LMFDB - Embedded newform 1575.2.bc.a.899.1

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			899.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1575.899
Dual form			1575.2.bc.a.1349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-2.59808 - 0.500000i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-2.59808 - 0.500000i) q^{7} -2.82843 q^{8} +(1.22474 + 0.707107i) q^{11} -5.19615 q^{13} +(1.22474 + 3.53553i) q^{14} +(2.00000 + 3.46410i) q^{16} +(4.24264 + 2.44949i) q^{17} +(-1.50000 + 0.866025i) q^{19} -2.00000i q^{22} +(2.82843 + 4.89898i) q^{23} +(3.67423 + 6.36396i) q^{26} -2.82843i q^{29} +(1.50000 + 0.866025i) q^{31} -6.92820i q^{34} +(-0.866025 + 0.500000i) q^{37} +(2.12132 + 1.22474i) q^{38} +7.34847 q^{41} +1.00000i q^{43} +(4.00000 - 6.92820i) q^{46} +(10.6066 - 6.12372i) q^{47} +(6.50000 + 2.59808i) q^{49} +(-1.41421 + 2.44949i) q^{53} +(7.34847 + 1.41421i) q^{56} +(-3.46410 + 2.00000i) q^{58} +(-2.44949 + 4.24264i) q^{59} +(-3.00000 + 1.73205i) q^{61} -2.44949i q^{62} +8.00000 q^{64} +(-9.52628 - 5.50000i) q^{67} +7.07107i q^{71} +(0.866025 - 1.50000i) q^{73} +(1.22474 + 0.707107i) q^{74} +(-2.82843 - 2.44949i) q^{77} +(2.50000 + 4.33013i) q^{79} +(-5.19615 - 9.00000i) q^{82} +7.34847i q^{83} +(1.22474 - 0.707107i) q^{86} +(-3.46410 - 2.00000i) q^{88} +(2.44949 + 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} +(-15.0000 - 8.66025i) q^{94} +10.3923 q^{97} +(-1.41421 - 9.79796i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

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

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	$-0.333333\pi$
$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i	−1.00000			$\pi$
$3$		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	$-0.264945\pi$
$11$	1.22474	+	0.707107i	0.369274	+	0.213201i	−0.303867	+	0.952714i	$0.598278\pi$
$12$		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	$-0.130846\pi$
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.112296	+	0.993675i	$0.464180\pi$
$18$		0			0
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	−0.662094	−	0.749421i	$-0.730332\pi$
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	0.317970	+	0.948101i	$0.396999\pi$
$20$		0			0
$21$		0			0
$22$		−	2.00000i		−	0.426401i
$23$	2.82843	+	4.89898i	0.589768	+	1.02151i	0.994263	+	0.106967i	$0.0341141\pi$
$23$	2.82843	+	4.89898i	0.589768	+	1.02151i	−0.404495	+	0.914540i	$0.632553\pi$
$24$		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	0.628619	−	0.777714i	$-0.283621\pi$
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	−0.359211	+	0.933257i	$0.616954\pi$
$32$		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	−0.569495	−	0.821995i	$-0.692861\pi$
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	0.427121	+	0.904194i	$0.359528\pi$
$38$	2.12132	+	1.22474i	0.344124	+	0.198680i
$39$		0			0
$40$		0			0
$41$	7.34847			1.14764			0.573819	−	0.818982i	$-0.305461\pi$
$41$	7.34847			1.14764			0.573819	+	0.818982i	$0.305461\pi$
$42$		0			0
$43$			1.00000i			0.152499i	0.997089	+	0.0762493i	$0.0242945\pi$
$43$			1.00000i			0.152499i	−0.997089	+	0.0762493i	$0.975706\pi$
$44$		0			0
$45$		0			0
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	10.6066	−	6.12372i	1.54713	−	0.893237i	0.548773	−	0.835971i	$-0.315095\pi$
$47$	10.6066	−	6.12372i	1.54713	−	0.893237i	0.998359	−	0.0572655i	$-0.0182382\pi$
$48$		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	$-0.895563\pi$
