LMFDB - Embedded newform 121.4.c.c.81.1

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			81.1
Root			$0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	121.81
Dual form			121.4.c.c.3.1

$q$-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	0.123964	−	0.992287i	$-0.460439\pi$
$2$	−2.21028	−	1.60586i	−0.781450	−	0.567757i	−0.905414	+	0.424530i	$0.860439\pi$
$3$	−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	0.973407	−	0.229081i	$-0.0735720\pi$
$7$	0.949237	+	2.92145i	0.0512540	+	0.157744i	−0.922153	+	0.386824i	$0.873572\pi$
$8$	−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	0.540576	−	0.841295i	$-0.318206\pi$
$13$	−4.33551	−	3.14993i	−0.0924964	−	0.0672026i	−0.633072	+	0.774093i	$0.718206\pi$
$14$	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	−0.323951	−	0.946074i	$-0.605011\pi$
$17$	33.3440	−	24.2258i	0.475712	−	0.345625i	0.799663	+	0.600449i	$0.205011\pi$
$18$	30.2718	+	93.1669i	0.396396	+	1.21998i
$19$	43.2386	−	133.075i	0.522085	−	1.60681i	−0.247924	−	0.968779i	$-0.579748\pi$
$19$	43.2386	−	133.075i	0.522085	−	1.60681i	0.770009	−	0.638033i	$-0.220252\pi$
$20$	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	0.923277	−	0.384134i	$-0.125500\pi$
$29$	−7.72383	−	23.7715i	−0.0494579	−	0.152216i	−0.972735	+	0.231918i	$0.925500\pi$
$30$	−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	$-0.734352\pi$
$41$	80.6756	−	248.294i	0.307303	−	0.945781i	0.978808	−	0.204781i	$-0.0656482\pi$
$42$	53.8287	+	39.1088i	0.197761	+	0.143681i
$43$	−57.7128			−0.204677			−0.102339	−	0.994750i	$-0.532633\pi$
$43$	−57.7128			−0.204677			−0.102339	+	0.994750i	$0.532633\pi$
$44$		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	−0.998468	−	0.0553387i	$-0.982376\pi$
$61$	−597.619	+	434.195i	−1.25438	+	0.911361i	−0.255913	+	0.966700i	$0.582376\pi$
$62$	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	$-0.799386\pi$
$73$	−312.293	−	961.138i	−0.500700	−	1.54100i	0.307182	−	0.951651i	$-0.400614\pi$
$74$	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	$-0.926888\pi$
$79$	−1047.05	−	760.727i	−1.49117	−	1.08340i	−0.517432	−	0.855725i	$-0.673112\pi$
$80$	−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	−0.798504	−	0.601990i	$-0.794375\pi$
$83$	−357.461	+	259.711i	−0.472728	+	0.343457i	0.325775	+	0.945447i	$0.394375\pi$
$84$	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	0.650268	−	0.759705i	$-0.274657\pi$
$101$	130.625	+	94.9046i	0.128690	+	0.0934986i	−0.521578	+	0.853203i	$0.674657\pi$
$102$	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	$-0.777322\pi$
$107$	257.158	−	791.450i	0.232340	−	0.715068i	0.997463	−	0.0711847i	$-0.0226780\pi$
$108$	−30.4419	−	22.1174i	−0.0271229	−	0.0197060i
$109$	1044.26			0.917629			0.458815	−	0.888532i	$-0.348274\pi$
$109$	1044.26			0.917629			0.458815	+	0.888532i	$0.348274\pi$
$110$		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	−0.149414	−	0.988775i	$-0.547739\pi$
$127$	1065.96	−	774.469i	0.744796	−	0.541126i	0.894209	+	0.447649i	$0.147739\pi$
$128$	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	$-0.679235\pi$
$131$	−1600.71			−1.06759			−0.533797	+	0.845612i	$0.679235\pi$
$132$		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	0.948008	−	0.318248i	$-0.103094\pi$
