LMFDB - Embedded newform 201.3.c.a.68.34

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			68.34
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37672i q^{2} +(-2.91725 - 0.699765i) q^{3} -1.64880 q^{4} +3.76639i q^{5} +(1.66315 - 6.93348i) q^{6} +9.72750 q^{7} +5.58814i q^{8} +(8.02066 + 4.08278i) q^{9} +O(q^{10})$	\(q+2.37672i q^{2} +(-2.91725 - 0.699765i) q^{3} -1.64880 q^{4} +3.76639i q^{5} +(1.66315 - 6.93348i) q^{6} +9.72750 q^{7} +5.58814i q^{8} +(8.02066 + 4.08278i) q^{9} -8.95165 q^{10} +6.42866i q^{11} +(4.80996 + 1.15377i) q^{12} -19.9265 q^{13} +23.1195i q^{14} +(2.63559 - 10.9875i) q^{15} -19.8767 q^{16} -12.2150i q^{17} +(-9.70362 + 19.0629i) q^{18} -16.2495 q^{19} -6.21003i q^{20} +(-28.3775 - 6.80696i) q^{21} -15.2791 q^{22} +29.8560i q^{23} +(3.91039 - 16.3020i) q^{24} +10.8143 q^{25} -47.3598i q^{26} +(-20.5413 - 17.5230i) q^{27} -16.0387 q^{28} +38.6422i q^{29} +(26.1142 + 6.26406i) q^{30} +11.7109 q^{31} -24.8887i q^{32} +(4.49855 - 18.7540i) q^{33} +29.0317 q^{34} +36.6375i q^{35} +(-13.2245 - 6.73169i) q^{36} +14.6187 q^{37} -38.6204i q^{38} +(58.1306 + 13.9439i) q^{39} -21.0471 q^{40} +6.17375i q^{41} +(16.1783 - 67.4454i) q^{42} -11.1638 q^{43} -10.5996i q^{44} +(-15.3773 + 30.2089i) q^{45} -70.9593 q^{46} +1.34781i q^{47} +(57.9851 + 13.9090i) q^{48} +45.6242 q^{49} +25.7026i q^{50} +(-8.54766 + 35.6343i) q^{51} +32.8549 q^{52} -74.6579i q^{53} +(41.6474 - 48.8208i) q^{54} -24.2128 q^{55} +54.3586i q^{56} +(47.4037 + 11.3708i) q^{57} -91.8418 q^{58} -58.8875i q^{59} +(-4.34556 + 18.1162i) q^{60} +36.2784 q^{61} +27.8336i q^{62} +(78.0209 + 39.7152i) q^{63} -20.3531 q^{64} -75.0510i q^{65} +(44.5730 + 10.6918i) q^{66} +8.18535 q^{67} +20.1402i q^{68} +(20.8922 - 87.0972i) q^{69} -87.0772 q^{70} +128.501i q^{71} +(-22.8151 + 44.8206i) q^{72} +105.916 q^{73} +34.7446i q^{74} +(-31.5480 - 7.56749i) q^{75} +26.7921 q^{76} +62.5348i q^{77} +(-33.1407 + 138.160i) q^{78} +117.249 q^{79} -74.8632i q^{80} +(47.6619 + 65.4931i) q^{81} -14.6733 q^{82} +56.8769i q^{83} +(46.7889 + 11.2233i) q^{84} +46.0066 q^{85} -26.5333i q^{86} +(27.0405 - 112.729i) q^{87} -35.9243 q^{88} +71.5967i q^{89} +(-71.7981 - 36.5476i) q^{90} -193.835 q^{91} -49.2266i q^{92} +(-34.1636 - 8.19490i) q^{93} -3.20338 q^{94} -61.2017i q^{95} +(-17.4163 + 72.6065i) q^{96} +118.807 q^{97} +108.436i q^{98} +(-26.2468 + 51.5621i) 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 $

$2$			2.37672i			1.18836i	0.804332	+	0.594180i	$0.202523\pi$
$2$			2.37672i			1.18836i	−0.804332	+	0.594180i	$0.797477\pi$
$3$	−2.91725	−	0.699765i	−0.972416	−	0.233255i
$3$	−2.91725	−	0.699765i	−0.972416	−	0.233255i
$4$	−1.64880			−0.412201
$5$			3.76639i			0.753278i	0.926360	+	0.376639i	$0.122920\pi$
$5$			3.76639i			0.753278i	−0.926360	+	0.376639i	$0.877080\pi$
$6$	1.66315	−	6.93348i	0.277191	−	1.15558i
$7$	9.72750			1.38964			0.694821	−	0.719183i	$-0.255484\pi$
$7$	9.72750			1.38964			0.694821	+	0.719183i	$0.255484\pi$
$8$			5.58814i			0.698518i
$9$	8.02066	+	4.08278i	0.891184	+	0.453642i
$10$	−8.95165			−0.895165
$11$			6.42866i			0.584424i	0.956354	+	0.292212i	$0.0943912\pi$
$11$			6.42866i			0.584424i	−0.956354	+	0.292212i	$0.905609\pi$
$12$	4.80996	+	1.15377i	0.400830	+	0.0961479i
$13$	−19.9265			−1.53281			−0.766405	−	0.642358i	$-0.777956\pi$
$13$	−19.9265			−1.53281			−0.766405	+	0.642358i	$0.777956\pi$
$14$			23.1195i			1.65140i
$15$	2.63559	−	10.9875i	0.175706	−	0.732499i
$16$	−19.8767			−1.24229
$17$		−	12.2150i		−	0.718532i	−0.933235	−	0.359266i	$-0.883027\pi$
$17$		−	12.2150i		−	0.718532i	0.933235	−	0.359266i	$-0.116973\pi$
$18$	−9.70362	+	19.0629i	−0.539090	+	1.05905i
$19$	−16.2495			−0.855234			−0.427617	−	0.903960i	$-0.640647\pi$
$19$	−16.2495			−0.855234			−0.427617	+	0.903960i	$0.640647\pi$
$20$		−	6.21003i		−	0.310501i
$21$	−28.3775	−	6.80696i	−1.35131	−	0.324141i
$22$	−15.2791			−0.694506
$23$			29.8560i			1.29808i	0.760752	+	0.649042i	$0.224830\pi$
$23$			29.8560i			1.29808i	−0.760752	+	0.649042i	$0.775170\pi$
$24$	3.91039	−	16.3020i	0.162933	−	0.679249i
$25$	10.8143			0.432573
$26$		−	47.3598i		−	1.82153i
$27$	−20.5413	−	17.5230i	−0.760787	−	0.649001i
$28$	−16.0387			−0.572811
$29$			38.6422i			1.33249i	0.745733	+	0.666245i	$0.232100\pi$
$29$			38.6422i			1.33249i	−0.745733	+	0.666245i	$0.767900\pi$
$30$	26.1142	+	6.26406i	0.870473	+	0.208802i
$31$	11.7109			0.377772			0.188886	−	0.981999i	$-0.439512\pi$
$31$	11.7109			0.377772			0.188886	+	0.981999i	$0.439512\pi$
$32$		−	24.8887i		−	0.777772i
$33$	4.49855	−	18.7540i	0.136320	−	0.568303i
$34$	29.0317			0.853874
$35$			36.6375i			1.04679i
$36$	−13.2245	−	6.73169i	−0.367347	−	0.186991i
$37$	14.6187			0.395100			0.197550	−	0.980293i	$-0.436702\pi$
$37$	14.6187			0.395100			0.197550	+	0.980293i	$0.436702\pi$
$38$		−	38.6204i		−	1.01633i
$39$	58.1306	+	13.9439i	1.49053	+	0.357536i
$40$	−21.0471			−0.526178
$41$			6.17375i			0.150579i	0.997162	+	0.0752896i	$0.0239881\pi$
$41$			6.17375i			0.150579i	−0.997162	+	0.0752896i	$0.976012\pi$
$42$	16.1783	−	67.4454i	0.385196	−	1.60584i
$43$	−11.1638			−0.259624			−0.129812	−	0.991539i	$-0.541437\pi$
$43$	−11.1638			−0.259624			−0.129812	+	0.991539i	$0.541437\pi$
$44$		−	10.5996i		−	0.240900i
$45$	−15.3773	+	30.2089i	−0.341718	+	0.671309i
$46$	−70.9593			−1.54259
$47$			1.34781i			0.0286769i	0.999897	+	0.0143385i	$0.00456423\pi$
$47$			1.34781i			0.0286769i	−0.999897	+	0.0143385i	$0.995436\pi$
$48$	57.9851	+	13.9090i	1.20802	+	0.289771i
$49$	45.6242			0.931106
$50$			25.7026i			0.514053i
$51$	−8.54766	+	35.6343i	−0.167601	+	0.698711i
$52$	32.8549			0.631825
$53$		−	74.6579i		−	1.40864i	−0.709883	−	0.704320i	$-0.751252\pi$
$53$		−	74.6579i		−	1.40864i	0.709883	−	0.704320i	$-0.248748\pi$
$54$	41.6474	−	48.8208i	0.771248	−	0.904089i
$55$	−24.2128			−0.440233
$56$			54.3586i			0.970690i
$57$	47.4037	+	11.3708i	0.831643	+	0.199488i
$58$	−91.8418			−1.58348
$59$		−	58.8875i		−	0.998094i	−0.866575	−	0.499047i	$-0.833684\pi$
$59$		−	58.8875i		−	0.998094i	0.866575	−	0.499047i	$-0.166316\pi$
$60$	−4.34556	+	18.1162i	−0.0724260	+	0.301936i
$61$	36.2784			0.594728			0.297364	−	0.954764i	$-0.403893\pi$
$61$	36.2784			0.594728			0.297364	+	0.954764i	$0.403893\pi$
$62$			27.8336i			0.448929i
$63$	78.0209	+	39.7152i	1.23843	+	0.630400i
$64$	−20.3531			−0.318017
$65$		−	75.0510i		−	1.15463i
$66$	44.5730	+	10.6918i	0.675348	+	0.161997i
$67$	8.18535			0.122169
$67$	8.18535			0.122169
$68$			20.1402i			0.296179i
$69$	20.8922	−	87.0972i	0.302785	−	1.26228i
$70$	−87.0772			−1.24396
$71$			128.501i			1.80987i	0.425550	+	0.904935i	$0.360081\pi$
$71$			128.501i			1.80987i	−0.425550	+	0.904935i	$0.639919\pi$
$72$	−22.8151	+	44.8206i	−0.316877	+	0.622508i
$73$	105.916			1.45090			0.725449	−	0.688276i	$-0.241632\pi$
$73$	105.916			1.45090			0.725449	+	0.688276i	$0.241632\pi$
$74$			34.7446i			0.469521i
$75$	−31.5480	−	7.56749i	−0.420641	−	0.100900i
$76$	26.7921			0.352528
$77$			62.5348i			0.812140i
$78$	−33.1407	+	138.160i	−0.424881	+	1.77128i
$79$	117.249			1.48417			0.742084	−	0.670307i	$-0.233837\pi$
