LMFDB - Embedded newform 175.2.o.d.82.6

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			82.6
Character	$\chi$	$=$	175.82
Dual form			175.2.o.d.143.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.41547 - 0.647225i) q^{2} +(-0.583228 + 2.17663i) q^{3} +(3.68357 - 2.12671i) q^{4} +5.63509i q^{6} +(-2.61922 - 0.373780i) q^{7} +(3.98461 - 3.98461i) q^{8} +(-1.79951 - 1.03895i) q^{9} +O(q^{10})$	\(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	0.733066	−	0.680157i	$-0.238089\pi$
$2$	2.41547	−	0.647225i	1.70800	−	0.457657i	0.974933	+	0.222501i	$0.0714219\pi$
$3$	−0.583228	+	2.17663i	−0.336727	+	1.25668i	0.565259	+	0.824914i	$0.308776\pi$
$3$	−0.583228	+	2.17663i	−0.336727	+	1.25668i	−0.901985	+	0.431767i	$0.857890\pi$
$4$	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	0.776515	−	0.630098i	$-0.216985\pi$
$13$	0.527913	+	0.527913i	0.146417	+	0.146417i	−0.630098	+	0.776515i	$0.716985\pi$
$14$	−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	0.0994797	−	0.995040i	$-0.468282\pi$
$17$	−1.28595	−	0.344569i	−0.311888	−	0.0835702i	−0.411368	+	0.911469i	$0.634949\pi$
$18$	−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	$0.0226316\pi$
$23$	0.811243	+	3.02760i	0.169156	+	0.631298i	−0.828318	+	0.560259i	$0.810702\pi$
$24$	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	0.360421	−	0.932790i	$-0.382633\pi$
$37$	6.92796	−	1.85634i	1.13895	−	0.305181i	0.778529	+	0.627609i	$0.215966\pi$
$38$	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	−0.993255	−	0.115952i	$-0.963008\pi$
$43$	−5.75286	+	5.75286i	−0.877303	+	0.877303i	0.115952	+	0.993255i	$0.463008\pi$
$44$	−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	$-0.872593\pi$
$47$	−2.18157	−	8.14173i	−0.318215	−	1.18759i	0.602744	−	0.797934i	$-0.294074\pi$
$48$	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	0.448504	−	0.893781i	$-0.351957\pi$
$53$	2.83945	+	0.760829i	0.390029	+	0.104508i	−0.0584750	+	0.998289i	$0.518624\pi$
$54$	−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	−0.889286	−	0.457352i	$-0.848798\pi$
$67$	0.896575	−	3.34607i	0.109534	−	0.408787i	0.998820	+	0.0485648i	$0.0154647\pi$
$68$	−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	−0.873981	−	0.485961i	$-0.838470\pi$
$73$	1.07560	−	4.01418i	0.125889	−	0.469824i	0.999870	+	0.0161362i	$0.00513654\pi$
$74$	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	$-0.909023\pi$
$83$	−11.3094	−	11.3094i	−1.24137	−	1.24137i	−0.281937	−	0.959433i	$-0.590977\pi$
$84$	−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	−0.438552	−	0.898706i	$-0.644508\pi$
$97$	4.53199	−	4.53199i	0.460154	−	0.460154i	0.898706	+	0.438552i	$0.144508\pi$
$98$	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	0.661952	−	0.749546i	$-0.269728\pi$
$103$	16.3396	−	4.37819i	1.60999	−	0.431396i	0.948040	+	0.318150i	$0.103062\pi$
$104$	4.20705			0.412535
$105$		0			0
$106$	7.35105			0.713997
$107$	−16.6725	+	4.46738i	−1.61179	+	0.431878i	−0.948576	−	0.316551i	$-0.897475\pi$
$107$	−16.6725	+	4.46738i	−1.61179	+	0.431878i	−0.663215	+	0.748429i	$0.730809\pi$
$108$	−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	−0.746933	−	0.664899i	$-0.768475\pi$
$113$	−0.872037	+	0.872037i	−0.0820344	+	0.0820344i	0.664899	+	0.746933i	$0.268475\pi$
