LMFDB - Embedded newform 121.4.c.c.3.1

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			3.1
Root			$0.535233 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	121.3
Dual form			121.4.c.c.81.1

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

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

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	−0.905414	−	0.424530i	$-0.860439\pi$
$2$	−2.21028	+	1.60586i	−0.781450	+	0.567757i	0.123964	+	0.992287i	$0.460439\pi$
$3$	−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	−0.922153	−	0.386824i	$-0.873572\pi$
$7$	0.949237	−	2.92145i	0.0512540	−	0.157744i	0.973407	+	0.229081i	$0.0735720\pi$
$8$	−7.20643	−	22.1791i	−0.318482	−	0.980188i
$9$	−29.0084	+	21.0759i	−1.07439	+	0.780588i
$10$	40.5885			1.28352
$11$		0			0
$11$		0			0
$12$	4.24871			0.102208
$13$	−4.33551	+	3.14993i	−0.0924964	+	0.0672026i	−0.633072	−	0.774093i	$-0.718206\pi$
$13$	−4.33551	+	3.14993i	−0.0924964	+	0.0672026i	0.540576	+	0.841295i	$0.318206\pi$
$14$	2.59336	+	7.98156i	0.0495076	+	0.152369i
$15$	−36.3974	+	112.020i	−0.626519	+	1.92823i
$16$	48.0763	+	34.9295i	0.751193	+	0.545774i
$17$	33.3440	+	24.2258i	0.475712	+	0.345625i	0.799663	−	0.600449i	$-0.205011\pi$
$17$	33.3440	+	24.2258i	0.475712	+	0.345625i	−0.323951	+	0.946074i	$0.605011\pi$
$18$	30.2718	−	93.1669i	0.396396	−	1.21998i
$19$	43.2386	+	133.075i	0.522085	+	1.60681i	0.770009	+	0.638033i	$0.220252\pi$
$19$	43.2386	+	133.075i	0.522085	+	1.60681i	−0.247924	+	0.968779i	$0.579748\pi$
$20$	6.44101	−	4.67967i	0.0720127	−	0.0523203i
$21$	−24.3538			−0.253069
$22$		0			0
$23$	−111.354			−1.00952			−0.504758	−	0.863261i	$-0.668418\pi$
$23$	−111.354			−1.00952			−0.504758	+	0.863261i	$0.668418\pi$
$24$	−149.579	+	108.675i	−1.27219	+	0.924304i
$25$	29.5769	+	91.0283i	0.236615	+	0.728226i
$26$	4.52432	−	13.9244i	0.0341266	−	0.105031i
$27$	56.8054	+	41.2716i	0.404897	+	0.294175i
$28$	1.33178	+	0.967595i	0.00898867	+	0.00653065i
$29$	−7.72383	+	23.7715i	−0.0494579	+	0.152216i	−0.972735	−	0.231918i	$-0.925500\pi$
$29$	−7.72383	+	23.7715i	−0.0494579	+	0.152216i	0.923277	+	0.384134i	$0.125500\pi$
$30$	−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	$0.0656482\pi$
$41$	80.6756	+	248.294i	0.307303	+	0.945781i	−0.671505	+	0.741000i	$0.734352\pi$
$42$	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	−0.969245	−	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	−0.255913	−	0.966700i	$-0.582376\pi$
$61$	−597.619	−	434.195i	−1.25438	−	0.911361i	−0.998468	+	0.0553387i	$0.982376\pi$
$62$	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	$0.400614\pi$
$73$	−312.293	+	961.138i	−0.500700	+	1.54100i	−0.807882	+	0.589344i	$0.799386\pi$
$74$	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	$0.673112\pi$
$79$	−1047.05	+	760.727i	−1.49117	+	1.08340i	−0.973738	+	0.227673i	$0.926888\pi$
$80$	−272.816	−	839.641i	−0.381272	−	1.17343i
$81$	−127.142	+	391.304i	−0.174406	+	0.536768i
$82$	−577.041	−	419.245i	−0.777116	−	0.564607i
$83$	−357.461	−	259.711i	−0.472728	−	0.343457i	0.325775	−	0.945447i	$-0.394375\pi$
$83$	−357.461	−	259.711i	−0.472728	−	0.343457i	−0.798504	+	0.601990i	$0.794375\pi$
