LMFDB - Embedded newform 1512.2.c.g.757.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.2
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.g.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40920 + 0.118957i) q^{2} +(1.97170 - 0.335269i) q^{4} +3.46300i q^{5} +1.00000 q^{7} +(-2.73864 + 0.707009i) q^{8} +O(q^{10})$	\(q+(-1.40920 + 0.118957i) q^{2} +(1.97170 - 0.335269i) q^{4} +3.46300i q^{5} +1.00000 q^{7} +(-2.73864 + 0.707009i) q^{8} +(-0.411948 - 4.88007i) q^{10} -3.31902i q^{11} -3.10840i q^{13} +(-1.40920 + 0.118957i) q^{14} +(3.77519 - 1.32210i) q^{16} +1.40277 q^{17} -4.80674i q^{19} +(1.16104 + 6.82800i) q^{20} +(0.394821 + 4.67717i) q^{22} -8.79960 q^{23} -6.99238 q^{25} +(0.369766 + 4.38037i) q^{26} +(1.97170 - 0.335269i) q^{28} -9.87397i q^{29} -7.83557 q^{31} +(-5.16273 + 2.31219i) q^{32} +(-1.97678 + 0.166869i) q^{34} +3.46300i q^{35} -5.42317i q^{37} +(0.571795 + 6.77366i) q^{38} +(-2.44837 - 9.48391i) q^{40} +11.5710 q^{41} -7.03957i q^{43} +(-1.11276 - 6.54411i) q^{44} +(12.4004 - 1.04677i) q^{46} -11.2916 q^{47} +1.00000 q^{49} +(9.85368 - 0.831793i) q^{50} +(-1.04215 - 6.12884i) q^{52} +6.51655i q^{53} +11.4938 q^{55} +(-2.73864 + 0.707009i) q^{56} +(1.17458 + 13.9144i) q^{58} -3.89654i q^{59} +9.42334i q^{61} +(11.0419 - 0.932096i) q^{62} +(7.00028 - 3.87248i) q^{64} +10.7644 q^{65} +0.909712i q^{67} +(2.76583 - 0.470304i) q^{68} +(-0.411948 - 4.88007i) q^{70} +6.42314 q^{71} +1.56257 q^{73} +(0.645124 + 7.64234i) q^{74} +(-1.61155 - 9.47744i) q^{76} -3.31902i q^{77} -11.1619 q^{79} +(4.57843 + 13.0735i) q^{80} +(-16.3059 + 1.37645i) q^{82} -0.370241i q^{83} +4.85778i q^{85} +(0.837406 + 9.92018i) q^{86} +(2.34658 + 9.08960i) q^{88} -4.85047 q^{89} -3.10840i q^{91} +(-17.3502 + 2.95023i) q^{92} +(15.9121 - 1.34321i) q^{94} +16.6457 q^{95} +1.63283 q^{97} +(-1.40920 + 0.118957i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 24 q^{7}+O(q^{10}) $ 24 * q + 6 * q^4 + 24 * q^7	$ 24 q + 6 q^{4} + 24 q^{7} - 16 q^{10} + 2 q^{16} + 16 q^{22} - 24 q^{25} + 6 q^{28} + 8 q^{31} + 22 q^{34} + 26 q^{46} + 24 q^{49} - 6 q^{52} + 16 q^{55} - 58 q^{58} + 6 q^{64} - 16 q^{70} + 60 q^{76} + 8 q^{79} - 28 q^{82} + 12 q^{88} + 36 q^{94}+O(q^{100}) $ 24 * q + 6 * q^4 + 24 * q^7 - 16 * q^10 + 2 * q^16 + 16 * q^22 - 24 * q^25 + 6 * q^28 + 8 * q^31 + 22 * q^34 + 26 * q^46 + 24 * q^49 - 6 * q^52 + 16 * q^55 - 58 * q^58 + 6 * q^64 - 16 * q^70 + 60 * q^76 + 8 * q^79 - 28 * q^82 + 12 * q^88 + 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	−1.40920	+	0.118957i	−0.996456	+	0.0841153i
$2$	−1.40920	+	0.118957i	−0.996456	+	0.0841153i
$3$		0			0
$3$		0			0
$4$	1.97170	−	0.335269i	0.985849	−	0.167634i
$5$			3.46300i			1.54870i	0.632757	+	0.774351i	$0.281923\pi$
$5$			3.46300i			1.54870i	−0.632757	+	0.774351i	$0.718077\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.73864	+	0.707009i	−0.968255	+	0.249965i
$9$		0			0
$10$	−0.411948	−	4.88007i	−0.130269	−	1.54321i
$11$		−	3.31902i		−	1.00072i	−0.865817	−	0.500361i	$-0.833201\pi$
$11$		−	3.31902i		−	1.00072i	0.865817	−	0.500361i	$-0.166799\pi$
$12$		0			0
$13$		−	3.10840i		−	0.862116i	−0.902324	−	0.431058i	$-0.858140\pi$
$13$		−	3.10840i		−	0.862116i	0.902324	−	0.431058i	$-0.141860\pi$
$14$	−1.40920	+	0.118957i	−0.376625	+	0.0317926i
$15$		0			0
$16$	3.77519	−	1.32210i	0.943797	−	0.330524i
$17$	1.40277			0.340221			0.170110	−	0.985425i	$-0.445588\pi$
$17$	1.40277			0.340221			0.170110	+	0.985425i	$0.445588\pi$
$18$		0			0
$19$		−	4.80674i		−	1.10274i	−0.834260	−	0.551371i	$-0.814105\pi$
$19$		−	4.80674i		−	1.10274i	0.834260	−	0.551371i	$-0.185895\pi$
$20$	1.16104	+	6.82800i	0.259616	+	1.52679i
$21$		0			0
$22$	0.394821	+	4.67717i	0.0841761	+	0.997176i
$23$	−8.79960			−1.83484			−0.917421	−	0.397917i	$-0.869733\pi$
$23$	−8.79960			−1.83484			−0.917421	+	0.397917i	$0.869733\pi$
$24$		0			0
$25$	−6.99238			−1.39848
$26$	0.369766	+	4.38037i	0.0725172	+	0.859061i
$27$		0			0
$28$	1.97170	−	0.335269i	0.372616	−	0.0633598i
$29$		−	9.87397i		−	1.83355i	−0.399404	−	0.916775i	$-0.630783\pi$
$29$		−	9.87397i		−	1.83355i	0.399404	−	0.916775i	$-0.369217\pi$
$30$		0			0
$31$	−7.83557			−1.40731			−0.703655	−	0.710541i	$-0.748450\pi$
$31$	−7.83557			−1.40731			−0.703655	+	0.710541i	$0.748450\pi$
$32$	−5.16273	+	2.31219i	−0.912650	+	0.408741i
$33$		0			0
$34$	−1.97678	+	0.166869i	−0.339015	+	0.0286178i
$35$			3.46300i			0.585354i
$36$		0			0
$37$		−	5.42317i		−	0.891564i	−0.895142	−	0.445782i	$-0.852926\pi$
$37$		−	5.42317i		−	0.891564i	0.895142	−	0.445782i	$-0.147074\pi$
$38$	0.571795	+	6.77366i	0.0927574	+	1.09883i
$39$		0			0
$40$	−2.44837	−	9.48391i	−0.387122	−	1.49954i
$41$	11.5710			1.80708			0.903542	−	0.428499i	$-0.140957\pi$
$41$	11.5710			1.80708			0.903542	+	0.428499i	$0.140957\pi$
$42$		0			0
$43$		−	7.03957i		−	1.07352i	−0.843733	−	0.536762i	$-0.819647\pi$
$43$		−	7.03957i		−	1.07352i	0.843733	−	0.536762i	$-0.180353\pi$
$44$	−1.11276	−	6.54411i	−0.167756	−	0.986562i
$45$		0			0
$46$	12.4004	−	1.04677i	1.82834	−	0.154338i
$47$	−11.2916			−1.64704			−0.823522	−	0.567284i	$-0.807994\pi$
$47$	−11.2916			−1.64704			−0.823522	+	0.567284i	$0.807994\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	9.85368	−	0.831793i	1.39352	−	0.117633i
$51$		0			0
$52$	−1.04215	−	6.12884i	−0.144520	−	0.849917i
$53$			6.51655i			0.895117i	0.894255	+	0.447559i	$0.147706\pi$
$53$			6.51655i			0.895117i	−0.894255	+	0.447559i	$0.852294\pi$
$54$		0			0
$55$	11.4938			1.54982
$56$	−2.73864	+	0.707009i	−0.365966	+	0.0944780i
$57$		0			0
$58$	1.17458	+	13.9144i	0.154230	+	1.82705i
$59$		−	3.89654i		−	0.507287i	−0.967298	−	0.253643i	$-0.918371\pi$
$59$		−	3.89654i		−	0.507287i	0.967298	−	0.253643i	$-0.0816290\pi$
$60$		0			0
$61$			9.42334i			1.20653i	0.797539	+	0.603267i	$0.206135\pi$
$61$			9.42334i			1.20653i	−0.797539	+	0.603267i	$0.793865\pi$
$62$	11.0419	−	0.932096i	1.40232	−	0.118376i
$63$		0			0
$64$	7.00028	−	3.87248i	0.875035	−	0.484060i
$65$	10.7644			1.33516
$66$		0			0
$67$			0.909712i			0.111139i	0.998455	+	0.0555695i	$0.0176974\pi$
$67$			0.909712i			0.111139i	−0.998455	+	0.0555695i	$0.982303\pi$
$68$	2.76583	−	0.470304i	0.335406	−	0.0570327i
$69$		0			0
$70$	−0.411948	−	4.88007i	−0.0492372	−	0.583280i
$71$	6.42314			0.762286			0.381143	−	0.924516i	$-0.375531\pi$
$71$	6.42314			0.762286			0.381143	+	0.924516i	$0.375531\pi$
$72$		0			0
$73$	1.56257			0.182884			0.0914422	−	0.995810i	$-0.470852\pi$
$73$	1.56257			0.182884			0.0914422	+	0.995810i	$0.470852\pi$
$74$	0.645124	+	7.64234i	0.0749942	+	0.888404i
