LMFDB - Embedded newform 945.2.bv.e.523.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(73,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 2]))

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

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

chi := DirichletCharacter("945.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bv (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			523.28
Character	$\chi$	$=$	945.523
Dual form			945.2.bv.e.262.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.690838 - 0.690838i) q^{2} +1.04549i q^{4} +(-1.77477 + 1.36022i) q^{5} +(-0.704044 - 2.55036i) q^{7} +(2.10394 + 2.10394i) q^{8} +O(q^{10})$	\(q+(0.690838 - 0.690838i) q^{2} +1.04549i q^{4} +(-1.77477 + 1.36022i) q^{5} +(-0.704044 - 2.55036i) q^{7} +(2.10394 + 2.10394i) q^{8} +(-0.286383 + 2.16577i) q^{10} +(-0.816710 + 1.41458i) q^{11} +(-0.137573 - 0.513429i) q^{13} +(-2.24826 - 1.27550i) q^{14} +0.815990 q^{16} +(-0.265268 + 0.989992i) q^{17} +(-2.99374 + 5.18531i) q^{19} +(-1.42209 - 1.85549i) q^{20} +(0.413034 + 1.54146i) q^{22} +(-1.92122 + 7.17009i) q^{23} +(1.29959 - 4.82815i) q^{25} +(-0.449737 - 0.259656i) q^{26} +(2.66636 - 0.736068i) q^{28} +(-5.82340 + 3.36214i) q^{29} -8.35659i q^{31} +(-3.64416 + 3.64416i) q^{32} +(0.500668 + 0.867182i) q^{34} +(4.71857 + 3.56863i) q^{35} +(1.47305 + 5.49748i) q^{37} +(1.51402 + 5.65040i) q^{38} +(-6.59582 - 0.872175i) q^{40} +(-6.13816 - 3.54387i) q^{41} +(-1.98612 + 7.41230i) q^{43} +(-1.47893 - 0.853858i) q^{44} +(3.62612 + 6.28062i) q^{46} +(-1.39656 - 1.39656i) q^{47} +(-6.00864 + 3.59113i) q^{49} +(-2.43767 - 4.23328i) q^{50} +(0.536782 - 0.143830i) q^{52} +(-0.361997 + 1.35099i) q^{53} +(-0.474678 - 3.62146i) q^{55} +(3.88453 - 6.84706i) q^{56} +(-1.70033 + 6.34572i) q^{58} +1.10522 q^{59} +13.7361i q^{61} +(-5.77305 - 5.77305i) q^{62} +6.66703i q^{64} +(0.942537 + 0.724087i) q^{65} +(3.95260 - 3.95260i) q^{67} +(-1.03502 - 0.277333i) q^{68} +(5.72511 - 0.794419i) q^{70} +6.35753 q^{71} +(6.07255 + 1.62714i) q^{73} +(4.81551 + 2.78023i) q^{74} +(-5.42116 - 3.12991i) q^{76} +(4.18269 + 1.08697i) q^{77} -6.73743i q^{79} +(-1.44819 + 1.10993i) q^{80} +(-6.68871 + 1.79224i) q^{82} +(-3.78491 - 1.01416i) q^{83} +(-0.875822 - 2.11783i) q^{85} +(3.74861 + 6.49278i) q^{86} +(-4.69450 + 1.25789i) q^{88} +(9.04644 - 15.6689i) q^{89} +(-1.21257 + 0.712336i) q^{91} +(-7.49622 - 2.00861i) q^{92} -1.92959 q^{94} +(-1.73998 - 13.2749i) q^{95} +(0.0399199 - 0.148983i) q^{97} +(-1.67011 + 6.63189i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.690838	−	0.690838i	0.488496	−	0.488496i	−0.419335	−	0.907832i	$-0.637737\pi$
$2$	0.690838	−	0.690838i	0.488496	−	0.488496i	0.907832	+	0.419335i	$0.137737\pi$
$3$		0			0
$3$		0			0
$4$			1.04549i			0.522743i
$5$	−1.77477	+	1.36022i	−0.793700	+	0.608310i
$5$	−1.77477	+	1.36022i	−0.793700	+	0.608310i
$6$		0			0
$7$	−0.704044	−	2.55036i	−0.266104	−	0.963944i
$7$	−0.704044	−	2.55036i	−0.266104	−	0.963944i
$8$	2.10394	+	2.10394i	0.743854	+	0.743854i
$9$		0			0
$10$	−0.286383	+	2.16577i	−0.0905622	+	0.684877i
$11$	−0.816710	+	1.41458i	−0.246247	+	0.426513i	−0.962482	−	0.271347i	$-0.912531\pi$
$11$	−0.816710	+	1.41458i	−0.246247	+	0.426513i	0.716234	+	0.697860i	$0.245864\pi$
$12$		0			0
$13$	−0.137573	−	0.513429i	−0.0381558	−	0.142400i	0.944220	−	0.329315i	$-0.106818\pi$
$13$	−0.137573	−	0.513429i	−0.0381558	−	0.142400i	−0.982376	+	0.186915i	$0.940151\pi$
$14$	−2.24826	−	1.27550i	−0.600874	−	0.340893i
$15$		0			0
$16$	0.815990			0.203998
$17$	−0.265268	+	0.989992i	−0.0643369	+	0.240108i	−0.990604	−	0.136758i	$-0.956332\pi$
$17$	−0.265268	+	0.989992i	−0.0643369	+	0.240108i	0.926268	+	0.376866i	$0.122998\pi$
$18$		0			0
$19$	−2.99374	+	5.18531i	−0.686811	+	1.18959i	0.286053	+	0.958214i	$0.407657\pi$
$19$	−2.99374	+	5.18531i	−0.686811	+	1.18959i	−0.972864	+	0.231377i	$0.925677\pi$
$20$	−1.42209	−	1.85549i	−0.317989	−	0.414901i
$21$		0			0
$22$	0.413034	+	1.54146i	0.0880591	+	0.328641i
$23$	−1.92122	+	7.17009i	−0.400602	+	1.49507i	0.411423	+	0.911444i	$0.365032\pi$
$23$	−1.92122	+	7.17009i	−0.400602	+	1.49507i	−0.812025	+	0.583622i	$0.801635\pi$
$24$		0			0
$25$	1.29959	−	4.82815i	0.259918	−	0.965631i
$26$	−0.449737	−	0.259656i	−0.0882006	−	0.0509227i
$27$		0			0
$28$	2.66636	−	0.736068i	0.503895	−	0.139104i
$29$	−5.82340	+	3.36214i	−1.08138	+	0.624334i	−0.931268	−	0.364335i	$-0.881296\pi$
$29$	−5.82340	+	3.36214i	−1.08138	+	0.624334i	−0.150110	+	0.988669i	$0.547963\pi$
$30$		0			0
$31$		−	8.35659i		−	1.50089i	−0.660934	−	0.750444i	$-0.729840\pi$
$31$		−	8.35659i		−	1.50089i	0.660934	−	0.750444i	$-0.270160\pi$
$32$	−3.64416	+	3.64416i	−0.644202	+	0.644202i
$33$		0			0
$34$	0.500668	+	0.867182i	0.0858638	+	0.148720i
$35$	4.71857	+	3.56863i	0.797583	+	0.603209i
$36$		0			0
$37$	1.47305	+	5.49748i	0.242167	+	0.903780i	0.974786	+	0.223141i	$0.0716311\pi$
$37$	1.47305	+	5.49748i	0.242167	+	0.903780i	−0.732619	+	0.680639i	$0.761702\pi$
$38$	1.51402	+	5.65040i	0.245606	+	0.916615i
$39$		0			0
$40$	−6.59582	−	0.872175i	−1.04289	−	0.137903i
$41$	−6.13816	−	3.54387i	−0.958619	−	0.553459i	−0.0628714	−	0.998022i	$-0.520026\pi$
$41$	−6.13816	−	3.54387i	−0.958619	−	0.553459i	−0.895748	+	0.444563i	$0.853359\pi$
$42$		0			0
$43$	−1.98612	+	7.41230i	−0.302880	+	1.13036i	0.631874	+	0.775071i	$0.282286\pi$
$43$	−1.98612	+	7.41230i	−0.302880	+	1.13036i	−0.934755	+	0.355294i	$0.884381\pi$
$44$	−1.47893	−	0.853858i	−0.222956	−	0.128724i
$45$		0			0
$46$	3.62612	+	6.28062i	0.534642	+	0.926027i
$47$	−1.39656	−	1.39656i	−0.203709	−	0.203709i	0.597878	−	0.801587i	$-0.296011\pi$
$47$	−1.39656	−	1.39656i	−0.203709	−	0.203709i	−0.801587	+	0.597878i	$0.796011\pi$
$48$		0			0
$49$	−6.00864	+	3.59113i	−0.858378	+	0.513018i
$50$	−2.43767	−	4.23328i	−0.344738	−	0.598676i
$51$		0			0
$52$	0.536782	−	0.143830i	0.0744383	−	0.0199457i
$53$	−0.361997	+	1.35099i	−0.0497241	+	0.185573i	−0.986321	−	0.164836i	$-0.947291\pi$
$53$	−0.361997	+	1.35099i	−0.0497241	+	0.185573i	0.936597	+	0.350409i	$0.113957\pi$
$54$		0			0
$55$	−0.474678	−	3.62146i	−0.0640056	−	0.488318i
$56$	3.88453	−	6.84706i	0.519092	−	0.914976i
$57$		0			0
$58$	−1.70033	+	6.34572i	−0.223264	+	0.833234i
$59$	1.10522			0.143887			0.0719437	−	0.997409i	$-0.477080\pi$
$59$	1.10522			0.143887			0.0719437	+	0.997409i	$0.477080\pi$
$60$		0			0
$61$			13.7361i			1.75873i	0.476153	+	0.879363i	$0.342031\pi$
$61$			13.7361i			1.75873i	−0.476153	+	0.879363i	$0.657969\pi$
$62$	−5.77305	−	5.77305i	−0.733178	−	0.733178i
$63$		0			0
$64$			6.66703i			0.833378i
$65$	0.942537	+	0.724087i	0.116907	+	0.0898119i
$66$		0			0
$67$	3.95260	−	3.95260i	0.482886	−	0.482886i	−0.423166	−	0.906052i	$-0.639081\pi$
$67$	3.95260	−	3.95260i	0.482886	−	0.482886i	0.906052	+	0.423166i	$0.139081\pi$
$68$	−1.03502	−	0.277333i	−0.125515	−	0.0336316i
$69$		0			0
$70$	5.72511	−	0.794419i	0.684282	−	0.0949512i
$71$	6.35753			0.754500			0.377250	−	0.926112i	$-0.376870\pi$
$71$	6.35753			0.754500			0.377250	+	0.926112i	$0.376870\pi$
$72$		0			0
$73$	6.07255	+	1.62714i	0.710739	+	0.190442i	0.596036	−	0.802958i	$-0.296742\pi$
$73$	6.07255	+	1.62714i	0.710739	+	0.190442i	0.114703	+	0.993400i	$0.463408\pi$
$74$	4.81551	+	2.78023i	0.559791	+	0.323196i
$75$		0			0
$76$	−5.42116	−	3.12991i	−0.621850	−	0.359025i
$77$	4.18269	+	1.08697i	0.476662	+	0.123872i
$78$		0			0
$79$		−	6.73743i		−	0.758020i	−0.925393	−	0.379010i	$-0.876265\pi$
$79$		−	6.73743i		−	0.758020i	0.925393	−	0.379010i	$-0.123735\pi$
$80$	−1.44819	+	1.10993i	−0.161913	+	0.124094i
$81$		0			0
