LMFDB - Embedded newform 175.2.o.d.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(68,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("175.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.o (of order $12$, degree $4$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.1
Character	$\chi$	$=$	175.82
Dual form			175.2.o.d.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41547 + 0.647225i) q^{2} +(0.583228 - 2.17663i) q^{3} +(3.68357 - 2.12671i) q^{4} +5.63509i q^{6} +(2.61922 + 0.373780i) q^{7} +(-3.98461 + 3.98461i) q^{8} +(-1.79951 - 1.03895i) q^{9} +O(q^{10})$	\(q+(-2.41547 + 0.647225i) q^{2} +(0.583228 - 2.17663i) q^{3} +(3.68357 - 2.12671i) q^{4} +5.63509i q^{6} +(2.61922 + 0.373780i) q^{7} +(-3.98461 + 3.98461i) q^{8} +(-1.79951 - 1.03895i) q^{9} +(-1.62671 - 2.81754i) q^{11} +(-2.48071 - 9.25814i) q^{12} +(-0.527913 - 0.527913i) q^{13} +(-6.56857 + 0.792364i) q^{14} +(2.79236 - 4.83652i) q^{16} +(1.28595 + 0.344569i) q^{17} +(5.01910 + 1.34486i) q^{18} +(2.88500 - 4.99697i) q^{19} +(2.34118 - 5.48308i) q^{21} +(5.75286 + 5.75286i) q^{22} +(-0.811243 - 3.02760i) q^{23} +(6.34910 + 10.9970i) q^{24} +(1.61684 + 0.933483i) q^{26} +(1.46929 - 1.46929i) q^{27} +(10.4430 - 4.19347i) q^{28} +0.824475i q^{29} +(-6.49697 + 3.75103i) q^{31} +(-0.697639 + 2.60362i) q^{32} +(-7.08150 + 1.89748i) q^{33} -3.32919 q^{34} -8.83815 q^{36} +(-6.92796 + 1.85634i) q^{37} +(-3.73449 + 13.9373i) q^{38} +(-1.45697 + 0.841181i) q^{39} +1.86697i q^{41} +(-2.10628 + 14.7595i) q^{42} +(5.75286 - 5.75286i) q^{43} +(-11.9842 - 6.91907i) q^{44} +(3.91907 + 6.78803i) q^{46} +(2.18157 + 8.14173i) q^{47} +(-8.89875 - 8.89875i) q^{48} +(6.72058 + 1.95802i) q^{49} +(1.50000 - 2.59808i) q^{51} +(-3.06732 - 0.821886i) q^{52} +(-2.83945 - 0.760829i) q^{53} +(-2.59808 + 4.50000i) q^{54} +(-11.9259 + 8.94718i) q^{56} +(-9.19396 - 9.19396i) q^{57} +(-0.533620 - 1.99150i) q^{58} +(5.41562 + 9.38013i) q^{59} +(6.26329 + 3.61611i) q^{61} +(13.2655 - 13.2655i) q^{62} +(-4.32496 - 3.39384i) q^{63} +4.42894i q^{64} +(15.8771 - 9.16664i) q^{66} +(-0.896575 + 3.34607i) q^{67} +(5.46967 - 1.46559i) q^{68} -7.06312 q^{69} +6.16946 q^{71} +(11.3101 - 3.03054i) q^{72} +(-1.07560 + 4.01418i) q^{73} +(15.5328 - 8.96789i) q^{74} -24.5422i q^{76} +(-3.20756 - 7.98778i) q^{77} +(2.97484 - 2.97484i) q^{78} +(2.66553 + 1.53895i) q^{79} +(-5.45802 - 9.45357i) q^{81} +(-1.20835 - 4.50961i) q^{82} +(11.3094 + 11.3094i) q^{83} +(-3.03701 - 25.1763i) q^{84} +(-10.1725 + 17.6193i) q^{86} +(1.79458 + 0.480856i) q^{87} +(17.7086 + 4.74500i) q^{88} +(1.66459 - 2.88316i) q^{89} +(-1.18539 - 1.58004i) q^{91} +(-9.42709 - 9.42709i) q^{92} +(4.37540 + 16.3292i) q^{93} +(-10.5391 - 18.2542i) q^{94} +(5.26025 + 3.03701i) q^{96} +(-4.53199 + 4.53199i) q^{97} +(-17.5007 - 0.379825i) q^{98} +6.76025i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{11} - 4 q^{16} - 28 q^{21} + 12 q^{26} - 36 q^{31} - 8 q^{36} - 8 q^{46} + 36 q^{51} - 60 q^{56} + 84 q^{61} + 168 q^{66} - 136 q^{71} - 20 q^{81} - 80 q^{86} + 20 q^{91} - 60 q^{96}+O(q^{100}) $ 24 * q - 8 * q^11 - 4 * q^16 - 28 * q^21 + 12 * q^26 - 36 * q^31 - 8 * q^36 - 8 * q^46 + 36 * q^51 - 60 * q^56 + 84 * q^61 + 168 * q^66 - 136 * q^71 - 20 * q^81 - 80 * q^86 + 20 * q^91 - 60 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.41547	+	0.647225i	−1.70800	+	0.457657i	−0.974933	−	0.222501i	$-0.928578\pi$
$2$	−2.41547	+	0.647225i	−1.70800	+	0.457657i	−0.733066	+	0.680157i	$0.761911\pi$
$3$	0.583228	−	2.17663i	0.336727	−	1.25668i	−0.565259	−	0.824914i	$-0.691224\pi$
$3$	0.583228	−	2.17663i	0.336727	−	1.25668i	0.901985	−	0.431767i	$-0.142110\pi$
$4$	3.68357	−	2.12671i	1.84178	−	1.06335i
$5$		0			0
$5$		0			0
$6$			5.63509i			2.30051i
$7$	2.61922	+	0.373780i	0.989970	+	0.141276i
$7$	2.61922	+	0.373780i	0.989970	+	0.141276i
$8$	−3.98461	+	3.98461i	−1.40877	+	1.40877i
$9$	−1.79951	−	1.03895i	−0.599836	−	0.346315i
$10$		0			0
$11$	−1.62671	−	2.81754i	−0.490471	−	0.849521i	0.509469	−	0.860489i	$-0.329842\pi$
$11$	−1.62671	−	2.81754i	−0.490471	−	0.849521i	−0.999940	+	0.0109682i	$0.996509\pi$
$12$	−2.48071	−	9.25814i	−0.716119	−	2.67259i
$13$	−0.527913	−	0.527913i	−0.146417	−	0.146417i	0.630098	−	0.776515i	$-0.283015\pi$
$13$	−0.527913	−	0.527913i	−0.146417	−	0.146417i	−0.776515	+	0.630098i	$0.783015\pi$
$14$	−6.56857	+	0.792364i	−1.75552	+	0.211768i
$15$		0			0
$16$	2.79236	−	4.83652i	0.698091	−	1.20913i
$17$	1.28595	+	0.344569i	0.311888	+	0.0835702i	0.411368	−	0.911469i	$-0.365051\pi$
$17$	1.28595	+	0.344569i	0.311888	+	0.0835702i	−0.0994797	+	0.995040i	$0.531718\pi$
$18$	5.01910	+	1.34486i	1.18301	+	0.316987i
$19$	2.88500	−	4.99697i	0.661864	−	1.14638i	−0.318261	−	0.948003i	$-0.603099\pi$
$19$	2.88500	−	4.99697i	0.661864	−	1.14638i	0.980125	−	0.198380i	$-0.0635679\pi$
$20$		0			0
$21$	2.34118	−	5.48308i	0.510887	−	1.19651i
$22$	5.75286	+	5.75286i	1.22651	+	1.22651i
$23$	−0.811243	−	3.02760i	−0.169156	−	0.631298i	−0.997474	−	0.0710395i	$-0.977368\pi$
$23$	−0.811243	−	3.02760i	−0.169156	−	0.631298i	0.828318	−	0.560259i	$-0.189298\pi$
$24$	6.34910	+	10.9970i	1.29600	+	2.24475i
$25$		0			0
$26$	1.61684	+	0.933483i	0.317088	+	0.183071i
$27$	1.46929	−	1.46929i	0.282765	−	0.282765i
$28$	10.4430	−	4.19347i	1.97354	−	0.792490i
$29$			0.824475i			0.153101i	0.997066	+	0.0765506i	$0.0243907\pi$
$29$			0.824475i			0.153101i	−0.997066	+	0.0765506i	$0.975609\pi$
$30$		0			0
$31$	−6.49697	+	3.75103i	−1.16689	+	0.673704i	−0.952945	−	0.303142i	$-0.901964\pi$
$31$	−6.49697	+	3.75103i	−1.16689	+	0.673704i	−0.213944	+	0.976846i	$0.568631\pi$
$32$	−0.697639	+	2.60362i	−0.123326	+	0.460260i
$33$	−7.08150	+	1.89748i	−1.23273	+	0.330309i
$34$	−3.32919			−0.570951
$35$		0			0
$36$	−8.83815			−1.47302
$37$	−6.92796	+	1.85634i	−1.13895	+	0.305181i	−0.778529	−	0.627609i	$-0.784034\pi$
$37$	−6.92796	+	1.85634i	−1.13895	+	0.305181i	−0.360421	+	0.932790i	$0.617367\pi$
$38$	−3.73449	+	13.9373i	−0.605814	+	2.26093i
$39$	−1.45697	+	0.841181i	−0.233302	+	0.134697i
$40$		0			0
$41$			1.86697i			0.291571i	0.989316	+	0.145785i	$0.0465709\pi$
$41$			1.86697i			0.291571i	−0.989316	+	0.145785i	$0.953429\pi$
$42$	−2.10628	+	14.7595i	−0.325006	+	2.27744i
$43$	5.75286	−	5.75286i	0.877303	−	0.877303i	−0.115952	−	0.993255i	$-0.536992\pi$
$43$	5.75286	−	5.75286i	0.877303	−	0.877303i	0.993255	+	0.115952i	$0.0369920\pi$
$44$	−11.9842	−	6.91907i	−1.80668	−	1.04309i
$45$		0			0
$46$	3.91907	+	6.78803i	0.577836	+	1.00084i
$47$	2.18157	+	8.14173i	0.318215	+	1.18759i	0.920959	+	0.389659i	$0.127407\pi$
$47$	2.18157	+	8.14173i	0.318215	+	1.18759i	−0.602744	+	0.797934i	$0.705926\pi$
$48$	−8.89875	−	8.89875i	−1.28442	−	1.28442i
$49$	6.72058	+	1.95802i	0.960082	+	0.279717i
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$	−3.06732	−	0.821886i	−0.425361	−	0.113975i
$53$	−2.83945	−	0.760829i	−0.390029	−	0.104508i	0.0584750	−	0.998289i	$-0.481376\pi$
$53$	−2.83945	−	0.760829i	−0.390029	−	0.104508i	−0.448504	+	0.893781i	$0.648043\pi$
$54$	−2.59808	+	4.50000i	−0.353553	+	0.612372i
$55$		0			0
$56$	−11.9259	+	8.94718i	−1.59367	+	1.19562i
$57$	−9.19396	−	9.19396i	−1.21777	−	1.21777i
$58$	−0.533620	−	1.99150i	−0.0700678	−	0.261497i
$59$	5.41562	+	9.38013i	0.705054	+	1.22119i	0.966672	+	0.256017i	$0.0824104\pi$
$59$	5.41562	+	9.38013i	0.705054	+	1.22119i	−0.261619	+	0.965171i	$0.584256\pi$
$60$		0			0
$61$	6.26329	+	3.61611i	0.801932	+	0.462996i	0.844146	−	0.536113i	$-0.180108\pi$
$61$	6.26329	+	3.61611i	0.801932	+	0.462996i	−0.0422144	+	0.999109i	$0.513441\pi$
$62$	13.2655	−	13.2655i	1.68472	−	1.68472i
$63$	−4.32496	−	3.39384i	−0.544894	−	0.427584i
$64$			4.42894i			0.553618i
$65$		0			0
$66$	15.8771	−	9.16664i	1.95434	−	1.12834i
$67$	−0.896575	+	3.34607i	−0.109534	+	0.408787i	−0.998820	−	0.0485648i	$-0.984535\pi$
$67$	−0.896575	+	3.34607i	−0.109534	+	0.408787i	0.889286	+	0.457352i	$0.151202\pi$
$68$	5.46967	−	1.46559i	0.663295	−	0.177729i
$69$	−7.06312			−0.850299
$70$		0			0
$71$	6.16946			0.732180			0.366090	−	0.930579i	$-0.380696\pi$
$71$	6.16946			0.732180			0.366090	+	0.930579i	$0.380696\pi$
$72$	11.3101	−	3.03054i	1.33291	−	0.357152i
