LMFDB - Embedded newform 945.2.m.a.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(323,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("945.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.m (of order $4$, degree $2$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.4
Character	$\chi$	$=$	945.323
Dual form			945.2.m.a.512.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66804 - 1.66804i) q^{2} +3.56469i q^{4} +(0.420676 + 2.19614i) q^{5} +(0.707107 - 0.707107i) q^{7} +(2.60996 - 2.60996i) q^{8} +O(q^{10})$	\(q+(-1.66804 - 1.66804i) q^{2} +3.56469i q^{4} +(0.420676 + 2.19614i) q^{5} +(0.707107 - 0.707107i) q^{7} +(2.60996 - 2.60996i) q^{8} +(2.96154 - 4.36494i) q^{10} +3.90505i q^{11} +(3.99143 + 3.99143i) q^{13} -2.35896 q^{14} -1.57763 q^{16} +(-5.52768 - 5.52768i) q^{17} +2.04710i q^{19} +(-7.82856 + 1.49958i) q^{20} +(6.51376 - 6.51376i) q^{22} +(-0.704206 + 0.704206i) q^{23} +(-4.64606 + 1.84773i) q^{25} -13.3157i q^{26} +(2.52062 + 2.52062i) q^{28} -3.13979 q^{29} -5.10144 q^{31} +(-2.58837 - 2.58837i) q^{32} +18.4407i q^{34} +(1.85037 + 1.25544i) q^{35} +(2.61698 - 2.61698i) q^{37} +(3.41463 - 3.41463i) q^{38} +(6.82978 + 4.63389i) q^{40} +7.05389i q^{41} +(-4.64400 - 4.64400i) q^{43} -13.9203 q^{44} +2.34928 q^{46} +(5.17704 + 5.17704i) q^{47} -1.00000i q^{49} +(10.8319 + 4.66772i) q^{50} +(-14.2282 + 14.2282i) q^{52} +(-4.29145 + 4.29145i) q^{53} +(-8.57603 + 1.64276i) q^{55} -3.69104i q^{56} +(5.23729 + 5.23729i) q^{58} -6.73665 q^{59} -14.6189 q^{61} +(8.50938 + 8.50938i) q^{62} +11.7903i q^{64} +(-7.08663 + 10.4448i) q^{65} +(-2.23789 + 2.23789i) q^{67} +(19.7045 - 19.7045i) q^{68} +(-0.992359 - 5.18061i) q^{70} +8.03487i q^{71} +(8.12090 + 8.12090i) q^{73} -8.73044 q^{74} -7.29726 q^{76} +(2.76129 + 2.76129i) q^{77} -5.60247i q^{79} +(-0.663673 - 3.46470i) q^{80} +(11.7661 - 11.7661i) q^{82} +(9.62012 - 9.62012i) q^{83} +(9.81419 - 14.4649i) q^{85} +15.4927i q^{86} +(10.1920 + 10.1920i) q^{88} +15.0877 q^{89} +5.64473 q^{91} +(-2.51028 - 2.51028i) q^{92} -17.2710i q^{94} +(-4.49571 + 0.861165i) q^{95} +(-1.81595 + 1.81595i) q^{97} +(-1.66804 + 1.66804i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 32 q^{10} + 8 q^{13} - 56 q^{16} + 16 q^{22} + 16 q^{25} + 48 q^{31} + 64 q^{37} - 16 q^{40} - 56 q^{43} - 8 q^{46} - 48 q^{52} - 64 q^{55} - 40 q^{58} - 32 q^{61} - 16 q^{70} + 16 q^{73} - 8 q^{76} - 16 q^{82} + 48 q^{85} - 24 q^{88} - 48 q^{97}+O(q^{100}) $ 48 * q - 32 * q^10 + 8 * q^13 - 56 * q^16 + 16 * q^22 + 16 * q^25 + 48 * q^31 + 64 * q^37 - 16 * q^40 - 56 * q^43 - 8 * q^46 - 48 * q^52 - 64 * q^55 - 40 * q^58 - 32 * q^61 - 16 * q^70 + 16 * q^73 - 8 * q^76 - 16 * q^82 + 48 * q^85 - 24 * q^88 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.66804	−	1.66804i	−1.17948	−	1.17948i	−0.979877	−	0.199603i	$-0.936035\pi$
$2$	−1.66804	−	1.66804i	−1.17948	−	1.17948i	−0.199603	−	0.979877i	$-0.563965\pi$
$3$		0			0
$3$		0			0
$4$			3.56469i			1.78234i
$5$	0.420676	+	2.19614i	0.188132	+	0.982144i
$5$	0.420676	+	2.19614i	0.188132	+	0.982144i
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	2.60996	−	2.60996i	0.922760	−	0.922760i
$9$		0			0
$10$	2.96154	−	4.36494i	0.936520	−	1.38032i
$11$			3.90505i			1.17742i	0.808346	+	0.588708i	$0.200363\pi$
$11$			3.90505i			1.17742i	−0.808346	+	0.588708i	$0.799637\pi$
$12$		0			0
$13$	3.99143	+	3.99143i	1.10702	+	1.10702i	0.993540	+	0.113482i	$0.0362005\pi$
$13$	3.99143	+	3.99143i	1.10702	+	1.10702i	0.113482	+	0.993540i	$0.463799\pi$
$14$	−2.35896			−0.630458
$15$		0			0
$16$	−1.57763			−0.394408
$17$	−5.52768	−	5.52768i	−1.34066	−	1.34066i	−0.895404	−	0.445255i	$-0.853113\pi$
$17$	−5.52768	−	5.52768i	−1.34066	−	1.34066i	−0.445255	−	0.895404i	$-0.646887\pi$
$18$		0			0
$19$			2.04710i			0.469636i	0.972039	+	0.234818i	$0.0754494\pi$
$19$			2.04710i			0.469636i	−0.972039	+	0.234818i	$0.924551\pi$
$20$	−7.82856	+	1.49958i	−1.75052	+	0.335317i
$21$		0			0
$22$	6.51376	−	6.51376i	1.38874	−	1.38874i
$23$	−0.704206	+	0.704206i	−0.146837	+	0.146837i	−0.776703	−	0.629866i	$-0.783110\pi$
$23$	−0.704206	+	0.704206i	−0.146837	+	0.146837i	0.629866	+	0.776703i	$0.283110\pi$
$24$		0			0
$25$	−4.64606	+	1.84773i	−0.929213	+	0.369546i
$26$		−	13.3157i		−	2.61142i
$27$		0			0
$28$	2.52062	+	2.52062i	0.476352	+	0.476352i
$29$	−3.13979			−0.583045			−0.291523	−	0.956564i	$-0.594162\pi$
$29$	−3.13979			−0.583045			−0.291523	+	0.956564i	$0.594162\pi$
$30$		0			0
$31$	−5.10144			−0.916245			−0.458122	−	0.888889i	$-0.651478\pi$
$31$	−5.10144			−0.916245			−0.458122	+	0.888889i	$0.651478\pi$
$32$	−2.58837	−	2.58837i	−0.457563	−	0.457563i
$33$		0			0
$34$			18.4407i			3.16256i
$35$	1.85037	+	1.25544i	0.312769	+	0.212208i
$36$		0			0
$37$	2.61698	−	2.61698i	0.430229	−	0.430229i	−0.458477	−	0.888706i	$-0.651605\pi$
$37$	2.61698	−	2.61698i	0.430229	−	0.430229i	0.888706	+	0.458477i	$0.151605\pi$
$38$	3.41463	−	3.41463i	0.553926	−	0.553926i
$39$		0			0
$40$	6.82978	+	4.63389i	1.07988	+	0.732682i
$41$			7.05389i			1.10163i	0.834627	+	0.550816i	$0.185684\pi$
$41$			7.05389i			1.10163i	−0.834627	+	0.550816i	$0.814316\pi$
$42$		0			0
$43$	−4.64400	−	4.64400i	−0.708204	−	0.708204i	0.257953	−	0.966157i	$-0.416952\pi$
$43$	−4.64400	−	4.64400i	−0.708204	−	0.708204i	−0.966157	+	0.257953i	$0.916952\pi$
$44$	−13.9203			−2.09856
$45$		0			0
$46$	2.34928			0.346383
$47$	5.17704	+	5.17704i	0.755149	+	0.755149i	0.975435	−	0.220286i	$-0.0706991\pi$
$47$	5.17704	+	5.17704i	0.755149	+	0.755149i	−0.220286	+	0.975435i	$0.570699\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	10.8319	+	4.66772i	1.53186	+	0.660116i
$51$		0			0
$52$	−14.2282	+	14.2282i	−1.97310	+	1.97310i
$53$	−4.29145	+	4.29145i	−0.589476	+	0.589476i	−0.937489	−	0.348014i	$-0.886856\pi$
$53$	−4.29145	+	4.29145i	−0.589476	+	0.589476i	0.348014	+	0.937489i	$0.386856\pi$
$54$		0			0
$55$	−8.57603	+	1.64276i	−1.15639	+	0.221510i
$56$		−	3.69104i		−	0.493236i
$57$		0			0
$58$	5.23729	+	5.23729i	0.687690	+	0.687690i
$59$	−6.73665			−0.877037			−0.438518	−	0.898722i	$-0.644497\pi$
$59$	−6.73665			−0.877037			−0.438518	+	0.898722i	$0.644497\pi$
$60$		0			0
$61$	−14.6189			−1.87176			−0.935882	−	0.352315i	$-0.885395\pi$
$61$	−14.6189			−1.87176			−0.935882	+	0.352315i	$0.885395\pi$
$62$	8.50938	+	8.50938i	1.08069	+	1.08069i
$63$		0			0
$64$			11.7903i			1.47378i
$65$	−7.08663	+	10.4448i	−0.878988	+	1.29552i
$66$		0			0
$67$	−2.23789	+	2.23789i	−0.273402	+	0.273402i	−0.830468	−	0.557066i	$-0.811927\pi$
$67$	−2.23789	+	2.23789i	−0.273402	+	0.273402i	0.557066	+	0.830468i	$0.311927\pi$
$68$	19.7045	−	19.7045i	2.38952	−	2.38952i
$69$		0			0
$70$	−0.992359	−	5.18061i	−0.118610	−	0.619201i
$71$			8.03487i			0.953563i	0.879022	+	0.476782i	$0.158197\pi$
$71$			8.03487i			0.953563i	−0.879022	+	0.476782i	$0.841803\pi$
$72$		0			0
