LMFDB - Embedded newform 1352.2.o.c.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1352,2,Mod(361,1352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1352, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1352.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,0,0,0,0,-6,0,0,0,0,0,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-2.21837 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	1352.361
Dual form			1352.2.o.c.1161.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28078 - 2.21837i) q^{3} -3.56155i q^{5} +(-2.21837 - 1.28078i) q^{7} +(-1.78078 + 3.08440i) q^{9} +(-2.21837 + 1.28078i) q^{11} +(-7.90084 + 4.56155i) q^{15} +(-2.50000 + 4.33013i) q^{17} +(2.21837 + 1.28078i) q^{19} +6.56155i q^{21} +(-1.84233 - 3.19101i) q^{23} -7.68466 q^{25} +1.43845 q^{27} +(2.50000 + 4.33013i) q^{29} -8.00000i q^{31} +(5.68247 + 3.28078i) q^{33} +(-4.56155 + 7.90084i) q^{35} +(0.866025 - 0.500000i) q^{37} +(8.00745 - 4.62311i) q^{41} +(-3.28078 + 5.68247i) q^{43} +(10.9852 + 6.34233i) q^{45} -4.00000i q^{47} +(-0.219224 - 0.379706i) q^{49} +12.8078 q^{51} +4.43845 q^{53} +(4.56155 + 7.90084i) q^{55} -6.56155i q^{57} +(-2.21837 - 1.28078i) q^{59} +(3.62311 - 6.27540i) q^{61} +(7.90084 - 4.56155i) q^{63} +(-8.17394 + 4.71922i) q^{67} +(-4.71922 + 8.17394i) q^{69} +(-6.65511 - 3.84233i) q^{71} +1.31534i q^{73} +(9.84233 + 17.0474i) q^{75} +6.56155 q^{77} -4.00000 q^{79} +(3.50000 + 6.06218i) q^{81} +2.24621i q^{83} +(15.4220 + 8.90388i) q^{85} +(6.40388 - 11.0918i) q^{87} +(8.38716 - 4.84233i) q^{89} +(-17.7470 + 10.2462i) q^{93} +(4.56155 - 7.90084i) q^{95} +(-2.43160 - 1.40388i) q^{97} -9.12311i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 6 q^{9} - 20 q^{17} + 10 q^{23} - 12 q^{25} + 28 q^{27} + 20 q^{29} - 20 q^{35} - 18 q^{43} - 10 q^{49} + 20 q^{51} + 52 q^{53} + 20 q^{55} - 4 q^{61} - 46 q^{69} + 54 q^{75} + 36 q^{77}+ \cdots + 20 q^{95}+O(q^{100}) $ 8 * q - 2 * q^3 - 6 * q^9 - 20 * q^17 + 10 * q^23 - 12 * q^25 + 28 * q^27 + 20 * q^29 - 20 * q^35 - 18 * q^43 - 10 * q^49 + 20 * q^51 + 52 * q^53 + 20 * q^55 - 4 * q^61 - 46 * q^69 + 54 * q^75 + 36 * q^77 - 32 * q^79 + 28 * q^81 + 10 * q^87 + 20 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.28078	−	2.21837i	−0.739457	−	1.28078i	−0.952740	−	0.303786i	$-0.901749\pi$
$3$	−1.28078	−	2.21837i	−0.739457	−	1.28078i	0.213284	−	0.976990i	$-0.431584\pi$
$4$		0			0
$5$		−	3.56155i		−	1.59277i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$		−	3.56155i		−	1.59277i	0.604787	−	0.796387i	$-0.293258\pi$
$6$		0			0
$7$	−2.21837	−	1.28078i	−0.838465	−	0.484088i	0.0182772	−	0.999833i	$-0.494182\pi$
$7$	−2.21837	−	1.28078i	−0.838465	−	0.484088i	−0.856742	+	0.515745i	$0.827515\pi$
$8$		0			0
$9$	−1.78078	+	3.08440i	−0.593592	+	1.02813i
$10$		0			0
$11$	−2.21837	+	1.28078i	−0.668864	+	0.386169i	−0.795646	−	0.605762i	$-0.792868\pi$
$11$	−2.21837	+	1.28078i	−0.668864	+	0.386169i	0.126782	+	0.991931i	$0.459535\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−7.90084	+	4.56155i	−2.03999	+	1.17779i
$16$		0			0
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$		0			0
$19$	2.21837	+	1.28078i	0.508929	+	0.293830i	0.732393	−	0.680882i	$-0.238403\pi$
$19$	2.21837	+	1.28078i	0.508929	+	0.293830i	−0.223464	+	0.974712i	$0.571737\pi$
$20$		0			0
$21$			6.56155i			1.43185i
$22$		0			0
$23$	−1.84233	−	3.19101i	−0.384152	−	0.665371i	0.607499	−	0.794320i	$-0.292173\pi$
$23$	−1.84233	−	3.19101i	−0.384152	−	0.665371i	−0.991651	+	0.128949i	$0.958840\pi$
$24$		0			0
$25$	−7.68466			−1.53693
$26$		0			0
$27$	1.43845			0.276829
$28$		0			0
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$		0			0
$31$		−	8.00000i		−	1.43684i	−0.695608	−	0.718421i	$-0.744865\pi$
$31$		−	8.00000i		−	1.43684i	0.695608	−	0.718421i	$-0.255135\pi$
$32$		0			0
$33$	5.68247	+	3.28078i	0.989191	+	0.571110i
$34$		0			0
$35$	−4.56155	+	7.90084i	−0.771043	+	1.33549i
$36$		0			0
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	0.569495	+	0.821995i	$0.307139\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.00745	−	4.62311i	1.25055	−	0.722008i	0.279335	−	0.960194i	$-0.409886\pi$
$41$	8.00745	−	4.62311i	1.25055	−	0.722008i	0.971220	+	0.238186i	$0.0765528\pi$
$42$		0			0
$43$	−3.28078	+	5.68247i	−0.500314	+	0.866569i	0.499686	+	0.866206i	$0.333449\pi$
$43$	−3.28078	+	5.68247i	−0.500314	+	0.866569i	−1.00000		0.000362281i	$0.999885\pi$
$44$		0			0
$45$	10.9852	+	6.34233i	1.63758	+	0.945459i
$46$		0			0
$47$		−	4.00000i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$		−	4.00000i		−	0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$		0			0
$49$	−0.219224	−	0.379706i	−0.0313177	−	0.0542438i
$50$		0			0
$51$	12.8078			1.79345
$52$		0			0
$53$	4.43845			0.609668			0.304834	−	0.952406i	$-0.401399\pi$
$53$	4.43845			0.609668			0.304834	+	0.952406i	$0.401399\pi$
$54$		0			0
$55$	4.56155	+	7.90084i	0.615080	+	1.06535i
$56$		0			0
$57$		−	6.56155i		−	0.869099i
$58$		0			0
$59$	−2.21837	−	1.28078i	−0.288807	−	0.166743i	0.348597	−	0.937273i	$-0.386658\pi$
$59$	−2.21837	−	1.28078i	−0.288807	−	0.166743i	−0.637404	+	0.770530i	$0.719992\pi$
$60$		0			0
$61$	3.62311	−	6.27540i	0.463891	−	0.803483i	−0.535260	−	0.844688i	$-0.679786\pi$
$61$	3.62311	−	6.27540i	0.463891	−	0.803483i	0.999151	+	0.0412046i	$0.0131195\pi$
$62$		0			0
$63$	7.90084	−	4.56155i	0.995412	−	0.574702i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.17394	+	4.71922i	−0.998605	+	0.576545i	−0.907835	−	0.419327i	$-0.862266\pi$
$67$	−8.17394	+	4.71922i	−0.998605	+	0.576545i	−0.0907698	+	0.995872i	$0.528933\pi$
$68$		0			0
$69$	−4.71922	+	8.17394i	−0.568128	+	0.984026i
$70$		0			0
$71$	−6.65511	−	3.84233i	−0.789816	−	0.456001i	0.0500816	−	0.998745i	$-0.484052\pi$
$71$	−6.65511	−	3.84233i	−0.789816	−	0.456001i	−0.839898	+	0.542745i	$0.817385\pi$
$72$		0			0
$73$			1.31534i			0.153949i	0.997033	+	0.0769745i	$0.0245260\pi$
$73$			1.31534i			0.153949i	−0.997033	+	0.0769745i	$0.975474\pi$
$74$		0			0
$75$	9.84233	+	17.0474i	1.13649	+	1.96847i
$76$		0			0
$77$	6.56155			0.747758
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$		0			0
$83$			2.24621i			0.246554i	0.992372	+	0.123277i	$0.0393403\pi$
$83$			2.24621i			0.246554i	−0.992372	+	0.123277i	$0.960660\pi$
$84$		0			0
$85$	15.4220	+	8.90388i	1.67275	+	0.965762i
$86$		0			0