$73$	−1.07560	+	4.01418i	−0.125889	+	0.469824i	−0.999870	−	0.0161362i	$-0.994863\pi$
$73$	−1.07560	+	4.01418i	−0.125889	+	0.469824i	0.873981	+	0.485961i	$0.161530\pi$
$74$	15.5328	−	8.96789i	1.80566	−	1.04250i
$75$		0			0
$76$		−	24.5422i		−	2.81519i
$77$	−3.20756	−	7.98778i	−0.365535	−	0.910292i
$78$	2.97484	−	2.97484i	0.336834	−	0.336834i
$79$	2.66553	+	1.53895i	0.299896	+	0.173145i	0.642396	−	0.766373i	$-0.277940\pi$
$79$	2.66553	+	1.53895i	0.299896	+	0.173145i	−0.342500	+	0.939518i	$0.611274\pi$
$80$		0			0
$81$	−5.45802	−	9.45357i	−0.606447	−	1.05040i
$82$	−1.20835	−	4.50961i	−0.133439	−	0.498003i
$83$	11.3094	+	11.3094i	1.24137	+	1.24137i	0.959433	+	0.281937i	$0.0909769\pi$
$83$	11.3094	+	11.3094i	1.24137	+	1.24137i	0.281937	+	0.959433i	$0.409023\pi$
$84$	−3.03701	−	25.1763i	−0.331365	−	2.74696i
$85$		0			0
$86$	−10.1725	+	17.6193i	−1.09693	+	1.89993i
$87$	1.79458	+	0.480856i	0.192399	+	0.0515532i
$88$	17.7086	+	4.74500i	1.88774	+	0.505819i
$89$	1.66459	−	2.88316i	0.176447	−	0.305614i	−0.764214	−	0.644962i	$-0.776873\pi$
$89$	1.66459	−	2.88316i	0.176447	−	0.305614i	0.940661	+	0.339348i	$0.110206\pi$
$90$		0			0
$91$	−1.18539	−	1.58004i	−0.124263	−	0.165633i
$92$	−9.42709	−	9.42709i	−0.982842	−	0.982842i
$93$	4.37540	+	16.3292i	0.453708	+	1.69326i
$94$	−10.5391	−	18.2542i	−1.08702	−	1.88278i
$95$		0			0
$96$	5.26025	+	3.03701i	0.536872	+	0.309963i
$97$	−4.53199	+	4.53199i	−0.460154	+	0.460154i	−0.898706	−	0.438552i	$-0.855492\pi$
$97$	−4.53199	+	4.53199i	−0.460154	+	0.460154i	0.438552	+	0.898706i	$0.355492\pi$
$98$	−17.5007	−	0.379825i	−1.76783	−	0.0383682i
$99$			6.76025i			0.679431i
$100$		0			0
$101$	−3.26329	+	1.88406i	−0.324709	+	0.187471i	−0.653490	−	0.756935i	$-0.726696\pi$
$101$	−3.26329	+	1.88406i	−0.324709	+	0.187471i	0.328780	+	0.944406i	$0.393362\pi$
$102$	−1.94167	+	7.24642i	−0.192254	+	0.717503i
$103$	−16.3396	+	4.37819i	−1.60999	+	0.431396i	−0.948040	−	0.318150i	$-0.896938\pi$
$103$	−16.3396	+	4.37819i	−1.60999	+	0.431396i	−0.661952	+	0.749546i	$0.730272\pi$
$104$	4.20705			0.412535
$105$		0			0
$106$	7.35105			0.713997
$107$	16.6725	−	4.46738i	1.61179	−	0.431878i	0.663215	−	0.748429i	$-0.269191\pi$
$107$	16.6725	−	4.46738i	1.61179	−	0.431878i	0.948576	+	0.316551i	$0.102525\pi$
$108$	2.28748	−	8.53699i	0.220113	−	0.821473i
$109$	−2.95246	+	1.70460i	−0.282794	+	0.163271i	−0.634688	−	0.772769i	$-0.718871\pi$
$109$	−2.95246	+	1.70460i	−0.282794	+	0.163271i	0.351894	+	0.936040i	$0.385538\pi$
$110$		0			0
$111$			16.1623i			1.53406i
$112$	9.12160	−	11.6241i	0.861910	−	1.09838i
$113$	0.872037	−	0.872037i	0.0820344	−	0.0820344i	−0.664899	−	0.746933i	$-0.731525\pi$
$113$	0.872037	−	0.872037i	0.0820344	−	0.0820344i	0.746933	+	0.664899i	$0.231525\pi$
$114$	28.1583	+	16.2572i	2.63727	+	1.52263i
$115$		0			0
$116$	1.75342	+	3.03701i	0.162801	+	0.281979i
$117$	0.401510	+	1.49846i	0.0371197	+	0.138532i
$118$	−19.1523	−	19.1523i	−1.76312	−	1.76312i
$119$	3.23938	+	1.38316i	0.296954	+	0.126794i
$120$		0			0
$121$	0.207636	−	0.359635i	0.0188760	−	0.0326941i
$122$	−17.4692	−	4.68087i	−1.58159	−	0.423786i
$123$	4.06370	+	1.08887i	0.366412	+	0.0981797i
$124$	−15.9547	+	27.6343i	−1.43277	+	2.48163i
$125$		0			0
$126$	12.6434	+	5.39852i	1.12636	+	0.480939i
$127$	3.57884	+	3.57884i	0.317570	+	0.317570i	0.847833	−	0.530263i	$-0.177907\pi$
$127$	3.57884	+	3.57884i	0.317570	+	0.317570i	−0.530263	+	0.847833i	$0.677907\pi$
$128$	−4.26180	−	15.9052i	−0.376693	−	1.40584i
$129$	−9.16664	−	15.8771i	−0.807078	−	1.39790i
$130$		0			0
$131$	−17.0175	−	9.82504i	−1.48682	−	0.858418i	−0.486936	−	0.873437i	$-0.661886\pi$
$131$	−17.0175	−	9.82504i	−1.48682	−	0.858418i	−0.999887	+	0.0150194i	$0.995219\pi$
$132$	−22.0498	+	22.0498i	−1.91919	+	1.91919i
$133$	9.42420	−	12.0098i	0.817182	−	1.04138i
$134$		−	8.66262i		−	0.748337i
$135$		0			0
$136$	−6.49697	+	3.75103i	−0.557110	+	0.321648i
$137$	−2.10569	+	7.85855i	−0.179901	+	0.671401i	0.815763	+	0.578386i	$0.196317\pi$
$137$	−2.10569	+	7.85855i	−0.179901	+	0.671401i	−0.995665	+	0.0930153i	$0.970349\pi$
$138$	17.0608	−	4.57142i	1.45231	−	0.389145i
$139$	1.29312			0.109681			0.0548404	−	0.998495i	$-0.482535\pi$
$139$	1.29312			0.109681			0.0548404	+	0.998495i	$0.482535\pi$
$140$		0			0
$141$	18.9939			1.59958
$142$	−14.9022	+	3.99302i	−1.25056	+	0.335087i
$143$	−0.628657	+	2.34618i	−0.0525709	+	0.196197i
$144$	−10.0498	+	5.80223i	−0.837480	+	0.483520i
$145$		0			0
$146$		−	10.3923i		−	0.860073i
$147$	8.18152	−	13.4863i	0.674800	−	1.11233i
$148$	−21.5717	+	21.5717i	−1.77318	+	1.77318i
$149$	−13.8853	−	8.01671i	−1.13753	−	0.656754i	−0.191713	−	0.981451i	$-0.561404\pi$
$149$	−13.8853	−	8.01671i	−1.13753	−	0.656754i	−0.945818	+	0.324697i	$0.894738\pi$
$150$		0			0
$151$	10.2504	+	17.7542i	0.834164	+	1.44482i	0.894709	+	0.446650i	$0.147383\pi$
$151$	10.2504	+	17.7542i	0.834164	+	1.44482i	−0.0605445	+	0.998166i	$0.519284\pi$
$152$	8.41536	+	31.4065i	0.682576	+	2.54741i
$153$	−1.95608	−	1.95608i	−0.158140	−	0.158140i
$154$	12.9177	+	17.2183i	1.04094	+	1.38749i
$155$		0			0
$156$	−3.57789	+	6.19709i	−0.286461	+	0.496164i
$157$	−7.97219	−	2.13614i	−0.636250	−	0.170483i	−0.0737458	−	0.997277i	$-0.523495\pi$
$157$	−7.97219	−	2.13614i	−0.636250	−	0.170483i	−0.562504	+	0.826794i	$0.690162\pi$
$158$	−7.43457	−	1.99209i	−0.591463	−	0.158482i
$159$	−3.31209	+	5.73671i	−0.262666	+	0.454951i
$160$		0			0
$161$	−0.993164	−	8.23316i	−0.0782723	−	0.648864i
$162$	19.3023	+	19.3023i	1.51653	+	1.51653i
$163$	−0.262127	−	0.978271i	−0.0205314	−	0.0766241i	0.954900	−	0.296927i	$-0.0959619\pi$
$163$	−0.262127	−	0.978271i	−0.0205314	−	0.0766241i	−0.975431	+	0.220303i	$0.929295\pi$
$164$	3.97049	+	6.87709i	0.310043	+	0.537011i
$165$		0			0
$166$	−34.6373	−	19.9979i	−2.68838	−	1.55214i
$167$	−5.01878	+	5.01878i	−0.388365	+	0.388365i	−0.874104	−	0.485739i	$-0.838551\pi$
$167$	−5.01878	+	5.01878i	−0.388365	+	0.388365i	0.485739	+	0.874104i	$0.338551\pi$
$168$	12.5192	+	31.1766i	0.965879	+	2.40533i
$169$		−	12.4426i		−	0.957124i
$170$		0			0
$171$	−10.3832	+	5.99472i	−0.794020	+	0.458428i
$172$	8.95639	−	33.4257i	0.682918	−	2.54869i
$173$	23.0391	−	6.17331i	1.75163	−	0.469348i	0.766657	−	0.642057i	$-0.221919\pi$
$173$	23.0391	−	6.17331i	1.75163	−	0.469348i	0.984973	+	0.172710i	$0.0552522\pi$
$174$	−4.64599			−0.352211
$175$		0			0
$176$	−18.1695			−1.36957
$177$	23.5756	−	6.31708i	1.77205	−	0.474820i
$178$	−2.15473	+	8.04157i	−0.161504	+	0.602741i
$179$	−8.52534	+	4.92211i	−0.637214	+	0.367896i	−0.783540	−	0.621341i	$-0.786588\pi$
$179$	−8.52534	+	4.92211i	−0.637214	+	0.367896i	0.146327	+	0.989236i	$0.453255\pi$
$180$		0			0
$181$			20.2344i			1.50401i	0.659155	+	0.752007i	$0.270914\pi$
$181$			20.2344i			1.50401i	−0.659155	+	0.752007i	$0.729086\pi$
$182$	3.88593	+	3.04933i	0.288045	+	0.226032i
$183$	11.5239	−	11.5239i	0.851869	−	0.851869i
$184$	15.2963	+	8.83131i	1.12766	+	0.651053i
$185$		0			0
$186$	−21.1373	−	36.6110i	−1.54987	−	2.68445i
$187$	−1.12103	−	4.18373i	−0.0819775	−	0.305944i
$188$	25.3511	+	25.3511i	1.84892	+	1.84892i
$189$	4.39758	−	3.29920i	0.319877	−	0.239982i
$190$		0			0
$191$	7.18236	−	12.4402i	0.519697	−	0.900142i	−0.480040	−	0.877246i	$-0.659378\pi$
$191$	7.18236	−	12.4402i	0.519697	−	0.900142i	0.999738	−	0.0228960i	$-0.00728865\pi$
$192$	9.64019	+	2.58308i	0.695721	+	0.186418i
$193$	−10.3070	−	2.76177i	−0.741918	−	0.198796i	−0.131987	−	0.991251i	$-0.542136\pi$
$193$	−10.3070	−	2.76177i	−0.741918	−	0.198796i	−0.609930	+	0.792455i	$0.708803\pi$
$194$	8.01370	−	13.8801i	0.575350	−	0.996535i
$195$		0			0
$196$	28.9198	−	7.08021i	2.06570	−	0.505729i
$197$	4.46762	+	4.46762i	0.318305	+	0.318305i	0.848116	−	0.529811i	$-0.177737\pi$
$197$	4.46762	+	4.46762i	0.318305	+	0.318305i	−0.529811	+	0.848116i	$0.677737\pi$
$198$	−4.37540	−	16.3292i	−0.310946	−	1.16047i
$199$	3.83558	+	6.64341i	0.271897	+	0.470939i	0.969348	−	0.245694i	$-0.0790157\pi$
$199$	3.83558	+	6.64341i	0.271897	+	0.470939i	−0.697451	+	0.716633i	$0.745682\pi$
$200$		0			0
$201$	6.76025	+	3.90303i	0.476832	+	0.275299i
$202$	6.66298	−	6.66298i	0.468806	−	0.468806i
