LMFDB - Embedded newform 960.3.i.b.929.64

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("960.929");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.64
Character	$\chi$	$=$	960.929
Dual form			960.3.i.b.929.59

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.90428 + 0.751787i) q^{3} +(1.38579 + 4.80412i) q^{5} +3.03946i q^{7} +(7.86963 + 4.36679i) q^{9} +O(q^{10})$	\(q+(2.90428 + 0.751787i) q^{3} +(1.38579 + 4.80412i) q^{5} +3.03946i q^{7} +(7.86963 + 4.36679i) q^{9} -11.4633 q^{11} +16.9968 q^{13} +(0.413034 + 14.9943i) q^{15} -18.1540 q^{17} +16.9311i q^{19} +(-2.28502 + 8.82743i) q^{21} +22.3489 q^{23} +(-21.1592 + 13.3150i) q^{25} +(19.5727 + 18.5987i) q^{27} +17.8986 q^{29} -16.9667 q^{31} +(-33.2924 - 8.61792i) q^{33} +(-14.6019 + 4.21205i) q^{35} +1.21295 q^{37} +(49.3634 + 12.7780i) q^{39} +42.0791i q^{41} +1.98640 q^{43} +(-10.0730 + 43.8581i) q^{45} -52.4557 q^{47} +39.7617 q^{49} +(-52.7244 - 13.6480i) q^{51} +8.58147i q^{53} +(-15.8856 - 55.0709i) q^{55} +(-12.7286 + 49.1727i) q^{57} -93.0686 q^{59} -80.4817i q^{61} +(-13.2727 + 23.9194i) q^{63} +(23.5540 + 81.6548i) q^{65} -38.1420 q^{67} +(64.9073 + 16.8016i) q^{69} +109.674i q^{71} +28.2759i q^{73} +(-71.4621 + 22.7632i) q^{75} -34.8421i q^{77} +56.1781 q^{79} +(42.8623 + 68.7301i) q^{81} -126.249i q^{83} +(-25.1577 - 87.2143i) q^{85} +(51.9824 + 13.4559i) q^{87} +126.786i q^{89} +51.6611i q^{91} +(-49.2761 - 12.7554i) q^{93} +(-81.3392 + 23.4630i) q^{95} -153.612i q^{97} +(-90.2116 - 50.0576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{9}+O(q^{10}) $ 64 * q - 32 * q^9	$ 64 q - 32 q^{9} - 32 q^{25} - 320 q^{49} + 448 q^{81}+O(q^{100}) $ 64 * q - 32 * q^9 - 32 * q^25 - 320 * q^49 + 448 * q^81

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.90428	+	0.751787i	0.968092	+	0.250596i
$3$	2.90428	+	0.751787i	0.968092	+	0.250596i
$4$		0			0
$5$	1.38579	+	4.80412i	0.277158	+	0.960824i
$5$	1.38579	+	4.80412i	0.277158	+	0.960824i
$6$		0			0
$7$			3.03946i			0.434208i	0.976148	+	0.217104i	$0.0696611\pi$
$7$			3.03946i			0.434208i	−0.976148	+	0.217104i	$0.930339\pi$
$8$		0			0
$9$	7.86963	+	4.36679i	0.874404	+	0.485199i
$10$		0			0
$11$	−11.4633			−1.04211			−0.521057	−	0.853522i	$-0.674462\pi$
$11$	−11.4633			−1.04211			−0.521057	+	0.853522i	$0.674462\pi$
$12$		0			0
$13$	16.9968			1.30745			0.653724	−	0.756733i	$-0.273206\pi$
$13$	16.9968			1.30745			0.653724	+	0.756733i	$0.273206\pi$
$14$		0			0
$15$	0.413034	+	14.9943i	0.0275356	+	0.999621i
$16$		0			0
$17$	−18.1540			−1.06789			−0.533943	−	0.845521i	$-0.679290\pi$
$17$	−18.1540			−1.06789			−0.533943	+	0.845521i	$0.679290\pi$
$18$		0			0
$19$			16.9311i			0.891112i	0.895254	+	0.445556i	$0.146994\pi$
$19$			16.9311i			0.891112i	−0.895254	+	0.445556i	$0.853006\pi$
$20$		0			0
$21$	−2.28502	+	8.82743i	−0.108811	+	0.420354i
$22$		0			0
$23$	22.3489			0.971690			0.485845	−	0.874045i	$-0.338512\pi$
$23$	22.3489			0.971690			0.485845	+	0.874045i	$0.338512\pi$
$24$		0			0
$25$	−21.1592	+	13.3150i	−0.846367	+	0.532600i
$26$		0			0
$27$	19.5727	+	18.5987i	0.724914	+	0.688839i
$28$		0			0
$29$	17.8986			0.617193			0.308596	−	0.951193i	$-0.400141\pi$
$29$	17.8986			0.617193			0.308596	+	0.951193i	$0.400141\pi$
$30$		0			0
$31$	−16.9667			−0.547314			−0.273657	−	0.961827i	$-0.588233\pi$
$31$	−16.9667			−0.547314			−0.273657	+	0.961827i	$0.588233\pi$
$32$		0			0
$33$	−33.2924	−	8.61792i	−1.00886	−	0.261149i
$34$		0			0
$35$	−14.6019	+	4.21205i	−0.417198	+	0.120344i
$36$		0			0
$37$	1.21295			0.0327823			0.0163912	−	0.999866i	$-0.494782\pi$
$37$	1.21295			0.0327823			0.0163912	+	0.999866i	$0.494782\pi$
$38$		0			0
$39$	49.3634	+	12.7780i	1.26573	+	0.327641i
$40$		0			0
$41$			42.0791i			1.02632i	0.858293	+	0.513160i	$0.171525\pi$
$41$			42.0791i			1.02632i	−0.858293	+	0.513160i	$0.828475\pi$
$42$		0			0
$43$	1.98640			0.0461954			0.0230977	−	0.999733i	$-0.492647\pi$
$43$	1.98640			0.0461954			0.0230977	+	0.999733i	$0.492647\pi$
$44$		0			0
$45$	−10.0730	+	43.8581i	−0.223844	+	0.974625i
$46$		0			0
$47$	−52.4557			−1.11608			−0.558039	−	0.829815i	$-0.688446\pi$
$47$	−52.4557			−1.11608			−0.558039	+	0.829815i	$0.688446\pi$
$48$		0			0
$49$	39.7617			0.811463
$50$		0			0
$51$	−52.7244	−	13.6480i	−1.03381	−	0.267607i
$52$		0			0
$53$			8.58147i			0.161915i	0.996718	+	0.0809573i	$0.0257977\pi$
$53$			8.58147i			0.161915i	−0.996718	+	0.0809573i	$0.974202\pi$
$54$		0			0
$55$	−15.8856	−	55.0709i	−0.288830	−	1.00129i
$56$		0			0
$57$	−12.7286	+	49.1727i	−0.223309	+	0.862678i
$58$		0			0
$59$	−93.0686			−1.57743			−0.788717	−	0.614756i	$-0.789254\pi$
$59$	−93.0686			−1.57743			−0.788717	+	0.614756i	$0.789254\pi$
$60$		0			0
$61$		−	80.4817i		−	1.31937i	−0.751541	−	0.659686i	$-0.770689\pi$
$61$		−	80.4817i		−	1.31937i	0.751541	−	0.659686i	$-0.229311\pi$
$62$		0			0
$63$	−13.2727	+	23.9194i	−0.210678	+	0.379673i
$64$		0			0
$65$	23.5540	+	81.6548i	0.362369	+	1.25623i
$66$		0			0
$67$	−38.1420			−0.569283			−0.284642	−	0.958634i	$-0.591875\pi$
$67$	−38.1420			−0.569283			−0.284642	+	0.958634i	$0.591875\pi$
$68$		0			0
$69$	64.9073	+	16.8016i	0.940685	+	0.243501i
$70$		0			0
$71$			109.674i			1.54470i	0.635197	+	0.772350i	$0.280919\pi$
$71$			109.674i			1.54470i	−0.635197	+	0.772350i	$0.719081\pi$
$72$		0			0
$73$			28.2759i			0.387341i	0.981067	+	0.193671i	$0.0620393\pi$
$73$			28.2759i			0.387341i	−0.981067	+	0.193671i	$0.937961\pi$
$74$		0			0
$75$	−71.4621	+	22.7632i	−0.952828	+	0.303509i
$76$		0			0
$77$		−	34.8421i		−	0.452495i
$78$		0			0
$79$	56.1781			0.711115			0.355558	−	0.934654i	$-0.384291\pi$
$79$	56.1781			0.711115			0.355558	+	0.934654i	$0.384291\pi$
$80$		0			0
$81$	42.8623	+	68.7301i	0.529164	+	0.848520i
$82$		0			0
$83$		−	126.249i		−	1.52108i	−0.649294	−	0.760538i	$-0.724935\pi$
$83$		−	126.249i		−	1.52108i	0.649294	−	0.760538i	$-0.275065\pi$
$84$		0			0
