LMFDB - Embedded newform 201.3.c.a.68.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.7
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.87376i q^{2} +(2.67705 - 1.35402i) q^{3} -4.25852 q^{4} +2.14706i q^{5} +(-3.89115 - 7.69322i) q^{6} +2.18513 q^{7} +0.742934i q^{8} +(5.33323 - 7.24959i) q^{9} +O(q^{10})$	\(q-2.87376i q^{2} +(2.67705 - 1.35402i) q^{3} -4.25852 q^{4} +2.14706i q^{5} +(-3.89115 - 7.69322i) q^{6} +2.18513 q^{7} +0.742934i q^{8} +(5.33323 - 7.24959i) q^{9} +6.17014 q^{10} -13.5238i q^{11} +(-11.4003 + 5.76615i) q^{12} -21.9908 q^{13} -6.27955i q^{14} +(2.90717 + 5.74779i) q^{15} -14.8991 q^{16} -16.0867i q^{17} +(-20.8336 - 15.3265i) q^{18} +32.4110 q^{19} -9.14329i q^{20} +(5.84971 - 2.95872i) q^{21} -38.8641 q^{22} +36.8270i q^{23} +(1.00595 + 1.98887i) q^{24} +20.3901 q^{25} +63.1964i q^{26} +(4.46122 - 26.6289i) q^{27} -9.30543 q^{28} +39.5658i q^{29} +(16.5178 - 8.35452i) q^{30} +37.7043 q^{31} +45.7882i q^{32} +(-18.3115 - 36.2038i) q^{33} -46.2294 q^{34} +4.69160i q^{35} +(-22.7117 + 30.8726i) q^{36} +26.3891 q^{37} -93.1417i q^{38} +(-58.8706 + 29.7761i) q^{39} -1.59512 q^{40} -24.8350i q^{41} +(-8.50267 - 16.8107i) q^{42} -24.4652 q^{43} +57.5912i q^{44} +(15.5653 + 11.4508i) q^{45} +105.832 q^{46} +60.4985i q^{47} +(-39.8856 + 20.1737i) q^{48} -44.2252 q^{49} -58.5965i q^{50} +(-21.7818 - 43.0650i) q^{51} +93.6484 q^{52} +34.4176i q^{53} +(-76.5251 - 12.8205i) q^{54} +29.0363 q^{55} +1.62341i q^{56} +(86.7661 - 43.8854i) q^{57} +113.703 q^{58} -14.1702i q^{59} +(-12.3802 - 24.4771i) q^{60} -28.5548 q^{61} -108.353i q^{62} +(11.6538 - 15.8413i) q^{63} +71.9881 q^{64} -47.2155i q^{65} +(-104.041 + 52.6229i) q^{66} -8.18535 q^{67} +68.5056i q^{68} +(49.8646 + 98.5878i) q^{69} +13.4826 q^{70} -56.0792i q^{71} +(5.38597 + 3.96224i) q^{72} +131.403 q^{73} -75.8361i q^{74} +(54.5855 - 27.6088i) q^{75} -138.023 q^{76} -29.5512i q^{77} +(85.5695 + 169.180i) q^{78} +48.9266 q^{79} -31.9892i q^{80} +(-24.1133 - 77.3276i) q^{81} -71.3698 q^{82} +128.899i q^{83} +(-24.9111 + 12.5998i) q^{84} +34.5391 q^{85} +70.3073i q^{86} +(53.5731 + 105.920i) q^{87} +10.0473 q^{88} +57.8911i q^{89} +(32.9068 - 44.7310i) q^{90} -48.0528 q^{91} -156.828i q^{92} +(100.936 - 51.0525i) q^{93} +173.858 q^{94} +69.5883i q^{95} +(61.9983 + 122.577i) q^{96} -80.5042 q^{97} +127.093i q^{98} +(-98.0417 - 72.1253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.87376i		−	1.43688i	−0.695588	−	0.718441i	$-0.744856\pi$
$2$		−	2.87376i		−	1.43688i	0.695588	−	0.718441i	$-0.255144\pi$
$3$	2.67705	−	1.35402i	0.892351	−	0.451342i
$3$	2.67705	−	1.35402i	0.892351	−	0.451342i
$4$	−4.25852			−1.06463
$5$			2.14706i			0.429411i	0.976679	+	0.214706i	$0.0688792\pi$
$5$			2.14706i			0.429411i	−0.976679	+	0.214706i	$0.931121\pi$
$6$	−3.89115	−	7.69322i	−0.648525	−	1.28220i
$7$	2.18513			0.312161			0.156081	−	0.987744i	$-0.450114\pi$
$7$	2.18513			0.312161			0.156081	+	0.987744i	$0.450114\pi$
$8$			0.742934i			0.0928668i
$9$	5.33323	−	7.24959i	0.592581	−	0.805511i
$10$	6.17014			0.617014
$11$		−	13.5238i		−	1.22943i	−0.788749	−	0.614716i	$-0.789271\pi$
$11$		−	13.5238i		−	1.22943i	0.788749	−	0.614716i	$-0.210729\pi$
$12$	−11.4003	+	5.76615i	−0.950025	+	0.480512i
$13$	−21.9908			−1.69160			−0.845800	−	0.533500i	$-0.820877\pi$
$13$	−21.9908			−1.69160			−0.845800	+	0.533500i	$0.820877\pi$
$14$		−	6.27955i		−	0.448539i
$15$	2.90717	+	5.74779i	0.193811	+	0.383186i
$16$	−14.8991			−0.931192
$17$		−	16.0867i		−	0.946277i	−0.880988	−	0.473139i	$-0.843121\pi$
$17$		−	16.0867i		−	0.946277i	0.880988	−	0.473139i	$-0.156879\pi$
$18$	−20.8336	−	15.3265i	−1.15742	−	0.851470i
$19$	32.4110			1.70584			0.852922	−	0.522038i	$-0.174828\pi$
$19$	32.4110			1.70584			0.852922	+	0.522038i	$0.174828\pi$
$20$		−	9.14329i		−	0.457165i
$21$	5.84971	−	2.95872i	0.278558	−	0.140891i
$22$	−38.8641			−1.76655
$23$			36.8270i			1.60117i	0.599217	+	0.800586i	$0.295478\pi$
$23$			36.8270i			1.60117i	−0.599217	+	0.800586i	$0.704522\pi$
$24$	1.00595	+	1.98887i	0.0419146	+	0.0828698i
$25$	20.3901			0.815606
$26$			63.1964i			2.43063i
$27$	4.46122	−	26.6289i	0.165230	−	0.986255i
$28$	−9.30543			−0.332337
$29$			39.5658i			1.36434i	0.731194	+	0.682169i	$0.238963\pi$
$29$			39.5658i			1.36434i	−0.731194	+	0.682169i	$0.761037\pi$
$30$	16.5178	−	8.35452i	0.550593	−	0.278484i
$31$	37.7043			1.21627			0.608133	−	0.793835i	$-0.291919\pi$
$31$	37.7043			1.21627			0.608133	+	0.793835i	$0.291919\pi$
$32$			45.7882i			1.43088i
$33$	−18.3115	−	36.2038i	−0.554894	−	1.09709i
$34$	−46.2294			−1.35969
$35$			4.69160i			0.134046i
$36$	−22.7117	+	30.8726i	−0.630880	+	0.857571i
$37$	26.3891			0.713219			0.356610	−	0.934254i	$-0.383933\pi$
$37$	26.3891			0.713219			0.356610	+	0.934254i	$0.383933\pi$
$38$		−	93.1417i		−	2.45110i
$39$	−58.8706	+	29.7761i	−1.50950	+	0.763490i
$40$	−1.59512			−0.0398780
$41$		−	24.8350i		−	0.605731i	−0.953033	−	0.302865i	$-0.902057\pi$
$41$		−	24.8350i		−	0.605731i	0.953033	−	0.302865i	$-0.0979433\pi$
$42$	−8.50267	−	16.8107i	−0.202444	−	0.400255i
$43$	−24.4652			−0.568959			−0.284479	−	0.958682i	$-0.591821\pi$
$43$	−24.4652			−0.568959			−0.284479	+	0.958682i	$0.591821\pi$
$44$			57.5912i			1.30889i
$45$	15.5653	+	11.4508i	0.345895	+	0.254461i
$46$	105.832			2.30070
$47$			60.4985i			1.28720i	0.765361	+	0.643601i	$0.222560\pi$
$47$			60.4985i			1.28720i	−0.765361	+	0.643601i	$0.777440\pi$
$48$	−39.8856	+	20.1737i	−0.830950	+	0.420286i
$49$	−44.2252			−0.902555
$50$		−	58.5965i		−	1.17193i
$51$	−21.7818	−	43.0650i	−0.427094	−	0.844412i
$52$	93.6484			1.80093
$53$			34.4176i			0.649389i	0.945819	+	0.324694i	$0.105261\pi$
$53$			34.4176i			0.649389i	−0.945819	+	0.324694i	$0.894739\pi$
$54$	−76.5251	−	12.8205i	−1.41713	−	0.237417i
$55$	29.0363			0.527932
$56$			1.62341i			0.0289894i
$57$	86.7661	−	43.8854i	1.52221	−	0.769919i
$58$	113.703			1.96039
$59$		−	14.1702i		−	0.240174i	−0.992763	−	0.120087i	$-0.961683\pi$
$59$		−	14.1702i		−	0.240174i	0.992763	−	0.120087i	$-0.0383173\pi$
$60$	−12.3802	−	24.4771i	−0.206337	−	0.407951i
$61$	−28.5548			−0.468111			−0.234056	−	0.972223i	$-0.575200\pi$
$61$	−28.5548			−0.468111			−0.234056	+	0.972223i	$0.575200\pi$
$62$		−	108.353i		−	1.74763i
$63$	11.6538	−	15.8413i	0.184981	−	0.251449i
$64$	71.9881			1.12481
$65$		−	47.2155i		−	0.726392i
$66$	−104.041	+	52.6229i	−1.57638	+	0.797317i
$67$	−8.18535			−0.122169
$67$	−8.18535			−0.122169
$68$			68.5056i			1.00744i
$69$	49.8646	+	98.5878i	0.722676	+	1.42881i
$70$	13.4826			0.192608
$71$		−	56.0792i		−	0.789848i	−0.918714	−	0.394924i	$-0.870771\pi$
$71$		−	56.0792i		−	0.789848i	0.918714	−	0.394924i	$-0.129229\pi$
$72$	5.38597	+	3.96224i	0.0748051	+	0.0550311i
$73$	131.403			1.80004			0.900021	−	0.435847i	$-0.143551\pi$
$73$	131.403			1.80004			0.900021	+	0.435847i	$0.143551\pi$
$74$		−	75.8361i		−	1.02481i
$75$	54.5855	−	27.6088i	0.727807	−	0.368117i
$76$	−138.023			−1.81609
$77$		−	29.5512i		−	0.383781i
$78$	85.5695	+	169.180i	1.09704	+	2.16898i
$79$	48.9266			0.619325			0.309662	−	0.950847i	$-0.399784\pi$
