LMFDB - Embedded newform 656.2.be.e.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(113,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("656.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.be (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 39x^{14} + 594x^{12} + 4428x^{10} + 16529x^{8} + 28236x^{6} + 17856x^{4} + 4032x^{2} + 256 $ x^16 + 39x^14 + 594x^12 + 4428x^10 + 16529x^8 + 28236x^6 + 17856x^4 + 4032*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 164)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.1
Root			$3.11423i$ of defining polynomial
Character	$\chi$	$=$	656.113
Dual form			656.2.be.e.209.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.11423i q^{3} +(0.234613 + 0.722064i) q^{5} +(0.334979 + 0.461059i) q^{7} -6.69841 q^{9} +O(q^{10})$	\(q-3.11423i q^{3} +(0.234613 + 0.722064i) q^{5} +(0.334979 + 0.461059i) q^{7} -6.69841 q^{9} +(-2.03752 - 0.662032i) q^{11} +(0.911006 - 1.25389i) q^{13} +(2.24867 - 0.730637i) q^{15} +(-5.57536 - 1.81154i) q^{17} +(-3.71496 - 5.11320i) q^{19} +(1.43584 - 1.04320i) q^{21} +(-6.10394 - 4.43478i) q^{23} +(3.57875 - 2.60012i) q^{25} +11.5177i q^{27} +(4.10984 - 1.33537i) q^{29} +(-2.71177 + 8.34596i) q^{31} +(-2.06172 + 6.34531i) q^{33} +(-0.254323 + 0.350046i) q^{35} +(-0.289804 - 0.891926i) q^{37} +(-3.90490 - 2.83708i) q^{39} +(-2.32565 + 5.96585i) q^{41} +(7.69171 + 5.58835i) q^{43} +(-1.57153 - 4.83668i) q^{45} +(5.55324 - 7.64338i) q^{47} +(2.06275 - 6.34851i) q^{49} +(-5.64156 + 17.3629i) q^{51} +(3.92714 - 1.27600i) q^{53} -1.62654i q^{55} +(-15.9237 + 11.5692i) q^{57} +(4.51093 + 3.27738i) q^{59} +(3.73050 - 2.71037i) q^{61} +(-2.24382 - 3.08836i) q^{63} +(1.11912 + 0.363625i) q^{65} +(-3.57383 + 1.16121i) q^{67} +(-13.8109 + 19.0091i) q^{69} +(-7.45067 - 2.42087i) q^{71} -1.26823 q^{73} +(-8.09735 - 11.1450i) q^{75} +(-0.377292 - 1.16119i) q^{77} -1.98372i q^{79} +15.7735 q^{81} +8.42095 q^{83} -4.45077i q^{85} +(-4.15864 - 12.7990i) q^{87} +(-6.90454 - 9.50329i) q^{89} +0.883285 q^{91} +(25.9912 + 8.44506i) q^{93} +(2.82048 - 3.88206i) q^{95} +(2.75953 - 0.896627i) q^{97} +(13.6482 + 4.43456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{5} - 30 q^{9}+O(q^{10}) $ 16 * q + 4 * q^5 - 30 * q^9	$ 16 q + 4 q^{5} - 30 q^{9} + 5 q^{11} + 10 q^{15} + 5 q^{17} - 15 q^{19} + 19 q^{21} - 12 q^{23} - 2 q^{25} + 20 q^{29} - 3 q^{31} - 25 q^{33} - 5 q^{35} + 2 q^{37} + 28 q^{39} - 4 q^{41} + 22 q^{43} - 48 q^{45} - 15 q^{47} - 28 q^{49} - 17 q^{51} + 25 q^{53} - 8 q^{57} - 8 q^{59} - 46 q^{61} + 40 q^{63} - 10 q^{65} + 45 q^{67} + 10 q^{69} - 15 q^{71} + 34 q^{73} - 135 q^{75} + 23 q^{77} + 108 q^{81} - 12 q^{83} - 14 q^{87} + 60 q^{93} + 30 q^{95} - 40 q^{97} - 70 q^{99}+O(q^{100}) $ 16 * q + 4 * q^5 - 30 * q^9 + 5 * q^11 + 10 * q^15 + 5 * q^17 - 15 * q^19 + 19 * q^21 - 12 * q^23 - 2 * q^25 + 20 * q^29 - 3 * q^31 - 25 * q^33 - 5 * q^35 + 2 * q^37 + 28 * q^39 - 4 * q^41 + 22 * q^43 - 48 * q^45 - 15 * q^47 - 28 * q^49 - 17 * q^51 + 25 * q^53 - 8 * q^57 - 8 * q^59 - 46 * q^61 + 40 * q^63 - 10 * q^65 + 45 * q^67 + 10 * q^69 - 15 * q^71 + 34 * q^73 - 135 * q^75 + 23 * q^77 + 108 * q^81 - 12 * q^83 - 14 * q^87 + 60 * q^93 + 30 * q^95 - 40 * q^97 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$1$

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
$3$		−	3.11423i		−	1.79800i	−0.437949	−	0.899000i	$-0.644295\pi$
$3$		−	3.11423i		−	1.79800i	0.437949	−	0.899000i	$-0.355705\pi$
$4$		0			0
$5$	0.234613	+	0.722064i	0.104922	+	0.322917i	0.989712	−	0.143073i	$-0.0456984\pi$
$5$	0.234613	+	0.722064i	0.104922	+	0.322917i	−0.884790	+	0.465990i	$0.845698\pi$
$6$		0			0
$7$	0.334979	+	0.461059i	0.126610	+	0.174264i	0.867616	−	0.497234i	$-0.165651\pi$
$7$	0.334979	+	0.461059i	0.126610	+	0.174264i	−0.741006	+	0.671498i	$0.765651\pi$
$8$		0			0
$9$	−6.69841			−2.23280
$10$		0			0
$11$	−2.03752	−	0.662032i	−0.614337	−	0.199610i	−0.0147125	−	0.999892i	$-0.504683\pi$
$11$	−2.03752	−	0.662032i	−0.614337	−	0.199610i	−0.599624	+	0.800282i	$0.704683\pi$
$12$		0			0
$13$	0.911006	−	1.25389i	0.252668	−	0.347767i	−0.663776	−	0.747932i	$-0.731047\pi$
$13$	0.911006	−	1.25389i	0.252668	−	0.347767i	0.916443	+	0.400165i	$0.131047\pi$
$14$		0			0
$15$	2.24867	−	0.730637i	0.580604	−	0.188650i
$16$		0			0
$17$	−5.57536	−	1.81154i	−1.35222	−	0.439364i	−0.458784	−	0.888548i	$-0.651715\pi$
$17$	−5.57536	−	1.81154i	−1.35222	−	0.439364i	−0.893439	+	0.449184i	$0.851715\pi$
$18$		0			0
$19$	−3.71496	−	5.11320i	−0.852270	−	1.17305i	−0.983358	−	0.181678i	$-0.941847\pi$
$19$	−3.71496	−	5.11320i	−0.852270	−	1.17305i	0.131088	−	0.991371i	$-0.458153\pi$
$20$		0			0
$21$	1.43584	−	1.04320i	0.313326	−	0.227645i
$22$		0			0
$23$	−6.10394	−	4.43478i	−1.27276	−	0.924715i	−0.273452	−	0.961886i	$-0.588165\pi$
$23$	−6.10394	−	4.43478i	−1.27276	−	0.924715i	−0.999309	+	0.0371711i	$0.988165\pi$
$24$		0			0
$25$	3.57875	−	2.60012i	0.715750	−	0.520023i
$26$		0			0
$27$			11.5177i			2.21658i
$28$		0			0
$29$	4.10984	−	1.33537i	0.763178	−	0.247972i	0.0985359	−	0.995133i	$-0.468584\pi$
$29$	4.10984	−	1.33537i	0.763178	−	0.247972i	0.664642	+	0.747162i	$0.268584\pi$
$30$		0			0
$31$	−2.71177	+	8.34596i	−0.487048	+	1.49898i	0.341945	+	0.939720i	$0.388914\pi$
$31$	−2.71177	+	8.34596i	−0.487048	+	1.49898i	−0.828993	+	0.559259i	$0.811086\pi$
$32$		0			0
$33$	−2.06172	+	6.34531i	−0.358899	+	1.10458i
$34$		0			0
$35$	−0.254323	+	0.350046i	−0.0429885	+	0.0591686i
$36$		0			0
$37$	−0.289804	−	0.891926i	−0.0476436	−	0.146632i	0.924405	−	0.381413i	$-0.124563\pi$
$37$	−0.289804	−	0.891926i	−0.0476436	−	0.146632i	−0.972048	+	0.234782i	$0.924563\pi$
$38$		0			0
$39$	−3.90490	−	2.83708i	−0.625285	−	0.454296i
$40$		0			0
$41$	−2.32565	+	5.96585i	−0.363205	+	0.931709i
$41$	−2.32565	+	5.96585i	−0.363205	+	0.931709i
$42$		0			0
$43$	7.69171	+	5.58835i	1.17297	+	0.852216i	0.991362	−	0.131154i	$-0.0418683\pi$
$43$	7.69171	+	5.58835i	1.17297	+	0.852216i	0.181613	+	0.983370i	$0.441868\pi$
$44$		0			0
$45$	−1.57153	−	4.83668i	−0.234270	−	0.721009i
$46$		0			0
$47$	5.55324	−	7.64338i	0.810024	−	1.11490i	−0.181296	−	0.983429i	$-0.558029\pi$
$47$	5.55324	−	7.64338i	0.810024	−	1.11490i	0.991320	−	0.131473i	$-0.0419708\pi$
$48$		0			0
$49$	2.06275	−	6.34851i	0.294679	−	0.906929i
$50$		0			0
$51$	−5.64156	+	17.3629i	−0.789976	+	2.43130i
$52$		0			0
$53$	3.92714	−	1.27600i	0.539434	−	0.175273i	−0.0266131	−	0.999646i	$-0.508472\pi$
$53$	3.92714	−	1.27600i	0.539434	−	0.175273i	0.566047	+	0.824373i	$0.308472\pi$
$54$		0			0
$55$		−	1.62654i		−	0.219323i
$56$		0			0
$57$	−15.9237	+	11.5692i	−2.10914	+	1.53238i
$58$		0			0
$59$	4.51093	+	3.27738i	0.587273	+	0.426679i	0.841339	−	0.540508i	$-0.181768\pi$
$59$	4.51093	+	3.27738i	0.587273	+	0.426679i	−0.254066	+	0.967187i	$0.581768\pi$
$60$		0			0
