LMFDB - Embedded newform 483.3.b.a.323.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(323,483)]

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([1, 0, 0]))

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

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

chi := DirichletCharacter("483.323");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.b (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:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.20
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.69

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47284i q^{2} +(-2.89906 + 0.771673i) q^{3} -2.11494 q^{4} +6.48523i q^{5} +(1.90823 + 7.16890i) q^{6} -2.64575 q^{7} -4.66144i q^{8} +(7.80904 - 4.47425i) q^{9} +O(q^{10})$	\(q-2.47284i q^{2} +(-2.89906 + 0.771673i) q^{3} -2.11494 q^{4} +6.48523i q^{5} +(1.90823 + 7.16890i) q^{6} -2.64575 q^{7} -4.66144i q^{8} +(7.80904 - 4.47425i) q^{9} +16.0370 q^{10} -9.37034i q^{11} +(6.13134 - 1.63205i) q^{12} +4.90351 q^{13} +6.54252i q^{14} +(-5.00448 - 18.8011i) q^{15} -19.9868 q^{16} +11.1062i q^{17} +(-11.0641 - 19.3105i) q^{18} -6.35410 q^{19} -13.7159i q^{20} +(7.67018 - 2.04166i) q^{21} -23.1714 q^{22} -4.79583i q^{23} +(3.59711 + 13.5138i) q^{24} -17.0583 q^{25} -12.1256i q^{26} +(-19.1862 + 18.9971i) q^{27} +5.59562 q^{28} +49.3977i q^{29} +(-46.4920 + 12.3753i) q^{30} -46.1462 q^{31} +30.7784i q^{32} +(7.23084 + 27.1651i) q^{33} +27.4638 q^{34} -17.1583i q^{35} +(-16.5157 + 9.46279i) q^{36} -65.6564 q^{37} +15.7127i q^{38} +(-14.2156 + 3.78391i) q^{39} +30.2305 q^{40} +44.1702i q^{41} +(-5.04869 - 18.9671i) q^{42} -77.9135 q^{43} +19.8178i q^{44} +(29.0165 + 50.6435i) q^{45} -11.8593 q^{46} -2.11060i q^{47} +(57.9428 - 15.4233i) q^{48} +7.00000 q^{49} +42.1824i q^{50} +(-8.57035 - 32.1974i) q^{51} -10.3707 q^{52} -66.3914i q^{53} +(46.9769 + 47.4444i) q^{54} +60.7688 q^{55} +12.3330i q^{56} +(18.4209 - 4.90329i) q^{57} +122.153 q^{58} -69.6173i q^{59} +(10.5842 + 39.7632i) q^{60} +22.3516 q^{61} +114.112i q^{62} +(-20.6608 + 11.8377i) q^{63} -3.83708 q^{64} +31.8004i q^{65} +(67.1751 - 17.8807i) q^{66} +85.5505 q^{67} -23.4890i q^{68} +(3.70082 + 13.9034i) q^{69} -42.4298 q^{70} +45.3965i q^{71} +(-20.8564 - 36.4014i) q^{72} -108.196 q^{73} +162.358i q^{74} +(49.4528 - 13.1634i) q^{75} +13.4386 q^{76} +24.7916i q^{77} +(9.35701 + 35.1528i) q^{78} -42.9889 q^{79} -129.619i q^{80} +(40.9622 - 69.8791i) q^{81} +109.226 q^{82} +143.377i q^{83} +(-16.2220 + 4.31799i) q^{84} -72.0262 q^{85} +192.668i q^{86} +(-38.1189 - 143.207i) q^{87} -43.6793 q^{88} -35.5329i q^{89} +(125.233 - 71.7533i) q^{90} -12.9735 q^{91} +10.1429i q^{92} +(133.780 - 35.6098i) q^{93} -5.21918 q^{94} -41.2078i q^{95} +(-23.7509 - 89.2282i) q^{96} -77.3480 q^{97} -17.3099i q^{98} +(-41.9252 - 73.1734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

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 $

$2$		−	2.47284i		−	1.23642i	−0.786013	−	0.618210i	$-0.787858\pi$
$2$		−	2.47284i		−	1.23642i	0.786013	−	0.618210i	$-0.212142\pi$
$3$	−2.89906	+	0.771673i	−0.966352	+	0.257224i
$3$	−2.89906	+	0.771673i	−0.966352	+	0.257224i
$4$	−2.11494			−0.528736
$5$			6.48523i			1.29705i	0.761195	+	0.648523i	$0.224613\pi$
$5$			6.48523i			1.29705i	−0.761195	+	0.648523i	$0.775387\pi$
$6$	1.90823	+	7.16890i	0.318038	+	1.19482i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		−	4.66144i		−	0.582680i
$9$	7.80904	−	4.47425i	0.867671	−	0.497139i
$10$	16.0370			1.60370
$11$		−	9.37034i		−	0.851849i	−0.904759	−	0.425925i	$-0.859949\pi$
$11$		−	9.37034i		−	0.851849i	0.904759	−	0.425925i	$-0.140051\pi$
$12$	6.13134	−	1.63205i	0.510945	−	0.136004i
$13$	4.90351			0.377193			0.188597	−	0.982055i	$-0.439606\pi$
$13$	4.90351			0.377193			0.188597	+	0.982055i	$0.439606\pi$
$14$			6.54252i			0.467323i
$15$	−5.00448	−	18.8011i	−0.333632	−	1.25340i
$16$	−19.9868			−1.24917
$17$			11.1062i			0.653305i	0.945144	+	0.326653i	$0.105921\pi$
$17$			11.1062i			0.653305i	−0.945144	+	0.326653i	$0.894079\pi$
$18$	−11.0641	−	19.3105i	−0.614672	−	1.07281i
$19$	−6.35410			−0.334426			−0.167213	−	0.985921i	$-0.553477\pi$
$19$	−6.35410			−0.334426			−0.167213	+	0.985921i	$0.553477\pi$
$20$		−	13.7159i		−	0.685796i
$21$	7.67018	−	2.04166i	0.365247	−	0.0972217i
$22$	−23.1714			−1.05324
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	3.59711	+	13.5138i	0.149880	+	0.563074i
$25$	−17.0583			−0.682330
$26$		−	12.1256i		−	0.466370i
$27$	−19.1862	+	18.9971i	−0.710599	+	0.703597i
$28$	5.59562			0.199844
$29$			49.3977i			1.70337i	0.524055	+	0.851684i	$0.324418\pi$
$29$			49.3977i			1.70337i	−0.524055	+	0.851684i	$0.675582\pi$
$30$	−46.4920	+	12.3753i	−1.54973	+	0.412510i
$31$	−46.1462			−1.48859			−0.744294	−	0.667852i	$-0.767214\pi$
$31$	−46.1462			−1.48859			−0.744294	+	0.667852i	$0.767214\pi$
$32$			30.7784i			0.961825i
$33$	7.23084	+	27.1651i	0.219116	+	0.823186i
$34$	27.4638			0.807760
$35$		−	17.1583i		−	0.490238i
$36$	−16.5157	+	9.46279i	−0.458769	+	0.262855i
$37$	−65.6564			−1.77450			−0.887249	−	0.461291i	$-0.847386\pi$
$37$	−65.6564			−1.77450			−0.887249	+	0.461291i	$0.847386\pi$
$38$			15.7127i			0.413491i
$39$	−14.2156	+	3.78391i	−0.364501	+	0.0970234i
$40$	30.2305			0.755764
$41$			44.1702i			1.07732i	0.842523	+	0.538661i	$0.181069\pi$
$41$			44.1702i			1.07732i	−0.842523	+	0.538661i	$0.818931\pi$
$42$	−5.04869	−	18.9671i	−0.120207	−	0.451598i
$43$	−77.9135			−1.81194			−0.905971	−	0.423340i	$-0.860858\pi$
$43$	−77.9135			−1.81194			−0.905971	+	0.423340i	$0.860858\pi$
$44$			19.8178i			0.450403i
$45$	29.0165	+	50.6435i	0.644812	+	1.12541i
$46$	−11.8593			−0.257812
$47$		−	2.11060i		−	0.0449064i	−0.999748	−	0.0224532i	$-0.992852\pi$
$47$		−	2.11060i		−	0.0449064i	0.999748	−	0.0224532i	$-0.00714768\pi$
$48$	57.9428	−	15.4233i	1.20714	−	0.321318i
$49$	7.00000			0.142857
$50$			42.1824i			0.843647i
$51$	−8.57035	−	32.1974i	−0.168046	−	0.631323i
$52$	−10.3707			−0.199436
$53$		−	66.3914i		−	1.25267i	−0.779555	−	0.626334i	$-0.784555\pi$
$53$		−	66.3914i		−	1.25267i	0.779555	−	0.626334i	$-0.215445\pi$
$54$	46.9769	+	47.4444i	0.869942	+	0.878600i
$55$	60.7688			1.10489
$56$			12.3330i			0.220232i
$57$	18.4209	−	4.90329i	0.323173	−	0.0860226i
$58$	122.153			2.10608
$59$		−	69.6173i		−	1.17995i	−0.807420	−	0.589977i	$-0.799137\pi$
$59$		−	69.6173i		−	1.17995i	0.807420	−	0.589977i	$-0.200863\pi$
$60$	10.5842	+	39.7632i	0.176403	+	0.662720i
$61$	22.3516			0.366420			0.183210	−	0.983074i	$-0.441351\pi$
$61$	22.3516			0.366420			0.183210	+	0.983074i	$0.441351\pi$
$62$			114.112i			1.84052i
$63$	−20.6608	+	11.8377i	−0.327949	+	0.187901i
$64$	−3.83708			−0.0599543
$65$			31.8004i			0.489237i
$66$	67.1751	−	17.8807i	1.01780	−	0.270920i
$67$	85.5505			1.27687			0.638437	−	0.769674i	$-0.279581\pi$
$67$	85.5505			1.27687			0.638437	+	0.769674i	$0.279581\pi$
$68$		−	23.4890i		−	0.345426i
$69$	3.70082	+	13.9034i	0.0536350	+	0.201498i
$70$	−42.4298			−0.606140
$71$			45.3965i			0.639388i	0.947521	+	0.319694i	$0.103580\pi$
$71$			45.3965i			0.639388i	−0.947521	+	0.319694i	$0.896420\pi$
$72$	−20.8564	−	36.4014i	−0.289673	−	0.505575i
