LMFDB - Embedded newform 925.2.bc.e.49.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(49,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14]))

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

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

chi := DirichletCharacter("925.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bc (of order $18$, degree $6$, 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.9
Character	$\chi$	$=$	925.49
Dual form			925.2.bc.e.774.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777601 - 0.926709i) q^{2} +(1.92015 - 2.28834i) q^{3} +(0.0931703 - 0.528395i) q^{4} -3.61374 q^{6} +(-0.899712 - 2.47194i) q^{7} +(-2.65744 + 1.53427i) q^{8} +(-1.02860 - 5.83350i) q^{9} +O(q^{10})$	\(q+(-0.777601 - 0.926709i) q^{2} +(1.92015 - 2.28834i) q^{3} +(0.0931703 - 0.528395i) q^{4} -3.61374 q^{6} +(-0.899712 - 2.47194i) q^{7} +(-2.65744 + 1.53427i) q^{8} +(-1.02860 - 5.83350i) q^{9} +(-2.05288 - 3.55569i) q^{11} +(-1.03025 - 1.22780i) q^{12} +(5.11585 + 0.902063i) q^{13} +(-1.59115 + 2.75595i) q^{14} +(2.47987 + 0.902600i) q^{16} +(3.80463 - 0.670858i) q^{17} +(-4.60612 + 5.48936i) q^{18} +(-3.00738 - 2.52349i) q^{19} +(-7.38423 - 2.68764i) q^{21} +(-1.69877 + 4.66732i) q^{22} +(7.59031 + 4.38227i) q^{23} +(-1.59173 + 9.02716i) q^{24} +(-3.14214 - 5.44235i) q^{26} +(-7.56311 - 4.36656i) q^{27} +(-1.38999 + 0.245092i) q^{28} +(4.63674 + 8.03107i) q^{29} -4.88813 q^{31} +(1.00710 + 2.76699i) q^{32} +(-12.0785 - 2.12976i) q^{33} +(-3.58017 - 3.00412i) q^{34} -3.17823 q^{36} +(-5.02721 + 3.42449i) q^{37} +4.74923i q^{38} +(11.8874 - 9.97474i) q^{39} +(-0.0686945 + 0.389586i) q^{41} +(3.25133 + 8.93295i) q^{42} +2.75281i q^{43} +(-2.07007 + 0.753445i) q^{44} +(-1.84115 - 10.4417i) q^{46} +(-1.83566 - 1.05982i) q^{47} +(6.82719 - 3.94168i) q^{48} +(0.0613108 - 0.0514458i) q^{49} +(5.77029 - 9.99444i) q^{51} +(0.953290 - 2.61914i) q^{52} +(0.660379 - 1.81438i) q^{53} +(1.83455 + 10.4043i) q^{54} +(6.18355 + 5.18862i) q^{56} +(-11.5492 + 2.03644i) q^{57} +(3.83693 - 10.5419i) q^{58} +(-3.30713 - 1.20370i) q^{59} +(-0.0936657 + 0.531205i) q^{61} +(3.80102 + 4.52988i) q^{62} +(-13.4946 + 7.79112i) q^{63} +(4.42010 - 7.65583i) q^{64} +(7.41856 + 12.8493i) q^{66} +(1.35225 + 3.71526i) q^{67} -2.07285i q^{68} +(24.6027 - 8.95463i) q^{69} +(4.29878 + 3.60710i) q^{71} +(11.6836 + 13.9240i) q^{72} -11.6830i q^{73} +(7.08267 + 1.99588i) q^{74} +(-1.61360 + 1.35397i) q^{76} +(-6.94244 + 8.27368i) q^{77} +(-18.4874 - 3.25982i) q^{78} +(-8.98019 + 3.26852i) q^{79} +(-7.81571 + 2.84469i) q^{81} +(0.414450 - 0.239283i) q^{82} +(15.3032 - 2.69836i) q^{83} +(-2.10813 + 3.65138i) q^{84} +(2.55105 - 2.14059i) q^{86} +(27.2811 + 4.81039i) q^{87} +(10.9108 + 6.29934i) q^{88} +(-3.42252 - 1.24570i) q^{89} +(-2.37295 - 13.4577i) q^{91} +(3.02276 - 3.60238i) q^{92} +(-9.38594 + 11.1857i) q^{93} +(0.445267 + 2.52524i) q^{94} +(8.26562 + 3.00844i) q^{96} +(-7.37135 - 4.25585i) q^{97} +(-0.0953507 - 0.0168129i) q^{98} +(-18.6305 + 15.6329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{4}+O(q^{10}) $ 156 * q - 6 * q^4	$ 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) $ 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.777601	−	0.926709i	−0.549847	−	0.655282i	0.417518	−	0.908669i	$-0.362900\pi$
$2$	−0.777601	−	0.926709i	−0.549847	−	0.655282i	−0.967365	+	0.253386i	$0.918456\pi$
$3$	1.92015	−	2.28834i	1.10860	−	1.32118i	0.166424	−	0.986054i	$-0.446778\pi$
$3$	1.92015	−	2.28834i	1.10860	−	1.32118i	0.942175	−	0.335122i	$-0.108778\pi$
$4$	0.0931703	−	0.528395i	0.0465851	−	0.264197i
$5$		0			0
$5$		0			0
$6$	−3.61374			−1.47530
$7$	−0.899712	−	2.47194i	−0.340059	−	0.934305i	−0.985377	−	0.170391i	$-0.945497\pi$
$7$	−0.899712	−	2.47194i	−0.340059	−	0.934305i	0.645317	−	0.763915i	$-0.276725\pi$
$8$	−2.65744	+	1.53427i	−0.939546	+	0.542447i
$9$	−1.02860	−	5.83350i	−0.342868	−	1.94450i
$10$		0			0
$11$	−2.05288	−	3.55569i	−0.618965	−	1.07208i	−0.989675	−	0.143331i	$-0.954219\pi$
$11$	−2.05288	−	3.55569i	−0.618965	−	1.07208i	0.370709	−	0.928749i	$-0.379115\pi$
$12$	−1.03025	−	1.22780i	−0.297407	−	0.354436i
$13$	5.11585	+	0.902063i	1.41888	+	0.250187i	0.829879	−	0.557944i	$-0.188410\pi$
$13$	5.11585	+	0.902063i	1.41888	+	0.250187i	0.589003	+	0.808131i	$0.299521\pi$
$14$	−1.59115	+	2.75595i	−0.425253	+	0.736560i
$15$		0			0
$16$	2.47987	+	0.902600i	0.619968	+	0.225650i
$17$	3.80463	−	0.670858i	0.922757	−	0.162707i	0.307966	−	0.951397i	$-0.400352\pi$
$17$	3.80463	−	0.670858i	0.922757	−	0.162707i	0.614791	+	0.788690i	$0.289240\pi$
$18$	−4.60612	+	5.48936i	−1.08567	+	1.29385i
$19$	−3.00738	−	2.52349i	−0.689939	−	0.578928i	0.228952	−	0.973438i	$-0.426470\pi$
$19$	−3.00738	−	2.52349i	−0.689939	−	0.578928i	−0.918892	+	0.394510i	$0.870914\pi$
$20$		0			0
$21$	−7.38423	−	2.68764i	−1.61137	−	0.586491i
$22$	−1.69877	+	4.66732i	−0.362178	+	0.995077i
$23$	7.59031	+	4.38227i	1.58269	+	0.913766i	0.994465	+	0.105067i	$0.0335056\pi$
$23$	7.59031	+	4.38227i	1.58269	+	0.913766i	0.588223	+	0.808699i	$0.299828\pi$
$24$	−1.59173	+	9.02716i	−0.324911	+	1.84266i
$25$		0			0
$26$	−3.14214	−	5.44235i	−0.616225	−	1.06733i
$27$	−7.56311	−	4.36656i	−1.45552	−	0.840346i
$28$	−1.38999	+	0.245092i	−0.262683	+	0.0463180i
$29$	4.63674	+	8.03107i	0.861021	+	1.49133i	0.870944	+	0.491382i	$0.163508\pi$
$29$	4.63674	+	8.03107i	0.861021	+	1.49133i	−0.00992263	+	0.999951i	$0.503159\pi$
$30$		0			0
$31$	−4.88813			−0.877935			−0.438967	−	0.898503i	$-0.644656\pi$
$31$	−4.88813			−0.877935			−0.438967	+	0.898503i	$0.644656\pi$
$32$	1.00710	+	2.76699i	0.178032	+	0.489140i
$33$	−12.0785	−	2.12976i	−2.10259	−	0.370743i
$34$	−3.58017	−	3.00412i	−0.613994	−	0.515203i
$35$		0			0
$36$	−3.17823			−0.529705
$37$	−5.02721	+	3.42449i	−0.826469	+	0.562982i
$37$	−5.02721	+	3.42449i	−0.826469	+	0.562982i
$38$			4.74923i			0.770427i
$39$	11.8874	−	9.97474i	1.90351	−	1.59724i
$40$		0			0
$41$	−0.0686945	+	0.389586i	−0.0107283	+	0.0608431i	−0.989702	−	0.143144i	$-0.954279\pi$
$41$	−0.0686945	+	0.389586i	−0.0107283	+	0.0608431i	0.978974	+	0.203987i	$0.0653900\pi$
$42$	3.25133	+	8.93295i	0.501691	+	1.37838i
$43$			2.75281i			0.419800i	0.977723	+	0.209900i	$0.0673138\pi$
$43$			2.75281i			0.419800i	−0.977723	+	0.209900i	$0.932686\pi$
$44$	−2.07007	+	0.753445i	−0.312075	+	0.113586i
$45$		0			0
$46$	−1.84115	−	10.4417i	−0.271462	−	1.53954i
$47$	−1.83566	−	1.05982i	−0.267758	−	0.154590i	0.360110	−	0.932910i	$-0.382739\pi$
$47$	−1.83566	−	1.05982i	−0.267758	−	0.154590i	−0.627868	+	0.778320i	$0.716072\pi$
$48$	6.82719	−	3.94168i	0.985420	−	0.568932i
$49$	0.0613108	−	0.0514458i	0.00875868	−	0.00734941i
$50$		0			0
$51$	5.77029	−	9.99444i	0.808003	−	1.39950i
$52$	0.953290	−	2.61914i	0.132198	−	0.363210i
$53$	0.660379	−	1.81438i	0.0907101	−	0.249224i	−0.886039	−	0.463612i	$-0.846553\pi$
$53$	0.660379	−	1.81438i	0.0907101	−	0.249224i	0.976749	+	0.214388i	$0.0687756\pi$
$54$	1.83455	+	10.4043i	0.249651	+	1.41584i
$55$		0			0
$56$	6.18355	+	5.18862i	0.826312	+	0.693358i
$57$	−11.5492	+	2.03644i	−1.52973	+	0.269733i
$58$	3.83693	−	10.5419i	0.503814	−	1.38422i
$59$	−3.30713	−	1.20370i	−0.430551	−	0.156708i	0.117649	−	0.993055i	$-0.462464\pi$
$59$	−3.30713	−	1.20370i	−0.430551	−	0.156708i	−0.548200	+	0.836348i	$0.684687\pi$
$60$		0			0
$61$	−0.0936657	+	0.531205i	−0.0119927	+	0.0680138i	−0.990217	−	0.139538i	$-0.955438\pi$
$61$	−0.0936657	+	0.531205i	−0.0119927	+	0.0680138i	0.978224	+	0.207551i	$0.0665495\pi$
$62$	3.80102	+	4.52988i	0.482730	+	0.575295i
$63$	−13.4946	+	7.79112i	−1.70016	+	0.981589i
$64$	4.42010	−	7.65583i	0.552512	−	0.956979i
$65$		0			0
$66$	7.41856	+	12.8493i	0.913162	+	1.58164i
$67$	1.35225	+	3.71526i	0.165203	+	0.453892i	0.994478	−	0.104950i	$-0.0334682\pi$
$67$	1.35225	+	3.71526i	0.165203	+	0.453892i	−0.829274	+	0.558842i	$0.811246\pi$
$68$		−	2.07285i		−	0.251370i
$69$	24.6027	−	8.95463i	2.96181	−	1.07801i
$70$		0			0
$71$	4.29878	+	3.60710i	0.510171	+	0.428084i	0.861189	−	0.508284i	$-0.169720\pi$
$71$	4.29878	+	3.60710i	0.510171	+	0.428084i	−0.351018	+	0.936369i	$0.614165\pi$
$72$	11.6836	+	13.9240i	1.37693	+	1.64096i
$73$		−	11.6830i		−	1.36739i	−0.729769	−	0.683694i	$-0.760372\pi$