$79$	48.9266			0.619325			0.309662	+	0.950847i	$0.399784\pi$
$80$		−	31.9892i		−	0.399864i
$81$	−24.1133	−	77.3276i	−0.297694	−	0.954661i
$82$	−71.3698			−0.870364
$83$			128.899i			1.55300i	0.630115	+	0.776502i	$0.283008\pi$
$83$			128.899i			1.55300i	−0.630115	+	0.776502i	$0.716992\pi$
$84$	−24.9111	+	12.5998i	−0.296561	+	0.149997i
$85$	34.5391			0.406342
$86$			70.3073i			0.817527i
$87$	53.5731	+	105.920i	0.615783	+	1.21747i
$88$	10.0473			0.114173
$89$			57.8911i			0.650462i	0.945635	+	0.325231i	$0.105442\pi$
$89$			57.8911i			0.650462i	−0.945635	+	0.325231i	$0.894558\pi$
$90$	32.9068	−	44.7310i	0.365631	−	0.497011i
$91$	−48.0528			−0.528053
$92$		−	156.828i		−	1.70466i
$93$	100.936	−	51.0525i	1.08534	−	0.548952i
$94$	173.858			1.84956
$95$			69.5883i			0.732509i
$96$	61.9983	+	122.577i	0.645816	+	1.27685i
$97$	−80.5042			−0.829940			−0.414970	−	0.909835i	$-0.636208\pi$
$97$	−80.5042			−0.829940			−0.414970	+	0.909835i	$0.636208\pi$
$98$			127.093i			1.29687i
$99$	−98.0417	−	72.1253i	−0.990320	−	0.728539i
$100$	−86.8319			−0.868319
$101$		−	138.343i		−	1.36974i	−0.728667	−	0.684868i	$-0.759860\pi$
$101$		−	138.343i		−	1.36974i	0.728667	−	0.684868i	$-0.240140\pi$
$102$	−123.759	+	62.5958i	−1.21332	+	0.613684i
$103$	9.11240			0.0884699			0.0442350	−	0.999021i	$-0.485915\pi$
$103$	9.11240			0.0884699			0.0442350	+	0.999021i	$0.485915\pi$
$104$		−	16.3377i		−	0.157093i
$105$	6.35254	+	12.5597i	0.0605004	+	0.119616i
$106$	98.9081			0.933095
$107$		−	68.1725i		−	0.637126i	−0.947902	−	0.318563i	$-0.896800\pi$
$107$		−	68.1725i		−	0.637126i	0.947902	−	0.318563i	$-0.103200\pi$
$108$	−18.9982	+	113.400i	−0.175909	+	1.05000i
$109$	−124.482			−1.14204			−0.571020	−	0.820936i	$-0.693452\pi$
$109$	−124.482			−1.14204			−0.571020	+	0.820936i	$0.693452\pi$
$110$		−	83.4434i		−	0.758576i
$111$	70.6451	−	35.7315i	0.636442	−	0.321905i
$112$	−32.5564			−0.290682
$113$			38.2699i			0.338672i	0.985558	+	0.169336i	$0.0541623\pi$
$113$			38.2699i			0.338672i	−0.985558	+	0.169336i	$0.945838\pi$
$114$	−126.116	−	249.345i	−1.10628	−	2.18724i
$115$	−79.0696			−0.687562
$116$		−	168.492i		−	1.45252i
$117$	−117.282	+	159.424i	−1.00241	+	1.36260i
$118$	−40.7219			−0.345101
$119$		−	35.1516i		−	0.295391i
$120$	−4.27023	+	2.15983i	−0.0355852	+	0.0179986i
$121$	−61.8919			−0.511503
$122$			82.0597i			0.672621i
$123$	−33.6272	−	66.4845i	−0.273392	−	0.540525i
$124$	−160.564			−1.29487
$125$			97.4552i			0.779642i
$126$	−45.5242	−	33.4903i	−0.361303	−	0.265796i
$127$	79.0158			0.622172			0.311086	−	0.950382i	$-0.399307\pi$
$127$	79.0158			0.622172			0.311086	+	0.950382i	$0.399307\pi$
$128$		−	23.7242i		−	0.185346i
$129$	−65.4947	+	33.1265i	−0.507711	+	0.256795i
$130$	−135.686			−1.04374
$131$		−	56.8033i		−	0.433613i	−0.976215	−	0.216806i	$-0.930436\pi$
$131$		−	56.8033i		−	0.433613i	0.976215	−	0.216806i	$-0.0695640\pi$
$132$	77.9799	+	154.175i	0.590757	+	1.16799i
$133$	70.8224			0.532499
$134$			23.5228i			0.175543i
$135$	57.1737	+	9.57849i	0.423509	+	0.0709518i
$136$	11.9514			0.0878777
$137$			78.8204i			0.575332i	0.957731	+	0.287666i	$0.0928792\pi$
$137$			78.8204i			0.575332i	−0.957731	+	0.287666i	$0.907121\pi$
$138$	283.318	−	143.299i	2.05303	−	1.03840i
$139$	−114.744			−0.825494			−0.412747	−	0.910846i	$-0.635431\pi$
$139$	−114.744			−0.825494			−0.412747	+	0.910846i	$0.635431\pi$
$140$		−	19.9793i		−	0.142709i
$141$	81.9165	+	161.958i	0.580968	+	1.14864i
$142$	−161.158			−1.13492
$143$			297.398i			2.07971i
$144$	−79.4602	+	108.012i	−0.551807	+	0.750085i
$145$	−84.9501			−0.585863
$146$		−	377.621i		−	2.58645i
$147$	−118.393	+	59.8820i	−0.805396	+	0.407361i
$148$	−112.379			−0.759315
$149$		−	116.914i		−	0.784656i	−0.919825	−	0.392328i	$-0.871670\pi$
$149$		−	116.914i		−	0.784656i	0.919825	−	0.392328i	$-0.128330\pi$
$150$	−79.3411	−	156.866i	−0.528941	−	1.04577i
$151$	−223.975			−1.48328			−0.741638	−	0.670800i	$-0.765951\pi$
$151$	−223.975			−1.48328			−0.741638	+	0.670800i	$0.765951\pi$
$152$			24.0793i			0.158416i
$153$	−116.622	−	85.7942i	−0.762236	−	0.560746i
$154$	−84.9231			−0.551449
$155$			80.9532i			0.522279i
$156$	250.702	−	126.802i	1.60706	−	0.812835i
$157$	−132.933			−0.846706			−0.423353	−	0.905965i	$-0.639147\pi$
$157$	−132.933			−0.846706			−0.423353	+	0.905965i	$0.639147\pi$
$158$		−	140.604i		−	0.889896i
$159$	46.6023	+	92.1378i	0.293096	+	0.579483i
$160$	−98.3098			−0.614436
$161$			80.4717i			0.499824i
$162$	−222.221	+	69.2958i	−1.37174	+	0.427752i
$163$	225.234			1.38180			0.690901	−	0.722949i	$-0.257214\pi$
$163$	225.234			1.38180			0.690901	+	0.722949i	$0.257214\pi$
$164$			105.760i			0.644880i
$165$	77.7316	−	39.3158i	0.471101	−	0.238278i
$166$	370.426			2.23148
$167$		−	10.0886i		−	0.0604107i	−0.999544	−	0.0302054i	$-0.990384\pi$
$167$		−	10.0886i		−	0.0604107i	0.999544	−	0.0302054i	$-0.00961612\pi$
$168$	2.19813	+	4.34595i	0.0130841	+	0.0258687i
$169$	314.596			1.86151
$170$		−	99.2572i		−	0.583866i
$171$	172.856	−	234.967i	1.01085	−	1.37408i
$172$	104.186			0.605731
$173$			27.4154i			0.158471i	0.996856	+	0.0792353i	$0.0252478\pi$
$173$			27.4154i			0.158471i	−0.996856	+	0.0792353i	$0.974752\pi$
$174$	304.389	−	153.957i	1.74936	−	0.884808i
$175$	44.5551			0.254601
$176$			201.491i			1.14484i
$177$	−19.1869	−	37.9345i	−0.108400	−	0.214319i
$178$	166.365			0.934637
$179$			171.762i			0.959563i	0.877388	+	0.479781i	$0.159284\pi$
$179$			171.762i			0.959563i	−0.877388	+	0.479781i	$0.840716\pi$
$180$	−66.2851	−	48.7633i	−0.368251	−	0.270907i
$181$	94.5772			0.522526			0.261263	−	0.965268i	$-0.415861\pi$
$181$	94.5772			0.522526			0.261263	+	0.965268i	$0.415861\pi$
$182$			138.092i			0.758749i
$183$	−76.4427	+	38.6639i	−0.417720	+	0.211278i
$184$	−27.3600			−0.148696
$185$			56.6589i			0.306264i
$186$	−146.713	−	290.067i	−0.788779	−	1.55950i
$187$	−217.553			−1.16338
$188$		−	257.634i		−	1.37039i
$189$	9.74835	−	58.1876i	0.0515785	−	0.307871i
$190$	199.981			1.05253
$191$		−	199.566i		−	1.04485i	−0.852686	−	0.522424i	$-0.825028\pi$
$191$		−	199.566i		−	1.04485i	0.852686	−	0.522424i	$-0.174972\pi$
$192$	192.716	−	97.4737i	1.00373	−	0.507676i
$193$	150.597			0.780297			0.390149	−	0.920752i	$-0.372424\pi$
$193$	150.597			0.780297			0.390149	+	0.920752i	$0.372424\pi$
$194$			231.350i			1.19253i
$195$	−63.9310	−	126.398i	−0.327851	−	0.648197i
$196$	188.334			0.960888
$197$		−	92.8384i		−	0.471261i	−0.971843	−	0.235630i	$-0.924285\pi$
$197$		−	92.8384i		−	0.471261i	0.971843	−	0.235630i	$-0.0757155\pi$
$198$	−207.271	+	281.749i	−1.04682	+	1.42297i
$199$	−150.615			−0.756859			−0.378430	−	0.925630i	$-0.623536\pi$
$199$	−150.615			−0.756859			−0.378430	+	0.925630i	$0.623536\pi$
$200$			15.1485i			0.0757427i
$201$	−21.9126	+	11.0832i	−0.109018	+	0.0551402i
$202$	−397.566			−1.96815
$203$			86.4565i			0.425894i
$204$	92.7584	+	183.393i	0.454698	+	0.898987i
$205$	53.3221			0.260108
$206$		−	26.1869i		−	0.127121i
$207$	266.981	+	196.407i	1.28976	+	0.948825i
$208$	327.643			1.57521
$209$		−	438.319i		−	2.09722i
$210$	36.0935	−	18.2557i	0.171874	−	0.0869320i