$75$		0			0
$76$	−1.61155	−	9.47744i	−0.184857	−	1.08714i
$77$		−	3.31902i		−	0.378238i
$78$		0			0
$79$	−11.1619			−1.25582			−0.627908	−	0.778288i	$-0.716088\pi$
$79$	−11.1619			−1.25582			−0.627908	+	0.778288i	$0.716088\pi$
$80$	4.57843	+	13.0735i	0.511884	+	1.46166i
$81$		0			0
$82$	−16.3059	+	1.37645i	−1.80068	+	0.152003i
$83$		−	0.370241i		−	0.0406392i	−0.999794	−	0.0203196i	$-0.993532\pi$
$83$		−	0.370241i		−	0.0406392i	0.999794	−	0.0203196i	$-0.00646837\pi$
$84$		0			0
$85$			4.85778i			0.526900i
$86$	0.837406	+	9.92018i	0.0902999	+	1.06972i
$87$		0			0
$88$	2.34658	+	9.08960i	0.250146	+	0.968954i
$89$	−4.85047			−0.514149			−0.257075	−	0.966392i	$-0.582759\pi$
$89$	−4.85047			−0.514149			−0.257075	+	0.966392i	$0.582759\pi$
$90$		0			0
$91$		−	3.10840i		−	0.325849i
$92$	−17.3502	+	2.95023i	−1.80888	+	0.307583i
$93$		0			0
$94$	15.9121	−	1.34321i	1.64121	−	0.138542i
$95$	16.6457			1.70782
$96$		0			0
$97$	1.63283			0.165789			0.0828946	−	0.996558i	$-0.473584\pi$
$97$	1.63283			0.165789			0.0828946	+	0.996558i	$0.473584\pi$
$98$	−1.40920	+	0.118957i	−0.142351	+	0.0120165i
$99$		0			0
$100$	−13.7869	+	2.34433i	−1.37869	+	0.234433i
$101$		−	13.1650i		−	1.30997i	−0.755643	−	0.654983i	$-0.772676\pi$
$101$		−	13.1650i		−	1.30997i	0.755643	−	0.654983i	$-0.227324\pi$
$102$		0			0
$103$	15.6983			1.54680			0.773399	−	0.633920i	$-0.218555\pi$
$103$	15.6983			1.54680			0.773399	+	0.633920i	$0.218555\pi$
$104$	2.19767	+	8.51280i	0.215499	+	0.834748i
$105$		0			0
$106$	−0.775190	−	9.18314i	−0.0752931	−	0.891945i
$107$		−	9.37257i		−	0.906081i	−0.891490	−	0.453040i	$-0.850339\pi$
$107$		−	9.37257i		−	0.906081i	0.891490	−	0.453040i	$-0.149661\pi$
$108$		0			0
$109$			7.31490i			0.700640i	0.936630	+	0.350320i	$0.113927\pi$
$109$			7.31490i			0.700640i	−0.936630	+	0.350320i	$0.886073\pi$
$110$	−16.1970	+	1.36727i	−1.54433	+	0.130364i
$111$		0			0
$112$	3.77519	−	1.32210i	0.356722	−	0.124927i
$113$	−10.9153			−1.02683			−0.513414	−	0.858141i	$-0.671620\pi$
$113$	−10.9153			−1.02683			−0.513414	+	0.858141i	$0.671620\pi$
$114$		0			0
$115$		−	30.4730i		−	2.84162i
$116$	−3.31043	−	19.4685i	−0.307366	−	1.80760i
$117$		0			0
$118$	0.463521	+	5.49102i	0.0426706	+	0.505489i
$119$	1.40277			0.128591
$120$		0			0
$121$	−0.0159016			−0.00144560
$122$	−1.12097	−	13.2794i	−0.101488	−	1.20226i
$123$		0			0
$124$	−15.4494	+	2.62702i	−1.38740	+	0.235914i
$125$		−	6.89962i		−	0.617121i
$126$		0			0
$127$	3.37545			0.299523			0.149761	−	0.988722i	$-0.452149\pi$
$127$	3.37545			0.299523			0.149761	+	0.988722i	$0.452149\pi$
$128$	−9.40414	+	6.28984i	−0.831217	+	0.555949i
$129$		0			0
$130$	−15.1692	+	1.28050i	−1.33043	+	0.112307i
$131$		−	7.15460i		−	0.625100i	−0.949901	−	0.312550i	$-0.898817\pi$
$131$		−	7.15460i		−	0.625100i	0.949901	−	0.312550i	$-0.101183\pi$
$132$		0			0
$133$		−	4.80674i		−	0.416797i
$134$	−0.108217	−	1.28197i	−0.00934850	−	0.110745i
$135$		0			0
$136$	−3.84167	+	0.991767i	−0.329420	+	0.0850434i
$137$	−4.22854			−0.361269			−0.180634	−	0.983550i	$-0.557815\pi$
$137$	−4.22854			−0.361269			−0.180634	+	0.983550i	$0.557815\pi$
$138$		0			0
$139$		−	3.31473i		−	0.281152i	−0.990070	−	0.140576i	$-0.955105\pi$
$139$		−	3.31473i		−	0.281152i	0.990070	−	0.140576i	$-0.0448954\pi$
$140$	1.16104	+	6.82800i	0.0981255	+	0.577071i
$141$		0			0
$142$	−9.05150	+	0.764077i	−0.759585	+	0.0641199i
$143$	−10.3169			−0.862739
$144$		0			0
$145$	34.1936			2.83962
$146$	−2.20197	+	0.185878i	−0.182236	+	0.0153834i
$147$		0			0
$148$	−1.81822	−	10.6929i	−0.149457	−	0.878948i
$149$		−	7.08433i		−	0.580371i	−0.956970	−	0.290185i	$-0.906283\pi$
$149$		−	7.08433i		−	0.580371i	0.956970	−	0.290185i	$-0.0937169\pi$
$150$		0			0
$151$	0.252443			0.0205436			0.0102718	−	0.999947i	$-0.496730\pi$
$151$	0.252443			0.0205436			0.0102718	+	0.999947i	$0.496730\pi$
$152$	3.39841	+	13.1639i	0.275647	+	1.06773i
$153$		0			0
$154$	0.394821	+	4.67717i	0.0318156	+	0.376897i
$155$		−	27.1346i		−	2.17950i
$156$		0			0
$157$		−	3.11021i		−	0.248222i	−0.992268	−	0.124111i	$-0.960392\pi$
$157$		−	3.11021i		−	0.248222i	0.992268	−	0.124111i	$-0.0396078\pi$
$158$	15.7294	−	1.32779i	1.25136	−	0.105633i
$159$		0			0
$160$	−8.00711	−	17.8785i	−0.633018	−	1.41342i
$161$	−8.79960			−0.693505
$162$		0			0
$163$			18.5595i			1.45369i	0.686800	+	0.726847i	$0.259015\pi$
$163$			18.5595i			1.45369i	−0.686800	+	0.726847i	$0.740985\pi$
$164$	22.8145	−	3.87939i	1.78151	−	0.302930i
$165$		0			0
$166$	0.0440427	+	0.521744i	0.00341838	+	0.0404952i
$167$	14.3221			1.10828			0.554140	−	0.832424i	$-0.313047\pi$
$167$	14.3221			1.10828			0.554140	+	0.832424i	$0.313047\pi$
$168$		0			0
$169$	3.33782			0.256755
$170$	−0.577867	−	6.84559i	−0.0443204	−	0.525033i
$171$		0			0
$172$	−2.36015	−	13.8799i	−0.179960	−	1.05833i
$173$			1.40183i			0.106579i	0.998579	+	0.0532896i	$0.0169707\pi$
$173$			1.40183i			0.106579i	−0.998579	+	0.0532896i	$0.983029\pi$
$174$		0			0
$175$	−6.99238			−0.528574
$176$	−4.38807	−	12.5299i	−0.330763	−	0.944479i
$177$		0			0
$178$	6.83530	−	0.576998i	0.512327	−	0.0432478i
$179$			3.46849i			0.259247i	0.991563	+	0.129624i	$0.0413769\pi$
$179$			3.46849i			0.259247i	−0.991563	+	0.129624i	$0.958623\pi$
$180$		0			0
$181$			19.3992i			1.44193i	0.692972	+	0.720965i	$0.256301\pi$
$181$			19.3992i			1.44193i	−0.692972	+	0.720965i	$0.743699\pi$
$182$	0.369766	+	4.38037i	0.0274089	+	0.324695i
$183$		0			0
$184$	24.0989	−	6.22139i	1.77660	−	0.458647i
$185$	18.7805			1.38077
$186$		0			0
$187$		−	4.65581i		−	0.340466i
$188$	−22.2636	+	3.78571i	−1.62374	+	0.276101i
$189$		0			0
$190$	−23.4572	+	1.98013i	−1.70176	+	0.143654i
$191$	−23.4610			−1.69758			−0.848790	−	0.528729i	$-0.822669\pi$
$191$	−23.4610			−1.69758			−0.848790	+	0.528729i	$0.822669\pi$
$192$		0			0
$193$	−15.5374			−1.11840			−0.559202	−	0.829031i	$-0.688893\pi$
$193$	−15.5374			−1.11840			−0.559202	+	0.829031i	$0.688893\pi$
$194$	−2.30099	+	0.194237i	−0.165202	+	0.0139454i
$195$		0			0
$196$	1.97170	−	0.335269i	0.140836	−	0.0239478i
$197$		−	14.8278i		−	1.05643i	−0.849109	−	0.528217i	$-0.822861\pi$
$197$		−	14.8278i		−	1.05643i	0.849109	−	0.528217i	$-0.177139\pi$
$198$		0			0
$199$	13.2095			0.936397			0.468199	−	0.883623i	$-0.344903\pi$
$199$	13.2095			0.936397			0.468199	+	0.883623i	$0.344903\pi$
$200$	19.1496	−	4.94367i	1.35408	−	0.349571i
$201$		0			0
$202$	1.56607	+	18.5521i	0.110188	+	1.30532i
$203$		−	9.87397i		−	0.693017i
$204$		0			0
$205$			40.0703i			2.79863i
$206$	−22.1220	+	1.86742i	−1.54132	+	0.130109i
$207$		0			0
$208$	−4.10962	−	11.7348i	−0.284951	−	0.813663i
