LMFDB - Embedded newform 945.2.m.a.323.21

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			323.21
Character	$\chi$	$=$	945.323
Dual form			945.2.m.a.512.21

$q$-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	$0.0639652\pi$
$2$	1.66804	+	1.66804i	1.17948	+	1.17948i	0.199603	+	0.979877i	$0.436035\pi$
$3$		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	$-0.799637\pi$
$11$		−	3.90505i		−	1.17742i	0.808346	−	0.588708i	$-0.200363\pi$
$12$		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	$0.146887\pi$
$17$	5.52768	+	5.52768i	1.34066	+	1.34066i	0.445255	+	0.895404i	$0.353113\pi$
$18$		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	−0.629866	−	0.776703i	$-0.716890\pi$
$23$	0.704206	−	0.704206i	0.146837	−	0.146837i	0.776703	+	0.629866i	$0.216890\pi$
$24$		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	$-0.405838\pi$
$29$	3.13979			0.583045			0.291523	+	0.956564i	$0.405838\pi$
$30$		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	$-0.814316\pi$
$41$		−	7.05389i		−	1.10163i	0.834627	−	0.550816i	$-0.185684\pi$
$42$		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	0.220286	−	0.975435i	$-0.429301\pi$
$47$	−5.17704	−	5.17704i	−0.755149	−	0.755149i	−0.975435	+	0.220286i	$0.929301\pi$
$48$		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	−0.348014	−	0.937489i	$-0.613144\pi$
$53$	4.29145	−	4.29145i	0.589476	−	0.589476i	0.937489	+	0.348014i	$0.113144\pi$
$54$		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	$-0.355503\pi$
$59$	6.73665			0.877037			0.438518	+	0.898722i	$0.355503\pi$
$60$		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	$-0.841803\pi$
$71$		−	8.03487i		−	0.953563i	0.879022	−	0.476782i	$-0.158197\pi$
$72$		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	$0.518347\pi$
$83$	−9.62012	+	9.62012i	−1.05595	+	1.05595i	−0.998339	+	0.0576065i	$0.981653\pi$
$84$		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	$-0.794979\pi$
$89$	−15.0877			−1.59929			−0.799645	+	0.600473i	$0.794979\pi$
$90$		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	$0.0681138\pi$
$101$			4.26831i			0.424713i	−0.977192	+	0.212357i	$0.931886\pi$
$102$		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	0.695468	−	0.718557i	$-0.255197\pi$
$107$	−0.238838	−	0.238838i	−0.0230894	−	0.0230894i	−0.718557	+	0.695468i	$0.755197\pi$
$108$		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	−0.906488	−	0.422231i	$-0.861247\pi$
$113$	−5.14772	+	5.14772i	−0.484257	+	0.484257i	0.422231	+	0.906488i	$0.361247\pi$
$114$		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	$0.0437067\pi$
$131$			3.13327i			0.273755i	−0.990588	+	0.136878i	$0.956293\pi$
$132$		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	0.147559	−	0.989053i	$-0.452858\pi$
$137$	−9.84944	−	9.84944i	−0.841494	−	0.841494i	−0.989053	+	0.147559i	$0.952858\pi$
$138$		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	$-0.606356\pi$
$149$	−8.00615			−0.655889			−0.327944	+	0.944697i	$0.606356\pi$
$150$		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	0.832032	−	0.554727i	$-0.187177\pi$
$167$	3.58358	+	3.58358i	0.277305	+	0.277305i	−0.554727	+	0.832032i	$0.687177\pi$
$168$		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	−0.465996	−	0.884787i	$-0.654304\pi$
$173$	5.50833	−	5.50833i	0.418791	−	0.418791i	0.884787	+	0.465996i	$0.154304\pi$
$174$		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	$-0.318743\pi$
$179$	14.4269			1.07831			0.539157	+	0.842205i	$0.318743\pi$
$180$		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	$-0.600992\pi$