$73$		−	11.6830i		−	1.36739i	0.729769	−	0.683694i	$-0.239628\pi$
$74$	7.08267	+	1.99588i	0.823344	+	0.232016i
$75$		0			0
$76$	−1.61360	+	1.35397i	−0.185092	+	0.155311i
$77$	−6.94244	+	8.27368i	−0.791164	+	0.942873i
$78$	−18.4874	−	3.25982i	−2.09328	−	0.369102i
$79$	−8.98019	+	3.26852i	−1.01035	+	0.367738i	−0.793567	−	0.608482i	$-0.791779\pi$
$79$	−8.98019	+	3.26852i	−1.01035	+	0.367738i	−0.216783	+	0.976220i	$0.569556\pi$
$80$		0			0
$81$	−7.81571	+	2.84469i	−0.868413	+	0.316076i
$82$	0.414450	−	0.239283i	0.0457683	−	0.0264243i
$83$	15.3032	−	2.69836i	1.67974	−	0.296183i	0.749192	−	0.662353i	$-0.230442\pi$
$83$	15.3032	−	2.69836i	1.67974	−	0.296183i	0.930548	+	0.366170i	$0.119331\pi$
$84$	−2.10813	+	3.65138i	−0.230015	+	0.398398i
$85$		0			0
$86$	2.55105	−	2.14059i	0.275087	−	0.230826i
$87$	27.2811	+	4.81039i	2.92484	+	0.515728i
$88$	10.9108	+	6.29934i	1.16309	+	0.671512i
$89$	−3.42252	−	1.24570i	−0.362786	−	0.132043i	0.154194	−	0.988041i	$-0.450722\pi$
$89$	−3.42252	−	1.24570i	−0.362786	−	0.132043i	−0.516981	+	0.855997i	$0.672944\pi$
$90$		0			0
$91$	−2.37295	−	13.4577i	−0.248753	−	1.41075i
$92$	3.02276	−	3.60238i	0.315144	−	0.375574i
$93$	−9.38594	+	11.1857i	−0.973277	+	1.15991i
$94$	0.445267	+	2.52524i	0.0459258	+	0.260458i
$95$		0			0
$96$	8.26562	+	3.00844i	0.843606	+	0.307047i
$97$	−7.37135	−	4.25585i	−0.748447	−	0.432116i	0.0766855	−	0.997055i	$-0.475566\pi$
$97$	−7.37135	−	4.25585i	−0.748447	−	0.432116i	−0.825132	+	0.564939i	$0.808900\pi$
$98$	−0.0953507	−	0.0168129i	−0.00963187	−	0.00169836i
$99$	−18.6305	+	15.6329i	−1.87244	+	1.57116i
$100$		0			0
$101$	−2.78746	+	4.82802i	−0.277362	+	0.480406i	−0.970728	−	0.240180i	$-0.922794\pi$
$101$	−2.78746	+	4.82802i	−0.277362	+	0.480406i	0.693366	+	0.720586i	$0.256127\pi$
$102$	−13.7489	+	2.42431i	−1.36135	+	0.240042i
$103$	−0.437589	+	0.252642i	−0.0431169	+	0.0248936i	−0.521404	−	0.853310i	$-0.674591\pi$
$103$	−0.437589	+	0.252642i	−0.0431169	+	0.0248936i	0.478287	+	0.878204i	$0.341258\pi$
$104$	−14.9791	+	5.45193i	−1.46882	+	0.534606i
$105$		0			0
$106$	−2.19491	+	0.798883i	−0.213189	+	0.0775943i
$107$	−7.83699	−	1.38187i	−0.757631	−	0.133591i	−0.218528	−	0.975831i	$-0.570125\pi$
$107$	−7.83699	−	1.38187i	−0.757631	−	0.133591i	−0.539103	+	0.842240i	$0.681237\pi$
$108$	−3.01193	+	3.58947i	−0.289823	+	0.345397i
$109$	−2.76511	+	2.32020i	−0.264849	+	0.222235i	−0.765535	−	0.643394i	$-0.777526\pi$
$109$	−2.76511	+	2.32020i	−0.264849	+	0.222235i	0.500686	+	0.865629i	$0.333081\pi$
$110$		0			0
$111$	−1.81659	+	18.0795i	−0.172423	+	1.71603i
$112$		−	6.94218i		−	0.655974i
$113$	7.50588	+	8.94516i	0.706094	+	0.841490i	0.993201	−	0.116408i	$-0.0371381\pi$
$113$	7.50588	+	8.94516i	0.706094	+	0.841490i	−0.287108	+	0.957898i	$0.592694\pi$
$114$	10.8679	+	9.11923i	1.01787	+	0.854094i
$115$		0			0
$116$	4.67558	−	1.70177i	0.434117	−	0.158006i
$117$		−	30.7712i		−	2.84480i
$118$	1.45615	+	4.00074i	0.134049	+	0.368298i
$119$	−5.08139	−	8.80122i	−0.465810	−	0.806807i
$120$		0			0
$121$	−2.92860	+	5.07248i	−0.266236	+	0.461135i
$122$	0.565107	−	0.326264i	0.0511624	−	0.0295386i
$123$	0.759603	+	0.905259i	0.0684911	+	0.0816245i
$124$	−0.455429	+	2.58286i	−0.0408987	+	0.231948i
$125$		0			0
$126$	17.7135	+	6.44720i	1.57805	+	0.574362i
$127$	7.22802	−	19.8588i	0.641383	−	1.76218i	−0.00595603	−	0.999982i	$-0.501896\pi$
$127$	7.22802	−	19.8588i	0.641383	−	1.76218i	0.647339	−	0.762202i	$-0.275882\pi$
$128$	−4.73213	+	0.834403i	−0.418266	+	0.0737515i
$129$	6.29938	+	5.28581i	0.554629	+	0.465389i
$130$		0			0
$131$	−3.33897	−	18.9362i	−0.291727	−	1.65447i	−0.680216	−	0.733012i	$-0.738114\pi$
$131$	−3.33897	−	18.9362i	−0.291727	−	1.65447i	0.388489	−	0.921453i	$-0.372997\pi$
$132$	−2.25071	+	6.18377i	−0.195899	+	0.538228i
$133$	−3.53214	+	9.70446i	−0.306275	+	0.841484i
$134$	2.39146	−	4.14213i	0.206591	−	0.357826i
$135$		0			0
$136$	−9.08127	+	7.62009i	−0.778713	+	0.653418i
$137$	−0.662374	+	0.382422i	−0.0565904	+	0.0326725i	−0.528028	−	0.849227i	$-0.677068\pi$
$137$	−0.662374	+	0.382422i	−0.0565904	+	0.0326725i	0.471438	+	0.881899i	$0.343735\pi$
$138$	−27.4294	−	15.8364i	−2.33495	−	1.34808i
$139$	−2.04372	−	11.5905i	−0.173346	−	0.983096i	−0.940035	−	0.341077i	$-0.889208\pi$
$139$	−2.04372	−	11.5905i	−0.173346	−	0.983096i	0.766689	−	0.642019i	$-0.221903\pi$
$140$		0			0
$141$	−5.94996	+	2.16561i	−0.501077	+	0.182377i
$142$		−	6.78860i		−	0.569687i
$143$	−7.29476	−	20.0422i	−0.610018	−	1.67601i
$144$	2.71451	−	15.3948i	0.226209	−	1.28290i
$145$		0			0
$146$	−10.8267	+	9.08469i	−0.896025	+	0.751854i
$147$		−	0.239084i		−	0.0197193i
$148$	1.34110	+	2.97541i	0.110237	+	0.244578i
$149$	3.51144			0.287668			0.143834	−	0.989602i	$-0.454057\pi$
$149$	3.51144			0.287668			0.143834	+	0.989602i	$0.454057\pi$
$150$		0			0
$151$	15.9941	+	13.4206i	1.30158	+	1.09216i	0.989870	+	0.141978i	$0.0453463\pi$
$151$	15.9941	+	13.4206i	1.30158	+	1.09216i	0.311710	+	0.950177i	$0.399098\pi$
$152$	11.8636	+	2.09188i	0.962267	+	0.169674i
$153$	−7.82691	−	21.5042i	−0.632768	−	1.73852i
$154$	13.0657			1.05287
$155$		0			0
$156$	−4.16304	−	7.21060i	−0.333310	−	0.577310i
$157$	−0.528408	+	0.0931725i	−0.0421715	+	0.00743598i	−0.194694	−	0.980864i	$-0.562371\pi$
$157$	−0.528408	+	0.0931725i	−0.0421715	+	0.00743598i	0.152523	+	0.988300i	$0.451260\pi$
$158$	10.0120	+	5.78042i	0.796510	+	0.459865i
$159$	−2.88389	−	4.99505i	−0.228708	−	0.396133i
$160$		0			0
$161$	4.00360	−	22.7056i	0.315528	−	1.78945i
$162$	8.71371	+	5.03086i	0.684613	+	0.395262i
$163$	−7.80017	+	21.4308i	−0.610956	+	1.67859i	0.117142	+	0.993115i	$0.462627\pi$
$163$	−7.80017	+	21.4308i	−0.610956	+	1.67859i	−0.728098	+	0.685473i	$0.759595\pi$
$164$	0.199455	+	0.0725956i	0.0155748	+	0.00566876i
$165$		0			0
$166$	−14.4004	−	12.0833i	−1.11768	−	0.937848i
$167$	3.30963	−	3.94426i	0.256107	−	0.305216i	−0.622636	−	0.782512i	$-0.713938\pi$
$167$	3.30963	−	3.94426i	0.256107	−	0.305216i	0.878743	+	0.477295i	$0.158383\pi$
$168$	23.7467	−	4.18718i	1.83210	−	0.323048i
$169$	13.1422	+	4.78337i	1.01094	+	0.367952i
$170$		0			0
$171$	−11.6274	+	20.1392i	−0.889168	+	1.54008i
$172$	1.45457	+	0.256480i	0.110910	+	0.0195564i
$173$	2.58846	+	3.08481i	0.196797	+	0.234534i	0.855414	−	0.517944i	$-0.173303\pi$
$173$	2.58846	+	3.08481i	0.196797	+	0.234534i	−0.658617	+	0.752478i	$0.728858\pi$
$174$	−16.7560	−	29.0222i	−1.27027	−	2.20017i
$175$		0			0
$176$	−1.88151	−	10.6706i	−0.141824	−	0.804325i
$177$	−9.10464	+	5.25657i	−0.684347	+	0.395108i
$178$	1.50696	+	4.14034i	0.112951	+	0.310331i
$179$	−8.85764			−0.662051			−0.331025	−	0.943622i	$-0.607395\pi$
$179$	−8.85764			−0.662051			−0.331025	+	0.943622i	$0.607395\pi$
$180$		0			0
$181$	−2.53534	+	14.3786i	−0.188450	+	1.06876i	0.732991	+	0.680238i	$0.238124\pi$
$181$	−2.53534	+	14.3786i	−0.188450	+	1.06876i	−0.921441	+	0.388517i	$0.872987\pi$
$182$	−10.6261	+	12.6637i	−0.787662	+	0.938699i
$183$	1.03573	+	1.23433i	0.0765631	+	0.0912444i
$184$	−26.8943			−1.98268
$185$		0			0
$186$	17.6644			1.29522
$187$	−10.1958	−	12.1509i	−0.745590	−	0.888559i
$188$	−0.731030	+	0.871208i	−0.0533159	+	0.0635394i
$189$	−3.98926	+	22.6242i	−0.290176	+	1.64567i
$190$		0			0
$191$	−13.2823			−0.961075			−0.480537	−	0.876974i	$-0.659558\pi$
$191$	−13.2823			−0.961075			−0.480537	+	0.876974i	$0.659558\pi$
$192$	−9.03194	−	24.8151i	−0.651824	−	1.79087i
$193$	6.18771	−	3.57247i	0.445401	−	0.257152i	−0.260485	−	0.965478i	$-0.583882\pi$
$193$	6.18771	−	3.57247i	0.445401	−	0.257152i	0.705886	+	0.708326i	$0.250549\pi$
$194$	1.78804	+	10.1405i	0.128373	+	0.728042i
$195$		0			0
$196$	−0.0214714	−	0.0371895i	−0.00153367	−	0.00265639i
$197$	16.7650	+	19.9798i	1.19446	+	1.42350i	0.880487	+	0.474070i	$0.157216\pi$
$197$	16.7650	+	19.9798i	1.19446	+	1.42350i	0.313973	+	0.949432i	$0.398340\pi$
$198$	28.9742	+	5.10894i	2.05911	+	0.363076i
$199$	5.01011	−	8.67776i	0.355157	−	0.615150i	−0.631988	−	0.774978i	$-0.717761\pi$
$199$	5.01011	−	8.67776i	0.355157	−	0.615150i	0.987145	+	0.159828i	$0.0510940\pi$
$200$		0			0
$201$	11.0983	+	4.03946i	0.782815	+	0.284921i
$202$	6.64170	−	1.17111i	0.467308	−	0.0823991i
$203$	15.6806	−	18.6874i	1.10056	−	1.31160i
$204$	−4.74339	−	3.98018i	−0.332104	−	0.278668i
$205$		0			0
