LMFDB - Embedded newform 1575.2.bc.a.1349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(899,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1575.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.bc (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:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1575.1349
Dual form			1575.2.bc.a.899.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-2.59808 + 0.500000i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-2.59808 + 0.500000i) q^{7} +2.82843 q^{8} +(-1.22474 + 0.707107i) q^{11} -5.19615 q^{13} +(-1.22474 + 3.53553i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-4.24264 + 2.44949i) q^{17} +(-1.50000 - 0.866025i) q^{19} +2.00000i q^{22} +(-2.82843 + 4.89898i) q^{23} +(-3.67423 + 6.36396i) q^{26} -2.82843i q^{29} +(1.50000 - 0.866025i) q^{31} +6.92820i q^{34} +(-0.866025 - 0.500000i) q^{37} +(-2.12132 + 1.22474i) q^{38} -7.34847 q^{41} -1.00000i q^{43} +(4.00000 + 6.92820i) q^{46} +(-10.6066 - 6.12372i) q^{47} +(6.50000 - 2.59808i) q^{49} +(1.41421 + 2.44949i) q^{53} +(-7.34847 + 1.41421i) q^{56} +(-3.46410 - 2.00000i) q^{58} +(2.44949 + 4.24264i) q^{59} +(-3.00000 - 1.73205i) q^{61} -2.44949i q^{62} +8.00000 q^{64} +(-9.52628 + 5.50000i) q^{67} +7.07107i q^{71} +(0.866025 + 1.50000i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(2.82843 - 2.44949i) q^{77} +(2.50000 - 4.33013i) q^{79} +(-5.19615 + 9.00000i) q^{82} +7.34847i q^{83} +(-1.22474 - 0.707107i) q^{86} +(-3.46410 + 2.00000i) q^{88} +(-2.44949 + 4.24264i) q^{89} +(13.5000 - 2.59808i) q^{91} +(-15.0000 + 8.66025i) q^{94} +10.3923 q^{97} +(1.41421 - 9.79796i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 16 q^{16} - 12 q^{19} + 12 q^{31} + 32 q^{46} + 52 q^{49} - 24 q^{61} + 64 q^{64} + 20 q^{79} + 108 q^{91} - 120 q^{94}+O(q^{100}) $ 8 * q + 16 * q^16 - 12 * q^19 + 12 * q^31 + 32 * q^46 + 52 * q^49 - 24 * q^61 + 64 * q^64 + 20 * q^79 + 108 * q^91 - 120 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	1.22474i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	0.707107	−	1.22474i	0.500000	−	0.866025i	1.00000			$0$
$3$		0			0
$3$		0			0
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$8$	2.82843			1.00000
$9$		0			0
$10$		0			0
$11$	−1.22474	+	0.707107i	−0.369274	+	0.213201i	−0.673141	−	0.739514i	$-0.735055\pi$
$11$	−1.22474	+	0.707107i	−0.369274	+	0.213201i	0.303867	+	0.952714i	$0.401722\pi$
$12$		0			0
$13$	−5.19615			−1.44115			−0.720577	−	0.693375i	$-0.756123\pi$
$13$	−5.19615			−1.44115			−0.720577	+	0.693375i	$0.756123\pi$
$14$	−1.22474	+	3.53553i	−0.327327	+	0.944911i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−4.24264	+	2.44949i	−1.02899	+	0.594089i	−0.916696	−	0.399586i	$-0.869154\pi$
$17$	−4.24264	+	2.44949i	−1.02899	+	0.594089i	−0.112296	+	0.993675i	$0.535820\pi$
$18$		0			0
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	0.317970	−	0.948101i	$-0.396999\pi$
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	−0.662094	+	0.749421i	$0.730332\pi$
$20$		0			0
$21$		0			0
$22$			2.00000i			0.426401i
$23$	−2.82843	+	4.89898i	−0.589768	+	1.02151i	0.404495	+	0.914540i	$0.367447\pi$
$23$	−2.82843	+	4.89898i	−0.589768	+	1.02151i	−0.994263	+	0.106967i	$0.965886\pi$
$24$		0			0
$25$		0			0
$26$	−3.67423	+	6.36396i	−0.720577	+	1.24808i
$27$		0			0
$28$		0			0
$29$		−	2.82843i		−	0.525226i	−0.964901	−	0.262613i	$-0.915416\pi$
$29$		−	2.82843i		−	0.525226i	0.964901	−	0.262613i	$-0.0845842\pi$
$30$		0			0
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$		0			0
$34$			6.92820i			1.18818i
$35$		0			0
$36$		0			0
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	0.427121	−	0.904194i	$-0.359528\pi$
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	−0.569495	+	0.821995i	$0.692861\pi$
$38$	−2.12132	+	1.22474i	−0.344124	+	0.198680i
$39$		0			0
$40$		0			0
$41$	−7.34847			−1.14764			−0.573819	−	0.818982i	$-0.694539\pi$
$41$	−7.34847			−1.14764			−0.573819	+	0.818982i	$0.694539\pi$
$42$		0			0
$43$		−	1.00000i		−	0.152499i	−0.997089	−	0.0762493i	$-0.975706\pi$
$43$		−	1.00000i		−	0.152499i	0.997089	−	0.0762493i	$-0.0242945\pi$
$44$		0			0
$45$		0			0
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$	−10.6066	−	6.12372i	−1.54713	−	0.893237i	−0.998359	−	0.0572655i	$-0.981762\pi$
$47$	−10.6066	−	6.12372i	−1.54713	−	0.893237i	−0.548773	−	0.835971i	$-0.684905\pi$
$48$		0			0
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.41421	+	2.44949i	0.194257	+	0.336463i	0.946657	−	0.322244i	$-0.104437\pi$
$53$	1.41421	+	2.44949i	0.194257	+	0.336463i	−0.752400	+	0.658707i	$0.771104\pi$
$54$		0			0
$55$		0			0
$56$	−7.34847	+	1.41421i	−0.981981	+	0.188982i
$57$		0			0
$58$	−3.46410	−	2.00000i	−0.454859	−	0.262613i
$59$	2.44949	+	4.24264i	0.318896	+	0.552345i	0.980258	−	0.197722i	$-0.0633545\pi$
$59$	2.44949	+	4.24264i	0.318896	+	0.552345i	−0.661362	+	0.750067i	$0.730021\pi$
$60$		0			0
$61$	−3.00000	−	1.73205i	−0.384111	−	0.221766i	0.295495	−	0.955344i	$-0.404516\pi$
$61$	−3.00000	−	1.73205i	−0.384111	−	0.221766i	−0.679605	+	0.733578i	$0.737849\pi$
$62$		−	2.44949i		−	0.311086i
$63$		0			0
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$	−9.52628	+	5.50000i	−1.16382	+	0.671932i	−0.952217	−	0.305424i	$-0.901202\pi$
$67$	−9.52628	+	5.50000i	−1.16382	+	0.671932i	−0.211604	+	0.977356i	$0.567869\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.07107i			0.839181i	0.907713	+	0.419591i	$0.137826\pi$
$71$			7.07107i			0.839181i	−0.907713	+	0.419591i	$0.862174\pi$
$72$		0			0
$73$	0.866025	+	1.50000i	0.101361	+	0.175562i	0.912245	−	0.409644i	$-0.134347\pi$
$73$	0.866025	+	1.50000i	0.101361	+	0.175562i	−0.810885	+	0.585206i	$0.801014\pi$
$74$	−1.22474	+	0.707107i	−0.142374	+	0.0821995i
$75$		0			0
$76$		0			0
$77$	2.82843	−	2.44949i	0.322329	−	0.279145i
$78$		0			0
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$		0			0
$81$		0			0
$82$	−5.19615	+	9.00000i	−0.573819	+	0.993884i
$83$			7.34847i			0.806599i	0.915068	+	0.403300i	$0.132137\pi$
$83$			7.34847i			0.806599i	−0.915068	+	0.403300i	$0.867863\pi$
$84$		0			0
$85$		0			0
$86$	−1.22474	−	0.707107i	−0.132068	−	0.0762493i
$87$		0			0
$88$	−3.46410	+	2.00000i	−0.369274	+	0.213201i
$89$	−2.44949	+	4.24264i	−0.259645	+	0.449719i	−0.966147	−	0.257993i	$-0.916939\pi$
