LMFDB - Embedded newform 1890.2.t.c.1151.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (of order $6$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.14
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.c.1601.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.80382 + 1.93552i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.80382 + 1.93552i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +0.781517i q^{11} +(-2.26905 - 1.31003i) q^{13} +(-2.52991 + 0.774302i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.02795 + 5.24457i) q^{17} +(6.09668 - 3.51992i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.390758 + 0.676813i) q^{22} -4.60919i q^{23} +1.00000 q^{25} +(-1.31003 - 2.26905i) q^{26} +(-2.57812 - 0.594391i) q^{28} +(-3.96237 + 2.28767i) q^{29} +(-6.47842 + 3.74031i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.24457 + 3.02795i) q^{34} +(1.80382 - 1.93552i) q^{35} +(-5.42975 - 9.40460i) q^{37} +7.03984 q^{38} -1.00000i q^{40} +(-5.46910 + 9.47275i) q^{41} +(-4.45098 - 7.70932i) q^{43} +(-0.676813 + 0.390758i) q^{44} +(2.30460 - 3.99168i) q^{46} +(-0.501266 + 0.868218i) q^{47} +(-0.492485 - 6.98265i) q^{49} +(0.866025 + 0.500000i) q^{50} -2.62007i q^{52} +(-8.30234 - 4.79336i) q^{53} -0.781517i q^{55} +(-1.93552 - 1.80382i) q^{56} -4.57535 q^{58} +(-1.32003 - 2.28635i) q^{59} +(1.84617 + 1.06588i) q^{61} -7.48063 q^{62} -1.00000 q^{64} +(2.26905 + 1.31003i) q^{65} +(-6.02939 - 10.4432i) q^{67} -6.05590 q^{68} +(2.52991 - 0.774302i) q^{70} +10.1200i q^{71} +(7.67003 + 4.42830i) q^{73} -10.8595i q^{74} +(6.09668 + 3.51992i) q^{76} +(-1.51264 - 1.40971i) q^{77} +(-7.96847 + 13.8018i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-9.47275 + 5.46910i) q^{82} +(2.03248 + 3.52036i) q^{83} +(3.02795 - 5.24457i) q^{85} -8.90195i q^{86} -0.781517 q^{88} +(3.78927 + 6.56320i) q^{89} +(6.62855 - 2.02872i) q^{91} +(3.99168 - 2.30460i) q^{92} +(-0.868218 + 0.501266i) q^{94} +(-6.09668 + 3.51992i) q^{95} +(5.00436 - 2.88927i) q^{97} +(3.06482 - 6.29340i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.80382	+	1.93552i	−0.681779	+	0.731558i
$7$	−1.80382	+	1.93552i	−0.681779	+	0.731558i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$			0.781517i			0.235636i	0.993035	+	0.117818i	$0.0375900\pi$
$11$			0.781517i			0.235636i	−0.993035	+	0.117818i	$0.962410\pi$
$12$		0			0
$13$	−2.26905	−	1.31003i	−0.629320	−	0.363338i	0.151168	−	0.988508i	$-0.451696\pi$
$13$	−2.26905	−	1.31003i	−0.629320	−	0.363338i	−0.780489	+	0.625170i	$0.785030\pi$
$14$	−2.52991	+	0.774302i	−0.676148	+	0.206941i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.02795	+	5.24457i	−0.734386	+	1.27199i	0.220606	+	0.975363i	$0.429197\pi$
$17$	−3.02795	+	5.24457i	−0.734386	+	1.27199i	−0.954992	+	0.296631i	$0.904137\pi$
$18$		0			0
$19$	6.09668	−	3.51992i	1.39867	−	0.807525i	0.404421	−	0.914573i	$-0.367473\pi$
$19$	6.09668	−	3.51992i	1.39867	−	0.807525i	0.994254	+	0.107048i	$0.0341397\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−0.390758	+	0.676813i	−0.0833100	+	0.144297i
$23$		−	4.60919i		−	0.961083i	−0.876972	−	0.480542i	$-0.840440\pi$
$23$		−	4.60919i		−	0.961083i	0.876972	−	0.480542i	$-0.159560\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.31003	−	2.26905i	−0.256919	−	0.444997i
$27$		0			0
$28$	−2.57812	−	0.594391i	−0.487219	−	0.112329i
$29$	−3.96237	+	2.28767i	−0.735793	+	0.424810i	−0.820538	−	0.571592i	$-0.806326\pi$
$29$	−3.96237	+	2.28767i	−0.735793	+	0.424810i	0.0847445	+	0.996403i	$0.472993\pi$
$30$		0			0
$31$	−6.47842	+	3.74031i	−1.16356	+	0.671780i	−0.952154	−	0.305618i	$-0.901137\pi$
$31$	−6.47842	+	3.74031i	−1.16356	+	0.671780i	−0.211404	+	0.977399i	$0.567803\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−5.24457	+	3.02795i	−0.899436	+	0.519289i
$35$	1.80382	−	1.93552i	0.304901	−	0.327163i
$36$		0			0
$37$	−5.42975	−	9.40460i	−0.892645	−	1.54611i	−0.836692	−	0.547673i	$-0.815514\pi$
$37$	−5.42975	−	9.40460i	−0.892645	−	1.54611i	−0.0559531	−	0.998433i	$-0.517820\pi$
$38$	7.03984			1.14201
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$	−5.46910	+	9.47275i	−0.854129	+	1.47940i	0.0233211	+	0.999728i	$0.492576\pi$
$41$	−5.46910	+	9.47275i	−0.854129	+	1.47940i	−0.877450	+	0.479667i	$0.840757\pi$
$42$		0			0
$43$	−4.45098	−	7.70932i	−0.678768	−	1.17566i	−0.975352	−	0.220654i	$-0.929181\pi$
$43$	−4.45098	−	7.70932i	−0.678768	−	1.17566i	0.296585	−	0.955007i	$-0.404152\pi$
$44$	−0.676813	+	0.390758i	−0.102033	+	0.0589090i
$45$		0			0
$46$	2.30460	−	3.99168i	0.339794	−	0.588541i
$47$	−0.501266	+	0.868218i	−0.0731172	+	0.126643i	−0.900266	−	0.435340i	$-0.856628\pi$
$47$	−0.501266	+	0.868218i	−0.0731172	+	0.126643i	0.827149	+	0.561983i	$0.189961\pi$
$48$		0			0
$49$	−0.492485	−	6.98265i	−0.0703549	−	0.997522i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$		−	2.62007i		−	0.363338i
$53$	−8.30234	−	4.79336i	−1.14041	−	0.658418i	−0.193881	−	0.981025i	$-0.562107\pi$
$53$	−8.30234	−	4.79336i	−1.14041	−	0.658418i	−0.946533	+	0.322607i	$0.895441\pi$
$54$		0			0
$55$		−	0.781517i		−	0.105380i
$56$	−1.93552	−	1.80382i	−0.258645	−	0.241045i
$57$		0			0
$58$	−4.57535			−0.600773
$59$	−1.32003	−	2.28635i	−0.171853	−	0.297658i	0.767215	−	0.641390i	$-0.221642\pi$
$59$	−1.32003	−	2.28635i	−0.171853	−	0.297658i	−0.939068	+	0.343733i	$0.888309\pi$
$60$		0			0
$61$	1.84617	+	1.06588i	0.236377	+	0.136473i	0.613511	−	0.789686i	$-0.289757\pi$
$61$	1.84617	+	1.06588i	0.236377	+	0.136473i	−0.377133	+	0.926159i	$0.623090\pi$
$62$	−7.48063			−0.950041
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.26905	+	1.31003i	0.281441	+	0.162490i
$66$		0			0
$67$	−6.02939	−	10.4432i	−0.736607	−	1.27584i	−0.954015	−	0.299760i	$-0.903093\pi$
$67$	−6.02939	−	10.4432i	−0.736607	−	1.27584i	0.217407	−	0.976081i	$-0.430240\pi$
$68$	−6.05590			−0.734386
$69$		0			0
$70$	2.52991	−	0.774302i	0.302382	−	0.0925468i
$71$			10.1200i			1.20103i	0.799614	+	0.600514i	$0.205037\pi$
$71$			10.1200i			1.20103i	−0.799614	+	0.600514i	$0.794963\pi$
$72$		0			0
$73$	7.67003	+	4.42830i	0.897710	+	0.518293i	0.876456	−	0.481481i	$-0.159901\pi$
$73$	7.67003	+	4.42830i	0.897710	+	0.518293i	0.0212532	+	0.999774i	$0.493234\pi$
$74$		−	10.8595i		−	1.26239i
$75$		0			0
$76$	6.09668	+	3.51992i	0.699337	+	0.403763i
$77$	−1.51264	−	1.40971i	−0.172382	−	0.160652i
$78$		0			0
$79$	−7.96847	+	13.8018i	−0.896523	+	1.55282i	−0.0646137	+	0.997910i	$0.520582\pi$
$79$	−7.96847	+	13.8018i	−0.896523	+	1.55282i	−0.831909	+	0.554912i	$0.812752\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−9.47275	+	5.46910i	−1.04609	+	0.603961i
$83$	2.03248	+	3.52036i	0.223094	+	0.386410i	0.955746	−	0.294194i	$-0.0950511\pi$
$83$	2.03248	+	3.52036i	0.223094	+	0.386410i	−0.732652	+	0.680603i	$0.761718\pi$
$84$		0			0
$85$	3.02795	−	5.24457i	0.328428	−	0.568853i
$86$		−	8.90195i		−	0.959922i
$87$		0			0
$88$	−0.781517			−0.0833100
$89$	3.78927	+	6.56320i	0.401662	+	0.695698i	0.993927	−	0.110045i	$-0.0350995\pi$