$53$	−1.41421	+	2.44949i	−0.194257	+	0.336463i	0.752400	+	0.658707i	$0.228896\pi$
$54$		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	$-0.936646\pi$
$59$	−2.44949	+	4.24264i	−0.318896	+	0.552345i	0.661362	+	0.750067i	$0.269979\pi$
$60$		0			0
$61$	−3.00000	+	1.73205i	−0.384111	+	0.221766i	−0.679605	−	0.733578i	$-0.737849\pi$
$61$	−3.00000	+	1.73205i	−0.384111	+	0.221766i	0.295495	+	0.955344i	$0.404516\pi$
$62$		−	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	−0.211604	−	0.977356i	$-0.567869\pi$
$67$	−9.52628	−	5.50000i	−1.16382	−	0.671932i	−0.952217	+	0.305424i	$0.901202\pi$
$68$		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	−0.810885	−	0.585206i	$-0.801014\pi$
$73$	0.866025	−	1.50000i	0.101361	−	0.175562i	0.912245	+	0.409644i	$0.134347\pi$
$74$	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	0.971698	−	0.236225i	$-0.0759104\pi$
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	−0.690426	+	0.723403i	$0.742577\pi$
$80$		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	$-0.0830610\pi$
$89$	2.44949	+	4.24264i	0.259645	+	0.449719i	−0.706502	+	0.707712i	$0.749728\pi$
$90$		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	0.0253604	+	0.999678i	$0.491927\pi$
$101$	−8.57321	+	14.8492i	−0.853067	+	1.47755i	−0.878427	+	0.477876i	$0.841407\pi$
$102$		0			0
$103$	4.33013	+	7.50000i	0.426660	+	0.738997i	0.996574	−	0.0827075i	$-0.0263567\pi$
$103$	4.33013	+	7.50000i	0.426660	+	0.738997i	−0.569914	+	0.821705i	$0.693023\pi$
$104$	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	$-0.123012\pi$
$107$	1.41421	+	2.44949i	0.136717	+	0.236801i	−0.789535	+	0.613706i	$0.789678\pi$
$108$		0			0
$109$	−0.500000	+	0.866025i	−0.0478913	+	0.0829502i	−0.888977	−	0.457951i	$-0.848583\pi$
$109$	−0.500000	+	0.866025i	−0.0478913	+	0.0829502i	0.841086	+	0.540901i	$0.181917\pi$
$110$		0			0
$111$		0			0
$112$	−3.46410	−	10.0000i	−0.327327	−	0.944911i
$113$	−1.41421			−0.133038			−0.0665190	−	0.997785i	$-0.521189\pi$
$113$	−1.41421			−0.133038			−0.0665190	+	0.997785i	$0.521189\pi$
$114$		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	$0.162290\pi$
$127$			11.0000i			0.976092i	−0.872818	+	0.488046i	$0.837710\pi$
$128$	−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	$-0.132540\pi$
$131$	1.22474	+	2.12132i	0.107006	+	0.185341i	−0.807550	+	0.589799i	$0.799207\pi$
$132$		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	$-0.672772\pi$
$137$	5.65685	−	9.79796i	0.483298	−	0.837096i	0.999816	+	0.0191800i	$0.00610555\pi$
$138$		0			0
$139$			5.19615i			0.440732i	0.975417	+	0.220366i	$0.0707252\pi$
$139$			5.19615i			0.440732i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		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	$-0.592233\pi$
$149$	4.89898	−	2.82843i	0.401340	−	0.231714i	0.687062	+	0.726599i	$0.258900\pi$
$150$		0			0
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.0615699	−	0.998103i	$-0.480389\pi$
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.833597	−	0.552372i	$-0.186277\pi$
$152$	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	0.280293	+	0.959914i	$0.409568\pi$
$157$	−8.66025	+	15.0000i	−0.691164	+	1.19713i	−0.971457	+	0.237216i	$0.923765\pi$
$158$	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	−0.120900	−	0.992665i	$-0.538578\pi$
$163$	8.66025	−	5.00000i	0.678323	−	0.391630i	0.799223	+	0.601035i	$0.205245\pi$
$164$		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	$-0.545180\pi$
$173$	8.48528	−	4.89898i	0.645124	−	0.372463i	0.786586	+	0.617481i	$0.211847\pi$
