LMFDB - Embedded newform 944.2.m.c.417.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [944,2,Mod(17,944)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(944, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 0, 40]))

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

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

chi := DirichletCharacter("944.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 944 = 2^{4} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	944.m (of order $29$, degree $28$, 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:	$7.53787795081$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$4$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 59)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			417.1
Character	$\chi$	$=$	944.417
Dual form			944.2.m.c.369.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.865386 + 1.01881i) q^{3} +(0.331060 + 0.251665i) q^{5} +(0.928345 - 2.32997i) q^{7} +(0.196262 + 1.19715i) q^{9} +O(q^{10})$	\(q+(-0.865386 + 1.01881i) q^{3} +(0.331060 + 0.251665i) q^{5} +(0.928345 - 2.32997i) q^{7} +(0.196262 + 1.19715i) q^{9} +(0.551218 - 0.255021i) q^{11} +(0.568579 - 3.46818i) q^{13} +(-0.542894 + 0.119500i) q^{15} +(-0.0439170 - 0.110223i) q^{17} +(3.52708 + 5.20206i) q^{19} +(1.57042 + 2.96213i) q^{21} +(0.233431 - 4.30537i) q^{23} +(-1.29138 - 4.65112i) q^{25} +(-4.82569 - 2.90352i) q^{27} +(7.91458 - 0.860763i) q^{29} +(1.03526 - 1.52689i) q^{31} +(-0.217199 + 0.782279i) q^{33} +(0.893711 - 0.537728i) q^{35} +(2.60938 - 0.879204i) q^{37} +(3.04138 + 3.58059i) q^{39} +(0.288828 + 5.32712i) q^{41} +(9.32450 + 4.31397i) q^{43} +(-0.236306 + 0.445720i) q^{45} +(-1.73583 + 1.31954i) q^{47} +(0.515030 + 0.487862i) q^{49} +(0.150302 + 0.0506426i) q^{51} +(-8.32319 + 7.88414i) q^{53} +(0.246666 + 0.0542954i) q^{55} +(-8.35221 - 0.908357i) q^{57} +(7.64516 + 0.742603i) q^{59} +(7.26914 + 0.790567i) q^{61} +(2.97152 + 0.654081i) q^{63} +(1.06105 - 1.00508i) q^{65} +(8.23909 + 2.77607i) q^{67} +(4.18436 + 3.96363i) q^{69} +(7.83962 - 5.95953i) q^{71} +(3.97436 - 7.49644i) q^{73} +(5.85615 + 2.70934i) q^{75} +(-0.0824700 - 1.52107i) q^{77} +(-5.82798 - 6.86122i) q^{79} +(3.68536 - 1.24174i) q^{81} +(-13.0446 + 7.84865i) q^{83} +(0.0132002 - 0.0475429i) q^{85} +(-5.97222 + 8.80836i) q^{87} +(7.04739 - 0.766450i) q^{89} +(-7.55292 - 4.54444i) q^{91} +(0.659715 + 2.37608i) q^{93} +(-0.141501 + 2.60984i) q^{95} +(-0.594592 - 1.12152i) q^{97} +(0.413481 + 0.609839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 23 q^{3} - 25 q^{5} + 23 q^{7} - 21 q^{9}+O(q^{10}) $ 112 * q + 23 * q^3 - 25 * q^5 + 23 * q^7 - 21 * q^9	$ 112 q + 23 q^{3} - 25 q^{5} + 23 q^{7} - 21 q^{9} + 15 q^{11} - 23 q^{13} - 4 q^{15} - 10 q^{17} + 15 q^{19} - 12 q^{21} - 3 q^{23} - 5 q^{25} - 22 q^{27} - 13 q^{29} - 3 q^{31} + 33 q^{33} - 28 q^{35} - 9 q^{37} - 45 q^{39} + 23 q^{41} - 19 q^{43} + 19 q^{45} - 10 q^{47} - 31 q^{49} + 61 q^{51} - 23 q^{53} + 24 q^{55} - 91 q^{57} + 33 q^{59} - 47 q^{61} + 58 q^{63} - 16 q^{65} + 19 q^{67} - 45 q^{69} + 18 q^{71} + 24 q^{73} - 58 q^{75} + 65 q^{77} - 41 q^{79} + 95 q^{81} - 49 q^{83} + 39 q^{85} - 80 q^{87} + 51 q^{89} - 77 q^{91} + 93 q^{93} - 65 q^{95} + 91 q^{97} - 44 q^{99}+O(q^{100}) $ 112 * q + 23 * q^3 - 25 * q^5 + 23 * q^7 - 21 * q^9 + 15 * q^11 - 23 * q^13 - 4 * q^15 - 10 * q^17 + 15 * q^19 - 12 * q^21 - 3 * q^23 - 5 * q^25 - 22 * q^27 - 13 * q^29 - 3 * q^31 + 33 * q^33 - 28 * q^35 - 9 * q^37 - 45 * q^39 + 23 * q^41 - 19 * q^43 + 19 * q^45 - 10 * q^47 - 31 * q^49 + 61 * q^51 - 23 * q^53 + 24 * q^55 - 91 * q^57 + 33 * q^59 - 47 * q^61 + 58 * q^63 - 16 * q^65 + 19 * q^67 - 45 * q^69 + 18 * q^71 + 24 * q^73 - 58 * q^75 + 65 * q^77 - 41 * q^79 + 95 * q^81 - 49 * q^83 + 39 * q^85 - 80 * q^87 + 51 * q^89 - 77 * q^91 + 93 * q^93 - 65 * q^95 + 91 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/944\mathbb{Z}\right)^\times$.

$n$	$591$	$709$	$769$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{29}\right)$

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			0
$2$		0			0
$3$	−0.865386	+	1.01881i	−0.499631	+	0.588211i	−0.952946	−	0.303139i	$-0.901965\pi$
$3$	−0.865386	+	1.01881i	−0.499631	+	0.588211i	0.453315	+	0.891350i	$0.350241\pi$
$4$		0			0
$5$	0.331060	+	0.251665i	0.148055	+	0.112548i	0.676579	−	0.736370i	$-0.263462\pi$
$5$	0.331060	+	0.251665i	0.148055	+	0.112548i	−0.528525	+	0.848918i	$0.677255\pi$
$6$		0			0
$7$	0.928345	−	2.32997i	0.350881	−	0.880646i	−0.642553	−	0.766241i	$-0.722125\pi$
$7$	0.928345	−	2.32997i	0.350881	−	0.880646i	0.993434	−	0.114405i	$-0.0364960\pi$
$8$		0			0
$9$	0.196262	+	1.19715i	0.0654208	+	0.399049i
$10$		0			0
$11$	0.551218	−	0.255021i	0.166199	−	0.0768917i	−0.335026	−	0.942209i	$-0.608745\pi$
$11$	0.551218	−	0.255021i	0.166199	−	0.0768917i	0.501225	+	0.865317i	$0.332883\pi$
$12$		0			0
$13$	0.568579	−	3.46818i	0.157695	−	0.961900i	−0.782845	−	0.622217i	$-0.786232\pi$
$13$	0.568579	−	3.46818i	0.157695	−	0.961900i	0.940540	−	0.339683i	$-0.110320\pi$
$14$		0			0
$15$	−0.542894	+	0.119500i	−0.140175	+	0.0308548i
$16$		0			0
$17$	−0.0439170	−	0.110223i	−0.0106514	−	0.0267331i	0.923555	−	0.383466i	$-0.125270\pi$
$17$	−0.0439170	−	0.110223i	−0.0106514	−	0.0267331i	−0.934206	+	0.356733i	$0.883890\pi$
$18$		0			0
$19$	3.52708	+	5.20206i	0.809168	+	1.19343i	0.978168	+	0.207818i	$0.0666361\pi$
$19$	3.52708	+	5.20206i	0.809168	+	1.19343i	−0.168999	+	0.985616i	$0.554054\pi$
$20$		0			0
$21$	1.57042	+	2.96213i	0.342695	+	0.646391i
$22$		0			0
$23$	0.233431	−	4.30537i	0.0486736	−	0.897732i	−0.867621	−	0.497227i	$-0.834352\pi$
$23$	0.233431	−	4.30537i	0.0486736	−	0.897732i	0.916294	−	0.400506i	$-0.131166\pi$
$24$		0			0
$25$	−1.29138	−	4.65112i	−0.258275	−	0.930223i
$26$		0			0
$27$	−4.82569	−	2.90352i	−0.928705	−	0.558783i
$28$		0			0
$29$	7.91458	−	0.860763i	1.46970	−	0.159840i	0.662032	−	0.749476i	$-0.269694\pi$
$29$	7.91458	−	0.860763i	1.46970	−	0.159840i	0.807669	+	0.589636i	$0.200729\pi$
$30$		0			0
$31$	1.03526	−	1.52689i	0.185937	−	0.274237i	−0.723283	−	0.690551i	$-0.757368\pi$
$31$	1.03526	−	1.52689i	0.185937	−	0.274237i	0.909221	+	0.416314i	$0.136678\pi$
$32$		0			0
$33$	−0.217199	+	0.782279i	−0.0378095	+	0.136177i
$34$		0			0
$35$	0.893711	−	0.537728i	0.151065	−	0.0908926i
$36$		0			0
$37$	2.60938	−	0.879204i	0.428980	−	0.144540i	−0.0965252	−	0.995331i	$-0.530773\pi$
$37$	2.60938	−	0.879204i	0.428980	−	0.144540i	0.525505	+	0.850790i	$0.323876\pi$
$38$		0			0
$39$	3.04138	+	3.58059i	0.487011	+	0.573353i
$40$		0			0
$41$	0.288828	+	5.32712i	0.0451074	+	0.831956i	0.930315	+	0.366761i	$0.119533\pi$
$41$	0.288828	+	5.32712i	0.0451074	+	0.831956i	−0.885208	+	0.465196i	$0.845984\pi$
$42$		0			0
$43$	9.32450	+	4.31397i	1.42197	+	0.657875i	0.971960	−	0.235147i	$-0.0755572\pi$
$43$	9.32450	+	4.31397i	1.42197	+	0.657875i	0.450013	+	0.893022i	$0.351419\pi$
$44$		0			0
$45$	−0.236306	+	0.445720i	−0.0352264	+	0.0664441i
$46$		0			0
$47$	−1.73583	+	1.31954i	−0.253197	+	0.192475i	−0.724072	−	0.689725i	$-0.757732\pi$
$47$	−1.73583	+	1.31954i	−0.253197	+	0.192475i	0.470875	+	0.882200i	$0.343938\pi$
$48$		0			0
$49$	0.515030	+	0.487862i	0.0735757	+	0.0696946i
$50$		0			0
$51$	0.150302	+	0.0506426i	0.0210465	+	0.00709139i
$52$		0			0