$89$	3.78927	+	6.56320i	0.401662	+	0.695698i	−0.592265	+	0.805743i	$0.701766\pi$
$90$		0			0
$91$	6.62855	−	2.02872i	0.694860	−	0.212668i
$92$	3.99168	−	2.30460i	0.416161	−	0.240271i
$93$		0			0
$94$	−0.868218	+	0.501266i	−0.0895499	+	0.0517017i
$95$	−6.09668	+	3.51992i	−0.625506	+	0.361136i
$96$		0			0
$97$	5.00436	−	2.88927i	0.508115	−	0.293361i	−0.223943	−	0.974602i	$-0.571893\pi$
$97$	5.00436	−	2.88927i	0.508115	−	0.293361i	0.732059	+	0.681242i	$0.238560\pi$
$98$	3.06482	−	6.29340i	0.309594	−	0.635729i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−0.998784			−0.0993827			−0.0496914	−	0.998765i	$-0.515824\pi$
$101$	−0.998784			−0.0993827			−0.0496914	+	0.998765i	$0.515824\pi$
$102$		0			0
$103$			5.87358i			0.578741i	0.957217	+	0.289370i	$0.0934459\pi$
$103$			5.87358i			0.578741i	−0.957217	+	0.289370i	$0.906554\pi$
$104$	1.31003	−	2.26905i	0.128459	−	0.222498i
$105$		0			0
$106$	−4.79336	−	8.30234i	−0.465572	−	0.806394i
$107$	−4.22082	+	2.43689i	−0.408042	+	0.235583i	−0.689948	−	0.723859i	$-0.742367\pi$
$107$	−4.22082	+	2.43689i	−0.408042	+	0.235583i	0.281906	+	0.959442i	$0.409033\pi$
$108$		0			0
$109$	0.338969	−	0.587111i	0.0324673	−	0.0562350i	−0.849335	−	0.527854i	$-0.822997\pi$
$109$	0.338969	−	0.587111i	0.0324673	−	0.0562350i	0.881802	+	0.471619i	$0.156330\pi$
$110$	0.390758	−	0.676813i	0.0372573	−	0.0645316i
$111$		0			0
$112$	−0.774302	−	2.52991i	−0.0731646	−	0.239054i
$113$	2.66192	+	1.53686i	0.250413	+	0.144576i	0.619953	−	0.784639i	$-0.287152\pi$
$113$	2.66192	+	1.53686i	0.250413	+	0.144576i	−0.369541	+	0.929215i	$0.620485\pi$
$114$		0			0
$115$			4.60919i			0.429809i
$116$	−3.96237	−	2.28767i	−0.367897	−	0.212405i
$117$		0			0
$118$		−	2.64005i		−	0.243036i
$119$	−4.68910	−	15.3209i	−0.429849	−	1.40447i
$120$		0			0
$121$	10.3892			0.944476
$122$	1.06588	+	1.84617i	0.0965006	+	0.167144i
$123$		0			0
$124$	−6.47842	−	3.74031i	−0.581779	−	0.335890i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.401239			−0.0356042			−0.0178021	−	0.999842i	$-0.505667\pi$
$127$	−0.401239			−0.0356042			−0.0178021	+	0.999842i	$0.505667\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	1.31003	+	2.26905i	0.114898	+	0.199009i
$131$	−22.1595			−1.93608			−0.968042	−	0.250787i	$-0.919311\pi$
$131$	−22.1595			−1.93608			−0.968042	+	0.250787i	$0.919311\pi$
$132$		0			0
$133$	−4.18442	+	18.1496i	−0.362835	+	1.57377i
$134$		−	12.0588i		−	1.04172i
$135$		0			0
$136$	−5.24457	−	3.02795i	−0.449718	−	0.259645i
$137$		−	19.2002i		−	1.64039i	−0.572086	−	0.820194i	$-0.693866\pi$
$137$		−	19.2002i		−	1.64039i	0.572086	−	0.820194i	$-0.306134\pi$
$138$		0			0
$139$	−0.151908	−	0.0877042i	−0.0128847	−	0.00743897i	0.493544	−	0.869721i	$-0.335701\pi$
$139$	−0.151908	−	0.0877042i	−0.0128847	−	0.00743897i	−0.506429	+	0.862282i	$0.669035\pi$
$140$	2.57812	+	0.594391i	0.217891	+	0.0502352i
$141$		0			0
$142$	−5.06002	+	8.76422i	−0.424628	+	0.735477i
$143$	1.02381	−	1.77330i	0.0856156	−	0.148291i
$144$		0			0
$145$	3.96237	−	2.28767i	0.329057	−	0.189981i
$146$	4.42830	+	7.67003i	0.366488	+	0.634777i
$147$		0			0
$148$	5.42975	−	9.40460i	0.446323	−	0.773053i
$149$			1.23022i			0.100784i	0.998730	+	0.0503918i	$0.0160470\pi$
$149$			1.23022i			0.100784i	−0.998730	+	0.0503918i	$0.983953\pi$
$150$		0			0
$151$	1.87265			0.152394			0.0761969	−	0.997093i	$-0.475722\pi$
$151$	1.87265			0.152394			0.0761969	+	0.997093i	$0.475722\pi$
$152$	3.51992	+	6.09668i	0.285503	+	0.494506i
$153$		0			0
$154$	−0.605130	−	1.97717i	−0.0487627	−	0.159325i
$155$	6.47842	−	3.74031i	0.520359	−	0.300429i
$156$		0			0
$157$	5.99822	−	3.46308i	0.478710	−	0.276383i	−0.241169	−	0.970483i	$-0.577531\pi$
$157$	5.99822	−	3.46308i	0.478710	−	0.276383i	0.719879	+	0.694100i	$0.244197\pi$
$158$	−13.8018	+	7.96847i	−1.09801	+	0.633937i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	8.92119	+	8.31414i	0.703088	+	0.655246i
$162$		0			0
$163$	9.12797	+	15.8101i	0.714958	+	1.23834i	0.962976	+	0.269588i	$0.0868876\pi$
$163$	9.12797	+	15.8101i	0.714958	+	1.23834i	−0.248018	+	0.968756i	$0.579779\pi$
$164$	−10.9382			−0.854129
$165$		0			0
$166$			4.06496i			0.315502i
$167$	−10.7511	+	18.6214i	−0.831942	+	1.44097i	0.0645545	+	0.997914i	$0.479437\pi$
$167$	−10.7511	+	18.6214i	−0.831942	+	1.44097i	−0.896496	+	0.443051i	$0.853896\pi$
$168$		0			0
$169$	−3.06762	−	5.31327i	−0.235971	−	0.408713i
$170$	5.24457	−	3.02795i	0.402240	−	0.232233i
$171$		0			0
$172$	4.45098	−	7.70932i	0.339384	−	0.587830i
$173$	3.31016	−	5.73336i	0.251667	−	0.435900i	−0.712318	−	0.701857i	$-0.752355\pi$
$173$	3.31016	−	5.73336i	0.251667	−	0.435900i	0.963985	+	0.265957i	$0.0856880\pi$
$174$		0			0
$175$	−1.80382	+	1.93552i	−0.136356	+	0.146312i
$176$	−0.676813	−	0.390758i	−0.0510167	−	0.0294545i
$177$		0			0
$178$			7.57854i			0.568035i
$179$	8.99427	+	5.19284i	0.672263	+	0.388131i	0.796934	−	0.604067i	$-0.206454\pi$
$179$	8.99427	+	5.19284i	0.672263	+	0.388131i	−0.124671	+	0.992198i	$0.539787\pi$
$180$		0			0
$181$		−	0.766824i		−	0.0569975i	−0.999594	−	0.0284988i	$-0.990927\pi$
$181$		−	0.766824i		−	0.0569975i	0.999594	−	0.0284988i	$-0.00907267\pi$
$182$	6.75485	+	1.55735i	0.500703	+	0.115438i
$183$		0			0
$184$	4.60919			0.339794
$185$	5.42975	+	9.40460i	0.399203	+	0.691440i
$186$		0			0
$187$	−4.09872	−	2.36639i	−0.299728	−	0.173048i
$188$	−1.00253			−0.0731172
$189$		0			0
$190$	−7.03984			−0.510724
$191$	11.7224	+	6.76794i	0.848204	+	0.489711i	0.860044	−	0.510219i	$-0.170436\pi$
$191$	11.7224	+	6.76794i	0.848204	+	0.489711i	−0.0118406	+	0.999930i	$0.503769\pi$
$192$		0			0
$193$	4.69750	+	8.13632i	0.338134	+	0.585665i	0.984082	−	0.177717i	$-0.0568710\pi$
$193$	4.69750	+	8.13632i	0.338134	+	0.585665i	−0.645948	+	0.763381i	$0.723538\pi$
$194$	5.77853			0.414874
$195$		0			0
$196$	5.80091	−	3.91783i	0.414351	−	0.279845i
$197$			12.0072i			0.855480i	0.903902	+	0.427740i	$0.140690\pi$
$197$			12.0072i			0.855480i	−0.903902	+	0.427740i	$0.859310\pi$
$198$		0			0
$199$	3.77973	+	2.18223i	0.267938	+	0.154694i	0.627950	−	0.778253i	$-0.283894\pi$
$199$	3.77973	+	2.18223i	0.267938	+	0.154694i	−0.360012	+	0.932948i	$0.617227\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−0.864973	−	0.499392i	−0.0608593	−	0.0351371i
$203$	2.71955	−	11.7958i	0.190875	−	0.827902i
$204$		0			0
$205$	5.46910	−	9.47275i	0.381978	−	0.661606i
$206$	−2.93679	+	5.08667i	−0.204616	+	0.354405i
$207$		0			0
$208$	2.26905	−	1.31003i	0.157330	−	0.0908346i
$209$	2.75088	+	4.76466i	0.190282	+	0.329578i
$210$		0			0
$211$	−5.82791	+	10.0942i	−0.401210	+	0.694916i	−0.993872	−	0.110535i	$-0.964744\pi$
$211$	−5.82791	+	10.0942i	−0.401210	+	0.694916i	0.592662	+	0.805451i	$0.298077\pi$
$212$		−	9.58671i		−	0.658418i
$213$		0			0
$214$	−4.87379			−0.333165
$215$	4.45098	+	7.70932i	0.303554	+	0.525771i
$216$		0			0
$217$	4.44642	−	19.2860i	0.301843	−	1.30922i
$218$	0.587111	−	0.338969i	0.0397642	−	0.0229579i
$219$		0			0
$220$	0.676813	−	0.390758i	0.0456307	−	0.0263449i
