LMFDB - Embedded newform 960.3.ba.a.913.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(817,960)]

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, 1, 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("960.817");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.ba (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			913.16
Character	$\chi$	$=$	960.913
Dual form			960.3.ba.a.817.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{3} +(3.23774 - 3.81012i) q^{5} +(2.47993 + 2.47993i) q^{7} -3.00000 q^{9} +O(q^{10})$	\(q-1.73205i q^{3} +(3.23774 - 3.81012i) q^{5} +(2.47993 + 2.47993i) q^{7} -3.00000 q^{9} +(-0.348209 + 0.348209i) q^{11} -6.32796i q^{13} +(-6.59933 - 5.60793i) q^{15} +(11.8771 - 11.8771i) q^{17} +(6.07794 - 6.07794i) q^{19} +(4.29537 - 4.29537i) q^{21} +(-17.0846 + 17.0846i) q^{23} +(-4.03408 - 24.6724i) q^{25} +5.19615i q^{27} +(21.6151 - 21.6151i) q^{29} -2.86002 q^{31} +(0.603116 + 0.603116i) q^{33} +(17.4782 - 1.41947i) q^{35} -53.4598i q^{37} -10.9604 q^{39} +10.1296i q^{41} +31.6559 q^{43} +(-9.71322 + 11.4304i) q^{45} +(-9.33506 + 9.33506i) q^{47} -36.6998i q^{49} +(-20.5718 - 20.5718i) q^{51} +21.2609 q^{53} +(0.199309 + 2.45413i) q^{55} +(-10.5273 - 10.5273i) q^{57} +(-24.4012 - 24.4012i) q^{59} +(47.9384 + 47.9384i) q^{61} +(-7.43980 - 7.43980i) q^{63} +(-24.1103 - 20.4883i) q^{65} -98.7782 q^{67} +(29.5913 + 29.5913i) q^{69} +7.58516i q^{71} +(-71.1095 + 71.1095i) q^{73} +(-42.7338 + 6.98723i) q^{75} -1.72707 q^{77} -146.874i q^{79} +9.00000 q^{81} +78.3344i q^{83} +(-6.79826 - 83.7083i) q^{85} +(-37.4385 - 37.4385i) q^{87} -129.469 q^{89} +(15.6929 - 15.6929i) q^{91} +4.95371i q^{93} +(-3.47891 - 42.8365i) q^{95} +(44.2193 - 44.2193i) q^{97} +(1.04463 - 1.04463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 288 q^{9}+O(q^{10}) $ 96 * q - 288 * q^9	$ 96 q - 288 q^{9} + 32 q^{19} + 96 q^{35} + 128 q^{43} - 96 q^{51} + 128 q^{59} + 32 q^{61} - 576 q^{67} + 96 q^{69} - 96 q^{73} + 192 q^{75} + 864 q^{81} + 384 q^{91} + 768 q^{95}+O(q^{100}) $ 96 * q - 288 * q^9 + 32 * q^19 + 96 * q^35 + 128 * q^43 - 96 * q^51 + 128 * q^59 + 32 * q^61 - 576 * q^67 + 96 * q^69 - 96 * q^73 + 192 * q^75 + 864 * q^81 + 384 * q^91 + 768 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$		0			0
$5$	3.23774	−	3.81012i	0.647548	−	0.762025i
$5$	3.23774	−	3.81012i	0.647548	−	0.762025i
$6$		0			0
$7$	2.47993	+	2.47993i	0.354276	+	0.354276i	0.861698	−	0.507422i	$-0.169401\pi$
$7$	2.47993	+	2.47993i	0.354276	+	0.354276i	−0.507422	+	0.861698i	$0.669401\pi$
$8$		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
$13$		−	6.32796i		−	0.486766i	−0.969930	−	0.243383i	$-0.921743\pi$
$13$		−	6.32796i		−	0.486766i	0.969930	−	0.243383i	$-0.0782572\pi$
$14$		0			0
$15$	−6.59933	−	5.60793i	−0.439955	−	0.373862i
$16$		0			0
$17$	11.8771	−	11.8771i	0.698654	−	0.698654i	−0.265466	−	0.964120i	$-0.585526\pi$
$17$	11.8771	−	11.8771i	0.698654	−	0.698654i	0.964120	+	0.265466i	$0.0855259\pi$
$18$		0			0
$19$	6.07794	−	6.07794i	0.319891	−	0.319891i	−0.528834	−	0.848725i	$-0.677371\pi$
$19$	6.07794	−	6.07794i	0.319891	−	0.319891i	0.848725	+	0.528834i	$0.177371\pi$
$20$		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	$-0.926026\pi$
$23$	−17.0846	+	17.0846i	−0.742807	+	0.742807i	0.230310	+	0.973117i	$0.426026\pi$
$24$		0			0
$25$	−4.03408	−	24.6724i	−0.161363	−	0.986895i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	21.6151	−	21.6151i	0.745350	−	0.745350i	−0.228252	−	0.973602i	$-0.573301\pi$
$29$	21.6151	−	21.6151i	0.745350	−	0.745350i	0.973602	+	0.228252i	$0.0733011\pi$
$30$		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
$35$	17.4782	−	1.41947i	0.499378	−	0.0405564i
$36$		0			0
$37$		−	53.4598i		−	1.44486i	−0.691444	−	0.722430i	$-0.743025\pi$
$37$		−	53.4598i		−	1.44486i	0.691444	−	0.722430i	$-0.256975\pi$
$38$		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
$43$	31.6559			0.736183			0.368091	−	0.929790i	$-0.380011\pi$
$43$	31.6559			0.736183			0.368091	+	0.929790i	$0.380011\pi$
$44$		0			0
$45$	−9.71322	+	11.4304i	−0.215849	+	0.254008i
$46$		0			0
$47$	−9.33506	+	9.33506i	−0.198618	+	0.198618i	−0.799407	−	0.600789i	$-0.794853\pi$
$47$	−9.33506	+	9.33506i	−0.198618	+	0.198618i	0.600789	+	0.799407i	$0.294853\pi$
$48$		0			0
$49$		−	36.6998i		−	0.748976i
$50$		0			0
$51$	−20.5718	−	20.5718i	−0.403368	−	0.403368i
$52$		0			0
$53$	21.2609			0.401150			0.200575	−	0.979678i	$-0.435719\pi$
$53$	21.2609			0.401150			0.200575	+	0.979678i	$0.435719\pi$
$54$		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	0.469404	−	0.882984i	$-0.344469\pi$
