LMFDB - Embedded newform 1472.2.i.b.367.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1472,2,Mod(367,1472)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1472, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1472.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1472 = 2^{6} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1472.i (of order $4$, degree $2$, 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:	$11.7539791775$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			367.12
Character	$\chi$	$=$	1472.367
Dual form			1472.2.i.b.1103.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.860099 + 0.860099i) q^{3} +(-0.0592628 - 0.0592628i) q^{5} -2.65917i q^{7} +1.52046i q^{9} +(3.23118 - 3.23118i) q^{11} +(1.32495 + 1.32495i) q^{13} +0.101944 q^{15} +1.27002i q^{17} +(-4.69664 - 4.69664i) q^{19} +(2.28715 + 2.28715i) q^{21} +(-2.50175 + 4.09161i) q^{23} -4.99298i q^{25} +(-3.88804 - 3.88804i) q^{27} +(-1.21823 - 1.21823i) q^{29} +2.31556i q^{31} +5.55826i q^{33} +(-0.157590 + 0.157590i) q^{35} +(1.54778 + 1.54778i) q^{37} -2.27918 q^{39} -2.46013i q^{41} +(8.21821 - 8.21821i) q^{43} +(0.0901066 - 0.0901066i) q^{45} -1.72980i q^{47} -0.0711808 q^{49} +(-1.09234 - 1.09234i) q^{51} +(-5.85076 - 5.85076i) q^{53} -0.382977 q^{55} +8.07915 q^{57} +(-10.2226 - 10.2226i) q^{59} +(9.18423 - 9.18423i) q^{61} +4.04316 q^{63} -0.157040i q^{65} +(0.241049 + 0.241049i) q^{67} +(-1.36744 - 5.67094i) q^{69} +15.0134 q^{71} +2.20672i q^{73} +(4.29446 + 4.29446i) q^{75} +(-8.59224 - 8.59224i) q^{77} -6.90459 q^{79} +2.12683 q^{81} +(6.96262 + 6.96262i) q^{83} +(0.0752648 - 0.0752648i) q^{85} +2.09559 q^{87} +14.2609 q^{89} +(3.52326 - 3.52326i) q^{91} +(-1.99162 - 1.99162i) q^{93} +0.556672i q^{95} -7.99512i q^{97} +(4.91287 + 4.91287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} - 4 q^{13} - 4 q^{23} - 44 q^{27} - 20 q^{29} - 16 q^{35} + 128 q^{39} - 160 q^{49} + 8 q^{55} - 80 q^{59} - 24 q^{69} + 8 q^{71} + 12 q^{75} + 40 q^{77} + 40 q^{81} - 16 q^{85} + 8 q^{87}+ \cdots - 28 q^{93}+O(q^{100}) $ 80 * q + 4 * q^3 - 4 * q^13 - 4 * q^23 - 44 * q^27 - 20 * q^29 - 16 * q^35 + 128 * q^39 - 160 * q^49 + 8 * q^55 - 80 * q^59 - 24 * q^69 + 8 * q^71 + 12 * q^75 + 40 * q^77 + 40 * q^81 - 16 * q^85 + 8 * q^87 - 28 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1472\mathbb{Z}\right)^\times$.

$n$	$645$	$833$	$1151$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.860099	+	0.860099i	−0.496579	+	0.496579i	−0.910371	−	0.413793i	$-0.864204\pi$
$3$	−0.860099	+	0.860099i	−0.496579	+	0.496579i	0.413793	+	0.910371i	$0.364204\pi$
$4$		0			0
$5$	−0.0592628	−	0.0592628i	−0.0265031	−	0.0265031i	0.693731	−	0.720234i	$-0.255966\pi$
$5$	−0.0592628	−	0.0592628i	−0.0265031	−	0.0265031i	−0.720234	+	0.693731i	$0.755966\pi$
$6$		0			0
$7$		−	2.65917i		−	1.00507i	−0.864556	−	0.502536i	$-0.832401\pi$
$7$		−	2.65917i		−	1.00507i	0.864556	−	0.502536i	$-0.167599\pi$
$8$		0			0
$9$			1.52046i			0.506819i
$10$		0			0
$11$	3.23118	−	3.23118i	0.974236	−	0.974236i	−0.0254403	−	0.999676i	$-0.508099\pi$
$11$	3.23118	−	3.23118i	0.974236	−	0.974236i	0.999676	+	0.0254403i	$0.00809877\pi$
$12$		0			0
$13$	1.32495	+	1.32495i	0.367475	+	0.367475i	0.866555	−	0.499081i	$-0.166329\pi$
$13$	1.32495	+	1.32495i	0.367475	+	0.367475i	−0.499081	+	0.866555i	$0.666329\pi$
$14$		0			0
$15$	0.101944			0.0263218
$16$		0			0
$17$			1.27002i			0.308025i	0.988069	+	0.154012i	$0.0492196\pi$
$17$			1.27002i			0.308025i	−0.988069	+	0.154012i	$0.950780\pi$
$18$		0			0
$19$	−4.69664	−	4.69664i	−1.07748	−	1.07748i	−0.996735	−	0.0807484i	$-0.974269\pi$
$19$	−4.69664	−	4.69664i	−1.07748	−	1.07748i	−0.0807484	−	0.996735i	$-0.525731\pi$
$20$		0			0
$21$	2.28715	+	2.28715i	0.499097	+	0.499097i
$22$		0			0
$23$	−2.50175	+	4.09161i	−0.521651	+	0.853159i
$23$	−2.50175	+	4.09161i	−0.521651	+	0.853159i
$24$		0			0
$25$		−	4.99298i		−	0.998595i
$26$		0			0
$27$	−3.88804	−	3.88804i	−0.748254	−	0.748254i
$28$		0			0
$29$	−1.21823	−	1.21823i	−0.226219	−	0.226219i	0.584892	−	0.811111i	$-0.301137\pi$
$29$	−1.21823	−	1.21823i	−0.226219	−	0.226219i	−0.811111	+	0.584892i	$0.801137\pi$
$30$		0			0
$31$			2.31556i			0.415888i	0.978141	+	0.207944i	$0.0666771\pi$
$31$			2.31556i			0.415888i	−0.978141	+	0.207944i	$0.933323\pi$
$32$		0			0
$33$			5.55826i			0.967570i
$34$		0			0
$35$	−0.157590	+	0.157590i	−0.0266375	+	0.0266375i
$36$		0			0
$37$	1.54778	+	1.54778i	0.254454	+	0.254454i	0.822794	−	0.568340i	$-0.192414\pi$
$37$	1.54778	+	1.54778i	0.254454	+	0.254454i	−0.568340	+	0.822794i	$0.692414\pi$
$38$		0			0
$39$	−2.27918			−0.364960
$40$		0			0
$41$		−	2.46013i		−	0.384208i	−0.981375	−	0.192104i	$-0.938469\pi$
$41$		−	2.46013i		−	0.384208i	0.981375	−	0.192104i	$-0.0615310\pi$
$42$		0			0
$43$	8.21821	−	8.21821i	1.25326	−	1.25326i	0.299017	−	0.954248i	$-0.403341\pi$
$43$	8.21821	−	8.21821i	1.25326	−	1.25326i	0.954248	−	0.299017i	$-0.0966588\pi$
$44$		0			0
$45$	0.0901066	−	0.0901066i	0.0134323	−	0.0134323i
$46$		0			0
$47$		−	1.72980i		−	0.252317i	−0.992010	−	0.126159i	$-0.959735\pi$
$47$		−	1.72980i		−	0.252317i	0.992010	−	0.126159i	$-0.0402648\pi$
$48$		0			0
$49$	−0.0711808			−0.0101687
$50$		0			0
$51$	−1.09234	−	1.09234i	−0.152959	−	0.152959i
$52$		0			0
$53$	−5.85076	−	5.85076i	−0.803663	−	0.803663i	0.180003	−	0.983666i	$-0.442389\pi$
$53$	−5.85076	−	5.85076i	−0.803663	−	0.803663i	−0.983666	+	0.180003i	$0.942389\pi$
$54$		0			0
$55$	−0.382977			−0.0516406
$56$		0			0
$57$	8.07915			1.07011
$58$		0			0
$59$	−10.2226	−	10.2226i	−1.33088	−	1.33088i	−0.904588	−	0.426287i	$-0.859821\pi$
$59$	−10.2226	−	10.2226i	−1.33088	−	1.33088i	−0.426287	−	0.904588i	$-0.640179\pi$
$60$		0			0
$61$	9.18423	−	9.18423i	1.17592	−	1.17592i	0.195146	−	0.980774i	$-0.437482\pi$
$61$	9.18423	−	9.18423i	1.17592	−	1.17592i	0.980774	−	0.195146i	$-0.0625180\pi$
$62$		0			0
$63$	4.04316			0.509390
$64$		0			0
$65$		−	0.157040i		−	0.0194785i
$66$		0			0
$67$	0.241049	+	0.241049i	0.0294489	+	0.0294489i	0.721678	−	0.692229i	$-0.243371\pi$
$67$	0.241049	+	0.241049i	0.0294489	+	0.0294489i	−0.692229	+	0.721678i	$0.743371\pi$
$68$		0			0
$69$	−1.36744	−	5.67094i	−0.164620	−	0.682701i
$70$		0			0
