LMFDB - Embedded newform 960.3.bg.c.193.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,3,Mod(193,960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("960.193"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3])) N = Newforms(chi, 3, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.2
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	960.193
Dual form			960.3.bg.c.577.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 1.22474i) q^{3} +(2.67423 - 4.22474i) q^{5} +(-5.44949 + 5.44949i) q^{7} +3.00000i q^{9} +6.44949 q^{11} +(-14.4495 - 14.4495i) q^{13} +(8.44949 - 1.89898i) q^{15} +(-23.1464 + 23.1464i) q^{17} +16.6969i q^{19} -13.3485 q^{21} +(-6.65153 - 6.65153i) q^{23} +(-10.6969 - 22.5959i) q^{25} +(-3.67423 + 3.67423i) q^{27} -0.0454077i q^{29} +4.49490 q^{31} +(7.89898 + 7.89898i) q^{33} +(8.44949 + 37.5959i) q^{35} +(-35.3485 + 35.3485i) q^{37} -35.3939i q^{39} +20.2929 q^{41} +(-32.2929 - 32.2929i) q^{43} +(12.6742 + 8.02270i) q^{45} +(-50.5403 + 50.5403i) q^{47} -10.3939i q^{49} -56.6969 q^{51} +(5.50510 + 5.50510i) q^{53} +(17.2474 - 27.2474i) q^{55} +(-20.4495 + 20.4495i) q^{57} +55.4393i q^{59} -47.8888 q^{61} +(-16.3485 - 16.3485i) q^{63} +(-99.6867 + 22.4041i) q^{65} +(85.2827 - 85.2827i) q^{67} -16.2929i q^{69} +48.4041 q^{71} +(-21.9898 - 21.9898i) q^{73} +(14.5732 - 40.7753i) q^{75} +(-35.1464 + 35.1464i) q^{77} +126.697i q^{79} -9.00000 q^{81} +(-94.9444 - 94.9444i) q^{83} +(35.8888 + 159.687i) q^{85} +(0.0556128 - 0.0556128i) q^{87} +71.7980i q^{89} +157.485 q^{91} +(5.50510 + 5.50510i) q^{93} +(70.5403 + 44.6515i) q^{95} +(-37.0000 + 37.0000i) q^{97} +19.3485i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} - 12 q^{7} + 16 q^{11} - 48 q^{13} + 24 q^{15} - 24 q^{17} - 24 q^{21} - 56 q^{23} + 16 q^{25} - 80 q^{31} + 12 q^{33} + 24 q^{35} - 112 q^{37} - 56 q^{41} + 8 q^{43} + 36 q^{45} - 16 q^{47}+ \cdots - 148 q^{97}+O(q^{100}) $ 4 * q - 4 * q^5 - 12 * q^7 + 16 * q^11 - 48 * q^13 + 24 * q^15 - 24 * q^17 - 24 * q^21 - 56 * q^23 + 16 * q^25 - 80 * q^31 + 12 * q^33 + 24 * q^35 - 112 * q^37 - 56 * q^41 + 8 * q^43 + 36 * q^45 - 16 * q^47 - 168 * q^51 + 120 * q^53 + 20 * q^55 - 72 * q^57 + 24 * q^61 - 36 * q^63 - 144 * q^65 + 8 * q^67 + 272 * q^71 + 108 * q^73 + 24 * q^75 - 72 * q^77 - 36 * q^81 - 272 * q^83 - 72 * q^85 + 108 * q^87 + 336 * q^91 + 120 * q^93 + 96 * q^95 - 148 * q^97

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		0			0
$5$	2.67423	−	4.22474i	0.534847	−	0.844949i
$5$	2.67423	−	4.22474i	0.534847	−	0.844949i
$6$		0			0
$7$	−5.44949	+	5.44949i	−0.778499	+	0.778499i	−0.979575	−	0.201077i	$-0.935556\pi$
$7$	−5.44949	+	5.44949i	−0.778499	+	0.778499i	0.201077	+	0.979575i	$0.435556\pi$
$8$		0			0
$9$			3.00000i			0.333333i
$10$		0			0
$11$	6.44949			0.586317			0.293159	−	0.956064i	$-0.405294\pi$
$11$	6.44949			0.586317			0.293159	+	0.956064i	$0.405294\pi$
$12$		0			0
$13$	−14.4495	−	14.4495i	−1.11150	−	1.11150i	−0.992948	−	0.118551i	$-0.962175\pi$
$13$	−14.4495	−	14.4495i	−1.11150	−	1.11150i	−0.118551	−	0.992948i	$-0.537825\pi$
$14$		0			0
$15$	8.44949	−	1.89898i	0.563299	−	0.126599i
$16$		0			0
$17$	−23.1464	+	23.1464i	−1.36155	+	1.36155i	−0.489617	+	0.871938i	$0.662863\pi$
$17$	−23.1464	+	23.1464i	−1.36155	+	1.36155i	−0.871938	+	0.489617i	$0.837137\pi$
$18$		0			0
$19$			16.6969i			0.878786i	0.898295	+	0.439393i	$0.144806\pi$
$19$			16.6969i			0.878786i	−0.898295	+	0.439393i	$0.855194\pi$
$20$		0			0
$21$	−13.3485			−0.635641
$22$		0			0
$23$	−6.65153	−	6.65153i	−0.289197	−	0.289197i	0.547566	−	0.836763i	$-0.315555\pi$
$23$	−6.65153	−	6.65153i	−0.289197	−	0.289197i	−0.836763	+	0.547566i	$0.815555\pi$
$24$		0			0
$25$	−10.6969	−	22.5959i	−0.427878	−	0.903837i
$26$		0			0
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	0.0454077i		−	0.00156578i	−1.00000		0.000782891i	$-0.999751\pi$
$29$		−	0.0454077i		−	0.00156578i	1.00000		0.000782891i	$-0.000249202\pi$
$30$		0			0
$31$	4.49490			0.144997			0.0724983	−	0.997369i	$-0.476903\pi$
$31$	4.49490			0.144997			0.0724983	+	0.997369i	$0.476903\pi$
$32$		0			0
$33$	7.89898	+	7.89898i	0.239363	+	0.239363i
$34$		0			0
$35$	8.44949	+	37.5959i	0.241414	+	1.07417i
$36$		0			0
$37$	−35.3485	+	35.3485i	−0.955364	+	0.955364i	−0.999046	−	0.0436815i	$-0.986091\pi$
$37$	−35.3485	+	35.3485i	−0.955364	+	0.955364i	0.0436815	+	0.999046i	$0.486091\pi$
$38$		0			0
$39$		−	35.3939i		−	0.907535i
$40$		0			0
$41$	20.2929			0.494948			0.247474	−	0.968895i	$-0.420400\pi$
$41$	20.2929			0.494948			0.247474	+	0.968895i	$0.420400\pi$
$42$		0			0
$43$	−32.2929	−	32.2929i	−0.750997	−	0.750997i	0.223669	−	0.974665i	$-0.428197\pi$
$43$	−32.2929	−	32.2929i	−0.750997	−	0.750997i	−0.974665	+	0.223669i	$0.928197\pi$
$44$		0			0
$45$	12.6742	+	8.02270i	0.281650	+	0.178282i
$46$		0			0
$47$	−50.5403	+	50.5403i	−1.07533	+	1.07533i	−0.0784040	+	0.996922i	$0.524982\pi$
$47$	−50.5403	+	50.5403i	−1.07533	+	1.07533i	−0.996922	+	0.0784040i	$0.975018\pi$
$48$		0			0
$49$		−	10.3939i		−	0.212120i
$50$		0			0
$51$	−56.6969			−1.11170
$52$		0			0
$53$	5.50510	+	5.50510i	0.103870	+	0.103870i	0.757132	−	0.653262i	$-0.226600\pi$
$53$	5.50510	+	5.50510i	0.103870	+	0.103870i	−0.653262	+	0.757132i	$0.726600\pi$
$54$		0			0
$55$	17.2474	−	27.2474i	0.313590	−	0.495408i
$56$		0			0
$57$	−20.4495	+	20.4495i	−0.358763	+	0.358763i
$58$		0			0
$59$			55.4393i			0.939649i	0.882760	+	0.469824i	$0.155683\pi$
$59$			55.4393i			0.939649i	−0.882760	+	0.469824i	$0.844317\pi$
$60$		0			0
$61$	−47.8888			−0.785062			−0.392531	−	0.919739i	$-0.628400\pi$
$61$	−47.8888			−0.785062			−0.392531	+	0.919739i	$0.628400\pi$
$62$		0			0
$63$	−16.3485	−	16.3485i	−0.259500	−	0.259500i
$64$		0			0
$65$	−99.6867	+	22.4041i	−1.53364	+	0.344678i
$66$		0			0
$67$	85.2827	−	85.2827i	1.27288	−	1.27288i	0.328303	−	0.944573i	$-0.393523\pi$
$67$	85.2827	−	85.2827i	1.27288	−	1.27288i	0.944573	−	0.328303i	$-0.106477\pi$
$68$		0			0
$69$		−	16.2929i		−	0.236128i
$70$		0			0
$71$	48.4041			0.681748			0.340874	−	0.940109i	$-0.389277\pi$
$71$	48.4041			0.681748			0.340874	+	0.940109i	$0.389277\pi$
$72$		0			0
$73$	−21.9898	−	21.9898i	−0.301230	−	0.301230i	0.540265	−	0.841495i	$-0.318324\pi$
$73$	−21.9898	−	21.9898i	−0.301230	−	0.301230i	−0.841495	+	0.540265i	$0.818324\pi$
$74$		0			0
$75$	14.5732	−	40.7753i	0.194310	−	0.543670i
$76$		0			0
