6085	−	30.8978i	−0.665550	−	1.31749i
$551$	5.92005	−	10.2538i	0.252203	−	0.436828i
$552$	−4.08329	+	3.75274i	−0.173796	+	0.159727i
$553$		0			0
$554$	6.85974	−	24.2335i	0.291443	−	1.02958i
$555$	−2.08090	+	0.811444i	−0.0883292	+	0.0344439i
$556$	−0.779807	+	27.7380i	−0.0330712	+	1.17635i
$557$	−22.0931	+	12.7555i	−0.936116	+	0.540467i	−0.888741	−	0.458411i	$-0.848419\pi$
$557$	−22.0931	+	12.7555i	−0.936116	+	0.540467i	−0.0473751	+	0.998877i	$0.515086\pi$
$558$	4.22598	−	4.10885i	0.178900	−	0.173941i
$559$	27.4502			1.16102
$560$		0			0
$561$	10.6004			0.447549
$562$	−30.0302	+	29.1978i	−1.26675	+	1.23163i
$563$	−27.2462	+	15.7306i	−1.14829	+	0.662965i	−0.948470	−	0.316868i	$-0.897369\pi$
$563$	−27.2462	+	15.7306i	−1.14829	+	0.662965i	−0.199819	+	0.979833i	$0.564035\pi$
$564$	0.290660	−	10.3389i	0.0122390	−	0.435344i
$565$	12.9380	+	33.1786i	0.544304	+	1.39583i
$566$	−1.37830	+	4.86912i	−0.0579342	+	0.204665i
$567$		0			0
$568$	29.8446	−	27.4286i	1.25225	−	1.15088i
$569$	−8.21728	+	14.2327i	−0.344486	+	0.596668i	−0.985260	−	0.171062i	$-0.945280\pi$
$569$	−8.21728	+	14.2327i	−0.344486	+	0.596668i	0.640774	+	0.767729i	$0.278614\pi$
$570$	−7.63389	−	3.47927i	−0.319748	−	0.145731i
$571$	−12.9962	+	7.50335i	−0.543873	+	0.314005i	−0.746647	−	0.665220i	$-0.768338\pi$
$571$	−12.9962	+	7.50335i	−0.543873	+	0.314005i	0.202774	+	0.979226i	$0.435004\pi$
$572$	−11.8554	−	21.9355i	−0.495697	−	0.917169i
$573$	−7.55580			−0.315648
$574$		0			0
$575$	5.05378	+	22.5972i	0.210757	+	0.942370i
$576$	−18.5230	−	12.8887i	−0.771793	−	0.537030i
$577$	−1.24966	−	2.16447i	−0.0520240	−	0.0901082i	0.838841	−	0.544377i	$-0.183234\pi$
$577$	−1.24966	−	2.16447i	−0.0520240	−	0.0901082i	−0.890865	+	0.454269i	$0.849901\pi$
$578$	−3.17524	−	12.5532i	−0.132073	−	0.522144i
$579$	−3.85983	+	6.68543i	−0.160409	+	0.277837i
$580$	2.84762	+	7.95620i	0.118241	+	0.330363i
$581$		0			0
$582$	0.558282	−	1.97225i	0.0231415	−	0.0817522i
$583$	−5.47369	+	9.48071i	−0.226697	+	0.392651i
$584$	6.66391	−	21.2444i	0.275754	−	0.879098i
$585$	2.42874	−	15.8779i	0.100416	−	0.656472i
$586$	18.0219	−	17.5224i	0.744477	−	0.723842i
$587$		−	22.1562i		−	0.914482i	−0.889343	−	0.457241i	$-0.848838\pi$
$587$		−	22.1562i		−	0.914482i	0.889343	−	0.457241i	$-0.151162\pi$
$588$		0			0
$589$	−9.25842			−0.381487
$590$	−17.9106	+	1.72399i	−0.737366	+	0.0709754i
$591$	−2.40419	−	4.16419i	−0.0988953	−	0.171292i
$592$	7.89451	+	5.17010i	0.324462	+	0.212490i
$593$	14.3251	−	24.8118i	0.588262	−	1.01890i	−0.406198	−	0.913785i	$-0.633146\pi$
$593$	14.3251	−	24.8118i	0.588262	−	1.01890i	0.994460	−	0.105115i	$-0.0335211\pi$
$594$	16.4169	+	4.64713i	0.673596	+	0.190674i
$595$		0			0
$596$	−9.30594	−	5.72737i	−0.381186	−	0.234602i
$597$	−3.31036	−	1.91123i	−0.135484	−	0.0782216i
$598$	4.08999	+	16.1696i	0.167252	+	0.661224i
$599$	−14.2033	+	8.20030i	−0.580333	+	0.335055i	−0.761266	−	0.648440i	$-0.775422\pi$
$599$	−14.2033	+	8.20030i	−0.580333	+	0.335055i	0.180933	+	0.983495i	$0.442088\pi$
$600$	5.41815	−	2.54855i	0.221195	−	0.104044i
$601$		−	22.1672i		−	0.904220i	−0.891962	−	0.452110i	$-0.850671\pi$
$601$		−	22.1672i		−	0.904220i	0.891962	−	0.452110i	$-0.149329\pi$
$602$		0			0
$603$	2.50851			0.102155
$604$	1.42269	+	2.63235i	0.0578885	+	0.107109i
$605$	4.38387	−	28.6596i	0.178230	−	1.16518i
$606$	1.07287	+	4.24155i	0.0435824	+	0.172301i
$607$	24.8986	+	14.3752i	1.01060	+	0.583472i	0.911368	−	0.411592i	$-0.135027\pi$
$607$	24.8986	+	14.3752i	1.01060	+	0.583472i	0.0992347	+	0.995064i	$0.468361\pi$
$608$	6.74768	+	34.7977i	0.273654	+	1.41123i
$609$		0			0
$610$	−9.96351	+	7.10640i	−0.403411	+	0.287730i
$611$	−26.9385	−	15.5530i	−1.08982	−	0.629206i
$612$	0.810812	−	28.8408i	0.0327751	−	1.16582i
$613$	−10.5198	+	6.07359i	−0.424890	+	0.245310i	−0.697167	−	0.716909i	$-0.745556\pi$
$613$	−10.5198	+	6.07359i	−0.424890	+	0.245310i	0.272278	+	0.962219i	$0.412223\pi$