$114$	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	0.530263	−	0.847833i	$-0.322093\pi$
$127$	−3.57884	−	3.57884i	−0.317570	−	0.317570i	−0.847833	+	0.530263i	$0.822093\pi$
$128$	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	$-0.803683\pi$
$137$	2.10569	−	7.85855i	0.179901	−	0.671401i	0.995665	−	0.0930153i	$-0.0296505\pi$
$138$	−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	0.562504	−	0.826794i	$-0.309838\pi$
$157$	7.97219	+	2.13614i	0.636250	+	0.170483i	0.0737458	+	0.997277i	$0.476505\pi$
$158$	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	0.975431	−	0.220303i	$-0.0707047\pi$
$163$	0.262127	+	0.978271i	0.0205314	+	0.0766241i	−0.954900	+	0.296927i	$0.904038\pi$
$164$	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	−0.485739	−	0.874104i	$-0.661449\pi$
$167$	5.01878	−	5.01878i	0.388365	−	0.388365i	0.874104	+	0.485739i	$0.161449\pi$
$168$	−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	−0.984973	−	0.172710i	$-0.944748\pi$
$173$	−23.0391	+	6.17331i	−1.75163	+	0.469348i	−0.766657	+	0.642057i	$0.778081\pi$
$174$	−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	0.609930	−	0.792455i	$-0.291197\pi$
$193$	10.3070	+	2.76177i	0.741918	+	0.198796i	0.131987	+	0.991251i	$0.457864\pi$
$194$	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	0.529811	−	0.848116i	$-0.322263\pi$
$197$	−4.46762	−	4.46762i	−0.318305	−	0.318305i	−0.848116	+	0.529811i	$0.822263\pi$
$198$	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	0.708482	−	0.705729i	$-0.249380\pi$
$223$	0.0411207	+	0.0411207i	0.00275364	+	0.00275364i	−0.705729	+	0.708482i	$0.749380\pi$
$224$	−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	0.541054	−	0.840988i	$-0.318026\pi$
$227$	8.87608	+	2.37834i	0.589126	+	0.157856i	0.0480724	+	0.998844i	$0.484692\pi$
$228$	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	$-0.974924\pi$
$233$	−2.63931	−	9.85005i	−0.172907	−	0.645298i	0.823992	−	0.566602i	$-0.191742\pi$
$234$	−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	$-0.924565\pi$
$257$	−3.96961	−	14.8148i	−0.247617	−	0.924120i	0.724433	−	0.689346i	$-0.242102\pi$
$258$	−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	0.508039	−	0.861334i	$-0.330370\pi$
$263$	8.38997	+	2.24809i	0.517348	+	0.138623i	0.00930819	+	0.999957i	$0.497037\pi$
$264$	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	−0.989611	−	0.143774i	$-0.954076\pi$
$277$	−1.01018	+	3.77004i	−0.0606958	+	0.226520i	0.928915	+	0.370294i	$0.120743\pi$
$278$	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	$-0.829765\pi$
$283$	2.34796	−	8.76271i	0.139572	−	0.520889i	0.999937	−	0.0112113i	$-0.00356873\pi$
$284$	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	0.931618	−	0.363438i	$-0.118397\pi$
$293$	9.72568	+	9.72568i	0.568180	+	0.568180i	−0.363438	+	0.931618i	$0.618397\pi$
$294$	−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	−0.827603	−	0.561313i	$-0.810296\pi$
$307$	−4.66577	+	4.66577i	−0.266290	+	0.266290i	0.561313	+	0.827603i	$0.310296\pi$
$308$	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	−0.164548	−	0.986369i	$-0.552617\pi$
$313$	3.29304	−	0.882367i	0.186134	−	0.0498743i	0.350682	+	0.936495i	$0.385950\pi$
$314$	20.6392			1.16474
$315$		0			0
$316$	13.0916			0.736458