$82$	−6.68871	+	1.79224i	−0.738645	+	0.197919i
$83$	−3.78491	−	1.01416i	−0.415448	−	0.111319i	0.0450392	−	0.998985i	$-0.485659\pi$
$83$	−3.78491	−	1.01416i	−0.415448	−	0.111319i	−0.460488	+	0.887666i	$0.652325\pi$
$84$		0			0
$85$	−0.875822	−	2.11783i	−0.0949962	−	0.229711i
$86$	3.74861	+	6.49278i	0.404223	+	0.700135i
$87$		0			0
$88$	−4.69450	+	1.25789i	−0.500436	+	0.134091i
$89$	9.04644	−	15.6689i	0.958921	−	1.66090i	0.233793	−	0.972286i	$-0.424886\pi$
$89$	9.04644	−	15.6689i	0.958921	−	1.66090i	0.725128	−	0.688614i	$-0.241780\pi$
$90$		0			0
$91$	−1.21257	+	0.712336i	−0.127112	+	0.0746731i
$92$	−7.49622	−	2.00861i	−0.781535	−	0.209412i
$93$		0			0
$94$	−1.92959			−0.199022
$95$	−1.73998	−	13.2749i	−0.178519	−	1.36197i
$96$		0			0
$97$	0.0399199	−	0.148983i	0.00405325	−	0.0151270i	−0.963870	−	0.266375i	$-0.914174\pi$
$97$	0.0399199	−	0.148983i	0.00405325	−	0.0151270i	0.967923	+	0.251248i	$0.0808409\pi$
$98$	−1.67011	+	6.63189i	−0.168707	+	0.669922i
$99$		0			0
$100$	5.04776	+	1.35870i	0.504776	+	0.135870i
$101$	−7.05201	−	4.07148i	−0.701701	−	0.405127i	0.106280	−	0.994336i	$-0.466106\pi$
$101$	−7.05201	−	4.07148i	−0.701701	−	0.405127i	−0.807981	+	0.589209i	$0.799439\pi$
$102$		0			0
$103$	9.91904	+	2.65780i	0.977352	+	0.261881i	0.711929	−	0.702252i	$-0.247822\pi$
$103$	9.91904	+	2.65780i	0.977352	+	0.261881i	0.265423	+	0.964132i	$0.414488\pi$
$104$	0.790777	−	1.36967i	0.0775421	−	0.134307i
$105$		0			0
$106$	0.683235	+	1.18340i	0.0663616	+	0.114942i
$107$	0.329306	+	1.22899i	0.0318352	+	0.118811i	0.980015	−	0.198924i	$-0.0637446\pi$
$107$	0.329306	+	1.22899i	0.0318352	+	0.118811i	−0.948180	+	0.317734i	$0.897078\pi$
$108$		0			0
$109$	10.0397	−	5.79643i	0.961630	−	0.555197i	0.0649556	−	0.997888i	$-0.479309\pi$
$109$	10.0397	−	5.79643i	0.961630	−	0.555197i	0.896674	+	0.442691i	$0.145976\pi$
$110$	−2.82977	−	2.17392i	−0.269808	−	0.207275i
$111$		0			0
$112$	−0.574493	−	2.08107i	−0.0542845	−	0.196642i
$113$	20.1005	−	5.38592i	1.89090	−	0.506664i	0.892438	−	0.451170i	$-0.148993\pi$
$113$	20.1005	−	5.38592i	1.89090	−	0.506664i	0.998459	−	0.0554944i	$-0.0176735\pi$
$114$		0			0
$115$	−6.34320	−	15.3385i	−0.591506	−	1.43032i
$116$	−3.51507	−	6.08828i	−0.326366	−	0.565282i
$117$		0			0
$118$	0.763528	−	0.763528i	0.0702884	−	0.0702884i
$119$	2.71159	−	0.0204710i	0.248571	−	0.00187657i
$120$		0			0
$121$	4.16597	+	7.21567i	0.378724	+	0.655970i
$122$	9.48941	+	9.48941i	0.859131	+	0.859131i
$123$		0			0
$124$	8.73669			0.784578
$125$	4.26089	+	10.3366i	0.381106	+	0.924531i
$126$		0			0
$127$	−1.86063	+	1.86063i	−0.165104	+	0.165104i	−0.784824	−	0.619719i	$-0.787246\pi$
$127$	−1.86063	+	1.86063i	−0.165104	+	0.165104i	0.619719	+	0.784824i	$0.287246\pi$
$128$	−2.68248	−	2.68248i	−0.237100	−	0.237100i
$129$		0			0
$130$	1.15137	−	0.150914i	0.100982	−	0.0132360i
$131$	−1.82517	+	1.05376i	−0.159465	+	0.0920674i	−0.577609	−	0.816313i	$-0.696014\pi$
$131$	−1.82517	+	1.05376i	−0.159465	+	0.0920674i	0.418144	+	0.908381i	$0.362681\pi$
$132$		0			0
$133$	15.3321	+	3.98442i	1.32946	+	0.345493i
$134$		−	5.46121i		−	0.471777i
$135$		0			0
$136$	−2.64099	+	1.52478i	−0.226463	+	0.130748i
$137$	3.50159	+	13.0681i	0.299161	+	1.11648i	0.937856	+	0.347024i	$0.112808\pi$
$137$	3.50159	+	13.0681i	0.299161	+	1.11648i	−0.638695	+	0.769460i	$0.720526\pi$
$138$		0			0
$139$	6.44269	−	11.1591i	0.546461	−	0.946499i	−0.452052	−	0.891992i	$-0.649308\pi$
$139$	6.44269	−	11.1591i	0.546461	−	0.946499i	0.998513	−	0.0545074i	$-0.0173588\pi$
$140$	−3.73095	+	4.93319i	−0.315323	+	0.416931i
$141$		0			0
$142$	4.39202	−	4.39202i	0.368570	−	0.368570i
$143$	0.838645	+	0.224714i	0.0701310	+	0.0187915i
$144$		0			0
$145$	5.76191	−	13.8881i	0.478501	−	1.15335i
$146$	5.31924	−	3.07106i	0.440223	−	0.254163i
$147$		0			0
$148$	−5.74753	+	1.54005i	−0.472444	+	0.126591i
$149$	−3.17238	+	1.83158i	−0.259892	+	0.150049i	−0.624285	−	0.781197i	$-0.714610\pi$
$149$	−3.17238	+	1.83158i	−0.259892	+	0.150049i	0.364393	+	0.931245i	$0.381276\pi$
$150$		0			0
$151$	−0.998652	+	1.72972i	−0.0812691	+	0.140762i	−0.903795	−	0.427965i	$-0.859231\pi$
$151$	−0.998652	+	1.72972i	−0.0812691	+	0.140762i	0.822526	+	0.568727i	$0.192564\pi$
$152$	−17.2082	+	4.61092i	−1.39577	+	0.373995i
$153$		0			0
$154$	3.64049	−	2.13864i	0.293359	−	0.172337i
$155$	11.3668	+	14.8310i	0.913005	+	1.19125i
$156$		0			0
$157$	−5.97391	−	5.97391i	−0.476770	−	0.476770i	0.427327	−	0.904097i	$-0.359455\pi$
$157$	−5.97391	−	5.97391i	−0.476770	−	0.476770i	−0.904097	+	0.427327i	$0.859455\pi$
$158$	−4.65447	−	4.65447i	−0.370290	−	0.370290i
$159$		0			0
$160$	1.51066	−	11.4244i	0.119428	−	0.903178i
$161$	19.6389	−	0.148263i	1.54776	−	0.0116847i
$162$		0			0
$163$	−2.14187	+	0.573913i	−0.167764	+	0.0449523i	−0.341723	−	0.939801i	$-0.611011\pi$
$163$	−2.14187	+	0.573913i	−0.167764	+	0.0449523i	0.173959	+	0.984753i	$0.444344\pi$
$164$	3.70506	−	6.41735i	0.289317	−	0.501111i
$165$		0			0
$166$	−3.31539	+	1.91414i	−0.257324	+	0.148566i
$167$	−1.31306	+	0.351833i	−0.101607	+	0.0272256i	−0.309265	−	0.950976i	$-0.600083\pi$
$167$	−1.31306	+	0.351833i	−0.101607	+	0.0272256i	0.207657	+	0.978202i	$0.433416\pi$
$168$		0			0
$169$	11.0136	−	6.35873i	0.847204	−	0.489133i
$170$	−2.06813	−	0.858026i	−0.158618	−	0.0658076i
$171$		0			0
$172$	−7.74945	−	2.07646i	−0.590890	−	0.158328i
$173$	−1.45010	+	1.45010i	−0.110249	+	0.110249i	−0.760079	−	0.649830i	$-0.774840\pi$
$173$	−1.45010	+	1.45010i	−0.110249	+	0.110249i	0.649830	+	0.760079i	$0.274840\pi$
$174$		0			0
$175$	−13.2285	+	0.0848112i	−0.999979	+	0.00641112i
$176$	−0.666427	+	1.15429i	−0.0502339	+	0.0870076i
$177$		0			0
$178$	−4.57505	−	17.0743i	−0.342914	−	1.27977i
$179$	−14.6028	+	8.43092i	−1.09146	+	0.630157i	−0.933966	−	0.357362i	$-0.883676\pi$
$179$	−14.6028	+	8.43092i	−1.09146	+	0.630157i	−0.157498	+	0.987519i	$0.550343\pi$
$180$		0			0
$181$			20.3678i			1.51392i	0.653459	+	0.756962i	$0.273317\pi$
$181$			20.3678i			1.51392i	−0.653459	+	0.756962i	$0.726683\pi$
$182$	−0.345580	+	1.32980i	−0.0256161	+	0.0985712i
$183$		0			0
$184$	−19.1275	+	11.0433i	−1.41010	+	0.814122i
$185$	−10.0921	−	7.75307i	−0.741986	−	0.570017i
$186$		0			0
$187$	−1.18378	−	1.18378i	−0.0865666	−	0.0865666i
$188$	1.46008	−	1.46008i	0.106487	−	0.106487i
$189$		0			0
$190$	−10.3728	−	7.96873i	−0.752524	−	0.578113i
$191$	−17.2341			−1.24701			−0.623506	−	0.781818i	$-0.714292\pi$
$191$	−17.2341			−1.24701			−0.623506	+	0.781818i	$0.714292\pi$
$192$		0			0
$193$	7.64872	+	7.64872i	0.550567	+	0.550567i	0.926604	−	0.376038i	$-0.122714\pi$
$193$	7.64872	+	7.64872i	0.550567	+	0.550567i	−0.376038	+	0.926604i	$0.622714\pi$
$194$	−0.0753451	−	0.130501i	−0.00540946	−	0.00936946i
$195$		0			0
$196$	−3.75447	−	6.28195i	−0.268176	−	0.448711i
$197$	−4.66542	+	4.66542i	−0.332398	+	0.332398i	−0.853496	−	0.521099i	$-0.825522\pi$
$197$	−4.66542	+	4.66542i	−0.332398	+	0.332398i	0.521099	+	0.853496i	$0.325522\pi$
$198$		0			0
$199$	−2.58318	−	4.47420i	−0.183117	−	0.317168i	0.759823	−	0.650130i	$-0.225285\pi$
$199$	−2.58318	−	4.47420i	−0.183117	−	0.317168i	−0.942940	+	0.332962i	$0.891952\pi$
$200$	12.8924	−	7.42387i	0.911630	−	0.524947i
$201$		0			0
$202$	−7.68453	+	2.05906i	−0.540682	+	0.144875i
$203$	12.6746	+	12.4847i	0.889582	+	0.876251i
$204$		0			0
$205$	15.7142	−	2.05972i	1.09753	−	0.143857i
$206$	8.68856	−	5.01634i	0.605360	−	0.349505i
$207$		0			0
$208$	−0.112258	−	0.418953i	−0.00778370	−	0.0290492i
$209$	−4.89003	−	8.46978i	−0.338251	−	0.585867i
$210$		0			0
$211$	0.273339	−	0.473437i	0.0188174	−	0.0325927i	−0.856463	−	0.516208i	$-0.827343\pi$