$89$	−2.44949	+	4.24264i	−0.259645	+	0.449719i	0.706502	+	0.707712i	$0.250272\pi$
$90$		0			0
$91$	13.5000	−	2.59808i	1.41518	−	0.272352i
$92$		0			0
$93$		0			0
$94$	−15.0000	+	8.66025i	−1.54713	+	0.893237i
$95$		0			0
$96$		0			0
$97$	10.3923			1.05518			0.527589	−	0.849500i	$-0.323096\pi$
$97$	10.3923			1.05518			0.527589	+	0.849500i	$0.323096\pi$
$98$	1.41421	−	9.79796i	0.142857	−	0.989743i
$99$		0			0
$100$		0			0
$101$	8.57321	+	14.8492i	0.853067	+	1.47755i	0.878427	+	0.477876i	$0.158593\pi$
$101$	8.57321	+	14.8492i	0.853067	+	1.47755i	−0.0253604	+	0.999678i	$0.508073\pi$
$102$		0			0
$103$	4.33013	−	7.50000i	0.426660	−	0.738997i	−0.569914	−	0.821705i	$-0.693023\pi$
$103$	4.33013	−	7.50000i	0.426660	−	0.738997i	0.996574	+	0.0827075i	$0.0263567\pi$
$104$	−14.6969			−1.44115
$105$		0			0
$106$	4.00000			0.388514
$107$	−1.41421	+	2.44949i	−0.136717	+	0.236801i	−0.926252	−	0.376905i	$-0.876988\pi$
$107$	−1.41421	+	2.44949i	−0.136717	+	0.236801i	0.789535	+	0.613706i	$0.210322\pi$
$108$		0			0
$109$	−0.500000	−	0.866025i	−0.0478913	−	0.0829502i	0.841086	−	0.540901i	$-0.181917\pi$
$109$	−0.500000	−	0.866025i	−0.0478913	−	0.0829502i	−0.888977	+	0.457951i	$0.848583\pi$
$110$		0			0
$111$		0			0
$112$	−3.46410	+	10.0000i	−0.327327	+	0.944911i
$113$	1.41421			0.133038			0.0665190	−	0.997785i	$-0.478811\pi$
$113$	1.41421			0.133038			0.0665190	+	0.997785i	$0.478811\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	6.92820			0.637793
$119$	9.79796	−	8.48528i	0.898177	−	0.777844i
$120$		0			0
$121$	−4.50000	+	7.79423i	−0.409091	+	0.708566i
$122$	−4.24264	+	2.44949i	−0.384111	+	0.221766i
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	11.0000i		−	0.976092i	−0.872818	−	0.488046i	$-0.837710\pi$
$127$		−	11.0000i		−	0.976092i	0.872818	−	0.488046i	$-0.162290\pi$
$128$	5.65685	−	9.79796i	0.500000	−	0.866025i
$129$		0			0
$130$		0			0
$131$	−1.22474	+	2.12132i	−0.107006	+	0.185341i	−0.914556	−	0.404459i	$-0.867460\pi$
$131$	−1.22474	+	2.12132i	−0.107006	+	0.185341i	0.807550	+	0.589799i	$0.200793\pi$
$132$		0			0
$133$	4.33013	+	1.50000i	0.375470	+	0.130066i
$134$			15.5563i			1.34386i
$135$		0			0
$136$	−12.0000	+	6.92820i	−1.02899	+	0.594089i
$137$	−5.65685	−	9.79796i	−0.483298	−	0.837096i	0.516518	−	0.856276i	$-0.327228\pi$
$137$	−5.65685	−	9.79796i	−0.483298	−	0.837096i	−0.999816	+	0.0191800i	$0.993894\pi$
$138$		0			0
$139$		−	5.19615i		−	0.440732i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$		−	5.19615i		−	0.440732i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$		0			0
$142$	8.66025	+	5.00000i	0.726752	+	0.419591i
$143$	6.36396	−	3.67423i	0.532181	−	0.307255i
$144$		0			0
$145$		0			0
$146$	2.44949			0.202721
$147$		0			0
$148$		0			0
$149$	−4.89898	−	2.82843i	−0.401340	−	0.231714i	0.285722	−	0.958313i	$-0.407767\pi$
$149$	−4.89898	−	2.82843i	−0.401340	−	0.231714i	−0.687062	+	0.726599i	$0.741100\pi$
$150$		0			0
$151$	11.0000	+	19.0526i	0.895167	+	1.55048i	0.833597	+	0.552372i	$0.186277\pi$
$151$	11.0000	+	19.0526i	0.895167	+	1.55048i	0.0615699	+	0.998103i	$0.480389\pi$
$152$	−4.24264	−	2.44949i	−0.344124	−	0.198680i
$153$		0			0
$154$	−1.00000	−	5.19615i	−0.0805823	−	0.418718i
$155$		0			0
$156$		0			0
$157$	−8.66025	−	15.0000i	−0.691164	−	1.19713i	−0.971457	−	0.237216i	$-0.923765\pi$
$157$	−8.66025	−	15.0000i	−0.691164	−	1.19713i	0.280293	−	0.959914i	$-0.409568\pi$
$158$	−3.53553	−	6.12372i	−0.281272	−	0.487177i
$159$		0			0
$160$		0			0
$161$	4.89898	−	14.1421i	0.386094	−	1.11456i
$162$		0			0
$163$	8.66025	+	5.00000i	0.678323	+	0.391630i	0.799223	−	0.601035i	$-0.205245\pi$
$163$	8.66025	+	5.00000i	0.678323	+	0.391630i	−0.120900	+	0.992665i	$0.538578\pi$
$164$		0			0
$165$		0			0
$166$	9.00000	+	5.19615i	0.698535	+	0.403300i
$167$			7.34847i			0.568642i	0.958729	+	0.284321i	$0.0917681\pi$
$167$			7.34847i			0.568642i	−0.958729	+	0.284321i	$0.908232\pi$
$168$		0			0
$169$	14.0000			1.07692
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.48528	−	4.89898i	−0.645124	−	0.372463i	0.141462	−	0.989944i	$-0.454820\pi$
$173$	−8.48528	−	4.89898i	−0.645124	−	0.372463i	−0.786586	+	0.617481i	$0.788153\pi$
$174$		0			0
$175$		0			0
$176$			5.65685i			0.426401i
$177$		0			0
$178$	3.46410	+	6.00000i	0.259645	+	0.449719i
$179$	8.57321	−	4.94975i	0.640792	−	0.369961i	−0.144127	−	0.989559i	$-0.546038\pi$
$179$	8.57321	−	4.94975i	0.640792	−	0.369961i	0.784920	+	0.619598i	$0.212704\pi$
$180$		0			0
$181$		−	15.5885i		−	1.15868i	−0.815086	−	0.579340i	$-0.803310\pi$
$181$		−	15.5885i		−	1.15868i	0.815086	−	0.579340i	$-0.196690\pi$
$182$	6.36396	−	18.3712i	0.471728	−	1.36176i
$183$		0			0
$184$	−8.00000	+	13.8564i	−0.589768	+	1.02151i
$185$		0			0
$186$		0			0
$187$	3.46410	−	6.00000i	0.253320	−	0.438763i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.22474	+	0.707107i	0.0886194	+	0.0511645i	0.543655	−	0.839309i	$-0.317040\pi$
$191$	1.22474	+	0.707107i	0.0886194	+	0.0511645i	−0.455035	+	0.890473i	$0.650373\pi$
$192$		0			0
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	−0.116289	−	0.993215i	$-0.537100\pi$
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	0.802005	+	0.597317i	$0.203766\pi$
$194$	7.34847	−	12.7279i	0.527589	−	0.913812i
$195$		0			0
$196$		0			0
$197$	19.7990			1.41062			0.705310	−	0.708899i	$-0.250808\pi$
$197$	19.7990			1.41062			0.705310	+	0.708899i	$0.250808\pi$
$198$		0			0
$199$	12.0000	−	6.92820i	0.850657	−	0.491127i	−0.0102152	−	0.999948i	$-0.503252\pi$
$199$	12.0000	−	6.92820i	0.850657	−	0.491127i	0.860873	+	0.508821i	$0.169918\pi$
$200$		0			0
$201$		0			0
$202$	24.2487			1.70613
$203$	1.41421	+	7.34847i	0.0992583	+	0.515761i
$204$		0			0
$205$		0			0
$206$	−6.12372	−	10.6066i	−0.426660	−	0.738997i
$207$		0			0
$208$	−10.3923	+	18.0000i	−0.720577	+	1.24808i
$209$	2.44949			0.169435
$210$		0			0
$211$	−22.0000			−1.51454			−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000			−1.51454			−0.757271	+	0.653101i	$0.773468\pi$
$212$		0			0
$213$		0			0
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$		0			0
$216$		0			0
$217$	−3.46410	+	3.00000i	−0.235159	+	0.203653i
$218$	−1.41421			−0.0957826
$219$		0			0
$220$		0			0
$221$	22.0454	−	12.7279i	1.48293	−	0.856173i
$222$		0			0
$223$	20.7846			1.39184			0.695920	−	0.718119i	$-0.254997\pi$
$223$	20.7846			1.39184			0.695920	+	0.718119i	$0.254997\pi$
