LMFDB - Embedded newform 960.3.i.b.929.50

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:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.50
Character	$\chi$	$=$	960.929
Dual form			960.3.i.b.929.53

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.54191 - 1.59332i) q^{3} +(-4.96076 + 0.625206i) q^{5} +5.93744i q^{7} +(3.92266 - 8.10017i) q^{9} +O(q^{10})$	\(q+(2.54191 - 1.59332i) q^{3} +(-4.96076 + 0.625206i) q^{5} +5.93744i q^{7} +(3.92266 - 8.10017i) q^{9} -5.99878 q^{11} +15.6160 q^{13} +(-11.6137 + 9.49330i) q^{15} -14.2275 q^{17} -29.6128i q^{19} +(9.46024 + 15.0925i) q^{21} +21.5275 q^{23} +(24.2182 - 6.20299i) q^{25} +(-2.93512 - 26.8400i) q^{27} +18.1383 q^{29} -8.55847 q^{31} +(-15.2484 + 9.55799i) q^{33} +(-3.71212 - 29.4542i) q^{35} -13.4855 q^{37} +(39.6947 - 24.8814i) q^{39} -18.8052i q^{41} +27.1036 q^{43} +(-14.3951 + 42.6355i) q^{45} +37.4498 q^{47} +13.7469 q^{49} +(-36.1651 + 22.6690i) q^{51} -93.5909i q^{53} +(29.7585 - 3.75047i) q^{55} +(-47.1827 - 75.2731i) q^{57} +83.7790 q^{59} -39.3326i q^{61} +(48.0942 + 23.2905i) q^{63} +(-77.4674 + 9.76324i) q^{65} +103.540 q^{67} +(54.7210 - 34.3002i) q^{69} +14.5589i q^{71} -95.8968i q^{73} +(51.6773 - 54.3549i) q^{75} -35.6174i q^{77} -133.154 q^{79} +(-50.2255 - 63.5484i) q^{81} -116.715i q^{83} +(70.5793 - 8.89513i) q^{85} +(46.1060 - 28.9001i) q^{87} +146.524i q^{89} +92.7193i q^{91} +(-21.7549 + 13.6364i) q^{93} +(18.5141 + 146.902i) q^{95} -19.9818i q^{97} +(-23.5312 + 48.5912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{9}+O(q^{10}) $ 64 * q - 32 * q^9	$ 64 q - 32 q^{9} - 32 q^{25} - 320 q^{49} + 448 q^{81}+O(q^{100}) $ 64 * q - 32 * q^9 - 32 * q^25 - 320 * q^49 + 448 * 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
$3$	2.54191	−	1.59332i	0.847305	−	0.531107i
$3$	2.54191	−	1.59332i	0.847305	−	0.531107i
$4$		0			0
$5$	−4.96076	+	0.625206i	−0.992152	+	0.125041i
$5$	−4.96076	+	0.625206i	−0.992152	+	0.125041i
$6$		0			0
$7$			5.93744i			0.848205i	0.905614	+	0.424103i	$0.139410\pi$
$7$			5.93744i			0.848205i	−0.905614	+	0.424103i	$0.860590\pi$
$8$		0			0
$9$	3.92266	−	8.10017i	0.435851	−	0.900019i
$10$		0			0
$11$	−5.99878			−0.545344			−0.272672	−	0.962107i	$-0.587907\pi$
$11$	−5.99878			−0.545344			−0.272672	+	0.962107i	$0.587907\pi$
$12$		0			0
$13$	15.6160			1.20123			0.600617	−	0.799537i	$-0.294922\pi$
$13$	15.6160			1.20123			0.600617	+	0.799537i	$0.294922\pi$
$14$		0			0
$15$	−11.6137	+	9.49330i	−0.774245	+	0.632887i
$16$		0			0
$17$	−14.2275			−0.836913			−0.418457	−	0.908237i	$-0.637429\pi$
$17$	−14.2275			−0.836913			−0.418457	+	0.908237i	$0.637429\pi$
$18$		0			0
$19$		−	29.6128i		−	1.55857i	−0.626672	−	0.779283i	$-0.715583\pi$
$19$		−	29.6128i		−	1.55857i	0.626672	−	0.779283i	$-0.284417\pi$
$20$		0			0
$21$	9.46024	+	15.0925i	0.450488	+	0.718688i
$22$		0			0
$23$	21.5275			0.935977			0.467989	−	0.883734i	$-0.344979\pi$
$23$	21.5275			0.935977			0.467989	+	0.883734i	$0.344979\pi$
$24$		0			0
$25$	24.2182	−	6.20299i	0.968729	−	0.248119i
$26$		0			0
$27$	−2.93512	−	26.8400i	−0.108708	−	0.994074i
$28$		0			0
$29$	18.1383			0.625459			0.312729	−	0.949842i	$-0.398757\pi$
$29$	18.1383			0.625459			0.312729	+	0.949842i	$0.398757\pi$
$30$		0			0
$31$	−8.55847			−0.276080			−0.138040	−	0.990427i	$-0.544080\pi$
$31$	−8.55847			−0.276080			−0.138040	+	0.990427i	$0.544080\pi$
$32$		0			0
$33$	−15.2484	+	9.55799i	−0.462072	+	0.289636i
$34$		0			0
$35$	−3.71212	−	29.4542i	−0.106060	−	0.841548i
$36$		0			0
$37$	−13.4855			−0.364473			−0.182236	−	0.983255i	$-0.558334\pi$
$37$	−13.4855			−0.364473			−0.182236	+	0.983255i	$0.558334\pi$
$38$		0			0
$39$	39.6947	−	24.8814i	1.01781	−	0.637984i
$40$		0			0
$41$		−	18.8052i		−	0.458664i	−0.973348	−	0.229332i	$-0.926346\pi$
$41$		−	18.8052i		−	0.458664i	0.973348	−	0.229332i	$-0.0736541\pi$
$42$		0			0
$43$	27.1036			0.630317			0.315158	−	0.949039i	$-0.397942\pi$
$43$	27.1036			0.630317			0.315158	+	0.949039i	$0.397942\pi$
$44$		0			0
$45$	−14.3951	+	42.6355i	−0.319891	+	0.947455i
$46$		0			0
$47$	37.4498			0.796805			0.398403	−	0.917211i	$-0.369565\pi$
$47$	37.4498			0.796805			0.398403	+	0.917211i	$0.369565\pi$
$48$		0			0
$49$	13.7469			0.280548
$50$		0			0
$51$	−36.1651	+	22.6690i	−0.709120	+	0.444490i
$52$		0			0
$53$		−	93.5909i		−	1.76587i	−0.469498	−	0.882933i	$-0.655565\pi$
$53$		−	93.5909i		−	1.76587i	0.469498	−	0.882933i	$-0.344435\pi$
$54$		0			0
$55$	29.7585	−	3.75047i	0.541064	−	0.0681904i
$56$		0			0
$57$	−47.1827	−	75.2731i	−0.827766	−	1.32058i
$58$		0			0
$59$	83.7790			1.41998			0.709992	−	0.704210i	$-0.248699\pi$
$59$	83.7790			1.41998			0.709992	+	0.704210i	$0.248699\pi$
$60$		0			0
$61$		−	39.3326i		−	0.644797i	−0.946604	−	0.322398i	$-0.895511\pi$
$61$		−	39.3326i		−	0.644797i	0.946604	−	0.322398i	$-0.104489\pi$
$62$		0			0
$63$	48.0942	+	23.2905i	0.763401	+	0.369691i
$64$		0			0
$65$	−77.4674	+	9.76324i	−1.19181	+	0.150204i
$66$		0			0
$67$	103.540			1.54538			0.772688	−	0.634785i	$-0.218912\pi$
$67$	103.540			1.54538			0.772688	+	0.634785i	$0.218912\pi$
$68$		0			0
$69$	54.7210	−	34.3002i	0.793058	−	0.497104i
$70$		0			0
$71$			14.5589i			0.205054i	0.994730	+	0.102527i	$0.0326928\pi$
$71$			14.5589i			0.205054i	−0.994730	+	0.102527i	$0.967307\pi$
$72$		0			0
$73$		−	95.8968i		−	1.31366i	−0.754041	−	0.656828i	$-0.771898\pi$
$73$		−	95.8968i		−	1.31366i	0.754041	−	0.656828i	$-0.228102\pi$
$74$		0			0
$75$	51.6773	−	54.3549i	0.689031	−	0.724732i
$76$		0			0
$77$		−	35.6174i		−	0.462563i
$78$		0			0
$79$	−133.154			−1.68549			−0.842747	−	0.538310i	$-0.819063\pi$
$79$	−133.154			−1.68549			−0.842747	+	0.538310i	$0.819063\pi$
$80$		0			0
$81$	−50.2255	−	63.5484i	−0.620068	−	0.784548i
$82$		0			0
$83$		−	116.715i		−	1.40621i	−0.711087	−	0.703104i	$-0.751797\pi$
$83$		−	116.715i		−	1.40621i	0.711087	−	0.703104i	$-0.248203\pi$
