LMFDB - Embedded newform 925.2.p.e.626.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(201,925)]

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([0, 2]))

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

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

chi := DirichletCharacter("925.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.p (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			626.9
Character	$\chi$	$=$	925.626
Dual form			925.2.p.e.826.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.926709 + 0.777601i) q^{2} +(-2.28834 + 1.92015i) q^{3} +(-0.0931703 - 0.528395i) q^{4} -3.61374 q^{6} +(2.47194 + 0.899712i) q^{7} +(1.53427 - 2.65744i) q^{8} +(1.02860 - 5.83350i) q^{9} +O(q^{10})$	\(q+(0.926709 + 0.777601i) q^{2} +(-2.28834 + 1.92015i) q^{3} +(-0.0931703 - 0.528395i) q^{4} -3.61374 q^{6} +(2.47194 + 0.899712i) q^{7} +(1.53427 - 2.65744i) q^{8} +(1.02860 - 5.83350i) q^{9} +(-2.05288 + 3.55569i) q^{11} +(1.22780 + 1.03025i) q^{12} +(0.902063 + 5.11585i) q^{13} +(1.59115 + 2.75595i) q^{14} +(2.47987 - 0.902600i) q^{16} +(0.670858 - 3.80463i) q^{17} +(5.48936 - 4.60612i) q^{18} +(3.00738 - 2.52349i) q^{19} +(-7.38423 + 2.68764i) q^{21} +(-4.66732 + 1.69877i) q^{22} +(4.38227 + 7.59031i) q^{23} +(1.59173 + 9.02716i) q^{24} +(-3.14214 + 5.44235i) q^{26} +(4.36656 + 7.56311i) q^{27} +(0.245092 - 1.38999i) q^{28} +(-4.63674 + 8.03107i) q^{29} -4.88813 q^{31} +(-2.76699 - 1.00710i) q^{32} +(-2.12976 - 12.0785i) q^{33} +(3.58017 - 3.00412i) q^{34} -3.17823 q^{36} +(-3.42449 + 5.02721i) q^{37} +4.74923 q^{38} +(-11.8874 - 9.97474i) q^{39} +(-0.0686945 - 0.389586i) q^{41} +(-8.93295 - 3.25133i) q^{42} +2.75281 q^{43} +(2.07007 + 0.753445i) q^{44} +(-1.84115 + 10.4417i) q^{46} +(1.05982 + 1.83566i) q^{47} +(-3.94168 + 6.82719i) q^{48} +(-0.0613108 - 0.0514458i) q^{49} +(5.77029 + 9.99444i) q^{51} +(2.61914 - 0.953290i) q^{52} +(-1.81438 + 0.660379i) q^{53} +(-1.83455 + 10.4043i) q^{54} +(6.18355 - 5.18862i) q^{56} +(-2.03644 + 11.5492i) q^{57} +(-10.5419 + 3.83693i) q^{58} +(3.30713 - 1.20370i) q^{59} +(-0.0936657 - 0.531205i) q^{61} +(-4.52988 - 3.80102i) q^{62} +(7.79112 - 13.4946i) q^{63} +(-4.42010 - 7.65583i) q^{64} +(7.41856 - 12.8493i) q^{66} +(-3.71526 - 1.35225i) q^{67} -2.07285 q^{68} +(-24.6027 - 8.95463i) q^{69} +(4.29878 - 3.60710i) q^{71} +(-13.9240 - 11.6836i) q^{72} -11.6830 q^{73} +(-7.08267 + 1.99588i) q^{74} +(-1.61360 - 1.35397i) q^{76} +(-8.27368 + 6.94244i) q^{77} +(-3.25982 - 18.4874i) q^{78} +(8.98019 + 3.26852i) q^{79} +(-7.81571 - 2.84469i) q^{81} +(0.239283 - 0.414450i) q^{82} +(-2.69836 + 15.3032i) q^{83} +(2.10813 + 3.65138i) q^{84} +(2.55105 + 2.14059i) q^{86} +(-4.81039 - 27.2811i) q^{87} +(6.29934 + 10.9108i) q^{88} +(3.42252 - 1.24570i) q^{89} +(-2.37295 + 13.4577i) q^{91} +(3.60238 - 3.02276i) q^{92} +(11.1857 - 9.38594i) q^{93} +(-0.445267 + 2.52524i) q^{94} +(8.26562 - 3.00844i) q^{96} +(4.25585 + 7.37135i) q^{97} +(-0.0168129 - 0.0953507i) q^{98} +(18.6305 + 15.6329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 3 q^{2} + 3 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 78 * q - 3 * q^2 + 3 * q^4 + 6 * q^7 - 6 * q^8	$ 78 q - 3 q^{2} + 3 q^{4} + 6 q^{7} - 6 q^{8} - 15 q^{12} + 27 q^{13} + 6 q^{14} + 21 q^{16} - 15 q^{18} - 12 q^{19} + 15 q^{21} + 30 q^{22} - 18 q^{23} + 15 q^{24} + 36 q^{27} - 3 q^{28} - 3 q^{29} - 36 q^{31} + 36 q^{32} + 30 q^{33} - 21 q^{34} + 108 q^{36} + 54 q^{37} - 60 q^{38} + 9 q^{39} - 3 q^{41} + 6 q^{42} + 12 q^{43} - 15 q^{44} - 36 q^{46} + 63 q^{47} + 54 q^{48} - 30 q^{49} - 30 q^{51} - 105 q^{52} + 24 q^{53} + 27 q^{54} + 120 q^{56} - 27 q^{57} - 33 q^{58} + 15 q^{59} - 6 q^{61} + 24 q^{62} + 48 q^{63} - 54 q^{64} - 6 q^{66} + 48 q^{67} - 246 q^{68} + 45 q^{69} + 72 q^{71} + 132 q^{72} - 36 q^{73} + 96 q^{74} + 21 q^{76} + 3 q^{77} - 186 q^{78} + 48 q^{79} + 48 q^{81} - 66 q^{82} - 18 q^{83} + 27 q^{84} + 108 q^{86} + 72 q^{87} - 42 q^{88} - 21 q^{89} - 27 q^{91} + 75 q^{92} + 48 q^{93} - 78 q^{94} - 126 q^{96} + 12 q^{97} + 30 q^{98} + 141 q^{99}+O(q^{100}) $ 78 * q - 3 * q^2 + 3 * q^4 + 6 * q^7 - 6 * q^8 - 15 * q^12 + 27 * q^13 + 6 * q^14 + 21 * q^16 - 15 * q^18 - 12 * q^19 + 15 * q^21 + 30 * q^22 - 18 * q^23 + 15 * q^24 + 36 * q^27 - 3 * q^28 - 3 * q^29 - 36 * q^31 + 36 * q^32 + 30 * q^33 - 21 * q^34 + 108 * q^36 + 54 * q^37 - 60 * q^38 + 9 * q^39 - 3 * q^41 + 6 * q^42 + 12 * q^43 - 15 * q^44 - 36 * q^46 + 63 * q^47 + 54 * q^48 - 30 * q^49 - 30 * q^51 - 105 * q^52 + 24 * q^53 + 27 * q^54 + 120 * q^56 - 27 * q^57 - 33 * q^58 + 15 * q^59 - 6 * q^61 + 24 * q^62 + 48 * q^63 - 54 * q^64 - 6 * q^66 + 48 * q^67 - 246 * q^68 + 45 * q^69 + 72 * q^71 + 132 * q^72 - 36 * q^73 + 96 * q^74 + 21 * q^76 + 3 * q^77 - 186 * q^78 + 48 * q^79 + 48 * q^81 - 66 * q^82 - 18 * q^83 + 27 * q^84 + 108 * q^86 + 72 * q^87 - 42 * q^88 - 21 * q^89 - 27 * q^91 + 75 * q^92 + 48 * q^93 - 78 * q^94 - 126 * q^96 + 12 * q^97 + 30 * q^98 + 141 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.926709	+	0.777601i	0.655282	+	0.549847i	0.908669	−	0.417518i	$-0.137100\pi$
$2$	0.926709	+	0.777601i	0.655282	+	0.549847i	−0.253386	+	0.967365i	$0.581544\pi$
$3$	−2.28834	+	1.92015i	−1.32118	+	1.10860i	−0.335122	+	0.942175i	$0.608778\pi$
$3$	−2.28834	+	1.92015i	−1.32118	+	1.10860i	−0.986054	+	0.166424i	$0.946778\pi$
$4$	−0.0931703	−	0.528395i	−0.0465851	−	0.264197i
$5$		0			0
$5$		0			0
$6$	−3.61374			−1.47530
$7$	2.47194	+	0.899712i	0.934305	+	0.340059i	0.763915	−	0.645317i	$-0.223275\pi$
$7$	2.47194	+	0.899712i	0.934305	+	0.340059i	0.170391	+	0.985377i	$0.445497\pi$
$8$	1.53427	−	2.65744i	0.542447	−	0.939546i
$9$	1.02860	−	5.83350i	0.342868	−	1.94450i
$10$		0			0
$11$	−2.05288	+	3.55569i	−0.618965	+	1.07208i	0.370709	+	0.928749i	$0.379115\pi$
$11$	−2.05288	+	3.55569i	−0.618965	+	1.07208i	−0.989675	+	0.143331i	$0.954219\pi$
$12$	1.22780	+	1.03025i	0.354436	+	0.297407i
$13$	0.902063	+	5.11585i	0.250187	+	1.41888i	0.808131	+	0.589003i	$0.200479\pi$
$13$	0.902063	+	5.11585i	0.250187	+	1.41888i	−0.557944	+	0.829879i	$0.688410\pi$
$14$	1.59115	+	2.75595i	0.425253	+	0.736560i
$15$		0			0
$16$	2.47987	−	0.902600i	0.619968	−	0.225650i
$17$	0.670858	−	3.80463i	0.162707	−	0.922757i	−0.788690	−	0.614791i	$-0.789240\pi$
$17$	0.670858	−	3.80463i	0.162707	−	0.922757i	0.951397	−	0.307966i	$-0.0996484\pi$
$18$	5.48936	−	4.60612i	1.29385	−	1.08567i
$19$	3.00738	−	2.52349i	0.689939	−	0.578928i	−0.228952	−	0.973438i	$-0.573530\pi$
$19$	3.00738	−	2.52349i	0.689939	−	0.578928i	0.918892	+	0.394510i	$0.129086\pi$
$20$		0			0
$21$	−7.38423	+	2.68764i	−1.61137	+	0.586491i
$22$	−4.66732	+	1.69877i	−0.995077	+	0.362178i
$23$	4.38227	+	7.59031i	0.913766	+	1.58269i	0.808699	+	0.588223i	$0.200172\pi$
$23$	4.38227	+	7.59031i	0.913766	+	1.58269i	0.105067	+	0.994465i	$0.466494\pi$
$24$	1.59173	+	9.02716i	0.324911	+	1.84266i
$25$		0			0
$26$	−3.14214	+	5.44235i	−0.616225	+	1.06733i
$27$	4.36656	+	7.56311i	0.840346	+	1.45552i
$28$	0.245092	−	1.38999i	0.0463180	−	0.262683i
$29$	−4.63674	+	8.03107i	−0.861021	+	1.49133i	0.00992263	+	0.999951i	$0.496841\pi$
$29$	−4.63674	+	8.03107i	−0.861021	+	1.49133i	−0.870944	+	0.491382i	$0.836492\pi$
$30$		0			0
$31$	−4.88813			−0.877935			−0.438967	−	0.898503i	$-0.644656\pi$
$31$	−4.88813			−0.877935			−0.438967	+	0.898503i	$0.644656\pi$
$32$	−2.76699	−	1.00710i	−0.489140	−	0.178032i
$33$	−2.12976	−	12.0785i	−0.370743	−	2.10259i
$34$	3.58017	−	3.00412i	0.613994	−	0.515203i
$35$		0			0
$36$	−3.17823			−0.529705
$37$	−3.42449	+	5.02721i	−0.562982	+	0.826469i
$37$	−3.42449	+	5.02721i	−0.562982	+	0.826469i
$38$	4.74923			0.770427
$39$	−11.8874	−	9.97474i	−1.90351	−	1.59724i
$40$		0			0
$41$	−0.0686945	−	0.389586i	−0.0107283	−	0.0608431i	0.978974	−	0.203987i	$-0.0653900\pi$
$41$	−0.0686945	−	0.389586i	−0.0107283	−	0.0608431i	−0.989702	+	0.143144i	$0.954279\pi$
$42$	−8.93295	−	3.25133i	−1.37838	−	0.501691i
$43$	2.75281			0.419800			0.209900	−	0.977723i	$-0.432686\pi$
$43$	2.75281			0.419800			0.209900	+	0.977723i	$0.432686\pi$
$44$	2.07007	+	0.753445i	0.312075	+	0.113586i
$45$		0			0
$46$	−1.84115	+	10.4417i	−0.271462	+	1.53954i
$47$	1.05982	+	1.83566i	0.154590	+	0.267758i	0.932910	−	0.360110i	$-0.117261\pi$
$47$	1.05982	+	1.83566i	0.154590	+	0.267758i	−0.778320	+	0.627868i	$0.783928\pi$
$48$	−3.94168	+	6.82719i	−0.568932	+	0.985420i
$49$	−0.0613108	−	0.0514458i	−0.00875868	−	0.00734941i
$50$		0			0
$51$	5.77029	+	9.99444i	0.808003	+	1.39950i
$52$	2.61914	−	0.953290i	0.363210	−	0.132198i
$53$	−1.81438	+	0.660379i	−0.249224	+	0.0907101i	−0.463612	−	0.886039i	$-0.653447\pi$
