LMFDB - Embedded newform 120.4.m.b.59.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(59,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("120.59");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.5
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73183 - 0.732884i) q^{2} +(-2.64167 - 4.47455i) q^{3} +(6.92576 + 4.00422i) q^{4} +(-10.4671 - 3.92924i) q^{5} +(3.93726 + 14.1597i) q^{6} -4.10158 q^{7} +(-15.9854 - 16.0146i) q^{8} +(-13.0432 + 23.6406i) q^{9} +O(q^{10})$	\(q+(-2.73183 - 0.732884i) q^{2} +(-2.64167 - 4.47455i) q^{3} +(6.92576 + 4.00422i) q^{4} +(-10.4671 - 3.92924i) q^{5} +(3.93726 + 14.1597i) q^{6} -4.10158 q^{7} +(-15.9854 - 16.0146i) q^{8} +(-13.0432 + 23.6406i) q^{9} +(25.7147 + 18.4052i) q^{10} -5.96978i q^{11} +(-0.378480 - 41.5675i) q^{12} -33.0570 q^{13} +(11.2048 + 3.00598i) q^{14} +(10.0691 + 57.2155i) q^{15} +(31.9324 + 55.4646i) q^{16} +50.6136 q^{17} +(52.9575 - 55.0228i) q^{18} +74.1386 q^{19} +(-56.7594 - 69.1258i) q^{20} +(10.8350 + 18.3527i) q^{21} +(-4.37515 + 16.3084i) q^{22} +184.927i q^{23} +(-29.4302 + 113.833i) q^{24} +(94.1221 + 82.2559i) q^{25} +(90.3061 + 24.2270i) q^{26} +(140.237 - 4.08828i) q^{27} +(-28.4065 - 16.4236i) q^{28} +98.3905 q^{29} +(14.4252 - 163.682i) q^{30} +192.624i q^{31} +(-46.5846 - 174.922i) q^{32} +(-26.7121 + 15.7702i) q^{33} +(-138.268 - 37.0939i) q^{34} +(42.9318 + 16.1161i) q^{35} +(-184.996 + 111.501i) q^{36} -350.946 q^{37} +(-202.534 - 54.3350i) q^{38} +(87.3258 + 147.915i) q^{39} +(104.396 + 230.438i) q^{40} -292.535i q^{41} +(-16.1490 - 58.0772i) q^{42} +80.8246i q^{43} +(23.9043 - 41.3453i) q^{44} +(229.414 - 196.199i) q^{45} +(135.530 - 505.188i) q^{46} +63.1702i q^{47} +(163.824 - 289.402i) q^{48} -326.177 q^{49} +(-196.841 - 293.689i) q^{50} +(-133.705 - 226.473i) q^{51} +(-228.945 - 132.368i) q^{52} +178.821i q^{53} +(-386.098 - 91.6086i) q^{54} +(-23.4567 + 62.4865i) q^{55} +(65.5652 + 65.6852i) q^{56} +(-195.850 - 331.737i) q^{57} +(-268.786 - 72.1088i) q^{58} +479.870i q^{59} +(-159.367 + 436.580i) q^{60} -635.627i q^{61} +(141.171 - 526.215i) q^{62} +(53.4975 - 96.9635i) q^{63} +(-0.936778 + 511.999i) q^{64} +(346.013 + 129.889i) q^{65} +(84.5304 - 23.5046i) q^{66} +288.505i q^{67} +(350.538 + 202.668i) q^{68} +(827.464 - 488.515i) q^{69} +(-105.471 - 75.4904i) q^{70} -1062.20 q^{71} +(587.094 - 169.021i) q^{72} +980.889i q^{73} +(958.725 + 257.203i) q^{74} +(119.418 - 638.447i) q^{75} +(513.467 + 296.868i) q^{76} +24.4855i q^{77} +(-130.154 - 468.079i) q^{78} +804.239i q^{79} +(-116.307 - 706.026i) q^{80} +(-388.752 - 616.695i) q^{81} +(-214.394 + 799.156i) q^{82} -300.045 q^{83} +(1.55237 + 170.492i) q^{84} +(-529.780 - 198.873i) q^{85} +(59.2350 - 220.799i) q^{86} +(-259.915 - 440.253i) q^{87} +(-95.6038 + 95.4290i) q^{88} +1112.49i q^{89} +(-770.511 + 367.849i) q^{90} +135.586 q^{91} +(-740.488 + 1280.76i) q^{92} +(861.905 - 508.849i) q^{93} +(46.2964 - 172.570i) q^{94} +(-776.020 - 291.309i) q^{95} +(-659.638 + 670.532i) q^{96} -1217.88i q^{97} +(891.059 + 239.050i) q^{98} +(141.129 + 77.8648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) $ 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9	$ 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) $ 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9 - 72 * q^10 - 128 * q^16 + 672 * q^19 - 416 * q^24 + 496 * q^25 - 248 * q^30 + 240 * q^34 - 608 * q^36 - 1344 * q^40 + 336 * q^46 + 3520 * q^49 - 544 * q^51 - 952 * q^54 - 2064 * q^60 + 2176 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 + 2304 * q^76 - 2304 * q^81 - 736 * q^84 - 1432 * q^90 - 2752 * q^91 + 4496 * q^94 + 640 * q^96 + 256 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.73183	−	0.732884i	−0.965847	−	0.259114i
$2$	−2.73183	−	0.732884i	−0.965847	−	0.259114i
$3$	−2.64167	−	4.47455i	−0.508390	−	0.861127i
$3$	−2.64167	−	4.47455i	−0.508390	−	0.861127i
$4$	6.92576	+	4.00422i	0.865720	+	0.500528i
$5$	−10.4671	−	3.92924i	−0.936210	−	0.351442i
$5$	−10.4671	−	3.92924i	−0.936210	−	0.351442i
$6$	3.93726	+	14.1597i	0.267897	+	0.963448i
$7$	−4.10158			−0.221464			−0.110732	−	0.993850i	$-0.535320\pi$
$7$	−4.10158			−0.221464			−0.110732	+	0.993850i	$0.535320\pi$
$8$	−15.9854	−	16.0146i	−0.706460	−	0.707753i
$9$	−13.0432	+	23.6406i	−0.483080	+	0.875576i
$10$	25.7147	+	18.4052i	0.813172	+	0.582024i
$11$		−	5.96978i		−	0.163632i	−0.996647	−	0.0818162i	$-0.973928\pi$
$11$		−	5.96978i		−	0.163632i	0.996647	−	0.0818162i	$-0.0260720\pi$
$12$	−0.378480	−	41.5675i	−0.00910482	−	0.999959i
$13$	−33.0570			−0.705259			−0.352630	−	0.935763i	$-0.614712\pi$
$13$	−33.0570			−0.705259			−0.352630	+	0.935763i	$0.614712\pi$
$14$	11.2048	+	3.00598i	0.213901	+	0.0573844i
$15$	10.0691	+	57.2155i	0.173323	+	0.984865i
$16$	31.9324	+	55.4646i	0.498943	+	0.866635i
$17$	50.6136			0.722095			0.361047	−	0.932547i	$-0.382419\pi$
$17$	50.6136			0.722095			0.361047	+	0.932547i	$0.382419\pi$
$18$	52.9575	−	55.0228i	0.693455	−	0.720500i
$19$	74.1386			0.895188			0.447594	−	0.894237i	$-0.352281\pi$
$19$	74.1386			0.895188			0.447594	+	0.894237i	$0.352281\pi$
$20$	−56.7594	−	69.1258i	−0.634589	−	0.772850i
$21$	10.8350	+	18.3527i	0.112590	+	0.190709i
$22$	−4.37515	+	16.3084i	−0.0423994	+	0.158044i
$23$			184.927i			1.67652i	0.545273	+	0.838259i	$0.316426\pi$
$23$			184.927i			1.67652i	−0.545273	+	0.838259i	$0.683574\pi$
$24$	−29.4302	+	113.833i	−0.250309	+	0.968166i
$25$	94.1221	+	82.2559i	0.752977	+	0.658047i
$26$	90.3061	+	24.2270i	0.681173	+	0.182742i
$27$	140.237	−	4.08828i	0.999575	−	0.0291404i
$28$	−28.4065	−	16.4236i	−0.191726	−	0.110849i
$29$	98.3905			0.630023			0.315011	−	0.949088i	$-0.397992\pi$
$29$	98.3905			0.630023			0.315011	+	0.949088i	$0.397992\pi$
$30$	14.4252	−	163.682i	0.0877887	−	0.996139i
$31$			192.624i			1.11601i	0.829838	+	0.558004i	$0.188433\pi$
$31$			192.624i			1.11601i	−0.829838	+	0.558004i	$0.811567\pi$
$32$	−46.5846	−	174.922i	−0.257346	−	0.966319i
$33$	−26.7121	+	15.7702i	−0.140908	+	0.0831890i
$34$	−138.268	−	37.0939i	−0.697433	−	0.187105i
$35$	42.9318	+	16.1161i	0.207337	+	0.0778319i
$36$	−184.996	+	111.501i	−0.856463	+	0.516209i
$37$	−350.946			−1.55933			−0.779665	−	0.626196i	$-0.784611\pi$
$37$	−350.946			−1.55933			−0.779665	+	0.626196i	$0.784611\pi$
$38$	−202.534	−	54.3350i	−0.864614	−	0.231955i
$39$	87.3258	+	147.915i	0.358547	+	0.607318i
$40$	104.396	+	230.438i	0.412660	+	0.910885i
$41$		−	292.535i		−	1.11430i	−0.830412	−	0.557150i	$-0.811895\pi$
$41$		−	292.535i		−	1.11430i	0.830412	−	0.557150i	$-0.188105\pi$
$42$	−16.1490	−	58.0772i	−0.0593296	−	0.213369i
$43$			80.8246i			0.286643i	0.989676	+	0.143321i	$0.0457782\pi$
$43$			80.8246i			0.286643i	−0.989676	+	0.143321i	$0.954222\pi$