$84$		0			0
$85$	70.5793	−	8.89513i	0.830345	−	0.104649i
$86$		0			0
$87$	46.1060	−	28.9001i	0.529954	−	0.332185i
$88$		0			0
$89$			146.524i			1.64634i	0.567794	+	0.823170i	$0.307797\pi$
$89$			146.524i			1.64634i	−0.567794	+	0.823170i	$0.692203\pi$
$90$		0			0
$91$			92.7193i			1.01889i
$92$		0			0
$93$	−21.7549	+	13.6364i	−0.233924	+	0.146628i
$94$		0			0
$95$	18.5141	+	146.902i	0.194885	+	1.54633i
$96$		0			0
$97$		−	19.9818i		−	0.205998i	−0.994681	−	0.102999i	$-0.967156\pi$
$97$		−	19.9818i		−	0.205998i	0.994681	−	0.102999i	$-0.0328439\pi$
$98$		0			0
$99$	−23.5312	+	48.5912i	−0.237688	+	0.490820i
$100$		0			0
$101$	−115.654			−1.14509			−0.572543	−	0.819874i	$-0.694043\pi$
$101$	−115.654			−1.14509			−0.572543	+	0.819874i	$0.694043\pi$
$102$		0			0
$103$			108.400i			1.05243i	0.850352	+	0.526214i	$0.176389\pi$
$103$			108.400i			1.05243i	−0.850352	+	0.526214i	$0.823611\pi$
$104$		0			0
$105$	−56.3658	−	68.9554i	−0.536818	−	0.656718i
$106$		0			0
$107$		−	74.1440i		−	0.692935i	−0.938062	−	0.346467i	$-0.887381\pi$
$107$		−	74.1440i		−	0.692935i	0.938062	−	0.346467i	$-0.112619\pi$
$108$		0			0
$109$		−	15.0213i		−	0.137810i	−0.997623	−	0.0689051i	$-0.978049\pi$
$109$		−	15.0213i		−	0.137810i	0.997623	−	0.0689051i	$-0.0219506\pi$
$110$		0			0
$111$	−34.2790	+	21.4867i	−0.308820	+	0.193574i
$112$		0			0
$113$	−164.159			−1.45273			−0.726366	−	0.687308i	$-0.758792\pi$
$113$	−164.159			−1.45273			−0.726366	+	0.687308i	$0.758792\pi$
$114$		0			0
$115$	−106.793	+	13.4591i	−0.928631	+	0.117036i
$116$		0			0
$117$	61.2564	−	126.493i	0.523559	−	1.08113i
$118$		0			0
$119$		−	84.4750i		−	0.709874i
$120$		0			0
$121$	−85.0146			−0.702600
$122$		0			0
$123$	−29.9627	−	47.8012i	−0.243600	−	0.388628i
$124$		0			0
$125$	−116.263	+	45.9129i	−0.930101	+	0.367303i
$126$		0			0
$127$		−	68.6273i		−	0.540372i	−0.962808	−	0.270186i	$-0.912915\pi$
$127$		−	68.6273i		−	0.540372i	0.962808	−	0.270186i	$-0.0870852\pi$
$128$		0			0
$129$	68.8951	−	43.1848i	0.534070	−	0.334766i
$130$		0			0
$131$	176.512			1.34742			0.673712	−	0.738994i	$-0.264699\pi$
$131$	176.512			1.34742			0.673712	+	0.738994i	$0.264699\pi$
$132$		0			0
$133$	175.824			1.32198
$134$		0			0
$135$	31.3409	+	131.312i	0.232155	+	0.972679i
$136$		0			0
$137$	−96.3424			−0.703229			−0.351615	−	0.936145i	$-0.614367\pi$
$137$	−96.3424			−0.703229			−0.351615	+	0.936145i	$0.614367\pi$
$138$		0			0
$139$			20.1883i			0.145240i	0.997360	+	0.0726198i	$0.0231360\pi$
$139$			20.1883i			0.145240i	−0.997360	+	0.0726198i	$0.976864\pi$
$140$		0			0
$141$	95.1943	−	59.6696i	0.675137	−	0.423189i
$142$		0			0
$143$	−93.6773			−0.655086
$144$		0			0
$145$	−89.9797	+	11.3402i	−0.620550	+	0.0782080i
$146$		0			0
$147$	34.9433	−	21.9032i	0.237710	−	0.149001i
$148$		0			0
$149$	138.759			0.931270			0.465635	−	0.884977i	$-0.345826\pi$
$149$	138.759			0.931270			0.465635	+	0.884977i	$0.345826\pi$
$150$		0			0
$151$	123.501			0.817888			0.408944	−	0.912559i	$-0.365897\pi$
$151$	123.501			0.817888			0.408944	+	0.912559i	$0.365897\pi$
$152$		0			0
$153$	−55.8097	+	115.245i	−0.364769	+	0.753238i
$154$		0			0
$155$	42.4565	−	5.35080i	0.273913	−	0.0345213i
$156$		0			0
$157$	−233.338			−1.48623			−0.743116	−	0.669162i	$-0.766653\pi$
$157$	−233.338			−1.48623			−0.743116	+	0.669162i	$0.766653\pi$
$158$		0			0
$159$	−149.120	−	237.900i	−0.937864	−	1.49623i
$160$		0			0
$161$			127.818i			0.793901i
$162$		0			0
$163$	98.7745			0.605979			0.302989	−	0.952994i	$-0.402015\pi$
$163$	98.7745			0.605979			0.302989	+	0.952994i	$0.402015\pi$
$164$		0			0
$165$	69.6679	−	56.9482i	0.422229	−	0.345141i
$166$		0			0
$167$	133.070			0.796825			0.398412	−	0.917206i	$-0.369561\pi$
$167$	133.070			0.796825			0.398412	+	0.917206i	$0.369561\pi$
$168$		0			0
$169$	74.8609			0.442964
$170$		0			0
$171$	−239.869	−	116.161i	−1.40274	−	0.679302i
$172$		0			0
$173$			323.270i			1.86861i	0.356474	+	0.934305i	$0.383979\pi$
$173$			323.270i			1.86861i	−0.356474	+	0.934305i	$0.616021\pi$
$174$		0			0
$175$	36.8298	+	143.794i	0.210456	+	0.821681i
$176$		0			0
$177$	212.959	−	133.487i	1.20316	−	0.754163i
$178$		0			0
$179$	183.645			1.02595			0.512975	−	0.858403i	$-0.328543\pi$
$179$	183.645			1.02595			0.512975	+	0.858403i	$0.328543\pi$
$180$		0			0
$181$			301.614i			1.66637i	0.552992	+	0.833187i	$0.313486\pi$
$181$			301.614i			1.66637i	−0.552992	+	0.833187i	$0.686514\pi$
$182$		0			0
$183$	−62.6695	−	99.9801i	−0.342456	−	0.546339i
$184$		0			0
$185$	66.8983	−	8.43121i	0.361612	−	0.0455741i
$186$		0			0
$187$	85.3478			0.456405
$188$		0			0
$189$	159.361	−	17.4271i	0.843178	−	0.0922068i
$190$		0			0
$191$			242.628i			1.27030i	0.772387	+	0.635152i	$0.219063\pi$
$191$			242.628i			1.27030i	−0.772387	+	0.635152i	$0.780937\pi$
$192$		0			0
$193$		−	13.6897i		−	0.0709311i	−0.999371	−	0.0354656i	$-0.988709\pi$
$193$		−	13.6897i		−	0.0709311i	0.999371	−	0.0354656i	$-0.0112914\pi$
$194$		0			0
$195$	−181.360	+	148.248i	−0.930049	+	0.760245i
$196$		0			0
$197$		−	361.518i		−	1.83511i	−0.397604	−	0.917557i	$-0.630158\pi$
$197$		−	361.518i		−	1.83511i	0.397604	−	0.917557i	$-0.369842\pi$
$198$		0			0
$199$	196.862			0.989258			0.494629	−	0.869104i	$-0.335304\pi$
$199$	196.862			0.989258			0.494629	+	0.869104i	$0.335304\pi$
$200$		0			0
$201$	263.190	−	164.973i	1.30941	−	0.820761i
$202$		0			0
$203$			107.695i			0.530517i
$204$		0			0
$205$	11.7571	+	93.2881i	0.0573518	+	0.455064i
$206$		0			0
$207$	84.4449	−	174.376i	0.407946	−	0.842397i
$208$		0			0
$209$			177.641i			0.849955i
$210$		0			0
$211$		−	202.277i		−	0.958658i	−0.877635	−	0.479329i	$-0.840880\pi$
$211$		−	202.277i		−	0.958658i	0.877635	−	0.479329i	$-0.159120\pi$
$212$		0			0
$213$	23.1969	+	37.0073i	0.108906	+	0.173743i
$214$		0			0
$215$	−134.454	+	16.9453i	−0.625370	+	0.0788155i
$216$		0			0
$217$		−	50.8153i		−	0.234172i
$218$		0			0
