LMFDB - Embedded newform 1360.2.bt.d.1041.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1360,2,Mod(81,1360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1360, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1360.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1360.bt (of order $4$, 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:	$10.8596546749$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1041.1
Root			$1.52346i$ of defining polynomial
Character	$\chi$	$=$	1360.1041
Dual form			1360.2.bt.d.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.78436 + 1.78436i) q^{3} +(-0.707107 + 0.707107i) q^{5} +(0.260895 + 0.260895i) q^{7} -3.36786i q^{9} +(1.76642 + 1.76642i) q^{11} -4.68778 q^{13} -2.52346i q^{15} +(3.84558 + 1.48711i) q^{17} +7.16938i q^{19} -0.931060 q^{21} +(-4.73801 - 4.73801i) q^{23} -1.00000i q^{25} +(0.656399 + 0.656399i) q^{27} +(-4.79535 + 4.79535i) q^{29} +(-3.40685 + 3.40685i) q^{31} -6.30387 q^{33} -0.368961 q^{35} +(-1.37133 + 1.37133i) q^{37} +(8.36467 - 8.36467i) q^{39} +(1.66858 + 1.66858i) q^{41} -11.7105i q^{43} +(2.38144 + 2.38144i) q^{45} +1.65317 q^{47} -6.86387i q^{49} +(-9.51543 + 4.20836i) q^{51} -6.81536i q^{53} -2.49810 q^{55} +(-12.7927 - 12.7927i) q^{57} -0.484372i q^{59} +(4.86706 + 4.86706i) q^{61} +(0.878658 - 0.878658i) q^{63} +(3.31476 - 3.31476i) q^{65} +1.87478 q^{67} +16.9086 q^{69} +(-1.21593 + 1.21593i) q^{71} +(0.202452 - 0.202452i) q^{73} +(1.78436 + 1.78436i) q^{75} +0.921703i q^{77} +(-3.80821 - 3.80821i) q^{79} +7.76109 q^{81} -9.94985i q^{83} +(-3.77078 + 1.66769i) q^{85} -17.1132i q^{87} -4.30781 q^{89} +(-1.22302 - 1.22302i) q^{91} -12.1581i q^{93} +(-5.06952 - 5.06952i) q^{95} +(9.01275 - 9.01275i) q^{97} +(5.94908 - 5.94908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 4 q^{11} + 12 q^{17} - 16 q^{21} - 12 q^{23} + 4 q^{27} - 12 q^{29} - 16 q^{33} - 16 q^{35} + 12 q^{37} + 20 q^{39} - 24 q^{41} + 8 q^{45} + 48 q^{47} - 32 q^{51} + 40 q^{61} - 12 q^{63}+ \cdots + 4 q^{97}+O(q^{100}) $ 12 * q + 4 * q^3 + 4 * q^11 + 12 * q^17 - 16 * q^21 - 12 * q^23 + 4 * q^27 - 12 * q^29 - 16 * q^33 - 16 * q^35 + 12 * q^37 + 20 * q^39 - 24 * q^41 + 8 * q^45 + 48 * q^47 - 32 * q^51 + 40 * q^61 - 12 * q^63 + 4 * q^65 + 8 * q^67 - 28 * q^71 - 48 * q^73 - 4 * q^75 + 8 * q^79 + 28 * q^81 - 4 * q^85 + 24 * q^89 + 36 * q^91 + 8 * q^95 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−1.78436	+	1.78436i	−1.03020	+	1.03020i	−0.0306697	+	0.999530i	$0.509764\pi$
$3$	−1.78436	+	1.78436i	−1.03020	+	1.03020i	−0.999530	+	0.0306697i	$0.990236\pi$
$4$		0			0
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$	0.260895	+	0.260895i	0.0986090	+	0.0986090i	0.754690	−	0.656081i	$-0.227787\pi$
$7$	0.260895	+	0.260895i	0.0986090	+	0.0986090i	−0.656081	+	0.754690i	$0.727787\pi$
$8$		0			0
$9$		−	3.36786i		−	1.12262i
$10$		0			0
$11$	1.76642	+	1.76642i	0.532597	+	0.532597i	0.921344	−	0.388747i	$-0.127092\pi$
$11$	1.76642	+	1.76642i	0.532597	+	0.532597i	−0.388747	+	0.921344i	$0.627092\pi$
$12$		0			0
$13$	−4.68778			−1.30016			−0.650078	−	0.759868i	$-0.725264\pi$
$13$	−4.68778			−1.30016			−0.650078	+	0.759868i	$0.725264\pi$
$14$		0			0
$15$		−	2.52346i		−	0.651555i
$16$		0			0
$17$	3.84558	+	1.48711i	0.932691	+	0.360676i
$17$	3.84558	+	1.48711i	0.932691	+	0.360676i
$18$		0			0
$19$			7.16938i			1.64477i	0.568933	+	0.822384i	$0.307356\pi$
$19$			7.16938i			1.64477i	−0.568933	+	0.822384i	$0.692644\pi$
$20$		0			0
$21$	−0.931060			−0.203174
$22$		0			0
$23$	−4.73801	−	4.73801i	−0.987943	−	0.987943i	0.0119854	−	0.999928i	$-0.496185\pi$
$23$	−4.73801	−	4.73801i	−0.987943	−	0.987943i	−0.999928	+	0.0119854i	$0.996185\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	0.656399	+	0.656399i	0.126324	+	0.126324i
$28$		0			0
$29$	−4.79535	+	4.79535i	−0.890475	+	0.890475i	−0.994568	−	0.104093i	$-0.966806\pi$
$29$	−4.79535	+	4.79535i	−0.890475	+	0.890475i	0.104093	+	0.994568i	$0.466806\pi$
$30$		0			0
$31$	−3.40685	+	3.40685i	−0.611888	+	0.611888i	−0.943438	−	0.331549i	$-0.892429\pi$
$31$	−3.40685	+	3.40685i	−0.611888	+	0.611888i	0.331549	+	0.943438i	$0.392429\pi$
$32$		0			0
$33$	−6.30387			−1.09736
$34$		0			0
$35$	−0.368961			−0.0623658
$36$		0			0
$37$	−1.37133	+	1.37133i	−0.225445	+	0.225445i	−0.810787	−	0.585342i	$-0.800960\pi$
$37$	−1.37133	+	1.37133i	−0.225445	+	0.225445i	0.585342	+	0.810787i	$0.300960\pi$
$38$		0			0
$39$	8.36467	−	8.36467i	1.33942	−	1.33942i
$40$		0			0
$41$	1.66858	+	1.66858i	0.260588	+	0.260588i	0.825293	−	0.564705i	$-0.191010\pi$
$41$	1.66858	+	1.66858i	0.260588	+	0.260588i	−0.564705	+	0.825293i	$0.691010\pi$
$42$		0			0
$43$		−	11.7105i		−	1.78584i	−0.450218	−	0.892918i	$-0.648654\pi$
$43$		−	11.7105i		−	1.78584i	0.450218	−	0.892918i	$-0.351346\pi$
$44$		0			0
$45$	2.38144	+	2.38144i	0.355004	+	0.355004i
$46$		0			0
$47$	1.65317			0.241140			0.120570	−	0.992705i	$-0.461528\pi$
$47$	1.65317			0.241140			0.120570	+	0.992705i	$0.461528\pi$
$48$		0			0
$49$		−	6.86387i		−	0.980553i
$50$		0			0
$51$	−9.51543	+	4.20836i	−1.33243	+	0.589289i
$52$		0			0
$53$		−	6.81536i		−	0.936162i	−0.883686	−	0.468081i	$-0.844946\pi$
$53$		−	6.81536i		−	0.936162i	0.883686	−	0.468081i	$-0.155054\pi$
$54$		0			0
$55$	−2.49810			−0.336844
$56$		0			0
$57$	−12.7927	−	12.7927i	−1.69444	−	1.69444i
$58$		0			0
$59$		−	0.484372i		−	0.0630598i	−0.999503	−	0.0315299i	$-0.989962\pi$
$59$		−	0.484372i		−	0.0630598i	0.999503	−	0.0315299i	$-0.0100379\pi$
$60$		0			0
$61$	4.86706	+	4.86706i	0.623164	+	0.623164i	0.946339	−	0.323175i	$-0.104750\pi$
$61$	4.86706	+	4.86706i	0.623164	+	0.623164i	−0.323175	+	0.946339i	$0.604750\pi$
$62$		0			0
$63$	0.878658	−	0.878658i	0.110701	−	0.110701i
$64$		0			0
$65$	3.31476	−	3.31476i	0.411145	−	0.411145i
$66$		0			0
$67$	1.87478			0.229041			0.114520	−	0.993421i	$-0.463467\pi$
$67$	1.87478			0.229041			0.114520	+	0.993421i	$0.463467\pi$
$68$		0			0
$69$	16.9086			2.03556
$70$		0			0
$71$	−1.21593	+	1.21593i	−0.144304	+	0.144304i	−0.775568	−	0.631264i	$-0.782536\pi$
$71$	−1.21593	+	1.21593i	−0.144304	+	0.144304i	0.631264	+	0.775568i	$0.282536\pi$
$72$		0			0
$73$	0.202452	−	0.202452i	0.0236952	−	0.0236952i	−0.695160	−	0.718855i	$-0.744666\pi$
$73$	0.202452	−	0.202452i	0.0236952	−	0.0236952i	0.718855	+	0.695160i	$0.244666\pi$
