LMFDB - Embedded newform 756.2.ca.a.173.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(173,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 13, 15]))

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

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

chi := DirichletCharacter("756.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ca (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.6
Character	$\chi$	$=$	756.173
Dual form			756.2.ca.a.437.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31609 + 1.12602i) q^{3} +(-0.481690 + 0.404186i) q^{5} +(2.64564 + 0.0243961i) q^{7} +(0.464163 - 2.96387i) q^{9} +O(q^{10})$	\(q+(-1.31609 + 1.12602i) q^{3} +(-0.481690 + 0.404186i) q^{5} +(2.64564 + 0.0243961i) q^{7} +(0.464163 - 2.96387i) q^{9} +(1.20589 - 1.43712i) q^{11} +(-0.235703 - 0.280900i) q^{13} +(0.178824 - 1.07434i) q^{15} +(1.98751 - 3.44247i) q^{17} +(-1.22027 + 0.704525i) q^{19} +(-3.50936 + 2.94693i) q^{21} +(1.66481 - 4.57403i) q^{23} +(-0.799582 + 4.53465i) q^{25} +(2.72650 + 4.42337i) q^{27} +(2.85223 - 3.39915i) q^{29} +(6.08987 + 7.25762i) q^{31} +(0.0311738 + 3.24923i) q^{33} +(-1.28424 + 1.05758i) q^{35} +0.392947 q^{37} +(0.626504 + 0.104282i) q^{39} +(0.337003 - 0.282779i) q^{41} +(8.15803 - 2.96928i) q^{43} +(0.974373 + 1.61528i) q^{45} +(7.50900 + 6.30080i) q^{47} +(6.99881 + 0.129086i) q^{49} +(1.26055 + 6.76857i) q^{51} +(-8.64238 + 4.98968i) q^{53} +1.17965i q^{55} +(0.812676 - 2.30127i) q^{57} +(-0.100302 - 0.568840i) q^{59} +(-3.75615 + 4.47641i) q^{61} +(1.30031 - 7.83002i) q^{63} +(0.227072 + 0.0400389i) q^{65} +(-3.34534 - 1.21760i) q^{67} +(2.95941 + 7.89443i) q^{69} +(12.2893 - 7.09525i) q^{71} +6.36345i q^{73} +(-4.05379 - 6.86834i) q^{75} +(3.22540 - 3.77268i) q^{77} +(9.49778 - 3.45691i) q^{79} +(-8.56911 - 2.75144i) q^{81} +(3.38160 + 2.83750i) q^{83} +(0.434034 + 2.46153i) q^{85} +(0.0737338 + 7.68524i) q^{87} +(-3.11200 - 5.39014i) q^{89} +(-0.616733 - 0.748910i) q^{91} +(-16.1870 - 2.69435i) q^{93} +(0.303034 - 0.832580i) q^{95} +(-2.12529 - 5.83919i) q^{97} +(-3.69972 - 4.24116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.31609	+	1.12602i	−0.759842	+	0.650107i
$3$	−1.31609	+	1.12602i	−0.759842	+	0.650107i
$4$		0			0
$5$	−0.481690	+	0.404186i	−0.215418	+	0.180757i	−0.744111	−	0.668056i	$-0.767127\pi$
$5$	−0.481690	+	0.404186i	−0.215418	+	0.180757i	0.528693	+	0.848813i	$0.322682\pi$
$6$		0			0
$7$	2.64564	+	0.0243961i	0.999957	+	0.00922085i
$7$	2.64564	+	0.0243961i	0.999957	+	0.00922085i
$8$		0			0
$9$	0.464163	−	2.96387i	0.154721	−	0.987958i
$10$		0			0
$11$	1.20589	−	1.43712i	0.363589	−	0.433308i	−0.552974	−	0.833198i	$-0.686507\pi$
$11$	1.20589	−	1.43712i	0.363589	−	0.433308i	0.916563	+	0.399890i	$0.130952\pi$
$12$		0			0
$13$	−0.235703	−	0.280900i	−0.0653723	−	0.0779077i	0.732367	−	0.680910i	$-0.238415\pi$
$13$	−0.235703	−	0.280900i	−0.0653723	−	0.0779077i	−0.797740	+	0.603002i	$0.793971\pi$
$14$		0			0
$15$	0.178824	−	1.07434i	0.0461722	−	0.277392i
$16$		0			0
$17$	1.98751	−	3.44247i	0.482043	−	0.834923i	−0.517745	−	0.855535i	$-0.673228\pi$
$17$	1.98751	−	3.44247i	0.482043	−	0.834923i	0.999788	+	0.0206125i	$0.00656162\pi$
$18$		0			0
$19$	−1.22027	+	0.704525i	−0.279950	+	0.161629i	−0.633401	−	0.773824i	$-0.718341\pi$
$19$	−1.22027	+	0.704525i	−0.279950	+	0.161629i	0.353451	+	0.935453i	$0.385008\pi$
$20$		0			0
$21$	−3.50936	+	2.94693i	−0.765805	+	0.643073i
$22$		0			0
$23$	1.66481	−	4.57403i	0.347137	−	0.953751i	−0.636130	−	0.771582i	$-0.719466\pi$
$23$	1.66481	−	4.57403i	0.347137	−	0.953751i	0.983267	−	0.182170i	$-0.0583120\pi$
$24$		0			0
$25$	−0.799582	+	4.53465i	−0.159916	+	0.906931i
$26$		0			0
$27$	2.72650	+	4.42337i	0.524715	+	0.851278i
$28$		0			0
$29$	2.85223	−	3.39915i	0.529646	−	0.631207i	−0.433188	−	0.901304i	$-0.642611\pi$
$29$	2.85223	−	3.39915i	0.529646	−	0.631207i	0.962833	+	0.270097i	$0.0870557\pi$
$30$		0			0
$31$	6.08987	+	7.25762i	1.09377	+	1.30351i	0.949430	+	0.313979i	$0.101662\pi$
$31$	6.08987	+	7.25762i	1.09377	+	1.30351i	0.144343	+	0.989528i	$0.453893\pi$
$32$		0			0
$33$	0.0311738	+	3.24923i	0.00542666	+	0.565618i
$34$		0			0
$35$	−1.28424	+	1.05758i	−0.217076	+	0.178763i
$36$		0			0
$37$	0.392947			0.0646000			0.0323000	−	0.999478i	$-0.489717\pi$
$37$	0.392947			0.0646000			0.0323000	+	0.999478i	$0.489717\pi$
$38$		0			0
$39$	0.626504	+	0.104282i	0.100321	+	0.0166985i
$40$		0			0
$41$	0.337003	−	0.282779i	0.0526311	−	0.0441627i	−0.616093	−	0.787674i	$-0.711285\pi$
$41$	0.337003	−	0.282779i	0.0526311	−	0.0441627i	0.668724	+	0.743511i	$0.266841\pi$
$42$		0			0
$43$	8.15803	−	2.96928i	1.24409	−	0.452811i	0.365688	−	0.930737i	$-0.380834\pi$
$43$	8.15803	−	2.96928i	1.24409	−	0.452811i	0.878400	+	0.477926i	$0.158611\pi$
$44$		0			0
$45$	0.974373	+	1.61528i	0.145251	+	0.240791i
$46$		0			0
$47$	7.50900	+	6.30080i	1.09530	+	0.919065i	0.997100	−	0.0761013i	$-0.0242473\pi$
$47$	7.50900	+	6.30080i	1.09530	+	0.919065i	0.0981994	+	0.995167i	$0.468692\pi$
$48$		0			0
$49$	6.99881	+	0.129086i	0.999830	+	0.0184409i
$50$		0			0
$51$	1.26055	+	6.76857i	0.176513	+	0.947789i
$52$		0			0
$53$	−8.64238	+	4.98968i	−1.18712	+	0.685385i	−0.957651	−	0.287930i	$-0.907033\pi$
$53$	−8.64238	+	4.98968i	−1.18712	+	0.685385i	−0.229471	+	0.973316i	$0.573700\pi$
$54$		0			0
$55$			1.17965i			0.159064i
$56$		0			0
$57$	0.812676	−	2.30127i	0.107642	−	0.304810i
$58$		0			0
$59$	−0.100302	−	0.568840i	−0.0130582	−	0.0740567i	0.977582	−	0.210554i	$-0.0675267\pi$
$59$	−0.100302	−	0.568840i	−0.0130582	−	0.0740567i	−0.990640	+	0.136497i	$0.956416\pi$
$60$		0			0
$61$	−3.75615	+	4.47641i	−0.480926	+	0.573145i	−0.950886	−	0.309543i	$-0.899824\pi$
$61$	−3.75615	+	4.47641i	−0.480926	+	0.573145i	0.469959	+	0.882688i	$0.344269\pi$
$62$		0			0
$63$	1.30031	−	7.83002i	0.163824	−	0.986490i
$64$		0			0
$65$	0.227072	+	0.0400389i	0.0281648	+	0.00496621i
$66$		0			0
$67$	−3.34534	−	1.21760i	−0.408698	−	0.148754i	0.129486	−	0.991581i	$-0.458667\pi$
$67$	−3.34534	−	1.21760i	−0.408698	−	0.148754i	−0.538184	+	0.842827i	$0.680890\pi$
$68$		0			0
$69$	2.95941	+	7.89443i	0.356271	+	0.950377i
$70$		0			0
$71$	12.2893	−	7.09525i	1.45848	−	0.842051i	0.459539	−	0.888157i	$-0.348014\pi$
$71$	12.2893	−	7.09525i	1.45848	−	0.842051i	0.998937	+	0.0461059i	$0.0146812\pi$
$72$		0			0
$73$			6.36345i			0.744785i	0.928075	+	0.372392i	$0.121462\pi$
$73$			6.36345i			0.744785i	−0.928075	+	0.372392i	$0.878538\pi$
$74$		0			0
$75$	−4.05379	−	6.86834i	−0.468091	−	0.793087i
$76$		0			0
$77$	3.22540	−	3.77268i	0.367569	−	0.429937i
$78$		0			0
$79$	9.49778	−	3.45691i	1.06858	−	0.388933i	0.252937	−	0.967483i	$-0.418603\pi$
$79$	9.49778	−	3.45691i	1.06858	−	0.388933i	0.815647	+	0.578550i	$0.196381\pi$
$80$		0			0
