LMFDB - Embedded newform 960.3.be.a.337.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(337,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))

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

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

chi := DirichletCharacter("960.337");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.be (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.16
Character	$\chi$	$=$	960.337
Dual form			960.3.be.a.433.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{3} +(3.81012 - 3.23774i) q^{5} +(-2.47993 + 2.47993i) q^{7} +3.00000 q^{9} +O(q^{10})$	\(q-1.73205 q^{3} +(3.81012 - 3.23774i) q^{5} +(-2.47993 + 2.47993i) q^{7} +3.00000 q^{9} +(-0.348209 + 0.348209i) q^{11} -6.32796 q^{13} +(-6.59933 + 5.60793i) q^{15} +(11.8771 + 11.8771i) q^{17} +(-6.07794 + 6.07794i) q^{19} +(4.29537 - 4.29537i) q^{21} +(17.0846 + 17.0846i) q^{23} +(4.03408 - 24.6724i) q^{25} -5.19615 q^{27} +(-21.6151 + 21.6151i) q^{29} -2.86002 q^{31} +(0.603116 - 0.603116i) q^{33} +(-1.41947 + 17.4782i) q^{35} +53.4598 q^{37} +10.9604 q^{39} +10.1296i q^{41} -31.6559i q^{43} +(11.4304 - 9.71322i) q^{45} +(-9.33506 - 9.33506i) q^{47} +36.6998i q^{49} +(-20.5718 - 20.5718i) q^{51} -21.2609i q^{53} +(-0.199309 + 2.45413i) q^{55} +(10.5273 - 10.5273i) q^{57} +(24.4012 + 24.4012i) q^{59} +(47.9384 + 47.9384i) q^{61} +(-7.43980 + 7.43980i) q^{63} +(-24.1103 + 20.4883i) q^{65} -98.7782i q^{67} +(-29.5913 - 29.5913i) q^{69} +7.58516i q^{71} +(71.1095 + 71.1095i) q^{73} +(-6.98723 + 42.7338i) q^{75} -1.72707i q^{77} +146.874i q^{79} +9.00000 q^{81} +78.3344 q^{83} +(83.7083 + 6.79826i) q^{85} +(37.4385 - 37.4385i) q^{87} +129.469 q^{89} +(15.6929 - 15.6929i) q^{91} +4.95371 q^{93} +(-3.47891 + 42.8365i) q^{95} +(44.2193 + 44.2193i) q^{97} +(-1.04463 + 1.04463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 288 q^{9}+O(q^{10}) $ 96 * q + 288 * q^9	$ 96 q + 288 q^{9} - 32 q^{19} + 96 q^{35} - 96 q^{51} - 128 q^{59} + 32 q^{61} - 96 q^{69} + 96 q^{73} - 192 q^{75} + 864 q^{81} + 320 q^{83} + 384 q^{91} + 768 q^{95}+O(q^{100}) $ 96 * q + 288 * q^9 - 32 * q^19 + 96 * q^35 - 96 * q^51 - 128 * q^59 + 32 * q^61 - 96 * q^69 + 96 * q^73 - 192 * q^75 + 864 * q^81 + 320 * q^83 + 384 * q^91 + 768 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$		0			0
$5$	3.81012	−	3.23774i	0.762025	−	0.647548i
$5$	3.81012	−	3.23774i	0.762025	−	0.647548i
$6$		0			0
$7$	−2.47993	+	2.47993i	−0.354276	+	0.354276i	−0.861698	−	0.507422i	$-0.830599\pi$
$7$	−2.47993	+	2.47993i	−0.354276	+	0.354276i	0.507422	+	0.861698i	$0.330599\pi$
$8$		0			0
$9$	3.00000			0.333333
$10$		0			0
$11$	−0.348209	+	0.348209i	−0.0316554	+	0.0316554i	−0.722757	−	0.691102i	$-0.757126\pi$
$11$	−0.348209	+	0.348209i	−0.0316554	+	0.0316554i	0.691102	+	0.722757i	$0.257126\pi$
$12$		0			0
$13$	−6.32796			−0.486766			−0.243383	−	0.969930i	$-0.578257\pi$
$13$	−6.32796			−0.486766			−0.243383	+	0.969930i	$0.578257\pi$
$14$		0			0
$15$	−6.59933	+	5.60793i	−0.439955	+	0.373862i
$16$		0			0
$17$	11.8771	+	11.8771i	0.698654	+	0.698654i	0.964120	−	0.265466i	$-0.0855259\pi$
$17$	11.8771	+	11.8771i	0.698654	+	0.698654i	−0.265466	+	0.964120i	$0.585526\pi$
$18$		0			0
$19$	−6.07794	+	6.07794i	−0.319891	+	0.319891i	−0.848725	−	0.528834i	$-0.822629\pi$
$19$	−6.07794	+	6.07794i	−0.319891	+	0.319891i	0.528834	+	0.848725i	$0.322629\pi$
$20$		0			0
$21$	4.29537	−	4.29537i	0.204542	−	0.204542i
$22$		0			0
$23$	17.0846	+	17.0846i	0.742807	+	0.742807i	0.973117	−	0.230310i	$-0.0739741\pi$
$23$	17.0846	+	17.0846i	0.742807	+	0.742807i	−0.230310	+	0.973117i	$0.573974\pi$
$24$		0			0
$25$	4.03408	−	24.6724i	0.161363	−	0.986895i
$26$		0			0
$27$	−5.19615			−0.192450
$28$		0			0
$29$	−21.6151	+	21.6151i	−0.745350	+	0.745350i	−0.973602	−	0.228252i	$-0.926699\pi$
$29$	−21.6151	+	21.6151i	−0.745350	+	0.745350i	0.228252	+	0.973602i	$0.426699\pi$
$30$		0			0
$31$	−2.86002			−0.0922588			−0.0461294	−	0.998935i	$-0.514689\pi$
$31$	−2.86002			−0.0922588			−0.0461294	+	0.998935i	$0.514689\pi$
$32$		0			0
$33$	0.603116	−	0.603116i	0.0182763	−	0.0182763i
$34$		0			0
$35$	−1.41947	+	17.4782i	−0.0405564	+	0.499378i
$36$		0			0
$37$	53.4598			1.44486			0.722430	−	0.691444i	$-0.243025\pi$
$37$	53.4598			1.44486			0.722430	+	0.691444i	$0.243025\pi$
$38$		0			0
$39$	10.9604			0.281035
$40$		0			0
$41$			10.1296i			0.247063i	0.992341	+	0.123532i	$0.0394221\pi$
$41$			10.1296i			0.247063i	−0.992341	+	0.123532i	$0.960578\pi$
$42$		0			0
$43$		−	31.6559i		−	0.736183i	−0.929790	−	0.368091i	$-0.880011\pi$
$43$		−	31.6559i		−	0.736183i	0.929790	−	0.368091i	$-0.119989\pi$
$44$		0			0
$45$	11.4304	−	9.71322i	0.254008	−	0.215849i
$46$		0			0
$47$	−9.33506	−	9.33506i	−0.198618	−	0.198618i	0.600789	−	0.799407i	$-0.294853\pi$
$47$	−9.33506	−	9.33506i	−0.198618	−	0.198618i	−0.799407	+	0.600789i	$0.794853\pi$
$48$		0			0
$49$			36.6998i			0.748976i
$50$		0			0
$51$	−20.5718	−	20.5718i	−0.403368	−	0.403368i
$52$		0			0
$53$		−	21.2609i		−	0.401150i	−0.979678	−	0.200575i	$-0.935719\pi$
$53$		−	21.2609i		−	0.401150i	0.979678	−	0.200575i	$-0.0642810\pi$
$54$		0			0
$55$	−0.199309	+	2.45413i	−0.00362380	+	0.0446206i
$56$		0			0
$57$	10.5273	−	10.5273i	0.184689	−	0.184689i
$58$		0			0
$59$	24.4012	+	24.4012i	0.413580	+	0.413580i	0.882984	−	0.469404i	$-0.155531\pi$
$59$	24.4012	+	24.4012i	0.413580	+	0.413580i	−0.469404	+	0.882984i	$0.655531\pi$
$60$		0			0
$61$	47.9384	+	47.9384i	0.785876	+	0.785876i	0.980815	−	0.194939i	$-0.0624510\pi$
$61$	47.9384	+	47.9384i	0.785876	+	0.785876i	−0.194939	+	0.980815i	$0.562451\pi$
$62$		0			0
$63$	−7.43980	+	7.43980i	−0.118092	+	0.118092i
$64$		0			0
$65$	−24.1103	+	20.4883i	−0.370928	+	0.315205i
$66$		0			0
$67$		−	98.7782i		−	1.47430i	−0.675729	−	0.737151i	$-0.736171\pi$
$67$		−	98.7782i		−	1.47430i	0.675729	−	0.737151i	$-0.263829\pi$
$68$		0			0
$69$	−29.5913	−	29.5913i	−0.428860	−	0.428860i
$70$		0			0
$71$			7.58516i			0.106833i	0.998572	+	0.0534166i	$0.0170111\pi$
$71$			7.58516i			0.106833i	−0.998572	+	0.0534166i	$0.982989\pi$
$72$		0			0
$73$	71.1095	+	71.1095i	0.974103	+	0.974103i	0.999673	−	0.0255703i	$-0.00814015\pi$
$73$	71.1095	+	71.1095i	0.974103	+	0.974103i	−0.0255703	+	0.999673i	$0.508140\pi$
$74$		0			0
