LMFDB - Embedded newform 656.2.bs.d.497.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(33,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

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

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

chi := DirichletCharacter("656.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.bs (of order $20$, degree $8$, 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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			497.2
Character	$\chi$	$=$	656.497
Dual form			656.2.bs.d.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.983583 + 0.983583i) q^{3} +(1.02071 + 0.331648i) q^{5} +(-0.625712 - 3.95059i) q^{7} -1.06513i q^{9} +O(q^{10})$	\(q+(0.983583 + 0.983583i) q^{3} +(1.02071 + 0.331648i) q^{5} +(-0.625712 - 3.95059i) q^{7} -1.06513i q^{9} +(1.14123 - 2.23980i) q^{11} +(4.25204 + 0.673457i) q^{13} +(0.677748 + 1.33015i) q^{15} +(-4.26144 - 2.17131i) q^{17} +(-0.967006 + 0.153159i) q^{19} +(3.27029 - 4.50117i) q^{21} +(1.78427 - 1.29635i) q^{23} +(-3.11323 - 2.26189i) q^{25} +(3.99839 - 3.99839i) q^{27} +(1.83197 - 0.933434i) q^{29} +(2.02631 + 6.23635i) q^{31} +(3.32552 - 1.08053i) q^{33} +(0.671536 - 4.23991i) q^{35} +(-3.34992 + 10.3100i) q^{37} +(3.51983 + 4.84464i) q^{39} +(6.18056 + 1.67354i) q^{41} +(1.18522 + 1.63132i) q^{43} +(0.353247 - 1.08718i) q^{45} +(-1.55707 + 9.83098i) q^{47} +(-8.55823 + 2.78074i) q^{49} +(-2.05581 - 6.32714i) q^{51} +(6.91813 - 3.52496i) q^{53} +(1.90769 - 1.90769i) q^{55} +(-1.10177 - 0.800486i) q^{57} +(-7.77045 + 5.64556i) q^{59} +(-0.263416 + 0.362561i) q^{61} +(-4.20788 + 0.666462i) q^{63} +(4.11674 + 2.09758i) q^{65} +(1.59206 + 3.12459i) q^{67} +(3.03004 + 0.479912i) q^{69} +(6.39610 - 12.5531i) q^{71} -8.75882i q^{73} +(-0.837360 - 5.28689i) q^{75} +(-9.56259 - 3.10707i) q^{77} +(1.93225 + 1.93225i) q^{79} +4.67012 q^{81} +2.79623 q^{83} +(-3.62957 - 3.62957i) q^{85} +(2.72000 + 0.883783i) q^{87} +(1.73754 + 10.9704i) q^{89} -17.2194i q^{91} +(-4.14092 + 8.12702i) q^{93} +(-1.03782 - 0.164375i) q^{95} +(1.70702 + 3.35021i) q^{97} +(-2.38567 - 1.21556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{11}{20}\right)$	$1$	$1$

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
$3$	0.983583	+	0.983583i	0.567872	+	0.567872i	0.931532	−	0.363660i	$-0.118473\pi$
$3$	0.983583	+	0.983583i	0.567872	+	0.567872i	−0.363660	+	0.931532i	$0.618473\pi$
$4$		0			0
$5$	1.02071	+	0.331648i	0.456474	+	0.148318i	0.528224	−	0.849105i	$-0.322858\pi$
$5$	1.02071	+	0.331648i	0.456474	+	0.148318i	−0.0717495	+	0.997423i	$0.522858\pi$
$6$		0			0
$7$	−0.625712	−	3.95059i	−0.236497	−	1.49318i	−0.764878	−	0.644175i	$-0.777201\pi$
$7$	−0.625712	−	3.95059i	−0.236497	−	1.49318i	0.528382	−	0.849007i	$-0.322799\pi$
$8$		0			0
$9$		−	1.06513i		−	0.355042i
$10$		0			0
$11$	1.14123	−	2.23980i	0.344095	−	0.675324i	−0.652499	−	0.757789i	$-0.726279\pi$
$11$	1.14123	−	2.23980i	0.344095	−	0.675324i	0.996594	+	0.0824655i	$0.0262794\pi$
$12$		0			0
$13$	4.25204	+	0.673457i	1.17930	+	0.186783i	0.715150	−	0.698971i	$-0.246359\pi$
$13$	4.25204	+	0.673457i	1.17930	+	0.186783i	0.464154	+	0.885755i	$0.346359\pi$
$14$		0			0
$15$	0.677748	+	1.33015i	0.174994	+	0.343444i
$16$		0			0
$17$	−4.26144	−	2.17131i	−1.03355	−	0.526620i	−0.146944	−	0.989145i	$-0.546944\pi$
$17$	−4.26144	−	2.17131i	−1.03355	−	0.526620i	−0.886606	+	0.462525i	$0.846944\pi$
$18$		0			0
$19$	−0.967006	+	0.153159i	−0.221846	+	0.0351370i	−0.266368	−	0.963871i	$-0.585824\pi$
$19$	−0.967006	+	0.153159i	−0.221846	+	0.0351370i	0.0445217	+	0.999008i	$0.485824\pi$
$20$		0			0
$21$	3.27029	−	4.50117i	0.713636	−	0.982236i
$22$		0			0
$23$	1.78427	−	1.29635i	0.372046	−	0.270307i	−0.386013	−	0.922493i	$-0.626148\pi$
$23$	1.78427	−	1.29635i	0.372046	−	0.270307i	0.758059	+	0.652186i	$0.226148\pi$
$24$		0			0
$25$	−3.11323	−	2.26189i	−0.622646	−	0.452379i
$26$		0			0
$27$	3.99839	−	3.99839i	0.769491	−	0.769491i
$28$		0			0
$29$	1.83197	−	0.933434i	0.340188	−	0.173334i	−0.275547	−	0.961287i	$-0.588859\pi$
$29$	1.83197	−	0.933434i	0.340188	−	0.173334i	0.615735	+	0.787953i	$0.288859\pi$
$30$		0			0
$31$	2.02631	+	6.23635i	0.363936	+	1.12008i	0.950644	+	0.310283i	$0.100424\pi$
$31$	2.02631	+	6.23635i	0.363936	+	1.12008i	−0.586708	+	0.809799i	$0.699576\pi$
$32$		0			0
$33$	3.32552	−	1.08053i	0.578900	−	0.188096i
$34$		0			0
$35$	0.671536	−	4.23991i	0.113510	−	0.716676i
$36$		0			0
$37$	−3.34992	+	10.3100i	−0.550724	+	1.69495i	0.156252	+	0.987717i	$0.450059\pi$
$37$	−3.34992	+	10.3100i	−0.550724	+	1.69495i	−0.706976	+	0.707237i	$0.749941\pi$
$38$		0			0
$39$	3.51983	+	4.84464i	0.563624	+	0.775763i
$40$		0			0
$41$	6.18056	+	1.67354i	0.965241	+	0.261363i
$41$	6.18056	+	1.67354i	0.965241	+	0.261363i
$42$		0			0
$43$	1.18522	+	1.63132i	0.180745	+	0.248773i	0.889770	−	0.456410i	$-0.150865\pi$
$43$	1.18522	+	1.63132i	0.180745	+	0.248773i	−0.709025	+	0.705183i	$0.750865\pi$
$44$		0			0
$45$	0.353247	−	1.08718i	0.0526590	−	0.162068i
$46$		0			0
$47$	−1.55707	+	9.83098i	−0.227123	+	1.43400i	0.565735	+	0.824587i	$0.308593\pi$
$47$	−1.55707	+	9.83098i	−0.227123	+	1.43400i	−0.792857	+	0.609408i	$0.791407\pi$
$48$		0			0
$49$	−8.55823	+	2.78074i	−1.22260	+	0.397248i
$50$		0			0
$51$	−2.05581	−	6.32714i	−0.287871	−	0.885977i
$52$		0			0
$53$	6.91813	−	3.52496i	0.950278	−	0.484191i	0.0910855	−	0.995843i	$-0.470966\pi$
$53$	6.91813	−	3.52496i	0.950278	−	0.484191i	0.859193	+	0.511652i	$0.170966\pi$
$54$		0			0
$55$	1.90769	−	1.90769i	0.257233	−	0.257233i
$56$		0			0
$57$	−1.10177	−	0.800486i	−0.145934	−	0.106027i
$58$		0			0
$59$	−7.77045	+	5.64556i	−1.01163	+	0.734989i	−0.964549	−	0.263902i	$-0.914990\pi$
$59$	−7.77045	+	5.64556i	−1.01163	+	0.734989i	−0.0470763	+	0.998891i	$0.514990\pi$
$60$		0			0
$61$	−0.263416	+	0.362561i	−0.0337269	+	0.0464211i	−0.825547	−	0.564333i	$-0.809134\pi$
$61$	−0.263416	+	0.362561i	−0.0337269	+	0.0464211i	0.791821	+	0.610754i	$0.209134\pi$
$62$		0			0
$63$	−4.20788	+	0.666462i	−0.530143	+	0.0839663i
$64$		0			0
$65$	4.11674	+	2.09758i	0.510618	+	0.260173i
$66$		0			0
$67$	1.59206	+	3.12459i	0.194501	+	0.381729i	0.967574	−	0.252587i	$-0.0812816\pi$
$67$	1.59206	+	3.12459i	0.194501	+	0.381729i	−0.773073	+	0.634317i	$0.781282\pi$
$68$		0			0
$69$	3.03004	+	0.479912i	0.364775	+	0.0577746i
$70$		0			0
$71$	6.39610	−	12.5531i	0.759078	−	1.48977i	−0.109374	−	0.994001i	$-0.534885\pi$
$71$	6.39610	−	12.5531i	0.759078	−	1.48977i	0.868452	−	0.495773i	$-0.165115\pi$
$72$		0			0
$73$		−	8.75882i		−	1.02514i	−0.858645	−	0.512571i	$-0.828693\pi$
$73$		−	8.75882i		−	1.02514i	0.858645	−	0.512571i	$-0.171307\pi$
$74$		0			0
$75$	−0.837360	−	5.28689i	−0.0966901	−	0.610477i
$76$		0			0
$77$	−9.56259	−	3.10707i	−1.08976	−	0.354084i