$84$	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	−0.521578	−	0.853203i	$-0.674657\pi$
$101$	130.625	−	94.9046i	0.128690	−	0.0934986i	0.650268	+	0.759705i	$0.274657\pi$
$102$	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	$0.0226780\pi$
$107$	257.158	+	791.450i	0.232340	+	0.715068i	−0.765123	+	0.643884i	$0.777322\pi$
$108$	−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	0.981811	−	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	0.894209	−	0.447649i	$-0.147739\pi$
$127$	1065.96	+	774.469i	0.744796	+	0.541126i	−0.149414	+	0.988775i	$0.547739\pi$
$128$	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	0.101613	−	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	−0.954016	−	0.299757i	$-0.903094\pi$
$139$	−9.84588	+	30.3025i	−0.00600803	+	0.0184908i	0.948008	+	0.318248i	$0.103094\pi$
$140$	−7.55738	−	23.2592i	−0.00456225	−	0.0140412i
$141$	−2205.45	+	1602.35i	−1.31725	+	0.957037i
$142$	−566.529			−0.334803
$143$		0			0
$144$	−2130.79			−1.23310
$145$	300.415	−	218.264i	0.172056	−	0.125006i
$146$	−853.199	−	2625.88i	−0.483639	−	1.48849i
$147$	817.215	−	2515.13i	0.458522	−	1.41119i
$148$	5.69842	+	4.14014i	0.00316491	+	0.00229944i
$149$	1964.57	+	1427.34i	1.08016	+	0.784782i	0.977711	−	0.209956i	$-0.0673320\pi$
$149$	1964.57	+	1427.34i	1.08016	+	0.784782i	0.102449	+	0.994738i	$0.467332\pi$
$150$	−640.643	+	1971.70i	−0.348722	+	1.07326i
$151$	−796.237	−	2450.57i	−0.429118	−	1.32069i	−0.898995	−	0.437958i	$-0.855702\pi$
$151$	−796.237	−	2450.57i	−0.429118	−	1.32069i	0.469877	−	0.882732i	$-0.344298\pi$
$152$	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	−0.967532	−	0.252750i	$-0.918665\pi$
$167$	−2214.52	+	1608.94i	−1.02614	+	0.745531i	−0.0586043	+	0.998281i	$0.518665\pi$
$168$	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	$0.0692536\pi$
$173$	713.031	+	2194.48i	0.313357	+	0.964413i	−0.663069	+	0.748558i	$0.730746\pi$
$174$	−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	0.366945	−	0.930243i	$-0.380404\pi$
$193$	−1084.23	−	787.740i	−0.404377	−	0.293797i	−0.771321	+	0.636446i	$0.780404\pi$
$194$	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	−0.573528	−	0.819186i	$-0.694426\pi$
$211$	86.8424	−	63.0947i	0.0283340	−	0.0205859i	0.601862	+	0.798600i	$0.294426\pi$
$212$	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	−0.998642	−	0.0521050i	$-0.983407\pi$
$227$	−547.548	+	1685.18i	−0.160097	+	0.492728i	0.838545	+	0.544833i	$0.183407\pi$
$228$	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	−0.962095	−	0.272716i	$-0.912078\pi$
$233$	−3556.70	+	2584.09i	−1.00003	+	0.726564i	−0.0379350	+	0.999280i	$0.512078\pi$
$234$	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	$-0.913587\pi$
$239$	−1262.18	−	3884.58i	−0.341604	−	1.05135i	0.621772	−	0.783198i	$-0.286413\pi$
$240$	−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	−0.693564	−	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	$-0.242078\pi$
$263$	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	0.493607	−	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	$-0.728543\pi$
$271$	1414.37	−	4352.98i	0.317036	−	0.975736i	0.974908	−	0.222607i	$-0.0714565\pi$
$272$	756.860	+	2329.38i	0.168718	+	0.519262i