$59$	−24.4012	−	24.4012i	−0.413580	−	0.413580i	−0.882984	+	0.469404i	$0.844469\pi$
$60$		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
$67$	−98.7782			−1.47430			−0.737151	−	0.675729i	$-0.763829\pi$
$67$	−98.7782			−1.47430			−0.737151	+	0.675729i	$0.763829\pi$
$68$		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	$-0.991860\pi$
$73$	−71.1095	+	71.1095i	−0.974103	+	0.974103i	0.0255703	+	0.999673i	$0.491860\pi$
$74$		0			0
$75$	−42.7338	+	6.98723i	−0.569784	+	0.0931631i
$76$		0			0
$77$	−1.72707			−0.0224295
$78$		0			0
$79$		−	146.874i		−	1.85917i	−0.368608	−	0.929585i	$-0.620165\pi$
$79$		−	146.874i		−	1.85917i	0.368608	−	0.929585i	$-0.379835\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		0			0
$83$			78.3344i			0.943788i	0.881655	+	0.471894i	$0.156430\pi$
$83$			78.3344i			0.943788i	−0.881655	+	0.471894i	$0.843570\pi$
$84$		0			0
$85$	−6.79826	−	83.7083i	−0.0799796	−	0.984803i
$86$		0			0
$87$	−37.4385	−	37.4385i	−0.430328	−	0.430328i
$88$		0			0
$89$	−129.469			−1.45471			−0.727353	−	0.686264i	$-0.759250\pi$
$89$	−129.469			−1.45471			−0.727353	+	0.686264i	$0.759250\pi$
$90$		0			0
$91$	15.6929	−	15.6929i	0.172450	−	0.172450i
$92$		0			0
$93$			4.95371i			0.0532657i
$94$		0			0
$95$	−3.47891	−	42.8365i	−0.0366201	−	0.450910i
$96$		0			0
$97$	44.2193	−	44.2193i	0.455869	−	0.455869i	−0.441428	−	0.897297i	$-0.645528\pi$
$97$	44.2193	−	44.2193i	0.455869	−	0.455869i	0.897297	+	0.441428i	$0.145528\pi$
$98$		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	$-0.512296\pi$
$103$	98.9454	−	98.9454i	0.960635	−	0.960635i	0.999254	+	0.0386192i	$0.0122959\pi$
$104$		0			0
$105$	−2.45860	−	30.2732i	−0.0234152	−	0.288316i
$106$		0			0
$107$		−	136.473i		−	1.27545i	−0.770266	−	0.637723i	$-0.779876\pi$
$107$		−	136.473i		−	1.27545i	0.770266	−	0.637723i	$-0.220124\pi$
$108$		0			0
$109$	−26.0921	+	26.0921i	−0.239377	+	0.239377i	−0.816592	−	0.577215i	$-0.804139\pi$
$109$	−26.0921	+	26.0921i	−0.239377	+	0.239377i	0.577215	+	0.816592i	$0.304139\pi$
$110$		0			0
$111$	−92.5951			−0.834190
$112$		0			0
$113$	−145.030	−	145.030i	−1.28345	−	1.28345i	−0.938693	−	0.344755i	$-0.887962\pi$
$113$	−145.030	−	145.030i	−1.28345	−	1.28345i	−0.344755	−	0.938693i	$-0.612038\pi$
$114$		0			0
$115$	9.77892	+	120.410i	0.0850341	+	1.04704i
$116$		0			0
$117$			18.9839i			0.162255i
$118$		0			0
$119$	58.9089			0.495033
$120$		0			0
$121$			120.758i			0.997996i
$122$		0			0
$123$	17.5450			0.142642
$124$		0			0
$125$	−107.066	−	64.5124i	−0.856529	−	0.516099i
$126$		0			0
$127$	150.676	−	150.676i	1.18643	−	1.18643i	0.208381	−	0.978048i	$-0.433180\pi$
$127$	150.676	−	150.676i	1.18643	−	1.18643i	0.978048	−	0.208381i	$-0.0668195\pi$
$128$		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
$133$	30.1458			0.226660
$134$		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	$-0.325099\pi$
$137$	−45.2883	−	45.2883i	−0.330571	−	0.330571i	−0.852803	+	0.522232i	$0.825099\pi$
$138$		0			0
$139$	−111.230	−	111.230i	−0.800218	−	0.800218i	0.182911	−	0.983129i	$-0.441448\pi$
$139$	−111.230	−	111.230i	−0.800218	−	0.800218i	−0.983129	+	0.182911i	$0.941448\pi$
$140$		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
$147$	−63.5660			−0.432422
$148$		0			0
$149$	147.057	+	147.057i	0.986962	+	0.986962i	0.999916	−	0.0129541i	$-0.00412353\pi$
$149$	147.057	+	147.057i	0.986962	+	0.986962i	−0.0129541	+	0.999916i	$0.504124\pi$
$150$		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
$155$	−9.26001	+	10.8970i	−0.0597420	+	0.0703035i
$156$		0			0
$157$	90.6356			0.577297			0.288648	−	0.957435i	$-0.406794\pi$
$157$	90.6356			0.577297			0.288648	+	0.957435i	$0.406794\pi$
$158$		0			0
$159$		−	36.8250i		−	0.231604i
$160$		0			0
$161$	−84.7372			−0.526318
$162$		0			0
$163$			136.683i			0.838549i	0.907860	+	0.419274i	$0.137715\pi$
$163$			136.683i			0.838549i	−0.907860	+	0.419274i	$0.862285\pi$
$164$		0			0
$165$	4.25068	−	0.345214i	0.0257617	−	0.00209220i
$166$		0			0
$167$	−93.7702	−	93.7702i	−0.561498	−	0.561498i	0.368235	−	0.929733i	$-0.379962\pi$
$167$	−93.7702	−	93.7702i	−0.561498	−	0.561498i	−0.929733	+	0.368235i	$0.879962\pi$
$168$		0			0
$169$	128.957			0.763059
$170$		0			0
$171$	−18.2338	+	18.2338i	−0.106630	+	0.106630i
$172$		0			0
$173$		−	147.827i		−	0.854490i	−0.904136	−	0.427245i	$-0.859484\pi$
$173$		−	147.827i		−	0.854490i	0.904136	−	0.427245i	$-0.140516\pi$
$174$		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	−0.734262	−	0.678866i	$-0.762472\pi$
$179$	−9.91598	+	9.91598i	−0.0553965	+	0.0553965i	0.678866	+	0.734262i	$0.262472\pi$
