LMFDB - Embedded newform 108.4.h.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.553553856144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 96x^{4} + 704x^{2} + 4096 $ x^8 + 11x^6 + 96x^4 + 704*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.1
Root			$2.14417 + 1.84460i$ of defining polynomial
Character	$\chi$	$=$	108.71
Dual form			108.4.h.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66955 - 0.934608i) q^{2} +(6.25302 + 4.98997i) q^{4} +(-4.30507 - 2.48553i) q^{5} +(3.07102 - 1.77306i) q^{7} +(-12.0291 - 19.1651i) q^{8} +O(q^{10})$	\(q+(-2.66955 - 0.934608i) q^{2} +(6.25302 + 4.98997i) q^{4} +(-4.30507 - 2.48553i) q^{5} +(3.07102 - 1.77306i) q^{7} +(-12.0291 - 19.1651i) q^{8} +(9.16960 + 10.6588i) q^{10} +(22.1867 + 38.4285i) q^{11} +(30.6949 - 53.1652i) q^{13} +(-9.85537 + 1.86306i) q^{14} +(14.2004 + 62.4047i) q^{16} -99.9210i q^{17} -85.6058i q^{19} +(-14.5169 - 37.0242i) q^{20} +(-23.3130 - 123.323i) q^{22} +(41.3024 - 71.5379i) q^{23} +(-50.1443 - 86.8524i) q^{25} +(-131.630 + 113.239i) q^{26} +(28.0507 + 4.23737i) q^{28} +(152.983 - 88.3250i) q^{29} +(171.407 + 98.9620i) q^{31} +(20.4153 - 179.864i) q^{32} +(-93.3870 + 266.744i) q^{34} -17.6280 q^{35} -172.780 q^{37} +(-80.0079 + 228.529i) q^{38} +(4.15053 + 112.406i) q^{40} +(-38.2467 - 22.0817i) q^{41} +(67.7220 - 39.0993i) q^{43} +(-53.0233 + 351.005i) q^{44} +(-177.119 + 152.373i) q^{46} +(229.919 + 398.231i) q^{47} +(-165.213 + 286.157i) q^{49} +(52.6897 + 278.722i) q^{50} +(457.229 - 179.276i) q^{52} +290.321i q^{53} -220.583i q^{55} +(-70.9224 - 37.5283i) q^{56} +(-490.947 + 92.8087i) q^{58} +(147.857 - 256.096i) q^{59} +(-247.340 - 428.406i) q^{61} +(-365.090 - 424.383i) q^{62} +(-222.602 + 461.077i) q^{64} +(-264.287 + 152.586i) q^{65} +(-19.4994 - 11.2580i) q^{67} +(498.603 - 624.808i) q^{68} +(47.0587 + 16.4752i) q^{70} -304.326 q^{71} +1163.14 q^{73} +(461.244 + 161.481i) q^{74} +(427.171 - 535.295i) q^{76} +(136.272 + 78.6767i) q^{77} +(-964.094 + 556.620i) q^{79} +(93.9752 - 303.952i) q^{80} +(81.4637 + 94.6940i) q^{82} +(-400.836 - 694.268i) q^{83} +(-248.357 + 430.167i) q^{85} +(-217.330 + 41.0841i) q^{86} +(469.601 - 887.471i) q^{88} -346.372i q^{89} -217.695i q^{91} +(615.237 - 241.230i) q^{92} +(-241.590 - 1277.98i) q^{94} +(-212.776 + 368.539i) q^{95} +(291.434 + 504.778i) q^{97} +(708.488 - 609.501i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 11 q^{4} - 66 q^{5}+O(q^{10}) $ 8 * q + 3 * q^2 + 11 * q^4 - 66 * q^5	$ 8 q + 3 q^{2} + 11 q^{4} - 66 q^{5} - 116 q^{10} + 214 q^{13} + 42 q^{14} + 71 q^{16} - 306 q^{20} + 207 q^{22} - 54 q^{25} + 540 q^{28} + 498 q^{29} - 327 q^{32} + 469 q^{34} - 1256 q^{37} - 1035 q^{38} - 602 q^{40} + 1272 q^{41} - 912 q^{46} - 154 q^{49} + 1329 q^{50} - 464 q^{52} + 1314 q^{56} - 830 q^{58} + 262 q^{61} - 550 q^{64} - 3282 q^{65} + 843 q^{68} - 480 q^{70} + 3940 q^{73} - 222 q^{74} + 105 q^{76} - 330 q^{77} + 4786 q^{82} - 472 q^{85} - 1209 q^{86} - 1425 q^{88} + 1308 q^{92} + 1356 q^{94} - 572 q^{97}+O(q^{100}) $ 8 * q + 3 * q^2 + 11 * q^4 - 66 * q^5 - 116 * q^10 + 214 * q^13 + 42 * q^14 + 71 * q^16 - 306 * q^20 + 207 * q^22 - 54 * q^25 + 540 * q^28 + 498 * q^29 - 327 * q^32 + 469 * q^34 - 1256 * q^37 - 1035 * q^38 - 602 * q^40 + 1272 * q^41 - 912 * q^46 - 154 * q^49 + 1329 * q^50 - 464 * q^52 + 1314 * q^56 - 830 * q^58 + 262 * q^61 - 550 * q^64 - 3282 * q^65 + 843 * q^68 - 480 * q^70 + 3940 * q^73 - 222 * q^74 + 105 * q^76 - 330 * q^77 + 4786 * q^82 - 472 * q^85 - 1209 * q^86 - 1425 * q^88 + 1308 * q^92 + 1356 * q^94 - 572 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−2.66955	−	0.934608i	−0.943829	−	0.330434i
$2$	−2.66955	−	0.934608i	−0.943829	−	0.330434i
$3$		0			0
$3$		0			0
$4$	6.25302	+	4.98997i	0.781627	+	0.623746i
$5$	−4.30507	−	2.48553i	−0.385057	−	0.222313i	0.294959	−	0.955510i	$-0.404694\pi$
$5$	−4.30507	−	2.48553i	−0.385057	−	0.222313i	−0.680016	+	0.733197i	$0.738027\pi$
$6$		0			0
$7$	3.07102	−	1.77306i	0.165820	−	0.0957361i	−0.414794	−	0.909916i	$-0.636146\pi$
$7$	3.07102	−	1.77306i	0.165820	−	0.0957361i	0.580613	+	0.814179i	$0.302813\pi$
$8$	−12.0291	−	19.1651i	−0.531615	−	0.846986i
$9$		0			0
$10$	9.16960	+	10.6588i	0.289968	+	0.337061i
$11$	22.1867	+	38.4285i	0.608141	+	1.05333i	0.991547	+	0.129751i	$0.0414178\pi$
$11$	22.1867	+	38.4285i	0.608141	+	1.05333i	−0.383406	+	0.923580i	$0.625249\pi$
$12$		0			0
$13$	30.6949	−	53.1652i	0.654865	−	1.13426i	−0.327063	−	0.945003i	$-0.606059\pi$
$13$	30.6949	−	53.1652i	0.654865	−	1.13426i	0.981928	−	0.189257i	$-0.0606078\pi$
$14$	−9.85537	+	1.86306i	−0.188140	+	0.0355660i
$15$		0			0
$16$	14.2004	+	62.4047i	0.221881	+	0.975074i
$17$		−	99.9210i		−	1.42555i	−0.701391	−	0.712777i	$-0.747437\pi$
