LMFDB - Embedded newform 950.2.l.l.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	950.101
Dual form			950.2.l.l.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-3.03100 - 1.10319i) q^{3} +(0.173648 - 0.984808i) q^{4} +(3.03100 - 1.10319i) q^{6} +(-1.36166 + 2.35847i) q^{7} +(0.500000 + 0.866025i) q^{8} +(5.67178 + 4.75918i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-3.03100 - 1.10319i) q^{3} +(0.173648 - 0.984808i) q^{4} +(3.03100 - 1.10319i) q^{6} +(-1.36166 + 2.35847i) q^{7} +(0.500000 + 0.866025i) q^{8} +(5.67178 + 4.75918i) q^{9} +(-1.18927 - 2.05988i) q^{11} +(-1.61276 + 2.79338i) q^{12} +(-0.0945198 + 0.0344024i) q^{13} +(-0.472900 - 2.68195i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(4.17630 - 3.50433i) q^{17} -7.40398 q^{18} +(1.18130 - 4.19577i) q^{19} +(6.72904 - 5.64633i) q^{21} +(2.23510 + 0.813512i) q^{22} +(0.235016 - 1.33284i) q^{23} +(-0.560106 - 3.17652i) q^{24} +(0.0502929 - 0.0871099i) q^{26} +(-7.10256 - 12.3020i) q^{27} +(2.08619 + 1.75052i) q^{28} +(-1.61211 - 1.35272i) q^{29} +(-5.26498 + 9.11921i) q^{31} +(0.939693 - 0.342020i) q^{32} +(1.33224 + 7.55550i) q^{33} +(-0.946690 + 5.36895i) q^{34} +(5.67178 - 4.75918i) q^{36} -1.18731 q^{37} +(1.79206 + 3.97348i) q^{38} +0.324442 q^{39} +(3.30679 + 1.20357i) q^{41} +(-1.52535 + 8.65069i) q^{42} +(-1.22895 - 6.96972i) q^{43} +(-2.23510 + 0.813512i) q^{44} +(0.676702 + 1.17208i) q^{46} +(6.13425 + 5.14725i) q^{47} +(2.47089 + 2.07332i) q^{48} +(-0.208248 - 0.360697i) q^{49} +(-16.5243 + 6.01435i) q^{51} +(0.0174665 + 0.0990577i) q^{52} +(-1.94049 + 11.0051i) q^{53} +(13.3484 + 4.85844i) q^{54} -2.72332 q^{56} +(-8.20927 + 11.4142i) q^{57} +2.10445 q^{58} +(-9.13030 + 7.66123i) q^{59} +(-0.0303598 + 0.172179i) q^{61} +(-1.82851 - 10.3700i) q^{62} +(-18.9474 + 6.89630i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.87714 - 4.93150i) q^{66} +(-4.17582 - 3.50393i) q^{67} +(-2.72588 - 4.72137i) q^{68} +(-2.18272 + 3.78057i) q^{69} +(0.240963 + 1.36657i) q^{71} +(-1.28569 + 7.29149i) q^{72} +(-11.3670 - 4.13725i) q^{73} +(0.909534 - 0.763190i) q^{74} +(-3.92690 - 1.89194i) q^{76} +6.47756 q^{77} +(-0.248537 + 0.208547i) q^{78} +(-3.51498 - 1.27935i) q^{79} +(4.09930 + 23.2483i) q^{81} +(-3.30679 + 1.20357i) q^{82} +(-4.50106 + 7.79606i) q^{83} +(-4.39207 - 7.60729i) q^{84} +(5.42148 + 4.54916i) q^{86} +(3.39398 + 5.87854i) q^{87} +(1.18927 - 2.05988i) q^{88} +(-7.26423 + 2.64396i) q^{89} +(0.0475671 - 0.269766i) q^{91} +(-1.27178 - 0.462891i) q^{92} +(26.0184 - 21.8320i) q^{93} -8.00769 q^{94} -3.22552 q^{96} +(-2.26235 + 1.89834i) q^{97} +(0.391379 + 0.142450i) q^{98} +(3.05807 - 17.3432i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−3.03100	−	1.10319i	−1.74995	−	0.636929i	−0.750241	−	0.661165i	$-0.770062\pi$
$3$	−3.03100	−	1.10319i	−1.74995	−	0.636929i	−0.999706	+	0.0242362i	$0.992285\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	3.03100	−	1.10319i	1.23740	−	0.450377i
$7$	−1.36166	+	2.35847i	−0.514660	+	0.891417i	0.485195	+	0.874406i	$0.338749\pi$
$7$	−1.36166	+	2.35847i	−0.514660	+	0.891417i	−0.999855	+	0.0170114i	$0.994585\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	5.67178	+	4.75918i	1.89059	+	1.58639i
$10$		0			0
$11$	−1.18927	−	2.05988i	−0.358580	−	0.621078i	0.629144	−	0.777289i	$-0.283406\pi$
$11$	−1.18927	−	2.05988i	−0.358580	−	0.621078i	−0.987724	+	0.156210i	$0.950072\pi$
$12$	−1.61276	+	2.79338i	−0.465564	+	0.806380i
$13$	−0.0945198	+	0.0344024i	−0.0262151	+	0.00954150i	−0.355094	−	0.934830i	$-0.615551\pi$
$13$	−0.0945198	+	0.0344024i	−0.0262151	+	0.00954150i	0.328879	+	0.944372i	$0.393329\pi$
$14$	−0.472900	−	2.68195i	−0.126388	−	0.716782i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	4.17630	−	3.50433i	1.01290	−	0.849925i	0.0241821	−	0.999708i	$-0.492302\pi$
$17$	4.17630	−	3.50433i	1.01290	−	0.849925i	0.988719	+	0.149783i	$0.0478574\pi$
$18$	−7.40398			−1.74513
$19$	1.18130	−	4.19577i	0.271009	−	0.962577i
$19$	1.18130	−	4.19577i	0.271009	−	0.962577i
$20$		0			0
$21$	6.72904	−	5.64633i	1.46840	−	1.23213i
$22$	2.23510	+	0.813512i	0.476526	+	0.173441i
$23$	0.235016	−	1.33284i	0.0490042	−	0.277917i	−0.950453	−	0.310869i	$-0.899380\pi$
$23$	0.235016	−	1.33284i	0.0490042	−	0.277917i	0.999457	+	0.0329524i	$0.0104910\pi$
$24$	−0.560106	−	3.17652i	−0.114331	−	0.648404i
$25$		0			0
$26$	0.0502929	−	0.0871099i	0.00986325	−	0.0170837i
$27$	−7.10256	−	12.3020i	−1.36689	−	2.36752i
$28$	2.08619	+	1.75052i	0.394252	+	0.330817i
$29$	−1.61211	−	1.35272i	−0.299360	−	0.251193i	0.480718	−	0.876875i	$-0.340376\pi$
$29$	−1.61211	−	1.35272i	−0.299360	−	0.251193i	−0.780078	+	0.625682i	$0.784821\pi$
$30$		0			0
$31$	−5.26498	+	9.11921i	−0.945618	+	1.63786i	−0.191109	+	0.981569i	$0.561208\pi$
$31$	−5.26498	+	9.11921i	−0.945618	+	1.63786i	−0.754509	+	0.656290i	$0.772125\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	1.33224	+	7.55550i	0.231913	+	1.31524i
$34$	−0.946690	+	5.36895i	−0.162356	+	0.920766i
$35$		0			0
$36$	5.67178	−	4.75918i	0.945296	−	0.793197i
$37$	−1.18731			−0.195193			−0.0975965	−	0.995226i	$-0.531115\pi$
$37$	−1.18731			−0.195193			−0.0975965	+	0.995226i	$0.531115\pi$
$38$	1.79206	+	3.97348i	0.290711	+	0.644583i
$39$	0.324442			0.0519522
$40$		0			0
$41$	3.30679	+	1.20357i	0.516433	+	0.187966i	0.587071	−	0.809536i	$-0.300281\pi$
$41$	3.30679	+	1.20357i	0.516433	+	0.187966i	−0.0706374	+	0.997502i	$0.522503\pi$
$42$	−1.52535	+	8.65069i	−0.235367	+	1.33483i
$43$	−1.22895	−	6.96972i	−0.187413	−	1.06287i	−0.922816	−	0.385242i	$-0.874118\pi$
$43$	−1.22895	−	6.96972i	−0.187413	−	1.06287i	0.735403	−	0.677630i	$-0.236993\pi$
$44$	−2.23510	+	0.813512i	−0.336955	+	0.122641i
$45$		0			0
$46$	0.676702	+	1.17208i	0.0997742	+	0.172814i
$47$	6.13425	+	5.14725i	0.894772	+	0.750803i	0.969162	−	0.246426i	$-0.0792564\pi$
$47$	6.13425	+	5.14725i	0.894772	+	0.750803i	−0.0743895	+	0.997229i	$0.523701\pi$
$48$	2.47089	+	2.07332i	0.356642	+	0.299259i
$49$	−0.208248	−	0.360697i	−0.0297498	−	0.0515281i
$50$		0			0
$51$	−16.5243	+	6.01435i	−2.31386	+	0.842178i
$52$	0.0174665	+	0.0990577i	0.00242217	+	0.0137368i
$53$	−1.94049	+	11.0051i	−0.266547	+	1.51166i	0.498046	+	0.867151i	$0.334051\pi$
$53$	−1.94049	+	11.0051i	−0.266547	+	1.51166i	−0.764593	+	0.644514i	$0.777060\pi$
$54$	13.3484	+	4.85844i	1.81649	+	0.661149i
$55$		0			0
$56$	−2.72332			−0.363920
$57$	−8.20927	+	11.4142i	−1.08734	+	1.51184i
$58$	2.10445			0.276328
$59$	−9.13030	+	7.66123i	−1.18866	+	0.997407i	−0.188782	+	0.982019i	$0.560454\pi$
$59$	−9.13030	+	7.66123i	−1.18866	+	0.997407i	−0.999882	+	0.0153883i	$0.995102\pi$
$60$		0			0
$61$	−0.0303598	+	0.172179i	−0.00388717	+	0.0220452i	−0.986690	−	0.162615i	$-0.948007\pi$
$61$	−0.0303598	+	0.172179i	−0.00388717	+	0.0220452i	0.982802	+	0.184660i	$0.0591184\pi$
$62$	−1.82851	−	10.3700i	−0.232221	−	1.31699i
$63$	−18.9474	+	6.89630i	−2.38715	+	0.868852i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−5.87714	−	4.93150i	−0.723425	−	0.607026i
$67$	−4.17582	−	3.50393i	−0.510157	−	0.428073i	0.351027	−	0.936365i	$-0.385832\pi$
$67$	−4.17582	−	3.50393i	−0.510157	−	0.428073i	−0.861184	+	0.508293i	$0.830277\pi$
$68$	−2.72588	−	4.72137i	−0.330562	−	0.572550i
$69$	−2.18272	+	3.78057i	−0.262768	+	0.455128i
$70$		0			0
$71$	0.240963	+	1.36657i	0.0285970	+	0.162182i	0.995762	−	0.0919676i	$-0.0293156\pi$
$71$	0.240963	+	1.36657i	0.0285970	+	0.162182i	−0.967165	+	0.254149i	$0.918205\pi$
$72$	−1.28569	+	7.29149i	−0.151520	+	0.859311i
$73$	−11.3670	−	4.13725i	−1.33041	−	0.484229i	−0.423629	−	0.905836i	$-0.639244\pi$
$73$	−11.3670	−	4.13725i	−1.33041	−	0.484229i	−0.906779	+	0.421607i	$0.861466\pi$
$74$	0.909534	−	0.763190i	0.105731	−	0.0887190i
$75$		0			0
$76$	−3.92690	−	1.89194i	−0.450446	−	0.217021i
$77$	6.47756			0.738187
$78$	−0.248537	+	0.208547i	−0.0281412	+	0.0236133i
$79$	−3.51498	−	1.27935i	−0.395466	−	0.143938i	0.136629	−	0.990622i	$-0.456373\pi$
$79$	−3.51498	−	1.27935i	−0.395466	−	0.143938i	−0.532095	+	0.846684i	$0.678595\pi$
$80$		0			0
$81$	4.09930	+	23.2483i	0.455478	+	2.58314i
$82$	−3.30679	+	1.20357i	−0.365173	+	0.132912i