$180$		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
$187$			8.27145i			0.0442323i
$188$		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	0.974800	−	0.223082i	$-0.0716119\pi$
$193$	145.081	+	145.081i	0.751717	+	0.751717i	−0.223082	+	0.974800i	$0.571612\pi$
$194$		0			0
$195$	−35.4868	+	41.7603i	−0.181983	+	0.214155i
$196$		0			0
$197$			391.730i			1.98848i	0.107189	+	0.994239i	$0.465815\pi$
$197$			391.730i			1.98848i	−0.107189	+	0.994239i	$0.534185\pi$
$198$		0			0
$199$	110.455			0.555050			0.277525	−	0.960718i	$-0.410486\pi$
$199$	110.455			0.555050			0.277525	+	0.960718i	$0.410486\pi$
$200$		0			0
$201$			171.089i			0.851188i
$202$		0			0
$203$	107.208			0.528120
$204$		0			0
$205$	38.5950	+	32.7970i	0.188268	+	0.159985i
$206$		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
$213$	13.1379			0.0616802
$214$		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	0.281557	−	0.959544i	$-0.409149\pi$
$223$	−151.191	−	151.191i	−0.677987	−	0.677987i	−0.959544	+	0.281557i	$0.909149\pi$
$224$		0			0
$225$	12.1022	+	74.0171i	0.0537877	+	0.328965i
$226$		0			0
$227$	−300.586			−1.32417			−0.662083	−	0.749431i	$-0.730327\pi$
$227$	−300.586			−1.32417			−0.662083	+	0.749431i	$0.730327\pi$
$228$		0			0
$229$	321.239	+	321.239i	1.40279	+	1.40279i	0.791082	+	0.611710i	$0.209518\pi$
$229$	321.239	+	321.239i	1.40279	+	1.40279i	0.611710	+	0.791082i	$0.290482\pi$
$230$		0			0
$231$			2.99138i			0.0129497i
$232$		0			0
$233$	−96.0956	+	96.0956i	−0.412427	+	0.412427i	−0.882583	−	0.470156i	$-0.844198\pi$
$233$	−96.0956	+	96.0956i	−0.412427	+	0.412427i	0.470156	+	0.882583i	$0.344198\pi$
$234$		0			0
$235$	5.34323	+	65.7922i	0.0227372	+	0.279967i
$236$		0			0
$237$	−254.394			−1.07339
$238$		0			0
$239$			397.633i			1.66374i	0.554974	+	0.831868i	$0.312728\pi$
$239$			397.633i			1.66374i	−0.554974	+	0.831868i	$0.687272\pi$
$240$		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
$243$		−	15.5885i		−	0.0641500i
$244$		0			0
$245$	−139.831	−	118.825i	−0.570739	−	0.484998i
$246$		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
$253$		−	11.8980i		−	0.0470277i
$254$		0			0
$255$	−144.987	+	11.7749i	−0.568577	+	0.0461762i
$256$		0			0
$257$	−321.383	+	321.383i	−1.25052	+	1.25052i	−0.295029	+	0.955488i	$0.595329\pi$
$257$	−321.383	+	321.383i	−1.25052	+	1.25052i	−0.955488	+	0.295029i	$0.904671\pi$
$258$		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	$-0.524108\pi$
$263$	242.346	−	242.346i	0.921467	−	0.921467i	0.997133	+	0.0756659i	$0.0241082\pi$
$264$		0			0
$265$	68.8374	−	81.0068i	0.259764	−	0.305686i
$266$		0			0
$267$			224.246i			0.839874i
$268$		0			0
$269$	164.004	−	164.004i	0.609681	−	0.609681i	−0.333182	−	0.942863i	$-0.608122\pi$
$269$	164.004	−	164.004i	0.609681	−	0.609681i	0.942863	+	0.333182i	$0.108122\pi$
$270$		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
$275$	9.99586	+	7.18645i	0.0363486	+	0.0261325i
$276$		0			0
$277$		−	257.269i		−	0.928769i	−0.885634	−	0.464384i	$-0.846276\pi$
$277$		−	257.269i		−	0.928769i	0.885634	−	0.464384i	$-0.153724\pi$
$278$		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
$283$	516.051			1.82350			0.911750	−	0.410745i	$-0.134731\pi$
$283$	516.051			1.82350			0.911750	+	0.410745i	$0.134731\pi$
$284$		0			0
$285$	−74.1949	+	6.02565i	−0.260333	+	0.0211426i
$286$		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
$293$	178.541			0.609356			0.304678	−	0.952455i	$-0.401451\pi$
$293$	178.541			0.609356			0.304678	+	0.952455i	$0.401451\pi$
$294$		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
$307$	−103.189			−0.336120			−0.168060	−	0.985777i	$-0.553750\pi$
$307$	−103.189			−0.336120			−0.168060	+	0.985777i	$0.553750\pi$
$308$		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	$-0.802031\pi$
$313$	−72.0336	+	72.0336i	−0.230139	+	0.230139i	0.582612	+	0.812751i	$0.302031\pi$
$314$		0			0
$315$	−52.4347	+	4.25842i	−0.166459	+	0.0135188i
$316$		0			0
$317$	470.061			1.48284			0.741421	−	0.671040i	$-0.234152\pi$
$317$	470.061			1.48284			0.741421	+	0.671040i	$0.234152\pi$
$318$		0			0
$319$			15.0532i			0.0471887i
$320$		0			0
$321$	−236.378			−0.736379
$322$		0			0
$323$		−	144.377i		−	0.446987i
$324$		0			0
$325$	−156.126	+	25.5275i	−0.480387	+	0.0785462i
$326$		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
$333$			160.379i			0.481620i
$334$		0			0
$335$	−319.818	+	376.357i	−0.954681	+	1.12345i
$336$		0			0
$337$	256.418	−	256.418i	0.760883	−	0.760883i	−0.215599	−	0.976482i	$-0.569170\pi$
$337$	256.418	−	256.418i	0.760883	−	0.760883i	0.976482	+	0.215599i	$0.0691704\pi$
$338$		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
