LMFDB - Embedded newform 960.3.i.a.929.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(929,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("960.929");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.i (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:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.21
Character	$\chi$	$=$	960.929
Dual form			960.3.i.a.929.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44379 + 2.62973i) q^{3} +(-2.67751 - 4.22267i) q^{5} -1.30019i q^{7} +(-4.83095 + 7.59354i) q^{9} +O(q^{10})$	\(q+(1.44379 + 2.62973i) q^{3} +(-2.67751 - 4.22267i) q^{5} -1.30019i q^{7} +(-4.83095 + 7.59354i) q^{9} -9.69683 q^{11} +15.3824 q^{13} +(7.23873 - 13.1378i) q^{15} +9.62982 q^{17} -9.66190i q^{19} +(3.41913 - 1.87719i) q^{21} -16.1769 q^{23} +(-10.6619 + 22.6125i) q^{25} +(-26.9438 - 1.74063i) q^{27} +47.2899 q^{29} +40.6635 q^{31} +(-14.0002 - 25.5000i) q^{33} +(-5.49025 + 3.48126i) q^{35} +43.5469 q^{37} +(22.2090 + 40.4516i) q^{39} +4.20658i q^{41} +53.8877 q^{43} +(44.9999 + 0.0677491i) q^{45} -48.5306 q^{47} +47.3095 q^{49} +(13.9034 + 25.3238i) q^{51} -9.87301i q^{53} +(25.9633 + 40.9465i) q^{55} +(25.4082 - 13.9497i) q^{57} +70.4452 q^{59} -92.5902i q^{61} +(9.87301 + 6.28113i) q^{63} +(-41.1866 - 64.9549i) q^{65} -25.9882 q^{67} +(-23.3559 - 42.5407i) q^{69} +41.0296i q^{71} -17.3255i q^{73} +(-74.8582 + 4.60969i) q^{75} +12.6077i q^{77} +92.5902 q^{79} +(-34.3238 - 73.3681i) q^{81} -54.2976i q^{83} +(-25.7839 - 40.6635i) q^{85} +(68.2766 + 124.360i) q^{87} +102.103i q^{89} -20.0000i q^{91} +(58.7095 + 106.934i) q^{93} +(-40.7990 + 25.8698i) q^{95} +97.2013i q^{97} +(46.8449 - 73.6333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{9}+O(q^{10}) $ 32 * q + 32 * q^9	$ 32 q + 32 q^{9} + 32 q^{25} - 352 q^{49} - 352 q^{81}+O(q^{100}) $ 32 * q + 32 * q^9 + 32 * q^25 - 352 * q^49 - 352 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	1.44379	+	2.62973i	0.481263	+	0.876576i
$3$	1.44379	+	2.62973i	0.481263	+	0.876576i
$4$		0			0
$5$	−2.67751	−	4.22267i	−0.535502	−	0.844534i
$5$	−2.67751	−	4.22267i	−0.535502	−	0.844534i
$6$		0			0
$7$		−	1.30019i		−	0.185741i	−0.995678	−	0.0928704i	$-0.970396\pi$
$7$		−	1.30019i		−	0.185741i	0.995678	−	0.0928704i	$-0.0296042\pi$
$8$		0			0
$9$	−4.83095	+	7.59354i	−0.536772	+	0.843727i
$10$		0			0
$11$	−9.69683			−0.881530			−0.440765	−	0.897622i	$-0.645293\pi$
$11$	−9.69683			−0.881530			−0.440765	+	0.897622i	$0.645293\pi$
$12$		0			0
$13$	15.3824			1.18326			0.591632	−	0.806208i	$-0.298484\pi$
$13$	15.3824			1.18326			0.591632	+	0.806208i	$0.298484\pi$
$14$		0			0
$15$	7.23873	−	13.1378i	0.482582	−	0.875851i
$16$		0			0
$17$	9.62982			0.566460			0.283230	−	0.959052i	$-0.408594\pi$
$17$	9.62982			0.566460			0.283230	+	0.959052i	$0.408594\pi$
$18$		0			0
$19$		−	9.66190i		−	0.508521i	−0.967136	−	0.254261i	$-0.918168\pi$
$19$		−	9.66190i		−	0.508521i	0.967136	−	0.254261i	$-0.0818321\pi$
$20$		0			0
$21$	3.41913	−	1.87719i	0.162816	−	0.0893901i
$22$		0			0
$23$	−16.1769			−0.703341			−0.351671	−	0.936124i	$-0.614386\pi$
$23$	−16.1769			−0.703341			−0.351671	+	0.936124i	$0.614386\pi$
$24$		0			0
$25$	−10.6619	+	22.6125i	−0.426476	+	0.904499i
$26$		0			0
$27$	−26.9438	−	1.74063i	−0.997920	−	0.0644677i
$28$		0			0
$29$	47.2899			1.63069			0.815343	−	0.578978i	$-0.196548\pi$
$29$	47.2899			1.63069			0.815343	+	0.578978i	$0.196548\pi$
$30$		0			0
$31$	40.6635			1.31173			0.655864	−	0.754879i	$-0.272305\pi$
$31$	40.6635			1.31173			0.655864	+	0.754879i	$0.272305\pi$
$32$		0			0
$33$	−14.0002	−	25.5000i	−0.424248	−	0.772729i
$34$		0			0
$35$	−5.49025	+	3.48126i	−0.156864	+	0.0994644i
$36$		0			0
$37$	43.5469			1.17694			0.588472	−	0.808518i	$-0.299730\pi$
$37$	43.5469			1.17694			0.588472	+	0.808518i	$0.299730\pi$
$38$		0			0
$39$	22.2090	+	40.4516i	0.569461	+	1.03722i
$40$		0			0
$41$			4.20658i			0.102600i	0.998683	+	0.0512998i	$0.0163364\pi$
$41$			4.20658i			0.102600i	−0.998683	+	0.0512998i	$0.983664\pi$
$42$		0			0
$43$	53.8877			1.25320			0.626601	−	0.779340i	$-0.284446\pi$
$43$	53.8877			1.25320			0.626601	+	0.779340i	$0.284446\pi$
$44$		0			0
$45$	44.9999	+	0.0677491i	0.999999	+	0.00150554i
$46$		0			0
$47$	−48.5306			−1.03256			−0.516282	−	0.856418i	$-0.672685\pi$
$47$	−48.5306			−1.03256			−0.516282	+	0.856418i	$0.672685\pi$
$48$		0			0
$49$	47.3095			0.965500
$50$		0			0
$51$	13.9034	+	25.3238i	0.272616	+	0.496545i
$52$		0			0
$53$		−	9.87301i		−	0.186283i	−0.995653	−	0.0931416i	$-0.970309\pi$
$53$		−	9.87301i		−	0.186283i	0.995653	−	0.0931416i	$-0.0296909\pi$
$54$		0			0
$55$	25.9633	+	40.9465i	0.472061	+	0.744483i
$56$		0			0
$57$	25.4082	−	13.9497i	0.445758	−	0.244732i
$58$		0			0
$59$	70.4452			1.19399			0.596993	−	0.802246i	$-0.296362\pi$
$59$	70.4452			1.19399			0.596993	+	0.802246i	$0.296362\pi$
$60$		0			0
$61$		−	92.5902i		−	1.51787i	−0.651165	−	0.758936i	$-0.725719\pi$
$61$		−	92.5902i		−	1.51787i	0.651165	−	0.758936i	$-0.274281\pi$
$62$		0			0
$63$	9.87301	+	6.28113i	0.156714	+	0.0997005i
$64$		0			0
$65$	−41.1866	−	64.9549i	−0.633639	−	0.999307i
$66$		0			0
$67$	−25.9882			−0.387883			−0.193942	−	0.981013i	$-0.562127\pi$
$67$	−25.9882			−0.387883			−0.193942	+	0.981013i	$0.562127\pi$
$68$		0			0
$69$	−23.3559	−	42.5407i	−0.338492	−	0.616532i
$70$		0			0
$71$			41.0296i			0.577882i	0.957347	+	0.288941i	$0.0933031\pi$
$71$			41.0296i			0.577882i	−0.957347	+	0.288941i	$0.906697\pi$
$72$		0			0
$73$		−	17.3255i		−	0.237335i	−0.992934	−	0.118668i	$-0.962138\pi$
$73$		−	17.3255i		−	0.237335i	0.992934	−	0.118668i	$-0.0378623\pi$
$74$		0			0
$75$	−74.8582	+	4.60969i	−0.998109	+	0.0614626i
$76$		0			0
$77$			12.6077i			0.163736i
$78$		0			0
$79$	92.5902			1.17203			0.586014	−	0.810301i	$-0.300696\pi$
$79$	92.5902			1.17203			0.586014	+	0.810301i	$0.300696\pi$
$80$		0			0
$81$	−34.3238	−	73.3681i	−0.423751	−	0.905779i