$203$	−0.308172	+	2.15948i	−0.0216294	+	0.151566i
$204$		−	12.7603i		−	0.893396i
$205$		0			0
$206$	36.6343	−	21.1508i	2.55243	−	1.47365i
$207$	−1.68568	+	6.29103i	−0.117163	+	0.437257i
$208$	−4.02739	+	1.07914i	−0.279249	+	0.0748246i
$209$	−18.7722			−1.29850
$210$		0			0
$211$	−4.68236			−0.322347			−0.161174	−	0.986926i	$-0.551528\pi$
$211$	−4.68236			−0.322347			−0.161174	+	0.986926i	$0.551528\pi$
$212$	−12.0774	+	3.23612i	−0.829477	+	0.222258i
$213$	3.59820	−	13.4287i	0.246544	−	0.920116i
$214$	−37.3806	+	21.5817i	−2.55528	+	1.47529i
$215$		0			0
$216$			11.7091i			0.796704i
$217$	−18.4190	+	7.39631i	−1.25036	+	0.502094i
$218$	6.02833	−	6.02833i	0.408290	−	0.408290i
$219$	8.11009	+	4.68236i	0.548029	+	0.316405i
$220$		0			0
$221$	−0.496966	−	0.860771i	−0.0334296	−	0.0579017i
$222$	−10.4606	−	39.0396i	−0.702072	−	2.62017i
$223$	−0.0411207	−	0.0411207i	−0.00275364	−	0.00275364i	0.705729	−	0.708482i	$-0.250620\pi$
$223$	−0.0411207	−	0.0411207i	−0.00275364	−	0.00275364i	−0.708482	+	0.705729i	$0.750620\pi$
$224$	−2.80045	+	6.55869i	−0.187113	+	0.438221i
$225$		0			0
$226$	−1.54198	+	2.67079i	−0.102571	+	0.177658i
$227$	−8.87608	−	2.37834i	−0.589126	−	0.157856i	−0.0480724	−	0.998844i	$-0.515308\pi$
$227$	−8.87608	−	2.37834i	−0.589126	−	0.157856i	−0.541054	+	0.840988i	$0.681974\pi$
$228$	−53.4194	−	14.3137i	−3.53779	−	0.947948i
$229$	5.11160	−	8.85355i	0.337784	−	0.585059i	−0.646232	−	0.763141i	$-0.723656\pi$
$229$	5.11160	−	8.85355i	0.337784	−	0.585059i	0.984016	+	0.178082i	$0.0569893\pi$
$230$		0			0
$231$	−19.2572	+	2.32299i	−1.26703	+	0.152842i
$232$	−3.28521	−	3.28521i	−0.215684	−	0.215684i
$233$	2.63931	+	9.85005i	0.172907	+	0.645298i	0.996899	+	0.0786960i	$0.0250756\pi$
$233$	2.63931	+	9.85005i	0.172907	+	0.645298i	−0.823992	+	0.566602i	$0.808258\pi$
$234$	−1.93968	−	3.35962i	−0.126801	−	0.219625i
$235$		0			0
$236$	39.8976	+	23.0349i	2.59711	+	1.49944i
$237$	4.90434	−	4.90434i	0.318571	−	0.318571i
$238$	−8.71986	−	1.24438i	−0.565224	−	0.0806614i
$239$			7.83815i			0.507008i	0.967334	+	0.253504i	$0.0815830\pi$
$239$			7.83815i			0.507008i	−0.967334	+	0.253504i	$0.918417\pi$
$240$		0			0
$241$	−10.8505	+	6.26455i	−0.698943	+	0.403535i	−0.806954	−	0.590615i	$-0.798885\pi$
$241$	−10.8505	+	6.26455i	−0.698943	+	0.403535i	0.108010	+	0.994150i	$0.465552\pi$
$242$	−0.268774	+	1.00308i	−0.0172774	+	0.0644802i
$243$	−17.7390	+	4.75314i	−1.13795	+	0.304914i
$244$	30.7617			1.96931
$245$		0			0
$246$	−10.5205			−0.670763
$247$	−4.16099	+	1.11493i	−0.264758	+	0.0709416i
$248$	10.9415	−	40.8342i	0.694786	−	2.59298i
$249$	31.2124	−	18.0205i	1.97801	−	1.14200i
$250$		0			0
$251$		−	2.01239i		−	0.127021i	−0.997981	−	0.0635104i	$-0.979770\pi$
$251$		−	2.01239i		−	0.127021i	0.997981	−	0.0635104i	$-0.0202296\pi$
$252$	−23.1490	−	3.30352i	−1.45825	−	0.208102i
$253$	−7.21074	+	7.21074i	−0.453335	+	0.453335i
$254$	−10.9609	−	6.32828i	−0.687748	−	0.397071i
$255$		0			0
$256$	16.1596	+	27.9892i	1.00997	+	1.74933i
$257$	3.96961	+	14.8148i	0.247617	+	0.924120i	0.972050	+	0.234774i	$0.0754351\pi$
$257$	3.96961	+	14.8148i	0.247617	+	0.924120i	−0.724433	+	0.689346i	$0.757898\pi$
$258$	32.4178	+	32.4178i	2.01825	+	2.01825i
$259$	−18.8397	+	2.27263i	−1.17064	+	0.141214i
$260$		0			0
$261$	0.856585	−	1.48365i	0.0530213	−	0.0918356i
$262$	47.4643	+	12.7180i	2.93235	+	0.785722i
$263$	−8.38997	−	2.24809i	−0.517348	−	0.138623i	−0.00930819	−	0.999957i	$-0.502963\pi$
$263$	−8.38997	−	2.24809i	−0.517348	−	0.138623i	−0.508039	+	0.861334i	$0.669630\pi$
$264$	20.6563	−	35.7777i	1.27131	−	2.20197i
$265$		0			0
$266$	−14.9909	+	35.1089i	−0.919151	+	2.15266i
$267$	−5.30475	−	5.30475i	−0.324645	−	0.324645i
$268$	3.81351	+	14.2322i	0.232947	+	0.869371i
$269$	−0.731111	−	1.26632i	−0.0445766	−	0.0772090i	0.842876	−	0.538107i	$-0.180861\pi$
$269$	−0.731111	−	1.26632i	−0.0445766	−	0.0772090i	−0.887453	+	0.460898i	$0.847527\pi$
$270$		0			0
$271$	5.35659	+	3.09263i	0.325389	+	0.187864i	0.653792	−	0.756674i	$-0.273177\pi$
$271$	5.35659	+	3.09263i	0.325389	+	0.187864i	−0.328403	+	0.944538i	$0.606510\pi$
$272$	5.25735	−	5.25735i	0.318773	−	0.318773i
$273$	−4.13053	+	1.65865i	−0.249991	+	0.100386i
$274$		−	20.3450i		−	1.22909i
$275$		0			0
$276$	−26.0175	+	15.0212i	−1.56607	+	0.904170i
$277$	1.01018	−	3.77004i	0.0606958	−	0.226520i	−0.928915	−	0.370294i	$-0.879257\pi$
$277$	1.01018	−	3.77004i	0.0606958	−	0.226520i	0.989611	+	0.143774i	$0.0459238\pi$
$278$	−3.12349	+	0.836938i	−0.187335	+	0.0501962i
$279$	15.5885			0.933257
$280$		0			0
$281$	−27.1695			−1.62079			−0.810397	−	0.585881i	$-0.800749\pi$
$281$	−27.1695			−1.62079			−0.810397	+	0.585881i	$0.800749\pi$
$282$	−45.8794	+	12.2933i	−2.73208	+	0.732058i
$283$	−2.34796	+	8.76271i	−0.139572	+	0.520889i	0.860365	+	0.509678i	$0.170235\pi$
$283$	−2.34796	+	8.76271i	−0.139572	+	0.520889i	−0.999937	+	0.0112113i	$0.996431\pi$
$284$	22.7256	−	13.1206i	1.34852	−	0.778567i
$285$		0			0
$286$		−	6.07402i		−	0.359164i
$287$	−0.697834	+	4.88998i	−0.0411918	+	0.288647i
$288$	3.96043	−	3.96043i	0.233371	−	0.233371i
$289$	−13.1875	−	7.61381i	−0.775735	−	0.447871i
$290$		0			0
$291$	7.22131	+	12.5077i	0.423321	+	0.733213i
$292$	4.57496	+	17.0740i	0.267729	+	0.999180i
$293$	−9.72568	−	9.72568i	−0.568180	−	0.568180i	0.363438	−	0.931618i	$-0.381603\pi$
$293$	−9.72568	−	9.72568i	−0.568180	−	0.568180i	−0.931618	+	0.363438i	$0.881603\pi$
$294$	−11.0336	+	37.8710i	−0.643493	+	2.20868i
$295$		0			0
$296$	20.2084	−	35.0020i	1.17459	−	2.03445i
$297$	−6.52990	−	1.74968i	−0.378903	−	0.101527i
$298$	38.7283	+	10.3772i	2.24347	+	0.601136i
$299$	−1.17004	+	2.02658i	−0.0676654	+	0.117200i
$300$		0			0
$301$	17.2183	−	12.9177i	0.992445	−	0.744562i
$302$	−36.2505	−	36.2505i	−2.08598	−	2.08598i
$303$	2.19767	+	8.20182i	0.126253	+	0.471182i
$304$	−16.1119	−	27.9067i	−0.924083	−	1.60056i
$305$		0			0
$306$	5.99090	+	3.45885i	0.342477	+	0.197729i
$307$	4.66577	−	4.66577i	0.266290	−	0.266290i	−0.561313	−	0.827603i	$-0.689704\pi$
$307$	4.66577	−	4.66577i	0.266290	−	0.266290i	0.827603	+	0.561313i	$0.189704\pi$
$308$	−28.8030	−	22.6020i	−1.64120	−	1.28787i
$309$			38.1189i			2.16851i
$310$		0			0
$311$	19.5205	−	11.2702i	1.10691	−	0.639073i	0.168880	−	0.985637i	$-0.445985\pi$
$311$	19.5205	−	11.2702i	1.10691	−	0.639073i	0.938026	+	0.346564i	$0.112652\pi$
$312$	2.45367	−	9.15722i	0.138912	−	0.518425i
$313$	−3.29304	+	0.882367i	−0.186134	+	0.0498743i	−0.350682	−	0.936495i	$-0.614050\pi$
$313$	−3.29304	+	0.882367i	−0.186134	+	0.0498743i	0.164548	+	0.986369i	$0.447383\pi$
$314$	20.6392			1.16474
$315$		0			0
$316$	13.0916			0.736458
$317$	0.188148	−	0.0504142i	0.0105675	−	0.00283154i	−0.253531	−	0.967327i	$-0.581592\pi$
$317$	0.188148	−	0.0504142i	0.0105675	−	0.00283154i	0.264099	+	0.964496i	$0.414925\pi$
$318$	4.28733	−	16.0006i	0.240422	−	0.897266i
$319$	2.32299	−	1.34118i	0.130063	−	0.0750917i
$320$		0			0
$321$		−	38.8954i		−	2.17093i
$322$	7.72767	+	19.2442i	0.430646	+	1.07244i
$323$	5.43176	−	5.43176i	0.302231	−	0.302231i
$324$	−40.2100	−	23.2152i	−2.23389	−	1.28974i
$325$		0			0
$326$	1.26632	+	2.19333i	0.0701351	+	0.121477i
$327$	1.98834	+	7.42059i	0.109956	+	0.410360i
$328$	−7.43912	−	7.43912i	−0.410757	−	0.410757i
$329$	2.67079	+	22.1404i	0.147245	+	1.22064i
$330$		0			0
$331$	14.6695	−	25.4082i	0.806306	−	1.39656i	−0.109099	−	0.994031i	$-0.534797\pi$
$331$	14.6695	−	25.4082i	0.806306	−	1.39656i	0.915406	−	0.402533i	$-0.131870\pi$
$332$	65.7109	+	17.6072i	3.60635	+	0.966319i
$333$	14.3956	+	3.85728i	0.788872	+	0.211378i
$334$	8.87447	−	15.3710i	0.485589	−	0.841065i
$335$		0			0
$336$	−19.9816	−	26.6339i	−1.09008	−	1.45300i
$337$	−7.09718	−	7.09718i	−0.386608	−	0.386608i	0.486868	−	0.873476i	$-0.338139\pi$
$337$	−7.09718	−	7.09718i	−0.386608	−	0.386608i	−0.873476	+	0.486868i	$0.838139\pi$
$338$	8.05317	+	30.0548i	0.438034	+	1.63477i
$339$	−1.38951	−	2.40670i	−0.0754678	−	0.130714i
$340$		0			0
$341$	21.1373	+	12.2037i	1.14465	+	0.660865i
$342$	21.2003	−	21.2003i	1.14638	−	1.14638i
$343$	16.8708	+	7.64049i	0.910936	+	0.412548i
$344$			45.8458i			2.47184i
$345$		0			0
$346$	−51.6548	+	29.8229i	−2.77698	+	1.60329i
