LMFDB - Embedded newform 680.2.cg.b.57.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(57,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 0, 4, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.57"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cg (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			57.11
Character	$\chi$	$=$	680.57
Dual form			680.2.cg.b.513.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19803 - 1.79298i) q^{3} +(-2.17385 + 0.523803i) q^{5} +(-0.696254 + 3.50030i) q^{7} +(-0.631450 - 1.52445i) q^{9} +(-0.584025 + 2.93609i) q^{11} +3.18928i q^{13} +(-1.66517 + 4.52521i) q^{15} +(3.77086 + 1.66751i) q^{17} +(0.568477 - 1.37243i) q^{19} +(5.44184 + 5.44184i) q^{21} +(-2.62616 + 1.75474i) q^{23} +(4.45126 - 2.27734i) q^{25} +(2.85508 + 0.567911i) q^{27} +(-4.59419 + 6.87569i) q^{29} +(-1.30893 - 6.58044i) q^{31} +(4.56468 + 4.56468i) q^{33} +(-0.319916 - 7.97384i) q^{35} +(-6.74179 - 4.50472i) q^{37} +(5.71832 + 3.82086i) q^{39} +(5.17262 + 7.74137i) q^{41} +(0.553869 - 1.33716i) q^{43} +(2.17119 + 2.98318i) q^{45} +2.76193 q^{47} +(-5.30020 - 2.19541i) q^{49} +(7.50743 - 4.76335i) q^{51} +(6.70106 - 2.77567i) q^{53} +(-0.268349 - 6.68854i) q^{55} +(-1.77968 - 2.66348i) q^{57} +(-7.46530 + 3.09223i) q^{59} +(-6.94772 + 4.64232i) q^{61} +(5.77570 - 1.14886i) q^{63} +(-1.67055 - 6.93303i) q^{65} +(3.73919 - 3.73919i) q^{67} +6.81089i q^{69} +(1.37331 - 0.273168i) q^{71} +(-0.629073 - 3.16256i) q^{73} +(1.24953 - 10.7093i) q^{75} +(-9.87059 - 4.08853i) q^{77} +(15.8369 + 3.15015i) q^{79} +(7.93903 - 7.93903i) q^{81} +(-3.12593 - 7.54667i) q^{83} +(-9.07074 - 1.64974i) q^{85} +(6.82400 + 16.4746i) q^{87} +(-11.6488 + 11.6488i) q^{89} +(-11.1635 - 2.22055i) q^{91} +(-13.3667 - 5.53669i) q^{93} +(-0.516905 + 3.28122i) q^{95} +(2.20206 + 11.0705i) q^{97} +(4.84472 - 0.963675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 16 q^{15} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 48 q^{33} - 32 q^{35} - 16 q^{37} - 16 q^{41} + 48 q^{43} - 24 q^{45} - 16 q^{47} - 80 q^{49} + 32 q^{51} - 8 q^{53} + 24 q^{55} - 80 q^{59} - 24 q^{61}+ \cdots + 48 q^{99}+O(q^{100}) $ 112 * q + 16 * q^15 - 24 * q^27 - 8 * q^29 + 16 * q^31 - 48 * q^33 - 32 * q^35 - 16 * q^37 - 16 * q^41 + 48 * q^43 - 24 * q^45 - 16 * q^47 - 80 * q^49 + 32 * q^51 - 8 * q^53 + 24 * q^55 - 80 * q^59 - 24 * q^61 - 72 * q^63 + 16 * q^65 - 48 * q^67 - 40 * q^71 - 16 * q^73 + 16 * q^75 + 24 * q^77 + 40 * q^79 - 24 * q^83 + 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^93 - 8 * q^95 + 64 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.19803	−	1.79298i	0.691684	−	1.03518i	−0.304884	−	0.952390i	$-0.598618\pi$
$3$	1.19803	−	1.79298i	0.691684	−	1.03518i	0.996567	−	0.0827881i	$-0.0263825\pi$
$4$		0			0
$5$	−2.17385	+	0.523803i	−0.972176	+	0.234252i
$5$	−2.17385	+	0.523803i	−0.972176	+	0.234252i
$6$		0			0
$7$	−0.696254	+	3.50030i	−0.263159	+	1.32299i	0.592550	+	0.805533i	$0.298121\pi$
$7$	−0.696254	+	3.50030i	−0.263159	+	1.32299i	−0.855709	+	0.517457i	$0.826879\pi$
$8$		0			0
$9$	−0.631450	−	1.52445i	−0.210483	−	0.508151i
$10$		0			0
$11$	−0.584025	+	2.93609i	−0.176090	+	0.885265i	0.787178	+	0.616725i	$0.211541\pi$
$11$	−0.584025	+	2.93609i	−0.176090	+	0.885265i	−0.963269	+	0.268540i	$0.913459\pi$
$12$		0			0
$13$			3.18928i			0.884548i	0.896880	+	0.442274i	$0.145828\pi$
$13$			3.18928i			0.884548i	−0.896880	+	0.442274i	$0.854172\pi$
$14$		0			0
$15$	−1.66517	+	4.52521i	−0.429946	+	1.16840i
$16$		0			0
$17$	3.77086	+	1.66751i	0.914568	+	0.404431i
$17$	3.77086	+	1.66751i	0.914568	+	0.404431i
$18$		0			0
$19$	0.568477	−	1.37243i	0.130418	−	0.314856i	−0.845159	−	0.534515i	$-0.820494\pi$
$19$	0.568477	−	1.37243i	0.130418	−	0.314856i	0.975577	+	0.219659i	$0.0704944\pi$
$20$		0			0
$21$	5.44184	+	5.44184i	1.18751	+	1.18751i
$22$		0			0
$23$	−2.62616	+	1.75474i	−0.547593	+	0.365890i	−0.798381	−	0.602152i	$-0.794310\pi$
$23$	−2.62616	+	1.75474i	−0.547593	+	0.365890i	0.250789	+	0.968042i	$0.419310\pi$
$24$		0			0
$25$	4.45126	−	2.27734i	0.890252	−	0.455468i
$26$		0			0
$27$	2.85508	+	0.567911i	0.549461	+	0.109295i
$28$		0			0
$29$	−4.59419	+	6.87569i	−0.853120	+	1.27678i	0.106167	+	0.994348i	$0.466142\pi$
$29$	−4.59419	+	6.87569i	−0.853120	+	1.27678i	−0.959286	+	0.282435i	$0.908858\pi$
$30$		0			0
$31$	−1.30893	−	6.58044i	−0.235091	−	1.18188i	−0.900315	−	0.435239i	$-0.856664\pi$
$31$	−1.30893	−	6.58044i	−0.235091	−	1.18188i	0.665224	−	0.746644i	$-0.268336\pi$
$32$		0			0
$33$	4.56468	+	4.56468i	0.794608	+	0.794608i
$34$		0			0
$35$	−0.319916	−	7.97384i	−0.0540757	−	1.34782i
$36$		0			0
$37$	−6.74179	−	4.50472i	−1.10834	−	0.740572i	−0.139990	−	0.990153i	$-0.544707\pi$
$37$	−6.74179	−	4.50472i	−1.10834	−	0.740572i	−0.968354	+	0.249581i	$0.919707\pi$
$38$		0			0
$39$	5.71832	+	3.82086i	0.915664	+	0.611827i
$40$		0			0
$41$	5.17262	+	7.74137i	0.807827	+	1.20900i	0.974810	+	0.223038i	$0.0715975\pi$
$41$	5.17262	+	7.74137i	0.807827	+	1.20900i	−0.166983	+	0.985960i	$0.553402\pi$
$42$		0			0
$43$	0.553869	−	1.33716i	0.0844642	−	0.203915i	−0.876004	−	0.482303i	$-0.839800\pi$
$43$	0.553869	−	1.33716i	0.0844642	−	0.203915i	0.960469	+	0.278389i	$0.0898003\pi$
$44$		0			0
$45$	2.17119	+	2.98318i	0.323662	+	0.444707i
$46$		0			0
$47$	2.76193			0.402869			0.201435	−	0.979502i	$-0.435440\pi$
$47$	2.76193			0.402869			0.201435	+	0.979502i	$0.435440\pi$
$48$		0			0
$49$	−5.30020	−	2.19541i	−0.757171	−	0.313630i
$50$		0			0
$51$	7.50743	−	4.76335i	1.05125	−	0.667002i
$52$		0			0
$53$	6.70106	−	2.77567i	0.920461	−	0.381267i	0.128409	−	0.991721i	$-0.459013\pi$
$53$	6.70106	−	2.77567i	0.920461	−	0.381267i	0.792052	+	0.610454i	$0.209013\pi$
$54$		0			0
$55$	−0.268349	−	6.68854i	−0.0361842	−	0.901883i
$56$		0			0
$57$	−1.77968	−	2.66348i	−0.235724	−	0.352786i
$58$		0			0
$59$	−7.46530	+	3.09223i	−0.971900	+	0.402574i	−0.811419	−	0.584465i	$-0.801304\pi$
$59$	−7.46530	+	3.09223i	−0.971900	+	0.402574i	−0.160481	+	0.987039i	$0.551304\pi$
$60$		0			0
$61$	−6.94772	+	4.64232i	−0.889564	+	0.594388i	−0.914180	−	0.405309i	$-0.867164\pi$
$61$	−6.94772	+	4.64232i	−0.889564	+	0.594388i	0.0246154	+	0.999697i	$0.492164\pi$
$62$		0			0
$63$	5.77570	−	1.14886i	0.727670	−	0.144743i
$64$		0			0
$65$	−1.67055	−	6.93303i	−0.207207	−	0.859936i
$66$		0			0
$67$	3.73919	−	3.73919i	0.456815	−	0.456815i	−0.440794	−	0.897608i	$-0.645303\pi$
$67$	3.73919	−	3.73919i	0.456815	−	0.456815i	0.897608	+	0.440794i	$0.145303\pi$
$68$		0			0
$69$			6.81089i			0.819935i
$70$		0			0
$71$	1.37331	−	0.273168i	0.162982	−	0.0324191i	−0.112925	−	0.993604i	$-0.536022\pi$
$71$	1.37331	−	0.273168i	0.162982	−	0.0324191i	0.275907	+	0.961184i	$0.411022\pi$
$72$		0			0
$73$	−0.629073	−	3.16256i	−0.0736274	−	0.370150i	0.926351	−	0.376660i	$-0.122928\pi$
