LMFDB - Embedded newform 1183.2.e.j.170.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.6
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.j.508.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0904119 + 0.156598i) q^{2} +(0.913006 + 1.58137i) q^{3} +(0.983651 + 1.70373i) q^{4} +(-1.34332 + 2.32670i) q^{5} -0.330186 q^{6} +(-1.64912 + 2.06892i) q^{7} -0.717383 q^{8} +(-0.167162 + 0.289532i) q^{9} +O(q^{10})$	\(q+(-0.0904119 + 0.156598i) q^{2} +(0.913006 + 1.58137i) q^{3} +(0.983651 + 1.70373i) q^{4} +(-1.34332 + 2.32670i) q^{5} -0.330186 q^{6} +(-1.64912 + 2.06892i) q^{7} -0.717383 q^{8} +(-0.167162 + 0.289532i) q^{9} +(-0.242904 - 0.420723i) q^{10} +(-1.34712 - 2.33328i) q^{11} +(-1.79616 + 3.11104i) q^{12} +(-0.174889 - 0.445303i) q^{14} -4.90584 q^{15} +(-1.90244 + 3.29513i) q^{16} +(-2.38247 - 4.12655i) q^{17} +(-0.0302268 - 0.0523543i) q^{18} +(-0.0942122 + 0.163180i) q^{19} -5.28544 q^{20} +(-4.77738 - 0.718933i) q^{21} +0.487183 q^{22} +(-2.19964 + 3.80989i) q^{23} +(-0.654975 - 1.13445i) q^{24} +(-1.10902 - 1.92088i) q^{25} +4.86756 q^{27} +(-5.14704 - 0.774561i) q^{28} +7.08560 q^{29} +(0.443546 - 0.768245i) q^{30} +(1.84965 + 3.20369i) q^{31} +(-1.06139 - 1.83838i) q^{32} +(2.45986 - 4.26060i) q^{33} +0.861613 q^{34} +(-2.59846 - 6.61622i) q^{35} -0.657715 q^{36} +(-3.97707 + 6.88848i) q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(0.963675 - 1.66913i) q^{40} +5.42958 q^{41} +(0.544516 - 0.683129i) q^{42} -8.01065 q^{43} +(2.65020 - 4.59027i) q^{44} +(-0.449103 - 0.777869i) q^{45} +(-0.397748 - 0.688919i) q^{46} +(0.924445 - 1.60118i) q^{47} -6.94777 q^{48} +(-1.56084 - 6.82377i) q^{49} +0.401075 q^{50} +(4.35041 - 7.53514i) q^{51} +(3.53622 + 6.12491i) q^{53} +(-0.440085 + 0.762250i) q^{54} +7.23846 q^{55} +(1.18305 - 1.48421i) q^{56} -0.344066 q^{57} +(-0.640623 + 1.10959i) q^{58} +(-3.79444 - 6.57216i) q^{59} +(-4.82564 - 8.35825i) q^{60} +(0.205782 - 0.356425i) q^{61} -0.668922 q^{62} +(-0.323350 - 0.823315i) q^{63} -7.22592 q^{64} +(0.444801 + 0.770418i) q^{66} +(-5.70051 - 9.87358i) q^{67} +(4.68703 - 8.11818i) q^{68} -8.03315 q^{69} +(1.27102 + 0.191271i) q^{70} -3.34488 q^{71} +(0.119919 - 0.207705i) q^{72} +(7.10790 + 12.3112i) q^{73} +(-0.719148 - 1.24560i) q^{74} +(2.02509 - 3.50756i) q^{75} -0.370688 q^{76} +(7.04893 + 1.06077i) q^{77} +(-4.55529 + 7.89000i) q^{79} +(-5.11118 - 8.85283i) q^{80} +(4.94560 + 8.56603i) q^{81} +(-0.490899 + 0.850261i) q^{82} +16.5866 q^{83} +(-3.47441 - 8.84657i) q^{84} +12.8017 q^{85} +(0.724258 - 1.25445i) q^{86} +(6.46920 + 11.2050i) q^{87} +(0.966401 + 1.67386i) q^{88} +(2.94582 - 5.10232i) q^{89} +0.162417 q^{90} -8.65473 q^{92} +(-3.37749 + 5.84998i) q^{93} +(0.167162 + 0.289532i) q^{94} +(-0.253115 - 0.438407i) q^{95} +(1.93811 - 3.35691i) q^{96} -0.451094 q^{97} +(1.20971 + 0.372526i) q^{98} +0.900747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0904119	+	0.156598i	−0.0639308	+	0.110731i	−0.896219	−	0.443611i	$-0.853697\pi$
$2$	−0.0904119	+	0.156598i	−0.0639308	+	0.110731i	0.832288	+	0.554343i	$0.187030\pi$
$3$	0.913006	+	1.58137i	0.527125	+	0.913006i	0.999500	+	0.0316092i	$0.0100632\pi$
$3$	0.913006	+	1.58137i	0.527125	+	0.913006i	−0.472376	+	0.881397i	$0.656603\pi$
$4$	0.983651	+	1.70373i	0.491826	+	0.851867i
$5$	−1.34332	+	2.32670i	−0.600751	+	1.04053i	0.391956	+	0.919984i	$0.371799\pi$
$5$	−1.34332	+	2.32670i	−0.600751	+	1.04053i	−0.992708	+	0.120548i	$0.961535\pi$
$6$	−0.330186			−0.134798
$7$	−1.64912	+	2.06892i	−0.623307	+	0.781977i
$7$	−1.64912	+	2.06892i	−0.623307	+	0.781977i
$8$	−0.717383			−0.253633
$9$	−0.167162	+	0.289532i	−0.0557205	+	0.0965108i
$10$	−0.242904	−	0.420723i	−0.0768131	−	0.133044i
$11$	−1.34712	−	2.33328i	−0.406172	−	0.703511i	0.588285	−	0.808654i	$-0.299803\pi$
$11$	−1.34712	−	2.33328i	−0.406172	−	0.703511i	−0.994457	+	0.105143i	$0.966470\pi$
$12$	−1.79616	+	3.11104i	−0.518507	+	0.898080i
$13$		0			0
$13$		0			0
$14$	−0.174889	−	0.445303i	−0.0467409	−	0.119012i
$15$	−4.90584			−1.26668
$16$	−1.90244	+	3.29513i	−0.475611	+	0.823782i
$17$	−2.38247	−	4.12655i	−0.577833	−	1.00084i	−0.995727	−	0.0923405i	$-0.970565\pi$
$17$	−2.38247	−	4.12655i	−0.577833	−	1.00084i	0.417894	−	0.908496i	$-0.362768\pi$
$18$	−0.0302268	−	0.0523543i	−0.00712452	−	0.0123400i
$19$	−0.0942122	+	0.163180i	−0.0216138	+	0.0374361i	−0.876630	−	0.481165i	$-0.840214\pi$
$19$	−0.0942122	+	0.163180i	−0.0216138	+	0.0374361i	0.855016	+	0.518601i	$0.173547\pi$
$20$	−5.28544			−1.18186
$21$	−4.77738	−	0.718933i	−1.04251	−	0.156884i
$22$	0.487183			0.103868
$23$	−2.19964	+	3.80989i	−0.458657	+	0.794418i	−0.998890	−	0.0470977i	$-0.985003\pi$
$23$	−2.19964	+	3.80989i	−0.458657	+	0.794418i	0.540233	+	0.841516i	$0.318336\pi$
$24$	−0.654975	−	1.13445i	−0.133696	−	0.231569i
$25$	−1.10902	−	1.92088i	−0.221804	−	0.384177i
$26$		0			0
$27$	4.86756			0.936762
$28$	−5.14704	−	0.774561i	−0.972699	−	0.146378i
$29$	7.08560			1.31576			0.657882	−	0.753121i	$-0.271453\pi$
$29$	7.08560			1.31576			0.657882	+	0.753121i	$0.271453\pi$
$30$	0.443546	−	0.768245i	0.0809801	−	0.140262i
$31$	1.84965	+	3.20369i	0.332207	+	0.575400i	0.982944	−	0.183903i	$-0.0588732\pi$
$31$	1.84965	+	3.20369i	0.332207	+	0.575400i	−0.650737	+	0.759303i	$0.725540\pi$
$32$	−1.06139	−	1.83838i	−0.187629	−	0.324983i
$33$	2.45986	−	4.26060i	0.428207	−	0.741676i
$34$	0.861613			0.147765
$35$	−2.59846	−	6.61622i	−0.439220	−	1.11834i
$36$	−0.657715			−0.109619
$37$	−3.97707	+	6.88848i	−0.653826	+	1.13246i	0.328361	+	0.944552i	$0.393504\pi$
$37$	−3.97707	+	6.88848i	−0.653826	+	1.13246i	−0.982187	+	0.187907i	$0.939830\pi$
$38$	−0.0170358	−	0.0295069i	−0.00276357	−	0.00478665i
$39$		0			0
$40$	0.963675	−	1.66913i	0.152370	−	0.263913i
$41$	5.42958			0.847958			0.423979	−	0.905672i	$-0.360633\pi$
$41$	5.42958			0.847958			0.423979	+	0.905672i	$0.360633\pi$
$42$	0.544516	−	0.683129i	0.0840206	−	0.105409i
$43$	−8.01065			−1.22161			−0.610807	−	0.791780i	$-0.709155\pi$
$43$	−8.01065			−1.22161			−0.610807	+	0.791780i	$0.709155\pi$
$44$	2.65020	−	4.59027i	0.399532	−	0.692010i
$45$	−0.449103	−	0.777869i	−0.0669483	−	0.115958i
$46$	−0.397748	−	0.688919i	−0.0586447	−	0.101576i
$47$	0.924445	−	1.60118i	0.134844	−	0.233557i	−0.790694	−	0.612212i	$-0.790280\pi$
$47$	0.924445	−	1.60118i	0.134844	−	0.233557i	0.925538	+	0.378655i	$0.123613\pi$
$48$	−6.94777			−1.00282
$49$	−1.56084	−	6.82377i	−0.222977	−	0.974824i
$50$	0.401075			0.0567206
$51$	4.35041	−	7.53514i	0.609180	−	1.05513i
$52$		0			0
$53$	3.53622	+	6.12491i	0.485737	+	0.841321i	0.999866	−	0.0163917i	$-0.00521788\pi$
$53$	3.53622	+	6.12491i	0.485737	+	0.841321i	−0.514128	+	0.857713i	$0.671885\pi$
$54$	−0.440085	+	0.762250i	−0.0598880	+	0.103729i
$55$	7.23846			0.976034
$56$	1.18305	−	1.48421i	0.158091	−	0.198335i
$57$	−0.344066			−0.0455726
$58$	−0.640623	+	1.10959i	−0.0841179	+	0.145696i
$59$	−3.79444	−	6.57216i	−0.493994	−	0.855623i	0.505982	−	0.862544i	$-0.331130\pi$
$59$	−3.79444	−	6.57216i	−0.493994	−	0.855623i	−0.999976	+	0.00692130i	$0.997797\pi$
$60$	−4.82564	−	8.35825i	−0.622987	−	1.07905i
$61$	0.205782	−	0.356425i	0.0263477	−	0.0456355i	−0.852551	−	0.522644i	$-0.824946\pi$
$61$	0.205782	−	0.356425i	0.0263477	−	0.0456355i	0.878899	+	0.477009i	$0.158279\pi$
$62$	−0.668922			−0.0849532
$63$	−0.323350	−	0.823315i	−0.0407382	−	0.103728i
$64$	−7.22592			−0.903240
$65$		0			0
$66$	0.444801	+	0.770418i	0.0547512	+	0.0948319i
$67$	−5.70051	−	9.87358i	−0.696429	−	1.20625i	−0.969697	−	0.244312i	$-0.921438\pi$
$67$	−5.70051	−	9.87358i	−0.696429	−	1.20625i	0.273268	−	0.961938i	$-0.411895\pi$
$68$	4.68703	−	8.11818i	0.568386	−	0.984474i
$69$	−8.03315			−0.967078
$70$	1.27102	+	0.191271i	0.151916	+	0.0228613i
$71$	−3.34488			−0.396965			−0.198482	−	0.980104i	$-0.563601\pi$
$71$	−3.34488			−0.396965			−0.198482	+	0.980104i	$0.563601\pi$
$72$	0.119919	−	0.207705i	0.0141326	−	0.0244783i
$73$	7.10790	+	12.3112i	0.831917	+	1.44092i	0.896516	+	0.443011i	$0.146090\pi$
$73$	7.10790	+	12.3112i	0.831917	+	1.44092i	−0.0645994	+	0.997911i	$0.520577\pi$
$74$	−0.719148	−	1.24560i	−0.0835993	−	0.144798i
$75$	2.02509	−	3.50756i	0.233837	−	0.405018i
$76$	−0.370688			−0.0425208
$77$	7.04893	+	1.06077i	0.803300	+	0.120886i
$78$		0			0
$79$	−4.55529	+	7.89000i	−0.512511	+	0.887695i	0.487384	+	0.873188i	$0.337951\pi$