$347$	5.84665	−	21.8200i	0.313864	−	1.17136i	−0.611178	−	0.791493i	$-0.709304\pi$
$347$	5.84665	−	21.8200i	0.313864	−	1.17136i	0.925042	−	0.379864i	$-0.124029\pi$
$348$	7.63310	−	2.04528i	0.409177	−	0.109639i
$349$	23.8230			1.27521			0.637607	−	0.770362i	$-0.279925\pi$
$349$	23.8230			1.27521			0.637607	+	0.770362i	$0.279925\pi$
$350$		0			0
$351$	−1.55132			−0.0828032
$352$	8.47067	−	2.26971i	0.451488	−	0.120976i
$353$	0.727489	−	2.71503i	0.0387203	−	0.144506i	−0.943860	−	0.330347i	$-0.892834\pi$
$353$	0.727489	−	2.71503i	0.0387203	−	0.144506i	0.982580	+	0.185841i	$0.0595009\pi$
$354$	−52.8578	+	30.5175i	−2.80936	+	1.62199i
$355$		0			0
$356$		−	14.1604i		−	0.750501i
$357$	4.89993	−	6.24425i	0.259332	−	0.330481i
$358$	17.4070	−	17.4070i	0.919990	−	0.919990i
$359$	25.4135	+	14.6725i	1.34127	+	0.774384i	0.986994	−	0.160755i	$-0.0513930\pi$
$359$	25.4135	+	14.6725i	1.34127	+	0.774384i	0.354279	+	0.935140i	$0.384726\pi$
$360$		0			0
$361$	−7.14645	−	12.3780i	−0.376129	−	0.651474i
$362$	−13.0962	−	48.8758i	−0.688322	−	2.56885i
$363$	−0.661696	−	0.661696i	−0.0347300	−	0.0347300i
$364$	−7.72677	−	3.29920i	−0.404993	−	0.172925i
$365$		0			0
$366$	−20.3771	+	35.2942i	−1.06513	+	1.84486i
$367$	−4.07138	−	1.09092i	−0.212524	−	0.0569457i	0.150986	−	0.988536i	$-0.451755\pi$
$367$	−4.07138	−	1.09092i	−0.212524	−	0.0569457i	−0.363510	+	0.931590i	$0.618422\pi$
$368$	−16.9083	−	4.53057i	−0.881407	−	0.236172i
$369$	1.93968	−	3.35962i	0.100976	−	0.174895i
$370$		0			0
$371$	−7.15275	−	3.05410i	−0.371352	−	0.158561i
$372$	50.8446	+	50.8446i	2.63617	+	2.63617i
$373$	−3.50762	−	13.0906i	−0.181617	−	0.677806i	−0.995329	−	0.0965373i	$-0.969223\pi$
$373$	−3.50762	−	13.0906i	−0.181617	−	0.677806i	0.813712	−	0.581268i	$-0.197443\pi$
$374$	5.41562	+	9.38013i	0.280035	+	0.485035i
$375$		0			0
$376$	−41.1343	−	23.7489i	−2.12134	−	1.22476i
$377$	0.435251	−	0.435251i	0.0224166	−	0.0224166i
$378$	−8.48693	+	10.8154i	−0.436521	+	0.556282i
$379$		−	17.8245i		−	0.915582i	−0.889060	−	0.457791i	$-0.848641\pi$
$379$		−	17.8245i		−	0.915582i	0.889060	−	0.457791i	$-0.151359\pi$
$380$		0			0
$381$	9.87709	−	5.70254i	0.506019	−	0.292150i
$382$	−9.29720	+	34.6976i	−0.475686	+	1.77528i
$383$	−29.3862	+	7.87402i	−1.50157	+	0.402344i	−0.913624	−	0.406559i	$-0.866728\pi$
$383$	−29.3862	+	7.87402i	−1.50157	+	0.402344i	−0.587942	+	0.808903i	$0.700062\pi$
$384$	−37.1055			−1.89353
$385$		0			0
$386$	26.6839			1.35817
$387$	−16.3292	+	4.37540i	−0.830061	+	0.222414i
$388$	−7.05567	+	26.3321i	−0.358197	+	1.33681i
$389$	−13.6659	+	7.89000i	−0.692887	+	0.400039i	−0.804693	−	0.593691i	$-0.797670\pi$
$389$	−13.6659	+	7.89000i	−0.692887	+	0.400039i	0.111805	+	0.993730i	$0.464337\pi$
$390$		0			0
$391$		−	4.17286i		−	0.211031i
$392$	−34.5808	+	18.9769i	−1.74659	+	0.958479i
$393$	−31.3106	+	31.3106i	−1.57941	+	1.57941i
$394$	−13.6830	−	7.89987i	−0.689338	−	0.397990i
$395$		0			0
$396$	14.3771	+	24.9019i	0.722476	+	1.25137i
$397$	0.121237	+	0.452461i	0.00608469	+	0.0227084i	0.968901	−	0.247447i	$-0.0795916\pi$
$397$	0.121237	+	0.452461i	0.00608469	+	0.0227084i	−0.962817	+	0.270155i	$0.912925\pi$
$398$	−13.5645	−	13.5645i	−0.679928	−	0.679928i
$399$	−20.6444	−	27.5175i	−1.03351	−	1.37760i
$400$		0			0
$401$	−12.5496	+	21.7365i	−0.626696	+	1.08547i	0.361514	+	0.932367i	$0.382260\pi$
$401$	−12.5496	+	21.7365i	−0.626696	+	1.08547i	−0.988210	+	0.153103i	$0.951073\pi$
$402$	−18.8554	−	5.05228i	−0.940420	−	0.251985i
$403$	5.41005	+	1.44962i	0.269494	+	0.0722106i
$404$	−8.01370	+	13.8801i	−0.398696	+	0.690562i
$405$		0			0
$406$	−0.653285	−	5.41562i	−0.0324220	−	0.268773i
$407$	16.5001	+	16.5001i	0.817879	+	0.817879i
$408$	4.37540	+	16.3292i	0.216615	+	0.808417i
$409$	12.1362	+	21.0205i	0.600096	+	1.03940i	0.992806	+	0.119735i	$0.0382044\pi$
$409$	12.1362	+	21.0205i	0.600096	+	1.03940i	−0.392710	+	0.919663i	$0.628462\pi$
$410$		0			0
$411$	15.8771	+	9.16664i	0.783159	+	0.452157i
$412$	−50.8770	+	50.8770i	−2.50653	+	2.50653i
$413$	10.6786	+	26.5928i	0.525458	+	1.30855i
$414$		−	16.2868i		−	0.800454i
$415$		0			0
$416$	1.74278	−	1.00619i	0.0854468	−	0.0493327i
$417$	0.754182	−	2.81465i	0.0369324	−	0.137834i
$418$	45.3438	−	12.1498i	2.21784	−	0.594268i
$419$	11.8203			0.577461			0.288731	−	0.957410i	$-0.406767\pi$
$419$	11.8203			0.577461			0.288731	+	0.957410i	$0.406767\pi$
$420$		0			0
$421$	−22.7481			−1.10868			−0.554338	−	0.832292i	$-0.687028\pi$
$421$	−22.7481			−1.10868			−0.554338	+	0.832292i	$0.687028\pi$
$422$	11.3101	−	3.03054i	0.550568	−	0.147524i
$423$	4.53307	−	16.9177i	0.220405	−	0.822564i
$424$	14.3457	−	8.28249i	0.696689	−	0.402234i
$425$		0			0
$426$			34.7654i			1.68439i
$427$	15.0533	+	11.8125i	0.728479	+	0.571645i
$428$	51.9135	−	51.9135i	2.50933	−	2.50933i
$429$	4.74012	+	2.73671i	0.228855	+	0.132130i
$430$		0			0
$431$	−13.0359	−	22.5789i	−0.627918	−	1.08759i	−0.987969	−	0.154653i	$-0.950574\pi$
$431$	−13.0359	−	22.5789i	−0.627918	−	1.08759i	0.360051	−	0.932933i	$-0.382759\pi$
$432$	−3.00346	−	11.2091i	−0.144504	−	0.539296i
$433$	−22.4028	−	22.4028i	−1.07661	−	1.07661i	−0.996811	−	0.0797995i	$-0.974572\pi$
$433$	−22.4028	−	22.4028i	−1.07661	−	1.07661i	−0.0797995	−	0.996811i	$-0.525428\pi$
$434$	39.7036	−	29.7868i	1.90583	−	1.42981i
$435$		0			0
$436$	−7.25038	+	12.5580i	−0.347230	+	0.601421i
$437$	−17.4692	−	4.68087i	−0.835668	−	0.223916i
$438$	−22.6203	−	6.06108i	−1.08084	−	0.289610i
$439$	3.40848	−	5.90367i	0.162678	−	0.281767i	−0.773150	−	0.634223i	$-0.781320\pi$
$439$	3.40848	−	5.90367i	0.162678	−	0.281767i	0.935828	+	0.352456i	$0.114653\pi$
$440$		0			0
$441$	−10.0595	−	10.5058i	−0.479022	−	0.500276i
$442$	1.75752	+	1.75752i	0.0835968	+	0.0835968i
$443$	−7.67471	−	28.6424i	−0.364637	−	1.36084i	−0.867913	−	0.496717i	$-0.834539\pi$
$443$	−7.67471	−	28.6424i	−0.364637	−	1.36084i	0.503276	−	0.864126i	$-0.332128\pi$
$444$	34.3725	+	59.5349i	1.63125	+	2.82540i
$445$		0			0
$446$	0.125940	+	0.0727116i	0.00596344	+	0.00344300i
$447$	−25.5478	+	25.5478i	−1.20837	+	1.20837i
$448$	−1.65545	+	11.6004i	−0.0782127	+	0.548065i
$449$		−	11.4947i		−	0.542469i	−0.962513	−	0.271234i	$-0.912568\pi$
$449$		−	11.4947i		−	0.542469i	0.962513	−	0.271234i	$-0.0874318\pi$
$450$		0			0
$451$	5.26025	−	3.03701i	0.247696	−	0.143007i
$452$	1.35764	−	5.06678i	0.0638580	−	0.238321i
$453$	44.6227	−	11.9566i	2.09656	−	0.561771i
$454$	22.9793			1.07847
$455$		0			0
$456$	73.2686			3.43112
$457$	4.70063	−	1.25953i	0.219886	−	0.0589184i	−0.147194	−	0.989108i	$-0.547024\pi$
$457$	4.70063	−	1.25953i	0.219886	−	0.0589184i	0.367080	+	0.930189i	$0.380357\pi$
$458$	−6.61671	+	24.6939i	−0.309178	+	1.15387i
$459$	2.39570	−	1.38316i	0.111822	−	0.0645604i
$460$		0			0
$461$			22.5745i			1.05140i	0.850670	+	0.525700i	$0.176197\pi$
$461$			22.5745i			1.05140i	−0.850670	+	0.525700i	$0.823803\pi$
$462$	45.0118	−	18.0749i	2.09414	−	0.840919i
$463$	12.8682	−	12.8682i	0.598036	−	0.598036i	−0.341754	−	0.939790i	$-0.611021\pi$
$463$	12.8682	−	12.8682i	0.598036	−	0.598036i	0.939790	+	0.341754i	$0.111021\pi$
$464$	3.98759	+	2.30223i	0.185119	+	0.106879i
$465$		0			0
$466$	−12.7504	−	22.0843i	−0.590650	−	1.02304i
$467$	3.48404	+	13.0026i	0.161222	+	0.601689i	0.998492	+	0.0548990i	$0.0174837\pi$
$467$	3.48404	+	13.0026i	0.161222	+	0.601689i	−0.837270	+	0.546790i	$0.815850\pi$
$468$	4.66577	+	4.66577i	0.215675	+	0.215675i
$469$	−3.59902	+	8.42894i	−0.166187	+	0.389212i
$470$		0			0
$471$	−9.29920	+	16.1067i	−0.428485	+	0.742157i
$472$	−58.9552	−	15.7970i	−2.71363	−	0.727116i
$473$	−25.5671	−	6.85070i	−1.17558	−	0.314995i
$474$	−8.67209	+	15.0205i	−0.398322	+	0.689915i
$475$		0			0
$476$	14.8741	−	1.79425i	0.681751	−	0.0822395i
$477$	4.31916	+	4.31916i	0.197761	+	0.197761i
$478$	−5.07304	−	18.9328i	−0.232035	−	0.865968i
$479$	−15.5157	−	26.8741i	−0.708933	−	1.22791i	−0.965253	−	0.261315i	$-0.915844\pi$
$479$	−15.5157	−	26.8741i	−0.708933	−	1.22791i	0.256321	−	0.966592i	$-0.417490\pi$
$480$		0			0
$481$	4.63735	+	2.67737i	0.211445	+	0.122078i
$482$	22.1546	−	22.1546i	1.00911	−	1.00911i
$483$	−18.4998	−	2.64005i	−0.841771	−	0.120126i
$484$		−	1.76632i		−	0.0802873i
$485$		0			0