$81$	−8.56911	−	2.75144i	−0.952123	−	0.305716i
$82$		0			0
$83$	3.38160	+	2.83750i	0.371178	+	0.311456i	0.809228	−	0.587495i	$-0.199886\pi$
$83$	3.38160	+	2.83750i	0.371178	+	0.311456i	−0.438049	+	0.898951i	$0.644330\pi$
$84$		0			0
$85$	0.434034	+	2.46153i	0.0470776	+	0.266990i
$86$		0			0
$87$	0.0737338	+	7.68524i	0.00790510	+	0.823944i
$88$		0			0
$89$	−3.11200	−	5.39014i	−0.329871	−	0.571354i	0.652615	−	0.757690i	$-0.273672\pi$
$89$	−3.11200	−	5.39014i	−0.329871	−	0.571354i	−0.982486	+	0.186336i	$0.940339\pi$
$90$		0			0
$91$	−0.616733	−	0.748910i	−0.0646511	−	0.0785071i
$92$		0			0
$93$	−16.1870	−	2.69435i	−1.67851	−	0.279391i
$94$		0			0
$95$	0.303034	−	0.832580i	0.0310907	−	0.0854209i
$96$		0			0
$97$	−2.12529	−	5.83919i	−0.215791	−	0.592880i	0.783814	−	0.620996i	$-0.213272\pi$
$97$	−2.12529	−	5.83919i	−0.215791	−	0.592880i	−0.999605	+	0.0281157i	$0.991049\pi$
$98$		0			0
$99$	−3.69972	−	4.24116i	−0.371836	−	0.426252i
$100$		0			0
$101$	−15.7817	+	5.74408i	−1.57034	+	0.571557i	−0.973075	−	0.230487i	$-0.925968\pi$
$101$	−15.7817	+	5.74408i	−1.57034	+	0.571557i	−0.597265	+	0.802044i	$0.703746\pi$
$102$		0			0
$103$	−2.51205	−	2.99375i	−0.247520	−	0.294983i	0.627952	−	0.778252i	$-0.283894\pi$
$103$	−2.51205	−	2.99375i	−0.247520	−	0.294983i	−0.875472	+	0.483269i	$0.839449\pi$
$104$		0			0
$105$	0.499314	−	2.83794i	0.0487281	−	0.276955i
$106$		0			0
$107$	−10.8698	−	6.27569i	−1.05082	−	0.606693i	−0.127944	−	0.991781i	$-0.540838\pi$
$107$	−10.8698	−	6.27569i	−1.05082	−	0.606693i	−0.922880	+	0.385088i	$0.874171\pi$
$108$		0			0
$109$	−0.894424	−	1.54919i	−0.0856703	−	0.148385i	0.820006	−	0.572354i	$-0.193970\pi$
$109$	−0.894424	−	1.54919i	−0.0856703	−	0.148385i	−0.905677	+	0.423969i	$0.860636\pi$
$110$		0			0
$111$	−0.517151	+	0.442465i	−0.0490858	+	0.0419969i
$112$		0			0
$113$	3.18174	−	8.74175i	0.299313	−	0.822355i	−0.695302	−	0.718717i	$-0.744730\pi$
$113$	3.18174	−	8.74175i	0.299313	−	0.822355i	0.994615	−	0.103638i	$-0.0330483\pi$
$114$		0			0
$115$	1.04684	+	2.87616i	0.0976179	+	0.268203i
$116$		0			0
$117$	−0.941957	+	0.568211i	−0.0870840	+	0.0525311i
$118$		0			0
$119$	5.34223	−	9.05906i	0.489721	−	0.830442i
$120$		0			0
$121$	1.29898	+	7.36687i	0.118089	+	0.669716i
$122$		0			0
$123$	−0.125110	+	0.751634i	−0.0112808	+	0.0677725i
$124$		0			0
$125$	−3.01970	−	5.23027i	−0.270090	−	0.467809i
$126$		0			0
$127$	−1.10888	+	1.92063i	−0.0983971	+	0.170429i	−0.911021	−	0.412359i	$-0.864705\pi$
$127$	−1.10888	+	1.92063i	−0.0983971	+	0.170429i	0.812624	+	0.582788i	$0.198038\pi$
$128$		0			0
$129$	−7.39320	+	13.0939i	−0.650935	+	1.15286i
$130$		0			0
$131$	2.83330	+	1.03124i	0.247546	+	0.0900995i	0.462813	−	0.886456i	$-0.346840\pi$
$131$	2.83330	+	1.03124i	0.247546	+	0.0900995i	−0.215267	+	0.976555i	$0.569062\pi$
$132$		0			0
$133$	−3.24559	+	1.83415i	−0.281428	+	0.159041i
$134$		0			0
$135$	−3.10119	−	1.02868i	−0.266908	−	0.0885347i
$136$		0			0
$137$	−13.0192	−	2.29563i	−1.11230	−	0.196129i	−0.412844	−	0.910802i	$-0.635465\pi$
$137$	−13.0192	−	2.29563i	−1.11230	−	0.196129i	−0.699459	+	0.714673i	$0.746576\pi$
$138$		0			0
$139$	21.1007	−	3.72062i	1.78974	−	0.315579i	0.822368	−	0.568956i	$-0.192653\pi$
$139$	21.1007	−	3.72062i	1.78974	−	0.315579i	0.967367	+	0.253378i	$0.0815415\pi$
$140$		0			0
$141$	−16.9773	+	0.162884i	−1.42975	+	0.0137173i
$142$		0			0
$143$	−0.687919			−0.0575267
$144$		0			0
$145$			2.79017i			0.231711i
$146$		0			0
$147$	−9.35639	+	7.71090i	−0.771702	+	0.635985i
$148$		0			0
$149$	15.9884	−	2.81918i	1.30982	−	0.230956i	0.525223	−	0.850965i	$-0.323982\pi$
$149$	15.9884	−	2.81918i	1.30982	−	0.230956i	0.784595	+	0.620009i	$0.212871\pi$
$150$		0			0
$151$	−11.1735	−	9.37564i	−0.909283	−	0.762979i	0.0626994	−	0.998032i	$-0.480029\pi$
$151$	−11.1735	−	9.37564i	−0.909283	−	0.762979i	−0.971982	+	0.235053i	$0.924473\pi$
$152$		0			0
$153$	−9.28053	−	7.48861i	−0.750287	−	0.605418i
$154$		0			0
$155$	−5.86686	−	1.03448i	−0.471237	−	0.0830918i
$156$		0			0
$157$	7.33393	−	1.29317i	0.585312	−	0.103206i	0.126852	−	0.991922i	$-0.459513\pi$
$157$	7.33393	−	1.29317i	0.585312	−	0.103206i	0.458459	+	0.888715i	$0.348401\pi$
$158$		0			0
$159$	5.75564	−	16.2983i	0.456452	−	1.29254i
$160$		0			0
$161$	4.51608	−	12.0606i	0.355917	−	0.950510i
$162$		0			0
$163$	−10.6878	+	18.5118i	−0.837134	+	1.44996i	0.0551466	+	0.998478i	$0.482437\pi$
$163$	−10.6878	+	18.5118i	−0.837134	+	1.44996i	−0.892281	+	0.451481i	$0.850896\pi$
$164$		0			0
$165$	−1.32831	−	1.55252i	−0.103409	−	0.120863i
$166$		0			0
$167$	−3.47846	−	1.26606i	−0.269172	−	0.0979704i	0.203908	−	0.978990i	$-0.434636\pi$
$167$	−3.47846	−	1.26606i	−0.269172	−	0.0979704i	−0.473080	+	0.881020i	$0.656858\pi$
$168$		0			0
$169$	2.23408	−	12.6701i	0.171852	−	0.974622i
$170$		0			0
$171$	1.52172	+	3.94375i	0.116369	+	0.301586i
$172$		0			0
$173$	0.204026	−	1.15709i	0.0155118	−	0.0879719i	−0.976069	−	0.217461i	$-0.930223\pi$
$173$	0.204026	−	1.15709i	0.0155118	−	0.0879719i	0.991581	+	0.129489i	$0.0413337\pi$
$174$		0			0
$175$	−2.22603	+	11.9776i	−0.168272	+	0.905418i
$176$		0			0
$177$	0.772530	+	0.635700i	0.0580669	+	0.0477822i
$178$		0			0
$179$	−3.63333	−	2.09770i	−0.271568	−	0.156790i	0.358032	−	0.933709i	$-0.383448\pi$
$179$	−3.63333	−	2.09770i	−0.271568	−	0.156790i	−0.629600	+	0.776920i	$0.716781\pi$
$180$		0			0
$181$	1.69261	+	0.977228i	0.125811	+	0.0726368i	0.561585	−	0.827419i	$-0.310192\pi$
$181$	1.69261	+	0.977228i	0.125811	+	0.0726368i	−0.435774	+	0.900056i	$0.643525\pi$
$182$		0			0
$183$	−0.0971014	−	10.1208i	−0.00717794	−	0.748154i
$184$		0			0
$185$	−0.189278	+	0.158823i	−0.0139160	+	0.0116769i
$186$		0			0
$187$	−2.55053	−	7.00754i	−0.186514	−	0.512442i
$188$		0			0
$189$	7.10542	+	11.7692i	0.516843	+	0.856080i
$190$		0			0
$191$	−0.379594	−	1.04293i	−0.0274664	−	0.0754634i	0.925202	−	0.379476i	$-0.123896\pi$
$191$	−0.379594	−	1.04293i	−0.0274664	−	0.0754634i	−0.952668	+	0.304013i	$0.901673\pi$
$192$		0			0
$193$	−1.76417	+	1.48032i	−0.126988	+	0.106556i	−0.704070	−	0.710131i	$-0.748636\pi$
$193$	−1.76417	+	1.48032i	−0.126988	+	0.106556i	0.577082	+	0.816686i	$0.304191\pi$
$194$		0			0
$195$	−0.343930	+	0.202992i	−0.0246294	+	0.0145366i
$196$		0			0
$197$	−16.4656	−	9.50640i	−1.17312	−	0.677303i	−0.218709	−	0.975790i	$-0.570185\pi$
$197$	−16.4656	−	9.50640i	−1.17312	−	0.677303i	−0.954414	+	0.298488i	$0.903518\pi$
$198$		0			0
$199$	−3.05294	−	1.76262i	−0.216417	−	0.124949i	0.387873	−	0.921713i	$-0.373210\pi$
$199$	−3.05294	−	1.76262i	−0.216417	−	0.124949i	−0.604290	+	0.796764i	$0.706543\pi$
$200$		0			0
$201$	5.77380	−	2.16444i	0.407252	−	0.152668i
$202$		0			0
$203$	7.62889	−	8.92335i	0.535443	−	0.626296i
$204$		0			0
$205$	−0.0480357	+	0.272424i	−0.00335496	+	0.0190269i
$206$		0			0