$191$		−	26.2610i		−	1.90018i	0.311980	−	0.950089i	$-0.399008\pi$
$192$		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	0.106997	−	0.994259i	$-0.465876\pi$
$197$	−12.4533	−	12.4533i	−0.887262	−	0.887262i	−0.994259	+	0.106997i	$0.965876\pi$
$198$		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	0.993249	−	0.116002i	$-0.0370080\pi$
$227$	13.2171	+	13.2171i	0.877246	+	0.877246i	−0.116002	+	0.993249i	$0.537008\pi$
$228$		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	−0.334909	−	0.942251i	$-0.608705\pi$
$233$	9.27067	−	9.27067i	0.607342	−	0.607342i	0.942251	+	0.334909i	$0.108705\pi$
$234$		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	$-0.502971\pi$
$239$	−0.288582			−0.0186668			−0.00933342	+	0.999956i	$0.502971\pi$
$240$		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	$0.131229\pi$
$251$			12.6962i			0.801375i	−0.916215	+	0.400687i	$0.868771\pi$
$252$		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	0.0969421	−	0.995290i	$-0.469094\pi$
$257$	−14.4016	−	14.4016i	−0.898348	−	0.898348i	−0.995290	+	0.0969421i	$0.969094\pi$
$258$		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	$-0.469934\pi$
$263$	17.6745	−	17.6745i	1.08986	−	1.08986i	0.995542	−	0.0943154i	$-0.0300662\pi$
$264$		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	$-0.708249\pi$
$269$	−19.9619			−1.21710			−0.608550	+	0.793515i	$0.708249\pi$
$270$		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	$-0.986128\pi$
$281$		−	1.46058i		−	0.0871308i	0.999051	−	0.0435654i	$-0.0138717\pi$
$282$		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	−0.937661	−	0.347552i	$-0.887013\pi$
$293$	−10.1010	+	10.1010i	−0.590108	+	0.590108i	0.347552	+	0.937661i	$0.387013\pi$
$294$		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	$0.143903\pi$
$311$			15.4076i			0.873684i	−0.899538	+	0.436842i	$0.856097\pi$
$312$		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	0.921408	−	0.388596i	$-0.127040\pi$
$317$	9.48645	+	9.48645i	0.532812	+	0.532812i	−0.388596	+	0.921408i	$0.627040\pi$
$318$		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	0.730410	−	0.683009i	$-0.239329\pi$
$347$	0.882971	+	0.882971i	0.0474003	+	0.0474003i	−0.683009	+	0.730410i	$0.739329\pi$
$348$		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	−0.501265	−	0.865294i	$-0.667132\pi$
$353$	6.83948	−	6.83948i	0.364029	−	0.364029i	0.865294	+	0.501265i	$0.167132\pi$
$354$		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	$-0.863786\pi$
$359$	−34.4775			−1.81965			−0.909827	+	0.414987i	$0.863786\pi$
$360$		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	−0.220449	−	0.975398i	$-0.570752\pi$
$383$	14.7746	−	14.7746i	0.754949	−	0.754949i	0.975398	+	0.220449i	$0.0707523\pi$
$384$		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	$-0.573314\pi$
$389$	−9.00529			−0.456586			−0.228293	+	0.973592i	$0.573314\pi$
$390$		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	$-0.935794\pi$
$401$		−	8.02382i		−	0.400690i	0.979725	−	0.200345i	$-0.0642064\pi$
$402$		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	$-0.814311\pi$
$419$	−34.1683			−1.66923			−0.834616	+	0.550832i	$0.814311\pi$
$420$		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	$0.0547672\pi$
$431$			7.10877i			0.342417i	−0.985235	+	0.171209i	$0.945233\pi$
$432$		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	−0.864032	−	0.503437i	$-0.832069\pi$
$443$	−7.58964	+	7.58964i	−0.360595	+	0.360595i	0.503437	+	0.864032i	$0.332069\pi$
$444$		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	$-0.353844\pi$
