LMFDB - Embedded newform 676.2.h.e.361.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [676,2,Mod(361,676)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("676.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(676, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.6
Root			$0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	676.361
Dual form			676.2.h.e.485.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52446 + 2.64044i) q^{3} +2.55496i q^{5} +(-2.73563 - 1.57942i) q^{7} +(-3.14795 + 5.45241i) q^{9} +(0.908389 - 0.524459i) q^{11} +(-6.74621 + 3.89493i) q^{15} +(-1.04407 + 1.80839i) q^{17} +(-2.13632 - 1.23341i) q^{19} -9.63102i q^{21} +(2.19202 + 3.79669i) q^{23} -1.52781 q^{25} -10.0489 q^{27} +(1.57942 + 2.73563i) q^{29} +4.93900i q^{31} +(2.76960 + 1.59903i) q^{33} +(4.03534 - 6.98942i) q^{35} +(-7.41720 + 4.28232i) q^{37} +(9.95406 - 5.74698i) q^{41} +(6.36443 - 11.0235i) q^{43} +(-13.9307 - 8.04288i) q^{45} -3.54288i q^{47} +(1.48911 + 2.57922i) q^{49} -6.36658 q^{51} -8.45473 q^{53} +(1.33997 + 2.32090i) q^{55} -7.52111i q^{57} +(10.8096 + 6.24094i) q^{59} +(-1.78836 + 3.09754i) q^{61} +(17.2232 - 9.94385i) q^{63} +(1.50770 - 0.870469i) q^{67} +(-6.68329 + 11.5758i) q^{69} +(4.06341 + 2.34601i) q^{71} +7.34481i q^{73} +(-2.32908 - 4.03409i) q^{75} -3.31336 q^{77} +6.73556 q^{79} +(-5.87531 - 10.1763i) q^{81} +2.19806i q^{83} +(-4.62035 - 2.66756i) q^{85} +(-4.81551 + 8.34071i) q^{87} +(-11.4194 + 6.59299i) q^{89} +(-13.0411 + 7.52930i) q^{93} +(3.15130 - 5.45821i) q^{95} +(11.4806 + 6.62833i) q^{97} +6.60388i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{9} - 20 q^{17} + 6 q^{23} - 44 q^{25} - 84 q^{27} + 2 q^{29} + 24 q^{35} + 10 q^{43} + 24 q^{49} + 28 q^{51} - 12 q^{53} - 32 q^{55} - 16 q^{61} - 28 q^{69} + 14 q^{75} - 48 q^{77} + 36 q^{79}+ \cdots + 54 q^{95}+O(q^{100}) $ 12 * q - 10 * q^9 - 20 * q^17 + 6 * q^23 - 44 * q^25 - 84 * q^27 + 2 * q^29 + 24 * q^35 + 10 * q^43 + 24 * q^49 + 28 * q^51 - 12 * q^53 - 32 * q^55 - 16 * q^61 - 28 * q^69 + 14 * q^75 - 48 * q^77 + 36 * q^79 + 2 * q^81 - 28 * q^87 + 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.52446	+	2.64044i	0.880147	+	1.52446i	0.851177	+	0.524878i	$0.175889\pi$
$3$	1.52446	+	2.64044i	0.880147	+	1.52446i	0.0289694	+	0.999580i	$0.490777\pi$
$4$		0			0
$5$			2.55496i			1.14261i	0.820737	+	0.571306i	$0.193563\pi$
$5$			2.55496i			1.14261i	−0.820737	+	0.571306i	$0.806437\pi$
$6$		0			0
$7$	−2.73563	−	1.57942i	−1.03397	−	0.596963i	−0.115851	−	0.993267i	$-0.536960\pi$
$7$	−2.73563	−	1.57942i	−1.03397	−	0.596963i	−0.918120	+	0.396303i	$0.870293\pi$
$8$		0			0
$9$	−3.14795	+	5.45241i	−1.04932	+	1.81747i
$10$		0			0
$11$	0.908389	−	0.524459i	0.273890	−	0.158130i	−0.356764	−	0.934194i	$-0.616120\pi$
$11$	0.908389	−	0.524459i	0.273890	−	0.158130i	0.630654	+	0.776064i	$0.282787\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−6.74621	+	3.89493i	−1.74186	+	1.00567i
$16$		0			0
$17$	−1.04407	+	1.80839i	−0.253225	+	0.438598i	−0.964412	−	0.264405i	$-0.914825\pi$
$17$	−1.04407	+	1.80839i	−0.253225	+	0.438598i	0.711187	+	0.703003i	$0.248158\pi$
$18$		0			0
$19$	−2.13632	−	1.23341i	−0.490106	−	0.282963i	0.234513	−	0.972113i	$-0.424651\pi$
$19$	−2.13632	−	1.23341i	−0.490106	−	0.282963i	−0.724618	+	0.689150i	$0.757984\pi$
$20$		0			0
$21$		−	9.63102i		−	2.10166i
$22$		0			0
$23$	2.19202	+	3.79669i	0.457068	+	0.791665i	0.998804	−	0.0488833i	$-0.0155662\pi$
$23$	2.19202	+	3.79669i	0.457068	+	0.791665i	−0.541736	+	0.840548i	$0.682233\pi$
$24$		0			0
$25$	−1.52781			−0.305562
$26$		0			0
$27$	−10.0489			−1.93392
$28$		0			0
$29$	1.57942	+	2.73563i	0.293290	+	0.507994i	0.974586	−	0.224015i	$-0.0719164\pi$
$29$	1.57942	+	2.73563i	0.293290	+	0.507994i	−0.681295	+	0.732009i	$0.738583\pi$
$30$		0			0
$31$			4.93900i			0.887071i	0.896257	+	0.443535i	$0.146276\pi$
$31$			4.93900i			0.887071i	−0.896257	+	0.443535i	$0.853724\pi$
$32$		0			0
$33$	2.76960	+	1.59903i	0.482126	+	0.278356i
$34$		0			0
$35$	4.03534	−	6.98942i	0.682098	−	1.18143i
$36$		0			0
$37$	−7.41720	+	4.28232i	−1.21938	+	0.704010i	−0.964785	−	0.263038i	$-0.915275\pi$
$37$	−7.41720	+	4.28232i	−1.21938	+	0.704010i	−0.254595	+	0.967048i	$0.581942\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	9.95406	−	5.74698i	1.55456	−	0.897527i	0.556802	−	0.830645i	$-0.312028\pi$
$41$	9.95406	−	5.74698i	1.55456	−	0.897527i	0.997761	−	0.0668823i	$-0.0213052\pi$
$42$		0			0
$43$	6.36443	−	11.0235i	0.970566	−	1.68107i	0.276715	−	0.960952i	$-0.410754\pi$
$43$	6.36443	−	11.0235i	0.970566	−	1.68107i	0.693852	−	0.720118i	$-0.255912\pi$
$44$		0			0
$45$	−13.9307	−	8.04288i	−2.07666	−	1.19896i
$46$		0			0
$47$		−	3.54288i		−	0.516782i	−0.966040	−	0.258391i	$-0.916808\pi$
$47$		−	3.54288i		−	0.516782i	0.966040	−	0.258391i	$-0.0831922\pi$
$48$		0			0
$49$	1.48911	+	2.57922i	0.212731	+	0.368460i
$50$		0			0
$51$	−6.36658			−0.891500
$52$		0			0
$53$	−8.45473			−1.16135			−0.580673	−	0.814137i	$-0.697211\pi$
$53$	−8.45473			−1.16135			−0.580673	+	0.814137i	$0.697211\pi$
$54$		0			0
$55$	1.33997	+	2.32090i	0.180682	+	0.312950i
$56$		0			0
$57$		−	7.52111i		−	0.996195i
$58$		0			0
$59$	10.8096	+	6.24094i	1.40729	+	0.812501i	0.995126	−	0.0986074i	$-0.0314388\pi$
$59$	10.8096	+	6.24094i	1.40729	+	0.812501i	0.412167	+	0.911108i	$0.364772\pi$
$60$		0			0
$61$	−1.78836	+	3.09754i	−0.228977	+	0.396599i	−0.957505	−	0.288416i	$-0.906871\pi$
$61$	−1.78836	+	3.09754i	−0.228977	+	0.396599i	0.728528	+	0.685015i	$0.240205\pi$
$62$		0			0
$63$	17.2232	−	9.94385i	2.16992	−	1.25281i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.50770	−	0.870469i	0.184195	−	0.106345i	−0.405067	−	0.914287i	$-0.632752\pi$
$67$	1.50770	−	0.870469i	0.184195	−	0.106345i	0.589262	+	0.807942i	$0.299419\pi$
$68$		0			0
$69$	−6.68329	+	11.5758i	−0.804574	+	1.39356i
$70$		0			0
$71$	4.06341	+	2.34601i	0.482238	+	0.278420i	0.721349	−	0.692572i	$-0.243523\pi$
$71$	4.06341	+	2.34601i	0.482238	+	0.278420i	−0.239111	+	0.970992i	$0.576856\pi$
$72$		0			0
$73$			7.34481i			0.859645i	0.902913	+	0.429823i	$0.141424\pi$
$73$			7.34481i			0.859645i	−0.902913	+	0.429823i	$0.858576\pi$
$74$		0			0
$75$	−2.32908	−	4.03409i	−0.268940	−	0.465817i
$76$		0			0
$77$	−3.31336			−0.377592
$78$		0			0
$79$	6.73556			0.757810			0.378905	−	0.925436i	$-0.376301\pi$