$17$		−	99.9210i		−	1.42555i	0.701391	−	0.712777i	$-0.252563\pi$
$18$		0			0
$19$		−	85.6058i		−	1.03365i	−0.856091	−	0.516824i	$-0.827114\pi$
$19$		−	85.6058i		−	1.03365i	0.856091	−	0.516824i	$-0.172886\pi$
$20$	−14.5169	−	37.0242i	−0.162304	−	0.413943i
$21$		0			0
$22$	−23.3130	−	123.323i	−0.225925	−	1.19512i
$23$	41.3024	−	71.5379i	0.374441	−	0.648552i	−0.615802	−	0.787901i	$-0.711168\pi$
$23$	41.3024	−	71.5379i	0.374441	−	0.648552i	0.990243	+	0.139349i	$0.0445011\pi$
$24$		0			0
$25$	−50.1443	−	86.8524i	−0.401154	−	0.694819i
$26$	−131.630	+	113.239i	−0.992878	+	0.854157i
$27$		0			0
$28$	28.0507	+	4.23737i	0.189324	+	0.0285996i
$29$	152.983	−	88.3250i	0.979597	−	0.565571i	0.0774487	−	0.996996i	$-0.475323\pi$
$29$	152.983	−	88.3250i	0.979597	−	0.565571i	0.902148	+	0.431426i	$0.141989\pi$
$30$		0			0
$31$	171.407	+	98.9620i	0.993086	+	0.573358i	0.906195	−	0.422860i	$-0.138974\pi$
$31$	171.407	+	98.9620i	0.993086	+	0.573358i	0.0868904	+	0.996218i	$0.472307\pi$
$32$	20.4153	−	179.864i	0.112780	−	0.993620i
$33$		0			0
$34$	−93.3870	+	266.744i	−0.471051	+	1.34548i
$35$	−17.6280			−0.0851334
$36$		0			0
$37$	−172.780			−0.767698			−0.383849	−	0.923396i	$-0.625402\pi$
$37$	−172.780			−0.767698			−0.383849	+	0.923396i	$0.625402\pi$
$38$	−80.0079	+	228.529i	−0.341553	+	0.975588i
$39$		0			0
$40$	4.15053	+	112.406i	0.0164064	+	0.444323i
$41$	−38.2467	−	22.0817i	−0.145686	−	0.0841119i	0.425385	−	0.905012i	$-0.360139\pi$
$41$	−38.2467	−	22.0817i	−0.145686	−	0.0841119i	−0.571071	+	0.820901i	$0.693472\pi$
$42$		0			0
$43$	67.7220	−	39.0993i	0.240175	−	0.138665i	−0.375082	−	0.926992i	$-0.622386\pi$
$43$	67.7220	−	39.0993i	0.240175	−	0.138665i	0.615257	+	0.788327i	$0.289052\pi$
$44$	−53.0233	+	351.005i	−0.181672	+	1.20264i
$45$		0			0
$46$	−177.119	+	152.373i	−0.567712	+	0.488394i
$47$	229.919	+	398.231i	0.713555	+	1.23591i	0.963514	+	0.267657i	$0.0862493\pi$
$47$	229.919	+	398.231i	0.713555	+	1.23591i	−0.249960	+	0.968256i	$0.580417\pi$
$48$		0			0
$49$	−165.213	+	286.157i	−0.481669	+	0.834276i
$50$	52.6897	+	278.722i	0.149029	+	0.788346i
$51$		0			0
$52$	457.229	−	179.276i	1.21935	−	0.478098i
$53$			290.321i			0.752427i	0.926533	+	0.376213i	$0.122774\pi$
$53$			290.321i			0.752427i	−0.926533	+	0.376213i	$0.877226\pi$
$54$		0			0
$55$		−	220.583i		−	0.540790i
$56$	−70.9224	−	37.5283i	−0.169239	−	0.0895522i
$57$		0			0
$58$	−490.947	+	92.8087i	−1.11146	+	0.210110i
$59$	147.857	−	256.096i	0.326260	−	0.565098i	−0.655507	−	0.755189i	$-0.727545\pi$
$59$	147.857	−	256.096i	0.326260	−	0.565098i	0.981766	+	0.190091i	$0.0608783\pi$
$60$		0			0
$61$	−247.340	−	428.406i	−0.519159	−	0.899209i	−0.999752	−	0.0222656i	$-0.992912\pi$
$61$	−247.340	−	428.406i	−0.519159	−	0.899209i	0.480593	−	0.876944i	$-0.340421\pi$
$62$	−365.090	−	424.383i	−0.747846	−	0.869301i
$63$		0			0
$64$	−222.602	+	461.077i	−0.434770	+	0.900541i
$65$	−264.287	+	152.586i	−0.504320	+	0.291170i
$66$		0			0
$67$	−19.4994	−	11.2580i	−0.0355557	−	0.0205281i	0.482117	−	0.876107i	$-0.339868\pi$
$67$	−19.4994	−	11.2580i	−0.0355557	−	0.0205281i	−0.517672	+	0.855579i	$0.673201\pi$
$68$	498.603	−	624.808i	0.889184	−	1.11425i
$69$		0			0
$70$	47.0587	+	16.4752i	0.0803514	+	0.0281310i
$71$	−304.326			−0.508688			−0.254344	−	0.967114i	$-0.581859\pi$
$71$	−304.326			−0.508688			−0.254344	+	0.967114i	$0.581859\pi$
$72$		0			0
$73$	1163.14			1.86486			0.932432	−	0.361345i	$-0.117682\pi$
$73$	1163.14			1.86486			0.932432	+	0.361345i	$0.117682\pi$
$74$	461.244	+	161.481i	0.724575	+	0.253673i
$75$		0			0
$76$	427.171	−	535.295i	0.644735	−	0.807928i
$77$	136.272	+	78.6767i	0.201684	+	0.116442i
$78$		0			0
$79$	−964.094	+	556.620i	−1.37303	+	0.792717i	−0.991308	−	0.131562i	$-0.958001\pi$
$79$	−964.094	+	556.620i	−1.37303	+	0.792717i	−0.381718	+	0.924279i	$0.624667\pi$
$80$	93.9752	−	303.952i	0.131334	−	0.424786i
$81$		0			0
$82$	81.4637	+	94.6940i	0.109709	+	0.127527i
$83$	−400.836	−	694.268i	−0.530090	−	0.918142i	−0.999384	−	0.0351004i	$-0.988825\pi$
$83$	−400.836	−	694.268i	−0.530090	−	0.918142i	0.469294	−	0.883042i	$-0.344508\pi$
$84$		0			0
$85$	−248.357	+	430.167i	−0.316919	+	0.548919i
$86$	−217.330	+	41.0841i	−0.272504	+	0.0515142i
$87$		0			0
$88$	469.601	−	887.471i	0.568860	−	1.07505i
$89$		−	346.372i		−	0.412532i	−0.978496	−	0.206266i	$-0.933869\pi$
$89$		−	346.372i		−	0.412532i	0.978496	−	0.206266i	$-0.0661312\pi$
$90$		0			0
$91$		−	217.695i		−	0.250777i
$92$	615.237	−	241.230i	0.697205	−	0.273369i
$93$		0			0
$94$	−241.590	−	1277.98i	−0.265086	−	1.40227i
$95$	−212.776	+	368.539i	−0.229793	+	0.398014i
$96$		0			0
$97$	291.434	+	504.778i	0.305058	+	0.528376i	0.977274	−	0.211979i	$-0.0679908\pi$