$347$			165.582i			0.477182i	0.971120	+	0.238591i	$0.0766855\pi$
$347$			165.582i			0.477182i	−0.971120	+	0.238591i	$0.923315\pi$
$348$		0			0
$349$	33.8885	−	33.8885i	0.0971016	−	0.0971016i	−0.656887	−	0.753989i	$-0.728127\pi$
$349$	33.8885	−	33.8885i	0.0971016	−	0.0971016i	0.753989	+	0.656887i	$0.228127\pi$
$350$		0			0
$351$	32.8811			0.0936782
$352$		0			0
$353$	121.788	+	121.788i	0.345009	+	0.345009i	0.858247	−	0.513238i	$-0.171554\pi$
$353$	121.788	+	121.788i	0.345009	+	0.345009i	−0.513238	+	0.858247i	$0.671554\pi$
$354$		0			0
$355$	28.9004	+	24.5588i	0.0814096	+	0.0691797i
$356$		0			0
$357$		−	102.033i		−	0.285808i
$358$		0			0
$359$	149.331			0.415963			0.207982	−	0.978133i	$-0.433311\pi$
$359$	149.331			0.415963			0.207982	+	0.978133i	$0.433311\pi$
$360$		0			0
$361$			287.117i			0.795339i
$362$		0			0
$363$	209.158			0.576193
$364$		0			0
$365$	40.7019	+	501.170i	0.111512	+	1.37307i
$366$		0			0
$367$	119.158	−	119.158i	0.324682	−	0.324682i	−0.525878	−	0.850560i	$-0.676263\pi$
$367$	119.158	−	119.158i	0.324682	−	0.324682i	0.850560	+	0.525878i	$0.176263\pi$
$368$		0			0
$369$		−	30.3888i		−	0.0823545i
$370$		0			0
$371$	52.7257	+	52.7257i	0.142118	+	0.142118i
$372$		0			0
$373$	172.603			0.462744			0.231372	−	0.972865i	$-0.425679\pi$
$373$	172.603			0.462744			0.231372	+	0.972865i	$0.425679\pi$
$374$		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	0.708233	−	0.705978i	$-0.249492\pi$
$379$	0.854693	+	0.854693i	0.00225513	+	0.00225513i	−0.705978	+	0.708233i	$0.749492\pi$
$380$		0			0
$381$	−260.979	−	260.979i	−0.684985	−	0.684985i
$382$		0			0
$383$	−217.613	−	217.613i	−0.568181	−	0.568181i	0.363438	−	0.931619i	$-0.381603\pi$
$383$	−217.613	−	217.613i	−0.568181	−	0.568181i	−0.931619	+	0.363438i	$0.881603\pi$
$384$		0			0
$385$	−5.59181	+	6.58036i	−0.0145242	+	0.0170918i
$386$		0			0
$387$	−94.9676			−0.245394
$388$		0			0
$389$	377.146	+	377.146i	0.969527	+	0.969527i	0.999549	−	0.0300219i	$-0.00955772\pi$
$389$	377.146	+	377.146i	0.969527	+	0.969527i	−0.0300219	+	0.999549i	$0.509558\pi$
$390$		0			0
$391$			405.831i			1.03793i
$392$		0			0
$393$	213.074	−	213.074i	0.542172	−	0.542172i
$394$		0			0
$395$	−559.610	−	475.541i	−1.41673	−	1.20390i
$396$		0			0
$397$	−78.3445			−0.197341			−0.0986706	−	0.995120i	$-0.531459\pi$
$397$	−78.3445			−0.197341			−0.0986706	+	0.995120i	$0.531459\pi$
$398$		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
$403$			18.0981i			0.0449085i
$404$		0			0
$405$	29.1397	−	34.2911i	0.0719498	−	0.0846694i
$406$		0			0
$407$	18.6152	+	18.6152i	0.0457376	+	0.0457376i
$408$		0			0
$409$	590.912			1.44477			0.722386	−	0.691490i	$-0.243045\pi$
$409$	590.912			1.44477			0.722386	+	0.691490i	$0.243045\pi$
$410$		0			0
$411$	−78.4416	+	78.4416i	−0.190855	+	0.190855i
$412$		0			0
$413$		−	121.027i		−	0.293043i
$414$		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	−0.140603	−	0.990066i	$-0.544904\pi$
$419$	355.925	−	355.925i	0.849463	−	0.849463i	0.990066	+	0.140603i	$0.0449041\pi$
$420$		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
$427$			237.768i			0.556835i
$428$		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	0.370658	−	0.928770i	$-0.379132\pi$
$433$	−241.662	−	241.662i	−0.558112	−	0.558112i	−0.928770	+	0.370658i	$0.879132\pi$
$434$		0			0
$435$	−263.862	+	21.4292i	−0.606578	+	0.0492625i
$436$		0			0
$437$			207.678i			0.475235i
$438$		0			0
$439$	−377.052			−0.858889			−0.429444	−	0.903093i	$-0.641291\pi$
$439$	−377.052			−0.858889			−0.429444	+	0.903093i	$0.641291\pi$
$440$		0			0
$441$			110.100i			0.249659i
$442$		0			0
$443$	−208.703			−0.471112			−0.235556	−	0.971861i	$-0.575691\pi$
$443$	−208.703			−0.471112			−0.235556	+	0.971861i	$0.575691\pi$
$444$		0			0
$445$	−419.186	+	493.292i	−0.941991	+	1.10852i
$446$		0			0
$447$	254.711	−	254.711i	0.569823	−	0.569823i
$448$		0			0
$449$			147.313i			0.328091i	0.986453	+	0.164046i	$0.0524544\pi$
$449$			147.313i			0.328091i	−0.986453	+	0.164046i	$0.947546\pi$
$450$		0			0
$451$	−3.52722	−	3.52722i	−0.00782089	−	0.00782089i
$452$		0			0
$453$	150.649			0.332559
$454$		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	$-0.416010\pi$
$457$	−321.992	−	321.992i	−0.704578	−	0.704578i	−0.965390	+	0.260812i	$0.916010\pi$
$458$		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	0.999861	+	0.0166443i	$0.00529830\pi$
$463$	470.642	+	470.642i	1.01651	+	1.01651i	0.0166443	+	0.999861i	$0.494702\pi$
$464$		0			0
$465$	18.8742	+	16.0388i	0.0405897	+	0.0344921i
$466$		0			0
$467$	112.993			0.241954			0.120977	−	0.992655i	$-0.461397\pi$