$85$	−25.1577	−	87.2143i	−0.295972	−	1.02605i
$86$		0			0
$87$	51.9824	+	13.4559i	0.597499	+	0.154666i
$88$		0			0
$89$			126.786i			1.42457i	0.701892	+	0.712283i	$0.252339\pi$
$89$			126.786i			1.42457i	−0.701892	+	0.712283i	$0.747661\pi$
$90$		0			0
$91$			51.6611i			0.567705i
$92$		0			0
$93$	−49.2761	−	12.7554i	−0.529850	−	0.137154i
$94$		0			0
$95$	−81.3392	+	23.4630i	−0.856202	+	0.246978i
$96$		0			0
$97$		−	153.612i		−	1.58363i	−0.610761	−	0.791815i	$-0.709136\pi$
$97$		−	153.612i		−	1.58363i	0.610761	−	0.791815i	$-0.290864\pi$
$98$		0			0
$99$	−90.2116	−	50.0576i	−0.911228	−	0.505633i
$100$		0			0
$101$	170.074			1.68390			0.841948	−	0.539559i	$-0.181409\pi$
$101$	170.074			1.68390			0.841948	+	0.539559i	$0.181409\pi$
$102$		0			0
$103$		−	14.7993i		−	0.143683i	−0.997416	−	0.0718415i	$-0.977112\pi$
$103$		−	14.7993i		−	0.143683i	0.997416	−	0.0718415i	$-0.0228876\pi$
$104$		0			0
$105$	−45.5746	+	1.25540i	−0.434044	+	0.0119562i
$106$		0			0
$107$		−	177.576i		−	1.65959i	−0.558069	−	0.829795i	$-0.688457\pi$
$107$		−	177.576i		−	1.65959i	0.558069	−	0.829795i	$-0.311543\pi$
$108$		0			0
$109$			189.527i			1.73878i	0.494130	+	0.869388i	$0.335487\pi$
$109$			189.527i			1.73878i	−0.494130	+	0.869388i	$0.664513\pi$
$110$		0			0
$111$	3.52273	+	0.911877i	0.0317363	+	0.00821511i
$112$		0			0
$113$	107.567			0.951924			0.475962	−	0.879466i	$-0.342100\pi$
$113$	107.567			0.951924			0.475962	+	0.879466i	$0.342100\pi$
$114$		0			0
$115$	30.9708	+	107.367i	0.269311	+	0.933624i
$116$		0			0
$117$	133.759	+	74.2216i	1.14324	+	0.634372i
$118$		0			0
$119$		−	55.1785i		−	0.463685i
$120$		0			0
$121$	10.4061			0.0860012
$122$		0			0
$123$	−31.6345	+	122.209i	−0.257191	+	0.993572i
$124$		0			0
$125$	−93.2890	−	83.1996i	−0.746312	−	0.665597i
$126$		0			0
$127$			209.938i			1.65305i	0.562897	+	0.826527i	$0.309687\pi$
$127$			209.938i			1.65305i	−0.562897	+	0.826527i	$0.690313\pi$
$128$		0			0
$129$	5.76906	+	1.49335i	0.0447214	+	0.0115764i
$130$		0			0
$131$	−28.0136			−0.213844			−0.106922	−	0.994267i	$-0.534100\pi$
$131$	−28.0136			−0.213844			−0.106922	+	0.994267i	$0.534100\pi$
$132$		0			0
$133$	−51.4615			−0.386928
$134$		0			0
$135$	−62.2266	+	119.803i	−0.460938	+	0.887432i
$136$		0			0
$137$	138.049			1.00766			0.503830	−	0.863803i	$-0.331924\pi$
$137$	138.049			1.00766			0.503830	+	0.863803i	$0.331924\pi$
$138$		0			0
$139$		−	162.141i		−	1.16648i	−0.812299	−	0.583242i	$-0.801784\pi$
$139$		−	162.141i		−	1.16648i	0.812299	−	0.583242i	$-0.198216\pi$
$140$		0			0
$141$	−152.346	−	39.4355i	−1.08047	−	0.279684i
$142$		0			0
$143$	−194.839			−1.36251
$144$		0			0
$145$	24.8036	+	85.9870i	0.171060	+	0.593014i
$146$		0			0
$147$	115.479	+	29.8923i	0.785571	+	0.203349i
$148$		0			0
$149$	237.883			1.59653			0.798266	−	0.602306i	$-0.205751\pi$
$149$	237.883			1.59653			0.798266	+	0.602306i	$0.205751\pi$
$150$		0			0
$151$	−70.2302			−0.465100			−0.232550	−	0.972584i	$-0.574707\pi$
$151$	−70.2302			−0.465100			−0.232550	+	0.972584i	$0.574707\pi$
$152$		0			0
$153$	−142.866	−	79.2750i	−0.933763	−	0.518137i
$154$		0			0
$155$	−23.5123	−	81.5103i	−0.151692	−	0.525873i
$156$		0			0
$157$	169.831			1.08173			0.540863	−	0.841111i	$-0.318098\pi$
$157$	169.831			1.08173			0.540863	+	0.841111i	$0.318098\pi$
$158$		0			0
$159$	−6.45144	+	24.9230i	−0.0405751	+	0.156748i
$160$		0			0
$161$			67.9285i			0.421916i
$162$		0			0
$163$	−137.171			−0.841538			−0.420769	−	0.907168i	$-0.638240\pi$
$163$	−137.171			−0.841538			−0.420769	+	0.907168i	$0.638240\pi$
$164$		0			0
$165$	−4.73471	−	171.884i	−0.0286952	−	1.04172i
$166$		0			0
$167$	121.223			0.725885			0.362943	−	0.931812i	$-0.381772\pi$
$167$	121.223			0.725885			0.362943	+	0.931812i	$0.381772\pi$
$168$		0			0
$169$	119.892			0.709418
$170$		0			0
$171$	−73.9347	+	133.242i	−0.432367	+	0.779192i
$172$		0			0
$173$		−	21.4234i		−	0.123835i	−0.998081	−	0.0619175i	$-0.980278\pi$
$173$		−	21.4234i		−	0.123835i	0.998081	−	0.0619175i	$-0.0197216\pi$
$174$		0			0
$175$	−40.4704	−	64.3125i	−0.231259	−	0.367500i
$176$		0			0
$177$	−270.297	−	69.9678i	−1.52710	−	0.395298i
$178$		0			0
$179$	29.4937			0.164769			0.0823847	−	0.996601i	$-0.473746\pi$
$179$	29.4937			0.164769			0.0823847	+	0.996601i	$0.473746\pi$
$180$		0			0
$181$			9.12992i			0.0504416i	0.999682	+	0.0252208i	$0.00802888\pi$
$181$			9.12992i			0.0504416i	−0.999682	+	0.0252208i	$0.991971\pi$
$182$		0			0
$183$	60.5051	−	233.741i	0.330629	−	1.27727i
$184$		0			0
$185$	1.68089	+	5.82714i	0.00908587	+	0.0314981i
$186$		0			0
$187$	208.104			1.11286
$188$		0			0
$189$	−56.5298	+	59.4904i	−0.299100	+	0.314764i
$190$		0			0
$191$		−	8.76163i		−	0.0458724i	−0.999737	−	0.0229362i	$-0.992699\pi$
$191$		−	8.76163i		−	0.0458724i	0.999737	−	0.0229362i	$-0.00730146\pi$
$192$		0			0
$193$			292.061i			1.51327i	0.653839	+	0.756634i	$0.273157\pi$
$193$			292.061i			1.51327i	−0.653839	+	0.756634i	$0.726843\pi$
$194$		0			0
$195$	7.02026	+	254.856i	0.0360013	+	1.30695i
$196$		0			0
$197$		−	128.223i		−	0.650877i	−0.945563	−	0.325438i	$-0.894488\pi$
$197$		−	128.223i		−	0.650877i	0.945563	−	0.325438i	$-0.105512\pi$
$198$		0			0
$199$	358.971			1.80387			0.901936	−	0.431869i	$-0.142146\pi$
$199$	358.971			1.80387			0.901936	+	0.431869i	$0.142146\pi$
$200$		0			0
$201$	−110.775	−	28.6746i	−0.551118	−	0.142660i
$202$		0			0
$203$			54.4020i			0.267990i
$204$		0			0
$205$	−202.153	+	58.3127i	−0.986114	+	0.284452i
$206$		0			0
$207$	175.877	+	97.5929i	0.849650	+	0.471463i
$208$		0			0
$209$		−	194.086i		−	0.928640i
$210$		0			0
$211$			19.4711i			0.0922803i	0.998935	+	0.0461402i	$0.0146921\pi$
$211$			19.4711i			0.0922803i	−0.998935	+	0.0461402i	$0.985308\pi$
$212$		0			0
$213$	−82.4513	+	318.523i	−0.387095	+	1.49541i
$214$		0			0
$215$	2.75273	+	9.54293i	0.0128034	+	0.0443857i
$216$		0			0
$217$		−	51.5697i		−	0.237648i
