LMFDB - Embedded newform 121.4.c.f.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not 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:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$-0.535233 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	121.81
Dual form			121.4.c.f.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.21028 + 1.60586i) q^{2} +(-2.44995 + 7.54017i) q^{3} +(-0.165602 - 0.509670i) q^{4} +(-12.0191 + 8.73238i) q^{5} +(-17.5235 + 12.7316i) q^{6} +(-0.949237 - 2.92145i) q^{7} +(7.20643 - 22.1791i) q^{8} +(-29.0084 - 21.0759i) q^{9} +O(q^{10})$	\(q+(2.21028 + 1.60586i) q^{2} +(-2.44995 + 7.54017i) q^{3} +(-0.165602 - 0.509670i) q^{4} +(-12.0191 + 8.73238i) q^{5} +(-17.5235 + 12.7316i) q^{6} +(-0.949237 - 2.92145i) q^{7} +(7.20643 - 22.1791i) q^{8} +(-29.0084 - 21.0759i) q^{9} -40.5885 q^{10} +4.24871 q^{12} +(4.33551 + 3.14993i) q^{13} +(2.59336 - 7.98156i) q^{14} +(-36.3974 - 112.020i) q^{15} +(48.0763 - 34.9295i) q^{16} +(-33.3440 + 24.2258i) q^{17} +(-30.2718 - 93.1669i) q^{18} +(-43.2386 + 133.075i) q^{19} +(6.44101 + 4.67967i) q^{20} +24.3538 q^{21} -111.354 q^{23} +(149.579 + 108.675i) q^{24} +(29.5769 - 91.0283i) q^{25} +(4.52432 + 13.9244i) q^{26} +(56.8054 - 41.2716i) q^{27} +(-1.33178 + 0.967595i) q^{28} +(7.72383 + 23.7715i) q^{29} +(99.4397 - 306.044i) q^{30} +(-25.4820 - 18.5137i) q^{31} -24.2102 q^{32} -112.603 q^{34} +(36.9202 + 26.8241i) q^{35} +(-5.93788 + 18.2749i) q^{36} +(4.06159 + 12.5003i) q^{37} +(-309.268 + 224.697i) q^{38} +(-34.3728 + 24.9733i) q^{39} +(107.062 + 329.502i) q^{40} +(-80.6756 + 248.294i) q^{41} +(53.8287 + 39.1088i) q^{42} +57.7128 q^{43} +532.697 q^{45} +(-246.123 - 178.819i) q^{46} +(-106.254 + 327.017i) q^{47} +(145.590 + 448.079i) q^{48} +(269.859 - 196.064i) q^{49} +(211.552 - 153.701i) q^{50} +(-100.976 - 310.771i) q^{51} +(0.887457 - 2.73131i) q^{52} +(277.489 + 201.607i) q^{53} +191.832 q^{54} -71.6359 q^{56} +(-897.474 - 652.053i) q^{57} +(-21.1019 + 64.9450i) q^{58} +(27.3076 + 84.0442i) q^{59} +(-51.0656 + 37.1013i) q^{60} +(597.619 - 434.195i) q^{61} +(-26.5917 - 81.8408i) q^{62} +(-34.0362 + 104.753i) q^{63} +(-438.122 - 318.314i) q^{64} -79.6152 q^{65} +342.359 q^{67} +(17.8690 + 12.9826i) q^{68} +(272.811 - 839.627i) q^{69} +(38.5281 + 118.577i) q^{70} +(167.761 - 121.886i) q^{71} +(-676.492 + 491.500i) q^{72} +(312.293 + 961.138i) q^{73} +(-11.0965 + 34.1515i) q^{74} +(613.907 + 446.029i) q^{75} +74.9845 q^{76} -116.077 q^{78} +(1047.05 + 760.727i) q^{79} +(-272.816 + 839.641i) q^{80} +(-127.142 - 391.304i) q^{81} +(-577.041 + 419.245i) q^{82} +(357.461 - 259.711i) q^{83} +(-4.03304 - 12.4124i) q^{84} +(189.215 - 582.344i) q^{85} +(127.561 + 92.6787i) q^{86} -198.164 q^{87} -1489.11 q^{89} +(1177.41 + 855.437i) q^{90} +(5.08695 - 15.6560i) q^{91} +(18.4404 + 56.7537i) q^{92} +(202.026 - 146.781i) q^{93} +(-759.995 + 552.168i) q^{94} +(-642.370 - 1977.01i) q^{95} +(59.3139 - 182.549i) q^{96} +(-1089.27 - 791.403i) q^{97} +911.314 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9} - 200 q^{10} - 160 q^{12} + 80 q^{13} + 4 q^{14} + 194 q^{15} + 8 q^{16} - 124 q^{17} + 92 q^{18} + 72 q^{19} - 88 q^{20} - 304 q^{21} - 392 q^{23} + 252 q^{24} - 136 q^{25} + 40 q^{26} + 182 q^{27} - 128 q^{28} + 144 q^{29} - 266 q^{30} + 34 q^{31} + 416 q^{32} - 208 q^{34} - 172 q^{35} + 80 q^{36} - 54 q^{37} - 432 q^{38} + 400 q^{39} - 492 q^{40} + 536 q^{41} + 140 q^{42} + 240 q^{43} + 1712 q^{45} - 314 q^{46} + 272 q^{47} - 776 q^{48} + 390 q^{49} + 232 q^{50} - 164 q^{51} - 560 q^{52} + 492 q^{53} + 440 q^{54} + 480 q^{56} - 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} + 840 q^{61} + 134 q^{62} + 248 q^{63} - 224 q^{64} + 3520 q^{65} + 3016 q^{67} + 640 q^{68} - 962 q^{69} - 284 q^{70} + 678 q^{71} - 744 q^{72} - 400 q^{73} + 6 q^{74} + 520 q^{75} - 1728 q^{76} - 1760 q^{78} + 316 q^{79} + 1544 q^{80} + 1294 q^{81} - 512 q^{82} + 468 q^{83} - 736 q^{84} + 452 q^{85} + 156 q^{86} - 4800 q^{87} - 7368 q^{89} + 1532 q^{90} - 1280 q^{91} + 40 q^{92} + 638 q^{93} - 992 q^{94} + 2952 q^{95} - 952 q^{96} - 2194 q^{97} + 3480 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9 - 200 * q^10 - 160 * q^12 + 80 * q^13 + 4 * q^14 + 194 * q^15 + 8 * q^16 - 124 * q^17 + 92 * q^18 + 72 * q^19 - 88 * q^20 - 304 * q^21 - 392 * q^23 + 252 * q^24 - 136 * q^25 + 40 * q^26 + 182 * q^27 - 128 * q^28 + 144 * q^29 - 266 * q^30 + 34 * q^31 + 416 * q^32 - 208 * q^34 - 172 * q^35 + 80 * q^36 - 54 * q^37 - 432 * q^38 + 400 * q^39 - 492 * q^40 + 536 * q^41 + 140 * q^42 + 240 * q^43 + 1712 * q^45 - 314 * q^46 + 272 * q^47 - 776 * q^48 + 390 * q^49 + 232 * q^50 - 164 * q^51 - 560 * q^52 + 492 * q^53 + 440 * q^54 + 480 * q^56 - 1512 * q^57 + 192 * q^58 - 634 * q^59 - 632 * q^60 + 840 * q^61 + 134 * q^62 + 248 * q^63 - 224 * q^64 + 3520 * q^65 + 3016 * q^67 + 640 * q^68 - 962 * q^69 - 284 * q^70 + 678 * q^71 - 744 * q^72 - 400 * q^73 + 6 * q^74 + 520 * q^75 - 1728 * q^76 - 1760 * q^78 + 316 * q^79 + 1544 * q^80 + 1294 * q^81 - 512 * q^82 + 468 * q^83 - 736 * q^84 + 452 * q^85 + 156 * q^86 - 4800 * q^87 - 7368 * q^89 + 1532 * q^90 - 1280 * q^91 + 40 * q^92 + 638 * q^93 - 992 * q^94 + 2952 * q^95 - 952 * q^96 - 2194 * q^97 + 3480 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	2.21028	+	1.60586i	0.781450	+	0.567757i	0.905414	−	0.424530i	$-0.139561\pi$
$2$	2.21028	+	1.60586i	0.781450	+	0.567757i	−0.123964	+	0.992287i	$0.539561\pi$
$3$	−2.44995	+	7.54017i	−0.471493	+	1.45111i	0.379137	+	0.925341i	$0.376221\pi$
$3$	−2.44995	+	7.54017i	−0.471493	+	1.45111i	−0.850630	+	0.525766i	$0.823779\pi$
$4$	−0.165602	−	0.509670i	−0.0207002	−	0.0637087i
$5$	−12.0191	+	8.73238i	−1.07502	+	0.781048i	−0.976808	−	0.214118i	$-0.931312\pi$
$5$	−12.0191	+	8.73238i	−1.07502	+	0.781048i	−0.0982119	+	0.995166i	$0.531312\pi$
$6$	−17.5235	+	12.7316i	−1.19232	+	0.866274i
$7$	−0.949237	−	2.92145i	−0.0512540	−	0.157744i	0.922153	−	0.386824i	$-0.126428\pi$
$7$	−0.949237	−	2.92145i	−0.0512540	−	0.157744i	−0.973407	+	0.229081i	$0.926428\pi$
$8$	7.20643	−	22.1791i	0.318482	−	0.980188i
$9$	−29.0084	−	21.0759i	−1.07439	−	0.780588i
$10$	−40.5885			−1.28352
$11$		0			0
$11$		0			0
$12$	4.24871			0.102208
$13$	4.33551	+	3.14993i	0.0924964	+	0.0672026i	0.633072	−	0.774093i	$-0.281794\pi$
$13$	4.33551	+	3.14993i	0.0924964	+	0.0672026i	−0.540576	+	0.841295i	$0.681794\pi$
$14$	2.59336	−	7.98156i	0.0495076	−	0.152369i
$15$	−36.3974	−	112.020i	−0.626519	−	1.92823i
$16$	48.0763	−	34.9295i	0.751193	−	0.545774i
$17$	−33.3440	+	24.2258i	−0.475712	+	0.345625i	−0.799663	−	0.600449i	$-0.794989\pi$
$17$	−33.3440	+	24.2258i	−0.475712	+	0.345625i	0.323951	+	0.946074i	$0.394989\pi$
$18$	−30.2718	−	93.1669i	−0.396396	−	1.21998i
$19$	−43.2386	+	133.075i	−0.522085	+	1.60681i	0.247924	+	0.968779i	$0.420252\pi$
$19$	−43.2386	+	133.075i	−0.522085	+	1.60681i	−0.770009	+	0.638033i	$0.779748\pi$
$20$	6.44101	+	4.67967i	0.0720127	+	0.0523203i
$21$	24.3538			0.253069
$22$		0			0
$23$	−111.354			−1.00952			−0.504758	−	0.863261i	$-0.668418\pi$
$23$	−111.354			−1.00952			−0.504758	+	0.863261i	$0.668418\pi$
$24$	149.579	+	108.675i	1.27219	+	0.924304i
$25$	29.5769	−	91.0283i	0.236615	−	0.728226i
$26$	4.52432	+	13.9244i	0.0341266	+	0.105031i
$27$	56.8054	−	41.2716i	0.404897	−	0.294175i
$28$	−1.33178	+	0.967595i	−0.00898867	+	0.00653065i
$29$	7.72383	+	23.7715i	0.0494579	+	0.152216i	0.972735	−	0.231918i	$-0.0745001\pi$
$29$	7.72383	+	23.7715i	0.0494579	+	0.152216i	−0.923277	+	0.384134i	$0.874500\pi$
$30$	99.4397	−	306.044i	0.605171	−	1.86252i
$31$	−25.4820	−	18.5137i	−0.147635	−	0.107263i	0.511516	−	0.859274i	$-0.329084\pi$
$31$	−25.4820	−	18.5137i	−0.147635	−	0.107263i	−0.659151	+	0.752011i	$0.729084\pi$
$32$	−24.2102			−0.133744
$33$		0			0
$34$	−112.603			−0.567976
$35$	36.9202	+	26.8241i	0.178304	+	0.129546i
$36$	−5.93788	+	18.2749i	−0.0274902	+	0.0846061i
$37$	4.06159	+	12.5003i	0.0180465	+	0.0555415i	0.959674	−	0.281114i	$-0.0907041\pi$
$37$	4.06159	+	12.5003i	0.0180465	+	0.0555415i	−0.941628	+	0.336656i	$0.890704\pi$
$38$	−309.268	+	224.697i	−1.32026	+	0.959227i
$39$	−34.3728	+	24.9733i	−0.141130	+	0.102537i
$40$	107.062	+	329.502i	0.423199	+	1.30247i
$41$	−80.6756	+	248.294i	−0.307303	+	0.945781i	0.671505	+	0.741000i	$0.265648\pi$
$41$	−80.6756	+	248.294i	−0.307303	+	0.945781i	−0.978808	+	0.204781i	$0.934352\pi$
$42$	53.8287	+	39.1088i	0.197761	+	0.143681i
$43$	57.7128			0.204677			0.102339	−	0.994750i	$-0.467367\pi$
$43$	57.7128			0.204677			0.102339	+	0.994750i	$0.467367\pi$
$44$		0			0
$45$	532.697			1.76466
$46$	−246.123	−	178.819i	−0.788887	−	0.573160i
$47$	−106.254	+	327.017i	−0.329761	+	1.01490i	0.639484	+	0.768804i	$0.279148\pi$
$47$	−106.254	+	327.017i	−0.329761	+	1.01490i	−0.969245	+	0.246097i	$0.920852\pi$
$48$	145.590	+	448.079i	0.437793	+	1.34739i
$49$	269.859	−	196.064i	0.786761	−	0.571615i
$50$	211.552	−	153.701i	0.598359	−	0.434733i
$51$	−100.976	−	310.771i	−0.277243	−	0.853268i
$52$	0.887457	−	2.73131i	0.00236669	−	0.00728394i