$614$	32.4268	+	33.3513i	1.30864	+	1.34595i
$615$	5.21205	+	4.17515i	0.210170	+	0.168358i
$616$		0			0
$617$			15.9265i			0.641175i	0.947219	+	0.320588i	$0.103880\pi$
$617$			15.9265i			0.641175i	−0.947219	+	0.320588i	$0.896120\pi$
$618$	2.89806	−	2.81773i	0.116577	−	0.113346i
$619$	−1.94167	−	3.36308i	−0.0780424	−	0.135173i	0.824363	−	0.566062i	$-0.191534\pi$
$619$	−1.94167	−	3.36308i	−0.0780424	−	0.135173i	−0.902405	+	0.430888i	$0.858200\pi$
$620$	4.27452	−	5.03908i	0.171669	−	0.202374i
$621$	−9.88396	−	5.70651i	−0.396630	−	0.228994i
$622$	−27.0446	−	7.65549i	−1.08439	−	0.306957i
$623$		0			0
$624$	3.85031	−	1.94319i	0.154136	−	0.0777897i
$625$	2.08628	−	24.9128i	0.0834513	−	0.996512i
$626$	2.20957	+	8.73546i	0.0883123	+	0.349139i
$627$	−6.49378	−	11.2476i	−0.259337	−	0.449184i
$628$	40.2980	−	21.7796i	1.60806	−	0.869101i
$629$			12.0656i			0.481089i
$630$		0			0
$631$			12.2743i			0.488633i	0.969696	+	0.244316i	$0.0785636\pi$
$631$			12.2743i			0.488633i	−0.969696	+	0.244316i	$0.921436\pi$
$632$	2.85925	+	12.8079i	0.113735	+	0.509470i
$633$	0.931800	+	1.61393i	0.0370357	+	0.0641478i
$634$	23.3107	−	5.89626i	0.925785	−	0.234171i
$635$	−25.4559	+	9.92651i	−1.01019	+	0.393922i
$636$	−1.61262	−	0.992493i	−0.0639446	−	0.0393549i
$637$		0			0
$638$	−3.56314	+	12.5875i	−0.141066	+	0.498345i
$639$	35.0084	+	20.2121i	1.38491	+	0.799578i
$640$	−22.0547	−	12.3932i	−0.871787	−	0.489884i
$641$	−7.41350	−	12.8406i	−0.292816	−	0.507172i	0.681659	−	0.731670i	$-0.261259\pi$
$641$	−7.41350	−	12.8406i	−0.292816	−	0.507172i	−0.974474	+	0.224499i	$0.927926\pi$
$642$	4.10298	+	4.21995i	0.161932	+	0.166548i
$643$			11.8058i			0.465577i	0.972527	+	0.232789i	$0.0747850\pi$
$643$			11.8058i			0.465577i	−0.972527	+	0.232789i	$0.925215\pi$
$644$		0			0
$645$	−6.37998	+	7.96444i	−0.251211	+	0.313600i
$646$	−32.4934	+	31.5927i	−1.27843	+	1.24300i
$647$	29.9706	−	17.3035i	1.17827	−	0.680272i	0.222653	−	0.974898i	$-0.428528\pi$
$647$	29.9706	−	17.3035i	1.17827	−	0.680272i	0.955613	+	0.294626i	$0.0951950\pi$
$648$	6.28037	−	20.0217i	0.246716	−	0.786526i
$649$	−24.1235	−	13.9277i	−0.946931	−	0.546711i
$650$	1.00478	−	17.9794i	0.0394109	−	0.705211i
$651$		0			0
$652$	3.28817	+	2.02372i	0.128775	+	0.0792549i
$653$	24.4111	+	14.0937i	0.955279	+	0.551531i	0.894717	−	0.446634i	$-0.147377\pi$
$653$	24.4111	+	14.0937i	0.955279	+	0.551531i	0.0605622	+	0.998164i	$0.480711\pi$
$654$	−5.46359	+	1.38198i	−0.213643	+	0.0540396i
$655$	−3.33053	+	21.7734i	−0.130134	+	0.850755i
$656$	1.58522	−	28.1712i	0.0618926	−	1.09990i
$657$	22.2045			0.866281
$658$		0			0
$659$			9.79123i			0.381412i	0.981647	+	0.190706i	$0.0610777\pi$
$659$			9.79123i			0.381412i	−0.981647	+	0.190706i	$0.938922\pi$
$660$	9.11982	+	1.65852i	0.354989	+	0.0645578i
$661$	0.707548	−	0.408503i	0.0275204	−	0.0158889i	−0.486177	−	0.873861i	$-0.661609\pi$
$661$	0.707548	−	0.408503i	0.0275204	−	0.0158889i	0.513697	+	0.857972i	$0.328276\pi$
$662$	−20.1011	+	5.08444i	−0.781253	+	0.197612i
$663$	4.77554	+	2.75716i	0.185467	+	0.107079i
$664$	−9.01470	+	8.28494i	−0.349838	+	0.321518i
$665$		0			0
$666$	−2.56329	+	9.05536i	−0.0993255	+	0.350888i
$667$	4.37540	−	7.57842i	0.169416	−	0.293438i
$668$	−33.9219	−	0.953659i	−1.31248	−	0.0368982i
$669$	2.98708	+	5.17377i	0.115487	+	0.200029i
$670$	2.79931	−	0.269448i	0.108147	−	0.0104097i
$671$	−18.9459			−0.731397
$672$		0			0
$673$		−	9.43129i		−	0.363550i	−0.983340	−	0.181775i	$-0.941816\pi$
$673$		−	9.43129i		−	0.363550i	0.983340	−	0.181775i	$-0.0581842\pi$
$674$	−15.0278	−	15.4562i	−0.578850	−	0.595352i
$675$	8.34161	+	9.06936i	0.321069	+	0.349080i
$676$	−0.366151	+	13.0241i	−0.0140827	+	0.500927i
$677$	1.23700	−	2.14255i	0.0475418	−	0.0823449i	−0.841275	−	0.540607i	$-0.818195\pi$
$677$	1.23700	−	2.14255i	0.0475418	−	0.0823449i	0.888817	+	0.458262i	$0.151528\pi$