$211$	0.273339	−	0.473437i	0.0188174	−	0.0325927i	0.875281	+	0.483615i	$0.160677\pi$
$212$	−1.41244	−	0.378462i	−0.0970068	−	0.0259929i
$213$		0			0
$214$	1.07653	+	0.621534i	0.0735900	+	0.0424872i
$215$	−6.55747	−	15.8567i	−0.447216	−	1.08141i
$216$		0			0
$217$	−21.3123	+	5.88341i	−1.44677	+	0.399392i
$218$	2.93142	−	10.9402i	0.198541	−	0.740965i
$219$		0			0
$220$	3.78618	−	0.496269i	0.255265	−	0.0334584i
$221$	0.544784			0.0366462
$222$		0			0
$223$	−25.6042	−	6.86061i	−1.71458	−	0.459421i	−0.738041	−	0.674756i	$-0.764249\pi$
$223$	−25.6042	−	6.86061i	−1.71458	−	0.459421i	−0.976540	+	0.215335i	$0.930916\pi$
$224$	11.8596	+	6.72826i	0.792400	+	0.449551i
$225$		0			0
$226$	10.1654	−	17.6070i	0.676193	−	1.17120i
$227$	16.4370	−	4.40428i	1.09096	−	0.292323i	0.331883	−	0.943321i	$-0.392316\pi$
$227$	16.4370	−	4.40428i	1.09096	−	0.292323i	0.759079	+	0.650998i	$0.225649\pi$
$228$		0			0
$229$	−6.99567	−	12.1169i	−0.462287	−	0.800705i	0.536787	−	0.843717i	$-0.319638\pi$
$229$	−6.99567	−	12.1169i	−0.462287	−	0.800705i	−0.999075	+	0.0430129i	$0.986304\pi$
$230$	−14.9786	−	6.21431i	−0.987657	−	0.409759i
$231$		0			0
$232$	−19.3258	−	5.17833i	−1.26880	−	0.339974i
$233$	−11.8929	+	3.18669i	−0.779130	+	0.208767i	−0.626401	−	0.779501i	$-0.715473\pi$
$233$	−11.8929	+	3.18669i	−0.779130	+	0.208767i	−0.152729	+	0.988268i	$0.548806\pi$
$234$		0			0
$235$	4.37819	+	0.578935i	0.285602	+	0.0377656i
$236$			1.15549i			0.0752160i
$237$		0			0
$238$	1.85913	−	1.88742i	0.120510	−	0.122343i
$239$	6.57367	+	3.79531i	0.425215	+	0.245498i	0.697306	−	0.716773i	$-0.254382\pi$
$239$	6.57367	+	3.79531i	0.425215	+	0.245498i	−0.272091	+	0.962272i	$0.587715\pi$
$240$		0			0
$241$	5.21861	+	3.01296i	0.336160	+	0.194082i	0.658573	−	0.752517i	$-0.271161\pi$
$241$	5.21861	+	3.01296i	0.336160	+	0.194082i	−0.322413	+	0.946599i	$0.604494\pi$
$242$	7.86287	+	2.10685i	0.505445	+	0.135433i
$243$		0			0
$244$	−14.3609			−0.919361
$245$	5.77921	−	14.5465i	0.369220	−	0.929342i
$246$		0			0
$247$	3.07414	+	0.823714i	0.195603	+	0.0524117i
$248$	17.5817	−	17.5817i	1.11644	−	1.11644i
$249$		0			0
$250$	10.0845	+	4.19732i	0.637799	+	0.265462i
$251$		−	4.81059i		−	0.303642i	−0.988408	−	0.151821i	$-0.951486\pi$
$251$		−	4.81059i		−	0.303642i	0.988408	−	0.151821i	$-0.0485137\pi$
$252$		0			0
$253$	−8.57361	−	8.57361i	−0.539018	−	0.539018i
$254$			2.57079i			0.161306i
$255$		0			0
$256$	−17.0404			−1.06502
$257$	−4.23796	+	15.8163i	−0.264357	+	0.986592i	0.698287	+	0.715818i	$0.253946\pi$
$257$	−4.23796	+	15.8163i	−0.264357	+	0.986592i	−0.962643	+	0.270774i	$0.912721\pi$
$258$		0			0
$259$	12.9835	−	7.62726i	0.806752	−	0.473935i
$260$	−0.757022	+	0.985408i	−0.0469485	+	0.0611124i
$261$		0			0
$262$	−0.532917	+	1.98887i	−0.0329237	+	0.122873i
$263$	8.05555	−	2.15848i	0.496726	−	0.133097i	−0.00175401	−	0.999998i	$-0.500558\pi$
$263$	8.05555	−	2.15848i	0.496726	−	0.133097i	0.498480	+	0.866901i	$0.333892\pi$
$264$		0			0
$265$	−1.19519	−	2.89009i	−0.0734198	−	0.177537i
$266$	13.3446	−	7.83942i	0.818210	−	0.480666i
$267$		0			0
$268$	4.13238	+	4.13238i	0.252425	+	0.252425i
$269$	1.86662	+	3.23307i	0.113810	+	0.197124i	0.917303	−	0.398189i	$-0.130361\pi$
$269$	1.86662	+	3.23307i	0.113810	+	0.197124i	−0.803494	+	0.595313i	$0.797028\pi$
$270$		0			0
$271$	5.54325	+	3.20039i	0.336728	+	0.194410i	0.658824	−	0.752297i	$-0.271054\pi$
$271$	5.54325	+	3.20039i	0.336728	+	0.194410i	−0.322096	+	0.946707i	$0.604387\pi$
$272$	−0.216456	+	0.807824i	−0.0131246	+	0.0489815i
$273$		0			0
$274$	11.4470	+	6.60892i	0.691537	+	0.399259i
$275$	5.76844	+	5.78158i	0.347850	+	0.348642i
$276$		0			0
$277$	0.148632	+	0.554701i	0.00893041	+	0.0333287i	0.970247	−	0.242116i	$-0.0778415\pi$
$277$	0.148632	+	0.554701i	0.00893041	+	0.0333287i	−0.961317	+	0.275445i	$0.911175\pi$
$278$	−3.25825	−	12.1600i	−0.195417	−	0.729306i
$279$		0			0
$280$	2.41939	+	17.4357i	0.144586	+	1.04199i
$281$	−2.21693	−	3.83984i	−0.132251	−	0.229065i	0.792293	−	0.610141i	$-0.208887\pi$
$281$	−2.21693	−	3.83984i	−0.132251	−	0.229065i	−0.924544	+	0.381075i	$0.875554\pi$
$282$		0			0
$283$	5.26619	−	5.26619i	0.313043	−	0.313043i	−0.533044	−	0.846087i	$-0.678952\pi$
$283$	5.26619	−	5.26619i	0.313043	−	0.313043i	0.846087	+	0.533044i	$0.178952\pi$
$284$			6.64670i			0.394409i
$285$		0			0
$286$	0.734609	−	0.424127i	0.0434383	−	0.0250791i
$287$	−4.71659	+	18.1495i	−0.278412	+	1.07133i
$288$		0			0
$289$	13.8127	+	7.97477i	0.812513	+	0.469104i
$290$	−5.61390	−	13.5750i	−0.329660	−	0.797152i
$291$		0			0
$292$	−1.70115	+	6.34877i	−0.0995521	+	0.371533i
$293$	4.98512	+	18.6047i	0.291234	+	1.08690i	0.944163	+	0.329480i	$0.106873\pi$
$293$	4.98512	+	18.6047i	0.291234	+	1.08690i	−0.652929	+	0.757419i	$0.726460\pi$
$294$		0			0
$295$	−1.96151	+	1.50334i	−0.114203	+	0.0875281i
$296$	−8.46716	+	14.6656i	−0.492144	+	0.852418i
$297$		0			0
$298$	−0.926280	+	3.45692i	−0.0536580	+	0.200254i
$299$	3.94564			0.228182
$300$		0			0
$301$	20.3023	−	0.153271i	1.17021	−	0.00883439i
$302$	0.505047	+	1.88486i	0.0290622	+	0.108462i
$303$		0			0
$304$	−2.44286	+	4.23116i	−0.140108	+	0.242674i
$305$	−18.6841	−	24.3783i	−1.06985	−	1.39590i
$306$		0			0
$307$	6.54479	+	6.54479i	0.373531	+	0.373531i	0.868761	−	0.495231i	$-0.164916\pi$
$307$	6.54479	+	6.54479i	0.373531	+	0.373531i	−0.495231	+	0.868761i	$0.664916\pi$
$308$	−1.13641	+	4.37294i	−0.0647532	+	0.249172i
$309$		0			0
$310$	18.0985	+	2.39319i	1.02792	+	0.135924i
$311$		−	24.6330i		−	1.39681i	−0.715702	−	0.698406i	$-0.753893\pi$
$311$		−	24.6330i		−	1.39681i	0.715702	−	0.698406i	$-0.246107\pi$
$312$		0			0
$313$	−17.9429	+	17.9429i	−1.01419	+	1.01419i	−0.0142930	+	0.999898i	$0.504550\pi$
$313$	−17.9429	+	17.9429i	−1.01419	+	1.01419i	−0.999898	+	0.0142930i	$0.995450\pi$
$314$	−8.25401			−0.465801
$315$		0			0
$316$	7.04388			0.396249
$317$	7.53443	−	7.53443i	0.423176	−	0.423176i	−0.463120	−	0.886296i	$-0.653270\pi$
$317$	7.53443	−	7.53443i	0.423176	−	0.423176i	0.886296	+	0.463120i	$0.153270\pi$
$318$		0			0
$319$		−	10.9836i		−	0.614962i
$320$	−9.06864	−	11.8324i	−0.506952	−	0.661452i
$321$		0			0
$322$	13.4649	−	13.6697i	0.750369	−	0.761785i
$323$	−4.33927	−	4.33927i	−0.241444	−	0.241444i
$324$		0			0
$325$	−2.65770	−	0.00302479i	−0.147423	−	0.000167785i
$326$	−1.08321	+	1.87617i	−0.0599932	+	0.103911i
$327$		0			0
$328$	−5.45823	−	20.3704i	−0.301380	−	1.12477i
$329$	−2.57848	+	4.54496i	−0.142156	+	0.250572i
$330$		0			0
$331$	6.24703			0.343368			0.171684	−	0.985152i	$-0.445079\pi$
$331$	6.24703			0.343368			0.171684	+	0.985152i	$0.445079\pi$
$332$	1.06029	−	3.95707i	0.0581912	−	0.217173i
$333$		0			0
$334$	−0.664051	+	1.15017i	−0.0363352	+	0.0629345i
$335$	−1.63853	+	12.3913i	−0.0895222	+	0.677011i
$336$		0			0
$337$	−3.31266	−	12.3630i	−0.180452	−	0.673457i	−0.995558	−	0.0941452i	$-0.969988\pi$
$337$	−3.31266	−	12.3630i	−0.180452	−	0.673457i	0.815106	−	0.579311i	$-0.196678\pi$
$338$	3.21579	−	12.0015i	0.174916	−	0.652796i
$339$		0			0
$340$	2.21416	−	0.915659i	0.120080	−	0.0496586i
$341$	11.8211	+	6.82491i	0.640148	+	0.369590i
$342$		0			0
$343$	13.3890	+	12.7959i	0.722939	+	0.690912i
$344$	−19.7737	+	11.4163i	−1.06613	+	0.615528i
$345$		0			0
$346$			2.00357i			0.107712i
$347$	9.47519	−	9.47519i	0.508655	−	0.508655i	−0.405459	−	0.914113i	$-0.632888\pi$
$347$	9.47519	−	9.47519i	0.508655	−	0.508655i	0.914113	+	0.405459i	$0.132888\pi$
$348$		0			0
$349$	15.4350	+	26.7341i	0.826215	+	1.43105i	0.900987	+	0.433846i	$0.142844\pi$
$349$	15.4350	+	26.7341i	0.826215	+	1.43105i	−0.0747724	+	0.997201i	$0.523823\pi$