$79$	−4.55529	+	7.89000i	−0.512511	+	0.887695i	−0.999895	+	0.0145069i	$0.995382\pi$
$80$	−5.11118	−	8.85283i	−0.571448	−	0.989776i
$81$	4.94560	+	8.56603i	0.549511	+	0.951781i
$82$	−0.490899	+	0.850261i	−0.0542107	+	0.0938956i
$83$	16.5866			1.82061			0.910307	−	0.413934i	$-0.135845\pi$
$83$	16.5866			1.82061			0.910307	+	0.413934i	$0.135845\pi$
$84$	−3.47441	−	8.84657i	−0.379089	−	0.965240i
$85$	12.8017			1.38854
$86$	0.724258	−	1.25445i	0.0780988	−	0.135271i
$87$	6.46920	+	11.2050i	0.693571	+	1.20130i
$88$	0.966401	+	1.67386i	0.103019	+	0.178434i
$89$	2.94582	−	5.10232i	0.312257	−	0.540844i	−0.666594	−	0.745421i	$-0.732248\pi$
$89$	2.94582	−	5.10232i	0.312257	−	0.540844i	0.978851	+	0.204577i	$0.0655818\pi$
$90$	0.162417			0.0171203
$91$		0			0
$92$	−8.65473			−0.902318
$93$	−3.37749	+	5.84998i	−0.350229	+	0.606615i
$94$	0.167162	+	0.289532i	0.0172414	+	0.0298630i
$95$	−0.253115	−	0.438407i	−0.0259690	−	0.0449796i
$96$	1.93811	−	3.35691i	0.197808	−	0.342613i
$97$	−0.451094			−0.0458016			−0.0229008	−	0.999738i	$-0.507290\pi$
$97$	−0.451094			−0.0458016			−0.0229008	+	0.999738i	$0.507290\pi$
$98$	1.20971	+	0.372526i	0.122199	+	0.0376308i
$99$	0.900747			0.0905285
$100$	2.18178	−	3.77896i	0.218178	−	0.377896i
$101$	3.82840	+	6.63098i	0.380940	+	0.659807i	0.991197	−	0.132396i	$-0.0422671\pi$
$101$	3.82840	+	6.63098i	0.380940	+	0.659807i	−0.610257	+	0.792204i	$0.708934\pi$
$102$	0.786658	+	1.36253i	0.0778908	+	0.134911i
$103$	−2.57870	+	4.46644i	−0.254087	+	0.440091i	−0.964647	−	0.263545i	$-0.915108\pi$
$103$	−2.57870	+	4.46644i	−0.254087	+	0.440091i	0.710560	+	0.703636i	$0.248442\pi$
$104$		0			0
$105$	8.09030	−	10.1498i	0.789532	−	0.990517i
$106$	−1.27887			−0.124214
$107$	−4.01644	+	6.95669i	−0.388284	+	0.672528i	−0.992219	−	0.124506i	$-0.960265\pi$
$107$	−4.01644	+	6.95669i	−0.388284	+	0.672528i	0.603935	+	0.797034i	$0.293599\pi$
$108$	4.78798	+	8.29303i	0.460724	+	0.797997i
$109$	−0.666781	−	1.15490i	−0.0638660	−	0.110619i	0.832324	−	0.554289i	$-0.187010\pi$
$109$	−0.666781	−	1.15490i	−0.0638660	−	0.110619i	−0.896190	+	0.443670i	$0.853676\pi$
$110$	−0.654443	+	1.13353i	−0.0623987	+	0.108078i
$111$	−14.5243			−1.37859
$112$	−3.68000	−	9.37004i	−0.347727	−	0.885386i
$113$	−19.9383			−1.87564			−0.937821	−	0.347119i	$-0.887160\pi$
$113$	−19.9383			−1.87564			−0.937821	+	0.347119i	$0.887160\pi$
$114$	0.0311076	−	0.0538800i	0.00291349	−	0.00504632i
$115$	−5.90965	−	10.2358i	−0.551078	−	0.954495i
$116$	6.96976	+	12.0720i	0.647126	+	1.12086i
$117$		0			0
$118$	1.37225			0.126326
$119$	12.4665	+	1.87604i	1.14280	+	0.171976i
$120$	3.51937			0.321273
$121$	1.87053	−	3.23985i	0.170048	−	0.294532i
$122$	0.0372103	+	0.0644501i	0.00336886	+	0.00583503i
$123$	4.95724	+	8.58619i	0.446979	+	0.774191i
$124$	−3.63883	+	6.30263i	−0.326776	+	0.565993i
$125$	−7.47412			−0.668505
$126$	0.158164	+	0.0238016i	0.0140904	+	0.00212042i
$127$	−7.96722			−0.706976			−0.353488	−	0.935439i	$-0.615005\pi$
$127$	−7.96722			−0.706976			−0.353488	+	0.935439i	$0.615005\pi$
$128$	2.77609	−	4.80833i	0.245374	−	0.425000i
$129$	−7.31378	−	12.6678i	−0.643942	−	1.11534i
$130$		0			0
$131$	−5.00897	+	8.67579i	−0.437636	+	0.758007i	−0.997507	−	0.0705727i	$-0.977517\pi$
$131$	−5.00897	+	8.67579i	−0.437636	+	0.758007i	0.559871	+	0.828580i	$0.310851\pi$
$132$	9.67858			0.842412
$133$	−0.182240	−	0.464021i	−0.0158022	−	0.0402357i
$134$	2.06158			0.178093
$135$	−6.53870	+	11.3254i	−0.562761	+	0.974731i
$136$	1.70914	+	2.96032i	0.146558	+	0.253845i
$137$	2.53348	+	4.38811i	0.216450	+	0.374902i	0.953720	−	0.300696i	$-0.0972189\pi$
$137$	2.53348	+	4.38811i	0.216450	+	0.374902i	−0.737270	+	0.675598i	$0.763886\pi$
$138$	0.726293	−	1.25798i	0.0618261	−	0.107086i
$139$	7.72578			0.655292			0.327646	−	0.944800i	$-0.393745\pi$
$139$	7.72578			0.655292			0.327646	+	0.944800i	$0.393745\pi$
$140$	8.71630	−	10.9351i	0.736662	−	0.924187i
$141$	3.37610			0.284319
$142$	0.302417	−	0.523802i	0.0253783	−	0.0439565i
$143$		0			0
$144$	−0.636031	−	1.10164i	−0.0530025	−	0.0918031i
$145$	−9.51824	+	16.4861i	−0.790447	+	1.36909i
$146$	−2.57055			−0.212741
$147$	9.36587	−	8.69841i	0.772484	−	0.717433i
$148$	−15.6482			−1.28627
$149$	−7.15924	+	12.4002i	−0.586507	+	1.01586i	0.408178	+	0.912902i	$0.366164\pi$
$149$	−7.15924	+	12.4002i	−0.586507	+	1.01586i	−0.994686	+	0.102958i	$0.967169\pi$
$150$	0.366184	+	0.634250i	0.0298988	+	0.0517863i
$151$	3.23624	+	5.60534i	0.263362	+	0.456156i	0.967133	−	0.254271i	$-0.0818354\pi$
$151$	3.23624	+	5.60534i	0.263362	+	0.456156i	−0.703771	+	0.710427i	$0.748502\pi$
$152$	0.0675862	−	0.117063i	0.00548197	−	0.00949504i
$153$	1.59303			0.128789
$154$	−0.803421	+	1.00794i	−0.0647415	+	0.0812222i
$155$	−9.93871			−0.798296
$156$		0			0
$157$	−7.95937	−	13.7860i	−0.635227	−	1.10025i	−0.986467	−	0.163960i	$-0.947573\pi$
$157$	−7.95937	−	13.7860i	−0.635227	−	1.10025i	0.351240	−	0.936285i	$-0.385760\pi$
$158$	−0.823705	−	1.42670i	−0.0655305	−	0.113502i
$159$	−6.45718	+	11.1842i	−0.512088	+	0.886962i
$160$	5.70315			0.450873
$161$	−4.25489	−	10.8338i	−0.335332	−	0.853826i
$162$	−1.78856			−0.140523
$163$	−2.39081	+	4.14100i	−0.187263	+	0.324348i	−0.944337	−	0.328981i	$-0.893295\pi$
$163$	−2.39081	+	4.14100i	−0.187263	+	0.324348i	0.757074	+	0.653329i	$0.226628\pi$
$164$	5.34081	+	9.25056i	0.417048	+	0.722348i
$165$	6.60876	+	11.4467i	0.514492	+	0.891126i
$166$	−1.49962	+	2.59743i	−0.116393	+	0.201599i
$167$	2.71042			0.209739			0.104869	−	0.994486i	$-0.466558\pi$
$167$	2.71042			0.209739			0.104869	+	0.994486i	$0.466558\pi$
$168$	3.42721	+	0.515750i	0.264415	+	0.0397910i
$169$		0			0
$170$	−1.15742	+	2.00472i	−0.0887703	+	0.153755i
$171$	−0.0314973	−	0.0545550i	−0.00240866	−	0.00417192i
$172$	−7.87969	−	13.6480i	−0.600821	−	1.04065i
$173$	0.449908	−	0.779264i	0.0342059	−	0.0592463i	−0.848416	−	0.529331i	$-0.822443\pi$
$173$	0.449908	−	0.779264i	0.0342059	−	0.0592463i	0.882622	+	0.470084i	$0.155776\pi$
$174$	−2.33957			−0.177362
$175$	5.80305	+	0.873282i	0.438670	+	0.0660139i
$176$	10.2513			0.772720
$177$	6.92870	−	12.0009i	0.520793	−	0.902039i
$178$	0.532675	+	0.922620i	0.0399257	+	0.0691533i
$179$	5.52791	+	9.57462i	0.413175	+	0.715641i	0.995235	−	0.0975054i	$-0.0310863\pi$
$179$	5.52791	+	9.57462i	0.413175	+	0.715641i	−0.582060	+	0.813146i	$0.697753\pi$
$180$	0.883522	−	1.53030i	0.0658538	−	0.114062i
$181$	3.52898			0.262307			0.131153	−	0.991362i	$-0.458132\pi$
$181$	3.52898			0.262307			0.131153	+	0.991362i	$0.458132\pi$
$182$		0			0
$183$	0.751521			0.0555540
$184$	1.57799	−	2.73315i	0.116331	−	0.201491i
$185$	−10.6850	−	18.5069i	−0.785573	−	1.36065i
$186$	−0.610730	−	1.05782i	−0.0447809	−	0.0775628i
$187$	−6.41894	+	11.1179i	−0.469400	+	0.813024i
$188$	3.63732			0.265279
$189$	−8.02717	+	10.0706i	−0.583891	+	0.732527i
$190$	0.0915382			0.00664088
$191$	10.2002	−	17.6672i	0.738059	−	1.27836i	−0.215309	−	0.976546i	$-0.569076\pi$
$191$	10.2002	−	17.6672i	0.738059	−	1.27836i	0.953368	−	0.301810i	$-0.0975909\pi$
$192$	−6.59731	−	11.4269i	−0.476120	−	0.824664i
$193$	8.63228	+	14.9515i	0.621365	+	1.07624i	0.989232	+	0.146357i	$0.0467549\pi$
$193$	8.63228	+	14.9515i	0.621365	+	1.07624i	−0.367867	+	0.929878i	$0.619912\pi$
$194$	0.0407842	−	0.0706403i	0.00292814	−	0.00507168i
$195$		0			0
$196$	10.0906	−	9.37146i	0.720755	−	0.669390i
$197$	−4.95672			−0.353152			−0.176576	−	0.984287i	$-0.556502\pi$
$197$	−4.95672			−0.353152			−0.176576	+	0.984287i	$0.556502\pi$
$198$	−0.0814383	+	0.141055i	−0.00578757	+	0.0100244i
$199$	−3.59097	−	6.21975i	−0.254557	−	0.440906i	0.710218	−	0.703982i	$-0.248596\pi$
$199$	−3.59097	−	6.21975i	−0.254557	−	0.440906i	−0.964775	+	0.263076i	$0.915263\pi$
$200$	0.795593	+	1.37801i	0.0562569	+	0.0974399i
$201$	10.4092	−	18.0293i	0.734209	−	1.27169i
$202$	−1.38453			−0.0974153
$203$	−11.6850	+	14.6595i	−0.820125	+	1.02890i
$204$	17.1172			1.19844
$205$	−7.29367	+	12.6330i	−0.509412	+	0.882327i
$206$	−0.466290	−	0.807638i	−0.0324880	−	0.0562708i
$207$	−0.735392	−	1.27374i	−0.0511132	−	0.0885307i
$208$		0			0
$209$	0.507661			0.0351157
$210$	0.857976	+	2.18459i	0.0592060	+	0.150751i
$211$	−17.5927			−1.21113			−0.605566	−	0.795795i	$-0.707053\pi$
$211$	−17.5927			−1.21113			−0.605566	+	0.795795i	$0.707053\pi$
$212$	−6.95682	+	12.0496i	−0.477796	+	0.827567i
$213$	−3.05390	−	5.28951i	−0.209250	−	0.362431i