$61$	3.73050	−	2.71037i	0.477642	−	0.347027i	−0.322770	−	0.946477i	$-0.604614\pi$
$61$	3.73050	−	2.71037i	0.477642	−	0.347027i	0.800412	+	0.599450i	$0.204614\pi$
$62$		0			0
$63$	−2.24382	−	3.08836i	−0.282695	−	0.389097i
$64$		0			0
$65$	1.11912	+	0.363625i	0.138810	+	0.0451022i
$66$		0			0
$67$	−3.57383	+	1.16121i	−0.436613	+	0.141864i	−0.519072	−	0.854730i	$-0.673723\pi$
$67$	−3.57383	+	1.16121i	−0.436613	+	0.141864i	0.0824594	+	0.996594i	$0.473723\pi$
$68$		0			0
$69$	−13.8109	+	19.0091i	−1.66264	+	2.28842i
$70$		0			0
$71$	−7.45067	−	2.42087i	−0.884231	−	0.287304i	−0.168518	−	0.985699i	$-0.553898\pi$
$71$	−7.45067	−	2.42087i	−0.884231	−	0.287304i	−0.715713	+	0.698394i	$0.753898\pi$
$72$		0			0
$73$	−1.26823			−0.148435			−0.0742177	−	0.997242i	$-0.523646\pi$
$73$	−1.26823			−0.148435			−0.0742177	+	0.997242i	$0.523646\pi$
$74$		0			0
$75$	−8.09735	−	11.1450i	−0.935001	−	1.28692i
$76$		0			0
$77$	−0.377292	−	1.16119i	−0.0429964	−	0.132329i
$78$		0			0
$79$		−	1.98372i		−	0.223186i	−0.993754	−	0.111593i	$-0.964405\pi$
$79$		−	1.98372i		−	0.223186i	0.993754	−	0.111593i	$-0.0355953\pi$
$80$		0			0
$81$	15.7735			1.75261
$82$		0			0
$83$	8.42095			0.924319			0.462160	−	0.886797i	$-0.347075\pi$
$83$	8.42095			0.924319			0.462160	+	0.886797i	$0.347075\pi$
$84$		0			0
$85$		−	4.45077i		−	0.482754i
$86$		0			0
$87$	−4.15864	−	12.7990i	−0.445853	−	1.37219i
$88$		0			0
$89$	−6.90454	−	9.50329i	−0.731880	−	1.00735i	−0.999045	−	0.0436955i	$-0.986087\pi$
$89$	−6.90454	−	9.50329i	−0.731880	−	1.00735i	0.267165	−	0.963651i	$-0.413913\pi$
$90$		0			0
$91$	0.883285			0.0925935
$92$		0			0
$93$	25.9912	+	8.44506i	2.69516	+	0.875712i
$94$		0			0
$95$	2.82048	−	3.88206i	0.289375	−	0.398291i
$96$		0			0
$97$	2.75953	−	0.896627i	0.280188	−	0.0910386i	−0.165552	−	0.986201i	$-0.552941\pi$
$97$	2.75953	−	0.896627i	0.280188	−	0.0910386i	0.445740	+	0.895162i	$0.352941\pi$
$98$		0			0
$99$	13.6482	+	4.43456i	1.37169	+	0.445690i
$100$		0			0
$101$	−2.40034	−	3.30379i	−0.238843	−	0.328739i	0.672722	−	0.739895i	$-0.265125\pi$
$101$	−2.40034	−	3.30379i	−0.238843	−	0.328739i	−0.911565	+	0.411156i	$0.865125\pi$
$102$		0			0
$103$	16.2748	−	11.8243i	1.60360	−	1.16508i	0.723470	−	0.690356i	$-0.242546\pi$
$103$	16.2748	−	11.8243i	1.60360	−	1.16508i	0.880132	−	0.474729i	$-0.157454\pi$
$104$		0			0
$105$	1.09012	+	0.792021i	0.106385	+	0.0772933i
$106$		0			0
$107$	5.13066	−	3.72764i	0.496000	−	0.360365i	−0.311487	−	0.950250i	$-0.600827\pi$
$107$	5.13066	−	3.72764i	0.496000	−	0.360365i	0.807487	+	0.589886i	$0.200827\pi$
$108$		0			0
$109$		−	18.7919i		−	1.79994i	−0.435957	−	0.899968i	$-0.643590\pi$
$109$		−	18.7919i		−	1.79994i	0.435957	−	0.899968i	$-0.356410\pi$
$110$		0			0
$111$	−2.77766	+	0.902517i	−0.263644	+	0.0856631i
$112$		0			0
$113$	−2.84389	+	8.75259i	−0.267531	+	0.823374i	0.723569	+	0.690252i	$0.242500\pi$
$113$	−2.84389	+	8.75259i	−0.267531	+	0.823374i	−0.991100	+	0.133122i	$0.957500\pi$
$114$		0			0
$115$	1.77013	−	5.44789i	0.165065	−	0.508018i
$116$		0			0
$117$	−6.10229	+	8.39908i	−0.564157	+	0.776495i
$118$		0			0
$119$	−1.03240	−	3.17740i	−0.0946398	−	0.291271i
$120$		0			0
$121$	−5.18597	−	3.76782i	−0.471451	−	0.342530i
$122$		0			0
$123$	18.5790	+	7.24259i	1.67521	+	0.653042i
$124$		0			0
$125$	5.78819	+	4.20537i	0.517711	+	0.376139i
$126$		0			0
$127$	5.85357	+	18.0154i	0.519420	+	1.59861i	0.775093	+	0.631847i	$0.217703\pi$
$127$	5.85357	+	18.0154i	0.519420	+	1.59861i	−0.255673	+	0.966763i	$0.582297\pi$
$128$		0			0
$129$	17.4034	−	23.9537i	1.53228	−	2.10901i
$130$		0			0
$131$	1.96208	−	6.03865i	0.171428	−	0.527600i	−0.828025	−	0.560692i	$-0.810535\pi$
$131$	1.96208	−	6.03865i	0.171428	−	0.527600i	0.999452	+	0.0330918i	$0.0105354\pi$
$132$		0			0
$133$	1.11305	−	3.42563i	0.0965140	−	0.297040i
$134$		0			0
$135$	−8.31650	+	2.70219i	−0.715770	+	0.232568i
$136$		0			0
$137$		−	10.6077i		−	0.906275i	−0.891441	−	0.453137i	$-0.850305\pi$
$137$		−	10.6077i		−	0.906275i	0.891441	−	0.453137i	$-0.149695\pi$
$138$		0			0
$139$	−6.45365	+	4.68885i	−0.547392	+	0.397703i	−0.826823	−	0.562462i	$-0.809854\pi$
$139$	−6.45365	+	4.68885i	−0.547392	+	0.397703i	0.279431	+	0.960166i	$0.409854\pi$
$140$		0			0
$141$	−23.8032	−	17.2941i	−2.00459	−	1.45642i
$142$		0			0
$143$	−2.68631	+	1.95172i	−0.224641	+	0.163211i
$144$		0			0
$145$	1.92844	+	2.65427i	0.160148	+	0.220425i
$146$		0			0
$147$	−19.7707	−	6.42389i	−1.63066	−	0.529833i
$148$		0			0
$149$	−10.7327	+	3.48725i	−0.879254	+	0.285687i	−0.713648	−	0.700505i	$-0.752958\pi$
$149$	−10.7327	+	3.48725i	−0.879254	+	0.285687i	−0.165607	+	0.986192i	$0.552958\pi$
$150$		0			0
$151$	1.42714	−	1.96428i	0.116139	−	0.159851i	−0.746990	−	0.664835i	$-0.768502\pi$
$151$	1.42714	−	1.96428i	0.116139	−	0.159851i	0.863129	+	0.504984i	$0.168502\pi$
$152$		0			0
$153$	37.3460	+	12.1345i	3.01925	+	0.981013i
$154$		0			0
$155$	−6.66253			−0.535147
$156$		0			0
$157$	11.2630	+	15.5022i	0.898886	+	1.23721i	0.970822	+	0.239801i	$0.0770822\pi$
$157$	11.2630	+	15.5022i	0.898886	+	1.23721i	−0.0719361	+	0.997409i	$0.522918\pi$
$158$		0			0
$159$	−3.97377	−	12.2300i	−0.315140	−	0.969901i
$160$		0			0
$161$		−	4.29983i		−	0.338874i
$162$		0			0
$163$	−6.71180			−0.525709			−0.262854	−	0.964836i	$-0.584664\pi$
$163$	−6.71180			−0.525709			−0.262854	+	0.964836i	$0.584664\pi$
$164$		0			0
$165$	−5.06543			−0.394343
$166$		0			0
$167$			8.47459i			0.655783i	0.944715	+	0.327892i	$0.106338\pi$
$167$			8.47459i			0.655783i	−0.944715	+	0.327892i	$0.893662\pi$
$168$		0			0
$169$	3.27491	+	10.0791i	0.251916	+	0.775318i
$170$		0			0
$171$	24.8843	+	34.2503i	1.90295	+	2.61919i
$172$		0			0
$173$	−12.4627			−0.947524			−0.473762	−	0.880653i	$-0.657104\pi$
$173$	−12.4627			−0.947524			−0.473762	+	0.880653i	$0.657104\pi$
$174$		0			0
$175$	2.39761	+	0.779031i	0.181242	+	0.0588892i
$176$		0			0
$177$	10.2065	−	14.0481i	0.767168	−	1.05592i
$178$		0			0
$179$	−12.9825	+	4.21826i	−0.970356	+	0.315288i	−0.750960	−	0.660348i	$-0.770409\pi$
$179$	−12.9825	+	4.21826i	−0.970356	+	0.315288i	−0.219396	+	0.975636i	$0.570409\pi$
$180$		0			0
$181$	16.1910	+	5.26076i	1.20346	+	0.391029i	0.841034	−	0.540982i	$-0.181947\pi$
$181$	16.1910	+	5.26076i	1.20346	+	0.391029i	0.362430	+	0.932011i	$0.381947\pi$
$182$		0			0
$183$	−8.44070	−	11.6176i	−0.623954	−	0.858800i
$184$		0			0
$185$	0.576036	−	0.418515i	0.0423510	−	0.0307698i
$186$		0			0
$187$	10.1606	+	7.38213i	0.743019	+	0.539835i
$188$		0			0
$189$	−5.31033	+	3.85818i	−0.386270	+	0.280641i
$190$		0			0
$191$			7.57160i			0.547862i	0.961749	+	0.273931i	$0.0883240\pi$
$191$			7.57160i			0.547862i	−0.961749	+	0.273931i	$0.911676\pi$
$192$		0			0
$193$	−4.32329	+	1.40472i	−0.311197	+	0.101114i	−0.460452	−	0.887685i	$-0.652313\pi$
$193$	−4.32329	+	1.40472i	−0.311197	+	0.101114i	0.149254	+	0.988799i	$0.452313\pi$
