LMFDB - Embedded newform 121.4.c.f.3.2

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			3.2
Root			$-0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	121.3
Dual form			121.4.c.f.81.2

$q$-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 $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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	$-0.539561\pi$
$2$	2.21028	−	1.60586i	0.781450	−	0.567757i	0.905414	+	0.424530i	$0.139561\pi$
$3$	−2.44995	−	7.54017i	−0.471493	−	1.45111i	−0.850630	−	0.525766i	$-0.823779\pi$
$3$	−2.44995	−	7.54017i	−0.471493	−	1.45111i	0.379137	−	0.925341i	$-0.376221\pi$
$4$	−0.165602	+	0.509670i	−0.0207002	+	0.0637087i
$5$	−12.0191	−	8.73238i	−1.07502	−	0.781048i	−0.0982119	−	0.995166i	$-0.531312\pi$
$5$	−12.0191	−	8.73238i	−1.07502	−	0.781048i	−0.976808	+	0.214118i	$0.931312\pi$
$6$	−17.5235	−	12.7316i	−1.19232	−	0.866274i
$7$	−0.949237	+	2.92145i	−0.0512540	+	0.157744i	−0.973407	−	0.229081i	$-0.926428\pi$
$7$	−0.949237	+	2.92145i	−0.0512540	+	0.157744i	0.922153	+	0.386824i	$0.126428\pi$
$8$	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	$-0.681794\pi$
$13$	4.33551	−	3.14993i	0.0924964	−	0.0672026i	0.633072	+	0.774093i	$0.281794\pi$
$14$	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	$-0.394989\pi$
$17$	−33.3440	−	24.2258i	−0.475712	−	0.345625i	−0.799663	+	0.600449i	$0.794989\pi$
$18$	−30.2718	+	93.1669i	−0.396396	+	1.21998i
$19$	−43.2386	−	133.075i	−0.522085	−	1.60681i	−0.770009	−	0.638033i	$-0.779748\pi$
$19$	−43.2386	−	133.075i	−0.522085	−	1.60681i	0.247924	−	0.968779i	$-0.420252\pi$
$20$	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	$-0.874500\pi$
$29$	7.72383	−	23.7715i	0.0494579	−	0.152216i	0.972735	+	0.231918i	$0.0745001\pi$
$30$	99.4397	+	306.044i	0.605171	+	1.86252i
$31$	−25.4820	+	18.5137i	−0.147635	+	0.107263i	−0.659151	−	0.752011i	$-0.729084\pi$
$31$	−25.4820	+	18.5137i	−0.147635	+	0.107263i	0.511516	+	0.859274i	$0.329084\pi$
$32$	−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	−0.941628	−	0.336656i	$-0.890704\pi$
$37$	4.06159	−	12.5003i	0.0180465	−	0.0555415i	0.959674	+	0.281114i	$0.0907041\pi$
$38$	−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	−0.978808	−	0.204781i	$-0.934352\pi$
$41$	−80.6756	−	248.294i	−0.307303	−	0.945781i	0.671505	−	0.741000i	$-0.265648\pi$
$42$	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	−0.969245	−	0.246097i	$-0.920852\pi$
$47$	−106.254	−	327.017i	−0.329761	−	1.01490i	0.639484	−	0.768804i	$-0.279148\pi$
$48$	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	−0.166949	−	0.985966i	$-0.553392\pi$
$53$	277.489	−	201.607i	0.719170	−	0.522507i	0.886119	+	0.463458i	$0.153392\pi$
$54$	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	−0.916397	−	0.400270i	$-0.868916\pi$
$59$	27.3076	−	84.0442i	0.0602568	−	0.185451i	0.976654	+	0.214819i	$0.0689162\pi$
$60$	−51.0656	−	37.1013i	−0.109876	−	0.0798294i
$61$	597.619	+	434.195i	1.25438	+	0.911361i	0.998468	−	0.0553387i	$-0.0176239\pi$
$61$	597.619	+	434.195i	1.25438	+	0.911361i	0.255913	+	0.966700i	$0.417624\pi$
$62$	−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	0.719099	−	0.694908i	$-0.244555\pi$
$71$	167.761	+	121.886i	0.280417	+	0.203735i	−0.438682	+	0.898642i	$0.644555\pi$
$72$	−676.492	−	491.500i	−1.10730	−	0.804498i
