LMFDB - Embedded newform 483.3.f.a.22.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(22,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.f (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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.43
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.65278 q^{2} +1.73205 q^{3} +9.34282 q^{4} -3.50425i q^{5} +6.32681 q^{6} -2.64575i q^{7} +19.5162 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+3.65278 q^{2} +1.73205 q^{3} +9.34282 q^{4} -3.50425i q^{5} +6.32681 q^{6} -2.64575i q^{7} +19.5162 q^{8} +3.00000 q^{9} -12.8003i q^{10} +4.35528i q^{11} +16.1822 q^{12} -8.22871 q^{13} -9.66436i q^{14} -6.06954i q^{15} +33.9171 q^{16} +11.9816i q^{17} +10.9583 q^{18} -15.8777i q^{19} -32.7396i q^{20} -4.58258i q^{21} +15.9089i q^{22} +(-8.55074 + 21.3515i) q^{23} +33.8030 q^{24} +12.7202 q^{25} -30.0577 q^{26} +5.19615 q^{27} -24.7188i q^{28} -0.402475 q^{29} -22.1707i q^{30} -32.4359 q^{31} +45.8270 q^{32} +7.54357i q^{33} +43.7661i q^{34} -9.27138 q^{35} +28.0285 q^{36} +10.0659i q^{37} -57.9977i q^{38} -14.2525 q^{39} -68.3896i q^{40} -15.1554 q^{41} -16.7392i q^{42} +44.7240i q^{43} +40.6906i q^{44} -10.5128i q^{45} +(-31.2340 + 77.9923i) q^{46} +64.3043 q^{47} +58.7461 q^{48} -7.00000 q^{49} +46.4642 q^{50} +20.7527i q^{51} -76.8794 q^{52} -40.9340i q^{53} +18.9804 q^{54} +15.2620 q^{55} -51.6349i q^{56} -27.5010i q^{57} -1.47015 q^{58} -40.4555 q^{59} -56.7066i q^{60} +21.4584i q^{61} -118.481 q^{62} -7.93725i q^{63} +31.7277 q^{64} +28.8355i q^{65} +27.5550i q^{66} +86.0524i q^{67} +111.942i q^{68} +(-14.8103 + 36.9818i) q^{69} -33.8663 q^{70} +6.72626 q^{71} +58.5485 q^{72} -81.7202 q^{73} +36.7686i q^{74} +22.0321 q^{75} -148.342i q^{76} +11.5230 q^{77} -52.0615 q^{78} +13.2576i q^{79} -118.854i q^{80} +9.00000 q^{81} -55.3593 q^{82} -156.866i q^{83} -42.8142i q^{84} +41.9864 q^{85} +163.367i q^{86} -0.697106 q^{87} +84.9985i q^{88} +124.601i q^{89} -38.4008i q^{90} +21.7711i q^{91} +(-79.8880 + 199.483i) q^{92} -56.1806 q^{93} +234.890 q^{94} -55.6394 q^{95} +79.3746 q^{96} -127.711i q^{97} -25.5695 q^{98} +13.0658i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	3.65278			1.82639			0.913196	−	0.407521i	$-0.133607\pi$
$2$	3.65278			1.82639			0.913196	+	0.407521i	$0.133607\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	9.34282			2.33571
$5$		−	3.50425i		−	0.700850i	−0.936591	−	0.350425i	$-0.886037\pi$
$5$		−	3.50425i		−	0.700850i	0.936591	−	0.350425i	$-0.113963\pi$
$6$	6.32681			1.05447
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	19.5162			2.43952
$9$	3.00000			0.333333
$10$		−	12.8003i		−	1.28003i
$11$			4.35528i			0.395935i	0.980209	+	0.197967i	$0.0634340\pi$
$11$			4.35528i			0.395935i	−0.980209	+	0.197967i	$0.936566\pi$
$12$	16.1822			1.34852
$13$	−8.22871			−0.632978			−0.316489	−	0.948596i	$-0.602504\pi$
$13$	−8.22871			−0.632978			−0.316489	+	0.948596i	$0.602504\pi$
$14$		−	9.66436i		−	0.690311i
$15$		−	6.06954i		−	0.404636i
$16$	33.9171			2.11982
$17$			11.9816i			0.704798i	0.935850	+	0.352399i	$0.114634\pi$
$17$			11.9816i			0.704798i	−0.935850	+	0.352399i	$0.885366\pi$
$18$	10.9583			0.608797
$19$		−	15.8777i		−	0.835668i	−0.908523	−	0.417834i	$-0.862789\pi$
$19$		−	15.8777i		−	0.835668i	0.908523	−	0.417834i	$-0.137211\pi$
$20$		−	32.7396i		−	1.63698i
$21$		−	4.58258i		−	0.218218i
$22$			15.9089i			0.723132i
$23$	−8.55074	+	21.3515i	−0.371771	+	0.928324i
$23$	−8.55074	+	21.3515i	−0.371771	+	0.928324i
$24$	33.8030			1.40846
$25$	12.7202			0.508809
$26$	−30.0577			−1.15607
$27$	5.19615			0.192450
$28$		−	24.7188i		−	0.882814i
$29$	−0.402475			−0.0138784			−0.00693922	−	0.999976i	$-0.502209\pi$
$29$	−0.402475			−0.0138784			−0.00693922	+	0.999976i	$0.502209\pi$
$30$		−	22.1707i		−	0.739024i
$31$	−32.4359			−1.04632			−0.523159	−	0.852235i	$-0.675247\pi$
$31$	−32.4359			−1.04632			−0.523159	+	0.852235i	$0.675247\pi$
$32$	45.8270			1.43209
$33$			7.54357i			0.228593i
$34$			43.7661i			1.28724i
$35$	−9.27138			−0.264896
$36$	28.0285			0.778569
$37$			10.0659i			0.272052i	0.990705	+	0.136026i	$0.0434330\pi$
$37$			10.0659i			0.272052i	−0.990705	+	0.136026i	$0.956567\pi$
$38$		−	57.9977i		−	1.52626i
$39$	−14.2525			−0.365450
$40$		−	68.3896i		−	1.70974i
$41$	−15.1554			−0.369643			−0.184822	−	0.982772i	$-0.559171\pi$
$41$	−15.1554			−0.369643			−0.184822	+	0.982772i	$0.559171\pi$
$42$		−	16.7392i		−	0.398551i
$43$			44.7240i			1.04009i	0.854138	+	0.520047i	$0.174085\pi$
$43$			44.7240i			1.04009i	−0.854138	+	0.520047i	$0.825915\pi$
$44$			40.6906i			0.924787i
$45$		−	10.5128i		−	0.233617i
$46$	−31.2340	+	77.9923i	−0.679000	+	1.69548i
$47$	64.3043			1.36818			0.684088	−	0.729400i	$-0.260200\pi$
$47$	64.3043			1.36818			0.684088	+	0.729400i	$0.260200\pi$
$48$	58.7461			1.22388
$49$	−7.00000			−0.142857
$50$	46.4642			0.929285
$51$			20.7527i			0.406916i
$52$	−76.8794			−1.47845
$53$		−	40.9340i		−	0.772339i	−0.922428	−	0.386170i	$-0.873798\pi$
$53$		−	40.9340i		−	0.772339i	0.922428	−	0.386170i	$-0.126202\pi$
$54$	18.9804			0.351489
$55$	15.2620			0.277491
$56$		−	51.6349i		−	0.922053i
$57$		−	27.5010i		−	0.482473i
$58$	−1.47015			−0.0253475
$59$	−40.4555			−0.685687			−0.342843	−	0.939393i	$-0.611390\pi$
$59$	−40.4555			−0.685687			−0.342843	+	0.939393i	$0.611390\pi$
$60$		−	56.7066i		−	0.945111i
$61$			21.4584i			0.351777i	0.984410	+	0.175889i	$0.0562799\pi$
$61$			21.4584i			0.351777i	−0.984410	+	0.175889i	$0.943720\pi$
$62$	−118.481			−1.91099
$63$		−	7.93725i		−	0.125988i
$64$	31.7277			0.495745
$65$			28.8355i			0.443623i
$66$			27.5550i			0.417500i
$67$			86.0524i			1.28436i	0.766552	+	0.642182i	$0.221971\pi$
$67$			86.0524i			1.28436i	−0.766552	+	0.642182i	$0.778029\pi$
$68$			111.942i			1.64620i
$69$	−14.8103	+	36.9818i	−0.214642	+	0.535968i
$70$	−33.8663			−0.483805
$71$	6.72626			0.0947361			0.0473680	−	0.998878i	$-0.484917\pi$
$71$	6.72626			0.0947361			0.0473680	+	0.998878i	$0.484917\pi$
$72$	58.5485			0.813174
$73$	−81.7202			−1.11946			−0.559728	−	0.828677i	$-0.689094\pi$
$73$	−81.7202			−1.11946			−0.559728	+	0.828677i	$0.689094\pi$
$74$			36.7686i			0.496873i
$75$	22.0321			0.293761
$76$		−	148.342i		−	1.95187i
$77$	11.5230			0.149649
$78$	−52.0615			−0.667455