$53$	−1.81438	+	0.660379i	−0.249224	+	0.0907101i	0.214388	+	0.976749i	$0.431224\pi$
$54$	−1.83455	+	10.4043i	−0.249651	+	1.41584i
$55$		0			0
$56$	6.18355	−	5.18862i	0.826312	−	0.693358i
$57$	−2.03644	+	11.5492i	−0.269733	+	1.52973i
$58$	−10.5419	+	3.83693i	−1.38422	+	0.503814i
$59$	3.30713	−	1.20370i	0.430551	−	0.156708i	−0.117649	−	0.993055i	$-0.537536\pi$
$59$	3.30713	−	1.20370i	0.430551	−	0.156708i	0.548200	+	0.836348i	$0.315313\pi$
$60$		0			0
$61$	−0.0936657	−	0.531205i	−0.0119927	−	0.0680138i	0.978224	−	0.207551i	$-0.0665495\pi$
$61$	−0.0936657	−	0.531205i	−0.0119927	−	0.0680138i	−0.990217	+	0.139538i	$0.955438\pi$
$62$	−4.52988	−	3.80102i	−0.575295	−	0.482730i
$63$	7.79112	−	13.4946i	0.981589	−	1.70016i
$64$	−4.42010	−	7.65583i	−0.552512	−	0.956979i
$65$		0			0
$66$	7.41856	−	12.8493i	0.913162	−	1.58164i
$67$	−3.71526	−	1.35225i	−0.453892	−	0.165203i	0.104950	−	0.994478i	$-0.466532\pi$
$67$	−3.71526	−	1.35225i	−0.453892	−	0.165203i	−0.558842	+	0.829274i	$0.688754\pi$
$68$	−2.07285			−0.251370
$69$	−24.6027	−	8.95463i	−2.96181	−	1.07801i
$70$		0			0
$71$	4.29878	−	3.60710i	0.510171	−	0.428084i	−0.351018	−	0.936369i	$-0.614165\pi$
$71$	4.29878	−	3.60710i	0.510171	−	0.428084i	0.861189	+	0.508284i	$0.169720\pi$
$72$	−13.9240	−	11.6836i	−1.64096	−	1.37693i
$73$	−11.6830			−1.36739			−0.683694	−	0.729769i	$-0.739628\pi$
$73$	−11.6830			−1.36739			−0.683694	+	0.729769i	$0.739628\pi$
$74$	−7.08267	+	1.99588i	−0.823344	+	0.232016i
$75$		0			0
$76$	−1.61360	−	1.35397i	−0.185092	−	0.155311i
$77$	−8.27368	+	6.94244i	−0.942873	+	0.791164i
$78$	−3.25982	−	18.4874i	−0.369102	−	2.09328i
$79$	8.98019	+	3.26852i	1.01035	+	0.367738i	0.793567	−	0.608482i	$-0.208221\pi$
$79$	8.98019	+	3.26852i	1.01035	+	0.367738i	0.216783	+	0.976220i	$0.430444\pi$
$80$		0			0
$81$	−7.81571	−	2.84469i	−0.868413	−	0.316076i
$82$	0.239283	−	0.414450i	0.0264243	−	0.0457683i
$83$	−2.69836	+	15.3032i	−0.296183	+	1.67974i	0.366170	+	0.930548i	$0.380669\pi$
$83$	−2.69836	+	15.3032i	−0.296183	+	1.67974i	−0.662353	+	0.749192i	$0.730442\pi$
$84$	2.10813	+	3.65138i	0.230015	+	0.398398i
$85$		0			0
$86$	2.55105	+	2.14059i	0.275087	+	0.230826i
$87$	−4.81039	−	27.2811i	−0.515728	−	2.92484i
$88$	6.29934	+	10.9108i	0.671512	+	1.16309i
$89$	3.42252	−	1.24570i	0.362786	−	0.132043i	−0.154194	−	0.988041i	$-0.549278\pi$
$89$	3.42252	−	1.24570i	0.362786	−	0.132043i	0.516981	+	0.855997i	$0.327056\pi$
$90$		0			0
$91$	−2.37295	+	13.4577i	−0.248753	+	1.41075i
$92$	3.60238	−	3.02276i	0.375574	−	0.315144i
$93$	11.1857	−	9.38594i	1.15991	−	0.973277i
$94$	−0.445267	+	2.52524i	−0.0459258	+	0.260458i
$95$		0			0
$96$	8.26562	−	3.00844i	0.843606	−	0.307047i
$97$	4.25585	+	7.37135i	0.432116	+	0.748447i	0.997055	−	0.0766855i	$-0.0244337\pi$
$97$	4.25585	+	7.37135i	0.432116	+	0.748447i	−0.564939	+	0.825132i	$0.691100\pi$
$98$	−0.0168129	−	0.0953507i	−0.00169836	−	0.00963187i
$99$	18.6305	+	15.6329i	1.87244	+	1.57116i
$100$		0			0
$101$	−2.78746	−	4.82802i	−0.277362	−	0.480406i	0.693366	−	0.720586i	$-0.256127\pi$
$101$	−2.78746	−	4.82802i	−0.277362	−	0.480406i	−0.970728	+	0.240180i	$0.922794\pi$
$102$	−2.42431	+	13.7489i	−0.240042	+	1.36135i
$103$	0.252642	−	0.437589i	0.0248936	−	0.0431169i	−0.853310	−	0.521404i	$-0.825409\pi$
$103$	0.252642	−	0.437589i	0.0248936	−	0.0431169i	0.878204	+	0.478287i	$0.158742\pi$
$104$	14.9791	+	5.45193i	1.46882	+	0.534606i
$105$		0			0
$106$	−2.19491	−	0.798883i	−0.213189	−	0.0775943i
$107$	1.38187	+	7.83699i	0.133591	+	0.757631i	0.975831	+	0.218528i	$0.0701255\pi$
$107$	1.38187	+	7.83699i	0.133591	+	0.757631i	−0.842240	+	0.539103i	$0.818763\pi$
$108$	3.58947	−	3.01193i	0.345397	−	0.289823i
$109$	2.76511	+	2.32020i	0.264849	+	0.222235i	0.765535	−	0.643394i	$-0.222474\pi$
$109$	2.76511	+	2.32020i	0.264849	+	0.222235i	−0.500686	+	0.865629i	$0.666919\pi$
$110$		0			0
$111$	−1.81659	−	18.0795i	−0.172423	−	1.71603i
$112$	6.94218			0.655974
$113$	8.94516	+	7.50588i	0.841490	+	0.706094i	0.957898	−	0.287108i	$-0.0926937\pi$
$113$	8.94516	+	7.50588i	0.841490	+	0.706094i	−0.116408	+	0.993201i	$0.537138\pi$
$114$	−10.8679	+	9.11923i	−1.01787	+	0.854094i
$115$		0			0
$116$	4.67558	+	1.70177i	0.434117	+	0.158006i
$117$	30.7712			2.84480
$118$	4.00074	+	1.45615i	0.368298	+	0.134049i
$119$	5.08139	−	8.80122i	0.465810	−	0.806807i
$120$		0			0
$121$	−2.92860	−	5.07248i	−0.266236	−	0.461135i
$122$	0.326264	−	0.565107i	0.0295386	−	0.0511624i
$123$	0.905259	+	0.759603i	0.0816245	+	0.0684911i
$124$	0.455429	+	2.58286i	0.0408987	+	0.231948i
$125$		0			0
$126$	17.7135	−	6.44720i	1.57805	−	0.574362i
$127$	19.8588	−	7.22802i	1.76218	−	0.641383i	0.762202	−	0.647339i	$-0.224118\pi$
$127$	19.8588	−	7.22802i	1.76218	−	0.641383i	0.999982	+	0.00595603i	$0.00189587\pi$
$128$	0.834403	−	4.73213i	0.0737515	−	0.418266i
$129$	−6.29938	+	5.28581i	−0.554629	+	0.465389i
$130$		0			0
$131$	−3.33897	+	18.9362i	−0.291727	+	1.65447i	0.388489	+	0.921453i	$0.372997\pi$
$131$	−3.33897	+	18.9362i	−0.291727	+	1.65447i	−0.680216	+	0.733012i	$0.738114\pi$
$132$	−6.18377	+	2.25071i	−0.538228	+	0.195899i
$133$	9.70446	−	3.53214i	0.841484	−	0.306275i
$134$	−2.39146	−	4.14213i	−0.206591	−	0.357826i
$135$		0			0
$136$	−9.08127	−	7.62009i	−0.778713	−	0.653418i
$137$	−0.382422	+	0.662374i	−0.0326725	+	0.0565904i	−0.881899	−	0.471438i	$-0.843735\pi$
$137$	−0.382422	+	0.662374i	−0.0326725	+	0.0565904i	0.849227	+	0.528028i	$0.177068\pi$
$138$	−15.8364	−	27.4294i	−1.34808	−	2.33495i
$139$	2.04372	−	11.5905i	0.173346	−	0.983096i	−0.766689	−	0.642019i	$-0.778097\pi$
$139$	2.04372	−	11.5905i	0.173346	−	0.983096i	0.940035	−	0.341077i	$-0.110792\pi$
$140$		0			0
$141$	−5.94996	−	2.16561i	−0.501077	−	0.182377i
$142$	6.78860			0.569687
$143$	−20.0422	−	7.29476i	−1.67601	−	0.610018i
$144$	−2.71451	−	15.3948i	−0.226209	−	1.28290i
$145$		0			0
$146$	−10.8267	−	9.08469i	−0.896025	−	0.751854i
$147$	0.239084			0.0197193
$148$	2.97541	+	1.34110i	0.244578	+	0.110237i
$149$	−3.51144			−0.287668			−0.143834	−	0.989602i	$-0.545943\pi$
$149$	−3.51144			−0.287668			−0.143834	+	0.989602i	$0.545943\pi$
$150$		0			0
$151$	15.9941	−	13.4206i	1.30158	−	1.09216i	0.311710	−	0.950177i	$-0.399098\pi$
$151$	15.9941	−	13.4206i	1.30158	−	1.09216i	0.989870	−	0.141978i	$-0.0453463\pi$
$152$	−2.09188	−	11.8636i	−0.169674	−	0.962267i
$153$	−21.5042	−	7.82691i	−1.73852	−	0.632768i
$154$	−13.0657			−1.05287
$155$		0			0
$156$	−4.16304	+	7.21060i	−0.333310	+	0.577310i
$157$	−0.0931725	+	0.528408i	−0.00743598	+	0.0421715i	−0.988300	−	0.152523i	$-0.951260\pi$
$157$	−0.0931725	+	0.528408i	−0.00743598	+	0.0421715i	0.980864	+	0.194694i	$0.0623714\pi$
$158$	5.78042	+	10.0120i	0.459865	+	0.796510i
$159$	2.88389	−	4.99505i	0.228708	−	0.396133i
$160$		0			0
$161$	4.00360	+	22.7056i	0.315528	+	1.78945i
$162$	−5.03086	−	8.71371i	−0.395262	−	0.684613i
$163$	21.4308	−	7.80017i	1.67859	−	0.610956i	0.685473	−	0.728098i	$-0.259595\pi$
$163$	21.4308	−	7.80017i	1.67859	−	0.610956i	0.993115	+	0.117142i	$0.0373732\pi$
$164$	−0.199455	+	0.0725956i	−0.0155748	+	0.00566876i
$165$		0			0
$166$	−14.4004	+	12.0833i	−1.11768	+	0.937848i
$167$	3.94426	−	3.30963i	0.305216	−	0.256107i	−0.477295	−	0.878743i	$-0.658383\pi$
$167$	3.94426	−	3.30963i	0.305216	−	0.256107i	0.782512	+	0.622636i	$0.213938\pi$
$168$	−4.18718	+	23.7467i	−0.323048	+	1.83210i
$169$	−13.1422	+	4.78337i	−1.01094	+	0.367952i
$170$		0			0
$171$	−11.6274	−	20.1392i	−0.889168	−	1.54008i
$172$	−0.256480	−	1.45457i	−0.0195564	−	0.110910i
$173$	3.08481	+	2.58846i	0.234534	+	0.196797i	0.752478	−	0.658617i	$-0.228858\pi$
$173$	3.08481	+	2.58846i	0.234534	+	0.196797i	−0.517944	+	0.855414i	$0.673303\pi$
$174$	16.7560	−	29.0222i	1.27027	−	2.20017i
$175$		0			0
$176$	−1.88151	+	10.6706i	−0.141824	+	0.804325i
$177$	−5.25657	+	9.10464i	−0.395108	+	0.684347i
$178$	4.14034	+	1.50696i	0.310331	+	0.112951i
$179$	8.85764			0.662051			0.331025	−	0.943622i	$-0.392605\pi$
$179$	8.85764			0.662051			0.331025	+	0.943622i	$0.392605\pi$
$180$		0			0
$181$	−2.53534	−	14.3786i	−0.188450	−	1.06876i	−0.921441	−	0.388517i	$-0.872987\pi$
$181$	−2.53534	−	14.3786i	−0.188450	−	1.06876i	0.732991	−	0.680238i	$-0.238124\pi$
$182$	−12.6637	+	10.6261i	−0.938699	+	0.787662i
$183$	1.23433	+	1.03573i	0.0912444	+	0.0765631i
$184$	26.8943			1.98268
$185$		0			0
$186$	17.6644			1.29522
$187$	12.1509	+	10.1958i	0.888559	+	0.745590i
$188$	0.871208	−	0.731030i	0.0635394	−	0.0533159i
$189$	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	$0.659558\pi$
$192$	24.8151	+	9.03194i	1.79087	+	0.651824i
$193$	−3.57247	+	6.18771i	−0.257152	+	0.445401i	−0.965478	−	0.260485i	$-0.916118\pi$