$211$	−322.065			−1.52638			−0.763188	−	0.646177i	$-0.776367\pi$
$211$	−322.065			−1.52638			−0.763188	+	0.646177i	$0.776367\pi$
$212$		−	146.568i		−	0.691359i
$213$	−75.9327	−	150.127i	−0.356491	−	0.704822i
$214$	−195.912			−0.915475
$215$		−	52.5282i		−	0.244317i
$216$	19.7835	+	3.31439i	0.0915903	+	0.0153444i
$217$	82.3887			0.379672
$218$			357.733i			1.64098i
$219$	351.773	−	177.923i	1.60627	−	0.812434i
$220$	−123.652			−0.562053
$221$			353.760i			1.60072i
$222$	−102.684	−	203.017i	−0.462540	−	0.914492i
$223$	−266.477			−1.19497			−0.597483	−	0.801882i	$-0.703832\pi$
$223$	−266.477			−1.19497			−0.597483	+	0.801882i	$0.703832\pi$
$224$			100.053i			0.446666i
$225$	108.745	−	147.820i	0.483313	−	0.656979i
$226$	109.979			0.486632
$227$			166.535i			0.733635i	0.930293	+	0.366817i	$0.119553\pi$
$227$			166.535i			0.733635i	−0.930293	+	0.366817i	$0.880447\pi$
$228$	−369.495	+	186.887i	−1.62059	+	0.819679i
$229$	−371.784			−1.62351			−0.811756	−	0.583996i	$-0.801488\pi$
$229$	−371.784			−1.62351			−0.811756	+	0.583996i	$0.801488\pi$
$230$			227.227i			0.987945i
$231$	−40.0130	−	79.1100i	−0.173216	−	0.342468i
$232$	−29.3948			−0.126702
$233$			262.767i			1.12776i	0.825858	+	0.563879i	$0.190691\pi$
$233$			262.767i			1.12776i	−0.825858	+	0.563879i	$0.809309\pi$
$234$	458.148	+	337.041i	1.95790	+	1.44035i
$235$	−129.894			−0.552739
$236$			60.3443i			0.255696i
$237$	130.979	−	66.2479i	0.552655	−	0.279527i
$238$	−101.017			−0.424443
$239$		−	323.796i		−	1.35480i	−0.735617	−	0.677398i	$-0.763108\pi$
$239$		−	323.796i		−	1.35480i	0.735617	−	0.677398i	$-0.236892\pi$
$240$	−43.3141	−	85.6367i	−0.180475	−	0.356820i
$241$	162.287			0.673388			0.336694	−	0.941614i	$-0.390691\pi$
$241$	162.287			0.673388			0.336694	+	0.941614i	$0.390691\pi$
$242$			177.863i			0.734970i
$243$	−169.256	−	174.360i	−0.696526	−	0.717531i
$244$	121.601			0.498365
$245$		−	94.9540i		−	0.387567i
$246$	−191.061	+	96.6365i	−0.776670	+	0.392831i
$247$	−712.745			−2.88561
$248$			28.0118i			0.112951i
$249$	174.533	+	345.071i	0.700936	+	1.38583i
$250$	280.063			1.12025
$251$			72.1779i			0.287561i	0.989610	+	0.143781i	$0.0459260\pi$
$251$			72.1779i			0.287561i	−0.989610	+	0.143781i	$0.954074\pi$
$252$	−49.6280	+	67.4606i	−0.196937	+	0.267701i
$253$	498.039			1.96853
$254$		−	227.073i		−	0.893987i
$255$	92.4630	−	46.7668i	0.362600	−	0.183399i
$256$	219.775			0.858495
$257$			267.300i			1.04008i	0.854143	+	0.520039i	$0.174083\pi$
$257$			267.300i			1.04008i	−0.854143	+	0.520039i	$0.825917\pi$
$258$	95.1978	+	188.216i	0.368984	+	0.729521i
$259$	57.6636			0.222640
$260$			201.068i			0.773340i
$261$	286.836	+	211.014i	1.09899	+	0.808482i
$262$	−163.239			−0.623050
$263$		−	342.930i		−	1.30392i	−0.758255	−	0.651958i	$-0.773948\pi$
$263$		−	342.930i		−	1.30392i	0.758255	−	0.651958i	$-0.226052\pi$
$264$	26.8970	−	13.6042i	0.101883	−	0.0515312i
$265$	−73.8965			−0.278855
$266$		−	203.527i		−	0.765138i
$267$	78.3860	+	154.978i	0.293581	+	0.580440i
$268$	34.8575			0.130065
$269$			84.6490i			0.314680i	0.987544	+	0.157340i	$0.0502919\pi$
$269$			84.6490i			0.314680i	−0.987544	+	0.157340i	$0.949708\pi$
$270$	27.5263	−	164.304i	0.101949	−	0.608533i
$271$	−282.343			−1.04185			−0.520927	−	0.853601i	$-0.674414\pi$
$271$	−282.343			−1.04185			−0.520927	+	0.853601i	$0.674414\pi$
$272$			239.677i			0.881166i
$273$	−128.640	+	65.0647i	−0.471208	+	0.238332i
$274$	226.511			0.826684
$275$		−	275.751i		−	1.00273i
$276$	−212.350	−	419.838i	−0.769383	−	1.52115i
$277$	247.725			0.894313			0.447156	−	0.894456i	$-0.352437\pi$
$277$	247.725			0.894313			0.447156	+	0.894456i	$0.352437\pi$
$278$			329.746i			1.18614i
$279$	201.086	−	273.341i	0.720737	−	0.979716i
$280$	−3.48555			−0.0124484
$281$		−	102.850i		−	0.366015i	−0.983111	−	0.183008i	$-0.941417\pi$
$281$		−	102.850i		−	0.366015i	0.983111	−	0.183008i	$-0.0585833\pi$
$282$	465.428	−	235.409i	1.65046	−	0.834782i
$283$	261.619			0.924448			0.462224	−	0.886763i	$-0.347052\pi$
$283$	261.619			0.924448			0.462224	+	0.886763i	$0.347052\pi$
$284$			238.815i			0.840897i
$285$	94.2244	+	186.292i	0.330612	+	0.653655i
$286$	854.652			2.98830
$287$		−	54.2676i		−	0.189086i
$288$	331.946	+	244.199i	1.15259	+	0.847913i
$289$	30.2176			0.104559
$290$			244.127i			0.841816i
$291$	−215.514	+	109.005i	−0.740598	+	0.374587i
$292$	−559.583			−1.91638
$293$			284.822i			0.972090i	0.873934	+	0.486045i	$0.161561\pi$
$293$			284.822i			0.972090i	−0.873934	+	0.486045i	$0.838439\pi$
$294$	172.087	+	340.234i	0.585329	+	1.15726i
$295$	30.4243			0.103133
$296$			19.6054i			0.0662343i
$297$	−360.122	−	60.3324i	−1.21253	−	0.203139i
$298$	−335.983			−1.12746
$299$		−	809.855i		−	2.70854i
$300$	−232.454	+	117.573i	−0.774846	+	0.391909i
$301$	−53.4597			−0.177607
$302$			643.651i			2.13129i
$303$	−187.320	−	370.353i	−0.618219	−	1.22229i
$304$	−482.895			−1.58847
$305$		−	61.3087i		−	0.201012i
$306$	−246.552	+	335.145i	−0.805727	+	1.09524i
$307$	−284.618			−0.927094			−0.463547	−	0.886072i	$-0.653423\pi$
$307$	−284.618			−0.927094			−0.463547	+	0.886072i	$0.653423\pi$
$308$			125.844i			0.408585i
$309$	24.3944	−	12.3384i	0.0789463	−	0.0399302i
$310$	232.640			0.750453
$311$			9.75878i			0.0313787i	0.999877	+	0.0156894i	$0.00499428\pi$
$311$			9.75878i			0.0313787i	−0.999877	+	0.0156894i	$0.995006\pi$
$312$	−22.1217	−	43.7369i	−0.0709028	−	0.140183i
$313$	89.5265			0.286027			0.143014	−	0.989721i	$-0.454321\pi$
$313$	89.5265			0.286027			0.143014	+	0.989721i	$0.454321\pi$
$314$			382.018i			1.21662i
$315$	34.0122	+	25.0214i	0.107975	+	0.0794330i
$316$	−208.355			−0.659352
$317$		−	87.8530i		−	0.277139i	−0.990353	−	0.138569i	$-0.955750\pi$
$317$		−	87.8530i		−	0.277139i	0.990353	−	0.138569i	$-0.0442504\pi$
$318$	264.782	−	133.924i	0.832649	−	0.421145i
$319$	535.078			1.67736
$320$			154.563i			0.483008i
$321$	−92.3073	−	182.501i	−0.287562	−	0.568540i
$322$	231.257			0.718189
$323$		−	521.387i		−	1.61420i
$324$	102.687	+	329.301i	0.316935	+	1.01636i
$325$	−448.396			−1.37968
$326$		−	647.269i		−	1.98549i
$327$	−333.246	+	168.552i	−1.01910	+	0.515450i
$328$	18.4507			0.0562522
$329$			132.197i			0.401815i
$330$	−112.984	−	223.382i	−0.342377	−	0.676916i
$331$	−96.8713			−0.292662			−0.146331	−	0.989236i	$-0.546747\pi$
$331$	−96.8713			−0.292662			−0.146331	+	0.989236i	$0.546747\pi$
$332$		−	548.921i		−	1.65338i
$333$	140.739	−	191.310i	0.422640	−	0.574506i
$334$	−28.9922			−0.0868031
$335$		−	17.5744i		−	0.0524609i
$336$	−87.1553	+	44.0822i	−0.259391	+	0.131197i
$337$	−252.981			−0.750686			−0.375343	−	0.926886i	$-0.622475\pi$
$337$	−252.981			−0.750686			−0.375343	+	0.926886i	$0.622475\pi$
$338$		−	904.074i		−	2.67477i
$339$	51.8184	+	102.451i	0.152857	+	0.302214i
$340$	−147.086			−0.432604
$341$		−	509.903i		−	1.49532i
$342$	−675.240	−	496.746i	−1.97438	−	1.45247i
$343$	−203.709			−0.593904
$344$		−	18.1760i		−	0.0528373i
$345$	−211.674	+	107.062i	−0.613546	+	0.310325i
$346$	78.7854			0.227703
$347$		−	434.830i		−	1.25311i	−0.779376	−	0.626556i	$-0.784464\pi$
$347$		−	434.830i		−	1.25311i	0.779376	−	0.626556i	$-0.215536\pi$