$486$	39.7717	−	22.9622i	1.80408	−	1.04159i
$487$	10.5157	−	39.2451i	0.476511	−	1.77836i	−0.139062	−	0.990284i	$-0.544409\pi$
$487$	10.5157	−	39.2451i	0.476511	−	1.77836i	0.615573	−	0.788080i	$-0.288925\pi$
$488$	−39.3655	+	10.5480i	−1.78199	+	0.477484i
$489$	−2.28222			−0.103205
$490$		0			0
$491$	−10.8184			−0.488228			−0.244114	−	0.969747i	$-0.578497\pi$
$491$	−10.8184			−0.488228			−0.244114	+	0.969747i	$0.578497\pi$
$492$	17.2846	−	4.63140i	0.779251	−	0.208800i
$493$	−0.284088	+	1.06023i	−0.0127947	+	0.0477504i
$494$	9.32916	−	5.38619i	0.419739	−	0.242336i
$495$		0			0
$496$			41.8969i			1.88123i
$497$	16.1591	+	2.30602i	0.724836	+	0.103439i
$498$	−63.7295	+	63.7295i	−2.85579	+	2.85579i
$499$	−21.7855	−	12.5779i	−0.975255	−	0.563064i	−0.0744209	−	0.997227i	$-0.523711\pi$
$499$	−21.7855	−	12.5779i	−0.975255	−	0.563064i	−0.900834	+	0.434163i	$0.857044\pi$
$500$		0			0
$501$	7.99697	+	13.8512i	0.357278	+	0.618824i
$502$	1.30247	+	4.86087i	0.0581320	+	0.216951i
$503$	3.30126	+	3.30126i	0.147196	+	0.147196i	0.776864	−	0.629668i	$-0.216809\pi$
$503$	3.30126	+	3.30126i	0.147196	+	0.147196i	−0.629668	+	0.776864i	$0.716809\pi$
$504$	30.7564	−	3.71014i	1.37000	−	0.165263i
$505$		0			0
$506$	12.7504	−	22.0843i	0.566824	−	0.981767i
$507$	−27.0830	−	7.25688i	−1.20280	−	0.322289i
$508$	20.7940	+	5.57174i	0.922586	+	0.247206i
$509$	−20.2003	+	34.9879i	−0.895360	+	1.55081i	−0.0620027	+	0.998076i	$0.519749\pi$
$509$	−20.2003	+	34.9879i	−0.895360	+	1.55081i	−0.833358	+	0.552734i	$0.813585\pi$
$510$		0			0
$511$	−4.31764	+	10.1120i	−0.191001	+	0.447327i
$512$	−33.8615	−	33.8615i	−1.49648	−	1.49648i
$513$	−3.10310	−	11.5809i	−0.137005	−	0.511310i
$514$	−19.1770	−	33.2155i	−0.845860	−	1.46507i
$515$		0			0
$516$	−67.5319	−	38.9896i	−2.97293	−	1.71642i
$517$	19.3909	−	19.3909i	0.852811	−	0.852811i
$518$	44.0359	−	17.6830i	1.93483	−	0.776945i
$519$		−	53.7481i		−	2.35928i
$520$		0			0
$521$	−15.5266	+	8.96427i	−0.680232	+	0.392732i	−0.799942	−	0.600077i	$-0.795137\pi$
$521$	−15.5266	+	8.96427i	−0.680232	+	0.392732i	0.119711	+	0.992809i	$0.461803\pi$
$522$	−1.10881	+	4.13812i	−0.0485311	+	0.181121i
$523$	7.70248	−	2.06387i	0.336806	−	0.0902469i	−0.0864523	−	0.996256i	$-0.527553\pi$
$523$	7.70248	−	2.06387i	0.336806	−	0.0902469i	0.423258	+	0.906009i	$0.360886\pi$
$524$	−83.5800			−3.65121
$525$		0			0
$526$	21.7208			0.947071
$527$	−9.64724	+	2.58497i	−0.420241	+	0.112603i
$528$	−10.5969	+	39.5483i	−0.461172	+	1.72112i
$529$	11.4103	−	6.58776i	0.496102	−	0.286424i
$530$		0			0
$531$		−	22.5062i		−	0.976684i
$532$	9.17339	−	64.2814i	0.397717	−	2.78695i
$533$	0.985596	−	0.985596i	0.0426909	−	0.0426909i
$534$	16.2469	+	9.38013i	0.703070	+	0.405918i
$535$		0			0
$536$	−9.76025	−	16.9053i	−0.421579	−	0.730196i
$537$	5.74142	+	21.4273i	0.247760	+	0.924654i
$538$	2.58557	+	2.58557i	0.111472	+	0.111472i
$539$	−5.41562	−	22.1206i	−0.233267	−	0.952803i
$540$		0			0
$541$	0.954986	−	1.65408i	0.0410581	−	0.0711147i	−0.844766	−	0.535136i	$-0.820260\pi$
$541$	0.954986	−	1.65408i	0.0410581	−	0.0711147i	0.885824	+	0.464021i	$0.153594\pi$
$542$	−14.9403	−	4.00325i	−0.641742	−	0.171954i
$543$	44.0430	+	11.8013i	1.89007	+	0.506442i
$544$	−1.79425	+	3.10774i	−0.0769280	+	0.133243i
$545$		0			0
$546$	8.90367	−	6.67980i	0.381042	−	0.285869i
$547$	13.5602	+	13.5602i	0.579791	+	0.579791i	0.934845	−	0.355055i	$-0.115538\pi$
$547$	13.5602	+	13.5602i	0.579791	+	0.579791i	−0.355055	+	0.934845i	$0.615538\pi$
$548$	8.95639	+	33.4257i	0.382598	+	1.42787i
$549$	−7.51389	−	13.0144i	−0.320685	−	0.555443i
$550$		0			0
$551$	4.11987	+	2.37861i	0.175512	+	0.101332i
$552$	28.1437	−	28.1437i	1.19788	−	1.19788i
$553$	6.40638	+	5.02715i	0.272427	+	0.213776i
$554$			9.76025i			0.414673i
$555$		0			0
$556$	4.76329	−	2.75009i	0.202008	−	0.116630i
$557$	−5.24984	+	19.5927i	−0.222443	+	0.830167i	0.760970	+	0.648787i	$0.224723\pi$
$557$	−5.24984	+	19.5927i	−0.222443	+	0.830167i	−0.983413	+	0.181381i	$0.941943\pi$
$558$	−37.6535	+	10.0892i	−1.59400	+	0.427111i
$559$	−6.07402			−0.256904
$560$		0			0
$561$	−9.76025			−0.412078
$562$	65.6271	−	17.5847i	2.76831	−	0.741767i
$563$	6.22227	−	23.2218i	0.262238	−	0.978684i	−0.701682	−	0.712490i	$-0.747567\pi$
$563$	6.22227	−	23.2218i	0.262238	−	0.978684i	0.963920	−	0.266194i	$-0.0857660\pi$
$564$	69.9654	−	40.3946i	2.94608	−	1.70092i
$565$		0			0
$566$		−	22.6858i		−	0.953554i
$567$	−10.7622	−	26.8010i	−0.451969	−	1.12554i
$568$	−24.5829	+	24.5829i	−1.03147	+	1.03147i
$569$	36.2461	+	20.9267i	1.51951	+	0.877292i	0.999736	+	0.0229910i	$0.00731891\pi$
$569$	36.2461	+	20.9267i	1.51951	+	0.877292i	0.519779	+	0.854301i	$0.326014\pi$
$570$		0			0
$571$	12.2243	+	21.1732i	0.511573	+	0.886070i	0.999910	+	0.0134150i	$0.00427026\pi$
$571$	12.2243	+	21.1732i	0.511573	+	0.886070i	−0.488337	+	0.872655i	$0.662396\pi$
$572$	2.67394	+	9.97928i	0.111803	+	0.417255i
$573$	−22.8889	−	22.8889i	−0.956196	−	0.956196i
$574$	−1.47932	−	12.2633i	−0.0617455	−	0.511860i
$575$		0			0
$576$	4.60143	−	7.96992i	0.191726	−	0.332080i
$577$	42.2335	+	11.3164i	1.75821	+	0.471110i	0.986346	−	0.164684i	$-0.0526605\pi$
$577$	42.2335	+	11.3164i	1.75821	+	0.471110i	0.771859	+	0.635794i	$0.219327\pi$
$578$	36.7819	+	9.85568i	1.52993	+	0.409942i
$579$	−12.0227	+	20.8239i	−0.499647	+	0.865414i
$580$		0			0
$581$	25.3946	+	33.8490i	1.05354	+	1.40429i
$582$	−25.5382	−	25.5382i	−1.05859	−	1.05859i
$583$	2.47529	+	9.23792i	0.102516	+	0.382596i
$584$	−11.7091	−	20.2808i	−0.484526	−	0.839224i
$585$		0			0
$586$	29.7868	+	17.1974i	1.23048	+	0.710419i
$587$	−14.2988	+	14.2988i	−0.590174	+	0.590174i	−0.937678	−	0.347504i	$-0.887029\pi$
$587$	−14.2988	+	14.2988i	−0.590174	+	0.590174i	0.347504	+	0.937678i	$0.387029\pi$
$588$	1.45581	−	67.0773i	0.0600366	−	2.76622i
$589$			43.2868i			1.78360i
$590$		0			0
$591$	12.3300	−	7.11873i	0.507189	−	0.292826i
$592$	−10.3672	+	38.6908i	−0.426088	+	1.59018i
$593$	14.6144	−	3.91593i	0.600143	−	0.160808i	0.0540583	−	0.998538i	$-0.482784\pi$
$593$	14.6144	−	3.91593i	0.600143	−	0.160808i	0.546085	+	0.837730i	$0.316118\pi$
$594$	16.9053			0.693631
$595$		0			0
$596$	−68.1968			−2.79345
$597$	16.6973	−	4.47403i	0.683375	−	0.183110i
$598$	1.51456	−	5.65242i	0.0619351	−	0.231145i
$599$	−28.1412	+	16.2474i	−1.14982	+	0.663849i	−0.948843	−	0.315747i	$-0.897745\pi$
$599$	−28.1412	+	16.2474i	−1.14982	+	0.663849i	−0.200976	+	0.979596i	$0.564411\pi$
$600$		0			0
$601$		−	31.3355i		−	1.27820i	−0.769123	−	0.639101i	$-0.779307\pi$
$601$		−	31.3355i		−	1.27820i	0.769123	−	0.639101i	$-0.220693\pi$
$602$	−33.2297	+	42.3464i	−1.35434	+	1.72591i
$603$	5.08978	−	5.08978i	0.207272	−	0.207272i
$604$	75.5160	+	43.5992i	3.07270	+	1.77403i
$605$		0			0
$606$	−10.6168	−	18.3889i	−0.431280	−	0.746998i
$607$	−10.8356	−	40.4390i	−0.439803	−	1.64137i	−0.729305	−	0.684189i	$-0.760156\pi$
$607$	−10.8356	−	40.4390i	−0.439803	−	1.64137i	0.289502	−	0.957178i	$-0.406510\pi$
$608$	10.9975	+	10.9975i	0.446009	+	0.446009i
$609$	4.52066	+	1.93024i	0.183186	+	0.0782175i
$610$		0			0
$611$	3.14645	−	5.44981i	0.127292	−	0.220476i
$612$	−11.3654	−	3.04535i	−0.459419	−	0.123101i
$613$	14.2424	+	3.81623i	0.575244	+	0.154136i	0.534700	−	0.845042i	$-0.320424\pi$
$613$	14.2424	+	3.81623i	0.575244	+	0.154136i	0.0405433	+	0.999178i	$0.487091\pi$
$614$	−8.25026	+	14.2899i	−0.332953	+	0.576692i
$615$		0			0
$616$	44.6090	+	19.0473i	1.79735	+	0.767438i
$617$	−18.8300	−	18.8300i	−0.758068	−	0.758068i	0.217903	−	0.975970i	$-0.430078\pi$
$617$	−18.8300	−	18.8300i	−0.758068	−	0.758068i	−0.975970	+	0.217903i	$0.930078\pi$
$618$	−24.6715	−	92.0753i	−0.992433	−	3.70381i
$619$	9.22226	+	15.9734i	0.370674	+	0.642026i	0.989669	−	0.143368i	$-0.0457934\pi$
$619$	9.22226	+	15.9734i	0.370674	+	0.642026i	−0.618995	+	0.785395i	$0.712460\pi$
$620$		0			0
$621$	−5.64038	−	3.25648i	−0.226341	−	0.130678i
$622$	−39.8570	+	39.8570i	−1.59812	+	1.59812i
$623$	5.43760	−	6.92943i	0.217853	−	0.277622i
$624$			9.39553i			0.376122i
$625$		0			0
$626$	7.38316	−	4.26267i	0.295090	−	0.170371i
$627$	−10.9485	+	40.8603i	−0.437240	+	1.63180i
$628$	−33.9091	+	9.08590i	−1.35312	+	0.362567i
