LMFDB - Embedded newform 930.2.k.a.433.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.k (of order $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.6
Character	$\chi$	$=$	930.433
Dual form			930.2.k.a.247.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.06824 + 1.96440i) q^{5} +1.00000i q^{6} +(-1.05833 + 1.05833i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.06824 + 1.96440i) q^{5} +1.00000i q^{6} +(-1.05833 + 1.05833i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-2.14440 - 0.633681i) q^{10} +5.04212i q^{11} +(-0.707107 - 0.707107i) q^{12} +(-4.63173 + 4.63173i) q^{13} -1.49670i q^{14} +(2.14440 + 0.633681i) q^{15} -1.00000 q^{16} +(-2.53121 - 2.53121i) q^{17} +(0.707107 + 0.707107i) q^{18} -7.83439i q^{19} +(1.96440 - 1.06824i) q^{20} +1.49670i q^{21} +(-3.56532 - 3.56532i) q^{22} +(-2.05623 + 2.05623i) q^{23} +1.00000 q^{24} +(-2.71773 + 4.19690i) q^{25} -6.55026i q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.05833 + 1.05833i) q^{28} -3.01575 q^{29} +(-1.96440 + 1.06824i) q^{30} +(-5.11803 - 2.19222i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.56532 + 3.56532i) q^{33} +3.57968 q^{34} +(-3.20952 - 0.948429i) q^{35} -1.00000 q^{36} +(2.29070 + 2.29070i) q^{37} +(5.53975 + 5.53975i) q^{38} +6.55026i q^{39} +(-0.633681 + 2.14440i) q^{40} +2.23428 q^{41} +(-1.05833 - 1.05833i) q^{42} +(-4.87703 + 4.87703i) q^{43} +5.04212 q^{44} +(1.96440 - 1.06824i) q^{45} -2.90795i q^{46} +(5.72583 - 5.72583i) q^{47} +(-0.707107 + 0.707107i) q^{48} +4.75989i q^{49} +(-1.04593 - 4.88938i) q^{50} -3.57968 q^{51} +(4.63173 + 4.63173i) q^{52} +(5.97851 - 5.97851i) q^{53} +1.00000 q^{54} +(-9.90473 + 5.38619i) q^{55} -1.49670 q^{56} +(-5.53975 - 5.53975i) q^{57} +(2.13246 - 2.13246i) q^{58} +5.06330i q^{59} +(0.633681 - 2.14440i) q^{60} +4.63816i q^{61} +(5.16912 - 2.06886i) q^{62} +(1.05833 + 1.05833i) q^{63} +1.00000i q^{64} +(-14.0464 - 4.15078i) q^{65} -5.04212 q^{66} +(-5.44255 + 5.44255i) q^{67} +(-2.53121 + 2.53121i) q^{68} +2.90795i q^{69} +(2.94011 - 1.59883i) q^{70} +15.4412 q^{71} +(0.707107 - 0.707107i) q^{72} +(-5.66109 + 5.66109i) q^{73} -3.23955 q^{74} +(1.04593 + 4.88938i) q^{75} -7.83439 q^{76} +(-5.33620 - 5.33620i) q^{77} +(-4.63173 - 4.63173i) q^{78} +12.7043 q^{79} +(-1.06824 - 1.96440i) q^{80} -1.00000 q^{81} +(-1.57987 + 1.57987i) q^{82} +(-8.45297 + 8.45297i) q^{83} +1.49670 q^{84} +(2.26837 - 7.67626i) q^{85} -6.89717i q^{86} +(-2.13246 + 2.13246i) q^{87} +(-3.56532 + 3.56532i) q^{88} -2.92224 q^{89} +(-0.633681 + 2.14440i) q^{90} -9.80376i q^{91} +(2.05623 + 2.05623i) q^{92} +(-5.16912 + 2.06886i) q^{93} +8.09754i q^{94} +(15.3899 - 8.36900i) q^{95} -1.00000i q^{96} +(-7.21512 + 7.21512i) q^{97} +(-3.36575 - 3.36575i) q^{98} +5.04212 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	1.06824	+	1.96440i	0.477731	+	0.878506i
$5$	1.06824	+	1.96440i	0.477731	+	0.878506i
$6$			1.00000i			0.408248i
$7$	−1.05833	+	1.05833i	−0.400009	+	0.400009i	−0.878236	−	0.478227i	$-0.841280\pi$
$7$	−1.05833	+	1.05833i	−0.400009	+	0.400009i	0.478227	+	0.878236i	$0.341280\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−2.14440	−	0.633681i	−0.678119	−	0.200388i
$11$			5.04212i			1.52026i	0.649774	+	0.760128i	$0.274864\pi$
$11$			5.04212i			1.52026i	−0.649774	+	0.760128i	$0.725136\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−4.63173	+	4.63173i	−1.28461	+	1.28461i	−0.346598	+	0.938014i	$0.612663\pi$
$13$	−4.63173	+	4.63173i	−1.28461	+	1.28461i	−0.938014	+	0.346598i	$0.887337\pi$
$14$		−	1.49670i		−	0.400009i
$15$	2.14440	+	0.633681i	0.553682	+	0.163616i
$16$	−1.00000			−0.250000
$17$	−2.53121	−	2.53121i	−0.613910	−	0.613910i	0.330053	−	0.943962i	$-0.392933\pi$
$17$	−2.53121	−	2.53121i	−0.613910	−	0.613910i	−0.943962	+	0.330053i	$0.892933\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$		−	7.83439i		−	1.79733i	−0.438634	−	0.898666i	$-0.644537\pi$
$19$		−	7.83439i		−	1.79733i	0.438634	−	0.898666i	$-0.355463\pi$
$20$	1.96440	−	1.06824i	0.439253	−	0.238866i
$21$			1.49670i			0.326606i
$22$	−3.56532	−	3.56532i	−0.760128	−	0.760128i
$23$	−2.05623	+	2.05623i	−0.428755	+	0.428755i	−0.888204	−	0.459449i	$-0.848047\pi$
$23$	−2.05623	+	2.05623i	−0.428755	+	0.428755i	0.459449	+	0.888204i	$0.348047\pi$
$24$	1.00000			0.204124
$25$	−2.71773	+	4.19690i	−0.543546	+	0.839379i
$26$		−	6.55026i		−	1.28461i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.05833	+	1.05833i	0.200005	+	0.200005i
$29$	−3.01575			−0.560010			−0.280005	−	0.959999i	$-0.590336\pi$
$29$	−3.01575			−0.560010			−0.280005	+	0.959999i	$0.590336\pi$
$30$	−1.96440	+	1.06824i	−0.358649	+	0.195033i
$31$	−5.11803	−	2.19222i	−0.919224	−	0.393734i
$31$	−5.11803	−	2.19222i	−0.919224	−	0.393734i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.56532	+	3.56532i	0.620642	+	0.620642i
$34$	3.57968			0.613910
$35$	−3.20952	−	0.948429i	−0.542508	−	0.160314i
$36$	−1.00000			−0.166667
$37$	2.29070	+	2.29070i	0.376590	+	0.376590i	0.869870	−	0.493281i	$-0.164202\pi$
$37$	2.29070	+	2.29070i	0.376590	+	0.376590i	−0.493281	+	0.869870i	$0.664202\pi$
$38$	5.53975	+	5.53975i	0.898666	+	0.898666i
$39$			6.55026i			1.04888i
$40$	−0.633681	+	2.14440i	−0.100194	+	0.339059i
$41$	2.23428			0.348935			0.174468	−	0.984663i	$-0.444180\pi$
$41$	2.23428			0.348935			0.174468	+	0.984663i	$0.444180\pi$
$42$	−1.05833	−	1.05833i	−0.163303	−	0.163303i
$43$	−4.87703	+	4.87703i	−0.743741	+	0.743741i	−0.973296	−	0.229555i	$-0.926273\pi$
$43$	−4.87703	+	4.87703i	−0.743741	+	0.743741i	0.229555	+	0.973296i	$0.426273\pi$
$44$	5.04212			0.760128
$45$	1.96440	−	1.06824i	0.292835	−	0.159244i
$46$		−	2.90795i		−	0.428755i
$47$	5.72583	−	5.72583i	0.835198	−	0.835198i	−0.153024	−	0.988222i	$-0.548901\pi$
$47$	5.72583	−	5.72583i	0.835198	−	0.835198i	0.988222	+	0.153024i	$0.0489013\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			4.75989i			0.679985i
$50$	−1.04593	−	4.88938i	−0.147917	−	0.691463i
$51$	−3.57968			−0.501255
$52$	4.63173	+	4.63173i	0.642306	+	0.642306i
$53$	5.97851	−	5.97851i	0.821212	−	0.821212i	−0.165070	−	0.986282i	$-0.552785\pi$
$53$	5.97851	−	5.97851i	0.821212	−	0.821212i	0.986282	+	0.165070i	$0.0527850\pi$
$54$	1.00000			0.136083
$55$	−9.90473	+	5.38619i	−1.33555	+	0.726273i
$56$	−1.49670			−0.200005
$57$	−5.53975	−	5.53975i	−0.733758	−	0.733758i
$58$	2.13246	−	2.13246i	0.280005	−	0.280005i
$59$			5.06330i			0.659186i	0.944123	+	0.329593i	$0.106912\pi$
$59$			5.06330i			0.659186i	−0.944123	+	0.329593i	$0.893088\pi$
$60$	0.633681	−	2.14440i	0.0818079	−	0.276841i
$61$			4.63816i			0.593855i	0.954900	+	0.296928i	$0.0959620\pi$
$61$			4.63816i			0.593855i	−0.954900	+	0.296928i	$0.904038\pi$
$62$	5.16912	−	2.06886i	0.656479	−	0.262745i
$63$	1.05833	+	1.05833i	0.133336	+	0.133336i
$64$			1.00000i			0.125000i
$65$	−14.0464	−	4.15078i	−1.74224	−	0.514840i
$66$	−5.04212			−0.620642
$67$	−5.44255	+	5.44255i	−0.664913	+	0.664913i	−0.956534	−	0.291621i	$-0.905805\pi$
$67$	−5.44255	+	5.44255i	−0.664913	+	0.664913i	0.291621	+	0.956534i	$0.405805\pi$
$68$	−2.53121	+	2.53121i	−0.306955	+	0.306955i
$69$			2.90795i			0.350077i
$70$	2.94011	−	1.59883i	0.351411	−	0.191097i
$71$	15.4412			1.83253			0.916266	−	0.400570i	$-0.131188\pi$
$71$	15.4412			1.83253			0.916266	+	0.400570i	$0.131188\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−5.66109	+	5.66109i	−0.662580	+	0.662580i	−0.955988	−	0.293407i	$-0.905211\pi$
$73$	−5.66109	+	5.66109i	−0.662580	+	0.662580i	0.293407	+	0.955988i	$0.405211\pi$
$74$	−3.23955			−0.376590
$75$	1.04593	+	4.88938i	0.120773	+	0.564577i
$76$	−7.83439			−0.898666
$77$	−5.33620	−	5.33620i	−0.608117	−	0.608117i
$78$	−4.63173	−	4.63173i	−0.524440	−	0.524440i
$79$	12.7043			1.42935			0.714673	−	0.699458i	$-0.246575\pi$
$79$	12.7043			1.42935			0.714673	+	0.699458i	$0.246575\pi$
$80$	−1.06824	−	1.96440i	−0.119433	−	0.219627i
$81$	−1.00000			−0.111111
$82$	−1.57987	+	1.57987i	−0.174468	+	0.174468i
$83$	−8.45297	+	8.45297i	−0.927834	+	0.927834i	−0.997566	−	0.0697314i	$-0.977786\pi$