$467$	112.993			0.241954			0.120977	+	0.992655i	$0.461397\pi$
$468$		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
$475$	−174.476	−	125.438i	−0.367318	−	0.264081i
$476$		0			0
$477$	−63.7828			−0.133717
$478$		0			0
$479$			731.858i			1.52789i	0.645283	+	0.763943i	$0.276739\pi$
$479$			731.858i			1.52789i	−0.645283	+	0.763943i	$0.723261\pi$
$480$		0			0
$481$	−338.292			−0.703309
$482$		0			0
$483$			146.769i			0.303870i
$484$		0			0
$485$	−25.3104	−	311.652i	−0.0521864	−	0.642581i
$486$		0			0
$487$	259.467	+	259.467i	0.532787	+	0.532787i	0.921401	−	0.388613i	$-0.127046\pi$
$487$	259.467	+	259.467i	0.532787	+	0.532787i	−0.388613	+	0.921401i	$0.627046\pi$
$488$		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
$493$		−	513.451i		−	1.04148i
$494$		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	−0.650575	−	0.759442i	$-0.725472\pi$
$499$	54.3250	−	54.3250i	0.108868	−	0.108868i	0.759442	+	0.650575i	$0.225472\pi$
$500$		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	$-0.885318\pi$
$503$	−293.378	+	293.378i	−0.583255	+	0.583255i	0.352541	+	0.935796i	$0.385318\pi$
$504$		0			0
$505$	−11.9884	−	147.616i	−0.0237395	−	0.292309i
$506$		0			0
$507$		−	223.360i		−	0.440552i
$508$		0			0
$509$	−123.743	+	123.743i	−0.243111	+	0.243111i	−0.818136	−	0.575025i	$-0.804992\pi$
$509$	−123.743	+	123.743i	−0.243111	+	0.243111i	0.575025	+	0.818136i	$0.304992\pi$
$510$		0			0
$511$	−352.694			−0.690203
$512$		0			0
$513$	31.5819	+	31.5819i	0.0615631	+	0.0615631i
$514$		0			0
$515$	−56.6347	−	697.354i	−0.109970	−	1.35408i
$516$		0			0
$517$		−	6.50111i		−	0.0125747i
$518$		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
$523$	608.027			1.16258			0.581288	−	0.813698i	$-0.302549\pi$
$523$	608.027			1.16258			0.581288	+	0.813698i	$0.302549\pi$
$524$		0			0
$525$	−123.305	−	88.6492i	−0.234867	−	0.168856i
$526$		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
$533$	64.0997			0.120262
$534$		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
$547$	235.706			0.430907			0.215454	−	0.976514i	$-0.430877\pi$
$547$	235.706			0.430907			0.215454	+	0.976514i	$0.430877\pi$
$548$		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
$555$	−299.799	+	352.799i	−0.540178	+	0.635673i
$556$		0			0
$557$	625.647			1.12324			0.561622	−	0.827394i	$-0.310178\pi$
$557$	625.647			1.12324			0.561622	+	0.827394i	$0.310178\pi$
$558$		0			0
$559$		−	200.317i		−	0.358349i
$560$		0			0
$561$	14.3266			0.0255376
$562$		0			0
$563$		−	488.327i		−	0.867366i	−0.901065	−	0.433683i	$-0.857214\pi$
$563$		−	488.327i		−	0.867366i	0.901065	−	0.433683i	$-0.142786\pi$
$564$		0			0
$565$	−1022.15	+	83.0125i	−1.80911	+	0.146925i
$566$		0			0
$567$	22.3194	+	22.3194i	0.0393640	+	0.0393640i
$568$		0			0
$569$	568.948			0.999908			0.499954	−	0.866052i	$-0.333350\pi$
$569$	568.948			0.999908			0.499954	+	0.866052i	$0.333350\pi$
$570$		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
$573$			223.664i			0.390339i
$574$		0			0
$575$	490.437	+	352.596i	0.852934	+	0.613211i
$576$		0			0
$577$	99.8357	−	99.8357i	0.173025	−	0.173025i	−0.615282	−	0.788307i	$-0.710958\pi$
$577$	99.8357	−	99.8357i	0.173025	−	0.173025i	0.788307	+	0.615282i	$0.210958\pi$
$578$		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
$587$		−	557.705i		−	0.950094i	−0.879960	−	0.475047i	$-0.842431\pi$
$587$		−	557.705i		−	0.950094i	0.879960	−	0.475047i	$-0.157569\pi$
$588$		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	0.898002	−	0.439991i	$-0.145018\pi$
$593$	271.601	+	271.601i	0.458012	+	0.458012i	−0.439991	+	0.898002i	$0.645018\pi$
$594$		0			0
$595$	190.732	−	224.450i	0.320558	−	0.377227i
$596$		0			0
$597$		−	191.313i		−	0.320458i
$598$		0			0
$599$	173.826			0.290194			0.145097	−	0.989417i	$-0.453651\pi$
$599$	173.826			0.290194			0.145097	+	0.989417i	$0.453651\pi$
$600$		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
$603$	296.335			0.491434
$604$		0			0
$605$	460.101	+	390.981i	0.760497	+	0.646250i
$606$		0			0
$607$	664.932	−	664.932i	1.09544	−	1.09544i	0.100502	−	0.994937i	$-0.467955\pi$
$607$	664.932	−	664.932i	1.09544	−	1.09544i	0.994937	−	0.100502i	$-0.0320450\pi$
$608$		0			0
$609$		−	185.690i		−	0.304910i
$610$		0			0
$611$	59.0719	+	59.0719i	0.0966807	+	0.0966807i
$612$		0			0
$613$	−474.479			−0.774027			−0.387014	−	0.922074i	$-0.626493\pi$
$613$	−474.479			−0.774027			−0.387014	+	0.922074i	$0.626493\pi$
$614$		0			0
$615$	56.8061	−	66.8486i	0.0923677	−	0.108697i
$616$		0			0
$617$	−807.635	−	807.635i	−1.30897	−	1.30897i	−0.922159	−	0.386812i	$-0.873576\pi$