$44$	23.9043	−	41.3453i	0.0819026	−	0.141660i
$45$	229.414	−	196.199i	0.759979	−	0.649948i
$46$	135.530	−	505.188i	0.434408	−	1.61926i
$47$			63.1702i			0.196049i	0.995184	+	0.0980246i	$0.0312524\pi$
$47$			63.1702i			0.196049i	−0.995184	+	0.0980246i	$0.968748\pi$
$48$	163.824	−	289.402i	0.492625	−	0.870242i
$49$	−326.177			−0.950954
$50$	−196.841	−	293.689i	−0.556751	−	0.830679i
$51$	−133.705	−	226.473i	−0.367105	−	0.621815i
$52$	−228.945	−	132.368i	−0.610557	−	0.353002i
$53$			178.821i			0.463453i	0.972781	+	0.231726i	$0.0744374\pi$
$53$			178.821i			0.463453i	−0.972781	+	0.231726i	$0.925563\pi$
$54$	−386.098	−	91.6086i	−0.972987	−	0.230858i
$55$	−23.4567	+	62.4865i	−0.0575073	+	0.153194i
$56$	65.5652	+	65.6852i	0.156456	+	0.156742i
$57$	−195.850	−	331.737i	−0.455104	−	0.770871i
$58$	−268.786	−	72.1088i	−0.608506	−	0.163247i
$59$			479.870i			1.05888i	0.848348	+	0.529439i	$0.177598\pi$
$59$			479.870i			1.05888i	−0.848348	+	0.529439i	$0.822402\pi$
$60$	−159.367	+	436.580i	−0.342904	+	0.939371i
$61$		−	635.627i		−	1.33416i	−0.744986	−	0.667080i	$-0.767544\pi$
$61$		−	635.627i		−	1.33416i	0.744986	−	0.667080i	$-0.232456\pi$
$62$	141.171	−	526.215i	0.289173	−	1.07789i
$63$	53.4975	−	96.9635i	0.106985	−	0.193909i
$64$	−0.936778	+	511.999i	−0.00182965	+	0.999998i
$65$	346.013	+	129.889i	0.660271	+	0.247858i
$66$	84.5304	−	23.5046i	0.157651	−	0.0438366i
$67$			288.505i			0.526067i	0.964787	+	0.263033i	$0.0847229\pi$
$67$			288.505i			0.526067i	−0.964787	+	0.263033i	$0.915277\pi$
$68$	350.538	+	202.668i	0.625132	+	0.361429i
$69$	827.464	−	488.515i	1.44369	−	0.852324i
$70$	−105.471	−	75.4904i	−0.180088	−	0.128898i
$71$	−1062.20			−1.77549			−0.887743	−	0.460340i	$-0.847727\pi$
$71$	−1062.20			−1.77549			−0.887743	+	0.460340i	$0.847727\pi$
$72$	587.094	−	169.021i	0.960969	−	0.276658i
$73$			980.889i			1.57266i	0.617805	+	0.786332i	$0.288022\pi$
$73$			980.889i			1.57266i	−0.617805	+	0.786332i	$0.711978\pi$
$74$	958.725	+	257.203i	1.50607	+	0.404044i
$75$	119.418	−	638.447i	0.183857	−	0.982953i
$76$	513.467	+	296.868i	0.774982	+	0.448067i
$77$			24.4855i			0.0362387i
$78$	−130.154	−	468.079i	−0.188937	−	0.679480i
$79$			804.239i			1.14537i	0.819777	+	0.572683i	$0.194097\pi$
$79$			804.239i			1.14537i	−0.819777	+	0.572683i	$0.805903\pi$
$80$	−116.307	−	706.026i	−0.162544	−	0.986701i
$81$	−388.752	−	616.695i	−0.533267	−	0.845947i
$82$	−214.394	+	799.156i	−0.288730	+	1.07624i
$83$	−300.045			−0.396798			−0.198399	−	0.980121i	$-0.563574\pi$
$83$	−300.045			−0.396798			−0.198399	+	0.980121i	$0.563574\pi$
$84$	1.55237	+	170.492i	0.00201639	+	0.221455i
$85$	−529.780	−	198.873i	−0.676032	−	0.253775i
$86$	59.2350	−	220.799i	0.0742730	−	0.276853i
$87$	−259.915	−	440.253i	−0.320297	−	0.542530i
$88$	−95.6038	+	95.4290i	−0.115811	+	0.115600i
$89$			1112.49i			1.32499i	0.749066	+	0.662495i	$0.230502\pi$
$89$			1112.49i			1.32499i	−0.749066	+	0.662495i	$0.769498\pi$
$90$	−770.511	+	367.849i	−0.902433	+	0.430830i
$91$	135.586			0.156190
$92$	−740.488	+	1280.76i	−0.839144	+	1.45139i
$93$	861.905	−	508.849i	0.961026	−	0.567367i
$94$	46.2964	−	172.570i	0.0507990	−	0.189354i
$95$	−776.020	−	291.309i	−0.838083	−	0.314607i
$96$	−659.638	+	670.532i	−0.701292	+	0.712874i
$97$		−	1217.88i		−	1.27481i	−0.770529	−	0.637405i	$-0.780008\pi$
$97$		−	1217.88i		−	1.27481i	0.770529	−	0.637405i	$-0.219992\pi$
$98$	891.059	+	239.050i	0.918476	+	0.246405i
$99$	141.129	+	77.8648i	0.143273	+	0.0790475i
$100$	322.496	+	946.571i	0.322496	+	0.946571i
$101$	−461.131			−0.454300			−0.227150	−	0.973860i	$-0.572941\pi$
$101$	−461.131			−0.454300			−0.227150	+	0.973860i	$0.572941\pi$
$102$	199.279	+	716.675i	0.193447	+	0.695700i
$103$	1363.74			1.30460			0.652299	−	0.757962i	$-0.273805\pi$
$103$	1363.74			1.30460			0.652299	+	0.757962i	$0.273805\pi$
$104$	528.428	+	529.396i	0.498237	+	0.499150i
$105$	−41.2994	−	234.674i	−0.0383848	−	0.218112i
$106$	131.055	−	488.509i	0.120087	−	0.447624i
$107$	626.784			0.566295			0.283147	−	0.959076i	$-0.408621\pi$
$107$	626.784			0.566295			0.283147	+	0.959076i	$0.408621\pi$
$108$	987.615	+	533.224i	0.879938	+	0.475088i
$109$			472.473i			0.415181i	0.978216	+	0.207590i	$0.0665621\pi$
$109$			472.473i			0.415181i	−0.978216	+	0.207590i	$0.933438\pi$
$110$	109.875	−	153.511i	0.0952379	−	0.133061i
$111$	927.084	+	1570.33i	0.792747	+	1.34278i
$112$	−130.973	−	227.492i	−0.110498	−	0.191929i
$113$	−507.424			−0.422429			−0.211214	−	0.977440i	$-0.567742\pi$
$113$	−507.424			−0.422429			−0.211214	+	0.977440i	$0.567742\pi$
$114$	291.903	+	1049.78i	0.239818	+	0.862467i
$115$	726.622	−	1935.65i	0.589199	−	1.56957i
$116$	681.429	+	393.978i	0.545424	+	0.315344i
$117$	431.168	−	781.487i	0.340697	−	0.617508i
$118$	351.689	−	1310.92i	0.274370	−	1.02271i
$119$	−207.596			−0.159918
$120$	755.326	−	1075.86i	0.574596	−	0.818437i
$121$	1295.36			0.973224
$122$	−465.841	+	1736.42i	−0.345699	+	1.28859i
$123$	−1308.96	+	772.781i	−0.959555	+	0.566499i
$124$	−771.309	+	1334.07i	−0.558594	+	0.966152i
$125$	−661.986	−	1230.81i	−0.473679	−	0.880698i
$126$	−217.209	+	225.680i	−0.153576	+	0.159565i
$127$	2049.23			1.43181			0.715903	−	0.698199i	$-0.246015\pi$
$127$	2049.23			1.43181			0.715903	+	0.698199i	$0.246015\pi$
$128$	377.795	−	1398.01i	0.260880	−	0.965371i
$129$	361.654	−	213.512i	0.246836	−	0.145726i
$130$	−850.053	−	608.422i	−0.573497	−	0.410478i
$131$			1677.53i			1.11883i	0.828888	+	0.559415i	$0.188974\pi$
$131$			1677.53i			1.11883i	−0.828888	+	0.559415i	$0.811026\pi$
$132$	−248.149	+	2.25944i	−0.163626	+	0.00148984i
$133$	−304.085			−0.198252
$134$	211.440	−	788.145i	0.136311	−	0.508100i
$135$	−1483.94	−	508.231i	−0.946053	−	0.324011i
$136$	−809.077	−	810.559i	−0.510131	−	0.511065i
$137$	−1839.77			−1.14731			−0.573657	−	0.819096i	$-0.694476\pi$
$137$	−1839.77			−1.14731			−0.573657	+	0.819096i	$0.694476\pi$
$138$	−2618.51	+	728.105i	−1.61524	+	0.449133i
$139$	−1598.25			−0.975264			−0.487632	−	0.873049i	$-0.662139\pi$
$139$	−1598.25			−0.975264			−0.487632	+	0.873049i	$0.662139\pi$
$140$	232.803	+	283.525i	0.140539	+	0.171159i
$141$	282.658	−	166.875i	0.168823	−	0.0996694i
$142$	2901.74	+	778.466i	1.71485	+	0.460052i
$143$			197.343i			0.115403i
$144$	−1727.71	+	31.4650i	−0.999834	+	0.0182089i
$145$	−1029.87	−	386.600i	−0.589833	−	0.221417i
$146$	718.878	−	2679.62i	0.407498	−	1.51895i
$147$	861.652	+	1459.50i	0.483455	+	0.818892i
$148$	−2430.57	−	1405.27i	−1.34994	−	0.780489i
$149$	−533.530			−0.293346			−0.146673	−	0.989185i	$-0.546856\pi$
$149$	−533.530			−0.293346			−0.146673	+	0.989185i	$0.546856\pi$
$150$	−794.138	+	1656.61i	−0.432274	+	0.901742i
$151$		−	3056.41i		−	1.64720i	−0.567173	−	0.823599i	$-0.691963\pi$