$73$	8.12090	+	8.12090i	0.950479	+	0.950479i	0.998830	−	0.0483513i	$-0.0153967\pi$
$73$	8.12090	+	8.12090i	0.950479	+	0.950479i	−0.0483513	+	0.998830i	$0.515397\pi$
$74$	−8.73044			−1.01489
$75$		0			0
$76$	−7.29726			−0.837053
$77$	2.76129	+	2.76129i	0.314678	+	0.314678i
$78$		0			0
$79$		−	5.60247i		−	0.630327i	−0.949037	−	0.315163i	$-0.897941\pi$
$79$		−	5.60247i		−	0.630327i	0.949037	−	0.315163i	$-0.102059\pi$
$80$	−0.663673	−	3.46470i	−0.0742009	−	0.387366i
$81$		0			0
$82$	11.7661	−	11.7661i	1.29935	−	1.29935i
$83$	9.62012	−	9.62012i	1.05595	−	1.05595i	0.0576065	−	0.998339i	$-0.481653\pi$
$83$	9.62012	−	9.62012i	1.05595	−	1.05595i	0.998339	−	0.0576065i	$-0.0183469\pi$
$84$		0			0
$85$	9.81419	−	14.4649i	1.06450	−	1.56894i
$86$			15.4927i			1.67062i
$87$		0			0
$88$	10.1920	+	10.1920i	1.08647	+	1.08647i
$89$	15.0877			1.59929			0.799645	−	0.600473i	$-0.205021\pi$
$89$	15.0877			1.59929			0.799645	+	0.600473i	$0.205021\pi$
$90$		0			0
$91$	5.64473			0.591728
$92$	−2.51028	−	2.51028i	−0.261714	−	0.261714i
$93$		0			0
$94$		−	17.2710i		−	1.78137i
$95$	−4.49571	+	0.861165i	−0.461250	+	0.0883537i
$96$		0			0
$97$	−1.81595	+	1.81595i	−0.184382	+	0.184382i	−0.793262	−	0.608880i	$-0.791619\pi$
$97$	−1.81595	+	1.81595i	−0.184382	+	0.184382i	0.608880	+	0.793262i	$0.291619\pi$
$98$	−1.66804	+	1.66804i	−0.168497	+	0.168497i
$99$		0			0
$100$	−6.58658	−	16.5618i	−0.658658	−	1.65618i
$101$		−	4.26831i		−	0.424713i	−0.977192	−	0.212357i	$-0.931886\pi$
$101$		−	4.26831i		−	0.424713i	0.977192	−	0.212357i	$-0.0681138\pi$
$102$		0			0
$103$	3.69083	+	3.69083i	0.363668	+	0.363668i	0.865162	−	0.501493i	$-0.167216\pi$
$103$	3.69083	+	3.69083i	0.363668	+	0.363668i	−0.501493	+	0.865162i	$0.667216\pi$
$104$	20.8349			2.04303
$105$		0			0
$106$	14.3166			1.39055
$107$	0.238838	+	0.238838i	0.0230894	+	0.0230894i	0.718557	−	0.695468i	$-0.244803\pi$
$107$	0.238838	+	0.238838i	0.0230894	+	0.0230894i	−0.695468	+	0.718557i	$0.744803\pi$
$108$		0			0
$109$			16.4616i			1.57674i	0.615205	+	0.788368i	$0.289073\pi$
$109$			16.4616i			1.57674i	−0.615205	+	0.788368i	$0.710927\pi$
$110$	17.0453	+	11.5649i	1.62521	+	1.10267i
$111$		0			0
$112$	−1.11556	+	1.11556i	−0.105410	+	0.105410i
$113$	5.14772	−	5.14772i	0.484257	−	0.484257i	−0.422231	−	0.906488i	$-0.638753\pi$
$113$	5.14772	−	5.14772i	0.484257	−	0.484257i	0.906488	+	0.422231i	$0.138753\pi$
$114$		0			0
$115$	−1.84278	−	1.25029i	−0.171840	−	0.116590i
$116$		−	11.1924i		−	1.03919i
$117$		0			0
$118$	11.2370	+	11.2370i	1.03445	+	1.03445i
$119$	−7.81732			−0.716612
$120$		0			0
$121$	−4.24941			−0.386310
$122$	24.3849	+	24.3849i	2.20771	+	2.20771i
$123$		0			0
$124$		−	18.1850i		−	1.63306i
$125$	−6.01236	−	9.42611i	−0.537762	−	0.843097i
$126$		0			0
$127$	−6.88044	+	6.88044i	−0.610541	+	0.610541i	−0.943087	−	0.332546i	$-0.892092\pi$
$127$	−6.88044	+	6.88044i	−0.610541	+	0.610541i	0.332546	+	0.943087i	$0.392092\pi$
$128$	14.4898	−	14.4898i	1.28073	−	1.28073i
$129$		0			0
$130$	29.2431	−	5.60160i	2.56479	−	0.491292i
$131$		−	3.13327i		−	0.273755i	−0.990588	−	0.136878i	$-0.956293\pi$
$131$		−	3.13327i		−	0.273755i	0.990588	−	0.136878i	$-0.0437067\pi$
$132$		0			0
$133$	1.44752	+	1.44752i	0.125515	+	0.125515i
$134$	7.46577			0.644944
$135$		0			0
$136$	−28.8540			−2.47421
$137$	9.84944	+	9.84944i	0.841494	+	0.841494i	0.989053	−	0.147559i	$-0.0471417\pi$
$137$	9.84944	+	9.84944i	0.841494	+	0.841494i	−0.147559	+	0.989053i	$0.547142\pi$
$138$		0			0
$139$		−	1.05274i		−	0.0892922i	−0.999003	−	0.0446461i	$-0.985784\pi$
$139$		−	1.05274i		−	0.0892922i	0.999003	−	0.0446461i	$-0.0142160\pi$
$140$	−4.47526	+	6.59599i	−0.378229	+	0.557463i
$141$		0			0
$142$	13.4025	−	13.4025i	1.12471	−	1.12471i
$143$	−15.5867	+	15.5867i	−1.30343	+	1.30343i
$144$		0			0
$145$	−1.32084	−	6.89543i	−0.109690	−	0.572634i
$146$		−	27.0919i		−	2.24214i
$147$		0			0
$148$	9.32873	+	9.32873i	0.766817	+	0.766817i
$149$	8.00615			0.655889			0.327944	−	0.944697i	$-0.393644\pi$
$149$	8.00615			0.655889			0.327944	+	0.944697i	$0.393644\pi$
$150$		0			0
$151$	−13.5211			−1.10034			−0.550168	−	0.835054i	$-0.685436\pi$
$151$	−13.5211			−1.10034			−0.550168	+	0.835054i	$0.685436\pi$
$152$	5.34284	+	5.34284i	0.433361	+	0.433361i
$153$		0			0
$154$		−	9.21185i		−	0.742312i
$155$	−2.14605	−	11.2035i	−0.172375	−	0.899884i
$156$		0			0
$157$	−4.38312	+	4.38312i	−0.349811	+	0.349811i	−0.860039	−	0.510228i	$-0.829561\pi$
$157$	−4.38312	+	4.38312i	−0.349811	+	0.349811i	0.510228	+	0.860039i	$0.329561\pi$
$158$	−9.34512	+	9.34512i	−0.743457	+	0.743457i
$159$		0			0
$160$	4.59556	−	6.77329i	0.363311	−	0.535475i
$161$			0.995898i			0.0784877i
$162$		0			0
$163$	−15.4170	−	15.4170i	−1.20755	−	1.20755i	−0.971817	−	0.235737i	$-0.924250\pi$
$163$	−15.4170	−	15.4170i	−1.20755	−	1.20755i	−0.235737	−	0.971817i	$-0.575750\pi$
$164$	−25.1449			−1.96349
$165$		0			0
$166$	−32.0934			−2.49093
$167$	−3.58358	−	3.58358i	−0.277305	−	0.277305i	0.554727	−	0.832032i	$-0.312823\pi$
$167$	−3.58358	−	3.58358i	−0.277305	−	0.277305i	−0.832032	+	0.554727i	$0.812823\pi$
$168$		0			0
$169$			18.8630i			1.45100i
$170$	−40.4984	+	7.75758i	−3.10609	+	0.594979i
$171$		0			0
$172$	16.5544	−	16.5544i	1.26226	−	1.26226i
$173$	−5.50833	+	5.50833i	−0.418791	+	0.418791i	−0.884787	−	0.465996i	$-0.845696\pi$
$173$	−5.50833	+	5.50833i	−0.418791	+	0.418791i	0.465996	+	0.884787i	$0.345696\pi$
$174$		0			0
$175$	−1.97872	+	4.59180i	−0.149577	+	0.347108i
$176$		−	6.16073i		−	0.464383i
$177$		0			0
$178$	−25.1668	−	25.1668i	−1.88633	−	1.88633i
$179$	−14.4269			−1.07831			−0.539157	−	0.842205i	$-0.681257\pi$
$179$	−14.4269			−1.07831			−0.539157	+	0.842205i	$0.681257\pi$
$180$		0			0
$181$	2.51038			0.186595			0.0932976	−	0.995638i	$-0.470259\pi$
$181$	2.51038			0.186595			0.0932976	+	0.995638i	$0.470259\pi$
$182$	−9.41561	−	9.41561i	−0.697932	−	0.697932i
$183$		0			0
$184$			3.67590i			0.270991i
$185$	6.84816	+	4.64635i	0.503487	+	0.341607i
$186$		0			0
$187$	21.5859	−	21.5859i	1.57851	−	1.57851i
$188$	−18.4546	+	18.4546i	−1.34594	+	1.34594i
$189$		0			0
$190$	8.93546	+	6.06255i	0.648246	+	0.439824i
$191$			26.2610i			1.90018i	0.311980	+	0.950089i	$0.399008\pi$
$191$			26.2610i			1.90018i	−0.311980	+	0.950089i	$0.600992\pi$
$192$		0			0
$193$	−5.62533	−	5.62533i	−0.404920	−	0.404920i	0.475043	−	0.879963i	$-0.342433\pi$
$193$	−5.62533	−	5.62533i	−0.404920	−	0.404920i	−0.879963	+	0.475043i	$0.842433\pi$
$194$	6.05815			0.434950
$195$		0			0
$196$	3.56469			0.254621
$197$	12.4533	+	12.4533i	0.887262	+	0.887262i	0.994259	−	0.106997i	$-0.0341235\pi$
$197$	12.4533	+	12.4533i	0.887262	+	0.887262i	−0.106997	+	0.994259i	$0.534124\pi$
$198$		0			0
$199$			13.6955i			0.970850i	0.874278	+	0.485425i	$0.161335\pi$
$199$			13.6955i			0.970850i	−0.874278	+	0.485425i	$0.838665\pi$
$200$	−7.30354	+	16.9485i	−0.516438	+	1.19844i
$201$		0			0
$202$	−7.11970	+	7.11970i	−0.500941	+	0.500941i