$224$		0			0
$225$		0			0
$226$	1.00000	−	1.73205i	0.0665190	−	0.115214i
$227$	−23.3345	+	13.4722i	−1.54877	+	0.894181i	−0.550530	+	0.834815i	$0.685575\pi$
$227$	−23.3345	+	13.4722i	−1.54877	+	0.894181i	−0.998236	+	0.0593658i	$0.981092\pi$
$228$		0			0
$229$	−19.5000	−	11.2583i	−1.28860	−	0.743971i	−0.310192	−	0.950674i	$-0.600393\pi$
$229$	−19.5000	−	11.2583i	−1.28860	−	0.743971i	−0.978404	+	0.206702i	$0.933727\pi$
$230$		0			0
$231$		0			0
$232$		−	8.00000i		−	0.525226i
$233$	−4.94975	+	8.57321i	−0.324269	+	0.561650i	−0.981364	−	0.192158i	$-0.938452\pi$
$233$	−4.94975	+	8.57321i	−0.324269	+	0.561650i	0.657095	+	0.753807i	$0.271785\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−3.46410	−	18.0000i	−0.224544	−	1.16677i
$239$			26.8701i			1.73808i	0.494742	+	0.869040i	$0.335262\pi$
$239$			26.8701i			1.73808i	−0.494742	+	0.869040i	$0.664738\pi$
$240$		0			0
$241$	−12.0000	+	6.92820i	−0.772988	+	0.446285i	−0.833939	−	0.551856i	$-0.813920\pi$
$241$	−12.0000	+	6.92820i	−0.772988	+	0.446285i	0.0609515	+	0.998141i	$0.480586\pi$
$242$	6.36396	+	11.0227i	0.409091	+	0.708566i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.79423	+	4.50000i	0.495935	+	0.286328i
$248$	4.24264	−	2.44949i	0.269408	−	0.155543i
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		−	8.00000i		−	0.502956i
$254$	−13.4722	−	7.77817i	−0.845321	−	0.488046i
$255$		0			0
$256$		0			0
$257$	2.12132	+	1.22474i	0.132324	+	0.0763975i	0.564701	−	0.825296i	$-0.308992\pi$
$257$	2.12132	+	1.22474i	0.132324	+	0.0763975i	−0.432377	+	0.901693i	$0.642325\pi$
$258$		0			0
$259$	2.50000	+	0.866025i	0.155342	+	0.0538122i
$260$		0			0
$261$		0			0
$262$	1.73205	+	3.00000i	0.107006	+	0.185341i
$263$	−7.07107	−	12.2474i	−0.436021	−	0.755210i	0.561358	−	0.827573i	$-0.310279\pi$
$263$	−7.07107	−	12.2474i	−0.436021	−	0.755210i	−0.997378	+	0.0723633i	$0.976946\pi$
$264$		0			0
$265$		0			0
$266$	4.89898	−	4.24264i	0.300376	−	0.260133i
$267$		0			0
$268$		0			0
$269$	−8.57321	−	14.8492i	−0.522718	−	0.905374i	−0.999651	−	0.0264343i	$-0.991585\pi$
$269$	−8.57321	−	14.8492i	−0.522718	−	0.905374i	0.476932	−	0.878940i	$-0.341749\pi$
$270$		0			0
$271$	−12.0000	−	6.92820i	−0.728948	−	0.420858i	0.0890891	−	0.996024i	$-0.471604\pi$
$271$	−12.0000	−	6.92820i	−0.728948	−	0.420858i	−0.818037	+	0.575165i	$0.804938\pi$
$272$			19.5959i			1.18818i
$273$		0			0
$274$	−16.0000			−0.966595
$275$		0			0
$276$		0			0
$277$	−19.9186	+	11.5000i	−1.19679	+	0.690968i	−0.959839	−	0.280553i	$-0.909482\pi$
$277$	−19.9186	+	11.5000i	−1.19679	+	0.690968i	−0.236953	+	0.971521i	$0.576149\pi$
$278$	−6.36396	−	3.67423i	−0.381685	−	0.220366i
$279$		0			0
$280$		0			0
$281$		−	22.6274i		−	1.34984i	−0.737892	−	0.674919i	$-0.764178\pi$
$281$		−	22.6274i		−	1.34984i	0.737892	−	0.674919i	$-0.235822\pi$
$282$		0			0
$283$	0.866025	+	1.50000i	0.0514799	+	0.0891657i	0.890617	−	0.454754i	$-0.150273\pi$
$283$	0.866025	+	1.50000i	0.0514799	+	0.0891657i	−0.839137	+	0.543920i	$0.816940\pi$
$284$		0			0
$285$		0			0
$286$		−	10.3923i		−	0.614510i
$287$	19.0919	−	3.67423i	1.12696	−	0.216883i
$288$		0			0
$289$	3.50000	−	6.06218i	0.205882	−	0.356599i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			14.6969i			0.858604i	0.903161	+	0.429302i	$0.141240\pi$
$293$			14.6969i			0.858604i	−0.903161	+	0.429302i	$0.858760\pi$
$294$		0			0
$295$		0			0
$296$	−2.44949	−	1.41421i	−0.142374	−	0.0821995i
$297$		0			0
$298$	−6.92820	+	4.00000i	−0.401340	+	0.231714i
$299$	14.6969	−	25.4558i	0.849946	−	1.47215i
$300$		0			0
$301$	0.500000	+	2.59808i	0.0288195	+	0.149751i
$302$	31.1127			1.79033
$303$		0			0
$304$	−6.00000	+	3.46410i	−0.344124	+	0.198680i
$305$		0			0
$306$		0			0
$307$	15.5885			0.889680			0.444840	−	0.895610i	$-0.353260\pi$
$307$	15.5885			0.889680			0.444840	+	0.895610i	$0.353260\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.57321	+	14.8492i	0.486142	+	0.842023i	0.999873	−	0.0159282i	$-0.00507031\pi$
$311$	8.57321	+	14.8492i	0.486142	+	0.842023i	−0.513731	+	0.857951i	$0.671737\pi$
$312$		0			0
$313$	−6.06218	+	10.5000i	−0.342655	+	0.593495i	−0.984925	−	0.172983i	$-0.944659\pi$
$313$	−6.06218	+	10.5000i	−0.342655	+	0.593495i	0.642270	+	0.766478i	$0.277993\pi$
$314$	−24.4949			−1.38233
$315$		0			0
$316$		0			0
$317$	7.07107	−	12.2474i	0.397151	−	0.687885i	−0.596222	−	0.802819i	$-0.703332\pi$
$317$	7.07107	−	12.2474i	0.397151	−	0.687885i	0.993373	+	0.114934i	$0.0366657\pi$
$318$		0			0
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$		0			0
$321$		0			0
$322$	−13.8564	−	16.0000i	−0.772187	−	0.891645i
$323$	8.48528			0.472134
$324$		0			0
$325$		0			0
$326$	12.2474	−	7.07107i	0.678323	−	0.391630i
$327$		0			0
$328$	−20.7846			−1.14764
$329$	30.6186	+	10.6066i	1.68806	+	0.584761i
$330$		0			0
$331$	15.5000	−	26.8468i	0.851957	−	1.47563i	−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	15.5000	−	26.8468i	0.851957	−	1.47563i	0.879440	−	0.476011i	$-0.157918\pi$
$332$		0			0
$333$		0			0
$334$	9.00000	+	5.19615i	0.492458	+	0.284321i
$335$		0			0
$336$		0			0
$337$		−	23.0000i		−	1.25289i	−0.779466	−	0.626445i	$-0.784509\pi$
$337$		−	23.0000i		−	1.25289i	0.779466	−	0.626445i	$-0.215491\pi$
$338$	9.89949	−	17.1464i	0.538462	−	0.932643i
$339$		0			0
$340$		0			0
$341$	−1.22474	+	2.12132i	−0.0663237	+	0.114876i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		−	2.82843i		−	0.152499i
$345$		0			0
$346$	−12.0000	+	6.92820i	−0.645124	+	0.372463i
$347$	15.5563	+	26.9444i	0.835109	+	1.44645i	0.893942	+	0.448183i	$0.147929\pi$
$347$	15.5563	+	26.9444i	0.835109	+	1.44645i	−0.0588334	+	0.998268i	$0.518738\pi$
$348$		0			0
$349$		−	10.3923i		−	0.556287i	−0.960539	−	0.278144i	$-0.910281\pi$
$349$		−	10.3923i		−	0.556287i	0.960539	−	0.278144i	$-0.0897191\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.8492	+	8.57321i	−0.790345	+	0.456306i	−0.840084	−	0.542456i	$-0.817494\pi$
$353$	−14.8492	+	8.57321i	−0.790345	+	0.456306i	0.0497387	+	0.998762i	$0.484161\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		−	14.0000i		−	0.739923i
$359$	24.4949	+	14.1421i	1.29279	+	0.746393i	0.979148	−	0.203148i	$-0.0651171\pi$
$359$	24.4949	+	14.1421i	1.29279	+	0.746393i	0.313643	+	0.949541i	$0.398450\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	−19.0919	−	11.0227i	−1.00345	−	0.579340i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.866025	−	1.50000i	−0.0452062	−	0.0782994i	0.842537	−	0.538639i	$-0.181061\pi$