$71$	15.0134			1.78176			0.890879	−	0.454241i	$-0.150089\pi$
$71$	15.0134			1.78176			0.890879	+	0.454241i	$0.150089\pi$
$72$		0			0
$73$			2.20672i			0.258277i	0.991627	+	0.129139i	$0.0412212\pi$
$73$			2.20672i			0.258277i	−0.991627	+	0.129139i	$0.958779\pi$
$74$		0			0
$75$	4.29446	+	4.29446i	0.495881	+	0.495881i
$76$		0			0
$77$	−8.59224	−	8.59224i	−0.979177	−	0.979177i
$78$		0			0
$79$	−6.90459			−0.776827			−0.388414	−	0.921485i	$-0.626977\pi$
$79$	−6.90459			−0.776827			−0.388414	+	0.921485i	$0.626977\pi$
$80$		0			0
$81$	2.12683			0.236315
$82$		0			0
$83$	6.96262	+	6.96262i	0.764247	+	0.764247i	0.977087	−	0.212840i	$-0.0682714\pi$
$83$	6.96262	+	6.96262i	0.764247	+	0.764247i	−0.212840	+	0.977087i	$0.568271\pi$
$84$		0			0
$85$	0.0752648	−	0.0752648i	0.00816362	−	0.00816362i
$86$		0			0
$87$	2.09559			0.224671
$88$		0			0
$89$	14.2609			1.51166			0.755828	−	0.654771i	$-0.227235\pi$
$89$	14.2609			1.51166			0.755828	+	0.654771i	$0.227235\pi$
$90$		0			0
$91$	3.52326	−	3.52326i	0.369338	−	0.369338i
$92$		0			0
$93$	−1.99162	−	1.99162i	−0.206521	−	0.206521i
$94$		0			0
$95$			0.556672i			0.0571133i
$96$		0			0
$97$		−	7.99512i		−	0.811781i	−0.913922	−	0.405891i	$-0.866961\pi$
$97$		−	7.99512i		−	0.811781i	0.913922	−	0.405891i	$-0.133039\pi$
$98$		0			0
$99$	4.91287	+	4.91287i	0.493762	+	0.493762i
$100$		0			0
$101$	−3.64570	+	3.64570i	−0.362760	+	0.362760i	−0.864828	−	0.502068i	$-0.832573\pi$
$101$	−3.64570	+	3.64570i	−0.362760	+	0.362760i	0.502068	+	0.864828i	$0.332573\pi$
$102$		0			0
$103$			13.3253i			1.31298i	0.754333	+	0.656492i	$0.227961\pi$
$103$			13.3253i			1.31298i	−0.754333	+	0.656492i	$0.772039\pi$
$104$		0			0
$105$		−	0.271086i		−	0.0264553i
$106$		0			0
$107$	7.02903	−	7.02903i	0.679522	−	0.679522i	−0.280370	−	0.959892i	$-0.590457\pi$
$107$	7.02903	−	7.02903i	0.679522	−	0.679522i	0.959892	+	0.280370i	$0.0904570\pi$
$108$		0			0
$109$	3.12657	−	3.12657i	0.299471	−	0.299471i	−0.541335	−	0.840807i	$-0.682081\pi$
$109$	3.12657	−	3.12657i	0.299471	−	0.299471i	0.840807	+	0.541335i	$0.182081\pi$
$110$		0			0
$111$	−2.66250			−0.252713
$112$		0			0
$113$		−	8.66950i		−	0.815558i	−0.913081	−	0.407779i	$-0.866303\pi$
$113$		−	8.66950i		−	0.815558i	0.913081	−	0.407779i	$-0.133697\pi$
$114$		0			0
$115$	0.390741	−	0.0942195i	0.0364367	−	0.00878601i
$116$		0			0
$117$	−2.01453	+	2.01453i	−0.186243	+	0.186243i
$118$		0			0
$119$	3.37719			0.309587
$120$		0			0
$121$		−	9.88099i		−	0.898272i
$122$		0			0
$123$	2.11596	+	2.11596i	0.190789	+	0.190789i
$124$		0			0
$125$	−0.592211	+	0.592211i	−0.0529690	+	0.0529690i
$126$		0			0
$127$		−	5.22135i		−	0.463320i	−0.972797	−	0.231660i	$-0.925584\pi$
$127$		−	5.22135i		−	0.463320i	0.972797	−	0.231660i	$-0.0744157\pi$
$128$		0			0
$129$			14.1370i			1.24469i
$130$		0			0
$131$	−3.33453	+	3.33453i	−0.291339	+	0.291339i	−0.837609	−	0.546270i	$-0.816047\pi$
$131$	−3.33453	+	3.33453i	−0.291339	+	0.291339i	0.546270	+	0.837609i	$0.316047\pi$
$132$		0			0
$133$	−12.4892	+	12.4892i	−1.08295	+	1.08295i
$134$		0			0
$135$			0.460832i			0.0396621i
$136$		0			0
$137$	7.42500			0.634361			0.317180	−	0.948365i	$-0.397264\pi$
$137$	7.42500			0.634361			0.317180	+	0.948365i	$0.397264\pi$
$138$		0			0
$139$	−6.66197	−	6.66197i	−0.565061	−	0.565061i	0.365680	−	0.930741i	$-0.380836\pi$
$139$	−6.66197	−	6.66197i	−0.565061	−	0.565061i	−0.930741	+	0.365680i	$0.880836\pi$
$140$		0			0
$141$	1.48780	+	1.48780i	0.125295	+	0.125295i
$142$		0			0
$143$	8.56229			0.716014
$144$		0			0
$145$			0.144391i			0.0119910i
$146$		0			0
$147$	0.0612226	−	0.0612226i	0.00504955	−	0.00504955i
$148$		0			0
$149$	−6.57835	−	6.57835i	−0.538920	−	0.538920i	0.384292	−	0.923212i	$-0.374446\pi$
$149$	−6.57835	−	6.57835i	−0.538920	−	0.538920i	−0.923212	+	0.384292i	$0.874446\pi$
$150$		0			0
$151$	−15.6057			−1.26997			−0.634986	−	0.772524i	$-0.718994\pi$
$151$	−15.6057			−1.26997			−0.634986	+	0.772524i	$0.718994\pi$
$152$		0			0
$153$	−1.93101			−0.156113
$154$		0			0
$155$	0.137227	−	0.137227i	0.0110223	−	0.0110223i
$156$		0			0
$157$	−6.05567	+	6.05567i	−0.483295	+	0.483295i	−0.906182	−	0.422887i	$-0.861017\pi$
$157$	−6.05567	+	6.05567i	−0.483295	+	0.483295i	0.422887	+	0.906182i	$0.361017\pi$
$158$		0			0
$159$	10.0645			0.798164
$160$		0			0
$161$	10.8803	+	6.65257i	0.857486	+	0.524296i
$162$		0			0
$163$	10.7888	−	10.7888i	0.845040	−	0.845040i	−0.144469	−	0.989509i	$-0.546147\pi$
$163$	10.7888	−	10.7888i	0.845040	−	0.845040i	0.989509	+	0.144469i	$0.0461474\pi$
$164$		0			0
$165$	0.329398	−	0.329398i	0.0256436	−	0.0256436i
$166$		0			0
$167$	6.67959			0.516882			0.258441	−	0.966027i	$-0.416791\pi$
$167$	6.67959			0.516882			0.258441	+	0.966027i	$0.416791\pi$
$168$		0			0
$169$		−	9.48902i		−	0.729925i
$170$		0			0
$171$	7.14104	−	7.14104i	0.546089	−	0.546089i
$172$		0			0
$173$	9.10911	+	9.10911i	0.692553	+	0.692553i	0.962793	−	0.270240i	$-0.0871030\pi$
$173$	9.10911	+	9.10911i	0.692553	+	0.692553i	−0.270240	+	0.962793i	$0.587103\pi$
$174$		0			0
$175$	−13.2772			−1.00366
$176$		0			0
$177$	17.5850			1.32177
$178$		0			0
$179$	−0.0909711	+	0.0909711i	−0.00679950	+	0.00679950i	−0.710498	−	0.703699i	$-0.751530\pi$
$179$	−0.0909711	+	0.0909711i	−0.00679950	+	0.00679950i	0.703699	+	0.710498i	$0.251530\pi$
$180$		0			0
$181$	−11.3170	−	11.3170i	−0.841187	−	0.841187i	0.147826	−	0.989013i	$-0.452772\pi$
$181$	−11.3170	−	11.3170i	−0.841187	−	0.841187i	−0.989013	+	0.147826i	$0.952772\pi$
$182$		0			0
$183$			15.7987i			1.16787i
$184$		0			0
$185$		−	0.183452i		−	0.0134877i
$186$		0			0
$187$	4.10365	+	4.10365i	0.300089	+	0.300089i
$188$		0			0
$189$	−10.3390	+	10.3390i	−0.752049	+	0.752049i
$190$		0			0
$191$	−15.7543			−1.13994			−0.569972	−	0.821664i	$-0.693046\pi$
$191$	−15.7543			−1.13994			−0.569972	+	0.821664i	$0.693046\pi$
$192$		0			0
$193$	−9.94979			−0.716202			−0.358101	−	0.933683i	$-0.616576\pi$
$193$	−9.94979			−0.716202			−0.358101	+	0.933683i	$0.616576\pi$
$194$		0			0
$195$	0.135070	+	0.135070i	0.00967258	+	0.00967258i
$196$		0			0
$197$	12.0238	−	12.0238i	0.856661	−	0.856661i	−0.134282	−	0.990943i	$-0.542873\pi$
$197$	12.0238	−	12.0238i	0.856661	−	0.856661i	0.990943	+	0.134282i	$0.0428729\pi$
$198$		0			0