$218$		0			0
$219$	−21.2575	+	82.1210i	−0.0970660	+	0.374982i
$220$		0			0
$221$	−308.561			−1.39620
$222$		0			0
$223$		−	229.348i		−	1.02847i	−0.857651	−	0.514233i	$-0.828077\pi$
$223$		−	229.348i		−	1.02847i	0.857651	−	0.514233i	$-0.171923\pi$
$224$		0			0
$225$	−224.659	+	12.3863i	−0.998484	+	0.0550503i
$226$		0			0
$227$		−	7.21047i		−	0.0317642i	−0.999874	−	0.0158821i	$-0.994944\pi$
$227$		−	7.21047i		−	0.0317642i	0.999874	−	0.0158821i	$-0.00505564\pi$
$228$		0			0
$229$		−	8.06181i		−	0.0352044i	−0.999845	−	0.0176022i	$-0.994397\pi$
$229$		−	8.06181i		−	0.0352044i	0.999845	−	0.0176022i	$-0.00560325\pi$
$230$		0			0
$231$	26.1938	−	101.191i	0.113393	−	0.438056i
$232$		0			0
$233$	147.853			0.634563			0.317282	−	0.948331i	$-0.397230\pi$
$233$	147.853			0.634563			0.317282	+	0.948331i	$0.397230\pi$
$234$		0			0
$235$	−72.6924	−	252.003i	−0.309329	−	1.07236i
$236$		0			0
$237$	163.157	+	42.2340i	0.688425	+	0.178202i
$238$		0			0
$239$		−	225.695i		−	0.944331i	−0.881510	−	0.472166i	$-0.843472\pi$
$239$		−	225.695i		−	0.944331i	0.881510	−	0.472166i	$-0.156528\pi$
$240$		0			0
$241$	−288.529			−1.19722			−0.598608	−	0.801042i	$-0.704279\pi$
$241$	−288.529			−1.19722			−0.598608	+	0.801042i	$0.704279\pi$
$242$		0			0
$243$	72.8134	+	231.834i	0.299644	+	0.954051i
$244$		0			0
$245$	55.1013	+	191.020i	0.224903	+	0.779674i
$246$		0			0
$247$			287.775i			1.16508i
$248$		0			0
$249$	94.9125	−	366.663i	0.381175	−	1.47254i
$250$		0			0
$251$	431.712			1.71997			0.859984	−	0.510321i	$-0.170473\pi$
$251$	431.712			1.71997			0.859984	+	0.510321i	$0.170473\pi$
$252$		0			0
$253$	−256.191			−1.01261
$254$		0			0
$255$	−7.49824	−	272.207i	−0.0294049	−	1.06748i
$256$		0			0
$257$	130.084			0.506162			0.253081	−	0.967445i	$-0.418556\pi$
$257$	130.084			0.506162			0.253081	+	0.967445i	$0.418556\pi$
$258$		0			0
$259$			3.68670i			0.0142344i
$260$		0			0
$261$	140.855	+	78.1594i	0.539676	+	0.299461i
$262$		0			0
$263$	−94.7069			−0.360102			−0.180051	−	0.983657i	$-0.557626\pi$
$263$	−94.7069			−0.360102			−0.180051	+	0.983657i	$0.557626\pi$
$264$		0			0
$265$	−41.2265	+	11.8921i	−0.155572	+	0.0448759i
$266$		0			0
$267$	−95.3164	+	368.223i	−0.356990	+	1.37911i
$268$		0			0
$269$	−470.172			−1.74785			−0.873926	−	0.486059i	$-0.838434\pi$
$269$	−470.172			−1.74785			−0.873926	+	0.486059i	$0.838434\pi$
$270$		0			0
$271$	−110.731			−0.408602			−0.204301	−	0.978908i	$-0.565492\pi$
$271$	−110.731			−0.408602			−0.204301	+	0.978908i	$0.565492\pi$
$272$		0			0
$273$	−38.8381	+	150.038i	−0.142264	+	0.549590i
$274$		0			0
$275$	242.553	−	152.633i	0.882011	−	0.555029i
$276$		0			0
$277$	455.593			1.64474			0.822371	−	0.568952i	$-0.192651\pi$
$277$	455.593			1.64474			0.822371	+	0.568952i	$0.192651\pi$
$278$		0			0
$279$	−133.522	−	74.0902i	−0.478573	−	0.265556i
$280$		0			0
$281$		−	209.415i		−	0.745250i	−0.927982	−	0.372625i	$-0.878458\pi$
$281$		−	209.415i		−	0.745250i	0.927982	−	0.372625i	$-0.121542\pi$
$282$		0			0
$283$	−16.4631			−0.0581734			−0.0290867	−	0.999577i	$-0.509260\pi$
$283$	−16.4631			−0.0581734			−0.0290867	+	0.999577i	$0.509260\pi$
$284$		0			0
$285$	−253.871	+	6.99313i	−0.890774	+	0.0245373i
$286$		0			0
$287$	−127.898			−0.445637
$288$		0			0
$289$	40.5695			0.140379
$290$		0			0
$291$	115.484	−	446.132i	0.396851	−	1.53310i
$292$		0			0
$293$		−	284.977i		−	0.972616i	−0.873787	−	0.486308i	$-0.838343\pi$
$293$		−	284.977i		−	0.972616i	0.873787	−	0.486308i	$-0.161657\pi$
$294$		0			0
$295$	−128.973	−	447.113i	−0.437198	−	1.51564i
$296$		0			0
$297$	−224.367	−	213.201i	−0.755443	−	0.717849i
$298$		0			0
$299$	379.860			1.27043
$300$		0			0
$301$			6.03759i			0.0200584i
$302$		0			0
$303$	493.940	+	127.859i	1.63017	+	0.421977i
$304$		0			0
$305$	386.644	−	111.531i	1.26769	−	0.365674i
$306$		0			0
$307$	517.938			1.68710			0.843548	−	0.537054i	$-0.180463\pi$
$307$	517.938			1.68710			0.843548	+	0.537054i	$0.180463\pi$
$308$		0			0
$309$	11.1259	−	42.9814i	0.0360063	−	0.139098i
$310$		0			0
$311$		−	309.426i		−	0.994940i	−0.867481	−	0.497470i	$-0.834262\pi$
$311$		−	309.426i		−	0.994940i	0.867481	−	0.497470i	$-0.165738\pi$
$312$		0			0
$313$		−	335.046i		−	1.07043i	−0.844715	−	0.535217i	$-0.820230\pi$
$313$		−	335.046i		−	1.07043i	0.844715	−	0.535217i	$-0.179770\pi$
$314$		0			0
$315$	−133.305	−	30.6164i	−0.423190	−	0.0971948i
$316$		0			0
$317$		−	589.116i		−	1.85841i	−0.369564	−	0.929205i	$-0.620493\pi$
$317$		−	589.116i		−	1.85841i	0.369564	−	0.929205i	$-0.379507\pi$
$318$		0			0
$319$	−205.176			−0.643185
$320$		0			0
$321$	133.499	−	515.730i	0.415886	−	1.60664i
$322$		0			0
$323$		−	307.369i		−	0.951605i
$324$		0			0
$325$	−359.639	+	226.312i	−1.10658	+	0.696346i
$326$		0			0
$327$	−142.484	+	550.437i	−0.435730	+	1.68329i
$328$		0			0
$329$		−	159.437i		−	0.484611i
$330$		0			0
$331$			259.902i			0.785203i	0.919709	+	0.392602i	$0.128425\pi$
$331$			259.902i			0.785203i	−0.919709	+	0.392602i	$0.871575\pi$
$332$		0			0
$333$	9.54544	+	5.29668i	0.0286650	+	0.0159060i
$334$		0			0
$335$	−52.8567	−	183.239i	−0.157781	−	0.546981i
$336$		0			0
$337$		−	313.844i		−	0.931288i	−0.884972	−	0.465644i	$-0.845823\pi$
$337$		−	313.844i		−	0.931288i	0.884972	−	0.465644i	$-0.154177\pi$
$338$		0			0
$339$	312.405	+	80.8677i	0.921550	+	0.238548i
$340$		0			0
$341$	194.494			0.570363
$342$		0			0
$343$			269.788i			0.786553i
$344$		0			0
$345$	9.23085	+	335.106i	0.0267561	+	0.971322i
$346$		0			0
$347$		−	372.311i		−	1.07294i	−0.843919	−	0.536471i	$-0.819757\pi$
$347$		−	372.311i		−	1.07294i	0.843919	−	0.536471i	$-0.180243\pi$
$348$		0			0
$349$		−	67.3243i		−	0.192906i	−0.995338	−	0.0964531i	$-0.969250\pi$
$349$		−	67.3243i		−	0.192906i	0.995338	−	0.0964531i	$-0.0307498\pi$
$350$		0			0
$351$	332.673	+	316.118i	0.947787	+	0.900621i
$352$		0			0
$353$	359.038			1.01710			0.508552	−	0.861031i	$-0.330181\pi$