$53$	−8.32319	+	7.88414i	−1.14328	+	1.08297i	−0.147699	+	0.989032i	$0.547187\pi$
$53$	−8.32319	+	7.88414i	−1.14328	+	1.08297i	−0.995578	+	0.0939376i	$0.970055\pi$
$54$		0			0
$55$	0.246666	+	0.0542954i	0.0332605	+	0.00732118i
$56$		0			0
$57$	−8.35221	−	0.908357i	−1.10628	−	0.120315i
$58$		0			0
$59$	7.64516	+	0.742603i	0.995316	+	0.0966787i
$59$	7.64516	+	0.742603i	0.995316	+	0.0966787i
$60$		0			0
$61$	7.26914	+	0.790567i	0.930718	+	0.101222i	0.560901	−	0.827883i	$-0.310455\pi$
$61$	7.26914	+	0.790567i	0.930718	+	0.101222i	0.369817	+	0.929105i	$0.379420\pi$
$62$		0			0
$63$	2.97152	+	0.654081i	0.374376	+	0.0824064i
$64$		0			0
$65$	1.06105	−	1.00508i	0.131608	−	0.124665i
$66$		0			0
$67$	8.23909	+	2.77607i	1.00657	+	0.339151i	0.773833	−	0.633390i	$-0.218337\pi$
$67$	8.23909	+	2.77607i	1.00657	+	0.339151i	0.232732	+	0.972541i	$0.425233\pi$
$68$		0			0
$69$	4.18436	+	3.96363i	0.503737	+	0.477165i
$70$		0			0
$71$	7.83962	−	5.95953i	0.930392	−	0.707266i	−0.0259045	−	0.999664i	$-0.508247\pi$
$71$	7.83962	−	5.95953i	0.930392	−	0.707266i	0.956296	+	0.292399i	$0.0944535\pi$
$72$		0			0
$73$	3.97436	−	7.49644i	0.465164	−	0.877392i	−0.534321	−	0.845282i	$-0.679432\pi$
$73$	3.97436	−	7.49644i	0.465164	−	0.877392i	0.999484	−	0.0321101i	$-0.0102227\pi$
$74$		0			0
$75$	5.85615	+	2.70934i	0.676210	+	0.312848i
$76$		0			0
$77$	−0.0824700	−	1.52107i	−0.00939833	−	0.173342i
$78$		0			0
$79$	−5.82798	−	6.86122i	−0.655698	−	0.771948i	0.329353	−	0.944207i	$-0.393169\pi$
$79$	−5.82798	−	6.86122i	−0.655698	−	0.771948i	−0.985052	+	0.172259i	$0.944893\pi$
$80$		0			0
$81$	3.68536	−	1.24174i	0.409484	−	0.137971i
$82$		0			0
$83$	−13.0446	+	7.84865i	−1.43183	+	0.861501i	−0.999197	−	0.0400707i	$-0.987242\pi$
$83$	−13.0446	+	7.84865i	−1.43183	+	0.861501i	−0.432629	+	0.901572i	$0.642414\pi$
$84$		0			0
$85$	0.0132002	−	0.0475429i	0.00143177	−	0.00515676i
$86$		0			0
$87$	−5.97222	+	8.80836i	−0.640289	+	0.944355i
$88$		0			0
$89$	7.04739	−	0.766450i	0.747022	−	0.0812435i	0.273313	−	0.961925i	$-0.411880\pi$
$89$	7.04739	−	0.766450i	0.747022	−	0.0812435i	0.473709	+	0.880682i	$0.342915\pi$
$90$		0			0
$91$	−7.55292	−	4.54444i	−0.791761	−	0.476387i
$92$		0			0
$93$	0.659715	+	2.37608i	0.0684093	+	0.246388i
$94$		0			0
$95$	−0.141501	+	2.60984i	−0.0145177	+	0.267764i
$96$		0			0
$97$	−0.594592	−	1.12152i	−0.0603717	−	0.113873i	0.851490	−	0.524371i	$-0.175700\pi$
$97$	−0.594592	−	1.12152i	−0.0603717	−	0.113873i	−0.911861	+	0.410498i	$0.865355\pi$
$98$		0			0
$99$	0.413481	+	0.609839i	0.0415564	+	0.0612911i
$100$		0			0
$101$	7.25377	+	18.2056i	0.721777	+	1.81152i	0.567270	+	0.823532i	$0.308000\pi$
$101$	7.25377	+	18.2056i	0.721777	+	1.81152i	0.154507	+	0.987992i	$0.450621\pi$
$102$		0			0
$103$	5.29482	−	1.16548i	0.521714	−	0.114838i	0.0536970	−	0.998557i	$-0.482900\pi$
$103$	5.29482	−	1.16548i	0.521714	−	0.114838i	0.468017	+	0.883719i	$0.344968\pi$
$104$		0			0
$105$	−0.225562	+	1.37587i	−0.0220126	+	0.134271i
$106$		0			0
$107$	−5.81159	+	2.68873i	−0.561828	+	0.259929i	−0.680183	−	0.733042i	$-0.738100\pi$
$107$	−5.81159	+	2.68873i	−0.561828	+	0.259929i	0.118356	+	0.992971i	$0.462238\pi$
$108$		0			0
$109$	−0.740993	−	4.51986i	−0.0709743	−	0.432924i	−0.998280	−	0.0586200i	$-0.981330\pi$
$109$	−0.740993	−	4.51986i	−0.0709743	−	0.432924i	0.927306	−	0.374304i	$-0.122118\pi$
$110$		0			0
$111$	−1.36238	+	3.41932i	−0.129312	+	0.324548i
$112$		0			0
$113$	−16.3893	−	12.4588i	−1.54177	−	1.17202i	−0.921966	−	0.387270i	$-0.873418\pi$
$113$	−16.3893	−	12.4588i	−1.54177	−	1.17202i	−0.619806	−	0.784755i	$-0.712789\pi$
$114$		0			0
$115$	1.16079	−	1.36659i	0.108244	−	0.127435i
$116$		0			0
$117$	4.26352			0.394162
$118$		0			0
$119$	−0.297587			−0.0272798
$120$		0			0
$121$	−6.88244	+	8.10264i	−0.625677	+	0.736603i
$122$		0			0
$123$	−5.67728	−	4.31576i	−0.511903	−	0.389139i
$124$		0			0
$125$	1.51262	−	3.79640i	0.135293	−	0.339560i
$126$		0			0
$127$	−0.590797	−	3.60370i	−0.0524248	−	0.319777i	−1.00000		0.000244181i	$-0.999922\pi$
$127$	−0.590797	−	3.60370i	−0.0524248	−	0.319777i	0.947575	−	0.319533i	$-0.103526\pi$
$128$		0			0
$129$	−12.4644	+	5.76666i	−1.09743	+	0.507726i
$130$		0			0
$131$	1.24020	−	7.56491i	0.108357	−	0.660949i	−0.875667	−	0.482915i	$-0.839578\pi$
$131$	1.24020	−	7.56491i	0.108357	−	0.660949i	0.984024	−	0.178034i	$-0.0569737\pi$
$132$		0			0
$133$	15.3950	−	3.38869i	1.33492	−	0.293837i
$134$		0			0
$135$	−0.866878	−	2.17570i	−0.0746090	−	0.187254i
$136$		0			0
$137$	−5.36322	−	7.91016i	−0.458211	−	0.675811i	0.526466	−	0.850196i	$-0.323517\pi$
$137$	−5.36322	−	7.91016i	−0.458211	−	0.675811i	−0.984678	+	0.174385i	$0.944206\pi$
$138$		0			0
$139$	−8.73833	−	16.4822i	−0.741176	−	1.39801i	−0.910947	−	0.412522i	$-0.864648\pi$
$139$	−8.73833	−	16.4822i	−0.741176	−	1.39801i	0.169772	−	0.985483i	$-0.445697\pi$
$140$		0			0
$141$	0.157797	−	2.91040i	0.0132889	−	0.245100i
$142$		0			0
$143$	−0.571047	−	2.05672i	−0.0477533	−	0.171992i
$144$		0			0
$145$	2.83683	+	1.70686i	0.235586	+	0.141747i
$146$		0			0
$147$	−0.942740	+	0.102529i	−0.0777559	+	0.00845646i
$148$		0			0
$149$	9.95866	−	14.6879i	0.815845	−	1.20328i	−0.160494	−	0.987037i	$-0.551309\pi$
$149$	9.95866	−	14.6879i	0.815845	−	1.20328i	0.976339	−	0.216245i	$-0.0693809\pi$
$150$		0			0
$151$	−3.88692	+	13.9994i	−0.316313	+	1.13926i	0.618987	+	0.785401i	$0.287543\pi$
$151$	−3.88692	+	13.9994i	−0.316313	+	1.13926i	−0.935300	+	0.353856i	$0.884870\pi$
$152$		0			0
$153$	0.123334	−	0.0742079i	0.00997100	−	0.00599935i
$154$		0			0
$155$	0.726997	−	0.244954i	0.0583938	−	0.0196752i
$156$		0			0
$157$	−8.58258	−	10.1042i	−0.684965	−	0.806403i	0.304294	−	0.952578i	$-0.401579\pi$
$157$	−8.58258	−	10.1042i	−0.684965	−	0.806403i	−0.989259	+	0.146176i	$0.953304\pi$
$158$		0			0
$159$	−0.829682	−	15.3026i	−0.0657981	−	1.21357i
$160$		0			0
$161$	−9.81469	−	4.54076i	−0.773506	−	0.357862i
$162$		0			0
$163$	2.51531	−	4.74438i	0.197014	−	0.371608i	−0.765247	−	0.643737i	$-0.777383\pi$
$163$	2.51531	−	4.74438i	0.197014	−	0.371608i	0.962261	+	0.272129i	$0.0877278\pi$
$164$		0			0
$165$	−0.268778	+	0.204320i	−0.0209244	+	0.0159063i
$166$		0			0
$167$	3.87366	+	3.66932i	0.299753	+	0.283941i	0.822762	−	0.568386i	$-0.192432\pi$
$167$	3.87366	+	3.66932i	0.299753	+	0.283941i	−0.523009	+	0.852327i	$0.675191\pi$
$168$		0			0
$169$	0.614505	+	0.207051i	0.0472696	+	0.0159270i
$170$		0			0
$171$	−5.53540	+	5.24341i	−0.423303	+	0.400974i
$172$		0			0
$173$	3.19129	+	0.702456i	0.242629	+	0.0534068i	0.334620	−	0.942353i	$-0.391392\pi$
$173$	3.19129	+	0.702456i	0.242629	+	0.0534068i	−0.0919908	+	0.995760i	$0.529323\pi$
$174$		0			0
$175$	−12.0358	−	1.30897i	−0.909822	−	0.0989491i
$176$		0			0
$177$	−7.37259	+	7.14634i	−0.554158	+	0.537152i
$178$		0			0
$179$	0.646032	+	0.0702602i	0.0482867	+	0.00525149i	0.132230	−	0.991219i	$-0.457786\pi$
$179$	0.646032	+	0.0702602i	0.0482867	+	0.00525149i	−0.0839438	+	0.996470i	$0.526752\pi$
$180$		0			0
$181$	−15.3542	−	3.37971i	−1.14127	−	0.251212i	−0.396176	−	0.918174i	$-0.629663\pi$
$181$	−15.3542	−	3.37971i	−1.14127	−	0.251212i	−0.745091	+	0.666962i	$0.767594\pi$
$182$		0			0
$183$	−7.09605	+	6.72174i	−0.524555	+	0.496885i
$184$		0			0
$185$	1.08513	+	0.365622i	0.0797802	+	0.0268811i
$186$		0			0
$187$	−0.0523171	−	0.0495574i	−0.00382581	−	0.00362400i
$188$		0			0
$189$	−11.2450	+	8.54825i	−0.817956	+	0.621794i