$73$	−108.196			−1.48214			−0.741069	−	0.671429i	$-0.765681\pi$
$73$	−108.196			−1.48214			−0.741069	+	0.671429i	$0.765681\pi$
$74$			162.358i			2.19403i
$75$	49.4528	−	13.1634i	0.659371	−	0.175512i
$76$	13.4386			0.176823
$77$			24.7916i			0.321969i
$78$	9.35701	+	35.1528i	0.119962	+	0.450677i
$79$	−42.9889			−0.544163			−0.272082	−	0.962274i	$-0.587712\pi$
$79$	−42.9889			−0.544163			−0.272082	+	0.962274i	$0.587712\pi$
$80$		−	129.619i		−	1.62024i
$81$	40.9622	−	69.8791i	0.505707	−	0.862706i
$82$	109.226			1.33202
$83$			143.377i			1.72744i	0.503976	+	0.863718i	$0.331870\pi$
$83$			143.377i			1.72744i	−0.503976	+	0.863718i	$0.668130\pi$
$84$	−16.2220	+	4.31799i	−0.193119	+	0.0514046i
$85$	−72.0262			−0.847367
$86$			192.668i			2.24032i
$87$	−38.1189	−	143.207i	−0.438148	−	1.64605i
$88$	−43.6793			−0.496356
$89$		−	35.5329i		−	0.399246i	−0.979873	−	0.199623i	$-0.936028\pi$
$89$		−	35.5329i		−	0.399246i	0.979873	−	0.199623i	$-0.0639717\pi$
$90$	125.233	−	71.7533i	1.39148	−	0.797259i
$91$	−12.9735			−0.142566
$92$			10.1429i			0.110249i
$93$	133.780	−	35.6098i	1.43850	−	0.382901i
$94$	−5.21918			−0.0555232
$95$		−	41.2078i		−	0.433766i
$96$	−23.7509	−	89.2282i	−0.247405	−	0.929461i
$97$	−77.3480			−0.797402			−0.398701	−	0.917081i	$-0.630539\pi$
$97$	−77.3480			−0.797402			−0.398701	+	0.917081i	$0.630539\pi$
$98$		−	17.3099i		−	0.176632i
$99$	−41.9252	−	73.1734i	−0.423487	−	0.739125i
$100$	36.0773			0.360773
$101$		−	9.10673i		−	0.0901657i	−0.998983	−	0.0450828i	$-0.985645\pi$
$101$		−	9.10673i		−	0.0901657i	0.998983	−	0.0450828i	$-0.0143552\pi$
$102$	−79.6192	+	21.1931i	−0.780580	+	0.207776i
$103$	−79.9841			−0.776545			−0.388273	−	0.921545i	$-0.626928\pi$
$103$	−79.9841			−0.776545			−0.388273	+	0.921545i	$0.626928\pi$
$104$		−	22.8574i		−	0.219783i
$105$	13.2406	+	49.7429i	0.126101	+	0.473742i
$106$	−164.175			−1.54882
$107$		−	140.356i		−	1.31174i	−0.754874	−	0.655870i	$-0.772302\pi$
$107$		−	140.356i		−	1.31174i	0.754874	−	0.655870i	$-0.227698\pi$
$108$	40.5777	−	40.1779i	0.375720	−	0.372017i
$109$	−5.45958			−0.0500879			−0.0250440	−	0.999686i	$-0.507973\pi$
$109$	−5.45958			−0.0500879			−0.0250440	+	0.999686i	$0.507973\pi$
$110$		−	150.272i		−	1.36611i
$111$	190.342	−	50.6653i	1.71479	−	0.456444i
$112$	52.8801			0.472143
$113$			186.367i			1.64927i	0.565669	+	0.824633i	$0.308618\pi$
$113$			186.367i			1.64927i	−0.565669	+	0.824633i	$0.691382\pi$
$114$	−12.1251	−	45.5519i	−0.106360	−	0.399578i
$115$	31.1021			0.270453
$116$		−	104.473i		−	0.900633i
$117$	38.2917	−	21.9395i	0.327280	−	0.187517i
$118$	−172.153			−1.45892
$119$		−	29.3842i		−	0.246926i
$120$	−87.6400	+	23.3281i	−0.730333	+	0.194401i
$121$	33.1967			0.274353
$122$		−	55.2719i		−	0.453049i
$123$	−34.0849	−	128.052i	−0.277113	−	1.04107i
$124$	97.5967			0.787070
$125$			51.5040i			0.412032i
$126$	29.2729	+	51.0908i	0.232324	+	0.405483i
$127$	−84.6987			−0.666919			−0.333460	−	0.942764i	$-0.608216\pi$
$127$	−84.6987			−0.666919			−0.333460	+	0.942764i	$0.608216\pi$
$128$			132.602i			1.03595i
$129$	225.876	−	60.1238i	1.75097	−	0.466076i
$130$	78.6374			0.604903
$131$			47.6742i			0.363925i	0.983305	+	0.181963i	$0.0582450\pi$
$131$			47.6742i			0.363925i	−0.983305	+	0.181963i	$0.941755\pi$
$132$	−15.2928	−	57.4528i	−0.115855	−	0.435248i
$133$	16.8114			0.126401
$134$		−	211.553i		−	1.57875i
$135$	−123.201	−	124.427i	−0.912598	−	0.921681i
$136$	51.7709			0.380668
$137$		−	101.027i		−	0.737424i	−0.929544	−	0.368712i	$-0.879799\pi$
$137$		−	101.027i		−	0.737424i	0.929544	−	0.368712i	$-0.120201\pi$
$138$	34.3809	−	9.15153i	0.249137	−	0.0663154i
$139$	−10.1719			−0.0731794			−0.0365897	−	0.999330i	$-0.511649\pi$
$139$	−10.1719			−0.0731794			−0.0365897	+	0.999330i	$0.511649\pi$
$140$			36.2889i			0.259206i
$141$	1.62869	+	6.11875i	0.0115510	+	0.0433954i
$142$	112.258			0.790552
$143$		−	45.9476i		−	0.321312i
$144$	−156.078	+	89.4258i	−1.08387	+	0.621013i
$145$	−320.356			−2.20935
$146$			267.552i			1.83255i
$147$	−20.2934	+	5.40171i	−0.138050	+	0.0367463i
$148$	138.860			0.938241
$149$			77.8584i			0.522540i	0.965266	+	0.261270i	$0.0841412\pi$
$149$			77.8584i			0.522540i	−0.965266	+	0.261270i	$0.915859\pi$
$150$	−32.5510	−	122.289i	−0.217007	−	0.815260i
$151$	128.369			0.850123			0.425061	−	0.905164i	$-0.360252\pi$
$151$	128.369			0.850123			0.425061	+	0.905164i	$0.360252\pi$
$152$			29.6193i			0.194864i
$153$	49.6918	+	86.7287i	0.324783	+	0.566854i
$154$	61.3057			0.398089
$155$		−	299.269i		−	1.93077i
$156$	30.0651	−	8.00276i	0.192725	−	0.0512998i
$157$	2.52852			0.0161052			0.00805262	−	0.999968i	$-0.497437\pi$
$157$	2.52852			0.0161052			0.00805262	+	0.999968i	$0.497437\pi$
$158$			106.305i			0.672814i
$159$	51.2324	+	192.472i	0.322217	+	1.21052i
$160$	−199.605			−1.24753
$161$			12.6886i			0.0788110i
$162$	−172.800	−	101.293i	−1.06667	−	0.625266i
$163$	108.571			0.666081			0.333041	−	0.942912i	$-0.391925\pi$
$163$	108.571			0.666081			0.333041	+	0.942912i	$0.391925\pi$
$164$		−	93.4175i		−	0.569619i
$165$	−176.172	+	46.8937i	−1.06771	+	0.284204i
$166$	354.549			2.13584
$167$		−	116.491i		−	0.697550i	−0.937207	−	0.348775i	$-0.886598\pi$
$167$		−	116.491i		−	0.697550i	0.937207	−	0.348775i	$-0.113402\pi$
$168$	−9.51706	−	35.7541i	−0.0566492	−	0.212822i
$169$	−144.956			−0.857725
$170$			178.109i			1.04770i
$171$	−49.6194	+	28.4298i	−0.290172	+	0.166256i
$172$	164.783			0.958039
$173$		−	241.995i		−	1.39881i	−0.714724	−	0.699407i	$-0.753448\pi$
$173$		−	241.995i		−	1.39881i	0.714724	−	0.699407i	$-0.246552\pi$
$174$	−354.127	+	94.2619i	−2.03521	+	0.541735i
$175$	45.1319			0.257897
$176$			187.283i			1.06411i
$177$	53.7218	+	201.824i	0.303513	+	1.14025i
$178$	−87.8672			−0.493636
$179$			88.2003i			0.492739i	0.969176	+	0.246370i	$0.0792377\pi$
$179$			88.2003i			0.492739i	−0.969176	+	0.246370i	$0.920762\pi$
$180$	−61.3684	−	107.108i	−0.340935	−	0.595045i
$181$	305.792			1.68946			0.844729	−	0.535194i	$-0.179761\pi$
$181$	305.792			1.68946			0.844729	+	0.535194i	$0.179761\pi$
$182$			32.0814i			0.176271i
$183$	−64.7985	+	17.2481i	−0.354090	+	0.0942521i
$184$	−22.3555			−0.121497
$185$		−	425.797i		−	2.30161i
$186$	−88.0574	−	330.818i	−0.473427	−	1.77859i
$187$	104.069			0.556517
$188$			4.46381i			0.0237436i
$189$	50.7619	−	50.2616i	0.268581	−	0.265935i
$190$	−101.900			−0.536318
$191$			108.716i			0.569193i	0.958647	+	0.284597i	$0.0918596\pi$
$191$			108.716i			0.569193i	−0.958647	+	0.284597i	$0.908140\pi$
$192$	11.1239	−	2.96097i	0.0579370	−	0.0154217i
$193$	126.865			0.657334			0.328667	−	0.944446i	$-0.393401\pi$
$193$	126.865			0.657334			0.328667	+	0.944446i	$0.393401\pi$
$194$			191.269i			0.985925i
$195$	−24.5395	−	92.1912i	−0.125844	−	0.472775i
$196$	−14.8046			−0.0755337
$197$			15.3832i			0.0780872i	0.999238	+	0.0390436i	$0.0124311\pi$
$197$			15.3832i			0.0780872i	−0.999238	+	0.0390436i	$0.987569\pi$
$198$	−180.946	+	103.674i	−0.913869	+	0.523608i
$199$	−198.522			−0.997599			−0.498800	−	0.866717i	$-0.666226\pi$
$199$	−198.522			−0.997599			−0.498800	+	0.866717i	$0.666226\pi$
$200$			79.5161i			0.397580i
$201$	−248.016	+	66.0171i	−1.23391	+	0.328443i