$209$	−15.9537			−1.10354
$210$		0			0
$211$		−	12.3790i		−	0.852206i	−0.904675	−	0.426103i	$-0.859886\pi$
$211$		−	12.3790i		−	0.852206i	0.904675	−	0.426103i	$-0.140114\pi$
$212$	2.18480	+	12.8487i	0.150052	+	0.882451i
$213$		0			0
$214$	1.11493	+	13.2078i	0.0762153	+	0.902870i
$215$	24.3781			1.66257
$216$		0			0
$217$	−7.83557			−0.531913
$218$	−0.870158	−	10.3082i	−0.0589345	−	0.698157i
$219$		0			0
$220$	22.6623	−	3.85350i	1.52789	−	0.259803i
$221$		−	4.36036i		−	0.293310i
$222$		0			0
$223$	2.91170			0.194982			0.0974910	−	0.995236i	$-0.468918\pi$
$223$	2.91170			0.194982			0.0974910	+	0.995236i	$0.468918\pi$
$224$	−5.16273	+	2.31219i	−0.344949	+	0.154490i
$225$		0			0
$226$	15.3819	−	1.29846i	1.02319	−	0.0863720i
$227$		−	11.3550i		−	0.753658i	−0.926283	−	0.376829i	$-0.877014\pi$
$227$		−	11.3550i		−	0.753658i	0.926283	−	0.376829i	$-0.122986\pi$
$228$		0			0
$229$		−	17.4776i		−	1.15495i	−0.816407	−	0.577477i	$-0.804037\pi$
$229$		−	17.4776i		−	1.15495i	0.816407	−	0.577477i	$-0.195963\pi$
$230$	3.62498	+	42.9426i	0.239024	+	2.83155i
$231$		0			0
$232$	6.98098	+	27.0412i	0.458324	+	1.77534i
$233$	−1.98827			−0.130256			−0.0651279	−	0.997877i	$-0.520746\pi$
$233$	−1.98827			−0.130256			−0.0651279	+	0.997877i	$0.520746\pi$
$234$		0			0
$235$		−	39.1027i		−	2.55078i
$236$	−1.30639	−	7.68281i	−0.0850387	−	0.500108i
$237$		0			0
$238$	−1.97678	+	0.166869i	−0.128136	+	0.0108165i
$239$	21.3430			1.38056			0.690282	−	0.723540i	$-0.257486\pi$
$239$	21.3430			1.38056			0.690282	+	0.723540i	$0.257486\pi$
$240$		0			0
$241$	−13.3714			−0.861330			−0.430665	−	0.902512i	$-0.641721\pi$
$241$	−13.3714			−0.861330			−0.430665	+	0.902512i	$0.641721\pi$
$242$	0.0224085	−	0.00189160i	0.00144047	−	0.000121597i
$243$		0			0
$244$	3.15935	+	18.5800i	0.202257	+	1.18946i
$245$			3.46300i			0.221243i
$246$		0			0
$247$	−14.9413			−0.950691
$248$	21.4588	−	5.53982i	1.36264	−	0.351779i
$249$		0			0
$250$	0.820758	+	9.72296i	0.0519093	+	0.614934i
$251$			1.92814i			0.121703i	0.998147	+	0.0608514i	$0.0193816\pi$
$251$			1.92814i			0.121703i	−0.998147	+	0.0608514i	$0.980618\pi$
$252$		0			0
$253$			29.2060i			1.83617i
$254$	−4.75669	+	0.401533i	−0.298461	+	0.0251944i
$255$		0			0
$256$	12.5041	−	9.98234i	0.781507	−	0.623896i
$257$	5.22415			0.325873			0.162937	−	0.986637i	$-0.447903\pi$
$257$	5.22415			0.325873			0.162937	+	0.986637i	$0.447903\pi$
$258$		0			0
$259$		−	5.42317i		−	0.336980i
$260$	21.2242	−	3.60897i	1.31627	−	0.223819i
$261$		0			0
$262$	0.851089	+	10.0823i	0.0525805	+	0.622885i
$263$	4.69624			0.289583			0.144791	−	0.989462i	$-0.453749\pi$
$263$	4.69624			0.289583			0.144791	+	0.989462i	$0.453749\pi$
$264$		0			0
$265$	−22.5668			−1.38627
$266$	0.571795	+	6.77366i	0.0350590	+	0.415320i
$267$		0			0
$268$	0.304998	+	1.79368i	0.0186307	+	0.109566i
$269$		−	26.9906i		−	1.64565i	−0.568297	−	0.822824i	$-0.692397\pi$
$269$		−	26.9906i		−	1.64565i	0.568297	−	0.822824i	$-0.307603\pi$
$270$		0			0
$271$	2.75175			0.167157			0.0835784	−	0.996501i	$-0.473365\pi$
$271$	2.75175			0.167157			0.0835784	+	0.996501i	$0.473365\pi$
$272$	5.29571	−	1.85459i	0.321099	−	0.112451i
$273$		0			0
$274$	5.95887	−	0.503015i	0.359988	−	0.0303882i
$275$			23.2079i			1.39949i
$276$		0			0
$277$			12.0526i			0.724173i	0.932145	+	0.362086i	$0.117935\pi$
$277$			12.0526i			0.724173i	−0.932145	+	0.362086i	$0.882065\pi$
$278$	0.394311	+	4.67113i	0.0236492	+	0.280156i
$279$		0			0
$280$	−2.44837	−	9.48391i	−0.146318	−	0.566772i
$281$	6.74449			0.402342			0.201171	−	0.979556i	$-0.435525\pi$
$281$	6.74449			0.402342			0.201171	+	0.979556i	$0.435525\pi$
$282$		0			0
$283$			8.53083i			0.507105i	0.967322	+	0.253552i	$0.0815991\pi$
$283$			8.53083i			0.507105i	−0.967322	+	0.253552i	$0.918401\pi$
$284$	12.6645	−	2.15348i	0.751499	−	0.127785i
$285$		0			0
$286$	14.5385	−	1.22726i	0.859682	−	0.0725696i
$287$	11.5710			0.683014
$288$		0			0
$289$	−15.0322			−0.884250
$290$	−48.1856	+	4.06756i	−2.82956	+	0.238856i
$291$		0			0
$292$	3.08091	−	0.523879i	0.180296	−	0.0306577i
$293$		−	11.2926i		−	0.659718i	−0.944030	−	0.329859i	$-0.892999\pi$
$293$		−	11.2926i		−	0.659718i	0.944030	−	0.329859i	$-0.107001\pi$
$294$		0			0
$295$	13.4937			0.785636
$296$	3.83423	+	14.8521i	0.222860	+	0.863261i
$297$		0			0
$298$	0.842730	+	9.98324i	0.0488180	+	0.578314i
$299$			27.3527i			1.58185i
$300$		0			0
$301$		−	7.03957i		−	0.405754i
$302$	−0.355744	+	0.0300299i	−0.0204708	+	0.00172803i
$303$		0			0
$304$	−6.35498	−	18.1463i	−0.364483	−	1.04076i
$305$	−32.6330			−1.86856
$306$		0			0
$307$			9.15810i			0.522680i	0.965247	+	0.261340i	$0.0841644\pi$
$307$			9.15810i			0.522680i	−0.965247	+	0.261340i	$0.915836\pi$
$308$	−1.11276	−	6.54411i	−0.0634056	−	0.372885i
$309$		0			0
$310$	3.22785	+	38.2381i	0.183330	+	2.17178i
$311$	−10.0122			−0.567741			−0.283870	−	0.958863i	$-0.591619\pi$
$311$	−10.0122			−0.567741			−0.283870	+	0.958863i	$0.591619\pi$
$312$		0			0
$313$	−10.3334			−0.584076			−0.292038	−	0.956407i	$-0.594333\pi$
$313$	−10.3334			−0.584076			−0.292038	+	0.956407i	$0.594333\pi$
$314$	0.369981	+	4.38291i	0.0208792	+	0.247342i
$315$		0			0
$316$	−22.0080	+	3.74225i	−1.23804	+	0.210518i
$317$			34.9339i			1.96208i	0.193794	+	0.981042i	$0.437921\pi$
$317$			34.9339i			1.96208i	−0.193794	+	0.981042i	$0.562079\pi$
$318$		0			0
$319$	−32.7719			−1.83487
$320$	13.4104	+	24.2420i	0.749665	+	1.35517i
$321$		0			0
$322$	12.4004	−	1.04677i	0.691048	−	0.0583344i
$323$		−	6.74273i		−	0.375175i
$324$		0			0
$325$			21.7352i			1.20565i
$326$	−2.20778	−	26.1541i	−0.122278	−	1.44854i
$327$		0			0
$328$	−31.6887	+	8.18079i	−1.74972	+	0.451708i
$329$	−11.2916			−0.622524
$330$		0			0
$331$		−	8.71488i		−	0.479013i	−0.970895	−	0.239507i	$-0.923014\pi$
$331$		−	8.71488i		−	0.479013i	0.970895	−	0.239507i	$-0.0769857\pi$
$332$	−0.124130	−	0.730003i	−0.00681252	−	0.0400641i
$333$		0			0
$334$	−20.1828	+	1.70372i	−1.10435	+	0.0932233i
$335$	−3.15034			−0.172121
$336$		0			0
$337$	−8.63703			−0.470489			−0.235244	−	0.971936i	$-0.575589\pi$
$337$	−8.63703			−0.470489			−0.235244	+	0.971936i	$0.575589\pi$
$338$	−4.70366	+	0.397057i	−0.255846	+	0.0215971i
$339$		0			0
$340$	1.62866	+	9.57808i	0.0883266	+	0.519444i
$341$			26.0064i			1.40833i
$342$		0			0
$343$	1.00000			0.0539949
$344$	4.97704	+	19.2788i	0.268344	+	1.03945i
$345$		0			0
$346$	−0.166758	−	1.97546i	−0.00896495	−	0.106202i
$347$			28.2190i			1.51488i	0.652907	+	0.757438i	$0.273549\pi$
$347$			28.2190i			1.51488i	−0.652907	+	0.757438i	$0.726451\pi$
$348$		0			0