$214$	−0.726269	−	1.25793i	−0.0496467	−	0.0859906i
$215$	10.7609	−	18.6384i	0.733886	−	1.27113i
$216$	−3.49190			−0.237594
$217$	−9.67847	−	1.45648i	−0.657017	−	0.0988723i
$218$	0.241140			0.0163320
$219$	−12.9791	+	22.4805i	−0.877048	+	1.51909i
$220$	7.12013	+	12.3324i	0.480039	+	0.831452i
$221$		0			0
$222$	1.31317	−	2.27448i	0.0881344	−	0.152653i
$223$	14.1054			0.944569			0.472284	−	0.881446i	$-0.343430\pi$
$223$	14.1054			0.944569			0.472284	+	0.881446i	$0.343430\pi$
$224$	5.55381	+	0.835775i	0.371080	+	0.0558425i
$225$	0.741543			0.0494362
$226$	1.80266	−	3.12230i	0.119911	−	0.207693i
$227$	−1.43439	−	2.48443i	−0.0952035	−	0.164897i	0.814490	−	0.580178i	$-0.197017\pi$
$227$	−1.43439	−	2.48443i	−0.0952035	−	0.164897i	−0.909694	+	0.415280i	$0.863684\pi$
$228$	−0.338441	−	0.586196i	−0.0224138	−	0.0388218i
$229$	−4.38706	+	7.59860i	−0.289905	+	0.502130i	−0.973787	−	0.227463i	$-0.926957\pi$
$229$	−4.38706	+	7.59860i	−0.289905	+	0.502130i	0.683882	+	0.729593i	$0.260290\pi$
$230$	2.13721			0.140924
$231$	4.75824	+	12.1155i	0.313069	+	0.797140i
$232$	−5.08309			−0.333721
$233$	−2.55371	+	4.42316i	−0.167299	+	0.289771i	−0.937469	−	0.348068i	$-0.886838\pi$
$233$	−2.55371	+	4.42316i	−0.167299	+	0.289771i	0.770170	+	0.637839i	$0.220171\pi$
$234$		0			0
$235$	2.48365	+	4.30181i	0.162016	+	0.280619i
$236$	7.46481	−	12.9294i	0.485918	−	0.841634i
$237$	−16.6361			−1.08063
$238$	−1.42090	+	1.78261i	−0.0921032	+	0.115549i
$239$	2.49797			0.161580			0.0807901	−	0.996731i	$-0.474256\pi$
$239$	2.49797			0.161580			0.0807901	+	0.996731i	$0.474256\pi$
$240$	9.33309	−	16.1654i	0.602448	−	1.04347i
$241$	3.99256	+	6.91532i	0.257183	+	0.445455i	0.965486	−	0.260454i	$-0.0838722\pi$
$241$	3.99256	+	6.91532i	0.257183	+	0.445455i	−0.708303	+	0.705909i	$0.750539\pi$
$242$	0.338236	+	0.585842i	0.0217426	+	0.0376593i
$243$	−1.72939	+	2.99538i	−0.110940	+	0.192154i
$244$	0.809671			0.0518339
$245$	17.9736	+	5.53491i	1.14829	+	0.353612i
$246$	−1.79277			−0.114303
$247$		0			0
$248$	−1.32691	−	2.29827i	−0.0842588	−	0.145941i
$249$	15.1437	+	26.2296i	0.959690	+	1.66223i
$250$	0.675749	−	1.17043i	0.0427381	−	0.0740246i
$251$	25.2570			1.59421			0.797105	−	0.603841i	$-0.206364\pi$
$251$	25.2570			1.59421			0.797105	+	0.603841i	$0.206364\pi$
$252$	1.08465	−	1.36076i	0.0683264	−	0.0857196i
$253$	11.8527			0.745176
$254$	0.720331	−	1.24765i	0.0451976	−	0.0782845i
$255$	11.6880	+	20.2442i	0.731931	+	1.26774i
$256$	−6.72394	−	11.6462i	−0.420246	−	0.727888i
$257$	1.68682	−	2.92165i	0.105221	−	0.182248i	−0.808608	−	0.588348i	$-0.799778\pi$
$257$	1.68682	−	2.92165i	0.105221	−	0.182248i	0.913828	+	0.406101i	$0.133112\pi$
$258$	2.64501			0.164671
$259$	−7.69305	−	19.5881i	−0.478023	−	1.21715i
$260$		0			0
$261$	−1.18444	+	2.05151i	−0.0733150	+	0.126985i
$262$	−0.905740	−	1.56879i	−0.0559568	−	0.0969201i
$263$	0.0794677	+	0.137642i	0.00490019	+	0.00848737i	0.868465	−	0.495750i	$-0.165107\pi$
$263$	0.0794677	+	0.137642i	0.00490019	+	0.00848737i	−0.863565	+	0.504238i	$0.831774\pi$
$264$	−1.76466	+	3.05648i	−0.108607	+	0.188114i
$265$	−19.0011			−1.16723
$266$	0.0891413	+	0.0134146i	0.00546561	+	0.000822501i
$267$	10.7582			0.658392
$268$	11.2146	−	19.4243i	0.685043	−	1.18653i
$269$	11.6633	+	20.2014i	0.711124	+	1.23170i	0.964435	+	0.264318i	$0.0851470\pi$
$269$	11.6633	+	20.2014i	0.711124	+	1.23170i	−0.253311	+	0.967385i	$0.581520\pi$
$270$	−1.18235	−	2.04789i	−0.0719556	−	0.124631i
$271$	−5.91049	+	10.2373i	−0.359037	+	0.621870i	−0.987800	−	0.155727i	$-0.950228\pi$
$271$	−5.91049	+	10.2373i	−0.359037	+	0.621870i	0.628763	+	0.777597i	$0.283561\pi$
$272$	18.1300			1.09929
$273$		0			0
$274$	−0.916226			−0.0553513
$275$	−2.98797	+	5.17532i	−0.180182	+	0.312084i
$276$	−7.90182	−	13.6864i	−0.475634	−	0.823822i
$277$	13.6827	+	23.6991i	0.822111	+	1.42394i	0.904107	+	0.427306i	$0.140537\pi$
$277$	13.6827	+	23.6991i	0.822111	+	1.42394i	−0.0819961	+	0.996633i	$0.526130\pi$
$278$	−0.698503	+	1.20984i	−0.0418934	+	0.0725615i
$279$	−1.23676			−0.0740431
$280$	1.86409	+	4.74636i	0.111401	+	0.283649i
$281$	28.5383			1.70245			0.851225	−	0.524801i	$-0.175860\pi$
$281$	28.5383			1.70245			0.851225	+	0.524801i	$0.175860\pi$
$282$	−0.305239	+	0.528690i	−0.0181767	+	0.0314830i
$283$	−8.98604	−	15.5643i	−0.534165	−	0.925201i	−0.999203	−	0.0399101i	$-0.987293\pi$
$283$	−8.98604	−	15.5643i	−0.534165	−	0.925201i	0.465038	−	0.885290i	$-0.346040\pi$
$284$	−3.29020	−	5.69879i	−0.195237	−	0.338161i
$285$	0.462190	−	0.800537i	0.0273778	−	0.0474197i
$286$		0			0
$287$	−8.95400	+	11.2334i	−0.528538	+	0.663084i
$288$	0.709694			0.0418191
$289$	−2.85229	+	4.94032i	−0.167782	+	0.290607i
$290$	−1.72112	−	2.98107i	−0.101068	−	0.175055i
$291$	−0.411851	−	0.713347i	−0.0241432	−	0.0418172i
$292$	−13.9834	+	24.2199i	−0.818316	+	1.41737i
$293$	14.8891			0.869828			0.434914	−	0.900472i	$-0.356779\pi$
$293$	14.8891			0.869828			0.434914	+	0.900472i	$0.356779\pi$
$294$	0.515367	+	2.25312i	0.0300568	+	0.131404i
$295$	20.3886			1.18707
$296$	2.85308	−	4.94168i	0.165832	−	0.287229i
$297$	−6.55719	−	11.3574i	−0.380487	−	0.659023i
$298$	−1.29456	−	2.24224i	−0.0749918	−	0.129890i
$299$		0			0
$300$	7.96793			0.460028
$301$	13.2105	−	16.5734i	0.761440	−	0.955274i
$302$	−1.17038			−0.0673478
$303$	−6.99071	+	12.1083i	−0.401606	+	0.695601i
$304$	−0.358467	−	0.620883i	−0.0205595	−	0.0356101i
$305$	0.552862	+	0.957586i	0.0316568	+	0.0548312i
$306$	−0.144029	+	0.249465i	−0.00823356	+	0.0142610i
$307$	−23.5161			−1.34214			−0.671068	−	0.741396i	$-0.734164\pi$
$307$	−23.5161			−1.34214			−0.671068	+	0.741396i	$0.734164\pi$
$308$	5.12642	+	13.0529i	0.292105	+	0.743759i
$309$	−9.41747			−0.535741
$310$	0.898577	−	1.55638i	0.0510358	−	0.0883965i
$311$	−0.815450	−	1.41240i	−0.0462399	−	0.0800899i	0.841979	−	0.539510i	$-0.181391\pi$
$311$	−0.815450	−	1.41240i	−0.0462399	−	0.0800899i	−0.888219	+	0.459420i	$0.848057\pi$
$312$		0			0
$313$	0.348367	−	0.603389i	0.0196909	−	0.0341056i	−0.856012	−	0.516956i	$-0.827065\pi$
$313$	0.348367	−	0.603389i	0.0196909	−	0.0341056i	0.875703	+	0.482850i	$0.160398\pi$
$314$	2.87849			0.162442
$315$	2.34997	+	0.353639i	0.132406	+	0.0199253i
$316$	−17.9233			−1.00826
$317$	10.7144	−	18.5579i	0.601780	−	1.04231i	−0.390771	−	0.920488i	$-0.627792\pi$
$317$	10.7144	−	18.5579i	0.601780	−	1.04231i	0.992551	−	0.121826i	$-0.0388751\pi$
$318$	−1.16761	−	2.02236i	−0.0654764	−	0.113409i
$319$	−9.54517	−	16.5327i	−0.534427	−	0.925654i
$320$	9.70673	−	16.8126i	0.542623	−	0.939850i
$321$	−14.6682			−0.818697
$322$	2.08125	+	0.313200i	0.115983	+	0.0174540i
$323$	0.897830			0.0499566
$324$	−9.72949	+	16.8520i	−0.540527	+	0.936221i
$325$		0			0
$326$	−0.432315	−	0.748792i	−0.0239437	−	0.0414717i
$327$	1.21755	−	2.10886i	0.0673307	−	0.116620i
$328$	−3.89509			−0.215070
$329$	1.78820	+	4.55314i	0.0985868	+	0.251023i
$330$	−2.39004			−0.131568
$331$	0.760232	−	1.31676i	0.0417861	−	0.0723757i	−0.844376	−	0.535751i	$-0.820029\pi$
$331$	0.760232	−	1.31676i	0.0417861	−	0.0723757i	0.886162	+	0.463375i	$0.153362\pi$
$332$	16.3154	+	28.2591i	0.895425	+	1.55092i
$333$	−1.32962	−	2.30298i	−0.0728630	−	0.126202i
$334$	−0.245054	+	0.424446i	−0.0134088	+	0.0232247i
$335$	30.6305			1.67352
$336$	11.4577	−	14.3744i	0.625067	−	0.784186i
$337$	32.2304			1.75570			0.877850	−	0.478936i	$-0.158977\pi$
$337$	32.2304			1.75570			0.877850	+	0.478936i	$0.158977\pi$
$338$		0			0
$339$	−18.2038	−	31.5300i	−0.988697	−	1.71247i
$340$	12.5924	+	21.8106i	0.682918	+	1.18285i
$341$	4.98341	−	8.63153i	0.269867	−	0.467423i
$342$	0.0113909			0.000615951
$343$	16.6918	+	8.02394i	0.901273	+	0.433252i
$344$	5.74670			0.309841
$345$	10.7911	−	18.6907i	0.580974	−	1.00628i
$346$	0.0813541	+	0.140909i	0.00437362	+	0.00757534i
$347$	−4.09215	−	7.08782i	−0.219678	−	0.380494i	0.735031	−	0.678033i	$-0.237167\pi$
$347$	−4.09215	−	7.08782i	−0.219678	−	0.380494i	−0.954710	+	0.297539i	$0.903834\pi$
$348$	−12.7269	+	22.0436i	−0.682232	+	1.18166i
$349$	21.8493			1.16956			0.584782	−	0.811190i	$-0.301180\pi$
$349$	21.8493			1.16956			0.584782	+	0.811190i	$0.301180\pi$
$350$	−0.661419	+	0.829791i	−0.0353543	+	0.0443542i
$351$		0			0
$352$	−2.85964	+	4.95304i	−0.152419	+	0.263998i
$353$	−0.283590	−	0.491192i	−0.0150940	−	0.0261435i	0.858380	−	0.513015i	$-0.171471\pi$
$353$	−0.283590	−	0.491192i	−0.0150940	−	0.0261435i	−0.873474	+	0.486871i	$0.838138\pi$