$350$	−9.08015	+	9.19733i	−0.485355	+	0.491618i
$351$		0			0
$352$	−2.17874	−	8.13118i	−0.116127	−	0.433394i
$353$	4.25417	+	15.8768i	0.226426	+	0.845035i	0.981828	+	0.189773i	$0.0607752\pi$
$353$	4.25417	+	15.8768i	0.226426	+	0.845035i	−0.755402	+	0.655262i	$0.772558\pi$
$354$		0			0
$355$	−11.2831	+	8.64765i	−0.598846	+	0.458970i
$356$	16.3816	+	9.45792i	0.868223	+	0.501269i
$357$		0			0
$358$	−4.26376	+	15.9126i	−0.225347	+	0.841005i
$359$	−1.40486	−	0.811094i	−0.0741455	−	0.0428079i	0.462469	−	0.886635i	$-0.346964\pi$
$359$	−1.40486	−	0.811094i	−0.0741455	−	0.0428079i	−0.536614	+	0.843828i	$0.680297\pi$
$360$		0			0
$361$	−8.42494	−	14.5924i	−0.443418	−	0.768022i
$362$	14.0708	+	14.0708i	0.739546	+	0.739546i
$363$		0			0
$364$	−0.744737	−	1.26772i	−0.0390348	−	0.0664468i
$365$	−12.9906	+	5.37224i	−0.679961	+	0.281196i
$366$		0			0
$367$	2.34101	−	0.627271i	0.122200	−	0.0327433i	−0.197201	−	0.980363i	$-0.563185\pi$
$367$	2.34101	−	0.627271i	0.122200	−	0.0327433i	0.319401	+	0.947620i	$0.396518\pi$
$368$	−1.56770	+	5.85072i	−0.0817218	+	0.304990i
$369$		0			0
$370$	−12.3281	+	1.61589i	−0.640909	+	0.0840063i
$371$	3.70037	−	0.0279357i	0.192114	−	0.00145035i
$372$		0			0
$373$	−8.27835	+	30.8952i	−0.428637	+	1.59969i	0.327214	+	0.944950i	$0.393890\pi$
$373$	−8.27835	+	30.8952i	−0.428637	+	1.59969i	−0.755851	+	0.654744i	$0.772777\pi$
$374$	−1.63560			−0.0845749
$375$		0			0
$376$		−	5.87654i		−	0.303060i
$377$	2.52736	+	2.52736i	0.130166	+	0.130166i
$378$		0			0
$379$		−	30.9678i		−	1.59071i	−0.606146	−	0.795353i	$-0.707285\pi$
$379$		−	30.9678i		−	1.59071i	0.606146	−	0.795353i	$-0.292715\pi$
$380$	13.8787	−	1.81913i	0.711961	−	0.0933193i
$381$		0			0
$382$	−11.9059	+	11.9059i	−0.609161	+	0.609161i
$383$	−18.1872	−	4.87326i	−0.929324	−	0.249012i	−0.237758	−	0.971324i	$-0.576412\pi$
$383$	−18.1872	−	4.87326i	−0.929324	−	0.249012i	−0.691567	+	0.722313i	$0.743079\pi$
$384$		0			0
$385$	−8.90183	+	3.76027i	−0.453679	+	0.191641i
$386$	10.5681			0.537900
$387$		0			0
$388$	0.155760	+	0.0417357i	0.00790750	+	0.00211881i
$389$	−20.5140	−	11.8438i	−1.04010	−	0.600503i	−0.120240	−	0.992745i	$-0.538366\pi$
$389$	−20.5140	−	11.8438i	−1.04010	−	0.600503i	−0.919862	+	0.392242i	$0.871700\pi$
$390$		0			0
$391$	−6.58870	−	3.80399i	−0.333205	−	0.192376i
$392$	−20.1973	−	5.08630i	−1.02012	−	0.256897i
$393$		0			0
$394$			6.44611i			0.324750i
$395$	9.16440	+	11.9574i	0.461111	+	0.601640i
$396$		0			0
$397$	−23.2158	+	6.22065i	−1.16517	+	0.312205i	−0.789027	−	0.614358i	$-0.789415\pi$
$397$	−23.2158	+	6.22065i	−1.16517	+	0.312205i	−0.376139	+	0.926563i	$0.622748\pi$
$398$	−4.87551	−	1.30639i	−0.244387	−	0.0654834i
$399$		0			0
$400$	1.06045	−	3.93973i	0.0530227	−	0.196986i
$401$	17.1072	+	29.6306i	0.854295	+	1.47968i	0.877298	+	0.479947i	$0.159344\pi$
$401$	17.1072	+	29.6306i	0.854295	+	1.47968i	−0.0230028	+	0.999735i	$0.507323\pi$
$402$		0			0
$403$	−4.29051	+	1.14964i	−0.213726	+	0.0572676i
$404$	4.25667	−	7.37277i	0.211777	−	0.366809i
$405$		0			0
$406$	17.3810	−	0.131216i	0.862603	−	0.00651216i
$407$	−8.97969	−	2.40610i	−0.445107	−	0.119266i
$408$		0			0
$409$	0.0910287			0.00450108			0.00225054	−	0.999997i	$-0.499284\pi$
$409$	0.0910287			0.00450108			0.00225054	+	0.999997i	$0.499284\pi$
$410$	9.43306	−	12.2789i	0.465866	−	0.606413i
$411$		0			0
$412$	−2.77869	+	10.3702i	−0.136896	+	0.510903i
$413$	−0.778123	−	2.81870i	−0.0382889	−	0.138699i
$414$		0			0
$415$	8.09683	−	3.34842i	0.397458	−	0.164367i
$416$	2.37235	+	1.36968i	0.116314	+	0.0671540i
$417$		0			0
$418$	−9.22947	−	2.47303i	−0.451428	−	0.120960i
$419$	13.7216	−	23.7665i	0.670343	−	1.16107i	−0.307464	−	0.951560i	$-0.599480\pi$
$419$	13.7216	−	23.7665i	0.670343	−	1.16107i	0.977807	−	0.209508i	$-0.0671862\pi$
$420$		0			0
$421$	−5.94319	−	10.2939i	−0.289653	−	0.501695i	0.684074	−	0.729413i	$-0.260207\pi$
$421$	−5.94319	−	10.2939i	−0.289653	−	0.501695i	−0.973727	+	0.227719i	$0.926873\pi$
$422$	−0.138235	−	0.515901i	−0.00672919	−	0.0251137i
$423$		0			0
$424$	−3.60402	+	2.08078i	−0.175027	+	0.101052i
$425$	4.43510	+	2.56734i	0.215134	+	0.124534i
$426$		0			0
$427$	35.0319	−	9.67081i	1.69531	−	0.468003i
$428$	−1.28489	+	0.344285i	−0.0621074	+	0.0166416i
$429$		0			0
$430$	−15.4845	−	6.42423i	−0.746731	−	0.309804i
$431$	11.1221	+	19.2640i	0.535732	+	0.927915i	0.999128	+	0.0417634i	$0.0132976\pi$
$431$	11.1221	+	19.2640i	0.535732	+	0.927915i	−0.463396	+	0.886152i	$0.653369\pi$
$432$		0			0
$433$	−5.23695	+	5.23695i	−0.251672	+	0.251672i	−0.821656	−	0.569984i	$-0.806949\pi$
$433$	−5.23695	+	5.23695i	−0.251672	+	0.251672i	0.569984	+	0.821656i	$0.306949\pi$
$434$	−10.6589	+	18.7878i	−0.511642	+	0.901845i
$435$		0			0
$436$	6.06008	+	10.4964i	0.290225	+	0.502685i
$437$	−31.4275	−	31.4275i	−1.50338	−	1.50338i
$438$		0			0
$439$	−19.5501			−0.933075			−0.466538	−	0.884501i	$-0.654499\pi$
$439$	−19.5501			−0.933075			−0.466538	+	0.884501i	$0.654499\pi$
$440$	6.62064	−	8.61802i	0.315626	−	0.410848i
$441$		0			0
$442$	0.376358	−	0.376358i	0.0179015	−	0.0179015i
$443$	26.5025	+	26.5025i	1.25917	+	1.25917i	0.951488	+	0.307685i	$0.0995544\pi$
$443$	26.5025	+	26.5025i	1.25917	+	1.25917i	0.307685	+	0.951488i	$0.400446\pi$
$444$		0			0
$445$	5.25786	+	40.1138i	0.249247	+	1.90158i
$446$	−22.4279	+	12.9488i	−1.06199	+	0.613141i
$447$		0			0
$448$	17.0033	−	4.69388i	0.803330	−	0.221765i
$449$		−	18.6203i		−	0.878748i	−0.898304	−	0.439374i	$-0.855200\pi$
$449$		−	18.6203i		−	0.878748i	0.898304	−	0.439374i	$-0.144800\pi$
$450$		0			0
$451$	10.0262	−	5.78862i	0.472115	−	0.272576i
$452$	5.63090	+	21.0148i	0.264855	+	0.988452i
$453$		0			0
$454$	8.31267	−	14.3980i	0.390133	−	0.675730i
$455$	1.18309	−	2.91359i	0.0554642	−	0.136591i
$456$		0			0
$457$	−20.6389	+	20.6389i	−0.965445	+	0.965445i	−0.999423	−	0.0339772i	$-0.989183\pi$
$457$	−20.6389	+	20.6389i	−0.965445	+	0.965445i	0.0339772	+	0.999423i	$0.489183\pi$
$458$	−13.2037	−	3.53791i	−0.616967	−	0.165316i
$459$		0			0
$460$	16.0362	−	6.63172i	0.747691	−	0.309206i
$461$	−13.2237	+	7.63473i	−0.615891	+	0.355585i	−0.775267	−	0.631633i	$-0.782385\pi$
$461$	−13.2237	+	7.63473i	−0.615891	+	0.355585i	0.159377	+	0.987218i	$0.449052\pi$
$462$		0			0
$463$	39.9841	−	10.7137i	1.85822	−	0.497908i	0.858333	−	0.513092i	$-0.171500\pi$
$463$	39.9841	−	10.7137i	1.85822	−	0.497908i	0.999885	+	0.0151842i	$0.00483345\pi$
$464$	−4.75184	+	2.74347i	−0.220599	+	0.127363i
$465$		0			0
$466$	−6.01458	+	10.4176i	−0.278620	+	0.482584i
$467$	−17.4657	+	4.67993i	−0.808217	+	0.216561i	−0.639189	−	0.769050i	$-0.720730\pi$
$467$	−17.4657	+	4.67993i	−0.808217	+	0.216561i	−0.169029	+	0.985611i	$0.554063\pi$
$468$		0			0
$469$	−12.8633	−	7.29773i	−0.593973	−	0.336978i
$470$	3.42457	−	2.62467i	0.157964	−	0.121067i
$471$		0			0
$472$	2.32531	+	2.32531i	0.107031	+	0.107031i
$473$	−8.86323	−	8.86323i	−0.407532	−	0.407532i
$474$		0			0
$475$	21.1448	+	21.1930i	0.970191	+	0.972402i
$476$	0.0214021	+	2.83493i	0.000980965	+	0.129939i
$477$		0			0
$478$	7.16329	−	1.91940i	0.327641	−	0.0877912i
$479$	−4.07569	+	7.05931i	−0.186223	+	0.322548i	−0.943988	−	0.329980i	$-0.892958\pi$
$479$	−4.07569	+	7.05931i	−0.186223	+	0.322548i	0.757765	+	0.652528i	$0.226291\pi$
$480$		0			0
$481$	2.61991	−	1.51261i	0.119458	−	0.0689690i
$482$	5.68668	−	1.52374i	0.259021	−	0.0694045i
$483$		0			0
$484$	−7.54388	+	4.35546i	−0.342903	+	0.197975i
$485$	0.131802	+	0.318710i	0.00598481	+	0.0144719i
$486$		0			0
$487$	3.93080	+	1.05326i	0.178122	+	0.0477276i	0.346777	−	0.937947i	$-0.387276\pi$