$74$		0			0
$75$	1.78436	+	1.78436i	0.206040	+	0.206040i
$76$		0			0
$77$			0.921703i			0.105038i
$78$		0			0
$79$	−3.80821	−	3.80821i	−0.428458	−	0.428458i	0.459645	−	0.888103i	$-0.347977\pi$
$79$	−3.80821	−	3.80821i	−0.428458	−	0.428458i	−0.888103	+	0.459645i	$0.847977\pi$
$80$		0			0
$81$	7.76109			0.862343
$82$		0			0
$83$		−	9.94985i		−	1.09214i	−0.837740	−	0.546069i	$-0.816124\pi$
$83$		−	9.94985i		−	1.09214i	0.837740	−	0.546069i	$-0.183876\pi$
$84$		0			0
$85$	−3.77078	+	1.66769i	−0.408999	+	0.180887i
$86$		0			0
$87$		−	17.1132i		−	1.83473i
$88$		0			0
$89$	−4.30781			−0.456627			−0.228314	−	0.973588i	$-0.573321\pi$
$89$	−4.30781			−0.456627			−0.228314	+	0.973588i	$0.573321\pi$
$90$		0			0
$91$	−1.22302	−	1.22302i	−0.128207	−	0.128207i
$92$		0			0
$93$		−	12.1581i		−	1.26073i
$94$		0			0
$95$	−5.06952	−	5.06952i	−0.520121	−	0.520121i
$96$		0			0
$97$	9.01275	−	9.01275i	0.915106	−	0.915106i	−0.0815619	−	0.996668i	$-0.525991\pi$
$97$	9.01275	−	9.01275i	0.915106	−	0.915106i	0.996668	+	0.0815619i	$0.0259908\pi$
$98$		0			0
$99$	5.94908	−	5.94908i	0.597905	−	0.597905i
$100$		0			0
$101$	−9.08552			−0.904043			−0.452021	−	0.892007i	$-0.649297\pi$
$101$	−9.08552			−0.904043			−0.452021	+	0.892007i	$0.649297\pi$
$102$		0			0
$103$	−4.77811			−0.470801			−0.235401	−	0.971898i	$-0.575640\pi$
$103$	−4.77811			−0.470801			−0.235401	+	0.971898i	$0.575640\pi$
$104$		0			0
$105$	0.658359	−	0.658359i	0.0642492	−	0.0642492i
$106$		0			0
$107$	−2.01673	+	2.01673i	−0.194965	+	0.194965i	−0.797837	−	0.602873i	$-0.794023\pi$
$107$	−2.01673	+	2.01673i	−0.194965	+	0.194965i	0.602873	+	0.797837i	$0.294023\pi$
$108$		0			0
$109$	−6.68119	−	6.68119i	−0.639942	−	0.639942i	0.310599	−	0.950541i	$-0.399470\pi$
$109$	−6.68119	−	6.68119i	−0.639942	−	0.639942i	−0.950541	+	0.310599i	$0.899470\pi$
$110$		0			0
$111$		−	4.89387i		−	0.464506i
$112$		0			0
$113$	−7.55112	−	7.55112i	−0.710349	−	0.710349i	0.256259	−	0.966608i	$-0.417510\pi$
$113$	−7.55112	−	7.55112i	−0.710349	−	0.710349i	−0.966608	+	0.256259i	$0.917510\pi$
$114$		0			0
$115$	6.70055			0.624830
$116$		0			0
$117$			15.7878i			1.45958i
$118$		0			0
$119$	0.615314	+	1.39127i	0.0564058	+	0.127538i
$120$		0			0
$121$		−	4.75949i		−	0.432681i
$122$		0			0
$123$	−5.95468			−0.536915
$124$		0			0
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$			15.7315i			1.39595i	0.716124	+	0.697974i	$0.245915\pi$
$127$			15.7315i			1.39595i	−0.716124	+	0.697974i	$0.754085\pi$
$128$		0			0
$129$	20.8957	+	20.8957i	1.83977	+	1.83977i
$130$		0			0
$131$	2.89320	−	2.89320i	0.252780	−	0.252780i	−0.569329	−	0.822109i	$-0.692797\pi$
$131$	2.89320	−	2.89320i	0.252780	−	0.252780i	0.822109	+	0.569329i	$0.192797\pi$
$132$		0			0
$133$	−1.87045	+	1.87045i	−0.162189	+	0.162189i
$134$		0			0
$135$	−0.928289			−0.0798944
$136$		0			0
$137$	−16.2144			−1.38529			−0.692644	−	0.721280i	$-0.743554\pi$
$137$	−16.2144			−1.38529			−0.692644	+	0.721280i	$0.743554\pi$
$138$		0			0
$139$	−7.57109	+	7.57109i	−0.642172	+	0.642172i	−0.951089	−	0.308917i	$-0.900033\pi$
$139$	−7.57109	+	7.57109i	−0.642172	+	0.642172i	0.308917	+	0.951089i	$0.400033\pi$
$140$		0			0
$141$	−2.94985	+	2.94985i	−0.248422	+	0.248422i
$142$		0			0
$143$	−8.28060	−	8.28060i	−0.692459	−	0.692459i
$144$		0			0
$145$		−	6.78165i		−	0.563186i
$146$		0			0
$147$	12.2476	+	12.2476i	1.01016	+	1.01016i
$148$		0			0
$149$	−11.1290			−0.911719			−0.455860	−	0.890052i	$-0.650668\pi$
$149$	−11.1290			−0.911719			−0.455860	+	0.890052i	$0.650668\pi$
$150$		0			0
$151$		−	16.0861i		−	1.30907i	−0.756032	−	0.654535i	$-0.772865\pi$
$151$		−	16.0861i		−	1.30907i	0.756032	−	0.654535i	$-0.227135\pi$
$152$		0			0
$153$	5.00837	−	12.9514i	0.404903	−	1.04706i
$154$		0			0
$155$		−	4.81801i		−	0.386992i
$156$		0			0
$157$	−2.63326			−0.210157			−0.105079	−	0.994464i	$-0.533509\pi$
$157$	−2.63326			−0.210157			−0.105079	+	0.994464i	$0.533509\pi$
$158$		0			0
$159$	12.1610	+	12.1610i	0.964434	+	0.964434i
$160$		0			0
$161$		−	2.47224i		−	0.194840i
$162$		0			0
$163$	13.5013	+	13.5013i	1.05751	+	1.05751i	0.998242	+	0.0592626i	$0.0188749\pi$
$163$	13.5013	+	13.5013i	1.05751	+	1.05751i	0.0592626	+	0.998242i	$0.481125\pi$
$164$		0			0
$165$	4.45751	−	4.45751i	0.347016	−	0.347016i
$166$		0			0
$167$	−2.81953	+	2.81953i	−0.218182	+	0.218182i	−0.807732	−	0.589550i	$-0.799305\pi$
$167$	−2.81953	+	2.81953i	−0.218182	+	0.218182i	0.589550	+	0.807732i	$0.299305\pi$
$168$		0			0
$169$	8.97524			0.690403
$170$		0			0
$171$	24.1455			1.84645
$172$		0			0
$173$	−10.3293	+	10.3293i	−0.785322	+	0.785322i	−0.980723	−	0.195401i	$-0.937399\pi$
$173$	−10.3293	+	10.3293i	−0.785322	+	0.785322i	0.195401	+	0.980723i	$0.437399\pi$
$174$		0			0
$175$	0.260895	−	0.260895i	0.0197218	−	0.0197218i
$176$		0			0
$177$	0.864292	+	0.864292i	0.0649642	+	0.0649642i
$178$		0			0
$179$			14.7452i			1.10211i	0.834469	+	0.551054i	$0.185774\pi$
$179$			14.7452i			1.10211i	−0.834469	+	0.551054i	$0.814226\pi$
$180$		0			0
$181$	7.96307	+	7.96307i	0.591890	+	0.591890i	0.938142	−	0.346252i	$-0.112546\pi$
$181$	7.96307	+	7.96307i	0.591890	+	0.591890i	−0.346252	+	0.938142i	$0.612546\pi$
$182$		0			0
$183$	−17.3692			−1.28397
$184$		0			0
$185$		−	1.93935i		−	0.142584i
$186$		0			0
$187$	4.16607	+	9.41980i	0.304653	+	0.688844i
$188$		0			0
$189$			0.342503i			0.0249134i
$190$		0			0
$191$	−21.4934			−1.55521			−0.777604	−	0.628754i	$-0.783565\pi$
$191$	−21.4934			−1.55521			−0.777604	+	0.628754i	$0.783565\pi$
$192$		0			0
$193$	−1.00556	−	1.00556i	−0.0723819	−	0.0723819i	0.669989	−	0.742371i	$-0.266299\pi$
$193$	−1.00556	−	1.00556i	−0.0723819	−	0.0723819i	−0.742371	+	0.669989i	$0.766299\pi$
$194$		0			0
$195$			11.8294i			0.847123i
$196$		0			0
$197$	12.3127	+	12.3127i	0.877240	+	0.877240i	0.993248	−	0.116008i	$-0.0370098\pi$
$197$	12.3127	+	12.3127i	0.877240	+	0.877240i	−0.116008	+	0.993248i	$0.537010\pi$
$198$		0			0
$199$	12.6485	−	12.6485i	0.896626	−	0.896626i	−0.0985101	−	0.995136i	$-0.531408\pi$
$199$	12.6485	−	12.6485i	0.896626	−	0.896626i	0.995136	+	0.0985101i	$0.0314077\pi$
$200$		0			0
$201$	−3.34527	+	3.34527i	−0.235957	+	0.235957i
$202$		0			0
$203$	−2.50217			−0.175618
$204$		0			0
$205$	−2.35972			−0.164810
$206$		0			0