$219$	−152.794	−	243.762i	−0.697692	−	1.11307i
$220$		0			0
$221$	−222.178			−1.00533
$222$		0			0
$223$			34.1739i			0.153246i	0.997060	+	0.0766232i	$0.0244138\pi$
$223$			34.1739i			0.153246i	−0.997060	+	0.0766232i	$0.975586\pi$
$224$		0			0
$225$	44.7545	−	220.504i	0.198909	−	0.980018i
$226$		0			0
$227$			316.667i			1.39501i	0.716580	+	0.697505i	$0.245706\pi$
$227$			316.667i			1.39501i	−0.716580	+	0.697505i	$0.754294\pi$
$228$		0			0
$229$		−	236.008i		−	1.03060i	−0.857009	−	0.515301i	$-0.827680\pi$
$229$		−	236.008i		−	1.03060i	0.857009	−	0.515301i	$-0.172320\pi$
$230$		0			0
$231$	−56.7499	−	90.5363i	−0.245671	−	0.391932i
$232$		0			0
$233$	195.417			0.838698			0.419349	−	0.907825i	$-0.362258\pi$
$233$	195.417			0.838698			0.419349	+	0.907825i	$0.362258\pi$
$234$		0			0
$235$	−185.780	+	23.4138i	−0.790551	+	0.0996334i
$236$		0			0
$237$	−338.466	+	212.157i	−1.42813	+	0.895177i
$238$		0			0
$239$			9.71717i			0.0406576i	0.999793	+	0.0203288i	$0.00647130\pi$
$239$			9.71717i			0.0406576i	−0.999793	+	0.0203288i	$0.993529\pi$
$240$		0			0
$241$	200.592			0.832331			0.416166	−	0.909289i	$-0.363374\pi$
$241$	200.592			0.832331			0.416166	+	0.909289i	$0.363374\pi$
$242$		0			0
$243$	−228.922	−	81.5091i	−0.942066	−	0.335428i
$244$		0			0
$245$	−68.1949	+	8.59462i	−0.278346	+	0.0350801i
$246$		0			0
$247$		−	462.434i		−	1.87220i
$248$		0			0
$249$	−185.965	−	296.680i	−0.746847	−	1.19149i
$250$		0			0
$251$	20.8698			0.0831465			0.0415733	−	0.999135i	$-0.486763\pi$
$251$	20.8698			0.0831465			0.0415733	+	0.999135i	$0.486763\pi$
$252$		0			0
$253$	−129.139			−0.510429
$254$		0			0
$255$	165.234	−	135.066i	0.647975	−	0.529671i
$256$		0			0
$257$	456.070			1.77459			0.887296	−	0.461199i	$-0.152581\pi$
$257$	456.070			1.77459			0.887296	+	0.461199i	$0.152581\pi$
$258$		0			0
$259$		−	80.0693i		−	0.309148i
$260$		0			0
$261$	71.1503	−	146.923i	0.272607	−	0.562925i
$262$		0			0
$263$	−161.431			−0.613807			−0.306904	−	0.951741i	$-0.599293\pi$
$263$	−161.431			−0.613807			−0.306904	+	0.951741i	$0.599293\pi$
$264$		0			0
$265$	58.5136	+	464.282i	0.220806	+	1.75201i
$266$		0			0
$267$	233.460	+	372.452i	0.874383	+	1.39495i
$268$		0			0
$269$	−129.135			−0.480054			−0.240027	−	0.970766i	$-0.577156\pi$
$269$	−129.135			−0.480054			−0.240027	+	0.970766i	$0.577156\pi$
$270$		0			0
$271$	230.676			0.851203			0.425601	−	0.904911i	$-0.360063\pi$
$271$	230.676			0.851203			0.425601	+	0.904911i	$0.360063\pi$
$272$		0			0
$273$	147.732	+	235.684i	0.541141	+	0.863313i
$274$		0			0
$275$	−145.280	+	37.2104i	−0.528291	+	0.135310i
$276$		0			0
$277$	−354.494			−1.27976			−0.639881	−	0.768474i	$-0.721016\pi$
$277$	−354.494			−1.27976			−0.639881	+	0.768474i	$0.721016\pi$
$278$		0			0
$279$	−33.5719	+	69.3251i	−0.120329	+	0.248477i
$280$		0			0
$281$			350.785i			1.24834i	0.781287	+	0.624172i	$0.214564\pi$
$281$			350.785i			1.24834i	−0.781287	+	0.624172i	$0.785436\pi$
$282$		0			0
$283$	−254.054			−0.897718			−0.448859	−	0.893602i	$-0.648170\pi$
$283$	−254.054			−0.897718			−0.448859	+	0.893602i	$0.648170\pi$
$284$		0			0
$285$	281.123	+	343.913i	0.986396	+	1.20671i
$286$		0			0
$287$	111.655			0.389041
$288$		0			0
$289$	−86.5776			−0.299576
$290$		0			0
$291$	−31.8375	−	50.7921i	−0.109407	−	0.174543i
$292$		0			0
$293$		−	198.349i		−	0.676958i	−0.940974	−	0.338479i	$-0.890088\pi$
$293$		−	198.349i		−	0.676958i	0.940974	−	0.338479i	$-0.109912\pi$
$294$		0			0
$295$	−415.608	+	52.3791i	−1.40884	+	0.177556i
$296$		0			0
$297$	17.6071	+	161.007i	0.0592833	+	0.542112i
$298$		0			0
$299$	336.174			1.12433
$300$		0			0
$301$			160.926i			0.534638i
$302$		0			0
$303$	−293.982	+	184.274i	−0.970237	+	0.608164i
$304$		0			0
$305$	24.5910	+	195.120i	0.0806261	+	0.639736i
$306$		0			0
$307$	−229.921			−0.748927			−0.374464	−	0.927242i	$-0.622173\pi$
$307$	−229.921			−0.748927			−0.374464	+	0.927242i	$0.622173\pi$
$308$		0			0
$309$	172.716	+	275.544i	0.558952	+	0.891728i
$310$		0			0
$311$		−	43.0855i		−	0.138538i	−0.997598	−	0.0692692i	$-0.977933\pi$
$311$		−	43.0855i		−	0.138538i	0.997598	−	0.0692692i	$-0.0220668\pi$
$312$		0			0
$313$			218.737i			0.698841i	0.936966	+	0.349420i	$0.113622\pi$
$313$			218.737i			0.698841i	−0.936966	+	0.349420i	$0.886378\pi$
$314$		0			0
$315$	−253.145	−	85.4698i	−0.803636	−	0.271333i
$316$		0			0
$317$			325.313i			1.02622i	0.858322	+	0.513111i	$0.171507\pi$
$317$			325.313i			1.02622i	−0.858322	+	0.513111i	$0.828493\pi$
$318$		0			0
$319$	−108.808			−0.341090
$320$		0			0
$321$	−118.135	−	188.468i	−0.368022	−	0.587127i
$322$		0			0
$323$			421.316i			1.30439i
$324$		0			0
$325$	378.193	−	96.8661i	1.16367	−	0.298050i
$326$		0			0
$327$	−23.9338	−	38.1829i	−0.0731919	−	0.116767i
$328$		0			0
$329$			222.356i			0.675854i
$330$		0			0
$331$			314.138i			0.949058i	0.880240	+	0.474529i	$0.157382\pi$
$331$			314.138i			0.949058i	−0.880240	+	0.474529i	$0.842618\pi$
$332$		0			0
$333$	−52.8990	+	109.235i	−0.158856	+	0.328033i
$334$		0			0
$335$	−513.638	+	64.7339i	−1.53325	+	0.193236i
$336$		0			0
$337$		−	325.048i		−	0.964534i	−0.876024	−	0.482267i	$-0.839813\pi$
$337$		−	325.048i		−	0.964534i	0.876024	−	0.482267i	$-0.160187\pi$
$338$		0			0
$339$	−417.277	+	261.558i	−1.23091	+	0.771556i
$340$		0			0
$341$	51.3404			0.150558
$342$		0			0
$343$			372.555i			1.08617i
$344$		0			0
$345$	−250.013	+	204.367i	−0.724675	+	0.592367i
$346$		0			0
$347$			415.143i			1.19638i	0.801355	+	0.598189i	$0.204113\pi$
$347$			415.143i			1.19638i	−0.801355	+	0.598189i	$0.795887\pi$
$348$		0			0
$349$		−	179.846i		−	0.515318i	−0.966236	−	0.257659i	$-0.917049\pi$
$349$		−	179.846i		−	0.515318i	0.966236	−	0.257659i	$-0.0829512\pi$
$350$		0			0
$351$	−45.8350	−	419.135i	−0.130584	−	1.19412i
$352$		0			0
$353$	103.250			0.292493			0.146246	−	0.989248i	$-0.453281\pi$
$353$	103.250			0.292493			0.146246	+	0.989248i	$0.453281\pi$