$79$			13.2576i			0.167818i	0.996473	+	0.0839090i	$0.0267405\pi$
$79$			13.2576i			0.167818i	−0.996473	+	0.0839090i	$0.973260\pi$
$80$		−	118.854i		−	1.48567i
$81$	9.00000			0.111111
$82$	−55.3593			−0.675114
$83$		−	156.866i		−	1.88995i	−0.327143	−	0.944975i	$-0.606086\pi$
$83$		−	156.866i		−	1.88995i	0.327143	−	0.944975i	$-0.393914\pi$
$84$		−	42.8142i		−	0.509693i
$85$	41.9864			0.493958
$86$			163.367i			1.89962i
$87$	−0.697106			−0.00801272
$88$			84.9985i			0.965892i
$89$			124.601i			1.40002i	0.714135	+	0.700008i	$0.246820\pi$
$89$			124.601i			1.40002i	−0.714135	+	0.700008i	$0.753180\pi$
$90$		−	38.4008i		−	0.426676i
$91$			21.7711i			0.239243i
$92$	−79.8880	+	199.483i	−0.868348	+	2.16829i
$93$	−56.1806			−0.604092
$94$	234.890			2.49882
$95$	−55.6394			−0.585678
$96$	79.3746			0.826819
$97$		−	127.711i		−	1.31661i	−0.752753	−	0.658303i	$-0.771275\pi$
$97$		−	127.711i		−	1.31661i	0.752753	−	0.658303i	$-0.228725\pi$
$98$	−25.5695			−0.260913
$99$			13.0658i			0.131978i
$100$	118.843			1.18843
$101$	7.77319			0.0769623			0.0384812	−	0.999259i	$-0.487748\pi$
$101$	7.77319			0.0769623			0.0384812	+	0.999259i	$0.487748\pi$
$102$			75.8051i			0.743187i
$103$		−	118.706i		−	1.15249i	−0.817278	−	0.576243i	$-0.804518\pi$
$103$		−	118.706i		−	1.15249i	0.817278	−	0.576243i	$-0.195482\pi$
$104$	−160.593			−1.54416
$105$	−16.0585			−0.152938
$106$		−	149.523i		−	1.41059i
$107$		−	162.591i		−	1.51954i	−0.650193	−	0.759769i	$-0.725312\pi$
$107$		−	162.591i		−	1.51954i	0.650193	−	0.759769i	$-0.274688\pi$
$108$	48.5467			0.449507
$109$			11.0718i			0.101576i	0.998709	+	0.0507879i	$0.0161732\pi$
$109$			11.0718i			0.101576i	−0.998709	+	0.0507879i	$0.983827\pi$
$110$	55.7488			0.506807
$111$			17.4347i			0.157069i
$112$		−	89.7361i		−	0.801215i
$113$			127.552i			1.12878i	0.825509	+	0.564389i	$0.190888\pi$
$113$			127.552i			1.12878i	−0.825509	+	0.564389i	$0.809112\pi$
$114$		−	100.455i		−	0.881185i
$115$	74.8209	+	29.9639i	0.650616	+	0.260556i
$116$	−3.76025			−0.0324159
$117$	−24.6861			−0.210993
$118$	−147.775			−1.25233
$119$	31.7003			0.266389
$120$		−	118.454i		−	0.987118i
$121$	102.032			0.843236
$122$			78.3830i			0.642483i
$123$	−26.2499			−0.213414
$124$	−303.043			−2.44389
$125$		−	132.181i		−	1.05745i
$126$		−	28.9931i		−	0.230104i
$127$	5.40583			0.0425656			0.0212828	−	0.999773i	$-0.493225\pi$
$127$	5.40583			0.0425656			0.0212828	+	0.999773i	$0.493225\pi$
$128$	−67.4135			−0.526668
$129$			77.4642i			0.600498i
$130$			105.330i			0.810229i
$131$	−85.4458			−0.652258			−0.326129	−	0.945325i	$-0.605744\pi$
$131$	−85.4458			−0.652258			−0.326129	+	0.945325i	$0.605744\pi$
$132$			70.4783i			0.533926i
$133$	−42.0084			−0.315853
$134$			314.331i			2.34575i
$135$		−	18.2086i		−	0.134879i
$136$			233.834i			1.71937i
$137$		−	35.2003i		−	0.256936i	−0.991714	−	0.128468i	$-0.958994\pi$
$137$		−	35.2003i		−	0.256936i	0.991714	−	0.128468i	$-0.0410060\pi$
$138$	−54.0989	+	135.087i	−0.392021	+	0.978888i
$139$	12.4535			0.0895937			0.0447968	−	0.998996i	$-0.485736\pi$
$139$	12.4535			0.0895937			0.0447968	+	0.998996i	$0.485736\pi$
$140$	−86.6208			−0.618720
$141$	111.378			0.789917
$142$	24.5696			0.173025
$143$		−	35.8384i		−	0.250618i
$144$	101.751			0.706605
$145$			1.41037i			0.00972670i
$146$	−298.506			−2.04456
$147$	−12.1244			−0.0824786
$148$			94.0440i			0.635433i
$149$		−	179.623i		−	1.20553i	−0.797920	−	0.602763i	$-0.794066\pi$
$149$		−	179.623i		−	1.20553i	0.797920	−	0.602763i	$-0.205934\pi$
$150$	80.4784			0.536523
$151$	57.1650			0.378576			0.189288	−	0.981922i	$-0.439382\pi$
$151$	57.1650			0.378576			0.189288	+	0.981922i	$0.439382\pi$
$152$		−	309.872i		−	2.03863i
$153$			35.9447i			0.234933i
$154$	42.0910			0.273318
$155$			113.663i			0.733313i
$156$	−133.159			−0.853584
$157$			49.9955i			0.318443i	0.987243	+	0.159221i	$0.0508984\pi$
$157$			49.9955i			0.318443i	−0.987243	+	0.159221i	$0.949102\pi$
$158$			48.4272i			0.306501i
$159$		−	70.8998i		−	0.445910i
$160$		−	160.589i		−	1.00368i
$161$	56.4907	+	22.6231i	0.350874	+	0.140516i
$162$	32.8750			0.202932
$163$	−222.948			−1.36778			−0.683890	−	0.729585i	$-0.739713\pi$
$163$	−222.948			−1.36778			−0.683890	+	0.729585i	$0.739713\pi$
$164$	−141.594			−0.863378
$165$	26.4346			0.160209
$166$		−	572.997i		−	3.45179i
$167$	114.615			0.686316			0.343158	−	0.939278i	$-0.388503\pi$
$167$	114.615			0.686316			0.343158	+	0.939278i	$0.388503\pi$
$168$		−	89.4344i		−	0.532347i
$169$	−101.288			−0.599339
$170$	153.367			0.902161
$171$		−	47.6331i		−	0.278556i
$172$			417.848i			2.42935i
$173$	213.191			1.23232			0.616160	−	0.787621i	$-0.288688\pi$
$173$	213.191			1.23232			0.616160	+	0.787621i	$0.288688\pi$
$174$	−2.54638			−0.0146344
$175$		−	33.6546i		−	0.192312i
$176$			147.718i			0.839309i
$177$	−70.0710			−0.395881
$178$			455.142i			2.55698i
$179$	70.1461			0.391878			0.195939	−	0.980616i	$-0.437225\pi$
$179$	70.1461			0.391878			0.195939	+	0.980616i	$0.437225\pi$
$180$		−	98.2188i		−	0.545660i
$181$		−	17.4458i		−	0.0963856i	−0.998838	−	0.0481928i	$-0.984654\pi$
$181$		−	17.4458i		−	0.0963856i	0.998838	−	0.0481928i	$-0.0153462\pi$
$182$			79.5252i			0.436952i
$183$			37.1671i			0.203099i
$184$	−166.878	+	416.699i	−0.906944	+	2.26467i
$185$	35.2735			0.190667
$186$	−205.216			−1.10331
$187$	−52.1831			−0.279054
$188$	600.783			3.19566
$189$		−	13.7477i		−	0.0727393i
$190$	−203.239			−1.06968
$191$			49.1482i			0.257321i	0.991689	+	0.128660i	$0.0410677\pi$
$191$			49.1482i			0.257321i	−0.991689	+	0.128660i	$0.958932\pi$
$192$	54.9540			0.286219
$193$	−65.9708			−0.341818			−0.170909	−	0.985287i	$-0.554670\pi$
$193$	−65.9708			−0.341818			−0.170909	+	0.985287i	$0.554670\pi$
$194$		−	466.499i		−	2.40464i
$195$			49.9445i			0.256126i
$196$	−65.3998			−0.333672
$197$	385.724			1.95799			0.978994	−	0.203889i	$-0.0653582\pi$
$197$	385.724			1.95799			0.978994	+	0.203889i	$0.0653582\pi$
$198$			47.7267i			0.241044i
$199$			93.6973i			0.470841i	0.971894	+	0.235420i	$0.0756467\pi$
$199$			93.6973i			0.470841i	−0.971894	+	0.235420i	$0.924353\pi$
$200$	248.250			1.24125
$201$			149.047i			0.741528i
$202$	28.3938			0.140563
$203$			1.06485i			0.00524555i
$204$			193.889i			0.950435i
$205$			53.1083i			0.259065i
$206$		−	433.608i		−	2.10489i
$207$	−25.6522	+	64.0544i	−0.123924	+	0.309441i