$82$		0			0
$83$		−	54.2976i		−	0.654188i	−0.944992	−	0.327094i	$-0.893931\pi$
$83$		−	54.2976i		−	0.654188i	0.944992	−	0.327094i	$-0.106069\pi$
$84$		0			0
$85$	−25.7839	−	40.6635i	−0.303340	−	0.478395i
$86$		0			0
$87$	68.2766	+	124.360i	0.784788	+	1.42942i
$88$		0			0
$89$			102.103i			1.14723i	0.819127	+	0.573613i	$0.194458\pi$
$89$			102.103i			1.14723i	−0.819127	+	0.573613i	$0.805542\pi$
$90$		0			0
$91$		−	20.0000i		−	0.219780i
$92$		0			0
$93$	58.7095	+	106.934i	0.631285	+	1.14983i
$94$		0			0
$95$	−40.7990	+	25.8698i	−0.429464	+	0.272314i
$96$		0			0
$97$			97.2013i			1.00208i	0.865425	+	0.501038i	$0.167048\pi$
$97$			97.2013i			1.00208i	−0.865425	+	0.501038i	$0.832952\pi$
$98$		0			0
$99$	46.8449	−	73.6333i	0.473181	−	0.743771i
$100$		0			0
$101$	100.840			0.998416			0.499208	−	0.866482i	$-0.333624\pi$
$101$	100.840			0.998416			0.499208	+	0.866482i	$0.333624\pi$
$102$		0			0
$103$			162.926i			1.58180i	0.611944	+	0.790901i	$0.290388\pi$
$103$			162.926i			1.58180i	−0.611944	+	0.790901i	$0.709612\pi$
$104$		0			0
$105$	−17.0815	−	9.41169i	−0.162681	−	0.0896351i
$106$		0			0
$107$			129.708i			1.21223i	0.795378	+	0.606113i	$0.207272\pi$
$107$			129.708i			1.21223i	−0.795378	+	0.606113i	$0.792728\pi$
$108$		0			0
$109$		−	173.917i		−	1.59557i	−0.602941	−	0.797786i	$-0.706005\pi$
$109$		−	173.917i		−	1.59557i	0.602941	−	0.797786i	$-0.293995\pi$
$110$		0			0
$111$	62.8725	+	114.517i	0.566419	+	1.03168i
$112$		0			0
$113$	−2.66730			−0.0236045			−0.0118022	−	0.999930i	$-0.503757\pi$
$113$	−2.66730			−0.0236045			−0.0118022	+	0.999930i	$0.503757\pi$
$114$		0			0
$115$	43.3136	+	68.3095i	0.376640	+	0.593996i
$116$		0			0
$117$	−74.3118	+	116.807i	−0.635143	+	0.998351i
$118$		0			0
$119$		−	12.5205i		−	0.105215i
$120$		0			0
$121$	−26.9714			−0.222904
$122$		0			0
$123$	−11.0622	+	6.07341i	−0.0899363	+	0.0493773i
$124$		0			0
$125$	124.032	−	15.5234i	0.992259	−	0.124187i
$126$		0			0
$127$		−	14.3020i		−	0.112614i	−0.998413	−	0.0563072i	$-0.982067\pi$
$127$		−	14.3020i		−	0.112614i	0.998413	−	0.0563072i	$-0.0179326\pi$
$128$		0			0
$129$	77.8024	+	141.710i	0.603119	+	1.09853i
$130$		0			0
$131$	−189.375			−1.44561			−0.722804	−	0.691054i	$-0.757147\pi$
$131$	−189.375			−1.44561			−0.722804	+	0.691054i	$0.757147\pi$
$132$		0			0
$133$	−12.5623			−0.0944531
$134$		0			0
$135$	64.7922	+	118.435i	0.479942	+	0.877300i
$136$		0			0
$137$	134.229			0.979773			0.489887	−	0.871786i	$-0.337038\pi$
$137$	134.229			0.979773			0.489887	+	0.871786i	$0.337038\pi$
$138$		0			0
$139$		−	86.2809i		−	0.620726i	−0.950618	−	0.310363i	$-0.899549\pi$
$139$		−	86.2809i		−	0.620726i	0.950618	−	0.310363i	$-0.100451\pi$
$140$		0			0
$141$	−70.0678	−	127.622i	−0.496935	−	0.905122i
$142$		0			0
$143$	−149.161			−1.04308
$144$		0			0
$145$	−126.619	−	199.690i	−0.873235	−	1.37717i
$146$		0			0
$147$	68.3049	+	124.411i	0.464659	+	0.846335i
$148$		0			0
$149$	−14.2545			−0.0956680			−0.0478340	−	0.998855i	$-0.515232\pi$
$149$	−14.2545			−0.0956680			−0.0478340	+	0.998855i	$0.515232\pi$
$150$		0			0
$151$	11.2631			0.0745904			0.0372952	−	0.999304i	$-0.488126\pi$
$151$	11.2631			0.0745904			0.0372952	+	0.999304i	$0.488126\pi$
$152$		0			0
$153$	−46.5212	+	73.1244i	−0.304060	+	0.477937i
$154$		0			0
$155$	−108.877	−	171.709i	−0.702432	−	1.10780i
$156$		0			0
$157$	145.803			0.928684			0.464342	−	0.885656i	$-0.346291\pi$
$157$	145.803			0.928684			0.464342	+	0.885656i	$0.346291\pi$
$158$		0			0
$159$	25.9633	−	14.2545i	0.163291	−	0.0896512i
$160$		0			0
$161$			21.0329i			0.130639i
$162$		0			0
$163$	−200.137			−1.22783			−0.613916	−	0.789372i	$-0.710407\pi$
$163$	−200.137			−1.22783			−0.613916	+	0.789372i	$0.710407\pi$
$164$		0			0
$165$	−70.1927	+	127.395i	−0.425411	+	0.772089i
$166$		0			0
$167$	−152.730			−0.914551			−0.457275	−	0.889325i	$-0.651175\pi$
$167$	−152.730			−0.914551			−0.457275	+	0.889325i	$0.651175\pi$
$168$		0			0
$169$	67.6190			0.400113
$170$		0			0
$171$	73.3681	+	46.6762i	0.429053	+	0.272960i
$172$		0			0
$173$		−	146.426i		−	0.846394i	−0.906038	−	0.423197i	$-0.860908\pi$
$173$		−	146.426i		−	0.846394i	0.906038	−	0.423197i	$-0.139092\pi$
$174$		0			0
$175$	29.4004	+	13.8624i	0.168002	+	0.0792140i
$176$		0			0
$177$	101.708	+	185.252i	0.574621	+	1.04662i
$178$		0			0
$179$	261.103			1.45868			0.729339	−	0.684152i	$-0.239828\pi$
$179$	261.103			1.45868			0.729339	+	0.684152i	$0.239828\pi$
$180$		0			0
$181$			185.180i			1.02310i	0.859255	+	0.511548i	$0.170928\pi$
$181$			185.180i			1.02310i	−0.859255	+	0.511548i	$0.829072\pi$
$182$		0			0
$183$	243.487	−	133.681i	1.33053	−	0.730496i
$184$		0			0
$185$	−116.597	−	183.884i	−0.630255	−	0.993969i
$186$		0			0
$187$	−93.3787			−0.499351
$188$		0			0
$189$	−2.26314	+	35.0320i	−0.0119743	+	0.185354i
$190$		0			0
$191$		−	242.710i		−	1.27073i	−0.772211	−	0.635366i	$-0.780849\pi$
$191$		−	242.710i		−	1.27073i	0.772211	−	0.635366i	$-0.219151\pi$
$192$		0			0
$193$		−	17.3255i		−	0.0897692i	−0.998992	−	0.0448846i	$-0.985708\pi$
$193$		−	17.3255i		−	0.0897692i	0.998992	−	0.0448846i	$-0.0142920\pi$
$194$		0			0
$195$	111.349	−	202.091i	0.571022	−	1.03636i
$196$		0			0
$197$		−	353.156i		−	1.79267i	−0.443377	−	0.896335i	$-0.646220\pi$
$197$		−	353.156i		−	1.79267i	0.443377	−	0.896335i	$-0.353780\pi$
$198$		0			0
$199$	−63.1898			−0.317537			−0.158768	−	0.987316i	$-0.550752\pi$
$199$	−63.1898			−0.317537			−0.158768	+	0.987316i	$0.550752\pi$
$200$		0			0
$201$	−37.5214	−	68.3419i	−0.186674	−	0.340009i
$202$		0			0
$203$		−	61.4856i		−	0.302885i
$204$		0			0
$205$	17.7630	−	11.2631i	0.0866488	−	0.0549422i
$206$		0			0
$207$	78.1496	−	122.840i	0.377534	−	0.593428i
$208$		0			0
$209$			93.6899i			0.448277i
$210$		0			0
$211$			122.900i			0.582464i	0.956652	+	0.291232i	$0.0940652\pi$
$211$			122.900i			0.582464i	−0.956652	+	0.291232i	$0.905935\pi$
$212$		0			0
$213$	−107.897	+	59.2381i	−0.506558	+	0.278113i