$78$		0			0
$79$	1.93225	+	1.93225i	0.217395	+	0.217395i	0.807400	−	0.590005i	$-0.200874\pi$
$79$	1.93225	+	1.93225i	0.217395	+	0.217395i	−0.590005	+	0.807400i	$0.700874\pi$
$80$		0			0
$81$	4.67012			0.518903
$82$		0			0
$83$	2.79623			0.306926			0.153463	−	0.988154i	$-0.450957\pi$
$83$	2.79623			0.306926			0.153463	+	0.988154i	$0.450957\pi$
$84$		0			0
$85$	−3.62957	−	3.62957i	−0.393682	−	0.393682i
$86$		0			0
$87$	2.72000	+	0.883783i	0.291615	+	0.0947515i
$88$		0			0
$89$	1.73754	+	10.9704i	0.184179	+	1.16286i	0.890505	+	0.454974i	$0.150351\pi$
$89$	1.73754	+	10.9704i	0.184179	+	1.16286i	−0.706326	+	0.707887i	$0.749649\pi$
$90$		0			0
$91$		−	17.2194i		−	1.80509i
$92$		0			0
$93$	−4.14092	+	8.12702i	−0.429394	+	0.842732i
$94$		0			0
$95$	−1.03782	−	0.164375i	−0.106479	−	0.0168645i
$96$		0			0
$97$	1.70702	+	3.35021i	0.173321	+	0.340162i	0.961283	−	0.275561i	$-0.0888637\pi$
$97$	1.70702	+	3.35021i	0.173321	+	0.340162i	−0.787962	+	0.615724i	$0.788864\pi$
$98$		0			0
$99$	−2.38567	−	1.21556i	−0.239769	−	0.122168i
$100$		0			0
$101$	−1.80537	+	0.285942i	−0.179641	+	0.0284523i	−0.245607	−	0.969370i	$-0.578987\pi$
$101$	−1.80537	+	0.285942i	−0.179641	+	0.0284523i	0.0659658	+	0.997822i	$0.478987\pi$
$102$		0			0
$103$	−6.53693	+	8.99731i	−0.644103	+	0.886531i	−0.998826	−	0.0484399i	$-0.984575\pi$
$103$	−6.53693	+	8.99731i	−0.644103	+	0.886531i	0.354723	+	0.934971i	$0.384575\pi$
$104$		0			0
$105$	4.83082	−	3.50979i	0.471440	−	0.342521i
$106$		0			0
$107$	−10.4582	−	7.59832i	−1.01103	−	0.734557i	−0.0466060	−	0.998913i	$-0.514841\pi$
$107$	−10.4582	−	7.59832i	−1.01103	−	0.734557i	−0.964425	+	0.264356i	$0.914841\pi$
$108$		0			0
$109$	−4.71687	+	4.71687i	−0.451794	+	0.451794i	−0.895950	−	0.444156i	$-0.853504\pi$
$109$	−4.71687	+	4.71687i	−0.451794	+	0.451794i	0.444156	+	0.895950i	$0.353504\pi$
$110$		0			0
$111$	−13.4357	+	6.84582i	−1.27526	+	0.649777i
$112$		0			0
$113$	−4.03978	−	12.4332i	−0.380031	−	1.16961i	−0.940021	−	0.341115i	$-0.889195\pi$
$113$	−4.03978	−	12.4332i	−0.380031	−	1.16961i	0.559991	−	0.828499i	$-0.310805\pi$
$114$		0			0
$115$	2.25115	−	0.731443i	0.209921	−	0.0682074i
$116$		0			0
$117$	0.717317	−	4.52896i	0.0663160	−	0.418703i
$118$		0			0
$119$	−5.91152	+	18.1938i	−0.541908	+	1.66782i
$120$		0			0
$121$	2.75136	+	3.78693i	0.250124	+	0.344266i
$122$		0			0
$123$	4.43303	+	7.72516i	0.399713	+	0.696554i
$124$		0			0
$125$	−5.58171	−	7.68256i	−0.499243	−	0.687149i
$126$		0			0
$127$	−2.84583	+	8.75856i	−0.252526	+	0.777196i	0.741781	+	0.670643i	$0.233982\pi$
$127$	−2.84583	+	8.75856i	−0.252526	+	0.777196i	−0.994307	+	0.106554i	$0.966018\pi$
$128$		0			0
$129$	−0.438772	+	2.77030i	−0.0386318	+	0.243911i
$130$		0			0
$131$	−0.179705	+	0.0583895i	−0.0157009	+	0.00510152i	−0.316857	−	0.948473i	$-0.602627\pi$
$131$	−0.179705	+	0.0583895i	−0.0157009	+	0.00510152i	0.301156	+	0.953575i	$0.402627\pi$
$132$		0			0
$133$	1.21013	+	3.72441i	0.104932	+	0.322947i
$134$		0			0
$135$	5.40725	−	2.75513i	0.465382	−	0.237124i
$136$		0			0
$137$	−4.54556	+	4.54556i	−0.388353	+	0.388353i	−0.874100	−	0.485746i	$-0.838548\pi$
$137$	−4.54556	+	4.54556i	−0.388353	+	0.388353i	0.485746	+	0.874100i	$0.338548\pi$
$138$		0			0
$139$	−5.82631	−	4.23306i	−0.494181	−	0.359043i	0.312609	−	0.949882i	$-0.398797\pi$
$139$	−5.82631	−	4.23306i	−0.494181	−	0.359043i	−0.806790	+	0.590838i	$0.798797\pi$
$140$		0			0
$141$	−11.2011	+	8.13807i	−0.943303	+	0.685349i
$142$		0			0
$143$	6.36097	−	8.75513i	0.531931	−	0.732141i
$144$		0			0
$145$	2.17948	−	0.345195i	0.180996	−	0.0286669i
$146$		0			0
$147$	−11.1528	−	5.68264i	−0.919869	−	0.468697i
$148$		0			0
$149$	−2.20761	−	4.33268i	−0.180855	−	0.354947i	0.782725	−	0.622367i	$-0.213829\pi$
$149$	−2.20761	−	4.33268i	−0.180855	−	0.354947i	−0.963580	+	0.267420i	$0.913829\pi$
$150$		0			0
$151$	9.40032	+	1.48886i	0.764987	+	0.121162i	0.526721	−	0.850038i	$-0.323421\pi$
$151$	9.40032	+	1.48886i	0.764987	+	0.121162i	0.238266	+	0.971200i	$0.423421\pi$
$152$		0			0
$153$	−2.31272	+	4.53897i	−0.186972	+	0.366954i
$154$		0			0
$155$			7.03751i			0.565266i
$156$		0			0
$157$	1.23051	+	7.76915i	0.0982056	+	0.620046i	0.986874	+	0.161495i	$0.0516314\pi$
$157$	1.23051	+	7.76915i	0.0982056	+	0.620046i	−0.888668	+	0.458551i	$0.848369\pi$
$158$		0			0
$159$	10.2717	+	3.33746i	0.814595	+	0.264678i
$160$		0			0
$161$	−6.23777	−	6.23777i	−0.491605	−	0.491605i
$162$		0			0
$163$	14.6310			1.14599			0.572994	−	0.819560i	$-0.305782\pi$
$163$	14.6310			1.14599			0.572994	+	0.819560i	$0.305782\pi$
$164$		0			0
$165$	3.75274			0.292151
$166$		0			0
$167$	−0.134117	−	0.134117i	−0.0103783	−	0.0103783i	0.701899	−	0.712277i	$-0.252336\pi$
$167$	−0.134117	−	0.134117i	−0.0103783	−	0.0103783i	−0.712277	+	0.701899i	$0.752336\pi$
$168$		0			0
$169$	5.26255	+	1.70991i	0.404812	+	0.131531i
$170$		0			0
$171$	0.163133	+	1.02998i	0.0124751	+	0.0787648i
$172$		0			0
$173$		−	5.31858i		−	0.404364i	−0.979348	−	0.202182i	$-0.935197\pi$
$173$		−	5.31858i		−	0.404364i	0.979348	−	0.202182i	$-0.0648033\pi$
$174$		0			0
$175$	−6.98783	+	13.7144i	−0.528230	+	1.03671i
$176$		0			0
$177$	−13.1958	−	2.09000i	−0.991854	−	0.157094i
$178$		0			0
$179$	−7.56349	−	14.8442i	−0.565322	−	1.10951i	−0.979899	−	0.199492i	$-0.936071\pi$
$179$	−7.56349	−	14.8442i	−0.565322	−	1.10951i	0.414578	−	0.910014i	$-0.363929\pi$
$180$		0			0
$181$	9.39816	+	4.78860i	0.698560	+	0.355934i	0.766934	−	0.641726i	$-0.221781\pi$
$181$	9.39816	+	4.78860i	0.698560	+	0.355934i	−0.0683744	+	0.997660i	$0.521781\pi$
$182$		0			0
$183$	−0.615700	+	0.0975173i	−0.0455138	+	0.00720868i
$184$		0			0
$185$	−6.83859	+	9.41251i	−0.502783	+	0.692021i
$186$		0			0
$187$	−9.72658	+	7.06678i	−0.711278	+	0.516774i
$188$		0			0
$189$	−18.2978	−	13.2942i	−1.33097	−	0.967007i
$190$		0			0
$191$	−11.1396	+	11.1396i	−0.806032	+	0.806032i	−0.984031	−	0.177999i	$-0.943038\pi$
$191$	−11.1396	+	11.1396i	−0.806032	+	0.806032i	0.177999	+	0.984031i	$0.443038\pi$
$192$		0			0
$193$	−20.8262	+	10.6115i	−1.49910	+	0.763831i	−0.995006	−	0.0998160i	$-0.968175\pi$
$193$	−20.8262	+	10.6115i	−1.49910	+	0.763831i	−0.504097	+	0.863647i	$0.668175\pi$
$194$		0			0
$195$	1.98601	+	6.11230i	0.142221	+	0.437711i
$196$		0			0
$197$	11.2628	−	3.65951i	0.802442	−	0.260729i	0.121048	−	0.992647i	$-0.461374\pi$
$197$	11.2628	−	3.65951i	0.802442	−	0.260729i	0.681393	+	0.731918i	$0.261374\pi$
$198$		0			0
$199$	−1.32526	+	8.36737i	−0.0939452	+	0.593147i	0.895138	+	0.445789i	$0.147077\pi$
$199$	−1.32526	+	8.36737i	−0.0939452	+	0.593147i	−0.989083	+	0.147358i	$0.952923\pi$
$200$		0			0
$201$	−1.50737	+	4.63921i	−0.106322	+	0.327225i
$202$		0			0
$203$	−4.83390	−	6.65329i	−0.339273	−	0.466969i
$204$		0			0
$205$	5.75351	+	3.75796i	0.401843	+	0.262468i