$208$	−279.094			−1.34180
$209$	69.1518			0.330870
$210$	−58.6582			−0.279325
$211$	7.18809			0.0340668			0.0170334	−	0.999855i	$-0.494578\pi$
$211$	7.18809			0.0340668			0.0170334	+	0.999855i	$0.494578\pi$
$212$		−	382.439i		−	1.80396i
$213$	11.6502			0.0546959
$214$		−	593.908i		−	2.77527i
$215$	156.724			0.728949
$216$	101.409			0.469486
$217$			85.8173i			0.395471i
$218$			40.4427i			0.185517i
$219$	−141.544			−0.646318
$220$	142.590			0.648137
$221$		−	98.5929i		−	0.446122i
$222$			63.6851i			0.286870i
$223$	−48.3677			−0.216895			−0.108448	−	0.994102i	$-0.534588\pi$
$223$	−48.3677			−0.216895			−0.108448	+	0.994102i	$0.534588\pi$
$224$		−	121.247i		−	0.541280i
$225$	38.1607			0.169603
$226$			465.920i			2.06159i
$227$		−	217.350i		−	0.957489i	−0.877954	−	0.478744i	$-0.841092\pi$
$227$		−	217.350i		−	0.957489i	0.877954	−	0.478744i	$-0.158908\pi$
$228$		−	256.937i		−	1.12692i
$229$		−	220.309i		−	0.962049i	−0.876707	−	0.481025i	$-0.840265\pi$
$229$		−	220.309i		−	0.962049i	0.876707	−	0.481025i	$-0.159735\pi$
$230$	273.304	+	109.452i	1.18828	+	0.475877i
$231$	19.9584			0.0864001
$232$	−7.85476			−0.0338567
$233$	278.201			1.19400			0.596998	−	0.802243i	$-0.296360\pi$
$233$	278.201			1.19400			0.596998	+	0.802243i	$0.296360\pi$
$234$	−90.1731			−0.385355
$235$		−	225.338i		−	0.958886i
$236$	−377.969			−1.60156
$237$			22.9629i			0.0968897i
$238$	115.794			0.486530
$239$	307.385			1.28613			0.643064	−	0.765813i	$-0.277663\pi$
$239$	307.385			1.28613			0.643064	+	0.765813i	$0.277663\pi$
$240$		−	205.861i		−	0.857754i
$241$			287.627i			1.19347i	0.802437	+	0.596737i	$0.203536\pi$
$241$			287.627i			1.19347i	−0.802437	+	0.596737i	$0.796464\pi$
$242$	372.699			1.54008
$243$	15.5885			0.0641500
$244$			200.482i			0.821649i
$245$			24.5298i			0.100121i
$246$	−95.8852			−0.389777
$247$			130.653i			0.528959i
$248$	−633.024			−2.55252
$249$		−	271.700i		−	1.09116i
$250$		−	482.829i		−	1.93132i
$251$			221.490i			0.882432i	0.897401	+	0.441216i	$0.145453\pi$
$251$			221.490i			0.882432i	−0.897401	+	0.441216i	$0.854547\pi$
$252$		−	74.1564i		−	0.294271i
$253$	−92.9917	−	37.2409i	−0.367556	−	0.147197i
$254$	19.7463			0.0777414
$255$	72.7226			0.285187
$256$	−373.157			−1.45765
$257$	−164.674			−0.640755			−0.320378	−	0.947290i	$-0.603810\pi$
$257$	−164.674			−0.640755			−0.320378	+	0.947290i	$0.603810\pi$
$258$			282.960i			1.09674i
$259$	26.6319			0.102826
$260$			269.405i			1.03617i
$261$	−1.20742			−0.00462614
$262$	−312.115			−1.19128
$263$		−	410.552i		−	1.56103i	−0.625134	−	0.780517i	$-0.714956\pi$
$263$		−	410.552i		−	1.56103i	0.625134	−	0.780517i	$-0.285044\pi$
$264$			147.222i			0.557658i
$265$	−143.443			−0.541294
$266$	−153.448			−0.576871
$267$			215.816i			0.808299i
$268$			803.972i			2.99990i
$269$	432.024			1.60604			0.803019	−	0.595953i	$-0.203226\pi$
$269$	432.024			1.60604			0.803019	+	0.595953i	$0.203226\pi$
$270$		−	66.5121i		−	0.246341i
$271$	−222.404			−0.820678			−0.410339	−	0.911933i	$-0.634590\pi$
$271$	−222.404			−0.820678			−0.410339	+	0.911933i	$0.634590\pi$
$272$			406.380i			1.49404i
$273$			37.7087i			0.138127i
$274$		−	128.579i		−	0.469267i
$275$			55.4002i			0.201455i
$276$	−138.370	+	345.515i	−0.501341	+	1.25186i
$277$	−494.271			−1.78437			−0.892187	−	0.451667i	$-0.850830\pi$
$277$	−494.271			−1.78437			−0.892187	+	0.451667i	$0.850830\pi$
$278$	45.4900			0.163633
$279$	−97.3076			−0.348773
$280$	−180.942			−0.646221
$281$			157.473i			0.560402i	0.959941	+	0.280201i	$0.0904011\pi$
$281$			157.473i			0.560402i	−0.959941	+	0.280201i	$0.909599\pi$
$282$	406.841			1.44270
$283$			218.075i			0.770585i	0.922795	+	0.385292i	$0.125899\pi$
$283$			218.075i			0.770585i	−0.922795	+	0.385292i	$0.874101\pi$
$284$	62.8423			0.221276
$285$	−96.3703			−0.338141
$286$		−	130.910i		−	0.457727i
$287$			40.0974i			0.139712i
$288$	137.481			0.477364
$289$	145.442			0.503259
$290$			5.15178i			0.0177648i
$291$		−	221.201i		−	0.760142i
$292$	−763.498			−2.61472
$293$			350.591i			1.19656i	0.801288	+	0.598279i	$0.204148\pi$
$293$			350.591i			1.19656i	−0.801288	+	0.598279i	$0.795852\pi$
$294$	−44.2876			−0.150638
$295$			141.766i			0.480564i
$296$			196.448i			0.663676i
$297$			22.6307i			0.0761977i
$298$		−	656.125i		−	2.20176i
$299$	70.3616	−	175.695i	0.235323	−	0.587609i
$300$	205.842			0.686140
$301$	118.329			0.393118
$302$	208.812			0.691429
$303$	13.4636			0.0444342
$304$		−	538.524i		−	1.77146i
$305$	75.1957			0.246543
$306$			131.298i			0.429079i
$307$	−41.8424			−0.136294			−0.0681472	−	0.997675i	$-0.521709\pi$
$307$	−41.8424			−0.136294			−0.0681472	+	0.997675i	$0.521709\pi$
$308$	107.657			0.349537
$309$		−	205.605i		−	0.665389i
$310$			415.188i			1.33932i
$311$	−253.907			−0.816422			−0.408211	−	0.912888i	$-0.633847\pi$
$311$	−253.907			−0.816422			−0.408211	+	0.912888i	$0.633847\pi$
$312$	−278.155			−0.891523
$313$		−	323.465i		−	1.03343i	−0.856156	−	0.516717i	$-0.827154\pi$
$313$		−	323.465i		−	1.03343i	0.856156	−	0.516717i	$-0.172846\pi$
$314$			182.623i			0.581601i
$315$	−27.8141			−0.0882988
$316$			123.864i			0.391973i
$317$	−135.481			−0.427386			−0.213693	−	0.976901i	$-0.568549\pi$
$317$	−135.481			−0.427386			−0.213693	+	0.976901i	$0.568549\pi$
$318$		−	258.981i		−	0.814407i
$319$		−	1.75289i		−	0.00549495i
$320$		−	111.182i		−	0.347443i
$321$		−	281.615i		−	0.877306i
$322$	206.348	+	82.6374i	0.640833	+	0.256638i
$323$	190.240			0.588977
$324$	84.0854			0.259523
$325$	−104.671			−0.322065
$326$	−814.382			−2.49810
$327$			19.1768i			0.0586448i
$328$	−295.775			−0.901753
$329$		−	170.133i		−	0.517122i
$330$	96.5597			0.292605
$331$	420.571			1.27061			0.635304	−	0.772262i	$-0.280875\pi$
$331$	420.571			1.27061			0.635304	+	0.772262i	$0.280875\pi$
$332$		−	1465.57i		−	4.41437i
$333$			30.1977i			0.0906839i
$334$	418.663			1.25348
$335$	301.549			0.900146
$336$		−	155.427i		−	0.462582i
$337$			205.027i			0.608387i	0.952610	+	0.304194i	$0.0983870\pi$
$337$			205.027i			0.608387i	−0.952610	+	0.304194i	$0.901613\pi$
$338$	−369.984			−1.09463
$339$			220.926i			0.651701i
$340$	392.272			1.15374
$341$		−	141.267i		−	0.414274i
$342$		−	173.993i		−	0.508752i
$343$			18.5203i			0.0539949i
$344$			872.842i			2.53733i
$345$	129.594	+	51.8990i	0.375633	+	0.150432i