$87$	6.40388	−	11.0918i	0.686568	−	1.18917i
$88$		0			0
$89$	8.38716	−	4.84233i	0.889037	−	0.513286i	0.0154098	−	0.999881i	$-0.495095\pi$
$89$	8.38716	−	4.84233i	0.889037	−	0.513286i	0.873627	+	0.486595i	$0.161761\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−17.7470	+	10.2462i	−1.84027	+	1.06248i
$94$		0			0
$95$	4.56155	−	7.90084i	0.468005	−	0.810609i
$96$		0			0
$97$	−2.43160	−	1.40388i	−0.246891	−	0.142543i	0.371449	−	0.928453i	$-0.378861\pi$
$97$	−2.43160	−	1.40388i	−0.246891	−	0.142543i	−0.618340	+	0.785911i	$0.712194\pi$
$98$		0			0
$99$		−	9.12311i		−	0.916907i
$100$		0			0
$101$	2.62311	+	4.54335i	0.261009	+	0.452080i	0.966510	−	0.256628i	$-0.0826115\pi$
$101$	2.62311	+	4.54335i	0.261009	+	0.452080i	−0.705501	+	0.708708i	$0.749278\pi$
$102$		0			0
$103$	−14.2462			−1.40372			−0.701860	−	0.712314i	$-0.747647\pi$
$103$	−14.2462			−1.40372			−0.701860	+	0.712314i	$0.747647\pi$
$104$		0			0
$105$	23.3693			2.28061
$106$		0			0
$107$	1.84233	+	3.19101i	0.178105	+	0.308486i	0.941231	−	0.337763i	$-0.109670\pi$
$107$	1.84233	+	3.19101i	0.178105	+	0.308486i	−0.763127	+	0.646249i	$0.776337\pi$
$108$		0			0
$109$			8.24621i			0.789844i	0.918715	+	0.394922i	$0.129228\pi$
$109$			8.24621i			0.789844i	−0.918715	+	0.394922i	$0.870772\pi$
$110$		0			0
$111$	−2.21837	−	1.28078i	−0.210558	−	0.121566i
$112$		0			0
$113$	−4.62311	+	8.00745i	−0.434905	+	0.753278i	−0.997288	−	0.0735992i	$-0.976551\pi$
$113$	−4.62311	+	8.00745i	−0.434905	+	0.753278i	0.562383	+	0.826877i	$0.309885\pi$
$114$		0			0
$115$	−11.3649	+	6.56155i	−1.05979	+	0.611868i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.0918	−	6.40388i	1.01679	−	0.587043i
$120$		0			0
$121$	−2.21922	+	3.84381i	−0.201748	+	0.349437i
$122$		0			0
$123$	−20.5115	−	11.8423i	−1.84946	−	1.06779i
$124$		0			0
$125$			9.56155i			0.855211i
$126$		0			0
$127$	6.40388	+	11.0918i	0.568253	+	0.984242i	0.996739	+	0.0806942i	$0.0257137\pi$
$127$	6.40388	+	11.0918i	0.568253	+	0.984242i	−0.428486	+	0.903548i	$0.640953\pi$
$128$		0			0
$129$	16.8078			1.47984
$130$		0			0
$131$	18.2462			1.59418			0.797089	−	0.603861i	$-0.206372\pi$
$131$	18.2462			1.59418			0.797089	+	0.603861i	$0.206372\pi$
$132$		0			0
$133$	−3.28078	−	5.68247i	−0.284479	−	0.492733i
$134$		0			0
$135$		−	5.12311i		−	0.440927i
$136$		0			0
$137$	−18.6130	−	10.7462i	−1.59021	−	0.918111i	−0.993269	−	0.115829i	$-0.963048\pi$
$137$	−18.6130	−	10.7462i	−1.59021	−	0.918111i	−0.596945	−	0.802282i	$-0.703619\pi$
$138$		0			0
$139$	−9.84233	+	17.0474i	−0.834815	+	1.44594i	0.0593651	+	0.998236i	$0.481092\pi$
$139$	−9.84233	+	17.0474i	−0.834815	+	1.44594i	−0.894181	+	0.447706i	$0.852241\pi$
$140$		0			0
$141$	−8.87348	+	5.12311i	−0.747282	+	0.431443i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	15.4220	−	8.90388i	1.28073	−	0.739427i
$146$		0			0
$147$	−0.561553	+	0.972638i	−0.0463161	+	0.0802218i
$148$		0			0
$149$	−11.4716	−	6.62311i	−0.939786	−	0.542586i	−0.0498931	−	0.998755i	$-0.515888\pi$
$149$	−11.4716	−	6.62311i	−0.939786	−	0.542586i	−0.889893	+	0.456169i	$0.849221\pi$
$150$		0			0
$151$			12.4924i			1.01662i	0.861174	+	0.508309i	$0.169729\pi$
$151$			12.4924i			1.01662i	−0.861174	+	0.508309i	$0.830271\pi$
$152$		0			0
$153$	−8.90388	−	15.4220i	−0.719836	−	1.24679i
$154$		0			0
$155$	−28.4924			−2.28857
$156$		0			0
$157$	−17.8078			−1.42121			−0.710607	−	0.703589i	$-0.751580\pi$
$157$	−17.8078			−1.42121			−0.710607	+	0.703589i	$0.751580\pi$
$158$		0			0
$159$	−5.68466	−	9.84612i	−0.450823	−	0.780848i
$160$		0			0
$161$			9.43845i			0.743854i
$162$		0			0
$163$	5.13628	+	2.96543i	0.402305	+	0.232271i	0.687478	−	0.726205i	$-0.258718\pi$
$163$	5.13628	+	2.96543i	0.402305	+	0.232271i	−0.285173	+	0.958476i	$0.592051\pi$
$164$		0			0
$165$	11.6847	−	20.2384i	0.909649	−	1.57556i
$166$		0			0
$167$	4.70983	−	2.71922i	0.364458	−	0.210420i	−0.306577	−	0.951846i	$-0.599184\pi$
$167$	4.70983	−	2.71922i	0.364458	−	0.210420i	0.671034	+	0.741426i	$0.265850\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−7.90084	+	4.56155i	−0.604192	+	0.348831i
$172$		0			0
$173$	−7.96543	+	13.7965i	−0.605601	+	1.04893i	0.386355	+	0.922350i	$0.373734\pi$
$173$	−7.96543	+	13.7965i	−0.605601	+	1.04893i	−0.991956	+	0.126581i	$0.959600\pi$
$174$		0			0
$175$	17.0474	+	9.84233i	1.28866	+	0.744010i
$176$		0			0
$177$			6.56155i			0.493197i
$178$		0			0
$179$	2.15767	+	3.73720i	0.161272	+	0.279331i	0.935325	−	0.353789i	$-0.115107\pi$
$179$	2.15767	+	3.73720i	0.161272	+	0.279331i	−0.774053	+	0.633121i	$0.781774\pi$
$180$		0			0
$181$	9.80776			0.729005			0.364503	−	0.931202i	$-0.381239\pi$
$181$	9.80776			0.729005			0.364503	+	0.931202i	$0.381239\pi$
$182$		0			0
$183$	−18.5616			−1.37211
$184$		0			0
$185$	−1.78078	−	3.08440i	−0.130925	−	0.226769i
$186$		0			0
$187$		−	12.8078i		−	0.936596i
$188$		0			0
$189$	−3.19101	−	1.84233i	−0.232112	−	0.134010i
$190$		0			0
$191$	2.15767	−	3.73720i	0.156124	−	0.270414i	−0.777344	−	0.629076i	$-0.783434\pi$
$191$	2.15767	−	3.73720i	0.156124	−	0.270414i	0.933468	+	0.358662i	$0.116767\pi$
$192$		0			0
$193$	−2.59808	+	1.50000i	−0.187014	+	0.107972i	−0.590584	−	0.806976i	$-0.701102\pi$
$193$	−2.59808	+	1.50000i	−0.187014	+	0.107972i	0.403570	+	0.914949i	$0.367769\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.00514	−	1.15767i	0.142861	−	0.0824806i	−0.426866	−	0.904315i	$-0.640382\pi$
$197$	2.00514	−	1.15767i	0.142861	−	0.0824806i	0.569727	+	0.821834i	$0.307049\pi$
$198$		0			0
$199$	4.71922	−	8.17394i	0.334537	−	0.579435i	−0.648859	−	0.760909i	$-0.724753\pi$
$199$	4.71922	−	8.17394i	0.334537	−	0.579435i	0.983396	+	0.181474i	$0.0580868\pi$
$200$		0			0
$201$	20.9380	+	12.0885i	1.47685	+	0.852660i
$202$		0			0
$203$		−	12.8078i		−	0.898929i
$204$		0			0
$205$	−16.4654	−	28.5190i	−1.15000	−	1.99185i
$206$		0			0
$207$	13.1231			0.912119
$208$		0			0
$209$	−6.56155			−0.453872
$210$		0			0
$211$	−6.15767	−	10.6654i	−0.423912	−	0.734236i	0.572407	−	0.819970i	$-0.306010\pi$
$211$	−6.15767	−	10.6654i	−0.423912	−	0.734236i	−0.996318	+	0.0857336i	$0.972677\pi$
$212$		0			0
$213$			19.6847i			1.34877i
$214$		0			0
$215$	20.2384	+	11.6847i	1.38025	+	0.796887i
$216$		0			0
$217$	−10.2462	+	17.7470i	−0.695558	+	1.20474i
$218$		0			0
