LMFDB - Embedded newform 1890.2.l.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(361,1890)]

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([2, 0, 4]))

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

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

chi := DirichletCharacter("1890.361");

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.l (of order $3$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1890.361
Dual form			1890.2.l.c.1801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +2.00000 q^{11} +(1.00000 - 1.73205i) q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} +4.00000 q^{23} +1.00000 q^{25} +(-1.00000 - 1.73205i) q^{26} +(-2.50000 + 0.866025i) q^{28} +(-0.500000 - 0.866025i) q^{29} +(-5.00000 - 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} +1.00000 q^{40} +(2.50000 - 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(2.00000 - 3.46410i) q^{46} +(-6.50000 + 11.2583i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} -2.00000 q^{52} +(-5.00000 + 8.66025i) q^{53} -2.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -1.00000 q^{58} +(-2.00000 - 3.46410i) q^{59} +(3.00000 - 5.19615i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-6.00000 - 10.3923i) q^{67} +(2.00000 + 1.73205i) q^{70} +12.0000 q^{71} -8.00000 q^{74} +(1.00000 - 5.19615i) q^{77} +(-5.00000 + 8.66025i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-2.50000 - 4.33013i) q^{82} +(-2.50000 - 4.33013i) q^{83} +1.00000 q^{86} -2.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(-2.00000 - 3.46410i) q^{92} +(6.50000 + 11.2583i) q^{94} +(-1.00000 - 1.73205i) q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 2 * q^5 + q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 2 q^{8} - q^{10} + 4 q^{11} + 2 q^{13} - 4 q^{14} - q^{16} + q^{20} + 2 q^{22} + 8 q^{23} + 2 q^{25} - 2 q^{26} - 5 q^{28} - q^{29} - 10 q^{31} + q^{32} - q^{35} - 8 q^{37} + 2 q^{40} + 5 q^{41} + q^{43} - 2 q^{44} + 4 q^{46} - 13 q^{47} - 13 q^{49} + q^{50} - 4 q^{52} - 10 q^{53} - 4 q^{55} - q^{56} - 2 q^{58} - 4 q^{59} + 6 q^{61} - 20 q^{62} + 2 q^{64} - 2 q^{65} - 12 q^{67} + 4 q^{70} + 24 q^{71} - 16 q^{74} + 2 q^{77} - 10 q^{79} + q^{80} - 5 q^{82} - 5 q^{83} + 2 q^{86} - 4 q^{88} - 14 q^{89} - 8 q^{91} - 4 q^{92} + 13 q^{94} - 2 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 2 * q^5 + q^7 - 2 * q^8 - q^10 + 4 * q^11 + 2 * q^13 - 4 * q^14 - q^16 + q^20 + 2 * q^22 + 8 * q^23 + 2 * q^25 - 2 * q^26 - 5 * q^28 - q^29 - 10 * q^31 + q^32 - q^35 - 8 * q^37 + 2 * q^40 + 5 * q^41 + q^43 - 2 * q^44 + 4 * q^46 - 13 * q^47 - 13 * q^49 + q^50 - 4 * q^52 - 10 * q^53 - 4 * q^55 - q^56 - 2 * q^58 - 4 * q^59 + 6 * q^61 - 20 * q^62 + 2 * q^64 - 2 * q^65 - 12 * q^67 + 4 * q^70 + 24 * q^71 - 16 * q^74 + 2 * q^77 - 10 * q^79 + q^80 - 5 * q^82 - 5 * q^83 + 2 * q^86 - 4 * q^88 - 14 * q^89 - 8 * q^91 - 4 * q^92 + 13 * q^94 - 2 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		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
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		0			0
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$	−0.500000	+	2.59808i	−0.0845154	+	0.439155i
$36$		0			0
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$		0			0
$39$		0			0
$40$	1.00000			0.158114
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	−0.602072	−	0.798441i	$-0.705658\pi$
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	0.992507	+	0.122189i	$0.0389915\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−6.50000	+	11.2583i	−0.948122	+	1.64220i	−0.198747	+	0.980051i	$0.563687\pi$
$47$	−6.50000	+	11.2583i	−0.948122	+	1.64220i	−0.749375	+	0.662145i	$0.769646\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	−2.00000			−0.277350
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	0.286064	+	0.958211i	$0.407653\pi$
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	−0.972867	+	0.231367i	$0.925680\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$		0			0
$58$	−1.00000			−0.131306
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$	−10.0000			−1.27000
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		0			0
$69$		0			0
$70$	2.00000	+	1.73205i	0.239046	+	0.207020i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$73$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$		0			0
$77$	1.00000	−	5.19615i	0.113961	−	0.592157i
$78$		0			0
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−2.50000	−	4.33013i	−0.276079	−	0.478183i
$83$	−2.50000	−	4.33013i	−0.274411	−	0.475293i	0.695576	−	0.718453i	$-0.255149\pi$
$83$	−2.50000	−	4.33013i	−0.274411	−	0.475293i	−0.969986	+	0.243160i	$0.921816\pi$
$84$		0			0
$85$		0			0
$86$	1.00000			0.107833
$87$		0			0
$88$	−2.00000			−0.213201
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$		0			0
$91$	−4.00000	−	3.46410i	−0.419314	−	0.363137i
$92$	−2.00000	−	3.46410i	−0.208514	−	0.361158i
$93$		0			0
$94$	6.50000	+	11.2583i	0.670424	+	1.16121i
$95$		0			0
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$		0			0
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	5.00000	+	8.66025i	0.485643	+	0.841158i
$107$	0.500000	+	0.866025i	0.0483368	+	0.0837218i	0.889182	−	0.457555i	$-0.151275\pi$
$107$	0.500000	+	0.866025i	0.0483368	+	0.0837218i	−0.840845	+	0.541276i	$0.817941\pi$
$108$		0			0
$109$	1.50000	−	2.59808i	0.143674	−	0.248851i	−0.785203	−	0.619238i	$-0.787442\pi$
$109$	1.50000	−	2.59808i	0.143674	−	0.248851i	0.928877	+	0.370387i	$0.120775\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$	−4.00000			−0.373002
$116$	−0.500000	+	0.866025i	−0.0464238	+	0.0804084i