$139$	−9.84588	−	30.3025i	−0.00600803	−	0.0184908i	−0.954016	+	0.299757i	$0.903094\pi$
$140$	−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	0.102449	−	0.994738i	$-0.467332\pi$
$149$	1964.57	−	1427.34i	1.08016	−	0.784782i	0.977711	+	0.209956i	$0.0673320\pi$
$150$	−640.643	−	1971.70i	−0.348722	−	1.07326i
$151$	−796.237	+	2450.57i	−0.429118	+	1.32069i	0.469877	+	0.882732i	$0.344298\pi$
$151$	−796.237	+	2450.57i	−0.429118	+	1.32069i	−0.898995	+	0.437958i	$0.855702\pi$
$152$	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	−0.0586043	−	0.998281i	$-0.518665\pi$
$167$	−2214.52	−	1608.94i	−1.02614	−	0.745531i	−0.967532	+	0.252750i	$0.918665\pi$
$168$	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	$-0.730746\pi$
$173$	713.031	−	2194.48i	0.313357	−	0.964413i	0.976426	−	0.215854i	$-0.0692536\pi$
$174$	−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	−0.771321	−	0.636446i	$-0.780404\pi$
$193$	−1084.23	+	787.740i	−0.404377	+	0.293797i	0.366945	+	0.930243i	$0.380404\pi$
$194$	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	$-0.719503\pi$
$197$	−3518.33			−1.27244			−0.636220	+	0.771508i	$0.719503\pi$
$198$		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	0.601862	−	0.798600i	$-0.294426\pi$
$211$	86.8424	+	63.0947i	0.0283340	+	0.0205859i	−0.573528	+	0.819186i	$0.694426\pi$
$212$	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	0.838545	−	0.544833i	$-0.183407\pi$
$227$	−547.548	−	1685.18i	−0.160097	−	0.492728i	−0.998642	+	0.0521050i	$0.983407\pi$
$228$	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	−0.0379350	−	0.999280i	$-0.512078\pi$
$233$	−3556.70	−	2584.09i	−1.00003	−	0.726564i	−0.962095	+	0.272716i	$0.912078\pi$
$234$	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	$0.286413\pi$
$239$	−1262.18	+	3884.58i	−0.341604	+	1.05135i	−0.963377	+	0.268152i	$0.913587\pi$
$240$	−5662.65	−	4114.16i	−1.52301	−	1.10653i
$241$	3908.58			1.04471			0.522353	−	0.852730i	$-0.325054\pi$
$241$	3908.58			1.04471			0.522353	+	0.852730i	$0.325054\pi$
$242$		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	$-0.242078\pi$
$263$	6180.06			1.44897			0.724484	+	0.689292i	$0.242078\pi$
$264$		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	$0.0714565\pi$
$271$	1414.37	+	4352.98i	0.317036	+	0.975736i	−0.657873	+	0.753129i	$0.728543\pi$
$272$	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	0.536846	−	0.843680i	$-0.319615\pi$
$277$	−459.389	−	333.766i	−0.0996462	−	0.0723972i	−0.636493	+	0.771283i	$0.719615\pi$
$278$	−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	−0.941563	−	0.336838i	$-0.890643\pi$
$281$	−4296.70	+	3121.74i	−0.912170	+	0.662730i	0.0293930	+	0.999568i	$0.490643\pi$
$282$	2301.49	+	7083.27i	0.486000	+	1.49575i
$283$	−1461.17	+	4497.01i	−0.306917	+	0.944593i	0.672038	+	0.740517i	$0.265419\pi$
$283$	−1461.17	+	4497.01i	−0.306917	+	0.944593i	−0.978955	+	0.204076i	$0.934581\pi$
$284$	−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	0.996814	−	0.0797574i	$-0.0254146\pi$
$293$	719.675	+	2214.93i	0.143494	+	0.441630i	−0.853320	+	0.521388i	$0.825415\pi$
$294$	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	$-0.549854\pi$
$307$	−1678.07			−0.311962			−0.155981	+	0.987760i	$0.549854\pi$
$308$		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	0.944905	−	0.327344i	$-0.106154\pi$