$79$	117.249			1.48417			0.742084	+	0.670307i	$0.233837\pi$
$80$		−	74.8632i		−	0.935790i
$81$	47.6619	+	65.4931i	0.588418	+	0.808557i
$82$	−14.6733			−0.178942
$83$			56.8769i			0.685264i	0.939470	+	0.342632i	$0.111318\pi$
$83$			56.8769i			0.685264i	−0.939470	+	0.342632i	$0.888682\pi$
$84$	46.7889	+	11.2233i	0.557011	+	0.133611i
$85$	46.0066			0.541254
$86$		−	26.5333i		−	0.308527i
$87$	27.0405	−	112.729i	0.310810	−	1.29573i
$88$	−35.9243			−0.408230
$89$			71.5967i			0.804457i	0.915539	+	0.402228i	$0.131764\pi$
$89$			71.5967i			0.804457i	−0.915539	+	0.402228i	$0.868236\pi$
$90$	−71.7981	−	36.5476i	−0.797757	−	0.406084i
$91$	−193.835			−2.13006
$92$		−	49.2266i		−	0.535071i
$93$	−34.1636	−	8.19490i	−0.367351	−	0.0881172i
$94$	−3.20338			−0.0340785
$95$		−	61.2017i		−	0.644229i
$96$	−17.4163	+	72.6065i	−0.181419	+	0.756318i
$97$	118.807			1.22482			0.612409	−	0.790541i	$-0.290201\pi$
$97$	118.807			1.22482			0.612409	+	0.790541i	$0.290201\pi$
$98$			108.436i			1.10649i
$99$	−26.2468	+	51.5621i	−0.265119	+	0.520829i
$100$	−17.8307			−0.178307
$101$		−	142.645i		−	1.41232i	−0.708050	−	0.706162i	$-0.750425\pi$
$101$		−	142.645i		−	1.41232i	0.708050	−	0.706162i	$-0.249575\pi$
$102$	−84.6927	−	20.3154i	−0.830321	−	0.199171i
$103$	−72.3124			−0.702062			−0.351031	−	0.936364i	$-0.614169\pi$
$103$	−72.3124			−0.702062			−0.351031	+	0.936364i	$0.614169\pi$
$104$		−	111.352i		−	1.07069i
$105$	25.6377	−	106.881i	0.244168	−	1.01791i
$106$	177.441			1.67397
$107$		−	128.769i		−	1.20345i	−0.798705	−	0.601723i	$-0.794481\pi$
$107$		−	128.769i		−	1.20345i	0.798705	−	0.601723i	$-0.205519\pi$
$108$	33.8685	+	28.8920i	0.313597	+	0.267519i
$109$	107.508			0.986311			0.493156	−	0.869941i	$-0.335843\pi$
$109$	107.508			0.986311			0.493156	+	0.869941i	$0.335843\pi$
$110$		−	57.5471i		−	0.523156i
$111$	−42.6463	−	10.2297i	−0.384201	−	0.0921591i
$112$	−193.350			−1.72634
$113$		−	186.185i		−	1.64766i	−0.566839	−	0.823829i	$-0.691834\pi$
$113$		−	186.185i		−	1.64766i	0.566839	−	0.823829i	$-0.308166\pi$
$114$	−27.0252	+	112.665i	−0.237063	+	0.988292i
$115$	−112.449			−0.977818
$116$		−	63.7134i		−	0.549253i
$117$	−159.824	−	81.3555i	−1.36602	−	0.695346i
$118$	139.959			1.18610
$119$		−	118.822i		−	0.998502i
$120$	61.3996	+	14.7280i	0.511663	+	0.122734i
$121$	79.6723			0.658449
$122$			86.2236i			0.706751i
$123$	4.32017	−	18.0103i	0.0351234	−	0.146426i
$124$	−19.3090			−0.155718
$125$			134.891i			1.07913i
$126$	−94.3919	+	185.434i	−0.749142	+	1.47170i
$127$	−183.200			−1.44252			−0.721260	−	0.692664i	$-0.756437\pi$
$127$	−183.200			−1.44252			−0.721260	+	0.692664i	$0.756437\pi$
$128$		−	147.929i		−	1.15569i
$129$	32.5677	+	7.81207i	0.252463	+	0.0605587i
$130$	178.375			1.37212
$131$			226.790i			1.73122i	0.500718	+	0.865610i	$0.333069\pi$
$131$			226.790i			1.73122i	−0.500718	+	0.865610i	$0.666931\pi$
$132$	−7.41722	+	30.9216i	−0.0561911	+	0.234255i
$133$	−158.066			−1.18847
$134$			19.4543i			0.145181i
$135$	65.9986	−	77.3663i	0.488878	−	0.573084i
$136$	68.2593			0.501907
$137$		−	62.6591i		−	0.457366i	−0.973501	−	0.228683i	$-0.926558\pi$
$137$		−	62.6591i		−	0.457366i	0.973501	−	0.228683i	$-0.0734419\pi$
$138$	207.006	+	49.6548i	1.50004	+	0.359818i
$139$	90.3218			0.649797			0.324899	−	0.945749i	$-0.394670\pi$
$139$	90.3218			0.649797			0.324899	+	0.945749i	$0.394670\pi$
$140$		−	60.4080i		−	0.431486i
$141$	0.943154	−	3.93191i	0.00668903	−	0.0278859i
$142$	−305.411			−2.15078
$143$		−	128.101i		−	0.895810i
$144$	−159.424	−	81.1519i	−1.10711	−	0.563555i
$145$	−145.542			−1.00373
$146$			251.732i			1.72419i
$147$	−133.097	−	31.9262i	−0.905422	−	0.217185i
$148$	−24.1033			−0.162860
$149$			166.755i			1.11916i	0.828776	+	0.559580i	$0.189037\pi$
$149$			166.755i			1.11916i	−0.828776	+	0.559580i	$0.810963\pi$
$150$	17.9858	−	74.9809i	0.119905	−	0.499873i
$151$	68.0234			0.450486			0.225243	−	0.974303i	$-0.427682\pi$
$151$	68.0234			0.450486			0.225243	+	0.974303i	$0.427682\pi$
$152$		−	90.8042i		−	0.597396i
$153$	49.8712	−	97.9726i	0.325956	−	0.640344i
$154$	−148.628			−0.965115
$155$			44.1079i			0.284567i
$156$	−95.8459	−	22.9907i	−0.614397	−	0.147376i
$157$	182.503			1.16244			0.581218	−	0.813748i	$-0.302576\pi$
$157$	182.503			1.16244			0.581218	+	0.813748i	$0.302576\pi$
$158$			278.669i			1.76373i
$159$	−52.2430	+	217.795i	−0.328572	+	1.36978i
$160$	93.7405			0.585878
$161$			290.424i			1.80387i
$162$	−155.659	+	113.279i	−0.960857	+	0.699253i
$163$	−133.849			−0.821157			−0.410578	−	0.911825i	$-0.634673\pi$
$163$	−133.849			−0.821157			−0.410578	+	0.911825i	$0.634673\pi$
$164$		−	10.1793i		−	0.0620688i
$165$	70.6348	+	16.9433i	0.428090	+	0.102687i
$166$	−135.180			−0.814340
$167$			34.4175i			0.206093i	0.994677	+	0.103046i	$0.0328590\pi$
$167$			34.4175i			0.206093i	−0.994677	+	0.103046i	$0.967141\pi$
$168$	38.0383	−	158.577i	0.226418	−	0.943914i
$169$	228.067			1.34951
$170$			109.345i			0.643204i
$171$	−130.331	−	66.3429i	−0.762171	−	0.387970i
$172$	18.4070			0.107017
$173$		−	110.176i		−	0.636858i	−0.947947	−	0.318429i	$-0.896845\pi$
$173$		−	110.176i		−	0.636858i	0.947947	−	0.318429i	$-0.103155\pi$
$174$	267.925	+	64.2677i	1.53980	+	0.369354i
$175$	105.196			0.601122
$176$		−	127.780i		−	0.726024i
$177$	−41.2074	+	171.789i	−0.232810	+	0.970562i
$178$	−170.165			−0.955985
$179$		−	309.605i		−	1.72964i	−0.502084	−	0.864819i	$-0.667433\pi$
$179$		−	309.605i		−	1.72964i	0.502084	−	0.864819i	$-0.332567\pi$
$180$	25.3542	−	49.8085i	0.140856	−	0.276714i
$181$	−16.1864			−0.0894277			−0.0447138	−	0.999000i	$-0.514238\pi$
$181$	−16.1864			−0.0894277			−0.0447138	+	0.999000i	$0.514238\pi$
$182$		−	460.692i		−	2.53128i
$183$	−105.833	−	25.3864i	−0.578322	−	0.138723i
$184$	−166.839			−0.906735
$185$			55.0597i			0.297620i
$186$	19.4770	−	81.1975i	0.104715	−	0.436545i
$187$	78.5263			0.419927
$188$		−	2.22228i		−	0.0118206i
$189$	−199.815	−	170.455i	−1.05722	−	0.901880i
$190$	145.459			0.765576
$191$			276.996i			1.45024i	0.688621	+	0.725122i	$0.258216\pi$
$191$			276.996i			1.45024i	−0.688621	+	0.725122i	$0.741784\pi$
$192$	59.3751	+	14.2424i	0.309245	+	0.0741792i
$193$	156.777			0.812315			0.406158	−	0.913803i	$-0.366868\pi$
$193$	156.777			0.812315			0.406158	+	0.913803i	$0.366868\pi$
$194$			282.372i			1.45552i
$195$	−52.5181	+	218.942i	−0.269324	+	1.12278i
$196$	−75.2253			−0.383802
$197$			126.802i			0.643665i	0.946797	+	0.321832i	$0.104299\pi$
$197$			126.802i			0.643665i	−0.946797	+	0.321832i	$0.895701\pi$
$198$	−122.549	−	62.3813i	−0.618933	−	0.315057i
$199$	−98.7033			−0.495996			−0.247998	−	0.968761i	$-0.579773\pi$
$199$	−98.7033			−0.495996			−0.247998	+	0.968761i	$0.579773\pi$
$200$			60.4319i			0.302160i
$201$	−23.8787	−	5.72782i	−0.118799	−	0.0284966i
$202$	339.027			1.67835
$203$			375.892i			1.85168i
$204$	14.0934	−	58.7539i	0.0690853	−	0.288009i
$205$	−23.2527			−0.113428
$206$		−	171.866i		−	0.834302i
$207$	−121.895	+	239.464i	−0.588865	+	1.15683i
$208$	396.073			1.90420
$209$		−	104.462i		−	0.499819i
$210$	254.026	+	60.9336i	1.20965	+	0.290160i
