LMFDB - Embedded newform 1445.2.d.g.866.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(866,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1445.866");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.d (of order $2$, degree $1$, 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:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.5
Root			$3.48265i$ of defining polynomial
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.g.866.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12708 q^{2} -2.48265i q^{3} -0.729699 q^{4} +1.00000i q^{5} +2.79814i q^{6} -2.44256i q^{7} +3.07658 q^{8} -3.16356 q^{9} +O(q^{10})$	\(q-1.12708 q^{2} -2.48265i q^{3} -0.729699 q^{4} +1.00000i q^{5} +2.79814i q^{6} -2.44256i q^{7} +3.07658 q^{8} -3.16356 q^{9} -1.12708i q^{10} -3.63808i q^{11} +1.81159i q^{12} -3.64168 q^{13} +2.75295i q^{14} +2.48265 q^{15} -2.00814 q^{16} +3.56558 q^{18} +2.61358 q^{19} -0.729699i q^{20} -6.06403 q^{21} +4.10039i q^{22} -1.40552i q^{23} -7.63808i q^{24} -1.00000 q^{25} +4.10445 q^{26} +0.406074i q^{27} +1.78234i q^{28} -0.850775i q^{29} -2.79814 q^{30} -9.44332i q^{31} -3.88983 q^{32} -9.03208 q^{33} +2.44256 q^{35} +2.30845 q^{36} +11.0054i q^{37} -2.94570 q^{38} +9.04103i q^{39} +3.07658i q^{40} -9.53958i q^{41} +6.83463 q^{42} -7.47280 q^{43} +2.65470i q^{44} -3.16356i q^{45} +1.58412i q^{46} +5.42683 q^{47} +4.98551i q^{48} +1.03389 q^{49} +1.12708 q^{50} +2.65733 q^{52} -12.9453 q^{53} -0.457676i q^{54} +3.63808 q^{55} -7.51473i q^{56} -6.48861i q^{57} +0.958888i q^{58} -1.40270 q^{59} -1.81159 q^{60} +1.13771i q^{61} +10.6433i q^{62} +7.72720i q^{63} +8.40042 q^{64} -3.64168i q^{65} +10.1798 q^{66} -2.07908 q^{67} -3.48941 q^{69} -2.75295 q^{70} +12.2919i q^{71} -9.73296 q^{72} -1.47586i q^{73} -12.4039i q^{74} +2.48265i q^{75} -1.90713 q^{76} -8.88623 q^{77} -10.1899i q^{78} -8.97276i q^{79} -2.00814i q^{80} -8.48255 q^{81} +10.7518i q^{82} +2.52680 q^{83} +4.42492 q^{84} +8.42242 q^{86} -2.11218 q^{87} -11.1928i q^{88} +1.66373 q^{89} +3.56558i q^{90} +8.89503i q^{91} +1.02560i q^{92} -23.4445 q^{93} -6.11645 q^{94} +2.61358i q^{95} +9.65710i q^{96} +12.2673i q^{97} -1.16527 q^{98} +11.5093i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 12 q^{4} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 12 * q^4 - 12 * q^8 - 4 * q^9	$ 12 q - 4 q^{2} + 12 q^{4} - 12 q^{8} - 4 q^{9} - 8 q^{15} + 4 q^{16} + 28 q^{18} + 24 q^{19} + 16 q^{21} - 12 q^{25} + 24 q^{26} + 8 q^{30} + 12 q^{32} - 16 q^{33} + 16 q^{35} + 20 q^{36} - 24 q^{38} + 16 q^{42} - 16 q^{43} + 48 q^{47} + 20 q^{49} + 4 q^{50} - 56 q^{52} + 32 q^{59} - 16 q^{60} - 28 q^{64} + 32 q^{66} - 8 q^{67} - 16 q^{70} - 20 q^{72} + 72 q^{76} - 48 q^{77} - 28 q^{81} - 40 q^{83} - 96 q^{86} - 48 q^{87} - 24 q^{89} - 72 q^{93} - 40 q^{94} - 44 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 - 12 * q^8 - 4 * q^9 - 8 * q^15 + 4 * q^16 + 28 * q^18 + 24 * q^19 + 16 * q^21 - 12 * q^25 + 24 * q^26 + 8 * q^30 + 12 * q^32 - 16 * q^33 + 16 * q^35 + 20 * q^36 - 24 * q^38 + 16 * q^42 - 16 * q^43 + 48 * q^47 + 20 * q^49 + 4 * q^50 - 56 * q^52 + 32 * q^59 - 16 * q^60 - 28 * q^64 + 32 * q^66 - 8 * q^67 - 16 * q^70 - 20 * q^72 + 72 * q^76 - 48 * q^77 - 28 * q^81 - 40 * q^83 - 96 * q^86 - 48 * q^87 - 24 * q^89 - 72 * q^93 - 40 * q^94 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.12708	−0.796963	−0.398482	−	0.917176i	$-0.630463\pi$
$2$	−1.12708	−0.796963	−0.398482	+	0.917176i	$0.630463\pi$
$3$	− 2.48265i	− 1.43336i	−0.697402	−	0.716680i	$-0.745661\pi$
$3$	− 2.48265i	− 1.43336i	0.697402	−	0.716680i	$-0.254339\pi$
$4$	−0.729699	−0.364850
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	2.79814i	1.14234i
$7$	− 2.44256i	− 0.923202i	−0.887088	−	0.461601i	$-0.847275\pi$
$7$	− 2.44256i	− 0.923202i	0.887088	−	0.461601i	$-0.152725\pi$
$8$	3.07658	1.08773
$9$	−3.16356	−1.05452
$10$	− 1.12708i	− 0.356413i
$11$	− 3.63808i	− 1.09692i	−0.836176	−	0.548461i	$-0.815214\pi$
$11$	− 3.63808i	− 1.09692i	0.836176	−	0.548461i	$-0.184786\pi$
$12$	1.81159i	0.522961i
$13$	−3.64168	−1.01002	−0.505010	−	0.863113i	$-0.668511\pi$
$13$	−3.64168	−1.01002	−0.505010	+	0.863113i	$0.668511\pi$
$14$	2.75295i	0.735758i
$15$	2.48265	0.641018
$16$	−2.00814	−0.502035
$17$	0	0
$17$	0	0
$18$	3.56558	0.840415
$19$	2.61358	0.599596	0.299798	−	0.954003i	$-0.403081\pi$
$19$	2.61358	0.599596	0.299798	+	0.954003i	$0.403081\pi$
$20$	− 0.729699i	− 0.163166i
$21$	−6.06403	−1.32328
$22$	4.10039i	0.874206i
$23$	− 1.40552i	− 0.293070i	−0.989205	−	0.146535i	$-0.953188\pi$
$23$	− 1.40552i	− 0.293070i	0.989205	−	0.146535i	$-0.0468122\pi$
$24$	− 7.63808i	− 1.55912i
$25$	−1.00000	−0.200000
$26$	4.10445	0.804949
$27$	0.406074i	0.0781489i
$28$	1.78234i	0.336830i
$29$	− 0.850775i	− 0.157985i	−0.996875	−	0.0789925i	$-0.974830\pi$
$29$	− 0.850775i	− 0.157985i	0.996875	−	0.0789925i	$-0.0251703\pi$
$30$	−2.79814	−0.510868
$31$	− 9.44332i	− 1.69607i	−0.529940	−	0.848035i	$-0.677785\pi$
$31$	− 9.44332i	− 1.69607i	0.529940	−	0.848035i	$-0.322215\pi$
$32$	−3.88983	−0.687632
$33$	−9.03208	−1.57228
$34$	0	0
$35$	2.44256	0.412868
$36$	2.30845	0.384742
$37$	11.0054i	1.80928i	0.426181	+	0.904638i	$0.359859\pi$
$37$	11.0054i	1.80928i	−0.426181	+	0.904638i	$0.640141\pi$
$38$	−2.94570	−0.477856
$39$	9.04103i	1.44772i
$40$	3.07658i	0.486450i
$41$	− 9.53958i	− 1.48983i	−0.667158	−	0.744916i	$-0.732489\pi$
$41$	− 9.53958i	− 1.48983i	0.667158	−	0.744916i	$-0.267511\pi$
$42$	6.83463	1.05461
$43$	−7.47280	−1.13959	−0.569796	−	0.821786i	$-0.692978\pi$
$43$	−7.47280	−1.13959	−0.569796	+	0.821786i	$0.692978\pi$
$44$	2.65470i	0.400212i
$45$	− 3.16356i	− 0.471596i
$46$	1.58412i	0.233566i
$47$	5.42683	0.791585	0.395792	−	0.918340i	$-0.370470\pi$
$47$	5.42683	0.791585	0.395792	+	0.918340i	$0.370470\pi$
$48$	4.98551i	0.719597i
$49$	1.03389	0.147699
$50$	1.12708	0.159393
$51$	0	0
$52$	2.65733	0.368506
$53$	−12.9453	−1.77817	−0.889087	−	0.457737i	$-0.848660\pi$
$53$	−12.9453	−1.77817	−0.889087	+	0.457737i	$0.848660\pi$
$54$	− 0.457676i	− 0.0622818i
$55$	3.63808	0.490558
$56$	− 7.51473i	− 1.00420i