$273$	105.586	−	76.7129i	0.0234079	−	0.0170069i
$274$	4403.18			0.970825
$275$		0			0
$276$	−473.110			−0.103181
$277$	−459.389	+	333.766i	−0.0996462	+	0.0723972i	−0.636493	−	0.771283i	$-0.719615\pi$
$277$	−459.389	+	333.766i	−0.0996462	+	0.0723972i	0.536846	+	0.843680i	$0.319615\pi$
$278$	−26.8994	−	82.7880i	−0.00580331	−	0.0178608i
$279$	348.999	−	1074.11i	0.0748890	−	0.230485i
$280$	860.998	+	625.551i	0.183766	+	0.133514i
$281$	−4296.70	−	3121.74i	−0.912170	−	0.662730i	0.0293930	−	0.999568i	$-0.490643\pi$
$281$	−4296.70	−	3121.74i	−0.912170	−	0.662730i	−0.941563	+	0.336838i	$0.890643\pi$
$282$	2301.49	−	7083.27i	0.486000	−	1.49575i
$283$	−1461.17	−	4497.01i	−0.306917	−	0.944593i	−0.978955	−	0.204076i	$-0.934581\pi$
$283$	−1461.17	−	4497.01i	−0.306917	−	0.944593i	0.672038	−	0.740517i	$-0.265419\pi$
$284$	−89.9029	+	65.3183i	−0.0187844	+	0.0136476i
$285$	−16480.8			−3.42539
$286$		0			0
$287$	801.960			0.164941
$288$	−702.301	+	510.252i	−0.143693	+	0.104399i
$289$	−993.271	−	3056.97i	−0.202172	−	0.622221i
$290$	−313.498	+	964.849i	−0.0634802	+	0.195372i
$291$	8635.98	+	6274.40i	1.73969	+	1.26396i
$292$	−438.146	−	318.332i	−0.0878102	−	0.0637979i
$293$	719.675	−	2214.93i	0.143494	−	0.441630i	−0.853320	−	0.521388i	$-0.825415\pi$
$293$	719.675	−	2214.93i	0.143494	−	0.441630i	0.996814	+	0.0797574i	$0.0254146\pi$
$294$	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	0.999845	+	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	−0.956852	−	0.290574i	$-0.906154\pi$
$337$	−73.9116	+	227.477i	−0.0119472	+	0.0367698i	0.944905	+	0.327344i	$0.106154\pi$
$338$	−1830.57	−	5633.92i	−0.294586	−	0.906642i
$339$	1892.67	−	1375.10i	0.303232	−	0.220311i
$340$	328.137			0.0523404
$341$		0			0
$342$	13707.1			2.16723
$343$	1681.35	−	1221.57i	0.264678	−	0.192300i
$344$	415.904	+	1280.02i	0.0651861	+	0.200622i
$345$	4052.99	−	12473.8i	0.632481	−	1.94658i
$346$	−5100.02	−	3705.38i	−0.792425	−	0.575730i
$347$	4743.10	+	3446.06i	0.733784	+	0.533125i	0.890758	−	0.454478i	$-0.150174\pi$
$347$	4743.10	+	3446.06i	0.733784	+	0.533125i	−0.156975	+	0.987603i	$0.550174\pi$
$348$	−32.8163	+	100.998i	−0.00505500	+	0.0155577i
$349$	1079.00	+	3320.83i	0.165495	+	0.509341i	0.999072	−	0.0430615i	$-0.0137111\pi$
$349$	1079.00	+	3320.83i	0.165495	+	0.509341i	−0.833577	+	0.552403i	$0.813711\pi$
$350$	−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	$0.420628\pi$
$359$	−3553.92	+	10937.8i	−0.522476	+	1.60802i	−0.769254	+	0.638943i	$0.779372\pi$
$360$	−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	$-0.620152\pi$
$373$	−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	0.632793	−	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	−0.363567	−	0.931568i	$-0.618441\pi$
$409$	3391.80	−	2464.29i	0.410059	−	0.297925i	0.773625	+	0.633643i	$0.218441\pi$
$410$	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	−0.787186	−	0.616715i	$-0.788463\pi$
$431$	−3972.00	+	2885.83i	−0.443909	+	0.322519i	0.343277	+	0.939234i	$0.388463\pi$
$432$	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	$-0.722208\pi$
$439$	−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	0.966819	+	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	0.931942	−	0.362608i	$-0.118114\pi$