$73$	312.293	−	961.138i	0.500700	−	1.54100i	−0.307182	−	0.951651i	$-0.599386\pi$
$73$	312.293	−	961.138i	0.500700	−	1.54100i	0.807882	−	0.589344i	$-0.200614\pi$
$74$	−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	0.517432	−	0.855725i	$-0.326888\pi$
$79$	1047.05	−	760.727i	1.49117	−	1.08340i	0.973738	−	0.227673i	$-0.0731118\pi$
$80$	−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	$-0.205625\pi$
$83$	357.461	+	259.711i	0.472728	+	0.343457i	−0.325775	+	0.945447i	$0.605625\pi$
$84$	−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	−0.987146	−	0.159819i	$-0.948909\pi$
$97$	−1089.27	+	791.403i	−1.14019	+	0.828400i	−0.153048	+	0.988219i	$0.548909\pi$
$98$	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	$-0.725343\pi$
$101$	−130.625	+	94.9046i	−0.128690	+	0.0934986i	0.521578	+	0.853203i	$0.325343\pi$
$102$	275.871	+	849.042i	0.267797	+	0.824193i
$103$	−10.7412	+	33.0580i	−0.0102753	+	0.0316243i	−0.956063	−	0.293162i	$-0.905292\pi$
$103$	−10.7412	+	33.0580i	−0.0102753	+	0.0316243i	0.945787	+	0.324786i	$0.105292\pi$
$104$	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	−0.997463	−	0.0711847i	$-0.977322\pi$
$107$	−257.158	−	791.450i	−0.232340	−	0.715068i	0.765123	−	0.643884i	$-0.222678\pi$
$108$	−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	0.981811	−	0.189861i	$-0.0608039\pi$
$113$	91.1853	+	280.639i	0.0759114	+	0.233631i	−0.905899	+	0.423493i	$0.860804\pi$
$114$	−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	$-0.452261\pi$
$127$	−1065.96	−	774.469i	−0.744796	−	0.541126i	−0.894209	+	0.447649i	$0.852261\pi$
$128$	−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	0.101613	−	0.994824i	$-0.467600\pi$
$137$	−1303.87	−	947.320i	−0.813120	−	0.590766i	−0.914734	+	0.404058i	$0.867600\pi$
$138$	1951.31	+	1417.71i	1.20367	+	0.874518i
$139$	9.84588	−	30.3025i	0.00600803	−	0.0184908i	−0.948008	−	0.318248i	$-0.896906\pi$
$139$	9.84588	−	30.3025i	0.00600803	−	0.0184908i	0.954016	+	0.299757i	$0.0969056\pi$
$140$	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	$-0.532668\pi$
$149$	−1964.57	−	1427.34i	−1.08016	−	0.784782i	−0.977711	+	0.209956i	$0.932668\pi$
$150$	640.643	−	1971.70i	0.348722	−	1.07326i
$151$	796.237	+	2450.57i	0.429118	+	1.32069i	0.898995	+	0.437958i	$0.144298\pi$
$151$	796.237	+	2450.57i	0.429118	+	1.32069i	−0.469877	+	0.882732i	$0.655702\pi$
$152$	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	0.933587	+	0.358350i	$0.116660\pi$
$157$	765.109	+	2354.76i	0.388932	+	1.19701i	−0.544656	+	0.838660i	$0.683340\pi$
$158$	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	0.0854225	−	0.996345i	$-0.472776\pi$
$163$	2204.66	−	1601.78i	1.05940	−	0.769699i	0.973977	+	0.226646i	$0.0727760\pi$
$164$	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	$-0.481335\pi$
$167$	2214.52	−	1608.94i	1.02614	−	0.745531i	0.967532	+	0.252750i	$0.0813350\pi$
$168$	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	−0.976426	−	0.215854i	$-0.930746\pi$
$173$	−713.031	−	2194.48i	−0.313357	−	0.964413i	0.663069	−	0.748558i	$-0.269254\pi$
$174$	−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	0.830016	−	0.557739i	$-0.188331\pi$
$179$	−405.478	−	1247.93i	−0.169312	−	0.521089i	−0.999328	+	0.0366506i	$0.988331\pi$
$180$	−88.2156	+	271.500i	−0.0365289	+	0.112424i
$181$	649.781	+	472.094i	0.266839	+	0.193870i	0.713157	−	0.701005i	$-0.247265\pi$