$73$	−0.629073	−	3.16256i	−0.0736274	−	0.370150i	−0.999979	+	0.00651048i	$0.997928\pi$
$74$		0			0
$75$	1.24953	−	10.7093i	0.144283	−	1.23661i
$76$		0			0
$77$	−9.87059	−	4.08853i	−1.12486	−	0.465931i
$78$		0			0
$79$	15.8369	+	3.15015i	1.78179	+	0.354420i	0.972484	−	0.232970i	$-0.0748442\pi$
$79$	15.8369	+	3.15015i	1.78179	+	0.354420i	0.809305	+	0.587389i	$0.199844\pi$
$80$		0			0
$81$	7.93903	−	7.93903i	0.882114	−	0.882114i
$82$		0			0
$83$	−3.12593	−	7.54667i	−0.343116	−	0.828355i	−0.997397	−	0.0721038i	$-0.977029\pi$
$83$	−3.12593	−	7.54667i	−0.343116	−	0.828355i	0.654281	−	0.756251i	$-0.272971\pi$
$84$		0			0
$85$	−9.07074	−	1.64974i	−0.983860	−	0.178939i
$86$		0			0
$87$	6.82400	+	16.4746i	0.731609	+	1.76626i
$88$		0			0
$89$	−11.6488	+	11.6488i	−1.23477	+	1.23477i	−0.272663	+	0.962109i	$0.587905\pi$
$89$	−11.6488	+	11.6488i	−1.23477	+	1.23477i	−0.962109	+	0.272663i	$0.912095\pi$
$90$		0			0
$91$	−11.1635	−	2.22055i	−1.17025	−	0.232777i
$92$		0			0
$93$	−13.3667	−	5.53669i	−1.38607	−	0.574128i
$94$		0			0
$95$	−0.516905	+	3.28122i	−0.0530333	+	0.336646i
$96$		0			0
$97$	2.20206	+	11.0705i	0.223585	+	1.12404i	0.915580	+	0.402137i	$0.131732\pi$
$97$	2.20206	+	11.0705i	0.223585	+	1.12404i	−0.691994	+	0.721903i	$0.743268\pi$
$98$		0			0
$99$	4.84472	−	0.963675i	0.486913	−	0.0968530i
$100$		0			0
$101$			16.9816i			1.68973i	0.534978	+	0.844866i	$0.320320\pi$
$101$			16.9816i			1.68973i	−0.534978	+	0.844866i	$0.679680\pi$
$102$		0			0
$103$	3.64303	−	3.64303i	0.358959	−	0.358959i	−0.504470	−	0.863429i	$-0.668312\pi$
$103$	3.64303	−	3.64303i	0.358959	−	0.358959i	0.863429	+	0.504470i	$0.168312\pi$
$104$		0			0
$105$	−14.6802	−	8.97930i	−1.43264	−	0.876290i
$106$		0			0
$107$	−0.944757	+	0.187924i	−0.0913331	+	0.0181673i	−0.240545	−	0.970638i	$-0.577326\pi$
$107$	−0.944757	+	0.187924i	−0.0913331	+	0.0181673i	0.149212	+	0.988805i	$0.452326\pi$
$108$		0			0
$109$	2.42146	−	1.61797i	0.231934	−	0.154973i	−0.434173	−	0.900829i	$-0.642959\pi$
$109$	2.42146	−	1.61797i	0.231934	−	0.154973i	0.666107	+	0.745856i	$0.267959\pi$
$110$		0			0
$111$	−16.1538	+	6.69110i	−1.53325	+	0.635091i
$112$		0			0
$113$	0.177729	+	0.265990i	0.0167193	+	0.0250222i	0.839735	−	0.542996i	$-0.182710\pi$
$113$	0.177729	+	0.265990i	0.0167193	+	0.0250222i	−0.823016	+	0.568018i	$0.807710\pi$
$114$		0			0
$115$	4.78975	−	5.19015i	0.446646	−	0.483984i
$116$		0			0
$117$	4.86191	−	2.01387i	0.449484	−	0.186182i
$118$		0			0
$119$	−8.46228	+	12.0381i	−0.775736	+	1.10354i
$120$		0			0
$121$	1.88312	+	0.780013i	0.171193	+	0.0709103i
$122$		0			0
$123$	20.0771			1.81029
$124$		0			0
$125$	−8.48351	+	7.28218i	−0.758788	+	0.651338i
$126$		0			0
$127$	1.56712	−	3.78336i	0.139059	−	0.335719i	−0.838973	−	0.544174i	$-0.816843\pi$
$127$	1.56712	−	3.78336i	0.139059	−	0.335719i	0.978032	+	0.208454i	$0.0668433\pi$
$128$		0			0
$129$	−1.73395	−	2.59503i	−0.152665	−	0.228480i
$130$		0			0
$131$	−14.6869	−	9.81350i	−1.28320	−	0.857410i	−0.288232	−	0.957561i	$-0.593067\pi$
$131$	−14.6869	−	9.81350i	−1.28320	−	0.857410i	−0.994972	+	0.100151i	$0.968067\pi$
$132$		0			0
$133$	4.40810	+	2.94540i	0.382231	+	0.255398i
$134$		0			0
$135$	−6.50400	+	0.260945i	−0.559775	+	0.0224586i
$136$		0			0
$137$	−1.21496	−	1.21496i	−0.103801	−	0.103801i	0.653299	−	0.757100i	$-0.273384\pi$
$137$	−1.21496	−	1.21496i	−0.103801	−	0.103801i	−0.757100	+	0.653299i	$0.773384\pi$
$138$		0			0
$139$	1.13885	+	5.72536i	0.0965956	+	0.485619i	0.998552	+	0.0537921i	$0.0171308\pi$
$139$	1.13885	+	5.72536i	0.0965956	+	0.485619i	−0.901957	+	0.431827i	$0.857869\pi$
$140$		0			0
$141$	3.30888	−	4.95209i	0.278658	−	0.417041i
$142$		0			0
$143$	−9.36403	−	1.86262i	−0.783059	−	0.155760i
$144$		0			0
$145$	6.38558	−	17.3532i	0.530294	−	1.44110i
$146$		0			0
$147$	−10.2861	+	6.87297i	−0.848386	+	0.566873i
$148$		0			0
$149$	14.3725	+	14.3725i	1.17744	+	1.17744i	0.980394	+	0.197045i	$0.0631345\pi$
$149$	14.3725	+	14.3725i	1.17744	+	1.17744i	0.197045	+	0.980394i	$0.436865\pi$
$150$		0			0
$151$	4.24187	−	10.2408i	0.345199	−	0.833384i	−0.651974	−	0.758241i	$-0.726059\pi$
$151$	4.24187	−	10.2408i	0.345199	−	0.833384i	0.997173	−	0.0751424i	$-0.0239411\pi$
$152$		0			0
$153$	0.160938	−	6.80146i	0.0130110	−	0.549865i
$154$		0			0
$155$	6.29228	+	13.6193i	0.505408	+	1.09393i
$156$		0			0
$157$		−	12.2792i		−	0.979984i	−0.871727	−	0.489992i	$-0.837000\pi$
$157$		−	12.2792i		−	0.979984i	0.871727	−	0.489992i	$-0.163000\pi$
$158$		0			0
$159$	3.05136	−	15.3402i	0.241988	−	1.21656i
$160$		0			0
$161$	−4.31366	−	10.4141i	−0.339964	−	0.820747i
$162$		0			0
$163$	0.706706	−	3.55285i	0.0553535	−	0.278281i	−0.943189	−	0.332257i	$-0.892190\pi$
$163$	0.706706	−	3.55285i	0.0553535	−	0.278281i	0.998542	+	0.0539768i	$0.0171897\pi$
$164$		0			0
$165$	−12.3139	−	7.53194i	−0.958637	−	0.586361i
$166$		0			0
$167$	9.93826	−	14.8737i	0.769046	−	1.15096i	−0.215615	−	0.976478i	$-0.569176\pi$
$167$	9.93826	−	14.8737i	0.769046	−	1.15096i	0.984661	−	0.174480i	$-0.0558244\pi$
$168$		0			0
$169$	2.82848			0.217575
$170$		0			0
$171$	−2.45116			−0.187445
$172$		0			0
$173$	11.2221	−	16.7951i	0.853202	−	1.27691i	−0.106052	−	0.994361i	$-0.533821\pi$
$173$	11.2221	−	16.7951i	0.853202	−	1.27691i	0.959254	−	0.282546i	$-0.0911791\pi$
$174$		0			0
$175$	4.87217	+	17.1664i	0.368301	+	1.29766i
$176$		0			0
$177$	−3.39936	+	17.0897i	−0.255511	+	1.28454i
$178$		0			0
$179$	−9.66314	−	23.3289i	−0.722257	−	1.74368i	−0.666819	−	0.745220i	$-0.732344\pi$
$179$	−9.66314	−	23.3289i	−0.722257	−	1.74368i	−0.0554380	−	0.998462i	$-0.517656\pi$
$180$		0			0
$181$	2.77423	−	13.9470i	0.206207	−	1.03667i	−0.729523	−	0.683956i	$-0.760258\pi$
$181$	2.77423	−	13.9470i	0.206207	−	1.03667i	0.935730	−	0.352717i	$-0.114742\pi$
$182$		0			0
$183$			18.0188i			1.33199i
$184$		0			0
$185$	17.0152	+	6.26123i	1.25099	+	0.460335i
$186$		0			0
$187$	−7.09825	+	10.0977i	−0.519076	+	0.738419i
$188$		0			0
$189$	−3.97572	+	9.59824i	−0.289191	+	0.698169i
$190$		0			0
$191$	−16.6356	−	16.6356i	−1.20371	−	1.20371i	−0.973029	−	0.230682i	$-0.925904\pi$
$191$	−16.6356	−	16.6356i	−1.20371	−	1.20371i	−0.230682	−	0.973029i	$-0.574096\pi$
$192$		0			0
$193$	−1.42491	+	0.952095i	−0.102567	+	0.0685333i	−0.605796	−	0.795620i	$-0.707145\pi$
$193$	−1.42491	+	0.952095i	−0.102567	+	0.0685333i	0.503229	+	0.864153i	$0.332145\pi$
$194$		0			0
$195$	−14.4322	−	5.31071i	−1.03351	−	0.380308i
$196$		0			0
$197$	7.37642	+	1.46726i	0.525548	+	0.104538i	0.450732	−	0.892659i	$-0.351163\pi$
$197$	7.37642	+	1.46726i	0.525548	+	0.104538i	0.0748160	+	0.997197i	$0.476163\pi$
$198$		0			0
$199$	−5.36549	+	8.03003i	−0.380350	+	0.569234i	−0.971414	−	0.237391i	$-0.923708\pi$
$199$	−5.36549	+	8.03003i	−0.380350	+	0.569234i	0.591064	+	0.806624i	$0.298708\pi$
$200$		0			0
$201$	−2.22463	−	11.1840i	−0.156913	−	0.788856i