$97$	291.434	+	504.778i	0.305058	+	0.528376i	−0.672216	+	0.740355i	$0.734657\pi$
$98$	708.488	−	609.501i	0.730286	−	0.628254i
$99$		0			0
$100$	119.838	−	793.308i	0.119838	−	0.793308i
$101$	−61.5958	+	35.5623i	−0.0606832	+	0.0350355i	−0.530035	−	0.847976i	$-0.677821\pi$
$101$	−61.5958	+	35.5623i	−0.0606832	+	0.0350355i	0.469351	+	0.883011i	$0.344488\pi$
$102$		0			0
$103$	652.974	+	376.995i	0.624655	+	0.360645i	0.778679	−	0.627422i	$-0.215890\pi$
$103$	652.974	+	376.995i	0.624655	+	0.360645i	−0.154024	+	0.988067i	$0.549223\pi$
$104$	−1388.15	+	51.2567i	−1.30884	+	0.0483282i
$105$		0			0
$106$	271.336	−	775.026i	0.248627	−	0.710162i
$107$	−883.464			−0.798203			−0.399102	−	0.916907i	$-0.630678\pi$
$107$	−883.464			−0.798203			−0.399102	+	0.916907i	$0.630678\pi$
$108$		0			0
$109$	627.057			0.551020			0.275510	−	0.961298i	$-0.411153\pi$
$109$	627.057			0.551020			0.275510	+	0.961298i	$0.411153\pi$
$110$	−206.159	+	588.858i	−0.178695	+	0.510413i
$111$		0			0
$112$	154.257	+	166.468i	0.130142	+	0.140444i
$113$	−590.118	−	340.705i	−0.491271	−	0.283635i	0.233831	−	0.972277i	$-0.424874\pi$
$113$	−590.118	−	340.705i	−0.491271	−	0.283635i	−0.725102	+	0.688642i	$0.758207\pi$
$114$		0			0
$115$	−355.619	+	205.317i	−0.288363	+	0.166486i
$116$	1397.35	+	211.085i	1.11845	+	0.168955i
$117$		0			0
$118$	−634.061	+	545.472i	−0.494661	+	0.425549i
$119$	−177.166	−	306.860i	−0.136477	−	0.236385i
$120$		0			0
$121$	−319.002	+	552.528i	−0.239671	+	0.415122i
$122$	259.896	+	1374.82i	0.192868	+	1.02025i
$123$		0			0
$124$	577.995	+	1474.13i	0.418592	+	1.06759i
$125$			1119.92i			0.801352i
$126$		0			0
$127$			48.2222i			0.0336931i	0.999858	+	0.0168466i	$0.00536268\pi$
$127$			48.2222i			0.0336931i	−0.999858	+	0.0168466i	$0.994637\pi$
$128$	1025.18	−	1022.82i	0.707918	−	0.706294i
$129$		0			0
$130$	848.138	−	160.332i	0.572205	−	0.108170i
$131$	−198.379	+	343.603i	−0.132309	+	0.229166i	−0.924566	−	0.381021i	$-0.875572\pi$
$131$	−198.379	+	343.603i	−0.132309	+	0.229166i	0.792257	+	0.610187i	$0.208906\pi$
$132$		0			0
$133$	−151.784	−	262.898i	−0.0989575	−	0.171399i
$134$	41.5328	+	48.2780i	0.0267753	+	0.0311238i
$135$		0			0
$136$	−1915.00	+	1201.96i	−1.20742	+	0.757846i
$137$	−568.672	+	328.323i	−0.354634	+	0.204748i	−0.666725	−	0.745304i	$-0.732304\pi$
$137$	−568.672	+	328.323i	−0.354634	+	0.204748i	0.312090	+	0.950052i	$0.398971\pi$
$138$		0			0
$139$	502.618	+	290.187i	0.306702	+	0.177074i	0.645450	−	0.763803i	$-0.276670\pi$
$139$	502.618	+	290.187i	0.306702	+	0.177074i	−0.338748	+	0.940877i	$0.610003\pi$
$140$	−110.228	−	87.9630i	−0.0665425	−	0.0531016i
$141$		0			0
$142$	812.414	+	284.425i	0.480114	+	0.168088i
$143$	2724.08			1.59300
$144$		0			0
$145$	−878.139			−0.502934
$146$	−3105.06	−	1087.08i	−1.76011	−	0.616214i
$147$		0			0
$148$	−1080.39	−	862.166i	−0.600053	−	0.478849i
$149$	1342.80	+	775.266i	0.738299	+	0.426257i	0.821450	−	0.570280i	$-0.193165\pi$
$149$	1342.80	+	775.266i	0.738299	+	0.426257i	−0.0831517	+	0.996537i	$0.526499\pi$
$150$		0			0
$151$	−1418.31	+	818.861i	−0.764373	+	0.441311i	−0.830864	−	0.556476i	$-0.812153\pi$
$151$	−1418.31	+	818.861i	−0.764373	+	0.441311i	0.0664908	+	0.997787i	$0.478820\pi$
$152$	−1640.64	+	1029.76i	−0.875486	+	0.549504i
$153$		0			0
$154$	−290.253	−	337.392i	−0.151878	−	0.176545i
$155$	−491.946	−	852.076i	−0.254930	−	0.441551i
$156$		0			0
$157$	233.169	−	403.860i	0.118528	−	0.205296i	−0.800657	−	0.599124i	$-0.795516\pi$
$157$	233.169	−	403.860i	0.118528	−	0.205296i	0.919184	+	0.393827i	$0.128849\pi$
$158$	3093.92	−	584.876i	1.55784	−	0.294495i
$159$		0			0
$160$	−534.948	+	723.586i	−0.264321	+	0.357528i
$161$		−	292.926i		−	0.143390i
$162$		0			0
$163$		−	3587.04i		−	1.72367i	−0.507185	−	0.861837i	$-0.669314\pi$
$163$		−	3587.04i		−	1.72367i	0.507185	−	0.861837i	$-0.330686\pi$
$164$	−128.970	−	328.927i	−0.0614076	−	0.156615i
$165$		0			0
$166$	421.183	+	2228.01i	0.196929	+	1.04173i
$167$	−682.164	+	1181.54i	−0.316092	+	0.547488i	−0.979669	−	0.200620i	$-0.935704\pi$
$167$	−682.164	+	1181.54i	−0.316092	+	0.547488i	0.663577	+	0.748108i	$0.269038\pi$
$168$		0			0
$169$	−785.858	−	1361.15i	−0.357696	−	0.619547i
$170$	1065.04	−	916.236i	0.480498	−	0.413365i
$171$		0			0
$172$	618.571	+	93.4422i	0.274219	+	0.0414239i
$173$	156.849	−	90.5569i	0.0689307	−	0.0397972i	−0.465139	−	0.885238i	$-0.653995\pi$
$173$	156.849	−	90.5569i	0.0689307	−	0.0397972i	0.534069	+	0.845441i	$0.320662\pi$
$174$		0			0
$175$	−307.989	−	177.817i	−0.133039	−	0.0768098i
$176$	−2083.06	+	1930.26i	−0.892140	+	0.826697i
$177$		0			0
$178$	−323.722	+	924.658i	−0.136315	+	0.389360i
$179$	1430.26			0.597220			0.298610	−	0.954375i	$-0.403477\pi$
$179$	1430.26			0.597220			0.298610	+	0.954375i	$0.403477\pi$
$180$		0			0