$151$		−	3056.41i		−	1.64720i	0.567173	−	0.823599i	$-0.308037\pi$
$152$	−1185.13	−	1187.30i	−0.632414	−	0.633572i
$153$	−660.162	+	1196.53i	−0.348830	+	0.632249i
$154$	17.9450	−	66.8901i	0.00938994	−	0.0350011i
$155$	756.866	−	2016.22i	0.392213	−	1.04482i
$156$	12.5114	+	1374.10i	0.00642126	+	0.705230i
$157$	−1429.75			−0.726794			−0.363397	−	0.931634i	$-0.618383\pi$
$157$	−1429.75			−0.726794			−0.363397	+	0.931634i	$0.618383\pi$
$158$	589.414	−	2197.04i	0.296780	−	1.10625i
$159$	800.145	−	472.387i	0.399092	−	0.235615i
$160$	−199.705	+	2013.98i	−0.0986756	+	0.995120i
$161$		−	758.491i		−	0.371289i
$162$	610.037	+	1969.61i	0.295858	+	0.955232i
$163$			600.115i			0.288372i	0.989551	+	0.144186i	$0.0460564\pi$
$163$			600.115i			0.288372i	−0.989551	+	0.144186i	$0.953944\pi$
$164$	1171.38	−	2026.03i	0.557739	−	0.964673i
$165$	341.564	−	60.1105i	0.161156	−	0.0283612i
$166$	819.671	+	219.898i	0.383246	+	0.102816i
$167$			1087.44i			0.503883i	0.967742	+	0.251942i	$0.0810691\pi$
$167$			1087.44i			0.503883i	−0.967742	+	0.251942i	$0.918931\pi$
$168$	120.710	−	466.893i	0.0554345	−	0.214414i
$169$	−1104.23			−0.502609
$170$	1301.52	+	931.555i	0.587187	+	0.420276i
$171$	−967.002	+	1752.68i	−0.432447	+	0.783805i
$172$	−323.640	+	559.772i	−0.143473	+	0.248152i
$173$			374.343i			0.164513i	0.996611	+	0.0822567i	$0.0262127\pi$
$173$			374.343i			0.164513i	−0.996611	+	0.0822567i	$0.973787\pi$
$174$	387.389	+	1393.18i	0.168781	+	0.606994i
$175$	−386.049	−	337.379i	−0.166757	−	0.145734i
$176$	331.111	−	190.629i	0.141809	−	0.0816433i
$177$	2147.20	−	1267.66i	0.911829	−	0.538322i
$178$	815.329	−	3039.14i	0.343323	−	1.27974i
$179$		−	1886.45i		−	0.787708i	−0.919173	−	0.393854i	$-0.871142\pi$
$179$		−	1886.45i		−	0.787708i	0.919173	−	0.393854i	$-0.128858\pi$
$180$	2374.49	−	440.204i	0.983246	−	0.182283i
$181$			986.271i			0.405022i	0.979280	+	0.202511i	$0.0649101\pi$
$181$			986.271i			0.405022i	−0.979280	+	0.202511i	$0.935090\pi$
$182$	−370.397	−	99.3688i	−0.150855	−	0.0404709i
$183$	−2844.15	+	1679.12i	−1.14888	+	0.678273i
$184$	2961.53	−	2956.12i	1.18656	−	1.18439i
$185$	3673.41	+	1378.95i	1.45986	+	0.548015i
$186$	−2727.50	+	758.411i	−1.07522	+	0.298975i
$187$		−	302.152i		−	0.118158i
$188$	−252.947	+	437.501i	−0.0981281	+	0.169724i
$189$	−575.191	+	16.7684i	−0.221370	+	0.00645355i
$190$	1906.46	+	1364.54i	0.727941	+	0.521021i
$191$	3513.46			1.33102			0.665510	−	0.746389i	$-0.268214\pi$
$191$	3513.46			1.33102			0.665510	+	0.746389i	$0.268214\pi$
$192$	2293.44	−	1348.34i	0.862056	−	0.506813i
$193$			3049.07i			1.13719i	0.822619	+	0.568593i	$0.192512\pi$
$193$			3049.07i			1.13719i	−0.822619	+	0.568593i	$0.807488\pi$
$194$	−892.561	+	3327.02i	−0.330320	+	1.23127i
$195$	−332.856	−	1891.37i	−0.122238	−	0.694585i
$196$	−2259.02	−	1306.09i	−0.823260	−	0.475979i
$197$			3893.24i			1.40803i	0.710186	+	0.704014i	$0.248611\pi$
$197$			3893.24i			1.40803i	−0.710186	+	0.704014i	$0.751389\pi$
$198$	−328.474	−	316.144i	−0.117897	−	0.113472i
$199$		−	2888.21i		−	1.02884i	−0.857537	−	0.514422i	$-0.828006\pi$
$199$		−	2888.21i		−	1.02884i	0.857537	−	0.514422i	$-0.171994\pi$
$200$	−187.278	−	2822.22i	−0.0662127	−	0.997806i
$201$	1290.93	−	762.134i	0.453010	−	0.267447i
$202$	1259.73	+	337.956i	0.438784	+	0.117715i
$203$	−403.556			−0.139528
$204$	−19.1563	−	2103.88i	−0.00657454	−	0.722065i
$205$	−1149.44	+	3062.01i	−0.391612	+	1.04322i
$206$	−3725.51	−	999.466i	−1.26004	−	0.338039i
$207$	−4371.77	−	2412.03i	−1.46792	−	0.809892i
$208$	−1055.59	−	1833.50i	−0.351884	−	0.611202i
$209$		−	442.591i		−	0.146482i
$210$	−59.1659	+	671.356i	−0.0194421	+	0.220609i
$211$	−1800.81			−0.587550			−0.293775	−	0.955875i	$-0.594912\pi$
$211$	−1800.81			−0.587550			−0.293775	+	0.955875i	$0.594912\pi$
$212$	−716.041	+	1238.47i	−0.231971	+	0.401220i
$213$	2805.97	+	4752.85i	0.902638	+	1.52892i
$214$	−1712.27	−	459.360i	−0.546954	−	0.146735i
$215$	317.579	−	846.003i	0.100738	−	0.268358i
$216$	−2307.20	−	2180.48i	−0.726784	−	0.686866i
$217$		−	790.062i		−	0.247156i
$218$	346.268	−	1290.71i	0.107579	−	0.401001i
$219$	4389.04	−	2591.19i	1.35426	−	0.799526i
$220$	−412.666	+	338.841i	−0.126463	+	0.103839i
$221$	−1673.14			−0.509264
$222$	−1381.77	−	4969.31i	−0.417740	−	1.50233i
$223$	3394.93			1.01947			0.509734	−	0.860332i	$-0.329744\pi$
$223$	3394.93			1.01947			0.509734	+	0.860332i	$0.329744\pi$
$224$	191.070	+	717.458i	0.0569929	+	0.214005i
$225$	−3172.22	+	1152.22i	−0.939918	+	0.341399i
$226$	1386.19	+	371.883i	0.408001	+	0.109457i
$227$	−1666.84			−0.487366			−0.243683	−	0.969855i	$-0.578356\pi$
$227$	−1666.84			−0.487366			−0.243683	+	0.969855i	$0.578356\pi$
$228$	−28.0600	−	3081.76i	−0.00815053	−	0.895151i
$229$			5278.56i			1.52322i	0.648037	+	0.761609i	$0.275590\pi$
$229$			5278.56i			1.52322i	−0.648037	+	0.761609i	$0.724410\pi$
$230$	−3403.62	+	4755.34i	−0.975773	+	1.36330i
$231$	109.562	−	64.6826i	0.0312061	−	0.0184234i
$232$	−1572.81	−	1575.69i	−0.445086	−	0.445901i
$233$	−469.587			−0.132033			−0.0660165	−	0.997819i	$-0.521029\pi$
$233$	−469.587			−0.132033			−0.0660165	+	0.997819i	$0.521029\pi$
$234$	−1750.62	+	1818.89i	−0.489066	+	0.508139i
$235$	248.211	−	661.211i	0.0689000	−	0.183543i
$236$	−1921.51	+	3323.47i	−0.529998	+	0.916692i
$237$	3598.61	−	2124.53i	0.986306	−	0.582292i
$238$	567.116	+	152.144i	0.154456	+	0.0414370i
$239$	130.148			0.0352242			0.0176121	−	0.999845i	$-0.494394\pi$
$239$	130.148			0.0352242			0.0176121	+	0.999845i	$0.494394\pi$
$240$	−2851.90	+	2385.51i	−0.767040	+	0.641599i
$241$	5560.04			1.48611			0.743057	−	0.669228i	$-0.233375\pi$
$241$	5560.04			1.48611			0.743057	+	0.669228i	$0.233375\pi$
$242$	−3538.70	−	949.350i	−0.939986	−	0.252176i
$243$	−1732.48	+	3368.59i	−0.457360	+	0.889281i
$244$	2545.19	−	4402.20i	0.667784	−	1.15501i
$245$	3414.14	+	1281.63i	0.890292	+	0.334205i
$246$	4142.22	−	1151.79i	1.07357	−	0.298517i
$247$	−2450.80			−0.631340
$248$	3084.80	−	3079.16i	0.789859	−	0.788415i
$249$	792.619	+	1342.57i	0.201728	+	0.341693i
$250$	906.389	+	3847.53i	0.229300	+	0.973356i
$251$			6537.02i			1.64388i	0.569576	+	0.821939i	$0.307107\pi$
$251$			6537.02i			1.64388i	−0.569576	+	0.821939i	$0.692893\pi$
$252$	758.775	−	457.330i	0.189676	−	0.114322i
$253$	1103.97			0.274332
$254$	−5598.13	−	1501.85i	−1.38291	−	0.371001i
$255$	509.636	+	2895.88i	0.125155	+	0.711166i
$256$	−2056.65	+	3542.23i	−0.502111	+	0.864803i
$257$	2769.77			0.672270			0.336135	−	0.941814i	$-0.390880\pi$
$257$	2769.77			0.672270			0.336135	+	0.941814i	$0.390880\pi$
$258$	−1144.45	+	318.228i	−0.276165	+	0.0767906i
$259$	1439.43			0.345336
$260$	1876.30	+	2285.09i	0.447550	+	0.545060i
$261$	−1283.32	+	2326.01i	−0.304351	+	0.551633i
