LMFDB - Embedded newform 624.2.cn.d.353.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.3
Root			$0.500000 - 1.00333i$ of defining polynomial
Character	$\chi$	$=$	624.353
Dual form			624.2.cn.d.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0795432 + 1.73022i) q^{3} +(2.02097 + 2.02097i) q^{5} +(-3.46723 + 0.929042i) q^{7} +(-2.98735 + 0.275255i) q^{9} +(4.05922 + 1.08766i) q^{11} +(-3.60121 - 0.176977i) q^{13} +(-3.33598 + 3.65748i) q^{15} +(-1.72704 + 2.99132i) q^{17} +(-0.581191 - 2.16903i) q^{19} +(-1.88324 - 5.92518i) q^{21} +(1.51618 + 2.62611i) q^{23} +3.16864i q^{25} +(-0.713876 - 5.14688i) q^{27} +(1.74432 - 1.00708i) q^{29} +(-1.21829 + 1.21829i) q^{31} +(-1.55902 + 7.10987i) q^{33} +(-8.88473 - 5.12960i) q^{35} +(-1.25335 + 4.67758i) q^{37} +(0.0197576 - 6.24497i) q^{39} +(2.05521 - 7.67015i) q^{41} +(1.68905 + 0.975173i) q^{43} +(-6.59362 - 5.48105i) q^{45} +(0.957390 - 0.957390i) q^{47} +(5.09639 - 2.94240i) q^{49} +(-5.31303 - 2.75023i) q^{51} +7.22186i q^{53} +(6.00542 + 10.4017i) q^{55} +(3.70668 - 1.17812i) q^{57} +(2.66284 + 9.93785i) q^{59} +(-0.137104 + 0.237470i) q^{61} +(10.1021 - 3.72974i) q^{63} +(-6.92026 - 7.63559i) q^{65} +(-4.10121 - 1.09891i) q^{67} +(-4.42315 + 2.83223i) q^{69} +(-10.6578 + 2.85575i) q^{71} +(10.0822 + 10.0822i) q^{73} +(-5.48246 + 0.252044i) q^{75} -15.0847 q^{77} -1.58051 q^{79} +(8.84847 - 1.64456i) q^{81} +(2.58938 + 2.58938i) q^{83} +(-9.53567 + 2.55507i) q^{85} +(1.88122 + 2.93795i) q^{87} +(9.50933 + 2.54802i) q^{89} +(12.6506 - 2.73205i) q^{91} +(-2.20483 - 2.01101i) q^{93} +(3.20898 - 5.55812i) q^{95} +(-2.07638 - 7.74915i) q^{97} +(-12.4257 - 2.13191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73}+ \cdots + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0795432	+	1.73022i	0.0459243	+	0.998945i
$3$	0.0795432	+	1.73022i	0.0459243	+	0.998945i
$4$		0			0
$5$	2.02097	+	2.02097i	0.903805	+	0.903805i	0.995763	−	0.0919576i	$-0.0293124\pi$
$5$	2.02097	+	2.02097i	0.903805	+	0.903805i	−0.0919576	+	0.995763i	$0.529312\pi$
$6$		0			0
$7$	−3.46723	+	0.929042i	−1.31049	+	0.351145i	−0.845407	−	0.534122i	$-0.820642\pi$
$7$	−3.46723	+	0.929042i	−1.31049	+	0.351145i	−0.465083	+	0.885267i	$0.653975\pi$
$8$		0			0
$9$	−2.98735	+	0.275255i	−0.995782	+	0.0917517i
$10$		0			0
$11$	4.05922	+	1.08766i	1.22390	+	0.327943i	0.812201	−	0.583377i	$-0.198269\pi$
$11$	4.05922	+	1.08766i	1.22390	+	0.327943i	0.411699	+	0.911320i	$0.364936\pi$
$12$		0			0
$13$	−3.60121	−	0.176977i	−0.998795	−	0.0490845i
$13$	−3.60121	−	0.176977i	−0.998795	−	0.0490845i
$14$		0			0
$15$	−3.33598	+	3.65748i	−0.861345	+	0.944358i
$16$		0			0
$17$	−1.72704	+	2.99132i	−0.418869	+	0.725502i	−0.995826	−	0.0912724i	$-0.970907\pi$
$17$	−1.72704	+	2.99132i	−0.418869	+	0.725502i	0.576957	+	0.816774i	$0.304240\pi$
$18$		0			0
$19$	−0.581191	−	2.16903i	−0.133334	−	0.497611i	0.866665	−	0.498891i	$-0.166259\pi$
$19$	−0.581191	−	2.16903i	−0.133334	−	0.497611i	−0.999999	+	0.00128023i	$0.999592\pi$
$20$		0			0
$21$	−1.88324	−	5.92518i	−0.410958	−	1.29298i
$22$		0			0
$23$	1.51618	+	2.62611i	0.316146	+	0.547581i	0.979680	−	0.200565i	$-0.0642777\pi$
$23$	1.51618	+	2.62611i	0.316146	+	0.547581i	−0.663534	+	0.748146i	$0.730944\pi$
$24$		0			0
$25$			3.16864i			0.633728i
$26$		0			0
$27$	−0.713876	−	5.14688i	−0.137386	−	0.990518i
$28$		0			0
$29$	1.74432	−	1.00708i	0.323911	−	0.187010i	−0.329223	−	0.944252i	$-0.606787\pi$
$29$	1.74432	−	1.00708i	0.323911	−	0.187010i	0.653135	+	0.757242i	$0.273454\pi$
$30$		0			0
$31$	−1.21829	+	1.21829i	−0.218812	+	0.218812i	−0.807998	−	0.589186i	$-0.799449\pi$
$31$	−1.21829	+	1.21829i	−0.218812	+	0.218812i	0.589186	+	0.807998i	$0.299449\pi$
$32$		0			0
$33$	−1.55902	+	7.10987i	−0.271390	+	1.23767i
$34$		0			0
$35$	−8.88473	−	5.12960i	−1.50179	−	0.867061i
$36$		0			0
$37$	−1.25335	+	4.67758i	−0.206050	+	0.768990i	0.783077	+	0.621925i	$0.213649\pi$
$37$	−1.25335	+	4.67758i	−0.206050	+	0.768990i	−0.989127	+	0.147065i	$0.953017\pi$
$38$		0			0
$39$	0.0197576	−	6.24497i	0.00316375	−	0.999995i
$40$		0			0
$41$	2.05521	−	7.67015i	0.320970	−	1.19788i	−0.597332	−	0.801994i	$-0.703772\pi$
$41$	2.05521	−	7.67015i	0.320970	−	1.19788i	0.918302	−	0.395881i	$-0.129561\pi$
$42$		0			0
$43$	1.68905	+	0.975173i	0.257578	+	0.148712i	0.623229	−	0.782039i	$-0.285820\pi$
$43$	1.68905	+	0.975173i	0.257578	+	0.148712i	−0.365651	+	0.930752i	$0.619154\pi$
$44$		0			0
$45$	−6.59362	−	5.48105i	−0.982919	−	0.817067i
$46$		0			0
$47$	0.957390	−	0.957390i	0.139650	−	0.139650i	−0.633826	−	0.773476i	$-0.718516\pi$
$47$	0.957390	−	0.957390i	0.139650	−	0.139650i	0.773476	+	0.633826i	$0.218516\pi$
$48$		0			0
$49$	5.09639	−	2.94240i	0.728056	−	0.420343i
$50$		0			0
$51$	−5.31303	−	2.75023i	−0.743973	−	0.385109i
$52$		0			0
$53$			7.22186i			0.991999i	0.868323	+	0.495999i	$0.165198\pi$
$53$			7.22186i			0.991999i	−0.868323	+	0.495999i	$0.834802\pi$
$54$		0			0
$55$	6.00542	+	10.4017i	0.809771	+	1.40256i
$56$		0			0
$57$	3.70668	−	1.17812i	0.490962	−	0.156046i
$58$		0			0
$59$	2.66284	+	9.93785i	0.346672	+	1.29380i	0.890647	+	0.454696i	$0.150252\pi$
$59$	2.66284	+	9.93785i	0.346672	+	1.29380i	−0.543975	+	0.839101i	$0.683081\pi$
$60$		0			0
$61$	−0.137104	+	0.237470i	−0.0175543	+	0.0304050i	−0.874669	−	0.484720i	$-0.838921\pi$
$61$	−0.137104	+	0.237470i	−0.0175543	+	0.0304050i	0.857115	+	0.515125i	$0.172255\pi$
$62$		0			0
$63$	10.1021	−	3.72974i	1.27274	−	0.469903i
$64$		0			0
$65$	−6.92026	−	7.63559i	−0.858353	−	0.947079i
$66$		0			0
$67$	−4.10121	−	1.09891i	−0.501042	−	0.134254i	−0.000558430	−	1.00000i	$-0.500178\pi$
$67$	−4.10121	−	1.09891i	−0.501042	−	0.134254i	−0.500484	+	0.865746i	$0.666844\pi$
$68$		0			0
$69$	−4.42315	+	2.83223i	−0.532485	+	0.340960i
$70$		0			0
$71$	−10.6578	+	2.85575i	−1.26485	+	0.338915i	−0.828055	−	0.560647i	$-0.810553\pi$
$71$	−10.6578	+	2.85575i	−1.26485	+	0.338915i	−0.436793	+	0.899562i	$0.643886\pi$
$72$		0			0
$73$	10.0822	+	10.0822i	1.18003	+	1.18003i	0.979735	+	0.200296i	$0.0641903\pi$
$73$	10.0822	+	10.0822i	1.18003	+	1.18003i	0.200296	+	0.979735i	$0.435810\pi$
$74$		0			0
$75$	−5.48246	+	0.252044i	−0.633059	+	0.0291035i
$76$		0			0
$77$	−15.0847			−1.71906
$78$		0			0
$79$	−1.58051			−0.177821			−0.0889105	−	0.996040i	$-0.528339\pi$
$79$	−1.58051			−0.177821			−0.0889105	+	0.996040i	$0.528339\pi$
$80$		0			0
$81$	8.84847	−	1.64456i	0.983163	−	0.182729i
$82$		0			0
$83$	2.58938	+	2.58938i	0.284221	+	0.284221i	0.834790	−	0.550569i	$-0.185589\pi$
$83$	2.58938	+	2.58938i	0.284221	+	0.284221i	−0.550569	+	0.834790i	$0.685589\pi$
$84$		0			0
$85$	−9.53567	+	2.55507i	−1.03429	+	0.277137i
$86$		0			0
$87$	1.88122	+	2.93795i	0.201688	+	0.314981i