$617$	−807.635	−	807.635i	−1.30897	−	1.30897i	−0.386812	−	0.922159i	$-0.626424\pi$
$618$		0			0
$619$	−461.288	−	461.288i	−0.745215	−	0.745215i	0.228361	−	0.973576i	$-0.426663\pi$
$619$	−461.288	−	461.288i	−0.745215	−	0.745215i	−0.973576	+	0.228361i	$0.926663\pi$
$620$		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
$627$	7.33141			0.0116928
$628$		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
$635$	−86.2447	−	1061.95i	−0.135818	−	1.67236i
$636$		0			0
$637$	−232.235			−0.364576
$638$		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
$643$		−	226.198i		−	0.351785i	−0.984409	−	0.175893i	$-0.943719\pi$
$643$		−	226.198i		−	0.351785i	0.984409	−	0.175893i	$-0.0562812\pi$
$644$		0			0
$645$	−208.907	−	177.524i	−0.323887	−	0.275231i
$646$		0			0
$647$	−537.803	−	537.803i	−0.831225	−	0.831225i	0.156459	−	0.987684i	$-0.449992\pi$
$647$	−537.803	−	537.803i	−0.831225	−	0.831225i	−0.987684	+	0.156459i	$0.949992\pi$
$648$		0			0
$649$	16.9935			0.0261841
$650$		0			0
$651$	−12.2849	+	12.2849i	−0.0188708	+	0.0188708i
$652$		0			0
$653$		−	747.369i		−	1.14452i	−0.820074	−	0.572258i	$-0.806068\pi$
$653$		−	747.369i		−	1.14452i	0.820074	−	0.572258i	$-0.193932\pi$
$654$		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	$-0.471680\pi$
$659$	714.948	−	714.948i	1.08490	−	1.08490i	0.996045	−	0.0888541i	$-0.0283205\pi$
$660$		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
$667$			738.570i			1.10730i
$668$		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	0.996920	−	0.0784214i	$-0.0249880\pi$
$673$	618.150	+	618.150i	0.918499	+	0.918499i	−0.0784214	+	0.996920i	$0.524988\pi$
$674$		0			0
$675$	128.201	−	20.9617i	0.189928	−	0.0310544i
$676$		0			0
$677$			523.647i			0.773481i	0.922189	+	0.386741i	$0.126399\pi$
$677$			523.647i			0.773481i	−0.922189	+	0.386741i	$0.873601\pi$
$678$		0			0
$679$	219.322			0.323007
$680$		0			0
$681$			520.629i			0.764507i
$682$		0			0
$683$	−1171.63			−1.71542			−0.857712	−	0.514130i	$-0.828115\pi$
$683$	−1171.63			−1.71542			−0.857712	+	0.514130i	$0.828115\pi$
$684$		0			0
$685$	−319.186	+	25.9223i	−0.465964	+	0.0378427i
$686$		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
$693$	5.18122			0.00747651
$694$		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
$707$	103.883			0.146935
$708$		0			0
$709$	−783.751	−	783.751i	−1.10543	−	1.10543i	−0.993743	−	0.111689i	$-0.964374\pi$
$709$	−783.751	−	783.751i	−1.10543	−	1.10543i	−0.111689	−	0.993743i	$-0.535626\pi$
$710$		0			0
$711$			440.623i			0.619723i
$712$		0			0
$713$	48.8623	−	48.8623i	0.0685305	−	0.0685305i
$714$		0			0
$715$	15.5297	−	1.26122i	0.0217198	−	0.00176395i
$716$		0			0
$717$	688.720			0.960558
$718$		0			0
$719$			1035.43i			1.44009i	0.693925	+	0.720047i	$0.255880\pi$
$719$			1035.43i			1.44009i	−0.693925	+	0.720047i	$0.744120\pi$
$720$		0			0
$721$	490.756			0.680660
$722$		0			0
$723$		−	305.856i		−	0.423037i
$724$		0			0
$725$	−620.494	−	446.100i	−0.855854	−	0.615310i
$726$		0			0
$727$	−564.170	−	564.170i	−0.776024	−	0.776024i	0.203128	−	0.979152i	$-0.434889\pi$
$727$	−564.170	−	564.170i	−0.776024	−	0.776024i	−0.979152	+	0.203128i	$0.934889\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	375.980	−	375.980i	0.514337	−	0.514337i
$732$		0			0
$733$		−	663.374i		−	0.905012i	−0.891761	−	0.452506i	$-0.850530\pi$
$733$		−	663.374i		−	0.905012i	0.891761	−	0.452506i	$-0.149470\pi$
$734$		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	−0.611952	−	0.790895i	$-0.709615\pi$
$739$	132.239	−	132.239i	0.178944	−	0.178944i	0.790895	+	0.611952i	$0.209615\pi$
$740$		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	$-0.964055\pi$
$743$	−654.544	+	654.544i	−0.880947	+	0.880947i	0.112684	+	0.993631i	$0.464055\pi$
$744$		0			0
$745$	1036.44	−	84.1732i	1.39119	−	0.112984i
$746$		0			0
$747$		−	235.003i		−	0.314596i
$748$		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
$755$	331.394	+	281.610i	0.438932	+	0.372993i
$756$		0			0
$757$		−	1058.07i		−	1.39771i	−0.715264	−	0.698855i	$-0.753693\pi$
$757$		−	1058.07i		−	1.39771i	0.715264	−	0.698855i	$-0.246307\pi$
$758$		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
$763$	−129.413			−0.169611
$764$		0			0
$765$	20.3948	+	251.125i	0.0266599	+	0.328268i
$766$		0			0
$767$	−154.410	+	154.410i	−0.201317	+	0.201317i
$768$		0			0
$769$			1321.92i			1.71901i	0.511127	+	0.859505i	$0.329228\pi$
$769$			1321.92i			1.71901i	−0.511127	+	0.859505i	$0.670772\pi$
$770$		0			0
$771$	556.651	+	556.651i	0.721986	+	0.721986i
$772$		0			0
$773$	−88.8442			−0.114934			−0.0574671	−	0.998347i	$-0.518302\pi$