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−3.00000	−	5.19615i	−0.271607	−	0.470438i
$123$		0			0
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−5.00000			−0.443678			−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000			−0.443678			−0.221839	+	0.975083i	$0.571206\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000			−1.03664
$135$		0			0
$136$		0			0
$137$	−12.0000			−1.02523			−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000			−1.02523			−0.512615	+	0.858619i	$0.671323\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$	2.50000	−	0.866025i	0.211289	−	0.0731925i
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$		0			0
$145$	0.500000	+	0.866025i	0.0415227	+	0.0719195i
$146$		0			0
$147$		0			0
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	18.0000			1.47462			0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000			1.47462			0.737309	+	0.675556i	$0.236096\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$		0			0
$153$		0			0
$154$	−4.00000	−	3.46410i	−0.322329	−	0.279145i
$155$	5.00000	+	8.66025i	0.401610	+	0.695608i
$156$		0			0
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	5.00000	+	8.66025i	0.397779	+	0.688973i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	2.00000	−	10.3923i	0.157622	−	0.819028i
$162$		0			0
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$	−5.00000			−0.390434
$165$		0			0
$166$	−5.00000			−0.388075
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	0.500000	−	2.59808i	0.0377964	−	0.196396i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$		0			0
$178$	−14.0000			−1.04934
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$		0			0
$181$	21.0000			1.56092			0.780459	−	0.625207i	$-0.214986\pi$
$181$	21.0000			1.56092			0.780459	+	0.625207i	$0.214986\pi$
$182$	−5.00000	+	1.73205i	−0.370625	+	0.128388i
$183$		0			0
$184$	−4.00000			−0.294884
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$		0			0
$187$		0			0
$188$	13.0000			0.948122
$189$		0			0
$190$		0			0
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	26.0000			1.85242			0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000			1.85242			0.926212	+	0.377004i	$0.123046\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$	1.50000	−	2.59808i	0.105540	−	0.182800i
$203$	−2.50000	+	0.866025i	−0.175466	+	0.0607831i
$204$		0			0
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$		0			0
$208$	1.00000	+	1.73205i	0.0693375	+	0.120096i
$209$		0			0
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	10.0000			0.686803
$213$		0			0
$214$	1.00000			0.0683586
$215$	−0.500000	−	0.866025i	−0.0340997	−	0.0590624i
$216$		0			0
$217$	−25.0000	+	8.66025i	−1.69711	+	0.587896i
$218$	−1.50000	−	2.59808i	−0.101593	−	0.175964i
$219$		0			0
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$		0			0
$222$		0			0
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	0.675098	−	0.737728i	$-0.264101\pi$
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	−0.976440	+	0.215788i	$0.930768\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$		0			0
$226$	−3.00000	−	5.19615i	−0.199557	−	0.345643i
$227$	−4.00000			−0.265489			−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$		0			0
$229$	−1.00000			−0.0660819			−0.0330409	−	0.999454i	$-0.510519\pi$
$229$	−1.00000			−0.0660819			−0.0330409	+	0.999454i	$0.510519\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$		0			0
$232$	0.500000	+	0.866025i	0.0328266	+	0.0568574i
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	6.50000	−	11.2583i	0.424013	−	0.734412i
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$		0			0
$238$		0			0
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	−0.752536	−	0.658551i	$-0.771170\pi$
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	0.946590	+	0.322440i	$0.104503\pi$
$240$		0			0
$241$	25.0000			1.61039			0.805196	−	0.593009i	$-0.202060\pi$
$241$	25.0000			1.61039			0.805196	+	0.593009i	$0.202060\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	−6.00000			−0.384111
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$		0			0
$248$	5.00000	+	8.66025i	0.317500	+	0.549927i
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−14.0000			−0.883672			−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000			−0.883672			−0.441836	+	0.897096i	$0.645673\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	−2.50000	+	4.33013i	−0.156864	+	0.271696i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.0000			−1.24757			−0.623783	−	0.781598i	$-0.714405\pi$
$257$	−20.0000			−1.24757			−0.623783	+	0.781598i	$0.714405\pi$
$258$		0			0
$259$	−20.0000	+	6.92820i	−1.24274	+	0.430498i
$260$	2.00000			0.124035
$261$		0			0
$262$	−10.0000	+	17.3205i	−0.617802	+	1.07006i
$263$	9.00000			0.554964			0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000			0.554964			0.277482	+	0.960731i	$0.410500\pi$
$264$		0			0
$265$	5.00000	−	8.66025i	0.307148	−	0.531995i
$266$		0			0
$267$		0			0
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	−0.996586	−	0.0825561i	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$		0			0
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	0.880812	+	0.473466i	$0.156997\pi$
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$		0			0
$273$		0			0
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$	2.00000			0.120605
$276$		0			0
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$	−8.00000	−	13.8564i	−0.479808	−	0.831052i
$279$		0			0
$280$	0.500000	−	2.59808i	0.0298807	−	0.155265i
$281$	6.50000	+	11.2583i	0.387757	+	0.671616i	0.992148	−	0.125073i	$-0.0399165\pi$