$194$		0			0
$195$	1.13241	−	3.48520i	0.0810937	−	0.249581i
$196$		0			0
$197$	5.77794	−	17.7827i	0.411661	−	1.26696i	−0.503542	−	0.863971i	$-0.667970\pi$
$197$	5.77794	−	17.7827i	0.411661	−	1.26696i	0.915203	−	0.402992i	$-0.132030\pi$
$198$		0			0
$199$	7.12837	−	9.81136i	0.505317	−	0.695509i	−0.477804	−	0.878466i	$-0.658567\pi$
$199$	7.12837	−	9.81136i	0.505317	−	0.695509i	0.983121	+	0.182958i	$0.0585671\pi$
$200$		0			0
$201$	3.61627	+	11.1297i	0.255072	+	0.785030i
$202$		0			0
$203$	1.99239	+	1.44756i	0.139838	+	0.101599i
$204$		0			0
$205$	−4.85335	−	0.279601i	−0.338973	−	0.0195282i
$206$		0			0
$207$	40.8867	+	29.7059i	2.84182	+	2.06471i
$208$		0			0
$209$	4.18422	+	12.8777i	0.289428	+	0.890769i
$210$		0			0
$211$	10.2054	−	14.0465i	0.702566	−	0.966999i	−0.297359	−	0.954766i	$-0.596106\pi$
$211$	10.2054	−	14.0465i	0.702566	−	0.966999i	0.999925	−	0.0122337i	$-0.00389421\pi$
$212$		0			0
$213$	−7.53913	+	23.2031i	−0.516573	+	1.58985i
$214$		0			0
$215$	−2.23057	+	6.86500i	−0.152124	+	0.468189i
$216$		0			0
$217$	−4.75636	+	1.54544i	−0.322883	+	0.104911i
$218$		0			0
$219$			3.94956i			0.266887i
$220$		0			0
$221$	−7.35066	+	5.34057i	−0.494459	+	0.359246i
$222$		0			0
$223$	−4.48432	−	3.25805i	−0.300292	−	0.218175i	0.427428	−	0.904050i	$-0.359420\pi$
$223$	−4.48432	−	3.25805i	−0.300292	−	0.218175i	−0.727720	+	0.685875i	$0.759420\pi$
$224$		0			0
$225$	−23.9719	+	17.4166i	−1.59813	+	1.16111i
$226$		0			0
$227$	−5.14243	−	7.07794i	−0.341315	−	0.469780i	0.603510	−	0.797355i	$-0.293768\pi$
$227$	−5.14243	−	7.07794i	−0.341315	−	0.469780i	−0.944825	+	0.327576i	$0.893768\pi$
$228$		0			0
$229$	12.4613	+	4.04891i	0.823464	+	0.267560i	0.690290	−	0.723533i	$-0.257483\pi$
$229$	12.4613	+	4.04891i	0.823464	+	0.267560i	0.133174	+	0.991093i	$0.457483\pi$
$230$		0			0
$231$	−3.61619	+	1.17497i	−0.237928	+	0.0773075i
$232$		0			0
$233$	−2.13508	+	2.93869i	−0.139874	+	0.192520i	−0.873207	−	0.487350i	$-0.837964\pi$
$233$	−2.13508	+	2.93869i	−0.139874	+	0.192520i	0.733333	+	0.679870i	$0.237964\pi$
$234$		0			0
$235$	6.82187	+	2.21656i	0.445010	+	0.144592i
$236$		0			0
$237$	−6.17776			−0.401289
$238$		0			0
$239$	−13.0264	−	17.9293i	−0.842610	−	1.15975i	−0.985443	−	0.170006i	$-0.945621\pi$
$239$	−13.0264	−	17.9293i	−0.842610	−	1.15975i	0.142833	−	0.989747i	$-0.454379\pi$
$240$		0			0
$241$	−3.31923	−	10.2155i	−0.213810	−	0.658041i	−0.999236	−	0.0390846i	$-0.987556\pi$
$241$	−3.31923	−	10.2155i	−0.213810	−	0.658041i	0.785425	−	0.618956i	$-0.212444\pi$
$242$		0			0
$243$		−	14.5691i		−	0.934606i
$244$		0			0
$245$	5.06797			0.323781
$246$		0			0
$247$	−9.79575			−0.623289
$248$		0			0
$249$		−	26.2248i		−	1.66193i
$250$		0			0
$251$	2.72545	+	8.38809i	0.172029	+	0.529451i	0.999485	−	0.0320790i	$-0.0102128\pi$
$251$	2.72545	+	8.38809i	0.172029	+	0.529451i	−0.827456	+	0.561530i	$0.810213\pi$
$252$		0			0
$253$	9.50098	+	13.0770i	0.597321	+	0.822142i
$254$		0			0
$255$	−13.8607			−0.867992
$256$		0			0
$257$	13.4091	+	4.35689i	0.836438	+	0.271775i	0.695754	−	0.718280i	$-0.255070\pi$
$257$	13.4091	+	4.35689i	0.836438	+	0.271775i	0.140683	+	0.990055i	$0.455070\pi$
$258$		0			0
$259$	0.314152	−	0.432393i	0.0195205	−	0.0268676i
$260$		0			0
$261$	−27.5294	+	8.94484i	−1.70403	+	0.553672i
$262$		0			0
$263$	−12.6462	−	4.10899i	−0.779796	−	0.253371i	−0.108043	−	0.994146i	$-0.534458\pi$
$263$	−12.6462	−	4.10899i	−0.779796	−	0.253371i	−0.671753	+	0.740775i	$0.734458\pi$
$264$		0			0
$265$	1.84271	+	2.53628i	0.113197	+	0.155802i
$266$		0			0
$267$	−29.5954	+	21.5023i	−1.81121	+	1.31592i
$268$		0			0
$269$	6.27047	+	4.55576i	0.382317	+	0.277770i	0.762300	−	0.647224i	$-0.224070\pi$
$269$	6.27047	+	4.55576i	0.382317	+	0.277770i	−0.379983	+	0.924994i	$0.624070\pi$
$270$		0			0
$271$	11.2237	−	8.15452i	0.681793	−	0.495352i	−0.192159	−	0.981364i	$-0.561549\pi$
$271$	11.2237	−	8.15452i	0.681793	−	0.495352i	0.873952	+	0.486012i	$0.161549\pi$
$272$		0			0
$273$		−	2.75075i		−	0.166483i
$274$		0			0
$275$	−9.01316	+	2.92855i	−0.543514	+	0.176598i
$276$		0			0
$277$	−2.91751	+	8.97918i	−0.175296	+	0.539507i	−0.999647	−	0.0265731i	$-0.991541\pi$
$277$	−2.91751	+	8.97918i	−0.175296	+	0.539507i	0.824351	+	0.566080i	$0.191541\pi$
$278$		0			0
$279$	18.1645	−	55.9047i	1.08748	−	3.34693i
$280$		0			0
$281$	−5.34867	+	7.36181i	−0.319075	+	0.439169i	−0.938184	−	0.346136i	$-0.887494\pi$
$281$	−5.34867	+	7.36181i	−0.319075	+	0.439169i	0.619110	+	0.785305i	$0.287494\pi$
$282$		0			0
$283$	−2.51955	−	7.75438i	−0.149772	−	0.460950i	0.847822	−	0.530281i	$-0.177914\pi$
$283$	−2.51955	−	7.75438i	−0.149772	−	0.460950i	−0.997594	+	0.0693308i	$0.977914\pi$
$284$		0			0
$285$	−12.0896	−	8.78361i	−0.716127	−	0.520296i
$286$		0			0
$287$	−3.52965	+	0.926173i	−0.208349	+	0.0546703i
$288$		0			0
$289$	14.0496	+	10.2077i	0.826449	+	0.600450i
$290$		0			0
$291$	−2.79230	−	8.59381i	−0.163687	−	0.503778i
$292$		0			0
$293$	4.20696	−	5.79039i	0.245773	−	0.338278i	−0.668252	−	0.743935i	$-0.732957\pi$
$293$	4.20696	−	5.79039i	0.245773	−	0.338278i	0.914025	+	0.405657i	$0.132957\pi$
$294$		0			0
$295$	−1.30816	+	4.02609i	−0.0761639	+	0.234408i
$296$		0			0
$297$	7.62508	−	23.4676i	0.442452	−	1.36173i
$298$		0			0
$299$	−11.1215	+	3.61358i	−0.643171	+	0.208979i
$300$		0			0
$301$			5.41831i			0.312306i
$302$		0			0
$303$	−10.2887	+	7.47521i	−0.591073	+	0.429440i
$304$		0			0
$305$	2.83228	+	2.05777i	0.162176	+	0.117828i
$306$		0			0
$307$	6.78851	−	4.93214i	0.387441	−	0.281492i	−0.376965	−	0.926227i	$-0.623032\pi$
$307$	6.78851	−	4.93214i	0.387441	−	0.281492i	0.764406	+	0.644735i	$0.223032\pi$
$308$		0			0
$309$	−36.8236	−	50.6834i	−2.09482	−	2.88328i
$310$		0			0
$311$	25.4957	+	8.28406i	1.44573	+	0.469746i	0.923678	−	0.383169i	$-0.125167\pi$
$311$	25.4957	+	8.28406i	1.44573	+	0.469746i	0.522050	+	0.852915i	$0.325167\pi$
$312$		0			0
$313$	0.330503	−	0.107387i	0.0186811	−	0.00606987i	−0.299662	−	0.954046i	$-0.596874\pi$
$313$	0.330503	−	0.107387i	0.0186811	−	0.00606987i	0.318343	+	0.947976i	$0.396874\pi$
$314$		0			0
$315$	1.70356	−	2.34475i	0.0959849	−	0.132112i
$316$		0			0
$317$	−15.2469	−	4.95402i	−0.856352	−	0.278246i	−0.152248	−	0.988342i	$-0.548651\pi$
$317$	−15.2469	−	4.95402i	−0.856352	−	0.278246i	−0.704104	+	0.710097i	$0.748651\pi$
$318$		0			0
$319$	−9.25795			−0.518346
$320$		0			0
$321$	−11.6087	−	15.9780i	−0.647936	−	0.891807i
$322$		0			0
$323$	11.4494	+	35.2377i	0.637063	+	1.96068i
$324$		0			0
$325$		−	6.85609i		−	0.380307i
$326$		0			0
$327$	−58.5222			−3.23628
$328$		0			0
$329$	5.38427			0.296844
$330$		0			0
$331$		−	23.7895i		−	1.30759i	−0.756673	−	0.653794i	$-0.773176\pi$
$331$		−	23.7895i		−	1.30759i	0.756673	−	0.653794i	$-0.226824\pi$
$332$		0			0
$333$	1.94123	+	5.97449i	0.106379	+	0.327400i
$334$		0			0
$335$	−1.67693	−	2.30810i	−0.0916206	−	0.126105i