$354$	1.25287	+	2.17004i	0.0665894	+	0.115336i
$355$	4.49325	−	7.78254i	0.238477	−	0.413054i
$356$	11.5907			0.614303
$357$	8.41524	+	21.4270i	0.445382	+	1.13404i
$358$	−1.99915			−0.105659
$359$	16.2022	−	28.0630i	0.855118	−	1.48111i	−0.0214184	−	0.999771i	$-0.506818\pi$
$359$	16.2022	−	28.0630i	0.855118	−	1.48111i	0.876536	−	0.481336i	$-0.159848\pi$
$360$	0.322179	+	0.558030i	0.0169803	+	0.0294108i
$361$	9.48225	+	16.4237i	0.499066	+	0.864407i
$362$	−0.319061	+	0.552631i	−0.0167695	+	0.0290456i
$363$	6.83122			0.358546
$364$		0			0
$365$	−38.1928			−1.99910
$366$	−0.0679464	+	0.117687i	−0.00355162	+	0.00615158i
$367$	3.93444	+	6.81465i	0.205376	+	0.355722i	0.950252	−	0.311481i	$-0.100825\pi$
$367$	3.93444	+	6.81465i	0.205376	+	0.355722i	−0.744876	+	0.667202i	$0.767492\pi$
$368$	−8.36939	−	14.4962i	−0.436285	−	0.755667i
$369$	−0.907617	+	1.57204i	−0.0472487	+	0.0818371i
$370$	3.86419			0.200889
$371$	−18.5036	−	2.78454i	−0.960658	−	0.144566i
$372$	−13.2891			−0.689007
$373$	1.04581	−	1.81140i	0.0541502	−	0.0937909i	−0.837680	−	0.546162i	$-0.816088\pi$
$373$	1.04581	−	1.81140i	0.0541502	−	0.0937909i	0.891830	+	0.452371i	$0.149422\pi$
$374$	−1.16070	−	2.01039i	−0.0600182	−	0.103955i
$375$	−6.82392	−	11.8194i	−0.352386	−	0.610350i
$376$	−0.663180	+	1.14866i	−0.0342009	+	0.0592377i
$377$		0			0
$378$	−0.851281	−	2.16754i	−0.0437852	−	0.111486i
$379$	14.3163			0.735381			0.367691	−	0.929948i	$-0.380149\pi$
$379$	14.3163			0.735381			0.367691	+	0.929948i	$0.380149\pi$
$380$	0.497953	−	0.862480i	0.0255444	−	0.0442443i
$381$	−7.27412	−	12.5991i	−0.372665	−	0.645474i
$382$	1.84444	+	3.19466i	0.0943695	+	0.163453i
$383$	−12.5937	+	21.8129i	−0.643507	+	1.11459i	0.341138	+	0.940013i	$0.389188\pi$
$383$	−12.5937	+	21.8129i	−0.643507	+	1.11459i	−0.984644	+	0.174573i	$0.944146\pi$
$384$	10.1383			0.517370
$385$	−11.9371	+	14.9758i	−0.608369	+	0.763237i
$386$	−3.12184			−0.158898
$387$	1.33907	−	2.31934i	0.0680689	−	0.117899i
$388$	−0.443719	−	0.768544i	−0.0225264	−	0.0390169i
$389$	−14.0512	−	24.3373i	−0.712422	−	1.23395i	−0.963946	−	0.266099i	$-0.914265\pi$
$389$	−14.0512	−	24.3373i	−0.712422	−	1.23395i	0.251524	−	0.967851i	$-0.419068\pi$
$390$		0			0
$391$	20.9623			1.06011
$392$	1.11972	+	4.89525i	0.0565543	+	0.247248i
$393$	−18.2929			−0.922754
$394$	0.448146	−	0.776212i	0.0225773	−	0.0391050i
$395$	−12.2384	−	21.1976i	−0.615783	−	1.06657i
$396$	0.886021	+	1.53463i	0.0445243	+	0.0771183i
$397$	−10.8882	+	18.8590i	−0.546465	+	0.946504i	0.452049	+	0.891993i	$0.350693\pi$
$397$	−10.8882	+	18.8590i	−0.546465	+	0.946504i	−0.998513	+	0.0545111i	$0.982640\pi$
$398$	1.29867			0.0650963
$399$	0.567404	−	0.711843i	0.0284057	−	0.0356367i
$400$	8.43941			0.421970
$401$	10.2645	−	17.7786i	0.512584	−	0.887821i	−0.487310	−	0.873229i	$-0.662022\pi$
$401$	10.2645	−	17.7786i	0.512584	−	0.887821i	0.999894	−	0.0145918i	$-0.00464489\pi$
$402$	1.88223	+	3.26012i	0.0938772	+	0.162600i
$403$		0			0
$404$	−7.53162	+	13.0451i	−0.374712	+	0.649020i
$405$	−26.5741			−1.32048
$406$	−1.23919	−	3.15524i	−0.0615000	−	0.156592i
$407$	21.4304			1.06226
$408$	−3.12091	+	5.40558i	−0.154508	+	0.267616i
$409$	−3.13431	−	5.42879i	−0.154982	−	0.268436i	0.778071	−	0.628177i	$-0.216199\pi$
$409$	−3.13431	−	5.42879i	−0.154982	−	0.268436i	−0.933052	+	0.359741i	$0.882865\pi$
$410$	−1.31887	−	2.28435i	−0.0651343	−	0.112816i
$411$	−4.62616	+	8.01275i	−0.228192	+	0.395240i
$412$	−10.1462			−0.499865
$413$	19.8547	+	2.98787i	0.976987	+	0.147024i
$414$	0.265953			0.0130709
$415$	−22.2811	+	38.5920i	−1.09374	+	1.89441i
$416$		0			0
$417$	7.05369	+	12.2174i	0.345421	+	0.598286i
$418$	−0.0458986	+	0.0794987i	−0.00224497	+	0.00388841i
$419$	34.1635			1.66899			0.834497	−	0.551013i	$-0.185758\pi$
$419$	34.1635			1.66899			0.834497	+	0.551013i	$0.185758\pi$
$420$	25.2506	+	3.79987i	1.23210	+	0.185415i
$421$	11.5233			0.561613			0.280806	−	0.959764i	$-0.409398\pi$
$421$	11.5233			0.561613			0.280806	+	0.959764i	$0.409398\pi$
$422$	1.59059	−	2.75498i	0.0774288	−	0.134111i
$423$	0.309063	+	0.535313i	0.0150272	+	0.0260278i
$424$	−2.53682	−	4.39391i	−0.123199	−	0.213387i
$425$	−5.28442	+	9.15288i	−0.256332	+	0.443980i
$426$	1.10444			0.0535101
$427$	0.398055	+	1.01353i	0.0192632	+	0.0490482i
$428$	−15.8031			−0.763873
$429$		0			0
$430$	1.94582	+	3.37026i	0.0938359	+	0.162529i
$431$	−4.38500	−	7.59505i	−0.211218	−	0.365841i	0.740878	−	0.671640i	$-0.234410\pi$
$431$	−4.38500	−	7.59505i	−0.211218	−	0.365841i	−0.952096	+	0.305799i	$0.901076\pi$
$432$	−9.26026	+	16.0392i	−0.445534	+	0.771688i
$433$	22.1069			1.06239			0.531196	−	0.847249i	$-0.321743\pi$
$433$	22.1069			1.06239			0.531196	+	0.847249i	$0.321743\pi$
$434$	1.10313	−	1.38394i	0.0529519	−	0.0664315i
$435$	−34.7609			−1.66666
$436$	1.31176	−	2.27203i	0.0628219	−	0.108811i
$437$	−0.414467	−	0.717877i	−0.0198266	−	0.0343407i
$438$	−2.34693	−	4.06501i	−0.112141	−	0.194234i
$439$	5.18547	−	8.98150i	0.247489	−	0.428664i	−0.715339	−	0.698777i	$-0.753728\pi$
$439$	5.18547	−	8.98150i	0.247489	−	0.428664i	0.962828	+	0.270114i	$0.0870612\pi$
$440$	−5.19275			−0.247555
$441$	2.23661	+	0.688759i	0.106505	+	0.0327980i
$442$		0			0
$443$	−17.9068	+	31.0156i	−0.850780	+	1.47359i	0.0297257	+	0.999558i	$0.490537\pi$
$443$	−17.9068	+	31.0156i	−0.850780	+	1.47359i	−0.880506	+	0.474036i	$0.842797\pi$
$444$	−14.2869	−	24.7456i	−0.678026	−	1.17438i
$445$	7.91437	+	13.7081i	0.375177	+	0.649826i
$446$	−1.27530	+	2.20888i	−0.0603871	+	0.104593i
$447$	−26.1457			−1.23665
$448$	11.9164	−	14.9498i	0.562996	−	0.706313i
$449$	−22.7502			−1.07365			−0.536825	−	0.843693i	$-0.680377\pi$
$449$	−22.7502			−1.07365			−0.536825	+	0.843693i	$0.680377\pi$
$450$	−0.0670443	+	0.116124i	−0.00316050	+	0.00547415i
$451$	−7.31430	−	12.6687i	−0.344417	−	0.596548i
$452$	−19.6124	−	33.9696i	−0.922489	−	1.59780i
$453$	−5.90942	+	10.2354i	−0.277649	+	0.480902i
$454$	0.518742			0.0243458
$455$		0			0
$456$	0.246827			0.0115587
$457$	−15.6586	+	27.1215i	−0.732478	+	1.26869i	0.223344	+	0.974740i	$0.428303\pi$
$457$	−15.6586	+	27.1215i	−0.732478	+	1.26869i	−0.955821	+	0.293949i	$0.905031\pi$
$458$	−0.793284	−	1.37401i	−0.0370677	−	0.0642032i
$459$	−11.5968	−	20.0862i	−0.541292	−	0.937546i
$460$	11.6261	−	20.1370i	0.542069	−	0.938891i
$461$	8.40753			0.391578			0.195789	−	0.980646i	$-0.437273\pi$
$461$	8.40753			0.391578			0.195789	+	0.980646i	$0.437273\pi$
$462$	−2.32746	−	0.350252i	−0.108283	−	0.0162952i
$463$	10.0392			0.466563			0.233281	−	0.972409i	$-0.425054\pi$
$463$	10.0392			0.466563			0.233281	+	0.972409i	$0.425054\pi$
$464$	−13.4800	+	23.3480i	−0.625791	+	1.08390i
$465$	−9.07411	−	15.7168i	−0.420802	−	0.728850i
$466$	−0.461772	−	0.799813i	−0.0213912	−	0.0370506i
$467$	13.1756	−	22.8209i	0.609696	−	1.05602i	−0.381594	−	0.924330i	$-0.624625\pi$
$467$	13.1756	−	22.8209i	0.609696	−	1.05602i	0.991290	−	0.131695i	$-0.0420418\pi$
$468$		0			0
$469$	29.8284	+	4.48878i	1.37735	+	0.207273i
$470$	−0.898206			−0.0414312
$471$	14.5339	−	25.1735i	0.669687	−	1.15993i
$472$	2.72206	+	4.71475i	0.125293	+	0.217014i
$473$	10.7913	+	18.6911i	0.496185	+	0.859418i
$474$	1.50410	−	2.60517i	0.0690855	−	0.119660i
$475$	0.417934			0.0191761
$476$	9.06638	+	23.0849i	0.415557	+	1.05809i
$477$	−2.36448			−0.108262
$478$	−0.225846	+	0.391177i	−0.0103300	+	0.0178920i
$479$	4.29207	+	7.43409i	0.196110	+	0.339672i	0.947264	−	0.320455i	$-0.103836\pi$
$479$	4.29207	+	7.43409i	0.196110	+	0.339672i	−0.751154	+	0.660127i	$0.770502\pi$
$480$	5.20701	+	9.01880i	0.237666	+	0.411650i
$481$		0			0
$482$	−1.44390			−0.0657678
$483$	13.2476	−	16.6199i	0.602787	−	0.756233i
$484$	7.35979			0.334536
$485$	0.605963	−	1.04956i	0.0275154	−	0.0476580i
$486$	−0.312714	−	0.541637i	−0.0141850	−	0.0245691i
$487$	−10.6281	−	18.4084i	−0.481606	−	0.834166i	0.518171	−	0.855277i	$-0.326613\pi$
$487$	−10.6281	−	18.4084i	−0.481606	−	0.834166i	−0.999777	+	0.0211110i	$0.993280\pi$
$488$	−0.147624	+	0.255693i	−0.00668264	+	0.0115747i
$489$	−8.73130			−0.394843
$490$	−2.49178	+	2.31420i	−0.112567	+	0.104545i
$491$	−22.4535			−1.01331			−0.506657	−	0.862148i	$-0.669119\pi$
$491$	−22.4535			−1.01331			−0.506657	+	0.862148i	$0.669119\pi$
$492$	−9.75240	+	16.8916i	−0.439672	+	0.761534i
$493$	−16.8812	−	29.2391i	−0.760292	−	1.31686i
$494$		0			0