$77$	−35.1464	+	35.1464i	−0.456447	+	0.456447i
$78$		0			0
$79$			126.697i			1.60376i	0.597486	+	0.801879i	$0.296166\pi$
$79$			126.697i			1.60376i	−0.597486	+	0.801879i	$0.703834\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	−94.9444	−	94.9444i	−1.14391	−	1.14391i	−0.987729	−	0.156180i	$-0.950082\pi$
$83$	−94.9444	−	94.9444i	−1.14391	−	1.14391i	−0.156180	−	0.987729i	$-0.549918\pi$
$84$		0			0
$85$	35.8888	+	159.687i	0.422221	+	1.87867i
$86$		0			0
$87$	0.0556128	−	0.0556128i	0.000639228	−	0.000639228i
$88$		0			0
$89$			71.7980i			0.806719i	0.915042	+	0.403359i	$0.132158\pi$
$89$			71.7980i			0.806719i	−0.915042	+	0.403359i	$0.867842\pi$
$90$		0			0
$91$	157.485			1.73060
$92$		0			0
$93$	5.50510	+	5.50510i	0.0591947	+	0.0591947i
$94$		0			0
$95$	70.5403	+	44.6515i	0.742530	+	0.470016i
$96$		0			0
$97$	−37.0000	+	37.0000i	−0.381443	+	0.381443i	−0.871622	−	0.490179i	$-0.836932\pi$
$97$	−37.0000	+	37.0000i	−0.381443	+	0.381443i	0.490179	+	0.871622i	$0.336932\pi$
$98$		0			0
$99$			19.3485i			0.195439i
$100$		0			0
$101$	−94.3383			−0.934042			−0.467021	−	0.884246i	$-0.654673\pi$
$101$	−94.3383			−0.934042			−0.467021	+	0.884246i	$0.654673\pi$
$102$		0			0
$103$	72.6413	+	72.6413i	0.705256	+	0.705256i	0.965534	−	0.260278i	$-0.0838142\pi$
$103$	72.6413	+	72.6413i	0.705256	+	0.705256i	−0.260278	+	0.965534i	$0.583814\pi$
$104$		0			0
$105$	−35.6969	+	56.3939i	−0.339971	+	0.537085i
$106$		0			0
$107$	13.0556	−	13.0556i	0.122015	−	0.122015i	−0.643463	−	0.765478i	$-0.722503\pi$
$107$	13.0556	−	13.0556i	0.122015	−	0.122015i	0.765478	+	0.643463i	$0.222503\pi$
$108$		0			0
$109$		−	69.2827i		−	0.635621i	−0.948154	−	0.317810i	$-0.897052\pi$
$109$		−	69.2827i		−	0.635621i	0.948154	−	0.317810i	$-0.102948\pi$
$110$		0			0
$111$	−86.5857			−0.780051
$112$		0			0
$113$	−102.136	−	102.136i	−0.903860	−	0.903860i	0.0919072	−	0.995768i	$-0.470704\pi$
$113$	−102.136	−	102.136i	−0.903860	−	0.903860i	−0.995768	+	0.0919072i	$0.970704\pi$
$114$		0			0
$115$	−45.8888	+	10.3133i	−0.399033	+	0.0896806i
$116$		0			0
$117$	43.3485	−	43.3485i	0.370500	−	0.370500i
$118$		0			0
$119$		−	252.272i		−	2.11994i
$120$		0			0
$121$	−79.4041			−0.656232
$122$		0			0
$123$	24.8536	+	24.8536i	0.202062	+	0.202062i
$124$		0			0
$125$	−124.068	−	15.2350i	−0.992545	−	0.121880i
$126$		0			0
$127$	119.944	−	119.944i	0.944444	−	0.944444i	−0.0540920	−	0.998536i	$-0.517226\pi$
$127$	119.944	−	119.944i	0.944444	−	0.944444i	0.998536	+	0.0540920i	$0.0172264\pi$
$128$		0			0
$129$		−	79.1010i		−	0.613186i
$130$		0			0
$131$	−121.146			−0.924782			−0.462391	−	0.886676i	$-0.653008\pi$
$131$	−121.146			−0.924782			−0.462391	+	0.886676i	$0.653008\pi$
$132$		0			0
$133$	−90.9898	−	90.9898i	−0.684134	−	0.684134i
$134$		0			0
$135$	5.69694	+	25.3485i	0.0421995	+	0.187766i
$136$		0			0
$137$	119.530	−	119.530i	0.872482	−	0.872482i	−0.120260	−	0.992742i	$-0.538373\pi$
$137$	119.530	−	119.530i	0.872482	−	0.872482i	0.992742	+	0.120260i	$0.0383728\pi$
$138$		0			0
$139$			140.788i			1.01286i	0.862281	+	0.506431i	$0.169035\pi$
$139$			140.788i			1.01286i	−0.862281	+	0.506431i	$0.830965\pi$
$140$		0			0
$141$	−123.798			−0.878000
$142$		0			0
$143$	−93.1918	−	93.1918i	−0.651691	−	0.651691i
$144$		0			0
$145$	−0.191836	−	0.121431i	−0.00132301	−	0.000837454i
$146$		0			0
$147$	12.7298	−	12.7298i	0.0865976	−	0.0865976i
$148$		0			0
$149$		−	53.5301i		−	0.359262i	−0.983734	−	0.179631i	$-0.942510\pi$
$149$		−	53.5301i		−	0.359262i	0.983734	−	0.179631i	$-0.0574904\pi$
$150$		0			0
$151$	−232.606			−1.54044			−0.770219	−	0.637780i	$-0.779853\pi$
$151$	−232.606			−1.54044			−0.770219	+	0.637780i	$0.779853\pi$
$152$		0			0
$153$	−69.4393	−	69.4393i	−0.453852	−	0.453852i
$154$		0			0
$155$	12.0204	−	18.9898i	0.0775510	−	0.122515i
$156$		0			0
$157$	−128.631	+	128.631i	−0.819306	+	0.819306i	−0.986007	−	0.166701i	$-0.946689\pi$
$157$	−128.631	+	128.631i	−0.819306	+	0.819306i	0.166701	+	0.986007i	$0.446689\pi$
$158$		0			0
$159$			13.4847i			0.0848094i
$160$		0			0
$161$	72.4949			0.450279
$162$		0			0
$163$	117.576	+	117.576i	0.721322	+	0.721322i	0.968875	−	0.247552i	$-0.0796262\pi$
$163$	117.576	+	117.576i	0.721322	+	0.721322i	−0.247552	+	0.968875i	$0.579626\pi$
$164$		0			0
$165$	54.4949	−	12.2474i	0.330272	−	0.0742270i
$166$		0			0
$167$	−33.6617	+	33.6617i	−0.201567	+	0.201567i	−0.800671	−	0.599104i	$-0.795524\pi$
$167$	−33.6617	+	33.6617i	−0.201567	+	0.201567i	0.599104	+	0.800671i	$0.295524\pi$
$168$		0			0
$169$			248.576i			1.47086i
$170$		0			0
$171$	−50.0908			−0.292929
$172$		0			0
$173$	−28.2474	−	28.2474i	−0.163280	−	0.163280i	0.620738	−	0.784018i	$-0.286833\pi$
$173$	−28.2474	−	28.2474i	−0.163280	−	0.163280i	−0.784018	+	0.620738i	$0.786833\pi$
$174$		0			0
$175$	181.429	+	64.8434i	1.03674	+	0.370534i
$176$		0			0
$177$	−67.8990	+	67.8990i	−0.383610	+	0.383610i
$178$		0			0
$179$		−	45.2372i		−	0.252722i	−0.991984	−	0.126361i	$-0.959670\pi$
$179$		−	45.2372i		−	0.252722i	0.991984	−	0.126361i	$-0.0403298\pi$
$180$		0			0
$181$	260.656			1.44009			0.720045	−	0.693928i	$-0.244121\pi$
$181$	260.656			1.44009			0.720045	+	0.693928i	$0.244121\pi$
$182$		0			0
$183$	−58.6515	−	58.6515i	−0.320500	−	0.320500i
$184$		0			0
$185$	54.8082	+	243.868i	0.296260	+	1.31821i
$186$		0			0
$187$	−149.283	+	149.283i	−0.798303	+	0.798303i
$188$		0			0
$189$		−	40.0454i		−	0.211880i
$190$		0			0
$191$	−51.8684			−0.271562			−0.135781	−	0.990739i	$-0.543354\pi$
$191$	−51.8684			−0.271562			−0.135781	+	0.990739i	$0.543354\pi$
$192$		0			0
$193$	16.6163	+	16.6163i	0.0860950	+	0.0860950i	0.748843	−	0.662748i	$-0.230610\pi$
$193$	16.6163	+	16.6163i	0.0860950	+	0.0860950i	−0.662748	+	0.748843i	$0.730610\pi$
$194$		0			0
$195$	−149.530	−	94.6515i	−0.766821	−	0.485392i
$196$		0			0
$197$	−86.0908	+	86.0908i	−0.437009	+	0.437009i	−0.891004	−	0.453995i	$-0.849998\pi$
$197$	−86.0908	+	86.0908i	−0.437009	+	0.437009i	0.453995	+	0.891004i	$0.349998\pi$
$198$		0			0
$199$		−	28.5653i		−	0.143544i	−0.997421	−	0.0717721i	$-0.977135\pi$
$199$		−	28.5653i		−	0.143544i	0.997421	−	0.0717721i	$-0.0228654\pi$
$200$		0			0
$201$	208.899			1.03930
$202$		0			0
$203$	0.247449	+	0.247449i	0.00121896	+	0.00121896i
$204$		0			0
$205$	54.2679	−	85.7321i	0.264721	−	0.418206i
$206$		0			0
$207$	19.9546	−	19.9546i	0.0963990	−	0.0963990i
$208$		0			0
$209$			107.687i			0.515248i
$210$		0			0