$367$	−0.866025	−	1.50000i	−0.0452062	−	0.0782994i	−0.887743	+	0.460339i	$0.847728\pi$
$368$	11.3137	+	19.5959i	0.589768	+	1.02151i
$369$		0			0
$370$		0			0
$371$	−4.89898	−	5.65685i	−0.254342	−	0.293689i
$372$		0			0
$373$	−25.1147	−	14.5000i	−1.30039	−	0.750782i	−0.319921	−	0.947444i	$-0.603656\pi$
$373$	−25.1147	−	14.5000i	−1.30039	−	0.750782i	−0.980471	+	0.196663i	$0.936990\pi$
$374$	−4.89898	−	8.48528i	−0.253320	−	0.438763i
$375$		0			0
$376$	−30.0000	−	17.3205i	−1.54713	−	0.893237i
$377$			14.6969i			0.756931i
$378$		0			0
$379$	7.00000			0.359566			0.179783	−	0.983706i	$-0.442460\pi$
$379$	7.00000			0.359566			0.179783	+	0.983706i	$0.442460\pi$
$380$		0			0
$381$		0			0
$382$	1.73205	−	1.00000i	0.0886194	−	0.0511645i
$383$	16.9706	+	9.79796i	0.867155	+	0.500652i	0.866402	−	0.499347i	$-0.166427\pi$
$383$	16.9706	+	9.79796i	0.867155	+	0.500652i	0.000753393		1.00000i	$0.499760\pi$
$384$		0			0
$385$		0			0
$386$		−	15.5563i		−	0.791797i
$387$		0			0
$388$		0			0
$389$	23.2702	−	13.4350i	1.17984	−	0.681183i	0.223865	−	0.974620i	$-0.428132\pi$
$389$	23.2702	−	13.4350i	1.17984	−	0.681183i	0.955978	+	0.293437i	$0.0947991\pi$
$390$		0			0
$391$		−	27.7128i		−	1.40150i
$392$	18.3848	−	7.34847i	0.928571	−	0.371154i
$393$		0			0
$394$	14.0000	−	24.2487i	0.705310	−	1.22163i
$395$		0			0
$396$		0			0
$397$	0.866025	−	1.50000i	0.0434646	−	0.0752828i	−0.843475	−	0.537169i	$-0.819494\pi$
$397$	0.866025	−	1.50000i	0.0434646	−	0.0752828i	0.886939	+	0.461886i	$0.152827\pi$
$398$		−	19.5959i		−	0.982255i
$399$		0			0
$400$		0			0
$401$	−17.1464	−	9.89949i	−0.856252	−	0.494357i	0.00650355	−	0.999979i	$-0.497930\pi$
$401$	−17.1464	−	9.89949i	−0.856252	−	0.494357i	−0.862755	+	0.505622i	$0.831263\pi$
$402$		0			0
$403$	−7.79423	+	4.50000i	−0.388258	+	0.224161i
$404$		0			0
$405$		0			0
$406$	10.0000	+	3.46410i	0.496292	+	0.171920i
$407$	1.41421			0.0701000
$408$		0			0
$409$	−28.5000	+	16.4545i	−1.40923	+	0.813622i	−0.995314	−	0.0966915i	$-0.969174\pi$
$409$	−28.5000	+	16.4545i	−1.40923	+	0.813622i	−0.413920	+	0.910313i	$0.635841\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.48528	−	9.79796i	−0.417533	−	0.482126i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	1.73205	−	3.00000i	0.0847174	−	0.146735i
$419$	−36.7423			−1.79498			−0.897491	−	0.441034i	$-0.854612\pi$
$419$	−36.7423			−1.79498			−0.897491	+	0.441034i	$0.854612\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$	−15.5563	+	26.9444i	−0.757271	+	1.31163i
$423$		0			0
$424$	4.00000	+	6.92820i	0.194257	+	0.336463i
$425$		0			0
$426$		0			0
$427$	8.66025	+	3.00000i	0.419099	+	0.145180i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.4722	−	7.77817i	0.648933	−	0.374661i	−0.139114	−	0.990276i	$-0.544426\pi$
$431$	13.4722	−	7.77817i	0.648933	−	0.374661i	0.788047	+	0.615615i	$0.211092\pi$
$432$		0			0
$433$	15.5885			0.749133			0.374567	−	0.927200i	$-0.377791\pi$
$433$	15.5885			0.749133			0.374567	+	0.927200i	$0.377791\pi$
$434$	1.22474	+	6.36396i	0.0587896	+	0.305480i
$435$		0			0
$436$		0			0
$437$	8.48528	−	4.89898i	0.405906	−	0.234350i
$438$		0			0
$439$	−24.0000	−	13.8564i	−1.14546	−	0.661330i	−0.197681	−	0.980266i	$-0.563341\pi$
$439$	−24.0000	−	13.8564i	−1.14546	−	0.661330i	−0.947776	+	0.318936i	$0.896674\pi$
$440$		0			0
$441$		0			0
$442$		−	36.0000i		−	1.71235i
$443$	−19.7990	+	34.2929i	−0.940678	+	1.62930i	−0.176497	+	0.984301i	$0.556477\pi$
$443$	−19.7990	+	34.2929i	−0.940678	+	1.62930i	−0.764181	+	0.645002i	$0.776857\pi$
$444$		0			0
$445$		0			0
$446$	14.6969	−	25.4558i	0.695920	−	1.20537i
$447$		0			0
$448$	−20.7846	+	4.00000i	−0.981981	+	0.188982i
$449$		−	7.07107i		−	0.333704i	−0.985982	−	0.166852i	$-0.946640\pi$
$449$		−	7.07107i		−	0.333704i	0.985982	−	0.166852i	$-0.0533603\pi$
$450$		0			0
$451$	9.00000	−	5.19615i	0.423793	−	0.244677i
$452$		0			0
$453$		0			0
$454$			38.1051i			1.78836i
$455$		0			0
$456$		0			0
$457$	4.33013	+	2.50000i	0.202555	+	0.116945i	0.597847	−	0.801611i	$-0.296023\pi$
$457$	4.33013	+	2.50000i	0.202555	+	0.116945i	−0.395292	+	0.918556i	$0.629357\pi$
$458$	−27.5772	+	15.9217i	−1.28860	+	0.743971i
$459$		0			0
$460$		0			0
$461$	−14.6969			−0.684505			−0.342252	−	0.939608i	$-0.611190\pi$
$461$	−14.6969			−0.684505			−0.342252	+	0.939608i	$0.611190\pi$
$462$		0			0
$463$		−	13.0000i		−	0.604161i	−0.953282	−	0.302081i	$-0.902319\pi$
$463$		−	13.0000i		−	0.604161i	0.953282	−	0.302081i	$-0.0976812\pi$
$464$	−9.79796	−	5.65685i	−0.454859	−	0.262613i
$465$		0			0
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−23.3345	−	13.4722i	−1.07979	−	0.623419i	−0.148952	−	0.988844i	$-0.547590\pi$
$467$	−23.3345	−	13.4722i	−1.07979	−	0.623419i	−0.930841	+	0.365426i	$0.880923\pi$
$468$		0			0
$469$	22.0000	−	19.0526i	1.01587	−	0.879765i
$470$		0			0
$471$		0			0
$472$	6.92820	+	12.0000i	0.318896	+	0.552345i
$473$	0.707107	+	1.22474i	0.0325128	+	0.0563138i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	32.9090	+	19.0000i	1.50522	+	0.869040i
$479$	2.44949	+	4.24264i	0.111920	+	0.193851i	0.916544	−	0.399933i	$-0.130967\pi$
$479$	2.44949	+	4.24264i	0.111920	+	0.193851i	−0.804624	+	0.593784i	$0.797633\pi$
$480$		0			0
$481$	4.50000	+	2.59808i	0.205182	+	0.118462i
$482$			19.5959i			0.892570i
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−14.7224	+	8.50000i	−0.667137	+	0.385172i	−0.794991	−	0.606621i	$-0.792524\pi$
$487$	−14.7224	+	8.50000i	−0.667137	+	0.385172i	0.127854	+	0.991793i	$0.459191\pi$
$488$	−8.48528	−	4.89898i	−0.384111	−	0.221766i
$489$		0			0
$490$		0			0
$491$			11.3137i			0.510581i	0.966864	+	0.255290i	$0.0821710\pi$
$491$			11.3137i			0.510581i	−0.966864	+	0.255290i	$0.917829\pi$
$492$		0			0
$493$	6.92820	+	12.0000i	0.312031	+	0.540453i
$494$	11.0227	−	6.36396i	0.495935	−	0.286328i
$495$		0			0
$496$		−	6.92820i		−	0.311086i
$497$	−3.53553	−	18.3712i	−0.158590	−	0.824060i
$498$		0			0
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	0.437955	+	0.898997i	$0.355703\pi$
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	−0.997532	+	0.0702185i	$0.977630\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			22.0454i			0.982956i	0.870890	+	0.491478i	$0.163543\pi$