$193$	−3.57247	+	6.18771i	−0.257152	+	0.445401i	0.708326	+	0.705886i	$0.249451\pi$
$194$	−1.78804	+	10.1405i	−0.128373	+	0.728042i
$195$		0			0
$196$	−0.0214714	+	0.0371895i	−0.00153367	+	0.00265639i
$197$	−19.9798	−	16.7650i	−1.42350	−	1.19446i	−0.949432	−	0.313973i	$-0.898340\pi$
$197$	−19.9798	−	16.7650i	−1.42350	−	1.19446i	−0.474070	−	0.880487i	$-0.657216\pi$
$198$	5.10894	+	28.9742i	0.363076	+	2.05911i
$199$	−5.01011	−	8.67776i	−0.355157	−	0.615150i	0.631988	−	0.774978i	$-0.282239\pi$
$199$	−5.01011	−	8.67776i	−0.355157	−	0.615150i	−0.987145	+	0.159828i	$0.948906\pi$
$200$		0			0
$201$	11.0983	−	4.03946i	0.782815	−	0.284921i
$202$	1.17111	−	6.64170i	0.0823991	−	0.467308i
$203$	−18.6874	+	15.6806i	−1.31160	+	1.10056i
$204$	4.74339	−	3.98018i	0.332104	−	0.278668i
$205$		0			0
$206$	0.574395	−	0.209063i	0.0400200	−	0.0145661i
$207$	48.7857	−	17.7565i	3.39084	−	1.23416i
$208$	6.85457	+	11.8725i	0.475279	+	0.823207i
$209$	2.79896	+	15.8737i	0.193608	+	1.09801i
$210$		0			0
$211$	2.84657	−	4.93040i	0.195966	−	0.339423i	−0.751251	−	0.660017i	$-0.770549\pi$
$211$	2.84657	−	4.93040i	0.195966	−	0.339423i	0.947217	+	0.320594i	$0.103882\pi$
$212$	0.517987	+	0.897180i	0.0355755	+	0.0616186i
$213$	−2.91091	+	16.5086i	−0.199452	+	1.13115i
$214$	−4.81346	+	8.33716i	−0.329041	+	0.569917i
$215$		0			0
$216$	26.7980			1.82337
$217$	−12.0832	−	4.39791i	−0.820259	−	0.298550i
$218$	0.758260	+	4.30031i	0.0513558	+	0.291253i
$219$	26.7347	−	22.4330i	1.80656	−	1.51588i
$220$		0			0
$221$	20.0691			1.34999
$222$	12.3752	−	18.1670i	0.830570	−	1.21929i
$223$	−18.5146			−1.23983			−0.619916	−	0.784668i	$-0.712833\pi$
$223$	−18.5146			−1.23983			−0.619916	+	0.784668i	$0.712833\pi$
$224$	−5.93373	−	4.97899i	−0.396464	−	0.332673i
$225$		0			0
$226$	2.45298	+	13.9115i	0.163170	+	0.925382i
$227$	−13.1626	−	4.79078i	−0.873630	−	0.317975i	−0.133994	−	0.990982i	$-0.542780\pi$
$227$	−13.1626	−	4.79078i	−0.873630	−	0.317975i	−0.739636	+	0.673007i	$0.765003\pi$
$228$	6.29229			0.416717
$229$	0.00233946		0.000851494i	0.000154596		5.62683e-5i	0.342097	−	0.939664i	$-0.388863\pi$
$229$	0.00233946		0.000851494i	0.000154596		5.62683e-5i	−0.341943	+	0.939721i	$0.611085\pi$
$230$		0			0
$231$	5.60251	−	31.7734i	0.368618	−	2.09054i
$232$	14.2280	+	24.6437i	0.934117	+	1.61794i
$233$	0.0223889	−	0.0387787i	0.00146675	−	0.00254048i	−0.865291	−	0.501270i	$-0.832866\pi$
$233$	0.0223889	−	0.0387787i	0.00146675	−	0.00254048i	0.866758	+	0.498729i	$0.166200\pi$
$234$	28.5160	+	23.9277i	1.86415	+	1.56420i
$235$		0			0
$236$	−0.944152	−	1.63532i	−0.0614591	−	0.106450i
$237$	−26.8258	+	9.76380i	−1.74252	+	0.634227i
$238$	11.5528	−	4.20488i	0.748858	−	0.272562i
$239$	4.40032	−	24.9555i	0.284633	−	1.61424i	−0.421959	−	0.906615i	$-0.638658\pi$
$239$	4.40032	−	24.9555i	0.284633	−	1.61424i	0.706593	−	0.707621i	$-0.250231\pi$
$240$		0			0
$241$	8.92689	−	7.49055i	0.575032	−	0.482509i	−0.308280	−	0.951296i	$-0.599753\pi$
$241$	8.92689	−	7.49055i	0.575032	−	0.482509i	0.883311	+	0.468787i	$0.155309\pi$
$242$	1.23041	−	6.97800i	0.0790937	−	0.448563i
$243$	−1.27210	+	0.463006i	−0.0816052	+	0.0297019i
$244$	−0.271959	+	0.0989849i	−0.0174104	+	0.00633686i
$245$		0			0
$246$	0.248244	+	1.40786i	0.0158275	+	0.0897620i
$247$	15.6226	+	13.1089i	0.994044	+	0.834102i
$248$	−7.49972	+	12.9899i	−0.476233	+	0.824860i
$249$	−23.2096	−	40.2002i	−1.47085	−	2.54758i
$250$		0			0
$251$	1.50934	−	2.61426i	0.0952688	−	0.165010i	−0.814452	−	0.580231i	$-0.802962\pi$
$251$	1.50934	−	2.61426i	0.0952688	−	0.165010i	0.909721	+	0.415221i	$0.136296\pi$
$252$	−7.85639	−	2.85949i	−0.494906	−	0.180131i
$253$	−35.9850			−2.26236
$254$	24.0239	+	8.74397i	1.50739	+	0.548645i
$255$		0			0
$256$	−9.09100	+	7.62826i	−0.568188	+	0.476766i
$257$	−15.0746	−	12.6491i	−0.940327	−	0.789028i	0.0373153	−	0.999304i	$-0.488119\pi$
$257$	−15.0746	−	12.6491i	−0.940327	−	0.789028i	−0.977642	+	0.210276i	$0.932564\pi$
$258$	−9.94794			−0.619332
$259$	−12.9882	+	9.34591i	−0.807046	+	0.580727i
$260$		0			0
$261$	42.0799	+	35.3093i	2.60468	+	2.18559i
$262$	−17.8191	+	14.9520i	−1.10087	+	0.923737i
$263$	4.60253	+	26.1022i	0.283804	+	1.60953i	0.709526	+	0.704679i	$0.248909\pi$
$263$	4.60253	+	26.1022i	0.283804	+	1.60953i	−0.425722	+	0.904854i	$0.639980\pi$
$264$	−35.3654	−	12.8719i	−2.17659	−	0.792213i
$265$		0			0
$266$	11.7398	+	4.27294i	0.719814	+	0.261991i
$267$	−5.43999	+	9.42233i	−0.332922	+	0.576637i
$268$	−0.368367	+	2.08911i	−0.0225016	+	0.127613i
$269$	−6.36638	−	11.0269i	−0.388165	−	0.672321i	0.604038	−	0.796956i	$-0.293558\pi$
$269$	−6.36638	−	11.0269i	−0.388165	−	0.672321i	−0.992203	+	0.124634i	$0.960224\pi$
$270$		0			0
$271$	−15.0559	−	12.6334i	−0.914578	−	0.767422i	0.0584062	−	0.998293i	$-0.481398\pi$
$271$	−15.0559	−	12.6334i	−0.914578	−	0.767422i	−0.972984	+	0.230871i	$0.925843\pi$
$272$	−1.77041	−	10.0405i	−0.107347	−	0.608795i
$273$	−20.4106	−	35.3522i	−1.23531	−	2.13961i
$274$	−0.869457	+	0.316456i	−0.0525258	+	0.0191178i
$275$		0			0
$276$	−2.43935	+	13.8342i	−0.146831	+	0.832722i
$277$	16.9190	−	14.1967i	1.01656	−	0.852996i	0.0273698	−	0.999625i	$-0.491287\pi$
$277$	16.9190	−	14.1967i	1.01656	−	0.852996i	0.989192	+	0.146629i	$0.0468424\pi$
$278$	10.9067	−	9.15185i	0.654143	−	0.548891i
$279$	−5.02795	+	28.5149i	−0.301016	+	1.70714i
$280$		0			0
$281$	9.09594	−	3.31065i	0.542618	−	0.197497i	−0.0561454	−	0.998423i	$-0.517881\pi$
$281$	9.09594	−	3.31065i	0.542618	−	0.197497i	0.598764	+	0.800926i	$0.295659\pi$
$282$	−3.82990	−	6.63359i	−0.228067	−	0.395024i
$283$	−2.82825	−	16.0398i	−0.168122	−	0.953466i	−0.945787	−	0.324787i	$-0.894707\pi$
$283$	−2.82825	−	16.0398i	−0.168122	−	0.953466i	0.777665	−	0.628679i	$-0.216404\pi$
$284$	−2.30649	−	1.93538i	−0.136865	−	0.114843i
$285$		0			0
$286$	−12.9009	−	22.3449i	−0.762844	−	1.32128i
$287$	0.180706	−	1.02484i	0.0106668	−	0.0604942i
$288$	−8.72107	+	15.1053i	−0.513894	+	0.890091i
$289$	1.94965	+	0.709615i	0.114685	+	0.0417420i
$290$		0			0
$291$	−23.8929	−	8.69632i	−1.40063	−	0.509787i
$292$	1.08851	+	6.17322i	0.0637000	+	0.361260i
$293$	21.9704	−	18.4353i	1.28352	−	1.07700i	0.290774	−	0.956792i	$-0.406087\pi$
$293$	21.9704	−	18.4353i	1.28352	−	1.07700i	0.992748	−	0.120212i	$-0.0383573\pi$
$294$	0.221561	+	0.185912i	0.0129217	+	0.0108426i
$295$		0			0
$296$	8.10540	+	16.8135i	0.471117	+	0.977263i
$297$	−35.8561			−2.08058
$298$	−3.25408	−	2.73050i	−0.188504	−	0.158174i
$299$	−34.8778	+	29.2659i	−2.01704	+	1.69249i
$300$		0			0
$301$	6.80478	+	2.47674i	0.392221	+	0.142757i
$302$	25.2578			1.45342
$303$	15.6492	+	5.69584i	0.899022	+	0.327217i
$304$	5.18021	−	8.97239i	0.297106	−	0.514602i
$305$		0			0
$306$	−13.8420	−	23.9750i	−0.791293	−	1.37056i
$307$	15.3112	−	26.5198i	0.873858	−	1.51357i	0.0158835	−	0.999874i	$-0.494944\pi$
$307$	15.3112	−	26.5198i	0.873858	−	1.51357i	0.857974	−	0.513692i	$-0.171723\pi$
$308$	4.43921	+	3.72494i	0.252947	+	0.212248i
$309$	0.262104	+	1.48646i	0.0149106	+	0.0845620i
$310$		0			0
$311$	−1.80612	+	0.657373i	−0.102415	+	0.0372762i	−0.392720	−	0.919658i	$-0.628466\pi$
$311$	−1.80612	+	0.657373i	−0.102415	+	0.0372762i	0.290304	+	0.956934i	$0.406244\pi$
$312$	−44.7458	+	16.2861i	−2.53323	+	0.922021i
$313$	3.42146	−	19.4040i	0.193392	−	1.09678i	−0.721298	−	0.692625i	$-0.756454\pi$
$313$	3.42146	−	19.4040i	0.193392	−	1.09678i	0.914690	−	0.404156i	$-0.132435\pi$
$314$	−0.497234	+	0.417229i	−0.0280606	+	0.0235456i
$315$		0			0
$316$	0.890384	−	5.04962i	0.0500880	−	0.284063i
$317$	−12.3984	+	4.51265i	−0.696363	+	0.253456i	−0.665857	−	0.746079i	$-0.731934\pi$
$317$	−12.3984	+	4.51265i	−0.696363	+	0.253456i	−0.0305060	+	0.999535i	$0.509712\pi$
$318$	6.55669	−	2.38644i	0.367681	−	0.133825i
$319$	−19.0373	−	32.9736i	−1.06588	−	1.84617i
$320$		0			0
$321$	−18.2104	−	15.2803i	−1.01641	−	0.852865i
$322$	−13.9457	+	24.1547i	−0.777163	+	1.34609i
$323$	−7.58341	−	13.1348i	−0.421952	−	0.730842i
$324$	−0.774926	+	4.39482i	−0.0430514	+	0.244157i
$325$		0			0
$326$	25.9255	+	9.43612i	1.43588	+	0.522618i
$327$	−10.7827			−0.596282
$328$	−1.14070	−	0.415179i	−0.0629844	−	0.0229244i
$329$	0.968240	+	5.49116i	0.0533808	+	0.302738i
$330$		0			0
$331$	13.0085	+	10.9155i	0.715014	+	0.599968i	0.926001	−	0.377521i	$-0.123223\pi$
$331$	13.0085	+	10.9155i	0.715014	+	0.599968i	−0.210987	+	0.977489i	$0.567668\pi$
$332$	8.33752			0.457581
$333$	25.8038	+	25.1478i	1.41404	+	1.37809i
$334$	6.22876			0.340823
$335$		0			0
$336$	−15.8861	+	13.3300i	−0.866657	+	0.727212i
$337$	3.97411	+	22.5383i	0.216484	+	1.22774i	0.878313	+	0.478086i	$0.158669\pi$
$337$	3.97411	+	22.5383i	0.216484	+	1.22774i	−0.661829	+	0.749655i	$0.730220\pi$