$181$	−2022.85			−0.830705			−0.415352	−	0.909661i	$-0.636342\pi$
$181$	−2022.85			−0.830705			−0.415352	+	0.909661i	$0.636342\pi$
$182$	−203.460	+	581.149i	−0.0828651	+	0.236690i
$183$		0			0
$184$	−1867.86	+	68.9700i	−0.748373	+	0.0276333i
$185$	743.828	+	429.449i	0.295607	+	0.170669i
$186$		0			0
$187$	3839.82	−	2216.92i	1.50158	−	0.866937i
$188$	−549.475	+	3637.43i	−0.213163	+	1.41110i
$189$		0			0
$190$	912.456	−	784.971i	0.348403	−	0.299725i
$191$	1356.81	+	2350.07i	0.514008	+	0.890288i	0.999868	+	0.0162510i	$0.00517309\pi$
$191$	1356.81	+	2350.07i	0.514008	+	0.890288i	−0.485860	+	0.874037i	$0.661494\pi$
$192$		0			0
$193$	357.929	−	619.952i	0.133494	−	0.231218i	−0.791527	−	0.611134i	$-0.790714\pi$
$193$	357.929	−	619.952i	0.133494	−	0.231218i	0.925021	+	0.379916i	$0.124047\pi$
$194$	−306.228	−	1619.91i	−0.113329	−	0.599498i
$195$		0			0
$196$	−2460.99	+	964.935i	−0.896862	+	0.351653i
$197$		−	4060.25i		−	1.46843i	−0.678917	−	0.734215i	$-0.737550\pi$
$197$		−	4060.25i		−	1.46843i	0.678917	−	0.734215i	$-0.262450\pi$
$198$		0			0
$199$			5080.79i			1.80989i	0.425532	+	0.904944i	$0.360087\pi$
$199$			5080.79i			1.80989i	−0.425532	+	0.904944i	$0.639913\pi$
$200$	−1061.35	+	2005.77i	−0.375243	+	0.709149i
$201$		0			0
$202$	197.670	−	37.3676i	0.0688515	−	0.0130157i
$203$	313.211	−	542.497i	0.108291	−	0.187566i
$204$		0			0
$205$	109.770	+	190.127i	0.0373983	+	0.0647757i
$206$	−1390.81	−	1616.68i	−0.470398	−	0.546794i
$207$		0			0
$208$	3753.64	+	1160.54i	1.25129	+	0.386871i
$209$	3289.71	−	1899.31i	1.08877	−	0.628604i
$210$		0			0
$211$	1879.85	+	1085.33i	0.613337	+	0.354110i	0.774270	−	0.632855i	$-0.218117\pi$
$211$	1879.85	+	1085.33i	0.613337	+	0.354110i	−0.160933	+	0.986965i	$0.551450\pi$
$212$	−1448.69	+	1815.38i	−0.469323	+	0.588117i
$213$		0			0
$214$	2358.45	+	825.693i	0.753367	+	0.263753i
$215$	−388.731			−0.123308
$216$		0			0
$217$	701.861			0.219564
$218$	−1673.96	−	586.053i	−0.520069	−	0.182076i
$219$		0			0
$220$	1100.70	−	1379.31i	0.337316	−	0.422696i
$221$	−5312.32	−	3067.07i	−1.61695	−	0.933545i
$222$		0			0
$223$	1500.22	−	866.150i	0.450502	−	0.260097i	−0.257540	−	0.966268i	$-0.582912\pi$
$223$	1500.22	−	866.150i	0.450502	−	0.260097i	0.708042	+	0.706170i	$0.249579\pi$
$224$	−256.214	−	588.566i	−0.0764242	−	0.175559i
$225$		0			0
$226$	1256.92	+	1461.06i	0.369953	+	0.430036i
$227$	−1643.44	−	2846.52i	−0.480523	−	0.832290i	0.519227	−	0.854636i	$-0.326220\pi$
$227$	−1643.44	−	2846.52i	−0.480523	−	0.832290i	−0.999750	+	0.0223459i	$0.992887\pi$
$228$		0			0
$229$	688.303	−	1192.18i	0.198622	−	0.344023i	−0.749460	−	0.662049i	$-0.769687\pi$
$229$	688.303	−	1192.18i	0.198622	−	0.344023i	0.948082	+	0.318027i	$0.103020\pi$
$230$	1141.24	−	215.740i	0.327178	−	0.0618498i
$231$		0			0
$232$	−3533.01	−	1869.47i	−0.999799	−	0.529039i
$233$			646.104i			0.181664i	0.995866	+	0.0908320i	$0.0289526\pi$
$233$			646.104i			0.181664i	−0.995866	+	0.0908320i	$0.971047\pi$
$234$		0			0
$235$		−	2285.88i		−	0.634529i
$236$	2202.46	−	863.568i	0.607491	−	0.238193i
$237$		0			0
$238$	186.159	+	984.759i	0.0507013	+	0.268204i
$239$	433.303	−	750.502i	0.117272	−	0.203121i	−0.801414	−	0.598110i	$-0.795918\pi$
$239$	433.303	−	750.502i	0.117272	−	0.203121i	0.918686	+	0.394989i	$0.129252\pi$
$240$		0			0
$241$	−1336.83	−	2315.45i	−0.357313	−	0.618885i	0.630198	−	0.776435i	$-0.282974\pi$
$241$	−1336.83	−	2315.45i	−0.357313	−	0.618885i	−0.987511	+	0.157550i	$0.949641\pi$
$242$	1367.99	−	1176.86i	0.363379	−	0.312609i
$243$		0			0
$244$	591.110	−	3913.05i	0.155090	−	1.02667i
$245$	1422.50	−	821.282i	0.370940	−	0.214162i
$246$		0			0
$247$	−4551.25	−	2627.67i	−1.17243	−	0.676900i
$248$	−165.254	−	4475.46i	−0.0423132	−	1.14594i
$249$		0			0
$250$	1046.69	−	2989.69i	0.264794	−	0.756339i
$251$	−4161.12			−1.04641			−0.523203	−	0.852208i	$-0.675263\pi$
$251$	−4161.12			−1.04641			−0.523203	+	0.852208i	$0.675263\pi$
$252$		0			0
$253$	3665.46			0.910853
$254$	45.0688	−	128.732i	0.0111333	−	0.0318005i
$255$		0			0
$256$	−3692.70	+	1772.34i	−0.901538	+	0.432701i
$257$	4067.29	+	2348.25i	0.987201	+	0.569961i	0.904437	−	0.426608i	$-0.140292\pi$
$257$	4067.29	+	2348.25i	0.987201	+	0.569961i	0.0827648	+	0.996569i	$0.473625\pi$
$258$		0			0
$259$	−530.611	+	306.348i	−0.127299	+	0.0734964i
$260$	−2414.00	−	364.661i	−0.575806	−	0.0869820i
$261$		0			0
$262$	850.718	−	731.859i	0.200601	−	0.172574i
$263$	3971.86	+	6879.47i	0.931238	+	1.61295i	0.781209	+	0.624269i	$0.214603\pi$
$263$	3971.86	+	6879.47i	0.931238	+	1.61295i	0.150028	+	0.988682i	$0.452064\pi$
$264$		0			0
$265$	721.601	−	1249.85i	0.167274	−	0.289727i
$266$	159.489	+	843.678i	0.0367628	+	0.194471i
$267$		0			0
$268$	−65.7530	−	167.698i	−0.0149870	−	0.0382230i