$207$	−15.9570	+	15.9570i	−1.10909	+	1.10909i
$208$		0			0
$209$	−12.6642	+	12.6642i	−0.875999	+	0.875999i
$210$		0			0
$211$	5.07688	+	5.07688i	0.349507	+	0.349507i	0.859926	−	0.510419i	$-0.170510\pi$
$211$	5.07688	+	5.07688i	0.349507	+	0.349507i	−0.510419	+	0.859926i	$0.670510\pi$
$212$		0			0
$213$		−	4.33930i		−	0.297324i
$214$		0			0
$215$	8.28059	+	8.28059i	0.564731	+	0.564731i
$216$		0			0
$217$	−1.77766			−0.120675
$218$		0			0
$219$			0.722494i			0.0488216i
$220$		0			0
$221$	−18.0272	−	6.97123i	−1.21264	−	0.468935i
$222$		0			0
$223$			3.93334i			0.263396i	0.991290	+	0.131698i	$0.0420428\pi$
$223$			3.93334i			0.263396i	−0.991290	+	0.131698i	$0.957957\pi$
$224$		0			0
$225$	−3.36786			−0.224524
$226$		0			0
$227$	−2.46062	−	2.46062i	−0.163317	−	0.163317i	0.620717	−	0.784034i	$-0.286841\pi$
$227$	−2.46062	−	2.46062i	−0.163317	−	0.163317i	−0.784034	+	0.620717i	$0.786841\pi$
$228$		0			0
$229$		−	4.41164i		−	0.291529i	−0.989319	−	0.145765i	$-0.953436\pi$
$229$		−	4.41164i		−	0.291529i	0.989319	−	0.145765i	$-0.0465642\pi$
$230$		0			0
$231$	−1.64465	−	1.64465i	−0.108210	−	0.108210i
$232$		0			0
$233$	−11.0779	+	11.0779i	−0.725739	+	0.725739i	−0.969768	−	0.244029i	$-0.921531\pi$
$233$	−11.0779	+	11.0779i	−0.725739	+	0.725739i	0.244029	+	0.969768i	$0.421531\pi$
$234$		0			0
$235$	−1.16897	+	1.16897i	−0.0762552	+	0.0762552i
$236$		0			0
$237$	13.5904			0.882793
$238$		0			0
$239$	6.59116			0.426346			0.213173	−	0.977014i	$-0.431620\pi$
$239$	6.59116			0.426346			0.213173	+	0.977014i	$0.431620\pi$
$240$		0			0
$241$	3.09742	−	3.09742i	0.199523	−	0.199523i	−0.600273	−	0.799795i	$-0.704941\pi$
$241$	3.09742	−	3.09742i	0.199523	−	0.199523i	0.799795	+	0.600273i	$0.204941\pi$
$242$		0			0
$243$	−15.8178	+	15.8178i	−1.01471	+	1.01471i
$244$		0			0
$245$	4.85349	+	4.85349i	0.310078	+	0.310078i
$246$		0			0
$247$		−	33.6084i		−	2.13845i
$248$		0			0
$249$	17.7541	+	17.7541i	1.12512	+	1.12512i
$250$		0			0
$251$	4.30290			0.271597			0.135798	−	0.990736i	$-0.456640\pi$
$251$	4.30290			0.271597			0.135798	+	0.990736i	$0.456640\pi$
$252$		0			0
$253$		−	16.7387i		−	1.05235i
$254$		0			0
$255$	3.75266	−	9.70419i	0.235001	−	0.607700i
$256$		0			0
$257$			10.5366i			0.657254i	0.944460	+	0.328627i	$0.106586\pi$
$257$			10.5366i			0.657254i	−0.944460	+	0.328627i	$0.893414\pi$
$258$		0			0
$259$	−0.715544			−0.0444618
$260$		0			0
$261$	16.1501	+	16.1501i	0.999665	+	0.999665i
$262$		0			0
$263$			13.6253i			0.840173i	0.907484	+	0.420086i	$0.138000\pi$
$263$			13.6253i			0.840173i	−0.907484	+	0.420086i	$0.862000\pi$
$264$		0			0
$265$	4.81919	+	4.81919i	0.296040	+	0.296040i
$266$		0			0
$267$	7.68668	−	7.68668i	0.470417	−	0.470417i
$268$		0			0
$269$	11.0360	−	11.0360i	0.672878	−	0.672878i	−0.285501	−	0.958378i	$-0.592160\pi$
$269$	11.0360	−	11.0360i	0.672878	−	0.672878i	0.958378	+	0.285501i	$0.0921599\pi$
$270$		0			0
$271$	9.66560			0.587143			0.293572	−	0.955937i	$-0.405156\pi$
$271$	9.66560			0.587143			0.293572	+	0.955937i	$0.405156\pi$
$272$		0			0
$273$	4.36460			0.264158
$274$		0			0
$275$	1.76642	−	1.76642i	0.106519	−	0.106519i
$276$		0			0
$277$	−0.955063	+	0.955063i	−0.0573842	+	0.0573842i	−0.735217	−	0.677832i	$-0.762920\pi$
$277$	−0.955063	+	0.955063i	−0.0573842	+	0.0573842i	0.677832	+	0.735217i	$0.262920\pi$
$278$		0			0
$279$	11.4738	+	11.4738i	0.686919	+	0.686919i
$280$		0			0
$281$			15.8582i			0.946020i	0.881057	+	0.473010i	$0.156833\pi$
$281$			15.8582i			0.946020i	−0.881057	+	0.473010i	$0.843167\pi$
$282$		0			0
$283$	−20.7458	−	20.7458i	−1.23321	−	1.23321i	−0.962725	−	0.270483i	$-0.912816\pi$
$283$	−20.7458	−	20.7458i	−1.23321	−	1.23321i	−0.270483	−	0.962725i	$-0.587184\pi$
$284$		0			0
$285$	18.0917			1.07166
$286$		0			0
$287$			0.870646i			0.0513926i
$288$		0			0
$289$	12.5770	+	11.4376i	0.739825	+	0.672799i
$290$		0			0
$291$			32.1639i			1.88548i
$292$		0			0
$293$	−20.6478			−1.20626			−0.603129	−	0.797644i	$-0.706080\pi$
$293$	−20.6478			−1.20626			−0.603129	+	0.797644i	$0.706080\pi$
$294$		0			0
$295$	0.342503	+	0.342503i	0.0199413	+	0.0199413i
$296$		0			0
$297$			2.31896i			0.134560i
$298$		0			0
$299$	22.2107	+	22.2107i	1.28448	+	1.28448i
$300$		0			0
$301$	3.05521	−	3.05521i	0.176100	−	0.176100i
$302$		0			0
$303$	16.2118	−	16.2118i	0.931344	−	0.931344i
$304$		0			0
$305$	−6.88307			−0.394123
$306$		0			0
$307$	−16.3437			−0.932787			−0.466393	−	0.884577i	$-0.654447\pi$
$307$	−16.3437			−0.932787			−0.466393	+	0.884577i	$0.654447\pi$
$308$		0			0
$309$	8.52586	−	8.52586i	0.485019	−	0.485019i
$310$		0			0
$311$	−24.8266	+	24.8266i	−1.40778	+	1.40778i	−0.636547	+	0.771238i	$0.719638\pi$
$311$	−24.8266	+	24.8266i	−1.40778	+	1.40778i	−0.771238	+	0.636547i	$0.780362\pi$
$312$		0			0
$313$	22.1419	+	22.1419i	1.25153	+	1.25153i	0.955032	+	0.296502i	$0.0958202\pi$
$313$	22.1419	+	22.1419i	1.25153	+	1.25153i	0.296502	+	0.955032i	$0.404180\pi$
$314$		0			0
$315$			1.24261i			0.0700132i
$316$		0			0
$317$	8.87399	+	8.87399i	0.498413	+	0.498413i	0.910944	−	0.412531i	$-0.135355\pi$
$317$	8.87399	+	8.87399i	0.498413	+	0.498413i	−0.412531	+	0.910944i	$0.635355\pi$
$318$		0			0
$319$	−16.9413			−0.948528
$320$		0			0
$321$		−	7.19714i		−	0.401705i
$322$		0			0
$323$	−10.6616	+	27.5704i	−0.593229	+	1.53406i
$324$		0			0
$325$			4.68778i			0.260031i
$326$		0			0
$327$	23.8433			1.31854
$328$		0			0
$329$	0.431305	+	0.431305i	0.0237786	+	0.0237786i
$330$		0			0
$331$		−	0.497450i		−	0.0273423i	−0.999907	−	0.0136712i	$-0.995648\pi$
$331$		−	0.497450i		−	0.0273423i	0.999907	−	0.0136712i	$-0.00435180\pi$
$332$		0			0
$333$	4.61844	+	4.61844i	0.253089	+	0.253089i
$334$		0			0
$335$	−1.32567	+	1.32567i	−0.0724290	+	0.0724290i
$336$		0			0
$337$	−23.7358	+	23.7358i	−1.29297	+	1.29297i	−0.360031	+	0.932940i	$0.617234\pi$
$337$	−23.7358	+	23.7358i	−1.29297	+	1.29297i	−0.932940	+	0.360031i	$0.882766\pi$
$338$		0			0
$339$	26.9478			1.46360
$340$		0			0
$341$	−12.0359			−0.651780
$342$		0			0
$343$	3.61701	−	3.61701i	0.195300	−	0.195300i
$344$		0			0
$345$	−11.9562	+	11.9562i	−0.643699	+	0.643699i
$346$		0			0
$347$	−18.5976	−	18.5976i	−0.998370	−	0.998370i	0.00162819	−	0.999999i	$-0.499482\pi$
$347$	−18.5976	−	18.5976i	−0.998370	−	0.998370i	−0.999999	+	0.00162819i	$0.999482\pi$
$348$		0			0