$202$	−22.5195			−0.111483
$203$		−	130.694i		−	0.643813i
$204$	18.1258	+	68.0958i	0.0888520	+	0.333803i
$205$	−286.454			−1.39734
$206$			197.788i			0.960136i
$207$	−21.4577	−	37.4508i	−0.103661	−	0.180922i
$208$	−98.0055			−0.471180
$209$			59.5401i			0.284881i
$210$	123.006	−	32.7419i	0.585744	−	0.155914i
$211$	197.714			0.937034			0.468517	−	0.883454i	$-0.344788\pi$
$211$	197.714			0.937034			0.468517	+	0.883454i	$0.344788\pi$
$212$			140.414i			0.662331i
$213$	−35.0313	−	131.607i	−0.164466	−	0.617873i
$214$	−347.079			−1.62186
$215$		−	505.287i		−	2.35017i
$216$	88.5540	+	89.4353i	0.409972	+	0.414052i
$217$	122.091			0.562633
$218$			13.5007i			0.0619298i
$219$	313.666	−	83.4920i	1.43227	−	0.381242i
$220$	−128.523			−0.584194
$221$			54.4593i			0.246422i
$222$	−125.287	−	470.684i	−0.564357	−	2.12020i
$223$	−175.117			−0.785277			−0.392639	−	0.919693i	$-0.628438\pi$
$223$	−175.117			−0.785277			−0.392639	+	0.919693i	$0.628438\pi$
$224$		−	81.4320i		−	0.363536i
$225$	−133.209	+	76.3229i	−0.592038	+	0.339213i
$226$	460.856			2.03919
$227$			134.376i			0.591964i	0.955194	+	0.295982i	$0.0956468\pi$
$227$			134.376i			0.591964i	−0.955194	+	0.295982i	$0.904353\pi$
$228$	−38.9591	+	10.3702i	−0.170873	+	0.0454833i
$229$	356.627			1.55732			0.778661	−	0.627445i	$-0.215899\pi$
$229$	356.627			1.55732			0.778661	+	0.627445i	$0.215899\pi$
$230$		−	76.9105i		−	0.334394i
$231$	−19.1310	−	71.8722i	−0.0828182	−	0.311135i
$232$	230.264			0.992519
$233$		−	205.741i		−	0.883010i	−0.897259	−	0.441505i	$-0.854445\pi$
$233$		−	205.741i		−	0.883010i	0.897259	−	0.441505i	$-0.145555\pi$
$234$	−54.2530	−	94.6894i	−0.231850	−	0.404656i
$235$	13.6877			0.0582457
$236$			147.237i			0.623885i
$237$	124.627	−	33.1734i	0.525853	−	0.139972i
$238$	−72.6625			−0.305305
$239$		−	345.433i		−	1.44533i	−0.691200	−	0.722663i	$-0.742918\pi$
$239$		−	345.433i		−	1.44533i	0.691200	−	0.722663i	$-0.257082\pi$
$240$	100.024	+	375.773i	0.416765	+	1.56572i
$241$	−300.193			−1.24561			−0.622807	−	0.782376i	$-0.714008\pi$
$241$	−300.193			−1.24561			−0.622807	+	0.782376i	$0.714008\pi$
$242$		−	82.0903i		−	0.339216i
$243$	−64.8279	+	234.193i	−0.266781	+	0.963757i
$244$	−47.2724			−0.193739
$245$			45.3966i			0.185292i
$246$	−316.652	+	84.2867i	−1.28720	+	0.342629i
$247$	−31.1574			−0.126143
$248$			215.108i			0.867371i
$249$	−110.640	−	415.658i	−0.444339	−	1.66931i
$250$	127.361			0.509445
$251$			55.1019i			0.219530i	0.993958	+	0.109765i	$0.0350098\pi$
$251$			55.1019i			0.219530i	−0.993958	+	0.109765i	$0.964990\pi$
$252$	43.6964	−	25.0362i	0.173398	−	0.0993499i
$253$	−44.9386			−0.177623
$254$			209.447i			0.824593i
$255$	208.808	−	55.5807i	0.818855	−	0.217964i
$256$	312.555			1.22092
$257$			66.5990i			0.259140i	0.991570	+	0.129570i	$0.0413597\pi$
$257$			66.5990i			0.259140i	−0.991570	+	0.129570i	$0.958640\pi$
$258$	−148.677	−	558.554i	−0.576266	−	2.16494i
$259$	173.711			0.670697
$260$		−	67.2562i		−	0.258678i
$261$	221.017	+	385.749i	0.846810	+	1.47796i
$262$	117.891			0.449965
$263$			105.995i			0.403022i	0.979486	+	0.201511i	$0.0645852\pi$
$263$			105.995i			0.403022i	−0.979486	+	0.201511i	$0.935415\pi$
$264$	126.629	−	33.7061i	0.479654	−	0.127675i
$265$	430.564			1.62477
$266$		−	41.5718i		−	0.156285i
$267$	27.4198	+	103.012i	0.102696	+	0.385812i
$268$	−180.935			−0.675129
$269$			471.762i			1.75376i	0.480706	+	0.876882i	$0.340380\pi$
$269$			471.762i			1.75376i	−0.480706	+	0.876882i	$0.659620\pi$
$270$	−307.688	+	304.656i	−1.13959	+	1.12836i
$271$	377.444			1.39278			0.696391	−	0.717663i	$-0.254788\pi$
$271$	377.444			1.39278			0.696391	+	0.717663i	$0.254788\pi$
$272$		−	221.977i		−	0.816092i
$273$	37.6108	−	10.0113i	0.137769	−	0.0366714i
$274$	−249.824			−0.911766
$275$			159.842i			0.581243i
$276$	−7.82702	−	29.4049i	−0.0283588	−	0.106539i
$277$	−67.2064			−0.242622			−0.121311	−	0.992615i	$-0.538710\pi$
$277$	−67.2064			−0.242622			−0.121311	+	0.992615i	$0.538710\pi$
$278$			25.1536i			0.0904805i
$279$	−360.358	+	206.470i	−1.29160	+	0.740034i
$280$	−79.9825			−0.285652
$281$			358.562i			1.27602i	0.770028	+	0.638011i	$0.220242\pi$
$281$			358.562i			1.27602i	−0.770028	+	0.638011i	$0.779758\pi$
$282$	15.1307	−	4.02750i	0.0536550	−	0.0142819i
$283$	−221.881			−0.784031			−0.392016	−	0.919959i	$-0.628222\pi$
$283$	−221.881			−0.784031			−0.392016	+	0.919959i	$0.628222\pi$
$284$		−	96.0111i		−	0.338067i
$285$	31.7990	+	119.464i	0.111575	+	0.419171i
$286$	−113.621			−0.397277
$287$		−	116.863i		−	0.407189i
$288$	137.710	+	240.350i	0.478160	+	0.834547i
$289$	165.653			0.573192
$290$			792.188i			2.73168i
$291$	224.236	−	59.6874i	0.770571	−	0.205111i
$292$	228.829			0.783660
$293$		−	211.225i		−	0.720903i	−0.932778	−	0.360452i	$-0.882623\pi$
$293$		−	211.225i		−	0.720903i	0.932778	−	0.360452i	$-0.117377\pi$
$294$	13.3576	+	50.1823i	0.0454339	+	0.170688i
$295$	451.485			1.53046
$296$			306.054i			1.03396i
$297$	178.009	+	179.781i	0.599358	+	0.605323i
$298$	192.531			0.646079
$299$		−	23.5164i		−	0.0786503i
$300$	−104.590	+	27.8399i	−0.348633	+	0.0927996i
$301$	206.140			0.684850
$302$		−	317.435i		−	1.05111i
$303$	7.02742	+	26.4009i	0.0231928	+	0.0871317i
$304$	126.998			0.417757
$305$			144.955i			0.475263i
$306$	214.466	−	122.880i	0.700870	−	0.401569i
$307$	512.344			1.66887			0.834437	−	0.551103i	$-0.185793\pi$
$307$	512.344			1.66887			0.834437	+	0.551103i	$0.185793\pi$
$308$		−	52.4328i		−	0.170237i
$309$	231.878	−	61.7216i	0.750416	−	0.199746i
$310$	−740.045			−2.38724
$311$		−	341.645i		−	1.09854i	−0.835646	−	0.549269i	$-0.814906\pi$
$311$		−	341.645i		−	1.09854i	0.835646	−	0.549269i	$-0.185094\pi$
$312$	17.6385	+	66.2650i	0.0565336	+	0.212388i
$313$	−303.251			−0.968853			−0.484426	−	0.874832i	$-0.660972\pi$
$313$	−303.251			−0.968853			−0.484426	+	0.874832i	$0.660972\pi$
$314$		−	6.25264i		−	0.0199129i
$315$	−76.7705	−	133.990i	−0.243716	−	0.425365i
$316$	90.9191			0.287719
$317$		−	295.965i		−	0.933644i	−0.884351	−	0.466822i	$-0.845399\pi$
$317$		−	295.965i		−	0.933644i	0.884351	−	0.466822i	$-0.154601\pi$
$318$	475.953	−	126.690i	1.49671	−	0.398395i
$319$	462.873			1.45101
$320$		−	24.8843i		−	0.0777636i
$321$	108.309	+	406.901i	0.337412	+	1.26760i
$322$	31.3768			0.0974436
$323$		−	70.5698i		−	0.218482i
$324$	−86.6329	+	147.791i	−0.267385	+	0.456144i
$325$	−83.6454			−0.257371
$326$		−	268.480i		−	0.823557i
$327$	15.8276	−	4.21302i	0.0484026	−	0.0128838i
$328$	205.897			0.627734
$329$			5.58413i			0.0169730i
$330$	115.961	+	435.646i	0.351396	+	1.32014i
$331$	−468.256			−1.41467			−0.707336	−	0.706877i	$-0.750103\pi$
$331$	−468.256			−1.41467			−0.707336	+	0.706877i	$0.750103\pi$
$332$		−	303.235i		−	0.913358i
$333$	−512.714	+	293.763i	−1.53968	+	0.882171i
$334$	−288.063			−0.862465
$335$			554.815i			1.65616i
$336$	−153.302	+	40.8061i	−0.456257	+	0.121447i
$337$	−447.490			−1.32786			−0.663932	−	0.747793i	$-0.731114\pi$
$337$	−447.490			−1.32786			−0.663932	+	0.747793i	$0.731114\pi$
$338$			358.452i			1.06051i
$339$	−143.814	−	540.288i	−0.424231	−	1.59377i
$340$	152.331			0.448034
$341$			432.406i			1.26805i
$342$	70.3024	+	122.701i	0.205563	+	0.358775i
$343$	−18.5203			−0.0539949