$219$	2.91791	−	1.68466i	0.197174	−	0.113839i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−3.19101	+	1.84233i	−0.213686	+	0.123371i	−0.603023	−	0.797724i	$-0.706037\pi$
$223$	−3.19101	+	1.84233i	−0.213686	+	0.123371i	0.389337	+	0.921095i	$0.372704\pi$
$224$		0			0
$225$	13.6847	−	23.7025i	0.912311	−	1.58017i
$226$		0			0
$227$	6.10892	+	3.52699i	0.405463	+	0.234094i	0.688839	−	0.724915i	$-0.258121\pi$
$227$	6.10892	+	3.52699i	0.405463	+	0.234094i	−0.283375	+	0.959009i	$0.591454\pi$
$228$		0			0
$229$			4.24621i			0.280598i	0.990109	+	0.140299i	$0.0448063\pi$
$229$			4.24621i			0.280598i	−0.990109	+	0.140299i	$0.955194\pi$
$230$		0			0
$231$	−8.40388	−	14.5560i	−0.552935	−	0.957711i
$232$		0			0
$233$	−4.24621			−0.278179			−0.139089	−	0.990280i	$-0.544417\pi$
$233$	−4.24621			−0.278179			−0.139089	+	0.990280i	$0.544417\pi$
$234$		0			0
$235$	−14.2462			−0.929320
$236$		0			0
$237$	5.12311	+	8.87348i	0.332781	+	0.576394i
$238$		0			0
$239$			1.75379i			0.113443i	0.998390	+	0.0567216i	$0.0180647\pi$
$239$			1.75379i			0.113443i	−0.998390	+	0.0567216i	$0.981935\pi$
$240$		0			0
$241$	−22.0771	−	12.7462i	−1.42211	−	0.821056i	−0.425631	−	0.904897i	$-0.639948\pi$
$241$	−22.0771	−	12.7462i	−1.42211	−	0.821056i	−0.996479	+	0.0838412i	$0.973281\pi$
$242$		0			0
$243$	11.1231	−	19.2658i	0.713548	−	1.23590i
$244$		0			0
$245$	−1.35234	+	0.780776i	−0.0863981	+	0.0498820i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	4.98293	−	2.87689i	0.315780	−	0.182316i
$250$		0			0
$251$	14.9654	−	25.9209i	0.944610	−	1.63611i	0.188079	−	0.982154i	$-0.439774\pi$
$251$	14.9654	−	25.9209i	0.944610	−	1.63611i	0.756530	−	0.653958i	$-0.226893\pi$
$252$		0			0
$253$	8.17394	+	4.71922i	0.513891	+	0.296695i
$254$		0			0
$255$		−	45.6155i		−	2.85656i
$256$		0			0
$257$	−5.62311	−	9.73950i	−0.350760	−	0.607534i	0.635623	−	0.772000i	$-0.280743\pi$
$257$	−5.62311	−	9.73950i	−0.350760	−	0.607534i	−0.986383	+	0.164466i	$0.947410\pi$
$258$		0			0
$259$	−2.56155			−0.159167
$260$		0			0
$261$	−17.8078			−1.10227
$262$		0			0
$263$	−4.40388	−	7.62775i	−0.271555	−	0.470347i	0.697705	−	0.716385i	$-0.254205\pi$
$263$	−4.40388	−	7.62775i	−0.271555	−	0.470347i	−0.969260	+	0.246038i	$0.920871\pi$
$264$		0			0
$265$		−	15.8078i		−	0.971063i
$266$		0			0
$267$	−21.4842	−	12.4039i	−1.31481	−	0.759105i
$268$		0			0
$269$	−7.40388	+	12.8239i	−0.451423	+	0.781887i	−0.998475	−	0.0552116i	$-0.982417\pi$
$269$	−7.40388	+	12.8239i	−0.451423	+	0.781887i	0.547052	+	0.837099i	$0.315750\pi$
$270$		0			0
$271$	4.70983	−	2.71922i	0.286102	−	0.165181i	−0.350081	−	0.936720i	$-0.613846\pi$
$271$	4.70983	−	2.71922i	0.286102	−	0.165181i	0.636183	+	0.771539i	$0.280512\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	17.0474	−	9.84233i	1.02800	−	0.593515i
$276$		0			0
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	−0.652140	−	0.758099i	$-0.726128\pi$
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	0.982603	+	0.185720i	$0.0594618\pi$
$278$		0			0
$279$	24.6752	+	14.2462i	1.47726	+	0.852898i
$280$		0			0
$281$		−	14.6847i		−	0.876013i	−0.898972	−	0.438007i	$-0.855685\pi$
$281$		−	14.6847i		−	0.876013i	0.898972	−	0.438007i	$-0.144315\pi$
$282$		0			0
$283$	−10.7192	−	18.5662i	−0.637192	−	1.10365i	−0.986046	−	0.166472i	$-0.946763\pi$
$283$	−10.7192	−	18.5662i	−0.637192	−	1.10365i	0.348855	−	0.937177i	$-0.386571\pi$
$284$		0			0
$285$	−23.3693			−1.38428
$286$		0			0
$287$	−23.6847			−1.39806
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$			7.19224i			0.421616i
$292$		0			0
$293$	9.95273	+	5.74621i	0.581445	+	0.335697i	0.761707	−	0.647921i	$-0.224361\pi$
$293$	9.95273	+	5.74621i	0.581445	+	0.335697i	−0.180263	+	0.983619i	$0.557695\pi$
$294$		0			0
$295$	−4.56155	+	7.90084i	−0.265584	+	0.460005i
$296$		0			0
$297$	−3.19101	+	1.84233i	−0.185161	+	0.106903i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	14.5560	−	8.40388i	0.838991	−	0.484392i
$302$		0			0
$303$	6.71922	−	11.6380i	0.386009	−	0.668588i
$304$		0			0
$305$	−22.3502	−	12.9039i	−1.27977	−	0.738874i
$306$		0			0
$307$			26.2462i			1.49795i	0.662598	+	0.748975i	$0.269454\pi$
$307$			26.2462i			1.49795i	−0.662598	+	0.748975i	$0.730546\pi$
$308$		0			0
$309$	18.2462	+	31.6034i	1.03799	+	1.79785i
$310$		0			0
$311$	14.2462			0.807829			0.403914	−	0.914797i	$-0.367649\pi$
$311$	14.2462			0.807829			0.403914	+	0.914797i	$0.367649\pi$
$312$		0			0
$313$	−32.2462			−1.82266			−0.911332	−	0.411673i	$-0.864945\pi$
$313$	−32.2462			−1.82266			−0.911332	+	0.411673i	$0.864945\pi$
$314$		0			0
$315$	−16.2462	−	28.1393i	−0.915370	−	1.58547i
$316$		0			0
$317$			16.4384i			0.923275i	0.887069	+	0.461638i	$0.152738\pi$
$317$			16.4384i			0.923275i	−0.887069	+	0.461638i	$0.847262\pi$
$318$		0			0
$319$	−11.0918	−	6.40388i	−0.621024	−	0.358549i
$320$		0			0
$321$	4.71922	−	8.17394i	0.263401	−	0.456225i
$322$		0			0
$323$	−11.0918	+	6.40388i	−0.617167	+	0.356322i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	18.2931	−	10.5616i	1.01161	−	0.584055i
$328$		0			0
$329$	−5.12311	+	8.87348i	−0.282446	+	0.489211i
$330$		0			0
$331$	−18.9927	−	10.9654i	−1.04393	−	0.602715i	−0.122988	−	0.992408i	$-0.539248\pi$
$331$	−18.9927	−	10.9654i	−1.04393	−	0.602715i	−0.920945	+	0.389693i	$0.872581\pi$
$332$		0			0
$333$			3.56155i			0.195172i
$334$		0			0
$335$	16.8078	+	29.1119i	0.918306	+	1.59055i
$336$		0			0
$337$	−16.4384			−0.895459			−0.447730	−	0.894169i	$-0.647767\pi$
$337$	−16.4384			−0.895459			−0.447730	+	0.894169i	$0.647767\pi$
$338$		0			0
$339$	23.6847			1.28637
$340$		0			0
$341$	10.2462	+	17.7470i	0.554863	+	0.961052i
$342$		0			0
$343$			19.0540i			1.02882i
$344$		0			0
$345$	29.1119	+	16.8078i	1.56733	+	0.904900i
$346$		0			0
$347$	17.5270	−	30.3576i	0.940898	−	1.62968i	0.177135	−	0.984187i	$-0.443317\pi$
$347$	17.5270	−	30.3576i	0.940898	−	1.62968i	0.763763	−	0.645497i	$-0.223350\pi$
$348$		0			0
$349$	−17.8068	+	10.2808i	−0.953178	+	0.550317i	−0.894067	−	0.447934i	$-0.852160\pi$
$349$	−17.8068	+	10.2808i	−0.953178	+	0.550317i	−0.0591110	+	0.998251i	$0.518827\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.79423	+	4.50000i	−0.414845	+	0.239511i	−0.692869	−	0.721063i	$-0.743654\pi$
$353$	−7.79423	+	4.50000i	−0.414845	+	0.239511i	0.278024	+	0.960574i	$0.410320\pi$
$354$		0			0
$355$	−13.6847	+	23.7025i	−0.726306	+	1.25800i
$356$		0			0
$357$	−28.4124	−	16.4039i	−1.50374	−	0.868186i