$206$		0			0
$207$	−1.38078	−	1.90047i	−0.0959705	−	0.132092i
$208$		0			0
$209$	−0.760535	+	2.34068i	−0.0526073	+	0.161909i
$210$		0			0
$211$	1.50316	−	9.49061i	0.103482	−	0.653360i	−0.880358	−	0.474310i	$-0.842698\pi$
$211$	1.50316	−	9.49061i	0.103482	−	0.653360i	0.983840	−	0.179050i	$-0.0573025\pi$
$212$		0			0
$213$	18.6381	−	6.05588i	1.27706	−	0.414942i
$214$		0			0
$215$	0.668741	+	2.05817i	0.0456078	+	0.140366i
$216$		0			0
$217$	23.3693	−	11.9073i	1.58641	−	0.808319i
$218$		0			0
$219$	8.61503	−	8.61503i	0.582150	−	0.582150i
$220$		0			0
$221$	−16.6575	−	12.1024i	−1.12051	−	0.814095i
$222$		0			0
$223$	4.32492	−	3.14224i	0.289618	−	0.210420i	−0.433484	−	0.901161i	$-0.642716\pi$
$223$	4.32492	−	3.14224i	0.289618	−	0.210420i	0.723102	+	0.690742i	$0.242716\pi$
$224$		0			0
$225$	−2.40921	+	3.31599i	−0.160614	+	0.221066i
$226$		0			0
$227$	−6.85453	+	1.08565i	−0.454951	+	0.0720571i	−0.379704	−	0.925108i	$-0.623974\pi$
$227$	−6.85453	+	1.08565i	−0.454951	+	0.0720571i	−0.0752464	+	0.997165i	$0.523974\pi$
$228$		0			0
$229$	15.9124	+	8.10777i	1.05152	+	0.535777i	0.892289	−	0.451465i	$-0.149098\pi$
$229$	15.9124	+	8.10777i	1.05152	+	0.535777i	0.159232	+	0.987241i	$0.449098\pi$
$230$		0			0
$231$	−6.34954	−	12.4617i	−0.417769	−	0.819918i
$232$		0			0
$233$	−4.30559	−	0.681939i	−0.282069	−	0.0446753i	0.0137971	−	0.999905i	$-0.495608\pi$
$233$	−4.30559	−	0.681939i	−0.282069	−	0.0446753i	−0.295866	+	0.955230i	$0.595608\pi$
$234$		0			0
$235$	−4.84974	+	9.51815i	−0.316362	+	0.620896i
$236$		0			0
$237$			3.80105i			0.246905i
$238$		0			0
$239$	−1.73930	−	10.9815i	−0.112506	−	0.710334i	−0.977874	−	0.209197i	$-0.932915\pi$
$239$	−1.73930	−	10.9815i	−0.112506	−	0.710334i	0.865368	−	0.501138i	$-0.167085\pi$
$240$		0			0
$241$	18.4604	+	5.99815i	1.18914	+	0.386375i	0.835755	−	0.549103i	$-0.185030\pi$
$241$	18.4604	+	5.99815i	1.18914	+	0.386375i	0.353385	+	0.935478i	$0.385030\pi$
$242$		0			0
$243$	−7.40172	−	7.40172i	−0.474821	−	0.474821i
$244$		0			0
$245$	−9.65767			−0.617006
$246$		0			0
$247$	−4.21489			−0.268187
$248$		0			0
$249$	2.75033	+	2.75033i	0.174295	+	0.174295i
$250$		0			0
$251$	2.21352	+	0.719217i	0.139716	+	0.0453966i	0.378040	−	0.925789i	$-0.376598\pi$
$251$	2.21352	+	0.719217i	0.139716	+	0.0453966i	−0.238324	+	0.971186i	$0.576598\pi$
$252$		0			0
$253$	−0.867287	−	5.47584i	−0.0545259	−	0.344263i
$254$		0			0
$255$		−	7.13997i		−	0.447122i
$256$		0			0
$257$	−8.86149	+	17.3916i	−0.552764	+	1.08486i	0.430485	+	0.902597i	$0.358342\pi$
$257$	−8.86149	+	17.3916i	−0.552764	+	1.08486i	−0.983250	+	0.182263i	$0.941658\pi$
$258$		0			0
$259$	42.8267	+	6.78308i	2.66112	+	0.421480i
$260$		0			0
$261$	−0.994226	−	1.95128i	−0.0615410	−	0.120781i
$262$		0			0
$263$	2.91538	+	1.48546i	0.179770	+	0.0915973i	0.541559	−	0.840662i	$-0.317834\pi$
$263$	2.91538	+	1.48546i	0.179770	+	0.0915973i	−0.361790	+	0.932260i	$0.617834\pi$
$264$		0			0
$265$	8.23043	−	1.30357i	0.505592	−	0.0800778i
$266$		0			0
$267$	−9.08129	+	12.4993i	−0.555766	+	0.764946i
$268$		0			0
$269$	−9.01598	+	6.55050i	−0.549714	+	0.399391i	−0.827680	−	0.561200i	$-0.810340\pi$
$269$	−9.01598	+	6.55050i	−0.549714	+	0.399391i	0.277966	+	0.960591i	$0.410340\pi$
$270$		0			0
$271$	5.17280	+	3.75826i	0.314225	+	0.228298i	0.733707	−	0.679466i	$-0.237788\pi$
$271$	5.17280	+	3.75826i	0.314225	+	0.228298i	−0.419482	+	0.907764i	$0.637788\pi$
$272$		0			0
$273$	16.9368	−	16.9368i	1.02506	−	1.02506i
$274$		0			0
$275$	−8.61911	+	4.39165i	−0.519752	+	0.264827i
$276$		0			0
$277$	7.78542	+	23.9611i	0.467781	+	1.43968i	0.855452	+	0.517883i	$0.173280\pi$
$277$	7.78542	+	23.9611i	0.467781	+	1.43968i	−0.387671	+	0.921798i	$0.626720\pi$
$278$		0			0
$279$	6.64250	−	2.15828i	0.397676	−	0.129213i
$280$		0			0
$281$	−0.531501	+	3.35577i	−0.0317067	+	0.200188i	−0.998457	−	0.0555350i	$-0.982314\pi$
$281$	−0.531501	+	3.35577i	−0.0317067	+	0.200188i	0.966750	+	0.255723i	$0.0823136\pi$
$282$		0			0
$283$	−2.32829	+	7.16575i	−0.138403	+	0.425959i	−0.996104	−	0.0881892i	$-0.971892\pi$
$283$	−2.32829	+	7.16575i	−0.138403	+	0.425959i	0.857701	+	0.514149i	$0.171892\pi$
$284$		0			0
$285$	−0.859110	−	1.18246i	−0.0508893	−	0.0700431i
$286$		0			0
$287$	2.74422	−	25.4640i	0.161986	−	1.50309i
$288$		0			0
$289$	3.45290	+	4.75251i	0.203112	+	0.279559i
$290$		0			0
$291$	−1.61622	+	4.97421i	−0.0947443	+	0.291593i
$292$		0			0
$293$	−0.934720	+	5.90159i	−0.0546069	+	0.344775i	0.945225	+	0.326421i	$0.105843\pi$
$293$	−0.934720	+	5.90159i	−0.0546069	+	0.344775i	−0.999832	+	0.0183540i	$0.994157\pi$
$294$		0			0
$295$	−9.80369	+	3.18541i	−0.570793	+	0.185462i
$296$		0			0
$297$	−4.39249	−	13.5187i	−0.254878	−	0.784433i
$298$		0			0
$299$	8.45982	−	4.31049i	0.489244	−	0.249282i
$300$		0			0
$301$	5.70305	−	5.70305i	0.328718	−	0.328718i
$302$		0			0
$303$	−2.05698	−	1.49448i	−0.118170	−	0.0858558i
$304$		0			0
$305$	−0.389113	+	0.282707i	−0.0222805	+	0.0161878i
$306$		0			0
$307$	−0.432807	+	0.595708i	−0.0247016	+	0.0339988i	−0.821189	−	0.570656i	$-0.806689\pi$
$307$	−0.432807	+	0.595708i	−0.0247016	+	0.0339988i	0.796488	+	0.604655i	$0.206689\pi$
$308$		0			0
$309$	−15.2792	+	2.41999i	−0.869205	+	0.137668i
$310$		0			0
$311$	25.7148	+	13.1024i	1.45816	+	0.742967i	0.990051	−	0.140706i	$-0.0449373\pi$
$311$	25.7148	+	13.1024i	1.45816	+	0.742967i	0.468104	+	0.883673i	$0.344937\pi$
$312$		0			0
$313$	−7.45211	−	14.6256i	−0.421218	−	0.826687i	−0.999938	−	0.0111603i	$-0.996447\pi$
$313$	−7.45211	−	14.6256i	−0.421218	−	0.826687i	0.578720	−	0.815526i	$-0.303553\pi$
$314$		0			0
$315$	−4.51604	−	0.715271i	−0.254450	−	0.0403010i
$316$		0			0
$317$	15.3313	−	30.0894i	0.861091	−	1.68999i	0.147917	−	0.989000i	$-0.452743\pi$
$317$	15.3313	−	30.0894i	0.861091	−	1.68999i	0.713174	−	0.700987i	$-0.247257\pi$
$318$		0			0
$319$		−	5.16850i		−	0.289380i
$320$		0			0
$321$	−2.81292	−	17.7601i	−0.157002	−	0.991271i
$322$		0			0
$323$	4.45339	+	1.44699i	0.247793	+	0.0805129i
$324$		0			0
$325$	−11.7143	−	11.7143i	−0.649792	−	0.649792i
$326$		0			0
$327$	−9.27886			−0.513122
$328$		0			0
$329$	39.8124			2.19493
$330$		0			0
$331$	8.52119	+	8.52119i	0.468367	+	0.468367i	0.901385	−	0.433018i	$-0.142551\pi$
$331$	8.52119	+	8.52119i	0.468367	+	0.468367i	−0.433018	+	0.901385i	$0.642551\pi$
$332$		0			0
$333$	10.9815	+	3.56809i	0.601781	+	0.195530i
$334$		0			0
$335$	0.588761	+	3.71729i	0.0321675	+	0.203097i
$336$		0			0
$337$			3.80509i			0.207276i	0.994615	+	0.103638i	$0.0330484\pi$
$337$			3.80509i			0.207276i	−0.994615	+	0.103638i	$0.966952\pi$
$338$		0			0
$339$	8.25560	−	16.2025i	0.448383	−	0.880000i
$340$		0			0
$341$	16.2806	+	2.57860i	0.881646	+	0.139639i
$342$		0			0
$343$	3.62932	+	7.12295i	0.195965	+	0.384603i
$344$		0			0