$83$	−4.50106	+	7.79606i	−0.494055	+	0.855729i	−0.999977	−	0.00685072i	$-0.997819\pi$
$83$	−4.50106	+	7.79606i	−0.494055	+	0.855729i	0.505921	+	0.862580i	$0.331153\pi$
$84$	−4.39207	−	7.60729i	−0.479214	−	0.830023i
$85$		0			0
$86$	5.42148	+	4.54916i	0.584613	+	0.490549i
$87$	3.39398	+	5.87854i	0.363873	+	0.630246i
$88$	1.18927	−	2.05988i	0.126777	−	0.219584i
$89$	−7.26423	+	2.64396i	−0.770007	+	0.280259i	−0.696999	−	0.717072i	$-0.745482\pi$
$89$	−7.26423	+	2.64396i	−0.770007	+	0.280259i	−0.0730074	+	0.997331i	$0.523260\pi$
$90$		0			0
$91$	0.0475671	−	0.269766i	0.00498638	−	0.0282792i
$92$	−1.27178	−	0.462891i	−0.132593	−	0.0482598i
$93$	26.0184	−	21.8320i	2.69798	−	2.26387i
$94$	−8.00769			−0.825930
$95$		0			0
$96$	−3.22552			−0.329203
$97$	−2.26235	+	1.89834i	−0.229707	+	0.192747i	−0.750375	−	0.661012i	$-0.770127\pi$
$97$	−2.26235	+	1.89834i	−0.229707	+	0.192747i	0.520668	+	0.853759i	$0.325683\pi$
$98$	0.391379	+	0.142450i	0.0395353	+	0.0143897i
$99$	3.05807	−	17.3432i	0.307348	−	1.74305i
$100$		0			0
$101$	−8.05071	+	2.93022i	−0.801075	+	0.291568i	−0.709932	−	0.704270i	$-0.751274\pi$
$101$	−8.05071	+	2.93022i	−0.801075	+	0.291568i	−0.0911434	+	0.995838i	$0.529052\pi$
$102$	8.79240	−	15.2289i	0.870577	−	1.50788i
$103$	−0.890417	−	1.54225i	−0.0877354	−	0.151962i	0.818818	−	0.574053i	$-0.194630\pi$
$103$	−0.890417	−	1.54225i	−0.0877354	−	0.151962i	−0.906554	+	0.422091i	$0.861296\pi$
$104$	−0.0770532	−	0.0646553i	−0.00755569	−	0.00633998i
$105$		0			0
$106$	−5.58743	−	9.67771i	−0.542699	−	0.939982i
$107$	4.24824	−	7.35816i	0.410693	−	0.711340i	−0.584273	−	0.811557i	$-0.698620\pi$
$107$	4.24824	−	7.35816i	0.410693	−	0.711340i	0.994966	+	0.100217i	$0.0319536\pi$
$108$	−13.3484	+	4.85844i	−1.28445	+	0.467503i
$109$	−1.33246	−	7.55678i	−0.127627	−	0.723808i	−0.979713	−	0.200406i	$-0.935774\pi$
$109$	−1.33246	−	7.55678i	−0.127627	−	0.723808i	0.852086	−	0.523402i	$-0.175337\pi$
$110$		0			0
$111$	3.59874	+	1.30983i	0.341577	+	0.124324i
$112$	2.08619	−	1.75052i	0.197126	−	0.165409i
$113$	3.14545			0.295899			0.147949	−	0.988995i	$-0.452733\pi$
$113$	3.14545			0.295899			0.147949	+	0.988995i	$0.452733\pi$
$114$	−1.04823	−	14.0206i	−0.0981755	−	1.31315i
$115$		0			0
$116$	−1.61211	+	1.35272i	−0.149680	+	0.125597i
$117$	−0.699822	−	0.254714i	−0.0646986	−	0.0235484i
$118$	2.06967	−	11.7377i	0.190529	−	1.08054i
$119$	2.57814	+	14.6214i	0.236338	+	1.34034i
$120$		0			0
$121$	2.67125	−	4.62675i	0.242841	−	0.420613i
$122$	−0.0874174	−	0.151411i	−0.00791440	−	0.0137081i
$123$	−8.69509	−	7.29604i	−0.784010	−	0.657862i
$124$	8.06641	+	6.76853i	0.724385	+	0.607832i
$125$		0			0
$126$	10.0817	−	17.4620i	0.898151	−	1.55564i
$127$	−10.1214	+	3.68389i	−0.898130	+	0.326893i	−0.749503	−	0.662001i	$-0.769708\pi$
$127$	−10.1214	+	3.68389i	−0.898130	+	0.326893i	−0.148627	+	0.988893i	$0.547485\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−3.96400	+	22.4810i	−0.349011	+	1.97934i
$130$		0			0
$131$	−3.31899	+	2.78497i	−0.289982	+	0.243324i	−0.776160	−	0.630536i	$-0.782835\pi$
$131$	−3.31899	+	2.78497i	−0.289982	+	0.243324i	0.486178	+	0.873860i	$0.338391\pi$
$132$	7.67206			0.667767
$133$	8.28707	+	8.49929i	0.718580	+	0.736982i
$134$	5.45114			0.470907
$135$		0			0
$136$	5.12299	+	1.86462i	0.439293	+	0.159889i
$137$	−1.25804	+	7.13470i	−0.107482	+	0.609559i	0.882718	+	0.469902i	$0.155711\pi$
$137$	−1.25804	+	7.13470i	−0.107482	+	0.609559i	−0.990200	+	0.139656i	$0.955400\pi$
$138$	−0.758049	−	4.29911i	−0.0645294	−	0.365964i
$139$	−13.8285	+	5.03317i	−1.17292	+	0.426908i	−0.853696	−	0.520771i	$-0.825644\pi$
$139$	−13.8285	+	5.03317i	−1.17292	+	0.426908i	−0.319224	+	0.947679i	$0.603422\pi$
$140$		0			0
$141$	−12.9145	−	22.3685i	−1.08760	−	1.88377i
$142$	−1.06300	−	0.891964i	−0.0892051	−	0.0748520i
$143$	0.183275	+	0.153786i	0.0153262	+	0.0128602i
$144$	−3.70199	−	6.41203i	−0.308499	−	0.534336i
$145$		0			0
$146$	11.3670	−	4.13725i	0.940740	−	0.342401i
$147$	0.233282	+	1.32301i	0.0192408	+	0.109120i
$148$	−0.206175	+	1.16927i	−0.0169474	+	0.0961137i
$149$	8.16373	+	2.97136i	0.668799	+	0.243423i	0.654031	−	0.756468i	$-0.273077\pi$
$149$	8.16373	+	2.97136i	0.668799	+	0.243423i	0.0147684	+	0.999891i	$0.495299\pi$
$150$		0			0
$151$	8.23583			0.670222			0.335111	−	0.942179i	$-0.391226\pi$
$151$	8.23583			0.670222			0.335111	+	0.942179i	$0.391226\pi$
$152$	4.22430	−	1.07485i	0.342636	−	0.0871819i
$153$	40.3648			3.26330
$154$	−4.96210	+	4.16370i	−0.399857	+	0.335520i
$155$		0			0
$156$	0.0563387	−	0.319513i	0.00451070	−	0.0255815i
$157$	2.03713	+	11.5531i	0.162581	+	0.922041i	0.951524	+	0.307575i	$0.0995175\pi$
$157$	2.03713	+	11.5531i	0.162581	+	0.922041i	−0.788943	+	0.614466i	$0.789371\pi$
$158$	3.51498	−	1.27935i	0.279637	−	0.101779i
$159$	18.0224	−	31.2156i	1.42927	−	2.47556i
$160$		0			0
$161$	2.82345	+	2.36916i	0.222519	+	0.186716i
$162$	−18.0840	−	15.1743i	−1.42081	−	1.19220i
$163$	9.83039	+	17.0267i	0.769975	+	1.33364i	0.937576	+	0.347781i	$0.113065\pi$
$163$	9.83039	+	17.0267i	0.769975	+	1.33364i	−0.167600	+	0.985855i	$0.553602\pi$
$164$	1.75950	−	3.04755i	0.137394	−	0.237974i
$165$		0			0
$166$	−1.56320	−	8.86535i	−0.121328	−	0.688085i
$167$	−2.91465	+	16.5298i	−0.225543	+	1.27912i	0.636103	+	0.771604i	$0.280545\pi$
$167$	−2.91465	+	16.5298i	−0.225543	+	1.27912i	−0.861645	+	0.507511i	$0.830566\pi$
$168$	8.25439	+	3.00435i	0.636840	+	0.231791i
$169$	−9.95083	+	8.34974i	−0.765448	+	0.642287i
$170$		0			0
$171$	26.6685	−	18.1755i	2.03939	−	1.38991i
$172$	−7.07724			−0.539634
$173$	−10.2431	+	8.59496i	−0.778766	+	0.653463i	−0.942938	−	0.332969i	$-0.891949\pi$
$173$	−10.2431	+	8.59496i	−0.778766	+	0.653463i	0.164171	+	0.986432i	$0.447505\pi$
$174$	−6.37859	−	2.32162i	−0.483560	−	0.176001i
$175$		0			0
$176$	0.413031	+	2.34241i	0.0311334	+	0.176566i
$177$	36.1257	−	13.1487i	2.71538	−	0.988316i
$178$	3.86521	−	6.69475i	0.289710	−	0.501793i
$179$	−10.8243	−	18.7483i	−0.809047	−	1.40131i	−0.913525	−	0.406784i	$-0.866650\pi$
$179$	−10.8243	−	18.7483i	−0.809047	−	1.40131i	0.104477	−	0.994527i	$-0.466683\pi$
$180$		0			0
$181$	−6.96216	−	5.84194i	−0.517493	−	0.434228i	0.346264	−	0.938137i	$-0.387450\pi$
$181$	−6.96216	−	5.84194i	−0.517493	−	0.434228i	−0.863757	+	0.503909i	$0.831895\pi$
$182$	0.136964	+	0.237228i	0.0101524	+	0.0175845i
$183$	0.281967	−	0.488380i	0.0208436	−	0.0361021i
$184$	1.27178	−	0.462891i	0.0937571	−	0.0341248i
$185$		0			0
$186$	−5.89789	+	33.4486i	−0.432454	+	2.45257i
$187$	−12.1853	−	4.43508i	−0.891076	−	0.324325i
$188$	6.13425	−	5.14725i	0.447386	−	0.375401i
$189$	38.6851			2.81393
$190$		0			0
$191$	6.95613			0.503328			0.251664	−	0.967815i	$-0.419022\pi$
$191$	6.95613			0.503328			0.251664	+	0.967815i	$0.419022\pi$
$192$	2.47089	−	2.07332i	0.178321	−	0.149629i
$193$	−15.3524	−	5.58781i	−1.10509	−	0.402220i	−0.275899	−	0.961187i	$-0.588976\pi$
$193$	−15.3524	−	5.58781i	−1.10509	−	0.402220i	−0.829190	+	0.558967i	$0.811198\pi$
$194$	0.512833	−	2.90842i	0.0368193	−	0.208812i
$195$		0			0
$196$	−0.391379	+	0.142450i	−0.0279557	+	0.0101750i
$197$	1.43752	−	2.48986i	0.102419	−	0.177395i	−0.810262	−	0.586068i	$-0.800675\pi$
$197$	1.43752	−	2.48986i	0.102419	−	0.177395i	0.912681	+	0.408673i	$0.134008\pi$
$198$	8.80536	+	15.2513i	0.625770	+	1.08386i
$199$	−14.2742	−	11.9774i	−1.01187	−	0.849058i	−0.0232838	−	0.999729i	$-0.507412\pi$
$199$	−14.2742	−	11.9774i	−1.01187	−	0.849058i	−0.988584	+	0.150671i	$0.951857\pi$
$200$		0			0
$201$	8.79138	+	15.2271i	0.620096	+	1.07404i
$202$	4.28369	−	7.41957i	0.301400	−	0.522039i
$203$	5.38548	−	1.96016i	0.377987	−	0.137576i
$204$	3.05357	+	17.3176i	0.213792	+	1.21248i
$205$		0			0
$206$	1.67344	+	0.609081i	0.116594	+	0.0424367i
$207$	7.67620	−	6.44110i	0.533533	−	0.447687i
$208$	0.100586			0.00697437
$209$	−10.0477	+	2.55658i	−0.695014	+	0.176843i
$210$		0			0
$211$	−3.41054	+	2.86178i	−0.234791	+	0.197013i	−0.752590	−	0.658489i	$-0.771196\pi$
$211$	−3.41054	+	2.86178i	−0.234791	+	0.197013i	0.517799	+	0.855502i	$0.326751\pi$
$212$	10.5009	+	3.82202i	0.721207	+	0.262498i
$213$	0.777231	−	4.40789i	0.0532550	−	0.302024i