$487$	3.93080	+	1.05326i	0.178122	+	0.0477276i	−0.168656	+	0.985675i	$0.553943\pi$
$488$	−28.8999	+	28.8999i	−1.30824	+	1.30824i
$489$		0			0
$490$	−6.05678	−	14.0418i	−0.273618	−	0.634343i
$491$	−14.1237	+	24.4629i	−0.637392	+	1.10399i	0.348612	+	0.937267i	$0.386653\pi$
$491$	−14.1237	+	24.4629i	−0.637392	+	1.10399i	−0.986003	+	0.166727i	$0.946680\pi$
$492$		0			0
$493$	−1.78373	−	6.65699i	−0.0803354	−	0.299816i
$494$	2.69279	−	1.55468i	0.121154	−	0.0699485i
$495$		0			0
$496$		−	6.81890i		−	0.306178i
$497$	−4.47598	−	16.2140i	−0.200775	−	0.727296i
$498$		0			0
$499$	21.4496	−	12.3840i	0.960218	−	0.554382i	0.0639775	−	0.997951i	$-0.479621\pi$
$499$	21.4496	−	12.3840i	0.960218	−	0.554382i	0.896240	+	0.443569i	$0.146288\pi$
$500$	−10.8067	+	4.45470i	−0.483292	+	0.199220i
$501$		0			0
$502$	−3.32334	−	3.32334i	−0.148328	−	0.148328i
$503$	22.1184	−	22.1184i	0.986211	−	0.986211i	−0.0136949	−	0.999906i	$-0.504359\pi$
$503$	22.1184	−	22.1184i	0.986211	−	0.986211i	0.999906	+	0.0136949i	$0.00435937\pi$
$504$		0			0
$505$	18.0538	−	2.36638i	0.803383	−	0.105302i
$506$	−11.8460			−0.526617
$507$		0			0
$508$	−1.94526	−	1.94526i	−0.0863071	−	0.0863071i
$509$	0.687693	+	1.19112i	0.0304815	+	0.0527955i	0.880864	−	0.473370i	$-0.156963\pi$
$509$	0.687693	+	1.19112i	0.0304815	+	0.0527955i	−0.850382	+	0.526165i	$0.823629\pi$
$510$		0			0
$511$	−0.125568	−	16.6328i	−0.00555480	−	0.735790i
$512$	−6.40718	+	6.40718i	−0.283160	+	0.283160i
$513$		0			0
$514$	7.99874	+	13.8542i	0.352809	+	0.611084i
$515$	−21.2192	+	8.77512i	−0.935028	+	0.386678i
$516$		0			0
$517$	3.11613	−	0.834965i	0.137047	−	0.0367217i
$518$	3.70026	−	14.2387i	0.162580	−	0.625611i
$519$		0			0
$520$	0.459606	+	3.50647i	0.0201551	+	0.153769i
$521$	22.4862	−	12.9824i	0.985140	−	0.568771i	0.0813222	−	0.996688i	$-0.474086\pi$
$521$	22.4862	−	12.9824i	0.985140	−	0.568771i	0.903818	+	0.427917i	$0.140752\pi$
$522$		0			0
$523$	0.697525	+	2.60320i	0.0305006	+	0.113830i	0.979498	−	0.201454i	$-0.0645668\pi$
$523$	0.697525	+	2.60320i	0.0305006	+	0.113830i	−0.948997	+	0.315284i	$0.897900\pi$
$524$	−1.10169	−	1.90818i	−0.0481276	−	0.0833594i
$525$		0			0
$526$	4.07392	−	7.05624i	0.177631	−	0.307667i
$527$	8.27296	+	2.21673i	0.360376	+	0.0965624i
$528$		0			0
$529$	−27.8005	−	16.0506i	−1.20872	−	0.697853i
$530$	−2.82226	−	1.17090i	−0.122591	−	0.0508607i
$531$		0			0
$532$	−4.16565	+	16.0295i	−0.180604	+	0.694967i
$533$	−0.975080	+	3.63905i	−0.0422354	+	0.157625i
$534$		0			0
$535$	−2.25614	−	1.73324i	−0.0975414	−	0.0749343i
$536$	16.6320			0.718394
$537$		0			0
$538$	3.52306	+	0.944001i	0.151890	+	0.0406988i
$539$	−0.172630	−	11.4326i	−0.00743569	−	0.492439i
$540$		0			0
$541$	−10.0369	+	17.3845i	−0.431522	+	0.747418i	−0.997005	−	0.0773420i	$-0.975357\pi$
$541$	−10.0369	+	17.3845i	−0.431522	+	0.747418i	0.565482	+	0.824760i	$0.308690\pi$
$542$	6.04044	−	1.61853i	0.259459	−	0.0695219i
$543$		0			0
$544$	−2.64101	−	4.57437i	−0.113232	−	0.196124i
$545$	−9.93371	+	23.9435i	−0.425513	+	1.02563i
$546$		0			0
$547$	14.4892	+	3.88238i	0.619515	+	0.165999i	0.554907	−	0.831912i	$-0.312754\pi$
$547$	14.4892	+	3.88238i	0.619515	+	0.165999i	0.0646077	+	0.997911i	$0.479420\pi$
$548$	−13.6625	+	3.66086i	−0.583634	+	0.156384i
$549$		0			0
$550$	7.97919	+	0.00908129i	0.340234	+	0.000387228i
$551$		−	40.2615i		−	1.71520i
$552$		0			0
$553$	−17.1829	+	4.74345i	−0.730689	+	0.201712i
$554$	0.485889	+	0.280528i	0.0206434	+	0.0119185i
$555$		0			0
$556$	11.6666	+	6.73573i	0.494775	+	0.285659i
$557$	−0.236144	−	0.0632745i	−0.0100057	−	0.00268103i	0.253813	−	0.967253i	$-0.418315\pi$
$557$	−0.236144	−	0.0632745i	−0.0100057	−	0.00268103i	−0.263818	+	0.964572i	$0.584982\pi$
$558$		0			0
$559$	4.07892			0.172520
$560$	3.85030	+	2.91197i	0.162705	+	0.123053i
$561$		0			0
$562$	−4.18424	−	1.12117i	−0.176502	−	0.0472935i
$563$	−0.0555045	+	0.0555045i	−0.00233924	+	0.00233924i	−0.708275	−	0.705936i	$-0.750527\pi$
$563$	−0.0555045	+	0.0555045i	−0.00233924	+	0.00233924i	0.705936	+	0.708275i	$0.250527\pi$
$564$		0			0
$565$	−28.3477	+	36.8999i	−1.19260	+	1.55239i
$566$		−	7.27618i		−	0.305840i
$567$		0			0
$568$	13.3758	+	13.3758i	0.561238	+	0.561238i
$569$			14.7549i			0.618556i	0.950972	+	0.309278i	$0.100087\pi$
$569$			14.7549i			0.618556i	−0.950972	+	0.309278i	$0.899913\pi$
$570$		0			0
$571$	−29.5516			−1.23669			−0.618347	−	0.785905i	$-0.712197\pi$
$571$	−29.5516			−1.23669			−0.618347	+	0.785905i	$0.712197\pi$
$572$	−0.234935	+	0.876791i	−0.00982314	+	0.0366605i
$573$		0			0
$574$	9.27999	+	15.7968i	0.387339	+	0.659345i
$575$	32.1215	+	18.5941i	1.33956	+	0.775429i
$576$		0			0
$577$	−2.16353	+	8.07441i	−0.0900690	+	0.336142i	−0.996226	−	0.0867998i	$-0.972336\pi$
$577$	−2.16353	+	8.07441i	−0.0900690	+	0.336142i	0.906157	+	0.422942i	$0.139003\pi$
$578$	15.0516	−	4.03307i	0.626065	−	0.167754i
$579$		0			0
$580$	14.5198	+	6.02400i	0.602903	+	0.250133i
$581$	0.0782642	+	10.3669i	0.00324695	+	0.430091i
$582$		0			0
$583$	−1.61544	−	1.61544i	−0.0669048	−	0.0669048i
$584$	9.35288	+	16.1997i	0.387025	+	0.670347i
$585$		0			0
$586$	16.2968	+	9.40894i	0.673213	+	0.388680i
$587$	−2.34352	+	8.74614i	−0.0967275	+	0.360992i	−0.997276	−	0.0737643i	$-0.976499\pi$
$587$	−2.34352	+	8.74614i	−0.0967275	+	0.360992i	0.900548	+	0.434756i	$0.143165\pi$
$588$		0			0
$589$	43.3315	+	25.0175i	1.78544	+	1.03083i
$590$	−0.316516	+	2.39365i	−0.0130308	+	0.0985450i
$591$		0			0
$592$	1.20199	+	4.48589i	0.0494015	+	0.184369i
$593$	7.48847	+	27.9474i	0.307515	+	1.14766i	0.930759	+	0.365633i	$0.119148\pi$
$593$	7.48847	+	27.9474i	0.307515	+	1.14766i	−0.623244	+	0.782027i	$0.714186\pi$
$594$		0			0
$595$	−4.78460	+	3.72470i	−0.196150	+	0.152698i
$596$	−1.91489	−	3.31668i	−0.0784367	−	0.135856i
$597$		0			0
$598$	2.72580	−	2.72580i	0.111466	−	0.111466i
$599$		−	10.0498i		−	0.410625i	−0.978696	−	0.205313i	$-0.934179\pi$
$599$		−	10.0498i		−	0.410625i	0.978696	−	0.205313i	$-0.0658211\pi$
$600$		0			0
$601$	27.4153	−	15.8282i	1.11829	−	0.645647i	0.177329	−	0.984152i	$-0.443254\pi$
$601$	27.4153	−	15.8282i	1.11829	−	0.645647i	0.940965	+	0.338505i	$0.109921\pi$
$602$	13.9197	−	14.1315i	0.567326	−	0.575957i
$603$		0			0
$604$	−1.80839	−	1.04408i	−0.0735824	−	0.0424828i
$605$	−17.2085	−	7.13949i	−0.699627	−	0.290261i
$606$		0			0
$607$	−2.86111	+	10.6778i	−0.116129	+	0.433398i	−0.999369	−	0.0355226i	$-0.988690\pi$
$607$	−2.86111	+	10.6778i	−0.116129	+	0.433398i	0.883240	+	0.468921i	$0.155357\pi$
$608$	−7.98642	−	29.8057i	−0.323892	−	1.20878i
$609$		0			0
$610$	−29.7492	−	3.93378i	−1.20451	−	0.159274i
$611$	−0.524905	+	0.909162i	−0.0212354	+	0.0367807i
$612$		0			0
$613$	6.18919	−	23.0984i	0.249979	−	0.932934i	−0.720836	−	0.693105i	$-0.756242\pi$
$613$	6.18919	−	23.0984i	0.249979	−	0.932934i	0.970815	−	0.239829i	$-0.0770913\pi$
$614$	9.04278			0.364937
$615$		0			0
$616$	6.51320	+	11.0870i	0.262424	+	0.446710i
$617$	1.79766	+	6.70895i	0.0723709	+	0.270092i	0.992624	−	0.121231i	$-0.0386842\pi$
$617$	1.79766	+	6.70895i	0.0723709	+	0.270092i	−0.920253	+	0.391323i	$0.872018\pi$
$618$		0			0
$619$	−15.6977	+	27.1893i	−0.630945	+	1.09283i	0.356414	+	0.934328i	$0.383999\pi$
$619$	−15.6977	+	27.1893i	−0.630945	+	1.09283i	−0.987359	+	0.158500i	$0.949334\pi$
$620$	−15.5056	+	11.8838i	−0.622719	+	0.477267i
$621$		0			0
$622$	−17.0174	−	17.0174i	−0.682337	−	0.682337i
$623$	−46.3304	−	12.0401i	−1.85619	−	0.482375i
$624$		0			0
$625$	−21.6221	−	12.5492i	−0.864885	−	0.501970i
$626$			24.7912i			0.990857i
$627$		0			0
$628$	6.24563	−	6.24563i	0.249228	−	0.249228i
$629$	−5.83322			−0.232586
$630$		0			0