$336$		0			0
$337$	−13.5518			−0.738212			−0.369106	−	0.929387i	$-0.620336\pi$
$337$	−13.5518			−0.738212			−0.369106	+	0.929387i	$0.620336\pi$
$338$		0			0
$339$	27.2575	+	8.85651i	1.48043	+	0.481020i
$340$		0			0
$341$	11.0506	−	15.2098i	0.598423	−	0.823658i
$342$		0			0
$343$	7.41206	−	2.40832i	0.400214	−	0.130037i
$344$		0			0
$345$	−16.9660	−	5.51258i	−0.913417	−	0.296787i
$346$		0			0
$347$	−10.3984	−	14.3122i	−0.558218	−	0.768321i	0.432881	−	0.901451i	$-0.357497\pi$
$347$	−10.3984	−	14.3122i	−0.558218	−	0.768321i	−0.991099	+	0.133130i	$0.957497\pi$
$348$		0			0
$349$	17.6212	−	12.8026i	0.943243	−	0.685306i	−0.00595577	−	0.999982i	$-0.501896\pi$
$349$	17.6212	−	12.8026i	0.943243	−	0.685306i	0.949199	+	0.314676i	$0.101896\pi$
$350$		0			0
$351$	14.4419	+	10.4927i	0.770853	+	0.560058i
$352$		0			0
$353$	−23.3719	+	16.9807i	−1.24396	+	0.903790i	−0.997856	−	0.0654527i	$-0.979151\pi$
$353$	−23.3719	+	16.9807i	−1.24396	+	0.903790i	−0.246105	+	0.969243i	$0.579151\pi$
$354$		0			0
$355$		−	5.94782i		−	0.315678i
$356$		0			0
$357$	−9.89513	+	3.21512i	−0.523706	+	0.170162i
$358$		0			0
$359$	−11.4425	+	35.2165i	−0.603914	+	1.85866i	−0.0998250	+	0.995005i	$0.531828\pi$
$359$	−11.4425	+	35.2165i	−0.603914	+	1.85866i	−0.504089	+	0.863652i	$0.668172\pi$
$360$		0			0
$361$	−6.47259	+	19.9206i	−0.340663	+	1.04845i
$362$		0			0
$363$	−11.7339	+	16.1503i	−0.615868	+	0.847670i
$364$		0			0
$365$	−0.297543	−	0.915745i	−0.0155741	−	0.0479323i
$366$		0			0
$367$	10.4756	+	7.61099i	0.546823	+	0.397290i	0.826613	−	0.562771i	$-0.190265\pi$
$367$	10.4756	+	7.61099i	0.546823	+	0.397290i	−0.279790	+	0.960061i	$0.590265\pi$
$368$		0			0
$369$	15.5781	−	39.9617i	0.810965	−	2.08032i
$370$		0			0
$371$	1.90382	+	1.38321i	0.0988414	+	0.0718125i
$372$		0			0
$373$	7.52597	+	23.1625i	0.389680	+	1.19931i	0.933028	+	0.359804i	$0.117156\pi$
$373$	7.52597	+	23.1625i	0.389680	+	1.19931i	−0.543348	+	0.839507i	$0.682844\pi$
$374$		0			0
$375$	13.0965	−	18.0257i	0.676298	−	0.930845i
$376$		0			0
$377$	2.06968	−	6.36982i	0.106594	−	0.328062i
$378$		0			0
$379$	6.34961	−	19.5421i	0.326157	−	1.00381i	−0.644758	−	0.764387i	$-0.723042\pi$
$379$	6.34961	−	19.5421i	0.326157	−	1.00381i	0.970916	−	0.239422i	$-0.0769581\pi$
$380$		0			0
$381$	56.1041	−	18.2293i	2.87430	−	0.933917i
$382$		0			0
$383$		−	22.1709i		−	1.13288i	−0.824102	−	0.566441i	$-0.808320\pi$
$383$		−	22.1709i		−	1.13288i	0.824102	−	0.566441i	$-0.191680\pi$
$384$		0			0
$385$	0.749932	−	0.544858i	0.0382201	−	0.0277685i
$386$		0			0
$387$	−51.5222	−	37.4331i	−2.61902	−	1.90283i
$388$		0			0
$389$	18.9810	−	13.7905i	0.962377	−	0.699208i	0.00867535	−	0.999962i	$-0.497239\pi$
$389$	18.9810	−	13.7905i	0.962377	−	0.699208i	0.953702	+	0.300755i	$0.0972385\pi$
$390$		0			0
$391$	25.9979	+	35.7830i	1.31477	+	1.80963i
$392$		0			0
$393$	−18.8057	−	6.11036i	−0.948624	−	0.308227i
$394$		0			0
$395$	1.43237	−	0.465406i	0.0720705	−	0.0234171i
$396$		0			0
$397$	3.63028	−	4.99666i	0.182199	−	0.250775i	−0.708142	−	0.706070i	$-0.750466\pi$
$397$	3.63028	−	4.99666i	0.182199	−	0.250775i	0.890341	+	0.455295i	$0.150466\pi$
$398$		0			0
$399$	−10.6682	−	3.46630i	−0.534077	−	0.173532i
$400$		0			0
$401$	−12.3637			−0.617411			−0.308706	−	0.951158i	$-0.599896\pi$
$401$	−12.3637			−0.617411			−0.308706	+	0.951158i	$0.599896\pi$
$402$		0			0
$403$	7.99450	+	11.0035i	0.398234	+	0.548123i
$404$		0			0
$405$	3.70065	+	11.3894i	0.183887	+	0.565946i
$406$		0			0
$407$			2.00918i			0.0995915i
$408$		0			0
$409$	−24.5334			−1.21310			−0.606548	−	0.795047i	$-0.707446\pi$
$409$	−24.5334			−1.21310			−0.606548	+	0.795047i	$0.707446\pi$
$410$		0			0
$411$	−33.0347			−1.62948
$412$		0			0
$413$			3.17766i			0.156362i
$414$		0			0
$415$	1.97566	+	6.08046i	0.0969814	+	0.298478i
$416$		0			0
$417$	14.6022	+	20.0981i	0.715071	+	0.984210i
$418$		0			0
$419$	−0.591836			−0.0289131			−0.0144565	−	0.999895i	$-0.504602\pi$
$419$	−0.591836			−0.0289131			−0.0144565	+	0.999895i	$0.504602\pi$
$420$		0			0
$421$	3.72489	+	1.21029i	0.181540	+	0.0589859i	0.398376	−	0.917222i	$-0.369574\pi$
$421$	3.72489	+	1.21029i	0.181540	+	0.0589859i	−0.216836	+	0.976208i	$0.569574\pi$
$422$		0			0
$423$	−37.1979	+	51.1985i	−1.80862	+	2.48936i
$424$		0			0
$425$	−24.6630	+	8.01351i	−1.19633	+	0.388712i
$426$		0			0
$427$	2.49928	+	0.812064i	0.120948	+	0.0392985i
$428$		0			0
$429$	6.07810	+	8.36579i	0.293454	+	0.403904i
$430$		0			0
$431$	−6.69486	+	4.86410i	−0.322480	+	0.234295i	−0.737233	−	0.675639i	$-0.763868\pi$
$431$	−6.69486	+	4.86410i	−0.322480	+	0.234295i	0.414753	+	0.909934i	$0.363868\pi$
$432$		0			0
$433$	15.3829	+	11.1763i	0.739253	+	0.537098i	0.892477	−	0.451093i	$-0.148966\pi$
$433$	15.3829	+	11.1763i	0.739253	+	0.537098i	−0.153224	+	0.988191i	$0.548966\pi$
$434$		0			0
$435$	8.26600	−	6.00560i	0.396324	−	0.287947i
$436$		0			0
$437$			47.6857i			2.28112i
$438$		0			0
$439$	−3.44577	+	1.11960i	−0.164458	+	0.0534355i	−0.390089	−	0.920777i	$-0.627556\pi$
$439$	−3.44577	+	1.11960i	−0.164458	+	0.0534355i	0.225631	+	0.974213i	$0.427556\pi$
$440$		0			0
$441$	−13.8172	+	42.5249i	−0.657961	+	2.02499i
$442$		0			0
$443$	2.06308	−	6.34952i	0.0980200	−	0.301675i	−0.890009	−	0.455943i	$-0.849302\pi$
$443$	2.06308	−	6.34952i	0.0980200	−	0.301675i	0.988029	+	0.154268i	$0.0493021\pi$
$444$		0			0
$445$	5.24208	−	7.21511i	0.248499	−	0.342029i
$446$		0			0
$447$	10.8601	+	33.4240i	0.513665	+	1.58090i
$448$		0			0
$449$	−30.4252	−	22.1052i	−1.43585	−	1.04321i	−0.988889	−	0.148656i	$-0.952505\pi$
$449$	−30.4252	−	22.1052i	−1.43585	−	1.04321i	−0.446964	−	0.894552i	$-0.647495\pi$
$450$		0			0
$451$	8.68815	−	10.6159i	0.409109	−	0.499884i
$452$		0			0
$453$	−6.11722	−	4.44442i	−0.287412	−	0.208817i
$454$		0			0
$455$	0.207230	+	0.637788i	0.00971509	+	0.0299000i
$456$		0			0
$457$	−13.3748	+	18.4088i	−0.625646	+	0.861127i	−0.997749	−	0.0670642i	$-0.978637\pi$
$457$	−13.3748	+	18.4088i	−0.625646	+	0.861127i	0.372103	+	0.928191i	$0.378637\pi$
$458$		0			0
$459$	20.8648	−	64.2152i	0.973885	−	2.99731i
$460$		0			0
$461$	5.40061	−	16.6214i	0.251532	−	0.774134i	−0.742962	−	0.669334i	$-0.766580\pi$
$461$	5.40061	−	16.6214i	0.251532	−	0.774134i	0.994493	−	0.104801i	$-0.0334204\pi$
$462$		0			0
$463$	−4.60270	+	1.49551i	−0.213906	+	0.0695022i	−0.414010	−	0.910273i	$-0.635872\pi$
$463$	−4.60270	+	1.49551i	−0.213906	+	0.0695022i	0.200104	+	0.979775i	$0.435872\pi$
$464$		0			0
$465$			20.7486i			0.962195i
$466$		0			0
$467$	−18.5306	+	13.4633i	−0.857495	+	0.623006i	−0.927202	−	0.374561i	$-0.877793\pi$
$467$	−18.5306	+	13.4633i	−0.857495	+	0.623006i	0.0697075	+	0.997567i	$0.477793\pi$
$468$		0			0
$469$	−1.73254	−	1.25877i	−0.0800014	−	0.0581244i
$470$		0			0
$471$	48.2774	−	35.0756i	2.22450	−	1.61620i
$472$		0			0
$473$	−11.9724	−	16.4786i	−0.550491	−	0.757685i