$79$	6.73556			0.757810			0.378905	+	0.925436i	$0.376301\pi$
$80$		0			0
$81$	−5.87531	−	10.1763i	−0.652813	−	1.13070i
$82$		0			0
$83$			2.19806i			0.241269i	0.992697	+	0.120634i	$0.0384929\pi$
$83$			2.19806i			0.241269i	−0.992697	+	0.120634i	$0.961507\pi$
$84$		0			0
$85$	−4.62035	−	2.66756i	−0.501148	−	0.289338i
$86$		0			0
$87$	−4.81551	+	8.34071i	−0.516277	+	0.894218i
$88$		0			0
$89$	−11.4194	+	6.59299i	−1.21045	+	0.698856i	−0.962858	−	0.270008i	$-0.912974\pi$
$89$	−11.4194	+	6.59299i	−1.21045	+	0.698856i	−0.247595	+	0.968864i	$0.579640\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−13.0411	+	7.52930i	−1.35230	+	0.780752i
$94$		0			0
$95$	3.15130	−	5.45821i	0.323317	−	0.560001i
$96$		0			0
$97$	11.4806	+	6.62833i	1.16568	+	0.673005i	0.952659	−	0.304042i	$-0.0983364\pi$
$97$	11.4806	+	6.62833i	1.16568	+	0.673005i	0.213021	+	0.977048i	$0.431670\pi$
$98$		0			0
$99$			6.60388i			0.663714i
$100$		0			0
$101$	0.751824	+	1.30220i	0.0748093	+	0.129573i	0.901003	−	0.433812i	$-0.142832\pi$
$101$	0.751824	+	1.30220i	0.0748093	+	0.129573i	−0.826194	+	0.563386i	$0.809499\pi$
$102$		0			0
$103$	5.07069			0.499630			0.249815	−	0.968294i	$-0.419630\pi$
$103$	5.07069			0.499630			0.249815	+	0.968294i	$0.419630\pi$
$104$		0			0
$105$	24.6069			2.40138
$106$		0			0
$107$	2.26391	+	3.92120i	0.218860	+	0.379077i	0.954460	−	0.298340i	$-0.0964329\pi$
$107$	2.26391	+	3.92120i	0.218860	+	0.379077i	−0.735600	+	0.677416i	$0.763100\pi$
$108$		0			0
$109$			12.8659i			1.23233i	0.787616	+	0.616166i	$0.211315\pi$
$109$			12.8659i			1.23233i	−0.787616	+	0.616166i	$0.788685\pi$
$110$		0			0
$111$	−22.6144	−	13.0565i	−2.14647	−	1.23926i
$112$		0			0
$113$	7.73005	−	13.3888i	0.727182	−	1.25952i	−0.230887	−	0.972981i	$-0.574163\pi$
$113$	7.73005	−	13.3888i	0.727182	−	1.25952i	0.958069	−	0.286536i	$-0.0925038\pi$
$114$		0			0
$115$	−9.70039	+	5.60052i	−0.904566	+	0.522251i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.71240	−	3.29805i	0.523654	−	0.302332i
$120$		0			0
$121$	−4.94989	+	8.57345i	−0.449990	+	0.779405i
$122$		0			0
$123$	30.3491	+	17.5221i	2.73649	+	1.57991i
$124$		0			0
$125$			8.87130i			0.793473i
$126$		0			0
$127$	−5.52446	−	9.56864i	−0.490216	−	0.849080i	0.509720	−	0.860340i	$-0.329749\pi$
$127$	−5.52446	−	9.56864i	−0.490216	−	0.849080i	−0.999937	+	0.0112605i	$0.996416\pi$
$128$		0			0
$129$	38.8092			3.41696
$130$		0			0
$131$	6.84117			0.597715			0.298858	−	0.954298i	$-0.403394\pi$
$131$	6.84117			0.597715			0.298858	+	0.954298i	$0.403394\pi$
$132$		0			0
$133$	3.89612	+	6.74829i	0.337837	+	0.585151i
$134$		0			0
$135$		−	25.6746i		−	2.20971i
$136$		0			0
$137$	5.00577	+	2.89008i	0.427672	+	0.246917i	0.698354	−	0.715752i	$-0.253916\pi$
$137$	5.00577	+	2.89008i	0.427672	+	0.246917i	−0.270682	+	0.962669i	$0.587249\pi$
$138$		0			0
$139$	0.263906	−	0.457098i	0.0223842	−	0.0387705i	−0.854616	−	0.519260i	$-0.826208\pi$
$139$	0.263906	−	0.457098i	0.0223842	−	0.0387705i	0.877001	+	0.480489i	$0.159541\pi$
$140$		0			0
$141$	9.35475	−	5.40097i	0.787812	−	0.454844i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−6.98942	+	4.03534i	−0.580440	+	0.335117i
$146$		0			0
$147$	−4.54019	+	7.86384i	−0.374468	+	0.648598i
$148$		0			0
$149$	−17.2912	−	9.98307i	−1.41655	−	0.817845i	−0.420556	−	0.907267i	$-0.638165\pi$
$149$	−17.2912	−	9.98307i	−1.41655	−	0.817845i	−0.995994	+	0.0894214i	$0.971498\pi$
$150$		0			0
$151$		−	3.41550i		−	0.277950i	−0.990296	−	0.138975i	$-0.955619\pi$
$151$		−	3.41550i		−	0.277950i	0.990296	−	0.138975i	$-0.0443807\pi$
$152$		0			0
$153$	−6.57338	−	11.3854i	−0.531426	−	0.920457i
$154$		0			0
$155$	−12.6189			−1.01358
$156$		0			0
$157$	6.32304			0.504634			0.252317	−	0.967645i	$-0.418807\pi$
$157$	6.32304			0.504634			0.252317	+	0.967645i	$0.418807\pi$
$158$		0			0
$159$	−12.8889	−	22.3242i	−1.02216	−	1.77042i
$160$		0			0
$161$		−	13.8485i		−	1.09141i
$162$		0			0
$163$	−9.74483	−	5.62618i	−0.763274	−	0.440676i	0.0671962	−	0.997740i	$-0.478595\pi$
$163$	−9.74483	−	5.62618i	−0.763274	−	0.440676i	−0.830470	+	0.557063i	$0.811928\pi$
$164$		0			0
$165$	−4.08546	+	7.07622i	−0.318052	+	0.550883i
$166$		0			0
$167$	4.61570	−	2.66487i	0.357173	−	0.206214i	−0.310667	−	0.950519i	$-0.600552\pi$
$167$	4.61570	−	2.66487i	0.357173	−	0.206214i	0.667840	+	0.744305i	$0.267219\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	13.4501	−	7.76540i	1.02855	−	0.593835i
$172$		0			0
$173$	9.60388	−	16.6344i	0.730169	−	1.26469i	−0.226642	−	0.973978i	$-0.572775\pi$
$173$	9.60388	−	16.6344i	0.730169	−	1.26469i	0.956811	−	0.290712i	$-0.0938921\pi$
$174$		0			0
$175$	4.17953	+	2.41305i	0.315942	+	0.182409i
$176$		0			0
$177$			38.0562i			2.86048i
$178$		0			0
$179$	−2.81820	−	4.88127i	−0.210642	−	0.364843i	0.741274	−	0.671203i	$-0.234222\pi$
$179$	−2.81820	−	4.88127i	−0.210642	−	0.364843i	−0.951916	+	0.306360i	$0.900889\pi$
$180$		0			0
$181$	−3.96615			−0.294801			−0.147401	−	0.989077i	$-0.547091\pi$
$181$	−3.96615			−0.294801			−0.147401	+	0.989077i	$0.547091\pi$
$182$		0			0
$183$	−10.9051			−0.806132
$184$		0			0
$185$	−10.9412	−	18.9506i	−0.804410	−	1.39328i
$186$		0			0
$187$			2.19029i			0.160170i
$188$		0			0
$189$	27.4901	+	15.8714i	1.99961	+	1.15448i
$190$		0			0
$191$	10.4526	−	18.1044i	0.756322	−	1.30999i	−0.188393	−	0.982094i	$-0.560328\pi$
$191$	10.4526	−	18.1044i	0.756322	−	1.30999i	0.944715	−	0.327894i	$-0.106339\pi$
$192$		0			0
$193$	11.1045	−	6.41119i	0.799320	−	0.461488i	−0.0439134	−	0.999035i	$-0.513983\pi$
$193$	11.1045	−	6.41119i	0.799320	−	0.461488i	0.843233	+	0.537548i	$0.180649\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	15.5571	−	8.98188i	1.10840	−	0.639932i	0.169982	−	0.985447i	$-0.445629\pi$
$197$	15.5571	−	8.98188i	1.10840	−	0.639932i	0.938413	+	0.345515i	$0.112296\pi$
$198$		0			0
$199$	−6.83728	+	11.8425i	−0.484682	+	0.839494i	−0.999845	−	0.0175983i	$-0.994398\pi$
$199$	−6.83728	+	11.8425i	−0.484682	+	0.839494i	0.515163	+	0.857092i	$0.327731\pi$
$200$		0			0
$201$	4.59684	+	2.65399i	0.324236	+	0.187198i
$202$		0			0
$203$		−	9.97823i		−	0.700334i
$204$		0			0
$205$	14.6833	+	25.4322i	1.02553	+	1.77626i
$206$		0			0
$207$	−27.6015			−1.91844
$208$		0			0
$209$	−2.58748			−0.178980
$210$		0			0
$211$	3.77144	+	6.53232i	0.259637	+	0.449704i	0.966145	−	0.258001i	$-0.0830639\pi$