$211$	197.151			0.934365			0.467183	−	0.884161i	$-0.345269\pi$
$211$	197.151			0.934365			0.467183	+	0.884161i	$0.345269\pi$
$212$		0			0
$213$	59.2827	+	59.2827i	0.278322	+	0.278322i
$214$		0			0
$215$	−222.788	+	50.0704i	−1.03622	+	0.232886i
$216$		0			0
$217$	−24.4949	+	24.4949i	−0.112880	+	0.112880i
$218$		0			0
$219$		−	53.8638i		−	0.245953i
$220$		0			0
$221$	668.908			3.02673
$222$		0			0
$223$	287.338	+	287.338i	1.28851	+	1.28851i	0.935690	+	0.352822i	$0.114778\pi$
$223$	287.338	+	287.338i	1.28851	+	1.28851i	0.352822	+	0.935690i	$0.385222\pi$
$224$		0			0
$225$	67.7878	−	32.0908i	0.301279	−	0.142626i
$226$		0			0
$227$	234.384	−	234.384i	1.03253	−	1.03253i	0.0330743	−	0.999453i	$-0.489470\pi$
$227$	234.384	−	234.384i	1.03253	−	1.03253i	0.999453	−	0.0330743i	$-0.0105298\pi$
$228$		0			0
$229$		−	284.969i		−	1.24441i	−0.782855	−	0.622204i	$-0.786237\pi$
$229$		−	284.969i		−	1.24441i	0.782855	−	0.622204i	$-0.213763\pi$
$230$		0			0
$231$	−86.0908			−0.372688
$232$		0			0
$233$	−241.530	−	241.530i	−1.03661	−	1.03661i	−0.999304	−	0.0373060i	$-0.988122\pi$
$233$	−241.530	−	241.530i	−1.03661	−	1.03661i	−0.0373060	−	0.999304i	$-0.511878\pi$
$234$		0			0
$235$	78.3633	+	348.677i	0.333461	+	1.48373i
$236$		0			0
$237$	−155.171	+	155.171i	−0.654732	+	0.654732i
$238$		0			0
$239$			327.737i			1.37128i	0.727939	+	0.685642i	$0.240478\pi$
$239$			327.737i			1.37128i	−0.727939	+	0.685642i	$0.759522\pi$
$240$		0			0
$241$	269.131			1.11672			0.558362	−	0.829597i	$-0.311430\pi$
$241$	269.131			1.11672			0.558362	+	0.829597i	$0.311430\pi$
$242$		0			0
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−43.9115	−	27.7957i	−0.179231	−	0.113452i
$246$		0			0
$247$	241.262	−	241.262i	0.976770	−	0.976770i
$248$		0			0
$249$		−	232.565i		−	0.933997i
$250$		0			0
$251$	−186.136			−0.741579			−0.370789	−	0.928717i	$-0.620913\pi$
$251$	−186.136			−0.741579			−0.370789	+	0.928717i	$0.620913\pi$
$252$		0			0
$253$	−42.8990	−	42.8990i	−0.169561	−	0.169561i
$254$		0			0
$255$	−151.621	+	239.530i	−0.594592	+	0.939334i
$256$		0			0
$257$	138.268	−	138.268i	0.538007	−	0.538007i	−0.384936	−	0.922943i	$-0.625776\pi$
$257$	138.268	−	138.268i	0.538007	−	0.538007i	0.922943	+	0.384936i	$0.125776\pi$
$258$		0			0
$259$		−	385.262i		−	1.48750i
$260$		0			0
$261$	0.136223			0.000521927
$262$		0			0
$263$	−163.146	−	163.146i	−0.620329	−	0.620329i	0.325287	−	0.945615i	$-0.394539\pi$
$263$	−163.146	−	163.146i	−0.620329	−	0.620329i	−0.945615	+	0.325287i	$0.894539\pi$
$264$		0			0
$265$	37.9796	−	8.53572i	0.143319	−	0.0322103i
$266$		0			0
$267$	−87.9342	+	87.9342i	−0.329342	+	0.329342i
$268$		0			0
$269$			108.227i			0.402331i	0.979557	+	0.201165i	$0.0644729\pi$
$269$			108.227i			0.402331i	−0.979557	+	0.201165i	$0.935527\pi$
$270$		0			0
$271$	324.384			1.19699			0.598494	−	0.801127i	$-0.295766\pi$
$271$	324.384			1.19699			0.598494	+	0.801127i	$0.295766\pi$
$272$		0			0
$273$	192.879	+	192.879i	0.706515	+	0.706515i
$274$		0			0
$275$	−68.9898	−	145.732i	−0.250872	−	0.529935i
$276$		0			0
$277$	165.864	−	165.864i	0.598786	−	0.598786i	−0.341203	−	0.939990i	$-0.610834\pi$
$277$	165.864	−	165.864i	0.598786	−	0.598786i	0.939990	+	0.341203i	$0.110834\pi$
$278$		0			0
$279$			13.4847i			0.0483322i
$280$		0			0
$281$	300.434			1.06916			0.534579	−	0.845118i	$-0.320470\pi$
$281$	300.434			1.06916			0.534579	+	0.845118i	$0.320470\pi$
$282$		0			0
$283$	352.161	+	352.161i	1.24439	+	1.24439i	0.958163	+	0.286223i	$0.0923998\pi$
$283$	352.161	+	352.161i	1.24439	+	1.24439i	0.286223	+	0.958163i	$0.407600\pi$
$284$		0			0
$285$	31.7071	+	141.081i	0.111253	+	0.495020i
$286$		0			0
$287$	−110.586	+	110.586i	−0.385316	+	0.385316i
$288$		0			0
$289$		−	782.514i		−	2.70766i
$290$		0			0
$291$	−90.6311			−0.311447
$292$		0			0
$293$	109.414	+	109.414i	0.373428	+	0.373428i	0.868724	−	0.495296i	$-0.164941\pi$
$293$	109.414	+	109.414i	0.373428	+	0.373428i	−0.495296	+	0.868724i	$0.664941\pi$
$294$		0			0
$295$	234.217	+	148.258i	0.793955	+	0.502568i
$296$		0			0
$297$	−23.6969	+	23.6969i	−0.0797877	+	0.0797877i
$298$		0			0
$299$			192.222i			0.642884i
$300$		0			0
$301$	351.959			1.16930
$302$		0			0
$303$	−115.540	−	115.540i	−0.381321	−	0.381321i
$304$		0			0
$305$	−128.066	+	202.318i	−0.419888	+	0.663337i
$306$		0			0
$307$	−110.627	+	110.627i	−0.360347	+	0.360347i	−0.863941	−	0.503594i	$-0.832011\pi$
$307$	−110.627	+	110.627i	−0.360347	+	0.360347i	0.503594	+	0.863941i	$0.332011\pi$
$308$		0			0
$309$			177.934i			0.575839i
$310$		0			0
$311$	2.38367			0.00766454			0.00383227	−	0.999993i	$-0.498780\pi$
$311$	2.38367			0.00766454			0.00383227	+	0.999993i	$0.498780\pi$
$312$		0			0
$313$	132.959	+	132.959i	0.424790	+	0.424790i	0.886849	−	0.462059i	$-0.152889\pi$
$313$	132.959	+	132.959i	0.424790	+	0.424790i	−0.462059	+	0.886849i	$0.652889\pi$
$314$		0			0
$315$	−112.788	+	25.3485i	−0.358056	+	0.0804713i
$316$		0			0
$317$	37.1464	−	37.1464i	0.117181	−	0.117181i	−0.646085	−	0.763266i	$-0.723595\pi$
$317$	37.1464	−	37.1464i	0.117181	−	0.117181i	0.763266	+	0.646085i	$0.223595\pi$
$318$		0			0
$319$		−	0.292856i		−	0.000918045i
$320$		0			0
$321$	31.9796			0.0996249
$322$		0			0
$323$	−386.474	−	386.474i	−1.19652	−	1.19652i
$324$		0			0
$325$	−171.934	+	481.065i	−0.529028	+	1.48020i
$326$		0			0
$327$	84.8536	−	84.8536i	0.259491	−	0.259491i
$328$		0			0
$329$		−	550.838i		−	1.67428i
$330$		0			0
$331$	−21.6459			−0.0653955			−0.0326978	−	0.999465i	$-0.510410\pi$
$331$	−21.6459			−0.0653955			−0.0326978	+	0.999465i	$0.510410\pi$
$332$		0			0
$333$	−106.045	−	106.045i	−0.318455	−	0.318455i
$334$		0			0
$335$	−132.232	−	588.363i	−0.394721	−	1.75631i
$336$		0			0
$337$	−136.757	+	136.757i	−0.405808	+	0.405808i	−0.880274	−	0.474466i	$-0.842641\pi$
$337$	−136.757	+	136.757i	−0.405808	+	0.405808i	0.474466	+	0.880274i	$0.342641\pi$
$338$		0			0
$339$		−	250.182i		−	0.737999i
$340$		0			0
$341$	28.9898			0.0850141
$342$		0			0
$343$	−210.384	−	210.384i	−0.613363	−	0.613363i
$344$		0			0
$345$	−68.8332	−	43.5709i	−0.199516	−	0.126293i
$346$		0			0
$347$	−33.8480	+	33.8480i	−0.0975445	+	0.0975445i	−0.754195	−	0.656650i	$-0.771973\pi$
$347$	−33.8480	+	33.8480i	−0.0975445	+	0.0975445i	0.656650	+	0.754195i	$0.271973\pi$
$348$		0			0
$349$		−	241.283i		−	0.691354i	−0.938354	−	0.345677i	$-0.887649\pi$
$349$		−	241.283i		−	0.691354i	0.938354	−	0.345677i	$-0.112351\pi$