$346$	778.741			2.25070
$347$	400.791			1.15502			0.577509	−	0.816384i	$-0.304025\pi$
$347$	400.791			1.15502			0.577509	+	0.816384i	$0.304025\pi$
$348$	−6.51294			−0.0187153
$349$	393.502			1.12751			0.563757	−	0.825941i	$-0.309355\pi$
$349$	393.502			1.12751			0.563757	+	0.825941i	$0.309355\pi$
$350$		−	122.933i		−	0.351237i
$351$	−42.7576			−0.121817
$352$			199.589i			0.567015i
$353$	−126.206			−0.357525			−0.178763	−	0.983892i	$-0.557209\pi$
$353$	−126.206			−0.357525			−0.178763	+	0.983892i	$0.557209\pi$
$354$	−255.954			−0.723035
$355$		−	23.5705i		−	0.0663958i
$356$			1164.13i			3.27002i
$357$	54.9065			0.153800
$358$	256.229			0.715722
$359$		−	462.778i		−	1.28908i	−0.764573	−	0.644538i	$-0.777050\pi$
$359$		−	462.778i		−	1.28908i	0.764573	−	0.644538i	$-0.222950\pi$
$360$		−	205.169i		−	0.569913i
$361$	108.899			0.301659
$362$		−	63.7257i		−	0.176038i
$363$	176.724			0.486842
$364$			203.404i			0.558802i
$365$			286.368i			0.784570i
$366$			135.763i			0.370938i
$367$		−	51.0623i		−	0.139134i	−0.997577	−	0.0695671i	$-0.977838\pi$
$367$		−	51.0623i		−	0.139134i	0.997577	−	0.0695671i	$-0.0221618\pi$
$368$	−290.016	+	724.179i	−0.788087	+	1.96788i
$369$	−45.4661			−0.123214
$370$	128.846			0.348233
$371$	−108.301			−0.291917
$372$	−524.885			−1.41098
$373$		−	371.140i		−	0.995013i	−0.867460	−	0.497506i	$-0.834249\pi$
$373$		−	371.140i		−	0.995013i	0.867460	−	0.497506i	$-0.165751\pi$
$374$	−190.614			−0.509662
$375$		−	228.944i		−	0.610518i
$376$	1254.97			3.33769
$377$	3.31185			0.00878474
$378$		−	50.2175i		−	0.132850i
$379$			566.191i			1.49391i	0.664876	+	0.746953i	$0.268484\pi$
$379$			566.191i			1.49391i	−0.664876	+	0.746953i	$0.731516\pi$
$380$	−519.829			−1.36797
$381$	9.36317			0.0245752
$382$			179.528i			0.469968i
$383$			100.060i			0.261254i	0.991432	+	0.130627i	$0.0416990\pi$
$383$			100.060i			0.261254i	−0.991432	+	0.130627i	$0.958301\pi$
$384$	−116.764			−0.304072
$385$		−	40.3795i		−	0.104882i
$386$	−240.977			−0.624293
$387$			134.172i			0.346698i
$388$		−	1193.18i		−	3.07520i
$389$		−	712.587i		−	1.83184i	−0.401358	−	0.915921i	$-0.631462\pi$
$389$		−	712.587i		−	1.83184i	0.401358	−	0.915921i	$-0.368538\pi$
$390$			182.436i			0.467786i
$391$	−255.824	−	102.451i	−0.654282	−	0.262024i
$392$	−136.613			−0.348503
$393$	−147.996			−0.376581
$394$	1408.96			3.57605
$395$	46.4580			0.117615
$396$			122.072i			0.308262i
$397$	42.3688			0.106722			0.0533612	−	0.998575i	$-0.483007\pi$
$397$	42.3688			0.106722			0.0533612	+	0.998575i	$0.483007\pi$
$398$			342.256i			0.859939i
$399$	−72.7607			−0.182358
$400$	431.433			1.07858
$401$		−	599.099i		−	1.49401i	−0.664818	−	0.747006i	$-0.731491\pi$
$401$		−	599.099i		−	1.49401i	0.664818	−	0.747006i	$-0.268509\pi$
$402$			544.437i			1.35432i
$403$	266.906			0.662297
$404$	72.6236			0.179761
$405$		−	31.5383i		−	0.0778722i
$406$			3.88966i			0.00958044i
$407$	−43.8399			−0.107715
$408$			405.013i			0.992679i
$409$	420.617			1.02840			0.514202	−	0.857669i	$-0.328088\pi$
$409$	420.617			1.02840			0.514202	+	0.857669i	$0.328088\pi$
$410$			193.993i			0.473153i
$411$		−	60.9687i		−	0.148342i
$412$		−	1109.05i		−	2.69187i
$413$			107.035i			0.259165i
$414$	−93.7020	+	233.977i	−0.226333	+	0.565161i
$415$	−549.697			−1.32457
$416$	−377.097			−0.906483
$417$	21.5701			0.0517269
$418$	252.597			0.604298
$419$			430.471i			1.02738i	0.857977	+	0.513688i	$0.171721\pi$
$419$			430.471i			1.02738i	−0.857977	+	0.513688i	$0.828279\pi$
$420$	−150.032			−0.357218
$421$		−	566.813i		−	1.34635i	−0.739484	−	0.673175i	$-0.764930\pi$
$421$		−	566.813i		−	1.34635i	0.739484	−	0.673175i	$-0.235070\pi$
$422$	26.2565			0.0622193
$423$	192.913			0.456059
$424$		−	798.875i		−	1.88414i
$425$			152.408i			0.358608i
$426$	42.5557			0.0998961
$427$	56.7737			0.132959
$428$		−	1519.06i		−	3.54919i
$429$		−	62.0739i		−	0.144694i
$430$	572.479			1.33135
$431$		−	446.544i		−	1.03606i	−0.855361	−	0.518032i	$-0.826665\pi$
$431$		−	446.544i		−	1.03606i	0.855361	−	0.518032i	$-0.173335\pi$
$432$	176.238			0.407959
$433$			655.015i			1.51274i	0.654146	+	0.756368i	$0.273028\pi$
$433$			655.015i			1.51274i	−0.654146	+	0.756368i	$0.726972\pi$
$434$			313.472i			0.722285i
$435$			2.44284i			0.00561571i
$436$			103.441i			0.237251i
$437$	339.012	+	135.766i	0.775771	+	0.310677i
$438$	−517.028			−1.18043
$439$	34.0544			0.0775728			0.0387864	−	0.999248i	$-0.487651\pi$
$439$	34.0544			0.0775728			0.0387864	+	0.999248i	$0.487651\pi$
$440$	297.856			0.676945
$441$	−21.0000			−0.0476190
$442$		−	360.139i		−	0.814793i
$443$	450.127			1.01609			0.508044	−	0.861331i	$-0.330369\pi$
$443$	450.127			1.01609			0.508044	+	0.861331i	$0.330369\pi$
$444$			162.889i			0.366867i
$445$	436.634			0.981201
$446$	−176.677			−0.396136
$447$		−	311.117i		−	0.696011i
$448$		−	83.9436i		−	0.187374i
$449$	656.094			1.46123			0.730617	−	0.682788i	$-0.239233\pi$
$449$	656.094			1.46123			0.730617	+	0.682788i	$0.239233\pi$
$450$	139.393			0.309762
$451$		−	66.0060i		−	0.146355i
$452$			1191.70i			2.63649i
$453$	99.0128			0.218571
$454$		−	793.932i		−	1.74875i
$455$	76.2915			0.167674
$456$		−	536.714i		−	1.17700i
$457$			32.0316i			0.0700910i	0.999386	+	0.0350455i	$0.0111576\pi$
$457$			32.0316i			0.0700910i	−0.999386	+	0.0350455i	$0.988842\pi$
$458$		−	804.742i		−	1.75708i
$459$			62.2581i			0.135639i
$460$	699.038	+	279.948i	1.51965	+	0.608582i
$461$	662.552			1.43721			0.718603	−	0.695420i	$-0.244782\pi$
$461$	662.552			1.43721			0.718603	+	0.695420i	$0.244782\pi$
$462$	72.9038			0.157800
$463$	−404.553			−0.873765			−0.436883	−	0.899519i	$-0.643917\pi$
$463$	−404.553			−0.873765			−0.436883	+	0.899519i	$0.643917\pi$
$464$	−13.6508			−0.0294197
$465$			196.871i			0.423378i
$466$	1016.21			2.18070
$467$			111.261i			0.238247i	0.992879	+	0.119123i	$0.0380084\pi$
$467$			111.261i			0.238247i	−0.992879	+	0.119123i	$0.961992\pi$
$468$	−230.638			−0.492817
$469$	227.673			0.485444
$470$		−	823.112i		−	1.75130i
$471$			86.5947i			0.183853i
$472$	−789.537			−1.67275
$473$	−194.786			−0.411809
$474$			83.8784i			0.176959i
$475$		−	201.968i		−	0.425195i
$476$	296.170			0.622206
$477$		−	122.802i		−	0.257446i
$478$	1122.81			2.34897
$479$			557.467i			1.16381i	0.813256	+	0.581907i	$0.197693\pi$