$353$	359.038			1.01710			0.508552	+	0.861031i	$0.330181\pi$
$354$		0			0
$355$	−526.886	+	151.985i	−1.48419	+	0.428126i
$356$		0			0
$357$	41.4825	−	160.254i	0.116197	−	0.448889i
$358$		0			0
$359$		−	59.4869i		−	0.165702i	−0.996562	−	0.0828509i	$-0.973597\pi$
$359$		−	59.4869i		−	0.165702i	0.996562	−	0.0828509i	$-0.0264025\pi$
$360$		0			0
$361$	74.3369			0.205919
$362$		0			0
$363$	30.2223	+	7.82320i	0.0832571	+	0.0215515i
$364$		0			0
$365$	−135.841	+	39.1844i	−0.372167	+	0.107355i
$366$		0			0
$367$			337.187i			0.918766i	0.888238	+	0.459383i	$0.151929\pi$
$367$			337.187i			0.918766i	−0.888238	+	0.459383i	$0.848071\pi$
$368$		0			0
$369$	−183.751	+	331.147i	−0.497970	+	0.897418i
$370$		0			0
$371$	−26.0830			−0.0703047
$372$		0			0
$373$	128.860			0.345469			0.172734	−	0.984968i	$-0.444740\pi$
$373$	128.860			0.345469			0.172734	+	0.984968i	$0.444740\pi$
$374$		0			0
$375$	−208.389	−	311.768i	−0.555703	−	0.831381i
$376$		0			0
$377$	304.219			0.806947
$378$		0			0
$379$		−	146.179i		−	0.385697i	−0.981229	−	0.192848i	$-0.938227\pi$
$379$		−	146.179i		−	0.385697i	0.981229	−	0.192848i	$-0.0617725\pi$
$380$		0			0
$381$	−157.829	+	609.718i	−0.414248	+	1.60031i
$382$		0			0
$383$	−108.089			−0.282216			−0.141108	−	0.989994i	$-0.545066\pi$
$383$	−108.089			−0.282216			−0.141108	+	0.989994i	$0.545066\pi$
$384$		0			0
$385$	167.386	−	48.2837i	0.434768	−	0.125412i
$386$		0			0
$387$	15.6323	+	8.67421i	0.0403935	+	0.0224140i
$388$		0			0
$389$	344.945			0.886748			0.443374	−	0.896337i	$-0.353781\pi$
$389$	344.945			0.886748			0.443374	+	0.896337i	$0.353781\pi$
$390$		0			0
$391$	−405.723			−1.03765
$392$		0			0
$393$	−81.3591	−	21.0602i	−0.207021	−	0.0535884i
$394$		0			0
$395$	77.8509	+	269.886i	0.197091	+	0.683257i
$396$		0			0
$397$	651.573			1.64124			0.820621	−	0.571473i	$-0.193628\pi$
$397$	651.573			1.64124			0.820621	+	0.571473i	$0.193628\pi$
$398$		0			0
$399$	−149.458	−	38.6881i	−0.374582	−	0.0969625i
$400$		0			0
$401$		−	35.6227i		−	0.0888346i	−0.999013	−	0.0444173i	$-0.985857\pi$
$401$		−	35.6227i		−	0.0888346i	0.999013	−	0.0444173i	$-0.0141431\pi$
$402$		0			0
$403$	−288.380			−0.715584
$404$		0			0
$405$	−270.790	+	301.161i	−0.668617	+	0.743607i
$406$		0			0
$407$	−13.9043			−0.0341629
$408$		0			0
$409$	−583.841			−1.42748			−0.713742	−	0.700409i	$-0.753001\pi$
$409$	−583.841			−1.42748			−0.713742	+	0.700409i	$0.753001\pi$
$410$		0			0
$411$	400.934	+	103.784i	0.975508	+	0.252515i
$412$		0			0
$413$		−	282.878i		−	0.684935i
$414$		0			0
$415$	606.517	−	174.955i	1.46149	−	0.421578i
$416$		0			0
$417$	121.896	−	470.903i	0.292316	−	1.12926i
$418$		0			0
$419$	349.798			0.834840			0.417420	−	0.908714i	$-0.362934\pi$
$419$	349.798			0.834840			0.417420	+	0.908714i	$0.362934\pi$
$420$		0			0
$421$		−	801.589i		−	1.90401i	−0.306078	−	0.952006i	$-0.599017\pi$
$421$		−	801.589i		−	1.90401i	0.306078	−	0.952006i	$-0.400983\pi$
$422$		0			0
$423$	−412.807	−	229.063i	−0.975903	−	0.541520i
$424$		0			0
$425$	384.125	−	241.721i	0.903823	−	0.568755i
$426$		0			0
$427$	244.621			0.572883
$428$		0			0
$429$	−565.865	−	146.477i	−1.31903	−	0.341439i
$430$		0			0
$431$		−	536.485i		−	1.24474i	−0.782721	−	0.622372i	$-0.786169\pi$
$431$		−	536.485i		−	1.24474i	0.782721	−	0.622372i	$-0.213831\pi$
$432$		0			0
$433$			147.436i			0.340499i	0.985401	+	0.170249i	$0.0544574\pi$
$433$			147.436i			0.340499i	−0.985401	+	0.170249i	$0.945543\pi$
$434$		0			0
$435$	7.39273	+	268.377i	0.0169948	+	0.616959i
$436$		0			0
$437$			378.392i			0.865885i
$438$		0			0
$439$	−668.581			−1.52296			−0.761482	−	0.648187i	$-0.775528\pi$
$439$	−668.581			−1.52296			−0.761482	+	0.648187i	$0.775528\pi$
$440$		0			0
$441$	312.910	+	173.631i	0.709546	+	0.393721i
$442$		0			0
$443$		−	198.439i		−	0.447944i	−0.974596	−	0.223972i	$-0.928098\pi$
$443$		−	198.439i		−	0.447944i	0.974596	−	0.223972i	$-0.0719025\pi$
$444$		0			0
$445$	−609.098	+	175.699i	−1.36876	+	0.394829i
$446$		0			0
$447$	690.878	+	178.837i	1.54559	+	0.400084i
$448$		0			0
$449$			44.5024i			0.0991144i	0.998771	+	0.0495572i	$0.0157810\pi$
$449$			44.5024i			0.0991144i	−0.998771	+	0.0495572i	$0.984219\pi$
$450$		0			0
$451$		−	482.364i		−	1.06954i
$452$		0			0
$453$	−203.968	−	52.7981i	−0.450260	−	0.116552i
$454$		0			0
$455$	−248.186	+	71.5914i	−0.545465	+	0.157344i
$456$		0			0
$457$			2.70201i			0.00591250i	0.999996	+	0.00295625i	$0.000941005\pi$
$457$			2.70201i			0.00591250i	−0.999996	+	0.00295625i	$0.999059\pi$
$458$		0			0
$459$	−355.324	−	337.641i	−0.774125	−	0.735601i
$460$		0			0
$461$	−530.641			−1.15107			−0.575533	−	0.817779i	$-0.695205\pi$
$461$	−530.641			−1.15107			−0.575533	+	0.817779i	$0.695205\pi$
$462$		0			0
$463$		−	775.407i		−	1.67475i	−0.546632	−	0.837373i	$-0.684090\pi$
$463$		−	775.407i		−	1.67475i	0.546632	−	0.837373i	$-0.315910\pi$
$464$		0			0
$465$	−7.00784	−	254.404i	−0.0150706	−	0.547106i
$466$		0			0
$467$		−	333.335i		−	0.713779i	−0.934147	−	0.356890i	$-0.883837\pi$
$467$		−	333.335i		−	0.713779i	0.934147	−	0.356890i	$-0.116163\pi$
$468$		0			0
$469$		−	115.931i		−	0.247187i
$470$		0			0
$471$	493.236	+	127.677i	1.04721	+	0.271076i
$472$		0			0
$473$	−22.7706			−0.0481409
$474$		0			0
$475$	−225.438	−	358.249i	−0.474606	−	0.754208i
$476$		0			0
$477$	−37.4735	+	67.5331i	−0.0785608	+	0.141579i
$478$		0			0
$479$			698.275i			1.45778i	0.684632	+	0.728889i	$0.259963\pi$
$479$			698.275i			1.45778i	−0.684632	+	0.728889i	$0.740037\pi$
$480$		0			0
$481$	20.6162			0.0428612
$482$		0			0
$483$	−51.0677	+	197.283i	−0.105730	+	0.408454i
$484$		0			0
$485$	737.971	−	212.874i	1.52159	−	0.438915i
$486$		0			0
$487$			409.379i			0.840614i	0.907382	+	0.420307i	$0.138078\pi$
$487$			409.379i			0.840614i	−0.907382	+	0.420307i	$0.861922\pi$
$488$		0			0
$489$	−398.381	−	103.123i	−0.814686	−	0.210886i
$490$		0			0