$203$	−2.22017	+	2.22017i	−0.155825	+	0.155825i
$204$		0			0
$205$	−15.4913	+	2.96741i	−1.08196	+	0.207253i
$206$		−	12.3129i		−	0.857879i
$207$		0			0
$208$	−6.29701	−	6.29701i	−0.436619	−	0.436619i
$209$	−7.99401			−0.552957
$210$		0			0
$211$	3.18450			0.219230			0.109615	−	0.993974i	$-0.465038\pi$
$211$	3.18450			0.219230			0.109615	+	0.993974i	$0.465038\pi$
$212$	−15.2977	−	15.2977i	−1.05065	−	1.05065i
$213$		0			0
$214$		−	0.796782i		−	0.0544669i
$215$	8.24526	−	12.1525i	0.562322	−	0.828794i
$216$		0			0
$217$	−3.60726	+	3.60726i	−0.244877	+	0.244877i
$218$	27.4585	−	27.4585i	1.85973	−	1.85973i
$219$		0			0
$220$	−5.85594	−	30.5709i	−0.394807	−	2.06109i
$221$		−	44.1266i		−	2.96828i
$222$		0			0
$223$	1.84405	+	1.84405i	0.123487	+	0.123487i	0.766149	−	0.642663i	$-0.222170\pi$
$223$	1.84405	+	1.84405i	0.123487	+	0.123487i	−0.642663	+	0.766149i	$0.722170\pi$
$224$	−3.66051			−0.244578
$225$		0			0
$226$	−17.1732			−1.14234
$227$	−13.2171	−	13.2171i	−0.877246	−	0.877246i	0.116002	−	0.993249i	$-0.462992\pi$
$227$	−13.2171	−	13.2171i	−0.877246	−	0.877246i	−0.993249	+	0.116002i	$0.962992\pi$
$228$		0			0
$229$			13.5368i			0.894539i	0.894399	+	0.447269i	$0.147603\pi$
$229$			13.5368i			0.894539i	−0.894399	+	0.447269i	$0.852397\pi$
$230$	0.988288	+	5.15935i	0.0651658	+	0.340198i
$231$		0			0
$232$	−8.19473	+	8.19473i	−0.538011	+	0.538011i
$233$	−9.27067	+	9.27067i	−0.607342	+	0.607342i	−0.942251	−	0.334909i	$-0.891295\pi$
$233$	−9.27067	+	9.27067i	−0.607342	+	0.607342i	0.334909	+	0.942251i	$0.391295\pi$
$234$		0			0
$235$	−9.19165	+	13.5474i	−0.599597	+	0.883733i
$236$		−	24.0141i		−	1.56318i
$237$		0			0
$238$	13.0396	+	13.0396i	0.845230	+	0.845230i
$239$	0.288582			0.0186668			0.00933342	−	0.999956i	$-0.497029\pi$
$239$	0.288582			0.0186668			0.00933342	+	0.999956i	$0.497029\pi$
$240$		0			0
$241$	19.8169			1.27652			0.638260	−	0.769821i	$-0.279655\pi$
$241$	19.8169			1.27652			0.638260	+	0.769821i	$0.279655\pi$
$242$	7.08816	+	7.08816i	0.455644	+	0.455644i
$243$		0			0
$244$		−	52.1120i		−	3.33613i
$245$	2.19614	−	0.420676i	0.140306	−	0.0268760i
$246$		0			0
$247$	−8.17083	+	8.17083i	−0.519897	+	0.519897i
$248$	−13.3145	+	13.3145i	−0.845474	+	0.845474i
$249$		0			0
$250$	−5.69425	+	25.7519i	−0.360136	+	1.62869i
$251$		−	12.6962i		−	0.801375i	−0.916215	−	0.400687i	$-0.868771\pi$
$251$		−	12.6962i		−	0.801375i	0.916215	−	0.400687i	$-0.131229\pi$
$252$		0			0
$253$	−2.74996	−	2.74996i	−0.172888	−	0.172888i
$254$	22.9537			1.44024
$255$		0			0
$256$	−24.7586			−1.54741
$257$	14.4016	+	14.4016i	0.898348	+	0.898348i	0.995290	−	0.0969421i	$-0.0309062\pi$
$257$	14.4016	+	14.4016i	0.898348	+	0.898348i	−0.0969421	+	0.995290i	$0.530906\pi$
$258$		0			0
$259$		−	3.70097i		−	0.229967i
$260$	−37.2326	−	25.2616i	−2.30907	−	1.56666i
$261$		0			0
$262$	−5.22641	+	5.22641i	−0.322889	+	0.322889i
$263$	−17.6745	+	17.6745i	−1.08986	+	1.08986i	−0.0943154	+	0.995542i	$0.530066\pi$
$263$	−17.6745	+	17.6745i	−1.08986	+	1.08986i	−0.995542	+	0.0943154i	$0.969934\pi$
$264$		0			0
$265$	−11.2299	−	7.61931i	−0.689849	−	0.468050i
$266$		−	4.82902i		−	0.296086i
$267$		0			0
$268$	−7.97739	−	7.97739i	−0.487296	−	0.487296i
$269$	19.9619			1.21710			0.608550	−	0.793515i	$-0.291751\pi$
$269$	19.9619			1.21710			0.608550	+	0.793515i	$0.291751\pi$
$270$		0			0
$271$	5.67023			0.344442			0.172221	−	0.985058i	$-0.444906\pi$
$271$	5.67023			0.344442			0.172221	+	0.985058i	$0.444906\pi$
$272$	8.72065	+	8.72065i	0.528767	+	0.528767i
$273$		0			0
$274$		−	32.8584i		−	1.98505i
$275$	−7.21547	−	18.1431i	−0.435109	−	1.09407i
$276$		0			0
$277$	6.13913	−	6.13913i	0.368865	−	0.368865i	−0.498198	−	0.867063i	$-0.666005\pi$
$277$	6.13913	−	6.13913i	0.368865	−	0.368865i	0.867063	+	0.498198i	$0.166005\pi$
$278$	−1.75601	+	1.75601i	−0.105318	+	0.105318i
$279$		0			0
$280$	8.10604	−	1.55273i	0.484429	−	0.0927936i
$281$			1.46058i			0.0871308i	0.999051	+	0.0435654i	$0.0138717\pi$
$281$			1.46058i			0.0871308i	−0.999051	+	0.0435654i	$0.986128\pi$
$282$		0			0
$283$	−16.9557	−	16.9557i	−1.00791	−	1.00791i	−0.999968	−	0.00794489i	$-0.997471\pi$
$283$	−16.9557	−	16.9557i	−1.00791	−	1.00791i	−0.00794489	−	0.999968i	$-0.502529\pi$
$284$	−28.6418			−1.69958
$285$		0			0
$286$	51.9984			3.07473
$287$	4.98785	+	4.98785i	0.294424	+	0.294424i
$288$		0			0
$289$			44.1105i			2.59473i
$290$	−9.29862	+	13.7050i	−0.546034	+	0.804787i
$291$		0			0
$292$	−28.9485	+	28.9485i	−1.69408	+	1.69408i
$293$	10.1010	−	10.1010i	0.590108	−	0.590108i	−0.347552	−	0.937661i	$-0.612987\pi$
$293$	10.1010	−	10.1010i	0.590108	−	0.590108i	0.937661	+	0.347552i	$0.112987\pi$
$294$		0			0
$295$	−2.83395	−	14.7946i	−0.164999	−	0.861376i
$296$		−	13.6604i		−	0.793996i
$297$		0			0
$298$	−13.3545	−	13.3545i	−0.773608	−	0.773608i
$299$	−5.62157			−0.325104
$300$		0			0
$301$	−6.56761			−0.378551
$302$	22.5538	+	22.5538i	1.29782	+	1.29782i
$303$		0			0
$304$		−	3.22957i		−	0.185228i
$305$	−6.14984	−	32.1052i	−0.352139	−	1.83834i
$306$		0			0
$307$	19.0235	−	19.0235i	1.08573	−	1.08573i	0.0897638	−	0.995963i	$-0.471389\pi$
$307$	19.0235	−	19.0235i	1.08573	−	1.08573i	0.995963	−	0.0897638i	$-0.0286112\pi$
$308$	−9.84313	+	9.84313i	−0.560864	+	0.560864i
$309$		0			0
$310$	−15.1081	+	22.2675i	−0.858082	+	1.26471i
$311$		−	15.4076i		−	0.873684i	−0.899538	−	0.436842i	$-0.856097\pi$
$311$		−	15.4076i		−	0.873684i	0.899538	−	0.436842i	$-0.143903\pi$
$312$		0			0
$313$	−9.81200	−	9.81200i	−0.554607	−	0.554607i	0.373160	−	0.927767i	$-0.378274\pi$
$313$	−9.81200	−	9.81200i	−0.554607	−	0.554607i	−0.927767	+	0.373160i	$0.878274\pi$
$314$	14.6224			0.825190
$315$		0			0
$316$	19.9711			1.12346
$317$	−9.48645	−	9.48645i	−0.532812	−	0.532812i	0.388596	−	0.921408i	$-0.372960\pi$
$317$	−9.48645	−	9.48645i	−0.532812	−	0.532812i	−0.921408	+	0.388596i	$0.872960\pi$
$318$		0			0
$319$		−	12.2610i		−	0.686487i
$320$	−25.8930	+	4.95988i	−1.44747	+	0.277266i
$321$		0			0
$322$	1.66119	−	1.66119i	0.0925747	−	0.0925747i
$323$	11.3157	−	11.3157i	0.629622	−	0.629622i
$324$		0			0
$325$	−25.9195	−	11.1693i	−1.43775	−	0.619564i
$326$			51.4323i			2.84857i
$327$		0			0
$328$	18.4104	+	18.4104i	1.01654	+	1.01654i
$329$	7.32144			0.403644
$330$		0			0
$331$	14.4590			0.794738			0.397369	−	0.917659i	$-0.369923\pi$
$331$	14.4590			0.794738			0.397369	+	0.917659i	$0.369923\pi$
$332$	34.2928	+	34.2928i	1.88206	+	1.88206i
$333$		0			0
$334$			11.9551i			0.654152i
$335$	−5.85615	−	3.97329i	−0.319956	−	0.217084i
$336$		0			0
$337$	11.5758	−	11.5758i	0.630575	−	0.630575i	−0.317638	−	0.948212i	$-0.602890\pi$
$337$	11.5758	−	11.5758i	0.630575	−	0.630575i	0.948212	+	0.317638i	$0.102890\pi$
$338$	31.4641	−	31.4641i	1.71142	−	1.71142i
$339$		0			0
$340$	51.5630	+	34.9845i	2.79639	+	1.89730i
$341$		−	19.9214i		−	1.07880i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−24.2413			−1.30700