$629$	−9.54863			−0.380729
$630$		0			0
$631$	−18.0471			−0.718443			−0.359222	−	0.933252i	$-0.616958\pi$
$631$	−18.0471			−0.718443			−0.359222	+	0.933252i	$0.616958\pi$
$632$	−16.7532	+	4.48901i	−0.666407	+	0.178563i
$633$	−2.73088	+	10.1918i	−0.108543	+	0.405087i
$634$	−0.421838	+	0.243548i	−0.0167533	+	0.00967254i
$635$		0			0
$636$			28.1754i			1.11723i
$637$	−2.51422	−	4.58155i	−0.0996169	−	0.181527i
$638$	−4.74309	+	4.74309i	−0.187781	+	0.187781i
$639$	−11.1020	−	6.40974i	−0.439188	−	0.253565i
$640$		0			0
$641$	12.4772	+	21.6112i	0.492821	+	0.853591i	0.999966	−	0.00827004i	$-0.00263247\pi$
$641$	12.4772	+	21.6112i	0.492821	+	0.853591i	−0.507145	+	0.861861i	$0.669299\pi$
$642$	25.1741	+	93.9509i	0.993542	+	3.70795i
$643$	23.0234	+	23.0234i	0.907954	+	0.907954i	0.996107	−	0.0881532i	$-0.0280965\pi$
$643$	23.0234	+	23.0234i	0.907954	+	0.907954i	−0.0881532	+	0.996107i	$0.528096\pi$
$644$	−21.1679	−	28.2152i	−0.834133	−	1.11184i
$645$		0			0
$646$	−9.60470	+	16.6358i	−0.377892	+	0.654528i
$647$	12.4686	+	3.34095i	0.490191	+	0.131346i	0.495444	−	0.868640i	$-0.335005\pi$
$647$	12.4686	+	3.34095i	0.490191	+	0.131346i	−0.00525299	+	0.999986i	$0.501672\pi$
$648$	59.4168	+	15.9207i	2.33411	+	0.625424i
$649$	17.6193	−	30.5175i	0.691617	−	1.19792i
$650$		0			0
$651$	5.35659	+	44.4052i	0.209941	+	1.74038i
$652$	−3.04606	−	3.04606i	−0.119293	−	0.119293i
$653$	7.12439	+	26.5886i	0.278799	+	1.04049i	0.953253	+	0.302175i	$0.0977126\pi$
$653$	7.12439	+	26.5886i	0.278799	+	1.04049i	−0.674454	+	0.738317i	$0.735621\pi$
$654$	−9.60558	−	16.6373i	−0.375608	−	0.650572i
$655$		0			0
$656$	9.02961	+	5.21325i	0.352547	+	0.203543i
$657$	6.10606	−	6.10606i	0.238220	−	0.238220i
$658$	−20.7810	−	51.7509i	−0.810128	−	2.01746i
$659$		−	39.9692i		−	1.55698i	−0.627658	−	0.778489i	$-0.715986\pi$
$659$		−	39.9692i		−	1.55698i	0.627658	−	0.778489i	$-0.284014\pi$
$660$		0			0
$661$	9.99393	−	5.77000i	0.388719	−	0.224427i	−0.292886	−	0.956147i	$-0.594616\pi$
$661$	9.99393	−	5.77000i	0.388719	−	0.224427i	0.681605	+	0.731720i	$0.261282\pi$
$662$	−18.9889	+	70.8674i	−0.738023	+	2.75434i
$663$	−2.16343	+	0.579689i	−0.0840206	+	0.0225133i
$664$	−90.1272			−3.49761
$665$		0			0
$666$	−37.2686			−1.44413
$667$	2.49618	−	0.668849i	0.0966525	−	0.0258979i
$668$	−7.81354	+	29.1605i	−0.302315	+	1.12825i
$669$	−0.113487	+	0.0655220i	−0.00438768	+	0.00253323i
$670$		0			0
$671$		−	23.5294i		−	0.908344i
$672$	12.6426	+	9.92076i	0.487698	+	0.382702i
$673$	−30.8611	+	30.8611i	−1.18961	+	1.18961i	−0.212431	+	0.977176i	$0.568138\pi$
$673$	−30.8611	+	30.8611i	−1.18961	+	1.18961i	−0.977176	+	0.212431i	$0.931862\pi$
$674$	21.7365	+	12.5496i	0.837259	+	0.483392i
$675$		0			0
$676$	−26.4618	−	45.8332i	−1.01776	−	1.76282i
$677$	1.50395	+	5.61280i	0.0578014	+	0.215718i	0.988786	−	0.149342i	$-0.0477154\pi$
$677$	1.50395	+	5.61280i	0.0578014	+	0.215718i	−0.930984	+	0.365059i	$0.881049\pi$
$678$	4.91400	+	4.91400i	0.188721	+	0.188721i
$679$	−13.5642	+	10.1763i	−0.520547	+	0.390530i
$680$		0			0
$681$	−10.3536	+	17.9329i	−0.396749	+	0.687189i
$682$	−58.9552	−	15.7970i	−2.25751	−	0.604899i
$683$	−30.1953	−	8.09080i	−1.15539	−	0.309586i	−0.370267	−	0.928925i	$-0.620734\pi$
$683$	−30.1953	−	8.09080i	−1.15539	−	0.309586i	−0.785123	+	0.619339i	$0.787401\pi$
$684$	−25.4981	+	44.1639i	−0.974942	+	1.68865i
$685$		0			0
$686$	−45.6960	−	7.53624i	−1.74468	−	0.287735i
$687$	−16.2897	−	16.2897i	−0.621492	−	0.621492i
$688$	−11.7597	−	43.8879i	−0.448335	−	1.67321i
$689$	1.09733	+	1.90064i	0.0418050	+	0.0724084i
$690$		0			0
$691$	6.63431	+	3.83032i	0.252381	+	0.145712i	0.620854	−	0.783926i	$-0.286786\pi$
$691$	6.63431	+	3.83032i	0.252381	+	0.145712i	−0.368473	+	0.929638i	$0.620119\pi$
$692$	71.7372	−	71.7372i	2.72704	−	2.72704i
$693$	−2.52685	+	17.7066i	−0.0959870	+	0.672617i
$694$			56.4897i			2.14432i
$695$		0			0
$696$	−9.06672	+	5.23467i	−0.343673	+	0.198420i
$697$	−0.643298	+	2.40082i	−0.0243666	+	0.0909375i
$698$	−57.5437	+	15.4188i	−2.17806	+	0.583610i
$699$	22.9793			0.869156
$700$		0			0
$701$	6.78500			0.256266			0.128133	−	0.991757i	$-0.459102\pi$
$701$	6.78500			0.256266			0.128133	+	0.991757i	$0.459102\pi$
$702$	3.74717	−	1.00405i	0.141428	−	0.0378954i
$703$	−10.7111	+	39.9743i	−0.403976	+	1.50766i
$704$	12.4787	−	7.20460i	0.470310	−	0.271534i
$705$		0			0
$706$			7.02893i			0.264537i
$707$	−9.25148	+	3.71501i	−0.347938	+	0.139717i
$708$	73.4079	−	73.4079i	2.75884	−	2.75884i
$709$	−31.2746	−	18.0564i	−1.17454	−	0.678123i	−0.219798	−	0.975545i	$-0.570540\pi$
$709$	−31.2746	−	18.0564i	−1.17454	−	0.678123i	−0.954746	+	0.297422i	$0.903873\pi$
$710$		0			0
$711$	−3.19777	−	5.53869i	−0.119926	−	0.207717i
$712$	4.85551	+	18.1210i	0.181968	+	0.679114i
$713$	16.6272	+	16.6272i	0.622694	+	0.622694i
$714$	−7.79423	+	18.2542i	−0.291692	+	0.683146i
$715$		0			0
$716$	−20.9358	+	36.2618i	−0.782407	+	1.35517i
$717$	17.0608	+	4.57142i	0.637147	+	0.170723i
$718$	−70.8821	−	18.9928i	−2.64530	−	0.708805i
$719$	−11.2531	+	19.4909i	−0.419669	+	0.726888i	−0.995906	−	0.0903947i	$-0.971187\pi$
$719$	−11.2531	+	19.4909i	−0.419669	+	0.726888i	0.576237	+	0.817283i	$0.304520\pi$
$720$		0			0
$721$	−44.4335	+	5.36000i	−1.65479	+	0.199617i
$722$	25.2734	+	25.2734i	0.940579	+	0.940579i
$723$	7.30732	+	27.2713i	0.271762	+	1.01423i
$724$	43.0328	+	74.5349i	1.59930	+	2.77007i
$725$		0			0
$726$	2.02658	+	1.17004i	0.0752133	+	0.0434244i
$727$	16.5442	−	16.5442i	0.613591	−	0.613591i	−0.330289	−	0.943880i	$-0.607146\pi$
$727$	16.5442	−	16.5442i	0.613591	−	0.613591i	0.943880	+	0.330289i	$0.107146\pi$
$728$	11.0192	+	1.57251i	0.408398	+	0.0582812i
$729$			8.63528i			0.319825i
$730$		0			0
$731$	9.38013	−	5.41562i	0.346937	−	0.200304i
$732$	17.9410	−	66.9569i	0.663120	−	2.47480i
$733$	22.5612	−	6.04527i	0.833319	−	0.223287i	0.183158	−	0.983084i	$-0.441368\pi$
$733$	22.5612	−	6.04527i	0.833319	−	0.223287i	0.650161	+	0.759797i	$0.274701\pi$
$734$	10.5404			0.389053
$735$		0			0
$736$	8.44868			0.311423
$737$	10.8861	−	2.91693i	0.400996	−	0.107447i
$738$	−2.51081	+	9.37048i	−0.0924243	+	0.344932i
$739$	−2.18282	+	1.26025i	−0.0802965	+	0.0463592i	−0.539611	−	0.841915i	$-0.681429\pi$
$739$	−2.18282	+	1.26025i	−0.0802965	+	0.0463592i	0.459314	+	0.888274i	$0.348095\pi$
$740$		0			0
$741$			9.70722i			0.356604i
$742$	19.2540	+	2.74767i	0.706836	+	0.100870i
$743$	−21.2539	+	21.2539i	−0.779730	+	0.779730i	−0.979785	−	0.200055i	$-0.935888\pi$
$743$	−21.2539	+	21.2539i	−0.779730	+	0.779730i	0.200055	+	0.979785i	$0.435888\pi$
$744$	−82.4998	−	47.6313i	−3.02459	−	1.74625i
$745$		0			0
$746$	16.9451	+	29.3498i	0.620405	+	1.07457i
$747$	−8.60151	−	32.1013i	−0.314713	−	1.17452i
$748$	−13.0269	−	13.0269i	−0.476312	−	0.476312i
$749$	45.3387	−	5.46919i	1.65664	−	0.199840i
$750$		0			0
$751$	17.5298	−	30.3626i	0.639673	−	1.10795i	−0.345831	−	0.938297i	$-0.612403\pi$
$751$	17.5298	−	30.3626i	0.639673	−	1.10795i	0.985504	−	0.169650i	$-0.0542636\pi$
$752$	45.4694	+	12.1835i	1.65810	+	0.444286i
$753$	−4.38023	−	1.17368i	−0.159625	−	0.0427713i
$754$	−0.769633	+	1.33304i	−0.0280284	+	0.0485466i
$755$		0			0
$756$	9.18236	−	21.5052i	0.333959	−	0.782137i
$757$	13.5662	+	13.5662i	0.493071	+	0.493071i	0.909272	−	0.416201i	$-0.136639\pi$
$757$	13.5662	+	13.5662i	0.493071	+	0.493071i	−0.416201	+	0.909272i	$0.636639\pi$
$758$	11.5364	+	43.0546i	0.419022	+	1.56381i
$759$	11.4896	+	19.9006i	0.417047	+	0.722347i
$760$		0			0
$761$	−31.3073	−	18.0753i	−1.13489	−	0.655229i	−0.189730	−	0.981836i	$-0.560761\pi$
$761$	−31.3073	−	18.0753i	−1.13489	−	0.655229i	−0.945160	+	0.326607i	$0.894095\pi$
$762$	−20.1670	+	20.1670i	−0.730575	+	0.730575i
$763$	−8.37027	+	3.36115i	−0.303024	+	0.121682i
$764$		−	61.0992i		−	2.21049i
$765$		0			0
$766$	65.8855	−	38.0390i	2.38054	−	1.37440i
$767$	2.09292	−	7.81087i	0.0755708	−	0.282034i
$768$	70.3470	−	18.8494i	2.53843	−	0.680170i
$769$	−38.4565			−1.38678			−0.693388	−	0.720564i	$-0.743883\pi$
$769$	−38.4565			−1.38678			−0.693388	+	0.720564i	$0.743883\pi$
$770$		0			0
$771$	34.5615			1.24470
$772$	−43.8402	+	11.7469i	−1.57784	+	0.422782i
$773$	9.68418	−	36.1419i	0.348316	−	1.29993i	−0.540375	−	0.841425i	$-0.681717\pi$