$479$			557.467i			1.16381i	−0.813256	+	0.581907i	$0.802307\pi$
$480$		−	278.149i		−	0.579476i
$481$		−	82.8295i		−	0.172203i
$482$			1050.64i			2.17975i
$483$	97.8447	+	39.1844i	0.202577	+	0.0811271i
$484$	953.262			1.96955
$485$	−447.530			−0.922743
$486$	56.9413			0.117163
$487$	−658.960			−1.35310			−0.676550	−	0.736396i	$-0.736526\pi$
$487$	−658.960			−1.35310			−0.676550	+	0.736396i	$0.736526\pi$
$488$			418.786i			0.858169i
$489$	−386.158			−0.789689
$490$			89.6019i			0.182861i
$491$	−558.020			−1.13650			−0.568248	−	0.822857i	$-0.692379\pi$
$491$	−558.020			−1.13650			−0.568248	+	0.822857i	$0.692379\pi$
$492$	−245.248			−0.498472
$493$		−	4.82228i		−	0.00978150i
$494$			477.247i			0.966087i
$495$	45.7860			0.0924970
$496$	−1100.13			−2.21800
$497$		−	17.7960i		−	0.0358069i
$498$		−	992.460i		−	1.99289i
$499$	−552.317			−1.10685			−0.553424	−	0.832900i	$-0.686679\pi$
$499$	−552.317			−1.10685			−0.553424	+	0.832900i	$0.686679\pi$
$500$		−	1234.94i		−	2.46989i
$501$	198.519			0.396245
$502$			809.057i			1.61167i
$503$			345.201i			0.686284i	0.939284	+	0.343142i	$0.111491\pi$
$503$			345.201i			0.686284i	−0.939284	+	0.343142i	$0.888509\pi$
$504$		−	154.905i		−	0.307351i
$505$		−	27.2392i		−	0.0539391i
$506$	−339.678	−	136.033i	−0.671301	−	0.268840i
$507$	−175.436			−0.346028
$508$	50.5057			0.0994206
$509$	−680.602			−1.33714			−0.668568	−	0.743651i	$-0.733092\pi$
$509$	−680.602			−1.33714			−0.668568	+	0.743651i	$0.733092\pi$
$510$	265.640			0.520863
$511$			216.211i			0.423114i
$512$	−1093.41			−2.13557
$513$		−	82.5029i		−	0.160824i
$514$	−601.519			−1.17027
$515$	−415.976			−0.807720
$516$			723.735i			1.40259i
$517$			280.063i			0.541708i
$518$	97.2805			0.187800
$519$	369.258			0.711480
$520$			562.758i			1.08223i
$521$			735.088i			1.41092i	0.708751	+	0.705459i	$0.249259\pi$
$521$			735.088i			1.41092i	−0.708751	+	0.705459i	$0.750741\pi$
$522$	−4.41046			−0.00844915
$523$			917.801i			1.75488i	0.479688	+	0.877439i	$0.340750\pi$
$523$			917.801i			1.75488i	−0.479688	+	0.877439i	$0.659250\pi$
$524$	−798.305			−1.52348
$525$		−	58.2914i		−	0.111031i
$526$		−	1499.66i		−	2.85106i
$527$		−	388.633i		−	0.737444i
$528$			255.856i			0.484575i
$529$	−382.770	−	365.141i	−0.723572	−	0.690249i
$530$	−523.966			−0.988615
$531$	−121.367			−0.228562
$532$	−392.477			−0.737739
$533$	124.709			0.233976
$534$			788.328i			1.47627i
$535$	−569.758			−1.06497
$536$			1679.41i			3.13323i
$537$	121.497			0.226251
$538$	1578.09			2.93325
$539$		−	30.4870i		−	0.0565621i
$540$		−	170.120i		−	0.315037i
$541$	−835.375			−1.54413			−0.772065	−	0.635543i	$-0.780776\pi$
$541$	−835.375			−1.54413			−0.772065	+	0.635543i	$0.780776\pi$
$542$	−812.393			−1.49888
$543$		−	30.2170i		−	0.0556483i
$544$			549.079i			1.00934i
$545$	38.7982			0.0711893
$546$			137.742i			0.252274i
$547$	−996.211			−1.82123			−0.910613	−	0.413260i	$-0.864390\pi$
$547$	−996.211			−1.82123			−0.910613	+	0.413260i	$0.864390\pi$
$548$		−	328.870i		−	0.600128i
$549$			64.3753i			0.117259i
$550$			202.365i			0.367936i
$551$			6.39036i			0.0115978i
$552$	−289.041	+	721.744i	−0.523624	+	1.30751i
$553$	35.0764			0.0634292
$554$	−1805.47			−3.25896
$555$	61.0954			0.110082
$556$	116.351			0.209264
$557$			794.172i			1.42580i	0.701265	+	0.712901i	$0.252619\pi$
$557$			794.172i			1.42580i	−0.701265	+	0.712901i	$0.747381\pi$
$558$	−355.444			−0.636996
$559$		−	368.021i		−	0.658356i
$560$	−314.458			−0.561532
$561$	−90.3838			−0.161112
$562$			575.215i			1.02351i
$563$		−	824.287i		−	1.46410i	−0.681252	−	0.732049i	$-0.738564\pi$
$563$		−	824.287i		−	1.46410i	0.681252	−	0.732049i	$-0.261436\pi$
$564$	1040.59			1.84501
$565$	446.974			0.791105
$566$			796.582i			1.40739i
$567$		−	23.8118i		−	0.0419961i
$568$	131.271			0.231111
$569$			85.8799i			0.150931i	0.997148	+	0.0754657i	$0.0240443\pi$
$569$			85.8799i			0.150931i	−0.997148	+	0.0754657i	$0.975956\pi$
$570$	−352.020			−0.617578
$571$			365.022i			0.639267i	0.947541	+	0.319634i	$0.103560\pi$
$571$			365.022i			0.639267i	−0.947541	+	0.319634i	$0.896440\pi$
$572$		−	334.832i		−	0.585370i
$573$			85.1273i			0.148564i
$574$			146.467i			0.255169i
$575$	−108.767	+	271.595i	−0.189161	+	0.472340i
$576$	95.1831			0.165248
$577$	−515.182			−0.892863			−0.446431	−	0.894818i	$-0.647305\pi$
$577$	−515.182			−0.892863			−0.446431	+	0.894818i	$0.647305\pi$
$578$	531.268			0.919148
$579$	−114.265			−0.197348
$580$			13.1769i			0.0227187i
$581$	−415.028			−0.714334
$582$		−	808.001i		−	1.38832i
$583$	178.279			0.305796
$584$	−1594.87			−2.73094
$585$			86.5064i			0.147874i
$586$			1280.63i			2.18538i
$587$	−1046.85			−1.78339			−0.891693	−	0.452641i	$-0.850482\pi$
$587$	−1046.85			−1.78339			−0.891693	+	0.452641i	$0.850482\pi$
$588$	−113.276			−0.192646
$589$			515.007i			0.874375i
$590$			517.841i			0.877697i
$591$	668.093			1.13044
$592$			341.406i			0.576699i
$593$	169.663			0.286109			0.143055	−	0.989715i	$-0.454308\pi$
$593$	169.663			0.286109			0.143055	+	0.989715i	$0.454308\pi$
$594$			82.6651i			0.139167i
$595$		−	111.086i		−	0.186699i
$596$		−	1678.19i		−	2.81576i
$597$			162.288i			0.271840i
$598$	257.016	−	641.776i	0.429792	−	1.07320i
$599$	−148.625			−0.248122			−0.124061	−	0.992275i	$-0.539592\pi$
$599$	−148.625			−0.248122			−0.124061	+	0.992275i	$0.539592\pi$
$600$	429.982			0.716637
$601$	277.812			0.462249			0.231124	−	0.972924i	$-0.425760\pi$
$601$	277.812			0.462249			0.231124	+	0.972924i	$0.425760\pi$
$602$	432.229			0.717988
$603$			258.157i			0.428121i
$604$	534.083			0.884243
$605$		−	357.544i		−	0.590982i
$606$	49.1795			0.0811543
$607$	−783.273			−1.29040			−0.645200	−	0.764014i	$-0.723226\pi$
$607$	−783.273			−1.29040			−0.645200	+	0.764014i	$0.723226\pi$
$608$		−	727.626i		−	1.19675i
$609$			1.84437i			0.00302852i
$610$	274.674			0.450285
$611$	−529.141			−0.866025
$612$			335.825i			0.548734i
$613$		−	771.270i		−	1.25819i	−0.777329	−	0.629095i	$-0.783426\pi$
$613$		−	771.270i		−	1.25819i	0.777329	−	0.629095i	$-0.216574\pi$
$614$	−152.841			−0.248927
$615$			91.9862i			0.149571i
$616$	224.885			0.365073
$617$		−	244.858i		−	0.396852i	−0.980116	−	0.198426i	$-0.936417\pi$
$617$		−	244.858i		−	0.396852i	0.980116	−	0.198426i	$-0.0635829\pi$
$618$		−	751.031i		−	1.21526i
$619$			116.726i			0.188572i	0.995545	+	0.0942858i	$0.0300567\pi$