$678$	−9.17542	−	2.59728i	−0.352380	−	0.0997479i
$679$		0			0
$680$	−2.19309	−	32.2712i	−0.0841010	−	1.23754i
$681$	2.32812	−	4.03243i	0.0892139	−	0.154523i
$682$	9.91728	−	2.50850i	0.379752	−	0.0960556i
$683$	9.37801	+	16.2432i	0.358840	+	0.621528i	0.987767	−	0.155935i	$-0.0498392\pi$
$683$	9.37801	+	16.2432i	0.358840	+	0.621528i	−0.628928	+	0.777464i	$0.716506\pi$
$684$	−31.0982	+	16.8075i	−1.18907	+	0.642651i
$685$	6.56332	−	8.19332i	0.250772	−	0.313051i
$686$		0			0
$687$	3.43341			0.130993
$688$	43.0478	+	2.42235i	1.64118	+	0.0923513i
$689$	−4.93186	+	2.84741i	−0.187889	+	0.108478i
$690$	−5.64207	−	2.57147i	−0.214790	−	0.0978941i
$691$	2.11063	−	3.65572i	0.0802923	−	0.139070i	−0.823083	−	0.567921i	$-0.807748\pi$
$691$	2.11063	−	3.65572i	0.0802923	−	0.139070i	0.903375	+	0.428851i	$0.141081\pi$
$692$	17.0945	+	10.5209i	0.649836	+	0.399943i
$693$		0			0
$694$	45.4753	+	12.8727i	1.72622	+	0.488640i
$695$	−28.9044	+	11.2712i	−1.09641	+	0.427543i
$696$	−2.15908	−	0.677258i	−0.0818398	−	0.0256714i
$697$	31.2426	−	18.0379i	1.18340	−	0.683236i
$698$	−15.9300	−	16.3841i	−0.602958	−	0.620147i
$699$	6.72095			0.254210
$700$		0			0
$701$	−12.2843			−0.463971			−0.231985	−	0.972719i	$-0.574522\pi$
$701$	−12.2843			−0.463971			−0.231985	+	0.972719i	$0.574522\pi$
$702$	6.18721	+	6.36360i	0.233521	+	0.240179i
$703$	12.8022	−	7.39138i	0.482846	−	0.278771i
$704$	−16.6561	−	35.4458i	−0.627749	−	1.33591i
$705$	10.7736	−	4.20116i	0.405758	−	0.158225i
$706$	−30.8691	−	8.73809i	−1.16177	−	0.328862i
$707$		0			0
$708$	2.52539	−	4.10329i	0.0949098	−	0.154211i
$709$	−1.46808	+	2.54279i	−0.0551348	+	0.0954963i	−0.892276	−	0.451491i	$-0.850892\pi$
$709$	−1.46808	+	2.54279i	−0.0551348	+	0.0954963i	0.837141	+	0.546988i	$0.184226\pi$
$710$	41.2376	+	18.7947i	1.54762	+	0.705354i
$711$	−11.3341	+	6.54374i	−0.425062	+	0.245410i
$712$	−1.34500	−	6.02485i	−0.0504060	−	0.225791i
$713$	−6.84273			−0.256262
$714$		0			0
$715$	17.4288	−	21.7573i	0.651802	−	0.813677i
$716$	3.37849	+	6.25108i	0.126260	+	0.233614i
$717$	5.18511	+	8.98088i	0.193642	+	0.335397i
$718$	22.9892	−	5.81496i	0.857951	−	0.217013i
$719$	−23.7638	+	41.1601i	−0.886240	+	1.53501i	−0.0419549	+	0.999120i	$0.513359\pi$
$719$	−23.7638	+	41.1601i	−0.886240	+	1.53501i	−0.844285	+	0.535894i	$0.819975\pi$
$720$	5.20994	−	24.6857i	0.194163	−	0.919982i
$721$		0			0
$722$	27.5726	+	7.80495i	1.02615	+	0.290470i
$723$	4.06160	−	7.03489i	0.151052	−	0.261630i
$724$	44.5255	+	1.25176i	1.65478	+	0.0465213i
$725$	−6.95383	+	6.39584i	−0.258259	+	0.237535i
$726$	5.41198	+	5.56627i	0.200857	+	0.206584i
$727$		−	8.28795i		−	0.307383i	−0.988119	−	0.153692i	$-0.950884\pi$
$727$		−	8.28795i		−	0.307383i	0.988119	−	0.153692i	$-0.0491162\pi$
$728$		0			0
$729$	17.7963			0.659124
$730$	24.7785	−	2.38506i	0.917094	−	0.0882751i
$731$	27.5634	+	47.7413i	1.01947	+	1.76578i
$732$	0.0920928	−	3.27577i	0.00340385	−	0.121076i
$733$	−20.9930	+	36.3610i	−0.775395	+	1.34302i	0.159178	+	0.987250i	$0.449116\pi$
$733$	−20.9930	+	36.3610i	−0.775395	+	1.34302i	−0.934572	+	0.355773i	$0.884218\pi$
$734$	6.02552	−	21.2864i	0.222406	−	0.785696i
$735$		0			0
$736$	4.98709	+	25.7184i	0.183826	+	0.947991i
$737$	3.77035	+	2.17681i	0.138883	+	0.0801840i
$738$	27.2799	−	6.90026i	1.00419	−	0.254002i
$739$	22.4500	−	12.9615i	0.825836	−	0.476796i	−0.0265891	−	0.999646i	$-0.508465\pi$
$739$	22.4500	−	12.9615i	0.825836	−	0.476796i	0.852425	+	0.522850i	$0.175131\pi$
$740$	−1.88777	+	10.3804i	−0.0693957	+	0.381591i
$741$		−	6.75612i		−	0.248192i
$742$		0			0
$743$	11.2976			0.414470			0.207235	−	0.978291i	$-0.433554\pi$
$743$	11.2976			0.414470			0.207235	+	0.978291i	$0.433554\pi$
$744$	0.385518	+	1.72691i	0.0141338	+	0.0633115i
$745$	1.84726	−	12.0765i	0.0676784	−	0.442448i
$746$	23.4509	−	5.93172i	0.858597	−	0.217176i
$747$	−10.5744	−	6.10515i	−0.386898	−	0.223376i