$53$	277.489	+	201.607i	0.719170	+	0.522507i	0.886119	−	0.463458i	$-0.153392\pi$
$53$	277.489	+	201.607i	0.719170	+	0.522507i	−0.166949	+	0.985966i	$0.553392\pi$
$54$	191.832			0.483426
$55$		0			0
$56$	−71.6359			−0.170942
$57$	−897.474	−	652.053i	−2.08550	−	1.51520i
$58$	−21.1019	+	64.9450i	−0.0477727	+	0.147029i
$59$	27.3076	+	84.0442i	0.0602568	+	0.185451i	0.976654	−	0.214819i	$-0.0689162\pi$
$59$	27.3076	+	84.0442i	0.0602568	+	0.185451i	−0.916397	+	0.400270i	$0.868916\pi$
$60$	−51.0656	+	37.1013i	−0.109876	+	0.0798294i
$61$	597.619	−	434.195i	1.25438	−	0.911361i	0.255913	−	0.966700i	$-0.417624\pi$
$61$	597.619	−	434.195i	1.25438	−	0.911361i	0.998468	+	0.0553387i	$0.0176239\pi$
$62$	−26.5917	−	81.8408i	−0.0544702	−	0.167642i
$63$	−34.0362	+	104.753i	−0.0680661	+	0.209486i
$64$	−438.122	−	318.314i	−0.855707	−	0.621708i
$65$	−79.6152			−0.151924
$66$		0			0
$67$	342.359			0.624266			0.312133	−	0.950038i	$-0.398957\pi$
$67$	342.359			0.624266			0.312133	+	0.950038i	$0.398957\pi$
$68$	17.8690	+	12.9826i	0.0318666	+	0.0231525i
$69$	272.811	−	839.627i	0.475980	−	1.46492i
$70$	38.5281	+	118.577i	0.0657855	+	0.202467i
$71$	167.761	−	121.886i	0.280417	−	0.203735i	−0.438682	−	0.898642i	$-0.644555\pi$
$71$	167.761	−	121.886i	0.280417	−	0.203735i	0.719099	+	0.694908i	$0.244555\pi$
$72$	−676.492	+	491.500i	−1.10730	+	0.804498i
$73$	312.293	+	961.138i	0.500700	+	1.54100i	0.807882	+	0.589344i	$0.200614\pi$
$73$	312.293	+	961.138i	0.500700	+	1.54100i	−0.307182	+	0.951651i	$0.599386\pi$
$74$	−11.0965	+	34.1515i	−0.0174316	+	0.0536490i
$75$	613.907	+	446.029i	0.945171	+	0.686707i
$76$	74.9845			0.113175
$77$		0			0
$78$	−116.077			−0.168502
$79$	1047.05	+	760.727i	1.49117	+	1.08340i	0.973738	+	0.227673i	$0.0731118\pi$
$79$	1047.05	+	760.727i	1.49117	+	1.08340i	0.517432	+	0.855725i	$0.326888\pi$
$80$	−272.816	+	839.641i	−0.381272	+	1.17343i
$81$	−127.142	−	391.304i	−0.174406	−	0.536768i
$82$	−577.041	+	419.245i	−0.777116	+	0.564607i
$83$	357.461	−	259.711i	0.472728	−	0.343457i	−0.325775	−	0.945447i	$-0.605625\pi$
$83$	357.461	−	259.711i	0.472728	−	0.343457i	0.798504	+	0.601990i	$0.205625\pi$
$84$	−4.03304	−	12.4124i	−0.00523857	−	0.0161227i
$85$	189.215	−	582.344i	0.241450	−	0.743107i
$86$	127.561	+	92.6787i	0.159945	+	0.116207i
$87$	−198.164			−0.244200
$88$		0			0
$89$	−1489.11			−1.77355			−0.886773	−	0.462205i	$-0.847058\pi$
$89$	−1489.11			−1.77355			−0.886773	+	0.462205i	$0.847058\pi$
$90$	1177.41	+	855.437i	1.37900	+	1.00190i
$91$	5.08695	−	15.6560i	0.00585997	−	0.0180351i
$92$	18.4404	+	56.7537i	0.0208972	+	0.0643150i
$93$	202.026	−	146.781i	0.225259	−	0.163661i
$94$	−759.995	+	552.168i	−0.833909	+	0.605870i
$95$	−642.370	−	1977.01i	−0.693745	−	2.13513i
$96$	59.3139	−	182.549i	0.0630593	−	0.194077i
$97$	−1089.27	−	791.403i	−1.14019	−	0.828400i	−0.153048	−	0.988219i	$-0.548909\pi$
$97$	−1089.27	−	791.403i	−1.14019	−	0.828400i	−0.987146	+	0.159819i	$0.948909\pi$
$98$	911.314			0.939353
$99$		0			0
$100$	−51.2923			−0.0512923
$101$	−130.625	−	94.9046i	−0.128690	−	0.0934986i	0.521578	−	0.853203i	$-0.325343\pi$
$101$	−130.625	−	94.9046i	−0.128690	−	0.0934986i	−0.650268	+	0.759705i	$0.725343\pi$
$102$	275.871	−	849.042i	0.267797	−	0.824193i
$103$	−10.7412	−	33.0580i	−0.0102753	−	0.0316243i	0.945787	−	0.324786i	$-0.105292\pi$
$103$	−10.7412	−	33.0580i	−0.0102753	−	0.0316243i	−0.956063	+	0.293162i	$0.905292\pi$
$104$	101.106	−	73.4580i	0.0953297	−	0.0692611i
$105$	−292.711	+	212.667i	−0.272054	+	0.197659i
$106$	289.573	+	891.215i	0.265338	+	0.816627i
$107$	−257.158	+	791.450i	−0.232340	+	0.715068i	0.765123	+	0.643884i	$0.222678\pi$
$107$	−257.158	+	791.450i	−0.232340	+	0.715068i	−0.997463	+	0.0711847i	$0.977322\pi$
$108$	−30.4419	−	22.1174i	−0.0271229	−	0.0197060i
$109$	−1044.26			−0.917629			−0.458815	−	0.888532i	$-0.651726\pi$
$109$	−1044.26			−0.917629			−0.458815	+	0.888532i	$0.651726\pi$
$110$		0			0
$111$	−104.205			−0.0891055
$112$	−147.681	−	107.296i	−0.124594	−	0.0905228i
$113$	91.1853	−	280.639i	0.0759114	−	0.233631i	−0.905899	−	0.423493i	$-0.860804\pi$
$113$	91.1853	−	280.639i	0.0759114	−	0.233631i	0.981811	+	0.189861i	$0.0608039\pi$
$114$	−936.559	−	2882.43i	−0.769446	−	2.36811i
$115$	1338.37	−	972.384i	1.08525	−	0.788480i
$116$	10.8365	−	7.87321i	0.00867368	−	0.00630180i
$117$	−59.3788	−	182.749i	−0.0469194	−	0.144403i
$118$	−74.6058	+	229.613i	−0.0582036	+	0.179132i
$119$	102.426	+	74.4167i	0.0789022	+	0.0573258i
$120$	−2746.80			−2.08956
$121$		0			0
$122$	2018.16			1.49767
$123$	−1674.53	−	1216.62i	−1.22754	−	0.891858i
$124$	−5.21603	+	16.0533i	−0.00377752	+	0.0116260i
$125$	−134.454	−	413.807i	−0.0962075	−	0.296096i
$126$	−243.448	+	176.875i	−0.172127	+	0.125058i
$127$	−1065.96	+	774.469i	−0.744796	+	0.541126i	−0.894209	−	0.447649i	$-0.852261\pi$
$127$	−1065.96	+	774.469i	−0.744796	+	0.541126i	0.149414	+	0.988775i	$0.452261\pi$
$128$	−397.351	−	1222.92i	−0.274385	−	0.844469i
$129$	−141.393	+	435.164i	−0.0965039	+	0.297008i
$130$	−175.972	−	127.851i	−0.118721	−	0.0862559i
$131$	1600.71			1.06759			0.533797	−	0.845612i	$-0.320765\pi$
$131$	1600.71			1.06759			0.533797	+	0.845612i	$0.320765\pi$
$132$		0			0
$133$	429.815			0.280223
$134$	756.708	+	549.780i	0.487833	+	0.354431i
$135$	−322.351	+	992.093i	−0.205508	+	0.632487i
$136$	297.016	+	914.121i	0.187271	+	0.576362i
$137$	−1303.87	+	947.320i	−0.813120	+	0.590766i	−0.914734	−	0.404058i	$-0.867600\pi$
$137$	−1303.87	+	947.320i	−0.813120	+	0.590766i	0.101613	+	0.994824i	$0.467600\pi$
$138$	1951.31	−	1417.71i	1.20367	−	0.874518i
$139$	9.84588	+	30.3025i	0.00600803	+	0.0184908i	0.954016	−	0.299757i	$-0.0969056\pi$
$139$	9.84588	+	30.3025i	0.00600803	+	0.0184908i	−0.948008	+	0.318248i	$0.896906\pi$
$140$	7.55738	−	23.2592i	0.00456225	−	0.0140412i
$141$	−2205.45	−	1602.35i	−1.31725	−	0.957037i
$142$	566.529			0.334803
$143$		0			0
$144$	−2130.79			−1.23310
$145$	−300.415	−	218.264i	−0.172056	−	0.125006i
$146$	−853.199	+	2625.88i	−0.483639	+	1.48849i
$147$	817.215	+	2515.13i	0.458522	+	1.41119i
$148$	5.69842	−	4.14014i	0.00316491	−	0.00229944i
$149$	−1964.57	+	1427.34i	−1.08016	+	0.784782i	−0.977711	−	0.209956i	$-0.932668\pi$
$149$	−1964.57	+	1427.34i	−1.08016	+	0.784782i	−0.102449	+	0.994738i	$0.532668\pi$
$150$	640.643	+	1971.70i	0.348722	+	1.07326i
$151$	796.237	−	2450.57i	0.429118	−	1.32069i	−0.469877	−	0.882732i	$-0.655702\pi$
$151$	796.237	−	2450.57i	0.429118	−	1.32069i	0.898995	−	0.437958i	$-0.144298\pi$
$152$	2639.88	+	1917.99i	1.40870	+	1.02348i
$153$	1477.84			0.780889
$154$		0			0
$155$	467.939			0.242489
$156$	18.4203	+	13.3832i	0.00945389	+	0.00686865i
$157$	765.109	−	2354.76i	0.388932	−	1.19701i	−0.544656	−	0.838660i	$-0.683340\pi$
$157$	765.109	−	2354.76i	0.388932	−	1.19701i	0.933587	−	0.358350i	$-0.116660\pi$
$158$	1092.65	+	3362.83i	0.550168	+	1.69324i
$159$	−2199.99	+	1598.38i	−1.09730	+	0.797233i
$160$	290.985	−	211.413i	0.143777	−	0.104460i
$161$	105.701	+	325.315i	0.0517418	+	0.159245i
$162$	347.359	−	1069.06i	0.168464	−	0.518478i
$163$	2204.66	+	1601.78i	1.05940	+	0.769699i	0.973977	−	0.226646i	$-0.0727760\pi$
$163$	2204.66	+	1601.78i	1.05940	+	0.769699i	0.0854225	+	0.996345i	$0.472776\pi$
$164$	139.908			0.0666157
$165$		0			0
$166$	1207.15			0.564414
$167$	2214.52	+	1608.94i	1.02614	+	0.745531i	0.967532	−	0.252750i	$-0.0813350\pi$
$167$	2214.52	+	1608.94i	1.02614	+	0.745531i	0.0586043	+	0.998281i	$0.481335\pi$
$168$	175.504	−	540.147i	0.0805979	−	0.248055i
$169$	−670.036	−	2062.16i	−0.304978	−	0.938625i
$170$	1353.38	−	983.288i	0.610585	−	0.443616i
$171$	4058.95	−	2949.00i	1.81518	−	1.31880i
$172$	−9.55734	−	29.4145i	−0.00423686	−	0.0130397i
$173$	−713.031	+	2194.48i	−0.313357	+	0.964413i	0.663069	+	0.748558i	$0.269254\pi$
$173$	−713.031	+	2194.48i	−0.313357	+	0.964413i	−0.976426	+	0.215854i	$0.930746\pi$
$174$	−437.998	−	318.224i	−0.190830	−	0.138646i
$175$	−294.010			−0.127001
$176$		0			0
$177$	−700.610			−0.297520
$178$	−3291.35	−	2391.31i	−1.38594	−	1.00694i
$179$	−405.478	+	1247.93i	−0.169312	+	0.521089i	−0.999328	−	0.0366506i	$-0.988331\pi$
$179$	−405.478	+	1247.93i	−0.169312	+	0.521089i	0.830016	+	0.557739i	$0.188331\pi$
$180$	−88.2156	−	271.500i	−0.0365289	−	0.112424i
$181$	649.781	−	472.094i	0.266839	−	0.193870i	−0.446318	−	0.894875i	$-0.647265\pi$
$181$	649.781	−	472.094i	0.266839	−	0.193870i	0.713157	+	0.701005i	$0.247265\pi$
$182$	36.3849	−	26.4352i	0.0148188	−	0.0107665i
$183$	1809.77	+	5569.90i	0.731050	+	2.24994i
$184$	−802.464	+	2469.73i	−0.321513	+	0.989516i
$185$	−157.974	−	114.775i	−0.0627810	−	0.0456130i
$186$	682.242			0.268949
$187$		0			0
$188$	184.267			0.0714842
$189$	−174.495	−	126.778i	−0.0671568	−	0.0487922i
$190$	1754.99	−	5401.30i	0.670106	−	2.06238i
$191$	530.967	+	1634.15i	0.201149	+	0.619073i	0.999850	+	0.0173442i	$0.00552110\pi$
$191$	530.967	+	1634.15i	0.201149	+	0.619073i	−0.798701	+	0.601729i	$0.794479\pi$
$192$	3473.52	−	2523.66i	1.30562	−	0.948591i
$193$	1084.23	−	787.740i	0.404377	−	0.293797i	−0.366945	−	0.930243i	$-0.619596\pi$