$83$	−8.45297	+	8.45297i	−0.927834	+	0.927834i	0.0697314	+	0.997566i	$0.477786\pi$
$84$	1.49670			0.163303
$85$	2.26837	−	7.67626i	0.246040	−	0.832607i
$86$		−	6.89717i		−	0.743741i
$87$	−2.13246	+	2.13246i	−0.228623	+	0.228623i
$88$	−3.56532	+	3.56532i	−0.380064	+	0.380064i
$89$	−2.92224			−0.309757			−0.154878	−	0.987934i	$-0.549499\pi$
$89$	−2.92224			−0.309757			−0.154878	+	0.987934i	$0.549499\pi$
$90$	−0.633681	+	2.14440i	−0.0667959	+	0.226040i
$91$		−	9.80376i		−	1.02771i
$92$	2.05623	+	2.05623i	0.214377	+	0.214377i
$93$	−5.16912	+	2.06886i	−0.536013	+	0.214531i
$94$			8.09754i			0.835198i
$95$	15.3899	−	8.36900i	1.57897	−	0.858641i
$96$		−	1.00000i		−	0.102062i
$97$	−7.21512	+	7.21512i	−0.732584	+	0.732584i	−0.971131	−	0.238547i	$-0.923329\pi$
$97$	−7.21512	+	7.21512i	−0.732584	+	0.732584i	0.238547	+	0.971131i	$0.423329\pi$
$98$	−3.36575	−	3.36575i	−0.339992	−	0.339992i
$99$	5.04212			0.506752
$100$	4.19690	+	2.71773i	0.419690	+	0.271773i
$101$	−8.30366			−0.826245			−0.413123	−	0.910675i	$-0.635562\pi$
$101$	−8.30366			−0.826245			−0.413123	+	0.910675i	$0.635562\pi$
$102$	2.53121	−	2.53121i	0.250628	−	0.250628i
$103$	11.0318	+	11.0318i	1.08700	+	1.08700i	0.995836	+	0.0911602i	$0.0290575\pi$
$103$	11.0318	+	11.0318i	1.08700	+	1.08700i	0.0911602	+	0.995836i	$0.470942\pi$
$104$	−6.55026			−0.642306
$105$	−2.94011	+	1.59883i	−0.286926	+	0.156030i
$106$			8.45489i			0.821212i
$107$	1.51957	−	1.51957i	0.146903	−	0.146903i	−0.629830	−	0.776733i	$-0.716875\pi$
$107$	1.51957	−	1.51957i	0.146903	−	0.146903i	0.776733	+	0.629830i	$0.216875\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$		−	10.4479i		−	1.00073i	−0.865815	−	0.500364i	$-0.833200\pi$
$109$		−	10.4479i		−	1.00073i	0.865815	−	0.500364i	$-0.166800\pi$
$110$	3.19509	−	10.8123i	0.304640	−	1.03091i
$111$	3.23955			0.307484
$112$	1.05833	−	1.05833i	0.100002	−	0.100002i
$113$	14.5661	+	14.5661i	1.37026	+	1.37026i	0.860046	+	0.510216i	$0.170435\pi$
$113$	14.5661	+	14.5661i	1.37026	+	1.37026i	0.510216	+	0.860046i	$0.329565\pi$
$114$	7.83439			0.733758
$115$	−6.23582	−	1.84272i	−0.581493	−	0.171834i
$116$			3.01575i			0.280005i
$117$	4.63173	+	4.63173i	0.428204	+	0.428204i
$118$	−3.58030	−	3.58030i	−0.329593	−	0.329593i
$119$	5.35770			0.491139
$120$	1.06824	+	1.96440i	0.0975164	+	0.179324i
$121$	−14.4230			−1.31118
$122$	−3.27967	−	3.27967i	−0.296928	−	0.296928i
$123$	1.57987	−	1.57987i	0.142452	−	0.142452i
$124$	−2.19222	+	5.11803i	−0.196867	+	0.459612i
$125$	−11.1476	−	0.855419i	−0.997069	−	0.0765110i
$126$	−1.49670			−0.133336
$127$	−2.15923	−	2.15923i	−0.191601	−	0.191601i	0.604787	−	0.796387i	$-0.293258\pi$
$127$	−2.15923	−	2.15923i	−0.191601	−	0.191601i	−0.796387	+	0.604787i	$0.793258\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$			6.89717i			0.607262i
$130$	12.8673	−	6.99724i	1.12854	−	0.613699i
$131$	0.0930152			0.00812678			0.00406339	−	0.999992i	$-0.498707\pi$
$131$	0.0930152			0.00812678			0.00406339	+	0.999992i	$0.498707\pi$
$132$	3.56532	−	3.56532i	0.310321	−	0.310321i
$133$	8.29133	+	8.29133i	0.718950	+	0.718950i
$134$		−	7.69692i		−	0.664913i
$135$	0.633681	−	2.14440i	0.0545386	−	0.184561i
$136$		−	3.57968i		−	0.306955i
$137$	−4.24973	−	4.24973i	−0.363079	−	0.363079i	0.501866	−	0.864945i	$-0.332647\pi$
$137$	−4.24973	−	4.24973i	−0.363079	−	0.363079i	−0.864945	+	0.501866i	$0.832647\pi$
$138$	−2.05623	−	2.05623i	−0.175038	−	0.175038i
$139$	4.79836			0.406991			0.203496	−	0.979076i	$-0.434770\pi$
$139$	4.79836			0.406991			0.203496	+	0.979076i	$0.434770\pi$
$140$	−0.948429	+	3.20952i	−0.0801569	+	0.271254i
$141$		−	8.09754i		−	0.681936i
$142$	−10.9186	+	10.9186i	−0.916266	+	0.916266i
$143$	−23.3537	−	23.3537i	−1.95294	−	1.95294i
$144$			1.00000i			0.0833333i
$145$	−3.22154	−	5.92413i	−0.267534	−	0.491972i
$146$		−	8.00599i		−	0.662580i
$147$	3.36575	+	3.36575i	0.277603	+	0.277603i
$148$	2.29070	−	2.29070i	0.188295	−	0.188295i
$149$		−	11.4909i		−	0.941373i	−0.882301	−	0.470686i	$-0.844006\pi$
$149$		−	11.4909i		−	0.941373i	0.882301	−	0.470686i	$-0.155994\pi$
$150$	−4.19690	−	2.71773i	−0.342675	−	0.221902i
$151$		−	6.44191i		−	0.524235i	−0.965036	−	0.262118i	$-0.915579\pi$
$151$		−	6.44191i		−	0.524235i	0.965036	−	0.262118i	$-0.0844209\pi$
$152$	5.53975	−	5.53975i	0.449333	−	0.449333i
$153$	−2.53121	+	2.53121i	−0.204637	+	0.204637i
$154$	7.54653			0.608117
$155$	−1.16088	−	12.3957i	−0.0932444	−	0.995643i
$156$	6.55026			0.524440
$157$	−3.09948	+	3.09948i	−0.247366	+	0.247366i	−0.819889	−	0.572523i	$-0.805965\pi$
$157$	−3.09948	+	3.09948i	−0.247366	+	0.247366i	0.572523	+	0.819889i	$0.305965\pi$
$158$	−8.98330	+	8.98330i	−0.714673	+	0.714673i
$159$		−	8.45489i		−	0.670517i
$160$	2.14440	+	0.633681i	0.169530	+	0.0500969i
$161$		−	4.35233i		−	0.343012i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−2.01708	−	2.01708i	−0.157990	−	0.157990i	0.623686	−	0.781675i	$-0.285635\pi$
$163$	−2.01708	−	2.01708i	−0.157990	−	0.157990i	−0.781675	+	0.623686i	$0.785635\pi$
$164$		−	2.23428i		−	0.174468i
$165$	−3.19509	+	10.8123i	−0.248738	+	0.841737i
$166$		−	11.9543i		−	0.927834i
$167$	16.2544	+	16.2544i	1.25780	+	1.25780i	0.952139	+	0.305666i	$0.0988791\pi$
$167$	16.2544	+	16.2544i	1.25780	+	1.25780i	0.305666	+	0.952139i	$0.401121\pi$
$168$	−1.05833	+	1.05833i	−0.0816516	+	0.0816516i
$169$		−	29.9059i		−	2.30045i
$170$	3.82395	+	7.03192i	0.293284	+	0.539323i
$171$	−7.83439			−0.599111
$172$	4.87703	+	4.87703i	0.371870	+	0.371870i
$173$	0.524672	+	0.524672i	0.0398901	+	0.0398901i	0.726770	−	0.686880i	$-0.241020\pi$
$173$	0.524672	+	0.524672i	0.0398901	+	0.0398901i	−0.686880	+	0.726770i	$0.741020\pi$
$174$		−	3.01575i		−	0.228623i
$175$	−1.56544	−	7.31792i	−0.118336	−	0.553183i
$176$		−	5.04212i		−	0.380064i
$177$	3.58030	+	3.58030i	0.269112	+	0.269112i
$178$	2.06634	−	2.06634i	0.154878	−	0.154878i
$179$	2.87084			0.214577			0.107288	−	0.994228i	$-0.465783\pi$
$179$	2.87084			0.214577			0.107288	+	0.994228i	$0.465783\pi$
$180$	−1.06824	−	1.96440i	−0.0796218	−	0.146418i
$181$			25.7303i			1.91252i	0.292526	+	0.956258i	$0.405504\pi$
$181$			25.7303i			1.91252i	−0.292526	+	0.956258i	$0.594496\pi$
$182$	6.93231	+	6.93231i	0.513857	+	0.513857i
$183$	3.27967	+	3.27967i	0.242440	+	0.242440i
$184$	−2.90795			−0.214377
$185$	−2.05284	+	6.94688i	−0.150928	+	0.510745i
$186$	2.19222	−	5.11803i	0.160741	−	0.375272i
$187$	12.7627	−	12.7627i	0.933299	−	0.933299i
$188$	−5.72583	−	5.72583i	−0.417599	−	0.417599i
$189$	1.49670			0.108869
$190$	−4.96450	+	16.8001i	−0.360163	+	1.21880i
$191$	19.7130			1.42638			0.713192	−	0.700969i	$-0.247249\pi$
$191$	19.7130			1.42638			0.713192	+	0.700969i	$0.247249\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−3.02398	−	3.02398i	−0.217671	−	0.217671i	0.589845	−	0.807516i	$-0.299189\pi$
$193$	−3.02398	−	3.02398i	−0.217671	−	0.217671i	−0.807516	+	0.589845i	$0.799189\pi$
$194$		−	10.2037i		−	0.732584i
$195$	−12.8673	+	6.99724i	−0.921448	+	0.501083i
$196$	4.75989			0.339992
$197$	3.98103	+	3.98103i	0.283636	+	0.283636i	0.834557	−	0.550921i	$-0.185723\pi$
$197$	3.98103	+	3.98103i	0.283636	+	0.283636i	−0.550921	+	0.834557i	$0.685723\pi$
$198$	−3.56532	+	3.56532i	−0.253376	+	0.253376i
$199$	14.3596			1.01793			0.508964	−	0.860788i	$-0.330029\pi$
$199$	14.3596			1.01793			0.508964	+	0.860788i	$0.330029\pi$
$200$	−4.88938	+	1.04593i	−0.345731	+	0.0739583i
$201$			7.69692i			0.542899i
$202$	5.87158	−	5.87158i	0.413123	−	0.413123i
$203$	3.19164	−	3.19164i	0.224009	−	0.224009i
$204$			3.57968i			0.250628i
$205$	2.38674	+	4.38901i	0.166697	+	0.306542i
$206$	−15.6013			−1.08700
$207$	2.05623	+	2.05623i	0.142918	+	0.142918i
$208$	4.63173	−	4.63173i	0.321153	−	0.321153i
$209$	39.5019			2.73240
$210$	0.948429	−	3.20952i	0.0654478	−	0.221478i
$211$	9.13202			0.628674			0.314337	−	0.949311i	$-0.398218\pi$
$211$	9.13202			0.628674			0.314337	+	0.949311i	$0.398218\pi$
$212$	−5.97851	−	5.97851i	−0.410606	−	0.410606i
$213$	10.9186	−	10.9186i	0.748128	−	0.748128i
$214$			2.14900i			0.146903i
$215$	−14.7903	−	4.37060i	−1.00869	−	0.298073i