$88$		0			0
$89$	9.50933	+	2.54802i	1.00799	+	0.270089i	0.724788	−	0.688972i	$-0.241938\pi$
$89$	9.50933	+	2.54802i	1.00799	+	0.270089i	0.283199	+	0.959061i	$0.408604\pi$
$90$		0			0
$91$	12.6506	−	2.73205i	1.32615	−	0.286397i
$92$		0			0
$93$	−2.20483	−	2.01101i	−0.228630	−	0.208533i
$94$		0			0
$95$	3.20898	−	5.55812i	0.329235	−	0.570251i
$96$		0			0
$97$	−2.07638	−	7.74915i	−0.210824	−	0.786807i	−0.987595	−	0.157023i	$-0.949810\pi$
$97$	−2.07638	−	7.74915i	−0.210824	−	0.786807i	0.776771	−	0.629784i	$-0.216856\pi$
$98$		0			0
$99$	−12.4257	−	2.13191i	−1.24883	−	0.214265i
$100$		0			0
$101$	1.05342	+	1.82458i	0.104820	+	0.181553i	0.913665	−	0.406469i	$-0.133240\pi$
$101$	1.05342	+	1.82458i	0.104820	+	0.181553i	−0.808845	+	0.588022i	$0.799907\pi$
$102$		0			0
$103$			14.2629i			1.40537i	0.711503	+	0.702683i	$0.248015\pi$
$103$			14.2629i			1.40537i	−0.711503	+	0.702683i	$0.751985\pi$
$104$		0			0
$105$	8.16864	−	15.7806i	0.797178	−	1.54003i
$106$		0			0
$107$	11.9906	−	6.92275i	1.15917	−	0.669248i	0.208066	−	0.978115i	$-0.433283\pi$
$107$	11.9906	−	6.92275i	1.15917	−	0.669248i	0.951105	+	0.308867i	$0.0999497\pi$
$108$		0			0
$109$	5.84220	−	5.84220i	0.559581	−	0.559581i	−0.369607	−	0.929188i	$-0.620508\pi$
$109$	5.84220	−	5.84220i	0.559581	−	0.559581i	0.929188	+	0.369607i	$0.120508\pi$
$110$		0			0
$111$	−8.19296	−	1.79651i	−0.777641	−	0.170518i
$112$		0			0
$113$	15.5920	+	9.00205i	1.46677	+	0.846841i	0.999309	−	0.0371710i	$-0.0118346\pi$
$113$	15.5920	+	9.00205i	1.46677	+	0.846841i	0.467463	+	0.884012i	$0.345168\pi$
$114$		0			0
$115$	−2.24312	+	8.37145i	−0.209172	+	0.780641i
$116$		0			0
$117$	10.8068	−	0.462560i	0.999085	−	0.0427637i
$118$		0			0
$119$	3.20898	−	11.9761i	0.294167	−	1.09785i
$120$		0			0
$121$	5.76795	+	3.33013i	0.524359	+	0.302739i
$122$		0			0
$123$	13.4345	+	2.94586i	1.21135	+	0.265620i
$124$		0			0
$125$	3.70112	−	3.70112i	0.331039	−	0.331039i
$126$		0			0
$127$	17.9209	−	10.3466i	1.59022	−	0.918114i	0.596952	−	0.802277i	$-0.296378\pi$
$127$	17.9209	−	10.3466i	1.59022	−	0.918114i	0.993268	−	0.115837i	$-0.0369549\pi$
$128$		0			0
$129$	−1.55291	+	3.00000i	−0.136726	+	0.264135i
$130$		0			0
$131$		−	4.68295i		−	0.409151i	−0.978851	−	0.204576i	$-0.934419\pi$
$131$		−	4.68295i		−	0.409151i	0.978851	−	0.204576i	$-0.0655814\pi$
$132$		0			0
$133$	4.03025	+	6.98059i	0.349467	+	0.605294i
$134$		0			0
$135$	8.95897	−	11.8444i	0.771065	−	1.01940i
$136$		0			0
$137$	−1.41832	−	5.29326i	−0.121176	−	0.452234i	0.878499	−	0.477744i	$-0.158545\pi$
$137$	−1.41832	−	5.29326i	−0.121176	−	0.452234i	−0.999675	+	0.0255107i	$0.991879\pi$
$138$		0			0
$139$	7.34662	−	12.7247i	0.623132	−	1.07930i	−0.365767	−	0.930706i	$-0.619193\pi$
$139$	7.34662	−	12.7247i	0.623132	−	1.07930i	0.988899	−	0.148590i	$-0.0474734\pi$
$140$		0			0
$141$	1.73265	+	1.58034i	0.145916	+	0.133089i
$142$		0			0
$143$	−14.4256	−	4.63529i	−1.20633	−	0.387622i
$144$		0			0
$145$	5.56049	+	1.48993i	0.461774	+	0.123732i
$146$		0			0
$147$	5.49640	+	8.58385i	0.453335	+	0.707984i
$148$		0			0
$149$	−9.98255	+	2.67482i	−0.817803	+	0.219130i	−0.643386	−	0.765542i	$-0.722471\pi$
$149$	−9.98255	+	2.67482i	−0.817803	+	0.219130i	−0.174417	+	0.984672i	$0.555804\pi$
$150$		0			0
$151$	6.48932	+	6.48932i	0.528094	+	0.528094i	0.920004	−	0.391910i	$-0.128186\pi$
$151$	6.48932	+	6.48932i	0.528094	+	0.528094i	−0.391910	+	0.920004i	$0.628186\pi$
$152$		0			0
$153$	4.33589	−	9.41149i	0.350536	−	0.760874i
$154$		0			0
$155$	−4.92427			−0.395527
$156$		0			0
$157$	−14.1431			−1.12874			−0.564372	−	0.825520i	$-0.690882\pi$
$157$	−14.1431			−1.12874			−0.564372	+	0.825520i	$0.690882\pi$
$158$		0			0
$159$	−12.4954	+	0.574450i	−0.990952	+	0.0455568i
$160$		0			0
$161$	−7.69672	−	7.69672i	−0.606587	−	0.606587i
$162$		0			0
$163$	−1.07638	+	0.288415i	−0.0843084	+	0.0225904i	−0.300727	−	0.953710i	$-0.597229\pi$
$163$	−1.07638	+	0.288415i	−0.0843084	+	0.0225904i	0.216418	+	0.976301i	$0.430563\pi$
$164$		0			0
$165$	−17.5196	+	11.2181i	−1.36390	+	0.873328i
$166$		0			0
$167$	−5.39478	−	1.44553i	−0.417461	−	0.111858i	0.0439735	−	0.999033i	$-0.485998\pi$
$167$	−5.39478	−	1.44553i	−0.417461	−	0.111858i	−0.461434	+	0.887174i	$0.652665\pi$
$168$		0			0
$169$	12.9374	+	1.27466i	0.995181	+	0.0980507i
$170$		0			0
$171$	2.33326	+	6.31968i	0.178429	+	0.483278i
$172$		0			0
$173$	8.74765	−	15.1514i	0.665072	−	1.15194i	−0.314194	−	0.949359i	$-0.601734\pi$
$173$	8.74765	−	15.1514i	0.665072	−	1.15194i	0.979266	−	0.202579i	$-0.0649324\pi$
$174$		0			0
$175$	−2.94380	−	10.9864i	−0.222530	−	0.830494i
$176$		0			0
$177$	−16.9829	+	5.39779i	−1.27651	+	0.405723i
$178$		0			0
$179$	4.60754	+	7.98049i	0.344384	+	0.596490i	0.985242	−	0.171169i	$-0.0547545\pi$
$179$	4.60754	+	7.98049i	0.344384	+	0.596490i	−0.640858	+	0.767660i	$0.721421\pi$
$180$		0			0
$181$		−	13.8110i		−	1.02656i	−0.858220	−	0.513282i	$-0.828429\pi$
$181$		−	13.8110i		−	1.02656i	0.858220	−	0.513282i	$-0.171571\pi$
$182$		0			0
$183$	−0.421783	−	0.218331i	−0.0311791	−	0.0161395i
$184$		0			0
$185$	−11.9862	+	6.92026i	−0.881246	+	0.508788i
$186$		0			0
$187$	−10.2640	+	10.2640i	−0.750577	+	0.750577i
$188$		0			0
$189$	7.25684	+	17.1822i	0.527857	+	1.24982i
$190$		0			0
$191$	19.6614	+	11.3515i	1.42265	+	0.821366i	0.996525	−	0.0832996i	$-0.0265458\pi$
$191$	19.6614	+	11.3515i	1.42265	+	0.821366i	0.426123	+	0.904665i	$0.359879\pi$
$192$		0			0
$193$	−5.18821	+	19.3627i	−0.373456	+	1.39376i	0.482133	+	0.876098i	$0.339862\pi$
$193$	−5.18821	+	19.3627i	−0.373456	+	1.39376i	−0.855588	+	0.517657i	$0.826804\pi$
$194$		0			0
$195$	12.6608	−	12.5810i	0.906660	−	0.900941i
$196$		0			0
$197$	−4.82369	+	18.0023i	−0.343674	+	1.28261i	0.550480	+	0.834849i	$0.314445\pi$
$197$	−4.82369	+	18.0023i	−0.343674	+	1.28261i	−0.894154	+	0.447760i	$0.852222\pi$
$198$		0			0
$199$	3.90611	+	2.25519i	0.276897	+	0.159866i	0.632018	−	0.774954i	$-0.282227\pi$
$199$	3.90611	+	2.25519i	0.276897	+	0.159866i	−0.355121	+	0.934820i	$0.615560\pi$
$200$		0			0
$201$	1.57514	−	7.18341i	0.111102	−	0.506679i
$202$		0			0
$203$	−5.11233	+	5.11233i	−0.358815	+	0.358815i
$204$		0			0
$205$	19.6547	−	11.3476i	1.37274	−	0.792552i
$206$		0			0
$207$	−5.25221	−	7.42775i	−0.365054	−	0.516264i
$208$		0			0
$209$		−	9.43672i		−	0.652752i
$210$		0			0
$211$	−4.28841	−	7.42775i	−0.295227	−	0.511348i	0.679811	−	0.733387i	$-0.262062\pi$
$211$	−4.28841	−	7.42775i	−0.295227	−	0.511348i	−0.975038	+	0.222040i	$0.928728\pi$
$212$		0			0
$213$	−5.78884	−	18.2132i	−0.396645	−	1.24795i
$214$		0			0
$215$	1.44272	+	5.38431i	0.0983928	+	0.367207i
$216$		0			0
$217$	3.09226	−	5.35596i	0.209916	−	0.363586i
$218$		0			0
$219$	−16.6425	+	18.2464i	−1.12459	+	1.23298i