$214$		0			0
$215$	−144.285	−	227.550i	−0.671091	−	1.05837i
$216$		0			0
$217$		−	52.8701i		−	0.243641i
$218$		0			0
$219$	45.5613	−	25.0143i	0.208042	−	0.114220i
$220$		0			0
$221$	148.130			0.670271
$222$		0			0
$223$		−	272.544i		−	1.22217i	−0.791566	−	0.611084i	$-0.790734\pi$
$223$		−	272.544i		−	1.22217i	0.791566	−	0.611084i	$-0.209266\pi$
$224$		0			0
$225$	−120.202	−	190.201i	−0.534229	−	0.845339i
$226$		0			0
$227$			305.124i			1.34416i	0.740480	+	0.672079i	$0.234598\pi$
$227$			305.124i			1.34416i	−0.740480	+	0.672079i	$0.765402\pi$
$228$		0			0
$229$			429.162i			1.87407i	0.349237	+	0.937034i	$0.386441\pi$
$229$			429.162i			1.87407i	−0.349237	+	0.937034i	$0.613559\pi$
$230$		0			0
$231$	−33.1548	+	18.2028i	−0.143527	+	0.0788001i
$232$		0			0
$233$	−281.343			−1.20748			−0.603741	−	0.797180i	$-0.706324\pi$
$233$	−281.343			−1.20748			−0.603741	+	0.797180i	$0.706324\pi$
$234$		0			0
$235$	129.941	+	204.929i	0.552940	+	0.872036i
$236$		0			0
$237$	133.681	+	243.487i	0.564054	+	1.02737i
$238$		0			0
$239$		−	94.5798i		−	0.395731i	−0.980229	−	0.197866i	$-0.936599\pi$
$239$		−	94.5798i		−	0.395731i	0.980229	−	0.197866i	$-0.0634010\pi$
$240$		0			0
$241$	129.662			0.538016			0.269008	−	0.963138i	$-0.413304\pi$
$241$	129.662			0.538016			0.269008	+	0.963138i	$0.413304\pi$
$242$		0			0
$243$	143.382	−	196.190i	0.590049	−	0.807367i
$244$		0			0
$245$	−126.672	−	199.773i	−0.517027	−	0.815398i
$246$		0			0
$247$		−	148.624i		−	0.601715i
$248$		0			0
$249$	142.788	−	78.3943i	0.573446	−	0.314836i
$250$		0			0
$251$	172.548			0.687443			0.343722	−	0.939072i	$-0.388312\pi$
$251$	172.548			0.687443			0.343722	+	0.939072i	$0.388312\pi$
$252$		0			0
$253$	156.864			0.620017
$254$		0			0
$255$	69.7076	−	126.514i	0.273363	−	0.496134i
$256$		0			0
$257$	466.977			1.81703			0.908516	−	0.417850i	$-0.137216\pi$
$257$	466.977			1.81703			0.908516	+	0.417850i	$0.137216\pi$
$258$		0			0
$259$		−	56.6190i		−	0.218606i
$260$		0			0
$261$	−228.455	+	359.098i	−0.875307	+	1.37585i
$262$		0			0
$263$	−276.675			−1.05200			−0.525999	−	0.850485i	$-0.676308\pi$
$263$	−276.675			−1.05200			−0.525999	+	0.850485i	$0.676308\pi$
$264$		0			0
$265$	−41.6905	+	26.4351i	−0.157323	+	0.0997550i
$266$		0			0
$267$	−268.503	+	147.415i	−1.00563	+	0.552117i
$268$		0			0
$269$	282.005			1.04835			0.524173	−	0.851612i	$-0.324374\pi$
$269$	282.005			1.04835			0.524173	+	0.851612i	$0.324374\pi$
$270$		0			0
$271$	−173.917			−0.641761			−0.320881	−	0.947120i	$-0.603979\pi$
$271$	−173.917			−0.641761			−0.320881	+	0.947120i	$0.603979\pi$
$272$		0			0
$273$	52.5946	−	28.8758i	0.192654	−	0.105772i
$274$		0			0
$275$	103.387	−	219.269i	0.375952	−	0.797343i
$276$		0			0
$277$	−514.542			−1.85755			−0.928776	−	0.370641i	$-0.879138\pi$
$277$	−514.542			−1.85755			−0.928776	+	0.370641i	$0.879138\pi$
$278$		0			0
$279$	−196.444	+	308.780i	−0.704099	+	1.10674i
$280$		0			0
$281$		−	139.962i		−	0.498086i	−0.968492	−	0.249043i	$-0.919884\pi$
$281$		−	139.962i		−	0.498086i	0.968492	−	0.249043i	$-0.0801161\pi$
$282$		0			0
$283$	338.740			1.19696			0.598481	−	0.801137i	$-0.295771\pi$
$283$	338.740			1.19696			0.598481	+	0.801137i	$0.295771\pi$
$284$		0			0
$285$	−126.936	−	69.9399i	−0.445389	−	0.245403i
$286$		0			0
$287$	5.46933			0.0190569
$288$		0			0
$289$	−196.267			−0.679123
$290$		0			0
$291$	−255.613	+	140.338i	−0.878396	+	0.482261i
$292$		0			0
$293$		−	346.018i		−	1.18095i	−0.807057	−	0.590474i	$-0.798941\pi$
$293$		−	346.018i		−	1.18095i	0.807057	−	0.590474i	$-0.201059\pi$
$294$		0			0
$295$	−188.618	−	297.467i	−0.639381	−	1.00836i
$296$		0			0
$297$	261.270	+	16.8786i	0.879697	+	0.0568302i
$298$		0			0
$299$	−248.839			−0.832238
$300$		0			0
$301$		−	70.0639i		−	0.232771i
$302$		0			0
$303$	145.592	+	265.182i	0.480500	+	0.875188i
$304$		0			0
$305$	−390.978	+	247.911i	−1.28190	+	0.812823i
$306$		0			0
$307$	−511.995			−1.66774			−0.833868	−	0.551964i	$-0.813878\pi$
$307$	−511.995			−1.66774			−0.833868	+	0.551964i	$0.813878\pi$
$308$		0			0
$309$	−428.450	+	235.230i	−1.38657	+	0.761262i
$310$		0			0
$311$		−	296.260i		−	0.952604i	−0.879282	−	0.476302i	$-0.841977\pi$
$311$		−	296.260i		−	0.952604i	0.879282	−	0.476302i	$-0.158023\pi$
$312$		0			0
$313$		−	162.681i		−	0.519746i	−0.965643	−	0.259873i	$-0.916319\pi$
$313$		−	162.681i		−	0.519746i	0.965643	−	0.259873i	$-0.0836807\pi$
$314$		0			0
$315$	0.0880864	−	58.5083i	0.000279639	−	0.185741i
$316$		0			0
$317$		−	178.780i		−	0.563974i	−0.959418	−	0.281987i	$-0.909006\pi$
$317$		−	178.780i		−	0.563974i	0.959418	−	0.281987i	$-0.0909936\pi$
$318$		0			0
$319$	−458.562			−1.43750
$320$		0			0
$321$	−341.098	+	187.271i	−1.06261	+	0.583400i
$322$		0			0
$323$		−	93.0424i		−	0.288057i
$324$		0			0
$325$	−164.006	+	347.835i	−0.504634	+	1.07026i
$326$		0			0
$327$	457.355	−	251.100i	1.39864	−	0.767889i
$328$		0			0
$329$			63.0987i			0.191789i
$330$		0			0
$331$		−	636.138i		−	1.92187i	−0.276779	−	0.960934i	$-0.589267\pi$
$331$		−	636.138i		−	1.92187i	0.276779	−	0.960934i	$-0.410733\pi$
$332$		0			0
$333$	−210.373	+	330.675i	−0.631751	+	0.993019i
$334$		0			0
$335$	69.5836	+	109.740i	0.207712	+	0.327581i
$336$		0			0
$337$			503.332i			1.49357i	0.665067	+	0.746783i	$0.268403\pi$
$337$			503.332i			1.49357i	−0.665067	+	0.746783i	$0.731597\pi$
$338$		0			0
$339$	−3.85102	−	7.01429i	−0.0113599	−	0.0206911i
$340$		0			0
$341$	−394.308			−1.15633
$342$		0			0
$343$		−	125.220i		−	0.365073i
$344$		0			0
$345$	−117.100	+	212.528i	−0.339420	+	0.616022i
$346$		0			0
$347$			508.389i			1.46510i	0.680714	+	0.732549i	$0.261670\pi$
$347$			508.389i			1.46510i	−0.680714	+	0.732549i	$0.738330\pi$
$348$		0			0
$349$		−	81.3271i		−	0.233029i	−0.993189	−	0.116514i	$-0.962828\pi$
$349$		−	81.3271i		−	0.233029i	0.993189	−	0.116514i	$-0.0371721\pi$
$350$		0			0
$351$	−414.462	−	26.7751i	−1.18080	−	0.0762823i
$352$		0			0
