LMFDB - Embedded newform 1890.2.t.b.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:	$28$
Relative dimension:	$14$ 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.b.1601.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-2.02958 + 1.69729i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-2.02958 + 1.69729i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -5.51168i q^{11} +(-5.67516 - 3.27655i) q^{13} +(-2.60632 + 0.455105i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.26666 + 2.19392i) q^{17} +(-6.11706 + 3.53169i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.75584 - 4.77326i) q^{22} -4.21229i q^{23} +1.00000 q^{25} +(-3.27655 - 5.67516i) q^{26} +(-2.48469 - 0.909025i) q^{28} +(-6.29071 + 3.63194i) q^{29} +(-5.33881 + 3.08236i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.19392 + 1.26666i) q^{34} +(-2.02958 + 1.69729i) q^{35} +(-1.00755 - 1.74514i) q^{37} -7.06338 q^{38} +1.00000i q^{40} +(2.97356 - 5.15035i) q^{41} +(2.74829 + 4.76018i) q^{43} +(4.77326 - 2.75584i) q^{44} +(2.10615 - 3.64795i) q^{46} +(-2.69332 + 4.66497i) q^{47} +(1.23841 - 6.88958i) q^{49} +(0.866025 + 0.500000i) q^{50} -6.55311i q^{52} +(-2.56943 - 1.48346i) q^{53} -5.51168i q^{55} +(-1.69729 - 2.02958i) q^{56} -7.26388 q^{58} +(1.95873 + 3.39263i) q^{59} +(0.512178 + 0.295706i) q^{61} -6.16472 q^{62} -1.00000 q^{64} +(-5.67516 - 3.27655i) q^{65} +(1.48818 + 2.57760i) q^{67} -2.53332 q^{68} +(-2.60632 + 0.455105i) q^{70} -14.8483i q^{71} +(9.76683 + 5.63888i) q^{73} -2.01511i q^{74} +(-6.11706 - 3.53169i) q^{76} +(9.35492 + 11.1864i) q^{77} +(-0.619617 + 1.07321i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.15035 - 2.97356i) q^{82} +(4.32347 + 7.48846i) q^{83} +(-1.26666 + 2.19392i) q^{85} +5.49658i q^{86} +5.51168 q^{88} +(-7.84313 - 13.5847i) q^{89} +(17.0795 - 2.98235i) q^{91} +(3.64795 - 2.10615i) q^{92} +(-4.66497 + 2.69332i) q^{94} +(-6.11706 + 3.53169i) q^{95} +(0.197336 - 0.113932i) q^{97} +(4.51729 - 5.34735i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * 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
$7$	−2.02958	+	1.69729i	−0.767110	+	0.641515i
$7$	−2.02958	+	1.69729i	−0.767110	+	0.641515i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	5.51168i		−	1.66183i	−0.556396	−	0.830917i	$-0.687816\pi$
$11$		−	5.51168i		−	1.66183i	0.556396	−	0.830917i	$-0.312184\pi$
$12$		0			0
$13$	−5.67516	−	3.27655i	−1.57400	−	0.908752i	−0.995671	−	0.0929524i	$-0.970370\pi$
$13$	−5.67516	−	3.27655i	−1.57400	−	0.908752i	−0.578334	−	0.815800i	$-0.696297\pi$
$14$	−2.60632	+	0.455105i	−0.696567	+	0.121632i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.26666	+	2.19392i	−0.307211	+	0.532104i	−0.977751	−	0.209769i	$-0.932729\pi$
$17$	−1.26666	+	2.19392i	−0.307211	+	0.532104i	0.670541	+	0.741873i	$0.266062\pi$
$18$		0			0
$19$	−6.11706	+	3.53169i	−1.40335	+	0.810225i	−0.994735	−	0.102482i	$-0.967322\pi$
$19$	−6.11706	+	3.53169i	−1.40335	+	0.810225i	−0.408616	+	0.912707i	$0.633988\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	2.75584	−	4.77326i	0.587547	−	1.01766i
$23$		−	4.21229i		−	0.878324i	−0.898408	−	0.439162i	$-0.855275\pi$
$23$		−	4.21229i		−	0.878324i	0.898408	−	0.439162i	$-0.144725\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−3.27655	−	5.67516i	−0.642585	−	1.11299i
$27$		0			0
$28$	−2.48469	−	0.909025i	−0.469562	−	0.171790i
$29$	−6.29071	+	3.63194i	−1.16815	+	0.674435i	−0.953245	−	0.302199i	$-0.902279\pi$
$29$	−6.29071	+	3.63194i	−1.16815	+	0.674435i	−0.214910	+	0.976634i	$0.568946\pi$
$30$		0			0
$31$	−5.33881	+	3.08236i	−0.958878	+	0.553608i	−0.895827	−	0.444402i	$-0.853416\pi$
$31$	−5.33881	+	3.08236i	−0.958878	+	0.553608i	−0.0630503	+	0.998010i	$0.520083\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−2.19392	+	1.26666i	−0.376255	+	0.217231i
$35$	−2.02958	+	1.69729i	−0.343062	+	0.286894i
$36$		0			0
$37$	−1.00755	−	1.74514i	−0.165641	−	0.286899i	0.771242	−	0.636542i	$-0.219636\pi$
$37$	−1.00755	−	1.74514i	−0.165641	−	0.286899i	−0.936883	+	0.349644i	$0.886303\pi$
$38$	−7.06338			−1.14583
$39$		0			0
$40$			1.00000i			0.158114i
$41$	2.97356	−	5.15035i	0.464392	−	0.804350i	−0.534782	−	0.844990i	$-0.679606\pi$
$41$	2.97356	−	5.15035i	0.464392	−	0.804350i	0.999174	+	0.0406401i	$0.0129397\pi$
$42$		0			0
$43$	2.74829	+	4.76018i	0.419110	+	0.725920i	0.995850	−	0.0910078i	$-0.0290088\pi$
$43$	2.74829	+	4.76018i	0.419110	+	0.725920i	−0.576740	+	0.816928i	$0.695675\pi$
$44$	4.77326	−	2.75584i	0.719595	−	0.415459i
$45$		0			0
$46$	2.10615	−	3.64795i	0.310534	−	0.537861i
$47$	−2.69332	+	4.66497i	−0.392861	+	0.680456i	−0.992826	−	0.119571i	$-0.961848\pi$
$47$	−2.69332	+	4.66497i	−0.392861	+	0.680456i	0.599964	+	0.800027i	$0.295181\pi$
$48$		0			0
$49$	1.23841	−	6.88958i	0.176916	−	0.984226i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$		−	6.55311i		−	0.908752i
$53$	−2.56943	−	1.48346i	−0.352938	−	0.203769i	0.313040	−	0.949740i	$-0.398652\pi$
$53$	−2.56943	−	1.48346i	−0.352938	−	0.203769i	−0.665979	+	0.745971i	$0.731986\pi$
$54$		0			0
$55$		−	5.51168i		−	0.743195i
$56$	−1.69729	−	2.02958i	−0.226810	−	0.271214i
$57$		0			0
$58$	−7.26388			−0.953795
$59$	1.95873	+	3.39263i	0.255005	+	0.441682i	0.964897	−	0.262629i	$-0.0845894\pi$
$59$	1.95873	+	3.39263i	0.255005	+	0.441682i	−0.709892	+	0.704311i	$0.751256\pi$
$60$		0			0
$61$	0.512178	+	0.295706i	0.0655776	+	0.0378613i	0.532430	−	0.846474i	$-0.321279\pi$
$61$	0.512178	+	0.295706i	0.0655776	+	0.0378613i	−0.466853	+	0.884335i	$0.654612\pi$
$62$	−6.16472			−0.782920
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.67516	−	3.27655i	−0.703916	−	0.406406i
$66$		0			0
$67$	1.48818	+	2.57760i	0.181810	+	0.314904i	0.942497	−	0.334215i	$-0.108471\pi$
$67$	1.48818	+	2.57760i	0.181810	+	0.314904i	−0.760687	+	0.649119i	$0.775138\pi$
$68$	−2.53332			−0.307211
$69$		0			0
$70$	−2.60632	+	0.455105i	−0.311514	+	0.0543955i
$71$		−	14.8483i		−	1.76217i	−0.472960	−	0.881084i	$-0.656815\pi$
$71$		−	14.8483i		−	1.76217i	0.472960	−	0.881084i	$-0.343185\pi$
$72$		0			0
$73$	9.76683	+	5.63888i	1.14312	+	0.659981i	0.947201	−	0.320639i	$-0.103898\pi$
$73$	9.76683	+	5.63888i	1.14312	+	0.659981i	0.195919	+	0.980620i	$0.437231\pi$
$74$		−	2.01511i		−	0.234252i
$75$		0			0
$76$	−6.11706	−	3.53169i	−0.701675	−	0.405112i
$77$	9.35492	+	11.1864i	1.06609	+	1.27481i
$78$		0			0
$79$	−0.619617	+	1.07321i	−0.0697124	+	0.120745i	−0.898775	−	0.438411i	$-0.855541\pi$
$79$	−0.619617	+	1.07321i	−0.0697124	+	0.120745i	0.829062	+	0.559156i	$0.188875\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	5.15035	−	2.97356i	0.568761	−	0.328374i
$83$	4.32347	+	7.48846i	0.474562	+	0.821966i	0.999576	−	0.0291281i	$-0.00927309\pi$
$83$	4.32347	+	7.48846i	0.474562	+	0.821966i	−0.525014	+	0.851094i	$0.675940\pi$
$84$		0			0
$85$	−1.26666	+	2.19392i	−0.137389	+	0.237964i
$86$			5.49658i			0.592711i
$87$		0			0
$88$	5.51168			0.587547
$89$	−7.84313	−	13.5847i	−0.831371	−	1.43998i	−0.896952	−	0.442129i	$-0.854223\pi$