$503$			22.0454i			0.982956i	−0.870890	+	0.491478i	$0.836457\pi$
$504$		0			0
$505$		0			0
$506$	−9.79796	−	5.65685i	−0.435572	−	0.251478i
$507$		0			0
$508$		0			0
$509$	1.22474	−	2.12132i	0.0542859	−	0.0940259i	−0.837605	−	0.546276i	$-0.816045\pi$
$509$	1.22474	−	2.12132i	0.0542859	−	0.0940259i	0.891891	+	0.452250i	$0.149378\pi$
$510$		0			0
$511$	−3.00000	−	3.46410i	−0.132712	−	0.153243i
$512$	22.6274			1.00000
$513$		0			0
$514$	3.00000	−	1.73205i	0.132324	−	0.0763975i
$515$		0			0
$516$		0			0
$517$	17.3205			0.761755
$518$	2.82843	−	2.44949i	0.124274	−	0.107624i
$519$		0			0
$520$		0			0
$521$	−2.44949	−	4.24264i	−0.107314	−	0.185873i	0.807367	−	0.590049i	$-0.200892\pi$
$521$	−2.44949	−	4.24264i	−0.107314	−	0.185873i	−0.914681	+	0.404176i	$0.867558\pi$
$522$		0			0
$523$	−0.866025	+	1.50000i	−0.0378686	+	0.0655904i	−0.884339	−	0.466846i	$-0.845390\pi$
$523$	−0.866025	+	1.50000i	−0.0378686	+	0.0655904i	0.846470	+	0.532437i	$0.178724\pi$
$524$		0			0
$525$		0			0
$526$	−20.0000			−0.872041
$527$	−4.24264	+	7.34847i	−0.184812	+	0.320104i
$528$		0			0
$529$	−4.50000	−	7.79423i	−0.195652	−	0.338880i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	38.1838			1.65392
$534$		0			0
$535$		0			0
$536$	−26.9444	+	15.5563i	−1.16382	+	0.671932i
$537$		0			0
$538$	−24.2487			−1.04544
$539$	−6.12372	+	7.77817i	−0.263767	+	0.335030i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$	−16.9706	+	9.79796i	−0.728948	+	0.420858i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$			10.0000i			0.427569i	0.976881	+	0.213785i	$0.0685791\pi$
$547$			10.0000i			0.427569i	−0.976881	+	0.213785i	$0.931421\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.44949	+	4.24264i	−0.104352	+	0.180743i
$552$		0			0
$553$	−4.33013	+	12.5000i	−0.184136	+	0.531554i
$554$			32.5269i			1.38194i
$555$		0			0
$556$		0			0
$557$	−7.77817	−	13.4722i	−0.329572	−	0.570835i	0.652855	−	0.757483i	$-0.273571\pi$
$557$	−7.77817	−	13.4722i	−0.329572	−	0.570835i	−0.982427	+	0.186648i	$0.940238\pi$
$558$		0			0
$559$			5.19615i			0.219774i
$560$		0			0
$561$		0			0
$562$	−27.7128	−	16.0000i	−1.16899	−	0.674919i
$563$	23.3345	−	13.4722i	0.983433	−	0.567785i	0.0801281	−	0.996785i	$-0.474467\pi$
$563$	23.3345	−	13.4722i	0.983433	−	0.567785i	0.903305	+	0.428999i	$0.141134\pi$
$564$		0			0
$565$		0			0
$566$	2.44949			0.102960
$567$		0			0
$568$			20.0000i			0.839181i
$569$	−1.22474	−	0.707107i	−0.0513440	−	0.0296435i	0.474108	−	0.880467i	$-0.342771\pi$
$569$	−1.22474	−	0.707107i	−0.0513440	−	0.0296435i	−0.525452	+	0.850823i	$0.676104\pi$
$570$		0			0
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	0.727690	−	0.685907i	$-0.240594\pi$
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	−0.957857	+	0.287244i	$0.907261\pi$
$572$		0			0
$573$		0			0
$574$	9.00000	−	25.9808i	0.375653	−	1.08442i
$575$		0			0
$576$		0			0
$577$	−0.866025	−	1.50000i	−0.0360531	−	0.0624458i	0.847436	−	0.530898i	$-0.178145\pi$
$577$	−0.866025	−	1.50000i	−0.0360531	−	0.0624458i	−0.883489	+	0.468452i	$0.844812\pi$
$578$	−4.94975	−	8.57321i	−0.205882	−	0.356599i
$579$		0			0
$580$		0			0
$581$	−3.67423	−	19.0919i	−0.152433	−	0.792065i
$582$		0			0
$583$	−3.46410	−	2.00000i	−0.143468	−	0.0828315i
$584$	2.44949	+	4.24264i	0.101361	+	0.175562i
$585$		0			0
$586$	18.0000	+	10.3923i	0.743573	+	0.429302i
$587$			14.6969i			0.606608i	0.952894	+	0.303304i	$0.0980897\pi$
$587$			14.6969i			0.606608i	−0.952894	+	0.303304i	$0.901910\pi$
$588$		0			0
$589$	−3.00000			−0.123613
$590$		0			0
$591$		0			0
$592$	−3.46410	+	2.00000i	−0.142374	+	0.0821995i
$593$	−14.8492	−	8.57321i	−0.609785	−	0.352060i	0.163096	−	0.986610i	$-0.447852\pi$
$593$	−14.8492	−	8.57321i	−0.609785	−	0.352060i	−0.772881	+	0.634550i	$0.781185\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−20.7846	−	36.0000i	−0.849946	−	1.47215i
$599$	4.89898	−	2.82843i	0.200167	−	0.115566i	−0.396566	−	0.918006i	$-0.629798\pi$
$599$	4.89898	−	2.82843i	0.200167	−	0.115566i	0.596733	+	0.802440i	$0.296465\pi$
$600$		0			0
$601$			25.9808i			1.05978i	0.848067	+	0.529889i	$0.177766\pi$
$601$			25.9808i			1.05978i	−0.848067	+	0.529889i	$0.822234\pi$
$602$	3.53553	+	1.22474i	0.144098	+	0.0499169i
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−19.9186	+	34.5000i	−0.808470	+	1.40031i	0.105453	+	0.994424i	$0.466371\pi$
$607$	−19.9186	+	34.5000i	−0.808470	+	1.40031i	−0.913923	+	0.405887i	$0.866962\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	55.1135	+	31.8198i	2.22965	+	1.28729i
$612$		0			0
$613$	6.92820	−	4.00000i	0.279827	−	0.161558i	−0.353518	−	0.935428i	$-0.615015\pi$
$613$	6.92820	−	4.00000i	0.279827	−	0.161558i	0.633345	+	0.773869i	$0.281681\pi$
$614$	11.0227	−	19.0919i	0.444840	−	0.770486i
$615$		0			0
$616$	8.00000	−	6.92820i	0.322329	−	0.279145i
$617$	24.0416			0.967880			0.483940	−	0.875101i	$-0.339205\pi$
$617$	24.0416			0.967880			0.483940	+	0.875101i	$0.339205\pi$
$618$		0			0
$619$	25.5000	−	14.7224i	1.02493	−	0.591744i	0.109403	−	0.993997i	$-0.465106\pi$
$619$	25.5000	−	14.7224i	1.02493	−	0.591744i	0.915529	+	0.402253i	$0.131773\pi$
$620$		0			0
$621$		0			0
$622$	24.2487			0.972285
$623$	4.24264	−	12.2474i	0.169978	−	0.490684i
$624$		0			0
$625$		0			0
$626$	8.57321	+	14.8492i	0.342655	+	0.593495i
$627$		0			0
$628$		0			0
$629$	4.89898			0.195335
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$	7.07107	−	12.2474i	0.281272	−	0.487177i
$633$		0			0
$634$	−10.0000	−	17.3205i	−0.397151	−	0.687885i
$635$		0			0
$636$		0			0
$637$	−33.7750	+	13.5000i	−1.33821	+	0.534889i
$638$	5.65685			0.223957
$639$		0			0
$640$		0			0
$641$	−12.2474	+	7.07107i	−0.483745	+	0.279290i	−0.721976	−	0.691918i	$-0.756766\pi$
$641$	−12.2474	+	7.07107i	−0.483745	+	0.279290i	0.238231	+	0.971209i	$0.423433\pi$
$642$		0			0
$643$	25.9808			1.02458			0.512291	−	0.858812i	$-0.328797\pi$
$643$	25.9808			1.02458			0.512291	+	0.858812i	$0.328797\pi$
$644$		0			0
$645$		0			0
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	14.8492	−	8.57321i	0.583784	−	0.337048i	−0.178852	−	0.983876i	$-0.557238\pi$
$647$	14.8492	−	8.57321i	0.583784	−	0.337048i	0.762636	+	0.646828i	$0.223905\pi$
$648$		0			0
$649$	−6.00000	−	3.46410i	−0.235521	−	0.135978i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.53553	−	6.12372i	0.138356	−	0.239640i	−0.788518	−	0.615011i	$-0.789151\pi$