$337$	−73.9116	−	227.477i	−0.0119472	−	0.0367698i	−0.956852	+	0.290574i	$0.906154\pi$
$338$	−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	−0.156975	−	0.987603i	$-0.550174\pi$
$347$	4743.10	−	3446.06i	0.733784	−	0.533125i	0.890758	+	0.454478i	$0.150174\pi$
$348$	−32.8163	−	100.998i	−0.00505500	−	0.0155577i
$349$	1079.00	−	3320.83i	0.165495	−	0.509341i	−0.833577	−	0.552403i	$-0.813711\pi$
$349$	1079.00	−	3320.83i	0.165495	−	0.509341i	0.999072	+	0.0430615i	$0.0137111\pi$
$350$	−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	$-0.779372\pi$
$359$	−3553.92	−	10937.8i	−0.522476	−	1.60802i	0.246778	−	0.969072i	$-0.420628\pi$
$360$	−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	$-0.620152\pi$
$373$	−5310.22			−0.737139			−0.368569	+	0.929600i	$0.620152\pi$
$374$		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	0.773625	−	0.633643i	$-0.218441\pi$
$409$	3391.80	+	2464.29i	0.410059	+	0.297925i	−0.363567	+	0.931568i	$0.618441\pi$
$410$	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	0.343277	−	0.939234i	$-0.388463\pi$
$431$	−3972.00	−	2885.83i	−0.443909	−	0.322519i	−0.787186	+	0.616715i	$0.788463\pi$
$432$	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	$-0.722208\pi$
$439$	−11824.2			−1.28551			−0.642754	+	0.766073i	$0.722208\pi$
$440$		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	−0.0568749	−	0.998381i	$-0.518114\pi$
$457$	8549.00	−	6211.21i	0.875067	−	0.635773i	0.931942	+	0.362608i	$0.118114\pi$
$458$	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	$-0.423136\pi$
$461$	4733.96			0.478270			0.239135	+	0.970986i	$0.423136\pi$
$462$		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	−0.936562	−	0.350502i	$-0.886011\pi$
$479$	−9357.81	+	6798.85i	−0.892629	+	0.648533i	0.0439333	+	0.999034i	$0.486011\pi$
$480$	−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	$-0.986155\pi$
$491$	−2353.96	−	7244.75i	−0.216360	−	0.665888i	0.782694	−	0.622407i	$-0.213845\pi$
$492$	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	$-0.751224\pi$
$503$	3141.36	−	9668.11i	0.278462	−	0.857017i	0.988283	−	0.152635i	$-0.0487759\pi$
$504$	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	−0.778991	−	0.627035i	$-0.784268\pi$
$523$	−5063.71	+	3679.00i	−0.423367	+	0.307594i	0.355624	+	0.934629i	$0.384268\pi$
$524$	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	0.938626	−	0.344937i	$-0.112100\pi$
$541$	11332.8	+	8233.79i	0.900623	+	0.654341i	−0.0380030	+	0.999278i	$0.512100\pi$
$542$	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	−0.992869	−	0.119208i	$-0.961964\pi$
$547$	−1529.46	+	4707.20i	−0.119552	+	0.367944i	0.873317	+	0.487152i	$0.161964\pi$
$548$	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	0.896380	−	0.443287i	$-0.146188\pi$
$557$	−1174.75	−	3615.51i	−0.0893641	−	0.275034i	−0.985744	+	0.168252i	$0.946188\pi$
$558$	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	0.845724	−	0.533621i	$-0.179169\pi$
$563$	8009.36	+	5819.14i	0.599564	+	0.435608i	−0.246160	+	0.969229i	$0.579169\pi$
$564$	−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	−0.871884	−	0.489713i	$-0.837102\pi$
$569$	1646.80	−	5068.33i	0.121331	−	0.373419i	0.993215	+	0.116294i	$0.0371015\pi$
$570$	36427.1	+	26465.8i	2.67678	+	1.94479i