$221$	13.7411	−	7.93344i	0.924328	−	0.533661i
$222$		0			0
$223$	8.63803	−	4.98717i	0.578446	−	0.333966i	−0.182070	−	0.983286i	$-0.558280\pi$
$223$	8.63803	−	4.98717i	0.578446	−	0.333966i	0.760515	+	0.649320i	$0.224946\pi$
$224$	0.594391	−	2.57812i	0.0397144	−	0.172258i
$225$		0			0
$226$	1.53686	+	2.66192i	0.102231	+	0.177068i
$227$	−17.1596			−1.13893			−0.569463	−	0.822017i	$-0.692849\pi$
$227$	−17.1596			−1.13893			−0.569463	+	0.822017i	$0.692849\pi$
$228$		0			0
$229$			12.8942i			0.852070i	0.904707	+	0.426035i	$0.140090\pi$
$229$			12.8942i			0.852070i	−0.904707	+	0.426035i	$0.859910\pi$
$230$	−2.30460	+	3.99168i	−0.151961	+	0.263203i
$231$		0			0
$232$	−2.28767	−	3.96237i	−0.150193	−	0.260142i
$233$	12.8761	−	7.43401i	0.843540	−	0.487018i	−0.0149261	−	0.999889i	$-0.504751\pi$
$233$	12.8761	−	7.43401i	0.843540	−	0.487018i	0.858466	+	0.512871i	$0.171418\pi$
$234$		0			0
$235$	0.501266	−	0.868218i	0.0326990	−	0.0566363i
$236$	1.32003	−	2.28635i	0.0859263	−	0.148829i
$237$		0			0
$238$	3.59958	−	15.6128i	0.233326	−	1.01203i
$239$	1.84122	+	1.06303i	0.119099	+	0.0687617i	0.558366	−	0.829595i	$-0.311429\pi$
$239$	1.84122	+	1.06303i	0.119099	+	0.0687617i	−0.439267	+	0.898356i	$0.644762\pi$
$240$		0			0
$241$		−	18.4443i		−	1.18810i	−0.804426	−	0.594052i	$-0.797527\pi$
$241$		−	18.4443i		−	1.18810i	0.804426	−	0.594052i	$-0.202473\pi$
$242$	8.99734	+	5.19462i	0.578371	+	0.333923i
$243$		0			0
$244$			2.13177i			0.136473i
$245$	0.492485	+	6.98265i	0.0314637	+	0.446105i
$246$		0			0
$247$	−18.4449			−1.17362
$248$	−3.74031	−	6.47842i	−0.237510	−	0.411380i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	14.4909			0.914655			0.457328	−	0.889298i	$-0.348807\pi$
$251$	14.4909			0.914655			0.457328	+	0.889298i	$0.348807\pi$
$252$		0			0
$253$	3.60216			0.226466
$254$	−0.347483	−	0.200619i	−0.0218030	−	0.0125880i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.81867			0.425337			0.212669	−	0.977124i	$-0.431785\pi$
$257$	6.81867			0.425337			0.212669	+	0.977124i	$0.431785\pi$
$258$		0			0
$259$	27.9971	+	6.45479i	1.73965	+	0.401081i
$260$			2.62007i			0.162490i
$261$		0			0
$262$	−19.1907	−	11.0798i	−1.18560	−	0.684509i
$263$		−	18.5629i		−	1.14464i	−0.820031	−	0.572319i	$-0.806044\pi$
$263$		−	18.5629i		−	1.14464i	0.820031	−	0.572319i	$-0.193956\pi$
$264$		0			0
$265$	8.30234	+	4.79336i	0.510008	+	0.294454i
$266$	−12.6986	+	13.6258i	−0.778601	+	0.835449i
$267$		0			0
$268$	6.02939	−	10.4432i	0.368304	−	0.637921i
$269$	0.646992	−	1.12062i	0.0394478	−	0.0683256i	−0.845627	−	0.533774i	$-0.820773\pi$
$269$	0.646992	−	1.12062i	0.0394478	−	0.0683256i	0.885075	+	0.465448i	$0.154107\pi$
$270$		0			0
$271$	−23.9309	+	13.8165i	−1.45370	+	0.839295i	−0.998689	−	0.0511902i	$-0.983699\pi$
$271$	−23.9309	+	13.8165i	−1.45370	+	0.839295i	−0.455012	+	0.890485i	$0.650365\pi$
$272$	−3.02795	−	5.24457i	−0.183597	−	0.317999i
$273$		0			0
$274$	9.60012	−	16.6279i	0.579964	−	1.00453i
$275$			0.781517i			0.0471272i
$276$		0			0
$277$	−24.4527			−1.46922			−0.734611	−	0.678488i	$-0.762635\pi$
$277$	−24.4527			−1.46922			−0.734611	+	0.678488i	$0.762635\pi$
$278$	−0.0877042	−	0.151908i	−0.00526015	−	0.00911084i
$279$		0			0
$280$	1.93552	+	1.80382i	0.115670	+	0.107799i
$281$	−2.32984	+	1.34513i	−0.138986	+	0.0802438i	−0.567881	−	0.823111i	$-0.692237\pi$
$281$	−2.32984	+	1.34513i	−0.138986	+	0.0802438i	0.428894	+	0.903355i	$0.358903\pi$
$282$		0			0
$283$	6.19520	−	3.57680i	0.368266	−	0.212619i	−0.304434	−	0.952533i	$-0.598467\pi$
$283$	6.19520	−	3.57680i	0.368266	−	0.212619i	0.672701	+	0.739915i	$0.265134\pi$
$284$	−8.76422	+	5.06002i	−0.520061	+	0.300257i
$285$		0			0
$286$	1.77330	−	1.02381i	0.104857	−	0.0605394i
$287$	−8.46946	−	27.6727i	−0.499936	−	1.63347i
$288$		0			0
$289$	−9.83699	−	17.0382i	−0.578646	−	1.00224i
$290$	4.57535			0.268674
$291$		0			0
$292$			8.85659i			0.518293i
$293$	2.65334	−	4.59573i	0.155010	−	0.268485i	−0.778053	−	0.628199i	$-0.783792\pi$
$293$	2.65334	−	4.59573i	0.155010	−	0.268485i	0.933063	+	0.359714i	$0.117126\pi$
$294$		0			0
$295$	1.32003	+	2.28635i	0.0768549	+	0.133117i
$296$	9.40460	−	5.42975i	0.546631	−	0.315598i
$297$		0			0
$298$	−0.615111	+	1.06540i	−0.0356324	+	0.0617171i
$299$	−6.03820	+	10.4585i	−0.349198	+	0.604829i
$300$		0			0
$301$	22.9503	+	5.29124i	1.32283	+	0.304982i
$302$	1.62176	+	0.936323i	0.0933218	+	0.0538794i
$303$		0			0
$304$			7.03984i			0.403763i
$305$	−1.84617	−	1.06588i	−0.105711	−	0.0610324i
$306$		0			0
$307$			28.5768i			1.63097i	0.578782	+	0.815483i	$0.303528\pi$
$307$			28.5768i			1.63097i	−0.578782	+	0.815483i	$0.696472\pi$
$308$	0.464527	−	2.01484i	0.0264689	−	0.114806i
$309$		0			0
$310$	7.48063			0.424871
$311$	14.1734	+	24.5491i	0.803702	+	1.39205i	0.917164	+	0.398510i	$0.130473\pi$
$311$	14.1734	+	24.5491i	0.803702	+	1.39205i	−0.113462	+	0.993542i	$0.536194\pi$
$312$		0			0
$313$	12.0568	+	6.96097i	0.681488	+	0.393457i	0.800416	−	0.599446i	$-0.204612\pi$
$313$	12.0568	+	6.96097i	0.681488	+	0.393457i	−0.118927	+	0.992903i	$0.537946\pi$
$314$	6.92615			0.390865
$315$		0			0
$316$	−15.9369			−0.896523
$317$	−5.61708	−	3.24302i	−0.315487	−	0.182146i	0.333892	−	0.942611i	$-0.391638\pi$
$317$	−5.61708	−	3.24302i	−0.315487	−	0.182146i	−0.649379	+	0.760465i	$0.724971\pi$
$318$		0			0
$319$	−1.78786	−	3.09666i	−0.100101	−	0.173379i
$320$	1.00000			0.0559017
$321$		0			0
$322$	3.56891	+	11.6609i	0.198887	+	0.649834i
$323$			42.6326i			2.37214i
$324$		0			0
$325$	−2.26905	−	1.31003i	−0.125864	−	0.0726677i
$326$			18.2559i			1.01110i
$327$		0			0
$328$	−9.47275	−	5.46910i	−0.523045	−	0.301980i
$329$	−0.776263	−	2.53632i	−0.0427967	−	0.139832i
$330$		0			0
$331$	10.1155	−	17.5206i	0.556001	−	0.963021i	−0.441824	−	0.897102i	$-0.645669\pi$
$331$	10.1155	−	17.5206i	0.556001	−	0.963021i	0.997825	−	0.0659198i	$-0.0209982\pi$
$332$	−2.03248	+	3.52036i	−0.111547	+	0.193205i
$333$		0			0
$334$	−18.6214	+	10.7511i	−1.01892	+	0.588272i
$335$	6.02939	+	10.4432i	0.329421	+	0.570574i
$336$		0			0
$337$	−6.26528	+	10.8518i	−0.341292	+	0.591134i	−0.984673	−	0.174412i	$-0.944198\pi$
$337$	−6.26528	+	10.8518i	−0.341292	+	0.591134i	0.643381	+	0.765546i	$0.277531\pi$
$338$		−	6.13524i		−	0.333713i
$339$		0			0
$340$	6.05590			0.328428
$341$	−2.92312	−	5.06299i	−0.158296	−	0.274176i
$342$		0			0
$343$	14.4034	+	11.6422i	0.777712	+	0.628621i
$344$	7.70932	−	4.45098i	0.415659	−	0.239981i
$345$		0			0
$346$	5.73336	−	3.31016i	0.308228	−	0.177955i
$347$	−0.249731	+	0.144182i	−0.0134063	+	0.00774011i	−0.506688	−	0.862129i	$-0.669130\pi$
$347$	−0.249731	+	0.144182i	−0.0134063	+	0.00774011i	0.493282	+	0.869870i	$0.335797\pi$
$348$		0			0
$349$	−6.77506	+	3.91159i	−0.362661	+	0.209382i	−0.670247	−	0.742138i	$-0.733812\pi$
$349$	−6.77506	+	3.91159i	−0.362661	+	0.209382i	0.307586	+	0.951520i	$0.400479\pi$
$350$	−2.52991	+	0.774302i	−0.135230	+	0.0413882i
$351$		0			0
$352$	−0.390758	−	0.676813i	−0.0208275	−	0.0360743i
$353$	−4.24919			−0.226162			−0.113081	−	0.993586i	$-0.536072\pi$