$174$		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	$-0.453962\pi$
$179$	−8.57321	−	4.94975i	−0.640792	−	0.369961i	−0.784920	+	0.619598i	$0.787296\pi$
$180$		0			0
$181$			15.5885i			1.15868i	0.815086	+	0.579340i	$0.196690\pi$
$181$			15.5885i			1.15868i	−0.815086	+	0.579340i	$0.803310\pi$
$182$	−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	$-0.682960\pi$
$191$	−1.22474	+	0.707107i	−0.0886194	+	0.0511645i	0.455035	+	0.890473i	$0.349627\pi$
$192$		0			0
$193$	9.52628	+	5.50000i	0.685717	+	0.395899i	0.802005	−	0.597317i	$-0.203766\pi$
$193$	9.52628	+	5.50000i	0.685717	+	0.395899i	−0.116289	+	0.993215i	$0.537100\pi$
$194$	−7.34847	−	12.7279i	−0.527589	−	0.913812i
$195$		0			0
$196$		0			0
$197$	−19.7990			−1.41062			−0.705310	−	0.708899i	$-0.749192\pi$
$197$	−19.7990			−1.41062			−0.705310	+	0.708899i	$0.749192\pi$
$198$		0			0
$199$	12.0000	+	6.92820i	0.850657	+	0.491127i	0.860873	−	0.508821i	$-0.169918\pi$
$199$	12.0000	+	6.92820i	0.850657	+	0.491127i	−0.0102152	+	0.999948i	$0.503252\pi$
$200$		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	0.998236	+	0.0593658i	$0.0189078\pi$
$227$	23.3345	+	13.4722i	1.54877	+	0.894181i	0.550530	+	0.834815i	$0.314425\pi$
$228$		0			0
$229$	−19.5000	+	11.2583i	−1.28860	+	0.743971i	−0.978404	−	0.206702i	$-0.933727\pi$
$229$	−19.5000	+	11.2583i	−1.28860	+	0.743971i	−0.310192	+	0.950674i	$0.600393\pi$
$230$		0			0
$231$		0			0
$232$			8.00000i			0.525226i
$233$	4.94975	+	8.57321i	0.324269	+	0.561650i	0.981364	−	0.192158i	$-0.0615485\pi$
$233$	4.94975	+	8.57321i	0.324269	+	0.561650i	−0.657095	+	0.753807i	$0.728215\pi$
$234$		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	0.0609515	−	0.998141i	$-0.480586\pi$
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	−0.833939	+	0.551856i	$0.813920\pi$
$242$	−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	$-0.691008\pi$
$257$	−2.12132	+	1.22474i	−0.132324	+	0.0763975i	0.432377	+	0.901693i	$0.357675\pi$
$258$		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	$-0.689721\pi$
$263$	7.07107	−	12.2474i	0.436021	−	0.755210i	0.997378	+	0.0723633i	$0.0230541\pi$
$264$		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	−0.476932	−	0.878940i	$-0.658251\pi$
$269$	8.57321	−	14.8492i	0.522718	−	0.905374i	0.999651	−	0.0264343i	$-0.00841529\pi$
$270$		0			0
$271$	−12.0000	+	6.92820i	−0.728948	+	0.420858i	−0.818037	−	0.575165i	$-0.804938\pi$
$271$	−12.0000	+	6.92820i	−0.728948	+	0.420858i	0.0890891	+	0.996024i	$0.471604\pi$
$272$			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	−0.236953	−	0.971521i	$-0.576149\pi$
$277$	−19.9186	−	11.5000i	−1.19679	−	0.690968i	−0.959839	+	0.280553i	$0.909482\pi$
$278$	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	−0.839137	−	0.543920i	$-0.816940\pi$
$283$	0.866025	−	1.50000i	0.0514799	−	0.0891657i	0.890617	+	0.454754i	$0.150273\pi$
$284$		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	$-0.994930\pi$
$311$	−8.57321	+	14.8492i	−0.486142	+	0.842023i	0.513731	+	0.857951i	$0.328263\pi$
$312$		0			0
$313$	−6.06218	−	10.5000i	−0.342655	−	0.593495i	0.642270	−	0.766478i	$-0.277993\pi$
$313$	−6.06218	−	10.5000i	−0.342655	−	0.593495i	−0.984925	+	0.172983i	$0.944659\pi$
$314$	24.4949			1.38233
$315$		0			0
$316$		0			0
$317$	−7.07107	−	12.2474i	−0.397151	−	0.687885i	0.596222	−	0.802819i	$-0.296668\pi$
$317$	−7.07107	−	12.2474i	−0.397151	−	0.687885i	−0.993373	+	0.114934i	$0.963334\pi$