$474$		0			0
$475$	−26.5898	−	8.63956i	−1.22002	−	0.396410i
$476$		0			0
$477$	−26.3056	+	8.54719i	−1.20445	+	0.391349i
$478$		0			0
$479$	−15.4619	+	21.2815i	−0.706474	+	0.972377i	0.293392	+	0.955992i	$0.405216\pi$
$479$	−15.4619	+	21.2815i	−0.706474	+	0.972377i	−0.999866	+	0.0163853i	$0.994784\pi$
$480$		0			0
$481$	−1.38239	−	0.449167i	−0.0630317	−	0.0204802i
$482$		0			0
$483$	−13.3907			−0.609296
$484$		0			0
$485$	1.29484	+	1.78220i	0.0587958	+	0.0809255i
$486$		0			0
$487$	8.00524	+	24.6376i	0.362752	+	1.11644i	0.951377	+	0.308030i	$0.0996697\pi$
$487$	8.00524	+	24.6376i	0.362752	+	1.11644i	−0.588624	+	0.808407i	$0.700330\pi$
$488$		0			0
$489$			20.9021i			0.945224i
$490$		0			0
$491$	30.6345			1.38251			0.691257	−	0.722609i	$-0.257057\pi$
$491$	30.6345			1.38251			0.691257	+	0.722609i	$0.257057\pi$
$492$		0			0
$493$	−25.3329			−1.14094
$494$		0			0
$495$			10.8953i			0.489705i
$496$		0			0
$497$	−1.37965	−	4.24613i	−0.0618859	−	0.190465i
$498$		0			0
$499$	1.35018	+	1.85836i	0.0604422	+	0.0831916i	0.838168	−	0.545412i	$-0.183627\pi$
$499$	1.35018	+	1.85836i	0.0604422	+	0.0831916i	−0.777726	+	0.628604i	$0.783627\pi$
$500$		0			0
$501$	26.3918			1.17910
$502$		0			0
$503$	33.5612	+	10.9047i	1.49642	+	0.486216i	0.938971	−	0.343997i	$-0.111781\pi$
$503$	33.5612	+	10.9047i	1.49642	+	0.486216i	0.557447	+	0.830212i	$0.311781\pi$
$504$		0			0
$505$	1.82239	−	2.50831i	0.0810955	−	0.111618i
$506$		0			0
$507$	31.3887	−	10.1988i	1.39402	−	0.452945i
$508$		0			0
$509$	17.6826	+	5.74544i	0.783769	+	0.254662i	0.673449	−	0.739234i	$-0.264812\pi$
$509$	17.6826	+	5.74544i	0.783769	+	0.254662i	0.110320	+	0.993896i	$0.464812\pi$
$510$		0			0
$511$	−0.424831	−	0.584730i	−0.0187934	−	0.0258669i
$512$		0			0
$513$	58.8922	−	42.7877i	2.60016	−	1.88912i
$514$		0			0
$515$	12.3562	+	8.97729i	0.544478	+	0.395587i
$516$		0			0
$517$	−16.3750	+	11.8972i	−0.720173	+	0.523236i
$518$		0			0
$519$			38.8118i			1.70365i
$520$		0			0
$521$	−14.3582	+	4.66527i	−0.629045	+	0.204389i	−0.606152	−	0.795349i	$-0.707288\pi$
$521$	−14.3582	+	4.66527i	−0.629045	+	0.204389i	−0.0228931	+	0.999738i	$0.507288\pi$
$522$		0			0
$523$	3.21172	−	9.88465i	0.140439	−	0.432226i	−0.855958	−	0.517046i	$-0.827032\pi$
$523$	3.21172	−	9.88465i	0.140439	−	0.432226i	0.996396	+	0.0848202i	$0.0270316\pi$
$524$		0			0
$525$	2.42608	−	7.46671i	0.105883	−	0.325874i
$526$		0			0
$527$	30.2381	−	41.6192i	1.31719	−	1.81296i
$528$		0			0
$529$	10.4835	+	32.2650i	0.455805	+	1.40282i
$530$		0			0
$531$	−30.2161	−	21.9532i	−1.31126	−	0.952690i
$532$		0			0
$533$	5.36185	+	8.35103i	0.232248	+	0.361723i
$534$		0			0
$535$	3.89531	+	2.83011i	0.168409	+	0.122356i
$536$		0			0
$537$	13.1366	+	40.4304i	0.566887	+	1.74470i
$538$		0			0
$539$	−8.40583	+	11.5696i	−0.362065	+	0.498339i
$540$		0			0
$541$	5.93295	−	18.2597i	0.255077	−	0.785047i	−0.738737	−	0.673994i	$-0.764578\pi$
$541$	5.93295	−	18.2597i	0.255077	−	0.785047i	0.993814	−	0.111053i	$-0.0354225\pi$
$542$		0			0
$543$	16.3832	−	50.4223i	0.703071	−	2.16383i
$544$		0			0
$545$	13.5689	−	4.40881i	0.581229	−	0.188853i
$546$		0			0
$547$			40.7375i			1.74181i	0.491453	+	0.870904i	$0.336466\pi$
$547$			40.7375i			1.74181i	−0.491453	+	0.870904i	$0.663534\pi$
$548$		0			0
$549$	−24.9884	+	18.1552i	−1.06648	+	0.774843i
$550$		0			0
$551$	−22.0959	−	16.0536i	−0.941316	−	0.683906i
$552$		0			0
$553$	0.914612	−	0.664505i	0.0388933	−	0.0282576i
$554$		0			0
$555$	−1.30335	−	1.79391i	−0.0553241	−	0.0761471i
$556$		0			0
$557$	40.4822	+	13.1534i	1.71528	+	0.557330i	0.991199	−	0.132381i	$-0.0422623\pi$
$557$	40.4822	+	13.1534i	1.71528	+	0.557330i	0.724085	+	0.689711i	$0.242262\pi$
$558$		0			0
$559$	14.0144	−	4.55355i	0.592745	−	0.192595i
$560$		0			0
$561$	22.9896	−	31.6425i	0.970623	−	1.33595i
$562$		0			0
$563$	25.8821	+	8.40960i	1.09080	+	0.354422i	0.798555	−	0.601921i	$-0.205598\pi$
$563$	25.8821	+	8.40960i	1.09080	+	0.354422i	0.292244	+	0.956344i	$0.405598\pi$
$564$		0			0
$565$	−6.98714			−0.293951
$566$		0			0
$567$	5.28377	+	7.27249i	0.221898	+	0.305416i
$568$		0			0
$569$	7.82531	+	24.0838i	0.328054	+	1.00965i	0.970043	+	0.242933i	$0.0781095\pi$
$569$	7.82531	+	24.0838i	0.328054	+	1.00965i	−0.641989	+	0.766714i	$0.721891\pi$
$570$		0			0
$571$			7.94379i			0.332437i	0.986089	+	0.166219i	$0.0531557\pi$
$571$			7.94379i			0.332437i	−0.986089	+	0.166219i	$0.946844\pi$
$572$		0			0
$573$	23.5797			0.985055
$574$		0			0
$575$	−33.3754			−1.39185
$576$		0			0
$577$		−	39.6444i		−	1.65042i	−0.564828	−	0.825208i	$-0.691058\pi$
$577$		−	39.6444i		−	1.65042i	0.564828	−	0.825208i	$-0.308942\pi$
$578$		0			0
$579$	4.37463	+	13.4637i	0.181803	+	0.559533i
$580$		0			0
$581$	2.82084	+	3.88255i	0.117028	+	0.161075i
$582$		0			0
$583$	−8.84639			−0.366380
$584$		0			0
$585$	−7.49634	−	2.43571i	−0.309936	−	0.100704i
$586$		0			0
$587$	−3.69794	+	5.08978i	−0.152630	+	0.210078i	−0.878484	−	0.477771i	$-0.841445\pi$
$587$	−3.69794	+	5.08978i	−0.152630	+	0.210078i	0.725854	+	0.687849i	$0.241445\pi$
$588$		0			0
$589$	52.7487	−	17.1391i	2.17347	−	0.706204i
$590$		0			0
$591$	−55.3793	−	17.9938i	−2.27800	−	0.740167i
$592$		0			0
$593$	−3.90297	−	5.37198i	−0.160276	−	0.220601i	0.721325	−	0.692597i	$-0.243534\pi$
$593$	−3.90297	−	5.37198i	−0.160276	−	0.220601i	−0.881600	+	0.471996i	$0.843534\pi$
$594$		0			0
$595$	2.05207	−	1.49091i	0.0841266	−	0.0611215i
$596$		0			0
$597$	−30.5548	−	22.1994i	−1.25052	−	0.908559i
$598$		0			0
$599$	13.5062	−	9.81280i	0.551847	−	0.400940i	−0.276619	−	0.960980i	$-0.589214\pi$
$599$	13.5062	−	9.81280i	0.551847	−	0.400940i	0.828466	+	0.560040i	$0.189214\pi$
$600$		0			0
$601$			30.3710i			1.23886i	0.785053	+	0.619429i	$0.212636\pi$
$601$			30.3710i			1.23886i	−0.785053	+	0.619429i	$0.787364\pi$
$602$		0			0
$603$	23.9390	−	7.77825i	0.974871	−	0.316755i
$604$		0			0
$605$	1.50392	−	4.62858i	0.0611429	−	0.188178i
$606$		0			0
$607$	−12.6273	+	38.8630i	−0.512528	+	1.57740i	0.275208	+	0.961385i	$0.411253\pi$
$607$	−12.6273	+	38.8630i	−0.512528	+	1.57740i	−0.787735	+	0.616014i	$0.788747\pi$
$608$		0			0
$609$	4.50802	−	6.20476i	0.182674	−	0.251430i
$610$		0			0
$611$	−4.52494	−	13.9263i	−0.183059	−	0.563399i
$612$		0			0
$613$	−31.7394	−	23.0601i	−1.28194	−	0.931387i	−0.282334	−	0.959316i	$-0.591109\pi$
$613$	−31.7394	−	23.0601i	−1.28194	−	0.931387i	−0.999610	+	0.0279294i	$0.991109\pi$
$614$		0			0
$615$	−0.870740	+	15.1144i	−0.0351116	+	0.609473i
$616$		0			0
$617$	−8.89734	−	6.46429i	−0.358193	−	0.260243i	0.394105	−	0.919065i	$-0.371055\pi$
$617$	−8.89734	−	6.46429i	−0.358193	−	0.260243i	−0.752298	+	0.658823i	$0.771055\pi$
$618$		0			0
$619$	−14.2654	−	43.9044i	−0.573374	−	1.76467i	−0.641649	−	0.766999i	$-0.721749\pi$
$619$	−14.2654	−	43.9044i	−0.573374	−	1.76467i	0.0682743	−	0.997667i	$-0.478251\pi$