$199$		−	12.1254i		−	0.859544i	−0.902937	−	0.429772i	$-0.858594\pi$
$199$		−	12.1254i		−	0.859544i	0.902937	−	0.429772i	$-0.141406\pi$
$200$		0			0
$201$	−0.414653			−0.0292473
$202$		0			0
$203$	−3.23947	+	3.23947i	−0.227366	+	0.227366i
$204$		0			0
$205$	−0.145794	+	0.145794i	−0.0101827	+	0.0101827i
$206$		0			0
$207$	−6.22112	−	3.80380i	−0.432398	−	0.264383i
$208$		0			0
$209$	−30.3513			−2.09945
$210$		0			0
$211$	−8.84817	+	8.84817i	−0.609133	+	0.609133i	−0.942720	−	0.333586i	$-0.891741\pi$
$211$	−8.84817	+	8.84817i	−0.609133	+	0.609133i	0.333586	+	0.942720i	$0.391741\pi$
$212$		0			0
$213$	−12.9130	+	12.9130i	−0.884783	+	0.884783i
$214$		0			0
$215$	−0.974067			−0.0664308
$216$		0			0
$217$	6.15748			0.417997
$218$		0			0
$219$	−1.89800	−	1.89800i	−0.128255	−	0.128255i
$220$		0			0
$221$	−1.68271	+	1.68271i	−0.113191	+	0.113191i
$222$		0			0
$223$			8.33600i			0.558220i	0.960259	+	0.279110i	$0.0900394\pi$
$223$			8.33600i			0.558220i	−0.960259	+	0.279110i	$0.909961\pi$
$224$		0			0
$225$	7.59161			0.506107
$226$		0			0
$227$	−4.72544	−	4.72544i	−0.313638	−	0.313638i	0.532679	−	0.846317i	$-0.321185\pi$
$227$	−4.72544	−	4.72544i	−0.313638	−	0.313638i	−0.846317	+	0.532679i	$0.821185\pi$
$228$		0			0
$229$	−15.7355	−	15.7355i	−1.03983	−	1.03983i	−0.999173	−	0.0406573i	$-0.987055\pi$
$229$	−15.7355	−	15.7355i	−1.03983	−	1.03983i	−0.0406573	−	0.999173i	$-0.512945\pi$
$230$		0			0
$231$	14.7804			0.972477
$232$		0			0
$233$			5.06132i			0.331578i	0.986161	+	0.165789i	$0.0530171\pi$
$233$			5.06132i			0.331578i	−0.986161	+	0.165789i	$0.946983\pi$
$234$		0			0
$235$	−0.102513	+	0.102513i	−0.00668720	+	0.00668720i
$236$		0			0
$237$	5.93863	−	5.93863i	0.385756	−	0.385756i
$238$		0			0
$239$			25.4452i			1.64591i	0.568105	+	0.822956i	$0.307677\pi$
$239$			25.4452i			1.64591i	−0.568105	+	0.822956i	$0.692323\pi$
$240$		0			0
$241$			7.67284i			0.494251i	0.968983	+	0.247126i	$0.0794860\pi$
$241$			7.67284i			0.494251i	−0.968983	+	0.247126i	$0.920514\pi$
$242$		0			0
$243$	9.83484	−	9.83484i	0.630905	−	0.630905i
$244$		0			0
$245$	0.00421837	+	0.00421837i	0.000269502	+	0.000269502i
$246$		0			0
$247$		−	12.4456i		−	0.791896i
$248$		0			0
$249$	−11.9771			−0.759017
$250$		0			0
$251$	−18.0092	+	18.0092i	−1.13673	+	1.13673i	−0.147695	+	0.989033i	$0.547186\pi$
$251$	−18.0092	+	18.0092i	−1.13673	+	1.13673i	−0.989033	+	0.147695i	$0.952814\pi$
$252$		0			0
$253$	5.13712	+	21.3043i	0.322968	+	1.33939i
$254$		0			0
$255$			0.129470i			0.00810776i
$256$		0			0
$257$	−11.5321			−0.719351			−0.359675	−	0.933077i	$-0.617113\pi$
$257$	−11.5321			−0.719351			−0.359675	+	0.933077i	$0.617113\pi$
$258$		0			0
$259$	4.11582	−	4.11582i	0.255745	−	0.255745i
$260$		0			0
$261$	1.85226	−	1.85226i	0.114652	−	0.114652i
$262$		0			0
$263$			25.8401i			1.59337i	0.604396	+	0.796684i	$0.293414\pi$
$263$			25.8401i			1.59337i	−0.604396	+	0.796684i	$0.706586\pi$
$264$		0			0
$265$			0.693464i			0.0425992i
$266$		0			0
$267$	−12.2658	+	12.2658i	−0.750656	+	0.750656i
$268$		0			0
$269$	12.0864	+	12.0864i	0.736922	+	0.736922i	0.971981	−	0.235059i	$-0.0755284\pi$
$269$	12.0864	+	12.0864i	0.736922	+	0.736922i	−0.235059	+	0.971981i	$0.575528\pi$
$270$		0			0
$271$			19.6896i			1.19606i	0.801474	+	0.598030i	$0.204050\pi$
$271$			19.6896i			1.19606i	−0.801474	+	0.598030i	$0.795950\pi$
$272$		0			0
$273$			6.06071i			0.366811i
$274$		0			0
$275$	−16.1332	−	16.1332i	−0.972867	−	0.972867i
$276$		0			0
$277$	−8.60109	+	8.60109i	−0.516789	+	0.516789i	−0.916598	−	0.399809i	$-0.869076\pi$
$277$	−8.60109	+	8.60109i	−0.516789	+	0.516789i	0.399809	+	0.916598i	$0.369076\pi$
$278$		0			0
$279$	−3.52072			−0.210780
$280$		0			0
$281$	28.6536			1.70933			0.854665	−	0.519181i	$-0.173763\pi$
$281$	28.6536			1.70933			0.854665	+	0.519181i	$0.173763\pi$
$282$		0			0
$283$	4.00191	−	4.00191i	0.237889	−	0.237889i	−0.578086	−	0.815976i	$-0.696200\pi$
$283$	4.00191	−	4.00191i	0.237889	−	0.237889i	0.815976	+	0.578086i	$0.196200\pi$
$284$		0			0
$285$	−0.478793	−	0.478793i	−0.0283612	−	0.0283612i
$286$		0			0
$287$	−6.54190			−0.386156
$288$		0			0
$289$	15.3871			0.905121
$290$		0			0
$291$	6.87660	+	6.87660i	0.403113	+	0.403113i
$292$		0			0
$293$	9.94696	+	9.94696i	0.581107	+	0.581107i	0.935208	−	0.354100i	$-0.115213\pi$
$293$	9.94696	+	9.94696i	0.581107	+	0.581107i	−0.354100	+	0.935208i	$0.615213\pi$
$294$		0			0
$295$			1.21164i			0.0705447i
$296$		0			0
$297$	−25.1259			−1.45795
$298$		0			0
$299$	−8.73586	+	2.10648i	−0.505208	+	0.121821i
$300$		0			0
$301$	−21.8536	−	21.8536i	−1.25962	−	1.25962i
$302$		0			0
$303$		−	6.27132i		−	0.360278i
$304$		0			0
$305$	−1.08857			−0.0623311
$306$		0			0
$307$	−10.7455	+	10.7455i	−0.613280	+	0.613280i	−0.943799	−	0.330519i	$-0.892776\pi$
$307$	−10.7455	+	10.7455i	−0.613280	+	0.613280i	0.330519	+	0.943799i	$0.392776\pi$
$308$		0			0
$309$	−11.4611	−	11.4611i	−0.652000	−	0.652000i
$310$		0			0
$311$	−14.1242			−0.800908			−0.400454	−	0.916317i	$-0.631148\pi$
$311$	−14.1242			−0.800908			−0.400454	+	0.916317i	$0.631148\pi$
$312$		0			0
$313$	−24.3707			−1.37751			−0.688757	−	0.724992i	$-0.741843\pi$
$313$	−24.3707			−1.37751			−0.688757	+	0.724992i	$0.741843\pi$
$314$		0			0
$315$	−0.239609	−	0.239609i	−0.0135004	−	0.0135004i
$316$		0			0
$317$	10.5047	+	10.5047i	0.590001	+	0.590001i	0.937632	−	0.347630i	$-0.113014\pi$
$317$	10.5047	+	10.5047i	0.590001	+	0.590001i	−0.347630	+	0.937632i	$0.613014\pi$
$318$		0			0
$319$	−7.87261			−0.440781
$320$		0			0
$321$			12.0913i			0.674873i
$322$		0			0
$323$	5.96482	−	5.96482i	0.331891	−	0.331891i
$324$		0			0
$325$	6.61544	−	6.61544i	0.366959	−	0.366959i
$326$		0			0
$327$			5.37833i			0.297422i
$328$		0			0
$329$	−4.59983			−0.253597
$330$		0			0
$331$	8.83567	+	8.83567i	0.485652	+	0.485652i	0.906931	−	0.421279i	$-0.138419\pi$
$331$	8.83567	+	8.83567i	0.485652	+	0.485652i	−0.421279	+	0.906931i	$0.638419\pi$
$332$		0			0
$333$	−2.35334	+	2.35334i	−0.128962	+	0.128962i
$334$		0			0
$335$		−	0.0285705i		−	0.00156097i
$336$		0			0
$337$		−	10.6494i		−	0.580110i	−0.957010	−	0.290055i	$-0.906326\pi$
$337$		−	10.6494i		−	0.580110i	0.957010	−	0.290055i	$-0.0936735\pi$
$338$		0			0
$339$	7.45663	+	7.45663i	0.404989	+	0.404989i
$340$		0			0