$354$		0			0
$355$	−9.10227	−	72.2229i	−0.0256402	−	0.203445i
$356$		0			0
$357$	−134.596	−	214.728i	−0.377019	−	0.601480i
$358$		0			0
$359$			353.673i			0.985161i	0.870267	+	0.492580i	$0.163946\pi$
$359$			353.673i			0.985161i	−0.870267	+	0.492580i	$0.836054\pi$
$360$		0			0
$361$	−515.916			−1.42913
$362$		0			0
$363$	−216.100	+	135.456i	−0.595316	+	0.373156i
$364$		0			0
$365$	59.9552	+	475.721i	0.164261	+	1.30335i
$366$		0			0
$367$		−	640.613i		−	1.74554i	−0.488133	−	0.872769i	$-0.662322\pi$
$367$		−	640.613i		−	1.74554i	0.488133	−	0.872769i	$-0.337678\pi$
$368$		0			0
$369$	−152.325	−	73.7664i	−0.412806	−	0.199909i
$370$		0			0
$371$	555.690			1.49782
$372$		0			0
$373$	503.724			1.35047			0.675233	−	0.737605i	$-0.264043\pi$
$373$	503.724			1.35047			0.675233	+	0.737605i	$0.264043\pi$
$374$		0			0
$375$	−222.376	+	301.950i	−0.593002	+	0.805201i
$376$		0			0
$377$	283.249			0.751322
$378$		0			0
$379$			138.570i			0.365620i	0.983148	+	0.182810i	$0.0585194\pi$
$379$			138.570i			0.365620i	−0.983148	+	0.182810i	$0.941481\pi$
$380$		0			0
$381$	−109.345	−	174.445i	−0.286995	−	0.457860i
$382$		0			0
$383$	149.537			0.390437			0.195219	−	0.980760i	$-0.437458\pi$
$383$	149.537			0.390437			0.195219	+	0.980760i	$0.437458\pi$
$384$		0			0
$385$	22.2682	+	176.689i	0.0578394	+	0.458933i
$386$		0			0
$387$	106.318	−	219.544i	0.274724	−	0.567297i
$388$		0			0
$389$	−585.106			−1.50413			−0.752064	−	0.659090i	$-0.770942\pi$
$389$	−585.106			−1.50413			−0.752064	+	0.659090i	$0.770942\pi$
$390$		0			0
$391$	−306.283			−0.783332
$392$		0			0
$393$	448.679	−	281.241i	1.14168	−	0.715626i
$394$		0			0
$395$	660.545	−	83.2486i	1.67226	−	0.210756i
$396$		0			0
$397$	−529.718			−1.33430			−0.667151	−	0.744922i	$-0.732487\pi$
$397$	−529.718			−1.33430			−0.667151	+	0.744922i	$0.732487\pi$
$398$		0			0
$399$	446.929	−	280.144i	1.12012	−	0.702115i
$400$		0			0
$401$			134.714i			0.335944i	0.985792	+	0.167972i	$0.0537219\pi$
$401$			134.714i			0.335944i	−0.985792	+	0.167972i	$0.946278\pi$
$402$		0			0
$403$	−133.649			−0.331636
$404$		0			0
$405$	288.888	+	283.847i	0.713303	+	0.700856i
$406$		0			0
$407$	80.8966			0.198763
$408$		0			0
$409$	221.882			0.542499			0.271249	−	0.962509i	$-0.412563\pi$
$409$	221.882			0.542499			0.271249	+	0.962509i	$0.412563\pi$
$410$		0			0
$411$	−244.894	+	153.504i	−0.595850	+	0.373490i
$412$		0			0
$413$			497.433i			1.20444i
$414$		0			0
$415$	72.9710	+	578.996i	0.175834	+	1.39517i
$416$		0			0
$417$	32.1664	+	51.3169i	0.0771378	+	0.123062i
$418$		0			0
$419$	−358.418			−0.855413			−0.427707	−	0.903918i	$-0.640678\pi$
$419$	−358.418			−0.855413			−0.427707	+	0.903918i	$0.640678\pi$
$420$		0			0
$421$		−	572.660i		−	1.36024i	−0.733102	−	0.680119i	$-0.761928\pi$
$421$		−	572.660i		−	1.36024i	0.733102	−	0.680119i	$-0.238072\pi$
$422$		0			0
$423$	146.903	−	303.350i	0.347288	−	0.717140i
$424$		0			0
$425$	−344.566	+	88.2531i	−0.810742	+	0.207654i
$426$		0			0
$427$	233.535			0.546920
$428$		0			0
$429$	−238.120	+	149.258i	−0.555057	+	0.347921i
$430$		0			0
$431$			190.360i			0.441672i	0.975311	+	0.220836i	$0.0708785\pi$
$431$			190.360i			0.441672i	−0.975311	+	0.220836i	$0.929122\pi$
$432$		0			0
$433$			725.584i			1.67571i	0.545891	+	0.837857i	$0.316191\pi$
$433$			725.584i			1.67571i	−0.545891	+	0.837857i	$0.683809\pi$
$434$		0			0
$435$	−210.652	+	172.192i	−0.484258	+	0.395844i
$436$		0			0
$437$		−	637.488i		−	1.45878i
$438$		0			0
$439$	−460.268			−1.04845			−0.524223	−	0.851581i	$-0.675644\pi$
$439$	−460.268			−1.04845			−0.524223	+	0.851581i	$0.675644\pi$
$440$		0			0
$441$	53.9242	−	111.352i	0.122277	−	0.252499i
$442$		0			0
$443$		−	121.292i		−	0.273796i	−0.990585	−	0.136898i	$-0.956287\pi$
$443$		−	121.292i		−	0.273796i	0.990585	−	0.136898i	$-0.0437133\pi$
$444$		0			0
$445$	−91.6078	−	726.872i	−0.205860	−	1.63342i
$446$		0			0
$447$	352.714	−	221.088i	0.789070	−	0.494604i
$448$		0			0
$449$			12.4215i			0.0276648i	0.999904	+	0.0138324i	$0.00440313\pi$
$449$			12.4215i			0.0276648i	−0.999904	+	0.0138324i	$0.995597\pi$
$450$		0			0
$451$			112.808i			0.250129i
$452$		0			0
$453$	313.929	−	196.777i	0.693000	−	0.434386i
$454$		0			0
$455$	−57.9686	−	459.958i	−0.127404	−	1.01090i
$456$		0			0
$457$		−	438.321i		−	0.959126i	−0.877507	−	0.479563i	$-0.840795\pi$
$457$		−	438.321i		−	0.959126i	0.877507	−	0.479563i	$-0.159205\pi$
$458$		0			0
$459$	41.7595	+	381.867i	0.0909792	+	0.831953i
$460$		0			0
$461$	290.164			0.629424			0.314712	−	0.949187i	$-0.398092\pi$
$461$	290.164			0.629424			0.314712	+	0.949187i	$0.398092\pi$
$462$		0			0
$463$		−	342.841i		−	0.740477i	−0.928937	−	0.370239i	$-0.879276\pi$
$463$		−	342.841i		−	0.740477i	0.928937	−	0.370239i	$-0.120724\pi$
$464$		0			0
$465$	99.3952	−	81.2481i	0.213753	−	0.174727i
$466$		0			0
$467$			217.840i			0.466466i	0.972421	+	0.233233i	$0.0749305\pi$
$467$			217.840i			0.466466i	−0.972421	+	0.233233i	$0.925069\pi$
$468$		0			0
$469$			614.764i			1.31080i
$470$		0			0
$471$	−593.126	+	371.783i	−1.25929	+	0.789348i
$472$		0			0
$473$	−162.589			−0.343739
$474$		0			0
$475$	−183.688	−	717.169i	−0.386711	−	1.50983i
$476$		0			0
$477$	−758.103	−	367.125i	−1.58931	−	0.769654i
$478$		0			0
$479$			577.121i			1.20485i	0.798177	+	0.602423i	$0.205798\pi$
$479$			577.121i			1.20485i	−0.798177	+	0.602423i	$0.794202\pi$
$480$		0			0
$481$	−210.590			−0.437817
$482$		0			0
$483$	203.655	+	324.902i	0.421646	+	0.672676i
$484$		0			0
$485$	12.4928	+	99.1251i	0.0257583	+	0.204382i
$486$		0			0
$487$		−	689.685i		−	1.41619i	−0.706117	−	0.708095i	$-0.749555\pi$
$487$		−	689.685i		−	1.41619i	0.706117	−	0.708095i	$-0.250445\pi$
$488$		0			0
$489$	251.076	−	157.380i	0.513449	−	0.321840i
$490$		0			0
$491$	−834.980			−1.70057			−0.850285	−	0.526323i	$-0.823570\pi$
$491$	−834.980			−1.70057			−0.850285	+	0.526323i	$0.823570\pi$
$492$		0			0