$57$	− 6.48861i	− 0.859437i
$58$	0.958888i	0.125908i
$59$	−1.40270	−0.182616	−0.0913081	−	0.995823i	$-0.529105\pi$
$59$	−1.40270	−0.182616	−0.0913081	+	0.995823i	$0.529105\pi$
$60$	−1.81159	−0.233875
$61$	1.13771i	0.145669i	0.997344	+	0.0728346i	$0.0232045\pi$
$61$	1.13771i	0.145669i	−0.997344	+	0.0728346i	$0.976795\pi$
$62$	10.6433i	1.35171i
$63$	7.72720i	0.973536i
$64$	8.40042	1.05005
$65$	− 3.64168i	− 0.451695i
$66$	10.1798	1.25305
$67$	−2.07908	−0.254000	−0.127000	−	0.991903i	$-0.540535\pi$
$67$	−2.07908	−0.254000	−0.127000	+	0.991903i	$0.540535\pi$
$68$	0	0
$69$	−3.48941	−0.420076
$70$	−2.75295	−0.329041
$71$	12.2919i	1.45878i	0.684099	+	0.729389i	$0.260196\pi$
$71$	12.2919i	1.45878i	−0.684099	+	0.729389i	$0.739804\pi$
$72$	−9.73296	−1.14704
$73$	− 1.47586i	− 0.172737i	−0.996263	−	0.0863684i	$-0.972474\pi$
$73$	− 1.47586i	− 0.172737i	0.996263	−	0.0863684i	$-0.0275262\pi$
$74$	− 12.4039i	− 1.44193i
$75$	2.48265i	0.286672i
$76$	−1.90713	−0.218762
$77$	−8.88623	−1.01268
$78$	− 10.1899i	− 1.15378i
$79$	− 8.97276i	− 1.00951i	−0.863261	−	0.504757i	$-0.831582\pi$
$79$	− 8.97276i	− 1.00951i	0.863261	−	0.504757i	$-0.168418\pi$
$80$	− 2.00814i	− 0.224517i
$81$	−8.48255	−0.942506
$82$	10.7518i	1.18734i
$83$	2.52680	0.277353	0.138676	−	0.990338i	$-0.455715\pi$
$83$	2.52680	0.277353	0.138676	+	0.990338i	$0.455715\pi$
$84$	4.42492	0.482799
$85$	0	0
$86$	8.42242	0.908213
$87$	−2.11218	−0.226449
$88$	− 11.1928i	− 1.19316i
$89$	1.66373	0.176355	0.0881775	−	0.996105i	$-0.471896\pi$
$89$	1.66373	0.176355	0.0881775	+	0.996105i	$0.471896\pi$
$90$	3.56558i	0.375845i
$91$	8.89503i	0.932452i
$92$	1.02560i	0.106927i
$93$	−23.4445	−2.43108
$94$	−6.11645	−0.630864
$95$	2.61358i	0.268147i
$96$	9.65710i	0.985624i
$97$	12.2673i	1.24556i	0.782397	+	0.622780i	$0.213997\pi$
$97$	12.2673i	1.24556i	−0.782397	+	0.622780i	$0.786003\pi$
$98$	−1.16527	−0.117710
$99$	11.5093i	1.15673i
$100$	0.729699	0.0729699
$101$	−4.18131	−0.416056	−0.208028	−	0.978123i	$-0.566704\pi$
$101$	−4.18131	−0.416056	−0.208028	+	0.978123i	$0.566704\pi$
$102$	0	0
$103$	8.08417	0.796557	0.398279	−	0.917265i	$-0.369608\pi$
$103$	8.08417	0.796557	0.398279	+	0.917265i	$0.369608\pi$
$104$	−11.2039	−1.09863
$105$	− 6.06403i	− 0.591789i
$106$	14.5903	1.41714
$107$	8.80071i	0.850796i	0.905006	+	0.425398i	$0.139866\pi$
$107$	8.80071i	0.850796i	−0.905006	+	0.425398i	$0.860134\pi$
$108$	− 0.296312i	− 0.0285126i
$109$	14.3144i	1.37107i	0.728038	+	0.685537i	$0.240433\pi$
$109$	14.3144i	1.37107i	−0.728038	+	0.685537i	$0.759567\pi$
$110$	−4.10039	−0.390957
$111$	27.3226	2.59334
$112$	4.90501i	0.463480i
$113$	11.4598i	1.07805i	0.842289	+	0.539026i	$0.181208\pi$
$113$	11.4598i	1.07805i	−0.842289	+	0.539026i	$0.818792\pi$
$114$	7.31315i	0.684940i
$115$	1.40552	0.131065
$116$	0.620810i	0.0576408i
$117$	11.5207	1.06509
$118$	1.58095	0.145538
$119$	0	0
$120$	7.63808	0.697258
$121$	−2.23561	−0.203237
$122$	− 1.28229i	− 0.116093i
$123$	−23.6835	−2.13547
$124$	6.89079i	0.618811i
$125$	− 1.00000i	− 0.0894427i
$126$	− 8.70915i	− 0.775872i
$127$	2.51562	0.223225	0.111613	−	0.993752i	$-0.464398\pi$
$127$	2.51562	0.223225	0.111613	+	0.993752i	$0.464398\pi$
$128$	−1.68825	−0.149221
$129$	18.5524i	1.63345i
$130$	4.10445i	0.359984i
$131$	2.22230i	0.194163i	0.995276	+	0.0970817i	$0.0309508\pi$
$131$	2.22230i	0.194163i	−0.995276	+	0.0970817i	$0.969049\pi$
$132$	6.59071	0.573647
$133$	− 6.38383i	− 0.553548i
$134$	2.34328	0.202428
$135$	−0.406074	−0.0349493
$136$	0	0
$137$	−22.1633	−1.89354	−0.946771	−	0.321908i	$-0.895676\pi$
$137$	−22.1633	−1.89354	−0.946771	+	0.321908i	$0.895676\pi$
$138$	3.93283	0.334785
$139$	13.8857i	1.17777i	0.808218	+	0.588884i	$0.200432\pi$
$139$	13.8857i	1.17777i	−0.808218	+	0.588884i	$0.799568\pi$
$140$	−1.78234	−0.150635
$141$	− 13.4729i	− 1.13463i
$142$	− 13.8539i	− 1.16259i
$143$	13.2487i	1.10791i
$144$	6.35288	0.529407
$145$	0.850775	0.0706530
$146$	1.66341i	0.137665i
$147$	− 2.56679i	− 0.211705i
$148$	− 8.03063i	− 0.660114i
$149$	11.6461	0.954087	0.477044	−	0.878880i	$-0.341708\pi$
$149$	11.6461	0.954087	0.477044	+	0.878880i	$0.341708\pi$
$150$	− 2.79814i	− 0.228467i
$151$	−2.82731	−0.230083	−0.115042	−	0.993361i	$-0.536700\pi$
$151$	−2.82731	−0.230083	−0.115042	+	0.993361i	$0.536700\pi$
$152$	8.04088	0.652201
$153$	0	0
$154$	10.0155	0.807068
$155$	9.44332	0.758506
$156$	− 6.59723i	− 0.528201i
$157$	−1.36913	−0.109268	−0.0546342	−	0.998506i	$-0.517399\pi$
$157$	−1.36913	−0.109268	−0.0546342	+	0.998506i	$0.517399\pi$
$158$	10.1130i	0.804545i
$159$	32.1387i	2.54877i
$160$	− 3.88983i	− 0.307518i
$161$	−3.43306	−0.270563
$162$	9.56048	0.751143
$163$	− 12.0913i	− 0.947063i	−0.880777	−	0.473532i	$-0.842979\pi$
$163$	− 12.0913i	− 0.947063i	0.880777	−	0.473532i	$-0.157021\pi$
$164$	6.96103i	0.543565i
$165$	− 9.03208i	− 0.703147i
$166$	−2.84790	−0.221040
$167$	5.89177i	0.455919i	0.973671	+	0.227959i	$0.0732054\pi$
$167$	5.89177i	0.455919i	−0.973671	+	0.227959i	$0.926795\pi$
$168$	−18.6565	−1.43938
$169$	0.261831	0.0201408
$170$	0	0
$171$	−8.26822	−0.632287
$172$	5.45290	0.415780
$173$	2.07551i	0.157798i	0.996883	+	0.0788992i	$0.0251405\pi$
$173$	2.07551i	0.157798i	−0.996883	+	0.0788992i	$0.974859\pi$
$174$	2.38059	0.180472
$175$	2.44256i	0.184640i
$176$	7.30577i	0.550693i
$177$	3.48242i	0.261755i
$178$	−1.87515	−0.140548
$179$	−10.5373	−0.787597	−0.393799	−	0.919197i	$-0.628839\pi$
$179$	−10.5373	−0.787597	−0.393799	+	0.919197i	$0.628839\pi$
$180$	2.30845i	0.172062i
$181$	3.39068i	0.252028i	0.992028	+	0.126014i	$0.0402184\pi$
$181$	3.39068i	0.252028i	−0.992028	+	0.126014i	$0.959782\pi$
$182$	− 10.0254i	− 0.743130i
$183$	2.82455	0.208797
$184$	− 4.32418i	− 0.318783i
$185$	−11.0054	−0.809133
$186$	26.4237	1.93748
$187$	0	0
$188$	−3.95995	−0.288809
$189$	0.991860	0.0721472
$190$	− 2.94570i	− 0.213704i
$191$	12.3426	0.893077	0.446538	−	0.894764i	$-0.352657\pi$
$191$	12.3426	0.893077	0.446538	+	0.894764i	$0.352657\pi$
$192$	− 20.8553i	− 1.50510i
$193$	− 11.9557i	− 0.860590i	−0.902688	−	0.430295i	$-0.858409\pi$
$193$	− 11.9557i	− 0.860590i	0.902688	−	0.430295i	$-0.141591\pi$