$211$	3.77144	+	6.53232i	0.259637	+	0.449704i	−0.706508	+	0.707705i	$0.749731\pi$
$212$		0			0
$213$			14.3056i			0.980203i
$214$		0			0
$215$	28.1646	+	16.2608i	1.92081	+	1.10898i
$216$		0			0
$217$	7.80074	−	13.5113i	0.529549	−	0.917205i
$218$		0			0
$219$	−19.3935	+	11.1969i	−1.31049	+	0.756614i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	13.1750	−	7.60656i	0.882260	−	0.509373i	0.0108573	−	0.999941i	$-0.496544\pi$
$223$	13.1750	−	7.60656i	0.882260	−	0.509373i	0.871403	+	0.490568i	$0.163211\pi$
$224$		0			0
$225$	4.80947	−	8.33025i	0.320631	−	0.555350i
$226$		0			0
$227$	−12.1281	−	7.00216i	−0.804970	−	0.464749i	0.0402363	−	0.999190i	$-0.487189\pi$
$227$	−12.1281	−	7.00216i	−0.804970	−	0.464749i	−0.845206	+	0.534441i	$0.820522\pi$
$228$		0			0
$229$		−	4.72886i		−	0.312492i	−0.987718	−	0.156246i	$-0.950061\pi$
$229$		−	4.72886i		−	0.312492i	0.987718	−	0.156246i	$-0.0499392\pi$
$230$		0			0
$231$	−5.05107	−	8.74872i	−0.332336	−	0.575623i
$232$		0			0
$233$	−19.8998			−1.30368			−0.651839	−	0.758358i	$-0.726002\pi$
$233$	−19.8998			−1.30368			−0.651839	+	0.758358i	$0.726002\pi$
$234$		0			0
$235$	9.05190			0.590481
$236$		0			0
$237$	10.2681	+	17.7848i	0.666984	+	1.15525i
$238$		0			0
$239$		−	3.51573i		−	0.227414i	−0.993514	−	0.113707i	$-0.963728\pi$
$239$		−	3.51573i		−	0.227414i	0.993514	−	0.113707i	$-0.0362725\pi$
$240$		0			0
$241$	6.21019	+	3.58546i	0.400034	+	0.230960i	0.686499	−	0.727131i	$-0.259147\pi$
$241$	6.21019	+	3.58546i	0.400034	+	0.230960i	−0.286465	+	0.958091i	$0.592480\pi$
$242$		0			0
$243$	2.83997	−	4.91897i	0.182184	−	0.315552i
$244$		0			0
$245$	−6.58981	+	3.80463i	−0.421007	+	0.243069i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−5.80385	+	3.35086i	−0.367804	+	0.212352i
$250$		0			0
$251$	8.89977	−	15.4149i	0.561749	−	0.972977i	−0.435595	−	0.900143i	$-0.643462\pi$
$251$	8.89977	−	15.4149i	0.561749	−	0.972977i	0.997344	−	0.0728346i	$-0.0232045\pi$
$252$		0			0
$253$	3.98242	+	2.29925i	0.250372	+	0.144553i
$254$		0			0
$255$		−	16.2664i		−	1.01864i
$256$		0			0
$257$	7.06129	+	12.2305i	0.440471	+	0.762919i	0.997724	−	0.0674239i	$-0.0214780\pi$
$257$	7.06129	+	12.2305i	0.440471	+	0.762919i	−0.557253	+	0.830343i	$0.688145\pi$
$258$		0			0
$259$	27.0543			1.68107
$260$		0			0
$261$	−19.8877			−1.23102
$262$		0			0
$263$	−12.2485	−	21.2150i	−0.755273	−	1.30817i	−0.945238	−	0.326381i	$-0.894171\pi$
$263$	−12.2485	−	21.2150i	−0.755273	−	1.30817i	0.189965	−	0.981791i	$-0.439162\pi$
$264$		0			0
$265$		−	21.6015i		−	1.32697i
$266$		0			0
$267$	−34.8168	−	20.1015i	−2.13075	−	1.23019i
$268$		0			0
$269$	−7.09448	+	12.2880i	−0.432558	+	0.749213i	−0.997093	−	0.0761966i	$-0.975722\pi$
$269$	−7.09448	+	12.2880i	−0.432558	+	0.749213i	0.564535	+	0.825409i	$0.309056\pi$
$270$		0			0
$271$	21.4628	−	12.3916i	1.30377	−	0.752735i	0.322725	−	0.946493i	$-0.395401\pi$
$271$	21.4628	−	12.3916i	1.30377	−	0.752735i	0.981049	+	0.193758i	$0.0620677\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.38785	+	0.801274i	−0.0836903	+	0.0483186i
$276$		0			0
$277$	−5.80947	+	10.0623i	−0.349057	+	0.604585i	−0.986082	−	0.166258i	$-0.946831\pi$
$277$	−5.80947	+	10.0623i	−0.349057	+	0.604585i	0.637025	+	0.770843i	$0.280165\pi$
$278$		0			0
$279$	−26.9294	−	15.5477i	−1.61222	−	0.930818i
$280$		0			0
$281$		−	4.10023i		−	0.244599i	−0.992493	−	0.122300i	$-0.960973\pi$
$281$		−	4.10023i		−	0.244599i	0.992493	−	0.122300i	$-0.0390269\pi$
$282$		0			0
$283$	−12.4547	−	21.5722i	−0.740357	−	1.28234i	−0.952333	−	0.305061i	$-0.901323\pi$
$283$	−12.4547	−	21.5722i	−0.740357	−	1.28234i	0.211976	−	0.977275i	$-0.432010\pi$
$284$		0			0
$285$	19.2161			1.13826
$286$		0			0
$287$	−36.3075			−2.14316
$288$		0			0
$289$	6.31982	+	10.9463i	0.371754	+	0.643897i
$290$		0			0
$291$			40.4185i			2.36937i
$292$		0			0
$293$	−19.3999	−	11.2005i	−1.13335	−	0.654341i	−0.188576	−	0.982059i	$-0.560387\pi$
$293$	−19.3999	−	11.2005i	−1.13335	−	0.654341i	−0.944776	+	0.327718i	$0.893721\pi$
$294$		0			0
$295$	−15.9453	+	27.6181i	−0.928373	+	1.60799i
$296$		0			0
$297$	−9.12833	+	5.27024i	−0.529679	+	0.305810i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−34.8214	+	20.1042i	−2.00707	+	1.15879i
$302$		0			0
$303$	−2.29225	+	3.97029i	−0.131686	+	0.228087i
$304$		0			0
$305$	−7.91408	−	4.56920i	−0.453159	−	0.261631i
$306$		0			0
$307$		−	13.4383i		−	0.766966i	−0.923548	−	0.383483i	$-0.874724\pi$
$307$		−	13.4383i		−	0.766966i	0.923548	−	0.383483i	$-0.125276\pi$
$308$		0			0
$309$	7.73005	+	13.3888i	0.439747	+	0.761665i
$310$		0			0
$311$	14.3424			0.813284			0.406642	−	0.913588i	$-0.366700\pi$
$311$	14.3424			0.813284			0.406642	+	0.913588i	$0.366700\pi$
$312$		0			0
$313$	4.52111			0.255548			0.127774	−	0.991803i	$-0.459217\pi$
$313$	4.52111			0.255548			0.127774	+	0.991803i	$0.459217\pi$
$314$		0			0
$315$	25.4061	+	44.0047i	1.43147	+	2.47938i
$316$		0			0
$317$		−	22.6655i		−	1.27302i	−0.771269	−	0.636510i	$-0.780378\pi$
$317$		−	22.6655i		−	1.27302i	0.771269	−	0.636510i	$-0.219622\pi$
$318$		0			0
$319$	2.86945	+	1.65668i	0.160658	+	0.0927561i
$320$		0			0
$321$	−6.90246	+	11.9554i	−0.385258	+	0.667286i
$322$		0			0
$323$	4.46095	−	2.57553i	0.248214	−	0.143306i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−33.9717	+	19.6136i	−1.87864	+	1.08463i
$328$		0			0
$329$	−5.59568	+	9.69200i	−0.308500	+	0.534337i
$330$		0			0
$331$	11.9168	+	6.88016i	0.655006	+	0.378168i	0.790371	−	0.612628i	$-0.209888\pi$
$331$	11.9168	+	6.88016i	0.655006	+	0.378168i	−0.135366	+	0.990796i	$0.543221\pi$
$332$		0			0
$333$		−	53.9221i		−	2.95491i
$334$		0			0
$335$	2.22401	+	3.85210i	0.121511	+	0.210463i
$336$		0			0
$337$	−9.84548			−0.536317			−0.268159	−	0.963375i	$-0.586415\pi$
$337$	−9.84548			−0.536317			−0.268159	+	0.963375i	$0.586415\pi$
$338$		0			0
$339$	47.1366			2.56011
$340$		0			0
$341$	2.59030	+	4.48653i	0.140273	+	0.242959i
$342$		0			0
$343$			12.7041i			0.685957i
$344$		0			0
$345$	−29.5757	−	17.0755i	−1.59230	−	0.919316i
$346$		0			0
$347$	1.46226	−	2.53271i	0.0784984	−	0.135963i	−0.824104	−	0.566439i	$-0.808321\pi$
$347$	1.46226	−	2.53271i	0.0784984	−	0.135963i	0.902602	+	0.430476i	$0.141654\pi$
$348$		0			0
$349$	−8.08653	+	4.66876i	−0.432862	+	0.249913i	−0.700565	−	0.713588i	$-0.747069\pi$