$220$		0			0
$221$	6.74882	−	10.4667i	0.453975	−	0.704067i
$222$		0			0
$223$	−20.3575	−	5.45476i	−1.36324	−	0.365278i	−0.498232	−	0.867043i	$-0.666017\pi$
$223$	−20.3575	−	5.45476i	−1.36324	−	0.365278i	−0.865004	+	0.501765i	$0.832684\pi$
$224$		0			0
$225$	−0.872184	−	9.46582i	−0.0581456	−	0.631055i
$226$		0			0
$227$	−4.85544	+	1.30101i	−0.322267	+	0.0863512i	−0.416326	−	0.909215i	$-0.636682\pi$
$227$	−4.85544	+	1.30101i	−0.322267	+	0.0863512i	0.0940589	+	0.995567i	$0.470016\pi$
$228$		0			0
$229$	−9.92484	−	9.92484i	−0.655852	−	0.655852i	0.298544	−	0.954396i	$-0.403499\pi$
$229$	−9.92484	−	9.92484i	−0.655852	−	0.655852i	−0.954396	+	0.298544i	$0.903499\pi$
$230$		0			0
$231$	−1.19989	−	26.0999i	−0.0789468	−	1.71725i
$232$		0			0
$233$	18.7944			1.23126			0.615630	−	0.788035i	$-0.288902\pi$
$233$	18.7944			1.23126			0.615630	+	0.788035i	$0.288902\pi$
$234$		0			0
$235$	3.86971			0.252432
$236$		0			0
$237$	−0.125719	−	2.73463i	−0.00816631	−	0.177633i
$238$		0			0
$239$	−6.82142	−	6.82142i	−0.441241	−	0.441241i	0.451188	−	0.892429i	$-0.351000\pi$
$239$	−6.82142	−	6.82142i	−0.441241	−	0.441241i	−0.892429	+	0.451188i	$0.851000\pi$
$240$		0			0
$241$	8.18821	−	2.19402i	0.527449	−	0.141330i	0.0147390	−	0.999891i	$-0.495308\pi$
$241$	8.18821	−	2.19402i	0.527449	−	0.141330i	0.512710	+	0.858562i	$0.328642\pi$
$242$		0			0
$243$	3.54930	+	15.1790i	0.227688	+	0.973734i
$244$		0			0
$245$	16.2462	+	4.35315i	1.03793	+	0.278112i
$246$		0			0
$247$	1.70912	+	7.91400i	0.108749	+	0.503555i
$248$		0			0
$249$	−4.27423	+	4.68617i	−0.270868	+	0.296974i
$250$		0			0
$251$	3.51988	−	6.09661i	0.222173	−	0.384814i	−0.733295	−	0.679911i	$-0.762018\pi$
$251$	3.51988	−	6.09661i	0.222173	−	0.384814i	0.955467	+	0.295096i	$0.0953518\pi$
$252$		0			0
$253$	3.29820	+	12.3090i	0.207356	+	0.773862i
$254$		0			0
$255$	−5.17935	−	16.2956i	−0.324343	−	1.02047i
$256$		0			0
$257$	−0.815993	−	1.41334i	−0.0509003	−	0.0881618i	0.839453	−	0.543433i	$-0.182876\pi$
$257$	−0.815993	−	1.41334i	−0.0509003	−	0.0881618i	−0.890353	+	0.455271i	$0.849542\pi$
$258$		0			0
$259$		−	17.3827i		−	1.08011i
$260$		0			0
$261$	−4.93367	+	3.48863i	−0.305387	+	0.215941i
$262$		0			0
$263$	9.15209	−	5.28396i	0.564342	−	0.325823i	−0.190544	−	0.981679i	$-0.561025\pi$
$263$	9.15209	−	5.28396i	0.564342	−	0.325823i	0.754886	+	0.655856i	$0.227692\pi$
$264$		0			0
$265$	−14.5952	+	14.5952i	−0.896574	+	0.896574i
$266$		0			0
$267$	−3.65223	+	16.6559i	−0.223513	+	1.01933i
$268$		0			0
$269$	−7.46392	−	4.30930i	−0.455083	−	0.262742i	0.254891	−	0.966970i	$-0.417960\pi$
$269$	−7.46392	−	4.30930i	−0.455083	−	0.262742i	−0.709975	+	0.704227i	$0.751294\pi$
$270$		0			0
$271$	−5.13290	+	19.1563i	−0.311802	+	1.16366i	0.615129	+	0.788427i	$0.289104\pi$
$271$	−5.13290	+	19.1563i	−0.311802	+	1.16366i	−0.926930	+	0.375233i	$0.877563\pi$
$272$		0			0
$273$	5.73333	+	21.6711i	0.346997	+	1.31159i
$274$		0			0
$275$	−3.44642	+	12.8622i	−0.207827	+	0.775620i
$276$		0			0
$277$	−13.4255	−	7.75123i	−0.806661	−	0.465726i	0.0391339	−	0.999234i	$-0.487540\pi$
$277$	−13.4255	−	7.75123i	−0.806661	−	0.465726i	−0.845795	+	0.533508i	$0.820873\pi$
$278$		0			0
$279$	3.30413	−	3.97481i	0.197813	−	0.237966i
$280$		0			0
$281$	−11.9452	+	11.9452i	−0.712591	+	0.712591i	−0.967077	−	0.254486i	$-0.918094\pi$
$281$	−11.9452	+	11.9452i	−0.712591	+	0.712591i	0.254486	+	0.967077i	$0.418094\pi$
$282$		0			0
$283$	1.36808	−	0.789860i	0.0813237	−	0.0469523i	−0.458787	−	0.888546i	$-0.651716\pi$
$283$	1.36808	−	0.789860i	0.0813237	−	0.0469523i	0.540110	+	0.841594i	$0.318382\pi$
$284$		0			0
$285$	9.87205	+	5.11015i	0.584770	+	0.302699i
$286$		0			0
$287$			28.5035i			1.68251i
$288$		0			0
$289$	2.53467	+	4.39017i	0.149098	+	0.258245i
$290$		0			0
$291$	13.2426	−	4.20899i	0.776295	−	0.246735i
$292$		0			0
$293$	−1.01073	−	3.77209i	−0.0590474	−	0.220368i	0.930097	−	0.367314i	$-0.119722\pi$
$293$	−1.01073	−	3.77209i	−0.0590474	−	0.220368i	−0.989145	+	0.146946i	$0.953056\pi$
$294$		0			0
$295$	−14.7026	+	25.4656i	−0.856017	+	1.48266i
$296$		0			0
$297$	2.70030	−	21.6688i	0.156687	−	1.25735i
$298$		0			0
$299$	−4.99533	−	9.72548i	−0.288887	−	0.562439i
$300$		0			0
$301$	−6.76230	−	1.81195i	−0.389772	−	0.104439i
$302$		0			0
$303$	−3.07315	+	1.96779i	−0.176548	+	0.113047i
$304$		0			0
$305$	−0.757003	+	0.202838i	−0.0433459	+	0.0116145i
$306$		0			0
$307$	−21.7994	−	21.7994i	−1.24416	−	1.24416i	−0.958260	−	0.285899i	$-0.907708\pi$
$307$	−21.7994	−	21.7994i	−1.24416	−	1.24416i	−0.285899	−	0.958260i	$-0.592292\pi$
$308$		0			0
$309$	−24.6780	+	1.13452i	−1.40388	+	0.0645404i
$310$		0			0
$311$	20.9295			1.18681			0.593403	−	0.804906i	$-0.297784\pi$
$311$	20.9295			1.18681			0.593403	+	0.804906i	$0.297784\pi$
$312$		0			0
$313$	−32.6685			−1.84653			−0.923267	−	0.384159i	$-0.874491\pi$
$313$	−32.6685			−1.84653			−0.923267	+	0.384159i	$0.874491\pi$
$314$		0			0
$315$	27.9537	+	12.8783i	1.57501	+	0.725612i
$316$		0			0
$317$	5.21085	+	5.21085i	0.292671	+	0.292671i	0.838134	−	0.545464i	$-0.183646\pi$
$317$	5.21085	+	5.21085i	0.292671	+	0.292671i	−0.545464	+	0.838134i	$0.683646\pi$
$318$		0			0
$319$	8.17593	−	2.19073i	0.457764	−	0.122657i
$320$		0			0
$321$	12.9317	+	20.1957i	0.721776	+	1.12721i
$322$		0			0
$323$	7.49202	+	2.00748i	0.416867	+	0.111699i
$324$		0			0
$325$	0.560775	−	11.4109i	0.0311062	−	0.632964i
$326$		0			0
$327$	10.5730	+	9.64360i	0.584689	+	0.533292i
$328$		0			0
$329$	−2.43004	+	4.20895i	−0.133972	+	0.232047i
$330$		0			0
$331$	−4.72013	−	17.6158i	−0.259442	−	0.968251i	−0.965565	−	0.260162i	$-0.916224\pi$
$331$	−4.72013	−	17.6158i	−0.259442	−	0.968251i	0.706123	−	0.708089i	$-0.250443\pi$
$332$		0			0
$333$	2.45667	−	14.3186i	0.134625	−	0.784652i
$334$		0			0
$335$	−6.06754	−	10.5093i	−0.331505	−	0.574184i
$336$		0			0
$337$			4.92484i			0.268273i	0.990963	+	0.134136i	$0.0428260\pi$
$337$			4.92484i			0.268273i	−0.990963	+	0.134136i	$0.957174\pi$
$338$		0			0
$339$	−14.3353	+	27.6937i	−0.778587	+	1.50412i
$340$		0			0
$341$	−6.27042	+	3.62023i	−0.339562	+	0.196046i
$342$		0			0
$343$	2.83057	−	2.83057i	0.152836	−	0.152836i
$344$		0			0
$345$	−14.6629	−	3.21521i	−0.789424	−	0.173101i
$346$		0			0
$347$	−12.9403	−	7.47108i	−0.694671	−	0.401069i	0.110688	−	0.993855i	$-0.464694\pi$
$347$	−12.9403	−	7.47108i	−0.694671	−	0.401069i	−0.805360	+	0.592787i	$0.798028\pi$
$348$		0			0
$349$	−8.08448	+	30.1717i	−0.432752	+	1.61505i	0.313636	+	0.949543i	$0.398453\pi$
$349$	−8.08448	+	30.1717i	−0.432752	+	1.61505i	−0.746388	+	0.665511i	$0.768214\pi$
$350$		0			0
$351$	1.65994	+	18.6613i	0.0886008	+	0.996067i
$352$		0			0
$353$	−2.67762	+	9.99302i	−0.142515	+	0.531875i	0.857338	+	0.514754i	$0.172117\pi$