$206$	0.574395	+	0.209063i	0.0400200	+	0.0145661i
$207$	17.7565	−	48.7857i	1.23416	−	3.39084i
$208$	11.8725	+	6.85457i	0.823207	+	0.475279i
$209$	−2.79896	+	15.8737i	−0.193608	+	1.09801i
$210$		0			0
$211$	2.84657	+	4.93040i	0.195966	+	0.339423i	0.947217	−	0.320594i	$-0.103882\pi$
$211$	2.84657	+	4.93040i	0.195966	+	0.339423i	−0.751251	+	0.660017i	$0.770549\pi$
$212$	−0.897180	−	0.517987i	−0.0616186	−	0.0355755i
$213$	16.5086	−	2.91091i	1.13115	−	0.199452i
$214$	4.81346	+	8.33716i	0.329041	+	0.569917i
$215$		0			0
$216$	26.7980			1.82337
$217$	4.39791	+	12.0832i	0.298550	+	0.820259i
$218$	4.30031	+	0.758260i	0.291253	+	0.0513558i
$219$	−26.7347	−	22.4330i	−1.80656	−	1.51588i
$220$		0			0
$221$	20.0691			1.34999
$222$	18.1670	−	12.3752i	1.21929	−	0.830570i
$223$		−	18.5146i		−	1.23983i	−0.784668	−	0.619916i	$-0.787167\pi$
$223$		−	18.5146i		−	1.23983i	0.784668	−	0.619916i	$-0.212833\pi$
$224$	5.93373	−	4.97899i	0.396464	−	0.332673i
$225$		0			0
$226$	2.45298	−	13.9115i	0.163170	−	0.925382i
$227$	4.79078	+	13.1626i	0.317975	+	0.873630i	0.990982	+	0.133994i	$0.0427803\pi$
$227$	4.79078	+	13.1626i	0.317975	+	0.873630i	−0.673007	+	0.739636i	$0.734997\pi$
$228$			6.29229i			0.416717i
$229$	−0.00233946		0.000851494i	−0.000154596		5.62683e-5i	−0.342097	−	0.939664i	$-0.611137\pi$
$229$	−0.00233946		0.000851494i	−0.000154596		5.62683e-5i	0.341943	+	0.939721i	$0.388915\pi$
$230$		0			0
$231$	5.60251	+	31.7734i	0.368618	+	2.09054i
$232$	−24.6437	−	14.2280i	−1.61794	−	0.934117i
$233$	−0.0387787	+	0.0223889i	−0.00254048	+	0.00146675i	−0.501270	−	0.865291i	$-0.667134\pi$
$233$	−0.0387787	+	0.0223889i	−0.00254048	+	0.00146675i	0.498729	+	0.866758i	$0.333800\pi$
$234$	−28.5160	+	23.9277i	−1.86415	+	1.56420i
$235$		0			0
$236$	−0.944152	+	1.63532i	−0.0614591	+	0.106450i
$237$	−9.76380	+	26.8258i	−0.634227	+	1.74252i
$238$	−4.20488	+	11.5528i	−0.272562	+	0.748858i
$239$	−4.40032	−	24.9555i	−0.284633	−	1.61424i	−0.706593	−	0.707621i	$-0.749769\pi$
$239$	−4.40032	−	24.9555i	−0.284633	−	1.61424i	0.421959	−	0.906615i	$-0.361342\pi$
$240$		0			0
$241$	8.92689	+	7.49055i	0.575032	+	0.482509i	0.883311	−	0.468787i	$-0.155309\pi$
$241$	8.92689	+	7.49055i	0.575032	+	0.482509i	−0.308280	+	0.951296i	$0.599753\pi$
$242$	6.97800	−	1.23041i	0.448563	−	0.0790937i
$243$	0.463006	−	1.27210i	0.0297019	−	0.0816052i
$244$	0.271959	+	0.0989849i	0.0174104	+	0.00633686i
$245$		0			0
$246$	0.248244	−	1.40786i	0.0158275	−	0.0897620i
$247$	−13.1089	−	15.6226i	−0.834102	−	0.994044i
$248$	12.9899	−	7.49972i	0.824860	−	0.476233i
$249$	23.2096	−	40.2002i	1.47085	−	2.54758i
$250$		0			0
$251$	1.50934	+	2.61426i	0.0952688	+	0.165010i	0.909721	−	0.415221i	$-0.136296\pi$
$251$	1.50934	+	2.61426i	0.0952688	+	0.165010i	−0.814452	+	0.580231i	$0.802962\pi$
$252$	2.85949	+	7.85639i	0.180131	+	0.494906i
$253$		−	35.9850i		−	2.26236i
$254$	−24.0239	+	8.74397i	−1.50739	+	0.548645i
$255$		0			0
$256$	−9.09100	−	7.62826i	−0.568188	−	0.476766i
$257$	12.6491	+	15.0746i	0.789028	+	0.940327i	0.999304	−	0.0373153i	$-0.0118806\pi$
$257$	12.6491	+	15.0746i	0.789028	+	0.940327i	−0.210276	+	0.977642i	$0.567436\pi$
$258$		−	9.94794i		−	0.619332i
$259$	12.9882	+	9.34591i	0.807046	+	0.580727i
$260$		0			0
$261$	42.0799	−	35.3093i	2.60468	−	2.18559i
$262$	−14.9520	+	17.8191i	−0.923737	+	1.10087i
$263$	26.1022	+	4.60253i	1.60953	+	0.283804i	0.904854	−	0.425722i	$-0.139980\pi$
$263$	26.1022	+	4.60253i	1.60953	+	0.283804i	0.704679	+	0.709526i	$0.251091\pi$
$264$	35.3654	−	12.8719i	2.17659	−	0.792213i
$265$		0			0
$266$	11.7398	−	4.27294i	0.719814	−	0.261991i
$267$	−9.42233	+	5.43999i	−0.576637	+	0.332922i
$268$	2.08911	−	0.368367i	0.127613	−	0.0225016i
$269$	6.36638	−	11.0269i	0.388165	−	0.672321i	−0.604038	−	0.796956i	$-0.706442\pi$
$269$	6.36638	−	11.0269i	0.388165	−	0.672321i	0.992203	+	0.124634i	$0.0397758\pi$
$270$		0			0
$271$	−15.0559	+	12.6334i	−0.914578	+	0.767422i	−0.972984	−	0.230871i	$-0.925843\pi$
$271$	−15.0559	+	12.6334i	−0.914578	+	0.767422i	0.0584062	+	0.998293i	$0.481398\pi$
$272$	10.0405	+	1.77041i	0.608795	+	0.107347i
$273$	−35.3522	−	20.4106i	−2.13961	−	1.23531i
$274$	0.869457	+	0.316456i	0.0525258	+	0.0191178i
$275$		0			0
$276$	−2.43935	−	13.8342i	−0.146831	−	0.832722i
$277$	14.1967	−	16.9190i	0.852996	−	1.01656i	−0.146629	−	0.989192i	$-0.546842\pi$
$277$	14.1967	−	16.9190i	0.852996	−	1.01656i	0.999625	−	0.0273698i	$-0.00871317\pi$
$278$	−9.15185	+	10.9067i	−0.548891	+	0.654143i
$279$	5.02795	+	28.5149i	0.301016	+	1.70714i
$280$		0			0
$281$	9.09594	+	3.31065i	0.542618	+	0.197497i	0.598764	−	0.800926i	$-0.295659\pi$
$281$	9.09594	+	3.31065i	0.542618	+	0.197497i	−0.0561454	+	0.998423i	$0.517881\pi$
$282$	6.63359	+	3.82990i	0.395024	+	0.228067i
$283$	−16.0398	−	2.82825i	−0.953466	−	0.168122i	−0.324787	−	0.945787i	$-0.605293\pi$
$283$	−16.0398	−	2.82825i	−0.953466	−	0.168122i	−0.628679	+	0.777665i	$0.716404\pi$
$284$	2.30649	−	1.93538i	0.136865	−	0.114843i
$285$		0			0
$286$	−12.9009	+	22.3449i	−0.762844	+	1.32128i
$287$	1.02484	−	0.180706i	0.0604942	−	0.0106668i
$288$	15.1053	−	8.72107i	0.890091	−	0.513894i
$289$	−1.94965	+	0.709615i	−0.114685	+	0.0417420i
$290$		0			0
$291$	−23.8929	+	8.69632i	−1.40063	+	0.509787i
$292$	−6.17322	−	1.08851i	−0.361260	−	0.0637000i
$293$	−18.4353	+	21.9704i	−1.07700	+	1.28352i	−0.120212	+	0.992748i	$0.538357\pi$
$293$	−18.4353	+	21.9704i	−1.07700	+	1.28352i	−0.956792	+	0.290774i	$0.906087\pi$
$294$	−0.221561	+	0.185912i	−0.0129217	+	0.0108426i
$295$		0			0
$296$	8.10540	−	16.8135i	0.471117	−	0.977263i
$297$			35.8561i			2.08058i
$298$	−2.73050	−	3.25408i	−0.158174	−	0.188504i
$299$	34.8778	+	29.2659i	2.01704	+	1.69249i
$300$		0			0
$301$	6.80478	−	2.47674i	0.392221	−	0.142757i
$302$		−	25.2578i		−	1.45342i
$303$	5.69584	+	15.6492i	0.327217	+	0.899022i
$304$	−5.18021	−	8.97239i	−0.297106	−	0.514602i
$305$		0			0
$306$	−13.8420	+	23.9750i	−0.791293	+	1.37056i
$307$	26.5198	−	15.3112i	1.51357	−	0.873858i	0.513692	−	0.857974i	$-0.328277\pi$
$307$	26.5198	−	15.3112i	1.51357	−	0.873858i	0.999874	−	0.0158835i	$-0.00505609\pi$
$308$	3.72494	+	4.43921i	0.212248	+	0.252947i
$309$	−0.262104	+	1.48646i	−0.0149106	+	0.0845620i
$310$		0			0
$311$	−1.80612	−	0.657373i	−0.102415	−	0.0372762i	0.290304	−	0.956934i	$-0.406244\pi$
$311$	−1.80612	−	0.657373i	−0.102415	−	0.0372762i	−0.392720	+	0.919658i	$0.628466\pi$
$312$	−16.2861	+	44.7458i	−0.922021	+	2.53323i
$313$	−19.4040	+	3.42146i	−1.09678	+	0.193392i	−0.692625	−	0.721298i	$-0.743546\pi$
$313$	−19.4040	+	3.42146i	−1.09678	+	0.193392i	−0.404156	+	0.914690i	$0.632435\pi$
$314$	0.497234	+	0.417229i	0.0280606	+	0.0235456i
$315$		0			0
$316$	0.890384	+	5.04962i	0.0500880	+	0.284063i
$317$	−4.51265	+	12.3984i	−0.253456	+	0.696363i	0.746079	+	0.665857i	$0.231934\pi$
$317$	−4.51265	+	12.3984i	−0.253456	+	0.696363i	−0.999535	+	0.0305060i	$0.990288\pi$
$318$	−2.38644	+	6.55669i	−0.133825	+	0.367681i
$319$	19.0373	−	32.9736i	1.06588	−	1.84617i
$320$		0			0
$321$	−18.2104	+	15.2803i	−1.01641	+	0.852865i
$322$	−24.1547	+	13.9457i	−1.34609	+	0.777163i
$323$	−13.1348	−	7.58341i	−0.730842	−	0.421952i
$324$	0.774926	+	4.39482i	0.0430514	+	0.244157i
$325$		0			0
$326$	25.9255	−	9.43612i	1.43588	−	0.522618i
$327$			10.7827i			0.596282i
$328$	−0.415179	−	1.14070i	−0.0229244	−	0.0629844i
$329$	−0.968240	+	5.49116i	−0.0533808	+	0.302738i
$330$		0			0
$331$	13.0085	−	10.9155i	0.715014	−	0.599968i	−0.210987	−	0.977489i	$-0.567668\pi$
$331$	13.0085	−	10.9155i	0.715014	−	0.599968i	0.926001	+	0.377521i	$0.123223\pi$
$332$		−	8.33752i		−	0.457581i
$333$	25.1478	+	25.8038i	1.37809	+	1.41404i
$334$	−6.22876			−0.340823
$335$		0			0
$336$	−15.8861	−	13.3300i	−0.866657	−	0.727212i
$337$	−22.5383	−	3.97411i	−1.22774	−	0.216484i	−0.478086	−	0.878313i	$-0.658669\pi$
$337$	−22.5383	−	3.97411i	−1.22774	−	0.216484i	−0.749655	+	0.661829i	$0.769780\pi$
$338$	−5.78660	−	15.8986i	−0.314750	−	0.864768i
$339$	34.8820			1.89453
$340$		0			0
$341$	10.0347	+	17.3807i	0.543411	+	0.941216i
$342$	27.7047	−	4.88508i	1.49810	−	0.264155i
$343$	−16.1294	−	9.31231i	−0.870905	−	0.502817i
$344$	−4.22356	−	7.31542i	−0.227719	−	0.394421i
$345$		0			0
$346$	0.845930	−	4.79751i	0.0454775	−	0.257916i