$353$	−69.0366			−0.195571			−0.0977856	−	0.995208i	$-0.531176\pi$
$353$	−69.0366			−0.195571			−0.0977856	+	0.995208i	$0.531176\pi$
$354$		0			0
$355$	173.255	−	109.857i	0.488041	−	0.309457i
$356$		0			0
$357$	32.9256	−	18.0770i	0.0922287	−	0.0506359i
$358$		0			0
$359$		−	646.070i		−	1.79964i	−0.436264	−	0.899819i	$-0.643699\pi$
$359$		−	646.070i		−	1.79964i	0.436264	−	0.899819i	$-0.356301\pi$
$360$		0			0
$361$	267.648			0.741406
$362$		0			0
$363$	−38.9410	−	70.9275i	−0.107276	−	0.195393i
$364$		0			0
$365$	−73.1597	+	46.3890i	−0.200438	+	0.127093i
$366$		0			0
$367$			337.553i			0.919762i	0.887980	+	0.459881i	$0.152108\pi$
$367$			337.553i			0.919762i	−0.887980	+	0.459881i	$0.847892\pi$
$368$		0			0
$369$	−31.9428	−	20.3218i	−0.0865660	−	0.0550726i
$370$		0			0
$371$	−12.8367			−0.0346004
$372$		0			0
$373$	−561.349			−1.50496			−0.752478	−	0.658617i	$-0.771142\pi$
$373$	−561.349			−1.50496			−0.752478	+	0.658617i	$0.771142\pi$
$374$		0			0
$375$	219.899	+	303.759i	0.586396	+	0.810024i
$376$		0			0
$377$	727.433			1.92953
$378$		0			0
$379$			439.519i			1.15968i	0.814730	+	0.579840i	$0.196885\pi$
$379$			439.519i			1.15968i	−0.814730	+	0.579840i	$0.803115\pi$
$380$		0			0
$381$	37.6105	−	20.6491i	0.0987152	−	0.0541971i
$382$		0			0
$383$	456.521			1.19196			0.595980	−	0.802999i	$-0.296764\pi$
$383$	456.521			1.19196			0.595980	+	0.802999i	$0.296764\pi$
$384$		0			0
$385$	53.2381	−	33.7572i	0.138281	−	0.0876809i
$386$		0			0
$387$	−260.329	+	409.198i	−0.672684	+	1.05736i
$388$		0			0
$389$	−190.894			−0.490729			−0.245364	−	0.969431i	$-0.578908\pi$
$389$	−190.894			−0.490729			−0.245364	+	0.969431i	$0.578908\pi$
$390$		0			0
$391$	−155.780			−0.398415
$392$		0			0
$393$	−273.417	−	498.004i	−0.695717	−	1.26719i
$394$		0			0
$395$	−247.911	−	390.978i	−0.627623	−	0.989818i
$396$		0			0
$397$	−247.218			−0.622715			−0.311357	−	0.950293i	$-0.600784\pi$
$397$	−247.218			−0.622715			−0.311357	+	0.950293i	$0.600784\pi$
$398$		0			0
$399$	−18.1372	−	33.0353i	−0.0454568	−	0.0827954i
$400$		0			0
$401$		−	14.2590i		−	0.0355585i	−0.999842	−	0.0177793i	$-0.994340\pi$
$401$		−	14.2590i		−	0.0355585i	0.999842	−	0.0177793i	$-0.00565961\pi$
$402$		0			0
$403$	625.504			1.55212
$404$		0			0
$405$	−217.907	+	341.382i	−0.538042	+	0.842918i
$406$		0			0
$407$	−422.267			−1.03751
$408$		0			0
$409$	−166.957			−0.408208			−0.204104	−	0.978949i	$-0.565428\pi$
$409$	−166.957			−0.408208			−0.204104	+	0.978949i	$0.565428\pi$
$410$		0			0
$411$	193.798	+	352.986i	0.471528	+	0.858846i
$412$		0			0
$413$		−	91.5918i		−	0.221772i
$414$		0			0
$415$	−229.281	+	145.382i	−0.552485	+	0.350319i
$416$		0			0
$417$	226.896	−	124.571i	0.544114	−	0.298732i
$418$		0			0
$419$	−369.052			−0.880793			−0.440396	−	0.897803i	$-0.645162\pi$
$419$	−369.052			−0.880793			−0.440396	+	0.897803i	$0.645162\pi$
$420$		0			0
$421$			417.899i			0.992633i	0.868142	+	0.496317i	$0.165314\pi$
$421$			417.899i			0.992633i	−0.868142	+	0.496317i	$0.834686\pi$
$422$		0			0
$423$	234.449	−	368.519i	0.554252	−	0.871203i
$424$		0			0
$425$	−102.672	+	217.754i	−0.241582	+	0.512362i
$426$		0			0
$427$	−120.384			−0.281931
$428$		0			0
$429$	−215.357	−	392.253i	−0.501997	−	0.914342i
$430$		0			0
$431$			419.349i			0.972967i	0.873690	+	0.486483i	$0.161721\pi$
$431$			419.349i			0.972967i	−0.873690	+	0.486483i	$0.838279\pi$
$432$		0			0
$433$		−	208.799i		−	0.482215i	−0.970498	−	0.241108i	$-0.922489\pi$
$433$		−	208.799i		−	0.482215i	0.970498	−	0.241108i	$-0.0775107\pi$
$434$		0			0
$435$	342.319	−	621.283i	0.786939	−	1.42824i
$436$		0			0
$437$			156.299i			0.357664i
$438$		0			0
$439$	121.991			0.277883			0.138941	−	0.990301i	$-0.455630\pi$
$439$	121.991			0.277883			0.138941	+	0.990301i	$0.455630\pi$
$440$		0			0
$441$	−228.550	+	359.247i	−0.518254	+	0.814619i
$442$		0			0
$443$		−	413.268i		−	0.932885i	−0.884551	−	0.466443i	$-0.845535\pi$
$443$		−	413.268i		−	0.932885i	0.884551	−	0.466443i	$-0.154465\pi$
$444$		0			0
$445$	431.148	−	273.382i	0.968871	−	0.614341i
$446$		0			0
$447$	−20.5805	−	37.4856i	−0.0460415	−	0.0838603i
$448$		0			0
$449$		−	836.712i		−	1.86350i	−0.363099	−	0.931751i	$-0.618281\pi$
$449$		−	836.712i		−	1.86350i	0.363099	−	0.931751i	$-0.381719\pi$
$450$		0			0
$451$		−	40.7905i		−	0.0904446i
$452$		0			0
$453$	16.2616	+	29.6190i	0.0358976	+	0.0653842i
$454$		0			0
$455$	−84.4534	+	53.5502i	−0.185612	+	0.117693i
$456$		0			0
$457$			868.060i			1.89948i	0.313046	+	0.949738i	$0.398650\pi$
$457$			868.060i			1.89948i	−0.313046	+	0.949738i	$0.601350\pi$
$458$		0			0
$459$	−259.464	−	16.7619i	−0.565281	−	0.0365184i
$460$		0			0
$461$	532.709			1.15555			0.577776	−	0.816196i	$-0.303921\pi$
$461$	532.709			1.15555			0.577776	+	0.816196i	$0.303921\pi$
$462$		0			0
$463$			215.775i			0.466037i	0.972472	+	0.233018i	$0.0748602\pi$
$463$			215.775i			0.466037i	−0.972472	+	0.233018i	$0.925140\pi$
$464$		0			0
$465$	294.352	−	534.228i	0.633016	−	1.14888i
$466$		0			0
$467$			545.281i			1.16762i	0.811889	+	0.583812i	$0.198440\pi$
$467$			545.281i			1.16762i	−0.811889	+	0.583812i	$0.801560\pi$
$468$		0			0
$469$			33.7894i			0.0720457i
$470$		0			0
$471$	210.509	+	383.423i	0.446941	+	0.814062i
$472$		0			0
$473$	−522.540			−1.10474
$474$		0			0
$475$	218.480	+	103.014i	0.459957	+	0.216872i
$476$		0			0
$477$	74.9711	+	47.6960i	0.157172	+	0.0999917i
$478$		0			0
$479$			160.650i			0.335387i	0.985839	+	0.167694i	$0.0536319\pi$
$479$			160.650i			0.335387i	−0.985839	+	0.167694i	$0.946368\pi$
$480$		0			0
$481$	669.857			1.39263
$482$		0			0
$483$	−55.3108	+	30.3670i	−0.114515	+	0.0628717i
$484$		0			0
$485$	410.449	−	260.257i	0.846287	−	0.536613i
$486$		0			0
$487$			26.4247i			0.0542602i	0.999632	+	0.0271301i	$0.00863684\pi$
$487$			26.4247i			0.0542602i	−0.999632	+	0.0271301i	$0.991363\pi$
$488$		0			0
$489$	−288.955	−	526.305i	−0.590909	−	1.07629i
$490$		0			0