$318$		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	0.879440	+	0.476011i	$0.157918\pi$
$331$	15.5000	+	26.8468i	0.851957	+	1.47563i	−0.0274825	+	0.999622i	$0.508749\pi$
$332$		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	$0.215491\pi$
$337$			23.0000i			1.25289i	−0.779466	+	0.626445i	$0.784509\pi$
$338$	−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	0.0588334	+	0.998268i	$0.481262\pi$
$347$	−15.5563	+	26.9444i	−0.835109	+	1.44645i	−0.893942	+	0.448183i	$0.852071\pi$
$348$		0			0
$349$			10.3923i			0.556287i	0.960539	+	0.278144i	$0.0897191\pi$
$349$			10.3923i			0.556287i	−0.960539	+	0.278144i	$0.910281\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.8492	+	8.57321i	0.790345	+	0.456306i	0.840084	−	0.542456i	$-0.182506\pi$
$353$	14.8492	+	8.57321i	0.790345	+	0.456306i	−0.0497387	+	0.998762i	$0.515839\pi$
$354$		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	$-0.934883\pi$
$359$	−24.4949	+	14.1421i	−1.29279	+	0.746393i	−0.313643	+	0.949541i	$0.601550\pi$
$360$		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	−0.887743	−	0.460339i	$-0.847728\pi$
$367$	−0.866025	+	1.50000i	−0.0452062	+	0.0782994i	0.842537	+	0.538639i	$0.181061\pi$
$368$	−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	−0.980471	−	0.196663i	$-0.936990\pi$
$373$	−25.1147	+	14.5000i	−1.30039	+	0.750782i	−0.319921	+	0.947444i	$0.603656\pi$
$374$	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	$-0.833573\pi$
$383$	−16.9706	+	9.79796i	−0.867155	+	0.500652i	−0.000753393		1.00000i	$0.500240\pi$
$384$		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	$-0.571868\pi$
$389$	−23.2702	−	13.4350i	−1.17984	−	0.681183i	−0.955978	+	0.293437i	$0.905201\pi$
$390$		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	0.886939	−	0.461886i	$-0.152827\pi$
$397$	0.866025	+	1.50000i	0.0434646	+	0.0752828i	−0.843475	+	0.537169i	$0.819494\pi$
$398$		−	19.5959i		−	0.982255i
$399$		0			0
$400$		0			0
$401$	17.1464	−	9.89949i	0.856252	−	0.494357i	−0.00650355	−	0.999979i	$-0.502070\pi$
$401$	17.1464	−	9.89949i	0.856252	−	0.494357i	0.862755	+	0.505622i	$0.168737\pi$
$402$		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	−0.413920	−	0.910313i	$-0.635841\pi$
$409$	−28.5000	−	16.4545i	−1.40923	−	0.813622i	−0.995314	+	0.0966915i	$0.969174\pi$
$410$		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	$-0.145388\pi$
$419$	36.7423			1.79498			0.897491	+	0.441034i	$0.145388\pi$
$420$		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	$-0.455574\pi$
$431$	−13.4722	−	7.77817i	−0.648933	−	0.374661i	−0.788047	+	0.615615i	$0.788908\pi$
$432$		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	−0.947776	−	0.318936i	$-0.896674\pi$
$439$	−24.0000	+	13.8564i	−1.14546	+	0.661330i	−0.197681	+	0.980266i	$0.563341\pi$
$440$		0			0
$441$		0			0
$442$			36.0000i			1.71235i
$443$	19.7990	+	34.2929i	0.940678	+	1.62930i	0.764181	+	0.645002i	$0.223143\pi$
$443$	19.7990	+	34.2929i	0.940678	+	1.62930i	0.176497	+	0.984301i	$0.443523\pi$
$444$		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	−0.395292	−	0.918556i	$-0.629357\pi$
$457$	4.33013	−	2.50000i	0.202555	−	0.116945i	0.597847	+	0.801611i	$0.296023\pi$
$458$	27.5772	+	15.9217i	1.28860	+	0.743971i
$459$		0			0
$460$		0			0
$461$	14.6969			0.684505			0.342252	−	0.939608i	$-0.388810\pi$
$461$	14.6969			0.684505			0.342252	+	0.939608i	$0.388810\pi$
$462$		0			0
$463$			13.0000i			0.604161i	0.953282	+	0.302081i	$0.0976812\pi$
$463$			13.0000i			0.604161i	−0.953282	+	0.302081i	$0.902319\pi$