$353$	−2.67762	+	9.99302i	−0.142515	+	0.531875i	−0.999853	+	0.0171211i	$0.994550\pi$
$354$		0			0
$355$	−27.3105	−	15.7677i	−1.44949	−	0.836864i
$356$		0			0
$357$	20.9766	+	4.59964i	1.11020	+	0.243439i
$358$		0			0
$359$	9.08944	−	9.08944i	0.479722	−	0.479722i	−0.425321	−	0.905043i	$-0.639839\pi$
$359$	9.08944	−	9.08944i	0.479722	−	0.479722i	0.905043	+	0.425321i	$0.139839\pi$
$360$		0			0
$361$	12.0876	−	6.97875i	0.636187	−	0.367303i
$362$		0			0
$363$	−5.30306	+	10.2447i	−0.278339	+	0.537709i
$364$		0			0
$365$			40.7516i			2.13304i
$366$		0			0
$367$	0.823475	+	1.42630i	0.0429850	+	0.0744522i	0.886717	−	0.462312i	$-0.152980\pi$
$367$	0.823475	+	1.42630i	0.0429850	+	0.0744522i	−0.843732	+	0.536764i	$0.819647\pi$
$368$		0			0
$369$	−4.02837	+	23.4791i	−0.209709	+	1.22227i
$370$		0			0
$371$	−6.70941	−	25.0398i	−0.348335	−	1.30000i
$372$		0			0
$373$	9.97578	−	17.2786i	0.516526	−	0.894650i	−0.483290	−	0.875461i	$-0.660558\pi$
$373$	9.97578	−	17.2786i	0.516526	−	0.894650i	0.999816	−	0.0191892i	$-0.00610849\pi$
$374$		0			0
$375$	6.69817	+	6.10937i	0.345892	+	0.315487i
$376$		0			0
$377$	−6.45987	+	3.31800i	−0.332700	+	0.170886i
$378$		0			0
$379$	11.8923	+	3.18653i	0.610865	+	0.163681i	0.550972	−	0.834524i	$-0.314257\pi$
$379$	11.8923	+	3.18653i	0.610865	+	0.163681i	0.0598936	+	0.998205i	$0.480924\pi$
$380$		0			0
$381$	19.3274	+	30.1841i	0.990175	+	1.54638i
$382$		0			0
$383$	−27.3800	+	7.33645i	−1.39905	+	0.374875i	−0.878005	−	0.478652i	$-0.841125\pi$
$383$	−27.3800	+	7.33645i	−1.39905	+	0.374875i	−0.521048	+	0.853527i	$0.674459\pi$
$384$		0			0
$385$	−30.4858	−	30.4858i	−1.55370	−	1.55370i
$386$		0			0
$387$	−5.31419	−	2.44826i	−0.270136	−	0.124452i
$388$		0			0
$389$	15.9504			0.808717			0.404359	−	0.914601i	$-0.367495\pi$
$389$	15.9504			0.808717			0.404359	+	0.914601i	$0.367495\pi$
$390$		0			0
$391$	−10.4740			−0.529695
$392$		0			0
$393$	8.10255	−	0.372497i	0.408720	−	0.0187900i
$394$		0			0
$395$	−3.19416	−	3.19416i	−0.160716	−	0.160716i
$396$		0			0
$397$	−12.2594	+	3.28489i	−0.615281	+	0.164864i	−0.552981	−	0.833194i	$-0.686510\pi$
$397$	−12.2594	+	3.28489i	−0.615281	+	0.164864i	−0.0622992	+	0.998058i	$0.519843\pi$
$398$		0			0
$399$	−11.7574	+	7.52849i	−0.588606	+	0.376896i
$400$		0			0
$401$	−15.8603	−	4.24976i	−0.792027	−	0.212223i	−0.159946	−	0.987126i	$-0.551132\pi$
$401$	−15.8603	−	4.24976i	−0.792027	−	0.212223i	−0.632080	+	0.774903i	$0.717799\pi$
$402$		0			0
$403$	4.60294	−	4.17172i	0.229289	−	0.207808i
$404$		0			0
$405$	21.2061	+	14.5589i	1.05374	+	0.723436i
$406$		0			0
$407$	−10.1753	+	17.6241i	−0.504370	+	0.873594i
$408$		0			0
$409$	−8.82005	−	32.9169i	−0.436123	−	1.62763i	−0.738364	−	0.674403i	$-0.764401\pi$
$409$	−8.82005	−	32.9169i	−0.436123	−	1.62763i	0.302240	−	0.953232i	$-0.402266\pi$
$410$		0			0
$411$	9.04570	−	2.87506i	0.446192	−	0.141816i
$412$		0			0
$413$	−18.4653	−	31.9829i	−0.908620	−	1.57378i
$414$		0			0
$415$			10.4661i			0.513761i
$416$		0			0
$417$	22.6010	+	11.6991i	1.10677	+	0.572909i
$418$		0			0
$419$	−28.4943	+	16.4512i	−1.39204	+	0.803693i	−0.993541	−	0.113477i	$-0.963801\pi$
$419$	−28.4943	+	16.4512i	−1.39204	+	0.803693i	−0.398496	+	0.917170i	$0.630468\pi$
$420$		0			0
$421$	17.0945	−	17.0945i	0.833137	−	0.833137i	−0.154808	−	0.987945i	$-0.549476\pi$
$421$	17.0945	−	17.0945i	0.833137	−	0.833137i	0.987945	+	0.154808i	$0.0494759\pi$
$422$		0			0
$423$	−2.59653	+	3.12358i	−0.126247	+	0.151874i
$424$		0			0
$425$	−9.47842	−	5.47237i	−0.459771	−	0.265449i
$426$		0			0
$427$	0.254750	−	0.950740i	0.0123282	−	0.0460095i
$428$		0			0
$429$	6.87263	−	25.3282i	0.331813	−	1.22286i
$430$		0			0
$431$	0.454427	−	1.69594i	0.0218890	−	0.0816908i	−0.954117	−	0.299433i	$-0.903203\pi$
$431$	0.454427	−	1.69594i	0.0218890	−	0.0816908i	0.976006	+	0.217742i	$0.0698692\pi$
$432$		0			0
$433$	−8.87140	−	5.12190i	−0.426332	−	0.246143i	0.271451	−	0.962452i	$-0.412497\pi$
$433$	−8.87140	−	5.12190i	−0.426332	−	0.246143i	−0.697783	+	0.716309i	$0.745830\pi$
$434$		0			0
$435$	−2.13561	+	9.73941i	−0.102395	+	0.466969i
$436$		0			0
$437$	4.81492	−	4.81492i	0.230329	−	0.230329i
$438$		0			0
$439$	4.67848	−	2.70112i	0.223292	−	0.128917i	−0.384182	−	0.923257i	$-0.625516\pi$
$439$	4.67848	−	2.70112i	0.223292	−	0.128917i	0.607473	+	0.794340i	$0.292183\pi$
$440$		0			0
$441$	−14.4148	+	10.1928i	−0.686418	+	0.485371i
$442$		0			0
$443$		−	13.5731i		−	0.644876i	−0.946591	−	0.322438i	$-0.895498\pi$
$443$		−	13.5731i		−	0.644876i	0.946591	−	0.322438i	$-0.104502\pi$
$444$		0			0
$445$	14.0686	+	24.3675i	0.666916	+	1.15513i
$446$		0			0
$447$	−5.42208	−	17.0593i	−0.256455	−	0.806877i
$448$		0			0
$449$	−0.525222	−	1.96016i	−0.0247868	−	0.0925055i	0.952424	−	0.304775i	$-0.0985812\pi$
$449$	−0.525222	−	1.96016i	−0.0247868	−	0.0925055i	−0.977211	+	0.212269i	$0.931915\pi$
$450$		0			0
$451$	16.6851	−	28.8994i	0.785670	−	1.36082i
$452$		0			0
$453$	−10.7118	+	11.7442i	−0.503284	+	0.551789i
$454$		0			0
$455$	31.0879	+	20.0451i	1.45742	+	0.939731i
$456$		0			0
$457$	−28.9328	−	7.75251i	−1.35342	−	0.362647i	−0.492022	−	0.870583i	$-0.663742\pi$
$457$	−28.9328	−	7.75251i	−1.35342	−	0.362647i	−0.861395	+	0.507936i	$0.830409\pi$
$458$		0			0
$459$	16.6289	+	6.75344i	0.776169	+	0.315223i
$460$		0			0
$461$	−15.5621	+	4.16985i	−0.724798	+	0.194209i	−0.602312	−	0.798261i	$-0.705754\pi$
$461$	−15.5621	+	4.16985i	−0.724798	+	0.194209i	−0.122487	+	0.992470i	$0.539087\pi$
$462$		0			0
$463$	4.07041	+	4.07041i	0.189168	+	0.189168i	0.795336	−	0.606168i	$-0.207294\pi$
$463$	4.07041	+	4.07041i	0.189168	+	0.189168i	−0.606168	+	0.795336i	$0.707294\pi$
$464$		0			0
$465$	−0.391693	−	8.52009i	−0.0181643	−	0.395110i
$466$		0			0
$467$	36.8536			1.70538			0.852690	−	0.522417i	$-0.174970\pi$
$467$	36.8536			1.70538			0.852690	+	0.522417i	$0.174970\pi$
$468$		0			0
$469$	15.2408			0.703753
$470$		0			0
$471$	−1.12499	−	24.4708i	−0.0518368	−	1.12755i
$472$		0			0
$473$	5.79555	+	5.79555i	0.266480	+	0.266480i
$474$		0			0
$475$	6.87289	−	1.84159i	0.315350	−	0.0844977i
$476$		0			0
$477$	−1.98785	−	21.5742i	−0.0910176	−	0.987814i
$478$		0			0
$479$	14.5305	+	3.89342i	0.663913	+	0.177895i	0.575011	−	0.818145i	$-0.304998\pi$
$479$	14.5305	+	3.89342i	0.663913	+	0.177895i	0.0889019	+	0.996040i	$0.471664\pi$
$480$		0			0
$481$	5.34141	−	16.6231i	0.243547	−	0.757949i
$482$		0			0
$483$	12.7048	−	13.9293i	0.578090	−	0.633804i
$484$		0			0
$485$	11.4645	−	19.8571i	0.520576	−	0.901664i
$486$		0			0
$487$	−4.33018	−	16.1605i	−0.196219	−	0.732301i	−0.991948	−	0.126647i	$-0.959578\pi$
$487$	−4.33018	−	16.1605i	−0.196219	−	0.732301i	0.795728	−	0.605654i	$-0.207088\pi$
$488$		0			0