$349$		−	16.7865i		−	0.898560i	−0.893391	−	0.449280i	$-0.851681\pi$
$349$		−	16.7865i		−	0.898560i	0.893391	−	0.449280i	$-0.148319\pi$
$350$		0			0
$351$	−3.07705	−	3.07705i	−0.164241	−	0.164241i
$352$		0			0
$353$	−23.4532			−1.24829			−0.624144	−	0.781309i	$-0.714552\pi$
$353$	−23.4532			−1.24829			−0.624144	+	0.781309i	$0.714552\pi$
$354$		0			0
$355$		−	1.71958i		−	0.0912660i
$356$		0			0
$357$	−3.58047	−	1.38459i	−0.189498	−	0.0732800i
$358$		0			0
$359$		−	18.1568i		−	0.958279i	−0.877739	−	0.479139i	$-0.840949\pi$
$359$		−	18.1568i		−	0.958279i	0.877739	−	0.479139i	$-0.159051\pi$
$360$		0			0
$361$	−32.4000			−1.70526
$362$		0			0
$363$	8.49263	+	8.49263i	0.445747	+	0.445747i
$364$		0			0
$365$			0.286310i			0.0149862i
$366$		0			0
$367$	9.68061	+	9.68061i	0.505324	+	0.505324i	0.913087	−	0.407764i	$-0.133691\pi$
$367$	9.68061	+	9.68061i	0.505324	+	0.505324i	−0.407764	+	0.913087i	$0.633691\pi$
$368$		0			0
$369$	5.61954	−	5.61954i	0.292541	−	0.292541i
$370$		0			0
$371$	1.77809	−	1.77809i	0.0923140	−	0.0923140i
$372$		0			0
$373$	−10.1594			−0.526035			−0.263018	−	0.964791i	$-0.584718\pi$
$373$	−10.1594			−0.526035			−0.263018	+	0.964791i	$0.584718\pi$
$374$		0			0
$375$	−2.52346			−0.130311
$376$		0			0
$377$	22.4795	−	22.4795i	1.15775	−	1.15775i
$378$		0			0
$379$	2.94447	−	2.94447i	0.151247	−	0.151247i	−0.627428	−	0.778675i	$-0.715892\pi$
$379$	2.94447	−	2.94447i	0.151247	−	0.151247i	0.778675	+	0.627428i	$0.215892\pi$
$380$		0			0
$381$	−28.0707	−	28.0707i	−1.43810	−	1.43810i
$382$		0			0
$383$			0.813273i			0.0415563i	0.999784	+	0.0207782i	$0.00661437\pi$
$383$			0.813273i			0.0415563i	−0.999784	+	0.0207782i	$0.993386\pi$
$384$		0			0
$385$	−0.651742	−	0.651742i	−0.0332159	−	0.0332159i
$386$		0			0
$387$	−39.4394			−2.00482
$388$		0			0
$389$			3.11676i			0.158026i	0.996874	+	0.0790131i	$0.0251769\pi$
$389$			3.11676i			0.158026i	−0.996874	+	0.0790131i	$0.974823\pi$
$390$		0			0
$391$	−11.1745	−	25.2663i	−0.565118	−	1.27777i
$392$		0			0
$393$			10.3250i			0.520828i
$394$		0			0
$395$	5.38563			0.270980
$396$		0			0
$397$	11.5998	+	11.5998i	0.582177	+	0.582177i	0.935501	−	0.353324i	$-0.114949\pi$
$397$	11.5998	+	11.5998i	0.582177	+	0.582177i	−0.353324	+	0.935501i	$0.614949\pi$
$398$		0			0
$399$		−	6.67512i		−	0.334174i
$400$		0			0
$401$	10.2143	+	10.2143i	0.510075	+	0.510075i	0.914549	−	0.404474i	$-0.132545\pi$
$401$	10.2143	+	10.2143i	0.510075	+	0.510075i	−0.404474	+	0.914549i	$0.632545\pi$
$402$		0			0
$403$	15.9706	−	15.9706i	0.795550	−	0.795550i
$404$		0			0
$405$	−5.48792	+	5.48792i	−0.272697	+	0.272697i
$406$		0			0
$407$	−4.84469			−0.240142
$408$		0			0
$409$	32.2867			1.59648			0.798238	−	0.602342i	$-0.205765\pi$
$409$	32.2867			1.59648			0.798238	+	0.602342i	$0.205765\pi$
$410$		0			0
$411$	28.9323	−	28.9323i	1.42712	−	1.42712i
$412$		0			0
$413$	0.126370	−	0.126370i	0.00621827	−	0.00621827i
$414$		0			0
$415$	7.03561	+	7.03561i	0.345364	+	0.345364i
$416$		0			0
$417$		−	27.0191i		−	1.32313i
$418$		0			0
$419$	−13.3485	−	13.3485i	−0.652115	−	0.652115i	0.301387	−	0.953502i	$-0.402550\pi$
$419$	−13.3485	−	13.3485i	−0.652115	−	0.652115i	−0.953502	+	0.301387i	$0.902550\pi$
$420$		0			0
$421$	−2.06006			−0.100401			−0.0502006	−	0.998739i	$-0.515986\pi$
$421$	−2.06006			−0.100401			−0.0502006	+	0.998739i	$0.515986\pi$
$422$		0			0
$423$		−	5.56766i		−	0.270709i
$424$		0			0
$425$	1.48711	−	3.84558i	0.0721353	−	0.186538i
$426$		0			0
$427$			2.53958i			0.122899i
$428$		0			0
$429$	29.5511			1.42674
$430$		0			0
$431$	2.63581	+	2.63581i	0.126962	+	0.126962i	0.767733	−	0.640770i	$-0.221385\pi$
$431$	2.63581	+	2.63581i	0.126962	+	0.126962i	−0.640770	+	0.767733i	$0.721385\pi$
$432$		0			0
$433$			27.9634i			1.34383i	0.740626	+	0.671917i	$0.234529\pi$
$433$			27.9634i			1.34383i	−0.740626	+	0.671917i	$0.765471\pi$
$434$		0			0
$435$	12.1009	+	12.1009i	0.580193	+	0.580193i
$436$		0			0
$437$	33.9686	−	33.9686i	1.62494	−	1.62494i
$438$		0			0
$439$	−8.87022	+	8.87022i	−0.423353	+	0.423353i	−0.886356	−	0.463004i	$-0.846772\pi$
$439$	−8.87022	+	8.87022i	−0.423353	+	0.423353i	0.463004	+	0.886356i	$0.346772\pi$
$440$		0			0
$441$	−23.1166			−1.10079
$442$		0			0
$443$	19.9529			0.947991			0.473995	−	0.880527i	$-0.342811\pi$
$443$	19.9529			0.947991			0.473995	+	0.880527i	$0.342811\pi$
$444$		0			0
$445$	3.04608	−	3.04608i	0.144398	−	0.144398i
$446$		0			0
$447$	19.8580	−	19.8580i	0.939252	−	0.939252i
$448$		0			0
$449$	14.2737	+	14.2737i	0.673618	+	0.673618i	0.958548	−	0.284930i	$-0.0919704\pi$
$449$	14.2737	+	14.2737i	0.673618	+	0.673618i	−0.284930	+	0.958548i	$0.591970\pi$
$450$		0			0
$451$			5.89483i			0.277577i
$452$		0			0
$453$	28.7034	+	28.7034i	1.34860	+	1.34860i
$454$		0			0
$455$	1.72961			0.0810852
$456$		0			0
$457$		−	37.7391i		−	1.76536i	−0.469973	−	0.882681i	$-0.655737\pi$
$457$		−	37.7391i		−	1.76536i	0.469973	−	0.882681i	$-0.344263\pi$
$458$		0			0
$459$	1.54810	+	3.50038i	0.0722592	+	0.163384i
$460$		0			0
$461$		−	38.1740i		−	1.77794i	−0.457966	−	0.888970i	$-0.651422\pi$
$461$		−	38.1740i		−	1.77794i	0.457966	−	0.888970i	$-0.348578\pi$
$462$		0			0
$463$	−13.1481			−0.611044			−0.305522	−	0.952185i	$-0.598831\pi$
$463$	−13.1481			−0.611044			−0.305522	+	0.952185i	$0.598831\pi$
$464$		0			0
$465$	8.59706	+	8.59706i	0.398679	+	0.398679i
$466$		0			0
$467$		−	16.2167i		−	0.750422i	−0.926940	−	0.375211i	$-0.877570\pi$
$467$		−	16.2167i		−	0.750422i	0.926940	−	0.375211i	$-0.122430\pi$
$468$		0			0
$469$	0.489120	+	0.489120i	0.0225855	+	0.0225855i
$470$		0			0
$471$	4.69869	−	4.69869i	0.216504	−	0.216504i
$472$		0			0
$473$	20.6857	−	20.6857i	0.951132	−	0.951132i
$474$		0			0
$475$	7.16938			0.328954
$476$		0			0
$477$	−22.9532			−1.05096
$478$		0			0
$479$	−1.46724	+	1.46724i	−0.0670398	+	0.0670398i	−0.739832	−	0.672792i	$-0.765095\pi$
$479$	−1.46724	+	1.46724i	−0.0670398	+	0.0670398i	0.672792	+	0.739832i	$0.265095\pi$
$480$		0			0
$481$	6.42847	−	6.42847i	0.293113	−	0.293113i
$482$		0			0
$483$	4.41137	+	4.41137i	0.200724	+	0.200724i
$484$		0			0
$485$			12.7460i			0.578764i
$486$		0			0
$487$	16.9890	+	16.9890i	0.769843	+	0.769843i	0.978079	−	0.208236i	$-0.0667721\pi$
$487$	16.9890	+	16.9890i	0.769843	+	0.769843i	−0.208236	+	0.978079i	$0.566772\pi$