$493$	−258.063			−0.523455
$494$		0			0
$495$	86.3529	−	255.761i	0.174450	−	0.516688i
$496$		0			0
$497$	−86.4422			−0.173928
$498$		0			0
$499$		−	145.508i		−	0.291600i	−0.989314	−	0.145800i	$-0.953424\pi$
$499$		−	145.508i		−	0.291600i	0.989314	−	0.145800i	$-0.0465755\pi$
$500$		0			0
$501$	338.252	−	212.023i	0.675153	−	0.423199i
$502$		0			0
$503$	−244.686			−0.486453			−0.243227	−	0.969969i	$-0.578206\pi$
$503$	−244.686			−0.486453			−0.243227	+	0.969969i	$0.578206\pi$
$504$		0			0
$505$	573.730	−	72.3074i	1.13610	−	0.143183i
$506$		0			0
$507$	190.290	−	119.278i	0.375326	−	0.235261i
$508$		0			0
$509$	−413.015			−0.811425			−0.405713	−	0.914001i	$-0.632977\pi$
$509$	−413.015			−0.811425			−0.405713	+	0.914001i	$0.632977\pi$
$510$		0			0
$511$	569.381			1.11425
$512$		0			0
$513$	−794.807	+	86.9170i	−1.54933	+	0.169429i
$514$		0			0
$515$	−67.7724	−	537.747i	−0.131597	−	1.04417i
$516$		0			0
$517$	−224.653			−0.434533
$518$		0			0
$519$	515.072	+	821.724i	0.992432	+	1.58328i
$520$		0			0
$521$		−	189.285i		−	0.363312i	−0.983362	−	0.181656i	$-0.941854\pi$
$521$		−	189.285i		−	0.363312i	0.983362	−	0.181656i	$-0.0581457\pi$
$522$		0			0
$523$	235.324			0.449950			0.224975	−	0.974365i	$-0.427770\pi$
$523$	235.324			0.449950			0.224975	+	0.974365i	$0.427770\pi$
$524$		0			0
$525$	322.729	+	306.831i	0.614721	+	0.584440i
$526$		0			0
$527$	121.766			0.231055
$528$		0			0
$529$	−65.5678			−0.123947
$530$		0			0
$531$	328.636	−	678.625i	0.618901	−	1.27801i
$532$		0			0
$533$		−	293.663i		−	0.550963i
$534$		0			0
$535$	46.3552	+	367.810i	0.0866453	+	0.687496i
$536$		0			0
$537$	466.810	−	292.606i	0.869293	−	0.544890i
$538$		0			0
$539$	−82.4644			−0.152995
$540$		0			0
$541$			789.168i			1.45872i	0.684130	+	0.729360i	$0.260182\pi$
$541$			789.168i			1.45872i	−0.684130	+	0.729360i	$0.739818\pi$
$542$		0			0
$543$	480.567	+	766.676i	0.885022	+	1.41193i
$544$		0			0
$545$	9.39140	+	74.5170i	0.0172319	+	0.136729i
$546$		0			0
$547$	905.745			1.65584			0.827921	−	0.560845i	$-0.189524\pi$
$547$	905.745			1.65584			0.827921	+	0.560845i	$0.189524\pi$
$548$		0			0
$549$	−318.601	−	154.288i	−0.580329	−	0.281035i
$550$		0			0
$551$		−	537.125i		−	0.974819i
$552$		0			0
$553$		−	790.593i		−	1.42964i
$554$		0			0
$555$	156.616	−	128.022i	0.282191	−	0.230670i
$556$		0			0
$557$		−	352.250i		−	0.632406i	−0.948692	−	0.316203i	$-0.897592\pi$
$557$		−	352.250i		−	0.632406i	0.948692	−	0.316203i	$-0.102408\pi$
$558$		0			0
$559$	423.251			0.757158
$560$		0			0
$561$	216.947	−	135.986i	0.386714	−	0.242400i
$562$		0			0
$563$		−	1028.02i		−	1.82597i	−0.407989	−	0.912987i	$-0.633770\pi$
$563$		−	1028.02i		−	1.82597i	0.407989	−	0.912987i	$-0.366230\pi$
$564$		0			0
$565$	814.352	−	102.633i	1.44133	−	0.181651i
$566$		0			0
$567$	377.314	−	298.211i	0.665457	−	0.525945i
$568$		0			0
$569$		−	612.176i		−	1.07588i	−0.842983	−	0.537941i	$-0.819202\pi$
$569$		−	612.176i		−	1.07588i	0.842983	−	0.537941i	$-0.180798\pi$
$570$		0			0
$571$			284.705i			0.498607i	0.968425	+	0.249304i	$0.0802017\pi$
$571$			284.705i			0.498607i	−0.968425	+	0.249304i	$0.919798\pi$
$572$		0			0
$573$	386.585	+	616.740i	0.674668	+	1.07633i
$574$		0			0
$575$	521.357	−	133.535i	0.906709	−	0.232234i
$576$		0			0
$577$		−	510.925i		−	0.885485i	−0.896649	−	0.442743i	$-0.854006\pi$
$577$		−	510.925i		−	0.885485i	0.896649	−	0.442743i	$-0.145994\pi$
$578$		0			0
$579$	−21.8121	−	34.7981i	−0.0376720	−	0.0601003i
$580$		0			0
$581$	692.989			1.19275
$582$		0			0
$583$			561.432i			0.963005i
$584$		0			0
$585$	−224.794	+	665.797i	−0.384264	+	1.13811i
$586$		0			0
$587$		−	425.221i		−	0.724396i	−0.932101	−	0.362198i	$-0.882026\pi$
$587$		−	425.221i		−	0.724396i	0.932101	−	0.362198i	$-0.117974\pi$
$588$		0			0
$589$			253.440i			0.430289i
$590$		0			0
$591$	−576.014	−	918.947i	−0.974642	−	1.55490i
$592$		0			0
$593$	−639.053			−1.07766			−0.538831	−	0.842414i	$-0.681134\pi$
$593$	−639.053			−1.07766			−0.538831	+	0.842414i	$0.681134\pi$
$594$		0			0
$595$	52.8142	+	419.060i	0.0887634	+	0.704302i
$596$		0			0
$597$	500.407	−	313.665i	0.838203	−	0.525402i
$598$		0			0
$599$		−	609.450i		−	1.01745i	−0.860930	−	0.508723i	$-0.830118\pi$
$599$		−	609.450i		−	1.01745i	0.860930	−	0.508723i	$-0.169882\pi$
$600$		0			0
$601$	443.553			0.738025			0.369012	−	0.929425i	$-0.379696\pi$
$601$	443.553			0.738025			0.369012	+	0.929425i	$0.379696\pi$
$602$		0			0
$603$	406.153	−	838.694i	0.673554	−	1.39087i
$604$		0			0
$605$	421.737	−	53.1516i	0.697086	−	0.0878539i
$606$		0			0
$607$			483.158i			0.795977i	0.917390	+	0.397988i	$0.130292\pi$
$607$			483.158i			0.795977i	−0.917390	+	0.397988i	$0.869708\pi$
$608$		0			0
$609$	171.593	+	273.751i	0.281761	+	0.449510i
$610$		0			0
$611$	584.818			0.957150
$612$		0			0
$613$	115.677			0.188706			0.0943532	−	0.995539i	$-0.469922\pi$
$613$	115.677			0.188706			0.0943532	+	0.995539i	$0.469922\pi$
$614$		0			0
$615$	178.524	+	218.398i	0.290282	+	0.355118i
$616$		0			0
$617$	−91.9068			−0.148958			−0.0744788	−	0.997223i	$-0.523729\pi$
$617$	−91.9068			−0.148958			−0.0744788	+	0.997223i	$0.523729\pi$
$618$		0			0
$619$		−	748.627i		−	1.20941i	−0.796448	−	0.604706i	$-0.793290\pi$
$619$		−	748.627i		−	1.20941i	0.796448	−	0.604706i	$-0.206710\pi$
$620$		0			0
$621$	−63.1857	−	577.797i	−0.101748	−	0.930430i
$622$		0			0
$623$	−869.979			−1.39643
$624$		0			0
$625$	548.046	−	300.451i	0.876873	−	0.480721i
$626$		0			0
$627$	283.038	+	451.547i	0.451417	+	0.720171i
$628$		0			0
$629$	191.865			0.305032
$630$		0			0
$631$	856.682			1.35766			0.678829	−	0.734296i	$-0.262488\pi$
$631$	856.682			1.35766			0.678829	+	0.734296i	$0.262488\pi$
$632$		0			0
$633$	−322.292	−	514.170i	−0.509150	−	0.812276i
$634$		0			0
$635$	42.9062	+	340.443i	0.0675687	+	0.536131i
$636$		0			0
$637$	214.672			0.337004
$638$		0			0
$639$	117.929	+	57.1094i	0.184553	+	0.0893730i