$317$	−0.188148	+	0.0504142i	−0.0105675	+	0.00283154i	−0.264099	−	0.964496i	$-0.585075\pi$
$317$	−0.188148	+	0.0504142i	−0.0105675	+	0.00283154i	0.253531	+	0.967327i	$0.418408\pi$
$318$	−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	0.873476	−	0.486868i	$-0.161861\pi$
$337$	7.09718	+	7.09718i	0.386608	+	0.386608i	−0.486868	+	0.873476i	$0.661861\pi$
$338$	−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	$0.290696\pi$
$347$	−5.84665	+	21.8200i	−0.313864	+	1.17136i	−0.925042	+	0.379864i	$0.875971\pi$
$348$	−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	−0.982580	−	0.185841i	$-0.940499\pi$
$353$	−0.727489	+	2.71503i	−0.0387203	+	0.144506i	0.943860	+	0.330347i	$0.107166\pi$
$354$	−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	0.363510	−	0.931590i	$-0.381578\pi$
$367$	4.07138	+	1.09092i	0.212524	+	0.0569457i	−0.150986	+	0.988536i	$0.548245\pi$
$368$	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	$0.0307767\pi$
$373$	3.50762	+	13.0906i	0.181617	+	0.677806i	−0.813712	+	0.581268i	$0.802557\pi$
$374$	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	0.587942	−	0.808903i	$-0.299938\pi$
$383$	29.3862	−	7.87402i	1.50157	−	0.402344i	0.913624	+	0.406559i	$0.133272\pi$
$384$	−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	0.962817	−	0.270155i	$-0.0870751\pi$
$397$	−0.121237	−	0.452461i	−0.00608469	−	0.0227084i	−0.968901	+	0.247447i	$0.920408\pi$
$398$	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	$0.0254280\pi$
$433$	22.4028	+	22.4028i	1.07661	+	1.07661i	0.0797995	+	0.996811i	$0.474572\pi$
$434$	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	$0.165461\pi$
$443$	7.67471	+	28.6424i	0.364637	+	1.36084i	−0.503276	+	0.864126i	$0.667872\pi$
$444$	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	−0.367080	−	0.930189i	$-0.619643\pi$
$457$	−4.70063	+	1.25953i	−0.219886	+	0.0589184i	0.147194	+	0.989108i	$0.452976\pi$
$458$	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	−0.939790	−	0.341754i	$-0.888979\pi$
$463$	−12.8682	+	12.8682i	−0.598036	+	0.598036i	0.341754	+	0.939790i	$0.388979\pi$
$464$	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	$-0.982516\pi$
$467$	−3.48404	−	13.0026i	−0.161222	−	0.601689i	0.837270	−	0.546790i	$-0.184150\pi$
$468$	−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	$0.455591\pi$
$487$	−10.5157	+	39.2451i	−0.476511	+	1.77836i	−0.615573	+	0.788080i	$0.711075\pi$
$488$	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	0.629668	−	0.776864i	$-0.283191\pi$
$503$	−3.30126	−	3.30126i	−0.147196	−	0.147196i	−0.776864	+	0.629668i	$0.783191\pi$
$504$	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	−0.423258	−	0.906009i	$-0.639114\pi$
$523$	−7.70248	+	2.06387i	−0.336806	+	0.0902469i	0.0864523	+	0.996256i	$0.472447\pi$
$524$	−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	0.355055	−	0.934845i	$-0.384462\pi$
$547$	−13.5602	−	13.5602i	−0.579791	−	0.579791i	−0.934845	+	0.355055i	$0.884462\pi$
$548$	−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	$-0.775277\pi$
$557$	5.24984	−	19.5927i	0.222443	−	0.830167i	0.983413	−	0.181381i	$-0.0580566\pi$
$558$	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	$0.252433\pi$
$563$	−6.22227	+	23.2218i	−0.262238	+	0.978684i	−0.963920	+	0.266194i	$0.914234\pi$