$214$	1.47540	+	8.36739i	0.100856	+	0.571983i
$215$		0			0
$216$	7.10256	−	12.3020i	0.483268	−	0.837044i
$217$	−14.3382	−	24.8346i	−0.973343	−	1.68588i
$218$	5.87813	+	4.93233i	0.398117	+	0.334060i
$219$	29.8892	+	25.0800i	2.01972	+	1.69475i
$220$		0			0
$221$	−0.274185	+	0.474903i	−0.0184437	+	0.0319454i
$222$	−3.59874	+	1.30983i	−0.241532	+	0.0879103i
$223$	−3.21314	−	18.2226i	−0.215168	−	1.22028i	−0.880615	−	0.473832i	$-0.842870\pi$
$223$	−3.21314	−	18.2226i	−0.215168	−	1.22028i	0.665448	−	0.746445i	$-0.268241\pi$
$224$	−0.472900	+	2.68195i	−0.0315970	+	0.179195i
$225$		0			0
$226$	−2.40955	+	2.02186i	−0.160281	+	0.134492i
$227$	1.50594			0.0999530			0.0499765	−	0.998750i	$-0.484085\pi$
$227$	1.50594			0.0999530			0.0499765	+	0.998750i	$0.484085\pi$
$228$	9.81525	+	10.0666i	0.650031	+	0.666677i
$229$	9.61539			0.635403			0.317702	−	0.948191i	$-0.397089\pi$
$229$	9.61539			0.635403			0.317702	+	0.948191i	$0.397089\pi$
$230$		0			0
$231$	−19.6335	−	7.14600i	−1.29179	−	0.470172i
$232$	0.365435	−	2.07248i	0.0239920	−	0.136065i
$233$	0.998532	+	5.66295i	0.0654160	+	0.370993i	0.999888	+	0.0149563i	$0.00476092\pi$
$233$	0.998532	+	5.66295i	0.0654160	+	0.370993i	−0.934472	+	0.356036i	$0.884128\pi$
$234$	0.699822	−	0.254714i	0.0457488	−	0.0166512i
$235$		0			0
$236$	5.95938	+	10.3219i	0.387923	+	0.671902i
$237$	9.24252	+	7.75540i	0.600366	+	0.503767i
$238$	−11.3734	−	9.54343i	−0.737229	−	0.618609i
$239$	8.72159	+	15.1062i	0.564153	+	0.977142i	0.997128	+	0.0757357i	$0.0241305\pi$
$239$	8.72159	+	15.1062i	0.564153	+	0.977142i	−0.432975	+	0.901406i	$0.642536\pi$
$240$		0			0
$241$	−14.2857	+	5.19958i	−0.920225	+	0.334935i	−0.758328	−	0.651873i	$-0.773984\pi$
$241$	−14.2857	+	5.19958i	−0.920225	+	0.334935i	−0.161897	+	0.986808i	$0.551761\pi$
$242$	0.927716	+	5.26134i	0.0596359	+	0.338212i
$243$	5.82231	−	33.0199i	0.373501	−	2.11823i
$244$	0.164291	+	0.0597970i	0.0105177	+	0.00382811i
$245$		0			0
$246$	11.3506			0.723690
$247$	0.0326883	+	0.437223i	0.00207991	+	0.0278198i
$248$	−10.5300			−0.668653
$249$	22.2433	−	18.6643i	1.40961	−	1.18280i
$250$		0			0
$251$	0.382644	−	2.17008i	0.0241523	−	0.136974i	−0.970347	−	0.241715i	$-0.922290\pi$
$251$	0.382644	−	2.17008i	0.0241523	−	0.136974i	0.994500	+	0.104741i	$0.0334012\pi$
$252$	3.50134	+	19.8571i	0.220564	+	1.25088i
$253$	−3.02500	+	1.10101i	−0.190180	+	0.0692199i
$254$	5.38549	−	9.32795i	0.337916	−	0.585287i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−8.80414	−	7.38755i	−0.549187	−	0.460823i	0.325479	−	0.945549i	$-0.394475\pi$
$257$	−8.80414	−	7.38755i	−0.549187	−	0.460823i	−0.874666	+	0.484727i	$0.838919\pi$
$258$	−11.4139	−	19.7694i	−0.710597	−	1.23079i
$259$	1.61672	−	2.80024i	0.100458	−	0.173998i
$260$		0			0
$261$	−2.70567	−	15.3446i	−0.167477	−	0.949808i
$262$	0.752355	−	4.26682i	0.0464806	−	0.263605i
$263$	16.7936	+	6.11237i	1.03554	+	0.376905i	0.803187	−	0.595727i	$-0.203136\pi$
$263$	16.7936	+	6.11237i	1.03554	+	0.376905i	0.232351	+	0.972632i	$0.425358\pi$
$264$	−5.87714	+	4.93150i	−0.361713	+	0.303513i
$265$		0			0
$266$	−11.8115	−	1.18401i	−0.724210	−	0.0725962i
$267$	24.9347			1.52598
$268$	−4.17582	+	3.50393i	−0.255079	+	0.214036i
$269$	0.485375	+	0.176662i	0.0295938	+	0.0107713i	0.356775	−	0.934190i	$-0.383876\pi$
$269$	0.485375	+	0.176662i	0.0295938	+	0.0107713i	−0.327181	+	0.944962i	$0.606099\pi$
$270$		0			0
$271$	−3.98871	−	22.6211i	−0.242297	−	1.37413i	−0.826687	−	0.562662i	$-0.809777\pi$
$271$	−3.98871	−	22.6211i	−0.242297	−	1.37413i	0.584390	−	0.811473i	$-0.301334\pi$
$272$	−5.12299	+	1.86462i	−0.310627	+	0.113059i
$273$	−0.441780	+	0.765185i	−0.0267377	+	0.0463111i
$274$	−3.62238	−	6.27415i	−0.218836	−	0.379035i
$275$		0			0
$276$	3.34411	+	2.80604i	0.201292	+	0.168904i
$277$	−5.05445	−	8.75457i	−0.303693	−	0.526011i	0.673277	−	0.739391i	$-0.264886\pi$
$277$	−5.05445	−	8.75457i	−0.303693	−	0.526011i	−0.976969	+	0.213379i	$0.931553\pi$
$278$	7.35801	−	12.7444i	0.441304	−	0.764361i
$279$	−73.2618	+	26.6651i	−4.38607	+	1.59640i
$280$		0			0
$281$	−5.01606	+	28.4475i	−0.299233	+	1.69703i	0.350248	+	0.936657i	$0.386097\pi$
$281$	−5.01606	+	28.4475i	−0.299233	+	1.69703i	−0.649481	+	0.760378i	$0.725014\pi$
$282$	24.2713	+	8.83403i	1.44533	+	0.526059i
$283$	−9.39720	+	7.88519i	−0.558605	+	0.468726i	−0.877843	−	0.478949i	$-0.841018\pi$
$283$	−9.39720	+	7.88519i	−0.558605	+	0.468726i	0.319237	+	0.947675i	$0.396573\pi$
$284$	1.38765			0.0823419
$285$		0			0
$286$	−0.239248			−0.0141470
$287$	−7.34131	+	6.16009i	−0.433344	+	0.363619i
$288$	6.95746	+	2.53231i	0.409972	+	0.149218i
$289$	2.20912	−	12.5285i	0.129948	−	0.736972i
$290$		0			0
$291$	8.95141	−	3.25805i	0.524741	−	0.190990i
$292$	−6.04826	+	10.4759i	−0.353947	+	0.613055i
$293$	−0.915093	−	1.58499i	−0.0534603	−	0.0925960i	0.838057	−	0.545583i	$-0.183692\pi$
$293$	−0.915093	−	1.58499i	−0.0534603	−	0.0925960i	−0.891517	+	0.452987i	$0.850358\pi$
$294$	−1.02912	−	0.863533i	−0.0600194	−	0.0503623i
$295$		0			0
$296$	−0.593656	−	1.02824i	−0.0345056	−	0.0597654i
$297$	−16.8938	+	29.2609i	−0.980277	+	1.69789i
$298$	−8.16373	+	2.97136i	−0.472912	+	0.172126i
$299$	0.0236393	+	0.134065i	0.00136710	+	0.00775318i
$300$		0			0
$301$	18.1113	+	6.59197i	1.04392	+	0.379955i
$302$	−6.30901	+	5.29389i	−0.363043	+	0.304629i
$303$	27.6343			1.58755
$304$	−2.54510	+	3.53871i	−0.145971	+	0.202959i
$305$		0			0
$306$	−30.9212	+	25.9460i	−1.76765	+	1.48323i
$307$	−1.36877	−	0.498191i	−0.0781197	−	0.0284333i	0.302665	−	0.953097i	$-0.402124\pi$
$307$	−1.36877	−	0.498191i	−0.0781197	−	0.0284333i	−0.380784	+	0.924664i	$0.624346\pi$
$308$	1.12482	−	6.37915i	0.0640924	−	0.363486i
$309$	0.997455	+	5.65685i	0.0567432	+	0.321807i
$310$		0			0
$311$	−9.85085	+	17.0622i	−0.558591	+	0.967507i	0.439024	+	0.898475i	$0.355324\pi$
$311$	−9.85085	+	17.0622i	−0.558591	+	0.967507i	−0.997614	+	0.0690320i	$0.978009\pi$
$312$	0.162221	+	0.280975i	0.00918394	+	0.0159071i
$313$	6.70515	+	5.62629i	0.378997	+	0.318017i	0.812309	−	0.583228i	$-0.198210\pi$
$313$	6.70515	+	5.62629i	0.378997	+	0.318017i	−0.433311	+	0.901244i	$0.642655\pi$
$314$	−8.98675	−	7.54078i	−0.507152	−	0.425551i
$315$		0			0
$316$	−1.87028	+	3.23942i	−0.105212	+	0.182232i
$317$	7.40399	−	2.69483i	0.415850	−	0.151357i	−0.125618	−	0.992079i	$-0.540091\pi$
$317$	7.40399	−	2.69483i	0.415850	−	0.151357i	0.541467	+	0.840722i	$0.317869\pi$
$318$	6.25910	+	35.4971i	0.350993	+	1.99058i
$319$	−0.869204	+	4.92950i	−0.0486661	+	0.275999i
$320$		0			0
$321$	−20.9939	+	17.6159i	−1.17176	+	0.983226i
$322$	−3.68576			−0.205399
$323$	−9.76991	−	21.6625i	−0.543613	−	1.20533i
$324$	23.6069			1.31150
$325$		0			0
$326$	−18.4751	−	6.72438i	−1.02324	−	0.372429i
$327$	−4.29789	+	24.3745i	−0.237674	+	1.34791i
$328$	0.611069	+	3.46555i	0.0337407	+	0.191353i
$329$	−20.4924	+	7.45862i	−1.12978	+	0.411207i
$330$		0			0
$331$	11.9264	+	20.6572i	0.655535	+	1.13542i	0.981759	+	0.190128i	$0.0608902\pi$
$331$	11.9264	+	20.6572i	0.655535	+	1.13542i	−0.326224	+	0.945292i	$0.605776\pi$
$332$	6.89602	+	5.78645i	0.378468	+	0.317573i
$333$	−6.73417	−	5.65064i	−0.369030	−	0.309653i
$334$	−8.39241	−	14.5361i	−0.459212	−	0.795379i
$335$		0			0
$336$	−8.25439	+	3.00435i	−0.450314	+	0.163901i
$337$	−3.80768	−	21.5944i	−0.207418	−	1.17632i	−0.893590	−	0.448885i	$-0.851821\pi$
$337$	−3.80768	−	21.5944i	−0.207418	−	1.17632i	0.686172	−	0.727439i	$-0.259290\pi$
$338$	2.25567	−	12.7925i	0.122692	−	0.695822i
$339$	−9.53385	−	3.47004i	−0.517808	−	0.188467i
$340$		0			0
$341$	25.0460			1.35632
$342$	−8.74633	+	31.0654i	−0.472947	+	1.67983i
$343$	−17.9290			−0.968076
$344$	5.42148	−	4.54916i	0.292307	−	0.245274i
$345$		0			0
$346$	2.32192	−	13.1682i	0.124827	−	0.707929i
$347$	−1.77470	−	10.0648i	−0.0952710	−	0.540308i	−0.994664	−	0.103168i	$-0.967102\pi$
$347$	−1.77470	−	10.0648i	−0.0952710	−	0.540308i	0.899393	−	0.437141i	$-0.144009\pi$
$348$	6.37859	−	2.32162i	0.341928	−	0.124452i
$349$	14.5918	−	25.2738i	0.781083	−	1.35288i	−0.150229	−	0.988651i	$-0.548001\pi$
$349$	14.5918	−	25.2738i	0.781083	−	1.35288i	0.931311	−	0.364224i	$-0.118666\pi$
$350$		0			0
$351$	1.09455	+	0.918436i	0.0584227	+	0.0490225i