$262$	1229.44	−	4582.73i	0.289904	−	1.08062i
$263$		−	2001.24i		−	0.469207i	−0.972091	−	0.234604i	$-0.924621\pi$
$263$		−	2001.24i		−	0.469207i	0.972091	−	0.234604i	$-0.0753792\pi$
$264$	679.555	+	175.692i	0.158423	+	0.0409586i
$265$	702.632	−	1871.75i	0.162877	−	0.433889i
$266$	830.708	+	222.859i	0.191481	+	0.0513698i
$267$	4977.91	−	2938.84i	1.14098	−	0.673611i
$268$	−1155.24	+	1998.12i	−0.263311	+	0.455427i
$269$	−2476.45			−0.561307			−0.280654	−	0.959809i	$-0.590551\pi$
$269$	−2476.45			−0.561307			−0.280654	+	0.959809i	$0.590551\pi$
$270$	3681.39	+	2475.95i	0.829787	+	0.558081i
$271$			1616.36i			0.362313i	0.983454	+	0.181156i	$0.0579840\pi$
$271$			1616.36i			0.362313i	−0.983454	+	0.181156i	$0.942016\pi$
$272$	1616.21	+	2807.27i	0.360284	+	0.625792i
$273$	−358.173	−	606.686i	−0.0794052	−	0.134499i
$274$	5025.93	+	1348.34i	1.10813	+	0.297285i
$275$	491.049	−	561.888i	0.107678	−	0.123211i
$276$	7686.94	−	69.9911i	1.67645	−	0.0152644i
$277$	−5749.66			−1.24716			−0.623580	−	0.781759i	$-0.714323\pi$
$277$	−5749.66			−1.24716			−0.623580	+	0.781759i	$0.714323\pi$
$278$	4366.14	+	1171.33i	0.941956	+	0.252704i
$279$	−4553.74	−	2512.43i	−0.977151	−	0.539122i
$280$	−428.187	−	945.158i	−0.0913894	−	0.201729i
$281$		−	7754.89i		−	1.64633i	−0.567804	−	0.823164i	$-0.692207\pi$
$281$		−	7754.89i		−	1.64633i	0.567804	−	0.823164i	$-0.307793\pi$
$282$	−894.472	+	248.717i	−0.188883	+	0.0525209i
$283$			4931.44i			1.03584i	0.855428	+	0.517922i	$0.173294\pi$
$283$			4931.44i			1.03584i	−0.855428	+	0.517922i	$0.826706\pi$
$284$	−7356.52	−	4253.27i	−1.53707	−	0.888680i
$285$	746.512	+	4241.88i	0.155156	+	0.881639i
$286$	144.630	−	539.107i	0.0299025	−	0.111462i
$287$			1199.86i			0.246778i
$288$	4742.88	+	1180.26i	0.970405	+	0.241484i
$289$	−2351.26			−0.478579
$290$	2530.09	+	1810.90i	0.512317	+	0.366688i
$291$	−5449.44	+	3217.22i	−1.09777	+	0.648100i
$292$	−3927.70	+	6793.41i	−0.787162	+	1.36149i
$293$		−	688.926i		−	0.137363i	−0.997639	−	0.0686817i	$-0.978121\pi$
$293$		−	688.926i		−	0.137363i	0.997639	−	0.0686817i	$-0.0218793\pi$
$294$	−1284.24	−	4618.58i	−0.254757	−	0.916194i
$295$	1885.53	−	5022.87i	0.372134	−	0.991332i
$296$	5610.00	+	5620.28i	1.10160	+	1.10362i
$297$	−24.4061	−	837.181i	−0.00476831	−	0.163563i
$298$	1457.51	+	391.016i	0.283327	+	0.0760099i
$299$		−	6113.13i		−	1.18238i
$300$	3383.55	−	3943.55i	0.651164	−	0.758937i
$301$		−	331.508i		−	0.0634811i
$302$	−2239.99	+	8349.58i	−0.426811	+	1.59094i
$303$	1218.16	+	2063.35i	0.230961	+	0.391210i
$304$	2367.42	+	4112.07i	0.446648	+	0.775801i
$305$	−2497.53	+	6653.20i	−0.468880	+	1.24905i
$306$	2680.37	−	2784.90i	0.500740	−	0.520269i
$307$		−	6625.29i		−	1.23168i	−0.787872	−	0.615839i	$-0.788817\pi$
$307$		−	6625.29i		−	1.23168i	0.787872	−	0.615839i	$-0.211183\pi$
$308$	−98.0454	+	169.581i	−0.0181385	+	0.0313726i
$309$	−3602.56	−	6102.14i	−0.663244	−	1.12343i
$310$	−3545.28	+	4953.28i	−0.649544	+	0.907507i
$311$	5355.88			0.976540			0.488270	−	0.872693i	$-0.337628\pi$
$311$	5355.88			0.976540			0.488270	+	0.872693i	$0.337628\pi$
$312$	972.875	−	3762.97i	0.176533	−	0.682808i
$313$		−	57.6042i		−	0.0104025i	−0.999986	−	0.00520125i	$-0.998344\pi$
$313$		−	57.6042i		−	0.0104025i	0.999986	−	0.00520125i	$-0.00165562\pi$
$314$	3905.84	+	1047.84i	0.701971	+	0.188322i
$315$	−940.959	+	804.726i	−0.168308	+	0.143940i
$316$	−3220.35	+	5569.97i	−0.573288	+	0.991567i
$317$		−	7806.30i		−	1.38311i	−0.722325	−	0.691554i	$-0.756926\pi$
$317$		−	7806.30i		−	1.38311i	0.722325	−	0.691554i	$-0.243074\pi$
$318$	−2532.06	+	704.066i	−0.446512	+	0.124157i
$319$		−	587.370i		−	0.103092i
$320$	2021.57	−	5355.49i	0.353155	−	0.935565i
$321$	−1655.76	−	2804.58i	−0.287898	−	0.487652i
$322$	−555.886	+	2072.07i	−0.0962059	+	0.358608i
$323$	3752.43			0.646410
$324$	−223.016	−	5827.73i	−0.0382401	−	0.999269i
$325$	−3111.40	−	2719.14i	−0.531044	−	0.464094i
$326$	439.815	−	1639.41i	0.0747212	−	0.278523i
$327$	2114.10	−	1248.12i	0.357523	−	0.211074i
$328$	−4684.84	+	4676.28i	−0.788650	+	0.787208i
$329$		−	259.097i		−	0.0434179i
$330$	−977.147	−	86.1149i	−0.163001	−	0.0143651i
$331$	−6218.44			−1.03262			−0.516308	−	0.856403i	$-0.672694\pi$
$331$	−6218.44			−1.03262			−0.516308	+	0.856403i	$0.672694\pi$
$332$	−2078.04	−	1201.45i	−0.343516	−	0.198608i
$333$	4577.45	−	8296.57i	0.753282	−	1.36531i
$334$	796.966	−	2970.69i	0.130563	−	0.486674i
$335$	1133.61	−	3019.82i	0.184882	−	0.492509i
$336$	−671.938	+	1187.00i	−0.109099	+	0.192727i
$337$			8547.36i			1.38162i	0.723038	+	0.690808i	$0.242745\pi$
$337$			8547.36i			1.38162i	−0.723038	+	0.690808i	$0.757255\pi$
$338$	3016.57	+	809.274i	0.485444	+	0.130233i
$339$	1340.45	+	2270.49i	0.214758	+	0.363765i
$340$	−2872.80	−	3498.71i	−0.458233	−	0.558071i
$341$	1149.92			0.182615
$342$	3926.19	−	4079.31i	0.620773	−	0.644983i
$343$	2744.68			0.432067
$344$	1294.38	−	1292.01i	0.202872	−	0.202501i
$345$	−10580.7	+	1862.05i	−1.65114	+	0.290579i
$346$	274.350	−	1022.64i	0.0426276	−	0.158895i
$347$	−11848.5			−1.83303			−0.916517	−	0.399996i	$-0.869012\pi$
$347$	−11848.5			−1.83303			−0.916517	+	0.399996i	$0.869012\pi$
$348$	−37.2389	−	4089.85i	−0.00573625	−	0.629997i
$349$		−	3765.09i		−	0.577480i	−0.957408	−	0.288740i	$-0.906764\pi$
$349$		−	3765.09i		−	0.577480i	0.957408	−	0.288740i	$-0.0932363\pi$
$350$	807.360	+	1204.59i	0.123301	+	0.183966i
$351$	−4635.80	+	135.146i	−0.704960	+	0.0205515i
$352$	−1044.25	+	278.100i	−0.158121	+	0.0421101i
$353$	−7721.18			−1.16418			−0.582092	−	0.813123i	$-0.697766\pi$
$353$	−7721.18			−1.16418			−0.582092	+	0.813123i	$0.697766\pi$
$354$	−6794.83	+	1889.37i	−1.02017	+	0.283670i
$355$	11118.2	+	4173.63i	1.66223	+	0.623980i
$356$	−4454.67	+	7704.87i	−0.663195	+	1.14707i
$357$	548.399	+	928.897i	0.0813007	+	0.137710i
$358$	−1382.55	+	5153.45i	−0.204106	+	0.760805i
$359$	−1277.28			−0.187778			−0.0938892	−	0.995583i	$-0.529930\pi$
$359$	−1277.28			−0.187778			−0.0938892	+	0.995583i	$0.529930\pi$
$360$	−6809.33	−	537.667i	−0.996897	−	0.0787154i
$361$	−1362.46			−0.198639
$362$	722.822	−	2694.32i	0.104947	−	0.391189i
$363$	−3421.92	−	5796.16i	−0.494777	−	0.838070i
$364$	939.036	+	542.917i	0.135217	+	0.0781774i
$365$	3854.15	−	10267.1i	0.552700	−	1.47234i
$366$	9000.31	−	2502.63i	1.28539	−	0.357417i
$367$	4874.49			0.693315			0.346657	−	0.937992i	$-0.387317\pi$
$367$	4874.49			0.693315			0.346657	+	0.937992i	$0.387317\pi$
$368$	−10256.9	+	5905.15i	−1.45293	+	0.836487i
$369$	6915.70	+	3815.58i	0.975655	+	0.538296i
$370$	−9024.50	−	6459.24i	−1.26800	−	0.907568i
$371$		−	733.449i		−	0.102638i
$372$	8006.89	−	72.9044i	1.11596	−	0.0101611i
$373$	−9969.36			−1.38390			−0.691949	−	0.721946i	$-0.743248\pi$