$488$		0			0
$489$	−48.1824			−2.17888
$490$		0			0
$491$			22.3803i			1.01001i	0.863116	+	0.505005i	$0.168509\pi$
$491$			22.3803i			1.01001i	−0.863116	+	0.505005i	$0.831491\pi$
$492$		0			0
$493$	−25.5721	+	11.3097i	−1.15171	+	0.509364i
$494$		0			0
$495$			8.41327i			0.378148i
$496$		0			0
$497$	−0.634459			−0.0284594
$498$		0			0
$499$	2.61493	+	2.61493i	0.117060	+	0.117060i	0.763210	−	0.646150i	$-0.223622\pi$
$499$	2.61493	+	2.61493i	0.117060	+	0.117060i	−0.646150	+	0.763210i	$0.723622\pi$
$500$		0			0
$501$		−	10.0621i		−	0.449541i
$502$		0			0
$503$	13.0544	+	13.0544i	0.582066	+	0.582066i	0.935471	−	0.353404i	$-0.114976\pi$
$503$	13.0544	+	13.0544i	0.582066	+	0.582066i	−0.353404	+	0.935471i	$0.614976\pi$
$504$		0			0
$505$	6.42443	−	6.42443i	0.285883	−	0.285883i
$506$		0			0
$507$	−16.0150	+	16.0150i	−0.711253	+	0.711253i
$508$		0			0
$509$	−17.3588			−0.769415			−0.384708	−	0.923039i	$-0.625698\pi$
$509$	−17.3588			−0.769415			−0.384708	+	0.923039i	$0.625698\pi$
$510$		0			0
$511$	0.105637			0.00467312
$512$		0			0
$513$	−4.70598	+	4.70598i	−0.207774	+	0.207774i
$514$		0			0
$515$	3.37863	−	3.37863i	0.148880	−	0.148880i
$516$		0			0
$517$	2.92021	+	2.92021i	0.128431	+	0.128431i
$518$		0			0
$519$		−	36.8623i		−	1.61808i
$520$		0			0
$521$	9.87476	+	9.87476i	0.432621	+	0.432621i	0.889519	−	0.456898i	$-0.151040\pi$
$521$	9.87476	+	9.87476i	0.432621	+	0.432621i	−0.456898	+	0.889519i	$0.651040\pi$
$522$		0			0
$523$	−5.59638			−0.244712			−0.122356	−	0.992486i	$-0.539045\pi$
$523$	−5.59638			−0.244712			−0.122356	+	0.992486i	$0.539045\pi$
$524$		0			0
$525$			0.931060i			0.0406348i
$526$		0			0
$527$	−18.1677	+	8.03498i	−0.791397	+	0.350009i
$528$		0			0
$529$			21.8974i			0.952062i
$530$		0			0
$531$	−1.63130			−0.0707923
$532$		0			0
$533$	−7.82191	−	7.82191i	−0.338805	−	0.338805i
$534$		0			0
$535$		−	2.85209i		−	0.123307i
$536$		0			0
$537$	−26.3107	−	26.3107i	−1.13539	−	1.13539i
$538$		0			0
$539$	12.1245	−	12.1245i	0.522239	−	0.522239i
$540$		0			0
$541$	27.6477	−	27.6477i	1.18867	−	1.18867i	0.211234	−	0.977436i	$-0.432252\pi$
$541$	27.6477	−	27.6477i	1.18867	−	1.18867i	0.977436	−	0.211234i	$-0.0677481\pi$
$542$		0			0
$543$	−28.4179			−1.21953
$544$		0			0
$545$	9.44863			0.404735
$546$		0			0
$547$	−20.7878	+	20.7878i	−0.888823	+	0.888823i	−0.994410	−	0.105588i	$-0.966328\pi$
$547$	−20.7878	+	20.7878i	−0.888823	+	0.888823i	0.105588	+	0.994410i	$0.466328\pi$
$548$		0			0
$549$	16.3916	−	16.3916i	0.699577	−	0.699577i
$550$		0			0
$551$	−34.3797	−	34.3797i	−1.46462	−	1.46462i
$552$		0			0
$553$		−	1.98709i		−	0.0844995i
$554$		0			0
$555$	3.46049	+	3.46049i	0.146890	+	0.146890i
$556$		0			0
$557$	−27.9399			−1.18385			−0.591927	−	0.805992i	$-0.701632\pi$
$557$	−27.9399			−1.18385			−0.591927	+	0.805992i	$0.701632\pi$
$558$		0			0
$559$			54.8963i			2.32186i
$560$		0			0
$561$	−24.2420	−	9.37453i	−1.02350	−	0.395793i
$562$		0			0
$563$			11.2994i			0.476213i	0.971239	+	0.238106i	$0.0765267\pi$
$563$			11.2994i			0.476213i	−0.971239	+	0.238106i	$0.923473\pi$
$564$		0			0
$565$	10.6789			0.449264
$566$		0			0
$567$	2.02483	+	2.02483i	0.0850348	+	0.0850348i
$568$		0			0
$569$			12.1204i			0.508114i	0.967189	+	0.254057i	$0.0817650\pi$
$569$			12.1204i			0.508114i	−0.967189	+	0.254057i	$0.918235\pi$
$570$		0			0
$571$	7.74264	+	7.74264i	0.324019	+	0.324019i	0.850307	−	0.526287i	$-0.176416\pi$
$571$	7.74264	+	7.74264i	0.324019	+	0.324019i	−0.526287	+	0.850307i	$0.676416\pi$
$572$		0			0
$573$	38.3519	−	38.3519i	1.60217	−	1.60217i
$574$		0			0
$575$	−4.73801	+	4.73801i	−0.197589	+	0.197589i
$576$		0			0
$577$	−9.09883			−0.378789			−0.189395	−	0.981901i	$-0.560653\pi$
$577$	−9.09883			−0.378789			−0.189395	+	0.981901i	$0.560653\pi$
$578$		0			0
$579$	3.58856			0.149135
$580$		0			0
$581$	2.59587	−	2.59587i	0.107695	−	0.107695i
$582$		0			0
$583$	12.0388	−	12.0388i	0.498597	−	0.498597i
$584$		0			0
$585$	−11.1637	−	11.1637i	−0.461560	−	0.461560i
$586$		0			0
$587$			11.2991i			0.466362i	0.972433	+	0.233181i	$0.0749134\pi$
$587$			11.2991i			0.466362i	−0.972433	+	0.233181i	$0.925087\pi$
$588$		0			0
$589$	−24.4250	−	24.4250i	−1.00641	−	1.00641i
$590$		0			0
$591$	−43.9403			−1.80746
$592$		0			0
$593$			42.8620i			1.76013i	0.474851	+	0.880066i	$0.342502\pi$
$593$			42.8620i			1.76013i	−0.474851	+	0.880066i	$0.657498\pi$
$594$		0			0
$595$	−1.41887	−	0.548685i	−0.0581680	−	0.0224939i
$596$		0			0
$597$			45.1388i			1.84741i
$598$		0			0
$599$	−21.0108			−0.858478			−0.429239	−	0.903191i	$-0.641218\pi$
$599$	−21.0108			−0.858478			−0.429239	+	0.903191i	$0.641218\pi$
$600$		0			0
$601$	−13.7533	−	13.7533i	−0.561009	−	0.561009i	0.368585	−	0.929594i	$-0.379842\pi$
$601$	−13.7533	−	13.7533i	−0.561009	−	0.561009i	−0.929594	+	0.368585i	$0.879842\pi$
$602$		0			0
$603$		−	6.31399i		−	0.257126i
$604$		0			0
$605$	3.36547	+	3.36547i	0.136826	+	0.136826i
$606$		0			0
$607$	19.3965	−	19.3965i	0.787281	−	0.787281i	−0.193767	−	0.981048i	$-0.562071\pi$
$607$	19.3965	−	19.3965i	0.787281	−	0.787281i	0.981048	+	0.193767i	$0.0620706\pi$
$608$		0			0
$609$	4.46476	−	4.46476i	0.180921	−	0.180921i
$610$		0			0
$611$	−7.74971			−0.313520
$612$		0			0
$613$	0.297602			0.0120200			0.00601001	−	0.999982i	$-0.498087\pi$
$613$	0.297602			0.0120200			0.00601001	+	0.999982i	$0.498087\pi$
$614$		0			0
$615$	4.21059	−	4.21059i	0.169787	−	0.169787i
$616$		0			0
$617$	8.95764	−	8.95764i	0.360621	−	0.360621i	−0.503421	−	0.864041i	$-0.667925\pi$
$617$	8.95764	−	8.95764i	0.360621	−	0.360621i	0.864041	+	0.503421i	$0.167925\pi$
$618$		0			0
$619$	−6.89991	−	6.89991i	−0.277331	−	0.277331i	0.554712	−	0.832043i	$-0.312829\pi$
$619$	−6.89991	−	6.89991i	−0.277331	−	0.277331i	−0.832043	+	0.554712i	$0.812829\pi$
$620$		0			0
$621$		−	6.22005i		−	0.249602i
$622$		0			0
$623$	−1.12389	−	1.12389i	−0.0450276	−	0.0450276i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		−	45.1948i		−	1.80491i
$628$		0			0
$629$	−7.31286	+	3.23424i	−0.291583	+	0.128958i
$630$		0			0
$631$		−	40.9574i		−	1.63049i	−0.579117	−	0.815244i	$-0.696603\pi$
$631$		−	40.9574i		−	1.63049i	0.579117	−	0.815244i	$-0.303397\pi$
$632$		0			0
$633$	−18.1179			−0.720123
$634$		0			0
$635$	−11.1239	−	11.1239i	−0.441437	−	0.441437i
$636$		0			0