$773$	−88.8442			−0.114934			−0.0574671	+	0.998347i	$0.518302\pi$
$774$		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
$787$	−1408.42			−1.78961			−0.894804	−	0.446459i	$-0.852685\pi$
$787$	−1408.42			−1.78961			−0.894804	+	0.446459i	$0.852685\pi$
$788$		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
$795$	−140.308	−	119.230i	−0.176488	−	0.149975i
$796$		0			0
$797$	−214.836			−0.269556			−0.134778	−	0.990876i	$-0.543032\pi$
$797$	−214.836			−0.269556			−0.134778	+	0.990876i	$0.543032\pi$
$798$		0			0
$799$			221.747i			0.277531i
$800$		0			0
$801$	388.406			0.484902
$802$		0			0
$803$		−	49.5220i		−	0.0616712i
$804$		0			0
$805$	−274.357	+	322.859i	−0.340816	+	0.401067i
$806$		0			0
$807$	−284.064	−	284.064i	−0.352000	−	0.352000i
$808$		0			0
$809$	−1149.79			−1.42124			−0.710622	−	0.703574i	$-0.751587\pi$
$809$	−1149.79			−1.42124			−0.710622	+	0.703574i	$0.751587\pi$
$810$		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
$813$		−	54.1346i		−	0.0665862i
$814$		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	$-0.892284\pi$
$823$	−503.108	+	503.108i	−0.611310	+	0.611310i	0.331978	+	0.943287i	$0.392284\pi$
$824$		0			0
$825$	12.4473	−	17.3133i	0.0150876	−	0.0209859i
$826$		0			0
$827$			1133.23i			1.37029i	0.728406	+	0.685145i	$0.240261\pi$
$827$			1133.23i			1.37029i	−0.728406	+	0.685145i	$0.759739\pi$
$828$		0			0
$829$	−1059.24	+	1059.24i	−1.27773	+	1.27773i	−0.335794	+	0.941935i	$0.609005\pi$
$829$	−1059.24	+	1059.24i	−1.27773	+	1.27773i	−0.941935	+	0.335794i	$0.890995\pi$
$830$		0			0
$831$	−445.603			−0.536225
$832$		0			0
$833$	−435.888	−	435.888i	−0.523275	−	0.523275i
$834$		0			0
$835$	−660.879	+	53.6725i	−0.791472	+	0.0642784i
$836$		0			0
$837$		−	14.8611i		−	0.0177552i
$838$		0			0
$839$	634.998			0.756851			0.378426	−	0.925632i	$-0.376466\pi$
$839$	634.998			0.756851			0.378426	+	0.925632i	$0.376466\pi$
$840$		0			0
$841$		−	93.4285i		−	0.111092i
$842$		0			0
$843$	241.184			0.286102
$844$		0			0
$845$	417.529	−	491.342i	0.494117	−	0.581469i
$846$		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
$853$	736.362			0.863261			0.431630	−	0.902051i	$-0.357938\pi$
$853$	736.362			0.863261			0.431630	+	0.902051i	$0.357938\pi$
$854$		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	$-0.325590\pi$
$857$	−285.114	−	285.114i	−0.332688	−	0.332688i	−0.853607	+	0.520918i	$0.825590\pi$
$858$		0			0
$859$	−535.646	−	535.646i	−0.623570	−	0.623570i	0.322873	−	0.946442i	$-0.395351\pi$
$859$	−535.646	−	535.646i	−0.623570	−	0.623570i	−0.946442	+	0.322873i	$0.895351\pi$
$860$		0			0
$861$	43.5104	+	43.5104i	0.0505348	+	0.0505348i
$862$		0			0
$863$	152.045	+	152.045i	0.176182	+	0.176182i	0.789689	−	0.613507i	$-0.210242\pi$
$863$	152.045	+	152.045i	0.176182	+	0.176182i	−0.613507	+	0.789689i	$0.710242\pi$
$864$		0			0
$865$	−563.238	−	478.624i	−0.651142	−	0.553323i
$866$		0			0
$867$	11.8961			0.0137210
$868$		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
$875$	−105.530	−	425.503i	−0.120606	−	0.486290i
$876$		0			0
$877$	777.146			0.886142			0.443071	−	0.896487i	$-0.353889\pi$
$877$	777.146			0.886142			0.443071	+	0.896487i	$0.353889\pi$
$878$		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
$883$			634.549i			0.718629i	0.933217	+	0.359314i	$0.116989\pi$
$883$			634.549i			0.718629i	−0.933217	+	0.359314i	$0.883011\pi$
$884$		0			0
$885$	24.1913	+	297.872i	0.0273348	+	0.336578i
$886$		0			0
$887$	1206.72	+	1206.72i	1.36045	+	1.36045i	0.873340	+	0.487112i	$0.161950\pi$
$887$	1206.72	+	1206.72i	1.36045	+	1.36045i	0.487112	+	0.873340i	$0.338050\pi$
$888$		0			0
$889$	747.336			0.840648
$890$		0			0
$891$	−3.13388	+	3.13388i	−0.00351727	+	0.00351727i
$892$		0			0
$893$			113.476i			0.127073i
$894$		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
$907$			1583.66i			1.74604i	0.487685	+	0.873020i	$0.337841\pi$
$907$			1583.66i			1.74604i	−0.487685	+	0.873020i	$0.662159\pi$
$908$		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
$915$	−47.5260	−	585.197i	−0.0519410	−	0.639559i
$916$		0			0
$917$			610.154i			0.665381i
$918$		0			0
$919$	840.571			0.914658			0.457329	−	0.889298i	$-0.348806\pi$
$919$	840.571			0.914658			0.457329	+	0.889298i	$0.348806\pi$
$920$		0			0
$921$			178.729i			0.194059i
$922$		0			0
$923$	47.9986			0.0520028
$924$		0			0
$925$	−1318.98	+	215.661i	−1.42592	+	0.233147i
$926$		0			0
$927$	−296.836	+	296.836i	−0.320212	+	0.320212i
$928$		0			0
$929$			211.525i			0.227691i	0.993498	+	0.113846i	$0.0363169\pi$
$929$			211.525i			0.227691i	−0.993498	+	0.113846i	$0.963683\pi$
$930$		0			0
$931$	−223.059	−	223.059i	−0.239591	−	0.239591i