$348$	−228.142	−	451.062i	−0.655581	−	1.29616i
$349$	−280.563			−0.803906			−0.401953	−	0.915660i	$-0.631669\pi$
$349$	−280.563			−0.803906			−0.401953	+	0.915660i	$0.631669\pi$
$350$		−	128.041i		−	0.365831i
$351$	−98.1058	+	585.591i	−0.279504	+	1.66835i
$352$	619.228			1.75917
$353$			348.733i			0.987912i	0.869487	+	0.493956i	$0.164450\pi$
$353$			348.733i			0.987912i	−0.869487	+	0.493956i	$0.835550\pi$
$354$	−109.015	+	55.1385i	−0.307952	+	0.155759i
$355$	120.405			0.339170
$356$		−	246.531i		−	0.692502i
$357$	−47.5961	−	94.1026i	−0.133322	−	0.263593i
$358$	493.603			1.37878
$359$			303.003i			0.844020i	0.906591	+	0.422010i	$0.138675\pi$
$359$			303.003i			0.844020i	−0.906591	+	0.422010i	$0.861325\pi$
$360$	−8.50715	+	11.5640i	−0.0236310	+	0.0321222i
$361$	689.476			1.90990
$362$		−	271.793i		−	0.750808i
$363$	−165.688	+	83.8031i	−0.456440	+	0.230863i
$364$	204.634			0.562181
$365$			282.130i			0.772958i
$366$	111.111	+	219.678i	0.303582	+	0.600214i
$367$	−440.327			−1.19980			−0.599900	−	0.800075i	$-0.704793\pi$
$367$	−440.327			−1.19980			−0.599900	+	0.800075i	$0.704793\pi$
$368$		−	548.688i		−	1.49100i
$369$	−180.043	−	132.451i	−0.487923	−	0.358945i
$370$	162.824			0.440066
$371$			75.2070i			0.202714i
$372$	−429.840	+	217.408i	−1.15548	+	0.584431i
$373$	199.584			0.535078			0.267539	−	0.963547i	$-0.413790\pi$
$373$	199.584			0.535078			0.267539	+	0.963547i	$0.413790\pi$
$374$			625.195i			1.67165i
$375$	131.957	+	260.893i	0.351885	+	0.695714i
$376$	−44.9464			−0.119538
$377$		−	870.084i		−	2.30792i
$378$	−167.217	−	28.0144i	−0.442374	−	0.0741123i
$379$	−69.2868			−0.182815			−0.0914074	−	0.995814i	$-0.529137\pi$
$379$	−69.2868			−0.182815			−0.0914074	+	0.995814i	$0.529137\pi$
$380$		−	296.344i		−	0.779851i
$381$	211.530	−	106.989i	0.555196	−	0.280812i
$382$	−573.506			−1.50132
$383$		−	395.231i		−	1.03193i	−0.856608	−	0.515967i	$-0.827433\pi$
$383$		−	395.231i		−	1.03193i	0.856608	−	0.515967i	$-0.172567\pi$
$384$	−32.1232	−	63.5111i	−0.0836542	−	0.165393i
$385$	63.4480			0.164800
$386$		−	432.781i		−	1.12120i
$387$	−130.479	+	177.363i	−0.337154	+	0.458302i
$388$	342.829			0.883580
$389$			189.284i			0.486590i	0.969952	+	0.243295i	$0.0782284\pi$
$389$			189.284i			0.486590i	−0.969952	+	0.243295i	$0.921772\pi$
$390$	−363.239	+	183.723i	−0.931383	+	0.471084i
$391$	592.425			1.51515
$392$		−	32.8564i		−	0.0838174i
$393$	−76.9130	−	152.065i	−0.195707	−	0.386935i
$394$	−266.796			−0.677146
$395$			105.048i			0.265945i
$396$	417.513	+	307.147i	1.05433	+	0.775625i
$397$	340.940			0.858791			0.429396	−	0.903117i	$-0.358727\pi$
$397$	340.940			0.858791			0.429396	+	0.903117i	$0.358727\pi$
$398$			432.832i			1.08752i
$399$	189.595	−	95.8952i	0.475176	−	0.240339i
$400$	−303.794			−0.759486
$401$			552.372i			1.37749i	0.725005	+	0.688744i	$0.241837\pi$
$401$			552.372i			1.37749i	−0.725005	+	0.688744i	$0.758163\pi$
$402$	31.8504	+	62.9717i	0.0792299	+	0.156646i
$403$	−829.147			−2.05744
$404$			589.139i			1.45826i
$405$	166.027	−	51.7725i	0.409942	−	0.127833i
$406$	248.456			0.611960
$407$		−	356.880i		−	0.876854i
$408$	31.9945	−	16.1825i	0.0784178	−	0.0396629i
$409$	−378.772			−0.926092			−0.463046	−	0.886334i	$-0.653243\pi$
$409$	−378.772			−0.926092			−0.463046	+	0.886334i	$0.653243\pi$
$410$		−	153.235i		−	0.373744i
$411$	106.725	+	211.007i	0.259671	+	0.513398i
$412$	−38.8054			−0.0941878
$413$		−	30.9638i		−	0.0749730i
$414$	564.427	−	767.239i	1.36335	−	1.85324i
$415$	−276.754			−0.666878
$416$		−	1006.92i		−	2.42048i
$417$	−307.175	+	155.366i	−0.736630	+	0.372580i
$418$	−1259.63			−3.01346
$419$			116.959i			0.279139i	0.990212	+	0.139569i	$0.0445718\pi$
$419$			116.959i			0.279139i	−0.990212	+	0.139569i	$0.955428\pi$
$420$	−27.0524	−	53.4856i	−0.0644106	−	0.127347i
$421$	588.105			1.39692			0.698462	−	0.715647i	$-0.253868\pi$
$421$	588.105			1.39692			0.698462	+	0.715647i	$0.253868\pi$
$422$			925.539i			2.19322i
$423$	438.590	+	322.653i	1.03685	+	0.762772i
$424$	−25.5700			−0.0603066
$425$		−	328.011i		−	0.771789i
$426$	−431.430	+	218.213i	−1.01275	+	0.512236i
$427$	−62.3959			−0.146126
$428$			290.314i			0.678304i
$429$	402.685	+	796.151i	0.938659	+	1.85583i
$430$	−150.954			−0.351055
$431$			15.4696i			0.0358923i	0.999839	+	0.0179462i	$0.00571275\pi$
$431$			15.4696i			0.0358923i	−0.999839	+	0.0179462i	$0.994287\pi$
$432$	−66.4680	+	396.746i	−0.153861	+	0.918393i
$433$	553.172			1.27753			0.638767	−	0.769401i	$-0.279445\pi$
$433$	553.172			1.27753			0.638767	+	0.769401i	$0.279445\pi$
$434$		−	236.766i		−	0.545543i
$435$	−227.416	+	115.025i	−0.522795	+	0.264424i
$436$	530.111			1.21585
$437$			1193.60i			2.73135i
$438$	−511.309	−	1010.91i	−1.16737	−	2.30802i
$439$	350.332			0.798022			0.399011	−	0.916946i	$-0.369353\pi$
$439$	350.332			0.798022			0.399011	+	0.916946i	$0.369353\pi$
$440$			21.5720i			0.0490273i
$441$	−235.863	+	320.615i	−0.534837	+	0.727018i
$442$	1016.62			2.30005
$443$			819.132i			1.84906i	0.381113	+	0.924529i	$0.375541\pi$
$443$			819.132i			1.84906i	−0.381113	+	0.924529i	$0.624459\pi$
$444$	−300.844	+	152.163i	−0.677576	+	0.342710i
$445$	−124.295			−0.279316
$446$			765.793i			1.71702i
$447$	−158.304	−	312.984i	−0.354148	−	0.700189i
$448$	157.303			0.351124
$449$		−	491.998i		−	1.09576i	−0.836556	−	0.547882i	$-0.815434\pi$
$449$		−	491.998i		−	1.09576i	0.836556	−	0.547882i	$-0.184566\pi$
$450$	−424.801	−	312.509i	−0.944002	−	0.694464i
$451$	−335.862			−0.744705
$452$		−	162.973i		−	0.360561i
$453$	−599.593	+	303.267i	−1.32360	+	0.669465i
$454$	478.583			1.05415
$455$		−	103.172i		−	0.226752i
$456$	32.6039	+	64.4615i	0.0714998	+	0.141363i
$457$	447.475			0.979158			0.489579	−	0.871959i	$-0.337151\pi$
$457$	447.475			0.979158			0.489579	+	0.871959i	$0.337151\pi$
$458$			1068.42i			2.33280i
$459$	−428.371	−	71.7664i	−0.933271	−	0.156354i
$460$	336.720			0.731999
$461$		−	86.1733i		−	0.186927i	−0.995623	−	0.0934635i	$-0.970206\pi$
$461$		−	86.1733i		−	0.186927i	0.995623	−	0.0934635i	$-0.0297938\pi$
$462$	−227.344	+	114.988i	−0.492086	+	0.248892i
$463$	−39.0841			−0.0844149			−0.0422074	−	0.999109i	$-0.513439\pi$
$463$	−39.0841			−0.0844149			−0.0422074	+	0.999109i	$0.513439\pi$
$464$		−	589.494i		−	1.27046i
$465$	109.613	+	216.716i	0.235726	+	0.466056i
$466$	755.132			1.62045
$467$			226.641i			0.485312i	0.970112	+	0.242656i	$0.0780187\pi$
$467$			226.641i			0.485312i	−0.970112	+	0.242656i	$0.921981\pi$
$468$	499.448	−	678.913i	1.06720	−	1.45067i
$469$	−17.8861			−0.0381366
$470$			373.284i			0.794221i
$471$	−355.868	+	179.994i	−0.755559	+	0.382154i
$472$	10.5276			0.0223041
$473$			330.862i			0.699496i
$474$	−190.381	−	376.403i	−0.401647	−	0.794100i
$475$	660.866			1.39130
$476$			149.694i			0.314483i
$477$	249.514	+	183.557i	0.523089	+	0.384816i
$478$	−930.514			−1.94668
$479$			394.098i			0.822751i	0.911466	+	0.411376i	$0.134952\pi$
$479$			394.098i			0.822751i	−0.911466	+	0.411376i	$0.865048\pi$
$480$	−263.181	+	133.114i	−0.548293	+	0.277321i
$481$	−580.318			−1.20648
$482$		−	466.373i		−	0.967579i
$483$	108.961	+	215.427i	0.225592	+	0.446019i