$495$	−1.20999	+	2.09577i	−0.0543851	+	0.0941978i
$496$	−14.0754			−0.632006
$497$	5.51610	−	6.92029i	0.247431	−	0.310417i
$498$	−5.47667			−0.245415
$499$	−19.4390	+	33.6694i	−0.870210	+	1.50725i	−0.00843082	+	0.999964i	$0.502684\pi$
$499$	−19.4390	+	33.6694i	−0.870210	+	1.50725i	−0.861779	+	0.507284i	$0.830650\pi$
$500$	−7.35193	−	12.7339i	−0.328788	−	0.569478i
$501$	2.47463	+	4.28619i	0.110558	+	0.191493i
$502$	−2.28354	+	3.95520i	−0.101919	+	0.176529i
$503$	5.45701			0.243316			0.121658	−	0.992572i	$-0.461179\pi$
$503$	5.45701			0.243316			0.121658	+	0.992572i	$0.461179\pi$
$504$	0.231965	+	0.590632i	0.0103326	+	0.0263088i
$505$	−20.5711			−0.915401
$506$	−1.07163	+	1.85612i	−0.0476397	+	0.0825144i
$507$		0			0
$508$	−7.83697	−	13.5740i	−0.347709	−	0.602250i
$509$	5.44623	−	9.43315i	0.241400	−	0.418117i	−0.719713	−	0.694271i	$-0.755727\pi$
$509$	5.44623	−	9.43315i	0.241400	−	0.418117i	0.961113	+	0.276154i	$0.0890601\pi$
$510$	−4.22694			−0.187172
$511$	−37.1927	−	5.59701i	−1.64531	−	0.247597i
$512$	13.5360			0.598214
$513$	−0.458584	+	0.794290i	−0.0202470	+	0.0350688i
$514$	0.305017	+	0.528304i	0.0134537	+	0.0233025i
$515$	−6.92804	−	11.9997i	−0.305286	−	0.528771i
$516$	14.3884	−	24.9215i	0.633415	−	1.09711i
$517$	−4.98136			−0.219080
$518$	3.76300	+	0.566282i	0.165337	+	0.0248810i
$519$	1.64308			0.0721230
$520$		0			0
$521$	−13.9480	−	24.1587i	−0.611074	−	1.05841i	−0.991060	−	0.133419i	$-0.957404\pi$
$521$	−13.9480	−	24.1587i	−0.611074	−	1.05841i	0.379985	−	0.924993i	$-0.375929\pi$
$522$	−0.214175	−	0.370962i	−0.00937418	−	0.0162366i
$523$	−8.36180	+	14.4831i	−0.365636	+	0.633300i	−0.988878	−	0.148729i	$-0.952482\pi$
$523$	−8.36180	+	14.4831i	−0.365636	+	0.633300i	0.623242	+	0.782029i	$0.285815\pi$
$524$	−19.7083			−0.860962
$525$	3.91724	+	9.97411i	0.170962	+	0.435306i
$526$	−0.0287393			−0.00125309
$527$	8.81347	−	15.2654i	0.383921	−	0.664970i
$528$	9.35949	+	16.2111i	0.407319	+	0.705498i
$529$	1.82314	+	3.15777i	0.0792668	+	0.137294i
$530$	1.71793	−	2.97554i	0.0746219	−	0.129249i
$531$	2.53714			0.110102
$532$	0.611307	−	0.766923i	0.0265035	−	0.0332503i
$533$		0			0
$534$	−0.972671	+	1.68472i	−0.0420916	+	0.0729048i
$535$	−10.7907	−	18.6901i	−0.466525	−	0.808045i
$536$	4.08945	+	7.08313i	0.176637	+	0.305945i
$537$	−10.0940	+	17.4834i	−0.435590	+	0.754464i
$538$	−4.21800			−0.181851
$539$	−13.8191	+	12.8343i	−0.595232	+	0.552813i
$540$	−25.7272			−1.10712
$541$	−5.58025	+	9.66528i	−0.239914	+	0.415543i	−0.960689	−	0.277626i	$-0.910453\pi$
$541$	−5.58025	+	9.66528i	−0.239914	+	0.415543i	0.720776	+	0.693169i	$0.243786\pi$
$542$	−1.06876	−	1.85114i	−0.0459070	−	0.0795133i
$543$	3.22198	+	5.58063i	0.138268	+	0.239488i
$544$	−5.05745	+	8.75976i	−0.216836	+	0.375572i
$545$	3.58280			0.153470
$546$		0			0
$547$	36.6556			1.56728			0.783640	−	0.621215i	$-0.213361\pi$
$547$	36.6556			1.56728			0.783640	+	0.621215i	$0.213361\pi$
$548$	−4.98412	+	8.63275i	−0.212911	+	0.368773i
$549$	0.0687976	+	0.119161i	0.00293621	+	0.00508567i
$550$	−0.540297	−	0.935821i	−0.0230383	−	0.0399036i
$551$	−0.667551	+	1.15623i	−0.0284386	+	0.0492571i
$552$	5.76285			0.245283
$553$	−8.81155	−	22.4361i	−0.374705	−	0.954078i
$554$	−4.94830			−0.210233
$555$	19.5109	−	33.7938i	0.828190	−	1.43447i
$556$	7.59948	+	13.1627i	0.322290	+	0.558222i
$557$	16.5388	+	28.6461i	0.700772	+	1.21377i	0.968196	+	0.250193i	$0.0804942\pi$
$557$	16.5388	+	28.6461i	0.700772	+	1.21377i	−0.267424	+	0.963579i	$0.586173\pi$
$558$	0.111818	−	0.193675i	0.00473364	−	0.00819890i
$559$		0			0
$560$	26.7447	+	4.02472i	1.13017	+	0.170076i
$561$	−23.4421			−0.989728
$562$	−2.58020	+	4.46903i	−0.108839	+	0.188515i
$563$	−8.89836	−	15.4124i	−0.375021	−	0.649556i	0.615309	−	0.788286i	$-0.289031\pi$
$563$	−8.89836	−	15.4124i	−0.375021	−	0.649556i	−0.990330	+	0.138730i	$0.955698\pi$
$564$	3.32090	+	5.75197i	0.139835	+	0.242202i
$565$	26.7836	−	46.3906i	1.12679	−	1.95167i
$566$	3.24978			0.136598
$567$	−25.8783	−	3.89433i	−1.08679	−	0.163547i
$568$	2.39956			0.100683
$569$	4.11047	−	7.11954i	0.172320	−	0.298467i	−0.766911	−	0.641754i	$-0.778207\pi$
$569$	4.11047	−	7.11954i	0.172320	−	0.298467i	0.939231	+	0.343287i	$0.111540\pi$
$570$	0.0835750	+	0.144756i	0.00350057	+	0.00606317i
$571$	12.8776	+	22.3047i	0.538912	+	0.933424i	0.998963	+	0.0455309i	$0.0144980\pi$
$571$	12.8776	+	22.3047i	0.538912	+	0.933424i	−0.460051	+	0.887893i	$0.652169\pi$
$572$		0			0
$573$	37.2513			1.55620
$574$	−0.949572	−	2.41781i	−0.0396344	−	0.100917i
$575$	9.75781			0.406929
$576$	1.20790	−	2.09214i	0.0503290	−	0.0871724i
$577$	0.384697	+	0.666314i	0.0160151	+	0.0277390i	0.873922	−	0.486066i	$-0.161569\pi$
$577$	0.384697	+	0.666314i	0.0160151	+	0.0277390i	−0.857907	+	0.513805i	$0.828235\pi$
$578$	−0.515762	−	0.893326i	−0.0214529	−	0.0371575i
$579$	−15.7626	+	27.3017i	−0.655073	+	1.13462i
$580$	−37.4505			−1.55505
$581$	−27.3532	+	34.3163i	−1.13480	+	1.42368i
$582$	0.148945			0.00617397
$583$	9.52743	−	16.5020i	0.394586	−	0.683443i
$584$	−5.09908	−	8.83187i	−0.211002	−	0.365465i
$585$		0			0
$586$	−1.34615	+	2.33159i	−0.0556088	+	0.0963173i
$587$	−12.0929			−0.499127			−0.249563	−	0.968358i	$-0.580287\pi$
$587$	−12.0929			−0.499127			−0.249563	+	0.968358i	$0.580287\pi$
$588$	24.0325	+	7.40075i	0.991085	+	0.305202i
$589$	−0.697040			−0.0287210
$590$	−1.84337	+	3.19281i	−0.0758904	+	0.131446i
$591$	−4.52552	−	7.83842i	−0.186155	−	0.322430i
$592$	−15.1323	−	26.2099i	−0.621933	−	1.07722i
$593$	7.97406	−	13.8115i	0.327456	−	0.567170i	−0.654551	−	0.756018i	$-0.727142\pi$
$593$	7.97406	−	13.8115i	0.327456	−	0.567170i	0.982006	+	0.188848i	$0.0604755\pi$
$594$	2.37139			0.0972994
$595$	−21.1114	+	26.4856i	−0.865484	+	1.08580i
$596$	−28.1688			−1.15384
$597$	6.55717	−	11.3573i	0.268367	−	0.464825i
$598$		0			0
$599$	3.55511	+	6.15763i	0.145258	+	0.251594i	0.929469	−	0.368900i	$-0.120266\pi$
$599$	3.55511	+	6.15763i	0.145258	+	0.251594i	−0.784211	+	0.620494i	$0.786932\pi$
$600$	−1.45276	+	2.51626i	−0.0593088	+	0.102726i
$601$	20.7905			0.848064			0.424032	−	0.905647i	$-0.360614\pi$
$601$	20.7905			0.848064			0.424032	+	0.905647i	$0.360614\pi$
$602$	1.40097	+	3.56717i	0.0570994	+	0.145387i
$603$	3.81163			0.155221
$604$	−6.36667	+	11.0274i	−0.259056	+	0.448698i
$605$	5.02544	+	8.70432i	0.204313	+	0.353881i
$606$	−1.26409	−	2.18946i	−0.0513500	−	0.0889408i
$607$	3.85702	−	6.68056i	0.156552	−	0.271156i	−0.777071	−	0.629413i	$-0.783296\pi$
$607$	3.85702	−	6.68056i	0.156552	−	0.271156i	0.933623	+	0.358257i	$0.116629\pi$
$608$	0.399983			0.0162215
$609$	−33.8507	−	5.09407i	−1.37170	−	0.206422i
$610$	−0.199941			−0.00809539
$611$		0			0
$612$	1.56698	+	2.71409i	0.0633415	+	0.109711i
$613$	−10.2189	−	17.6997i	−0.412738	−	0.714883i	0.582450	−	0.812867i	$-0.302094\pi$
$613$	−10.2189	−	17.6997i	−0.412738	−	0.714883i	−0.995188	+	0.0979832i	$0.968761\pi$
$614$	2.12614	−	3.68257i	0.0858038	−	0.148617i
$615$	−26.6367			−1.07409
$616$	−5.05678	−	0.760978i	−0.203743	−	0.0306607i
$617$	4.59812			0.185113			0.0925567	−	0.995707i	$-0.470496\pi$
$617$	4.59812			0.185113			0.0925567	+	0.995707i	$0.470496\pi$
$618$	0.851451	−	1.47476i	0.0342504	−	0.0593234i
$619$	−5.02641	−	8.70599i	−0.202028	−	0.349923i	0.747154	−	0.664651i	$-0.231420\pi$
$619$	−5.02641	−	8.70599i	−0.202028	−	0.349923i	−0.949182	+	0.314728i	$0.898087\pi$
$620$	−9.77623	−	16.9329i	−0.392623	−	0.680042i
$621$	−10.7069	+	18.5449i	−0.429653	+	0.744181i
$622$	0.294906			0.0118246
$623$	5.69827	+	14.5090i	0.228296	+	0.581290i
$624$		0			0
$625$	15.5853	−	26.9944i	0.623410	−	1.07978i
$626$	0.0629930	+	0.109107i	0.00251771	+	0.00436080i
$627$	0.463498	+	0.802802i	0.0185103	+	0.0320608i
$628$	15.6585	−	27.1213i	0.624842	−	1.08226i
$629$	37.9009			1.51121
$630$	−0.267844	+	0.336027i	−0.0106712	+	0.0133877i
$631$	−7.27372			−0.289562			−0.144781	−	0.989464i	$-0.546248\pi$
$631$	−7.27372			−0.289562			−0.144781	+	0.989464i	$0.546248\pi$
$632$	3.26789	−	5.66015i	0.129990	−	0.225149i
$633$	−16.0623	−	27.8207i	−0.638418	−	1.10577i
$634$	1.93742	+	3.35570i	0.0769447	+	0.133272i
$635$	10.7025	−	18.5373i	0.424717	−	0.735631i
$636$	−25.4065			−1.00743
$637$		0			0
$638$	3.45199			0.136665
$639$	0.559136	−	0.968451i	0.0221191	−	0.0383113i
$640$	7.45835	+	12.9182i	0.294817	+	0.510639i
$641$	−1.92516	−	3.33448i	−0.0760394	−	0.131704i	0.825498	−	0.564404i	$-0.190894\pi$