$748$	26.2459	−	42.6448i	0.959644	−	1.55925i
$749$		0			0
$750$	4.98304	+	4.47031i	0.181955	+	0.163233i
$751$	4.86553	+	2.80911i	0.177546	+	0.102506i	0.586139	−	0.810210i	$-0.300647\pi$
$751$	4.86553	+	2.80911i	0.177546	+	0.102506i	−0.408593	+	0.912717i	$0.633981\pi$
$752$	−40.8730	−	26.7676i	−1.49048	−	0.976114i
$753$	7.74847	−	4.47358i	0.282370	−	0.163026i
$754$	−4.87922	+	4.74398i	−0.177691	+	0.172765i
$755$	−2.09153	+	2.61097i	−0.0761187	+	0.0950228i
$756$		0			0
$757$		−	27.0456i		−	0.982990i	−0.870880	−	0.491495i	$-0.836451\pi$
$757$		−	27.0456i		−	0.982990i	0.870880	−	0.491495i	$-0.163549\pi$
$758$	−10.2294	−	10.5210i	−0.371547	−	0.382139i
$759$	−4.79944	−	8.31287i	−0.174208	−	0.301738i
$760$	−32.8979	+	22.0962i	−1.19333	+	0.801514i
$761$	22.3558	+	12.9071i	0.810396	+	0.467883i	0.847094	−	0.531444i	$-0.178350\pi$
$761$	22.3558	+	12.9071i	0.810396	+	0.467883i	−0.0366971	+	0.999326i	$0.511684\pi$
$762$	1.99274	−	7.03975i	0.0721892	−	0.255023i
$763$		0			0
$764$	−18.7076	+	30.3965i	−0.676818	+	1.09971i
$765$	30.0536	−	11.7194i	1.08659	−	0.423715i
$766$	12.6653	−	3.20360i	0.457617	−	0.115751i
$767$	−7.24519	−	12.5490i	−0.261609	−	0.453119i
$768$	6.20959	−	2.70756i	0.224069	−	0.0977007i
$769$			5.58909i			0.201548i	0.994909	+	0.100774i	$0.0321319\pi$
$769$			5.58909i			0.201548i	−0.994909	+	0.100774i	$0.967868\pi$
$770$		0			0
$771$		−	10.8608i		−	0.391140i
$772$	17.3384	+	32.0805i	0.624022	+	1.15460i
$773$	4.38608	+	7.59692i	0.157756	+	0.273242i	0.934059	−	0.357118i	$-0.116241\pi$
$773$	4.38608	+	7.59692i	0.157756	+	0.273242i	−0.776303	+	0.630360i	$0.782907\pi$
$774$	10.5442	+	41.6859i	0.379002	+	1.49837i
$775$	7.05000	+	2.20846i	0.253244	+	0.0793301i
$776$	−6.55196	−	7.12908i	−0.235202	−	0.255919i
$777$		0			0
$778$	23.2474	+	6.58062i	0.833459	+	0.235927i
$779$	−38.2783	−	22.1000i	−1.37146	−	0.791814i
$780$	3.67715	+	3.11923i	0.131663	+	0.111686i
$781$	35.0789	+	60.7584i	1.25522	+	2.17411i
$782$	−24.0153	+	23.3496i	−0.858784	+	0.834980i
$783$		−	4.65674i		−	0.166418i
$784$		0			0
$785$	39.9706	+	32.0187i	1.42661	+	1.14280i
$786$	−4.11161	−	4.22882i	−0.146656	−	0.150837i
$787$	−8.56726	+	4.94631i	−0.305390	+	0.176317i	−0.644862	−	0.764299i	$-0.723085\pi$
$787$	−8.56726	+	4.94631i	−0.305390	+	0.176317i	0.339472	+	0.940616i	$0.389752\pi$
$788$	−22.7049	−	0.638310i	−0.808828	−	0.0227389i
$789$	3.67389	+	2.12112i	0.130794	+	0.0755140i
$790$	−11.9451	+	8.51974i	−0.424987	+	0.303119i
$791$		0			0
$792$	28.7574	−	26.4294i	1.02185	−	0.939129i
$793$	−8.53522	−	4.92781i	−0.303094	−	0.174992i
$794$	−11.6302	−	45.9796i	−0.412741	−	1.63176i
$795$	0.320111	−	2.09273i	0.0113532	−	0.0742215i
$796$	−15.8850	+	8.58527i	−0.563029	+	0.304297i
$797$	31.5699			1.11826			0.559132	−	0.829079i	$-0.311135\pi$
$797$	31.5699			1.11826			0.559132	+	0.829079i	$0.311135\pi$
$798$		0			0
$799$		−	62.4685i		−	2.20998i
$800$	3.16232	−	28.1069i	0.111805	−	0.993730i
$801$	5.33158	−	3.07819i	0.188382	−	0.108762i
$802$	4.44885	+	17.5884i	0.157095	+	0.621067i
$803$	33.3739	+	19.2684i	1.17774	+	0.679968i
$804$	−0.394702	+	0.641319i	−0.0139200	+	0.0226176i
$805$		0			0
$806$	5.12025	+	1.44938i	0.180353	+	0.0510524i
$807$	2.89903	−	5.02128i	0.102051	−	0.176757i
$808$	19.7199	+	6.18570i	0.693742	+	0.217612i
$809$	−15.3882	−	26.6532i	−0.541021	−	0.937076i	−0.998846	−	0.0480338i	$-0.984704\pi$
$809$	−15.3882	−	26.6532i	−0.541021	−	0.937076i	0.457824	−	0.889043i	$-0.348629\pi$
$810$	23.3524	−	2.24779i	0.820521	−	0.0789794i
$811$	−19.0962			−0.670557			−0.335278	−	0.942119i	$-0.608830\pi$
$811$	−19.0962			−0.670557			−0.335278	+	0.942119i	$0.608830\pi$
$812$		0			0
$813$		−	6.50362i		−	0.228092i
$814$	−11.7106	+	11.3860i	−0.410458	+	0.399081i
$815$	−0.652714	+	4.26712i	−0.0228636	+	0.149471i
$816$	7.24577	+	4.74524i	0.253653	+	0.166117i
$817$	33.7706	−	58.4924i	1.18148	−	2.04639i