$349$	−8.08653	+	4.66876i	−0.432862	+	0.249913i	0.267703	+	0.963501i	$0.413735\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.6614	−	7.88740i	0.727121	−	0.419804i	−0.0902468	−	0.995919i	$-0.528766\pi$
$353$	13.6614	−	7.88740i	0.727121	−	0.419804i	0.817368	+	0.576116i	$0.195432\pi$
$354$		0			0
$355$	−5.99396	+	10.3818i	−0.318126	+	0.551011i
$356$		0			0
$357$	17.4166	+	10.0555i	0.921785	+	0.532193i
$358$		0			0
$359$			21.5676i			1.13830i	0.822235	+	0.569148i	$0.192727\pi$
$359$			21.5676i			1.13830i	−0.822235	+	0.569148i	$0.807273\pi$
$360$		0			0
$361$	−6.45742	−	11.1846i	−0.339864	−	0.588662i
$362$		0			0
$363$	−30.1836			−1.58423
$364$		0			0
$365$	−18.7657			−0.982241
$366$		0			0
$367$	6.90030	+	11.9517i	0.360193	+	0.623873i	0.987992	−	0.154503i	$-0.0493775\pi$
$367$	6.90030	+	11.9517i	0.360193	+	0.623873i	−0.627799	+	0.778375i	$0.716044\pi$
$368$		0			0
$369$			72.3648i			3.76716i
$370$		0			0
$371$	23.1290	+	13.3535i	1.20080	+	0.693281i
$372$		0			0
$373$	−12.0390	+	20.8521i	−0.623355	+	1.07968i	0.365501	+	0.930811i	$0.380898\pi$
$373$	−12.0390	+	20.8521i	−0.623355	+	1.07968i	−0.988856	+	0.148872i	$0.952436\pi$
$374$		0			0
$375$	−23.4241	+	13.5239i	−1.20962	+	0.698373i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−14.1660	+	8.17874i	−0.727659	+	0.420114i	−0.817565	−	0.575836i	$-0.804677\pi$
$379$	−14.1660	+	8.17874i	−0.727659	+	0.420114i	0.0899065	+	0.995950i	$0.471343\pi$
$380$		0			0
$381$	16.8436	−	29.1740i	0.862925	−	1.49463i
$382$		0			0
$383$	−6.05171	−	3.49396i	−0.309228	−	0.178533i	0.337353	−	0.941378i	$-0.390468\pi$
$383$	−6.05171	−	3.49396i	−0.309228	−	0.178533i	−0.646581	+	0.762845i	$0.723802\pi$
$384$		0			0
$385$		−	8.46548i		−	0.431441i
$386$		0			0
$387$	40.0698	+	69.4029i	2.03686	+	3.52795i
$388$		0			0
$389$	−9.57971			−0.485711			−0.242855	−	0.970063i	$-0.578084\pi$
$389$	−9.57971			−0.485711			−0.242855	+	0.970063i	$0.578084\pi$
$390$		0			0
$391$	−9.15452			−0.462964
$392$		0			0
$393$	10.4291	+	18.0637i	0.526077	+	0.911193i
$394$		0			0
$395$			17.2091i			0.865883i
$396$		0			0
$397$	−14.6838	−	8.47770i	−0.736959	−	0.425483i	0.0840036	−	0.996465i	$-0.473229\pi$
$397$	−14.6838	−	8.47770i	−0.736959	−	0.425483i	−0.820963	+	0.570982i	$0.806563\pi$
$398$		0			0
$399$	−11.8790	+	20.5750i	−0.594692	+	1.03004i
$400$		0			0
$401$	16.6831	−	9.63198i	0.833113	−	0.480998i	−0.0218041	−	0.999762i	$-0.506941\pi$
$401$	16.6831	−	9.63198i	0.833113	−	0.480998i	0.854917	+	0.518764i	$0.173608\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	26.0001	−	15.0112i	1.29196	−	0.745912i
$406$		0			0
$407$	−4.49180	+	7.78003i	−0.222650	+	0.385642i
$408$		0			0
$409$	−18.4831	−	10.6712i	−0.913929	−	0.527657i	−0.0322361	−	0.999480i	$-0.510263\pi$
$409$	−18.4831	−	10.6712i	−0.913929	−	0.527657i	−0.881693	+	0.471823i	$0.843596\pi$
$410$		0			0
$411$			17.6233i			0.869291i
$412$		0			0
$413$	−19.7141	−	34.1458i	−0.970067	−	1.68021i
$414$		0			0
$415$	−5.61596			−0.275676
$416$		0			0
$417$	1.60925			0.0788054
$418$		0			0
$419$	−6.90097	−	11.9528i	−0.337134	−	0.583934i	0.646758	−	0.762695i	$-0.276124\pi$
$419$	−6.90097	−	11.9528i	−0.337134	−	0.583934i	−0.983892	+	0.178761i	$0.942791\pi$
$420$		0			0
$421$		−	16.9836i		−	0.827730i	−0.910338	−	0.413865i	$-0.864178\pi$
$421$		−	16.9836i		−	0.827730i	0.910338	−	0.413865i	$-0.135822\pi$
$422$		0			0
$423$	19.3172	+	11.1528i	0.939235	+	0.542267i
$424$		0			0
$425$	1.59515	−	2.76287i	0.0773760	−	0.134019i
$426$		0			0
$427$	9.78461	−	5.64914i	0.473510	−	0.273381i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−14.4548	+	8.34548i	−0.696263	+	0.401988i	−0.805954	−	0.591978i	$-0.798347\pi$
$431$	−14.4548	+	8.34548i	−0.696263	+	0.401988i	0.109691	+	0.993966i	$0.465014\pi$
$432$		0			0
$433$	−1.27210	+	2.20335i	−0.0611333	+	0.105886i	−0.894972	−	0.446122i	$-0.852805\pi$
$433$	−1.27210	+	2.20335i	−0.0611333	+	0.105886i	0.833839	+	0.552008i	$0.186138\pi$
$434$		0			0
$435$	−21.3102	−	12.3034i	−1.02174	−	0.589904i
$436$		0			0
$437$		−	10.8146i		−	0.517333i
$438$		0			0
$439$	−3.05376	−	5.28927i	−0.145748	−	0.252443i	0.783904	−	0.620882i	$-0.213226\pi$
$439$	−3.05376	−	5.28927i	−0.145748	−	0.252443i	−0.929652	+	0.368439i	$0.879892\pi$
$440$		0			0
$441$	−18.7506			−0.892887
$442$		0			0
$443$	−29.2030			−1.38747			−0.693737	−	0.720228i	$-0.744037\pi$
$443$	−29.2030			−1.38747			−0.693737	+	0.720228i	$0.744037\pi$
$444$		0			0
$445$	−16.8448	−	29.1761i	−0.798521	−	1.38308i
$446$		0			0
$447$		−	60.8751i		−	2.87930i
$448$		0			0
$449$	28.2929	+	16.3349i	1.33522	+	0.770891i	0.986095	−	0.166184i	$-0.0531446\pi$
$449$	28.2929	+	16.3349i	1.33522	+	0.770891i	0.349128	+	0.937075i	$0.386478\pi$
$450$		0			0
$451$	6.02811	−	10.4410i	0.283852	−	0.491647i
$452$		0			0
$453$	9.01843	−	5.20679i	0.423723	−	0.244636i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.79685	−	1.61476i	0.130831	−	0.0755353i	−0.433156	−	0.901319i	$-0.642600\pi$
$457$	2.79685	−	1.61476i	0.130831	−	0.0755353i	0.563987	+	0.825784i	$0.309267\pi$
$458$		0			0
$459$	10.4918	−	18.1723i	0.489715	−	0.848212i
$460$		0			0
$461$	−9.03728	−	5.21768i	−0.420908	−	0.243011i	0.274558	−	0.961571i	$-0.411469\pi$
$461$	−9.03728	−	5.21768i	−0.420908	−	0.243011i	−0.695466	+	0.718559i	$0.744802\pi$
$462$		0			0
$463$			6.17928i			0.287175i	0.989638	+	0.143588i	$0.0458639\pi$
$463$			6.17928i			0.287175i	−0.989638	+	0.143588i	$0.954136\pi$
$464$		0			0
$465$	−19.2371	−	33.3196i	−0.892097	−	1.54516i
$466$		0			0
$467$	16.4601			0.761683			0.380841	−	0.924640i	$-0.375634\pi$
$467$	16.4601			0.761683			0.380841	+	0.924640i	$0.375634\pi$
$468$		0			0
$469$	−5.49934			−0.253936
$470$		0			0
$471$	9.63922	+	16.6956i	0.444152	+	0.769293i
$472$		0			0
$473$		−	13.3515i		−	0.613904i
$474$		0			0
$475$	3.26390	+	1.88441i	0.149758	+	0.0864627i
$476$		0			0
$477$	26.6151	−	46.0986i	1.21862	−	2.11071i
$478$		0			0
$479$	33.1338	−	19.1298i	1.51392	−	0.874064i	0.514056	−	0.857756i	$-0.328142\pi$
$479$	33.1338	−	19.1298i	1.51392	−	0.874064i	0.999867	−	0.0163076i	$-0.00519112\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	36.5660	−	21.1114i	1.66381	−	0.960602i
$484$		0			0
$485$	−16.9351	+	29.3325i	−0.768984	+	1.33192i
$486$		0			0
$487$	−25.6289	−	14.7969i	−1.16136	−	0.670510i	−0.209728	−	0.977760i	$-0.567258\pi$
$487$	−25.6289	−	14.7969i	−1.16136	−	0.670510i	−0.951629	+	0.307250i	$0.900591\pi$
$488$		0			0