$216$		−	1.00000i		−	0.0680414i
$217$	7.73662	−	3.09646i	0.525196	−	0.210201i
$218$	7.38778	+	7.38778i	0.500364	+	0.500364i
$219$			8.00599i			0.540994i
$220$	5.38619	+	9.90473i	0.363137	+	0.667777i
$221$	23.4478			1.57727
$222$	−2.29070	+	2.29070i	−0.153742	+	0.153742i
$223$	4.77518	−	4.77518i	0.319770	−	0.319770i	−0.528909	−	0.848679i	$-0.677399\pi$
$223$	4.77518	−	4.77518i	0.319770	−	0.319770i	0.848679	+	0.528909i	$0.177399\pi$
$224$			1.49670i			0.100002i
$225$	4.19690	+	2.71773i	0.279793	+	0.181182i
$226$	−20.5996			−1.37026
$227$	−4.70595	+	4.70595i	−0.312345	+	0.312345i	−0.845817	−	0.533473i	$-0.820887\pi$
$227$	−4.70595	+	4.70595i	−0.312345	+	0.312345i	0.533473	+	0.845817i	$0.320887\pi$
$228$	−5.53975	+	5.53975i	−0.366879	+	0.366879i
$229$	−25.0935			−1.65823			−0.829114	−	0.559080i	$-0.811154\pi$
$229$	−25.0935			−1.65823			−0.829114	+	0.559080i	$0.811154\pi$
$230$	5.71238	−	3.10639i	0.376663	−	0.204829i
$231$	−7.54653			−0.496525
$232$	−2.13246	−	2.13246i	−0.140003	−	0.140003i
$233$	19.4361	+	19.4361i	1.27330	+	1.27330i	0.944345	+	0.328958i	$0.106697\pi$
$233$	19.4361	+	19.4361i	1.27330	+	1.27330i	0.328958	+	0.944345i	$0.393303\pi$
$234$	−6.55026			−0.428204
$235$	17.3644	+	5.13126i	1.13273	+	0.334727i
$236$	5.06330			0.329593
$237$	8.98330	−	8.98330i	0.583528	−	0.583528i
$238$	−3.78846	+	3.78846i	−0.245570	+	0.245570i
$239$	29.7199			1.92242			0.961211	−	0.275813i	$-0.0889472\pi$
$239$	29.7199			1.92242			0.961211	+	0.275813i	$0.0889472\pi$
$240$	−2.14440	−	0.633681i	−0.138420	−	0.0409039i
$241$		−	12.5924i		−	0.811150i	−0.914062	−	0.405575i	$-0.867071\pi$
$241$		−	12.5924i		−	0.811150i	0.914062	−	0.405575i	$-0.132929\pi$
$242$	10.1986	−	10.1986i	0.655589	−	0.655589i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	4.63816			0.296928
$245$	−9.35034	+	5.08471i	−0.597371	+	0.324850i
$246$			2.23428i			0.142452i
$247$	36.2868	+	36.2868i	2.30887	+	2.30887i
$248$	−2.06886	−	5.16912i	−0.131373	−	0.328240i
$249$			11.9543i			0.757574i
$250$	8.48739	−	7.27765i	0.536790	−	0.460279i
$251$		−	19.1678i		−	1.20986i	−0.796279	−	0.604930i	$-0.793201\pi$
$251$		−	19.1678i		−	1.20986i	0.796279	−	0.604930i	$-0.206799\pi$
$252$	1.05833	−	1.05833i	0.0666682	−	0.0666682i
$253$	−10.3678	−	10.3678i	−0.651817	−	0.651817i
$254$	3.05361			0.191601
$255$	−3.82395	−	7.03192i	−0.239465	−	0.440356i
$256$	1.00000			0.0625000
$257$	−2.79449	+	2.79449i	−0.174315	+	0.174315i	−0.788872	−	0.614557i	$-0.789335\pi$
$257$	−2.79449	+	2.79449i	−0.174315	+	0.174315i	0.614557	+	0.788872i	$0.289335\pi$
$258$	−4.87703	−	4.87703i	−0.303631	−	0.303631i
$259$	−4.84862			−0.301279
$260$	−4.15078	+	14.0464i	−0.257420	+	0.871119i
$261$			3.01575i			0.186670i
$262$	−0.0657717	+	0.0657717i	−0.00406339	+	0.00406339i
$263$	−5.66131	+	5.66131i	−0.349091	+	0.349091i	−0.859771	−	0.510680i	$-0.829394\pi$
$263$	−5.66131	+	5.66131i	−0.349091	+	0.349091i	0.510680	+	0.859771i	$0.329394\pi$
$264$			5.04212i			0.310321i
$265$	18.1307	+	5.35771i	1.11376	+	0.329121i
$266$	−11.7257			−0.718950
$267$	−2.06634	+	2.06634i	−0.126458	+	0.126458i
$268$	5.44255	+	5.44255i	0.332456	+	0.332456i
$269$	−5.20425			−0.317309			−0.158654	−	0.987334i	$-0.550716\pi$
$269$	−5.20425			−0.317309			−0.158654	+	0.987334i	$0.550716\pi$
$270$	1.06824	+	1.96440i	0.0650110	+	0.119550i
$271$			15.3617i			0.933156i	0.884480	+	0.466578i	$0.154513\pi$
$271$			15.3617i			0.933156i	−0.884480	+	0.466578i	$0.845487\pi$
$272$	2.53121	+	2.53121i	0.153477	+	0.153477i
$273$	−6.93231	−	6.93231i	−0.419562	−	0.419562i
$274$	6.01002			0.363079
$275$	−21.1612	−	13.7031i	−1.27607	−	0.826329i
$276$	2.90795			0.175038
$277$	−8.05810	−	8.05810i	−0.484165	−	0.484165i	0.422294	−	0.906459i	$-0.361225\pi$
$277$	−8.05810	−	8.05810i	−0.484165	−	0.484165i	−0.906459	+	0.422294i	$0.861225\pi$
$278$	−3.39295	+	3.39295i	−0.203496	+	0.203496i
$279$	−2.19222	+	5.11803i	−0.131245	+	0.306408i
$280$	−1.59883	−	2.94011i	−0.0955484	−	0.175705i
$281$	−19.3095			−1.15191			−0.575956	−	0.817481i	$-0.695370\pi$
$281$	−19.3095			−1.15191			−0.575956	+	0.817481i	$0.695370\pi$
$282$	5.72583	+	5.72583i	0.340968	+	0.340968i
$283$	−8.89357	−	8.89357i	−0.528668	−	0.528668i	0.391507	−	0.920175i	$-0.371954\pi$
$283$	−8.89357	−	8.89357i	−0.528668	−	0.528668i	−0.920175	+	0.391507i	$0.871954\pi$
$284$		−	15.4412i		−	0.916266i
$285$	4.96450	−	16.8001i	0.294072	−	0.995149i
$286$	33.0272			1.95294
$287$	−2.36459	+	2.36459i	−0.139577	+	0.139577i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	4.18591i		−	0.246230i
$290$	6.46697	+	1.91102i	0.379753	+	0.112219i
$291$			10.2037i			0.598153i
$292$	5.66109	+	5.66109i	0.331290	+	0.331290i
$293$	8.83411	+	8.83411i	0.516094	+	0.516094i	0.916387	−	0.400293i	$-0.131092\pi$
$293$	8.83411	+	8.83411i	0.516094	+	0.516094i	−0.400293	+	0.916387i	$0.631092\pi$
$294$	−4.75989			−0.277603
$295$	−9.94635	+	5.40882i	−0.579099	+	0.314914i
$296$			3.23955i			0.188295i
$297$	3.56532	−	3.56532i	0.206881	−	0.206881i
$298$	8.12531	+	8.12531i	0.470686	+	0.470686i
$299$		−	19.0479i		−	1.10157i
$300$	4.88938	−	1.04593i	0.282288	−	0.0603867i
$301$		−	10.3230i		−	0.595006i
$302$	4.55512	+	4.55512i	0.262118	+	0.262118i
$303$	−5.87158	+	5.87158i	−0.337313	+	0.337313i
$304$			7.83439i			0.449333i
$305$	−9.11119	+	4.95466i	−0.521705	+	0.283703i
$306$		−	3.57968i		−	0.204637i
$307$	6.62807	−	6.62807i	0.378284	−	0.378284i	−0.492199	−	0.870483i	$-0.663807\pi$
$307$	6.62807	−	6.62807i	0.378284	−	0.378284i	0.870483	+	0.492199i	$0.163807\pi$
$308$	−5.33620	+	5.33620i	−0.304058	+	0.304058i
$309$	15.6013			0.887529
$310$	9.58592	+	7.94419i	0.544444	+	0.451199i
$311$	−1.91776			−0.108746			−0.0543730	−	0.998521i	$-0.517316\pi$
$311$	−1.91776			−0.108746			−0.0543730	+	0.998521i	$0.517316\pi$
$312$	−4.63173	+	4.63173i	−0.262220	+	0.262220i
$313$	7.23497	−	7.23497i	0.408945	−	0.408945i	−0.472426	−	0.881370i	$-0.656622\pi$
$313$	7.23497	−	7.23497i	0.408945	−	0.408945i	0.881370	+	0.472426i	$0.156622\pi$
$314$		−	4.38333i		−	0.247366i
$315$	−0.948429	+	3.20952i	−0.0534379	+	0.180836i
$316$		−	12.7043i		−	0.714673i
$317$	−14.1306	+	14.1306i	−0.793656	+	0.793656i	−0.982087	−	0.188430i	$-0.939660\pi$
$317$	−14.1306	+	14.1306i	−0.793656	+	0.793656i	0.188430	+	0.982087i	$0.439660\pi$
$318$	5.97851	+	5.97851i	0.335258	+	0.335258i
$319$		−	15.2058i		−	0.851359i
$320$	−1.96440	+	1.06824i	−0.109813	+	0.0597164i
$321$		−	2.14900i		−	0.119946i
$322$	3.07756	+	3.07756i	0.171506	+	0.171506i
$323$	−19.8305	+	19.8305i	−1.10340	+	1.10340i
$324$			1.00000i			0.0555556i
$325$	−6.85110	−	32.0267i	−0.380031	−	1.77652i
$326$	2.85258			0.157990
$327$	−7.38778	−	7.38778i	−0.408545	−	0.408545i
$328$	1.57987	+	1.57987i	0.0872338	+	0.0872338i
$329$			12.1196i			0.668174i
$330$	−5.38619	−	9.90473i	−0.296500	−	0.545238i
$331$			10.6923i			0.587704i	0.955851	+	0.293852i	$0.0949372\pi$
$331$			10.6923i			0.587704i	−0.955851	+	0.293852i	$0.905063\pi$
$332$	8.45297	+	8.45297i	0.463917	+	0.463917i
$333$	2.29070	−	2.29070i	0.125530	−	0.125530i
$334$	−22.9872			−1.25780
$335$	−16.5053	−	4.87739i	−0.901779	−	0.266480i
$336$		−	1.49670i		−	0.0816516i
$337$	−8.95306	−	8.95306i	−0.487704	−	0.487704i	0.419877	−	0.907581i	$-0.362073\pi$
$337$	−8.95306	−	8.95306i	−0.487704	−	0.487704i	−0.907581	+	0.419877i	$0.862073\pi$
$338$	21.1467	+	21.1467i	1.15023	+	1.15023i
$339$	20.5996			1.11881
$340$	−7.67626	−	2.26837i	−0.416303	−	0.123020i
$341$	11.0534	−	25.8057i	0.598576	−	1.39746i
$342$	5.53975	−	5.53975i	0.299555	−	0.299555i
$343$	−12.4458	−	12.4458i	−0.672010	−	0.672010i
$344$	−6.89717			−0.371870
$345$	−5.71238	+	3.10639i	−0.307544	+	0.167242i
$346$	−0.741998			−0.0398901
$347$	−9.87072	−	9.87072i	−0.529888	−	0.529888i	0.390651	−	0.920539i	$-0.372250\pi$
$347$	−9.87072	−	9.87072i	−0.529888	−	0.529888i	−0.920539	+	0.390651i	$0.872250\pi$
$348$	2.13246	+	2.13246i	0.114312	+	0.114312i
$349$		−	7.65781i		−	0.409913i	−0.978771	−	0.204957i	$-0.934295\pi$
$349$		−	7.65781i		−	0.409913i	0.978771	−	0.204957i	$-0.0657053\pi$
$350$	6.28149	+	4.06762i	0.335760	+	0.217424i