$464$	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	$-0.452410\pi$
$467$	23.3345	−	13.4722i	1.07979	−	0.623419i	0.930841	+	0.365426i	$0.119077\pi$
$468$		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	$-0.869033\pi$
$479$	−2.44949	+	4.24264i	−0.111920	+	0.193851i	0.804624	+	0.593784i	$0.202367\pi$
$480$		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	0.127854	−	0.991793i	$-0.459191\pi$
$487$	−14.7224	−	8.50000i	−0.667137	−	0.385172i	−0.794991	+	0.606621i	$0.792524\pi$
$488$	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	−0.997532	−	0.0702185i	$-0.977630\pi$
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	0.437955	−	0.898997i	$-0.355703\pi$
$500$		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	$-0.183955\pi$
$509$	−1.22474	−	2.12132i	−0.0542859	−	0.0940259i	−0.891891	+	0.452250i	$0.850622\pi$
$510$		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	$-0.799108\pi$
$521$	2.44949	−	4.24264i	0.107314	−	0.185873i	0.914681	+	0.404176i	$0.132442\pi$
$522$		0			0
$523$	−0.866025	−	1.50000i	−0.0378686	−	0.0655904i	0.846470	−	0.532437i	$-0.178724\pi$
$523$	−0.866025	−	1.50000i	−0.0378686	−	0.0655904i	−0.884339	+	0.466846i	$0.845390\pi$
$524$		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	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	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	$-0.931421\pi$
$547$		−	10.0000i		−	0.427569i	0.976881	−	0.213785i	$-0.0685791\pi$
$548$		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	$-0.726429\pi$
$557$	7.77817	−	13.4722i	0.329572	−	0.570835i	0.982427	+	0.186648i	$0.0597623\pi$
$558$		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	$-0.525533\pi$
$563$	−23.3345	−	13.4722i	−0.983433	−	0.567785i	−0.903305	+	0.428999i	$0.858866\pi$
$564$		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	$-0.657229\pi$
$569$	1.22474	−	0.707107i	0.0513440	−	0.0296435i	0.525452	+	0.850823i	$0.323896\pi$
$570$		0			0
$571$	−5.50000	+	9.52628i	−0.230168	+	0.398662i	−0.957857	−	0.287244i	$-0.907261\pi$
$571$	−5.50000	+	9.52628i	−0.230168	+	0.398662i	0.727690	+	0.685907i	$0.240594\pi$
$572$		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	−0.883489	−	0.468452i	$-0.844812\pi$
$577$	−0.866025	+	1.50000i	−0.0360531	+	0.0624458i	0.847436	+	0.530898i	$0.178145\pi$
$578$	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	$-0.552148\pi$
$593$	14.8492	−	8.57321i	0.609785	−	0.352060i	0.772881	+	0.634550i	$0.218815\pi$
$594$		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	$-0.370202\pi$
$599$	−4.89898	−	2.82843i	−0.200167	−	0.115566i	−0.596733	+	0.802440i	$0.703535\pi$
$600$		0			0
$601$		−	25.9808i		−	1.05978i	−0.848067	−	0.529889i	$-0.822234\pi$
$601$		−	25.9808i		−	1.05978i	0.848067	−	0.529889i	$-0.177766\pi$
$602$	−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	−0.913923	−	0.405887i	$-0.866962\pi$
$607$	−19.9186	−	34.5000i	−0.808470	−	1.40031i	0.105453	−	0.994424i	$-0.466371\pi$
$608$		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	0.633345	−	0.773869i	$-0.281681\pi$
$613$	6.92820	+	4.00000i	0.279827	+	0.161558i	−0.353518	+	0.935428i	$0.615015\pi$
$614$	−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	$-0.660795\pi$
$617$	−24.0416			−0.967880			−0.483940	+	0.875101i	$0.660795\pi$
$618$		0			0
$619$	25.5000	+	14.7224i	1.02493	+	0.591744i	0.915529	−	0.402253i	$-0.131773\pi$
$619$	25.5000	+	14.7224i	1.02493	+	0.591744i	0.109403	+	0.993997i	$0.465106\pi$