$571$	−16962.6			−1.24319			−0.621597	−	0.783337i	$-0.713516\pi$
$571$	−16962.6			−1.24319			−0.621597	+	0.783337i	$0.713516\pi$
$572$		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	$-0.451877\pi$
$593$	4349.68			0.301214			0.150607	+	0.988594i	$0.451877\pi$
$594$		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	$-0.880255\pi$
$601$	−5798.71	−	17846.6i	−0.393568	−	1.21128i	0.536503	−	0.843898i	$-0.319745\pi$
$602$	−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	−0.190652	−	0.981658i	$-0.561060\pi$
$607$	−17694.3	−	12855.7i	−1.18318	−	0.859629i	−0.992527	+	0.122028i	$0.961060\pi$
$608$	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	−0.980526	−	0.196389i	$-0.937079\pi$
$613$	−1090.17	+	3355.19i	−0.0718294	+	0.221068i	0.908697	+	0.417457i	$0.137079\pi$
$614$	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	$-0.600647\pi$
$659$	−10520.7			−0.621897			−0.310948	+	0.950427i	$0.600647\pi$
$660$		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	0.614961	−	0.788557i	$-0.289172\pi$
$673$	960.819	+	698.076i	0.0550325	+	0.0399834i	−0.559929	+	0.828541i	$0.689172\pi$
$674$	−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	−0.848437	−	0.529297i	$-0.822456\pi$
$677$	−10696.3	+	7771.33i	−0.607227	+	0.441177i	0.241210	+	0.970473i	$0.422456\pi$
$678$	−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	$-0.601177\pi$
$701$	9254.98	−	28483.9i	0.498653	−	1.53470i	0.811185	−	0.584789i	$-0.198823\pi$
$702$	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	0.995497	−	0.0947978i	$-0.0302204\pi$
$733$	2667.24	+	8208.93i	0.134402	+	0.413647i	−0.861094	+	0.508445i	$0.830220\pi$
$734$	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	0.892483	−	0.451080i	$-0.148961\pi$
$739$	14851.5	+	10790.3i	0.739273	+	0.537113i	−0.153210	+	0.988194i	$0.548961\pi$
$740$	−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	−0.788293	−	0.615300i	$-0.789035\pi$
$743$	−9046.95	+	6572.99i	−0.446703	+	0.324549i	0.341590	+	0.939849i	$0.389035\pi$
$744$	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	0.412510	−	0.910953i	$-0.364652\pi$
$761$	−6851.83	−	4978.15i	−0.326385	−	0.237132i	−0.738895	+	0.673821i	$0.764652\pi$
$762$	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	$-0.220324\pi$
$769$	32834.7			1.53973			0.769864	+	0.638208i	$0.220324\pi$
$770$		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	−0.837419	−	0.546561i	$-0.815937\pi$
$787$	−12725.5	+	9245.63i	−0.576386	+	0.418769i	0.261033	+	0.965330i	$0.415937\pi$
$788$	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	−0.686605	−	0.727030i	$-0.740900\pi$
$809$	−4770.75	+	3466.15i	−0.207331	+	0.150635i	0.479274	+	0.877665i	$0.340900\pi$
$810$	−5160.51	−	15882.4i	−0.223854	−	0.688952i
$811$	4387.41	−	13503.0i	0.189966	−	0.584656i	−0.810032	−	0.586385i	$-0.800550\pi$
$811$	4387.41	−	13503.0i	0.189966	−	0.584656i	0.999999	+	0.00172932i	$0.000550460\pi$
$812$	−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	$-0.961423\pi$
$821$	−6131.42	−	18870.6i	−0.260643	−	0.802177i	0.732022	−	0.681281i	$-0.238577\pi$
$822$	−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	−0.168164	−	0.985759i	$-0.553784\pi$
$827$	−27531.7	−	20002.9i	−1.15764	−	0.841076i	−0.989478	+	0.144683i	$0.953784\pi$