$193$	1084.23	−	787.740i	0.404377	−	0.293797i	0.771321	+	0.636446i	$0.219596\pi$
$194$	−1136.71	−	3498.44i	−0.420676	−	1.29471i
$195$	195.053	−	600.312i	0.0716311	−	0.220458i
$196$	−144.617	−	105.070i	−0.0527030	−	0.0382910i
$197$	3518.33			1.27244			0.636220	−	0.771508i	$-0.280497\pi$
$197$	3518.33			1.27244			0.636220	+	0.771508i	$0.280497\pi$
$198$		0			0
$199$	823.692			0.293417			0.146709	−	0.989180i	$-0.453132\pi$
$199$	823.692			0.293417			0.146709	+	0.989180i	$0.453132\pi$
$200$	−1805.78	−	1311.98i	−0.638441	−	0.463855i
$201$	−838.762	+	2581.44i	−0.294337	+	0.905876i
$202$	−136.314	−	419.531i	−0.0474802	−	0.146129i
$203$	62.1156	−	45.1296i	0.0214762	−	0.0156033i
$204$	−141.669	+	102.928i	−0.0486216	+	0.0353256i
$205$	−1198.55	−	3688.76i	−0.408343	−	1.25675i
$206$	29.3455	−	90.3161i	0.00992522	−	0.0305467i
$207$	3230.20	+	2346.88i	1.08461	+	0.788016i
$208$	318.461			0.106160
$209$		0			0
$210$	−988.484			−0.324819
$211$	−86.8424	−	63.0947i	−0.0283340	−	0.0205859i	0.573528	−	0.819186i	$-0.305574\pi$
$211$	−86.8424	−	63.0947i	−0.0283340	−	0.0205859i	−0.601862	+	0.798600i	$0.705574\pi$
$212$	56.8005	−	174.814i	0.0184013	−	0.0566334i
$213$	508.032	+	1563.56i	0.163426	+	0.502974i
$214$	−1839.35	+	1336.36i	−0.587547	+	0.426878i
$215$	−693.655	+	503.970i	−0.220032	+	0.159863i
$216$	−506.003	−	1557.32i	−0.159394	−	0.490564i
$217$	−29.8985	+	92.0182i	−0.00935320	+	0.0287862i
$218$	−2308.09	−	1676.93i	−0.717082	−	0.520990i
$219$	−8012.24			−2.47222
$220$		0			0
$221$	−220.873			−0.0672285
$222$	−230.322	−	167.339i	−0.0696315	−	0.0505903i
$223$	−1215.57	+	3741.15i	−0.365026	+	1.12344i	0.584938	+	0.811078i	$0.301119\pi$
$223$	−1215.57	+	3741.15i	−0.365026	+	1.12344i	−0.949965	+	0.312358i	$0.898881\pi$
$224$	22.9813	+	70.7290i	0.00685491	+	0.0210972i
$225$	−2776.48	+	2017.23i	−0.822661	+	0.597698i
$226$	652.212	−	473.860i	0.191967	−	0.139472i
$227$	547.548	+	1685.18i	0.160097	+	0.492728i	0.998642	−	0.0521050i	$-0.0165931\pi$
$227$	547.548	+	1685.18i	0.160097	+	0.492728i	−0.838545	+	0.544833i	$0.816593\pi$
$228$	−183.708	+	565.396i	−0.0533613	+	0.164229i
$229$	−1549.57	−	1125.83i	−0.447154	−	0.324876i	0.341317	−	0.939948i	$-0.389127\pi$
$229$	−1549.57	−	1125.83i	−0.447154	−	0.324876i	−0.788471	+	0.615072i	$0.789127\pi$
$230$	4519.68			1.29573
$231$		0			0
$232$	582.892			0.164952
$233$	3556.70	+	2584.09i	1.00003	+	0.726564i	0.962095	−	0.272716i	$-0.0879220\pi$
$233$	3556.70	+	2584.09i	1.00003	+	0.726564i	0.0379350	+	0.999280i	$0.487922\pi$
$234$	162.226	−	499.280i	0.0453207	−	0.139483i
$235$	−1578.56	−	4858.30i	−0.438186	−	1.34860i
$236$	38.3126	−	27.8357i	0.0105675	−	0.00767776i
$237$	−8301.23	+	6031.19i	−2.27520	+	1.65303i
$238$	106.887	+	328.963i	0.0291110	+	0.0895945i
$239$	1262.18	−	3884.58i	0.341604	−	1.05135i	−0.621772	−	0.783198i	$-0.713587\pi$
$239$	1262.18	−	3884.58i	0.341604	−	1.05135i	0.963377	−	0.268152i	$-0.0864130\pi$
$240$	−5662.65	−	4114.16i	−1.52301	−	1.10653i
$241$	−3908.58			−1.04471			−0.522353	−	0.852730i	$-0.674946\pi$
$241$	−3908.58			−1.04471			−0.522353	+	0.852730i	$0.674946\pi$
$242$		0			0
$243$	5157.80			1.36162
$244$	−320.263	−	232.685i	−0.0840276	−	0.0610496i
$245$	−1531.35	+	4713.02i	−0.399325	+	1.22900i
$246$	−1747.45	−	5378.11i	−0.452901	−	1.39389i
$247$	−606.638	+	440.748i	−0.156273	+	0.113539i
$248$	−594.252	+	431.749i	−0.152157	+	0.110549i
$249$	1082.50	+	3331.59i	0.275505	+	0.847917i
$250$	367.335	−	1130.54i	0.0929293	−	0.286007i
$251$	−885.786	−	643.561i	−0.222750	−	0.161838i	0.470813	−	0.882233i	$-0.343960\pi$
$251$	−885.786	−	643.561i	−0.222750	−	0.161838i	−0.693564	+	0.720395i	$0.743960\pi$
$252$	59.0258			0.0147551
$253$		0			0
$254$	−3599.76			−0.889249
$255$	3927.40	+	2853.43i	0.964485	+	0.700739i
$256$	−253.197	+	779.261i	−0.0618158	+	0.190249i
$257$	242.016	+	744.847i	0.0587413	+	0.180787i	0.976122	−	0.217224i	$-0.0697004\pi$
$257$	242.016	+	744.847i	0.0587413	+	0.180787i	−0.917380	+	0.398012i	$0.869700\pi$
$258$	−1011.33	+	734.775i	−0.244042	+	0.177307i
$259$	32.6636	−	23.7315i	0.00783636	−	0.00569345i
$260$	13.1844	+	40.5775i	0.00314486	+	0.00967888i
$261$	276.949	−	852.361i	0.0656809	−	0.202145i
$262$	3538.02	+	2570.52i	0.834272	+	0.606134i
$263$	−6180.06			−1.44897			−0.724484	−	0.689292i	$-0.757922\pi$
$263$	−6180.06			−1.44897			−0.724484	+	0.689292i	$0.757922\pi$
$264$		0			0
$265$	−5095.67			−1.18122
$266$	950.010	+	690.223i	0.218981	+	0.159099i
$267$	3648.25	−	11228.2i	0.836215	−	2.57360i
$268$	−56.6952	−	174.490i	−0.0129224	−	0.0397712i
$269$	−798.471	+	580.123i	−0.180980	+	0.131490i	−0.674587	−	0.738195i	$-0.735678\pi$
$269$	−798.471	+	580.123i	−0.180980	+	0.131490i	0.493607	+	0.869685i	$0.335678\pi$
$270$	−2305.65	+	1675.15i	−0.519693	+	0.377579i
$271$	−1414.37	−	4352.98i	−0.317036	−	0.975736i	−0.974908	−	0.222607i	$-0.928543\pi$
$271$	−1414.37	−	4352.98i	−0.317036	−	0.975736i	0.657873	−	0.753129i	$-0.271457\pi$
$272$	−756.860	+	2329.38i	−0.168718	+	0.519262i
$273$	105.586	+	76.7129i	0.0234079	+	0.0170069i
$274$	−4403.18			−0.970825
$275$		0			0
$276$	−473.110			−0.103181
$277$	459.389	+	333.766i	0.0996462	+	0.0723972i	0.636493	−	0.771283i	$-0.280385\pi$
$277$	459.389	+	333.766i	0.0996462	+	0.0723972i	−0.536846	+	0.843680i	$0.680385\pi$
$278$	−26.8994	+	82.7880i	−0.00580331	+	0.0178608i
$279$	348.999	+	1074.11i	0.0748890	+	0.230485i
$280$	860.998	−	625.551i	0.183766	−	0.133514i
$281$	4296.70	−	3121.74i	0.912170	−	0.662730i	−0.0293930	−	0.999568i	$-0.509357\pi$
$281$	4296.70	−	3121.74i	0.912170	−	0.662730i	0.941563	+	0.336838i	$0.109357\pi$
$282$	−2301.49	−	7083.27i	−0.486000	−	1.49575i
$283$	1461.17	−	4497.01i	0.306917	−	0.944593i	−0.672038	−	0.740517i	$-0.734581\pi$
$283$	1461.17	−	4497.01i	0.306917	−	0.944593i	0.978955	−	0.204076i	$-0.0654191\pi$
$284$	−89.9029	−	65.3183i	−0.0187844	−	0.0136476i
$285$	16480.8			3.42539
$286$		0			0
$287$	801.960			0.164941
$288$	702.301	+	510.252i	0.143693	+	0.104399i
$289$	−993.271	+	3056.97i	−0.202172	+	0.622221i
$290$	−313.498	−	964.849i	−0.0634802	−	0.195372i
$291$	8635.98	−	6274.40i	1.73969	−	1.26396i
$292$	438.146	−	318.332i	0.0878102	−	0.0637979i
$293$	−719.675	−	2214.93i	−0.143494	−	0.441630i	0.853320	−	0.521388i	$-0.174585\pi$
$293$	−719.675	−	2214.93i	−0.143494	−	0.441630i	−0.996814	+	0.0797574i	$0.974585\pi$
$294$	−2232.67	+	6871.46i	−0.442898	+	1.36310i
$295$	−1062.12	−	771.674i	−0.209623	−	0.152300i
$296$	306.515			0.0601886
$297$		0			0
$298$	−6634.36			−1.28966
$299$	−482.776	−	350.757i	−0.0933767	−	0.0678421i
$300$	125.664	−	386.753i	0.0241840	−	0.0744306i
$301$	−54.7832	−	168.605i	−0.0104905	−	0.0322865i
$302$	5695.17	−	4137.78i	1.08517	−	0.788419i
$303$	1035.62	−	752.423i	0.196353	−	0.142659i
$304$	2569.48	+	7908.05i	0.484769	+	1.49197i
$305$	−3391.27	+	10437.3i	−0.636668	+	1.95946i
$306$	3266.42	+	2373.20i	0.610226	+	0.443355i
$307$	1678.07			0.311962			0.155981	−	0.987760i	$-0.450146\pi$
$307$	1678.07			0.311962			0.155981	+	0.987760i	$0.450146\pi$
$308$		0			0
$309$	275.578			0.0507349
$310$	1034.27	+	751.443i	0.189493	+	0.137675i
$311$	1104.03	−	3397.85i	0.201298	−	0.619531i	−0.798547	−	0.601932i	$-0.794398\pi$
$311$	1104.03	−	3397.85i	0.201298	−	0.619531i	0.999845	−	0.0175989i	$-0.00560221\pi$
$312$	306.181	+	942.327i	0.0555579	+	0.170990i
$313$	−5812.27	+	4222.86i	−1.04961	+	0.762589i	−0.972139	−	0.234405i	$-0.924686\pi$
$313$	−5812.27	+	4222.86i	−1.04961	+	0.762589i	−0.0774746	+	0.996994i	$0.524686\pi$
$314$	5472.52	−	3976.02i	0.983541	−	0.714585i
$315$	−505.656	−	1556.25i	−0.0904460	−	0.278364i
$316$	214.326	−	659.627i	0.0381544	−	0.117427i
$317$	12.7078	+	9.23273i	0.00225154	+	0.00163584i	0.588910	−	0.808198i	$-0.299557\pi$
$317$	12.7078	+	9.23273i	0.00225154	+	0.00163584i	−0.586659	+	0.809834i	$0.699557\pi$
$318$	−7429.36			−1.31012
$319$		0			0
$320$	8045.47			1.40549
$321$	−5337.64	−	3878.02i	−0.928094	−	0.674299i
$322$	−288.781	+	888.777i	−0.0499787	+	0.153819i
$323$	−1782.10	−	5484.73i	−0.306992	−	0.944825i
$324$	−178.381	+	129.601i	−0.0305865	+	0.0222224i
$325$	414.964	−	301.489i	0.0708248	−	0.0514572i
$326$	2300.67	+	7080.74i	0.390866	+	1.20296i
$327$	2558.38	−	7873.87i	0.432656	−	1.33158i
$328$	4925.56	+	3578.63i	0.829172	+	0.602429i
$329$	1056.23			0.176996
$330$		0			0
$331$	−1318.95			−0.219022			−0.109511	−	0.993986i	$-0.534928\pi$
$331$	−1318.95			−0.219022			−0.109511	+	0.993986i	$0.534928\pi$
$332$	−191.563	−	139.179i	−0.0316668	−	0.0230073i
$333$	145.634	−	448.216i	0.0239661	−	0.0737600i
$334$	2310.96	+	7112.41i	0.378594	+	1.16519i
$335$	−4114.84	+	2989.61i	−0.671098	+	0.487581i
$336$	1170.84	−	850.667i	0.190103	−	0.138118i
$337$	73.9116	+	227.477i	0.0119472	+	0.0367698i	0.956852	−	0.290574i	$-0.0938464\pi$
$337$	73.9116	+	227.477i	0.0119472	+	0.0367698i	−0.944905	+	0.327344i	$0.893846\pi$
$338$	1830.57	−	5633.92i	0.294586	−	0.906642i
$339$	1892.67	+	1375.10i	0.303232	+	0.220311i
$340$	−328.137			−0.0523404
$341$		0			0
$342$	13707.1			2.16723
$343$	−1681.35	−	1221.57i	−0.264678	−	0.192300i
$344$	415.904	−	1280.02i	0.0651861	−	0.200622i