$489$		−	34.3075i		−	1.55144i
$490$		0			0
$491$	18.8497	+	32.6486i	0.850673	+	1.47341i	0.880602	+	0.473857i	$0.157139\pi$
$491$	18.8497	+	32.6486i	0.850673	+	1.47341i	−0.0299285	+	0.999552i	$0.509528\pi$
$492$		0			0
$493$	−6.59611			−0.297074
$494$		0			0
$495$	−16.8726			−0.758368
$496$		0			0
$497$	−7.41066	−	12.8356i	−0.332413	−	0.575757i
$498$		0			0
$499$		−	13.0774i		−	0.585424i	−0.956201	−	0.292712i	$-0.905442\pi$
$499$		−	13.0774i		−	0.585424i	0.956201	−	0.292712i	$-0.0945578\pi$
$500$		0			0
$501$	14.0729	+	8.12498i	0.628730	+	0.362997i
$502$		0			0
$503$	1.41305	−	2.44748i	0.0630048	−	0.109128i	−0.832802	−	0.553570i	$-0.813265\pi$
$503$	1.41305	−	2.44748i	0.0630048	−	0.109128i	0.895807	+	0.444443i	$0.146598\pi$
$504$		0			0
$505$	−3.32706	+	1.92088i	−0.148052	+	0.0854780i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	32.1586	−	18.5668i	1.42541	−	0.822959i	0.428653	−	0.903469i	$-0.358988\pi$
$509$	32.1586	−	18.5668i	1.42541	−	0.822959i	0.996754	+	0.0805101i	$0.0256549\pi$
$510$		0			0
$511$	11.6005	−	20.0927i	0.513177	−	0.888849i
$512$		0			0
$513$	21.4677	+	12.3944i	0.947823	+	0.547226i
$514$		0			0
$515$			12.9554i			0.570883i
$516$		0			0
$517$	−1.85809	−	3.21831i	−0.0817188	−	0.141541i
$518$		0			0
$519$	58.5628			2.57062
$520$		0			0
$521$	−29.5375			−1.29406			−0.647031	−	0.762464i	$-0.723989\pi$
$521$	−29.5375			−1.29406			−0.647031	+	0.762464i	$0.723989\pi$
$522$		0			0
$523$	−15.5819	−	26.9886i	−0.681348	−	1.18013i	−0.974570	−	0.224084i	$-0.928061\pi$
$523$	−15.5819	−	26.9886i	−0.681348	−	1.18013i	0.293222	−	0.956044i	$-0.405272\pi$
$524$		0			0
$525$			14.7144i			0.642188i
$526$		0			0
$527$	−8.93163	−	5.15668i	−0.389068	−	0.224628i
$528$		0			0
$529$	1.89008	−	3.27372i	0.0821776	−	0.142336i
$530$		0			0
$531$	−68.0563	+	39.2923i	−2.95339	+	1.70514i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−10.0185	+	5.78418i	−0.433138	+	0.250072i
$536$		0			0
$537$	8.59246	−	14.8826i	0.370792	−	0.642230i
$538$		0			0
$539$	2.70539	+	1.56196i	0.116529	+	0.0672783i
$540$		0			0
$541$			40.0810i			1.72322i	0.507575	+	0.861608i	$0.330542\pi$
$541$			40.0810i			1.72322i	−0.507575	+	0.861608i	$0.669458\pi$
$542$		0			0
$543$	−6.04623	−	10.4724i	−0.259469	−	0.449413i
$544$		0			0
$545$	−32.8719			−1.40808
$546$		0			0
$547$	16.4534			0.703497			0.351748	−	0.936095i	$-0.385587\pi$
$547$	16.4534			0.703497			0.351748	+	0.936095i	$0.385587\pi$
$548$		0			0
$549$	−11.2594	−	19.5018i	−0.480538	−	0.832316i
$550$		0			0
$551$		−	7.79225i		−	0.331961i
$552$		0			0
$553$	−18.4260	−	10.6383i	−0.783553	−	0.452385i
$554$		0			0
$555$	33.3587	−	57.7789i	1.41600	−	2.45258i
$556$		0			0
$557$	−10.9812	+	6.33997i	−0.465286	+	0.268633i	−0.714264	−	0.699876i	$-0.753239\pi$
$557$	−10.9812	+	6.33997i	−0.465286	+	0.268633i	0.248978	+	0.968509i	$0.419905\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−5.78334	+	3.33901i	−0.244173	+	0.140973i
$562$		0			0
$563$	11.0794	−	19.1901i	0.466942	−	0.808767i	−0.532345	−	0.846527i	$-0.678689\pi$
$563$	11.0794	−	19.1901i	0.466942	−	0.808767i	0.999287	+	0.0377606i	$0.0120224\pi$
$564$		0			0
$565$	34.2079	+	19.7500i	1.43914	+	0.830887i
$566$		0			0
$567$			37.1183i			1.55882i
$568$		0			0
$569$	1.65734	+	2.87060i	0.0694794	+	0.120342i	0.898672	−	0.438621i	$-0.144533\pi$
$569$	1.65734	+	2.87060i	0.0694794	+	0.120342i	−0.829193	+	0.558963i	$0.811200\pi$
$570$		0			0
$571$	15.7429			0.658818			0.329409	−	0.944187i	$-0.393150\pi$
$571$	15.7429			0.658818			0.329409	+	0.944187i	$0.393150\pi$
$572$		0			0
$573$	63.7381			2.66270
$574$		0			0
$575$	−3.34899	−	5.80063i	−0.139663	−	0.241903i
$576$		0			0
$577$		−	2.05131i		−	0.0853972i	−0.999088	−	0.0426986i	$-0.986404\pi$
$577$		−	2.05131i		−	0.0853972i	0.999088	−	0.0426986i	$-0.0135955\pi$
$578$		0			0
$579$	33.8567	+	19.5472i	1.40704	+	0.812353i
$580$		0			0
$581$	3.47166	−	6.01309i	0.144029	−	0.249465i
$582$		0			0
$583$	−7.68018	+	4.43416i	−0.318081	+	0.183644i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.55679	−	0.898813i	0.0642556	−	0.0370980i	−0.467528	−	0.883978i	$-0.654855\pi$
$587$	1.55679	−	0.898813i	0.0642556	−	0.0370980i	0.531784	+	0.846880i	$0.321522\pi$
$588$		0			0
$589$	6.09179	−	10.5513i	0.251008	−	0.434759i
$590$		0			0
$591$	47.4322	+	27.3850i	1.95110	+	1.12647i
$592$		0			0
$593$		−	28.7332i		−	1.17993i	−0.807429	−	0.589965i	$-0.799142\pi$
$593$		−	28.7332i		−	1.17993i	0.807429	−	0.589965i	$-0.200858\pi$
$594$		0			0
$595$	8.42639	+	14.5949i	0.345448	+	0.598334i
$596$		0			0
$597$	−41.6926			−1.70637
$598$		0			0
$599$	44.5840			1.82165			0.910827	−	0.412788i	$-0.135445\pi$
$599$	44.5840			1.82165			0.910827	+	0.412788i	$0.135445\pi$
$600$		0			0
$601$	4.86227	+	8.42170i	0.198336	+	0.343528i	0.947989	−	0.318303i	$-0.103113\pi$
$601$	4.86227	+	8.42170i	0.198336	+	0.343528i	−0.749653	+	0.661831i	$0.769780\pi$
$602$		0			0
$603$			10.9608i			0.446357i
$604$		0			0
$605$	−21.9048	−	12.6468i	−0.890557	−	0.514164i
$606$		0			0
$607$	−22.9324	+	39.7201i	−0.930799	+	1.61219i	−0.148839	+	0.988861i	$0.547554\pi$
$607$	−22.9324	+	39.7201i	−0.930799	+	1.61219i	−0.781960	+	0.623329i	$0.785780\pi$
$608$		0			0
$609$	26.3469	−	15.2114i	1.06763	−	0.616397i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−8.69423	+	5.01961i	−0.351157	+	0.202740i	−0.665195	−	0.746670i	$-0.731651\pi$
$613$	−8.69423	+	5.01961i	−0.351157	+	0.202740i	0.314038	+	0.949410i	$0.398318\pi$
$614$		0			0
$615$	−44.7681	+	77.5407i	−1.80523	+	3.12674i
$616$		0			0
$617$	10.2124	+	5.89612i	0.411135	+	0.237369i	0.691277	−	0.722589i	$-0.257048\pi$
$617$	10.2124	+	5.89612i	0.411135	+	0.237369i	−0.280142	+	0.959959i	$0.590382\pi$
$618$		0			0
$619$		−	21.2711i		−	0.854959i	−0.904025	−	0.427480i	$-0.859402\pi$
$619$		−	21.2711i		−	0.854959i	0.904025	−	0.427480i	$-0.140598\pi$
$620$		0			0
$621$	−22.0274	−	38.1526i	−0.883931	−	1.53101i
$622$		0			0
$623$	41.6523			1.66876
$624$		0			0
$625$	−30.3048			−1.21219
$626$		0			0
$627$	−3.94451	−	6.83209i	−0.157529	−	0.272847i
$628$		0			0
$629$		−	17.8842i		−	0.713091i
$630$		0			0
$631$	−3.31350	−	1.91305i	−0.131908	−	0.0761573i	0.432594	−	0.901589i	$-0.357598\pi$
$631$	−3.31350	−	1.91305i	−0.131908	−	0.0761573i	−0.564502	+	0.825432i	$0.690932\pi$
$632$		0			0
$633$	−11.4988	+	19.9165i	−0.457036	+	0.791610i
$634$		0			0