$194$	− 13.8262i	− 0.992665i
$195$	−9.04103	−0.647441
$196$	−0.754430	−0.0538878
$197$	1.22210i	0.0870711i	0.999052	+	0.0435356i	$0.0138622\pi$
$197$	1.22210i	0.0870711i	−0.999052	+	0.0435356i	$0.986138\pi$
$198$	− 12.9718i	− 0.921869i
$199$	− 21.7349i	− 1.54075i	−0.637592	−	0.770374i	$-0.720070\pi$
$199$	− 21.7349i	− 1.54075i	0.637592	−	0.770374i	$-0.279930\pi$
$200$	−3.07658	−0.217547
$201$	5.16162i	0.364073i
$202$	4.71265	0.331581
$203$	−2.07807	−0.145852
$204$	0	0
$205$	9.53958	0.666273
$206$	−9.11148	−0.634827
$207$	4.44644i	0.309049i
$208$	7.31300	0.507065
$209$	− 9.50840i	− 0.657710i
$210$	6.83463i	0.471634i
$211$	− 16.8853i	− 1.16243i	−0.813749	−	0.581217i	$-0.802577\pi$
$211$	− 16.8853i	− 1.16243i	0.813749	−	0.581217i	$-0.197423\pi$
$212$	9.44618	0.648767
$213$	30.5165	2.09096
$214$	− 9.91907i	− 0.678053i
$215$	− 7.47280i	− 0.509641i
$216$	1.24932i	0.0850053i
$217$	−23.0659	−1.56582
$218$	− 16.1335i	− 1.09270i
$219$	−3.66406	−0.247594
$220$	−2.65470	−0.178980
$221$	0	0
$222$	−30.7946	−2.06680
$223$	−9.61320	−0.643748	−0.321874	−	0.946783i	$-0.604313\pi$
$223$	−9.61320	−0.643748	−0.321874	+	0.946783i	$0.604313\pi$
$224$	9.50115i	0.634823i
$225$	3.16356	0.210904
$226$	− 12.9161i	− 0.859168i
$227$	− 1.77929i	− 0.118096i	−0.998255	−	0.0590479i	$-0.981194\pi$
$227$	− 1.77929i	− 0.118096i	0.998255	−	0.0590479i	$-0.0188065\pi$
$228$	4.73473i	0.313565i
$229$	16.7429	1.10640	0.553201	−	0.833048i	$-0.313406\pi$
$229$	16.7429	1.10640	0.553201	+	0.833048i	$0.313406\pi$
$230$	−1.58412	−0.104454
$231$	22.0614i	1.45153i
$232$	− 2.61748i	− 0.171846i
$233$	− 13.0860i	− 0.857295i	−0.903472	−	0.428648i	$-0.858990\pi$
$233$	− 13.0860i	− 0.857295i	0.903472	−	0.428648i	$-0.141010\pi$
$234$	−12.9847	−0.848836
$235$	5.42683i	0.354007i
$236$	1.02355	0.0666275
$237$	−22.2762	−1.44700
$238$	0	0
$239$	−23.9469	−1.54900	−0.774498	−	0.632577i	$-0.781997\pi$
$239$	−23.9469	−1.54900	−0.774498	+	0.632577i	$0.781997\pi$
$240$	−4.98551	−0.321814
$241$	− 17.2911i	− 1.11382i	−0.830574	−	0.556908i	$-0.811988\pi$
$241$	− 17.2911i	− 1.11382i	0.830574	−	0.556908i	$-0.188012\pi$
$242$	2.51970	0.161972
$243$	22.2775i	1.42910i
$244$	− 0.830189i	− 0.0531474i
$245$	1.03389i	0.0660529i
$246$	26.6931	1.70189
$247$	−9.51781	−0.605604
$248$	− 29.0531i	− 1.84488i
$249$	− 6.27318i	− 0.397546i
$250$	1.12708i	0.0712826i
$251$	−18.2106	−1.14944	−0.574722	−	0.818349i	$-0.694890\pi$
$251$	−18.2106	−1.14944	−0.574722	+	0.818349i	$0.694890\pi$
$252$	− 5.63854i	− 0.355194i
$253$	−5.11338	−0.321475
$254$	−2.83529	−0.177902
$255$	0	0
$256$	−14.8981	−0.931128
$257$	−2.58018	−0.160947	−0.0804735	−	0.996757i	$-0.525643\pi$
$257$	−2.58018	−0.160947	−0.0804735	+	0.996757i	$0.525643\pi$
$258$	− 20.9099i	− 1.30180i
$259$	26.8814	1.67033
$260$	2.65733i	0.164801i
$261$	2.69148i	0.166599i
$262$	− 2.50470i	− 0.154741i
$263$	−9.58787	−0.591213	−0.295607	−	0.955310i	$-0.595522\pi$
$263$	−9.58787	−0.591213	−0.295607	+	0.955310i	$0.595522\pi$
$264$	−27.7879	−1.71023
$265$	− 12.9453i	− 0.795224i
$266$	7.19506i	0.441157i
$267$	− 4.13046i	− 0.252780i
$268$	1.51710	0.0926717
$269$	− 7.08590i	− 0.432035i	−0.976389	−	0.216018i	$-0.930693\pi$
$269$	− 7.08590i	− 0.432035i	0.976389	−	0.216018i	$-0.0693069\pi$
$270$	0.457676	0.0278533
$271$	−13.7773	−0.836909	−0.418454	−	0.908238i	$-0.637428\pi$
$271$	−13.7773	−0.836909	−0.418454	+	0.908238i	$0.637428\pi$
$272$	0	0
$273$	22.0833	1.33654
$274$	24.9798	1.50908
$275$	3.63808i	0.219384i
$276$	2.54622	0.153264
$277$	− 4.51506i	− 0.271284i	−0.990758	−	0.135642i	$-0.956690\pi$
$277$	− 4.51506i	− 0.271284i	0.990758	−	0.135642i	$-0.0433096\pi$
$278$	− 15.6502i	− 0.938637i
$279$	29.8746i	1.78854i
$280$	7.51473	0.449091
$281$	3.44172	0.205316	0.102658	−	0.994717i	$-0.467265\pi$
$281$	3.44172	0.205316	0.102658	+	0.994717i	$0.467265\pi$
$282$	15.1850i	0.904255i
$283$	− 23.5408i	− 1.39935i	−0.714459	−	0.699677i	$-0.753327\pi$
$283$	− 23.5408i	− 1.39935i	0.714459	−	0.699677i	$-0.246673\pi$
$284$	− 8.96938i	− 0.532235i
$285$	6.48861	0.384352
$286$	− 14.9323i	− 0.882966i
$287$	−23.3010	−1.37542
$288$	12.3057	0.725122
$289$	0	0
$290$	−0.958888	−0.0563079
$291$	30.4555	1.78534
$292$	1.07694i	0.0630230i
$293$	−15.5924	−0.910918	−0.455459	−	0.890257i	$-0.650525\pi$
$293$	−15.5924	−0.910918	−0.455459	+	0.890257i	$0.650525\pi$
$294$	2.89297i	0.168721i
$295$	− 1.40270i	− 0.0816685i
$296$	33.8590i	1.96801i
$297$	1.47733	0.0857232
$298$	−13.1261	−0.760372
$299$	5.11844i	0.296007i
$300$	− 1.81159i	− 0.104592i
$301$	18.2528i	1.05207i
$302$	3.18660	0.183368
$303$	10.3807i	0.596358i
$304$	−5.24843	−0.301018
$305$	−1.13771	−0.0651453
$306$	0	0
$307$	21.6549	1.23591	0.617955	−	0.786214i	$-0.287962\pi$
$307$	21.6549	1.23591	0.617955	+	0.786214i	$0.287962\pi$
$308$	6.48428	0.369476
$309$	− 20.0702i	− 1.14175i
$310$	−10.6433	−0.604501
$311$	8.86449i	0.502659i	0.967902	+	0.251330i	$0.0808678\pi$
$311$	8.86449i	0.502659i	−0.967902	+	0.251330i	$0.919132\pi$
$312$	27.8154i	1.57474i
$313$	− 17.1141i	− 0.967345i	−0.875249	−	0.483672i	$-0.839303\pi$
$313$	− 17.1141i	− 0.967345i	0.875249	−	0.483672i	$-0.160697\pi$
$314$	1.54311	0.0870828
$315$	−7.72720	−0.435379
$316$	6.54742i	0.368321i
$317$	− 10.3241i	− 0.579862i	−0.957048	−	0.289931i	$-0.906368\pi$
$317$	− 10.3241i	− 0.579862i	0.957048	−	0.289931i	$-0.0936323\pi$
$318$	− 36.2228i	− 2.03127i
$319$	−3.09519	−0.173297
$320$	8.40042i	0.469598i
$321$	21.8491	1.21950
$322$	3.86932	0.215629
$323$	0	0
$324$	6.18971	0.343873
$325$	3.64168	0.202004
$326$	13.6278i	0.754775i
$327$	35.5378	1.96524
$328$	− 29.3493i	− 1.62054i
$329$	− 13.2554i	− 0.730792i
$330$	10.1798i	0.560382i
$331$	6.56727	0.360970	0.180485	−	0.983578i	$-0.442233\pi$
$331$	6.56727	0.360970	0.180485	+	0.983578i	$0.442233\pi$
$332$	−1.84381	−0.101192
$333$	− 34.8163i	− 1.90792i
$334$	− 6.64048i	− 0.363351i
$335$	− 2.07908i	− 0.113592i
$336$	12.1774	0.664333
$337$	− 30.1761i	− 1.64380i	−0.569633	−	0.821899i	$-0.692915\pi$
$337$	− 30.1761i	− 1.64380i	0.569633	−	0.821899i	$-0.307085\pi$
$338$	−0.295103	−0.0160515
$339$	28.4508	1.54524
$340$	0	0
$341$	−34.3555	−1.86046