$457$	8549.00	+	6211.21i	0.875067	+	0.635773i	−0.0568749	+	0.998381i	$0.518114\pi$
$458$	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	0.363483	−	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	0.0439333	−	0.999034i	$-0.486011\pi$
$479$	−9357.81	−	6798.85i	−0.892629	−	0.648533i	−0.936562	+	0.350502i	$0.886011\pi$
$480$	−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	$0.213845\pi$
$491$	−2353.96	+	7244.75i	−0.216360	+	0.665888i	−0.999054	+	0.0434814i	$0.986155\pi$
$492$	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	$0.0487759\pi$
$503$	3141.36	+	9668.11i	0.278462	+	0.857017i	−0.709821	+	0.704382i	$0.751224\pi$
$504$	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	0.355624	−	0.934629i	$-0.384268\pi$
$523$	−5063.71	−	3679.00i	−0.423367	−	0.307594i	−0.778991	+	0.627035i	$0.784268\pi$
$524$	265.081	−	815.835i	0.0220994	−	0.0680151i
$525$	−720.310	−	2216.89i	−0.0598799	−	0.184291i
$526$	−13659.6	+	9924.30i	−1.13230	+	0.822662i
$527$	−1298.18			−0.107305
$528$		0			0
$529$	232.675			0.0191235
$530$	11262.8	−	8182.93i	0.923069	−	0.670649i
$531$	979.153	+	3013.52i	0.0800219	+	0.246282i
$532$	−71.1781	+	219.064i	−0.00580068	+	0.0178527i
$533$	−1131.88	−	822.358i	−0.0919834	−	0.0668298i
$534$	−26094.5	−	18958.8i	−2.11464	−	1.53638i
$535$	3820.44	−	11758.1i	0.308733	−	0.950181i
$536$	−2467.19	−	7593.22i	−0.198818	−	0.611898i
$537$	−8416.22	+	6114.75i	−0.676326	+	0.491379i
$538$	2696.44			0.216081
$539$		0			0
$540$	559.022			0.0445490
$541$	11332.8	−	8233.79i	0.900623	−	0.654341i	−0.0380030	−	0.999278i	$-0.512100\pi$
$541$	11332.8	−	8233.79i	0.900623	−	0.654341i	0.938626	+	0.344937i	$0.112100\pi$
$542$	3864.12	+	11892.6i	0.306233	+	0.942489i
$543$	1967.74	−	6056.07i	0.155513	−	0.478620i
$544$	807.265	+	586.512i	0.0636235	+	0.0462252i
$545$	−12551.0	−	9118.84i	−0.986470	−	0.716712i
$546$	−110.185	+	339.113i	−0.00863638	+	0.0265801i
$547$	−1529.46	−	4707.20i	−0.119552	−	0.367944i	0.873317	−	0.487152i	$-0.161964\pi$
$547$	−1529.46	−	4707.20i	−0.119552	−	0.367944i	−0.992869	+	0.119208i	$0.961964\pi$
$548$	698.744	−	507.667i	0.0544687	−	0.0395738i
$549$	26487.0			2.05909
$550$		0			0
$551$	−3497.35			−0.270404
$552$	16656.2	−	12101.4i	1.28430	−	0.933100i
$553$	1228.53	+	3781.02i	0.0944707	+	0.290751i
$554$	479.395	−	1475.43i	0.0367645	−	0.113150i
$555$	1252.45	+	909.958i	0.0957901	+	0.0695956i
$556$	−13.8138	−	10.0363i	−0.00105366	−	0.000765528i
$557$	−1174.75	+	3615.51i	−0.0893641	+	0.275034i	−0.985744	−	0.168252i	$-0.946188\pi$
$557$	−1174.75	+	3615.51i	−0.0893641	+	0.275034i	0.896380	+	0.443287i	$0.146188\pi$
$558$	953.483	+	2934.52i	0.0723372	+	0.222631i
$559$	250.214	−	181.791i	0.0189319	−	0.0137548i
$560$	−2711.94			−0.204644
$561$		0			0
$562$	14510.0			1.08908
$563$	8009.36	−	5819.14i	0.599564	−	0.435608i	−0.246160	−	0.969229i	$-0.579169\pi$
$563$	8009.36	−	5819.14i	0.599564	−	0.435608i	0.845724	+	0.533621i	$0.179169\pi$
$564$	−451.444	−	1389.40i	−0.0337043	−	0.103731i
$565$	1354.69	−	4169.29i	0.100871	−	0.310449i
$566$	10451.2	+	7593.21i	0.776139	+	0.563898i
$567$	1022.49	+	742.880i	0.0757327	+	0.0550230i
$568$	1494.36	−	4599.15i	0.110390	−	0.339747i