$344$			363.189i			1.05578i
$345$	−90.1667	+	24.0007i	−0.261353	+	0.0695671i
$346$	−598.415			−1.72952
$347$		−	445.859i		−	1.28490i	−0.766329	−	0.642448i	$-0.777919\pi$
$347$		−	445.859i		−	1.28490i	0.766329	−	0.642448i	$-0.222081\pi$
$348$	80.6193	+	302.874i	0.231665	+	0.870328i
$349$	244.524			0.700641			0.350321	−	0.936630i	$-0.386073\pi$
$349$	244.524			0.700641			0.350321	+	0.936630i	$0.386073\pi$
$350$		−	111.604i		−	0.318869i
$351$	−94.0797	+	93.1526i	−0.268033	+	0.265392i
$352$	288.404			0.819329
$353$		−	462.070i		−	1.30898i	−0.756070	−	0.654490i	$-0.772883\pi$
$353$		−	462.070i		−	1.30898i	0.756070	−	0.654490i	$-0.227117\pi$
$354$	499.080	−	132.846i	1.40983	−	0.375270i
$355$	−294.407			−0.829316
$356$			75.1501i			0.211096i
$357$	22.6750	+	85.1864i	0.0635154	+	0.238617i
$358$	218.105			0.609233
$359$			126.693i			0.352906i	0.984309	+	0.176453i	$0.0564624\pi$
$359$			126.693i			0.352906i	−0.984309	+	0.176453i	$0.943538\pi$
$360$	236.072	−	135.259i	0.655754	−	0.375719i
$361$	−320.625			−0.888159
$362$		−	756.175i		−	2.08888i
$363$	−96.2392	+	25.6170i	−0.265122	+	0.0705703i
$364$	27.4382			0.0753796
$365$		−	701.677i		−	1.92240i
$366$	42.6519	+	160.236i	0.116535	+	0.437804i
$367$	76.1305			0.207440			0.103720	−	0.994607i	$-0.466925\pi$
$367$	76.1305			0.207440			0.103720	+	0.994607i	$0.466925\pi$
$368$			95.8533i			0.260471i
$369$	197.628	+	344.927i	0.535578	+	0.934761i
$370$	−1052.93			−2.84575
$371$			175.655i			0.473464i
$372$	−282.938	+	75.3128i	−0.760587	+	0.202454i
$373$	−61.9538			−0.166096			−0.0830480	−	0.996546i	$-0.526465\pi$
$373$	−61.9538			−0.166096			−0.0830480	+	0.996546i	$0.526465\pi$
$374$		−	257.346i		−	0.688090i
$375$	−39.7443	−	149.313i	−0.105985	−	0.398168i
$376$	−9.83845			−0.0261661
$377$			242.222i			0.642499i
$378$	−124.289	−	125.526i	−0.328807	−	0.332079i
$379$	−297.702			−0.785493			−0.392746	−	0.919647i	$-0.628475\pi$
$379$	−297.702			−0.785493			−0.392746	+	0.919647i	$0.628475\pi$
$380$			87.1523i			0.229348i
$381$	245.546	−	65.3597i	0.644478	−	0.171548i
$382$	268.837			0.703762
$383$			152.685i			0.398655i	0.979933	+	0.199327i	$0.0638757\pi$
$383$			152.685i			0.398655i	−0.979933	+	0.199327i	$0.936124\pi$
$384$	−102.325	−	384.421i	−0.266473	−	1.00110i
$385$	−160.779			−0.417608
$386$		−	313.718i		−	0.812741i
$387$	−608.430	+	348.604i	−1.57217	+	0.900786i
$388$	163.587			0.421615
$389$		−	16.6356i		−	0.0427649i	−0.999771	−	0.0213825i	$-0.993193\pi$
$389$		−	16.6356i		−	0.0427649i	0.999771	−	0.0213825i	$-0.00680677\pi$
$390$	−227.974	+	60.6824i	−0.584549	+	0.155596i
$391$	53.2634			0.136224
$392$		−	32.6301i		−	0.0832400i
$393$	−36.7889	−	138.210i	−0.0936104	−	0.351680i
$394$	38.0402			0.0965487
$395$		−	278.793i		−	0.705805i
$396$	88.6695	+	154.758i	0.223913	+	0.390802i
$397$	−331.880			−0.835969			−0.417985	−	0.908454i	$-0.637263\pi$
$397$	−331.880			−0.835969			−0.417985	+	0.908454i	$0.637263\pi$
$398$			490.914i			1.23345i
$399$	−48.7371	+	12.9729i	−0.122148	+	0.0325135i
$400$	340.940			0.852350
$401$			473.095i			1.17979i	0.807481	+	0.589894i	$0.200830\pi$
$401$			473.095i			1.17979i	−0.807481	+	0.589894i	$0.799170\pi$
$402$	163.250	+	613.304i	0.406094	+	1.52563i
$403$	−226.279			−0.561486
$404$			19.2602i			0.0476739i
$405$	453.183	+	265.650i	1.11897	+	0.655925i
$406$	−323.185			−0.796023
$407$			615.223i			1.51160i
$408$	−150.087	+	39.9502i	−0.367859	+	0.0979171i
$409$	414.368			1.01312			0.506562	−	0.862204i	$-0.330916\pi$
$409$	414.368			1.01312			0.506562	+	0.862204i	$0.330916\pi$
$410$			708.355i			1.72770i
$411$	77.9599	+	292.883i	0.189683	+	0.712611i
$412$	169.162			0.410588
$413$			184.190i			0.445981i
$414$	−92.6100	+	53.0616i	−0.223696	+	0.128168i
$415$	−929.834			−2.24056
$416$			150.922i			0.362794i
$417$	29.4890	−	7.84941i	0.0707171	−	0.0188235i
$418$	147.233			0.352232
$419$		−	128.102i		−	0.305733i	−0.988247	−	0.152866i	$-0.951150\pi$
$419$		−	128.102i		−	0.305733i	0.988247	−	0.152866i	$-0.0488504\pi$
$420$	−28.0032	−	105.204i	−0.0666742	−	0.250485i
$421$	728.059			1.72936			0.864678	−	0.502327i	$-0.167523\pi$
$421$	728.059			1.72936			0.864678	+	0.502327i	$0.167523\pi$
$422$		−	488.916i		−	1.15857i
$423$	−9.44335	−	16.4818i	−0.0223247	−	0.0389640i
$424$	−309.480			−0.729905
$425$		−	189.452i		−	0.445770i
$426$	−325.443	+	86.6268i	−0.763951	+	0.203349i
$427$	−59.1367			−0.138494
$428$			296.846i			0.693565i
$429$	35.4565	+	133.205i	0.0826493	+	0.310500i
$430$	−1249.50			−2.90580
$431$		−	166.062i		−	0.385295i	−0.981268	−	0.192648i	$-0.938293\pi$
$431$		−	166.062i		−	0.385295i	0.981268	−	0.192648i	$-0.0617075\pi$
$432$	383.470	−	379.691i	0.887662	−	0.878915i
$433$	−797.847			−1.84260			−0.921301	−	0.388850i	$-0.872872\pi$
$433$	−797.847			−1.84260			−0.921301	+	0.388850i	$0.872872\pi$
$434$		−	301.913i		−	0.695652i
$435$	928.728	−	247.210i	2.13501	−	0.568298i
$436$	11.5467			0.0264833
$437$			30.4732i			0.0697327i
$438$	−206.462	−	775.647i	−0.471376	−	1.77088i
$439$	255.993			0.583128			0.291564	−	0.956551i	$-0.405824\pi$
$439$	255.993			0.583128			0.291564	+	0.956551i	$0.405824\pi$
$440$		−	283.270i		−	0.643797i
$441$	54.6633	−	31.3197i	0.123953	−	0.0710198i
$442$	134.669			0.304682
$443$			31.4921i			0.0710884i	0.999368	+	0.0355442i	$0.0113164\pi$
$443$			31.4921i			0.0710884i	−0.999368	+	0.0355442i	$0.988684\pi$
$444$	−402.562	+	107.154i	−0.906671	+	0.241339i
$445$	230.439			0.517840
$446$			433.036i			0.970933i
$447$	−60.0812	−	225.716i	−0.134410	−	0.504957i
$448$	10.1520			0.0226606
$449$			244.886i			0.545404i	0.962099	+	0.272702i	$0.0879173\pi$
$449$			244.886i			0.545404i	−0.962099	+	0.272702i	$0.912083\pi$
$450$	188.734	+	329.404i	0.419410	+	0.732009i
$451$	413.889			0.917715
$452$		−	394.156i		−	0.872026i
$453$	−372.148	+	99.0586i	−0.821518	+	0.218672i
$454$	332.290			0.731916
$455$		−	84.1360i		−	0.184914i
$456$	−22.8564	−	85.8679i	−0.0501237	−	0.188307i
$457$	−744.424			−1.62894			−0.814468	−	0.580208i	$-0.802971\pi$
$457$	−744.424			−1.62894			−0.814468	+	0.580208i	$0.802971\pi$
$458$		−	881.881i		−	1.92551i
$459$	−210.986	−	213.085i	−0.459663	−	0.464238i
$460$	−65.7792			−0.142998
$461$		−	29.0619i		−	0.0630409i	−0.999503	−	0.0315205i	$-0.989965\pi$
$461$		−	29.0619i		−	0.0630409i	0.999503	−	0.0315205i	$-0.0100349\pi$
$462$	−177.729	+	47.3079i	−0.384694	+	0.102398i
$463$	573.741			1.23918			0.619590	−	0.784925i	$-0.287299\pi$
$463$	573.741			1.23918			0.619590	+	0.784925i	$0.287299\pi$
$464$		−	987.301i		−	2.12780i
$465$	230.938	+	867.598i	0.496641	+	1.86580i
$466$	−508.766			−1.09177
$467$		−	503.322i		−	1.07778i	−0.842377	−	0.538889i	$-0.818844\pi$
$467$		−	503.322i		−	1.07778i	0.842377	−	0.538889i	$-0.181156\pi$
$468$	−80.9849	+	46.4009i	−0.173045	+	0.0991472i
$469$	−226.345			−0.482613
$470$		−	33.8476i		−	0.0720162i
$471$	−7.33033	+	1.95119i	−0.0155633	+	0.00414266i
$472$	−324.517			−0.687536
$473$			730.076i			1.54350i
$474$	−82.0325	−	308.183i	−0.173064	−	0.650175i
$475$	108.390			0.228189
$476$			62.1460i			0.130559i
$477$	−297.051	−	518.453i	−0.622749	−	1.08690i
$478$	−854.201			−1.78703
$479$			376.752i			0.786538i	0.919423	+	0.393269i	$0.128656\pi$