$269$			3191.82i			0.723452i	0.932284	+	0.361726i	$0.117812\pi$
$269$			3191.82i			0.723452i	−0.932284	+	0.361726i	$0.882188\pi$
$270$		0			0
$271$			4131.13i			0.926007i	0.886356	+	0.463004i	$0.153228\pi$
$271$			4131.13i			0.926007i	−0.886356	+	0.463004i	$0.846772\pi$
$272$	6235.54	−	1418.92i	1.39002	−	0.316303i
$273$		0			0
$274$	1824.95	−	344.989i	0.402370	−	0.0760641i
$275$	2225.07	−	3853.94i	0.487917	−	0.845096i
$276$		0			0
$277$	3886.23	+	6731.15i	0.842964	+	1.46006i	0.887378	+	0.461043i	$0.152524\pi$
$277$	3886.23	+	6731.15i	0.842964	+	1.46006i	−0.0444143	+	0.999013i	$0.514142\pi$
$278$	−1070.55	−	1244.42i	−0.230962	−	0.268472i
$279$		0			0
$280$	212.048	+	337.842i	0.0452582	+	0.0721068i
$281$	−7359.18	+	4248.83i	−1.56232	+	0.902006i	−0.565298	+	0.824887i	$0.691239\pi$
$281$	−7359.18	+	4248.83i	−1.56232	+	0.902006i	−0.997022	+	0.0771194i	$0.975428\pi$
$282$		0			0
$283$	−7381.63	−	4261.78i	−1.55050	−	0.895183i	−0.998101	−	0.0616051i	$-0.980378\pi$
$283$	−7381.63	−	4261.78i	−1.55050	−	0.895183i	−0.552402	−	0.833578i	$-0.686289\pi$
$284$	−1902.95	−	1518.58i	−0.397604	−	0.317292i
$285$		0			0
$286$	−7272.08	−	2545.95i	−1.50352	−	0.526381i
$287$	−156.609			−0.0322102
$288$		0			0
$289$	−5071.21			−1.03220
$290$	2344.24	+	820.716i	0.474684	+	0.166186i
$291$		0			0
$292$	7273.12	+	5804.03i	1.45763	+	1.16320i
$293$	975.941	+	563.460i	0.194591	+	0.112347i	0.594130	−	0.804369i	$-0.297496\pi$
$293$	975.941	+	563.460i	0.194591	+	0.112347i	−0.399539	+	0.916716i	$0.630830\pi$
$294$		0			0
$295$	−1273.07	+	735.006i	−0.251257	+	0.145063i
$296$	2078.38	+	3311.34i	0.408120	+	0.650229i
$297$		0			0
$298$	−2860.11	−	3324.61i	−0.555978	−	0.646273i
$299$	−2535.55	−	4391.70i	−0.490417	−	0.849427i
$300$		0			0
$301$	138.651	−	240.150i	0.0265505	−	0.0459868i
$302$	4551.56	−	860.428i	0.867261	−	0.163947i
$303$		0			0
$304$	5342.21	−	1215.64i	1.00788	−	0.229347i
$305$			2459.09i			0.461662i
$306$		0			0
$307$			4979.02i			0.925628i	0.886456	+	0.462814i	$0.153160\pi$
$307$			4979.02i			0.925628i	−0.886456	+	0.462814i	$0.846840\pi$
$308$	459.517	+	1171.96i	0.0850110	+	0.216814i
$309$		0			0
$310$	516.919	+	2734.44i	0.0947066	+	0.500986i
$311$	−829.382	+	1436.53i	−0.151222	+	0.261924i	−0.931677	−	0.363288i	$-0.881654\pi$
$311$	−829.382	+	1436.53i	−0.151222	+	0.261924i	0.780455	+	0.625212i	$0.214987\pi$
$312$		0			0
$313$	2982.28	+	5165.45i	0.538556	+	0.932807i	0.998982	+	0.0451088i	$0.0143634\pi$
$313$	2982.28	+	5165.45i	0.538556	+	0.932807i	−0.460426	+	0.887698i	$0.652303\pi$
$314$	−999.906	+	860.203i	−0.179707	+	0.154599i
$315$		0			0
$316$	−8806.01	−	1330.25i	−1.56765	−	0.236811i
$317$	−3332.18	+	1923.83i	−0.590390	+	0.340862i	−0.765252	−	0.643731i	$-0.777386\pi$
$317$	−3332.18	+	1923.83i	−0.590390	+	0.340862i	0.174862	+	0.984593i	$0.444052\pi$
$318$		0			0
$319$	6788.41	+	3919.29i	1.19147	+	0.687893i
$320$	2104.34	−	1431.68i	0.367613	−	0.250105i
$321$		0			0
$322$	−273.771	+	781.982i	−0.0473810	+	0.135336i
$323$	−8553.82			−1.47352
$324$		0			0
$325$	−6156.70			−1.05081
$326$	−3352.48	+	9575.80i	−0.569560	+	1.62685i
$327$		0			0
$328$	36.8738	+	998.624i	0.00620735	+	0.168109i
$329$	1412.17	+	815.317i	0.236643	+	0.136626i
$330$		0			0
$331$	4097.97	−	2365.96i	0.680497	−	0.392885i	−0.119545	−	0.992829i	$-0.538144\pi$
$331$	4097.97	−	2365.96i	0.680497	−	0.392885i	0.800042	+	0.599943i	$0.204810\pi$
$332$	957.944	−	6341.43i	0.158355	−	1.04829i
$333$		0			0
$334$	2925.35	−	2516.63i	0.479246	−	0.412287i
$335$	55.9641	+	96.9327i	0.00912730	+	0.0158089i
$336$		0			0
$337$	−1637.93	+	2836.98i	−0.264759	+	0.458576i	−0.967500	−	0.252870i	$-0.918626\pi$
$337$	−1637.93	+	2836.98i	−0.264759	+	0.458576i	0.702742	+	0.711445i	$0.251959\pi$
$338$	825.750	+	4368.12i	0.132884	+	0.702942i
$339$		0			0
$340$	−3699.50	+	1450.55i	−0.590098	+	0.231373i
$341$			8782.58i			1.39473i
$342$		0			0
$343$			2388.04i			0.375925i
$344$	−1563.98	−	827.571i	−0.245128	−	0.129708i
$345$		0			0
$346$	−503.352	+	95.1538i	−0.0782092	+	0.0147847i
$347$	1878.44	−	3253.55i	0.290604	−	0.503342i	−0.683348	−	0.730092i	$-0.739477\pi$
$347$	1878.44	−	3253.55i	0.290604	−	0.503342i	0.973953	+	0.226751i	$0.0728103\pi$
$348$		0			0
$349$	2406.87	+	4168.83i	0.369160	+	0.639404i	0.989434	−	0.144981i	$-0.0463120\pi$
$349$	2406.87	+	4168.83i	0.369160	+	0.639404i	−0.620274	+	0.784385i	$0.712979\pi$
$350$	656.002	+	762.541i	0.100185	+	0.116456i
$351$		0			0
$352$	7364.88	−	3206.07i	1.11520	−	0.485467i
$353$	2525.32	−	1457.99i	0.380762	−	0.219833i	−0.297387	−	0.954757i	$-0.596115\pi$
$353$	2525.32	−	1457.99i	0.380762	−	0.219833i	0.678150	+	0.734924i	$0.262782\pi$
$354$		0			0
$355$	1310.14	+	756.411i	0.195874	+	0.113088i
$356$	1728.39	−	2165.87i	0.257315	−	0.322446i