$75$	−6.98723	+	42.7338i	−0.0931631	+	0.569784i
$76$		0			0
$77$		−	1.72707i		−	0.0224295i
$78$		0			0
$79$			146.874i			1.85917i	0.368608	+	0.929585i	$0.379835\pi$
$79$			146.874i			1.85917i	−0.368608	+	0.929585i	$0.620165\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		0			0
$83$	78.3344			0.943788			0.471894	−	0.881655i	$-0.343570\pi$
$83$	78.3344			0.943788			0.471894	+	0.881655i	$0.343570\pi$
$84$		0			0
$85$	83.7083	+	6.79826i	0.984803	+	0.0799796i
$86$		0			0
$87$	37.4385	−	37.4385i	0.430328	−	0.430328i
$88$		0			0
$89$	129.469			1.45471			0.727353	−	0.686264i	$-0.240750\pi$
$89$	129.469			1.45471			0.727353	+	0.686264i	$0.240750\pi$
$90$		0			0
$91$	15.6929	−	15.6929i	0.172450	−	0.172450i
$92$		0			0
$93$	4.95371			0.0532657
$94$		0			0
$95$	−3.47891	+	42.8365i	−0.0366201	+	0.450910i
$96$		0			0
$97$	44.2193	+	44.2193i	0.455869	+	0.455869i	0.897297	−	0.441428i	$-0.145528\pi$
$97$	44.2193	+	44.2193i	0.455869	+	0.455869i	−0.441428	+	0.897297i	$0.645528\pi$
$98$		0			0
$99$	−1.04463	+	1.04463i	−0.0105518	+	0.0105518i
$100$		0			0
$101$	20.9448	−	20.9448i	0.207374	−	0.207374i	−0.595776	−	0.803150i	$-0.703156\pi$
$101$	20.9448	−	20.9448i	0.207374	−	0.207374i	0.803150	+	0.595776i	$0.203156\pi$
$102$		0			0
$103$	−98.9454	−	98.9454i	−0.960635	−	0.960635i	0.0386192	−	0.999254i	$-0.487704\pi$
$103$	−98.9454	−	98.9454i	−0.960635	−	0.960635i	−0.999254	+	0.0386192i	$0.987704\pi$
$104$		0			0
$105$	2.45860	−	30.2732i	0.0234152	−	0.288316i
$106$		0			0
$107$	136.473			1.27545			0.637723	−	0.770266i	$-0.279876\pi$
$107$	136.473			1.27545			0.637723	+	0.770266i	$0.279876\pi$
$108$		0			0
$109$	26.0921	−	26.0921i	0.239377	−	0.239377i	−0.577215	−	0.816592i	$-0.695861\pi$
$109$	26.0921	−	26.0921i	0.239377	−	0.239377i	0.816592	+	0.577215i	$0.195861\pi$
$110$		0			0
$111$	−92.5951			−0.834190
$112$		0			0
$113$	−145.030	+	145.030i	−1.28345	+	1.28345i	−0.344755	+	0.938693i	$0.612038\pi$
$113$	−145.030	+	145.030i	−1.28345	+	1.28345i	−0.938693	+	0.344755i	$0.887962\pi$
$114$		0			0
$115$	120.410	+	9.77892i	1.04704	+	0.0850341i
$116$		0			0
$117$	−18.9839			−0.162255
$118$		0			0
$119$	−58.9089			−0.495033
$120$		0			0
$121$			120.758i			0.997996i
$122$		0			0
$123$		−	17.5450i		−	0.142642i
$124$		0			0
$125$	−64.5124	−	107.066i	−0.516099	−	0.856529i
$126$		0			0
$127$	150.676	+	150.676i	1.18643	+	1.18643i	0.978048	+	0.208381i	$0.0668195\pi$
$127$	150.676	+	150.676i	1.18643	+	1.18643i	0.208381	+	0.978048i	$0.433180\pi$
$128$		0			0
$129$			54.8295i			0.425035i
$130$		0			0
$131$	123.018	+	123.018i	0.939070	+	0.939070i	0.998247	−	0.0591777i	$-0.0188478\pi$
$131$	123.018	+	123.018i	0.939070	+	0.939070i	−0.0591777	+	0.998247i	$0.518848\pi$
$132$		0			0
$133$		−	30.1458i		−	0.226660i
$134$		0			0
$135$	−19.7980	+	16.8238i	−0.146652	+	0.124621i
$136$		0			0
$137$	45.2883	−	45.2883i	0.330571	−	0.330571i	−0.522232	−	0.852803i	$-0.674901\pi$
$137$	45.2883	−	45.2883i	0.330571	−	0.330571i	0.852803	+	0.522232i	$0.174901\pi$
$138$		0			0
$139$	111.230	+	111.230i	0.800218	+	0.800218i	0.983129	−	0.182911i	$-0.0585522\pi$
$139$	111.230	+	111.230i	0.800218	+	0.800218i	−0.182911	+	0.983129i	$0.558552\pi$
$140$		0			0
$141$	16.1688	+	16.1688i	0.114672	+	0.114672i
$142$		0			0
$143$	2.20346	−	2.20346i	0.0154088	−	0.0154088i
$144$		0			0
$145$	−12.3721	+	152.341i	−0.0853251	+	1.05062i
$146$		0			0
$147$		−	63.5660i		−	0.432422i
$148$		0			0
$149$	−147.057	−	147.057i	−0.986962	−	0.986962i	0.0129541	−	0.999916i	$-0.495876\pi$
$149$	−147.057	−	147.057i	−0.986962	−	0.986962i	−0.999916	+	0.0129541i	$0.995876\pi$
$150$		0			0
$151$			86.9772i			0.576008i	0.957629	+	0.288004i	$0.0929917\pi$
$151$			86.9772i			0.576008i	−0.957629	+	0.288004i	$0.907008\pi$
$152$		0			0
$153$	35.6313	+	35.6313i	0.232885	+	0.232885i
$154$		0			0
$155$	−10.8970	+	9.26001i	−0.0703035	+	0.0597420i
$156$		0			0
$157$			90.6356i			0.577297i	0.957435	+	0.288648i	$0.0932058\pi$
$157$			90.6356i			0.577297i	−0.957435	+	0.288648i	$0.906794\pi$
$158$		0			0
$159$			36.8250i			0.231604i
$160$		0			0
$161$	−84.7372			−0.526318
$162$		0			0
$163$	136.683			0.838549			0.419274	−	0.907860i	$-0.362285\pi$
$163$	136.683			0.838549			0.419274	+	0.907860i	$0.362285\pi$
$164$		0			0
$165$	0.345214	−	4.25068i	0.00209220	−	0.0257617i
$166$		0			0
$167$	93.7702	−	93.7702i	0.561498	−	0.561498i	−0.368235	−	0.929733i	$-0.620038\pi$
$167$	93.7702	−	93.7702i	0.561498	−	0.561498i	0.929733	+	0.368235i	$0.120038\pi$
$168$		0			0
$169$	−128.957			−0.763059
$170$		0			0
$171$	−18.2338	+	18.2338i	−0.106630	+	0.106630i
$172$		0			0
$173$	−147.827			−0.854490			−0.427245	−	0.904136i	$-0.640516\pi$
$173$	−147.827			−0.854490			−0.427245	+	0.904136i	$0.640516\pi$
$174$		0			0
$175$	51.1816	+	71.1901i	0.292466	+	0.406801i
$176$		0			0
$177$	−42.2641	−	42.2641i	−0.238780	−	0.238780i
$178$		0			0
$179$	9.91598	−	9.91598i	0.0553965	−	0.0553965i	−0.678866	−	0.734262i	$-0.737528\pi$
$179$	9.91598	−	9.91598i	0.0553965	−	0.0553965i	0.734262	+	0.678866i	$0.237528\pi$
$180$		0			0
$181$	106.279	−	106.279i	0.587175	−	0.587175i	−0.349690	−	0.936865i	$-0.613713\pi$
$181$	106.279	−	106.279i	0.587175	−	0.587175i	0.936865	+	0.349690i	$0.113713\pi$
$182$		0			0
$183$	−83.0318	−	83.0318i	−0.453726	−	0.453726i
$184$		0			0
$185$	203.688	−	173.089i	1.10102	−	0.935616i
$186$		0			0
$187$	−8.27145			−0.0442323
$188$		0			0
$189$	12.8861	−	12.8861i	0.0681805	−	0.0681805i
$190$		0			0
$191$	−129.132			−0.676086			−0.338043	−	0.941131i	$-0.609765\pi$
$191$	−129.132			−0.676086			−0.338043	+	0.941131i	$0.609765\pi$
$192$		0			0
$193$	145.081	−	145.081i	0.751717	−	0.751717i	−0.223082	−	0.974800i	$-0.571612\pi$
$193$	145.081	−	145.081i	0.751717	−	0.751717i	0.974800	+	0.223082i	$0.0716119\pi$
$194$		0			0
$195$	41.7603	−	35.4868i	0.214155	−	0.181983i
$196$		0			0
$197$	−391.730			−1.98848			−0.994239	−	0.107189i	$-0.965815\pi$
$197$	−391.730			−1.98848			−0.994239	+	0.107189i	$0.965815\pi$
$198$		0			0
$199$	−110.455			−0.555050			−0.277525	−	0.960718i	$-0.589514\pi$
$199$	−110.455			−0.555050			−0.277525	+	0.960718i	$0.589514\pi$
$200$		0			0
$201$			171.089i			0.851188i
$202$		0			0
$203$		−	107.208i		−	0.528120i
$204$		0			0
$205$	32.7970	+	38.5950i	0.159985	+	0.188268i