$479$			376.752i			0.786538i	−0.919423	+	0.393269i	$0.871344\pi$
$480$	578.666	−	154.030i	1.20555	−	0.320896i
$481$	−321.947			−0.669329
$482$			742.330i			1.54010i
$483$	−9.79144	−	36.7849i	−0.0202721	−	0.0761592i
$484$	−70.2093			−0.145060
$485$		−	501.620i		−	1.03427i
$486$	579.122	+	160.309i	1.19161	+	0.329854i
$487$	578.691			1.18828			0.594139	−	0.804363i	$-0.297493\pi$
$487$	578.691			1.18828			0.594139	+	0.804363i	$0.297493\pi$
$488$		−	104.191i		−	0.213505i
$489$	−314.754	+	83.7816i	−0.643669	+	0.171332i
$490$	112.259			0.229099
$491$		−	757.202i		−	1.54216i	−0.636736	−	0.771082i	$-0.719716\pi$
$491$		−	757.202i		−	1.54216i	0.636736	−	0.771082i	$-0.280284\pi$
$492$	72.0878	+	270.822i	0.146520	+	0.550452i
$493$	−548.620			−1.11282
$494$			77.0473i			0.155966i
$495$	474.546	−	271.895i	0.958680	−	0.549282i
$496$	922.315			1.85951
$497$		−	120.108i		−	0.241666i
$498$	−1027.86	+	273.596i	−2.06397	+	0.549390i
$499$	107.228			0.214885			0.107443	−	0.994211i	$-0.465734\pi$
$499$	107.228			0.214885			0.107443	+	0.994211i	$0.465734\pi$
$500$		−	108.928i		−	0.217856i
$501$	89.8929	+	337.713i	0.179427	+	0.674078i
$502$	136.258			0.271431
$503$			460.261i			0.915032i	0.889201	+	0.457516i	$0.151261\pi$
$503$			460.261i			0.915032i	−0.889201	+	0.457516i	$0.848739\pi$
$504$	55.1810	+	96.3090i	0.109486	+	0.191089i
$505$	59.0593			0.116949
$506$			111.126i			0.219617i
$507$	420.234	−	111.858i	0.828864	−	0.220628i
$508$	179.133			0.352624
$509$			166.878i			0.327854i	0.986472	+	0.163927i	$0.0524162\pi$
$509$			166.878i			0.327854i	−0.986472	+	0.163927i	$0.947584\pi$
$510$	−137.442	−	516.349i	−0.269495	−	1.01245i
$511$	286.260			0.560195
$512$		−	242.492i		−	0.473617i
$513$	121.911	−	120.710i	0.237643	−	0.235301i
$514$	164.689			0.320406
$515$		−	518.716i		−	1.00722i
$516$	−477.714	+	127.158i	−0.925803	+	0.246431i
$517$	−19.7771			−0.0382535
$518$		−	429.559i		−	0.829264i
$519$	186.741	+	701.556i	0.359809	+	1.35175i
$520$	148.236			0.285069
$521$			450.149i			0.864010i	0.901871	+	0.432005i	$0.142194\pi$
$521$			450.149i			0.864010i	−0.901871	+	0.432005i	$0.857806\pi$
$522$	953.895	−	546.541i	1.82738	−	1.04701i
$523$	−1041.91			−1.99218			−0.996089	−	0.0883611i	$-0.971837\pi$
$523$	−1041.91			−1.99218			−0.996089	+	0.0883611i	$0.971837\pi$
$524$		−	100.828i		−	0.192420i
$525$	−130.840	+	34.8271i	−0.249219	+	0.0663373i
$526$	262.108			0.498305
$527$		−	512.509i		−	0.972502i
$528$	−144.521	−	542.944i	−0.273715	−	1.02830i
$529$	−23.0000			−0.0434783
$530$		−	1064.72i		−	2.00890i
$531$	−311.485	−	543.644i	−0.586601	−	1.02381i
$532$	−35.5551			−0.0668329
$533$			216.589i			0.406358i
$534$	254.732	−	67.8047i	0.477026	−	0.126975i
$535$	910.243			1.70139
$536$		−	398.789i		−	0.744009i
$537$	−68.0618	−	255.698i	−0.126745	−	0.476159i
$538$	1166.59			2.16839
$539$		−	65.5924i		−	0.121693i
$540$	260.563	+	263.156i	0.482524	+	0.487326i
$541$	834.844			1.54315			0.771575	−	0.636139i	$-0.219469\pi$
$541$	834.844			1.54315			0.771575	+	0.636139i	$0.219469\pi$
$542$		−	933.359i		−	1.72206i
$543$	−886.508	+	235.972i	−1.63261	+	0.434570i
$544$	−341.831			−0.628365
$545$		−	35.4067i		−	0.0649664i
$546$	−24.7563	−	93.0056i	−0.0453413	−	0.170340i
$547$	694.609			1.26985			0.634926	−	0.772573i	$-0.281031\pi$
$547$	694.609			1.26985			0.634926	+	0.772573i	$0.281031\pi$
$548$			213.667i			0.389903i
$549$	174.544	−	100.007i	0.317932	−	0.182161i
$550$	395.263			0.718660
$551$		−	313.878i		−	0.569651i
$552$	64.8098	−	17.2511i	0.117409	−	0.0312521i
$553$	113.738			0.205674
$554$			166.191i			0.299983i
$555$	328.576	+	1234.41i	0.592029	+	2.22416i
$556$	21.5131			0.0386926
$557$		−	246.580i		−	0.442693i	−0.975195	−	0.221346i	$-0.928955\pi$
$557$		−	246.580i		−	0.442693i	0.975195	−	0.221346i	$-0.0710451\pi$
$558$	510.567	+	891.108i	0.914994	+	1.59697i
$559$	−382.050			−0.683453
$560$			342.940i			0.612392i
$561$	−301.701	+	80.3071i	−0.537791	+	0.143150i
$562$	886.667			1.57770
$563$			797.047i			1.41571i	0.706356	+	0.707857i	$0.250338\pi$
$563$			797.047i			1.41571i	−0.706356	+	0.707857i	$0.749662\pi$
$564$	−3.44460	−	12.9408i	−0.00610745	−	0.0229447i
$565$	−1208.63			−2.13917
$566$			548.676i			0.969393i
$567$	−108.376	+	184.883i	−0.191139	+	0.326072i
$568$	211.613			0.372559
$569$			72.7169i			0.127798i	0.997956	+	0.0638989i	$0.0203535\pi$
$569$			72.7169i			0.127798i	−0.997956	+	0.0638989i	$0.979646\pi$
$570$	295.415	−	78.6338i	0.518272	−	0.137954i
$571$	160.628			0.281310			0.140655	−	0.990059i	$-0.455079\pi$
$571$	160.628			0.281310			0.140655	+	0.990059i	$0.455079\pi$
$572$			97.1766i			0.169889i
$573$	−83.8931	−	315.173i	−0.146410	−	0.550041i
$574$	−288.984			−0.503457
$575$			81.8085i			0.142276i
$576$	−29.9639	+	17.1680i	−0.0520207	+	0.0298056i
$577$	206.558			0.357987			0.178993	−	0.983850i	$-0.442716\pi$
$577$	206.558			0.357987			0.178993	+	0.983850i	$0.442716\pi$
$578$		−	409.633i		−	0.708707i
$579$	−367.790	+	97.8987i	−0.635216	+	0.169082i
$580$	677.534			1.16816
$581$		−	379.340i		−	0.652909i
$582$	−147.597	−	554.500i	−0.253604	−	0.952750i
$583$	−622.110			−1.06708
$584$			504.350i			0.863612i
$585$	142.283	+	248.331i	0.243219	+	0.424497i
$586$	−522.325			−0.891340
$587$			66.4275i			0.113164i	0.998398	+	0.0565822i	$0.0180203\pi$
$587$			66.4275i			0.113164i	−0.998398	+	0.0565822i	$0.981980\pi$
$588$	42.9194	−	11.4243i	0.0729922	−	0.0194291i
$589$	293.218			0.497823
$590$		−	1116.45i		−	1.89229i
$591$	−11.8708	−	44.5967i	−0.0200859	−	0.0754597i
$592$	1312.26			2.21666
$593$			127.083i			0.214305i	0.994243	+	0.107153i	$0.0341734\pi$
$593$			127.083i			0.214305i	−0.994243	+	0.107153i	$0.965827\pi$
$594$	444.570	−	440.189i	0.748434	−	0.741059i
$595$	190.563			0.320275
$596$		−	164.666i		−	0.276286i
$597$	575.527	−	153.194i	0.964032	−	0.256607i
$598$	−58.1524			−0.0972448
$599$		−	108.791i		−	0.181621i	−0.995868	−	0.0908106i	$-0.971054\pi$
$599$		−	108.791i		−	0.181621i	0.995868	−	0.0908106i	$-0.0289458\pi$
$600$	−61.3605	−	230.522i	−0.102267	−	0.384203i
$601$	−926.924			−1.54230			−0.771152	−	0.636652i	$-0.780319\pi$
$601$	−926.924			−1.54230			−0.771152	+	0.636652i	$0.780319\pi$
$602$		−	509.751i		−	0.846762i
$603$	668.068	−	382.774i	1.10791	−	0.634783i
$604$	−271.492			−0.449491
$605$			215.289i			0.355849i
$606$	65.2853	−	17.3777i	0.107731	−	0.0286761i
$607$	−18.9826			−0.0312728			−0.0156364	−	0.999878i	$-0.504977\pi$
$607$	−18.9826			−0.0312728			−0.0156364	+	0.999878i	$0.504977\pi$
$608$		−	195.569i		−	0.321659i
$609$	100.853	+	378.889i	0.165604	+	0.622150i
$610$	358.451			0.587625
$611$		−	10.3494i		−	0.0169384i
$612$	−105.095	−	183.426i	−0.171725	−	0.299716i
$613$	−486.235			−0.793206			−0.396603	−	0.917990i	$-0.629811\pi$
$613$	−486.235			−0.793206			−0.396603	+	0.917990i	$0.629811\pi$
$614$		−	1266.95i		−	2.06343i
$615$	830.446	−	221.049i	1.35032	−	0.359429i
$616$	115.565			0.187605
$617$			644.372i			1.04436i	0.852835	+	0.522181i	$0.174882\pi$
$617$			644.372i			1.04436i	−0.852835	+	0.522181i	$0.825118\pi$
$618$	−152.628	−	573.399i	−0.246971	−	0.927830i
$619$	822.044			1.32802			0.664010	−	0.747724i	$-0.268853\pi$