$345$		0			0
$346$	18.3762			0.987910
$347$	−0.882971	−	0.882971i	−0.0474003	−	0.0474003i	0.683009	−	0.730410i	$-0.260671\pi$
$347$	−0.882971	−	0.882971i	−0.0474003	−	0.0474003i	−0.730410	+	0.683009i	$0.760671\pi$
$348$		0			0
$349$		−	15.8042i		−	0.845981i	−0.906134	−	0.422990i	$-0.860980\pi$
$349$		−	15.8042i		−	0.845981i	0.906134	−	0.422990i	$-0.139020\pi$
$350$	10.9599	−	4.35872i	0.585830	−	0.232983i
$351$		0			0
$352$	10.1077	−	10.1077i	0.538743	−	0.538743i
$353$	−6.83948	+	6.83948i	−0.364029	+	0.364029i	−0.865294	−	0.501265i	$-0.832868\pi$
$353$	−6.83948	+	6.83948i	−0.364029	+	0.364029i	0.501265	+	0.865294i	$0.332868\pi$
$354$		0			0
$355$	−17.6457	+	3.38008i	−0.936536	+	0.179396i
$356$			53.7829i			2.85049i
$357$		0			0
$358$	24.0645	+	24.0645i	1.27185	+	1.27185i
$359$	34.4775			1.81965			0.909827	−	0.414987i	$-0.136214\pi$
$359$	34.4775			1.81965			0.909827	+	0.414987i	$0.136214\pi$
$360$		0			0
$361$	14.8094			0.779442
$362$	−4.18741	−	4.18741i	−0.220085	−	0.220085i
$363$		0			0
$364$			20.1217i			1.05466i
$365$	−14.4184	+	21.2509i	−0.754691	+	1.11232i
$366$		0			0
$367$	6.86931	−	6.86931i	0.358575	−	0.358575i	−0.504712	−	0.863288i	$-0.668401\pi$
$367$	6.86931	−	6.86931i	0.358575	−	0.358575i	0.863288	+	0.504712i	$0.168401\pi$
$368$	1.11098	−	1.11098i	0.0579138	−	0.0579138i
$369$		0			0
$370$	−3.67269	−	19.1733i	−0.190934	−	0.996771i
$371$			6.06902i			0.315088i
$372$		0			0
$373$	2.07997	+	2.07997i	0.107697	+	0.107697i	0.758902	−	0.651205i	$-0.225736\pi$
$373$	2.07997	+	2.07997i	0.107697	+	0.107697i	−0.651205	+	0.758902i	$0.725736\pi$
$374$	−72.0120			−3.72365
$375$		0			0
$376$	27.0237			1.39364
$377$	−12.5323	−	12.5323i	−0.645444	−	0.645444i
$378$		0			0
$379$			31.2820i			1.60685i	0.595408	+	0.803423i	$0.296990\pi$
$379$			31.2820i			1.60685i	−0.595408	+	0.803423i	$0.703010\pi$
$380$	−3.06979	−	16.0258i	−0.157477	−	0.822107i
$381$		0			0
$382$	43.8043	−	43.8043i	2.24122	−	2.24122i
$383$	−14.7746	+	14.7746i	−0.754949	+	0.754949i	−0.975398	−	0.220449i	$-0.929248\pi$
$383$	−14.7746	+	14.7746i	−0.754949	+	0.754949i	0.220449	+	0.975398i	$0.429248\pi$
$384$		0			0
$385$	−4.90256	+	7.22578i	−0.249858	+	0.368260i
$386$			18.7665i			0.955190i
$387$		0			0
$388$	−6.47331	−	6.47331i	−0.328632	−	0.328632i
$389$	9.00529			0.456586			0.228293	−	0.973592i	$-0.426686\pi$
$389$	9.00529			0.456586			0.228293	+	0.973592i	$0.426686\pi$
$390$		0			0
$391$	7.78525			0.393717
$392$	−2.60996	−	2.60996i	−0.131823	−	0.131823i
$393$		0			0
$394$		−	41.5452i		−	2.09302i
$395$	12.3038	−	2.35683i	0.619071	−	0.118585i
$396$		0			0
$397$	−3.09700	+	3.09700i	−0.155434	+	0.155434i	−0.780540	−	0.625106i	$-0.785056\pi$
$397$	−3.09700	+	3.09700i	−0.155434	+	0.155434i	0.625106	+	0.780540i	$0.285056\pi$
$398$	22.8446	−	22.8446i	1.14510	−	1.14510i
$399$		0			0
$400$	7.32978	−	2.91504i	0.366489	−	0.145752i
$401$			8.02382i			0.400690i	0.979725	+	0.200345i	$0.0642064\pi$
$401$			8.02382i			0.400690i	−0.979725	+	0.200345i	$0.935794\pi$
$402$		0			0
$403$	−20.3620	−	20.3620i	−1.01430	−	1.01430i
$404$	15.2152			0.756985
$405$		0			0
$406$	7.40665			0.367586
$407$	10.2194	+	10.2194i	0.506559	+	0.506559i
$408$		0			0
$409$		−	16.3062i		−	0.806288i	−0.915136	−	0.403144i	$-0.867917\pi$
$409$		−	16.3062i		−	0.806288i	0.915136	−	0.403144i	$-0.132083\pi$
$410$	30.7898	+	20.8904i	1.52060	+	1.03170i
$411$		0			0
$412$	−13.1567	+	13.1567i	−0.648182	+	0.648182i
$413$	−4.76353	+	4.76353i	−0.234398	+	0.234398i
$414$		0			0
$415$	25.1741	+	17.0802i	1.23575	+	0.838433i
$416$		−	20.6626i		−	1.01307i
$417$		0			0
$418$	13.3343	+	13.3343i	0.652202	+	0.652202i
$419$	34.1683			1.66923			0.834616	−	0.550832i	$-0.185689\pi$
$419$	34.1683			1.66923			0.834616	+	0.550832i	$0.185689\pi$
$420$		0			0
$421$	−2.67756			−0.130496			−0.0652481	−	0.997869i	$-0.520784\pi$
$421$	−2.67756			−0.130496			−0.0652481	+	0.997869i	$0.520784\pi$
$422$	−5.31186	−	5.31186i	−0.258577	−	0.258577i
$423$		0			0
$424$			22.4010i			1.08789i
$425$	35.8956	+	15.4683i	1.74119	+	0.750322i
$426$		0			0
$427$	−10.3371	+	10.3371i	−0.500250	+	0.500250i
$428$	−0.851385	+	0.851385i	−0.0411532	+	0.0411532i
$429$		0			0
$430$	−34.0242	+	6.51743i	−1.64079	+	0.314298i
$431$		−	7.10877i		−	0.342417i	−0.985235	−	0.171209i	$-0.945233\pi$
$431$		−	7.10877i		−	0.342417i	0.985235	−	0.171209i	$-0.0547672\pi$
$432$		0			0
$433$	21.8806	+	21.8806i	1.05151	+	1.05151i	0.998599	+	0.0529135i	$0.0168508\pi$
$433$	21.8806	+	21.8806i	1.05151	+	1.05151i	0.0529135	+	0.998599i	$0.483149\pi$
$434$	12.0341			0.577654
$435$		0			0
$436$	−58.6805			−2.81029
$437$	−1.44158	−	1.44158i	−0.0689600	−	0.0689600i
$438$		0			0
$439$		−	20.9078i		−	0.997875i	−0.866638	−	0.498938i	$-0.833724\pi$
$439$		−	20.9078i		−	0.997875i	0.866638	−	0.498938i	$-0.166276\pi$
$440$	−18.0956	+	26.6706i	−0.862672	+	1.27147i
$441$		0			0
$442$	−73.6048	+	73.6048i	−3.50102	+	3.50102i
$443$	7.58964	−	7.58964i	0.360595	−	0.360595i	−0.503437	−	0.864032i	$-0.667931\pi$
$443$	7.58964	−	7.58964i	0.360595	−	0.360595i	0.864032	+	0.503437i	$0.167931\pi$
$444$		0			0
$445$	6.34703	+	33.1346i	0.300878	+	1.57073i
$446$		−	6.15187i		−	0.291300i
$447$		0			0
$448$	8.33697	+	8.33697i	0.393885	+	0.393885i
$449$	−18.7824			−0.886395			−0.443198	−	0.896424i	$-0.646156\pi$
$449$	−18.7824			−0.886395			−0.443198	+	0.896424i	$0.646156\pi$
$450$		0			0
$451$	−27.5458			−1.29708
$452$	18.3500	+	18.3500i	0.863113	+	0.863113i
$453$		0			0
$454$			44.0930i			2.06939i
$455$	2.37460	+	12.3966i	0.111323	+	0.581162i
$456$		0			0
$457$	−23.7922	+	23.7922i	−1.11295	+	1.11295i	−0.120201	+	0.992750i	$0.538354\pi$
$457$	−23.7922	+	23.7922i	−1.11295	+	1.11295i	−0.992750	+	0.120201i	$0.961646\pi$
$458$	22.5799	−	22.5799i	1.05509	−	1.05509i
$459$		0			0
$460$	4.45690	−	6.56893i	0.207804	−	0.306278i
$461$			1.65023i			0.0768587i	0.999261	+	0.0384294i	$0.0122355\pi$
$461$			1.65023i			0.0768587i	−0.999261	+	0.0384294i	$0.987765\pi$
$462$		0			0
$463$	−8.74262	−	8.74262i	−0.406304	−	0.406304i	0.474144	−	0.880448i	$-0.342758\pi$
$463$	−8.74262	−	8.74262i	−0.406304	−	0.406304i	−0.880448	+	0.474144i	$0.842758\pi$
$464$	4.95344			0.229958
$465$		0			0
$466$	30.9276			1.43270
$467$	7.80242	+	7.80242i	0.361053	+	0.361053i	0.864201	−	0.503148i	$-0.167825\pi$
$467$	7.80242	+	7.80242i	0.361053	+	0.361053i	−0.503148	+	0.864201i	$0.667825\pi$
$468$		0			0
$469$			3.16486i			0.146139i
$470$	37.9295	−	7.26550i	1.74956	−	0.335132i
$471$		0			0
$472$	−17.5824	+	17.5824i	−0.809294	+	0.809294i
$473$	18.1351	−	18.1351i	0.833851	−	0.833851i
$474$		0			0
$475$	−3.78248	−	9.51093i	−0.173552	−	0.436392i
$476$		−	27.8663i		−	1.27725i
$477$		0			0
$478$	−0.481366	−	0.481366i	−0.0220172	−	0.0220172i
$479$	0.0699366			0.00319549			0.00159774	−	0.999999i	$-0.499491\pi$
$479$	0.0699366			0.00319549			0.00159774	+	0.999999i	$0.499491\pi$