$342$	9.31892	0.503909
$343$	− 19.6233i	− 1.05956i
$344$	−22.9907	−1.23957
$345$	− 3.48941i	− 0.187863i
$346$	− 2.33926i	− 0.125759i
$347$	7.04017i	0.377936i	0.981983	+	0.188968i	$0.0605142\pi$
$347$	7.04017i	0.377936i	−0.981983	+	0.188968i	$0.939486\pi$
$348$	1.54126	0.0826200
$349$	35.4396	1.89704	0.948518	−	0.316723i	$-0.102583\pi$
$349$	35.4396	1.89704	0.948518	+	0.316723i	$0.102583\pi$
$350$	− 2.75295i	− 0.147152i
$351$	− 1.47879i	− 0.0789320i
$352$	14.1515i	0.754278i
$353$	8.54669	0.454895	0.227447	−	0.973790i	$-0.426962\pi$
$353$	8.54669	0.454895	0.227447	+	0.973790i	$0.426962\pi$
$354$	− 3.92495i	− 0.208609i
$355$	−12.2919	−0.652386
$356$	−1.21402	−0.0643430
$357$	0	0
$358$	11.8764	0.627686
$359$	20.2839	1.07054	0.535271	−	0.844681i	$-0.320210\pi$
$359$	20.2839	1.07054	0.535271	+	0.844681i	$0.320210\pi$
$360$	− 9.73296i	− 0.512972i
$361$	−12.1692	−0.640485
$362$	− 3.82156i	− 0.200857i
$363$	5.55023i	0.291312i
$364$	− 6.49070i	− 0.340205i
$365$	1.47586	0.0772503
$366$	−3.18348	−0.166403
$367$	− 12.7223i	− 0.664097i	−0.943262	−	0.332048i	$-0.892260\pi$
$367$	− 12.7223i	− 0.664097i	0.943262	−	0.332048i	$-0.107740\pi$
$368$	2.82247i	0.147132i
$369$	30.1791i	1.57106i
$370$	12.4039	0.644849
$371$	31.6197i	1.64161i
$372$	17.1074	0.886979
$373$	−11.1454	−0.577086	−0.288543	−	0.957467i	$-0.593171\pi$
$373$	−11.1454	−0.577086	−0.288543	+	0.957467i	$0.593171\pi$
$374$	0	0
$375$	−2.48265	−0.128204
$376$	16.6961	0.861034
$377$	3.09825i	0.159568i
$378$	−1.11790	−0.0574987
$379$	− 12.6811i	− 0.651386i	−0.945476	−	0.325693i	$-0.894402\pi$
$379$	− 12.6811i	− 0.651386i	0.945476	−	0.325693i	$-0.105598\pi$
$380$	− 1.90713i	− 0.0978335i
$381$	− 6.24541i	− 0.319962i
$382$	−13.9110	−0.711749
$383$	−17.3523	−0.886661	−0.443331	−	0.896358i	$-0.646203\pi$
$383$	−17.3523	−0.886661	−0.443331	+	0.896358i	$0.646203\pi$
$384$	4.19133i	0.213888i
$385$	− 8.88623i	− 0.452884i
$386$	13.4750i	0.685859i
$387$	23.6407	1.20172
$388$	− 8.95147i	− 0.454442i
$389$	−19.4510	−0.986205	−0.493103	−	0.869971i	$-0.664137\pi$
$389$	−19.4510	−0.986205	−0.493103	+	0.869971i	$0.664137\pi$
$390$	10.1899	0.515987
$391$	0	0
$392$	3.18085	0.160657
$393$	5.51720	0.278306
$394$	− 1.37740i	− 0.0693925i
$395$	8.97276	0.451468
$396$	− 8.39832i	− 0.422032i
$397$	4.75987i	0.238891i	0.992841	+	0.119446i	$0.0381117\pi$
$397$	4.75987i	0.238891i	−0.992841	+	0.119446i	$0.961888\pi$
$398$	24.4969i	1.22792i
$399$	−15.8488	−0.793434
$400$	2.00814	0.100407
$401$	24.2040i	1.20869i	0.796723	+	0.604345i	$0.206565\pi$
$401$	24.2040i	1.20869i	−0.796723	+	0.604345i	$0.793435\pi$
$402$	− 5.81754i	− 0.290153i
$403$	34.3896i	1.71307i
$404$	3.05110	0.151798
$405$	− 8.48255i	− 0.421501i
$406$	2.34214	0.116239
$407$	40.0385	1.98463
$408$	0	0
$409$	18.2463	0.902221	0.451111	−	0.892468i	$-0.351028\pi$
$409$	18.2463	0.902221	0.451111	+	0.892468i	$0.351028\pi$
$410$	−10.7518	−0.530995
$411$	55.0239i	2.71413i
$412$	−5.89901	−0.290624
$413$	3.42619i	0.168592i
$414$	− 5.01148i	− 0.246301i
$415$	2.52680i	0.124036i
$416$	14.1655	0.694522
$417$	34.4733	1.68816
$418$	10.7167i	0.524170i
$419$	− 1.74273i	− 0.0851377i	−0.999094	−	0.0425689i	$-0.986446\pi$
$419$	− 1.74273i	− 0.0851377i	0.999094	−	0.0425689i	$-0.0135542\pi$
$420$	4.42492i	0.215914i
$421$	37.0251	1.80449	0.902247	−	0.431220i	$-0.141917\pi$
$421$	37.0251	1.80449	0.902247	+	0.431220i	$0.141917\pi$
$422$	19.0310i	0.926417i
$423$	−17.1681	−0.834743
$424$	−39.8273	−1.93418
$425$	0	0
$426$	−34.3944	−1.66641
$427$	2.77894	0.134482
$428$	− 6.42187i	− 0.310413i
$429$	32.8920	1.58804
$430$	8.42242i	0.406165i
$431$	− 30.3883i	− 1.46375i	−0.681438	−	0.731876i	$-0.738645\pi$
$431$	− 30.3883i	− 1.46375i	0.681438	−	0.731876i	$-0.261355\pi$
$432$	− 0.815453i	− 0.0392335i
$433$	−15.8246	−0.760483	−0.380242	−	0.924887i	$-0.624159\pi$
$433$	−15.8246	−0.760483	−0.380242	+	0.924887i	$0.624159\pi$
$434$	25.9970	1.24790
$435$	− 2.11218i	− 0.101271i
$436$	− 10.4452i	− 0.500236i
$437$	− 3.67343i	− 0.175724i
$438$	4.12967	0.197323
$439$	− 4.16714i	− 0.198887i	−0.995043	−	0.0994434i	$-0.968294\pi$
$439$	− 4.16714i	− 0.198887i	0.995043	−	0.0994434i	$-0.0317062\pi$
$440$	11.1928	0.533597
$441$	−3.27078	−0.155751
$442$	0	0
$443$	15.7201	0.746884	0.373442	−	0.927654i	$-0.378177\pi$
$443$	15.7201	0.746884	0.373442	+	0.927654i	$0.378177\pi$
$444$	−19.9373	−0.946181
$445$	1.66373i	0.0788683i
$446$	10.8348	0.513043
$447$	− 28.9133i	− 1.36755i
$448$	− 20.5185i	− 0.969410i
$449$	− 16.5469i	− 0.780895i	−0.920625	−	0.390447i	$-0.872320\pi$
$449$	− 16.5469i	− 0.780895i	0.920625	−	0.390447i	$-0.127680\pi$
$450$	−3.56558	−0.168083
$451$	−34.7057	−1.63423
$452$	− 8.36224i	− 0.393327i
$453$	7.01924i	0.329792i
$454$	2.00540i	0.0941181i
$455$	−8.89503	−0.417005
$456$	− 19.9627i	− 0.934839i
$457$	1.42830	0.0668131	0.0334066	−	0.999442i	$-0.489364\pi$
$457$	1.42830	0.0668131	0.0334066	+	0.999442i	$0.489364\pi$
$458$	−18.8705	−0.881761
$459$	0	0
$460$	−1.02560	−0.0478191
$461$	−11.1662	−0.520062	−0.260031	−	0.965600i	$-0.583733\pi$
$461$	−11.1662	−0.520062	−0.260031	+	0.965600i	$0.583733\pi$
$462$	− 24.8649i	− 1.15682i
$463$	29.2204	1.35799	0.678994	−	0.734144i	$-0.262416\pi$
$463$	29.2204	1.35799	0.678994	+	0.734144i	$0.262416\pi$
$464$	1.70848i	0.0793140i
$465$	− 23.4445i	− 1.08721i
$466$	14.7490i	0.683233i
$467$	10.9388	0.506187	0.253093	−	0.967442i	$-0.418552\pi$
$467$	10.9388	0.506187	0.253093	+	0.967442i	$0.418552\pi$
$468$	−8.40664	−0.388597
$469$	5.07827i	0.234493i
$470$	− 6.11645i	− 0.282131i
$471$	3.39907i	0.156621i
$472$	−4.31552	−0.198638
$473$	27.1866i	1.25004i
$474$	25.1070	1.15320
$475$	−2.61358	−0.119919
$476$	0	0
$477$	40.9533	1.87512
$478$	26.9900	1.23449
$479$	− 17.1996i	− 0.785871i	−0.919566	−	0.392935i	$-0.871460\pi$
$479$	− 17.1996i	− 0.785871i	0.919566	−	0.392935i	$-0.128540\pi$
$480$	−9.65710	−0.440784
$481$	− 40.0781i	− 1.82741i
$482$	19.4884i	0.887670i
$483$	8.52310i	0.387814i
$484$	1.63132	0.0741509
$485$	−12.2673	−0.557031
$486$	− 25.1084i	− 1.13894i
$487$	25.8446i	1.17113i	0.810626	+	0.585564i	$0.199127\pi$