$181$	649.781	+	472.094i	0.266839	+	0.193870i	−0.446318	+	0.894875i	$0.647265\pi$
$182$	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	−0.798701	−	0.601729i	$-0.794479\pi$
$191$	530.967	−	1634.15i	0.201149	−	0.619073i	0.999850	−	0.0173442i	$-0.00552110\pi$
$192$	3473.52	+	2523.66i	1.30562	+	0.948591i
$193$	1084.23	+	787.740i	0.404377	+	0.293797i	0.771321	−	0.636446i	$-0.219596\pi$
$193$	1084.23	+	787.740i	0.404377	+	0.293797i	−0.366945	+	0.930243i	$0.619596\pi$
$194$	−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	−0.601862	−	0.798600i	$-0.705574\pi$
$211$	−86.8424	+	63.0947i	−0.0283340	+	0.0205859i	0.573528	+	0.819186i	$0.305574\pi$
$212$	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	−0.949965	−	0.312358i	$-0.898881\pi$
$223$	−1215.57	−	3741.15i	−0.365026	−	1.12344i	0.584938	−	0.811078i	$-0.301119\pi$
$224$	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	$-0.816593\pi$
$227$	547.548	−	1685.18i	0.160097	−	0.492728i	0.998642	+	0.0521050i	$0.0165931\pi$
$228$	−183.708	−	565.396i	−0.0533613	−	0.164229i
$229$	−1549.57	+	1125.83i	−0.447154	+	0.324876i	−0.788471	−	0.615072i	$-0.789127\pi$
$229$	−1549.57	+	1125.83i	−0.447154	+	0.324876i	0.341317	+	0.939948i	$0.389127\pi$
$230$	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	$-0.487922\pi$
$233$	3556.70	−	2584.09i	1.00003	−	0.726564i	0.962095	+	0.272716i	$0.0879220\pi$
$234$	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	0.963377	+	0.268152i	$0.0864130\pi$
$239$	1262.18	+	3884.58i	0.341604	+	1.05135i	−0.621772	+	0.783198i	$0.713587\pi$
$240$	−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	−0.693564	−	0.720395i	$-0.743960\pi$
$251$	−885.786	+	643.561i	−0.222750	+	0.161838i	0.470813	+	0.882233i	$0.343960\pi$
$252$	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	−0.917380	−	0.398012i	$-0.869700\pi$
$257$	242.016	−	744.847i	0.0587413	−	0.180787i	0.976122	+	0.217224i	$0.0697004\pi$
$258$	−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	0.493607	−	0.869685i	$-0.335678\pi$
$269$	−798.471	−	580.123i	−0.180980	−	0.131490i	−0.674587	+	0.738195i	$0.735678\pi$
$270$	−2305.65	−	1675.15i	−0.519693	−	0.377579i
$271$	−1414.37	+	4352.98i	−0.317036	+	0.975736i	0.657873	+	0.753129i	$0.271457\pi$
$271$	−1414.37	+	4352.98i	−0.317036	+	0.975736i	−0.974908	+	0.222607i	$0.928543\pi$
$272$	−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	$-0.680385\pi$
$277$	459.389	−	333.766i	0.0996462	−	0.0723972i	0.636493	+	0.771283i	$0.280385\pi$
$278$	−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	$-0.109357\pi$
$281$	4296.70	+	3121.74i	0.912170	+	0.662730i	−0.0293930	+	0.999568i	$0.509357\pi$
$282$	−2301.49	+	7083.27i	−0.486000	+	1.49575i
$283$	1461.17	+	4497.01i	0.306917	+	0.944593i	0.978955	+	0.204076i	$0.0654191\pi$
$283$	1461.17	+	4497.01i	0.306917	+	0.944593i	−0.672038	+	0.740517i	$0.734581\pi$
$284$	−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	$-0.974585\pi$
$293$	−719.675	+	2214.93i	−0.143494	+	0.441630i	0.853320	+	0.521388i	$0.174585\pi$
$294$	−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	0.999845	+	0.0175989i	$0.00560221\pi$
$311$	1104.03	+	3397.85i	0.201298	+	0.619531i	−0.798547	+	0.601932i	$0.794398\pi$
$312$	306.181	−	942.327i	0.0555579	−	0.170990i
$313$	−5812.27	−	4222.86i	−1.04961	−	0.762589i	−0.0774746	−	0.996994i	$-0.524686\pi$