$350$		0			0
$351$	106.182			0.302512
$352$		0			0
$353$	126.833	+	126.833i	0.359301	+	0.359301i	0.863555	−	0.504254i	$-0.168233\pi$
$353$	126.833	+	126.833i	0.359301	+	0.359301i	−0.504254	+	0.863555i	$0.668233\pi$
$354$		0			0
$355$	129.444	−	204.495i	0.364631	−	0.576042i
$356$		0			0
$357$	308.969	−	308.969i	0.865460	−	0.865460i
$358$		0			0
$359$			22.1112i			0.0615912i	0.999526	+	0.0307956i	$0.00980409\pi$
$359$			22.1112i			0.0615912i	−0.999526	+	0.0307956i	$0.990196\pi$
$360$		0			0
$361$	82.2122			0.227735
$362$		0			0
$363$	−97.2497	−	97.2497i	−0.267906	−	0.267906i
$364$		0			0
$365$	−151.707	+	34.0954i	−0.415636	+	0.0934121i
$366$		0			0
$367$	−213.944	+	213.944i	−0.582955	+	0.582955i	−0.935714	−	0.352759i	$-0.885243\pi$
$367$	−213.944	+	213.944i	−0.582955	+	0.582955i	0.352759	+	0.935714i	$0.385243\pi$
$368$		0			0
$369$			60.8786i			0.164983i
$370$		0			0
$371$	−60.0000			−0.161725
$372$		0			0
$373$	−210.025	−	210.025i	−0.563070	−	0.563070i	0.367108	−	0.930178i	$-0.380348\pi$
$373$	−210.025	−	210.025i	−0.563070	−	0.563070i	−0.930178	+	0.367108i	$0.880348\pi$
$374$		0			0
$375$	−133.293	−	170.611i	−0.355448	−	0.454962i
$376$		0			0
$377$	−0.656118	+	0.656118i	−0.00174037	+	0.00174037i
$378$		0			0
$379$		−	124.343i		−	0.328081i	−0.986454	−	0.164041i	$-0.947547\pi$
$379$		−	124.343i		−	0.328081i	0.986454	−	0.164041i	$-0.0524528\pi$
$380$		0			0
$381$	293.803			0.771135
$382$		0			0
$383$	418.540	+	418.540i	1.09279	+	1.09279i	0.995229	+	0.0975654i	$0.0311055\pi$
$383$	418.540	+	418.540i	1.09279	+	1.09279i	0.0975654	+	0.995229i	$0.468894\pi$
$384$		0			0
$385$	54.4949	+	242.474i	0.141545	+	0.629804i
$386$		0			0
$387$	96.8786	−	96.8786i	0.250332	−	0.250332i
$388$		0			0
$389$		−	369.884i		−	0.950859i	−0.879754	−	0.475430i	$-0.842293\pi$
$389$		−	369.884i		−	0.950859i	0.879754	−	0.475430i	$-0.157707\pi$
$390$		0			0
$391$	307.918			0.787515
$392$		0			0
$393$	−148.373	−	148.373i	−0.377541	−	0.377541i
$394$		0			0
$395$	535.262	+	338.817i	1.35509	+	0.857765i
$396$		0			0
$397$	373.984	−	373.984i	0.942026	−	0.942026i	−0.0563835	−	0.998409i	$-0.517957\pi$
$397$	373.984	−	373.984i	0.942026	−	0.942026i	0.998409	+	0.0563835i	$0.0179570\pi$
$398$		0			0
$399$		−	222.879i		−	0.558593i
$400$		0			0
$401$	113.151			0.282172			0.141086	−	0.989997i	$-0.454941\pi$
$401$	113.151			0.282172			0.141086	+	0.989997i	$0.454941\pi$
$402$		0			0
$403$	−64.9490	−	64.9490i	−0.161164	−	0.161164i
$404$		0			0
$405$	−24.0681	+	38.0227i	−0.0594274	+	0.0938832i
$406$		0			0
$407$	−227.980	+	227.980i	−0.560146	+	0.560146i
$408$		0			0
$409$		−	90.3837i		−	0.220987i	−0.993877	−	0.110493i	$-0.964757\pi$
$409$		−	90.3837i		−	0.220987i	0.993877	−	0.110493i	$-0.0352431\pi$
$410$		0			0
$411$	292.788			0.712379
$412$		0			0
$413$	−302.116	−	302.116i	−0.731515	−	0.731515i
$414$		0			0
$415$	−655.019	+	147.212i	−1.57836	+	0.354728i
$416$		0			0
$417$	−172.429	+	172.429i	−0.413499	+	0.413499i
$418$		0			0
$419$			334.772i			0.798978i	0.916738	+	0.399489i	$0.130812\pi$
$419$			334.772i			0.798978i	−0.916738	+	0.399489i	$0.869188\pi$
$420$		0			0
$421$	−57.2735			−0.136042			−0.0680208	−	0.997684i	$-0.521668\pi$
$421$	−57.2735			−0.136042			−0.0680208	+	0.997684i	$0.521668\pi$
$422$		0			0
$423$	−151.621	−	151.621i	−0.358442	−	0.358442i
$424$		0			0
$425$	770.611	+	275.419i	1.81320	+	0.648044i
$426$		0			0
$427$	260.969	−	260.969i	0.611170	−	0.611170i
$428$		0			0
$429$		−	228.272i		−	0.532104i
$430$		0			0
$431$	442.656			1.02704			0.513522	−	0.858076i	$-0.328340\pi$
$431$	442.656			1.02704			0.513522	+	0.858076i	$0.328340\pi$
$432$		0			0
$433$	−14.8684	−	14.8684i	−0.0343380	−	0.0343380i	0.689729	−	0.724067i	$-0.257730\pi$
$433$	−14.8684	−	14.8684i	−0.0343380	−	0.0343380i	−0.724067	+	0.689729i	$0.757730\pi$
$434$		0			0
$435$	−0.0862283	−	0.383672i	−0.000198226	−	0.000882004i
$436$		0			0
$437$	111.060	−	111.060i	0.254142	−	0.254142i
$438$		0			0
$439$		−	233.818i		−	0.532616i	−0.963888	−	0.266308i	$-0.914196\pi$
$439$		−	233.818i		−	0.532616i	0.963888	−	0.266308i	$-0.0858038\pi$
$440$		0			0
$441$	31.1816			0.0707066
$442$		0			0
$443$	246.747	+	246.747i	0.556991	+	0.556991i	0.928449	−	0.371459i	$-0.121142\pi$
$443$	246.747	+	246.747i	0.556991	+	0.556991i	−0.371459	+	0.928449i	$0.621142\pi$
$444$		0			0
$445$	303.328	+	192.005i	0.681636	+	0.431471i
$446$		0			0
$447$	65.5607	−	65.5607i	0.146668	−	0.146668i
$448$		0			0
$449$			282.758i			0.629751i	0.949133	+	0.314875i	$0.101963\pi$
$449$			282.758i			0.629751i	−0.949133	+	0.314875i	$0.898037\pi$
$450$		0			0
$451$	130.879			0.290196
$452$		0			0
$453$	−284.883	−	284.883i	−0.628881	−	0.628881i
$454$		0			0
$455$	421.151	−	665.333i	0.925607	−	1.46227i
$456$		0			0
$457$	−298.171	+	298.171i	−0.652454	+	0.652454i	−0.953583	−	0.301129i	$-0.902636\pi$
$457$	−298.171	+	298.171i	−0.652454	+	0.652454i	0.301129	+	0.953583i	$0.402636\pi$
$458$		0			0
$459$		−	170.091i		−	0.370568i
$460$		0			0
$461$	264.318			0.573358			0.286679	−	0.958027i	$-0.407449\pi$
$461$	264.318			0.573358			0.286679	+	0.958027i	$0.407449\pi$
$462$		0			0
$463$	135.116	+	135.116i	0.291827	+	0.291827i	0.837802	−	0.545975i	$-0.183841\pi$
$463$	135.116	+	135.116i	0.291827	+	0.291827i	−0.545975	+	0.837802i	$0.683841\pi$
$464$		0			0
$465$	37.9796	−	8.53572i	0.0816765	−	0.0183564i
$466$		0			0
$467$	−558.631	+	558.631i	−1.19621	+	1.19621i	−0.220920	+	0.975292i	$0.570906\pi$
$467$	−558.631	+	558.631i	−1.19621	+	1.19621i	−0.975292	+	0.220920i	$0.929094\pi$
$468$		0			0
$469$			929.494i			1.98186i
$470$		0			0
$471$	−315.081			−0.668961
$472$		0			0
$473$	−208.272	−	208.272i	−0.440322	−	0.440322i
$474$		0			0
$475$	377.283	−	178.606i	0.794279	−	0.376013i
$476$		0			0
$477$	−16.5153	+	16.5153i	−0.0346233	+	0.0346233i
$478$		0			0
$479$			456.141i			0.952277i	0.879370	+	0.476139i	$0.157964\pi$
$479$			456.141i			0.952277i	−0.879370	+	0.476139i	$0.842036\pi$
$480$		0			0
$481$	1021.53			2.12377
$482$		0			0
$483$	88.7878	+	88.7878i	0.183826	+	0.183826i
$484$		0			0
$485$	57.3689	+	255.262i	0.118286	+	0.526314i
$486$		0			0
$487$	11.9444	−	11.9444i	0.0245265	−	0.0245265i	−0.694737	−	0.719264i	$-0.744479\pi$
$487$	11.9444	−	11.9444i	0.0245265	−	0.0245265i	0.719264	+	0.694737i	$0.244479\pi$
$488$		0			0
$489$			288.000i			0.588957i
$490$		0			0