$620$		0			0
$621$	51.0783	−	70.3033i	2.04970	−	2.82117i
$622$		0			0
$623$	2.06870	−	6.36680i	0.0828806	−	0.255080i
$624$		0			0
$625$	5.15625	−	15.8693i	0.206250	−	0.634772i
$626$		0			0
$627$	40.1041	−	13.0306i	1.60160	−	0.520392i
$628$		0			0
$629$			5.49780i			0.219212i
$630$		0			0
$631$	−14.2763	+	10.3723i	−0.568330	+	0.412916i	−0.834498	−	0.551011i	$-0.814242\pi$
$631$	−14.2763	+	10.3723i	−0.568330	+	0.412916i	0.266168	+	0.963927i	$0.414242\pi$
$632$		0			0
$633$	−43.7439	−	31.7818i	−1.73866	−	1.26321i
$634$		0			0
$635$	−11.6350	+	8.45330i	−0.461719	+	0.335459i
$636$		0			0
$637$	−6.08116	−	8.37000i	−0.240944	−	0.331631i
$638$		0			0
$639$	49.9076	+	16.2160i	1.97431	+	0.641494i
$640$		0			0
$641$	−18.9225	+	6.14829i	−0.747394	+	0.242843i	−0.657859	−	0.753141i	$-0.728538\pi$
$641$	−18.9225	+	6.14829i	−0.747394	+	0.242843i	−0.0895343	+	0.995984i	$0.528538\pi$
$642$		0			0
$643$	17.7002	−	24.3622i	0.698027	−	0.960751i	−0.301946	−	0.953325i	$-0.597636\pi$
$643$	17.7002	−	24.3622i	0.698027	−	0.960751i	0.999972	−	0.00742616i	$-0.00236384\pi$
$644$		0			0
$645$	21.3792	+	6.94651i	0.841804	+	0.273519i
$646$		0			0
$647$	6.44925			0.253546			0.126773	−	0.991932i	$-0.459538\pi$
$647$	6.44925			0.253546			0.126773	+	0.991932i	$0.459538\pi$
$648$		0			0
$649$	−7.02140	−	9.66413i	−0.275614	−	0.379350i
$650$		0			0
$651$	4.81284	+	14.8124i	0.188630	+	0.580543i
$652$		0			0
$653$			5.49051i			0.214860i	0.994213	+	0.107430i	$0.0342622\pi$
$653$			5.49051i			0.214860i	−0.994213	+	0.107430i	$0.965738\pi$
$654$		0			0
$655$	4.82062			0.188357
$656$		0			0
$657$	8.49514			0.331427
$658$		0			0
$659$		−	0.0139596i		−	0.000543791i	−1.00000		0.000271895i	$-0.999913\pi$
$659$		−	0.0139596i		−	0.000543791i	1.00000		0.000271895i	$-8.65470e-5\pi$
$660$		0			0
$661$	−0.195685	−	0.602258i	−0.00761128	−	0.0234251i	0.947179	−	0.320706i	$-0.103920\pi$
$661$	−0.195685	−	0.602258i	−0.00761128	−	0.0234251i	−0.954790	+	0.297281i	$0.903920\pi$
$662$		0			0
$663$	16.6317	+	22.8916i	0.645923	+	0.889037i
$664$		0			0
$665$	2.73466			0.106045
$666$		0			0
$667$	−31.0083	−	10.0752i	−1.20065	−	0.390113i
$668$		0			0
$669$	−10.1463	+	13.9652i	−0.392278	+	0.539925i
$670$		0			0
$671$	−9.39534	+	3.05273i	−0.362703	+	0.117849i
$672$		0			0
$673$	21.0849	+	6.85090i	0.812763	+	0.264083i	0.685767	−	0.727821i	$-0.259467\pi$
$673$	21.0849	+	6.85090i	0.812763	+	0.264083i	0.126995	+	0.991903i	$0.459467\pi$
$674$		0			0
$675$	29.9473	+	41.2189i	1.15267	+	1.58652i
$676$		0			0
$677$	−37.7831	+	27.4510i	−1.45212	+	1.05503i	−0.466793	+	0.884367i	$0.654591\pi$
$677$	−37.7831	+	27.4510i	−1.45212	+	1.05503i	−0.985330	+	0.170662i	$0.945409\pi$
$678$		0			0
$679$	1.33778	+	0.971956i	0.0513394	+	0.0373002i
$680$		0			0
$681$	−22.0423	+	16.0147i	−0.844664	+	0.613684i
$682$		0			0
$683$			4.17441i			0.159729i	0.996806	+	0.0798646i	$0.0254488\pi$
$683$			4.17441i			0.159729i	−0.996806	+	0.0798646i	$0.974551\pi$
$684$		0			0
$685$	7.65941	−	2.48869i	0.292651	−	0.0950881i
$686$		0			0
$687$	12.6092	−	38.8072i	0.481072	−	1.48059i
$688$		0			0
$689$	1.97767	−	6.08665i	0.0753433	−	0.231883i
$690$		0			0
$691$	−13.8589	+	19.0751i	−0.527217	+	0.725652i	−0.986703	−	0.162533i	$-0.948034\pi$
$691$	−13.8589	+	19.0751i	−0.527217	+	0.725652i	0.459486	+	0.888185i	$0.348034\pi$
$692$		0			0
$693$	2.52726	+	7.77809i	0.0960025	+	0.295465i
$694$		0			0
$695$	−4.89976	−	3.55988i	−0.185858	−	0.135034i
$696$		0			0
$697$	23.7737	−	29.0487i	0.900493	−	1.10030i
$698$		0			0
$699$	9.15174	+	6.64913i	0.346150	+	0.251493i
$700$		0			0
$701$	−11.9550	−	36.7937i	−0.451533	−	1.38968i	−0.875157	−	0.483839i	$-0.839242\pi$
$701$	−11.9550	−	36.7937i	−0.451533	−	1.38968i	0.423624	−	0.905838i	$-0.360758\pi$
$702$		0			0
$703$	−3.48399	+	4.79530i	−0.131401	+	0.180858i
$704$		0			0
$705$	6.90287	−	21.2449i	0.259977	−	0.800127i
$706$		0			0
$707$	0.719176	−	2.21340i	0.0270474	−	0.0832434i
$708$		0			0
$709$	6.60736	−	2.14686i	0.248145	−	0.0806271i	−0.182304	−	0.983242i	$-0.558355\pi$
$709$	6.60736	−	2.14686i	0.248145	−	0.0806271i	0.430448	+	0.902615i	$0.358355\pi$
$710$		0			0
$711$			13.2878i			0.498331i
$712$		0			0
$713$	53.5650	−	38.9172i	2.00602	−	1.45746i
$714$		0			0
$715$	−2.03951	−	1.48179i	−0.0762733	−	0.0554158i
$716$		0			0
$717$	−55.8361	+	40.5673i	−2.08524	+	1.51501i
$718$		0			0
$719$	−8.08843	−	11.1328i	−0.301648	−	0.415182i	0.631106	−	0.775696i	$-0.282601\pi$
$719$	−8.08843	−	11.1328i	−0.301648	−	0.415182i	−0.932754	+	0.360514i	$0.882601\pi$
$720$		0			0
$721$	10.9034	+	3.54273i	0.406064	+	0.131938i
$722$		0			0
$723$	−31.8135	+	10.3368i	−1.18316	+	0.384431i
$724$		0			0
$725$	11.2360	−	15.4650i	0.417294	−	0.574356i
$726$		0			0
$727$	19.2854	+	6.26619i	0.715254	+	0.232400i	0.643964	−	0.765055i	$-0.277288\pi$
$727$	19.2854	+	6.26619i	0.715254	+	0.232400i	0.0712898	+	0.997456i	$0.477288\pi$
$728$		0			0
$729$	1.94899			0.0721849
$730$		0			0
$731$	−32.7605	−	45.0909i	−1.21169	−	1.66775i
$732$		0			0
$733$	4.55216	+	14.0101i	0.168138	+	0.517476i	0.999254	−	0.0386238i	$-0.0122974\pi$
$733$	4.55216	+	14.0101i	0.168138	+	0.517476i	−0.831116	+	0.556099i	$0.812297\pi$
$734$		0			0
$735$		−	15.7828i		−	0.582158i
$736$		0			0
$737$	8.05053			0.296545
$738$		0			0
$739$	16.0697			0.591134			0.295567	−	0.955322i	$-0.404491\pi$
$739$	16.0697			0.591134			0.295567	+	0.955322i	$0.404491\pi$
$740$		0			0
$741$			30.5062i			1.12067i
$742$		0			0
$743$	−8.08643	−	24.8875i	−0.296662	−	0.913033i	−0.982658	−	0.185427i	$-0.940633\pi$
$743$	−8.08643	−	24.8875i	−0.296662	−	0.913033i	0.685996	−	0.727606i	$-0.259367\pi$
$744$		0			0
$745$	−5.03604	−	6.93151i	−0.184506	−	0.253951i
$746$		0			0
$747$	−56.4070			−2.06382
$748$		0			0
$749$	3.43732	+	1.11685i	0.125597	+	0.0408090i
$750$		0			0
$751$	7.88100	−	10.8473i	0.287582	−	0.395822i	−0.640645	−	0.767837i	$-0.721333\pi$
$751$	7.88100	−	10.8473i	0.287582	−	0.395822i	0.928227	+	0.372015i	$0.121333\pi$
$752$		0			0
$753$	26.1224	−	8.48768i	0.951953	−	0.309308i
$754$		0			0
$755$	1.75316	+	0.569637i	0.0638041	+	0.0207312i
$756$		0			0
$757$	5.32375	+	7.32752i	0.193495	+	0.266323i	0.894730	−	0.446607i	$-0.147368\pi$
$757$	5.32375	+	7.32752i	0.193495	+	0.266323i	−0.701235	+	0.712930i	$0.747368\pi$
$758$		0			0
$759$	40.7247	−	29.5882i	1.47821	−	1.07398i
$760$		0			0
$761$	30.9720	+	22.5025i	1.12273	+	0.815714i	0.984621	−	0.174702i	$-0.0558963\pi$
$761$	30.9720	+	22.5025i	1.12273	+	0.815714i	0.138113	+	0.990416i	$0.455896\pi$
$762$		0			0
$763$	8.66416	−	6.29488i	0.313664	−	0.227890i
$764$		0			0
$765$			29.8131i			1.07790i
$766$		0			0
$767$	8.21897	−	2.67050i	0.296770	−	0.0964263i
$768$		0			0
$769$	−5.28000	+	16.2502i	−0.190402	+	0.585997i	−1.00000		0.000988576i	$-0.999685\pi$
$769$	−5.28000	+	16.2502i	−0.190402	+	0.585997i	0.809598	+	0.586985i	$0.199685\pi$