$487$	25.8446i	1.17113i	−0.810626	+	0.585564i	$0.800873\pi$
$488$	3.50026i	0.158450i
$489$	−30.0185	−1.35748
$490$	− 1.16527i	− 0.0526417i
$491$	−12.2373	−0.552261	−0.276131	−	0.961120i	$-0.589052\pi$
$491$	−12.2373	−0.552261	−0.276131	+	0.961120i	$0.589052\pi$
$492$	17.2818	0.779124
$493$	0	0
$494$	10.7273	0.482644
$495$	−11.5093	−0.517304
$496$	18.9635i	0.851487i
$497$	30.0237	1.34675
$498$	7.07035i	0.316830i
$499$	− 6.41606i	− 0.287222i	−0.989634	−	0.143611i	$-0.954129\pi$
$499$	− 6.41606i	− 0.287222i	0.989634	−	0.143611i	$-0.0458715\pi$
$500$	0.729699i	0.0326332i
$501$	14.6272	0.653496
$502$	20.5248	0.916065
$503$	21.3299i	0.951054i	0.879701	+	0.475527i	$0.157743\pi$
$503$	21.3299i	0.951054i	−0.879701	+	0.475527i	$0.842257\pi$
$504$	23.7733i	1.05895i
$505$	− 4.18131i	− 0.186066i
$506$	5.76317	0.256204
$507$	− 0.650034i	− 0.0288690i
$508$	−1.83565	−0.0814436
$509$	14.2265	0.630577	0.315289	−	0.948996i	$-0.397899\pi$
$509$	14.2265	0.630577	0.315289	+	0.948996i	$0.397899\pi$
$510$	0	0
$511$	−3.60489	−0.159471
$512$	20.1677	0.891296
$513$	1.06131i	0.0468578i
$514$	2.90805	0.128269
$515$	8.08417i	0.356231i
$516$	− 13.5377i	− 0.595962i
$517$	− 19.7432i	− 0.868306i
$518$	−30.2973	−1.33119
$519$	5.15278	0.226182
$520$	− 11.2039i	− 0.491324i
$521$	24.5559i	1.07581i	0.843005	+	0.537906i	$0.180784\pi$
$521$	24.5559i	1.07581i	−0.843005	+	0.537906i	$0.819216\pi$
$522$	− 3.03351i	− 0.132773i
$523$	−39.8642	−1.74314	−0.871570	−	0.490271i	$-0.836898\pi$
$523$	−39.8642	−1.74314	−0.871570	+	0.490271i	$0.836898\pi$
$524$	− 1.62161i	− 0.0708404i
$525$	6.06403	0.264656
$526$	10.8063	0.471175
$527$	0	0
$528$	18.1377	0.789341
$529$	21.0245	0.914110
$530$	14.5903i	0.633764i
$531$	4.43754	0.192573
$532$	4.65827i	0.201962i
$533$	34.7401i	1.50476i
$534$	4.65534i	0.201456i
$535$	−8.80071	−0.380488
$536$	−6.39644	−0.276284
$537$	26.1605i	1.12891i
$538$	7.98635i	0.344316i
$539$	− 3.76138i	− 0.162014i
$540$	0.296312	0.0127512
$541$	22.8827i	0.983803i	0.870651	+	0.491901i	$0.163698\pi$
$541$	22.8827i	0.983803i	−0.870651	+	0.491901i	$0.836302\pi$
$542$	15.5280	0.666985
$543$	8.41789	0.361246
$544$	0	0
$545$	−14.3144	−0.613163
$546$	−24.8895	−1.06517
$547$	15.5350i	0.664231i	0.943239	+	0.332115i	$0.107762\pi$
$547$	15.5350i	0.664231i	−0.943239	+	0.332115i	$0.892238\pi$
$548$	16.1726	0.690858
$549$	− 3.59923i	− 0.153611i
$550$	− 4.10039i	− 0.174841i
$551$	− 2.22357i	− 0.0947271i
$552$	−10.7354	−0.456931
$553$	−21.9165	−0.931985
$554$	5.08882i	0.216203i
$555$	27.3226i	1.15978i
$556$	− 10.1324i	− 0.429708i
$557$	0.980081	0.0415274	0.0207637	−	0.999784i	$-0.493390\pi$
$557$	0.980081	0.0415274	0.0207637	+	0.999784i	$0.493390\pi$
$558$	− 33.6709i	− 1.42540i
$559$	27.2136	1.15101
$560$	−4.90501	−0.207274
$561$	0	0
$562$	−3.87908	−0.163629
$563$	−28.8837	−1.21730	−0.608652	−	0.793437i	$-0.708289\pi$
$563$	−28.8837	−1.21730	−0.608652	+	0.793437i	$0.708289\pi$
$564$	9.83119i	0.413968i
$565$	−11.4598	−0.482119
$566$	26.5322i	1.11523i
$567$	20.7192i	0.870123i
$568$	37.8170i	1.58676i
$569$	−18.2893	−0.766729	−0.383365	−	0.923597i	$-0.625235\pi$
$569$	−18.2893	−0.766729	−0.383365	+	0.923597i	$0.625235\pi$
$570$	−7.31315	−0.306314
$571$	− 10.4044i	− 0.435410i	−0.976015	−	0.217705i	$-0.930143\pi$
$571$	− 10.4044i	− 0.435410i	0.976015	−	0.217705i	$-0.0698571\pi$
$572$	− 9.66758i	− 0.404222i
$573$	− 30.6423i	− 1.28010i
$574$	26.2620	1.09616
$575$	1.40552i	0.0586141i
$576$	−26.5753	−1.10730
$577$	−28.3066	−1.17842	−0.589209	−	0.807980i	$-0.700561\pi$
$577$	−28.3066	−1.17842	−0.589209	+	0.807980i	$0.700561\pi$
$578$	0	0
$579$	−29.6819	−1.23354
$580$	−0.620810	−0.0257777
$581$	− 6.17187i	− 0.256052i
$582$	−34.3257	−1.42285
$583$	47.0960i	1.95052i
$584$	− 4.54061i	− 0.187892i
$585$	11.5207i	0.476322i
$586$	17.5738	0.725968
$587$	−2.68137	−0.110672	−0.0553360	−	0.998468i	$-0.517623\pi$
$587$	−2.68137	−0.110672	−0.0553360	+	0.998468i	$0.517623\pi$
$588$	1.87299i	0.0772407i
$589$	− 24.6809i	− 1.01696i
$590$	1.58095i	0.0650868i
$591$	3.03405	0.124804
$592$	− 22.1004i	− 0.908320i
$593$	15.3155	0.628934	0.314467	−	0.949268i	$-0.398174\pi$
$593$	15.3155	0.628934	0.314467	+	0.949268i	$0.398174\pi$
$594$	−1.66506	−0.0683183
$595$	0	0
$596$	−8.49817	−0.348098
$597$	−53.9603	−2.20845
$598$	− 5.76887i	− 0.235907i
$599$	−43.5243	−1.77836	−0.889178	−	0.457561i	$-0.848723\pi$
$599$	−43.5243	−1.77836	−0.889178	+	0.457561i	$0.848723\pi$
$600$	7.63808i	0.311823i
$601$	− 30.7307i	− 1.25353i	−0.779208	−	0.626766i	$-0.784378\pi$
$601$	− 30.7307i	− 1.25353i	0.779208	−	0.626766i	$-0.215622\pi$
$602$	− 20.5723i	− 0.838463i
$603$	6.57729	0.267848
$604$	2.06309	0.0839459
$605$	− 2.23561i	− 0.0908903i
$606$	− 11.6999i	− 0.475275i
$607$	14.7075i	0.596957i	0.954416	+	0.298479i	$0.0964791\pi$
$607$	14.7075i	0.596957i	−0.954416	+	0.298479i	$0.903521\pi$
$608$	−10.1664	−0.412301
$609$	5.15913i	0.209058i
$610$	1.28229	0.0519184
$611$	−19.7628	−0.799516
$612$	0	0
$613$	23.6535	0.955354	0.477677	−	0.878535i	$-0.341479\pi$
$613$	23.6535	0.955354	0.477677	+	0.878535i	$0.341479\pi$
$614$	−24.4067	−0.984974
$615$	− 23.6835i	− 0.955009i
$616$	−27.3392	−1.10153
$617$	− 10.0479i	− 0.404512i	−0.979333	−	0.202256i	$-0.935173\pi$
$617$	− 10.0479i	− 0.404512i	0.979333	−	0.202256i	$-0.0648273\pi$
$618$	22.6206i	0.909935i
$619$	− 34.3858i	− 1.38208i	−0.722815	−	0.691042i	$-0.757152\pi$
$619$	− 34.3858i	− 1.38208i	0.722815	−	0.691042i	$-0.242848\pi$
$620$	−6.89079	−0.276741
$621$	0.570743	0.0229031
$622$	− 9.99096i	− 0.400601i
$623$	− 4.06376i	− 0.162811i
$624$	− 18.1556i	− 0.726807i
$625$	1.00000	0.0400000
$626$	19.2889i	0.770938i
$627$	−23.6060	−0.942735
$628$	0.999052	0.0398665
$629$	0	0
$630$	8.70915	0.346981
$631$	−8.25061	−0.328451	−0.164226	−	0.986423i	$-0.552513\pi$
$631$	−8.25061	−0.328451	−0.164226	+	0.986423i	$0.552513\pi$
$632$	− 27.6054i	− 1.09808i
$633$	−41.9204	−1.66619
$634$	11.6361i	0.462128i
$635$	2.51562i	0.0998293i
$636$	− 23.4516i	− 0.929916i
$637$	−3.76510	−0.149179
$638$	3.48851	0.138111
$639$	− 38.8862i	− 1.53831i
$640$	− 1.68825i	− 0.0667337i
$641$	− 17.2231i	− 0.680271i	−0.940376	−	0.340136i	$-0.889527\pi$