$631$	−36.8622			−1.46746			−0.733730	−	0.679441i	$-0.762222\pi$
$631$	−36.8622			−1.46746			−0.733730	+	0.679441i	$0.762222\pi$
$632$	14.1751	−	14.1751i	0.563856	−	0.563856i
$633$		0			0
$634$		−	10.4101i		−	0.413440i
$635$	0.771314	−	5.83306i	0.0306087	−	0.231478i
$636$		0			0
$637$	2.67041	+	2.59097i	0.105806	+	0.102658i
$638$	−7.58787	−	7.58787i	−0.300407	−	0.300407i
$639$		0			0
$640$	8.40954	+	1.11201i	0.332416	+	0.0439559i
$641$	7.53215	−	13.0461i	0.297502	−	0.515289i	−0.678062	−	0.735005i	$-0.737180\pi$
$641$	7.53215	−	13.0461i	0.297502	−	0.515289i	0.975564	+	0.219716i	$0.0705131\pi$
$642$		0			0
$643$	−4.70433	−	17.5568i	−0.185521	−	0.692372i	−0.994518	−	0.104561i	$-0.966656\pi$
$643$	−4.70433	−	17.5568i	−0.185521	−	0.692372i	0.808998	−	0.587812i	$-0.200010\pi$
$644$	0.155006	+	20.5322i	0.00610811	+	0.809082i
$645$		0			0
$646$	−5.99547			−0.235889
$647$	1.04775	−	3.91026i	0.0411913	−	0.153728i	−0.942267	−	0.334862i	$-0.891310\pi$
$647$	1.04775	−	3.91026i	0.0411913	−	0.153728i	0.983458	+	0.181134i	$0.0579769\pi$
$648$		0			0
$649$	−0.902644	+	1.56342i	−0.0354319	+	0.0613698i
$650$	−1.83813	+	1.83395i	−0.0720974	+	0.0719335i
$651$		0			0
$652$	−0.600017	−	2.23930i	−0.0234985	−	0.0876976i
$653$	−5.98559	+	22.3385i	−0.234234	+	0.874174i	0.744258	+	0.667892i	$0.232803\pi$
$653$	−5.98559	+	22.3385i	−0.234234	+	0.874174i	−0.978493	+	0.206282i	$0.933864\pi$
$654$		0			0
$655$	1.80589	−	4.35281i	0.0705622	−	0.170078i
$656$	−5.00868	−	2.89176i	−0.195556	−	0.112904i
$657$		0			0
$658$	1.35852	+	4.92115i	0.0529605	+	0.191846i
$659$	38.7647	−	22.3808i	1.51006	−	0.871834i	0.510129	−	0.860098i	$-0.329598\pi$
$659$	38.7647	−	22.3808i	1.51006	−	0.871834i	0.999931	−	0.0117356i	$-0.00373563\pi$
$660$		0			0
$661$			17.5421i			0.682309i	0.940007	+	0.341155i	$0.110818\pi$
$661$			17.5421i			0.682309i	−0.940007	+	0.341155i	$0.889182\pi$
$662$	4.31569	−	4.31569i	0.167734	−	0.167734i
$663$		0			0
$664$	−5.82948	−	10.0970i	−0.226228	−	0.391838i
$665$	−32.6306	+	13.7837i	−1.26536	+	0.534508i
$666$		0			0
$667$	−12.9188	−	48.2137i	−0.500219	−	1.86684i
$668$	−0.367836	−	1.37278i	−0.0142320	−	0.0531145i
$669$		0			0
$670$	7.42846	+	9.69237i	0.286986	+	0.374449i
$671$	−19.4308	−	11.2184i	−0.750119	−	0.433081i
$672$		0			0
$673$	−12.8090	+	47.8039i	−0.493751	+	1.84270i	0.0431629	+	0.999068i	$0.486257\pi$
$673$	−12.8090	+	47.8039i	−0.493751	+	1.84270i	−0.536914	+	0.843637i	$0.680410\pi$
$674$	−10.8294	−	6.25233i	−0.417131	−	0.240831i
$675$		0			0
$676$	6.64796	+	11.5146i	0.255691	+	0.442869i
$677$	−26.4976	−	26.4976i	−1.01839	−	1.01839i	−0.999828	−	0.0185585i	$-0.994092\pi$
$677$	−26.4976	−	26.4976i	−1.01839	−	1.01839i	−0.0185585	−	0.999828i	$-0.505908\pi$
$678$		0			0
$679$	−0.408066	+	0.00308066i	−0.0156601	+	0.000118225i
$680$	2.61310	−	6.29845i	0.100208	−	0.241535i
$681$		0			0
$682$	12.8814	−	3.45155i	0.493253	−	0.132167i
$683$	6.76683	−	25.2542i	0.258926	−	0.966324i	−0.706939	−	0.707275i	$-0.749924\pi$
$683$	6.76683	−	25.2542i	0.258926	−	0.966324i	0.965864	−	0.259049i	$-0.0834090\pi$
$684$		0			0
$685$	−23.9900	−	18.4299i	−0.916612	−	0.704170i
$686$	18.0895	−	0.409759i	0.690661	−	0.0156447i
$687$		0			0
$688$	−1.62065	+	6.04836i	−0.0617868	+	0.230592i
$689$	0.743438			0.0283227
$690$		0			0
$691$			21.1336i			0.803961i	0.915648	+	0.401980i	$0.131678\pi$
$691$			21.1336i			0.803961i	−0.915648	+	0.401980i	$0.868322\pi$
$692$	−1.51606	−	1.51606i	−0.0576318	−	0.0576318i
$693$		0			0
$694$		−	13.0916i		−	0.496952i
$695$	3.74454	+	28.5682i	0.142038	+	1.08365i
$696$		0			0
$697$	5.13666	−	5.13666i	0.194565	−	0.194565i
$698$	29.1320	+	7.80591i	1.10266	+	0.295458i
$699$		0			0
$700$	−0.0886688	−	13.8302i	−0.00335137	−	0.522732i
$701$	−17.0822			−0.645186			−0.322593	−	0.946538i	$-0.604554\pi$
$701$	−17.0822			−0.645186			−0.322593	+	0.946538i	$0.604554\pi$
$702$		0			0
$703$	−32.9160	−	8.81983i	−1.24145	−	0.332646i
$704$	−9.43107	−	5.44503i	−0.355447	−	0.205217i
$705$		0			0
$706$	13.9072	+	8.02934i	0.523405	+	0.302188i
$707$	−5.41880	+	20.8516i	−0.203795	+	0.784207i
$708$		0			0
$709$		−	43.7377i		−	1.64260i	−0.570494	−	0.821302i	$-0.693248\pi$
$709$		−	43.7377i		−	1.64260i	0.570494	−	0.821302i	$-0.306752\pi$
$710$	−1.82069	+	13.7689i	−0.0683292	+	0.516739i
$711$		0			0
$712$	51.9995	−	13.9332i	1.94877	−	0.522170i
$713$	59.9175	+	16.0548i	2.24393	+	0.601259i
$714$		0			0
$715$	−1.79406	+	0.741928i	−0.0670940	+	0.0277465i
$716$	−8.81441	−	15.2670i	−0.329410	−	0.570555i
$717$		0			0
$718$	−1.53086	+	0.410194i	−0.0571313	+	0.0153083i
$719$	9.10099	−	15.7634i	0.339410	−	0.587875i	−0.644912	−	0.764257i	$-0.723106\pi$
$719$	9.10099	−	15.7634i	0.339410	−	0.587875i	0.984322	+	0.176382i	$0.0564394\pi$
$720$		0			0
$721$	−0.205105	−	27.1683i	−0.00763851	−	1.01180i
$722$	−15.9013	−	4.26073i	−0.591784	−	0.158568i
$723$		0			0
$724$	−21.2942			−0.791392
$725$	8.66489	+	32.4857i	0.321806	+	1.20649i
$726$		0			0
$727$	−12.6674	+	47.2752i	−0.469806	+	1.75334i	0.170635	+	0.985334i	$0.445418\pi$
$727$	−12.6674	+	47.2752i	−0.469806	+	1.75334i	−0.640441	+	0.768007i	$0.721248\pi$
$728$	−4.04988	−	1.05246i	−0.150099	−	0.0390067i
$729$		0			0
$730$	−5.26308	+	12.6858i	−0.194795	+	0.469521i
$731$	−6.81126	−	3.93249i	−0.251924	−	0.145448i
$732$		0			0
$733$	19.2445	+	5.15655i	0.710812	+	0.190461i	0.596068	−	0.802934i	$-0.296729\pi$
$733$	19.2445	+	5.15655i	0.710812	+	0.190461i	0.114744	+	0.993395i	$0.463395\pi$
$734$	1.18391	−	2.05060i	0.0436991	−	0.0756890i
$735$		0			0
$736$	−19.1277	−	33.1302i	−0.705057	−	1.22119i
$737$	2.36315	+	8.81940i	0.0870478	+	0.324867i
$738$		0			0
$739$	−41.8852	+	24.1825i	−1.54077	+	0.889566i	−0.541984	+	0.840389i	$0.682327\pi$
$739$	−41.8852	+	24.1825i	−1.54077	+	0.889566i	−0.998790	+	0.0491770i	$0.984340\pi$
$740$	8.10572	−	10.5511i	0.297972	−	0.387868i
$741$		0			0
$742$	2.53706	−	2.57566i	0.0931383	−	0.0945553i
$743$	31.7951	−	8.51948i	1.16645	−	0.312549i	0.376911	−	0.926250i	$-0.376986\pi$
$743$	31.7951	−	8.51948i	1.16645	−	0.312549i	0.789539	+	0.613700i	$0.210320\pi$
$744$		0			0
$745$	3.13889	−	7.56576i	0.115000	−	0.277188i
$746$	15.6246	+	27.0626i	0.572057	+	0.990832i
$747$		0			0
$748$	1.23762	−	1.23762i	0.0452520	−	0.0452520i
$749$	2.90251	−	1.70511i	0.106055	−	0.0623034i
$750$		0			0
$751$	6.76017	+	11.7090i	0.246682	+	0.427266i	0.962603	−	0.270915i	$-0.0873263\pi$
$751$	6.76017	+	11.7090i	0.246682	+	0.427266i	−0.715921	+	0.698181i	$0.753993\pi$
$752$	−1.13958	−	1.13958i	−0.0415561	−	0.0415561i
$753$		0			0
$754$	3.49200			0.127171
$755$	−0.580424	−	4.42823i	−0.0211238	−	0.161160i
$756$		0			0
$757$	28.4104	−	28.4104i	1.03260	−	1.03260i	0.0331447	−	0.999451i	$-0.489448\pi$
$757$	28.4104	−	28.4104i	1.03260	−	1.03260i	0.999451	−	0.0331447i	$-0.0105522\pi$
$758$	−21.3937	−	21.3937i	−0.777055	−	0.777055i
$759$		0			0
$760$	24.2687	−	31.5903i	0.880317	−	1.14590i
$761$	−13.6962	+	7.90749i	−0.496486	+	0.286646i	−0.727261	−	0.686361i	$-0.759207\pi$
$761$	−13.6962	+	7.90749i	−0.496486	+	0.286646i	0.230775	+	0.973007i	$0.425874\pi$
$762$		0			0
$763$	−21.8514	−	21.5239i	−0.791072	−	0.779218i
$764$		−	18.0179i		−	0.651866i
$765$		0			0
$766$	−15.9311	+	9.19781i	−0.575613	+	0.332330i
$767$	−0.152048	−	0.567451i	−0.00549014	−	0.0204895i
$768$		0			0
$769$	−10.7002	+	18.5333i	−0.385860	+	0.668328i	−0.991888	−	0.127115i	$-0.959428\pi$
$769$	−10.7002	+	18.5333i	−0.385860	+	0.668328i	0.606028	+	0.795443i	$0.292762\pi$
$770$	−3.55199	+	8.74746i	−0.128005	+	0.315237i
$771$		0			0
$772$	−7.99662	+	7.99662i	−0.287805	+	0.287805i