$207$	−12.7841	−	7.05739i	−0.888557	−	0.490522i
$208$		0			0
$209$	−0.459025	+	2.60326i	−0.0317514	+	0.180071i
$210$		0			0
$211$	9.65706	+	3.51488i	0.664820	+	0.241975i	0.652316	−	0.757947i	$-0.273798\pi$
$211$	9.65706	+	3.51488i	0.664820	+	0.241975i	0.0125038	+	0.999922i	$0.496020\pi$
$212$		0			0
$213$	−8.18443	+	23.1760i	−0.560788	+	1.58799i
$214$		0			0
$215$	−2.72950	+	4.72763i	−0.186150	+	0.322422i
$216$		0			0
$217$	15.9345	+	19.3496i	1.08171	+	1.31354i
$218$		0			0
$219$	−7.16536	−	8.37484i	−0.484190	−	0.565919i
$220$		0			0
$221$	−1.43545	+	0.253109i	−0.0965591	+	0.0170260i
$222$		0			0
$223$	−27.8071	−	4.90315i	−1.86210	−	0.328339i	−0.874465	−	0.485088i	$-0.838788\pi$
$223$	−27.8071	−	4.90315i	−1.86210	−	0.328339i	−0.987638	+	0.156749i	$0.949899\pi$
$224$		0			0
$225$	13.0690	+	4.47468i	0.871267	+	0.298312i
$226$		0			0
$227$	5.74075	+	4.81706i	0.381027	+	0.319720i	0.813105	−	0.582116i	$-0.197775\pi$
$227$	5.74075	+	4.81706i	0.381027	+	0.319720i	−0.432079	+	0.901836i	$0.642220\pi$
$228$		0			0
$229$	1.53572	−	0.270789i	0.101483	−	0.0178942i	−0.122676	−	0.992447i	$-0.539148\pi$
$229$	1.53572	−	0.270789i	0.101483	−	0.0178942i	0.224159	+	0.974553i	$0.428036\pi$
$230$		0			0
$231$	0.00320611	+	8.59704i	0.000210946	+	0.565644i
$232$		0			0
$233$		−	13.3406i		−	0.873969i	−0.899469	−	0.436984i	$-0.856046\pi$
$233$		−	13.3406i		−	0.873969i	0.899469	−	0.436984i	$-0.143954\pi$
$234$		0			0
$235$	−6.16370			−0.402075
$236$		0			0
$237$	−8.60735	+	15.2443i	−0.559107	+	0.990222i
$238$		0			0
$239$	8.46669	−	1.49291i	0.547665	−	0.0965680i	0.107032	−	0.994256i	$-0.465865\pi$
$239$	8.46669	−	1.49291i	0.547665	−	0.0965680i	0.440633	+	0.897688i	$0.354754\pi$
$240$		0			0
$241$	10.4639	+	1.84507i	0.674038	+	0.118851i	0.500182	−	0.865920i	$-0.333266\pi$
$241$	10.4639	+	1.84507i	0.674038	+	0.118851i	0.173856	+	0.984771i	$0.444377\pi$
$242$		0			0
$243$	14.3759	−	6.02784i	0.922211	−	0.386686i
$244$		0			0
$245$	−3.42343	+	2.76664i	−0.218715	+	0.176754i
$246$		0			0
$247$	0.485523	+	0.176716i	0.0308931	+	0.0112442i
$248$		0			0
$249$	−7.64555	+	0.0733530i	−0.484517	+	0.00464856i
$250$		0			0
$251$	−11.6262	+	20.1372i	−0.733839	+	1.27105i	0.221391	+	0.975185i	$0.428940\pi$
$251$	−11.6262	+	20.1372i	−0.733839	+	1.27105i	−0.955231	+	0.295862i	$0.904393\pi$
$252$		0			0
$253$	−4.56586	−	7.90830i	−0.287053	−	0.497191i
$254$		0			0
$255$	−3.34296	−	2.75085i	−0.209344	−	0.172265i
$256$		0			0
$257$	2.09659	+	11.8903i	0.130782	+	0.741699i	0.977705	+	0.209984i	$0.0673412\pi$
$257$	2.09659	+	11.8903i	0.130782	+	0.741699i	−0.846923	+	0.531715i	$0.821548\pi$
$258$		0			0
$259$	1.03959	+	0.00958636i	0.0645973	+	0.000595667i
$260$		0			0
$261$	−8.75077	−	10.0314i	−0.541659	−	0.620929i
$262$		0			0
$263$	8.55417	+	23.5024i	0.527473	+	1.44922i	0.862036	+	0.506847i	$0.169189\pi$
$263$	8.55417	+	23.5024i	0.527473	+	1.44922i	−0.334563	+	0.942373i	$0.608589\pi$
$264$		0			0
$265$	2.14619	−	5.89661i	0.131839	−	0.362226i
$266$		0			0
$267$	10.1651	+	3.58972i	0.622091	+	0.219687i
$268$		0			0
$269$	−7.62612	−	13.2088i	−0.464973	−	0.805356i	0.534228	−	0.845341i	$-0.320603\pi$
$269$	−7.62612	−	13.2088i	−0.464973	−	0.805356i	−0.999200	+	0.0399844i	$0.987269\pi$
$270$		0			0
$271$	−18.4322	−	10.6418i	−1.11967	−	0.646444i	−0.178356	−	0.983966i	$-0.557078\pi$
$271$	−18.4322	−	10.6418i	−1.11967	−	0.646444i	−0.941318	+	0.337522i	$0.890411\pi$
$272$		0			0
$273$	1.65496	+	0.291178i	0.100163	+	0.0176229i
$274$		0			0
$275$	5.55264	+	6.61738i	0.334837	+	0.399043i
$276$		0			0
$277$	1.17892	−	0.429093i	0.0708346	−	0.0257817i	−0.306360	−	0.951916i	$-0.599111\pi$
$277$	1.17892	−	0.429093i	0.0708346	−	0.0257817i	0.377194	+	0.926134i	$0.376889\pi$
$278$		0			0
$279$	24.3374	−	14.6809i	1.45704	−	0.878921i
$280$		0			0
$281$	3.55922	+	9.77886i	0.212325	+	0.583358i	0.999440	−	0.0334475i	$-0.0106487\pi$
$281$	3.55922	+	9.77886i	0.212325	+	0.583358i	−0.787115	+	0.616806i	$0.788426\pi$
$282$		0			0
$283$	−3.26981	+	8.98372i	−0.194370	+	0.534027i	−0.998143	−	0.0609088i	$-0.980600\pi$
$283$	−3.26981	+	8.98372i	−0.194370	+	0.534027i	0.803774	+	0.594935i	$0.202822\pi$
$284$		0			0
$285$	0.538681	+	1.43697i	0.0319087	+	0.0851187i
$286$		0			0
$287$	0.898487	−	0.739910i	0.0530360	−	0.0436755i
$288$		0			0
$289$	0.599580	+	1.03850i	0.0352694	+	0.0610884i
$290$		0			0
$291$	9.37210	+	5.29176i	0.549402	+	0.310208i
$292$		0			0
$293$	−3.33317	−	18.9033i	−0.194726	−	1.10435i	−0.912809	−	0.408388i	$-0.866091\pi$
$293$	−3.33317	−	18.9033i	−0.194726	−	1.10435i	0.718083	−	0.695958i	$-0.245020\pi$
$294$		0			0
$295$	0.278231	+	0.233464i	0.0161993	+	0.0135928i
$296$		0			0
$297$	9.64477	+	1.41578i	0.559646	+	0.0821517i
$298$		0			0
$299$	−1.67725	+	0.610468i	−0.0969977	+	0.0353043i
$300$		0			0
$301$	21.6556	−	7.65662i	1.24821	−	0.441320i
$302$		0			0
$303$	14.3022	−	25.3302i	0.821638	−	1.45518i
$304$		0			0
$305$		−	3.67442i		−	0.210397i
$306$		0			0
$307$	−21.9964	+	12.6996i	−1.25540	+	0.724807i	−0.972177	−	0.234246i	$-0.924738\pi$
$307$	−21.9964	+	12.6996i	−1.25540	+	0.724807i	−0.283225	+	0.959053i	$0.591404\pi$
$308$		0			0
$309$	6.67710	+	1.11141i	0.379847	+	0.0632259i
$310$		0			0
$311$	12.3001	+	4.47688i	0.697476	+	0.253860i	0.666333	−	0.745654i	$-0.267863\pi$
$311$	12.3001	+	4.47688i	0.697476	+	0.253860i	0.0311431	+	0.999515i	$0.490085\pi$
$312$		0			0
$313$	−5.84980	−	1.03148i	−0.330651	−	0.0583026i	0.00585853	−	0.999983i	$-0.498135\pi$
$313$	−5.84980	−	1.03148i	−0.330651	−	0.0583026i	−0.336509	+	0.941680i	$0.609246\pi$
$314$		0			0
$315$	2.53843	+	4.29721i	0.143025	+	0.242120i
$316$		0			0
$317$	−19.7893	+	23.5839i	−1.11148	+	1.32461i	−0.170798	+	0.985306i	$0.554635\pi$
$317$	−19.7893	+	23.5839i	−1.11148	+	1.32461i	−0.940678	+	0.339300i	$0.889810\pi$
$318$		0			0
$319$	−1.44553	−	8.19800i	−0.0809340	−	0.459000i
$320$		0			0
$321$	21.3721	−	3.98027i	1.19288	−	0.222157i
$322$		0			0
$323$			5.60101i			0.311649i
$324$		0			0
$325$	1.46225	−	0.844230i	0.0811110	−	0.0468294i
$326$		0			0
$327$	2.92155	+	1.03173i	0.161562	+	0.0570545i
$328$		0			0
$329$	19.7124	+	16.8528i	1.08678	+	0.929126i
$330$		0			0
$331$	−13.0648	−	10.9626i	−0.718104	−	0.602561i	0.208756	−	0.977968i	$-0.433058\pi$
$331$	−13.0648	−	10.9626i	−0.718104	−	0.602561i	−0.926860	+	0.375407i	$0.877503\pi$
$332$		0			0
$333$	0.182391	−	1.16464i	0.00999498	−	0.0638221i
$334$		0			0
$335$	2.10356	−	0.765631i	0.114929	−	0.0418309i
$336$		0			0
$337$	13.1848	−	11.0634i	0.718221	−	0.602659i	−0.208671	−	0.977986i	$-0.566914\pi$
$337$	13.1848	−	11.0634i	0.718221	−	0.602659i	0.926893	+	0.375327i	$0.122469\pi$
$338$		0			0
$339$	5.65594	+	15.0876i	0.307188	+	0.819446i
$340$		0			0
$341$	17.7738			0.962504
$342$		0			0
$343$	18.5132	+	0.512260i	0.999617	+	0.0276594i
$344$		0			0