$281$	6.50000	+	11.2583i	0.387757	+	0.671616i	−0.604390	+	0.796689i	$0.706583\pi$
$282$		0			0
$283$	5.50000	+	9.52628i	0.326941	+	0.566279i	0.981903	−	0.189383i	$-0.0606488\pi$
$283$	5.50000	+	9.52628i	0.326941	+	0.566279i	−0.654962	+	0.755662i	$0.727315\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$	−10.0000	−	8.66025i	−0.590281	−	0.511199i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	1.00000			0.0587220
$291$		0			0
$292$		0			0
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	−0.635818	−	0.771839i	$-0.719337\pi$
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	0.986341	+	0.164714i	$0.0526703\pi$
$294$		0			0
$295$	2.00000	+	3.46410i	0.116445	+	0.201688i
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$		0			0
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	4.00000	−	6.92820i	0.231326	−	0.400668i
$300$		0			0
$301$	2.50000	−	0.866025i	0.144098	−	0.0499169i
$302$	6.00000	−	10.3923i	0.345261	−	0.598010i
$303$		0			0
$304$		0			0
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	−5.00000	+	1.73205i	−0.284901	+	0.0986928i
$309$		0			0
$310$	10.0000			0.567962
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	−0.768699	−	0.639611i	$-0.779095\pi$
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	0.938269	+	0.345907i	$0.112429\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	10.0000			0.562544
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$		0			0
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−8.00000	−	6.92820i	−0.445823	−	0.386094i
$323$		0			0
$324$		0			0
$325$	1.00000	−	1.73205i	0.0554700	−	0.0960769i
$326$	20.0000			1.10770
$327$		0			0
$328$	−2.50000	+	4.33013i	−0.138039	+	0.239091i
$329$	26.0000	+	22.5167i	1.43343	+	1.24138i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−2.50000	+	4.33013i	−0.137205	+	0.237647i
$333$		0			0
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$		0			0
$337$	−3.00000	+	5.19615i	−0.163420	+	0.283052i	−0.936093	−	0.351752i	$-0.885586\pi$
$337$	−3.00000	+	5.19615i	−0.163420	+	0.283052i	0.772673	+	0.634804i	$0.218919\pi$
$338$	9.00000			0.489535
$339$		0			0
$340$		0			0
$341$	−10.0000	−	17.3205i	−0.541530	−	0.937958i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	9.50000	+	16.4545i	0.509987	+	0.883323i	0.999933	+	0.0115703i	$0.00368303\pi$
$347$	9.50000	+	16.4545i	0.509987	+	0.883323i	−0.489946	+	0.871753i	$0.662984\pi$
$348$		0			0
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	−0.917679	−	0.397324i	$-0.869939\pi$
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	0.114747	−	0.993395i	$-0.463394\pi$
$350$	−2.00000	−	1.73205i	−0.106904	−	0.0925820i
$351$		0			0
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	24.0000			1.27739			0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000			1.27739			0.638696	+	0.769460i	$0.279474\pi$
$354$		0			0
$355$	−12.0000			−0.636894
$356$	−7.00000	+	12.1244i	−0.370999	+	0.642590i
$357$		0			0
$358$	−2.00000	−	3.46410i	−0.105703	−	0.183083i
$359$	−17.0000	−	29.4449i	−0.897226	−	1.55404i	−0.831026	−	0.556234i	$-0.812246\pi$
$359$	−17.0000	−	29.4449i	−0.897226	−	1.55404i	−0.0662000	−	0.997806i	$-0.521088\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	10.5000	−	18.1865i	0.551868	−	0.955863i
$363$		0			0
$364$	−1.00000	+	5.19615i	−0.0524142	+	0.272352i
$365$		0			0
$366$		0			0
$367$	−17.0000			−0.887393			−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000			−0.887393			−0.443696	+	0.896177i	$0.646333\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$		0			0
$370$	8.00000			0.415900
$371$	20.0000	+	17.3205i	1.03835	+	0.899236i
$372$		0			0
$373$	24.0000			1.24267			0.621336	−	0.783544i	$-0.286590\pi$
$373$	24.0000			1.24267			0.621336	+	0.783544i	$0.286590\pi$
$374$		0			0
$375$		0			0
$376$	6.50000	−	11.2583i	0.335212	−	0.580604i
$377$	−2.00000			−0.103005
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$		0			0
$381$		0			0
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	−13.0000			−0.664269			−0.332134	−	0.943232i	$-0.607769\pi$
$383$	−13.0000			−0.664269			−0.332134	+	0.943232i	$0.607769\pi$
$384$		0			0
$385$	−1.00000	+	5.19615i	−0.0509647	+	0.264820i
$386$	2.00000			0.101797
$387$		0			0
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	−5.00000			−0.253510			−0.126755	−	0.991934i	$-0.540456\pi$
$389$	−5.00000			−0.253510			−0.126755	+	0.991934i	$0.540456\pi$
$390$		0			0
$391$		0			0
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$		0			0
$394$	13.0000	−	22.5167i	0.654931	−	1.13437i
$395$	5.00000	−	8.66025i	0.251577	−	0.435745i
$396$		0			0
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	25.0000			1.24844			0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000			1.24844			0.624220	+	0.781248i	$0.285417\pi$
$402$		0			0
$403$	−20.0000			−0.996271
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$		0			0
$406$	−0.500000	+	2.59808i	−0.0248146	+	0.128940i
$407$	−8.00000	−	13.8564i	−0.396545	−	0.686837i
$408$		0			0
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$	2.50000	+	4.33013i	0.123466	+	0.213850i
$411$		0			0
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$	−10.0000	+	3.46410i	−0.492068	+	0.170457i
$414$		0			0
$415$	2.50000	+	4.33013i	0.122720	+	0.212558i
$416$	2.00000			0.0980581
$417$		0			0
$418$		0			0
$419$	13.0000	−	22.5167i	0.635092	−	1.10001i	−0.351404	−	0.936224i	$-0.614296\pi$
$419$	13.0000	−	22.5167i	0.635092	−	1.10001i	0.986496	−	0.163787i	$-0.0523710\pi$
$420$		0			0
$421$	14.5000	+	25.1147i	0.706687	+	1.22402i	0.966079	+	0.258245i	$0.0831443\pi$
$421$	14.5000	+	25.1147i	0.706687	+	1.22402i	−0.259393	+	0.965772i	$0.583522\pi$