$358$		0			0
$359$			4.49242i			0.237101i	0.992948	+	0.118550i	$0.0378247\pi$
$359$			4.49242i			0.237101i	−0.992948	+	0.118550i	$0.962175\pi$
$360$		0			0
$361$	−6.21922	−	10.7720i	−0.327328	−	0.566948i
$362$		0			0
$363$	11.3693			0.596734
$364$		0			0
$365$	4.68466			0.245206
$366$		0			0
$367$	16.0885	+	27.8662i	0.839815	+	1.45460i	0.890049	+	0.455865i	$0.150670\pi$
$367$	16.0885	+	27.8662i	0.839815	+	1.45460i	−0.0502341	+	0.998737i	$0.515997\pi$
$368$		0			0
$369$			32.9309i			1.71431i
$370$		0			0
$371$	−9.84612	−	5.68466i	−0.511185	−	0.295133i
$372$		0			0
$373$	5.62311	−	9.73950i	0.291153	−	0.504292i	−0.682929	−	0.730484i	$-0.739294\pi$
$373$	5.62311	−	9.73950i	0.291153	−	0.504292i	0.974083	+	0.226192i	$0.0726277\pi$
$374$		0			0
$375$	21.2111	−	12.2462i	1.09533	−	0.632392i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−22.4568	+	12.9654i	−1.15353	+	0.665990i	−0.949744	−	0.313026i	$-0.898657\pi$
$379$	−22.4568	+	12.9654i	−1.15353	+	0.665990i	−0.203783	+	0.979016i	$0.565324\pi$
$380$		0			0
$381$	16.4039	−	28.4124i	0.840396	−	1.45561i
$382$		0			0
$383$	−14.0098	−	8.08854i	−0.715865	−	0.413305i	0.0973636	−	0.995249i	$-0.468959\pi$
$383$	−14.0098	−	8.08854i	−0.715865	−	0.413305i	−0.813229	+	0.581944i	$0.802292\pi$
$384$		0			0
$385$		−	23.3693i		−	1.19101i
$386$		0			0
$387$	−11.6847	−	20.2384i	−0.593965	−	1.02878i
$388$		0			0
$389$	17.3153			0.877923			0.438961	−	0.898506i	$-0.355347\pi$
$389$	17.3153			0.877923			0.438961	+	0.898506i	$0.355347\pi$
$390$		0			0
$391$	18.4233			0.931706
$392$		0			0
$393$	−23.3693	−	40.4768i	−1.17883	−	2.04179i
$394$		0			0
$395$			14.2462i			0.716805i
$396$		0			0
$397$	−18.7795	−	10.8423i	−0.942514	−	0.544161i	−0.0517667	−	0.998659i	$-0.516485\pi$
$397$	−18.7795	−	10.8423i	−0.942514	−	0.544161i	−0.890748	+	0.454498i	$0.849819\pi$
$398$		0			0
$399$	−8.40388	+	14.5560i	−0.420720	+	0.728709i
$400$		0			0
$401$	8.22068	−	4.74621i	0.410521	−	0.237014i	−0.280492	−	0.959856i	$-0.590498\pi$
$401$	8.22068	−	4.74621i	0.410521	−	0.237014i	0.691014	+	0.722842i	$0.257164\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	21.5908	−	12.4654i	1.07285	−	0.619412i
$406$		0			0
$407$	−1.28078	+	2.21837i	−0.0634857	+	0.109961i
$408$		0			0
$409$	−1.07925	−	0.623106i	−0.0533655	−	0.0308106i	0.473080	−	0.881020i	$-0.343142\pi$
$409$	−1.07925	−	0.623106i	−0.0533655	−	0.0308106i	−0.526445	+	0.850209i	$0.676476\pi$
$410$		0			0
$411$			55.0540i			2.71561i
$412$		0			0
$413$	3.28078	+	5.68247i	0.161436	+	0.279616i
$414$		0			0
$415$	8.00000			0.392705
$416$		0			0
$417$	50.4233			2.46924
$418$		0			0
$419$	6.96543	+	12.0645i	0.340284	+	0.589389i	0.984485	−	0.175467i	$-0.0561435\pi$
$419$	6.96543	+	12.0645i	0.340284	+	0.589389i	−0.644202	+	0.764856i	$0.722810\pi$
$420$		0			0
$421$		−	21.3153i		−	1.03885i	−0.854517	−	0.519423i	$-0.826147\pi$
$421$		−	21.3153i		−	1.03885i	0.854517	−	0.519423i	$-0.173853\pi$
$422$		0			0
$423$	12.3376	+	7.12311i	0.599874	+	0.346337i
$424$		0			0
$425$	19.2116	−	33.2755i	0.931902	−	1.61410i
$426$		0			0
$427$	−16.0748	+	9.28078i	−0.777913	+	0.449128i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.79192	−	1.03457i	0.0863137	−	0.0498333i	−0.456222	−	0.889866i	$-0.650798\pi$
$431$	1.79192	−	1.03457i	0.0863137	−	0.0498333i	0.542536	+	0.840033i	$0.317464\pi$
$432$		0			0
$433$	−0.746211	+	1.29248i	−0.0358606	+	0.0621124i	−0.883399	−	0.468622i	$-0.844751\pi$
$433$	−0.746211	+	1.29248i	−0.0358606	+	0.0621124i	0.847538	+	0.530735i	$0.178084\pi$
$434$		0			0
$435$	−39.5042	−	22.8078i	−1.89408	−	1.09355i
$436$		0			0
$437$		−	9.43845i		−	0.451502i
$438$		0			0
$439$	−18.9654	−	32.8491i	−0.905171	−	1.56780i	−0.820688	−	0.571377i	$-0.806409\pi$
$439$	−18.9654	−	32.8491i	−0.905171	−	1.56780i	−0.0844831	−	0.996425i	$-0.526924\pi$
$440$		0			0
$441$	1.56155			0.0743597
$442$		0			0
$443$	21.7538			1.03355			0.516777	−	0.856120i	$-0.327132\pi$
$443$	21.7538			1.03355			0.516777	+	0.856120i	$0.327132\pi$
$444$		0			0
$445$	−17.2462	−	29.8713i	−0.817549	−	1.41604i
$446$		0			0
$447$			33.9309i			1.60488i
$448$		0			0
$449$	11.3051	+	6.52699i	0.533519	+	0.308028i	0.742448	−	0.669903i	$-0.233664\pi$
$449$	11.3051	+	6.52699i	0.533519	+	0.308028i	−0.208929	+	0.977931i	$0.566998\pi$
$450$		0			0
$451$	−11.8423	+	20.5115i	−0.557634	+	0.965850i
$452$		0			0
$453$	27.7128	−	16.0000i	1.30206	−	0.751746i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.79423	+	4.50000i	−0.364599	+	0.210501i	−0.671096	−	0.741370i	$-0.734176\pi$
$457$	−7.79423	+	4.50000i	−0.364599	+	0.210501i	0.306497	+	0.951871i	$0.400843\pi$
$458$		0			0
$459$	−3.59612	+	6.22866i	−0.167852	+	0.290729i
$460$		0			0
$461$	8.22068	+	4.74621i	0.382875	+	0.221053i	0.679068	−	0.734075i	$-0.262384\pi$
$461$	8.22068	+	4.74621i	0.382875	+	0.221053i	−0.296193	+	0.955128i	$0.595717\pi$
$462$		0			0
$463$		−	32.9848i		−	1.53294i	−0.642283	−	0.766468i	$-0.722012\pi$
$463$		−	32.9848i		−	1.53294i	0.642283	−	0.766468i	$-0.277988\pi$
$464$		0			0
$465$	36.4924	+	63.2067i	1.69230	+	2.93114i
$466$		0			0
$467$	−9.75379			−0.451352			−0.225676	−	0.974202i	$-0.572459\pi$
$467$	−9.75379			−0.451352			−0.225676	+	0.974202i	$0.572459\pi$
$468$		0			0
$469$	24.1771			1.11639
$470$		0			0
$471$	22.8078	+	39.5042i	1.05093	+	1.82026i
$472$		0			0
$473$		−	16.8078i		−	0.772822i
$474$		0			0
$475$	−17.0474	−	9.84233i	−0.782189	−	0.451597i
$476$		0			0
$477$	−7.90388	+	13.6899i	−0.361894	+	0.626819i
$478$		0			0
$479$	−28.8388	+	16.6501i	−1.31768	+	0.760762i	−0.983355	−	0.181696i	$-0.941841\pi$
$479$	−28.8388	+	16.6501i	−1.31768	+	0.760762i	−0.334324	+	0.942458i	$0.608508\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	20.9380	−	12.0885i	0.952710	−	0.550048i
$484$		0			0
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$		0			0
$487$	33.3953	+	19.2808i	1.51328	+	0.873695i	0.999879	+	0.0155493i	$0.00494971\pi$
$487$	33.3953	+	19.2808i	1.51328	+	0.873695i	0.513406	+	0.858146i	$0.328384\pi$
$488$		0			0
$489$		−	15.1922i		−	0.687017i
$490$		0			0
$491$	17.5270	+	30.3576i	0.790982	+	1.37002i	0.925360	+	0.379091i	$0.123763\pi$
$491$	17.5270	+	30.3576i	0.790982	+	1.37002i	−0.134378	+	0.990930i	$0.542904\pi$
$492$		0			0
$493$	−25.0000			−1.12594
$494$		0			0
$495$	−32.4924			−1.46043
$496$		0			0
$497$	9.84233	+	17.0474i	0.441489	+	0.764681i