$818$	8.31894	−	29.3884i	0.290865	−	1.02754i
$819$		0			0
$820$	29.7011	−	10.6304i	1.03721	−	0.371229i
$821$	−24.0855	+	41.7174i	−0.840591	+	1.45595i	0.0488054	+	0.998808i	$0.484459\pi$
$821$	−24.0855	+	41.7174i	−0.840591	+	1.45595i	−0.889396	+	0.457137i	$0.848875\pi$
$822$	0.689335	+	2.72526i	0.0240433	+	0.0950543i
$823$	4.76754	+	8.25762i	0.166186	+	0.287843i	0.937076	−	0.349126i	$-0.113521\pi$
$823$	4.76754	+	8.25762i	0.166186	+	0.287843i	−0.770890	+	0.636969i	$0.780188\pi$
$824$	−4.16016	−	18.6352i	−0.144926	−	0.649188i
$825$	2.26188	+	10.1137i	0.0787485	+	0.352113i
$826$		0			0
$827$	−0.650873			−0.0226331			−0.0113165	−	0.999936i	$-0.503602\pi$
$827$	−0.650873			−0.0226331			−0.0113165	+	0.999936i	$0.503602\pi$
$828$	−22.9842	+	12.4221i	−0.798755	+	0.431699i
$829$	40.5282	−	23.3989i	1.40760	−	0.812679i	0.412445	−	0.910983i	$-0.364675\pi$
$829$	40.5282	−	23.3989i	1.40760	−	0.812679i	0.995156	+	0.0983034i	$0.0313416\pi$
$830$	−12.4560	−	5.67704i	−0.432355	−	0.197053i
$831$	−3.77005	+	6.52991i	−0.130781	+	0.226520i
$832$	1.71578	−	20.3008i	0.0594841	−	0.703802i
$833$		0			0
$834$	2.26269	−	7.99342i	0.0783505	−	0.276789i
$835$	−13.7841	−	35.3484i	−0.477018	−	1.22328i
$836$	−61.3264	−	1.72409i	−2.12102	−	0.0596289i
$837$	−3.15351	+	1.82068i	−0.109001	+	0.0629318i
$838$	−18.9895	+	18.4631i	−0.655980	+	0.637797i
$839$	−50.2124			−1.73353			−0.866763	−	0.498720i	$-0.833803\pi$
$839$	−50.2124			−1.73353			−0.866763	+	0.498720i	$0.833803\pi$
$840$		0			0
$841$	−25.4295			−0.876879
$842$	19.2312	−	18.6981i	0.662750	−	0.644379i
$843$	10.8595	−	6.26972i	0.374020	−	0.215941i
$844$	8.79980	+	0.247392i	0.302901	+	0.00851557i
$845$	−13.5718	+	5.29230i	−0.466883	+	0.182061i
$846$	13.2712	−	46.8831i	0.456272	−	1.61187i
$847$		0			0
$848$	−7.98548	+	4.03014i	−0.274223	+	0.138395i
$849$	0.757499	−	1.31203i	0.0259973	−	0.0450286i
$850$	32.2787	−	16.3061i	1.10715	−	0.559294i
$851$	9.46191	−	5.46284i	0.324350	−	0.187264i
$852$	−10.6757	+	5.76986i	−0.365745	+	0.197672i
$853$	12.0132			0.411323			0.205661	−	0.978623i	$-0.434065\pi$
$853$	12.0132			0.411323			0.205661	+	0.978623i	$0.434065\pi$
$854$		0			0
$855$	−30.8456	−	24.7091i	−1.05490	−	0.845034i
$856$	27.1353	−	6.05774i	0.927466	−	0.207049i
$857$	13.5132	+	23.4056i	0.461603	+	0.799519i	0.999041	−	0.0437838i	$-0.0139413\pi$
$857$	13.5132	+	23.4056i	0.461603	+	0.799519i	−0.537438	+	0.843303i	$0.680608\pi$
$858$	1.83052	+	7.23690i	0.0624930	+	0.247064i
$859$	10.2882	−	17.8197i	0.351030	−	0.608002i	−0.635400	−	0.772183i	$-0.719165\pi$
$859$	10.2882	−	17.8197i	0.351030	−	0.608002i	0.986430	+	0.164181i	$0.0524982\pi$
$860$	16.2441	+	45.3857i	0.553919	+	1.54764i
$861$		0			0
$862$	−10.4093	+	36.7731i	−0.354543	+	1.25250i
$863$	−4.73195	+	8.19598i	−0.161078	+	0.278994i	−0.935255	−	0.353974i	$-0.884830\pi$
$863$	−4.73195	+	8.19598i	−0.161078	+	0.278994i	0.774178	+	0.632968i	$0.218164\pi$
$864$	9.14132	+	10.5255i	0.310994	+	0.358084i
$865$	−3.39332	+	22.1839i	−0.115376	+	0.754274i
$866$	−15.2109	+	14.7892i	−0.516886	+	0.502559i
$867$			3.87654i			0.131654i
$868$		0			0
$869$	−22.7139			−0.770515
$870$	−0.242396	−	2.51826i	−0.00821798	−	0.0853770i
$871$	1.13238	+	1.96133i	0.0383691	+	0.0664573i
$872$	−7.96787	+	25.4014i	−0.269826	+	0.860199i
$873$	4.82813	−	8.36256i	0.163407	−	0.283030i
$874$	39.4868	+	11.1775i	1.33566	+	0.378084i
$875$		0			0
$876$	−3.49377	+	5.67674i	−0.118043	+	0.191799i
$877$	17.5315	+	10.1218i	0.591996	+	0.341789i	0.765886	−	0.642976i	$-0.222300\pi$
$877$	17.5315	+	10.1218i	0.591996	+	0.341789i	−0.173890	+	0.984765i	$0.555634\pi$
$878$	6.39417	+	25.2791i	0.215793	+	0.853128i
$879$	−6.51705	+	3.76262i	−0.219815	+	0.126910i
$880$	29.2522	−	32.5821i	0.986090	−	1.09834i
$881$		−	58.2514i		−	1.96254i	−0.192638	−	0.981270i	$-0.561704\pi$
$881$		−	58.2514i		−	1.96254i	0.192638	−	0.981270i	$-0.438296\pi$
$882$		0			0