$422$	−11.0000	−	19.0526i	−0.535472	−	0.927464i
$423$		0			0
$424$	5.00000	−	8.66025i	0.242821	−	0.420579i
$425$		0			0
$426$		0			0
$427$	−12.0000	−	10.3923i	−0.580721	−	0.502919i
$428$	0.500000	−	0.866025i	0.0241684	−	0.0418609i
$429$		0			0
$430$	−1.00000			−0.0482243
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	0.997173	+	0.0751385i	$0.0239399\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−5.00000	+	25.9808i	−0.240008	+	1.24712i
$435$		0			0
$436$	−3.00000			−0.143674
$437$		0			0
$438$		0			0
$439$	17.0000	−	29.4449i	0.811366	−	1.40533i	−0.100543	−	0.994933i	$-0.532058\pi$
$439$	17.0000	−	29.4449i	0.811366	−	1.40533i	0.911908	−	0.410394i	$-0.134609\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$		0			0
$443$	8.50000	−	14.7224i	0.403847	−	0.699484i	−0.590339	−	0.807155i	$-0.701006\pi$
$443$	8.50000	−	14.7224i	0.403847	−	0.699484i	0.994187	+	0.107671i	$0.0343394\pi$
$444$		0			0
$445$	7.00000	+	12.1244i	0.331832	+	0.574750i
$446$	−9.00000			−0.426162
$447$		0			0
$448$	0.500000	−	2.59808i	0.0236228	−	0.122748i
$449$	5.00000			0.235965			0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000			0.235965			0.117982	+	0.993016i	$0.462357\pi$
$450$		0			0
$451$	5.00000	−	8.66025i	0.235441	−	0.407795i
$452$	−6.00000			−0.282216
$453$		0			0
$454$	−2.00000	+	3.46410i	−0.0938647	+	0.162578i
$455$	4.00000	+	3.46410i	0.187523	+	0.162400i
$456$		0			0
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	−0.575036	−	0.818128i	$-0.695012\pi$
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	0.996038	+	0.0889312i	$0.0283451\pi$
$458$	−0.500000	+	0.866025i	−0.0233635	+	0.0404667i
$459$		0			0
$460$	2.00000	+	3.46410i	0.0932505	+	0.161515i
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	0.951584	−	0.307388i	$-0.0994551\pi$
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	−0.741998	+	0.670402i	$0.766122\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$	1.00000			0.0464238
$465$		0			0
$466$	−6.00000			−0.277945
$467$	−10.5000	−	18.1865i	−0.485882	−	0.841572i	0.513986	−	0.857798i	$-0.328168\pi$
$467$	−10.5000	−	18.1865i	−0.485882	−	0.841572i	−0.999868	+	0.0162260i	$0.994835\pi$
$468$		0			0
$469$	−30.0000	+	10.3923i	−1.38527	+	0.479872i
$470$	−6.50000	−	11.2583i	−0.299823	−	0.519308i
$471$		0			0
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$	1.00000	+	1.73205i	0.0459800	+	0.0796398i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	10.0000			0.456912			0.228456	−	0.973554i	$-0.426632\pi$
$479$	10.0000			0.456912			0.228456	+	0.973554i	$0.426632\pi$
$480$		0			0
$481$	−16.0000			−0.729537
$482$	12.5000	−	21.6506i	0.569359	−	0.986159i
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	0.233933	+	0.972253i	$0.424840\pi$
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	−0.958962	+	0.283535i	$0.908493\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$		0			0
$490$	5.50000	−	4.33013i	0.248465	−	0.195615i
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	−0.942057	−	0.335453i	$-0.891111\pi$
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	0.761539	+	0.648119i	$0.224444\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	10.0000			0.449013
$497$	6.00000	−	31.1769i	0.269137	−	1.39848i
$498$		0			0
$499$	10.0000			0.447661			0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000			0.447661			0.223831	+	0.974628i	$0.428144\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−7.00000	+	12.1244i	−0.312425	+	0.541136i
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$	4.00000	−	6.92820i	0.177822	−	0.307996i
$507$		0			0
$508$	2.50000	+	4.33013i	0.110920	+	0.192118i
$509$	29.0000			1.28540			0.642701	−	0.766117i	$-0.277814\pi$
$509$	29.0000			1.28540			0.642701	+	0.766117i	$0.277814\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−10.0000	+	17.3205i	−0.441081	+	0.763975i
$515$	1.00000			0.0440653
$516$		0			0
$517$	−13.0000	+	22.5167i	−0.571739	+	0.990282i
$518$	−4.00000	+	20.7846i	−0.175750	+	0.913223i
$519$		0			0
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	−0.998961	−	0.0455727i	$-0.985489\pi$
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	0.538948	+	0.842339i	$0.318822\pi$
$522$		0			0
$523$	−17.5000	−	30.3109i	−0.765222	−	1.32540i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$	−17.5000	−	30.3109i	−0.765222	−	1.32540i	0.174908	−	0.984585i	$-0.444037\pi$
$524$	10.0000	+	17.3205i	0.436852	+	0.756650i
$525$		0			0
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$		0			0
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−5.00000	−	8.66025i	−0.217186	−	0.376177i
$531$		0			0
$532$		0			0
$533$	−5.00000	−	8.66025i	−0.216574	−	0.375117i
$534$		0			0
$535$	−0.500000	−	0.866025i	−0.0216169	−	0.0374415i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$		0			0
$538$	7.00000	+	12.1244i	0.301791	+	0.522718i
$539$	−13.0000	−	5.19615i	−0.559950	−	0.223814i
$540$		0			0
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	0.956504	+	0.291718i	$0.0942267\pi$
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	−0.225617	+	0.974216i	$0.572440\pi$
$542$	28.0000			1.20270
$543$		0			0
$544$		0			0
$545$	−1.50000	+	2.59808i	−0.0642529	+	0.111289i
$546$		0			0
$547$	−6.50000	−	11.2583i	−0.277920	−	0.481371i	0.692948	−	0.720988i	$-0.256312\pi$
$547$	−6.50000	−	11.2583i	−0.277920	−	0.481371i	−0.970868	+	0.239616i	$0.922978\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$		0			0
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$		0			0
$552$		0			0
$553$	20.0000	+	17.3205i	0.850487	+	0.736543i
$554$	13.0000	−	22.5167i	0.552317	−	0.956641i
$555$		0			0
$556$	−16.0000			−0.678551