$338$	−15.8986	−	5.78660i	−0.864768	−	0.314750i
$339$	−34.8820			−1.89453
$340$		0			0
$341$	10.0347	−	17.3807i	0.543411	−	0.941216i
$342$	4.88508	−	27.7047i	0.264155	−	1.49810i
$343$	−9.31231	−	16.1294i	−0.502817	−	0.870905i
$344$	4.22356	−	7.31542i	0.227719	−	0.394421i
$345$		0			0
$346$	0.845930	+	4.79751i	0.0454775	+	0.257916i
$347$	15.1470	+	26.2354i	0.813134	+	1.40839i	0.910660	+	0.413156i	$0.135574\pi$
$347$	15.1470	+	26.2354i	0.813134	+	1.40839i	−0.0975267	+	0.995233i	$0.531093\pi$
$348$	−13.9670	+	5.08358i	−0.748710	+	0.272508i
$349$	18.9605	−	6.90106i	1.01493	−	0.369405i	0.219607	−	0.975588i	$-0.429522\pi$
$349$	18.9605	−	6.90106i	1.01493	−	0.369405i	0.795325	+	0.606183i	$0.207300\pi$
$350$		0			0
$351$	−34.7528	+	29.1611i	−1.85497	+	1.55650i
$352$	9.26123	−	7.77109i	0.493625	−	0.414201i
$353$	1.41651	−	8.03343i	0.0753933	−	0.427576i	−0.923626	−	0.383295i	$-0.874789\pi$
$353$	1.41651	−	8.03343i	0.0753933	−	0.427576i	0.999019	−	0.0442811i	$-0.0140997\pi$
$354$	−11.9511	+	4.34984i	−0.635194	+	0.231192i
$355$		0			0
$356$	−0.977096	−	1.69238i	−0.0517860	−	0.0896960i
$357$	5.27169	+	29.8973i	0.279008	+	1.58233i
$358$	8.20846	+	6.88771i	0.433830	+	0.364027i
$359$	1.06949	−	1.85241i	0.0564454	−	0.0977663i	−0.836422	−	0.548086i	$-0.815357\pi$
$359$	1.06949	−	1.85241i	0.0564454	−	0.0977663i	0.892867	+	0.450320i	$0.148690\pi$
$360$		0			0
$361$	−0.622996	+	3.53319i	−0.0327893	+	0.185957i
$362$	8.83132	−	15.2963i	0.464164	−	0.803956i
$363$	16.4416	+	5.98424i	0.862958	+	0.314091i
$364$	7.33205			0.384304
$365$		0			0
$366$	0.338484	+	1.91964i	0.0176928	+	0.100341i
$367$	−19.3521	+	16.2383i	−1.01017	+	0.847634i	−0.988361	−	0.152128i	$-0.951387\pi$
$367$	−19.3521	+	16.2383i	−1.01017	+	0.847634i	−0.0218099	+	0.999762i	$0.506943\pi$
$368$	17.7185	+	14.8676i	0.923639	+	0.775025i
$369$	−2.34331			−0.121988
$370$		0			0
$371$	−5.07918			−0.263698
$372$	−6.00166	−	5.03599i	−0.311172	−	0.261104i
$373$	−11.6858	+	9.80558i	−0.605070	+	0.507714i	−0.893071	−	0.449916i	$-0.851454\pi$
$373$	−11.6858	+	9.80558i	−0.605070	+	0.507714i	0.288001	+	0.957630i	$0.407009\pi$
$374$	3.33206	+	18.8971i	0.172297	+	0.977143i
$375$		0			0
$376$	6.50419			0.335428
$377$	−45.2684	−	16.4764i	−2.33144	−	0.848575i
$378$	−13.8957	+	24.0681i	−0.714719	+	1.23793i
$379$	0.825541	−	4.68187i	0.0424052	−	0.240492i	−0.956237	−	0.292595i	$-0.905481\pi$
$379$	0.825541	−	4.68187i	0.0424052	−	0.240492i	0.998642	+	0.0521031i	$0.0165924\pi$
$380$		0			0
$381$	−31.5649	+	54.6721i	−1.61712	+	2.80094i
$382$	−12.3088	−	10.3283i	−0.629775	−	0.528444i
$383$	−1.55773	−	8.83431i	−0.0795962	−	0.451412i	−0.998392	−	0.0566801i	$-0.981948\pi$
$383$	−1.55773	−	8.83431i	−0.0795962	−	0.451412i	0.918796	−	0.394732i	$-0.129163\pi$
$384$	7.17700	+	12.4309i	0.366250	+	0.634363i
$385$		0			0
$386$	−8.12221	+	2.95624i	−0.413410	+	0.150469i
$387$	2.83155	−	16.0585i	0.143936	−	0.816301i
$388$	3.49846	−	2.93556i	0.177608	−	0.149030i
$389$	−19.2415	+	16.1456i	−0.975584	+	0.818612i	−0.983417	−	0.181357i	$-0.941951\pi$
$389$	−19.2415	+	16.1456i	−0.975584	+	0.818612i	0.00783338	+	0.999969i	$0.497507\pi$
$390$		0			0
$391$	31.8182	−	11.5809i	1.60911	−	0.585669i
$392$	−0.230781	+	0.0839976i	−0.0116562	+	0.00424252i
$393$	−28.7197	−	49.7439i	−1.44872	−	2.50925i
$394$	−5.47894	−	31.0726i	−0.276025	−	1.56542i
$395$		0			0
$396$	6.52451	−	11.3008i	0.327869	−	0.567886i
$397$	0.366345	+	0.634528i	0.0183863	+	0.0318461i	0.875072	−	0.483992i	$-0.160814\pi$
$397$	0.366345	+	0.634528i	0.0183863	+	0.0318461i	−0.856686	+	0.515839i	$0.827480\pi$
$398$	2.10493	−	11.9376i	0.105510	−	0.598379i
$399$	−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	$0.482847\pi$
$402$	13.4260	+	4.88666i	0.669628	+	0.243725i
$403$	−4.40940	−	25.0070i	−0.219648	−	1.24569i
$404$	−2.29139	+	1.92271i	−0.114001	+	0.0956582i
$405$		0			0
$406$	−29.5110			−1.46461
$407$	−10.8451	−	22.4967i	−0.537574	−	1.11512i
$408$	35.4128			1.75319
$409$	22.5739	+	18.9418i	1.11621	+	0.936610i	0.998407	−	0.0564271i	$-0.0179709\pi$
$409$	22.5739	+	18.9418i	1.11621	+	0.936610i	0.117802	+	0.993037i	$0.462415\pi$
$410$		0			0
$411$	−0.396744	−	2.25005i	−0.0195699	−	0.110987i
$412$	−0.254758	−	0.0927245i	−0.0125510	−	0.00456821i
$413$	9.25799			0.455556
$414$	59.0177	+	21.4807i	2.90056	+	1.05572i
$415$		0			0
$416$	2.65619	−	15.0640i	0.130230	−	0.738573i
$417$	17.5788	+	30.4474i	0.860838	+	1.49101i
$418$	−9.74958	+	16.8868i	−0.476868	+	0.825959i
$419$	21.1305	+	17.7306i	1.03229	+	0.866198i	0.991122	−	0.132954i	$-0.0424463\pi$
$419$	21.1305	+	17.7306i	1.03229	+	0.866198i	0.0411722	+	0.999152i	$0.486891\pi$
$420$		0			0
$421$	−9.22474	−	15.9777i	−0.449587	−	0.778707i	0.548772	−	0.835972i	$-0.315095\pi$
$421$	−9.22474	−	15.9777i	−0.449587	−	0.778707i	−0.998359	+	0.0572651i	$0.981762\pi$
$422$	6.47183	−	2.35555i	0.315044	−	0.114667i
$423$	11.7984	−	4.29428i	0.573660	−	0.208795i
$424$	−1.02883	+	5.83479i	−0.0499645	+	0.283363i
$425$		0			0
$426$	−15.5347	+	13.0351i	−0.752657	+	0.631554i
$427$	0.246395	−	1.39738i	0.0119239	−	0.0676238i
$428$	4.01228	−	1.46035i	0.193941	−	0.0705887i
$429$	59.8704	−	21.7911i	2.89057	−	1.05208i
$430$		0			0
$431$	−3.00270	−	17.0292i	−0.144635	−	0.820266i	−0.967660	−	0.252260i	$-0.918826\pi$
$431$	−3.00270	−	17.0292i	−0.144635	−	0.820266i	0.823025	−	0.568006i	$-0.192285\pi$
$432$	17.6550	+	14.8143i	0.849426	+	0.712753i
$433$	9.37889	−	16.2447i	0.450721	−	0.780671i	−0.547710	−	0.836668i	$-0.684500\pi$
$433$	9.37889	−	16.2447i	0.450721	−	0.780671i	0.998431	+	0.0559969i	$0.0178337\pi$
$434$	−7.77776	−	13.4715i	−0.373344	−	0.646651i
$435$		0			0
$436$	0.968357	−	1.67724i	0.0463759	−	0.0803254i
$437$	32.3332	+	11.7683i	1.54671	+	0.562955i
$438$	42.2192			2.01731
$439$	−11.2582	−	4.09764i	−0.537323	−	0.195570i	0.0590820	−	0.998253i	$-0.481183\pi$
$439$	−11.2582	−	4.09764i	−0.537323	−	0.195570i	−0.596405	+	0.802683i	$0.703405\pi$
$440$		0			0
$441$	−0.363174	+	0.304739i	−0.0172940	+	0.0145114i
$442$	18.5982	+	15.6057i	0.884625	+	0.742289i
$443$	32.0677			1.52358			0.761792	−	0.647822i	$-0.224320\pi$
$443$	32.0677			1.52358			0.761792	+	0.647822i	$0.224320\pi$
$444$	−9.38388	+	2.64435i	−0.445339	+	0.125495i
$445$		0			0
$446$	−17.1577	−	14.3970i	−0.812440	−	0.681718i
$447$	8.03539	−	6.74249i	0.380061	−	0.318909i
$448$	−4.03816	−	22.9016i	−0.190785	−	1.08200i
$449$	−2.57650	−	0.937768i	−0.121592	−	0.0442560i	0.280507	−	0.959852i	$-0.409497\pi$
$449$	−2.57650	−	0.937768i	−0.121592	−	0.0442560i	−0.402100	+	0.915596i	$0.631720\pi$
$450$		0			0
$451$	1.52627	+	0.555515i	0.0718690	+	0.0261582i
$452$	3.13265	−	5.42590i	0.147347	−	0.255213i
$453$	−10.8304	+	61.4221i	−0.508855	+	2.88586i
$454$	−8.47255	−	14.6749i	−0.397637	−	0.688727i
$455$		0			0
$456$	27.5669	+	23.1314i	1.29094	+	1.08323i
$457$	−4.94224	−	28.0288i	−0.231188	−	1.31113i	−0.850494	−	0.525984i	$-0.823697\pi$
$457$	−4.94224	−	28.0288i	−0.231188	−	1.31113i	0.619306	−	0.785150i	$-0.287414\pi$
$458$	0.00150588	+	0.00260825i	7.03650e−5	+	0.000121876i
$459$	31.7042	−	11.5394i	1.47982	−	0.538612i
$460$		0			0
$461$	−2.97465	+	16.8701i	−0.138543	+	0.785717i	0.833784	+	0.552092i	$0.186170\pi$
$461$	−2.97465	+	16.8701i	−0.138543	+	0.785717i	−0.972327	+	0.233626i	$0.924941\pi$
$462$	29.8989	−	25.0882i	1.39102	−	1.16721i
$463$	−3.56668	+	2.99280i	−0.165758	+	0.139087i	−0.721893	−	0.692004i	$-0.756728\pi$
$463$	−3.56668	+	2.99280i	−0.165758	+	0.139087i	0.556136	+	0.831091i	$0.312283\pi$
$464$	−4.24969	+	24.1012i	−0.197287	+	1.11887i
$465$		0			0
$466$	0.0509024	−	0.0185270i	0.00235801	−	0.000858245i
$467$	4.55808	+	7.89482i	0.210923	+	0.365329i	0.952004	−	0.306087i	$-0.0990199\pi$
$467$	4.55808	+	7.89482i	0.210923	+	0.365329i	−0.741081	+	0.671416i	$0.765687\pi$
$468$	−2.86696	−	16.2593i	−0.132525	−	0.751588i
$469$	−7.96727	−	6.68533i	−0.367894	−	0.308700i
$470$		0			0
$471$	−0.801411	−	1.38808i	−0.0369271	−	0.0639595i
$472$	1.87529	−	10.6353i	0.0863170	−	0.489528i
$473$	−5.65118	+	9.78813i	−0.259841	+	0.450058i
$474$	−32.4521	−	11.8116i	−1.49057	−	0.542524i
$475$		0			0
$476$	−5.12395	−	1.86497i	−0.234856	−	0.0854806i
$477$	1.98605	+	11.2634i	0.0909350	+	0.515718i
$478$	23.4832	−	19.7048i	1.07410	−	0.901275i
$479$	10.3231	+	8.66210i	0.471674	+	0.395781i	0.847405	−	0.530947i	$-0.178164\pi$
$479$	10.3231	+	8.66210i	0.471674	+	0.395781i	−0.375731	+	0.926729i	$0.622608\pi$
$480$		0			0
$481$	−28.8076	−	12.9843i	−1.31351	−	0.592034i
$482$	14.0973			0.642114
$483$	−52.7597	−	44.2706i	−2.40065	−	2.01438i
$484$	−2.40741	+	2.02006i	−0.109428	+	0.0918210i
$485$		0			0
$486$	−1.53890	−	0.560114i	−0.0698059	−	0.0254073i