$653$	3.53553	−	6.12372i	0.138356	−	0.239640i	0.926875	+	0.375371i	$0.122485\pi$
$654$		0			0
$655$		0			0
$656$	−14.6969	+	25.4558i	−0.573819	+	0.993884i
$657$		0			0
$658$	34.6410	−	30.0000i	1.35045	−	1.16952i
$659$			22.6274i			0.881439i	0.897645	+	0.440720i	$0.145277\pi$
$659$			22.6274i			0.881439i	−0.897645	+	0.440720i	$0.854723\pi$
$660$		0			0
$661$	−25.5000	+	14.7224i	−0.991835	+	0.572636i	−0.905822	−	0.423658i	$-0.860746\pi$
$661$	−25.5000	+	14.7224i	−0.991835	+	0.572636i	−0.0860127	+	0.996294i	$0.527413\pi$
$662$	−21.9203	−	37.9671i	−0.851957	−	1.47563i
$663$		0			0
$664$			20.7846i			0.806599i
$665$		0			0
$666$		0			0
$667$	13.8564	+	8.00000i	0.536522	+	0.309761i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.89898			0.189123
$672$		0			0
$673$			35.0000i			1.34915i	0.738206	+	0.674575i	$0.235673\pi$
$673$			35.0000i			1.34915i	−0.738206	+	0.674575i	$0.764327\pi$
$674$	−28.1691	−	16.2635i	−1.08503	−	0.626445i
$675$		0			0
$676$		0			0
$677$	8.48528	+	4.89898i	0.326116	+	0.188283i	0.654115	−	0.756395i	$-0.273041\pi$
$677$	8.48528	+	4.89898i	0.326116	+	0.188283i	−0.327999	+	0.944678i	$0.606374\pi$
$678$		0			0
$679$	−27.0000	+	5.19615i	−1.03616	+	0.199410i
$680$		0			0
$681$		0			0
$682$	1.73205	+	3.00000i	0.0663237	+	0.114876i
$683$	−24.0416	−	41.6413i	−0.919927	−	1.59336i	−0.799522	−	0.600636i	$-0.794914\pi$
$683$	−24.0416	−	41.6413i	−0.919927	−	1.59336i	−0.120405	−	0.992725i	$-0.538419\pi$
$684$		0			0
$685$		0			0
$686$	1.22474	+	26.1630i	0.0467610	+	0.998906i
$687$		0			0
$688$	−3.46410	−	2.00000i	−0.132068	−	0.0762493i
$689$	−7.34847	−	12.7279i	−0.279954	−	0.484895i
$690$		0			0
$691$	37.5000	+	21.6506i	1.42657	+	0.823629i	0.996848	−	0.0793336i	$-0.0252792\pi$
$691$	37.5000	+	21.6506i	1.42657	+	0.823629i	0.429719	+	0.902963i	$0.358613\pi$
$692$		0			0
$693$		0			0
$694$	44.0000			1.67022
$695$		0			0
$696$		0			0
$697$	31.1769	−	18.0000i	1.18091	−	0.681799i
$698$	−12.7279	−	7.34847i	−0.481759	−	0.278144i
$699$		0			0
$700$		0			0
$701$		−	5.65685i		−	0.213656i	−0.994277	−	0.106828i	$-0.965931\pi$
$701$		−	5.65685i		−	0.213656i	0.994277	−	0.106828i	$-0.0340695\pi$
$702$		0			0
$703$	0.866025	+	1.50000i	0.0326628	+	0.0565736i
$704$	−9.79796	+	5.65685i	−0.369274	+	0.213201i
$705$		0			0
$706$			24.2487i			0.912612i
$707$	−29.6985	−	34.2929i	−1.11693	−	1.28972i
$708$		0			0
$709$	−20.0000	+	34.6410i	−0.751116	+	1.30097i	0.196167	+	0.980571i	$0.437151\pi$
$709$	−20.0000	+	34.6410i	−0.751116	+	1.30097i	−0.947282	+	0.320400i	$0.896183\pi$
$710$		0			0
$711$		0			0
$712$	−6.92820	+	12.0000i	−0.259645	+	0.449719i
$713$			9.79796i			0.366936i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	34.6410	−	20.0000i	1.29279	−	0.746393i
$719$	−13.4722	+	23.3345i	−0.502428	+	0.870231i	0.497568	+	0.867425i	$0.334226\pi$
$719$	−13.4722	+	23.3345i	−0.502428	+	0.870231i	−0.999996	+	0.00280593i	$0.999107\pi$
$720$		0			0
$721$	−7.50000	+	21.6506i	−0.279315	+	0.806312i
$722$	−22.6274			−0.842105
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	25.9808			0.963573			0.481787	−	0.876289i	$-0.339988\pi$
$727$	25.9808			0.963573			0.481787	+	0.876289i	$0.339988\pi$
$728$	38.1838	−	7.34847i	1.41518	−	0.272352i
$729$		0			0
$730$		0			0
$731$	2.44949	+	4.24264i	0.0905977	+	0.156920i
$732$		0			0
$733$	19.9186	−	34.5000i	0.735710	−	1.27429i	−0.218702	−	0.975792i	$-0.570182\pi$
$733$	19.9186	−	34.5000i	0.735710	−	1.27429i	0.954411	−	0.298495i	$-0.0964845\pi$
$734$	−2.44949			−0.0904123
$735$		0			0
$736$		0			0
$737$	7.77817	−	13.4722i	0.286513	−	0.496255i
$738$		0			0
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	0.856683	−	0.515844i	$-0.172522\pi$
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	−0.875075	+	0.483987i	$0.839188\pi$
$740$		0			0
$741$		0			0
$742$	−10.3923	+	2.00000i	−0.381514	+	0.0734223i
$743$	−24.0416			−0.882002			−0.441001	−	0.897507i	$-0.645376\pi$
$743$	−24.0416			−0.882002			−0.441001	+	0.897507i	$0.645376\pi$
$744$		0			0
$745$		0			0
$746$	−35.5176	+	20.5061i	−1.30039	+	0.750782i
$747$		0			0
$748$		0			0
$749$	2.44949	−	7.07107i	0.0895024	−	0.258371i
$750$		0			0
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$	−42.4264	+	24.4949i	−1.54713	+	0.893237i
$753$		0			0
$754$	18.0000	+	10.3923i	0.655521	+	0.378465i
$755$		0			0
$756$		0			0
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$	4.94975	−	8.57321i	0.179783	−	0.311393i
$759$		0			0
$760$		0			0
$761$	−12.2474	+	21.2132i	−0.443970	+	0.768978i	−0.997980	−	0.0635319i	$-0.979764\pi$
$761$	−12.2474	+	21.2132i	−0.443970	+	0.768978i	0.554010	+	0.832510i	$0.313097\pi$
$762$		0			0
$763$	1.73205	+	2.00000i	0.0627044	+	0.0724049i
$764$		0			0
$765$		0			0
$766$	24.0000	−	13.8564i	0.867155	−	0.500652i
$767$	−12.7279	−	22.0454i	−0.459579	−	0.796014i
$768$		0			0
$769$			25.9808i			0.936890i	0.883493	+	0.468445i	$0.155186\pi$
$769$			25.9808i			0.936890i	−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	23.3345	−	13.4722i	0.839284	−	0.484561i	−0.0177365	−	0.999843i	$-0.505646\pi$
$773$	23.3345	−	13.4722i	0.839284	−	0.484561i	0.857021	+	0.515282i	$0.172313\pi$
$774$		0			0
$775$		0			0
$776$	29.3939			1.05518
$777$		0			0
$778$		−	38.0000i		−	1.36237i
$779$	11.0227	+	6.36396i	0.394929	+	0.228013i
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$	−33.9411	−	19.5959i	−1.21373	−	0.700749i
$783$		0			0
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$		0			0
$786$		0			0
$787$	22.5167	+	39.0000i	0.802632	+	1.39020i	0.917878	+	0.396863i	$0.129901\pi$
$787$	22.5167	+	39.0000i	0.802632	+	1.39020i	−0.115246	+	0.993337i	$0.536766\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.67423	+	0.707107i	−0.130641	+	0.0251418i
$792$		0			0
$793$	15.5885	+	9.00000i	0.553562	+	0.319599i
$794$	−1.22474	−	2.12132i	−0.0434646	−	0.0752828i
$795$		0			0
$796$		0			0
$797$			29.3939i			1.04118i	0.853805	+	0.520592i	$0.174289\pi$
$797$			29.3939i			1.04118i	−0.853805	+	0.520592i	$0.825711\pi$
$798$		0			0
$799$	60.0000			2.12265
$800$		0			0
$801$		0			0
$802$	−24.2487	+	14.0000i	−0.856252	+	0.494357i
$803$	−2.12132	−	1.22474i	−0.0748598	−	0.0432203i
$804$		0			0
$805$		0			0
$806$			12.7279i			0.448322i
$807$		0			0
$808$	24.2487	+	42.0000i	0.853067	+	1.47755i
$809$	−35.5176	+	20.5061i	−1.24873	+	0.720956i	−0.970857	−	0.239661i	$-0.922964\pi$