$341$	7.48199	+	7.48199i	0.405173	+	0.405173i
$342$		0			0
$343$		−	18.4249i		−	0.994851i
$344$		0			0
$345$	−0.255038	+	0.417114i	−0.0137308	+	0.0224567i
$346$		0			0
$347$	16.4276	+	16.4276i	0.881879	+	0.881879i	0.993725	−	0.111847i	$-0.0356765\pi$
$347$	16.4276	+	16.4276i	0.881879	+	0.881879i	−0.111847	+	0.993725i	$0.535677\pi$
$348$		0			0
$349$	−5.53040	−	5.53040i	−0.296036	−	0.296036i	0.543423	−	0.839459i	$-0.317128\pi$
$349$	−5.53040	−	5.53040i	−0.296036	−	0.296036i	−0.839459	+	0.543423i	$0.817128\pi$
$350$		0			0
$351$		−	10.3029i		−	0.549929i
$352$		0			0
$353$	32.2050			1.71410			0.857050	−	0.515233i	$-0.172295\pi$
$353$	32.2050			1.71410			0.857050	+	0.515233i	$0.172295\pi$
$354$		0			0
$355$	−0.889733	−	0.889733i	−0.0472221	−	0.0472221i
$356$		0			0
$357$	−2.90472	+	2.90472i	−0.153734	+	0.153734i
$358$		0			0
$359$		−	13.6769i		−	0.721838i	−0.932597	−	0.360919i	$-0.882463\pi$
$359$		−	13.6769i		−	0.721838i	0.932597	−	0.360919i	$-0.117537\pi$
$360$		0			0
$361$			25.1168i			1.32194i
$362$		0			0
$363$	8.49863	+	8.49863i	0.446063	+	0.446063i
$364$		0			0
$365$	0.130776	−	0.130776i	0.00684515	−	0.00684515i
$366$		0			0
$367$	−18.4813			−0.964716			−0.482358	−	0.875974i	$-0.660220\pi$
$367$	−18.4813			−0.964716			−0.482358	+	0.875974i	$0.660220\pi$
$368$		0			0
$369$	3.74052			0.194724
$370$		0			0
$371$	−15.5582	+	15.5582i	−0.807739	+	0.807739i
$372$		0			0
$373$	2.68817	+	2.68817i	0.139188	+	0.139188i	0.773268	−	0.634080i	$-0.218621\pi$
$373$	2.68817	+	2.68817i	0.139188	+	0.139188i	−0.634080	+	0.773268i	$0.718621\pi$
$374$		0			0
$375$		−	1.01872i		−	0.0526065i
$376$		0			0
$377$		−	3.22818i		−	0.166260i
$378$		0			0
$379$	17.1581	−	17.1581i	0.881353	−	0.881353i	−0.112319	−	0.993672i	$-0.535828\pi$
$379$	17.1581	−	17.1581i	0.881353	−	0.881353i	0.993672	+	0.112319i	$0.0358279\pi$
$380$		0			0
$381$	4.49088	+	4.49088i	0.230075	+	0.230075i
$382$		0			0
$383$	9.20129			0.470164			0.235082	−	0.971976i	$-0.424464\pi$
$383$	9.20129			0.470164			0.235082	+	0.971976i	$0.424464\pi$
$384$		0			0
$385$			1.01840i			0.0519025i
$386$		0			0
$387$	12.4954	+	12.4954i	0.635179	+	0.635179i
$388$		0			0
$389$	19.1433	+	19.1433i	0.970606	+	0.970606i	0.999580	−	0.0289741i	$-0.00922403\pi$
$389$	19.1433	+	19.1433i	0.970606	+	0.970606i	−0.0289741	+	0.999580i	$0.509224\pi$
$390$		0			0
$391$	−5.19642	−	3.17727i	−0.262794	−	0.160681i
$392$		0			0
$393$		−	5.73606i		−	0.289346i
$394$		0			0
$395$	0.409185	+	0.409185i	0.0205883	+	0.0205883i
$396$		0			0
$397$	4.43182	+	4.43182i	0.222426	+	0.222426i	0.809519	−	0.587093i	$-0.199728\pi$
$397$	4.43182	+	4.43182i	0.222426	+	0.222426i	−0.587093	+	0.809519i	$0.699728\pi$
$398$		0			0
$399$		−	21.4838i		−	1.07554i
$400$		0			0
$401$			9.14611i			0.456735i	0.973575	+	0.228367i	$0.0733388\pi$
$401$			9.14611i			0.456735i	−0.973575	+	0.228367i	$0.926661\pi$
$402$		0			0
$403$	−3.06801	+	3.06801i	−0.152828	+	0.152828i
$404$		0			0
$405$	−0.126042	−	0.126042i	−0.00626308	−	0.00626308i
$406$		0			0
$407$	10.0023			0.495797
$408$		0			0
$409$			38.6304i			1.91015i	0.296365	+	0.955075i	$0.404225\pi$
$409$			38.6304i			1.91015i	−0.296365	+	0.955075i	$0.595775\pi$
$410$		0			0
$411$	−6.38624	+	6.38624i	−0.315010	+	0.315010i
$412$		0			0
$413$	−27.1837	+	27.1837i	−1.33762	+	1.33762i
$414$		0			0
$415$		−	0.825248i		−	0.0405098i
$416$		0			0
$417$	11.4599			0.561194
$418$		0			0
$419$	−12.1063	−	12.1063i	−0.591429	−	0.591429i	0.346588	−	0.938017i	$-0.387340\pi$
$419$	−12.1063	−	12.1063i	−0.591429	−	0.591429i	−0.938017	+	0.346588i	$0.887340\pi$
$420$		0			0
$421$	13.6001	+	13.6001i	0.662827	+	0.662827i	0.956045	−	0.293219i	$-0.0947264\pi$
$421$	13.6001	+	13.6001i	0.662827	+	0.662827i	−0.293219	+	0.956045i	$0.594726\pi$
$422$		0			0
$423$	2.63009			0.127879
$424$		0			0
$425$	6.34117			0.307592
$426$		0			0
$427$	−24.4224	−	24.4224i	−1.18188	−	1.18188i
$428$		0			0
$429$	−7.36442	+	7.36442i	−0.355557	+	0.355557i
$430$		0			0
$431$	−6.75253			−0.325258			−0.162629	−	0.986687i	$-0.551997\pi$
$431$	−6.75253			−0.325258			−0.162629	+	0.986687i	$0.551997\pi$
$432$		0			0
$433$		−	8.63103i		−	0.414781i	−0.978258	−	0.207390i	$-0.933503\pi$
$433$		−	8.63103i		−	0.414781i	0.978258	−	0.207390i	$-0.0664970\pi$
$434$		0			0
$435$	−0.124191	−	0.124191i	−0.00595448	−	0.00595448i
$436$		0			0
$437$	30.9666	−	7.46700i	1.48133	−	0.357195i
$438$		0			0
$439$	23.6988			1.13108			0.565540	−	0.824721i	$-0.308668\pi$
$439$	23.6988			1.13108			0.565540	+	0.824721i	$0.308668\pi$
$440$		0			0
$441$		−	0.108227i		−	0.00515369i
$442$		0			0
$443$	16.5520	+	16.5520i	0.786407	+	0.786407i	0.980903	−	0.194496i	$-0.0623071\pi$
$443$	16.5520	+	16.5520i	0.786407	+	0.786407i	−0.194496	+	0.980903i	$0.562307\pi$
$444$		0			0
$445$	−0.845142	−	0.845142i	−0.0400636	−	0.0400636i
$446$		0			0
$447$	11.3161			0.535232
$448$		0			0
$449$	−22.5417			−1.06381			−0.531904	−	0.846804i	$-0.678523\pi$
$449$	−22.5417			−1.06381			−0.531904	+	0.846804i	$0.678523\pi$
$450$		0			0
$451$	−7.94911	−	7.94911i	−0.374309	−	0.374309i
$452$		0			0
$453$	13.4224	−	13.4224i	0.630641	−	0.630641i
$454$		0			0
$455$	−0.417597			−0.0195772
$456$		0			0
$457$	−19.8676			−0.929365			−0.464683	−	0.885477i	$-0.653832\pi$
$457$	−19.8676			−0.929365			−0.464683	+	0.885477i	$0.653832\pi$
$458$		0			0
$459$	4.93789	−	4.93789i	0.230481	−	0.230481i
$460$		0			0
$461$	−28.8571	−	28.8571i	−1.34401	−	1.34401i	−0.892027	−	0.451982i	$-0.850717\pi$
$461$	−28.8571	−	28.8571i	−1.34401	−	1.34401i	−0.451982	−	0.892027i	$-0.649283\pi$
$462$		0			0
$463$		−	23.6252i		−	1.09796i	−0.835837	−	0.548978i	$-0.815017\pi$
$463$		−	23.6252i		−	1.09796i	0.835837	−	0.548978i	$-0.184983\pi$
$464$		0			0
$465$			0.236057i			0.0109469i
$466$		0			0
$467$	−2.66814	−	2.66814i	−0.123467	−	0.123467i	0.642674	−	0.766140i	$-0.277825\pi$
$467$	−2.66814	−	2.66814i	−0.123467	−	0.123467i	−0.766140	+	0.642674i	$0.777825\pi$
$468$		0			0
$469$	0.640991	−	0.640991i	0.0295982	−	0.0295982i
$470$		0			0
$471$		−	10.4170i		−	0.479988i
$472$		0			0
$473$		−	53.1089i		−	2.44195i
$474$		0			0
$475$	−23.4502	+	23.4502i	−1.07597	+	1.07597i
$476$		0			0
$477$	8.89583	−	8.89583i	0.407312	−	0.407312i
$478$		0			0
$479$	13.6769			0.624914			0.312457	−	0.949932i	$-0.398848\pi$