$491$	893.826			1.82042			0.910210	−	0.414147i	$-0.135920\pi$
$491$	893.826			1.82042			0.910210	+	0.414147i	$0.135920\pi$
$492$		0			0
$493$	455.393			0.923718
$494$		0			0
$495$	−436.357	−	0.656952i	−0.881529	−	0.00132718i
$496$		0			0
$497$	53.3461			0.107336
$498$		0			0
$499$			156.929i			0.314486i	0.987560	+	0.157243i	$0.0502606\pi$
$499$			156.929i			0.314486i	−0.987560	+	0.157243i	$0.949739\pi$
$500$		0			0
$501$	−220.510	−	401.639i	−0.440139	−	0.801674i
$502$		0			0
$503$	−709.881			−1.41129			−0.705647	−	0.708563i	$-0.749344\pi$
$503$	−709.881			−1.41129			−0.705647	+	0.708563i	$0.749344\pi$
$504$		0			0
$505$	−270.000	−	425.814i	−0.534653	−	0.843197i
$506$		0			0
$507$	97.6276	+	177.820i	0.192559	+	0.350729i
$508$		0			0
$509$	−138.402			−0.271909			−0.135954	−	0.990715i	$-0.543410\pi$
$509$	−138.402			−0.271909			−0.135954	+	0.990715i	$0.543410\pi$
$510$		0			0
$511$	−22.5263			−0.0440828
$512$		0			0
$513$	−16.8178	+	260.329i	−0.0327832	+	0.507463i
$514$		0			0
$515$	687.981	−	436.234i	1.33589	−	0.847057i
$516$		0			0
$517$	470.593			0.910237
$518$		0			0
$519$	385.061	−	211.408i	0.741929	−	0.407338i
$520$		0			0
$521$			104.670i			0.200903i	0.994942	+	0.100451i	$0.0320287\pi$
$521$			104.670i			0.200903i	−0.994942	+	0.100451i	$0.967971\pi$
$522$		0			0
$523$	−617.735			−1.18114			−0.590569	−	0.806987i	$-0.701097\pi$
$523$	−617.735			−1.18114			−0.590569	+	0.806987i	$0.701097\pi$
$524$		0			0
$525$	5.99346	+	97.3295i	0.0114161	+	0.185390i
$526$		0			0
$527$	391.582			0.743041
$528$		0			0
$529$	−267.310			−0.505311
$530$		0			0
$531$	−340.317	+	534.929i	−0.640899	+	1.00740i
$532$		0			0
$533$			64.7074i			0.121402i
$534$		0			0
$535$	547.715	−	347.295i	1.02377	−	0.649149i
$536$		0			0
$537$	376.978	+	686.631i	0.702007	+	1.27864i
$538$		0			0
$539$	−458.753			−0.851118
$540$		0			0
$541$		−	415.414i		−	0.767862i	−0.923362	−	0.383931i	$-0.874570\pi$
$541$		−	415.414i		−	0.767862i	0.923362	−	0.383931i	$-0.125430\pi$
$542$		0			0
$543$	−486.975	+	267.361i	−0.896822	+	0.492378i
$544$		0			0
$545$	−734.396	+	465.665i	−1.34752	+	0.854431i
$546$		0			0
$547$	218.356			0.399188			0.199594	−	0.979879i	$-0.436038\pi$
$547$	218.356			0.399188			0.199594	+	0.979879i	$0.436038\pi$
$548$		0			0
$549$	703.088	+	447.299i	1.28067	+	0.814752i
$550$		0			0
$551$		−	456.910i		−	0.829238i
$552$		0			0
$553$		−	120.384i		−	0.217693i
$554$		0			0
$555$	315.224	−	572.109i	0.567972	−	1.03083i
$556$		0			0
$557$			8.20400i			0.0147289i	0.999973	+	0.00736445i	$0.00234420\pi$
$557$			8.20400i			0.0147289i	−0.999973	+	0.00736445i	$0.997656\pi$
$558$		0			0
$559$	828.923			1.48287
$560$		0			0
$561$	−134.819	−	245.561i	−0.240319	−	0.437720i
$562$		0			0
$563$		−	222.751i		−	0.395649i	−0.980237	−	0.197825i	$-0.936612\pi$
$563$		−	222.751i		−	0.395649i	0.980237	−	0.197825i	$-0.0633877\pi$
$564$		0			0
$565$	7.14173	+	11.2631i	0.0126402	+	0.0199348i
$566$		0			0
$567$	−95.3921	+	44.6273i	−0.168240	+	0.0787078i
$568$		0			0
$569$			196.287i			0.344968i	0.985012	+	0.172484i	$0.0551794\pi$
$569$			196.287i			0.344968i	−0.985012	+	0.172484i	$0.944821\pi$
$570$		0			0
$571$		−	830.167i		−	1.45388i	−0.686700	−	0.726941i	$-0.740941\pi$
$571$		−	830.167i		−	1.45388i	0.686700	−	0.726941i	$-0.259059\pi$
$572$		0			0
$573$	638.261	−	350.421i	1.11389	−	0.611556i
$574$		0			0
$575$	172.476	−	365.799i	0.299958	−	0.636171i
$576$		0			0
$577$		−	574.421i		−	0.995531i	−0.867312	−	0.497765i	$-0.834154\pi$
$577$		−	574.421i		−	0.995531i	0.867312	−	0.497765i	$-0.165846\pi$
$578$		0			0
$579$	45.5613	−	25.0143i	0.0786896	−	0.0432026i
$580$		0			0
$581$	−70.5970			−0.121509
$582$		0			0
$583$			95.7369i			0.164214i
$584$		0			0
$585$	692.208	+	1.04215i	1.18326	+	0.00178145i
$586$		0			0
$587$			962.030i			1.63889i	0.573156	+	0.819446i	$0.305719\pi$
$587$			962.030i			1.63889i	−0.573156	+	0.819446i	$0.694281\pi$
$588$		0			0
$589$		−	392.887i		−	0.667041i
$590$		0			0
$591$	928.705	−	509.882i	1.57141	−	0.862745i
$592$		0			0
$593$	621.054			1.04731			0.523655	−	0.851931i	$-0.324568\pi$
$593$	621.054			1.04731			0.523655	+	0.851931i	$0.324568\pi$
$594$		0			0
$595$	−52.8701	+	33.5238i	−0.0888574	+	0.0563426i
$596$		0			0
$597$	−91.2327	−	166.172i	−0.152819	−	0.278345i
$598$		0			0
$599$			958.318i			1.59986i	0.600091	+	0.799932i	$0.295131\pi$
$599$			958.318i			1.59986i	−0.600091	+	0.799932i	$0.704869\pi$
$600$		0			0
$601$	356.424			0.593051			0.296526	−	0.955025i	$-0.404172\pi$
$601$	356.424			0.593051			0.296526	+	0.955025i	$0.404172\pi$
$602$		0			0
$603$	125.548	−	197.342i	0.208205	−	0.327268i
$604$		0			0
$605$	72.2162	+	113.891i	0.119366	+	0.188250i
$606$		0			0
$607$		−	303.308i		−	0.499684i	−0.968287	−	0.249842i	$-0.919621\pi$
$607$		−	303.308i		−	0.499684i	0.968287	−	0.249842i	$-0.0803787\pi$
$608$		0			0
$609$	161.690	−	88.7722i	0.265502	−	0.145767i
$610$		0			0
$611$	−746.518			−1.22180
$612$		0			0
$613$	547.468			0.893096			0.446548	−	0.894760i	$-0.352653\pi$
$613$	547.468			0.893096			0.446548	+	0.894760i	$0.352653\pi$
$614$		0			0
$615$	55.2650	+	30.4503i	0.0898619	+	0.0495127i
$616$		0			0
$617$	707.134			1.14608			0.573042	−	0.819526i	$-0.305763\pi$
$617$	707.134			1.14608			0.573042	+	0.819526i	$0.305763\pi$
$618$		0			0
$619$			979.405i			1.58224i	0.611663	+	0.791119i	$0.290501\pi$
$619$			979.405i			1.58224i	−0.611663	+	0.791119i	$0.709499\pi$
$620$		0			0
$621$	435.866	+	28.1579i	0.701878	+	0.0453428i
$622$		0			0
$623$	132.753			0.213086
$624$		0			0
$625$	−397.648	−	482.184i	−0.636236	−	0.771494i
$626$		0			0
$627$	−246.379	+	135.268i	−0.392949	+	0.215739i
$628$		0			0
$629$	419.349			0.666691
$630$		0			0
$631$	596.205			0.944857			0.472429	−	0.881369i	$-0.343377\pi$
$631$	596.205			0.944857			0.472429	+	0.881369i	$0.343377\pi$
$632$		0			0
$633$	−323.194	+	177.442i	−0.510575	+	0.280318i
$634$		0			0
$635$	−60.3928	+	38.2938i	−0.0951068	+	0.0603052i