$347$	−26.2354	−	15.1470i	−1.40839	−	0.813134i	−0.413156	−	0.910660i	$-0.635574\pi$
$347$	−26.2354	−	15.1470i	−1.40839	−	0.813134i	−0.995233	+	0.0975267i	$0.968907\pi$
$348$	5.08358	−	13.9670i	0.272508	−	0.748710i
$349$	−18.9605	−	6.90106i	−1.01493	−	0.369405i	−0.219607	−	0.975588i	$-0.570478\pi$
$349$	−18.9605	−	6.90106i	−1.01493	−	0.369405i	−0.795325	+	0.606183i	$0.792700\pi$
$350$		0			0
$351$	−34.7528	−	29.1611i	−1.85497	−	1.55650i
$352$	7.77109	−	9.26123i	0.414201	−	0.493625i
$353$	−8.03343	+	1.41651i	−0.427576	+	0.0753933i	−0.383295	−	0.923626i	$-0.625211\pi$
$353$	−8.03343	+	1.41651i	−0.427576	+	0.0753933i	−0.0442811	+	0.999019i	$0.514100\pi$
$354$	11.9511	+	4.34984i	0.635194	+	0.231192i
$355$		0			0
$356$	−0.977096	+	1.69238i	−0.0517860	+	0.0896960i
$357$	−29.8973	−	5.27169i	−1.58233	−	0.279008i
$358$	6.88771	+	8.20846i	0.364027	+	0.433830i
$359$	−1.06949	−	1.85241i	−0.0564454	−	0.0977663i	0.836422	−	0.548086i	$-0.184643\pi$
$359$	−1.06949	−	1.85241i	−0.0564454	−	0.0977663i	−0.892867	+	0.450320i	$0.851310\pi$
$360$		0			0
$361$	−0.622996	−	3.53319i	−0.0327893	−	0.185957i
$362$	15.2963	−	8.83132i	0.803956	−	0.464164i
$363$	5.98424	+	16.4416i	0.314091	+	0.862958i
$364$	−7.33205			−0.384304
$365$		0			0
$366$	0.338484	−	1.91964i	0.0176928	−	0.100341i
$367$	−16.2383	+	19.3521i	−0.847634	+	1.01017i	0.152128	+	0.988361i	$0.451387\pi$
$367$	−16.2383	+	19.3521i	−0.847634	+	1.01017i	−0.999762	+	0.0218099i	$0.993057\pi$
$368$	14.8676	+	17.7185i	0.775025	+	0.923639i
$369$	2.34331			0.121988
$370$		0			0
$371$	−5.07918			−0.263698
$372$	5.03599	+	6.00166i	0.261104	+	0.311172i
$373$	9.80558	−	11.6858i	0.507714	−	0.605070i	−0.449916	−	0.893071i	$-0.648546\pi$
$373$	9.80558	−	11.6858i	0.507714	−	0.605070i	0.957630	+	0.288001i	$0.0929906\pi$
$374$	−3.33206	+	18.8971i	−0.172297	+	0.977143i
$375$		0			0
$376$	6.50419			0.335428
$377$	16.4764	+	45.2684i	0.848575	+	2.33144i
$378$	24.0681	−	13.8957i	1.23793	−	0.714719i
$379$	−0.825541	−	4.68187i	−0.0424052	−	0.240492i	0.956237	−	0.292595i	$-0.0945187\pi$
$379$	−0.825541	−	4.68187i	−0.0424052	−	0.240492i	−0.998642	+	0.0521031i	$0.983408\pi$
$380$		0			0
$381$	−31.5649	−	54.6721i	−1.61712	−	2.80094i
$382$	10.3283	+	12.3088i	0.528444	+	0.629775i
$383$	−8.83431	−	1.55773i	−0.451412	−	0.0795962i	−0.0566801	−	0.998392i	$-0.518052\pi$
$383$	−8.83431	−	1.55773i	−0.451412	−	0.0795962i	−0.394732	+	0.918796i	$0.629163\pi$
$384$	−7.17700	+	12.4309i	−0.366250	+	0.634363i
$385$		0			0
$386$	−8.12221	−	2.95624i	−0.413410	−	0.150469i
$387$	16.0585	−	2.83155i	0.816301	−	0.143936i
$388$	−2.93556	+	3.49846i	−0.149030	+	0.177608i
$389$	19.2415	+	16.1456i	0.975584	+	0.818612i	0.983417	−	0.181357i	$-0.0580490\pi$
$389$	19.2415	+	16.1456i	0.975584	+	0.818612i	−0.00783338	+	0.999969i	$0.502493\pi$
$390$		0			0
$391$	31.8182	+	11.5809i	1.60911	+	0.585669i
$392$	−0.0839976	+	0.230781i	−0.00424252	+	0.0116562i
$393$	−49.7439	−	28.7197i	−2.50925	−	1.44872i
$394$	5.47894	−	31.0726i	0.276025	−	1.56542i
$395$		0			0
$396$	6.52451	+	11.3008i	0.327869	+	0.567886i
$397$	−0.634528	−	0.366345i	−0.0318461	−	0.0183863i	0.483992	−	0.875072i	$-0.339186\pi$
$397$	−0.634528	−	0.366345i	−0.0318461	−	0.0183863i	−0.515839	+	0.856686i	$0.672520\pi$
$398$	−11.9376	+	2.10493i	−0.598379	+	0.105510i
$399$	15.4249	+	26.7168i	0.772212	+	1.33751i
$400$		0			0
$401$	2.15719			0.107725			0.0538625	−	0.998548i	$-0.482847\pi$
$401$	2.15719			0.107725			0.0538625	+	0.998548i	$0.482847\pi$
$402$	−4.88666	−	13.4260i	−0.243725	−	0.669628i
$403$	−25.0070	−	4.40940i	−1.24569	−	0.219648i
$404$	2.29139	+	1.92271i	0.114001	+	0.0956582i
$405$		0			0
$406$	−29.5110			−1.46461
$407$	22.4967	+	10.8451i	1.11512	+	0.537574i
$408$			35.4128i			1.75319i
$409$	−22.5739	+	18.9418i	−1.11621	+	0.936610i	−0.998407	−	0.0564271i	$-0.982029\pi$
$409$	−22.5739	+	18.9418i	−1.11621	+	0.936610i	−0.117802	+	0.993037i	$0.537585\pi$
$410$		0			0
$411$	−0.396744	+	2.25005i	−0.0195699	+	0.110987i
$412$	0.0927245	+	0.254758i	0.00456821	+	0.0125510i
$413$			9.25799i			0.455556i
$414$	−59.0177	+	21.4807i	−2.90056	+	1.05572i
$415$		0			0
$416$	2.65619	+	15.0640i	0.130230	+	0.738573i
$417$	−30.4474	−	17.5788i	−1.49101	−	0.860838i
$418$	16.8868	−	9.74958i	0.825959	−	0.476868i
$419$	−21.1305	+	17.7306i	−1.03229	+	0.866198i	−0.991122	−	0.132954i	$-0.957554\pi$
$419$	−21.1305	+	17.7306i	−1.03229	+	0.866198i	−0.0411722	+	0.999152i	$0.513109\pi$
$420$		0			0
$421$	−9.22474	+	15.9777i	−0.449587	+	0.778707i	−0.998359	−	0.0572651i	$-0.981762\pi$
$421$	−9.22474	+	15.9777i	−0.449587	+	0.778707i	0.548772	+	0.835972i	$0.315095\pi$
$422$	2.35555	−	6.47183i	0.114667	−	0.315044i
$423$	−4.29428	+	11.7984i	−0.208795	+	0.573660i
$424$	1.02883	+	5.83479i	0.0499645	+	0.283363i
$425$		0			0
$426$	−15.5347	−	13.0351i	−0.752657	−	0.631554i
$427$	1.39738	−	0.246395i	0.0676238	−	0.0119239i
$428$	−1.46035	+	4.01228i	−0.0705887	+	0.193941i
$429$	−59.8704	−	21.7911i	−2.89057	−	1.05208i
$430$		0			0
$431$	−3.00270	+	17.0292i	−0.144635	+	0.820266i	0.823025	+	0.568006i	$0.192285\pi$
$431$	−3.00270	+	17.0292i	−0.144635	+	0.820266i	−0.967660	+	0.252260i	$0.918826\pi$
$432$	−14.8143	−	17.6550i	−0.712753	−	0.849426i
$433$	−16.2447	+	9.37889i	−0.780671	+	0.450721i	−0.836668	−	0.547710i	$-0.815500\pi$
$433$	−16.2447	+	9.37889i	−0.780671	+	0.450721i	0.0559969	+	0.998431i	$0.482166\pi$
$434$	7.77776	−	13.4715i	0.373344	−	0.646651i
$435$		0			0
$436$	0.968357	+	1.67724i	0.0463759	+	0.0803254i
$437$	−11.7683	−	32.3332i	−0.562955	−	1.54671i
$438$			42.2192i			2.01731i
$439$	11.2582	−	4.09764i	0.537323	−	0.195570i	−0.0590820	−	0.998253i	$-0.518817\pi$
$439$	11.2582	−	4.09764i	0.537323	−	0.195570i	0.596405	+	0.802683i	$0.296595\pi$
$440$		0			0
$441$	−0.363174	−	0.304739i	−0.0172940	−	0.0145114i
$442$	−15.6057	−	18.5982i	−0.742289	−	0.884625i
$443$			32.0677i			1.52358i	0.647822	+	0.761792i	$0.275680\pi$
$443$			32.0677i			1.52358i	−0.647822	+	0.761792i	$0.724320\pi$
$444$	9.38388	+	2.64435i	0.445339	+	0.125495i
$445$		0			0
$446$	−17.1577	+	14.3970i	−0.812440	+	0.681718i
$447$	6.74249	−	8.03539i	0.318909	−	0.380061i
$448$	−22.9016	−	4.03816i	−1.08200	−	0.190785i
$449$	2.57650	−	0.937768i	0.121592	−	0.0442560i	−0.280507	−	0.959852i	$-0.590503\pi$
$449$	2.57650	−	0.937768i	0.121592	−	0.0442560i	0.402100	+	0.915596i	$0.368280\pi$
$450$		0			0
$451$	1.52627	−	0.555515i	0.0718690	−	0.0261582i
$452$	5.42590	−	3.13265i	0.255213	−	0.147347i
$453$	61.4221	−	10.8304i	2.88586	−	0.508855i
$454$	8.47255	−	14.6749i	0.397637	−	0.688727i
$455$		0			0
$456$	27.5669	−	23.1314i	1.29094	−	1.08323i
$457$	28.0288	+	4.94224i	1.31113	+	0.231188i	0.785150	−	0.619306i	$-0.212586\pi$
$457$	28.0288	+	4.94224i	1.31113	+	0.231188i	0.525984	+	0.850494i	$0.323697\pi$
$458$	0.00260825	+	0.00150588i	0.000121876	+	7.03650e-5i
$459$	−31.7042	−	11.5394i	−1.47982	−	0.538612i
$460$		0			0
$461$	−2.97465	−	16.8701i	−0.138543	−	0.785717i	−0.972327	−	0.233626i	$-0.924941\pi$
$461$	−2.97465	−	16.8701i	−0.138543	−	0.785717i	0.833784	−	0.552092i	$-0.186170\pi$
$462$	25.0882	−	29.8989i	1.16721	−	1.39102i
$463$	2.99280	−	3.56668i	0.139087	−	0.165758i	−0.692004	−	0.721893i	$-0.743272\pi$
$463$	2.99280	−	3.56668i	0.139087	−	0.165758i	0.831091	+	0.556136i	$0.187717\pi$
$464$	4.24969	+	24.1012i	0.197287	+	1.11887i
$465$		0			0
$466$	0.0509024	+	0.0185270i	0.00235801	+	0.000858245i
$467$	−7.89482	−	4.55808i	−0.365329	−	0.210923i	0.306087	−	0.952004i	$-0.400980\pi$
$467$	−7.89482	−	4.55808i	−0.365329	−	0.210923i	−0.671416	+	0.741081i	$0.734313\pi$
$468$	−16.2593	−	2.86696i	−0.751588	−	0.132525i
$469$	7.96727	−	6.68533i	0.367894	−	0.308700i
$470$		0			0
$471$	−0.801411	+	1.38808i	−0.0369271	+	0.0639595i
$472$	10.6353	−	1.87529i	0.489528	−	0.0863170i
$473$	9.78813	−	5.65118i	0.450058	−	0.259841i
$474$	32.4521	−	11.8116i	1.49057	−	0.542524i
$475$		0			0
$476$	−5.12395	+	1.86497i	−0.234856	+	0.0854806i
$477$	−11.2634	−	1.98605i	−0.515718	−	0.0909350i
$478$	−19.7048	+	23.4832i	−0.901275	+	1.07410i
$479$	−10.3231	+	8.66210i	−0.471674	+	0.395781i	−0.847405	−	0.530947i	$-0.821836\pi$
$479$	−10.3231	+	8.66210i	−0.471674	+	0.395781i	0.375731	+	0.926729i	$0.377392\pi$
$480$		0			0
$481$	−28.8076	+	12.9843i	−1.31351	+	0.592034i