$89$	−7.84313	−	13.5847i	−0.831371	−	1.43998i	0.0655810	−	0.997847i	$-0.479110\pi$
$90$		0			0
$91$	17.0795	−	2.98235i	1.79041	−	0.312635i
$92$	3.64795	−	2.10615i	0.380326	−	0.219581i
$93$		0			0
$94$	−4.66497	+	2.69332i	−0.481155	+	0.277795i
$95$	−6.11706	+	3.53169i	−0.627597	+	0.362344i
$96$		0			0
$97$	0.197336	−	0.113932i	0.0200365	−	0.0115681i	−0.489948	−	0.871751i	$-0.662984\pi$
$97$	0.197336	−	0.113932i	0.0200365	−	0.0115681i	0.509985	+	0.860183i	$0.329651\pi$
$98$	4.51729	−	5.34735i	0.456315	−	0.540164i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−2.76769			−0.275396			−0.137698	−	0.990474i	$-0.543970\pi$
$101$	−2.76769			−0.275396			−0.137698	+	0.990474i	$0.543970\pi$
$102$		0			0
$103$			3.30139i			0.325295i	0.986684	+	0.162648i	$0.0520034\pi$
$103$			3.30139i			0.325295i	−0.986684	+	0.162648i	$0.947997\pi$
$104$	3.27655	−	5.67516i	0.321292	−	0.556495i
$105$		0			0
$106$	−1.48346	−	2.56943i	−0.144086	−	0.249565i
$107$	−4.81501	+	2.77994i	−0.465484	+	0.268747i	−0.714347	−	0.699791i	$-0.753276\pi$
$107$	−4.81501	+	2.77994i	−0.465484	+	0.268747i	0.248863	+	0.968539i	$0.419943\pi$
$108$		0			0
$109$	9.12223	−	15.8002i	0.873751	−	1.51338i	0.0156644	−	0.999877i	$-0.495014\pi$
$109$	9.12223	−	15.8002i	0.873751	−	1.51338i	0.858087	−	0.513504i	$-0.171653\pi$
$110$	2.75584	−	4.77326i	0.262759	−	0.455112i
$111$		0			0
$112$	−0.455105	−	2.60632i	−0.0430034	−	0.246274i
$113$	−1.41503	−	0.816970i	−0.133115	−	0.0768540i	0.431964	−	0.901891i	$-0.357821\pi$
$113$	−1.41503	−	0.816970i	−0.133115	−	0.0768540i	−0.565079	+	0.825037i	$0.691154\pi$
$114$		0			0
$115$		−	4.21229i		−	0.392798i
$116$	−6.29071	−	3.63194i	−0.584077	−	0.337217i
$117$		0			0
$118$			3.91747i			0.360632i
$119$	−1.15293	−	6.60264i	−0.105689	−	0.605263i
$120$		0			0
$121$	−19.3786			−1.76169
$122$	0.295706	+	0.512178i	0.0267720	+	0.0463704i
$123$		0			0
$124$	−5.33881	−	3.08236i	−0.479439	−	0.276804i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−11.2316			−0.996643			−0.498322	−	0.866992i	$-0.666050\pi$
$127$	−11.2316			−0.996643			−0.498322	+	0.866992i	$0.666050\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−3.27655	−	5.67516i	−0.287373	−	0.497744i
$131$	4.16723			0.364092			0.182046	−	0.983290i	$-0.441728\pi$
$131$	4.16723			0.364092			0.182046	+	0.983290i	$0.441728\pi$
$132$		0			0
$133$	6.42079	−	17.5503i	0.556753	−	1.52180i
$134$			2.97636i			0.257118i
$135$		0			0
$136$	−2.19392	−	1.26666i	−0.188127	−	0.108615i
$137$			9.27120i			0.792092i	0.918231	+	0.396046i	$0.129618\pi$
$137$			9.27120i			0.792092i	−0.918231	+	0.396046i	$0.870382\pi$
$138$		0			0
$139$	3.08961	+	1.78379i	0.262057	+	0.151299i	0.625273	−	0.780406i	$-0.284988\pi$
$139$	3.08961	+	1.78379i	0.262057	+	0.151299i	−0.363216	+	0.931705i	$0.618321\pi$
$140$	−2.48469	−	0.909025i	−0.209994	−	0.0768266i
$141$		0			0
$142$	7.42414	−	12.8590i	0.623020	−	1.07910i
$143$	−18.0593	+	31.2796i	−1.51020	+	2.61574i
$144$		0			0
$145$	−6.29071	+	3.63194i	−0.522415	+	0.301616i
$146$	5.63888	+	9.76683i	0.466677	+	0.808308i
$147$		0			0
$148$	1.00755	−	1.74514i	0.0828205	−	0.143449i
$149$			10.3904i			0.851216i	0.904908	+	0.425608i	$0.139940\pi$
$149$			10.3904i			0.851216i	−0.904908	+	0.425608i	$0.860060\pi$
$150$		0			0
$151$	−8.76778			−0.713512			−0.356756	−	0.934198i	$-0.616117\pi$
$151$	−8.76778			−0.713512			−0.356756	+	0.934198i	$0.616117\pi$
$152$	−3.53169	−	6.11706i	−0.286458	−	0.496159i
$153$		0			0
$154$	2.50839	+	14.3652i	0.202132	+	1.15758i
$155$	−5.33881	+	3.08236i	−0.428823	+	0.247581i
$156$		0			0
$157$	10.3942	−	6.00109i	0.829547	−	0.478939i	−0.0241507	−	0.999708i	$-0.507688\pi$
$157$	10.3942	−	6.00109i	0.829547	−	0.478939i	0.853697	+	0.520769i	$0.174355\pi$
$158$	−1.07321	+	0.619617i	−0.0853799	+	0.0492941i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	7.14949	+	8.54920i	0.563458	+	0.673771i
$162$		0			0
$163$	−5.40261	−	9.35760i	−0.423165	−	0.732944i	0.573082	−	0.819498i	$-0.305748\pi$
$163$	−5.40261	−	9.35760i	−0.423165	−	0.732944i	−0.996247	+	0.0865542i	$0.972414\pi$
$164$	5.94711			0.464392
$165$		0			0
$166$			8.64693i			0.671132i
$167$	−10.7866	+	18.6830i	−0.834695	+	1.44573i	0.0595841	+	0.998223i	$0.481023\pi$
$167$	−10.7866	+	18.6830i	−0.834695	+	1.44573i	−0.894279	+	0.447510i	$0.852311\pi$
$168$		0			0
$169$	14.9716	+	25.9316i	1.15166	+	1.99474i
$170$	−2.19392	+	1.26666i	−0.168266	+	0.0971485i
$171$		0			0
$172$	−2.74829	+	4.76018i	−0.209555	+	0.362960i
$173$	0.639733	−	1.10805i	0.0486380	−	0.0842435i	−0.840681	−	0.541530i	$-0.817845\pi$
$173$	0.639733	−	1.10805i	0.0486380	−	0.0842435i	0.889319	+	0.457286i	$0.151179\pi$
$174$		0			0
$175$	−2.02958	+	1.69729i	−0.153422	+	0.128303i
$176$	4.77326	+	2.75584i	0.359798	+	0.207729i
$177$		0			0
$178$		−	15.6863i		−	1.17574i
$179$	−10.2660	−	5.92708i	−0.767317	−	0.443010i	0.0645999	−	0.997911i	$-0.479423\pi$
$179$	−10.2660	−	5.92708i	−0.767317	−	0.443010i	−0.831917	+	0.554901i	$0.812756\pi$
$180$		0			0
$181$			13.3188i			0.989978i	0.868899	+	0.494989i	$0.164828\pi$
$181$			13.3188i			0.989978i	−0.868899	+	0.494989i	$0.835172\pi$
$182$	16.2824	+	5.95694i	1.20693	+	0.441558i
$183$		0			0
$184$	4.21229			0.310534
$185$	−1.00755	−	1.74514i	−0.0740769	−	0.128305i
$186$		0			0
$187$	12.0922	+	6.98143i	0.884269	+	0.510533i
$188$	−5.38665			−0.392861
$189$		0			0
$190$	−7.06338			−0.512431
$191$	−7.09826	−	4.09818i	−0.513612	−	0.296534i	0.220705	−	0.975341i	$-0.429164\pi$
$191$	−7.09826	−	4.09818i	−0.513612	−	0.296534i	−0.734317	+	0.678806i	$0.762498\pi$
$192$		0			0
$193$	−1.49743	−	2.59363i	−0.107787	−	0.186693i	0.807086	−	0.590434i	$-0.201043\pi$
$193$	−1.49743	−	2.59363i	−0.107787	−	0.186693i	−0.914874	+	0.403740i	$0.867710\pi$
$194$	0.227864			0.0163597
$195$		0			0
$196$	6.58576	−	2.37229i	0.470411	−	0.169450i
$197$		−	11.9427i		−	0.850883i	−0.904986	−	0.425441i	$-0.860119\pi$
$197$		−	11.9427i		−	0.850883i	0.904986	−	0.425441i	$-0.139881\pi$
$198$		0			0
$199$	−2.73876	−	1.58122i	−0.194145	−	0.112090i	0.399776	−	0.916613i	$-0.369088\pi$
$199$	−2.73876	−	1.58122i	−0.194145	−	0.112090i	−0.593922	+	0.804523i	$0.702421\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−2.39689	−	1.38385i	−0.168645	−	0.0973670i
$203$	6.60305	−	18.0485i	0.463443	−	1.26676i
$204$		0			0
$205$	2.97356	−	5.15035i	0.207682	−	0.359716i
$206$	−1.65069	+	2.85909i	−0.115009	+	0.199202i
$207$		0			0
$208$	5.67516	−	3.27655i	0.393501	−	0.227188i
$209$	19.4655	+	33.7153i	1.34646	+	2.33214i
$210$		0			0
$211$	6.04072	−	10.4628i	0.415860	−	0.720291i	−0.579658	−	0.814860i	$-0.696814\pi$
$211$	6.04072	−	10.4628i	0.415860	−	0.720291i	0.995518	+	0.0945689i	$0.0301473\pi$
$212$		−	2.96692i		−	0.203769i
$213$		0			0
$214$	−5.55989			−0.380066
$215$	2.74829	+	4.76018i	0.187432	+	0.324641i
$216$		0			0
$217$	5.60389	−	15.3174i	0.380417	−	1.03981i
$218$	15.8002	−	9.12223i	1.07012	−	0.617835i
$219$		0			0
$220$	4.77326	−	2.75584i	0.321813	−	0.185799i