$636$		0			0
$637$	727.735			1.14244
$638$		0			0
$639$	−311.560	−	198.212i	−0.487575	−	0.310191i
$640$		0			0
$641$			249.767i			0.389653i	0.980838	+	0.194826i	$0.0624143\pi$
$641$			249.767i			0.389653i	−0.980838	+	0.194826i	$0.937586\pi$
$642$		0			0
$643$	−280.012			−0.435478			−0.217739	−	0.976007i	$-0.569868\pi$
$643$	−280.012			−0.435478			−0.217739	+	0.976007i	$0.569868\pi$
$644$		0			0
$645$	390.078	−	707.963i	0.604772	−	1.09762i
$646$		0			0
$647$	−496.013			−0.766635			−0.383318	−	0.923617i	$-0.625219\pi$
$647$	−496.013			−0.766635			−0.383318	+	0.923617i	$0.625219\pi$
$648$		0			0
$649$	−683.095			−1.05253
$650$		0			0
$651$	139.034	−	76.3333i	0.213570	−	0.117255i
$652$		0			0
$653$			800.639i			1.22609i	0.790047	+	0.613046i	$0.210056\pi$
$653$			800.639i			1.22609i	−0.790047	+	0.613046i	$0.789944\pi$
$654$		0			0
$655$	507.052	+	799.666i	0.774125	+	1.22086i
$656$		0			0
$657$	131.562	+	83.6984i	0.200246	+	0.127395i
$658$		0			0
$659$	−270.228			−0.410057			−0.205029	−	0.978756i	$-0.565729\pi$
$659$	−270.228			−0.410057			−0.205029	+	0.978756i	$0.565729\pi$
$660$		0			0
$661$		−	521.752i		−	0.789337i	−0.918824	−	0.394669i	$-0.870859\pi$
$661$		−	521.752i		−	0.789337i	0.918824	−	0.394669i	$-0.129141\pi$
$662$		0			0
$663$	213.868	+	389.542i	0.322577	+	0.587544i
$664$		0			0
$665$	33.6356	+	53.0463i	0.0505798	+	0.0797689i
$666$		0			0
$667$	−765.001			−1.14693
$668$		0			0
$669$	716.716	−	393.495i	1.07132	−	0.588184i
$670$		0			0
$671$			897.832i			1.33805i
$672$		0			0
$673$			895.960i			1.33129i	0.746267	+	0.665646i	$0.231844\pi$
$673$			895.960i			1.33129i	−0.746267	+	0.665646i	$0.768156\pi$
$674$		0			0
$675$	326.632	−	590.708i	0.483900	−	0.875123i
$676$		0			0
$677$			119.542i			0.176576i	0.996095	+	0.0882879i	$0.0281395\pi$
$677$			119.542i			0.176576i	−0.996095	+	0.0882879i	$0.971860\pi$
$678$		0			0
$679$	126.380			0.186126
$680$		0			0
$681$	−802.393	+	440.534i	−1.17826	+	0.646893i
$682$		0			0
$683$		−	259.642i		−	0.380149i	−0.981770	−	0.190075i	$-0.939127\pi$
$683$		−	259.642i		−	0.380149i	0.981770	−	0.190075i	$-0.0608730\pi$
$684$		0			0
$685$	−359.399	−	566.805i	−0.524670	−	0.827452i
$686$		0			0
$687$	−1128.58	+	619.619i	−1.64276	+	0.901919i
$688$		0			0
$689$		−	151.871i		−	0.220422i
$690$		0			0
$691$		−	609.662i		−	0.882289i	−0.897436	−	0.441145i	$-0.854573\pi$
$691$		−	609.662i		−	0.882289i	0.897436	−	0.441145i	$-0.145427\pi$
$692$		0			0
$693$	−95.7369	−	60.9071i	−0.138149	−	0.0878890i
$694$		0			0
$695$	−364.336	+	231.018i	−0.524225	+	0.332400i
$696$		0			0
$697$			40.5086i			0.0581185i
$698$		0			0
$699$	−406.200	−	739.857i	−0.581116	−	1.05845i
$700$		0			0
$701$	−51.8162			−0.0739175			−0.0369587	−	0.999317i	$-0.511767\pi$
$701$	−51.8162			−0.0739175			−0.0369587	+	0.999317i	$0.511767\pi$
$702$		0			0
$703$		−	420.746i		−	0.598501i
$704$		0			0
$705$	−351.299	+	637.583i	−0.498297	+	0.904373i
$706$		0			0
$707$		−	131.111i		−	0.185447i
$708$		0			0
$709$		−	614.342i		−	0.866491i	−0.901276	−	0.433246i	$-0.857368\pi$
$709$		−	614.342i		−	0.866491i	0.901276	−	0.433246i	$-0.142632\pi$
$710$		0			0
$711$	−447.299	+	703.088i	−0.629113	+	0.988872i
$712$		0			0
$713$	−657.808			−0.922592
$714$		0			0
$715$	399.379	+	629.857i	0.558572	+	0.880919i
$716$		0			0
$717$	248.719	−	136.553i	0.346889	−	0.190451i
$718$		0			0
$719$			822.709i			1.14424i	0.820170	+	0.572120i	$0.193879\pi$
$719$			822.709i			1.14424i	−0.820170	+	0.572120i	$0.806121\pi$
$720$		0			0
$721$	211.833			0.293805
$722$		0			0
$723$	187.204	+	340.976i	0.258927	+	0.471612i
$724$		0			0
$725$	−504.200	+	1069.34i	−0.695449	+	1.47495i
$726$		0			0
$727$			406.884i			0.559675i	0.960047	+	0.279837i	$0.0902806\pi$
$727$			406.884i			0.559675i	−0.960047	+	0.279837i	$0.909719\pi$
$728$		0			0
$729$	722.940	+	93.7984i	0.991688	+	0.128667i
$730$		0			0
$731$	518.928			0.709888
$732$		0			0
$733$	−757.218			−1.03304			−0.516520	−	0.856275i	$-0.672773\pi$
$733$	−757.218			−1.03304			−0.516520	+	0.856275i	$0.672773\pi$
$734$		0			0
$735$	342.461	−	621.541i	0.465933	−	0.845634i
$736$		0			0
$737$	252.003			0.341931
$738$		0			0
$739$		−	36.3095i		−	0.0491333i	−0.999698	−	0.0245667i	$-0.992179\pi$
$739$		−	36.3095i		−	0.0491333i	0.999698	−	0.0245667i	$-0.00782060\pi$
$740$		0			0
$741$	390.840	−	214.581i	0.527449	−	0.289583i
$742$		0			0
$743$	769.119			1.03515			0.517577	−	0.855637i	$-0.326834\pi$
$743$	769.119			1.03515			0.517577	+	0.855637i	$0.326834\pi$
$744$		0			0
$745$	38.1666	+	60.1922i	0.0512304	+	0.0807949i
$746$		0			0
$747$	412.311	+	262.309i	0.551956	+	0.351150i
$748$		0			0
$749$	168.645			0.225160
$750$		0			0
$751$	907.765			1.20874			0.604371	−	0.796703i	$-0.293425\pi$
$751$	907.765			1.20874			0.604371	+	0.796703i	$0.293425\pi$
$752$		0			0
$753$	249.123	+	453.755i	0.330841	+	0.602596i
$754$		0			0
$755$	−30.1572	−	47.5606i	−0.0399433	−	0.0629941i
$756$		0			0
$757$	114.599			0.151386			0.0756928	−	0.997131i	$-0.475883\pi$
$757$	114.599			0.151386			0.0756928	+	0.997131i	$0.475883\pi$
$758$		0			0
$759$	226.479	+	412.510i	0.298391	+	0.543492i
$760$		0			0
$761$		−	200.928i		−	0.264031i	−0.991248	−	0.132016i	$-0.957855\pi$
$761$		−	200.928i		−	0.264031i	0.991248	−	0.132016i	$-0.0421449\pi$
$762$		0			0
$763$	−226.125			−0.296363
$764$		0			0
$765$	433.341	+	0.652411i	0.566459	+	0.000852825i
$766$		0			0
$767$	1083.62			1.41280
$768$		0			0
$769$	−285.267			−0.370958			−0.185479	−	0.982648i	$-0.559384\pi$
$769$	−285.267			−0.370958			−0.185479	+	0.982648i	$0.559384\pi$
$770$		0			0
$771$	674.216	+	1228.02i	0.874470	+	1.59277i
$772$		0			0
$773$			229.211i			0.296521i	0.988948	+	0.148260i	$0.0473674\pi$
$773$			229.211i			0.296521i	−0.988948	+	0.148260i	$0.952633\pi$
$774$		0			0
$775$	−433.551	+	919.503i	−0.559420	+	1.18646i
$776$		0			0
$777$	148.893	−	81.7459i	0.191625	−	0.105207i
$778$		0			0