$352$	−1.82207	−	1.52890i	−0.0971169	−	0.0814907i
$353$	−10.6172	−	18.3895i	−0.565095	−	0.978773i	−0.997041	−	0.0768738i	$-0.975506\pi$
$353$	−10.6172	−	18.3895i	−0.565095	−	0.978773i	0.431946	−	0.901900i	$-0.357827\pi$
$354$	−19.2221	+	33.2936i	−1.02164	+	1.76954i
$355$		0			0
$356$	1.34237	+	7.61299i	0.0711457	+	0.403487i
$357$	8.31585	−	47.1615i	0.440122	−	2.49605i
$358$	20.3431	+	7.40427i	1.07516	+	0.391328i
$359$	18.4389	−	15.4721i	0.973170	−	0.816586i	−0.00987517	−	0.999951i	$-0.503143\pi$
$359$	18.4389	−	15.4721i	0.973170	−	0.816586i	0.983045	+	0.183365i	$0.0586990\pi$
$360$		0			0
$361$	−16.2091	−	9.91295i	−0.853108	−	0.521734i
$362$	9.08845			0.477678
$363$	−13.2008	+	11.0767i	−0.692860	+	0.581378i
$364$	−0.257408	−	0.0936888i	−0.0134918	−	0.00491063i
$365$		0			0
$366$	0.0979260	+	0.555366i	0.00511867	+	0.0290294i
$367$	−18.1506	+	6.60629i	−0.947456	+	0.344846i	−0.769106	−	0.639121i	$-0.779298\pi$
$367$	−18.1506	+	6.60629i	−0.947456	+	0.344846i	−0.178350	+	0.983967i	$0.557076\pi$
$368$	−0.676702	+	1.17208i	−0.0352755	+	0.0610990i
$369$	13.0273	+	22.5640i	0.678176	+	1.17463i
$370$		0			0
$371$	−23.3128	−	19.5618i	−1.21034	−	1.01560i
$372$	−16.9823	−	29.4142i	−0.880491	−	1.52505i
$373$	−16.6405	+	28.8223i	−0.861615	+	1.49236i	0.00875464	+	0.999962i	$0.497213\pi$
$373$	−16.6405	+	28.8223i	−0.861615	+	1.49236i	−0.870370	+	0.492399i	$0.836120\pi$
$374$	12.1853	−	4.43508i	0.630086	−	0.229332i
$375$		0			0
$376$	−1.39052	+	7.88604i	−0.0717106	+	0.406691i
$377$	0.198912	+	0.0723982i	0.0102445	+	0.00372870i
$378$	−29.6345	+	24.8663i	−1.52424	+	1.27899i
$379$	17.9416			0.921600			0.460800	−	0.887504i	$-0.347563\pi$
$379$	17.9416			0.921600			0.460800	+	0.887504i	$0.347563\pi$
$380$		0			0
$381$	34.7420			1.77989
$382$	−5.32870	+	4.47131i	−0.272640	+	0.228772i
$383$	24.5918	+	8.95070i	1.25658	+	0.457359i	0.882621	−	0.470084i	$-0.155777\pi$
$383$	24.5918	+	8.95070i	1.25658	+	0.457359i	0.373963	+	0.927444i	$0.377999\pi$
$384$	−0.560106	+	3.17652i	−0.0285828	+	0.162101i
$385$		0			0
$386$	15.3524	−	5.58781i	0.781416	−	0.284412i
$387$	26.1999	−	45.3795i	1.33181	−	2.30677i
$388$	1.47664	+	2.55762i	0.0749653	+	0.129844i
$389$	12.5930	+	10.5668i	0.638492	+	0.535758i	0.903555	−	0.428473i	$-0.140948\pi$
$389$	12.5930	+	10.5668i	0.638492	+	0.535758i	−0.265063	+	0.964231i	$0.585393\pi$
$390$		0			0
$391$	−3.68922	−	6.38992i	−0.186572	−	0.323152i
$392$	0.208248	−	0.360697i	0.0105181	−	0.0182179i
$393$	13.1322	−	4.77974i	0.662433	−	0.241106i
$394$	0.499246	+	2.83137i	0.0251517	+	0.142642i
$395$		0			0
$396$	−16.5487	−	6.02322i	−0.831602	−	0.302678i
$397$	−7.56400	+	6.34695i	−0.379626	+	0.318544i	−0.812556	−	0.582884i	$-0.801924\pi$
$397$	−7.56400	+	6.34695i	−0.379626	+	0.318544i	0.432929	+	0.901428i	$0.357480\pi$
$398$	18.6336			0.934017
$399$	−15.7417	−	34.9036i	−0.788072	−	1.74736i
$400$		0			0
$401$	22.0410	−	18.4946i	1.10067	−	0.923574i	0.103202	−	0.994660i	$-0.467091\pi$
$401$	22.0410	−	18.4946i	1.10067	−	0.923574i	0.997470	+	0.0710864i	$0.0226466\pi$
$402$	−16.5224	−	6.01366i	−0.824062	−	0.299934i
$403$	0.183922	−	1.04307i	0.00916181	−	0.0519592i
$404$	1.48771	+	8.43723i	0.0740164	+	0.419768i
$405$		0			0
$406$	−2.86556	+	4.96329i	−0.142215	+	0.246324i
$407$	1.41204	+	2.44573i	0.0699922	+	0.121230i
$408$	−13.4707	−	11.3033i	−0.666901	−	0.559596i
$409$	19.6383	+	16.4785i	0.971052	+	0.814810i	0.982715	−	0.185122i	$-0.0592682\pi$
$409$	19.6383	+	16.4785i	0.971052	+	0.814810i	−0.0116633	+	0.999932i	$0.503713\pi$
$410$		0			0
$411$	11.6841	−	20.2374i	0.576333	−	0.998238i
$412$	−1.67344	+	0.609081i	−0.0824443	+	0.0300073i
$413$	−5.63639	−	31.9655i	−0.277348	−	1.57292i
$414$	−1.74005	+	9.86833i	−0.0855190	+	0.485002i
$415$		0			0
$416$	−0.0770532	+	0.0646553i	−0.00377784	+	0.00316999i
$417$	47.4668			2.32446
$418$	6.05364	−	8.41699i	0.296093	−	0.411689i
$419$	−33.3178			−1.62768			−0.813840	−	0.581090i	$-0.802627\pi$
$419$	−33.3178			−1.62768			−0.813840	+	0.581090i	$0.802627\pi$
$420$		0			0
$421$	0.609988	+	0.222018i	0.0297290	+	0.0108205i	0.356842	−	0.934165i	$-0.383854\pi$
$421$	0.609988	+	0.222018i	0.0297290	+	0.0108205i	−0.327113	+	0.944985i	$0.606076\pi$
$422$	0.773107	−	4.38451i	0.0376343	−	0.213435i
$423$	10.2954	+	58.3880i	0.500579	+	2.83892i
$424$	−10.5009	+	3.82202i	−0.509970	+	0.185614i
$425$		0			0
$426$	2.23795	+	3.87624i	0.108429	+	0.187804i
$427$	−0.364738	−	0.306052i	−0.0176509	−	0.0148109i
$428$	−6.50868	−	5.46143i	−0.314609	−	0.263988i
$429$	−0.385850	−	0.668312i	−0.0186290	−	0.0322664i
$430$		0			0
$431$	0.898248	−	0.326936i	0.0432671	−	0.0157479i	−0.320296	−	0.947318i	$-0.603782\pi$
$431$	0.898248	−	0.326936i	0.0432671	−	0.0157479i	0.363563	+	0.931570i	$0.381560\pi$
$432$	2.46669	+	13.9893i	0.118679	+	0.673061i
$433$	0.438254	−	2.48546i	0.0210611	−	0.119444i	−0.972465	−	0.233050i	$-0.925129\pi$
$433$	0.438254	−	2.48546i	0.0210611	−	0.119444i	0.993526	+	0.113607i	$0.0362404\pi$
$434$	26.9471	+	9.80794i	1.29350	+	0.470796i
$435$		0			0
$436$	−7.67335			−0.367487
$437$	−5.31468	−	2.56056i	−0.254236	−	0.122488i
$438$	−39.0175			−1.86433
$439$	−8.97963	+	7.53481i	−0.428575	+	0.359617i	−0.831414	−	0.555654i	$-0.812468\pi$
$439$	−8.97963	+	7.53481i	−0.428575	+	0.359617i	0.402839	+	0.915271i	$0.368023\pi$
$440$		0			0
$441$	0.535485	−	3.03689i	0.0254993	−	0.144614i
$442$	−0.0952236	−	0.540040i	−0.00452932	−	0.0256871i
$443$	17.9136	−	6.52000i	0.851099	−	0.309775i	0.120610	−	0.992700i	$-0.461515\pi$
$443$	17.9136	−	6.52000i	0.851099	−	0.309775i	0.730488	+	0.682925i	$0.239293\pi$
$444$	1.91485	−	3.31662i	0.0908747	−	0.157400i
$445$		0			0
$446$	14.1747	+	11.8940i	0.671190	+	0.563196i
$447$	−21.4663	−	18.0123i	−1.01532	−	0.851955i
$448$	−1.36166	−	2.35847i	−0.0643325	−	0.111427i
$449$	13.4465	−	23.2900i	0.634579	−	1.09912i	−0.352025	−	0.935991i	$-0.614507\pi$
$449$	13.4465	−	23.2900i	0.634579	−	1.09912i	0.986604	−	0.163133i	$-0.0521600\pi$
$450$		0			0
$451$	−1.45346	−	8.24297i	−0.0684407	−	0.388146i
$452$	0.546202	−	3.09766i	0.0256912	−	0.145702i
$453$	−24.9628	−	9.08571i	−1.17285	−	0.426884i
$454$	−1.15362	+	0.968002i	−0.0541421	+	0.0454306i
$455$		0			0
$456$	−13.9896	−	1.40235i	−0.655123	−	0.0656709i
$457$	−30.4123			−1.42263			−0.711313	−	0.702876i	$-0.751899\pi$
$457$	−30.4123			−1.42263			−0.711313	+	0.702876i	$0.751899\pi$
$458$	−7.36582	+	6.18066i	−0.344182	+	0.288803i
$459$	−72.7726	−	26.4871i	−3.39674	−	1.23631i
$460$		0			0
$461$	−1.02335	−	5.80373i	−0.0476623	−	0.270306i	0.951658	−	0.307158i	$-0.0993781\pi$
$461$	−1.02335	−	5.80373i	−0.0476623	−	0.270306i	−0.999321	+	0.0368519i	$0.988267\pi$
$462$	19.6335	−	7.14600i	0.913432	−	0.332462i
$463$	−16.2882	+	28.2119i	−0.756975	+	1.31112i	0.187412	+	0.982281i	$0.439990\pi$
$463$	−16.2882	+	28.2119i	−0.756975	+	1.31112i	−0.944387	+	0.328837i	$0.893343\pi$
$464$	1.05223	+	1.82251i	0.0488484	+	0.0846079i
$465$		0			0
$466$	−4.40500	−	3.69623i	−0.204058	−	0.171225i
$467$	3.11229	+	5.39065i	0.144020	+	0.249449i	0.929007	−	0.370063i	$-0.120664\pi$
$467$	3.11229	+	5.39065i	0.144020	+	0.249449i	−0.784987	+	0.619512i	$0.787330\pi$
$468$	−0.372368	+	0.644960i	−0.0172127	+	0.0298133i
$469$	13.9499	−	5.07737i	0.644149	−	0.234451i
$470$		0			0
$471$	6.57081	−	37.2649i	0.302767	−	1.71708i
$472$	−11.2000	−	4.07646i	−0.515520	−	0.187634i
$473$	−12.8953	+	10.8204i	−0.592924	+	0.497523i
$474$	−12.0653			−0.554176
$475$		0			0
$476$	14.8469			0.680508
$477$	−63.3813	+	53.1832i	−2.90203	+	2.43509i
$478$	−16.3912	−	5.96592i	−0.749718	−	0.272875i
$479$	−0.252128	+	1.42989i	−0.0115200	+	0.0653334i	−0.990026	−	0.140886i	$-0.955005\pi$
$479$	−0.252128	+	1.42989i	−0.0115200	+	0.0653334i	0.978506	+	0.206219i	$0.0661160\pi$
$480$		0			0
$481$	0.112224	−	0.0408464i	0.00511699	−	0.00186243i
$482$	7.60128	−	13.1658i	0.346229	−	0.599686i
$483$	−5.94424	−	10.2957i	−0.270472	−	0.468472i
$484$	−4.09260	−	3.43410i	−0.186027	−	0.156095i
$485$		0			0
$486$	16.7647	+	29.0372i	0.760461	+	1.31716i
$487$	−11.3216	+	19.6095i	−0.513029	+	0.888593i	0.486856	+	0.873482i	$0.338144\pi$
$487$	−11.3216	+	19.6095i	−0.513029	+	0.888593i	−0.999886	+	0.0151111i	$0.995190\pi$