$221$	14.3770	−	8.30057i	0.967102	−	0.558357i
$222$		0			0
$223$	−13.6952	+	7.90695i	−0.917101	+	0.529488i	−0.882709	−	0.469920i	$-0.844283\pi$
$223$	−13.6952	+	7.90695i	−0.917101	+	0.529488i	−0.0343917	+	0.999408i	$0.510949\pi$
$224$	0.909025	−	2.48469i	0.0607368	−	0.166015i
$225$		0			0
$226$	−0.816970	−	1.41503i	−0.0543440	−	0.0941266i
$227$	−2.12883			−0.141296			−0.0706478	−	0.997501i	$-0.522507\pi$
$227$	−2.12883			−0.141296			−0.0706478	+	0.997501i	$0.522507\pi$
$228$		0			0
$229$		−	20.3062i		−	1.34187i	−0.741517	−	0.670934i	$-0.765893\pi$
$229$		−	20.3062i		−	1.34187i	0.741517	−	0.670934i	$-0.234107\pi$
$230$	2.10615	−	3.64795i	0.138875	−	0.240539i
$231$		0			0
$232$	−3.63194	−	6.29071i	−0.238449	−	0.413005i
$233$	11.1623	−	6.44458i	0.731269	−	0.422198i	−0.0876172	−	0.996154i	$-0.527925\pi$
$233$	11.1623	−	6.44458i	0.731269	−	0.422198i	0.818886	+	0.573956i	$0.194592\pi$
$234$		0			0
$235$	−2.69332	+	4.66497i	−0.175693	+	0.304309i
$236$	−1.95873	+	3.39263i	−0.127503	+	0.220841i
$237$		0			0
$238$	2.30285	−	6.29452i	0.149272	−	0.408013i
$239$	0.970335	+	0.560223i	0.0627658	+	0.0362378i	0.531054	−	0.847338i	$-0.321796\pi$
$239$	0.970335	+	0.560223i	0.0627658	+	0.0362378i	−0.468289	+	0.883576i	$0.655129\pi$
$240$		0			0
$241$		−	1.45223i		−	0.0935465i	−0.998906	−	0.0467732i	$-0.985106\pi$
$241$		−	1.45223i		−	0.0935465i	0.998906	−	0.0467732i	$-0.0148938\pi$
$242$	−16.7824	−	9.68931i	−1.07881	−	0.622853i
$243$		0			0
$244$			0.591412i			0.0378613i
$245$	1.23841	−	6.88958i	0.0791192	−	0.440159i
$246$		0			0
$247$	46.2871			2.94517
$248$	−3.08236	−	5.33881i	−0.195730	−	0.339014i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−14.7760			−0.932653			−0.466327	−	0.884613i	$-0.654423\pi$
$251$	−14.7760			−0.932653			−0.466327	+	0.884613i	$0.654423\pi$
$252$		0			0
$253$	−23.2168			−1.45963
$254$	−9.72685	−	5.61580i	−0.610317	−	0.352367i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.7853			1.10942			0.554708	−	0.832045i	$-0.312830\pi$
$257$	17.7853			1.10942			0.554708	+	0.832045i	$0.312830\pi$
$258$		0			0
$259$	5.00692	+	1.83179i	0.311115	+	0.113822i
$260$		−	6.55311i		−	0.406406i
$261$		0			0
$262$	3.60893	+	2.08361i	0.222960	+	0.128726i
$263$			7.71730i			0.475869i	0.971281	+	0.237935i	$0.0764704\pi$
$263$			7.71730i			0.475869i	−0.971281	+	0.237935i	$0.923530\pi$
$264$		0			0
$265$	−2.56943	−	1.48346i	−0.157839	−	0.0911282i
$266$	14.3357	−	11.9886i	0.878979	−	0.735068i
$267$		0			0
$268$	−1.48818	+	2.57760i	−0.0909049	+	0.157452i
$269$	11.2244	−	19.4412i	0.684361	−	1.18535i	−0.289276	−	0.957246i	$-0.593414\pi$
$269$	11.2244	−	19.4412i	0.684361	−	1.18535i	0.973637	−	0.228103i	$-0.0732522\pi$
$270$		0			0
$271$	−0.353310	+	0.203983i	−0.0214620	+	0.0123911i	−0.510693	−	0.859763i	$-0.670611\pi$
$271$	−0.353310	+	0.203983i	−0.0214620	+	0.0123911i	0.489231	+	0.872154i	$0.337278\pi$
$272$	−1.26666	−	2.19392i	−0.0768026	−	0.133026i
$273$		0			0
$274$	−4.63560	+	8.02909i	−0.280047	+	0.485055i
$275$		−	5.51168i		−	0.332367i
$276$		0			0
$277$	25.7859			1.54932			0.774662	−	0.632376i	$-0.217920\pi$
$277$	25.7859			1.54932			0.774662	+	0.632376i	$0.217920\pi$
$278$	1.78379	+	3.08961i	0.106984	+	0.185302i
$279$		0			0
$280$	−1.69729	−	2.02958i	−0.101432	−	0.121291i
$281$	−11.9347	+	6.89052i	−0.711966	+	0.411054i	−0.811788	−	0.583952i	$-0.801506\pi$
$281$	−11.9347	+	6.89052i	−0.711966	+	0.411054i	0.0998226	+	0.995005i	$0.468172\pi$
$282$		0			0
$283$	2.84397	−	1.64197i	0.169056	−	0.0976048i	−0.413084	−	0.910693i	$-0.635549\pi$
$283$	2.84397	−	1.64197i	0.169056	−	0.0976048i	0.582141	+	0.813088i	$0.302215\pi$
$284$	12.8590	−	7.42414i	0.763041	−	0.440542i
$285$		0			0
$286$	−31.2796	+	18.0593i	−1.84960	+	1.06787i
$287$	2.70656	+	15.5001i	0.159763	+	0.914939i
$288$		0			0
$289$	5.29114	+	9.16452i	0.311243	+	0.539089i
$290$	−7.26388			−0.426550
$291$		0			0
$292$			11.2778i			0.659981i
$293$	5.22757	−	9.05442i	0.305398	−	0.528965i	−0.671952	−	0.740595i	$-0.734544\pi$
$293$	5.22757	−	9.05442i	0.305398	−	0.528965i	0.977350	+	0.211630i	$0.0678772\pi$
$294$		0			0
$295$	1.95873	+	3.39263i	0.114042	+	0.197526i
$296$	1.74514	−	1.00755i	0.101434	−	0.0585629i
$297$		0			0
$298$	−5.19521	+	8.99836i	−0.300950	+	0.521261i
$299$	−13.8018	+	23.9054i	−0.798179	+	1.38249i
$300$		0			0
$301$	−13.6573	−	4.99653i	−0.787192	−	0.287995i
$302$	−7.59312	−	4.38389i	−0.436935	−	0.252264i
$303$		0			0
$304$		−	7.06338i		−	0.405112i
$305$	0.512178	+	0.295706i	0.0293272	+	0.0169321i
$306$		0			0
$307$			32.9003i			1.87772i	0.344297	+	0.938861i	$0.388117\pi$
$307$			32.9003i			1.87772i	−0.344297	+	0.938861i	$0.611883\pi$
$308$	−5.01026	+	13.6948i	−0.285486	+	0.780334i
$309$		0			0
$310$	−6.16472			−0.350133
$311$	−12.9216	−	22.3808i	−0.732715	−	1.26910i	−0.955719	−	0.294282i	$-0.904920\pi$
$311$	−12.9216	−	22.3808i	−0.732715	−	1.26910i	0.223004	−	0.974818i	$-0.428414\pi$
$312$		0			0
$313$	−16.2102	−	9.35899i	−0.916257	−	0.529002i	−0.0338183	−	0.999428i	$-0.510767\pi$
$313$	−16.2102	−	9.35899i	−0.916257	−	0.529002i	−0.882439	+	0.470426i	$0.844100\pi$
$314$	12.0022			0.677322
$315$		0			0
$316$	−1.23923			−0.0697124
$317$	15.9904	+	9.23209i	0.898113	+	0.518526i	0.876587	−	0.481243i	$-0.159814\pi$
$317$	15.9904	+	9.23209i	0.898113	+	0.518526i	0.0215255	+	0.999768i	$0.493148\pi$
$318$		0			0
$319$	20.0181	+	34.6724i	1.12080	+	1.94128i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	1.91704	+	10.9786i	0.106832	+	0.611812i
$323$		−	17.8938i		−	0.995638i
$324$		0			0
$325$	−5.67516	−	3.27655i	−0.314801	−	0.181750i
$326$		−	10.8052i		−	0.598446i
$327$		0			0
$328$	5.15035	+	2.97356i	0.284381	+	0.164187i
$329$	−2.45149	−	14.0393i	−0.135155	−	0.774011i
$330$		0			0
$331$	−11.7514	+	20.3540i	−0.645913	+	1.11875i	0.338176	+	0.941083i	$0.390190\pi$
$331$	−11.7514	+	20.3540i	−0.645913	+	1.11875i	−0.984090	+	0.177672i	$0.943143\pi$
$332$	−4.32347	+	7.48846i	−0.237281	+	0.410983i
$333$		0			0
$334$	−18.6830	+	10.7866i	−1.02229	+	0.590218i
$335$	1.48818	+	2.57760i	0.0813078	+	0.140829i
$336$		0			0
$337$	−8.75258	+	15.1599i	−0.476783	+	0.825813i	−0.999646	−	0.0266040i	$-0.991531\pi$
$337$	−8.75258	+	15.1599i	−0.476783	+	0.825813i	0.522863	+	0.852417i	$0.324864\pi$
$338$			29.9432i			1.62869i
$339$		0			0
$340$	−2.53332			−0.137389
$341$	16.9890	+	29.4258i	0.920005	+	1.59350i
$342$		0			0
$343$	9.18016	+	16.0849i	0.495682	+	0.868504i
$344$	−4.76018	+	2.74829i	−0.256651	+	0.148178i
$345$		0			0
$346$	1.10805	−	0.639733i	0.0595691	−	0.0343923i
$347$	8.88116	−	5.12754i	0.476766	−	0.275261i	−0.242302	−	0.970201i	$-0.577902\pi$
$347$	8.88116	−	5.12754i	0.476766	−	0.275261i	0.719068	+	0.694940i	$0.244569\pi$
$348$		0			0
$349$	0.861681	−	0.497492i	0.0461247	−	0.0266301i	−0.476760	−	0.879033i	$-0.658189\pi$
$349$	0.861681	−	0.497492i	0.0461247	−	0.0266301i	0.522885	+	0.852403i	$0.324856\pi$
$350$	−2.60632	+	0.455105i	−0.139313	+	0.0243264i
$351$		0			0
$352$	2.75584	+	4.77326i	0.146887	+	0.254415i