$641$	−1.92516	−	3.33448i	−0.0760394	−	0.131704i	−0.901538	+	0.432700i	$0.857561\pi$
$642$	1.32618	−	2.29700i	0.0523400	−	0.0906555i
$643$	−2.87709			−0.113461			−0.0567307	−	0.998390i	$-0.518068\pi$
$643$	−2.87709			−0.113461			−0.0567307	+	0.998390i	$0.518068\pi$
$644$	14.2726	−	17.9059i	0.562421	−	0.705592i
$645$	39.2990			1.54740
$646$	−0.0811745	+	0.140598i	−0.00319377	+	0.00553177i
$647$	−18.5501	−	32.1296i	−0.729278	−	1.26315i	−0.957189	−	0.289464i	$-0.906523\pi$
$647$	−18.5501	−	32.1296i	−0.729278	−	1.26315i	0.227911	−	0.973682i	$-0.426810\pi$
$648$	−3.54789	−	6.14512i	−0.139374	−	0.241403i
$649$	−10.2231	+	17.7070i	−0.401293	+	0.695061i
$650$		0			0
$651$	−6.53326	−	16.6350i	−0.256059	−	0.651979i
$652$	−9.40689			−0.368402
$653$	−10.0475	+	17.4028i	−0.393189	+	0.681023i	−0.992868	−	0.119218i	$-0.961961\pi$
$653$	−10.0475	+	17.4028i	−0.393189	+	0.681023i	0.599679	+	0.800240i	$0.295295\pi$
$654$	0.220162	+	0.381332i	0.00860902	+	0.0149113i
$655$	−13.4573	−	23.3087i	−0.525820	−	0.910748i
$656$	−10.3295	+	17.8912i	−0.403298	+	0.698532i
$657$	−4.75267			−0.185419
$658$	−0.874687	−	0.131629i	−0.0340988	−	0.00513142i
$659$	9.91058			0.386061			0.193031	−	0.981193i	$-0.438168\pi$
$659$	9.91058			0.386061			0.193031	+	0.981193i	$0.438168\pi$
$660$	−13.0014	+	22.5192i	−0.506080	+	0.876557i
$661$	−23.6133	−	40.8994i	−0.918450	−	1.59080i	−0.801770	−	0.597633i	$-0.796108\pi$
$661$	−23.6133	−	40.8994i	−0.918450	−	1.59080i	−0.116680	−	0.993170i	$-0.537225\pi$
$662$	0.137468	+	0.238102i	0.00534284	+	0.00925408i
$663$		0			0
$664$	−11.8989			−0.461768
$665$	1.32444	+	0.199311i	0.0513597	+	0.00772895i
$666$	0.480855			0.0186328
$667$	−15.5858	+	26.9954i	−0.603485	+	1.04527i
$668$	2.66611	+	4.61783i	0.103155	+	0.178669i
$669$	12.8783	+	22.3059i	0.497905	+	0.862397i
$670$	−2.76936	+	4.79667i	−0.106990	+	0.185312i
$671$	−1.10885			−0.0428068
$672$	3.74899	+	9.54572i	0.144621	+	0.368234i
$673$	6.91689			0.266627			0.133313	−	0.991074i	$-0.457438\pi$
$673$	6.91689			0.266627			0.133313	+	0.991074i	$0.457438\pi$
$674$	−2.91401	+	5.04721i	−0.112243	+	0.194411i
$675$	−5.39823	−	9.35001i	−0.207778	−	0.359882i
$676$		0			0
$677$	6.16453	−	10.6773i	0.236922	−	0.410361i	−0.722908	−	0.690945i	$-0.757195\pi$
$677$	6.16453	−	10.6773i	0.236922	−	0.410361i	0.959830	+	0.280584i	$0.0905281\pi$
$678$	6.58337			0.252833
$679$	0.743905	−	0.933275i	0.0285485	−	0.0358158i
$680$	−9.18369			−0.352179
$681$	2.61921	−	4.53660i	0.100368	−	0.173843i
$682$	0.901120	+	1.56078i	0.0345057	+	0.0597655i
$683$	12.2682	+	21.2491i	0.469430	+	0.813076i	0.999389	−	0.0349470i	$-0.0111262\pi$
$683$	12.2682	+	21.2491i	0.469430	+	0.813076i	−0.529960	+	0.848023i	$0.677793\pi$
$684$	0.0619648	−	0.107326i	0.00236928	−	0.00410372i
$685$	−13.6131			−0.520130
$686$	−2.76567	+	1.88844i	−0.105594	+	0.0721011i
$687$	−16.0216			−0.611264
$688$	15.2398	−	26.3961i	0.581012	−	1.00634i
$689$		0			0
$690$	1.95129	+	3.37973i	0.0742843	+	0.128664i
$691$	−4.55358	+	7.88703i	−0.173226	+	0.300037i	−0.939546	−	0.342423i	$-0.888753\pi$
$691$	−4.55358	+	7.88703i	−0.173226	+	0.300037i	0.766320	+	0.642459i	$0.222086\pi$
$692$	1.77021			0.0672933
$693$	−1.48544	+	1.86357i	−0.0564271	+	0.0707912i
$694$	1.47992			0.0561769
$695$	−10.3782	+	17.9756i	−0.393668	+	0.681853i
$696$	−4.64089	−	8.03826i	−0.175913	−	0.304690i
$697$	−12.9358	−	22.4055i	−0.489978	−	0.848667i
$698$	−1.97543	+	3.42155i	−0.0747712	+	0.129508i
$699$	−9.32623			−0.352750
$700$	4.22034	+	10.7459i	0.159514	+	0.406156i
$701$	−0.286950			−0.0108380			−0.00541898	−	0.999985i	$-0.501725\pi$
$701$	−0.286950			−0.0108380			−0.00541898	+	0.999985i	$0.501725\pi$
$702$		0			0
$703$	−0.749377	−	1.29796i	−0.0282633	−	0.0489534i
$704$	9.73419	+	16.8601i	0.366871	+	0.635440i
$705$	−4.53518	+	7.85516i	−0.170805	+	0.295842i
$706$	0.102559			0.00385988
$707$	−20.0324	−	3.01461i	−0.753397	−	0.113376i
$708$	27.2617			1.02456
$709$	9.29241	−	16.0949i	0.348984	−	0.604457i	−0.637086	−	0.770793i	$-0.719860\pi$
$709$	9.29241	−	16.0949i	0.348984	−	0.604457i	0.986069	+	0.166336i	$0.0531936\pi$
$710$	0.812486	+	1.40727i	0.0304921	+	0.0528138i
$711$	−1.52294	−	2.63781i	−0.0571147	−	0.0989256i
$712$	−2.11328	+	3.66031i	−0.0791986	+	0.137176i
$713$	−16.2743			−0.609478
$714$	−4.11626	−	0.619442i	−0.154047	−	0.0231820i
$715$		0			0
$716$	−10.8751	+	18.8362i	−0.406421	+	0.703941i
$717$	2.28066	+	3.95022i	0.0851729	+	0.147524i
$718$	2.92974	+	5.07445i	0.109337	+	0.189377i
$719$	−20.8475	+	36.1088i	−0.777479	+	1.34663i	0.155912	+	0.987771i	$0.450168\pi$
$719$	−20.8475	+	36.1088i	−0.777479	+	1.34663i	−0.933391	+	0.358862i	$0.883165\pi$
$720$	3.41757			0.127365
$721$	−4.98812	−	12.7008i	−0.185767	−	0.473002i
$722$	−3.42923			−0.127623
$723$	−7.29046	+	12.6275i	−0.271135	+	0.469620i
$724$	3.47128	+	6.01244i	0.129009	+	0.223451i
$725$	−7.85809	−	13.6106i	−0.291842	−	0.505486i
$726$	−0.617623	+	1.06975i	−0.0229221	+	0.0397023i
$727$	−32.7039			−1.21292			−0.606461	−	0.795113i	$-0.707411\pi$
$727$	−32.7039			−1.21292			−0.606461	+	0.795113i	$0.707411\pi$
$728$		0			0
$729$	23.3578			0.865105
$730$	3.45308	−	5.98091i	0.127804	−	0.221363i
$731$	19.0851	+	33.0564i	0.705888	+	1.22263i
$732$	0.739235	+	1.28039i	0.0273229	+	0.0473246i
$733$	4.96765	−	8.60423i	0.183484	−	0.317804i	−0.759580	−	0.650413i	$-0.774596\pi$
$733$	4.96765	−	8.60423i	0.183484	−	0.317804i	0.943065	+	0.332609i	$0.107929\pi$
$734$	−1.42288			−0.0525195
$735$	7.65722	+	33.4763i	0.282441	+	1.23479i
$736$	9.33871			0.344230
$737$	−15.3586	+	26.6018i	−0.565740	+	0.979891i
$738$	−0.164119	−	0.284262i	−0.00604129	−	0.0104638i
$739$	5.20108	+	9.00853i	0.191325	+	0.331384i	0.945690	−	0.325071i	$-0.105388\pi$
$739$	5.20108	+	9.00853i	0.191325	+	0.331384i	−0.754365	+	0.656455i	$0.772055\pi$
$740$	21.0205	−	36.4086i	0.772730	−	1.33841i
$741$		0			0
$742$	2.10900	−	2.64587i	0.0774237	−	0.0971328i
$743$	−1.70863			−0.0626837			−0.0313419	−	0.999509i	$-0.509978\pi$
$743$	−1.70863			−0.0626837			−0.0313419	+	0.999509i	$0.509978\pi$
$744$	2.42295	−	4.19668i	0.0888297	−	0.153858i
$745$	−19.2343	−	33.3148i	−0.704690	−	1.22056i
$746$	0.189108	+	0.327545i	0.00692374	+	0.0119923i
$747$	−2.77264	+	4.80235i	−0.101446	+	0.175709i
$748$	−25.2560			−0.923451
$749$	−7.76923	−	19.7821i	−0.283881	−	0.722821i
$750$	2.46785			0.0901132
$751$	−14.9906	+	25.9645i	−0.547015	+	0.947458i	0.451462	+	0.892290i	$0.350903\pi$
$751$	−14.9906	+	25.9645i	−0.547015	+	0.947458i	−0.998477	+	0.0551673i	$0.982431\pi$
$752$	3.51741	+	6.09233i	0.128267	+	0.222164i
$753$	23.0598	+	39.9408i	0.840347	+	1.45552i
$754$		0			0
$755$	−17.3893			−0.632860
$756$	−25.0535	−	3.77022i	−0.911188	−	0.137122i
$757$	8.40458			0.305470			0.152735	−	0.988267i	$-0.451192\pi$
$757$	8.40458			0.305470			0.152735	+	0.988267i	$0.451192\pi$
$758$	−1.29437	+	2.24191i	−0.0470136	+	0.0814299i
$759$	10.8216	+	18.7436i	0.392800	+	0.680350i
$760$	0.181580	+	0.314506i	0.00658660	+	0.0114083i
$761$	25.5295	−	44.2184i	0.925444	−	1.60292i	0.134598	−	0.990900i	$-0.457026\pi$
$761$	25.5295	−	44.2184i	0.925444	−	1.60292i	0.790846	−	0.612015i	$-0.209641\pi$
$762$	2.63067			0.0952990
$763$	3.48899	+	0.525046i	0.126310	+	0.0190079i
$764$	40.1337			1.45199
$765$	−2.13995	+	3.70650i	−0.0773699	+	0.134009i
$766$	−2.27723	−	3.94429i	−0.0822798	−	0.142513i
$767$		0			0
$768$	12.2780	−	21.2661i	0.443044	−	0.767375i
$769$	−0.704439			−0.0254027			−0.0127014	−	0.999919i	$-0.504043\pi$
$769$	−0.704439			−0.0254027			−0.0127014	+	0.999919i	$0.504043\pi$
$770$	−1.26592	−	3.22331i	−0.0456208	−	0.116160i
$771$	6.16030			0.221858
$772$	−16.9823	+	29.4142i	−0.611206	+	1.05864i
$773$	0.632607	+	1.09571i	0.0227533	+	0.0394099i	0.877178	−	0.480166i	$-0.159423\pi$
$773$	0.632607	+	1.09571i	0.0227533	+	0.0394099i	−0.854425	+	0.519575i	$0.826090\pi$
$774$	0.242136	+	0.419392i	0.00870341	+	0.0150747i
$775$	4.10261	−	7.10593i	0.147370	−	0.255253i
$776$	0.323607			0.0116168
$777$	23.9523	−	30.0497i	0.859285	−	1.07803i
$778$	5.08156			0.182183
$779$	−0.511533	+	0.886001i	−0.0183276	+	0.0317443i
$780$		0			0
$781$	4.50596	+	7.80456i	0.161236	+	0.279269i
$782$	−1.89524	+	3.28265i	−0.0677737	+	0.117387i
$783$	34.4896			1.23256
$784$	25.4546	+	7.83867i	0.909092	+	0.279952i
$785$	42.7679			1.52645
$786$	1.65389	−	2.86463i	0.0589924	−	0.102178i