$488$	−0.164291	+	0.0597970i	−0.00743710	+	0.00270688i
$489$	−11.0121	−	62.4528i	−0.497985	−	2.82421i
$490$		0			0
$491$	5.70304	+	2.07574i	0.257375	+	0.0936767i	0.467485	−	0.884001i	$-0.345160\pi$
$491$	5.70304	+	2.07574i	0.257375	+	0.0936767i	−0.210110	+	0.977678i	$0.567382\pi$
$492$	−8.69509	+	7.29604i	−0.392005	+	0.328931i
$493$	−11.4730			−0.516718
$494$	−0.306082	−	0.313921i	−0.0137713	−	0.0141240i
$495$		0			0
$496$	8.06641	−	6.76853i	0.362193	−	0.303916i
$497$	−3.55112	−	1.29250i	−0.159289	−	0.0579766i
$498$	−5.04214	+	28.5954i	−0.225944	+	1.28139i
$499$	0.998143	+	5.66075i	0.0446830	+	0.253410i	0.998964	−	0.0454999i	$-0.0144881\pi$
$499$	0.998143	+	5.66075i	0.0446830	+	0.253410i	−0.954281	+	0.298910i	$0.903377\pi$
$500$		0			0
$501$	27.0699	−	46.8864i	1.20939	−	2.09473i
$502$	1.10178	+	1.90834i	0.0491748	+	0.0851733i
$503$	−8.87376	−	7.44597i	−0.395661	−	0.331999i	0.423152	−	0.906059i	$-0.360923\pi$
$503$	−8.87376	−	7.44597i	−0.395661	−	0.331999i	−0.818814	+	0.574059i	$0.805368\pi$
$504$	−15.4461	−	12.9608i	−0.688023	−	0.577320i
$505$		0			0
$506$	1.60957	−	2.78785i	0.0715540	−	0.123935i
$507$	39.3723	−	14.3303i	1.74859	−	0.636433i
$508$	1.87036	+	10.6073i	0.0829839	+	0.470625i
$509$	−5.74516	+	32.5824i	−0.254650	+	1.44419i	0.542321	+	0.840171i	$0.317546\pi$
$509$	−5.74516	+	32.5824i	−0.254650	+	1.44419i	−0.796971	+	0.604018i	$0.793565\pi$
$510$		0			0
$511$	25.2356	−	21.1752i	1.11636	−	0.936735i
$512$	−1.00000			−0.0441942
$513$	−60.0066	+	15.2684i	−2.64936	+	0.674115i
$514$	11.4930			0.506934
$515$		0			0
$516$	21.4511	+	7.80756i	0.944331	+	0.343709i
$517$	3.30742	−	18.7573i	0.145460	−	0.824946i
$518$	0.561480	+	3.18431i	0.0246700	+	0.139911i
$519$	40.5286	−	14.7512i	1.77901	−	0.647506i
$520$		0			0
$521$	4.23276	+	7.33136i	0.185441	+	0.321193i	0.943725	−	0.330731i	$-0.107295\pi$
$521$	4.23276	+	7.33136i	0.185441	+	0.321193i	−0.758284	+	0.651924i	$0.773962\pi$
$522$	11.9360	+	10.0155i	0.522424	+	0.438366i
$523$	3.35434	+	2.81463i	0.146675	+	0.123075i	0.713173	−	0.700988i	$-0.247258\pi$
$523$	3.35434	+	2.81463i	0.146675	+	0.123075i	−0.566498	+	0.824063i	$0.691702\pi$
$524$	2.16632	+	3.75218i	0.0946361	+	0.163915i
$525$		0			0
$526$	−16.7936	+	6.11237i	−0.732236	+	0.266512i
$527$	9.96860	+	56.5348i	0.434239	+	2.46269i
$528$	1.33224	−	7.55550i	0.0579782	−	0.328811i
$529$	19.8917	+	7.23998i	0.864856	+	0.314782i
$530$		0			0
$531$	−88.2462			−3.82956
$532$	9.80920	−	6.68528i	0.425283	−	0.289844i
$533$	−0.353962			−0.0153318
$534$	−19.1011	+	16.0277i	−0.826583	+	0.693586i
$535$		0			0
$536$	0.946580	−	5.36832i	0.0408861	−	0.231876i
$537$	12.1255	+	68.7672i	0.523255	+	2.96753i
$538$	−0.485375	+	0.176662i	−0.0209260	+	0.00761644i
$539$	−0.495329	+	0.857935i	−0.0213353	+	0.0369539i
$540$		0			0
$541$	−11.8358	−	9.93142i	−0.508861	−	0.426985i	0.351867	−	0.936050i	$-0.385547\pi$
$541$	−11.8358	−	9.93142i	−0.508861	−	0.426985i	−0.860728	+	0.509065i	$0.829991\pi$
$542$	17.5961	+	14.7649i	0.755817	+	0.634206i
$543$	14.6575	+	25.3875i	0.629013	+	1.08948i
$544$	2.72588	−	4.72137i	0.116871	−	0.202427i
$545$		0			0
$546$	−0.153429	−	0.870136i	−0.00656614	−	0.0372384i
$547$	−0.467667	+	2.65227i	−0.0199960	+	0.113403i	−0.993172	−	0.116659i	$-0.962782\pi$
$547$	−0.467667	+	2.65227i	−0.0199960	+	0.113403i	0.973176	+	0.230062i	$0.0738928\pi$
$548$	6.80786	+	2.47786i	0.290817	+	0.105849i
$549$	−0.991624	+	0.832071i	−0.0423215	+	0.0355119i
$550$		0			0
$551$	−7.58008	+	5.16606i	−0.322922	+	0.220082i
$552$	−4.36543			−0.185805
$553$	7.80352	−	6.54793i	0.331839	−	0.278446i
$554$	9.49926	+	3.45745i	0.403585	+	0.146893i
$555$		0			0
$556$	2.55541	+	14.4924i	0.108373	+	0.614616i
$557$	−18.0263	+	6.56103i	−0.763798	+	0.278000i	−0.694400	−	0.719589i	$-0.744330\pi$
$557$	−18.0263	+	6.56103i	−0.763798	+	0.278000i	−0.0693982	+	0.997589i	$0.522108\pi$
$558$	38.9818	−	67.5184i	1.65023	−	2.85828i
$559$	0.355935	+	0.616497i	0.0150544	+	0.0260751i
$560$		0			0
$561$	32.0408	+	26.8854i	1.35276	+	1.13510i
$562$	−14.4432	−	25.0163i	−0.609248	−	1.05525i
$563$	−11.2236	+	19.4398i	−0.473016	+	0.819289i	−0.999523	−	0.0308825i	$-0.990168\pi$
$563$	−11.2236	+	19.4398i	−0.473016	+	0.819289i	0.526507	+	0.850171i	$0.323502\pi$
$564$	−24.2713	+	8.83403i	−1.02201	+	0.371980i
$565$		0			0
$566$	2.13017	−	12.0808i	0.0895378	−	0.507794i
$567$	−60.4123	−	21.9883i	−2.53708	−	0.923420i
$568$	−1.06300	+	0.891964i	−0.0446026	+	0.0374260i
$569$	−25.7630			−1.08004			−0.540020	−	0.841652i	$-0.681583\pi$
$569$	−25.7630			−1.08004			−0.540020	+	0.841652i	$0.681583\pi$
$570$		0			0
$571$	22.1970			0.928914			0.464457	−	0.885596i	$-0.346250\pi$
$571$	22.1970			0.928914			0.464457	+	0.885596i	$0.346250\pi$
$572$	0.183275	−	0.153786i	0.00766311	−	0.00643011i
$573$	−21.0840	−	7.67395i	−0.880797	−	0.320584i
$574$	1.66414	−	9.43781i	0.0694599	−	0.393926i
$575$		0			0
$576$	−6.95746	+	2.53231i	−0.289894	+	0.105513i
$577$	−11.5629	+	20.0275i	−0.481370	+	0.833758i	−0.999771	−	0.0213798i	$-0.993194\pi$
$577$	−11.5629	+	20.0275i	−0.481370	+	0.833758i	0.518401	+	0.855138i	$0.326527\pi$
$578$	6.36090	+	11.0174i	0.264578	+	0.458263i
$579$	40.3686	+	33.8733i	1.67766	+	1.40773i
$580$		0			0
$581$	−12.2578	−	21.2312i	−0.508541	−	0.880819i
$582$	−4.76295	+	8.24966i	−0.197430	+	0.341960i
$583$	24.9770	−	9.09087i	1.03444	−	0.376505i
$584$	−2.10054	−	11.9127i	−0.0869209	−	0.492953i
$585$		0			0
$586$	1.71981	+	0.625960i	0.0710448	+	0.0258582i
$587$	26.9830	−	22.6414i	1.11371	−	0.934512i	0.115438	−	0.993315i	$-0.463173\pi$
$587$	26.9830	−	22.6414i	1.11371	−	0.934512i	0.998270	+	0.0588030i	$0.0187284\pi$
$588$	1.34342			0.0554017
$589$	32.0426	+	32.8632i	1.32029	+	1.35410i
$590$		0			0
$591$	−7.10392	+	5.96090i	−0.292216	+	0.245199i
$592$	1.11571	+	0.406085i	0.0458553	+	0.0166900i
$593$	−3.60643	+	20.4531i	−0.148098	+	0.839908i	0.816728	+	0.577022i	$0.195785\pi$
$593$	−3.60643	+	20.4531i	−0.148098	+	0.839908i	−0.964827	+	0.262886i	$0.915326\pi$
$594$	−5.86715	−	33.2743i	−0.240732	−	1.36526i
$595$		0			0
$596$	4.34383	−	7.52374i	0.177930	−	0.308184i
$597$	30.0515	+	52.0507i	1.22993	+	2.13029i
$598$	−0.104284	−	0.0875048i	−0.00426449	−	0.00357834i
$599$	−2.03068	−	1.70394i	−0.0829713	−	0.0696212i	0.600359	−	0.799731i	$-0.295024\pi$
$599$	−2.03068	−	1.70394i	−0.0829713	−	0.0696212i	−0.683330	+	0.730110i	$0.739469\pi$
$600$		0			0
$601$	−7.70749	+	13.3498i	−0.314395	+	0.544548i	−0.979309	−	0.202372i	$-0.935135\pi$
$601$	−7.70749	+	13.3498i	−0.314395	+	0.544548i	0.664914	+	0.746920i	$0.268468\pi$
$602$	−18.1113	+	6.59197i	−0.738160	+	0.268668i
$603$	−7.00846	−	39.7470i	−0.285407	−	1.61862i
$604$	1.43014	−	8.11071i	0.0581914	−	0.330020i
$605$		0			0
$606$	−21.1691	+	17.7630i	−0.859935	+	0.721571i
$607$	30.5539			1.24015			0.620073	−	0.784544i	$-0.287103\pi$
$607$	30.5539			1.24015			0.620073	+	0.784544i	$0.287103\pi$
$608$	−0.324980	−	4.34677i	−0.0131797	−	0.176285i
$609$	−18.4858			−0.749083
$610$		0			0
$611$	−0.756885	−	0.275484i	−0.0306203	−	0.0111449i
$612$	7.00927	−	39.7515i	0.283333	−	1.60686i
$613$	0.724114	+	4.10666i	0.0292467	+	0.165866i	0.995933	−	0.0900982i	$-0.0287181\pi$
$613$	0.724114	+	4.10666i	0.0292467	+	0.165866i	−0.966686	+	0.255964i	$0.917607\pi$
$614$	1.36877	−	0.498191i	0.0552390	−	0.0201053i
$615$		0			0
$616$	3.23878	+	5.60973i	0.130494	+	0.226023i
$617$	12.5821	+	10.5577i	0.506538	+	0.425036i	0.859909	−	0.510447i	$-0.170520\pi$
$617$	12.5821	+	10.5577i	0.506538	+	0.425036i	−0.353371	+	0.935483i	$0.614965\pi$
$618$	−4.40025	−	3.69225i	−0.177004	−	0.148524i
$619$	−3.76167	−	6.51540i	−0.151194	−	0.261876i	0.780473	−	0.625190i	$-0.214979\pi$
$619$	−3.76167	−	6.51540i	−0.151194	−	0.261876i	−0.931667	+	0.363314i	$0.881645\pi$
$620$		0			0
$621$	−18.0658	+	6.57542i	−0.724957	+	0.263863i
$622$	−3.42117	−	19.4024i	−0.137176	−	0.777965i
$623$	3.65572	−	20.7326i	0.146463	−	0.830635i
$624$	−0.304875	−	0.110966i	−0.0122048	−	0.00444218i
$625$		0			0
$626$	−8.75295			−0.349838
$627$	33.2750	+	3.33555i	1.32887	+	0.133209i
$628$	11.7314			0.468133
$629$	−4.95857	+	4.16073i	−0.197711	+	0.165899i