$640$		0			0
$641$			29.0978i			0.0453944i	0.999742	+	0.0226972i	$0.00722536\pi$
$641$			29.0978i			0.0453944i	−0.999742	+	0.0226972i	$0.992775\pi$
$642$		0			0
$643$	−873.920			−1.35913			−0.679564	−	0.733616i	$-0.737831\pi$
$643$	−873.920			−1.35913			−0.679564	+	0.733616i	$0.737831\pi$
$644$		0			0
$645$	−314.772	+	257.303i	−0.488019	+	0.398919i
$646$		0			0
$647$	1152.62			1.78149			0.890743	−	0.454507i	$-0.150184\pi$
$647$	1152.62			1.78149			0.890743	+	0.454507i	$0.150184\pi$
$648$		0			0
$649$	−502.572			−0.774379
$650$		0			0
$651$	−80.9652	−	129.168i	−0.124370	−	0.198415i
$652$		0			0
$653$		−	143.894i		−	0.220358i	−0.993912	−	0.110179i	$-0.964858\pi$
$653$		−	143.894i		−	0.220358i	0.993912	−	0.110179i	$-0.0351424\pi$
$654$		0			0
$655$	−875.635	+	110.357i	−1.33685	+	0.168483i
$656$		0			0
$657$	−776.781	−	376.170i	−1.18231	−	0.572557i
$658$		0			0
$659$	−410.806			−0.623379			−0.311689	−	0.950184i	$-0.600895\pi$
$659$	−410.806			−0.623379			−0.311689	+	0.950184i	$0.600895\pi$
$660$		0			0
$661$			1129.32i			1.70851i	0.519855	+	0.854254i	$0.325986\pi$
$661$			1129.32i			1.70851i	−0.519855	+	0.854254i	$0.674014\pi$
$662$		0			0
$663$	−564.757	+	354.000i	−0.851820	+	0.533937i
$664$		0			0
$665$	−872.220	+	109.926i	−1.31161	+	0.165302i
$666$		0			0
$667$	390.472			0.585415
$668$		0			0
$669$	54.4500	+	86.8672i	0.0813902	+	0.129846i
$670$		0			0
$671$			235.948i			0.351636i
$672$		0			0
$673$			630.561i			0.936940i	0.883479	+	0.468470i	$0.155195\pi$
$673$			630.561i			0.936940i	−0.883479	+	0.468470i	$0.844805\pi$
$674$		0			0
$675$	−237.572	−	631.811i	−0.351958	−	0.936016i
$676$		0			0
$677$		−	412.121i		−	0.608746i	−0.952553	−	0.304373i	$-0.901553\pi$
$677$		−	412.121i		−	0.608746i	0.952553	−	0.304373i	$-0.0984470\pi$
$678$		0			0
$679$	118.641			0.174729
$680$		0			0
$681$	504.552	+	804.941i	0.740899	+	1.18200i
$682$		0			0
$683$		−	538.782i		−	0.788847i	−0.918929	−	0.394423i	$-0.870944\pi$
$683$		−	538.782i		−	0.788847i	0.918929	−	0.394423i	$-0.129056\pi$
$684$		0			0
$685$	477.931	−	60.2338i	0.697710	−	0.0879326i
$686$		0			0
$687$	−376.036	−	599.912i	−0.547360	−	0.873234i
$688$		0			0
$689$		−	1461.52i		−	2.12122i
$690$		0			0
$691$			617.899i			0.894210i	0.894482	+	0.447105i	$0.147545\pi$
$691$			617.899i			0.894210i	−0.894482	+	0.447105i	$0.852455\pi$
$692$		0			0
$693$	−288.507	−	139.715i	−0.416316	−	0.201609i
$694$		0			0
$695$	−12.6218	−	100.149i	−0.0181609	−	0.144100i
$696$		0			0
$697$			267.552i			0.383862i
$698$		0			0
$699$	496.732	−	311.361i	0.710633	−	0.445438i
$700$		0			0
$701$	−583.091			−0.831799			−0.415900	−	0.909410i	$-0.636533\pi$
$701$	−583.091			−0.831799			−0.415900	+	0.909410i	$0.636533\pi$
$702$		0			0
$703$			399.343i			0.568055i
$704$		0			0
$705$	−434.930	+	355.523i	−0.616922	+	0.504287i
$706$		0			0
$707$		−	686.687i		−	0.971268i
$708$		0			0
$709$		−	291.529i		−	0.411184i	−0.978638	−	0.205592i	$-0.934088\pi$
$709$		−	291.529i		−	0.411184i	0.978638	−	0.205592i	$-0.0659119\pi$
$710$		0			0
$711$	−522.317	+	1078.57i	−0.734623	+	1.51698i
$712$		0			0
$713$	−184.242			−0.258404
$714$		0			0
$715$	464.710	−	58.5675i	0.649944	−	0.0819127i
$716$		0			0
$717$	15.4826	+	24.7002i	0.0215935	+	0.0344494i
$718$		0			0
$719$			1189.83i			1.65483i	0.561588	+	0.827417i	$0.310191\pi$
$719$			1189.83i			1.65483i	−0.561588	+	0.827417i	$0.689809\pi$
$720$		0			0
$721$	−643.619			−0.892675
$722$		0			0
$723$	509.887	−	319.607i	0.705238	−	0.442057i
$724$		0			0
$725$	439.278	−	112.512i	0.605900	−	0.155188i
$726$		0			0
$727$			332.813i			0.457790i	0.973451	+	0.228895i	$0.0735112\pi$
$727$			332.813i			0.457790i	−0.973451	+	0.228895i	$0.926489\pi$
$728$		0			0
$729$	−711.770	+	157.557i	−0.976365	+	0.216128i
$730$		0			0
$731$	−385.617			−0.527520
$732$		0			0
$733$	430.132			0.586810			0.293405	−	0.955988i	$-0.405212\pi$
$733$	430.132			0.586810			0.293405	+	0.955988i	$0.405212\pi$
$734$		0			0
$735$	−159.652	+	130.503i	−0.217213	+	0.177555i
$736$		0			0
$737$	−621.115			−0.842762
$738$		0			0
$739$			824.829i			1.11614i	0.829793	+	0.558071i	$0.188458\pi$
$739$			824.829i			1.11614i	−0.829793	+	0.558071i	$0.811542\pi$
$740$		0			0
$741$	−736.807	−	1175.47i	−0.994341	−	1.58633i
$742$		0			0
$743$	848.265			1.14168			0.570838	−	0.821063i	$-0.306619\pi$
$743$	848.265			1.14168			0.570838	+	0.821063i	$0.306619\pi$
$744$		0			0
$745$	−688.351	+	86.7531i	−0.923961	+	0.116447i
$746$		0			0
$747$	−945.414	−	457.834i	−1.26561	−	0.612897i
$748$		0			0
$749$	440.225			0.587751
$750$		0			0
$751$	63.2095			0.0841671			0.0420836	−	0.999114i	$-0.486600\pi$
$751$	63.2095			0.0841671			0.0420836	+	0.999114i	$0.486600\pi$
$752$		0			0
$753$	53.0492	−	33.2522i	0.0704504	−	0.0441597i
$754$		0			0
$755$	−612.659	+	77.2136i	−0.811469	+	0.102270i
$756$		0			0
$757$	−1255.62			−1.65868			−0.829340	−	0.558744i	$-0.811283\pi$
$757$	−1255.62			−1.65868			−0.829340	+	0.558744i	$0.811283\pi$
$758$		0			0
$759$	−328.259	+	205.759i	−0.432489	+	0.271093i
$760$		0			0
$761$		−	819.598i		−	1.07700i	−0.842625	−	0.538501i	$-0.818991\pi$
$761$		−	819.598i		−	1.07700i	0.842625	−	0.538501i	$-0.181009\pi$
$762$		0			0
$763$	89.1880			0.116891
$764$		0			0
$765$	204.806	−	606.597i	0.267721	−	0.792937i
$766$		0			0
$767$	1308.30			1.70573
$768$		0			0
$769$	275.299			0.357997			0.178998	−	0.983849i	$-0.442714\pi$
$769$	275.299			0.357997			0.178998	+	0.983849i	$0.442714\pi$
$770$		0			0
$771$	1159.29	−	726.667i	1.50362	−	0.942499i
$772$		0			0
$773$			310.696i			0.401935i	0.979598	+	0.200968i	$0.0644086\pi$
$773$			310.696i			0.401935i	−0.979598	+	0.200968i	$0.935591\pi$
$774$		0			0
$775$	−207.271	+	53.0881i	−0.267446	+	0.0685007i
$776$		0			0
$777$	−127.576	−	203.529i	−0.164191	−	0.261942i
$778$		0			0
$779$	−556.875			−0.714858
$780$		0			0
$781$		−	87.3354i		−	0.111825i
$782$		0			0