$480$		0			0
$481$	20.8910			0.952546
$482$	−33.0553	−	33.0553i	−1.50563	−	1.50563i
$483$		0			0
$484$		−	15.1478i		−	0.688537i
$485$	−4.75201	−	3.22416i	−0.215778	−	0.146401i
$486$		0			0
$487$	29.5762	−	29.5762i	1.34023	−	1.34023i	0.444397	−	0.895830i	$-0.353418\pi$
$487$	29.5762	−	29.5762i	1.34023	−	1.34023i	0.895830	−	0.444397i	$-0.146582\pi$
$488$	−38.1548	+	38.1548i	−1.72719	+	1.72719i
$489$		0			0
$490$	−4.36494	−	2.96154i	−0.197188	−	0.133789i
$491$		−	10.2626i		−	0.463144i	−0.972818	−	0.231572i	$-0.925613\pi$
$491$		−	10.2626i		−	0.463144i	0.972818	−	0.231572i	$-0.0743870\pi$
$492$		0			0
$493$	17.3558	+	17.3558i	0.781664	+	0.781664i
$494$	27.2585			1.22642
$495$		0			0
$496$	8.04819			0.361375
$497$	5.68151	+	5.68151i	0.254851	+	0.254851i
$498$		0			0
$499$			17.0229i			0.762050i	0.924565	+	0.381025i	$0.124429\pi$
$499$			17.0229i			0.762050i	−0.924565	+	0.381025i	$0.875571\pi$
$500$	33.6012	−	21.4322i	1.50269	−	0.958477i
$501$		0			0
$502$	−21.1777	+	21.1777i	−0.945205	+	0.945205i
$503$	12.9647	−	12.9647i	0.578069	−	0.578069i	−0.356302	−	0.934371i	$-0.615962\pi$
$503$	12.9647	−	12.9647i	0.578069	−	0.578069i	0.934371	+	0.356302i	$0.115962\pi$
$504$		0			0
$505$	9.37382	−	1.79558i	0.417129	−	0.0799022i
$506$			9.17406i			0.407837i
$507$		0			0
$508$	−24.5266	−	24.5266i	−1.08819	−	1.08819i
$509$	−17.3978			−0.771142			−0.385571	−	0.922678i	$-0.625995\pi$
$509$	−17.3978			−0.771142			−0.385571	+	0.922678i	$0.625995\pi$
$510$		0			0
$511$	11.4847			0.508052
$512$	12.3186	+	12.3186i	0.544411	+	0.544411i
$513$		0			0
$514$		−	48.0448i		−	2.11917i
$515$	−6.55293	+	9.65823i	−0.288757	+	0.425592i
$516$		0			0
$517$	−20.2166	+	20.2166i	−0.889125	+	0.889125i
$518$	−6.17335	+	6.17335i	−0.271242	+	0.271242i
$519$		0			0
$520$	8.76476	+	45.7564i	0.384360	+	2.00655i
$521$		−	25.3312i		−	1.10978i	−0.831924	−	0.554890i	$-0.812760\pi$
$521$		−	25.3312i		−	1.10978i	0.831924	−	0.554890i	$-0.187240\pi$
$522$		0			0
$523$	−14.8923	−	14.8923i	−0.651194	−	0.651194i	0.302086	−	0.953281i	$-0.402317\pi$
$523$	−14.8923	−	14.8923i	−0.651194	−	0.651194i	−0.953281	+	0.302086i	$0.902317\pi$
$524$	11.1691			0.487926
$525$		0			0
$526$	58.9635			2.57093
$527$	28.1991	+	28.1991i	1.22837	+	1.22837i
$528$		0			0
$529$			22.0082i			0.956878i
$530$	6.02265	+	31.4412i	0.261607	+	1.36572i
$531$		0			0
$532$	−5.15994	+	5.15994i	−0.223712	+	0.223712i
$533$	−28.1551	+	28.1551i	−1.21953	+	1.21953i
$534$		0			0
$535$	−0.424049	+	0.624996i	−0.0183332	+	0.0270210i
$536$			11.6816i			0.504569i
$537$		0			0
$538$	−33.2972	−	33.2972i	−1.43555	−	1.43555i
$539$	3.90505			0.168202
$540$		0			0
$541$	33.2048			1.42758			0.713792	−	0.700358i	$-0.246976\pi$
$541$	33.2048			1.42758			0.713792	+	0.700358i	$0.246976\pi$
$542$	−9.45815	−	9.45815i	−0.406263	−	0.406263i
$543$		0			0
$544$			28.6153i			1.22687i
$545$	−36.1520	+	6.92501i	−1.54858	+	0.296635i
$546$		0			0
$547$	−9.55534	+	9.55534i	−0.408557	+	0.408557i	−0.881235	−	0.472678i	$-0.843287\pi$
$547$	−9.55534	+	9.55534i	−0.408557	+	0.408557i	0.472678	+	0.881235i	$0.343287\pi$
$548$	−35.1102	+	35.1102i	−1.49983	+	1.49983i
$549$		0			0
$550$	−18.2277	+	42.2990i	−0.777231	+	1.80364i
$551$		−	6.42746i		−	0.273819i
$552$		0			0
$553$	−3.96154	−	3.96154i	−0.168462	−	0.168462i
$554$	−20.4806			−0.870137
$555$		0			0
$556$	3.75269			0.159150
$557$	6.23261	+	6.23261i	0.264084	+	0.264084i	0.826711	−	0.562627i	$-0.190209\pi$
$557$	6.23261	+	6.23261i	0.264084	+	0.264084i	−0.562627	+	0.826711i	$0.690209\pi$
$558$		0			0
$559$		−	37.0724i		−	1.56800i
$560$	−2.91920	−	1.98063i	−0.123359	−	0.0836968i
$561$		0			0
$562$	2.43630	−	2.43630i	0.102769	−	0.102769i
$563$	28.6524	−	28.6524i	1.20755	−	1.20755i	0.235737	−	0.971817i	$-0.424250\pi$
$563$	28.6524	−	28.6524i	1.20755	−	1.20755i	0.971817	−	0.235737i	$-0.0757503\pi$
$564$		0			0
$565$	13.4706	+	9.13959i	0.566714	+	0.384505i
$566$			56.5655i			2.37763i
$567$		0			0
$568$	20.9707	+	20.9707i	0.879910	+	0.879910i
$569$	39.5328			1.65730			0.828652	−	0.559765i	$-0.189109\pi$
$569$	39.5328			1.65730			0.828652	+	0.559765i	$0.189109\pi$
$570$		0			0
$571$	−7.31893			−0.306288			−0.153144	−	0.988204i	$-0.548940\pi$
$571$	−7.31893			−0.306288			−0.153144	+	0.988204i	$0.548940\pi$
$572$	−55.5618	−	55.5618i	−2.32316	−	2.32316i
$573$		0			0
$574$		−	16.6398i		−	0.694534i
$575$	1.97060	−	4.57297i	0.0821798	−	0.190706i
$576$		0			0
$577$	−28.0510	+	28.0510i	−1.16778	+	1.16778i	−0.185049	+	0.982729i	$0.559244\pi$
$577$	−28.0510	+	28.0510i	−1.16778	+	1.16778i	−0.982729	+	0.185049i	$0.940756\pi$
$578$	73.5778	−	73.5778i	3.06043	−	3.06043i
$579$		0			0
$580$	24.5801	−	4.70837i	1.02063	−	0.195505i
$581$		−	13.6049i		−	0.564427i
$582$		0			0
$583$	−16.7583	−	16.7583i	−0.694058	−	0.694058i
$584$	42.3904			1.75413
$585$		0			0
$586$	−33.6977			−1.39204
$587$	−22.5108	−	22.5108i	−0.929118	−	0.929118i	0.0685309	−	0.997649i	$-0.478169\pi$
$587$	−22.5108	−	22.5108i	−0.929118	−	0.929118i	−0.997649	+	0.0685309i	$0.978169\pi$
$588$		0			0
$589$		−	10.4431i		−	0.430302i
$590$	−19.9508	+	29.4051i	−0.821363	+	1.21059i
$591$		0			0
$592$	−4.12864	+	4.12864i	−0.169686	+	0.169686i
$593$	−14.9506	+	14.9506i	−0.613948	+	0.613948i	−0.943972	−	0.330025i	$-0.892943\pi$
$593$	−14.9506	+	14.9506i	−0.613948	+	0.613948i	0.330025	+	0.943972i	$0.392943\pi$
$594$		0			0
$595$	−3.28856	−	17.1679i	−0.134818	−	0.703816i
$596$			28.5394i			1.16902i
$597$		0			0
$598$	9.37698	+	9.37698i	0.383453	+	0.383453i
$599$	−12.2321			−0.499788			−0.249894	−	0.968273i	$-0.580396\pi$
$599$	−12.2321			−0.499788			−0.249894	+	0.968273i	$0.580396\pi$
$600$		0			0
$601$	34.9245			1.42460			0.712300	−	0.701875i	$-0.247653\pi$
$601$	34.9245			1.42460			0.712300	+	0.701875i	$0.247653\pi$
$602$	10.9550	+	10.9550i	0.446493	+	0.446493i
$603$		0			0
$604$		−	48.1987i		−	1.96118i
$605$	−1.78762	−	9.33229i	−0.0726773	−	0.379412i
$606$		0			0
$607$	30.9003	−	30.9003i	1.25420	−	1.25420i	0.300386	−	0.953818i	$-0.402884\pi$
$607$	30.9003	−	30.9003i	1.25420	−	1.25420i	0.953818	−	0.300386i	$-0.0971157\pi$
$608$	5.29864	−	5.29864i	0.214888	−	0.214888i
$609$		0			0
$610$	−43.2945	+	63.8109i	−1.75294	+	2.58363i
$611$			41.3276i			1.67193i
$612$		0			0
$613$	30.2877	+	30.2877i	1.22331	+	1.22331i	0.966449	+	0.256860i	$0.0826879\pi$
$613$	30.2877	+	30.2877i	1.22331	+	1.22331i	0.256860	+	0.966449i	$0.417312\pi$
$614$	−63.4637			−2.56119
$615$		0			0
$616$	14.4137			0.580744
$617$	−16.7504	−	16.7504i	−0.674345	−	0.674345i	0.284370	−	0.958715i	$-0.408216\pi$
$617$	−16.7504	−	16.7504i	−0.674345	−	0.674345i	−0.958715	+	0.284370i	$0.908216\pi$
$618$		0			0
$619$			5.10632i			0.205240i	0.994721	+	0.102620i	$0.0327226\pi$
$619$			5.10632i			0.205240i	−0.994721	+	0.102620i	$0.967277\pi$
$620$	39.9369	−	7.65002i	1.60390	−	0.307232i
$621$		0			0
$622$	−25.7004	+	25.7004i	−1.03049	+	1.03049i