$353$	−13.3768			−0.711976			−0.355988	−	0.934491i	$-0.615856\pi$
$353$	−13.3768			−0.711976			−0.355988	+	0.934491i	$0.615856\pi$
$354$		0			0
$355$		−	14.8483i		−	0.788065i
$356$	7.84313	−	13.5847i	0.415685	−	0.719988i
$357$		0			0
$358$	−5.92708	−	10.2660i	−0.313256	−	0.542575i
$359$	14.3453	−	8.28227i	0.757116	−	0.437121i	−0.0711432	−	0.997466i	$-0.522665\pi$
$359$	14.3453	−	8.28227i	0.757116	−	0.437121i	0.828259	+	0.560345i	$0.189331\pi$
$360$		0			0
$361$	15.4456	−	26.7526i	0.812929	−	1.40803i
$362$	−6.65940	+	11.5344i	−0.350010	+	0.606235i
$363$		0			0
$364$	11.1225	+	13.3001i	0.582979	+	0.697113i
$365$	9.76683	+	5.63888i	0.511219	+	0.295153i
$366$		0			0
$367$			11.4300i			0.596639i	0.954466	+	0.298319i	$0.0964260\pi$
$367$			11.4300i			0.596639i	−0.954466	+	0.298319i	$0.903574\pi$
$368$	3.64795	+	2.10615i	0.190163	+	0.109791i
$369$		0			0
$370$		−	2.01511i		−	0.104761i
$371$	7.73273	−	1.35026i	0.401463	−	0.0701020i
$372$		0			0
$373$	−23.5637			−1.22008			−0.610040	−	0.792371i	$-0.708847\pi$
$373$	−23.5637			−1.22008			−0.610040	+	0.792371i	$0.708847\pi$
$374$	6.98143	+	12.0922i	0.361001	+	0.625273i
$375$		0			0
$376$	−4.66497	−	2.69332i	−0.240578	−	0.138898i
$377$	47.6010			2.45158
$378$		0			0
$379$	17.5149			0.899678			0.449839	−	0.893110i	$-0.351481\pi$
$379$	17.5149			0.899678			0.449839	+	0.893110i	$0.351481\pi$
$380$	−6.11706	−	3.53169i	−0.313799	−	0.181172i
$381$		0			0
$382$	−4.09818	−	7.09826i	−0.209681	−	0.363179i
$383$	−19.9087			−1.01729			−0.508645	−	0.860977i	$-0.669853\pi$
$383$	−19.9087			−1.01729			−0.508645	+	0.860977i	$0.669853\pi$
$384$		0			0
$385$	9.35492	+	11.1864i	0.476771	+	0.570112i
$386$		−	2.99486i		−	0.152435i
$387$		0			0
$388$	0.197336	+	0.113932i	0.0100182	+	0.00578403i
$389$		−	34.4294i		−	1.74564i	−0.488044	−	0.872819i	$-0.662289\pi$
$389$		−	34.4294i		−	1.74564i	0.488044	−	0.872819i	$-0.337711\pi$
$390$		0			0
$391$	9.24145	+	5.33555i	0.467360	+	0.269830i
$392$	6.88958	+	1.23841i	0.347976	+	0.0625493i
$393$		0			0
$394$	5.97136	−	10.3427i	0.300833	−	0.521057i
$395$	−0.619617	+	1.07321i	−0.0311763	+	0.0539990i
$396$		0			0
$397$	−10.0202	+	5.78514i	−0.502897	+	0.290348i	−0.729909	−	0.683544i	$-0.760438\pi$
$397$	−10.0202	+	5.78514i	−0.502897	+	0.290348i	0.227012	+	0.973892i	$0.427104\pi$
$398$	−1.58122	−	2.73876i	−0.0792595	−	0.137282i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	13.9512i		−	0.696687i	−0.937367	−	0.348344i	$-0.886744\pi$
$401$		−	13.9512i		−	0.696687i	0.937367	−	0.348344i	$-0.113256\pi$
$402$		0			0
$403$	40.3981			2.01237
$404$	−1.38385	−	2.39689i	−0.0688489	−	0.119250i
$405$		0			0
$406$	14.7427	−	12.3289i	0.731665	−	0.611874i
$407$	−9.61863	+	5.55332i	−0.476778	+	0.275268i
$408$		0			0
$409$	−19.3854	+	11.1922i	−0.958546	+	0.553417i	−0.895725	−	0.444608i	$-0.853343\pi$
$409$	−19.3854	+	11.1922i	−0.958546	+	0.553417i	−0.0628208	+	0.998025i	$0.520010\pi$
$410$	5.15035	−	2.97356i	0.254358	−	0.146854i
$411$		0			0
$412$	−2.85909	+	1.65069i	−0.140857	+	0.0813239i
$413$	−9.73368	−	3.56108i	−0.478963	−	0.175229i
$414$		0			0
$415$	4.32347	+	7.48846i	0.212231	+	0.367594i
$416$	6.55311			0.321292
$417$		0			0
$418$			38.9311i			1.90418i
$419$	−19.0389	+	32.9764i	−0.930112	+	1.61100i	−0.146985	+	0.989139i	$0.546957\pi$
$419$	−19.0389	+	32.9764i	−0.930112	+	1.61100i	−0.783127	+	0.621862i	$0.786377\pi$
$420$		0			0
$421$	17.9992	+	31.1755i	0.877227	+	1.51940i	0.854371	+	0.519664i	$0.173943\pi$
$421$	17.9992	+	31.1755i	0.877227	+	1.51940i	0.0228566	+	0.999739i	$0.492724\pi$
$422$	10.4628	−	6.04072i	0.509323	−	0.294058i
$423$		0			0
$424$	1.48346	−	2.56943i	0.0720432	−	0.124782i
$425$	−1.26666	+	2.19392i	−0.0614421	+	0.106421i
$426$		0			0
$427$	−1.54141	+	0.269155i	−0.0745939	+	0.0130253i
$428$	−4.81501	−	2.77994i	−0.232742	−	0.134374i
$429$		0			0
$430$			5.49658i			0.265068i
$431$	−23.2779	−	13.4395i	−1.12126	−	0.647359i	−0.179537	−	0.983751i	$-0.557460\pi$
$431$	−23.2779	−	13.4395i	−1.12126	−	0.647359i	−0.941722	+	0.336392i	$0.890793\pi$
$432$		0			0
$433$			26.3834i			1.26790i	0.773372	+	0.633952i	$0.218568\pi$
$433$			26.3834i			1.26790i	−0.773372	+	0.633952i	$0.781432\pi$
$434$	12.5118	−	10.4633i	0.600586	−	0.502255i
$435$		0			0
$436$	18.2445			0.873751
$437$	14.8765	+	25.7669i	0.711640	+	1.23260i
$438$		0			0
$439$	−21.6627	−	12.5070i	−1.03391	−	0.596926i	−0.115804	−	0.993272i	$-0.536945\pi$
$439$	−21.6627	−	12.5070i	−1.03391	−	0.596926i	−0.918101	+	0.396346i	$0.870278\pi$
$440$	5.51168			0.262759
$441$		0			0
$442$	16.6011			0.789635
$443$	8.24251	+	4.75881i	0.391613	+	0.226098i	0.682859	−	0.730550i	$-0.260736\pi$
$443$	8.24251	+	4.75881i	0.391613	+	0.226098i	−0.291246	+	0.956648i	$0.594070\pi$
$444$		0			0
$445$	−7.84313	−	13.5847i	−0.371800	−	0.643977i
$446$	−15.8139			−0.748810
$447$		0			0
$448$	2.02958	−	1.69729i	0.0958888	−	0.0801894i
$449$			26.9921i			1.27383i	0.770932	+	0.636917i	$0.219791\pi$
$449$			26.9921i			1.27383i	−0.770932	+	0.636917i	$0.780209\pi$
$450$		0			0
$451$	−28.3871	−	16.3893i	−1.33670	−	0.771742i
$452$		−	1.63394i		−	0.0768540i
$453$		0			0
$454$	−1.84362	−	1.06442i	−0.0865256	−	0.0499556i
$455$	17.0795	−	2.98235i	0.800697	−	0.139815i
$456$		0			0
$457$	2.38587	−	4.13245i	0.111606	−	0.193308i	−0.804812	−	0.593530i	$-0.797734\pi$
$457$	2.38587	−	4.13245i	0.111606	−	0.193308i	0.916418	+	0.400222i	$0.131067\pi$
$458$	10.1531	−	17.5856i	0.474422	−	0.821723i
$459$		0			0
$460$	3.64795	−	2.10615i	0.170087	−	0.0981996i
$461$	−11.0704	−	19.1745i	−0.515600	−	0.893046i	−0.999836	−	0.0181082i	$-0.994236\pi$
$461$	−11.0704	−	19.1745i	−0.515600	−	0.893046i	0.484236	−	0.874938i	$-0.339098\pi$
$462$		0			0
$463$	10.8244	−	18.7483i	0.503051	−	0.871309i	−0.496943	−	0.867783i	$-0.665544\pi$
$463$	10.8244	−	18.7483i	0.503051	−	0.871309i	0.999994	−	0.00352608i	$-0.00112239\pi$
$464$		−	7.26388i		−	0.337217i
$465$		0			0
$466$	12.8892			0.597079
$467$	1.97116	+	3.41416i	0.0912146	+	0.157988i	0.908022	−	0.418921i	$-0.137592\pi$
$467$	1.97116	+	3.41416i	0.0912146	+	0.157988i	−0.816808	+	0.576910i	$0.804258\pi$
$468$		0			0
$469$	−7.39531	−	2.70558i	−0.341484	−	0.124932i
$470$	−4.66497	+	2.69332i	−0.215179	+	0.124234i
$471$		0			0
$472$	−3.39263	+	1.95873i	−0.156158	+	0.0901580i
$473$	26.2366	−	15.1477i	1.20636	−	0.696491i
$474$		0			0
$475$	−6.11706	+	3.53169i	−0.280670	+	0.162045i
$476$	5.14159	−	4.29978i	0.235664	−	0.197080i
$477$		0			0
$478$	0.560223	+	0.970335i	0.0256240	+	0.0443821i
$479$	−6.94520			−0.317334			−0.158667	−	0.987332i	$-0.550720\pi$
$479$	−6.94520			−0.317334			−0.158667	+	0.987332i	$0.550720\pi$
$480$		0			0
$481$			13.2052i			0.602106i
$482$	0.726116	−	1.25767i	0.0330737	−	0.0572853i
$483$		0			0
$484$	−9.68931	−	16.7824i	−0.440423	−	0.762836i
$485$	0.197336	−	0.113932i	0.00896058	−	0.00517339i
$486$		0			0
$487$	−9.68011	+	16.7664i	−0.438648	+	0.759760i	−0.997585	−	0.0694495i	$-0.977876\pi$
$487$	−9.68011	+	16.7664i	−0.438648	+	0.759760i	0.558938	+	0.829210i	$0.311209\pi$