$569$	1646.80	+	5068.33i	0.121331	+	0.373419i	0.993215	−	0.116294i	$-0.0371015\pi$
$569$	1646.80	+	5068.33i	0.121331	+	0.373419i	−0.871884	+	0.489713i	$0.837102\pi$
$570$	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	0.939486	−	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	$-0.451877\pi$
$593$	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	0.161239	−	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	$0.319745\pi$
$601$	−5798.71	+	17846.6i	−0.393568	+	1.21128i	−0.930071	+	0.367379i	$0.880255\pi$
$602$	−149.670	−	460.638i	−0.0101331	−	0.0311864i
$603$	−9931.30	+	7215.51i	−0.670703	+	0.487294i
$604$	1380.84			0.0930223
$605$		0			0
$606$	3497.29			0.234435
$607$	−17694.3	+	12855.7i	−1.18318	+	0.859629i	−0.992527	−	0.122028i	$-0.961060\pi$
$607$	−17694.3	+	12855.7i	−1.18318	+	0.859629i	−0.190652	+	0.981658i	$0.561060\pi$
$608$	1046.82	+	3221.77i	0.0698257	+	0.214901i
$609$	188.105	−	578.927i	0.0125162	−	0.0385210i
$610$	−24256.4	−	17623.3i	−1.61002	−	1.16975i
$611$	1490.75	+	1083.09i	0.0987057	+	0.0717139i
$612$	244.732	−	753.208i	0.0161646	−	0.0497494i
$613$	−1090.17	−	3355.19i	−0.0718294	−	0.221068i	0.908697	−	0.417457i	$-0.137079\pi$
$613$	−1090.17	−	3355.19i	−0.0718294	−	0.221068i	−0.980526	+	0.196389i	$0.937079\pi$
$614$	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	$-0.600647\pi$
$659$	−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	−0.559929	−	0.828541i	$-0.689172\pi$
$673$	960.819	−	698.076i	0.0550325	−	0.0399834i	0.614961	+	0.788557i	$0.289172\pi$
$674$	−201.930	−	621.477i	−0.0115402	−	0.0355169i
$675$	−2076.75	+	6391.59i	−0.118421	+	0.364463i
$676$	−940.060	−	682.994i	−0.0534855	−	0.0388595i
$677$	−10696.3	−	7771.33i	−0.607227	−	0.441177i	0.241210	−	0.970473i	$-0.422456\pi$
$677$	−10696.3	−	7771.33i	−0.607227	−	0.441177i	−0.848437	+	0.529297i	$0.822456\pi$
$678$	−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	$0.198823\pi$
$701$	9254.98	+	28483.9i	0.498653	+	1.53470i	−0.312532	+	0.949907i	$0.601177\pi$
$702$	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	−0.861094	−	0.508445i	$-0.830220\pi$
$733$	2667.24	−	8208.93i	0.134402	−	0.413647i	0.995497	+	0.0947978i	$0.0302204\pi$
$734$	5713.05	+	17582.9i	0.287292	+	0.884194i
$735$	−31785.2	+	23093.3i	−1.59512	+	1.15893i
$736$	−2695.90			−0.135017
$737$		0			0
$738$	25575.0			1.27565
$739$	14851.5	−	10790.3i	0.739273	−	0.537113i	−0.153210	−	0.988194i	$-0.548961\pi$
$739$	14851.5	−	10790.3i	0.739273	−	0.537113i	0.892483	+	0.451080i	$0.148961\pi$
$740$	−32.3365	−	99.5214i	−0.00160637	−	0.00494389i
$741$	−1837.08	+	5653.96i	−0.0910755	+	0.280302i
$742$	2328.77	+	1691.95i	0.115218	+	0.0837108i
$743$	−9046.95	−	6572.99i	−0.446703	−	0.324549i	0.341590	−	0.939849i	$-0.389035\pi$
$743$	−9046.95	−	6572.99i	−0.446703	−	0.324549i	−0.788293	+	0.615300i	$0.789035\pi$
$744$	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	−0.738895	−	0.673821i	$-0.764652\pi$
$761$	−6851.83	+	4978.15i	−0.326385	+	0.237132i	0.412510	+	0.910953i	$0.364652\pi$
$762$	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

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

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