$357$		0			0
$358$	−3818.14	−	1336.73i	−0.563674	−	0.197342i
$359$	2282.01			0.335487			0.167744	−	0.985831i	$-0.446352\pi$
$359$	2282.01			0.335487			0.167744	+	0.985831i	$0.446352\pi$
$360$		0			0
$361$	−469.360			−0.0684298
$362$	5400.12	+	1890.58i	0.784043	+	0.274493i
$363$		0			0
$364$	1086.29	−	1361.25i	0.156421	−	0.196014i
$365$	−5007.39	−	2891.02i	−0.718079	−	0.414583i
$366$		0			0
$367$	−9728.22	+	5616.59i	−1.38368	+	0.798866i	−0.992593	−	0.121490i	$-0.961233\pi$
$367$	−9728.22	+	5616.59i	−1.38368	+	0.798866i	−0.391083	+	0.920355i	$0.627899\pi$
$368$	5050.81	+	1561.60i	0.715467	+	0.221207i
$369$		0			0
$370$	−1584.32	−	1841.63i	−0.222608	−	0.258761i
$371$	514.755	+	891.582i	0.0720344	+	0.124767i
$372$		0			0
$373$	997.078	−	1726.99i	0.138409	−	0.239732i	−0.788485	−	0.615054i	$-0.789134\pi$
$373$	997.078	−	1726.99i	0.138409	−	0.239732i	0.926895	+	0.375321i	$0.122468\pi$
$374$	−12322.5	+	2329.46i	−1.70370	+	0.322068i
$375$		0			0
$376$	4866.42	−	9196.76i	0.667464	−	1.26140i
$377$		−	10844.5i		−	1.48149i
$378$		0			0
$379$		−	7704.47i		−	1.04420i	−0.852884	−	0.522101i	$-0.825149\pi$
$379$		−	7704.47i		−	1.04420i	0.852884	−	0.522101i	$-0.174851\pi$
$380$	−3169.49	+	1242.73i	−0.427872	+	0.167765i
$381$		0			0
$382$	−1425.69	−	7541.72i	−0.190954	−	1.01012i
$383$	−3270.48	+	5664.65i	−0.436329	+	0.755744i	−0.997403	−	0.0720217i	$-0.977055\pi$
$383$	−3270.48	+	5664.65i	−0.436329	+	0.755744i	0.561074	+	0.827766i	$0.310388\pi$
$384$		0			0
$385$	−391.107	−	677.417i	−0.0517731	−	0.0896736i
$386$	−1534.92	+	1320.47i	−0.202398	+	0.174120i
$387$		0			0
$388$	−696.488	+	4610.63i	−0.0911310	+	0.603272i
$389$	12148.9	−	7014.20i	1.58349	−	0.914226i	0.589141	−	0.808031i	$-0.299466\pi$
$389$	12148.9	−	7014.20i	1.58349	−	0.914226i	0.994345	−	0.106195i	$-0.0338669\pi$
$390$		0			0
$391$	−7148.14	−	4126.98i	−0.924545	−	0.533786i
$392$	7471.57	−	275.884i	0.962682	−	0.0355466i
$393$		0			0
$394$	−3794.74	+	10839.0i	−0.485219	+	1.38595i
$395$	5533.98			0.704924
$396$		0			0
$397$	5393.79			0.681881			0.340940	−	0.940085i	$-0.389255\pi$
$397$	5393.79			0.681881			0.340940	+	0.940085i	$0.389255\pi$
$398$	4748.55	−	13563.4i	0.598048	−	1.70822i
$399$		0			0
$400$	4707.93	−	4362.58i	0.588492	−	0.545322i
$401$	2512.43	+	1450.55i	0.312880	+	0.180641i	0.648215	−	0.761458i	$-0.275516\pi$
$401$	2512.43	+	1450.55i	0.312880	+	0.180641i	−0.335334	+	0.942099i	$0.608849\pi$
$402$		0			0
$403$	10522.7	−	6075.27i	1.30067	−	0.750944i
$404$	−562.614	−	84.9892i	−0.0692849	−	0.0104663i
$405$		0			0
$406$	−1343.15	+	1155.49i	−0.164186	+	0.141247i
$407$	−3833.42	−	6639.67i	−0.466868	−	0.808640i
$408$		0			0
$409$	6841.43	−	11849.7i	0.827108	−	1.43259i	−0.0731902	−	0.997318i	$-0.523318\pi$
$409$	6841.43	−	11849.7i	0.827108	−	1.43259i	0.900298	−	0.435274i	$-0.143349\pi$
$410$	−115.342	−	610.144i	−0.0138935	−	0.0734948i
$411$		0			0
$412$	2201.86	+	5615.68i	0.263296	+	0.671516i
$413$		−	1048.63i		−	0.124939i
$414$		0			0
$415$			3985.16i			0.471383i
$416$	−8935.88	−	6606.31i	−1.05317	−	0.778608i
$417$		0			0
$418$	−10557.2	+	1995.73i	−1.23533	+	0.233527i
$419$	−621.302	+	1076.13i	−0.0724406	+	0.125471i	−0.899970	−	0.435951i	$-0.856412\pi$
$419$	−621.302	+	1076.13i	−0.0724406	+	0.125471i	0.827530	+	0.561422i	$0.189745\pi$
$420$		0			0
$421$	−8254.66	−	14297.5i	−0.955600	−	1.65515i	−0.732989	−	0.680241i	$-0.761875\pi$
$421$	−8254.66	−	14297.5i	−0.955600	−	1.65515i	−0.222612	−	0.974907i	$-0.571458\pi$
$422$	−4003.99	−	4654.27i	−0.461875	−	0.536887i
$423$		0			0
$424$	5564.03	−	3492.29i	0.637295	−	0.400002i
$425$	−8678.38	+	5010.47i	−0.990502	+	0.571867i
$426$		0			0
$427$	−1519.18	−	877.097i	−0.172174	−	0.0994044i
$428$	−5524.32	−	4408.46i	−0.623897	−	0.497876i
$429$		0			0
$430$	1037.74	+	363.311i	0.116382	+	0.0407451i
$431$	9018.30			1.00788			0.503940	−	0.863739i	$-0.331883\pi$
$431$	9018.30			1.00788			0.503940	+	0.863739i	$0.331883\pi$
$432$		0			0
$433$	3108.94			0.345048			0.172524	−	0.985005i	$-0.444808\pi$
$433$	3108.94			0.345048			0.172524	+	0.985005i	$0.444808\pi$
$434$	−1873.66	−	655.965i	−0.207231	−	0.0725515i
$435$		0			0
$436$	3921.00	+	3129.00i	0.430692	+	0.343697i
$437$	−6124.06	−	3535.73i	−0.670375	−	0.387041i
$438$		0			0
$439$	6391.17	−	3689.94i	0.694838	−	0.401165i	−0.110584	−	0.993867i	$-0.535272\pi$
$439$	6391.17	−	3689.94i	0.694838	−	0.401165i	0.805422	+	0.592702i	$0.201939\pi$
$440$	−4227.50	+	2653.41i	−0.458041	+	0.287492i
$441$		0			0
$442$	11315.0	+	13152.6i	1.21765	+	1.41540i
$443$	1359.33	+	2354.44i	0.145788	+	0.252512i	0.929667	−	0.368402i	$-0.120095\pi$
$443$	1359.33	+	2354.44i	0.145788	+	0.252512i	−0.783879	+	0.620914i	$0.786762\pi$
$444$		0			0
$445$	−860.918	+	1491.15i	−0.0917111	+	0.158848i