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	0.491496	+	0.870880i	$0.336450\pi$
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	−0.999952	+	0.00979220i	$0.996883\pi$
$558$		0			0
$559$	2.00000			0.0845910
$560$	−2.00000	−	1.73205i	−0.0845154	−	0.0731925i
$561$		0			0
$562$	13.0000			0.548372
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$		0			0
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	11.0000			0.462364
$567$		0			0
$568$	−12.0000			−0.503509
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	1.00000	+	1.73205i	0.0418487	+	0.0724841i	0.886191	−	0.463320i	$-0.153342\pi$
$571$	1.00000	+	1.73205i	0.0418487	+	0.0724841i	−0.844342	+	0.535804i	$0.820009\pi$
$572$	−4.00000			−0.167248
$573$		0			0
$574$	−12.5000	+	4.33013i	−0.521740	+	0.180736i
$575$	4.00000			0.166812
$576$		0			0
$577$	−14.0000	+	24.2487i	−0.582828	+	1.00949i	0.412315	+	0.911041i	$0.364720\pi$
$577$	−14.0000	+	24.2487i	−0.582828	+	1.00949i	−0.995142	+	0.0984456i	$0.968613\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$	0.500000	−	0.866025i	0.0207614	−	0.0359597i
$581$	−12.5000	+	4.33013i	−0.518587	+	0.179644i
$582$		0			0
$583$	−10.0000	+	17.3205i	−0.414158	+	0.717342i
$584$		0			0
$585$		0			0
$586$	−6.00000	−	10.3923i	−0.247858	−	0.429302i
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	−0.974668	−	0.223659i	$-0.928200\pi$
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	0.293640	−	0.955916i	$-0.405133\pi$
$588$		0			0
$589$		0			0
$590$	4.00000			0.164677
$591$		0			0
$592$	8.00000			0.328798
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	0.973202	−	0.229953i	$-0.0738573\pi$
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	−0.685746	+	0.727841i	$0.740524\pi$
$594$		0			0
$595$		0			0
$596$	−9.00000	−	15.5885i	−0.368654	−	0.638528i
$597$		0			0
$598$	−4.00000	−	6.92820i	−0.163572	−	0.283315i
$599$	−22.0000	−	38.1051i	−0.898896	−	1.55693i	−0.828908	−	0.559385i	$-0.811037\pi$
$599$	−22.0000	−	38.1051i	−0.898896	−	1.55693i	−0.0699877	−	0.997548i	$-0.522296\pi$
$600$		0			0
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$	0.500000	−	2.59808i	0.0203785	−	0.105890i
$603$		0			0
$604$	−6.00000	−	10.3923i	−0.244137	−	0.422857i
$605$	7.00000			0.284590
$606$		0			0
$607$	−43.0000			−1.74532			−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000			−1.74532			−0.872658	+	0.488332i	$0.837606\pi$
$608$		0			0
$609$		0			0
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$	13.0000	+	22.5167i	0.525924	+	0.910927i
$612$		0			0
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	−0.171564	−	0.985173i	$-0.554882\pi$
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	0.938967	−	0.344008i	$-0.111785\pi$
$614$	−3.50000	+	6.06218i	−0.141249	+	0.244650i
$615$		0			0
$616$	−1.00000	+	5.19615i	−0.0402911	+	0.209359i
$617$	10.0000	−	17.3205i	0.402585	−	0.697297i	−0.591452	−	0.806340i	$-0.701445\pi$
$617$	10.0000	−	17.3205i	0.402585	−	0.697297i	0.994037	+	0.109043i	$0.0347785\pi$
$618$		0			0
$619$	32.0000			1.28619			0.643094	−	0.765787i	$-0.277650\pi$
$619$	32.0000			1.28619			0.643094	+	0.765787i	$0.277650\pi$
$620$	5.00000	−	8.66025i	0.200805	−	0.347804i
$621$		0			0
$622$	24.0000			0.962312
$623$	−35.0000	+	12.1244i	−1.40225	+	0.485752i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$		0			0
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$		0			0
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	5.00000	−	8.66025i	0.198889	−	0.344486i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	5.00000			0.198419
$636$		0			0
$637$	−11.0000	+	8.66025i	−0.435836	+	0.343132i
$638$	−2.00000			−0.0791808
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$	−23.5000	+	40.7032i	−0.926750	+	1.60518i	−0.138027	+	0.990429i	$0.544076\pi$
$643$	−23.5000	+	40.7032i	−0.926750	+	1.60518i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−10.0000	+	3.46410i	−0.394055	+	0.136505i
$645$		0			0
$646$		0			0
$647$	−3.50000	+	6.06218i	−0.137599	+	0.238329i	−0.926587	−	0.376080i	$-0.877272\pi$
$647$	−3.50000	+	6.06218i	−0.137599	+	0.238329i	0.788988	+	0.614408i	$0.210605\pi$
$648$		0			0
$649$	−4.00000	−	6.92820i	−0.157014	−	0.271956i
$650$	−1.00000	−	1.73205i	−0.0392232	−	0.0679366i
$651$		0			0
$652$	10.0000	−	17.3205i	0.391630	−	0.678323i
$653$	4.00000			0.156532			0.0782660	−	0.996933i	$-0.475062\pi$
$653$	4.00000			0.156532			0.0782660	+	0.996933i	$0.475062\pi$
$654$		0			0
$655$	20.0000			0.781465
$656$	2.50000	+	4.33013i	0.0976086	+	0.169063i
$657$		0			0
$658$	32.5000	−	11.2583i	1.26698	−	0.438895i
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	−1.50000	−	2.59808i	−0.0583432	−	0.101053i	0.835379	−	0.549675i	$-0.185248\pi$
$661$	−1.50000	−	2.59808i	−0.0583432	−	0.101053i	−0.893722	+	0.448622i	$0.851915\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	2.50000	+	4.33013i	0.0970188	+	0.168042i
$665$		0			0
$666$		0			0
$667$	−2.00000	−	3.46410i	−0.0774403	−	0.134131i
$668$	−12.0000			−0.464294
$669$		0			0
$670$	12.0000			0.463600
$671$	6.00000	−	10.3923i	0.231627	−	0.401190i
$672$		0			0
$673$	4.00000	+	6.92820i	0.154189	+	0.267063i	0.932763	−	0.360489i	$-0.117390\pi$
$673$	4.00000	+	6.92820i	0.154189	+	0.267063i	−0.778575	+	0.627552i	$0.784057\pi$
$674$	3.00000	+	5.19615i	0.115556	+	0.200148i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−10.0000	+	17.3205i	−0.384331	+	0.665681i	−0.991676	−	0.128757i	$-0.958901\pi$
$677$	−10.0000	+	17.3205i	−0.384331	+	0.665681i	0.607345	+	0.794438i	$0.292235\pi$
$678$		0			0
$679$	−5.00000	+	1.73205i	−0.191882	+	0.0664700i
$680$		0			0
$681$		0			0
$682$	−20.0000			−0.765840