$353$	−4.24919			−0.226162			−0.113081	+	0.993586i	$0.536072\pi$
$354$		0			0
$355$		−	10.1200i		−	0.537116i
$356$	−3.78927	+	6.56320i	−0.200831	+	0.347849i
$357$		0			0
$358$	5.19284	+	8.99427i	0.274450	+	0.475362i
$359$	−9.71995	+	5.61182i	−0.513000	+	0.296180i	−0.734066	−	0.679078i	$-0.762380\pi$
$359$	−9.71995	+	5.61182i	−0.513000	+	0.296180i	0.221066	+	0.975259i	$0.429046\pi$
$360$		0			0
$361$	15.2797	−	26.4652i	0.804194	−	1.39291i
$362$	0.383412	−	0.664089i	0.0201517	−	0.0349037i
$363$		0			0
$364$	5.07120	+	4.72613i	0.265803	+	0.247716i
$365$	−7.67003	−	4.42830i	−0.401468	−	0.231788i
$366$		0			0
$367$		−	6.63431i		−	0.346308i	−0.984895	−	0.173154i	$-0.944604\pi$
$367$		−	6.63431i		−	0.346308i	0.984895	−	0.173154i	$-0.0553958\pi$
$368$	3.99168	+	2.30460i	0.208081	+	0.120135i
$369$		0			0
$370$			10.8595i			0.564558i
$371$	24.2535	−	7.42301i	1.25918	−	0.385383i
$372$		0			0
$373$	−30.4025			−1.57418			−0.787091	−	0.616837i	$-0.788414\pi$
$373$	−30.4025			−1.57418			−0.787091	+	0.616837i	$0.788414\pi$
$374$	−2.36639	−	4.09872i	−0.122363	−	0.211940i
$375$		0			0
$376$	−0.868218	−	0.501266i	−0.0447749	−	0.0258508i
$377$	11.9877			0.617400
$378$		0			0
$379$	−7.50620			−0.385568			−0.192784	−	0.981241i	$-0.561752\pi$
$379$	−7.50620			−0.385568			−0.192784	+	0.981241i	$0.561752\pi$
$380$	−6.09668	−	3.51992i	−0.312753	−	0.180568i
$381$		0			0
$382$	6.76794	+	11.7224i	0.346278	+	0.599771i
$383$	4.17818			0.213495			0.106748	−	0.994286i	$-0.465956\pi$
$383$	4.17818			0.213495			0.106748	+	0.994286i	$0.465956\pi$
$384$		0			0
$385$	1.51264	+	1.40971i	0.0770914	+	0.0718456i
$386$			9.39501i			0.478193i
$387$		0			0
$388$	5.00436	+	2.88927i	0.254058	+	0.146680i
$389$		−	14.2487i		−	0.722439i	−0.932481	−	0.361220i	$-0.882360\pi$
$389$		−	14.2487i		−	0.722439i	0.932481	−	0.361220i	$-0.117640\pi$
$390$		0			0
$391$	24.1732	+	13.9564i	1.22249	+	0.705806i
$392$	6.98265	−	0.492485i	0.352677	−	0.0248742i
$393$		0			0
$394$	−6.00362	+	10.3986i	−0.302458	+	0.523872i
$395$	7.96847	−	13.8018i	0.400937	−	0.694443i
$396$		0			0
$397$	15.1562	−	8.75045i	0.760669	−	0.439172i	−0.0688669	−	0.997626i	$-0.521938\pi$
$397$	15.1562	−	8.75045i	0.760669	−	0.439172i	0.829536	+	0.558453i	$0.188605\pi$
$398$	2.18223	+	3.77973i	0.109385	+	0.189461i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	12.0735i		−	0.602924i	−0.953478	−	0.301462i	$-0.902525\pi$
$401$		−	12.0735i		−	0.602924i	0.953478	−	0.301462i	$-0.0974746\pi$
$402$		0			0
$403$	19.5998			0.976334
$404$	−0.499392	−	0.864973i	−0.0248457	−	0.0430340i
$405$		0			0
$406$	8.25309	−	8.85568i	0.409594	−	0.439500i
$407$	7.34985	−	4.24344i	0.364319	−	0.210339i
$408$		0			0
$409$	−30.4287	+	17.5680i	−1.50460	+	0.868683i	−0.504617	+	0.863344i	$0.668366\pi$
$409$	−30.4287	+	17.5680i	−1.50460	+	0.868683i	−0.999986	+	0.00533893i	$0.998301\pi$
$410$	9.47275	−	5.46910i	0.467826	−	0.270099i
$411$		0			0
$412$	−5.08667	+	2.93679i	−0.250602	+	0.144685i
$413$	6.80637	+	1.56922i	0.334919	+	0.0772164i
$414$		0			0
$415$	−2.03248	−	3.52036i	−0.0997706	−	0.172808i
$416$	2.62007			0.128459
$417$		0			0
$418$			5.50175i			0.269100i
$419$	1.20192	−	2.08178i	0.0587176	−	0.101702i	−0.835172	−	0.549988i	$-0.814632\pi$
$419$	1.20192	−	2.08178i	0.0587176	−	0.101702i	0.893890	+	0.448286i	$0.147966\pi$
$420$		0			0
$421$	0.667716	+	1.15652i	0.0325425	+	0.0563652i	0.881838	−	0.471553i	$-0.156306\pi$
$421$	0.667716	+	1.15652i	0.0325425	+	0.0563652i	−0.849295	+	0.527918i	$0.822973\pi$
$422$	−10.0942	+	5.82791i	−0.491380	+	0.283698i
$423$		0			0
$424$	4.79336	−	8.30234i	0.232786	−	0.403197i
$425$	−3.02795	+	5.24457i	−0.146877	+	0.254399i
$426$		0			0
$427$	−5.39319	+	1.65063i	−0.260995	+	0.0798797i
$428$	−4.22082	−	2.43689i	−0.204021	−	0.117792i
$429$		0			0
$430$			8.90195i			0.429290i
$431$	27.5465	+	15.9040i	1.32687	+	0.766067i	0.984814	−	0.173613i	$-0.0555442\pi$
$431$	27.5465	+	15.9040i	1.32687	+	0.766067i	0.342054	+	0.939680i	$0.388878\pi$
$432$		0			0
$433$			33.1620i			1.59367i	0.604200	+	0.796833i	$0.293493\pi$
$433$			33.1620i			1.59367i	−0.604200	+	0.796833i	$0.706507\pi$
$434$	13.4937	−	14.4789i	0.647718	−	0.695010i
$435$		0			0
$436$	0.677937			0.0324673
$437$	−16.2240	−	28.1008i	−0.776099	−	1.34424i
$438$		0			0
$439$	−24.7576	−	14.2938i	−1.18162	−	0.682207i	−0.225229	−	0.974306i	$-0.572313\pi$
$439$	−24.7576	−	14.2938i	−1.18162	−	0.682207i	−0.956388	+	0.292099i	$0.905646\pi$
$440$	0.781517			0.0372573
$441$		0			0
$442$	15.8669			0.754711
$443$	30.2830	+	17.4839i	1.43879	+	0.830684i	0.997766	−	0.0668124i	$-0.0212829\pi$
$443$	30.2830	+	17.4839i	1.43879	+	0.830684i	0.441022	+	0.897497i	$0.354616\pi$
$444$		0			0
$445$	−3.78927	−	6.56320i	−0.179629	−	0.311126i
$446$	9.97434			0.472299
$447$		0			0
$448$	1.80382	−	1.93552i	0.0852224	−	0.0914448i
$449$			12.6187i			0.595515i	0.954642	+	0.297758i	$0.0962387\pi$
$449$			12.6187i			0.595515i	−0.954642	+	0.297758i	$0.903761\pi$
$450$		0			0
$451$	−7.40311	−	4.27419i	−0.348599	−	0.201264i
$452$			3.07372i			0.144576i
$453$		0			0
$454$	−14.8607	−	8.57982i	−0.697447	−	0.402671i
$455$	−6.62855	+	2.02872i	−0.310751	+	0.0951081i
$456$		0			0
$457$	−15.1831	+	26.2979i	−0.710236	+	1.23016i	0.254533	+	0.967064i	$0.418078\pi$
$457$	−15.1831	+	26.2979i	−0.710236	+	1.23016i	−0.964768	+	0.263100i	$0.915255\pi$
$458$	−6.44708	+	11.1667i	−0.301252	+	0.521784i
$459$		0			0
$460$	−3.99168	+	2.30460i	−0.186113	+	0.107452i
$461$	−0.772644	−	1.33826i	−0.0359856	−	0.0623289i	0.847472	−	0.530841i	$-0.178124\pi$
$461$	−0.772644	−	1.33826i	−0.0359856	−	0.0623289i	−0.883457	+	0.468512i	$0.844790\pi$
$462$		0			0
$463$	−7.01500	+	12.1503i	−0.326015	+	0.564674i	−0.981717	−	0.190346i	$-0.939039\pi$
$463$	−7.01500	+	12.1503i	−0.326015	+	0.564674i	0.655703	+	0.755019i	$0.272373\pi$
$464$		−	4.57535i		−	0.212405i
$465$		0			0
$466$	14.8680			0.688747
$467$	−5.25258	−	9.09774i	−0.243061	−	0.420993i	0.718524	−	0.695502i	$-0.244818\pi$
$467$	−5.25258	−	9.09774i	−0.243061	−	0.420993i	−0.961585	+	0.274509i	$0.911485\pi$
$468$		0			0
$469$	31.0890	+	7.16763i	1.43556	+	0.330971i
$470$	0.868218	−	0.501266i	0.0400479	−	0.0231217i
$471$		0			0
$472$	2.28635	−	1.32003i	0.105238	−	0.0607591i
$473$	6.02496	−	3.47851i	0.277028	−	0.159942i
$474$		0			0
$475$	6.09668	−	3.51992i	0.279735	−	0.161505i
$476$	10.9237	−	11.7213i	0.500689	−	0.537246i
$477$		0			0
$478$	1.06303	+	1.84122i	0.0486219	+	0.0842155i
$479$	−9.77353			−0.446564			−0.223282	−	0.974754i	$-0.571677\pi$
$479$	−9.77353			−0.446564			−0.223282	+	0.974754i	$0.571677\pi$
$480$		0			0
$481$			28.4526i			1.29733i
$482$	9.22217	−	15.9733i	0.420058	−	0.727563i
$483$		0			0
$484$	5.19462	+	8.99734i	0.236119	+	0.408970i
$485$	−5.00436	+	2.88927i	−0.227236	+	0.131195i
$486$		0			0
$487$	0.414656	−	0.718204i	0.0187898	−	0.0325449i	−0.856478	−	0.516184i	$-0.827352\pi$
$487$	0.414656	−	0.718204i	0.0187898	−	0.0325449i	0.875267	+	0.483639i	$0.160685\pi$