$345$	4052.99	+	12473.8i	0.632481	+	1.94658i
$346$	−5100.02	+	3705.38i	−0.792425	+	0.575730i
$347$	−4743.10	+	3446.06i	−0.733784	+	0.533125i	−0.890758	−	0.454478i	$-0.849826\pi$
$347$	−4743.10	+	3446.06i	−0.733784	+	0.533125i	0.156975	+	0.987603i	$0.449826\pi$
$348$	32.8163	+	100.998i	0.00505500	+	0.0155577i
$349$	−1079.00	+	3320.83i	−0.165495	+	0.509341i	−0.999072	−	0.0430615i	$-0.986289\pi$
$349$	−1079.00	+	3320.83i	−0.165495	+	0.509341i	0.833577	+	0.552403i	$0.186289\pi$
$350$	−649.844	−	472.139i	−0.0992446	−	0.0721054i
$351$	376.283			0.0572208
$352$		0			0
$353$	−10916.7			−1.64600			−0.822999	−	0.568043i	$-0.807701\pi$
$353$	−10916.7			−1.64600			−0.822999	+	0.568043i	$0.807701\pi$
$354$	−1548.54	−	1125.08i	−0.232497	−	0.168919i
$355$	−951.984	+	2929.91i	−0.142327	+	0.438037i
$356$	246.600	+	758.956i	0.0367128	+	0.112990i
$357$	−812.053	+	589.991i	−0.120388	+	0.0874668i
$358$	−2900.22	+	2107.13i	−0.428161	+	0.311077i
$359$	3553.92	+	10937.8i	0.522476	+	1.60802i	0.769254	+	0.638943i	$0.220628\pi$
$359$	3553.92	+	10937.8i	0.522476	+	1.60802i	−0.246778	+	0.969072i	$0.579372\pi$
$360$	3838.85	−	11814.8i	0.562014	−	1.72970i
$361$	−10290.3	−	7476.31i	−1.50026	−	1.09000i
$362$	2194.31			0.318592
$363$		0			0
$364$	−8.82180			−0.00127030
$365$	−12146.5	−	8824.94i	−1.74185	−	1.26553i
$366$	−4944.39	+	15217.3i	−0.706140	+	2.17328i
$367$	2091.12	+	6435.80i	0.297427	+	0.915385i	0.982396	+	0.186813i	$0.0598157\pi$
$367$	2091.12	+	6435.80i	0.297427	+	0.915385i	−0.684969	+	0.728572i	$0.740184\pi$
$368$	−5353.48	+	3889.53i	−0.758342	+	0.550967i
$369$	7573.29	−	5502.31i	1.06843	−	0.776258i
$370$	−164.854	−	507.368i	−0.0231631	−	0.0712887i
$371$	325.584	−	1002.04i	0.0455619	−	0.140225i
$372$	−108.265	−	78.6595i	−0.0150895	−	0.0109632i
$373$	5310.22			0.737139			0.368569	−	0.929600i	$-0.379848\pi$
$373$	5310.22			0.737139			0.368569	+	0.929600i	$0.379848\pi$
$374$		0			0
$375$	3449.58			0.475028
$376$	6487.24	+	4713.25i	0.889770	+	0.646456i
$377$	−41.3919	+	127.391i	−0.00565462	+	0.0174031i
$378$	−182.094	−	560.428i	−0.0247775	−	0.0762574i
$379$	678.172	−	492.721i	0.0919139	−	0.0667794i	−0.540879	−	0.841100i	$-0.681908\pi$
$379$	678.172	−	492.721i	0.0919139	−	0.0667794i	0.632793	+	0.774321i	$0.281908\pi$
$380$	−901.246	+	654.793i	−0.121666	+	0.0883952i
$381$	−3228.07	−	9934.96i	−0.434065	−	1.33592i
$382$	−1450.63	+	4464.58i	−0.194295	+	0.597978i
$383$	2291.27	+	1664.70i	0.305688	+	0.222095i	0.730044	−	0.683400i	$-0.239500\pi$
$383$	2291.27	+	1664.70i	0.305688	+	0.222095i	−0.424356	+	0.905495i	$0.639500\pi$
$384$	10194.5			1.35479
$385$		0			0
$386$	3661.45			0.482806
$387$	−1674.16	−	1216.35i	−0.219903	−	0.159769i
$388$	−222.969	+	686.227i	−0.0291740	+	0.0897884i
$389$	961.431	+	2958.98i	0.125312	+	0.385671i	0.993958	−	0.109763i	$-0.0350090\pi$
$389$	961.431	+	2958.98i	0.125312	+	0.385671i	−0.868646	+	0.495434i	$0.835009\pi$
$390$	1395.14	−	1013.63i	0.181143	−	0.131608i
$391$	3712.98	−	2697.64i	0.480239	−	0.348914i
$392$	−2403.81	−	7398.16i	−0.309721	−	0.953223i
$393$	−3921.66	+	12069.6i	−0.503363	+	1.54919i
$394$	7776.48	+	5649.94i	0.994348	+	0.722436i
$395$	−19227.5			−2.44922
$396$		0			0
$397$	14208.7			1.79626			0.898131	−	0.439728i	$-0.144925\pi$
$397$	14208.7			1.79626			0.898131	+	0.439728i	$0.144925\pi$
$398$	1820.59	+	1322.73i	0.229291	+	0.166590i
$399$	−1053.03	+	3240.88i	−0.132123	+	0.406634i
$400$	−1757.62	−	5409.41i	−0.219703	−	0.676177i
$401$	5065.81	−	3680.52i	0.630859	−	0.458346i	−0.225839	−	0.974165i	$-0.572512\pi$
$401$	5065.81	−	3680.52i	0.630859	−	0.458346i	0.856698	+	0.515819i	$0.172512\pi$
$402$	−5999.33	+	4358.77i	−0.744327	+	0.540785i
$403$	−52.1603	−	160.533i	−0.00644737	−	0.0198429i
$404$	−26.7383	+	82.2919i	−0.00329277	+	0.0101341i
$405$	4945.15	+	3592.86i	0.606732	+	0.440816i
$406$	209.764			0.0256415
$407$		0			0
$408$	−7620.30			−0.924660
$409$	−3391.80	−	2464.29i	−0.410059	−	0.297925i	0.363567	−	0.931568i	$-0.381559\pi$
$409$	−3391.80	−	2464.29i	−0.410059	−	0.297925i	−0.773625	+	0.633643i	$0.781559\pi$
$410$	3274.50	−	10077.9i	0.394429	−	1.21393i
$411$	−3948.53	−	12152.3i	−0.473884	−	1.45847i
$412$	−15.0699	+	10.9489i	−0.00180204	+	0.00130926i
$413$	219.610	−	159.556i	0.0261653	−	0.0190102i
$414$	3370.88	+	10374.5i	0.400168	+	1.23159i
$415$	−2028.46	+	6242.97i	−0.239936	+	0.738446i
$416$	−104.964	−	76.2606i	−0.0123708	−	0.00898794i
$417$	−252.608			−0.0296649
$418$		0			0
$419$	−9287.15			−1.08283			−0.541416	−	0.840755i	$-0.682112\pi$
$419$	−9287.15			−1.08283			−0.541416	+	0.840755i	$0.682112\pi$
$420$	156.863	+	113.968i	0.0182241	+	0.0132406i
$421$	4062.34	−	12502.6i	0.470276	−	1.44736i	−0.381947	−	0.924184i	$-0.624746\pi$
$421$	4062.34	−	12502.6i	0.470276	−	1.44736i	0.852224	−	0.523178i	$-0.175254\pi$
$422$	−90.6245	−	278.913i	−0.0104539	−	0.0321737i
$423$	9974.44	−	7246.85i	1.14651	−	0.832988i
$424$	6471.18	−	4701.58i	0.741198	−	0.538512i
$425$	1219.02	+	3751.77i	0.139132	+	0.428206i
$426$	−1387.97	+	4271.73i	−0.157857	+	0.485835i
$427$	−1835.76	−	1333.76i	−0.208053	−	0.151160i
$428$	445.964			0.0503656
$429$		0			0
$430$	−2342.47			−0.262707
$431$	3972.00	+	2885.83i	0.443909	+	0.322519i	0.787186	−	0.616715i	$-0.211537\pi$
$431$	3972.00	+	2885.83i	0.443909	+	0.322519i	−0.343277	+	0.939234i	$0.611537\pi$
$432$	1289.40	−	3968.37i	0.143603	−	0.441964i
$433$	−3628.88	−	11168.5i	−0.402755	−	1.23955i	−0.922755	−	0.385386i	$-0.874068\pi$
$433$	−3628.88	−	11168.5i	−0.402755	−	1.23955i	0.520000	−	0.854166i	$-0.325932\pi$
$434$	−213.852	+	155.373i	−0.0236526	+	0.0171846i
$435$	2381.75	−	1730.44i	0.262520	−	0.190732i
$436$	172.931	+	532.226i	0.0189951	+	0.0584610i
$437$	4814.78	−	14818.4i	0.527053	−	1.62210i
$438$	−17709.3	−	12866.5i	−1.93192	−	1.40362i
$439$	11824.2			1.28551			0.642754	−	0.766073i	$-0.277792\pi$
$439$	11824.2			1.28551			0.642754	+	0.766073i	$0.277792\pi$
$440$		0			0
$441$	−11960.4			−1.29148
$442$	−488.189	−	354.690i	−0.0525357	−	0.0381695i
$443$	3121.72	−	9607.68i	0.334803	−	1.03042i	−0.632016	−	0.774955i	$-0.717772\pi$
$443$	3121.72	−	9607.68i	0.334803	−	1.03042i	0.966819	−	0.255462i	$-0.0822275\pi$
$444$	17.2565	+	53.1102i	0.00184450	+	0.00567680i
$445$	17897.8	−	13003.5i	1.90660	−	1.38522i
$446$	−8694.52	+	6316.94i	−0.923088	+	0.670663i
$447$	−5949.32	−	18310.1i	−0.629515	−	1.93745i
$448$	−514.058	+	1582.11i	−0.0542120	+	0.166847i
$449$	279.316	+	202.935i	0.0293580	+	0.0213299i	0.602368	−	0.798219i	$-0.294224\pi$
$449$	279.316	+	202.935i	0.0293580	+	0.0213299i	−0.573009	+	0.819549i	$0.694224\pi$
$450$	−9376.17			−0.982216
$451$		0			0
$452$	−158.134			−0.0164557
$453$	16526.9	+	12007.5i	1.71414	+	1.24539i
$454$	−1495.93	+	4603.99i	−0.154642	+	0.475939i
$455$	75.5738	+	232.592i	0.00778671	+	0.0239650i
$456$	−20929.5	+	15206.2i	−2.14938	+	1.56161i
$457$	−8549.00	+	6211.21i	−0.875067	+	0.635773i	−0.931942	−	0.362608i	$-0.881886\pi$
$457$	−8549.00	+	6211.21i	−0.875067	+	0.635773i	0.0568749	+	0.998381i	$0.481886\pi$
$458$	−1617.05	−	4976.77i	−0.164978	−	0.507749i
$459$	−894.281	+	2752.31i	−0.0909400	+	0.279885i
$460$	−717.231	−	521.099i	−0.0726980	−	0.0528182i
$461$	−4733.96			−0.478270			−0.239135	−	0.970986i	$-0.576864\pi$
$461$	−4733.96			−0.478270			−0.239135	+	0.970986i	$0.576864\pi$
$462$		0			0
$463$	3431.20			0.344409			0.172204	−	0.985061i	$-0.444911\pi$
$463$	3431.20			0.344409			0.172204	+	0.985061i	$0.444911\pi$
$464$	1201.66	+	873.058i	0.120228	+	0.0873506i
$465$	−1146.43	+	3528.34i	−0.114332	+	0.351877i
$466$	3711.59	+	11423.1i	0.368962	+	1.13555i
$467$	−4139.71	+	3007.67i	−0.410199	+	0.298027i	−0.773682	−	0.633574i	$-0.781587\pi$
$467$	−4139.71	+	3007.67i	−0.410199	+	0.298027i	0.363483	+	0.931601i	$0.381587\pi$
$468$	−83.3085	+	60.5272i	−0.00822850	+	0.00597835i
$469$	−324.980	−	1000.19i	−0.0319961	−	0.0984739i
$470$	4312.70	−	13273.1i	0.423255	−	1.30265i
$471$	15880.8	+	11538.1i	1.55361	+	1.12876i
$472$	2060.82			0.200968
$473$		0			0
$474$	−28033.2			−2.71648
$475$	10834.7	+	7871.87i	1.04659	+	0.760392i
$476$	20.9661	−	64.5269i	0.00201886	−	0.00621341i
$477$	−3800.46	−	11696.6i	−0.364804	−	1.12275i
$478$	9027.85	−	6559.12i	0.863858	−	0.627630i
$479$	9357.81	−	6798.85i	0.892629	−	0.648533i	−0.0439333	−	0.999034i	$-0.513989\pi$
$479$	9357.81	−	6798.85i	0.892629	−	0.648533i	0.936562	+	0.350502i	$0.113989\pi$
$480$	881.191	+	2712.03i	0.0837931	+	0.257889i
$481$	−21.7660	+	66.9889i	−0.00206329	+	0.00635017i
$482$	−8639.05	−	6276.64i	−0.816386	−	0.593139i
$483$	−2711.89			−0.255477
$484$		0			0
$485$	20002.9			1.87275
$486$	11400.2	+	8282.71i	1.06404	+	0.773068i
$487$	−5663.21	+	17429.6i	−0.526950	+	1.62179i	0.233477	+	0.972362i	$0.424990\pi$
$487$	−5663.21	+	17429.6i	−0.526950	+	1.62179i	−0.760427	+	0.649423i	$0.775010\pi$
$488$	−5323.37	−	16383.7i	−0.493807	−	1.51978i
$489$	−17479.0	+	12699.2i	−1.61641	+	1.17439i
$490$	−10953.2	+	7957.94i	−1.00982	+	0.733679i
$491$	2353.96	+	7244.75i	0.216360	+	0.665888i	0.999054	+	0.0434814i	$0.0138449\pi$
$491$	2353.96	+	7244.75i	0.216360	+	0.665888i	−0.782694	+	0.622407i	$0.786155\pi$