$190$		0			0
$191$	−9.16877	+	17.2941i	−0.663429	+	1.25136i	0.292079	+	0.956394i	$0.405653\pi$
$191$	−9.16877	+	17.2941i	−0.663429	+	1.25136i	−0.955508	+	0.294965i	$0.904692\pi$
$192$		0			0
$193$	−15.1968	−	7.03079i	−1.09389	−	0.506087i	−0.211869	−	0.977298i	$-0.567955\pi$
$193$	−15.1968	−	7.03079i	−1.09389	−	0.506087i	−0.882021	+	0.471211i	$0.843817\pi$
$194$		0			0
$195$	0.105769	+	1.95080i	0.00757430	+	0.139700i
$196$		0			0
$197$	6.66937	+	7.85179i	0.475173	+	0.559417i	0.946568	−	0.322506i	$-0.104525\pi$
$197$	6.66937	+	7.85179i	0.475173	+	0.559417i	−0.471395	+	0.881922i	$0.656249\pi$
$198$		0			0
$199$	−11.2078	+	3.77635i	−0.794500	+	0.267698i	−0.687143	−	0.726522i	$-0.741135\pi$
$199$	−11.2078	+	3.77635i	−0.794500	+	0.267698i	−0.107357	+	0.994221i	$0.534239\pi$
$200$		0			0
$201$	−9.95829	+	5.99171i	−0.702404	+	0.422622i
$202$		0			0
$203$	5.34191	−	19.2398i	0.374929	−	1.35037i
$204$		0			0
$205$	−1.24503	+	1.83628i	−0.0869568	+	0.128252i
$206$		0			0
$207$	5.19998	−	0.565532i	0.361424	−	0.0393072i
$208$		0			0
$209$	3.27083	+	1.96799i	0.226248	+	0.136129i
$210$		0			0
$211$	−0.612996	−	2.20781i	−0.0422004	−	0.151992i	0.939448	−	0.342691i	$-0.111338\pi$
$211$	−0.612996	−	2.20781i	−0.0422004	−	0.151992i	−0.981649	+	0.190699i	$0.938925\pi$
$212$		0			0
$213$	−0.712668	+	13.1444i	−0.0488312	+	0.900639i
$214$		0			0
$215$	2.00129	+	3.77484i	0.136487	+	0.257442i
$216$		0			0
$217$	−2.59653	−	3.82960i	−0.176264	−	0.259970i
$218$		0			0
$219$	4.19810	+	10.5364i	0.283681	+	0.711987i
$220$		0			0
$221$	−0.407245	+	0.0896413i	−0.0273942	+	0.00602993i
$222$		0			0
$223$	1.86529	−	11.3778i	0.124909	−	0.761912i	−0.847875	−	0.530197i	$-0.822118\pi$
$223$	1.86529	−	11.3778i	0.124909	−	0.761912i	0.972784	−	0.231715i	$-0.0744337\pi$
$224$		0			0
$225$	5.31463	−	2.45881i	0.354309	−	0.163921i
$226$		0			0
$227$	2.91545	+	17.7835i	0.193506	+	1.18033i	0.887658	+	0.460503i	$0.152331\pi$
$227$	2.91545	+	17.7835i	0.193506	+	1.18033i	−0.694152	+	0.719828i	$0.744221\pi$
$228$		0			0
$229$	0.565931	−	1.42038i	0.0373978	−	0.0938614i	−0.909092	−	0.416596i	$-0.863223\pi$
$229$	0.565931	−	1.42038i	0.0373978	−	0.0938614i	0.946489	+	0.322735i	$0.104602\pi$
$230$		0			0
$231$	1.62105	+	1.23229i	0.106657	+	0.0810789i
$232$		0			0
$233$	−11.0021	+	12.9527i	−0.720773	+	0.848560i	−0.993536	−	0.113521i	$-0.963787\pi$
$233$	−11.0021	+	12.9527i	−0.720773	+	0.848560i	0.272762	+	0.962081i	$0.412063\pi$
$234$		0			0
$235$	−0.906748			−0.0591497
$236$		0			0
$237$	12.0337			0.781676
$238$		0			0
$239$	11.0311	−	12.9869i	0.713545	−	0.840050i	−0.279207	−	0.960231i	$-0.590072\pi$
$239$	11.0311	−	12.9869i	0.713545	−	0.840050i	0.992752	+	0.120181i	$0.0383475\pi$
$240$		0			0
$241$	−17.7671	−	13.5062i	−1.14448	−	0.870010i	−0.151518	−	0.988455i	$-0.548416\pi$
$241$	−17.7671	−	13.5062i	−1.14448	−	0.870010i	−0.992961	+	0.118445i	$0.962209\pi$
$242$		0			0
$243$	4.32953	−	10.8663i	0.277740	−	0.697074i
$244$		0			0
$245$	0.0477278	+	0.291127i	0.00304922	+	0.0185994i
$246$		0			0
$247$	20.0471	−	9.27477i	1.27557	−	0.590140i
$248$		0			0
$249$	3.29229	−	20.0821i	0.208640	−	1.27265i
$250$		0			0
$251$	−17.0154	+	3.74537i	−1.07400	+	0.236405i	−0.716557	−	0.697529i	$-0.754283\pi$
$251$	−17.0154	+	3.74537i	−1.07400	+	0.236405i	−0.357444	+	0.933934i	$0.616352\pi$
$252$		0			0
$253$	−0.969289	−	2.43273i	−0.0609386	−	0.152944i
$254$		0			0
$255$	0.0370140	+	0.0545916i	0.00231791	+	0.00341866i
$256$		0			0
$257$	0.0639778	+	0.120675i	0.00399083	+	0.00752750i	0.885499	−	0.464640i	$-0.153816\pi$
$257$	0.0639778	+	0.120675i	0.00399083	+	0.00752750i	−0.881509	+	0.472168i	$0.843472\pi$
$258$		0			0
$259$	0.373890	−	6.89599i	0.0232324	−	0.428496i
$260$		0			0
$261$	2.58380	+	9.30599i	0.159933	+	0.576026i
$262$		0			0
$263$	−4.42645	−	2.66330i	−0.272946	−	0.164226i	0.372500	−	0.928032i	$-0.378501\pi$
$263$	−4.42645	−	2.66330i	−0.272946	−	0.164226i	−0.645446	+	0.763806i	$0.723328\pi$
$264$		0			0
$265$	−4.73964	+	0.515467i	−0.291154	+	0.0316649i
$266$		0			0
$267$	−5.31785	+	7.84324i	−0.325447	+	0.479998i
$268$		0			0
$269$	−6.13774	+	22.1062i	−0.374225	+	1.34784i	0.501555	+	0.865126i	$0.332761\pi$
$269$	−6.13774	+	22.1062i	−0.374225	+	1.34784i	−0.875780	+	0.482710i	$0.839652\pi$
$270$		0			0
$271$	−15.5343	+	9.34666i	−0.943639	+	0.567769i	−0.902175	−	0.431371i	$-0.858030\pi$
$271$	−15.5343	+	9.34666i	−0.943639	+	0.567769i	−0.0414646	+	0.999140i	$0.513202\pi$
$272$		0			0
$273$	11.1661	−	3.76230i	0.675804	−	0.227705i
$274$		0			0
$275$	−1.89796	−	2.23445i	−0.114451	−	0.134743i
$276$		0			0
$277$	−0.612755	−	11.3016i	−0.0368169	−	0.679048i	−0.957447	−	0.288611i	$-0.906807\pi$
$277$	−0.612755	−	11.3016i	−0.0368169	−	0.679048i	0.920630	−	0.390437i	$-0.127676\pi$
$278$		0			0
$279$	2.03109	+	0.939684i	0.121598	+	0.0562574i
$280$		0			0
$281$	−6.97268	+	13.1519i	−0.415955	+	0.784575i	−0.999624	−	0.0274168i	$-0.991272\pi$
$281$	−6.97268	+	13.1519i	−0.415955	+	0.784575i	0.583669	+	0.811992i	$0.301617\pi$
$282$		0			0
$283$	−17.6479	+	13.4156i	−1.04906	+	0.797475i	−0.979771	−	0.200122i	$-0.935866\pi$
$283$	−17.6479	+	13.4156i	−1.04906	+	0.797475i	−0.0692893	+	0.997597i	$0.522073\pi$
$284$		0			0
$285$	−2.53648	−	2.40268i	−0.150248	−	0.142323i
$286$		0			0
$287$	12.6802	+	4.27245i	0.748487	+	0.252194i
$288$		0			0
$289$	12.3317	−	11.6812i	0.725394	−	0.687130i
$290$		0			0
$291$	1.65717	+	0.364771i	0.0971450	+	0.0213832i
$292$		0			0
$293$	4.00059	+	0.435090i	0.233717	+	0.0254182i	0.224228	−	0.974537i	$-0.428014\pi$
$293$	4.00059	+	0.435090i	0.233717	+	0.0254182i	0.00948898	+	0.999955i	$0.496980\pi$
$294$		0			0
$295$	2.34412	+	2.16987i	0.136480	+	0.126335i
$296$		0			0
$297$	−3.40047	−	0.369823i	−0.197315	−	0.0214593i
$298$		0			0
$299$	−14.7991	−	3.25752i	−0.855853	−	0.188388i
$300$		0			0
$301$	18.7078	−	17.7210i	1.07830	−	1.02142i
$302$		0			0
$303$	−24.8254	−	8.36464i	−1.42618	−	0.480536i
$304$		0			0
$305$	2.20756	+	2.09112i	0.126405	+	0.119737i
$306$		0			0
$307$	3.82546	−	2.90804i	0.218330	−	0.165970i	−0.490292	−	0.871558i	$-0.663110\pi$
$307$	3.82546	−	2.90804i	0.218330	−	0.165970i	0.708623	+	0.705588i	$0.249317\pi$
$308$		0			0
$309$	−3.39466	+	6.40302i	−0.193116	+	0.364255i
$310$		0			0
$311$	9.48515	+	4.38830i	0.537854	+	0.248838i	0.669959	−	0.742398i	$-0.266312\pi$
$311$	9.48515	+	4.38830i	0.537854	+	0.248838i	−0.132105	+	0.991236i	$0.542174\pi$
$312$		0			0
$313$	−0.0553862	−	1.02154i	−0.00313062	−	0.0577408i	0.996551	−	0.0829867i	$-0.0264459\pi$
$313$	−0.0553862	−	1.02154i	−0.00313062	−	0.0577408i	−0.999681	+	0.0252459i	$0.991963\pi$
$314$		0			0
$315$	0.819142	+	0.964368i	0.0461534	+	0.0543360i
$316$		0			0
$317$	14.4414	−	4.86587i	0.811109	−	0.273294i	0.116970	−	0.993135i	$-0.462682\pi$
$317$	14.4414	−	4.86587i	0.811109	−	0.273294i	0.694139	+	0.719841i	$0.255785\pi$
$318$		0			0
$319$	4.14315	−	2.49285i	0.231972	−	0.139573i
$320$		0			0
$321$	2.28996	−	8.24770i	0.127813	−	0.460342i
$322$		0			0
$323$	0.418489	−	0.617226i	0.0232854	−	0.0343434i
$324$		0			0
$325$	−16.8652	+	1.83420i	−0.935511	+	0.101743i
$326$		0			0
$327$	5.24613	+	3.15649i	0.290112	+	0.174554i
$328$		0			0
$329$	1.46305	+	5.26943i	0.0806605	+	0.290513i
$330$		0			0
$331$	0.459232	−	8.47004i	0.0252417	−	0.465556i	−0.958401	−	0.285425i	$-0.907865\pi$