$211$	117.646			0.557563			0.278781	−	0.960355i	$-0.410069\pi$
$211$	117.646			0.557563			0.278781	+	0.960355i	$0.410069\pi$
$212$			123.096i			0.580642i
$213$	89.9204	−	374.868i	0.422161	−	1.75995i
$214$	306.047			1.43013
$215$		−	42.0474i		−	0.195569i
$216$	97.9212	−	114.787i	0.453339	−	0.531423i
$217$	113.918			0.524967
$218$			255.516i			1.17209i
$219$	−308.982	−	74.1160i	−1.41088	−	0.338429i
$220$	39.9222			0.181464
$221$			243.403i			1.10137i
$222$	24.3130	−	101.358i	0.109518	−	0.456570i
$223$	−362.520			−1.62565			−0.812825	−	0.582508i	$-0.802071\pi$
$223$	−362.520			−1.62565			−0.812825	+	0.582508i	$0.802071\pi$
$224$		−	242.105i		−	1.08083i
$225$	86.7380	+	44.1524i	0.385502	+	0.196233i
$226$	442.510			1.95801
$227$		−	37.3389i		−	0.164489i	−0.996612	−	0.0822443i	$-0.973791\pi$
$227$		−	37.3389i		−	0.164489i	0.996612	−	0.0822443i	$-0.0262088\pi$
$228$	−78.1593	−	18.7482i	−0.342804	−	0.0822290i
$229$	363.114			1.58565			0.792825	−	0.609450i	$-0.208610\pi$
$229$	363.114			1.58565			0.792825	+	0.609450i	$0.208610\pi$
$230$		−	267.260i		−	1.16200i
$231$	43.7596	−	182.429i	0.189436	−	0.789737i
$232$	−215.938			−0.930768
$233$			169.553i			0.727697i	0.931458	+	0.363848i	$0.118537\pi$
$233$			169.553i			0.727697i	−0.931458	+	0.363848i	$0.881463\pi$
$234$	193.359	−	379.857i	0.826322	−	1.62332i
$235$	−5.07639			−0.0216017
$236$			97.0939i			0.411415i
$237$	−342.045	−	82.0470i	−1.44323	−	0.346190i
$238$	282.406			1.18658
$239$		−	183.112i		−	0.766159i	−0.923715	−	0.383079i	$-0.874864\pi$
$239$		−	183.112i		−	0.766159i	0.923715	−	0.383079i	$-0.125136\pi$
$240$	−52.3867	+	218.394i	−0.218278	+	0.909977i
$241$	−11.0008			−0.0456464			−0.0228232	−	0.999740i	$-0.507265\pi$
$241$	−11.0008			−0.0456464			−0.0228232	+	0.999740i	$0.507265\pi$
$242$			189.359i			0.782475i
$243$	−93.2117	−	224.412i	−0.383587	−	0.923505i
$244$	−59.8159			−0.245147
$245$			171.838i			0.701381i
$246$	42.8056	+	10.2678i	0.174006	+	0.0417392i
$247$	323.795			1.31091
$248$			65.4423i			0.263880i
$249$	39.8005	−	165.924i	0.159841	−	0.666361i
$250$	−320.597			−1.28239
$251$		−	166.776i		−	0.664447i	−0.943201	−	0.332223i	$-0.892201\pi$
$251$		−	166.776i		−	0.664447i	0.943201	−	0.332223i	$-0.107799\pi$
$252$	−128.641	−	65.4825i	−0.510480	−	0.259851i
$253$	−191.934			−0.758631
$254$		−	435.416i		−	1.71423i
$255$	−134.212	−	32.1938i	−0.526324	−	0.126250i
$256$	270.172			1.05536
$257$		−	323.219i		−	1.25766i	−0.777542	−	0.628831i	$-0.783534\pi$
$257$		−	323.219i		−	1.25766i	0.777542	−	0.628831i	$-0.216466\pi$
$258$	−18.5671	+	77.4043i	−0.0719655	+	0.300017i
$259$	142.203			0.549048
$260$			123.744i			0.475940i
$261$	−157.767	+	309.936i	−0.604473	+	1.18749i
$262$	−539.016			−2.05731
$263$		−	165.415i		−	0.628954i	−0.949265	−	0.314477i	$-0.898171\pi$
$263$		−	165.415i		−	0.628954i	0.949265	−	0.314477i	$-0.101829\pi$
$264$	104.800	+	25.1385i	0.396969	+	0.0952217i
$265$	281.191			1.06110
$266$		−	375.680i		−	1.41233i
$267$	50.1008	−	208.865i	0.187644	−	0.782266i
$268$	−13.4960			−0.0503583
$269$		−	92.9279i		−	0.345457i	−0.984969	−	0.172728i	$-0.944742\pi$
$269$		−	92.9279i		−	0.345457i	0.984969	−	0.172728i	$-0.0552583\pi$
$270$	183.878	+	156.860i	0.681030	+	0.580964i
$271$	−320.804			−1.18378			−0.591889	−	0.806020i	$-0.701618\pi$
$271$	−320.804			−1.18378			−0.591889	+	0.806020i	$0.701618\pi$
$272$			242.794i			0.892625i
$273$	565.465	+	135.639i	2.07130	+	0.496847i
$274$	148.923			0.543515
$275$			69.5216i			0.252806i
$276$	−34.4470	+	143.606i	−0.124808	+	0.520312i
$277$	−330.812			−1.19427			−0.597133	−	0.802142i	$-0.703693\pi$
$277$	−330.812			−1.19427			−0.597133	+	0.802142i	$0.703693\pi$
$278$			214.670i			0.772193i
$279$	93.9293	+	47.8131i	0.336664	+	0.171373i
$280$	−204.736			−0.731199
$281$		−	214.789i		−	0.764373i	−0.924085	−	0.382186i	$-0.875171\pi$
$281$		−	214.789i		−	0.764373i	0.924085	−	0.382186i	$-0.124829\pi$
$282$	9.34505	+	2.24161i	0.0331385	+	0.00794898i
$283$	199.344			0.704397			0.352199	−	0.935925i	$-0.385434\pi$
$283$	199.344			0.704397			0.352199	+	0.935925i	$0.385434\pi$
$284$		−	211.872i		−	0.746030i
$285$	−42.8268	+	178.541i	−0.150270	+	0.626458i
$286$	304.460			1.06455
$287$			60.0551i			0.209251i
$288$	101.615	−	199.624i	0.352830	−	0.693138i
$289$	139.793			0.483712
$290$		−	345.912i		−	1.19280i
$291$	−346.590	−	83.1372i	−1.19103	−	0.285695i
$292$	−174.634			−0.598061
$293$			115.477i			0.394118i	0.980392	+	0.197059i	$0.0631391\pi$
$293$			115.477i			0.394118i	−0.980392	+	0.197059i	$0.936861\pi$
$294$	75.8797	−	316.334i	0.258094	−	1.07597i
$295$	221.793			0.751842
$296$			81.6913i			0.275984i
$297$	112.650	−	132.053i	0.379292	−	0.444622i
$298$	−396.330			−1.32997
$299$		−	594.926i		−	1.98972i
$300$	52.0165	+	12.4773i	0.173388	+	0.0415910i
$301$	−108.596			−0.360785
$302$			161.673i			0.535340i
$303$	−99.8179	+	416.130i	−0.329432	+	1.37337i
$304$	322.985			1.06245
$305$			136.638i			0.447995i
$306$	232.854	+	118.530i	0.760959	+	0.387353i
$307$	524.968			1.70999			0.854996	−	0.518634i	$-0.173559\pi$
$307$	524.968			1.70999			0.854996	+	0.518634i	$0.173559\pi$
$308$		−	103.107i		−	0.334765i
$309$	210.953	+	50.6017i	0.682696	+	0.163759i
$310$	−104.832			−0.338168
$311$			490.463i			1.57705i	0.615002	+	0.788526i	$0.289155\pi$
$311$			490.463i			1.57705i	−0.615002	+	0.788526i	$0.710845\pi$
$312$	−77.9204	+	324.842i	−0.249745	+	1.04116i
$313$	−593.678			−1.89673			−0.948367	−	0.317175i	$-0.897266\pi$
$313$	−593.678			−1.89673			−0.948367	+	0.317175i	$0.897266\pi$
$314$			433.758i			1.38139i
$315$	−149.583	+	293.857i	−0.474866	+	0.932879i
$316$	−193.321			−0.611775
$317$			314.640i			0.992556i	0.868164	+	0.496278i	$0.165300\pi$
$317$			314.640i			0.992556i	−0.868164	+	0.496278i	$0.834700\pi$
$318$	−517.639	−	124.167i	−1.62780	−	0.390462i
$319$	−248.418			−0.778739
$320$		−	76.6577i		−	0.239555i
$321$	−90.1079	+	375.650i	−0.280710	+	1.17025i
$322$	−690.256			−2.14365
$323$			198.488i			0.614513i
$324$	−78.5850	−	107.985i	−0.242546	−	0.333288i
$325$	−215.492			−0.663052
$326$		−	318.121i		−	0.975830i
$327$	−313.627	−	75.2303i	−0.959104	−	0.230062i
$328$	−34.4998			−0.105182
$329$			13.1109i			0.0398506i
$330$	−40.2695	+	167.879i	−0.122029	+	0.508725i
$331$	−10.0998			−0.0305129			−0.0152565	−	0.999884i	$-0.504856\pi$
$331$	−10.0998			−0.0305129			−0.0152565	+	0.999884i	$0.504856\pi$
$332$		−	93.7787i		−	0.282466i
$333$	117.252	+	59.6849i	0.352107	+	0.179234i
$334$	−81.8008			−0.244912
$335$			30.8292i			0.0920275i
$336$	564.050	+	135.300i	1.67872	+	0.402678i
$337$	−333.156			−0.988594			−0.494297	−	0.869293i	$-0.664574\pi$
$337$	−333.156			−0.988594			−0.494297	+	0.869293i	$0.664574\pi$
$338$			542.050i			1.60370i
$339$	−130.286	+	543.148i	−0.384324	+	1.60221i
$340$	−75.8557			−0.223105
$341$			75.2855i			0.220779i
$342$	157.678	−	309.761i	0.461048	−	0.905734i
$343$	−32.8383			−0.0957383
$344$		−	62.3851i		−	0.181352i
$345$	328.042	+	78.6880i	0.950846	+	0.228081i
$346$	261.859			0.756817
$347$		−	83.3785i		−	0.240284i	−0.992757	−	0.120142i	$-0.961665\pi$
$347$		−	83.3785i		−	0.240284i	0.992757	−	0.120142i	$-0.0383350\pi$