$773$	9.68418	−	36.1419i	0.348316	−	1.29993i	0.888690	−	0.458508i	$-0.151616\pi$
$774$	36.6110	−	21.1373i	1.31595	−	0.759766i
$775$		0			0
$776$		−	36.1164i		−	1.29650i
$777$	−6.04114	+	42.3326i	−0.216725	+	1.51867i
$778$	27.9030	−	27.9030i	1.00037	−	1.00037i
$779$	9.32916	+	5.38619i	0.334252	+	0.192980i
$780$		0			0
$781$	−10.0359	−	17.3827i	−0.359113	−	0.622002i
$782$	2.70078	+	10.0794i	0.0965797	+	0.360440i
$783$	1.21139	+	1.21139i	0.0432917	+	0.0432917i
$784$	28.2363	−	27.0367i	1.00844	−	0.965596i
$785$		0			0
$786$	55.3650	−	95.8949i	1.97480	−	3.42046i
$787$	−22.9433	−	6.14764i	−0.817840	−	0.219140i	−0.174438	−	0.984668i	$-0.555811\pi$
$787$	−22.9433	−	6.14764i	−0.817840	−	0.219140i	−0.643402	+	0.765528i	$0.722478\pi$
$788$	25.9581	+	6.95545i	0.924719	+	0.247778i
$789$	−9.78652	+	16.9508i	−0.348409	+	0.603463i
$790$		0			0
$791$	2.61000	−	1.95810i	0.0928010	−	0.0696221i
$792$	−26.9370	−	26.9370i	−0.957163	−	0.957163i
$793$	−1.39748	−	5.21546i	−0.0496260	−	0.185207i
$794$	−0.585688	−	1.01444i	−0.0207853	−	0.0360012i
$795$		0			0
$796$	28.2572	+	16.3143i	1.00155	+	0.578246i
$797$	4.44975	−	4.44975i	0.157618	−	0.157618i	−0.623892	−	0.781510i	$-0.714450\pi$
$797$	4.44975	−	4.44975i	0.157618	−	0.157618i	0.781510	+	0.623892i	$0.214450\pi$
$798$	67.6761	+	53.1062i	2.39571	+	1.87994i
$799$			11.2215i			0.396990i
$800$		0			0
$801$	−5.99090	+	3.45885i	−0.211678	+	0.122212i
$802$	16.2448	−	60.6264i	0.573624	−	2.14079i
$803$	13.0598	−	3.49937i	0.460871	−	0.123490i
$804$	33.2025			1.17096
$805$		0			0
$806$	−14.0061			−0.493343
$807$	−3.18272	+	0.852808i	−0.112037	+	0.0300203i
$808$	5.49568	−	20.5102i	0.193337	−	0.721545i
$809$	−12.4231	+	7.17249i	−0.436774	+	0.252171i	−0.702228	−	0.711952i	$-0.747811\pi$
$809$	−12.4231	+	7.17249i	−0.436774	+	0.252171i	0.265454	+	0.964123i	$0.414478\pi$
$810$		0			0
$811$			22.9214i			0.804879i	0.915447	+	0.402440i	$0.131838\pi$
$811$			22.9214i			0.804879i	−0.915447	+	0.402440i	$0.868162\pi$
$812$	3.45741	+	8.60997i	0.121331	+	0.302151i
$813$	9.85562	−	9.85562i	0.345652	−	0.345652i
$814$	−50.5348	−	29.1763i	−1.77124	−	1.02263i
$815$		0			0
$816$	−8.37709	−	14.5096i	−0.293257	−	0.507936i
$817$	−12.1498	−	45.3438i	−0.425069	−	1.58638i
$818$	−42.9197	−	42.9197i	−1.50065	−	1.50065i
$819$	0.491549	+	4.07486i	0.0171761	+	0.142387i
$820$		0			0
$821$	5.65275	−	9.79085i	0.197282	−	0.341703i	−0.750364	−	0.661025i	$-0.770122\pi$
$821$	5.65275	−	9.79085i	0.197282	−	0.341703i	0.947646	+	0.319322i	$0.103455\pi$
$822$	−44.2836	−	11.8658i	−1.54457	−	0.413866i
$823$	−11.9617	−	3.20513i	−0.416959	−	0.111724i	0.0442392	−	0.999021i	$-0.485914\pi$
$823$	−11.9617	−	3.20513i	−0.416959	−	0.111724i	−0.461198	+	0.887297i	$0.652580\pi$
$824$	47.6617	−	82.5524i	1.66037	−	2.87585i
$825$		0			0
$826$	−43.0053	−	57.3229i	−1.49635	−	1.99452i
$827$	1.19586	+	1.19586i	0.0415840	+	0.0415840i	0.727593	−	0.686009i	$-0.240639\pi$
$827$	1.19586	+	1.19586i	0.0415840	+	0.0415840i	−0.686009	+	0.727593i	$0.740639\pi$
$828$	7.16988	+	26.7584i	0.249171	+	0.929918i
$829$	15.5105	+	26.8650i	0.538702	+	0.933059i	0.998974	+	0.0452810i	$0.0144183\pi$
$829$	15.5105	+	26.8650i	0.538702	+	0.933059i	−0.460273	+	0.887778i	$0.652248\pi$
$830$		0			0
$831$	−7.61684	−	4.39758i	−0.264225	−	0.152551i
$832$	2.33810	−	2.33810i	0.0810589	−	0.0810589i
$833$	7.96764	+	4.83361i	0.276062	+	0.167475i
$834$			7.28683i			0.252322i
$835$		0			0
$836$	−69.1488	+	39.9231i	−2.39156	+	1.38077i
$837$	−4.03459	+	15.0573i	−0.139456	+	0.520456i
$838$	−28.5517	+	7.65041i	−0.986303	+	0.264279i
$839$	36.7350			1.26823			0.634116	−	0.773238i	$-0.281364\pi$
$839$	36.7350			1.26823			0.634116	+	0.773238i	$0.281364\pi$
$840$		0			0
$841$	28.3202			0.976560
$842$	54.9475	−	14.7231i	1.89362	−	0.507393i
$843$	−15.8460	+	59.1380i	−0.545764	+	2.03682i
$844$	−17.2478	+	9.95802i	−0.593694	+	0.342769i
$845$		0			0
$846$			43.7981i			1.50581i
$847$	0.678267	−	0.864352i	0.0233055	−	0.0296995i
$848$	−11.6085	+	11.6085i	−0.398639	+	0.398639i
$849$	17.7038	+	10.2213i	0.607594	+	0.350794i
$850$		0			0
$851$	11.2405	+	19.4691i	0.385320	+	0.667394i
$852$	−15.3046	−	57.1177i	−0.524328	−	1.95682i
$853$	−10.5655	−	10.5655i	−0.361755	−	0.361755i	0.502704	−	0.864459i	$-0.332339\pi$
$853$	−10.5655	−	10.5655i	−0.361755	−	0.361755i	−0.864459	+	0.502704i	$0.832339\pi$
$854$	−44.0061	−	18.7899i	−1.50586	−	0.642976i
$855$		0			0
$856$	−48.6326	+	84.2341i	−1.66223	+	2.87906i
$857$	27.3230	+	7.32117i	0.933335	+	0.250086i	0.693276	−	0.720672i	$-0.256167\pi$
$857$	27.3230	+	7.32117i	0.933335	+	0.250086i	0.240059	+	0.970758i	$0.422833\pi$
$858$	−13.2209	−	3.54253i	−0.451355	−	0.120940i
$859$	9.29630	−	16.1017i	0.317186	−	0.549382i	−0.662714	−	0.748873i	$-0.730595\pi$
$859$	9.29630	−	16.1017i	0.317186	−	0.549382i	0.979900	+	0.199491i	$0.0639288\pi$
$860$		0			0
$861$	10.2367	+	4.37090i	0.348866	+	0.148960i
$862$	46.1015	+	46.1015i	1.57022	+	1.57022i
$863$	−5.17387	−	19.3091i	−0.176121	−	0.657291i	−0.996358	−	0.0852678i	$-0.972825\pi$
$863$	−5.17387	−	19.3091i	−0.176121	−	0.657291i	0.820238	−	0.572023i	$-0.193841\pi$
$864$	2.80045	+	4.85052i	0.0952732	+	0.165018i
$865$		0			0
$866$	68.6131	+	39.6138i	2.33157	+	1.34613i
$867$	−24.2638	+	24.2638i	−0.824041	+	0.824041i
$868$	−52.1179	+	66.4167i	−1.76900	+	2.25433i
$869$		−	10.0137i		−	0.339691i
$870$		0			0
$871$	2.23975	−	1.29312i	0.0758909	−	0.0438156i
$872$	4.97221	−	18.5565i	0.168380	−	0.628404i
$873$	12.8639	−	3.44686i	0.435375	−	0.116658i
$874$	45.2261			1.52980
$875$		0			0
$876$	39.8321			1.34580
$877$	−46.5640	+	12.4768i	−1.57235	+	0.421311i	−0.936548	−	0.350538i	$-0.885999\pi$
$877$	−46.5640	+	12.4768i	−1.57235	+	0.421311i	−0.635805	+	0.771849i	$0.719332\pi$
$878$	−4.41211	+	16.4662i	−0.148901	+	0.555708i
$879$	−26.8415	+	15.4970i	−0.905342	+	0.522700i
$880$		0			0
$881$			29.5693i			0.996214i	0.867116	+	0.498107i	$0.165971\pi$
$881$			29.5693i			0.996214i	−0.867116	+	0.498107i	$0.834029\pi$
$882$	31.0980	+	18.8658i	1.04712	+	0.635243i
$883$	−8.22652	+	8.22652i	−0.276845	+	0.276845i	−0.831848	−	0.555003i	$-0.812717\pi$
$883$	−8.22652	+	8.22652i	−0.276845	+	0.276845i	0.555003	+	0.831848i	$0.312717\pi$
$884$	−3.66122	−	2.11381i	−0.123140	−	0.0710950i
$885$		0			0
$886$	37.0762	+	64.2178i	1.24560	+	2.15744i
$887$	−8.30591	−	30.9981i	−0.278885	−	1.04081i	−0.953193	−	0.302363i	$-0.902225\pi$
$887$	−8.30591	−	30.9981i	−0.278885	−	1.04081i	0.674308	−	0.738450i	$-0.264442\pi$
$888$	−64.4004	−	64.4004i	−2.16114	−	2.16114i
$889$	8.03604	+	10.7114i	0.269520	+	0.359250i
$890$		0			0
$891$	−17.7572	+	30.7564i	−0.594889	+	1.03038i
$892$	−0.238922	−	0.0640191i	−0.00799972	−	0.00214352i
$893$	46.9778	+	12.5877i	1.57205	+	0.421230i
$894$	45.1748	−	78.2451i	1.51087	−	2.61691i
$895$		0			0
$896$	−5.21751	−	43.2522i	−0.174305	−	1.44496i
$897$	3.72871	+	3.72871i	0.124498	+	0.124498i
$898$	7.43965	+	27.7652i	0.248264	+	0.926535i
$899$	−3.09263	−	5.35659i	−0.103145	−	0.178652i
$900$		0			0
$901$	−3.38923	−	1.95677i	−0.112912	−	0.0651895i
$902$	−10.7404	+	10.7404i	−0.357616	+	0.357616i
$903$	−18.0749	−	45.0118i	−0.601494	−	1.49790i
$904$			6.94945i			0.231135i
$905$		0			0
$906$	−100.046	+	57.7618i	−3.32382	+	1.91901i
$907$	−13.4803	+	50.3092i	−0.447606	+	1.67049i	0.261355	+	0.965243i	$0.415831\pi$
$907$	−13.4803	+	50.3092i	−0.447606	+	1.67049i	−0.708961	+	0.705247i	$0.750836\pi$
$908$	−37.7537	+	10.1161i	−1.25290	+	0.335714i
$909$	7.82975			0.259696
$910$		0			0
$911$	5.80580			0.192355			0.0961774	−	0.995364i	$-0.469338\pi$
$911$	5.80580			0.192355			0.0961774	+	0.995364i	$0.469338\pi$
$912$	−70.1396	+	18.7939i	−2.32256	+	0.622327i
$913$	13.4676	−	50.2619i	0.445714	−	1.66343i
$914$	−10.5391	+	6.08473i	−0.348601	+	0.201265i
$915$		0			0
$916$		−	43.4835i		−	1.43674i
$917$	−40.9000	−	32.0947i	−1.35064	−	1.05986i
$918$	−4.89155	+	4.89155i	−0.161445	+	0.161445i
$919$	−16.5500	−	9.55512i	−0.545933	−	0.315194i	0.201547	−	0.979479i	$-0.435403\pi$
$919$	−16.5500	−	9.55512i	−0.545933	−	0.315194i	−0.747480	+	0.664284i	$0.768736\pi$
$920$		0			0
$921$	−7.43448	−	12.8769i	−0.244974	−	0.424308i