$345$	2.93363	+	1.49476i	0.157941	+	0.0804751i
$346$		0			0
$347$	15.9515	−	2.52648i	0.856324	−	0.135628i	0.287190	−	0.957874i	$-0.407279\pi$
$347$	15.9515	−	2.52648i	0.856324	−	0.135628i	0.569134	+	0.822245i	$0.307279\pi$
$348$		0			0
$349$	−0.538696	+	0.741452i	−0.0288358	+	0.0396890i	−0.823191	−	0.567764i	$-0.807809\pi$
$349$	−0.538696	+	0.741452i	−0.0288358	+	0.0396890i	0.794356	+	0.607453i	$0.207809\pi$
$350$		0			0
$351$	19.6941	−	14.3086i	1.05119	−	0.763735i
$352$		0			0
$353$	−3.48494	−	2.53196i	−0.185485	−	0.134763i	0.491168	−	0.871065i	$-0.336570\pi$
$353$	−3.48494	−	2.53196i	−0.185485	−	0.134763i	−0.676653	+	0.736302i	$0.736570\pi$
$354$		0			0
$355$	10.6917	−	10.6917i	0.567459	−	0.567459i
$356$		0			0
$357$	−23.7096	+	12.0806i	−1.25484	+	0.639375i
$358$		0			0
$359$	−8.03083	−	24.7164i	−0.423851	−	1.30448i	−0.904090	−	0.427342i	$-0.859450\pi$
$359$	−8.03083	−	24.7164i	−0.423851	−	1.30448i	0.480239	−	0.877138i	$-0.340550\pi$
$360$		0			0
$361$	−17.1584	+	5.57511i	−0.903075	+	0.293427i
$362$		0			0
$363$	−1.01856	+	6.43096i	−0.0534607	+	0.337538i
$364$		0			0
$365$	2.90485	−	8.94020i	0.152047	−	0.467951i
$366$		0			0
$367$	−8.09990	−	11.1486i	−0.422811	−	0.581950i	0.543473	−	0.839427i	$-0.317109\pi$
$367$	−8.09990	−	11.1486i	−0.422811	−	0.581950i	−0.966285	+	0.257477i	$0.917109\pi$
$368$		0			0
$369$	1.78253	−	6.58308i	0.0927949	−	0.342701i
$370$		0			0
$371$	−18.2544	−	25.1251i	−0.947723	−	1.30443i
$372$		0			0
$373$	10.7077	−	32.9549i	0.554424	−	1.70634i	−0.143036	−	0.989717i	$-0.545687\pi$
$373$	10.7077	−	32.9549i	0.554424	−	1.70634i	0.697460	−	0.716624i	$-0.254313\pi$
$374$		0			0
$375$	2.06636	−	13.0465i	0.106707	−	0.673719i
$376$		0			0
$377$	8.41822	−	2.73525i	0.433561	−	0.140872i
$378$		0			0
$379$	2.94287	+	9.05722i	0.151165	+	0.465238i	0.997752	−	0.0670121i	$-0.0213466\pi$
$379$	2.94287	+	9.05722i	0.151165	+	0.465238i	−0.846587	+	0.532250i	$0.821347\pi$
$380$		0			0
$381$	−11.4139	+	5.81566i	−0.584751	+	0.297945i
$382$		0			0
$383$	16.7656	−	16.7656i	0.856684	−	0.856684i	−0.134262	−	0.990946i	$-0.542866\pi$
$383$	16.7656	−	16.7656i	0.856684	−	0.856684i	0.990946	+	0.134262i	$0.0428663\pi$
$384$		0			0
$385$	−8.73016	−	6.34283i	−0.444930	−	0.323261i
$386$		0			0
$387$	1.73756	−	1.26241i	0.0883251	−	0.0641720i
$388$		0			0
$389$	−6.45082	+	8.87880i	−0.327070	+	0.450173i	−0.940609	−	0.339491i	$-0.889745\pi$
$389$	−6.45082	+	8.87880i	−0.327070	+	0.450173i	0.613540	+	0.789664i	$0.289745\pi$
$390$		0			0
$391$	−10.4183	+	1.65010i	−0.526877	+	0.0834492i
$392$		0			0
$393$	−0.234185	−	0.119323i	−0.0118131	−	0.00601907i
$394$		0			0
$395$	1.33143	+	2.61308i	0.0669916	+	0.131479i
$396$		0			0
$397$	−25.3501	−	4.01506i	−1.27228	−	0.201510i	−0.516476	−	0.856302i	$-0.672756\pi$
$397$	−25.3501	−	4.01506i	−1.27228	−	0.201510i	−0.755809	+	0.654792i	$0.772756\pi$
$398$		0			0
$399$	−2.47300	+	4.85353i	−0.123805	+	0.242980i
$400$		0			0
$401$		−	26.7180i		−	1.33423i	−0.744953	−	0.667117i	$-0.767528\pi$
$401$		−	26.7180i		−	1.33423i	0.744953	−	0.667117i	$-0.232472\pi$
$402$		0			0
$403$	4.41605	+	27.8818i	0.219979	+	1.38889i
$404$		0			0
$405$	4.76683	+	1.54884i	0.236866	+	0.0769623i
$406$		0			0
$407$	19.2693	+	19.2693i	0.955142	+	0.955142i
$408$		0			0
$409$	35.3318			1.74704			0.873522	−	0.486785i	$-0.161831\pi$
$409$	35.3318			1.74704			0.873522	+	0.486785i	$0.161831\pi$
$410$		0			0
$411$	−8.94188			−0.441070
$412$		0			0
$413$	27.1653	+	27.1653i	1.33672	+	1.33672i
$414$		0			0
$415$	2.85414	+	0.927365i	0.140104	+	0.0455225i
$416$		0			0
$417$	−1.56709	−	9.89423i	−0.0767408	−	0.484522i
$418$		0			0
$419$			28.5341i			1.39398i	0.717080	+	0.696991i	$0.245478\pi$
$419$			28.5341i			1.39398i	−0.717080	+	0.696991i	$0.754522\pi$
$420$		0			0
$421$	4.65405	−	9.13410i	0.226825	−	0.445169i	−0.749344	−	0.662181i	$-0.769631\pi$
$421$	4.65405	−	9.13410i	0.226825	−	0.445169i	0.976169	+	0.217012i	$0.0696311\pi$
$422$		0			0
$423$	10.4712	+	1.65848i	0.509129	+	0.0806381i
$424$		0			0
$425$	8.35556	+	16.3987i	0.405304	+	0.795454i
$426$		0			0
$427$	1.59715	+	0.813788i	0.0772915	+	0.0393820i
$428$		0			0
$429$	14.8679	−	2.35485i	0.717831	−	0.113693i
$430$		0			0
$431$	−12.2049	+	16.7986i	−0.587891	+	0.809162i	−0.994533	−	0.104425i	$-0.966700\pi$
$431$	−12.2049	+	16.7986i	−0.587891	+	0.809162i	0.406642	+	0.913588i	$0.366700\pi$
$432$		0			0
$433$	−13.3108	+	9.67086i	−0.639676	+	0.464752i	−0.859739	−	0.510734i	$-0.829374\pi$
$433$	−13.3108	+	9.67086i	−0.639676	+	0.464752i	0.220063	+	0.975486i	$0.429374\pi$
$434$		0			0
$435$	2.48322	+	1.80417i	0.119061	+	0.0865032i
$436$		0			0
$437$	−1.52685	+	1.52685i	−0.0730392	+	0.0730392i
$438$		0			0
$439$	−20.4889	+	10.4396i	−0.977882	+	0.498256i	−0.868470	−	0.495741i	$-0.834897\pi$
$439$	−20.4889	+	10.4396i	−0.977882	+	0.498256i	−0.109411	+	0.993997i	$0.534897\pi$
$440$		0			0
$441$	2.96184	+	9.11560i	0.141040	+	0.434076i
$442$		0			0
$443$	−0.331688	+	0.107772i	−0.0157590	+	0.00512040i	−0.316886	−	0.948464i	$-0.602637\pi$
$443$	−0.331688	+	0.107772i	−0.0157590	+	0.00512040i	0.301127	+	0.953584i	$0.402637\pi$
$444$		0			0
$445$	−1.86479	+	11.7738i	−0.0883996	+	0.558133i
$446$		0			0
$447$	2.09018	−	6.43293i	0.0988623	−	0.304267i
$448$		0			0
$449$	−17.2577	−	23.7532i	−0.814440	−	1.12098i	−0.990623	−	0.136623i	$-0.956375\pi$
$449$	−17.2577	−	23.7532i	−0.814440	−	1.12098i	0.176183	−	0.984357i	$-0.443625\pi$
$450$		0			0
$451$	10.8018	−	11.9333i	0.508639	−	0.561917i
$452$		0			0
$453$	7.78157	+	10.7104i	0.365610	+	0.503219i
$454$		0			0
$455$	5.71079	−	17.5760i	0.267726	−	0.823976i
$456$		0			0
$457$	−1.33751	+	8.44470i	−0.0625660	+	0.395026i	0.936455	+	0.350788i	$0.114086\pi$
$457$	−1.33751	+	8.44470i	−0.0625660	+	0.395026i	−0.999021	+	0.0442385i	$0.985914\pi$
$458$		0			0
$459$	−25.7206	+	8.35714i	−1.20054	+	0.390078i
$460$		0			0
$461$	10.8222	+	33.3073i	0.504041	+	1.55128i	0.802378	+	0.596817i	$0.203568\pi$
$461$	10.8222	+	33.3073i	0.504041	+	1.55128i	−0.298337	+	0.954461i	$0.596432\pi$
$462$		0			0
$463$	4.11872	−	2.09859i	0.191413	−	0.0975298i	−0.355657	−	0.934616i	$-0.615743\pi$
$463$	4.11872	−	2.09859i	0.191413	−	0.0975298i	0.547070	+	0.837087i	$0.315743\pi$
$464$		0			0
$465$	−6.92198	+	6.92198i	−0.320999	+	0.320999i
$466$		0			0
$467$	−22.3850	−	16.2637i	−1.03585	−	0.752592i	−0.0663821	−	0.997794i	$-0.521146\pi$
$467$	−22.3850	−	16.2637i	−1.03585	−	0.752592i	−0.969472	+	0.245202i	$0.921146\pi$
$468$		0			0
$469$	11.3478	−	8.24465i	0.523992	−	0.380703i
$470$		0			0
$471$	−6.43130	+	8.85192i	−0.296338	+	0.407875i
$472$		0			0
$473$	5.00643	−	0.792941i	0.230196	−	0.0364595i
$474$		0			0
$475$	3.35694	+	1.71045i	0.154027	+	0.0784807i
$476$		0			0
$477$	−3.75453	−	7.36869i	−0.171908	−	0.337389i
$478$		0			0