$373$	−9969.36			−1.38390			−0.691949	+	0.721946i	$0.743248\pi$
$374$	−221.442	+	825.428i	−0.0306164	+	0.114123i
$375$	−3758.58	+	6213.49i	−0.517580	+	0.855635i
$376$	1011.65	−	1009.80i	0.138755	−	0.138501i
$377$	−3252.50			−0.444330
$378$	1583.61	+	375.740i	0.215482	+	0.0511269i
$379$	−3910.73			−0.530028			−0.265014	−	0.964245i	$-0.585377\pi$
$379$	−3910.73			−0.530028			−0.265014	+	0.964245i	$0.585377\pi$
$380$	−4208.06	−	5124.89i	−0.568076	−	0.691846i
$381$	−5413.38	−	9169.36i	−0.727916	−	1.23297i
$382$	−9598.16	−	2574.96i	−1.28556	−	0.344886i
$383$		−	2301.53i		−	0.307056i	−0.988144	−	0.153528i	$-0.950936\pi$
$383$		−	2301.53i		−	0.307056i	0.988144	−	0.153528i	$-0.0490636\pi$
$384$	−7253.46	+	2002.61i	−0.963936	+	0.266133i
$385$	96.2095	−	256.293i	0.0127358	−	0.0339270i
$386$	2234.61	−	8329.53i	0.294660	−	1.09835i
$387$	−1910.74	−	1054.21i	−0.250978	−	0.138471i
$388$	4876.65	−	8434.71i	0.638078	−	1.10363i
$389$	13438.1			1.75152			0.875758	−	0.482751i	$-0.160362\pi$
$389$	13438.1			1.75152			0.875758	+	0.482751i	$0.160362\pi$
$390$	−476.853	+	5410.85i	−0.0619138	+	0.702536i
$391$			9359.82i			1.21060i
$392$	5214.06	+	5223.61i	0.671810	+	0.673041i
$393$	7506.20	−	4431.49i	0.963455	−	0.568801i
$394$	2853.29	−	10635.6i	0.364839	−	1.35994i
$395$	3160.05	−	8418.08i	0.402530	−	1.07230i
$396$	665.637	+	1104.38i	0.0844685	+	0.140145i
$397$	10501.3			1.32757			0.663786	−	0.747922i	$-0.268949\pi$
$397$	10501.3			1.32757			0.663786	+	0.747922i	$0.268949\pi$
$398$	−2116.73	+	7890.10i	−0.266588	+	0.993706i
$399$	803.293	+	1360.64i	0.100789	+	0.170720i
$400$	−1556.75	+	7847.07i	−0.194594	+	0.980884i
$401$		−	13566.8i		−	1.68951i	−0.535155	−	0.844754i	$-0.679747\pi$
$401$		−	13566.8i		−	1.68951i	0.535155	−	0.844754i	$-0.320253\pi$
$402$	−4085.15	+	1135.92i	−0.506838	+	0.140932i
$403$		−	6367.58i		−	0.787076i
$404$	−3193.69	−	1846.47i	−0.393297	−	0.227390i
$405$	1645.97	+	7982.54i	0.201948	+	0.979396i
$406$	1102.45	+	295.760i	0.134762	+	0.0361535i
$407$			2095.07i			0.255157i
$408$	−1489.57	+	5761.48i	−0.180747	+	0.699108i
$409$	−7673.26			−0.927674			−0.463837	−	0.885921i	$-0.653528\pi$
$409$	−7673.26			−0.927674			−0.463837	+	0.885921i	$0.653528\pi$
$410$	5384.17	−	7522.47i	0.648550	−	0.906118i
$411$	4860.06	+	8232.13i	0.583282	+	0.987983i
$412$	9444.96	+	5460.73i	1.12942	+	0.652988i
$413$		−	1968.22i		−	0.234504i
$414$	10175.2	+	9793.25i	1.20793	+	1.16259i
$415$	3140.61	+	1178.95i	0.371486	+	0.139451i
$416$	1539.95	+	5782.42i	0.181496	+	0.681506i
$417$	4222.05	+	7151.44i	0.495814	+	0.839827i
$418$	−324.368	+	1209.08i	−0.0379554	+	0.141479i
$419$			1239.80i			0.144554i	0.997385	+	0.0722768i	$0.0230265\pi$
$419$			1239.80i			0.144554i	−0.997385	+	0.0722768i	$0.976973\pi$
$420$	653.657	−	1790.67i	0.0759409	−	0.208037i
$421$		−	1701.96i		−	0.197027i	−0.995136	−	0.0985134i	$-0.968591\pi$
$421$		−	1701.96i		−	0.197027i	0.995136	−	0.0985134i	$-0.0314087\pi$
$422$	4919.51	+	1319.79i	0.567483	+	0.152242i
$423$	−1493.38	−	823.939i	−0.171656	−	0.0947075i
$424$	2863.76	−	2858.52i	0.328010	−	0.327411i
$425$	4763.86	+	4163.27i	0.543721	+	0.475172i
$426$	−4182.14	−	15040.4i	−0.475647	−	1.71059i
$427$			2607.07i			0.295469i
$428$	4340.96	+	2509.79i	0.490253	+	0.283446i
$429$	883.021	−	521.315i	0.0993769	−	0.0586698i
$430$	−1487.59	+	2078.38i	−0.166833	+	0.233090i
$431$	−9669.03			−1.08061			−0.540303	−	0.841471i	$-0.681690\pi$
$431$	−9669.03			−1.08061			−0.540303	+	0.841471i	$0.681690\pi$
$432$	4704.84	+	7647.62i	0.523985	+	0.851727i
$433$		−	11871.2i		−	1.31753i	−0.752348	−	0.658766i	$-0.771079\pi$
$433$		−	11871.2i		−	1.31753i	0.752348	−	0.658766i	$-0.228921\pi$
$434$	−579.023	+	2158.31i	−0.0640415	+	0.238715i
$435$	990.708	+	5629.46i	0.109197	+	0.620487i
$436$	−1891.89	+	3272.24i	−0.207810	+	0.359430i
$437$			13710.2i			1.50080i
$438$	−13889.1	+	3862.02i	−1.51518	+	0.421311i
$439$			16373.4i			1.78009i	0.455868	+	0.890047i	$0.349329\pi$
$439$			16373.4i			1.78009i	−0.455868	+	0.890047i	$0.650671\pi$
$440$	1375.66	−	623.219i	0.149050	−	0.0675245i
$441$	4254.38	−	7711.01i	0.459387	−	0.832632i
$442$	4570.72	+	1226.21i	0.491871	+	0.131957i
$443$	13008.8			1.39519			0.697594	−	0.716493i	$-0.254254\pi$
$443$	13008.8			1.39519			0.697594	+	0.716493i	$0.254254\pi$
$444$	132.826	+	14588.0i	0.0141974	+	1.55927i
$445$	4371.26	−	11644.6i	0.465657	−	1.24047i
$446$	−9274.36	−	2488.09i	−0.984650	−	0.264158i
$447$	1409.41	+	2387.31i	0.149134	+	0.252608i
$448$	3.84227	−	2100.00i	0.000405201	−	0.221464i
$449$			9615.94i			1.01070i	0.862914	+	0.505350i	$0.168637\pi$
$449$			9615.94i			1.01070i	−0.862914	+	0.505350i	$0.831363\pi$
$450$	9510.42	−	822.799i	0.996278	−	0.0861936i
$451$	−1746.37			−0.182336
$452$	−3514.30	−	2031.84i	−0.365705	−	0.211437i
$453$	−13676.0	+	8074.02i	−1.41845	+	0.837418i
$454$	4553.52	+	1221.60i	0.470721	+	0.126283i
$455$	−1419.20	−	532.750i	−0.146226	−	0.0548917i
$456$	−2181.92	+	8439.39i	−0.224074	+	0.866690i
$457$			3926.38i			0.401900i	0.979601	+	0.200950i	$0.0644030\pi$
$457$			3926.38i			0.401900i	−0.979601	+	0.200950i	$0.935597\pi$
$458$	3868.57	−	14420.1i	0.394687	−	1.47120i
$459$	7097.88	−	206.923i	0.721788	−	0.0210421i
$460$	12783.2	−	10496.3i	1.29570	−	1.06390i
$461$	−360.528			−0.0364240			−0.0182120	−	0.999834i	$-0.505797\pi$
$461$	−360.528			−0.0364240			−0.0182120	+	0.999834i	$0.505797\pi$
$462$	−346.708	+	96.4058i	−0.0349141	+	0.00970823i
$463$	−14036.6			−1.40894			−0.704468	−	0.709735i	$-0.748815\pi$
$463$	−14036.6			−1.40894			−0.704468	+	0.709735i	$0.748815\pi$
$464$	3141.84	+	5457.19i	0.314346	+	0.546000i
$465$	−11021.1	+	1939.56i	−1.09912	+	0.193430i
$466$	1282.83	+	344.153i	0.127524	+	0.0342115i
$467$	4186.44			0.414829			0.207415	−	0.978253i	$-0.433495\pi$
$467$	4186.44			0.414829			0.207415	+	0.978253i	$0.433495\pi$
$468$	6115.42	−	3685.90i	0.604028	−	0.364061i
$469$		−	1183.32i		−	0.116505i
$470$	−1162.66	+	1624.40i	−0.114105	+	0.159422i
$471$	3776.93	+	6397.49i	0.369494	+	0.625862i
$472$	7684.95	−	7670.90i	0.749424	−	0.748054i
$473$	482.505			0.0469040
$474$	−11387.8	+	3166.50i	−1.10350	+	0.306840i
$475$	6978.08	+	6098.34i	0.674056	+	0.589076i
$476$	−1437.76	−	831.260i	−0.138444	−	0.0800435i
$477$	−4227.44	−	2332.40i	−0.405788	−	0.223885i
$478$	−355.543	−	95.3836i	−0.0340212	−	0.00912708i
$479$	−3466.07			−0.330624			−0.165312	−	0.986241i	$-0.552863\pi$
$479$	−3466.07			−0.330624			−0.165312	+	0.986241i	$0.552863\pi$
$480$	9539.21	−	4426.68i	0.907090	−	0.420936i
$481$	11601.2			1.09973
$482$	−15189.1	−	4074.86i	−1.43536	−	0.385072i
$483$	−3393.91	+	2003.68i	−0.319727	+	0.188759i
$484$	8971.37	+	5186.92i	0.842540	+	0.487126i
$485$	−4785.33	+	12747.7i	−0.448022	+	1.19349i
$486$	7201.62	−	7932.71i	0.672165	−	0.740401i