$491$	−275.334			−0.560763			−0.280381	−	0.959889i	$-0.590461\pi$
$491$	−275.334			−0.560763			−0.280381	+	0.959889i	$0.590461\pi$
$492$		0			0
$493$	−324.932			−0.659091
$494$		0			0
$495$	115.469	−	502.757i	0.233270	−	1.01567i
$496$		0			0
$497$	−333.349			−0.670722
$498$		0			0
$499$			421.784i			0.845258i	0.906303	+	0.422629i	$0.138893\pi$
$499$			421.784i			0.845258i	−0.906303	+	0.422629i	$0.861107\pi$
$500$		0			0
$501$	352.064	+	91.1337i	0.702723	+	0.181904i
$502$		0			0
$503$	190.452			0.378633			0.189316	−	0.981916i	$-0.439373\pi$
$503$	190.452			0.378633			0.189316	+	0.981916i	$0.439373\pi$
$504$		0			0
$505$	235.686	+	817.054i	0.466705	+	1.61793i
$506$		0			0
$507$	348.199	+	90.1330i	0.686782	+	0.177777i
$508$		0			0
$509$	−300.150			−0.589685			−0.294843	−	0.955546i	$-0.595267\pi$
$509$	−300.150			−0.589685			−0.294843	+	0.955546i	$0.595267\pi$
$510$		0			0
$511$	−85.9435			−0.168187
$512$		0			0
$513$	−314.896	+	331.388i	−0.613833	+	0.645980i
$514$		0			0
$515$	71.0979	−	20.5087i	0.138054	−	0.0398228i
$516$		0			0
$517$	601.313			1.16308
$518$		0			0
$519$	16.1059	−	62.2196i	0.0310325	−	0.119884i
$520$		0			0
$521$			232.372i			0.446012i	0.974817	+	0.223006i	$0.0715870\pi$
$521$			232.372i			0.446012i	−0.974817	+	0.223006i	$0.928413\pi$
$522$		0			0
$523$	−249.629			−0.477303			−0.238651	−	0.971105i	$-0.576705\pi$
$523$	−249.629			−0.477303			−0.238651	+	0.971105i	$0.576705\pi$
$524$		0			0
$525$	−69.1878	−	217.206i	−0.131786	−	0.413726i
$526$		0			0
$527$	308.015			0.584468
$528$		0			0
$529$	−29.5278			−0.0558182
$530$		0			0
$531$	−732.416	−	406.411i	−1.37931	−	0.765370i
$532$		0			0
$533$			715.211i			1.34186i
$534$		0			0
$535$	853.097	−	246.083i	1.59457	−	0.459968i
$536$		0			0
$537$	85.6579	+	22.1730i	0.159512	+	0.0412905i
$538$		0			0
$539$	−455.798			−0.845637
$540$		0			0
$541$			349.843i			0.646661i	0.946286	+	0.323330i	$0.104802\pi$
$541$			349.843i			0.646661i	−0.946286	+	0.323330i	$0.895198\pi$
$542$		0			0
$543$	−6.86376	+	26.5158i	−0.0126404	+	0.0488321i
$544$		0			0
$545$	−910.509	+	262.644i	−1.67066	+	0.481915i
$546$		0			0
$547$	116.234			0.212493			0.106247	−	0.994340i	$-0.466117\pi$
$547$	116.234			0.212493			0.106247	+	0.994340i	$0.466117\pi$
$548$		0			0
$549$	351.447	−	633.362i	0.640158	−	1.15366i
$550$		0			0
$551$			303.043i			0.549988i
$552$		0			0
$553$			170.751i			0.308772i
$554$		0			0
$555$	0.500988	+	18.1873i	0.000902681	+	0.0327699i
$556$		0			0
$557$			87.2444i			0.156633i	0.996929	+	0.0783163i	$0.0249544\pi$
$557$			87.2444i			0.156633i	−0.996929	+	0.0783163i	$0.975046\pi$
$558$		0			0
$559$	33.7625			0.0603981
$560$		0			0
$561$	604.393	+	156.450i	1.07735	+	0.278877i
$562$		0			0
$563$			967.995i			1.71935i	0.510839	+	0.859676i	$0.329335\pi$
$563$			967.995i			1.71935i	−0.510839	+	0.859676i	$0.670665\pi$
$564$		0			0
$565$	149.066	+	516.767i	0.263833	+	0.914632i
$566$		0			0
$567$	−208.902	+	130.278i	−0.368434	+	0.229767i
$568$		0			0
$569$			827.215i			1.45380i	0.686741	+	0.726902i	$0.259041\pi$
$569$			827.215i			1.45380i	−0.686741	+	0.726902i	$0.740959\pi$
$570$		0			0
$571$			862.968i			1.51133i	0.654960	+	0.755664i	$0.272686\pi$
$571$			862.968i			1.51133i	−0.654960	+	0.755664i	$0.727314\pi$
$572$		0			0
$573$	6.58688	−	25.4462i	0.0114954	−	0.0444087i
$574$		0			0
$575$	−472.884	+	297.575i	−0.822407	+	0.517522i
$576$		0			0
$577$		−	345.725i		−	0.599176i	−0.954069	−	0.299588i	$-0.903151\pi$
$577$		−	345.725i		−	0.599176i	0.954069	−	0.299588i	$-0.0968493\pi$
$578$		0			0
$579$	−219.567	+	848.225i	−0.379218	+	1.46498i
$580$		0			0
$581$	383.729			0.660464
$582$		0			0
$583$		−	98.3716i		−	0.168733i
$584$		0			0
$585$	−171.208	+	745.448i	−0.292664	+	1.27427i
$586$		0			0
$587$			231.353i			0.394129i	0.980391	+	0.197064i	$0.0631408\pi$
$587$			231.353i			0.394129i	−0.980391	+	0.197064i	$0.936859\pi$
$588$		0			0
$589$		−	287.266i		−	0.487718i
$590$		0			0
$591$	96.3962	−	372.394i	0.163107	−	0.630109i
$592$		0			0
$593$	−152.452			−0.257087			−0.128543	−	0.991704i	$-0.541030\pi$
$593$	−152.452			−0.257087			−0.128543	+	0.991704i	$0.541030\pi$
$594$		0			0
$595$	265.084	−	76.4657i	0.445520	−	0.128514i
$596$		0			0
$597$	1042.55	+	269.869i	1.74631	+	0.452043i
$598$		0			0
$599$			636.180i			1.06207i	0.847350	+	0.531035i	$0.178197\pi$
$599$			636.180i			1.06207i	−0.847350	+	0.531035i	$0.821803\pi$
$600$		0			0
$601$	−388.977			−0.647217			−0.323609	−	0.946191i	$-0.604896\pi$
$601$	−388.977			−0.647217			−0.323609	+	0.946191i	$0.604896\pi$
$602$		0			0
$603$	−300.163	−	166.558i	−0.497783	−	0.276216i
$604$		0			0
$605$	14.4207	+	49.9924i	0.0238359	+	0.0826321i
$606$		0			0
$607$			913.941i			1.50567i	0.658210	+	0.752835i	$0.271314\pi$
$607$			913.941i			1.50567i	−0.658210	+	0.752835i	$0.728686\pi$
$608$		0			0
$609$	−40.8987	+	157.998i	−0.0671572	+	0.259439i
$610$		0			0
$611$	−891.579			−1.45921
$612$		0			0
$613$	−854.218			−1.39350			−0.696752	−	0.717312i	$-0.745372\pi$
$613$	−854.218			−1.39350			−0.696752	+	0.717312i	$0.745372\pi$
$614$		0			0
$615$	−630.948	+	17.3801i	−1.02593	+	0.0282603i
$616$		0			0
$617$	−992.683			−1.60889			−0.804443	−	0.594029i	$-0.797536\pi$
$617$	−992.683			−1.60889			−0.804443	+	0.594029i	$0.797536\pi$
$618$		0			0
$619$			695.874i			1.12419i	0.827072	+	0.562095i	$0.190005\pi$
$619$			695.874i			1.12419i	−0.827072	+	0.562095i	$0.809995\pi$
$620$		0			0
$621$	437.428	+	415.659i	0.704392	+	0.669338i
$622$		0			0
$623$	−385.362			−0.618559
$624$		0			0
$625$	270.422	−	563.469i	0.432675	−	0.901550i
$626$		0			0
$627$	145.911	−	563.679i	0.232713	−	0.899009i
$628$		0			0
$629$	−22.0199			−0.0350078
$630$		0			0
$631$	142.981			0.226594			0.113297	−	0.993561i	$-0.463859\pi$
$631$	142.981			0.226594			0.113297	+	0.993561i	$0.463859\pi$
$632$		0			0
$633$	−14.6381	+	56.5496i	−0.0231250	+	0.0893358i
$634$		0			0
$635$	−1008.57	+	290.929i	−1.58830	+	0.458157i