$479$	−5.04854	−	0.799610i	−0.230674	−	0.0365351i	0.0400274	−	0.999199i	$-0.487255\pi$
$479$	−5.04854	−	0.799610i	−0.230674	−	0.0365351i	−0.270701	+	0.962663i	$0.587255\pi$
$480$		0			0
$481$	−21.1873	+	41.5825i	−0.966060	+	1.89600i
$482$		0			0
$483$		−	12.2707i		−	0.558338i
$484$		0			0
$485$	0.631275	+	3.98571i	0.0286647	+	0.180982i
$486$		0			0
$487$	−21.2814	−	6.91475i	−0.964353	−	0.313337i	−0.215819	−	0.976433i	$-0.569242\pi$
$487$	−21.2814	−	6.91475i	−0.964353	−	0.313337i	−0.748534	+	0.663096i	$0.769242\pi$
$488$		0			0
$489$	14.3908	+	14.3908i	0.650774	+	0.650774i
$490$		0			0
$491$	40.1125			1.81025			0.905125	−	0.425146i	$-0.139777\pi$
$491$	40.1125			1.81025			0.905125	+	0.425146i	$0.139777\pi$
$492$		0			0
$493$	−9.83359			−0.442883
$494$		0			0
$495$	−2.03193	−	2.03193i	−0.0913285	−	0.0913285i
$496$		0			0
$497$	−53.5941	−	17.4138i	−2.40402	−	0.781114i
$498$		0			0
$499$	4.96084	+	31.3215i	0.222078	+	1.40214i	0.806759	+	0.590880i	$0.201219\pi$
$499$	4.96084	+	31.3215i	0.222078	+	1.40214i	−0.584682	+	0.811263i	$0.698781\pi$
$500$		0			0
$501$		−	0.263831i		−	0.0117871i
$502$		0			0
$503$	−1.60627	+	3.15248i	−0.0716200	+	0.140562i	−0.924040	−	0.382295i	$-0.875134\pi$
$503$	−1.60627	+	3.15248i	−0.0716200	+	0.140562i	0.852420	+	0.522857i	$0.175134\pi$
$504$		0			0
$505$	−1.93759	−	0.306883i	−0.0862214	−	0.0136561i
$506$		0			0
$507$	3.49432	+	6.85799i	0.155188	+	0.304574i
$508$		0			0
$509$	−4.40168	−	2.24277i	−0.195101	−	0.0994090i	0.353711	−	0.935355i	$-0.384920\pi$
$509$	−4.40168	−	2.24277i	−0.195101	−	0.0994090i	−0.548812	+	0.835946i	$0.684920\pi$
$510$		0			0
$511$	−34.6025	+	5.48050i	−1.53072	+	0.242443i
$512$		0			0
$513$	−3.25408	+	4.47886i	−0.143671	+	0.197746i
$514$		0			0
$515$	−9.65623	+	7.01567i	−0.425505	+	0.309147i
$516$		0			0
$517$	20.2424	+	14.7070i	0.890260	+	0.646811i
$518$		0			0
$519$	5.23127	−	5.23127i	0.229627	−	0.229627i
$520$		0			0
$521$	−1.05069	+	0.535356i	−0.0460318	+	0.0234544i	−0.476855	−	0.878982i	$-0.658223\pi$
$521$	−1.05069	+	0.535356i	−0.0460318	+	0.0234544i	0.430823	+	0.902436i	$0.358223\pi$
$522$		0			0
$523$	−0.00907992	−	0.0279451i	−0.000397037	−	0.00122195i	0.950858	−	0.309628i	$-0.100204\pi$
$523$	−0.00907992	−	0.0279451i	−0.000397037	−	0.00122195i	−0.951255	+	0.308406i	$0.900204\pi$
$524$		0			0
$525$	−20.3624	+	6.61613i	−0.888686	+	0.288752i
$526$		0			0
$527$	4.90605	−	30.9756i	0.213711	−	1.34932i
$528$		0			0
$529$	−5.60429	+	17.2482i	−0.243665	+	0.749923i
$530$		0			0
$531$	6.01324	+	8.27651i	0.260952	+	0.359170i
$532$		0			0
$533$	25.1529	+	11.2783i	1.08949	+	0.488517i
$534$		0			0
$535$	−8.15478	−	11.2241i	−0.352562	−	0.485260i
$536$		0			0
$537$	7.16117	−	22.0398i	0.309027	−	0.951088i
$538$		0			0
$539$	−3.53865	+	22.3422i	−0.152420	+	0.962345i
$540$		0			0
$541$	33.9890	−	11.0437i	1.46130	−	0.474806i	0.532834	−	0.846220i	$-0.321127\pi$
$541$	33.9890	−	11.0437i	1.46130	−	0.474806i	0.928467	+	0.371414i	$0.121127\pi$
$542$		0			0
$543$	4.53389	+	13.9539i	0.194568	+	0.598818i
$544$		0			0
$545$	−6.37888	+	3.25020i	−0.273241	+	0.139223i
$546$		0			0
$547$	4.84258	−	4.84258i	0.207054	−	0.207054i	−0.595960	−	0.803014i	$-0.703228\pi$
$547$	4.84258	−	4.84258i	0.207054	−	0.207054i	0.803014	+	0.595960i	$0.203228\pi$
$548$		0			0
$549$	0.386173	+	0.280571i	0.0164815	+	0.0119745i
$550$		0			0
$551$	−1.62856	+	1.18322i	−0.0693790	+	0.0504068i
$552$		0			0
$553$	6.42448	−	8.84253i	0.273197	−	0.376023i
$554$		0			0
$555$	−15.9843	+	2.53167i	−0.678496	+	0.107463i
$556$		0			0
$557$	−21.5323	−	10.9713i	−0.912355	−	0.464868i	−0.0662005	−	0.997806i	$-0.521088\pi$
$557$	−21.5323	−	10.9713i	−0.912355	−	0.464868i	−0.846154	+	0.532938i	$0.821088\pi$
$558$		0			0
$559$	3.94098	+	7.73462i	0.166686	+	0.327139i
$560$		0			0
$561$	−16.5177	−	2.61614i	−0.697377	−	0.110454i
$562$		0			0
$563$	−3.35567	+	6.58588i	−0.141425	+	0.277562i	−0.950844	−	0.309669i	$-0.899782\pi$
$563$	−3.35567	+	6.58588i	−0.141425	+	0.277562i	0.809420	+	0.587231i	$0.199782\pi$
$564$		0			0
$565$		−	14.0304i		−	0.590264i
$566$		0			0
$567$	−2.92215	−	18.4497i	−0.122719	−	0.774816i
$568$		0			0
$569$	−3.63848	−	1.18221i	−0.152533	−	0.0495609i	0.231755	−	0.972774i	$-0.425553\pi$
$569$	−3.63848	−	1.18221i	−0.152533	−	0.0495609i	−0.384288	+	0.923213i	$0.625553\pi$
$570$		0			0
$571$	7.80695	+	7.80695i	0.326710	+	0.326710i	0.851334	−	0.524624i	$-0.175794\pi$
$571$	7.80695	+	7.80695i	0.326710	+	0.326710i	−0.524624	+	0.851334i	$0.675794\pi$
$572$		0			0
$573$	−21.9134			−0.915446
$574$		0			0
$575$	−8.48705			−0.353934
$576$		0			0
$577$	−7.23096	−	7.23096i	−0.301029	−	0.301029i	0.540388	−	0.841416i	$-0.318278\pi$
$577$	−7.23096	−	7.23096i	−0.301029	−	0.301029i	−0.841416	+	0.540388i	$0.818278\pi$
$578$		0			0
$579$	−30.9216	−	10.0470i	−1.28506	−	0.417540i
$580$		0			0
$581$	−1.74963	−	11.0468i	−0.0725871	−	0.458297i
$582$		0			0
$583$		−	19.5180i		−	0.808353i
$584$		0			0
$585$	2.23419	−	4.38485i	0.0923725	−	0.181291i
$586$		0			0
$587$	−11.6235	−	1.84098i	−0.479754	−	0.0759855i	−0.0881260	−	0.996109i	$-0.528088\pi$
$587$	−11.6235	−	1.84098i	−0.479754	−	0.0759855i	−0.391628	+	0.920124i	$0.628088\pi$
$588$		0			0
$589$	−2.91461	−	5.72024i	−0.120094	−	0.235698i
$590$		0			0
$591$	14.6773	+	7.47848i	0.603745	+	0.307623i
$592$		0			0
$593$	−26.9781	+	4.27291i	−1.10786	+	0.175467i	−0.683445	−	0.730002i	$-0.739519\pi$
$593$	−26.9781	+	4.27291i	−1.10786	+	0.175467i	−0.424412	+	0.905469i	$0.639519\pi$
$594$		0			0
$595$	−12.0679	+	16.6100i	−0.494734	+	0.680943i
$596$		0			0
$597$	−9.53351	+	6.92650i	−0.390181	+	0.283483i
$598$		0			0
$599$	−8.16465	−	5.93196i	−0.333598	−	0.242373i	0.408358	−	0.912822i	$-0.366102\pi$
$599$	−8.16465	−	5.93196i	−0.333598	−	0.242373i	−0.741956	+	0.670449i	$0.766102\pi$
$600$		0			0
$601$	−9.88133	+	9.88133i	−0.403068	+	0.403068i	−0.879313	−	0.476245i	$-0.841998\pi$
$601$	−9.88133	+	9.88133i	−0.403068	+	0.403068i	0.476245	+	0.879313i	$0.341998\pi$
$602$		0			0
$603$	3.32808	−	1.69574i	0.135530	−	0.0690560i
$604$		0			0
$605$	1.55241	+	4.77783i	0.0631145	+	0.194246i
$606$		0			0
$607$	−5.95620	+	1.93529i	−0.241755	+	0.0785509i	−0.427388	−	0.904068i	$-0.640566\pi$
$607$	−5.95620	+	1.93529i	−0.241755	+	0.0785509i	0.185634	+	0.982619i	$0.440566\pi$
$608$		0			0
$609$	1.78952	−	11.2986i	0.0725151	−	0.457843i
$610$		0			0
$611$	−13.2415	+	40.7531i	−0.535693	+	1.64869i
$612$		0			0
$613$	13.8469	+	19.0586i	0.559270	+	0.769769i	0.991233	−	0.132122i	$-0.0421790\pi$
$613$	13.8469	+	19.0586i	0.559270	+	0.769769i	−0.431963	+	0.901891i	$0.642179\pi$
$614$		0			0
$615$	1.96279	+	9.35533i	0.0791474	+	0.377243i
$616$		0			0
$617$	−19.5926	−	26.9669i	−0.788768	−	1.08565i	−0.994260	−	0.106988i	$-0.965879\pi$