$637$			32.1763i			1.27487i
$638$		0			0
$639$	4.09508	+	4.09508i	0.161999	+	0.161999i
$640$		0			0
$641$	2.80367	−	2.80367i	0.110738	−	0.110738i	−0.649567	−	0.760305i	$-0.725050\pi$
$641$	2.80367	−	2.80367i	0.110738	−	0.110738i	0.760305	+	0.649567i	$0.225050\pi$
$642$		0			0
$643$	−10.9095	+	10.9095i	−0.430227	+	0.430227i	−0.888706	−	0.458478i	$-0.848395\pi$
$643$	−10.9095	+	10.9095i	−0.430227	+	0.430227i	0.458478	+	0.888706i	$0.348395\pi$
$644$		0			0
$645$	−29.5510			−1.16357
$646$		0			0
$647$	10.5735			0.415687			0.207843	−	0.978162i	$-0.433356\pi$
$647$	10.5735			0.415687			0.207843	+	0.978162i	$0.433356\pi$
$648$		0			0
$649$	0.855606	−	0.855606i	0.0335855	−	0.0335855i
$650$		0			0
$651$	3.17198	−	3.17198i	0.124320	−	0.124320i
$652$		0			0
$653$	−10.3029	−	10.3029i	−0.403184	−	0.403184i	0.476169	−	0.879354i	$-0.342025\pi$
$653$	−10.3029	−	10.3029i	−0.403184	−	0.403184i	−0.879354	+	0.476169i	$0.842025\pi$
$654$		0			0
$655$			4.09160i			0.159872i
$656$		0			0
$657$	−0.681831	−	0.681831i	−0.0266007	−	0.0266007i
$658$		0			0
$659$	−23.7883			−0.926660			−0.463330	−	0.886186i	$-0.653346\pi$
$659$	−23.7883			−0.926660			−0.463330	+	0.886186i	$0.653346\pi$
$660$		0			0
$661$			9.91502i			0.385650i	0.981233	+	0.192825i	$0.0617649\pi$
$661$			9.91502i			0.385650i	−0.981233	+	0.192825i	$0.938235\pi$
$662$		0			0
$663$	44.6062	−	19.7279i	1.73236	−	0.766167i
$664$		0			0
$665$		−	2.64522i		−	0.102577i
$666$		0			0
$667$	45.4408			1.75948
$668$		0			0
$669$	−7.01848	−	7.01848i	−0.271350	−	0.271350i
$670$		0			0
$671$			17.1946i			0.663790i
$672$		0			0
$673$	−2.81097	−	2.81097i	−0.108355	−	0.108355i	0.650851	−	0.759206i	$-0.274412\pi$
$673$	−2.81097	−	2.81097i	−0.108355	−	0.108355i	−0.759206	+	0.650851i	$0.774412\pi$
$674$		0			0
$675$	0.656399	−	0.656399i	0.0252648	−	0.0252648i
$676$		0			0
$677$	−14.4022	+	14.4022i	−0.553523	+	0.553523i	−0.927456	−	0.373933i	$-0.878009\pi$
$677$	−14.4022	+	14.4022i	−0.553523	+	0.553523i	0.373933	+	0.927456i	$0.378009\pi$
$678$		0			0
$679$	4.70276			0.180475
$680$		0			0
$681$	8.78125			0.336498
$682$		0			0
$683$	−20.4617	+	20.4617i	−0.782944	+	0.782944i	−0.980327	−	0.197383i	$-0.936756\pi$
$683$	−20.4617	+	20.4617i	−0.782944	+	0.782944i	0.197383	+	0.980327i	$0.436756\pi$
$684$		0			0
$685$	11.4653	−	11.4653i	0.438067	−	0.438067i
$686$		0			0
$687$	7.87193	+	7.87193i	0.300333	+	0.300333i
$688$		0			0
$689$			31.9489i			1.21716i
$690$		0			0
$691$	3.76661	+	3.76661i	0.143289	+	0.143289i	0.775112	−	0.631824i	$-0.217693\pi$
$691$	3.76661	+	3.76661i	0.143289	+	0.143289i	−0.631824	+	0.775112i	$0.717693\pi$
$692$		0			0
$693$	3.10417			0.117918
$694$		0			0
$695$		−	10.7071i		−	0.406145i
$696$		0			0
$697$	3.93530	+	8.89800i	0.149060	+	0.337036i
$698$		0			0
$699$		−	39.5340i		−	1.49531i
$700$		0			0
$701$	−42.2699			−1.59651			−0.798256	−	0.602318i	$-0.794244\pi$
$701$	−42.2699			−1.59651			−0.798256	+	0.602318i	$0.794244\pi$
$702$		0			0
$703$	−9.83156	−	9.83156i	−0.370804	−	0.370804i
$704$		0			0
$705$		−	4.17172i		−	0.157116i
$706$		0			0
$707$	−2.37037	−	2.37037i	−0.0891468	−	0.0891468i
$708$		0			0
$709$	−34.1983	+	34.1983i	−1.28435	+	1.28435i	−0.346176	+	0.938170i	$0.612520\pi$
$709$	−34.1983	+	34.1983i	−1.28435	+	1.28435i	−0.938170	+	0.346176i	$0.887480\pi$
$710$		0			0
$711$	−12.8255	+	12.8255i	−0.480995	+	0.480995i
$712$		0			0
$713$	32.2834			1.20902
$714$		0			0
$715$	11.7105			0.437949
$716$		0			0
$717$	−11.7610	+	11.7610i	−0.439222	+	0.439222i
$718$		0			0
$719$	−5.83066	+	5.83066i	−0.217447	+	0.217447i	−0.807422	−	0.589975i	$-0.799138\pi$
$719$	−5.83066	+	5.83066i	−0.217447	+	0.217447i	0.589975	+	0.807422i	$0.299138\pi$
$720$		0			0
$721$	−1.24658	−	1.24658i	−0.0464252	−	0.0464252i
$722$		0			0
$723$			11.0538i			0.411096i
$724$		0			0
$725$	4.79535	+	4.79535i	0.178095	+	0.178095i
$726$		0			0
$727$	−6.46089			−0.239621			−0.119811	−	0.992797i	$-0.538229\pi$
$727$	−6.46089			−0.239621			−0.119811	+	0.992797i	$0.538229\pi$
$728$		0			0
$729$		−	33.1658i		−	1.22836i
$730$		0			0
$731$	17.4148	−	45.0338i	0.644109	−	1.66563i
$732$		0			0
$733$		−	15.9605i		−	0.589515i	−0.955572	−	0.294758i	$-0.904761\pi$
$733$		−	15.9605i		−	0.589515i	0.955572	−	0.294758i	$-0.0952389\pi$
$734$		0			0
$735$	−17.3207			−0.638884
$736$		0			0
$737$	3.31165	+	3.31165i	0.121986	+	0.121986i
$738$		0			0
$739$		−	0.760943i		−	0.0279918i	−0.999902	−	0.0139959i	$-0.995545\pi$
$739$		−	0.760943i		−	0.0279918i	0.999902	−	0.0139959i	$-0.00445517\pi$
$740$		0			0
$741$	59.9695	+	59.9695i	2.20303	+	2.20303i
$742$		0			0
$743$	−27.8096	+	27.8096i	−1.02024	+	1.02024i	−0.0204461	+	0.999791i	$0.506509\pi$
$743$	−27.8096	+	27.8096i	−1.02024	+	1.02024i	−0.999791	+	0.0204461i	$0.993491\pi$
$744$		0			0
$745$	7.86936	−	7.86936i	0.288311	−	0.288311i
$746$		0			0
$747$	−33.5097			−1.22606
$748$		0			0
$749$	−1.05231			−0.0384506
$750$		0			0
$751$	23.8937	−	23.8937i	0.871892	−	0.871892i	−0.120786	−	0.992679i	$-0.538542\pi$
$751$	23.8937	−	23.8937i	0.871892	−	0.871892i	0.992679	+	0.120786i	$0.0385416\pi$
$752$		0			0
$753$	−7.67792	+	7.67792i	−0.279799	+	0.279799i
$754$		0			0
$755$	11.3746	+	11.3746i	0.413964	+	0.413964i
$756$		0			0
$757$		−	23.0663i		−	0.838359i	−0.907903	−	0.419180i	$-0.862318\pi$
$757$		−	23.0663i		−	0.838359i	0.907903	−	0.419180i	$-0.137682\pi$
$758$		0			0
$759$	29.8678	+	29.8678i	1.08413	+	1.08413i
$760$		0			0
$761$	22.8435			0.828076			0.414038	−	0.910260i	$-0.364118\pi$
$761$	22.8435			0.828076			0.414038	+	0.910260i	$0.364118\pi$
$762$		0			0
$763$		−	3.48618i		−	0.126208i
$764$		0			0
$765$	5.61657	+	12.6995i	0.203067	+	0.459151i
$766$		0			0
$767$			2.27063i			0.0819876i
$768$		0			0
$769$	3.68785			0.132987			0.0664936	−	0.997787i	$-0.478819\pi$
$769$	3.68785			0.132987			0.0664936	+	0.997787i	$0.478819\pi$
$770$		0			0
$771$	−18.8010	−	18.8010i	−0.677102	−	0.677102i
$772$		0			0
$773$			5.04027i			0.181286i	0.995883	+	0.0906430i	$0.0288922\pi$
$773$			5.04027i			0.181286i	−0.995883	+	0.0906430i	$0.971108\pi$
$774$		0			0
$775$	3.40685	+	3.40685i	0.122378	+	0.122378i
$776$		0			0
$777$	1.27679	−	1.27679i	0.0458045	−	0.0458045i
$778$		0			0
$779$	−11.9627	+	11.9627i	−0.428607	+	0.428607i
$780$		0			0
$781$	−4.29569			−0.153712
$782$		0			0