$636$		0			0
$637$	675.822			1.06095
$638$		0			0
$639$	−478.922	+	863.092i	−0.749487	+	1.35069i
$640$		0			0
$641$			658.955i			1.02801i	0.857787	+	0.514005i	$0.171839\pi$
$641$			658.955i			1.02801i	−0.857787	+	0.514005i	$0.828161\pi$
$642$		0			0
$643$	986.709			1.53454			0.767270	−	0.641324i	$-0.221615\pi$
$643$	986.709			1.53454			0.767270	+	0.641324i	$0.221615\pi$
$644$		0			0
$645$	0.820452	+	29.7848i	0.00127202	+	0.0461779i
$646$		0			0
$647$	875.183			1.35268			0.676339	−	0.736590i	$-0.263565\pi$
$647$	875.183			1.35268			0.676339	+	0.736590i	$0.263565\pi$
$648$		0			0
$649$	1066.87			1.64387
$650$		0			0
$651$	38.7694	−	149.773i	0.0595536	−	0.230065i
$652$		0			0
$653$			683.228i			1.04629i	0.852243	+	0.523145i	$0.175242\pi$
$653$			683.228i			1.04629i	−0.852243	+	0.523145i	$0.824758\pi$
$654$		0			0
$655$	−38.8209	−	134.581i	−0.0592685	−	0.205467i
$656$		0			0
$657$	−123.475	+	222.521i	−0.187938	+	0.338693i
$658$		0			0
$659$	−299.346			−0.454242			−0.227121	−	0.973866i	$-0.572931\pi$
$659$	−299.346			−0.454242			−0.227121	+	0.973866i	$0.572931\pi$
$660$		0			0
$661$		−	305.186i		−	0.461704i	−0.972989	−	0.230852i	$-0.925849\pi$
$661$		−	305.186i		−	0.461704i	0.972989	−	0.230852i	$-0.0741513\pi$
$662$		0			0
$663$	−896.146	−	231.972i	−1.35165	−	0.349882i
$664$		0			0
$665$	−71.3147	−	247.227i	−0.107240	−	0.371770i
$666$		0			0
$667$	400.013			0.599720
$668$		0			0
$669$	172.421	−	666.089i	0.257729	−	0.995649i
$670$		0			0
$671$			922.582i			1.37494i
$672$		0			0
$673$			725.482i			1.07798i	0.842312	+	0.538991i	$0.181194\pi$
$673$			725.482i			1.07798i	−0.842312	+	0.538991i	$0.818806\pi$
$674$		0			0
$675$	−661.783	−	132.922i	−0.980419	−	0.196922i
$676$		0			0
$677$		−	794.175i		−	1.17308i	−0.809920	−	0.586540i	$-0.800490\pi$
$677$		−	794.175i		−	1.17308i	0.809920	−	0.586540i	$-0.199510\pi$
$678$		0			0
$679$	466.898			0.687625
$680$		0			0
$681$	5.42074	−	20.9412i	0.00795996	−	0.0307506i
$682$		0			0
$683$		−	697.731i		−	1.02157i	−0.859709	−	0.510784i	$-0.829355\pi$
$683$		−	697.731i		−	1.02157i	0.859709	−	0.510784i	$-0.170645\pi$
$684$		0			0
$685$	191.307	+	663.207i	0.279281	+	0.968185i
$686$		0			0
$687$	6.06076	−	23.4137i	0.00882207	−	0.0340811i
$688$		0			0
$689$			145.858i			0.211695i
$690$		0			0
$691$		−	531.954i		−	0.769832i	−0.922952	−	0.384916i	$-0.874230\pi$
$691$		−	531.954i		−	0.769832i	0.922952	−	0.384916i	$-0.125770\pi$
$692$		0			0
$693$	152.148	−	274.194i	0.219550	−	0.395663i
$694$		0			0
$695$	778.946	−	224.693i	1.12079	−	0.323300i
$696$		0			0
$697$		−	763.907i		−	1.09599i
$698$		0			0
$699$	429.406	+	111.154i	0.614315	+	0.159019i
$700$		0			0
$701$	880.504			1.25607			0.628034	−	0.778186i	$-0.283860\pi$
$701$	880.504			1.25607			0.628034	+	0.778186i	$0.283860\pi$
$702$		0			0
$703$			20.5366i			0.0292127i
$704$		0			0
$705$	−21.6660	−	786.537i	−0.0307319	−	1.11565i
$706$		0			0
$707$			516.931i			0.731162i
$708$		0			0
$709$			279.807i			0.394650i	0.980338	+	0.197325i	$0.0632255\pi$
$709$			279.807i			0.394650i	−0.980338	+	0.197325i	$0.936775\pi$
$710$		0			0
$711$	442.101	+	245.318i	0.621802	+	0.345032i
$712$		0			0
$713$	−379.187			−0.531820
$714$		0			0
$715$	−270.005	−	936.029i	−0.377630	−	1.30913i
$716$		0			0
$717$	169.675	−	655.481i	0.236645	−	0.914199i
$718$		0			0
$719$		−	1100.16i		−	1.53013i	−0.643953	−	0.765065i	$-0.722707\pi$
$719$		−	1100.16i		−	1.53013i	0.643953	−	0.765065i	$-0.277293\pi$
$720$		0			0
$721$	44.9820			0.0623883
$722$		0			0
$723$	−837.968	−	216.912i	−1.15902	−	0.300017i
$724$		0			0
$725$	−378.719	+	238.319i	−0.522372	+	0.328717i
$726$		0			0
$727$			595.579i			0.819229i	0.912259	+	0.409614i	$0.134337\pi$
$727$			595.579i			0.819229i	−0.912259	+	0.409614i	$0.865663\pi$
$728$		0			0
$729$	37.1802	+	728.051i	0.0510017	+	0.998699i
$730$		0			0
$731$	−36.0613			−0.0493314
$732$		0			0
$733$	94.7325			0.129239			0.0646197	−	0.997910i	$-0.479417\pi$
$733$	94.7325			0.129239			0.0646197	+	0.997910i	$0.479417\pi$
$734$		0			0
$735$	16.4229	+	596.199i	0.0223441	+	0.811155i
$736$		0			0
$737$	437.231			0.593258
$738$		0			0
$739$		−	618.484i		−	0.836920i	−0.908235	−	0.418460i	$-0.862570\pi$
$739$		−	618.484i		−	0.836920i	0.908235	−	0.418460i	$-0.137430\pi$
$740$		0			0
$741$	−216.346	+	835.779i	−0.291964	+	1.12791i
$742$		0			0
$743$	1000.33			1.34634			0.673172	−	0.739486i	$-0.264931\pi$
$743$	1000.33			1.34634			0.673172	+	0.739486i	$0.264931\pi$
$744$		0			0
$745$	329.656	+	1142.82i	0.442491	+	1.53399i
$746$		0			0
$747$	551.304	−	993.535i	0.738024	−	1.33003i
$748$		0			0
$749$	539.735			0.720608
$750$		0			0
$751$	−839.947			−1.11844			−0.559219	−	0.829020i	$-0.688899\pi$
$751$	−839.947			−1.11844			−0.559219	+	0.829020i	$0.688899\pi$
$752$		0			0
$753$	1253.81	+	324.555i	1.66509	+	0.431016i
$754$		0			0
$755$	−97.3241	−	337.394i	−0.128906	−	0.446880i
$756$		0			0
$757$	−994.763			−1.31409			−0.657043	−	0.753853i	$-0.728193\pi$
$757$	−994.763			−1.31409			−0.657043	+	0.753853i	$0.728193\pi$
$758$		0			0
$759$	−744.049	−	192.601i	−0.980301	−	0.253756i
$760$		0			0
$761$		−	182.129i		−	0.239329i	−0.992814	−	0.119665i	$-0.961818\pi$
$761$		−	182.129i		−	0.239329i	0.992814	−	0.119665i	$-0.0381819\pi$
$762$		0			0
$763$	−576.058			−0.754991
$764$		0			0
$765$	182.865	−	796.203i	0.239039	−	1.04079i
$766$		0			0
$767$	−1581.87			−2.06241
$768$		0			0
$769$	238.214			0.309771			0.154886	−	0.987932i	$-0.450499\pi$
$769$	238.214			0.309771			0.154886	+	0.987932i	$0.450499\pi$
$770$		0			0
$771$	377.799	+	97.7952i	0.490012	+	0.126842i
$772$		0			0
$773$			420.519i			0.544009i	0.962296	+	0.272004i	$0.0876865\pi$
$773$			420.519i			0.544009i	−0.962296	+	0.272004i	$0.912313\pi$
$774$		0			0
$775$	359.002	−	225.912i	0.463229	−	0.291499i
$776$		0			0
$777$	−2.77161	+	10.7072i	−0.00356707	+	0.0137802i
$778$		0			0
$779$	−712.447			−0.914566