$487$	2.28645			0.103609			0.0518044	−	0.998657i	$-0.483503\pi$
$487$	2.28645			0.103609			0.0518044	+	0.998657i	$0.483503\pi$
$488$	−1.55535	−	0.566101i	−0.0704074	−	0.0256262i
$489$	−34.0635	+	58.9998i	−1.54041	+	2.66806i
$490$		0			0
$491$	5.53323	+	9.58383i	0.249711	+	0.432512i	0.963446	−	0.267904i	$-0.0863310\pi$
$491$	5.53323	+	9.58383i	0.249711	+	0.432512i	−0.713734	+	0.700416i	$0.752998\pi$
$492$	0.317027	−	0.549107i	0.0142927	−	0.0247556i
$493$	27.4446	+	23.0288i	1.23604	+	1.03716i
$494$	4.28410	+	24.2964i	0.192751	+	1.09314i
$495$		0			0
$496$	−12.1219	+	4.41203i	−0.544292	+	0.198106i
$497$	13.8717	−	5.04887i	0.622229	−	0.226473i
$498$	9.75117	−	55.3017i	0.436961	−	2.47813i
$499$	18.1310	−	15.2137i	0.811655	−	0.681059i	−0.139347	−	0.990244i	$-0.544500\pi$
$499$	18.1310	−	15.2137i	0.811655	−	0.681059i	0.951002	+	0.309184i	$0.100056\pi$
$500$		0			0
$501$	−2.67085	+	15.1472i	−0.119325	+	0.676725i
$502$	3.43157	−	1.24899i	0.153158	−	0.0557451i
$503$	−26.7985	+	9.75384i	−1.19488	+	0.434902i	−0.861436	−	0.507866i	$-0.830434\pi$
$503$	−26.7985	+	9.75384i	−1.19488	+	0.434902i	−0.333448	+	0.942768i	$0.608212\pi$
$504$	−23.9074	−	41.4088i	−1.06492	−	1.84450i
$505$		0			0
$506$	−33.3476	−	27.9820i	−1.48248	−	1.24395i
$507$	20.8891	−	36.1810i	0.927718	−	1.60686i
$508$	−5.66950	−	9.81986i	−0.251543	−	0.435686i
$509$	3.99880	−	22.6783i	0.177244	−	1.00520i	−0.758279	−	0.651930i	$-0.773959\pi$
$509$	3.99880	−	22.6783i	0.177244	−	1.00520i	0.935522	−	0.353268i	$-0.114929\pi$
$510$		0			0
$511$	−28.8796	−	10.5113i	−1.27756	−	0.464993i
$512$	−23.9667			−1.05919
$513$	32.2173	+	11.7261i	1.42243	+	0.517722i
$514$	−4.13382	−	23.4440i	−0.182335	−	1.03407i
$515$		0			0
$516$	3.37991	+	2.83608i	0.148792	+	0.124851i
$517$	−8.70269			−0.382744
$518$	−19.3037	−	1.43868i	−0.848154	−	0.0632119i
$519$	−12.0294			−0.528030
$520$		0			0
$521$	19.8046	−	16.6180i	0.867654	−	0.728048i	−0.0959487	−	0.995386i	$-0.530588\pi$
$521$	19.8046	−	16.6180i	0.867654	−	0.728048i	0.963603	+	0.267338i	$0.0861440\pi$
$522$	11.5393	+	65.4428i	0.505063	+	2.86435i
$523$	29.2385	+	10.6419i	1.27851	+	0.465339i	0.889939	−	0.456080i	$-0.150747\pi$
$523$	29.2385	+	10.6419i	1.27851	+	0.465339i	0.388570	+	0.921419i	$0.372969\pi$
$524$	10.3169			0.450696
$525$		0			0
$526$	−16.0319	+	27.7681i	−0.699025	+	1.21075i
$527$	−3.27924	+	18.5975i	−0.142846	+	0.810120i
$528$	−16.1836	−	28.0307i	−0.704299	−	1.21988i
$529$	−26.9085	+	46.6069i	−1.16993	+	2.02639i
$530$		0			0
$531$	−3.62004	−	20.5303i	−0.157096	−	0.890937i
$532$	−2.77053	−	4.79870i	−0.120118	−	0.208050i
$533$	1.93110	−	0.702861i	0.0836450	−	0.0304443i
$534$	−12.3681	+	4.50162i	−0.535220	+	0.194804i
$535$		0			0
$536$	−9.29373	+	7.79836i	−0.401428	+	0.336838i
$537$	−20.2693	+	17.0080i	−0.874686	+	0.733949i
$538$	2.67474	−	15.1692i	0.115316	−	0.653991i
$539$	0.308789	−	0.112390i	0.0133005	−	0.00484097i
$540$		0			0
$541$	10.2174	+	17.6971i	0.439282	+	0.760858i	0.997634	−	0.0687454i	$-0.0218996\pi$
$541$	10.2174	+	17.6971i	0.439282	+	0.760858i	−0.558352	+	0.829604i	$0.688566\pi$
$542$	−4.12868	−	23.4149i	−0.177342	−	1.00576i
$543$	33.4109	+	28.0350i	1.43380	+	1.20310i
$544$	−5.68791	+	9.85174i	−0.243867	+	0.422390i
$545$		0			0
$546$	8.57523	−	48.6325i	0.366986	−	2.08128i
$547$	1.06355	−	1.84213i	0.0454743	−	0.0787637i	−0.842392	−	0.538865i	$-0.818853\pi$
$547$	1.06355	−	1.84213i	0.0454743	−	0.0787637i	0.887867	+	0.460101i	$0.152187\pi$
$548$	0.385625	+	0.140356i	0.0164731	+	0.00599572i
$549$	−3.19513			−0.136365
$550$		0			0
$551$	6.32189	+	35.8532i	0.269322	+	1.52740i
$552$	−61.5435	+	51.6412i	−2.61947	+	2.19799i
$553$	19.2578	+	16.1592i	0.818923	+	0.687158i
$554$	26.7183			1.13515
$555$		0			0
$556$	−6.31479			−0.267807
$557$	−20.4257	−	17.1392i	−0.865465	−	0.726211i	0.0976735	−	0.995219i	$-0.468860\pi$
$557$	−20.4257	−	17.1392i	−0.865465	−	0.726211i	−0.963138	+	0.269007i	$0.913304\pi$
$558$	−26.8327	+	22.5153i	−1.13592	+	0.953149i
$559$	2.48321	+	14.0830i	0.105028	+	0.595646i
$560$		0			0
$561$	−47.3828			−2.00050
$562$	11.0037	+	4.00500i	0.464161	+	0.168941i
$563$	−0.574887	+	0.995734i	−0.0242286	+	0.0419652i	−0.877885	−	0.478871i	$-0.841046\pi$
$563$	−0.574887	+	0.995734i	−0.0242286	+	0.0419652i	0.853657	+	0.520836i	$0.174380\pi$
$564$	−0.589937	+	3.34570i	−0.0248408	+	0.140879i
$565$		0			0
$566$	9.85159	−	17.0635i	0.414093	−	0.717231i
$567$	−16.7606	−	14.0638i	−0.703878	−	0.590623i
$568$	−2.99015	−	16.9580i	−0.125464	−	0.711542i
$569$	17.6008	+	30.4855i	0.737864	+	1.27802i	0.953455	+	0.301534i	$0.0974987\pi$
$569$	17.6008	+	30.4855i	0.737864	+	1.27802i	−0.215591	+	0.976484i	$0.569168\pi$
$570$		0			0
$571$	28.9070	−	10.5213i	1.20972	−	0.440302i	0.343113	−	0.939294i	$-0.388519\pi$
$571$	28.9070	−	10.5213i	1.20972	−	0.440302i	0.866606	+	0.498992i	$0.166296\pi$
$572$	−1.98718	+	11.2698i	−0.0830880	+	0.471216i
$573$	30.3945	−	25.5040i	1.26975	−	1.06545i
$574$	0.964377	−	0.809209i	0.0402523	−	0.0337757i
$575$		0			0
$576$	−49.2069	+	17.9098i	−2.05029	+	0.746243i
$577$	−23.7359	+	8.63917i	−0.988140	+	0.359654i	−0.785000	−	0.619496i	$-0.787337\pi$
$577$	−23.7359	+	8.63917i	−0.988140	+	0.359654i	−0.203140	+	0.979150i	$0.565115\pi$
$578$	1.25496	+	2.17366i	0.0521995	+	0.0904122i
$579$	−3.70627	−	21.0193i	−0.154027	−	0.873532i
$580$		0			0
$581$	−20.4386	+	35.4007i	−0.847937	+	1.46867i
$582$	−15.3795	−	26.6381i	−0.637502	−	1.10419i
$583$	1.37659	−	7.80703i	0.0570126	−	0.323334i
$584$	−17.9248	+	31.0467i	−0.741735	+	1.28472i
$585$		0			0
$586$	34.6955			1.43326
$587$	−13.1804	−	4.79726i	−0.544012	−	0.198004i	0.0553719	−	0.998466i	$-0.482366\pi$
$587$	−13.1804	−	4.79726i	−0.544012	−	0.198004i	−0.599384	+	0.800462i	$0.704588\pi$
$588$	−0.0222755	−	0.126331i	−0.000918626	−	0.00520979i
$589$	−14.7005	+	12.3351i	−0.605722	+	0.508261i
$590$		0			0
$591$	77.9121			3.20487
$592$	−3.95473	+	15.5578i	−0.162539	+	0.639421i
$593$	20.0133			0.821849			0.410925	−	0.911669i	$-0.365206\pi$
$593$	20.0133			0.821849			0.410925	+	0.911669i	$0.365206\pi$
$594$	−33.2281	−	27.8817i	−1.36337	−	1.14400i
$595$		0			0
$596$	0.327162	+	1.85543i	0.0134011	+	0.0760013i
$597$	28.1274	+	10.2376i	1.15118	+	0.418995i
$598$	−55.0788			−2.25234
$599$	26.9488	+	9.80858i	1.10110	+	0.400768i	0.827722	−	0.561139i	$-0.189637\pi$
$599$	26.9488	+	9.80858i	1.10110	+	0.400768i	0.273378	+	0.961907i	$0.411859\pi$
$600$		0			0
$601$	−3.52558	+	19.9945i	−0.143811	+	0.815594i	0.824503	+	0.565858i	$0.191455\pi$
$601$	−3.52558	+	19.9945i	−0.143811	+	0.815594i	−0.968314	+	0.249736i	$0.919656\pi$
$602$	4.38014	+	7.58662i	0.178521	+	0.309207i
$603$	−11.7099	+	20.2821i	−0.476862	+	0.825950i
$604$	−8.58156	−	7.20079i	−0.349179	−	0.292996i
$605$		0			0
$606$	10.0731	+	17.4472i	0.409194	+	0.708744i
$607$	−3.46235	+	1.26019i	−0.140533	+	0.0511497i	−0.411329	−	0.911487i	$-0.634935\pi$
$607$	−3.46235	+	1.26019i	−0.140533	+	0.0511497i	0.270796	+	0.962637i	$0.412713\pi$
$608$	−10.8628	+	3.95373i	−0.440545	+	0.160345i
$609$	12.6541	−	71.7652i	0.512772	−	2.90807i
$610$		0			0
$611$	−8.43493	+	7.07774i	−0.341241	+	0.286335i
$612$	−2.13214	+	12.0920i	−0.0861867	+	0.488789i
$613$	−2.51967	+	0.917084i	−0.101768	+	0.0370407i	−0.392403	−	0.919794i	$-0.628356\pi$
$613$	−2.51967	+	0.917084i	−0.101768	+	0.0370407i	0.290634	+	0.956834i	$0.406134\pi$
$614$	34.8109	−	12.6701i	1.40485	−	0.511325i
$615$		0			0
$616$	5.75502	+	32.6384i	0.231877	+	1.31504i
$617$	−7.46322	−	6.26239i	−0.300458	−	0.252114i	0.480077	−	0.877226i	$-0.340609\pi$
$617$	−7.46322	−	6.26239i	−0.300458	−	0.252114i	−0.780535	+	0.625112i	$0.785053\pi$
$618$	−0.912983	+	1.58133i	−0.0367256	+	0.0636105i
$619$	−7.81784	−	13.5409i	−0.314226	−	0.544255i	0.665047	−	0.746802i	$-0.268412\pi$
$619$	−7.81784	−	13.5409i	−0.314226	−	0.544255i	−0.979273	+	0.202547i	$0.935078\pi$
$620$		0			0
$621$	−38.2709	+	66.2871i	−1.53576	+	2.66001i
$622$	−2.18492	−	0.795245i	−0.0876073	−	0.0318864i
$623$	9.58103			0.383856
$624$	−38.4825	−	14.0065i	−1.54053	−	0.560708i
$625$		0			0
$626$	18.2593	−	15.3214i	0.729789	−	0.612365i
$627$	−36.8848	−	30.9501i	−1.47304	−	1.23603i
$628$	0.287889			0.0114880
$629$	16.8293	+	16.4014i	0.671029	+	0.653968i
$630$		0			0
$631$	−17.7946	−	14.9314i	−0.708391	−	0.594411i	0.215756	−	0.976447i	$-0.430778\pi$
$631$	−17.7946	−	14.9314i	−0.708391	−	0.594411i	−0.924147	+	0.382037i	$0.875223\pi$
$632$	22.4639	−	18.8495i	0.893568	−	0.749792i
$633$	2.95318	+	16.7483i	0.117378	+	0.665685i
$634$	−14.9988	−	5.45910i	−0.595676	−	0.216809i
$635$		0			0
$636$	−2.90805	−	1.05844i	−0.115312	−	0.0419701i
$637$	0.207883	−	0.360064i	0.00823663	−	0.0142663i