$349$		−	13.6266i		−	0.729416i	−0.931122	−	0.364708i	$-0.881169\pi$
$349$		−	13.6266i		−	0.729416i	0.931122	−	0.364708i	$-0.118831\pi$
$350$	9.85368	−	0.831793i	0.526701	−	0.0444612i
$351$		0			0
$352$	7.67420	+	17.1352i	0.409036	+	0.913310i
$353$	32.4282			1.72598			0.862990	−	0.505220i	$-0.168589\pi$
$353$	32.4282			1.72598			0.862990	+	0.505220i	$0.168589\pi$
$354$		0			0
$355$			22.2433i			1.18055i
$356$	−9.56367	+	1.62621i	−0.506874	+	0.0861891i
$357$		0			0
$358$	−0.412602	−	4.88781i	−0.0218067	−	0.258329i
$359$	12.9995			0.686087			0.343044	−	0.939319i	$-0.388542\pi$
$359$	12.9995			0.686087			0.343044	+	0.939319i	$0.388542\pi$
$360$		0			0
$361$	−4.10474			−0.216039
$362$	−2.30767	−	27.3374i	−0.121288	−	1.43682i
$363$		0			0
$364$	−1.04215	−	6.12884i	−0.0546236	−	0.321238i
$365$			5.41117i			0.283233i
$366$		0			0
$367$	−7.55576			−0.394408			−0.197204	−	0.980363i	$-0.563186\pi$
$367$	−7.55576			−0.394408			−0.197204	+	0.980363i	$0.563186\pi$
$368$	−33.2201	+	11.6339i	−1.73172	+	0.606460i
$369$		0			0
$370$	−26.4654	+	2.23407i	−1.37587	+	0.116144i
$371$			6.51655i			0.338323i
$372$		0			0
$373$			34.6651i			1.79489i	0.441124	+	0.897446i	$0.354580\pi$
$373$			34.6651i			1.79489i	−0.441124	+	0.897446i	$0.645420\pi$
$374$	0.553841	+	6.56097i	0.0286384	+	0.339260i
$375$		0			0
$376$	30.9235	−	7.98324i	1.59476	−	0.411704i
$377$	−30.6923			−1.58073
$378$		0			0
$379$		−	0.308373i		−	0.0158401i	−0.999969	−	0.00792004i	$-0.997479\pi$
$379$		−	0.308373i		−	0.0158401i	0.999969	−	0.00792004i	$-0.00252105\pi$
$380$	32.8204	−	5.58080i	1.68365	−	0.286289i
$381$		0			0
$382$	33.0613	−	2.79085i	1.69156	−	0.142793i
$383$	−4.36024			−0.222798			−0.111399	−	0.993776i	$-0.535533\pi$
$383$	−4.36024			−0.222798			−0.111399	+	0.993776i	$0.535533\pi$
$384$		0			0
$385$	11.4938			0.585777
$386$	21.8953	−	1.84828i	1.11444	−	0.0940750i
$387$		0			0
$388$	3.21946	−	0.547439i	0.163443	−	0.0277920i
$389$			1.33391i			0.0676317i	0.999428	+	0.0338159i	$0.0107660\pi$
$389$			1.33391i			0.0676317i	−0.999428	+	0.0338159i	$0.989234\pi$
$390$		0			0
$391$	−12.3438			−0.624251
$392$	−2.73864	+	0.707009i	−0.138322	+	0.0357093i
$393$		0			0
$394$	1.76387	+	20.8953i	0.0888623	+	1.05269i
$395$		−	38.6538i		−	1.94488i
$396$		0			0
$397$		−	6.92952i		−	0.347783i	−0.984765	−	0.173891i	$-0.944366\pi$
$397$		−	6.92952i		−	0.347783i	0.984765	−	0.173891i	$-0.0556342\pi$
$398$	−18.6149	+	1.57136i	−0.933079	+	0.0787653i
$399$		0			0
$400$	−26.3976	+	9.24461i	−1.31988	+	0.462231i
$401$	23.9669			1.19685			0.598426	−	0.801178i	$-0.295793\pi$
$401$	23.9669			1.19685			0.598426	+	0.801178i	$0.295793\pi$
$402$		0			0
$403$			24.3561i			1.21327i
$404$	−4.41382	−	25.9574i	−0.219596	−	1.29143i
$405$		0			0
$406$	1.17458	+	13.9144i	0.0582933	+	0.690561i
$407$	−17.9996			−0.892208
$408$		0			0
$409$	21.6936			1.07268			0.536340	−	0.844002i	$-0.319807\pi$
$409$	21.6936			1.07268			0.536340	+	0.844002i	$0.319807\pi$
$410$	−4.76665	−	56.4672i	−0.235408	−	2.78872i
$411$		0			0
$412$	30.9523	−	5.26314i	1.52491	−	0.259296i
$413$		−	3.89654i		−	0.191736i
$414$		0			0
$415$	1.28214			0.0629380
$416$	7.18722	+	16.0479i	0.352382	+	0.786811i
$417$		0			0
$418$	22.4819	−	1.89780i	1.09963	−	0.0928245i
$419$		−	27.5910i		−	1.34791i	−0.738772	−	0.673955i	$-0.764594\pi$
$419$		−	27.5910i		−	1.34791i	0.738772	−	0.673955i	$-0.235406\pi$
$420$		0			0
$421$			38.3335i			1.86826i	0.356929	+	0.934131i	$0.383824\pi$
$421$			38.3335i			1.86826i	−0.356929	+	0.934131i	$0.616176\pi$
$422$	1.47257	+	17.4445i	0.0716836	+	0.849186i
$423$		0			0
$424$	−4.60726	−	17.8465i	−0.223748	−	0.866702i
$425$	−9.80867			−0.475790
$426$		0			0
$427$			9.42334i			0.456027i
$428$	−3.14233	−	18.4799i	−0.151890	−	0.893259i
$429$		0			0
$430$	−34.3536	+	2.89994i	−1.65668	+	0.139848i
$431$	−2.22510			−0.107179			−0.0535896	−	0.998563i	$-0.517066\pi$
$431$	−2.22510			−0.107179			−0.0535896	+	0.998563i	$0.517066\pi$
$432$		0			0
$433$	28.2235			1.35633			0.678167	−	0.734908i	$-0.262775\pi$
$433$	28.2235			1.35633			0.678167	+	0.734908i	$0.262775\pi$
$434$	11.0419	−	0.932096i	0.530028	−	0.0447421i
$435$		0			0
$436$	2.45246	+	14.4228i	0.117451	+	0.690725i
$437$			42.2974i			2.02336i
$438$		0			0
$439$	−5.63936			−0.269152			−0.134576	−	0.990903i	$-0.542967\pi$
$439$	−5.63936			−0.269152			−0.134576	+	0.990903i	$0.542967\pi$
$440$	−31.4773	+	8.12620i	−1.50062	+	0.387401i
$441$		0			0
$442$	0.518696	+	6.14463i	0.0246718	+	0.292270i
$443$			5.81672i			0.276361i	0.990407	+	0.138180i	$0.0441254\pi$
$443$			5.81672i			0.276361i	−0.990407	+	0.138180i	$0.955875\pi$
$444$		0			0
$445$		−	16.7972i		−	0.796264i
$446$	−4.10318	+	0.346367i	−0.194291	+	0.0164010i
$447$		0			0
$448$	7.00028	−	3.87248i	0.330732	−	0.182958i
$449$	1.66921			0.0787748			0.0393874	−	0.999224i	$-0.487459\pi$
$449$	1.66921			0.0787748			0.0393874	+	0.999224i	$0.487459\pi$
$450$		0			0
$451$		−	38.4043i		−	1.80839i
$452$	−21.5218	+	3.65957i	−1.01230	+	0.172132i
$453$		0			0
$454$	1.35076	+	16.0015i	0.0633942	+	0.750987i
$455$	10.7644			0.504643
$456$		0			0
$457$	−16.4606			−0.769994			−0.384997	−	0.922918i	$-0.625797\pi$
$457$	−16.4606			−0.769994			−0.384997	+	0.922918i	$0.625797\pi$
$458$	2.07908	+	24.6295i	0.0971493	+	1.15086i
$459$		0			0
$460$	−10.2167	−	60.0836i	−0.476354	−	2.80141i
$461$			22.7915i			1.06151i	0.847527	+	0.530753i	$0.178091\pi$
$461$			22.7915i			1.06151i	−0.847527	+	0.530753i	$0.821909\pi$
$462$		0			0
$463$	−16.3165			−0.758293			−0.379146	−	0.925337i	$-0.623782\pi$
$463$	−16.3165			−0.758293			−0.379146	+	0.925337i	$0.623782\pi$
$464$	−13.0544	−	37.2761i	−0.606033	−	1.73050i
$465$		0			0
$466$	2.80187	−	0.236518i	0.129794	−	0.0109565i
$467$			33.3073i			1.54128i	0.637271	+	0.770639i	$0.280063\pi$
$467$			33.3073i			1.54128i	−0.637271	+	0.770639i	$0.719937\pi$
$468$		0			0
$469$			0.909712i			0.0420066i
$470$	4.65154	+	55.1036i	0.214560	+	2.54174i
$471$		0			0
$472$	2.75489	+	10.6712i	0.126804	+	0.491183i
$473$	−23.3645			−1.07430
$474$		0			0
$475$			33.6105i			1.54216i
$476$	2.76583	−	0.470304i	0.126772	−	0.0215563i
$477$		0			0
$478$	−30.0766	+	2.53890i	−1.37567	+	0.116127i
$479$	−28.5717			−1.30547			−0.652737	−	0.757584i	$-0.726379\pi$
$479$	−28.5717			−1.30547			−0.652737	+	0.757584i	$0.726379\pi$
$480$		0			0
$481$	−16.8574			−0.768632
$482$	18.8430	−	1.59063i	0.858277	−	0.0724510i
$483$		0			0
$484$	−0.0313531	+	0.00533130i	−0.00142514	+	0.000242332i
$485$			5.65451i			0.256758i
$486$		0			0
$487$	39.0149			1.76793			0.883967	−	0.467550i	$-0.154863\pi$