$635$	24.4475	−	14.1148i	0.970169	−	0.560127i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−25.5828	+	14.7702i	−1.01204	+	0.584302i
$640$		0			0
$641$	−14.0209	+	24.2849i	−0.553791	+	0.959194i	0.444205	+	0.895925i	$0.353486\pi$
$641$	−14.0209	+	24.2849i	−0.553791	+	0.959194i	−0.997996	+	0.0632693i	$0.979847\pi$
$642$		0			0
$643$	−9.83743	−	5.67964i	−0.387950	−	0.223983i	0.293321	−	0.956014i	$-0.405239\pi$
$643$	−9.83743	−	5.67964i	−0.387950	−	0.223983i	−0.681272	+	0.732031i	$0.738573\pi$
$644$		0			0
$645$			99.1560i			3.90426i
$646$		0			0
$647$	−9.06638	−	15.7034i	−0.356436	−	0.617365i	0.630927	−	0.775843i	$-0.282675\pi$
$647$	−9.06638	−	15.7034i	−0.356436	−	0.617365i	−0.987363	+	0.158477i	$0.949342\pi$
$648$		0			0
$649$	13.0925			0.513924
$650$		0			0
$651$	47.5676			1.86432
$652$		0			0
$653$	4.45957	+	7.72421i	0.174517	+	0.302272i	0.939994	−	0.341191i	$-0.110830\pi$
$653$	4.45957	+	7.72421i	0.174517	+	0.302272i	−0.765477	+	0.643463i	$0.777497\pi$
$654$		0			0
$655$			17.4789i			0.682957i
$656$		0			0
$657$	−40.0469	−	23.1211i	−1.56238	−	0.902040i
$658$		0			0
$659$	−9.02877	+	15.6383i	−0.351711	+	0.609181i	−0.986549	−	0.163464i	$-0.947733\pi$
$659$	−9.02877	+	15.6383i	−0.351711	+	0.609181i	0.634838	+	0.772645i	$0.281067\pi$
$660$		0			0
$661$	34.1092	−	19.6930i	1.32670	−	0.765968i	0.341909	−	0.939733i	$-0.388927\pi$
$661$	34.1092	−	19.6930i	1.32670	−	0.765968i	0.984787	+	0.173765i	$0.0555933\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−17.2416	+	9.95444i	−0.668600	+	0.386016i
$666$		0			0
$667$	−6.92423	+	11.9931i	−0.268107	+	0.464375i
$668$		0			0
$669$	40.1693	+	23.1918i	1.55304	+	0.896646i
$670$		0			0
$671$			3.75169i			0.144832i
$672$		0			0
$673$	11.8101	+	20.4558i	0.455247	+	0.788511i	0.998702	−	0.0509269i	$-0.0162175\pi$
$673$	11.8101	+	20.4558i	0.455247	+	0.788511i	−0.543455	+	0.839438i	$0.682884\pi$
$674$		0			0
$675$	15.3528			0.590931
$676$		0			0
$677$	46.7741			1.79767			0.898836	−	0.438284i	$-0.144414\pi$
$677$	46.7741			1.79767			0.898836	+	0.438284i	$0.144414\pi$
$678$		0			0
$679$	−20.9378	−	36.2653i	−0.803519	−	1.39174i
$680$		0			0
$681$		−	42.6980i		−	1.63619i
$682$		0			0
$683$	5.83782	+	3.37047i	0.223378	+	0.128967i	0.607513	−	0.794309i	$-0.292167\pi$
$683$	5.83782	+	3.37047i	0.223378	+	0.128967i	−0.384135	+	0.923277i	$0.625500\pi$
$684$		0			0
$685$	−7.38404	+	12.7895i	−0.282130	+	0.488663i
$686$		0			0
$687$	12.4863	−	7.20895i	0.476381	−	0.275038i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	24.4114	−	14.0939i	0.928655	−	0.536159i	0.0422690	−	0.999106i	$-0.486541\pi$
$691$	24.4114	−	14.0939i	0.928655	−	0.536159i	0.886386	+	0.462947i	$0.153208\pi$
$692$		0			0
$693$	10.4303	−	18.0658i	0.396213	−	0.686262i
$694$		0			0
$695$	1.16787	+	0.674268i	0.0442997	+	0.0255764i
$696$		0			0
$697$			24.0011i			0.909105i
$698$		0			0
$699$	−30.3364	−	52.5442i	−1.14743	−	1.98740i
$700$		0			0
$701$	18.2078			0.687697			0.343849	−	0.939025i	$-0.388269\pi$
$701$	18.2078			0.687697			0.343849	+	0.939025i	$0.388269\pi$
$702$		0			0
$703$	21.1274			0.796834
$704$		0			0
$705$	13.7992	+	23.9010i	0.519710	+	0.900164i
$706$		0			0
$707$		−	4.74977i		−	0.178634i
$708$		0			0
$709$	−21.5873	−	12.4635i	−0.810730	−	0.468075i	0.0364795	−	0.999334i	$-0.488386\pi$
$709$	−21.5873	−	12.4635i	−0.810730	−	0.468075i	−0.847209	+	0.531259i	$0.821719\pi$
$710$		0			0
$711$	−21.2032	+	36.7250i	−0.795182	+	1.37730i
$712$		0			0
$713$	−18.7519	+	10.8264i	−0.702263	+	0.405452i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	9.28307	−	5.35958i	0.346683	−	0.200157i
$718$		0			0
$719$	16.5981	−	28.7488i	0.619006	−	1.07215i	−0.370662	−	0.928768i	$-0.620869\pi$
$719$	16.5981	−	28.7488i	0.619006	−	1.07215i	0.989667	−	0.143382i	$-0.0457976\pi$
$720$		0			0
$721$	−13.8715	−	8.00873i	−0.516603	−	0.298261i
$722$		0			0
$723$			21.8635i			0.813113i
$724$		0			0
$725$	−2.41305	−	4.17953i	−0.0896184	−	0.155224i
$726$		0			0
$727$	−36.0006			−1.33519			−0.667594	−	0.744526i	$-0.732676\pi$
$727$	−36.0006			−1.33519			−0.667594	+	0.744526i	$0.732676\pi$
$728$		0			0
$729$	−17.9342			−0.664230
$730$		0			0
$731$	13.2899	+	23.0187i	0.491543	+	0.851378i
$732$		0			0
$733$			7.47757i			0.276190i	0.990419	+	0.138095i	$0.0440980\pi$
$733$			7.47757i			0.276190i	−0.990419	+	0.138095i	$0.955902\pi$
$734$		0			0
$735$	−20.0918	−	11.6000i	−0.741096	−	0.427872i
$736$		0			0
$737$	0.913050	−	1.58145i	0.0336326	−	0.0582535i
$738$		0			0
$739$	−33.8493	+	19.5429i	−1.24516	+	0.718896i	−0.970141	−	0.242541i	$-0.922019\pi$
$739$	−33.8493	+	19.5429i	−1.24516	+	0.718896i	−0.275024	+	0.961437i	$0.588686\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−28.1713	+	16.2647i	−1.03351	+	0.596695i	−0.917987	−	0.396610i	$-0.870187\pi$
$743$	−28.1713	+	16.2647i	−1.03351	+	0.596695i	−0.115519	+	0.993305i	$0.536853\pi$
$744$		0			0
$745$	25.5063	−	44.1783i	0.934480	−	1.61857i
$746$		0			0
$747$	−11.9847	−	6.91939i	−0.438498	−	0.253167i
$748$		0			0
$749$		−	14.3026i		−	0.522606i
$750$		0			0
$751$	−9.16315	−	15.8710i	−0.334368	−	0.579142i	0.648995	−	0.760792i	$-0.275189\pi$
$751$	−9.16315	−	15.8710i	−0.334368	−	0.579142i	−0.983363	+	0.181650i	$0.941856\pi$
$752$		0			0
$753$	54.2693			1.97768
$754$		0			0
$755$	8.72646			0.317589
$756$		0			0
$757$	11.5586	+	20.0201i	0.420105	+	0.727643i	0.995949	−	0.0899165i	$-0.0286600\pi$
$757$	11.5586	+	20.0201i	0.420105	+	0.727643i	−0.575845	+	0.817559i	$0.695327\pi$
$758$		0			0
$759$			14.0204i			0.508910i
$760$		0			0
$761$	11.8634	+	6.84936i	0.430050	+	0.248289i	0.699368	−	0.714762i	$-0.253465\pi$
$761$	11.8634	+	6.84936i	0.430050	+	0.248289i	−0.269318	+	0.963051i	$0.586798\pi$
$762$		0			0
$763$	20.3207	−	35.1964i	0.735657	−	1.27420i
$764$		0			0
$765$	29.0893	−	16.7947i	1.05172	−	0.607214i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	21.1726	−	12.2240i	0.763504	−	0.440809i	−0.0670485	−	0.997750i	$-0.521358\pi$
$769$	21.1726	−	12.2240i	0.763504	−	0.440809i	0.830552	+	0.556941i	$0.188025\pi$
$770$		0			0
$771$	−21.5293	+	37.2898i	−0.775359	+	1.34296i
$772$		0			0
$773$	29.5049	+	17.0347i	1.06122	+	0.612695i	0.925769	−	0.378089i	$-0.123419\pi$
$773$	29.5049	+	17.0347i	1.06122	+	0.612695i	0.135450	+	0.990784i	$0.456752\pi$
$774$		0			0
$775$		−	7.54586i		−	0.271055i
$776$		0			0
$777$	41.2432	+	71.4352i	1.47959	+	2.56272i