$331$	0.459232	−	8.47004i	0.0252417	−	0.465556i	0.983643	−	0.180131i	$-0.0576520\pi$
$332$		0			0
$333$	1.56466	+	2.95126i	0.0857429	+	0.161728i
$334$		0			0
$335$	2.02899	+	2.99254i	0.110856	+	0.163500i
$336$		0			0
$337$	1.97275	+	4.95124i	0.107463	+	0.269711i	0.972868	−	0.231362i	$-0.0743181\pi$
$337$	1.97275	+	4.95124i	0.107463	+	0.269711i	−0.865405	+	0.501073i	$0.832939\pi$
$338$		0			0
$339$	26.8762	−	5.91590i	1.45972	−	0.321308i
$340$		0			0
$341$	0.181264	−	1.10566i	0.00981599	−	0.0598749i
$342$		0			0
$343$	17.5489	−	8.11898i	0.947551	−	0.438384i
$344$		0			0
$345$	0.387764	+	2.36526i	0.0208765	+	0.127341i
$346$		0			0
$347$	−4.81722	+	12.0903i	−0.258602	+	0.649042i	−0.999751	−	0.0222982i	$-0.992902\pi$
$347$	−4.81722	+	12.0903i	−0.258602	+	0.649042i	0.741149	+	0.671340i	$0.234281\pi$
$348$		0			0
$349$	7.98107	+	6.06705i	0.427217	+	0.324762i	0.796591	−	0.604519i	$-0.206635\pi$
$349$	7.98107	+	6.06705i	0.427217	+	0.324762i	−0.369374	+	0.929281i	$0.620428\pi$
$350$		0			0
$351$	−12.8137	+	15.0855i	−0.683946	+	0.805204i
$352$		0			0
$353$	11.0078			0.585885			0.292943	−	0.956130i	$-0.405365\pi$
$353$	11.0078			0.585885			0.292943	+	0.956130i	$0.405365\pi$
$354$		0			0
$355$	4.09519			0.217350
$356$		0			0
$357$	0.257528	−	0.303185i	0.0136298	−	0.0160463i
$358$		0			0
$359$	2.64665	+	2.01193i	0.139685	+	0.106185i	0.672683	−	0.739931i	$-0.265142\pi$
$359$	2.64665	+	2.01193i	0.139685	+	0.106185i	−0.532998	+	0.846116i	$0.678935\pi$
$360$		0			0
$361$	−7.58847	+	19.0456i	−0.399393	+	1.00240i
$362$		0			0
$363$	−2.29909	−	14.0238i	−0.120671	−	0.736060i
$364$		0			0
$365$	3.20235	−	1.48156i	0.167618	−	0.0775486i
$366$		0			0
$367$	2.09670	−	12.7893i	0.109447	−	0.667597i	−0.873934	−	0.486044i	$-0.838439\pi$
$367$	2.09670	−	12.7893i	0.109447	−	0.667597i	0.983381	−	0.181553i	$-0.0581124\pi$
$368$		0			0
$369$	−6.32067	+	1.39128i	−0.329041	+	0.0724273i
$370$		0			0
$371$	10.6430	+	26.7120i	0.552558	+	1.38682i
$372$		0			0
$373$	5.75751	+	8.49169i	0.298112	+	0.439683i	0.947015	−	0.321188i	$-0.104082\pi$
$373$	5.75751	+	8.49169i	0.298112	+	0.439683i	−0.648903	+	0.760871i	$0.724772\pi$
$374$		0			0
$375$	2.55881	+	4.82643i	0.132136	+	0.249236i
$376$		0			0
$377$	1.51479	−	27.9386i	0.0780155	−	1.43891i
$378$		0			0
$379$	−4.71791	−	16.9924i	−0.242343	−	0.872840i	−0.980221	−	0.197906i	$-0.936586\pi$
$379$	−4.71791	−	16.9924i	−0.242343	−	0.872840i	0.737878	−	0.674934i	$-0.235828\pi$
$380$		0			0
$381$	4.18276	+	2.51669i	0.214290	+	0.128934i
$382$		0			0
$383$	−5.46013	+	0.593824i	−0.278999	+	0.0303430i	−0.246549	−	0.969130i	$-0.579297\pi$
$383$	−5.46013	+	0.593824i	−0.278999	+	0.0303430i	−0.0324504	+	0.999473i	$0.510331\pi$
$384$		0			0
$385$	0.355498	−	0.524320i	0.0181179	−	0.0267218i
$386$		0			0
$387$	−3.33442	+	12.0095i	−0.169498	+	0.610476i
$388$		0			0
$389$	−25.9437	+	15.6098i	−1.31540	+	0.791449i	−0.988150	−	0.153490i	$-0.950949\pi$
$389$	−25.9437	+	15.6098i	−1.31540	+	0.791449i	−0.327248	+	0.944938i	$0.606121\pi$
$390$		0			0
$391$	−0.484804	+	0.163350i	−0.0245176	+	0.00826094i
$392$		0			0
$393$	6.63396	+	7.81010i	0.334639	+	0.393968i
$394$		0			0
$395$	−0.202678	−	3.73818i	−0.0101978	−	0.188088i
$396$		0			0
$397$	2.60860	+	1.20687i	0.130922	+	0.0605710i	0.484257	−	0.874926i	$-0.339090\pi$
$397$	2.60860	+	1.20687i	0.130922	+	0.0605710i	−0.353334	+	0.935497i	$0.614952\pi$
$398$		0			0
$399$	−9.87018	+	18.6171i	−0.494127	+	0.932022i
$400$		0			0
$401$	−14.5043	+	11.0259i	−0.724310	+	0.550606i	−0.901084	−	0.433645i	$-0.857227\pi$
$401$	−14.5043	+	11.0259i	−0.724310	+	0.550606i	0.176774	+	0.984252i	$0.443434\pi$
$402$		0			0
$403$	−4.70690	−	4.45861i	−0.234467	−	0.222099i
$404$		0			0
$405$	1.53258	+	0.516385i	0.0761544	+	0.0256594i
$406$		0			0
$407$	1.21413	−	1.15008i	0.0601820	−	0.0570074i
$408$		0			0
$409$	26.3149	+	5.79235i	1.30119	+	0.286413i	0.810920	−	0.585157i	$-0.198967\pi$
$409$	26.3149	+	5.79235i	1.30119	+	0.286413i	0.490270	+	0.871571i	$0.336898\pi$
$410$		0			0
$411$	12.7002	+	1.38123i	0.626456	+	0.0681312i
$412$		0			0
$413$	8.82759	−	17.1236i	0.434378	−	0.842598i
$414$		0			0
$415$	−6.29376	−	0.684488i	−0.308949	−	0.0336002i
$416$		0			0
$417$	24.3543	+	5.36080i	1.19264	+	0.262519i
$418$		0			0
$419$	6.14125	−	5.81730i	0.300020	−	0.284194i	−0.522849	−	0.852425i	$-0.675131\pi$
$419$	6.14125	−	5.81730i	0.300020	−	0.284194i	0.822869	+	0.568232i	$0.192372\pi$
$420$		0			0
$421$	0.375044	+	0.126367i	0.0182785	+	0.00615875i	0.328426	−	0.944530i	$-0.393482\pi$
$421$	0.375044	+	0.126367i	0.0182785	+	0.00615875i	−0.310147	+	0.950688i	$0.600378\pi$
$422$		0			0
$423$	−1.92037	−	1.81907i	−0.0933715	−	0.0884462i
$424$		0			0
$425$	−0.455948	+	0.346603i	−0.0221167	+	0.0168127i
$426$		0			0
$427$	8.59027	−	16.2030i	0.415712	−	0.784117i
$428$		0			0
$429$	2.58959	+	1.19807i	0.125027	+	0.0578435i
$430$		0			0
$431$	−0.358843	−	6.61847i	−0.0172849	−	0.318800i	−0.994371	−	0.105956i	$-0.966210\pi$
$431$	−0.358843	−	6.61847i	−0.0172849	−	0.318800i	0.977086	−	0.212845i	$-0.0682729\pi$
$432$		0			0
$433$	17.1717	+	20.2160i	0.825217	+	0.971520i	0.999914	−	0.0131017i	$-0.00417053\pi$
$433$	17.1717	+	20.2160i	0.825217	+	0.971520i	−0.174697	+	0.984622i	$0.555895\pi$
$434$		0			0
$435$	−4.19392	+	1.41310i	−0.201083	+	0.0677528i
$436$		0			0
$437$	23.2201	−	13.9711i	1.11077	−	0.668328i
$438$		0			0
$439$	−8.51822	+	30.6799i	−0.406553	+	1.46427i	0.423148	+	0.906061i	$0.360925\pi$
$439$	−8.51822	+	30.6799i	−0.406553	+	1.46427i	−0.829700	+	0.558209i	$0.811489\pi$
$440$		0			0
$441$	−0.482962	+	0.712316i	−0.0229982	+	0.0339198i
$442$		0			0
$443$	−17.3478	+	1.88668i	−0.824217	+	0.0896390i	−0.510500	−	0.859878i	$-0.670540\pi$
$443$	−17.3478	+	1.88668i	−0.824217	+	0.0896390i	−0.313717	+	0.949517i	$0.601574\pi$
$444$		0			0
$445$	2.52600	+	1.51984i	0.119744	+	0.0720475i
$446$		0			0
$447$	6.34614	+	22.8567i	0.300162	+	1.08109i
$448$		0			0
$449$	1.07247	−	19.7805i	0.0506128	−	0.933499i	−0.857425	−	0.514610i	$-0.827937\pi$
$449$	1.07247	−	19.7805i	0.0506128	−	0.933499i	0.908037	−	0.418889i	$-0.137580\pi$
$450$		0			0
$451$	1.51773	+	2.86275i	0.0714673	+	0.134802i
$452$		0			0
$453$	−10.8991	−	16.0750i	−0.512084	−	0.755267i
$454$		0			0
$455$	−1.35679	−	3.40529i	−0.0636074	−	0.159642i
$456$		0			0
$457$	−14.7095	+	3.23780i	−0.688080	+	0.151458i	−0.545230	−	0.838287i	$-0.683558\pi$
$457$	−14.7095	+	3.23780i	−0.688080	+	0.151458i	−0.142850	+	0.989744i	$0.545627\pi$
$458$		0			0
$459$	−0.108106	+	0.659418i	−0.00504596	+	0.0307790i
$460$		0			0
$461$	−18.3239	+	8.47753i	−0.853428	+	0.394838i	−0.797298	−	0.603586i	$-0.793738\pi$
$461$	−18.3239	+	8.47753i	−0.853428	+	0.394838i	−0.0561298	+	0.998423i	$0.517876\pi$
$462$		0			0
$463$	−4.50564	−	27.4832i	−0.209395	−	1.27725i	−0.857016	−	0.515289i	$-0.827684\pi$
$463$	−4.50564	−	27.4832i	−0.209395	−	1.27725i	0.647622	−	0.761962i	$-0.275764\pi$
$464$		0			0
$465$	−0.379571	+	0.952652i	−0.0176022	+	0.0441782i
$466$		0			0
$467$	7.83232	+	5.95398i	0.362437	+	0.275517i	0.770505	−	0.637434i	$-0.220004\pi$
$467$	7.83232	+	5.95398i	0.362437	+	0.275517i	−0.408068	+	0.912952i	$0.633797\pi$
$468$		0			0
$469$	14.1169	−	16.6197i	0.651857	−	0.767426i
$470$		0			0
$471$	17.7215			0.816565
$472$		0			0
$473$	6.23999			0.286915
$474$		0			0
$475$	19.6406	−	23.1227i	0.901172	−	1.06094i
$476$		0			0