$779$	40.6436			0.0521740
$780$		0			0
$781$		−	397.857i		−	0.509420i
$782$		0			0
$783$	−1274.17	−	82.3141i	−1.62729	−	0.105127i
$784$		0			0
$785$	−390.390	−	615.680i	−0.497312	−	0.784305i
$786$		0			0
$787$	−453.267			−0.575943			−0.287971	−	0.957639i	$-0.592981\pi$
$787$	−453.267			−0.575943			−0.287971	+	0.957639i	$0.592981\pi$
$788$		0			0
$789$	−399.461	−	727.582i	−0.506287	−	0.922157i
$790$		0			0
$791$			3.46799i			0.00438431i
$792$		0			0
$793$		−	1424.26i		−	1.79604i
$794$		0			0
$795$	−129.709	−	71.4680i	−0.163156	−	0.0898969i
$796$		0			0
$797$			1276.67i			1.60185i	0.598765	+	0.800925i	$0.295658\pi$
$797$			1276.67i			1.60185i	−0.598765	+	0.800925i	$0.704342\pi$
$798$		0			0
$799$	−467.340			−0.584906
$800$		0			0
$801$	−775.324	−	493.255i	−0.967945	−	0.615799i
$802$		0			0
$803$			168.002i			0.209218i
$804$		0			0
$805$	88.8150	−	56.3157i	0.110329	−	0.0699575i
$806$		0			0
$807$	407.156	+	741.598i	0.504530	+	0.918956i
$808$		0			0
$809$		−	797.708i		−	0.986042i	−0.870018	−	0.493021i	$-0.835893\pi$
$809$		−	797.708i		−	0.986042i	0.870018	−	0.493021i	$-0.164107\pi$
$810$		0			0
$811$		−	449.833i		−	0.554665i	−0.960774	−	0.277333i	$-0.910550\pi$
$811$		−	449.833i		−	0.554665i	0.960774	−	0.277333i	$-0.0894504\pi$
$812$		0			0
$813$	−251.100	−	457.355i	−0.308856	−	0.562553i
$814$		0			0
$815$	535.867	+	845.111i	0.657506	+	1.03695i
$816$		0			0
$817$		−	520.657i		−	0.637280i
$818$		0			0
$819$	151.871	+	96.6190i	0.185435	+	0.117972i
$820$		0			0
$821$	42.7636			0.0520872			0.0260436	−	0.999661i	$-0.491709\pi$
$821$	42.7636			0.0520872			0.0260436	+	0.999661i	$0.491709\pi$
$822$		0			0
$823$			1434.25i			1.74271i	0.490657	+	0.871353i	$0.336757\pi$
$823$			1434.25i			1.74271i	−0.490657	+	0.871353i	$0.663243\pi$
$824$		0			0
$825$	725.888	−	44.6994i	0.879864	−	0.0541811i
$826$		0			0
$827$		−	679.647i		−	0.821822i	−0.911675	−	0.410911i	$-0.865211\pi$
$827$		−	679.647i		−	0.821822i	0.911675	−	0.410911i	$-0.134789\pi$
$828$		0			0
$829$			336.572i			0.405997i	0.979179	+	0.202998i	$0.0650687\pi$
$829$			336.572i			0.405997i	−0.979179	+	0.202998i	$0.934931\pi$
$830$		0			0
$831$	−742.890	−	1353.11i	−0.893971	−	1.62829i
$832$		0			0
$833$	455.582			0.546917
$834$		0			0
$835$	408.936	+	644.929i	0.489743	+	0.772370i
$836$		0			0
$837$	−1095.63	−	70.7801i	−1.30900	−	0.0845640i
$838$		0			0
$839$		−	835.229i		−	0.995506i	−0.867319	−	0.497753i	$-0.834159\pi$
$839$		−	835.229i		−	0.995506i	0.867319	−	0.497753i	$-0.165841\pi$
$840$		0			0
$841$	1395.33			1.65914
$842$		0			0
$843$	368.063	−	202.076i	0.436611	−	0.239710i
$844$		0			0
$845$	−181.051	−	285.533i	−0.214261	−	0.337909i
$846$		0			0
$847$			35.0678i			0.0414024i
$848$		0			0
$849$	489.069	+	890.795i	0.576053	+	1.04923i
$850$		0			0
$851$	−704.452			−0.827793
$852$		0			0
$853$	131.483			0.154142			0.0770708	−	0.997026i	$-0.475443\pi$
$853$	131.483			0.154142			0.0770708	+	0.997026i	$0.475443\pi$
$854$		0			0
$855$	0.654585	−	434.785i	0.000765597	−	0.508521i
$856$		0			0
$857$	126.816			0.147976			0.0739880	−	0.997259i	$-0.476427\pi$
$857$	126.816			0.147976			0.0739880	+	0.997259i	$0.476427\pi$
$858$		0			0
$859$			63.1858i			0.0735573i	0.999323	+	0.0367787i	$0.0117097\pi$
$859$			63.1858i			0.0735573i	−0.999323	+	0.0367787i	$0.988290\pi$
$860$		0			0
$861$	7.89656	+	14.3829i	0.00917138	+	0.0167048i
$862$		0			0
$863$	742.235			0.860064			0.430032	−	0.902814i	$-0.358502\pi$
$863$	742.235			0.860064			0.430032	+	0.902814i	$0.358502\pi$
$864$		0			0
$865$	−618.310	+	392.057i	−0.714809	+	0.453245i
$866$		0			0
$867$	−283.367	−	516.128i	−0.326837	−	0.595304i
$868$		0			0
$869$	−897.832			−1.03318
$870$		0			0
$871$	−399.761			−0.458968
$872$		0			0
$873$	−738.102	−	469.575i	−0.845478	−	0.537886i
$874$		0			0
$875$	−20.1832	−	161.265i	−0.0230665	−	0.184303i
$876$		0			0
$877$	−253.700			−0.289282			−0.144641	−	0.989484i	$-0.546203\pi$
$877$	−253.700			−0.289282			−0.144641	+	0.989484i	$0.546203\pi$
$878$		0			0
$879$	909.933	−	499.576i	1.03519	−	0.568346i
$880$		0			0
$881$			536.960i			0.609489i	0.952434	+	0.304745i	$0.0985711\pi$
$881$			536.960i			0.609489i	−0.952434	+	0.304745i	$0.901429\pi$
$882$		0			0
$883$	1329.87			1.50608			0.753039	−	0.657976i	$-0.228587\pi$
$883$	1329.87			1.50608			0.753039	+	0.657976i	$0.228587\pi$
$884$		0			0
$885$	509.934	−	925.492i	0.576196	−	1.04575i
$886$		0			0
$887$	1035.09			1.16695			0.583476	−	0.812130i	$-0.301692\pi$
$887$	1035.09			1.16695			0.583476	+	0.812130i	$0.301692\pi$
$888$		0			0
$889$	−18.5953			−0.0209171
$890$		0			0
$891$	332.832	+	711.438i	0.373549	+	0.798472i
$892$		0			0
$893$			468.898i			0.525081i
$894$		0			0
$895$	−699.106	−	1102.55i	−0.781124	−	1.23190i
$896$		0			0
$897$	−359.271	−	654.380i	−0.400525	−	0.729520i
$898$		0			0
$899$	1922.97			2.13901
$900$		0			0
$901$		−	95.0753i		−	0.105522i
$902$		0			0
$903$	184.249	−	101.157i	0.204041	−	0.112024i
$904$		0			0
$905$	781.956	−	495.822i	0.864040	−	0.547870i
$906$		0			0
$907$	−172.237			−0.189898			−0.0949488	−	0.995482i	$-0.530269\pi$
$907$	−172.237			−0.189898			−0.0949488	+	0.995482i	$0.530269\pi$
$908$		0			0
$909$	−487.153	+	765.733i	−0.535922	+	0.842391i
$910$		0			0
$911$			790.732i			0.867982i	0.900917	+	0.433991i	$0.142895\pi$
$911$			790.732i			0.867982i	−0.900917	+	0.433991i	$0.857105\pi$
$912$		0			0
$913$			526.515i			0.576687i
$914$		0			0
$915$	−1216.43	−	670.236i	−1.32943	−	0.732498i
$916$		0			0
$917$			246.222i			0.268508i
$918$		0			0
$919$	−187.666			−0.204206			−0.102103	−	0.994774i	$-0.532557\pi$
$919$	−187.666			−0.204206			−0.102103	+	0.994774i	$0.532557\pi$
$920$		0			0
$921$	−739.212	−	1346.41i	−0.802619	−	1.46190i
$922$		0			0
$923$			631.135i			0.683787i
$924$		0			0
$925$	−464.293	+	984.703i	−0.501938	+	1.06454i
$926$		0			0
$927$	−1237.18	−	787.086i	−1.33461	−	0.849067i
$928$		0			0
$929$			1157.28i			1.24573i	0.782331	+	0.622863i	$0.214031\pi$