$479$	13.6769			0.624914			0.312457	+	0.949932i	$0.398848\pi$
$480$		0			0
$481$			4.10147i			0.187011i
$482$		0			0
$483$	−15.0800	+	3.63625i	−0.686163	+	0.165455i
$484$		0			0
$485$	−0.473813	+	0.473813i	−0.0215147	+	0.0215147i
$486$		0			0
$487$	−15.9805			−0.724144			−0.362072	−	0.932150i	$-0.617931\pi$
$487$	−15.9805			−0.724144			−0.362072	+	0.932150i	$0.617931\pi$
$488$		0			0
$489$			18.5588i			0.839258i
$490$		0			0
$491$	−23.4883	−	23.4883i	−1.06001	−	1.06001i	−0.998081	−	0.0619296i	$-0.980275\pi$
$491$	−23.4883	−	23.4883i	−1.06001	−	1.06001i	−0.0619296	−	0.998081i	$-0.519725\pi$
$492$		0			0
$493$	1.54717	−	1.54717i	0.0696811	−	0.0696811i
$494$		0			0
$495$		−	0.582300i		−	0.0261724i
$496$		0			0
$497$		−	39.9231i		−	1.79079i
$498$		0			0
$499$	−25.4995	+	25.4995i	−1.14152	+	1.14152i	−0.153343	+	0.988173i	$0.549004\pi$
$499$	−25.4995	+	25.4995i	−1.14152	+	1.14152i	−0.988173	+	0.153343i	$0.950996\pi$
$500$		0			0
$501$	−5.74511	+	5.74511i	−0.256673	+	0.256673i
$502$		0			0
$503$			19.6250i			0.875035i	0.899210	+	0.437517i	$0.144142\pi$
$503$			19.6250i			0.875035i	−0.899210	+	0.437517i	$0.855858\pi$
$504$		0			0
$505$	0.432108			0.0192286
$506$		0			0
$507$	8.16150	+	8.16150i	0.362465	+	0.362465i
$508$		0			0
$509$	12.6219	+	12.6219i	0.559456	+	0.559456i	0.929153	−	0.369697i	$-0.120538\pi$
$509$	12.6219	+	12.6219i	0.559456	+	0.559456i	−0.369697	+	0.929153i	$0.620538\pi$
$510$		0			0
$511$	5.86805			0.259587
$512$		0			0
$513$			36.5215i			1.61246i
$514$		0			0
$515$	0.789696	−	0.789696i	0.0347982	−	0.0347982i
$516$		0			0
$517$	−5.58929	−	5.58929i	−0.245817	−	0.245817i
$518$		0			0
$519$	−15.6695			−0.687814
$520$		0			0
$521$	−12.0617			−0.528434			−0.264217	−	0.964463i	$-0.585114\pi$
$521$	−12.0617			−0.528434			−0.264217	+	0.964463i	$0.585114\pi$
$522$		0			0
$523$	−1.82928	+	1.82928i	−0.0799888	+	0.0799888i	−0.745969	−	0.665980i	$-0.768013\pi$
$523$	−1.82928	+	1.82928i	−0.0799888	+	0.0799888i	0.665980	+	0.745969i	$0.268013\pi$
$524$		0			0
$525$	11.4197	−	11.4197i	0.498396	−	0.498396i
$526$		0			0
$527$	−2.94081			−0.128104
$528$		0			0
$529$	−10.4825	−	20.4723i	−0.455761	−	0.890102i
$530$		0			0
$531$	15.5431	−	15.5431i	0.674513	−	0.674513i
$532$		0			0
$533$	3.25955	−	3.25955i	0.141187	−	0.141187i
$534$		0			0
$535$	−0.833120			−0.0360189
$536$		0			0
$537$		−	0.156488i		−	0.00675297i
$538$		0			0
$539$	−0.229998	+	0.229998i	−0.00990670	+	0.00990670i
$540$		0			0
$541$	−1.64738	−	1.64738i	−0.0708265	−	0.0708265i	0.670806	−	0.741633i	$-0.265948\pi$
$541$	−1.64738	−	1.64738i	−0.0708265	−	0.0708265i	−0.741633	+	0.670806i	$0.765948\pi$
$542$		0			0
$543$	19.4675			0.835431
$544$		0			0
$545$	−0.370579			−0.0158738
$546$		0			0
$547$	18.0346	−	18.0346i	0.771105	−	0.771105i	−0.207195	−	0.978300i	$-0.566433\pi$
$547$	18.0346	−	18.0346i	0.771105	−	0.771105i	0.978300	+	0.207195i	$0.0664333\pi$
$548$		0			0
$549$	13.9642	+	13.9642i	0.595979	+	0.595979i
$550$		0			0
$551$			11.4431i			0.487494i
$552$		0			0
$553$			18.3605i			0.780767i
$554$		0			0
$555$	0.157787	+	0.157787i	0.00669768	+	0.00669768i
$556$		0			0
$557$	14.7445	−	14.7445i	0.624743	−	0.624743i	−0.321997	−	0.946741i	$-0.604354\pi$
$557$	14.7445	−	14.7445i	0.624743	−	0.624743i	0.946741	+	0.321997i	$0.104354\pi$
$558$		0			0
$559$	21.7774			0.921086
$560$		0			0
$561$	−7.05910			−0.298035
$562$		0			0
$563$	−7.74891	−	7.74891i	−0.326578	−	0.326578i	0.524706	−	0.851284i	$-0.324175\pi$
$563$	−7.74891	−	7.74891i	−0.326578	−	0.326578i	−0.851284	+	0.524706i	$0.824175\pi$
$564$		0			0
$565$	−0.513779	+	0.513779i	−0.0216148	+	0.0216148i
$566$		0			0
$567$		−	5.65561i		−	0.237513i
$568$		0			0
$569$	−3.63750			−0.152492			−0.0762460	−	0.997089i	$-0.524293\pi$
$569$	−3.63750			−0.152492			−0.0762460	+	0.997089i	$0.524293\pi$
$570$		0			0
$571$	−12.0122	+	12.0122i	−0.502695	+	0.502695i	−0.912275	−	0.409579i	$-0.865676\pi$
$571$	−12.0122	+	12.0122i	−0.502695	+	0.502695i	0.409579	+	0.912275i	$0.365676\pi$
$572$		0			0
$573$	13.5503	−	13.5503i	0.566072	−	0.566072i
$574$		0			0
$575$	20.4293	+	12.4912i	0.851961	+	0.520918i
$576$		0			0
$577$	−20.4216			−0.850164			−0.425082	−	0.905155i	$-0.639755\pi$
$577$	−20.4216			−0.850164			−0.425082	+	0.905155i	$0.639755\pi$
$578$		0			0
$579$	8.55781	−	8.55781i	0.355650	−	0.355650i
$580$		0			0
$581$	18.5148	−	18.5148i	0.768123	−	0.768123i
$582$		0			0
$583$	−37.8097			−1.56592
$584$		0			0
$585$	0.238773			0.00987206
$586$		0			0
$587$	17.0110	+	17.0110i	0.702118	+	0.702118i	0.964865	−	0.262747i	$-0.0846284\pi$
$587$	17.0110	+	17.0110i	0.702118	+	0.702118i	−0.262747	+	0.964865i	$0.584628\pi$
$588$		0			0
$589$	10.8754	−	10.8754i	0.448112	−	0.448112i
$590$		0			0
$591$			20.6833i			0.850799i
$592$		0			0
$593$	−3.97528			−0.163245			−0.0816226	−	0.996663i	$-0.526010\pi$
$593$	−3.97528			−0.163245			−0.0816226	+	0.996663i	$0.526010\pi$
$594$		0			0
$595$	−0.200142	−	0.200142i	−0.00820502	−	0.00820502i
$596$		0			0
$597$	10.4290	+	10.4290i	0.426831	+	0.426831i
$598$		0			0
$599$	22.1613			0.905487			0.452744	−	0.891641i	$-0.350445\pi$
$599$	22.1613			0.905487			0.452744	+	0.891641i	$0.350445\pi$
$600$		0			0
$601$			16.7533i			0.683381i	0.939813	+	0.341690i	$0.110999\pi$
$601$			16.7533i			0.683381i	−0.939813	+	0.341690i	$0.889001\pi$
$602$		0			0
$603$	−0.366505	+	0.366505i	−0.0149253	+	0.0149253i
$604$		0			0
$605$	−0.585575	+	0.585575i	−0.0238070	+	0.0238070i
$606$		0			0
$607$			36.1916i			1.46897i	0.678624	+	0.734486i	$0.262577\pi$
$607$			36.1916i			1.46897i	−0.678624	+	0.734486i	$0.737423\pi$
$608$		0			0
$609$		−	5.57253i		−	0.225810i
$610$		0			0
$611$	2.29190	−	2.29190i	0.0927203	−	0.0927203i
$612$		0			0
$613$	30.4776	+	30.4776i	1.23098	+	1.23098i	0.963588	+	0.267392i	$0.0861619\pi$
$613$	30.4776	+	30.4776i	1.23098	+	1.23098i	0.267392	+	0.963588i	$0.413838\pi$
$614$		0			0
$615$		−	0.250795i		−	0.0101130i
$616$		0			0
$617$	16.7959			0.676176			0.338088	−	0.941114i	$-0.390220\pi$
$617$	16.7959			0.676176			0.338088	+	0.941114i	$0.390220\pi$
$618$		0			0
$619$	10.5813	−	10.5813i	0.425300	−	0.425300i	−0.461724	−	0.887024i	$-0.652769\pi$
$619$	10.5813	−	10.5813i	0.425300	−	0.425300i	0.887024	+	0.461724i	$0.152769\pi$