$477$	−11.0720	−	8.41673i	−0.506953	−	0.385375i
$478$		0			0
$479$	−0.724963	+	1.81952i	−0.0331244	+	0.0831360i	−0.944608	−	0.328199i	$-0.893558\pi$
$479$	−0.724963	+	1.81952i	−0.0331244	+	0.0831360i	0.911484	+	0.411335i	$0.134938\pi$
$480$		0			0
$481$	−1.56560	−	9.54971i	−0.0713850	−	0.435429i
$482$		0			0
$483$	13.1197	−	6.06981i	0.596966	−	0.276186i
$484$		0			0
$485$	0.0854019	−	0.520929i	0.00387790	−	0.0236542i
$486$		0			0
$487$	26.3448	−	5.79892i	1.19380	−	0.262774i	0.426752	−	0.904369i	$-0.359658\pi$
$487$	26.3448	−	5.79892i	1.19380	−	0.262774i	0.767044	+	0.641595i	$0.221727\pi$
$488$		0			0
$489$	2.65691	+	6.66834i	0.120150	+	0.301553i
$490$		0			0
$491$	−3.19296	−	4.70927i	−0.144096	−	0.212526i	0.748791	−	0.662806i	$-0.230635\pi$
$491$	−3.19296	−	4.70927i	−0.144096	−	0.212526i	−0.892888	+	0.450280i	$0.851324\pi$
$492$		0			0
$493$	−0.442461	−	0.834570i	−0.0199274	−	0.0375871i
$494$		0			0
$495$	−0.0165882	+	0.305952i	−0.000745586	+	0.0137515i
$496$		0			0
$497$	−6.60764	−	23.7986i	−0.296393	−	1.06751i
$498$		0			0
$499$	12.7761	+	7.68715i	0.571939	+	0.344124i	0.771964	−	0.635667i	$-0.219275\pi$
$499$	12.7761	+	7.68715i	0.571939	+	0.344124i	−0.200025	+	0.979791i	$0.564102\pi$
$500$		0			0
$501$	−7.09056	+	0.771145i	−0.316783	+	0.0344522i
$502$		0			0
$503$	11.0447	−	16.2898i	0.492460	−	0.726325i	−0.497532	−	0.867446i	$-0.665760\pi$
$503$	11.0447	−	16.2898i	0.492460	−	0.726325i	0.989992	+	0.141121i	$0.0450706\pi$
$504$		0			0
$505$	−2.18028	+	7.85267i	−0.0970213	+	0.349439i
$506$		0			0
$507$	−0.742730	+	0.446886i	−0.0329858	+	0.0198469i
$508$		0			0
$509$	−40.2488	+	13.5614i	−1.78400	+	0.601098i	−0.999811	−	0.0194284i	$-0.993815\pi$
$509$	−40.2488	+	13.5614i	−1.78400	+	0.601098i	−0.784185	+	0.620527i	$0.786919\pi$
$510$		0			0
$511$	−13.7769	−	16.2194i	−0.609455	−	0.717505i
$512$		0			0
$513$	−1.91632	−	35.3445i	−0.0846078	−	1.56050i
$514$		0			0
$515$	2.04621	+	0.946680i	0.0901670	+	0.0417157i
$516$		0			0
$517$	−0.620311	+	1.17003i	−0.0272812	+	0.0514579i
$518$		0			0
$519$	−3.47737	+	2.64343i	−0.152640	+	0.116034i
$520$		0			0
$521$	26.7050	+	25.2963i	1.16997	+	1.10825i	0.992261	+	0.124167i	$0.0396259\pi$
$521$	26.7050	+	25.2963i	1.16997	+	1.10825i	0.177705	+	0.984084i	$0.443133\pi$
$522$		0			0
$523$	11.9159	+	4.01493i	0.521046	+	0.175561i	0.567521	−	0.823359i	$-0.307902\pi$
$523$	11.9159	+	4.01493i	0.521046	+	0.175561i	−0.0464755	+	0.998919i	$0.514799\pi$
$524$		0			0
$525$	11.7492	−	11.1295i	0.512778	−	0.485729i
$526$		0			0
$527$	−0.213764	−	0.0470530i	−0.00931171	−	0.00204966i
$528$		0			0
$529$	4.38342	+	0.476726i	0.190584	+	0.0207272i
$530$		0			0
$531$	0.611453	+	9.29814i	0.0265348	+	0.403505i
$532$		0			0
$533$	18.6396	+	2.02718i	0.807372	+	0.0878070i
$534$		0			0
$535$	−2.60065	−	0.572445i	−0.112436	−	0.0247490i
$536$		0			0
$537$	−0.630649	+	0.597382i	−0.0272145	+	0.0257790i
$538$		0			0
$539$	0.408309	+	0.137575i	0.0175871	+	0.00592579i
$540$		0			0
$541$	3.27688	+	3.10402i	0.140884	+	0.133452i	0.754897	−	0.655844i	$-0.227687\pi$
$541$	3.27688	+	3.10402i	0.140884	+	0.133452i	−0.614013	+	0.789296i	$0.710446\pi$
$542$		0			0
$543$	16.7306	−	12.7183i	0.717978	−	0.545793i
$544$		0			0
$545$	0.892178	−	1.68283i	0.0382167	−	0.0720844i
$546$		0			0
$547$	−36.2322	−	16.7628i	−1.54918	−	0.716726i	−0.555768	−	0.831338i	$-0.687576\pi$
$547$	−36.2322	−	16.7628i	−1.54918	−	0.716726i	−0.993410	+	0.114612i	$0.963438\pi$
$548$		0			0
$549$	0.480234	+	8.85740i	0.0204959	+	0.378025i
$550$		0			0
$551$	32.3931	+	38.1361i	1.37999	+	1.62465i
$552$		0			0
$553$	−21.3968	+	7.20943i	−0.909885	+	0.306576i
$554$		0			0
$555$	−1.31156	+	0.789136i	−0.0556724	+	0.0334970i
$556$		0			0
$557$	−6.95556	+	25.0517i	−0.294717	+	1.06147i	0.656848	+	0.754023i	$0.271890\pi$
$557$	−6.95556	+	25.0517i	−0.294717	+	1.06147i	−0.951564	+	0.307450i	$0.900524\pi$
$558$		0			0
$559$	20.2633	−	29.8862i	0.857048	−	1.26405i
$560$		0			0
$561$	0.0957642	−	0.0104150i	0.00404317	−	0.000439721i
$562$		0			0
$563$	19.8422	+	11.9386i	0.836248	+	0.503154i	0.868130	−	0.496338i	$-0.165322\pi$
$563$	19.8422	+	11.9386i	0.836248	+	0.503154i	−0.0318811	+	0.999492i	$0.510150\pi$
$564$		0			0
$565$	−2.29038	−	8.24922i	−0.0963572	−	0.347047i
$566$		0			0
$567$	0.528062	−	9.73954i	0.0221765	−	0.409022i
$568$		0			0
$569$	−5.99073	−	11.2997i	−0.251144	−	0.473709i	0.725600	−	0.688117i	$-0.241562\pi$
$569$	−5.99073	−	11.2997i	−0.251144	−	0.473709i	−0.976744	+	0.214408i	$0.931218\pi$
$570$		0			0
$571$	9.23035	+	13.6138i	0.386278	+	0.569718i	0.970265	−	0.242045i	$-0.0778183\pi$
$571$	9.23035	+	13.6138i	0.386278	+	0.569718i	−0.583987	+	0.811763i	$0.698508\pi$
$572$		0			0
$573$	−9.68493	−	24.3073i	−0.404594	−	1.01545i
$574$		0			0
$575$	−20.3262	+	4.47414i	−0.847663	+	0.186585i
$576$		0			0
$577$	−5.46240	+	33.3192i	−0.227403	+	1.38710i	0.588309	+	0.808636i	$0.299794\pi$
$577$	−5.46240	+	33.3192i	−0.227403	+	1.38710i	−0.815712	+	0.578459i	$0.803654\pi$
$578$		0			0
$579$	20.3142	−	9.39833i	0.844228	−	0.390581i
$580$		0			0
$581$	6.17727	+	37.6797i	0.256276	+	1.56322i
$582$		0			0
$583$	−2.57727	+	6.46847i	−0.106740	+	0.267897i
$584$		0			0
$585$	1.41148	+	1.07298i	0.0583575	+	0.0443622i
$586$		0			0
$587$	−3.31987	+	3.90845i	−0.137026	+	0.161319i	−0.826395	−	0.563091i	$-0.809612\pi$
$587$	−3.31987	+	3.90845i	−0.137026	+	0.161319i	0.689369	+	0.724410i	$0.257888\pi$
$588$		0			0
$589$	11.5944			0.477739
$590$		0			0
$591$	−13.7711			−0.566466
$592$		0			0
$593$	16.7944	−	19.7719i	0.689665	−	0.811937i	−0.300211	−	0.953873i	$-0.597057\pi$
$593$	16.7944	−	19.7719i	0.689665	−	0.811937i	0.989876	+	0.141936i	$0.0453328\pi$
$594$		0			0
$595$	−0.0985193	−	0.0748924i	−0.00403890	−	0.00307029i
$596$		0			0
$597$	5.85169	−	14.6866i	0.239494	−	0.601084i
$598$		0			0
$599$	3.26675	+	19.9263i	0.133476	+	0.814167i	0.965687	+	0.259708i	$0.0836264\pi$
$599$	3.26675	+	19.9263i	0.133476	+	0.814167i	−0.832211	+	0.554459i	$0.812925\pi$
$600$		0			0
$601$	30.1128	−	13.9317i	1.22833	−	0.568284i	0.305019	−	0.952346i	$-0.401337\pi$
$601$	30.1128	−	13.9317i	1.22833	−	0.568284i	0.923307	+	0.384062i	$0.125475\pi$
$602$		0			0
$603$	−1.70635	+	10.4083i	−0.0694878	+	0.423857i
$604$		0			0
$605$	−4.31765	+	0.950388i	−0.175538	+	0.0386388i
$606$		0			0
$607$	3.23282	+	8.11376i	0.131216	+	0.329327i	0.979875	−	0.199614i	$-0.0639687\pi$
$607$	3.23282	+	8.11376i	0.131216	+	0.329327i	−0.848659	+	0.528941i	$0.822589\pi$
$608$		0			0
$609$	14.9789	+	22.0923i	0.606977	+	0.895225i
$610$		0			0
$611$	3.58946	+	6.77044i	0.145214	+	0.273903i
$612$		0			0
$613$	2.45688	−	45.3144i	0.0992323	−	1.83023i	−0.349922	−	0.936779i	$-0.613792\pi$
$613$	2.45688	−	45.3144i	0.0992323	−	1.83023i	0.449155	−	0.893454i	$-0.351725\pi$
$614$		0			0
$615$	−0.793395	−	2.85755i	−0.0319928	−	0.115227i
$616$		0			0
$617$	23.1753	+	13.9441i	0.933001	+	0.561368i	0.898950	−	0.438052i	$-0.144332\pi$
$617$	23.1753	+	13.9441i	0.933001	+	0.561368i	0.0340511	+	0.999420i	$0.489159\pi$
$618$		0			0
$619$	−30.0907	+	3.27256i	−1.20945	+	0.131535i	−0.690539	−	0.723296i	$-0.742626\pi$
$619$	−30.0907	+	3.27256i	−1.20945	+	0.131535i	−0.518907	+	0.854831i	$0.673661\pi$
$620$		0			0
$621$	−13.6272	+	20.0986i	−0.546841	+	0.806531i
$622$		0			0
$623$	4.75661	−	17.1317i	0.190569	−	0.686369i
$624$		0			0