$482$		−	14.0973i		−	0.642114i
$483$	−44.2706	−	52.7597i	−2.01438	−	2.40065i
$484$	2.40741	+	2.02006i	0.109428	+	0.0918210i
$485$		0			0
$486$	−1.53890	+	0.560114i	−0.0698059	+	0.0254073i
$487$		−	2.28645i		−	0.103609i	−0.998657	−	0.0518044i	$-0.983503\pi$
$487$		−	2.28645i		−	0.103609i	0.998657	−	0.0518044i	$-0.0164972\pi$
$488$	−0.566101	−	1.55535i	−0.0256262	−	0.0704074i
$489$	34.0635	+	58.9998i	1.54041	+	2.66806i
$490$		0			0
$491$	5.53323	−	9.58383i	0.249711	−	0.432512i	−0.713734	−	0.700416i	$-0.752998\pi$
$491$	5.53323	−	9.58383i	0.249711	−	0.432512i	0.963446	+	0.267904i	$0.0863310\pi$
$492$	0.549107	−	0.317027i	0.0247556	−	0.0142927i
$493$	23.0288	+	27.4446i	1.03716	+	1.23604i
$494$	−4.28410	+	24.2964i	−0.192751	+	1.09314i
$495$		0			0
$496$	−12.1219	−	4.41203i	−0.544292	−	0.198106i
$497$	5.04887	−	13.8717i	0.226473	−	0.622229i
$498$	−55.3017	+	9.75117i	−2.47813	+	0.436961i
$499$	−18.1310	−	15.2137i	−0.811655	−	0.681059i	0.139347	−	0.990244i	$-0.455500\pi$
$499$	−18.1310	−	15.2137i	−0.811655	−	0.681059i	−0.951002	+	0.309184i	$0.899944\pi$
$500$		0			0
$501$	−2.67085	−	15.1472i	−0.119325	−	0.676725i
$502$	1.24899	−	3.43157i	0.0557451	−	0.153158i
$503$	9.75384	−	26.7985i	0.434902	−	1.19488i	−0.507866	−	0.861436i	$-0.669566\pi$
$503$	9.75384	−	26.7985i	0.434902	−	1.19488i	0.942768	−	0.333448i	$-0.108212\pi$
$504$	23.9074	−	41.4088i	1.06492	−	1.84450i
$505$		0			0
$506$	−33.3476	+	27.9820i	−1.48248	+	1.24395i
$507$	36.1810	−	20.8891i	1.60686	−	0.927718i
$508$	−9.81986	−	5.66950i	−0.435686	−	0.251543i
$509$	−3.99880	−	22.6783i	−0.177244	−	1.00520i	−0.935522	−	0.353268i	$-0.885071\pi$
$509$	−3.99880	−	22.6783i	−0.177244	−	1.00520i	0.758279	−	0.651930i	$-0.226041\pi$
$510$		0			0
$511$	−28.8796	+	10.5113i	−1.27756	+	0.464993i
$512$			23.9667i			1.05919i
$513$	11.7261	+	32.2173i	0.517722	+	1.42243i
$514$	4.13382	−	23.4440i	0.182335	−	1.03407i
$515$		0			0
$516$	3.37991	−	2.83608i	0.148792	−	0.124851i
$517$			8.70269i			0.382744i
$518$	−1.43868	−	19.3037i	−0.0632119	−	0.848154i
$519$	12.0294			0.528030
$520$		0			0
$521$	19.8046	+	16.6180i	0.867654	+	0.728048i	0.963603	−	0.267338i	$-0.0861440\pi$
$521$	19.8046	+	16.6180i	0.867654	+	0.728048i	−0.0959487	+	0.995386i	$0.530588\pi$
$522$	−65.4428	−	11.5393i	−2.86435	−	0.505063i
$523$	10.6419	+	29.2385i	0.465339	+	1.27851i	0.921419	+	0.388570i	$0.127031\pi$
$523$	10.6419	+	29.2385i	0.465339	+	1.27851i	−0.456080	+	0.889939i	$0.650747\pi$
$524$	−10.3169			−0.450696
$525$		0			0
$526$	−16.0319	−	27.7681i	−0.699025	−	1.21075i
$527$	−18.5975	+	3.27924i	−0.810120	+	0.142846i
$528$	−28.0307	−	16.1836i	−1.21988	−	0.704299i
$529$	26.9085	+	46.6069i	1.16993	+	2.02639i
$530$		0			0
$531$	−3.62004	+	20.5303i	−0.157096	+	0.890937i
$532$	4.79870	+	2.77053i	0.208050	+	0.120118i
$533$	−0.702861	+	1.93110i	−0.0304443	+	0.0836450i
$534$	12.3681	+	4.50162i	0.535220	+	0.194804i
$535$		0			0
$536$	−9.29373	−	7.79836i	−0.401428	−	0.336838i
$537$	−17.0080	+	20.2693i	−0.733949	+	0.874686i
$538$	−15.1692	+	2.67474i	−0.653991	+	0.115316i
$539$	−0.308789	−	0.112390i	−0.0133005	−	0.00484097i
$540$		0			0
$541$	10.2174	−	17.6971i	0.439282	−	0.760858i	−0.558352	−	0.829604i	$-0.688566\pi$
$541$	10.2174	−	17.6971i	0.439282	−	0.760858i	0.997634	+	0.0687454i	$0.0218996\pi$
$542$	23.4149	+	4.12868i	1.00576	+	0.177342i
$543$	28.0350	+	33.4109i	1.20310	+	1.43380i
$544$	5.68791	+	9.85174i	0.243867	+	0.422390i
$545$		0			0
$546$	8.57523	+	48.6325i	0.366986	+	2.08128i
$547$	1.84213	−	1.06355i	0.0787637	−	0.0454743i	−0.460101	−	0.887867i	$-0.652187\pi$
$547$	1.84213	−	1.06355i	0.0787637	−	0.0454743i	0.538865	+	0.842392i	$0.318853\pi$
$548$	0.140356	+	0.385625i	0.00599572	+	0.0164731i
$549$	3.19513			0.136365
$550$		0			0
$551$	6.32189	−	35.8532i	0.269322	−	1.52740i
$552$	−51.6412	+	61.5435i	−2.19799	+	2.61947i
$553$	16.1592	+	19.2578i	0.687158	+	0.818923i
$554$	−26.7183			−1.13515
$555$		0			0
$556$	−6.31479			−0.267807
$557$	17.1392	+	20.4257i	0.726211	+	0.865465i	0.995219	−	0.0976735i	$-0.0311401\pi$
$557$	17.1392	+	20.4257i	0.726211	+	0.865465i	−0.269007	+	0.963138i	$0.586696\pi$
$558$	22.5153	−	26.8327i	0.953149	−	1.13592i
$559$	−2.48321	+	14.0830i	−0.105028	+	0.595646i
$560$		0			0
$561$	−47.3828			−2.00050
$562$	−4.00500	−	11.0037i	−0.168941	−	0.464161i
$563$	0.995734	−	0.574887i	0.0419652	−	0.0242286i	−0.478871	−	0.877885i	$-0.658954\pi$
$563$	0.995734	−	0.574887i	0.0419652	−	0.0242286i	0.520836	+	0.853657i	$0.325620\pi$
$564$	0.589937	+	3.34570i	0.0248408	+	0.140879i
$565$		0			0
$566$	9.85159	+	17.0635i	0.414093	+	0.717231i
$567$	14.0638	+	16.7606i	0.590623	+	0.703878i
$568$	−16.9580	−	2.99015i	−0.711542	−	0.125464i
$569$	−17.6008	+	30.4855i	−0.737864	+	1.27802i	0.215591	+	0.976484i	$0.430832\pi$
$569$	−17.6008	+	30.4855i	−0.737864	+	1.27802i	−0.953455	+	0.301534i	$0.902501\pi$
$570$		0			0
$571$	28.9070	+	10.5213i	1.20972	+	0.440302i	0.866606	−	0.498992i	$-0.166296\pi$
$571$	28.9070	+	10.5213i	1.20972	+	0.440302i	0.343113	+	0.939294i	$0.388519\pi$
$572$	−11.2698	+	1.98718i	−0.471216	+	0.0830880i
$573$	−25.5040	+	30.3945i	−1.06545	+	1.26975i
$574$	−0.964377	−	0.809209i	−0.0402523	−	0.0337757i
$575$		0			0
$576$	−49.2069	−	17.9098i	−2.05029	−	0.746243i
$577$	−8.63917	+	23.7359i	−0.359654	+	0.988140i	0.619496	+	0.785000i	$0.287337\pi$
$577$	−8.63917	+	23.7359i	−0.359654	+	0.988140i	−0.979150	+	0.203140i	$0.934885\pi$
$578$	2.17366	+	1.25496i	0.0904122	+	0.0521995i
$579$	3.70627	−	21.0193i	0.154027	−	0.873532i
$580$		0			0
$581$	−20.4386	−	35.4007i	−0.847937	−	1.46867i
$582$	26.6381	+	15.3795i	1.10419	+	0.637502i
$583$	−7.80703	+	1.37659i	−0.323334	+	0.0570126i
$584$	17.9248	+	31.0467i	0.741735	+	1.28472i
$585$		0			0
$586$	34.6955			1.43326
$587$	4.79726	+	13.1804i	0.198004	+	0.544012i	0.998466	−	0.0553719i	$-0.0176344\pi$
$587$	4.79726	+	13.1804i	0.198004	+	0.544012i	−0.800462	+	0.599384i	$0.795412\pi$
$588$	−0.126331	−	0.0222755i	−0.00520979	−	0.000918626i
$589$	14.7005	+	12.3351i	0.605722	+	0.508261i
$590$		0			0
$591$	77.9121			3.20487
$592$	−15.5578	+	3.95473i	−0.639421	+	0.162539i
$593$			20.0133i			0.821849i	0.911669	+	0.410925i	$0.134794\pi$
$593$			20.0133i			0.821849i	−0.911669	+	0.410925i	$0.865206\pi$
$594$	33.2281	−	27.8817i	1.36337	−	1.14400i
$595$		0			0
$596$	0.327162	−	1.85543i	0.0134011	−	0.0760013i
$597$	−10.2376	−	28.1274i	−0.418995	−	1.15118i
$598$		−	55.0788i		−	2.25234i
$599$	−26.9488	+	9.80858i	−1.10110	+	0.400768i	−0.827722	−	0.561139i	$-0.810363\pi$
$599$	−26.9488	+	9.80858i	−1.10110	+	0.400768i	−0.273378	+	0.961907i	$0.588141\pi$
$600$		0			0
$601$	−3.52558	−	19.9945i	−0.143811	−	0.815594i	−0.968314	−	0.249736i	$-0.919656\pi$
$601$	−3.52558	−	19.9945i	−0.143811	−	0.815594i	0.824503	−	0.565858i	$-0.191455\pi$
$602$	−7.58662	−	4.38014i	−0.309207	−	0.178521i
$603$	20.2821	−	11.7099i	0.825950	−	0.476862i
$604$	8.58156	−	7.20079i	0.349179	−	0.292996i
$605$		0			0
$606$	10.0731	−	17.4472i	0.409194	−	0.708744i
$607$	−1.26019	+	3.46235i	−0.0511497	+	0.140533i	−0.962637	−	0.270796i	$-0.912713\pi$
$607$	−1.26019	+	3.46235i	−0.0511497	+	0.140533i	0.911487	+	0.411329i	$0.134935\pi$
$608$	3.95373	−	10.8628i	0.160345	−	0.440545i
$609$	−12.6541	−	71.7652i	−0.512772	−	2.90807i
$610$		0			0
$611$	−8.43493	−	7.07774i	−0.341241	−	0.286335i
$612$	−12.0920	+	2.13214i	−0.488789	+	0.0861867i
$613$	0.917084	−	2.51967i	0.0370407	−	0.101768i	−0.919794	−	0.392403i	$-0.871644\pi$
$613$	0.917084	−	2.51967i	0.0370407	−	0.101768i	0.956834	+	0.290634i	$0.0938663\pi$
$614$	−34.8109	−	12.6701i	−1.40485	−	0.511325i
$615$		0			0
$616$	5.75502	−	32.6384i	0.231877	−	1.31504i
$617$	6.26239	+	7.46322i	0.252114	+	0.300458i	0.877226	−	0.480077i	$-0.159391\pi$
$617$	6.26239	+	7.46322i	0.252114	+	0.300458i	−0.625112	+	0.780535i	$0.714947\pi$
$618$	1.58133	−	0.912983i	0.0636105	−	0.0367256i
$619$	7.81784	−	13.5409i	0.314226	−	0.544255i	−0.665047	−	0.746802i	$-0.731588\pi$
$619$	7.81784	−	13.5409i	0.314226	−	0.544255i	0.979273	+	0.202547i	$0.0649218\pi$
$620$		0			0
$621$	−38.2709	−	66.2871i	−1.53576	−	2.66001i
$622$	0.795245	+	2.18492i	0.0318864	+	0.0876073i
$623$			9.58103i			0.383856i
$624$	38.4825	−	14.0065i	1.54053	−	0.560708i
$625$		0			0