$620$		0			0
$621$	25.6353	−	6.18144i	1.02871	−	0.248053i
$622$		0			0
$623$		−	37.9222i		−	1.51932i
$624$		0			0
$625$	−24.8947			−0.995787
$626$		0			0
$627$	26.1052	−	26.1052i	1.04254	−	1.04254i
$628$		0			0
$629$	−1.96571	+	1.96571i	−0.0783782	+	0.0783782i
$630$		0			0
$631$		−	44.3752i		−	1.76655i	−0.468857	−	0.883274i	$-0.655334\pi$
$631$		−	44.3752i		−	1.76655i	0.468857	−	0.883274i	$-0.344666\pi$
$632$		0			0
$633$		−	15.2206i		−	0.604965i
$634$		0			0
$635$	−0.309432	+	0.309432i	−0.0122794	+	0.0122794i
$636$		0			0
$637$	−0.0943110	−	0.0943110i	−0.00373674	−	0.00373674i
$638$		0			0
$639$			22.8272i			0.903029i
$640$		0			0
$641$		−	22.6166i		−	0.893303i	−0.894708	−	0.446652i	$-0.852616\pi$
$641$		−	22.6166i		−	0.893303i	0.894708	−	0.446652i	$-0.147384\pi$
$642$		0			0
$643$	25.9171	+	25.9171i	1.02207	+	1.02207i	0.999751	+	0.0223210i	$0.00710559\pi$
$643$	25.9171	+	25.9171i	1.02207	+	1.02207i	0.0223210	+	0.999751i	$0.492894\pi$
$644$		0			0
$645$	0.837795	−	0.837795i	0.0329881	−	0.0329881i
$646$		0			0
$647$	16.0802			0.632179			0.316090	−	0.948729i	$-0.397630\pi$
$647$	16.0802			0.632179			0.316090	+	0.948729i	$0.397630\pi$
$648$		0			0
$649$	−66.0623			−2.59317
$650$		0			0
$651$	−5.29604	+	5.29604i	−0.207568	+	0.207568i
$652$		0			0
$653$	25.6456	+	25.6456i	1.00359	+	1.00359i	0.999994	+	0.00359817i	$0.00114534\pi$
$653$	25.6456	+	25.6456i	1.00359	+	1.00359i	0.00359817	+	0.999994i	$0.498855\pi$
$654$		0			0
$655$	0.395227			0.0154428
$656$		0			0
$657$	−3.35523			−0.130900
$658$		0			0
$659$	−5.67720	−	5.67720i	−0.221152	−	0.221152i	0.587831	−	0.808984i	$-0.299982\pi$
$659$	−5.67720	−	5.67720i	−0.221152	−	0.221152i	−0.808984	+	0.587831i	$0.799982\pi$
$660$		0			0
$661$	−25.6539	−	25.6539i	−0.997820	−	0.997820i	0.00217783	−	0.999998i	$-0.499307\pi$
$661$	−25.6539	−	25.6539i	−0.997820	−	0.997820i	−0.999998	+	0.00217783i	$0.999307\pi$
$662$		0			0
$663$		−	2.89460i		−	0.112417i
$664$		0			0
$665$	1.48028			0.0574030
$666$		0			0
$667$	8.03220	−	1.93681i	0.311008	−	0.0749936i
$668$		0			0
$669$	−7.16979	−	7.16979i	−0.277200	−	0.277200i
$670$		0			0
$671$		−	59.3517i		−	2.29125i
$672$		0			0
$673$	−14.3871			−0.554583			−0.277291	−	0.960786i	$-0.589437\pi$
$673$	−14.3871			−0.554583			−0.277291	+	0.960786i	$0.589437\pi$
$674$		0			0
$675$	−19.4129	+	19.4129i	−0.747203	+	0.747203i
$676$		0			0
$677$	9.48874	+	9.48874i	0.364682	+	0.364682i	0.865533	−	0.500851i	$-0.166980\pi$
$677$	9.48874	+	9.48874i	0.364682	+	0.364682i	−0.500851	+	0.865533i	$0.666980\pi$
$678$		0			0
$679$	−21.2604			−0.815898
$680$		0			0
$681$	8.12869			0.311492
$682$		0			0
$683$	10.0685	+	10.0685i	0.385260	+	0.385260i	0.872993	−	0.487733i	$-0.162176\pi$
$683$	10.0685	+	10.0685i	0.385260	+	0.385260i	−0.487733	+	0.872993i	$0.662176\pi$
$684$		0			0
$685$	−0.440026	−	0.440026i	−0.0168125	−	0.0168125i
$686$		0			0
$687$	27.0682			1.03272
$688$		0			0
$689$		−	15.5039i		−	0.590652i
$690$		0			0
$691$	25.0974	−	25.0974i	0.954750	−	0.954750i	−0.0442700	−	0.999020i	$-0.514096\pi$
$691$	25.0974	−	25.0974i	0.954750	−	0.954750i	0.999020	+	0.0442700i	$0.0140962\pi$
$692$		0			0
$693$	13.0641	−	13.0641i	0.496266	−	0.496266i
$694$		0			0
$695$			0.789613i			0.0299517i
$696$		0			0
$697$	3.12441			0.118346
$698$		0			0
$699$	−4.35324	−	4.35324i	−0.164655	−	0.164655i
$700$		0			0
$701$	−1.25488	+	1.25488i	−0.0473963	+	0.0473963i	−0.730408	−	0.683011i	$-0.760670\pi$
$701$	−1.25488	+	1.25488i	−0.0473963	+	0.0473963i	0.683011	+	0.730408i	$0.260670\pi$
$702$		0			0
$703$		−	14.5388i		−	0.548340i
$704$		0			0
$705$		−	0.176342i		−	0.00664144i
$706$		0			0
$707$	9.69453	+	9.69453i	0.364600	+	0.364600i
$708$		0			0
$709$	−17.0708	−	17.0708i	−0.641106	−	0.641106i	0.309721	−	0.950827i	$-0.399764\pi$
$709$	−17.0708	−	17.0708i	−0.641106	−	0.641106i	−0.950827	+	0.309721i	$0.899764\pi$
$710$		0			0
$711$		−	10.4981i		−	0.393711i
$712$		0			0
$713$	−9.47438	−	5.79296i	−0.354818	−	0.216948i
$714$		0			0
$715$	−0.507425	−	0.507425i	−0.0189766	−	0.0189766i
$716$		0			0
$717$	−21.8854	−	21.8854i	−0.817325	−	0.817325i
$718$		0			0
$719$			10.8401i			0.404268i	0.979358	+	0.202134i	$0.0647876\pi$
$719$			10.8401i			0.404268i	−0.979358	+	0.202134i	$0.935212\pi$
$720$		0			0
$721$	35.4343			1.31964
$722$		0			0
$723$	−6.59940	−	6.59940i	−0.245434	−	0.245434i
$724$		0			0
$725$	−6.08258	+	6.08258i	−0.225901	+	0.225901i
$726$		0			0
$727$		−	10.3403i		−	0.383501i	−0.981444	−	0.191751i	$-0.938583\pi$
$727$		−	10.3403i		−	0.383501i	0.981444	−	0.191751i	$-0.0614165\pi$
$728$		0			0
$729$			23.2984i			0.862903i
$730$		0			0
$731$	10.4373	+	10.4373i	0.386037	+	0.386037i
$732$		0			0
$733$	−18.2971	+	18.2971i	−0.675819	+	0.675819i	−0.959051	−	0.283232i	$-0.908593\pi$
$733$	−18.2971	+	18.2971i	−0.675819	+	0.675819i	0.283232	+	0.959051i	$0.408593\pi$
$734$		0			0
$735$	−0.00725644			−0.000267658
$736$		0			0
$737$	1.55775			0.0573803
$738$		0			0
$739$	−29.3914	+	29.3914i	−1.08118	+	1.08118i	−0.0847802	+	0.996400i	$0.527019\pi$
$739$	−29.3914	+	29.3914i	−1.08118	+	1.08118i	−0.996400	+	0.0847802i	$0.972981\pi$
$740$		0			0
$741$	10.7045	+	10.7045i	0.393238	+	0.393238i
$742$		0			0
$743$			15.4325i			0.566163i	0.959096	+	0.283081i	$0.0913566\pi$
$743$			15.4325i			0.566163i	−0.959096	+	0.283081i	$0.908643\pi$
$744$		0			0
$745$			0.779703i			0.0285661i
$746$		0			0
$747$	−10.5864	+	10.5864i	−0.387335	+	0.387335i
$748$		0			0
$749$	−18.6914	−	18.6914i	−0.682969	−	0.682969i
$750$		0			0
$751$	14.9635			0.546026			0.273013	−	0.962010i	$-0.411980\pi$
$751$	14.9635			0.546026			0.273013	+	0.962010i	$0.411980\pi$
$752$		0			0
$753$		−	30.9793i		−	1.12895i
$754$		0			0
$755$	0.924836	+	0.924836i	0.0336582	+	0.0336582i
$756$		0			0
$757$	−11.8442	−	11.8442i	−0.430485	−	0.430485i	0.458308	−	0.888793i	$-0.348456\pi$
$757$	−11.8442	−	11.8442i	−0.430485	−	0.430485i	−0.888793	+	0.458308i	$0.848456\pi$
$758$		0			0
$759$	−22.7422	−	13.9054i	−0.825491	−	0.504733i
$760$		0			0
$761$			0.408106i			0.0147938i	0.999973	+	0.00739692i	$0.00235453\pi$
$761$			0.408106i			0.0147938i	−0.999973	+	0.00739692i	$0.997645\pi$
$762$		0			0
$763$	−8.31408	−	8.31408i	−0.300990	−	0.300990i
$764$		0			0