$809$	−35.5176	+	20.5061i	−1.24873	+	0.720956i	−0.277876	+	0.960617i	$0.589630\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$		0			0
$813$		0			0
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$		0			0
$816$		0			0
$817$	−0.866025	+	1.50000i	−0.0302984	+	0.0524784i
$818$			46.5403i			1.62724i
$819$		0			0
$820$		0			0
$821$	−20.8207	−	12.0208i	−0.726646	−	0.419529i	0.0905478	−	0.995892i	$-0.471138\pi$
$821$	−20.8207	−	12.0208i	−0.726646	−	0.419529i	−0.817194	+	0.576363i	$0.804472\pi$
$822$		0			0
$823$	−29.4449	+	17.0000i	−1.02638	+	0.592583i	−0.915947	−	0.401300i	$-0.868558\pi$
$823$	−29.4449	+	17.0000i	−1.02638	+	0.592583i	−0.110437	+	0.993883i	$0.535225\pi$
$824$	12.2474	−	21.2132i	0.426660	−	0.738997i
$825$		0			0
$826$	−18.0000	+	3.46410i	−0.626300	+	0.120532i
$827$	7.07107			0.245885			0.122943	−	0.992414i	$-0.460767\pi$
$827$	7.07107			0.245885			0.122943	+	0.992414i	$0.460767\pi$
$828$		0			0
$829$	−1.50000	+	0.866025i	−0.0520972	+	0.0300783i	−0.525822	−	0.850594i	$-0.676242\pi$
$829$	−1.50000	+	0.866025i	−0.0520972	+	0.0300783i	0.473725	+	0.880673i	$0.342909\pi$
$830$		0			0
$831$		0			0
$832$	−41.5692			−1.44115
$833$	−21.2132	+	26.9444i	−0.734994	+	0.933568i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−25.9808	+	45.0000i	−0.897491	+	1.55450i
$839$	14.6969			0.507395			0.253697	−	0.967284i	$-0.418353\pi$
$839$	14.6969			0.507395			0.253697	+	0.967284i	$0.418353\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$	−0.707107	+	1.22474i	−0.0243685	+	0.0422075i
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$	7.79423	−	22.5000i	0.267813	−	0.773109i
$848$	11.3137			0.388514
$849$		0			0
$850$		0			0
$851$	4.89898	−	2.82843i	0.167935	−	0.0969572i
$852$		0			0
$853$	36.3731			1.24539			0.622695	−	0.782465i	$-0.286038\pi$
$853$	36.3731			1.24539			0.622695	+	0.782465i	$0.286038\pi$
$854$	9.79796	−	8.48528i	0.335279	−	0.290360i
$855$		0			0
$856$	−4.00000	+	6.92820i	−0.136717	+	0.236801i
$857$	33.9411	−	19.5959i	1.15941	−	0.669384i	0.208245	−	0.978077i	$-0.433225\pi$
$857$	33.9411	−	19.5959i	1.15941	−	0.669384i	0.951162	+	0.308693i	$0.0998915\pi$
$858$		0			0
$859$	−33.0000	−	19.0526i	−1.12595	−	0.650065i	−0.183033	−	0.983107i	$-0.558592\pi$
$859$	−33.0000	−	19.0526i	−1.12595	−	0.650065i	−0.942912	+	0.333042i	$0.891925\pi$
$860$		0			0
$861$		0			0
$862$		−	22.0000i		−	0.749323i
$863$	20.5061	−	35.5176i	0.698036	−	1.20903i	−0.271111	−	0.962548i	$-0.587391\pi$
$863$	20.5061	−	35.5176i	0.698036	−	1.20903i	0.969147	−	0.246485i	$-0.0792756\pi$
$864$		0			0
$865$		0			0
$866$	11.0227	−	19.0919i	0.374567	−	0.648769i
$867$		0			0
$868$		0			0
$869$			7.07107i			0.239870i
$870$		0			0
$871$	49.5000	−	28.5788i	1.67724	−	0.968357i
$872$	−1.41421	−	2.44949i	−0.0478913	−	0.0829502i
$873$		0			0
$874$		−	13.8564i		−	0.468700i
$875$		0			0
$876$		0			0
$877$	17.3205	+	10.0000i	0.584872	+	0.337676i	0.763067	−	0.646319i	$-0.223693\pi$
$877$	17.3205	+	10.0000i	0.584872	+	0.337676i	−0.178195	+	0.983995i	$0.557026\pi$
$878$	−33.9411	+	19.5959i	−1.14546	+	0.661330i
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$			11.0000i			0.370179i	0.982722	+	0.185090i	$0.0592576\pi$
$883$			11.0000i			0.370179i	−0.982722	+	0.185090i	$0.940742\pi$
$884$		0			0
$885$		0			0
$886$	28.0000	+	48.4974i	0.940678	+	1.62930i
$887$	−36.0624	−	20.8207i	−1.21086	−	0.699089i	−0.247912	−	0.968783i	$-0.579744\pi$
$887$	−36.0624	−	20.8207i	−1.21086	−	0.699089i	−0.962946	+	0.269693i	$0.913078\pi$
$888$		0			0
$889$	5.50000	+	28.5788i	0.184464	+	0.958503i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	10.6066	+	18.3712i	0.354936	+	0.614768i
$894$		0			0
$895$		0			0
$896$	−9.79796	+	28.2843i	−0.327327	+	0.944911i
$897$		0			0
$898$	−8.66025	−	5.00000i	−0.288996	−	0.166852i
$899$	−2.44949	−	4.24264i	−0.0816951	−	0.141500i
$900$		0			0
$901$	−12.0000	−	6.92820i	−0.399778	−	0.230812i
$902$		−	14.6969i		−	0.489355i
$903$		0			0
$904$	4.00000			0.133038
$905$		0			0
$906$		0			0
$907$	−4.33013	+	2.50000i	−0.143780	+	0.0830111i	−0.570164	−	0.821531i	$-0.693120\pi$
$907$	−4.33013	+	2.50000i	−0.143780	+	0.0830111i	0.426385	+	0.904542i	$0.359787\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			53.7401i			1.78049i	0.455483	+	0.890245i	$0.349467\pi$
$911$			53.7401i			1.78049i	−0.455483	+	0.890245i	$0.650533\pi$
$912$		0			0
$913$	−5.19615	−	9.00000i	−0.171968	−	0.297857i
$914$	6.12372	−	3.53553i	0.202555	−	0.116945i
$915$		0			0
$916$		0			0
$917$	2.12132	−	6.12372i	0.0700522	−	0.202223i
$918$		0			0
$919$	8.50000	−	14.7224i	0.280389	−	0.485648i	−0.691091	−	0.722767i	$-0.742870\pi$
$919$	8.50000	−	14.7224i	0.280389	−	0.485648i	0.971481	+	0.237119i	$0.0762032\pi$
$920$		0			0
$921$		0			0
$922$	−10.3923	+	18.0000i	−0.342252	+	0.592798i
$923$		−	36.7423i		−	1.20939i
$924$		0			0
$925$		0			0
$926$	−15.9217	−	9.19239i	−0.523219	−	0.302081i
$927$		0			0
$928$		0			0
$929$	−28.1691	+	48.7904i	−0.924199	+	1.60076i	−0.131355	+	0.991335i	$0.541933\pi$
$929$	−28.1691	+	48.7904i	−0.924199	+	1.60076i	−0.792844	+	0.609425i	$0.791400\pi$
$930$		0			0
$931$	−12.0000	−	1.73205i	−0.393284	−	0.0567657i
$932$		0			0
$933$		0			0
$934$	−33.0000	+	19.0526i	−1.07979	+	0.623419i
$935$		0			0
$936$		0			0
$937$	−46.7654			−1.52776			−0.763879	−	0.645359i	$-0.776708\pi$
$937$	−46.7654			−1.52776			−0.763879	+	0.645359i	$0.776708\pi$
$938$	−7.77817	−	40.4166i	−0.253966	−	1.31965i
$939$		0			0
$940$		0			0
$941$	−24.4949	−	42.4264i	−0.798511	−	1.38306i	−0.920586	−	0.390540i	$-0.872288\pi$
$941$	−24.4949	−	42.4264i	−0.798511	−	1.38306i	0.122075	−	0.992521i	$-0.461045\pi$
$942$		0			0
$943$	20.7846	−	36.0000i	0.676840	−	1.17232i
$944$	19.5959			0.637793
$945$		0			0
$946$	2.00000			0.0650256
$947$	−24.7487	+	42.8661i	−0.804226	+	1.39296i	0.112586	+	0.993642i	$0.464086\pi$
$947$	−24.7487	+	42.8661i	−0.804226	+	1.39296i	−0.916812	+	0.399318i	$0.869247\pi$
$948$		0			0
$949$	−4.50000	−	7.79423i	−0.146076	−	0.253011i
$950$		0			0
$951$		0			0
$952$	27.7128	−	24.0000i	0.898177	−	0.777844i
$953$	5.65685			0.183243			0.0916217	−	0.995794i	$-0.470795\pi$
$953$	5.65685			0.183243			0.0916217	+	0.995794i	$0.470795\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	6.92820			0.223840