$626$	18.2593	+	15.3214i	0.729789	+	0.612365i
$627$	30.9501	+	36.8848i	1.23603	+	1.47304i
$628$			0.287889i			0.0114880i
$629$	−16.8293	+	16.4014i	−0.671029	+	0.653968i
$630$		0			0
$631$	−17.7946	+	14.9314i	−0.708391	+	0.594411i	−0.924147	−	0.382037i	$-0.875223\pi$
$631$	−17.7946	+	14.9314i	−0.708391	+	0.594411i	0.215756	+	0.976447i	$0.430778\pi$
$632$	18.8495	−	22.4639i	0.749792	−	0.893568i
$633$	16.7483	+	2.95318i	0.665685	+	0.117378i
$634$	14.9988	−	5.45910i	0.595676	−	0.216809i
$635$		0			0
$636$	−2.90805	+	1.05844i	−0.115312	+	0.0419701i
$637$	0.360064	−	0.207883i	0.0142663	−	0.00823663i
$638$	−45.3604	+	7.99826i	−1.79583	+	0.316654i
$639$	16.6203	−	28.7872i	0.657489	−	1.13880i
$640$		0			0
$641$	19.1875	−	16.1002i	0.757862	−	0.635922i	−0.179708	−	0.983720i	$-0.557515\pi$
$641$	19.1875	−	16.1002i	0.757862	−	0.635922i	0.937569	+	0.347799i	$0.113071\pi$
$642$	28.3209	+	4.99373i	1.11774	+	0.197087i
$643$	31.6537	+	18.2753i	1.24830	+	0.720707i	0.970770	−	0.240010i	$-0.0771507\pi$
$643$	31.6537	+	18.2753i	1.24830	+	0.720707i	0.277531	+	0.960717i	$0.410484\pi$
$644$	−11.6245	−	4.23096i	−0.458069	−	0.166723i
$645$		0			0
$646$	3.18606	+	18.0690i	0.125354	+	0.710917i
$647$	2.39906	−	2.85909i	0.0943169	−	0.112403i	−0.716822	−	0.697257i	$-0.754404\pi$
$647$	2.39906	−	2.85909i	0.0943169	−	0.112403i	0.811138	+	0.584854i	$0.198848\pi$
$648$	16.4052	−	19.5510i	0.644459	−	0.768036i
$649$	2.50916	+	14.2301i	0.0984930	+	0.558582i
$650$		0			0
$651$	36.0951	+	13.1375i	1.41468	+	0.514901i
$652$	10.5972	+	6.11828i	0.415017	+	0.239610i
$653$	10.4880	+	1.84932i	0.410427	+	0.0723693i	0.375050	−	0.927005i	$-0.377626\pi$
$653$	10.4880	+	1.84932i	0.410427	+	0.0723693i	0.0353772	+	0.999374i	$0.488737\pi$
$654$	9.99239	−	8.38461i	0.390733	−	0.327864i
$655$		0			0
$656$	−0.521994	+	0.904119i	−0.0203804	+	0.0352999i
$657$	−68.1526	+	12.0171i	−2.65889	+	0.468834i
$658$	5.84162	−	3.37266i	0.227730	−	0.131480i
$659$	15.5823	−	5.67151i	0.607002	−	0.220931i	−0.0201889	−	0.999796i	$-0.506427\pi$
$659$	15.5823	−	5.67151i	0.607002	−	0.220931i	0.627191	+	0.778865i	$0.284205\pi$
$660$		0			0
$661$	17.9941	−	6.54931i	0.699888	−	0.254739i	0.0325252	−	0.999471i	$-0.489645\pi$
$661$	17.9941	−	6.54931i	0.699888	−	0.254739i	0.667363	+	0.744732i	$0.267423\pi$
$662$	−20.2309	−	3.56726i	−0.786297	−	0.138645i
$663$	38.5356	−	45.9249i	1.49660	−	1.78358i
$664$	−36.5272	+	30.6499i	−1.41753	+	1.18945i
$665$		0			0
$666$	4.35769	−	43.3698i	0.168857	−	1.68054i
$667$			81.2777i			3.14709i
$668$	−1.77577	−	2.11628i	−0.0687066	−	0.0818813i
$669$	−42.3679	−	35.5509i	−1.63804	−	1.37448i
$670$		0			0
$671$	2.08108	−	0.757451i	0.0803392	−	0.0292411i
$672$		−	23.1388i		−	0.892600i
$673$	−9.25971	−	25.4408i	−0.356936	−	0.980673i	−0.980087	−	0.198571i	$-0.936370\pi$
$673$	−9.25971	−	25.4408i	−0.356936	−	0.980673i	0.623151	−	0.782102i	$-0.285852\pi$
$674$	13.8430	+	23.9767i	0.533212	+	0.923550i
$675$		0			0
$676$	3.75197	−	6.49861i	0.144307	−	0.249946i
$677$	16.2809	−	9.39978i	0.625726	−	0.361263i	−0.153369	−	0.988169i	$-0.549012\pi$
$677$	16.2809	−	9.39978i	0.625726	−	0.361263i	0.779095	+	0.626906i	$0.215679\pi$
$678$	−27.1243	−	32.3255i	−1.04170	−	1.24145i
$679$	−3.88811	+	22.0506i	−0.149212	+	0.846223i
$680$		0			0
$681$	39.3195	+	14.3111i	1.50673	+	0.548404i
$682$	8.30380	−	22.8145i	0.317969	−	0.873612i
$683$	24.8583	−	4.38318i	0.951175	−	0.167718i	0.323531	−	0.946218i	$-0.395130\pi$
$683$	24.8583	−	4.38318i	0.951175	−	0.167718i	0.627645	+	0.778500i	$0.284019\pi$
$684$	9.55813	+	8.02022i	0.365464	+	0.306661i
$685$		0			0
$686$	3.91243	+	22.1885i	0.149377	+	0.847162i
$687$	−0.00254360	+	0.00698849i	−9.70444e−5	+	0.000266627i
$688$	−2.48469	+	6.82662i	−0.0947278	+	0.260262i
$689$	5.01508	−	8.68638i	0.191060	−	0.330925i
$690$		0			0
$691$	26.7478	−	22.4441i	1.01753	−	0.853812i	0.0282184	−	0.999602i	$-0.491017\pi$
$691$	26.7478	−	22.4441i	1.01753	−	0.853812i	0.989316	+	0.145789i	$0.0465722\pi$
$692$	1.87117	−	1.08032i	0.0711311	−	0.0410676i
$693$	55.4056	+	31.9884i	2.10468	+	1.21514i
$694$	6.36380	+	36.0909i	0.241566	+	1.36999i
$695$		0			0
$696$	−79.8783	+	29.0733i	−3.02778	+	1.10202i
$697$			1.52831i			0.0578889i
$698$	8.34844	+	22.9371i	0.315993	+	0.868184i
$699$	−0.0232274	+	0.131729i	−0.000878541	+	0.00498246i
$700$		0			0
$701$	−17.7678	+	14.9090i	−0.671081	+	0.563104i	−0.913385	−	0.407096i	$-0.866541\pi$
$701$	−17.7678	+	14.9090i	−0.671081	+	0.563104i	0.242304	+	0.970200i	$0.422097\pi$
$702$			54.8815i			2.07137i
$703$	23.7604	+	2.38739i	0.896140	+	0.0900421i
$704$	−36.2956			−1.36794
$705$		0			0
$706$	7.55950	+	6.34317i	0.284506	+	0.238729i
$707$	14.4425	+	2.54660i	0.543165	+	0.0957747i
$708$	1.92926	+	5.30060i	0.0725061	+	0.199209i
$709$	32.9756			1.23843			0.619213	−	0.785223i	$-0.287452\pi$
$709$	32.9756			1.23843			0.619213	+	0.785223i	$0.287452\pi$
$710$		0			0
$711$	28.3040	+	49.0240i	1.06148	+	1.83854i
$712$	11.0064	−	1.94072i	0.412481	−	0.0727315i
$713$	−37.1024	−	21.4211i	−1.38950	−	0.802226i
$714$	18.3628	+	31.8053i	0.687211	+	1.19028i
$715$		0			0
$716$	−0.825269	+	4.68033i	−0.0308417	+	0.174912i
$717$	−65.5560	−	37.8488i	−2.44823	−	1.41349i
$718$	−0.885007	+	2.43154i	−0.0330282	+	0.0907442i
$719$	−0.0608811	−	0.0221589i	−0.00227048	−	0.000826388i	0.340885	−	0.940105i	$-0.389273\pi$
$719$	−0.0608811	−	0.0221589i	−0.00227048	−	0.000826388i	−0.343155	+	0.939279i	$0.611496\pi$
$720$		0			0
$721$	1.01822	+	0.854388i	0.0379205	+	0.0318191i
$722$	−2.78979	+	3.32475i	−0.103825	+	0.123734i
$723$	34.2819	−	6.04483i	1.27496	−	0.224810i
$724$	7.36138	+	2.67932i	0.273583	+	0.0995762i
$725$		0			0
$726$	10.5832	−	18.3306i	0.392779	−	0.680314i
$727$	19.7361	+	3.48001i	0.731973	+	0.129067i	0.527198	−	0.849743i	$-0.323243\pi$
$727$	19.7361	+	3.48001i	0.731973	+	0.129067i	0.204775	+	0.978809i	$0.434354\pi$
$728$	26.9537	+	32.1222i	0.998970	+	1.19053i
$729$	−14.4979	−	25.1111i	−0.536960	−	0.930042i
$730$		0			0
$731$	1.84674	+	10.4734i	0.0683043	+	0.387373i
$732$	0.748713	−	0.432270i	0.0276732	−	0.0159772i
$733$	−12.1033	−	33.2536i	−0.447046	−	1.22825i	−0.934771	−	0.355252i	$-0.884395\pi$
$733$	−12.1033	−	33.2536i	−0.447046	−	1.22825i	0.487724	−	0.872998i	$-0.337827\pi$
$734$	30.5607			1.12802
$735$		0			0
$736$	−4.48147	+	25.4157i	−0.165189	+	0.936835i
$737$	10.4343	−	12.4351i	0.384353	−	0.458054i
$738$	−1.82216	−	2.17157i	−0.0670746	−	0.0799364i
$739$	16.6665			0.613089			0.306544	−	0.951856i	$-0.400827\pi$
$739$	16.6665			0.613089			0.306544	+	0.951856i	$0.400827\pi$
$740$		0			0
$741$	−60.9211			−2.23799
$742$	3.94958	+	4.70692i	0.144994	+	0.172797i
$743$	12.4086	−	14.7880i	0.455228	−	0.542520i	−0.488795	−	0.872399i	$-0.662563\pi$
$743$	12.4086	−	14.7880i	0.455228	−	0.542520i	0.944023	+	0.329879i	$0.107008\pi$
$744$	7.78060	−	44.1260i	0.285251	−	1.61774i
$745$		0			0
$746$	−18.4542			−0.675657
$747$	−31.4818	−	86.4955i	−1.15186	−	3.16470i
$748$	−7.37040	+	4.25530i	−0.269488	+	0.155589i
$749$	3.63513	+	20.6159i	0.132825	+	0.753287i
$750$		0			0
$751$	23.1755	+	40.1412i	0.845686	+	1.46477i	0.885024	+	0.465546i	$0.154142\pi$
$751$	23.1755	+	40.1412i	0.845686	+	1.46477i	−0.0393375	+	0.999226i	$0.512525\pi$
$752$	−3.59561	−	4.28508i	−0.131118	−	0.156261i
$753$	8.88048	+	1.56587i	0.323623	+	0.0570634i
$754$	29.1386	−	50.4696i	1.06117	−	1.83799i
$755$		0			0
$756$	11.5828	+	4.21581i	0.421263	+	0.153327i
$757$	15.4254	−	2.71992i	0.560646	−	0.0988571i	0.113858	−	0.993497i	$-0.463679\pi$
$757$	15.4254	−	2.71992i	0.560646	−	0.0988571i	0.446788	+	0.894640i	$0.352568\pi$
$758$	−3.69679	+	4.40567i	−0.134274	+	0.160021i
$759$	−82.3461	−	69.0965i	−2.98897	−	2.50805i
$760$		0			0
$761$	0.726263	+	0.264338i	0.0263270	+	0.00958224i	0.355150	−	0.934809i	$-0.384430\pi$
$761$	0.726263	+	0.264338i	0.0263270	+	0.00958224i	−0.328823	+	0.944392i	$0.606652\pi$
$762$	−26.1202	+	71.7646i	−0.946234	+	2.59976i
$763$	8.22320	+	4.74767i	0.297700	+	0.171877i
$764$	−1.23752	+	7.01831i	−0.0447718	+	0.253913i
$765$		0			0
$766$	5.42601	+	9.39813i	0.196050	+	0.339568i
$767$	−15.8330	−	9.14116i	−0.571695	−	0.330068i
$768$	−34.9122	+	6.15596i	−1.25978	+	0.222134i
$769$	7.13677	+	12.3612i	0.257358	+	0.445758i	0.965533	−	0.260279i	$-0.0838146\pi$