$351$	6.55026			0.349627
$352$	3.56532	+	3.56532i	0.190032	+	0.190032i
$353$	0.693301	−	0.693301i	0.0369007	−	0.0369007i	−0.688416	−	0.725316i	$-0.741693\pi$
$353$	0.693301	−	0.693301i	0.0369007	−	0.0369007i	0.725316	+	0.688416i	$0.241693\pi$
$354$	−5.06330			−0.269112
$355$	16.4949	+	30.3327i	0.875457	+	1.60989i
$356$			2.92224i			0.154878i
$357$	3.78846	−	3.78846i	0.200507	−	0.200507i
$358$	−2.02999	+	2.02999i	−0.107288	+	0.107288i
$359$			12.9348i			0.682672i	0.939941	+	0.341336i	$0.110879\pi$
$359$			12.9348i			0.682672i	−0.939941	+	0.341336i	$0.889121\pi$
$360$	2.14440	+	0.633681i	0.113020	+	0.0333979i
$361$	−42.3776			−2.23040
$362$	−18.1940	−	18.1940i	−0.956258	−	0.956258i
$363$	−10.1986	+	10.1986i	−0.535286	+	0.535286i
$364$	−9.80376			−0.513857
$365$	−17.1680	−	5.07324i	−0.898616	−	0.265546i
$366$	−4.63816			−0.242440
$367$	−16.9386	−	16.9386i	−0.884189	−	0.884189i	0.109768	−	0.993957i	$-0.464989\pi$
$367$	−16.9386	−	16.9386i	−0.884189	−	0.884189i	−0.993957	+	0.109768i	$0.964989\pi$
$368$	2.05623	−	2.05623i	0.107189	−	0.107189i
$369$		−	2.23428i		−	0.116312i
$370$	−3.46061	−	6.36376i	−0.179909	−	0.330836i
$371$			12.6544i			0.656985i
$372$	2.06886	+	5.16912i	0.107265	+	0.268007i
$373$	−12.2249	−	12.2249i	−0.632981	−	0.632981i	0.315833	−	0.948815i	$-0.397716\pi$
$373$	−12.2249	−	12.2249i	−0.632981	−	0.632981i	−0.948815	+	0.315833i	$0.897716\pi$
$374$			18.0492i			0.933299i
$375$	−8.48739	+	7.27765i	−0.438287	+	0.375816i
$376$	8.09754			0.417599
$377$	13.9681	−	13.9681i	0.719395	−	0.719395i
$378$	−1.05833	+	1.05833i	−0.0544344	+	0.0544344i
$379$		−	20.4677i		−	1.05135i	−0.850685	−	0.525676i	$-0.823812\pi$
$379$		−	20.4677i		−	1.05135i	0.850685	−	0.525676i	$-0.176188\pi$
$380$	−8.36900	−	15.3899i	−0.429321	−	0.789484i
$381$	−3.05361			−0.156441
$382$	−13.9392	+	13.9392i	−0.713192	+	0.713192i
$383$	25.2058	−	25.2058i	1.28796	−	1.28796i	0.351928	−	0.936027i	$-0.385526\pi$
$383$	25.2058	−	25.2058i	1.28796	−	1.28796i	0.936027	−	0.351928i	$-0.114474\pi$
$384$	−1.00000			−0.0510310
$385$	4.78209	−	16.1828i	0.243718	−	0.824750i
$386$	4.27656			0.217671
$387$	4.87703	+	4.87703i	0.247914	+	0.247914i
$388$	7.21512	+	7.21512i	0.366292	+	0.366292i
$389$	18.4973			0.937849			0.468924	−	0.883238i	$-0.344642\pi$
$389$	18.4973			0.937849			0.468924	+	0.883238i	$0.344642\pi$
$390$	4.15078	−	14.0464i	0.210183	−	0.711266i
$391$	10.4095			0.526433
$392$	−3.36575	+	3.36575i	−0.169996	+	0.169996i
$393$	0.0657717	−	0.0657717i	0.00331774	−	0.00331774i
$394$	−5.63002			−0.283636
$395$	13.5712	+	24.9563i	0.682843	+	1.25569i
$396$		−	5.04212i		−	0.253376i
$397$	−8.45450	+	8.45450i	−0.424319	+	0.424319i	−0.886688	−	0.462368i	$-0.847000\pi$
$397$	−8.45450	+	8.45450i	−0.424319	+	0.424319i	0.462368	+	0.886688i	$0.347000\pi$
$398$	−10.1538	+	10.1538i	−0.508964	+	0.508964i
$399$	11.7257			0.587020
$400$	2.71773	−	4.19690i	0.135887	−	0.209845i
$401$			7.64200i			0.381623i	0.981627	+	0.190812i	$0.0611119\pi$
$401$			7.64200i			0.381623i	−0.981627	+	0.190812i	$0.938888\pi$
$402$	−5.44255	−	5.44255i	−0.271450	−	0.271450i
$403$	33.8591	−	13.5516i	1.68664	−	0.675051i
$404$			8.30366i			0.413123i
$405$	−1.06824	−	1.96440i	−0.0530812	−	0.0976118i
$406$			4.51366i			0.224009i
$407$	−11.5500	+	11.5500i	−0.572512	+	0.572512i
$408$	−2.53121	−	2.53121i	−0.125314	−	0.125314i
$409$	−22.9311			−1.13387			−0.566935	−	0.823762i	$-0.691871\pi$
$409$	−22.9311			−1.13387			−0.566935	+	0.823762i	$0.691871\pi$
$410$	−4.79118	−	1.41582i	−0.236619	−	0.0699223i
$411$	−6.01002			−0.296453
$412$	11.0318	−	11.0318i	0.543498	−	0.543498i
$413$	−5.35862	−	5.35862i	−0.263681	−	0.263681i
$414$	−2.90795			−0.142918
$415$	−25.6348	−	7.57522i	−1.25836	−	0.371853i
$416$			6.55026i			0.321153i
$417$	3.39295	−	3.39295i	0.166154	−	0.166154i
$418$	−27.9321	+	27.9321i	−1.36620	+	1.36620i
$419$			30.5175i			1.49088i	0.666575	+	0.745438i	$0.267760\pi$
$419$			30.5175i			1.49088i	−0.666575	+	0.745438i	$0.732240\pi$
$420$	1.59883	+	2.94011i	0.0780150	+	0.143463i
$421$	21.7751			1.06125			0.530627	−	0.847605i	$-0.321956\pi$
$421$	21.7751			1.06125			0.530627	+	0.847605i	$0.321956\pi$
$422$	−6.45731	+	6.45731i	−0.314337	+	0.314337i
$423$	−5.72583	−	5.72583i	−0.278399	−	0.278399i
$424$	8.45489			0.410606
$425$	17.5024	−	3.74409i	0.848991	−	0.181615i
$426$			15.4412i			0.748128i
$427$	−4.90868	−	4.90868i	−0.237548	−	0.237548i
$428$	−1.51957	−	1.51957i	−0.0734514	−	0.0734514i
$429$	−33.0272			−1.59457
$430$	13.5488	−	7.36782i	0.653381	−	0.355308i
$431$	0.781118			0.0376251			0.0188126	−	0.999823i	$-0.494011\pi$
$431$	0.781118			0.0376251			0.0188126	+	0.999823i	$0.494011\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−4.95534	+	4.95534i	−0.238138	+	0.238138i	−0.816079	−	0.577941i	$-0.803857\pi$
$433$	−4.95534	+	4.95534i	−0.238138	+	0.238138i	0.577941	+	0.816079i	$0.303857\pi$
$434$	−3.28109	+	7.66014i	−0.157497	+	0.367698i
$435$	−6.46697	−	1.91102i	−0.310067	−	0.0916265i
$436$	−10.4479			−0.500364
$437$	16.1093	+	16.1093i	0.770614	+	0.770614i
$438$	−5.66109	−	5.66109i	−0.270497	−	0.270497i
$439$		−	4.02017i		−	0.191872i	−0.995387	−	0.0959362i	$-0.969416\pi$
$439$		−	4.02017i		−	0.191872i	0.995387	−	0.0959362i	$-0.0305845\pi$
$440$	−10.8123	−	3.19509i	−0.515457	−	0.152320i
$441$	4.75989			0.226662
$442$	−16.5801	+	16.5801i	−0.788635	+	0.788635i
$443$	15.2507	+	15.2507i	0.724582	+	0.724582i	0.969535	−	0.244953i	$-0.0787726\pi$
$443$	15.2507	+	15.2507i	0.724582	+	0.724582i	−0.244953	+	0.969535i	$0.578773\pi$
$444$		−	3.23955i		−	0.153742i
$445$	−3.12165	−	5.74045i	−0.147980	−	0.272123i
$446$			6.75312i			0.319770i
$447$	−8.12531	−	8.12531i	−0.384314	−	0.384314i
$448$	−1.05833	−	1.05833i	−0.0500012	−	0.0500012i
$449$	−14.0081			−0.661085			−0.330542	−	0.943791i	$-0.607232\pi$
$449$	−14.0081			−0.661085			−0.330542	+	0.943791i	$0.607232\pi$
$450$	−4.88938	+	1.04593i	−0.230488	+	0.0493055i
$451$			11.2655i			0.530471i
$452$	14.5661	−	14.5661i	0.685131	−	0.685131i
$453$	−4.55512	−	4.55512i	−0.214018	−	0.214018i
$454$		−	6.65522i		−	0.312345i
$455$	19.2585	−	10.4728i	0.902853	−	0.490971i
$456$		−	7.83439i		−	0.366879i
$457$	−21.3948	−	21.3948i	−1.00081	−	1.00081i	−1.00000		0.000807496i	$-0.999743\pi$
$457$	−21.3948	−	21.3948i	−1.00081	−	1.00081i	−0.000807496	−	1.00000i	$-0.500257\pi$
$458$	17.7438	−	17.7438i	0.829114	−	0.829114i
$459$			3.57968i			0.167085i
$460$	−1.84272	+	6.23582i	−0.0859171	+	0.290746i
$461$		−	13.2812i		−	0.618569i	−0.950970	−	0.309284i	$-0.899911\pi$
$461$		−	13.2812i		−	0.618569i	0.950970	−	0.309284i	$-0.100089\pi$
$462$	5.33620	−	5.33620i	0.248263	−	0.248263i
$463$	−5.97931	+	5.97931i	−0.277882	+	0.277882i	−0.832263	−	0.554381i	$-0.812955\pi$
$463$	−5.97931	+	5.97931i	−0.277882	+	0.277882i	0.554381	+	0.832263i	$0.312955\pi$
$464$	3.01575			0.140003
$465$	−9.58592	−	7.94419i	−0.444537	−	0.368403i
$466$	−27.4868			−1.27330
$467$	−9.72180	+	9.72180i	−0.449871	+	0.449871i	−0.895312	−	0.445440i	$-0.853047\pi$
$467$	−9.72180	+	9.72180i	−0.449871	+	0.449871i	0.445440	+	0.895312i	$0.353047\pi$
$468$	4.63173	−	4.63173i	0.214102	−	0.214102i
$469$		−	11.5200i		−	0.531943i
$470$	−15.9068	+	8.65011i	−0.733727	+	0.399000i
$471$			4.38333i			0.201973i
$472$	−3.58030	+	3.58030i	−0.164797	+	0.164797i
$473$	−24.5906	−	24.5906i	−1.13068	−	1.13068i
$474$			12.7043i			0.583528i
$475$	32.8801	+	21.2918i	1.50864	+	0.976933i
$476$		−	5.35770i		−	0.245570i
$477$	−5.97851	−	5.97851i	−0.273737	−	0.273737i
$478$	−21.0152	+	21.0152i	−0.961211	+	0.961211i
$479$			15.8991i			0.726446i	0.931702	+	0.363223i	$0.118324\pi$
$479$			15.8991i			0.726446i	−0.931702	+	0.363223i	$0.881676\pi$
$480$	1.96440	−	1.06824i	0.0896622	−	0.0487582i
$481$	−21.2199			−0.967543
$482$	8.90420	+	8.90420i	0.405575	+	0.405575i
$483$	−3.07756	−	3.07756i	−0.140034	−	0.140034i
$484$			14.4230i			0.655589i
$485$	−21.8809	−	6.46590i	−0.993558	−	0.293602i
$486$		−	1.00000i		−	0.0453609i
$487$	−2.16804	−	2.16804i	−0.0982432	−	0.0982432i	0.656277	−	0.754520i	$-0.272130\pi$