$487$	2368.19			0.220355			0.110178	−	0.993912i	$-0.464858\pi$
$487$	2368.19			0.220355			0.110178	+	0.993912i	$0.464858\pi$
$488$	−10179.3	+	10160.7i	−0.944256	+	0.942530i
$489$	2685.25	−	1585.31i	0.248325	−	0.146605i
$490$	−8387.56	−	6003.36i	−0.773288	−	0.553478i
$491$			19310.1i			1.77485i	0.460953	+	0.887424i	$0.347508\pi$
$491$			19310.1i			1.77485i	−0.460953	+	0.887424i	$0.652492\pi$
$492$	−12160.0	+	110.719i	−1.11425	+	0.0101455i
$493$	4979.90			0.454936
$494$	6695.17	+	1796.15i	0.609777	+	0.163589i
$495$	−1171.27	−	1369.55i	−0.106353	−	0.124357i
$496$	−10683.8	+	6150.94i	−0.967172	+	0.556825i
$497$	4356.68			0.393207
$498$	−1181.36	−	4248.55i	−0.106301	−	0.382294i
$499$	−2257.79			−0.202551			−0.101275	−	0.994858i	$-0.532292\pi$
$499$	−2257.79			−0.202551			−0.101275	+	0.994858i	$0.532292\pi$
$500$	343.693	−	11175.1i	0.0307408	−	0.999527i
$501$	4865.79	−	2872.65i	0.433907	−	0.256169i
$502$	4790.88	−	17858.0i	0.425951	−	1.58773i
$503$		−	171.197i		−	0.0151755i	−0.999971	−	0.00758776i	$-0.997585\pi$
$503$		−	171.197i		−	0.0151755i	0.999971	−	0.00758776i	$-0.00241528\pi$
$504$	−2408.01	+	693.254i	−0.212820	+	0.0612698i
$505$	4826.73	+	1811.90i	0.425320	+	0.159660i
$506$	−3015.86	−	809.083i	−0.264963	−	0.0710833i
$507$	2917.02	+	4940.94i	0.255521	+	0.432810i
$508$	14192.5	+	8205.57i	1.23954	+	0.716660i
$509$	−872.727			−0.0759979			−0.0379989	−	0.999278i	$-0.512098\pi$
$509$	−872.727			−0.0759979			−0.0379989	+	0.999278i	$0.512098\pi$
$510$	730.109	−	8284.56i	0.0633917	−	0.719307i
$511$		−	4023.19i		−	0.348289i
$512$	8214.45	−	8169.49i	0.709045	−	0.705163i
$513$	10396.9	−	303.099i	0.894808	−	0.0260861i
$514$	−7566.53	−	2029.92i	−0.649310	−	0.174194i
$515$	−14274.5	−	5358.48i	−1.22138	−	0.458491i
$516$	3359.68	−	30.5905i	0.286631	−	0.00260983i
$517$	377.112			0.0320800
$518$	−3932.28	−	1054.94i	−0.333542	−	0.0894813i
$519$	1675.02	−	988.892i	0.141667	−	0.0836368i
$520$	−3451.01	−	7617.59i	−0.291032	−	0.642410i
$521$			783.069i			0.0658481i	0.999458	+	0.0329240i	$0.0104819\pi$
$521$			783.069i			0.0658481i	−0.999458	+	0.0329240i	$0.989518\pi$
$522$	5210.51	−	5413.72i	0.436893	−	0.453931i
$523$		−	10952.6i		−	0.915727i	−0.889023	−	0.457863i	$-0.848615\pi$
$523$		−	10952.6i		−	0.915727i	0.889023	−	0.457863i	$-0.151385\pi$
$524$	−6717.22	+	11618.2i	−0.560006	+	0.968593i
$525$	−489.804	+	2618.64i	−0.0407177	+	0.217689i
$526$	−1466.67	+	5467.03i	−0.121578	+	0.453182i
$527$			9749.40i			0.805864i
$528$	−1727.67	−	977.995i	−0.142400	−	0.0806094i
$529$	−22030.9			−1.81071
$530$	−3291.24	+	4598.34i	−0.269741	+	0.376867i
$531$	−11344.4	−	6259.03i	−0.927128	−	0.511523i
$532$	−2106.02	−	1217.63i	−0.171631	−	0.0992308i
$533$			9670.35i			0.785871i
$534$	−15752.6	+	4380.18i	−1.27656	+	0.354960i
$535$	−6560.64	−	2462.79i	−0.530170	−	0.199020i
$536$	4620.30	−	4611.85i	0.372325	−	0.371645i
$537$	−8441.00	+	4983.37i	−0.678317	+	0.400463i
$538$	6765.23	+	1814.95i	0.542137	+	0.145442i
$539$			1947.20i			0.155607i
$540$	−8242.34	−	9461.91i	−0.656841	−	0.754029i
$541$		−	8779.37i		−	0.697698i	−0.937179	−	0.348849i	$-0.886573\pi$
$541$		−	8779.37i		−	0.697698i	0.937179	−	0.348849i	$-0.113427\pi$
$542$	1184.60	−	4415.61i	0.0938801	−	0.349939i
$543$	4413.12	−	2605.40i	0.348775	−	0.205909i
$544$	−2357.82	−	8853.46i	−0.185828	−	0.697774i
$545$	1856.46	−	4945.44i	0.145912	−	0.388696i
$546$	533.837	+	1919.86i	0.0418427	+	0.150481i
$547$			4135.81i			0.323281i	0.986850	+	0.161640i	$0.0516784\pi$
$547$			4135.81i			0.323281i	−0.986850	+	0.161640i	$0.948322\pi$
$548$	−12741.8	−	7366.85i	−0.993253	−	0.574263i
$549$	15026.6	+	8290.59i	1.16816	+	0.644506i
$550$	−1753.26	+	1175.10i	−0.135926	+	0.0911025i
$551$	7294.54			0.563989
$552$	−21050.7	−	5442.43i	−1.62315	−	0.419647i
$553$		−	3298.65i		−	0.253658i
$554$	15707.1	+	4213.83i	1.20457	+	0.323156i
$555$	−3533.73	−	20079.6i	−0.270267	−	1.53573i
$556$	−11069.1	−	6399.75i	−0.844306	−	0.488147i
$557$		−	13645.6i		−	1.03803i	−0.854765	−	0.519015i	$-0.826299\pi$
$557$		−	13645.6i		−	1.03803i	0.854765	−	0.519015i	$-0.173701\pi$
$558$	10598.7	+	10200.9i	0.804084	+	0.773902i
$559$		−	2671.82i		−	0.202157i
$560$	477.041	+	2895.82i	0.0359976	+	0.218519i
$561$	−1351.99	+	798.186i	−0.101749	+	0.0600703i
$562$	−5683.43	+	21185.0i	−0.426586	+	1.59010i
$563$	10861.6			0.813076			0.406538	−	0.913634i	$-0.366736\pi$
$563$	10861.6			0.813076			0.406538	+	0.913634i	$0.366736\pi$
$564$	2625.83	−	23.9087i	0.196041	−	0.00178499i
$565$	5311.28	+	1993.79i	0.395482	+	0.148459i
$566$	3614.18	−	13471.9i	0.268401	−	1.00047i
$567$	1594.50	+	2529.42i	0.118100	+	0.187347i
$568$	16979.6	+	17010.7i	1.25431	+	1.25661i
$569$			4479.34i			0.330024i	0.986292	+	0.165012i	$0.0527663\pi$
$569$			4479.34i			0.330024i	−0.986292	+	0.165012i	$0.947234\pi$
$570$	1069.46	−	12135.2i	0.0785873	−	0.891732i
$571$	9122.59			0.668596			0.334298	−	0.942467i	$-0.391501\pi$
$571$	9122.59			0.668596			0.334298	+	0.942467i	$0.391501\pi$
$572$	−790.206	+	1366.75i	−0.0577626	+	0.0999069i
$573$	−9281.40	−	15721.1i	−0.676677	−	1.14618i
$574$	879.355	−	3277.80i	0.0639435	−	0.238350i
$575$	−15211.3	+	17405.7i	−1.10323	+	1.26238i
$576$	−12091.7	−	6700.23i	−0.874691	−	0.484681i
$577$		−	12703.2i		−	0.916533i	−0.888815	−	0.458267i	$-0.848471\pi$
$577$		−	12703.2i		−	0.916533i	0.888815	−	0.458267i	$-0.151529\pi$
$578$	6423.24	+	1723.20i	0.462234	+	0.124006i
$579$	13643.2	−	8054.64i	0.979262	−	0.578134i
$580$	−5584.58	−	6801.32i	−0.399806	−	0.486913i
$581$	1230.66			0.0878765
$582$	17244.8	−	4795.09i	1.22821	−	0.341517i
$583$	1067.52			0.0758359
$584$	15708.6	−	15679.9i	1.11306	−	1.11102i
$585$	−7583.75	+	6485.77i	−0.535982	+	0.458382i
$586$	−504.903	+	1882.03i	−0.0355927	+	0.132672i
$587$	584.550			0.0411021			0.0205511	−	0.999789i	$-0.493458\pi$
$587$	584.550			0.0411021			0.0205511	+	0.999789i	$0.493458\pi$
$588$	123.452	+	13558.4i	0.00865826	+	0.950914i
$589$			14280.9i			0.999038i
$590$	−8832.12	+	12339.7i	−0.616292	+	0.861049i
$591$	17420.5	−	10284.6i	1.21249	−	0.715827i
$592$	−11206.6	−	19465.1i	−0.778018	−	1.35137i
$593$	9207.43			0.637612			0.318806	−	0.947820i	$-0.396718\pi$
$593$	9207.43			0.637612			0.318806	+	0.947820i	$0.396718\pi$
$594$	−546.883	+	2304.92i	−0.0377759	+	0.159212i
$595$	2172.93	+	815.694i	0.149717	+	0.0562020i
$596$	−3695.11	−	2136.38i	−0.253955	−	0.146828i
$597$	−12923.5	+	7629.71i	−0.885966	+	0.523054i
$598$	−4480.21	+	16700.0i	−0.306371	+	1.14200i
$599$	14077.4			0.960246			0.480123	−	0.877201i	$-0.340592\pi$
$599$	14077.4			0.960246			0.480123	+	0.877201i	$0.340592\pi$
$600$	−12133.4	+	8293.36i	−0.825576	+	0.564291i
$601$	9056.37			0.614670			0.307335	−	0.951601i	$-0.400563\pi$