$498$		0			0
$499$			16.4924i			0.738302i	0.929369	+	0.369151i	$0.120352\pi$
$499$			16.4924i			0.738302i	−0.929369	+	0.369151i	$0.879648\pi$
$500$		0			0
$501$	−12.0645	−	6.96543i	−0.539002	−	0.311193i
$502$		0			0
$503$	10.1577	−	17.5936i	0.452908	−	0.784460i	−0.545657	−	0.838009i	$-0.683720\pi$
$503$	10.1577	−	17.5936i	0.452908	−	0.784460i	0.998565	+	0.0535486i	$0.0170532\pi$
$504$		0			0
$505$	16.1814	−	9.34233i	0.720062	−	0.415728i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−28.5788	+	16.5000i	−1.26673	+	0.731350i	−0.974369	−	0.224957i	$-0.927776\pi$
$509$	−28.5788	+	16.5000i	−1.26673	+	0.731350i	−0.292366	+	0.956306i	$0.594443\pi$
$510$		0			0
$511$	1.68466	−	2.91791i	0.0745249	−	0.129081i
$512$		0			0
$513$	3.19101	+	1.84233i	0.140886	+	0.0813408i
$514$		0			0
$515$			50.7386i			2.23581i
$516$		0			0
$517$	5.12311	+	8.87348i	0.225314	+	0.390255i
$518$		0			0
$519$	40.8078			1.79126
$520$		0			0
$521$	−28.0540			−1.22907			−0.614533	−	0.788891i	$-0.710656\pi$
$521$	−28.0540			−1.22907			−0.614533	+	0.788891i	$0.710656\pi$
$522$		0			0
$523$	−20.6501	−	35.7670i	−0.902966	−	1.56398i	−0.823625	−	0.567135i	$-0.808052\pi$
$523$	−20.6501	−	35.7670i	−0.902966	−	1.56398i	−0.0793404	−	0.996848i	$-0.525281\pi$
$524$		0			0
$525$		−	50.4233i		−	2.20065i
$526$		0			0
$527$	34.6410	+	20.0000i	1.50899	+	0.871214i
$528$		0			0
$529$	4.71165	−	8.16081i	0.204854	−	0.354818i
$530$		0			0
$531$	7.90084	−	4.56155i	0.342867	−	0.197955i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	11.3649	−	6.56155i	0.491349	−	0.283681i
$536$		0			0
$537$	5.52699	−	9.57302i	0.238507	−	0.413106i
$538$		0			0
$539$	0.972638	+	0.561553i	0.0418945	+	0.0241878i
$540$		0			0
$541$		−	6.68466i		−	0.287396i	−0.989622	−	0.143698i	$-0.954101\pi$
$541$		−	6.68466i		−	0.287396i	0.989622	−	0.143698i	$-0.0458994\pi$
$542$		0			0
$543$	−12.5616	−	21.7572i	−0.539068	−	0.933693i
$544$		0			0
$545$	29.3693			1.25804
$546$		0			0
$547$	−16.4924			−0.705165			−0.352583	−	0.935781i	$-0.614696\pi$
$547$	−16.4924			−0.705165			−0.352583	+	0.935781i	$0.614696\pi$
$548$		0			0
$549$	12.9039	+	22.3502i	0.550724	+	0.953882i
$550$		0			0
$551$			12.8078i			0.545629i
$552$		0			0
$553$	8.87348	+	5.12311i	0.377339	+	0.217857i
$554$		0			0
$555$	−4.56155	+	7.90084i	−0.193627	+	0.335372i
$556$		0			0
$557$	1.29248	−	0.746211i	0.0547640	−	0.0316180i	−0.472368	−	0.881401i	$-0.656601\pi$
$557$	1.29248	−	0.746211i	0.0547640	−	0.0316180i	0.527132	+	0.849783i	$0.323267\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−28.4124	+	16.4039i	−1.19957	+	0.692572i
$562$		0			0
$563$	−15.5270	+	26.8935i	−0.654385	+	1.13343i	0.327663	+	0.944795i	$0.393739\pi$
$563$	−15.5270	+	26.8935i	−0.654385	+	1.13343i	−0.982048	+	0.188633i	$0.939594\pi$
$564$		0			0
$565$	28.5190	+	16.4654i	1.19980	+	0.692706i
$566$		0			0
$567$		−	17.9309i		−	0.753026i
$568$		0			0
$569$	3.15767	+	5.46925i	0.132376	+	0.229283i	0.924592	−	0.380958i	$-0.124406\pi$
$569$	3.15767	+	5.46925i	0.132376	+	0.229283i	−0.792216	+	0.610241i	$0.791073\pi$
$570$		0			0
$571$	−24.4924			−1.02498			−0.512488	−	0.858694i	$-0.671276\pi$
$571$	−24.4924			−1.02498			−0.512488	+	0.858694i	$0.671276\pi$
$572$		0			0
$573$	−11.0540			−0.461786
$574$		0			0
$575$	14.1577	+	24.5218i	0.590416	+	1.02263i
$576$		0			0
$577$		−	31.5616i		−	1.31392i	−0.753923	−	0.656962i	$-0.771841\pi$
$577$		−	31.5616i		−	1.31392i	0.753923	−	0.656962i	$-0.228159\pi$
$578$		0			0
$579$	6.65511	+	3.84233i	0.276577	+	0.159682i
$580$		0			0
$581$	2.87689	−	4.98293i	0.119354	−	0.206727i
$582$		0			0
$583$	−9.84612	+	5.68466i	−0.407785	+	0.235434i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.0645	+	6.96543i	−0.497955	+	0.287494i	−0.727869	−	0.685717i	$-0.759489\pi$
$587$	−12.0645	+	6.96543i	−0.497955	+	0.287494i	0.229914	+	0.973211i	$0.426156\pi$
$588$		0			0
$589$	10.2462	−	17.7470i	0.422188	−	0.731251i
$590$		0			0
$591$	−5.13628	−	2.96543i	−0.211278	−	0.121982i
$592$		0			0
$593$			23.5616i			0.967557i	0.875190	+	0.483779i	$0.160736\pi$
$593$			23.5616i			0.967557i	−0.875190	+	0.483779i	$0.839264\pi$
$594$		0			0
$595$	−22.8078	−	39.5042i	−0.935027	−	1.61951i
$596$		0			0
$597$	−24.1771			−0.989502
$598$		0			0
$599$	−22.7386			−0.929075			−0.464538	−	0.885553i	$-0.653779\pi$
$599$	−22.7386			−0.929075			−0.464538	+	0.885553i	$0.653779\pi$
$600$		0			0
$601$	18.9924	+	32.8958i	0.774717	+	1.34185i	0.934953	+	0.354771i	$0.115441\pi$
$601$	18.9924	+	32.8958i	0.774717	+	1.34185i	−0.160236	+	0.987079i	$0.551226\pi$
$602$		0			0
$603$		−	33.6155i		−	1.36893i
$604$		0			0
$605$	13.6899	+	7.90388i	0.556575	+	0.321339i
$606$		0			0
$607$	−15.8423	+	27.4397i	−0.643020	+	1.11374i	0.341735	+	0.939796i	$0.388986\pi$
$607$	−15.8423	+	27.4397i	−0.643020	+	1.11374i	−0.984755	+	0.173947i	$0.944348\pi$
$608$		0			0
$609$	−28.4124	+	16.4039i	−1.15133	+	0.664719i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−7.79423	+	4.50000i	−0.314806	+	0.181753i	−0.649075	−	0.760724i	$-0.724844\pi$
$613$	−7.79423	+	4.50000i	−0.314806	+	0.181753i	0.334269	+	0.942478i	$0.391511\pi$
$614$		0			0
$615$	−42.1771	+	73.0528i	−1.70074	+	2.94578i
$616$		0			0
$617$	−7.58100	−	4.37689i	−0.305200	−	0.176207i	0.339577	−	0.940578i	$-0.389716\pi$
$617$	−7.58100	−	4.37689i	−0.305200	−	0.176207i	−0.644776	+	0.764371i	$0.723050\pi$
$618$		0			0
$619$		−	36.9848i		−	1.48655i	−0.668988	−	0.743273i	$-0.733272\pi$
$619$		−	36.9848i		−	1.48655i	0.668988	−	0.743273i	$-0.266728\pi$
$620$		0			0
$621$	−2.65009	−	4.59010i	−0.106345	−	0.184194i
$622$		0			0
$623$	−24.8078			−0.993902
$624$		0			0
$625$	−4.36932			−0.174773
$626$		0			0
$627$	8.40388	+	14.5560i	0.335619	+	0.581309i
$628$		0			0
$629$			5.00000i			0.199363i
$630$		0			0
$631$	−23.4294	−	13.5270i	−0.932711	−	0.538501i	−0.0450430	−	0.998985i	$-0.514342\pi$
$631$	−23.4294	−	13.5270i	−0.932711	−	0.538501i	−0.887668	+	0.460484i	$0.847676\pi$
$632$		0			0
$633$	−15.7732	+	27.3200i	−0.626928	+	1.08587i
$634$		0			0
$635$	39.5042	−	22.8078i	1.56768	−	0.905099i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	23.7025	−	13.6847i	0.937657	−	0.541357i
$640$		0			0
$641$	15.7462	−	27.2732i	0.621938	−	1.07723i	−0.367187	−	0.930147i	$-0.619679\pi$
$641$	15.7462	−	27.2732i	0.621938	−	1.07723i	0.989124	−	0.147081i	$-0.0469877\pi$