$313$	−5812.27	−	4222.86i	−1.04961	−	0.762589i	−0.972139	+	0.234405i	$0.924686\pi$
$314$	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	−0.586659	−	0.809834i	$-0.699557\pi$
$317$	12.7078	−	9.23273i	0.00225154	−	0.00163584i	0.588910	+	0.808198i	$0.299557\pi$
$318$	−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	$-0.893846\pi$
$337$	73.9116	−	227.477i	0.0119472	−	0.0367698i	0.956852	+	0.290574i	$0.0938464\pi$
$338$	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	$-0.449826\pi$
$347$	−4743.10	−	3446.06i	−0.733784	−	0.533125i	−0.890758	+	0.454478i	$0.849826\pi$
$348$	32.8163	−	100.998i	0.00505500	−	0.0155577i
$349$	−1079.00	−	3320.83i	−0.165495	−	0.509341i	0.833577	−	0.552403i	$-0.186289\pi$
$349$	−1079.00	−	3320.83i	−0.165495	−	0.509341i	−0.999072	+	0.0430615i	$0.986289\pi$
$350$	−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	−0.246778	−	0.969072i	$-0.579372\pi$
$359$	3553.92	−	10937.8i	0.522476	−	1.60802i	0.769254	−	0.638943i	$-0.220628\pi$
$360$	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	−0.684969	−	0.728572i	$-0.740184\pi$
$367$	2091.12	−	6435.80i	0.297427	−	0.915385i	0.982396	−	0.186813i	$-0.0598157\pi$
$368$	−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	0.632793	−	0.774321i	$-0.281908\pi$
$379$	678.172	+	492.721i	0.0919139	+	0.0667794i	−0.540879	+	0.841100i	$0.681908\pi$
$380$	−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	−0.424356	−	0.905495i	$-0.639500\pi$
$383$	2291.27	−	1664.70i	0.305688	−	0.222095i	0.730044	+	0.683400i	$0.239500\pi$
$384$	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	−0.868646	−	0.495434i	$-0.835009\pi$
$389$	961.431	−	2958.98i	0.125312	−	0.385671i	0.993958	+	0.109763i	$0.0350090\pi$
$390$	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	0.856698	−	0.515819i	$-0.172512\pi$
$401$	5065.81	+	3680.52i	0.630859	+	0.458346i	−0.225839	+	0.974165i	$0.572512\pi$
$402$	−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	$-0.781559\pi$
$409$	−3391.80	+	2464.29i	−0.410059	+	0.297925i	0.363567	+	0.931568i	$0.381559\pi$
$410$	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	0.852224	+	0.523178i	$0.175254\pi$
$421$	4062.34	+	12502.6i	0.470276	+	1.44736i	−0.381947	+	0.924184i	$0.624746\pi$
$422$	−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	$-0.611537\pi$
$431$	3972.00	−	2885.83i	0.443909	−	0.322519i	0.787186	+	0.616715i	$0.211537\pi$
$432$	1289.40	+	3968.37i	0.143603	+	0.441964i
$433$	−3628.88	+	11168.5i	−0.402755	+	1.23955i	0.520000	+	0.854166i	$0.325932\pi$
$433$	−3628.88	+	11168.5i	−0.402755	+	1.23955i	−0.922755	+	0.385386i	$0.874068\pi$
$434$	−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	0.966819	+	0.255462i	$0.0822275\pi$
$443$	3121.72	+	9607.68i	0.334803	+	1.03042i	−0.632016	+	0.774955i	$0.717772\pi$
$444$	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	−0.573009	−	0.819549i	$-0.694224\pi$
$449$	279.316	−	202.935i	0.0293580	−	0.0213299i	0.602368	+	0.798219i	$0.294224\pi$
$450$	−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	$-0.481886\pi$
$457$	−8549.00	−	6211.21i	−0.875067	−	0.635773i	−0.931942	+	0.362608i	$0.881886\pi$
$458$	−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	0.363483	−	0.931601i	$-0.381587\pi$
$467$	−4139.71	−	3007.67i	−0.410199	−	0.298027i	−0.773682	+	0.633574i	$0.781587\pi$