$206$		0			0
$207$	51.2537	+	51.2537i	0.247602	+	0.247602i
$208$		0			0
$209$		−	4.23279i		−	0.0202526i
$210$		0			0
$211$	195.650	+	195.650i	0.927250	+	0.927250i	0.997527	−	0.0702773i	$-0.0223884\pi$
$211$	195.650	+	195.650i	0.927250	+	0.927250i	−0.0702773	+	0.997527i	$0.522388\pi$
$212$		0			0
$213$		−	13.1379i		−	0.0616802i
$214$		0			0
$215$	−102.493	−	120.613i	−0.476714	−	0.560989i
$216$		0			0
$217$	7.09267	−	7.09267i	0.0326851	−	0.0326851i
$218$		0			0
$219$	−123.165	−	123.165i	−0.562398	−	0.562398i
$220$		0			0
$221$	−75.1579	−	75.1579i	−0.340081	−	0.340081i
$222$		0			0
$223$	−151.191	+	151.191i	−0.677987	+	0.677987i	−0.959544	−	0.281557i	$-0.909149\pi$
$223$	−151.191	+	151.191i	−0.677987	+	0.677987i	0.281557	+	0.959544i	$0.409149\pi$
$224$		0			0
$225$	12.1022	−	74.0171i	0.0537877	−	0.328965i
$226$		0			0
$227$		−	300.586i		−	1.32417i	−0.749431	−	0.662083i	$-0.769673\pi$
$227$		−	300.586i		−	1.32417i	0.749431	−	0.662083i	$-0.230327\pi$
$228$		0			0
$229$	−321.239	−	321.239i	−1.40279	−	1.40279i	−0.791082	−	0.611710i	$-0.790482\pi$
$229$	−321.239	−	321.239i	−1.40279	−	1.40279i	−0.611710	−	0.791082i	$-0.709518\pi$
$230$		0			0
$231$			2.99138i			0.0129497i
$232$		0			0
$233$	96.0956	+	96.0956i	0.412427	+	0.412427i	0.882583	−	0.470156i	$-0.155802\pi$
$233$	96.0956	+	96.0956i	0.412427	+	0.412427i	−0.470156	+	0.882583i	$0.655802\pi$
$234$		0			0
$235$	−65.7922	−	5.34323i	−0.279967	−	0.0227372i
$236$		0			0
$237$		−	254.394i		−	1.07339i
$238$		0			0
$239$		−	397.633i		−	1.66374i	−0.554974	−	0.831868i	$-0.687272\pi$
$239$		−	397.633i		−	1.66374i	0.554974	−	0.831868i	$-0.312728\pi$
$240$		0			0
$241$	176.586			0.732722			0.366361	−	0.930473i	$-0.380603\pi$
$241$	176.586			0.732722			0.366361	+	0.930473i	$0.380603\pi$
$242$		0			0
$243$	−15.5885			−0.0641500
$244$		0			0
$245$	118.825	+	139.831i	0.484998	+	0.570739i
$246$		0			0
$247$	38.4609	−	38.4609i	0.155712	−	0.155712i
$248$		0			0
$249$	−135.679			−0.544896
$250$		0			0
$251$	−155.376	+	155.376i	−0.619029	+	0.619029i	−0.945282	−	0.326254i	$-0.894214\pi$
$251$	−155.376	+	155.376i	−0.619029	+	0.619029i	0.326254	+	0.945282i	$0.394214\pi$
$252$		0			0
$253$	−11.8980			−0.0470277
$254$		0			0
$255$	−144.987	−	11.7749i	−0.568577	−	0.0461762i
$256$		0			0
$257$	−321.383	−	321.383i	−1.25052	−	1.25052i	−0.955488	−	0.295029i	$-0.904671\pi$
$257$	−321.383	−	321.383i	−1.25052	−	1.25052i	−0.295029	−	0.955488i	$-0.595329\pi$
$258$		0			0
$259$	−132.577	+	132.577i	−0.511880	+	0.511880i
$260$		0			0
$261$	−64.8454	+	64.8454i	−0.248450	+	0.248450i
$262$		0			0
$263$	−242.346	−	242.346i	−0.921467	−	0.921467i	0.0756659	−	0.997133i	$-0.475892\pi$
$263$	−242.346	−	242.346i	−0.921467	−	0.921467i	−0.997133	+	0.0756659i	$0.975892\pi$
$264$		0			0
$265$	−68.8374	−	81.0068i	−0.259764	−	0.305686i
$266$		0			0
$267$	−224.246			−0.839874
$268$		0			0
$269$	−164.004	+	164.004i	−0.609681	+	0.609681i	−0.942863	−	0.333182i	$-0.891878\pi$
$269$	−164.004	+	164.004i	−0.609681	+	0.609681i	0.333182	+	0.942863i	$0.391878\pi$
$270$		0			0
$271$	31.2546			0.115331			0.0576654	−	0.998336i	$-0.481634\pi$
$271$	31.2546			0.115331			0.0576654	+	0.998336i	$0.481634\pi$
$272$		0			0
$273$	−27.1810	+	27.1810i	−0.0995639	+	0.0995639i
$274$		0			0
$275$	7.18645	+	9.99586i	0.0261325	+	0.0363486i
$276$		0			0
$277$	257.269			0.928769			0.464384	−	0.885634i	$-0.346276\pi$
$277$	257.269			0.928769			0.464384	+	0.885634i	$0.346276\pi$
$278$		0			0
$279$	−8.58007			−0.0307529
$280$		0			0
$281$			139.247i			0.495543i	0.968819	+	0.247771i	$0.0796981\pi$
$281$			139.247i			0.495543i	−0.968819	+	0.247771i	$0.920302\pi$
$282$		0			0
$283$		−	516.051i		−	1.82350i	−0.410745	−	0.911750i	$-0.634731\pi$
$283$		−	516.051i		−	1.82350i	0.410745	−	0.911750i	$-0.365269\pi$
$284$		0			0
$285$	6.02565	−	74.1949i	0.0211426	−	0.260333i
$286$		0			0
$287$	−25.1208	−	25.1208i	−0.0875288	−	0.0875288i
$288$		0			0
$289$		−	6.86821i		−	0.0237654i
$290$		0			0
$291$	−76.5901	−	76.5901i	−0.263196	−	0.263196i
$292$		0			0
$293$		−	178.541i		−	0.609356i	−0.952455	−	0.304678i	$-0.901451\pi$
$293$		−	178.541i		−	0.609356i	0.952455	−	0.304678i	$-0.0985488\pi$
$294$		0			0
$295$	171.976	+	13.9668i	0.582971	+	0.0473452i
$296$		0			0
$297$	1.80935	−	1.80935i	0.00609208	−	0.00609208i
$298$		0			0
$299$	−108.110	−	108.110i	−0.361573	−	0.361573i
$300$		0			0
$301$	78.5044	+	78.5044i	0.260812	+	0.260812i
$302$		0			0
$303$	−36.2774	+	36.2774i	−0.119727	+	0.119727i
$304$		0			0
$305$	337.864	+	27.4392i	1.10775	+	0.0899645i
$306$		0			0
$307$		−	103.189i		−	0.336120i	−0.985777	−	0.168060i	$-0.946250\pi$
$307$		−	103.189i		−	0.336120i	0.985777	−	0.168060i	$-0.0537503\pi$
$308$		0			0
$309$	171.378	+	171.378i	0.554623	+	0.554623i
$310$		0			0
$311$			577.264i			1.85615i	0.372388	+	0.928077i	$0.378539\pi$
$311$			577.264i			1.85615i	−0.372388	+	0.928077i	$0.621461\pi$
$312$		0			0
$313$	72.0336	+	72.0336i	0.230139	+	0.230139i	0.812751	−	0.582612i	$-0.197969\pi$
$313$	72.0336	+	72.0336i	0.230139	+	0.230139i	−0.582612	+	0.812751i	$0.697969\pi$
$314$		0			0
$315$	−4.25842	+	52.4347i	−0.0135188	+	0.166459i
$316$		0			0
$317$			470.061i			1.48284i	0.671040	+	0.741421i	$0.265848\pi$
$317$			470.061i			1.48284i	−0.671040	+	0.741421i	$0.734152\pi$
$318$		0			0
$319$		−	15.0532i		−	0.0471887i
$320$		0			0
$321$	−236.378			−0.736379
$322$		0			0
$323$	−144.377			−0.446987
$324$		0			0
$325$	−25.5275	+	156.126i	−0.0785462	+	0.480387i
$326$		0			0
$327$	−45.1928	+	45.1928i	−0.138204	+	0.138204i
$328$		0			0
$329$	46.3007			0.140732
$330$		0			0
$331$	−192.710	+	192.710i	−0.582206	+	0.582206i	−0.935509	−	0.353303i	$-0.885058\pi$
$331$	−192.710	+	192.710i	−0.582206	+	0.582206i	0.353303	+	0.935509i	$0.385058\pi$
$332$		0			0
$333$	160.379			0.481620
$334$		0			0
$335$	−319.818	−	376.357i	−0.954681	−	1.12345i
$336$		0			0
$337$	256.418	+	256.418i	0.760883	+	0.760883i	0.976482	−	0.215599i	$-0.0691704\pi$
$337$	256.418	+	256.418i	0.760883	+	0.760883i	−0.215599	+	0.976482i	$0.569170\pi$
$338$		0			0
$339$	251.199	−	251.199i	0.740999	−	0.740999i
$340$		0			0
$341$	0.995887	−	0.995887i	0.00292049	−	0.00292049i
$342$		0			0
$343$	−212.530	−	212.530i	−0.619621	−	0.619621i
$344$		0			0
$345$	−208.556	−	16.9376i	−0.604509	−	0.0490944i