$487$	39.0149			1.76793			0.883967	+	0.467550i	$0.154863\pi$
$488$	−6.66238	−	25.8071i	−0.301592	−	1.16823i
$489$		0			0
$490$	−0.411948	−	4.88007i	−0.0186099	−	0.220459i
$491$			12.5799i			0.567722i	0.958866	+	0.283861i	$0.0916153\pi$
$491$			12.5799i			0.567722i	−0.958866	+	0.283861i	$0.908385\pi$
$492$		0			0
$493$		−	13.8509i		−	0.623811i
$494$	21.0553	−	1.77737i	0.947322	−	0.0799677i
$495$		0			0
$496$	−29.5808	+	10.3594i	−1.32822	+	0.465151i
$497$	6.42314			0.288117
$498$		0			0
$499$		−	17.3054i		−	0.774697i	−0.921933	−	0.387349i	$-0.873391\pi$
$499$		−	17.3054i		−	0.774697i	0.921933	−	0.387349i	$-0.126609\pi$
$500$	−2.31323	−	13.6040i	−0.103451	−	0.608388i
$501$		0			0
$502$	−0.229365	−	2.71713i	−0.0102371	−	0.121272i
$503$	−18.1289			−0.808326			−0.404163	−	0.914687i	$-0.632437\pi$
$503$	−18.1289			−0.808326			−0.404163	+	0.914687i	$0.632437\pi$
$504$		0			0
$505$	45.5904			2.02875
$506$	−3.47426	−	41.1572i	−0.154450	−	1.82966i
$507$		0			0
$508$	6.65537	−	1.13168i	0.295284	−	0.0502103i
$509$		−	17.3445i		−	0.768780i	−0.923171	−	0.384390i	$-0.874412\pi$
$509$		−	17.3445i		−	0.768780i	0.923171	−	0.384390i	$-0.125588\pi$
$510$		0			0
$511$	1.56257			0.0691238
$512$	−16.4333	+	15.5546i	−0.726258	+	0.687422i
$513$		0			0
$514$	−7.36188	+	0.621449i	−0.324719	+	0.0274109i
$515$			54.3632i			2.39553i
$516$		0			0
$517$			37.4770i			1.64823i
$518$	0.645124	+	7.64234i	0.0283451	+	0.335785i
$519$		0			0
$520$	−29.4798	+	7.61053i	−1.29278	+	0.333744i
$521$	16.7507			0.733861			0.366930	−	0.930248i	$-0.380409\pi$
$521$	16.7507			0.733861			0.366930	+	0.930248i	$0.380409\pi$
$522$		0			0
$523$		−	20.8692i		−	0.912545i	−0.889840	−	0.456273i	$-0.849184\pi$
$523$		−	20.8692i		−	0.912545i	0.889840	−	0.456273i	$-0.150816\pi$
$524$	−2.39871	−	14.1067i	−0.104788	−	0.616254i
$525$		0			0
$526$	−6.61795	+	0.558651i	−0.288556	+	0.0243583i
$527$	−10.9915			−0.478796
$528$		0			0
$529$	54.4329			2.36665
$530$	31.8012	−	2.68448i	1.38136	−	0.116606i
$531$		0			0
$532$	−1.61155	−	9.47744i	−0.0698695	−	0.410899i
$533$		−	35.9673i		−	1.55792i
$534$		0			0
$535$	32.4572			1.40325
$536$	−0.643175	−	2.49137i	−0.0277809	−	0.107611i
$537$		0			0
$538$	3.21072	+	38.0352i	0.138424	+	1.63982i
$539$		−	3.31902i		−	0.142960i
$540$		0			0
$541$		−	37.7498i		−	1.62299i	−0.584359	−	0.811495i	$-0.698654\pi$
$541$		−	37.7498i		−	1.62299i	0.584359	−	0.811495i	$-0.301346\pi$
$542$	−3.87777	+	0.327340i	−0.166564	+	0.0140604i
$543$		0			0
$544$	−7.24210	+	3.24346i	−0.310503	+	0.139062i
$545$	−25.3315			−1.08508
$546$		0			0
$547$		−	34.4520i		−	1.47306i	−0.676404	−	0.736531i	$-0.736463\pi$
$547$		−	34.4520i		−	1.47306i	0.676404	−	0.736531i	$-0.263537\pi$
$548$	−8.33741	+	1.41770i	−0.356156	+	0.0605611i
$549$		0			0
$550$	−2.76074	−	32.7046i	−0.117718	−	1.39453i
$551$	−47.4616			−2.02193
$552$		0			0
$553$	−11.1619			−0.474653
$554$	−1.43375	−	16.9846i	−0.0609140	−	0.721606i
$555$		0			0
$556$	−1.11133	−	6.53566i	−0.0471308	−	0.277174i
$557$			27.7136i			1.17426i	0.809491	+	0.587132i	$0.199743\pi$
$557$			27.7136i			1.17426i	−0.809491	+	0.587132i	$0.800257\pi$
$558$		0			0
$559$	−21.8818			−0.925503
$560$	4.57843	+	13.0735i	0.193474	+	0.552456i
$561$		0			0
$562$	−9.50434	+	0.802304i	−0.400917	+	0.0338432i
$563$			0.570384i			0.0240388i	0.999928	+	0.0120194i	$0.00382599\pi$
$563$			0.570384i			0.0240388i	−0.999928	+	0.0120194i	$0.996174\pi$
$564$		0			0
$565$		−	37.7998i		−	1.59025i
$566$	−1.01480	−	12.0217i	−0.0426553	−	0.505308i
$567$		0			0
$568$	−17.5907	+	4.54121i	−0.738087	+	0.190545i
$569$	18.4090			0.771745			0.385872	−	0.922552i	$-0.373901\pi$
$569$	18.4090			0.771745			0.385872	+	0.922552i	$0.373901\pi$
$570$		0			0
$571$		−	43.3534i		−	1.81428i	−0.420824	−	0.907142i	$-0.638259\pi$
$571$		−	43.3534i		−	1.81428i	0.420824	−	0.907142i	$-0.361741\pi$
$572$	−20.3417	+	3.45892i	−0.850531	+	0.144625i
$573$		0			0
$574$	−16.3059	+	1.37645i	−0.680593	+	0.0574519i
$575$	61.5301			2.56598
$576$		0			0
$577$	−39.6209			−1.64944			−0.824720	−	0.565541i	$-0.808667\pi$
$577$	−39.6209			−1.64944			−0.824720	+	0.565541i	$0.808667\pi$
$578$	21.1835	−	1.78819i	0.881116	−	0.0743790i
$579$		0			0
$580$	67.4194	−	11.4640i	2.79944	−	0.476018i
$581$		−	0.370241i		−	0.0153602i
$582$		0			0
$583$	21.6286			0.895764
$584$	−4.27930	+	1.10475i	−0.177079	+	0.0457148i
$585$		0			0
$586$	1.34333	+	15.9135i	0.0554924	+	0.657380i
$587$		−	13.4388i		−	0.554677i	−0.960772	−	0.277338i	$-0.910548\pi$
$587$		−	13.4388i		−	0.554677i	0.960772	−	0.277338i	$-0.0894523\pi$
$588$		0			0
$589$			37.6636i			1.55190i
$590$	−19.0154	+	1.60518i	−0.782852	+	0.0660840i
$591$		0			0
$592$	−7.16997	−	20.4735i	−0.294684	−	0.841456i
$593$	22.3157			0.916395			0.458198	−	0.888850i	$-0.348495\pi$
$593$	22.3157			0.916395			0.458198	+	0.888850i	$0.348495\pi$
$594$		0			0
$595$			4.85778i			0.199150i
$596$	−2.37515	−	13.9682i	−0.0972901	−	0.572158i
$597$		0			0
$598$	−3.25380	−	38.5455i	−0.133058	−	1.57624i
$599$	−14.2622			−0.582740			−0.291370	−	0.956610i	$-0.594111\pi$
$599$	−14.2622			−0.582740			−0.291370	+	0.956610i	$0.594111\pi$
$600$		0			0
$601$	−2.40215			−0.0979858			−0.0489929	−	0.998799i	$-0.515601\pi$
$601$	−2.40215			−0.0979858			−0.0489929	+	0.998799i	$0.515601\pi$
$602$	0.837406	+	9.92018i	0.0341301	+	0.404316i
$603$		0			0
$604$	0.497742	−	0.0846364i	0.0202529	−	0.00344381i
$605$		−	0.0550671i		−	0.00223880i
$606$		0			0
$607$	−10.0506			−0.407940			−0.203970	−	0.978977i	$-0.565385\pi$
$607$	−10.0506			−0.407940			−0.203970	+	0.978977i	$0.565385\pi$
$608$	11.1141	+	24.8159i	0.450736	+	1.00642i
$609$		0			0
$610$	45.9865	−	3.88193i	1.86194	−	0.157175i
$611$			35.0988i			1.41994i
$612$		0			0
$613$			2.57394i			0.103961i	0.998648	+	0.0519803i	$0.0165533\pi$
$613$			2.57394i			0.103961i	−0.998648	+	0.0519803i	$0.983447\pi$
$614$	−1.08942	−	12.9056i	−0.0439654	−	0.520828i
$615$		0			0
$616$	2.34658	+	9.08960i	0.0945463	+	0.366230i
$617$	−36.3495			−1.46337			−0.731687	−	0.681640i	$-0.761267\pi$
$617$	−36.3495			−1.46337			−0.731687	+	0.681640i	$0.761267\pi$
$618$		0			0
$619$			16.6498i			0.669211i	0.942358	+	0.334606i	$0.108603\pi$
$619$			16.6498i			0.669211i	−0.942358	+	0.334606i	$0.891397\pi$
$620$	−9.09739	−	53.5013i	−0.365360	−	2.14866i
$621$		0			0
$622$	14.1092	−	1.19102i	0.565729	−	0.0477557i
$623$	−4.85047			−0.194330
$624$		0			0
$625$	−11.0685			−0.442740
$626$	14.5618	−	1.22923i	0.582006	−	0.0491297i
$627$		0			0
$628$	−1.04276	−	6.13240i	−0.0416105	−	0.244709i
$629$		−	7.60744i		−	0.303328i
$630$		0			0
$631$	14.7898			0.588773			0.294387	−	0.955686i	$-0.404885\pi$