$449$	18.7824			0.886395			0.443198	+	0.896424i	$0.353844\pi$
$450$		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	$-0.987765\pi$
$461$		−	1.65023i		−	0.0768587i	0.999261	−	0.0384294i	$-0.0122355\pi$
$462$		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	0.503148	−	0.864201i	$-0.332175\pi$
$467$	−7.80242	−	7.80242i	−0.361053	−	0.361053i	−0.864201	+	0.503148i	$0.832175\pi$
$468$		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	$-0.500509\pi$
$479$	−0.0699366			−0.00319549			−0.00159774	+	0.999999i	$0.500509\pi$
$480$		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	$0.0743870\pi$
$491$			10.2626i			0.463144i	−0.972818	+	0.231572i	$0.925613\pi$
$492$		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	−0.934371	−	0.356302i	$-0.884038\pi$
$503$	−12.9647	+	12.9647i	−0.578069	+	0.578069i	0.356302	+	0.934371i	$0.384038\pi$
$504$		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	$-0.374005\pi$
$509$	17.3978			0.771142			0.385571	+	0.922678i	$0.374005\pi$
$510$		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	$0.187240\pi$
$521$			25.3312i			1.10978i	−0.831924	+	0.554890i	$0.812760\pi$
$522$		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	0.562627	−	0.826711i	$-0.309791\pi$
$557$	−6.23261	−	6.23261i	−0.264084	−	0.264084i	−0.826711	+	0.562627i	$0.809791\pi$
$558$		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	$0.575750\pi$
$563$	−28.6524	+	28.6524i	−1.20755	+	1.20755i	−0.971817	+	0.235737i	$0.924250\pi$
$564$		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	$-0.810891\pi$
$569$	−39.5328			−1.65730			−0.828652	+	0.559765i	$0.810891\pi$
$570$		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	0.997649	−	0.0685309i	$-0.0218312\pi$
$587$	22.5108	+	22.5108i	0.929118	+	0.929118i	−0.0685309	+	0.997649i	$0.521831\pi$
$588$		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	−0.330025	−	0.943972i	$-0.607057\pi$
$593$	14.9506	−	14.9506i	0.613948	−	0.613948i	0.943972	+	0.330025i	$0.107057\pi$
$594$		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	$-0.419604\pi$
$599$	12.2321			0.499788			0.249894	+	0.968273i	$0.419604\pi$
$600$		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	0.958715	−	0.284370i	$-0.0917844\pi$
$617$	16.7504	+	16.7504i	0.674345	+	0.674345i	−0.284370	+	0.958715i	$0.591784\pi$
$618$		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	$0.230867\pi$
$641$			33.5895i			1.32670i	−0.748307	+	0.663352i	$0.769133\pi$
$642$		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	0.621863	−	0.783126i	$-0.286376\pi$
$647$	−4.10192	−	4.10192i	−0.161263	−	0.161263i	−0.783126	+	0.621863i	$0.786376\pi$
$648$		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	−0.901307	−	0.433180i	$-0.857391\pi$
$653$	−11.9625	+	11.9625i	−0.468127	+	0.468127i	0.433180	+	0.901307i	$0.357391\pi$
$654$		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	$-0.642593\pi$
$659$	−22.2380			−0.866270			−0.433135	+	0.901329i	$0.642593\pi$
$660$		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	0.846178	−	0.532900i	$-0.178898\pi$
$677$	8.15127	+	8.15127i	0.313279	+	0.313279i	−0.532900	+	0.846178i	$0.678898\pi$
$678$		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	−0.729550	−	0.683928i	$-0.760270\pi$
$683$	−1.19230	+	1.19230i	−0.0456222	+	0.0456222i	0.683928	+	0.729550i	$0.260270\pi$
$684$		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	$-0.833761\pi$
$701$		−	26.4148i		−	0.997672i	0.866696	−	0.498836i	$-0.166239\pi$
$702$		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	$-0.624971\pi$