$638$	7.99826	−	45.3604i	0.316654	−	1.79583i
$639$	−16.6203	−	28.7872i	−0.657489	−	1.13880i
$640$		0			0
$641$	19.1875	+	16.1002i	0.757862	+	0.635922i	0.937569	−	0.347799i	$-0.113071\pi$
$641$	19.1875	+	16.1002i	0.757862	+	0.635922i	−0.179708	+	0.983720i	$0.557515\pi$
$642$	−4.99373	−	28.3209i	−0.197087	−	1.11774i
$643$	18.2753	+	31.6537i	0.720707	+	1.24830i	0.960717	+	0.277531i	$0.0895160\pi$
$643$	18.2753	+	31.6537i	0.720707	+	1.24830i	−0.240010	+	0.970770i	$0.577151\pi$
$644$	11.6245	−	4.23096i	0.458069	−	0.166723i
$645$		0			0
$646$	3.18606	−	18.0690i	0.125354	−	0.710917i
$647$	2.85909	−	2.39906i	0.112403	−	0.0943169i	−0.584854	−	0.811138i	$-0.698848\pi$
$647$	2.85909	−	2.39906i	0.112403	−	0.0943169i	0.697257	+	0.716822i	$0.254404\pi$
$648$	−19.5510	+	16.4052i	−0.768036	+	0.644459i
$649$	−2.50916	+	14.2301i	−0.0984930	+	0.558582i
$650$		0			0
$651$	36.0951	−	13.1375i	1.41468	−	0.514901i
$652$	−6.11828	−	10.5972i	−0.239610	−	0.415017i
$653$	1.84932	+	10.4880i	0.0723693	+	0.410427i	0.999374	+	0.0353772i	$0.0112633\pi$
$653$	1.84932	+	10.4880i	0.0723693	+	0.410427i	−0.927005	+	0.375050i	$0.877626\pi$
$654$	−9.99239	−	8.38461i	−0.390733	−	0.327864i
$655$		0			0
$656$	−0.521994	−	0.904119i	−0.0203804	−	0.0352999i
$657$	−12.0171	+	68.1526i	−0.468834	+	2.65889i
$658$	−3.37266	+	5.84162i	−0.131480	+	0.227730i
$659$	−15.5823	−	5.67151i	−0.607002	−	0.220931i	0.0201889	−	0.999796i	$-0.493573\pi$
$659$	−15.5823	−	5.67151i	−0.607002	−	0.220931i	−0.627191	+	0.778865i	$0.715795\pi$
$660$		0			0
$661$	17.9941	+	6.54931i	0.699888	+	0.254739i	0.667363	−	0.744732i	$-0.267423\pi$
$661$	17.9941	+	6.54931i	0.699888	+	0.254739i	0.0325252	+	0.999471i	$0.489645\pi$
$662$	3.56726	+	20.2309i	0.138645	+	0.786297i
$663$	−45.9249	+	38.5356i	−1.78358	+	1.49660i
$664$	36.5272	+	30.6499i	1.41753	+	1.18945i
$665$		0			0
$666$	4.35769	+	43.3698i	0.168857	+	1.68054i
$667$	−81.2777			−3.14709
$668$	−2.11628	−	1.77577i	−0.0818813	−	0.0687066i
$669$	42.3679	−	35.5509i	1.63804	−	1.37448i
$670$		0			0
$671$	2.08108	+	0.757451i	0.0803392	+	0.0292411i
$672$	23.1388			0.892600
$673$	−25.4408	−	9.25971i	−0.980673	−	0.356936i	−0.198571	−	0.980087i	$-0.563630\pi$
$673$	−25.4408	−	9.25971i	−0.980673	−	0.356936i	−0.782102	+	0.623151i	$0.785852\pi$
$674$	−13.8430	+	23.9767i	−0.533212	+	0.923550i
$675$		0			0
$676$	3.75197	+	6.49861i	0.144307	+	0.249946i
$677$	9.39978	−	16.2809i	0.361263	−	0.625726i	−0.626906	−	0.779095i	$-0.715679\pi$
$677$	9.39978	−	16.2809i	0.361263	−	0.625726i	0.988169	+	0.153369i	$0.0490124\pi$
$678$	−32.3255	−	27.1243i	−1.24145	−	1.04170i
$679$	3.88811	+	22.0506i	0.149212	+	0.846223i
$680$		0			0
$681$	39.3195	−	14.3111i	1.50673	−	0.548404i
$682$	22.8145	−	8.30380i	0.873612	−	0.317969i
$683$	−4.38318	+	24.8583i	−0.167718	+	0.951175i	0.778500	+	0.627645i	$0.215981\pi$
$683$	−4.38318	+	24.8583i	−0.167718	+	0.951175i	−0.946218	+	0.323531i	$0.895130\pi$
$684$	−9.55813	+	8.02022i	−0.365464	+	0.306661i
$685$		0			0
$686$	3.91243	−	22.1885i	0.149377	−	0.847162i
$687$	−0.00698849	+	0.00254360i	−0.000266627	+	9.70444e-5i
$688$	6.82662	−	2.48469i	0.260262	−	0.0947278i
$689$	−5.01508	−	8.68638i	−0.191060	−	0.330925i
$690$		0			0
$691$	26.7478	+	22.4441i	1.01753	+	0.853812i	0.989316	−	0.145789i	$-0.0465722\pi$
$691$	26.7478	+	22.4441i	1.01753	+	0.853812i	0.0282184	+	0.999602i	$0.491017\pi$
$692$	1.08032	−	1.87117i	0.0410676	−	0.0711311i
$693$	31.9884	+	55.4056i	1.21514	+	2.10468i
$694$	−6.36380	+	36.0909i	−0.241566	+	1.36999i
$695$		0			0
$696$	−79.8783	−	29.0733i	−3.02778	−	1.10202i
$697$	−1.52831			−0.0578889
$698$	22.9371	+	8.34844i	0.868184	+	0.315993i
$699$	0.0232274	+	0.131729i	0.000878541	+	0.00498246i
$700$		0			0
$701$	−17.7678	−	14.9090i	−0.671081	−	0.563104i	0.242304	−	0.970200i	$-0.422097\pi$
$701$	−17.7678	−	14.9090i	−0.671081	−	0.563104i	−0.913385	+	0.407096i	$0.866541\pi$
$702$	−54.8815			−2.07137
$703$	2.38739	+	23.7604i	0.0900421	+	0.896140i
$704$	36.2956			1.36794
$705$		0			0
$706$	7.55950	−	6.34317i	0.284506	−	0.238729i
$707$	−2.54660	−	14.4425i	−0.0957747	−	0.543165i
$708$	5.30060	+	1.92926i	0.199209	+	0.0725061i
$709$	−32.9756			−1.23843			−0.619213	−	0.785223i	$-0.712548\pi$
$709$	−32.9756			−1.23843			−0.619213	+	0.785223i	$0.712548\pi$
$710$		0			0
$711$	28.3040	−	49.0240i	1.06148	−	1.83854i
$712$	1.94072	−	11.0064i	0.0727315	−	0.412481i
$713$	−21.4211	−	37.1024i	−0.802226	−	1.38950i
$714$	−18.3628	+	31.8053i	−0.687211	+	1.19028i
$715$		0			0
$716$	−0.825269	−	4.68033i	−0.0308417	−	0.174912i
$717$	37.8488	+	65.5560i	1.41349	+	2.44823i
$718$	2.43154	−	0.885007i	0.0907442	−	0.0330282i
$719$	0.0608811	−	0.0221589i	0.00227048	−	0.000826388i	−0.340885	−	0.940105i	$-0.610727\pi$
$719$	0.0608811	−	0.0221589i	0.00227048	−	0.000826388i	0.343155	+	0.939279i	$0.388504\pi$
$720$		0			0
$721$	1.01822	−	0.854388i	0.0379205	−	0.0318191i
$722$	−3.32475	+	2.78979i	−0.123734	+	0.103825i
$723$	−6.04483	+	34.2819i	−0.224810	+	1.27496i
$724$	−7.36138	+	2.67932i	−0.273583	+	0.0995762i
$725$		0			0
$726$	10.5832	+	18.3306i	0.392779	+	0.680314i
$727$	−3.48001	−	19.7361i	−0.129067	−	0.731973i	−0.978809	−	0.204775i	$-0.934354\pi$
$727$	−3.48001	−	19.7361i	−0.129067	−	0.731973i	0.849743	−	0.527198i	$-0.176757\pi$
$728$	32.1222	+	26.9537i	1.19053	+	0.998970i
$729$	14.4979	−	25.1111i	0.536960	−	0.930042i
$730$		0			0
$731$	1.84674	−	10.4734i	0.0683043	−	0.387373i
$732$	0.432270	−	0.748713i	0.0159772	−	0.0276732i
$733$	−33.2536	−	12.1033i	−1.22825	−	0.447046i	−0.355252	−	0.934771i	$-0.615605\pi$
$733$	−33.2536	−	12.1033i	−1.22825	−	0.447046i	−0.872998	+	0.487724i	$0.837827\pi$
$734$	−30.5607			−1.12802
$735$		0			0
$736$	−4.48147	−	25.4157i	−0.165189	−	0.936835i
$737$	12.4351	−	10.4343i	0.458054	−	0.384353i
$738$	−2.17157	−	1.82216i	−0.0799364	−	0.0670746i
$739$	−16.6665			−0.613089			−0.306544	−	0.951856i	$-0.599173\pi$
$739$	−16.6665			−0.613089			−0.306544	+	0.951856i	$0.599173\pi$
$740$		0			0
$741$	−60.9211			−2.23799
$742$	−4.70692	−	3.94958i	−0.172797	−	0.144994i
$743$	−14.7880	+	12.4086i	−0.542520	+	0.455228i	−0.872399	−	0.488795i	$-0.837437\pi$
$743$	−14.7880	+	12.4086i	−0.542520	+	0.455228i	0.329879	+	0.944023i	$0.392992\pi$
$744$	−7.78060	−	44.1260i	−0.285251	−	1.61774i
$745$		0			0
$746$	−18.4542			−0.675657
$747$	86.4955	+	31.4818i	3.16470	+	1.15186i
$748$	4.25530	−	7.37040i	0.155589	−	0.269488i
$749$	−3.63513	+	20.6159i	−0.132825	+	0.753287i
$750$		0			0
$751$	23.1755	−	40.1412i	0.845686	−	1.46477i	−0.0393375	−	0.999226i	$-0.512525\pi$
$751$	23.1755	−	40.1412i	0.845686	−	1.46477i	0.885024	−	0.465546i	$-0.154142\pi$
$752$	4.28508	+	3.59561i	0.156261	+	0.131118i
$753$	1.56587	+	8.88048i	0.0570634	+	0.323623i
$754$	−29.1386	−	50.4696i	−1.06117	−	1.83799i
$755$		0			0
$756$	11.5828	−	4.21581i	0.421263	−	0.153327i
$757$	2.71992	−	15.4254i	0.0988571	−	0.560646i	−0.894640	−	0.446788i	$-0.852568\pi$
$757$	2.71992	−	15.4254i	0.0988571	−	0.560646i	0.993497	−	0.113858i	$-0.0363210\pi$
$758$	4.40567	−	3.69679i	0.160021	−	0.134274i
$759$	82.3461	−	69.0965i	2.98897	−	2.50805i
$760$		0			0
$761$	0.726263	−	0.264338i	0.0263270	−	0.00958224i	−0.328823	−	0.944392i	$-0.606652\pi$
$761$	0.726263	−	0.264338i	0.0263270	−	0.00958224i	0.355150	+	0.934809i	$0.384430\pi$
$762$	−71.7646	+	26.1202i	−2.59976	+	0.946234i
$763$	4.74767	+	8.22320i	0.171877	+	0.297700i
$764$	1.23752	+	7.01831i	0.0447718	+	0.253913i
$765$		0			0
$766$	5.42601	−	9.39813i	0.196050	−	0.339568i
$767$	9.14116	+	15.8330i	0.330068	+	0.571695i
$768$	6.15596	−	34.9122i	0.222134	−	1.25978i
$769$	−7.13677	+	12.3612i	−0.257358	+	0.445758i	−0.965533	−	0.260279i	$-0.916185\pi$
$769$	−7.13677	+	12.3612i	−0.257358	+	0.445758i	0.708175	+	0.706037i	$0.249519\pi$
$770$		0			0
$771$	58.7840			2.11705
$772$	3.60240	+	1.31117i	0.129653	+	0.0471899i
$773$	−4.68831	−	26.5887i	−0.168627	−	0.956330i	−0.945246	−	0.326359i	$-0.894178\pi$
$773$	−4.68831	−	26.5887i	−0.168627	−	0.956330i	0.776619	−	0.629970i	$-0.216933\pi$
$774$	15.1112	−	12.6798i	0.543159	−	0.455765i
$775$		0			0
$776$	26.1185			0.937600
$777$	11.7759	−	46.3259i	0.422457	−	1.66193i
$778$	−30.3861			−1.08939
$779$	−1.18971	−	0.998281i	−0.0426256	−	0.0357671i
$780$		0			0
$781$	4.00086	+	22.6900i	0.143162	+	0.811913i
$782$	38.4915	+	14.0097i	1.37645	+	0.500988i
$783$	−80.9865			−2.89422
$784$	−0.198478	−	0.0722401i	−0.00708850	−	0.00258000i
$785$		0			0
$786$	12.0662	−	68.4306i	0.430386	−	2.44084i
$787$	−24.3067	−	42.1004i	−0.866440	−	1.50072i	−0.865610	−	0.500719i	$-0.833069\pi$
$787$	−24.3067	−	42.1004i	−0.866440	−	1.50072i	−0.000829899	−	1.00000i	$-0.500264\pi$