$883$	−39.7551			−1.33786			−0.668932	−	0.743323i	$-0.733248\pi$
$883$	−39.7551			−1.33786			−0.668932	+	0.743323i	$0.733248\pi$
$884$	22.9158	−	12.3852i	0.770742	−	0.416559i
$885$	5.32492	+	0.814518i	0.178995	+	0.0273797i
$886$	−7.23395	−	28.5991i	−0.243029	−	0.960807i
$887$	39.2114	+	22.6387i	1.31659	+	0.760134i	0.983178	−	0.182648i	$-0.0584667\pi$
$887$	39.2114	+	22.6387i	1.31659	+	0.760134i	0.333412	+	0.942781i	$0.391800\pi$
$888$	−1.91174	−	2.08014i	−0.0641539	−	0.0698048i
$889$		0			0
$890$	5.61899	−	4.00770i	0.188349	−	0.134339i
$891$	31.4531	+	18.1595i	1.05372	+	0.608365i
$892$	28.2095	+	0.793064i	0.944525	+	0.0265538i
$893$	−66.2822	+	38.2681i	−2.21805	+	1.28059i
$894$	2.28048	+	2.34550i	0.0762708	+	0.0784451i
$895$	−4.96680	+	6.20030i	−0.166022	+	0.207253i
$896$		0			0
$897$		−	4.99333i		−	0.166722i
$898$	−14.8527	+	14.4410i	−0.495642	+	0.481904i
$899$	−1.39598	−	2.41792i	−0.0465587	−	0.0806420i
$900$	27.6895	−	5.38038i	0.922985	−	0.179346i
$901$	−9.90440	−	5.71831i	−0.329963	−	0.190504i
$902$	46.9901	+	13.3015i	1.56460	+	0.442890i
$903$		0			0
$904$	−33.1664	+	30.4815i	−1.10310	+	1.01380i
$905$	18.0928	+	46.3978i	0.601425	+	1.54232i
$906$	−0.219670	−	0.868459i	−0.00729806	−	0.0288526i
$907$	25.2789	+	43.7844i	0.839373	+	1.45384i	0.890420	+	0.455140i	$0.150411\pi$
$907$	25.2789	+	43.7844i	0.839373	+	1.45384i	−0.0510468	+	0.998696i	$0.516256\pi$
$908$	−10.4579	−	19.3499i	−0.347059	−	0.642150i
$909$			20.6111i			0.683627i
$910$		0			0
$911$			0.524910i			0.0173910i	0.999962	+	0.00869552i	$0.00276790\pi$
$911$			0.524910i			0.0173910i	−0.999962	+	0.00869552i	$0.997232\pi$
$912$	0.596196	−	10.5950i	0.0197420	−	0.350837i
$913$	−10.5957	−	18.3524i	−0.350668	−	0.607374i
$914$	1.63154	−	0.412687i	0.0539666	−	0.0136505i
$915$	3.41352	−	1.33110i	0.112847	−	0.0440048i
$916$	8.50089	−	13.8124i	0.280877	−	0.456375i
$917$		0			0
$918$	−4.85481	+	17.1506i	−0.160233	+	0.566055i
$919$	−18.6304	−	10.7563i	−0.614561	−	0.354817i	0.160187	−	0.987087i	$-0.448790\pi$
$919$	−18.6304	−	10.7563i	−0.614561	−	0.354817i	−0.774749	+	0.632269i	$0.782124\pi$
$920$	−24.3142	+	16.3309i	−0.801616	+	0.538415i
$921$	−6.96310	−	12.0604i	−0.229442	−	0.397405i
$922$	−14.3584	−	14.7677i	−0.472868	−	0.486349i
$923$			36.4960i			1.20128i
$924$		0			0
$925$	−11.5116	+	2.57453i	−0.378500	+	0.0846499i
$926$	−4.75941	+	4.62749i	−0.156404	+	0.152069i
$927$	16.4909	−	9.52103i	0.541632	−	0.312711i
$928$	−8.07030	+	7.00901i	−0.264921	+	0.230082i
$929$	13.5117	+	7.80096i	0.443303	+	0.255941i	0.704998	−	0.709210i	$-0.250948\pi$
$929$	13.5117	+	7.80096i	0.443303	+	0.255941i	−0.261695	+	0.965151i	$0.584281\pi$
$930$	−1.61058	+	1.14873i	−0.0528129	+	0.0376684i
$931$		0			0
$932$	16.6406	−	27.0380i	0.545081	−	0.885658i
$933$	7.28740	+	4.20738i	0.238579	+	0.137743i
$934$	−34.6623	+	8.76757i	−1.13418	+	0.286884i
$935$	55.3409	+	8.46514i	1.80984	+	0.276840i
$936$	19.8297	−	4.42681i	0.648153	−	0.144695i
$937$	7.15521			0.233751			0.116875	−	0.993147i	$-0.462712\pi$
$937$	7.15521			0.233751			0.116875	+	0.993147i	$0.462712\pi$
$938$		0			0
$939$		−	2.69759i		−	0.0880326i
$940$	9.77371	−	53.7434i	0.318783	−	1.75292i
$941$	−6.17342	+	3.56423i	−0.201248	+	0.116191i	−0.597237	−	0.802065i	$-0.703735\pi$
$941$	−6.17342	+	3.56423i	−0.201248	+	0.116191i	0.395990	+	0.918255i	$0.370402\pi$
$942$	−13.2950	+	3.36287i	−0.433174	+	0.109568i
$943$	−28.2908	−	16.3337i	−0.921275	−	0.531899i
$944$	−10.2546	−	20.3189i	−0.333760	−	0.661325i
$945$		0			0
$946$	−20.3257	+	71.8048i	−0.660846	+	2.33457i
$947$	−11.5507	+	20.0064i	−0.375348	+	0.650122i	−0.990379	−	0.138381i	$-0.955810\pi$
$947$	−11.5507	+	20.0064i	−0.375348	+	0.650122i	0.615031	+	0.788503i	$0.289143\pi$
$948$	0.110408	−	3.92726i	0.00358590	−	0.127552i
$949$	10.0234	+	17.3611i	0.325374	+	0.563564i
$950$	−37.0754	−	24.2602i	−1.20288	−	0.787105i
$951$	−7.19855			−0.233429