$783$	−6.29533			−0.224977
$784$		0			0
$785$	1.86200	−	1.86200i	0.0664576	−	0.0664576i
$786$		0			0
$787$	9.65129	−	9.65129i	0.344031	−	0.344031i	−0.513849	−	0.857880i	$-0.671781\pi$
$787$	9.65129	−	9.65129i	0.344031	−	0.344031i	0.857880	+	0.513849i	$0.171781\pi$
$788$		0			0
$789$	−24.3124	−	24.3124i	−0.865545	−	0.865545i
$790$		0			0
$791$		−	3.94010i		−	0.140094i
$792$		0			0
$793$	−22.8157	−	22.8157i	−0.810209	−	0.810209i
$794$		0			0
$795$	−17.1983			−0.609961
$796$		0			0
$797$		−	16.6869i		−	0.591081i	−0.955330	−	0.295541i	$-0.904500\pi$
$797$		−	16.6869i		−	0.591081i	0.955330	−	0.295541i	$-0.0954997\pi$
$798$		0			0
$799$	6.35742	+	2.45845i	0.224909	+	0.0869736i
$800$		0			0
$801$			14.5081i			0.512619i
$802$		0			0
$803$	0.715232			0.0252400
$804$		0			0
$805$	1.74814	+	1.74814i	0.0616139	+	0.0616139i
$806$		0			0
$807$			39.3844i			1.38640i
$808$		0			0
$809$	−21.7364	−	21.7364i	−0.764211	−	0.764211i	0.212870	−	0.977081i	$-0.431719\pi$
$809$	−21.7364	−	21.7364i	−0.764211	−	0.764211i	−0.977081	+	0.212870i	$0.931719\pi$
$810$		0			0
$811$	−15.1208	+	15.1208i	−0.530962	+	0.530962i	−0.920859	−	0.389896i	$-0.872511\pi$
$811$	−15.1208	+	15.1208i	−0.530962	+	0.530962i	0.389896	+	0.920859i	$0.372511\pi$
$812$		0			0
$813$	−17.2469	+	17.2469i	−0.604874	+	0.604874i
$814$		0			0
$815$	−19.0937			−0.668825
$816$		0			0
$817$	83.9571			2.93729
$818$		0			0
$819$	−4.11895	+	4.11895i	−0.143928	+	0.143928i
$820$		0			0
$821$	−8.42091	+	8.42091i	−0.293892	+	0.293892i	−0.838616	−	0.544724i	$-0.816634\pi$
$821$	−8.42091	+	8.42091i	−0.293892	+	0.293892i	0.544724	+	0.838616i	$0.316634\pi$
$822$		0			0
$823$	13.8553	+	13.8553i	0.482965	+	0.482965i	0.906077	−	0.423113i	$-0.139063\pi$
$823$	13.8553	+	13.8553i	0.482965	+	0.482965i	−0.423113	+	0.906077i	$0.639063\pi$
$824$		0			0
$825$			6.30387i			0.219472i
$826$		0			0
$827$	−24.8128	−	24.8128i	−0.862827	−	0.862827i	0.128838	−	0.991666i	$-0.458875\pi$
$827$	−24.8128	−	24.8128i	−0.862827	−	0.862827i	−0.991666	+	0.128838i	$0.958875\pi$
$828$		0			0
$829$	46.3683			1.61044			0.805219	−	0.592978i	$-0.202048\pi$
$829$	46.3683			1.61044			0.805219	+	0.592978i	$0.202048\pi$
$830$		0			0
$831$		−	3.40835i		−	0.118234i
$832$		0			0
$833$	10.2073	−	26.3956i	0.353662	−	0.914552i
$834$		0			0
$835$		−	3.98742i		−	0.137990i
$836$		0			0
$837$	−4.47251			−0.154593
$838$		0			0
$839$	17.6001	+	17.6001i	0.607623	+	0.607623i	0.942324	−	0.334701i	$-0.108635\pi$
$839$	17.6001	+	17.6001i	0.607623	+	0.607623i	−0.334701	+	0.942324i	$0.608635\pi$
$840$		0			0
$841$		−	16.9908i		−	0.585890i
$842$		0			0
$843$	−28.2967	−	28.2967i	−0.974589	−	0.974589i
$844$		0			0
$845$	−6.34645	+	6.34645i	−0.218325	+	0.218325i
$846$		0			0
$847$	1.24173	−	1.24173i	0.0426662	−	0.0426662i
$848$		0			0
$849$	74.0357			2.54090
$850$		0			0
$851$	12.9947			0.445453
$852$		0			0
$853$	−19.8742	+	19.8742i	−0.680478	+	0.680478i	−0.960108	−	0.279629i	$-0.909788\pi$
$853$	−19.8742	+	19.8742i	−0.680478	+	0.680478i	0.279629	+	0.960108i	$0.409788\pi$
$854$		0			0
$855$	−17.0734	+	17.0734i	−0.583899	+	0.583899i
$856$		0			0
$857$	−17.3313	−	17.3313i	−0.592025	−	0.592025i	0.346153	−	0.938178i	$-0.387488\pi$
$857$	−17.3313	−	17.3313i	−0.592025	−	0.592025i	−0.938178	+	0.346153i	$0.887488\pi$
$858$		0			0
$859$		−	12.8979i		−	0.440069i	−0.975492	−	0.220034i	$-0.929383\pi$
$859$		−	12.8979i		−	0.440069i	0.975492	−	0.220034i	$-0.0706170\pi$
$860$		0			0
$861$	−1.55354	−	1.55354i	−0.0529447	−	0.0529447i
$862$		0			0
$863$	5.83668			0.198683			0.0993414	−	0.995053i	$-0.468326\pi$
$863$	5.83668			0.198683			0.0993414	+	0.995053i	$0.468326\pi$
$864$		0			0
$865$		−	14.6078i		−	0.496681i
$866$		0			0
$867$	−42.8507	+	2.03316i	−1.45528	+	0.0690496i
$868$		0			0
$869$		−	13.4538i		−	0.456390i
$870$		0			0
$871$	−8.78854			−0.297788
$872$		0			0
$873$	−30.3537	−	30.3537i	−1.02732	−	1.02732i
$874$		0			0
$875$			0.368961i			0.0124732i
$876$		0			0
$877$	−13.2827	−	13.2827i	−0.448526	−	0.448526i	0.446338	−	0.894864i	$-0.352728\pi$
$877$	−13.2827	−	13.2827i	−0.448526	−	0.448526i	−0.894864	+	0.446338i	$0.852728\pi$
$878$		0			0
$879$	36.8431	−	36.8431i	1.24269	−	1.24269i
$880$		0			0
$881$	−32.3447	+	32.3447i	−1.08972	+	1.08972i	−0.0941649	+	0.995557i	$0.530018\pi$
$881$	−32.3447	+	32.3447i	−1.08972	+	1.08972i	−0.995557	+	0.0941649i	$0.969982\pi$
$882$		0			0
$883$	−6.15932			−0.207277			−0.103639	−	0.994615i	$-0.533049\pi$
$883$	−6.15932			−0.207277			−0.103639	+	0.994615i	$0.533049\pi$
$884$		0			0
$885$	−1.22229			−0.0410870
$886$		0			0
$887$	11.8423	−	11.8423i	0.397627	−	0.397627i	−0.479768	−	0.877395i	$-0.659279\pi$
$887$	11.8423	−	11.8423i	0.397627	−	0.397627i	0.877395	+	0.479768i	$0.159279\pi$
$888$		0			0
$889$	−4.10428	+	4.10428i	−0.137653	+	0.137653i
$890$		0			0
$891$	13.7094	+	13.7094i	0.459281	+	0.459281i
$892$		0			0
$893$			11.8522i			0.396620i
$894$		0			0
$895$	−10.4264	−	10.4264i	−0.348517	−	0.348517i
$896$		0			0
$897$	−79.2637			−2.64654
$898$		0			0
$899$		−	32.6741i		−	1.08974i
$900$		0			0
$901$	10.1352	−	26.2091i	0.337652	−	0.873150i
$902$		0			0
$903$			10.9032i			0.362835i
$904$		0			0
$905$	−11.2615			−0.374344
$906$		0			0
$907$	−5.74762	−	5.74762i	−0.190847	−	0.190847i	0.605215	−	0.796062i	$-0.293087\pi$
$907$	−5.74762	−	5.74762i	−0.190847	−	0.190847i	−0.796062	+	0.605215i	$0.793087\pi$
$908$		0			0
$909$			30.5988i			1.01490i
$910$		0			0
$911$	25.2063	+	25.2063i	0.835121	+	0.835121i	0.988212	−	0.153091i	$-0.0489227\pi$
$911$	25.2063	+	25.2063i	0.835121	+	0.835121i	−0.153091	+	0.988212i	$0.548923\pi$
$912$		0			0
$913$	17.5757	−	17.5757i	0.581670	−	0.581670i
$914$		0			0
$915$	12.2819	−	12.2819i	0.406025	−	0.406025i
$916$		0			0
$917$	1.50964			0.0498528
$918$		0			0
$919$	24.2398			0.799596			0.399798	−	0.916603i	$-0.369080\pi$
$919$	24.2398			0.799596			0.399798	+	0.916603i	$0.369080\pi$
$920$		0			0
$921$	29.1631	−	29.1631i	0.960956	−	0.960956i
$922$		0			0
$923$	5.70000	−	5.70000i	0.187618	−	0.187618i
$924$		0			0
$925$	1.37133	+	1.37133i	0.0450889	+	0.0450889i
$926$		0			0
$927$			16.0920i			0.528531i
$928$		0			0
$929$	−23.6454	−	23.6454i	−0.775781	−	0.775781i	0.203329	−	0.979110i	$-0.434824\pi$
$929$	−23.6454	−	23.6454i	−0.775781	−	0.775781i	−0.979110	+	0.203329i	$0.934824\pi$