$492$	−342.767	+	1054.93i	−0.0314088	+	0.0966665i
$493$	−833.427	−	605.520i	−0.0761372	−	0.0553169i
$494$	−2048.62			−0.186582
$495$		0			0
$496$	−1871.75			−0.169444
$497$	−515.328	−	374.408i	−0.0465103	−	0.0337917i
$498$	−2957.45	+	9102.09i	−0.266117	+	0.819024i
$499$	3989.14	+	12277.3i	0.357872	+	1.10142i	0.954325	+	0.298770i	$0.0965763\pi$
$499$	3989.14	+	12277.3i	0.357872	+	1.10142i	−0.596453	+	0.802648i	$0.703424\pi$
$500$	−188.639	+	137.054i	−0.0168724	+	0.0122585i
$501$	−17557.2	+	12756.0i	−1.56566	+	1.13752i
$502$	−924.363	−	2844.90i	−0.0821839	−	0.252936i
$503$	−3141.36	+	9668.11i	−0.278462	+	0.857017i	0.709821	+	0.704382i	$0.248776\pi$
$503$	−3141.36	+	9668.11i	−0.278462	+	0.857017i	−0.988283	+	0.152635i	$0.951224\pi$
$504$	2078.04	+	1509.79i	0.183658	+	0.133435i
$505$	2398.74			0.211371
$506$		0			0
$507$	17190.6			1.50584
$508$	571.249	+	415.037i	0.0498919	+	0.0362486i
$509$	1993.14	−	6134.25i	0.173564	−	0.534177i	−0.826001	−	0.563669i	$-0.809389\pi$
$509$	1993.14	−	6134.25i	0.173564	−	0.534177i	0.999565	+	0.0294928i	$0.00938922\pi$
$510$	4098.44	+	12613.7i	0.355847	+	1.09519i
$511$	2511.48	−	1824.70i	0.217419	−	0.157964i
$512$	−10133.3	+	7362.24i	−0.874670	+	0.635485i
$513$	3036.02	+	9343.89i	0.261293	+	0.804177i
$514$	−661.199	+	2034.96i	−0.0567398	+	0.174627i
$515$	417.774	+	303.530i	0.0357462	+	0.0259712i
$516$	245.205			0.0209197
$517$		0			0
$518$	110.305			0.00935623
$519$	−14799.9	−	10752.7i	−1.25172	−	0.909428i
$520$	−573.742	+	1765.80i	−0.0483851	+	0.148914i
$521$	−5972.50	−	18381.5i	−0.502227	−	1.54569i	−0.805383	−	0.592754i	$-0.798041\pi$
$521$	−5972.50	−	18381.5i	−0.502227	−	1.54569i	0.303157	−	0.952941i	$-0.401959\pi$
$522$	1980.90	−	1439.21i	0.166096	−	0.120675i
$523$	5063.71	−	3679.00i	0.423367	−	0.307594i	−0.355624	−	0.934629i	$-0.615732\pi$
$523$	5063.71	−	3679.00i	0.423367	−	0.307594i	0.778991	+	0.627035i	$0.215732\pi$
$524$	−265.081	−	815.835i	−0.0220994	−	0.0680151i
$525$	720.310	−	2216.89i	0.0598799	−	0.184291i
$526$	−13659.6	−	9924.30i	−1.13230	−	0.822662i
$527$	1298.18			0.107305
$528$		0			0
$529$	232.675			0.0191235
$530$	−11262.8	−	8182.93i	−0.923069	−	0.670649i
$531$	979.153	−	3013.52i	0.0800219	−	0.246282i
$532$	−71.1781	−	219.064i	−0.00580068	−	0.0178527i
$533$	−1131.88	+	822.358i	−0.0919834	+	0.0668298i
$534$	26094.5	−	18958.8i	2.11464	−	1.53638i
$535$	−3820.44	−	11758.1i	−0.308733	−	0.950181i
$536$	2467.19	−	7593.22i	0.198818	−	0.611898i
$537$	−8416.22	−	6114.75i	−0.676326	−	0.491379i
$538$	−2696.44			−0.216081
$539$		0			0
$540$	559.022			0.0445490
$541$	−11332.8	−	8233.79i	−0.900623	−	0.654341i	0.0380030	−	0.999278i	$-0.487900\pi$
$541$	−11332.8	−	8233.79i	−0.900623	−	0.654341i	−0.938626	+	0.344937i	$0.887900\pi$
$542$	3864.12	−	11892.6i	0.306233	−	0.942489i
$543$	1967.74	+	6056.07i	0.155513	+	0.478620i
$544$	807.265	−	586.512i	0.0636235	−	0.0462252i
$545$	12551.0	−	9118.84i	0.986470	−	0.716712i
$546$	110.185	+	339.113i	0.00863638	+	0.0265801i
$547$	1529.46	−	4707.20i	0.119552	−	0.367944i	−0.873317	−	0.487152i	$-0.838036\pi$
$547$	1529.46	−	4707.20i	0.119552	−	0.367944i	0.992869	+	0.119208i	$0.0380356\pi$
$548$	698.744	+	507.667i	0.0544687	+	0.0395738i
$549$	−26487.0			−2.05909
$550$		0			0
$551$	−3497.35			−0.270404
$552$	−16656.2	−	12101.4i	−1.28430	−	0.933100i
$553$	1228.53	−	3781.02i	0.0944707	−	0.290751i
$554$	479.395	+	1475.43i	0.0367645	+	0.113150i
$555$	1252.45	−	909.958i	0.0957901	−	0.0695956i
$556$	13.8138	−	10.0363i	0.00105366	−	0.000765528i
$557$	1174.75	+	3615.51i	0.0893641	+	0.275034i	0.985744	−	0.168252i	$-0.0538123\pi$
$557$	1174.75	+	3615.51i	0.0893641	+	0.275034i	−0.896380	+	0.443287i	$0.853812\pi$
$558$	−953.483	+	2934.52i	−0.0723372	+	0.222631i
$559$	250.214	+	181.791i	0.0189319	+	0.0137548i
$560$	2711.94			0.204644
$561$		0			0
$562$	14510.0			1.08908
$563$	−8009.36	−	5819.14i	−0.599564	−	0.435608i	0.246160	−	0.969229i	$-0.420831\pi$
$563$	−8009.36	−	5819.14i	−0.599564	−	0.435608i	−0.845724	+	0.533621i	$0.820831\pi$
$564$	−451.444	+	1389.40i	−0.0337043	+	0.103731i
$565$	1354.69	+	4169.29i	0.100871	+	0.310449i
$566$	10451.2	−	7593.21i	0.776139	−	0.563898i
$567$	−1022.49	+	742.880i	−0.0757327	+	0.0550230i
$568$	−1494.36	−	4599.15i	−0.110390	−	0.339747i
$569$	−1646.80	+	5068.33i	−0.121331	+	0.373419i	−0.993215	−	0.116294i	$-0.962898\pi$
$569$	−1646.80	+	5068.33i	−0.121331	+	0.373419i	0.871884	+	0.489713i	$0.162898\pi$
$570$	36427.1	+	26465.8i	2.67678	+	1.94479i
$571$	16962.6			1.24319			0.621597	−	0.783337i	$-0.286484\pi$
$571$	16962.6			1.24319			0.621597	+	0.783337i	$0.286484\pi$
$572$		0			0
$573$	−13622.6			−0.993181
$574$	1772.55	+	1287.83i	0.128893	+	0.0936466i
$575$	−3293.50	+	10136.3i	−0.238867	+	0.735156i
$576$	6000.49	+	18467.6i	0.434063	+	1.33591i
$577$	12529.2	−	9103.01i	0.903983	−	0.656782i	−0.0355028	−	0.999370i	$-0.511303\pi$
$577$	12529.2	−	9103.01i	0.903983	−	0.656782i	0.939486	+	0.342587i	$0.111303\pi$
$578$	−7104.47	+	5161.70i	−0.511258	+	0.371451i
$579$	3283.38	+	10105.2i	0.235670	+	0.725317i
$580$	−61.4935	+	189.257i	−0.00440238	+	0.0135491i
$581$	−1098.05	−	797.778i	−0.0784074	−	0.0569663i
$582$	29163.7			2.07710
$583$		0			0
$584$	23567.7			1.66993
$585$	2309.51	+	1677.96i	0.163225	+	0.118590i
$586$	1966.19	−	6051.30i	0.138605	−	0.426582i
$587$	3425.19	+	10541.7i	0.240839	+	0.741228i	0.996293	+	0.0860254i	$0.0274166\pi$
$587$	3425.19	+	10541.7i	0.240839	+	0.741228i	−0.755453	+	0.655202i	$0.772583\pi$
$588$	1146.55	−	833.019i	0.0804133	−	0.0584237i
$589$	3565.51	−	2590.50i	0.249430	−	0.181222i
$590$	−1108.37	−	3411.22i	−0.0773407	−	0.238030i
$591$	−8619.73	+	26528.8i	−0.599946	+	1.84644i
$592$	631.896	+	459.099i	0.0438695	+	0.0318731i
$593$	−4349.68			−0.301214			−0.150607	−	0.988594i	$-0.548123\pi$
$593$	−4349.68			−0.301214			−0.150607	+	0.988594i	$0.548123\pi$
$594$		0			0
$595$	−1880.90			−0.129596
$596$	1052.81	+	764.911i	0.0723570	+	0.0525705i
$597$	−2018.00	+	6210.78i	−0.138344	+	0.425779i
$598$	−503.801	−	1550.54i	−0.0344514	−	0.106031i
$599$	−10666.0	+	7749.31i	−0.727548	+	0.528595i	−0.888787	−	0.458321i	$-0.848451\pi$
$599$	−10666.0	+	7749.31i	−0.727548	+	0.528595i	0.161239	+	0.986915i	$0.448451\pi$
$600$	14316.6	−	10401.6i	0.974123	−	0.707742i
$601$	5798.71	+	17846.6i	0.393568	+	1.21128i	0.930071	+	0.367379i	$0.119745\pi$
$601$	5798.71	+	17846.6i	0.393568	+	1.21128i	−0.536503	+	0.843898i	$0.680255\pi$
$602$	149.670	−	460.638i	0.0101331	−	0.0311864i
$603$	−9931.30	−	7215.51i	−0.670703	−	0.487294i
$604$	−1380.84			−0.0930223
$605$		0			0
$606$	3497.29			0.234435
$607$	17694.3	+	12855.7i	1.18318	+	0.859629i	0.992527	−	0.122028i	$-0.0389399\pi$
$607$	17694.3	+	12855.7i	1.18318	+	0.859629i	0.190652	+	0.981658i	$0.438940\pi$
$608$	1046.82	−	3221.77i	0.0698257	−	0.214901i
$609$	188.105	+	578.927i	0.0125162	+	0.0385210i
$610$	−24256.4	+	17623.3i	−1.61002	+	1.16975i
$611$	−1490.75	+	1083.09i	−0.0987057	+	0.0717139i
$612$	−244.732	−	753.208i	−0.0161646	−	0.0497494i
$613$	1090.17	−	3355.19i	0.0718294	−	0.221068i	−0.908697	−	0.417457i	$-0.862921\pi$
$613$	1090.17	−	3355.19i	0.0718294	−	0.221068i	0.980526	+	0.196389i	$0.0629215\pi$
$614$	3708.99	+	2694.74i	0.243783	+	0.177119i
$615$	30750.2			2.01621
$616$		0			0
$617$	−22728.1			−1.48298			−0.741490	−	0.670963i	$-0.765881\pi$
$617$	−22728.1			−1.48298			−0.741490	+	0.670963i	$0.765881\pi$
$618$	609.103	+	442.540i	0.0396468	+	0.0288051i
$619$	−6626.35	+	20393.8i	−0.430267	+	1.32423i	0.467592	+	0.883944i	$0.345121\pi$
$619$	−6626.35	+	20393.8i	−0.430267	+	1.32423i	−0.897860	+	0.440282i	$0.854879\pi$
$620$	−77.4914	−	238.494i	−0.00501956	−	0.0154486i
$621$	−6325.50	+	4595.75i	−0.408750	+	0.296974i
$622$	7896.67	−	5737.26i	0.509047	−	0.369845i
$623$	1413.52	+	4350.37i	0.0909013	+	0.279766i
$624$	−780.213	+	2401.25i	−0.0500537	+	0.154050i
$625$	14908.7	+	10831.8i	0.954156	+	0.693235i
$626$	−19628.0			−1.25319
$627$		0			0
$628$	−1326.85			−0.0843109
$629$	−438.259	−	318.414i	−0.0277815	−	0.0201844i
$630$	1381.48	−	4251.75i	0.0873642	−	0.268879i
$631$	6653.74	+	20478.1i	0.419780	+	1.29195i	0.907905	+	0.419177i	$0.137681\pi$
$631$	6653.74	+	20478.1i	0.419780	+	1.29195i	−0.488124	+	0.872774i	$0.662319\pi$
$632$	24417.7	−	17740.5i	1.53684	−	1.11658i
$633$	688.504	−	500.228i	0.0432316	−	0.0314096i
$634$	13.2612	+	40.8138i	0.000830709	+	0.00255666i
$635$	6048.97	−	18616.8i	0.378025	−	1.16344i
$636$	1178.97	+	856.571i	0.0735050	+	0.0534045i
$637$	1787.56			0.111187
$638$		0			0
$639$	−7435.33			−0.460309
$640$	15454.8	+	11228.6i	0.954540	+	0.693514i
$641$	6226.16	−	19162.1i	0.383648	−	1.18075i	−0.553808	−	0.832644i	$-0.686826\pi$
$641$	6226.16	−	19162.1i	0.383648	−	1.18075i	0.937456	−	0.348103i	$-0.113174\pi$
$642$	−5570.10	−	17143.0i	−0.342421	−	1.05386i
$643$	−23356.1	+	16969.2i	−1.43246	+	1.04074i	−0.442911	+	0.896566i	$0.646054\pi$
$643$	−23356.1	+	16969.2i	−1.43246	+	1.04074i	−0.989552	+	0.144179i	$0.953946\pi$
$644$	148.299	−	107.745i	0.00907421	−	0.00659280i