$765$	0.114437	+	0.114437i	0.00413748	+	0.00413748i
$766$		0			0
$767$		−	27.0890i		−	0.978126i
$768$		0			0
$769$		−	44.9499i		−	1.62093i	−0.585784	−	0.810467i	$-0.699213\pi$
$769$		−	44.9499i		−	1.62093i	0.585784	−	0.810467i	$-0.300787\pi$
$770$		0			0
$771$	9.91873	−	9.91873i	0.357214	−	0.357214i
$772$		0			0
$773$	28.2917	+	28.2917i	1.01758	+	1.01758i	0.999843	+	0.0177385i	$0.00564664\pi$
$773$	28.2917	+	28.2917i	1.01758	+	1.01758i	0.0177385	+	0.999843i	$0.494353\pi$
$774$		0			0
$775$	11.5616			0.415303
$776$		0			0
$777$			7.08003i			0.253995i
$778$		0			0
$779$	−11.5543	+	11.5543i	−0.413977	+	0.413977i
$780$		0			0
$781$	48.5108	−	48.5108i	1.73585	−	1.73585i
$782$		0			0
$783$			9.47304i			0.338539i
$784$		0			0
$785$	0.717752			0.0256177
$786$		0			0
$787$	23.2407	+	23.2407i	0.828442	+	0.828442i	0.987301	−	0.158859i	$-0.0507815\pi$
$787$	23.2407	+	23.2407i	0.828442	+	0.828442i	−0.158859	+	0.987301i	$0.550782\pi$
$788$		0			0
$789$	−22.2250	−	22.2250i	−0.791232	−	0.791232i
$790$		0			0
$791$	−23.0537			−0.819694
$792$		0			0
$793$	24.3373			0.864242
$794$		0			0
$795$	−0.596448	−	0.596448i	−0.0211538	−	0.0211538i
$796$		0			0
$797$	−16.5321	+	16.5321i	−0.585598	+	0.585598i	−0.936436	−	0.350838i	$-0.885897\pi$
$797$	−16.5321	+	16.5321i	−0.585598	+	0.585598i	0.350838	+	0.936436i	$0.385897\pi$
$798$		0			0
$799$	2.19688			0.0777200
$800$		0			0
$801$			21.6831i			0.766136i
$802$		0			0
$803$	7.13030	+	7.13030i	0.251623	+	0.251623i
$804$		0			0
$805$	−0.250546	−	1.03905i	−0.00883057	−	0.0366215i
$806$		0			0
$807$	−20.7910			−0.731879
$808$		0			0
$809$			3.22326i			0.113324i	0.998393	+	0.0566618i	$0.0180457\pi$
$809$			3.22326i			0.113324i	−0.998393	+	0.0566618i	$0.981954\pi$
$810$		0			0
$811$	12.6982	+	12.6982i	0.445893	+	0.445893i	0.893987	−	0.448093i	$-0.147897\pi$
$811$	12.6982	+	12.6982i	0.445893	+	0.445893i	−0.448093	+	0.893987i	$0.647897\pi$
$812$		0			0
$813$	−16.9350	−	16.9350i	−0.593937	−	0.593937i
$814$		0			0
$815$	−1.27874			−0.0447924
$816$		0			0
$817$	−77.1959			−2.70074
$818$		0			0
$819$	5.35698	+	5.35698i	0.187188	+	0.187188i
$820$		0			0
$821$	−24.5612	+	24.5612i	−0.857192	+	0.857192i	−0.991006	−	0.133814i	$-0.957277\pi$
$821$	−24.5612	+	24.5612i	−0.857192	+	0.857192i	0.133814	+	0.991006i	$0.457277\pi$
$822$		0			0
$823$	45.6245			1.59037			0.795185	−	0.606367i	$-0.207374\pi$
$823$	45.6245			1.59037			0.795185	+	0.606367i	$0.207374\pi$
$824$		0			0
$825$	27.7523			0.966210
$826$		0			0
$827$	0.390922	−	0.390922i	0.0135937	−	0.0135937i	−0.700277	−	0.713871i	$-0.746940\pi$
$827$	0.390922	−	0.390922i	0.0135937	−	0.0135937i	0.713871	+	0.700277i	$0.246940\pi$
$828$		0			0
$829$	−12.4079	−	12.4079i	−0.430943	−	0.430943i	0.458006	−	0.888949i	$-0.348564\pi$
$829$	−12.4079	−	12.4079i	−0.430943	−	0.430943i	−0.888949	+	0.458006i	$0.848564\pi$
$830$		0			0
$831$		−	14.7956i		−	0.513253i
$832$		0			0
$833$		−	0.0904010i		−	0.00313221i
$834$		0			0
$835$	−0.395851	−	0.395851i	−0.0136990	−	0.0136990i
$836$		0			0
$837$	9.00301	−	9.00301i	0.311190	−	0.311190i
$838$		0			0
$839$			2.88285i			0.0995269i	0.998761	+	0.0497635i	$0.0158467\pi$
$839$			2.88285i			0.0995269i	−0.998761	+	0.0497635i	$0.984153\pi$
$840$		0			0
$841$		−	26.0318i		−	0.897650i
$842$		0			0
$843$	−24.6449	+	24.6449i	−0.848816	+	0.848816i
$844$		0			0
$845$	−0.562346	+	0.562346i	−0.0193453	+	0.0193453i
$846$		0			0
$847$	−26.2752			−0.902827
$848$		0			0
$849$			6.88409i			0.236261i
$850$		0			0
$851$	−10.2051	+	2.46076i	−0.349826	+	0.0843538i
$852$		0			0
$853$	−4.58595	+	4.58595i	−0.157020	+	0.157020i	−0.781245	−	0.624225i	$-0.785415\pi$
$853$	−4.58595	+	4.58595i	−0.157020	+	0.157020i	0.624225	+	0.781245i	$0.285415\pi$
$854$		0			0
$855$	−0.846396			−0.0289461
$856$		0			0
$857$		−	18.1650i		−	0.620506i	−0.950654	−	0.310253i	$-0.899586\pi$
$857$		−	18.1650i		−	0.620506i	0.950654	−	0.310253i	$-0.100414\pi$
$858$		0			0
$859$	−24.8997	−	24.8997i	−0.849566	−	0.849566i	0.140513	−	0.990079i	$-0.455125\pi$
$859$	−24.8997	−	24.8997i	−0.849566	−	0.849566i	−0.990079	+	0.140513i	$0.955125\pi$
$860$		0			0
$861$	5.62669	−	5.62669i	0.191757	−	0.191757i
$862$		0			0
$863$		−	17.1216i		−	0.582825i	−0.956598	−	0.291412i	$-0.905875\pi$
$863$		−	17.1216i		−	0.582825i	0.956598	−	0.291412i	$-0.0941252\pi$
$864$		0			0
$865$		−	1.07966i		−	0.0367096i
$866$		0			0
$867$	−13.2344	+	13.2344i	−0.449464	+	0.449464i
$868$		0			0
$869$	−22.3099	+	22.3099i	−0.756813	+	0.756813i
$870$		0			0
$871$			0.638756i			0.0216434i
$872$		0			0
$873$	12.1562			0.411426
$874$		0			0
$875$	1.57479	+	1.57479i	0.0532376	+	0.0532376i
$876$		0			0
$877$	−15.2309	−	15.2309i	−0.514312	−	0.514312i	0.401532	−	0.915845i	$-0.368478\pi$
$877$	−15.2309	−	15.2309i	−0.514312	−	0.514312i	−0.915845	+	0.401532i	$0.868478\pi$
$878$		0			0
$879$	−17.1107			−0.577131
$880$		0			0
$881$		−	51.1387i		−	1.72291i	−0.507837	−	0.861453i	$-0.669555\pi$
$881$		−	51.1387i		−	1.72291i	0.507837	−	0.861453i	$-0.330445\pi$
$882$		0			0
$883$	2.24931	−	2.24931i	0.0756953	−	0.0756953i	−0.668245	−	0.743941i	$-0.732954\pi$
$883$	2.24931	−	2.24931i	0.0756953	−	0.0756953i	0.743941	+	0.668245i	$0.232954\pi$
$884$		0			0
$885$	−1.04213	−	1.04213i	−0.0350310	−	0.0350310i
$886$		0			0
$887$	−41.9597			−1.40887			−0.704435	−	0.709769i	$-0.748799\pi$
$887$	−41.9597			−1.40887			−0.704435	+	0.709769i	$0.748799\pi$
$888$		0			0
$889$	−13.8845			−0.465670
$890$		0			0
$891$	6.87217	−	6.87217i	0.230226	−	0.230226i
$892$		0			0
$893$	−8.12425	+	8.12425i	−0.271868	+	0.271868i
$894$		0			0
$895$	0.0107824			0.000360416
$896$		0			0
$897$	5.70192	−	9.32549i	0.190382	−	0.311369i
$898$		0			0
$899$	2.82088	−	2.82088i	0.0940817	−	0.0940817i
$900$		0			0
$901$	7.43057	−	7.43057i	0.247548	−	0.247548i
$902$		0			0
$903$	37.5925			1.25100
$904$		0			0
$905$			1.34136i			0.0445882i
$906$		0			0
$907$	−6.73858	+	6.73858i	−0.223751	+	0.223751i	−0.810076	−	0.586325i	$-0.800574\pi$
$907$	−6.73858	+	6.73858i	−0.223751	+	0.223751i	0.586325	+	0.810076i	$0.300574\pi$
$908$		0			0
$909$	−5.54313	−	5.54313i	−0.183854	−	0.183854i
$910$		0			0
$911$	58.1801			1.92759			0.963796	−	0.266642i	$-0.0859142\pi$
$911$	58.1801			1.92759			0.963796	+	0.266642i	$0.0859142\pi$
$912$		0			0