$780$		0			0
$781$		−	1257.22i		−	1.60975i
$782$		0			0
$783$	350.323	+	332.890i	0.447412	+	0.425146i
$784$		0			0
$785$	235.350	+	815.888i	0.299808	+	1.03935i
$786$		0			0
$787$	−746.996			−0.949169			−0.474585	−	0.880210i	$-0.657402\pi$
$787$	−746.996			−0.949169			−0.474585	+	0.880210i	$0.657402\pi$
$788$		0			0
$789$	−275.055	−	71.1994i	−0.348612	−	0.0902401i
$790$		0			0
$791$			326.947i			0.413333i
$792$		0			0
$793$		−	1367.93i		−	1.72501i
$794$		0			0
$795$	−128.673	+	3.54444i	−0.161853	+	0.00445842i
$796$		0			0
$797$			598.627i			0.751100i	0.926802	+	0.375550i	$0.122546\pi$
$797$			598.627i			0.751100i	−0.926802	+	0.375550i	$0.877454\pi$
$798$		0			0
$799$	952.283			1.19184
$800$		0			0
$801$	−553.650	+	997.763i	−0.691198	+	1.24565i
$802$		0			0
$803$		−	324.134i		−	0.403654i
$804$		0			0
$805$	−326.337	+	94.1345i	−0.405387	+	0.116937i
$806$		0			0
$807$	−1365.51	−	353.469i	−1.69208	−	0.438004i
$808$		0			0
$809$			412.050i			0.509332i	0.967029	+	0.254666i	$0.0819655\pi$
$809$			412.050i			0.509332i	−0.967029	+	0.254666i	$0.918034\pi$
$810$		0			0
$811$			1455.03i			1.79411i	0.441915	+	0.897057i	$0.354299\pi$
$811$			1455.03i			1.79411i	−0.441915	+	0.897057i	$0.645701\pi$
$812$		0			0
$813$	−321.594	−	83.2463i	−0.395565	−	0.102394i
$814$		0			0
$815$	−190.089	−	658.985i	−0.233239	−	0.808570i
$816$		0			0
$817$			33.6321i			0.0411653i
$818$		0			0
$819$	−225.593	+	406.554i	−0.275450	+	0.496403i
$820$		0			0
$821$	−169.674			−0.206668			−0.103334	−	0.994647i	$-0.532951\pi$
$821$	−169.674			−0.206668			−0.103334	+	0.994647i	$0.532951\pi$
$822$		0			0
$823$		−	701.170i		−	0.851968i	−0.904731	−	0.425984i	$-0.859928\pi$
$823$		−	701.170i		−	0.851968i	0.904731	−	0.425984i	$-0.140072\pi$
$824$		0			0
$825$	819.188	−	260.940i	0.992956	−	0.316291i
$826$		0			0
$827$			453.999i			0.548972i	0.961591	+	0.274486i	$0.0885076\pi$
$827$			453.999i			0.548972i	−0.961591	+	0.274486i	$0.911492\pi$
$828$		0			0
$829$			400.990i			0.483703i	0.970313	+	0.241852i	$0.0777547\pi$
$829$			400.990i			0.483703i	−0.970313	+	0.241852i	$0.922245\pi$
$830$		0			0
$831$	1323.17	+	342.509i	1.59226	+	0.412165i
$832$		0			0
$833$	−721.836			−0.866549
$834$		0			0
$835$	167.989	+	582.369i	0.201185	+	0.697448i
$836$		0			0
$837$	−332.085	−	315.558i	−0.396756	−	0.377011i
$838$		0			0
$839$			841.266i			1.00270i	0.865244	+	0.501351i	$0.167163\pi$
$839$			841.266i			1.00270i	−0.865244	+	0.501351i	$0.832837\pi$
$840$		0			0
$841$	−520.641			−0.619073
$842$		0			0
$843$	157.436	−	608.199i	0.186756	−	0.721470i
$844$		0			0
$845$	166.144	+	575.974i	0.196621	+	0.681627i
$846$		0			0
$847$			31.6291i			0.0373425i
$848$		0			0
$849$	−47.8133	−	12.3767i	−0.0563172	−	0.0145780i
$850$		0			0
$851$	27.1080			0.0318543
$852$		0			0
$853$	539.313			0.632255			0.316127	−	0.948717i	$-0.397617\pi$
$853$	539.313			0.632255			0.316127	+	0.948717i	$0.397617\pi$
$854$		0			0
$855$	−742.568	−	170.547i	−0.868500	−	0.199470i
$856$		0			0
$857$	−409.842			−0.478228			−0.239114	−	0.970991i	$-0.576857\pi$
$857$	−409.842			−0.478228			−0.239114	+	0.970991i	$0.576857\pi$
$858$		0			0
$859$		−	831.792i		−	0.968326i	−0.874978	−	0.484163i	$-0.839124\pi$
$859$		−	831.792i		−	0.968326i	0.874978	−	0.484163i	$-0.160876\pi$
$860$		0			0
$861$	−371.450	−	96.1519i	−0.431417	−	0.111675i
$862$		0			0
$863$	−1214.06			−1.40679			−0.703395	−	0.710799i	$-0.748334\pi$
$863$	−1214.06			−1.40679			−0.703395	+	0.710799i	$0.748334\pi$
$864$		0			0
$865$	102.921	−	29.6883i	0.118984	−	0.0343218i
$866$		0			0
$867$	117.825	+	30.4996i	0.135900	+	0.0351783i
$868$		0			0
$869$	−643.984			−0.741063
$870$		0			0
$871$	−648.292			−0.744308
$872$		0			0
$873$	670.792	−	1208.87i	0.768376	−	1.38473i
$874$		0			0
$875$	252.882	−	283.548i	0.289008	−	0.324055i
$876$		0			0
$877$	−343.642			−0.391838			−0.195919	−	0.980620i	$-0.562769\pi$
$877$	−343.642			−0.391838			−0.195919	+	0.980620i	$0.562769\pi$
$878$		0			0
$879$	214.242	−	827.650i	0.243733	−	0.941582i
$880$		0			0
$881$		−	464.129i		−	0.526821i	−0.964684	−	0.263410i	$-0.915153\pi$
$881$		−	464.129i		−	0.526821i	0.964684	−	0.263410i	$-0.0848473\pi$
$882$		0			0
$883$	−543.338			−0.615332			−0.307666	−	0.951494i	$-0.599548\pi$
$883$	−543.338			−0.615332			−0.307666	+	0.951494i	$0.599548\pi$
$884$		0			0
$885$	−38.4405	−	1395.50i	−0.0434356	−	1.57684i
$886$		0			0
$887$	1616.28			1.82219			0.911093	−	0.412200i	$-0.135240\pi$
$887$	1616.28			1.82219			0.911093	+	0.412200i	$0.135240\pi$
$888$		0			0
$889$	−638.098			−0.717770
$890$		0			0
$891$	−491.341	−	787.870i	−0.551449	−	0.884254i
$892$		0			0
$893$		−	888.134i		−	0.994551i
$894$		0			0
$895$	40.8720	+	141.691i	0.0456671	+	0.158314i
$896$		0			0
$897$	1103.22	+	285.573i	1.22990	+	0.318365i
$898$		0			0
$899$	−303.680			−0.337798
$900$		0			0
$901$		−	155.788i		−	0.172906i
$902$		0			0
$903$	−4.53898	+	17.5348i	−0.00502656	+	0.0194184i
$904$		0			0
$905$	−43.8613	+	12.6521i	−0.0484655	+	0.0139803i
$906$		0			0
$907$	−1189.11			−1.31104			−0.655521	−	0.755177i	$-0.727551\pi$
$907$	−1189.11			−1.31104			−0.655521	+	0.755177i	$0.727551\pi$
$908$		0			0
$909$	1338.42	+	742.676i	1.47241	+	0.817025i
$910$		0			0
$911$		−	1003.01i		−	1.10100i	−0.834834	−	0.550502i	$-0.814436\pi$
$911$		−	1003.01i		−	1.10100i	0.834834	−	0.550502i	$-0.185564\pi$
$912$		0			0
$913$			1447.23i			1.58513i
$914$		0			0
$915$	1206.77	−	33.2417i	1.31887	−	0.0363297i
$916$		0			0
$917$		−	85.1461i		−	0.0928529i
$918$		0			0
$919$	118.618			0.129073			0.0645363	−	0.997915i	$-0.479443\pi$
$919$	118.618			0.129073			0.0645363	+	0.997915i	$0.479443\pi$
$920$		0			0
$921$	1504.24	+	389.379i	1.63326	+	0.422779i
$922$		0			0
$923$			1864.10i			2.01961i
$924$		0			0
$925$	−25.6650	+	16.1504i	−0.0277459	+	0.0174599i
$926$		0			0
$927$	64.6256	−	116.465i	0.0697148	−	0.125637i
$928$		0			0