$491$	−822.468			−1.67509			−0.837544	−	0.546370i	$-0.816009\pi$
$491$	−822.468			−1.67509			−0.837544	+	0.546370i	$0.816009\pi$
$492$		0			0
$493$	1.05103	+	1.05103i	0.00213190	+	0.00213190i
$494$		0			0
$495$	81.7423	+	51.7423i	0.165136	+	0.104530i
$496$		0			0
$497$	−263.778	+	263.778i	−0.530740	+	0.530740i
$498$		0			0
$499$			312.474i			0.626201i	0.949720	+	0.313101i	$0.101368\pi$
$499$			312.474i			0.626201i	−0.949720	+	0.313101i	$0.898632\pi$
$500$		0			0
$501$	−82.4541			−0.164579
$502$		0			0
$503$	−371.530	−	371.530i	−0.738628	−	0.738628i	0.233684	−	0.972313i	$-0.424922\pi$
$503$	−371.530	−	371.530i	−0.738628	−	0.738628i	−0.972313	+	0.233684i	$0.924922\pi$
$504$		0			0
$505$	−252.283	+	398.555i	−0.499570	+	0.789218i
$506$		0			0
$507$	−304.442	+	304.442i	−0.600476	+	0.600476i
$508$		0			0
$509$			171.228i			0.336401i	0.985753	+	0.168200i	$0.0537956\pi$
$509$			171.228i			0.336401i	−0.985753	+	0.168200i	$0.946204\pi$
$510$		0			0
$511$	239.666			0.469014
$512$		0			0
$513$	−61.3485	−	61.3485i	−0.119588	−	0.119588i
$514$		0			0
$515$	501.151	−	112.631i	0.973109	−	0.218701i
$516$		0			0
$517$	−325.959	+	325.959i	−0.630482	+	0.630482i
$518$		0			0
$519$		−	69.1918i		−	0.133318i
$520$		0			0
$521$	−206.313			−0.395995			−0.197997	−	0.980203i	$-0.563444\pi$
$521$	−206.313			−0.395995			−0.197997	+	0.980203i	$0.563444\pi$
$522$		0			0
$523$	135.526	+	135.526i	0.259131	+	0.259131i	0.824701	−	0.565570i	$-0.191344\pi$
$523$	135.526	+	135.526i	0.259131	+	0.259131i	−0.565570	+	0.824701i	$0.691344\pi$
$524$		0			0
$525$	142.788	+	301.621i	0.271977	+	0.574516i
$526$		0			0
$527$	−104.041	+	104.041i	−0.197421	+	0.197421i
$528$		0			0
$529$		−	440.514i		−	0.832730i
$530$		0			0
$531$	−166.318			−0.313216
$532$		0			0
$533$	−293.221	−	293.221i	−0.550134	−	0.550134i
$534$		0			0
$535$	−20.2429	−	90.0704i	−0.0378371	−	0.168356i
$536$		0			0
$537$	55.4041	−	55.4041i	0.103173	−	0.103173i
$538$		0			0
$539$		−	67.0352i		−	0.124370i
$540$		0			0
$541$	−303.485			−0.560970			−0.280485	−	0.959858i	$-0.590495\pi$
$541$	−303.485			−0.560970			−0.280485	+	0.959858i	$0.590495\pi$
$542$		0			0
$543$	319.237	+	319.237i	0.587914	+	0.587914i
$544$		0			0
$545$	−292.702	−	185.278i	−0.537067	−	0.339960i
$546$		0			0
$547$	71.3939	−	71.3939i	0.130519	−	0.130519i	−0.638829	−	0.769348i	$-0.720581\pi$
$547$	71.3939	−	71.3939i	0.130519	−	0.130519i	0.769348	+	0.638829i	$0.220581\pi$
$548$		0			0
$549$		−	143.666i		−	0.261687i
$550$		0			0
$551$	0.758169			0.00137599
$552$		0			0
$553$	−690.434	−	690.434i	−1.24852	−	1.24852i
$554$		0			0
$555$	−231.551	+	365.803i	−0.417208	+	0.659104i
$556$		0			0
$557$	−753.019	+	753.019i	−1.35192	+	1.35192i	−0.468407	+	0.883513i	$0.655172\pi$
$557$	−753.019	+	753.019i	−1.35192	+	1.35192i	−0.883513	+	0.468407i	$0.844828\pi$
$558$		0			0
$559$			933.231i			1.66946i
$560$		0			0
$561$	−365.666			−0.651812
$562$		0			0
$563$	−703.464	−	703.464i	−1.24949	−	1.24949i	−0.955944	−	0.293548i	$-0.905164\pi$
$563$	−703.464	−	703.464i	−1.24949	−	1.24949i	−0.293548	−	0.955944i	$-0.594836\pi$
$564$		0			0
$565$	−704.636	+	158.363i	−1.24714	+	0.280289i
$566$		0			0
$567$	49.0454	−	49.0454i	0.0864998	−	0.0864998i
$568$		0			0
$569$		−	434.504i		−	0.763628i	−0.924239	−	0.381814i	$-0.875300\pi$
$569$		−	434.504i		−	0.763628i	0.924239	−	0.381814i	$-0.124700\pi$
$570$		0			0
$571$	131.040			0.229492			0.114746	−	0.993395i	$-0.463395\pi$
$571$	131.040			0.229492			0.114746	+	0.993395i	$0.463395\pi$
$572$		0			0
$573$	−63.5255	−	63.5255i	−0.110865	−	0.110865i
$574$		0			0
$575$	−79.1464	+	221.448i	−0.137646	+	0.385128i
$576$		0			0
$577$	290.444	−	290.444i	0.503369	−	0.503369i	−0.409114	−	0.912483i	$-0.634162\pi$
$577$	290.444	−	290.444i	0.503369	−	0.503369i	0.912483	+	0.409114i	$0.134162\pi$
$578$		0			0
$579$			40.7015i			0.0702962i
$580$		0			0
$581$	1034.80			1.78106
$582$		0			0
$583$	35.5051	+	35.5051i	0.0609007	+	0.0609007i
$584$		0			0
$585$	−67.2122	−	299.060i	−0.114893	−	0.511214i
$586$		0			0
$587$	−180.288	+	180.288i	−0.307135	+	0.307135i	−0.843797	−	0.536662i	$-0.819685\pi$
$587$	−180.288	+	180.288i	−0.307135	+	0.307135i	0.536662	+	0.843797i	$0.319685\pi$
$588$		0			0
$589$			75.0510i			0.127421i
$590$		0			0
$591$	−210.879			−0.356817
$592$		0			0
$593$	−25.0556	−	25.0556i	−0.0422523	−	0.0422523i	0.685665	−	0.727917i	$-0.259512\pi$
$593$	−25.0556	−	25.0556i	−0.0422523	−	0.0422523i	−0.727917	+	0.685665i	$0.759512\pi$
$594$		0			0
$595$	−1065.79	−	674.636i	−1.79124	−	1.13384i
$596$		0			0
$597$	34.9852	−	34.9852i	0.0586017	−	0.0586017i
$598$		0			0
$599$		−	509.807i		−	0.851097i	−0.904936	−	0.425549i	$-0.860081\pi$
$599$		−	509.807i		−	0.851097i	0.904936	−	0.425549i	$-0.139919\pi$
$600$		0			0
$601$	179.757			0.299097			0.149548	−	0.988754i	$-0.452218\pi$
$601$	179.757			0.299097			0.149548	+	0.988754i	$0.452218\pi$
$602$		0			0
$603$	255.848	+	255.848i	0.424292	+	0.424292i
$604$		0			0
$605$	−212.345	+	335.462i	−0.350984	+	0.554483i
$606$		0			0
$607$	33.1566	−	33.1566i	0.0546238	−	0.0546238i	−0.679267	−	0.733891i	$-0.737702\pi$
$607$	33.1566	−	33.1566i	0.0546238	−	0.0546238i	0.733891	+	0.679267i	$0.237702\pi$
$608$		0			0
$609$			0.606123i			0.000995276i
$610$		0			0
$611$	1460.56			2.39045
$612$		0			0
$613$	261.712	+	261.712i	0.426936	+	0.426936i	0.887583	−	0.460647i	$-0.152383\pi$
$613$	261.712	+	261.712i	0.426936	+	0.426936i	−0.460647	+	0.887583i	$0.652383\pi$
$614$		0			0
$615$	171.464	−	38.5357i	0.278804	−	0.0626597i
$616$		0			0
$617$	−762.075	+	762.075i	−1.23513	+	1.23513i	−0.273161	+	0.961968i	$0.588069\pi$
$617$	−762.075	+	762.075i	−1.23513	+	1.23513i	−0.961968	+	0.273161i	$0.911931\pi$
$618$		0			0
$619$		−	81.6367i		−	0.131885i	−0.997823	−	0.0659424i	$-0.978995\pi$
$619$		−	81.6367i		−	0.131885i	0.997823	−	0.0659424i	$-0.0210054\pi$
$620$		0			0
$621$	48.8786			0.0787095
$622$		0			0
$623$	−391.262	−	391.262i	−0.628029	−	0.628029i
$624$		0			0
$625$	−396.151	+	483.414i	−0.633842	+	0.773463i
$626$		0			0
$627$	−131.889	+	131.889i	−0.210349	+	0.210349i
$628$		0			0
$629$		−	1636.38i		−	2.60156i
$630$		0			0
$631$	−16.4133			−0.0260115			−0.0130057	−	0.999915i	$-0.504140\pi$
$631$	−16.4133			−0.0260115			−0.0130057	+	0.999915i	$0.504140\pi$
$632$		0			0
$633$	241.460	+	241.460i	0.381453	+	0.381453i
$634$		0			0
$635$	−185.975	−	827.494i	−0.292874	−	1.30314i
$636$		0			0