$345$	−4.61633	−	2.60651i	−0.248535	−	0.140330i
$346$		0			0
$347$	−1.58853	−	1.89314i	−0.0852770	−	0.101629i	0.721719	−	0.692186i	$-0.243352\pi$
$347$	−1.58853	−	1.89314i	−0.0852770	−	0.101629i	−0.806996	+	0.590557i	$0.798908\pi$
$348$		0			0
$349$	9.60242	−	11.4437i	0.514006	−	0.612568i	−0.445147	−	0.895458i	$-0.646848\pi$
$349$	9.60242	−	11.4437i	0.514006	−	0.612568i	0.959153	+	0.282889i	$0.0912929\pi$
$350$		0			0
$351$	0.599880	−	1.80848i	0.0320192	−	0.0965293i
$352$		0			0
$353$	−4.18500	+	23.7343i	−0.222745	+	1.26325i	0.644204	+	0.764854i	$0.277189\pi$
$353$	−4.18500	+	23.7343i	−0.222745	+	1.26325i	−0.866949	+	0.498396i	$0.833922\pi$
$354$		0			0
$355$	−3.05185	+	8.38489i	−0.161975	+	0.445024i
$356$		0			0
$357$	3.16984	+	17.9379i	0.167766	+	0.949377i
$358$		0			0
$359$	23.9777	−	13.8436i	1.26550	−	0.730635i	0.291364	−	0.956612i	$-0.405891\pi$
$359$	23.9777	−	13.8436i	1.26550	−	0.730635i	0.974133	+	0.225977i	$0.0725575\pi$
$360$		0			0
$361$	−8.50729	+	14.7351i	−0.447752	+	0.775529i
$362$		0			0
$363$	−10.0048	−	8.23276i	−0.525116	−	0.432108i
$364$		0			0
$365$	−2.57201	−	3.06521i	−0.134625	−	0.160440i
$366$		0			0
$367$	19.6544	−	23.4232i	1.02595	−	1.22268i	0.0513624	−	0.998680i	$-0.483644\pi$
$367$	19.6544	−	23.4232i	1.02595	−	1.22268i	0.974589	−	0.224001i	$-0.0719119\pi$
$368$		0			0
$369$	−0.681698	−	1.13009i	−0.0354878	−	0.0588302i
$370$		0			0
$371$	−22.9863	+	12.9901i	−1.19339	+	0.674410i
$372$		0			0
$373$	−4.21369	+	3.53570i	−0.218176	+	0.183072i	−0.745325	−	0.666701i	$-0.767706\pi$
$373$	−4.21369	+	3.53570i	−0.218176	+	0.183072i	0.527148	+	0.849773i	$0.323261\pi$
$374$		0			0
$375$	9.86356	+	3.48325i	0.509352	+	0.179874i
$376$		0			0
$377$	−1.62710			−0.0838000
$378$		0			0
$379$	−20.4096			−1.04837			−0.524185	−	0.851604i	$-0.675630\pi$
$379$	−20.4096			−1.04837			−0.524185	+	0.851604i	$0.675630\pi$
$380$		0			0
$381$	−0.703291	−	3.77634i	−0.0360307	−	0.193468i
$382$		0			0
$383$	−12.4747	+	10.4675i	−0.637426	+	0.534864i	−0.903226	−	0.429164i	$-0.858808\pi$
$383$	−12.4747	+	10.4675i	−0.637426	+	0.534864i	0.265801	+	0.964028i	$0.414364\pi$
$384$		0			0
$385$	−0.0287788	+	3.12093i	−0.00146670	+	0.159057i
$386$		0			0
$387$	−5.01392	−	25.5576i	−0.254872	−	1.29917i
$388$		0			0
$389$	10.5003	−	12.5137i	0.532385	−	0.634471i	−0.431078	−	0.902315i	$-0.641867\pi$
$389$	10.5003	−	12.5137i	0.532385	−	0.634471i	0.963462	+	0.267843i	$0.0863110\pi$
$390$		0			0
$391$	−12.4372	−	14.8220i	−0.628974	−	0.749582i
$392$		0			0
$393$	−4.89005	+	1.83315i	−0.246671	+	0.0924703i
$394$		0			0
$395$	−3.17775	+	5.50403i	−0.159890	+	0.276938i
$396$		0			0
$397$	7.93620	−	4.58196i	0.398306	−	0.229962i	−0.287447	−	0.957797i	$-0.592806\pi$
$397$	7.93620	−	4.58196i	0.398306	−	0.229962i	0.685753	+	0.727834i	$0.259473\pi$
$398$		0			0
$399$	2.20619	−	6.06849i	0.110448	−	0.303805i
$400$		0			0
$401$	6.70302	−	18.4164i	0.334733	−	0.919670i	−0.652130	−	0.758107i	$-0.726124\pi$
$401$	6.70302	−	18.4164i	0.334733	−	0.919670i	0.986862	−	0.161563i	$-0.0516535\pi$
$402$		0			0
$403$	0.603265	−	3.42129i	0.0300508	−	0.170427i
$404$		0			0
$405$	5.23975	−	2.13817i	0.260365	−	0.106246i
$406$		0			0
$407$	0.473849	−	0.564712i	0.0234878	−	0.0279917i
$408$		0			0
$409$	−10.4798	−	12.4893i	−0.518191	−	0.617556i	0.441961	−	0.897034i	$-0.354283\pi$
$409$	−10.4798	−	12.4893i	−0.518191	−	0.617556i	−0.960152	+	0.279478i	$0.909838\pi$
$410$		0			0
$411$	19.7193	−	11.6386i	0.972680	−	0.574089i
$412$		0			0
$413$	−0.251485	−	1.50739i	−0.0123748	−	0.0741739i
$414$		0			0
$415$	−2.77576			−0.136257
$416$		0			0
$417$	−23.5808	+	28.6564i	−1.15476	+	1.40331i
$418$		0			0
$419$	−6.43393	+	5.39871i	−0.314318	+	0.263744i	−0.786274	−	0.617878i	$-0.787993\pi$
$419$	−6.43393	+	5.39871i	−0.314318	+	0.263744i	0.471956	+	0.881622i	$0.343548\pi$
$420$		0			0
$421$	20.1286	−	7.32622i	0.981009	−	0.357058i	0.198777	−	0.980045i	$-0.436303\pi$
$421$	20.1286	−	7.32622i	0.981009	−	0.357058i	0.782232	+	0.622987i	$0.214081\pi$
$422$		0			0
$423$	22.1602	−	19.3311i	1.07746	−	0.939911i
$424$		0			0
$425$	14.0213	+	11.7652i	0.680131	+	0.570697i
$426$		0			0
$427$	−10.0466	+	11.7513i	−0.486191	+	0.568686i
$428$		0			0
$429$	0.905360	−	0.774610i	0.0437112	−	0.0373985i
$430$		0			0
$431$	−23.7130	+	13.6907i	−1.14222	+	0.659459i	−0.946978	−	0.321297i	$-0.895881\pi$
$431$	−23.7130	+	13.6907i	−1.14222	+	0.659459i	−0.195237	+	0.980756i	$0.562548\pi$
$432$		0			0
$433$			9.79725i			0.470826i	0.971895	+	0.235413i	$0.0756443\pi$
$433$			9.79725i			0.470826i	−0.971895	+	0.235413i	$0.924356\pi$
$434$		0			0
$435$	−3.14178	−	3.67210i	−0.150637	−	0.176064i
$436$		0			0
$437$	1.19100	+	6.75447i	0.0569730	+	0.323110i
$438$		0			0
$439$	15.3141	−	18.2506i	0.730901	−	0.871054i	−0.264740	−	0.964320i	$-0.585286\pi$
$439$	15.3141	−	18.2506i	0.730901	−	0.871054i	0.995641	+	0.0932656i	$0.0297306\pi$
$440$		0			0
$441$	3.63119	−	20.6837i	0.172914	−	0.984937i
$442$		0			0
$443$	31.9047	+	5.62567i	1.51584	+	0.267283i	0.868796	−	0.495170i	$-0.164894\pi$
$443$	31.9047	+	5.62567i	1.51584	+	0.267283i	0.647043	+	0.762453i	$0.276005\pi$
$444$		0			0
$445$	3.67764	+	1.33855i	0.174337	+	0.0634534i
$446$		0			0
$447$	−17.8676	+	21.7135i	−0.845109	+	1.02701i
$448$		0			0
$449$	−27.4242	+	15.8334i	−1.29423	+	0.747223i	−0.979401	−	0.201927i	$-0.935280\pi$
$449$	−27.4242	+	15.8334i	−1.29423	+	0.747223i	−0.314827	+	0.949149i	$0.601946\pi$
$450$		0			0
$451$		−	0.825314i		−	0.0388625i
$452$		0			0
$453$	25.2624	−	0.242373i	1.18693	−	0.0113877i
$454$		0			0
$455$	0.599773	+	0.111468i	0.0281178	+	0.00522570i
$456$		0			0
$457$	−33.4224	+	12.1648i	−1.56344	+	0.569044i	−0.971520	−	0.236956i	$-0.923850\pi$
$457$	−33.4224	+	12.1648i	−1.56344	+	0.569044i	−0.591915	+	0.806000i	$0.701628\pi$
$458$		0			0
$459$	20.6463	−	0.594400i	0.963686	−	0.0277442i
$460$		0			0
$461$	−20.6320	−	17.3123i	−0.960927	−	0.806313i	0.0201766	−	0.999796i	$-0.493577\pi$
$461$	−20.6320	−	17.3123i	−0.960927	−	0.806313i	−0.981104	+	0.193483i	$0.938022\pi$
$462$		0			0
$463$	5.46034	+	30.9671i	0.253763	+	1.43916i	0.799227	+	0.601029i	$0.205242\pi$
$463$	5.46034	+	30.9671i	0.253763	+	1.43916i	−0.545464	+	0.838134i	$0.683647\pi$
$464$		0			0
$465$	8.88613	−	5.24472i	0.412085	−	0.243218i
$466$		0			0
$467$	18.0645	+	31.2887i	0.835926	+	1.44787i	0.893274	+	0.449513i	$0.148402\pi$
$467$	18.0645	+	31.2887i	0.835926	+	1.44787i	−0.0573474	+	0.998354i	$0.518264\pi$
$468$		0			0
$469$	−8.82086	−	3.30295i	−0.407309	−	0.152516i
$470$		0			0
$471$	−8.19595	+	9.96007i	−0.377650	+	0.458936i
$472$		0			0
$473$	5.57045	−	15.3047i	0.256130	−	0.703711i
$474$		0			0
$475$	−2.21907	−	6.09684i	−0.101818	−	0.279742i
$476$		0			0
$477$	10.7773	+	27.9310i	0.493459	+	1.27887i
$478$		0			0