$788$	−6.99704	+	12.1192i	−0.249259	+	0.431730i
$789$	−60.6524	−	50.8934i	−2.15928	−	1.81185i
$790$		0			0
$791$	15.3588	+	26.6022i	0.546095	+	0.945864i
$792$	70.1276	−	25.5243i	2.49187	−	0.906968i
$793$	2.63307	−	0.958359i	0.0935031	−	0.0340323i
$794$	−0.153915	+	0.872893i	−0.00546223	+	0.0309778i
$795$		0			0
$796$	−4.11849	+	3.45582i	−0.145976	+	0.122488i
$797$	−5.50622	+	31.2273i	−0.195040	+	1.10613i	0.717321	+	0.696743i	$0.245368\pi$
$797$	−5.50622	+	31.2273i	−0.195040	+	1.10613i	−0.912361	+	0.409386i	$0.865743\pi$
$798$	−35.0694	+	12.7642i	−1.24144	+	0.451849i
$799$	7.69497	−	2.80074i	0.272229	−	0.0990831i
$800$		0			0
$801$	−3.74635	−	21.2466i	−0.132371	−	0.750712i
$802$	1.99909	+	1.67744i	0.0705903	+	0.0592323i
$803$	23.9837	−	41.5410i	0.846366	−	1.46595i
$804$	−3.16846	−	5.48793i	−0.111743	−	0.193545i
$805$		0			0
$806$	15.3592	−	26.6029i	0.541005	−	0.937048i
$807$	35.7417	+	13.0089i	1.25817	+	0.457936i
$808$	−17.1069			−0.601818
$809$	−2.41252	−	0.878086i	−0.0848197	−	0.0308719i	0.299262	−	0.954171i	$-0.403260\pi$
$809$	−2.41252	−	0.878086i	−0.0848197	−	0.0308719i	−0.384082	+	0.923299i	$0.625482\pi$
$810$		0			0
$811$	4.61093	−	3.86903i	0.161911	−	0.135860i	−0.558232	−	0.829685i	$-0.688520\pi$
$811$	4.61093	−	3.86903i	0.161911	−	0.135860i	0.720144	+	0.693825i	$0.244076\pi$
$812$	10.0267	+	8.41336i	0.351867	+	0.295251i
$813$	58.7109			2.05908
$814$	7.44314	−	29.2810i	0.260882	−	1.02630i
$815$		0			0
$816$	23.3306	+	19.5767i	0.816734	+	0.685321i
$817$	8.27874	−	6.94668i	0.289636	−	0.243034i
$818$	6.19031	+	35.1070i	0.216439	+	1.22749i
$819$	76.0645	+	27.6852i	2.65791	+	0.967400i
$820$		0			0
$821$	−13.5004	−	4.91375i	−0.471167	−	0.171491i	0.0955137	−	0.995428i	$-0.469551\pi$
$821$	−13.5004	−	4.91375i	−0.471167	−	0.171491i	−0.566681	+	0.823937i	$0.691773\pi$
$822$	1.38197	−	2.39365i	0.0482018	−	0.0834880i
$823$	4.23314	−	24.0073i	0.147558	−	0.836843i	−0.817720	−	0.575617i	$-0.804762\pi$
$823$	4.23314	−	24.0073i	0.147558	−	0.836843i	0.965278	−	0.261226i	$-0.0841268\pi$
$824$	−0.775243	−	1.34276i	−0.0270069	−	0.0467773i
$825$		0			0
$826$	8.57947	+	7.19903i	0.298518	+	0.250486i
$827$	0.556935	+	3.15854i	0.0193665	+	0.109833i	0.992959	−	0.118461i	$-0.0377962\pi$
$827$	0.556935	+	3.15854i	0.0193665	+	0.109833i	−0.973592	+	0.228295i	$0.926685\pi$
$828$	−13.9278	−	24.1237i	−0.484026	−	0.838358i
$829$	5.46591	−	1.98943i	0.189839	−	0.0690957i	−0.245351	−	0.969434i	$-0.578903\pi$
$829$	5.46591	−	1.98943i	0.189839	−	0.0690957i	0.435190	+	0.900339i	$0.356681\pi$
$830$		0			0
$831$	−11.4566	+	64.9738i	−0.397426	+	2.25392i
$832$	35.1789	−	29.5186i	1.21961	−	1.02337i
$833$	−0.236863	+	0.198752i	−0.00820682	+	0.00688634i
$834$	−7.38548	+	41.8852i	−0.255738	+	1.45036i
$835$		0			0
$836$	8.12680	−	2.95791i	0.281071	−	0.102302i
$837$	−21.3443	−	36.9695i	−0.737769	−	1.27785i
$838$	5.79451	+	32.8623i	0.200168	+	1.13521i
$839$	2.04936	+	1.71961i	0.0707516	+	0.0593677i	0.677478	−	0.735543i	$-0.263073\pi$
$839$	2.04936	+	1.71961i	0.0707516	+	0.0593677i	−0.606726	+	0.794911i	$0.707517\pi$
$840$		0			0
$841$	−28.4988	−	49.3613i	−0.982716	−	1.70211i
$842$	3.87565	−	21.9799i	0.133564	−	0.757477i
$843$	−14.4577	+	25.0415i	−0.497950	+	0.862474i
$844$	−2.87041	−	1.04475i	−0.0988037	−	0.0359616i
$845$		0			0
$846$	14.2730	+	5.19493i	0.490715	+	0.178606i
$847$	−2.67554	−	15.1738i	−0.0919328	−	0.521377i
$848$	−3.90337	+	3.27531i	−0.134042	+	0.112475i
$849$	37.2708	+	31.2739i	1.27913	+	1.07332i
$850$		0			0
$851$	−53.1651	−	3.96234i	−1.82248	−	0.135827i
$852$	8.99426			0.308138
$853$	−16.9109	−	14.1899i	−0.579018	−	0.485853i	0.305607	−	0.952158i	$-0.401141\pi$
$853$	−16.9109	−	14.1899i	−0.579018	−	0.485853i	−0.884624	+	0.466304i	$0.845585\pi$
$854$	1.31494	−	1.10337i	0.0449963	−	0.0377564i
$855$		0			0
$856$	22.9465	+	8.35184i	0.784295	+	0.285460i
$857$	−13.4850			−0.460638			−0.230319	−	0.973115i	$-0.573977\pi$
$857$	−13.4850			−0.460638			−0.230319	+	0.973115i	$0.573977\pi$
$858$	72.4272	+	26.3614i	2.47263	+	0.899962i
$859$	−7.28037	+	12.6100i	−0.248403	+	0.430247i	−0.963083	−	0.269205i	$-0.913239\pi$
$859$	−7.28037	+	12.6100i	−0.248403	+	0.430247i	0.714680	+	0.699452i	$0.246572\pi$
$860$		0			0
$861$	1.55432	+	2.69216i	0.0529711	+	0.0917487i
$862$	10.4593	−	18.1160i	0.356244	−	0.617033i
$863$	24.2323	+	20.3333i	0.824877	+	0.692154i	0.954109	−	0.299461i	$-0.0968067\pi$
$863$	24.2323	+	20.3333i	0.824877	+	0.692154i	−0.129232	+	0.991614i	$0.541251\pi$
$864$	−4.46542	−	25.3246i	−0.151917	−	0.861562i
$865$		0			0
$866$	21.3234	−	7.76109i	0.724599	−	0.263733i
$867$	−5.82404	+	2.11978i	−0.197795	+	0.0719914i
$868$	−1.19804	+	6.79444i	−0.0406642	+	0.230618i
$869$	−30.0571	+	25.2209i	−1.01962	+	0.855559i
$870$		0			0
$871$	3.56648	−	20.2265i	0.120846	−	0.685350i
$872$	10.4082	−	3.78828i	0.352467	−	0.128287i
$873$	47.3784	−	17.2443i	1.60351	−	0.583632i
$874$	20.8124	+	36.0481i	0.703990	+	1.21935i
$875$		0			0
$876$	−14.3444	−	12.0364i	−0.484652	−	0.406671i
$877$	−6.11832	+	10.5972i	−0.206601	+	0.357843i	−0.950642	−	0.310291i	$-0.899574\pi$
$877$	−6.11832	+	10.5972i	−0.206601	+	0.357843i	0.744041	+	0.668134i	$0.232907\pi$
$878$	−7.24672	−	12.5517i	−0.244565	−	0.423599i
$879$	−14.8772	+	84.3728i	−0.501795	+	2.84582i
$880$		0			0
$881$	5.34083	+	1.94390i	0.179937	+	0.0654918i	0.430418	−	0.902630i	$-0.358366\pi$
$881$	5.34083	+	1.94390i	0.179937	+	0.0654918i	−0.250480	+	0.968122i	$0.580589\pi$
$882$	−0.573522			−0.0193115
$883$	−0.289230	−	0.105271i	−0.00973338	−	0.00354266i	0.337149	−	0.941451i	$-0.390537\pi$
$883$	−0.289230	−	0.105271i	−0.00973338	−	0.00354266i	−0.346882	+	0.937909i	$0.612760\pi$
$884$	−1.86984	−	10.6044i	−0.0628895	−	0.356664i
$885$		0			0
$886$	29.7174	+	24.9359i	0.998377	+	0.837738i
$887$	−37.7764			−1.26841			−0.634204	−	0.773166i	$-0.718672\pi$
$887$	−37.7764			−1.26841			−0.634204	+	0.773166i	$0.718672\pi$
$888$	−50.8323	−	22.9114i	−1.70582	−	0.768858i
$889$	55.5929			1.86453
$890$		0			0
$891$	26.1595	−	21.9504i	0.876376	−	0.735367i
$892$	1.72501	+	9.78304i	0.0577577	+	0.327560i
$893$	7.81953	+	2.84608i	0.261671	+	0.0952403i
$894$	12.6894			0.424398
$895$		0			0
$896$	6.32015	−	10.9468i	0.211141	−	0.365708i
$897$	23.6174	−	133.941i	0.788563	−	4.47217i
$898$	−1.65845	−	2.87253i	−0.0553433	−	0.0958574i
$899$	22.6650	−	39.2570i	0.755921	−	1.30929i
$900$		0			0
$901$	1.29531	+	7.34605i	0.0431529	+	0.244732i
$902$	0.982435	+	1.70163i	0.0327115	+	0.0566580i
$903$	−20.3274	+	7.39856i	−0.676453	+	0.246209i
$904$	33.6707	−	12.2551i	1.11987	−	0.407600i
$905$		0			0
$906$	−57.7985	+	48.4987i	−1.92023	+	1.61126i
$907$	−38.1422	+	32.0051i	−1.26649	+	1.06271i	−0.271532	+	0.962430i	$0.587530\pi$
$907$	−38.1422	+	32.0051i	−1.26649	+	1.06271i	−0.994959	+	0.100282i	$0.968025\pi$
$908$	−1.30507	+	7.40139i	−0.0433101	+	0.245624i
$909$	−31.0315	+	11.2945i	−1.02925	+	0.374616i
$910$		0			0
$911$	0.683516	+	1.18389i	0.0226459	+	0.0392239i	0.877126	−	0.480260i	$-0.159458\pi$
$911$	0.683516	+	1.18389i	0.0226459	+	0.0392239i	−0.854480	+	0.519484i	$0.826124\pi$
$912$	5.37422	+	30.4787i	0.177958	+	1.00925i
$913$	−48.8738	−	41.0100i	−1.61749	−	1.35723i
$914$	17.2152	−	29.8177i	0.569430	−	0.986281i
$915$		0			0
$916$	0.000231957	−	0.00131549i	7.66407e−6	−	4.34651e-5i
$917$	−25.2909	+	43.8051i	−0.835178	+	1.44657i
$918$	38.3536	+	13.9596i	1.26586	+	0.460734i
$919$	−13.3894			−0.441676			−0.220838	−	0.975310i	$-0.570879\pi$
$919$	−13.3894			−0.441676			−0.220838	+	0.975310i	$0.570879\pi$
$920$		0			0
$921$	15.8847	+	90.0863i	0.523417	+	2.96845i
$922$	−15.8748	+	13.3206i	−0.522809	+	0.438689i
$923$	22.3312	+	18.7381i	0.735039	+	0.616771i
$924$	−17.3109			−0.569486
$925$		0			0
$926$	−5.63248			−0.185095
$927$	−2.29281	−	1.92389i	−0.0753057	−	0.0631890i
$928$	20.9179	−	17.5522i	0.686665	−	0.576180i
$929$	1.76707	+	10.0215i	0.0579756	+	0.328796i	0.999977	−	0.00681348i	$-0.00216882\pi$
$929$	1.76707	+	10.0215i	0.0579756	+	0.328796i	−0.942001	+	0.335610i	$0.891058\pi$
$930$		0			0
$931$	−0.314208			−0.0102977
$932$	−0.0225765	−	0.00821716i	−0.000739517	−	0.000269162i
$933$	2.87076	−	4.97231i	0.0939846	−	0.162786i
$934$	−1.91501	+	10.8606i	−0.0626611	+	0.355369i
$935$		0			0
$936$	47.2114	−	81.7725i	1.54315	−	2.67282i
$937$	35.7939	+	30.0346i	1.16934	+	0.981189i	0.999990	−	0.00436754i	$-0.00139023\pi$
$937$	35.7939	+	30.0346i	1.16934	+	0.981189i	0.169345	+	0.985557i	$0.445835\pi$
$938$	−2.18482	−	12.3907i	−0.0713369	−	0.404571i
$939$	29.4292	+	50.9729i	0.960385	+	1.66344i
$940$		0			0
$941$	−24.3819	+	8.87429i	−0.794827	+	0.289294i	−0.707341	−	0.706872i	$-0.750106\pi$