$637$	−150.186	+	150.186i	−0.235771	+	0.235771i
$638$		0			0
$639$			145.212i			0.227249i
$640$		0			0
$641$	−546.041			−0.851858			−0.425929	−	0.904757i	$-0.640053\pi$
$641$	−546.041			−0.851858			−0.425929	+	0.904757i	$0.640053\pi$
$642$		0			0
$643$	142.879	+	142.879i	0.222206	+	0.222206i	0.809427	−	0.587221i	$-0.199778\pi$
$643$	142.879	+	142.879i	0.222206	+	0.222206i	−0.587221	+	0.809427i	$0.699778\pi$
$644$		0			0
$645$	−334.182	−	211.535i	−0.518111	−	0.327961i
$646$		0			0
$647$	−649.691	+	649.691i	−1.00416	+	1.00416i	−0.00416838	+	0.999991i	$0.501327\pi$
$647$	−649.691	+	649.691i	−1.00416	+	1.00416i	−0.999991	+	0.00416838i	$0.998673\pi$
$648$		0			0
$649$			357.555i			0.550932i
$650$		0			0
$651$	−60.0000			−0.0921659
$652$		0			0
$653$	150.904	+	150.904i	0.231093	+	0.231093i	0.813149	−	0.582056i	$-0.197752\pi$
$653$	150.904	+	150.904i	0.231093	+	0.231093i	−0.582056	+	0.813149i	$0.697752\pi$
$654$		0			0
$655$	−323.974	+	511.813i	−0.494617	+	0.781394i
$656$		0			0
$657$	65.9694	−	65.9694i	0.100410	−	0.100410i
$658$		0			0
$659$		−	268.802i		−	0.407893i	−0.978982	−	0.203947i	$-0.934623\pi$
$659$		−	268.802i		−	0.407893i	0.978982	−	0.203947i	$-0.0653769\pi$
$660$		0			0
$661$	−311.162			−0.470745			−0.235372	−	0.971905i	$-0.575631\pi$
$661$	−311.162			−0.470745			−0.235372	+	0.971905i	$0.575631\pi$
$662$		0			0
$663$	819.242	+	819.242i	1.23566	+	1.23566i
$664$		0			0
$665$	−627.737	+	141.081i	−0.943965	+	0.212151i
$666$		0			0
$667$	−0.302031	+	0.302031i	−0.000452820	+	0.000452820i
$668$		0			0
$669$			703.832i			1.05207i
$670$		0			0
$671$	−308.858			−0.460295
$672$		0			0
$673$	−547.756	−	547.756i	−0.813902	−	0.813902i	0.171314	−	0.985216i	$-0.445199\pi$
$673$	−547.756	−	547.756i	−0.813902	−	0.813902i	−0.985216	+	0.171314i	$0.945199\pi$
$674$		0			0
$675$	122.326	+	43.7196i	0.181223	+	0.0647698i
$676$		0			0
$677$	−696.257	+	696.257i	−1.02844	+	1.02844i	−0.0288606	+	0.999583i	$0.509188\pi$
$677$	−696.257	+	696.257i	−1.02844	+	1.02844i	−0.999583	+	0.0288606i	$0.990812\pi$
$678$		0			0
$679$		−	403.262i		−	0.593906i
$680$		0			0
$681$	574.120			0.843055
$682$		0			0
$683$	84.0250	+	84.0250i	0.123023	+	0.123023i	0.765938	−	0.642915i	$-0.222275\pi$
$683$	84.0250	+	84.0250i	0.123023	+	0.123023i	−0.642915	+	0.765938i	$0.722275\pi$
$684$		0			0
$685$	−185.333	−	824.636i	−0.270559	−	1.20385i
$686$		0			0
$687$	349.015	−	349.015i	0.508027	−	0.508027i
$688$		0			0
$689$		−	159.092i		−	0.230903i
$690$		0			0
$691$	−1157.06			−1.67447			−0.837236	−	0.546842i	$-0.815830\pi$
$691$	−1157.06			−1.67447			−0.837236	+	0.546842i	$0.815830\pi$
$692$		0			0
$693$	−105.439	−	105.439i	−0.152149	−	0.152149i
$694$		0			0
$695$	594.792	+	376.499i	0.855816	+	0.541726i
$696$		0			0
$697$	−469.707	+	469.707i	−0.673898	+	0.673898i
$698$		0			0
$699$		−	591.626i		−	0.846388i
$700$		0			0
$701$	−843.691			−1.20355			−0.601777	−	0.798664i	$-0.705540\pi$
$701$	−843.691			−1.20355			−0.601777	+	0.798664i	$0.705540\pi$
$702$		0			0
$703$	−590.211	−	590.211i	−0.839561	−	0.839561i
$704$		0			0
$705$	−331.065	+	523.015i	−0.469595	+	0.741865i
$706$		0			0
$707$	514.095	−	514.095i	0.727150	−	0.727150i
$708$		0			0
$709$		−	170.686i		−	0.240741i	−0.992729	−	0.120371i	$-0.961592\pi$
$709$		−	170.686i		−	0.240741i	0.992729	−	0.120371i	$-0.0384083\pi$
$710$		0			0
$711$	−380.091			−0.534586
$712$		0			0
$713$	−29.8979	−	29.8979i	−0.0419326	−	0.0419326i
$714$		0			0
$715$	−642.929	+	144.495i	−0.899201	+	0.202091i
$716$		0			0
$717$	−401.394	+	401.394i	−0.559824	+	0.559824i
$718$		0			0
$719$			605.435i			0.842051i	0.907049	+	0.421026i	$0.138330\pi$
$719$			605.435i			0.842051i	−0.907049	+	0.421026i	$0.861670\pi$
$720$		0			0
$721$	−791.716			−1.09808
$722$		0			0
$723$	329.616	+	329.616i	0.455901	+	0.455901i
$724$		0			0
$725$	−1.02603	+	0.485723i	−0.00141521	+	0.000669963i
$726$		0			0
$727$	−50.8025	+	50.8025i	−0.0698797	+	0.0698797i	−0.741183	−	0.671303i	$-0.765735\pi$
$727$	−50.8025	+	50.8025i	−0.0698797	+	0.0698797i	0.671303	+	0.741183i	$0.265735\pi$
$728$		0			0
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	1494.93			2.04505
$732$		0			0
$733$	−516.529	−	516.529i	−0.704678	−	0.704678i	0.260733	−	0.965411i	$-0.416036\pi$
$733$	−516.529	−	516.529i	−0.704678	−	0.704678i	−0.965411	+	0.260733i	$0.916036\pi$
$734$		0			0
$735$	−19.7378	−	87.8230i	−0.0268541	−	0.119487i
$736$		0			0
$737$	550.030	−	550.030i	0.746309	−	0.746309i
$738$		0			0
$739$			650.109i			0.879715i	0.898068	+	0.439857i	$0.144971\pi$
$739$			650.109i			0.879715i	−0.898068	+	0.439857i	$0.855029\pi$
$740$		0			0
$741$	590.969			0.797530
$742$		0			0
$743$	90.6811	+	90.6811i	0.122047	+	0.122047i	0.765492	−	0.643445i	$-0.222496\pi$
$743$	90.6811	+	90.6811i	0.122047	+	0.122047i	−0.643445	+	0.765492i	$0.722496\pi$
$744$		0			0
$745$	−226.151	−	143.152i	−0.303558	−	0.192150i
$746$		0			0
$747$	284.833	−	284.833i	0.381303	−	0.381303i
$748$		0			0
$749$			142.293i			0.189977i
$750$		0			0
$751$	−300.050			−0.399534			−0.199767	−	0.979843i	$-0.564019\pi$
$751$	−300.050			−0.399534			−0.199767	+	0.979843i	$0.564019\pi$
$752$		0			0
$753$	−227.969	−	227.969i	−0.302748	−	0.302748i
$754$		0			0
$755$	−622.043	+	982.702i	−0.823898	+	1.30159i
$756$		0			0
$757$	−523.176	+	523.176i	−0.691118	+	0.691118i	−0.962478	−	0.271360i	$-0.912527\pi$
$757$	−523.176	+	523.176i	−0.691118	+	0.691118i	0.271360	+	0.962478i	$0.412527\pi$
$758$		0			0
$759$		−	105.081i		−	0.138446i
$760$		0			0
$761$	−724.130			−0.951550			−0.475775	−	0.879567i	$-0.657832\pi$
$761$	−724.130			−0.951550			−0.475775	+	0.879567i	$0.657832\pi$
$762$		0			0
$763$	377.555	+	377.555i	0.494830	+	0.494830i
$764$		0			0
$765$	−479.060	+	107.666i	−0.626222	+	0.140740i
$766$		0			0
$767$	801.069	−	801.069i	1.04442	−	1.04442i
$768$		0			0
$769$			13.7775i			0.0179162i	0.999960	+	0.00895809i	$0.00285149\pi$
$769$			13.7775i			0.0179162i	−0.999960	+	0.00895809i	$0.997149\pi$
$770$		0			0
$771$	338.686			0.439281
$772$		0			0
$773$	564.207	+	564.207i	0.729892	+	0.729892i	0.970598	−	0.240706i	$-0.0773789\pi$
$773$	564.207	+	564.207i	0.729892	+	0.729892i	−0.240706	+	0.970598i	$0.577379\pi$
$774$		0			0
$775$	−48.0816	−	101.566i	−0.0620408	−	0.131053i
$776$		0			0
$777$	471.848	−	471.848i	0.607269	−	0.607269i
$778$		0			0
$779$			338.829i			0.434953i
$780$		0			0
$781$	312.182			0.399720