$952$		0			0
$953$			36.2840i			1.17535i	0.809096	+	0.587677i	$0.199957\pi$
$953$			36.2840i			1.17535i	−0.809096	+	0.587677i	$0.800043\pi$
$954$	−6.21850	−	6.39578i	−0.201331	−	0.207071i
$955$	−39.4461	−	6.03381i	−1.27645	−	0.195250i
$956$	48.9675	+	1.37664i	1.58372	+	0.0445237i
$957$	1.95826	−	3.39181i	0.0633017	−	0.109642i
$958$	−5.58295	−	1.58036i	−0.180377	−	0.0510592i
$959$		0			0
$960$	5.49131	+	5.21612i	0.177231	+	0.168350i
$961$	14.4084	−	24.9561i	0.464787	−	0.805035i
$962$	−8.23722	+	2.08355i	−0.265579	+	0.0671762i
$963$	13.8639	+	24.0129i	0.446757	+	0.773805i
$964$	−18.2447	−	33.7575i	−0.587622	−	1.08725i
$965$	−25.4896	+	31.8199i	−0.820539	+	1.02432i
$966$		0			0
$967$	−41.0345			−1.31958			−0.659790	−	0.751450i	$-0.729355\pi$
$967$	−41.0345			−1.31958			−0.659790	+	0.751450i	$0.729355\pi$
$968$	35.7924	−	7.99037i	1.15041	−	0.256820i
$969$	11.7502	−	6.78399i	0.377471	−	0.217933i
$970$	4.48956	−	9.85057i	0.144151	−	0.316283i
$971$	−22.1241	+	38.3201i	−0.709997	+	1.22975i	0.254860	+	0.966978i	$0.417970\pi$
$971$	−22.1241	+	38.3201i	−0.709997	+	1.22975i	−0.964858	+	0.262773i	$0.915363\pi$
$972$	−11.0429	+	17.9428i	−0.354202	+	0.575514i
$973$		0			0
$974$	46.0089	+	13.0237i	1.47422	+	0.417306i
$975$	−1.61157	+	5.14458i	−0.0516116	+	0.164758i
$976$	−12.9502	−	8.48106i	−0.414526	−	0.271472i
$977$	−9.99116	+	5.76840i	−0.319646	+	0.184547i	−0.651235	−	0.758876i	$-0.725749\pi$
$977$	−9.99116	+	5.76840i	−0.319646	+	0.184547i	0.331589	+	0.943424i	$0.392415\pi$
$978$	−0.805789	−	0.828761i	−0.0257663	−	0.0265009i
$979$	10.6846			0.341483
$980$		0			0
$981$	−26.5494			−0.847658
$982$	−25.5449	−	26.2731i	−0.815170	−	0.838409i
$983$	13.6399	−	7.87503i	0.435047	−	0.251174i	−0.266448	−	0.963849i	$-0.585850\pi$
$983$	13.6399	−	7.87503i	0.435047	−	0.251174i	0.701494	+	0.712675i	$0.252517\pi$
$984$	−2.52825	+	8.06001i	−0.0805978	+	0.256944i
$985$	−9.22606	−	23.6597i	−0.293967	−	0.753859i
$986$	−13.1501	−	3.72237i	−0.418783	−	0.118545i
$987$		0			0
$988$	−27.1795	−	16.7277i	−0.864694	−	0.532178i
$989$	24.9592	−	43.2307i	0.793658	−	1.37466i
$990$	39.7354	+	18.1101i	1.26287	+	0.575576i
$991$	−2.35222	+	1.35806i	−0.0747208	+	0.0431401i	−0.536895	−	0.843649i	$-0.680403\pi$
$991$	−2.35222	+	1.35806i	−0.0747208	+	0.0431401i	0.462174	+	0.886789i	$0.347070\pi$
$992$	7.90176	+	2.72479i	0.250881	+	0.0865120i
$993$	6.20742			0.196986
$994$		0			0
$995$	−15.7559	−	12.6214i	−0.499497	−	0.400126i
$996$	3.22466	−	1.74281i	0.102177	−	0.0552231i
$997$	4.48080	+	7.76097i	0.141908	+	0.245792i	0.928215	−	0.372044i	$-0.121343\pi$
$997$	4.48080	+	7.76097i	0.141908	+	0.245792i	−0.786307	+	0.617836i	$0.788010\pi$
$998$	−33.3194	+	8.42791i	−1.05471	+	0.266781i
$999$	2.90704	−	5.03515i	0.0919748	−	0.159305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.g.19.12		96
4.3	odd	2	inner	980.2.s.g.19.29		96
5.4	even	2	inner	980.2.s.g.19.37		96
7.2	even	3		980.2.c.e.979.44	yes	48
7.3	odd	6	inner	980.2.s.g.619.20		96
7.4	even	3	inner	980.2.s.g.619.19		96
7.5	odd	6		980.2.c.e.979.43	yes	48
7.6	odd	2	inner	980.2.s.g.19.11		96
20.19	odd	2	inner	980.2.s.g.19.20		96
28.3	even	6	inner	980.2.s.g.619.37		96
28.11	odd	6	inner	980.2.s.g.619.38		96
28.19	even	6		980.2.c.e.979.8	yes	48
28.23	odd	6		980.2.c.e.979.7	yes	48
28.27	even	2	inner	980.2.s.g.19.30		96
35.4	even	6	inner	980.2.s.g.619.30		96
35.9	even	6		980.2.c.e.979.5	✓	48
35.19	odd	6		980.2.c.e.979.6	yes	48
35.24	odd	6	inner	980.2.s.g.619.29		96
35.34	odd	2	inner	980.2.s.g.19.38		96
140.19	even	6		980.2.c.e.979.41	yes	48
140.39	odd	6	inner	980.2.s.g.619.11		96
140.59	even	6	inner	980.2.s.g.619.12		96
140.79	odd	6		980.2.c.e.979.42	yes	48
140.139	even	2	inner	980.2.s.g.19.19		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.c.e.979.5	✓	48	35.9	even	6
980.2.c.e.979.6	yes	48	35.19	odd	6
980.2.c.e.979.7	yes	48	28.23	odd	6
980.2.c.e.979.8	yes	48	28.19	even	6