$787$	21.8984	+	37.9292i	0.780595	+	1.35203i	0.931595	+	0.363497i	$0.118417\pi$
$787$	21.8984	+	37.9292i	0.780595	+	1.35203i	−0.151000	+	0.988534i	$0.548249\pi$
$788$	−4.87568	−	8.44493i	−0.173689	−	0.300838i
$789$	−0.145109	+	0.251336i	−0.00516602	+	0.00894780i
$790$	4.42600			0.157470
$791$	32.8806	−	41.2508i	1.16910	−	1.46671i
$792$	−0.646180			−0.0229610
$793$		0			0
$794$	−1.96885	−	3.41015i	−0.0698719	−	0.121022i
$795$	−17.3481	−	30.0479i	−0.615275	−	1.06569i
$796$	7.06453	−	12.2361i	0.250396	−	0.433698i
$797$	13.6837			0.484700			0.242350	−	0.970189i	$-0.422082\pi$
$797$	13.6837			0.484700			0.242350	+	0.970189i	$0.422082\pi$
$798$	0.0601731	+	0.153213i	0.00213011	+	0.00542369i
$799$	−8.80983			−0.311669
$800$	−2.35421	+	4.07761i	−0.0832338	+	0.144165i
$801$	0.984857	+	1.70582i	0.0347982	+	0.0602722i
$802$	1.85606	+	3.21479i	0.0655398	+	0.113518i
$803$	19.1504	−	33.1695i	0.675803	−	1.17053i
$804$	40.9561			1.44441
$805$	30.9228	+	4.65347i	1.08988	+	0.164013i
$806$		0			0
$807$	−21.2973	+	36.8881i	−0.749702	+	1.29852i
$808$	−2.74643	−	4.75695i	−0.0966189	−	0.167349i
$809$	−4.55688	−	7.89274i	−0.160211	−	0.277494i	0.774733	−	0.632288i	$-0.217884\pi$
$809$	−4.55688	−	7.89274i	−0.160211	−	0.277494i	−0.934944	+	0.354794i	$0.884551\pi$
$810$	2.40261	−	4.16145i	0.0844193	−	0.146218i
$811$	−2.31899			−0.0814309			−0.0407154	−	0.999171i	$-0.512964\pi$
$811$	−2.31899			−0.0814309			−0.0407154	+	0.999171i	$0.512964\pi$
$812$	−36.4699	−	5.48823i	−1.27984	−	0.192599i
$813$	−21.5853			−0.757028
$814$	−1.93756	+	3.35595i	−0.0679114	+	0.117626i
$815$	−6.42325	−	11.1254i	−0.224997	−	0.389706i
$816$	16.5528	+	28.6703i	0.579465	+	1.00366i
$817$	0.754702	−	1.30718i	0.0264037	−	0.0457325i
$818$	1.13352			0.0396325
$819$		0			0
$820$	−28.6977			−1.00217
$821$	5.07235	−	8.78557i	0.177026	−	0.306619i	−0.763834	−	0.645412i	$-0.776686\pi$
$821$	5.07235	−	8.78557i	0.177026	−	0.306619i	0.940861	+	0.338794i	$0.110019\pi$
$822$	−0.836520	−	1.44890i	−0.0291770	−	0.0505360i
$823$	13.4089	+	23.2249i	0.467405	+	0.809570i	0.999306	−	0.0372366i	$-0.0118555\pi$
$823$	13.4089	+	23.2249i	0.467405	+	0.809570i	−0.531901	+	0.846806i	$0.678522\pi$
$824$	1.84991	−	3.20414i	0.0644448	−	0.111622i
$825$	−10.9122			−0.379913
$826$	−2.26300	+	2.83907i	−0.0787398	+	0.0987839i
$827$	−33.6015			−1.16844			−0.584219	−	0.811596i	$-0.698599\pi$
$827$	−33.6015			−1.16844			−0.584219	+	0.811596i	$0.698599\pi$
$828$	1.44674	−	2.50582i	0.0502776	−	0.0870834i
$829$	−5.93328	−	10.2767i	−0.206071	−	0.356926i	0.744402	−	0.667731i	$-0.232735\pi$
$829$	−5.93328	−	10.2767i	−0.206071	−	0.356926i	−0.950473	+	0.310806i	$0.899401\pi$
$830$	−4.02895	−	6.97835i	−0.139847	−	0.242222i
$831$	−24.9847	+	43.2748i	−0.866710	+	1.50119i
$832$		0			0
$833$	−24.4400	+	22.6983i	−0.846796	+	0.786448i
$834$	−2.55095			−0.0883322
$835$	−3.64096	+	6.30633i	−0.126001	+	0.218240i
$836$	0.499362	+	0.864920i	0.0172708	+	0.0299139i
$837$	9.00330	+	15.5942i	0.311199	+	0.539013i
$838$	−3.08878	+	5.34993i	−0.106700	+	0.184810i
$839$	−34.6177			−1.19514			−0.597568	−	0.801818i	$-0.703866\pi$
$839$	−34.6177			−1.19514			−0.597568	+	0.801818i	$0.703866\pi$
$840$	−5.80384	+	7.28128i	−0.200252	+	0.251228i
$841$	21.2058			0.731234
$842$	−1.04185	+	1.80453i	−0.0359044	+	0.0621882i
$843$	26.0556	+	45.1296i	0.897403	+	1.55435i
$844$	−17.3051	−	29.9733i	−0.595666	−	1.03172i
$845$		0			0
$846$	−0.111772			−0.00384280
$847$	3.61826	+	9.21286i	0.124325	+	0.316557i
$848$	−26.9098			−0.924087
$849$	16.4086	−	28.4206i	0.563143	−	0.975392i
$850$	−0.955548	−	1.65506i	−0.0327750	−	0.0567680i
$851$	−17.4963	−	30.3044i	−0.599764	−	1.03882i
$852$	6.00795	−	10.4061i	0.205829	−	0.356506i
$853$	29.1897			0.999436			0.499718	−	0.866188i	$-0.333437\pi$
$853$	29.1897			0.999436			0.499718	+	0.866188i	$0.333437\pi$
$854$	−0.194706	−	0.0293006i	−0.00666270	−	0.00100265i
$855$	0.169244			0.00578802
$856$	2.88133	−	4.99061i	0.0984817	−	0.170575i
$857$	12.6599	+	21.9276i	0.432455	+	0.749033i	0.997084	−	0.0763112i	$-0.0243142\pi$
$857$	12.6599	+	21.9276i	0.432455	+	0.749033i	−0.564629	+	0.825345i	$0.690981\pi$
$858$		0			0
$859$	−13.0424	+	22.5902i	−0.445002	+	0.770766i	−0.998052	−	0.0623818i	$-0.980130\pi$
$859$	−13.0424	+	22.5902i	−0.445002	+	0.770766i	0.553050	+	0.833148i	$0.313464\pi$
$860$	42.3398			1.44378
$861$	−25.9392	−	3.90350i	−0.884005	−	0.133031i
$862$	1.58583			0.0540134
$863$	18.0169	−	31.2061i	0.613302	−	1.06227i	−0.377378	−	0.926059i	$-0.623174\pi$
$863$	18.0169	−	31.2061i	0.613302	−	1.06227i	0.990680	−	0.136210i	$-0.0434923\pi$
$864$	−5.16638	−	8.94843i	−0.175764	−	0.304432i
$865$	1.20874	+	2.09360i	0.0410985	+	0.0711846i
$866$	−1.99873	+	3.46190i	−0.0679196	+	0.117640i
$867$	−10.4166			−0.353768
$868$	−7.03878	−	17.9222i	−0.238912	−	0.608319i
$869$	24.5461			0.832671
$870$	3.14279	−	5.44348i	0.106551	−	0.184551i
$871$		0			0
$872$	0.478337	+	0.828504i	0.0161985	+	0.0280567i
$873$	0.0754055	−	0.130606i	0.00255209	−	0.00442035i
$874$	0.149891			0.00507013
$875$	12.3257	−	15.4633i	0.416684	−	0.522756i
$876$	−51.0677			−1.72542
$877$	−4.56084	+	7.89961i	−0.154009	+	0.266751i	−0.932698	−	0.360659i	$-0.882552\pi$
$877$	−4.56084	+	7.89961i	−0.154009	+	0.266751i	0.778689	+	0.627410i	$0.215885\pi$
$878$	0.937657	+	1.62407i	0.0316444	+	0.0548097i
$879$	13.5938	+	23.5452i	0.458507	+	0.794158i
$880$	−13.7708	+	23.8517i	−0.464212	+	0.804039i
$881$	13.0331			0.439095			0.219548	−	0.975602i	$-0.429542\pi$
$881$	13.0331			0.439095			0.219548	+	0.975602i	$0.429542\pi$
$882$	−0.310075	+	0.287977i	−0.0104408	+	0.00969669i
$883$	2.13222			0.0717548			0.0358774	−	0.999356i	$-0.488577\pi$
$883$	2.13222			0.0717548			0.0358774	+	0.999356i	$0.488577\pi$
$884$		0			0
$885$	18.6149	+	32.2420i	0.625734	+	1.08380i
$886$	−3.23798	−	5.60835i	−0.108782	−	0.188416i
$887$	23.5857	−	40.8517i	0.791932	−	1.37167i	−0.132838	−	0.991138i	$-0.542409\pi$
$887$	23.5857	−	40.8517i	0.791932	−	1.37167i	0.924769	−	0.380528i	$-0.124258\pi$
$888$	10.4195			0.349656
$889$	13.1389	−	16.4835i	0.440663	−	0.552839i
$890$	−2.86221			−0.0959416
$891$	13.3246	−	23.0790i	0.446392	−	0.773174i
$892$	13.8748	+	24.0319i	0.464563	+	0.804647i
$893$	0.174188	+	0.301702i	0.00582898	+	0.0100961i
$894$	2.36388	−	4.09437i	0.0790601	−	0.136936i
$895$	−29.7030			−0.992863
$896$	5.36994	+	13.6730i	0.179397	+	0.456782i
$897$		0			0
$898$	2.05689	−	3.56264i	0.0686394	−	0.118887i
$899$	13.1059	+	22.7001i	0.437107	+	0.757091i
$900$	0.729420	+	1.26339i	0.0243140	+	0.0421131i
$901$	16.8499	−	29.1848i	0.561350	−	0.972287i
$902$	2.64520			0.0880755
$903$	38.2700	+	5.75912i	1.27354	+	0.191652i
$904$	14.3034			0.475725
$905$	−4.74055	+	8.21087i	−0.157581	+	0.272939i
$906$	−1.06856	−	1.85081i	−0.0355007	−	0.0614889i
$907$	−8.02154	−	13.8937i	−0.266351	−	0.461333i	0.701566	−	0.712605i	$-0.252485\pi$
$907$	−8.02154	−	13.8937i	−0.266351	−	0.461333i	−0.967917	+	0.251271i	$0.919151\pi$
$908$	2.82187	−	4.88763i	0.0936471	−	0.162202i
$909$	−2.55984			−0.0849047
$910$		0			0
$911$	−24.4319			−0.809466			−0.404733	−	0.914435i	$-0.632636\pi$
$911$	−24.4319			−0.809466			−0.404733	+	0.914435i	$0.632636\pi$
$912$	0.654565	−	1.13374i	0.0216748	−	0.0375419i
$913$	−22.3441	−	38.7012i	−0.739483	−	1.28082i
$914$	−2.83144	−	4.90420i	−0.0936558	−	0.162217i
$915$	−1.00953	+	1.74856i	−0.0333742	+	0.0578057i
$916$	−17.2613			−0.570331
$917$	−9.68912	−	24.6705i	−0.319963	−	0.814692i
$918$	4.19395			0.138421
$919$	−7.95800	+	13.7837i	−0.262510	+	0.454681i	−0.966908	−	0.255124i	$-0.917884\pi$
$919$	−7.95800	+	13.7837i	−0.262510	+	0.454681i	0.704398	+	0.709805i	$0.251217\pi$
$920$	4.23948	+	7.34300i	0.139772	+	0.242092i
$921$	−21.4704	−	37.1878i	−0.707472	−	1.22538i
$922$	−0.760140	+	1.31660i	−0.0250339	+	0.0433600i
$923$		0			0
$924$	−15.9611	+	20.0242i	−0.525082	+	0.658747i
$925$	17.6426			0.580086
$926$	−0.907665	+	1.57212i	−0.0298277	+	0.0516632i
$927$	−0.862118	−	1.49323i	−0.0283157	−	0.0490442i
$928$	−7.52059	−	13.0260i	−0.246875	−	0.427601i
$929$	23.6618	−	40.9834i	0.776317	−	1.34462i	−0.157734	−	0.987482i	$-0.550419\pi$
$929$	23.6618	−	40.9834i	0.776317	−	1.34462i	0.934051	−	0.357139i	$-0.116248\pi$
$930$	3.28163			0.107609
$931$	1.26055	+	0.388184i	0.0413130	+	0.0127222i
$932$	−10.0479			−0.329129
$933$	1.48902	−	2.57906i	0.0487484	−	0.0844347i
$934$	2.38247	+	4.12656i	0.0779568	+	0.135025i