$631$	14.7898			0.588773			0.294387	+	0.955686i	$0.404885\pi$
$632$	30.5685	−	7.89158i	1.21595	−	0.313910i
$633$		0			0
$634$	−4.15563	−	49.2289i	−0.165041	−	1.95513i
$635$			11.6892i			0.463871i
$636$		0			0
$637$		−	3.10840i		−	0.123159i
$638$	46.1822	−	3.89845i	1.82837	−	0.154341i
$639$		0			0
$640$	−21.7817	−	32.5666i	−0.860998	−	1.28731i
$641$	32.8085			1.29586			0.647928	−	0.761701i	$-0.275636\pi$
$641$	32.8085			1.29586			0.647928	+	0.761701i	$0.275636\pi$
$642$		0			0
$643$		−	15.3479i		−	0.605263i	−0.953108	−	0.302631i	$-0.902135\pi$
$643$		−	15.3479i		−	0.605263i	0.953108	−	0.302631i	$-0.0978651\pi$
$644$	−17.3502	+	2.95023i	−0.683692	+	0.116255i
$645$		0			0
$646$	0.802095	+	9.50186i	0.0315580	+	0.373846i
$647$	−6.19107			−0.243396			−0.121698	−	0.992567i	$-0.538834\pi$
$647$	−6.19107			−0.243396			−0.121698	+	0.992567i	$0.538834\pi$
$648$		0			0
$649$	−12.9327			−0.507653
$650$	−2.58555	−	30.6292i	−0.101414	−	1.20138i
$651$		0			0
$652$	6.22243	+	36.5938i	0.243689	+	1.43312i
$653$		−	17.4848i		−	0.684234i	−0.939657	−	0.342117i	$-0.888856\pi$
$653$		−	17.4848i		−	0.684234i	0.939657	−	0.342117i	$-0.111144\pi$
$654$		0			0
$655$	24.7764			0.968093
$656$	43.6827	−	15.2980i	1.70552	−	0.597286i
$657$		0			0
$658$	15.9121	−	1.34321i	0.620318	−	0.0523638i
$659$		−	13.8987i		−	0.541416i	−0.962661	−	0.270708i	$-0.912742\pi$
$659$		−	13.8987i		−	0.541416i	0.962661	−	0.270708i	$-0.0872578\pi$
$660$		0			0
$661$			1.69978i			0.0661137i	0.999453	+	0.0330568i	$0.0105242\pi$
$661$			1.69978i			0.0661137i	−0.999453	+	0.0330568i	$0.989476\pi$
$662$	1.03670	+	12.2810i	0.0402923	+	0.477316i
$663$		0			0
$664$	0.261763	+	1.01395i	0.0101584	+	0.0393491i
$665$	16.6457			0.645494
$666$		0			0
$667$			86.8869i			3.36428i
$668$	28.2389	−	4.80176i	1.09260	−	0.185786i
$669$		0			0
$670$	4.43946	−	0.374755i	0.171511	−	0.0144780i
$671$	31.2762			1.20741
$672$		0			0
$673$	−22.7847			−0.878284			−0.439142	−	0.898418i	$-0.644718\pi$
$673$	−22.7847			−0.878284			−0.439142	+	0.898418i	$0.644718\pi$
$674$	12.1713	−	1.02743i	0.468821	−	0.0395753i
$675$		0			0
$676$	6.58118	−	1.11907i	0.253122	−	0.0430410i
$677$			34.2963i			1.31811i	0.752093	+	0.659057i	$0.229044\pi$
$677$			34.2963i			1.31811i	−0.752093	+	0.659057i	$0.770956\pi$
$678$		0			0
$679$	1.63283			0.0626624
$680$	−3.43449	−	13.3037i	−0.131707	−	0.510174i
$681$		0			0
$682$	−3.09365	−	36.6483i	−0.118462	−	1.40334i
$683$		−	10.5590i		−	0.404029i	−0.979383	−	0.202014i	$-0.935251\pi$
$683$		−	10.5590i		−	0.404029i	0.979383	−	0.202014i	$-0.0647487\pi$
$684$		0			0
$685$		−	14.6434i		−	0.559497i
$686$	−1.40920	+	0.118957i	−0.0538036	+	0.00454180i
$687$		0			0
$688$	−9.30700	−	26.5757i	−0.354826	−	1.01319i
$689$	20.2561			0.771695
$690$		0			0
$691$		−	14.3879i		−	0.547342i	−0.961823	−	0.273671i	$-0.911762\pi$
$691$		−	14.3879i		−	0.547342i	0.961823	−	0.273671i	$-0.0882380\pi$
$692$	0.469990	+	2.76399i	0.0178664	+	0.105071i
$693$		0			0
$694$	−3.35685	−	39.7663i	−0.127424	−	1.50951i
$695$	11.4789			0.435421
$696$		0			0
$697$	16.2314			0.614807
$698$	1.62098	+	19.2027i	0.0613551	+	0.726831i
$699$		0			0
$700$	−13.7869	+	2.34433i	−0.521095	+	0.0886072i
$701$			17.8913i			0.675746i	0.941192	+	0.337873i	$0.109708\pi$
$701$			17.8913i			0.675746i	−0.941192	+	0.337873i	$0.890292\pi$
$702$		0			0
$703$	−26.0678			−0.983165
$704$	−12.8528	−	23.2341i	−0.484410	−	0.875667i
$705$		0			0
$706$	−45.6979	+	3.85757i	−1.71986	+	0.145181i
$707$		−	13.1650i		−	0.495121i
$708$		0			0
$709$		−	22.0614i		−	0.828535i	−0.910155	−	0.414267i	$-0.864038\pi$
$709$		−	22.0614i		−	0.828535i	0.910155	−	0.414267i	$-0.135962\pi$
$710$	−2.64600	−	31.3453i	−0.0993026	−	1.17637i
$711$		0			0
$712$	13.2837	−	3.42933i	0.497828	−	0.128519i
$713$	68.9499			2.58219
$714$		0			0
$715$		−	35.7273i		−	1.33613i
$716$	1.16288	+	6.83883i	0.0434588	+	0.255579i
$717$		0			0
$718$	−18.3189	+	1.54638i	−0.683656	+	0.0577104i
$719$	−15.8888			−0.592552			−0.296276	−	0.955102i	$-0.595745\pi$
$719$	−15.8888			−0.592552			−0.296276	+	0.955102i	$0.595745\pi$
$720$		0			0
$721$	15.6983			0.584634
$722$	5.78440	−	0.488287i	0.215273	−	0.0181722i
$723$		0			0
$724$	6.50394	+	38.2493i	0.241717	+	1.42153i
$725$			69.0425i			2.56418i
$726$		0			0
$727$	−26.2510			−0.973595			−0.486798	−	0.873515i	$-0.661835\pi$
$727$	−26.2510			−0.973595			−0.486798	+	0.873515i	$0.661835\pi$
$728$	2.19767	+	8.51280i	0.0814510	+	0.315505i
$729$		0			0
$730$	−0.643696	−	7.62542i	−0.0238243	−	0.282230i
$731$		−	9.87487i		−	0.365235i
$732$		0			0
$733$		−	23.1441i		−	0.854848i	−0.904051	−	0.427424i	$-0.859421\pi$
$733$		−	23.1441i		−	0.854848i	0.904051	−	0.427424i	$-0.140579\pi$
$734$	10.6476	−	0.898811i	0.393010	−	0.0331757i
$735$		0			0
$736$	45.4299	−	20.3463i	1.67457	−	0.749975i
$737$	3.01935			0.111219
$738$		0			0
$739$		−	11.2767i		−	0.414819i	−0.978254	−	0.207409i	$-0.933497\pi$
$739$		−	11.2767i		−	0.414819i	0.978254	−	0.207409i	$-0.0665032\pi$
$740$	37.0294	−	6.29650i	1.36123	−	0.231464i
$741$		0			0
$742$	−0.775190	−	9.18314i	−0.0284581	−	0.337124i
$743$	−5.16580			−0.189515			−0.0947575	−	0.995500i	$-0.530208\pi$
$743$	−5.16580			−0.189515			−0.0947575	+	0.995500i	$0.530208\pi$
$744$		0			0
$745$	24.5330			0.898821
$746$	−4.12366	−	48.8502i	−0.150978	−	1.78853i
$747$		0			0
$748$	−1.56095	−	9.17985i	−0.0570739	−	0.335649i
$749$		−	9.37257i		−	0.342466i
$750$		0			0
$751$	35.7670			1.30516			0.652578	−	0.757722i	$-0.273687\pi$
$751$	35.7670			1.30516			0.652578	+	0.757722i	$0.273687\pi$
$752$	−42.6278	+	14.9286i	−1.55448	+	0.544389i
$753$		0			0
$754$	43.2516	−	3.65106i	1.57513	−	0.132964i
$755$			0.874212i			0.0318158i
$756$		0			0
$757$		−	31.6174i		−	1.14916i	−0.818450	−	0.574578i	$-0.805166\pi$
$757$		−	31.6174i		−	1.14916i	0.818450	−	0.574578i	$-0.194834\pi$
$758$	0.0366832	+	0.434560i	0.00133239	+	0.0157839i
$759$		0			0
$760$	−45.5867	+	11.7687i	−1.65360	+	0.426895i
$761$	12.7856			0.463477			0.231738	−	0.972778i	$-0.425559\pi$
$761$	12.7856			0.463477			0.231738	+	0.972778i	$0.425559\pi$
$762$		0			0
$763$			7.31490i			0.264817i
$764$	−46.2581	+	7.86575i	−1.67356	+	0.284573i
$765$		0			0
$766$	6.14446	−	0.518681i	0.222008	−	0.0187407i
$767$	−12.1120			−0.437340
$768$		0			0
$769$	6.55622			0.236423			0.118212	−	0.992988i	$-0.462284\pi$
$769$	6.55622			0.236423			0.118212	+	0.992988i	$0.462284\pi$
$770$	−16.1970	+	1.36727i	−0.583701	+	0.0492728i
$771$		0			0
$772$	−30.6350	+	5.20920i	−1.10258	+	0.187483i
$773$		−	27.7250i		−	0.997197i	−0.866833	−	0.498599i	$-0.833848\pi$