$642$		0			0
$643$	28.8388	+	16.6501i	1.13729	+	0.656616i	0.945758	−	0.324871i	$-0.105321\pi$
$643$	28.8388	+	16.6501i	1.13729	+	0.656616i	0.191533	+	0.981486i	$0.438654\pi$
$644$		0			0
$645$		−	59.8617i		−	2.35705i
$646$		0			0
$647$	−2.96543	−	5.13628i	−0.116583	−	0.201928i	0.801828	−	0.597555i	$-0.203861\pi$
$647$	−2.96543	−	5.13628i	−0.116583	−	0.201928i	−0.918412	+	0.395626i	$0.870528\pi$
$648$		0			0
$649$	6.56155			0.257563
$650$		0			0
$651$	52.4924			2.05734
$652$		0			0
$653$	−22.7732	−	39.4443i	−0.891184	−	1.54358i	−0.838457	−	0.544967i	$-0.816542\pi$
$653$	−22.7732	−	39.4443i	−0.891184	−	1.54358i	−0.0527268	−	0.998609i	$-0.516791\pi$
$654$		0			0
$655$		−	64.9848i		−	2.53917i
$656$		0			0
$657$	−4.05703	−	2.34233i	−0.158280	−	0.0913830i
$658$		0			0
$659$	−8.71922	+	15.1021i	−0.339653	+	0.588296i	−0.984367	−	0.176128i	$-0.943643\pi$
$659$	−8.71922	+	15.1021i	−0.339653	+	0.588296i	0.644715	+	0.764423i	$0.276976\pi$
$660$		0			0
$661$	37.8788	−	21.8693i	1.47331	−	0.850618i	0.473764	−	0.880652i	$-0.342895\pi$
$661$	37.8788	−	21.8693i	1.47331	−	0.850618i	0.999549	+	0.0300338i	$0.00956148\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−20.2384	+	11.6847i	−0.784812	+	0.453112i
$666$		0			0
$667$	9.21165	−	15.9550i	0.356676	−	0.617782i
$668$		0			0
$669$	8.17394	+	4.71922i	0.316023	+	0.182456i
$670$		0			0
$671$			18.5616i			0.716561i
$672$		0			0
$673$	0.376894	+	0.652800i	0.0145282	+	0.0251636i	0.873198	−	0.487365i	$-0.162042\pi$
$673$	0.376894	+	0.652800i	0.0145282	+	0.0251636i	−0.858670	+	0.512529i	$0.828709\pi$
$674$		0			0
$675$	−11.0540			−0.425468
$676$		0			0
$677$	20.7386			0.797050			0.398525	−	0.917157i	$-0.369522\pi$
$677$	20.7386			0.797050			0.398525	+	0.917157i	$0.369522\pi$
$678$		0			0
$679$	3.59612	+	6.22866i	0.138006	+	0.239034i
$680$		0			0
$681$		−	18.0691i		−	0.692411i
$682$		0			0
$683$	17.0474	+	9.84233i	0.652301	+	0.376606i	0.789337	−	0.613960i	$-0.210424\pi$
$683$	17.0474	+	9.84233i	0.652301	+	0.376606i	−0.137036	+	0.990566i	$0.543758\pi$
$684$		0			0
$685$	−38.2732	+	66.2911i	−1.46234	+	2.53285i
$686$		0			0
$687$	9.41967	−	5.43845i	0.359383	−	0.207490i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−18.5662	+	10.7192i	−0.706293	+	0.407778i	−0.809687	−	0.586862i	$-0.800363\pi$
$691$	−18.5662	+	10.7192i	−0.706293	+	0.407778i	0.103394	+	0.994640i	$0.467030\pi$
$692$		0			0
$693$	−11.6847	+	20.2384i	−0.443863	+	0.768794i
$694$		0			0
$695$	60.7153	+	35.0540i	2.30306	+	1.32967i
$696$		0			0
$697$			46.2311i			1.75113i
$698$		0			0
$699$	5.43845	+	9.41967i	0.205701	+	0.356285i
$700$		0			0
$701$	16.7386			0.632209			0.316105	−	0.948724i	$-0.397625\pi$
$701$	16.7386			0.632209			0.316105	+	0.948724i	$0.397625\pi$
$702$		0			0
$703$	2.56155			0.0966108
$704$		0			0
$705$	18.2462	+	31.6034i	0.687192	+	1.19025i
$706$		0			0
$707$		−	13.4384i		−	0.505405i
$708$		0			0
$709$	−13.6301	−	7.86932i	−0.511888	−	0.295538i	0.221722	−	0.975110i	$-0.428832\pi$
$709$	−13.6301	−	7.86932i	−0.511888	−	0.295538i	−0.733609	+	0.679572i	$0.762166\pi$
$710$		0			0
$711$	7.12311	−	12.3376i	0.267137	−	0.462695i
$712$		0			0
$713$	−25.5281	+	14.7386i	−0.956033	+	0.551966i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.89055	−	2.24621i	0.145295	−	0.0838863i
$718$		0			0
$719$	−7.03457	+	12.1842i	−0.262345	+	0.454395i	−0.966865	−	0.255290i	$-0.917829\pi$
$719$	−7.03457	+	12.1842i	−0.262345	+	0.454395i	0.704520	+	0.709685i	$0.251163\pi$
$720$		0			0
$721$	31.6034	+	18.2462i	1.17697	+	0.679524i
$722$		0			0
$723$			65.3002i			2.42854i
$724$		0			0
$725$	−19.2116	−	33.2755i	−0.713503	−	1.23582i
$726$		0			0
$727$	42.7386			1.58509			0.792544	−	0.609815i	$-0.208756\pi$
$727$	42.7386			1.58509			0.792544	+	0.609815i	$0.208756\pi$
$728$		0			0
$729$	−35.9848			−1.33277
$730$		0			0
$731$	−16.4039	−	28.4124i	−0.606719	−	1.05087i
$732$		0			0
$733$		−	21.8078i		−	0.805488i	−0.915313	−	0.402744i	$-0.868056\pi$
$733$		−	21.8078i		−	0.805488i	0.915313	−	0.402744i	$-0.131944\pi$
$734$		0			0
$735$	3.46410	+	2.00000i	0.127775	+	0.0737711i
$736$		0			0
$737$	12.0885	−	20.9380i	0.445287	−	0.771260i
$738$		0			0
$739$	−15.6483	+	9.03457i	−0.575633	+	0.332342i	−0.759396	−	0.650629i	$-0.774505\pi$
$739$	−15.6483	+	9.03457i	−0.575633	+	0.332342i	0.183763	+	0.982971i	$0.441172\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−32.8491	+	18.9654i	−1.20512	+	0.695774i	−0.961688	−	0.274145i	$-0.911605\pi$
$743$	−32.8491	+	18.9654i	−1.20512	+	0.695774i	−0.243428	+	0.969919i	$0.578272\pi$
$744$		0			0
$745$	−23.5885	+	40.8566i	−0.864217	+	1.49687i
$746$		0			0
$747$	−6.92820	−	4.00000i	−0.253490	−	0.146352i
$748$		0			0
$749$		−	9.43845i		−	0.344873i
$750$		0			0
$751$	2.65009	+	4.59010i	0.0967033	+	0.167495i	0.910318	−	0.413909i	$-0.135837\pi$
$751$	2.65009	+	4.59010i	0.0967033	+	0.167495i	−0.813615	+	0.581404i	$0.802504\pi$
$752$		0			0
$753$	−76.6695			−2.79399
$754$		0			0
$755$	44.4924			1.61925
$756$		0			0
$757$	−26.7732	−	46.3725i	−0.973088	−	1.68544i	−0.686104	−	0.727503i	$-0.740681\pi$
$757$	−26.7732	−	46.3725i	−0.973088	−	1.68544i	−0.286984	−	0.957935i	$-0.592653\pi$
$758$		0			0
$759$		−	24.1771i		−	0.877572i
$760$		0			0
$761$	−44.9735	−	25.9654i	−1.63029	−	0.941246i	−0.984004	−	0.178148i	$-0.942989\pi$
$761$	−44.9735	−	25.9654i	−1.63029	−	0.941246i	−0.646283	−	0.763098i	$-0.723677\pi$
$762$		0			0
$763$	10.5616	−	18.2931i	0.382354	−	0.662256i
$764$		0			0
$765$	−54.9262	+	31.7116i	−1.98586	+	1.14654i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−24.1888	+	13.9654i	−0.872272	+	0.503606i	−0.868103	−	0.496385i	$-0.834660\pi$
$769$	−24.1888	+	13.9654i	−0.872272	+	0.503606i	−0.00416940	+	0.999991i	$0.501327\pi$
$770$		0			0
$771$	−14.4039	+	24.9483i	−0.518743	+	0.898489i
$772$		0			0
$773$	−47.4649	−	27.4039i	−1.70719	−	0.985649i	−0.938001	−	0.346633i	$-0.887325\pi$
$773$	−47.4649	−	27.4039i	−1.70719	−	0.985649i	−0.769194	−	0.639016i	$-0.779342\pi$
$774$		0			0
$775$			61.4773i			2.20833i
$776$		0			0
$777$	3.28078	+	5.68247i	0.117697	+	0.203858i
$778$		0			0
$779$	23.6847			0.848591
$780$		0			0
$781$	19.6847			0.704372
$782$		0			0
$783$	3.59612	+	6.22866i	0.128515	+	0.222594i
$784$		0			0
$785$			63.4233i			2.26367i
$786$		0			0
$787$	29.8114	+	17.2116i	1.06266	+	0.613529i	0.926168	−	0.377112i	$-0.123083\pi$