$489$	−0.584640	−	1.83943i	−0.0264383	−	0.0831820i
$490$		0			0
$491$	−12.6333	−	21.8815i	−0.570132	−	0.987498i	−0.996552	−	0.0829727i	$-0.973559\pi$
$491$	−12.6333	−	21.8815i	−0.570132	−	0.987498i	0.426419	−	0.904526i	$-0.359775\pi$
$492$		0			0
$493$			6.95708i			0.313331i
$494$		0			0
$495$	−20.8034	−	29.4204i	−0.935043	−	1.32235i
$496$		0			0
$497$	34.3000	−	19.8031i	1.53856	−	0.888290i
$498$		0			0
$499$	−1.37946	+	1.37946i	−0.0617533	+	0.0617533i	−0.737309	−	0.675556i	$-0.763904\pi$
$499$	−1.37946	+	1.37946i	−0.0617533	+	0.0617533i	0.675556	+	0.737309i	$0.263904\pi$
$500$		0			0
$501$	2.07197	−	9.44916i	0.0925687	−	0.422157i
$502$		0			0
$503$	9.77777	+	5.64520i	0.435969	+	0.251707i	0.701886	−	0.712289i	$-0.252341\pi$
$503$	9.77777	+	5.64520i	0.435969	+	0.251707i	−0.265917	+	0.963996i	$0.585675\pi$
$504$		0			0
$505$	−1.55849	+	5.81637i	−0.0693520	+	0.258825i
$506$		0			0
$507$	−1.17636	+	22.4859i	−0.0522442	+	0.998634i
$508$		0			0
$509$	9.73260	−	36.3226i	0.431390	−	1.60997i	−0.318171	−	0.948033i	$-0.603069\pi$
$509$	9.73260	−	36.3226i	0.431390	−	1.60997i	0.749561	−	0.661936i	$-0.230265\pi$
$510$		0			0
$511$	−44.3241	−	25.5905i	−1.96078	−	1.13206i
$512$		0			0
$513$	−10.7489	+	4.53974i	−0.474574	+	0.200435i
$514$		0			0
$515$	−28.8249	+	28.8249i	−1.27018	+	1.27018i
$516$		0			0
$517$	4.92757	−	2.84493i	0.216714	−	0.125120i
$518$		0			0
$519$	26.9111	+	13.9302i	1.18127	+	0.611468i
$520$		0			0
$521$		−	18.2111i		−	0.797843i	−0.916985	−	0.398922i	$-0.869385\pi$
$521$		−	18.2111i		−	0.797843i	0.916985	−	0.398922i	$-0.130615\pi$
$522$		0			0
$523$	16.9049	+	29.2801i	0.739199	+	1.28033i	0.952857	+	0.303421i	$0.0981289\pi$
$523$	16.9049	+	29.2801i	0.739199	+	1.28033i	−0.213658	+	0.976909i	$0.568538\pi$
$524$		0			0
$525$	18.7748	−	5.96732i	0.819398	−	0.260435i
$526$		0			0
$527$	−1.54027	−	5.74835i	−0.0670951	−	0.250402i
$528$		0			0
$529$	6.90238	−	11.9553i	0.300103	−	0.519794i
$530$		0			0
$531$	−10.6903	−	28.9548i	−0.463918	−	1.25653i
$532$		0			0
$533$	−8.75867	+	27.2580i	−0.379380	+	1.18068i
$534$		0			0
$535$	38.2233	+	10.2419i	1.65254	+	0.442795i
$536$		0			0
$537$	−13.4415	+	8.60687i	−0.580045	+	0.371414i
$538$		0			0
$539$	23.8877	−	6.40069i	1.02892	−	0.275697i
$540$		0			0
$541$	−4.97355	−	4.97355i	−0.213829	−	0.213829i	0.592063	−	0.805892i	$-0.298314\pi$
$541$	−4.97355	−	4.97355i	−0.213829	−	0.213829i	−0.805892	+	0.592063i	$0.798314\pi$
$542$		0			0
$543$	23.8961	−	1.09857i	1.02548	−	0.0471442i
$544$		0			0
$545$	23.6138			1.01150
$546$		0			0
$547$	2.15870			0.0922995			0.0461497	−	0.998935i	$-0.485305\pi$
$547$	2.15870			0.0922995			0.0461497	+	0.998935i	$0.485305\pi$
$548$		0			0
$549$	0.344211	−	0.747145i	0.0146906	−	0.0318874i
$550$		0			0
$551$	−3.19818	−	3.19818i	−0.136247	−	0.136247i
$552$		0			0
$553$	5.47999	−	1.46836i	0.233033	−	0.0624409i
$554$		0			0
$555$	−12.9270	−	20.1884i	−0.548722	−	0.856951i
$556$		0			0
$557$	−2.17782	−	0.583545i	−0.0922772	−	0.0247256i	0.212385	−	0.977186i	$-0.431877\pi$
$557$	−2.17782	−	0.583545i	−0.0922772	−	0.0247256i	−0.304662	+	0.952460i	$0.598544\pi$
$558$		0			0
$559$	−5.91003	−	3.81072i	−0.249968	−	0.161176i
$560$		0			0
$561$	−18.5754	−	16.9426i	−0.784254	−	0.715315i
$562$		0			0
$563$	18.1490	−	31.4349i	0.764888	−	1.32482i	−0.175418	−	0.984494i	$-0.556128\pi$
$563$	18.1490	−	31.4349i	0.764888	−	1.32482i	0.940306	−	0.340330i	$-0.110539\pi$
$564$		0			0
$565$	13.3181	+	49.7038i	0.560297	+	2.09106i
$566$		0			0
$567$	−29.1518	+	13.9227i	−1.22426	+	0.584698i
$568$		0			0
$569$	19.5376	+	33.8400i	0.819057	+	1.41865i	0.906378	+	0.422468i	$0.138836\pi$
$569$	19.5376	+	33.8400i	0.819057	+	1.41865i	−0.0873209	+	0.996180i	$0.527831\pi$
$570$		0			0
$571$			31.9061i			1.33523i	0.744508	+	0.667614i	$0.232684\pi$
$571$			31.9061i			1.33523i	−0.744508	+	0.667614i	$0.767316\pi$
$572$		0			0
$573$	−18.0767	+	34.9215i	−0.755165	+	1.45887i
$574$		0			0
$575$	−8.32119	+	4.80424i	−0.347018	+	0.200351i
$576$		0			0
$577$	9.31011	−	9.31011i	0.387585	−	0.387585i	−0.486240	−	0.873825i	$-0.661632\pi$
$577$	9.31011	−	9.31011i	0.387585	−	0.387585i	0.873825	+	0.486240i	$0.161632\pi$
$578$		0			0
$579$	−33.9144	−	7.43659i	−1.40944	−	0.309054i
$580$		0			0
$581$	−11.3836	−	6.57233i	−0.472271	−	0.272666i
$582$		0			0
$583$	−7.85495	+	29.3151i	−0.325319	+	1.21411i
$584$		0			0
$585$	22.7750	+	20.9053i	0.941629	+	0.864328i
$586$		0			0
$587$	−7.58008	+	28.2892i	−0.312863	+	1.16762i	0.613099	+	0.790006i	$0.289923\pi$
$587$	−7.58008	+	28.2892i	−0.312863	+	1.16762i	−0.925962	+	0.377615i	$0.876744\pi$
$588$		0			0
$589$	3.35059	+	1.93446i	0.138058	+	0.0797081i
$590$		0			0
$591$	−31.5316	−	6.91411i	−1.29704	−	0.284408i
$592$		0			0
$593$	−12.7368	+	12.7368i	−0.523037	+	0.523037i	−0.918487	−	0.395450i	$-0.870589\pi$
$593$	−12.7368	+	12.7368i	−0.523037	+	0.523037i	0.395450	+	0.918487i	$0.370589\pi$
$594$		0			0
$595$	30.6886	−	17.7181i	1.25811	−	0.726370i
$596$		0			0
$597$	−3.59128	+	6.93783i	−0.146981	+	0.283946i
$598$		0			0
$599$		−	15.6579i		−	0.639764i	−0.947457	−	0.319882i	$-0.896357\pi$
$599$		−	15.6579i		−	0.639764i	0.947457	−	0.319882i	$-0.103643\pi$
$600$		0			0
$601$	−3.99832	−	6.92529i	−0.163095	−	0.282488i	0.772882	−	0.634549i	$-0.218814\pi$
$601$	−3.99832	−	6.92529i	−0.163095	−	0.282488i	−0.935977	+	0.352061i	$0.885481\pi$
$602$		0			0
$603$	12.5542	+	2.15396i	0.511247	+	0.0877160i
$604$		0			0
$605$	4.92677	+	18.3869i	0.200302	+	0.747535i
$606$		0			0
$607$	2.24581	−	3.88985i	0.0911545	−	0.157884i	−0.816843	−	0.576860i	$-0.804278\pi$
$607$	2.24581	−	3.88985i	0.0911545	−	0.157884i	0.907997	+	0.418976i	$0.137611\pi$
$608$		0			0
$609$	−9.25212	−	8.43882i	−0.374915	−	0.341958i
$610$		0			0
$611$	−3.61719	+	3.27832i	−0.146336	+	0.132627i
$612$		0			0
$613$	30.5112	+	8.17546i	1.23234	+	0.330204i	0.815489	−	0.578773i	$-0.196468\pi$
$613$	30.5112	+	8.17546i	1.23234	+	0.330204i	0.416848	+	0.908976i	$0.363135\pi$
$614$		0			0
$615$	21.1973	+	33.1043i	0.854758	+	1.33489i
$616$		0			0
$617$	−5.23513	+	1.40275i	−0.210758	+	0.0564725i	−0.362653	−	0.931924i	$-0.618129\pi$
$617$	−5.23513	+	1.40275i	−0.210758	+	0.0564725i	0.151895	+	0.988397i	$0.451462\pi$
$618$		0			0
$619$	−7.22455	−	7.22455i	−0.290379	−	0.290379i	0.546851	−	0.837230i	$-0.315826\pi$
$619$	−7.22455	−	7.22455i	−0.290379	−	0.290379i	−0.837230	+	0.546851i	$0.815826\pi$
$620$		0			0
$621$	12.4339	−	9.67833i	0.498955	−	0.388378i
$622$		0			0
$623$	−35.3382			−1.41580
$624$		0			0
$625$	30.8029			1.23212
$626$		0			0
$627$	16.3276	−	0.750627i	0.652063	−	0.0299772i
$628$		0			0
$629$	−11.8276	−	11.8276i	−0.471596	−	0.471596i
$630$		0			0
$631$	20.2844	−	5.43520i	0.807511	−	0.216372i	0.168632	−	0.985679i	$-0.446065\pi$