$935$	−17.2454	−	29.8699i	−0.563985	−	0.976850i
$936$		0			0
$937$	−29.7044			−0.970401			−0.485200	−	0.874403i	$-0.661253\pi$
$937$	−29.7044			−0.970401			−0.485200	+	0.874403i	$0.661253\pi$
$938$	−3.39978	+	4.26523i	−0.111007	+	0.139265i
$939$	1.27224			0.0415181
$940$	−4.88609	+	8.46296i	−0.159367	+	0.276031i
$941$	−20.2112	−	35.0068i	−0.658866	−	1.14119i	−0.980909	−	0.194465i	$-0.937703\pi$
$941$	−20.2112	−	35.0068i	−0.658866	−	1.14119i	0.322043	−	0.946725i	$-0.395630\pi$
$942$	2.62808	+	4.55196i	0.0856273	+	0.148311i
$943$	−11.9431	+	20.6861i	−0.388922	+	0.673633i
$944$	28.8748			0.939795
$945$	−12.6482	−	32.2048i	−0.411444	−	1.04762i
$946$	−3.90265			−0.126886
$947$	−22.9614	+	39.7703i	−0.746146	+	1.29236i	0.203512	+	0.979072i	$0.434764\pi$
$947$	−22.9614	+	39.7703i	−0.746146	+	1.29236i	−0.949658	+	0.313290i	$0.898569\pi$
$948$	−16.3641	−	28.3434i	−0.531481	−	0.920551i
$949$		0			0
$950$	−0.0377862	+	0.0654476i	−0.00122595	+	0.00212340i
$951$	39.1292			1.26885
$952$	−8.94322	−	1.34584i	−0.289851	−	0.0436188i
$953$	12.3893			0.401329			0.200664	−	0.979660i	$-0.435690\pi$
$953$	12.3893			0.401329			0.200664	+	0.979660i	$0.435690\pi$
$954$	0.213777	−	0.370273i	0.00692129	−	0.0119880i
$955$	27.4042	+	47.4655i	0.886780	+	1.53595i
$956$	2.45713	+	4.25587i	0.0794693	+	0.137645i
$957$	17.4296	−	30.1890i	0.563419	−	0.975870i
$958$	−1.55222			−0.0501499
$959$	−13.2566	−	1.99495i	−0.428079	−	0.0644202i
$960$	35.4492			1.14412
$961$	8.65757	−	14.9953i	0.279276	−	0.483721i
$962$		0			0
$963$	−1.34279	−	2.32578i	−0.0432708	−	0.0749472i
$964$	−7.85457	+	13.6045i	−0.252979	+	0.438172i
$965$	−46.3837			−1.49314
$966$	1.40491	+	3.57719i	0.0452021	+	0.115094i
$967$	9.44932			0.303870			0.151935	−	0.988391i	$-0.451450\pi$
$967$	9.44932			0.303870			0.151935	+	0.988391i	$0.451450\pi$
$968$	−1.34188	+	2.32421i	−0.0431298	+	0.0747030i
$969$	0.819725	+	1.41980i	0.0263333	+	0.0456107i
$970$	0.109573	+	0.189785i	0.00351816	+	0.00609364i
$971$	10.4882	−	18.1660i	0.336581	−	0.582976i	−0.647206	−	0.762315i	$-0.724063\pi$
$971$	10.4882	−	18.1660i	0.336581	−	0.582976i	0.983787	+	0.179339i	$0.0573959\pi$
$972$	−6.80445			−0.218253
$973$	−12.7407	+	15.9840i	−0.408448	+	0.512424i
$974$	3.84363			0.123158
$975$		0			0
$976$	0.782977	+	1.35616i	0.0250625	+	0.0434095i
$977$	−6.59214	−	11.4179i	−0.210901	−	0.365292i	0.741096	−	0.671400i	$-0.234307\pi$
$977$	−6.59214	−	11.4179i	−0.210901	−	0.365292i	−0.951997	+	0.306108i	$0.900973\pi$
$978$	0.789413	−	1.36730i	0.0252426	−	0.0437215i
$979$	−15.8735			−0.507320
$980$	8.24971	+	36.0666i	0.263527	+	1.15211i
$981$	0.445840			0.0142346
$982$	2.03007	−	3.51618i	0.0647820	−	0.112206i
$983$	−11.6794	−	20.2294i	−0.372516	−	0.645216i	0.617436	−	0.786621i	$-0.288171\pi$
$983$	−11.6794	−	20.2294i	−0.372516	−	0.645216i	−0.989952	+	0.141405i	$0.954838\pi$
$984$	−3.55624	−	6.15959i	−0.113369	−	0.196360i
$985$	6.65846	−	11.5328i	0.212156	−	0.367465i
$986$	6.10505			0.194424
$987$	−5.56757	+	6.98486i	−0.177218	+	0.222331i
$988$		0			0
$989$	17.6206	−	30.5197i	0.560302	−	0.970471i
$990$	−0.218795	−	0.378965i	−0.00695378	−	0.0120443i
$991$	−19.7465	−	34.2019i	−0.627267	−	1.08646i	−0.988098	−	0.153827i	$-0.950840\pi$
$991$	−19.7465	−	34.2019i	−0.627267	−	1.08646i	0.360831	−	0.932631i	$-0.382493\pi$
$992$	3.92640	−	6.80073i	0.124663	−	0.215923i
$993$	2.77639			0.0881060
$994$	0.584982	+	1.48949i	0.0185545	+	0.0472436i
$995$	19.2953			0.611703
$996$	−29.7922	+	51.6015i	−0.944001	+	1.63506i
$997$	25.7396	+	44.5822i	0.815180	+	1.41193i	0.909199	+	0.416363i	$0.136695\pi$
$997$	25.7396	+	44.5822i	0.815180	+	1.41193i	−0.0940184	+	0.995570i	$0.529971\pi$
$998$	−3.51504	−	6.08822i	−0.111267	−	0.192719i
$999$	−19.3586	+	33.5301i	−0.612479	+	1.06085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.j.170.6		24
7.2	even	3		8281.2.a.cp.1.7		12
7.4	even	3	inner	1183.2.e.j.508.6		24
7.5	odd	6		8281.2.a.co.1.7		12
13.2	odd	12		91.2.u.b.30.3	yes	12
13.7	odd	12		91.2.k.b.23.4	yes	12
13.12	even	2	inner	1183.2.e.j.170.7		24
39.2	even	12		819.2.do.e.667.4		12
39.20	even	12		819.2.bm.f.478.3		12
91.2	odd	12		637.2.q.g.589.4		12
91.12	odd	6		8281.2.a.co.1.6		12
91.20	even	12		637.2.k.i.569.4		12
91.25	even	6	inner	1183.2.e.j.508.7		24
91.33	even	12		637.2.q.i.491.4		12
91.41	even	12		637.2.u.g.30.3		12
91.46	odd	12		91.2.u.b.88.3	yes	12
91.51	even	6		8281.2.a.cp.1.6		12
91.54	even	12		637.2.q.i.589.4		12
91.59	even	12		637.2.u.g.361.3		12
91.67	odd	12		91.2.k.b.4.3	✓	12
91.72	odd	12		637.2.q.g.491.4		12
91.80	even	12		637.2.k.i.459.3		12
273.137	even	12		819.2.do.e.361.4		12
273.158	even	12		819.2.bm.f.550.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.3	✓	12	91.67	odd	12
91.2.k.b.23.4	yes	12	13.7	odd	12
91.2.u.b.30.3	yes	12	13.2	odd	12
91.2.u.b.88.3	yes	12	91.46	odd	12
637.2.k.i.459.3		12	91.80	even	12
637.2.k.i.569.4		12	91.20	even	12
637.2.q.g.491.4		12	91.72	odd	12
637.2.q.g.589.4		12	91.2	odd	12
637.2.q.i.491.4		12	91.33	even	12
637.2.q.i.589.4		12	91.54	even	12
637.2.u.g.30.3		12	91.41	even	12
637.2.u.g.361.3		12	91.59	even	12
819.2.bm.f.478.3		12	39.20	even	12
819.2.bm.f.550.4		12	273.158	even	12
819.2.do.e.361.4		12	273.137	even	12
819.2.do.e.667.4		12	39.2	even	12
1183.2.e.j.170.6		24	1.1	even	1	trivial
1183.2.e.j.170.7		24	13.12	even	2	inner
1183.2.e.j.508.6		24	7.4	even	3	inner
1183.2.e.j.508.7		24	91.25	even	6	inner
8281.2.a.co.1.6		12	91.12	odd	6
8281.2.a.co.1.7		12	7.5	odd	6
8281.2.a.cp.1.6		12	91.51	even	6
8281.2.a.cp.1.7		12	7.2	even	3

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0904119 + 0.156598i) q^{2} +(0.913006 + 1.58137i) q^{3} +(0.983651 + 1.70373i) q^{4} +(-1.34332 + 2.32670i) q^{5} -0.330186 q^{6} +(-1.64912 + 2.06892i) q^{7} -0.717383 q^{8} +(-0.167162 + 0.289532i) q^{9} +O(q^{10})\)	\(q+(-0.0904119 + 0.156598i) q^{2} +(0.913006 + 1.58137i) q^{3} +(0.983651 + 1.70373i) q^{4} +(-1.34332 + 2.32670i) q^{5} -0.330186 q^{6} +(-1.64912 + 2.06892i) q^{7} -0.717383 q^{8} +(-0.167162 + 0.289532i) q^{9} +(-0.242904 - 0.420723i) q^{10} +(-1.34712 - 2.33328i) q^{11} +(-1.79616 + 3.11104i) q^{12} +(-0.174889 - 0.445303i) q^{14} -4.90584 q^{15} +(-1.90244 + 3.29513i) q^{16} +(-2.38247 - 4.12655i) q^{17} +(-0.0302268 - 0.0523543i) q^{18} +(-0.0942122 + 0.163180i) q^{19} -5.28544 q^{20} +(-4.77738 - 0.718933i) q^{21} +0.487183 q^{22} +(-2.19964 + 3.80989i) q^{23} +(-0.654975 - 1.13445i) q^{24} +(-1.10902 - 1.92088i) q^{25} +4.86756 q^{27} +(-5.14704 - 0.774561i) q^{28} +7.08560 q^{29} +(0.443546 - 0.768245i) q^{30} +(1.84965 + 3.20369i) q^{31} +(-1.06139 - 1.83838i) q^{32} +(2.45986 - 4.26060i) q^{33} +0.861613 q^{34} +(-2.59846 - 6.61622i) q^{35} -0.657715 q^{36} +(-3.97707 + 6.88848i) q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(0.963675 - 1.66913i) q^{40} +5.42958 q^{41} +(0.544516 - 0.683129i) q^{42} -8.01065 q^{43} +(2.65020 - 4.59027i) q^{44} +(-0.449103 - 0.777869i) q^{45} +(-0.397748 - 0.688919i) q^{46} +(0.924445 - 1.60118i) q^{47} -6.94777 q^{48} +(-1.56084 - 6.82377i) q^{49} +0.401075 q^{50} +(4.35041 - 7.53514i) q^{51} +(3.53622 + 6.12491i) q^{53} +(-0.440085 + 0.762250i) q^{54} +7.23846 q^{55} +(1.18305 - 1.48421i) q^{56} -0.344066 q^{57} +(-0.640623 + 1.10959i) q^{58} +(-3.79444 - 6.57216i) q^{59} +(-4.82564 - 8.35825i) q^{60} +(0.205782 - 0.356425i) q^{61} -0.668922 q^{62} +(-0.323350 - 0.823315i) q^{63} -7.22592 q^{64} +(0.444801 + 0.770418i) q^{66} +(-5.70051 - 9.87358i) q^{67} +(4.68703 - 8.11818i) q^{68} -8.03315 q^{69} +(1.27102 + 0.191271i) q^{70} -3.34488 q^{71} +(0.119919 - 0.207705i) q^{72} +(7.10790 + 12.3112i) q^{73} +(-0.719148 - 1.24560i) q^{74} +(2.02509 - 3.50756i) q^{75} -0.370688 q^{76} +(7.04893 + 1.06077i) q^{77} +(-4.55529 + 7.89000i) q^{79} +(-5.11118 - 8.85283i) q^{80} +(4.94560 + 8.56603i) q^{81} +(-0.490899 + 0.850261i) q^{82} +16.5866 q^{83} +(-3.47441 - 8.84657i) q^{84} +12.8017 q^{85} +(0.724258 - 1.25445i) q^{86} +(6.46920 + 11.2050i) q^{87} +(0.966401 + 1.67386i) q^{88} +(2.94582 - 5.10232i) q^{89} +0.162417 q^{90} -8.65473 q^{92} +(-3.37749 + 5.84998i) q^{93} +(0.167162 + 0.289532i) q^{94} +(-0.253115 - 0.438407i) q^{95} +(1.93811 - 3.35691i) q^{96} -0.451094 q^{97} +(1.20971 + 0.372526i) q^{98} +0.900747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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