$922$	−14.6108	−	54.5282i	−0.481181	−	1.79579i
$923$	−3.25694	−	3.25694i	−0.107203	−	0.107203i
$924$	−65.9950	+	49.5114i	−2.17107	+	1.62881i
$925$		0			0
$926$	−22.7542	+	39.4114i	−0.747749	+	1.29514i
$927$	33.9520	+	9.09742i	1.11513	+	0.298798i
$928$	−2.14662	−	0.575186i	−0.0704663	−	0.0188814i
$929$	26.4937	−	45.8885i	0.869231	−	1.50555i	0.00644791	−	0.999979i	$-0.497948\pi$
$929$	26.4937	−	45.8885i	0.869231	−	1.50555i	0.862783	−	0.505574i	$-0.168719\pi$
$930$		0			0
$931$	29.1730	−	27.9336i	0.956107	−	0.915487i
$932$	30.6703	+	30.6703i	1.00464	+	1.00464i
$933$	−13.1461	−	49.0621i	−0.430386	−	1.60622i
$934$	−16.8312	−	29.1525i	−0.550734	−	0.953899i
$935$		0			0
$936$	−7.57063	−	4.37090i	−0.247454	−	0.142867i
$937$	−5.68048	+	5.68048i	−0.185573	+	0.185573i	−0.793779	−	0.608206i	$-0.791889\pi$
$937$	−5.68048	+	5.68048i	−0.185573	+	0.185573i	0.608206	+	0.793779i	$0.291889\pi$
$938$	3.23791	−	22.6893i	0.105722	−	0.740831i
$939$			7.68236i			0.250704i
$940$		0			0
$941$	−18.6343	+	10.7585i	−0.607461	+	0.350718i	−0.771971	−	0.635657i	$-0.780729\pi$
$941$	−18.6343	+	10.7585i	−0.607461	+	0.350718i	0.164510	+	0.986375i	$0.447396\pi$
$942$	12.0373	−	44.9240i	0.392198	−	1.46370i
$943$	5.65242	−	1.51456i	0.184068	−	0.0493209i
$944$	60.4895			1.96877
$945$		0			0
$946$	66.1907			2.15205
$947$	−40.2481	+	10.7845i	−1.30789	+	0.350448i	−0.844428	−	0.535669i	$-0.820059\pi$
$947$	−40.2481	+	10.7845i	−1.30789	+	0.350448i	−0.463461	+	0.886117i	$0.653393\pi$
$948$	7.63536	−	28.4956i	0.247985	−	0.925493i
$949$	2.68696	−	1.55132i	0.0872224	−	0.0503579i
$950$		0			0
$951$		−	0.438933i		−	0.0142334i
$952$	−18.4190	+	7.39631i	−0.596964	+	0.239716i
$953$	−7.82075	+	7.82075i	−0.253339	+	0.253339i	−0.822338	−	0.568999i	$-0.807331\pi$
$953$	−7.82075	+	7.82075i	−0.253339	+	0.253339i	0.568999	+	0.822338i	$0.307331\pi$
$954$	−13.2283	−	7.63735i	−0.428281	−	0.247268i
$955$		0			0
$956$	16.6695	+	28.8723i	0.539129	+	0.933798i
$957$	−1.56443	−	5.83852i	−0.0505707	−	0.188733i
$958$	54.8714	+	54.8714i	1.77282	+	1.77282i
$959$	−8.45263	+	19.7962i	−0.272950	+	0.639252i
$960$		0			0
$961$	12.6404	−	21.8938i	0.407754	−	0.706251i
$962$	−12.9343	−	3.46572i	−0.417017	−	0.111739i
$963$	−34.6437	−	9.28274i	−1.11638	−	0.299132i
$964$	−26.6457	+	46.1518i	−0.858202	+	1.48645i
$965$		0			0
$966$	46.3946	−	5.59656i	1.49272	−	0.180066i
$967$	6.14790	+	6.14790i	0.197703	+	0.197703i	0.799015	−	0.601312i	$-0.205355\pi$
$967$	6.14790	+	6.14790i	0.197703	+	0.197703i	−0.601312	+	0.799015i	$0.705355\pi$
$968$	0.605659	+	2.26035i	0.0194666	+	0.0726504i
$969$	−8.65500	−	14.9909i	−0.278039	−	0.481577i
$970$		0			0
$971$	−19.9674	−	11.5282i	−0.640783	−	0.369956i	0.144133	−	0.989558i	$-0.453961\pi$
$971$	−19.9674	−	11.5282i	−0.640783	−	0.369956i	−0.784916	+	0.619602i	$0.787294\pi$
$972$	−55.2341	+	55.2341i	−1.77164	+	1.77164i
$973$	3.38695	+	0.483341i	0.108581	+	0.0154952i
$974$			101.601i			3.25552i
$975$		0			0
$976$	34.9788	−	20.1950i	1.11964	−	0.646426i
$977$	6.28268	−	23.4473i	0.201001	−	0.750144i	−0.789631	−	0.613582i	$-0.789728\pi$
$977$	6.28268	−	23.4473i	0.201001	−	0.750144i	0.990631	−	0.136562i	$-0.0436054\pi$
$978$	5.51264	−	1.47711i	0.176275	−	0.0472327i
$979$	−10.8312			−0.346168
$980$		0			0
$981$	7.08396			0.226173
$982$	26.1316	−	7.00194i	0.833893	−	0.223441i
$983$	−4.40830	+	16.4520i	−0.140603	+	0.524737i	0.859309	+	0.511457i	$0.170894\pi$
$983$	−4.40830	+	16.4520i	−0.140603	+	0.524737i	−0.999912	+	0.0132800i	$0.995773\pi$
$984$	−20.5310	+	11.8536i	−0.654503	+	0.377877i
$985$		0			0
$986$		−	2.74483i		−	0.0874132i
$987$	49.7492	+	7.09955i	1.58353	+	0.225981i
$988$	−12.9562	+	12.9562i	−0.412190	+	0.412190i
$989$	−22.0843	−	12.7504i	−0.702240	−	0.405439i
$990$		0			0
$991$	−29.2739	−	50.7039i	−0.929917	−	1.61066i	−0.783456	−	0.621447i	$-0.786545\pi$
$991$	−29.2739	−	50.7039i	−0.929917	−	1.61066i	−0.146461	−	0.989217i	$-0.546788\pi$
$992$	−5.23372	−	19.5325i	−0.166171	−	0.620158i
$993$	−46.7488	−	46.7488i	−1.48353	−	1.48353i
$994$	−40.5245	+	4.88846i	−1.28536	+	0.155053i
$995$		0			0
$996$	76.6488	−	132.760i	2.42871	−	4.20665i
$997$	52.8636	+	14.1647i	1.67421	+	0.448602i	0.966240	−	0.257645i	$-0.0829464\pi$
$997$	52.8636	+	14.1647i	1.67421	+	0.448602i	0.707966	+	0.706247i	$0.249613\pi$
$998$	60.7632	+	16.2814i	1.92342	+	0.515380i
$999$	−7.45169	+	12.9067i	−0.235761	+	0.408350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.o.d.82.1	yes	24
5.2	odd	4	inner	175.2.o.d.68.1	✓	24
5.3	odd	4	inner	175.2.o.d.68.6	yes	24
5.4	even	2	inner	175.2.o.d.82.6	yes	24
7.3	odd	6	inner	175.2.o.d.157.6	yes	24
35.3	even	12	inner	175.2.o.d.143.1	yes	24
35.17	even	12	inner	175.2.o.d.143.6	yes	24
35.24	odd	6	inner	175.2.o.d.157.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.o.d.68.1	✓	24	5.2	odd	4	inner
175.2.o.d.68.6	yes	24	5.3	odd	4	inner
175.2.o.d.82.1	yes	24	1.1	even	1	trivial
175.2.o.d.82.6	yes	24	5.4	even	2	inner
175.2.o.d.143.1	yes	24	35.3	even	12	inner
175.2.o.d.143.6	yes	24	35.17	even	12	inner
175.2.o.d.157.1	yes	24	35.24	odd	6	inner
175.2.o.d.157.6	yes	24	7.3	odd	6	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.41547 + 0.647225i) q^{2} +(0.583228 - 2.17663i) q^{3} +(3.68357 - 2.12671i) q^{4} +5.63509i q^{6} +(2.61922 + 0.373780i) q^{7} +(-3.98461 + 3.98461i) q^{8} +(-1.79951 - 1.03895i) q^{9} +O(q^{10})\)	\(q+(-2.41547 + 0.647225i) q^{2} +(0.583228 - 2.17663i) q^{3} +(3.68357 - 2.12671i) q^{4} +5.63509i q^{6} +(2.61922 + 0.373780i) q^{7} +(-3.98461 + 3.98461i) q^{8} +(-1.79951 - 1.03895i) q^{9} +(-1.62671 - 2.81754i) q^{11} +(-2.48071 - 9.25814i) q^{12} +(-0.527913 - 0.527913i) q^{13} +(-6.56857 + 0.792364i) q^{14} +(2.79236 - 4.83652i) q^{16} +(1.28595 + 0.344569i) q^{17} +(5.01910 + 1.34486i) q^{18} +(2.88500 - 4.99697i) q^{19} +(2.34118 - 5.48308i) q^{21} +(5.75286 + 5.75286i) q^{22} +(-0.811243 - 3.02760i) q^{23} +(6.34910 + 10.9970i) q^{24} +(1.61684 + 0.933483i) q^{26} +(1.46929 - 1.46929i) q^{27} +(10.4430 - 4.19347i) q^{28} +0.824475i q^{29} +(-6.49697 + 3.75103i) q^{31} +(-0.697639 + 2.60362i) q^{32} +(-7.08150 + 1.89748i) q^{33} -3.32919 q^{34} -8.83815 q^{36} +(-6.92796 + 1.85634i) q^{37} +(-3.73449 + 13.9373i) q^{38} +(-1.45697 + 0.841181i) q^{39} +1.86697i q^{41} +(-2.10628 + 14.7595i) q^{42} +(5.75286 - 5.75286i) q^{43} +(-11.9842 - 6.91907i) q^{44} +(3.91907 + 6.78803i) q^{46} +(2.18157 + 8.14173i) q^{47} +(-8.89875 - 8.89875i) q^{48} +(6.72058 + 1.95802i) q^{49} +(1.50000 - 2.59808i) q^{51} +(-3.06732 - 0.821886i) q^{52} +(-2.83945 - 0.760829i) q^{53} +(-2.59808 + 4.50000i) q^{54} +(-11.9259 + 8.94718i) q^{56} +(-9.19396 - 9.19396i) q^{57} +(-0.533620 - 1.99150i) q^{58} +(5.41562 + 9.38013i) q^{59} +(6.26329 + 3.61611i) q^{61} +(13.2655 - 13.2655i) q^{62} +(-4.32496 - 3.39384i) q^{63} +4.42894i q^{64} +(15.8771 - 9.16664i) q^{66} +(-0.896575 + 3.34607i) q^{67} +(5.46967 - 1.46559i) q^{68} -7.06312 q^{69} +6.16946 q^{71} +(11.3101 - 3.03054i) q^{72} +(-1.07560 + 4.01418i) q^{73} +(15.5328 - 8.96789i) q^{74} -24.5422i q^{76} +(-3.20756 - 7.98778i) q^{77} +(2.97484 - 2.97484i) q^{78} +(2.66553 + 1.53895i) q^{79} +(-5.45802 - 9.45357i) q^{81} +(-1.20835 - 4.50961i) q^{82} +(11.3094 + 11.3094i) q^{83} +(-3.03701 - 25.1763i) q^{84} +(-10.1725 + 17.6193i) q^{86} +(1.79458 + 0.480856i) q^{87} +(17.7086 + 4.74500i) q^{88} +(1.66459 - 2.88316i) q^{89} +(-1.18539 - 1.58004i) q^{91} +(-9.42709 - 9.42709i) q^{92} +(4.37540 + 16.3292i) q^{93} +(-10.5391 - 18.2542i) q^{94} +(5.26025 + 3.03701i) q^{96} +(-4.53199 + 4.53199i) q^{97} +(-17.5007 - 0.379825i) q^{98} +6.76025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{11} - 4 q^{16} - 28 q^{21} + 12 q^{26} - 36 q^{31} - 8 q^{36} - 8 q^{46} + 36 q^{51} - 60 q^{56} + 84 q^{61} + 168 q^{66} - 136 q^{71} - 20 q^{81} - 80 q^{86} + 20 q^{91} - 60 q^{96}+O(q^{100}) \) 24 * q - 8 * q^11 - 4 * q^16 - 28 * q^21 + 12 * q^26 - 36 * q^31 - 8 * q^36 - 8 * q^46 + 36 * q^51 - 60 * q^56 + 84 * q^61 + 168 * q^66 - 136 * q^71 - 20 * q^81 - 80 * q^86 + 20 * q^91 - 60 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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