$631$	20.2844	−	5.43520i	0.807511	−	0.216372i	0.638879	+	0.769307i	$0.279398\pi$
$632$		0			0
$633$	12.5106	−	8.01074i	0.497250	−	0.318398i
$634$		0			0
$635$	57.1277	+	15.3073i	2.26705	+	0.607453i
$636$		0			0
$637$	−18.8739	+	9.69426i	−0.747811	+	0.384100i
$638$		0			0
$639$	31.0525	−	11.4647i	1.22842	−	0.453538i
$640$		0			0
$641$	−21.3437	+	36.9683i	−0.843024	+	1.46016i	0.0443019	+	0.999018i	$0.485894\pi$
$641$	−21.3437	+	36.9683i	−0.843024	+	1.46016i	−0.887326	+	0.461143i	$0.847440\pi$
$642$		0			0
$643$	0.813185	+	3.03485i	0.0320689	+	0.119683i	0.980105	−	0.198481i	$-0.0636007\pi$
$643$	0.813185	+	3.03485i	0.0320689	+	0.119683i	−0.948036	+	0.318163i	$0.896934\pi$
$644$		0			0
$645$	−9.20130	+	2.92452i	−0.362301	+	0.115153i
$646$		0			0
$647$	−18.2351	−	31.5841i	−0.716895	−	1.24170i	−0.962224	−	0.272258i	$-0.912229\pi$
$647$	−18.2351	−	31.5841i	−0.716895	−	1.24170i	0.245329	−	0.969440i	$-0.421104\pi$
$648$		0			0
$649$			43.2361i			1.69717i
$650$		0			0
$651$	9.51297	+	4.92427i	0.372843	+	0.192998i
$652$		0			0
$653$	39.3421	−	22.7142i	1.53957	−	0.888874i	0.540711	−	0.841208i	$-0.318155\pi$
$653$	39.3421	−	22.7142i	1.53957	−	0.888874i	0.998863	−	0.0476658i	$-0.0151782\pi$
$654$		0			0
$655$	9.46410	−	9.46410i	0.369793	−	0.369793i
$656$		0			0
$657$	−32.8942	−	27.3438i	−1.28332	−	1.06678i
$658$		0			0
$659$	−11.4858	−	6.63132i	−0.447422	−	0.258319i	0.259319	−	0.965792i	$-0.416502\pi$
$659$	−11.4858	−	6.63132i	−0.447422	−	0.258319i	−0.706741	+	0.707472i	$0.749835\pi$
$660$		0			0
$661$	2.40763	−	8.98541i	0.0936460	−	0.349492i	−0.903165	−	0.429294i	$-0.858762\pi$
$661$	2.40763	−	8.98541i	0.0936460	−	0.349492i	0.996811	+	0.0798025i	$0.0254290\pi$
$662$		0			0
$663$	18.6466	+	10.8444i	0.724173	+	0.421162i
$664$		0			0
$665$	−5.96256	+	22.2526i	−0.231218	+	0.862918i
$666$		0			0
$667$	5.28941	+	3.05384i	0.204807	+	0.118245i
$668$		0			0
$669$	7.81866	−	35.6568i	0.302287	−	1.37857i
$670$		0			0
$671$	−0.814821	+	0.814821i	−0.0314558	+	0.0314558i
$672$		0			0
$673$	−22.9273	+	13.2371i	−0.883782	+	0.510252i	−0.871904	−	0.489678i	$-0.837114\pi$
$673$	−22.9273	+	13.2371i	−0.883782	+	0.510252i	−0.0118785	+	0.999929i	$0.503781\pi$
$674$		0			0
$675$	16.3086	−	2.26202i	0.627719	−	0.0870650i
$676$		0			0
$677$		−	41.0789i		−	1.57879i	−0.613885	−	0.789396i	$-0.710394\pi$
$677$		−	41.0789i		−	1.57879i	0.613885	−	0.789396i	$-0.289606\pi$
$678$		0			0
$679$	14.3986	+	24.9390i	0.552566	+	0.957073i
$680$		0			0
$681$	−2.63726	−	8.29751i	−0.101060	−	0.317961i
$682$		0			0
$683$	−1.54160	−	5.75334i	−0.0589878	−	0.220145i	0.930140	−	0.367206i	$-0.119685\pi$
$683$	−1.54160	−	5.75334i	−0.0589878	−	0.220145i	−0.989128	+	0.147060i	$0.953019\pi$
$684$		0			0
$685$	7.83113	−	13.5639i	0.299212	−	0.518250i
$686$		0			0
$687$	16.3827	−	17.9616i	0.625040	−	0.685279i
$688$		0			0
$689$	1.27810	−	26.0074i	0.0486917	−	0.990803i
$690$		0			0
$691$	−27.6429	−	7.40689i	−1.05159	−	0.281771i	−0.308679	−	0.951166i	$-0.599887\pi$
$691$	−27.6429	−	7.40689i	−1.05159	−	0.281771i	−0.742907	+	0.669395i	$0.766553\pi$
$692$		0			0
$693$	45.0633	−	4.15215i	1.71181	−	0.157727i
$694$		0			0
$695$	40.5636	−	10.8690i	1.53866	−	0.412284i
$696$		0			0
$697$	19.3944	+	19.3944i	0.734617	+	0.734617i
$698$		0			0
$699$	1.49497	+	32.5185i	0.0565448	+	1.22996i
$700$		0			0
$701$	−0.672924			−0.0254160			−0.0127080	−	0.999919i	$-0.504045\pi$
$701$	−0.672924			−0.0254160			−0.0127080	+	0.999919i	$0.504045\pi$
$702$		0			0
$703$	10.8743			0.410131
$704$		0			0
$705$	0.307809	+	6.69546i	0.0115928	+	0.252166i
$706$		0			0
$707$	−5.34758	−	5.34758i	−0.201116	−	0.201116i
$708$		0			0
$709$	29.5534	−	7.91881i	1.10990	−	0.297397i	0.343111	−	0.939295i	$-0.388519\pi$
$709$	29.5534	−	7.91881i	1.10990	−	0.297397i	0.766790	+	0.641898i	$0.221853\pi$
$710$		0			0
$711$	4.72152	−	0.435043i	0.177071	−	0.0163154i
$712$		0			0
$713$	−5.04653	−	1.35221i	−0.188994	−	0.0506408i
$714$		0			0
$715$	−19.7859	−	38.5214i	−0.739950	−	1.44062i
$716$		0			0
$717$	11.2600	−	12.3452i	0.420512	−	0.461039i
$718$		0			0
$719$	−11.5566	+	20.0165i	−0.430987	+	0.746491i	−0.996959	−	0.0779336i	$-0.975168\pi$
$719$	−11.5566	+	20.0165i	−0.430987	+	0.746491i	0.565972	+	0.824425i	$0.308501\pi$
$720$		0			0
$721$	−13.2508	−	49.4528i	−0.493487	−	1.84172i
$722$		0			0
$723$	4.44747	+	13.9929i	0.165403	+	0.520402i
$724$		0			0
$725$	3.19108	+	5.52711i	0.118514	+	0.205272i
$726$		0			0
$727$		−	11.5379i		−	0.427917i	−0.976843	−	0.213959i	$-0.931364\pi$
$727$		−	11.5379i		−	0.427917i	0.976843	−	0.213959i	$-0.0686357\pi$
$728$		0			0
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$		0			0
$731$	−5.83411	+	3.36832i	−0.215782	+	0.124582i
$732$		0			0
$733$	−0.910162	+	0.910162i	−0.0336176	+	0.0336176i	−0.723716	−	0.690098i	$-0.757567\pi$
$733$	−0.910162	+	0.910162i	−0.0336176	+	0.0336176i	0.690098	+	0.723716i	$0.257567\pi$
$734$		0			0
$735$	−6.23964	+	28.4558i	−0.230153	+	1.04961i
$736$		0			0
$737$	−15.4524	−	8.92147i	−0.569198	−	0.328626i
$738$		0			0
$739$	3.23160	−	12.0605i	0.118876	−	0.443652i	−0.880671	−	0.473728i	$-0.842908\pi$
$739$	3.23160	−	12.0605i	0.118876	−	0.443652i	0.999548	+	0.0300754i	$0.00957473\pi$
$740$		0			0
$741$	−13.5570	+	3.58666i	−0.498030	+	0.131759i
$742$		0			0
$743$	11.8573	−	44.2519i	0.435001	−	1.62345i	−0.306063	−	0.952011i	$-0.599012\pi$
$743$	11.8573	−	44.2519i	0.435001	−	1.62345i	0.741064	−	0.671435i	$-0.234322\pi$
$744$		0			0
$745$	−25.5802	−	14.7687i	−0.937185	−	0.541084i
$746$		0			0
$747$	−8.44810	−	7.02262i	−0.309100	−	0.256944i
$748$		0			0
$749$	−35.1425	+	35.1425i	−1.28408	+	1.28408i
$750$		0			0
$751$	−13.8766	+	8.01168i	−0.506366	+	0.292350i	−0.731338	−	0.682015i	$-0.761104\pi$
$751$	−13.8766	+	8.01168i	−0.506366	+	0.292350i	0.224973	+	0.974365i	$0.427771\pi$
$752$		0			0
$753$	10.8285	+	5.60523i	0.394611	+	0.204266i
$754$		0			0
$755$			26.2295i			0.954588i
$756$		0			0
$757$	15.6277	+	27.0680i	0.567998	+	0.983802i	0.996764	+	0.0803861i	$0.0256153\pi$
$757$	15.6277	+	27.0680i	0.567998	+	0.983802i	−0.428765	+	0.903416i	$0.641051\pi$
$758$		0			0
$759$	−21.0350	+	6.68572i	−0.763523	+	0.242676i
$760$		0			0
$761$	4.45283	+	16.6182i	0.161415	+	0.602409i	0.998470	+	0.0552906i	$0.0176085\pi$
$761$	4.45283	+	16.6182i	0.161415	+	0.602409i	−0.837055	+	0.547118i	$0.815725\pi$
$762$		0			0
$763$	−14.8286	+	25.6839i	−0.536832	+	0.929820i
$764$		0			0
$765$	27.7830	−	10.2576i	1.00450	−	0.370865i
$766$		0			0
$767$	−7.83066	−	36.2595i	−0.282749	−	1.30925i
$768$		0			0
$769$	0.224553	+	0.0601687i	0.00809758	+	0.00216974i	0.262866	−	0.964832i	$-0.415332\pi$
$769$	0.224553	+	0.0601687i	0.00809758	+	0.00216974i	−0.254768	+	0.967002i	$0.581999\pi$