$601$	9056.37			0.614670			0.307335	+	0.951601i	$0.400563\pi$
$602$	−242.957	+	905.623i	−0.0164488	+	0.0613130i
$603$	−6820.41	−	3763.01i	−0.460611	−	0.254132i
$604$	12238.5	−	21168.0i	0.824469	−	1.42601i
$605$	−13558.7	−	5089.79i	−0.911142	−	0.342032i
$606$	−1815.59	−	6529.50i	−0.121705	−	0.437694i
$607$	−21455.8			−1.43470			−0.717350	−	0.696713i	$-0.754645\pi$
$607$	−21455.8			−1.43470			−0.717350	+	0.696713i	$0.754645\pi$
$608$	−3453.72	−	12968.5i	−0.230373	−	0.865037i
$609$	1066.06	+	1805.73i	0.0709344	+	0.120151i
$610$	11698.9	−	16345.0i	0.776513	−	1.08490i
$611$		−	2088.22i		−	0.138266i
$612$	−9363.32	+	5643.48i	−0.618447	+	0.372752i
$613$	9740.71			0.641800			0.320900	−	0.947113i	$-0.396015\pi$
$613$	9740.71			0.641800			0.320900	+	0.947113i	$0.396015\pi$
$614$	−4855.57	+	18099.1i	−0.319145	+	1.18961i
$615$	16737.5	−	2945.58i	1.09744	−	0.193134i
$616$	392.126	−	391.409i	0.0256481	−	0.0256012i
$617$	3739.84			0.244020			0.122010	−	0.992529i	$-0.461066\pi$
$617$	3739.84			0.244020			0.122010	+	0.992529i	$0.461066\pi$
$618$	5369.41	+	19310.2i	0.349498	+	1.25691i
$619$	−21751.2			−1.41237			−0.706183	−	0.708029i	$-0.749585\pi$
$619$	−21751.2			−1.41237			−0.706183	+	0.708029i	$0.749585\pi$
$620$	13315.3	−	10933.2i	0.862507	−	0.708207i
$621$	756.032	+	25933.5i	0.0488543	+	1.67581i
$622$	−14631.3	−	3925.24i	−0.943188	−	0.253035i
$623$		−	4562.98i		−	0.293438i
$624$	−5415.55	+	9566.78i	−0.347428	+	0.613746i
$625$	2092.94	+	15484.2i	0.133948	+	0.990988i
$626$	−42.2172	+	157.365i	−0.00269543	+	0.0100472i
$627$	−1980.40	+	1169.18i	−0.126139	+	0.0744698i
$628$	−9902.12	−	5725.05i	−0.629200	−	0.363781i
$629$	−17762.7			−1.12598
$630$	3160.31	−	1508.76i	0.199857	−	0.0954133i
$631$		−	5974.16i		−	0.376906i	−0.982082	−	0.188453i	$-0.939653\pi$
$631$		−	5974.16i		−	0.376906i	0.982082	−	0.188453i	$-0.0603472\pi$
$632$	12879.6	−	12856.0i	0.810637	−	0.809155i
$633$	4757.15	+	8057.82i	0.298704	+	0.505955i
$634$	−5721.11	+	21325.5i	−0.358382	+	1.33587i
$635$	−21449.5	−	8051.91i	−1.34047	−	0.503197i
$636$	7433.15	−	67.6803i	0.463434	−	0.00421965i
$637$	10782.4			0.670669
$638$	−430.474	+	1604.59i	−0.0267126	+	0.0995712i
$639$	13854.4	−	25110.9i	0.857702	−	1.55457i
$640$	−9447.54	+	13148.7i	−0.583511	+	0.812105i
$641$			7044.53i			0.434075i	0.976163	+	0.217038i	$0.0696394\pi$
$641$			7044.53i			0.434075i	−0.976163	+	0.217038i	$0.930361\pi$
$642$	2467.81	+	8875.10i	0.151708	+	0.545595i
$643$		−	2177.00i		−	0.133519i	−0.997769	−	0.0667595i	$-0.978734\pi$
$643$		−	2177.00i		−	0.133519i	0.997769	−	0.0667595i	$-0.0212660\pi$
$644$	3037.17	−	5253.13i	0.185840	−	0.321432i
$645$	−4624.42	+	813.834i	−0.282304	+	0.0496817i
$646$	−10251.0	−	2750.09i	−0.624333	−	0.167494i
$647$		−	15827.7i		−	0.961747i	−0.876790	−	0.480873i	$-0.840320\pi$
$647$		−	15827.7i		−	0.961747i	0.876790	−	0.480873i	$-0.159680\pi$
$648$	−3661.81	+	16083.8i	−0.221990	+	0.975049i
$649$	2864.72			0.173267
$650$	6506.99	+	9708.50i	0.392654	+	0.585844i
$651$	−3535.17	+	2087.08i	−0.212833	+	0.125652i
$652$	−2403.00	+	4156.26i	−0.144338	+	0.249650i
$653$		−	18484.0i		−	1.10771i	−0.832613	−	0.553856i	$-0.813156\pi$
$653$		−	18484.0i		−	1.10771i	0.832613	−	0.553856i	$-0.186844\pi$
$654$	−6690.09	+	1860.25i	−0.400005	+	0.111226i
$655$	6591.43	−	17559.0i	0.393204	−	1.04746i
$656$	16225.4	−	9341.34i	0.965691	−	0.555973i
$657$	−23188.8	−	12793.9i	−1.37699	−	0.759722i
$658$	−189.888	+	707.809i	−0.0112502	+	0.0419350i
$659$			11168.2i			0.660169i	0.943951	+	0.330084i	$0.107077\pi$
$659$			11168.2i			0.660169i	−0.943951	+	0.330084i	$0.892923\pi$
$660$	2606.29	+	951.387i	0.153711	+	0.0561101i
$661$		−	6525.85i		−	0.384003i	−0.981395	−	0.192002i	$-0.938502\pi$
$661$		−	6525.85i		−	0.384003i	0.981395	−	0.192002i	$-0.0614979\pi$
$662$	16987.7	+	4557.39i	0.997350	+	0.267565i
$663$	4419.87	+	7486.53i	0.258905	+	0.438541i
$664$	4796.32	+	4805.11i	0.280321	+	0.280835i
$665$	3182.90	+	1194.82i	0.185606	+	0.0696742i
$666$	−18585.2	+	19310.1i	−1.08133	+	1.12350i
$667$			18195.0i			1.05624i
$668$	−4354.35	+	7531.34i	−0.252208	+	0.436222i
$669$	−8968.28	−	15190.8i	−0.518287	−	0.877892i
$670$	−5309.99	+	7418.83i	−0.306183	+	0.427782i
$671$	−3794.55			−0.218312
$672$	2705.56	−	2750.24i	0.155311	−	0.157876i
$673$		−	10707.9i		−	0.613313i	−0.951820	−	0.306656i	$-0.900790\pi$
$673$		−	10707.9i		−	0.613313i	0.951820	−	0.306656i	$-0.0992103\pi$
$674$	6264.22	−	23349.9i	0.357995	−	1.33443i
$675$	13535.6	+	11150.5i	0.771833	+	0.635826i
$676$	−7647.65	−	4421.59i	−0.435119	−	0.251570i
$677$			5626.13i			0.319394i	0.987166	+	0.159697i	$0.0510517\pi$
$677$			5626.13i			0.319394i	−0.987166	+	0.159697i	$0.948948\pi$
$678$	−1997.86	−	7184.99i	−0.113167	−	0.406988i
$679$			4995.21i			0.282325i
$680$	5283.84	+	11663.3i	0.297980	+	0.657745i
$681$	4403.24	+	7458.35i	0.247772	+	0.419684i
$682$	−3141.39	−	842.759i	−0.176378	−	0.0473181i
$683$	8947.12			0.501247			0.250624	−	0.968085i	$-0.419364\pi$
$683$	8947.12			0.501247			0.250624	+	0.968085i	$0.419364\pi$
$684$	−13715.3	+	8266.54i	−0.766695	+	0.462104i
$685$	19257.1	+	7228.90i	1.07413	+	0.403215i
$686$	−7497.99	−	2011.53i	−0.417310	−	0.111954i
$687$	23619.2	−	13944.2i	1.31168	−	0.774388i
$688$	−4482.91	+	2580.92i	−0.248414	+	0.143018i
$689$		−	5911.30i		−	0.326854i
$690$	30269.2	+	2667.60i	1.67004	+	0.147179i
$691$	−2216.99			−0.122053			−0.0610263	−	0.998136i	$-0.519437\pi$
$691$	−2216.99			−0.122053			−0.0610263	+	0.998136i	$0.519437\pi$
$692$	−1498.96	+	2592.61i	−0.0823435	+	0.142423i
$693$	−578.851	−	319.368i	−0.0317298	−	0.0175062i
$694$	32368.2	+	8683.60i	1.77043	+	0.474964i
$695$	16729.1	+	6279.91i	0.913052	+	0.342749i
$696$	−2895.65	+	11200.1i	−0.157700	+	0.609967i
$697$		−	14806.3i		−	0.804631i
$698$	−2759.37	+	10285.6i	−0.149633	+	0.557757i
$699$	1240.49	+	2101.19i	0.0671242	+	0.113697i
$700$	−1322.74	−	3882.43i	−0.0714214	−	0.209632i
$701$	−34614.1			−1.86499			−0.932493	−	0.361188i	$-0.882371\pi$
$701$	−34614.1			−1.86499			−0.932493	+	0.361188i	$0.882371\pi$
$702$	12763.3	+	3028.31i	0.686208	+	0.162815i
$703$	−26018.7			−1.39589
$704$	3056.52	+	5.59236i	0.163632	+	0.000299389i
$705$	−3614.31	+	636.069i	−0.193082	+	0.0339798i
$706$	21092.9	+	5658.73i	1.12442	+	0.301656i
$707$	1891.37			0.100611
$708$	19947.0	−	181.621i	1.05883	−	0.00964089i
$709$			21114.8i			1.11845i	0.829015	+	0.559226i	$0.188902\pi$
$709$			21114.8i			1.11845i	−0.829015	+	0.559226i	$0.811098\pi$
$710$	−27314.1	−	19549.9i	−1.44377	−	1.03337i
$711$	−19012.7	−	10489.8i	−1.00286	−	0.553304i
$712$	17816.2	−	17783.6i	0.937766	−	0.936052i
$713$	−35621.3			−1.87101
$714$	−817.358	−	2939.50i	−0.0428416	−	0.154073i
$715$	775.409	−	2065.62i	0.0405576	−	0.108042i
$716$	7553.76	−	13065.1i	0.394270	−	0.681935i