$787$	29.8114	+	17.2116i	1.06266	+	0.613529i	0.136496	+	0.990641i	$0.456416\pi$
$788$		0			0
$789$	−11.2808	+	19.5389i	−0.401606	+	0.695602i
$790$		0			0
$791$	20.5115	−	11.8423i	0.729306	−	0.421065i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−35.0675	+	20.2462i	−1.24371	+	0.718059i
$796$		0			0
$797$	−7.96543	+	13.7965i	−0.282150	+	0.488698i	−0.971914	−	0.235336i	$-0.924381\pi$
$797$	−7.96543	+	13.7965i	−0.282150	+	0.488698i	0.689764	+	0.724034i	$0.257714\pi$
$798$		0			0
$799$	17.3205	+	10.0000i	0.612756	+	0.353775i
$800$		0			0
$801$			34.4924i			1.21873i
$802$		0			0
$803$	−1.68466	−	2.91791i	−0.0594503	−	0.102971i
$804$		0			0
$805$	33.6155			1.18479
$806$		0			0
$807$	37.9309			1.33523
$808$		0			0
$809$	3.37689	+	5.84895i	0.118725	+	0.205638i	0.919263	−	0.393644i	$-0.128786\pi$
$809$	3.37689	+	5.84895i	0.118725	+	0.205638i	−0.800537	+	0.599283i	$0.795453\pi$
$810$		0			0
$811$			8.00000i			0.280918i	0.990086	+	0.140459i	$0.0448578\pi$
$811$			8.00000i			0.280918i	−0.990086	+	0.140459i	$0.955142\pi$
$812$		0			0
$813$	−12.0645	−	6.96543i	−0.423120	−	0.244288i
$814$		0			0
$815$	10.5616	−	18.2931i	0.369955	−	0.640781i
$816$		0			0
$817$	−14.5560	+	8.40388i	−0.509248	+	0.294015i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.89570	−	3.40388i	0.205761	−	0.118796i	−0.393579	−	0.919291i	$-0.628763\pi$
$821$	5.89570	−	3.40388i	0.205761	−	0.118796i	0.599340	+	0.800495i	$0.295430\pi$
$822$		0			0
$823$	22.0885	−	38.2585i	0.769958	−	1.33361i	−0.167627	−	0.985851i	$-0.553610\pi$
$823$	22.0885	−	38.2585i	0.769958	−	1.33361i	0.937585	−	0.347756i	$-0.113056\pi$
$824$		0			0
$825$	−43.6679	−	25.2116i	−1.52032	−	0.877757i
$826$		0			0
$827$		−	28.9848i		−	1.00790i	−0.863732	−	0.503951i	$-0.831879\pi$
$827$		−	28.9848i		−	1.00790i	0.863732	−	0.503951i	$-0.168121\pi$
$828$		0			0
$829$	19.7462	+	34.2014i	0.685814	+	1.18787i	0.973180	+	0.230044i	$0.0738871\pi$
$829$	19.7462	+	34.2014i	0.685814	+	1.18787i	−0.287366	+	0.957821i	$0.592780\pi$
$830$		0			0
$831$	−28.1771			−0.977452
$832$		0			0
$833$	2.19224			0.0759565
$834$		0			0
$835$	−9.68466	−	16.7743i	−0.335151	−	0.580499i
$836$		0			0
$837$		−	11.5076i		−	0.397760i
$838$		0			0
$839$	34.3679	+	19.8423i	1.18651	+	0.685033i	0.957512	−	0.288393i	$-0.0931210\pi$
$839$	34.3679	+	19.8423i	1.18651	+	0.685033i	0.229000	+	0.973426i	$0.426454\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$		0			0
$843$	−32.5760	+	18.8078i	−1.12198	+	0.647774i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	9.84612	−	5.68466i	0.338317	−	0.195327i
$848$		0			0
$849$	−27.4579	+	47.5584i	−0.942351	+	1.63220i
$850$		0			0
$851$	−3.19101	−	1.84233i	−0.109386	−	0.0631542i
$852$		0			0
$853$		−	13.4233i		−	0.459605i	−0.973237	−	0.229802i	$-0.926192\pi$
$853$		−	13.4233i		−	0.459605i	0.973237	−	0.229802i	$-0.0738080\pi$
$854$		0			0
$855$	16.2462	+	28.1393i	0.555609	+	0.962343i
$856$		0			0
$857$	52.0540			1.77813			0.889065	−	0.457781i	$-0.151356\pi$
$857$	52.0540			1.77813			0.889065	+	0.457781i	$0.151356\pi$
$858$		0			0
$859$	−5.75379			−0.196317			−0.0981584	−	0.995171i	$-0.531295\pi$
$859$	−5.75379			−0.196317			−0.0981584	+	0.995171i	$0.531295\pi$
$860$		0			0
$861$	30.3348	+	52.5413i	1.03381	+	1.79060i
$862$		0			0
$863$		−	38.2462i		−	1.30192i	−0.759114	−	0.650958i	$-0.774367\pi$
$863$		−	38.2462i		−	1.30192i	0.759114	−	0.650958i	$-0.225633\pi$
$864$		0			0
$865$	49.1371	+	28.3693i	1.67071	+	0.964586i
$866$		0			0
$867$	−10.2462	+	17.7470i	−0.347980	+	0.602718i
$868$		0			0
$869$	8.87348	−	5.12311i	0.301012	−	0.173789i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	8.66025	−	5.00000i	0.293105	−	0.169224i
$874$		0			0
$875$	12.2462	−	21.2111i	0.413998	−	0.717065i
$876$		0			0
$877$	−8.43390	−	4.86932i	−0.284793	−	0.164425i	0.350798	−	0.936451i	$-0.385910\pi$
$877$	−8.43390	−	4.86932i	−0.284793	−	0.164425i	−0.635591	+	0.772026i	$0.719244\pi$
$878$		0			0
$879$		−	29.4384i		−	0.992934i
$880$		0			0
$881$	0.623106	+	1.07925i	0.0209930	+	0.0363609i	0.876331	−	0.481709i	$-0.159984\pi$
$881$	0.623106	+	1.07925i	0.0209930	+	0.0363609i	−0.855338	+	0.518070i	$0.826651\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	23.3693			0.785551
$886$		0			0
$887$	−4.15767	−	7.20130i	−0.139601	−	0.241796i	0.787745	−	0.616002i	$-0.211249\pi$
$887$	−4.15767	−	7.20130i	−0.139601	−	0.241796i	−0.927346	+	0.374206i	$0.877915\pi$
$888$		0			0
$889$		−	32.8078i		−	1.10034i
$890$		0			0
$891$	−15.5286	−	8.96543i	−0.520227	−	0.300353i
$892$		0			0
$893$	5.12311	−	8.87348i	0.171438	−	0.296940i
$894$		0			0
$895$	13.3102	−	7.68466i	0.444912	−	0.256870i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	34.6410	−	20.0000i	1.15534	−	0.667037i
$900$		0			0
$901$	−11.0961	+	19.2190i	−0.369665	+	0.640279i
$902$		0			0
$903$	−37.2858	−	21.5270i	−1.24079	−	0.716373i
$904$		0			0
$905$		−	34.9309i		−	1.16114i
$906$		0			0
$907$	6.65009	+	11.5183i	0.220813	+	0.382459i	0.955055	−	0.296429i	$-0.0957957\pi$
$907$	6.65009	+	11.5183i	0.220813	+	0.382459i	−0.734242	+	0.678888i	$0.762462\pi$
$908$		0			0
$909$	−18.6847			−0.619731
$910$		0			0
$911$	18.7386			0.620839			0.310419	−	0.950600i	$-0.399531\pi$
$911$	18.7386			0.620839			0.310419	+	0.950600i	$0.399531\pi$
$912$		0			0
$913$	−2.87689	−	4.98293i	−0.0952113	−	0.164911i
$914$		0			0
$915$			66.1080i			2.18546i
$916$		0			0
$917$	−40.4768	−	23.3693i	−1.33666	−	0.771723i
$918$		0			0
$919$	5.77320	−	9.99947i	0.190440	−	0.329852i	−0.754956	−	0.655775i	$-0.772342\pi$
$919$	5.77320	−	9.99947i	0.190440	−	0.329852i	0.945396	+	0.325923i	$0.105675\pi$
$920$		0			0
$921$	58.2238	−	33.6155i	1.91854	−	1.10767i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−6.65511	+	3.84233i	−0.218819	+	0.126335i
$926$		0			0
$927$	25.3693	−	43.9409i	0.833238	−	1.44321i
$928$		0			0
$929$	−24.2356	−	13.9924i	−0.795144	−	0.459076i	0.0466265	−	0.998912i	$-0.485153\pi$
$929$	−24.2356	−	13.9924i	−0.795144	−	0.459076i	−0.841770	+	0.539836i	$0.818486\pi$
$930$		0			0
$931$		−	1.12311i		−	0.0368083i
$932$		0			0
$933$	−18.2462	−	31.6034i	−0.597354	−	1.03465i
$934$		0			0
$935$	−45.6155			−1.49179
$936$		0			0
$937$	−1.31534			−0.0429703			−0.0214852	−	0.999769i	$-0.506839\pi$
$937$	−1.31534			−0.0429703			−0.0214852	+	0.999769i	$0.506839\pi$
$938$		0			0