$783$	−53.2381	−	486.832i	−0.0679924	−	0.621752i
$784$		0			0
$785$	1157.54	−	145.885i	1.47457	−	0.185840i
$786$		0			0
$787$	882.041			1.12076			0.560382	−	0.828234i	$-0.310654\pi$
$787$	882.041			1.12076			0.560382	+	0.828234i	$0.310654\pi$
$788$		0			0
$789$	−410.344	+	257.212i	−0.520082	+	0.325997i
$790$		0			0
$791$		−	974.682i		−	1.23221i
$792$		0			0
$793$		−	614.220i		−	0.774552i
$794$		0			0
$795$	888.487	+	1086.93i	1.11759	+	1.36721i
$796$		0			0
$797$		−	572.739i		−	0.718619i	−0.933218	−	0.359309i	$-0.883012\pi$
$797$		−	572.739i		−	0.718619i	0.933218	−	0.359309i	$-0.116988\pi$
$798$		0			0
$799$	−532.818			−0.666857
$800$		0			0
$801$	1186.87	+	574.765i	1.48174	+	0.717559i
$802$		0			0
$803$			575.264i			0.716394i
$804$		0			0
$805$	−79.9125	−	634.074i	−0.0992702	−	0.787670i
$806$		0			0
$807$	−328.249	+	205.753i	−0.406752	+	0.254960i
$808$		0			0
$809$			1122.50i			1.38751i	0.720210	+	0.693756i	$0.244045\pi$
$809$			1122.50i			1.38751i	−0.720210	+	0.693756i	$0.755955\pi$
$810$		0			0
$811$			76.3000i			0.0940814i	0.998893	+	0.0470407i	$0.0149791\pi$
$811$			76.3000i			0.0940814i	−0.998893	+	0.0470407i	$0.985021\pi$
$812$		0			0
$813$	586.358	−	367.541i	0.721228	−	0.452080i
$814$		0			0
$815$	−489.997	+	61.7544i	−0.601223	+	0.0757723i
$816$		0			0
$817$		−	802.613i		−	0.982391i
$818$		0			0
$819$	751.042	+	363.706i	0.917023	+	0.444085i
$820$		0			0
$821$	−499.762			−0.608724			−0.304362	−	0.952557i	$-0.598443\pi$
$821$	−499.762			−0.608724			−0.304362	+	0.952557i	$0.598443\pi$
$822$		0			0
$823$		−	1081.64i		−	1.31426i	−0.753777	−	0.657131i	$-0.771770\pi$
$823$		−	1081.64i		−	1.31426i	0.753777	−	0.657131i	$-0.228230\pi$
$824$		0			0
$825$	−310.001	+	326.063i	−0.375759	+	0.395228i
$826$		0			0
$827$			221.353i			0.267658i	0.991004	+	0.133829i	$0.0427272\pi$
$827$			221.353i			0.267658i	−0.991004	+	0.133829i	$0.957273\pi$
$828$		0			0
$829$		−	1010.54i		−	1.21899i	−0.792789	−	0.609496i	$-0.791372\pi$
$829$		−	1010.54i		−	1.21899i	0.792789	−	0.609496i	$-0.208628\pi$
$830$		0			0
$831$	−901.094	+	564.823i	−1.08435	+	0.679691i
$832$		0			0
$833$	−195.584			−0.234794
$834$		0			0
$835$	−660.127	+	83.1959i	−0.790571	+	0.0996358i
$836$		0			0
$837$	25.1201	+	229.709i	0.0300121	+	0.274443i
$838$		0			0
$839$		−	1554.32i		−	1.85259i	−0.376803	−	0.926294i	$-0.622976\pi$
$839$		−	1554.32i		−	1.85259i	0.376803	−	0.926294i	$-0.377024\pi$
$840$		0			0
$841$	−512.002			−0.608802
$842$		0			0
$843$	558.913	+	891.665i	0.663004	+	1.05773i
$844$		0			0
$845$	−371.367	+	46.8035i	−0.439488	+	0.0553887i
$846$		0			0
$847$		−	504.769i		−	0.595949i
$848$		0			0
$849$	−645.784	+	404.790i	−0.760641	+	0.476785i
$850$		0			0
$851$	−290.309			−0.341138
$852$		0			0
$853$	−79.6953			−0.0934295			−0.0467147	−	0.998908i	$-0.514875\pi$
$853$	−79.6953			−0.0934295			−0.0467147	+	0.998908i	$0.514875\pi$
$854$		0			0
$855$	1262.55	+	426.278i	1.47667	+	0.498571i
$856$		0			0
$857$	−169.805			−0.198139			−0.0990693	−	0.995081i	$-0.531587\pi$
$857$	−169.805			−0.198139			−0.0990693	+	0.995081i	$0.531587\pi$
$858$		0			0
$859$			811.495i			0.944698i	0.881412	+	0.472349i	$0.156594\pi$
$859$			811.495i			0.944698i	−0.881412	+	0.472349i	$0.843406\pi$
$860$		0			0
$861$	283.817	−	177.902i	0.329636	−	0.206622i
$862$		0			0
$863$	925.135			1.07200			0.535999	−	0.844218i	$-0.319935\pi$
$863$	925.135			1.07200			0.535999	+	0.844218i	$0.319935\pi$
$864$		0			0
$865$	−202.110	−	1603.66i	−0.233653	−	1.85394i
$866$		0			0
$867$	−220.073	+	137.946i	−0.253833	+	0.159107i
$868$		0			0
$869$	798.762			0.919173
$870$		0			0
$871$	1616.89			1.85636
$872$		0			0
$873$	−161.856	−	78.3819i	−0.185402	−	0.0897845i
$874$		0			0
$875$	−272.605	−	690.302i	−0.311548	−	0.788917i
$876$		0			0
$877$	425.026			0.484636			0.242318	−	0.970197i	$-0.422092\pi$
$877$	425.026			0.484636			0.242318	+	0.970197i	$0.422092\pi$
$878$		0			0
$879$	−316.033	−	504.185i	−0.359537	−	0.573590i
$880$		0			0
$881$		−	41.8218i		−	0.0474709i	−0.999718	−	0.0237354i	$-0.992444\pi$
$881$		−	41.8218i		−	0.0474709i	0.999718	−	0.0237354i	$-0.00755593\pi$
$882$		0			0
$883$	549.203			0.621973			0.310987	−	0.950414i	$-0.399341\pi$
$883$	549.203			0.621973			0.310987	+	0.950414i	$0.399341\pi$
$884$		0			0
$885$	−972.982	+	795.339i	−1.09941	+	0.898689i
$886$		0			0
$887$	−1315.99			−1.48364			−0.741819	−	0.670600i	$-0.766037\pi$
$887$	−1315.99			−1.48364			−0.741819	+	0.670600i	$0.766037\pi$
$888$		0			0
$889$	407.470			0.458346
$890$		0			0
$891$	301.292	+	381.213i	0.338150	+	0.427848i
$892$		0			0
$893$		−	1108.99i		−	1.24187i
$894$		0			0
$895$	−911.019	+	114.816i	−1.01790	+	0.128286i
$896$		0			0
$897$	854.526	−	535.633i	0.952648	−	0.597139i
$898$		0			0
$899$	−155.236			−0.172676
$900$		0			0
$901$			1331.57i			1.47788i
$902$		0			0
$903$	256.407	+	409.060i	0.283950	+	0.453001i
$904$		0			0
$905$	−188.570	−	1496.23i	−0.208365	−	1.65329i
$906$		0			0
$907$	−103.221			−0.113804			−0.0569022	−	0.998380i	$-0.518122\pi$
$907$	−103.221			−0.113804			−0.0569022	+	0.998380i	$0.518122\pi$
$908$		0			0
$909$	−453.670	+	936.815i	−0.499087	+	1.03060i
$910$		0			0
$911$			937.234i			1.02880i	0.857551	+	0.514399i	$0.171985\pi$
$911$			937.234i			1.02880i	−0.857551	+	0.514399i	$0.828015\pi$
$912$		0			0
$913$			700.149i			0.766867i
$914$		0			0
$915$	373.396	+	456.796i	0.408083	+	0.499230i
$916$		0			0
$917$			1048.03i			1.14289i
$918$		0			0
$919$	−565.469			−0.615309			−0.307655	−	0.951498i	$-0.599544\pi$
$919$	−565.469			−0.615309			−0.307655	+	0.951498i	$0.599544\pi$
$920$		0			0
$921$	−584.439	+	366.337i	−0.634570	+	0.397761i
$922$		0			0
$923$			227.352i			0.246318i
$924$		0			0
$925$	−326.595	+	83.6504i	−0.353076	+	0.0904328i
$926$		0			0
$927$	878.060	+	425.217i	0.947206	+	0.458702i
$928$		0			0
$929$			561.412i			0.604318i	0.953258	+	0.302159i	$0.0977074\pi$