$770$		0			0
$771$	2.38049	−	1.52427i	0.0857313	−	0.0548953i
$772$		0			0
$773$	42.7466	−	11.4539i	1.53749	−	0.411968i	0.612034	−	0.790831i	$-0.290352\pi$
$773$	42.7466	−	11.4539i	1.53749	−	0.411968i	0.925453	+	0.378863i	$0.123685\pi$
$774$		0			0
$775$	−3.86034	−	3.86034i	−0.138667	−	0.138667i
$776$		0			0
$777$	30.0759	−	1.38267i	1.07897	−	0.0496032i
$778$		0			0
$779$	−17.8313			−0.638872
$780$		0			0
$781$	−46.3684			−1.65919
$782$		0			0
$783$	−6.42856	−	8.25886i	−0.229738	−	0.295148i
$784$		0			0
$785$	−28.5828	−	28.5828i	−1.02017	−	1.02017i
$786$		0			0
$787$	−20.4083	+	5.46839i	−0.727478	+	0.194927i	−0.603506	−	0.797358i	$-0.706230\pi$
$787$	−20.4083	+	5.46839i	−0.727478	+	0.194927i	−0.123972	+	0.992286i	$0.539563\pi$
$788$		0			0
$789$	9.87042	+	15.4149i	0.351396	+	0.548783i
$790$		0			0
$791$	−62.4244	−	16.7266i	−2.21955	−	0.594728i
$792$		0			0
$793$	0.535765	−	0.830916i	0.0190256	−	0.0295067i
$794$		0			0
$795$	−26.4138	−	24.0919i	−0.936802	−	0.854453i
$796$		0			0
$797$	−12.0370	+	20.8487i	−0.426373	+	0.738501i	−0.996548	−	0.0830233i	$-0.973542\pi$
$797$	−12.0370	+	20.8487i	−0.426373	+	0.738501i	0.570174	+	0.821524i	$0.306876\pi$
$798$		0			0
$799$	1.21041	+	4.51731i	0.0428212	+	0.159811i
$800$		0			0
$801$	−29.1090	−	4.99431i	−1.02852	−	0.176465i
$802$		0			0
$803$	29.9598	+	51.8918i	1.05726	+	1.83122i
$804$		0			0
$805$		−	31.1097i		−	1.09647i
$806$		0			0
$807$	6.86234	−	13.2570i	0.241566	−	0.466669i
$808$		0			0
$809$	−22.2703	+	12.8578i	−0.782982	+	0.452055i	−0.837486	−	0.546459i	$-0.815975\pi$
$809$	−22.2703	+	12.8578i	−0.782982	+	0.452055i	0.0545042	+	0.998514i	$0.482642\pi$
$810$		0			0
$811$	−5.99463	+	5.99463i	−0.210500	+	0.210500i	−0.804480	−	0.593980i	$-0.797556\pi$
$811$	−5.99463	+	5.99463i	−0.210500	+	0.210500i	0.593980	+	0.804480i	$0.297556\pi$
$812$		0			0
$813$	−33.5529	−	7.35732i	−1.17675	−	0.258032i
$814$		0			0
$815$	−2.75821	−	1.59245i	−0.0966157	−	0.0557811i
$816$		0			0
$817$	1.13352	−	4.23037i	0.0396570	−	0.148002i
$818$		0			0
$819$	−37.0398	+	11.6437i	−1.29427	+	0.406865i
$820$		0			0
$821$	13.7528	−	51.3262i	0.479977	−	1.79130i	−0.121710	−	0.992566i	$-0.538838\pi$
$821$	13.7528	−	51.3262i	0.479977	−	1.79130i	0.601687	−	0.798732i	$-0.294496\pi$
$822$		0			0
$823$	9.92634	+	5.73097i	0.346010	+	0.199769i	0.662927	−	0.748684i	$-0.269314\pi$
$823$	9.92634	+	5.73097i	0.346010	+	0.199769i	−0.316916	+	0.948454i	$0.602647\pi$
$824$		0			0
$825$	−22.5286	−	4.93997i	−0.784346	−	0.171988i
$826$		0			0
$827$	4.57665	−	4.57665i	0.159146	−	0.159146i	−0.623042	−	0.782188i	$-0.714104\pi$
$827$	4.57665	−	4.57665i	0.159146	−	0.159146i	0.782188	+	0.623042i	$0.214104\pi$
$828$		0			0
$829$	43.2625	−	24.9776i	1.50257	−	0.867509i	0.502574	−	0.864534i	$-0.332387\pi$
$829$	43.2625	−	24.9776i	1.50257	−	0.867509i	0.999996	−	0.00297446i	$-0.000946803\pi$
$830$		0			0
$831$	12.3434	−	23.8457i	0.428189	−	0.827198i
$832$		0			0
$833$			20.3266i			0.704275i
$834$		0			0
$835$	−7.98133	−	13.8241i	−0.276205	−	0.478401i
$836$		0			0
$837$	7.14013	+	5.40071i	0.246799	+	0.186676i
$838$		0			0
$839$	3.00183	+	11.2030i	0.103635	+	0.386770i	0.998187	−	0.0601939i	$-0.0191719\pi$
$839$	3.00183	+	11.2030i	0.103635	+	0.386770i	−0.894552	+	0.446964i	$0.852505\pi$
$840$		0			0
$841$	−12.4716	+	21.6014i	−0.430054	+	0.744876i
$842$		0			0
$843$	−21.6180	−	19.7177i	−0.744564	−	0.679114i
$844$		0			0
$845$	23.5700	+	28.7221i	0.810832	+	0.988069i
$846$		0			0
$847$	−23.0926	−	6.18765i	−0.793472	−	0.212610i
$848$		0			0
$849$	1.47545	+	2.30425i	0.0506375	+	0.0790817i
$850$		0			0
$851$	−14.1841	+	3.80063i	−0.486226	+	0.130284i
$852$		0			0
$853$	−1.56247	−	1.56247i	−0.0534978	−	0.0534978i	0.679852	−	0.733350i	$-0.262044\pi$
$853$	−1.56247	−	1.56247i	−0.0534978	−	0.0534978i	−0.733350	+	0.679852i	$0.762044\pi$
$854$		0			0
$855$	−8.05644	+	17.4873i	−0.275525	+	0.598054i
$856$		0			0
$857$	−21.5804			−0.737174			−0.368587	−	0.929593i	$-0.620158\pi$
$857$	−21.5804			−0.737174			−0.368587	+	0.929593i	$0.620158\pi$
$858$		0			0
$859$	−10.5544			−0.360110			−0.180055	−	0.983657i	$-0.557628\pi$
$859$	−10.5544			−0.360110			−0.180055	+	0.983657i	$0.557628\pi$
$860$		0			0
$861$	−49.3175	+	2.26726i	−1.68074	+	0.0772681i
$862$		0			0
$863$	21.4177	+	21.4177i	0.729066	+	0.729066i	0.970434	−	0.241368i	$-0.0775960\pi$
$863$	21.4177	+	21.4177i	0.729066	+	0.729066i	−0.241368	+	0.970434i	$0.577596\pi$
$864$		0			0
$865$	48.2992	−	12.9417i	1.64222	−	0.440032i
$866$		0			0
$867$	−7.39436	+	4.73475i	−0.251126	+	0.160800i
$868$		0			0
$869$	−6.41562	−	1.71906i	−0.217635	−	0.0583152i
$870$		0			0
$871$	14.5748	+	4.68323i	0.493848	+	0.158685i
$872$		0			0
$873$	8.33585	+	22.5779i	0.282126	+	0.764144i
$874$		0			0
$875$	−9.39415	+	16.2711i	−0.317580	+	0.550065i
$876$		0			0
$877$	10.1109	+	37.7342i	0.341420	+	1.27419i	0.896740	+	0.442558i	$0.145929\pi$
$877$	10.1109	+	37.7342i	0.341420	+	1.27419i	−0.555320	+	0.831637i	$0.687404\pi$
$878$		0			0
$879$	6.44617	−	2.04883i	0.217424	−	0.0691054i
$880$		0			0
$881$	−3.39708	−	5.88391i	−0.114450	−	0.198234i	0.803110	−	0.595831i	$-0.203177\pi$
$881$	−3.39708	−	5.88391i	−0.114450	−	0.198234i	−0.917560	+	0.397598i	$0.869844\pi$
$882$		0			0
$883$			40.6560i			1.36818i	0.729397	+	0.684091i	$0.239801\pi$
$883$			40.6560i			1.36818i	−0.729397	+	0.684091i	$0.760199\pi$
$884$		0			0
$885$	−45.2307	−	23.4131i	−1.52041	−	0.787023i
$886$		0			0
$887$	9.04299	−	5.22097i	0.303634	−	0.175303i	−0.340440	−	0.940266i	$-0.610576\pi$
$887$	9.04299	−	5.22097i	0.303634	−	0.175303i	0.644074	+	0.764963i	$0.277243\pi$
$888$		0			0
$889$	−52.5233	+	52.5233i	−1.76158	+	1.76158i
$890$		0			0
$891$	37.7066	+	2.94852i	1.26322	+	0.0987790i
$892$		0			0
$893$	−2.63304	−	1.52018i	−0.0881112	−	0.0508710i
$894$		0			0
$895$	−6.81664	+	25.4400i	−0.227855	+	0.850367i
$896$		0			0
$897$	16.4299	−	9.41663i	0.548579	−	0.314412i
$898$		0			0
$899$	−0.898169	+	3.35201i	−0.0299556	+	0.111796i
$900$		0			0
$901$	−21.6029	−	12.4724i	−0.719697	−	0.415517i
$902$		0			0
$903$	2.59719	−	11.8444i	0.0864290	−	0.394157i
$904$		0			0
$905$	27.9116	−	27.9116i	0.927814	−	0.927814i
$906$		0			0
$907$	33.9759	−	19.6160i	1.12815	−	0.651338i	0.184681	−	0.982799i	$-0.440875\pi$
$907$	33.9759	−	19.6160i	1.12815	−	0.651338i	0.943469	+	0.331461i	$0.107542\pi$
$908$		0			0
$909$	−3.64917	−	5.16071i	−0.121035	−	0.171170i
$910$		0			0
$911$			32.0923i			1.06326i	0.846975	+	0.531632i	$0.178421\pi$
$911$			32.0923i			1.06326i	−0.846975	+	0.531632i	$0.821579\pi$
$912$		0			0
$913$	7.69447	+	13.3272i	0.254650	+	0.441066i
$914$		0			0
$915$	−0.411170	−	1.29365i	−0.0135929	−	0.0427667i
$916$		0			0
$917$	4.35066	+	16.2369i	0.143671	+	0.536189i