$346$		0			0
$347$	−165.582			−0.477182			−0.238591	−	0.971120i	$-0.576685\pi$
$347$	−165.582			−0.477182			−0.238591	+	0.971120i	$0.576685\pi$
$348$		0			0
$349$	−33.8885	+	33.8885i	−0.0971016	+	0.0971016i	−0.753989	−	0.656887i	$-0.771873\pi$
$349$	−33.8885	+	33.8885i	−0.0971016	+	0.0971016i	0.656887	+	0.753989i	$0.271873\pi$
$350$		0			0
$351$	32.8811			0.0936782
$352$		0			0
$353$	121.788	−	121.788i	0.345009	−	0.345009i	−0.513238	−	0.858247i	$-0.671554\pi$
$353$	121.788	−	121.788i	0.345009	−	0.345009i	0.858247	+	0.513238i	$0.171554\pi$
$354$		0			0
$355$	24.5588	+	28.9004i	0.0691797	+	0.0814096i
$356$		0			0
$357$	102.033			0.285808
$358$		0			0
$359$	−149.331			−0.415963			−0.207982	−	0.978133i	$-0.566689\pi$
$359$	−149.331			−0.415963			−0.207982	+	0.978133i	$0.566689\pi$
$360$		0			0
$361$			287.117i			0.795339i
$362$		0			0
$363$		−	209.158i		−	0.576193i
$364$		0			0
$365$	501.170	+	40.7019i	1.37307	+	0.111512i
$366$		0			0
$367$	119.158	+	119.158i	0.324682	+	0.324682i	0.850560	−	0.525878i	$-0.176263\pi$
$367$	119.158	+	119.158i	0.324682	+	0.324682i	−0.525878	+	0.850560i	$0.676263\pi$
$368$		0			0
$369$			30.3888i			0.0823545i
$370$		0			0
$371$	52.7257	+	52.7257i	0.142118	+	0.142118i
$372$		0			0
$373$		−	172.603i		−	0.462744i	−0.972865	−	0.231372i	$-0.925679\pi$
$373$		−	172.603i		−	0.462744i	0.972865	−	0.231372i	$-0.0743214\pi$
$374$		0			0
$375$	111.739	+	185.444i	0.297970	+	0.494517i
$376$		0			0
$377$	136.780	−	136.780i	0.362811	−	0.362811i
$378$		0			0
$379$	−0.854693	−	0.854693i	−0.00225513	−	0.00225513i	0.705978	−	0.708233i	$-0.250508\pi$
$379$	−0.854693	−	0.854693i	−0.00225513	−	0.00225513i	−0.708233	+	0.705978i	$0.750508\pi$
$380$		0			0
$381$	−260.979	−	260.979i	−0.684985	−	0.684985i
$382$		0			0
$383$	−217.613	+	217.613i	−0.568181	+	0.568181i	−0.931619	−	0.363438i	$-0.881603\pi$
$383$	−217.613	+	217.613i	−0.568181	+	0.568181i	0.363438	+	0.931619i	$0.381603\pi$
$384$		0			0
$385$	−5.59181	−	6.58036i	−0.0145242	−	0.0170918i
$386$		0			0
$387$		−	94.9676i		−	0.245394i
$388$		0			0
$389$	−377.146	−	377.146i	−0.969527	−	0.969527i	0.0300219	−	0.999549i	$-0.490442\pi$
$389$	−377.146	−	377.146i	−0.969527	−	0.969527i	−0.999549	+	0.0300219i	$0.990442\pi$
$390$		0			0
$391$			405.831i			1.03793i
$392$		0			0
$393$	−213.074	−	213.074i	−0.542172	−	0.542172i
$394$		0			0
$395$	475.541	+	559.610i	1.20390	+	1.41673i
$396$		0			0
$397$		−	78.3445i		−	0.197341i	−0.995120	−	0.0986706i	$-0.968541\pi$
$397$		−	78.3445i		−	0.197341i	0.995120	−	0.0986706i	$-0.0314590\pi$
$398$		0			0
$399$			52.2140i			0.130862i
$400$		0			0
$401$	−107.929			−0.269149			−0.134574	−	0.990903i	$-0.542967\pi$
$401$	−107.929			−0.269149			−0.134574	+	0.990903i	$0.542967\pi$
$402$		0			0
$403$	18.0981			0.0449085
$404$		0			0
$405$	34.2911	−	29.1397i	0.0846694	−	0.0719498i
$406$		0			0
$407$	−18.6152	+	18.6152i	−0.0457376	+	0.0457376i
$408$		0			0
$409$	−590.912			−1.44477			−0.722386	−	0.691490i	$-0.756955\pi$
$409$	−590.912			−1.44477			−0.722386	+	0.691490i	$0.756955\pi$
$410$		0			0
$411$	−78.4416	+	78.4416i	−0.190855	+	0.190855i
$412$		0			0
$413$	−121.027			−0.293043
$414$		0			0
$415$	298.464	−	253.626i	0.719190	−	0.611148i
$416$		0			0
$417$	−192.657	−	192.657i	−0.462006	−	0.462006i
$418$		0			0
$419$	−355.925	+	355.925i	−0.849463	+	0.849463i	−0.990066	−	0.140603i	$-0.955096\pi$
$419$	−355.925	+	355.925i	−0.849463	+	0.849463i	0.140603	+	0.990066i	$0.455096\pi$
$420$		0			0
$421$	6.82808	−	6.82808i	0.0162187	−	0.0162187i	−0.698951	−	0.715170i	$-0.746349\pi$
$421$	6.82808	−	6.82808i	0.0162187	−	0.0162187i	0.715170	+	0.698951i	$0.246349\pi$
$422$		0			0
$423$	−28.0052	−	28.0052i	−0.0662061	−	0.0662061i
$424$		0			0
$425$	340.950	−	245.123i	0.802235	−	0.576761i
$426$		0			0
$427$	−237.768			−0.556835
$428$		0			0
$429$	−3.81650	+	3.81650i	−0.00889626	+	0.00889626i
$430$		0			0
$431$	−195.688			−0.454033			−0.227016	−	0.973891i	$-0.572897\pi$
$431$	−195.688			−0.454033			−0.227016	+	0.973891i	$0.572897\pi$
$432$		0			0
$433$	−241.662	+	241.662i	−0.558112	+	0.558112i	−0.928770	−	0.370658i	$-0.879132\pi$
$433$	−241.662	+	241.662i	−0.558112	+	0.558112i	0.370658	+	0.928770i	$0.379132\pi$
$434$		0			0
$435$	21.4292	−	263.862i	0.0492625	−	0.606578i
$436$		0			0
$437$	−207.678			−0.475235
$438$		0			0
$439$	377.052			0.858889			0.429444	−	0.903093i	$-0.358709\pi$
$439$	377.052			0.858889			0.429444	+	0.903093i	$0.358709\pi$
$440$		0			0
$441$			110.100i			0.249659i
$442$		0			0
$443$			208.703i			0.471112i	0.971861	+	0.235556i	$0.0756911\pi$
$443$			208.703i			0.471112i	−0.971861	+	0.235556i	$0.924309\pi$
$444$		0			0
$445$	493.292	−	419.186i	1.10852	−	0.941991i
$446$		0			0
$447$	254.711	+	254.711i	0.569823	+	0.569823i
$448$		0			0
$449$		−	147.313i		−	0.328091i	−0.986453	−	0.164046i	$-0.947546\pi$
$449$		−	147.313i		−	0.328091i	0.986453	−	0.164046i	$-0.0524544\pi$
$450$		0			0
$451$	−3.52722	−	3.52722i	−0.00782089	−	0.00782089i
$452$		0			0
$453$		−	150.649i		−	0.332559i
$454$		0			0
$455$	8.98237	−	110.602i	0.0197415	−	0.243081i
$456$		0			0
$457$	321.992	−	321.992i	0.704578	−	0.704578i	−0.260812	−	0.965390i	$-0.583990\pi$
$457$	321.992	−	321.992i	0.704578	−	0.704578i	0.965390	+	0.260812i	$0.0839901\pi$
$458$		0			0
$459$	−61.7153	−	61.7153i	−0.134456	−	0.134456i
$460$		0			0
$461$	−14.3839	−	14.3839i	−0.0312014	−	0.0312014i	0.691334	−	0.722535i	$-0.257023\pi$
$461$	−14.3839	−	14.3839i	−0.0312014	−	0.0312014i	−0.722535	+	0.691334i	$0.757023\pi$
$462$		0			0
$463$	470.642	−	470.642i	1.01651	−	1.01651i	0.0166443	−	0.999861i	$-0.494702\pi$
$463$	470.642	−	470.642i	1.01651	−	1.01651i	0.999861	−	0.0166443i	$-0.00529830\pi$
$464$		0			0
$465$	18.8742	−	16.0388i	0.0405897	−	0.0344921i
$466$		0			0
$467$			112.993i			0.241954i	0.992655	+	0.120977i	$0.0386028\pi$
$467$			112.993i			0.241954i	−0.992655	+	0.120977i	$0.961397\pi$
$468$		0			0
$469$	244.963	+	244.963i	0.522310	+	0.522310i
$470$		0			0
$471$		−	156.985i		−	0.333302i
$472$		0			0
$473$	11.0229	+	11.0229i	0.0233042	+	0.0233042i
$474$		0			0
$475$	125.438	+	174.476i	0.264081	+	0.367318i
$476$		0			0
$477$		−	63.7828i		−	0.133717i
$478$		0			0
$479$		−	731.858i		−	1.52789i	−0.645283	−	0.763943i	$-0.723261\pi$