$939$	41.3002	+	71.5340i	1.34778	+	2.33442i
$940$		0			0
$941$			14.0000i			0.456387i	0.973616	+	0.228193i	$0.0732819\pi$
$941$			14.0000i			0.456387i	−0.973616	+	0.228193i	$0.926718\pi$
$942$		0			0
$943$	−29.5047	−	17.0346i	−0.960806	−	0.554722i
$944$		0			0
$945$	−6.56155	+	11.3649i	−0.213447	+	0.369702i
$946$		0			0
$947$	40.2038	−	23.2116i	1.30645	−	0.754277i	0.324945	−	0.945733i	$-0.394654\pi$
$947$	40.2038	−	23.2116i	1.30645	−	0.754277i	0.981501	+	0.191456i	$0.0613208\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	36.4666	−	21.0540i	1.18251	−	0.682722i
$952$		0			0
$953$	−2.59612	+	4.49661i	−0.0840965	+	0.145659i	−0.905006	−	0.425399i	$-0.860134\pi$
$953$	−2.59612	+	4.49661i	−0.0840965	+	0.145659i	0.820909	+	0.571059i	$0.193467\pi$
$954$		0			0
$955$	−13.3102	−	7.68466i	−0.430709	−	0.248670i
$956$		0			0
$957$			32.8078i			1.06052i
$958$		0			0
$959$	27.5270	+	47.6781i	0.888893	+	1.53961i
$960$		0			0
$961$	−33.0000			−1.06452
$962$		0			0
$963$	−13.1231			−0.422886
$964$		0			0
$965$	5.34233	+	9.25319i	0.171976	+	0.297871i
$966$		0			0
$967$			22.2462i			0.715390i	0.933838	+	0.357695i	$0.116437\pi$
$967$			22.2462i			0.715390i	−0.933838	+	0.357695i	$0.883563\pi$
$968$		0			0
$969$	28.4124	+	16.4039i	0.912736	+	0.526969i
$970$		0			0
$971$	−15.8423	+	27.4397i	−0.508405	+	0.880582i	0.491548	+	0.870850i	$0.336431\pi$
$971$	−15.8423	+	27.4397i	−0.508405	+	0.880582i	−0.999953	+	0.00973207i	$0.996902\pi$
$972$		0			0
$973$	43.6679	−	25.2116i	1.39993	−	0.808248i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.2036	+	7.62311i	−0.422421	+	0.243885i	−0.696113	−	0.717933i	$-0.745089\pi$
$977$	−13.2036	+	7.62311i	−0.422421	+	0.243885i	0.273692	+	0.961817i	$0.411755\pi$
$978$		0			0
$979$	−12.4039	+	21.4842i	−0.396430	+	0.686637i
$980$		0			0
$981$	−25.4346	−	14.6847i	−0.812063	−	0.468845i
$982$		0			0
$983$		−	40.9848i		−	1.30721i	−0.756834	−	0.653607i	$-0.773255\pi$
$983$		−	40.9848i		−	1.30721i	0.756834	−	0.653607i	$-0.226745\pi$
$984$		0			0
$985$	−4.12311	−	7.14143i	−0.131373	−	0.227545i
$986$		0			0
$987$	26.2462			0.835426
$988$		0			0
$989$	24.1771			0.768786
$990$		0			0
$991$	−28.6501	−	49.6234i	−0.910100	−	1.57634i	−0.813921	−	0.580976i	$-0.802671\pi$
$991$	−28.6501	−	49.6234i	−0.910100	−	1.57634i	−0.0961794	−	0.995364i	$-0.530662\pi$
$992$		0			0
$993$			56.1771i			1.78273i
$994$		0			0
$995$	−29.1119	−	16.8078i	−0.922909	−	0.532842i
$996$		0			0
$997$	13.3769	−	23.1695i	0.423650	−	0.733784i	−0.572643	−	0.819805i	$-0.694082\pi$
$997$	13.3769	−	23.1695i	0.423650	−	0.733784i	0.996293	+	0.0860208i	$0.0274151\pi$
$998$		0			0
$999$	1.24573	−	0.719224i	0.0394132	−	0.0227552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.o.c.361.1		8
13.2	odd	12		1352.2.a.f.1.2		2
13.3	even	3		1352.2.f.d.337.3		4
13.4	even	6	inner	1352.2.o.c.1161.2		8
13.5	odd	4		104.2.i.b.81.1	yes	4
13.6	odd	12		104.2.i.b.9.1	✓	4
13.7	odd	12		1352.2.i.e.529.1		4
13.8	odd	4		1352.2.i.e.1329.1		4
13.9	even	3	inner	1352.2.o.c.1161.1		8
13.10	even	6		1352.2.f.d.337.4		4
13.11	odd	12		1352.2.a.h.1.2		2
13.12	even	2	inner	1352.2.o.c.361.2		8
39.5	even	4		936.2.t.f.289.2		4
39.32	even	12		936.2.t.f.217.2		4
52.3	odd	6		2704.2.f.l.337.1		4
52.11	even	12		2704.2.a.r.1.1		2
52.15	even	12		2704.2.a.q.1.1		2
52.19	even	12		208.2.i.e.113.2		4
52.23	odd	6		2704.2.f.l.337.2		4
52.31	even	4		208.2.i.e.81.2		4
104.5	odd	4		832.2.i.o.705.2		4
104.19	even	12		832.2.i.l.321.1		4
104.45	odd	12		832.2.i.o.321.2		4
104.83	even	4		832.2.i.l.705.1		4
156.71	odd	12		1872.2.t.s.1153.2		4
156.83	odd	4		1872.2.t.s.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.i.b.9.1	✓	4	13.6	odd	12
104.2.i.b.81.1	yes	4	13.5	odd	4
208.2.i.e.81.2		4	52.31	even	4
208.2.i.e.113.2		4	52.19	even	12
832.2.i.l.321.1		4	104.19	even	12
832.2.i.l.705.1		4	104.83	even	4
832.2.i.o.321.2		4	104.45	odd	12
832.2.i.o.705.2		4	104.5	odd	4
936.2.t.f.217.2		4	39.32	even	12
936.2.t.f.289.2		4	39.5	even	4
1352.2.a.f.1.2		2	13.2	odd	12
1352.2.a.h.1.2		2	13.11	odd	12
1352.2.f.d.337.3		4	13.3	even	3
1352.2.f.d.337.4		4	13.10	even	6
1352.2.i.e.529.1		4	13.7	odd	12
1352.2.i.e.1329.1		4	13.8	odd	4
1352.2.o.c.361.1		8	1.1	even	1	trivial
1352.2.o.c.361.2		8	13.12	even	2	inner
1352.2.o.c.1161.1		8	13.9	even	3	inner
1352.2.o.c.1161.2		8	13.4	even	6	inner
1872.2.t.s.289.2		4	156.83	odd	4
1872.2.t.s.1153.2		4	156.71	odd	12
2704.2.a.q.1.1		2	52.15	even	12
2704.2.a.r.1.1		2	52.11	even	12
2704.2.f.l.337.1		4	52.3	odd	6
2704.2.f.l.337.2		4	52.23	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28078 - 2.21837i) q^{3} -3.56155i q^{5} +(-2.21837 - 1.28078i) q^{7} +(-1.78078 + 3.08440i) q^{9} +(-2.21837 + 1.28078i) q^{11} +(-7.90084 + 4.56155i) q^{15} +(-2.50000 + 4.33013i) q^{17} +(2.21837 + 1.28078i) q^{19} +6.56155i q^{21} +(-1.84233 - 3.19101i) q^{23} -7.68466 q^{25} +1.43845 q^{27} +(2.50000 + 4.33013i) q^{29} -8.00000i q^{31} +(5.68247 + 3.28078i) q^{33} +(-4.56155 + 7.90084i) q^{35} +(0.866025 - 0.500000i) q^{37} +(8.00745 - 4.62311i) q^{41} +(-3.28078 + 5.68247i) q^{43} +(10.9852 + 6.34233i) q^{45} -4.00000i q^{47} +(-0.219224 - 0.379706i) q^{49} +12.8078 q^{51} +4.43845 q^{53} +(4.56155 + 7.90084i) q^{55} -6.56155i q^{57} +(-2.21837 - 1.28078i) q^{59} +(3.62311 - 6.27540i) q^{61} +(7.90084 - 4.56155i) q^{63} +(-8.17394 + 4.71922i) q^{67} +(-4.71922 + 8.17394i) q^{69} +(-6.65511 - 3.84233i) q^{71} +1.31534i q^{73} +(9.84233 + 17.0474i) q^{75} +6.56155 q^{77} -4.00000 q^{79} +(3.50000 + 6.06218i) q^{81} +2.24621i q^{83} +(15.4220 + 8.90388i) q^{85} +(6.40388 - 11.0918i) q^{87} +(8.38716 - 4.84233i) q^{89} +(-17.7470 + 10.2462i) q^{93} +(4.56155 - 7.90084i) q^{95} +(-2.43160 - 1.40388i) q^{97} -9.12311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 6 q^{9} - 20 q^{17} + 10 q^{23} - 12 q^{25} + 28 q^{27} + 20 q^{29} - 20 q^{35} - 18 q^{43} - 10 q^{49} + 20 q^{51} + 52 q^{53} + 20 q^{55} - 4 q^{61} - 46 q^{69} + 54 q^{75} + 36 q^{77}+ \cdots + 20 q^{95}+O(q^{100}) \) 8 * q - 2 * q^3 - 6 * q^9 - 20 * q^17 + 10 * q^23 - 12 * q^25 + 28 * q^27 + 20 * q^29 - 20 * q^35 - 18 * q^43 - 10 * q^49 + 20 * q^51 + 52 * q^53 + 20 * q^55 - 4 * q^61 - 46 * q^69 + 54 * q^75 + 36 * q^77 - 32 * q^79 + 28 * q^81 + 10 * q^87 + 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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