$932$		0			0
$933$	999.850			1.07165
$934$		0			0
$935$	31.5152	+	26.7808i	0.0337061	+	0.0286426i
$936$		0			0
$937$	−1120.07	−	1120.07i	−1.19538	−	1.19538i	−0.975535	−	0.219846i	$-0.929445\pi$
$937$	−1120.07	−	1120.07i	−1.19538	−	1.19538i	−0.219846	−	0.975535i	$-0.570555\pi$
$938$		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
$947$	296.948			0.313567			0.156784	−	0.987633i	$-0.449887\pi$
$947$	296.948			0.313567			0.156784	+	0.987633i	$0.449887\pi$
$948$		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	$-0.994581\pi$
$953$	−936.638	+	936.638i	−0.982831	+	0.982831i	0.0170241	+	0.999855i	$0.494581\pi$
$954$		0			0
$955$	−418.097	+	492.011i	−0.437798	+	0.515194i
$956$		0			0
$957$	26.0729			0.0272444
$958$		0			0
$959$		−	224.624i		−	0.234227i
$960$		0			0
$961$	−952.820			−0.991488
$962$		0			0
$963$			409.418i			0.425149i
$964$		0			0
$965$	1022.51	−	83.0422i	1.05960	−	0.0860541i
$966$		0			0
$967$	−547.943	−	547.943i	−0.566643	−	0.566643i	0.364544	−	0.931186i	$-0.381225\pi$
$967$	−547.943	−	547.943i	−0.566643	−	0.566643i	−0.931186	+	0.364544i	$0.881225\pi$
$968$		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
$973$		−	551.688i		−	0.566997i
$974$		0			0
$975$	44.2149	+	270.418i	0.0453486	+	0.277352i
$976$		0			0
$977$	24.5422	−	24.5422i	0.0251200	−	0.0251200i	−0.694435	−	0.719555i	$-0.744346\pi$
$977$	24.5422	−	24.5422i	0.0251200	−	0.0251200i	0.719555	+	0.694435i	$0.244346\pi$
$978$		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	$-0.734432\pi$
$983$	67.9656	−	67.9656i	0.0691410	−	0.0691410i	0.740832	+	0.671691i	$0.234432\pi$
$984$		0			0
$985$	1492.54	+	1268.32i	1.51527	+	1.28763i
$986$		0			0
$987$			80.1951i			0.0812514i
$988$		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
$995$	357.624	−	420.847i	0.359421	−	0.422961i
$996$		0			0
$997$			1682.45i			1.68752i	0.536723	+	0.843758i	$0.319662\pi$
$997$			1682.45i			1.68752i	−0.536723	+	0.843758i	$0.680338\pi$
$998$		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.ba.a.913.16		96
4.3	odd	2		240.3.ba.a.13.8	✓	96
5.2	odd	4		960.3.be.a.337.16		96
16.5	even	4		960.3.be.a.433.16		96
16.11	odd	4		240.3.be.a.133.32	yes	96
20.7	even	4		240.3.be.a.157.32	yes	96
80.27	even	4		240.3.ba.a.37.8	yes	96
80.37	odd	4	inner	960.3.ba.a.817.33		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.3.ba.a.13.8	✓	96	4.3	odd	2
240.3.ba.a.37.8	yes	96	80.27	even	4
240.3.be.a.133.32	yes	96	16.11	odd	4
240.3.be.a.157.32	yes	96	20.7	even	4
960.3.ba.a.817.33		96	80.37	odd	4	inner
960.3.ba.a.913.16		96	1.1	even	1	trivial
960.3.be.a.337.16		96	5.2	odd	4
960.3.be.a.433.16		96	16.5	even	4

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.ba (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{3} +(3.23774 - 3.81012i) q^{5} +(2.47993 + 2.47993i) q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q-1.73205i q^{3} +(3.23774 - 3.81012i) q^{5} +(2.47993 + 2.47993i) q^{7} -3.00000 q^{9} +(-0.348209 + 0.348209i) q^{11} -6.32796i q^{13} +(-6.59933 - 5.60793i) q^{15} +(11.8771 - 11.8771i) q^{17} +(6.07794 - 6.07794i) q^{19} +(4.29537 - 4.29537i) q^{21} +(-17.0846 + 17.0846i) q^{23} +(-4.03408 - 24.6724i) q^{25} +5.19615i q^{27} +(21.6151 - 21.6151i) q^{29} -2.86002 q^{31} +(0.603116 + 0.603116i) q^{33} +(17.4782 - 1.41947i) q^{35} -53.4598i q^{37} -10.9604 q^{39} +10.1296i q^{41} +31.6559 q^{43} +(-9.71322 + 11.4304i) q^{45} +(-9.33506 + 9.33506i) q^{47} -36.6998i q^{49} +(-20.5718 - 20.5718i) q^{51} +21.2609 q^{53} +(0.199309 + 2.45413i) q^{55} +(-10.5273 - 10.5273i) q^{57} +(-24.4012 - 24.4012i) q^{59} +(47.9384 + 47.9384i) q^{61} +(-7.43980 - 7.43980i) q^{63} +(-24.1103 - 20.4883i) q^{65} -98.7782 q^{67} +(29.5913 + 29.5913i) q^{69} +7.58516i q^{71} +(-71.1095 + 71.1095i) q^{73} +(-42.7338 + 6.98723i) q^{75} -1.72707 q^{77} -146.874i q^{79} +9.00000 q^{81} +78.3344i q^{83} +(-6.79826 - 83.7083i) q^{85} +(-37.4385 - 37.4385i) q^{87} -129.469 q^{89} +(15.6929 - 15.6929i) q^{91} +4.95371i q^{93} +(-3.47891 - 42.8365i) q^{95} +(44.2193 - 44.2193i) q^{97} +(1.04463 - 1.04463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 288 q^{9}+O(q^{10}) \) 96 * q - 288 * q^9	\( 96 q - 288 q^{9} + 32 q^{19} + 96 q^{35} + 128 q^{43} - 96 q^{51} + 128 q^{59} + 32 q^{61} - 576 q^{67} + 96 q^{69} - 96 q^{73} + 192 q^{75} + 864 q^{81} + 384 q^{91} + 768 q^{95}+O(q^{100}) \) 96 * q - 288 * q^9 + 32 * q^19 + 96 * q^35 + 128 * q^43 - 96 * q^51 + 128 * q^59 + 32 * q^61 - 576 * q^67 + 96 * q^69 - 96 * q^73 + 192 * q^75 + 864 * q^81 + 384 * q^91 + 768 * q^95

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