$479$	−9.27108	+	3.37440i	−0.423607	+	0.154180i	−0.545022	−	0.838422i	$-0.683479\pi$
$479$	−9.27108	+	3.37440i	−0.423607	+	0.154180i	0.121416	+	0.992602i	$0.461257\pi$
$480$		0			0
$481$	−0.0926187	−	0.110379i	−0.00422305	−	0.00503284i
$482$		0			0
$483$	7.63694	+	20.9580i	0.347493	+	0.953622i
$484$		0			0
$485$	3.38385	+	1.95367i	0.153653	+	0.0887114i
$486$		0			0
$487$	−5.29343	−	9.16849i	−0.239868	−	0.415464i	0.720808	−	0.693135i	$-0.243771\pi$
$487$	−5.29343	−	9.16849i	−0.239868	−	0.415464i	−0.960676	+	0.277671i	$0.910438\pi$
$488$		0			0
$489$	−6.77860	−	36.3978i	−0.306539	−	1.64597i
$490$		0			0
$491$	1.98343	−	5.44942i	0.0895107	−	0.245929i	−0.886857	−	0.462044i	$-0.847116\pi$
$491$	1.98343	−	5.44942i	0.0895107	−	0.245929i	0.976368	+	0.216115i	$0.0693386\pi$
$492$		0			0
$493$	−6.03266	−	16.5746i	−0.271697	−	0.746482i
$494$		0			0
$495$	3.49633	+	0.547550i	0.157148	+	0.0246105i
$496$		0			0
$497$	32.6862	−	18.4717i	1.46618	−	0.828567i
$498$		0			0
$499$	3.52894	+	20.0136i	0.157977	+	0.895932i	0.956014	+	0.293323i	$0.0947610\pi$
$499$	3.52894	+	20.0136i	0.157977	+	0.895932i	−0.798037	+	0.602609i	$0.794128\pi$
$500$		0			0
$501$	6.00356	−	2.25058i	0.268219	−	0.100548i
$502$		0			0
$503$	6.84793	+	11.8610i	0.305334	+	0.528854i	0.977336	−	0.211695i	$-0.0678985\pi$
$503$	6.84793	+	11.8610i	0.305334	+	0.528854i	−0.672001	+	0.740550i	$0.734565\pi$
$504$		0			0
$505$	5.28022	−	9.14561i	0.234967	−	0.406974i
$506$		0			0
$507$	11.3265	+	19.1905i	0.503028	+	0.852281i
$508$		0			0
$509$	3.69572	+	1.34513i	0.163810	+	0.0596219i	0.422623	−	0.906305i	$-0.361109\pi$
$509$	3.69572	+	1.34513i	0.163810	+	0.0596219i	−0.258814	+	0.965927i	$0.583332\pi$
$510$		0			0
$511$	−0.155243	+	16.8354i	−0.00686755	+	0.744753i
$512$		0			0
$513$	−6.44345	−	3.47683i	−0.284485	−	0.153506i
$514$		0			0
$515$	2.42006	+	0.426722i	0.106641	+	0.0188036i
$516$		0			0
$517$	18.1100	−	3.19328i	0.796477	−	0.140440i
$518$		0			0
$519$	1.03439	+	1.75257i	0.0454046	+	0.0769291i
$520$		0			0
$521$	−38.5339			−1.68820			−0.844100	−	0.536185i	$-0.819865\pi$
$521$	−38.5339			−1.68820			−0.844100	+	0.536185i	$0.819865\pi$
$522$		0			0
$523$		−	28.6821i		−	1.25418i	−0.778947	−	0.627090i	$-0.784246\pi$
$523$		−	28.6821i		−	1.25418i	0.778947	−	0.627090i	$-0.215754\pi$
$524$		0			0
$525$	−10.5573	−	18.2700i	−0.460758	−	0.797370i
$526$		0			0
$527$	37.0879	−	6.53959i	1.61557	−	0.284869i
$528$		0			0
$529$	−0.531142	−	0.445681i	−0.0230931	−	0.0193774i
$530$		0			0
$531$	−1.73253	+	0.0332475i	−0.0751853	+	0.00144282i
$532$		0			0
$533$	−0.158865	−	0.0280123i	−0.00688122	−	0.00121335i
$534$		0			0
$535$	7.77242	−	1.37049i	0.336031	−	0.0592513i
$536$		0			0
$537$	7.14382	−	1.33044i	0.308279	−	0.0574127i
$538$		0			0
$539$	8.62529	−	9.90247i	0.371518	−	0.426530i
$540$		0			0
$541$	−6.07663	+	10.5250i	−0.261255	+	0.452507i	−0.966576	−	0.256382i	$-0.917470\pi$
$541$	−6.07663	+	10.5250i	−0.261255	+	0.452507i	0.705321	+	0.708888i	$0.250803\pi$
$542$		0			0
$543$	−3.32800	+	0.619794i	−0.142818	+	0.0265979i
$544$		0			0
$545$	1.05699	+	0.384715i	0.0452767	+	0.0164794i
$546$		0			0
$547$	0.380983	−	2.16066i	0.0162897	−	0.0923832i	−0.975579	−	0.219649i	$-0.929509\pi$
$547$	0.380983	−	2.16066i	0.0162897	−	0.0923832i	0.991869	+	0.127265i	$0.0406200\pi$
$548$		0			0
$549$	11.5240	+	13.2105i	0.491834	+	0.563813i
$550$		0			0
$551$	−1.08571	+	6.15736i	−0.0462528	+	0.262313i
$552$		0			0
$553$	25.2120	−	8.91403i	1.07212	−	0.379063i
$554$		0			0
$555$	0.0702684	−	0.422156i	0.00298273	−	0.0179195i
$556$		0			0
$557$	−18.2457	−	10.5342i	−0.773096	−	0.446347i	0.0608821	−	0.998145i	$-0.480609\pi$
$557$	−18.2457	−	10.5342i	−0.773096	−	0.446347i	−0.833978	+	0.551798i	$0.813942\pi$
$558$		0			0
$559$	−2.75694	−	1.59172i	−0.116606	−	0.0673227i
$560$		0			0
$561$	11.2473	+	6.35057i	0.474863	+	0.268121i
$562$		0			0
$563$	−32.1563	+	26.9824i	−1.35523	+	1.13717i	−0.377803	+	0.925886i	$0.623320\pi$
$563$	−32.1563	+	26.9824i	−1.35523	+	1.13717i	−0.977424	+	0.211285i	$0.932235\pi$
$564$		0			0
$565$	2.00068	+	5.49683i	0.0841693	+	0.231253i
$566$		0			0
$567$	−22.6036	−	7.48838i	−0.949263	−	0.314482i
$568$		0			0
$569$	5.60812	+	15.4082i	0.235105	+	0.645945i	0.999998	+	0.00178842i	$0.000569273\pi$
$569$	5.60812	+	15.4082i	0.235105	+	0.645945i	−0.764894	+	0.644157i	$0.777209\pi$
$570$		0			0
$571$	−12.5246	+	10.5094i	−0.524138	+	0.439804i	−0.866072	−	0.499920i	$-0.833363\pi$
$571$	−12.5246	+	10.5094i	−0.524138	+	0.439804i	0.341933	+	0.939724i	$0.388918\pi$
$572$		0			0
$573$	1.67393	+	0.945149i	0.0699295	+	0.0394842i
$574$		0			0
$575$	19.4105	+	11.2067i	0.809474	+	0.467350i
$576$		0			0
$577$	−3.10380	−	1.79198i	−0.129213	−	0.0746011i	0.434000	−	0.900913i	$-0.357102\pi$
$577$	−3.10380	−	1.79198i	−0.129213	−	0.0746011i	−0.563213	+	0.826312i	$0.690435\pi$
$578$		0			0
$579$	0.654939	−	3.93472i	0.0272183	−	0.163521i
$580$		0			0
$581$	8.87726	+	7.58949i	0.368291	+	0.314865i
$582$		0			0
$583$	−3.25097	+	18.4371i	−0.134641	+	0.763588i
$584$		0			0
$585$	0.224068	−	0.654427i	0.00926409	−	0.0270572i
$586$		0			0
$587$	−6.72409	+	38.1342i	−0.277533	+	1.57397i	0.453266	+	0.891375i	$0.350259\pi$
$587$	−6.72409	+	38.1342i	−0.277533	+	1.57397i	−0.730799	+	0.682593i	$0.760852\pi$
$588$		0			0
$589$	−12.5445	−	4.56582i	−0.516886	−	0.188131i
$590$		0			0
$591$	32.3745	−	6.02930i	1.33171	−	0.248012i
$592$		0			0
$593$	−3.48794	+	6.04130i	−0.143233	+	0.248086i	−0.928712	−	0.370801i	$-0.879083\pi$
$593$	−3.48794	+	6.04130i	−0.143233	+	0.248086i	0.785479	+	0.618888i	$0.212416\pi$
$594$		0			0
$595$	1.08825	+	6.52291i	0.0446137	+	0.267413i
$596$		0			0
$597$	6.00268	−	1.11792i	0.245673	−	0.0457533i
$598$		0			0
$599$	−7.01251	+	1.23650i	−0.286524	+	0.0505218i	−0.315063	−	0.949071i	$-0.602026\pi$
$599$	−7.01251	+	1.23650i	−0.286524	+	0.0505218i	0.0285392	+	0.999593i	$0.490914\pi$
$600$		0			0
$601$	−17.0560	−	3.00744i	−0.695730	−	0.122676i	−0.185411	−	0.982661i	$-0.559362\pi$
$601$	−17.0560	−	3.00744i	−0.695730	−	0.122676i	−0.510319	+	0.859985i	$0.670473\pi$
$602$		0			0
$603$	−5.16161	+	9.35000i	−0.210197	+	0.380762i
$604$		0			0
$605$	−3.60329	−	3.02352i	−0.146495	−	0.122924i
$606$		0			0
$607$	−41.6036	+	7.33583i	−1.68864	+	0.297752i	−0.933703	−	0.358049i	$-0.883442\pi$
$607$	−41.6036	+	7.33583i	−1.68864	+	0.297752i	−0.754934	+	0.655801i	$0.772331\pi$
$608$		0			0
$609$	0.00758326	+	20.3342i	0.000307289	+	0.823982i
$610$		0			0
$611$		−	3.59439i		−	0.145414i
$612$		0			0
$613$	2.96371			0.119703			0.0598515	−	0.998207i	$-0.480937\pi$
$613$	2.96371			0.119703			0.0598515	+	0.998207i	$0.480937\pi$
$614$		0			0
$615$	−0.243535	−	0.412622i	−0.00982029	−	0.0166385i
$616$		0			0
$617$	−22.7707	+	4.01508i	−0.916713	+	0.161641i	−0.612050	−	0.790819i	$-0.709655\pi$