$484$	263.568			0.544562
$485$		−	172.847i		−	0.356386i
$486$	−501.070	+	486.402i	−1.03101	+	1.00083i
$487$	−656.977			−1.34903			−0.674514	−	0.738262i	$-0.735647\pi$
$487$	−656.977			−1.34903			−0.674514	+	0.738262i	$0.735647\pi$
$488$		−	21.2143i		−	0.0434720i
$489$	602.963	−	304.972i	1.23305	−	0.623665i
$490$	−272.876			−0.556889
$491$			125.514i			0.255628i	0.991798	+	0.127814i	$0.0407961\pi$
$491$			125.514i			0.255628i	−0.991798	+	0.127814i	$0.959204\pi$
$492$	143.202	+	283.126i	0.291061	+	0.575459i
$493$	636.484			1.29104
$494$			2048.26i			4.14628i
$495$	154.857	−	210.501i	0.312843	−	0.425255i
$496$	−561.759			−1.13258
$497$		−	122.540i		−	0.246560i
$498$	991.651	−	501.567i	1.99127	−	1.00716i
$499$	−46.5613			−0.0933092			−0.0466546	−	0.998911i	$-0.514856\pi$
$499$	−46.5613			−0.0933092			−0.0466546	+	0.998911i	$0.514856\pi$
$500$		−	415.015i		−	0.830031i
$501$	−13.6602	−	27.0077i	−0.0272659	−	0.0539076i
$502$	207.422			0.413192
$503$		−	372.085i		−	0.739732i	−0.929085	−	0.369866i	$-0.879404\pi$
$503$		−	372.085i		−	0.739732i	0.929085	−	0.369866i	$-0.120596\pi$
$504$	11.7690	+	8.65801i	0.0233513	+	0.0171786i
$505$	297.031			0.588181
$506$		−	1431.25i		−	2.82855i
$507$	842.189	−	425.970i	1.66112	−	0.840178i
$508$	−336.491			−0.662383
$509$		−	361.954i		−	0.711108i	−0.934656	−	0.355554i	$-0.884292\pi$
$509$		−	361.954i		−	0.711108i	0.934656	−	0.355554i	$-0.115708\pi$
$510$	−134.397	−	265.717i	−0.263523	−	0.521014i
$511$	287.133			0.561904
$512$		−	726.477i		−	1.41890i
$513$	144.593	−	863.070i	0.281857	−	1.68240i
$514$	768.157			1.49447
$515$			19.5648i			0.0379900i
$516$	278.911	−	141.070i	0.540525	−	0.273392i
$517$	818.167			1.58253
$518$		−	165.712i		−	0.319907i
$519$	37.1211	+	73.3925i	0.0715243	+	0.141411i
$520$	35.0780			0.0674577
$521$		−	288.202i		−	0.553171i	−0.960989	−	0.276585i	$-0.910797\pi$
$521$		−	288.202i		−	0.553171i	0.960989	−	0.276585i	$-0.0892029\pi$
$522$	606.404	−	824.300i	1.16169	−	1.57912i
$523$	−101.280			−0.193652			−0.0968258	−	0.995301i	$-0.530869\pi$
$523$	−101.280			−0.193652			−0.0968258	+	0.995301i	$0.530869\pi$
$524$			241.898i			0.461637i
$525$	119.276	−	60.3288i	0.227193	−	0.114912i
$526$	−985.499			−1.87357
$527$		−	606.538i		−	1.15093i
$528$	272.824	+	539.403i	0.516713	+	1.02160i
$529$	−827.226			−1.56375
$530$			212.361i			0.400682i
$531$	−102.729	−	75.5732i	−0.193462	−	0.142322i
$532$	−301.599			−0.566915
$533$			546.141i			1.02465i
$534$	445.369	−	225.263i	0.834025	−	0.421841i
$535$	146.370			0.273589
$536$		−	6.08118i		−	0.0113455i
$537$	232.570	+	459.815i	0.433091	+	0.856267i
$538$	243.261			0.452159
$539$			598.091i			1.10963i
$540$	−243.476	−	40.7902i	−0.450881	−	0.0755374i
$541$	−340.372			−0.629153			−0.314577	−	0.949232i	$-0.601863\pi$
$541$	−340.372			−0.629153			−0.314577	+	0.949232i	$0.601863\pi$
$542$			811.386i			1.49702i
$543$	253.188	−	128.060i	0.466277	−	0.235838i
$544$	736.581			1.35401
$545$		−	267.271i		−	0.490405i
$546$	186.981	+	369.681i	0.342455	+	0.677071i
$547$	227.309			0.415556			0.207778	−	0.978176i	$-0.433377\pi$
$547$	227.309			0.415556			0.207778	+	0.978176i	$0.433377\pi$
$548$		−	335.659i		−	0.612516i
$549$	−152.289	+	207.011i	−0.277394	+	0.377068i
$550$	−792.444			−1.44081
$551$			1282.37i			2.32735i
$552$	−73.2442	+	37.0461i	−0.132689	+	0.0671126i
$553$	106.911			0.193329
$554$		−	711.902i		−	1.28502i
$555$	76.7176	+	151.679i	0.138230	+	0.273295i
$556$	488.638			0.878846
$557$		−	570.562i		−	1.02435i	−0.858881	−	0.512174i	$-0.828840\pi$
$557$		−	570.562i		−	1.02435i	0.858881	−	0.512174i	$-0.171160\pi$
$558$	−785.517	−	577.873i	−1.40774	−	1.03561i
$559$	538.010			0.962451
$560$		−	69.9005i		−	0.124822i
$561$	−582.400	+	294.572i	−1.03815	+	0.525084i
$562$	−295.568			−0.525921
$563$			621.349i			1.10364i	0.833963	+	0.551820i	$0.186066\pi$
$563$			621.349i			1.10364i	−0.833963	+	0.551820i	$0.813934\pi$
$564$	−348.843	−	689.701i	−0.618516	−	1.22287i
$565$	−82.1677			−0.145430
$566$		−	751.831i		−	1.32832i
$567$	−52.6906	−	168.971i	−0.0929287	−	0.298008i
$568$	41.6632			0.0733506
$569$			431.250i			0.757909i	0.925415	+	0.378954i	$0.123716\pi$
$569$			431.250i			0.757909i	−0.925415	+	0.378954i	$0.876284\pi$
$570$	535.359	−	270.779i	0.939226	−	0.475050i
$571$	−532.033			−0.931756			−0.465878	−	0.884849i	$-0.654262\pi$
$571$	−532.033			−0.931756			−0.465878	+	0.884849i	$0.654262\pi$
$572$		−	1266.48i		−	2.21412i
$573$	−270.217	−	534.249i	−0.471584	−	0.932372i
$574$	−155.952			−0.271694
$575$			750.907i			1.30593i
$576$	383.929	−	521.885i	0.666544	−	0.906050i
$577$	−1007.23			−1.74563			−0.872817	−	0.488048i	$-0.837709\pi$
$577$	−1007.23			−1.74563			−0.872817	+	0.488048i	$0.837709\pi$
$578$		−	86.8382i		−	0.150239i
$579$	403.157	−	203.913i	0.696299	−	0.352181i
$580$	361.762			0.623727
$581$			281.662i			0.484788i
$582$	313.254	+	619.337i	0.538237	+	1.06415i
$583$	465.455			0.798379
$584$			97.6238i			0.167164i
$585$	−342.293	−	251.811i	−0.585117	−	0.430447i
$586$	818.512			1.39678
$587$			471.583i			0.803378i	0.915776	+	0.401689i	$0.131577\pi$
$587$			471.583i			0.803378i	−0.915776	+	0.401689i	$0.868423\pi$
$588$	504.180	−	255.009i	0.857450	−	0.433689i
$589$	1222.03			2.07476
$590$		−	87.4323i		−	0.148190i
$591$	−125.706	−	248.533i	−0.212700	−	0.420530i
$592$	−393.173			−0.664144
$593$			777.627i			1.31134i	0.755046	+	0.655672i	$0.227614\pi$
$593$			777.627i			1.31134i	−0.755046	+	0.655672i	$0.772386\pi$
$594$	−173.381	+	1034.91i	−0.291887	+	1.74227i
$595$	75.4724			0.126844
$596$			497.880i			0.835369i
$597$	−403.204	+	203.936i	−0.675384	+	0.341602i
$598$	−2327.33			−3.89186
$599$		−	53.5934i		−	0.0894714i	−0.998999	−	0.0447357i	$-0.985755\pi$
$599$		−	53.5934i		−	0.0894714i	0.998999	−	0.0447357i	$-0.0142446\pi$
$600$	20.5115	+	40.5534i	0.0341858	+	0.0675891i
$601$	137.456			0.228713			0.114356	−	0.993440i	$-0.463519\pi$
$601$	137.456			0.228713			0.114356	+	0.993440i	$0.463519\pi$
$602$			153.631i			0.255200i
$603$	−43.6544	+	59.3405i	−0.0723953	+	0.0984088i
$604$	953.802			1.57914
$605$		−	132.885i		−	0.219645i
$606$	−1064.31	+	538.315i	−1.75628	+	0.888308i
$607$	720.863			1.18758			0.593792	−	0.804619i	$-0.297630\pi$
$607$	720.863			1.18758			0.593792	+	0.804619i	$0.297630\pi$
$608$			1484.04i			2.44086i
$609$	117.064	+	231.449i	0.192224	+	0.380047i
$610$	−176.187			−0.288831
$611$		−	1330.41i		−	2.17743i
$612$	496.638	+	365.357i	0.811500	+	0.596988i
$613$	−196.934			−0.321262			−0.160631	−	0.987015i	$-0.551353\pi$
$613$	−196.934			−0.321262			−0.160631	+	0.987015i	$0.551353\pi$
$614$			817.924i			1.33212i
$615$	142.746	−	72.1994i	0.232107	−	0.117397i
$616$	21.9546			0.0356405
$617$		−	1099.11i		−	1.78137i	−0.454617	−	0.890687i	$-0.650224\pi$
$617$		−	1099.11i		−	1.78137i	0.454617	−	0.890687i	$-0.349776\pi$
$618$	−35.4577	−	70.1037i	−0.0573750	−	0.113436i
$619$	−410.506			−0.663176			−0.331588	−	0.943424i	$-0.607584\pi$
$619$	−410.506			−0.663176			−0.331588	+	0.943424i	$0.607584\pi$
$620$		−	344.741i		−	0.556034i
$621$	980.661	+	164.293i	1.57916	+	0.264562i