$941$	−24.3819	+	8.87429i	−0.794827	+	0.289294i	−0.0874862	+	0.996166i	$0.527883\pi$
$942$	0.336701	−	1.90953i	0.0109703	−	0.0622158i
$943$	2.65604	−	2.22868i	0.0864925	−	0.0725758i
$944$	7.11480	−	5.97002i	0.231567	−	0.194308i
$945$		0			0
$946$	−12.8483	+	4.67638i	−0.417733	+	0.152042i
$947$	36.0218	−	13.1109i	1.17055	−	0.426046i	0.317696	−	0.948193i	$-0.397091\pi$
$947$	36.0218	−	13.1109i	1.17055	−	0.426046i	0.852855	+	0.522147i	$0.174869\pi$
$948$	7.65851	+	13.2649i	0.248737	+	0.430825i
$949$	−10.5388	−	59.7683i	−0.342103	−	1.94016i
$950$		0			0
$951$	19.7069	−	34.1333i	0.639038	−	1.10685i
$952$	−15.5925	−	27.0069i	−0.505355	−	0.875300i
$953$	−4.32189	+	24.5106i	−0.140000	+	0.793978i	0.831247	+	0.555903i	$0.187627\pi$
$953$	−4.32189	+	24.5106i	−0.140000	+	0.793978i	−0.971247	+	0.238075i	$0.923484\pi$
$954$	−6.91798	+	11.9823i	−0.223978	+	0.387941i
$955$		0			0
$956$	−13.5963			−0.439736
$957$	106.878	+	38.9005i	3.45488	+	1.25747i
$958$	2.83084	+	16.0545i	0.0914603	+	0.518697i
$959$	−1.54127	+	1.29328i	−0.0497702	+	0.0417621i
$960$		0			0
$961$	−7.10616			−0.229231
$962$	−16.5996	−	34.4335i	−0.535194	−	1.11018i
$963$	47.1385			1.51902
$964$	−4.78969	−	4.01903i	−0.154266	−	0.129444i
$965$		0			0
$966$	−14.4680	−	82.0520i	−0.465500	−	2.63998i
$967$	36.3618	+	13.2346i	1.16932	+	0.425596i	0.852417	−	0.522863i	$-0.175136\pi$
$967$	36.3618	+	13.2346i	1.16932	+	0.425596i	0.316899	+	0.948459i	$0.397358\pi$
$968$	−17.9731			−0.577676
$969$	42.5743	+	15.4958i	1.36768	+	0.497796i
$970$		0			0
$971$	−4.16513	+	23.6216i	−0.133665	+	0.758054i	0.842115	+	0.539299i	$0.181311\pi$
$971$	−4.16513	+	23.6216i	−0.133665	+	0.758054i	−0.975780	+	0.218755i	$0.929800\pi$
$972$	0.363172	+	0.629032i	0.0116487	+	0.0201762i
$973$	15.4801	−	26.8123i	0.496269	−	0.859563i
$974$	2.11887	+	1.77794i	0.0678930	+	0.0569690i
$975$		0			0
$976$	−0.711744	−	1.23278i	−0.0227824	−	0.0394602i
$977$	40.6124	−	14.7817i	1.29931	−	0.472909i	0.402536	−	0.915404i	$-0.368129\pi$
$977$	40.6124	−	14.7817i	1.29931	−	0.472909i	0.896771	+	0.442495i	$0.145907\pi$
$978$	−77.4453	+	28.1878i	−2.47643	+	0.901346i
$979$	−2.59671	+	14.7267i	−0.0829912	+	0.470666i
$980$		0			0
$981$	16.3791	−	13.7437i	0.522945	−	0.438803i
$982$	−2.32471	+	13.1841i	−0.0741844	+	0.420721i
$983$	51.4954	−	18.7428i	1.64245	−	0.597802i	0.654984	−	0.755643i	$-0.272675\pi$
$983$	51.4954	−	18.7428i	1.64245	−	0.597802i	0.987465	+	0.157841i	$0.0504532\pi$
$984$	3.40751	−	1.24023i	0.108627	−	0.0395372i
$985$		0			0
$986$	7.52598	+	42.6820i	0.239676	+	1.35927i
$987$	−12.7595	−	10.7065i	−0.406140	−	0.340792i
$988$	5.47113	−	9.47628i	0.174060	−	0.301481i
$989$	12.0635	+	20.8947i	0.383598	+	0.664412i
$990$		0			0
$991$	−15.9937	+	27.7019i	−0.508056	+	0.879979i	0.491900	+	0.870652i	$0.336302\pi$
$991$	−15.9937	+	27.7019i	−0.508056	+	0.879979i	−0.999956	+	0.00932754i	$0.997031\pi$
$992$	13.5254	+	4.92285i	0.429433	+	0.156301i
$993$	−50.7273			−1.60978
$994$	16.7810	+	6.10779i	0.532261	+	0.193727i
$995$		0			0
$996$	−19.0791	+	16.0093i	−0.604545	+	0.507273i
$997$	−38.2123	−	32.0639i	−1.21020	−	1.01547i	−0.999279	−	0.0379709i	$-0.987911\pi$
$997$	−38.2123	−	32.0639i	−1.21020	−	1.01547i	−0.210917	−	0.977504i	$-0.567645\pi$
$998$	28.6324			0.906342
$999$	−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.p.e.626.9	✓	78
5.2	odd	4		925.2.bc.e.774.9		156
5.3	odd	4		925.2.bc.e.774.18		156
5.4	even	2		925.2.p.f.626.5	yes	78
37.12	even	9	inner	925.2.p.e.826.9	yes	78
185.12	odd	36		925.2.bc.e.49.18		156
185.49	even	18		925.2.p.f.826.5	yes	78
185.123	odd	36		925.2.bc.e.49.9		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.p.e.626.9	✓	78	1.1	even	1	trivial
925.2.p.e.826.9	yes	78	37.12	even	9	inner
925.2.p.f.626.5	yes	78	5.4	even	2
925.2.p.f.826.5	yes	78	185.49	even	18
925.2.bc.e.49.9		156	185.123	odd	36
925.2.bc.e.49.18		156	185.12	odd	36
925.2.bc.e.774.9		156	5.2	odd	4
925.2.bc.e.774.18		156	5.3	odd	4

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.p (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.926709 + 0.777601i) q^{2} +(-2.28834 + 1.92015i) q^{3} +(-0.0931703 - 0.528395i) q^{4} -3.61374 q^{6} +(2.47194 + 0.899712i) q^{7} +(1.53427 - 2.65744i) q^{8} +(1.02860 - 5.83350i) q^{9} +O(q^{10})\)	\(q+(0.926709 + 0.777601i) q^{2} +(-2.28834 + 1.92015i) q^{3} +(-0.0931703 - 0.528395i) q^{4} -3.61374 q^{6} +(2.47194 + 0.899712i) q^{7} +(1.53427 - 2.65744i) q^{8} +(1.02860 - 5.83350i) q^{9} +(-2.05288 + 3.55569i) q^{11} +(1.22780 + 1.03025i) q^{12} +(0.902063 + 5.11585i) q^{13} +(1.59115 + 2.75595i) q^{14} +(2.47987 - 0.902600i) q^{16} +(0.670858 - 3.80463i) q^{17} +(5.48936 - 4.60612i) q^{18} +(3.00738 - 2.52349i) q^{19} +(-7.38423 + 2.68764i) q^{21} +(-4.66732 + 1.69877i) q^{22} +(4.38227 + 7.59031i) q^{23} +(1.59173 + 9.02716i) q^{24} +(-3.14214 + 5.44235i) q^{26} +(4.36656 + 7.56311i) q^{27} +(0.245092 - 1.38999i) q^{28} +(-4.63674 + 8.03107i) q^{29} -4.88813 q^{31} +(-2.76699 - 1.00710i) q^{32} +(-2.12976 - 12.0785i) q^{33} +(3.58017 - 3.00412i) q^{34} -3.17823 q^{36} +(-3.42449 + 5.02721i) q^{37} +4.74923 q^{38} +(-11.8874 - 9.97474i) q^{39} +(-0.0686945 - 0.389586i) q^{41} +(-8.93295 - 3.25133i) q^{42} +2.75281 q^{43} +(2.07007 + 0.753445i) q^{44} +(-1.84115 + 10.4417i) q^{46} +(1.05982 + 1.83566i) q^{47} +(-3.94168 + 6.82719i) q^{48} +(-0.0613108 - 0.0514458i) q^{49} +(5.77029 + 9.99444i) q^{51} +(2.61914 - 0.953290i) q^{52} +(-1.81438 + 0.660379i) q^{53} +(-1.83455 + 10.4043i) q^{54} +(6.18355 - 5.18862i) q^{56} +(-2.03644 + 11.5492i) q^{57} +(-10.5419 + 3.83693i) q^{58} +(3.30713 - 1.20370i) q^{59} +(-0.0936657 - 0.531205i) q^{61} +(-4.52988 - 3.80102i) q^{62} +(7.79112 - 13.4946i) q^{63} +(-4.42010 - 7.65583i) q^{64} +(7.41856 - 12.8493i) q^{66} +(-3.71526 - 1.35225i) q^{67} -2.07285 q^{68} +(-24.6027 - 8.95463i) q^{69} +(4.29878 - 3.60710i) q^{71} +(-13.9240 - 11.6836i) q^{72} -11.6830 q^{73} +(-7.08267 + 1.99588i) q^{74} +(-1.61360 - 1.35397i) q^{76} +(-8.27368 + 6.94244i) q^{77} +(-3.25982 - 18.4874i) q^{78} +(8.98019 + 3.26852i) q^{79} +(-7.81571 - 2.84469i) q^{81} +(0.239283 - 0.414450i) q^{82} +(-2.69836 + 15.3032i) q^{83} +(2.10813 + 3.65138i) q^{84} +(2.55105 + 2.14059i) q^{86} +(-4.81039 - 27.2811i) q^{87} +(6.29934 + 10.9108i) q^{88} +(3.42252 - 1.24570i) q^{89} +(-2.37295 + 13.4577i) q^{91} +(3.60238 - 3.02276i) q^{92} +(11.1857 - 9.38594i) q^{93} +(-0.445267 + 2.52524i) q^{94} +(8.26562 - 3.00844i) q^{96} +(4.25585 + 7.37135i) q^{97} +(-0.0168129 - 0.0953507i) q^{98} +(18.6305 + 15.6329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 3 q^{2} + 3 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 78 * q - 3 * q^2 + 3 * q^4 + 6 * q^7 - 6 * q^8	\( 78 q - 3 q^{2} + 3 q^{4} + 6 q^{7} - 6 q^{8} - 15 q^{12} + 27 q^{13} + 6 q^{14} + 21 q^{16} - 15 q^{18} - 12 q^{19} + 15 q^{21} + 30 q^{22} - 18 q^{23} + 15 q^{24} + 36 q^{27} - 3 q^{28} - 3 q^{29} - 36 q^{31} + 36 q^{32} + 30 q^{33} - 21 q^{34} + 108 q^{36} + 54 q^{37} - 60 q^{38} + 9 q^{39} - 3 q^{41} + 6 q^{42} + 12 q^{43} - 15 q^{44} - 36 q^{46} + 63 q^{47} + 54 q^{48} - 30 q^{49} - 30 q^{51} - 105 q^{52} + 24 q^{53} + 27 q^{54} + 120 q^{56} - 27 q^{57} - 33 q^{58} + 15 q^{59} - 6 q^{61} + 24 q^{62} + 48 q^{63} - 54 q^{64} - 6 q^{66} + 48 q^{67} - 246 q^{68} + 45 q^{69} + 72 q^{71} + 132 q^{72} - 36 q^{73} + 96 q^{74} + 21 q^{76} + 3 q^{77} - 186 q^{78} + 48 q^{79} + 48 q^{81} - 66 q^{82} - 18 q^{83} + 27 q^{84} + 108 q^{86} + 72 q^{87} - 42 q^{88} - 21 q^{89} - 27 q^{91} + 75 q^{92} + 48 q^{93} - 78 q^{94} - 126 q^{96} + 12 q^{97} + 30 q^{98} + 141 q^{99}+O(q^{100}) \) 78 * q - 3 * q^2 + 3 * q^4 + 6 * q^7 - 6 * q^8 - 15 * q^12 + 27 * q^13 + 6 * q^14 + 21 * q^16 - 15 * q^18 - 12 * q^19 + 15 * q^21 + 30 * q^22 - 18 * q^23 + 15 * q^24 + 36 * q^27 - 3 * q^28 - 3 * q^29 - 36 * q^31 + 36 * q^32 + 30 * q^33 - 21 * q^34 + 108 * q^36 + 54 * q^37 - 60 * q^38 + 9 * q^39 - 3 * q^41 + 6 * q^42 + 12 * q^43 - 15 * q^44 - 36 * q^46 + 63 * q^47 + 54 * q^48 - 30 * q^49 - 30 * q^51 - 105 * q^52 + 24 * q^53 + 27 * q^54 + 120 * q^56 - 27 * q^57 - 33 * q^58 + 15 * q^59 - 6 * q^61 + 24 * q^62 + 48 * q^63 - 54 * q^64 - 6 * q^66 + 48 * q^67 - 246 * q^68 + 45 * q^69 + 72 * q^71 + 132 * q^72 - 36 * q^73 + 96 * q^74 + 21 * q^76 + 3 * q^77 - 186 * q^78 + 48 * q^79 + 48 * q^81 - 66 * q^82 - 18 * q^83 + 27 * q^84 + 108 * q^86 + 72 * q^87 - 42 * q^88 - 21 * q^89 - 27 * q^91 + 75 * q^92 + 48 * q^93 - 78 * q^94 - 126 * q^96 + 12 * q^97 + 30 * q^98 + 141 * q^99

Introduction

L-functions

Modular forms

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Database

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