$769$	7.13677	+	12.3612i	0.257358	+	0.445758i	−0.708175	+	0.706037i	$0.750481\pi$
$770$		0			0
$771$	58.7840			2.11705
$772$	−1.31117	−	3.60240i	−0.0471899	−	0.129653i
$773$	−26.5887	−	4.68831i	−0.956330	−	0.168627i	−0.326359	−	0.945246i	$-0.605822\pi$
$773$	−26.5887	−	4.68831i	−0.956330	−	0.168627i	−0.629970	+	0.776619i	$0.716933\pi$
$774$	−15.1112	−	12.6798i	−0.543159	−	0.455765i
$775$		0			0
$776$	26.1185			0.937600
$777$	46.3259	−	11.7759i	1.66193	−	0.422457i
$778$		−	30.3861i		−	1.08939i
$779$	1.18971	−	0.998281i	0.0426256	−	0.0357671i
$780$		0			0
$781$	4.00086	−	22.6900i	0.143162	−	0.811913i
$782$	−14.0097	−	38.4915i	−0.500988	−	1.37645i
$783$		−	80.9865i		−	2.89422i
$784$	0.198478	−	0.0722401i	0.00708850	−	0.00258000i
$785$		0			0
$786$	12.0662	+	68.4306i	0.430386	+	2.44084i
$787$	42.1004	+	24.3067i	1.50072	+	0.866440i	1.00000		0.000829899i	$0.000264165\pi$
$787$	42.1004	+	24.3067i	1.50072	+	0.866440i	0.500719	+	0.865610i	$0.333069\pi$
$788$	12.1192	−	6.99704i	0.431730	−	0.249259i
$789$	60.6524	−	50.8934i	2.15928	−	1.81185i
$790$		0			0
$791$	15.3588	−	26.6022i	0.546095	−	0.945864i
$792$	25.5243	−	70.1276i	0.906968	−	2.49187i
$793$	−0.958359	+	2.63307i	−0.0340323	+	0.0935031i
$794$	0.153915	+	0.872893i	0.00546223	+	0.0309778i
$795$		0			0
$796$	−4.11849	−	3.45582i	−0.145976	−	0.122488i
$797$	−31.2273	+	5.50622i	−1.10613	+	0.195040i	−0.696743	−	0.717321i	$-0.745368\pi$
$797$	−31.2273	+	5.50622i	−1.10613	+	0.195040i	−0.409386	+	0.912361i	$0.634257\pi$
$798$	12.7642	−	35.0694i	0.451849	−	1.24144i
$799$	−7.69497	−	2.80074i	−0.272229	−	0.0990831i
$800$		0			0
$801$	−3.74635	+	21.2466i	−0.132371	+	0.750712i
$802$	−1.67744	−	1.99909i	−0.0592323	−	0.0705903i
$803$	−41.5410	+	23.9837i	−1.46595	+	0.846366i
$804$	3.16846	−	5.48793i	0.111743	−	0.193545i
$805$		0			0
$806$	15.3592	+	26.6029i	0.541005	+	0.937048i
$807$	−13.0089	−	35.7417i	−0.457936	−	1.25817i
$808$		−	17.1069i		−	0.601818i
$809$	2.41252	−	0.878086i	0.0848197	−	0.0308719i	−0.299262	−	0.954171i	$-0.596740\pi$
$809$	2.41252	−	0.878086i	0.0848197	−	0.0308719i	0.384082	+	0.923299i	$0.374518\pi$
$810$		0			0
$811$	4.61093	+	3.86903i	0.161911	+	0.135860i	0.720144	−	0.693825i	$-0.244076\pi$
$811$	4.61093	+	3.86903i	0.161911	+	0.135860i	−0.558232	+	0.829685i	$0.688520\pi$
$812$	−8.41336	−	10.0267i	−0.295251	−	0.351867i
$813$			58.7109i			2.05908i
$814$	−7.44314	−	29.2810i	−0.260882	−	1.02630i
$815$		0			0
$816$	23.3306	−	19.5767i	0.816734	−	0.685321i
$817$	6.94668	−	8.27874i	0.243034	−	0.289636i
$818$	35.1070	+	6.19031i	1.22749	+	0.216439i
$819$	−76.0645	+	27.6852i	−2.65791	+	0.967400i
$820$		0			0
$821$	−13.5004	+	4.91375i	−0.471167	+	0.171491i	−0.566681	−	0.823937i	$-0.691773\pi$
$821$	−13.5004	+	4.91375i	−0.471167	+	0.171491i	0.0955137	+	0.995428i	$0.469551\pi$
$822$	2.39365	−	1.38197i	0.0834880	−	0.0482018i
$823$	−24.0073	+	4.23314i	−0.836843	+	0.147558i	−0.575617	−	0.817720i	$-0.695238\pi$
$823$	−24.0073	+	4.23314i	−0.836843	+	0.147558i	−0.261226	+	0.965278i	$0.584127\pi$
$824$	0.775243	−	1.34276i	0.0270069	−	0.0467773i
$825$		0			0
$826$	8.57947	−	7.19903i	0.298518	−	0.250486i
$827$	−3.15854	−	0.556935i	−0.109833	−	0.0193665i	0.118461	−	0.992959i	$-0.462204\pi$
$827$	−3.15854	−	0.556935i	−0.109833	−	0.0193665i	−0.228295	+	0.973592i	$0.573315\pi$
$828$	−24.1237	−	13.9278i	−0.838358	−	0.484026i
$829$	−5.46591	−	1.98943i	−0.189839	−	0.0690957i	0.245351	−	0.969434i	$-0.421097\pi$
$829$	−5.46591	−	1.98943i	−0.189839	−	0.0690957i	−0.435190	+	0.900339i	$0.643319\pi$
$830$		0			0
$831$	−11.4566	−	64.9738i	−0.397426	−	2.25392i
$832$	29.5186	−	35.1789i	1.02337	−	1.21961i
$833$	0.198752	−	0.236863i	0.00688634	−	0.00820682i
$834$	7.38548	+	41.8852i	0.255738	+	1.45036i
$835$		0			0
$836$	8.12680	+	2.95791i	0.281071	+	0.102302i
$837$	36.9695	+	21.3443i	1.27785	+	0.737769i
$838$	32.8623	+	5.79451i	1.13521	+	0.200168i
$839$	−2.04936	+	1.71961i	−0.0707516	+	0.0593677i	−0.677478	−	0.735543i	$-0.736927\pi$
$839$	−2.04936	+	1.71961i	−0.0707516	+	0.0593677i	0.606726	+	0.794911i	$0.292483\pi$
$840$		0			0
$841$	−28.4988	+	49.3613i	−0.982716	+	1.70211i
$842$	21.9799	−	3.87565i	0.757477	−	0.133564i
$843$	25.0415	−	14.4577i	0.862474	−	0.497950i
$844$	2.87041	−	1.04475i	0.0988037	−	0.0359616i
$845$		0			0
$846$	14.2730	−	5.19493i	0.490715	−	0.178606i
$847$	15.1738	+	2.67554i	0.521377	+	0.0919328i
$848$	3.27531	−	3.90337i	0.112475	−	0.134042i
$849$	−37.2708	+	31.2739i	−1.27913	+	1.07332i
$850$		0			0
$851$	−53.1651	+	3.96234i	−1.82248	+	0.135827i
$852$		−	8.99426i		−	0.308138i
$853$	−14.1899	−	16.9109i	−0.485853	−	0.579018i	0.466304	−	0.884624i	$-0.345585\pi$
$853$	−14.1899	−	16.9109i	−0.485853	−	0.579018i	−0.952158	+	0.305607i	$0.901141\pi$
$854$	−1.31494	−	1.10337i	−0.0449963	−	0.0377564i
$855$		0			0
$856$	22.9465	−	8.35184i	0.784295	−	0.285460i
$857$			13.4850i			0.460638i	0.973115	+	0.230319i	$0.0739770\pi$
$857$			13.4850i			0.460638i	−0.973115	+	0.230319i	$0.926023\pi$
$858$	26.3614	+	72.4272i	0.899962	+	2.47263i
$859$	7.28037	+	12.6100i	0.248403	+	0.430247i	0.963083	−	0.269205i	$-0.0867609\pi$
$859$	7.28037	+	12.6100i	0.248403	+	0.430247i	−0.714680	+	0.699452i	$0.753428\pi$
$860$		0			0
$861$	1.55432	−	2.69216i	0.0529711	−	0.0917487i
$862$	18.1160	−	10.4593i	0.617033	−	0.356244i
$863$	20.3333	+	24.2323i	0.692154	+	0.824877i	0.991614	−	0.129232i	$-0.0412512\pi$
$863$	20.3333	+	24.2323i	0.692154	+	0.824877i	−0.299461	+	0.954109i	$0.596807\pi$
$864$	4.46542	−	25.3246i	0.151917	−	0.861562i
$865$		0			0
$866$	21.3234	+	7.76109i	0.724599	+	0.263733i
$867$	−2.11978	+	5.82404i	−0.0719914	+	0.197795i
$868$	6.79444	−	1.19804i	0.230618	−	0.0406642i
$869$	30.0571	+	25.2209i	1.01962	+	0.855559i
$870$		0			0
$871$	3.56648	+	20.2265i	0.120846	+	0.685350i
$872$	3.78828	−	10.4082i	0.128287	−	0.352467i
$873$	−17.2443	+	47.3784i	−0.583632	+	1.60351i
$874$	−20.8124	+	36.0481i	−0.703990	+	1.21935i
$875$		0			0
$876$	−14.3444	+	12.0364i	−0.484652	+	0.406671i
$877$	−10.5972	+	6.11832i	−0.357843	+	0.206601i	−0.668134	−	0.744041i	$-0.732907\pi$
$877$	−10.5972	+	6.11832i	−0.357843	+	0.206601i	0.310291	+	0.950642i	$0.399574\pi$
$878$	−12.5517	−	7.24672i	−0.423599	−	0.244565i
$879$	14.8772	+	84.3728i	0.501795	+	2.84582i
$880$		0			0
$881$	5.34083	−	1.94390i	0.179937	−	0.0654918i	−0.250480	−	0.968122i	$-0.580589\pi$
$881$	5.34083	−	1.94390i	0.179937	−	0.0654918i	0.430418	+	0.902630i	$0.358366\pi$
$882$			0.573522i			0.0193115i
$883$	−0.105271	−	0.289230i	−0.00354266	−	0.00973338i	0.937909	−	0.346882i	$-0.112760\pi$
$883$	−0.105271	−	0.289230i	−0.00354266	−	0.00973338i	−0.941451	+	0.337149i	$0.890537\pi$
$884$	1.86984	−	10.6044i	0.0628895	−	0.356664i
$885$		0			0
$886$	29.7174	−	24.9359i	0.998377	−	0.837738i
$887$			37.7764i			1.26841i	0.773166	+	0.634204i	$0.218672\pi$
$887$			37.7764i			1.26841i	−0.773166	+	0.634204i	$0.781328\pi$
$888$	−22.9114	−	50.8323i	−0.768858	−	1.70582i
$889$	−55.5929			−1.86453
$890$		0			0
$891$	26.1595	+	21.9504i	0.876376	+	0.735367i
$892$	−9.78304	−	1.72501i	−0.327560	−	0.0577577i
$893$	2.84608	+	7.81953i	0.0952403	+	0.261671i
$894$	−12.6894			−0.424398
$895$		0			0
$896$	6.32015	+	10.9468i	0.211141	+	0.365708i
$897$	133.941	−	23.6174i	4.47217	−	0.788563i
$898$	−2.87253	−	1.65845i	−0.0958574	−	0.0553433i
$899$	−22.6650	−	39.2570i	−0.755921	−	1.30929i
$900$		0			0
$901$	1.29531	−	7.34605i	0.0431529	−	0.244732i
$902$	−1.70163	−	0.982435i	−0.0566580	−	0.0327115i
$903$	7.39856	−	20.3274i	0.246209	−	0.676453i
$904$	−33.6707	−	12.2551i	−1.11987	−	0.407600i
$905$		0			0
$906$	−57.7985	−	48.4987i	−1.92023	−	1.61126i
$907$	−32.0051	+	38.1422i	−1.06271	+	1.26649i	−0.100282	+	0.994959i	$0.531975\pi$
$907$	−32.0051	+	38.1422i	−1.06271	+	1.26649i	−0.962430	+	0.271532i	$0.912470\pi$
$908$	7.40139	−	1.30507i	0.245624	−	0.0433101i
$909$	31.0315	+	11.2945i	1.02925	+	0.374616i
$910$		0			0
$911$	0.683516	−	1.18389i	0.0226459	−	0.0392239i	−0.854480	−	0.519484i	$-0.826124\pi$
$911$	0.683516	−	1.18389i	0.0226459	−	0.0392239i	0.877126	+	0.480260i	$0.159458\pi$
$912$	−30.4787	−	5.37422i	−1.00925	−	0.177958i
$913$	−41.0100	−	48.8738i	−1.35723	−	1.61749i
$914$	−17.2152	−	29.8177i	−0.569430	−	0.986281i
$915$		0			0
$916$	0.000231957		0.00131549i	7.66407e−6		4.34651e-5i