$622$	28.0444			0.0450875
$623$			126.500i			0.203049i
$624$	877.117	−	443.636i	1.40564	−	0.710956i
$625$	300.512			0.480819
$626$		−	257.278i		−	0.410987i
$627$	−593.495	−	1173.40i	−0.946563	−	1.87146i
$628$	566.098			0.901429
$629$		−	424.514i		−	0.674903i
$630$	71.9056	−	97.7430i	0.114136	−	0.155148i
$631$	448.778			0.711217			0.355609	−	0.934635i	$-0.384274\pi$
$631$	448.778			0.711217			0.355609	+	0.934635i	$0.384274\pi$
$632$			36.3493i			0.0575147i
$633$	−862.186	+	436.084i	−1.36206	+	0.688917i
$634$	−252.469			−0.398216
$635$			169.651i			0.267168i
$636$	−198.457	−	392.371i	−0.312039	−	0.616935i
$637$	972.548			1.52676
$638$		−	1537.69i		−	2.41017i
$639$	−406.552	−	299.084i	−0.636231	−	0.468049i
$640$	50.9373			0.0795895
$641$		−	3.30370i		−	0.00515398i	−0.999997	−	0.00257699i	$-0.999180\pi$
$641$		−	3.30370i		−	0.00515398i	0.999997	−	0.00257699i	$-0.000820282\pi$
$642$	−524.466	+	265.269i	−0.816925	+	0.413192i
$643$	−1241.25			−1.93040			−0.965202	−	0.261505i	$-0.915781\pi$
$643$	−1241.25			−1.93040			−0.965202	+	0.261505i	$0.915781\pi$
$644$		−	342.691i		−	0.532128i
$645$	−71.1245	−	140.621i	−0.110271	−	0.218017i
$646$	−1498.34			−2.31942
$647$			597.478i			0.923459i	0.887021	+	0.461730i	$0.152771\pi$
$647$			597.478i			0.923459i	−0.887021	+	0.461730i	$0.847229\pi$
$648$	57.4493	−	17.9146i	0.0886563	−	0.0276459i
$649$	−191.635			−0.295277
$650$			1288.58i			1.98244i
$651$	220.559	−	111.556i	0.338800	−	0.171362i
$652$	−959.163			−1.47111
$653$		−	1037.88i		−	1.58940i	−0.607005	−	0.794698i	$-0.707629\pi$
$653$		−	1037.88i		−	1.58940i	0.607005	−	0.794698i	$-0.292371\pi$
$654$	484.379	+	957.670i	0.740641	+	1.46433i
$655$	121.960			0.186198
$656$			370.018i			0.564052i
$657$	700.803	−	952.619i	1.06667	−	1.44995i
$658$	379.903			0.577361
$659$		−	579.574i		−	0.879475i	−0.898126	−	0.439737i	$-0.855071\pi$
$659$		−	579.574i		−	0.879475i	0.898126	−	0.439737i	$-0.144929\pi$
$660$	−331.022	+	167.427i	−0.501548	+	0.253678i
$661$	247.574			0.374545			0.187272	−	0.982308i	$-0.440035\pi$
$661$	247.574			0.374545			0.187272	+	0.982308i	$0.440035\pi$
$662$			278.385i			0.420521i
$663$	479.000	+	947.034i	0.722473	+	1.42841i
$664$	−95.7637			−0.144222
$665$			152.060i			0.228661i
$666$	−549.781	−	404.451i	−0.825497	−	0.607285i
$667$	−1457.09			−2.18454
$668$			42.9625i			0.0643151i
$669$	−713.374	+	360.817i	−1.06633	+	0.539338i
$670$	−50.5047			−0.0753802
$671$			386.168i			0.575511i
$672$	135.474	+	267.848i	0.201599	+	0.398583i
$673$	897.147			1.33306			0.666528	−	0.745480i	$-0.267780\pi$
$673$	897.147			1.33306			0.666528	+	0.745480i	$0.267780\pi$
$674$			727.009i			1.07865i
$675$	90.9649	−	542.967i	0.134763	−	0.804395i
$676$	−1339.71			−1.98182
$677$			828.009i			1.22306i	0.791223	+	0.611528i	$0.209445\pi$
$677$			828.009i			1.22306i	−0.791223	+	0.611528i	$0.790555\pi$
$678$	294.419	−	148.914i	0.434246	−	0.219637i
$679$	−175.912			−0.259075
$680$			25.6603i			0.0377357i
$681$	225.493	+	445.823i	0.331120	+	0.654660i
$682$	−1465.34			−2.14859
$683$		−	630.381i		−	0.922959i	−0.887151	−	0.461479i	$-0.847319\pi$
$683$		−	630.381i		−	0.922959i	0.887151	−	0.461479i	$-0.152681\pi$
$684$	−736.110	+	1000.61i	−1.07618	+	1.46288i
$685$	−169.232			−0.247054
$686$			585.412i			0.853371i
$687$	−995.287	+	503.405i	−1.44874	+	0.732759i
$688$	364.509			0.529810
$689$		−	756.871i		−	1.09851i
$690$	307.672	+	608.300i	0.445901	+	0.881594i
$691$	79.8080			0.115496			0.0577482	−	0.998331i	$-0.481608\pi$
$691$	79.8080			0.115496			0.0577482	+	0.998331i	$0.481608\pi$
$692$		−	116.749i		−	0.168713i
$693$	−214.234	−	157.603i	−0.309140	−	0.227422i
$694$	−1249.60			−1.80058
$695$		−	246.361i		−	0.354476i
$696$	−78.6915	+	39.8013i	−0.113062	+	0.0571858i
$697$	−399.513			−0.573189
$698$			806.273i			1.15512i
$699$	355.794	+	703.443i	0.509004	+	1.00636i
$700$	−189.739			−0.271056
$701$			89.2716i			0.127349i	0.997971	+	0.0636744i	$0.0202819\pi$
$701$			89.2716i			0.127349i	−0.997971	+	0.0636744i	$0.979718\pi$
$702$	1682.85	+	281.933i	2.39722	+	0.401614i
$703$	855.298			1.21664
$704$		−	973.549i		−	1.38288i
$705$	−347.732	+	175.879i	−0.493237	+	0.249474i
$706$	1002.18			1.41951
$707$		−	302.298i		−	0.427579i
$708$	81.7077	+	161.545i	0.115406	+	0.228171i
$709$	−122.915			−0.173364			−0.0866821	−	0.996236i	$-0.527626\pi$
$709$	−122.915			−0.173364			−0.0866821	+	0.996236i	$0.527626\pi$
$710$		−	346.016i		−	0.487347i
$711$	260.937	−	354.698i	0.367000	−	0.498872i
$712$	−43.0093			−0.0604063
$713$			1388.53i			1.94745i
$714$	−270.429	+	136.780i	−0.378752	+	0.191569i
$715$	−638.531			−0.893050
$716$		−	731.451i		−	1.02158i
$717$	−438.428	−	866.820i	−0.611476	−	1.20895i
$718$	870.760			1.21276
$719$		−	893.522i		−	1.24273i	−0.783522	−	0.621365i	$-0.786579\pi$
$719$		−	893.522i		−	1.24273i	0.783522	−	0.621365i	$-0.213421\pi$
$720$	−231.908	−	170.606i	−0.322095	−	0.236952i
$721$	19.9118			0.0276169
$722$		−	1981.39i		−	2.74431i
$723$	434.450	−	219.740i	0.600899	−	0.303928i
$724$	−402.759			−0.556297
$725$			806.753i			1.11276i
$726$	240.830	+	476.148i	0.331722	+	0.655851i
$727$	−211.125			−0.290405			−0.145203	−	0.989402i	$-0.546383\pi$
$727$	−211.125			−0.290405			−0.145203	+	0.989402i	$0.546383\pi$
$728$		−	35.7000i		−	0.0490385i
$729$	−689.195	−	237.595i	−0.945398	−	0.325918i
$730$	810.774			1.11065
$731$			393.565i			0.538393i
$732$	325.533	−	164.651i	0.444717	−	0.224933i
$733$	−970.103			−1.32347			−0.661735	−	0.749738i	$-0.730180\pi$
$733$	−970.103			−1.32347			−0.661735	+	0.749738i	$0.730180\pi$
$734$			1265.39i			1.72397i
$735$	−128.570	−	254.197i	−0.174925	−	0.345846i
$736$	−1686.24			−2.29109
$737$			110.697i			0.150199i
$738$	−380.632	+	517.402i	−0.515761	+	0.701087i
$739$	817.308			1.10596			0.552982	−	0.833193i	$-0.313490\pi$
$739$	817.308			1.10596			0.552982	+	0.833193i	$0.313490\pi$
$740$		−	241.283i		−	0.326058i
$741$	−1908.06	+	965.074i	−2.57498	+	1.30239i
$742$	216.127			0.291276
$743$		−	1131.34i		−	1.52267i	−0.648362	−	0.761333i	$-0.724546\pi$
$743$		−	1131.34i		−	1.52267i	0.648362	−	0.761333i	$-0.275454\pi$
$744$	37.9286	+	74.9890i	0.0509794	+	0.100792i
$745$	251.020			0.336940
$746$		−	573.558i		−	0.768844i
$747$	934.468	+	687.450i	1.25096	+	0.920282i
$748$	926.453			1.23857
$749$		−	148.966i		−	0.198886i
$750$	749.745	−	379.213i	0.999660	−	0.505617i
$751$	694.066			0.924189			0.462095	−	0.886831i	$-0.347098\pi$
$751$	694.066			0.924189			0.462095	+	0.886831i	$0.347098\pi$
$752$		−	901.372i		−	1.19863i
$753$	97.7307	+	193.224i	0.129788	+	0.256606i
$754$	−2500.42			−3.31620
$755$		−	480.887i		−	0.636936i
$756$	−41.5136	+	247.793i	−0.0549121	+	0.327769i
$757$	294.161			0.388588			0.194294	−	0.980943i	$-0.437758\pi$
$757$	294.161			0.388588			0.194294	+	0.980943i	$0.437758\pi$
$758$			199.114i			0.262683i
$759$	1333.28	−	674.357i	1.75662	−	0.888481i
$760$	−51.6995			−0.0680257
$761$		−	154.178i		−	0.202599i	−0.994856	−	0.101299i	$-0.967700\pi$
$761$		−	154.178i		−	0.202599i	0.994856	−	0.101299i	$-0.0323000\pi$
$762$	−307.462	−	607.886i	−0.403494	−	0.797751i
$763$	−272.010			−0.356501