$348$	−44.5844	+	185.868i	−0.128116	+	0.534102i
$349$	−41.2805			−0.118282			−0.0591411	−	0.998250i	$-0.518836\pi$
$349$	−41.2805			−0.118282			−0.0591411	+	0.998250i	$0.518836\pi$
$350$			250.022i			0.714349i
$351$	409.316	+	349.173i	1.16614	+	0.994796i
$352$	160.001			0.454548
$353$		−	546.447i		−	1.54801i	−0.633180	−	0.774005i	$-0.718251\pi$
$353$		−	546.447i		−	1.54801i	0.633180	−	0.774005i	$-0.281749\pi$
$354$	−408.296	−	97.9386i	−1.15338	−	0.276663i
$355$	−483.984			−1.36333
$356$		−	118.049i		−	0.331598i
$357$	−83.1473	+	346.632i	−0.232906	+	0.970959i
$358$	735.845			2.05543
$359$			29.9422i			0.0834043i	0.999130	+	0.0417022i	$0.0132781\pi$
$359$			29.9422i			0.0834043i	−0.999130	+	0.0417022i	$0.986722\pi$
$360$	−168.812	−	85.9306i	−0.468921	−	0.238696i
$361$	−96.9553			−0.268574
$362$		−	38.4706i		−	0.106272i
$363$	−232.424	−	55.7519i	−0.640286	−	0.153587i
$364$	319.596			0.878011
$365$			398.919i			1.09293i
$366$	60.3363	−	251.536i	0.164853	−	0.687256i
$367$	180.381			0.491502			0.245751	−	0.969333i	$-0.420965\pi$
$367$	180.381			0.491502			0.245751	+	0.969333i	$0.420965\pi$
$368$		−	593.437i		−	1.61260i
$369$	−25.2060	+	49.5175i	−0.0683090	+	0.134194i
$370$	−130.862			−0.353680
$371$		−	726.234i		−	1.95750i
$372$	56.3291	+	13.5118i	0.151422	+	0.0363219i
$373$	405.844			1.08805			0.544027	−	0.839068i	$-0.316899\pi$
$373$	405.844			1.08805			0.544027	+	0.839068i	$0.316899\pi$
$374$			186.635i			0.499024i
$375$	94.3918	−	393.509i	0.251711	−	1.04936i
$376$	−7.53178			−0.0200313
$377$		−	770.005i		−	2.04245i
$378$	405.125	−	474.904i	1.07176	−	1.25636i
$379$	496.264			1.30940			0.654702	−	0.755887i	$-0.272794\pi$
$379$	496.264			1.30940			0.654702	+	0.755887i	$0.272794\pi$
$380$			100.910i			0.265552i
$381$	534.440	+	128.197i	1.40273	+	0.336475i
$382$	−658.343			−1.72341
$383$			212.915i			0.555915i	0.960593	+	0.277957i	$0.0896574\pi$
$383$			212.915i			0.555915i	−0.960593	+	0.277957i	$0.910343\pi$
$384$	−103.515	+	431.544i	−0.269571	+	1.12381i
$385$	−235.530			−0.611767
$386$			372.615i			0.965323i
$387$	−89.5413	−	45.5795i	−0.231373	−	0.117776i
$388$	−195.890			−0.504870
$389$		−	228.124i		−	0.586437i	−0.956045	−	0.293219i	$-0.905274\pi$
$389$		−	228.124i		−	0.586437i	0.956045	−	0.293219i	$-0.0947264\pi$
$390$	−520.365	−	124.821i	−1.33427	−	0.320054i
$391$	364.692			0.932715
$392$			254.954i			0.650394i
$393$	158.700	−	661.602i	0.403816	−	1.68347i
$394$	−301.373			−0.764906
$395$			441.606i			1.11799i
$396$	43.2757	−	85.0157i	0.109282	−	0.214686i
$397$	4.30743			0.0108500			0.00542498	−	0.999985i	$-0.498273\pi$
$397$	4.30743			0.0108500			0.00542498	+	0.999985i	$0.498273\pi$
$398$		−	234.590i		−	0.589422i
$399$	461.119	+	110.609i	1.15569	+	0.277217i
$400$	−214.953			−0.537382
$401$		−	353.290i		−	0.881022i	−0.897747	−	0.440511i	$-0.854797\pi$
$401$		−	353.290i		−	0.881022i	0.897747	−	0.440511i	$-0.145203\pi$
$402$	13.6134	−	56.7530i	0.0338643	−	0.141177i
$403$	−233.358			−0.579052
$404$			235.193i			0.582161i
$405$	−246.672	+	179.513i	−0.609068	+	0.443242i
$406$	−893.390			−2.20047
$407$			93.9786i			0.230906i
$408$	−199.129	−	47.7655i	−0.488062	−	0.117072i
$409$	−434.929			−1.06340			−0.531698	−	0.846934i	$-0.678446\pi$
$409$	−434.929			−1.06340			−0.531698	+	0.846934i	$0.678446\pi$
$410$		−	55.2652i		−	0.134793i
$411$	−43.8466	+	182.792i	−0.106683	+	0.444749i
$412$	119.229			0.289390
$413$		−	572.828i		−	1.38699i
$414$	−569.140	−	289.711i	−1.37473	−	0.699784i
$415$	−214.220			−0.516194
$416$			495.946i			1.19218i
$417$	−263.491	−	63.2041i	−0.631873	−	0.151569i
$418$	248.277			0.593965
$419$			228.130i			0.544462i	0.962232	+	0.272231i	$0.0877615\pi$
$419$			228.130i			0.544462i	−0.962232	+	0.272231i	$0.912239\pi$
$420$	−42.2714	+	176.225i	−0.100646	+	0.419584i
$421$	−604.828			−1.43664			−0.718322	−	0.695710i	$-0.755090\pi$
$421$	−604.828			−1.43664			−0.718322	+	0.695710i	$0.755090\pi$
$422$			279.611i			0.662586i
$423$	−5.50282	+	10.8104i	−0.0130090	+	0.0255564i
$424$	417.199			0.983959
$425$		−	132.097i		−	0.310817i
$426$	890.958	+	213.716i	2.09145	+	0.501680i
$427$	352.898			0.826459
$428$			212.314i			0.496061i
$429$	−89.6405	+	373.702i	−0.208952	+	0.871100i
$430$	99.9348			0.232407
$431$		−	123.936i		−	0.287554i	−0.989610	−	0.143777i	$-0.954075\pi$
$431$		−	123.936i		−	0.287554i	0.989610	−	0.143777i	$-0.0459247\pi$
$432$	408.292	+	348.300i	0.945119	+	0.806249i
$433$	−146.653			−0.338690			−0.169345	−	0.985557i	$-0.554165\pi$
$433$	−146.653			−0.338690			−0.169345	+	0.985557i	$0.554165\pi$
$434$			270.751i			0.623851i
$435$	424.581	+	101.845i	0.976048	+	0.234126i
$436$	−177.259			−0.406558
$437$		−	485.143i		−	1.11017i
$438$	176.153	−	734.363i	0.402176	−	1.67663i
$439$	196.544			0.447708			0.223854	−	0.974623i	$-0.428136\pi$
$439$	196.544			0.447708			0.223854	+	0.974623i	$0.428136\pi$
$440$		−	135.305i		−	0.307511i
$441$	365.936	+	186.273i	0.829787	+	0.422388i
$442$	−578.502			−1.30883
$443$			55.5423i			0.125378i	0.998033	+	0.0626889i	$0.0199676\pi$
$443$			55.5423i			0.125378i	−0.998033	+	0.0626889i	$0.980032\pi$
$444$	70.3154	+	16.8667i	0.158368	+	0.0379880i
$445$	−269.661			−0.605979
$446$		−	861.609i		−	1.93186i
$447$	116.689	−	486.465i	0.261050	−	1.08829i
$448$	−197.985			−0.441930
$449$			222.399i			0.495320i	0.968847	+	0.247660i	$0.0796616\pi$
$449$			222.399i			0.495320i	−0.968847	+	0.247660i	$0.920338\pi$
$450$	−104.938	+	206.152i	−0.233196	+	0.458115i
$451$	−39.6889			−0.0880020
$452$			306.983i			0.679165i
$453$	−198.441	−	47.6004i	−0.438060	−	0.105078i
$454$	88.7442			0.195472
$455$		−	730.059i		−	1.60452i
$456$	−63.5416	+	264.898i	−0.139346	+	0.580917i
$457$	181.967			0.398177			0.199089	−	0.979981i	$-0.436202\pi$
$457$	181.967			0.398177			0.199089	+	0.979981i	$0.436202\pi$
$458$			863.020i			1.88432i
$459$	−214.045	+	250.912i	−0.466328	+	0.546650i
$460$	185.406			0.403057
$461$			392.741i			0.851933i	0.904739	+	0.425966i	$0.140066\pi$
$461$			392.741i			0.851933i	−0.904739	+	0.425966i	$0.859934\pi$
$462$	433.584	+	104.004i	0.938493	+	0.225118i
$463$	−64.9453			−0.140271			−0.0701354	−	0.997537i	$-0.522343\pi$
$463$	−64.9453			−0.140271			−0.0701354	+	0.997537i	$0.522343\pi$
$464$		−	768.078i		−	1.65534i
$465$	30.8652	−	128.674i	0.0663767	−	0.276717i
$466$	−402.981			−0.864766
$467$		−	260.604i		−	0.558039i	−0.960286	−	0.279019i	$-0.909991\pi$
$467$		−	260.604i		−	0.558039i	0.960286	−	0.279019i	$-0.0900093\pi$
$468$	263.518	+	134.139i	0.563073	+	0.286622i
$469$	79.6230			0.169772
$470$		−	12.0652i		−	0.0256706i
$471$	−532.405	−	127.709i	−1.13037	−	0.271144i
$472$	329.072			0.697186
$473$		−	71.7685i		−	0.151731i
$474$	195.003	−	812.946i	0.411398	−	1.71508i
$475$	−175.727			−0.369951
$476$			195.914i			0.411583i
$477$	304.811	−	598.805i	0.639018	−	1.25536i
$478$	435.206			0.910473
$479$			324.065i			0.676546i	0.941048	+	0.338273i	$0.109843\pi$
$479$			324.065i			0.676546i	−0.941048	+	0.338273i	$0.890157\pi$
$480$	−273.464	−	65.5964i	−0.569717	−	0.136659i
$481$	−291.300			−0.605613
$482$		−	26.1458i		−	0.0542444i