$488$	−0.295706	+	0.512178i	−0.0133860	+	0.0231852i
$489$		0			0
$490$	4.51729	−	5.34735i	0.204070	−	0.241569i
$491$	23.8914	+	13.7937i	1.07820	+	0.622500i	0.930411	−	0.366518i	$-0.119450\pi$
$491$	23.8914	+	13.7937i	1.07820	+	0.622500i	0.147792	+	0.989019i	$0.452784\pi$
$492$		0			0
$493$		−	18.4018i		−	0.828774i
$494$	40.0858	+	23.1435i	1.80354	+	1.04128i
$495$		0			0
$496$		−	6.16472i		−	0.276804i
$497$	25.2019	+	30.1358i	1.13046	+	1.35178i
$498$		0			0
$499$	15.6163			0.699080			0.349540	−	0.936921i	$-0.386338\pi$
$499$	15.6163			0.699080			0.349540	+	0.936921i	$0.386338\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−12.7964	−	7.38800i	−0.571131	−	0.329743i
$503$	1.51651			0.0676180			0.0338090	−	0.999428i	$-0.489236\pi$
$503$	1.51651			0.0676180			0.0338090	+	0.999428i	$0.489236\pi$
$504$		0			0
$505$	−2.76769			−0.123161
$506$	−20.1064	−	11.6084i	−0.893837	−	0.516057i
$507$		0			0
$508$	−5.61580	−	9.72685i	−0.249161	−	0.431559i
$509$	2.70222			0.119774			0.0598869	−	0.998205i	$-0.480926\pi$
$509$	2.70222			0.119774			0.0598869	+	0.998205i	$0.480926\pi$
$510$		0			0
$511$	−29.3934	+	5.13257i	−1.30029	+	0.227051i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	15.4025	+	8.89265i	0.679376	+	0.392238i
$515$			3.30139i			0.145477i
$516$		0			0
$517$	25.7118	+	14.8447i	1.13081	+	0.652871i
$518$	3.42023	+	4.08983i	0.150276	+	0.179697i
$519$		0			0
$520$	3.27655	−	5.67516i	0.143686	−	0.248872i
$521$	−8.63108	+	14.9495i	−0.378134	+	0.654948i	−0.990791	−	0.135401i	$-0.956768\pi$
$521$	−8.63108	+	14.9495i	−0.378134	+	0.654948i	0.612656	+	0.790349i	$0.290101\pi$
$522$		0			0
$523$	−34.8556	+	20.1239i	−1.52413	+	0.879956i	−0.524536	+	0.851388i	$0.675761\pi$
$523$	−34.8556	+	20.1239i	−1.52413	+	0.879956i	−0.999592	+	0.0285673i	$0.990906\pi$
$524$	2.08361	+	3.60893i	0.0910231	+	0.157657i
$525$		0			0
$526$	−3.85865	+	6.68338i	−0.168245	+	0.291409i
$527$		−	15.6172i		−	0.680297i
$528$		0			0
$529$	5.25657			0.228547
$530$	−1.48346	−	2.56943i	−0.0644374	−	0.111609i
$531$		0			0
$532$	18.4094	−	3.21458i	0.798148	−	0.139370i
$533$	−33.7508	+	19.4860i	−1.46191	+	0.844034i
$534$		0			0
$535$	−4.81501	+	2.77994i	−0.208171	+	0.120187i
$536$	−2.57760	+	1.48818i	−0.111335	+	0.0642795i
$537$		0			0
$538$	19.4412	−	11.2244i	0.838168	−	0.483917i
$539$	−37.9732	−	6.82573i	−1.63562	−	0.294005i
$540$		0			0
$541$	−9.02742	−	15.6359i	−0.388119	−	0.672242i	0.604077	−	0.796926i	$-0.293542\pi$
$541$	−9.02742	−	15.6359i	−0.388119	−	0.672242i	−0.992197	+	0.124684i	$0.960208\pi$
$542$	−0.407967			−0.0175237
$543$		0			0
$544$		−	2.53332i		−	0.108615i
$545$	9.12223	−	15.8002i	0.390753	−	0.676805i
$546$		0			0
$547$	−17.3408	−	30.0351i	−0.741438	−	1.28421i	−0.951841	−	0.306593i	$-0.900811\pi$
$547$	−17.3408	−	30.0351i	−0.741438	−	1.28421i	0.210403	−	0.977615i	$-0.432523\pi$
$548$	−8.02909	+	4.63560i	−0.342986	+	0.198023i
$549$		0			0
$550$	2.75584	−	4.77326i	0.117509	−	0.203532i
$551$	25.6538	−	44.4336i	1.09289	−	1.89294i
$552$		0			0
$553$	−0.563982	−	3.22984i	−0.0239830	−	0.137347i
$554$	22.3312	+	12.8929i	0.948763	+	0.547769i
$555$		0			0
$556$			3.56757i			0.151299i
$557$	−22.4858	−	12.9822i	−0.952753	−	0.550072i	−0.0588180	−	0.998269i	$-0.518733\pi$
$557$	−22.4858	−	12.9822i	−0.952753	−	0.550072i	−0.893935	+	0.448196i	$0.852066\pi$
$558$		0			0
$559$		−	36.0196i		−	1.52347i
$560$	−0.455105	−	2.60632i	−0.0192317	−	0.110137i
$561$		0			0
$562$	−13.7810			−0.581318
$563$	5.60094	+	9.70110i	0.236051	+	0.408853i	0.959578	−	0.281444i	$-0.0908133\pi$
$563$	5.60094	+	9.70110i	0.236051	+	0.408853i	−0.723526	+	0.690297i	$0.757480\pi$
$564$		0			0
$565$	−1.41503	−	0.816970i	−0.0595309	−	0.0343702i
$566$	3.28393			0.138034
$567$		0			0
$568$	14.8483			0.623020
$569$	−8.70803	−	5.02758i	−0.365059	−	0.210767i	0.306238	−	0.951955i	$-0.400930\pi$
$569$	−8.70803	−	5.02758i	−0.365059	−	0.210767i	−0.671298	+	0.741188i	$0.734263\pi$
$570$		0			0
$571$	−0.983905	−	1.70417i	−0.0411752	−	0.0713175i	0.844703	−	0.535235i	$-0.179777\pi$
$571$	−0.983905	−	1.70417i	−0.0411752	−	0.0713175i	−0.885879	+	0.463917i	$0.846443\pi$
$572$	−36.1186			−1.51020
$573$		0			0
$574$	−5.40608	+	14.7767i	−0.225645	+	0.616768i
$575$		−	4.21229i		−	0.175665i
$576$		0			0
$577$	−20.3522	−	11.7503i	−0.847272	−	0.489173i	0.0124575	−	0.999922i	$-0.496035\pi$
$577$	−20.3522	−	11.7503i	−0.847272	−	0.489173i	−0.859729	+	0.510750i	$0.829368\pi$
$578$			10.5823i			0.440165i
$579$		0			0
$580$	−6.29071	−	3.63194i	−0.261207	−	0.150808i
$581$	−21.4849	−	7.86028i	−0.891345	−	0.326099i
$582$		0			0
$583$	−8.17636	+	14.1619i	−0.338630	+	0.586525i
$584$	−5.63888	+	9.76683i	−0.233339	+	0.404154i
$585$		0			0
$586$	9.05442	−	5.22757i	0.374035	−	0.215949i
$587$	6.90407	+	11.9582i	0.284962	+	0.493568i	0.972600	−	0.232485i	$-0.0746858\pi$
$587$	6.90407	+	11.9582i	0.284962	+	0.493568i	−0.687638	+	0.726053i	$0.741352\pi$
$588$		0			0
$589$	21.7719	−	37.7100i	0.897094	−	1.55381i
$590$			3.91747i			0.161280i
$591$		0			0
$592$	2.01511			0.0828205
$593$	−14.5740	−	25.2428i	−0.598480	−	1.03660i	−0.993046	−	0.117731i	$-0.962438\pi$
$593$	−14.5740	−	25.2428i	−0.598480	−	1.03660i	0.394565	−	0.918868i	$-0.370895\pi$
$594$		0			0
$595$	−1.15293	−	6.60264i	−0.0472654	−	0.270682i
$596$	−8.99836	+	5.19521i	−0.368587	+	0.212804i
$597$		0			0
$598$	−23.9054	+	13.8018i	−0.977566	+	0.564398i
$599$	1.79110	−	1.03409i	0.0731824	−	0.0422519i	−0.462962	−	0.886378i	$-0.653213\pi$
$599$	1.79110	−	1.03409i	0.0731824	−	0.0422519i	0.536145	+	0.844126i	$0.319880\pi$
$600$		0			0
$601$	−16.7765	+	9.68589i	−0.684326	+	0.395096i	−0.801483	−	0.598018i	$-0.795955\pi$
$601$	−16.7765	+	9.68589i	−0.684326	+	0.395096i	0.117157	+	0.993113i	$0.462622\pi$
$602$	−9.32929	−	11.1558i	−0.380233	−	0.454675i
$603$		0			0
$604$	−4.38389	−	7.59312i	−0.178378	−	0.308960i
$605$	−19.3786			−0.787853
$606$		0			0
$607$			36.2789i			1.47252i	0.676701	+	0.736258i	$0.263409\pi$
$607$			36.2789i			1.47252i	−0.676701	+	0.736258i	$0.736591\pi$
$608$	3.53169	−	6.11706i	0.143229	−	0.248080i
$609$		0			0
$610$	0.295706	+	0.512178i	0.0119728	+	0.0207375i
$611$	30.5701	−	17.6496i	1.23673	−	0.714027i
$612$		0			0
$613$	10.2743	−	17.7956i	0.414974	−	0.718756i	−0.580452	−	0.814295i	$-0.697124\pi$
$613$	10.2743	−	17.7956i	0.414974	−	0.718756i	0.995426	+	0.0955386i	$0.0304573\pi$
$614$	−16.4502	+	28.4925i	−0.663875	+	1.14986i
$615$		0			0
$616$	−11.1864	+	9.35492i	−0.450713	+	0.376921i
$617$	−31.4987	−	18.1858i	−1.26809	−	0.732132i	−0.293463	−	0.955970i	$-0.594808\pi$
$617$	−31.4987	−	18.1858i	−1.26809	−	0.732132i	−0.974626	+	0.223838i	$0.928141\pi$
$618$		0			0
$619$		−	48.3608i		−	1.94378i	−0.235426	−	0.971892i	$-0.575649\pi$
$619$		−	48.3608i		−	1.94378i	0.235426	−	0.971892i	$-0.424351\pi$
$620$	−5.33881	−	3.08236i	−0.214412	−	0.123791i
$621$		0			0
$622$		−	25.8431i		−	1.03622i
$623$	38.9755	+	14.2592i	1.56152	+	0.571283i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−9.35899	−	16.2102i	−0.374061	−	0.647892i