$619$	822.044			1.32802			0.664010	+	0.747724i	$0.268853\pi$
$620$			632.938i			1.02087i
$621$	91.1070	+	92.0137i	0.146710	+	0.148170i
$622$	−844.834			−1.35825
$623$			94.0111i			0.150901i
$624$	284.123	−	75.6282i	0.455326	−	0.121199i
$625$	−760.472			−1.21676
$626$			749.891i			1.19791i
$627$	−45.9455	−	172.610i	−0.0732783	−	0.275295i
$628$	−5.34769			−0.00851543
$629$		−	729.192i		−	1.15929i
$630$	−331.336	+	189.841i	−0.525930	+	0.301336i
$631$	−106.688			−0.169077			−0.0845387	−	0.996420i	$-0.526942\pi$
$631$	−106.688			−0.169077			−0.0845387	+	0.996420i	$0.526942\pi$
$632$			200.390i			0.317073i
$633$	−573.184	+	152.571i	−0.905505	+	0.241028i
$634$	−731.875			−1.15438
$635$		−	549.291i		−	0.865025i
$636$	−108.354	−	407.068i	−0.170368	−	0.640044i
$637$	34.3246			0.0538848
$638$		−	1144.61i		−	1.79406i
$639$	203.115	+	354.503i	0.317864	+	0.554778i
$640$	−859.955			−1.34368
$641$		−	1009.45i		−	1.57481i	−0.616435	−	0.787406i	$-0.711424\pi$
$641$		−	1009.45i		−	1.57481i	0.616435	−	0.787406i	$-0.288576\pi$
$642$	1006.20	−	267.831i	1.56729	−	0.417183i
$643$	286.431			0.445460			0.222730	−	0.974880i	$-0.428503\pi$
$643$	286.431			0.445460			0.222730	+	0.974880i	$0.428503\pi$
$644$		−	26.8356i		−	0.0416703i
$645$	389.917	+	1464.86i	0.604522	+	2.27109i
$646$	−174.508			−0.270136
$647$		−	445.032i		−	0.687840i	−0.938999	−	0.343920i	$-0.888245\pi$
$647$		−	445.032i		−	0.687840i	0.938999	−	0.343920i	$-0.111755\pi$
$648$	−325.738	−	190.943i	−0.502682	−	0.294665i
$649$	−652.338			−1.00514
$650$			206.842i			0.318218i
$651$	−353.950	+	94.2147i	−0.543702	+	0.144723i
$652$	−229.622			−0.352181
$653$			393.889i			0.603199i	0.953435	+	0.301600i	$0.0975206\pi$
$653$			393.889i			0.603199i	−0.953435	+	0.301600i	$0.902479\pi$
$654$	−10.4181	−	39.1392i	−0.0159298	−	0.0598459i
$655$	−309.178			−0.472028
$656$		−	882.820i		−	1.34576i
$657$	−844.907	+	484.096i	−1.28601	+	0.736828i
$658$	13.8087			0.0209858
$659$		−	418.827i		−	0.635549i	−0.948166	−	0.317774i	$-0.897065\pi$
$659$		−	418.827i		−	0.635549i	0.948166	−	0.317774i	$-0.102935\pi$
$660$	372.595	−	99.1776i	0.564537	−	0.150269i
$661$	702.800			1.06324			0.531619	−	0.846984i	$-0.321584\pi$
$661$	702.800			1.06324			0.531619	+	0.846984i	$0.321584\pi$
$662$			1157.92i			1.74913i
$663$	−42.0248	−	157.881i	−0.0633859	−	0.238131i
$664$	668.344			1.00654
$665$			109.026i			0.163948i
$666$	726.429	+	1267.86i	1.09073	+	1.90369i
$667$	236.903			0.355177
$668$			246.372i			0.368820i
$669$	507.673	−	135.133i	0.758854	−	0.201992i
$670$	1371.97			2.04772
$671$		−	209.442i		−	0.312134i
$672$	62.8389	+	236.076i	0.0935102	+	0.351303i
$673$	149.524			0.222175			0.111088	−	0.993811i	$-0.464567\pi$
$673$	149.524			0.222175			0.111088	+	0.993811i	$0.464567\pi$
$674$			1106.57i			1.64180i
$675$	327.283	−	324.058i	0.484864	−	0.480086i
$676$	306.573			0.453510
$677$			570.278i			0.842361i	0.906977	+	0.421180i	$0.138384\pi$
$677$			570.278i			0.842361i	−0.906977	+	0.421180i	$0.861616\pi$
$678$	−1336.05	+	355.630i	−1.97057	+	0.524528i
$679$	204.644			0.301390
$680$			335.746i			0.493744i
$681$	−103.694	−	389.563i	−0.152268	−	0.572045i
$682$	1069.27			1.56785
$683$			434.547i			0.636232i	0.948052	+	0.318116i	$0.103050\pi$
$683$			434.547i			0.636232i	−0.948052	+	0.318116i	$0.896950\pi$
$684$	104.942	−	60.1275i	0.153424	−	0.0879056i
$685$	655.184			0.956473
$686$			45.7977i			0.0667604i
$687$	−1033.88	+	275.199i	−1.50492	+	0.400581i
$688$	1557.24			2.26343
$689$		−	325.551i		−	0.472498i
$690$	59.3498	+	222.968i	0.0860142	+	0.323142i
$691$	−789.343			−1.14232			−0.571160	−	0.820839i	$-0.693506\pi$
$691$	−789.343			−1.14232			−0.571160	+	0.820839i	$0.693506\pi$
$692$			511.805i			0.739603i
$693$	110.924	+	193.599i	0.160063	+	0.279363i
$694$	−1102.54			−1.58867
$695$		−	65.9674i		−	0.0949171i
$696$	−667.549	+	177.689i	−0.959123	+	0.255300i
$697$	−490.562			−0.703819
$698$		−	604.669i		−	0.866287i
$699$	158.765	+	596.456i	0.227132	+	0.853299i
$700$	−95.4515			−0.136359
$701$		−	1045.78i		−	1.49184i	−0.666035	−	0.745921i	$-0.732010\pi$
$701$		−	1045.78i		−	1.49184i	0.666035	−	0.745921i	$-0.267990\pi$
$702$	230.352	+	232.644i	0.328136	+	0.331402i
$703$	417.187			0.593439
$704$			35.9547i			0.0510720i
$705$	−39.6815	+	10.5625i	−0.0562859	+	0.0149822i
$706$	−1142.63			−1.61845
$707$			24.0941i			0.0340794i
$708$	−113.619	−	426.847i	−0.160478	−	0.602892i
$709$	−16.3184			−0.0230161			−0.0115081	−	0.999934i	$-0.503663\pi$
$709$	−16.3184			−0.0230161			−0.0115081	+	0.999934i	$0.503663\pi$
$710$			728.022i			1.02538i
$711$	−335.702	+	192.343i	−0.472155	+	0.270524i
$712$	−165.634			−0.232633
$713$			221.310i			0.310392i
$714$	210.653	−	56.0717i	0.295032	−	0.0785318i
$715$	297.981			0.416756
$716$		−	186.539i		−	0.260529i
$717$	266.561	+	1001.43i	0.371773	+	1.39669i
$718$	313.293			0.436341
$719$			74.7121i			0.103911i	0.998649	+	0.0519555i	$0.0165454\pi$
$719$			74.7121i			0.103911i	−0.998649	+	0.0519555i	$0.983455\pi$
$720$	−579.947	−	1012.20i	−0.805482	−	1.40583i
$721$	211.618			0.293506
$722$			792.856i			1.09814i
$723$	870.276	−	231.651i	1.20370	−	0.320402i
$724$	−646.733			−0.893278
$725$		−	842.639i		−	1.16226i
$726$	63.3469	+	237.984i	0.0872546	+	0.327802i
$727$	−306.940			−0.422201			−0.211101	−	0.977464i	$-0.567705\pi$
$727$	−306.940			−0.422201			−0.211101	+	0.977464i	$0.567705\pi$
$728$			60.4751i			0.0830702i
$729$	7.21917	−	728.964i	0.00990285	−	0.999951i
$730$	−1735.14			−2.37690
$731$		−	865.322i		−	1.18375i
$732$	137.045	−	36.4788i	0.187220	−	0.0498345i
$733$	−766.418			−1.04559			−0.522795	−	0.852458i	$-0.675111\pi$
$733$	−766.418			−1.04559			−0.522795	+	0.852458i	$0.675111\pi$
$734$		−	188.259i		−	0.256483i
$735$	−35.0314	−	131.607i	−0.0476617	−	0.179058i
$736$	147.608			0.200554
$737$		−	801.638i		−	1.08770i
$738$	852.949	−	488.703i	1.15576	−	0.662200i
$739$	−1055.00			−1.42761			−0.713804	−	0.700346i	$-0.753029\pi$
$739$	−1055.00			−1.42761			−0.713804	+	0.700346i	$0.753029\pi$
$740$			900.538i			1.21694i
$741$	90.3270	−	24.0433i	0.121899	−	0.0324472i
$742$	434.367			0.585400
$743$			123.625i			0.166387i	0.996533	+	0.0831933i	$0.0265119\pi$
$743$			123.625i			0.166387i	−0.996533	+	0.0831933i	$0.973488\pi$
$744$	−165.993	−	623.610i	−0.223109	−	0.838185i
$745$	−504.930			−0.677758
$746$			153.202i			0.205364i
$747$	641.505	+	1119.64i	0.858775	+	1.49885i
$748$	−220.100			−0.294251
$749$			371.348i			0.495791i
$750$	−369.227	+	98.2813i	−0.492303	+	0.131042i
$751$	−644.742			−0.858512			−0.429256	−	0.903183i	$-0.641224\pi$
$751$	−644.742			−0.858512			−0.429256	+	0.903183i	$0.641224\pi$
$752$			42.1841i			0.0560959i
$753$	−42.5207	−	159.744i	−0.0564684	−	0.212143i
$754$	598.977			0.794399
$755$			832.500i			1.10265i
$756$	−107.359	+	106.301i	−0.142009	+	0.140609i
$757$	670.147			0.885267			0.442634	−	0.896703i	$-0.354044\pi$
$757$	670.147			0.885267			0.442634	+	0.896703i	$0.354044\pi$
$758$			736.169i			0.971199i
$759$	130.279	−	34.6779i	0.171646	−	0.0456889i
$760$	−192.088			−0.252747
$761$			1006.28i			1.32231i	0.750249	+	0.661155i	$0.229934\pi$
$761$			1006.28i			1.32231i	−0.750249	+	0.661155i	$0.770066\pi$
$762$	−161.624	−	607.197i	−0.212105	−	0.796846i