$782$		0			0
$783$	0.166838	+	0.166838i	0.000213076	+	0.000213076i
$784$		0			0
$785$	199.444	+	887.423i	0.254069	+	1.13048i
$786$		0			0
$787$	212.424	−	212.424i	0.269917	−	0.269917i	−0.559150	−	0.829067i	$-0.688872\pi$
$787$	212.424	−	212.424i	0.269917	−	0.269917i	0.829067	+	0.559150i	$0.188872\pi$
$788$		0			0
$789$		−	399.626i		−	0.506496i
$790$		0			0
$791$	1113.18			1.40731
$792$		0			0
$793$	691.968	+	691.968i	0.872596	+	0.872596i
$794$		0			0
$795$	56.9694	+	36.0612i	0.0716596	+	0.0453600i
$796$		0			0
$797$	15.6617	−	15.6617i	0.0196509	−	0.0196509i	−0.697213	−	0.716864i	$-0.745577\pi$
$797$	15.6617	−	15.6617i	0.0196509	−	0.0196509i	0.716864	+	0.697213i	$0.245577\pi$
$798$		0			0
$799$		−	2339.66i		−	2.92823i
$800$		0			0
$801$	−215.394			−0.268906
$802$		0			0
$803$	−141.823	−	141.823i	−0.176616	−	0.176616i
$804$		0			0
$805$	193.868	−	306.272i	0.240830	−	0.380463i
$806$		0			0
$807$	−132.551	+	132.551i	−0.164251	+	0.164251i
$808$		0			0
$809$			816.788i			1.00963i	0.863229	+	0.504813i	$0.168439\pi$
$809$			816.788i			1.00963i	−0.863229	+	0.504813i	$0.831561\pi$
$810$		0			0
$811$	−830.504			−1.02405			−0.512025	−	0.858971i	$-0.671104\pi$
$811$	−830.504			−1.02405			−0.512025	+	0.858971i	$0.671104\pi$
$812$		0			0
$813$	397.287	+	397.287i	0.488668	+	0.488668i
$814$		0			0
$815$	811.151	−	182.302i	0.995277	−	0.223683i
$816$		0			0
$817$	539.192	−	539.192i	0.659966	−	0.659966i
$818$		0			0
$819$			472.454i			0.576867i
$820$		0			0
$821$	−569.217			−0.693321			−0.346661	−	0.937991i	$-0.612684\pi$
$821$	−569.217			−0.693321			−0.346661	+	0.937991i	$0.612684\pi$
$822$		0			0
$823$	497.095	+	497.095i	0.604004	+	0.604004i	0.941373	−	0.337369i	$-0.109537\pi$
$823$	497.095	+	497.095i	0.604004	+	0.604004i	−0.337369	+	0.941373i	$0.609537\pi$
$824$		0			0
$825$	93.9898	−	262.980i	0.113927	−	0.318763i
$826$		0			0
$827$	−874.070	+	874.070i	−1.05692	+	1.05692i	−0.0586377	+	0.998279i	$0.518676\pi$
$827$	−874.070	+	874.070i	−1.05692	+	1.05692i	−0.998279	+	0.0586377i	$0.981324\pi$
$828$		0			0
$829$		−	1548.77i		−	1.86824i	−0.356954	−	0.934122i	$-0.616185\pi$
$829$		−	1548.77i		−	1.86824i	0.356954	−	0.934122i	$-0.383815\pi$
$830$		0			0
$831$	406.282			0.488907
$832$		0			0
$833$	240.581	+	240.581i	0.288813	+	0.288813i
$834$		0			0
$835$	52.1929	+	232.232i	0.0625064	+	0.278122i
$836$		0			0
$837$	−16.5153	+	16.5153i	−0.0197316	+	0.0197316i
$838$		0			0
$839$		−	731.523i		−	0.871899i	−0.899971	−	0.435950i	$-0.856413\pi$
$839$		−	731.523i		−	0.871899i	0.899971	−	0.435950i	$-0.143587\pi$
$840$		0			0
$841$	840.998			0.999998
$842$		0			0
$843$	367.955	+	367.955i	0.436482	+	0.436482i
$844$		0			0
$845$	1050.17	+	664.749i	1.24280	+	0.786685i
$846$		0			0
$847$	432.712	−	432.712i	0.510876	−	0.510876i
$848$		0			0
$849$			862.615i			1.01604i
$850$		0			0
$851$	470.243			0.552577
$852$		0			0
$853$	554.166	+	554.166i	0.649667	+	0.649667i	0.952912	−	0.303246i	$-0.0980703\pi$
$853$	554.166	+	554.166i	0.649667	+	0.649667i	−0.303246	+	0.952912i	$0.598070\pi$
$854$		0			0
$855$	−133.955	+	211.621i	−0.156672	+	0.247510i
$856$		0			0
$857$	687.206	−	687.206i	0.801874	−	0.801874i	−0.181515	−	0.983388i	$-0.558100\pi$
$857$	687.206	−	687.206i	0.801874	−	0.801874i	0.983388	+	0.181515i	$0.0581000\pi$
$858$		0			0
$859$		−	1285.29i		−	1.49627i	−0.663549	−	0.748133i	$-0.730951\pi$
$859$		−	1285.29i		−	1.49627i	0.663549	−	0.748133i	$-0.269049\pi$
$860$		0			0
$861$	−270.879			−0.314609
$862$		0			0
$863$	−712.985	−	712.985i	−0.826171	−	0.826171i	0.160814	−	0.986985i	$-0.448588\pi$
$863$	−712.985	−	712.985i	−0.826171	−	0.826171i	−0.986985	+	0.160814i	$0.948588\pi$
$864$		0			0
$865$	−194.879	+	43.7980i	−0.225293	+	0.0506335i
$866$		0			0
$867$	958.380	−	958.380i	1.10540	−	1.10540i
$868$		0			0
$869$			817.131i			0.940311i
$870$		0			0
$871$	−2464.58			−2.82960
$872$		0			0
$873$	−111.000	−	111.000i	−0.127148	−	0.127148i
$874$		0			0
$875$	759.131	−	593.085i	0.867578	−	0.677812i
$876$		0			0
$877$	474.297	−	474.297i	0.540818	−	0.540818i	−0.382951	−	0.923769i	$-0.625092\pi$
$877$	474.297	−	474.297i	0.540818	−	0.540818i	0.923769	+	0.382951i	$0.125092\pi$
$878$		0			0
$879$			268.009i			0.304902i
$880$		0			0
$881$	1652.71			1.87594			0.937972	−	0.346712i	$-0.112702\pi$
$881$	1652.71			1.87594			0.937972	+	0.346712i	$0.112702\pi$
$882$		0			0
$883$	−18.9286	−	18.9286i	−0.0214367	−	0.0214367i	0.696307	−	0.717744i	$-0.254825\pi$
$883$	−18.9286	−	18.9286i	−0.0214367	−	0.0214367i	−0.717744	+	0.696307i	$0.754825\pi$
$884$		0			0
$885$	105.278	+	468.434i	0.118958	+	0.529304i
$886$		0			0
$887$	−382.338	+	382.338i	−0.431047	+	0.431047i	−0.888984	−	0.457938i	$-0.848588\pi$
$887$	−382.338	+	382.338i	−0.431047	+	0.431047i	0.457938	+	0.888984i	$0.348588\pi$
$888$		0			0
$889$			1307.27i			1.47050i
$890$		0			0
$891$	−58.0454			−0.0651464
$892$		0			0
$893$	−843.868	−	843.868i	−0.944981	−	0.944981i
$894$		0			0
$895$	−191.116	−	120.975i	−0.213537	−	0.135168i
$896$		0			0
$897$	−235.423	+	235.423i	−0.262456	+	0.262456i
$898$		0			0
$899$		−	0.204103i		−	0.000227033i
$900$		0			0
$901$	−254.847			−0.282849
$902$		0			0
$903$	431.060	+	431.060i	0.477365	+	0.477365i
$904$		0			0
$905$	697.056	−	1101.21i	0.770227	−	1.21680i
$906$		0			0
$907$	−725.485	+	725.485i	−0.799873	+	0.799873i	−0.983075	−	0.183202i	$-0.941354\pi$
$907$	−725.485	+	725.485i	−0.799873	+	0.799873i	0.183202	+	0.983075i	$0.441354\pi$
$908$		0			0
$909$		−	283.015i		−	0.311347i
$910$		0			0
$911$	−154.474			−0.169566			−0.0847829	−	0.996399i	$-0.527020\pi$
$911$	−154.474			−0.169566			−0.0847829	+	0.996399i	$0.527020\pi$
$912$		0			0
$913$	−612.343	−	612.343i	−0.670693	−	0.670693i
$914$		0			0
$915$	−404.636	+	90.9398i	−0.442225	+	0.0993878i
$916$		0			0
$917$	660.186	−	660.186i	0.719941	−	0.719941i
$918$		0			0
$919$		−	659.079i		−	0.717169i	−0.933497	−	0.358585i	$-0.883259\pi$
$919$		−	659.079i		−	0.717169i	0.933497	−	0.358585i	$-0.116741\pi$
$920$		0			0
$921$	−270.979			−0.294222
$922$		0			0
$923$	−699.414	−	699.414i	−0.757762	−	0.757762i
$924$		0			0
$925$	1176.85	+	420.611i	1.27227	+	0.454714i
$926$		0			0
$927$	−217.924	+	217.924i	−0.235085	+	0.235085i
$928$		0			0
$929$		−	368.556i		−	0.396723i	−0.980129	−	0.198362i	$-0.936438\pi$
$929$		−	368.556i		−	0.396723i	0.980129	−	0.198362i	$-0.0635621\pi$
$930$		0			0
$931$	173.546			0.186408
$932$		0			0