$929$			1157.28i			1.24573i	−0.782331	+	0.622863i	$0.785969\pi$
$930$		0			0
$931$		−	457.100i		−	0.490977i
$932$		0			0
$933$	779.083	−	427.736i	0.835030	−	0.458453i
$934$		0			0
$935$	250.022	+	394.308i	0.267403	+	0.421719i
$936$		0			0
$937$			1321.20i			1.41004i	0.709190	+	0.705018i	$0.249061\pi$
$937$			1321.20i			1.41004i	−0.709190	+	0.705018i	$0.750939\pi$
$938$		0			0
$939$	427.806	−	234.876i	0.455597	−	0.250134i
$940$		0			0
$941$	−1594.66			−1.69464			−0.847322	−	0.531080i	$-0.821787\pi$
$941$	−1594.66			−1.69464			−0.847322	+	0.531080i	$0.821787\pi$
$942$		0			0
$943$		−	68.0492i		−	0.0721625i
$944$		0			0
$945$	153.988	−	84.2419i	0.162950	−	0.0891449i
$946$		0			0
$947$			368.963i			0.389613i	0.980842	+	0.194806i	$0.0624079\pi$
$947$			368.963i			0.389613i	−0.980842	+	0.194806i	$0.937592\pi$
$948$		0			0
$949$		−	266.508i		−	0.280830i
$950$		0			0
$951$	470.143	−	258.120i	0.494367	−	0.271420i
$952$		0			0
$953$	−1432.04			−1.50266			−0.751331	−	0.659925i	$-0.770588\pi$
$953$	−1432.04			−1.50266			−0.751331	+	0.659925i	$0.770588\pi$
$954$		0			0
$955$	−1024.88	+	649.857i	−1.07318	+	0.680479i
$956$		0			0
$957$	−662.067	−	1205.89i	−0.691815	−	1.26008i
$958$		0			0
$959$		−	174.522i		−	0.181984i
$960$		0			0
$961$	692.524			0.720628
$962$		0			0
$963$	−984.945	−	626.614i	−1.02279	−	0.650690i
$964$		0			0
$965$	−73.1597	+	46.3890i	−0.0758132	+	0.0480716i
$966$		0			0
$967$		−	729.658i		−	0.754558i	−0.926100	−	0.377279i	$-0.876860\pi$
$967$		−	729.658i		−	0.754558i	0.926100	−	0.377279i	$-0.123140\pi$
$968$		0			0
$969$	244.676	−	134.333i	0.252504	−	0.138631i
$970$		0			0
$971$	−959.275			−0.987925			−0.493963	−	0.869483i	$-0.664452\pi$
$971$	−959.275			−0.987925			−0.493963	+	0.869483i	$0.664452\pi$
$972$		0			0
$973$	−112.181			−0.115294
$974$		0			0
$975$	−1151.50	+	70.9083i	−1.18103	+	0.0727265i
$976$		0			0
$977$	−901.809			−0.923039			−0.461520	−	0.887130i	$-0.652696\pi$
$977$	−901.809			−0.923039			−0.461520	+	0.887130i	$0.652696\pi$
$978$		0			0
$979$		−	990.076i		−	1.01131i
$980$		0			0
$981$	1320.65	+	840.186i	1.34623	+	0.856459i
$982$		0			0
$983$	−477.936			−0.486201			−0.243101	−	0.970001i	$-0.578165\pi$
$983$	−477.936			−0.486201			−0.243101	+	0.970001i	$0.578165\pi$
$984$		0			0
$985$	−1491.26	+	945.578i	−1.51397	+	0.959978i
$986$		0			0
$987$	−165.932	+	91.1011i	−0.168118	+	0.0923011i
$988$		0			0
$989$	−871.733			−0.881428
$990$		0			0
$991$	−1099.82			−1.10981			−0.554904	−	0.831914i	$-0.687245\pi$
$991$	−1099.82			−1.10981			−0.554904	+	0.831914i	$0.687245\pi$
$992$		0			0
$993$	1672.87	−	918.449i	1.68466	−	0.924923i
$994$		0			0
$995$	169.191	+	266.830i	0.170042	+	0.268171i
$996$		0			0
$997$	884.637			0.887298			0.443649	−	0.896201i	$-0.353684\pi$
$997$	884.637			0.887298			0.443649	+	0.896201i	$0.353684\pi$
$998$		0			0
$999$	−1173.32	−	75.7990i	−1.17450	−	0.0758748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.i.a.929.21	yes	32
3.2	odd	2	inner	960.3.i.a.929.20	yes	32
4.3	odd	2	inner	960.3.i.a.929.9	✓	32
5.4	even	2	inner	960.3.i.a.929.10	yes	32
8.3	odd	2	inner	960.3.i.a.929.24	yes	32
8.5	even	2	inner	960.3.i.a.929.12	yes	32
12.11	even	2	inner	960.3.i.a.929.16	yes	32
15.14	odd	2	inner	960.3.i.a.929.15	yes	32
20.19	odd	2	inner	960.3.i.a.929.22	yes	32
24.5	odd	2	inner	960.3.i.a.929.13	yes	32
24.11	even	2	inner	960.3.i.a.929.17	yes	32
40.19	odd	2	inner	960.3.i.a.929.11	yes	32
40.29	even	2	inner	960.3.i.a.929.23	yes	32
60.59	even	2	inner	960.3.i.a.929.19	yes	32
120.29	odd	2	inner	960.3.i.a.929.18	yes	32
120.59	even	2	inner	960.3.i.a.929.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.3.i.a.929.9	✓	32	4.3	odd	2	inner
960.3.i.a.929.10	yes	32	5.4	even	2	inner
960.3.i.a.929.11	yes	32	40.19	odd	2	inner
960.3.i.a.929.12	yes	32	8.5	even	2	inner
960.3.i.a.929.13	yes	32	24.5	odd	2	inner
960.3.i.a.929.14	yes	32	120.59	even	2	inner
960.3.i.a.929.15	yes	32	15.14	odd	2	inner
960.3.i.a.929.16	yes	32	12.11	even	2	inner
960.3.i.a.929.17	yes	32	24.11	even	2	inner
960.3.i.a.929.18	yes	32	120.29	odd	2	inner
960.3.i.a.929.19	yes	32	60.59	even	2	inner
960.3.i.a.929.20	yes	32	3.2	odd	2	inner
960.3.i.a.929.21	yes	32	1.1	even	1	trivial
960.3.i.a.929.22	yes	32	20.19	odd	2	inner
960.3.i.a.929.23	yes	32	40.29	even	2	inner
960.3.i.a.929.24	yes	32	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44379 + 2.62973i) q^{3} +(-2.67751 - 4.22267i) q^{5} -1.30019i q^{7} +(-4.83095 + 7.59354i) q^{9} +O(q^{10})\)	\(q+(1.44379 + 2.62973i) q^{3} +(-2.67751 - 4.22267i) q^{5} -1.30019i q^{7} +(-4.83095 + 7.59354i) q^{9} -9.69683 q^{11} +15.3824 q^{13} +(7.23873 - 13.1378i) q^{15} +9.62982 q^{17} -9.66190i q^{19} +(3.41913 - 1.87719i) q^{21} -16.1769 q^{23} +(-10.6619 + 22.6125i) q^{25} +(-26.9438 - 1.74063i) q^{27} +47.2899 q^{29} +40.6635 q^{31} +(-14.0002 - 25.5000i) q^{33} +(-5.49025 + 3.48126i) q^{35} +43.5469 q^{37} +(22.2090 + 40.4516i) q^{39} +4.20658i q^{41} +53.8877 q^{43} +(44.9999 + 0.0677491i) q^{45} -48.5306 q^{47} +47.3095 q^{49} +(13.9034 + 25.3238i) q^{51} -9.87301i q^{53} +(25.9633 + 40.9465i) q^{55} +(25.4082 - 13.9497i) q^{57} +70.4452 q^{59} -92.5902i q^{61} +(9.87301 + 6.28113i) q^{63} +(-41.1866 - 64.9549i) q^{65} -25.9882 q^{67} +(-23.3559 - 42.5407i) q^{69} +41.0296i q^{71} -17.3255i q^{73} +(-74.8582 + 4.60969i) q^{75} +12.6077i q^{77} +92.5902 q^{79} +(-34.3238 - 73.3681i) q^{81} -54.2976i q^{83} +(-25.7839 - 40.6635i) q^{85} +(68.2766 + 124.360i) q^{87} +102.103i q^{89} -20.0000i q^{91} +(58.7095 + 106.934i) q^{93} +(-40.7990 + 25.8698i) q^{95} +97.2013i q^{97} +(46.8449 - 73.6333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{9}+O(q^{10}) \) 32 * q + 32 * q^9	\( 32 q + 32 q^{9} + 32 q^{25} - 352 q^{49} - 352 q^{81}+O(q^{100}) \) 32 * q + 32 * q^9 + 32 * q^25 - 352 * q^49 - 352 * q^81

Introduction

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