$719$	−20.5182			−0.765200			−0.382600	+	0.923914i	$0.624971\pi$
$720$		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	−0.686421	−	0.727204i	$-0.740819\pi$
$743$	1.11168	−	1.11168i	0.0407834	−	0.0407834i	0.727204	+	0.686421i	$0.240819\pi$
$744$		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	$-0.638663\pi$
$761$		−	50.0198i		−	1.81322i	0.421974	−	0.906608i	$-0.361337\pi$
$762$		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	−0.387986	−	0.921665i	$-0.626829\pi$
$773$	14.8378	−	14.8378i	0.533680	−	0.533680i	0.921665	+	0.387986i	$0.126829\pi$
$774$		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	0.812647	−	0.582757i	$-0.198026\pi$
$797$	6.49007	+	6.49007i	0.229890	+	0.229890i	−0.582757	+	0.812647i	$0.698026\pi$
$798$		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	$-0.529508\pi$
$809$	−5.26585			−0.185137			−0.0925686	+	0.995706i	$0.529508\pi$
$810$		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	$-0.891459\pi$
$821$		−	19.1644i		−	0.668841i	0.942424	−	0.334420i	$-0.108541\pi$
$822$		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	0.840196	−	0.542283i	$-0.182440\pi$
$827$	8.56728	+	8.56728i	0.297914	+	0.297914i	−0.542283	+	0.840196i	$0.682440\pi$
$828$		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	$-0.372710\pi$
$839$	22.5537			0.778639			0.389319	+	0.921103i	$0.372710\pi$
$840$		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	$-0.971114\pi$
$857$	−31.8071	−	31.8071i	−1.08651	−	1.08651i	−0.0906234	−	0.995885i	$-0.528886\pi$
$858$		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	−0.179585	−	0.983743i	$-0.557475\pi$
$863$	23.6236	−	23.6236i	0.804158	−	0.804158i	0.983743	+	0.179585i	$0.0574754\pi$
$864$		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	$0.0131613\pi$
$881$			2.45383i			0.0826715i	−0.999145	+	0.0413358i	$0.986839\pi$
$882$		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	0.336378	−	0.941727i	$-0.390798\pi$
$887$	−18.0288	−	18.0288i	−0.605349	−	0.605349i	−0.941727	+	0.336378i	$0.890798\pi$
$888$		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	$-0.854817\pi$
$911$		−	26.5883i		−	0.880908i	0.897775	−	0.440454i	$-0.145183\pi$
$912$		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	$-0.251449\pi$
$929$	42.9079			1.40776			0.703881	+	0.710317i	$0.251449\pi$
$930$		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	$-0.917234\pi$
$941$		−	15.7734i		−	0.514197i	0.966385	−	0.257098i	$-0.0827665\pi$
$942$		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	0.799019	−	0.601305i	$-0.205352\pi$
$947$	6.08433	+	6.08433i	0.197714	+	0.197714i	−0.601305	+	0.799019i	$0.705352\pi$
$948$		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	−0.760468	−	0.649376i	$-0.775030\pi$
$953$	−3.42948	+	3.42948i	−0.111092	+	0.111092i	0.649376	+	0.760468i	$0.275030\pi$
$954$		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	$-0.919714\pi$
$971$		−	15.5529i		−	0.499118i	0.968360	−	0.249559i	$-0.0802856\pi$
$972$		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	0.110178	−	0.993912i	$-0.464858\pi$
$977$	−27.6229	−	27.6229i	−0.883734	−	0.883734i	−0.993912	+	0.110178i	$0.964858\pi$
$978$		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	−0.594262	−	0.804272i	$-0.702556\pi$
$983$	6.58441	−	6.58441i	0.210010	−	0.210010i	0.804272	+	0.594262i	$0.202556\pi$
$984$		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.323.21	yes	48
3.2	odd	2	inner	945.2.m.a.323.4	✓	48
5.2	odd	4	inner	945.2.m.a.512.4	yes	48
15.2	even	4	inner	945.2.m.a.512.21	yes	48

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