$625$	−19.2243	+	11.5669i	−0.768973	+	0.462676i
$626$		0			0
$627$	−4.83554	+	1.62928i	−0.193113	+	0.0650673i
$628$		0			0
$629$	−0.211505	−	0.249003i	−0.00843326	−	0.00992840i
$630$		0			0
$631$	−0.967251	−	17.8399i	−0.0385056	−	0.710195i	−0.952513	−	0.304497i	$-0.901512\pi$
$631$	−0.967251	−	17.8399i	−0.0385056	−	0.710195i	0.914008	−	0.405697i	$-0.132971\pi$
$632$		0			0
$633$	2.77982	+	1.28608i	0.110488	+	0.0511172i
$634$		0			0
$635$	0.711338	−	1.34173i	0.0282286	−	0.0532448i
$636$		0			0
$637$	1.98483	−	1.50883i	0.0786418	−	0.0597819i
$638$		0			0
$639$	8.67306	+	8.21556i	0.343101	+	0.325002i
$640$		0			0
$641$	27.0493	+	9.11396i	1.06838	+	0.359980i	0.797928	−	0.602753i	$-0.205930\pi$
$641$	27.0493	+	9.11396i	1.06838	+	0.359980i	0.270454	+	0.962733i	$0.412826\pi$
$642$		0			0
$643$	−25.7522	+	24.3938i	−1.01557	+	0.961998i	−0.999283	−	0.0378699i	$-0.987943\pi$
$643$	−25.7522	+	24.3938i	−1.01557	+	0.961998i	−0.0162857	+	0.999867i	$0.505184\pi$
$644$		0			0
$645$	−5.57774	−	1.22775i	−0.219623	−	0.0483427i
$646$		0			0
$647$	−38.5452	−	4.19204i	−1.51537	−	0.164806i	−0.687688	−	0.726006i	$-0.741374\pi$
$647$	−38.5452	−	4.19204i	−1.51537	−	0.164806i	−0.827680	+	0.561200i	$0.810340\pi$
$648$		0			0
$649$	4.40353	−	1.54034i	0.172854	−	0.0604636i
$650$		0			0
$651$	6.14864	+	0.668705i	0.240984	+	0.0262086i
$652$		0			0
$653$	−37.6612	−	8.28985i	−1.47380	−	0.324407i	−0.595822	−	0.803116i	$-0.703174\pi$
$653$	−37.6612	−	8.28985i	−1.47380	−	0.324407i	−0.877973	+	0.478710i	$0.841105\pi$
$654$		0			0
$655$	2.31441	−	2.19232i	0.0904314	−	0.0856611i
$656$		0			0
$657$	9.75437	+	3.28663i	0.380554	+	0.128224i
$658$		0			0
$659$	−10.0528	−	9.52253i	−0.391602	−	0.370945i	0.466415	−	0.884566i	$-0.345545\pi$
$659$	−10.0528	−	9.52253i	−0.391602	−	0.370945i	−0.858017	+	0.513621i	$0.828304\pi$
$660$		0			0
$661$	22.1917	−	16.8697i	0.863157	−	0.656155i	−0.0769498	−	0.997035i	$-0.524518\pi$
$661$	22.1917	−	16.8697i	0.863157	−	0.656155i	0.940107	+	0.340880i	$0.110725\pi$
$662$		0			0
$663$	0.261096	−	0.492480i	0.0101401	−	0.0191263i
$664$		0			0
$665$	5.94948	+	2.75252i	0.230711	+	0.106738i
$666$		0			0
$667$	−1.85840	−	34.2762i	−0.0719575	−	1.32718i
$668$		0			0
$669$	9.97761	+	11.7465i	0.385757	+	0.454148i
$670$		0			0
$671$	4.20850	−	1.41801i	0.162467	−	0.0547416i
$672$		0			0
$673$	−10.8454	+	6.52549i	−0.418061	+	0.251539i	−0.709008	−	0.705200i	$-0.750857\pi$
$673$	−10.8454	+	6.52549i	−0.418061	+	0.251539i	0.290947	+	0.956739i	$0.406030\pi$
$674$		0			0
$675$	−7.27284	+	26.1944i	−0.279932	+	1.00822i
$676$		0			0
$677$	−5.92107	+	8.73293i	−0.227565	+	0.335634i	−0.924280	−	0.381714i	$-0.875334\pi$
$677$	−5.92107	+	8.73293i	−0.227565	+	0.335634i	0.696715	+	0.717348i	$0.254644\pi$
$678$		0			0
$679$	−3.16510	+	0.344225i	−0.121465	+	0.0132101i
$680$		0			0
$681$	−20.6410	−	12.4193i	−0.790966	−	0.475908i
$682$		0			0
$683$	7.68162	+	27.6667i	0.293929	+	1.05864i	0.952105	+	0.305772i	$0.0989147\pi$
$683$	7.68162	+	27.6667i	0.293929	+	1.05864i	−0.658176	+	0.752865i	$0.728672\pi$
$684$		0			0
$685$	0.215165	−	3.96848i	0.00822102	−	0.151628i
$686$		0			0
$687$	0.957351	+	1.80576i	0.0365252	+	0.0688939i
$688$		0			0
$689$	22.6112	+	33.3491i	0.861419	+	1.27050i
$690$		0			0
$691$	16.8023	+	42.1706i	0.639189	+	1.60424i	0.788208	+	0.615409i	$0.211009\pi$
$691$	16.8023	+	42.1706i	0.639189	+	1.60424i	−0.149019	+	0.988834i	$0.547612\pi$
$692$		0			0
$693$	1.80476	−	0.397258i	0.0685572	−	0.0150906i
$694$		0			0
$695$	1.25510	−	7.65575i	0.0476085	−	0.290399i
$696$		0			0
$697$	0.574489	−	0.265787i	0.0217603	−	0.0100674i
$698$		0			0
$699$	−3.67528	−	22.4182i	−0.139012	−	0.847934i
$700$		0			0
$701$	0.00703909	−	0.0176668i	0.000265863	−	0.000667265i	−0.928844	−	0.370472i	$-0.879196\pi$
$701$	0.00703909	−	0.0176668i	0.000265863	−	0.000667265i	0.929110	+	0.369804i	$0.120575\pi$
$702$		0			0
$703$	13.7772	+	10.4731i	0.519616	+	0.395002i
$704$		0			0
$705$	0.784687	−	0.923805i	0.0295530	−	0.0347925i
$706$		0			0
$707$	49.1525			1.84857
$708$		0			0
$709$	−23.3896			−0.878416			−0.439208	−	0.898385i	$-0.644741\pi$
$709$	−23.3896			−0.878416			−0.439208	+	0.898385i	$0.644741\pi$
$710$		0			0
$711$	7.07009	−	8.32355i	0.265149	−	0.312158i
$712$		0			0
$713$	−6.33216	−	4.81359i	−0.237141	−	0.180270i
$714$		0			0
$715$	0.328555	−	0.824612i	0.0122873	−	0.0308387i
$716$		0			0
$717$	3.68496	+	22.4773i	0.137618	+	0.839430i
$718$		0			0
$719$	−42.5763	+	19.6979i	−1.58783	+	0.734608i	−0.997371	−	0.0724608i	$-0.976915\pi$
$719$	−42.5763	+	19.6979i	−1.58783	+	0.734608i	−0.590458	+	0.807069i	$0.701053\pi$
$720$		0			0
$721$	2.19989	−	13.4187i	0.0819282	−	0.499740i
$722$		0			0
$723$	29.1357	−	6.41324i	1.08357	−	0.238511i
$724$		0			0
$725$	−14.2242	−	35.7001i	−0.528274	−	1.32587i
$726$		0			0
$727$	16.0220	+	23.6306i	0.594222	+	0.876411i	0.999282	−	0.0378785i	$-0.0120600\pi$
$727$	16.0220	+	23.6306i	0.594222	+	0.876411i	−0.405061	+	0.914290i	$0.632750\pi$
$728$		0			0
$729$	12.7888	+	24.1223i	0.473660	+	0.893418i
$730$		0			0
$731$	0.0659965	−	1.21723i	0.00244097	−	0.0450210i
$732$		0			0
$733$	2.52437	+	9.09197i	0.0932398	+	0.335820i	0.995427	−	0.0955252i	$-0.0304531\pi$
$733$	2.52437	+	9.09197i	0.0932398	+	0.335820i	−0.902187	+	0.431345i	$0.858039\pi$
$734$		0			0
$735$	−0.337906	−	0.203312i	−0.0124639	−	0.00749926i
$736$		0			0
$737$	5.24949	−	0.570917i	0.193368	−	0.0210300i
$738$		0			0
$739$	−6.12324	+	9.03110i	−0.225247	+	0.332214i	−0.923473	−	0.383663i	$-0.874663\pi$
$739$	−6.12324	+	9.03110i	−0.225247	+	0.332214i	0.698226	+	0.715877i	$0.253973\pi$
$740$		0			0
$741$	−7.89924	+	28.4505i	−0.290186	+	1.04515i
$742$		0			0
$743$	3.97060	−	2.38903i	0.145667	−	0.0876451i	−0.440854	−	0.897579i	$-0.645324\pi$
$743$	3.97060	−	2.38903i	0.145667	−	0.0876451i	0.586522	+	0.809934i	$0.300497\pi$
$744$		0			0
$745$	6.99336	−	2.35634i	0.256217	−	0.0863295i
$746$		0			0
$747$	−11.9562	−	14.0759i	−0.437453	−	0.515009i
$748$		0			0
$749$	0.869496	+	16.0369i	0.0317707	+	0.585976i
$750$		0			0
$751$	−46.3978	−	21.4659i	−1.69308	−	0.783302i	−0.997921	−	0.0644455i	$-0.979472\pi$
$751$	−46.3978	−	21.4659i	−1.69308	−	0.783302i	−0.695158	−	0.718857i	$-0.744666\pi$
$752$		0			0
$753$	10.9090	−	20.5766i	0.397548	−	0.749855i
$754$		0			0
$755$	−4.80997	+	3.65645i	−0.175053	+	0.133072i
$756$		0			0
$757$	−15.2529	−	14.4483i	−0.554377	−	0.525133i	0.358413	−	0.933563i	$-0.383318\pi$
$757$	−15.2529	−	14.4483i	−0.554377	−	0.525133i	−0.912790	+	0.408430i	$0.866077\pi$
$758$		0			0
$759$	3.31730	+	1.11773i	0.120410	+	0.0405710i
$760$		0			0
$761$	−3.20241	+	3.03348i	−0.116087	+	0.109964i	−0.743542	−	0.668690i	$-0.766856\pi$
$761$	−3.20241	+	3.03348i	−0.116087	+	0.109964i	0.627454	+	0.778653i	$0.284097\pi$
$762$		0			0
$763$	−11.2190	−	2.46950i	−0.406156	−	0.0894018i
$764$		0			0
$765$	0.0595067	+	0.00647174i	0.00215147	+	0.000233986i
$766$		0			0
$767$	6.92236	−	26.0926i	0.249952	−	0.942148i
$768$		0			0
$769$	−51.1424	−	5.56208i	−1.84424	−	0.200574i	−0.881720	−	0.471772i	$-0.843614\pi$
$769$	−51.1424	−	5.56208i	−1.84424	−	0.200574i	−0.962523	+	0.271199i	$0.912580\pi$
$770$		0			0
$771$	−0.178311	−	0.0392491i	−0.00642170	−	0.00141352i
$772$		0			0
$773$	−11.1114	+	10.5253i	−0.399650	+	0.378568i	−0.860962	−	0.508670i	$-0.830137\pi$
$773$	−11.1114	+	10.5253i	−0.399650	+	0.378568i	0.461312	+	0.887238i	$0.347379\pi$