$202$		0			0
$203$	−20.8683	−	20.8683i	−1.46467	−	1.46467i
$204$		0			0
$205$	−15.2994	−	14.1192i	−1.06856	−	0.986124i
$206$		0			0
$207$	4.33332	+	2.89543i	0.301186	+	0.201246i
$208$		0			0
$209$	3.69756	+	2.47063i	0.255766	+	0.170897i
$210$		0			0
$211$	−3.82382	−	5.72275i	−0.263242	−	0.393970i	0.676177	−	0.736739i	$-0.263635\pi$
$211$	−3.82382	−	5.72275i	−0.263242	−	0.393970i	−0.939420	+	0.342769i	$0.888635\pi$
$212$		0			0
$213$	1.15548	−	2.78958i	0.0791722	−	0.191139i
$214$		0			0
$215$	−0.503622	+	3.19690i	−0.0343467	+	0.218027i
$216$		0			0
$217$	23.9449			1.62549
$218$		0			0
$219$	−6.42406	−	2.66093i	−0.434098	−	0.179809i
$220$		0			0
$221$	−5.31817	+	12.0263i	−0.357739	+	0.808979i
$222$		0			0
$223$	19.6506	−	8.13956i	1.31590	−	0.545065i	0.389303	−	0.921110i	$-0.372716\pi$
$223$	19.6506	−	8.13956i	1.31590	−	0.545065i	0.926602	+	0.376044i	$0.122716\pi$
$224$		0			0
$225$	−6.28244	−	5.34772i	−0.418830	−	0.356515i
$226$		0			0
$227$	9.26430	+	13.8650i	0.614893	+	0.920252i	0.999997	−	0.00262106i	$-0.000834311\pi$
$227$	9.26430	+	13.8650i	0.614893	+	0.920252i	−0.385104	+	0.922873i	$0.625834\pi$
$228$		0			0
$229$	1.26501	−	0.523985i	0.0835944	−	0.0346259i	−0.340494	−	0.940247i	$-0.610594\pi$
$229$	1.26501	−	0.523985i	0.0835944	−	0.0346259i	0.424089	+	0.905621i	$0.360594\pi$
$230$		0			0
$231$	−19.1559	+	12.7996i	−1.26037	+	0.842150i
$232$		0			0
$233$	13.0065	−	2.58715i	0.852082	−	0.169490i	0.250318	−	0.968164i	$-0.419465\pi$
$233$	13.0065	−	2.58715i	0.852082	−	0.169490i	0.601764	+	0.798674i	$0.294465\pi$
$234$		0			0
$235$	−6.00403	+	1.44671i	−0.391660	+	0.0943728i
$236$		0			0
$237$	24.6212	−	24.6212i	1.59932	−	1.59932i
$238$		0			0
$239$			2.74304i			0.177432i	0.996057	+	0.0887162i	$0.0282764\pi$
$239$			2.74304i			0.177432i	−0.996057	+	0.0887162i	$0.971724\pi$
$240$		0			0
$241$	−20.2804	+	4.03402i	−1.30638	+	0.259854i	−0.798719	−	0.601705i	$-0.794488\pi$
$241$	−20.2804	+	4.03402i	−1.30638	+	0.259854i	−0.507657	+	0.861559i	$0.669488\pi$
$242$		0			0
$243$	−3.01959	−	15.1805i	−0.193707	−	0.973829i
$244$		0			0
$245$	12.6718	+	1.99625i	0.809572	+	0.127535i
$246$		0			0
$247$	4.37705	+	1.81303i	0.278505	+	0.115361i
$248$		0			0
$249$	−17.2760	−	3.43641i	−1.09482	−	0.217774i
$250$		0			0
$251$	5.97237	−	5.97237i	0.376973	−	0.376973i	−0.493036	−	0.870009i	$-0.664113\pi$
$251$	5.97237	−	5.97237i	0.376973	−	0.376973i	0.870009	+	0.493036i	$0.164113\pi$
$252$		0			0
$253$	−3.61835	−	8.73547i	−0.227484	−	0.549194i
$254$		0			0
$255$	−13.8250	+	14.2872i	−0.865754	+	0.894701i
$256$		0			0
$257$	−5.67211	−	13.6937i	−0.353817	−	0.854189i	−0.996142	−	0.0877570i	$-0.972030\pi$
$257$	−5.67211	−	13.6937i	−0.353817	−	0.854189i	0.642325	−	0.766432i	$-0.277970\pi$
$258$		0			0
$259$	20.4619	−	20.4619i	1.27144	−	1.27144i
$260$		0			0
$261$	13.3827	+	2.66198i	0.828367	+	0.164772i
$262$		0			0
$263$	21.9410	+	9.08824i	1.35294	+	0.560405i	0.937109	−	0.349038i	$-0.113492\pi$
$263$	21.9410	+	9.08824i	1.35294	+	0.560405i	0.415829	+	0.909443i	$0.363492\pi$
$264$		0			0
$265$	−13.1132	+	9.54392i	−0.805537	+	0.586278i
$266$		0			0
$267$	6.93046	+	34.8418i	0.424137	+	2.13228i
$268$		0			0
$269$	6.27724	−	1.24862i	0.382730	−	0.0761297i	2.42140e−5	−	1.00000i	$-0.499992\pi$
$269$	6.27724	−	1.24862i	0.382730	−	0.0761297i	0.382706	+	0.923870i	$0.374992\pi$
$270$		0			0
$271$			1.45756i			0.0885406i	0.999020	+	0.0442703i	$0.0140963\pi$
$271$			1.45756i			0.0885406i	−0.999020	+	0.0442703i	$0.985904\pi$
$272$		0			0
$273$	−17.3556	+	17.3556i	−1.05041	+	1.05041i
$274$		0			0
$275$	4.08683	+	14.3993i	0.246445	+	0.868313i
$276$		0			0
$277$	17.4271	−	3.46646i	1.04709	−	0.208280i	0.358576	−	0.933501i	$-0.383262\pi$
$277$	17.4271	−	3.46646i	1.04709	−	0.208280i	0.688516	+	0.725221i	$0.258262\pi$
$278$		0			0
$279$	−9.20506	+	6.15062i	−0.551092	+	0.368228i
$280$		0			0
$281$	−10.2518	+	4.24643i	−0.611570	+	0.253321i	−0.666900	−	0.745148i	$-0.732379\pi$
$281$	−10.2518	+	4.24643i	−0.611570	+	0.253321i	0.0553296	+	0.998468i	$0.482379\pi$
$282$		0			0
$283$	9.98430	+	14.9426i	0.593505	+	0.888243i	0.999673	−	0.0255551i	$-0.00813533\pi$
$283$	9.98430	+	14.9426i	0.593505	+	0.888243i	−0.406168	+	0.913798i	$0.633135\pi$
$284$		0			0
$285$	5.26389	+	4.85780i	0.311806	+	0.287751i
$286$		0			0
$287$	−30.6986	+	12.7158i	−1.81208	+	0.750588i
$288$		0			0
$289$	11.4388	+	12.5759i	0.672871	+	0.739760i
$290$		0			0
$291$	22.4873	+	9.31456i	1.31823	+	0.546029i
$292$		0			0
$293$	9.67627			0.565294			0.282647	−	0.959224i	$-0.408788\pi$
$293$	9.67627			0.565294			0.282647	+	0.959224i	$0.408788\pi$
$294$		0			0
$295$	14.6087	−	10.6324i	0.850554	−	0.619042i
$296$		0			0
$297$	−3.33488	+	8.05111i	−0.193509	+	0.467173i
$298$		0			0
$299$	−5.59638	−	8.37557i	−0.323647	−	0.484372i
$300$		0			0
$301$	4.29482	+	2.86971i	0.247549	+	0.165407i
$302$		0			0
$303$	30.4477	+	20.3445i	1.74917	+	1.16876i
$304$		0			0
$305$	12.6717	−	13.7309i	0.725577	−	0.786231i
$306$		0			0
$307$	−11.0018	−	11.0018i	−0.627906	−	0.627906i	0.319635	−	0.947541i	$-0.396440\pi$
$307$	−11.0018	−	11.0018i	−0.627906	−	0.627906i	−0.947541	+	0.319635i	$0.896440\pi$
$308$		0			0
$309$	−2.16742	−	10.8964i	−0.123300	−	0.619872i
$310$		0			0
$311$	3.14541	−	4.70744i	0.178360	−	0.266934i	−0.731508	−	0.681833i	$-0.761183\pi$
$311$	3.14541	−	4.70744i	0.178360	−	0.266934i	0.909868	+	0.414899i	$0.136183\pi$
$312$		0			0
$313$	31.4220	+	6.25022i	1.77607	+	0.353283i	0.970850	−	0.239687i	$-0.0770449\pi$
$313$	31.4220	+	6.25022i	1.77607	+	0.353283i	0.805224	+	0.592971i	$0.202045\pi$
$314$		0			0
$315$	−11.9537	+	5.52277i	−0.673517	+	0.311173i
$316$		0			0
$317$	−12.5675	+	8.39736i	−0.705863	+	0.471643i	−0.855969	−	0.517027i	$-0.827039\pi$
$317$	−12.5675	+	8.39736i	−0.705863	+	0.471643i	0.150106	+	0.988670i	$0.452039\pi$
$318$		0			0
$319$	−17.5045	−	17.5045i	−0.980066	−	0.980066i
$320$		0			0
$321$	−0.794905	+	1.91907i	−0.0443673	+	0.107112i
$322$		0			0
$323$	4.43219	−	4.22728i	0.246613	−	0.235212i
$324$		0			0
$325$	7.26307	+	14.1963i	0.402883	+	0.787471i
$326$		0			0
$327$		−	6.28000i		−	0.347285i
$328$		0			0
$329$	−1.92301	+	9.66760i	−0.106019	+	0.532992i
$330$		0			0
$331$	−0.944647	−	2.28058i	−0.0519225	−	0.125352i	0.895790	−	0.444478i	$-0.146611\pi$
$331$	−0.944647	−	2.28058i	−0.0519225	−	0.125352i	−0.947712	+	0.319126i	$0.896611\pi$
$332$		0			0
$333$	−2.61014	+	13.1221i	−0.143035	+	0.719084i
$334$		0			0
$335$	−6.16985	+	10.0870i	−0.337095	+	0.551114i
$336$		0			0
$337$	−9.92520	+	14.8541i	−0.540660	+	0.809155i	−0.996731	−	0.0807881i	$-0.974256\pi$
$337$	−9.92520	+	14.8541i	−0.540660	+	0.809155i	0.456071	+	0.889943i	$0.349256\pi$
$338$		0			0
$339$	0.689840			0.0374670
$340$		0			0
$341$	20.0852			1.08768
$342$		0			0
$343$	−2.50445	+	3.74817i	−0.135227	+	0.202382i
$344$		0			0