$778$		0			0
$779$	−28.3534			−1.01587
$780$		0			0
$781$	4.92154			0.176107
$782$		0			0
$783$	−15.8714	−	27.4901i	−0.567199	−	0.982417i
$784$		0			0
$785$			16.1551i			0.576601i
$786$		0			0
$787$	−1.79907	−	1.03870i	−0.0641301	−	0.0370255i	0.467592	−	0.883944i	$-0.345122\pi$
$787$	−1.79907	−	1.03870i	−0.0641301	−	0.0370255i	−0.531722	+	0.846919i	$0.678455\pi$
$788$		0			0
$789$	37.3446	−	64.6827i	1.32950	−	2.30277i
$790$		0			0
$791$	−42.2931	+	24.4180i	−1.50377	+	0.868202i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	57.0374	−	32.9306i	2.02291	−	1.16793i
$796$		0			0
$797$	−13.5649	+	23.4952i	−0.480495	+	0.832242i	−0.999750	−	0.0223780i	$-0.992876\pi$
$797$	−13.5649	+	23.4952i	−0.480495	+	0.832242i	0.519255	+	0.854620i	$0.326210\pi$
$798$		0			0
$799$	6.40689	+	3.69902i	0.226660	+	0.130862i
$800$		0			0
$801$		−	83.0176i		−	2.93328i
$802$		0			0
$803$	3.85205	+	6.67195i	0.135936	+	0.235448i
$804$		0			0
$805$	35.3822			1.24706
$806$		0			0
$807$	−43.2610			−1.52286
$808$		0			0
$809$	6.09352	+	10.5543i	0.214237	+	0.371069i	0.953036	−	0.302856i	$-0.0979402\pi$
$809$	6.09352	+	10.5543i	0.214237	+	0.371069i	−0.738799	+	0.673925i	$0.764607\pi$
$810$		0			0
$811$			17.7178i			0.622158i	0.950384	+	0.311079i	$0.100690\pi$
$811$			17.7178i			0.622158i	−0.950384	+	0.311079i	$0.899310\pi$
$812$		0			0
$813$	65.4384	+	37.7809i	2.29503	+	1.32503i
$814$		0			0
$815$	14.3746	−	24.8976i	0.503522	−	0.872126i
$816$		0			0
$817$	−27.1929	+	15.6998i	−0.951360	+	0.549268i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.0766	+	14.4780i	−0.875180	+	0.505285i	−0.869066	−	0.494696i	$-0.835279\pi$
$821$	−25.0766	+	14.4780i	−0.875180	+	0.505285i	−0.00611388	+	0.999981i	$0.501946\pi$
$822$		0			0
$823$	−20.3442	+	35.2371i	−0.709152	+	1.22829i	0.256019	+	0.966672i	$0.417589\pi$
$823$	−20.3442	+	35.2371i	−0.709152	+	1.22829i	−0.965172	+	0.261617i	$0.915744\pi$
$824$		0			0
$825$	−4.23143	−	2.44302i	−0.147319	−	0.0850550i
$826$		0			0
$827$			20.5244i			0.713702i	0.934161	+	0.356851i	$0.116150\pi$
$827$			20.5244i			0.713702i	−0.934161	+	0.356851i	$0.883850\pi$
$828$		0			0
$829$	−15.8077	−	27.3798i	−0.549026	−	0.950940i	−0.998342	−	0.0575673i	$-0.981666\pi$
$829$	−15.8077	−	27.3798i	−0.549026	−	0.950940i	0.449316	−	0.893373i	$-0.351668\pi$
$830$		0			0
$831$	−35.4252			−1.22889
$832$		0			0
$833$	−6.21898			−0.215475
$834$		0			0
$835$	6.80864	+	11.7929i	0.235623	+	0.408111i
$836$		0			0
$837$		−	49.6316i		−	1.71552i
$838$		0			0
$839$	−8.85995	−	5.11529i	−0.305879	−	0.176600i	0.339202	−	0.940714i	$-0.389843\pi$
$839$	−8.85995	−	5.11529i	−0.305879	−	0.176600i	−0.645081	+	0.764114i	$0.723176\pi$
$840$		0			0
$841$	9.51089	−	16.4733i	0.327962	−	0.568046i
$842$		0			0
$843$	10.8264	−	6.25063i	0.372881	−	0.215283i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	27.0821	−	15.6359i	0.930553	−	0.537255i
$848$		0			0
$849$	37.9734	−	65.7719i	1.30325	−	2.25729i
$850$		0			0
$851$	−32.5173	−	18.7739i	−1.11468	−	0.643561i
$852$		0			0
$853$			21.6233i			0.740366i	0.928959	+	0.370183i	$0.120705\pi$
$853$			21.6233i			0.740366i	−0.928959	+	0.370183i	$0.879295\pi$
$854$		0			0
$855$	19.8403	+	34.3643i	0.678523	+	1.17524i
$856$		0			0
$857$	−43.6082			−1.48963			−0.744814	−	0.667273i	$-0.767462\pi$
$857$	−43.6082			−1.48963			−0.744814	+	0.667273i	$0.767462\pi$
$858$		0			0
$859$	−45.5991			−1.55582			−0.777910	−	0.628375i	$-0.783720\pi$
$859$	−45.5991			−1.55582			−0.777910	+	0.628375i	$0.783720\pi$
$860$		0			0
$861$	−55.3493	−	95.8678i	−1.88630	−	3.26717i
$862$		0			0
$863$		−	16.3104i		−	0.555212i	−0.960695	−	0.277606i	$-0.910459\pi$
$863$		−	16.3104i		−	0.555212i	0.960695	−	0.277606i	$-0.0895409\pi$
$864$		0			0
$865$	42.5002	+	24.5375i	1.44505	+	0.834300i
$866$		0			0
$867$	−19.2686	+	33.3742i	−0.654397	+	1.13345i
$868$		0			0
$869$	6.11851	−	3.53252i	0.207556	−	0.119833i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−72.2807	+	41.7313i	−2.44633	+	1.41239i
$874$		0			0
$875$	14.0115	−	24.2686i	0.473674	−	0.820428i
$876$		0			0
$877$	−11.0487	−	6.37896i	−0.373088	−	0.215402i	0.301719	−	0.953397i	$-0.402440\pi$
$877$	−11.0487	−	6.37896i	−0.373088	−	0.215402i	−0.674807	+	0.737995i	$0.735773\pi$
$878$		0			0
$879$		−	68.2989i		−	2.30366i
$880$		0			0
$881$	−4.92908	−	8.53741i	−0.166065	−	0.287633i	0.770968	−	0.636874i	$-0.219773\pi$
$881$	−4.92908	−	8.53741i	−0.166065	−	0.287633i	−0.937033	+	0.349241i	$0.886439\pi$
$882$		0			0
$883$	−15.8649			−0.533895			−0.266947	−	0.963711i	$-0.586015\pi$
$883$	−15.8649			−0.533895			−0.266947	+	0.963711i	$0.586015\pi$
$884$		0			0
$885$	−97.2320			−3.26842
$886$		0			0
$887$	1.47703	+	2.55830i	0.0495939	+	0.0858992i	0.889757	−	0.456435i	$-0.150874\pi$
$887$	1.47703	+	2.55830i	0.0495939	+	0.0858992i	−0.840163	+	0.542334i	$0.817541\pi$
$888$		0			0
$889$			34.9017i			1.17057i
$890$		0			0
$891$	−10.6741	−	6.16272i	−0.357597	−	0.206459i
$892$		0			0
$893$	−4.36981	+	7.56873i	−0.146230	+	0.253278i
$894$		0			0
$895$	12.4714	−	7.20038i	0.416874	−	0.240682i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.5113	+	7.80074i	−0.450626	+	0.260169i
$900$		0			0
$901$	8.82736	−	15.2894i	0.294082	−	0.509365i
$902$		0			0
$903$	−106.168	−	61.2960i	−3.53304	−	2.03980i
$904$		0			0
$905$		−	10.1333i		−	0.336844i
$906$		0			0
$907$	−5.49665	−	9.52047i	−0.182513	−	0.316122i	0.760223	−	0.649663i	$-0.225090\pi$
$907$	−5.49665	−	9.52047i	−0.182513	−	0.316122i	−0.942736	+	0.333541i	$0.891757\pi$
$908$		0			0
$909$	−9.46681			−0.313994
$910$		0			0
$911$	11.5104			0.381355			0.190677	−	0.981653i	$-0.438932\pi$
$911$	11.5104			0.381355			0.190677	+	0.981653i	$0.438932\pi$
$912$		0			0
$913$	1.15279	+	1.99670i	0.0381519	+	0.0660810i
$914$		0			0
$915$		−	27.8622i		−	0.921096i
$916$		0			0
$917$	−18.7149	−	10.8051i	−0.618020	−	0.356814i
$918$		0			0
$919$	12.5407	−	21.7212i	0.413680	−	0.716515i	−0.581609	−	0.813469i	$-0.697577\pi$
$919$	12.5407	−	21.7212i	0.413680	−	0.716515i	0.995289	+	0.0969536i	$0.0309098\pi$
$920$		0			0
$921$	35.4831	−	20.4862i	1.16921	−	0.675043i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	11.3321	−	6.54258i	0.372597	−	0.215119i
$926$		0			0
$927$	−15.9623	+	27.6475i	−0.524270	+	0.908061i
$928$		0			0
$929$	8.04117	+	4.64257i	0.263822	+	0.152318i	0.626077	−	0.779761i	$-0.284660\pi$