$619$			116.726i			0.188572i	−0.995545	+	0.0942858i	$0.969943\pi$
$620$			1061.94i			1.71280i
$621$	−44.4309	+	110.945i	−0.0715474	+	0.178656i
$622$	−927.469			−1.49111
$623$	329.664			0.529156
$624$	−483.405			−0.774687
$625$	−145.190			−0.232304
$626$		−	1181.55i		−	1.88746i
$627$	119.774			0.191028
$628$			467.099i			0.743788i
$629$	−120.605			−0.191742
$630$	−101.599			−0.161268
$631$		−	244.117i		−	0.386873i	−0.981113	−	0.193436i	$-0.938037\pi$
$631$		−	244.117i		−	0.386873i	0.981113	−	0.193436i	$-0.0619633\pi$
$632$			258.738i			0.409396i
$633$	12.4501			0.0196685
$634$	−494.884			−0.780574
$635$		−	18.9434i		−	0.0298321i
$636$		−	662.404i		−	1.04152i
$637$	57.6010			0.0904254
$638$		−	6.40293i		−	0.0100359i
$639$	20.1788			0.0315787
$640$			236.234i			0.369115i
$641$			174.599i			0.272385i	0.990682	+	0.136193i	$0.0434866\pi$
$641$			174.599i			0.272385i	−0.990682	+	0.136193i	$0.956513\pi$
$642$		−	1028.68i		−	1.60230i
$643$			228.519i			0.355394i	0.984085	+	0.177697i	$0.0568647\pi$
$643$			228.519i			0.355394i	−0.984085	+	0.177697i	$0.943135\pi$
$644$	527.782	+	211.364i	0.819538	+	0.328205i
$645$	271.454			0.420859
$646$	694.904			1.07570
$647$	−829.893			−1.28268			−0.641339	−	0.767257i	$-0.721621\pi$
$647$	−829.893			−1.28268			−0.641339	+	0.767257i	$0.721621\pi$
$648$	175.646			0.271058
$649$		−	176.195i		−	0.271487i
$650$	−382.341			−0.588217
$651$			148.640i			0.228325i
$652$	−2082.97			−3.19473
$653$	420.112			0.643356			0.321678	−	0.946849i	$-0.395753\pi$
$653$	420.112			0.643356			0.321678	+	0.946849i	$0.395753\pi$
$654$			70.0488i			0.107108i
$655$			299.424i			0.457135i
$656$	−514.026			−0.783576
$657$	−245.161			−0.373152
$658$		−	621.459i		−	0.944467i
$659$			808.978i			1.22758i	0.789468	+	0.613792i	$0.210357\pi$
$659$			808.978i			1.22758i	−0.789468	+	0.613792i	$0.789643\pi$
$660$	246.973			0.374202
$661$			584.947i			0.884943i	0.896783	+	0.442471i	$0.145898\pi$
$661$			584.947i			0.884943i	−0.896783	+	0.442471i	$0.854102\pi$
$662$	1536.25			2.32063
$663$		−	170.768i		−	0.257569i
$664$		−	3061.42i		−	4.61057i
$665$			147.208i			0.221365i
$666$			110.306i			0.165624i
$667$	3.44145	−	8.59342i	0.00515960	−	0.0128837i
$668$	1070.83			1.60303
$669$	−83.7753			−0.125225
$670$	1101.49			1.64402
$671$	−93.4575			−0.139281
$672$		−	210.006i		−	0.312508i
$673$	1106.50			1.64413			0.822065	−	0.569394i	$-0.192822\pi$
$673$	1106.50			1.64413			0.822065	+	0.569394i	$0.192822\pi$
$674$			748.918i			1.11115i
$675$	66.0962			0.0979204
$676$	−946.319			−1.39988
$677$		−	38.6642i		−	0.0571111i	−0.999592	−	0.0285556i	$-0.990909\pi$
$677$		−	38.6642i		−	0.0571111i	0.999592	−	0.0285556i	$-0.00909076\pi$
$678$			806.997i			1.19026i
$679$	−337.891			−0.497630
$680$	819.415			1.20502
$681$		−	376.461i		−	0.552806i
$682$		−	516.019i		−	0.756627i
$683$	−932.971			−1.36599			−0.682995	−	0.730423i	$-0.739323\pi$
$683$	−932.971			−1.36599			−0.682995	+	0.730423i	$0.739323\pi$
$684$		−	445.027i		−	0.650625i
$685$	−123.351			−0.180074
$686$			67.6505i			0.0986159i
$687$		−	381.587i		−	0.555439i
$688$			1516.91i			2.20481i
$689$			336.834i			0.488874i
$690$	473.377	+	189.576i	0.686054	+	0.274748i
$691$	−1227.83			−1.77688			−0.888441	−	0.458991i	$-0.848211\pi$
$691$	−1227.83			−1.77688			−0.888441	+	0.458991i	$0.848211\pi$
$692$	1991.81			2.87834
$693$	34.5690			0.0498831
$694$	1464.00			2.10951
$695$		−	43.6402i		−	0.0627917i
$696$	−13.6048			−0.0195472
$697$		−	181.585i		−	0.260524i
$698$	1437.38			2.05928
$699$	481.858			0.689354
$700$		−	314.429i		−	0.449184i
$701$		−	133.888i		−	0.190995i	−0.995430	−	0.0954976i	$-0.969556\pi$
$701$		−	133.888i		−	0.190995i	0.995430	−	0.0954976i	$-0.0304442\pi$
$702$	−156.184			−0.222485
$703$	159.823			0.227345
$704$			138.183i			0.196283i
$705$		−	390.297i		−	0.553613i
$706$	−461.005			−0.652981
$707$		−	20.5659i		−	0.0290890i
$708$	−654.661			−0.924663
$709$		−	926.034i		−	1.30611i	−0.757309	−	0.653056i	$-0.773486\pi$
$709$		−	926.034i		−	1.30611i	0.757309	−	0.653056i	$-0.226514\pi$
$710$		−	86.0979i		−	0.121265i
$711$			39.7729i			0.0559393i
$712$			2431.74i			3.41537i
$713$	277.351	−	692.553i	0.388991	−	0.971323i
$714$	200.561			0.280898
$715$	−125.587			−0.175646
$716$	655.363			0.915311
$717$	532.406			0.742546
$718$		−	1690.43i		−	2.35436i
$719$	−175.539			−0.244143			−0.122072	−	0.992521i	$-0.538954\pi$
$719$	−175.539			−0.244143			−0.122072	+	0.992521i	$0.538954\pi$
$720$		−	356.562i		−	0.495224i
$721$	−314.067			−0.435599
$722$	397.785			0.550948
$723$			498.185i			0.689053i
$724$		−	162.993i		−	0.225129i
$725$	−5.11957			−0.00706147
$726$	645.534			0.889165
$727$			1131.32i			1.55615i	0.628174	+	0.778073i	$0.283803\pi$
$727$			1131.32i			1.55615i	−0.628174	+	0.778073i	$0.716197\pi$
$728$			424.889i			0.583639i
$729$	27.0000			0.0370370
$730$			1046.04i			1.43293i
$731$	−535.864			−0.733056
$732$			347.245i			0.474379i
$733$		−	1447.49i		−	1.97475i	−0.158409	−	0.987374i	$-0.550636\pi$
$733$		−	1447.49i		−	1.97475i	0.158409	−	0.987374i	$-0.449364\pi$
$734$		−	186.519i		−	0.254114i
$735$			42.4868i			0.0578051i
$736$	−391.854	+	978.473i	−0.532411	+	1.32945i
$737$	−374.782			−0.508524
$738$	−166.078			−0.225038
$739$	−951.337			−1.28733			−0.643665	−	0.765307i	$-0.722587\pi$
$739$	−951.337			−1.28733			−0.643665	+	0.765307i	$0.722587\pi$
$740$	329.554			0.445343
$741$			226.298i			0.305395i
$742$	−395.601			−0.533155
$743$			992.366i			1.33562i	0.744331	+	0.667810i	$0.232768\pi$
$743$			992.366i			1.33562i	−0.744331	+	0.667810i	$0.767232\pi$
$744$	−1096.43			−1.47370
$745$	−629.446			−0.844893
$746$		−	1355.69i		−	1.81728i
$747$		−	470.597i		−	0.629983i
$748$	−487.538			−0.651789
$749$	−430.174			−0.574331
$750$		−	836.284i		−	1.11505i
$751$			1039.21i			1.38377i	0.722005	+	0.691887i	$0.243221\pi$
$751$			1039.21i			1.38377i	−0.722005	+	0.691887i	$0.756779\pi$
$752$	2181.01			2.90028
$753$			383.633i			0.509473i
$754$	12.0975			0.0160444
$755$		−	200.321i		−	0.265325i
$756$		−	128.443i		−	0.169898i
$757$			940.353i			1.24221i	0.783727	+	0.621105i	$0.213316\pi$
$757$			940.353i			1.24221i	−0.783727	+	0.621105i	$0.786684\pi$
$758$			2068.17i			2.72846i
$759$	−161.066	−	64.5031i	−0.212209	−	0.0849843i
$760$	−1085.87			−1.42877