$774$		0			0
$775$	−8.43864	−	2.84331i	−0.303125	−	0.102135i
$776$		0			0
$777$	6.70216	+	6.34862i	0.240439	+	0.227756i
$778$		0			0
$779$	−26.6933	+	20.2917i	−0.956386	+	0.727025i
$780$		0			0
$781$	2.80154	−	5.28427i	0.100247	−	0.189086i
$782$		0			0
$783$	−40.6926	−	18.8264i	−1.45423	−	0.672801i
$784$		0			0
$785$	−0.298474	−	5.50503i	−0.0106530	−	0.196483i
$786$		0			0
$787$	15.1165	+	17.7965i	0.538844	+	0.634376i	0.962446	−	0.271472i	$-0.0875104\pi$
$787$	15.1165	+	17.7965i	0.538844	+	0.634376i	−0.423602	+	0.905848i	$0.639235\pi$
$788$		0			0
$789$	6.54399	−	2.20493i	0.232972	−	0.0784975i
$790$		0			0
$791$	−44.2435	+	26.6204i	−1.57312	+	0.946514i
$792$		0			0
$793$	6.87491	−	24.7612i	0.244135	−	0.879296i
$794$		0			0
$795$	3.57646	−	5.27488i	0.126844	−	0.187081i
$796$		0			0
$797$	2.55891	−	0.278299i	0.0906414	−	0.00985784i	−0.0626859	−	0.998033i	$-0.519967\pi$
$797$	2.55891	−	0.278299i	0.0906414	−	0.00985784i	0.153327	+	0.988175i	$0.451001\pi$
$798$		0			0
$799$	0.221677	+	0.133379i	0.00784237	+	0.00471860i
$800$		0			0
$801$	2.30069	+	8.28635i	0.0812910	+	0.292784i
$802$		0			0
$803$	0.278993	−	5.14572i	0.00984544	−	0.181589i
$804$		0			0
$805$	−2.10650	−	3.97328i	−0.0742444	−	0.140040i
$806$		0			0
$807$	−17.2105	−	25.3836i	−0.605838	−	0.893544i
$808$		0			0
$809$	−12.3409	−	30.9732i	−0.433881	−	1.08896i	−0.969629	−	0.244582i	$-0.921349\pi$
$809$	−12.3409	−	30.9732i	−0.433881	−	1.08896i	0.535747	−	0.844378i	$-0.320030\pi$
$810$		0			0
$811$	−13.4748	+	2.96603i	−0.473165	+	0.104151i	−0.445150	−	0.895456i	$-0.646850\pi$
$811$	−13.4748	+	2.96603i	−0.473165	+	0.104151i	−0.0280147	+	0.999608i	$0.508919\pi$
$812$		0			0
$813$	3.92066	−	23.9150i	0.137503	−	0.838734i
$814$		0			0
$815$	2.02671	−	0.937657i	0.0709927	−	0.0328447i
$816$		0			0
$817$	10.4467	+	63.7223i	0.365485	+	2.22936i
$818$		0			0
$819$	3.95801	−	9.93387i	0.138304	−	0.347117i
$820$		0			0
$821$	−23.1188	−	17.5744i	−0.806851	−	0.613352i	0.118289	−	0.992979i	$-0.462259\pi$
$821$	−23.1188	−	17.5744i	−0.806851	−	0.613352i	−0.925139	+	0.379627i	$0.876052\pi$
$822$		0			0
$823$	17.6563	−	20.7866i	0.615458	−	0.724574i	−0.362822	−	0.931858i	$-0.618187\pi$
$823$	17.6563	−	20.7866i	0.615458	−	0.724574i	0.978281	+	0.207285i	$0.0664627\pi$
$824$		0			0
$825$	3.91896			0.136441
$826$		0			0
$827$	−51.4773			−1.79004			−0.895020	−	0.446026i	$-0.852839\pi$
$827$	−51.4773			−1.79004			−0.895020	+	0.446026i	$0.852839\pi$
$828$		0			0
$829$	25.1870	−	29.6524i	0.874781	−	1.02987i	−0.124510	−	0.992218i	$-0.539736\pi$
$829$	25.1870	−	29.6524i	0.874781	−	1.02987i	0.999291	−	0.0376534i	$-0.0119883\pi$
$830$		0			0
$831$	12.0445	+	9.15598i	0.417818	+	0.317617i
$832$		0			0
$833$	0.0311552	−	0.0781938i	0.00107947	−	0.00270925i
$834$		0			0
$835$	0.358972	+	2.18963i	0.0124227	+	0.0757753i
$836$		0			0
$837$	−9.42918	+	4.36241i	−0.325920	+	0.150787i
$838$		0			0
$839$	7.57216	−	46.1881i	0.261420	−	1.59459i	−0.450794	−	0.892628i	$-0.648859\pi$
$839$	7.57216	−	46.1881i	0.261420	−	1.59459i	0.712214	−	0.701963i	$-0.247693\pi$
$840$		0			0
$841$	33.5777	−	7.39101i	1.15785	−	0.254862i
$842$		0			0
$843$	−7.36522	−	18.4853i	−0.253672	−	0.636668i
$844$		0			0
$845$	0.151330	+	0.223196i	0.00520593	+	0.00767817i
$846$		0			0
$847$	12.4896	+	23.5579i	0.429149	+	0.809460i
$848$		0			0
$849$	1.60430	−	29.5896i	0.0550595	−	1.01551i
$850$		0			0
$851$	−3.17619	−	11.4396i	−0.108878	−	0.392145i
$852$		0			0
$853$	−19.1617	−	11.5292i	−0.656084	−	0.394753i	0.148234	−	0.988952i	$-0.452641\pi$
$853$	−19.1617	−	11.5292i	−0.656084	−	0.394753i	−0.804317	+	0.594200i	$0.797469\pi$
$854$		0			0
$855$	−3.15213	+	0.342815i	−0.107801	+	0.0117240i
$856$		0			0
$857$	−21.5554	+	31.7919i	−0.736319	+	1.08599i	0.256521	+	0.966539i	$0.417424\pi$
$857$	−21.5554	+	31.7919i	−0.736319	+	1.08599i	−0.992840	+	0.119451i	$0.961887\pi$
$858$		0			0
$859$	−4.26217	+	15.3509i	−0.145423	+	0.523767i	0.854567	+	0.519341i	$0.173823\pi$
$859$	−4.26217	+	15.3509i	−0.145423	+	0.523767i	−0.999990	+	0.00442592i	$0.998591\pi$
$860$		0			0
$861$	−15.3261	+	9.22138i	−0.522311	+	0.314264i
$862$		0			0
$863$	20.3347	−	6.85157i	0.692202	−	0.233230i	0.0488565	−	0.998806i	$-0.484442\pi$
$863$	20.3347	−	6.85157i	0.692202	−	0.233230i	0.643346	+	0.765576i	$0.277546\pi$
$864$		0			0
$865$	0.879725	+	1.03569i	0.0299116	+	0.0352146i
$866$		0			0
$867$	1.22926	+	22.6724i	0.0417480	+	0.769996i
$868$		0			0
$869$	−4.96224	−	2.29578i	−0.168333	−	0.0778789i
$870$		0			0
$871$	14.3125	−	26.9962i	0.484960	−	0.914732i
$872$		0			0
$873$	1.22593	−	0.931927i	0.0414914	−	0.0315410i
$874$		0			0
$875$	−7.44126	−	7.04873i	−0.251560	−	0.238291i
$876$		0			0
$877$	−53.5554	−	18.0449i	−1.80844	−	0.609334i	−0.999778	−	0.0210582i	$-0.993296\pi$
$877$	−53.5554	−	18.0449i	−1.80844	−	0.609334i	−0.808660	−	0.588276i	$-0.799807\pi$
$878$		0			0
$879$	−3.90533	+	3.69932i	−0.131724	+	0.124775i
$880$		0			0
$881$	−2.07576	−	0.456910i	−0.0699343	−	0.0153937i	0.179865	−	0.983691i	$-0.442434\pi$
$881$	−2.07576	−	0.456910i	−0.0699343	−	0.0153937i	−0.249800	+	0.968298i	$0.580365\pi$
$882$		0			0
$883$	14.9786	+	1.62902i	0.504069	+	0.0548208i	0.356621	−	0.934249i	$-0.383929\pi$
$883$	14.9786	+	1.62902i	0.504069	+	0.0548208i	0.147448	+	0.989070i	$0.452894\pi$
$884$		0			0
$885$	−4.23926	+	0.510443i	−0.142501	+	0.0171584i
$886$		0			0
$887$	23.6388	+	2.57087i	0.793713	+	0.0863215i	0.495987	−	0.868330i	$-0.334806\pi$
$887$	23.6388	+	2.57087i	0.793713	+	0.0863215i	0.297726	+	0.954651i	$0.403772\pi$
$888$		0			0
$889$	−8.94499	−	1.96894i	−0.300005	−	0.0660362i
$890$		0			0
$891$	1.71477	−	1.62431i	0.0574468	−	0.0544165i
$892$		0			0
$893$	−12.9868	−	4.37575i	−0.434586	−	0.146429i
$894$		0			0
$895$	0.196193	+	0.185844i	0.00655802	+	0.00621208i
$896$		0			0
$897$	16.1257	−	12.2585i	0.538422	−	0.409298i
$898$		0			0
$899$	6.87933	−	12.9758i	0.229438	−	0.432767i
$900$		0			0
$901$	1.23455	+	0.571162i	0.0411287	+	0.0190282i
$902$		0			0
$903$	1.86485	+	34.3952i	0.0620584	+	1.14460i
$904$		0			0
$905$	−4.23260	−	4.98300i	−0.140696	−	0.165641i
$906$		0			0
$907$	0.251060	−	0.0845921i	0.00833633	−	0.00280884i	−0.315130	−	0.949048i	$-0.602048\pi$
$907$	0.251060	−	0.0845921i	0.00833633	−	0.00280884i	0.323467	+	0.946240i	$0.395152\pi$
$908$		0			0
$909$	−20.3711	+	12.2569i	−0.675668	+	0.406536i
$910$		0			0
$911$	13.7994	−	49.7008i	0.457193	−	1.64666i	−0.271959	−	0.962309i	$-0.587671\pi$
$911$	13.7994	−	49.7008i	0.457193	−	1.64666i	0.729152	−	0.684352i	$-0.239915\pi$
$912$		0			0
$913$	−5.18883	+	7.65295i	−0.171725	+	0.253276i
$914$		0			0
$915$	−4.04085	+	0.439469i	−0.133586	+	0.0145284i
$916$		0			0
$917$	−16.4747	−	9.91248i	−0.544042	−	0.327339i
$918$		0			0
$919$	−0.989065	−	3.56229i	−0.0326262	−	0.117509i	0.945444	−	0.325785i	$-0.105629\pi$
$919$	−0.989065	−	3.56229i	−0.0326262	−	0.117509i	−0.978070	+	0.208276i	$0.933215\pi$
$920$		0			0
$921$	−0.347757	+	6.41399i	−0.0114590	+	0.211348i
$922$		0			0
$923$	−16.2113	−	30.5777i	−0.533600	−	1.00648i
$924$		0			0
$925$	−7.45898	−	11.0012i	−0.245250	−	0.361716i
$926$		0			0
$927$	2.43443	+	6.10995i	0.0799570	+	0.200677i
$928$		0			0
$929$	−34.9187	+	7.68618i	−1.14564	+	0.252175i	−0.746932	−	0.664900i	$-0.768474\pi$
$929$	−34.9187	+	7.68618i	−1.14564	+	0.252175i	−0.398713	+	0.917076i	$0.630543\pi$