$620$		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	$-0.243234\pi$
$641$	12.2474	+	7.07107i	0.483745	+	0.279290i	−0.238231	+	0.971209i	$0.576567\pi$
$642$		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	$-0.442762\pi$
$647$	−14.8492	−	8.57321i	−0.583784	−	0.337048i	−0.762636	+	0.646828i	$0.776095\pi$
$648$		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	$-0.210849\pi$
$653$	−3.53553	−	6.12372i	−0.138356	−	0.239640i	−0.926875	+	0.375371i	$0.877515\pi$
$654$		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	−0.0860127	−	0.996294i	$-0.527413\pi$
$661$	−25.5000	−	14.7224i	−0.991835	−	0.572636i	−0.905822	+	0.423658i	$0.860746\pi$
$662$	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	$-0.764327\pi$
$673$		−	35.0000i		−	1.34915i	0.738206	−	0.674575i	$-0.235673\pi$
$674$	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	$-0.726959\pi$
$677$	−8.48528	+	4.89898i	−0.326116	+	0.188283i	0.327999	+	0.944678i	$0.393626\pi$
$678$		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	0.120405	−	0.992725i	$-0.461581\pi$
$683$	24.0416	−	41.6413i	0.919927	−	1.59336i	0.799522	−	0.600636i	$-0.205086\pi$
$684$		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	0.429719	−	0.902963i	$-0.358613\pi$
$691$	37.5000	−	21.6506i	1.42657	−	0.823629i	0.996848	+	0.0793336i	$0.0252792\pi$
$692$		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	−0.947282	−	0.320400i	$-0.896183\pi$
$709$	−20.0000	−	34.6410i	−0.751116	−	1.30097i	0.196167	−	0.980571i	$-0.437151\pi$
$710$		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	0.999996	+	0.00280593i	$0.000893157\pi$
$719$	13.4722	+	23.3345i	0.502428	+	0.870231i	−0.497568	+	0.867425i	$0.665774\pi$
$720$		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	0.954411	+	0.298495i	$0.0964845\pi$
$733$	19.9186	+	34.5000i	0.735710	+	1.27429i	−0.218702	+	0.975792i	$0.570182\pi$
$734$	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	−0.875075	−	0.483987i	$-0.839188\pi$
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	0.856683	+	0.515844i	$0.172522\pi$
$740$		0			0
$741$		0			0
$742$	−10.3923	−	2.00000i	−0.381514	−	0.0734223i
$743$	24.0416			0.882002			0.441001	−	0.897507i	$-0.354624\pi$
$743$	24.0416			0.882002			0.441001	+	0.897507i	$0.354624\pi$
$744$		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	−0.999424	−	0.0339490i	$-0.989192\pi$
$751$	−14.5000	−	25.1147i	−0.529113	−	0.916450i	0.470311	−	0.882501i	$-0.344142\pi$
$752$	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	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	−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	$-0.0202365\pi$
$761$	12.2474	+	21.2132i	0.443970	+	0.768978i	−0.554010	+	0.832510i	$0.686903\pi$
$762$		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	$-0.844814\pi$
$769$		−	25.9808i		−	0.936890i	0.883493	−	0.468445i	$-0.155186\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−23.3345	−	13.4722i	−0.839284	−	0.484561i	0.0177365	−	0.999843i	$-0.494354\pi$
$773$	−23.3345	−	13.4722i	−0.839284	−	0.484561i	−0.857021	+	0.515282i	$0.827687\pi$
$774$		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	−0.115246	−	0.993337i	$-0.536766\pi$
$787$	22.5167	−	39.0000i	0.802632	−	1.39020i	0.917878	−	0.396863i	$-0.129901\pi$
$788$		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	$-0.0770363\pi$
$809$	35.5176	+	20.5061i	1.24873	+	0.720956i	0.277876	+	0.960617i	$0.410370\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$		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	$-0.528862\pi$