$828$	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	$0.631003\pi$
$853$	−34760.9	+	25255.3i	−1.39530	+	1.01374i	−0.995260	+	0.0972464i	$0.968997\pi$
$854$	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	$-0.611922\pi$
$857$	−17281.5			−0.688828			−0.344414	+	0.938818i	$0.611922\pi$
$858$		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	$-0.775989\pi$
$877$	6096.50	−	18763.1i	0.234737	−	0.722445i	0.997156	−	0.0753623i	$-0.0240113\pi$
$878$	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	0.990582	−	0.136921i	$-0.0437207\pi$
$887$	2871.65	+	8838.03i	0.108704	+	0.334557i	−0.881878	+	0.471478i	$0.843721\pi$
$888$	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	−0.198562	−	0.980088i	$-0.563627\pi$
$919$	18727.1	−	13606.0i	0.672198	−	0.488381i	0.870760	+	0.491708i	$0.163627\pi$
$920$	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	0.956637	−	0.291283i	$-0.0940820\pi$
$937$	27971.5	+	20322.5i	0.975228	+	0.708545i	0.0185910	+	0.999827i	$0.494082\pi$
$938$	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	−0.991293	−	0.131672i	$-0.957966\pi$
$941$	−33842.1	+	24587.7i	−1.17239	+	0.851793i	−0.181099	+	0.983465i	$0.557966\pi$
$942$	−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	$0.144942\pi$
$953$	12651.0	+	38935.7i	0.430016	+	1.32345i	−0.468092	+	0.883680i	$0.655058\pi$
$954$	−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	$-0.778624\pi$
$967$	−46173.1			−1.53550			−0.767750	+	0.640750i	$0.778624\pi$
$968$		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	$-0.930619\pi$
$997$	−9871.35	−	30380.9i	−0.313570	−	0.965068i	0.662770	−	0.748823i	$-0.269381\pi$
$998$	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.c.81.1		8
11.2	odd	10		121.4.c.f.27.1		8
11.3	even	5	inner	121.4.c.c.3.1		8
11.4	even	5	inner	121.4.c.c.9.2		8
11.5	even	5		11.4.a.a.1.2	✓	2
11.6	odd	10		121.4.a.c.1.1		2
11.7	odd	10		121.4.c.f.9.1		8
11.8	odd	10		121.4.c.f.3.2		8
11.9	even	5	inner	121.4.c.c.27.2		8
11.10	odd	2		121.4.c.f.81.2		8
33.5	odd	10		99.4.a.c.1.1		2
33.17	even	10		1089.4.a.v.1.2		2
44.27	odd	10		176.4.a.i.1.2		2
44.39	even	10		1936.4.a.w.1.2		2
55.27	odd	20		275.4.b.c.199.4		4
55.38	odd	20		275.4.b.c.199.1		4
55.49	even	10		275.4.a.b.1.1		2
77.27	odd	10		539.4.a.e.1.2		2
88.5	even	10		704.4.a.p.1.2		2
88.27	odd	10		704.4.a.n.1.1		2
132.71	even	10		1584.4.a.bc.1.1		2
143.38	even	10		1859.4.a.a.1.1		2
165.104	odd	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	11.5	even	5
99.4.a.c.1.1		2	33.5	odd	10
121.4.a.c.1.1		2	11.6	odd	10
121.4.c.c.3.1		8	11.3	even	5	inner
121.4.c.c.9.2		8	11.4	even	5	inner
121.4.c.c.27.2		8	11.9	even	5	inner
121.4.c.c.81.1		8	1.1	even	1	trivial
121.4.c.f.3.2		8	11.8	odd	10
121.4.c.f.9.1		8	11.7	odd	10
121.4.c.f.27.1		8	11.2	odd	10
121.4.c.f.81.2		8	11.10	odd	2
176.4.a.i.1.2		2	44.27	odd	10
275.4.a.b.1.1		2	55.49	even	10
275.4.b.c.199.1		4	55.38	odd	20
275.4.b.c.199.4		4	55.27	odd	20
539.4.a.e.1.2		2	77.27	odd	10
704.4.a.n.1.1		2	88.27	odd	10
704.4.a.p.1.2		2	88.5	even	10
1089.4.a.v.1.2		2	33.17	even	10
1584.4.a.bc.1.1		2	132.71	even	10
1859.4.a.a.1.1		2	143.38	even	10
1936.4.a.w.1.2		2	44.39	even	10
2475.4.a.q.1.2		2	165.104	odd	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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