$930$		0			0
$931$	49.2097			1.61278
$932$		0			0
$933$		−	88.5989i		−	2.90060i
$934$		0			0
$935$	−9.60666	−	3.71495i	−0.314171	−	0.121492i
$936$		0			0
$937$			25.6264i			0.837177i	0.908176	+	0.418588i	$0.137475\pi$
$937$			25.6264i			0.837177i	−0.908176	+	0.418588i	$0.862525\pi$
$938$		0			0
$939$	−79.0181			−2.57866
$940$		0			0
$941$	37.8063	+	37.8063i	1.23245	+	1.23245i	0.963020	+	0.269429i	$0.0868348\pi$
$941$	37.8063	+	37.8063i	1.23245	+	1.23245i	0.269429	+	0.963020i	$0.413165\pi$
$942$		0			0
$943$		−	15.8115i		−	0.514892i
$944$		0			0
$945$	−0.242186	−	0.242186i	−0.00787831	−	0.00787831i
$946$		0			0
$947$	8.32772	−	8.32772i	0.270615	−	0.270615i	−0.558733	−	0.829348i	$-0.688712\pi$
$947$	8.32772	−	8.32772i	0.270615	−	0.270615i	0.829348	+	0.558733i	$0.188712\pi$
$948$		0			0
$949$	−0.949050	+	0.949050i	−0.0308075	+	0.0308075i
$950$		0			0
$951$	−31.6687			−1.02693
$952$		0			0
$953$	23.9735			0.776576			0.388288	−	0.921538i	$-0.373067\pi$
$953$	23.9735			0.776576			0.388288	+	0.921538i	$0.373067\pi$
$954$		0			0
$955$	15.1981	−	15.1981i	0.491800	−	0.491800i
$956$		0			0
$957$	30.2293	−	30.2293i	0.977173	−	0.977173i
$958$		0			0
$959$	−4.23025	−	4.23025i	−0.136602	−	0.136602i
$960$		0			0
$961$			7.78674i			0.251185i
$962$		0			0
$963$	6.79208	+	6.79208i	0.218872	+	0.218872i
$964$		0			0
$965$	1.42208			0.0457783
$966$		0			0
$967$		−	45.6312i		−	1.46740i	−0.679473	−	0.733700i	$-0.737792\pi$
$967$		−	45.6312i		−	1.46740i	0.679473	−	0.733700i	$-0.262208\pi$
$968$		0			0
$969$	−30.1714	−	68.2197i	−0.969243	−	2.19153i
$970$		0			0
$971$			58.9182i			1.89078i	0.325946	+	0.945388i	$0.394317\pi$
$971$			58.9182i			1.89078i	−0.325946	+	0.945388i	$0.605683\pi$
$972$		0			0
$973$	−3.95052			−0.126648
$974$		0			0
$975$	−8.36467	−	8.36467i	−0.267884	−	0.267884i
$976$		0			0
$977$			24.7610i			0.792176i	0.918213	+	0.396088i	$0.129632\pi$
$977$			24.7610i			0.792176i	−0.918213	+	0.396088i	$0.870368\pi$
$978$		0			0
$979$	−7.60943	−	7.60943i	−0.243198	−	0.243198i
$980$		0			0
$981$	−22.5013	+	22.5013i	−0.718412	+	0.718412i
$982$		0			0
$983$	−6.99814	+	6.99814i	−0.223206	+	0.223206i	−0.809847	−	0.586641i	$-0.800450\pi$
$983$	−6.99814	+	6.99814i	−0.223206	+	0.223206i	0.586641	+	0.809847i	$0.300450\pi$
$984$		0			0
$985$	−17.4127			−0.554815
$986$		0			0
$987$	−1.53920			−0.0489934
$988$		0			0
$989$	−55.4845	+	55.4845i	−1.76430	+	1.76430i
$990$		0			0
$991$	−0.624955	+	0.624955i	−0.0198524	+	0.0198524i	−0.716963	−	0.697111i	$-0.754468\pi$
$991$	−0.624955	+	0.624955i	−0.0198524	+	0.0198524i	0.697111	+	0.716963i	$0.254468\pi$
$992$		0			0
$993$	0.887628	+	0.887628i	0.0281680	+	0.0281680i
$994$		0			0
$995$			17.8876i			0.567076i
$996$		0			0
$997$	−20.5067	−	20.5067i	−0.649455	−	0.649455i	0.303407	−	0.952861i	$-0.401876\pi$
$997$	−20.5067	−	20.5067i	−0.649455	−	0.649455i	−0.952861	+	0.303407i	$0.901876\pi$
$998$		0			0
$999$	−1.80028			−0.0569582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bt.d.1041.1		12
4.3	odd	2		85.2.e.a.21.5	✓	12
12.11	even	2		765.2.k.b.361.2		12
17.13	even	4	inner	1360.2.bt.d.81.1		12
20.3	even	4		425.2.j.c.174.5		12
20.7	even	4		425.2.j.b.174.2		12
20.19	odd	2		425.2.e.f.276.2		12
68.15	odd	8		1445.2.d.g.866.4		12
68.19	odd	8		1445.2.d.g.866.3		12
68.43	odd	8		1445.2.a.o.1.5		6
68.47	odd	4		85.2.e.a.81.2	yes	12
68.59	odd	8		1445.2.a.n.1.5		6
204.47	even	4		765.2.k.b.676.5		12
340.47	even	4		425.2.j.c.149.5		12
340.59	odd	8		7225.2.a.bb.1.2		6
340.179	odd	8		7225.2.a.z.1.2		6
340.183	even	4		425.2.j.b.149.2		12
340.319	odd	4		425.2.e.f.251.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.5	✓	12	4.3	odd	2
85.2.e.a.81.2	yes	12	68.47	odd	4
425.2.e.f.251.5		12	340.319	odd	4
425.2.e.f.276.2		12	20.19	odd	2
425.2.j.b.149.2		12	340.183	even	4
425.2.j.b.174.2		12	20.7	even	4
425.2.j.c.149.5		12	340.47	even	4
425.2.j.c.174.5		12	20.3	even	4
765.2.k.b.361.2		12	12.11	even	2
765.2.k.b.676.5		12	204.47	even	4
1360.2.bt.d.81.1		12	17.13	even	4	inner
1360.2.bt.d.1041.1		12	1.1	even	1	trivial
1445.2.a.n.1.5		6	68.59	odd	8
1445.2.a.o.1.5		6	68.43	odd	8
1445.2.d.g.866.3		12	68.19	odd	8
1445.2.d.g.866.4		12	68.15	odd	8
7225.2.a.z.1.2		6	340.179	odd	8
7225.2.a.bb.1.2		6	340.59	odd	8

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:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bt (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.78436 + 1.78436i) q^{3} +(-0.707107 + 0.707107i) q^{5} +(0.260895 + 0.260895i) q^{7} -3.36786i q^{9} +(1.76642 + 1.76642i) q^{11} -4.68778 q^{13} -2.52346i q^{15} +(3.84558 + 1.48711i) q^{17} +7.16938i q^{19} -0.931060 q^{21} +(-4.73801 - 4.73801i) q^{23} -1.00000i q^{25} +(0.656399 + 0.656399i) q^{27} +(-4.79535 + 4.79535i) q^{29} +(-3.40685 + 3.40685i) q^{31} -6.30387 q^{33} -0.368961 q^{35} +(-1.37133 + 1.37133i) q^{37} +(8.36467 - 8.36467i) q^{39} +(1.66858 + 1.66858i) q^{41} -11.7105i q^{43} +(2.38144 + 2.38144i) q^{45} +1.65317 q^{47} -6.86387i q^{49} +(-9.51543 + 4.20836i) q^{51} -6.81536i q^{53} -2.49810 q^{55} +(-12.7927 - 12.7927i) q^{57} -0.484372i q^{59} +(4.86706 + 4.86706i) q^{61} +(0.878658 - 0.878658i) q^{63} +(3.31476 - 3.31476i) q^{65} +1.87478 q^{67} +16.9086 q^{69} +(-1.21593 + 1.21593i) q^{71} +(0.202452 - 0.202452i) q^{73} +(1.78436 + 1.78436i) q^{75} +0.921703i q^{77} +(-3.80821 - 3.80821i) q^{79} +7.76109 q^{81} -9.94985i q^{83} +(-3.77078 + 1.66769i) q^{85} -17.1132i q^{87} -4.30781 q^{89} +(-1.22302 - 1.22302i) q^{91} -12.1581i q^{93} +(-5.06952 - 5.06952i) q^{95} +(9.01275 - 9.01275i) q^{97} +(5.94908 - 5.94908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 4 q^{11} + 12 q^{17} - 16 q^{21} - 12 q^{23} + 4 q^{27} - 12 q^{29} - 16 q^{33} - 16 q^{35} + 12 q^{37} + 20 q^{39} - 24 q^{41} + 8 q^{45} + 48 q^{47} - 32 q^{51} + 40 q^{61} - 12 q^{63}+ \cdots + 4 q^{97}+O(q^{100}) \) 12 * q + 4 * q^3 + 4 * q^11 + 12 * q^17 - 16 * q^21 - 12 * q^23 + 4 * q^27 - 12 * q^29 - 16 * q^33 - 16 * q^35 + 12 * q^37 + 20 * q^39 - 24 * q^41 + 8 * q^45 + 48 * q^47 - 32 * q^51 + 40 * q^61 - 12 * q^63 + 4 * q^65 + 8 * q^67 - 28 * q^71 - 48 * q^73 - 4 * q^75 + 8 * q^79 + 28 * q^81 - 4 * q^85 + 24 * q^89 + 36 * q^91 + 8 * q^95 + 4 * q^97

Introduction

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