$483$	203.228	−	847.238i	0.420763	−	1.75412i
$484$	−131.364			−0.271413
$485$			447.474i			0.922627i
$486$	533.364	−	221.538i	1.09746	−	0.455840i
$487$	−372.910			−0.765729			−0.382865	−	0.923804i	$-0.625062\pi$
$487$	−372.910			−0.765729			−0.382865	+	0.923804i	$0.625062\pi$
$488$			202.729i			0.415428i
$489$	390.469	+	93.6625i	0.798506	+	0.191539i
$490$	−408.412			−0.833494
$491$			241.715i			0.492290i	0.969233	+	0.246145i	$0.0791640\pi$
$491$			241.715i			0.492290i	−0.969233	+	0.246145i	$0.920836\pi$
$492$	−7.12311	+	29.6955i	−0.0144779	+	0.0603567i
$493$	472.016			0.957436
$494$			769.571i			1.55784i
$495$	−194.203	−	98.8555i	−0.392329	−	0.199708i
$496$	−232.774			−0.469302
$497$			1249.99i			2.51507i
$498$	394.355	+	94.5946i	0.791877	+	0.189949i
$499$	231.947			0.464825			0.232412	−	0.972617i	$-0.425338\pi$
$499$	231.947			0.464825			0.232412	+	0.972617i	$0.425338\pi$
$500$		−	222.408i		−	0.444816i
$501$	24.0842	−	100.404i	0.0480722	−	0.200408i
$502$	396.380			0.789602
$503$		−	666.213i		−	1.32448i	−0.749292	−	0.662240i	$-0.769606\pi$
$503$		−	666.213i		−	1.32448i	0.749292	−	0.662240i	$-0.230394\pi$
$504$	−221.934	+	435.992i	−0.440345	+	0.865063i
$505$	537.256			1.06387
$506$		−	456.173i		−	0.901528i
$507$	−665.326	−	159.593i	−1.31228	−	0.314779i
$508$	302.061			0.594608
$509$		−	549.506i		−	1.07958i	−0.841800	−	0.539790i	$-0.818504\pi$
$509$		−	549.506i		−	1.07958i	0.841800	−	0.539790i	$-0.181496\pi$
$510$	76.5157	−	318.986i	0.150031	−	0.625462i
$511$	1030.29			2.01623
$512$			50.4102i			0.0984575i
$513$	333.784	+	284.740i	0.650651	+	0.555048i
$514$	768.202			1.49456
$515$		−	272.356i		−	0.528847i
$516$	−53.6977	−	12.8806i	−0.104065	−	0.0249623i
$517$	−8.66464			−0.0167595
$518$			337.978i			0.652466i
$519$	−77.0977	+	321.412i	−0.148550	+	0.619291i
$520$	419.396			0.806530
$521$		−	795.439i		−	1.52675i	−0.645953	−	0.763377i	$-0.723540\pi$
$521$		−	795.439i		−	1.52675i	0.645953	−	0.763377i	$-0.276460\pi$
$522$	−736.631	−	374.969i	−1.41117	−	0.718332i
$523$	−945.016			−1.80691			−0.903457	−	0.428678i	$-0.858980\pi$
$523$	−945.016			−1.80691			−0.903457	+	0.428678i	$0.858980\pi$
$524$		−	373.932i		−	0.713610i
$525$	−306.883	−	73.6127i	−0.584540	−	0.140215i
$526$	393.145			0.747424
$527$		−	143.049i		−	0.271441i
$528$	−89.4162	+	372.767i	−0.169349	+	0.705997i
$529$	−362.378			−0.685025
$530$			668.311i			1.26096i
$531$	240.425	−	472.317i	0.452777	−	0.889485i
$532$	260.620			0.489888
$533$		−	123.021i		−	0.230809i
$534$	496.414	+	119.076i	0.929614	+	0.222988i
$535$	484.993			0.906529
$536$			45.7409i			0.0853375i
$537$	−216.651	+	903.195i	−0.403447	+	1.68193i
$538$	220.864			0.410527
$539$			293.302i			0.544160i
$540$	−108.819	+	127.562i	−0.201516	+	0.236226i
$541$	−185.288			−0.342492			−0.171246	−	0.985228i	$-0.554779\pi$
$541$	−185.288			−0.342492			−0.171246	+	0.985228i	$0.554779\pi$
$542$		−	762.461i		−	1.40675i
$543$	47.2198	+	11.3267i	0.0869609	+	0.0208595i
$544$	−304.017			−0.558854
$545$			404.916i			0.742966i
$546$	−322.376	+	1343.95i	−0.590433	+	2.46145i
$547$	−926.684			−1.69412			−0.847061	−	0.531496i	$-0.821630\pi$
$547$	−926.684			−1.69412			−0.847061	+	0.531496i	$0.821630\pi$
$548$			103.312i			0.188526i
$549$	290.977	+	148.117i	0.530012	+	0.269793i
$550$	−165.233			−0.300424
$551$		−	627.915i		−	1.13959i
$552$	486.711	+	116.748i	0.881723	+	0.211501i
$553$	1140.54			2.06246
$554$		−	786.247i		−	1.41922i
$555$	38.5289	−	160.623i	0.0694214	−	0.289410i
$556$	−148.923			−0.267847
$557$		−	579.691i		−	1.04074i	−0.853942	−	0.520369i	$-0.825794\pi$
$557$		−	579.691i		−	1.04074i	0.853942	−	0.520369i	$-0.174206\pi$
$558$	−113.638	+	223.244i	−0.203653	+	0.400078i
$559$	222.457			0.397955
$560$		−	728.232i		−	1.30041i
$561$	−229.081	−	54.9500i	−0.408343	−	0.0979500i
$562$	510.493			0.908350
$563$			989.788i			1.75806i	0.476765	+	0.879031i	$0.341809\pi$
$563$			989.788i			1.75806i	−0.476765	+	0.879031i	$0.658191\pi$
$564$	−1.55507	+	6.48294i	−0.00275722	+	0.0114946i
$565$	701.246			1.24114
$566$			473.786i			0.837078i
$567$	463.631	+	637.084i	0.817691	+	1.12360i
$568$	−718.080			−1.26423
$569$			838.459i			1.47357i	0.676129	+	0.736783i	$0.263656\pi$
$569$			838.459i			1.47357i	−0.676129	+	0.736783i	$0.736344\pi$
$570$	−424.341	−	101.787i	−0.744458	−	0.178574i
$571$	205.255			0.359466			0.179733	−	0.983715i	$-0.442477\pi$
$571$	205.255			0.359466			0.179733	+	0.983715i	$0.442477\pi$
$572$			211.213i			0.369254i
$573$	193.832	−	808.067i	0.338277	−	1.41024i
$574$	−142.734			−0.248666
$575$			322.872i			0.561516i
$576$	−163.245	−	83.0972i	−0.283412	−	0.144266i
$577$	879.703			1.52461			0.762307	−	0.647215i	$-0.224067\pi$
$577$	879.703			1.52461			0.762307	+	0.647215i	$0.224067\pi$
$578$			332.249i			0.574825i
$579$	−457.357	−	109.707i	−0.789908	−	0.189477i
$580$	239.969			0.413740
$581$			553.270i			0.952271i
$582$	197.594	−	823.748i	0.339508	−	1.41537i
$583$	479.950			0.823242
$584$			591.871i			1.01348i
$585$	306.417	−	601.959i	0.523789	−	1.02899i
$586$	−274.456			−0.468355
$587$			972.376i			1.65652i	0.560346	+	0.828259i	$0.310668\pi$
$587$			972.376i			1.65652i	−0.560346	+	0.828259i	$0.689332\pi$
$588$	219.451	+	52.6400i	0.373215	+	0.0895238i
$589$	−190.296			−0.323083
$590$			527.141i			0.893459i
$591$	88.7316	−	369.913i	0.150138	−	0.625910i
$592$	−290.571			−0.490829
$593$		−	171.805i		−	0.289722i	−0.989452	−	0.144861i	$-0.953726\pi$
$593$		−	171.805i		−	0.289722i	0.989452	−	0.144861i	$-0.0462736\pi$
$594$	313.852	+	267.737i	0.528371	+	0.450735i
$595$	447.529			0.752149
$596$		−	274.946i		−	0.461318i
$597$	287.942	+	69.0691i	0.482315	+	0.115694i
$598$	1413.97			2.36450
$599$			907.589i			1.51517i	0.652734	+	0.757587i	$0.273622\pi$
$599$			907.589i			1.51517i	−0.652734	+	0.757587i	$0.726378\pi$
$600$	42.2882	−	176.295i	0.0704803	−	0.293825i
$601$	−607.994			−1.01164			−0.505819	−	0.862640i	$-0.668810\pi$
$601$	−607.994			−1.01164			−0.505819	+	0.862640i	$0.668810\pi$
$602$		−	258.103i		−	0.428742i
$603$	65.6519	+	33.4190i	0.108875	+	0.0554212i
$604$	−112.157			−0.185691
$605$			300.077i			0.495995i
$606$	−989.025	−	237.239i	−1.63205	−	0.391484i
$607$	−1027.14			−1.69215			−0.846077	−	0.533061i	$-0.821041\pi$
$607$	−1027.14			−1.69215			−0.846077	+	0.533061i	$0.821041\pi$
$608$			404.428i			0.665178i
$609$	263.036	−	1096.57i	0.431915	−	1.80061i
$610$	−324.752			−0.532380
$611$		−	26.8573i		−	0.0439562i
$612$	−82.2278	+	161.537i	−0.134359	+	0.263950i
$613$	982.822			1.60330			0.801649	−	0.597795i	$-0.203956\pi$
$613$	982.822			1.60330			0.801649	+	0.597795i	$0.203956\pi$
$614$			1247.70i			2.03209i
$615$	67.8339	+	16.2714i	0.110299	+	0.0264576i
$616$	−349.453			−0.567294
$617$		−	891.078i		−	1.44421i	−0.691783	−	0.722105i	$-0.743175\pi$
$617$		−	891.078i		−	1.44421i	0.691783	−	0.722105i	$-0.256825\pi$
$618$	−120.266	+	501.376i	−0.194605	+	0.811289i
$619$	694.526			1.12201			0.561006	−	0.827811i	$-0.310414\pi$
$619$	694.526			1.12201			0.561006	+	0.827811i	$0.310414\pi$
$620$		−	72.7252i		−	0.117299i
$621$	523.167	−	613.279i	0.842459	−	0.987566i
$622$	−1165.69			−1.87411