$488$	−1.06588	+	1.84617i	−0.0482503	+	0.0835720i
$489$		0			0
$490$	−3.06482	+	6.29340i	−0.138455	+	0.284307i
$491$	−21.3419	−	12.3218i	−0.963147	−	0.556073i	−0.0660068	−	0.997819i	$-0.521026\pi$
$491$	−21.3419	−	12.3218i	−0.963147	−	0.556073i	−0.897140	+	0.441746i	$0.854359\pi$
$492$		0			0
$493$		−	27.7079i		−	1.24790i
$494$	−15.9737	−	9.22244i	−0.718692	−	0.414937i
$495$		0			0
$496$		−	7.48063i		−	0.335890i
$497$	−19.5876	−	18.2547i	−0.878623	−	0.818836i
$498$		0			0
$499$	29.0471			1.30033			0.650164	−	0.759794i	$-0.274700\pi$
$499$	29.0471			1.30033			0.650164	+	0.759794i	$0.274700\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	12.5495	+	7.24543i	0.560110	+	0.323379i
$503$	1.72372			0.0768570			0.0384285	−	0.999261i	$-0.487765\pi$
$503$	1.72372			0.0768570			0.0384285	+	0.999261i	$0.487765\pi$
$504$		0			0
$505$	0.998784			0.0444453
$506$	3.11956	+	1.80108i	0.138681	+	0.0800678i
$507$		0			0
$508$	−0.200619	−	0.347483i	−0.00890105	−	0.0154171i
$509$	12.6782			0.561952			0.280976	−	0.959715i	$-0.409342\pi$
$509$	12.6782			0.561952			0.280976	+	0.959715i	$0.409342\pi$
$510$		0			0
$511$	−22.4064	+	6.85768i	−0.991201	+	0.303366i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	5.90514	+	3.40934i	0.260465	+	0.150379i
$515$		−	5.87358i		−	0.258821i
$516$		0			0
$517$	−0.678527	−	0.391748i	−0.0298416	−	0.0172291i
$518$	21.0188	+	19.5886i	0.923513	+	0.860672i
$519$		0			0
$520$	−1.31003	+	2.26905i	−0.0574488	+	0.0995043i
$521$	−20.9088	+	36.2152i	−0.916032	+	1.58661i	−0.110650	+	0.993859i	$0.535293\pi$
$521$	−20.9088	+	36.2152i	−0.916032	+	1.58661i	−0.805383	+	0.592755i	$0.798040\pi$
$522$		0			0
$523$	−23.2073	+	13.3987i	−1.01478	+	0.585885i	−0.912589	−	0.408879i	$-0.865920\pi$
$523$	−23.2073	+	13.3987i	−1.01478	+	0.585885i	−0.102195	+	0.994764i	$0.532586\pi$
$524$	−11.0798	−	19.1907i	−0.484021	−	0.838349i
$525$		0			0
$526$	9.28146	−	16.0760i	0.404691	−	0.700945i
$527$		−	45.3020i		−	1.97339i
$528$		0			0
$529$	1.75534			0.0763192
$530$	4.79336	+	8.30234i	0.208210	+	0.360630i
$531$		0			0
$532$	−17.8102	+	5.45096i	−0.772169	+	0.236329i
$533$	24.8193	−	14.3294i	1.07504	−	0.620676i
$534$		0			0
$535$	4.22082	−	2.43689i	0.182482	−	0.105356i
$536$	10.4432	−	6.02939i	0.451078	−	0.260430i
$537$		0			0
$538$	1.12062	−	0.646992i	0.0483135	−	0.0278938i
$539$	5.45706	−	0.384885i	0.235052	−	0.0165782i
$540$		0			0
$541$	5.58077	+	9.66618i	0.239936	+	0.415581i	0.960696	−	0.277604i	$-0.0895402\pi$
$541$	5.58077	+	9.66618i	0.239936	+	0.415581i	−0.720760	+	0.693185i	$0.756207\pi$
$542$	−27.6331			−1.18694
$543$		0			0
$544$		−	6.05590i		−	0.259645i
$545$	−0.338969	+	0.587111i	−0.0145198	+	0.0251491i
$546$		0			0
$547$	1.68877	+	2.92504i	0.0722067	+	0.125066i	0.899868	−	0.436162i	$-0.143663\pi$
$547$	1.68877	+	2.92504i	0.0722067	+	0.125066i	−0.827661	+	0.561228i	$0.810329\pi$
$548$	16.6279	−	9.60012i	0.710308	−	0.410097i
$549$		0			0
$550$	−0.390758	+	0.676813i	−0.0166620	+	0.0288594i
$551$	−16.1049	+	27.8944i	−0.686090	+	1.18834i
$552$		0			0
$553$	−12.3400	−	40.3190i	−0.524750	−	1.71454i
$554$	−21.1767	−	12.2264i	−0.899711	−	0.519449i
$555$		0			0
$556$		−	0.175408i		−	0.00743897i
$557$	−19.1518	−	11.0573i	−0.811489	−	0.468513i	0.0359839	−	0.999352i	$-0.488544\pi$
$557$	−19.1518	−	11.0573i	−0.811489	−	0.468513i	−0.847473	+	0.530839i	$0.821877\pi$
$558$		0			0
$559$			23.3237i			0.986489i
$560$	0.774302	+	2.52991i	0.0327202	+	0.106908i
$561$		0			0
$562$	−2.69026			−0.113482
$563$	6.56999	+	11.3796i	0.276892	+	0.479591i	0.970611	−	0.240655i	$-0.0773622\pi$
$563$	6.56999	+	11.3796i	0.276892	+	0.479591i	−0.693719	+	0.720246i	$0.744029\pi$
$564$		0			0
$565$	−2.66192	−	1.53686i	−0.111988	−	0.0646563i
$566$	7.15360			0.300688
$567$		0			0
$568$	−10.1200			−0.424628
$569$	−14.3290	−	8.27287i	−0.600704	−	0.346817i	0.168614	−	0.985682i	$-0.446071\pi$
$569$	−14.3290	−	8.27287i	−0.600704	−	0.346817i	−0.769319	+	0.638865i	$0.779404\pi$
$570$		0			0
$571$	20.9898	+	36.3554i	0.878397	+	1.52143i	0.853100	+	0.521748i	$0.174720\pi$
$571$	20.9898	+	36.3554i	0.878397	+	1.52143i	0.0252972	+	0.999680i	$0.491947\pi$
$572$	2.04763			0.0856156
$573$		0			0
$574$	6.50157	−	28.2000i	0.271370	−	1.17704i
$575$		−	4.60919i		−	0.192217i
$576$		0			0
$577$	0.965716	+	0.557556i	0.0402033	+	0.0232114i	0.519967	−	0.854186i	$-0.325944\pi$
$577$	0.965716	+	0.557556i	0.0402033	+	0.0232114i	−0.479764	+	0.877398i	$0.659278\pi$
$578$		−	19.6740i		−	0.818329i
$579$		0			0
$580$	3.96237	+	2.28767i	0.164528	+	0.0949905i
$581$	−10.4800	−	2.41618i	−0.434782	−	0.100240i
$582$		0			0
$583$	3.74609	−	6.48841i	0.155147	−	0.268723i
$584$	−4.42830	+	7.67003i	−0.183244	+	0.317388i
$585$		0			0
$586$	4.59573	−	2.65334i	0.189848	−	0.109609i
$587$	−7.06492	−	12.2368i	−0.291600	−	0.505067i	0.682588	−	0.730803i	$-0.260854\pi$
$587$	−7.06492	−	12.2368i	−0.291600	−	0.505067i	−0.974188	+	0.225737i	$0.927521\pi$
$588$		0			0
$589$	−26.3312	+	45.6070i	−1.08496	+	1.87920i
$590$			2.64005i			0.108689i
$591$		0			0
$592$	10.8595			0.446323
$593$	−1.63329	−	2.82894i	−0.0670711	−	0.116171i	0.830540	−	0.556959i	$-0.188032\pi$
$593$	−1.63329	−	2.82894i	−0.0670711	−	0.116171i	−0.897611	+	0.440789i	$0.854699\pi$
$594$		0			0
$595$	4.68910	+	15.3209i	0.192234	+	0.628096i
$596$	−1.06540	+	0.615111i	−0.0436406	+	0.0251959i
$597$		0			0
$598$	−10.4585	+	6.03820i	−0.427679	+	0.246920i
$599$	−9.28550	+	5.36099i	−0.379395	+	0.219044i	−0.677555	−	0.735472i	$-0.736960\pi$
$599$	−9.28550	+	5.36099i	−0.379395	+	0.219044i	0.298160	+	0.954516i	$0.403627\pi$
$600$		0			0
$601$	34.1874	−	19.7381i	1.39453	−	0.805134i	0.400720	−	0.916201i	$-0.368760\pi$
$601$	34.1874	−	19.7381i	1.39453	−	0.805134i	0.993813	+	0.111067i	$0.0354268\pi$
$602$	17.2299	+	16.0575i	0.702239	+	0.654455i
$603$		0			0
$604$	0.936323	+	1.62176i	0.0380985	+	0.0659885i
$605$	−10.3892			−0.422382
$606$		0			0
$607$		−	23.4972i		−	0.953721i	−0.878979	−	0.476861i	$-0.841775\pi$
$607$		−	23.4972i		−	0.953721i	0.878979	−	0.476861i	$-0.158225\pi$
$608$	−3.51992	+	6.09668i	−0.142752	+	0.247253i
$609$		0			0
$610$	−1.06588	−	1.84617i	−0.0431564	−	0.0747491i
$611$	2.27479	−	1.31335i	0.0920283	−	0.0531325i
$612$		0			0
$613$	4.76729	−	8.25719i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$613$	4.76729	−	8.25719i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$614$	−14.2884	+	24.7483i	−0.576633	+	0.998758i
$615$		0			0
$616$	1.40971	−	1.51264i	0.0567990	−	0.0609461i
$617$	22.4936	+	12.9867i	0.905559	+	0.522825i	0.879000	−	0.476823i	$-0.158212\pi$
$617$	22.4936	+	12.9867i	0.905559	+	0.522825i	0.0265594	+	0.999647i	$0.491545\pi$
$618$		0			0
$619$		−	12.8707i		−	0.517317i	−0.965969	−	0.258658i	$-0.916720\pi$
$619$		−	12.8707i		−	0.517317i	0.965969	−	0.258658i	$-0.0832804\pi$
$620$	6.47842	+	3.74031i	0.260179	+	0.150215i
$621$		0			0
$622$			28.3469i			1.13661i
$623$	−19.5384	−	4.50461i	−0.782788	−	0.180474i
$624$		0			0
$625$	1.00000			0.0400000
$626$	6.96097	+	12.0568i	0.278216	+	0.481885i
$627$		0			0