$630$		0			0
$631$	−5.83962	+	33.1181i	−0.232472	+	1.31841i	0.615402	+	0.788214i	$0.288994\pi$
$631$	−5.83962	+	33.1181i	−0.232472	+	1.31841i	−0.847873	+	0.530199i	$0.822117\pi$
$632$	−0.649542	−	3.68373i	−0.0258374	−	0.146531i
$633$	13.4944	−	4.91158i	0.536356	−	0.195218i
$634$	−3.93958	+	6.82356i	−0.156461	+	0.270998i
$635$		0			0
$636$	−27.6118	−	23.1691i	−1.09488	−	0.918714i
$637$	0.0320924	+	0.0269287i	0.00127155	+	0.00106696i
$638$	−2.50277	−	4.33493i	−0.0990857	−	0.171622i
$639$	−5.13706	+	8.89766i	−0.203219	+	0.351986i
$640$		0			0
$641$	−0.0427768	−	0.242599i	−0.00168958	−	0.00958210i	0.983951	−	0.178437i	$-0.0571041\pi$
$641$	−0.0427768	−	0.242599i	−0.00168958	−	0.00958210i	−0.985641	+	0.168855i	$0.945993\pi$
$642$	4.75892	−	26.9892i	0.187820	−	1.06518i
$643$	−14.0111	−	5.09961i	−0.552542	−	0.201109i	0.0506335	−	0.998717i	$-0.483876\pi$
$643$	−14.0111	−	5.09961i	−0.552542	−	0.201109i	−0.603176	+	0.797608i	$0.706098\pi$
$644$	2.82345	−	2.36916i	0.111260	−	0.0933580i
$645$		0			0
$646$	21.4086	+	10.3144i	0.842308	+	0.405816i
$647$	28.3920			1.11620			0.558101	−	0.829773i	$-0.311530\pi$
$647$	28.3920			1.11620			0.558101	+	0.829773i	$0.311530\pi$
$648$	−18.0840	+	15.1743i	−0.710405	+	0.596101i
$649$	26.6397	+	9.69605i	1.04570	+	0.380603i
$650$		0			0
$651$	16.0619	+	91.0913i	0.629514	+	3.57015i
$652$	18.4751	−	6.72438i	0.723540	−	0.263347i
$653$	−14.1587	+	24.5237i	−0.554074	+	0.959685i	0.443901	+	0.896076i	$0.353594\pi$
$653$	−14.1587	+	24.5237i	−0.554074	+	0.959685i	−0.997975	+	0.0636088i	$0.979739\pi$
$654$	−12.3753	−	21.4346i	−0.483911	−	0.838159i
$655$		0			0
$656$	−2.69572	−	2.26197i	−0.105250	−	0.0883153i
$657$	−44.7812	−	77.5632i	−1.74708	−	3.02603i
$658$	10.9038	−	18.8859i	0.425073	−	0.736249i
$659$	36.0245	−	13.1118i	1.40331	−	0.510765i	0.474154	−	0.880442i	$-0.342754\pi$
$659$	36.0245	−	13.1118i	1.40331	−	0.510765i	0.929160	+	0.369677i	$0.120532\pi$
$660$		0			0
$661$	−4.12371	+	23.3867i	−0.160394	+	0.909637i	0.793294	+	0.608839i	$0.208364\pi$
$661$	−4.12371	+	23.3867i	−0.160394	+	0.909637i	−0.953688	+	0.300799i	$0.902747\pi$
$662$	−22.4143	−	8.15815i	−0.871158	−	0.317075i
$663$	1.35496	−	1.13695i	0.0526225	−	0.0441555i
$664$	−9.00212			−0.349350
$665$		0			0
$666$	8.79083			0.340638
$667$	−2.18183	+	1.83077i	−0.0844807	+	0.0708878i
$668$	15.7726	+	5.74075i	0.610259	+	0.222116i
$669$	−10.3640	+	58.7774i	−0.400697	+	2.27247i
$670$		0			0
$671$	0.390774	−	0.142230i	0.0150857	−	0.00549074i
$672$	4.39207	−	7.60729i	0.169428	−	0.293457i
$673$	−15.5006	−	26.8478i	−0.597504	−	1.03491i	−0.993188	−	0.116521i	$-0.962826\pi$
$673$	−15.5006	−	26.8478i	−0.597504	−	1.03491i	0.395684	−	0.918387i	$-0.370508\pi$
$674$	16.7975	+	14.0948i	0.647015	+	0.542910i
$675$		0			0
$676$	6.49494	+	11.2496i	0.249805	+	0.432676i
$677$	0.919318	−	1.59230i	0.0353322	−	0.0611972i	−0.847819	−	0.530286i	$-0.822084\pi$
$677$	0.919318	−	1.59230i	0.0353322	−	0.0611972i	0.883151	+	0.469089i	$0.155418\pi$
$678$	9.53385	−	3.47004i	0.366145	−	0.133266i
$679$	−1.39661	−	7.92058i	−0.0535970	−	0.303964i
$680$		0			0
$681$	−4.56451	−	1.66135i	−0.174912	−	0.0636629i
$682$	−19.1864	+	16.0993i	−0.734684	+	0.616473i
$683$	19.0534			0.729059			0.364530	−	0.931192i	$-0.381230\pi$
$683$	19.0534			0.729059			0.364530	+	0.931192i	$0.381230\pi$
$684$	−13.2684	−	29.4195i	−0.507330	−	1.12488i
$685$		0			0
$686$	13.7344	−	11.5245i	0.524383	−	0.440009i
$687$	−29.1442	−	10.6076i	−1.11192	−	0.404706i
$688$	−1.22895	+	6.96972i	−0.0468533	+	0.265718i
$689$	−0.195186	−	1.10696i	−0.00743600	−	0.0421716i
$690$		0			0
$691$	12.6346	−	21.8838i	0.480643	−	0.832499i	−0.519110	−	0.854708i	$-0.673736\pi$
$691$	12.6346	−	21.8838i	0.480643	−	0.832499i	0.999753	+	0.0222086i	$0.00706979\pi$
$692$	6.68569	+	11.5800i	0.254152	+	0.440204i
$693$	36.7393	+	30.8279i	1.39561	+	1.17106i
$694$	7.82905	+	6.56935i	0.297187	+	0.249369i
$695$		0			0
$696$	−3.39398	+	5.87854i	−0.128648	+	0.222826i
$697$	18.0278	−	6.56160i	0.682853	−	0.248538i
$698$	5.06769	+	28.7403i	0.191815	+	1.08784i
$699$	3.22078	−	18.2660i	0.121821	−	0.690883i
$700$		0			0
$701$	−12.7045	+	10.6603i	−0.479841	+	0.402635i	−0.850369	−	0.526187i	$-0.823621\pi$
$701$	−12.7045	+	10.6603i	−0.479841	+	0.402635i	0.370528	+	0.928821i	$0.379177\pi$
$702$	−1.42883			−0.0539278
$703$	−1.40257	+	4.98169i	−0.0528991	+	0.187888i
$704$	2.37855			0.0896449
$705$		0			0
$706$	19.9538	+	7.26257i	0.750970	+	0.273331i
$707$	4.05152	−	22.9773i	0.152373	−	0.864151i
$708$	−6.67576	−	37.8601i	−0.250891	−	1.42287i
$709$	−27.5288	+	10.0197i	−1.03386	+	0.376296i	−0.802551	−	0.596583i	$-0.796525\pi$
$709$	−27.5288	+	10.0197i	−1.03386	+	0.376296i	−0.231314	+	0.972879i	$0.574302\pi$
$710$		0			0
$711$	−13.8475	−	23.9846i	−0.519323	−	0.899493i
$712$	−5.92185	−	4.96902i	−0.221931	−	0.186222i
$713$	10.9171	+	9.16055i	0.408849	+	0.343065i
$714$	23.9445	+	41.4732i	0.896102	+	1.55209i
$715$		0			0
$716$	−20.3431	+	7.40427i	−0.760256	+	0.276710i
$717$	−9.77003	−	55.4086i	−0.364868	−	2.06927i
$718$	−4.17977	+	23.7046i	−0.155988	+	0.884649i
$719$	5.87107	+	2.13690i	0.218954	+	0.0796928i	0.449168	−	0.893447i	$-0.351720\pi$
$719$	5.87107	+	2.13690i	0.218954	+	0.0796928i	−0.230214	+	0.973140i	$0.573943\pi$
$720$		0			0
$721$	4.84979			0.180616
$722$	18.7888	−	2.82522i	0.699246	−	0.105144i
$723$	49.0362			1.82368
$724$	−6.96216	+	5.84194i	−0.258747	+	0.217114i
$725$		0			0
$726$	2.99237	−	16.9706i	0.111057	−	0.629836i
$727$	5.05158	+	28.6489i	0.187353	+	1.06253i	0.922895	+	0.385051i	$0.125816\pi$
$727$	5.05158	+	28.6489i	0.187353	+	1.06253i	−0.735543	+	0.677479i	$0.763073\pi$
$728$	0.257408	−	0.0936888i	0.00954017	−	0.00347234i
$729$	−18.6643	+	32.3276i	−0.691271	+	1.19732i
$730$		0			0
$731$	−29.5567	−	24.8010i	−1.09319	−	0.917297i
$732$	−0.431998	−	0.362489i	−0.0159671	−	0.0133980i
$733$	−23.6849	−	41.0234i	−0.874821	−	1.51523i	−0.856953	−	0.515394i	$-0.827646\pi$
$733$	−23.6849	−	41.0234i	−0.874821	−	1.51523i	−0.0178674	−	0.999840i	$-0.505688\pi$
$734$	9.65775	−	16.7277i	0.356474	−	0.617431i
$735$		0			0
$736$	−0.235016	−	1.33284i	−0.00866281	−	0.0491292i
$737$	−2.25149	+	12.7688i	−0.0829346	+	0.470346i
$738$	−24.4834	−	8.91122i	−0.901245	−	0.328026i
$739$	−6.34777	+	5.32642i	−0.233507	+	0.195935i	−0.752031	−	0.659127i	$-0.770926\pi$
$739$	−6.34777	+	5.32642i	−0.233507	+	0.195935i	0.518525	+	0.855063i	$0.326481\pi$
$740$		0			0
$741$	0.383263	−	1.36128i	0.0140795	−	0.0500080i
$742$	30.4328			1.11722
$743$	−4.45699	+	3.73986i	−0.163511	+	0.137202i	−0.720872	−	0.693068i	$-0.756258\pi$
$743$	−4.45699	+	3.73986i	−0.163511	+	0.137202i	0.557361	+	0.830270i	$0.311814\pi$
$744$	31.9163	+	11.6166i	1.17011	+	0.425884i
$745$		0			0
$746$	−5.77920	−	32.7755i	−0.211592	−	1.20000i
$747$	−62.6319	+	22.7961i	−2.29158	+	0.834067i
$748$	−6.48365	+	11.2300i	−0.237066	+	0.410610i
$749$	11.5693	+	20.0387i	0.422734	+	0.732197i
$750$		0			0
$751$	14.5050	+	12.1712i	0.529296	+	0.444132i	0.867858	−	0.496812i	$-0.165496\pi$
$751$	14.5050	+	12.1712i	0.529296	+	0.444132i	−0.338562	+	0.940944i	$0.609941\pi$
$752$	−4.00385	−	6.93486i	−0.146005	−	0.252888i
$753$	−3.55381	+	6.15538i	−0.129508	+	0.224315i
$754$	−0.198912	+	0.0723982i	−0.00724396	+	0.00263659i
$755$		0			0
$756$	6.71760	−	38.0974i	0.244317	−	1.38559i
$757$	14.1638	+	5.15520i	0.514792	+	0.187369i	0.586335	−	0.810069i	$-0.300570\pi$
$757$	14.1638	+	5.15520i	0.514792	+	0.187369i	−0.0715433	+	0.997437i	$0.522792\pi$
$758$	−13.7441	+	11.5327i	−0.499208	+	0.418885i
$759$	10.3834			0.376893
$760$		0			0
$761$	−6.63681			−0.240584			−0.120292	−	0.992739i	$-0.538383\pi$
$761$	−6.63681			−0.240584			−0.120292	+	0.992739i	$0.538383\pi$
$762$	−26.6139	+	22.3317i	−0.964121	+	0.808994i
$763$	19.6368	+	7.14720i	0.710899	+	0.258746i
$764$	1.20792	−	6.85045i	0.0437010	−	0.247841i
$765$		0			0
$766$	−24.5918	+	8.95070i	−0.888539	+	0.323402i
$767$	0.599429	−	1.03824i	0.0216441	−	0.0374887i
$768$	−1.61276	−	2.79338i	−0.0581955	−	0.100797i
$769$	−24.9327	−	20.9210i	−0.899095	−	0.754430i	0.0709184	−	0.997482i	$-0.477407\pi$
$769$	−24.9327	−	20.9210i	−0.899095	−	0.754430i	−0.970013	+	0.243052i	$0.921851\pi$