$487$	−2.16804	−	2.16804i	−0.0982432	−	0.0982432i	−0.754520	+	0.656277i	$0.772130\pi$
$488$	−3.27967	+	3.27967i	−0.148464	+	0.148464i
$489$	−2.85258			−0.128998
$490$	3.01626	−	10.2071i	0.136261	−	0.461110i
$491$		−	19.8973i		−	0.897951i	−0.893544	−	0.448975i	$-0.851789\pi$
$491$		−	19.8973i		−	0.897951i	0.893544	−	0.448975i	$-0.148211\pi$
$492$	−1.57987	−	1.57987i	−0.0712261	−	0.0712261i
$493$	7.63350	+	7.63350i	0.343796	+	0.343796i
$494$	−51.3173			−2.30887
$495$	5.38619	+	9.90473i	0.242091	+	0.445185i
$496$	5.11803	+	2.19222i	0.229806	+	0.0984335i
$497$	−16.3418	+	16.3418i	−0.733030	+	0.733030i
$498$	−8.45297	−	8.45297i	−0.378787	−	0.378787i
$499$	3.74882			0.167820			0.0839100	−	0.996473i	$-0.473259\pi$
$499$	3.74882			0.167820			0.0839100	+	0.996473i	$0.473259\pi$
$500$	−0.855419	+	11.1476i	−0.0382555	+	0.498534i
$501$	22.9872			1.02699
$502$	13.5537	+	13.5537i	0.604930	+	0.604930i
$503$	−26.1897	−	26.1897i	−1.16774	−	1.16774i	−0.982738	−	0.185003i	$-0.940771\pi$
$503$	−26.1897	−	26.1897i	−1.16774	−	1.16774i	−0.185003	−	0.982738i	$-0.559229\pi$
$504$			1.49670i			0.0666682i
$505$	−8.87030	−	16.3117i	−0.394723	−	0.725861i
$506$	14.6623			0.651817
$507$	−21.1467	−	21.1467i	−0.939156	−	0.939156i
$508$	−2.15923	+	2.15923i	−0.0958003	+	0.0958003i
$509$	−40.5226			−1.79613			−0.898067	−	0.439859i	$-0.855028\pi$
$509$	−40.5226			−1.79613			−0.898067	+	0.439859i	$0.855028\pi$
$510$	7.67626	+	2.26837i	0.339910	+	0.100445i
$511$		−	11.9825i		−	0.530077i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−5.53975	+	5.53975i	−0.244586	+	0.244586i
$514$		−	3.95200i		−	0.174315i
$515$	−9.88627	+	33.4555i	−0.435641	+	1.47422i
$516$	6.89717			0.303631
$517$	28.8703	+	28.8703i	1.26971	+	1.26971i
$518$	3.42849	−	3.42849i	0.150639	−	0.150639i
$519$	0.741998			0.0325701
$520$	−6.99724	−	12.8673i	−0.306849	−	0.564270i
$521$	13.8583			0.607142			0.303571	−	0.952809i	$-0.401821\pi$
$521$	13.8583			0.607142			0.303571	+	0.952809i	$0.401821\pi$
$522$	−2.13246	−	2.13246i	−0.0933350	−	0.0933350i
$523$	−17.8505	+	17.8505i	−0.780546	+	0.780546i	−0.979923	−	0.199377i	$-0.936108\pi$
$523$	−17.8505	+	17.8505i	−0.780546	+	0.780546i	0.199377	+	0.979923i	$0.436108\pi$
$524$		−	0.0930152i		−	0.00406339i
$525$	−6.28149	−	4.06762i	−0.274147	−	0.177526i
$526$		−	8.00630i		−	0.349091i
$527$	7.40584	+	18.5038i	0.322604	+	0.806038i
$528$	−3.56532	−	3.56532i	−0.155160	−	0.155160i
$529$			14.5438i			0.632339i
$530$	−16.6088	+	9.03185i	−0.721440	+	0.392318i
$531$	5.06330			0.219729
$532$	8.29133	−	8.29133i	0.359475	−	0.359475i
$533$	−10.3486	+	10.3486i	−0.448246	+	0.448246i
$534$		−	2.92224i		−	0.126458i
$535$	4.60832	+	1.36178i	0.199235	+	0.0588750i
$536$	−7.69692			−0.332456
$537$	2.02999	−	2.02999i	0.0876007	−	0.0876007i
$538$	3.67996	−	3.67996i	0.158654	−	0.158654i
$539$	−24.0000			−1.03375
$540$	−2.14440	−	0.633681i	−0.0922803	−	0.0272693i
$541$	35.7301			1.53616			0.768078	−	0.640356i	$-0.221213\pi$
$541$	35.7301			1.53616			0.768078	+	0.640356i	$0.221213\pi$
$542$	−10.8624	−	10.8624i	−0.466578	−	0.466578i
$543$	18.1940	+	18.1940i	0.780781	+	0.780781i
$544$	−3.57968			−0.153477
$545$	20.5239	−	11.1609i	0.879145	−	0.478079i
$546$	9.80376			0.419562
$547$	30.1622	−	30.1622i	1.28964	−	1.28964i	0.354642	−	0.935002i	$-0.384603\pi$
$547$	30.1622	−	30.1622i	1.28964	−	1.28964i	0.935002	−	0.354642i	$-0.115397\pi$
$548$	−4.24973	+	4.24973i	−0.181539	+	0.181539i
$549$	4.63816			0.197952
$550$	24.6528	−	5.27369i	1.05120	−	0.224871i
$551$			23.6265i			1.00652i
$552$	−2.05623	+	2.05623i	−0.0875192	+	0.0875192i
$553$	−13.4453	+	13.4453i	−0.571752	+	0.571752i
$554$	11.3959			0.484165
$555$	3.46061	+	6.36376i	0.146895	+	0.270127i
$556$		−	4.79836i		−	0.203496i
$557$	16.5286	+	16.5286i	0.700339	+	0.700339i	0.964483	−	0.264144i	$-0.0850896\pi$
$557$	16.5286	+	16.5286i	0.700339	+	0.700339i	−0.264144	+	0.964483i	$0.585090\pi$
$558$	−2.06886	−	5.16912i	−0.0875818	−	0.218826i
$559$		−	45.1782i		−	1.91084i
$560$	3.20952	+	0.948429i	0.135627	+	0.0400784i
$561$		−	18.0492i		−	0.762036i
$562$	13.6539	−	13.6539i	0.575956	−	0.575956i
$563$	−4.44405	−	4.44405i	−0.187294	−	0.187294i	0.607231	−	0.794525i	$-0.292280\pi$
$563$	−4.44405	−	4.44405i	−0.187294	−	0.187294i	−0.794525	+	0.607231i	$0.792280\pi$
$564$	−8.09754			−0.340968
$565$	−13.0536	+	44.1737i	−0.549167	+	1.85840i
$566$	12.5774			0.528668
$567$	1.05833	−	1.05833i	0.0444455	−	0.0444455i
$568$	10.9186	+	10.9186i	0.458133	+	0.458133i
$569$	−25.1454			−1.05415			−0.527075	−	0.849819i	$-0.676711\pi$
$569$	−25.1454			−1.05415			−0.527075	+	0.849819i	$0.676711\pi$
$570$	8.36900	+	15.3899i	0.350539	+	0.644611i
$571$			16.7647i			0.701581i	0.936454	+	0.350790i	$0.114087\pi$
$571$			16.7647i			0.701581i	−0.936454	+	0.350790i	$0.885913\pi$
$572$	−23.3537	+	23.3537i	−0.976469	+	0.976469i
$573$	13.9392	−	13.9392i	0.582319	−	0.582319i
$574$		−	3.34404i		−	0.139577i
$575$	−3.04151	−	14.2181i	−0.126840	−	0.592936i
$576$	1.00000			0.0416667
$577$	−2.00618	+	2.00618i	−0.0835185	+	0.0835185i	−0.747632	−	0.664113i	$-0.768809\pi$
$577$	−2.00618	+	2.00618i	−0.0835185	+	0.0835185i	0.664113	+	0.747632i	$0.268809\pi$
$578$	2.95989	+	2.95989i	0.123115	+	0.123115i
$579$	−4.27656			−0.177728
$580$	−5.92413	+	3.22154i	−0.245986	+	0.133767i
$581$		−	17.8920i		−	0.742285i
$582$	−7.21512	−	7.21512i	−0.299076	−	0.299076i
$583$	30.1444	+	30.1444i	1.24845	+	1.24845i
$584$	−8.00599			−0.331290
$585$	−4.15078	+	14.0464i	−0.171613	+	0.580746i
$586$	−12.4933			−0.516094
$587$	−0.268866	−	0.268866i	−0.0110973	−	0.0110973i	0.701536	−	0.712634i	$-0.252498\pi$
$587$	−0.268866	−	0.268866i	−0.0110973	−	0.0110973i	−0.712634	+	0.701536i	$0.752498\pi$
$588$	3.36575	−	3.36575i	0.138801	−	0.138801i
$589$	−17.1747	+	40.0966i	−0.707670	+	1.65215i
$590$	3.20852	−	10.8577i	0.132093	−	0.447006i
$591$	5.63002			0.231588
$592$	−2.29070	−	2.29070i	−0.0941474	−	0.0941474i
$593$	−11.4240	−	11.4240i	−0.469128	−	0.469128i	0.432504	−	0.901632i	$-0.357630\pi$
$593$	−11.4240	−	11.4240i	−0.469128	−	0.469128i	−0.901632	+	0.432504i	$0.857630\pi$
$594$			5.04212i			0.206881i
$595$	5.72330	+	10.5247i	0.234632	+	0.431469i
$596$	−11.4909			−0.470686
$597$	10.1538	−	10.1538i	0.415567	−	0.415567i
$598$	13.4689	+	13.4689i	0.550783	+	0.550783i
$599$		−	19.1063i		−	0.780662i	−0.920675	−	0.390331i	$-0.872361\pi$
$599$		−	19.1063i		−	0.780662i	0.920675	−	0.390331i	$-0.127639\pi$
$600$	−2.71773	+	4.19690i	−0.110951	+	0.171338i
$601$			43.1864i			1.76161i	0.473479	+	0.880805i	$0.342998\pi$
$601$			43.1864i			1.76161i	−0.473479	+	0.880805i	$0.657002\pi$
$602$	7.29945	+	7.29945i	0.297503	+	0.297503i
$603$	5.44255	+	5.44255i	0.221638	+	0.221638i
$604$	−6.44191			−0.262118
$605$	−15.4072	−	28.3324i	−0.626390	−	1.15188i
$606$		−	8.30366i		−	0.337313i
$607$	−26.2758	+	26.2758i	−1.06650	+	1.06650i	−0.0688749	+	0.997625i	$0.521941\pi$
$607$	−26.2758	+	26.2758i	−1.06650	+	1.06650i	−0.997625	+	0.0688749i	$0.978059\pi$
$608$	−5.53975	−	5.53975i	−0.224666	−	0.224666i
$609$		−	4.51366i		−	0.182903i
$610$	2.93911	−	9.94606i	0.119001	−	0.402704i
$611$			53.0410i			2.14581i
$612$	2.53121	+	2.53121i	0.102318	+	0.102318i
$613$	9.84589	−	9.84589i	0.397672	−	0.397672i	−0.479739	−	0.877411i	$-0.659269\pi$
$613$	9.84589	−	9.84589i	0.397672	−	0.397672i	0.877411	+	0.479739i	$0.159269\pi$
$614$			9.37351i			0.378284i
$615$	4.79118	+	1.41582i	0.193199	+	0.0570913i
$616$		−	7.54653i		−	0.304058i
$617$	0.731349	−	0.731349i	0.0294430	−	0.0294430i	−0.692232	−	0.721675i	$-0.743373\pi$
$617$	0.731349	−	0.731349i	0.0294430	−	0.0294430i	0.721675	+	0.692232i	$0.243373\pi$
$618$	−11.0318	+	11.0318i	−0.443764	+	0.443764i
$619$	47.6445			1.91500			0.957498	−	0.288441i	$-0.0931371\pi$
$619$	47.6445			1.91500			0.957498	+	0.288441i	$0.0931371\pi$
$620$	−12.3957	+	1.16088i	−0.497822	+	0.0466222i
$621$	2.90795			0.116692
$622$	1.35606	−	1.35606i	0.0543730	−	0.0543730i
$623$	3.09268	−	3.09268i	0.123906	−	0.123906i
$624$		−	6.55026i		−	0.262220i
$625$	−10.2279	−	22.8121i	−0.409115	−	0.912483i
$626$			10.2318i			0.408945i