$929$		−	1417.18i		−	1.52549i	−0.646699	−	0.762745i	$-0.723851\pi$
$929$		−	1417.18i		−	1.52549i	0.646699	−	0.762745i	$-0.276149\pi$
$930$		0			0
$931$			673.210i			0.723105i
$932$		0			0
$933$	232.623	−	898.659i	0.249328	−	0.963193i
$934$		0			0
$935$	288.389	+	999.759i	0.308437	+	1.06926i
$936$		0			0
$937$			495.393i			0.528701i	0.964427	+	0.264351i	$0.0851576\pi$
$937$			495.393i			0.528701i	−0.964427	+	0.264351i	$0.914842\pi$
$938$		0			0
$939$	251.883	−	973.065i	0.268246	−	1.03628i
$940$		0			0
$941$	120.337			0.127883			0.0639413	−	0.997954i	$-0.479633\pi$
$941$	120.337			0.127883			0.0639413	+	0.997954i	$0.479633\pi$
$942$		0			0
$943$			940.421i			0.997265i
$944$		0			0
$945$	−364.137	−	189.135i	−0.385331	−	0.200143i
$946$		0			0
$947$			119.186i			0.125857i	0.998018	+	0.0629283i	$0.0200439\pi$
$947$			119.186i			0.125857i	−0.998018	+	0.0629283i	$0.979956\pi$
$948$		0			0
$949$			480.600i			0.506428i
$950$		0			0
$951$	442.890	−	1710.96i	0.465710	−	1.79911i
$952$		0			0
$953$	−617.067			−0.647499			−0.323750	−	0.946143i	$-0.604944\pi$
$953$	−617.067			−0.647499			−0.323750	+	0.946143i	$0.604944\pi$
$954$		0			0
$955$	42.0919	−	12.1418i	0.0440753	−	0.0127139i
$956$		0			0
$957$	−595.888	−	154.249i	−0.622662	−	0.161179i
$958$		0			0
$959$			419.596i			0.437535i
$960$		0			0
$961$	−673.130			−0.700447
$962$		0			0
$963$	775.438	−	1397.46i	0.805231	−	1.45115i
$964$		0			0
$965$	−1403.10	+	404.734i	−1.45398	+	0.419414i
$966$		0			0
$967$		−	784.649i		−	0.811426i	−0.914001	−	0.405713i	$-0.867023\pi$
$967$		−	784.649i		−	0.811426i	0.914001	−	0.405713i	$-0.132977\pi$
$968$		0			0
$969$	231.076	−	892.683i	0.238468	−	0.921241i
$970$		0			0
$971$	1364.14			1.40488			0.702440	−	0.711743i	$-0.252094\pi$
$971$	1364.14			1.40488			0.702440	+	0.711743i	$0.252094\pi$
$972$		0			0
$973$	492.822			0.506497
$974$		0			0
$975$	−1214.63	+	386.902i	−1.24577	+	0.396822i
$976$		0			0
$977$	−1116.73			−1.14302			−0.571511	−	0.820595i	$-0.693642\pi$
$977$	−1116.73			−1.14302			−0.571511	+	0.820595i	$0.693642\pi$
$978$		0			0
$979$		−	1453.38i		−	1.48456i
$980$		0			0
$981$	−827.623	+	1491.50i	−0.843652	+	1.52039i
$982$		0			0
$983$	1737.11			1.76715			0.883574	−	0.468292i	$-0.155130\pi$
$983$	1737.11			1.76715			0.883574	+	0.468292i	$0.155130\pi$
$984$		0			0
$985$	615.998	−	177.690i	0.625378	−	0.180395i
$986$		0			0
$987$	119.863	−	463.049i	0.121441	−	0.469147i
$988$		0			0
$989$	44.3939			0.0448877
$990$		0			0
$991$	−1343.20			−1.35540			−0.677699	−	0.735339i	$-0.737023\pi$
$991$	−1343.20			−1.35540			−0.677699	+	0.735339i	$0.737023\pi$
$992$		0			0
$993$	−195.391	+	754.828i	−0.196768	+	0.760149i
$994$		0			0
$995$	497.457	+	1724.54i	0.499957	+	1.73321i
$996$		0			0
$997$	281.483			0.282330			0.141165	−	0.989986i	$-0.454915\pi$
$997$	281.483			0.282330			0.141165	+	0.989986i	$0.454915\pi$
$998$		0			0
$999$	23.7406	+	22.5592i	0.0237644	+	0.0225818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.i.b.929.64	yes	64
3.2	odd	2	inner	960.3.i.b.929.57	yes	64
4.3	odd	2	inner	960.3.i.b.929.4	yes	64
5.4	even	2	inner	960.3.i.b.929.3	yes	64
8.3	odd	2	inner	960.3.i.b.929.61	yes	64
8.5	even	2	inner	960.3.i.b.929.1	✓	64
12.11	even	2	inner	960.3.i.b.929.5	yes	64
15.14	odd	2	inner	960.3.i.b.929.6	yes	64
20.19	odd	2	inner	960.3.i.b.929.63	yes	64
24.5	odd	2	inner	960.3.i.b.929.8	yes	64
24.11	even	2	inner	960.3.i.b.929.60	yes	64
40.19	odd	2	inner	960.3.i.b.929.2	yes	64
40.29	even	2	inner	960.3.i.b.929.62	yes	64
60.59	even	2	inner	960.3.i.b.929.58	yes	64
120.29	odd	2	inner	960.3.i.b.929.59	yes	64
120.59	even	2	inner	960.3.i.b.929.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.3.i.b.929.1	✓	64	8.5	even	2	inner
960.3.i.b.929.2	yes	64	40.19	odd	2	inner
960.3.i.b.929.3	yes	64	5.4	even	2	inner
960.3.i.b.929.4	yes	64	4.3	odd	2	inner
960.3.i.b.929.5	yes	64	12.11	even	2	inner
960.3.i.b.929.6	yes	64	15.14	odd	2	inner
960.3.i.b.929.7	yes	64	120.59	even	2	inner
960.3.i.b.929.8	yes	64	24.5	odd	2	inner
960.3.i.b.929.57	yes	64	3.2	odd	2	inner
960.3.i.b.929.58	yes	64	60.59	even	2	inner
960.3.i.b.929.59	yes	64	120.29	odd	2	inner
960.3.i.b.929.60	yes	64	24.11	even	2	inner
960.3.i.b.929.61	yes	64	8.3	odd	2	inner
960.3.i.b.929.62	yes	64	40.29	even	2	inner
960.3.i.b.929.63	yes	64	20.19	odd	2	inner
960.3.i.b.929.64	yes	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.90428 + 0.751787i) q^{3} +(1.38579 + 4.80412i) q^{5} +3.03946i q^{7} +(7.86963 + 4.36679i) q^{9} +O(q^{10})\)	\(q+(2.90428 + 0.751787i) q^{3} +(1.38579 + 4.80412i) q^{5} +3.03946i q^{7} +(7.86963 + 4.36679i) q^{9} -11.4633 q^{11} +16.9968 q^{13} +(0.413034 + 14.9943i) q^{15} -18.1540 q^{17} +16.9311i q^{19} +(-2.28502 + 8.82743i) q^{21} +22.3489 q^{23} +(-21.1592 + 13.3150i) q^{25} +(19.5727 + 18.5987i) q^{27} +17.8986 q^{29} -16.9667 q^{31} +(-33.2924 - 8.61792i) q^{33} +(-14.6019 + 4.21205i) q^{35} +1.21295 q^{37} +(49.3634 + 12.7780i) q^{39} +42.0791i q^{41} +1.98640 q^{43} +(-10.0730 + 43.8581i) q^{45} -52.4557 q^{47} +39.7617 q^{49} +(-52.7244 - 13.6480i) q^{51} +8.58147i q^{53} +(-15.8856 - 55.0709i) q^{55} +(-12.7286 + 49.1727i) q^{57} -93.0686 q^{59} -80.4817i q^{61} +(-13.2727 + 23.9194i) q^{63} +(23.5540 + 81.6548i) q^{65} -38.1420 q^{67} +(64.9073 + 16.8016i) q^{69} +109.674i q^{71} +28.2759i q^{73} +(-71.4621 + 22.7632i) q^{75} -34.8421i q^{77} +56.1781 q^{79} +(42.8623 + 68.7301i) q^{81} -126.249i q^{83} +(-25.1577 - 87.2143i) q^{85} +(51.9824 + 13.4559i) q^{87} +126.786i q^{89} +51.6611i q^{91} +(-49.2761 - 12.7554i) q^{93} +(-81.3392 + 23.4630i) q^{95} -153.612i q^{97} +(-90.2116 - 50.0576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{9}+O(q^{10}) \) 64 * q - 32 * q^9	\( 64 q - 32 q^{9} - 32 q^{25} - 320 q^{49} + 448 q^{81}+O(q^{100}) \) 64 * q - 32 * q^9 - 32 * q^25 - 320 * q^49 + 448 * q^81

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