$617$	−22.7707	+	4.01508i	−0.916713	+	0.161641i	−0.304663	+	0.952460i	$0.598544\pi$
$618$		0			0
$619$	2.61726	+	0.461494i	0.105197	+	0.0185490i	0.225999	−	0.974128i	$-0.427436\pi$
$619$	2.61726	+	0.461494i	0.105197	+	0.0185490i	−0.120802	+	0.992677i	$0.538547\pi$
$620$		0			0
$621$	24.7717	−	5.10702i	0.994056	−	0.204938i
$622$		0			0
$623$	−8.10173	−	14.3363i	−0.324589	−	0.574371i
$624$		0			0
$625$	−18.0660	−	6.57550i	−0.722641	−	0.263020i
$626$		0			0
$627$	−2.32720	−	3.94298i	−0.0929395	−	0.157468i
$628$		0			0
$629$	0.780987	−	1.35271i	0.0311400	−	0.0539360i
$630$		0			0
$631$	−10.8636	−	18.8163i	−0.432473	−	0.749065i	0.564613	−	0.825356i	$-0.309026\pi$
$631$	−10.8636	−	18.8163i	−0.432473	−	0.749065i	−0.997086	+	0.0762910i	$0.975692\pi$
$632$		0			0
$633$	−16.6673	+	6.24815i	−0.662468	+	0.248342i
$634$		0			0
$635$	−0.242157	−	1.37334i	−0.00960973	−	0.0544995i
$636$		0			0
$637$	−1.61338	−	1.99639i	−0.0639245	−	0.0790999i
$638$		0			0
$639$	−15.3252	−	39.7174i	−0.606255	−	1.57120i
$640$		0			0
$641$	5.48719	+	15.0759i	0.216731	+	0.595464i	0.999644	−	0.0266670i	$-0.00848936\pi$
$641$	5.48719	+	15.0759i	0.216731	+	0.595464i	−0.782913	+	0.622131i	$0.786267\pi$
$642$		0			0
$643$	6.32054	−	17.3655i	0.249258	−	0.684830i	−0.750456	−	0.660920i	$-0.770166\pi$
$643$	6.32054	−	17.3655i	0.249258	−	0.684830i	0.999714	−	0.0239099i	$-0.00761148\pi$
$644$		0			0
$645$	−1.73115	−	9.29544i	−0.0681639	−	0.366008i
$646$		0			0
$647$	−12.7137	−	22.0208i	−0.499828	−	0.865727i	0.500172	−	0.865926i	$-0.333270\pi$
$647$	−12.7137	−	22.0208i	−0.499828	−	0.865727i	−1.00000		0.000199058i	$0.999937\pi$
$648$		0			0
$649$	−0.938445	−	0.541811i	−0.0368372	−	0.0212680i
$650$		0			0
$651$	−42.7592	−	7.52317i	−1.67587	−	0.294856i
$652$		0			0
$653$	10.3161	+	12.2943i	0.403700	+	0.481111i	0.929145	−	0.369717i	$-0.120545\pi$
$653$	10.3161	+	12.2943i	0.403700	+	0.481111i	−0.525444	+	0.850828i	$0.676101\pi$
$654$		0			0
$655$	−1.78158	+	0.648443i	−0.0696122	+	0.0253368i
$656$		0			0
$657$	18.8605	+	2.95368i	0.735816	+	0.115234i
$658$		0			0
$659$	−2.85356	−	7.84009i	−0.111159	−	0.305407i	0.871623	−	0.490177i	$-0.163068\pi$
$659$	−2.85356	−	7.84009i	−0.111159	−	0.305407i	−0.982782	+	0.184771i	$0.940846\pi$
$660$		0			0
$661$	6.48152	−	17.8078i	0.252102	−	0.692644i	−0.747495	−	0.664267i	$-0.768744\pi$
$661$	6.48152	−	17.8078i	0.252102	−	0.692644i	0.999597	−	0.0283771i	$-0.00903393\pi$
$662$		0			0
$663$	1.60418	−	1.94946i	0.0623010	−	0.0757108i
$664$		0			0
$665$	0.822031	−	2.19531i	0.0318770	−	0.0851306i
$666$		0			0
$667$	−10.7994	−	18.7051i	−0.418155	−	0.724266i
$668$		0			0
$669$	42.1176	−	24.8584i	1.62836	−	0.961081i
$670$		0			0
$671$	1.90364	+	10.7961i	0.0734893	+	0.416779i
$672$		0			0
$673$	−29.7861	−	24.9935i	−1.14817	−	0.963428i	−0.148493	−	0.988913i	$-0.547442\pi$
$673$	−29.7861	−	24.9935i	−1.14817	−	0.963428i	−0.999675	+	0.0254859i	$0.991887\pi$
$674$		0			0
$675$	−22.2385	+	8.82689i	−0.855961	+	0.339747i
$676$		0			0
$677$	−36.9649	+	13.4541i	−1.42067	+	0.517083i	−0.934244	−	0.356636i	$-0.883924\pi$
$677$	−36.9649	+	13.4541i	−1.42067	+	0.517083i	−0.486431	+	0.873719i	$0.661702\pi$
$678$		0			0
$679$	−5.48030	−	15.5002i	−0.210315	−	0.594844i
$680$		0			0
$681$	−12.9794	+	0.124527i	−0.497372	+	0.00477190i
$682$		0			0
$683$			15.4883i			0.592645i	0.955088	+	0.296323i	$0.0957603\pi$
$683$			15.4883i			0.592645i	−0.955088	+	0.296323i	$0.904240\pi$
$684$		0			0
$685$	7.19907	−	4.15638i	0.275062	−	0.158807i
$686$		0			0
$687$	−1.71623	+	2.08563i	−0.0654781	+	0.0795718i
$688$		0			0
$689$	3.43864	+	1.25156i	0.131002	+	0.0476807i
$690$		0			0
$691$	−38.8918	−	6.85767i	−1.47951	−	0.260878i	−0.625129	−	0.780521i	$-0.714954\pi$
$691$	−38.8918	−	6.85767i	−1.47951	−	0.260878i	−0.854383	+	0.519643i	$0.826065\pi$
$692$		0			0
$693$	−9.68465	−	11.3108i	−0.367889	−	0.429663i
$694$		0			0
$695$	−8.66016	+	10.3208i	−0.328499	+	0.391489i
$696$		0			0
$697$	−0.303662	−	1.72215i	−0.0115020	−	0.0652312i
$698$		0			0
$699$	15.0217	+	17.5573i	0.568174	+	0.664079i
$700$		0			0
$701$		−	17.7766i		−	0.671415i	−0.941966	−	0.335707i	$-0.891025\pi$
$701$		−	17.7766i		−	0.671415i	0.941966	−	0.335707i	$-0.108975\pi$
$702$		0			0
$703$	−0.479502	+	0.276841i	−0.0180848	+	0.0104412i
$704$		0			0
$705$	8.11196	−	6.94044i	0.305514	−	0.261392i
$706$		0			0
$707$	−41.8929	+	14.8117i	−1.57554	+	0.557053i
$708$		0			0
$709$	36.3063	+	30.4646i	1.36351	+	1.14412i	0.974880	+	0.222731i	$0.0714972\pi$
$709$	36.3063	+	30.4646i	1.36351	+	1.14412i	0.388633	+	0.921392i	$0.372947\pi$
$710$		0			0
$711$	−5.83733	−	29.7548i	−0.218917	−	1.11589i
$712$		0			0
$713$	43.3351	−	15.7727i	1.62291	−	0.590691i
$714$		0			0
$715$	0.331364	−	0.278047i	0.0123923	−	0.0103984i
$716$		0			0
$717$	−9.46185	+	11.4984i	−0.353359	+	0.429417i
$718$		0			0
$719$	−47.5090			−1.77179			−0.885894	−	0.463888i	$-0.846454\pi$
$719$	−47.5090			−1.77179			−0.885894	+	0.463888i	$0.846454\pi$
$720$		0			0
$721$	−6.57295	−	7.98166i	−0.244790	−	0.297253i
$722$		0			0
$723$	−15.8489	+	9.35427i	−0.589429	+	0.347889i
$724$		0			0
$725$	13.1334	+	15.6518i	0.487762	+	0.581292i
$726$		0			0
$727$	−8.50270	+	10.1331i	−0.315348	+	0.375817i	−0.900314	−	0.435241i	$-0.856663\pi$
$727$	−8.50270	+	10.1331i	−0.315348	+	0.375817i	0.584966	+	0.811057i	$0.301108\pi$
$728$		0			0
$729$	−12.1324	+	24.1206i	−0.449348	+	0.893357i
$730$		0			0
$731$	5.99253	−	33.9853i	0.221642	−	1.25699i
$732$		0			0
$733$	7.43997	−	20.4411i	0.274802	−	0.755011i	−0.723129	−	0.690713i	$-0.757297\pi$
$733$	7.43997	−	20.4411i	0.274802	−	0.755011i	0.997931	−	0.0642982i	$-0.0204809\pi$
$734$		0			0
$735$	1.39024	−	7.49598i	0.0512798	−	0.276493i
$736$		0			0
$737$	−5.78395	+	3.33937i	−0.213055	+	0.123007i
$738$		0			0
$739$	4.07174	−	7.05246i	0.149781	−	0.259429i	−0.781365	−	0.624074i	$-0.785476\pi$
$739$	4.07174	−	7.05246i	0.149781	−	0.259429i	0.931147	+	0.364645i	$0.118810\pi$
$740$		0			0
$741$	−0.837976	+	0.314135i	−0.0307838	+	0.0115400i
$742$		0			0
$743$	−20.7786	−	24.7630i	−0.762294	−	0.908466i	0.235697	−	0.971827i	$-0.424263\pi$
$743$	−20.7786	−	24.7630i	−0.762294	−	0.908466i	−0.997991	+	0.0633603i	$0.979818\pi$
$744$		0			0
$745$	−6.56196	+	7.82024i	−0.240412	+	0.286511i
$746$		0			0
$747$	9.97960	−	8.70557i	0.365134	−	0.318520i
$748$		0			0
$749$	−28.6045	−	16.8684i	−1.04518	−	0.616357i
$750$		0			0
$751$	−10.1401	+	8.50853i	−0.370016	+	0.310481i	−0.808768	−	0.588128i	$-0.799865\pi$
$751$	−10.1401	+	8.50853i	−0.370016	+	0.310481i	0.438752	+	0.898608i	$0.355421\pi$
$752$		0			0
$753$	−7.37376	−	39.5936i	−0.268715	−	1.44287i
$754$		0			0
$755$	9.17164			0.333790
$756$		0			0
$757$	−11.8523			−0.430780			−0.215390	−	0.976528i	$-0.569102\pi$
$757$	−11.8523			−0.430780			−0.215390	+	0.976528i	$0.569102\pi$