$683$	5.50000	−	9.52628i	0.210452	−	0.364513i	−0.741404	−	0.671059i	$-0.765840\pi$
$683$	5.50000	−	9.52628i	0.210452	−	0.364513i	0.951856	+	0.306546i	$0.0991732\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$		0			0
$688$	−1.00000			−0.0381246
$689$	10.0000	+	17.3205i	0.380970	+	0.659859i
$690$		0			0
$691$	24.0000	−	41.5692i	0.913003	−	1.58137i	0.103204	−	0.994660i	$-0.467091\pi$
$691$	24.0000	−	41.5692i	0.913003	−	1.58137i	0.809799	−	0.586707i	$-0.199576\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	19.0000			0.721230
$695$	−8.00000	+	13.8564i	−0.303457	+	0.525603i
$696$		0			0
$697$		0			0
$698$	−30.0000			−1.13552
$699$		0			0
$700$	−2.50000	+	0.866025i	−0.0944911	+	0.0327327i
$701$	33.0000			1.24639			0.623196	−	0.782065i	$-0.285834\pi$
$701$	33.0000			1.24639			0.623196	+	0.782065i	$0.285834\pi$
$702$		0			0
$703$		0			0
$704$	2.00000			0.0753778
$705$		0			0
$706$	12.0000	−	20.7846i	0.451626	−	0.782239i
$707$	1.50000	−	7.79423i	0.0564133	−	0.293132i
$708$		0			0
$709$	23.0000	−	39.8372i	0.863783	−	1.49612i	−0.00446726	−	0.999990i	$-0.501422\pi$
$709$	23.0000	−	39.8372i	0.863783	−	1.49612i	0.868250	−	0.496126i	$-0.165245\pi$
$710$	−6.00000	+	10.3923i	−0.225176	+	0.390016i
$711$		0			0
$712$	7.00000	+	12.1244i	0.262336	+	0.454379i
$713$	−20.0000	−	34.6410i	−0.749006	−	1.29732i
$714$		0			0
$715$	−2.00000	+	3.46410i	−0.0747958	+	0.129550i
$716$	−4.00000			−0.149487
$717$		0			0
$718$	−34.0000			−1.26887
$719$	14.0000	+	24.2487i	0.522112	+	0.904324i	0.999669	+	0.0257237i	$0.00818900\pi$
$719$	14.0000	+	24.2487i	0.522112	+	0.904324i	−0.477557	+	0.878601i	$0.658478\pi$
$720$		0			0
$721$	−0.500000	+	2.59808i	−0.0186210	+	0.0967574i
$722$	−9.50000	−	16.4545i	−0.353553	−	0.612372i
$723$		0			0
$724$	−10.5000	−	18.1865i	−0.390229	−	0.675897i
$725$	−0.500000	−	0.866025i	−0.0185695	−	0.0321634i
$726$		0			0
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	0.951694	+	0.307049i	$0.0993415\pi$
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	−0.209935	+	0.977715i	$0.567325\pi$
$728$	4.00000	+	3.46410i	0.148250	+	0.128388i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	20.0000			0.738717			0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000			0.738717			0.369358	+	0.929287i	$0.379577\pi$
$734$	−8.50000	+	14.7224i	−0.313741	+	0.543415i
$735$		0			0
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$		0			0
$739$	−16.0000	+	27.7128i	−0.588570	+	1.01943i	0.405851	+	0.913939i	$0.366975\pi$
$739$	−16.0000	+	27.7128i	−0.588570	+	1.01943i	−0.994420	+	0.105493i	$0.966358\pi$
$740$	4.00000	−	6.92820i	0.147043	−	0.254686i
$741$		0			0
$742$	25.0000	−	8.66025i	0.917779	−	0.317928i
$743$	−21.5000	+	37.2391i	−0.788759	+	1.36617i	0.137969	+	0.990437i	$0.455942\pi$
$743$	−21.5000	+	37.2391i	−0.788759	+	1.36617i	−0.926728	+	0.375733i	$0.877391\pi$
$744$		0			0
$745$	−18.0000			−0.659469
$746$	12.0000	−	20.7846i	0.439351	−	0.760979i
$747$		0			0
$748$		0			0
$749$	2.50000	−	0.866025i	0.0913480	−	0.0316439i
$750$		0			0
$751$	−46.0000			−1.67856			−0.839282	−	0.543696i	$-0.817024\pi$
$751$	−46.0000			−1.67856			−0.839282	+	0.543696i	$0.817024\pi$
$752$	−6.50000	−	11.2583i	−0.237031	−	0.410549i
$753$		0			0
$754$	−1.00000	+	1.73205i	−0.0364179	+	0.0630776i
$755$	−12.0000			−0.436725
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	1.00000	−	1.73205i	0.0363216	−	0.0629109i
$759$		0			0
$760$		0			0
$761$	−27.0000			−0.978749			−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000			−0.978749			−0.489375	+	0.872074i	$0.662775\pi$
$762$		0			0
$763$	−6.00000	−	5.19615i	−0.217215	−	0.188113i
$764$	18.0000			0.651217
$765$		0			0
$766$	−6.50000	+	11.2583i	−0.234855	+	0.406780i
$767$	−8.00000			−0.288863
$768$		0			0
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$	4.00000	+	3.46410i	0.144150	+	0.124838i
$771$		0			0
$772$	1.00000	−	1.73205i	0.0359908	−	0.0623379i
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	0.189899	+	0.981804i	$0.439184\pi$
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	−0.945216	+	0.326445i	$0.894149\pi$
$774$		0			0
$775$	−5.00000	−	8.66025i	−0.179605	−	0.311086i
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$		0			0
$778$	−2.50000	+	4.33013i	−0.0896293	+	0.155243i
$779$		0			0
$780$		0			0
$781$	24.0000			0.858788
$782$		0			0
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−2.00000	−	3.46410i	−0.0713831	−	0.123639i
$786$		0			0
$787$	−15.5000	−	26.8468i	−0.552515	−	0.956985i	−0.998092	−	0.0617409i	$-0.980335\pi$
$787$	−15.5000	−	26.8468i	−0.552515	−	0.956985i	0.445577	−	0.895244i	$-0.352999\pi$
$788$	−13.0000	−	22.5167i	−0.463106	−	0.802123i
$789$		0			0
$790$	−5.00000	−	8.66025i	−0.177892	−	0.308118i
$791$	−12.0000	−	10.3923i	−0.426671	−	0.369508i
$792$		0			0
$793$	−6.00000	−	10.3923i	−0.213066	−	0.369042i
$794$	−14.0000			−0.496841
$795$		0			0
$796$		0			0
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	0.468004	+	0.883726i	$0.344973\pi$
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	−0.999331	+	0.0365596i	$0.988360\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	12.5000	−	21.6506i	0.441390	−	0.764511i
$803$		0			0
$804$		0			0
$805$	−2.00000	+	10.3923i	−0.0704907	+	0.366281i
$806$	−10.0000	+	17.3205i	−0.352235	+	0.610089i
$807$		0			0
$808$	−3.00000			−0.105540
$809$	−1.50000	+	2.59808i	−0.0527372	+	0.0913435i	−0.891189	−	0.453632i	$-0.850128\pi$
$809$	−1.50000	+	2.59808i	−0.0527372	+	0.0913435i	0.838452	+	0.544976i	$0.183461\pi$
$810$		0			0
$811$	−42.0000			−1.47482			−0.737410	−	0.675446i	$-0.763951\pi$
$811$	−42.0000			−1.47482			−0.737410	+	0.675446i	$0.763951\pi$