$930$		0			0
$931$	−0.721335	+	4.39995i	−0.0236408	+	0.144202i
$932$		0			0
$933$	−12.6792	+	5.86601i	−0.415097	+	0.192045i
$934$		0			0
$935$	−0.00484823	−	0.0295729i	−0.000158554	−	0.000967136i
$936$		0			0
$937$	2.12358	−	5.32978i	0.0693742	−	0.174116i	−0.890201	−	0.455567i	$-0.849436\pi$
$937$	2.12358	−	5.32978i	0.0693742	−	0.174116i	0.959576	+	0.281451i	$0.0908157\pi$
$938$		0			0
$939$	1.08869	+	0.827598i	0.0355279	+	0.0270076i
$940$		0			0
$941$	1.67253	−	1.96906i	0.0545229	−	0.0641894i	−0.734225	−	0.678907i	$-0.762454\pi$
$941$	1.67253	−	1.96906i	0.0545229	−	0.0641894i	0.788747	+	0.614717i	$0.210730\pi$
$942$		0			0
$943$	23.0027			0.749070
$944$		0			0
$945$	−5.87408			−0.191084
$946$		0			0
$947$	−6.10044	+	7.18200i	−0.198238	+	0.233384i	−0.852295	−	0.523062i	$-0.824790\pi$
$947$	−6.10044	+	7.18200i	−0.198238	+	0.233384i	0.654057	+	0.756445i	$0.273066\pi$
$948$		0			0
$949$	−23.7393	−	18.0461i	−0.770609	−	0.585802i
$950$		0			0
$951$	−7.53997	+	18.9239i	−0.244500	+	0.613650i
$952$		0			0
$953$	−4.55467	−	27.7823i	−0.147540	−	0.899956i	−0.952033	−	0.305994i	$-0.901011\pi$
$953$	−4.55467	−	27.7823i	−0.147540	−	0.899956i	0.804493	−	0.593962i	$-0.202437\pi$
$954$		0			0
$955$	−7.38774	+	3.41793i	−0.239062	+	0.110602i
$956$		0			0
$957$	−1.04568	+	6.37837i	−0.0338021	+	0.206183i
$958$		0			0
$959$	−23.4094	+	5.15279i	−0.755928	+	0.166392i
$960$		0			0
$961$	10.2147	+	25.6368i	0.329505	+	0.826995i
$962$		0			0
$963$	−4.35940	−	6.42964i	−0.140480	−	0.207192i
$964$		0			0
$965$	−3.26165	−	6.15212i	−0.104996	−	0.198044i
$966$		0			0
$967$	−1.10288	+	20.3414i	−0.0354662	+	0.654135i	0.925716	+	0.378220i	$0.123464\pi$
$967$	−1.10288	+	20.3414i	−0.0354662	+	0.654135i	−0.961182	+	0.275915i	$0.911019\pi$
$968$		0			0
$969$	0.266682	+	0.960501i	0.00856705	+	0.0308557i
$970$		0			0
$971$	22.1258	+	13.3127i	0.710051	+	0.427223i	0.824244	−	0.566235i	$-0.191601\pi$
$971$	22.1258	+	13.3127i	0.710051	+	0.427223i	−0.114193	+	0.993459i	$0.536428\pi$
$972$		0			0
$973$	−46.5153	+	5.05885i	−1.49121	+	0.162179i
$974$		0			0
$975$	12.7262	−	18.7697i	0.407564	−	0.601112i
$976$		0			0
$977$	−10.7109	+	38.5773i	−0.342673	+	1.23420i	0.568676	+	0.822562i	$0.307456\pi$
$977$	−10.7109	+	38.5773i	−0.342673	+	1.23420i	−0.911349	+	0.411635i	$0.864958\pi$
$978$		0			0
$979$	3.68919	−	2.21971i	0.117907	−	0.0709423i
$980$		0			0
$981$	5.26551	−	1.77416i	0.168115	−	0.0566445i
$982$		0			0
$983$	25.3893	+	29.8906i	0.809792	+	0.953361i	0.999595	−	0.0284614i	$-0.00906077\pi$
$983$	25.3893	+	29.8906i	0.809792	+	0.953361i	−0.189803	+	0.981822i	$0.560785\pi$
$984$		0			0
$985$	0.231939	+	4.27786i	0.00739019	+	0.136304i
$986$		0			0
$987$	−6.63466	−	3.06952i	−0.211184	−	0.0977039i
$988$		0			0
$989$	20.7499	−	39.1384i	0.659808	−	1.24453i
$990$		0			0
$991$	−25.7810	+	19.5982i	−0.818961	+	0.622558i	−0.928461	−	0.371429i	$-0.878868\pi$
$991$	−25.7810	+	19.5982i	−0.818961	+	0.622558i	0.109501	+	0.993987i	$0.465075\pi$
$992$		0			0
$993$	8.23196	+	7.79773i	0.261233	+	0.247454i
$994$		0			0
$995$	−4.66083	−	1.57042i	−0.147758	−	0.0497856i
$996$		0			0
$997$	−2.64116	+	2.50184i	−0.0836464	+	0.0792341i	−0.728381	−	0.685173i	$-0.759727\pi$
$997$	−2.64116	+	2.50184i	−0.0836464	+	0.0792341i	0.644734	+	0.764407i	$0.276968\pi$
$998$		0			0
$999$	−15.1449	−	3.33364i	−0.479163	−	0.105472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	944.2.m.c.417.1		112
4.3	odd	2		59.2.c.a.4.3	✓	112
12.11	even	2		531.2.i.a.181.2		112
59.15	even	29	inner	944.2.m.c.369.1		112
236.15	odd	58		59.2.c.a.15.3	yes	112
236.147	odd	58		3481.2.a.p.1.25		56
236.207	even	58		3481.2.a.q.1.32		56
708.251	even	58		531.2.i.a.487.2		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.c.a.4.3	✓	112	4.3	odd	2
59.2.c.a.15.3	yes	112	236.15	odd	58
531.2.i.a.181.2		112	12.11	even	2
531.2.i.a.487.2		112	708.251	even	58
944.2.m.c.369.1		112	59.15	even	29	inner
944.2.m.c.417.1		112	1.1	even	1	trivial
3481.2.a.p.1.25		56	236.147	odd	58
3481.2.a.q.1.32		56	236.207	even	58

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:	\( N \)	\(=\)	\( 944 = 2^{4} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	944.m (of order \(29\), degree \(28\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.865386 + 1.01881i) q^{3} +(0.331060 + 0.251665i) q^{5} +(0.928345 - 2.32997i) q^{7} +(0.196262 + 1.19715i) q^{9} +O(q^{10})\)	\(q+(-0.865386 + 1.01881i) q^{3} +(0.331060 + 0.251665i) q^{5} +(0.928345 - 2.32997i) q^{7} +(0.196262 + 1.19715i) q^{9} +(0.551218 - 0.255021i) q^{11} +(0.568579 - 3.46818i) q^{13} +(-0.542894 + 0.119500i) q^{15} +(-0.0439170 - 0.110223i) q^{17} +(3.52708 + 5.20206i) q^{19} +(1.57042 + 2.96213i) q^{21} +(0.233431 - 4.30537i) q^{23} +(-1.29138 - 4.65112i) q^{25} +(-4.82569 - 2.90352i) q^{27} +(7.91458 - 0.860763i) q^{29} +(1.03526 - 1.52689i) q^{31} +(-0.217199 + 0.782279i) q^{33} +(0.893711 - 0.537728i) q^{35} +(2.60938 - 0.879204i) q^{37} +(3.04138 + 3.58059i) q^{39} +(0.288828 + 5.32712i) q^{41} +(9.32450 + 4.31397i) q^{43} +(-0.236306 + 0.445720i) q^{45} +(-1.73583 + 1.31954i) q^{47} +(0.515030 + 0.487862i) q^{49} +(0.150302 + 0.0506426i) q^{51} +(-8.32319 + 7.88414i) q^{53} +(0.246666 + 0.0542954i) q^{55} +(-8.35221 - 0.908357i) q^{57} +(7.64516 + 0.742603i) q^{59} +(7.26914 + 0.790567i) q^{61} +(2.97152 + 0.654081i) q^{63} +(1.06105 - 1.00508i) q^{65} +(8.23909 + 2.77607i) q^{67} +(4.18436 + 3.96363i) q^{69} +(7.83962 - 5.95953i) q^{71} +(3.97436 - 7.49644i) q^{73} +(5.85615 + 2.70934i) q^{75} +(-0.0824700 - 1.52107i) q^{77} +(-5.82798 - 6.86122i) q^{79} +(3.68536 - 1.24174i) q^{81} +(-13.0446 + 7.84865i) q^{83} +(0.0132002 - 0.0475429i) q^{85} +(-5.97222 + 8.80836i) q^{87} +(7.04739 - 0.766450i) q^{89} +(-7.55292 - 4.54444i) q^{91} +(0.659715 + 2.37608i) q^{93} +(-0.141501 + 2.60984i) q^{95} +(-0.594592 - 1.12152i) q^{97} +(0.413481 + 0.609839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 23 q^{3} - 25 q^{5} + 23 q^{7} - 21 q^{9}+O(q^{10}) \) 112 * q + 23 * q^3 - 25 * q^5 + 23 * q^7 - 21 * q^9	\( 112 q + 23 q^{3} - 25 q^{5} + 23 q^{7} - 21 q^{9} + 15 q^{11} - 23 q^{13} - 4 q^{15} - 10 q^{17} + 15 q^{19} - 12 q^{21} - 3 q^{23} - 5 q^{25} - 22 q^{27} - 13 q^{29} - 3 q^{31} + 33 q^{33} - 28 q^{35} - 9 q^{37} - 45 q^{39} + 23 q^{41} - 19 q^{43} + 19 q^{45} - 10 q^{47} - 31 q^{49} + 61 q^{51} - 23 q^{53} + 24 q^{55} - 91 q^{57} + 33 q^{59} - 47 q^{61} + 58 q^{63} - 16 q^{65} + 19 q^{67} - 45 q^{69} + 18 q^{71} + 24 q^{73} - 58 q^{75} + 65 q^{77} - 41 q^{79} + 95 q^{81} - 49 q^{83} + 39 q^{85} - 80 q^{87} + 51 q^{89} - 77 q^{91} + 93 q^{93} - 65 q^{95} + 91 q^{97} - 44 q^{99}+O(q^{100}) \) 112 * q + 23 * q^3 - 25 * q^5 + 23 * q^7 - 21 * q^9 + 15 * q^11 - 23 * q^13 - 4 * q^15 - 10 * q^17 + 15 * q^19 - 12 * q^21 - 3 * q^23 - 5 * q^25 - 22 * q^27 - 13 * q^29 - 3 * q^31 + 33 * q^33 - 28 * q^35 - 9 * q^37 - 45 * q^39 + 23 * q^41 - 19 * q^43 + 19 * q^45 - 10 * q^47 - 31 * q^49 + 61 * q^51 - 23 * q^53 + 24 * q^55 - 91 * q^57 + 33 * q^59 - 47 * q^61 + 58 * q^63 - 16 * q^65 + 19 * q^67 - 45 * q^69 + 18 * q^71 + 24 * q^73 - 58 * q^75 + 65 * q^77 - 41 * q^79 + 95 * q^81 - 49 * q^83 + 39 * q^85 - 80 * q^87 + 51 * q^89 - 77 * q^91 + 93 * q^93 - 65 * q^95 + 91 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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