$345$	−3.56756	−	14.8059i	−0.192071	−	0.797122i
$346$		0			0
$347$	−6.76613	+	34.0157i	−0.363225	+	1.82606i	0.176605	+	0.984282i	$0.443489\pi$
$347$	−6.76613	+	34.0157i	−0.363225	+	1.82606i	−0.539830	+	0.841774i	$0.681511\pi$
$348$		0			0
$349$	−6.94292	−	16.7617i	−0.371646	−	0.897233i	−0.993472	−	0.114078i	$-0.963609\pi$
$349$	−6.94292	−	16.7617i	−0.371646	−	0.897233i	0.621826	−	0.783156i	$-0.286391\pi$
$350$		0			0
$351$	−1.81123	+	9.10566i	−0.0966762	+	0.486024i
$352$		0			0
$353$			2.72376i			0.144971i	0.997369	+	0.0724855i	$0.0230931\pi$
$353$			2.72376i			0.144971i	−0.997369	+	0.0724855i	$0.976907\pi$
$354$		0			0
$355$	−2.84228	+	1.31317i	−0.150853	+	0.0696958i
$356$		0			0
$357$	11.4461	+	29.5948i	0.605791	+	1.56632i
$358$		0			0
$359$	−10.9942	+	26.5422i	−0.580249	+	1.40085i	0.312338	+	0.949971i	$0.398888\pi$
$359$	−10.9942	+	26.5422i	−0.580249	+	1.40085i	−0.892587	+	0.450875i	$0.851112\pi$
$360$		0			0
$361$	11.8746	+	11.8746i	0.624981	+	0.624981i
$362$		0			0
$363$	3.65458	−	2.44191i	0.191816	−	0.128167i
$364$		0			0
$365$	3.02407	+	6.54543i	0.158287	+	0.342604i
$366$		0			0
$367$	−21.0419	−	4.18549i	−1.09838	−	0.218481i	−0.387551	−	0.921848i	$-0.626679\pi$
$367$	−21.0419	−	4.18549i	−1.09838	−	0.218481i	−0.710827	+	0.703367i	$0.751679\pi$
$368$		0			0
$369$	8.53511	−	12.7737i	0.444320	−	0.664972i
$370$		0			0
$371$	5.05005	+	25.3883i	0.262185	+	1.31809i
$372$		0			0
$373$	−19.6466	−	19.6466i	−1.01726	−	1.01726i	−0.999848	−	0.0174135i	$-0.994457\pi$
$373$	−19.6466	−	19.6466i	−1.01726	−	1.01726i	−0.0174135	−	0.999848i	$-0.505543\pi$
$374$		0			0
$375$	2.89330	+	23.9350i	0.149409	+	1.23600i
$376$		0			0
$377$	−21.9285	−	14.6522i	−1.12938	−	0.754625i
$378$		0			0
$379$	25.0333	+	16.7267i	1.28587	+	0.859194i	0.995222	−	0.0976345i	$-0.0311276\pi$
$379$	25.0333	+	16.7267i	1.28587	+	0.859194i	0.290653	+	0.956829i	$0.406128\pi$
$380$		0			0
$381$	−4.90603	−	7.34240i	−0.251344	−	0.376163i
$382$		0			0
$383$	−3.61821	+	8.73512i	−0.184882	+	0.446344i	−0.988961	−	0.148179i	$-0.952659\pi$
$383$	−3.61821	+	8.73512i	−0.184882	+	0.446344i	0.804079	+	0.594523i	$0.202659\pi$
$384$		0			0
$385$	23.5988	+	3.71762i	1.20270	+	0.189467i
$386$		0			0
$387$	−2.38818			−0.121398
$388$		0			0
$389$	−1.74313	−	0.722027i	−0.0883801	−	0.0366082i	0.338055	−	0.941126i	$-0.390231\pi$
$389$	−1.74313	−	0.722027i	−0.0883801	−	0.0366082i	−0.426435	+	0.904518i	$0.640231\pi$
$390$		0			0
$391$	−12.8290	+	2.23774i	−0.648788	+	0.113168i
$392$		0			0
$393$	−35.1908	+	14.5765i	−1.77514	+	0.735288i
$394$		0			0
$395$	−36.0771	+	1.44744i	−1.81524	+	0.0728285i
$396$		0			0
$397$	−14.8627	−	22.2437i	−0.745940	−	1.11638i	−0.989222	−	0.146422i	$-0.953224\pi$
$397$	−14.8627	−	22.2437i	−0.745940	−	1.11638i	0.243282	−	0.969956i	$-0.421776\pi$
$398$		0			0
$399$	10.5621	−	4.37496i	0.528766	−	0.219022i
$400$		0			0
$401$	−4.11241	+	2.74783i	−0.205364	+	0.137220i	−0.654000	−	0.756495i	$-0.726910\pi$
$401$	−4.11241	+	2.74783i	−0.205364	+	0.137220i	0.448635	+	0.893715i	$0.351910\pi$
$402$		0			0
$403$	20.9869	−	4.17455i	1.04543	−	0.207949i
$404$		0			0
$405$	−13.0998	+	21.4168i	−0.650934	+	1.06421i
$406$		0			0
$407$	17.1637	−	17.1637i	0.850771	−	0.850771i
$408$		0			0
$409$		−	9.36133i		−	0.462888i	−0.972848	−	0.231444i	$-0.925655\pi$
$409$		−	9.36133i		−	0.462888i	0.972848	−	0.231444i	$-0.0743450\pi$
$410$		0			0
$411$	−3.63396	+	0.722840i	−0.179250	+	0.0356551i
$412$		0			0
$413$	−5.62600	−	28.2838i	−0.276837	−	1.39175i
$414$		0			0
$415$	10.7483	+	14.7680i	0.527613	+	0.724931i
$416$		0			0
$417$	11.6298	+	4.81723i	0.569515	+	0.235901i
$418$		0			0
$419$	6.29873	+	1.25289i	0.307713	+	0.0612079i	0.346531	−	0.938038i	$-0.387359\pi$
$419$	6.29873	+	1.25289i	0.307713	+	0.0612079i	−0.0388184	+	0.999246i	$0.512359\pi$
$420$		0			0
$421$	−6.28214	+	6.28214i	−0.306173	+	0.306173i	−0.843423	−	0.537250i	$-0.819463\pi$
$421$	−6.28214	+	6.28214i	−0.306173	+	0.306173i	0.537250	+	0.843423i	$0.319463\pi$
$422$		0			0
$423$	−1.74402	−	4.21044i	−0.0847972	−	0.204719i
$424$		0			0
$425$	20.5826	−	1.16499i	0.998402	−	0.0565104i
$426$		0			0
$427$	−11.4121	−	27.5514i	−0.552272	−	1.33330i
$428$		0			0
$429$	−14.5580	+	14.5580i	−0.702869	+	0.702869i
$430$		0			0
$431$	15.9001	+	3.16274i	0.765883	+	0.152344i	0.562547	−	0.826765i	$-0.309822\pi$
$431$	15.9001	+	3.16274i	0.765883	+	0.152344i	0.203336	+	0.979109i	$0.434822\pi$
$432$		0			0
$433$	13.0881	+	5.42127i	0.628974	+	0.260530i	0.674317	−	0.738442i	$-0.264438\pi$
$433$	13.0881	+	5.42127i	0.628974	+	0.260530i	−0.0453430	+	0.998971i	$0.514438\pi$
$434$		0			0
$435$	−23.4638	−	32.2389i	−1.12500	−	1.54574i
$436$		0			0
$437$	0.915344	+	4.60174i	0.0437868	+	0.220131i
$438$		0			0
$439$	18.9806	−	3.77549i	0.905897	−	0.180194i	0.279909	−	0.960027i	$-0.409696\pi$
$439$	18.9806	−	3.77549i	0.905897	−	0.180194i	0.625988	+	0.779833i	$0.284696\pi$
$440$		0			0
$441$			9.46620i			0.450771i
$442$		0			0
$443$	21.0038	−	21.0038i	0.997920	−	0.997920i	−0.00207769	−	0.999998i	$-0.500661\pi$
$443$	21.0038	−	21.0038i	0.997920	−	0.997920i	0.999998	+	0.00207769i	$0.000661348\pi$
$444$		0			0
$445$	19.2211	−	31.4245i	0.911169	−	1.48966i
$446$		0			0
$447$	42.9883	−	8.55090i	2.03327	−	0.404444i
$448$		0			0
$449$	−6.79732	+	4.54183i	−0.320786	+	0.214342i	−0.705528	−	0.708682i	$-0.749290\pi$
$449$	−6.79732	+	4.54183i	−0.320786	+	0.214342i	0.384743	+	0.923024i	$0.374290\pi$
$450$		0			0
$451$	−25.7503	+	10.6661i	−1.21253	+	0.502248i
$452$		0			0
$453$	−13.2796	−	19.8744i	−0.623932	−	0.933780i
$454$		0			0
$455$	25.4308	−	1.02030i	1.19222	−	0.0478325i
$456$		0			0
$457$	−0.0610986	+	0.0253079i	−0.00285807	+	0.00118385i	−0.384112	−	0.923287i	$-0.625492\pi$
$457$	−0.0610986	+	0.0253079i	−0.00285807	+	0.00118385i	0.381254	+	0.924470i	$0.375492\pi$
$458$		0			0
$459$	9.81912	+	6.90240i	0.458317	+	0.322176i
$460$		0			0
$461$	30.9050	+	12.8013i	1.43939	+	0.596215i	0.959650	−	0.281197i	$-0.0907313\pi$
$461$	30.9050	+	12.8013i	1.43939	+	0.596215i	0.479739	+	0.877411i	$0.340731\pi$
$462$		0			0
$463$	9.16247			0.425816			0.212908	−	0.977072i	$-0.431707\pi$
$463$	9.16247			0.425816			0.212908	+	0.977072i	$0.431707\pi$
$464$		0			0
$465$	31.9575	+	5.03440i	1.48199	+	0.233465i
$466$		0			0
$467$	13.0930	−	31.6094i	0.605874	−	1.46271i	−0.261576	−	0.965183i	$-0.584242\pi$
$467$	13.0930	−	31.6094i	0.605874	−	1.46271i	0.867450	−	0.497525i	$-0.165758\pi$
$468$		0			0
$469$	10.4849	+	15.6917i	0.484146	+	0.724576i
$470$		0			0
$471$	−22.0163	−	14.7108i	−1.01446	−	0.677839i
$472$		0			0
$473$	3.60255	+	2.40714i	0.165645	+	0.110681i
$474$		0			0
$475$	−0.595036	−	7.40364i	−0.0273021	−	0.339702i
$476$		0			0
$477$	−8.46276	−	8.46276i	−0.387483	−	0.387483i
$478$		0			0
$479$	5.82737	+	29.2962i	0.266259	+	1.33858i	0.850063	+	0.526681i	$0.176564\pi$