$479$		−	731.858i		−	1.52789i	0.645283	−	0.763943i	$-0.276739\pi$
$480$		0			0
$481$	−338.292			−0.703309
$482$		0			0
$483$	146.769			0.303870
$484$		0			0
$485$	311.652	+	25.3104i	0.642581	+	0.0521864i
$486$		0			0
$487$	−259.467	+	259.467i	−0.532787	+	0.532787i	−0.921401	−	0.388613i	$-0.872954\pi$
$487$	−259.467	+	259.467i	−0.532787	+	0.532787i	0.388613	+	0.921401i	$0.372954\pi$
$488$		0			0
$489$	−236.743			−0.484136
$490$		0			0
$491$	316.449	−	316.449i	0.644500	−	0.644500i	−0.307159	−	0.951658i	$-0.599378\pi$
$491$	316.449	−	316.449i	0.644500	−	0.644500i	0.951658	+	0.307159i	$0.0993783\pi$
$492$		0			0
$493$	−513.451			−1.04148
$494$		0			0
$495$	−0.597928	+	7.36240i	−0.00120793	+	0.0148735i
$496$		0			0
$497$	−18.8107	−	18.8107i	−0.0378485	−	0.0378485i
$498$		0			0
$499$	−54.3250	+	54.3250i	−0.108868	+	0.108868i	−0.759442	−	0.650575i	$-0.774528\pi$
$499$	−54.3250	+	54.3250i	−0.108868	+	0.108868i	0.650575	+	0.759442i	$0.274528\pi$
$500$		0			0
$501$	−162.415	+	162.415i	−0.324181	+	0.324181i
$502$		0			0
$503$	293.378	+	293.378i	0.583255	+	0.583255i	0.935796	−	0.352541i	$-0.114682\pi$
$503$	293.378	+	293.378i	0.583255	+	0.583255i	−0.352541	+	0.935796i	$0.614682\pi$
$504$		0			0
$505$	11.9884	−	147.616i	0.0237395	−	0.292309i
$506$		0			0
$507$	223.360			0.440552
$508$		0			0
$509$	123.743	−	123.743i	0.243111	−	0.243111i	−0.575025	−	0.818136i	$-0.695008\pi$
$509$	123.743	−	123.743i	0.243111	−	0.243111i	0.818136	+	0.575025i	$0.195008\pi$
$510$		0			0
$511$	−352.694			−0.690203
$512$		0			0
$513$	31.5819	−	31.5819i	0.0615631	−	0.0615631i
$514$		0			0
$515$	−697.354	−	56.6347i	−1.35408	−	0.109970i
$516$		0			0
$517$	6.50111			0.0125747
$518$		0			0
$519$	256.043			0.493340
$520$		0			0
$521$			507.415i			0.973925i	0.873423	+	0.486963i	$0.161895\pi$
$521$			507.415i			0.973925i	−0.873423	+	0.486963i	$0.838105\pi$
$522$		0			0
$523$		−	608.027i		−	1.16258i	−0.813698	−	0.581288i	$-0.802549\pi$
$523$		−	608.027i		−	1.16258i	0.813698	−	0.581288i	$-0.197451\pi$
$524$		0			0
$525$	−88.6492	−	123.305i	−0.168856	−	0.234867i
$526$		0			0
$527$	−33.9688	−	33.9688i	−0.0644570	−	0.0644570i
$528$		0			0
$529$			54.7646i			0.103525i
$530$		0			0
$531$	73.2036	+	73.2036i	0.137860	+	0.137860i
$532$		0			0
$533$		−	64.0997i		−	0.120262i
$534$		0			0
$535$	519.978	−	441.863i	0.971921	−	0.825913i
$536$		0			0
$537$	−17.1750	+	17.1750i	−0.0319832	+	0.0319832i
$538$		0			0
$539$	−12.7792	−	12.7792i	−0.0237092	−	0.0237092i
$540$		0			0
$541$	184.245	+	184.245i	0.340563	+	0.340563i	0.856579	−	0.516016i	$-0.172585\pi$
$541$	184.245	+	184.245i	0.340563	+	0.340563i	−0.516016	+	0.856579i	$0.672585\pi$
$542$		0			0
$543$	−184.080	+	184.080i	−0.339006	+	0.339006i
$544$		0			0
$545$	14.9347	−	183.893i	0.0274030	−	0.337419i
$546$		0			0
$547$			235.706i			0.430907i	0.976514	+	0.215454i	$0.0691230\pi$
$547$			235.706i			0.430907i	−0.976514	+	0.215454i	$0.930877\pi$
$548$		0			0
$549$	143.815	+	143.815i	0.261959	+	0.261959i
$550$		0			0
$551$		−	262.751i		−	0.476862i
$552$		0			0
$553$	−364.239	−	364.239i	−0.658660	−	0.658660i
$554$		0			0
$555$	−352.799	+	299.799i	−0.635673	+	0.540178i
$556$		0			0
$557$			625.647i			1.12324i	0.827394	+	0.561622i	$0.189822\pi$
$557$			625.647i			1.12324i	−0.827394	+	0.561622i	$0.810178\pi$
$558$		0			0
$559$			200.317i			0.358349i
$560$		0			0
$561$	14.3266			0.0255376
$562$		0			0
$563$	−488.327			−0.867366			−0.433683	−	0.901065i	$-0.642786\pi$
$563$	−488.327			−0.867366			−0.433683	+	0.901065i	$0.642786\pi$
$564$		0			0
$565$	−83.0125	+	1022.15i	−0.146925	+	1.80911i
$566$		0			0
$567$	−22.3194	+	22.3194i	−0.0393640	+	0.0393640i
$568$		0			0
$569$	−568.948			−0.999908			−0.499954	−	0.866052i	$-0.666650\pi$
$569$	−568.948			−0.999908			−0.499954	+	0.866052i	$0.666650\pi$
$570$		0			0
$571$	278.362	−	278.362i	0.487500	−	0.487500i	−0.420017	−	0.907516i	$-0.637976\pi$
$571$	278.362	−	278.362i	0.487500	−	0.487500i	0.907516	+	0.420017i	$0.137976\pi$
$572$		0			0
$573$	223.664			0.390339
$574$		0			0
$575$	490.437	−	352.596i	0.852934	−	0.613211i
$576$		0			0
$577$	99.8357	+	99.8357i	0.173025	+	0.173025i	0.788307	−	0.615282i	$-0.210958\pi$
$577$	99.8357	+	99.8357i	0.173025	+	0.173025i	−0.615282	+	0.788307i	$0.710958\pi$
$578$		0			0
$579$	−251.288	+	251.288i	−0.434004	+	0.434004i
$580$		0			0
$581$	−194.264	+	194.264i	−0.334362	+	0.334362i
$582$		0			0
$583$	7.40326	+	7.40326i	0.0126986	+	0.0126986i
$584$		0			0
$585$	−72.3309	+	61.4649i	−0.123643	+	0.105068i
$586$		0			0
$587$	557.705			0.950094			0.475047	−	0.879960i	$-0.342431\pi$
$587$	557.705			0.950094			0.475047	+	0.879960i	$0.342431\pi$
$588$		0			0
$589$	17.3830	−	17.3830i	0.0295128	−	0.0295128i
$590$		0			0
$591$	678.496			1.14805
$592$		0			0
$593$	271.601	−	271.601i	0.458012	−	0.458012i	−0.439991	−	0.898002i	$-0.645018\pi$
$593$	271.601	−	271.601i	0.458012	−	0.458012i	0.898002	+	0.439991i	$0.145018\pi$
$594$		0			0
$595$	−224.450	+	190.732i	−0.377227	+	0.320558i
$596$		0			0
$597$	191.313			0.320458
$598$		0			0
$599$	−173.826			−0.290194			−0.145097	−	0.989417i	$-0.546349\pi$
$599$	−173.826			−0.290194			−0.145097	+	0.989417i	$0.546349\pi$
$600$		0			0
$601$			502.850i			0.836689i	0.908288	+	0.418345i	$0.137390\pi$
$601$			502.850i			0.836689i	−0.908288	+	0.418345i	$0.862610\pi$
$602$		0			0
$603$		−	296.335i		−	0.491434i
$604$		0			0
$605$	390.981	+	460.101i	0.646250	+	0.760497i
$606$		0			0
$607$	664.932	+	664.932i	1.09544	+	1.09544i	0.994937	+	0.100502i	$0.0320450\pi$
$607$	664.932	+	664.932i	1.09544	+	1.09544i	0.100502	+	0.994937i	$0.467955\pi$
$608$		0			0
$609$			185.690i			0.304910i
$610$		0			0
$611$	59.0719	+	59.0719i	0.0966807	+	0.0966807i
$612$		0			0
$613$			474.479i			0.774027i	0.922074	+	0.387014i	$0.126493\pi$
$613$			474.479i			0.774027i	−0.922074	+	0.387014i	$0.873507\pi$
$614$		0			0
$615$	−56.8061	−	66.8486i	−0.0923677	−	0.108697i
$616$		0			0
$617$	807.635	−	807.635i	1.30897	−	1.30897i	0.386812	−	0.922159i	$-0.373576\pi$
$617$	807.635	−	807.635i	1.30897	−	1.30897i	0.922159	−	0.386812i	$-0.126424\pi$
$618$		0			0
$619$	461.288	+	461.288i	0.745215	+	0.745215i	0.973576	−	0.228361i	$-0.0733367\pi$
$619$	461.288	+	461.288i	0.745215	+	0.745215i	−0.228361	+	0.973576i	$0.573337\pi$