$623$	10.6686	−	10.6686i	0.427428	−	0.427428i
$624$		0			0
$625$	18.1718	−	17.1693i	0.726872	−	0.686773i
$626$			32.7336i			1.30830i
$627$		0			0
$628$	−15.6245	−	15.6245i	−0.623484	−	0.623484i
$629$	−28.9317			−1.15358
$630$		0			0
$631$	19.0518			0.758441			0.379220	−	0.925306i	$-0.376192\pi$
$631$	19.0518			0.758441			0.379220	+	0.925306i	$0.376192\pi$
$632$	−14.6222	−	14.6222i	−0.581640	−	0.581640i
$633$		0			0
$634$			31.6475i			1.25688i
$635$	−18.0049	−	12.2160i	−0.714501	−	0.484776i
$636$		0			0
$637$	3.99143	−	3.99143i	0.158146	−	0.158146i
$638$	−20.4519	+	20.4519i	−0.809697	+	0.809697i
$639$		0			0
$640$	37.9172	+	25.7262i	1.49881	+	1.01692i
$641$		−	33.5895i		−	1.32670i	−0.748307	−	0.663352i	$-0.769133\pi$
$641$		−	33.5895i		−	1.32670i	0.748307	−	0.663352i	$-0.230867\pi$
$642$		0			0
$643$	−29.8074	−	29.8074i	−1.17549	−	1.17549i	−0.980881	−	0.194610i	$-0.937656\pi$
$643$	−29.8074	−	29.8074i	−1.17549	−	1.17549i	−0.194610	−	0.980881i	$-0.562344\pi$
$644$	−3.55007			−0.139892
$645$		0			0
$646$	−37.7499			−1.48525
$647$	4.10192	+	4.10192i	0.161263	+	0.161263i	0.783126	−	0.621863i	$-0.213624\pi$
$647$	4.10192	+	4.10192i	0.161263	+	0.161263i	−0.621863	+	0.783126i	$0.713624\pi$
$648$		0			0
$649$		−	26.3069i		−	1.03264i
$650$	24.6038	+	61.8655i	0.965040	+	2.42656i
$651$		0			0
$652$	54.9569	−	54.9569i	2.15228	−	2.15228i
$653$	11.9625	−	11.9625i	0.468127	−	0.468127i	−0.433180	−	0.901307i	$-0.642609\pi$
$653$	11.9625	−	11.9625i	0.468127	−	0.468127i	0.901307	+	0.433180i	$0.142609\pi$
$654$		0			0
$655$	6.88110	−	1.31809i	0.268867	−	0.0515022i
$656$		−	11.1284i		−	0.434493i
$657$		0			0
$658$	−12.2124	−	12.2124i	−0.476090	−	0.476090i
$659$	22.2380			0.866270			0.433135	−	0.901329i	$-0.357407\pi$
$659$	22.2380			0.866270			0.433135	+	0.901329i	$0.357407\pi$
$660$		0			0
$661$	28.8512			1.12218			0.561090	−	0.827755i	$-0.310382\pi$
$661$	28.8512			1.12218			0.561090	+	0.827755i	$0.310382\pi$
$662$	−24.1181	−	24.1181i	−0.937378	−	0.937378i
$663$		0			0
$664$		−	50.2163i		−	1.94877i
$665$	−2.57001	+	3.78788i	−0.0996607	+	0.146888i
$666$		0			0
$667$	2.21106	−	2.21106i	0.0856126	−	0.0856126i
$668$	12.7743	−	12.7743i	0.494254	−	0.494254i
$669$		0			0
$670$	3.14067	+	16.3959i	0.121335	+	0.633428i
$671$		−	57.0877i		−	2.20384i
$672$		0			0
$673$	24.6972	+	24.6972i	0.952006	+	0.952006i	0.998900	−	0.0468939i	$-0.0149323\pi$
$673$	24.6972	+	24.6972i	0.952006	+	0.952006i	−0.0468939	+	0.998900i	$0.514932\pi$
$674$	−38.6177			−1.48750
$675$		0			0
$676$	−67.2406			−2.58618
$677$	−8.15127	−	8.15127i	−0.313279	−	0.313279i	0.532900	−	0.846178i	$-0.321102\pi$
$677$	−8.15127	−	8.15127i	−0.313279	−	0.313279i	−0.846178	+	0.532900i	$0.821102\pi$
$678$		0			0
$679$			2.56814i			0.0985563i
$680$	−12.1382	−	63.3675i	−0.465479	−	2.43003i
$681$		0			0
$682$	−33.2295	+	33.2295i	−1.27243	+	1.27243i
$683$	1.19230	−	1.19230i	0.0456222	−	0.0456222i	−0.683928	−	0.729550i	$-0.739730\pi$
$683$	1.19230	−	1.19230i	0.0456222	−	0.0456222i	0.729550	+	0.683928i	$0.239730\pi$
$684$		0			0
$685$	−17.4873	+	25.7742i	−0.668156	+	0.984780i
$686$			2.35896i			0.0900655i
$687$		0			0
$688$	7.32653	+	7.32653i	0.279322	+	0.279322i
$689$	−34.2580			−1.30513
$690$		0			0
$691$	3.67643			0.139858			0.0699290	−	0.997552i	$-0.477723\pi$
$691$	3.67643			0.139858			0.0699290	+	0.997552i	$0.477723\pi$
$692$	−19.6355	−	19.6355i	−0.746429	−	0.746429i
$693$		0			0
$694$			2.94565i			0.111815i
$695$	2.31196	−	0.442863i	0.0876978	−	0.0167987i
$696$		0			0
$697$	38.9916	−	38.9916i	1.47691	−	1.47691i
$698$	−26.3620	+	26.3620i	−0.997817	+	0.997817i
$699$		0			0
$700$	−16.3684	−	7.05353i	−0.618666	−	0.266598i
$701$			26.4148i			0.997672i	0.866696	+	0.498836i	$0.166239\pi$
$701$			26.4148i			0.997672i	−0.866696	+	0.498836i	$0.833761\pi$
$702$		0			0
$703$	5.35721	+	5.35721i	0.202051	+	0.202051i
$704$	−46.0415			−1.73525
$705$		0			0
$706$	22.8170			0.858730
$707$	−3.01815	−	3.01815i	−0.113509	−	0.113509i
$708$		0			0
$709$			5.48277i			0.205910i	0.994686	+	0.102955i	$0.0328298\pi$
$709$			5.48277i			0.205910i	−0.994686	+	0.102955i	$0.967170\pi$
$710$	35.0718	+	23.7956i	1.31622	+	0.893032i
$711$		0			0
$712$	39.3782	−	39.3782i	1.47576	−	1.47576i
$713$	3.59246	−	3.59246i	0.134539	−	0.134539i
$714$		0			0
$715$	−40.7876	−	27.6736i	−1.52537	−	1.03494i
$716$		−	51.4272i		−	1.92193i
$717$		0			0
$718$	−57.5098	−	57.5098i	−2.14625	−	2.14625i
$719$	20.5182			0.765200			0.382600	−	0.923914i	$-0.375029\pi$
$719$	20.5182			0.765200			0.382600	+	0.923914i	$0.375029\pi$
$720$		0			0
$721$	5.21962			0.194389
$722$	−24.7026	−	24.7026i	−0.919336	−	0.919336i
$723$		0			0
$724$			8.94874i			0.332577i
$725$	14.5877	−	5.80149i	0.541773	−	0.215462i
$726$		0			0
$727$	−26.4968	+	26.4968i	−0.982713	+	0.982713i	−0.999853	−	0.0171404i	$-0.994544\pi$
$727$	−26.4968	+	26.4968i	−0.982713	+	0.982713i	0.0171404	+	0.999853i	$0.494544\pi$
$728$	14.7325	−	14.7325i	0.546023	−	0.546023i
$729$		0			0
$730$	59.4976	−	11.3969i	2.20211	−	0.421819i
$731$			51.3411i			1.89892i
$732$		0			0
$733$	−2.79551	−	2.79551i	−0.103255	−	0.103255i	0.653592	−	0.756847i	$-0.273261\pi$
$733$	−2.79551	−	2.79551i	−0.103255	−	0.103255i	−0.756847	+	0.653592i	$0.773261\pi$
$734$	−22.9165			−0.845865
$735$		0			0
$736$	3.64549			0.134375
$737$	−8.73907	−	8.73907i	−0.321908	−	0.321908i
$738$		0			0
$739$			11.1286i			0.409371i	0.978828	+	0.204685i	$0.0656171\pi$
$739$			11.1286i			0.409371i	−0.978828	+	0.204685i	$0.934383\pi$
$740$	−16.5628	+	24.4116i	−0.608861	+	0.897387i
$741$		0			0
$742$	10.1234	−	10.1234i	0.371640	−	0.371640i
$743$	−1.11168	+	1.11168i	−0.0407834	+	0.0407834i	−0.727204	−	0.686421i	$-0.759181\pi$
$743$	−1.11168	+	1.11168i	−0.0407834	+	0.0407834i	0.686421	+	0.727204i	$0.259181\pi$
$744$		0			0
$745$	3.36800	+	17.5826i	0.123394	+	0.644177i
$746$		−	6.93892i		−	0.254052i
$747$		0			0
$748$	76.9469	+	76.9469i	2.81346	+	2.81346i
$749$	0.337769			0.0123418
$750$		0			0
$751$	13.5122			0.493066			0.246533	−	0.969134i	$-0.420709\pi$
$751$	13.5122			0.493066			0.246533	+	0.969134i	$0.420709\pi$
$752$	−8.16747	−	8.16747i	−0.297837	−	0.297837i
$753$		0			0
$754$			41.8085i			1.52258i
$755$	−5.68803	−	29.6943i	−0.207009	−	1.08069i
$756$		0			0
$757$	18.4088	−	18.4088i	0.669080	−	0.669080i	−0.288423	−	0.957503i	$-0.593131\pi$
$757$	18.4088	−	18.4088i	0.669080	−	0.669080i	0.957503	+	0.288423i	$0.0931311\pi$
$758$	52.1794	−	52.1794i	1.89524	−	1.89524i
$759$		0			0
$760$	−9.48601	+	13.9812i	−0.344094	+	0.507152i
$761$			50.0198i			1.81322i	0.421974	+	0.906608i	$0.361337\pi$
$761$			50.0198i			1.81322i	−0.421974	+	0.906608i	$0.638663\pi$
$762$		0			0
$763$	11.6401	+	11.6401i	0.421400	+	0.421400i
$764$	−93.6122			−3.38677
$765$		0			0
$766$	49.2893			1.78089
$767$	−26.8888	−	26.8888i	−0.970899	−	0.970899i
$768$		0			0