$812$	2.00000	+	1.73205i	0.0701862	+	0.0607831i
$813$		0			0
$814$	−16.0000			−0.560800
$815$	−10.0000	−	17.3205i	−0.350285	−	0.606711i
$816$		0			0
$817$		0			0
$818$	25.0000			0.874105
$819$		0			0
$820$	5.00000			0.174608
$821$	1.50000	−	2.59808i	0.0523504	−	0.0906735i	−0.838663	−	0.544651i	$-0.816662\pi$
$821$	1.50000	−	2.59808i	0.0523504	−	0.0906735i	0.891013	+	0.453978i	$0.149995\pi$
$822$		0			0
$823$	4.50000	+	7.79423i	0.156860	+	0.271690i	0.933735	−	0.357966i	$-0.116529\pi$
$823$	4.50000	+	7.79423i	0.156860	+	0.271690i	−0.776875	+	0.629655i	$0.783196\pi$
$824$	1.00000			0.0348367
$825$		0			0
$826$	−2.00000	+	10.3923i	−0.0695889	+	0.361595i
$827$	5.00000			0.173867			0.0869335	−	0.996214i	$-0.472293\pi$
$827$	5.00000			0.173867			0.0869335	+	0.996214i	$0.472293\pi$
$828$		0			0
$829$	17.5000	−	30.3109i	0.607800	−	1.05274i	−0.383802	−	0.923415i	$-0.625386\pi$
$829$	17.5000	−	30.3109i	0.607800	−	1.05274i	0.991602	−	0.129325i	$-0.0412811\pi$
$830$	5.00000			0.173553
$831$		0			0
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$		0			0
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$		0			0
$837$		0			0
$838$	−13.0000	−	22.5167i	−0.449078	−	0.777825i
$839$	8.00000	+	13.8564i	0.276191	+	0.478376i	0.970435	−	0.241363i	$-0.0775945\pi$
$839$	8.00000	+	13.8564i	0.276191	+	0.478376i	−0.694244	+	0.719740i	$0.744261\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	29.0000			0.999406
$843$		0			0
$844$	−22.0000			−0.757271
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	−3.50000	+	18.1865i	−0.120261	+	0.624897i
$848$	−5.00000	−	8.66025i	−0.171701	−	0.297394i
$849$		0			0
$850$		0			0
$851$	−16.0000	−	27.7128i	−0.548473	−	0.949983i
$852$		0			0
$853$	−8.00000	−	13.8564i	−0.273915	−	0.474434i	0.695946	−	0.718094i	$-0.254985\pi$
$853$	−8.00000	−	13.8564i	−0.273915	−	0.474434i	−0.969861	+	0.243660i	$0.921652\pi$
$854$	−15.0000	+	5.19615i	−0.513289	+	0.177809i
$855$		0			0
$856$	−0.500000	−	0.866025i	−0.0170896	−	0.0296001i
$857$	10.0000			0.341593			0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000			0.341593			0.170797	+	0.985306i	$0.445366\pi$
$858$		0			0
$859$	−36.0000			−1.22830			−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000			−1.22830			−0.614152	+	0.789188i	$0.710502\pi$
$860$	−0.500000	+	0.866025i	−0.0170499	+	0.0295312i
$861$		0			0
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$	4.00000	+	6.92820i	0.136162	+	0.235839i	0.926041	−	0.377424i	$-0.123190\pi$
$863$	4.00000	+	6.92820i	0.136162	+	0.235839i	−0.789879	+	0.613263i	$0.789857\pi$
$864$		0			0
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$		0			0
$868$	20.0000	+	17.3205i	0.678844	+	0.587896i
$869$	−10.0000	+	17.3205i	−0.339227	+	0.587558i
$870$		0			0
$871$	−24.0000			−0.813209
$872$	−1.50000	+	2.59808i	−0.0507964	+	0.0879820i
$873$		0			0
$874$		0			0
$875$	−0.500000	+	2.59808i	−0.0169031	+	0.0878310i
$876$		0			0
$877$	−4.00000			−0.135070			−0.0675352	−	0.997717i	$-0.521513\pi$
$877$	−4.00000			−0.135070			−0.0675352	+	0.997717i	$0.521513\pi$
$878$	−17.0000	−	29.4449i	−0.573722	−	0.993716i
$879$		0			0
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	−14.0000			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$882$		0			0
$883$	51.0000			1.71629			0.858143	−	0.513410i	$-0.171618\pi$
$883$	51.0000			1.71629			0.858143	+	0.513410i	$0.171618\pi$
$884$		0			0
$885$		0			0
$886$	−8.50000	−	14.7224i	−0.285563	−	0.494610i
$887$	−55.0000			−1.84672			−0.923360	−	0.383936i	$-0.874568\pi$
$887$	−55.0000			−1.84672			−0.923360	+	0.383936i	$0.874568\pi$
$888$		0			0
$889$	−2.50000	+	12.9904i	−0.0838473	+	0.435683i
$890$	14.0000			0.469281
$891$		0			0
$892$	−4.50000	+	7.79423i	−0.150671	+	0.260970i
$893$		0			0
$894$		0			0
$895$	−2.00000	+	3.46410i	−0.0668526	+	0.115792i
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$		0			0
$898$	2.50000	−	4.33013i	0.0834261	−	0.144498i
$899$	−5.00000	+	8.66025i	−0.166759	+	0.288836i
$900$		0			0
$901$		0			0
$902$	−5.00000	−	8.66025i	−0.166482	−	0.288355i
$903$		0			0
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	−21.0000			−0.698064
$906$		0			0
$907$	−37.0000			−1.22856			−0.614282	−	0.789086i	$-0.710554\pi$
$907$	−37.0000			−1.22856			−0.614282	+	0.789086i	$0.710554\pi$
$908$	2.00000	+	3.46410i	0.0663723	+	0.114960i
$909$		0			0
$910$	5.00000	−	1.73205i	0.165748	−	0.0574169i
$911$	10.0000	+	17.3205i	0.331315	+	0.573854i	0.982770	−	0.184833i	$-0.0591745\pi$
$911$	10.0000	+	17.3205i	0.331315	+	0.573854i	−0.651455	+	0.758687i	$0.725841\pi$
$912$		0			0
$913$	−5.00000	−	8.66025i	−0.165476	−	0.286613i
$914$	−9.00000	−	15.5885i	−0.297694	−	0.515620i
$915$		0			0
$916$	0.500000	+	0.866025i	0.0165205	+	0.0286143i
$917$	−10.0000	+	51.9615i	−0.330229	+	1.71592i
$918$		0			0
$919$	24.0000	+	41.5692i	0.791687	+	1.37124i	0.924922	+	0.380158i	$0.124130\pi$
$919$	24.0000	+	41.5692i	0.791687	+	1.37124i	−0.133235	+	0.991084i	$0.542536\pi$
$920$	4.00000			0.131876
$921$		0			0
$922$	9.00000			0.296399
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	−0.500000	−	0.866025i	−0.0164310	−	0.0284594i
$927$		0			0
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	−0.716364	−	0.697727i	$-0.754195\pi$
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	0.962431	+	0.271526i	$0.0875283\pi$
$930$		0			0
$931$		0			0
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$		0			0
$934$	−21.0000			−0.687141
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−6.00000	+	31.1769i	−0.195907	+	1.01796i
$939$		0			0
$940$	−13.0000			−0.424013
$941$	22.5000	+	38.9711i	0.733479	+	1.27042i	0.955387	+	0.295355i	$0.0954381\pi$