$929$	8.04117	+	4.64257i	0.263822	+	0.152318i	−0.362255	+	0.932079i	$0.617993\pi$
$930$		0			0
$931$		−	7.34673i		−	0.240779i
$932$		0			0
$933$	21.8644	+	37.8703i	0.715809	+	1.23982i
$934$		0			0
$935$	−5.59611			−0.183012
$936$		0			0
$937$	−34.3830			−1.12324			−0.561621	−	0.827394i	$-0.689822\pi$
$937$	−34.3830			−1.12324			−0.561621	+	0.827394i	$0.689822\pi$
$938$		0			0
$939$	6.89224	+	11.9377i	0.224920	+	0.389572i
$940$		0			0
$941$			37.3284i			1.21687i	0.793603	+	0.608436i	$0.208203\pi$
$941$			37.3284i			1.21687i	−0.793603	+	0.608436i	$0.791797\pi$
$942$		0			0
$943$	43.6390	+	25.1950i	1.42108	+	0.820462i
$944$		0			0
$945$	−40.5508	+	70.2361i	−1.31912	+	2.28478i
$946$		0			0
$947$	−25.3648	+	14.6444i	−0.824244	+	0.475878i	−0.851878	−	0.523740i	$-0.824536\pi$
$947$	−25.3648	+	14.6444i	−0.824244	+	0.475878i	0.0276335	+	0.999618i	$0.491203\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	59.8468	−	34.5526i	1.94067	−	1.12044i
$952$		0			0
$953$	3.67294	−	6.36172i	0.118978	−	0.206076i	−0.800385	−	0.599487i	$-0.795371\pi$
$953$	3.67294	−	6.36172i	0.118978	−	0.206076i	0.919363	+	0.393410i	$0.128705\pi$
$954$		0			0
$955$	46.2560	+	26.7059i	1.49681	+	0.864182i
$956$		0			0
$957$			10.1021i			0.326556i
$958$		0			0
$959$	−9.12929	−	15.8124i	−0.294800	−	0.510609i
$960$		0			0
$961$	6.60627			0.213105
$962$		0			0
$963$	−28.5066			−0.918613
$964$		0			0
$965$	16.3803	+	28.3716i	0.527301	+	0.913313i
$966$		0			0
$967$		−	40.6859i		−	1.30837i	−0.756334	−	0.654185i	$-0.773012\pi$
$967$		−	40.6859i		−	1.30837i	0.756334	−	0.654185i	$-0.226988\pi$
$968$		0			0
$969$	13.6011	+	7.85258i	0.436929	+	0.252261i
$970$		0			0
$971$	−15.2603	+	26.4316i	−0.489727	+	0.848232i	−0.999930	−	0.0118221i	$-0.996237\pi$
$971$	−15.2603	+	26.4316i	−0.489727	+	0.848232i	0.510203	+	0.860054i	$0.329570\pi$
$972$		0			0
$973$	−1.44390	+	0.833634i	−0.0462892	+	0.0267251i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	31.3960	−	18.1265i	1.00445	−	0.579917i	0.0948854	−	0.995488i	$-0.469752\pi$
$977$	31.3960	−	18.1265i	1.00445	−	0.579917i	0.909561	+	0.415571i	$0.136418\pi$
$978$		0			0
$979$	−6.91550	+	11.9780i	−0.221020	+	0.382819i
$980$		0			0
$981$	−70.1502	−	40.5013i	−2.23972	−	1.29311i
$982$		0			0
$983$			13.9632i			0.445356i	0.974892	+	0.222678i	$0.0714798\pi$
$983$			13.9632i			0.445356i	−0.974892	+	0.222678i	$0.928520\pi$
$984$		0			0
$985$	22.9483	+	39.7477i	0.731194	+	1.26647i
$986$		0			0
$987$	−34.1215			−1.08610
$988$		0			0
$989$	55.8039			1.77446
$990$		0			0
$991$	20.3771	+	35.2942i	0.647300	+	1.12116i	0.983765	+	0.179461i	$0.0574352\pi$
$991$	20.3771	+	35.2942i	0.647300	+	1.12116i	−0.336465	+	0.941696i	$0.609231\pi$
$992$		0			0
$993$			41.9541i			1.33137i
$994$		0			0
$995$	−30.2571	−	17.4690i	−0.959216	−	0.553804i
$996$		0			0
$997$	24.8555	−	43.0509i	0.787180	−	1.36344i	−0.140507	−	0.990080i	$-0.544873\pi$
$997$	24.8555	−	43.0509i	0.787180	−	1.36344i	0.927688	−	0.373357i	$-0.121793\pi$
$998$		0			0
$999$	74.5348	−	43.0327i	2.35818	−	1.36149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.h.e.361.6		12
13.2	odd	12		676.2.a.h.1.1	yes	3
13.3	even	3		676.2.d.e.337.2		6
13.4	even	6	inner	676.2.h.e.485.5		12
13.5	odd	4		676.2.e.g.653.3		6
13.6	odd	12		676.2.e.g.529.3		6
13.7	odd	12		676.2.e.f.529.3		6
13.8	odd	4		676.2.e.f.653.3		6
13.9	even	3	inner	676.2.h.e.485.6		12
13.10	even	6		676.2.d.e.337.1		6
13.11	odd	12		676.2.a.g.1.1	✓	3
13.12	even	2	inner	676.2.h.e.361.5		12
39.2	even	12		6084.2.a.x.1.2		3
39.11	even	12		6084.2.a.bc.1.2		3
39.23	odd	6		6084.2.b.p.4393.5		6
39.29	odd	6		6084.2.b.p.4393.2		6
52.3	odd	6		2704.2.f.n.337.6		6
52.11	even	12		2704.2.a.x.1.3		3
52.15	even	12		2704.2.a.y.1.3		3
52.23	odd	6		2704.2.f.n.337.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
676.2.a.g.1.1	✓	3	13.11	odd	12
676.2.a.h.1.1	yes	3	13.2	odd	12
676.2.d.e.337.1		6	13.10	even	6
676.2.d.e.337.2		6	13.3	even	3
676.2.e.f.529.3		6	13.7	odd	12
676.2.e.f.653.3		6	13.8	odd	4
676.2.e.g.529.3		6	13.6	odd	12
676.2.e.g.653.3		6	13.5	odd	4
676.2.h.e.361.5		12	13.12	even	2	inner
676.2.h.e.361.6		12	1.1	even	1	trivial
676.2.h.e.485.5		12	13.4	even	6	inner
676.2.h.e.485.6		12	13.9	even	3	inner
2704.2.a.x.1.3		3	52.11	even	12
2704.2.a.y.1.3		3	52.15	even	12
2704.2.f.n.337.5		6	52.23	odd	6
2704.2.f.n.337.6		6	52.3	odd	6
6084.2.a.x.1.2		3	39.2	even	12
6084.2.a.bc.1.2		3	39.11	even	12
6084.2.b.p.4393.2		6	39.29	odd	6
6084.2.b.p.4393.5		6	39.23	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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.52446 + 2.64044i) q^{3} +2.55496i q^{5} +(-2.73563 - 1.57942i) q^{7} +(-3.14795 + 5.45241i) q^{9} +(0.908389 - 0.524459i) q^{11} +(-6.74621 + 3.89493i) q^{15} +(-1.04407 + 1.80839i) q^{17} +(-2.13632 - 1.23341i) q^{19} -9.63102i q^{21} +(2.19202 + 3.79669i) q^{23} -1.52781 q^{25} -10.0489 q^{27} +(1.57942 + 2.73563i) q^{29} +4.93900i q^{31} +(2.76960 + 1.59903i) q^{33} +(4.03534 - 6.98942i) q^{35} +(-7.41720 + 4.28232i) q^{37} +(9.95406 - 5.74698i) q^{41} +(6.36443 - 11.0235i) q^{43} +(-13.9307 - 8.04288i) q^{45} -3.54288i q^{47} +(1.48911 + 2.57922i) q^{49} -6.36658 q^{51} -8.45473 q^{53} +(1.33997 + 2.32090i) q^{55} -7.52111i q^{57} +(10.8096 + 6.24094i) q^{59} +(-1.78836 + 3.09754i) q^{61} +(17.2232 - 9.94385i) q^{63} +(1.50770 - 0.870469i) q^{67} +(-6.68329 + 11.5758i) q^{69} +(4.06341 + 2.34601i) q^{71} +7.34481i q^{73} +(-2.32908 - 4.03409i) q^{75} -3.31336 q^{77} +6.73556 q^{79} +(-5.87531 - 10.1763i) q^{81} +2.19806i q^{83} +(-4.62035 - 2.66756i) q^{85} +(-4.81551 + 8.34071i) q^{87} +(-11.4194 + 6.59299i) q^{89} +(-13.0411 + 7.52930i) q^{93} +(3.15130 - 5.45821i) q^{95} +(11.4806 + 6.62833i) q^{97} +6.60388i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{9} - 20 q^{17} + 6 q^{23} - 44 q^{25} - 84 q^{27} + 2 q^{29} + 24 q^{35} + 10 q^{43} + 24 q^{49} + 28 q^{51} - 12 q^{53} - 32 q^{55} - 16 q^{61} - 28 q^{69} + 14 q^{75} - 48 q^{77} + 36 q^{79}+ \cdots + 54 q^{95}+O(q^{100}) \) 12 * q - 10 * q^9 - 20 * q^17 + 6 * q^23 - 44 * q^25 - 84 * q^27 + 2 * q^29 + 24 * q^35 + 10 * q^43 + 24 * q^49 + 28 * q^51 - 12 * q^53 - 32 * q^55 - 16 * q^61 - 28 * q^69 + 14 * q^75 - 48 * q^77 + 36 * q^79 + 2 * q^81 - 28 * q^87 + 54 * q^95

Introduction

L-functions

Modular forms

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