$645$	−2100.60	−	6464.98i	−0.128234	−	0.394664i
$646$	4868.78	−	14984.6i	0.296532	−	0.912631i
$647$	1286.35	+	934.591i	0.0781636	+	0.0567891i	0.626181	−	0.779678i	$-0.284617\pi$
$647$	1286.35	+	934.591i	0.0781636	+	0.0567891i	−0.548017	+	0.836467i	$0.684617\pi$
$648$	−9595.02			−0.581679
$649$		0			0
$650$	1401.33			0.0845612
$651$	−620.583	−	450.880i	−0.0373619	−	0.0271450i
$652$	451.282	−	1388.90i	0.0271067	−	0.0834259i
$653$	6189.01	+	19047.8i	0.370896	+	1.14150i	0.946206	+	0.323564i	$0.104881\pi$
$653$	6189.01	+	19047.8i	0.370896	+	1.14150i	−0.575311	+	0.817935i	$0.695119\pi$
$654$	18299.0	−	13295.0i	1.09411	−	0.794919i
$655$	−19239.1	+	13978.0i	−1.14769	+	0.833842i
$656$	4794.20	+	14755.0i	0.285338	+	0.878182i
$657$	11197.7	−	34462.9i	0.664937	−	2.04646i
$658$	2334.55	+	1696.15i	0.138313	+	0.100491i
$659$	10520.7			0.621897			0.310948	−	0.950427i	$-0.399353\pi$
$659$	10520.7			0.621897			0.310948	+	0.950427i	$0.399353\pi$
$660$		0			0
$661$	3295.83			0.193938			0.0969690	−	0.995287i	$-0.469085\pi$
$661$	3295.83			0.193938			0.0969690	+	0.995287i	$0.469085\pi$
$662$	−2915.25	−	2118.05i	−0.171155	−	0.124351i
$663$	541.127	−	1665.42i	0.0316978	−	0.0975557i
$664$	−3184.13	−	9799.76i	−0.186097	−	0.572748i
$665$	−5165.99	+	3753.31i	−0.301246	+	0.218868i
$666$	1041.66	−	756.813i	0.0606060	−	0.0440329i
$667$	−860.078	−	2647.05i	−0.0499286	−	0.153664i
$668$	453.301	−	1395.12i	0.0262556	−	0.0808064i
$669$	−25230.8	−	18331.3i	−1.45812	−	1.05938i
$670$	−13895.8			−0.801257
$671$		0			0
$672$	−589.612			−0.0338464
$673$	−960.819	−	698.076i	−0.0550325	−	0.0399834i	0.559929	−	0.828541i	$-0.310828\pi$
$673$	−960.819	−	698.076i	−0.0550325	−	0.0399834i	−0.614961	+	0.788557i	$0.710828\pi$
$674$	−201.930	+	621.477i	−0.0115402	+	0.0355169i
$675$	−2076.75	−	6391.59i	−0.118421	−	0.364463i
$676$	−940.060	+	682.994i	−0.0534855	+	0.0388595i
$677$	10696.3	−	7771.33i	0.607227	−	0.441177i	−0.241210	−	0.970473i	$-0.577544\pi$
$677$	10696.3	−	7771.33i	0.607227	−	0.441177i	0.848437	+	0.529297i	$0.177544\pi$
$678$	1975.10	+	6078.72i	0.111878	+	0.344324i
$679$	−1278.07	+	3933.49i	−0.0722353	+	0.222317i
$680$	−11552.3	−	8393.24i	−0.651487	−	0.473333i
$681$	−14048.0			−0.790485
$682$		0			0
$683$	−13831.4			−0.774882			−0.387441	−	0.921894i	$-0.626641\pi$
$683$	−13831.4			−0.774882			−0.387441	+	0.921894i	$0.626641\pi$
$684$	−2175.18	−	1580.36i	−0.121594	−	0.0883432i
$685$	7399.02	−	22771.8i	0.412704	−	1.27017i
$686$	−1754.58	−	5400.03i	−0.0976532	−	0.300546i
$687$	12285.3	−	8925.78i	0.682260	−	0.495691i
$688$	2774.62	−	2015.88i	0.153752	−	0.111707i
$689$	568.005	+	1748.14i	0.0314068	+	0.0966602i
$690$	−11073.0	+	34079.2i	−0.610930	+	1.88025i
$691$	7942.18	+	5770.33i	0.437243	+	0.317675i	0.784538	−	0.620080i	$-0.212900\pi$
$691$	7942.18	+	5770.33i	0.437243	+	0.317675i	−0.347296	+	0.937756i	$0.612900\pi$
$692$	1236.54			0.0679280
$693$		0			0
$694$	−16017.4			−0.876101
$695$	−382.951	−	278.230i	−0.0209010	−	0.0151854i
$696$	−1428.06	+	4395.11i	−0.0777735	+	0.239362i
$697$	−3325.08	−	10233.5i	−0.180698	−	0.556130i
$698$	−7717.68	+	5607.22i	−0.418508	+	0.304064i
$699$	−28198.2	+	20487.2i	−1.52583	+	1.10858i
$700$	48.6886	+	149.848i	0.00262894	+	0.00809104i
$701$	−9254.98	+	28483.9i	−0.498653	+	1.53470i	0.312532	+	0.949907i	$0.398823\pi$
$701$	−9254.98	+	28483.9i	−0.498653	+	1.53470i	−0.811185	+	0.584789i	$0.801177\pi$
$702$	831.689	+	604.258i	0.0447152	+	0.0324875i
$703$	−1839.09			−0.0986667
$704$		0			0
$705$	40499.8			2.16356
$706$	−24128.9	−	17530.7i	−1.28627	−	0.934527i
$707$	−153.265	+	471.702i	−0.00815294	+	0.0250922i
$708$	116.022	+	357.080i	0.00615873	+	0.0189546i
$709$	−9147.95	+	6646.38i	−0.484568	+	0.352059i	−0.803091	−	0.595856i	$-0.796813\pi$
$709$	−9147.95	+	6646.38i	−0.484568	+	0.352059i	0.318524	+	0.947915i	$0.396813\pi$
$710$	−6809.16	+	4947.15i	−0.359920	+	0.261497i
$711$	−14340.3	−	44135.0i	−0.756405	−	2.32798i
$712$	−10731.2	+	33027.2i	−0.564843	+	1.73841i
$713$	2837.51	+	2061.57i	0.149040	+	0.108284i
$714$	−2742.30			−0.143737
$715$		0			0
$716$	703.181			0.0367027
$717$	26198.1	+	19034.1i	1.36456	+	0.991409i
$718$	−9709.49	+	29882.8i	−0.504673	+	1.55322i
$719$	−10081.2	−	31026.7i	−0.522900	−	1.60932i	−0.768431	−	0.639933i	$-0.778962\pi$
$719$	−10081.2	−	31026.7i	−0.522900	−	1.60932i	0.245531	−	0.969389i	$-0.421038\pi$
$720$	25610.1	−	18606.9i	1.32560	−	0.963106i
$721$	−86.3813	+	62.7597i	−0.00446187	+	0.00324174i
$722$	−10738.4	−	33049.4i	−0.553521	−	1.70356i
$723$	9575.83	−	29471.4i	0.492571	−	1.51598i
$724$	−348.217	−	252.994i	−0.0178748	−	0.0129868i
$725$	2392.33			0.122550
$726$		0			0
$727$	−502.545			−0.0256373			−0.0128187	−	0.999918i	$-0.504080\pi$
$727$	−502.545			−0.0256373			−0.0128187	+	0.999918i	$0.504080\pi$
$728$	−310.578	−	225.648i	−0.0158115	−	0.0114877i
$729$	−9203.52	+	28325.5i	−0.467587	+	1.43909i
$730$	−12675.5	−	39011.1i	−0.642658	−	1.97790i
$731$	−1924.37	+	1398.14i	−0.0973673	+	0.0707415i
$732$	2539.11	−	1844.77i	0.128208	−	0.0931485i
$733$	−2667.24	−	8208.93i	−0.134402	−	0.413647i	0.861094	−	0.508445i	$-0.169780\pi$
$733$	−2667.24	−	8208.93i	−0.134402	−	0.413647i	−0.995497	+	0.0947978i	$0.969780\pi$
$734$	−5713.05	+	17582.9i	−0.287292	+	0.884194i
$735$	−31785.2	−	23093.3i	−1.59512	−	1.15893i
$736$	2695.90			0.135017
$737$		0			0
$738$	25575.0			1.27565
$739$	−14851.5	−	10790.3i	−0.739273	−	0.537113i	0.153210	−	0.988194i	$-0.451039\pi$
$739$	−14851.5	−	10790.3i	−0.739273	−	0.537113i	−0.892483	+	0.451080i	$0.851039\pi$
$740$	−32.3365	+	99.5214i	−0.00160637	+	0.00494389i
$741$	−1837.08	−	5653.96i	−0.0910755	−	0.280302i
$742$	2328.77	−	1691.95i	0.115218	−	0.0837108i
$743$	9046.95	−	6572.99i	0.446703	−	0.324549i	−0.341590	−	0.939849i	$-0.610965\pi$
$743$	9046.95	−	6572.99i	0.446703	−	0.324549i	0.788293	+	0.615300i	$0.210965\pi$
$744$	−1799.58	−	5538.53i	−0.0886770	−	0.272920i
$745$	11148.2	−	34310.7i	0.548241	−	1.68731i
$746$	11737.0	+	8527.47i	0.576037	+	0.418516i
$747$	−15843.0			−0.775991
$748$		0			0
$749$	2556.29			0.124706
$750$	7624.52	+	5539.54i	0.371211	+	0.269701i
$751$	5170.90	−	15914.4i	0.251250	−	0.773269i	−0.743295	−	0.668964i	$-0.766738\pi$
$751$	5170.90	−	15914.4i	0.251250	−	0.773269i	0.994545	−	0.104305i	$-0.0332618\pi$
$752$	6314.23	+	19433.2i	0.306192	+	0.942361i
$753$	7022.69	−	5102.29i	0.339869	−	0.246929i
$754$	−296.060	+	215.100i	−0.0142995	+	0.0103892i
$755$	11829.2	+	36406.6i	0.570211	+	1.75493i
$756$	−35.7182	+	109.929i	−0.00171833	+	0.00528848i
$757$	19742.0	+	14343.4i	0.947865	+	0.688664i	0.950301	−	0.311333i	$-0.100775\pi$
$757$	19742.0	+	14343.4i	0.947865	+	0.688664i	−0.00243609	+	0.999997i	$0.500775\pi$
$758$	2290.19			0.109741
$759$		0			0
$760$	−48477.6			−2.31377
$761$	6851.83	+	4978.15i	0.326385	+	0.237132i	0.738895	−	0.673821i	$-0.235348\pi$
$761$	6851.83	+	4978.15i	0.326385	+	0.237132i	−0.412510	+	0.910953i	$0.635348\pi$
$762$	8819.24	−	27142.8i	0.419275	−	1.29039i
$763$	991.247	+	3050.74i	0.0470322	+	0.144750i
$764$	744.947	−	541.236i	0.0352765	−	0.0256299i
$765$	−17762.2	+	12905.0i	−0.839471	+	0.609911i
$766$	2391.06	+	7358.91i	0.112784	+	0.347113i
$767$	−146.341	+	450.391i	−0.00688927	+	0.0212030i
$768$	−5255.44	−	3818.30i	−0.246926	−	0.179402i
$769$	−32834.7			−1.53973			−0.769864	−	0.638208i	$-0.779676\pi$
$769$	−32834.7			−1.53973			−0.769864	+	0.638208i	$0.779676\pi$
$770$		0			0
$771$	−6209.20			−0.290038
$772$	−581.038	−	422.149i	−0.0270881	−	0.0196807i
$773$	−10992.2	+	33830.4i	−0.511463	+	1.57412i	0.278164	+	0.960533i	$0.410274\pi$
$773$	−10992.2	+	33830.4i	−0.511463	+	1.57412i	−0.789627	+	0.613587i	$0.789726\pi$
$774$	−1747.07	−	5376.93i	−0.0811332	−	0.249702i
$775$	−2438.95	+	1772.00i	−0.113045	+	0.0821318i
$776$	−25402.4	+	18455.9i	−1.17512	+	0.853774i
$777$	98.9154	+	304.430i	0.00456701	+	0.0140558i
$778$	−2626.68	+	8084.08i	−0.121042	+	0.372530i
$779$	−29553.4	−	21471.8i	−1.35925	−	0.987556i
$780$	−338.262			−0.0155279
$781$		0			0
$782$	12538.7			0.573381
$783$	1419.84	+	1031.58i	0.0648034	+	0.0470824i
$784$	6125.41	−	18852.1i	0.279037	−	0.858787i
$785$	11366.8	+	34983.3i	0.516812	+	1.59058i
$786$	−28050.1	+	20379.6i	−1.27292	+	0.924830i
$787$	12725.5	−	9245.63i	0.576386	−	0.418769i	−0.261033	−	0.965330i	$-0.584063\pi$
$787$	12725.5	−	9245.63i	0.576386	−	0.418769i	0.837419	+	0.546561i	$0.184063\pi$
$788$	−582.641	−	1793.19i	−0.0263398	−	0.0810655i
$789$	15140.8	−	46598.7i	0.683178	−	2.10261i
$790$	−42498.2	−	30876.7i	−1.91394	−	1.39056i
$791$	−906.431			−0.0407446
$792$		0			0
$793$	3958.67			0.177272
$794$	31405.2	+	22817.2i	1.40369	+	1.01984i
$795$	12484.1	−	38422.2i	0.556939	−	1.71408i
$796$	−136.405	−	419.811i	−0.00607380	−	0.0186932i
$797$	−6381.58	+	4636.49i	−0.283623	+	0.206064i	−0.720496	−	0.693459i	$-0.756086\pi$
$797$	−6381.58	+	4636.49i	−0.283623	+	0.206064i	0.436873	+	0.899523i	$0.356086\pi$
$798$	−7531.87	+	5472.23i	−0.334117	+	0.242750i
$799$	−4379.31	−	13478.1i	−0.193904	−	0.596774i
$800$	−716.063	+	2203.82i	−0.0316458	+	0.0973958i
$801$	43196.8	+	31384.3i	1.90547	+	1.38441i