$627$	27.9321	−	27.9321i	1.11550	−	1.11550i
$628$	3.09948	+	3.09948i	0.123683	+	0.123683i
$629$		−	11.5965i		−	0.462384i
$630$	−1.59883	−	2.94011i	−0.0636990	−	0.117137i
$631$			9.24375i			0.367988i	0.982927	+	0.183994i	$0.0589027\pi$
$631$			9.24375i			0.367988i	−0.982927	+	0.183994i	$0.941097\pi$
$632$	8.98330	+	8.98330i	0.357337	+	0.357337i
$633$	6.45731	−	6.45731i	0.256655	−	0.256655i
$634$		−	19.9838i		−	0.793656i
$635$	1.93502	−	6.54816i	0.0767888	−	0.259856i
$636$	−8.45489			−0.335258
$637$	−22.0466	−	22.0466i	−0.873517	−	0.873517i
$638$	10.7521	+	10.7521i	0.425679	+	0.425679i
$639$		−	15.4412i		−	0.610844i
$640$	0.633681	−	2.14440i	0.0250484	−	0.0847648i
$641$			38.8629i			1.53499i	0.641055	+	0.767495i	$0.278497\pi$
$641$			38.8629i			1.53499i	−0.641055	+	0.767495i	$0.721503\pi$
$642$	1.51957	+	1.51957i	0.0599728	+	0.0599728i
$643$	16.8017	−	16.8017i	0.662595	−	0.662595i	−0.293396	−	0.955991i	$-0.594785\pi$
$643$	16.8017	−	16.8017i	0.662595	−	0.662595i	0.955991	+	0.293396i	$0.0947854\pi$
$644$	−4.35233			−0.171506
$645$	−13.5488	+	7.36782i	−0.533483	+	0.290108i
$646$		−	28.0446i		−	1.10340i
$647$	10.8269	+	10.8269i	0.425650	+	0.425650i	0.887144	−	0.461494i	$-0.152686\pi$
$647$	10.8269	+	10.8269i	0.425650	+	0.425650i	−0.461494	+	0.887144i	$0.652686\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−25.5298			−1.00213
$650$	27.4908	+	17.8018i	1.07828	+	0.698246i
$651$	3.28109	−	7.66014i	0.128596	−	0.300224i
$652$	−2.01708	+	2.01708i	−0.0789949	+	0.0789949i
$653$	2.85826	+	2.85826i	0.111852	+	0.111852i	0.760818	−	0.648965i	$-0.224798\pi$
$653$	2.85826	+	2.85826i	0.111852	+	0.111852i	−0.648965	+	0.760818i	$0.724798\pi$
$654$	10.4479			0.408545
$655$	0.0993625	+	0.182719i	0.00388241	+	0.00713942i
$656$	−2.23428			−0.0872338
$657$	5.66109	+	5.66109i	0.220860	+	0.220860i
$658$	−8.56984	−	8.56984i	−0.334087	−	0.334087i
$659$			31.5214i			1.22790i	0.789345	+	0.613950i	$0.210420\pi$
$659$			31.5214i			1.22790i	−0.789345	+	0.613950i	$0.789580\pi$
$660$	10.8123	+	3.19509i	0.420869	+	0.124369i
$661$	−16.6869			−0.649047			−0.324523	−	0.945878i	$-0.605204\pi$
$661$	−16.6869			−0.649047			−0.324523	+	0.945878i	$0.605204\pi$
$662$	−7.56062	−	7.56062i	−0.293852	−	0.293852i
$663$	16.5801	−	16.5801i	0.643918	−	0.643918i
$664$	−11.9543			−0.463917
$665$	−7.43036	+	25.1446i	−0.288137	+	0.975066i
$666$			3.23955i			0.125530i
$667$	6.20108	−	6.20108i	0.240107	−	0.240107i
$668$	16.2544	−	16.2544i	0.628902	−	0.628902i
$669$		−	6.75312i		−	0.261091i
$670$	15.1198	−	8.22215i	0.584130	−	0.317649i
$671$	−23.3861			−0.902812
$672$	1.05833	+	1.05833i	0.0408258	+	0.0408258i
$673$	27.7515	−	27.7515i	1.06974	−	1.06974i	0.0723632	−	0.997378i	$-0.476946\pi$
$673$	27.7515	−	27.7515i	1.06974	−	1.06974i	0.997378	−	0.0723632i	$-0.0230541\pi$
$674$	12.6615			0.487704
$675$	4.88938	−	1.04593i	0.188192	−	0.0402578i
$676$	−29.9059			−1.15023
$677$	−25.1068	−	25.1068i	−0.964933	−	0.964933i	0.0344722	−	0.999406i	$-0.489025\pi$
$677$	−25.1068	−	25.1068i	−0.964933	−	0.964933i	−0.999406	+	0.0344722i	$0.989025\pi$
$678$	−14.5661	+	14.5661i	−0.559407	+	0.559407i
$679$		−	15.2719i		−	0.586081i
$680$	7.03192	−	3.82395i	0.269662	−	0.146642i
$681$			6.65522i			0.255028i
$682$	10.4314	+	26.0633i	0.399440	+	0.998016i
$683$	4.29572	+	4.29572i	0.164371	+	0.164371i	0.784500	−	0.620129i	$-0.212920\pi$
$683$	4.29572	+	4.29572i	0.164371	+	0.164371i	−0.620129	+	0.784500i	$0.712920\pi$
$684$			7.83439i			0.299555i
$685$	3.80844	−	12.8879i	0.145513	−	0.492421i
$686$	17.6010			0.672010
$687$	−17.7438	+	17.7438i	−0.676968	+	0.676968i
$688$	4.87703	−	4.87703i	0.185935	−	0.185935i
$689$			55.3817i			2.10988i
$690$	1.84272	−	6.23582i	0.0701510	−	0.237393i
$691$	−39.6224			−1.50731			−0.753654	−	0.657271i	$-0.771711\pi$
$691$	−39.6224			−1.50731			−0.753654	+	0.657271i	$0.771711\pi$
$692$	0.524672	−	0.524672i	0.0199450	−	0.0199450i
$693$	−5.33620	+	5.33620i	−0.202706	+	0.202706i
$694$	13.9593			0.529888
$695$	5.12579	+	9.42589i	0.194432	+	0.357544i
$696$	−3.01575			−0.114312
$697$	−5.65543	−	5.65543i	−0.214215	−	0.214215i
$698$	5.41489	+	5.41489i	0.204957	+	0.204957i
$699$	27.4868			1.03965
$700$	−7.31792	+	1.56544i	−0.276592	+	0.0591680i
$701$	27.1869			1.02683			0.513417	−	0.858139i	$-0.328379\pi$
$701$	27.1869			1.02683			0.513417	+	0.858139i	$0.328379\pi$
$702$	−4.63173	+	4.63173i	−0.174813	+	0.174813i
$703$	17.9463	−	17.9463i	0.676856	−	0.676856i
$704$	−5.04212			−0.190032
$705$	15.9068	−	8.65011i	0.599085	−	0.325782i
$706$			0.980476i			0.0369007i
$707$	8.78798	−	8.78798i	0.330506	−	0.330506i
$708$	3.58030	−	3.58030i	0.134556	−	0.134556i
$709$	18.1008			0.679790			0.339895	−	0.940463i	$-0.389608\pi$
$709$	18.1008			0.679790			0.339895	+	0.940463i	$0.389608\pi$
$710$	−33.1121	−	9.78479i	−1.24267	−	0.367217i
$711$		−	12.7043i		−	0.476449i
$712$	−2.06634	−	2.06634i	−0.0774392	−	0.0774392i
$713$	15.0316	−	6.01615i	0.562937	−	0.225306i
$714$			5.35770i			0.200507i
$715$	20.9287	−	70.8235i	0.782689	−	2.64865i
$716$		−	2.87084i		−	0.107288i
$717$	21.0152	−	21.0152i	0.784826	−	0.784826i
$718$	−9.14628	−	9.14628i	−0.341336	−	0.341336i
$719$	38.6292			1.44062			0.720312	−	0.693650i	$-0.243998\pi$
$719$	38.6292			1.44062			0.720312	+	0.693650i	$0.243998\pi$
$720$	−1.96440	+	1.06824i	−0.0732088	+	0.0398109i
$721$	−23.3505			−0.869618
$722$	29.9655	−	29.9655i	1.11520	−	1.11520i
$723$	−8.90420	−	8.90420i	−0.331151	−	0.331151i
$724$	25.7303			0.956258
$725$	8.19599	−	12.6568i	0.304391	−	0.470061i
$726$		−	14.4230i		−	0.535286i
$727$	−11.1771	+	11.1771i	−0.414537	+	0.414537i	−0.883316	−	0.468779i	$-0.844694\pi$
$727$	−11.1771	+	11.1771i	−0.414537	+	0.414537i	0.468779	+	0.883316i	$0.344694\pi$
$728$	6.93231	−	6.93231i	0.256928	−	0.256928i
$729$			1.00000i			0.0370370i
$730$	15.7270	−	8.55231i	0.582081	−	0.316535i
$731$	24.6896			0.913179
$732$	3.27967	−	3.27967i	0.121220	−	0.121220i
$733$	24.3154	+	24.3154i	0.898109	+	0.898109i	0.995269	−	0.0971596i	$-0.0309757\pi$
$733$	24.3154	+	24.3154i	0.898109	+	0.898109i	−0.0971596	+	0.995269i	$0.530976\pi$
$734$	23.9548			0.884189
$735$	−3.01626	+	10.2071i	−0.111256	+	0.376495i
$736$			2.90795i			0.107189i
$737$	−27.4420	−	27.4420i	−1.01084	−	1.01084i
$738$	1.57987	+	1.57987i	0.0581559	+	0.0581559i
$739$	−49.5046			−1.82106			−0.910528	−	0.413447i	$-0.864325\pi$
$739$	−49.5046			−1.82106			−0.910528	+	0.413447i	$0.864325\pi$
$740$	6.94688	+	2.05284i	0.255372	+	0.0754639i
$741$	51.3173			1.88519
$742$	−8.94803	−	8.94803i	−0.328492	−	0.328492i
$743$	31.5991	−	31.5991i	1.15926	−	1.15926i	0.174624	−	0.984635i	$-0.444129\pi$
$743$	31.5991	−	31.5991i	1.15926	−	1.15926i	0.984635	−	0.174624i	$-0.0558711\pi$
$744$	−5.11803	−	2.19222i	−0.187636	−	0.0803706i
$745$	22.5728	−	12.2751i	0.827002	−	0.449723i
$746$	17.2886			0.632981
$747$	8.45297	+	8.45297i	0.309278	+	0.309278i
$748$	−12.7627	−	12.7627i	−0.466650	−	0.466650i
$749$			3.21641i			0.117525i
$750$	0.855419	−	11.1476i	0.0312355	−	0.407052i
$751$	25.3950			0.926677			0.463338	−	0.886181i	$-0.346651\pi$
$751$	25.3950			0.926677			0.463338	+	0.886181i	$0.346651\pi$
$752$	−5.72583	+	5.72583i	−0.208799	+	0.208799i
$753$	−13.5537	−	13.5537i	−0.493923	−	0.493923i
$754$			19.7539i			0.719395i
$755$	12.6545	−	6.88150i	0.460544	−	0.250444i
$756$		−	1.49670i		−	0.0544344i
$757$	0.171583	+	0.171583i	0.00623630	+	0.00623630i	0.710218	−	0.703982i	$-0.248596\pi$
$757$	0.171583	+	0.171583i	0.00623630	+	0.00623630i	−0.703982	+	0.710218i	$0.748596\pi$
$758$	14.4728	+	14.4728i	0.525676	+	0.525676i
$759$	−14.6623			−0.532206
$760$	16.8001	+	4.96450i	0.609402	+	0.180081i
$761$			0.0579901i			0.00210214i	0.999999	+	0.00105107i	$0.000334566\pi$
$761$			0.0579901i			0.00210214i	−0.999999	+	0.00105107i	$0.999665\pi$
$762$	2.15923	−	2.15923i	0.0782206	−	0.0782206i
$763$	11.0573	+	11.0573i	0.400300	+	0.400300i
$764$		−	19.7130i		−	0.713192i
$765$	−7.67626	−	2.26837i	−0.277536	−	0.0820132i
$766$			35.6464i			1.28796i