$479$	5.82737	+	29.2962i	0.266259	+	1.33858i	−0.583804	+	0.811895i	$0.698436\pi$
$480$		0			0
$481$	14.3668	−	21.5015i	0.655071	−	0.980383i
$482$		0			0
$483$	−23.8402	−	4.74211i	−1.08477	−	0.215773i
$484$		0			0
$485$	−10.5857	−	22.9122i	−0.480672	−	1.04039i
$486$		0			0
$487$	−15.8788	+	10.6099i	−0.719537	+	0.480779i	−0.860639	−	0.509216i	$-0.829936\pi$
$487$	−15.8788	+	10.6099i	−0.719537	+	0.480779i	0.141102	+	0.989995i	$0.454936\pi$
$488$		0			0
$489$	−5.52353	−	5.52353i	−0.249783	−	0.249783i
$490$		0			0
$491$	−3.23201	+	7.80276i	−0.145859	+	0.352134i	−0.979877	−	0.199603i	$-0.936035\pi$
$491$	−3.23201	+	7.80276i	−0.145859	+	0.352134i	0.834018	+	0.551737i	$0.186035\pi$
$492$		0			0
$493$	−28.7894	+	18.2664i	−1.29661	+	0.822678i
$494$		0			0
$495$	−10.0269	+	4.63256i	−0.450677	+	0.208218i
$496$		0			0
$497$			4.99719i			0.224154i
$498$		0			0
$499$	1.09321	−	5.49594i	0.0489388	−	0.246032i	−0.948571	−	0.316566i	$-0.897470\pi$
$499$	1.09321	−	5.49594i	0.0489388	−	0.246032i	0.997509	+	0.0705337i	$0.0224702\pi$
$500$		0			0
$501$	−14.7618	−	35.6382i	−0.659510	−	1.59220i
$502$		0			0
$503$	−5.77203	+	29.0180i	−0.257362	+	1.29385i	0.608496	+	0.793557i	$0.291773\pi$
$503$	−5.77203	+	29.0180i	−0.257362	+	1.29385i	−0.865858	+	0.500290i	$0.833227\pi$
$504$		0			0
$505$	−8.89500	−	36.9155i	−0.395822	−	1.64272i
$506$		0			0
$507$	3.38861	−	5.07141i	0.150493	−	0.225229i
$508$		0			0
$509$	31.9241			1.41501			0.707506	−	0.706708i	$-0.249820\pi$
$509$	31.9241			1.41501			0.707506	+	0.706708i	$0.249820\pi$
$510$		0			0
$511$	11.5079			0.509080
$512$		0			0
$513$	2.40246	−	3.59554i	0.106071	−	0.158747i
$514$		0			0
$515$	−6.01119	+	9.82765i	−0.264884	+	0.433058i
$516$		0			0
$517$	−1.61304	+	8.10929i	−0.0709413	+	0.356646i
$518$		0			0
$519$	−16.6688	−	40.2421i	−0.731680	−	1.76643i
$520$		0			0
$521$	4.13347	−	20.7803i	0.181090	−	0.910403i	−0.778208	−	0.628007i	$-0.783871\pi$
$521$	4.13347	−	20.7803i	0.181090	−	0.910403i	0.959298	−	0.282396i	$-0.0911292\pi$
$522$		0			0
$523$		−	15.7160i		−	0.687211i	−0.939114	−	0.343605i	$-0.888352\pi$
$523$		−	15.7160i		−	0.687211i	0.939114	−	0.343605i	$-0.111648\pi$
$524$		0			0
$525$	36.6160	+	11.8301i	1.59805	+	0.516310i
$526$		0			0
$527$	6.03717	−	26.9966i	0.262983	−	1.17599i
$528$		0			0
$529$	−4.98413	+	12.0327i	−0.216701	+	0.523163i
$530$		0			0
$531$	9.42792	+	9.42792i	0.409137	+	0.409137i
$532$		0			0
$533$	−24.6894	+	16.4969i	−1.06942	+	0.714561i
$534$		0			0
$535$	1.95533	−	0.903385i	0.0845362	−	0.0390567i
$536$		0			0
$537$	−53.4050	−	10.6229i	−2.30459	−	0.458412i
$538$		0			0
$539$	9.54138	−	14.2797i	0.410976	−	0.615070i
$540$		0			0
$541$	4.63140	+	23.2836i	0.199119	+	1.00104i	0.943016	+	0.332746i	$0.107975\pi$
$541$	4.63140	+	23.2836i	0.199119	+	1.00104i	−0.743897	+	0.668294i	$0.767025\pi$
$542$		0			0
$543$	−21.6831	−	21.6831i	−0.930510	−	0.930510i
$544$		0			0
$545$	−4.41640	+	4.78559i	−0.189178	+	0.204992i
$546$		0			0
$547$	−3.57141	−	2.38634i	−0.152702	−	0.102032i	0.476872	−	0.878973i	$-0.341771\pi$
$547$	−3.57141	−	2.38634i	−0.152702	−	0.102032i	−0.629574	+	0.776940i	$0.716771\pi$
$548$		0			0
$549$	11.4641	+	7.66009i	0.489277	+	0.326925i
$550$		0			0
$551$	6.82468	+	10.2139i	0.290741	+	0.435125i
$552$		0			0
$553$	−22.0530	+	53.2406i	−0.937788	+	2.26402i
$554$		0			0
$555$	31.6110	−	23.0068i	1.34181	−	0.976586i
$556$		0			0
$557$	−13.8976			−0.588861			−0.294430	−	0.955673i	$-0.595130\pi$
$557$	−13.8976			−0.588861			−0.294430	+	0.955673i	$0.595130\pi$
$558$		0			0
$559$	4.26457	+	1.76644i	0.180372	+	0.0747126i
$560$		0			0
$561$	9.60111	+	24.8244i	0.405359	+	1.04809i
$562$		0			0
$563$	−21.0126	+	8.70372i	−0.885577	+	0.366818i	−0.778657	−	0.627450i	$-0.784099\pi$
$563$	−21.0126	+	8.70372i	−0.885577	+	0.366818i	−0.106920	+	0.994268i	$0.534099\pi$
$564$		0			0
$565$	−0.525683	−	0.485128i	−0.0221156	−	0.0204095i
$566$		0			0
$567$	22.2614	+	33.3166i	0.934892	+	1.39917i
$568$		0			0
$569$	26.9528	−	11.1642i	1.12992	−	0.468029i	0.262167	−	0.965023i	$-0.415563\pi$
$569$	26.9528	−	11.1642i	1.12992	−	0.468029i	0.867754	+	0.496994i	$0.165563\pi$
$570$		0			0
$571$	27.8405	−	18.6024i	1.16509	−	0.778488i	0.186127	−	0.982526i	$-0.440406\pi$
$571$	27.8405	−	18.6024i	1.16509	−	0.778488i	0.978963	+	0.204037i	$0.0654064\pi$
$572$		0			0
$573$	−49.7573	+	9.89735i	−2.07864	+	0.413468i
$574$		0			0
$575$	−7.69358	+	13.7915i	−0.320845	+	0.575145i
$576$		0			0
$577$	23.5100	−	23.5100i	0.978732	−	0.978732i	−0.0210461	−	0.999779i	$-0.506700\pi$
$577$	23.5100	−	23.5100i	0.978732	−	0.978732i	0.999779	+	0.0210461i	$0.00669969\pi$
$578$		0			0
$579$			3.69548i			0.153579i
$580$		0			0
$581$	28.5921	−	5.68732i	1.18620	−	0.235950i
$582$		0			0
$583$	4.23603	+	21.2960i	0.175439	+	0.881990i
$584$		0			0
$585$	−9.51421	+	6.92454i	−0.393364	+	0.286294i
$586$		0			0
$587$	−7.28609	−	3.01800i	−0.300729	−	0.124566i	0.227217	−	0.973844i	$-0.427037\pi$
$587$	−7.28609	−	3.01800i	−0.300729	−	0.124566i	−0.527945	+	0.849278i	$0.677037\pi$
$588$		0			0
$589$	−9.77526	−	1.94442i	−0.402783	−	0.0801185i
$590$		0			0
$591$	11.4679	−	11.4679i	0.471728	−	0.471728i
$592$		0			0
$593$	4.93059	+	11.9035i	0.202475	+	0.488819i	0.992202	−	0.124640i	$-0.0397777\pi$
$593$	4.93059	+	11.9035i	0.202475	+	0.488819i	−0.789727	+	0.613459i	$0.789778\pi$
$594$		0			0
$595$	12.0901	−	30.6017i	0.495647	−	1.25455i
$596$		0			0
$597$	7.96966	+	19.2405i	0.326176	+	0.787459i
$598$		0			0
$599$	−13.5320	+	13.5320i	−0.552902	+	0.552902i	−0.927277	−	0.374375i	$-0.877857\pi$
$599$	−13.5320	+	13.5320i	−0.552902	+	0.552902i	0.374375	+	0.927277i	$0.377857\pi$
$600$		0			0
$601$	−37.8568	−	7.53019i	−1.54421	−	0.307163i	−0.651802	−	0.758389i	$-0.725987\pi$
$601$	−37.8568	−	7.53019i	−1.54421	−	0.307163i	−0.892409	+	0.451227i	$0.850987\pi$
$602$		0			0
$603$	−8.06133	−	3.33911i	−0.328283	−	0.135979i
$604$		0			0
$605$	−4.50219	−	0.709250i	−0.183040	−	0.0288351i
$606$		0			0
$607$	−9.29925	−	46.7505i	−0.377445	−	1.89754i	−0.437262	−	0.899334i	$-0.644052\pi$
$607$	−9.29925	−	46.7505i	−0.377445	−	1.89754i	0.0598176	−	0.998209i	$-0.480948\pi$
$608$		0			0
$609$	−62.4173	+	12.4156i	−2.52928	+	0.503104i
$610$		0			0
$611$			8.80858i			0.356357i
$612$		0			0
$613$	−14.3208	+	14.3208i	−0.578410	+	0.578410i	−0.934465	−	0.356055i	$-0.884121\pi$
$613$	−14.3208	+	14.3208i	−0.578410	+	0.578410i	0.356055	+	0.934465i	$0.384121\pi$
$614$		0			0
$615$	−43.6446	+	10.5164i	−1.75992	+	0.424063i
$616$		0			0
$617$	−31.5294	+	6.27158i	−1.26932	+	0.252484i	−0.783401	−	0.621517i	$-0.786517\pi$
$617$	−31.5294	+	6.27158i	−1.26932	+	0.252484i	−0.485924	+	0.874001i	$0.661517\pi$
$618$		0			0
$619$	−25.3671	+	16.9498i	−1.01959	+	0.681269i	−0.948688	−	0.316214i	$-0.897588\pi$
$619$	−25.3671	+	16.9498i	−1.01959	+	0.681269i	−0.0709038	+	0.997483i	$0.522588\pi$