$913$	44.9949			1.48911
$914$		0			0
$915$	0.936275	−	0.936275i	0.0309523	−	0.0309523i
$916$		0			0
$917$	8.86708	+	8.86708i	0.292817	+	0.292817i
$918$		0			0
$919$		−	45.9219i		−	1.51482i	−0.652938	−	0.757411i	$-0.726464\pi$
$919$		−	45.9219i		−	1.51482i	0.652938	−	0.757411i	$-0.273536\pi$
$920$		0			0
$921$		−	18.4845i		−	0.609083i
$922$		0			0
$923$	19.8919	+	19.8919i	0.654751	+	0.654751i
$924$		0			0
$925$	7.72805	−	7.72805i	0.254097	−	0.254097i
$926$		0			0
$927$	−20.2606			−0.665446
$928$		0			0
$929$	18.0479			0.592132			0.296066	−	0.955167i	$-0.404325\pi$
$929$	18.0479			0.592132			0.296066	+	0.955167i	$0.404325\pi$
$930$		0			0
$931$	0.334311	+	0.334311i	0.0109566	+	0.0109566i
$932$		0			0
$933$	12.1482	−	12.1482i	0.397714	−	0.397714i
$934$		0			0
$935$		−	0.486388i		−	0.0159066i
$936$		0			0
$937$	−3.77047			−0.123176			−0.0615879	−	0.998102i	$-0.519616\pi$
$937$	−3.77047			−0.123176			−0.0615879	+	0.998102i	$0.519616\pi$
$938$		0			0
$939$	20.9612	−	20.9612i	0.684044	−	0.684044i
$940$		0			0
$941$	−19.3322	+	19.3322i	−0.630212	+	0.630212i	−0.948121	−	0.317909i	$-0.897019\pi$
$941$	−19.3322	+	19.3322i	−0.630212	+	0.630212i	0.317909	+	0.948121i	$0.397019\pi$
$942$		0			0
$943$	10.0659	+	6.15462i	0.327790	+	0.200422i
$944$		0			0
$945$	1.22543			0.0398633
$946$		0			0
$947$	−0.659158	+	0.659158i	−0.0214197	+	0.0214197i	−0.717736	−	0.696316i	$-0.754821\pi$
$947$	−0.659158	+	0.659158i	−0.0214197	+	0.0214197i	0.696316	+	0.717736i	$0.254821\pi$
$948$		0			0
$949$	−2.92379	+	2.92379i	−0.0949104	+	0.0949104i
$950$		0			0
$951$	−18.0701			−0.585964
$952$		0			0
$953$	26.8329			0.869203			0.434601	−	0.900623i	$-0.356889\pi$
$953$	26.8329			0.869203			0.434601	+	0.900623i	$0.356889\pi$
$954$		0			0
$955$	0.933645	+	0.933645i	0.0302121	+	0.0302121i
$956$		0			0
$957$	6.77123	−	6.77123i	0.218883	−	0.218883i
$958$		0			0
$959$		−	19.7443i		−	0.637578i
$960$		0			0
$961$	25.6382			0.827037
$962$		0			0
$963$	10.6874	+	10.6874i	0.344395	+	0.344395i
$964$		0			0
$965$	0.589652	+	0.589652i	0.0189816	+	0.0189816i
$966$		0			0
$967$	15.2802			0.491379			0.245690	−	0.969349i	$-0.420986\pi$
$967$	15.2802			0.491379			0.245690	+	0.969349i	$0.420986\pi$
$968$		0			0
$969$			10.2607i			0.329620i
$970$		0			0
$971$	−5.62452	+	5.62452i	−0.180499	+	0.180499i	−0.791573	−	0.611074i	$-0.790738\pi$
$971$	−5.62452	+	5.62452i	−0.180499	+	0.180499i	0.611074	+	0.791573i	$0.290738\pi$
$972$		0			0
$973$	−17.7153	+	17.7153i	−0.567926	+	0.567926i
$974$		0			0
$975$			11.3799i			0.364448i
$976$		0			0
$977$			15.3837i			0.492169i	0.969248	+	0.246085i	$0.0791441\pi$
$977$			15.3837i			0.492169i	−0.969248	+	0.246085i	$0.920856\pi$
$978$		0			0
$979$	46.0796	−	46.0796i	1.47271	−	1.47271i
$980$		0			0
$981$	4.75382	+	4.75382i	0.151778	+	0.151778i
$982$		0			0
$983$			31.2924i			0.998073i	0.866581	+	0.499037i	$0.166313\pi$
$983$			31.2924i			0.998073i	−0.866581	+	0.499037i	$0.833687\pi$
$984$		0			0
$985$	−1.42513			−0.0454084
$986$		0			0
$987$	3.95631	−	3.95631i	0.125931	−	0.125931i
$988$		0			0
$989$	13.0658	+	54.1856i	0.415468	+	1.72300i
$990$		0			0
$991$		−	27.6157i		−	0.877241i	−0.898672	−	0.438620i	$-0.855467\pi$
$991$		−	27.6157i		−	0.877241i	0.898672	−	0.438620i	$-0.144533\pi$
$992$		0			0
$993$	−15.1991			−0.482329
$994$		0			0
$995$	−0.718583	+	0.718583i	−0.0227806	+	0.0227806i
$996$		0			0
$997$	26.4275	−	26.4275i	0.836969	−	0.836969i	−0.151490	−	0.988459i	$-0.548407\pi$
$997$	26.4275	−	26.4275i	0.836969	−	0.836969i	0.988459	+	0.151490i	$0.0484072\pi$
$998$		0			0
$999$		−	12.0357i		−	0.380793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1472.2.i.b.367.12		80
4.3	odd	2		368.2.i.b.275.5	yes	80
16.5	even	4		368.2.i.b.91.6	yes	80
16.11	odd	4	inner	1472.2.i.b.1103.11		80
23.22	odd	2	inner	1472.2.i.b.367.11		80
92.91	even	2		368.2.i.b.275.6	yes	80
368.91	even	4	inner	1472.2.i.b.1103.12		80
368.229	odd	4		368.2.i.b.91.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.i.b.91.5	✓	80	368.229	odd	4
368.2.i.b.91.6	yes	80	16.5	even	4
368.2.i.b.275.5	yes	80	4.3	odd	2
368.2.i.b.275.6	yes	80	92.91	even	2
1472.2.i.b.367.11		80	23.22	odd	2	inner
1472.2.i.b.367.12		80	1.1	even	1	trivial
1472.2.i.b.1103.11		80	16.11	odd	4	inner
1472.2.i.b.1103.12		80	368.91	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1472.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.860099 + 0.860099i) q^{3} +(-0.0592628 - 0.0592628i) q^{5} -2.65917i q^{7} +1.52046i q^{9} +(3.23118 - 3.23118i) q^{11} +(1.32495 + 1.32495i) q^{13} +0.101944 q^{15} +1.27002i q^{17} +(-4.69664 - 4.69664i) q^{19} +(2.28715 + 2.28715i) q^{21} +(-2.50175 + 4.09161i) q^{23} -4.99298i q^{25} +(-3.88804 - 3.88804i) q^{27} +(-1.21823 - 1.21823i) q^{29} +2.31556i q^{31} +5.55826i q^{33} +(-0.157590 + 0.157590i) q^{35} +(1.54778 + 1.54778i) q^{37} -2.27918 q^{39} -2.46013i q^{41} +(8.21821 - 8.21821i) q^{43} +(0.0901066 - 0.0901066i) q^{45} -1.72980i q^{47} -0.0711808 q^{49} +(-1.09234 - 1.09234i) q^{51} +(-5.85076 - 5.85076i) q^{53} -0.382977 q^{55} +8.07915 q^{57} +(-10.2226 - 10.2226i) q^{59} +(9.18423 - 9.18423i) q^{61} +4.04316 q^{63} -0.157040i q^{65} +(0.241049 + 0.241049i) q^{67} +(-1.36744 - 5.67094i) q^{69} +15.0134 q^{71} +2.20672i q^{73} +(4.29446 + 4.29446i) q^{75} +(-8.59224 - 8.59224i) q^{77} -6.90459 q^{79} +2.12683 q^{81} +(6.96262 + 6.96262i) q^{83} +(0.0752648 - 0.0752648i) q^{85} +2.09559 q^{87} +14.2609 q^{89} +(3.52326 - 3.52326i) q^{91} +(-1.99162 - 1.99162i) q^{93} +0.556672i q^{95} -7.99512i q^{97} +(4.91287 + 4.91287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} - 4 q^{13} - 4 q^{23} - 44 q^{27} - 20 q^{29} - 16 q^{35} + 128 q^{39} - 160 q^{49} + 8 q^{55} - 80 q^{59} - 24 q^{69} + 8 q^{71} + 12 q^{75} + 40 q^{77} + 40 q^{81} - 16 q^{85} + 8 q^{87}+ \cdots - 28 q^{93}+O(q^{100}) \) 80 * q + 4 * q^3 - 4 * q^13 - 4 * q^23 - 44 * q^27 - 20 * q^29 - 16 * q^35 + 128 * q^39 - 160 * q^49 + 8 * q^55 - 80 * q^59 - 24 * q^69 + 8 * q^71 + 12 * q^75 + 40 * q^77 + 40 * q^81 - 16 * q^85 + 8 * q^87 - 28 * q^93

Introduction

L-functions

Modular forms

Varieties

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Database

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