$758$		0			0
$759$	14.9140	+	5.26676i	0.541343	+	0.191171i
$760$		0			0
$761$	30.5805	−	25.6601i	1.10854	−	0.930178i	0.110573	−	0.993868i	$-0.464731\pi$
$761$	30.5805	−	25.6601i	1.10854	−	0.930178i	0.997970	+	0.0636903i	$0.0202870\pi$
$762$		0			0
$763$	−2.32853	−	4.12041i	−0.0842984	−	0.149169i
$764$		0			0
$765$	7.49713	−	0.143871i	0.271059	−	0.00520168i
$766$		0			0
$767$	−0.136146	+	0.162252i	−0.00491594	+	0.00585859i
$768$		0			0
$769$	14.9148	+	17.7747i	0.537840	+	0.640973i	0.964702	−	0.263344i	$-0.0848254\pi$
$769$	14.9148	+	17.7747i	0.537840	+	0.640973i	−0.426862	+	0.904317i	$0.640381\pi$
$770$		0			0
$771$	−16.1480	−	13.2879i	−0.581557	−	0.478552i
$772$		0			0
$773$	8.73044	−	15.1216i	0.314012	−	0.543885i	−0.665215	−	0.746652i	$-0.731660\pi$
$773$	8.73044	−	15.1216i	0.314012	−	0.543885i	0.979227	+	0.202767i	$0.0649934\pi$
$774$		0			0
$775$	−37.7802	+	21.8124i	−1.35710	+	0.783524i
$776$		0			0
$777$	−1.37899	+	1.15799i	−0.0494710	+	0.0415425i
$778$		0			0
$779$	−0.212011	+	0.582495i	−0.00759608	+	0.0208701i
$780$		0			0
$781$	4.62282	−	26.2173i	0.165418	−	0.938130i
$782$		0			0
$783$	22.8123	+	3.34867i	0.815246	+	0.119672i
$784$		0			0
$785$	−3.01000	+	3.58718i	−0.107432	+	0.128032i
$786$		0			0
$787$	−7.22694	−	8.61273i	−0.257612	−	0.307011i	0.621700	−	0.783255i	$-0.286442\pi$
$787$	−7.22694	−	8.61273i	−0.257612	−	0.307011i	−0.879313	+	0.476245i	$0.841998\pi$
$788$		0			0
$789$	−37.7222	−	21.2990i	−1.34294	−	0.758265i
$790$		0			0
$791$	8.63100	−	23.0499i	0.306883	−	0.819560i
$792$		0			0
$793$	2.14276			0.0760917
$794$		0			0
$795$	3.81512	+	10.1771i	0.135308	+	0.360944i
$796$		0			0
$797$	−37.0264	+	31.0688i	−1.31154	+	1.10051i	−0.323517	+	0.946222i	$0.604865\pi$
$797$	−37.0264	+	31.0688i	−1.31154	+	1.10051i	−0.988025	+	0.154292i	$0.950690\pi$
$798$		0			0
$799$	36.6146	−	13.3266i	1.29533	−	0.471462i
$800$		0			0
$801$	−17.4202	+	6.72167i	−0.615512	+	0.237499i
$802$		0			0
$803$	9.14504	+	7.67360i	0.322721	+	0.270795i
$804$		0			0
$805$	2.69938	+	7.63481i	0.0951407	+	0.269092i
$806$		0			0
$807$	24.9100	+	8.79679i	0.876874	+	0.309662i
$808$		0			0
$809$	40.4168	−	23.3346i	1.42098	−	0.820402i	0.424596	−	0.905383i	$-0.360416\pi$
$809$	40.4168	−	23.3346i	1.42098	−	0.820402i	0.996383	+	0.0849808i	$0.0270829\pi$
$810$		0			0
$811$			21.4580i			0.753491i	0.926317	+	0.376746i	$0.122957\pi$
$811$			21.4580i			0.753491i	−0.926317	+	0.376746i	$0.877043\pi$
$812$		0			0
$813$	36.2412	−	6.74942i	1.27103	−	0.236713i
$814$		0			0
$815$	−2.33401	−	13.2368i	−0.0817568	−	0.463666i
$816$		0			0
$817$	−7.86310	+	9.37087i	−0.275095	+	0.327845i
$818$		0			0
$819$	−2.50594	+	1.48030i	−0.0875647	+	0.0517259i
$820$		0			0
$821$	28.7816	+	5.07498i	1.00449	+	0.177118i	0.651612	−	0.758553i	$-0.274093\pi$
$821$	28.7816	+	5.07498i	1.00449	+	0.177118i	0.352874	+	0.935671i	$0.385204\pi$
$822$		0			0
$823$	1.05269	+	0.383146i	0.0366943	+	0.0133556i	0.360302	−	0.932836i	$-0.382674\pi$
$823$	1.05269	+	0.383146i	0.0366943	+	0.0133556i	−0.323608	+	0.946191i	$0.604896\pi$
$824$		0			0
$825$	−14.7590	−	2.45666i	−0.513844	−	0.0855299i
$826$		0			0
$827$	−31.2630	+	18.0497i	−1.08712	+	0.627650i	−0.932809	−	0.360372i	$-0.882650\pi$
$827$	−31.2630	+	18.0497i	−1.08712	+	0.627650i	−0.154313	+	0.988022i	$0.549316\pi$
$828$		0			0
$829$		−	17.2255i		−	0.598265i	−0.954212	−	0.299133i	$-0.903303\pi$
$829$		−	17.2255i		−	0.598265i	0.954212	−	0.299133i	$-0.0966973\pi$
$830$		0			0
$831$	−1.06840	+	1.89221i	−0.0370623	+	0.0656401i
$832$		0			0
$833$	14.3546	−	23.8367i	0.497358	−	0.825891i
$834$		0			0
$835$	2.18726	−	0.796099i	0.0756933	−	0.0275501i
$836$		0			0
$837$	−15.4991	+	46.7256i	−0.535728	+	1.61507i
$838$		0			0
$839$	−27.8026	−	23.3291i	−0.959851	−	0.805411i	0.0210778	−	0.999778i	$-0.493290\pi$
$839$	−27.8026	−	23.3291i	−0.959851	−	0.805411i	−0.980929	+	0.194367i	$0.937735\pi$
$840$		0			0
$841$	1.61676	+	9.16909i	0.0557503	+	0.316176i
$842$		0			0
$843$	−15.6954	−	8.86208i	−0.540579	−	0.305226i
$844$		0			0
$845$	4.04494	+	7.00603i	0.139150	+	0.241015i
$846$		0			0
$847$	3.25690	+	19.5218i	0.111909	+	0.670776i
$848$		0			0
$849$	−5.81249	−	15.5052i	−0.199484	−	0.532137i
$850$		0			0
$851$	0.654182	−	1.79735i	0.0224251	−	0.0616124i
$852$		0			0
$853$	−12.7651	−	35.0719i	−0.437069	−	1.20084i	−0.941390	−	0.337321i	$-0.890479\pi$
$853$	−12.7651	−	35.0719i	−0.437069	−	1.20084i	0.504320	−	0.863517i	$-0.331743\pi$
$854$		0			0
$855$	−2.32700	−	1.28461i	−0.0795819	−	0.0439327i
$856$		0			0
$857$	−32.6970	+	11.9007i	−1.11691	+	0.406521i	−0.833523	−	0.552485i	$-0.813679\pi$
$857$	−32.6970	+	11.9007i	−1.11691	+	0.406521i	−0.283385	+	0.959006i	$0.591457\pi$
$858$		0			0
$859$	−25.0043	−	29.7990i	−0.853136	−	1.01673i	−0.999621	−	0.0275149i	$-0.991241\pi$
$859$	−25.0043	−	29.7990i	−0.853136	−	1.01673i	0.146486	−	0.989213i	$-0.453204\pi$
$860$		0			0
$861$	−0.349334	+	1.98550i	−0.0119053	+	0.0676656i
$862$		0			0
$863$	11.7694	+	6.79505i	0.400634	+	0.231306i	0.686758	−	0.726886i	$-0.259033\pi$
$863$	11.7694	+	6.79505i	0.400634	+	0.231306i	−0.286123	+	0.958193i	$0.592367\pi$
$864$		0			0
$865$	0.369402	+	0.639823i	0.0125600	+	0.0217546i
$866$		0			0
$867$	−1.95847	−	0.691620i	−0.0665132	−	0.0234887i
$868$		0			0
$869$	6.48526	−	17.8181i	0.219997	−	0.604438i
$870$		0			0
$871$	0.446482	+	1.22670i	0.0151285	+	0.0415651i
$872$		0			0
$873$	−18.2931	+	3.58876i	−0.619128	+	0.121461i
$874$		0			0
$875$	−7.86143	−	13.9111i	−0.265765	−	0.470280i
$876$		0			0
$877$	4.61299	+	26.1616i	0.155770	+	0.883413i	0.958079	+	0.286505i	$0.0924934\pi$
$877$	4.61299	+	26.1616i	0.155770	+	0.883413i	−0.802309	+	0.596909i	$0.796395\pi$
$878$		0			0
$879$	25.6723	+	21.1252i	0.865904	+	0.712536i
$880$		0			0
$881$	22.4911	+	38.9557i	0.757744	+	1.31245i	0.943999	+	0.329949i	$0.107032\pi$
$881$	22.4911	+	38.9557i	0.757744	+	1.31245i	−0.186255	+	0.982501i	$0.559635\pi$
$882$		0			0
$883$	−19.4761	+	33.7336i	−0.655423	+	1.13523i	0.326365	+	0.945244i	$0.394176\pi$
$883$	−19.4761	+	33.7336i	−0.655423	+	1.13523i	−0.981788	+	0.189982i	$0.939157\pi$
$884$		0			0
$885$	−0.629061	+	0.00603534i	−0.0211457	+	0.000202876i
$886$		0			0
$887$	3.54138	+	1.28896i	0.118908	+	0.0432789i	0.400789	−	0.916170i	$-0.368736\pi$
$887$	3.54138	+	1.28896i	0.118908	+	0.0432789i	−0.281881	+	0.959449i	$0.590958\pi$
$888$		0			0
$889$	−2.98055	+	5.05425i	−0.0999644	+	0.169514i
$890$		0			0
$891$	−14.2875	+	8.99691i	−0.478650	+	0.301408i
$892$		0			0
$893$	−13.6021	−	2.39842i	−0.455177	−	0.0802599i
$894$		0			0
$895$	2.59800	−	0.458097i	0.0868415	−	0.0153125i
$896$		0			0
$897$	1.52000	−	2.69204i	0.0507514	−	0.0898846i
$898$		0			0
$899$	42.0395			1.40209
$900$		0			0
$901$			39.6682i			1.32154i
$902$		0			0
$903$	−19.8792	+	34.4614i	−0.661538	+	1.14680i