$620$		0			0
$621$	−8.49444	+	3.51851i	−0.340870	+	0.141193i
$622$		0			0
$623$	−32.6639	−	48.8850i	−1.30865	−	1.95853i
$624$		0			0
$625$	14.6275	−	20.2741i	0.585098	−	0.810962i
$626$		0			0
$627$	8.85959	−	3.66976i	0.353818	−	0.146556i
$628$		0			0
$629$	−17.9107	−	28.2287i	−0.714146	−	1.12555i
$630$		0			0
$631$	32.5727	+	13.4921i	1.29670	+	0.537111i	0.920976	−	0.389620i	$-0.127394\pi$
$631$	32.5727	+	13.4921i	1.29670	+	0.537111i	0.375725	+	0.926731i	$0.377394\pi$
$632$		0			0
$633$	−14.8418			−0.589909
$634$		0			0
$635$	−1.42495	+	9.04533i	−0.0565475	+	0.358953i
$636$		0			0
$637$	7.00179	−	16.9038i	0.277421	−	0.669754i
$638$		0			0
$639$	−1.28361	−	1.92105i	−0.0507787	−	0.0759957i
$640$		0			0
$641$	17.4144	+	11.6359i	0.687827	+	0.459592i	0.849732	−	0.527215i	$-0.176764\pi$
$641$	17.4144	+	11.6359i	0.687827	+	0.459592i	−0.161905	+	0.986806i	$0.551764\pi$
$642$		0			0
$643$	−25.8230	−	17.2544i	−1.01836	−	0.680445i	−0.0699674	−	0.997549i	$-0.522290\pi$
$643$	−25.8230	−	17.2544i	−1.01836	−	0.680445i	−0.948391	+	0.317104i	$0.897290\pi$
$644$		0			0
$645$	5.12862	+	4.73297i	0.201939	+	0.186361i
$646$		0			0
$647$	2.86127	+	2.86127i	0.112488	+	0.112488i	0.761111	−	0.648622i	$-0.224654\pi$
$647$	2.86127	+	2.86127i	0.112488	+	0.112488i	−0.648622	+	0.761111i	$0.724654\pi$
$648$		0			0
$649$	−4.71915	−	23.7248i	−0.185243	−	0.931278i
$650$		0			0
$651$	28.6867	−	42.9327i	1.12432	−	1.68267i
$652$		0			0
$653$	16.6024	+	3.30242i	0.649702	+	0.129234i	0.508929	−	0.860808i	$-0.330041\pi$
$653$	16.6024	+	3.30242i	0.649702	+	0.129234i	0.140772	+	0.990042i	$0.455041\pi$
$654$		0			0
$655$	37.0676	+	13.6400i	1.44835	+	0.532960i
$656$		0			0
$657$	−4.42395	+	2.95599i	−0.172595	+	0.115324i
$658$		0			0
$659$	10.2584	+	10.2584i	0.399609	+	0.399609i	0.878095	−	0.478486i	$-0.158814\pi$
$659$	10.2584	+	10.2584i	0.399609	+	0.399609i	−0.478486	+	0.878095i	$0.658814\pi$
$660$		0			0
$661$	−4.25104	+	10.2629i	−0.165346	+	0.399181i	−0.984736	−	0.174056i	$-0.944313\pi$
$661$	−4.25104	+	10.2629i	−0.165346	+	0.399181i	0.819389	+	0.573237i	$0.194313\pi$
$662$		0			0
$663$	15.1917	+	23.9433i	0.589995	+	0.929881i
$664$		0			0
$665$	−11.1254	−	4.09388i	−0.431423	−	0.158754i
$666$		0			0
$667$		−	26.1183i		−	1.01130i
$668$		0			0
$669$	8.94801	−	44.9847i	0.345950	−	1.73921i
$670$		0			0
$671$	−9.57263	−	23.1104i	−0.369547	−	0.892166i
$672$		0			0
$673$	4.21841	−	21.2074i	0.162608	−	0.817484i	−0.810251	−	0.586083i	$-0.800669\pi$
$673$	4.21841	−	21.2074i	0.162608	−	0.817484i	0.972858	−	0.231401i	$-0.0743309\pi$
$674$		0			0
$675$	14.0020	−	3.97407i	0.538939	−	0.152962i
$676$		0			0
$677$	4.46590	−	6.68370i	0.171639	−	0.256875i	−0.735670	−	0.677340i	$-0.763133\pi$
$677$	4.46590	−	6.68370i	0.171639	−	0.256875i	0.907309	+	0.420464i	$0.138133\pi$
$678$		0			0
$679$	−40.2833			−1.54593
$680$		0			0
$681$	35.9586			1.37794
$682$		0			0
$683$	−11.6381	+	17.4176i	−0.445319	+	0.666467i	−0.984432	−	0.175767i	$-0.943760\pi$
$683$	−11.6381	+	17.4176i	−0.445319	+	0.666467i	0.539113	+	0.842233i	$0.318760\pi$
$684$		0			0
$685$	3.27754	+	2.00474i	0.125228	+	0.0765973i
$686$		0			0
$687$	0.576029	−	2.89589i	0.0219769	−	0.110485i
$688$		0			0
$689$	8.85239	+	21.3716i	0.337249	+	0.814192i
$690$		0			0
$691$	−7.00516	+	35.2173i	−0.266489	+	1.33973i	0.583150	+	0.812364i	$0.301820\pi$
$691$	−7.00516	+	35.2173i	−0.266489	+	1.33973i	−0.849639	+	0.527365i	$0.823180\pi$
$692$		0			0
$693$			17.6290i			0.669669i
$694$		0			0
$695$	−5.47464	−	11.8496i	−0.207665	−	0.449479i
$696$		0			0
$697$	6.59639	+	37.8170i	0.249856	+	1.43242i
$698$		0			0
$699$	10.9434	−	26.4198i	0.413919	−	0.999289i
$700$		0			0
$701$	−28.5896	−	28.5896i	−1.07981	−	1.07981i	−0.996526	−	0.0832873i	$-0.973458\pi$
$701$	−28.5896	−	28.5896i	−1.07981	−	1.07981i	−0.0832873	−	0.996526i	$-0.526542\pi$
$702$		0			0
$703$	−10.0149	+	6.69177i	−0.377721	+	0.252385i
$704$		0			0
$705$	−4.59910	+	12.4983i	−0.173212	+	0.470714i
$706$		0			0
$707$	−59.4407	−	11.8235i	−2.23550	−	0.444668i
$708$		0			0
$709$	2.69657	−	4.03571i	0.101272	−	0.151564i	−0.777373	−	0.629040i	$-0.783448\pi$
$709$	2.69657	−	4.03571i	0.101272	−	0.151564i	0.878645	+	0.477476i	$0.158448\pi$
$710$		0			0
$711$	−5.19793	−	26.1318i	−0.194938	−	0.980018i
$712$		0			0
$713$	14.9845	+	14.9845i	0.561173	+	0.561173i
$714$		0			0
$715$	21.3317	−	0.855841i	0.797759	−	0.0320066i
$716$		0			0
$717$	4.91821	+	3.28624i	0.183674	+	0.122727i
$718$		0			0
$719$	−33.2804	−	22.2373i	−1.24115	−	0.829311i	−0.250820	−	0.968034i	$-0.580700\pi$
$719$	−33.2804	−	22.2373i	−1.24115	−	0.829311i	−0.990331	+	0.138723i	$0.955700\pi$
$720$		0			0
$721$	10.2152	+	15.2882i	0.380436	+	0.569362i
$722$		0			0
$723$	−17.0636	+	41.1953i	−0.634604	+	1.53207i
$724$		0			0
$725$	−4.79167	+	41.0680i	−0.177958	+	1.52523i
$726$		0			0
$727$	21.2943			0.789761			0.394881	−	0.918732i	$-0.370786\pi$
$727$	21.2943			0.789761			0.394881	+	0.918732i	$0.370786\pi$
$728$		0			0
$729$	0.282656	+	0.117080i	0.0104687	+	0.00433629i
$730$		0			0
$731$	4.31829	−	4.11865i	0.159718	−	0.152334i
$732$		0			0
$733$	25.7969	−	10.6854i	0.952829	−	0.394675i	0.148536	−	0.988907i	$-0.452544\pi$
$733$	25.7969	−	10.6854i	0.952829	−	0.394675i	0.804293	+	0.594232i	$0.202544\pi$
$734$		0			0
$735$	18.7604	−	20.3287i	0.691989	−	0.749836i
$736$		0			0
$737$	8.79483	+	13.1624i	0.323962	+	0.484843i
$738$		0			0
$739$	19.2440	−	7.97111i	0.707901	−	0.293222i	0.000465157	−	1.00000i	$-0.499852\pi$
$739$	19.2440	−	7.97111i	0.707901	−	0.293222i	0.707436	+	0.706778i	$0.249852\pi$
$740$		0			0
$741$	8.49458	−	5.67590i	0.312056	−	0.208509i
$742$		0			0
$743$	8.87467	−	1.76528i	0.325580	−	0.0647619i	−0.0295943	−	0.999562i	$-0.509422\pi$
$743$	8.87467	−	1.76528i	0.325580	−	0.0647619i	0.355174	+	0.934800i	$0.384422\pi$
$744$		0			0
$745$	−38.7720	−	23.7153i	−1.42050	−	0.868861i
$746$		0			0
$747$	−9.53069	+	9.53069i	−0.348710	+	0.348710i
$748$		0			0
$749$		−	3.43778i		−	0.125614i
$750$		0			0
$751$	−3.50805	+	0.697795i	−0.128011	+	0.0254629i	−0.258680	−	0.965963i	$-0.583287\pi$
$751$	−3.50805	+	0.697795i	−0.128011	+	0.0254629i	0.130669	+	0.991426i	$0.458287\pi$
$752$		0			0
$753$	−3.55326	−	17.8634i	−0.129488	−	0.650979i
$754$		0			0
$755$	−3.85705	+	24.4839i	−0.140373	+	0.891059i
$756$		0			0
$757$	38.6967	+	16.0287i	1.40645	+	0.582573i	0.951419	−	0.307900i	$-0.0996263\pi$
$757$	38.6967	+	16.0287i	1.40645	+	0.582573i	0.455036	+	0.890473i	$0.349626\pi$
$758$		0			0
$759$	−19.9974	−	3.97773i	−0.725860	−	0.144383i
$760$		0			0
$761$	13.8766	−	13.8766i	0.503028	−	0.503028i	−0.409350	−	0.912378i	$-0.634244\pi$
$761$	13.8766	−	13.8766i	0.503028	−	0.503028i	0.912378	+	0.409350i	$0.134244\pi$
$762$		0			0
$763$	3.97743	+	9.60235i	0.143992	+	0.347629i
$764$		0			0
$765$	3.21277	+	14.8697i	0.116158	+	0.537614i