$764$			849.856i			1.11238i
$765$	184.205	−	250.394i	0.240791	−	0.327313i
$766$	−1135.80			−1.48277
$767$			311.615i			0.406278i
$768$	588.348	−	297.580i	0.766079	−	0.387474i
$769$	1226.47			1.59489			0.797447	−	0.603389i	$-0.206184\pi$
$769$	1226.47			1.59489			0.797447	+	0.603389i	$0.206184\pi$
$770$		−	182.335i		−	0.236798i
$771$	361.931	+	715.577i	0.469430	+	0.928115i
$772$	−641.322			−0.830729
$773$		−	381.344i		−	0.493330i	−0.969101	−	0.246665i	$-0.920665\pi$
$773$		−	381.344i		−	0.493330i	0.969101	−	0.246665i	$-0.0793347\pi$
$774$	509.699	+	374.965i	0.658526	+	0.484451i
$775$	768.796			0.991994
$776$		−	59.8093i		−	0.0770739i
$777$	154.369	−	78.0780i	0.198673	−	0.100486i
$778$	543.957			0.699173
$779$		−	804.927i		−	1.03328i
$780$	272.252	+	538.271i	0.349040	+	0.690091i
$781$	−758.401			−0.971065
$782$		−	1702.49i		−	2.17710i
$783$	1053.59	+	176.512i	1.34559	+	0.225430i
$784$	658.915			0.840452
$785$		−	285.414i		−	0.363585i
$786$	−437.000	+	221.030i	−0.555980	+	0.281209i
$787$	−92.1286			−0.117063			−0.0585315	−	0.998286i	$-0.518642\pi$
$787$	−92.1286			−0.117063			−0.0585315	+	0.998286i	$0.518642\pi$
$788$			395.354i			0.501719i
$789$	−464.335	−	918.041i	−0.588511	−	1.16355i
$790$	301.884			0.382132
$791$			83.6248i			0.105720i
$792$	53.5844	−	72.8385i	0.0676570	−	0.0919678i
$793$	627.943			0.791857
$794$		−	979.782i		−	1.23398i
$795$	−197.825	+	100.058i	−0.248837	+	0.125859i
$796$	641.397			0.805776
$797$		−	770.584i		−	0.966855i	−0.875384	−	0.483428i	$-0.839392\pi$
$797$		−	770.584i		−	0.966855i	0.875384	−	0.483428i	$-0.160608\pi$
$798$	−275.580	−	544.852i	−0.345339	−	0.682772i
$799$	973.222			1.21805
$800$			933.628i			1.16703i
$801$	419.687	+	308.747i	0.523954	+	0.385452i
$802$	1587.39			1.97929
$803$		−	1777.06i		−	2.21303i
$804$	93.3154	−	47.1979i	0.116064	−	0.0587039i
$805$	−172.777			−0.214630
$806$			2382.77i			2.95629i
$807$	114.617	+	226.610i	0.142028	+	0.280805i
$808$	102.780			0.127203
$809$		−	1338.40i		−	1.65438i	−0.561919	−	0.827192i	$-0.689937\pi$
$809$		−	1338.40i		−	1.65438i	0.561919	−	0.827192i	$-0.310063\pi$
$810$	−148.782	−	477.121i	−0.183682	−	0.589039i
$811$	375.725			0.463285			0.231643	−	0.972801i	$-0.425590\pi$
$811$	375.725			0.463285			0.231643	+	0.972801i	$0.425590\pi$
$812$		−	368.177i		−	0.453420i
$813$	−755.846	+	382.299i	−0.929700	+	0.470232i
$814$	−1025.59			−1.25994
$815$			483.590i			0.593362i
$816$	324.529	+	641.629i	0.397707	+	0.786310i
$817$	−792.943			−0.970555
$818$			1088.50i			1.33068i
$819$	−256.277	+	348.363i	−0.312914	+	0.425352i
$820$	−227.073			−0.276919
$821$			69.9084i			0.0851504i	0.999093	+	0.0425752i	$0.0135562\pi$
$821$			69.9084i			0.0851504i	−0.999093	+	0.0425752i	$0.986444\pi$
$822$	606.383	−	306.702i	0.737692	−	0.373117i
$823$	−193.903			−0.235605			−0.117803	−	0.993037i	$-0.537585\pi$
$823$	−193.903			−0.235605			−0.117803	+	0.993037i	$0.537585\pi$
$824$			6.76991i			0.00821592i
$825$	−373.374	−	738.201i	−0.452575	−	0.894789i
$826$	−88.9828			−0.107727
$827$		−	1019.32i		−	1.23255i	−0.787529	−	0.616277i	$-0.788640\pi$
$827$		−	1019.32i		−	1.23255i	0.787529	−	0.616277i	$-0.211360\pi$
$828$	−1136.94	−	836.403i	−1.37312	−	1.01015i
$829$	−788.301			−0.950905			−0.475453	−	0.879741i	$-0.657716\pi$
$829$	−788.301			−0.950905			−0.475453	+	0.879741i	$0.657716\pi$
$830$			795.327i			0.958225i
$831$	663.172	−	335.425i	0.798041	−	0.403641i
$832$	−1583.08			−1.90274
$833$			711.438i			0.854068i
$834$	446.484	+	882.748i	0.535353	+	1.05845i
$835$	21.6608			0.0259410
$836$			1866.59i			2.23276i
$837$	168.207	−	1004.02i	0.200964	−	1.19955i
$838$	336.113			0.401090
$839$			1617.94i			1.92842i	0.265146	+	0.964208i	$0.414580\pi$
$839$			1617.94i			1.92842i	−0.265146	+	0.964208i	$0.585420\pi$
$840$	−9.33100	+	4.71952i	−0.0111083	+	0.00561848i
$841$	−724.455			−0.861421
$842$		−	1690.08i		−	2.00722i
$843$	−139.262	−	275.336i	−0.165198	−	0.326614i
$844$	1371.52			1.62503
$845$			675.454i			0.799354i
$846$	927.227	−	1260.40i	1.09601	−	1.48984i
$847$	−135.242			−0.159672
$848$		−	512.790i		−	0.604706i
$849$	700.367	−	354.238i	0.824932	−	0.417242i
$850$	−942.625			−1.10897
$851$			971.831i			1.14199i
$852$	323.361	+	639.320i	0.379532	+	0.750375i
$853$	−444.936			−0.521613			−0.260807	−	0.965391i	$-0.583989\pi$
$853$	−444.936			−0.521613			−0.260807	+	0.965391i	$0.583989\pi$
$854$			179.311i			0.209966i
$855$	504.487	+	371.131i	0.590044	+	0.434071i
$856$	50.6477			0.0591678
$857$		−	1115.27i		−	1.30136i	−0.759351	−	0.650681i	$-0.774484\pi$
$857$		−	1115.27i		−	1.30136i	0.759351	−	0.650681i	$-0.225516\pi$
$858$	2287.95	−	1157.22i	2.66661	−	1.34874i
$859$	−803.797			−0.935736			−0.467868	−	0.883798i	$-0.654978\pi$
$859$	−803.797			−0.935736			−0.467868	+	0.883798i	$0.654978\pi$
$860$			223.693i			0.260108i
$861$	−73.4797	−	145.277i	−0.0853423	−	0.168731i
$862$	44.4560			0.0515731
$863$			1710.78i			1.98236i	0.132509	+	0.991182i	$0.457697\pi$
$863$			1710.78i			1.98236i	−0.132509	+	0.991182i	$0.542303\pi$
$864$	1219.29	+	204.271i	1.41121	+	0.236425i
$865$	−58.8624			−0.0680490
$866$		−	1589.69i		−	1.83566i
$867$	80.8941	−	40.9154i	0.0933035	−	0.0471919i
$868$	−350.854			−0.404210
$869$		−	661.672i		−	0.761417i
$870$	330.553	+	653.540i	0.379946	+	0.751195i
$871$	180.003			0.206662
$872$		−	92.4821i		−	0.106057i
$873$	−429.348	+	583.623i	−0.491807	+	0.668526i
$874$	3430.13			3.92463
$875$			212.952i			0.243374i
$876$	−1498.03	+	757.689i	−1.71008	+	0.864942i
$877$	−637.070			−0.726420			−0.363210	−	0.931707i	$-0.618319\pi$
$877$	−637.070			−0.726420			−0.363210	+	0.931707i	$0.618319\pi$
$878$		−	1006.77i		−	1.14666i
$879$	385.656	+	762.485i	0.438745	+	0.867445i
$880$	−432.613			−0.491606
$881$		−	173.837i		−	0.197317i	−0.995121	−	0.0986587i	$-0.968545\pi$
$881$		−	173.837i		−	0.197317i	0.995121	−	0.0986587i	$-0.0314552\pi$
$882$	921.372	+	677.816i	1.04464	+	0.768498i
$883$	534.475			0.605295			0.302647	−	0.953103i	$-0.402130\pi$
$883$	534.475			0.605295			0.302647	+	0.953103i	$0.402130\pi$
$884$		−	1506.49i		−	1.70418i
$885$	81.4475	−	41.1953i	0.0920311	−	0.0465483i
$886$	2353.99			2.65688
$887$			339.977i			0.383289i	0.981464	+	0.191644i	$0.0613820\pi$
$887$			339.977i			0.383289i	−0.981464	+	0.191644i	$0.938618\pi$
$888$	26.5462	+	52.4846i	0.0298943	+	0.0591043i
$889$	172.660			0.194218
$890$			357.196i			0.401344i
$891$	−1045.76	+	326.102i	−1.17369	+	0.365995i
$892$	1134.80			1.27220
$893$			1960.82i			2.19577i
$894$	−899.443	+	454.929i	−1.00609	+	0.508869i
$895$	−368.782			−0.412047
$896$		−	51.8405i		−	0.0578578i
$897$	−1096.56	−	2168.02i	−1.22248	−	2.41697i
$898$	−1413.89			−1.57448
$899$			1491.80i			1.65940i
$900$	−463.095	+	629.496i	−0.514550	+	0.699440i
$901$	553.666			0.614502
$902$			965.188i			1.07005i
$903$	−143.114	+	72.3858i	−0.158488	+	0.0801614i
$904$	−28.4320			−0.0314514
$905$			203.063i			0.224379i
$906$	871.519	+	1723.09i	0.961942	+	1.90186i
$907$	−779.092			−0.858977			−0.429489	−	0.903072i	$-0.641306\pi$
$907$	−779.092			−0.858977			−0.429489	+	0.903072i	$0.641306\pi$
$908$		−	709.193i		−	0.781050i