$770$		0			0
$771$	18.5354	+	32.1043i	0.667537	+	1.15621i
$772$	−8.16884	+	14.1488i	−0.294003	+	0.509228i
$773$	0.612613	−	0.222973i	0.0220342	−	0.00801978i	−0.330980	−	0.943638i	$-0.607379\pi$
$773$	0.612613	−	0.222973i	0.0220342	−	0.00801978i	0.353014	+	0.935618i	$0.385157\pi$
$774$	9.09911	+	51.6036i	0.327061	+	1.85485i
$775$		0			0
$776$	−2.77518	−	1.01008i	−0.0996233	−	0.0362599i
$777$	−7.98947	+	6.70396i	−0.286621	+	0.240503i
$778$	−16.4390			−0.589368
$779$	8.95623	−	12.4527i	0.320890	−	0.446166i
$780$		0			0
$781$	2.52840	−	2.12158i	0.0904733	−	0.0759161i
$782$	6.93347	+	2.52358i	0.247940	+	0.0902429i
$783$	−5.19104	+	29.4398i	−0.185513	+	1.05209i
$784$	0.0723239	+	0.410169i	0.00258300	+	0.0146489i
$785$		0			0
$786$	−6.98751	+	12.1027i	−0.249236	+	0.431690i
$787$	6.32936	+	10.9628i	0.225617	+	0.390781i	0.956504	−	0.291718i	$-0.0942267\pi$
$787$	6.32936	+	10.9628i	0.225617	+	0.390781i	−0.730887	+	0.682498i	$0.760893\pi$
$788$	−2.20241	−	1.84804i	−0.0784577	−	0.0658338i
$789$	−44.1583	−	37.0532i	−1.57208	−	1.31913i
$790$		0			0
$791$	−4.28304	+	7.41844i	−0.152287	+	0.263769i
$792$	16.5487	−	6.02322i	0.588031	−	0.214026i
$793$	−0.00305376	−	0.0173187i	−0.000108442	−	0.000615006i
$794$	1.71462	−	9.72409i	0.0608496	−	0.345095i
$795$		0			0
$796$	−14.2742	+	11.9774i	−0.505934	+	0.424529i
$797$	−47.2820			−1.67482			−0.837408	−	0.546578i	$-0.815930\pi$
$797$	−47.2820			−1.67482			−0.837408	+	0.546578i	$0.815930\pi$
$798$	34.4944	+	16.6191i	1.22109	+	0.588309i
$799$	43.6561			1.54444
$800$		0			0
$801$	−53.7842	−	19.5758i	−1.90037	−	0.691678i
$802$	−4.99628	+	28.3353i	−0.176425	+	1.00055i
$803$	4.99623	+	28.3350i	0.176313	+	0.999922i
$804$	16.5224	−	6.01366i	0.582700	−	0.212085i
$805$		0			0
$806$	0.529582	+	0.917263i	0.0186537	+	0.0323092i
$807$	−1.27628	−	1.07092i	−0.0449271	−	0.0376983i
$808$	−6.56300	−	5.50701i	−0.230885	−	0.193736i
$809$	−24.1710	−	41.8655i	−0.849809	−	1.47191i	−0.881379	−	0.472410i	$-0.843384\pi$
$809$	−24.1710	−	41.8655i	−0.849809	−	1.47191i	0.0315702	−	0.999502i	$-0.489949\pi$
$810$		0			0
$811$	34.8288	−	12.6766i	1.22300	−	0.445137i	0.351808	−	0.936072i	$-0.385567\pi$
$811$	34.8288	−	12.6766i	1.22300	−	0.445137i	0.871196	+	0.490935i	$0.163345\pi$
$812$	−0.995197	−	5.64404i	−0.0349246	−	0.198067i
$813$	−12.8657	+	72.9649i	−0.451219	+	2.55899i
$814$	−2.65377	−	0.965892i	−0.0930145	−	0.0338545i
$815$		0			0
$816$	17.5848			0.615591
$817$	−30.6951	−	3.07694i	−1.07389	−	0.107649i
$818$	−25.6360			−0.896342
$819$	1.55366	−	1.30367i	0.0542892	−	0.0455540i
$820$		0			0
$821$	−4.86215	+	27.5746i	−0.169690	+	0.962362i	0.774405	+	0.632690i	$0.218049\pi$
$821$	−4.86215	+	27.5746i	−0.169690	+	0.962362i	−0.944096	+	0.329672i	$0.893062\pi$
$822$	4.05784	+	23.0131i	0.141533	+	0.802675i
$823$	7.12142	−	2.59198i	0.248237	−	0.0903509i	−0.214905	−	0.976635i	$-0.568944\pi$
$823$	7.12142	−	2.59198i	0.248237	−	0.0903509i	0.463142	+	0.886284i	$0.346722\pi$
$824$	0.890417	−	1.54225i	0.0310191	−	0.0537267i
$825$		0			0
$826$	24.8648	+	20.8640i	0.865156	+	0.725952i
$827$	−26.6363	−	22.3505i	−0.926236	−	0.777204i	0.0489016	−	0.998804i	$-0.484428\pi$
$827$	−26.6363	−	22.3505i	−0.926236	−	0.777204i	−0.975138	+	0.221599i	$0.928872\pi$
$828$	−5.01028	−	8.67807i	−0.174119	−	0.301584i
$829$	9.63690	−	16.6916i	0.334703	−	0.579723i	−0.648724	−	0.761023i	$-0.724697\pi$
$829$	9.63690	−	16.6916i	0.334703	−	0.579723i	0.983428	+	0.181300i	$0.0580306\pi$
$830$		0			0
$831$	5.66206	+	32.1111i	0.196415	+	1.11392i
$832$	0.0174665	−	0.0990577i	0.000605544	−	0.00343421i
$833$	−2.13371	−	0.776606i	−0.0739286	−	0.0269078i
$834$	−36.3617	+	30.5111i	−1.25910	+	1.05651i
$835$		0			0
$836$	0.772980	+	10.3390i	0.0267341	+	0.357582i
$837$	149.579			5.17021
$838$	25.5229	−	21.4162i	0.881674	−	0.739812i
$839$	−28.6196	−	10.4167i	−0.988059	−	0.359624i	−0.203091	−	0.979160i	$-0.565099\pi$
$839$	−28.6196	−	10.4167i	−0.988059	−	0.359624i	−0.784969	+	0.619536i	$0.787321\pi$
$840$		0			0
$841$	−4.26676	−	24.1980i	−0.147130	−	0.834413i
$842$	−0.609988	+	0.222018i	−0.0210216	+	0.00765123i
$843$	46.5867	−	80.6906i	1.60453	−	2.77913i
$844$	2.22607	+	3.85567i	0.0766246	+	0.132718i
$845$		0			0
$846$	−45.4178	−	38.1101i	−1.56150	−	1.31025i
$847$	7.27469	+	12.6001i	0.249961	+	0.432946i
$848$	5.58743	−	9.67771i	0.191873	−	0.332334i
$849$	37.1818	−	13.5331i	1.27607	−	0.464453i
$850$		0			0
$851$	−0.279037	+	1.58250i	−0.00956528	+	0.0542474i
$852$	−4.20596	−	1.53085i	−0.144094	−	0.0524459i
$853$	42.4989	−	35.6608i	1.45513	−	1.22100i	0.526411	−	0.850230i	$-0.323537\pi$
$853$	42.4989	−	35.6608i	1.45513	−	1.22100i	0.928723	−	0.370773i	$-0.120907\pi$
$854$	0.476132			0.0162929
$855$		0			0
$856$	8.49647			0.290403
$857$	40.4823	−	33.9686i	1.38285	−	1.16035i	0.414702	−	0.909957i	$-0.363886\pi$
$857$	40.4823	−	33.9686i	1.38285	−	1.16035i	0.968145	−	0.250390i	$-0.0805588\pi$
$858$	0.725161	+	0.263937i	0.0247566	+	0.00901066i
$859$	−0.271832	+	1.54164i	−0.00927480	+	0.0526000i	−0.989094	−	0.147286i	$-0.952946\pi$
$859$	−0.271832	+	1.54164i	−0.00927480	+	0.0526000i	0.979819	+	0.199886i	$0.0640573\pi$
$860$		0			0
$861$	29.0473	−	10.5723i	0.989928	−	0.360304i
$862$	−0.477948	+	0.827830i	−0.0162790	+	0.0281960i
$863$	−27.3298	−	47.3366i	−0.930318	−	1.61136i	−0.782778	−	0.622301i	$-0.786198\pi$
$863$	−27.3298	−	47.3366i	−0.930318	−	1.61136i	−0.147540	−	0.989056i	$-0.547135\pi$
$864$	−10.8817	−	9.13087i	−0.370205	−	0.310639i
$865$		0			0
$866$	1.26190	+	2.18568i	0.0428812	+	0.0742724i
$867$	−20.5172	+	35.5368i	−0.696800	+	1.20689i
$868$	−26.9471	+	9.80794i	−0.914644	+	0.332903i
$869$	1.54497	+	8.76194i	0.0524094	+	0.297229i
$870$		0			0
$871$	0.515240	+	0.187532i	0.0174583	+	0.00635429i
$872$	5.87813	−	4.93233i	0.199059	−	0.167030i
$873$	−21.8661			−0.740055
$874$	5.71718	−	1.45471i	0.193387	−	0.0492062i
$875$		0			0
$876$	29.8892	−	25.0800i	1.00986	−	0.847375i
$877$	−30.1850	−	10.9865i	−1.01928	−	0.370986i	−0.222288	−	0.974981i	$-0.571353\pi$
$877$	−30.1850	−	10.9865i	−1.01928	−	0.370986i	−0.796988	+	0.603995i	$0.793575\pi$
$878$	2.03552	−	11.5440i	0.0686954	−	0.389591i
$879$	1.02510	+	5.81362i	0.0345757	+	0.196088i
$880$		0			0
$881$	−12.5921	+	21.8102i	−0.424239	+	0.734804i	−0.996349	−	0.0853728i	$-0.972792\pi$
$881$	−12.5921	+	21.8102i	−0.424239	+	0.734804i	0.572110	+	0.820177i	$0.306125\pi$
$882$	1.54187	+	2.67059i	0.0519174	+	0.0899235i
$883$	19.4168	+	16.2926i	0.653426	+	0.548290i	0.908108	−	0.418735i	$-0.137526\pi$
$883$	19.4168	+	16.2926i	0.653426	+	0.548290i	−0.254682	+	0.967025i	$0.581971\pi$
$884$	0.420076	+	0.352486i	0.0141287	+	0.0118554i
$885$		0			0
$886$	−9.53160	+	16.5092i	−0.320220	+	0.554638i
$887$	37.9087	−	13.7977i	1.27285	−	0.463280i	0.384790	−	0.923004i	$-0.374274\pi$
$887$	37.9087	−	13.7977i	1.27285	−	0.463280i	0.888062	+	0.459724i	$0.152052\pi$
$888$	0.665020	+	3.77152i	0.0223166	+	0.126564i
$889$	5.09360	−	28.8873i	0.170834	−	0.968847i
$890$		0			0
$891$	43.0136	−	36.0927i	1.44101	−	1.20915i
$892$	−18.5037			−0.619551
$893$	28.8431	−	19.6575i	0.965197	−	0.657812i
$894$	28.0222			0.937204
$895$		0			0
$896$	2.55909	+	0.931432i	0.0854931	+	0.0311170i
$897$	0.0762490	−	0.432429i	0.00254588	−	0.0144384i
$898$	4.66992	+	26.4844i	0.155837	+	0.883797i
$899$	20.8234	−	7.57910i	0.694499	−	0.252777i
$900$		0			0
$901$	30.4614	+	52.7606i	1.01482	+	1.75771i
$902$	6.41189	+	5.38022i	0.213493	+	0.179142i
$903$	−47.6230	−	39.9605i	−1.58479	−	1.32980i
$904$	1.57272	+	2.72404i	0.0523080	+	0.0906002i
$905$		0			0
$906$	24.9628	−	9.08571i	0.829332	−	0.301852i
$907$	−3.16525	−	17.9510i	−0.105100	−	0.596053i	−0.991180	−	0.132521i	$-0.957693\pi$
$907$	−3.16525	−	17.9510i	−0.105100	−	0.596053i	0.886080	−	0.463532i	$-0.153418\pi$
$908$	0.261504	−	1.48307i	0.00867833	−	0.0492172i
$909$	−59.6073	−	21.6953i	−1.97705	−	0.719587i
$910$		0			0
$911$	31.5891			1.04659			0.523297	−	0.852150i	$-0.324702\pi$
$911$	31.5891			1.04659			0.523297	+	0.852150i	$0.324702\pi$
$912$	11.6181	−	7.91808i	0.384713	−	0.262194i
$913$	21.4120			0.708633
$914$	23.2971	−	19.5486i	0.770601	−	0.646611i