$468$	−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	$-0.113989\pi$
$479$	9357.81	+	6798.85i	0.892629	+	0.648533i	−0.0439333	+	0.999034i	$0.513989\pi$
$480$	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	−0.760427	−	0.649423i	$-0.775010\pi$
$487$	−5663.21	−	17429.6i	−0.526950	−	1.62179i	0.233477	−	0.972362i	$-0.424990\pi$
$488$	−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	−0.782694	−	0.622407i	$-0.786155\pi$
$491$	2353.96	−	7244.75i	0.216360	−	0.665888i	0.999054	−	0.0434814i	$-0.0138449\pi$
$492$	−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	−0.596453	−	0.802648i	$-0.703424\pi$
$499$	3989.14	−	12277.3i	0.357872	−	1.10142i	0.954325	−	0.298770i	$-0.0965763\pi$
$500$	−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	−0.988283	−	0.152635i	$-0.951224\pi$
$503$	−3141.36	−	9668.11i	−0.278462	−	0.857017i	0.709821	−	0.704382i	$-0.248776\pi$
$504$	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	0.999565	−	0.0294928i	$-0.00938922\pi$
$509$	1993.14	+	6134.25i	0.173564	+	0.534177i	−0.826001	+	0.563669i	$0.809389\pi$
$510$	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	0.303157	+	0.952941i	$0.401959\pi$
$521$	−5972.50	+	18381.5i	−0.502227	+	1.54569i	−0.805383	+	0.592754i	$0.798041\pi$
$522$	1980.90	+	1439.21i	0.166096	+	0.120675i
$523$	5063.71	+	3679.00i	0.423367	+	0.307594i	0.778991	−	0.627035i	$-0.215732\pi$
$523$	5063.71	+	3679.00i	0.423367	+	0.307594i	−0.355624	+	0.934629i	$0.615732\pi$
$524$	−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	$-0.887900\pi$
$541$	−11332.8	+	8233.79i	−0.900623	+	0.654341i	0.0380030	+	0.999278i	$0.487900\pi$
$542$	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	$-0.0380356\pi$
$547$	1529.46	+	4707.20i	0.119552	+	0.367944i	−0.873317	+	0.487152i	$0.838036\pi$
$548$	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	$-0.853812\pi$
$557$	1174.75	−	3615.51i	0.0893641	−	0.275034i	0.985744	+	0.168252i	$0.0538123\pi$
$558$	−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	$-0.820831\pi$
$563$	−8009.36	+	5819.14i	−0.599564	+	0.435608i	0.246160	+	0.969229i	$0.420831\pi$
$564$	−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	$-0.162898\pi$
$569$	−1646.80	−	5068.33i	−0.121331	−	0.373419i	−0.993215	+	0.116294i	$0.962898\pi$
$570$	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	0.939486	−	0.342587i	$-0.111303\pi$
$577$	12529.2	+	9103.01i	0.903983	+	0.656782i	−0.0355028	+	0.999370i	$0.511303\pi$
$578$	−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	−0.755453	−	0.655202i	$-0.772583\pi$
$587$	3425.19	−	10541.7i	0.240839	−	0.741228i	0.996293	−	0.0860254i	$-0.0274166\pi$
$588$	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	0.161239	−	0.986915i	$-0.448451\pi$
$599$	−10666.0	−	7749.31i	−0.727548	−	0.528595i	−0.888787	+	0.458321i	$0.848451\pi$
$600$	14316.6	+	10401.6i	0.974123	+	0.707742i
$601$	5798.71	−	17846.6i	0.393568	−	1.21128i	−0.536503	−	0.843898i	$-0.680255\pi$
$601$	5798.71	−	17846.6i	0.393568	−	1.21128i	0.930071	−	0.367379i	$-0.119745\pi$
$602$	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	$-0.438940\pi$
$607$	17694.3	−	12855.7i	1.18318	−	0.859629i	0.992527	+	0.122028i	$0.0389399\pi$
$608$	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	$-0.0629215\pi$
$613$	1090.17	+	3355.19i	0.0718294	+	0.221068i	−0.908697	+	0.417457i	$0.862921\pi$