$446$	−4814.42	+	910.119i	−0.511142	+	0.0966264i
$447$		0			0
$448$	133.899	+	1810.67i	0.0141208	+	0.190951i
$449$		−	10822.9i		−	1.13756i	−0.822491	−	0.568778i	$-0.807416\pi$
$449$		−	10822.9i		−	1.13756i	0.822491	−	0.568778i	$-0.192584\pi$
$450$		0			0
$451$		−	1959.69i		−	0.204608i
$452$	−1989.91	−	5075.10i	−0.207074	−	0.528126i
$453$		0			0
$454$	1726.86	+	9134.89i	0.178515	+	0.944321i
$455$	−541.089	+	937.193i	−0.0557509	+	0.0965633i
$456$		0			0
$457$	555.262	+	961.742i	0.0568360	+	0.0984429i	0.893044	−	0.449970i	$-0.148565\pi$
$457$	555.262	+	961.742i	0.0568360	+	0.0984429i	−0.836207	+	0.548413i	$0.815232\pi$
$458$	−2951.68	+	2539.28i	−0.301142	+	0.259067i
$459$		0			0
$460$	−3248.22	−	490.680i	−0.329237	−	0.0497350i
$461$	4288.85	−	2476.17i	0.433301	−	0.250167i	−0.267451	−	0.963572i	$-0.586181\pi$
$461$	4288.85	−	2476.17i	0.433301	−	0.250167i	0.700752	+	0.713405i	$0.252848\pi$
$462$		0			0
$463$	9164.57	+	5291.16i	0.919900	+	0.531104i	0.883603	−	0.468237i	$-0.155111\pi$
$463$	9164.57	+	5291.16i	0.919900	+	0.531104i	0.0362966	+	0.999341i	$0.488444\pi$
$464$	7684.33	+	8292.64i	0.768827	+	0.829690i
$465$		0			0
$466$	603.854	−	1724.81i	0.0600279	−	0.171460i
$467$	11595.9			1.14902			0.574511	−	0.818497i	$-0.305192\pi$
$467$	11595.9			1.14902			0.574511	+	0.818497i	$0.305192\pi$
$468$		0			0
$469$	−79.8441			−0.00786111
$470$	−2136.40	+	6102.27i	−0.209670	+	0.598887i
$471$		0			0
$472$	−6686.68	+	246.903i	−0.652075	+	0.0240776i
$473$	3005.06	+	1734.97i	0.292120	+	0.168656i
$474$		0			0
$475$	−7435.07	+	4292.64i	−0.718199	+	0.414652i
$476$	423.402	−	2802.85i	0.0407702	−	0.269892i
$477$		0			0
$478$	−1858.15	+	1598.54i	−0.177803	+	0.152961i
$479$	5354.57	+	9274.39i	0.510765	+	0.884671i	0.999922	+	0.0124755i	$0.00397116\pi$
$479$	5354.57	+	9274.39i	0.510765	+	0.884671i	−0.489157	+	0.872196i	$0.662696\pi$
$480$		0			0
$481$	−5303.46	+	9185.87i	−0.502738	+	0.870768i
$482$	1404.69	+	7430.62i	0.132742	+	0.702190i
$483$		0			0
$484$	−4751.82	+	1863.15i	−0.446264	+	0.174977i
$485$		−	2897.47i		−	0.271273i
$486$		0			0
$487$		−	15654.6i		−	1.45663i	−0.685243	−	0.728314i	$-0.740304\pi$
$487$		−	15654.6i		−	1.45663i	0.685243	−	0.728314i	$-0.259696\pi$
$488$	−5235.17	+	9893.63i	−0.485625	+	0.917753i
$489$		0			0
$490$	−4565.02	+	862.973i	−0.420871	+	0.0795615i
$491$	−8454.61	+	14643.8i	−0.777090	+	1.34596i	0.156523	+	0.987674i	$0.449972\pi$
$491$	−8454.61	+	14643.8i	−0.777090	+	1.34596i	−0.933613	+	0.358284i	$0.883362\pi$
$492$		0			0
$493$	−8825.53	−	15286.3i	−0.806251	−	1.39647i
$494$	9693.96	+	11268.3i	0.882899	+	1.02629i
$495$		0			0
$496$	−3741.65	+	12101.9i	−0.338720	+	1.09555i
$497$	−934.592	+	539.587i	−0.0843505	+	0.0486998i
$498$		0			0
$499$	6235.20	+	3599.90i	0.559371	+	0.322953i	0.752893	−	0.658143i	$-0.228658\pi$
$499$	6235.20	+	3599.90i	0.559371	+	0.322953i	−0.193522	+	0.981096i	$0.561991\pi$
$500$	−5588.38	+	7002.90i	−0.499840	+	0.626358i
$501$		0			0
$502$	11108.3	+	3889.02i	0.987628	+	0.345768i
$503$	−747.770			−0.0662852			−0.0331426	−	0.999451i	$-0.510552\pi$
$503$	−747.770			−0.0662852			−0.0331426	+	0.999451i	$0.510552\pi$
$504$		0			0
$505$	353.565			0.0311553
$506$	−9785.15	−	3425.77i	−0.859690	−	0.300977i
$507$		0			0
$508$	−240.627	+	301.534i	−0.0210159	+	0.0263354i
$509$	12246.8	+	7070.68i	1.06646	+	0.615722i	0.927213	−	0.374535i	$-0.122198\pi$
$509$	12246.8	+	7070.68i	1.06646	+	0.615722i	0.139249	+	0.990257i	$0.455531\pi$
$510$		0			0
$511$	3572.03	−	2062.31i	0.309231	−	0.178535i
$512$	11514.3	−	1280.14i	0.993876	−	0.110497i
$513$		0			0
$514$	−8663.15	−	10070.1i	−0.743415	−	0.864151i
$515$	−1874.07	−	3245.98i	−0.160352	−	0.277737i
$516$		0			0
$517$	−10202.3	+	17670.9i	−0.867884	+	1.50322i
$518$	1702.81	−	321.899i	0.144435	−	0.0273040i
$519$		0			0
$520$	6103.47	+	3229.62i	0.514721	+	0.272362i
$521$			4172.34i			0.350851i	0.984493	+	0.175426i	$0.0561302\pi$
$521$			4172.34i			0.350851i	−0.984493	+	0.175426i	$0.943870\pi$
$522$		0			0
$523$			8599.53i			0.718989i	0.933147	+	0.359495i	$0.117051\pi$
$523$			8599.53i			0.718989i	−0.933147	+	0.359495i	$0.882949\pi$
$524$	−2955.04	+	1158.65i	−0.246358	+	0.0965950i
$525$		0			0
$526$	−4173.49	−	22077.2i	−0.345956	−	1.83006i
$527$	9888.39	−	17127.2i	0.817353	−	1.41570i
$528$		0			0
$529$	2671.72	+	4627.55i	0.219587	+	0.380336i
$530$	−3094.47	+	2662.12i	−0.253614	+	0.218180i
$531$		0			0
$532$	362.744	−	2401.30i	0.0295619	−	0.195695i
$533$	−2347.96	+	1355.59i	−0.190809	+	0.110164i
$534$		0			0
$535$	3803.37	+	2195.88i	0.307354	+	0.177451i
$536$	18.7994	+	509.131i	0.00151495	+	0.0410282i
$537$		0			0
$538$	2983.10	−	8520.73i	0.239053	−	0.682815i
$539$	−14662.1			−1.17169
$540$		0			0