$620$		0			0
$621$	−88.7740	−	88.7740i	−0.142953	−	0.142953i
$622$		0			0
$623$	−321.074	+	321.074i	−0.515368	+	0.515368i
$624$		0			0
$625$	−592.452	−	199.061i	−0.947924	−	0.318497i
$626$		0			0
$627$			7.33141i			0.0116928i
$628$		0			0
$629$	634.948	+	634.948i	1.00946	+	1.00946i
$630$		0			0
$631$			278.307i			0.441057i	0.975381	+	0.220529i	$0.0707782\pi$
$631$			278.307i			0.441057i	−0.975381	+	0.220529i	$0.929222\pi$
$632$		0			0
$633$	−338.875	−	338.875i	−0.535348	−	0.535348i
$634$		0			0
$635$	1061.95	+	86.2447i	1.67236	+	0.135818i
$636$		0			0
$637$		−	232.235i		−	0.364576i
$638$		0			0
$639$			22.7555i			0.0356111i
$640$		0			0
$641$	565.878			0.882804			0.441402	−	0.897309i	$-0.354481\pi$
$641$	565.878			0.882804			0.441402	+	0.897309i	$0.354481\pi$
$642$		0			0
$643$	−226.198			−0.351785			−0.175893	−	0.984409i	$-0.556281\pi$
$643$	−226.198			−0.351785			−0.175893	+	0.984409i	$0.556281\pi$
$644$		0			0
$645$	177.524	+	208.907i	0.275231	+	0.323887i
$646$		0			0
$647$	537.803	−	537.803i	0.831225	−	0.831225i	−0.156459	−	0.987684i	$-0.550008\pi$
$647$	537.803	−	537.803i	0.831225	−	0.831225i	0.987684	+	0.156459i	$0.0500080\pi$
$648$		0			0
$649$	−16.9935			−0.0261841
$650$		0			0
$651$	−12.2849	+	12.2849i	−0.0188708	+	0.0188708i
$652$		0			0
$653$	−747.369			−1.14452			−0.572258	−	0.820074i	$-0.693932\pi$
$653$	−747.369			−1.14452			−0.572258	+	0.820074i	$0.693932\pi$
$654$		0			0
$655$	867.015	+	70.4135i	1.32369	+	0.107502i
$656$		0			0
$657$	213.329	+	213.329i	0.324701	+	0.324701i
$658$		0			0
$659$	−714.948	+	714.948i	−1.08490	+	1.08490i	−0.0888541	+	0.996045i	$0.528320\pi$
$659$	−714.948	+	714.948i	−1.08490	+	1.08490i	−0.996045	+	0.0888541i	$0.971680\pi$
$660$		0			0
$661$	1.34879	−	1.34879i	0.00204053	−	0.00204053i	−0.706086	−	0.708126i	$-0.749541\pi$
$661$	1.34879	−	1.34879i	0.00204053	−	0.00204053i	0.708126	+	0.706086i	$0.249541\pi$
$662$		0			0
$663$	130.177	+	130.177i	0.196346	+	0.196346i
$664$		0			0
$665$	−97.6042	−	114.859i	−0.146773	−	0.172720i
$666$		0			0
$667$	−738.570			−1.10730
$668$		0			0
$669$	261.871	−	261.871i	0.391436	−	0.391436i
$670$		0			0
$671$	−33.3852			−0.0497544
$672$		0			0
$673$	618.150	−	618.150i	0.918499	−	0.918499i	−0.0784214	−	0.996920i	$-0.524988\pi$
$673$	618.150	−	618.150i	0.918499	−	0.918499i	0.996920	+	0.0784214i	$0.0249880\pi$
$674$		0			0
$675$	−20.9617	+	128.201i	−0.0310544	+	0.189928i
$676$		0			0
$677$	−523.647			−0.773481			−0.386741	−	0.922189i	$-0.626399\pi$
$677$	−523.647			−0.773481			−0.386741	+	0.922189i	$0.626399\pi$
$678$		0			0
$679$	−219.322			−0.323007
$680$		0			0
$681$			520.629i			0.764507i
$682$		0			0
$683$			1171.63i			1.71542i	0.514130	+	0.857712i	$0.328115\pi$
$683$			1171.63i			1.71542i	−0.514130	+	0.857712i	$0.671885\pi$
$684$		0			0
$685$	25.9223	−	319.186i	0.0378427	−	0.465964i
$686$		0			0
$687$	556.403	+	556.403i	0.809902	+	0.809902i
$688$		0			0
$689$			134.538i			0.195266i
$690$		0			0
$691$	−462.015	−	462.015i	−0.668618	−	0.668618i	0.288778	−	0.957396i	$-0.406751\pi$
$691$	−462.015	−	462.015i	−0.668618	−	0.668618i	−0.957396	+	0.288778i	$0.906751\pi$
$692$		0			0
$693$		−	5.18122i		−	0.00747651i
$694$		0			0
$695$	783.936	+	63.6664i	1.12797	+	0.0916063i
$696$		0			0
$697$	−120.310	+	120.310i	−0.172612	+	0.172612i
$698$		0			0
$699$	−166.442	−	166.442i	−0.238115	−	0.238115i
$700$		0			0
$701$	−389.869	−	389.869i	−0.556161	−	0.556161i	0.372051	−	0.928212i	$-0.378655\pi$
$701$	−389.869	−	389.869i	−0.556161	−	0.556161i	−0.928212	+	0.372051i	$0.878655\pi$
$702$		0			0
$703$	−324.925	+	324.925i	−0.462198	+	0.462198i
$704$		0			0
$705$	113.955	+	9.25475i	0.161639	+	0.0131273i
$706$		0			0
$707$			103.883i			0.146935i
$708$		0			0
$709$	783.751	+	783.751i	1.10543	+	1.10543i	0.993743	+	0.111689i	$0.0356260\pi$
$709$	783.751	+	783.751i	1.10543	+	1.10543i	0.111689	+	0.993743i	$0.464374\pi$
$710$		0			0
$711$			440.623i			0.619723i
$712$		0			0
$713$	−48.8623	−	48.8623i	−0.0685305	−	0.0685305i
$714$		0			0
$715$	1.26122	−	15.5297i	0.00176395	−	0.0217198i
$716$		0			0
$717$			688.720i			0.960558i
$718$		0			0
$719$		−	1035.43i		−	1.44009i	−0.693925	−	0.720047i	$-0.744120\pi$
$719$		−	1035.43i		−	1.44009i	0.693925	−	0.720047i	$-0.255880\pi$
$720$		0			0
$721$	490.756			0.680660
$722$		0			0
$723$	−305.856			−0.423037
$724$		0			0
$725$	446.100	+	620.494i	0.615310	+	0.855854i
$726$		0			0
$727$	564.170	−	564.170i	0.776024	−	0.776024i	−0.203128	−	0.979152i	$-0.565111\pi$
$727$	564.170	−	564.170i	0.776024	−	0.776024i	0.979152	+	0.203128i	$0.0651107\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$		0			0
$731$	375.980	−	375.980i	0.514337	−	0.514337i
$732$		0			0
$733$	−663.374			−0.905012			−0.452506	−	0.891761i	$-0.649470\pi$
$733$	−663.374			−0.905012			−0.452506	+	0.891761i	$0.649470\pi$
$734$		0			0
$735$	−205.810	−	242.194i	−0.280014	−	0.329516i
$736$		0			0
$737$	34.3955	+	34.3955i	0.0466696	+	0.0466696i
$738$		0			0
$739$	−132.239	+	132.239i	−0.178944	+	0.178944i	−0.790895	−	0.611952i	$-0.790385\pi$
$739$	−132.239	+	132.239i	−0.178944	+	0.178944i	0.611952	+	0.790895i	$0.290385\pi$
$740$		0			0
$741$	−66.6163	+	66.6163i	−0.0899006	+	0.0899006i
$742$		0			0
$743$	654.544	+	654.544i	0.880947	+	0.880947i	0.993631	−	0.112684i	$-0.0359448\pi$
$743$	654.544	+	654.544i	0.880947	+	0.880947i	−0.112684	+	0.993631i	$0.535945\pi$
$744$		0			0
$745$	−1036.44	−	84.1732i	−1.39119	−	0.112984i
$746$		0			0
$747$	235.003			0.314596
$748$		0			0
$749$	−338.443	+	338.443i	−0.451860	+	0.451860i
$750$		0			0
$751$	−1444.23			−1.92308			−0.961539	−	0.274668i	$-0.911432\pi$
$751$	−1444.23			−1.92308			−0.961539	+	0.274668i	$0.911432\pi$
$752$		0			0
$753$	269.119	−	269.119i	0.357396	−	0.357396i
$754$		0			0
$755$	281.610	+	331.394i	0.372993	+	0.438932i
$756$		0			0
$757$	1058.07			1.39771			0.698855	−	0.715264i	$-0.253693\pi$
$757$	1058.07			1.39771			0.698855	+	0.715264i	$0.253693\pi$
$758$		0			0
$759$	20.6080			0.0271515
$760$		0			0
$761$		−	282.437i		−	0.371139i	−0.982631	−	0.185569i	$-0.940587\pi$
$761$		−	282.437i		−	0.371139i	0.982631	−	0.185569i	$-0.0594129\pi$
$762$		0			0
$763$			129.413i			0.169611i
$764$		0			0
$765$	251.125	+	20.3948i	0.328268	+	0.0266599i
$766$		0			0