$623$			696.456i			1.11791i
$624$	−1155.44	−	277.158i	−1.85167	−	0.444163i
$625$	−237.692			−0.380308
$626$		−	1411.01i		−	2.25400i
$627$	−73.0990	+	304.742i	−0.116585	+	0.486032i
$628$	−300.911			−0.479157
$629$		−	178.568i		−	0.283892i
$630$	−698.416	−	355.517i	−1.10860	−	0.564312i
$631$	−164.099			−0.260062			−0.130031	−	0.991510i	$-0.541508\pi$
$631$	−164.099			−0.260062			−0.130031	+	0.991510i	$0.541508\pi$
$632$			655.206i			1.03672i
$633$	−343.202	−	82.3244i	−0.542183	−	0.130054i
$634$	−747.812			−1.17951
$635$		−	690.003i		−	1.08662i
$636$	86.1384	−	359.102i	0.135438	−	0.564625i
$637$	−909.132			−1.42721
$638$		−	590.419i		−	0.925422i
$639$	−524.640	+	1030.66i	−0.821033	+	1.61293i
$640$	557.156			0.870557
$641$		−	345.410i		−	0.538861i	−0.963020	−	0.269430i	$-0.913165\pi$
$641$		−	345.410i		−	0.538861i	0.963020	−	0.269430i	$-0.0868354\pi$
$642$	−892.816	−	214.161i	−1.39068	−	0.333585i
$643$	−447.033			−0.695230			−0.347615	−	0.937637i	$-0.613008\pi$
$643$	−447.033			−0.695230			−0.347615	+	0.937637i	$0.613008\pi$
$644$		−	478.851i		−	0.743558i
$645$	−29.4233	+	122.663i	−0.0456175	+	0.190174i
$646$	−471.750			−0.730263
$647$		−	508.173i		−	0.785430i	−0.919660	−	0.392715i	$-0.871536\pi$
$647$		−	508.173i		−	0.785430i	0.919660	−	0.392715i	$-0.128464\pi$
$648$	−365.985	+	266.341i	−0.564791	+	0.411021i
$649$	378.568			0.583309
$650$		−	512.164i		−	0.787945i
$651$	−332.327	−	79.7158i	−0.510487	−	0.122451i
$652$	220.690			0.338481
$653$			739.707i			1.13278i	0.824136	+	0.566391i	$0.191661\pi$
$653$			739.707i			1.13278i	−0.824136	+	0.566391i	$0.808339\pi$
$654$	178.801	−	745.404i	0.273397	−	1.13976i
$655$	−854.179			−1.30409
$656$		−	122.713i		−	0.187063i
$657$	849.512	+	432.429i	1.29302	+	0.658188i
$658$	−31.1609			−0.0473569
$659$			554.974i			0.842146i	0.907027	+	0.421073i	$0.138346\pi$
$659$			554.974i			0.842146i	−0.907027	+	0.421073i	$0.861654\pi$
$660$	−116.463	−	27.9361i	−0.176459	−	0.0423275i
$661$	−370.474			−0.560476			−0.280238	−	0.959931i	$-0.590413\pi$
$661$	−370.474			−0.560476			−0.280238	+	0.959931i	$0.590413\pi$
$662$		−	24.0044i		−	0.0362604i
$663$	170.325	−	710.067i	0.256901	−	1.07099i
$664$	−317.836			−0.478669
$665$		−	595.340i		−	0.895248i
$666$	−141.854	+	278.674i	−0.212994	+	0.418430i
$667$	−1153.70			−1.72969
$668$		−	56.7476i		−	0.0849516i
$669$	1057.56	+	253.679i	1.58081	+	0.379191i
$670$	−73.2724			−0.109362
$671$			233.221i			0.347573i
$672$	−169.417	+	706.280i	−0.252108	+	1.05101i
$673$	−221.928			−0.329759			−0.164879	−	0.986314i	$-0.552723\pi$
$673$	−221.928			−0.329759			−0.164879	+	0.986314i	$0.552723\pi$
$674$		−	791.819i		−	1.17481i
$675$	−222.140	−	189.500i	−0.329096	−	0.280740i
$676$	−376.037			−0.556267
$677$		−	1040.16i		−	1.53642i	−0.640199	−	0.768209i	$-0.721148\pi$
$677$		−	1040.16i		−	1.53642i	0.640199	−	0.768209i	$-0.278852\pi$
$678$	−1290.91	−	309.653i	−1.90400	−	0.456716i
$679$	1155.70			1.70206
$680$			257.091i			0.378075i
$681$	−26.1285	+	108.927i	−0.0383678	+	0.159951i
$682$	−178.933			−0.262365
$683$			590.665i			0.864810i	0.901680	+	0.432405i	$0.142335\pi$
$683$			590.665i			0.864810i	−0.901680	+	0.432405i	$0.857665\pi$
$684$	214.891	+	109.386i	0.314167	+	0.159921i
$685$	235.998			0.344523
$686$		−	78.0474i		−	0.113772i
$687$	−1059.29	−	254.094i	−1.54191	−	0.369861i
$688$	221.900			0.322529
$689$			1487.67i			2.15918i
$690$	−187.019	+	779.664i	−0.271043	+	1.12995i
$691$	−50.2634			−0.0727401			−0.0363700	−	0.999338i	$-0.511579\pi$
$691$	−50.2634			−0.0727401			−0.0363700	+	0.999338i	$0.511579\pi$
$692$			181.659i			0.262513i
$693$	−255.315	+	501.570i	−0.368420	+	0.723766i
$694$	198.167			0.285544
$695$			340.187i			0.489478i
$696$	629.945	+	151.106i	0.905093	+	0.217106i
$697$	75.4125			0.108196
$698$		−	98.1121i		−	0.140562i
$699$	118.648	−	494.629i	0.169739	−	0.707624i
$700$	−173.448			−0.247783
$701$		−	673.977i		−	0.961450i	−0.876871	−	0.480725i	$-0.840373\pi$
$701$		−	673.977i		−	0.961450i	0.876871	−	0.480725i	$-0.159627\pi$
$702$	−829.888	+	972.830i	−1.18218	+	1.38580i
$703$	−237.546			−0.337903
$704$		−	130.843i		−	0.185857i
$705$	14.8091	+	3.55228i	0.0210058	+	0.00503870i
$706$	1298.75			1.83959
$707$		−	1387.58i		−	1.96263i
$708$	67.9429	−	283.247i	0.0959646	−	0.400066i
$709$	837.017			1.18056			0.590280	−	0.807199i	$-0.299017\pi$
$709$	837.017			1.18056			0.590280	+	0.807199i	$0.299017\pi$
$710$		−	1150.29i		−	1.62013i
$711$	940.417	+	478.703i	1.32267	+	0.673281i
$712$	−400.092			−0.561927
$713$			349.641i			0.490380i
$714$	−823.848	−	197.618i	−1.15385	−	0.276776i
$715$	482.478			0.674794
$716$			510.478i			0.712958i
$717$	−128.135	+	534.183i	−0.178710	+	0.745025i
$718$	−71.1641			−0.0991144
$719$		−	1332.80i		−	1.85369i	−0.375447	−	0.926844i	$-0.622511\pi$
$719$		−	1332.80i		−	1.85369i	0.375447	−	0.926844i	$-0.377489\pi$
$720$	305.650	−	600.452i	0.424513	−	0.833961i
$721$	−703.418			−0.975615
$722$		−	230.436i		−	0.319163i
$723$	32.0920	+	7.69797i	0.0443873	+	0.0106473i
$724$	26.6882			0.0368622
$725$			417.889i			0.576399i
$726$	132.507	−	552.407i	0.182516	−	0.760891i
$727$	1178.15			1.62056			0.810281	−	0.586041i	$-0.199314\pi$
$727$	1178.15			1.62056			0.810281	+	0.586041i	$0.199314\pi$
$728$		−	1083.18i		−	1.48788i
$729$	114.886	+	719.890i	0.157594	+	0.987504i
$730$	−948.119			−1.29879
$731$			136.367i			0.186548i
$732$	174.498	+	41.8571i	0.238385	+	0.0571818i
$733$	392.919			0.536043			0.268021	−	0.963413i	$-0.413630\pi$
$733$	392.919			0.536043			0.268021	+	0.963413i	$0.413630\pi$
$734$			428.716i			0.584082i
$735$	120.247	−	501.295i	0.163601	−	0.682034i
$736$	743.076			1.00961
$737$			52.6208i			0.0713987i
$738$	−117.689	−	59.9077i	−0.159471	−	0.0811757i
$739$	−787.654			−1.06584			−0.532919	−	0.846167i	$-0.678905\pi$
$739$	−787.654			−1.06584			−0.532919	+	0.846167i	$0.678905\pi$
$740$		−	90.7825i		−	0.122679i
$741$	−944.590	−	226.581i	−1.27475	−	0.305777i
$742$	1726.06			2.32622
$743$		−	188.675i		−	0.253937i	−0.991907	−	0.126968i	$-0.959475\pi$
$743$		−	188.675i		−	0.253937i	0.991907	−	0.126968i	$-0.0405247\pi$
$744$	45.7942	−	190.911i	0.0615514	−	0.256601i
$745$	−628.063			−0.843038
$746$			964.578i			1.29300i
$747$	−232.216	+	456.190i	−0.310864	+	0.610696i
$748$	−129.474			−0.173094
$749$		−	1252.60i		−	1.67236i
$750$	935.262	+	224.343i	1.24702	+	0.299124i
$751$	−620.652			−0.826434			−0.413217	−	0.910633i	$-0.635595\pi$
$751$	−620.652			−0.826434			−0.413217	+	0.910633i	$0.635595\pi$
$752$		−	26.7901i		−	0.0356251i
$753$	−116.704	+	486.527i	−0.154986	+	0.646118i
$754$	1830.09			2.42717
$755$			256.203i			0.339341i
$756$	329.455	+	281.047i	0.435788	+	0.371755i
$757$	−135.808			−0.179403			−0.0897015	−	0.995969i	$-0.528591\pi$
$757$	−135.808			−0.179403			−0.0897015	+	0.995969i	$0.528591\pi$
$758$			1179.48i			1.55604i
$759$	559.918	+	134.309i	0.737705	+	0.176955i
$760$	342.004			0.450005
$761$			449.571i			0.590764i	0.955379	+	0.295382i	$0.0954469\pi$
$761$			449.571i			0.590764i	−0.955379	+	0.295382i	$0.904553\pi$
$762$	−304.689	+	1270.21i	−0.399854	+	1.66695i
$763$	1045.78			1.37062