$766$		0			0
$767$	−9.86199	−	23.8090i	−0.356096	−	0.859692i
$768$		0			0
$769$	−31.1138	+	31.1138i	−1.12199	+	1.12199i	−0.130551	+	0.991442i	$0.541675\pi$
$769$	−31.1138	+	31.1138i	−1.12199	+	1.12199i	−0.991442	+	0.130551i	$0.958325\pi$
$770$		0			0
$771$	−31.3479	−	6.23548i	−1.12897	−	0.224565i
$772$		0			0
$773$	11.5956	+	4.80306i	0.417065	+	0.172754i	0.581340	−	0.813661i	$-0.302529\pi$
$773$	11.5956	+	4.80306i	0.417065	+	0.172754i	−0.164275	+	0.986415i	$0.552529\pi$
$774$		0			0
$775$	−20.8123	−	26.3104i	−0.747600	−	0.945097i
$776$		0			0
$777$	−12.1738	−	61.2017i	−0.436732	−	2.19560i
$778$		0			0
$779$	13.5650	−	2.69824i	0.486015	−	0.0966744i
$780$		0			0
$781$			4.19170i			0.149991i
$782$		0			0
$783$	−17.0216	+	17.0216i	−0.608301	+	0.608301i
$784$		0			0
$785$	6.43186	+	26.6931i	0.229563	+	0.952717i
$786$		0			0
$787$	44.3586	−	8.82347i	1.58121	−	0.314523i	0.675155	−	0.737676i	$-0.264077\pi$
$787$	44.3586	−	8.82347i	1.58121	−	0.314523i	0.906058	+	0.423154i	$0.139077\pi$
$788$		0			0
$789$	42.5810	−	28.4517i	1.51592	−	1.01291i
$790$		0			0
$791$	−1.05479	+	0.436909i	−0.0375040	+	0.0155347i
$792$		0			0
$793$	−14.8057	−	22.1582i	−0.525764	−	0.786862i
$794$		0			0
$795$	1.40204	+	34.9456i	0.0497253	+	1.23939i
$796$		0			0
$797$	−27.2550	+	11.2894i	−0.965423	+	0.399891i	−0.809006	−	0.587800i	$-0.799994\pi$
$797$	−27.2550	+	11.2894i	−0.965423	+	0.399891i	−0.156417	+	0.987691i	$0.549994\pi$
$798$		0			0
$799$	10.4149	+	4.60556i	0.368451	+	0.162933i
$800$		0			0
$801$	25.1137	+	10.4025i	0.887350	+	0.367553i
$802$		0			0
$803$	9.65297			0.340646
$804$		0			0
$805$	14.8322	+	20.3792i	0.522767	+	0.718273i
$806$		0			0
$807$	5.28158	−	12.7509i	0.185920	−	0.448851i
$808$		0			0
$809$	5.88904	+	8.81358i	0.207048	+	0.309869i	0.920431	−	0.390905i	$-0.127838\pi$
$809$	5.88904	+	8.81358i	0.207048	+	0.309869i	−0.713383	+	0.700774i	$0.752838\pi$
$810$		0			0
$811$	−43.8676	−	29.3114i	−1.54040	−	1.02926i	−0.979515	−	0.201369i	$-0.935461\pi$
$811$	−43.8676	−	29.3114i	−1.54040	−	1.02926i	−0.560885	−	0.827894i	$-0.689539\pi$
$812$		0			0
$813$	2.61338	+	1.74620i	0.0916552	+	0.0612421i
$814$		0			0
$815$	0.324718	+	8.09354i	0.0113744	+	0.283504i
$816$		0			0
$817$	−1.52029	−	1.52029i	−0.0531881	−	0.0531881i
$818$		0			0
$819$	3.66403	+	18.4203i	0.128032	+	0.643659i
$820$		0			0
$821$	−10.1260	+	15.1546i	−0.353399	+	0.528900i	−0.964994	−	0.262272i	$-0.915528\pi$
$821$	−10.1260	+	15.1546i	−0.353399	+	0.528900i	0.611595	+	0.791171i	$0.290528\pi$
$822$		0			0
$823$	−27.5076	−	5.47160i	−0.958854	−	0.190728i	−0.309233	−	0.950986i	$-0.600072\pi$
$823$	−27.5076	−	5.47160i	−0.958854	−	0.190728i	−0.649621	+	0.760258i	$0.725072\pi$
$824$		0			0
$825$	30.7139	+	9.92326i	1.06932	+	0.345483i
$826$		0			0
$827$	−34.9529	+	23.3548i	−1.21543	+	0.812125i	−0.986888	−	0.161409i	$-0.948396\pi$
$827$	−34.9529	+	23.3548i	−1.21543	+	0.812125i	−0.228543	+	0.973534i	$0.573396\pi$
$828$		0			0
$829$	−29.9305	−	29.9305i	−1.03953	−	1.03953i	−0.999186	−	0.0403449i	$-0.987154\pi$
$829$	−29.9305	−	29.9305i	−1.03953	−	1.03953i	−0.0403449	−	0.999186i	$-0.512846\pi$
$830$		0			0
$831$	14.6629	−	35.3993i	0.508650	−	1.22799i
$832$		0			0
$833$	−16.3254	−	17.1167i	−0.565643	−	0.593060i
$834$		0			0
$835$	−13.8134	+	37.5388i	−0.478034	+	1.29908i
$836$		0			0
$837$		−	19.5311i		−	0.675092i
$838$		0			0
$839$	6.98750	−	35.1285i	0.241235	−	1.21277i	−0.650249	−	0.759721i	$-0.725336\pi$
$839$	6.98750	−	35.1285i	0.241235	−	1.21277i	0.891485	−	0.453051i	$-0.149664\pi$
$840$		0			0
$841$	−15.0707	−	36.3840i	−0.519680	−	1.25462i
$842$		0			0
$843$	−4.66819	+	23.4686i	−0.160781	+	0.808301i
$844$		0			0
$845$	−6.14869	+	1.48156i	−0.211521	+	0.0509674i
$846$		0			0
$847$	−4.04141	+	6.04840i	−0.138864	+	0.207825i
$848$		0			0
$849$	38.7532			1.33001
$850$		0			0
$851$	25.6097			0.877888
$852$		0			0
$853$	−15.9963	+	23.9402i	−0.547704	+	0.819697i	−0.997292	−	0.0735388i	$-0.976571\pi$
$853$	−15.9963	+	23.9402i	−0.547704	+	0.819697i	0.449588	+	0.893236i	$0.351571\pi$
$854$		0			0
$855$	5.32847	−	1.28393i	0.182230	−	0.0439093i
$856$		0			0
$857$	2.46498	−	12.3923i	0.0842022	−	0.423313i	−0.915574	−	0.402150i	$-0.868263\pi$
$857$	2.46498	−	12.3923i	0.0842022	−	0.423313i	0.999776	−	0.0211631i	$-0.00673694\pi$
$858$		0			0
$859$	2.93187	+	7.07817i	0.100034	+	0.241504i	0.965971	−	0.258649i	$-0.0832772\pi$
$859$	2.93187	+	7.07817i	0.100034	+	0.241504i	−0.865937	+	0.500153i	$0.833277\pi$
$860$		0			0
$861$	−13.9787	+	70.2758i	−0.476394	+	2.39499i
$862$		0			0
$863$		−	24.1609i		−	0.822445i	−0.911535	−	0.411223i	$-0.865102\pi$
$863$		−	24.1609i		−	0.822445i	0.911535	−	0.411223i	$-0.134898\pi$
$864$		0			0
$865$	−15.5979	+	42.3882i	−0.530345	+	1.44124i
$866$		0			0
$867$	36.2524	−	5.44320i	1.23120	−	0.184861i
$868$		0			0
$869$	−18.4983	+	44.6588i	−0.627511	+	1.51495i
$870$		0			0
$871$	11.9253	+	11.9253i	0.404074	+	0.404074i
$872$		0			0
$873$	15.4860	−	10.3474i	0.524121	−	0.350207i
$874$		0			0
$875$	−19.5832	−	34.7651i	−0.662032	−	1.17527i
$876$		0			0
$877$	27.0479	+	5.38016i	0.913342	+	0.181675i	0.629323	−	0.777144i	$-0.283332\pi$
$877$	27.0479	+	5.38016i	0.913342	+	0.181675i	0.284019	+	0.958819i	$0.408332\pi$
$878$		0			0
$879$	11.5925	−	17.3494i	0.391004	−	0.585180i
$880$		0			0
$881$	3.30989	+	16.6399i	0.111513	+	0.560614i	0.995633	+	0.0933539i	$0.0297588\pi$
$881$	3.30989	+	16.6399i	0.111513	+	0.560614i	−0.884120	+	0.467260i	$0.845241\pi$
$882$		0			0
$883$	36.7432	+	36.7432i	1.23651	+	1.23651i	0.961419	+	0.275089i	$0.0887073\pi$
$883$	36.7432	+	36.7432i	1.23651	+	1.23651i	0.275089	+	0.961419i	$0.411293\pi$
$884$		0			0
$885$	−1.56194	−	38.9311i	−0.0525042	−	1.30866i
$886$		0			0
$887$	−17.5033	−	11.6953i	−0.587702	−	0.392690i	0.225867	−	0.974158i	$-0.427479\pi$
$887$	−17.5033	−	11.6953i	−0.587702	−	0.392690i	−0.813569	+	0.581468i	$0.802479\pi$
$888$		0			0
$889$	12.1518	+	8.11957i	0.407558	+	0.272322i
$890$		0			0
$891$	18.6731	+	27.9463i	0.625574	+	0.936237i
$892$		0			0
$893$	1.57010	−	3.79055i	0.0525412	−	0.126846i
$894$		0			0
$895$	33.2260	+	45.6519i	1.11062	+	1.52598i
$896$		0			0
$897$	−21.7219			−0.725272
$898$		0			0
$899$	51.2586	+	21.2320i	1.70957	+	0.708127i
$900$		0			0
$901$	29.8972	+	0.707435i	0.996021	+	0.0235681i
$902$		0			0
$903$	10.2907	−	4.26253i	0.342452	−	0.141848i
$904$		0			0
$905$	1.27471	+	31.7719i	0.0423728	+	1.05613i
$906$		0			0
$907$	4.86472	+	7.28057i	0.161530	+	0.241747i	0.903402	−	0.428795i	$-0.141062\pi$
$907$	4.86472	+	7.28057i	0.161530	+	0.241747i	−0.741872	+	0.670542i	$0.766062\pi$
$908$		0			0
$909$	25.8877	−	10.7230i	0.858639	−	0.355660i
$910$		0			0
$911$	40.6501	−	27.1615i	1.34680	−	0.899902i	0.347512	−	0.937675i	$-0.387026\pi$
$911$	40.6501	−	27.1615i	1.34680	−	0.899902i	0.999286	+	0.0377733i	$0.0120265\pi$