$773$	−8.90050	−	2.38488i	−0.320129	−	0.0857782i	0.0951763	−	0.995460i	$-0.469659\pi$
$773$	−8.90050	−	2.38488i	−0.320129	−	0.0857782i	−0.415305	+	0.909682i	$0.636325\pi$
$774$		0			0
$775$	−40.3469	−	10.8602i	−1.44930	−	0.390108i
$776$	0.397440	−	0.229462i	0.0142673	−	0.00823722i
$777$		0			0
$778$	−22.3540	+	5.98973i	−0.801430	+	0.214742i
$779$	36.7521	−	21.2188i	1.31678	−	0.760243i
$780$		0			0
$781$	−5.19226	+	8.99325i	−0.185794	+	0.321804i
$782$	−7.17966	+	1.92378i	−0.256744	+	0.0687944i
$783$		0			0
$784$	−4.90300	+	2.93033i	−0.175107	+	0.104654i
$785$	18.7281	+	2.47645i	0.668436	+	0.0883882i
$786$		0			0
$787$	36.7451	+	36.7451i	1.30982	+	1.30982i	0.921541	+	0.388282i	$0.126931\pi$
$787$	36.7451	+	36.7451i	1.30982	+	1.30982i	0.388282	+	0.921541i	$0.373069\pi$
$788$	−4.87763	−	4.87763i	−0.173758	−	0.173758i
$789$		0			0
$790$	14.5917	+	1.92948i	0.519150	+	0.0686480i
$791$	−27.8877	−	47.4716i	−0.991571	−	1.68789i
$792$		0			0
$793$	7.05250	−	1.88971i	0.250442	−	0.0671056i
$794$	−11.7409	+	20.3358i	−0.416668	+	0.721691i
$795$		0			0
$796$	4.67771	−	2.70068i	0.165797	−	0.0957230i
$797$	4.61563	−	1.23676i	0.163494	−	0.0438081i	−0.176143	−	0.984365i	$-0.556362\pi$
$797$	4.61563	−	1.23676i	0.163494	−	0.0438081i	0.339638	+	0.940556i	$0.389696\pi$
$798$		0			0
$799$	1.75304	−	1.01212i	0.0620182	−	0.0358062i
$800$	12.8586	+	22.3305i	0.454621	+	0.789501i
$801$		0			0
$802$	32.2883	+	8.65162i	1.14014	+	0.305499i
$803$	−7.26124	+	7.26124i	−0.256243	+	0.256243i
$804$		0			0
$805$	−34.6528	+	26.9764i	−1.22135	+	0.950794i
$806$	−2.16984	+	3.75827i	−0.0764292	+	0.132379i
$807$		0			0
$808$	−6.27085	−	23.4031i	−0.220608	−	0.823319i
$809$	−16.7030	+	9.64348i	−0.587246	+	0.339047i	−0.764008	−	0.645207i	$-0.776771\pi$
$809$	−16.7030	+	9.64348i	−0.587246	+	0.339047i	0.176762	+	0.984254i	$0.443438\pi$
$810$		0			0
$811$			7.57899i			0.266134i	0.991107	+	0.133067i	$0.0424826\pi$
$811$			7.57899i			0.266134i	−0.991107	+	0.133067i	$0.957517\pi$
$812$	−13.0525	+	13.2511i	−0.458054	+	0.465022i
$813$		0			0
$814$	−7.86574	+	4.54129i	−0.275694	+	0.159172i
$815$	3.02067	−	3.93198i	0.105810	−	0.137731i
$816$		0			0
$817$	−32.4891	−	32.4891i	−1.13665	−	1.13665i
$818$	0.0628861	−	0.0628861i	0.00219876	−	0.00219876i
$819$		0			0
$820$	2.15341	+	16.4290i	0.0752003	+	0.573726i
$821$	−22.8142			−0.796220			−0.398110	−	0.917338i	$-0.630334\pi$
$821$	−22.8142			−0.796220			−0.398110	+	0.917338i	$0.630334\pi$
$822$		0			0
$823$	5.27512	+	5.27512i	0.183879	+	0.183879i	0.793044	−	0.609165i	$-0.208495\pi$
$823$	5.27512	+	5.27512i	0.183879	+	0.183879i	−0.609165	+	0.793044i	$0.708495\pi$
$824$	15.2772	+	26.4609i	0.532206	+	0.921808i
$825$		0			0
$826$	−2.48483	−	1.40971i	−0.0864581	−	0.0490501i
$827$	21.2830	−	21.2830i	0.740083	−	0.740083i	−0.232511	−	0.972594i	$-0.574694\pi$
$827$	21.2830	−	21.2830i	0.740083	−	0.740083i	0.972594	+	0.232511i	$0.0746942\pi$
$828$		0			0
$829$	4.24336	+	7.34971i	0.147378	+	0.255266i	0.930258	−	0.366907i	$-0.119583\pi$
$829$	4.24336	+	7.34971i	0.147378	+	0.255266i	−0.782880	+	0.622173i	$0.786250\pi$
$830$	3.28038	−	7.90681i	0.113864	−	0.274449i
$831$		0			0
$832$	3.42304	−	0.917202i	0.118673	−	0.0317983i
$833$	−1.96129	−	6.90112i	−0.0679547	−	0.239110i
$834$		0			0
$835$	1.85180	−	2.41047i	0.0640841	−	0.0834177i
$836$	8.85503	−	5.11246i	0.306258	−	0.176818i
$837$		0			0
$838$	−6.93939	−	25.8982i	−0.239717	−	0.894637i
$839$	−0.839410	−	1.45390i	−0.0289797	−	0.0501942i	0.851172	−	0.524887i	$-0.175892\pi$
$839$	−0.839410	−	1.45390i	−0.0289797	−	0.0501942i	−0.880152	+	0.474693i	$0.842559\pi$
$840$		0			0
$841$	8.10798	−	14.0434i	0.279586	−	0.484256i
$842$	−11.2172	−	3.00564i	−0.386571	−	0.103581i
$843$		0			0
$844$	0.494971	+	0.285772i	0.0170376	+	0.00983667i
$845$	−10.8974	+	26.2663i	−0.374881	+	0.903587i
$846$		0			0
$847$	15.4695	−	15.7049i	0.531539	−	0.539625i
$848$	−0.295386	+	1.10240i	−0.0101436	+	0.0378564i
$849$		0			0
$850$	4.83755	−	1.29032i	0.165927	−	0.0442575i
$851$	−42.2475			−1.44822
$852$		0			0
$853$	41.0407	+	10.9968i	1.40521	+	0.376524i	0.880212	−	0.474581i	$-0.157401\pi$
$853$	41.0407	+	10.9968i	1.40521	+	0.376524i	0.524995	+	0.851105i	$0.324067\pi$
$854$	17.5204	−	30.8824i	0.599537	−	1.05677i
$855$		0			0
$856$	−1.89287	+	3.27855i	−0.0646971	+	0.112059i
$857$	49.8017	−	13.3443i	1.70119	−	0.455833i	0.727953	−	0.685627i	$-0.240472\pi$
$857$	49.8017	−	13.3443i	1.70119	−	0.455833i	0.973239	+	0.229794i	$0.0738051\pi$
$858$		0			0
$859$	−9.69220	−	16.7874i	−0.330694	−	0.572778i	0.651954	−	0.758258i	$-0.273949\pi$
$859$	−9.69220	−	16.7874i	−0.330694	−	0.572778i	−0.982648	+	0.185480i	$0.940616\pi$
$860$	16.5779	−	6.85574i	0.565302	−	0.233779i
$861$		0			0
$862$	20.9919	+	5.62476i	0.714986	+	0.191580i
$863$	−0.409122	+	0.109624i	−0.0139267	+	0.00373165i	−0.265776	−	0.964035i	$-0.585628\pi$
$863$	−0.409122	+	0.109624i	−0.0139267	+	0.00373165i	0.251849	+	0.967767i	$0.418961\pi$
$864$		0			0
$865$	0.601130	−	4.54604i	0.0204390	−	0.154570i
$866$			7.23577i			0.245881i
$867$		0			0
$868$	−6.15102	−	22.2817i	−0.208779	−	0.756290i
$869$	9.53065	+	5.50253i	0.323305	+	0.186660i
$870$		0			0
$871$	−2.57315	−	1.48561i	−0.0871877	−	0.0503379i
$872$	33.3182	+	8.92760i	1.12830	+	0.302327i
$873$		0			0
$874$	−43.4226			−1.46879
$875$	23.3621	−	18.1442i	0.789783	−	0.613386i
$876$		0			0
$877$	−37.7802	−	10.1232i	−1.27575	−	0.341836i	−0.443518	−	0.896266i	$-0.646270\pi$
$877$	−37.7802	−	10.1232i	−1.27575	−	0.341836i	−0.832230	+	0.554430i	$0.812936\pi$
$878$	−13.5060	+	13.5060i	−0.455804	+	0.455804i
$879$		0			0
$880$	−0.387333	−	2.95508i	−0.0130570	−	0.0996157i
$881$			34.8974i			1.17572i	0.808961	+	0.587862i	$0.200030\pi$
$881$			34.8974i			1.17572i	−0.808961	+	0.587862i	$0.799970\pi$
$882$		0			0
$883$	−38.1289	−	38.1289i	−1.28314	−	1.28314i	−0.938872	−	0.344268i	$-0.888127\pi$
$883$	−38.1289	−	38.1289i	−1.28314	−	1.28314i	−0.344268	−	0.938872i	$-0.611873\pi$
$884$			0.569564i			0.0191565i
$885$		0			0
$886$	36.6179			1.23020
$887$	12.2126	−	45.5781i	0.410060	−	1.53036i	−0.384469	−	0.923138i	$-0.625616\pi$
$887$	12.2126	−	45.5781i	0.410060	−	1.53036i	0.794529	−	0.607226i	$-0.207718\pi$
$888$		0			0
$889$	6.05524	+	3.43531i	0.203086	+	0.115217i
$890$	31.3445	+	24.0798i	1.05067	+	0.807157i
$891$		0			0
$892$	7.17267	−	26.7688i	0.240159	−	0.896285i
$893$	11.4225	−	3.06065i	0.382240	−	0.102421i
$894$		0			0
$895$	14.4486	−	34.8260i	0.482964	−	1.16410i
$896$	−4.95269	+	8.72986i	−0.165458	+	0.291644i
$897$		0			0
$898$	−12.8636	−	12.8636i	−0.429265	−	0.429265i
$899$	28.0960	+	48.6638i	0.937055	+	1.62303i
$900$		0			0
$901$	−1.24144	−	0.716748i	−0.0413585	−	0.0238783i
$902$	2.92747	−	10.9255i	0.0974742	−	0.363779i
$903$		0			0
$904$	53.6218	+	30.9586i	1.78344	+	1.02967i
$905$	−27.7047	−	36.1480i	−0.920935	−	1.20160i
$906$		0			0
$907$	6.49758	+	24.2493i	0.215749	+	0.805185i	0.985902	+	0.167326i	$0.0535131\pi$
$907$	6.49758	+	24.2493i	0.215749	+	0.805185i	−0.770153	+	0.637859i	$0.779820\pi$
$908$	4.60461	+	17.1846i	0.152809	+	0.570293i
$909$		0			0
$910$	−1.19550	−	2.83015i	−0.0396304	−	0.0938185i
$911$	−18.7147	−	32.4148i	−0.620045	−	1.07395i	−0.989477	−	0.144692i	$-0.953781\pi$
$911$	−18.7147	−	32.4148i	−0.620045	−	1.07395i	0.369431	−	0.929258i	$-0.379552\pi$
$912$		0			0
$913$	4.52580	−	4.52580i	0.149782	−	0.149782i
$914$			28.5162i			0.943233i
$915$		0			0
$916$	12.6680	−	7.31387i	0.418562	−	0.241657i
$917$	3.97246	+	3.91293i	0.131182	+	0.129216i
$918$		0			0
$919$	31.8867	+	18.4098i	1.05184	+	0.607283i	0.923165	−	0.384403i	$-0.125593\pi$