$627$		0			0
$628$	10.3942	+	6.00109i	0.414773	+	0.239470i
$629$	5.10492			0.203547
$630$		0			0
$631$	−33.2300			−1.32287			−0.661433	−	0.750004i	$-0.730051\pi$
$631$	−33.2300			−1.32287			−0.661433	+	0.750004i	$0.730051\pi$
$632$	−1.07321	−	0.619617i	−0.0426900	−	0.0246471i
$633$		0			0
$634$	9.23209	+	15.9904i	0.366653	+	0.635062i
$635$	−11.2316			−0.445712
$636$		0			0
$637$	−29.6023	+	35.0417i	−1.17288	+	1.38840i
$638$			40.0362i			1.58505i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	10.7186i		−	0.423359i	−0.977339	−	0.211679i	$-0.932107\pi$
$641$		−	10.7186i		−	0.423359i	0.977339	−	0.211679i	$-0.0678932\pi$
$642$		0			0
$643$	22.4608	+	12.9678i	0.885768	+	0.511398i	0.872556	−	0.488515i	$-0.162461\pi$
$643$	22.4608	+	12.9678i	0.885768	+	0.511398i	0.0132119	+	0.999913i	$0.495794\pi$
$644$	−3.82908	+	10.4662i	−0.150887	+	0.412428i
$645$		0			0
$646$	8.94691	−	15.4965i	0.352011	−	0.609702i
$647$	0.701476	−	1.21499i	0.0275779	−	0.0477663i	−0.851907	−	0.523693i	$-0.824554\pi$
$647$	0.701476	−	1.21499i	0.0275779	−	0.0477663i	0.879485	+	0.475927i	$0.157887\pi$
$648$		0			0
$649$	18.6991	−	10.7959i	0.734003	−	0.423777i
$650$	−3.27655	−	5.67516i	−0.128517	−	0.222598i
$651$		0			0
$652$	5.40261	−	9.35760i	0.211583	−	0.366472i
$653$		−	23.6102i		−	0.923939i	−0.886896	−	0.461969i	$-0.847143\pi$
$653$		−	23.6102i		−	0.923939i	0.886896	−	0.461969i	$-0.152857\pi$
$654$		0			0
$655$	4.16723			0.162827
$656$	2.97356	+	5.15035i	0.116098	+	0.201087i
$657$		0			0
$658$	4.89660	−	13.3841i	0.190889	−	0.521768i
$659$	9.61215	−	5.54958i	0.374436	−	0.216181i	−0.300958	−	0.953637i	$-0.597307\pi$
$659$	9.61215	−	5.54958i	0.374436	−	0.216181i	0.675395	+	0.737456i	$0.263973\pi$
$660$		0			0
$661$	27.2557	−	15.7361i	1.06012	−	0.612063i	0.134657	−	0.990892i	$-0.457007\pi$
$661$	27.2557	−	15.7361i	1.06012	−	0.612063i	0.925466	+	0.378830i	$0.123673\pi$
$662$	−20.3540	+	11.7514i	−0.791079	+	0.456730i
$663$		0			0
$664$	−7.48846	+	4.32347i	−0.290609	+	0.167783i
$665$	6.42079	−	17.5503i	0.248987	−	0.680571i
$666$		0			0
$667$	15.2988	+	26.4983i	0.592372	+	1.02602i
$668$	−21.5733			−0.834695
$669$		0			0
$670$			2.97636i			0.114987i
$671$	1.62984	−	2.82296i	0.0629192	−	0.108979i
$672$		0			0
$673$	14.7243	+	25.5033i	0.567580	+	0.983078i	0.996804	+	0.0798801i	$0.0254538\pi$
$673$	14.7243	+	25.5033i	0.567580	+	0.983078i	−0.429224	+	0.903198i	$0.641213\pi$
$674$	−15.1599	+	8.75258i	−0.583938	+	0.337137i
$675$		0			0
$676$	−14.9716	+	25.9316i	−0.575831	+	0.997368i
$677$	−5.29070	+	9.16376i	−0.203338	+	0.352192i	−0.949602	−	0.313458i	$-0.898512\pi$
$677$	−5.29070	+	9.16376i	−0.203338	+	0.352192i	0.746264	+	0.665650i	$0.231846\pi$
$678$		0			0
$679$	−0.207134	+	0.566172i	−0.00794909	+	0.0217277i
$680$	−2.19392	−	1.26666i	−0.0841331	−	0.0485743i
$681$		0			0
$682$			33.9780i			1.30108i
$683$	−16.4839	−	9.51701i	−0.630741	−	0.364158i	0.150298	−	0.988641i	$-0.451977\pi$
$683$	−16.4839	−	9.51701i	−0.630741	−	0.364158i	−0.781039	+	0.624482i	$0.785310\pi$
$684$		0			0
$685$			9.27120i			0.354234i
$686$	−0.0922085	+	18.5200i	−0.00352054	+	0.707098i
$687$		0			0
$688$	−5.49658			−0.209555
$689$	9.72127	+	16.8377i	0.370351	+	0.641467i
$690$		0			0
$691$	−1.91825	−	1.10750i	−0.0729735	−	0.0421313i	0.463069	−	0.886322i	$-0.346748\pi$
$691$	−1.91825	−	1.10750i	−0.0729735	−	0.0421313i	−0.536043	+	0.844191i	$0.680081\pi$
$692$	1.27947			0.0486380
$693$		0			0
$694$	10.2551			0.389278
$695$	3.08961	+	1.78379i	0.117195	+	0.0676628i
$696$		0			0
$697$	7.53298	+	13.0475i	0.285332	+	0.494209i
$698$	0.994983			0.0376607
$699$		0			0
$700$	−2.48469	−	0.909025i	−0.0939124	−	0.0343579i
$701$			14.6720i			0.554154i	0.960848	+	0.277077i	$0.0893656\pi$
$701$			14.6720i			0.554154i	−0.960848	+	0.277077i	$0.910634\pi$
$702$		0			0
$703$	12.3266	+	7.11674i	0.464905	+	0.268413i
$704$			5.51168i			0.207729i
$705$		0			0
$706$	−11.5847	−	6.68840i	−0.435994	−	0.251721i
$707$	5.61726	−	4.69757i	0.211259	−	0.176670i
$708$		0			0
$709$	14.5615	−	25.2213i	0.546870	−	0.947207i	−0.451617	−	0.892212i	$-0.649152\pi$
$709$	14.5615	−	25.2213i	0.546870	−	0.947207i	0.998487	−	0.0549947i	$-0.0175142\pi$
$710$	7.42414	−	12.8590i	0.278623	−	0.482589i
$711$		0			0
$712$	13.5847	−	7.84313i	0.509108	−	0.293934i
$713$	12.9838	+	22.4886i	0.486248	+	0.842205i
$714$		0			0
$715$	−18.0593	+	31.2796i	−0.675380	+	1.16979i
$716$		−	11.8542i		−	0.443010i
$717$		0			0
$718$	16.5645			0.618183
$719$	17.5750	+	30.4408i	0.655438	+	1.13525i	0.981784	+	0.190001i	$0.0608492\pi$
$719$	17.5750	+	30.4408i	0.655438	+	1.13525i	−0.326346	+	0.945250i	$0.605817\pi$
$720$		0			0
$721$	−5.60341	−	6.70044i	−0.208682	−	0.249537i
$722$	26.7526	−	15.4456i	0.995630	−	0.574827i
$723$		0			0
$724$	−11.5344	+	6.65940i	−0.428673	+	0.247495i
$725$	−6.29071	+	3.63194i	−0.233631	+	0.134887i
$726$		0			0
$727$	12.6948	−	7.32936i	0.470825	−	0.271831i	−0.245760	−	0.969331i	$-0.579038\pi$
$727$	12.6948	−	7.32936i	0.470825	−	0.271831i	0.716585	+	0.697500i	$0.245704\pi$
$728$	2.98235	+	17.0795i	0.110533	+	0.633007i
$729$		0			0
$730$	5.63888	+	9.76683i	0.208704	+	0.361487i
$731$	−13.9246			−0.515020
$732$		0			0
$733$		−	25.3896i		−	0.937785i	−0.883255	−	0.468893i	$-0.844653\pi$
$733$		−	25.3896i		−	0.937785i	0.883255	−	0.468893i	$-0.155347\pi$
$734$	−5.71498	+	9.89863i	−0.210944	+	0.365365i
$735$		0			0
$736$	2.10615	+	3.64795i	0.0776336	+	0.134465i
$737$	14.2069	−	8.20236i	0.523318	−	0.302138i
$738$		0			0
$739$	6.28334	−	10.8831i	0.231136	−	0.400340i	−0.727006	−	0.686631i	$-0.759089\pi$
$739$	6.28334	−	10.8831i	0.231136	−	0.400340i	0.958143	+	0.286291i	$0.0924223\pi$
$740$	1.00755	−	1.74514i	0.0370385	−	0.0641525i
$741$		0			0
$742$	7.37187	+	2.69701i	0.270630	+	0.0990102i
$743$	15.1504	+	8.74709i	0.555814	+	0.320899i	0.751464	−	0.659774i	$-0.229348\pi$
$743$	15.1504	+	8.74709i	0.555814	+	0.320899i	−0.195650	+	0.980674i	$0.562682\pi$
$744$		0			0
$745$			10.3904i			0.380675i
$746$	−20.4067	−	11.7818i	−0.747143	−	0.431363i
$747$		0			0
$748$			13.9629i			0.510533i
$749$	5.05408	−	13.8146i	0.184672	−	0.504774i
$750$		0			0
$751$	−32.8476			−1.19863			−0.599313	−	0.800515i	$-0.704560\pi$
$751$	−32.8476			−1.19863			−0.599313	+	0.800515i	$0.704560\pi$
$752$	−2.69332	−	4.66497i	−0.0982154	−	0.170114i
$753$		0			0
$754$	41.2237	+	23.8005i	1.50128	+	0.866763i
$755$	−8.76778			−0.319092
$756$		0			0
$757$	−34.4952			−1.25375			−0.626874	−	0.779120i	$-0.715666\pi$
$757$	−34.4952			−1.25375			−0.626874	+	0.779120i	$0.715666\pi$
$758$	15.1683	+	8.75743i	0.550938	+	0.318084i
$759$		0			0
$760$	−3.53169	−	6.11706i	−0.128108	−	0.221889i
$761$	−41.8797			−1.51814			−0.759069	−	0.651010i	$-0.774346\pi$
$761$	−41.8797			−1.51814			−0.759069	+	0.651010i	$0.774346\pi$
$762$		0			0
$763$	8.30315	+	47.5508i	0.300594	+	1.72146i
$764$		−	8.19637i		−	0.296534i
$765$		0			0
$766$	−17.2415	−	9.95437i	−0.622960	−	0.359666i
$767$		−	25.6716i		−	0.926947i