$767$	−154.410	−	154.410i	−0.201317	−	0.201317i
$768$		0			0
$769$		−	1321.92i		−	1.71901i	−0.511127	−	0.859505i	$-0.670772\pi$
$769$		−	1321.92i		−	1.71901i	0.511127	−	0.859505i	$-0.329228\pi$
$770$		0			0
$771$	556.651	+	556.651i	0.721986	+	0.721986i
$772$		0			0
$773$			88.8442i			0.114934i	0.998347	+	0.0574671i	$0.0183024\pi$
$773$			88.8442i			0.114934i	−0.998347	+	0.0574671i	$0.981698\pi$
$774$		0			0
$775$	−11.5376	+	70.5636i	−0.0148872	+	0.0910498i
$776$		0			0
$777$	229.630	−	229.630i	0.295534	−	0.295534i
$778$		0			0
$779$	−61.5671	−	61.5671i	−0.0790335	−	0.0790335i
$780$		0			0
$781$	−2.64122	−	2.64122i	−0.00338185	−	0.00338185i
$782$		0			0
$783$	112.316	−	112.316i	0.143443	−	0.143443i
$784$		0			0
$785$	293.454	+	345.333i	0.373827	+	0.439914i
$786$		0			0
$787$		−	1408.42i		−	1.78961i	−0.446459	−	0.894804i	$-0.647315\pi$
$787$		−	1408.42i		−	1.78961i	0.446459	−	0.894804i	$-0.352685\pi$
$788$		0			0
$789$	419.755	+	419.755i	0.532009	+	0.532009i
$790$		0			0
$791$		−	719.328i		−	0.909390i
$792$		0			0
$793$	−303.353	−	303.353i	−0.382538	−	0.382538i
$794$		0			0
$795$	119.230	+	140.308i	0.149975	+	0.176488i
$796$		0			0
$797$		−	214.836i		−	0.269556i	−0.990876	−	0.134778i	$-0.956968\pi$
$797$		−	214.836i		−	0.269556i	0.990876	−	0.134778i	$-0.0430321\pi$
$798$		0			0
$799$		−	221.747i		−	0.277531i
$800$		0			0
$801$	388.406			0.484902
$802$		0			0
$803$	−49.5220			−0.0616712
$804$		0			0
$805$	−322.859	+	274.357i	−0.401067	+	0.340816i
$806$		0			0
$807$	284.064	−	284.064i	0.352000	−	0.352000i
$808$		0			0
$809$	1149.79			1.42124			0.710622	−	0.703574i	$-0.248413\pi$
$809$	1149.79			1.42124			0.710622	+	0.703574i	$0.248413\pi$
$810$		0			0
$811$	−612.466	+	612.466i	−0.755198	+	0.755198i	−0.975444	−	0.220246i	$-0.929314\pi$
$811$	−612.466	+	612.466i	−0.755198	+	0.755198i	0.220246	+	0.975444i	$0.429314\pi$
$812$		0			0
$813$	−54.1346			−0.0665862
$814$		0			0
$815$	520.781	−	442.545i	0.638995	−	0.543000i
$816$		0			0
$817$	192.402	+	192.402i	0.235498	+	0.235498i
$818$		0			0
$819$	47.0788	−	47.0788i	0.0574833	−	0.0574833i
$820$		0			0
$821$	117.719	−	117.719i	0.143385	−	0.143385i	−0.631771	−	0.775155i	$-0.717672\pi$
$821$	117.719	−	117.719i	0.143385	−	0.143385i	0.775155	+	0.631771i	$0.217672\pi$
$822$		0			0
$823$	503.108	+	503.108i	0.611310	+	0.611310i	0.943287	−	0.331978i	$-0.107716\pi$
$823$	503.108	+	503.108i	0.611310	+	0.611310i	−0.331978	+	0.943287i	$0.607716\pi$
$824$		0			0
$825$	−12.4473	−	17.3133i	−0.0150876	−	0.0209859i
$826$		0			0
$827$	−1133.23			−1.37029			−0.685145	−	0.728406i	$-0.740261\pi$
$827$	−1133.23			−1.37029			−0.685145	+	0.728406i	$0.740261\pi$
$828$		0			0
$829$	1059.24	−	1059.24i	1.27773	−	1.27773i	0.335794	−	0.941935i	$-0.390995\pi$
$829$	1059.24	−	1059.24i	1.27773	−	1.27773i	0.941935	−	0.335794i	$-0.109005\pi$
$830$		0			0
$831$	−445.603			−0.536225
$832$		0			0
$833$	−435.888	+	435.888i	−0.523275	+	0.523275i
$834$		0			0
$835$	53.6725	−	660.879i	0.0642784	−	0.791472i
$836$		0			0
$837$	14.8611			0.0177552
$838$		0			0
$839$	−634.998			−0.756851			−0.378426	−	0.925632i	$-0.623534\pi$
$839$	−634.998			−0.756851			−0.378426	+	0.925632i	$0.623534\pi$
$840$		0			0
$841$		−	93.4285i		−	0.111092i
$842$		0			0
$843$		−	241.184i		−	0.286102i
$844$		0			0
$845$	−491.342	+	417.529i	−0.581469	+	0.494117i
$846$		0			0
$847$	−299.471	−	299.471i	−0.353566	−	0.353566i
$848$		0			0
$849$			893.826i			1.05280i
$850$		0			0
$851$	913.337	+	913.337i	1.07325	+	1.07325i
$852$		0			0
$853$		−	736.362i		−	0.863261i	−0.902051	−	0.431630i	$-0.857938\pi$
$853$		−	736.362i		−	0.863261i	0.902051	−	0.431630i	$-0.142062\pi$
$854$		0			0
$855$	−10.4367	+	128.509i	−0.0122067	+	0.150303i
$856$		0			0
$857$	285.114	−	285.114i	0.332688	−	0.332688i	−0.520918	−	0.853607i	$-0.674410\pi$
$857$	285.114	−	285.114i	0.332688	−	0.332688i	0.853607	+	0.520918i	$0.174410\pi$
$858$		0			0
$859$	535.646	+	535.646i	0.623570	+	0.623570i	0.946442	−	0.322873i	$-0.104649\pi$
$859$	535.646	+	535.646i	0.623570	+	0.623570i	−0.322873	+	0.946442i	$0.604649\pi$
$860$		0			0
$861$	43.5104	+	43.5104i	0.0505348	+	0.0505348i
$862$		0			0
$863$	152.045	−	152.045i	0.176182	−	0.176182i	−0.613507	−	0.789689i	$-0.710242\pi$
$863$	152.045	−	152.045i	0.176182	−	0.176182i	0.789689	+	0.613507i	$0.210242\pi$
$864$		0			0
$865$	−563.238	+	478.624i	−0.651142	+	0.553323i
$866$		0			0
$867$			11.8961i			0.0137210i
$868$		0			0
$869$	−51.1431	−	51.1431i	−0.0588528	−	0.0588528i
$870$		0			0
$871$			625.065i			0.717640i
$872$		0			0
$873$	132.658	+	132.658i	0.151956	+	0.151956i
$874$		0			0
$875$	425.503	+	105.530i	0.486290	+	0.120606i
$876$		0			0
$877$			777.146i			0.886142i	0.896487	+	0.443071i	$0.146111\pi$
$877$			777.146i			0.886142i	−0.896487	+	0.443071i	$0.853889\pi$
$878$		0			0
$879$			309.242i			0.351812i
$880$		0			0
$881$	359.196			0.407715			0.203857	−	0.979001i	$-0.434652\pi$
$881$	359.196			0.407715			0.203857	+	0.979001i	$0.434652\pi$
$882$		0			0
$883$	634.549			0.718629			0.359314	−	0.933217i	$-0.383011\pi$
$883$	634.549			0.718629			0.359314	+	0.933217i	$0.383011\pi$
$884$		0			0
$885$	−297.872	−	24.1913i	−0.336578	−	0.0273348i
$886$		0			0
$887$	−1206.72	+	1206.72i	−1.36045	+	1.36045i	−0.487112	+	0.873340i	$0.661950\pi$
$887$	−1206.72	+	1206.72i	−1.36045	+	1.36045i	−0.873340	+	0.487112i	$0.838050\pi$
$888$		0			0
$889$	−747.336			−0.840648
$890$		0			0
$891$	−3.13388	+	3.13388i	−0.00351727	+	0.00351727i
$892$		0			0
$893$	113.476			0.127073
$894$		0			0
$895$	5.67574	−	69.8864i	0.00634161	−	0.0780854i
$896$		0			0
$897$	187.253	+	187.253i	0.208755	+	0.208755i
$898$		0			0
$899$	61.8198	−	61.8198i	0.0687651	−	0.0687651i
$900$		0			0
$901$	252.519	−	252.519i	0.280265	−	0.280265i
$902$		0			0
$903$	−135.974	−	135.974i	−0.150580	−	0.150580i
$904$		0			0
$905$	60.8322	−	749.038i	0.0672179	−	0.827666i
$906$		0			0
$907$	−1583.66			−1.74604			−0.873020	−	0.487685i	$-0.837841\pi$
$907$	−1583.66			−1.74604			−0.873020	+	0.487685i	$0.837841\pi$
$908$		0			0
$909$	62.8343	−	62.8343i	0.0691247	−	0.0691247i
$910$		0			0
$911$	518.048			0.568658			0.284329	−	0.958727i	$-0.408229\pi$
$911$	518.048			0.568658			0.284329	+	0.958727i	$0.408229\pi$
$912$		0			0
$913$	−27.2768	+	27.2768i	−0.0298760	+	0.0298760i