$919$	31.8867	+	18.4098i	1.05184	+	0.607283i	0.128680	+	0.991686i	$0.458926\pi$
$920$	18.9256	−	45.6170i	0.623958	−	1.50395i
$921$		0			0
$922$	−3.86110	+	14.4098i	−0.127159	+	0.474562i
$923$	−0.874623	−	3.26414i	−0.0287886	−	0.107440i
$924$		0			0
$925$	28.4570	+	0.0323876i	0.935662	+	0.00106490i
$926$	20.2211	−	35.0240i	0.664507	−	1.15096i
$927$		0			0
$928$	8.96921	−	33.4736i	0.294429	−	1.09882i
$929$	−10.8700			−0.356635			−0.178317	−	0.983973i	$-0.557065\pi$
$929$	−10.8700			−0.356635			−0.178317	+	0.983973i	$0.557065\pi$
$930$		0			0
$931$	−0.632793	−	41.9076i	−0.0207389	−	1.37346i
$932$	−3.33164	−	12.4339i	−0.109132	−	0.407284i
$933$		0			0
$934$	−8.83292	+	15.2991i	−0.289022	+	0.500600i
$935$	3.71114	+	0.490729i	0.121367	+	0.0160486i
$936$		0			0
$937$	22.9760	+	22.9760i	0.750592	+	0.750592i	0.974590	−	0.223998i	$-0.0719108\pi$
$937$	22.9760	+	22.9760i	0.750592	+	0.750592i	−0.223998	+	0.974590i	$0.571911\pi$
$938$	−13.9280	+	3.84493i	−0.454766	+	0.125541i
$939$		0			0
$940$	−0.605268	+	4.57734i	−0.0197417	+	0.149296i
$941$			36.3208i			1.18402i	0.805929	+	0.592012i	$0.201666\pi$
$941$			36.3208i			1.18402i	−0.805929	+	0.592012i	$0.798334\pi$
$942$		0			0
$943$	37.2026	−	37.2026i	1.21148	−	1.21148i
$944$	0.901848			0.0293527
$945$		0			0
$946$	−12.2461			−0.398155
$947$	8.17811	−	8.17811i	0.265753	−	0.265753i	−0.561633	−	0.827386i	$-0.689827\pi$
$947$	8.17811	−	8.17811i	0.265753	−	0.265753i	0.827386	+	0.561633i	$0.189827\pi$
$948$		0			0
$949$		−	3.34167i		−	0.108475i
$950$	29.2486	+	0.0332885i	0.948950	+	0.00108002i
$951$		0			0
$952$	5.74810	+	5.66196i	0.186297	+	0.183505i
$953$	−39.2129	−	39.2129i	−1.27023	−	1.27023i	−0.945967	−	0.324263i	$-0.894884\pi$
$953$	−39.2129	−	39.2129i	−1.27023	−	1.27023i	−0.324263	−	0.945967i	$-0.605116\pi$
$954$		0			0
$955$	30.5864	−	23.4421i	0.989753	−	0.758570i
$956$	−3.96794	+	6.87267i	−0.128332	+	0.222278i
$957$		0			0
$958$	2.06120	+	7.69249i	0.0665942	+	0.248533i
$959$	30.8631	−	18.1308i	0.996621	−	0.585475i
$960$		0			0
$961$	−38.8326			−1.25267
$962$	0.764969	−	2.85490i	0.0246636	−	0.0920458i
$963$		0			0
$964$	−3.15001	+	5.45598i	−0.101455	+	0.175725i
$965$	−23.9786	−	3.17073i	−0.771900	−	0.102069i
$966$		0			0
$967$	−0.320359	−	1.19560i	−0.0103021	−	0.0384478i	0.960583	−	0.277992i	$-0.0896688\pi$
$967$	−0.320359	−	1.19560i	−0.0103021	−	0.0384478i	−0.970886	+	0.239544i	$0.923002\pi$
$968$	−6.41638	+	23.9463i	−0.206230	+	0.769662i
$969$		0			0
$970$	0.311231	+	0.129124i	0.00999302	+	0.00414591i
$971$	36.8435	+	21.2716i	1.18237	+	0.682639i	0.956561	−	0.291533i	$-0.0941654\pi$
$971$	36.8435	+	21.2716i	1.18237	+	0.682639i	0.225805	+	0.974173i	$0.427499\pi$
$972$		0			0
$973$	−32.9955	−	8.57468i	−1.05779	−	0.274892i
$974$	3.44318	−	1.98792i	0.110327	−	0.0636971i
$975$		0			0
$976$			11.2085i			0.358776i
$977$	5.18957	−	5.18957i	0.166029	−	0.166029i	−0.619202	−	0.785231i	$-0.712544\pi$
$977$	5.18957	−	5.18957i	0.166029	−	0.166029i	0.785231	+	0.619202i	$0.212544\pi$
$978$		0			0
$979$	14.7766	+	25.5939i	0.472264	+	0.817985i
$980$	15.2082	+	6.04208i	0.485807	+	0.193007i
$981$		0			0
$982$	7.14274	+	26.6571i	0.227934	+	0.850661i
$983$	−7.81104	−	29.1512i	−0.249133	−	0.929778i	−0.971261	−	0.238018i	$-0.923502\pi$
$983$	−7.81104	−	29.1512i	−0.249133	−	0.929778i	0.722127	−	0.691760i	$-0.243164\pi$
$984$		0			0
$985$	1.93402	−	14.6261i	0.0616231	−	0.466025i
$986$	−5.83117	−	3.36663i	−0.185702	−	0.107215i
$987$		0			0
$988$	−0.861181	+	3.21397i	−0.0273978	+	0.102250i
$989$	−49.3310	−	28.4813i	−1.56864	−	0.905652i
$990$		0			0
$991$	−25.4329	−	44.0511i	−0.807903	−	1.39933i	−0.914314	−	0.405007i	$-0.867269\pi$
$991$	−25.4329	−	44.0511i	−0.807903	−	1.39933i	0.106411	−	0.994322i	$-0.466064\pi$
$992$	30.4527	+	30.4527i	0.966875	+	0.966875i
$993$		0			0
$994$	−14.2934	−	8.10905i	−0.453359	−	0.257203i
$995$	10.6705	+	4.42696i	0.338276	+	0.140344i
$996$		0			0
$997$	−6.06203	+	1.62432i	−0.191986	+	0.0514426i	−0.353531	−	0.935423i	$-0.615019\pi$
$997$	−6.06203	+	1.62432i	−0.191986	+	0.0514426i	0.161545	+	0.986865i	$0.448352\pi$
$998$	6.26292	−	23.3735i	0.198249	−	0.739876i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bv.e.523.28		160
3.2	odd	2		315.2.bs.e.103.13	yes	160
5.2	odd	4	inner	945.2.bv.e.712.28		160
7.3	odd	6		945.2.cj.e.388.28		160
9.2	odd	6		315.2.cg.e.313.28	yes	160
9.7	even	3		945.2.cj.e.208.13		160
15.2	even	4		315.2.bs.e.292.13	yes	160
21.17	even	6		315.2.cg.e.283.13	yes	160
35.17	even	12		945.2.cj.e.577.13		160
45.2	even	12		315.2.cg.e.187.13	yes	160
45.7	odd	12		945.2.cj.e.397.28		160
63.38	even	6		315.2.bs.e.178.13	yes	160
63.52	odd	6	inner	945.2.bv.e.73.28		160
105.17	odd	12		315.2.cg.e.157.28	yes	160
315.52	even	12	inner	945.2.bv.e.262.28		160
315.227	odd	12		315.2.bs.e.52.13	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.13	✓	160	315.227	odd	12
315.2.bs.e.103.13	yes	160	3.2	odd	2
315.2.bs.e.178.13	yes	160	63.38	even	6
315.2.bs.e.292.13	yes	160	15.2	even	4
315.2.cg.e.157.28	yes	160	105.17	odd	12
315.2.cg.e.187.13	yes	160	45.2	even	12
315.2.cg.e.283.13	yes	160	21.17	even	6
315.2.cg.e.313.28	yes	160	9.2	odd	6
945.2.bv.e.73.28		160	63.52	odd	6	inner
945.2.bv.e.262.28		160	315.52	even	12	inner
945.2.bv.e.523.28		160	1.1	even	1	trivial
945.2.bv.e.712.28		160	5.2	odd	4	inner
945.2.cj.e.208.13		160	9.7	even	3
945.2.cj.e.388.28		160	7.3	odd	6
945.2.cj.e.397.28		160	45.7	odd	12
945.2.cj.e.577.13		160	35.17	even	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bv (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.690838 - 0.690838i) q^{2} +1.04549i q^{4} +(-1.77477 + 1.36022i) q^{5} +(-0.704044 - 2.55036i) q^{7} +(2.10394 + 2.10394i) q^{8} +O(q^{10})\)	\(q+(0.690838 - 0.690838i) q^{2} +1.04549i q^{4} +(-1.77477 + 1.36022i) q^{5} +(-0.704044 - 2.55036i) q^{7} +(2.10394 + 2.10394i) q^{8} +(-0.286383 + 2.16577i) q^{10} +(-0.816710 + 1.41458i) q^{11} +(-0.137573 - 0.513429i) q^{13} +(-2.24826 - 1.27550i) q^{14} +0.815990 q^{16} +(-0.265268 + 0.989992i) q^{17} +(-2.99374 + 5.18531i) q^{19} +(-1.42209 - 1.85549i) q^{20} +(0.413034 + 1.54146i) q^{22} +(-1.92122 + 7.17009i) q^{23} +(1.29959 - 4.82815i) q^{25} +(-0.449737 - 0.259656i) q^{26} +(2.66636 - 0.736068i) q^{28} +(-5.82340 + 3.36214i) q^{29} -8.35659i q^{31} +(-3.64416 + 3.64416i) q^{32} +(0.500668 + 0.867182i) q^{34} +(4.71857 + 3.56863i) q^{35} +(1.47305 + 5.49748i) q^{37} +(1.51402 + 5.65040i) q^{38} +(-6.59582 - 0.872175i) q^{40} +(-6.13816 - 3.54387i) q^{41} +(-1.98612 + 7.41230i) q^{43} +(-1.47893 - 0.853858i) q^{44} +(3.62612 + 6.28062i) q^{46} +(-1.39656 - 1.39656i) q^{47} +(-6.00864 + 3.59113i) q^{49} +(-2.43767 - 4.23328i) q^{50} +(0.536782 - 0.143830i) q^{52} +(-0.361997 + 1.35099i) q^{53} +(-0.474678 - 3.62146i) q^{55} +(3.88453 - 6.84706i) q^{56} +(-1.70033 + 6.34572i) q^{58} +1.10522 q^{59} +13.7361i q^{61} +(-5.77305 - 5.77305i) q^{62} +6.66703i q^{64} +(0.942537 + 0.724087i) q^{65} +(3.95260 - 3.95260i) q^{67} +(-1.03502 - 0.277333i) q^{68} +(5.72511 - 0.794419i) q^{70} +6.35753 q^{71} +(6.07255 + 1.62714i) q^{73} +(4.81551 + 2.78023i) q^{74} +(-5.42116 - 3.12991i) q^{76} +(4.18269 + 1.08697i) q^{77} -6.73743i q^{79} +(-1.44819 + 1.10993i) q^{80} +(-6.68871 + 1.79224i) q^{82} +(-3.78491 - 1.01416i) q^{83} +(-0.875822 - 2.11783i) q^{85} +(3.74861 + 6.49278i) q^{86} +(-4.69450 + 1.25789i) q^{88} +(9.04644 - 15.6689i) q^{89} +(-1.21257 + 0.712336i) q^{91} +(-7.49622 - 2.00861i) q^{92} -1.92959 q^{94} +(-1.73998 - 13.2749i) q^{95} +(0.0399199 - 0.148983i) q^{97} +(-1.67011 + 6.63189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more