$912$		0			0
$913$	23.9834	−	4.77059i	0.793733	−	0.157883i
$914$		0			0
$915$	−9.43828	−	39.1701i	−0.312020	−	1.29492i
$916$		0			0
$917$	44.5761	−	44.5761i	1.47203	−	1.47203i
$918$		0			0
$919$			40.5315i			1.33701i	0.743707	+	0.668506i	$0.233066\pi$
$919$			40.5315i			1.33701i	−0.743707	+	0.668506i	$0.766934\pi$
$920$		0			0
$921$	−32.9065	+	6.54552i	−1.08431	+	0.215682i
$922$		0			0
$923$	0.871209	+	4.37987i	0.0286762	+	0.144165i
$924$		0			0
$925$	−40.2682	−	4.69835i	−1.32401	−	0.154481i
$926$		0			0
$927$	−7.85403	−	3.25325i	−0.257960	−	0.106851i
$928$		0			0
$929$	−46.4806	−	9.24556i	−1.52498	−	0.303337i	−0.639782	−	0.768556i	$-0.720975\pi$
$929$	−46.4806	−	9.24556i	−1.52498	−	0.303337i	−0.885195	+	0.465219i	$0.845975\pi$
$930$		0			0
$931$	−6.02608	+	6.02608i	−0.197497	+	0.197497i
$932$		0			0
$933$	−4.67205	−	11.2793i	−0.152956	−	0.369268i
$934$		0			0
$935$	10.1413	−	25.6691i	0.331657	−	0.839468i
$936$		0			0
$937$	2.47014	+	5.96345i	0.0806961	+	0.194818i	0.959078	−	0.283142i	$-0.0913767\pi$
$937$	2.47014	+	5.96345i	0.0806961	+	0.194818i	−0.878382	+	0.477959i	$0.841377\pi$
$938$		0			0
$939$	48.8510	−	48.8510i	1.59419	−	1.59419i
$940$		0			0
$941$	−54.0330	−	10.7478i	−1.76143	−	0.350370i	−0.794862	−	0.606790i	$-0.792457\pi$
$941$	−54.0330	−	10.7478i	−1.76143	−	0.350370i	−0.966565	+	0.256421i	$0.917457\pi$
$942$		0			0
$943$	−27.1682	−	11.2535i	−0.884720	−	0.366463i
$944$		0			0
$945$	3.61504	−	22.9476i	0.117597	−	0.746487i
$946$		0			0
$947$	3.10538	+	15.6118i	0.100911	+	0.507316i	0.997872	+	0.0652053i	$0.0207702\pi$
$947$	3.10538	+	15.6118i	0.100911	+	0.507316i	−0.896960	+	0.442111i	$0.854230\pi$
$948$		0			0
$949$	10.0863	−	2.00629i	0.327415	−	0.0651270i
$950$		0			0
$951$			32.5937i			1.05692i
$952$		0			0
$953$	4.56692	−	4.56692i	0.147937	−	0.147937i	−0.629259	−	0.777196i	$-0.716641\pi$
$953$	4.56692	−	4.56692i	0.147937	−	0.147937i	0.777196	+	0.629259i	$0.216641\pi$
$954$		0			0
$955$	44.8771	+	27.4496i	1.45219	+	0.888248i
$956$		0			0
$957$	−52.3563	+	10.4143i	−1.69244	+	0.336647i
$958$		0			0
$959$	5.09865	−	3.40681i	0.164644	−	0.110012i
$960$		0			0
$961$	−12.9487	+	5.36351i	−0.417699	+	0.173016i
$962$		0			0
$963$	0.883048	+	1.32157i	0.0284558	+	0.0425872i
$964$		0			0
$965$	2.59884	−	2.81609i	0.0836595	−	0.0906530i
$966$		0			0
$967$	6.95922	−	2.88260i	0.223793	−	0.0926982i	−0.267970	−	0.963427i	$-0.586353\pi$
$967$	6.95922	−	2.88260i	0.223793	−	0.0926982i	0.491763	+	0.870729i	$0.336353\pi$
$968$		0			0
$969$	−2.26954	−	13.0112i	−0.0729081	−	0.417981i
$970$		0			0
$971$	−0.743896	−	0.308132i	−0.0238728	−	0.00988843i	0.370715	−	0.928747i	$-0.379113\pi$
$971$	−0.743896	−	0.308132i	−0.0238728	−	0.00988843i	−0.394588	+	0.918858i	$0.629113\pi$
$972$		0			0
$973$	−20.8334			−0.667889
$974$		0			0
$975$	34.1551	+	3.98510i	1.09384	+	0.127625i
$976$		0			0
$977$	4.49689	−	10.8565i	0.143868	−	0.347329i	−0.835476	−	0.549526i	$-0.814808\pi$
$977$	4.49689	−	10.8565i	0.143868	−	0.347329i	0.979345	+	0.202197i	$0.0648082\pi$
$978$		0			0
$979$	−27.3988	−	41.0052i	−0.875670	−	1.31053i
$980$		0			0
$981$	−3.99555	−	2.66974i	−0.127568	−	0.0852382i
$982$		0			0
$983$	40.4189	+	27.0070i	1.28916	+	0.861390i	0.995522	−	0.0945262i	$-0.0301336\pi$
$983$	40.4189	+	27.0070i	1.28916	+	0.861390i	0.293639	+	0.955916i	$0.405134\pi$
$984$		0			0
$985$	−16.8038	+	0.674180i	−0.535413	+	0.0214812i
$986$		0			0
$987$	15.0300	+	15.0300i	0.478410	+	0.478410i
$988$		0			0
$989$	0.891822	+	4.48349i	0.0283583	+	0.142567i
$990$		0			0
$991$	−20.6524	+	30.9084i	−0.656044	+	0.981839i	0.343052	+	0.939316i	$0.388539\pi$
$991$	−20.6524	+	30.9084i	−0.656044	+	0.981839i	−0.999096	+	0.0425222i	$0.986461\pi$
$992$		0			0
$993$	−5.22075	−	1.03847i	−0.165675	−	0.0329549i
$994$		0			0
$995$	7.45764	−	20.2666i	0.236423	−	0.642493i
$996$		0			0
$997$	−44.8830	+	29.9899i	−1.42146	+	0.949789i	−0.422400	+	0.906409i	$0.638812\pi$
$997$	−44.8830	+	29.9899i	−1.42146	+	0.949789i	−0.999059	+	0.0433793i	$0.986188\pi$
$998$		0			0
$999$	−16.6901	−	16.6901i	−0.528051	−	0.528051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cg.b.57.11	✓	112
5.3	odd	4		680.2.cq.b.193.11	yes	112
17.3	odd	16		680.2.cq.b.377.11	yes	112
85.3	even	16	inner	680.2.cg.b.513.11	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cg.b.57.11	✓	112	1.1	even	1	trivial
680.2.cg.b.513.11	yes	112	85.3	even	16	inner
680.2.cq.b.193.11	yes	112	5.3	odd	4
680.2.cq.b.377.11	yes	112	17.3	odd	16

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cg (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19803 - 1.79298i) q^{3} +(-2.17385 + 0.523803i) q^{5} +(-0.696254 + 3.50030i) q^{7} +(-0.631450 - 1.52445i) q^{9} +(-0.584025 + 2.93609i) q^{11} +3.18928i q^{13} +(-1.66517 + 4.52521i) q^{15} +(3.77086 + 1.66751i) q^{17} +(0.568477 - 1.37243i) q^{19} +(5.44184 + 5.44184i) q^{21} +(-2.62616 + 1.75474i) q^{23} +(4.45126 - 2.27734i) q^{25} +(2.85508 + 0.567911i) q^{27} +(-4.59419 + 6.87569i) q^{29} +(-1.30893 - 6.58044i) q^{31} +(4.56468 + 4.56468i) q^{33} +(-0.319916 - 7.97384i) q^{35} +(-6.74179 - 4.50472i) q^{37} +(5.71832 + 3.82086i) q^{39} +(5.17262 + 7.74137i) q^{41} +(0.553869 - 1.33716i) q^{43} +(2.17119 + 2.98318i) q^{45} +2.76193 q^{47} +(-5.30020 - 2.19541i) q^{49} +(7.50743 - 4.76335i) q^{51} +(6.70106 - 2.77567i) q^{53} +(-0.268349 - 6.68854i) q^{55} +(-1.77968 - 2.66348i) q^{57} +(-7.46530 + 3.09223i) q^{59} +(-6.94772 + 4.64232i) q^{61} +(5.77570 - 1.14886i) q^{63} +(-1.67055 - 6.93303i) q^{65} +(3.73919 - 3.73919i) q^{67} +6.81089i q^{69} +(1.37331 - 0.273168i) q^{71} +(-0.629073 - 3.16256i) q^{73} +(1.24953 - 10.7093i) q^{75} +(-9.87059 - 4.08853i) q^{77} +(15.8369 + 3.15015i) q^{79} +(7.93903 - 7.93903i) q^{81} +(-3.12593 - 7.54667i) q^{83} +(-9.07074 - 1.64974i) q^{85} +(6.82400 + 16.4746i) q^{87} +(-11.6488 + 11.6488i) q^{89} +(-11.1635 - 2.22055i) q^{91} +(-13.3667 - 5.53669i) q^{93} +(-0.516905 + 3.28122i) q^{95} +(2.20206 + 11.0705i) q^{97} +(4.84472 - 0.963675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 16 q^{15} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 48 q^{33} - 32 q^{35} - 16 q^{37} - 16 q^{41} + 48 q^{43} - 24 q^{45} - 16 q^{47} - 80 q^{49} + 32 q^{51} - 8 q^{53} + 24 q^{55} - 80 q^{59} - 24 q^{61}+ \cdots + 48 q^{99}+O(q^{100}) \) 112 * q + 16 * q^15 - 24 * q^27 - 8 * q^29 + 16 * q^31 - 48 * q^33 - 32 * q^35 - 16 * q^37 - 16 * q^41 + 48 * q^43 - 24 * q^45 - 16 * q^47 - 80 * q^49 + 32 * q^51 - 8 * q^53 + 24 * q^55 - 80 * q^59 - 24 * q^61 - 72 * q^63 + 16 * q^65 - 48 * q^67 - 40 * q^71 - 16 * q^73 + 16 * q^75 + 24 * q^77 + 40 * q^79 - 24 * q^83 + 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^93 - 8 * q^95 + 64 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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