$641$	− 17.2231i	− 0.680271i	0.940376	−	0.340136i	$-0.110473\pi$
$642$	−24.6256	−0.971895
$643$	− 12.5592i	− 0.495287i	−0.968851	−	0.247644i	$-0.920344\pi$
$643$	− 12.5592i	− 0.495287i	0.968851	−	0.247644i	$-0.0796562\pi$
$644$	2.50510	0.0987149
$645$	−18.5524	−0.730499
$646$	0	0
$647$	−3.62337	−0.142449	−0.0712247	−	0.997460i	$-0.522691\pi$
$647$	−3.62337	−0.142449	−0.0712247	+	0.997460i	$0.522691\pi$
$648$	−26.0972	−1.02520
$649$	5.10314i	0.200316i
$650$	−4.10445	−0.160990
$651$	57.2646i	2.24438i
$652$	8.82301i	0.345536i
$653$	9.74594i	0.381388i	0.981650	+	0.190694i	$0.0610739\pi$
$653$	9.74594i	0.381388i	−0.981650	+	0.190694i	$0.938926\pi$
$654$	−40.0538	−1.56623
$655$	−2.22230	−0.0868325
$656$	19.1568i	0.747948i
$657$	4.66899i	0.182155i
$658$	14.9398i	0.582414i
$659$	7.19930	0.280445	0.140222	−	0.990120i	$-0.455218\pi$
$659$	7.19930	0.280445	0.140222	+	0.990120i	$0.455218\pi$
$660$	6.59071i	0.256543i
$661$	11.0362	0.429258	0.214629	−	0.976696i	$-0.431146\pi$
$661$	11.0362	0.429258	0.214629	+	0.976696i	$0.431146\pi$
$662$	−7.40181	−0.287680
$663$	0	0
$664$	7.77391	0.301686
$665$	6.38383	0.247554
$666$	39.2406i	1.52054i
$667$	−1.19578	−0.0463007
$668$	− 4.29922i	− 0.166342i
$669$	23.8662i	0.922722i
$670$	2.34328i	0.0905287i
$671$	4.13909	0.159788
$672$	23.5881	0.909929
$673$	29.5111i	1.13757i	0.822487	+	0.568784i	$0.192586\pi$
$673$	29.5111i	1.13757i	−0.822487	+	0.568784i	$0.807414\pi$
$674$	34.0108i	1.31005i
$675$	− 0.406074i	− 0.0156298i
$676$	−0.191058	−0.00734837
$677$	0.557951i	0.0214438i	0.999943	+	0.0107219i	$0.00341295\pi$
$677$	0.557951i	0.0214438i	−0.999943	+	0.0107219i	$0.996587\pi$
$678$	−32.0662	−1.23150
$679$	29.9637	1.14990
$680$	0	0
$681$	−4.41737	−0.169274
$682$	38.7213	1.48272
$683$	− 36.1564i	− 1.38348i	−0.722144	−	0.691742i	$-0.756843\pi$
$683$	− 36.1564i	− 1.38348i	0.722144	−	0.691742i	$-0.243157\pi$
$684$	6.03332	0.230690
$685$	− 22.1633i	− 0.846818i
$686$	22.1169i	0.844428i
$687$	− 41.5668i	− 1.58587i
$688$	15.0064	0.572115
$689$	47.1427	1.79599
$690$	3.93283i	0.149720i
$691$	− 39.8226i	− 1.51492i	−0.652880	−	0.757461i	$-0.726439\pi$
$691$	− 39.8226i	− 1.51492i	0.652880	−	0.757461i	$-0.273561\pi$
$692$	− 1.51450i	− 0.0575727i
$693$	28.1122	1.06789
$694$	− 7.93480i	− 0.301201i
$695$	−13.8857	−0.526714
$696$	−6.49829	−0.246317
$697$	0	0
$698$	−39.9431	−1.51187
$699$	−32.4881	−1.22881
$700$	− 1.78234i	− 0.0673660i
$701$	−20.0299	−0.756520	−0.378260	−	0.925699i	$-0.623478\pi$
$701$	−20.0299	−0.756520	−0.378260	+	0.925699i	$0.623478\pi$
$702$	1.66671i	0.0629059i
$703$	28.7635i	1.08483i
$704$	− 30.5614i	− 1.15182i
$705$	13.4729	0.507420
$706$	−9.63277	−0.362534
$707$	10.2131i	0.384103i
$708$	− 2.54112i	− 0.0955012i
$709$	9.70848i	0.364610i	0.983242	+	0.182305i	$0.0583558\pi$
$709$	9.70848i	0.364610i	−0.983242	+	0.182305i	$0.941644\pi$
$710$	13.8539	0.519927
$711$	28.3859i	1.06455i
$712$	5.11859	0.191827
$713$	−13.2727	−0.497068
$714$	0	0
$715$	−13.2487	−0.495474
$716$	7.68909	0.287355
$717$	59.4518i	2.22027i
$718$	−22.8615	−0.853182
$719$	− 20.8091i	− 0.776050i	−0.921649	−	0.388025i	$-0.873157\pi$
$719$	− 20.8091i	− 0.776050i	0.921649	−	0.388025i	$-0.126843\pi$
$720$	6.35288i	0.236758i
$721$	− 19.7461i	− 0.735383i
$722$	13.7156	0.510443
$723$	−42.9277	−1.59650
$724$	− 2.47418i	− 0.0919522i
$725$	0.850775i	0.0315970i
$726$	− 6.25554i	− 0.232165i
$727$	−39.1557	−1.45220	−0.726102	−	0.687587i	$-0.758670\pi$
$727$	−39.1557	−1.45220	−0.726102	+	0.687587i	$0.758670\pi$
$728$	27.3663i	1.01426i
$729$	29.8595	1.10591
$730$	−1.66341	−0.0615656
$731$	0	0
$732$	−2.06107	−0.0761793
$733$	−12.9215	−0.477265	−0.238633	−	0.971110i	$-0.576699\pi$
$733$	−12.9215	−0.477265	−0.238633	+	0.971110i	$0.576699\pi$
$734$	14.3390i	0.529261i
$735$	2.56679	0.0946776
$736$	5.46722i	0.201525i
$737$	7.56384i	0.278618i
$738$	− 34.0141i	− 1.25208i
$739$	37.9866	1.39736	0.698680	−	0.715434i	$-0.253771\pi$
$739$	37.9866	1.39736	0.698680	+	0.715434i	$0.253771\pi$
$740$	8.03063	0.295212
$741$	23.6294i	0.868049i
$742$	− 35.6378i	− 1.30831i
$743$	− 12.2402i	− 0.449050i	−0.974468	−	0.224525i	$-0.927917\pi$
$743$	− 12.2402i	− 0.449050i	0.974468	−	0.224525i	$-0.0720830\pi$
$744$	−72.1288	−2.64437
$745$	11.6461i	0.426681i
$746$	12.5617	0.459916
$747$	−7.99371	−0.292474
$748$	0	0
$749$	21.4963	0.785457
$750$	2.79814	0.102174
$751$	− 14.1068i	− 0.514766i	−0.966309	−	0.257383i	$-0.917140\pi$
$751$	− 14.1068i	− 0.514766i	0.966309	−	0.257383i	$-0.0828602\pi$
$752$	−10.8978	−0.397403
$753$	45.2107i	1.64757i
$754$	− 3.49196i	− 0.127170i
$755$	− 2.82731i	− 0.102896i
$756$	−0.723760	−0.0263229
$757$	0.782070	0.0284248	0.0142124	−	0.999899i	$-0.495476\pi$
$757$	0.782070	0.0284248	0.0142124	+	0.999899i	$0.495476\pi$
$758$	14.2926i	0.519130i
$759$	12.6947i	0.460790i
$760$	8.04088i	0.291673i
$761$	−2.86350	−0.103802	−0.0519009	−	0.998652i	$-0.516528\pi$
$761$	−2.86350	−0.103802	−0.0519009	+	0.998652i	$0.516528\pi$
$762$	7.03905i	0.254998i
$763$	34.9639	1.26578
$764$	−9.00636	−0.325839
$765$	0	0
$766$	19.5574	0.706636
$767$	5.10819	0.184446
$768$	36.9867i	1.33464i
$769$	−38.6633	−1.39423	−0.697117	−	0.716957i	$-0.745534\pi$
$769$	−38.6633	−1.39423	−0.697117	+	0.716957i	$0.745534\pi$
$770$	10.0155i	0.360932i
$771$	6.40568i	0.230695i
$772$	8.72407i	0.313986i
$773$	37.9989	1.36672	0.683362	−	0.730080i	$-0.260517\pi$
$773$	37.9989	1.36672	0.683362	+	0.730080i	$0.260517\pi$
$774$	−26.6449	−0.957730
$775$	9.44332i	0.339214i
$776$	37.7414i	1.35484i
$777$	− 66.7371i	− 2.39418i
$778$	21.9228	0.785969
$779$	− 24.9324i	− 0.893297i
$780$	6.59723	0.236219
$781$	44.7188	1.60017
$782$	0	0
$783$	0.345477	0.0123464
$784$	−2.07620	−0.0741499
$785$	− 1.36913i	− 0.0488663i
$786$	−6.21831	−0.221800
$787$	35.3733i	1.26092i	0.776221	+	0.630461i	$0.217134\pi$
$787$	35.3733i	1.26092i	−0.776221	+	0.630461i	$0.782866\pi$
$788$	− 0.891767i	− 0.0317679i
$789$	23.8033i	0.847421i
$790$	−10.1130	−0.359804
$791$	27.9914	0.995259
$792$	35.4092i	1.25821i
$793$	− 4.14319i	− 0.147129i
$794$	− 5.36474i	− 0.190387i
$795$	−32.1387	−1.13984
$796$	15.8600i	0.562141i