$915$		0			0
$916$	1.66970	−	9.46931i	0.0551683	−	0.312875i
$917$	−2.04891	−	11.6199i	−0.0676609	−	0.383724i
$918$	72.7726	−	26.4871i	2.40185	−	0.874204i
$919$	−15.8297	+	27.4179i	−0.522174	+	0.904432i	0.477493	+	0.878636i	$0.341546\pi$
$919$	−15.8297	+	27.4179i	−0.522174	+	0.904432i	−0.999667	+	0.0257967i	$0.991788\pi$
$920$		0			0
$921$	3.59913	+	3.02003i	0.118595	+	0.0995134i
$922$	4.51450	+	3.78811i	0.148677	+	0.124755i
$923$	−0.0697890	−	0.120878i	−0.00229713	−	0.00397875i
$924$	−10.4467	+	18.0943i	−0.343673	+	0.595259i
$925$		0			0
$926$	−5.65682	−	32.0814i	−0.185895	−	1.05426i
$927$	2.28960	−	12.9849i	0.0752002	−	0.426481i
$928$	−1.97754	−	0.719766i	−0.0649159	−	0.0236275i
$929$	−17.2986	+	14.5152i	−0.567548	+	0.476229i	−0.880831	−	0.473430i	$-0.843016\pi$
$929$	−17.2986	+	14.5152i	−0.567548	+	0.476229i	0.313283	+	0.949660i	$0.398571\pi$
$930$		0			0
$931$	−1.75941	+	0.447672i	−0.0576622	+	0.0146719i
$932$	5.75032			0.188358
$933$	48.6808	−	40.8480i	1.59374	−	1.33730i
$934$	−5.84919	−	2.12893i	−0.191391	−	0.0696608i
$935$		0			0
$936$	−0.129322	−	0.733421i	−0.00422702	−	0.0239726i
$937$	29.1391	−	10.6058i	0.951932	−	0.346475i	0.181065	−	0.983471i	$-0.442045\pi$
$937$	29.1391	−	10.6058i	0.951932	−	0.346475i	0.770867	+	0.636996i	$0.219823\pi$
$938$	−7.42261	+	12.8563i	−0.242357	+	0.419774i
$939$	−14.1164	−	24.4503i	−0.460671	−	0.797906i
$940$		0			0
$941$	−1.60557	−	1.34723i	−0.0523401	−	0.0439186i	0.616242	−	0.787557i	$-0.288654\pi$
$941$	−1.60557	−	1.34723i	−0.0523401	−	0.0439186i	−0.668582	+	0.743638i	$0.733099\pi$
$942$	18.9199	+	32.7702i	0.616443	+	1.06771i
$943$	2.38132	−	4.12457i	0.0775464	−	0.134314i
$944$	11.2000	−	4.07646i	0.364528	−	0.132677i
$945$		0			0
$946$	2.92312	−	16.5778i	0.0950387	−	0.538991i
$947$	−16.5253	−	6.01473i	−0.537001	−	0.195453i	0.0592604	−	0.998243i	$-0.481126\pi$
$947$	−16.5253	−	6.01473i	−0.537001	−	0.195453i	−0.596262	+	0.802790i	$0.703348\pi$
$948$	9.24252	−	7.75540i	0.300183	−	0.251884i
$949$	1.21674			0.0394970
$950$		0			0
$951$	−25.4144			−0.824118
$952$	−11.3734	+	9.54343i	−0.368614	+	0.309304i
$953$	10.4716	+	3.81135i	0.339208	+	0.123462i	0.506007	−	0.862529i	$-0.331121\pi$
$953$	10.4716	+	3.81135i	0.339208	+	0.123462i	−0.166799	+	0.985991i	$0.553343\pi$
$954$	14.3674	−	81.4814i	0.465161	−	2.63806i
$955$		0			0
$956$	16.3912	−	5.96592i	0.530130	−	0.192952i
$957$	8.07274	−	13.9824i	0.260955	−	0.451987i
$958$	−0.725975	−	1.25743i	−0.0234552	−	0.0406256i
$959$	−15.1139	−	12.6821i	−0.488055	−	0.409527i
$960$		0			0
$961$	−39.9400	−	69.1781i	−1.28839	−	2.23155i
$962$	−0.0597134	+	0.103427i	−0.00192524	+	0.00333461i
$963$	59.1139	−	21.5157i	1.90492	−	0.693334i
$964$	2.63990	+	14.9716i	0.0850254	+	0.482203i
$965$		0			0
$966$	11.1715	+	4.06610i	0.359438	+	0.130825i
$967$	28.4207	−	23.8478i	0.913950	−	0.766895i	−0.0589166	−	0.998263i	$-0.518765\pi$
$967$	28.4207	−	23.8478i	0.913950	−	0.766895i	0.972866	+	0.231368i	$0.0743202\pi$
$968$	5.34251			0.171715
$969$	5.71470	+	76.4370i	0.183583	+	2.45551i
$970$		0			0
$971$	7.90649	−	6.63434i	0.253731	−	0.212906i	−0.507046	−	0.861919i	$-0.669262\pi$
$971$	7.90649	−	6.63434i	0.253731	−	0.212906i	0.760777	+	0.649013i	$0.224818\pi$
$972$	−31.5073	−	11.4677i	−1.01060	−	0.367827i
$973$	6.95921	−	39.4676i	0.223102	−	1.26527i
$974$	−3.93194	−	22.2991i	−0.125988	−	0.714511i
$975$		0			0
$976$	0.0874174	−	0.151411i	0.00279816	−	0.00484656i
$977$	−17.3817	−	30.1060i	−0.556089	−	0.963175i	−0.997818	−	0.0660264i	$-0.978968\pi$
$977$	−17.3817	−	30.1060i	−0.556089	−	0.963175i	0.441728	−	0.897149i	$-0.354365\pi$
$978$	48.5796	+	40.7632i	1.55341	+	1.30346i
$979$	14.0854	+	11.8191i	0.450172	+	0.377739i
$980$		0			0
$981$	28.4067	−	49.2018i	0.906955	−	1.57089i
$982$	−5.70304	+	2.07574i	−0.181991	+	0.0662395i
$983$	6.82528	+	38.7081i	0.217693	+	1.23460i	0.876173	+	0.481998i	$0.160089\pi$
$983$	6.82528	+	38.7081i	0.217693	+	1.23460i	−0.658480	+	0.752598i	$0.728800\pi$
$984$	1.97102	−	11.1782i	0.0628337	−	0.356348i
$985$		0			0
$986$	8.78883	−	7.37470i	0.279893	−	0.234858i
$987$	70.3407			2.23897
$988$	0.436257	+	0.0437313i	0.0138792	+	0.00139128i
$989$	−9.57836			−0.304574
$990$		0			0
$991$	−15.3142	−	5.57390i	−0.486470	−	0.177061i	0.0871286	−	0.996197i	$-0.472231\pi$
$991$	−15.3142	−	5.57390i	−0.486470	−	0.177061i	−0.573599	+	0.819136i	$0.694453\pi$
$992$	−1.82851	+	10.3700i	−0.0580552	+	0.329247i
$993$	−13.3601	−	75.7689i	−0.423970	−	2.40445i
$994$	3.55112	−	1.29250i	0.112635	−	0.0409957i
$995$		0			0
$996$	−14.5183	−	25.1464i	−0.460028	−	0.796793i
$997$	−7.22006	−	6.05835i	−0.228662	−	0.191870i	0.521257	−	0.853399i	$-0.325463\pi$
$997$	−7.22006	−	6.05835i	−0.228662	−	0.191870i	−0.749919	+	0.661530i	$0.769908\pi$
$998$	−4.40328	−	3.69479i	−0.139383	−	0.116957i
$999$	8.43295	+	14.6063i	0.266807	+	0.462123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.l.101.1		30
5.2	odd	4		190.2.p.a.139.1	✓	60
5.3	odd	4		190.2.p.a.139.10	yes	60
5.4	even	2		950.2.l.m.101.5		30
19.16	even	9	inner	950.2.l.l.301.1		30
95.54	even	18		950.2.l.m.301.5		30
95.73	odd	36		190.2.p.a.149.1	yes	60
95.92	odd	36		190.2.p.a.149.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.139.1	✓	60	5.2	odd	4
190.2.p.a.139.10	yes	60	5.3	odd	4
190.2.p.a.149.1	yes	60	95.73	odd	36
190.2.p.a.149.10	yes	60	95.92	odd	36
950.2.l.l.101.1		30	1.1	even	1	trivial
950.2.l.l.301.1		30	19.16	even	9	inner
950.2.l.m.101.5		30	5.4	even	2
950.2.l.m.301.5		30	95.54	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-3.03100 - 1.10319i) q^{3} +(0.173648 - 0.984808i) q^{4} +(3.03100 - 1.10319i) q^{6} +(-1.36166 + 2.35847i) q^{7} +(0.500000 + 0.866025i) q^{8} +(5.67178 + 4.75918i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-3.03100 - 1.10319i) q^{3} +(0.173648 - 0.984808i) q^{4} +(3.03100 - 1.10319i) q^{6} +(-1.36166 + 2.35847i) q^{7} +(0.500000 + 0.866025i) q^{8} +(5.67178 + 4.75918i) q^{9} +(-1.18927 - 2.05988i) q^{11} +(-1.61276 + 2.79338i) q^{12} +(-0.0945198 + 0.0344024i) q^{13} +(-0.472900 - 2.68195i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(4.17630 - 3.50433i) q^{17} -7.40398 q^{18} +(1.18130 - 4.19577i) q^{19} +(6.72904 - 5.64633i) q^{21} +(2.23510 + 0.813512i) q^{22} +(0.235016 - 1.33284i) q^{23} +(-0.560106 - 3.17652i) q^{24} +(0.0502929 - 0.0871099i) q^{26} +(-7.10256 - 12.3020i) q^{27} +(2.08619 + 1.75052i) q^{28} +(-1.61211 - 1.35272i) q^{29} +(-5.26498 + 9.11921i) q^{31} +(0.939693 - 0.342020i) q^{32} +(1.33224 + 7.55550i) q^{33} +(-0.946690 + 5.36895i) q^{34} +(5.67178 - 4.75918i) q^{36} -1.18731 q^{37} +(1.79206 + 3.97348i) q^{38} +0.324442 q^{39} +(3.30679 + 1.20357i) q^{41} +(-1.52535 + 8.65069i) q^{42} +(-1.22895 - 6.96972i) q^{43} +(-2.23510 + 0.813512i) q^{44} +(0.676702 + 1.17208i) q^{46} +(6.13425 + 5.14725i) q^{47} +(2.47089 + 2.07332i) q^{48} +(-0.208248 - 0.360697i) q^{49} +(-16.5243 + 6.01435i) q^{51} +(0.0174665 + 0.0990577i) q^{52} +(-1.94049 + 11.0051i) q^{53} +(13.3484 + 4.85844i) q^{54} -2.72332 q^{56} +(-8.20927 + 11.4142i) q^{57} +2.10445 q^{58} +(-9.13030 + 7.66123i) q^{59} +(-0.0303598 + 0.172179i) q^{61} +(-1.82851 - 10.3700i) q^{62} +(-18.9474 + 6.89630i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.87714 - 4.93150i) q^{66} +(-4.17582 - 3.50393i) q^{67} +(-2.72588 - 4.72137i) q^{68} +(-2.18272 + 3.78057i) q^{69} +(0.240963 + 1.36657i) q^{71} +(-1.28569 + 7.29149i) q^{72} +(-11.3670 - 4.13725i) q^{73} +(0.909534 - 0.763190i) q^{74} +(-3.92690 - 1.89194i) q^{76} +6.47756 q^{77} +(-0.248537 + 0.208547i) q^{78} +(-3.51498 - 1.27935i) q^{79} +(4.09930 + 23.2483i) q^{81} +(-3.30679 + 1.20357i) q^{82} +(-4.50106 + 7.79606i) q^{83} +(-4.39207 - 7.60729i) q^{84} +(5.42148 + 4.54916i) q^{86} +(3.39398 + 5.87854i) q^{87} +(1.18927 - 2.05988i) q^{88} +(-7.26423 + 2.64396i) q^{89} +(0.0475671 - 0.269766i) q^{91} +(-1.27178 - 0.462891i) q^{92} +(26.0184 - 21.8320i) q^{93} -8.00769 q^{94} -3.22552 q^{96} +(-2.26235 + 1.89834i) q^{97} +(0.391379 + 0.142450i) q^{98} +(3.05807 - 17.3432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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