980.2.c.e.979.41	yes	48	140.19	even	6
980.2.c.e.979.42	yes	48	140.79	odd	6
980.2.c.e.979.43	yes	48	7.5	odd	6
980.2.c.e.979.44	yes	48	7.2	even	3
980.2.s.g.19.11		96	7.6	odd	2	inner
980.2.s.g.19.12		96	1.1	even	1	trivial
980.2.s.g.19.19		96	140.139	even	2	inner
980.2.s.g.19.20		96	20.19	odd	2	inner
980.2.s.g.19.29		96	4.3	odd	2	inner
980.2.s.g.19.30		96	28.27	even	2	inner
980.2.s.g.19.37		96	5.4	even	2	inner
980.2.s.g.19.38		96	35.34	odd	2	inner
980.2.s.g.619.11		96	140.39	odd	6	inner
980.2.s.g.619.12		96	140.59	even	6	inner
980.2.s.g.619.19		96	7.4	even	3	inner
980.2.s.g.619.20		96	7.3	odd	6	inner
980.2.s.g.619.29		96	35.24	odd	6	inner
980.2.s.g.619.30		96	35.4	even	6	inner
980.2.s.g.619.37		96	28.3	even	6	inner
980.2.s.g.619.38		96	28.11	odd	6	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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.01395 + 0.985849i) q^{2} +(0.366665 - 0.211694i) q^{3} +(0.0562045 - 1.99921i) q^{4} +(2.08328 - 0.812373i) q^{5} +(-0.163083 + 0.576124i) q^{6} +(1.91393 + 2.08252i) q^{8} +(-1.41037 + 2.44283i) q^{9} +(-1.31147 + 2.87751i) q^{10} +(-4.23964 + 2.44776i) q^{11} +(-0.402613 - 0.744938i) q^{12} -2.54664 q^{13} +(0.591890 - 0.738886i) q^{15} +(-3.99368 - 0.224729i) q^{16} +(-2.55715 - 4.42911i) q^{17} +(-0.978214 - 3.86733i) q^{18} +(-3.13300 + 5.42652i) q^{19} +(-1.50701 - 4.21057i) q^{20} +(1.88568 - 6.66155i) q^{22} +(-2.31555 + 4.01064i) q^{23} +(1.14263 + 0.358418i) q^{24} +(3.68010 - 3.38480i) q^{25} +(2.58218 - 2.51060i) q^{26} +2.46443i q^{27} -1.88958 q^{29} +(0.128280 + 1.33271i) q^{30} +(0.738782 + 1.27961i) q^{31} +(4.27096 - 3.70930i) q^{32} +(-1.03635 + 1.79501i) q^{33} +(6.95926 + 1.96995i) q^{34} +(4.80447 + 2.95693i) q^{36} +(-2.04313 - 1.17960i) q^{37} +(-2.17301 - 8.59091i) q^{38} +(-0.933764 + 0.539109i) q^{39} +(5.67903 + 2.78364i) q^{40} +7.05393i q^{41} -10.7790 q^{43} +(4.65529 + 8.61350i) q^{44} +(-0.953704 + 6.23485i) q^{45} +(-1.60603 - 6.34939i) q^{46} +(10.5781 + 6.10725i) q^{47} +(-1.51192 + 0.763038i) q^{48} +(-0.394553 + 7.06005i) q^{50} +(-1.87523 - 1.08267i) q^{51} +(-0.143133 + 5.09127i) q^{52} +(1.93661 - 1.11810i) q^{53} +(-2.42956 - 2.49882i) q^{54} +(-6.84386 + 8.54352i) q^{55} +2.65295i q^{57} +(1.91594 - 1.86284i) q^{58} +(2.84500 + 4.92768i) q^{59} +(-1.44392 - 1.22484i) q^{60} +(3.35156 + 1.93502i) q^{61} +(-2.01059 - 0.569136i) q^{62} +(-0.673743 + 7.97158i) q^{64} +(-5.30536 + 2.06882i) q^{65} +(-0.718799 - 2.84174i) q^{66} +(-0.444655 - 0.770165i) q^{67} +(-8.99844 + 4.86334i) q^{68} +1.96075i q^{69} -14.3310i q^{71} +(-7.78659 + 1.73829i) q^{72} +(-3.93594 - 6.81724i) q^{73} +(3.23454 - 0.818154i) q^{74} +(0.632822 - 2.02014i) q^{75} +(10.6727 + 6.56853i) q^{76} +(0.415314 - 1.46718i) q^{78} +(4.01812 + 2.31987i) q^{79} +(-8.50252 + 2.77619i) q^{80} +(-3.70941 - 6.42488i) q^{81} +(-6.95411 - 7.15236i) q^{82} +4.32876i q^{83} +(-8.92534 - 7.14971i) q^{85} +(10.9294 - 10.6264i) q^{86} +(-0.692841 + 0.400012i) q^{87} +(-13.2119 - 4.14428i) q^{88} +(-1.89013 - 1.09127i) q^{89} +(-5.17961 - 7.26206i) q^{90} +(7.88798 + 4.85468i) q^{92} +(0.541770 + 0.312791i) q^{93} +(-16.7465 + 4.23590i) q^{94} +(-2.11856 + 13.8501i) q^{95} +(0.780773 - 2.26421i) q^{96} -3.42330 q^{97} -13.8090i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 16 q^{4} + 64 q^{9} - 16 q^{16} + 16 q^{25} - 96 q^{29} + 8 q^{30} + 352 q^{36} + 48 q^{44} + 32 q^{46} + 64 q^{50} - 24 q^{60} - 160 q^{64} + 16 q^{65} + 112 q^{74} + 48 q^{81} - 128 q^{85} + 112 q^{86}+O(q^{100}) \) 96 * q - 16 * q^4 + 64 * q^9 - 16 * q^16 + 16 * q^25 - 96 * q^29 + 8 * q^30 + 352 * q^36 + 48 * q^44 + 32 * q^46 + 64 * q^50 - 24 * q^60 - 160 * q^64 + 16 * q^65 + 112 * q^74 + 48 * q^81 - 128 * q^85 + 112 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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