$904$		0			0
$905$	−1.21029	+	0.213408i	−0.0402316	+	0.00709391i
$906$		0			0
$907$	26.1527	+	21.9447i	0.868387	+	0.728663i	0.963758	−	0.266778i	$-0.0859592\pi$
$907$	26.1527	+	21.9447i	0.868387	+	0.728663i	−0.0953706	+	0.995442i	$0.530404\pi$
$908$		0			0
$909$	9.69943	+	49.4412i	0.321710	+	1.63986i
$910$		0			0
$911$	50.5872	+	8.91989i	1.67603	+	0.295529i	0.929225	−	0.369515i	$-0.120476\pi$
$911$	50.5872	+	8.91989i	1.67603	+	0.295529i	0.746804	+	0.665044i	$0.231587\pi$
$912$		0			0
$913$	8.15565	−	1.43806i	0.269913	−	0.0475929i
$914$		0			0
$915$	4.13747	+	4.83586i	0.136781	+	0.159869i
$916$		0			0
$917$	7.47072	+	2.79740i	0.246705	+	0.0923783i
$918$		0			0
$919$	21.6545	−	37.5066i	0.714315	−	1.23723i	−0.248908	−	0.968527i	$-0.580072\pi$
$919$	21.6545	−	37.5066i	0.714315	−	1.23723i	0.963223	−	0.268703i	$-0.0865949\pi$
$920$		0			0
$921$	14.6491	−	41.4822i	0.482706	−	1.36689i
$922$		0			0
$923$	−4.88969	−	1.77970i	−0.160946	−	0.0585796i
$924$		0			0
$925$	−0.314193	+	1.78188i	−0.0103306	+	0.0585877i
$926$		0			0
$927$	−10.0391	+	6.05583i	−0.329727	+	0.198899i
$928$		0			0
$929$	−4.20184	+	23.8298i	−0.137858	+	0.781830i	0.834969	+	0.550297i	$0.185485\pi$
$929$	−4.20184	+	23.8298i	−0.137858	+	0.781830i	−0.972827	+	0.231533i	$0.925626\pi$
$930$		0			0
$931$	−8.63140	+	4.77332i	−0.282883	+	0.156439i
$932$		0			0
$933$	−21.2291	+	7.95821i	−0.695008	+	0.260540i
$934$		0			0
$935$	4.06091	+	2.34457i	0.132806	+	0.0766756i
$936$		0			0
$937$	37.1975	+	21.4760i	1.21519	+	0.701590i	0.963885	−	0.266318i	$-0.0858072\pi$
$937$	37.1975	+	21.4760i	1.21519	+	0.701590i	0.251304	+	0.967908i	$0.419141\pi$
$938$		0			0
$939$	8.86031	−	5.22948i	0.289145	−	0.170658i
$940$		0			0
$941$	27.9910	−	23.4872i	0.912479	−	0.765661i	−0.0601099	−	0.998192i	$-0.519145\pi$
$941$	27.9910	−	23.4872i	0.912479	−	0.765661i	0.972589	+	0.232531i	$0.0747007\pi$
$942$		0			0
$943$	−0.732394	−	2.01224i	−0.0238500	−	0.0655275i
$944$		0			0
$945$	−8.17954	−	2.79717i	−0.266080	−	0.0909920i
$946$		0			0
$947$	−17.6951	−	48.6169i	−0.575014	−	1.57984i	−0.796477	−	0.604669i	$-0.793306\pi$
$947$	−17.6951	−	48.6169i	−0.575014	−	1.57984i	0.221463	−	0.975169i	$-0.428917\pi$
$948$		0			0
$949$	1.78749	−	1.49988i	0.0580244	−	0.0486883i
$950$		0			0
$951$	−0.511578	−	53.3216i	−0.0165891	−	1.72907i
$952$		0			0
$953$	−26.8149	−	15.4816i	−0.868620	−	0.501498i	−0.00173046	−	0.999999i	$-0.500551\pi$
$953$	−26.8149	−	15.4816i	−0.868620	−	0.501498i	−0.866889	+	0.498501i	$0.833884\pi$
$954$		0			0
$955$	0.604382	+	0.348940i	0.0195573	+	0.0112914i
$956$		0			0
$957$	11.1335	+	9.16157i	0.359896	+	0.296152i
$958$		0			0
$959$	−34.3880	−	6.39103i	−1.11045	−	0.206377i
$960$		0			0
$961$	−10.2035	+	57.8669i	−0.329145	+	1.86667i
$962$		0			0
$963$	−23.6457	+	29.3038i	−0.761972	+	0.944302i
$964$		0			0
$965$	0.251461	−	1.42611i	0.00809483	−	0.0459081i
$966$		0			0
$967$	42.8851	+	15.6089i	1.37909	+	0.501948i	0.921903	−	0.387421i	$-0.126634\pi$
$967$	42.8851	+	15.6089i	1.37909	+	0.501948i	0.457189	+	0.889369i	$0.348856\pi$
$968$		0			0
$969$	−6.30685	−	7.37141i	−0.202605	−	0.236804i
$970$		0			0
$971$	−8.12697	+	14.0763i	−0.260807	+	0.451731i	−0.966457	−	0.256830i	$-0.917322\pi$
$971$	−8.12697	+	14.0763i	−0.260807	+	0.451731i	0.705650	+	0.708561i	$0.250655\pi$
$972$		0			0
$973$	55.9155	−	9.32864i	1.79257	−	0.299062i
$974$		0			0
$975$	−0.973826	+	2.75760i	−0.0311874	+	0.0883138i
$976$		0			0
$977$	−2.34163	+	0.412893i	−0.0749154	+	0.0132096i	−0.210980	−	0.977490i	$-0.567666\pi$
$977$	−2.34163	+	0.412893i	−0.0749154	+	0.0132096i	0.136065	+	0.990700i	$0.456554\pi$
$978$		0			0
$979$	−11.4990	−	2.02758i	−0.367510	−	0.0648019i
$980$		0			0
$981$	−5.00676	+	1.93188i	−0.159853	+	0.0616803i
$982$		0			0
$983$	−22.9817	−	19.2840i	−0.733004	−	0.615063i	0.197945	−	0.980213i	$-0.436573\pi$
$983$	−22.9817	−	19.2840i	−0.733004	−	0.615063i	−0.930949	+	0.365150i	$0.881018\pi$
$984$		0			0
$985$	11.7736	−	2.07601i	0.375139	−	0.0661472i
$986$		0			0
$987$	−44.9198	+	0.0167520i	−1.42981	+	0.000533222i
$988$		0			0
$989$		−	42.2584i		−	1.34374i
$990$		0			0
$991$	28.7117			0.912058			0.456029	−	0.889965i	$-0.349271\pi$
$991$	28.7117			0.912058			0.456029	+	0.889965i	$0.349271\pi$
$992$		0			0
$993$	29.5385	−	0.283398i	0.937375	−	0.00899337i
$994$		0			0
$995$	2.18300	−	0.384921i	0.0692057	−	0.0122028i
$996$		0			0
$997$	37.4768	+	6.60817i	1.18690	+	0.209283i	0.732029	−	0.681273i	$-0.238573\pi$
$997$	37.4768	+	6.60817i	1.18690	+	0.209283i	0.454873	+	0.890556i	$0.349685\pi$
$998$		0			0
$999$	1.07137	+	1.73815i	0.0338966	+	0.0549926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ca.a.173.6	✓	144
7.3	odd	6		756.2.ck.a.605.3	yes	144
27.5	odd	18		756.2.ck.a.5.3	yes	144
189.59	even	18	inner	756.2.ca.a.437.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.6	✓	144	1.1	even	1	trivial
756.2.ca.a.437.6	yes	144	189.59	even	18	inner
756.2.ck.a.5.3	yes	144	27.5	odd	18
756.2.ck.a.605.3	yes	144	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ca (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31609 + 1.12602i) q^{3} +(-0.481690 + 0.404186i) q^{5} +(2.64564 + 0.0243961i) q^{7} +(0.464163 - 2.96387i) q^{9} +O(q^{10})\)	\(q+(-1.31609 + 1.12602i) q^{3} +(-0.481690 + 0.404186i) q^{5} +(2.64564 + 0.0243961i) q^{7} +(0.464163 - 2.96387i) q^{9} +(1.20589 - 1.43712i) q^{11} +(-0.235703 - 0.280900i) q^{13} +(0.178824 - 1.07434i) q^{15} +(1.98751 - 3.44247i) q^{17} +(-1.22027 + 0.704525i) q^{19} +(-3.50936 + 2.94693i) q^{21} +(1.66481 - 4.57403i) q^{23} +(-0.799582 + 4.53465i) q^{25} +(2.72650 + 4.42337i) q^{27} +(2.85223 - 3.39915i) q^{29} +(6.08987 + 7.25762i) q^{31} +(0.0311738 + 3.24923i) q^{33} +(-1.28424 + 1.05758i) q^{35} +0.392947 q^{37} +(0.626504 + 0.104282i) q^{39} +(0.337003 - 0.282779i) q^{41} +(8.15803 - 2.96928i) q^{43} +(0.974373 + 1.61528i) q^{45} +(7.50900 + 6.30080i) q^{47} +(6.99881 + 0.129086i) q^{49} +(1.26055 + 6.76857i) q^{51} +(-8.64238 + 4.98968i) q^{53} +1.17965i q^{55} +(0.812676 - 2.30127i) q^{57} +(-0.100302 - 0.568840i) q^{59} +(-3.75615 + 4.47641i) q^{61} +(1.30031 - 7.83002i) q^{63} +(0.227072 + 0.0400389i) q^{65} +(-3.34534 - 1.21760i) q^{67} +(2.95941 + 7.89443i) q^{69} +(12.2893 - 7.09525i) q^{71} +6.36345i q^{73} +(-4.05379 - 6.86834i) q^{75} +(3.22540 - 3.77268i) q^{77} +(9.49778 - 3.45691i) q^{79} +(-8.56911 - 2.75144i) q^{81} +(3.38160 + 2.83750i) q^{83} +(0.434034 + 2.46153i) q^{85} +(0.0737338 + 7.68524i) q^{87} +(-3.11200 - 5.39014i) q^{89} +(-0.616733 - 0.748910i) q^{91} +(-16.1870 - 2.69435i) q^{93} +(0.303034 - 0.832580i) q^{95} +(-2.12529 - 5.83919i) q^{97} +(-3.69972 - 4.24116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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