$768$		0			0
$769$	40.9461	+	23.6402i	1.47655	+	0.852489i	0.999650	−	0.0264667i	$-0.00842558\pi$
$769$	40.9461	+	23.6402i	1.47655	+	0.852489i	0.476904	+	0.878955i	$0.341759\pi$
$770$	2.50839	+	14.3652i	0.0903962	+	0.517685i
$771$		0			0
$772$	1.49743	−	2.59363i	0.0538937	−	0.0933467i
$773$	−3.88458	+	6.72829i	−0.139719	+	0.242000i	−0.927390	−	0.374096i	$-0.877953\pi$
$773$	−3.88458	+	6.72829i	−0.139719	+	0.242000i	0.787671	+	0.616096i	$0.211287\pi$
$774$		0			0
$775$	−5.33881	+	3.08236i	−0.191776	+	0.110722i
$776$	0.113932	+	0.197336i	0.00408993	+	0.00708396i
$777$		0			0
$778$	17.2147	−	29.8167i	0.617176	−	1.06898i
$779$			42.0067i			1.50505i
$780$		0			0
$781$	−81.8390			−2.92843
$782$	5.33555	+	9.24145i	0.190799	+	0.330473i
$783$		0			0
$784$	5.34735	+	4.51729i	0.190977	+	0.161332i
$785$	10.3942	−	6.00109i	0.370985	−	0.214188i
$786$		0			0
$787$	24.8482	−	14.3461i	0.885743	−	0.511384i	0.0131953	−	0.999913i	$-0.495800\pi$
$787$	24.8482	−	14.3461i	0.885743	−	0.511384i	0.872548	+	0.488529i	$0.162466\pi$
$788$	10.3427	−	5.97136i	0.368443	−	0.212721i
$789$		0			0
$790$	−1.07321	+	0.619617i	−0.0381831	+	0.0220450i
$791$	4.25856	−	0.743614i	0.151417	−	0.0264399i
$792$		0			0
$793$	−1.93779	−	3.35635i	−0.0688130	−	0.119188i
$794$	−11.5703			−0.410614
$795$		0			0
$796$		−	3.16245i		−	0.112090i
$797$	18.1502	−	31.4371i	0.642914	−	1.11356i	−0.341866	−	0.939749i	$-0.611059\pi$
$797$	18.1502	−	31.4371i	0.642914	−	1.11356i	0.984779	−	0.173810i	$-0.0556079\pi$
$798$		0			0
$799$	−6.82306	−	11.8179i	−0.241382	−	0.418087i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	6.97558	−	12.0821i	0.246316	−	0.426632i
$803$	31.0797	−	53.8316i	1.09678	−	1.89968i
$804$		0			0
$805$	7.14949	+	8.54920i	0.251986	+	0.301320i
$806$	34.9858	+	20.1990i	1.23232	+	0.711481i
$807$		0			0
$808$		−	2.76769i		−	0.0973670i
$809$	−27.0602	−	15.6232i	−0.951384	−	0.549282i	−0.0578737	−	0.998324i	$-0.518432\pi$
$809$	−27.0602	−	15.6232i	−0.951384	−	0.549282i	−0.893511	+	0.449042i	$0.851765\pi$
$810$		0			0
$811$		−	21.8513i		−	0.767304i	−0.923478	−	0.383652i	$-0.874666\pi$
$811$		−	21.8513i		−	0.767304i	0.923478	−	0.383652i	$-0.125334\pi$
$812$	18.9320	−	3.30583i	0.664382	−	0.116012i
$813$		0			0
$814$	−11.1066			−0.389288
$815$	−5.40261	−	9.35760i	−0.189245	−	0.327783i
$816$		0			0
$817$	−33.6229	−	19.4122i	−1.17632	−	0.679147i
$818$	−22.3843			−0.782650
$819$		0			0
$820$	5.94711			0.207682
$821$	46.4550	+	26.8208i	1.62129	+	0.936052i	0.986576	+	0.163304i	$0.0522151\pi$
$821$	46.4550	+	26.8208i	1.62129	+	0.936052i	0.634713	+	0.772748i	$0.281118\pi$
$822$		0			0
$823$	−25.8325	−	44.7432i	−0.900464	−	1.55965i	−0.826894	−	0.562359i	$-0.809894\pi$
$823$	−25.8325	−	44.7432i	−0.900464	−	1.55965i	−0.0735700	−	0.997290i	$-0.523439\pi$
$824$	−3.30139			−0.115009
$825$		0			0
$826$	−6.64908	−	7.95082i	−0.231351	−	0.276645i
$827$		−	4.96328i		−	0.172590i	−0.996270	−	0.0862950i	$-0.972497\pi$
$827$		−	4.96328i		−	0.172590i	0.996270	−	0.0862950i	$-0.0275028\pi$
$828$		0			0
$829$	−29.7958	−	17.2026i	−1.03485	−	0.597471i	−0.116480	−	0.993193i	$-0.537161\pi$
$829$	−29.7958	−	17.2026i	−1.03485	−	0.597471i	−0.918370	+	0.395722i	$0.870494\pi$
$830$			8.64693i			0.300139i
$831$		0			0
$832$	5.67516	+	3.27655i	0.196751	+	0.113594i
$833$	13.5466	+	11.4437i	0.469360	+	0.396502i
$834$		0			0
$835$	−10.7866	+	18.6830i	−0.373287	+	0.646552i
$836$	−19.4655	+	33.7153i	−0.673230	+	1.16607i
$837$		0			0
$838$	−32.9764	+	19.0389i	−1.13915	+	0.657688i
$839$	−14.9698	−	25.9285i	−0.516815	−	0.895151i	−0.999809	−	0.0195269i	$-0.993784\pi$
$839$	−14.9698	−	25.9285i	−0.516815	−	0.895151i	0.482994	−	0.875624i	$-0.339549\pi$
$840$		0			0
$841$	11.8820	−	20.5802i	0.409724	−	0.709663i
$842$			35.9984i			1.24059i
$843$		0			0
$844$	12.0814			0.415860
$845$	14.9716	+	25.9316i	0.515039	+	0.892073i
$846$		0			0
$847$	39.3305	−	32.8912i	1.35141	−	1.13015i
$848$	2.56943	−	1.48346i	0.0882345	−	0.0509422i
$849$		0			0
$850$	−2.19392	+	1.26666i	−0.0752509	+	0.0434461i
$851$	−7.35103	+	4.24412i	−0.251990	+	0.145486i
$852$		0			0
$853$	31.4260	−	18.1438i	1.07600	−	0.621232i	0.146189	−	0.989257i	$-0.453299\pi$
$853$	31.4260	−	18.1438i	1.07600	−	0.621232i	0.929816	+	0.368025i	$0.119966\pi$
$854$	−1.46947	−	0.537608i	−0.0502844	−	0.0183966i
$855$		0			0
$856$	−2.77994	−	4.81501i	−0.0950166	−	0.164573i
$857$	−8.61419			−0.294255			−0.147128	−	0.989118i	$-0.547003\pi$
$857$	−8.61419			−0.294255			−0.147128	+	0.989118i	$0.547003\pi$
$858$		0			0
$859$		−	46.3923i		−	1.58289i	−0.611244	−	0.791443i	$-0.709330\pi$
$859$		−	46.3923i		−	1.58289i	0.611244	−	0.791443i	$-0.290670\pi$
$860$	−2.74829	+	4.76018i	−0.0937159	+	0.162321i
$861$		0			0
$862$	−13.4395	−	23.2779i	−0.457752	−	0.792850i
$863$	−1.40487	+	0.811104i	−0.0478225	+	0.0276103i	−0.523721	−	0.851890i	$-0.675456\pi$
$863$	−1.40487	+	0.811104i	−0.0478225	+	0.0276103i	0.475898	+	0.879500i	$0.342123\pi$
$864$		0			0
$865$	0.639733	−	1.10805i	0.0217516	−	0.0376748i
$866$	−13.1917	+	22.8487i	−0.448272	+	0.776430i
$867$		0			0
$868$	16.0672	−	2.80560i	0.545357	−	0.0952281i
$869$	5.91518	+	3.41513i	0.200659	+	0.115850i
$870$		0			0
$871$		−	19.5044i		−	0.660880i
$872$	15.8002	+	9.12223i	0.535061	+	0.308918i
$873$		0			0
$874$			29.7530i			1.00641i
$875$	−2.02958	+	1.69729i	−0.0686124	+	0.0573789i
$876$		0			0
$877$	−33.5380			−1.13250			−0.566249	−	0.824234i	$-0.691606\pi$
$877$	−33.5380			−1.13250			−0.566249	+	0.824234i	$0.691606\pi$
$878$	−12.5070	−	21.6627i	−0.422090	−	0.731082i
$879$		0			0
$880$	4.77326	+	2.75584i	0.160906	+	0.0928994i
$881$	−39.1144			−1.31780			−0.658899	−	0.752231i	$-0.728978\pi$
$881$	−39.1144			−1.31780			−0.658899	+	0.752231i	$0.728978\pi$
$882$		0			0
$883$	1.14778			0.0386258			0.0193129	−	0.999813i	$-0.493852\pi$
$883$	1.14778			0.0386258			0.0193129	+	0.999813i	$0.493852\pi$
$884$	14.3770	+	8.30057i	0.483551	+	0.279178i
$885$		0			0
$886$	4.75881	+	8.24251i	0.159875	+	0.276912i
$887$	−18.3937			−0.617599			−0.308800	−	0.951127i	$-0.599927\pi$
$887$	−18.3937			−0.617599			−0.308800	+	0.951127i	$0.599927\pi$
$888$		0			0
$889$	22.7955	−	19.0633i	0.764535	−	0.639362i
$890$		−	15.6863i		−	0.525805i
$891$		0			0
$892$	−13.6952	−	7.90695i	−0.458550	−	0.264744i
$893$		−	38.0479i		−	1.27322i
$894$		0			0
$895$	−10.2660	−	5.92708i	−0.343154	−	0.198120i
$896$	2.60632	−	0.455105i	0.0870709	−	0.0152040i
$897$		0			0
$898$	−13.4960	+	23.3758i	−0.450369	+	0.780061i
$899$	22.3899	−	38.7805i	0.746745	−	1.29340i
$900$		0			0
$901$	6.50919	−	3.75808i	0.216853	−	0.125200i
$902$	−16.3893	−	28.3871i	−0.545704	−	0.945187i
$903$		0			0
$904$	0.816970	−	1.41503i	0.0271720	−	0.0470633i
$905$			13.3188i			0.442732i
$906$		0			0
$907$	17.7344			0.588861			0.294430	−	0.955673i	$-0.404870\pi$
$907$	17.7344			0.588861			0.294430	+	0.955673i	$0.404870\pi$
$908$	−1.06442	−	1.84362i	−0.0353239	−	0.0611828i
$909$		0			0
$910$	16.2824	+	5.95694i	0.539757	+	0.197471i