$764$		−	456.712i		−	0.597791i
$765$	369.003	+	187.834i	0.482357	+	0.245535i
$766$	−506.040			−0.660627
$767$			1173.42i			1.52989i
$768$	−788.159	−	189.057i	−1.02625	−	0.246168i
$769$	−523.756			−0.681088			−0.340544	−	0.940229i	$-0.610611\pi$
$769$	−523.756			−0.681088			−0.340544	+	0.940229i	$0.610611\pi$
$770$		−	559.789i		−	0.726999i
$771$	−226.178	+	942.910i	−0.293356	+	1.22297i
$772$	−258.494			−0.334837
$773$		−	1319.96i		−	1.70758i	−0.520618	−	0.853790i	$-0.674298\pi$
$773$		−	1319.96i		−	1.70758i	0.520618	−	0.853790i	$-0.325702\pi$
$774$	108.330	−	212.815i	0.139961	−	0.274955i
$775$	126.646			0.163414
$776$			663.912i			0.855556i
$777$	−414.842	−	99.5089i	−0.533902	−	0.128068i
$778$	542.187			0.696899
$779$		−	100.320i		−	0.128780i
$780$	86.5920	−	360.993i	0.111015	−	0.462811i
$781$	−826.088			−1.05773
$782$			866.770i			1.10840i
$783$	677.129	−	793.760i	0.864788	−	1.01374i
$784$	−906.856			−1.15670
$785$			687.375i			0.875637i
$786$	1572.44	+	377.185i	2.00056	+	0.479879i
$787$	899.843			1.14338			0.571692	−	0.820468i	$-0.306287\pi$
$787$	899.843			1.14338			0.571692	+	0.820468i	$0.306287\pi$
$788$		−	209.071i		−	0.265319i
$789$	−115.752	+	482.556i	−0.146707	+	0.611604i
$790$	−1049.58			−1.32858
$791$		−	1811.12i		−	2.28965i
$792$	−288.136	−	146.671i	−0.363808	−	0.185190i
$793$	−722.902			−0.911604
$794$			10.2376i			0.0128937i
$795$	−820.302	−	196.767i	−1.03183	−	0.247506i
$796$	162.742			0.204450
$797$			838.270i			1.05178i	0.850552	+	0.525891i	$0.176268\pi$
$797$			838.270i			1.05178i	−0.850552	+	0.525891i	$0.823732\pi$
$798$	−262.888	+	1095.95i	−0.329433	+	1.37337i
$799$	16.4636			0.0206053
$800$		−	269.155i		−	0.336443i
$801$	−292.313	+	574.252i	−0.364935	+	0.716919i
$802$	839.671			1.04697
$803$			680.895i			0.847939i
$804$	39.3712	+	9.44405i	0.0489692	+	0.0117463i
$805$	−1093.85			−1.35882
$806$		−	554.627i		−	0.688123i
$807$	−65.0277	+	271.094i	−0.0805796	+	0.335928i
$808$	797.119			0.986534
$809$		−	194.037i		−	0.239848i	−0.992783	−	0.119924i	$-0.961735\pi$
$809$		−	194.037i		−	0.239848i	0.992783	−	0.119924i	$-0.0382651\pi$
$810$	−426.653	−	586.271i	−0.526732	−	0.723792i
$811$	979.185			1.20738			0.603690	−	0.797219i	$-0.293697\pi$
$811$	979.185			1.20738			0.603690	+	0.797219i	$0.293697\pi$
$812$		−	619.772i		−	0.763266i
$813$	935.864	+	224.487i	1.15112	+	0.276122i
$814$	−223.361			−0.274399
$815$		−	504.126i		−	0.618559i
$816$	169.899	−	708.290i	0.208209	−	0.868003i
$817$	181.406			0.222040
$818$		−	1033.70i		−	1.26370i
$819$	−1554.69	−	791.386i	−1.89827	−	0.966283i
$820$	38.3391			0.0467551
$821$			9.41351i			0.0114659i	0.999984	+	0.00573295i	$0.00182487\pi$
$821$			9.41351i			0.0114659i	−0.999984	+	0.00573295i	$0.998175\pi$
$822$	−434.446	−	104.211i	−0.528523	−	0.126778i
$823$	1307.15			1.58827			0.794136	−	0.607740i	$-0.207924\pi$
$823$	1307.15			1.58827			0.794136	+	0.607740i	$0.207924\pi$
$824$		−	404.092i		−	0.490402i
$825$	48.6488	−	202.812i	0.0589682	−	0.245832i
$826$	1361.45			1.64825
$827$			1318.83i			1.59472i	0.603505	+	0.797359i	$0.293770\pi$
$827$			1318.83i			1.59472i	−0.603505	+	0.797359i	$0.706230\pi$
$828$	200.981	−	394.829i	0.242731	−	0.476847i
$829$	−1511.44			−1.82320			−0.911601	−	0.411075i	$-0.865153\pi$
$829$	−1511.44			−1.82320			−0.911601	+	0.411075i	$0.865153\pi$
$830$		−	509.142i		−	0.613424i
$831$	965.059	+	231.490i	1.16132	+	0.278569i
$832$	405.567			0.487460
$833$		−	557.301i		−	0.669029i
$834$	150.218	−	626.245i	0.180118	−	0.750893i
$835$	−129.630			−0.155245
$836$			172.238i			0.206026i
$837$	−240.557	−	205.211i	−0.287404	−	0.245174i
$838$	−542.200			−0.647017
$839$			1441.85i			1.71853i	0.511527	+	0.859267i	$0.329080\pi$
$839$			1441.85i			1.71853i	−0.511527	+	0.859267i	$0.670920\pi$
$840$	597.264	+	143.267i	0.711029	+	0.170556i
$841$	−652.221			−0.775530
$842$		−	1437.51i		−	1.70725i
$843$	−150.302	+	626.592i	−0.178294	+	0.743288i
$844$	−193.975			−0.229828
$845$			858.987i			1.01655i
$846$	−25.6932	−	13.0787i	−0.0303702	−	0.0154594i
$847$	775.012			0.915009
$848$			1483.95i			1.74994i
$849$	−581.537	−	139.494i	−0.684967	−	0.164304i
$850$	313.958			0.369363
$851$			436.455i			0.512873i
$852$	−148.261	+	618.084i	−0.174015	+	0.725451i
$853$	380.381			0.445934			0.222967	−	0.974826i	$-0.428426\pi$
$853$	380.381			0.445934			0.222967	+	0.974826i	$0.428426\pi$
$854$			838.740i			0.982131i
$855$	249.873	−	490.878i	0.292249	−	0.574127i
$856$	719.578			0.840628
$857$			977.992i			1.14118i	0.821235	+	0.570590i	$0.193286\pi$
$857$			977.992i			1.14118i	−0.821235	+	0.570590i	$0.806714\pi$
$858$	−888.185	−	213.051i	−1.03518	−	0.248311i
$859$	493.660			0.574691			0.287346	−	0.957827i	$-0.407227\pi$
$859$	493.660			0.574691			0.287346	+	0.957827i	$0.407227\pi$
$860$			69.3278i			0.0806137i
$861$	42.0245	−	175.196i	0.0488089	−	0.203479i
$862$	294.560			0.341717
$863$		−	992.547i		−	1.15011i	−0.818114	−	0.575056i	$-0.804980\pi$
$863$		−	992.547i		−	1.15011i	0.818114	−	0.575056i	$-0.195020\pi$
$864$	−436.126	+	511.245i	−0.504775	+	0.591719i
$865$	414.967			0.479731
$866$		−	348.553i		−	0.402486i
$867$	−407.810	−	97.8222i	−0.470370	−	0.112828i
$868$	−187.828			−0.216392
$869$			753.756i			0.867383i
$870$	−242.057	+	1009.11i	−0.278226	+	1.15990i
$871$	−163.106			−0.187263
$872$			600.769i			0.688956i
$873$	952.913	+	485.063i	1.09154	+	0.555628i
$874$	1153.05			1.31928
$875$			1312.15i			1.49960i
$876$	509.450	+	122.203i	0.581564	+	0.139501i
$877$	463.028			0.527968			0.263984	−	0.964527i	$-0.414963\pi$
$877$	463.028			0.527968			0.263984	+	0.964527i	$0.414963\pi$
$878$			467.130i			0.532039i
$879$	80.8066	−	336.874i	0.0919301	−	0.383247i
$880$	481.270			0.546898
$881$		−	699.997i		−	0.794548i	−0.917700	−	0.397274i	$-0.869956\pi$
$881$		−	699.997i		−	0.794548i	0.917700	−	0.397274i	$-0.130044\pi$
$882$	−442.720	+	869.728i	−0.501950	+	0.986086i
$883$	−406.667			−0.460552			−0.230276	−	0.973125i	$-0.573963\pi$
$883$	−406.667			−0.460552			−0.230276	+	0.973125i	$0.573963\pi$
$884$		−	401.324i		−	0.453986i
$885$	−647.026	−	155.203i	−0.731102	−	0.175371i
$886$	−132.009			−0.148994
$887$		−	131.822i		−	0.148615i	−0.997235	−	0.0743076i	$-0.976325\pi$
$887$		−	131.822i		−	0.148615i	0.997235	−	0.0743076i	$-0.0236747\pi$
$888$	57.1648	−	238.314i	0.0643747	−	0.268371i
$889$	−1782.08			−2.00459
$890$		−	640.908i		−	0.720122i
$891$	−421.033	+	306.402i	−0.472540	+	0.343886i
$892$	597.724			0.670094
$893$		−	21.9012i		−	0.0245255i
$894$	1156.19	+	277.338i	1.29328	+	0.310221i
$895$	1166.09			1.30290
$896$		−	1438.97i		−	1.60600i
$897$	−416.308	+	1735.54i	−0.464112	+	1.93483i
$898$	−528.580			−0.588619
$899$			452.536i			0.503377i
$900$	−143.014	−	72.7987i	−0.158904	−	0.0808874i
$901$	−911.949			−1.01215
$902$		−	94.3295i		−	0.104578i
$903$	316.802	+	75.9919i	0.350833	+	0.0841549i
$904$	1040.43			1.15092
$905$		−	60.9643i		−	0.0673639i
$906$	113.133	−	471.639i	0.124871	−	0.520573i
$907$	−153.372			−0.169098			−0.0845492	−	0.996419i	$-0.526945\pi$
$907$	−153.372			−0.169098			−0.0845492	+	0.996419i	$0.526945\pi$
$908$			61.5645i			0.0678023i