$769$			49.7738i			1.79489i	0.441127	+	0.897445i	$0.354579\pi$
$769$			49.7738i			1.79489i	−0.441127	+	0.897445i	$0.645421\pi$
$770$	20.2305	−	3.87521i	0.729057	−	0.139653i
$771$		0			0
$772$	20.0526	−	20.0526i	0.721707	−	0.721707i
$773$	−14.8378	+	14.8378i	−0.533680	+	0.533680i	−0.921665	−	0.387986i	$-0.873171\pi$
$773$	−14.8378	+	14.8378i	−0.533680	+	0.533680i	0.387986	+	0.921665i	$0.373171\pi$
$774$		0			0
$775$	23.7016	−	9.42607i	0.851386	−	0.338594i
$776$			9.47912i			0.340281i
$777$		0			0
$778$	−15.0212	−	15.0212i	−0.538534	−	0.538534i
$779$	−14.4400			−0.517366
$780$		0			0
$781$	−31.3766			−1.12274
$782$	−12.9861	−	12.9861i	−0.464381	−	0.464381i
$783$		0			0
$784$			1.57763i			0.0563440i
$785$	−11.4698	−	7.78207i	−0.409376	−	0.277754i
$786$		0			0
$787$	17.0814	−	17.0814i	0.608888	−	0.608888i	−0.333768	−	0.942655i	$-0.608320\pi$
$787$	17.0814	−	17.0814i	0.608888	−	0.608888i	0.942655	+	0.333768i	$0.108320\pi$
$788$	−44.3922	+	44.3922i	−1.58141	+	1.58141i
$789$		0			0
$790$	−24.4545	−	16.5919i	−0.870050	−	0.590314i
$791$		−	7.27998i		−	0.258846i
$792$		0			0
$793$	−58.3504	−	58.3504i	−2.07208	−	2.07208i
$794$	10.3318			0.366663
$795$		0			0
$796$	−48.8203			−1.73039
$797$	−6.49007	−	6.49007i	−0.229890	−	0.229890i	0.582757	−	0.812647i	$-0.301974\pi$
$797$	−6.49007	−	6.49007i	−0.229890	−	0.229890i	−0.812647	+	0.582757i	$0.801974\pi$
$798$		0			0
$799$		−	57.2341i		−	2.02480i
$800$	16.8083	+	7.24312i	0.594264	+	0.256083i
$801$		0			0
$802$	13.3840	−	13.3840i	0.472606	−	0.472606i
$803$	−31.7125	+	31.7125i	−1.11911	+	1.11911i
$804$		0			0
$805$	−2.18713	+	0.418951i	−0.0770862	+	0.0147661i
$806$			67.9291i			2.39270i
$807$		0			0
$808$	−11.1401	−	11.1401i	−0.391908	−	0.391908i
$809$	5.26585			0.185137			0.0925686	−	0.995706i	$-0.470492\pi$
$809$	5.26585			0.185137			0.0925686	+	0.995706i	$0.470492\pi$
$810$		0			0
$811$	0.646408			0.0226984			0.0113492	−	0.999936i	$-0.496387\pi$
$811$	0.646408			0.0226984			0.0113492	+	0.999936i	$0.496387\pi$
$812$	−7.91421	−	7.91421i	−0.277734	−	0.277734i
$813$		0			0
$814$		−	34.0928i		−	1.19495i
$815$	27.3724	−	40.3435i	0.958812	−	1.41317i
$816$		0			0
$817$	9.50672	−	9.50672i	0.332598	−	0.332598i
$818$	−27.1993	+	27.1993i	−0.951001	+	0.951001i
$819$		0			0
$820$	−10.5779	−	55.2218i	−0.369396	−	1.92843i
$821$			19.1644i			0.668841i	0.942424	+	0.334420i	$0.108541\pi$
$821$			19.1644i			0.668841i	−0.942424	+	0.334420i	$0.891459\pi$
$822$		0			0
$823$	31.5090	+	31.5090i	1.09834	+	1.09834i	0.994605	+	0.103731i	$0.0330781\pi$
$823$	31.5090	+	31.5090i	1.09834	+	1.09834i	0.103731	+	0.994605i	$0.466922\pi$
$824$	19.2658			0.671157
$825$		0			0
$826$	15.8915			0.552935
$827$	−8.56728	−	8.56728i	−0.297914	−	0.297914i	0.542283	−	0.840196i	$-0.317560\pi$
$827$	−8.56728	−	8.56728i	−0.297914	−	0.297914i	−0.840196	+	0.542283i	$0.817560\pi$
$828$		0			0
$829$		−	11.5860i		−	0.402398i	−0.979550	−	0.201199i	$-0.935516\pi$
$829$		−	11.5860i		−	0.402398i	0.979550	−	0.201199i	$-0.0644838\pi$
$830$	−13.5010	−	70.4817i	−0.468625	−	2.44645i
$831$		0			0
$832$	−47.0599	+	47.0599i	−1.63151	+	1.63151i
$833$	−5.52768	+	5.52768i	−0.191523	+	0.191523i
$834$		0			0
$835$	6.36251	−	9.37756i	0.220184	−	0.324524i
$836$		−	28.4962i		−	0.985560i
$837$		0			0
$838$	−56.9940	−	56.9940i	−1.96883	−	1.96883i
$839$	−22.5537			−0.778639			−0.389319	−	0.921103i	$-0.627290\pi$
$839$	−22.5537			−0.778639			−0.389319	+	0.921103i	$0.627290\pi$
$840$		0			0
$841$	−19.1417			−0.660059
$842$	4.46626	+	4.46626i	0.153918	+	0.153918i
$843$		0			0
$844$			11.3518i			0.390744i
$845$	−41.4257	+	7.93520i	−1.42509	+	0.272979i
$846$		0			0
$847$	−3.00478	+	3.00478i	−0.103246	+	0.103246i
$848$	6.77033	−	6.77033i	0.232494	−	0.232494i
$849$		0			0
$850$	−34.0735	−	85.6768i	−1.16871	−	2.93869i
$851$			3.68579i			0.126347i
$852$		0			0
$853$	−8.13850	−	8.13850i	−0.278657	−	0.278657i	0.553916	−	0.832573i	$-0.313133\pi$
$853$	−8.13850	−	8.13850i	−0.278657	−	0.278657i	−0.832573	+	0.553916i	$0.813133\pi$
$854$	34.4855			1.18007
$855$		0			0
$856$	1.24672			0.0426119
$857$	31.8071	+	31.8071i	1.08651	+	1.08651i	0.995885	+	0.0906234i	$0.0288860\pi$
$857$	31.8071	+	31.8071i	1.08651	+	1.08651i	0.0906234	+	0.995885i	$0.471114\pi$
$858$		0			0
$859$		−	19.4270i		−	0.662840i	−0.943483	−	0.331420i	$-0.892472\pi$
$859$		−	19.4270i		−	0.662840i	0.943483	−	0.331420i	$-0.107528\pi$
$860$	43.3199	+	29.3918i	1.47720	+	1.00225i
$861$		0			0
$862$	−11.8577	+	11.8577i	−0.403874	+	0.403874i
$863$	−23.6236	+	23.6236i	−0.804158	+	0.804158i	−0.983743	−	0.179585i	$-0.942525\pi$
$863$	−23.6236	+	23.6236i	−0.804158	+	0.804158i	0.179585	+	0.983743i	$0.442525\pi$
$864$		0			0
$865$	−14.4143	−	9.77984i	−0.490101	−	0.332525i
$866$		−	72.9951i		−	2.48048i
$867$		0			0
$868$	−12.8588	−	12.8588i	−0.436455	−	0.436455i
$869$	21.8779			0.742157
$870$		0			0
$871$	−17.8647			−0.605324
$872$	42.9641	+	42.9641i	1.45495	+	1.45495i
$873$		0			0
$874$			4.80920i			0.162674i
$875$	−10.9166	−	2.41388i	−0.369050	−	0.0816042i
$876$		0			0
$877$	1.23188	−	1.23188i	0.0415978	−	0.0415978i	−0.686002	−	0.727600i	$-0.740636\pi$
$877$	1.23188	−	1.23188i	0.0415978	−	0.0415978i	0.727600	+	0.686002i	$0.240636\pi$
$878$	−34.8750	+	34.8750i	−1.17697	+	1.17697i
$879$		0			0
$880$	13.5298	−	2.59168i	0.456091	−	0.0873654i
$881$		−	2.45383i		−	0.0826715i	−0.999145	−	0.0413358i	$-0.986839\pi$
$881$		−	2.45383i		−	0.0826715i	0.999145	−	0.0413358i	$-0.0131613\pi$
$882$		0			0
$883$	2.51868	+	2.51868i	0.0847603	+	0.0847603i	0.748216	−	0.663455i	$-0.230911\pi$
$883$	2.51868	+	2.51868i	0.0847603	+	0.0847603i	−0.663455	+	0.748216i	$0.730911\pi$
$884$	157.298			5.29050
$885$		0			0
$886$	−25.3196			−0.850628
$887$	18.0288	+	18.0288i	0.605349	+	0.605349i	0.941727	−	0.336378i	$-0.109202\pi$
$887$	18.0288	+	18.0288i	0.605349	+	0.605349i	−0.336378	+	0.941727i	$0.609202\pi$
$888$		0			0
$889$			9.73041i			0.326348i
$890$	44.6827	−	65.8569i	1.49777	−	2.20753i
$891$		0			0
$892$	−6.57345	+	6.57345i	−0.220096	+	0.220096i
$893$	−10.5979	+	10.5979i	−0.354645	+	0.354645i
$894$		0			0
$895$	−6.06904	−	31.6834i	−0.202866	−	1.05906i
$896$		−	20.4917i		−	0.684580i
$897$		0			0
$898$	31.3297	+	31.3297i	1.04549	+	1.04549i
$899$	16.0175			0.534212
$900$		0			0
$901$	47.4435			1.58057
$902$	45.9474	+	45.9474i	1.52988	+	1.52988i
$903$		0			0
$904$		−	26.8707i		−	0.893705i
$905$	1.05606	+	5.51315i	0.0351046	+	0.183263i
$906$		0			0
$907$	−30.8634	+	30.8634i	−1.02480	+	1.02480i	−0.0251188	+	0.999684i	$0.507996\pi$
$907$	−30.8634	+	30.8634i	−1.02480	+	1.02480i	−0.999684	+	0.0251188i	$0.992004\pi$
$908$	47.1147	−	47.1147i	1.56356	−	1.56356i
$909$		0			0
$910$	16.7171	−	24.6389i	0.554166	−	0.816773i
$911$			26.5883i			0.880908i	0.897775	+	0.440454i	$0.145183\pi$
$911$			26.5883i			0.880908i	−0.897775	+	0.440454i	$0.854817\pi$
$912$		0			0
$913$	37.5671	+	37.5671i	1.24329	+	1.24329i