$717$	−343.809	−	582.355i	−0.0179076	−	0.0303325i
$718$	3489.32	+	936.101i	0.181365	+	0.0486560i
$719$	−26234.0			−1.36073			−0.680363	−	0.732875i	$-0.738178\pi$
$719$	−26234.0			−1.36073			−0.680363	+	0.732875i	$0.738178\pi$
$720$	18207.9	+	6459.26i	0.942454	+	0.334337i
$721$	−5593.50			−0.288922
$722$	3722.02	+	998.528i	0.191855	+	0.0514700i
$723$	−14687.8	−	24878.7i	−0.755525	−	1.27973i
$724$	−3949.25	+	6830.68i	−0.202725	+	0.350636i
$725$	9260.72	+	8093.20i	0.474393	+	0.414585i
$726$	5100.18	+	18342.0i	0.260724	+	0.937651i
$727$	1445.23			0.0737287			0.0368643	−	0.999320i	$-0.488263\pi$
$727$	1445.23			0.0737287			0.0368643	+	0.999320i	$0.488263\pi$
$728$	−2167.39	−	2171.36i	−0.110342	−	0.110544i
$729$	19649.6	−	1146.65i	0.998302	−	0.0582560i
$730$	−18053.5	+	25223.3i	−0.915328	+	1.27885i
$731$			4090.83i			0.206983i
$732$	−26421.4	+	240.572i	−1.33410	+	0.0121473i
$733$	19855.7			1.00053			0.500265	−	0.865872i	$-0.333236\pi$
$733$	19855.7			1.00053			0.500265	+	0.865872i	$0.333236\pi$
$734$	−13316.3	−	3572.44i	−0.669636	−	0.179647i
$735$	−3284.32	−	18662.4i	−0.164822	−	0.936561i
$736$	32347.8	−	8614.74i	1.62005	−	0.431445i
$737$	1722.31			0.0860815
$738$	−16096.1	−	15491.9i	−0.802853	−	0.772717i
$739$	−6549.70			−0.326028			−0.163014	−	0.986624i	$-0.552122\pi$
$739$	−6549.70			−0.326028			−0.163014	+	0.986624i	$0.552122\pi$
$740$	19919.5	+	24259.4i	0.989534	+	1.20513i
$741$	6474.21	+	10966.2i	0.320966	+	0.543664i
$742$	−537.533	+	2003.66i	−0.0265950	+	0.0991328i
$743$		−	22234.5i		−	1.09785i	−0.835870	−	0.548927i	$-0.815037\pi$
$743$		−	22234.5i		−	1.09785i	0.835870	−	0.548927i	$-0.184963\pi$
$744$	−21926.9	−	5668.96i	−1.08048	−	0.279347i
$745$	5584.54	+	2096.37i	0.274633	+	0.103094i
$746$	27234.6	+	7306.39i	1.33663	+	0.358587i
$747$	3913.53	−	7093.23i	0.191685	−	0.347427i
$748$	1209.89	−	2092.63i	0.0591414	−	0.102292i
$749$	−2570.80			−0.125414
$750$	14821.6	−	14219.6i	0.721609	−	0.692301i
$751$		−	9278.78i		−	0.450849i	−0.974261	−	0.225424i	$-0.927623\pi$
$751$		−	9278.78i		−	0.450849i	0.974261	−	0.225424i	$-0.0723769\pi$
$752$	−3503.71	+	2017.17i	−0.169903	+	0.0978174i
$753$	29250.2	−	17268.7i	1.41559	−	0.835730i
$754$	8885.27	+	2383.70i	0.429154	+	0.115132i
$755$	−12009.4	+	31991.8i	−0.578895	+	1.54212i
$756$	−4050.78	−	2187.06i	−0.194875	−	0.105215i
$757$	990.407			0.0475521			0.0237761	−	0.999717i	$-0.492431\pi$
$757$	990.407			0.0475521			0.0237761	+	0.999717i	$0.492431\pi$
$758$	10683.4	+	2866.11i	0.511926	+	0.137337i
$759$	−2916.33	−	4939.77i	−0.139468	−	0.236235i
$760$	7739.75	+	17084.3i	0.369408	+	0.815413i
$761$			10150.9i			0.483533i	0.970334	+	0.241766i	$0.0777268\pi$
$761$			10150.9i			0.483533i	−0.970334	+	0.241766i	$0.922273\pi$
$762$	8068.34	+	29016.5i	0.383576	+	1.37947i
$763$		−	1937.88i		−	0.0919477i
$764$	24333.4	+	14068.7i	1.15229	+	0.666213i
$765$	11611.5	−	9930.36i	0.548777	−	0.469324i
$766$	−1686.75	+	6287.38i	−0.0795625	+	0.296569i
$767$		−	15863.1i		−	0.746784i
$768$	21282.9	−	154.842i	0.999974	−	0.00727524i
$769$	10878.0			0.510103			0.255051	−	0.966927i	$-0.417908\pi$
$769$	10878.0			0.510103			0.255051	+	0.966927i	$0.417908\pi$
$770$	−450.661	+	629.638i	−0.0210918	+	0.0294683i

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.73183 - 0.732884i) q^{2} +(-2.64167 - 4.47455i) q^{3} +(6.92576 + 4.00422i) q^{4} +(-10.4671 - 3.92924i) q^{5} +(3.93726 + 14.1597i) q^{6} -4.10158 q^{7} +(-15.9854 - 16.0146i) q^{8} +(-13.0432 + 23.6406i) q^{9} +O(q^{10})\)	\(q+(-2.73183 - 0.732884i) q^{2} +(-2.64167 - 4.47455i) q^{3} +(6.92576 + 4.00422i) q^{4} +(-10.4671 - 3.92924i) q^{5} +(3.93726 + 14.1597i) q^{6} -4.10158 q^{7} +(-15.9854 - 16.0146i) q^{8} +(-13.0432 + 23.6406i) q^{9} +(25.7147 + 18.4052i) q^{10} -5.96978i q^{11} +(-0.378480 - 41.5675i) q^{12} -33.0570 q^{13} +(11.2048 + 3.00598i) q^{14} +(10.0691 + 57.2155i) q^{15} +(31.9324 + 55.4646i) q^{16} +50.6136 q^{17} +(52.9575 - 55.0228i) q^{18} +74.1386 q^{19} +(-56.7594 - 69.1258i) q^{20} +(10.8350 + 18.3527i) q^{21} +(-4.37515 + 16.3084i) q^{22} +184.927i q^{23} +(-29.4302 + 113.833i) q^{24} +(94.1221 + 82.2559i) q^{25} +(90.3061 + 24.2270i) q^{26} +(140.237 - 4.08828i) q^{27} +(-28.4065 - 16.4236i) q^{28} +98.3905 q^{29} +(14.4252 - 163.682i) q^{30} +192.624i q^{31} +(-46.5846 - 174.922i) q^{32} +(-26.7121 + 15.7702i) q^{33} +(-138.268 - 37.0939i) q^{34} +(42.9318 + 16.1161i) q^{35} +(-184.996 + 111.501i) q^{36} -350.946 q^{37} +(-202.534 - 54.3350i) q^{38} +(87.3258 + 147.915i) q^{39} +(104.396 + 230.438i) q^{40} -292.535i q^{41} +(-16.1490 - 58.0772i) q^{42} +80.8246i q^{43} +(23.9043 - 41.3453i) q^{44} +(229.414 - 196.199i) q^{45} +(135.530 - 505.188i) q^{46} +63.1702i q^{47} +(163.824 - 289.402i) q^{48} -326.177 q^{49} +(-196.841 - 293.689i) q^{50} +(-133.705 - 226.473i) q^{51} +(-228.945 - 132.368i) q^{52} +178.821i q^{53} +(-386.098 - 91.6086i) q^{54} +(-23.4567 + 62.4865i) q^{55} +(65.5652 + 65.6852i) q^{56} +(-195.850 - 331.737i) q^{57} +(-268.786 - 72.1088i) q^{58} +479.870i q^{59} +(-159.367 + 436.580i) q^{60} -635.627i q^{61} +(141.171 - 526.215i) q^{62} +(53.4975 - 96.9635i) q^{63} +(-0.936778 + 511.999i) q^{64} +(346.013 + 129.889i) q^{65} +(84.5304 - 23.5046i) q^{66} +288.505i q^{67} +(350.538 + 202.668i) q^{68} +(827.464 - 488.515i) q^{69} +(-105.471 - 75.4904i) q^{70} -1062.20 q^{71} +(587.094 - 169.021i) q^{72} +980.889i q^{73} +(958.725 + 257.203i) q^{74} +(119.418 - 638.447i) q^{75} +(513.467 + 296.868i) q^{76} +24.4855i q^{77} +(-130.154 - 468.079i) q^{78} +804.239i q^{79} +(-116.307 - 706.026i) q^{80} +(-388.752 - 616.695i) q^{81} +(-214.394 + 799.156i) q^{82} -300.045 q^{83} +(1.55237 + 170.492i) q^{84} +(-529.780 - 198.873i) q^{85} +(59.2350 - 220.799i) q^{86} +(-259.915 - 440.253i) q^{87} +(-95.6038 + 95.4290i) q^{88} +1112.49i q^{89} +(-770.511 + 367.849i) q^{90} +135.586 q^{91} +(-740.488 + 1280.76i) q^{92} +(861.905 - 508.849i) q^{93} +(46.2964 - 172.570i) q^{94} +(-776.020 - 291.309i) q^{95} +(-659.638 + 670.532i) q^{96} -1217.88i q^{97} +(891.059 + 239.050i) q^{98} +(141.129 + 77.8648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) \) 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) \) 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9 - 72 * q^10 - 128 * q^16 + 672 * q^19 - 416 * q^24 + 496 * q^25 - 248 * q^30 + 240 * q^34 - 608 * q^36 - 1344 * q^40 + 336 * q^46 + 3520 * q^49 - 544 * q^51 - 952 * q^54 - 2064 * q^60 + 2176 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 + 2304 * q^76 - 2304 * q^81 - 736 * q^84 - 1432 * q^90 - 2752 * q^91 + 4496 * q^94 + 640 * q^96 + 256 * q^99

Introduction

L-functions

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