$617$	−19.5926	−	26.9669i	−0.788768	−	1.08565i	0.205492	−	0.978659i	$-0.434121\pi$
$618$		0			0
$619$	13.3135	−	40.9747i	0.535115	−	1.64691i	−0.208286	−	0.978068i	$-0.566789\pi$
$619$	13.3135	−	40.9747i	0.535115	−	1.64691i	0.743401	−	0.668846i	$-0.233211\pi$
$620$		0			0
$621$	1.95090	−	12.3175i	0.0782870	−	0.494285i
$622$		0			0
$623$	42.2523	−	13.7286i	1.69280	−	0.550025i
$624$		0			0
$625$	2.79636	+	8.60631i	0.111854	+	0.344252i
$626$		0			0
$627$	−3.05031	+	1.55421i	−0.121818	+	0.0620692i
$628$		0			0
$629$	36.6617	−	36.6617i	1.46180	−	1.46180i
$630$		0			0
$631$	−5.88538	−	4.27598i	−0.234293	−	0.170224i	0.464444	−	0.885603i	$-0.346254\pi$
$631$	−5.88538	−	4.27598i	−0.234293	−	0.170224i	−0.698737	+	0.715379i	$0.746254\pi$
$632$		0			0
$633$	10.8133	−	7.85632i	0.429790	−	0.312261i
$634$		0			0
$635$	−5.80952	+	7.99611i	−0.230544	+	0.317316i
$636$		0			0
$637$	−38.2626	+	6.06020i	−1.51602	+	0.240114i
$638$		0			0
$639$	−13.3706	−	6.81266i	−0.528933	−	0.269505i
$640$		0			0
$641$	13.9831	+	27.4433i	0.552297	+	1.08394i	0.983368	+	0.181626i	$0.0581361\pi$
$641$	13.9831	+	27.4433i	0.552297	+	1.08394i	−0.431070	+	0.902318i	$0.641864\pi$
$642$		0			0
$643$	−15.0094	−	2.37726i	−0.591914	−	0.0937500i	−0.146711	−	0.989179i	$-0.546869\pi$
$643$	−15.0094	−	2.37726i	−0.591914	−	0.0937500i	−0.445203	+	0.895429i	$0.646869\pi$
$644$		0			0
$645$	−1.36662	+	2.68215i	−0.0538107	+	0.105609i
$646$		0			0
$647$		−	5.82135i		−	0.228861i	−0.993431	−	0.114430i	$-0.963496\pi$
$647$		−	5.82135i		−	0.228861i	0.993431	−	0.114430i	$-0.0365043\pi$
$648$		0			0
$649$	3.77701	+	23.8471i	0.148261	+	0.936081i
$650$		0			0
$651$	34.6975	+	11.2739i	1.35990	+	0.441859i
$652$		0			0
$653$	−7.96838	−	7.96838i	−0.311827	−	0.311827i	0.533790	−	0.845617i	$-0.320767\pi$
$653$	−7.96838	−	7.96838i	−0.311827	−	0.311827i	−0.845617	+	0.533790i	$0.820767\pi$
$654$		0			0
$655$	−0.202791			−0.00792368
$656$		0			0
$657$	−9.32926			−0.363969
$658$		0			0
$659$	18.7955	+	18.7955i	0.732169	+	0.732169i	0.971049	−	0.238880i	$-0.0767802\pi$
$659$	18.7955	+	18.7955i	0.732169	+	0.732169i	−0.238880	+	0.971049i	$0.576780\pi$
$660$		0			0
$661$	2.86486	+	0.930849i	0.111430	+	0.0362058i	0.364201	−	0.931320i	$-0.381342\pi$
$661$	2.86486	+	0.930849i	0.111430	+	0.0362058i	−0.252771	+	0.967526i	$0.581342\pi$
$662$		0			0
$663$	−4.48034	−	28.2878i	−0.174002	−	1.09861i
$664$		0			0
$665$			4.20287i			0.162980i
$666$		0			0
$667$	2.05867	−	4.04037i	0.0797120	−	0.156444i
$668$		0			0
$669$	7.34458	+	1.16327i	0.283958	+	0.0449745i
$670$		0			0
$671$	0.511443	+	1.00376i	0.0197440	+	0.0387499i
$672$		0			0
$673$	5.27484	+	2.68766i	0.203330	+	0.103602i	0.552691	−	0.833387i	$-0.313601\pi$
$673$	5.27484	+	2.68766i	0.203330	+	0.103602i	−0.349361	+	0.936988i	$0.613601\pi$
$674$		0			0
$675$	−21.4919	+	3.40398i	−0.827222	+	0.131019i
$676$		0			0
$677$	−6.10855	+	8.40769i	−0.234770	+	0.323134i	−0.910105	−	0.414378i	$-0.863999\pi$
$677$	−6.10855	+	8.40769i	−0.234770	+	0.323134i	0.675335	+	0.737512i	$0.263999\pi$
$678$		0			0
$679$	12.1672	−	8.83999i	0.466934	−	0.339248i
$680$		0			0
$681$	−7.80983	−	5.67417i	−0.299273	−	0.217435i
$682$		0			0
$683$	−25.5356	+	25.5356i	−0.977093	+	0.977093i	−0.999743	−	0.0226507i	$-0.992789\pi$
$683$	−25.5356	+	25.5356i	−0.977093	+	0.977093i	0.0226507	+	0.999743i	$0.492789\pi$
$684$		0			0
$685$	−6.14721	+	3.13216i	−0.234873	+	0.119674i
$686$		0			0
$687$	7.67650	+	23.6258i	0.292877	+	0.901382i
$688$		0			0
$689$	31.7901	−	10.3292i	1.21110	−	0.393512i
$690$		0			0
$691$	−0.650080	+	4.10445i	−0.0247302	+	0.156140i	−0.996963	−	0.0778748i	$-0.975187\pi$
$691$	−0.650080	+	4.10445i	−0.0247302	+	0.156140i	0.972233	+	0.234015i	$0.0751866\pi$
$692$		0			0
$693$	−3.30943	+	10.1854i	−0.125715	+	0.386910i
$694$		0			0
$695$	−4.54307	−	6.25300i	−0.172328	−	0.237190i
$696$		0			0
$697$	−22.7043	−	20.5516i	−0.859986	−	0.778447i
$698$		0			0
$699$	−3.56417	−	4.90565i	−0.134809	−	0.185549i
$700$		0			0
$701$	−2.84581	+	8.75851i	−0.107485	+	0.330805i	−0.990306	−	0.138906i	$-0.955642\pi$
$701$	−2.84581	+	8.75851i	−0.107485	+	0.330805i	0.882821	+	0.469710i	$0.155642\pi$
$702$		0			0
$703$	1.66033	−	10.4829i	0.0626205	−	0.395370i
$704$		0			0
$705$	−14.1320	+	4.59177i	−0.532243	+	0.172936i
$706$		0			0
$707$	2.25928	+	6.95335i	0.0849689	+	0.261507i
$708$		0			0
$709$	−29.0044	+	14.7785i	−1.08928	+	0.555018i	−0.903941	−	0.427656i	$-0.859339\pi$
$709$	−29.0044	+	14.7785i	−1.08928	+	0.555018i	−0.185342	+	0.982674i	$0.559339\pi$
$710$		0			0
$711$	2.05809	−	2.05809i	0.0771843	−	0.0771843i
$712$		0			0
$713$	11.7000	+	8.50052i	0.438167	+	0.318347i
$714$		0			0
$715$	9.39631	−	6.82682i	0.351402	−	0.255309i
$716$		0			0
$717$	9.09048	−	12.5120i	0.339490	−	0.467268i
$718$		0			0
$719$	10.0466	−	1.59122i	0.374675	−	0.0593427i	0.0337427	−	0.999431i	$-0.489257\pi$
$719$	10.0466	−	1.59122i	0.374675	−	0.0593427i	0.340932	+	0.940088i	$0.389257\pi$
$720$		0			0
$721$	39.6349	+	20.1950i	1.47608	+	0.752101i
$722$		0			0
$723$	12.2577	+	24.0570i	0.455868	+	0.894691i
$724$		0			0
$725$	−7.81467	−	1.23772i	−0.290230	−	0.0459678i
$726$		0			0
$727$	−20.8419	+	40.9046i	−0.772985	+	1.51707i	0.0809673	+	0.996717i	$0.474199\pi$
$727$	−20.8419	+	40.9046i	−0.772985	+	1.51707i	−0.853952	+	0.520352i	$0.825801\pi$
$728$		0			0
$729$		−	28.5708i		−	1.05818i
$730$		0			0
$731$	−1.50865	−	9.52523i	−0.0557994	−	0.352304i
$732$		0			0
$733$	−35.9271	−	11.6734i	−1.32700	−	0.431167i	−0.442104	−	0.896964i	$-0.645768\pi$
$733$	−35.9271	−	11.6734i	−1.32700	−	0.431167i	−0.884892	+	0.465797i	$0.845768\pi$
$734$		0			0
$735$	−9.49913	−	9.49913i	−0.350381	−	0.350381i
$736$		0			0
$737$	8.81535			0.324718
$738$		0			0
$739$	37.9331			1.39539			0.697697	−	0.716393i	$-0.254208\pi$
$739$	37.9331			1.39539			0.697697	+	0.716393i	$0.254208\pi$
$740$		0			0
$741$	−4.14570	−	4.14570i	−0.152296	−	0.152296i
$742$		0			0
$743$	−18.8073	−	6.11086i	−0.689973	−	0.224186i	−0.0570164	−	0.998373i	$-0.518159\pi$
$743$	−18.8073	−	6.11086i	−0.689973	−	0.224186i	−0.632956	+	0.774188i	$0.718159\pi$
$744$		0			0
$745$	−0.816401	−	5.15455i	−0.0299106	−	0.188848i
$746$		0			0
$747$		−	2.97834i		−	0.108972i
$748$		0			0
$749$	−23.4740	+	46.0703i	−0.857721	+	1.68337i
$750$		0			0
$751$	−15.6451	−	2.47795i	−0.570899	−	0.0904216i	−0.135691	−	0.990751i	$-0.543325\pi$
$751$	−15.6451	−	2.47795i	−0.570899	−	0.0904216i	−0.435209	+	0.900330i	$0.643325\pi$
$752$		0			0
$753$	1.46977	+	2.88459i	0.0535615	+	0.105120i
$754$		0			0
$755$	9.10120	+	4.63729i	0.331226	+	0.168768i
$756$		0			0
$757$	22.6735	−	3.59113i	0.824083	−	0.130522i	0.269870	−	0.962897i	$-0.413019\pi$
$757$	22.6735	−	3.59113i	0.824083	−	0.130522i	0.554213	+	0.832375i	$0.313019\pi$
$758$		0			0
$759$	4.53289	−	6.23899i	0.164534	−	0.226461i