$797$	26.7826	0.948688	0.474344	−	0.880340i	$-0.342685\pi$
$797$	26.7826	0.948688	0.474344	+	0.880340i	$0.342685\pi$
$798$	17.8628	0.632337
$799$	0	0
$800$	3.88983	0.137526
$801$	−5.26331	−0.185970
$802$	− 27.2797i	− 0.963281i
$803$	−5.36931	−0.189479
$804$	− 3.76643i	− 0.132832i
$805$	− 3.43306i	− 0.121000i
$806$	− 38.7596i	− 1.36525i
$807$	−17.5918	−0.619262
$808$	−12.8641	−0.452558
$809$	− 54.0086i	− 1.89884i	−0.314009	−	0.949420i	$-0.601672\pi$
$809$	− 54.0086i	− 1.89884i	0.314009	−	0.949420i	$-0.398328\pi$
$810$	9.56048i	0.335921i
$811$	52.7965i	1.85394i	0.375141	+	0.926968i	$0.377594\pi$
$811$	52.7965i	1.85394i	−0.375141	+	0.926968i	$0.622406\pi$
$812$	1.51637	0.0532141
$813$	34.2041i	1.19959i
$814$	−45.1264	−1.58168
$815$	12.0913	0.423540
$816$	0	0
$817$	−19.5308	−0.683295
$818$	−20.5650	−0.719037
$819$	− 28.1400i	− 0.983291i
$820$	−6.96103	−0.243090
$821$	11.9083i	0.415601i	0.978171	+	0.207801i	$0.0666305\pi$
$821$	11.9083i	0.415601i	−0.978171	+	0.207801i	$0.933369\pi$
$822$	− 62.0161i	− 2.16306i
$823$	− 39.5415i	− 1.37833i	−0.724604	−	0.689165i	$-0.757977\pi$
$823$	− 39.5415i	− 1.37833i	0.724604	−	0.689165i	$-0.242023\pi$
$824$	24.8716	0.866443
$825$	9.03208	0.314457
$826$	− 3.86157i	− 0.134361i
$827$	18.3299i	0.637392i	0.947857	+	0.318696i	$0.103245\pi$
$827$	18.3299i	0.637392i	−0.947857	+	0.318696i	$0.896755\pi$
$828$	− 3.24457i	− 0.112756i
$829$	39.4065	1.36864	0.684322	−	0.729180i	$-0.260098\pi$
$829$	39.4065	1.36864	0.684322	+	0.729180i	$0.260098\pi$
$830$	− 2.84790i	− 0.0988521i
$831$	−11.2093	−0.388847
$832$	−30.5916	−1.06057
$833$	0	0
$834$	−38.8540	−1.34541
$835$	−5.89177	−0.203893
$836$	6.93827i	0.239965i
$837$	3.83468	0.132546
$838$	1.96418i	0.0678516i
$839$	20.6064i	0.711410i	0.934598	+	0.355705i	$0.115759\pi$
$839$	20.6064i	0.711410i	−0.934598	+	0.355705i	$0.884241\pi$
$840$	− 18.6565i	− 0.643710i
$841$	28.2762	0.975041
$842$	−41.7301	−1.43812
$843$	− 8.54459i	− 0.294291i
$844$	12.3212i	0.424114i
$845$	0.261831i	0.00900725i
$846$	19.3498	0.665259
$847$	5.46061i	0.187629i
$848$	25.9960	0.892706
$849$	−58.4436	−2.00578
$850$	0	0
$851$	15.4683	0.530245
$852$	−22.2679	−0.762884
$853$	8.24316i	0.282241i	0.989992	+	0.141120i	$0.0450704\pi$
$853$	8.24316i	0.282241i	−0.989992	+	0.141120i	$0.954930\pi$
$854$	−3.13207	−0.107177
$855$	− 8.26822i	− 0.282767i
$856$	27.0761i	0.925441i
$857$	27.7260i	0.947104i	0.880766	+	0.473552i	$0.157028\pi$
$857$	27.7260i	0.947104i	−0.880766	+	0.473552i	$0.842972\pi$
$858$	−37.0717	−1.26561
$859$	7.00671	0.239066	0.119533	−	0.992830i	$-0.461860\pi$
$859$	7.00671	0.239066	0.119533	+	0.992830i	$0.461860\pi$
$860$	5.45290i	0.185942i
$861$	57.8483i	1.97147i
$862$	34.2499i	1.16656i
$863$	−29.4176	−1.00139	−0.500693	−	0.865625i	$-0.666921\pi$
$863$	−29.4176	−1.00139	−0.500693	+	0.865625i	$0.666921\pi$
$864$	− 1.57956i	− 0.0537377i
$865$	−2.07551	−0.0705696
$866$	17.8356	0.606077
$867$	0	0
$868$	16.8312	0.571287
$869$	−32.6436	−1.10736
$870$	2.38059i	0.0807095i
$871$	7.57133	0.256545
$872$	44.0395i	1.49137i
$873$	− 38.8085i	− 1.31347i
$874$	4.14023i	0.140045i
$875$	−2.44256	−0.0825737
$876$	2.67366	0.0903347
$877$	− 51.5386i	− 1.74034i	−0.492755	−	0.870168i	$-0.664010\pi$
$877$	− 51.5386i	− 1.74034i	0.492755	−	0.870168i	$-0.335990\pi$
$878$	4.69668i	0.158505i
$879$	38.7105i	1.30567i
$880$	−7.30577	−0.246277
$881$	− 46.6768i	− 1.57258i	−0.617856	−	0.786291i	$-0.711998\pi$
$881$	− 46.6768i	− 1.57258i	0.617856	−	0.786291i	$-0.288002\pi$
$882$	3.68642	0.124128
$883$	9.95880	0.335140	0.167570	−	0.985860i	$-0.446408\pi$
$883$	9.95880	0.335140	0.167570	+	0.985860i	$0.446408\pi$
$884$	0	0
$885$	−3.48242	−0.117060
$886$	−17.7177	−0.595239
$887$	18.8375i	0.632502i	0.948676	+	0.316251i	$0.102424\pi$
$887$	18.8375i	0.632502i	−0.948676	+	0.316251i	$0.897576\pi$
$888$	84.0601	2.82087
$889$	− 6.14455i	− 0.206082i
$890$	− 1.87515i	− 0.0628551i
$891$	30.8602i	1.03386i
$892$	7.01475	0.234871
$893$	14.1834	0.474631
$894$	32.5875i	1.08989i
$895$	− 10.5373i	− 0.352224i
$896$	4.12364i	0.137761i
$897$	12.7073	0.424285
$898$	18.6496i	0.622344i
$899$	−8.03414	−0.267954
$900$	−2.30845	−0.0769484
$901$	0	0
$902$	39.1160	1.30242
$903$	45.3153	1.50800
$904$	35.2571i	1.17263i
$905$	−3.39068	−0.112710
$906$	− 7.91121i	− 0.262832i
$907$	− 26.7419i	− 0.887950i	−0.896039	−	0.443975i	$-0.853568\pi$
$907$	− 26.7419i	− 0.887950i	0.896039	−	0.443975i	$-0.146432\pi$
$908$	1.29835i	0.0430872i
$909$	13.2278	0.438740
$910$	10.0254	0.332338
$911$	10.3831i	0.344008i	0.985096	+	0.172004i	$0.0550241\pi$
$911$	10.3831i	0.344008i	−0.985096	+	0.172004i	$0.944976\pi$
$912$	13.0300i	0.431467i
$913$	− 9.19271i	− 0.304234i
$914$	−1.60980	−0.0532476
$915$	2.82455i	0.0933766i
$916$	−12.2173	−0.403670
$917$	5.42811	0.179252
$918$	0	0
$919$	20.4602	0.674919	0.337460	−	0.941340i	$-0.390432\pi$
$919$	20.4602	0.674919	0.337460	+	0.941340i	$0.390432\pi$
$920$	4.32418	0.142564
$921$	− 53.7615i	− 1.77150i
$922$	12.5852	0.414470
$923$	− 44.7631i	− 1.47340i
$924$	− 16.0982i	− 0.529592i
$925$	− 11.0054i	− 0.361855i
$926$	−32.9337	−1.08227
$927$	−25.5748	−0.839986
$928$	3.30937i	0.108635i
$929$	− 4.56763i	− 0.149859i	−0.997189	−	0.0749296i	$-0.976127\pi$
$929$	− 4.56763i	− 0.149859i	0.997189	−	0.0749296i	$-0.0238732\pi$
$930$	26.4237i	0.866468i
$931$	2.70215	0.0885595
$932$	9.54888i	0.312784i
$933$	22.0075	0.720492
$934$	−12.3288	−0.403412
$935$	0	0
$936$	35.4443	1.15853
$937$	−2.90874	−0.0950243	−0.0475122	−	0.998871i	$-0.515129\pi$
$937$	−2.90874	−0.0950243	−0.0475122	+	0.998871i	$0.515129\pi$
$938$	− 5.72360i	− 0.186882i
$939$	−42.4883	−1.38655
$940$	− 3.95995i	− 0.129159i
$941$	15.3951i	0.501865i	0.968005	+	0.250933i	$0.0807373\pi$
$941$	15.3951i	0.501865i	−0.968005	+	0.250933i	$0.919263\pi$
$942$	− 3.83101i	− 0.124821i
$943$	−13.4080	−0.436626
$944$	2.81682	0.0916797
$945$	0.991860i	0.0322652i
$946$	− 30.6414i	− 0.996238i
$947$	− 23.9883i	− 0.779514i	−0.920918	−	0.389757i	$-0.872559\pi$
$947$	− 23.9883i	− 0.779514i	0.920918	−	0.389757i	$-0.127441\pi$
$948$	16.2550	0.527937
$949$	5.37463i	0.174468i
$950$	2.94570	0.0955712