$918$		0			0
$919$	16.6421	−	28.8249i	0.548972	−	0.950847i	−0.449374	−	0.893344i	$-0.648353\pi$
$919$	16.6421	−	28.8249i	0.548972	−	0.950847i	0.998345	−	0.0575028i	$-0.0183138\pi$
$920$		0			0
$921$	35.9839	−	39.4519i	1.18571	−	1.29998i
$922$		0			0
$923$	38.8863	−	8.39796i	1.27996	−	0.276422i
$924$		0			0
$925$	−14.8216	−	3.97143i	−0.487330	−	0.130580i
$926$		0			0
$927$	−3.92594	−	42.6082i	−0.128945	−	1.39944i
$928$		0			0
$929$	−21.2156	+	5.68470i	−0.696060	+	0.186509i	−0.589465	−	0.807794i	$-0.700662\pi$
$929$	−21.2156	+	5.68470i	−0.696060	+	0.186509i	−0.106595	+	0.994303i	$0.533995\pi$
$930$		0			0
$931$	−9.34415	−	9.34415i	−0.306242	−	0.306242i
$932$		0			0
$933$	1.66480	+	36.2128i	0.0545032	+	1.18555i
$934$		0			0
$935$	−41.4864			−1.35675
$936$		0			0
$937$	55.9423			1.82755			0.913777	−	0.406216i	$-0.133152\pi$
$937$	55.9423			1.82755			0.913777	+	0.406216i	$0.133152\pi$
$938$		0			0
$939$	−2.59856	−	56.5238i	−0.0848008	−	1.84459i
$940$		0			0
$941$	17.1600	+	17.1600i	0.559401	+	0.559401i	0.929137	−	0.369736i	$-0.120552\pi$
$941$	17.1600	+	17.1600i	0.559401	+	0.559401i	−0.369736	+	0.929137i	$0.620552\pi$
$942$		0			0
$943$	23.2587	−	6.23215i	0.757407	−	0.202947i
$944$		0			0
$945$	−20.0589	+	49.3906i	−0.652515	+	1.60668i
$946$		0			0
$947$	−46.0604	−	12.3419i	−1.49676	−	0.401056i	−0.584748	−	0.811215i	$-0.698807\pi$
$947$	−46.0604	−	12.3419i	−1.49676	−	0.401056i	−0.912014	+	0.410159i	$0.865473\pi$
$948$		0			0
$949$	−34.5237	−	38.0924i	−1.12069	−	1.23653i
$950$		0			0
$951$	−8.60145	+	9.43043i	−0.278921	+	0.305803i
$952$		0			0
$953$	21.5278	−	37.2872i	0.697353	−	1.20785i	−0.272029	−	0.962289i	$-0.587695\pi$
$953$	21.5278	−	37.2872i	0.697353	−	1.20785i	0.969381	−	0.245561i	$-0.0789721\pi$
$954$		0			0
$955$	16.7940	+	62.6761i	0.543441	+	2.02815i
$956$		0			0
$957$	4.44080	+	13.9719i	0.143551	+	0.451648i
$958$		0			0
$959$	9.83532	+	17.0353i	0.317599	+	0.550098i
$960$		0			0
$961$			28.0315i			0.904242i
$962$		0			0
$963$	−33.9144	+	23.9811i	−1.09288	+	0.772781i
$964$		0			0
$965$	−49.6166	+	28.6461i	−1.59721	+	0.922152i
$966$		0			0
$967$	4.96226	−	4.96226i	0.159576	−	0.159576i	−0.622803	−	0.782379i	$-0.714006\pi$
$967$	4.96226	−	4.96226i	0.159576	−	0.159576i	0.782379	+	0.622803i	$0.214006\pi$
$968$		0			0
$969$	−2.87745	+	13.1225i	−0.0924370	+	0.421557i
$970$		0			0
$971$	27.5285	+	15.8936i	0.883432	+	0.510050i	0.871789	−	0.489882i	$-0.162960\pi$
$971$	27.5285	+	15.8936i	0.883432	+	0.510050i	0.0116437	+	0.999932i	$0.496294\pi$
$972$		0			0
$973$	−13.6506	+	50.9448i	−0.437619	+	1.63322i
$974$		0			0
$975$	19.7881	+	0.0626048i	0.633725	+	0.00200496i
$976$		0			0
$977$	1.80392	−	6.73232i	0.0577125	−	0.215386i	−0.931047	−	0.364898i	$-0.881104\pi$
$977$	1.80392	−	6.73232i	0.0577125	−	0.215386i	0.988760	+	0.149512i	$0.0477704\pi$
$978$		0			0
$979$	35.8290	+	20.6859i	1.14510	+	0.661124i
$980$		0			0
$981$	−15.8446	+	19.0608i	−0.505878	+	0.608563i
$982$		0			0
$983$	−10.5636	+	10.5636i	−0.336926	+	0.336926i	−0.855209	−	0.518283i	$-0.826571\pi$
$983$	−10.5636	+	10.5636i	−0.336926	+	0.336926i	0.518283	+	0.855209i	$0.326571\pi$
$984$		0			0
$985$	−46.1306	+	26.6335i	−1.46984	+	0.848614i
$986$		0			0
$987$	−7.47571	−	3.86971i	−0.237954	−	0.123174i
$988$		0			0
$989$			5.91416i			0.188059i
$990$		0			0
$991$	13.1927	+	22.8505i	0.419081	+	0.725870i	0.995847	−	0.0910396i	$-0.0290190\pi$
$991$	13.1927	+	22.8505i	0.419081	+	0.725870i	−0.576766	+	0.816909i	$0.695686\pi$
$992$		0			0
$993$	30.1038	−	9.56810i	0.955315	−	0.303635i
$994$		0			0
$995$	3.33645	+	12.4518i	0.105773	+	0.394749i
$996$		0			0
$997$	−14.6325	+	25.3443i	−0.463416	+	0.802660i	−0.999129	−	0.0417401i	$-0.986710\pi$
$997$	−14.6325	+	25.3443i	−0.463416	+	0.802660i	0.535712	+	0.844401i	$0.320043\pi$
$998$		0			0
$999$	24.9697	+	3.11165i	0.790006	+	0.0984483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.d.353.3		16
3.2	odd	2	inner	624.2.cn.d.353.4		16
4.3	odd	2		78.2.k.a.41.1	✓	16
12.11	even	2		78.2.k.a.41.3	yes	16
13.7	odd	12	inner	624.2.cn.d.449.4		16
39.20	even	12	inner	624.2.cn.d.449.3		16
52.3	odd	6		1014.2.g.c.239.4		16
52.7	even	12		78.2.k.a.59.3	yes	16
52.11	even	12		1014.2.g.c.437.8		16
52.15	even	12		1014.2.g.d.437.4		16
52.23	odd	6		1014.2.g.d.239.8		16
156.11	odd	12		1014.2.g.c.437.4		16
156.23	even	6		1014.2.g.d.239.4		16
156.59	odd	12		78.2.k.a.59.1	yes	16
156.107	even	6		1014.2.g.c.239.8		16
156.119	odd	12		1014.2.g.d.437.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.1	✓	16	4.3	odd	2
78.2.k.a.41.3	yes	16	12.11	even	2
78.2.k.a.59.1	yes	16	156.59	odd	12
78.2.k.a.59.3	yes	16	52.7	even	12
624.2.cn.d.353.3		16	1.1	even	1	trivial
624.2.cn.d.353.4		16	3.2	odd	2	inner
624.2.cn.d.449.3		16	39.20	even	12	inner
624.2.cn.d.449.4		16	13.7	odd	12	inner
1014.2.g.c.239.4		16	52.3	odd	6
1014.2.g.c.239.8		16	156.107	even	6
1014.2.g.c.437.4		16	156.11	odd	12
1014.2.g.c.437.8		16	52.11	even	12
1014.2.g.d.239.4		16	156.23	even	6
1014.2.g.d.239.8		16	52.23	odd	6
1014.2.g.d.437.4		16	52.15	even	12
1014.2.g.d.437.8		16	156.119	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0795432 + 1.73022i) q^{3} +(2.02097 + 2.02097i) q^{5} +(-3.46723 + 0.929042i) q^{7} +(-2.98735 + 0.275255i) q^{9} +(4.05922 + 1.08766i) q^{11} +(-3.60121 - 0.176977i) q^{13} +(-3.33598 + 3.65748i) q^{15} +(-1.72704 + 2.99132i) q^{17} +(-0.581191 - 2.16903i) q^{19} +(-1.88324 - 5.92518i) q^{21} +(1.51618 + 2.62611i) q^{23} +3.16864i q^{25} +(-0.713876 - 5.14688i) q^{27} +(1.74432 - 1.00708i) q^{29} +(-1.21829 + 1.21829i) q^{31} +(-1.55902 + 7.10987i) q^{33} +(-8.88473 - 5.12960i) q^{35} +(-1.25335 + 4.67758i) q^{37} +(0.0197576 - 6.24497i) q^{39} +(2.05521 - 7.67015i) q^{41} +(1.68905 + 0.975173i) q^{43} +(-6.59362 - 5.48105i) q^{45} +(0.957390 - 0.957390i) q^{47} +(5.09639 - 2.94240i) q^{49} +(-5.31303 - 2.75023i) q^{51} +7.22186i q^{53} +(6.00542 + 10.4017i) q^{55} +(3.70668 - 1.17812i) q^{57} +(2.66284 + 9.93785i) q^{59} +(-0.137104 + 0.237470i) q^{61} +(10.1021 - 3.72974i) q^{63} +(-6.92026 - 7.63559i) q^{65} +(-4.10121 - 1.09891i) q^{67} +(-4.42315 + 2.83223i) q^{69} +(-10.6578 + 2.85575i) q^{71} +(10.0822 + 10.0822i) q^{73} +(-5.48246 + 0.252044i) q^{75} -15.0847 q^{77} -1.58051 q^{79} +(8.84847 - 1.64456i) q^{81} +(2.58938 + 2.58938i) q^{83} +(-9.53567 + 2.55507i) q^{85} +(1.88122 + 2.93795i) q^{87} +(9.50933 + 2.54802i) q^{89} +(12.6506 - 2.73205i) q^{91} +(-2.20483 - 2.01101i) q^{93} +(3.20898 - 5.55812i) q^{95} +(-2.07638 - 7.74915i) q^{97} +(-12.4257 - 2.13191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73}+ \cdots + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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