$914$		0			0
$915$	−585.197	−	47.5260i	−0.639559	−	0.0519410i
$916$		0			0
$917$	−610.154			−0.665381
$918$		0			0
$919$	−840.571			−0.914658			−0.457329	−	0.889298i	$-0.651194\pi$
$919$	−840.571			−0.914658			−0.457329	+	0.889298i	$0.651194\pi$
$920$		0			0
$921$			178.729i			0.194059i
$922$		0			0
$923$		−	47.9986i		−	0.0520028i
$924$		0			0
$925$	215.661	−	1318.98i	0.233147	−	1.42592i
$926$		0			0
$927$	−296.836	−	296.836i	−0.320212	−	0.320212i
$928$		0			0
$929$		−	211.525i		−	0.227691i	−0.993498	−	0.113846i	$-0.963683\pi$
$929$		−	211.525i		−	0.227691i	0.993498	−	0.113846i	$-0.0363169\pi$
$930$		0			0
$931$	−223.059	−	223.059i	−0.239591	−	0.239591i
$932$		0			0
$933$		−	999.850i		−	1.07165i
$934$		0			0
$935$	−31.5152	+	26.7808i	−0.0337061	+	0.0286426i
$936$		0			0
$937$	1120.07	−	1120.07i	1.19538	−	1.19538i	0.219846	−	0.975535i	$-0.429445\pi$
$937$	1120.07	−	1120.07i	1.19538	−	1.19538i	0.975535	−	0.219846i	$-0.0705554\pi$
$938$		0			0
$939$	−124.766	−	124.766i	−0.132871	−	0.132871i
$940$		0			0
$941$	694.013	+	694.013i	0.737527	+	0.737527i	0.972099	−	0.234572i	$-0.0753688\pi$
$941$	694.013	+	694.013i	0.737527	+	0.737527i	−0.234572	+	0.972099i	$0.575369\pi$
$942$		0			0
$943$	−173.060	+	173.060i	−0.183521	+	0.183521i
$944$		0			0
$945$	7.37580	−	90.8196i	0.00780508	−	0.0961054i
$946$		0			0
$947$			296.948i			0.313567i	0.987633	+	0.156784i	$0.0501126\pi$
$947$			296.948i			0.313567i	−0.987633	+	0.156784i	$0.949887\pi$
$948$		0			0
$949$	−449.978	−	449.978i	−0.474160	−	0.474160i
$950$		0			0
$951$		−	814.169i		−	0.856119i
$952$		0			0
$953$	936.638	+	936.638i	0.982831	+	0.982831i	0.999855	−	0.0170241i	$-0.00541920\pi$
$953$	936.638	+	936.638i	0.982831	+	0.982831i	−0.0170241	+	0.999855i	$0.505419\pi$
$954$		0			0
$955$	−492.011	+	418.097i	−0.515194	+	0.437798i
$956$		0			0
$957$			26.0729i			0.0272444i
$958$		0			0
$959$			224.624i			0.234227i
$960$		0			0
$961$	−952.820			−0.991488
$962$		0			0
$963$	409.418			0.425149
$964$		0			0
$965$	83.0422	−	1022.51i	0.0860541	−	1.05960i
$966$		0			0
$967$	547.943	−	547.943i	0.566643	−	0.566643i	−0.364544	−	0.931186i	$-0.618775\pi$
$967$	547.943	−	547.943i	0.566643	−	0.566643i	0.931186	+	0.364544i	$0.118775\pi$
$968$		0			0
$969$	250.068			0.258068
$970$		0			0
$971$	473.250	−	473.250i	0.487384	−	0.487384i	−0.420096	−	0.907480i	$-0.638004\pi$
$971$	473.250	−	473.250i	0.487384	−	0.487384i	0.907480	+	0.420096i	$0.138004\pi$
$972$		0			0
$973$	−551.688			−0.566997
$974$		0			0
$975$	44.2149	−	270.418i	0.0453486	−	0.277352i
$976$		0			0
$977$	24.5422	+	24.5422i	0.0251200	+	0.0251200i	0.719555	−	0.694435i	$-0.244346\pi$
$977$	24.5422	+	24.5422i	0.0251200	+	0.0251200i	−0.694435	+	0.719555i	$0.744346\pi$
$978$		0			0
$979$	−45.0822	+	45.0822i	−0.0460493	+	0.0460493i
$980$		0			0
$981$	78.2762	−	78.2762i	0.0797922	−	0.0797922i
$982$		0			0
$983$	−67.9656	−	67.9656i	−0.0691410	−	0.0691410i	0.671691	−	0.740832i	$-0.265568\pi$
$983$	−67.9656	−	67.9656i	−0.0691410	−	0.0691410i	−0.740832	+	0.671691i	$0.765568\pi$
$984$		0			0
$985$	−1492.54	+	1268.32i	−1.51527	+	1.28763i
$986$		0			0
$987$	−80.1951			−0.0812514
$988$		0			0
$989$	540.826	−	540.826i	0.546842	−	0.546842i
$990$		0			0
$991$	−1243.98			−1.25528			−0.627641	−	0.778503i	$-0.715979\pi$
$991$	−1243.98			−1.25528			−0.627641	+	0.778503i	$0.715979\pi$
$992$		0			0
$993$	333.784	−	333.784i	0.336137	−	0.336137i
$994$		0			0
$995$	−420.847	+	357.624i	−0.422961	+	0.359421i
$996$		0			0
$997$	−1682.45			−1.68752			−0.843758	−	0.536723i	$-0.819662\pi$
$997$	−1682.45			−1.68752			−0.843758	+	0.536723i	$0.819662\pi$
$998$		0			0
$999$	−277.785			−0.278063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.be.a.337.16		96
4.3	odd	2		240.3.be.a.157.32	yes	96
5.3	odd	4		960.3.ba.a.913.16		96
16.5	even	4		960.3.ba.a.817.33		96
16.11	odd	4		240.3.ba.a.37.8	yes	96
20.3	even	4		240.3.ba.a.13.8	✓	96
80.43	even	4		240.3.be.a.133.32	yes	96
80.53	odd	4	inner	960.3.be.a.433.16		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.3.ba.a.13.8	✓	96	20.3	even	4
240.3.ba.a.37.8	yes	96	16.11	odd	4
240.3.be.a.133.32	yes	96	80.43	even	4
240.3.be.a.157.32	yes	96	4.3	odd	2
960.3.ba.a.817.33		96	16.5	even	4
960.3.ba.a.913.16		96	5.3	odd	4
960.3.be.a.337.16		96	1.1	even	1	trivial
960.3.be.a.433.16		96	80.53	odd	4	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.be (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205 q^{3} +(3.81012 - 3.23774i) q^{5} +(-2.47993 + 2.47993i) q^{7} +3.00000 q^{9} +O(q^{10})\)	\(q-1.73205 q^{3} +(3.81012 - 3.23774i) q^{5} +(-2.47993 + 2.47993i) q^{7} +3.00000 q^{9} +(-0.348209 + 0.348209i) q^{11} -6.32796 q^{13} +(-6.59933 + 5.60793i) q^{15} +(11.8771 + 11.8771i) q^{17} +(-6.07794 + 6.07794i) q^{19} +(4.29537 - 4.29537i) q^{21} +(17.0846 + 17.0846i) q^{23} +(4.03408 - 24.6724i) q^{25} -5.19615 q^{27} +(-21.6151 + 21.6151i) q^{29} -2.86002 q^{31} +(0.603116 - 0.603116i) q^{33} +(-1.41947 + 17.4782i) q^{35} +53.4598 q^{37} +10.9604 q^{39} +10.1296i q^{41} -31.6559i q^{43} +(11.4304 - 9.71322i) q^{45} +(-9.33506 - 9.33506i) q^{47} +36.6998i q^{49} +(-20.5718 - 20.5718i) q^{51} -21.2609i q^{53} +(-0.199309 + 2.45413i) q^{55} +(10.5273 - 10.5273i) q^{57} +(24.4012 + 24.4012i) q^{59} +(47.9384 + 47.9384i) q^{61} +(-7.43980 + 7.43980i) q^{63} +(-24.1103 + 20.4883i) q^{65} -98.7782i q^{67} +(-29.5913 - 29.5913i) q^{69} +7.58516i q^{71} +(71.1095 + 71.1095i) q^{73} +(-6.98723 + 42.7338i) q^{75} -1.72707i q^{77} +146.874i q^{79} +9.00000 q^{81} +78.3344 q^{83} +(83.7083 + 6.79826i) q^{85} +(37.4385 - 37.4385i) q^{87} +129.469 q^{89} +(15.6929 - 15.6929i) q^{91} +4.95371 q^{93} +(-3.47891 + 42.8365i) q^{95} +(44.2193 + 44.2193i) q^{97} +(-1.04463 + 1.04463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 288 q^{9}+O(q^{10}) \) 96 * q + 288 * q^9	\( 96 q + 288 q^{9} - 32 q^{19} + 96 q^{35} - 96 q^{51} - 128 q^{59} + 32 q^{61} - 96 q^{69} + 96 q^{73} - 192 q^{75} + 864 q^{81} + 320 q^{83} + 384 q^{91} + 768 q^{95}+O(q^{100}) \) 96 * q + 288 * q^9 - 32 * q^19 + 96 * q^35 - 96 * q^51 - 128 * q^59 + 32 * q^61 - 96 * q^69 + 96 * q^73 - 192 * q^75 + 864 * q^81 + 320 * q^83 + 384 * q^91 + 768 * q^95

Introduction

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