$761$	856.775			1.12585			0.562927	−	0.826507i	$-0.309675\pi$
$761$	856.775			1.12585			0.562927	+	0.826507i	$0.309675\pi$
$762$	34.2016			0.0448840
$763$	29.2931			0.0383920
$764$			459.183i			0.601025i
$765$	125.959			0.164653
$766$			365.498i			0.477152i
$767$	332.897			0.434025
$768$	−646.328			−0.841573
$769$			298.366i			0.387992i	0.981002	+	0.193996i	$0.0621449\pi$
$769$			298.366i			0.387992i	−0.981002	+	0.193996i	$0.937855\pi$
$770$		−	147.497i		−	0.191555i
$771$	−285.224			−0.369940
$772$	−616.354			−0.798385
$773$		−	1191.65i		−	1.54160i	−0.637080	−	0.770798i	$-0.719858\pi$
$773$		−	1191.65i		−	1.54160i	0.637080	−	0.770798i	$-0.280142\pi$
$774$			490.101i			0.633206i
$775$	−412.592			−0.532377
$776$		−	2492.42i		−	3.21189i
$777$	46.1278			0.0593665
$778$		−	2602.93i		−	3.34566i
$779$			240.632i			0.308899i
$780$			466.623i			0.598234i
$781$			29.2948i			0.0375093i
$782$	−934.470	−	374.232i	−1.19497	−	0.478558i
$783$	−2.09132			−0.00267091
$784$	−237.419			−0.302831
$785$	175.197			0.223181
$786$	−540.599			−0.687785
$787$			1263.54i			1.60551i	0.596307	+	0.802756i	$0.296634\pi$
$787$			1263.54i			1.60551i	−0.596307	+	0.802756i	$0.703366\pi$
$788$	3603.75			4.57328
$789$		−	711.097i		−	0.901264i
$790$	169.701			0.214811
$791$	337.471			0.426638
$792$			254.995i			0.321964i
$793$		−	176.575i		−	0.222667i
$794$	154.764			0.194917
$795$	−248.450			−0.312516
$796$			875.397i			1.09975i
$797$			741.391i			0.930227i	0.885251	+	0.465114i	$0.153987\pi$
$797$			741.391i			0.930227i	−0.885251	+	0.465114i	$0.846013\pi$
$798$	−265.779			−0.333056
$799$			770.466i			0.964288i
$800$	582.929			0.728662
$801$			373.804i			0.466672i
$802$		−	2188.38i		−	2.72865i
$803$		−	355.915i		−	0.443231i
$804$			1392.52i			1.73199i
$805$	79.2771	−	197.957i	0.0984809	−	0.245910i
$806$	974.948			1.20961
$807$	748.288			0.927247
$808$	151.703			0.187751
$809$	−1574.25			−1.94592			−0.972958	−	0.230980i	$-0.925807\pi$
$809$	−1574.25			−1.94592			−0.972958	+	0.230980i	$0.925807\pi$
$810$		−	115.202i		−	0.142225i
$811$	−802.240			−0.989198			−0.494599	−	0.869121i	$-0.664685\pi$
$811$	−802.240			−0.989198			−0.494599	+	0.869121i	$0.664685\pi$
$812$			9.94868i			0.0122521i
$813$	−385.215			−0.473819
$814$	−160.138			−0.196729
$815$			781.267i			0.958609i
$816$			703.870i			0.862586i
$817$	710.114			0.869172
$818$	1536.42			1.87827
$819$			65.3134i			0.0797477i
$820$			496.181i			0.605099i
$821$	−140.087			−0.170630			−0.0853151	−	0.996354i	$-0.527190\pi$
$821$	−140.087			−0.170630			−0.0853151	+	0.996354i	$0.527190\pi$
$822$		−	222.705i		−	0.270931i
$823$	1076.64			1.30819			0.654096	−	0.756411i	$-0.273049\pi$
$823$	1076.64			1.30819			0.654096	+	0.756411i	$0.273049\pi$
$824$		−	2316.69i		−	2.81152i
$825$			95.9559i			0.116310i
$826$			390.977i			0.473337i
$827$		−	6.14571i		−	0.00743133i	−0.999993	−	0.00371566i	$-0.998817\pi$
$827$		−	6.14571i		−	0.00743133i	0.999993	−	0.00371566i	$-0.00118274\pi$
$828$	−239.664	+	598.449i	−0.289449	+	0.722764i
$829$	1440.92			1.73815			0.869074	−	0.494683i	$-0.164716\pi$
$829$	1440.92			1.73815			0.869074	+	0.494683i	$0.164716\pi$
$830$	−2007.92			−2.41919
$831$	−856.103			−1.03021
$832$	−261.078			−0.313796
$833$		−	83.8710i		−	0.100685i
$834$	78.7910			0.0944736
$835$		−	401.639i		−	0.481004i
$836$	646.073			0.772815
$837$	−168.542			−0.201364
$838$			1572.42i			1.87639i
$839$			45.1178i			0.0537757i	0.999638	+	0.0268878i	$0.00855970\pi$
$839$			45.1178i			0.0537757i	−0.999638	+	0.0268878i	$0.991440\pi$
$840$	−313.400			−0.373096
$841$	−840.838			−0.999807
$842$		−	2070.44i		−	2.45896i
$843$			272.751i			0.323548i
$844$	67.1571			0.0795700
$845$			354.940i			0.420047i
$846$	704.669			0.832942
$847$		−	269.950i		−	0.318713i
$848$		−	1388.36i		−	1.63722i
$849$			377.718i			0.444897i
$850$			556.715i			0.654958i
$851$	−214.922	−	86.0710i	−0.252552	−	0.101141i
$852$	108.846			0.127754
$853$	251.889			0.295298			0.147649	−	0.989040i	$-0.452829\pi$
$853$	251.889			0.295298			0.147649	+	0.989040i	$0.452829\pi$
$854$	207.382			0.242836
$855$	−166.918			−0.195226
$856$		−	3173.15i		−	3.70695i
$857$	576.607			0.672821			0.336410	−	0.941716i	$-0.390787\pi$
$857$	576.607			0.672821			0.336410	+	0.941716i	$0.390787\pi$
$858$		−	226.742i		−	0.264269i
$859$	250.000			0.291036			0.145518	−	0.989356i	$-0.453515\pi$
$859$	250.000			0.291036			0.145518	+	0.989356i	$0.453515\pi$
$860$	1464.25			1.70261
$861$			69.4507i			0.0806628i
$862$		−	1631.13i		−	1.89226i
$863$	1157.60			1.34137			0.670683	−	0.741744i	$-0.266001\pi$
$863$	1157.60			1.34137			0.670683	+	0.741744i	$0.266001\pi$
$864$	238.124			0.275606
$865$		−	747.075i		−	0.863671i
$866$			2392.63i			2.76285i
$867$	251.913			0.290557
$868$			801.776i			0.923705i
$869$	−57.7407			−0.0664450
$870$			8.92315i			0.0102565i
$871$		−	708.100i		−	0.812974i
$872$			216.078i			0.247796i
$873$		−	383.132i		−	0.438868i
$874$	1238.34	+	495.924i	1.41686	+	0.567418i
$875$	−349.718			−0.399678
$876$	−1322.42			−1.50961
$877$	121.560			0.138608			0.0693042	−	0.997596i	$-0.477922\pi$
$877$	121.560			0.138608			0.0693042	+	0.997596i	$0.477922\pi$
$878$	124.393			0.141678
$879$			607.242i			0.690833i
$880$	517.642			0.588230
$881$			560.238i			0.635911i	0.948106	+	0.317956i	$0.102996\pi$
$881$			560.238i			0.635911i	−0.948106	+	0.317956i	$0.897004\pi$
$882$	−76.7084			−0.0869710
$883$	−192.344			−0.217830			−0.108915	−	0.994051i	$-0.534738\pi$
$883$	−192.344			−0.217830			−0.108915	+	0.994051i	$0.534738\pi$
$884$		−	921.136i		−	1.04201i
$885$			245.546i			0.277454i
$886$	1644.22			1.85578
$887$	−790.542			−0.891254			−0.445627	−	0.895219i	$-0.647019\pi$
$887$	−790.542			−0.891254			−0.445627	+	0.895219i	$0.647019\pi$
$888$			340.258i			0.383173i
$889$		−	14.3025i		−	0.0160883i
$890$	1594.93			1.79206
$891$			39.1975i			0.0439928i
$892$	−451.891			−0.506604
$893$		−	1021.00i		−	1.14334i
$894$		−	1136.44i		−	1.27119i
$895$		−	245.810i		−	0.274648i
$896$			178.359i			0.199062i
$897$	121.870	−	304.313i	0.135864	−	0.339256i
$898$	2396.57			2.66879
$899$	13.0546			0.0145213
$900$	356.529			0.396143
$901$	490.454			0.544344
$902$		−	241.105i		−	0.267301i
$903$	204.951			0.226967
$904$			2489.33i			2.75368i
$905$	−61.1345			−0.0675519
$906$	361.672			0.399197