$917$	−43.8051	+	25.2909i	−1.44657	+	0.835178i
$918$	13.9596	+	38.3536i	0.460734	+	1.26586i
$919$	13.3894			0.441676			0.220838	−	0.975310i	$-0.429121\pi$
$919$	13.3894			0.441676			0.220838	+	0.975310i	$0.429121\pi$
$920$		0			0
$921$	15.8847	−	90.0863i	0.523417	−	2.96845i
$922$	−13.3206	+	15.8748i	−0.438689	+	0.522809i
$923$	18.7381	+	22.3312i	0.616771	+	0.735039i
$924$	17.3109			0.569486
$925$		0			0
$926$	−5.63248			−0.185095
$927$	1.92389	+	2.29281i	0.0631890	+	0.0753057i
$928$	−17.5522	+	20.9179i	−0.576180	+	0.686665i
$929$	−1.76707	+	10.0215i	−0.0579756	+	0.328796i	−0.999977	−	0.00681348i	$-0.997831\pi$
$929$	−1.76707	+	10.0215i	−0.0579756	+	0.328796i	0.942001	+	0.335610i	$0.108942\pi$
$930$		0			0
$931$	−0.314208			−0.0102977
$932$	0.00821716	+	0.0225765i	0.000269162	+	0.000739517i
$933$	−4.97231	+	2.87076i	−0.162786	+	0.0939846i
$934$	1.91501	+	10.8606i	0.0626611	+	0.355369i
$935$		0			0
$936$	47.2114	+	81.7725i	1.54315	+	2.67282i
$937$	−30.0346	−	35.7939i	−0.981189	−	1.16934i	−0.985557	−	0.169345i	$-0.945835\pi$
$937$	−30.0346	−	35.7939i	−0.981189	−	1.16934i	0.00436754	−	0.999990i	$-0.498610\pi$
$938$	−12.3907	−	2.18482i	−0.404571	−	0.0713369i
$939$	−29.4292	+	50.9729i	−0.960385	+	1.66344i
$940$		0			0
$941$	−24.3819	−	8.87429i	−0.794827	−	0.289294i	−0.0874862	−	0.996166i	$-0.527883\pi$
$941$	−24.3819	−	8.87429i	−0.794827	−	0.289294i	−0.707341	+	0.706872i	$0.750106\pi$
$942$	1.90953	−	0.336701i	0.0622158	−	0.0109703i
$943$	−2.22868	+	2.65604i	−0.0725758	+	0.0864925i
$944$	−7.11480	−	5.97002i	−0.231567	−	0.194308i
$945$		0			0
$946$	−12.8483	−	4.67638i	−0.417733	−	0.152042i
$947$	13.1109	−	36.0218i	0.426046	−	1.17055i	−0.522147	−	0.852855i	$-0.674869\pi$
$947$	13.1109	−	36.0218i	0.426046	−	1.17055i	0.948193	−	0.317696i	$-0.102909\pi$
$948$	13.2649	+	7.65851i	0.430825	+	0.248737i
$949$	10.5388	−	59.7683i	0.342103	−	1.94016i
$950$		0			0
$951$	19.7069	+	34.1333i	0.639038	+	1.10685i
$952$	27.0069	+	15.5925i	0.875300	+	0.505355i
$953$	24.5106	−	4.32189i	0.793978	−	0.140000i	0.238075	−	0.971247i	$-0.423484\pi$
$953$	24.5106	−	4.32189i	0.793978	−	0.140000i	0.555903	+	0.831247i	$0.312373\pi$
$954$	6.91798	+	11.9823i	0.223978	+	0.387941i
$955$		0			0
$956$	−13.5963			−0.439736
$957$	−38.9005	−	106.878i	−1.25747	−	3.45488i
$958$	16.0545	+	2.83084i	0.518697	+	0.0914603i
$959$	1.54127	+	1.29328i	0.0497702	+	0.0417621i
$960$		0			0
$961$	−7.10616			−0.229231
$962$	34.4335	+	16.5996i	1.11018	+	0.535194i
$963$			47.1385i			1.51902i
$964$	4.78969	−	4.01903i	0.154266	−	0.129444i
$965$		0			0
$966$	−14.4680	+	82.0520i	−0.465500	+	2.63998i
$967$	−13.2346	−	36.3618i	−0.425596	−	1.16932i	−0.948459	−	0.316899i	$-0.897358\pi$
$967$	−13.2346	−	36.3618i	−0.425596	−	1.16932i	0.522863	−	0.852417i	$-0.324864\pi$
$968$		−	17.9731i		−	0.577676i
$969$	−42.5743	+	15.4958i	−1.36768	+	0.497796i
$970$		0			0
$971$	−4.16513	−	23.6216i	−0.133665	−	0.758054i	−0.975780	−	0.218755i	$-0.929800\pi$
$971$	−4.16513	−	23.6216i	−0.133665	−	0.758054i	0.842115	−	0.539299i	$-0.181311\pi$
$972$	−0.629032	−	0.363172i	−0.0201762	−	0.0116487i
$973$	−26.8123	+	15.4801i	−0.859563	+	0.496269i
$974$	−2.11887	+	1.77794i	−0.0678930	+	0.0569690i
$975$		0			0
$976$	−0.711744	+	1.23278i	−0.0227824	+	0.0394602i
$977$	14.7817	−	40.6124i	0.472909	−	1.29931i	−0.442495	−	0.896771i	$-0.645907\pi$
$977$	14.7817	−	40.6124i	0.472909	−	1.29931i	0.915404	−	0.402536i	$-0.131871\pi$
$978$	28.1878	−	77.4453i	0.901346	−	2.47643i
$979$	2.59671	+	14.7267i	0.0829912	+	0.470666i
$980$		0			0
$981$	16.3791	+	13.7437i	0.522945	+	0.438803i
$982$	−13.1841	+	2.32471i	−0.420721	+	0.0741844i
$983$	−18.7428	+	51.4954i	−0.597802	+	1.64245i	0.157841	+	0.987465i	$0.449547\pi$
$983$	−18.7428	+	51.4954i	−0.597802	+	1.64245i	−0.755643	+	0.654984i	$0.772675\pi$
$984$	−3.40751	−	1.24023i	−0.108627	−	0.0395372i
$985$		0			0
$986$	7.52598	−	42.6820i	0.239676	−	1.35927i
$987$	10.7065	+	12.7595i	0.340792	+	0.406140i
$988$	−9.47628	+	5.47113i	−0.301481	+	0.174060i
$989$	−12.0635	+	20.8947i	−0.383598	+	0.664412i
$990$		0			0
$991$	−15.9937	−	27.7019i	−0.508056	−	0.879979i	−0.999956	−	0.00932754i	$-0.997031\pi$
$991$	−15.9937	−	27.7019i	−0.508056	−	0.879979i	0.491900	−	0.870652i	$-0.336302\pi$
$992$	−4.92285	−	13.5254i	−0.156301	−	0.429433i
$993$		−	50.7273i		−	1.60978i
$994$	−16.7810	+	6.10779i	−0.532261	+	0.193727i
$995$		0			0
$996$	−19.0791	−	16.0093i	−0.604545	−	0.507273i
$997$	32.0639	+	38.2123i	1.01547	+	1.21020i	0.977504	+	0.210917i	$0.0676450\pi$
$997$	32.0639	+	38.2123i	1.01547	+	1.21020i	0.0379709	+	0.999279i	$0.487911\pi$
$998$			28.6324i			0.906342i
$999$	52.9746	−	3.94814i	1.67604	−	0.124914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bc.e.49.9		156
5.2	odd	4		925.2.p.e.826.9	yes	78
5.3	odd	4		925.2.p.f.826.5	yes	78
5.4	even	2	inner	925.2.bc.e.49.18		156
37.34	even	9	inner	925.2.bc.e.774.18		156
185.34	even	18	inner	925.2.bc.e.774.9		156
185.108	odd	36		925.2.p.f.626.5	yes	78
185.182	odd	36		925.2.p.e.626.9	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.p.e.626.9	✓	78	185.182	odd	36
925.2.p.e.826.9	yes	78	5.2	odd	4
925.2.p.f.626.5	yes	78	185.108	odd	36
925.2.p.f.826.5	yes	78	5.3	odd	4
925.2.bc.e.49.9		156	1.1	even	1	trivial
925.2.bc.e.49.18		156	5.4	even	2	inner
925.2.bc.e.774.9		156	185.34	even	18	inner
925.2.bc.e.774.18		156	37.34	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.777601 - 0.926709i) q^{2} +(1.92015 - 2.28834i) q^{3} +(0.0931703 - 0.528395i) q^{4} -3.61374 q^{6} +(-0.899712 - 2.47194i) q^{7} +(-2.65744 + 1.53427i) q^{8} +(-1.02860 - 5.83350i) q^{9} +O(q^{10})\)	\(q+(-0.777601 - 0.926709i) q^{2} +(1.92015 - 2.28834i) q^{3} +(0.0931703 - 0.528395i) q^{4} -3.61374 q^{6} +(-0.899712 - 2.47194i) q^{7} +(-2.65744 + 1.53427i) q^{8} +(-1.02860 - 5.83350i) q^{9} +(-2.05288 - 3.55569i) q^{11} +(-1.03025 - 1.22780i) q^{12} +(5.11585 + 0.902063i) q^{13} +(-1.59115 + 2.75595i) q^{14} +(2.47987 + 0.902600i) q^{16} +(3.80463 - 0.670858i) q^{17} +(-4.60612 + 5.48936i) q^{18} +(-3.00738 - 2.52349i) q^{19} +(-7.38423 - 2.68764i) q^{21} +(-1.69877 + 4.66732i) q^{22} +(7.59031 + 4.38227i) q^{23} +(-1.59173 + 9.02716i) q^{24} +(-3.14214 - 5.44235i) q^{26} +(-7.56311 - 4.36656i) q^{27} +(-1.38999 + 0.245092i) q^{28} +(4.63674 + 8.03107i) q^{29} -4.88813 q^{31} +(1.00710 + 2.76699i) q^{32} +(-12.0785 - 2.12976i) q^{33} +(-3.58017 - 3.00412i) q^{34} -3.17823 q^{36} +(-5.02721 + 3.42449i) q^{37} +4.74923i q^{38} +(11.8874 - 9.97474i) q^{39} +(-0.0686945 + 0.389586i) q^{41} +(3.25133 + 8.93295i) q^{42} +2.75281i q^{43} +(-2.07007 + 0.753445i) q^{44} +(-1.84115 - 10.4417i) q^{46} +(-1.83566 - 1.05982i) q^{47} +(6.82719 - 3.94168i) q^{48} +(0.0613108 - 0.0514458i) q^{49} +(5.77029 - 9.99444i) q^{51} +(0.953290 - 2.61914i) q^{52} +(0.660379 - 1.81438i) q^{53} +(1.83455 + 10.4043i) q^{54} +(6.18355 + 5.18862i) q^{56} +(-11.5492 + 2.03644i) q^{57} +(3.83693 - 10.5419i) q^{58} +(-3.30713 - 1.20370i) q^{59} +(-0.0936657 + 0.531205i) q^{61} +(3.80102 + 4.52988i) q^{62} +(-13.4946 + 7.79112i) q^{63} +(4.42010 - 7.65583i) q^{64} +(7.41856 + 12.8493i) q^{66} +(1.35225 + 3.71526i) q^{67} -2.07285i q^{68} +(24.6027 - 8.95463i) q^{69} +(4.29878 + 3.60710i) q^{71} +(11.6836 + 13.9240i) q^{72} -11.6830i q^{73} +(7.08267 + 1.99588i) q^{74} +(-1.61360 + 1.35397i) q^{76} +(-6.94244 + 8.27368i) q^{77} +(-18.4874 - 3.25982i) q^{78} +(-8.98019 + 3.26852i) q^{79} +(-7.81571 + 2.84469i) q^{81} +(0.414450 - 0.239283i) q^{82} +(15.3032 - 2.69836i) q^{83} +(-2.10813 + 3.65138i) q^{84} +(2.55105 - 2.14059i) q^{86} +(27.2811 + 4.81039i) q^{87} +(10.9108 + 6.29934i) q^{88} +(-3.42252 - 1.24570i) q^{89} +(-2.37295 - 13.4577i) q^{91} +(3.02276 - 3.60238i) q^{92} +(-9.38594 + 11.1857i) q^{93} +(0.445267 + 2.52524i) q^{94} +(8.26562 + 3.00844i) q^{96} +(-7.37135 - 4.25585i) q^{97} +(-0.0953507 - 0.0168129i) q^{98} +(-18.6305 + 15.6329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{4}+O(q^{10}) \) 156 * q - 6 * q^4	\( 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) \) 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Introduction

L-functions

Modular forms

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