$802$	17107.2			0.753214
$803$		0			0
$804$	1454.58			0.0638050
$805$	−4111.20	−	2986.96i	−0.180001	−	0.130778i
$806$	142.505	−	438.584i	0.00622768	−	0.0191668i
$807$	−2418.01	−	7441.88i	−0.105475	−	0.324618i
$808$	−3046.24	+	2213.22i	−0.132632	+	0.0963625i
$809$	4770.75	−	3466.15i	0.207331	−	0.150635i	−0.479274	−	0.877665i	$-0.659100\pi$
$809$	4770.75	−	3466.15i	0.207331	−	0.150635i	0.686605	+	0.727030i	$0.259100\pi$
$810$	5160.51	+	15882.4i	0.223854	+	0.688952i
$811$	−4387.41	+	13503.0i	−0.189966	+	0.584656i	−0.999999	−	0.00172932i	$-0.999450\pi$
$811$	−4387.41	+	13503.0i	−0.189966	+	0.584656i	0.810032	+	0.586385i	$0.199450\pi$
$812$	−33.2876	−	24.1849i	−0.00143863	−	0.00104523i
$813$	36287.3			1.56538
$814$		0			0
$815$	−40485.3			−1.74005
$816$	−15709.6	−	11413.7i	−0.673954	−	0.489656i
$817$	−2495.42	+	7680.12i	−0.106859	+	0.328878i
$818$	−3539.52	−	10893.5i	−0.151291	−	0.465627i
$819$	−477.529	+	346.945i	−0.0203739	+	0.0148025i
$820$	−1681.57	+	1221.73i	−0.0716132	+	0.0520300i
$821$	6131.42	+	18870.6i	0.260643	+	0.802177i	0.992665	+	0.120896i	$0.0385768\pi$
$821$	6131.42	+	18870.6i	0.260643	+	0.802177i	−0.732022	+	0.681281i	$0.761423\pi$
$822$	10787.6	−	33200.7i	0.457737	−	1.40877i
$823$	22816.0	+	16576.8i	0.966364	+	0.702104i	0.954620	−	0.297827i	$-0.0962617\pi$
$823$	22816.0	+	16576.8i	0.966364	+	0.702104i	0.0117439	+	0.999931i	$0.496262\pi$
$824$	−810.602			−0.0342702
$825$		0			0
$826$	741.622			0.0312401
$827$	27531.7	+	20002.9i	1.15764	+	0.841076i	0.989478	−	0.144683i	$-0.0462161\pi$
$827$	27531.7	+	20002.9i	1.15764	+	0.841076i	0.168164	+	0.985759i	$0.446216\pi$
$828$	661.206	−	2034.98i	0.0277518	−	0.0854113i
$829$	1523.93	+	4690.19i	0.0638461	+	0.196498i	0.977891	−	0.209115i	$-0.0670582\pi$
$829$	1523.93	+	4690.19i	0.0638461	+	0.196498i	−0.914045	+	0.405613i	$0.867058\pi$
$830$	−14508.8	+	10541.3i	−0.606756	+	0.440834i
$831$	−3642.13	+	2646.16i	−0.152039	+	0.110462i
$832$	−896.814	−	2760.11i	−0.0373695	−	0.115011i
$833$	−4248.36	+	13075.1i	−0.176707	+	0.543848i
$834$	−558.333	−	405.653i	−0.0231816	−	0.0168424i
$835$	−40666.4			−1.68541
$836$		0			0
$837$	−2211.60			−0.0913312
$838$	−20527.2	−	14913.9i	−0.846180	−	0.614786i
$839$	−11801.3	+	36320.6i	−0.485609	+	1.49455i	0.345489	+	0.938423i	$0.387713\pi$
$839$	−11801.3	+	36320.6i	−0.485609	+	1.49455i	−0.831097	+	0.556127i	$0.812287\pi$
$840$	2607.36	+	8024.64i	0.107098	+	0.329615i
$841$	19225.7	−	13968.3i	0.788293	−	0.572729i
$842$	29056.3	−	21110.6i	1.18925	−	0.864039i
$843$	13011.7	+	40045.9i	0.531610	+	1.63613i
$844$	−17.7762	+	54.7095i	−0.000724979	+	0.00223126i
$845$	26060.8	+	18934.2i	1.06097	+	0.770838i
$846$	33683.7			1.36888
$847$		0			0
$848$	20382.7			0.825406
$849$	30328.5	+	22034.9i	1.22600	+	0.890738i
$850$	−3330.43	+	10250.0i	−0.134392	+	0.413615i
$851$	−452.274	−	1391.96i	−0.0182183	−	0.0560701i
$852$	712.769	−	517.857i	0.0286609	−	0.0208233i
$853$	34760.9	−	25255.3i	1.39530	−	1.01374i	0.400039	−	0.916498i	$-0.368997\pi$
$853$	34760.9	−	25255.3i	1.39530	−	1.01374i	0.995260	−	0.0972464i	$-0.0310035\pi$
$854$	−1915.71	−	5895.95i	−0.0767615	−	0.236248i
$855$	−23033.1	+	70888.6i	−0.921304	+	2.83548i
$856$	15700.5	+	11407.1i	0.626905	+	0.455473i
$857$	17281.5			0.688828			0.344414	−	0.938818i	$-0.388078\pi$
$857$	17281.5			0.688828			0.344414	+	0.938818i	$0.388078\pi$
$858$		0			0
$859$	9316.75			0.370062			0.185031	−	0.982733i	$-0.440761\pi$
$859$	9316.75			0.370062			0.185031	+	0.982733i	$0.440761\pi$
$860$	371.729	+	270.077i	0.0147394	+	0.0107088i
$861$	−1964.76	+	6046.91i	−0.0777687	+	0.239347i
$862$	4144.99	+	12757.0i	0.163780	+	0.504065i
$863$	7805.11	−	5670.75i	0.307867	−	0.223678i	−0.423114	−	0.906077i	$-0.639063\pi$
$863$	7805.11	−	5670.75i	0.307867	−	0.223678i	0.730981	+	0.682398i	$0.239063\pi$
$864$	−1375.27	+	999.194i	−0.0541525	+	0.0393441i
$865$	−10593.1	−	32602.1i	−0.416388	−	1.28151i
$866$	9914.29	−	30513.0i	0.389031	−	1.19732i
$867$	−20616.6	−	14978.9i	−0.807586	−	0.586746i
$868$	51.8501			0.00202754
$869$		0			0
$870$	8043.18			0.313436
$871$	1484.30	+	1078.41i	0.0577424	+	0.0419523i
$872$	−7525.36	+	23160.7i	−0.292249	+	0.899449i
$873$	14918.6	+	45914.7i	0.578371	+	1.78004i
$874$	34438.2	−	25020.8i	1.33283	−	0.968355i
$875$	−1081.29	+	785.602i	−0.0417763	+	0.0303522i
$876$	1326.84	+	4083.60i	0.0511756	+	0.157502i
$877$	−6096.50	+	18763.1i	−0.234737	+	0.722445i	0.762419	+	0.647083i	$0.224011\pi$
$877$	−6096.50	+	18763.1i	−0.234737	+	0.722445i	−0.997156	+	0.0753623i	$0.975989\pi$
$878$	26134.7	+	18988.0i	1.00456	+	0.729856i
$879$	18464.1			0.708509
$880$		0			0
$881$	19473.9			0.744712			0.372356	−	0.928090i	$-0.378550\pi$
$881$	19473.9			0.744712			0.372356	+	0.928090i	$0.378550\pi$
$882$	−26435.8	−	19206.7i	−1.00923	−	0.733248i
$883$	15170.4	−	46689.7i	0.578170	−	1.77943i	−0.0469507	−	0.998897i	$-0.514950\pi$
$883$	15170.4	−	46689.7i	0.578170	−	1.77943i	0.625121	−	0.780528i	$-0.285050\pi$
$884$	36.5769	+	112.572i	0.00139164	+	0.00428304i
$885$	8420.69	−	6117.99i	0.319840	−	0.232377i
$886$	22328.5	−	16222.6i	0.846658	−	0.615133i
$887$	−2871.65	−	8838.03i	−0.108704	−	0.334557i	0.881878	−	0.471478i	$-0.156279\pi$
$887$	−2871.65	−	8838.03i	−0.108704	−	0.334557i	−0.990582	+	0.136921i	$0.956279\pi$
$888$	−750.947	+	2311.18i	−0.0283785	+	0.0873401i
$889$	3274.43	+	2379.01i	0.123533	+	0.0897519i
$890$	60440.8			2.27638
$891$		0			0
$892$	2108.05			0.0791288
$893$	−38923.4	−	28279.5i	−1.45859	−	1.05973i
$894$	16253.8	−	50024.2i	0.608064	−	1.87143i
$895$	−6023.95	−	18539.8i	−0.224981	−	0.692421i
$896$	−3195.53	+	2321.69i	−0.119146	+	0.0865649i
$897$	3827.54	−	2780.87i	0.142473	−	0.103512i
$898$	291.481	+	897.086i	0.0108317	+	0.0333365i
$899$	243.281	−	748.741i	0.00902544	−	0.0277774i
$900$	1487.91	+	1081.03i	0.0551078	+	0.0400382i
$901$	−14136.7			−0.522709
$902$		0			0
$903$	1405.53			0.0517974
$904$	−5567.21	−	4044.82i	−0.204826	−	0.148815i
$905$	−3687.28	+	11348.3i	−0.135436	+	0.416828i
$906$	17246.7	+	53079.9i	0.632432	+	1.94642i
$907$	−30490.8	+	22152.9i	−1.11624	+	0.810997i	−0.983635	−	0.180172i	$-0.942335\pi$
$907$	−30490.8	+	22152.9i	−1.11624	+	0.810997i	−0.132606	+	0.991169i	$0.542335\pi$
$908$	768.210	−	558.137i	0.0280770	−	0.0203991i
$909$	1789.03	+	5506.07i	0.0652788	+	0.200907i
$910$	−206.471	+	635.454i	−0.00752138	+	0.0231484i
$911$	−26737.7	−	19426.1i	−0.972404	−	0.706493i	−0.0164061	−	0.999865i	$-0.505222\pi$
$911$	−26737.7	−	19426.1i	−0.972404	−	0.706493i	−0.955998	+	0.293372i	$0.905222\pi$
$912$	−65923.1			−2.39357
$913$		0			0
$914$	−28870.0			−1.04479
$915$	−70390.3	−	51141.5i	−2.54320	−	1.84775i
$916$	−317.188	+	976.206i	−0.0114413	+	0.0352126i
$917$	−1519.46	−	4676.41i	−0.0547185	−	0.168406i
$918$	−6396.44	+	4647.28i	−0.229972	+	0.167084i
$919$	−18727.1	+	13606.0i	−0.672198	+	0.488381i	−0.870760	−	0.491708i	$-0.836373\pi$
$919$	−18727.1	+	13606.0i	−0.672198	+	0.488381i	0.198562	+	0.980088i	$0.436373\pi$
$920$	−11921.7	−	36691.3i	−0.427226	−	1.31487i
$921$	−4111.18	+	12652.9i	−0.147088	+	0.452690i
$922$	−10463.4	−	7602.07i	−0.373744	−	0.271541i
$923$	1111.26			0.0396290
$924$		0			0
$925$	1258.01			0.0447169
$926$	7583.89	+	5510.02i	0.269138	+	0.195541i
$927$	−385.140	+	1185.34i	−0.0136458	+	0.0419975i
$928$	−186.996	−	575.514i	−0.00661470	−	0.0203579i
$929$	18751.3	−	13623.6i	0.662230	−	0.481138i	−0.205186	−	0.978723i	$-0.565780\pi$
$929$	18751.3	−	13623.6i	0.662230	−	0.481138i	0.867415	+	0.497585i	$0.165780\pi$
$930$	−8199.93	+	5957.60i	−0.289125	+	0.210062i
$931$	14422.8	+	44388.9i	0.507722	+	1.56261i
$932$	728.038	−	2240.67i	0.0255876	−	0.0787506i
$933$	22915.5	+	16649.1i	0.804095	+	0.584209i
$934$	−13979.8			−0.489757
$935$		0			0
$936$	−4481.13			−0.156485
$937$	−27971.5	−	20322.5i	−0.975228	−	0.708545i	−0.0185910	−	0.999827i	$-0.505918\pi$
$937$	−27971.5	−	20322.5i	−0.975228	−	0.708545i	−0.956637	+	0.291283i	$0.905918\pi$
$938$	887.862	−	2732.56i	0.0309059	−	0.0951185i
$939$	−17601.3	−	54171.3i	−0.611712	−	1.88266i
$940$	−2214.72	+	1609.09i	−0.0768469	+	0.0558325i
$941$	33842.1	−	24587.7i	1.17239	−	0.851793i	0.181099	−	0.983465i	$-0.442034\pi$
$941$	33842.1	−	24587.7i	1.17239	−	0.851793i	0.991293	+	0.131672i	$0.0420345\pi$
$942$	16572.4	+	51004.7i	0.573205	+	1.76414i
$943$	8983.54	−	27648.5i	0.310227	−	0.954781i
$944$	4248.47	+	3086.70i	0.146479	+	0.106423i
$945$	3204.34			0.110304
$946$		0			0
$947$	27231.2			0.934419			0.467209	−	0.884147i	$-0.345259\pi$
$947$	27231.2			0.934419			0.467209	+	0.884147i	$0.345259\pi$
$948$	4448.61	+	3232.11i	0.152410	+	0.110732i
$949$	−1673.57	+	5150.72i	−0.0572459	+	0.176185i
$950$	11306.6	+	34798.0i	0.386140	+	1.18842i
$951$	−100.750	+	73.1990i	−0.00343537	+	0.00249594i
$952$	2388.62	−	1735.44i	0.0813190	−	0.0590817i
$953$	−12651.0	−	38935.7i	−0.430016	−	1.32345i	−0.898108	−	0.439774i	$-0.855058\pi$
$953$	−12651.0	−	38935.7i	−0.430016	−	1.32345i	0.468092	−	0.883680i	$-0.344942\pi$
$954$	10383.1	−	31955.8i	0.352373	−	1.08449i
$955$	−20651.7	−	15004.4i	−0.699764	−	0.508409i
$956$	−2188.87			−0.0740515
$957$		0			0