$929$			561.412i			0.604318i	−0.953258	+	0.302159i	$0.902293\pi$
$930$		0			0
$931$		−	407.083i		−	0.437253i
$932$		0			0
$933$	−68.6490	−	109.520i	−0.0735787	−	0.117384i
$934$		0			0
$935$	−423.390	+	53.3599i	−0.452823	+	0.0570694i
$936$		0			0
$937$			1293.38i			1.38034i	0.723647	+	0.690170i	$0.242464\pi$
$937$			1293.38i			1.38034i	−0.723647	+	0.690170i	$0.757536\pi$
$938$		0			0
$939$	348.519	+	556.011i	0.371159	+	0.592131i
$940$		0			0
$941$	1509.76			1.60442			0.802209	−	0.597043i	$-0.203658\pi$
$941$	1509.76			1.60442			0.802209	+	0.597043i	$0.203658\pi$
$942$		0			0
$943$		−	404.829i		−	0.429299i
$944$		0			0
$945$	−779.654	+	186.085i	−0.825031	+	0.196915i
$946$		0			0
$947$			368.756i			0.389394i	0.980863	+	0.194697i	$0.0623723\pi$
$947$			368.756i			0.389394i	−0.980863	+	0.194697i	$0.937628\pi$
$948$		0			0
$949$		−	1497.53i		−	1.57801i
$950$		0			0
$951$	518.327	+	826.917i	0.545034	+	0.869523i
$952$		0			0
$953$	1580.92			1.65889			0.829443	−	0.558591i	$-0.188658\pi$
$953$	1580.92			1.65889			0.829443	+	0.558591i	$0.188658\pi$
$954$		0			0
$955$	−151.692	−	1203.62i	−0.158840	−	1.26033i
$956$		0			0
$957$	−276.580	+	173.366i	−0.289007	+	0.181155i
$958$		0			0
$959$		−	572.027i		−	0.596483i
$960$		0			0
$961$	−887.753			−0.923780
$962$		0			0
$963$	−600.579	−	290.841i	−0.623654	−	0.302016i
$964$		0			0
$965$	8.55888	+	67.9113i	0.00886931	+	0.0703744i
$966$		0			0
$967$			653.389i			0.675686i	0.941202	+	0.337843i	$0.109697\pi$
$967$			653.389i			0.675686i	−0.941202	+	0.337843i	$0.890303\pi$
$968$		0			0
$969$	671.292	+	1070.95i	0.692768	+	1.10521i
$970$		0			0
$971$	−414.882			−0.427273			−0.213636	−	0.976913i	$-0.568531\pi$
$971$	−414.882			−0.427273			−0.213636	+	0.976913i	$0.568531\pi$
$972$		0			0
$973$	−119.867			−0.123193
$974$		0			0
$975$	806.996	−	848.808i	0.827688	−	0.870573i
$976$		0			0
$977$	829.934			0.849472			0.424736	−	0.905317i	$-0.360367\pi$
$977$	829.934			0.849472			0.424736	+	0.905317i	$0.360367\pi$
$978$		0			0
$979$		−	878.968i		−	0.897822i
$980$		0			0
$981$	−121.675	−	58.9234i	−0.124032	−	0.0600646i
$982$		0			0
$983$	43.3930			0.0441435			0.0220717	−	0.999756i	$-0.492974\pi$
$983$	43.3930			0.0441435			0.0220717	+	0.999756i	$0.492974\pi$
$984$		0			0
$985$	226.023	+	1793.40i	0.229465	+	1.82071i
$986$		0			0
$987$	354.284	+	565.210i	0.358951	+	0.572654i
$988$		0			0
$989$	583.472			0.589962
$990$		0			0
$991$	−325.761			−0.328719			−0.164360	−	0.986400i	$-0.552556\pi$
$991$	−325.761			−0.328719			−0.164360	+	0.986400i	$0.552556\pi$
$992$		0			0
$993$	500.523	+	798.513i	0.504052	+	0.804142i
$994$		0			0
$995$	−976.586	+	123.079i	−0.981493	+	0.123698i
$996$		0			0
$997$	487.259			0.488725			0.244363	−	0.969684i	$-0.421421\pi$
$997$	487.259			0.488725			0.244363	+	0.969684i	$0.421421\pi$
$998$		0			0
$999$	39.5815	+	361.951i	0.0396212	+	0.362313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.i.b.929.50	yes	64
3.2	odd	2	inner	960.3.i.b.929.55	yes	64
4.3	odd	2	inner	960.3.i.b.929.14	yes	64
5.4	even	2	inner	960.3.i.b.929.13	yes	64
8.3	odd	2	inner	960.3.i.b.929.51	yes	64
8.5	even	2	inner	960.3.i.b.929.15	yes	64
12.11	even	2	inner	960.3.i.b.929.11	yes	64
15.14	odd	2	inner	960.3.i.b.929.12	yes	64
20.19	odd	2	inner	960.3.i.b.929.49	yes	64
24.5	odd	2	inner	960.3.i.b.929.10	yes	64
24.11	even	2	inner	960.3.i.b.929.54	yes	64
40.19	odd	2	inner	960.3.i.b.929.16	yes	64
40.29	even	2	inner	960.3.i.b.929.52	yes	64
60.59	even	2	inner	960.3.i.b.929.56	yes	64
120.29	odd	2	inner	960.3.i.b.929.53	yes	64
120.59	even	2	inner	960.3.i.b.929.9	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.3.i.b.929.9	✓	64	120.59	even	2	inner
960.3.i.b.929.10	yes	64	24.5	odd	2	inner
960.3.i.b.929.11	yes	64	12.11	even	2	inner
960.3.i.b.929.12	yes	64	15.14	odd	2	inner
960.3.i.b.929.13	yes	64	5.4	even	2	inner
960.3.i.b.929.14	yes	64	4.3	odd	2	inner
960.3.i.b.929.15	yes	64	8.5	even	2	inner
960.3.i.b.929.16	yes	64	40.19	odd	2	inner
960.3.i.b.929.49	yes	64	20.19	odd	2	inner
960.3.i.b.929.50	yes	64	1.1	even	1	trivial
960.3.i.b.929.51	yes	64	8.3	odd	2	inner
960.3.i.b.929.52	yes	64	40.29	even	2	inner
960.3.i.b.929.53	yes	64	120.29	odd	2	inner
960.3.i.b.929.54	yes	64	24.11	even	2	inner
960.3.i.b.929.55	yes	64	3.2	odd	2	inner
960.3.i.b.929.56	yes	64	60.59	even	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)

\(f(q)\)	\(=\)	\(q+(2.54191 - 1.59332i) q^{3} +(-4.96076 + 0.625206i) q^{5} +5.93744i q^{7} +(3.92266 - 8.10017i) q^{9} +O(q^{10})\)	\(q+(2.54191 - 1.59332i) q^{3} +(-4.96076 + 0.625206i) q^{5} +5.93744i q^{7} +(3.92266 - 8.10017i) q^{9} -5.99878 q^{11} +15.6160 q^{13} +(-11.6137 + 9.49330i) q^{15} -14.2275 q^{17} -29.6128i q^{19} +(9.46024 + 15.0925i) q^{21} +21.5275 q^{23} +(24.2182 - 6.20299i) q^{25} +(-2.93512 - 26.8400i) q^{27} +18.1383 q^{29} -8.55847 q^{31} +(-15.2484 + 9.55799i) q^{33} +(-3.71212 - 29.4542i) q^{35} -13.4855 q^{37} +(39.6947 - 24.8814i) q^{39} -18.8052i q^{41} +27.1036 q^{43} +(-14.3951 + 42.6355i) q^{45} +37.4498 q^{47} +13.7469 q^{49} +(-36.1651 + 22.6690i) q^{51} -93.5909i q^{53} +(29.7585 - 3.75047i) q^{55} +(-47.1827 - 75.2731i) q^{57} +83.7790 q^{59} -39.3326i q^{61} +(48.0942 + 23.2905i) q^{63} +(-77.4674 + 9.76324i) q^{65} +103.540 q^{67} +(54.7210 - 34.3002i) q^{69} +14.5589i q^{71} -95.8968i q^{73} +(51.6773 - 54.3549i) q^{75} -35.6174i q^{77} -133.154 q^{79} +(-50.2255 - 63.5484i) q^{81} -116.715i q^{83} +(70.5793 - 8.89513i) q^{85} +(46.1060 - 28.9001i) q^{87} +146.524i q^{89} +92.7193i q^{91} +(-21.7549 + 13.6364i) q^{93} +(18.5141 + 146.902i) q^{95} -19.9818i q^{97} +(-23.5312 + 48.5912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{9}+O(q^{10}) \) 64 * q - 32 * q^9	\( 64 q - 32 q^{9} - 32 q^{25} - 320 q^{49} + 448 q^{81}+O(q^{100}) \) 64 * q - 32 * q^9 - 32 * q^25 - 320 * q^49 + 448 * q^81

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