$763$	14.4447			0.0189315
$764$		−	229.928i		−	0.300953i
$765$	−562.456	+	322.263i	−0.735236	+	0.421259i
$766$	377.565			0.492905
$767$		−	341.369i		−	0.445071i
$768$	−906.116	+	241.191i	−1.17984	+	0.314050i
$769$	−596.916			−0.776224			−0.388112	−	0.921612i	$-0.626873\pi$
$769$	−596.916			−0.776224			−0.388112	+	0.921612i	$0.626873\pi$
$770$			397.582i			0.516340i
$771$	−51.3927	−	193.074i	−0.0666572	−	0.250420i
$772$	−268.313			−0.347556
$773$		−	961.508i		−	1.24387i	−0.783071	−	0.621933i	$-0.786348\pi$
$773$		−	961.508i		−	1.24387i	0.783071	−	0.621933i	$-0.213652\pi$
$774$	862.043	+	1504.55i	1.11375	+	1.94386i
$775$	787.174			1.01571
$776$			360.553i			0.464631i
$777$	−503.596	+	134.048i	−0.648129	+	0.172520i
$778$	−41.1371			−0.0528755
$779$		−	280.662i		−	0.360284i
$780$	51.8998	+	194.979i	0.0665382	+	0.249974i
$781$	425.381			0.544662
$782$		−	131.712i		−	0.168430i
$783$	−938.413	−	947.753i	−1.19848	−	1.21041i
$784$	−139.908			−0.178453
$785$			16.3981i			0.0208893i
$786$	−341.772	+	90.9731i	−0.434824	+	0.115742i
$787$	−469.049			−0.595997			−0.297998	−	0.954566i	$-0.596319\pi$
$787$	−469.049			−0.595997			−0.297998	+	0.954566i	$0.596319\pi$
$788$		−	32.5346i		−	0.0412875i
$789$	−81.7934	−	307.285i	−0.103667	−	0.389461i
$790$	−689.411			−0.872672
$791$		−	493.081i		−	0.623364i
$792$	−341.093	+	195.432i	−0.430674	+	0.246758i
$793$	109.601			0.138211
$794$			820.686i			1.03361i
$795$	−1248.23	+	332.254i	−1.57010	+	0.417930i
$796$	419.864			0.527467
$797$			517.984i			0.649917i	0.945728	+	0.324958i	$0.105350\pi$
$797$			517.984i			0.649917i	−0.945728	+	0.324958i	$0.894650\pi$
$798$	32.0799	+	120.519i	0.0402003	+	0.151026i
$799$	23.4407			0.0293376
$800$		−	525.026i		−	0.656282i
$801$	−158.983	−	277.478i	−0.198480	−	0.346414i
$802$	1169.89			1.45871
$803$			1013.83i			1.26256i
$804$	524.540	−	139.622i	0.652412	−	0.173660i
$805$	−82.2884			−0.102222
$806$			559.551i			0.694232i
$807$	−364.046	−	1367.66i	−0.451111	−	1.69475i
$808$	−42.4505			−0.0525378
$809$			589.209i			0.728318i	0.931337	+	0.364159i	$0.118644\pi$
$809$			589.209i			0.728318i	−0.931337	+	0.364159i	$0.881356\pi$
$810$	656.909	−	1120.65i	0.810999	−	1.38352i
$811$	−704.104			−0.868192			−0.434096	−	0.900867i	$-0.642932\pi$
$811$	−704.104			−0.868192			−0.434096	+	0.900867i	$0.642932\pi$
$812$			276.411i			0.340407i
$813$	−1094.23	+	291.263i	−1.34592	+	0.358257i
$814$	1521.35			1.86898
$815$			704.110i			0.863939i
$816$	171.294	+	643.524i	0.209919	+	0.788632i
$817$	495.070			0.605961
$818$		−	1024.67i		−	1.25265i
$819$	−101.310	+	58.0465i	−0.123700	+	0.0708749i
$820$	605.834			0.738822
$821$			776.407i			0.945684i	0.881147	+	0.472842i	$0.156772\pi$
$821$			776.407i			0.945684i	−0.881147	+	0.472842i	$0.843228\pi$
$822$	724.253	−	192.782i	0.881086	−	0.234528i
$823$	−1271.36			−1.54479			−0.772396	−	0.635141i	$-0.780942\pi$
$823$	−1271.36			−1.54479			−0.772396	+	0.635141i	$0.780942\pi$
$824$			372.841i			0.452478i
$825$	−123.346	−	463.390i	−0.149510	−	0.561685i
$826$	455.473			0.551420
$827$			602.754i			0.728845i	0.931234	+	0.364422i	$0.118734\pi$
$827$			602.754i			0.728845i	−0.931234	+	0.364422i	$0.881266\pi$
$828$	45.3819	+	79.2065i	0.0548091	+	0.0956600i
$829$	−372.049			−0.448792			−0.224396	−	0.974498i	$-0.572041\pi$
$829$	−372.049			−0.448792			−0.224396	+	0.974498i	$0.572041\pi$
$830$			2299.33i			2.77028i
$831$	194.835	−	51.8614i	0.234459	−	0.0624084i
$832$	−18.8152			−0.0226144
$833$			77.7433i			0.0933293i
$834$	−19.4104	−	72.9216i	−0.0232738	−	0.0874360i
$835$	755.470			0.904755
$836$		−	125.924i		−	0.150627i
$837$	885.370	−	876.645i	1.05779	−	1.04737i
$838$	−316.776			−0.378014
$839$			44.1144i			0.0525798i	0.999654	+	0.0262899i	$0.00836929\pi$
$839$			44.1144i			0.0525798i	−0.999654	+	0.0262899i	$0.991631\pi$
$840$	231.874	−	61.7204i	0.276040	−	0.0734766i
$841$	−1599.13			−1.90146
$842$		−	1800.37i		−	2.13821i
$843$	−276.693	−	1039.49i	−0.328224	−	1.23309i
$844$	−418.155			−0.495444
$845$		−	940.071i		−	1.11251i
$846$	−40.7568	+	23.3519i	−0.0481759	+	0.0276027i
$847$	−87.8303			−0.103696
$848$			1326.95i			1.56480i
$849$	643.245	−	171.220i	0.757650	−	0.201672i
$850$	−468.485			−0.551159
$851$			314.877i			0.370008i
$852$	74.0892	+	278.342i	0.0869592	+	0.326692i
$853$	−336.859			−0.394911			−0.197455	−	0.980312i	$-0.563268\pi$
$853$	−336.859			−0.394911			−0.197455	+	0.980312i	$0.563268\pi$
$854$			146.236i			0.171236i
$855$	−184.374	−	321.793i	−0.215642	−	0.376367i
$856$	−654.263			−0.764325
$857$		−	417.100i		−	0.486697i	−0.969939	−	0.243349i	$-0.921754\pi$
$857$		−	417.100i		−	0.486697i	0.969939	−	0.243349i	$-0.0782459\pi$
$858$	329.394	−	87.6784i	0.383909	−	0.102189i
$859$	814.724			0.948457			0.474228	−	0.880402i	$-0.342727\pi$
$859$	814.724			0.948457			0.474228	+	0.880402i	$0.342727\pi$
$860$			1068.65i			1.24262i
$861$	90.1803	+	338.793i	0.104739	+	0.393488i
$862$	−410.646			−0.476387
$863$		−	856.034i		−	0.991928i	−0.868343	−	0.495964i	$-0.834815\pi$
$863$		−	856.034i		−	0.991928i	0.868343	−	0.495964i	$-0.165185\pi$
$864$	−584.701	−	590.520i	−0.676737	−	0.683472i
$865$	1569.39			1.81433
$866$			1972.95i			2.27823i
$867$	−480.236	+	127.830i	−0.553905	+	0.147439i
$868$	−258.217			−0.297485
$869$			402.820i			0.463545i
$870$	−611.311	−	2296.60i	−0.702656	−	2.63977i
$871$	419.498			0.481628
$872$			25.4495i			0.0291852i
$873$	−604.014	+	346.074i	−0.691883	+	0.396419i
$874$	75.3554			0.0862189
$875$		−	136.267i		−	0.155734i
$876$	−663.387	+	176.581i	−0.757291	+	0.201576i
$877$	1605.37			1.83052			0.915261	−	0.402863i	$-0.131985\pi$
$877$	1605.37			1.83052			0.915261	+	0.402863i	$0.131985\pi$
$878$		−	633.030i		−	0.720991i
$879$	162.996	+	612.352i	0.185434	+	0.696646i
$880$	−1214.57			−1.38020
$881$			572.450i			0.649773i	0.945753	+	0.324887i	$0.105326\pi$
$881$			572.450i			0.649773i	−0.945753	+	0.324887i	$0.894674\pi$
$882$	−77.4487	−	135.174i	−0.0878103	−	0.153258i
$883$	71.3942			0.0808542			0.0404271	−	0.999182i	$-0.487128\pi$
$883$	71.3942			0.0808542			0.0404271	+	0.999182i	$0.487128\pi$
$884$		−	115.179i		−	0.130292i
$885$	−1308.88	+	348.399i	−1.47896	+	0.393671i
$886$	77.8751			0.0878951
$887$			857.904i			0.967197i	0.875290	+	0.483599i	$0.160671\pi$
$887$			857.904i			0.967197i	−0.875290	+	0.483599i	$0.839329\pi$
$888$	−236.173	−	887.266i	−0.265961	−	0.999174i
$889$	224.092			0.252072
$890$		−	569.839i		−	0.640269i
$891$	−654.791	−	383.830i	−0.734895	−	0.430786i
$892$	370.362			0.415205
$893$			13.4110i			0.0150179i
$894$	−558.159	+	148.571i	−0.624339	+	0.166187i
$895$	−572.000			−0.639106
$896$		−	350.832i		−	0.391554i
$897$	18.1470	+	68.1754i	0.0202308	+	0.0760038i
$898$	605.565			0.674349
$899$		−	2279.52i		−	2.53561i
$900$	281.729	−	161.419i	0.313032	−	0.179354i
$901$	737.355			0.818374
$902$		−	1023.48i		−	1.13468i
$903$	−597.611	+	159.073i	−0.661806	+	0.176160i
$904$	868.739			0.960994
$905$			1983.13i			2.19131i
$906$	244.956	+	920.262i	0.270371	+	1.01574i
$907$	−949.561			−1.04693			−0.523463	−	0.852049i	$-0.675360\pi$
$907$	−949.561			−1.04693			−0.523463	+	0.852049i	$0.675360\pi$
$908$		−	284.197i		−	0.312993i