$958$	31601.3			1.06575
$959$	4005.24	+	2909.97i	0.134865	+	0.0979854i
$960$	−19711.0	+	60664.2i	−0.662676	+	2.03951i
$961$	−8899.35	−	27389.4i	−0.298726	−	0.919385i
$962$	−155.684	+	113.111i	−0.00521772	+	0.00379089i
$963$	24140.2	−	17538.9i	0.807796	−	0.586898i
$964$	647.268	+	1992.09i	0.0216256	+	0.0665568i
$965$	−6152.63	+	18935.8i	−0.205244	+	0.631675i
$966$	−5994.03	−	4354.92i	−0.199643	−	0.145049i
$967$	46173.1			1.53550			0.767750	−	0.640750i	$-0.221376\pi$
$967$	46173.1			1.53550			0.767750	+	0.640750i	$0.221376\pi$
$968$		0			0
$969$	45721.8			1.51579
$970$	44211.9	+	32121.8i	1.46346	+	1.06327i
$971$	−1592.65	+	4901.66i	−0.0526369	+	0.162000i	−0.973919	−	0.226894i	$-0.927143\pi$
$971$	−1592.65	+	4901.66i	−0.0526369	+	0.162000i	0.921282	+	0.388894i	$0.127143\pi$
$972$	−854.141	−	2628.78i	−0.0281858	−	0.0867470i
$973$	79.1812	−	57.5285i	0.00260887	−	0.00189546i
$974$	−40506.7	+	29429.8i	−1.33257	+	0.968165i
$975$	1256.64	+	3867.53i	0.0412765	+	0.127036i
$976$	13565.1	−	41749.1i	0.444885	−	1.36922i
$977$	−7841.10	−	5696.89i	−0.256765	−	0.186550i	0.451955	−	0.892041i	$-0.350727\pi$
$977$	−7841.10	−	5696.89i	−0.256765	−	0.186550i	−0.708719	+	0.705490i	$0.750727\pi$
$978$	−59026.5			−1.92992
$979$		0			0
$980$	2655.68			0.0865638
$981$	30292.2	+	22008.6i	0.985889	+	0.716290i
$982$	−6431.14	+	19793.0i	−0.208988	+	0.643198i
$983$	10171.5	+	31304.7i	0.330031	+	1.01573i	0.969118	+	0.246597i	$0.0793125\pi$
$983$	10171.5	+	31304.7i	0.330031	+	1.01573i	−0.639087	+	0.769135i	$0.720687\pi$
$984$	−39050.8	+	28372.1i	−1.26514	+	0.919176i
$985$	−42287.1	+	30723.4i	−1.36790	+	0.993835i
$986$	−869.723	−	2676.73i	−0.0280909	−	0.0864549i
$987$	−2587.70	+	7964.12i	−0.0834522	+	0.256840i
$988$	325.096	+	236.196i	0.0104683	+	0.00760567i
$989$	−6426.54			−0.206625
$990$		0			0
$991$	29477.9			0.944901			0.472451	−	0.881357i	$-0.343370\pi$
$991$	29477.9			0.944901			0.472451	+	0.881357i	$0.343370\pi$
$992$	616.924	+	448.222i	0.0197453	+	0.0143458i
$993$	3231.37	−	9945.13i	0.103267	−	0.317824i
$994$	−537.771	−	1655.09i	−0.0171600	−	0.0528131i
$995$	−9900.03	+	7192.79i	−0.315429	+	0.229173i
$996$	1518.75	−	1103.44i	0.0483167	−	0.0351041i
$997$	9871.35	+	30380.9i	0.313570	+	0.965068i	0.976339	+	0.216245i	$0.0693808\pi$
$997$	9871.35	+	30380.9i	0.313570	+	0.965068i	−0.662770	+	0.748823i	$0.730619\pi$
$998$	−10898.5	+	33542.2i	−0.345678	+	1.06389i
$999$	746.628	+	542.457i	0.0236459	+	0.0171798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.c.f.81.2		8
11.2	odd	10		121.4.c.c.27.2		8
11.3	even	5	inner	121.4.c.f.3.2		8
11.4	even	5	inner	121.4.c.f.9.1		8
11.5	even	5		121.4.a.c.1.1		2
11.6	odd	10		11.4.a.a.1.2	✓	2
11.7	odd	10		121.4.c.c.9.2		8
11.8	odd	10		121.4.c.c.3.1		8
11.9	even	5	inner	121.4.c.f.27.1		8
11.10	odd	2		121.4.c.c.81.1		8
33.5	odd	10		1089.4.a.v.1.2		2
33.17	even	10		99.4.a.c.1.1		2
44.27	odd	10		1936.4.a.w.1.2		2
44.39	even	10		176.4.a.i.1.2		2
55.17	even	20		275.4.b.c.199.4		4
55.28	even	20		275.4.b.c.199.1		4
55.39	odd	10		275.4.a.b.1.1		2
77.6	even	10		539.4.a.e.1.2		2
88.61	odd	10		704.4.a.p.1.2		2
88.83	even	10		704.4.a.n.1.1		2
132.83	odd	10		1584.4.a.bc.1.1		2
143.116	odd	10		1859.4.a.a.1.1		2
165.149	even	10		2475.4.a.q.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.a.a.1.2	✓	2	11.6	odd	10
99.4.a.c.1.1		2	33.17	even	10
121.4.a.c.1.1		2	11.5	even	5
121.4.c.c.3.1		8	11.8	odd	10
121.4.c.c.9.2		8	11.7	odd	10
121.4.c.c.27.2		8	11.2	odd	10
121.4.c.c.81.1		8	11.10	odd	2
121.4.c.f.3.2		8	11.3	even	5	inner
121.4.c.f.9.1		8	11.4	even	5	inner
121.4.c.f.27.1		8	11.9	even	5	inner
121.4.c.f.81.2		8	1.1	even	1	trivial
176.4.a.i.1.2		2	44.39	even	10
275.4.a.b.1.1		2	55.39	odd	10
275.4.b.c.199.1		4	55.28	even	20
275.4.b.c.199.4		4	55.17	even	20
539.4.a.e.1.2		2	77.6	even	10
704.4.a.n.1.1		2	88.83	even	10
704.4.a.p.1.2		2	88.61	odd	10
1089.4.a.v.1.2		2	33.5	odd	10
1584.4.a.bc.1.1		2	132.83	odd	10
1859.4.a.a.1.1		2	143.116	odd	10
1936.4.a.w.1.2		2	44.27	odd	10
2475.4.a.q.1.2		2	165.149	even	10

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.21028 + 1.60586i) q^{2} +(-2.44995 + 7.54017i) q^{3} +(-0.165602 - 0.509670i) q^{4} +(-12.0191 + 8.73238i) q^{5} +(-17.5235 + 12.7316i) q^{6} +(-0.949237 - 2.92145i) q^{7} +(7.20643 - 22.1791i) q^{8} +(-29.0084 - 21.0759i) q^{9} +O(q^{10})\)	\(q+(2.21028 + 1.60586i) q^{2} +(-2.44995 + 7.54017i) q^{3} +(-0.165602 - 0.509670i) q^{4} +(-12.0191 + 8.73238i) q^{5} +(-17.5235 + 12.7316i) q^{6} +(-0.949237 - 2.92145i) q^{7} +(7.20643 - 22.1791i) q^{8} +(-29.0084 - 21.0759i) q^{9} -40.5885 q^{10} +4.24871 q^{12} +(4.33551 + 3.14993i) q^{13} +(2.59336 - 7.98156i) q^{14} +(-36.3974 - 112.020i) q^{15} +(48.0763 - 34.9295i) q^{16} +(-33.3440 + 24.2258i) q^{17} +(-30.2718 - 93.1669i) q^{18} +(-43.2386 + 133.075i) q^{19} +(6.44101 + 4.67967i) q^{20} +24.3538 q^{21} -111.354 q^{23} +(149.579 + 108.675i) q^{24} +(29.5769 - 91.0283i) q^{25} +(4.52432 + 13.9244i) q^{26} +(56.8054 - 41.2716i) q^{27} +(-1.33178 + 0.967595i) q^{28} +(7.72383 + 23.7715i) q^{29} +(99.4397 - 306.044i) q^{30} +(-25.4820 - 18.5137i) q^{31} -24.2102 q^{32} -112.603 q^{34} +(36.9202 + 26.8241i) q^{35} +(-5.93788 + 18.2749i) q^{36} +(4.06159 + 12.5003i) q^{37} +(-309.268 + 224.697i) q^{38} +(-34.3728 + 24.9733i) q^{39} +(107.062 + 329.502i) q^{40} +(-80.6756 + 248.294i) q^{41} +(53.8287 + 39.1088i) q^{42} +57.7128 q^{43} +532.697 q^{45} +(-246.123 - 178.819i) q^{46} +(-106.254 + 327.017i) q^{47} +(145.590 + 448.079i) q^{48} +(269.859 - 196.064i) q^{49} +(211.552 - 153.701i) q^{50} +(-100.976 - 310.771i) q^{51} +(0.887457 - 2.73131i) q^{52} +(277.489 + 201.607i) q^{53} +191.832 q^{54} -71.6359 q^{56} +(-897.474 - 652.053i) q^{57} +(-21.1019 + 64.9450i) q^{58} +(27.3076 + 84.0442i) q^{59} +(-51.0656 + 37.1013i) q^{60} +(597.619 - 434.195i) q^{61} +(-26.5917 - 81.8408i) q^{62} +(-34.0362 + 104.753i) q^{63} +(-438.122 - 318.314i) q^{64} -79.6152 q^{65} +342.359 q^{67} +(17.8690 + 12.9826i) q^{68} +(272.811 - 839.627i) q^{69} +(38.5281 + 118.577i) q^{70} +(167.761 - 121.886i) q^{71} +(-676.492 + 491.500i) q^{72} +(312.293 + 961.138i) q^{73} +(-11.0965 + 34.1515i) q^{74} +(613.907 + 446.029i) q^{75} +74.9845 q^{76} -116.077 q^{78} +(1047.05 + 760.727i) q^{79} +(-272.816 + 839.641i) q^{80} +(-127.142 - 391.304i) q^{81} +(-577.041 + 419.245i) q^{82} +(357.461 - 259.711i) q^{83} +(-4.03304 - 12.4124i) q^{84} +(189.215 - 582.344i) q^{85} +(127.561 + 92.6787i) q^{86} -198.164 q^{87} -1489.11 q^{89} +(1177.41 + 855.437i) q^{90} +(5.08695 - 15.6560i) q^{91} +(18.4404 + 56.7537i) q^{92} +(202.026 - 146.781i) q^{93} +(-759.995 + 552.168i) q^{94} +(-642.370 - 1977.01i) q^{95} +(59.3139 - 182.549i) q^{96} +(-1089.27 - 791.403i) q^{97} +911.314 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9} - 200 q^{10} - 160 q^{12} + 80 q^{13} + 4 q^{14} + 194 q^{15} + 8 q^{16} - 124 q^{17} + 92 q^{18} + 72 q^{19} - 88 q^{20} - 304 q^{21} - 392 q^{23} + 252 q^{24} - 136 q^{25} + 40 q^{26} + 182 q^{27} - 128 q^{28} + 144 q^{29} - 266 q^{30} + 34 q^{31} + 416 q^{32} - 208 q^{34} - 172 q^{35} + 80 q^{36} - 54 q^{37} - 432 q^{38} + 400 q^{39} - 492 q^{40} + 536 q^{41} + 140 q^{42} + 240 q^{43} + 1712 q^{45} - 314 q^{46} + 272 q^{47} - 776 q^{48} + 390 q^{49} + 232 q^{50} - 164 q^{51} - 560 q^{52} + 492 q^{53} + 440 q^{54} + 480 q^{56} - 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} + 840 q^{61} + 134 q^{62} + 248 q^{63} - 224 q^{64} + 3520 q^{65} + 3016 q^{67} + 640 q^{68} - 962 q^{69} - 284 q^{70} + 678 q^{71} - 744 q^{72} - 400 q^{73} + 6 q^{74} + 520 q^{75} - 1728 q^{76} - 1760 q^{78} + 316 q^{79} + 1544 q^{80} + 1294 q^{81} - 512 q^{82} + 468 q^{83} - 736 q^{84} + 452 q^{85} + 156 q^{86} - 4800 q^{87} - 7368 q^{89} + 1532 q^{90} - 1280 q^{91} + 40 q^{92} + 638 q^{93} - 992 q^{94} + 2952 q^{95} - 952 q^{96} - 2194 q^{97} + 3480 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9 - 200 * q^10 - 160 * q^12 + 80 * q^13 + 4 * q^14 + 194 * q^15 + 8 * q^16 - 124 * q^17 + 92 * q^18 + 72 * q^19 - 88 * q^20 - 304 * q^21 - 392 * q^23 + 252 * q^24 - 136 * q^25 + 40 * q^26 + 182 * q^27 - 128 * q^28 + 144 * q^29 - 266 * q^30 + 34 * q^31 + 416 * q^32 - 208 * q^34 - 172 * q^35 + 80 * q^36 - 54 * q^37 - 432 * q^38 + 400 * q^39 - 492 * q^40 + 536 * q^41 + 140 * q^42 + 240 * q^43 + 1712 * q^45 - 314 * q^46 + 272 * q^47 - 776 * q^48 + 390 * q^49 + 232 * q^50 - 164 * q^51 - 560 * q^52 + 492 * q^53 + 440 * q^54 + 480 * q^56 - 1512 * q^57 + 192 * q^58 - 634 * q^59 - 632 * q^60 + 840 * q^61 + 134 * q^62 + 248 * q^63 - 224 * q^64 + 3520 * q^65 + 3016 * q^67 + 640 * q^68 - 962 * q^69 - 284 * q^70 + 678 * q^71 - 744 * q^72 - 400 * q^73 + 6 * q^74 + 520 * q^75 - 1728 * q^76 - 1760 * q^78 + 316 * q^79 + 1544 * q^80 + 1294 * q^81 - 512 * q^82 + 468 * q^83 - 736 * q^84 + 452 * q^85 + 156 * q^86 - 4800 * q^87 - 7368 * q^89 + 1532 * q^90 - 1280 * q^91 + 40 * q^92 + 638 * q^93 - 992 * q^94 + 2952 * q^95 - 952 * q^96 - 2194 * q^97 + 3480 * q^98

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