$614$	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	−0.897860	−	0.440282i	$-0.854879\pi$
$619$	−6626.35	−	20393.8i	−0.430267	−	1.32423i	0.467592	−	0.883944i	$-0.345121\pi$
$620$	−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	−0.488124	−	0.872774i	$-0.662319\pi$
$631$	6653.74	−	20478.1i	0.419780	−	1.29195i	0.907905	−	0.419177i	$-0.137681\pi$
$632$	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	0.937456	+	0.348103i	$0.113174\pi$
$641$	6226.16	+	19162.1i	0.383648	+	1.18075i	−0.553808	+	0.832644i	$0.686826\pi$
$642$	−5570.10	+	17143.0i	−0.342421	+	1.05386i
$643$	−23356.1	−	16969.2i	−1.43246	−	1.04074i	−0.989552	−	0.144179i	$-0.953946\pi$
$643$	−23356.1	−	16969.2i	−1.43246	−	1.04074i	−0.442911	−	0.896566i	$-0.646054\pi$
$644$	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	−0.548017	−	0.836467i	$-0.684617\pi$
$647$	1286.35	−	934.591i	0.0781636	−	0.0567891i	0.626181	+	0.779678i	$0.284617\pi$
$648$	−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	−0.575311	−	0.817935i	$-0.695119\pi$
$653$	6189.01	−	19047.8i	0.370896	−	1.14150i	0.946206	−	0.323564i	$-0.104881\pi$
$654$	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	−0.614961	−	0.788557i	$-0.710828\pi$
$673$	−960.819	+	698.076i	−0.0550325	+	0.0399834i	0.559929	+	0.828541i	$0.310828\pi$
$674$	−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	$-0.177544\pi$
$677$	10696.3	+	7771.33i	0.607227	+	0.441177i	−0.241210	+	0.970473i	$0.577544\pi$
$678$	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	−0.347296	−	0.937756i	$-0.612900\pi$
$691$	7942.18	−	5770.33i	0.437243	−	0.317675i	0.784538	+	0.620080i	$0.212900\pi$
$692$	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	−0.811185	−	0.584789i	$-0.801177\pi$
$701$	−9254.98	−	28483.9i	−0.498653	−	1.53470i	0.312532	−	0.949907i	$-0.398823\pi$
$702$	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	0.318524	−	0.947915i	$-0.396813\pi$
$709$	−9147.95	−	6646.38i	−0.484568	−	0.352059i	−0.803091	+	0.595856i	$0.796813\pi$
$710$	−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	0.245531	+	0.969389i	$0.421038\pi$
$719$	−10081.2	+	31026.7i	−0.522900	+	1.60932i	−0.768431	+	0.639933i	$0.778962\pi$
$720$	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	$-0.969780\pi$
$733$	−2667.24	+	8208.93i	−0.134402	+	0.413647i	0.861094	+	0.508445i	$0.169780\pi$
$734$	−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	$-0.851039\pi$
$739$	−14851.5	+	10790.3i	−0.739273	+	0.537113i	0.153210	+	0.988194i	$0.451039\pi$
$740$	−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	$-0.210965\pi$
$743$	9046.95	+	6572.99i	0.446703	+	0.324549i	−0.341590	+	0.939849i	$0.610965\pi$
$744$	−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	0.994545	+	0.104305i	$0.0332618\pi$
$751$	5170.90	+	15914.4i	0.251250	+	0.773269i	−0.743295	+	0.668964i	$0.766738\pi$
$752$	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	−0.00243609	−	0.999997i	$-0.500775\pi$
$757$	19742.0	−	14343.4i	0.947865	−	0.688664i	0.950301	+	0.311333i	$0.100775\pi$
$758$	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	$-0.635348\pi$
$761$	6851.83	−	4978.15i	0.326385	−	0.237132i	0.738895	+	0.673821i	$0.235348\pi$
$762$	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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more