$564$	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	−0.771859	−	0.635794i	$-0.780673\pi$
$577$	−42.2335	−	11.3164i	−1.75821	−	0.471110i	−0.986346	+	0.164684i	$0.947340\pi$
$578$	−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	−0.347504	−	0.937678i	$-0.612971\pi$
$587$	14.2988	−	14.2988i	0.590174	−	0.590174i	0.937678	+	0.347504i	$0.112971\pi$
$588$	−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	−0.546085	−	0.837730i	$-0.683882\pi$
$593$	−14.6144	+	3.91593i	−0.600143	+	0.160808i	−0.0540583	+	0.998538i	$0.517216\pi$
$594$	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	$0.239844\pi$
$607$	10.8356	+	40.4390i	0.439803	+	1.64137i	−0.289502	+	0.957178i	$0.593490\pi$
$608$	−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	−0.0405433	−	0.999178i	$-0.512909\pi$
$613$	−14.2424	−	3.81623i	−0.575244	−	0.154136i	−0.534700	+	0.845042i	$0.679576\pi$
$614$	−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	0.975970	−	0.217903i	$-0.0699216\pi$
$617$	18.8300	+	18.8300i	0.758068	+	0.758068i	−0.217903	+	0.975970i	$0.569922\pi$
$618$	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	0.0881532	−	0.996107i	$-0.471904\pi$
$643$	−23.0234	−	23.0234i	−0.907954	−	0.907954i	−0.996107	+	0.0881532i	$0.971904\pi$
$644$	−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	0.00525299	−	0.999986i	$-0.498328\pi$
$647$	−12.4686	−	3.34095i	−0.490191	−	0.131346i	−0.495444	+	0.868640i	$0.664995\pi$
$648$	−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	$-0.902287\pi$
$653$	−7.12439	−	26.5886i	−0.278799	−	1.04049i	0.674454	−	0.738317i	$-0.264379\pi$
$654$	−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	$-0.431862\pi$
$673$	30.8611	−	30.8611i	1.18961	−	1.18961i	0.977176	−	0.212431i	$-0.0681380\pi$
$674$	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	0.930984	−	0.365059i	$-0.118951\pi$
$677$	−1.50395	−	5.61280i	−0.0578014	−	0.215718i	−0.988786	+	0.149342i	$0.952285\pi$
$678$	−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	0.785123	−	0.619339i	$-0.212599\pi$
$683$	30.1953	+	8.09080i	1.15539	+	0.309586i	0.370267	+	0.928925i	$0.379266\pi$
$684$	−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	−0.943880	−	0.330289i	$-0.892854\pi$
$727$	−16.5442	+	16.5442i	−0.613591	+	0.613591i	0.330289	+	0.943880i	$0.392854\pi$
$728$	−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	−0.650161	−	0.759797i	$-0.725299\pi$
$733$	−22.5612	+	6.04527i	−0.833319	+	0.223287i	−0.183158	+	0.983084i	$0.558632\pi$
$734$	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	−0.200055	−	0.979785i	$-0.564112\pi$
$743$	21.2539	−	21.2539i	0.779730	−	0.779730i	0.979785	+	0.200055i	$0.0641119\pi$
$744$	−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	0.416201	−	0.909272i	$-0.363361\pi$
$757$	−13.5662	−	13.5662i	−0.493071	−	0.493071i	−0.909272	+	0.416201i	$0.863361\pi$
$758$	−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	$0.318283\pi$
$773$	−9.68418	+	36.1419i	−0.348316	+	1.29993i	−0.888690	+	0.458508i	$0.848384\pi$
$774$	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	0.643402	−	0.765528i	$-0.277522\pi$
$787$	22.9433	+	6.14764i	0.817840	+	0.219140i	0.174438	+	0.984668i	$0.444189\pi$
$788$	−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	−0.781510	−	0.623892i	$-0.785550\pi$