$907$		−	392.988i		−	0.433284i	−0.976251	−	0.216642i	$-0.930490\pi$
$907$		−	392.988i		−	0.433284i	0.976251	−	0.216642i	$-0.0695104\pi$
$908$		−	2030.66i		−	2.23641i
$909$	23.3196			0.0256541
$910$	278.676			0.306238
$911$		−	257.598i		−	0.282764i	−0.989955	−	0.141382i	$-0.954845\pi$
$911$		−	257.598i		−	0.282764i	0.989955	−	0.141382i	$-0.0451546\pi$
$912$		−	932.752i		−	1.02275i
$913$	683.195			0.748297
$914$			117.004i			0.128014i
$915$	130.243			0.142342
$916$		−	2058.31i		−	2.24706i
$917$			226.068i			0.246530i
$918$			227.415i			0.247729i
$919$		−	953.073i		−	1.03708i	−0.855054	−	0.518538i	$-0.826476\pi$
$919$		−	953.073i		−	1.03708i	0.855054	−	0.518538i	$-0.173524\pi$
$920$	1460.22	+	584.781i	1.58719	+	0.635632i
$921$	−72.4731			−0.0786896
$922$	2420.16			2.62490
$923$	−55.3485			−0.0599658
$924$	186.468			0.201805
$925$			128.041i			0.138422i
$926$	−1477.75			−1.59584
$927$		−	356.118i		−	0.384162i
$928$	−18.4442			−0.0198752
$929$	−105.836			−0.113924			−0.0569622	−	0.998376i	$-0.518141\pi$
$929$	−105.836			−0.113924			−0.0569622	+	0.998376i	$0.518141\pi$
$930$			719.127i			0.773254i
$931$			111.144i			0.119381i
$932$	2599.18			2.78882
$933$	−439.780			−0.471362
$934$			406.413i			0.435132i
$935$			182.863i			0.195575i
$936$	−481.779			−0.514721
$937$			1094.07i			1.16763i	0.811888	+	0.583813i	$0.198440\pi$
$937$			1094.07i			1.16763i	−0.811888	+	0.583813i	$0.801560\pi$
$938$	831.641			0.886610
$939$		−	560.258i		−	0.596654i
$940$		−	2105.30i		−	2.23968i
$941$		−	217.665i		−	0.231312i	−0.993289	−	0.115656i	$-0.963103\pi$
$941$		−	217.665i		−	0.231312i	0.993289	−	0.115656i	$-0.0368970\pi$
$942$			316.312i			0.335788i
$943$	129.590	−	323.590i	0.137423	−	0.343149i
$944$	−1372.13			−1.45353
$945$	−48.1755			−0.0509793
$946$	−711.510			−0.752125
$947$	−152.903			−0.161460			−0.0807302	−	0.996736i	$-0.525725\pi$
$947$	−152.903			−0.161460			−0.0807302	+	0.996736i	$0.525725\pi$
$948$			214.538i			0.226306i
$949$	672.452			0.708591
$950$		−	737.745i		−	0.776573i
$951$	−234.661			−0.246751
$952$	618.668			0.649861
$953$			1129.40i			1.18510i	0.805533	+	0.592551i	$0.201879\pi$
$953$			1129.40i			1.18510i	−0.805533	+	0.592551i	$0.798121\pi$
$954$		−	448.569i		−	0.470198i
$955$	172.228			0.180343
$956$	2871.84			3.00402
$957$		−	3.03610i		−	0.00317251i
$958$			2036.30i			2.12558i
$959$	−93.1312			−0.0971129
$960$		−	192.573i		−	0.200596i
$961$	91.0865			0.0947831
$962$		−	302.558i		−	0.314510i
$963$		−	487.772i		−	0.506513i
$964$			2687.25i			2.78760i
$965$			231.178i			0.239563i
$966$	357.405	+	143.132i	0.369985	+	0.148170i
$967$	1463.93			1.51389			0.756943	−	0.653481i	$-0.226692\pi$
$967$	1463.93			1.51389			0.756943	+	0.653481i	$0.226692\pi$
$968$	1991.26			2.05709
$969$	329.505			0.340046
$970$	−1634.73			−1.68529
$971$			358.572i			0.369281i	0.982806	+	0.184641i	$0.0591121\pi$
$971$			358.572i			0.369281i	−0.982806	+	0.184641i	$0.940888\pi$
$972$	145.640			0.149836
$973$		−	32.9489i		−	0.0338632i
$974$	−2407.04			−2.47129
$975$	−181.296			−0.185944
$976$			727.807i			0.745704i
$977$		−	1618.98i		−	1.65709i	−0.559924	−	0.828544i	$-0.689170\pi$
$977$		−	1618.98i		−	1.65709i	0.559924	−	0.828544i	$-0.310830\pi$
$978$	−1410.55			−1.44228
$979$	−542.674			−0.554315
$980$			229.177i			0.233854i
$981$			33.2153i			0.0338586i
$982$	−2038.33			−2.07569
$983$			854.580i			0.869360i	0.900585	+	0.434680i	$0.143138\pi$
$983$			854.580i			0.869360i	−0.900585	+	0.434680i	$0.856862\pi$
$984$	−512.297			−0.520628
$985$		−	1351.67i		−	1.37226i
$986$		−	17.6147i		−	0.0178648i
$987$		−	294.679i		−	0.298560i
$988$			1220.67i			1.23549i
$989$	−954.923	−	382.423i	−0.965544	−	0.386677i
$990$	167.246			0.168936
$991$	−1426.46			−1.43941			−0.719706	−	0.694279i	$-0.755724\pi$
$991$	−1426.46			−1.43941			−0.719706	+	0.694279i	$0.755724\pi$
$992$	−1486.44			−1.49843
$993$	728.451			0.733586
$994$		−	65.0050i		−	0.0653973i
$995$	328.339			0.329989
$996$		−	2538.44i		−	2.54864i
$997$	97.0237			0.0973156			0.0486578	−	0.998816i	$-0.484506\pi$
$997$	97.0237			0.0973156			0.0486578	+	0.998816i	$0.484506\pi$
$998$	−2017.50			−2.02154
$999$			52.3040i			0.0523564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.43	✓	48
23.22	odd	2	inner	483.3.f.a.22.44	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.43	✓	48	1.1	even	1	trivial
483.3.f.a.22.44	yes	48	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.65278 q^{2} +1.73205 q^{3} +9.34282 q^{4} -3.50425i q^{5} +6.32681 q^{6} -2.64575i q^{7} +19.5162 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+3.65278 q^{2} +1.73205 q^{3} +9.34282 q^{4} -3.50425i q^{5} +6.32681 q^{6} -2.64575i q^{7} +19.5162 q^{8} +3.00000 q^{9} -12.8003i q^{10} +4.35528i q^{11} +16.1822 q^{12} -8.22871 q^{13} -9.66436i q^{14} -6.06954i q^{15} +33.9171 q^{16} +11.9816i q^{17} +10.9583 q^{18} -15.8777i q^{19} -32.7396i q^{20} -4.58258i q^{21} +15.9089i q^{22} +(-8.55074 + 21.3515i) q^{23} +33.8030 q^{24} +12.7202 q^{25} -30.0577 q^{26} +5.19615 q^{27} -24.7188i q^{28} -0.402475 q^{29} -22.1707i q^{30} -32.4359 q^{31} +45.8270 q^{32} +7.54357i q^{33} +43.7661i q^{34} -9.27138 q^{35} +28.0285 q^{36} +10.0659i q^{37} -57.9977i q^{38} -14.2525 q^{39} -68.3896i q^{40} -15.1554 q^{41} -16.7392i q^{42} +44.7240i q^{43} +40.6906i q^{44} -10.5128i q^{45} +(-31.2340 + 77.9923i) q^{46} +64.3043 q^{47} +58.7461 q^{48} -7.00000 q^{49} +46.4642 q^{50} +20.7527i q^{51} -76.8794 q^{52} -40.9340i q^{53} +18.9804 q^{54} +15.2620 q^{55} -51.6349i q^{56} -27.5010i q^{57} -1.47015 q^{58} -40.4555 q^{59} -56.7066i q^{60} +21.4584i q^{61} -118.481 q^{62} -7.93725i q^{63} +31.7277 q^{64} +28.8355i q^{65} +27.5550i q^{66} +86.0524i q^{67} +111.942i q^{68} +(-14.8103 + 36.9818i) q^{69} -33.8663 q^{70} +6.72626 q^{71} +58.5485 q^{72} -81.7202 q^{73} +36.7686i q^{74} +22.0321 q^{75} -148.342i q^{76} +11.5230 q^{77} -52.0615 q^{78} +13.2576i q^{79} -118.854i q^{80} +9.00000 q^{81} -55.3593 q^{82} -156.866i q^{83} -42.8142i q^{84} +41.9864 q^{85} +163.367i q^{86} -0.697106 q^{87} +84.9985i q^{88} +124.601i q^{89} -38.4008i q^{90} +21.7711i q^{91} +(-79.8880 + 199.483i) q^{92} -56.1806 q^{93} +234.890 q^{94} -55.6394 q^{95} +79.3746 q^{96} -127.711i q^{97} -25.5695 q^{98} +13.0658i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more