$760$		0			0
$761$	36.5322	−	26.5422i	1.32429	−	0.962155i	0.324424	−	0.945912i	$-0.394830\pi$
$761$	36.5322	−	26.5422i	1.32429	−	0.962155i	0.999868	−	0.0162427i	$-0.00517045\pi$
$762$		0			0
$763$	21.5858	+	15.6830i	0.781458	+	0.567762i
$764$		0			0
$765$	−3.86595	+	3.86595i	−0.139774	+	0.139774i
$766$		0			0
$767$	−36.8423	+	18.7721i	−1.33030	+	0.677820i
$768$		0			0
$769$	−6.93059	−	21.3302i	−0.249924	−	0.769186i	−0.994788	−	0.101969i	$-0.967486\pi$
$769$	−6.93059	−	21.3302i	−0.249924	−	0.769186i	0.744864	−	0.667216i	$-0.232514\pi$
$770$		0			0
$771$	−25.8221	+	8.39012i	−0.929962	+	0.302163i
$772$		0			0
$773$	1.69195	−	10.6826i	0.0608553	−	0.384225i	−0.938397	−	0.345559i	$-0.887689\pi$
$773$	1.69195	−	10.6826i	0.0608553	−	0.384225i	0.999252	−	0.0386657i	$-0.0123108\pi$
$774$		0			0
$775$	7.79759	−	23.9985i	0.280098	−	0.862052i
$776$		0			0
$777$	35.4519	+	48.7953i	1.27183	+	1.75052i
$778$		0			0
$779$	−6.23295	−	0.671716i	−0.223319	−	0.0240667i
$780$		0			0
$781$	−20.8169	−	28.6519i	−0.744885	−	1.02525i
$782$		0			0
$783$	3.59269	−	11.0572i	0.128392	−	0.395151i
$784$		0			0
$785$	−1.32063	+	8.33813i	−0.0471353	+	0.297601i
$786$		0			0
$787$	27.7465	−	9.01540i	0.989057	−	0.321364i	0.230573	−	0.973055i	$-0.425940\pi$
$787$	27.7465	−	9.01540i	0.989057	−	0.321364i	0.758485	+	0.651691i	$0.225940\pi$
$788$		0			0
$789$	1.40644	+	4.32859i	0.0500707	+	0.154102i
$790$		0			0
$791$	−46.5906	+	23.7391i	−1.65657	+	0.844065i
$792$		0			0
$793$	−1.36422	+	1.36422i	−0.0484449	+	0.0484449i
$794$		0			0
$795$	9.37749	+	6.81315i	0.332585	+	0.241637i
$796$		0			0
$797$	−17.5913	+	12.7808i	−0.623115	+	0.452720i	−0.854008	−	0.520259i	$-0.825835\pi$
$797$	−17.5913	+	12.7808i	−0.623115	+	0.452720i	0.230893	+	0.972979i	$0.425835\pi$
$798$		0			0
$799$	27.9815	−	38.5132i	0.989913	−	1.36250i
$800$		0			0
$801$	11.6849	−	1.85070i	0.412865	−	0.0653913i
$802$		0			0
$803$	−19.6180	−	9.99586i	−0.692303	−	0.352746i
$804$		0			0
$805$	−4.29820	−	8.43569i	−0.151492	−	0.297319i
$806$		0			0
$807$	−15.3109	−	2.42501i	−0.538970	−	0.0853645i
$808$		0			0
$809$	−21.4765	+	42.1499i	−0.755072	+	1.48191i	0.117314	+	0.993095i	$0.462571\pi$
$809$	−21.4765	+	42.1499i	−0.755072	+	1.48191i	−0.872386	+	0.488817i	$0.837429\pi$
$810$		0			0
$811$		−	53.0392i		−	1.86246i	−0.364436	−	0.931228i	$-0.618738\pi$
$811$		−	53.0392i		−	1.86246i	0.364436	−	0.931228i	$-0.381262\pi$
$812$		0			0
$813$	1.39132	+	8.78445i	0.0487957	+	0.308084i
$814$		0			0
$815$	14.9340	+	4.85234i	0.523114	+	0.169970i
$816$		0			0
$817$	−1.39597	−	1.39597i	−0.0488386	−	0.0488386i
$818$		0			0
$819$	−18.3409			−0.640882
$820$		0			0
$821$	−38.9809			−1.36044			−0.680222	−	0.733006i	$-0.738117\pi$
$821$	−38.9809			−1.36044			−0.680222	+	0.733006i	$0.738117\pi$
$822$		0			0
$823$	−1.02441	−	1.02441i	−0.0357087	−	0.0357087i	0.689027	−	0.724736i	$-0.258038\pi$
$823$	−1.02441	−	1.02441i	−0.0357087	−	0.0357087i	−0.724736	+	0.689027i	$0.758038\pi$
$824$		0			0
$825$	−12.7972	−	4.15805i	−0.445540	−	0.144765i
$826$		0			0
$827$	−6.74246	−	42.5702i	−0.234458	−	1.48031i	−0.771215	−	0.636575i	$-0.780351\pi$
$827$	−6.74246	−	42.5702i	−0.234458	−	1.48031i	0.536756	−	0.843737i	$-0.319649\pi$
$828$		0			0
$829$		−	12.8894i		−	0.447667i	−0.974627	−	0.223834i	$-0.928143\pi$
$829$		−	12.8894i		−	0.447667i	0.974627	−	0.223834i	$-0.0718572\pi$
$830$		0			0
$831$	−15.9101	+	31.2253i	−0.551915	+	1.08319i
$832$		0			0
$833$	42.5082	+	6.73263i	1.47282	+	0.233272i
$834$		0			0
$835$	−0.0924146	−	0.181374i	−0.00319814	−	0.00627670i
$836$		0			0
$837$	33.0374	+	16.8334i	1.14194	+	0.581846i
$838$		0			0
$839$	41.2093	−	6.52691i	1.42270	−	0.225334i	0.602825	−	0.797873i	$-0.294042\pi$
$839$	41.2093	−	6.52691i	1.42270	−	0.225334i	0.819877	+	0.572539i	$0.194042\pi$
$840$		0			0
$841$	−14.5610	+	20.0414i	−0.502102	+	0.691084i
$842$		0			0
$843$	−3.82345	+	2.77790i	−0.131687	+	0.0956760i
$844$		0			0
$845$	4.80444	+	3.49063i	0.165278	+	0.120081i
$846$		0			0
$847$	13.2390	−	13.2390i	0.454898	−	0.454898i
$848$		0			0
$849$	−9.33818	+	4.75804i	−0.320485	+	0.163295i
$850$		0			0
$851$	7.38819	+	22.7385i	0.253264	+	0.779466i
$852$		0			0
$853$	32.3174	−	10.5005i	1.10653	−	0.359532i	0.301915	−	0.953335i	$-0.402374\pi$
$853$	32.3174	−	10.5005i	1.10653	−	0.359532i	0.804610	+	0.593803i	$0.202374\pi$
$854$		0			0
$855$	−0.175081	+	1.10542i	−0.00598763	+	0.0378044i
$856$		0			0
$857$	−5.10325	+	15.7062i	−0.174324	+	0.536513i	−0.999602	−	0.0282132i	$-0.991018\pi$
$857$	−5.10325	+	15.7062i	−0.174324	+	0.536513i	0.825278	+	0.564726i	$0.191018\pi$
$858$		0			0
$859$	24.0112	+	33.0486i	0.819252	+	1.12760i	0.989829	+	0.142260i	$0.0454369\pi$
$859$	24.0112	+	33.0486i	0.819252	+	1.12760i	−0.170577	+	0.985344i	$0.554563\pi$
$860$		0			0
$861$	27.7451	−	22.3468i	0.945551	−	0.761576i
$862$		0			0
$863$	−19.3968	−	26.6975i	−0.660276	−	0.908792i	0.339214	−	0.940709i	$-0.389839\pi$
$863$	−19.3968	−	26.6975i	−0.660276	−	0.908792i	−0.999491	+	0.0319168i	$0.989839\pi$
$864$		0			0
$865$	1.76390	−	5.42872i	0.0599743	−	0.184582i
$866$		0			0
$867$	−1.27827	+	8.07071i	−0.0434125	+	0.274096i
$868$		0			0
$869$	6.53298	−	2.12269i	0.221616	−	0.0720075i
$870$		0			0
$871$	4.66521	+	14.3580i	0.158075	+	0.486504i
$872$		0			0
$873$	3.56840	−	1.81819i	0.120772	−	0.0615364i
$874$		0			0
$875$	−26.8581	+	26.8581i	−0.907969	+	0.907969i
$876$		0			0
$877$	−9.01360	−	6.54877i	−0.304368	−	0.221136i	0.425108	−	0.905143i	$-0.360236\pi$
$877$	−9.01360	−	6.54877i	−0.304368	−	0.221136i	−0.729476	+	0.684006i	$0.760236\pi$
$878$		0			0
$879$	−6.72408	+	4.88533i	−0.226798	+	0.164778i
$880$		0			0
$881$	14.5003	−	19.9579i	0.488527	−	0.672400i	−0.491589	−	0.870828i	$-0.663584\pi$
$881$	14.5003	−	19.9579i	0.488527	−	0.672400i	0.980115	+	0.198428i	$0.0635836\pi$
$882$		0			0
$883$	−21.4782	+	3.40182i	−0.722800	+	0.114480i	−0.506986	−	0.861954i	$-0.669240\pi$
$883$	−21.4782	+	3.40182i	−0.722800	+	0.114480i	−0.215814	+	0.976435i	$0.569240\pi$
$884$		0			0
$885$	−12.7759	−	6.50963i	−0.429456	−	0.218819i
$886$		0			0
$887$	20.8531	+	40.9264i	0.700177	+	1.37418i	0.917366	+	0.398045i	$0.130311\pi$
$887$	20.8531	+	40.9264i	0.700177	+	1.37418i	−0.217189	+	0.976130i	$0.569689\pi$
$888$		0			0
$889$	36.3821	+	5.76236i	1.22022	+	0.193263i
$890$		0			0
$891$	5.32970	−	10.4601i	0.178552	−	0.350427i
$892$		0			0
$893$		−	9.74509i		−	0.326107i
$894$		0			0
$895$	−2.79707	−	17.6600i	−0.0934956	−	0.590308i
$896$		0			0
$897$	12.5607	+	4.08121i	0.419388	+	0.136268i
$898$		0			0
$899$	9.53336	+	9.53336i	0.317955	+	0.317955i
$900$		0			0
$901$	−37.1350			−1.23714
$902$		0			0
$903$	11.2189			0.373340
$904$		0			0
$905$	8.00464	+	8.00464i	0.266083	+	0.266083i
$906$		0			0