$909$	−40.7458	−	71.1148i	−0.0448248	−	0.0782342i
$910$	−208.055			−0.228632
$911$			549.807i			0.603520i	0.953384	+	0.301760i	$0.0975742\pi$
$911$			549.807i			0.603520i	−0.953384	+	0.301760i	$0.902426\pi$
$912$	−368.174	+	98.0010i	−0.403700	+	0.107457i
$913$	1343.49			1.47151
$914$			1840.84i			2.01405i
$915$	−111.858	−	420.233i	−0.122249	−	0.459271i
$916$	−754.246			−0.823413
$917$		−	126.134i		−	0.137551i
$918$	−526.926	+	521.734i	−0.573994	+	0.568337i
$919$	1204.90			1.31110			0.655552	−	0.755150i	$-0.272436\pi$
$919$	1204.90			1.31110			0.655552	+	0.755150i	$0.272436\pi$
$920$		−	144.981i		−	0.157588i
$921$	−1485.31	+	395.362i	−1.61272	+	0.429275i
$922$	−71.8654			−0.0779451
$923$			222.602i			0.241173i
$924$	40.4610	+	152.006i	0.0437890	+	0.164508i
$925$	1119.98			1.21079
$926$		−	1418.77i		−	1.53215i
$927$	−624.599	+	357.869i	−0.673786	+	0.386051i
$928$	−1520.38			−1.63834
$929$			469.976i			0.505894i	0.967480	+	0.252947i	$0.0813999\pi$
$929$			469.976i			0.505894i	−0.967480	+	0.252947i	$0.918600\pi$
$930$	2145.43	−	571.073i	2.30692	−	0.614057i
$931$	−44.4787			−0.0477752
$932$			435.132i			0.466880i
$933$	263.638	+	990.448i	0.282571	+	1.06157i
$934$	−1244.64			−1.33259
$935$			674.910i			0.721829i
$936$	−102.270	−	178.495i	−0.109263	−	0.190700i
$937$	1484.30			1.58410			0.792051	−	0.610455i	$-0.209013\pi$
$937$	1484.30			1.58410			0.792051	+	0.610455i	$0.209013\pi$
$938$			559.716i			0.596713i
$939$	879.141	−	234.011i	0.936253	−	0.249213i
$940$	−28.9488			−0.0307966
$941$			69.0345i			0.0733629i	0.999327	+	0.0366814i	$0.0116787\pi$
$941$			69.0345i			0.0733629i	−0.999327	+	0.0366814i	$0.988321\pi$
$942$	4.82499	+	18.1267i	0.00512207	+	0.0192428i
$943$	211.833			0.224637
$944$			1391.43i			1.47397i
$945$	325.959	+	329.203i	0.344930	+	0.348363i
$946$	1805.36			1.90842
$947$		−	1885.38i		−	1.99090i	−0.0953097	−	0.995448i	$-0.530384\pi$
$947$		−	1885.38i		−	1.99090i	0.0953097	−	0.995448i	$-0.469616\pi$
$948$	−263.579	+	70.1598i	−0.278037	+	0.0740083i
$949$	−530.541			−0.559052
$950$		−	268.031i		−	0.282138i
$951$	228.389	+	858.020i	0.240156	+	0.902229i
$952$	−136.973			−0.143879
$953$		−	1106.21i		−	1.16076i	−0.814345	−	0.580381i	$-0.802904\pi$
$953$		−	1106.21i		−	1.16076i	0.814345	−	0.580381i	$-0.197096\pi$
$954$	−1282.05	+	734.561i	−1.34387	+	0.769980i
$955$	−705.048			−0.738270
$956$			730.572i			0.764197i
$957$	−1341.89	+	357.187i	−1.40219	+	0.373236i
$958$	931.648			0.972492
$959$			267.292i			0.278720i
$960$	19.2026	+	72.1411i	0.0200027	+	0.0751470i
$961$	1168.47			1.21589
$962$			796.124i			0.827572i
$963$	−627.989	−	1096.05i	−0.652117	−	1.13816i
$964$	634.892			0.658601
$965$			822.752i			0.852593i
$966$	−90.9632	+	24.2127i	−0.0941648	+	0.0250649i
$967$	74.2664			0.0768008			0.0384004	−	0.999262i	$-0.487774\pi$
$967$	74.2664			0.0768008			0.0384004	+	0.999262i	$0.487774\pi$
$968$		−	154.745i		−	0.159860i
$969$	54.4568	+	204.586i	0.0561990	+	0.211131i
$970$	−1240.43			−1.27879
$971$			386.354i			0.397893i	0.980010	+	0.198947i	$0.0637521\pi$
$971$			386.354i			0.397893i	−0.980010	+	0.198947i	$0.936248\pi$
$972$	137.107	−	495.305i	0.141057	−	0.509573i
$973$	26.9124			0.0276592
$974$		−	1431.01i		−	1.46921i
$975$	242.493	−	64.5469i	0.248710	−	0.0662020i
$976$	−446.736			−0.457722
$977$		−	1331.18i		−	1.36251i	−0.732045	−	0.681257i	$-0.761434\pi$
$977$		−	1331.18i		−	1.36251i	0.732045	−	0.681257i	$-0.238566\pi$
$978$	207.178	+	778.337i	0.211839	+	0.795846i
$979$	−332.955			−0.340097
$980$		−	96.0114i		−	0.0979708i
$981$	−42.6341	+	24.4275i	−0.0434599	+	0.0249006i
$982$	−1872.44			−1.90676
$983$			1373.69i			1.39745i	0.715393	+	0.698723i	$0.246248\pi$
$983$			1373.69i			1.39745i	−0.715393	+	0.698723i	$0.753752\pi$
$984$	−596.906	+	158.885i	−0.606612	+	0.161468i
$985$	−99.7636			−0.101283
$986$			1356.65i			1.37591i
$987$	−4.30912	−	16.1887i	−0.00436588	−	0.0164019i
$988$	65.8962			0.0666966
$989$			373.660i			0.377816i
$990$	−672.353	−	1173.48i	−0.679144	−	1.18533i
$991$	−1178.37			−1.18908			−0.594538	−	0.804067i	$-0.702665\pi$
$991$	−1178.37			−1.18908			−0.594538	+	0.804067i	$0.702665\pi$
$992$		−	1420.31i		−	1.43176i
$993$	1357.50	−	361.341i	1.36707	−	0.363888i
$994$	−297.008			−0.298801
$995$		−	1287.46i		−	1.29393i
$996$	233.998	+	879.094i	0.234938	+	0.882625i
$997$	1079.56			1.08281			0.541405	−	0.840762i	$-0.317892\pi$
$997$	1079.56			1.08281			0.541405	+	0.840762i	$0.317892\pi$
$998$		−	265.157i		−	0.265689i
$999$	1259.70	−	1247.28i	1.26096	−	1.24853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.20	✓	88
3.2	odd	2	inner	483.3.b.a.323.69	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.20	✓	88	1.1	even	1	trivial
483.3.b.a.323.69	yes	88	3.2	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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.47284i q^{2} +(-2.89906 + 0.771673i) q^{3} -2.11494 q^{4} +6.48523i q^{5} +(1.90823 + 7.16890i) q^{6} -2.64575 q^{7} -4.66144i q^{8} +(7.80904 - 4.47425i) q^{9} +O(q^{10})\)	\(q-2.47284i q^{2} +(-2.89906 + 0.771673i) q^{3} -2.11494 q^{4} +6.48523i q^{5} +(1.90823 + 7.16890i) q^{6} -2.64575 q^{7} -4.66144i q^{8} +(7.80904 - 4.47425i) q^{9} +16.0370 q^{10} -9.37034i q^{11} +(6.13134 - 1.63205i) q^{12} +4.90351 q^{13} +6.54252i q^{14} +(-5.00448 - 18.8011i) q^{15} -19.9868 q^{16} +11.1062i q^{17} +(-11.0641 - 19.3105i) q^{18} -6.35410 q^{19} -13.7159i q^{20} +(7.67018 - 2.04166i) q^{21} -23.1714 q^{22} -4.79583i q^{23} +(3.59711 + 13.5138i) q^{24} -17.0583 q^{25} -12.1256i q^{26} +(-19.1862 + 18.9971i) q^{27} +5.59562 q^{28} +49.3977i q^{29} +(-46.4920 + 12.3753i) q^{30} -46.1462 q^{31} +30.7784i q^{32} +(7.23084 + 27.1651i) q^{33} +27.4638 q^{34} -17.1583i q^{35} +(-16.5157 + 9.46279i) q^{36} -65.6564 q^{37} +15.7127i q^{38} +(-14.2156 + 3.78391i) q^{39} +30.2305 q^{40} +44.1702i q^{41} +(-5.04869 - 18.9671i) q^{42} -77.9135 q^{43} +19.8178i q^{44} +(29.0165 + 50.6435i) q^{45} -11.8593 q^{46} -2.11060i q^{47} +(57.9428 - 15.4233i) q^{48} +7.00000 q^{49} +42.1824i q^{50} +(-8.57035 - 32.1974i) q^{51} -10.3707 q^{52} -66.3914i q^{53} +(46.9769 + 47.4444i) q^{54} +60.7688 q^{55} +12.3330i q^{56} +(18.4209 - 4.90329i) q^{57} +122.153 q^{58} -69.6173i q^{59} +(10.5842 + 39.7632i) q^{60} +22.3516 q^{61} +114.112i q^{62} +(-20.6608 + 11.8377i) q^{63} -3.83708 q^{64} +31.8004i q^{65} +(67.1751 - 17.8807i) q^{66} +85.5505 q^{67} -23.4890i q^{68} +(3.70082 + 13.9034i) q^{69} -42.4298 q^{70} +45.3965i q^{71} +(-20.8564 - 36.4014i) q^{72} -108.196 q^{73} +162.358i q^{74} +(49.4528 - 13.1634i) q^{75} +13.4386 q^{76} +24.7916i q^{77} +(9.35701 + 35.1528i) q^{78} -42.9889 q^{79} -129.619i q^{80} +(40.9622 - 69.8791i) q^{81} +109.226 q^{82} +143.377i q^{83} +(-16.2220 + 4.31799i) q^{84} -72.0262 q^{85} +192.668i q^{86} +(-38.1189 - 143.207i) q^{87} -43.6793 q^{88} -35.5329i q^{89} +(125.233 - 71.7533i) q^{90} -12.9735 q^{91} +10.1429i q^{92} +(133.780 - 35.6098i) q^{93} -5.21918 q^{94} -41.2078i q^{95} +(-23.7509 - 89.2282i) q^{96} -77.3480 q^{97} -17.3099i q^{98} +(-41.9252 - 73.1734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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