$628$	5.99822	+	3.46308i	0.239355	+	0.138192i
$629$	65.7641			2.62219
$630$		0			0
$631$	25.3213			1.00802			0.504012	−	0.863697i	$-0.331857\pi$
$631$	25.3213			1.00802			0.504012	+	0.863697i	$0.331857\pi$
$632$	−13.8018	−	7.96847i	−0.549006	−	0.316969i
$633$		0			0
$634$	−3.24302	−	5.61708i	−0.128797	−	0.223083i
$635$	0.401239			0.0159227
$636$		0			0
$637$	−8.03005	+	16.4891i	−0.318162	+	0.653324i
$638$		−	3.57571i		−	0.141564i
$639$		0			0
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$		−	20.8838i		−	0.824859i	−0.910989	−	0.412430i	$-0.864680\pi$
$641$		−	20.8838i		−	0.824859i	0.910989	−	0.412430i	$-0.135320\pi$
$642$		0			0
$643$	−1.18971	−	0.686880i	−0.0469177	−	0.0270879i	0.476358	−	0.879252i	$-0.341957\pi$
$643$	−1.18971	−	0.686880i	−0.0469177	−	0.0270879i	−0.523275	+	0.852164i	$0.675290\pi$
$644$	−2.73966	+	11.8830i	−0.107958	+	0.468258i
$645$		0			0
$646$	−21.3163	+	36.9209i	−0.838679	+	1.45263i
$647$	−18.1195	+	31.3838i	−0.712349	+	1.23383i	0.251624	+	0.967825i	$0.419036\pi$
$647$	−18.1195	+	31.3838i	−0.712349	+	1.23383i	−0.963973	+	0.266000i	$0.914298\pi$
$648$		0			0
$649$	1.78682	−	1.03162i	0.0701389	−	0.0404947i
$650$	−1.31003	−	2.26905i	−0.0513838	−	0.0889993i
$651$		0			0
$652$	−9.12797	+	15.8101i	−0.357479	+	0.619172i
$653$		−	31.8472i		−	1.24628i	−0.782112	−	0.623138i	$-0.785857\pi$
$653$		−	31.8472i		−	1.24628i	0.782112	−	0.623138i	$-0.214143\pi$
$654$		0			0
$655$	22.1595			0.865843
$656$	−5.46910	−	9.47275i	−0.213532	−	0.369849i
$657$		0			0
$658$	0.595896	−	2.58465i	0.0232305	−	0.100760i
$659$	−20.7307	+	11.9689i	−0.807552	+	0.466240i	−0.846105	−	0.533016i	$-0.821058\pi$
$659$	−20.7307	+	11.9689i	−0.807552	+	0.466240i	0.0385530	+	0.999257i	$0.487725\pi$
$660$		0			0
$661$	33.4391	−	19.3061i	1.30063	−	0.750920i	0.320119	−	0.947378i	$-0.396277\pi$
$661$	33.4391	−	19.3061i	1.30063	−	0.750920i	0.980512	+	0.196458i	$0.0629439\pi$
$662$	17.5206	−	10.1155i	0.680959	−	0.393152i
$663$		0			0
$664$	−3.52036	+	2.03248i	−0.136616	+	0.0788755i
$665$	4.18442	−	18.1496i	0.162265	−	0.703810i
$666$		0			0
$667$	10.5443	+	18.2633i	0.408278	+	0.707158i
$668$	−21.5021			−0.831942
$669$		0			0
$670$			12.0588i			0.465871i
$671$	−0.833006	+	1.44281i	−0.0321579	+	0.0556990i
$672$		0			0
$673$	−7.83794	−	13.5757i	−0.302131	−	0.523305i	0.674488	−	0.738286i	$-0.264365\pi$
$673$	−7.83794	−	13.5757i	−0.302131	−	0.523305i	−0.976618	+	0.214981i	$0.931031\pi$
$674$	−10.8518	+	6.26528i	−0.417995	+	0.241330i
$675$		0			0
$676$	3.06762	−	5.31327i	0.117985	−	0.204357i
$677$	0.750432	−	1.29979i	0.0288414	−	0.0499548i	−0.851244	−	0.524769i	$-0.824152\pi$
$677$	0.750432	−	1.29979i	0.0288414	−	0.0499548i	0.880086	+	0.474815i	$0.157485\pi$
$678$		0			0
$679$	−3.43471	+	14.8977i	−0.131812	+	0.571723i
$680$	5.24457	+	3.02795i	0.201120	+	0.116117i
$681$		0			0
$682$		−	5.84624i		−	0.223864i
$683$	−42.4921	−	24.5328i	−1.62591	−	0.938722i	−0.985295	−	0.170862i	$-0.945345\pi$
$683$	−42.4921	−	24.5328i	−1.62591	−	0.938722i	−0.640619	−	0.767859i	$-0.721322\pi$
$684$		0			0
$685$			19.2002i			0.733603i
$686$	6.65262	+	17.2842i	0.253998	+	0.659913i
$687$		0			0
$688$	8.90195			0.339384
$689$	12.5589	+	21.7527i	0.478457	+	0.828712i
$690$		0			0
$691$	−14.7193	−	8.49821i	−0.559950	−	0.323287i	0.193175	−	0.981164i	$-0.438121\pi$
$691$	−14.7193	−	8.49821i	−0.559950	−	0.323287i	−0.753125	+	0.657877i	$0.771455\pi$
$692$	6.62032			0.251667
$693$		0			0
$694$	−0.288364			−0.0109462
$695$	0.151908	+	0.0877042i	0.00576220	+	0.00332681i
$696$		0			0
$697$	−33.1203	−	57.3661i	−1.25452	−	2.17290i
$698$	−7.82317			−0.296111
$699$		0			0
$700$	−2.57812	−	0.594391i	−0.0974437	−	0.0224659i
$701$		−	27.6593i		−	1.04468i	−0.852738	−	0.522338i	$-0.825060\pi$
$701$		−	27.6593i		−	1.04468i	0.852738	−	0.522338i	$-0.174940\pi$
$702$		0			0
$703$	−66.2069	−	38.2246i	−2.49704	−	1.44167i
$704$		−	0.781517i		−	0.0294545i
$705$		0			0
$706$	−3.67991	−	2.12459i	−0.138495	−	0.0799602i
$707$	1.80162	−	1.93317i	0.0677571	−	0.0727043i
$708$		0			0
$709$	14.5417	−	25.1870i	0.546125	−	0.945917i	−0.452410	−	0.891810i	$-0.649436\pi$
$709$	14.5417	−	25.1870i	0.546125	−	0.945917i	0.998535	−	0.0541066i	$-0.0172311\pi$
$710$	5.06002	−	8.76422i	0.189899	−	0.328915i
$711$		0			0
$712$	−6.56320	+	3.78927i	−0.245966	+	0.142009i
$713$	17.2398	+	29.8603i	0.645637	+	1.11828i
$714$		0			0
$715$	−1.02381	+	1.77330i	−0.0382885	+	0.0663176i
$716$			10.3857i			0.388131i
$717$		0			0
$718$	−11.2236			−0.418862
$719$	−19.0668	−	33.0246i	−0.711070	−	1.23161i	−0.964456	−	0.264245i	$-0.914877\pi$
$719$	−19.0668	−	33.0246i	−0.711070	−	1.23161i	0.253385	−	0.967365i	$-0.418456\pi$
$720$		0			0
$721$	−11.3684	−	10.5949i	−0.423383	−	0.394573i
$722$	26.4652	−	15.2797i	0.984933	−	0.568651i
$723$		0			0
$724$	0.664089	−	0.383412i	0.0246807	−	0.0142494i
$725$	−3.96237	+	2.28767i	−0.147159	+	0.0849621i
$726$		0			0
$727$	−9.20054	+	5.31193i	−0.341229	+	0.197009i	−0.660815	−	0.750548i	$-0.729789\pi$
$727$	−9.20054	+	5.31193i	−0.341229	+	0.197009i	0.319586	+	0.947557i	$0.396456\pi$
$728$	2.02872	+	6.62855i	0.0751895	+	0.245670i
$729$		0			0
$730$	−4.42830	−	7.67003i	−0.163899	−	0.283881i
$731$	53.9094			1.99391
$732$		0			0
$733$		−	3.60653i		−	0.133210i	−0.997779	−	0.0666051i	$-0.978783\pi$
$733$		−	3.60653i		−	0.133210i	0.997779	−	0.0666051i	$-0.0212168\pi$
$734$	3.31715	−	5.74548i	0.122438	−	0.212070i
$735$		0			0
$736$	2.30460	+	3.99168i	0.0849485	+	0.147135i
$737$	8.16154	−	4.71207i	0.300634	−	0.173571i
$738$		0			0
$739$	−5.13310	+	8.89079i	−0.188824	+	0.327053i	−0.944858	−	0.327479i	$-0.893801\pi$
$739$	−5.13310	+	8.89079i	−0.188824	+	0.327053i	0.756034	+	0.654532i	$0.227134\pi$
$740$	−5.42975	+	9.40460i	−0.199602	+	0.345720i
$741$		0			0
$742$	24.7157	+	5.69826i	0.907341	+	0.209190i
$743$	−35.2305	−	20.3403i	−1.29248	−	0.746214i	−0.313388	−	0.949625i	$-0.601464\pi$
$743$	−35.2305	−	20.3403i	−1.29248	−	0.746214i	−0.979093	+	0.203411i	$0.934797\pi$
$744$		0			0
$745$		−	1.23022i		−	0.0450718i
$746$	−26.3293	−	15.2013i	−0.963986	−	0.556557i
$747$		0			0
$748$		−	4.73279i		−	0.173048i
$749$	2.89694	−	12.5652i	0.105852	−	0.459122i
$750$		0			0
$751$	−22.2824			−0.813095			−0.406547	−	0.913630i	$-0.633267\pi$
$751$	−22.2824			−0.813095			−0.406547	+	0.913630i	$0.633267\pi$
$752$	−0.501266	−	0.868218i	−0.0182793	−	0.0316607i
$753$		0			0
$754$	10.3817	+	5.99387i	0.378078	+	0.218284i
$755$	−1.87265			−0.0681526
$756$		0			0
$757$	40.9255			1.48746			0.743732	−	0.668478i	$-0.233054\pi$
$757$	40.9255			1.48746			0.743732	+	0.668478i	$0.233054\pi$
$758$	−6.50056	−	3.75310i	−0.236111	−	0.136319i
$759$		0			0
$760$	−3.51992	−	6.09668i	−0.127681	−	0.221150i
$761$	29.3512			1.06398			0.531990	−	0.846750i	$-0.321444\pi$
$761$	29.3512			1.06398			0.531990	+	0.846750i	$0.321444\pi$
$762$		0			0
$763$	0.524928	+	1.71512i	0.0190037	+	0.0620916i
$764$			13.5359i			0.489711i
$765$		0			0
$766$	3.61841	+	2.08909i	0.130738	+	0.0754819i
$767$			6.91712i			0.249763i