$821$	20.8207	−	12.0208i	0.726646	−	0.419529i	0.817194	+	0.576363i	$0.195528\pi$
$822$		0			0
$823$	−29.4449	−	17.0000i	−1.02638	−	0.592583i	−0.110437	−	0.993883i	$-0.535225\pi$
$823$	−29.4449	−	17.0000i	−1.02638	−	0.592583i	−0.915947	+	0.401300i	$0.868558\pi$
$824$	−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	$-0.539233\pi$
$827$	−7.07107			−0.245885			−0.122943	+	0.992414i	$0.539233\pi$
$828$		0			0
$829$	−1.50000	−	0.866025i	−0.0520972	−	0.0300783i	0.473725	−	0.880673i	$-0.342909\pi$
$829$	−1.50000	−	0.866025i	−0.0520972	−	0.0300783i	−0.525822	+	0.850594i	$0.676242\pi$
$830$		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	$-0.581647\pi$
$839$	−14.6969			−0.507395			−0.253697	+	0.967284i	$0.581647\pi$
$840$		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	$-0.566775\pi$
$857$	−33.9411	−	19.5959i	−1.15941	−	0.669384i	−0.951162	+	0.308693i	$0.900108\pi$
$858$		0			0
$859$	−33.0000	+	19.0526i	−1.12595	+	0.650065i	−0.942912	−	0.333042i	$-0.891925\pi$
$859$	−33.0000	+	19.0526i	−1.12595	+	0.650065i	−0.183033	+	0.983107i	$0.558592\pi$
$860$		0			0
$861$		0			0
$862$			22.0000i			0.749323i
$863$	−20.5061	−	35.5176i	−0.698036	−	1.20903i	−0.969147	−	0.246485i	$-0.920724\pi$
$863$	−20.5061	−	35.5176i	−0.698036	−	1.20903i	0.271111	−	0.962548i	$-0.412609\pi$
$864$		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	−0.178195	−	0.983995i	$-0.557026\pi$
$877$	17.3205	−	10.0000i	0.584872	−	0.337676i	0.763067	+	0.646319i	$0.223693\pi$
$878$	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	$-0.940742\pi$
$883$		−	11.0000i		−	0.370179i	0.982722	−	0.185090i	$-0.0592576\pi$
$884$		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	$-0.420256\pi$
$887$	36.0624	−	20.8207i	1.21086	−	0.699089i	0.962946	+	0.269693i	$0.0869222\pi$
$888$		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	0.426385	−	0.904542i	$-0.359787\pi$
$907$	−4.33013	−	2.50000i	−0.143780	−	0.0830111i	−0.570164	+	0.821531i	$0.693120\pi$
$908$		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	0.971481	−	0.237119i	$-0.0762032\pi$
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	−0.691091	+	0.722767i	$0.742870\pi$
$920$		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	0.792844	+	0.609425i	$0.208600\pi$
$929$	28.1691	+	48.7904i	0.924199	+	1.60076i	0.131355	+	0.991335i	$0.458067\pi$
$930$		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	−0.122075	−	0.992521i	$-0.538955\pi$
$941$	24.4949	−	42.4264i	0.798511	−	1.38306i	0.920586	−	0.390540i	$-0.127712\pi$
$942$		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	0.916812	+	0.399318i	$0.130753\pi$
$947$	24.7487	+	42.8661i	0.804226	+	1.39296i	−0.112586	+	0.993642i	$0.535914\pi$
$948$		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	$-0.529205\pi$
$953$	−5.65685			−0.183243			−0.0916217	+	0.995794i	$0.529205\pi$
$954$		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	$-0.932971\pi$
$967$		−	13.0000i		−	0.418052i	0.977910	−	0.209026i	$-0.0670293\pi$
$968$	12.7279	+	22.0454i	0.409091	+	0.708566i
$969$		0			0
$970$		0			0
$971$	19.5959	+	33.9411i	0.628863	+	1.08922i	0.987780	+	0.155853i	$0.0498127\pi$
$971$	19.5959	+	33.9411i	0.628863	+	1.08922i	−0.358917	+	0.933369i	$0.616854\pi$
$972$		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	$-0.797252\pi$
$977$	3.53553	−	6.12372i	0.113112	−	0.195915i	0.917023	+	0.398833i	$0.130585\pi$
$978$		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	$-0.358227\pi$