$770$		0			0
$771$	13.5683	−	41.7590i	0.488651	−	1.50391i
$772$		0			0
$773$	−5.05808	+	6.96185i	−0.181926	+	0.250400i	−0.890234	−	0.455504i	$-0.849459\pi$
$773$	−5.05808	+	6.96185i	−0.181926	+	0.250400i	0.708307	+	0.705904i	$0.249459\pi$
$774$		0			0
$775$	11.9957	+	36.9190i	0.430899	+	1.32617i
$776$		0			0
$777$	−1.34657	−	0.978341i	−0.0483080	−	0.0350978i
$778$		0			0
$779$	39.1443	−	10.2714i	1.40249	−	0.368010i
$780$		0			0
$781$	13.5782	+	9.86516i	0.485867	+	0.353003i
$782$		0			0
$783$	15.3803	+	47.3358i	0.549649	+	1.69164i
$784$		0			0
$785$	−8.55113	+	11.7696i	−0.305203	+	0.420076i
$786$		0			0
$787$	1.95733	−	6.02403i	0.0697711	−	0.214734i	−0.910091	−	0.414408i	$-0.863989\pi$
$787$	1.95733	−	6.02403i	0.0697711	−	0.214734i	0.979862	+	0.199675i	$0.0639886\pi$
$788$		0			0
$789$	−12.7963	+	39.3831i	−0.455561	+	1.40207i
$790$		0			0
$791$	−4.98810	+	1.62073i	−0.177356	+	0.0576266i
$792$		0			0
$793$		−	7.14681i		−	0.253791i
$794$		0			0
$795$	7.89854	−	5.73862i	0.280132	−	0.203528i
$796$		0			0
$797$	11.0215	+	8.00762i	0.390403	+	0.283644i	0.765621	−	0.643292i	$-0.222432\pi$
$797$	11.0215	+	8.00762i	0.390403	+	0.283644i	−0.375218	+	0.926937i	$0.622432\pi$
$798$		0			0
$799$	−44.8076	+	32.5547i	−1.58518	+	1.15170i
$800$		0			0
$801$	46.2494	+	63.6569i	1.63414	+	2.24921i
$802$		0			0
$803$	2.58406	+	0.839610i	0.0911893	+	0.0296292i
$804$		0			0
$805$	3.10475	−	1.00880i	0.109428	−	0.0355554i
$806$		0			0
$807$	14.1877	−	19.5277i	0.499430	−	0.687407i
$808$		0			0
$809$	1.09004	+	0.354177i	0.0383239	+	0.0124522i	0.328116	−	0.944637i	$-0.393586\pi$
$809$	1.09004	+	0.354177i	0.0383239	+	0.0124522i	−0.289792	+	0.957090i	$0.593586\pi$
$810$		0			0
$811$	−51.9986			−1.82592			−0.912958	−	0.408053i	$-0.866208\pi$
$811$	−51.9986			−1.82592			−0.912958	+	0.408053i	$0.866208\pi$
$812$		0			0
$813$	−25.3950	−	34.9532i	−0.890642	−	1.22586i
$814$		0			0
$815$	−1.57467	−	4.84635i	−0.0551584	−	0.169760i
$816$		0			0
$817$		−	60.0898i		−	2.10227i
$818$		0			0
$819$	−5.91661			−0.206743
$820$		0			0
$821$	−21.3265			−0.744298			−0.372149	−	0.928173i	$-0.621379\pi$
$821$	−21.3265			−0.744298			−0.372149	+	0.928173i	$0.621379\pi$
$822$		0			0
$823$			29.8000i			1.03876i	0.854543	+	0.519381i	$0.173837\pi$
$823$			29.8000i			1.03876i	−0.854543	+	0.519381i	$0.826163\pi$
$824$		0			0
$825$	9.12018	+	28.0690i	0.317524	+	0.977238i
$826$		0			0
$827$	2.29167	+	3.15421i	0.0796892	+	0.109683i	0.847001	−	0.531592i	$-0.178406\pi$
$827$	2.29167	+	3.15421i	0.0796892	+	0.109683i	−0.767311	+	0.641275i	$0.778406\pi$
$828$		0			0
$829$	−4.49666			−0.156175			−0.0780877	−	0.996946i	$-0.524881\pi$
$829$	−4.49666			−0.156175			−0.0780877	+	0.996946i	$0.524881\pi$
$830$		0			0
$831$	27.9632	+	9.08579i	0.970033	+	0.315183i
$832$		0			0
$833$	−23.0012	+	31.6584i	−0.796944	+	1.09690i
$834$		0			0
$835$	−6.11919	+	1.98825i	−0.211763	+	0.0688061i
$836$		0			0
$837$	−96.1262	−	31.2333i	−3.32261	−	1.07958i
$838$		0			0
$839$	5.54340	+	7.62983i	0.191379	+	0.263411i	0.893914	−	0.448238i	$-0.147948\pi$
$839$	5.54340	+	7.62983i	0.191379	+	0.263411i	−0.702535	+	0.711649i	$0.747948\pi$
$840$		0			0
$841$	−8.35392	+	6.06948i	−0.288066	+	0.209292i
$842$		0			0
$843$	22.9263	+	16.6570i	0.789625	+	0.573696i
$844$		0			0
$845$	−6.50944	+	4.72938i	−0.223931	+	0.162696i
$846$		0			0
$847$		−	3.65318i		−	0.125525i
$848$		0			0
$849$	−24.1489	+	7.84646i	−0.828788	+	0.269290i
$850$		0			0
$851$	−2.18654	+	6.72949i	−0.0749537	+	0.230684i
$852$		0			0
$853$	5.57764	−	17.1662i	0.190975	−	0.587760i	−0.809025	−	0.587774i	$-0.800004\pi$
$853$	5.57764	−	17.1662i	0.190975	−	0.587760i	1.00000		1.40098e-5i	$4.45947e-6\pi$
$854$		0			0
$855$	−18.8927	+	26.0036i	−0.646118	+	0.889305i
$856$		0			0
$857$	9.63694	+	29.6594i	0.329191	+	1.01315i	0.969513	+	0.245040i	$0.0788011\pi$
$857$	9.63694	+	29.6594i	0.329191	+	1.01315i	−0.640321	+	0.768107i	$0.721199\pi$
$858$		0			0
$859$	−5.38859	−	3.91504i	−0.183856	−	0.133579i	0.492050	−	0.870567i	$-0.336248\pi$
$859$	−5.38859	−	3.91504i	−0.183856	−	0.133579i	−0.675906	+	0.736987i	$0.736248\pi$
$860$		0			0
$861$	2.88431	+	10.9921i	0.0982971	+	0.374611i
$862$		0			0
$863$	−19.7831	−	14.3733i	−0.673424	−	0.489271i	0.197746	−	0.980253i	$-0.436638\pi$
$863$	−19.7831	−	14.3733i	−0.673424	−	0.489271i	−0.871170	+	0.490982i	$0.836638\pi$
$864$		0			0
$865$	−2.92392	−	8.99889i	−0.0994161	−	0.305971i
$866$		0			0
$867$	31.7890	−	43.7537i	1.07961	−	1.48596i
$868$		0			0
$869$	−1.31329	+	4.04188i	−0.0445502	+	0.137111i
$870$		0			0
$871$	−1.79975	+	5.53907i	−0.0609823	+	0.187684i
$872$		0			0
$873$	−18.4845	+	6.00597i	−0.625605	+	0.203271i
$874$		0			0
$875$			4.07740i			0.137841i
$876$		0			0
$877$	−31.3231	+	22.7576i	−1.05771	+	0.768469i	−0.973663	−	0.227993i	$-0.926784\pi$
$877$	−31.3231	+	22.7576i	−1.05771	+	0.768469i	−0.0840441	+	0.996462i	$0.526784\pi$
$878$		0			0
$879$	−18.0326	−	13.1014i	−0.608224	−	0.441900i
$880$		0			0
$881$	24.8319	−	18.0415i	0.836609	−	0.607832i	−0.0848122	−	0.996397i	$-0.527029\pi$
$881$	24.8319	−	18.0415i	0.836609	−	0.607832i	0.921421	+	0.388565i	$0.127029\pi$
$882$		0			0
$883$	−1.45653	−	2.00474i	−0.0490161	−	0.0674649i	0.783805	−	0.621007i	$-0.213276\pi$
$883$	−1.45653	−	2.00474i	−0.0490161	−	0.0674649i	−0.832821	+	0.553542i	$0.813276\pi$
$884$		0			0
$885$	12.5382	+	4.07390i	0.421466	+	0.136943i
$886$		0			0
$887$	28.3511	−	9.21183i	0.951937	−	0.309303i	0.208435	−	0.978036i	$-0.433163\pi$
$887$	28.3511	−	9.21183i	0.951937	−	0.309303i	0.743502	+	0.668733i	$0.233163\pi$
$888$		0			0
$889$	−6.34535	+	8.73362i	−0.212816	+	0.292916i
$890$		0			0
$891$	−32.1388	−	10.4425i	−1.07669	−	0.349838i
$892$		0			0
$893$	−59.7122			−1.99819
$894$		0			0
$895$	−6.09171	−	8.38452i	−0.203623	−	0.280264i
$896$		0			0
$897$	11.2535	+	34.6347i	0.375744	+	1.15642i
$898$		0			0
$899$			37.9218i			1.26476i
$900$		0			0
$901$	−24.2067			−0.806443
$902$		0			0
$903$	16.8738			0.561526
$904$		0			0
$905$			12.9251i			0.429646i
$906$		0			0
$907$	−3.81119	−	11.7296i	−0.126549	−	0.389476i	0.867632	−	0.497208i	$-0.165641\pi$
$907$	−3.81119	−	11.7296i	−0.126549	−	0.389476i	−0.994180	+	0.107731i	$0.965641\pi$
$908$		0			0
$909$	16.0785	+	22.1301i	0.533289	+	0.734010i
$910$		0			0
$911$	22.7054			0.752264			0.376132	−	0.926566i	$-0.377254\pi$
$911$	22.7054			0.752264			0.376132	+	0.926566i	$0.377254\pi$
$912$		0			0
$913$	−17.1579	−	5.57494i	−0.567844	−	0.184504i
$914$		0			0
$915$	6.40837	−	8.82037i	0.211854	−	0.291592i
$916$		0			0
$917$	3.44143	−	1.11819i	0.113646	−	0.0369258i
$918$		0			0
$919$	−26.0930	−	8.47814i	−0.860729	−	0.279668i	−0.154796	−	0.987946i	$-0.549472\pi$
$919$	−26.0930	−	8.47814i	−0.860729	−	0.279668i	−0.705933	+	0.708278i	$0.749472\pi$
$920$		0			0
$921$	−15.3598	−	21.1410i	−0.506123	−	0.696619i