$909$	−1002.93	−	737.818i	−1.10334	−	0.811681i
$910$	−296.492			−0.325816
$911$			996.515i			1.09387i	0.837175	+	0.546934i	$0.184205\pi$
$911$			996.515i			1.09387i	−0.837175	+	0.546934i	$0.815795\pi$
$912$	−1292.73	+	653.851i	−1.41747	+	0.716942i
$913$	1743.20			1.90931
$914$		−	1285.94i		−	1.40693i
$915$	−83.0135	−	164.127i	−0.0907252	−	0.179374i
$916$	1583.25			1.72844
$917$		−	124.123i		−	0.135357i
$918$	−206.240	+	1231.04i	−0.224662	+	1.34100i
$919$	519.675			0.565479			0.282739	−	0.959197i	$-0.408757\pi$
$919$	519.675			0.565479			0.282739	+	0.959197i	$0.408757\pi$
$920$		−	58.7435i		−	0.0638516i
$921$	−761.937	+	385.380i	−0.827293	+	0.418436i
$922$	−247.642			−0.268592
$923$			1233.23i			1.33611i
$924$	170.396	+	336.892i	0.184412	+	0.364602i
$925$	538.078			0.581706
$926$			112.318i			0.121294i
$927$	48.5986	−	66.0612i	0.0524256	−	0.0712635i
$928$	−1811.65			−1.95221
$929$			475.851i			0.512219i	0.966648	+	0.256109i	$0.0824407\pi$
$929$			475.851i			0.512219i	−0.966648	+	0.256109i	$0.917559\pi$
$930$	622.791	−	315.001i	0.669668	−	0.338711i
$931$	−1433.38			−1.53962
$932$		−	1119.00i		−	1.20064i
$933$	13.2136	+	26.1248i	0.0141625	+	0.0280008i
$934$	651.313			0.697337
$935$		−	467.098i		−	0.499570i
$936$	−118.442	−	87.1329i	−0.126540	−	0.0930907i
$937$	−949.326			−1.01316			−0.506578	−	0.862194i	$-0.669090\pi$
$937$	−949.326			−1.01316			−0.506578	+	0.862194i	$0.669090\pi$
$938$			51.4003i			0.0547978i
$939$	239.667	−	121.221i	0.255237	−	0.129096i
$940$	553.155			0.588463
$941$		−	1198.39i		−	1.27352i	−0.771060	−	0.636762i	$-0.780273\pi$
$941$		−	1198.39i		−	1.27352i	0.771060	−	0.636762i	$-0.219727\pi$
$942$	517.262	+	1022.68i	0.549110	+	1.08565i
$943$	914.596			0.969880
$944$			211.124i			0.223648i
$945$	124.932	+	20.9302i	0.132203	+	0.0221484i
$946$	950.818			1.00509
$947$			1328.10i			1.40243i	0.712952	+	0.701213i	$0.247358\pi$
$947$			1328.10i			1.40243i	−0.712952	+	0.701213i	$0.752642\pi$
$948$	−557.778	+	282.118i	−0.588373	+	0.297593i
$949$	−2889.66			−3.04495
$950$		−	1899.17i		−	1.99913i
$951$	−118.955	−	235.187i	−0.125084	−	0.247305i
$952$	26.1153			0.0274320
$953$		−	565.628i		−	0.593524i	−0.954952	−	0.296762i	$-0.904093\pi$
$953$		−	565.628i		−	0.593524i	0.954952	−	0.296762i	$-0.0959067\pi$
$954$	527.500	−	717.044i	0.552935	−	0.751618i
$955$	428.480			0.448670
$956$			1378.89i			1.44236i
$957$	1432.43	−	724.510i	1.49680	−	0.757063i
$958$	1132.54			1.18220
$959$			172.233i			0.179596i
$960$	209.282	+	413.772i	0.218002	+	0.431013i
$961$	460.612			0.479304
$962$			1667.70i			1.73357i
$963$	−494.223	−	363.580i	−0.513212	−	0.377549i
$964$	−691.101			−0.716910
$965$			323.341i			0.335069i
$966$	619.087	−	313.127i	0.640877	−	0.324149i
$967$	1305.69			1.35025			0.675126	−	0.737702i	$-0.264089\pi$
$967$	1305.69			1.35025			0.675126	+	0.737702i	$0.264089\pi$
$968$		−	45.9816i		−	0.0475016i
$969$	−705.971	−	1395.78i	−0.728557	−	1.44044i
$970$	−496.722			−0.512084
$971$		−	345.529i		−	0.355849i	−0.984044	−	0.177924i	$-0.943062\pi$
$971$		−	345.529i		−	0.355849i	0.984044	−	0.177924i	$-0.0569382\pi$
$972$	720.780	+	742.516i	0.741543	+	0.763906i
$973$	−250.730			−0.257687
$974$			1888.00i			1.93840i
$975$	−1200.38	+	607.139i	−1.23116	+	0.622707i
$976$	425.440			0.435901
$977$			1069.85i			1.09504i	0.836794	+	0.547518i	$0.184427\pi$
$977$			1069.85i			1.09504i	−0.836794	+	0.547518i	$0.815573\pi$
$978$	−876.418	−	1732.77i	−0.896133	−	1.77175i
$979$	782.905			0.799699
$980$			404.364i			0.412616i
$981$	−663.893	+	902.446i	−0.676751	+	0.919925i
$982$	360.696			0.367308
$983$			1250.67i			1.27229i	0.771568	+	0.636147i	$0.219473\pi$
$983$			1250.67i			1.27229i	−0.771568	+	0.636147i	$0.780527\pi$
$984$	49.3936	−	24.9828i	0.0501968	−	0.0253890i
$985$	199.329			0.202365
$986$		−	1829.11i		−	1.85508i
$987$	178.998	+	353.899i	0.181356	+	0.358560i
$988$	3035.24			3.07211
$989$		−	900.980i		−	0.911001i
$990$	−604.931	−	445.023i	−0.611041	−	0.449518i
$991$	892.579			0.900685			0.450343	−	0.892856i	$-0.351302\pi$
$991$	892.579			0.900685			0.450343	+	0.892856i	$0.351302\pi$
$992$			1726.41i			1.74033i
$993$	−259.330	+	131.166i	−0.261158	+	0.132091i
$994$	−352.152			−0.354278
$995$		−	323.379i		−	0.325004i
$996$	−743.253	−	1469.49i	−0.746238	−	1.47539i
$997$	1362.80			1.36690			0.683452	−	0.729995i	$-0.260478\pi$
$997$	1362.80			1.36690			0.683452	+	0.729995i	$0.260478\pi$
$998$			133.806i			0.134074i
$999$	117.728	−	702.712i	0.117845	−	0.703416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.7	✓	44
3.2	odd	2	inner	201.3.c.a.68.38	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.7	✓	44	1.1	even	1	trivial
201.3.c.a.68.38	yes	44	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.87376i q^{2} +(2.67705 - 1.35402i) q^{3} -4.25852 q^{4} +2.14706i q^{5} +(-3.89115 - 7.69322i) q^{6} +2.18513 q^{7} +0.742934i q^{8} +(5.33323 - 7.24959i) q^{9} +O(q^{10})\)	\(q-2.87376i q^{2} +(2.67705 - 1.35402i) q^{3} -4.25852 q^{4} +2.14706i q^{5} +(-3.89115 - 7.69322i) q^{6} +2.18513 q^{7} +0.742934i q^{8} +(5.33323 - 7.24959i) q^{9} +6.17014 q^{10} -13.5238i q^{11} +(-11.4003 + 5.76615i) q^{12} -21.9908 q^{13} -6.27955i q^{14} +(2.90717 + 5.74779i) q^{15} -14.8991 q^{16} -16.0867i q^{17} +(-20.8336 - 15.3265i) q^{18} +32.4110 q^{19} -9.14329i q^{20} +(5.84971 - 2.95872i) q^{21} -38.8641 q^{22} +36.8270i q^{23} +(1.00595 + 1.98887i) q^{24} +20.3901 q^{25} +63.1964i q^{26} +(4.46122 - 26.6289i) q^{27} -9.30543 q^{28} +39.5658i q^{29} +(16.5178 - 8.35452i) q^{30} +37.7043 q^{31} +45.7882i q^{32} +(-18.3115 - 36.2038i) q^{33} -46.2294 q^{34} +4.69160i q^{35} +(-22.7117 + 30.8726i) q^{36} +26.3891 q^{37} -93.1417i q^{38} +(-58.8706 + 29.7761i) q^{39} -1.59512 q^{40} -24.8350i q^{41} +(-8.50267 - 16.8107i) q^{42} -24.4652 q^{43} +57.5912i q^{44} +(15.5653 + 11.4508i) q^{45} +105.832 q^{46} +60.4985i q^{47} +(-39.8856 + 20.1737i) q^{48} -44.2252 q^{49} -58.5965i q^{50} +(-21.7818 - 43.0650i) q^{51} +93.6484 q^{52} +34.4176i q^{53} +(-76.5251 - 12.8205i) q^{54} +29.0363 q^{55} +1.62341i q^{56} +(86.7661 - 43.8854i) q^{57} +113.703 q^{58} -14.1702i q^{59} +(-12.3802 - 24.4771i) q^{60} -28.5548 q^{61} -108.353i q^{62} +(11.6538 - 15.8413i) q^{63} +71.9881 q^{64} -47.2155i q^{65} +(-104.041 + 52.6229i) q^{66} -8.18535 q^{67} +68.5056i q^{68} +(49.8646 + 98.5878i) q^{69} +13.4826 q^{70} -56.0792i q^{71} +(5.38597 + 3.96224i) q^{72} +131.403 q^{73} -75.8361i q^{74} +(54.5855 - 27.6088i) q^{75} -138.023 q^{76} -29.5512i q^{77} +(85.5695 + 169.180i) q^{78} +48.9266 q^{79} -31.9892i q^{80} +(-24.1133 - 77.3276i) q^{81} -71.3698 q^{82} +128.899i q^{83} +(-24.9111 + 12.5998i) q^{84} +34.5391 q^{85} +70.3073i q^{86} +(53.5731 + 105.920i) q^{87} +10.0473 q^{88} +57.8911i q^{89} +(32.9068 - 44.7310i) q^{90} -48.0528 q^{91} -156.828i q^{92} +(100.936 - 51.0525i) q^{93} +173.858 q^{94} +69.5883i q^{95} +(61.9983 + 122.577i) q^{96} -80.5042 q^{97} +127.093i q^{98} +(-98.0417 - 72.1253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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