$951$	−25.6313	−0.831151
$952$	0	0
$953$	−9.31030	−0.301590	−0.150795	−	0.988565i	$-0.548183\pi$
$953$	−9.31030	−0.301590	−0.150795	+	0.988565i	$0.548183\pi$
$954$	−46.1575	−1.49440
$955$	12.3426i	0.399396i
$956$	17.4740	0.565151
$957$	7.68427i	0.248397i
$958$	19.3853i	0.626310i
$959$	54.1353i	1.74812i
$960$	20.8553	0.673102
$961$	−58.1763	−1.87666
$962$	45.1711i	1.45637i
$963$	− 27.8416i	− 0.897183i
$964$	12.6173i	0.406375i
$965$	11.9557	0.384868
$966$	− 9.60618i	− 0.309074i
$967$	1.29315	0.0415848	0.0207924	−	0.999784i	$-0.493381\pi$
$967$	1.29315	0.0415848	0.0207924	+	0.999784i	$0.493381\pi$
$968$	−6.87802	−0.221068
$969$	0	0
$970$	13.8262	0.443933
$971$	39.3251	1.26200	0.631002	−	0.775781i	$-0.282644\pi$
$971$	39.3251	1.26200	0.631002	+	0.775781i	$0.282644\pi$
$972$	− 16.2558i	− 0.521407i
$973$	33.9166	1.08732
$974$	− 29.1288i	− 0.933346i
$975$	− 9.04103i	− 0.289545i
$976$	− 2.28469i	− 0.0731311i
$977$	−53.3750	−1.70762	−0.853809	−	0.520586i	$-0.825714\pi$
$977$	−53.3750	−1.70762	−0.853809	+	0.520586i	$0.825714\pi$
$978$	33.8331	1.08186
$979$	− 6.05277i	− 0.193448i
$980$	− 0.754430i	− 0.0240994i
$981$	− 45.2846i	− 1.44583i
$982$	13.7924	0.440132
$983$	− 51.0753i	− 1.62905i	−0.580129	−	0.814524i	$-0.696998\pi$
$983$	− 51.0753i	− 1.62905i	0.580129	−	0.814524i	$-0.303002\pi$
$984$	−72.8641	−2.32282
$985$	−1.22210	−0.0389394
$986$	0	0
$987$	−32.9085	−1.04749
$988$	6.94514	0.220954
$989$	10.5031i	0.333981i
$990$	12.9718	0.412272
$991$	− 10.5889i	− 0.336369i	−0.985756	−	0.168185i	$-0.946210\pi$
$991$	− 10.5889i	− 0.336369i	0.985756	−	0.168185i	$-0.0537904\pi$
$992$	36.7329i	1.16627i
$993$	− 16.3042i	− 0.517400i
$994$	−33.8390	−1.07331
$995$	21.7349	0.689043
$996$	4.57753i	0.145045i
$997$	3.44530i	0.109114i	0.998511	+	0.0545568i	$0.0173746\pi$
$997$	3.44530i	0.109114i	−0.998511	+	0.0545568i	$0.982625\pi$
$998$	7.23139i	0.228906i
$999$	−4.46900	−0.141393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.g.866.5		12
17.2	even	8		85.2.e.a.81.3	yes	12
17.4	even	4		1445.2.a.o.1.4		6
17.8	even	8		85.2.e.a.21.4	✓	12
17.13	even	4		1445.2.a.n.1.4		6
17.16	even	2	inner	1445.2.d.g.866.6		12
51.2	odd	8		765.2.k.b.676.4		12
51.8	odd	8		765.2.k.b.361.3		12
68.19	odd	8		1360.2.bt.d.81.6		12
68.59	odd	8		1360.2.bt.d.1041.6		12
85.2	odd	8		425.2.j.c.149.4		12
85.4	even	4		7225.2.a.z.1.3		6
85.8	odd	8		425.2.j.c.174.4		12
85.19	even	8		425.2.e.f.251.4		12
85.42	odd	8		425.2.j.b.174.3		12
85.53	odd	8		425.2.j.b.149.3		12
85.59	even	8		425.2.e.f.276.3		12
85.64	even	4		7225.2.a.bb.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.4	✓	12	17.8	even	8
85.2.e.a.81.3	yes	12	17.2	even	8
425.2.e.f.251.4		12	85.19	even	8
425.2.e.f.276.3		12	85.59	even	8
425.2.j.b.149.3		12	85.53	odd	8
425.2.j.b.174.3		12	85.42	odd	8
425.2.j.c.149.4		12	85.2	odd	8
425.2.j.c.174.4		12	85.8	odd	8
765.2.k.b.361.3		12	51.8	odd	8
765.2.k.b.676.4		12	51.2	odd	8
1360.2.bt.d.81.6		12	68.19	odd	8
1360.2.bt.d.1041.6		12	68.59	odd	8
1445.2.a.n.1.4		6	17.13	even	4
1445.2.a.o.1.4		6	17.4	even	4
1445.2.d.g.866.5		12	1.1	even	1	trivial
1445.2.d.g.866.6		12	17.16	even	2	inner
7225.2.a.z.1.3		6	85.4	even	4
7225.2.a.bb.1.3		6	85.64	even	4

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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.12708 q^{2} -2.48265i q^{3} -0.729699 q^{4} +1.00000i q^{5} +2.79814i q^{6} -2.44256i q^{7} +3.07658 q^{8} -3.16356 q^{9} +O(q^{10})\)	\(q-1.12708 q^{2} -2.48265i q^{3} -0.729699 q^{4} +1.00000i q^{5} +2.79814i q^{6} -2.44256i q^{7} +3.07658 q^{8} -3.16356 q^{9} -1.12708i q^{10} -3.63808i q^{11} +1.81159i q^{12} -3.64168 q^{13} +2.75295i q^{14} +2.48265 q^{15} -2.00814 q^{16} +3.56558 q^{18} +2.61358 q^{19} -0.729699i q^{20} -6.06403 q^{21} +4.10039i q^{22} -1.40552i q^{23} -7.63808i q^{24} -1.00000 q^{25} +4.10445 q^{26} +0.406074i q^{27} +1.78234i q^{28} -0.850775i q^{29} -2.79814 q^{30} -9.44332i q^{31} -3.88983 q^{32} -9.03208 q^{33} +2.44256 q^{35} +2.30845 q^{36} +11.0054i q^{37} -2.94570 q^{38} +9.04103i q^{39} +3.07658i q^{40} -9.53958i q^{41} +6.83463 q^{42} -7.47280 q^{43} +2.65470i q^{44} -3.16356i q^{45} +1.58412i q^{46} +5.42683 q^{47} +4.98551i q^{48} +1.03389 q^{49} +1.12708 q^{50} +2.65733 q^{52} -12.9453 q^{53} -0.457676i q^{54} +3.63808 q^{55} -7.51473i q^{56} -6.48861i q^{57} +0.958888i q^{58} -1.40270 q^{59} -1.81159 q^{60} +1.13771i q^{61} +10.6433i q^{62} +7.72720i q^{63} +8.40042 q^{64} -3.64168i q^{65} +10.1798 q^{66} -2.07908 q^{67} -3.48941 q^{69} -2.75295 q^{70} +12.2919i q^{71} -9.73296 q^{72} -1.47586i q^{73} -12.4039i q^{74} +2.48265i q^{75} -1.90713 q^{76} -8.88623 q^{77} -10.1899i q^{78} -8.97276i q^{79} -2.00814i q^{80} -8.48255 q^{81} +10.7518i q^{82} +2.52680 q^{83} +4.42492 q^{84} +8.42242 q^{86} -2.11218 q^{87} -11.1928i q^{88} +1.66373 q^{89} +3.56558i q^{90} +8.89503i q^{91} +1.02560i q^{92} -23.4445 q^{93} -6.11645 q^{94} +2.61358i q^{95} +9.65710i q^{96} +12.2673i q^{97} -1.16527 q^{98} +11.5093i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 12 * q^4 - 12 * q^8 - 4 * q^9	\( 12 q - 4 q^{2} + 12 q^{4} - 12 q^{8} - 4 q^{9} - 8 q^{15} + 4 q^{16} + 28 q^{18} + 24 q^{19} + 16 q^{21} - 12 q^{25} + 24 q^{26} + 8 q^{30} + 12 q^{32} - 16 q^{33} + 16 q^{35} + 20 q^{36} - 24 q^{38} + 16 q^{42} - 16 q^{43} + 48 q^{47} + 20 q^{49} + 4 q^{50} - 56 q^{52} + 32 q^{59} - 16 q^{60} - 28 q^{64} + 32 q^{66} - 8 q^{67} - 16 q^{70} - 20 q^{72} + 72 q^{76} - 48 q^{77} - 28 q^{81} - 40 q^{83} - 96 q^{86} - 48 q^{87} - 24 q^{89} - 72 q^{93} - 40 q^{94} - 44 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 - 12 * q^8 - 4 * q^9 - 8 * q^15 + 4 * q^16 + 28 * q^18 + 24 * q^19 + 16 * q^21 - 12 * q^25 + 24 * q^26 + 8 * q^30 + 12 * q^32 - 16 * q^33 + 16 * q^35 + 20 * q^36 - 24 * q^38 + 16 * q^42 - 16 * q^43 + 48 * q^47 + 20 * q^49 + 4 * q^50 - 56 * q^52 + 32 * q^59 - 16 * q^60 - 28 * q^64 + 32 * q^66 - 8 * q^67 - 16 * q^70 - 20 * q^72 + 72 * q^76 - 48 * q^77 - 28 * q^81 - 40 * q^83 - 96 * q^86 - 48 * q^87 - 24 * q^89 - 72 * q^93 - 40 * q^94 - 44 * q^98

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