$768$		0			0
$769$	−31.8034	−	18.3617i	−1.14686	−	0.662141i	−0.198741	−	0.980052i	$-0.563685\pi$
$769$	−31.8034	−	18.3617i	−1.14686	−	0.662141i	−0.948120	+	0.317912i	$0.897018\pi$
$770$	0.605130	+	1.97717i	0.0218074	+	0.0712522i
$771$		0			0
$772$	−4.69750	+	8.13632i	−0.169067	+	0.292832i
$773$	−16.9345	+	29.3314i	−0.609091	+	1.05498i	0.382299	+	0.924039i	$0.375132\pi$
$773$	−16.9345	+	29.3314i	−0.609091	+	1.05498i	−0.991391	+	0.130938i	$0.958201\pi$
$774$		0			0
$775$	−6.47842	+	3.74031i	−0.232712	+	0.134356i
$776$	2.88927	+	5.00436i	0.103719	+	0.179646i
$777$		0			0
$778$	7.12437	−	12.3398i	0.255421	−	0.442402i
$779$			77.0032i			2.75892i
$780$		0			0
$781$	−7.90899			−0.283006
$782$	13.9564	+	24.1732i	0.499080	+	0.864433i
$783$		0			0
$784$	6.29340	+	3.06482i	0.224764	+	0.109458i
$785$	−5.99822	+	3.46308i	−0.214086	+	0.123602i
$786$		0			0
$787$	−2.83010	+	1.63396i	−0.100882	+	0.0582443i	−0.549592	−	0.835433i	$-0.685217\pi$
$787$	−2.83010	+	1.63396i	−0.100882	+	0.0582443i	0.448710	+	0.893677i	$0.351884\pi$
$788$	−10.3986	+	6.00362i	−0.370434	+	0.213870i
$789$		0			0
$790$	13.8018	−	7.96847i	0.491046	−	0.283505i
$791$	−7.77625	+	2.37999i	−0.276492	+	0.0846227i
$792$		0			0
$793$	−2.79269	−	4.83708i	−0.0991714	−	0.171770i
$794$	17.5009			0.621084
$795$		0			0
$796$			4.36446i			0.154694i
$797$	−13.7568	+	23.8275i	−0.487292	+	0.844014i	−0.999893	−	0.0146125i	$-0.995349\pi$
$797$	−13.7568	+	23.8275i	−0.487292	+	0.844014i	0.512601	+	0.858627i	$0.328682\pi$
$798$		0			0
$799$	−3.03562	−	5.25785i	−0.107393	−	0.186009i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	6.03677	−	10.4560i	0.213166	−	0.369214i
$803$	−3.46079	+	5.99426i	−0.122129	+	0.211533i
$804$		0			0
$805$	−8.92119	−	8.31414i	−0.314431	−	0.293035i
$806$	16.9739	+	9.79988i	0.597880	+	0.345186i
$807$		0			0
$808$		−	0.998784i		−	0.0351371i
$809$	−6.97997	−	4.02989i	−0.245403	−	0.141683i	0.372255	−	0.928131i	$-0.378585\pi$
$809$	−6.97997	−	4.02989i	−0.245403	−	0.141683i	−0.617657	+	0.786447i	$0.711918\pi$
$810$		0			0
$811$			22.0290i			0.773544i	0.922175	+	0.386772i	$0.126410\pi$
$811$			22.0290i			0.773544i	−0.922175	+	0.386772i	$0.873590\pi$
$812$	11.5752	−	3.54270i	0.406211	−	0.124324i
$813$		0			0
$814$	8.48688			0.297465
$815$	−9.12797	−	15.8101i	−0.319739	−	0.553804i
$816$		0			0
$817$	−54.2724	−	31.3342i	−1.89875	−	1.09624i
$818$	−35.1360			−1.22850
$819$		0			0
$820$	10.9382			0.381978
$821$	25.5537	+	14.7535i	0.891832	+	0.514899i	0.874541	−	0.484951i	$-0.161163\pi$
$821$	25.5537	+	14.7535i	0.891832	+	0.514899i	0.0172906	+	0.999851i	$0.494496\pi$
$822$		0			0
$823$	−12.6232	−	21.8640i	−0.440017	−	0.762132i	0.557673	−	0.830061i	$-0.311694\pi$
$823$	−12.6232	−	21.8640i	−0.440017	−	0.762132i	−0.997690	+	0.0679284i	$0.978361\pi$
$824$	−5.87358			−0.204616
$825$		0			0
$826$	5.10988	+	4.76217i	0.177795	+	0.165697i
$827$		−	30.4760i		−	1.05975i	−0.848075	−	0.529877i	$-0.822238\pi$
$827$		−	30.4760i		−	1.05975i	0.848075	−	0.529877i	$-0.177762\pi$
$828$		0			0
$829$	−29.4517	−	17.0040i	−1.02290	−	0.590572i	−0.107958	−	0.994156i	$-0.534431\pi$
$829$	−29.4517	−	17.0040i	−1.02290	−	0.590572i	−0.914943	+	0.403584i	$0.867764\pi$
$830$		−	4.06496i		−	0.141097i
$831$		0			0
$832$	2.26905	+	1.31003i	0.0786650	+	0.0454173i
$833$	38.1122	+	18.5603i	1.32051	+	0.643075i
$834$		0			0
$835$	10.7511	−	18.6214i	0.372056	−	0.644419i
$836$	−2.75088	+	4.76466i	−0.0951411	+	0.164789i
$837$		0			0
$838$	2.08178	−	1.20192i	0.0719140	−	0.0415196i
$839$	11.5670	+	20.0346i	0.399336	+	0.691670i	0.993644	−	0.112567i	$-0.0359073\pi$
$839$	11.5670	+	20.0346i	0.399336	+	0.691670i	−0.594308	+	0.804237i	$0.702574\pi$
$840$		0			0
$841$	−4.03309	+	6.98552i	−0.139072	+	0.240880i
$842$			1.33543i			0.0460220i
$843$		0			0
$844$	−11.6558			−0.401210
$845$	3.06762	+	5.31327i	0.105529	+	0.182782i
$846$		0			0
$847$	−18.7403	+	20.1086i	−0.643924	+	0.690939i
$848$	8.30234	−	4.79336i	0.285103	−	0.164605i
$849$		0			0
$850$	−5.24457	+	3.02795i	−0.179887	+	0.103858i
$851$	−43.3476	+	25.0268i	−1.48594	+	0.857906i
$852$		0			0
$853$	19.2922	−	11.1383i	0.660551	−	0.381369i	−0.131936	−	0.991258i	$-0.542119\pi$
$853$	19.2922	−	11.1383i	0.660551	−	0.381369i	0.792487	+	0.609889i	$0.208786\pi$
$854$	−5.49595	−	1.26710i	−0.188068	−	0.0433594i
$855$		0			0
$856$	−2.43689	−	4.22082i	−0.0832913	−	0.144265i
$857$	−2.17164			−0.0741817			−0.0370908	−	0.999312i	$-0.511809\pi$
$857$	−2.17164			−0.0741817			−0.0370908	+	0.999312i	$0.511809\pi$
$858$		0			0
$859$		−	3.62921i		−	0.123827i	−0.998082	−	0.0619135i	$-0.980280\pi$
$859$		−	3.62921i		−	0.123827i	0.998082	−	0.0619135i	$-0.0197203\pi$
$860$	−4.45098	+	7.70932i	−0.151777	+	0.262886i
$861$		0			0
$862$	15.9040	+	27.5465i	0.541691	+	0.938237i
$863$	−16.4116	+	9.47522i	−0.558656	+	0.322540i	−0.752606	−	0.658471i	$-0.771203\pi$
$863$	−16.4116	+	9.47522i	−0.558656	+	0.322540i	0.193950	+	0.981011i	$0.437870\pi$
$864$		0			0
$865$	−3.31016	+	5.73336i	−0.112549	+	0.194940i
$866$	−16.5810	+	28.7192i	−0.563446	+	0.975917i
$867$		0			0
$868$	18.9253	−	5.79226i	0.642368	−	0.196602i
$869$	−10.7863	−	6.22749i	−0.365901	−	0.211253i
$870$		0			0
$871$			31.5949i			1.07055i
$872$	0.587111	+	0.338969i	0.0198821	+	0.0114789i
$873$		0			0
$874$		−	32.4480i		−	1.09757i
$875$	1.80382	−	1.93552i	0.0609802	−	0.0654326i
$876$		0			0
$877$	5.59790			0.189028			0.0945138	−	0.995524i	$-0.469870\pi$
$877$	5.59790			0.189028			0.0945138	+	0.995524i	$0.469870\pi$
$878$	−14.2938	−	24.7576i	−0.482393	−	0.835529i
$879$		0			0
$880$	0.676813	+	0.390758i	0.0228154	+	0.0131725i
$881$	39.1755			1.31985			0.659927	−	0.751330i	$-0.270587\pi$
$881$	39.1755			1.31985			0.659927	+	0.751330i	$0.270587\pi$
$882$		0			0
$883$	−30.6078			−1.03003			−0.515017	−	0.857180i	$-0.672214\pi$
$883$	−30.6078			−1.03003			−0.515017	+	0.857180i	$0.672214\pi$
$884$	13.7411	+	7.93344i	0.462164	+	0.266831i
$885$		0			0
$886$	17.4839	+	30.2830i	0.587382	+	1.01738i
$887$	−37.7239			−1.26664			−0.633322	−	0.773888i	$-0.718309\pi$
$887$	−37.7239			−1.26664			−0.633322	+	0.773888i	$0.718309\pi$
$888$		0			0
$889$	0.723762	−	0.776606i	0.0242742	−	0.0260465i
$890$		−	7.57854i		−	0.254033i
$891$		0			0
$892$	8.63803	+	4.98717i	0.289223	+	0.166983i
$893$			7.05767i			0.236176i
$894$		0			0
$895$	−8.99427	−	5.19284i	−0.300645	−	0.173578i
$896$	2.52991	−	0.774302i	0.0845184	−	0.0258676i
$897$		0			0
$898$	−6.30937	+	10.9281i	−0.210546	+	0.364677i
$899$	17.1132	−	29.6410i	0.570759	−	0.988583i
$900$		0			0
$901$	50.2782	−	29.0281i	1.67501	−	0.967066i
$902$	−4.27419	−	7.40311i	−0.142315	−	0.246497i
$903$		0			0
$904$	−1.53686	+	2.66192i	−0.0511153	+	0.0885342i
$905$			0.766824i			0.0254901i
$906$		0			0
$907$	0.665419			0.0220949			0.0110474	−	0.999939i	$-0.496483\pi$
$907$	0.665419			0.0220949			0.0110474	+	0.999939i	$0.496483\pi$
$908$	−8.57982	−	14.8607i	−0.284731	−	0.493169i
$909$		0			0
$910$	−6.75485	−	1.55735i	−0.223921	−	0.0516255i