$922$		0			0
$923$	−9.82311	+	7.13690i	−0.323331	+	0.234914i
$924$		0			0
$925$	−3.35625	−	2.43846i	−0.110353	−	0.0801760i
$926$		0			0
$927$	−109.015	+	79.2041i	−3.58053	+	2.60141i
$928$		0			0
$929$		−	40.7217i		−	1.33604i	−0.744145	−	0.668018i	$-0.767143\pi$
$929$		−	40.7217i		−	1.33604i	0.744145	−	0.668018i	$-0.232857\pi$
$930$		0			0
$931$	−40.1242	+	13.0372i	−1.31502	+	0.427275i
$932$		0			0
$933$	25.7984	−	79.3994i	0.844603	−	2.59942i
$934$		0			0
$935$	−2.94655	+	9.06856i	−0.0963626	+	0.296574i
$936$		0			0
$937$	−16.4894	+	22.6957i	−0.538686	+	0.741437i	−0.988423	−	0.151724i	$-0.951518\pi$
$937$	−16.4894	+	22.6957i	−0.538686	+	0.741437i	0.449737	+	0.893161i	$0.351518\pi$
$938$		0			0
$939$	−0.334427	−	1.02926i	−0.0109136	−	0.0335887i
$940$		0			0
$941$	30.1292	+	21.8902i	0.982185	+	0.713599i	0.958196	−	0.286113i	$-0.0923633\pi$
$941$	30.1292	+	21.8902i	0.982185	+	0.713599i	0.0239892	+	0.999712i	$0.492363\pi$
$942$		0			0
$943$	40.6528	−	26.1015i	1.32384	−	0.849982i
$944$		0			0
$945$	−4.03172	−	2.92922i	−0.131152	−	0.0952874i
$946$		0			0
$947$	2.79266	+	8.59491i	0.0907491	+	0.279297i	0.986123	−	0.166019i	$-0.0530913\pi$
$947$	2.79266	+	8.59491i	0.0907491	+	0.279297i	−0.895373	+	0.445316i	$0.853091\pi$
$948$		0			0
$949$	−1.15537	+	1.59023i	−0.0375048	+	0.0516209i
$950$		0			0
$951$	−15.4280	+	47.4824i	−0.500286	+	1.53972i
$952$		0			0
$953$	10.3675	−	31.9080i	0.335837	−	1.03360i	−0.630471	−	0.776213i	$-0.717138\pi$
$953$	10.3675	−	31.9080i	0.335837	−	1.03360i	0.966308	−	0.257388i	$-0.0828619\pi$
$954$		0			0
$955$	−5.46718	+	1.77639i	−0.176914	+	0.0574827i
$956$		0			0
$957$			28.8314i			0.931986i
$958$		0			0
$959$	4.89076	−	3.55334i	0.157931	−	0.114743i
$960$		0			0
$961$	−37.2219	−	27.0433i	−1.20071	−	0.872364i
$962$		0			0
$963$	−34.3673	+	24.9693i	−1.10747	+	0.804623i
$964$		0			0
$965$	−2.02860	−	2.79213i	−0.0653029	−	0.0898818i
$966$		0			0
$967$	−0.174664	−	0.0567517i	−0.00561681	−	0.00182501i	0.306207	−	0.951965i	$-0.400940\pi$
$967$	−0.174664	−	0.0567517i	−0.00561681	−	0.00182501i	−0.311824	+	0.950140i	$0.600940\pi$
$968$		0			0
$969$	109.738	−	35.6561i	3.52530	−	1.14544i
$970$		0			0
$971$	15.1785	−	20.8915i	0.487102	−	0.670439i	−0.492748	−	0.870172i	$-0.664008\pi$
$971$	15.1785	−	20.8915i	0.487102	−	0.670439i	0.979850	+	0.199733i	$0.0640076\pi$
$972$		0			0
$973$	−4.32367	−	1.40485i	−0.138611	−	0.0450373i
$974$		0			0
$975$	−21.3514			−0.683793
$976$		0			0
$977$	34.4068	+	47.3569i	1.10077	+	1.51508i	0.834357	+	0.551224i	$0.185839\pi$
$977$	34.4068	+	47.3569i	1.10077	+	1.51508i	0.266415	+	0.963859i	$0.414161\pi$
$978$		0			0
$979$	7.77670	+	23.9342i	0.248544	+	0.764941i
$980$		0			0
$981$			125.876i			4.01890i
$982$		0			0
$983$	19.0639			0.608043			0.304021	−	0.952665i	$-0.401671\pi$
$983$	19.0639			0.608043			0.304021	+	0.952665i	$0.401671\pi$
$984$		0			0
$985$	14.1958			0.452316
$986$		0			0
$987$		−	16.7678i		−	0.533726i
$988$		0			0
$989$	−22.1667	−	68.2220i	−0.704859	−	2.16933i
$990$		0			0
$991$	−15.5516	−	21.4049i	−0.494011	−	0.679948i	0.487110	−	0.873341i	$-0.338051\pi$
$991$	−15.5516	−	21.4049i	−0.494011	−	0.679948i	−0.981122	+	0.193392i	$0.938051\pi$
$992$		0			0
$993$	−74.0858			−2.35104
$994$		0			0
$995$	8.75683	+	2.84527i	0.277610	+	0.0902010i
$996$		0			0
$997$	7.99547	−	11.0048i	0.253219	−	0.348526i	−0.663416	−	0.748250i	$-0.730894\pi$
$997$	7.99547	−	11.0048i	0.253219	−	0.348526i	0.916635	+	0.399724i	$0.130894\pi$
$998$		0			0
$999$	10.2729	−	3.33788i	0.325021	−	0.105606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.be.e.113.1		16
4.3	odd	2		164.2.k.a.113.4	yes	16
12.11	even	2		1476.2.bb.b.1261.2		16
41.4	even	10	inner	656.2.be.e.209.4		16
164.39	odd	20		6724.2.a.j.1.3		16
164.43	odd	20		6724.2.a.j.1.14		16
164.127	odd	10		164.2.k.a.45.1	✓	16
492.455	even	10		1476.2.bb.b.865.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.k.a.45.1	✓	16	164.127	odd	10
164.2.k.a.113.4	yes	16	4.3	odd	2
656.2.be.e.113.1		16	1.1	even	1	trivial
656.2.be.e.209.4		16	41.4	even	10	inner
1476.2.bb.b.865.2		16	492.455	even	10
1476.2.bb.b.1261.2		16	12.11	even	2
6724.2.a.j.1.3		16	164.39	odd	20
6724.2.a.j.1.14		16	164.43	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q-3.11423i q^{3} +(0.234613 + 0.722064i) q^{5} +(0.334979 + 0.461059i) q^{7} -6.69841 q^{9} +O(q^{10})\)	\(q-3.11423i q^{3} +(0.234613 + 0.722064i) q^{5} +(0.334979 + 0.461059i) q^{7} -6.69841 q^{9} +(-2.03752 - 0.662032i) q^{11} +(0.911006 - 1.25389i) q^{13} +(2.24867 - 0.730637i) q^{15} +(-5.57536 - 1.81154i) q^{17} +(-3.71496 - 5.11320i) q^{19} +(1.43584 - 1.04320i) q^{21} +(-6.10394 - 4.43478i) q^{23} +(3.57875 - 2.60012i) q^{25} +11.5177i q^{27} +(4.10984 - 1.33537i) q^{29} +(-2.71177 + 8.34596i) q^{31} +(-2.06172 + 6.34531i) q^{33} +(-0.254323 + 0.350046i) q^{35} +(-0.289804 - 0.891926i) q^{37} +(-3.90490 - 2.83708i) q^{39} +(-2.32565 + 5.96585i) q^{41} +(7.69171 + 5.58835i) q^{43} +(-1.57153 - 4.83668i) q^{45} +(5.55324 - 7.64338i) q^{47} +(2.06275 - 6.34851i) q^{49} +(-5.64156 + 17.3629i) q^{51} +(3.92714 - 1.27600i) q^{53} -1.62654i q^{55} +(-15.9237 + 11.5692i) q^{57} +(4.51093 + 3.27738i) q^{59} +(3.73050 - 2.71037i) q^{61} +(-2.24382 - 3.08836i) q^{63} +(1.11912 + 0.363625i) q^{65} +(-3.57383 + 1.16121i) q^{67} +(-13.8109 + 19.0091i) q^{69} +(-7.45067 - 2.42087i) q^{71} -1.26823 q^{73} +(-8.09735 - 11.1450i) q^{75} +(-0.377292 - 1.16119i) q^{77} -1.98372i q^{79} +15.7735 q^{81} +8.42095 q^{83} -4.45077i q^{85} +(-4.15864 - 12.7990i) q^{87} +(-6.90454 - 9.50329i) q^{89} +0.883285 q^{91} +(25.9912 + 8.44506i) q^{93} +(2.82048 - 3.88206i) q^{95} +(2.75953 - 0.896627i) q^{97} +(13.6482 + 4.43456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{5} - 30 q^{9}+O(q^{10}) \) 16 * q + 4 * q^5 - 30 * q^9	\( 16 q + 4 q^{5} - 30 q^{9} + 5 q^{11} + 10 q^{15} + 5 q^{17} - 15 q^{19} + 19 q^{21} - 12 q^{23} - 2 q^{25} + 20 q^{29} - 3 q^{31} - 25 q^{33} - 5 q^{35} + 2 q^{37} + 28 q^{39} - 4 q^{41} + 22 q^{43} - 48 q^{45} - 15 q^{47} - 28 q^{49} - 17 q^{51} + 25 q^{53} - 8 q^{57} - 8 q^{59} - 46 q^{61} + 40 q^{63} - 10 q^{65} + 45 q^{67} + 10 q^{69} - 15 q^{71} + 34 q^{73} - 135 q^{75} + 23 q^{77} + 108 q^{81} - 12 q^{83} - 14 q^{87} + 60 q^{93} + 30 q^{95} - 40 q^{97} - 70 q^{99}+O(q^{100}) \) 16 * q + 4 * q^5 - 30 * q^9 + 5 * q^11 + 10 * q^15 + 5 * q^17 - 15 * q^19 + 19 * q^21 - 12 * q^23 - 2 * q^25 + 20 * q^29 - 3 * q^31 - 25 * q^33 - 5 * q^35 + 2 * q^37 + 28 * q^39 - 4 * q^41 + 22 * q^43 - 48 * q^45 - 15 * q^47 - 28 * q^49 - 17 * q^51 + 25 * q^53 - 8 * q^57 - 8 * q^59 - 46 * q^61 + 40 * q^63 - 10 * q^65 + 45 * q^67 + 10 * q^69 - 15 * q^71 + 34 * q^73 - 135 * q^75 + 23 * q^77 + 108 * q^81 - 12 * q^83 - 14 * q^87 + 60 * q^93 + 30 * q^95 - 40 * q^97 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more