$914$	79.3724			2.62541
$915$		0			0
$916$	−48.2546			−1.59438
$917$	−2.21556	−	2.21556i	−0.0731642	−	0.0731642i
$918$		0			0
$919$			9.47447i			0.312534i	0.987715	+	0.156267i	$0.0499460\pi$
$919$			9.47447i			0.312534i	−0.987715	+	0.156267i	$0.950054\pi$
$920$	−8.07278	+	1.54636i	−0.266152	+	0.0509821i
$921$		0			0
$922$	2.75264	−	2.75264i	0.0906533	−	0.0906533i
$923$	−32.0706	+	32.0706i	−1.05562	+	1.05562i
$924$		0			0
$925$	−7.32319	+	16.9941i	−0.240785	+	0.558764i
$926$			29.1660i			0.958454i
$927$		0			0
$928$	8.12694	+	8.12694i	0.266780	+	0.266780i
$929$	−42.9079			−1.40776			−0.703881	−	0.710317i	$-0.748551\pi$
$929$	−42.9079			−1.40776			−0.703881	+	0.710317i	$0.748551\pi$
$930$		0			0
$931$	2.04710			0.0670908
$932$	−33.0471	−	33.0471i	−1.08249	−	1.08249i
$933$		0			0
$934$		−	26.0294i		−	0.851709i
$935$	56.4862	+	38.3249i	1.84730	+	1.25336i
$936$		0			0
$937$	13.4588	−	13.4588i	0.439680	−	0.439680i	−0.452224	−	0.891904i	$-0.649369\pi$
$937$	13.4588	−	13.4588i	0.439680	−	0.439680i	0.891904	+	0.452224i	$0.149369\pi$
$938$	5.27909	−	5.27909i	0.172369	−	0.172369i
$939$		0			0
$940$	−48.2922	−	32.7654i	−1.57512	−	1.06869i
$941$			15.7734i			0.514197i	0.966385	+	0.257098i	$0.0827665\pi$
$941$			15.7734i			0.514197i	−0.966385	+	0.257098i	$0.917234\pi$
$942$		0			0
$943$	−4.96739	−	4.96739i	−0.161761	−	0.161761i
$944$	10.6280			0.345911
$945$		0			0
$946$	−60.4999			−1.96702
$947$	−6.08433	−	6.08433i	−0.197714	−	0.197714i	0.601305	−	0.799019i	$-0.294648\pi$
$947$	−6.08433	−	6.08433i	−0.197714	−	0.197714i	−0.799019	+	0.601305i	$0.794648\pi$
$948$		0			0
$949$			64.8279i			2.10440i
$950$	−9.55527	+	22.1739i	−0.310014	+	0.719416i
$951$		0			0
$952$	−20.4029	+	20.4029i	−0.661261	+	0.661261i
$953$	3.42948	−	3.42948i	0.111092	−	0.111092i	−0.649376	−	0.760468i	$-0.724970\pi$
$953$	3.42948	−	3.42948i	0.111092	−	0.111092i	0.760468	+	0.649376i	$0.224970\pi$
$954$		0			0
$955$	−57.6728	+	11.0474i	−1.86625	+	0.357485i
$956$			1.02871i			0.0332707i
$957$		0			0
$958$	−0.116657	−	0.116657i	−0.00376901	−	0.00376901i
$959$	13.9292			0.449798
$960$		0			0
$961$	−4.97535			−0.160495
$962$	−34.8469	−	34.8469i	−1.12351	−	1.12351i
$963$		0			0
$964$			70.6411i			2.27520i
$965$	9.98757	−	14.7205i	0.321511	−	0.473868i
$966$		0			0
$967$	29.9517	−	29.9517i	0.963181	−	0.963181i	−0.0361644	−	0.999346i	$-0.511514\pi$
$967$	29.9517	−	29.9517i	0.963181	−	0.963181i	0.999346	+	0.0361644i	$0.0115140\pi$
$968$	−11.0908	+	11.0908i	−0.356471	+	0.356471i
$969$		0			0
$970$	2.54852	+	13.3045i	0.0818280	+	0.427183i
$971$			15.5529i			0.499118i	0.968360	+	0.249559i	$0.0802856\pi$
$971$			15.5529i			0.499118i	−0.968360	+	0.249559i	$0.919714\pi$
$972$		0			0
$973$	−0.744399	−	0.744399i	−0.0238643	−	0.0238643i
$974$	−98.6685			−3.16154
$975$		0			0
$976$	23.0633			0.738239
$977$	27.6229	+	27.6229i	0.883734	+	0.883734i	0.993912	−	0.110178i	$-0.0351422\pi$
$977$	27.6229	+	27.6229i	0.883734	+	0.883734i	−0.110178	+	0.993912i	$0.535142\pi$
$978$		0			0
$979$			58.9181i			1.88303i
$980$	1.49958	+	7.82856i	0.0479024	+	0.250074i
$981$		0			0
$982$	−17.1184	+	17.1184i	−0.546269	+	0.546269i
$983$	−6.58441	+	6.58441i	−0.210010	+	0.210010i	−0.804272	−	0.594262i	$-0.797444\pi$
$983$	−6.58441	+	6.58441i	−0.210010	+	0.210010i	0.594262	+	0.804272i	$0.297444\pi$
$984$		0			0
$985$	−22.1104	+	32.5881i	−0.704496	+	1.03834i
$986$		−	57.9001i		−	1.84391i
$987$		0			0
$988$	−29.1265	−	29.1265i	−0.926637	−	0.926637i
$989$	6.54067			0.207981
$990$		0			0
$991$	−52.7013			−1.67411			−0.837056	−	0.547117i	$-0.815725\pi$
$991$	−52.7013			−1.67411			−0.837056	+	0.547117i	$0.815725\pi$
$992$	13.2044	+	13.2044i	0.419240	+	0.419240i
$993$		0			0
$994$		−	18.9539i		−	0.601182i
$995$	−30.0773	+	5.76138i	−0.953514	+	0.182648i
$996$		0			0
$997$	14.3967	−	14.3967i	0.455949	−	0.455949i	−0.441374	−	0.897323i	$-0.645509\pi$
$997$	14.3967	−	14.3967i	0.455949	−	0.455949i	0.897323	+	0.441374i	$0.145509\pi$
$998$	28.3948	−	28.3948i	0.898822	−	0.898822i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.m.a.323.4	✓	48
3.2	odd	2	inner	945.2.m.a.323.21	yes	48
5.2	odd	4	inner	945.2.m.a.512.21	yes	48
15.2	even	4	inner	945.2.m.a.512.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.m.a.323.4	✓	48	1.1	even	1	trivial
945.2.m.a.323.21	yes	48	3.2	odd	2	inner
945.2.m.a.512.4	yes	48	15.2	even	4	inner
945.2.m.a.512.21	yes	48	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66804 - 1.66804i) q^{2} +3.56469i q^{4} +(0.420676 + 2.19614i) q^{5} +(0.707107 - 0.707107i) q^{7} +(2.60996 - 2.60996i) q^{8} +O(q^{10})\)	\(q+(-1.66804 - 1.66804i) q^{2} +3.56469i q^{4} +(0.420676 + 2.19614i) q^{5} +(0.707107 - 0.707107i) q^{7} +(2.60996 - 2.60996i) q^{8} +(2.96154 - 4.36494i) q^{10} +3.90505i q^{11} +(3.99143 + 3.99143i) q^{13} -2.35896 q^{14} -1.57763 q^{16} +(-5.52768 - 5.52768i) q^{17} +2.04710i q^{19} +(-7.82856 + 1.49958i) q^{20} +(6.51376 - 6.51376i) q^{22} +(-0.704206 + 0.704206i) q^{23} +(-4.64606 + 1.84773i) q^{25} -13.3157i q^{26} +(2.52062 + 2.52062i) q^{28} -3.13979 q^{29} -5.10144 q^{31} +(-2.58837 - 2.58837i) q^{32} +18.4407i q^{34} +(1.85037 + 1.25544i) q^{35} +(2.61698 - 2.61698i) q^{37} +(3.41463 - 3.41463i) q^{38} +(6.82978 + 4.63389i) q^{40} +7.05389i q^{41} +(-4.64400 - 4.64400i) q^{43} -13.9203 q^{44} +2.34928 q^{46} +(5.17704 + 5.17704i) q^{47} -1.00000i q^{49} +(10.8319 + 4.66772i) q^{50} +(-14.2282 + 14.2282i) q^{52} +(-4.29145 + 4.29145i) q^{53} +(-8.57603 + 1.64276i) q^{55} -3.69104i q^{56} +(5.23729 + 5.23729i) q^{58} -6.73665 q^{59} -14.6189 q^{61} +(8.50938 + 8.50938i) q^{62} +11.7903i q^{64} +(-7.08663 + 10.4448i) q^{65} +(-2.23789 + 2.23789i) q^{67} +(19.7045 - 19.7045i) q^{68} +(-0.992359 - 5.18061i) q^{70} +8.03487i q^{71} +(8.12090 + 8.12090i) q^{73} -8.73044 q^{74} -7.29726 q^{76} +(2.76129 + 2.76129i) q^{77} -5.60247i q^{79} +(-0.663673 - 3.46470i) q^{80} +(11.7661 - 11.7661i) q^{82} +(9.62012 - 9.62012i) q^{83} +(9.81419 - 14.4649i) q^{85} +15.4927i q^{86} +(10.1920 + 10.1920i) q^{88} +15.0877 q^{89} +5.64473 q^{91} +(-2.51028 - 2.51028i) q^{92} -17.2710i q^{94} +(-4.49571 + 0.861165i) q^{95} +(-1.81595 + 1.81595i) q^{97} +(-1.66804 + 1.66804i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 32 q^{10} + 8 q^{13} - 56 q^{16} + 16 q^{22} + 16 q^{25} + 48 q^{31} + 64 q^{37} - 16 q^{40} - 56 q^{43} - 8 q^{46} - 48 q^{52} - 64 q^{55} - 40 q^{58} - 32 q^{61} - 16 q^{70} + 16 q^{73} - 8 q^{76} - 16 q^{82} + 48 q^{85} - 24 q^{88} - 48 q^{97}+O(q^{100}) \) 48 * q - 32 * q^10 + 8 * q^13 - 56 * q^16 + 16 * q^22 + 16 * q^25 + 48 * q^31 + 64 * q^37 - 16 * q^40 - 56 * q^43 - 8 * q^46 - 48 * q^52 - 64 * q^55 - 40 * q^58 - 32 * q^61 - 16 * q^70 + 16 * q^73 - 8 * q^76 - 16 * q^82 + 48 * q^85 - 24 * q^88 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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