$773$		−	27.7250i		−	0.997197i	0.866833	−	0.498599i	$-0.166152\pi$
$774$		0			0
$775$	54.7893			1.96809
$776$	−4.47174	+	1.15443i	−0.160526	+	0.0414416i
$777$		0			0
$778$	−0.158677	−	1.87974i	−0.00568886	−	0.0673920i
$779$		−	55.6187i		−	1.99275i
$780$		0			0
$781$		−	21.3185i		−	0.762837i
$782$	17.3949	−	1.46838i	0.622039	−	0.0525091i
$783$		0			0
$784$	3.77519	−	1.32210i	0.134828	−	0.0472178i
$785$	10.7707			0.384421
$786$		0			0
$787$		−	25.9751i		−	0.925911i	−0.886382	−	0.462955i	$-0.846789\pi$
$787$		−	25.9751i		−	0.925911i	0.886382	−	0.462955i	$-0.153211\pi$
$788$	−4.97128	−	29.2359i	−0.177095	−	1.04148i
$789$		0			0
$790$	4.59814	+	54.4710i	0.163594	+	1.93799i
$791$	−10.9153			−0.388105
$792$		0			0
$793$	29.2915			1.04017
$794$	0.824315	+	9.76509i	0.0292538	+	0.346550i
$795$		0			0
$796$	26.0452	−	4.42874i	0.923146	−	0.156972i
$797$		−	45.5049i		−	1.61187i	−0.592006	−	0.805934i	$-0.701664\pi$
$797$		−	45.5049i		−	1.61187i	0.592006	−	0.805934i	$-0.298336\pi$
$798$		0			0
$799$	−15.8394			−0.560358
$800$	36.0998	−	16.1677i	1.27632	−	0.571614i
$801$		0			0
$802$	−33.7742	+	2.85103i	−1.19261	+	0.100674i
$803$		−	5.18619i		−	0.183017i
$804$		0			0
$805$		−	30.4730i		−	1.07403i
$806$	−2.89733	−	34.3227i	−0.102054	−	1.20897i
$807$		0			0
$808$	9.30777	+	36.0542i	0.327446	+	1.26838i
$809$	−20.8396			−0.732682			−0.366341	−	0.930481i	$-0.619390\pi$
$809$	−20.8396			−0.732682			−0.366341	+	0.930481i	$0.619390\pi$
$810$		0			0
$811$			52.1223i			1.83026i	0.403158	+	0.915130i	$0.367912\pi$
$811$			52.1223i			1.83026i	−0.403158	+	0.915130i	$0.632088\pi$
$812$	−3.31043	−	19.4685i	−0.116173	−	0.683210i
$813$		0			0
$814$	25.3651	−	2.14118i	0.889046	−	0.0750484i
$815$	−64.2716			−2.25134
$816$		0			0
$817$	−33.8374			−1.18382
$818$	−30.5707	+	2.58061i	−1.06888	+	0.0902288i
$819$		0			0
$820$	13.4343	+	79.0066i	0.469147	+	2.75903i
$821$		−	13.9160i		−	0.485673i	−0.970067	−	0.242837i	$-0.921922\pi$
$821$		−	13.9160i		−	0.485673i	0.970067	−	0.242837i	$-0.0780779\pi$
$822$		0			0
$823$	1.31771			0.0459323			0.0229662	−	0.999736i	$-0.492689\pi$
$823$	1.31771			0.0459323			0.0229662	+	0.999736i	$0.492689\pi$
$824$	−42.9919	+	11.0988i	−1.49769	+	0.386646i
$825$		0			0
$826$	0.463521	+	5.49102i	0.0161280	+	0.191057i
$827$			21.9111i			0.761925i	0.924591	+	0.380962i	$0.124407\pi$
$827$			21.9111i			0.761925i	−0.924591	+	0.380962i	$0.875593\pi$
$828$		0			0
$829$			33.0419i			1.14759i	0.818999	+	0.573795i	$0.194530\pi$
$829$			33.0419i			1.14759i	−0.818999	+	0.573795i	$0.805470\pi$
$830$	−1.80680	+	0.152520i	−0.0627149	+	0.00529405i
$831$		0			0
$832$	−12.0372	−	21.7597i	−0.417316	−	0.754382i
$833$	1.40277			0.0486029
$834$		0			0
$835$			49.5976i			1.71639i
$836$	−31.4558	+	5.34877i	−1.08792	+	0.184991i
$837$		0			0
$838$	3.28215	+	38.8814i	0.113380	+	1.34313i
$839$	−16.2548			−0.561177			−0.280589	−	0.959828i	$-0.590530\pi$
$839$	−16.2548			−0.561177			−0.280589	+	0.959828i	$0.590530\pi$
$840$		0			0
$841$	−68.4952			−2.36190
$842$	−4.56004	−	54.0197i	−0.157149	−	1.86164i
$843$		0			0
$844$	−4.15029	−	24.4077i	−0.142859	−	0.840147i
$845$			11.5589i			0.397638i
$846$		0			0
$847$	−0.0159016			−0.000546384
$848$	8.61552	+	24.6012i	0.295858	+	0.844810i
$849$		0			0
$850$	13.8224	−	1.16681i	0.474104	−	0.0400213i
$851$			47.7217i			1.63588i
$852$		0			0
$853$		−	43.5342i		−	1.49058i	−0.666738	−	0.745292i	$-0.732310\pi$
$853$		−	43.5342i		−	1.49058i	0.666738	−	0.745292i	$-0.267690\pi$
$854$	−1.12097	−	13.2794i	−0.0383589	−	0.454411i
$855$		0			0
$856$	6.62649	+	25.6681i	0.226489	+	0.877317i
$857$	0.968943			0.0330985			0.0165492	−	0.999863i	$-0.494732\pi$
$857$	0.968943			0.0330985			0.0165492	+	0.999863i	$0.494732\pi$
$858$		0			0
$859$		−	11.9386i		−	0.407341i	−0.979040	−	0.203670i	$-0.934713\pi$
$859$		−	11.9386i		−	0.407341i	0.979040	−	0.203670i	$-0.0652871\pi$
$860$	48.0662	−	8.17320i	1.63904	−	0.278704i
$861$		0			0
$862$	3.13561	−	0.264691i	0.106799	−	0.00901542i
$863$	7.95989			0.270958			0.135479	−	0.990780i	$-0.456743\pi$
$863$	7.95989			0.270958			0.135479	+	0.990780i	$0.456743\pi$
$864$		0			0
$865$	−4.85455			−0.165059
$866$	−39.7726	+	3.35738i	−1.35153	+	0.114088i
$867$		0			0
$868$	−15.4494	+	2.62702i	−0.524386	+	0.0891670i
$869$			37.0467i			1.25672i
$870$		0			0
$871$	2.82775			0.0958148
$872$	−5.17170	−	20.0329i	−0.175136	−	0.678398i
$873$		0			0
$874$	−5.03157	−	59.6055i	−0.170195	−	2.01619i
$875$		−	6.89962i		−	0.233250i
$876$		0			0
$877$			26.3998i			0.891459i	0.895168	+	0.445730i	$0.147056\pi$
$877$			26.3998i			0.891459i	−0.895168	+	0.445730i	$0.852944\pi$
$878$	7.94699	−	0.670841i	0.268198	−	0.0226398i
$879$		0			0
$880$	43.3912	−	15.1959i	1.46272	−	0.512254i
$881$	−32.4550			−1.09344			−0.546718	−	0.837317i	$-0.684123\pi$
$881$	−32.4550			−1.09344			−0.546718	+	0.837317i	$0.684123\pi$
$882$		0			0
$883$			3.46140i			0.116486i	0.998302	+	0.0582428i	$0.0185497\pi$
$883$			3.46140i			0.116486i	−0.998302	+	0.0582428i	$0.981450\pi$
$884$	−1.46189	−	8.59732i	−0.0491688	−	0.289159i
$885$		0			0
$886$	−0.691940	−	8.19694i	−0.0232462	−	0.275381i
$887$	−16.9279			−0.568385			−0.284192	−	0.958767i	$-0.591725\pi$
$887$	−16.9279			−0.568385			−0.284192	+	0.958767i	$0.591725\pi$
$888$		0			0
$889$	3.37545			0.113209
$890$	1.99814	+	23.6706i	0.0669780	+	0.793442i
$891$		0			0
$892$	5.74100	−	0.976203i	0.192223	−	0.0326857i
$893$			54.2756i			1.81626i
$894$		0			0
$895$	−12.0114			−0.401497
$896$	−9.40414	+	6.28984i	−0.314170	+	0.210129i
$897$		0			0
$898$	−2.35225	+	0.198564i	−0.0784956	+	0.00662616i
$899$			77.3682i			2.58037i
$900$		0			0
$901$			9.14120i			0.304537i
$902$	4.56847	+	54.1195i	0.152113	+	1.80198i
$903$		0			0
$904$	29.8932	−	7.71724i	0.994232	−	0.256672i
$905$	−67.1794			−2.23312
$906$		0			0
$907$		−	29.1236i		−	0.967034i	−0.875335	−	0.483517i	$-0.839359\pi$
$907$		−	29.1236i		−	0.967034i	0.875335	−	0.483517i	$-0.160641\pi$
$908$	−3.80698	−	22.3886i	−0.126339	−	0.742993i
$909$		0			0
$910$	−15.1692	+	1.28050i	−0.502855	+	0.0424482i
$911$	−6.85198			−0.227016			−0.113508	−	0.993537i	$-0.536209\pi$
$911$	−6.85198			−0.227016			−0.113508	+	0.993537i	$0.536209\pi$
$912$		0			0
$913$	−1.22884			−0.0406685
$914$	23.1963	−	1.95810i	0.767265	−	0.0647682i
$915$		0			0
$916$	−5.85970	−	34.4606i	−0.193610	−	1.13861i
$917$		−	7.15460i		−	0.236266i
$918$		0			0
$919$	−37.3468			−1.23196			−0.615979	−	0.787763i	$-0.711239\pi$
$919$	−37.3468			−1.23196			−0.615979	+	0.787763i	$0.711239\pi$
$920$	21.5447	+	83.4546i	0.710307	+	2.75142i
$921$		0			0