$933$	2.91939	+	2.91939i	0.00312904	+	0.00312904i
$934$		0			0
$935$	231.464	+	1029.90i	0.247555	+	1.10150i
$936$		0			0
$937$	−820.898	+	820.898i	−0.876092	+	0.876092i	−0.993128	−	0.117036i	$-0.962661\pi$
$937$	−820.898	+	820.898i	−0.876092	+	0.876092i	0.117036	+	0.993128i	$0.462661\pi$
$938$		0			0
$939$			325.682i			0.346839i
$940$		0			0
$941$	−1758.50			−1.86875			−0.934377	−	0.356286i	$-0.884043\pi$
$941$	−1758.50			−1.86875			−0.934377	+	0.356286i	$0.884043\pi$
$942$		0			0
$943$	−134.979	−	134.979i	−0.143137	−	0.143137i
$944$		0			0
$945$	−169.182	−	107.091i	−0.179028	−	0.113324i
$946$		0			0
$947$	118.080	−	118.080i	0.124688	−	0.124688i	−0.642009	−	0.766697i	$-0.721899\pi$
$947$	118.080	−	118.080i	0.124688	−	0.124688i	0.766697	+	0.642009i	$0.221899\pi$
$948$		0			0
$949$			635.483i			0.669634i
$950$		0			0
$951$	90.9898			0.0956780
$952$		0			0
$953$	−217.955	−	217.955i	−0.228704	−	0.228704i	0.583447	−	0.812151i	$-0.301703\pi$
$953$	−217.955	−	217.955i	−0.228704	−	0.228704i	−0.812151	+	0.583447i	$0.801703\pi$
$954$		0			0
$955$	−138.708	+	219.131i	−0.145244	+	0.229456i
$956$		0			0
$957$	0.358674	−	0.358674i	0.000374790	−	0.000374790i
$958$		0			0
$959$			1302.76i			1.35845i
$960$		0			0
$961$	−940.796			−0.978976
$962$		0			0
$963$	39.1668	+	39.1668i	0.0406717	+	0.0406717i
$964$		0			0
$965$	114.636	−	25.7638i	0.118793	−	0.0266982i
$966$		0			0
$967$	−323.983	+	323.983i	−0.335039	+	0.335039i	−0.854497	−	0.519457i	$-0.826134\pi$
$967$	−323.983	+	323.983i	−0.335039	+	0.335039i	0.519457	+	0.854497i	$0.326134\pi$
$968$		0			0
$969$		−	946.665i		−	0.976951i
$970$		0			0
$971$	−743.743			−0.765956			−0.382978	−	0.923757i	$-0.625102\pi$
$971$	−743.743			−0.765956			−0.382978	+	0.923757i	$0.625102\pi$
$972$		0			0
$973$	−767.221	−	767.221i	−0.788511	−	0.788511i
$974$		0			0
$975$	−799.757	+	378.606i	−0.820264	+	0.388314i
$976$		0			0
$977$	−1050.52	+	1050.52i	−1.07525	+	1.07525i	−0.0783226	+	0.996928i	$0.524956\pi$
$977$	−1050.52	+	1050.52i	−1.07525	+	1.07525i	−0.996928	+	0.0783226i	$0.975044\pi$
$978$		0			0
$979$			463.060i			0.472993i
$980$		0			0
$981$	207.848			0.211874
$982$		0			0
$983$	72.9648	+	72.9648i	0.0742267	+	0.0742267i	0.743245	−	0.669019i	$-0.233285\pi$
$983$	72.9648	+	72.9648i	0.0742267	+	0.0742267i	−0.669019	+	0.743245i	$0.733285\pi$
$984$		0			0
$985$	133.485	+	593.939i	0.135517	+	0.602984i
$986$		0			0
$987$	674.636	−	674.636i	0.683521	−	0.683521i
$988$		0			0
$989$			429.594i			0.434372i
$990$		0			0
$991$	444.624			0.448662			0.224331	−	0.974513i	$-0.427980\pi$
$991$	444.624			0.448662			0.224331	+	0.974513i	$0.427980\pi$
$992$		0			0
$993$	−26.5107	−	26.5107i	−0.0266976	−	0.0266976i
$994$		0			0
$995$	−120.681	−	76.3903i	−0.121288	−	0.0767742i
$996$		0			0
$997$	−12.6424	+	12.6424i	−0.0126804	+	0.0126804i	−0.713419	−	0.700738i	$-0.752854\pi$
$997$	−12.6424	+	12.6424i	−0.0126804	+	0.0126804i	0.700738	+	0.713419i	$0.252854\pi$
$998$		0			0
$999$		−	259.757i		−	0.260017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.bg.c.193.2		4
4.3	odd	2		960.3.bg.d.193.1		4
5.2	odd	4	inner	960.3.bg.c.577.2		4
8.3	odd	2		240.3.bg.c.193.2		4
8.5	even	2		120.3.u.a.73.1	✓	4
20.7	even	4		960.3.bg.d.577.1		4
24.5	odd	2		360.3.v.b.73.2		4
24.11	even	2		720.3.bh.g.433.2		4
40.3	even	4		1200.3.bg.e.1057.1		4
40.13	odd	4		600.3.u.e.457.2		4
40.19	odd	2		1200.3.bg.e.193.1		4
40.27	even	4		240.3.bg.c.97.2		4
40.29	even	2		600.3.u.e.193.2		4
40.37	odd	4		120.3.u.a.97.1	yes	4
120.29	odd	2		1800.3.v.n.793.2		4
120.53	even	4		1800.3.v.n.1657.2		4
120.77	even	4		360.3.v.b.217.2		4
120.107	odd	4		720.3.bh.g.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.u.a.73.1	✓	4	8.5	even	2
120.3.u.a.97.1	yes	4	40.37	odd	4
240.3.bg.c.97.2		4	40.27	even	4
240.3.bg.c.193.2		4	8.3	odd	2
360.3.v.b.73.2		4	24.5	odd	2
360.3.v.b.217.2		4	120.77	even	4
600.3.u.e.193.2		4	40.29	even	2
600.3.u.e.457.2		4	40.13	odd	4
720.3.bh.g.433.2		4	24.11	even	2
720.3.bh.g.577.2		4	120.107	odd	4
960.3.bg.c.193.2		4	1.1	even	1	trivial
960.3.bg.c.577.2		4	5.2	odd	4	inner
960.3.bg.d.193.1		4	4.3	odd	2
960.3.bg.d.577.1		4	20.7	even	4
1200.3.bg.e.193.1		4	40.19	odd	2
1200.3.bg.e.1057.1		4	40.3	even	4
1800.3.v.n.793.2		4	120.29	odd	2
1800.3.v.n.1657.2		4	120.53	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.22474 + 1.22474i) q^{3} +(2.67423 - 4.22474i) q^{5} +(-5.44949 + 5.44949i) q^{7} +3.00000i q^{9} +6.44949 q^{11} +(-14.4495 - 14.4495i) q^{13} +(8.44949 - 1.89898i) q^{15} +(-23.1464 + 23.1464i) q^{17} +16.6969i q^{19} -13.3485 q^{21} +(-6.65153 - 6.65153i) q^{23} +(-10.6969 - 22.5959i) q^{25} +(-3.67423 + 3.67423i) q^{27} -0.0454077i q^{29} +4.49490 q^{31} +(7.89898 + 7.89898i) q^{33} +(8.44949 + 37.5959i) q^{35} +(-35.3485 + 35.3485i) q^{37} -35.3939i q^{39} +20.2929 q^{41} +(-32.2929 - 32.2929i) q^{43} +(12.6742 + 8.02270i) q^{45} +(-50.5403 + 50.5403i) q^{47} -10.3939i q^{49} -56.6969 q^{51} +(5.50510 + 5.50510i) q^{53} +(17.2474 - 27.2474i) q^{55} +(-20.4495 + 20.4495i) q^{57} +55.4393i q^{59} -47.8888 q^{61} +(-16.3485 - 16.3485i) q^{63} +(-99.6867 + 22.4041i) q^{65} +(85.2827 - 85.2827i) q^{67} -16.2929i q^{69} +48.4041 q^{71} +(-21.9898 - 21.9898i) q^{73} +(14.5732 - 40.7753i) q^{75} +(-35.1464 + 35.1464i) q^{77} +126.697i q^{79} -9.00000 q^{81} +(-94.9444 - 94.9444i) q^{83} +(35.8888 + 159.687i) q^{85} +(0.0556128 - 0.0556128i) q^{87} +71.7980i q^{89} +157.485 q^{91} +(5.50510 + 5.50510i) q^{93} +(70.5403 + 44.6515i) q^{95} +(-37.0000 + 37.0000i) q^{97} +19.3485i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 12 q^{7} + 16 q^{11} - 48 q^{13} + 24 q^{15} - 24 q^{17} - 24 q^{21} - 56 q^{23} + 16 q^{25} - 80 q^{31} + 12 q^{33} + 24 q^{35} - 112 q^{37} - 56 q^{41} + 8 q^{43} + 36 q^{45} - 16 q^{47}+ \cdots - 148 q^{97}+O(q^{100}) \) 4 * q - 4 * q^5 - 12 * q^7 + 16 * q^11 - 48 * q^13 + 24 * q^15 - 24 * q^17 - 24 * q^21 - 56 * q^23 + 16 * q^25 - 80 * q^31 + 12 * q^33 + 24 * q^35 - 112 * q^37 - 56 * q^41 + 8 * q^43 + 36 * q^45 - 16 * q^47 - 168 * q^51 + 120 * q^53 + 20 * q^55 - 72 * q^57 + 24 * q^61 - 36 * q^63 - 144 * q^65 + 8 * q^67 + 272 * q^71 + 108 * q^73 + 24 * q^75 - 72 * q^77 - 36 * q^81 - 272 * q^83 - 72 * q^85 + 108 * q^87 + 336 * q^91 + 120 * q^93 + 96 * q^95 - 148 * q^97

Introduction

L-functions

Modular forms

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