$959$	19.5959	+	22.6274i	0.632785	+	0.730677i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$	6.36396	−	3.67423i	0.205182	−	0.118462i
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$			13.0000i			0.418052i	0.977910	+	0.209026i	$0.0670293\pi$
$967$			13.0000i			0.418052i	−0.977910	+	0.209026i	$0.932971\pi$
$968$	−12.7279	+	22.0454i	−0.409091	+	0.708566i
$969$		0			0
$970$		0			0
$971$	−19.5959	+	33.9411i	−0.628863	+	1.08922i	0.358917	+	0.933369i	$0.383146\pi$
$971$	−19.5959	+	33.9411i	−0.628863	+	1.08922i	−0.987780	+	0.155853i	$0.950187\pi$
$972$		0			0
$973$	2.59808	+	13.5000i	0.0832905	+	0.432790i
$974$			24.0416i			0.770344i
$975$		0			0
$976$	−12.0000	+	6.92820i	−0.384111	+	0.221766i
$977$	−3.53553	−	6.12372i	−0.113112	−	0.195915i	0.803912	−	0.594749i	$-0.202748\pi$
$977$	−3.53553	−	6.12372i	−0.113112	−	0.195915i	−0.917023	+	0.398833i	$0.869415\pi$
$978$		0			0
$979$		−	6.92820i		−	0.221426i
$980$		0			0
$981$		0			0
$982$	13.8564	+	8.00000i	0.442176	+	0.255290i
$983$	4.24264	−	2.44949i	0.135319	−	0.0781266i	−0.430812	−	0.902442i	$-0.641773\pi$
$983$	4.24264	−	2.44949i	0.135319	−	0.0781266i	0.566131	+	0.824315i	$0.308439\pi$
$984$		0			0
$985$		0			0
$986$	19.5959			0.624061
$987$		0			0
$988$		0			0
$989$	4.89898	+	2.82843i	0.155778	+	0.0899388i
$990$		0			0
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	−0.997832	−	0.0658059i	$-0.979038\pi$
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	0.441927	−	0.897051i	$-0.354295\pi$
$992$		0			0
$993$		0			0
$994$	−25.0000	−	8.66025i	−0.792952	−	0.274687i
$995$		0			0
$996$		0			0
$997$	14.7224	+	25.5000i	0.466264	+	0.807593i	0.999258	−	0.0385262i	$-0.0122663\pi$
$997$	14.7224	+	25.5000i	0.466264	+	0.807593i	−0.532993	+	0.846119i	$0.678933\pi$
$998$	17.6777	+	30.6186i	0.559577	+	0.969216i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.bc.a.1349.3		8
3.2	odd	2	inner	1575.2.bc.a.1349.1		8
5.2	odd	4		63.2.p.a.26.2	yes	4
5.3	odd	4		1575.2.bk.c.26.1		4
5.4	even	2	inner	1575.2.bc.a.1349.2		8
7.3	odd	6	inner	1575.2.bc.a.899.4		8
15.2	even	4		63.2.p.a.26.1	yes	4
15.8	even	4		1575.2.bk.c.26.2		4
15.14	odd	2	inner	1575.2.bc.a.1349.4		8
20.7	even	4		1008.2.bt.b.593.1		4
21.17	even	6	inner	1575.2.bc.a.899.2		8
35.2	odd	12		441.2.c.a.440.2		4
35.3	even	12		1575.2.bk.c.1151.2		4
35.12	even	12		441.2.c.a.440.1		4
35.17	even	12		63.2.p.a.17.1	✓	4
35.24	odd	6	inner	1575.2.bc.a.899.1		8
35.27	even	4		441.2.p.a.215.2		4
35.32	odd	12		441.2.p.a.80.1		4
45.2	even	12		567.2.i.d.215.2		4
45.7	odd	12		567.2.i.d.215.1		4
45.22	odd	12		567.2.s.d.26.1		4
45.32	even	12		567.2.s.d.26.2		4
60.47	odd	4		1008.2.bt.b.593.2		4
105.2	even	12		441.2.c.a.440.3		4
105.17	odd	12		63.2.p.a.17.2	yes	4
105.32	even	12		441.2.p.a.80.2		4
105.38	odd	12		1575.2.bk.c.1151.1		4
105.47	odd	12		441.2.c.a.440.4		4
105.59	even	6	inner	1575.2.bc.a.899.3		8
105.62	odd	4		441.2.p.a.215.1		4
140.47	odd	12		7056.2.k.b.881.2		4
140.87	odd	12		1008.2.bt.b.17.2		4
140.107	even	12		7056.2.k.b.881.4		4
315.52	even	12		567.2.s.d.458.2		4
315.122	odd	12		567.2.i.d.269.2		4
315.157	even	12		567.2.i.d.269.1		4
315.227	odd	12		567.2.s.d.458.1		4
420.47	even	12		7056.2.k.b.881.3		4
420.107	odd	12		7056.2.k.b.881.1		4
420.227	even	12		1008.2.bt.b.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.p.a.17.1	✓	4	35.17	even	12
63.2.p.a.17.2	yes	4	105.17	odd	12
63.2.p.a.26.1	yes	4	15.2	even	4
63.2.p.a.26.2	yes	4	5.2	odd	4
441.2.c.a.440.1		4	35.12	even	12
441.2.c.a.440.2		4	35.2	odd	12
441.2.c.a.440.3		4	105.2	even	12
441.2.c.a.440.4		4	105.47	odd	12
441.2.p.a.80.1		4	35.32	odd	12
441.2.p.a.80.2		4	105.32	even	12
441.2.p.a.215.1		4	105.62	odd	4
441.2.p.a.215.2		4	35.27	even	4
567.2.i.d.215.1		4	45.7	odd	12
567.2.i.d.215.2		4	45.2	even	12
567.2.i.d.269.1		4	315.157	even	12
567.2.i.d.269.2		4	315.122	odd	12
567.2.s.d.26.1		4	45.22	odd	12
567.2.s.d.26.2		4	45.32	even	12
567.2.s.d.458.1		4	315.227	odd	12
567.2.s.d.458.2		4	315.52	even	12
1008.2.bt.b.17.1		4	420.227	even	12
1008.2.bt.b.17.2		4	140.87	odd	12
1008.2.bt.b.593.1		4	20.7	even	4
1008.2.bt.b.593.2		4	60.47	odd	4
1575.2.bc.a.899.1		8	35.24	odd	6	inner
1575.2.bc.a.899.2		8	21.17	even	6	inner
1575.2.bc.a.899.3		8	105.59	even	6	inner
1575.2.bc.a.899.4		8	7.3	odd	6	inner
1575.2.bc.a.1349.1		8	3.2	odd	2	inner
1575.2.bc.a.1349.2		8	5.4	even	2	inner
1575.2.bc.a.1349.3		8	1.1	even	1	trivial
1575.2.bc.a.1349.4		8	15.14	odd	2	inner
1575.2.bk.c.26.1		4	5.3	odd	4
1575.2.bk.c.26.2		4	15.8	even	4
1575.2.bk.c.1151.1		4	105.38	odd	12
1575.2.bk.c.1151.2		4	35.3	even	12
7056.2.k.b.881.1		4	420.107	odd	12
7056.2.k.b.881.2		4	140.47	odd	12
7056.2.k.b.881.3		4	420.47	even	12
7056.2.k.b.881.4		4	140.107	even	12

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-2.59808 + 0.500000i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-2.59808 + 0.500000i) q^{7} +2.82843 q^{8} +(-1.22474 + 0.707107i) q^{11} -5.19615 q^{13} +(-1.22474 + 3.53553i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-4.24264 + 2.44949i) q^{17} +(-1.50000 - 0.866025i) q^{19} +2.00000i q^{22} +(-2.82843 + 4.89898i) q^{23} +(-3.67423 + 6.36396i) q^{26} -2.82843i q^{29} +(1.50000 - 0.866025i) q^{31} +6.92820i q^{34} +(-0.866025 - 0.500000i) q^{37} +(-2.12132 + 1.22474i) q^{38} -7.34847 q^{41} -1.00000i q^{43} +(4.00000 + 6.92820i) q^{46} +(-10.6066 - 6.12372i) q^{47} +(6.50000 - 2.59808i) q^{49} +(1.41421 + 2.44949i) q^{53} +(-7.34847 + 1.41421i) q^{56} +(-3.46410 - 2.00000i) q^{58} +(2.44949 + 4.24264i) q^{59} +(-3.00000 - 1.73205i) q^{61} -2.44949i q^{62} +8.00000 q^{64} +(-9.52628 + 5.50000i) q^{67} +7.07107i q^{71} +(0.866025 + 1.50000i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(2.82843 - 2.44949i) q^{77} +(2.50000 - 4.33013i) q^{79} +(-5.19615 + 9.00000i) q^{82} +7.34847i q^{83} +(-1.22474 - 0.707107i) q^{86} +(-3.46410 + 2.00000i) q^{88} +(-2.44949 + 4.24264i) q^{89} +(13.5000 - 2.59808i) q^{91} +(-15.0000 + 8.66025i) q^{94} +10.3923 q^{97} +(1.41421 - 9.79796i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 16 q^{16} - 12 q^{19} + 12 q^{31} + 32 q^{46} + 52 q^{49} - 24 q^{61} + 64 q^{64} + 20 q^{79} + 108 q^{91} - 120 q^{94}+O(q^{100}) \) 8 * q + 16 * q^16 - 12 * q^19 + 12 * q^31 + 32 * q^46 + 52 * q^49 - 24 * q^61 + 64 * q^64 + 20 * q^79 + 108 * q^91 - 120 * q^94

Introduction

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