$922$	−2.71121	−	32.1178i	−0.0892889	−	1.05774i
$923$		−	19.9657i		−	0.657179i
$924$		0			0
$925$			37.9209i			1.24683i
$926$	22.9933	−	1.94096i	0.755606	−	0.0637840i
$927$		0			0
$928$	22.8305	+	50.9766i	0.749447	+	1.67339i
$929$	38.8771			1.27552			0.637758	−	0.770236i	$-0.279862\pi$
$929$	38.8771			1.27552			0.637758	+	0.770236i	$0.279862\pi$
$930$		0			0
$931$		−	4.80674i		−	0.157534i
$932$	−3.92027	+	0.666604i	−0.128413	+	0.0218354i
$933$		0			0
$934$	−3.96214	−	46.9367i	−0.129645	−	1.53582i
$935$	16.1231			0.527281
$936$		0			0
$937$	−12.3583			−0.403727			−0.201863	−	0.979414i	$-0.564700\pi$
$937$	−12.3583			−0.403727			−0.201863	+	0.979414i	$0.564700\pi$
$938$	−0.108217	−	1.28197i	−0.00353340	−	0.0418577i
$939$		0			0
$940$	−13.1099	−	77.0988i	−0.427598	−	2.51468i
$941$		−	40.1798i		−	1.30982i	−0.755705	−	0.654912i	$-0.772706\pi$
$941$		−	40.1798i		−	1.30982i	0.755705	−	0.654912i	$-0.227294\pi$
$942$		0			0
$943$	−101.820			−3.31572
$944$	−5.15161	−	14.7102i	−0.167671	−	0.478776i
$945$		0			0
$946$	32.9253	−	2.77937i	1.07049	−	0.0903651i
$947$			14.7512i			0.479351i	0.970853	+	0.239676i	$0.0770411\pi$
$947$			14.7512i			0.479351i	−0.970853	+	0.239676i	$0.922959\pi$
$948$		0			0
$949$		−	4.85708i		−	0.157668i
$950$	−3.99821	−	47.3640i	−0.129719	−	1.53669i
$951$		0			0
$952$	−3.84167	+	0.991767i	−0.124509	+	0.0321434i
$953$	−36.2336			−1.17372			−0.586861	−	0.809687i	$-0.699637\pi$
$953$	−36.2336			−1.17372			−0.586861	+	0.809687i	$0.699637\pi$
$954$		0			0
$955$		−	81.2456i		−	2.62905i
$956$	42.0820	−	7.15564i	1.36103	−	0.231430i
$957$		0			0
$958$	40.2633	−	3.39880i	1.30085	−	0.109810i
$959$	−4.22854			−0.136547
$960$		0			0
$961$	30.3962			0.980523
$962$	23.7555	−	2.00531i	0.765908	−	0.0646537i
$963$		0			0
$964$	−26.3644	+	4.48303i	−0.849141	+	0.144389i
$965$		−	53.8060i		−	1.73208i
$966$		0			0
$967$	−32.6101			−1.04867			−0.524335	−	0.851512i	$-0.675686\pi$
$967$	−32.6101			−1.04867			−0.524335	+	0.851512i	$0.675686\pi$
$968$	0.0435486	−	0.0112425i	0.00139971	−	0.000361349i
$969$		0			0
$970$	−0.672644	−	7.96834i	−0.0215973	−	0.255848i
$971$		−	37.3897i		−	1.19989i	−0.800040	−	0.599947i	$-0.795188\pi$
$971$		−	37.3897i		−	1.19989i	0.800040	−	0.599947i	$-0.204812\pi$
$972$		0			0
$973$		−	3.31473i		−	0.106265i
$974$	−54.9798	+	4.64109i	−1.76167	+	0.148710i
$975$		0			0
$976$	12.4586	+	35.5749i	0.398789	+	1.13872i
$977$	−3.76353			−0.120406			−0.0602029	−	0.998186i	$-0.519175\pi$
$977$	−3.76353			−0.120406			−0.0602029	+	0.998186i	$0.519175\pi$
$978$		0			0
$979$			16.0988i			0.514521i
$980$	1.16104	+	6.82800i	0.0370879	+	0.218112i
$981$		0			0
$982$	−1.49646	−	17.7276i	−0.0477541	−	0.565710i
$983$	36.8112			1.17410			0.587048	−	0.809552i	$-0.300290\pi$
$983$	36.8112			1.17410			0.587048	+	0.809552i	$0.300290\pi$
$984$		0			0
$985$	51.3485			1.63610
$986$	1.64766	+	19.5187i	0.0524721	+	0.621601i
$987$		0			0
$988$	−29.4597	+	5.00935i	−0.937238	+	0.159369i
$989$			61.9454i			1.96975i
$990$		0			0
$991$	−53.0994			−1.68676			−0.843379	−	0.537319i	$-0.819437\pi$
$991$	−53.0994			−1.68676			−0.843379	+	0.537319i	$0.819437\pi$
$992$	40.4530	−	18.1173i	1.28438	−	0.575225i
$993$		0			0
$994$	−9.05150	+	0.764077i	−0.287096	+	0.0242351i
$995$			45.7445i			1.45020i
$996$		0			0
$997$		−	29.5497i		−	0.935847i	−0.883769	−	0.467923i	$-0.845002\pi$
$997$		−	29.5497i		−	0.935847i	0.883769	−	0.467923i	$-0.154998\pi$
$998$	2.05860	+	24.3868i	0.0651639	+	0.771952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.g.757.2	yes	24
3.2	odd	2	inner	1512.2.c.g.757.23	yes	24
4.3	odd	2		6048.2.c.f.3025.23		24
8.3	odd	2		6048.2.c.f.3025.2		24
8.5	even	2	inner	1512.2.c.g.757.1	✓	24
12.11	even	2		6048.2.c.f.3025.1		24
24.5	odd	2	inner	1512.2.c.g.757.24	yes	24
24.11	even	2		6048.2.c.f.3025.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.g.757.1	✓	24	8.5	even	2	inner
1512.2.c.g.757.2	yes	24	1.1	even	1	trivial
1512.2.c.g.757.23	yes	24	3.2	odd	2	inner
1512.2.c.g.757.24	yes	24	24.5	odd	2	inner
6048.2.c.f.3025.1		24	12.11	even	2
6048.2.c.f.3025.2		24	8.3	odd	2
6048.2.c.f.3025.23		24	4.3	odd	2
6048.2.c.f.3025.24		24	24.11	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40920 + 0.118957i) q^{2} +(1.97170 - 0.335269i) q^{4} +3.46300i q^{5} +1.00000 q^{7} +(-2.73864 + 0.707009i) q^{8} +O(q^{10})\)	\(q+(-1.40920 + 0.118957i) q^{2} +(1.97170 - 0.335269i) q^{4} +3.46300i q^{5} +1.00000 q^{7} +(-2.73864 + 0.707009i) q^{8} +(-0.411948 - 4.88007i) q^{10} -3.31902i q^{11} -3.10840i q^{13} +(-1.40920 + 0.118957i) q^{14} +(3.77519 - 1.32210i) q^{16} +1.40277 q^{17} -4.80674i q^{19} +(1.16104 + 6.82800i) q^{20} +(0.394821 + 4.67717i) q^{22} -8.79960 q^{23} -6.99238 q^{25} +(0.369766 + 4.38037i) q^{26} +(1.97170 - 0.335269i) q^{28} -9.87397i q^{29} -7.83557 q^{31} +(-5.16273 + 2.31219i) q^{32} +(-1.97678 + 0.166869i) q^{34} +3.46300i q^{35} -5.42317i q^{37} +(0.571795 + 6.77366i) q^{38} +(-2.44837 - 9.48391i) q^{40} +11.5710 q^{41} -7.03957i q^{43} +(-1.11276 - 6.54411i) q^{44} +(12.4004 - 1.04677i) q^{46} -11.2916 q^{47} +1.00000 q^{49} +(9.85368 - 0.831793i) q^{50} +(-1.04215 - 6.12884i) q^{52} +6.51655i q^{53} +11.4938 q^{55} +(-2.73864 + 0.707009i) q^{56} +(1.17458 + 13.9144i) q^{58} -3.89654i q^{59} +9.42334i q^{61} +(11.0419 - 0.932096i) q^{62} +(7.00028 - 3.87248i) q^{64} +10.7644 q^{65} +0.909712i q^{67} +(2.76583 - 0.470304i) q^{68} +(-0.411948 - 4.88007i) q^{70} +6.42314 q^{71} +1.56257 q^{73} +(0.645124 + 7.64234i) q^{74} +(-1.61155 - 9.47744i) q^{76} -3.31902i q^{77} -11.1619 q^{79} +(4.57843 + 13.0735i) q^{80} +(-16.3059 + 1.37645i) q^{82} -0.370241i q^{83} +4.85778i q^{85} +(0.837406 + 9.92018i) q^{86} +(2.34658 + 9.08960i) q^{88} -4.85047 q^{89} -3.10840i q^{91} +(-17.3502 + 2.95023i) q^{92} +(15.9121 - 1.34321i) q^{94} +16.6457 q^{95} +1.63283 q^{97} +(-1.40920 + 0.118957i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 24 q^{7}+O(q^{10}) \) 24 * q + 6 * q^4 + 24 * q^7	\( 24 q + 6 q^{4} + 24 q^{7} - 16 q^{10} + 2 q^{16} + 16 q^{22} - 24 q^{25} + 6 q^{28} + 8 q^{31} + 22 q^{34} + 26 q^{46} + 24 q^{49} - 6 q^{52} + 16 q^{55} - 58 q^{58} + 6 q^{64} - 16 q^{70} + 60 q^{76} + 8 q^{79} - 28 q^{82} + 12 q^{88} + 36 q^{94}+O(q^{100}) \) 24 * q + 6 * q^4 + 24 * q^7 - 16 * q^10 + 2 * q^16 + 16 * q^22 - 24 * q^25 + 6 * q^28 + 8 * q^31 + 22 * q^34 + 26 * q^46 + 24 * q^49 - 6 * q^52 + 16 * q^55 - 58 * q^58 + 6 * q^64 - 16 * q^70 + 60 * q^76 + 8 * q^79 - 28 * q^82 + 12 * q^88 + 36 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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