$941$	22.5000	+	38.9711i	0.733479	+	1.27042i	−0.221908	+	0.975068i	$0.571229\pi$
$942$		0			0
$943$	10.0000	−	17.3205i	0.325645	−	0.564033i
$944$	4.00000			0.130189
$945$		0			0
$946$	2.00000			0.0650256
$947$	−2.00000	+	3.46410i	−0.0649913	+	0.112568i	−0.896690	−	0.442659i	$-0.854035\pi$
$947$	−2.00000	+	3.46410i	−0.0649913	+	0.112568i	0.831699	+	0.555227i	$0.187369\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$		0			0
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$	−6.00000			−0.194054
$957$		0			0
$958$	5.00000	−	8.66025i	0.161543	−	0.279800i
$959$	−6.00000	+	31.1769i	−0.193750	+	1.00676i
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	−8.00000	+	13.8564i	−0.257930	+	0.446748i
$963$		0			0
$964$	−12.5000	−	21.6506i	−0.402598	−	0.697320i
$965$	−1.00000	−	1.73205i	−0.0321911	−	0.0557567i
$966$		0			0
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	−0.794515	−	0.607244i	$-0.792275\pi$
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	0.923147	+	0.384448i	$0.125608\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	2.00000			0.0642161
$971$	21.0000	+	36.3731i	0.673922	+	1.16727i	0.976783	+	0.214232i	$0.0687250\pi$
$971$	21.0000	+	36.3731i	0.673922	+	1.16727i	−0.302861	+	0.953035i	$0.597942\pi$
$972$		0			0
$973$	−32.0000	−	27.7128i	−1.02587	−	0.888432i
$974$	16.0000	+	27.7128i	0.512673	+	0.887976i
$975$		0			0
$976$	3.00000	+	5.19615i	0.0960277	+	0.166325i
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$	−14.0000	−	24.2487i	−0.447442	−	0.774992i
$980$	−1.00000	−	6.92820i	−0.0319438	−	0.221313i
$981$		0			0
$982$	4.00000	+	6.92820i	0.127645	+	0.221088i
$983$	31.0000			0.988746			0.494373	−	0.869250i	$-0.335398\pi$
$983$	31.0000			0.988746			0.494373	+	0.869250i	$0.335398\pi$
$984$		0			0
$985$	−26.0000			−0.828429
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.00000	+	3.46410i	0.0635963	+	0.110152i
$990$		0			0
$991$	−23.0000	+	39.8372i	−0.730619	+	1.26547i	0.226000	+	0.974127i	$0.427435\pi$
$991$	−23.0000	+	39.8372i	−0.730619	+	1.26547i	−0.956619	+	0.291342i	$0.905898\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$		0			0
$994$	−24.0000	−	20.7846i	−0.761234	−	0.659248i
$995$		0			0
$996$		0			0
$997$	32.0000			1.01345			0.506725	−	0.862108i	$-0.330856\pi$
$997$	32.0000			1.01345			0.506725	+	0.862108i	$0.330856\pi$
$998$	5.00000	−	8.66025i	0.158272	−	0.274136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.l.c.361.1		2
3.2	odd	2		630.2.l.a.571.1	yes	2
7.2	even	3		1890.2.i.b.1171.1		2
9.2	odd	6		630.2.i.c.151.1	yes	2
9.7	even	3		1890.2.i.b.991.1		2
21.2	odd	6		630.2.i.c.121.1	✓	2
63.2	odd	6		630.2.l.a.331.1	yes	2
63.16	even	3	inner	1890.2.l.c.1801.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.c.121.1	✓	2	21.2	odd	6
630.2.i.c.151.1	yes	2	9.2	odd	6
630.2.l.a.331.1	yes	2	63.2	odd	6
630.2.l.a.571.1	yes	2	3.2	odd	2
1890.2.i.b.991.1		2	9.7	even	3
1890.2.i.b.1171.1		2	7.2	even	3
1890.2.l.c.361.1		2	1.1	even	1	trivial
1890.2.l.c.1801.1		2	63.16	even	3	inner

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.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +2.00000 q^{11} +(1.00000 - 1.73205i) q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} +4.00000 q^{23} +1.00000 q^{25} +(-1.00000 - 1.73205i) q^{26} +(-2.50000 + 0.866025i) q^{28} +(-0.500000 - 0.866025i) q^{29} +(-5.00000 - 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} +1.00000 q^{40} +(2.50000 - 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(2.00000 - 3.46410i) q^{46} +(-6.50000 + 11.2583i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} -2.00000 q^{52} +(-5.00000 + 8.66025i) q^{53} -2.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -1.00000 q^{58} +(-2.00000 - 3.46410i) q^{59} +(3.00000 - 5.19615i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-6.00000 - 10.3923i) q^{67} +(2.00000 + 1.73205i) q^{70} +12.0000 q^{71} -8.00000 q^{74} +(1.00000 - 5.19615i) q^{77} +(-5.00000 + 8.66025i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-2.50000 - 4.33013i) q^{82} +(-2.50000 - 4.33013i) q^{83} +1.00000 q^{86} -2.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(-2.00000 - 3.46410i) q^{92} +(6.50000 + 11.2583i) q^{94} +(-1.00000 - 1.73205i) q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 2 * q^5 + q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 2 q^{8} - q^{10} + 4 q^{11} + 2 q^{13} - 4 q^{14} - q^{16} + q^{20} + 2 q^{22} + 8 q^{23} + 2 q^{25} - 2 q^{26} - 5 q^{28} - q^{29} - 10 q^{31} + q^{32} - q^{35} - 8 q^{37} + 2 q^{40} + 5 q^{41} + q^{43} - 2 q^{44} + 4 q^{46} - 13 q^{47} - 13 q^{49} + q^{50} - 4 q^{52} - 10 q^{53} - 4 q^{55} - q^{56} - 2 q^{58} - 4 q^{59} + 6 q^{61} - 20 q^{62} + 2 q^{64} - 2 q^{65} - 12 q^{67} + 4 q^{70} + 24 q^{71} - 16 q^{74} + 2 q^{77} - 10 q^{79} + q^{80} - 5 q^{82} - 5 q^{83} + 2 q^{86} - 4 q^{88} - 14 q^{89} - 8 q^{91} - 4 q^{92} + 13 q^{94} - 2 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 2 * q^5 + q^7 - 2 * q^8 - q^10 + 4 * q^11 + 2 * q^13 - 4 * q^14 - q^16 + q^20 + 2 * q^22 + 8 * q^23 + 2 * q^25 - 2 * q^26 - 5 * q^28 - q^29 - 10 * q^31 + q^32 - q^35 - 8 * q^37 + 2 * q^40 + 5 * q^41 + q^43 - 2 * q^44 + 4 * q^46 - 13 * q^47 - 13 * q^49 + q^50 - 4 * q^52 - 10 * q^53 - 4 * q^55 - q^56 - 2 * q^58 - 4 * q^59 + 6 * q^61 - 20 * q^62 + 2 * q^64 - 2 * q^65 - 12 * q^67 + 4 * q^70 + 24 * q^71 - 16 * q^74 + 2 * q^77 - 10 * q^79 + q^80 - 5 * q^82 - 5 * q^83 + 2 * q^86 - 4 * q^88 - 14 * q^89 - 8 * q^91 - 4 * q^92 + 13 * q^94 - 2 * q^97 - 11 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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