$983$	−4.24264	−	2.44949i	−0.135319	−	0.0781266i	−0.566131	+	0.824315i	$0.691561\pi$
$984$		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	0.441927	+	0.897051i	$0.354295\pi$
$991$	−17.5000	+	30.3109i	−0.555906	+	0.962857i	−0.997832	+	0.0658059i	$0.979038\pi$
$992$		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	−0.532993	−	0.846119i	$-0.678933\pi$
$997$	14.7224	−	25.5000i	0.466264	−	0.807593i	0.999258	+	0.0385262i	$0.0122663\pi$
$998$	−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.899.1		8
3.2	odd	2	inner	1575.2.bc.a.899.3		8
5.2	odd	4		1575.2.bk.c.1151.2		4
5.3	odd	4		63.2.p.a.17.1	✓	4
5.4	even	2	inner	1575.2.bc.a.899.4		8
7.5	odd	6	inner	1575.2.bc.a.1349.2		8
15.2	even	4		1575.2.bk.c.1151.1		4
15.8	even	4		63.2.p.a.17.2	yes	4
15.14	odd	2	inner	1575.2.bc.a.899.2		8
20.3	even	4		1008.2.bt.b.17.2		4
21.5	even	6	inner	1575.2.bc.a.1349.4		8
35.3	even	12		441.2.c.a.440.2		4
35.12	even	12		1575.2.bk.c.26.1		4
35.13	even	4		441.2.p.a.80.1		4
35.18	odd	12		441.2.c.a.440.1		4
35.19	odd	6	inner	1575.2.bc.a.1349.3		8
35.23	odd	12		441.2.p.a.215.2		4
35.33	even	12		63.2.p.a.26.2	yes	4
45.13	odd	12		567.2.i.d.269.1		4
45.23	even	12		567.2.i.d.269.2		4
45.38	even	12		567.2.s.d.458.1		4
45.43	odd	12		567.2.s.d.458.2		4
60.23	odd	4		1008.2.bt.b.17.1		4
105.23	even	12		441.2.p.a.215.1		4
105.38	odd	12		441.2.c.a.440.3		4
105.47	odd	12		1575.2.bk.c.26.2		4
105.53	even	12		441.2.c.a.440.4		4
105.68	odd	12		63.2.p.a.26.1	yes	4
105.83	odd	4		441.2.p.a.80.2		4
105.89	even	6	inner	1575.2.bc.a.1349.1		8
140.3	odd	12		7056.2.k.b.881.4		4
140.103	odd	12		1008.2.bt.b.593.1		4
140.123	even	12		7056.2.k.b.881.2		4
315.68	odd	12		567.2.s.d.26.2		4
315.103	even	12		567.2.s.d.26.1		4
315.173	odd	12		567.2.i.d.215.2		4
315.313	even	12		567.2.i.d.215.1		4
420.143	even	12		7056.2.k.b.881.1		4
420.263	odd	12		7056.2.k.b.881.3		4
420.383	even	12		1008.2.bt.b.593.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.p.a.17.1	✓	4	5.3	odd	4
63.2.p.a.17.2	yes	4	15.8	even	4
63.2.p.a.26.1	yes	4	105.68	odd	12
63.2.p.a.26.2	yes	4	35.33	even	12
441.2.c.a.440.1		4	35.18	odd	12
441.2.c.a.440.2		4	35.3	even	12
441.2.c.a.440.3		4	105.38	odd	12
441.2.c.a.440.4		4	105.53	even	12
441.2.p.a.80.1		4	35.13	even	4
441.2.p.a.80.2		4	105.83	odd	4
441.2.p.a.215.1		4	105.23	even	12
441.2.p.a.215.2		4	35.23	odd	12
567.2.i.d.215.1		4	315.313	even	12
567.2.i.d.215.2		4	315.173	odd	12
567.2.i.d.269.1		4	45.13	odd	12
567.2.i.d.269.2		4	45.23	even	12
567.2.s.d.26.1		4	315.103	even	12
567.2.s.d.26.2		4	315.68	odd	12
567.2.s.d.458.1		4	45.38	even	12
567.2.s.d.458.2		4	45.43	odd	12
1008.2.bt.b.17.1		4	60.23	odd	4
1008.2.bt.b.17.2		4	20.3	even	4
1008.2.bt.b.593.1		4	140.103	odd	12
1008.2.bt.b.593.2		4	420.383	even	12
1575.2.bc.a.899.1		8	1.1	even	1	trivial
1575.2.bc.a.899.2		8	15.14	odd	2	inner
1575.2.bc.a.899.3		8	3.2	odd	2	inner
1575.2.bc.a.899.4		8	5.4	even	2	inner
1575.2.bc.a.1349.1		8	105.89	even	6	inner
1575.2.bc.a.1349.2		8	7.5	odd	6	inner
1575.2.bc.a.1349.3		8	35.19	odd	6	inner
1575.2.bc.a.1349.4		8	21.5	even	6	inner
1575.2.bk.c.26.1		4	35.12	even	12
1575.2.bk.c.26.2		4	105.47	odd	12
1575.2.bk.c.1151.1		4	15.2	even	4
1575.2.bk.c.1151.2		4	5.2	odd	4
7056.2.k.b.881.1		4	420.143	even	12
7056.2.k.b.881.2		4	140.123	even	12
7056.2.k.b.881.3		4	420.263	odd	12
7056.2.k.b.881.4		4	140.3	odd	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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