$911$	−36.1849	+	20.8914i	−1.19886	+	0.692162i	−0.960301	−	0.278966i	$-0.910008\pi$
$911$	−36.1849	+	20.8914i	−1.19886	+	0.692162i	−0.238559	+	0.971128i	$0.576675\pi$
$912$		0			0
$913$	41.2740	−	23.8296i	1.36597	−	0.788644i
$914$	4.13245	−	2.38587i	0.136689	−	0.0789176i
$915$		0			0
$916$	17.5856	−	10.1531i	0.581046	−	0.335467i
$917$	−8.45773	+	7.07300i	−0.279299	+	0.233571i
$918$		0			0
$919$	14.9114	+	25.8273i	0.491882	+	0.851964i	0.999956	−	0.00934919i	$-0.00297598\pi$
$919$	14.9114	+	25.8273i	0.491882	+	0.851964i	−0.508075	+	0.861313i	$0.669643\pi$
$920$	4.21229			0.138875
$921$		0			0
$922$		−	22.1408i		−	0.729169i
$923$	−48.6512	+	84.2663i	−1.60137	+	2.77366i
$924$		0			0
$925$	−1.00755	−	1.74514i	−0.0331282	−	0.0573797i
$926$	18.7483	−	10.8244i	0.616109	−	0.355710i
$927$		0			0
$928$	3.63194	−	6.29071i	0.119224	−	0.206503i
$929$	11.8119	−	20.4588i	0.387535	−	0.671230i	−0.604582	−	0.796543i	$-0.706660\pi$
$929$	11.8119	−	20.4588i	0.387535	−	0.671230i	0.992117	+	0.125312i	$0.0399933\pi$
$930$		0			0
$931$	16.7564	+	46.5177i	0.549169	+	1.52456i
$932$	11.1623	+	6.44458i	0.365634	+	0.211099i
$933$		0			0
$934$			3.94233i			0.128997i
$935$	12.0922	+	6.98143i	0.395457	+	0.228317i
$936$		0			0
$937$		−	45.0608i		−	1.47207i	−0.676943	−	0.736035i	$-0.736696\pi$
$937$		−	45.0608i		−	1.47207i	0.676943	−	0.736035i	$-0.263304\pi$
$938$	−5.05174	−	6.04076i	−0.164945	−	0.197238i
$939$		0			0
$940$	−5.38665			−0.175693
$941$	−17.2029	−	29.7963i	−0.560799	−	0.971332i	−0.997427	−	0.0716900i	$-0.977161\pi$
$941$	−17.2029	−	29.7963i	−0.560799	−	0.971332i	0.436628	−	0.899642i	$-0.356173\pi$
$942$		0			0
$943$	−21.6948	−	12.5255i	−0.706480	−	0.407886i
$944$	−3.91747			−0.127503
$945$		0			0
$946$	30.2954			0.984988
$947$	−8.90645	−	5.14214i	−0.289421	−	0.167097i	0.348260	−	0.937398i	$-0.386773\pi$
$947$	−8.90645	−	5.14214i	−0.289421	−	0.167097i	−0.637681	+	0.770301i	$0.720106\pi$
$948$		0			0
$949$	−36.9522	−	64.0031i	−1.19952	−	2.07763i
$950$	−7.06338			−0.229166
$951$		0			0
$952$	6.60264	−	1.15293i	0.213993	−	0.0373666i
$953$			21.5003i			0.696464i	0.937408	+	0.348232i	$0.113218\pi$
$953$			21.5003i			0.696464i	−0.937408	+	0.348232i	$0.886782\pi$
$954$		0			0
$955$	−7.09826	−	4.09818i	−0.229694	−	0.132614i
$956$			1.12045i			0.0362378i
$957$		0			0
$958$	−6.01472	−	3.47260i	−0.194327	−	0.112195i
$959$	−15.7359	−	18.8167i	−0.508139	−	0.607622i
$960$		0			0
$961$	3.50189	−	6.06546i	0.112964	−	0.195660i
$962$	−6.60261	+	11.4361i	−0.212877	+	0.368713i
$963$		0			0
$964$	1.25767	−	0.726116i	0.0405068	−	0.0233866i
$965$	−1.49743	−	2.59363i	−0.0482040	−	0.0834918i
$966$		0			0
$967$	−19.1245	+	33.1246i	−0.615001	+	1.06521i	0.375383	+	0.926870i	$0.377511\pi$
$967$	−19.1245	+	33.1246i	−0.615001	+	1.06521i	−0.990384	+	0.138344i	$0.955822\pi$
$968$		−	19.3786i		−	0.622853i
$969$		0			0
$970$	0.227864			0.00731628
$971$	0.760849	+	1.31783i	0.0244168	+	0.0422911i	0.877976	−	0.478705i	$-0.158894\pi$
$971$	0.760849	+	1.31783i	0.0244168	+	0.0422911i	−0.853559	+	0.520997i	$0.825560\pi$
$972$		0			0
$973$	−9.29822	+	1.62362i	−0.298087	+	0.0520509i
$974$	−16.7664	+	9.68011i	−0.537232	+	0.310171i
$975$		0			0
$976$	−0.512178	+	0.295706i	−0.0163944	+	0.00946532i
$977$	29.6515	−	17.1193i	0.948637	−	0.547696i	0.0559798	−	0.998432i	$-0.482172\pi$
$977$	29.6515	−	17.1193i	0.948637	−	0.547696i	0.892657	+	0.450736i	$0.148838\pi$
$978$		0			0
$979$	−74.8746	+	43.2289i	−2.39300	+	1.38160i
$980$	6.58576	−	2.37229i	0.210374	−	0.0757802i
$981$		0			0
$982$	13.7937	+	23.8914i	0.440174	+	0.762404i
$983$	−0.677174			−0.0215985			−0.0107992	−	0.999942i	$-0.503438\pi$
$983$	−0.677174			−0.0215985			−0.0107992	+	0.999942i	$0.503438\pi$
$984$		0			0
$985$		−	11.9427i		−	0.380526i
$986$	9.20088	−	15.9364i	0.293016	−	0.507518i
$987$		0			0
$988$	23.1435	+	40.0858i	0.736294	+	1.27530i
$989$	20.0513	−	11.5766i	0.637593	−	0.368114i
$990$		0			0
$991$	24.5136	−	42.4589i	0.778701	−	1.34875i	−0.153989	−	0.988073i	$-0.549212\pi$
$991$	24.5136	−	42.4589i	0.778701	−	1.34875i	0.932691	−	0.360678i	$-0.117455\pi$
$992$	3.08236	−	5.33881i	0.0978650	−	0.169507i
$993$		0			0
$994$	6.75753	+	38.6993i	0.214336	+	1.22747i
$995$	−2.73876	−	1.58122i	−0.0868245	−	0.0501281i
$996$		0			0
$997$		−	3.64007i		−	0.115282i	−0.998337	−	0.0576411i	$-0.981642\pi$
$997$		−	3.64007i		−	0.115282i	0.998337	−	0.0576411i	$-0.0183579\pi$
$998$	13.5241	+	7.80813i	0.428097	+	0.247162i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1151.14		28
3.2	odd	2		630.2.t.b.311.6	✓	28
7.5	odd	6		1890.2.bk.b.341.1		28
9.2	odd	6		1890.2.bk.b.521.1		28
9.7	even	3		630.2.bk.b.101.6	yes	28
21.5	even	6		630.2.bk.b.131.13	yes	28
63.47	even	6	inner	1890.2.t.b.1601.14		28
63.61	odd	6		630.2.t.b.551.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.6	✓	28	3.2	odd	2
630.2.t.b.551.6	yes	28	63.61	odd	6
630.2.bk.b.101.6	yes	28	9.7	even	3
630.2.bk.b.131.13	yes	28	21.5	even	6
1890.2.t.b.1151.14		28	1.1	even	1	trivial
1890.2.t.b.1601.14		28	63.47	even	6	inner
1890.2.bk.b.341.1		28	7.5	odd	6
1890.2.bk.b.521.1		28	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-2.02958 + 1.69729i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-2.02958 + 1.69729i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -5.51168i q^{11} +(-5.67516 - 3.27655i) q^{13} +(-2.60632 + 0.455105i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.26666 + 2.19392i) q^{17} +(-6.11706 + 3.53169i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.75584 - 4.77326i) q^{22} -4.21229i q^{23} +1.00000 q^{25} +(-3.27655 - 5.67516i) q^{26} +(-2.48469 - 0.909025i) q^{28} +(-6.29071 + 3.63194i) q^{29} +(-5.33881 + 3.08236i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.19392 + 1.26666i) q^{34} +(-2.02958 + 1.69729i) q^{35} +(-1.00755 - 1.74514i) q^{37} -7.06338 q^{38} +1.00000i q^{40} +(2.97356 - 5.15035i) q^{41} +(2.74829 + 4.76018i) q^{43} +(4.77326 - 2.75584i) q^{44} +(2.10615 - 3.64795i) q^{46} +(-2.69332 + 4.66497i) q^{47} +(1.23841 - 6.88958i) q^{49} +(0.866025 + 0.500000i) q^{50} -6.55311i q^{52} +(-2.56943 - 1.48346i) q^{53} -5.51168i q^{55} +(-1.69729 - 2.02958i) q^{56} -7.26388 q^{58} +(1.95873 + 3.39263i) q^{59} +(0.512178 + 0.295706i) q^{61} -6.16472 q^{62} -1.00000 q^{64} +(-5.67516 - 3.27655i) q^{65} +(1.48818 + 2.57760i) q^{67} -2.53332 q^{68} +(-2.60632 + 0.455105i) q^{70} -14.8483i q^{71} +(9.76683 + 5.63888i) q^{73} -2.01511i q^{74} +(-6.11706 - 3.53169i) q^{76} +(9.35492 + 11.1864i) q^{77} +(-0.619617 + 1.07321i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.15035 - 2.97356i) q^{82} +(4.32347 + 7.48846i) q^{83} +(-1.26666 + 2.19392i) q^{85} +5.49658i q^{86} +5.51168 q^{88} +(-7.84313 - 13.5847i) q^{89} +(17.0795 - 2.98235i) q^{91} +(3.64795 - 2.10615i) q^{92} +(-4.66497 + 2.69332i) q^{94} +(-6.11706 + 3.53169i) q^{95} +(0.197336 - 0.113932i) q^{97} +(4.51729 - 5.34735i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

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