$767$	−23.4519	−	23.4519i	−0.846798	−	0.846798i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$			3.84574i			0.138681i	0.997593	+	0.0693405i	$0.0220895\pi$
$769$			3.84574i			0.138681i	−0.997593	+	0.0693405i	$0.977911\pi$
$770$	8.06150	+	14.8244i	0.290516	+	0.534234i
$771$			3.95200i			0.142328i
$772$	−3.02398	+	3.02398i	−0.108836	+	0.108836i
$773$	−5.69371	+	5.69371i	−0.204788	+	0.204788i	−0.802048	−	0.597260i	$-0.796256\pi$
$773$	−5.69371	+	5.69371i	−0.204788	+	0.204788i	0.597260	+	0.802048i	$0.296256\pi$
$774$	−6.89717			−0.247914
$775$	23.1099	−	15.5220i	0.830133	−	0.557565i
$776$	−10.2037			−0.366292
$777$	−3.42849	+	3.42849i	−0.122997	+	0.122997i
$778$	−13.0795	+	13.0795i	−0.468924	+	0.468924i
$779$		−	17.5042i		−	0.627152i
$780$	6.99724	+	12.8673i	0.250541	+	0.460724i
$781$			77.8563i			2.78592i
$782$	−7.36066	+	7.36066i	−0.263216	+	0.263216i
$783$	2.13246	+	2.13246i	0.0762077	+	0.0762077i
$784$		−	4.75989i		−	0.169996i
$785$	−9.39961	−	2.77763i	−0.335487	−	0.0991380i
$786$			0.0930152i			0.00331774i
$787$	−31.0306	−	31.0306i	−1.10612	−	1.10612i	−0.993655	−	0.112467i	$-0.964125\pi$
$787$	−31.0306	−	31.0306i	−1.10612	−	1.10612i	−0.112467	−	0.993655i	$-0.535875\pi$
$788$	3.98103	−	3.98103i	0.141818	−	0.141818i
$789$			8.00630i			0.285032i
$790$	−27.2431	−	8.05048i	−0.969267	−	0.286423i
$791$	−30.8313			−1.09624
$792$	3.56532	+	3.56532i	0.126688	+	0.126688i
$793$	−21.4827	−	21.4827i	−0.762873	−	0.762873i
$794$		−	11.9565i		−	0.424319i
$795$	16.6088	−	9.03185i	0.589053	−	0.320327i
$796$		−	14.3596i		−	0.508964i
$797$	12.8535	+	12.8535i	0.455296	+	0.455296i	0.897108	−	0.441812i	$-0.145664\pi$
$797$	12.8535	+	12.8535i	0.455296	+	0.455296i	−0.441812	+	0.897108i	$0.645664\pi$
$798$	−8.29133	+	8.29133i	−0.293510	+	0.293510i
$799$	−28.9866			−1.02547
$800$	1.04593	+	4.88938i	0.0369792	+	0.172866i
$801$			2.92224i			0.103252i
$802$	−5.40371	−	5.40371i	−0.190812	−	0.190812i
$803$	−28.5439	−	28.5439i	−1.00729	−	1.00729i
$804$	7.69692			0.271450
$805$	8.54971	−	4.64933i	0.301338	−	0.163867i
$806$	−14.3596	+	33.5244i	−0.505795	+	1.18085i
$807$	−3.67996	+	3.67996i	−0.129541	+	0.129541i
$808$	−5.87158	−	5.87158i	−0.206561	−	0.206561i
$809$	32.9889			1.15983			0.579913	−	0.814678i	$-0.303086\pi$
$809$	32.9889			1.15983			0.579913	+	0.814678i	$0.303086\pi$
$810$	2.14440	+	0.633681i	0.0753465	+	0.0222653i
$811$	−51.3364			−1.80267			−0.901333	−	0.433127i	$-0.857410\pi$
$811$	−51.3364			−1.80267			−0.901333	+	0.433127i	$0.857410\pi$
$812$	−3.19164	−	3.19164i	−0.112005	−	0.112005i
$813$	10.8624	+	10.8624i	0.380959	+	0.380959i
$814$		−	16.3342i		−	0.572512i
$815$	1.80763	−	6.11707i	0.0633184	−	0.214272i
$816$	3.57968			0.125314
$817$	38.2086	+	38.2086i	1.33675	+	1.33675i
$818$	16.2147	−	16.2147i	0.566935	−	0.566935i
$819$	−9.80376			−0.342571
$820$	4.38901	−	2.38674i	0.153271	−	0.0833486i
$821$			3.93571i			0.137357i	0.997639	+	0.0686786i	$0.0218783\pi$
$821$			3.93571i			0.137357i	−0.997639	+	0.0686786i	$0.978122\pi$
$822$	4.24973	−	4.24973i	0.148226	−	0.148226i
$823$	31.8846	−	31.8846i	1.11143	−	1.11143i	0.118468	−	0.992958i	$-0.462202\pi$
$823$	31.8846	−	31.8846i	1.11143	−	1.11143i	0.992958	−	0.118468i	$-0.0377982\pi$
$824$			15.6013i			0.543498i
$825$	−24.6528	+	5.27369i	−0.858301	+	0.183606i
$826$	7.57824			0.263681
$827$	33.8426	+	33.8426i	1.17682	+	1.17682i	0.980549	+	0.196272i	$0.0628837\pi$
$827$	33.8426	+	33.8426i	1.17682	+	1.17682i	0.196272	+	0.980549i	$0.437116\pi$
$828$	2.05623	−	2.05623i	0.0714591	−	0.0714591i
$829$	39.8409			1.38373			0.691866	−	0.722026i	$-0.256789\pi$
$829$	39.8409			1.38373			0.691866	+	0.722026i	$0.256789\pi$
$830$	23.4830	−	12.7701i	0.815108	−	0.443255i
$831$	−11.3959			−0.395319
$832$	−4.63173	−	4.63173i	−0.160576	−	0.160576i
$833$	12.0483	−	12.0483i	0.417449	−	0.417449i
$834$			4.79836i			0.166154i
$835$	−14.5666	+	49.2938i	−0.504097	+	1.70588i
$836$		−	39.5019i		−	1.36620i
$837$	2.06886	+	5.16912i	0.0715102	+	0.178671i
$838$	−21.5791	−	21.5791i	−0.745438	−	0.745438i
$839$			35.9863i			1.24239i	0.783657	+	0.621193i	$0.213352\pi$
$839$			35.9863i			1.24239i	−0.783657	+	0.621193i	$0.786648\pi$
$840$	−3.20952	−	0.948429i	−0.110739	−	0.0327239i
$841$	−19.9053			−0.686389
$842$	−15.3973	+	15.3973i	−0.530627	+	0.530627i
$843$	−13.6539	+	13.6539i	−0.470266	+	0.470266i
$844$		−	9.13202i		−	0.314337i
$845$	58.7471	−	31.9467i	2.02096	−	1.09900i
$846$	8.09754			0.278399
$847$	15.2642	−	15.2642i	0.524483	−	0.524483i
$848$	−5.97851	+	5.97851i	−0.205303	+	0.205303i
$849$	−12.5774			−0.431655
$850$	−9.72860	+	15.0235i	−0.333688	+	0.515303i
$851$	−9.42045			−0.322929
$852$	−10.9186	−	10.9186i	−0.374064	−	0.374064i
$853$	34.2863	+	34.2863i	1.17394	+	1.17394i	0.981262	+	0.192680i	$0.0617181\pi$
$853$	34.2863	+	34.2863i	1.17394	+	1.17394i	0.192680	+	0.981262i	$0.438282\pi$
$854$	6.94192			0.237548
$855$	−8.36900	−	15.3899i	−0.286214	−	0.526322i
$856$	2.14900			0.0734514
$857$	1.05382	−	1.05382i	0.0359978	−	0.0359978i	−0.688879	−	0.724877i	$-0.741897\pi$
$857$	1.05382	−	1.05382i	0.0359978	−	0.0359978i	0.724877	+	0.688879i	$0.241897\pi$
$858$	23.3537	−	23.3537i	0.797284	−	0.797284i
$859$	−7.56805			−0.258219			−0.129109	−	0.991630i	$-0.541212\pi$
$859$	−7.56805			−0.258219			−0.129109	+	0.991630i	$0.541212\pi$
$860$	−4.37060	+	14.7903i	−0.149036	+	0.504344i
$861$			3.34404i			0.113964i
$862$	−0.552334	+	0.552334i	−0.0188126	+	0.0188126i
$863$	−20.5693	+	20.5693i	−0.700187	+	0.700187i	−0.964450	−	0.264264i	$-0.914871\pi$
$863$	−20.5693	+	20.5693i	−0.700187	+	0.700187i	0.264264	+	0.964450i	$0.414871\pi$
$864$	−1.00000			−0.0340207
$865$	−0.470190	+	1.59114i	−0.0159869	+	0.0541004i
$866$		−	7.00791i		−	0.238138i
$867$	−2.95989	−	2.95989i	−0.100523	−	0.100523i
$868$	−3.09646	−	7.73662i	−0.105101	−	0.262598i
$869$			64.0566i			2.17297i
$870$	5.92413	−	3.22154i	0.200847	−	0.109220i
$871$		−	50.4168i		−	1.70831i
$872$	7.38778	−	7.38778i	0.250182	−	0.250182i
$873$	7.21512	+	7.21512i	0.244195	+	0.244195i
$874$	−22.7820			−0.770614
$875$	12.7031	−	10.8924i	0.429442	−	0.368232i
$876$	8.00599			0.270497
$877$	−34.9011	+	34.9011i	−1.17853	+	1.17853i	−0.198406	+	0.980120i	$0.563576\pi$
$877$	−34.9011	+	34.9011i	−1.17853	+	1.17853i	−0.980120	+	0.198406i	$0.936424\pi$
$878$	2.84269	+	2.84269i	0.0959362	+	0.0959362i
$879$	12.4933			0.421389
$880$	9.90473	−	5.38619i	0.333889	−	0.181568i
$881$			15.2410i			0.513484i	0.966480	+	0.256742i	$0.0826490\pi$
$881$			15.2410i			0.513484i	−0.966480	+	0.256742i	$0.917351\pi$
$882$	−3.36575	+	3.36575i	−0.113331	+	0.113331i
$883$	6.41003	−	6.41003i	0.215715	−	0.215715i	−0.590975	−	0.806690i	$-0.701257\pi$
$883$	6.41003	−	6.41003i	0.215715	−	0.215715i	0.806690	+	0.590975i	$0.201257\pi$
$884$		−	23.4478i		−	0.788635i
$885$	−3.20852	+	10.8577i	−0.107853	+	0.364979i
$886$	−21.5677			−0.724582
$887$	−23.7037	+	23.7037i	−0.795893	+	0.795893i	−0.982445	−	0.186552i	$-0.940269\pi$
$887$	−23.7037	+	23.7037i	−0.795893	+	0.795893i	0.186552	+	0.982445i	$0.440269\pi$
$888$	2.29070	+	2.29070i	0.0768710	+	0.0768710i
$889$	4.57033			0.153284
$890$	6.26645	+	1.85177i	0.210052	+	0.0620714i
$891$		−	5.04212i		−	0.168917i
$892$	−4.77518	−	4.77518i	−0.159885	−	0.159885i
$893$	−44.8584	−	44.8584i	−1.50113	−	1.50113i
$894$	11.4909			0.384314
$895$	3.06675	+	5.63948i	0.102510	+	0.188507i
$896$	1.49670			0.0500012
$897$	−13.4689	−	13.4689i	−0.449712	−	0.449712i
$898$	9.90525	−	9.90525i	0.330542	−	0.330542i
$899$	15.4347	+	6.61117i	0.514775	+	0.220495i
$900$	2.71773	−	4.19690i	0.0905910	−	0.139897i
$901$	−30.2658			−1.00830
$902$	−7.96590	−	7.96590i	−0.265235	−	0.265235i
$903$	−7.29945	−	7.29945i	−0.242910	−	0.242910i
$904$			20.5996i			0.685131i
$905$	−50.5445	+	27.4861i	−1.68016	+	0.913668i
$906$	6.44191			0.214018
$907$	−12.9844	+	12.9844i	−0.431139	+	0.431139i	−0.889016	−	0.457877i	$-0.848610\pi$
$907$	−12.9844	+	12.9844i	−0.431139	+	0.431139i	0.457877	+	0.889016i	$0.348610\pi$
$908$	4.70595	+	4.70595i	0.156172	+	0.156172i
$909$			8.30366i			0.275415i
$910$	−6.21246	+	21.0232i	−0.205941	+	0.696912i
$911$			10.0038i			0.331441i	0.986173	+	0.165720i	$0.0529949\pi$