$907$	−46.8965	−	15.2376i	−1.55717	−	0.505956i	−0.601121	−	0.799158i	$-0.705279\pi$
$907$	−46.8965	−	15.2376i	−1.55717	−	0.505956i	−0.956050	+	0.293203i	$0.905279\pi$
$908$		0			0
$909$	0.304565	+	1.92295i	0.0101018	+	0.0637801i
$910$		0			0
$911$		−	8.88306i		−	0.294309i	−0.989114	−	0.147154i	$-0.952989\pi$
$911$		−	8.88306i		−	0.294309i	0.989114	−	0.147154i	$-0.0470114\pi$
$912$		0			0
$913$	3.19115	−	6.26299i	0.105612	−	0.207275i
$914$		0			0
$915$	−0.660791	−	0.104659i	−0.0218451	−	0.00345992i
$916$		0			0
$917$	0.343116	+	0.673403i	0.0113307	+	0.0222377i
$918$		0			0
$919$	10.9177	+	5.56284i	0.360141	+	0.183501i	0.624693	−	0.780870i	$-0.285224\pi$
$919$	10.9177	+	5.56284i	0.360141	+	0.183501i	−0.264552	+	0.964371i	$0.585224\pi$
$920$		0			0
$921$	−1.01163	+	0.160226i	−0.0333343	+	0.00527964i
$922$		0			0
$923$	35.6504	−	49.0686i	1.17345	−	1.61511i
$924$		0			0
$925$	33.7492	−	24.5203i	1.10967	−	0.806221i
$926$		0			0
$927$	9.58328	+	6.96266i	0.314756	+	0.228684i
$928$		0			0
$929$	20.0281	−	20.0281i	0.657099	−	0.657099i	−0.297593	−	0.954693i	$-0.596184\pi$
$929$	20.0281	−	20.0281i	0.657099	−	0.657099i	0.954693	+	0.297593i	$0.0961839\pi$
$930$		0			0
$931$	7.84996	−	3.99975i	0.257272	−	0.131087i
$932$		0			0
$933$	12.4054	+	38.1800i	0.406135	+	1.24996i
$934$		0			0
$935$	−12.2717	+	3.98731i	−0.401327	+	0.130399i
$936$		0			0
$937$	6.70744	−	42.3491i	0.219122	−	1.38348i	−0.595436	−	0.803403i	$-0.703021\pi$
$937$	6.70744	−	42.3491i	0.219122	−	1.38348i	0.814558	−	0.580082i	$-0.196979\pi$
$938$		0			0
$939$	7.05571	−	21.7153i	0.230254	−	0.708650i
$940$		0			0
$941$	−24.8897	−	34.2578i	−0.811382	−	1.11677i	−0.991109	−	0.133055i	$-0.957521\pi$
$941$	−24.8897	−	34.2578i	−0.811382	−	1.11677i	0.179727	−	0.983717i	$-0.442479\pi$
$942$		0			0
$943$	13.1973	−	5.02611i	0.429762	−	0.163673i
$944$		0			0
$945$	−14.2678	−	19.6379i	−0.464130	−	0.638820i
$946$		0			0
$947$	1.31206	−	4.03811i	0.0426362	−	0.131221i	−0.927473	−	0.373891i	$-0.878023\pi$
$947$	1.31206	−	4.03811i	0.0426362	−	0.131221i	0.970109	+	0.242670i	$0.0780233\pi$
$948$		0			0
$949$	5.89869	−	37.2428i	0.191479	−	1.20895i
$950$		0			0
$951$	44.6750	−	14.5158i	1.44869	−	0.470707i
$952$		0			0
$953$	11.2759	+	34.7035i	0.365261	+	1.12416i	0.949818	+	0.312804i	$0.101268\pi$
$953$	11.2759	+	34.7035i	0.365261	+	1.12416i	−0.584557	+	0.811353i	$0.698732\pi$
$954$		0			0
$955$	−15.0647	+	7.67584i	−0.487482	+	0.248384i
$956$		0			0
$957$	5.08365	−	5.08365i	0.164331	−	0.164331i
$958$		0			0
$959$	20.8018	+	15.1134i	0.671726	+	0.488038i
$960$		0			0
$961$	−9.70657	+	7.05224i	−0.313115	+	0.227491i
$962$		0			0
$963$	−8.09317	+	11.1393i	−0.260799	+	0.358959i
$964$		0			0
$965$	−24.7767	+	3.92425i	−0.797592	+	0.126326i
$966$		0			0
$967$	−35.6031	−	18.1407i	−1.14492	−	0.583365i	−0.224567	−	0.974459i	$-0.572097\pi$
$967$	−35.6031	−	18.1407i	−1.14492	−	0.583365i	−0.920351	+	0.391094i	$0.872097\pi$
$968$		0			0
$969$	2.95704	+	5.80352i	0.0949938	+	0.186436i
$970$		0			0
$971$	24.6105	+	3.89792i	0.789788	+	0.125090i	0.538281	−	0.842765i	$-0.319074\pi$
$971$	24.6105	+	3.89792i	0.789788	+	0.125090i	0.251507	+	0.967855i	$0.419074\pi$
$972$		0			0
$973$	−13.0775	+	25.6660i	−0.419245	+	0.822814i
$974$		0			0
$975$		−	23.0440i		−	0.737998i
$976$		0			0
$977$	1.49380	+	9.43148i	0.0477909	+	0.301740i	0.999993	−	0.00372882i	$-0.00118692\pi$
$977$	1.49380	+	9.43148i	0.0477909	+	0.301740i	−0.952202	+	0.305469i	$0.901187\pi$
$978$		0			0
$979$	26.5544	+	8.62805i	0.848683	+	0.275754i
$980$		0			0
$981$	5.02406	+	5.02406i	0.160406	+	0.160406i
$982$		0			0
$983$	21.0349			0.670908			0.335454	−	0.942057i	$-0.391110\pi$
$983$	21.0349			0.670908			0.335454	+	0.942057i	$0.391110\pi$
$984$		0			0
$985$	12.7097			0.404965
$986$		0			0
$987$	39.1588	+	39.1588i	1.24644	+	1.24644i
$988$		0			0
$989$	4.22951	+	1.37425i	0.134491	+	0.0436986i
$990$		0			0
$991$	1.31916	+	8.32884i	0.0419045	+	0.264574i	0.999741	−	0.0227378i	$-0.00723829\pi$
$991$	1.31916	+	8.32884i	0.0419045	+	0.264574i	−0.957837	+	0.287312i	$0.907238\pi$
$992$		0			0
$993$			16.7626i			0.531945i
$994$		0			0
$995$	−4.12772	+	8.10111i	−0.130858	+	0.256823i
$996$		0			0
$997$	11.9561	+	1.89365i	0.378652	+	0.0599726i	0.342860	−	0.939387i	$-0.388604\pi$
$997$	11.9561	+	1.89365i	0.378652	+	0.0599726i	0.0357924	+	0.999359i	$0.488604\pi$
$998$		0			0
$999$	27.8291	+	54.6178i	0.880475	+	1.72803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.bs.d.497.2		24
4.3	odd	2		41.2.g.a.5.2	✓	24
12.11	even	2		369.2.u.a.46.2		24
41.33	even	20	inner	656.2.bs.d.33.2		24
164.19	even	40		1681.2.a.m.1.8		24
164.63	even	40		1681.2.a.m.1.7		24
164.115	odd	20		41.2.g.a.33.2	yes	24
492.443	even	20		369.2.u.a.361.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.2	✓	24	4.3	odd	2
41.2.g.a.33.2	yes	24	164.115	odd	20
369.2.u.a.46.2		24	12.11	even	2
369.2.u.a.361.2		24	492.443	even	20
656.2.bs.d.33.2		24	41.33	even	20	inner
656.2.bs.d.497.2		24	1.1	even	1	trivial
1681.2.a.m.1.7		24	164.63	even	40
1681.2.a.m.1.8		24	164.19	even	40

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.bs (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.983583 + 0.983583i) q^{3} +(1.02071 + 0.331648i) q^{5} +(-0.625712 - 3.95059i) q^{7} -1.06513i q^{9} +O(q^{10})\)	\(q+(0.983583 + 0.983583i) q^{3} +(1.02071 + 0.331648i) q^{5} +(-0.625712 - 3.95059i) q^{7} -1.06513i q^{9} +(1.14123 - 2.23980i) q^{11} +(4.25204 + 0.673457i) q^{13} +(0.677748 + 1.33015i) q^{15} +(-4.26144 - 2.17131i) q^{17} +(-0.967006 + 0.153159i) q^{19} +(3.27029 - 4.50117i) q^{21} +(1.78427 - 1.29635i) q^{23} +(-3.11323 - 2.26189i) q^{25} +(3.99839 - 3.99839i) q^{27} +(1.83197 - 0.933434i) q^{29} +(2.02631 + 6.23635i) q^{31} +(3.32552 - 1.08053i) q^{33} +(0.671536 - 4.23991i) q^{35} +(-3.34992 + 10.3100i) q^{37} +(3.51983 + 4.84464i) q^{39} +(6.18056 + 1.67354i) q^{41} +(1.18522 + 1.63132i) q^{43} +(0.353247 - 1.08718i) q^{45} +(-1.55707 + 9.83098i) q^{47} +(-8.55823 + 2.78074i) q^{49} +(-2.05581 - 6.32714i) q^{51} +(6.91813 - 3.52496i) q^{53} +(1.90769 - 1.90769i) q^{55} +(-1.10177 - 0.800486i) q^{57} +(-7.77045 + 5.64556i) q^{59} +(-0.263416 + 0.362561i) q^{61} +(-4.20788 + 0.666462i) q^{63} +(4.11674 + 2.09758i) q^{65} +(1.59206 + 3.12459i) q^{67} +(3.03004 + 0.479912i) q^{69} +(6.39610 - 12.5531i) q^{71} -8.75882i q^{73} +(-0.837360 - 5.28689i) q^{75} +(-9.56259 - 3.10707i) q^{77} +(1.93225 + 1.93225i) q^{79} +4.67012 q^{81} +2.79623 q^{83} +(-3.62957 - 3.62957i) q^{85} +(2.72000 + 0.883783i) q^{87} +(1.73754 + 10.9704i) q^{89} -17.2194i q^{91} +(-4.14092 + 8.12702i) q^{93} +(-1.03782 - 0.164375i) q^{95} +(1.70702 + 3.35021i) q^{97} +(-2.38567 - 1.21556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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