$909$	582.387	−	1144.10i	0.640689	−	1.25864i
$910$	1735.15			1.90675
$911$		−	1488.44i		−	1.63385i	−0.576743	−	0.816926i	$-0.695677\pi$
$911$		−	1488.44i		−	1.63385i	0.576743	−	0.816926i	$-0.304323\pi$
$912$	−942.226	−	226.014i	−1.03314	−	0.247822i
$913$	−365.642			−0.400484
$914$			432.485i			0.473178i
$915$	95.6148	−	398.608i	0.104497	−	0.435637i
$916$	−598.703			−0.653606
$917$			2206.10i			2.40578i
$918$	−596.348	−	508.724i	−0.649617	−	0.554166i
$919$	1108.72			1.20645			0.603223	−	0.797572i	$-0.293883\pi$
$919$	1108.72			1.20645			0.603223	+	0.797572i	$0.293883\pi$
$920$		−	628.381i		−	0.683023i
$921$	−1531.46	−	367.354i	−1.66282	−	0.398865i
$922$	−933.436			−1.01240
$923$		−	2560.57i		−	2.77419i
$924$	−72.1510	+	300.790i	−0.0780855	+	0.325530i
$925$	158.091			0.170910
$926$		−	154.357i		−	0.166692i
$927$	−579.993	−	295.235i	−0.625666	−	0.318484i
$928$	961.755			1.03637
$929$		−	1374.91i		−	1.47999i	−0.672611	−	0.739996i	$-0.734827\pi$
$929$		−	1374.91i		−	1.47999i	0.672611	−	0.739996i	$-0.265173\pi$
$930$	305.821	+	73.3579i	0.328840	+	0.0788794i
$931$	−741.368			−0.796314
$932$		−	279.560i		−	0.299957i
$933$	343.209	−	1430.80i	0.367855	−	1.53355i
$934$	619.383			0.663151
$935$			295.761i			0.316321i
$936$	454.626	−	893.118i	0.485712	−	0.954186i
$937$	77.9062			0.0831443			0.0415722	−	0.999136i	$-0.486763\pi$
$937$	77.9062			0.0831443			0.0415722	+	0.999136i	$0.486763\pi$
$938$			189.242i			0.201750i
$939$	1731.90	+	415.435i	1.84441	+	0.442423i
$940$	8.36997			0.00890422
$941$			108.785i			0.115606i	0.998328	+	0.0578029i	$0.0184095\pi$
$941$			108.785i			0.115606i	−0.998328	+	0.0578029i	$0.981591\pi$
$942$	303.528	−	1265.38i	0.322217	−	1.34329i
$943$	−184.323			−0.195465
$944$			1170.49i			1.23992i
$945$	642.001	−	752.581i	0.679366	−	0.796382i
$946$	170.574			0.180311
$947$			81.5080i			0.0860696i	0.999074	+	0.0430348i	$0.0137026\pi$
$947$			81.5080i			0.0860696i	−0.999074	+	0.0430348i	$0.986297\pi$
$948$	563.965	+	135.279i	0.594900	+	0.142700i
$949$	−2110.53			−2.22395
$950$		−	417.654i		−	0.439635i
$951$	220.174	−	917.883i	0.231519	−	0.965177i
$952$	663.992			0.697471
$953$			150.409i			0.157827i	0.996881	+	0.0789135i	$0.0251451\pi$
$953$			150.409i			0.157827i	−0.996881	+	0.0789135i	$0.974855\pi$
$954$	1423.19	+	724.452i	1.49182	+	0.759383i
$955$	−1043.28			−1.09244
$956$			301.915i			0.315811i
$957$	724.696	+	173.834i	0.757258	+	0.181645i
$958$	−770.213			−0.803980
$959$		−	609.516i		−	0.635575i
$960$	−53.6424	+	223.630i	−0.0558775	+	0.232947i
$961$	−823.854			−0.857289
$962$		−	692.339i		−	0.719687i
$963$	525.734	−	1032.81i	0.545933	−	1.07249i
$964$	18.1381			0.0188155
$965$			590.482i			0.611899i
$966$	2013.65	+	483.017i	2.08452	+	0.500018i
$967$	1135.47			1.17422			0.587108	−	0.809509i	$-0.300267\pi$
$967$	1135.47			1.17422			0.587108	+	0.809509i	$0.300267\pi$
$968$			445.220i			0.459938i
$969$	138.895	−	579.037i	0.143338	−	0.597562i
$970$	−1063.52			−1.09641
$971$		−	436.508i		−	0.449545i	−0.974411	−	0.224772i	$-0.927836\pi$
$971$		−	436.508i		−	0.449545i	0.974411	−	0.224772i	$-0.0721638\pi$
$972$	153.688	+	370.010i	0.158115	+	0.380669i
$973$	878.605			0.902986
$974$		−	886.304i		−	0.909963i
$975$	628.643	+	150.794i	0.644762	+	0.154660i
$976$	−721.093			−0.738825
$977$		−	1337.51i		−	1.36899i	−0.729016	−	0.684497i	$-0.760022\pi$
$977$		−	1337.51i		−	1.36899i	0.729016	−	0.684497i	$-0.239978\pi$
$978$	−222.610	+	928.036i	−0.227617	+	0.948912i
$979$	−460.270			−0.470144
$980$		−	283.328i		−	0.289110i
$981$	862.284	+	438.931i	0.878985	+	0.447432i
$982$	−574.488			−0.585019
$983$			693.250i			0.705239i	0.935767	+	0.352619i	$0.114709\pi$
$983$			693.250i			0.705239i	−0.935767	+	0.352619i	$0.885291\pi$
$984$	100.644	+	24.1417i	0.102281	+	0.0245343i
$985$	−477.585			−0.484858
$986$			1121.85i			1.13778i
$987$	9.17452	−	38.2476i	0.00929536	−	0.0387514i
$988$	−533.874			−0.540359
$989$		−	333.307i		−	0.337014i
$990$	234.952	−	461.566i	0.237325	−	0.466228i
$991$	−746.846			−0.753629			−0.376814	−	0.926289i	$-0.622981\pi$
$991$	−746.846			−0.753629			−0.376814	+	0.926289i	$0.622981\pi$
$992$		−	291.470i		−	0.293820i
$993$	29.4635	+	7.06747i	0.0296712	+	0.00711730i
$994$	−2970.88			−2.98881
$995$		−	371.755i		−	0.373623i
$996$	−65.6231	+	273.576i	−0.0658866	+	0.274674i
$997$	239.018			0.239737			0.119868	−	0.992790i	$-0.461753\pi$
$997$	239.018			0.239737			0.119868	+	0.992790i	$0.461753\pi$
$998$			551.274i			0.552379i
$999$	−300.286	−	256.164i	−0.300587	−	0.256420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.34	yes	44
3.2	odd	2	inner	201.3.c.a.68.11	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.11	✓	44	3.2	odd	2	inner
201.3.c.a.68.34	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.37672i q^{2} +(-2.91725 - 0.699765i) q^{3} -1.64880 q^{4} +3.76639i q^{5} +(1.66315 - 6.93348i) q^{6} +9.72750 q^{7} +5.58814i q^{8} +(8.02066 + 4.08278i) q^{9} +O(q^{10})\)	\(q+2.37672i q^{2} +(-2.91725 - 0.699765i) q^{3} -1.64880 q^{4} +3.76639i q^{5} +(1.66315 - 6.93348i) q^{6} +9.72750 q^{7} +5.58814i q^{8} +(8.02066 + 4.08278i) q^{9} -8.95165 q^{10} +6.42866i q^{11} +(4.80996 + 1.15377i) q^{12} -19.9265 q^{13} +23.1195i q^{14} +(2.63559 - 10.9875i) q^{15} -19.8767 q^{16} -12.2150i q^{17} +(-9.70362 + 19.0629i) q^{18} -16.2495 q^{19} -6.21003i q^{20} +(-28.3775 - 6.80696i) q^{21} -15.2791 q^{22} +29.8560i q^{23} +(3.91039 - 16.3020i) q^{24} +10.8143 q^{25} -47.3598i q^{26} +(-20.5413 - 17.5230i) q^{27} -16.0387 q^{28} +38.6422i q^{29} +(26.1142 + 6.26406i) q^{30} +11.7109 q^{31} -24.8887i q^{32} +(4.49855 - 18.7540i) q^{33} +29.0317 q^{34} +36.6375i q^{35} +(-13.2245 - 6.73169i) q^{36} +14.6187 q^{37} -38.6204i q^{38} +(58.1306 + 13.9439i) q^{39} -21.0471 q^{40} +6.17375i q^{41} +(16.1783 - 67.4454i) q^{42} -11.1638 q^{43} -10.5996i q^{44} +(-15.3773 + 30.2089i) q^{45} -70.9593 q^{46} +1.34781i q^{47} +(57.9851 + 13.9090i) q^{48} +45.6242 q^{49} +25.7026i q^{50} +(-8.54766 + 35.6343i) q^{51} +32.8549 q^{52} -74.6579i q^{53} +(41.6474 - 48.8208i) q^{54} -24.2128 q^{55} +54.3586i q^{56} +(47.4037 + 11.3708i) q^{57} -91.8418 q^{58} -58.8875i q^{59} +(-4.34556 + 18.1162i) q^{60} +36.2784 q^{61} +27.8336i q^{62} +(78.0209 + 39.7152i) q^{63} -20.3531 q^{64} -75.0510i q^{65} +(44.5730 + 10.6918i) q^{66} +8.18535 q^{67} +20.1402i q^{68} +(20.8922 - 87.0972i) q^{69} -87.0772 q^{70} +128.501i q^{71} +(-22.8151 + 44.8206i) q^{72} +105.916 q^{73} +34.7446i q^{74} +(-31.5480 - 7.56749i) q^{75} +26.7921 q^{76} +62.5348i q^{77} +(-33.1407 + 138.160i) q^{78} +117.249 q^{79} -74.8632i q^{80} +(47.6619 + 65.4931i) q^{81} -14.6733 q^{82} +56.8769i q^{83} +(46.7889 + 11.2233i) q^{84} +46.0066 q^{85} -26.5333i q^{86} +(27.0405 - 112.729i) q^{87} -35.9243 q^{88} +71.5967i q^{89} +(-71.7981 - 36.5476i) q^{90} -193.835 q^{91} -49.2266i q^{92} +(-34.1636 - 8.19490i) q^{93} -3.20338 q^{94} -61.2017i q^{95} +(-17.4163 + 72.6065i) q^{96} +118.807 q^{97} +108.436i q^{98} +(-26.2468 + 51.5621i) 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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