$911$			10.0038i			0.331441i	−0.986173	+	0.165720i	$0.947005\pi$
$912$	5.53975	+	5.53975i	0.183439	+	0.183439i
$913$	−42.6209	−	42.6209i	−1.41055	−	1.41055i
$914$	30.2568			1.00081
$915$	−2.93911	+	9.94606i	−0.0971640	+	0.328807i
$916$			25.0935i			0.829114i
$917$	−0.0984403	+	0.0984403i	−0.00325079	+	0.00325079i
$918$	−2.53121	−	2.53121i	−0.0835425	−	0.0835425i
$919$			26.5931i			0.877224i	0.898676	+	0.438612i	$0.144530\pi$
$919$			26.5931i			0.877224i	−0.898676	+	0.438612i	$0.855470\pi$
$920$	−3.10639	−	5.71238i	−0.102415	−	0.188332i
$921$		−	9.37351i		−	0.308868i
$922$	9.39125	+	9.39125i	0.309284	+	0.309284i
$923$	−71.5195	+	71.5195i	−2.35409	+	2.35409i
$924$			7.54653i			0.248263i
$925$	−15.8394	+	3.38833i	−0.520795	+	0.111408i
$926$		−	8.45602i		−	0.277882i
$927$	11.0318	−	11.0318i	0.362332	−	0.362332i
$928$	−2.13246	+	2.13246i	−0.0700013	+	0.0700013i
$929$	26.4741			0.868588			0.434294	−	0.900771i	$-0.356998\pi$
$929$	26.4741			0.868588			0.434294	+	0.900771i	$0.356998\pi$
$930$	12.3957	−	1.16088i	0.406470	−	0.0380669i
$931$	37.2909			1.22216
$932$	19.4361	−	19.4361i	0.636651	−	0.636651i
$933$	−1.35606	+	1.35606i	−0.0443954	+	0.0443954i
$934$		−	13.7487i		−	0.449871i
$935$	38.7046	+	11.4374i	1.26578	+	0.374043i
$936$			6.55026i			0.214102i
$937$	23.7864	−	23.7864i	0.777067	−	0.777067i	−0.202264	−	0.979331i	$-0.564830\pi$
$937$	23.7864	−	23.7864i	0.777067	−	0.777067i	0.979331	+	0.202264i	$0.0648298\pi$
$938$	8.14585	+	8.14585i	0.265971	+	0.265971i
$939$		−	10.2318i		−	0.333902i
$940$	5.13126	−	17.3644i	0.167363	−	0.566363i
$941$			1.41436i			0.0461067i	0.999734	+	0.0230534i	$0.00733877\pi$
$941$			1.41436i			0.0461067i	−0.999734	+	0.0230534i	$0.992661\pi$
$942$	−3.09948	−	3.09948i	−0.100987	−	0.100987i
$943$	−4.59419	+	4.59419i	−0.149608	+	0.149608i
$944$		−	5.06330i		−	0.164797i
$945$	1.59883	+	2.94011i	0.0520100	+	0.0956419i
$946$	34.7763			1.13068
$947$	19.7136	+	19.7136i	0.640605	+	0.640605i	0.950704	−	0.310100i	$-0.100362\pi$
$947$	19.7136	+	19.7136i	0.640605	+	0.640605i	−0.310100	+	0.950704i	$0.600362\pi$
$948$	−8.98330	−	8.98330i	−0.291764	−	0.291764i
$949$		−	52.4413i		−	1.70232i
$950$	−38.3053	+	8.19421i	−1.24279	+	0.265855i
$951$			19.9838i			0.648018i
$952$	3.78846	+	3.78846i	0.122785	+	0.122785i
$953$	34.0418	−	34.0418i	1.10272	−	1.10272i	0.108642	−	0.994081i	$-0.465350\pi$
$953$	34.0418	−	34.0418i	1.10272	−	1.10272i	0.994081	−	0.108642i	$-0.0346501\pi$
$954$	8.45489			0.273737
$955$	21.0582	+	38.7242i	0.681428	+	1.25309i
$956$		−	29.7199i		−	0.961211i
$957$	−10.7521	−	10.7521i	−0.347566	−	0.347566i
$958$	−11.2423	−	11.2423i	−0.363223	−	0.363223i
$959$	8.99519			0.290470
$960$	−0.633681	+	2.14440i	−0.0204520	+	0.0692102i
$961$	21.3884	+	22.4396i	0.689947	+	0.723860i
$962$	15.0047	−	15.0047i	0.483771	−	0.483771i
$963$	−1.51957	−	1.51957i	−0.0489676	−	0.0489676i
$964$	−12.5924			−0.405575
$965$	2.70997	−	9.17065i	0.0872371	−	0.295214i
$966$	4.35233			0.140034
$967$	7.33819	+	7.33819i	0.235980	+	0.235980i	0.815183	−	0.579203i	$-0.196636\pi$
$967$	7.33819	+	7.33819i	0.235980	+	0.235980i	−0.579203	+	0.815183i	$0.696636\pi$
$968$	−10.1986	−	10.1986i	−0.327794	−	0.327794i
$969$			28.0446i			0.900922i
$970$	20.0442	−	10.9000i	0.643580	−	0.349978i
$971$	−3.20869			−0.102972			−0.0514858	−	0.998674i	$-0.516396\pi$
$971$	−3.20869			−0.102972			−0.0514858	+	0.998674i	$0.516396\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−5.07822	+	5.07822i	−0.162800	+	0.162800i
$974$	3.06607			0.0982432
$975$	−27.4908	−	17.8018i	−0.880409	−	0.570115i
$976$		−	4.63816i		−	0.148464i
$977$	21.2352	−	21.2352i	0.679373	−	0.679373i	−0.280485	−	0.959858i	$-0.590495\pi$
$977$	21.2352	−	21.2352i	0.679373	−	0.679373i	0.959858	+	0.280485i	$0.0904955\pi$
$978$	2.01708	−	2.01708i	0.0644990	−	0.0644990i
$979$		−	14.7343i		−	0.470909i
$980$	5.08471	+	9.35034i	0.162425	+	0.298686i
$981$	−10.4479			−0.333576
$982$	14.0695	+	14.0695i	0.448975	+	0.448975i
$983$	14.4629	−	14.4629i	0.461294	−	0.461294i	−0.437785	−	0.899080i	$-0.644237\pi$
$983$	14.4629	−	14.4629i	0.461294	−	0.461294i	0.899080	+	0.437785i	$0.144237\pi$
$984$	2.23428			0.0712261
$985$	−3.56764	+	12.0730i	−0.113674	+	0.384678i
$986$	−10.7954			−0.343796
$987$	8.56984	+	8.56984i	0.272781	+	0.272781i
$988$	36.2868	−	36.2868i	1.15444	−	1.15444i
$989$		−	20.0567i		−	0.637764i
$990$	−10.8123	−	3.19509i	−0.343638	−	0.101547i
$991$		−	34.1173i		−	1.08377i	−0.840452	−	0.541886i	$-0.817710\pi$
$991$		−	34.1173i		−	1.08377i	0.840452	−	0.541886i	$-0.182290\pi$
$992$	−5.16912	+	2.06886i	−0.164120	+	0.0656863i
$993$	7.56062	+	7.56062i	0.239929	+	0.239929i
$994$		−	23.1108i		−	0.733030i
$995$	15.3395	+	28.2081i	0.486296	+	0.894256i
$996$	11.9543			0.378787
$997$	10.4258	−	10.4258i	0.330188	−	0.330188i	−0.522470	−	0.852658i	$-0.674989\pi$
$997$	10.4258	−	10.4258i	0.330188	−	0.330188i	0.852658	+	0.522470i	$0.174989\pi$
$998$	−2.65081	+	2.65081i	−0.0839100	+	0.0839100i
$999$		−	3.23955i		−	0.102495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.a.433.6	yes	32
5.2	odd	4		930.2.k.b.247.6	yes	32
31.30	odd	2		930.2.k.b.433.6	yes	32
155.92	even	4	inner	930.2.k.a.247.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.6	✓	32	155.92	even	4	inner
930.2.k.a.433.6	yes	32	1.1	even	1	trivial
930.2.k.b.247.6	yes	32	5.2	odd	4
930.2.k.b.433.6	yes	32	31.30	odd	2

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.06824 + 1.96440i) q^{5} +1.00000i q^{6} +(-1.05833 + 1.05833i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.06824 + 1.96440i) q^{5} +1.00000i q^{6} +(-1.05833 + 1.05833i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-2.14440 - 0.633681i) q^{10} +5.04212i q^{11} +(-0.707107 - 0.707107i) q^{12} +(-4.63173 + 4.63173i) q^{13} -1.49670i q^{14} +(2.14440 + 0.633681i) q^{15} -1.00000 q^{16} +(-2.53121 - 2.53121i) q^{17} +(0.707107 + 0.707107i) q^{18} -7.83439i q^{19} +(1.96440 - 1.06824i) q^{20} +1.49670i q^{21} +(-3.56532 - 3.56532i) q^{22} +(-2.05623 + 2.05623i) q^{23} +1.00000 q^{24} +(-2.71773 + 4.19690i) q^{25} -6.55026i q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.05833 + 1.05833i) q^{28} -3.01575 q^{29} +(-1.96440 + 1.06824i) q^{30} +(-5.11803 - 2.19222i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.56532 + 3.56532i) q^{33} +3.57968 q^{34} +(-3.20952 - 0.948429i) q^{35} -1.00000 q^{36} +(2.29070 + 2.29070i) q^{37} +(5.53975 + 5.53975i) q^{38} +6.55026i q^{39} +(-0.633681 + 2.14440i) q^{40} +2.23428 q^{41} +(-1.05833 - 1.05833i) q^{42} +(-4.87703 + 4.87703i) q^{43} +5.04212 q^{44} +(1.96440 - 1.06824i) q^{45} -2.90795i q^{46} +(5.72583 - 5.72583i) q^{47} +(-0.707107 + 0.707107i) q^{48} +4.75989i q^{49} +(-1.04593 - 4.88938i) q^{50} -3.57968 q^{51} +(4.63173 + 4.63173i) q^{52} +(5.97851 - 5.97851i) q^{53} +1.00000 q^{54} +(-9.90473 + 5.38619i) q^{55} -1.49670 q^{56} +(-5.53975 - 5.53975i) q^{57} +(2.13246 - 2.13246i) q^{58} +5.06330i q^{59} +(0.633681 - 2.14440i) q^{60} +4.63816i q^{61} +(5.16912 - 2.06886i) q^{62} +(1.05833 + 1.05833i) q^{63} +1.00000i q^{64} +(-14.0464 - 4.15078i) q^{65} -5.04212 q^{66} +(-5.44255 + 5.44255i) q^{67} +(-2.53121 + 2.53121i) q^{68} +2.90795i q^{69} +(2.94011 - 1.59883i) q^{70} +15.4412 q^{71} +(0.707107 - 0.707107i) q^{72} +(-5.66109 + 5.66109i) q^{73} -3.23955 q^{74} +(1.04593 + 4.88938i) q^{75} -7.83439 q^{76} +(-5.33620 - 5.33620i) q^{77} +(-4.63173 - 4.63173i) q^{78} +12.7043 q^{79} +(-1.06824 - 1.96440i) q^{80} -1.00000 q^{81} +(-1.57987 + 1.57987i) q^{82} +(-8.45297 + 8.45297i) q^{83} +1.49670 q^{84} +(2.26837 - 7.67626i) q^{85} -6.89717i q^{86} +(-2.13246 + 2.13246i) q^{87} +(-3.56532 + 3.56532i) q^{88} -2.92224 q^{89} +(-0.633681 + 2.14440i) q^{90} -9.80376i q^{91} +(2.05623 + 2.05623i) q^{92} +(-5.16912 + 2.06886i) q^{93} +8.09754i q^{94} +(15.3899 - 8.36900i) q^{95} -1.00000i q^{96} +(-7.21512 + 7.21512i) q^{97} +(-3.36575 - 3.36575i) q^{98} +5.04212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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