$911$	−16.9363	+	9.77817i	−0.561124	+	0.323965i	−0.753597	−	0.657337i	$-0.771683\pi$
$911$	−16.9363	+	9.77817i	−0.561124	+	0.323965i	0.192472	+	0.981302i	$0.438349\pi$
$912$		0			0
$913$	−2.75122	+	1.58842i	−0.0910521	+	0.0525689i
$914$	−26.2979	+	15.1831i	−0.869858	+	0.502213i
$915$		0			0
$916$	−11.1667	+	6.44708i	−0.368957	+	0.213017i
$917$	39.9717	−	42.8902i	1.31998	−	1.41636i
$918$		0			0
$919$	−0.579801	−	1.00424i	−0.0191259	−	0.0331270i	0.856304	−	0.516472i	$-0.172755\pi$
$919$	−0.579801	−	1.00424i	−0.0191259	−	0.0331270i	−0.875430	+	0.483345i	$0.839422\pi$
$920$	−4.60919			−0.151961
$921$		0			0
$922$		−	1.54529i		−	0.0508913i
$923$	13.2576	−	22.9629i	0.436380	−	0.755832i
$924$		0			0
$925$	−5.42975	−	9.40460i	−0.178529	−	0.309221i
$926$	−12.1503	+	7.01500i	−0.399285	+	0.230527i
$927$		0			0
$928$	2.28767	−	3.96237i	0.0750966	−	0.130071i
$929$	13.2868	−	23.0135i	0.435927	−	0.755048i	−0.561444	−	0.827515i	$-0.689754\pi$
$929$	13.2868	−	23.0135i	0.435927	−	0.755048i	0.997371	+	0.0724671i	$0.0230872\pi$
$930$		0			0
$931$	−27.5809	−	40.8375i	−0.903928	−	1.33840i
$932$	12.8761	+	7.43401i	0.421770	+	0.243509i
$933$		0			0
$934$		−	10.5052i		−	0.343740i
$935$	4.09872	+	2.36639i	0.134042	+	0.0773894i
$936$		0			0
$937$		−	23.9521i		−	0.782482i	−0.920288	−	0.391241i	$-0.872046\pi$
$937$		−	23.9521i		−	0.782482i	0.920288	−	0.391241i	$-0.127954\pi$
$938$	23.3400	+	21.7518i	0.762079	+	0.710223i
$939$		0			0
$940$	1.00253			0.0326990
$941$	−21.6730	−	37.5387i	−0.706519	−	1.22373i	−0.966140	−	0.258017i	$-0.916931\pi$
$941$	−21.6730	−	37.5387i	−0.706519	−	1.22373i	0.259621	−	0.965711i	$-0.416402\pi$
$942$		0			0
$943$	43.6617	+	25.2081i	1.42182	+	0.820889i
$944$	2.64005			0.0859263
$945$		0			0
$946$	6.95703			0.226192
$947$	25.1709	+	14.5324i	0.817944	+	0.472240i	0.849707	−	0.527255i	$-0.176779\pi$
$947$	25.1709	+	14.5324i	0.817944	+	0.472240i	−0.0317631	+	0.999495i	$0.510112\pi$
$948$		0			0
$949$	−11.6024	−	20.0960i	−0.376631	−	0.652344i
$950$	7.03984			0.228403
$951$		0			0
$952$	15.3209	−	4.68910i	0.496553	−	0.151975i
$953$		−	11.6767i		−	0.378247i	−0.981953	−	0.189123i	$-0.939435\pi$
$953$		−	11.6767i		−	0.378247i	0.981953	−	0.189123i	$-0.0605646\pi$
$954$		0			0
$955$	−11.7224	−	6.76794i	−0.379328	−	0.219005i
$956$			2.12606i			0.0687617i
$957$		0			0
$958$	−8.46413	−	4.88677i	−0.273464	−	0.157884i
$959$	37.1625	+	34.6337i	1.20004	+	1.11838i
$960$		0			0
$961$	12.4799	−	21.6158i	0.402578	−	0.697285i
$962$	−14.2263	+	24.6407i	−0.458675	+	0.794448i
$963$		0			0
$964$	15.9733	−	9.22217i	0.514464	−	0.297026i
$965$	−4.69750	−	8.13632i	−0.151218	−	0.261917i
$966$		0			0
$967$	7.59505	−	13.1550i	0.244240	−	0.423037i	−0.717677	−	0.696376i	$-0.754795\pi$
$967$	7.59505	−	13.1550i	0.244240	−	0.423037i	0.961918	+	0.273339i	$0.0881280\pi$
$968$			10.3892i			0.333923i
$969$		0			0
$970$	−5.77853			−0.185538
$971$	−21.6059	−	37.4226i	−0.693368	−	1.20095i	−0.970728	−	0.240182i	$-0.922793\pi$
$971$	−21.6059	−	37.4226i	−0.693368	−	1.20095i	0.277360	−	0.960766i	$-0.410540\pi$
$972$		0			0
$973$	0.443768	−	0.135819i	0.0142265	−	0.00435416i
$974$	0.718204	−	0.414656i	0.0230128	−	0.0132864i
$975$		0			0
$976$	−1.84617	+	1.06588i	−0.0590943	+	0.0341181i
$977$	−3.52150	+	2.03314i	−0.112663	+	0.0650459i	−0.555273	−	0.831668i	$-0.687386\pi$
$977$	−3.52150	+	2.03314i	−0.112663	+	0.0650459i	0.442610	+	0.896714i	$0.354053\pi$
$978$		0			0
$979$	−5.12925	+	2.96138i	−0.163932	+	0.0946460i
$980$	−5.80091	+	3.91783i	−0.185303	+	0.125151i
$981$		0			0
$982$	−12.3218	−	21.3419i	−0.393203	−	0.681048i
$983$	−36.3092			−1.15808			−0.579041	−	0.815298i	$-0.696573\pi$
$983$	−36.3092			−1.15808			−0.579041	+	0.815298i	$0.696573\pi$
$984$		0			0
$985$		−	12.0072i		−	0.382582i
$986$	13.8539	−	23.9957i	0.441199	−	0.764179i
$987$		0			0
$988$	−9.22244	−	15.9737i	−0.293405	−	0.508192i
$989$	−35.5337	+	20.5154i	−1.12991	+	0.652352i
$990$		0			0
$991$	22.0204	−	38.1404i	0.699501	−	1.21157i	−0.269139	−	0.963101i	$-0.586739\pi$
$991$	22.0204	−	38.1404i	0.699501	−	1.21157i	0.968640	−	0.248469i	$-0.0799275\pi$
$992$	3.74031	−	6.47842i	0.118755	−	0.205690i
$993$		0			0
$994$	−7.83597	−	25.6028i	−0.248542	−	0.812073i
$995$	−3.77973	−	2.18223i	−0.119826	−	0.0691814i
$996$		0			0
$997$		−	4.71325i		−	0.149270i	−0.997211	−	0.0746350i	$-0.976221\pi$
$997$		−	4.71325i		−	0.149270i	0.997211	−	0.0746350i	$-0.0237792\pi$
$998$	25.1555	+	14.5236i	0.796285	+	0.459735i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.c.1151.14		32
3.2	odd	2		630.2.t.c.311.2	✓	32
7.5	odd	6		1890.2.bk.c.341.7		32
9.2	odd	6		1890.2.bk.c.521.7		32
9.7	even	3		630.2.bk.c.101.2	yes	32
21.5	even	6		630.2.bk.c.131.10	yes	32
63.47	even	6	inner	1890.2.t.c.1601.14		32
63.61	odd	6		630.2.t.c.551.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.2	✓	32	3.2	odd	2
630.2.t.c.551.2	yes	32	63.61	odd	6
630.2.bk.c.101.2	yes	32	9.7	even	3
630.2.bk.c.131.10	yes	32	21.5	even	6
1890.2.t.c.1151.14		32	1.1	even	1	trivial
1890.2.t.c.1601.14		32	63.47	even	6	inner
1890.2.bk.c.341.7		32	7.5	odd	6
1890.2.bk.c.521.7		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.80382 + 1.93552i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.80382 + 1.93552i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +0.781517i q^{11} +(-2.26905 - 1.31003i) q^{13} +(-2.52991 + 0.774302i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.02795 + 5.24457i) q^{17} +(6.09668 - 3.51992i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.390758 + 0.676813i) q^{22} -4.60919i q^{23} +1.00000 q^{25} +(-1.31003 - 2.26905i) q^{26} +(-2.57812 - 0.594391i) q^{28} +(-3.96237 + 2.28767i) q^{29} +(-6.47842 + 3.74031i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.24457 + 3.02795i) q^{34} +(1.80382 - 1.93552i) q^{35} +(-5.42975 - 9.40460i) q^{37} +7.03984 q^{38} -1.00000i q^{40} +(-5.46910 + 9.47275i) q^{41} +(-4.45098 - 7.70932i) q^{43} +(-0.676813 + 0.390758i) q^{44} +(2.30460 - 3.99168i) q^{46} +(-0.501266 + 0.868218i) q^{47} +(-0.492485 - 6.98265i) q^{49} +(0.866025 + 0.500000i) q^{50} -2.62007i q^{52} +(-8.30234 - 4.79336i) q^{53} -0.781517i q^{55} +(-1.93552 - 1.80382i) q^{56} -4.57535 q^{58} +(-1.32003 - 2.28635i) q^{59} +(1.84617 + 1.06588i) q^{61} -7.48063 q^{62} -1.00000 q^{64} +(2.26905 + 1.31003i) q^{65} +(-6.02939 - 10.4432i) q^{67} -6.05590 q^{68} +(2.52991 - 0.774302i) q^{70} +10.1200i q^{71} +(7.67003 + 4.42830i) q^{73} -10.8595i q^{74} +(6.09668 + 3.51992i) q^{76} +(-1.51264 - 1.40971i) q^{77} +(-7.96847 + 13.8018i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-9.47275 + 5.46910i) q^{82} +(2.03248 + 3.52036i) q^{83} +(3.02795 - 5.24457i) q^{85} -8.90195i q^{86} -0.781517 q^{88} +(3.78927 + 6.56320i) q^{89} +(6.62855 - 2.02872i) q^{91} +(3.99168 - 2.30460i) q^{92} +(-0.868218 + 0.501266i) q^{94} +(-6.09668 + 3.51992i) q^{95} +(5.00436 - 2.88927i) q^{97} +(3.06482 - 6.29340i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

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