$797$	−4.44975	+	4.44975i	−0.157618	+	0.157618i	0.623892	+	0.781510i	$0.285550\pi$
$798$	−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	0.461198	−	0.887297i	$-0.347420\pi$
$823$	11.9617	+	3.20513i	0.416959	+	0.111724i	−0.0442392	+	0.999021i	$0.514086\pi$
$824$	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	0.686009	−	0.727593i	$-0.259361\pi$
$827$	−1.19586	−	1.19586i	−0.0415840	−	0.0415840i	−0.727593	+	0.686009i	$0.759361\pi$
$828$	−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	0.864459	−	0.502704i	$-0.167661\pi$
$853$	10.5655	+	10.5655i	0.361755	+	0.361755i	−0.502704	+	0.864459i	$0.667661\pi$
$854$	−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	−0.240059	−	0.970758i	$-0.577167\pi$
$857$	−27.3230	−	7.32117i	−0.933335	−	0.250086i	−0.693276	+	0.720672i	$0.743833\pi$
$858$	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	$0.0271746\pi$
$863$	5.17387	+	19.3091i	0.176121	+	0.657291i	−0.820238	+	0.572023i	$0.806159\pi$
$864$	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	0.635805	−	0.771849i	$-0.280668\pi$
$877$	46.5640	−	12.4768i	1.57235	−	0.421311i	0.936548	+	0.350538i	$0.114001\pi$
$878$	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	−0.555003	−	0.831848i	$-0.687283\pi$
$883$	8.22652	−	8.22652i	0.276845	−	0.276845i	0.831848	+	0.555003i	$0.187283\pi$
$884$	−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	$0.0977755\pi$
$887$	8.30591	+	30.9981i	0.278885	+	1.04081i	−0.674308	+	0.738450i	$0.735558\pi$
$888$	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	$-0.584169\pi$
$907$	13.4803	−	50.3092i	0.447606	−	1.67049i	0.708961	−	0.705247i	$-0.249164\pi$
$908$	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	−0.608206	−	0.793779i	$-0.708111\pi$
$937$	5.68048	−	5.68048i	0.185573	−	0.185573i	0.793779	+	0.608206i	$0.208111\pi$
$938$	−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	0.463461	−	0.886117i	$-0.346607\pi$
$947$	40.2481	−	10.7845i	1.30789	−	0.350448i	0.844428	+	0.535669i	$0.179941\pi$
$948$	−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	−0.568999	−	0.822338i	$-0.692669\pi$
$953$	7.82075	−	7.82075i	0.253339	−	0.253339i	0.822338	+	0.568999i	$0.192669\pi$
$954$	−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	0.601312	−	0.799015i	$-0.294645\pi$
$967$	−6.14790	−	6.14790i	−0.197703	−	0.197703i	−0.799015	+	0.601312i	$0.794645\pi$
$968$	−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	$0.210272\pi$
$977$	−6.28268	+	23.4473i	−0.201001	+	0.750144i	−0.990631	+	0.136562i	$0.956395\pi$
$978$	−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	$-0.829106\pi$
$983$	4.40830	−	16.4520i	0.140603	−	0.524737i	0.999912	−	0.0132800i	$-0.00422729\pi$
$984$	−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	−0.707966	−	0.706247i	$-0.750387\pi$
$997$	−52.8636	−	14.1647i	−1.67421	−	0.448602i	−0.966240	+	0.257645i	$0.917054\pi$
$998$	−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.82.6	yes	24
5.2	odd	4	inner	175.2.o.d.68.6	yes	24
5.3	odd	4	inner	175.2.o.d.68.1	✓	24
5.4	even	2	inner	175.2.o.d.82.1	yes	24
7.3	odd	6	inner	175.2.o.d.157.1	yes	24
35.3	even	12	inner	175.2.o.d.143.6	yes	24
35.17	even	12	inner	175.2.o.d.143.1	yes	24
35.24	odd	6	inner	175.2.o.d.157.6	yes	24

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