$541$	−4579.04			−0.363897			−0.181948	−	0.983308i	$-0.558240\pi$
$541$	−4579.04			−0.363897			−0.181948	+	0.983308i	$0.558240\pi$
$542$	3860.98	−	11028.3i	0.305984	−	0.873993i
$543$		0			0
$544$	−17972.2	−	2039.91i	−1.41646	−	0.160773i
$545$	−2699.52	−	1558.57i	−0.212174	−	0.122499i
$546$		0			0
$547$	−8822.88	+	5093.89i	−0.689651	+	0.398170i	−0.803481	−	0.595330i	$-0.797021\pi$
$547$	−8822.88	+	5093.89i	−0.689651	+	0.398170i	0.113830	+	0.993500i	$0.463688\pi$
$548$	−5194.23	−	784.648i	−0.404903	−	0.0611651i
$549$		0			0
$550$	−9541.88	+	8208.73i	−0.739758	+	0.636402i
$551$	−7561.14	−	13096.3i	−0.584601	−	1.01256i
$552$		0			0
$553$	−1973.84	+	3418.79i	−0.151783	+	0.262896i
$554$	−4083.51	−	21601.3i	−0.313162	−	1.65659i
$555$		0			0
$556$	1694.86	+	4322.59i	0.129277	+	0.329710i
$557$			19157.5i			1.45732i	0.684874	+	0.728661i	$0.259857\pi$
$557$			19157.5i			1.45732i	−0.684874	+	0.728661i	$0.740143\pi$
$558$		0			0
$559$		−	4800.61i		−	0.363227i
$560$	−250.324	−	1100.07i	−0.0188895	−	0.0830113i
$561$		0			0
$562$	23616.7	−	4464.51i	1.77262	−	0.335096i
$563$	4860.90	−	8419.32i	0.363876	−	0.630252i	−0.624719	−	0.780850i	$-0.714786\pi$
$563$	4860.90	−	8419.32i	0.363876	−	0.630252i	0.988595	+	0.150598i	$0.0481198\pi$
$564$		0			0
$565$	1693.66	+	2933.51i	0.126112	+	0.218432i
$566$	15722.5	+	18276.0i	1.16761	+	1.35724i
$567$		0			0
$568$	3660.76	+	5832.44i	0.270426	+	0.430851i
$569$	1525.83	−	880.938i	0.112418	−	0.0649048i	−0.442737	−	0.896652i	$-0.645992\pi$
$569$	1525.83	−	880.938i	0.112418	−	0.0649048i	0.555155	+	0.831747i	$0.312659\pi$
$570$		0			0
$571$	3701.00	+	2136.77i	0.271247	+	0.156605i	0.629454	−	0.777038i	$-0.283278\pi$
$571$	3701.00	+	2136.77i	0.271247	+	0.156605i	−0.358207	+	0.933642i	$0.616612\pi$
$572$	17033.7	+	13593.1i	1.24513	+	0.993628i
$573$		0			0
$574$	418.075	+	146.368i	0.0304009	+	0.0106433i
$575$	−8284.32			−0.600835
$576$		0			0
$577$	6274.37			0.452696			0.226348	−	0.974047i	$-0.427321\pi$
$577$	6274.37			0.452696			0.226348	+	0.974047i	$0.427321\pi$
$578$	13537.9	+	4739.59i	0.974222	+	0.341075i
$579$		0			0
$580$	−5491.01	−	4381.89i	−0.393107	−	0.313703i
$581$	−2461.95	−	1421.41i	−0.175799	−	0.101497i
$582$		0			0
$583$	−11156.6	+	6441.27i	−0.792554	+	0.457582i
$584$	−13991.5	−	22291.7i	−0.991390	−	1.57951i
$585$		0			0
$586$	−2078.71	−	2416.31i	−0.146537	−	0.170336i
$587$	−1247.63	−	2160.97i	−0.0877263	−	0.151946i	0.818823	−	0.574046i	$-0.194627\pi$
$587$	−1247.63	−	2160.97i	−0.0877263	−	0.151946i	−0.906550	+	0.422099i	$0.861293\pi$
$588$		0			0
$589$	8471.73	−	14673.5i	0.592651	−	1.02650i
$590$	4085.46	−	772.317i	0.285078	−	0.0538911i
$591$		0			0
$592$	−2453.54	−	10782.3i	−0.170338	−	0.748562i
$593$		−	10094.4i		−	0.699031i	−0.936931	−	0.349516i	$-0.886346\pi$
$593$		−	10094.4i		−	0.699031i	0.936931	−	0.349516i	$-0.113654\pi$
$594$		0			0
$595$			1761.40i			0.121362i
$596$	4528.00	+	11548.3i	0.311198	+	0.793685i
$597$		0			0
$598$	2664.26	+	14093.6i	0.182190	+	0.963765i
$599$	−11725.3	+	20308.7i	−0.799801	+	1.38530i	0.119944	+	0.992781i	$0.461729\pi$
$599$	−11725.3	+	20308.7i	−0.799801	+	1.38530i	−0.919745	+	0.392516i	$0.871605\pi$
$600$		0			0
$601$	1962.30	+	3398.81i	0.133185	+	0.230683i	0.924903	−	0.380204i	$-0.124146\pi$
$601$	1962.30	+	3398.81i	0.133185	+	0.230683i	−0.791718	+	0.610887i	$0.790813\pi$
$602$	−594.582	+	511.509i	−0.0402547	+	0.0346305i
$603$		0			0
$604$	−12954.8	−	1956.97i	−0.872720	−	0.131834i
$605$	2746.65	−	1585.78i	0.184574	−	0.106564i
$606$		0			0
$607$	−11255.5	−	6498.36i	−0.752630	−	0.434531i	0.0740137	−	0.997257i	$-0.476419\pi$
$607$	−11255.5	−	6498.36i	−0.752630	−	0.434531i	−0.826643	+	0.562726i	$0.809752\pi$
$608$	−15397.4	−	1747.67i	−1.02705	−	0.116574i
$609$		0			0
$610$	2298.28	−	6564.66i	0.152549	−	0.435730i
$611$	28229.3			1.86913
$612$		0			0
$613$	12133.0			0.799427			0.399713	−	0.916640i	$-0.369110\pi$
$613$	12133.0			0.799427			0.399713	+	0.916640i	$0.369110\pi$
$614$	4653.43	−	13291.8i	0.305859	−	0.873634i
$615$		0			0
$616$	−131.380	−	3558.08i	−0.00859329	−	0.232726i
$617$	−7349.86	−	4243.44i	−0.479569	−	0.276879i	0.240668	−	0.970608i	$-0.422634\pi$
$617$	−7349.86	−	4243.44i	−0.479569	−	0.276879i	−0.720237	+	0.693728i	$0.755967\pi$
$618$		0			0
$619$	−15253.5	+	8806.64i	−0.990455	+	0.571840i	−0.905410	−	0.424537i	$-0.860437\pi$
$619$	−15253.5	+	8806.64i	−0.990455	+	0.571840i	−0.0850450	+	0.996377i	$0.527103\pi$
$620$	1175.69	−	7782.84i	0.0761560	−	0.504140i
$621$		0			0
$622$	3556.67	−	3059.75i	0.229276	−	0.197242i
$623$	−614.137	−	1063.72i	−0.0394942	−	0.0684060i
$624$		0			0
$625$	−3484.43	+	6035.21i	−0.223003	+	0.386253i
$626$	−3133.66	−	16576.7i	−0.200074	−	1.05837i
$627$		0			0
$628$	3473.25	−	1361.84i	0.220697	−	0.0865338i
$629$			17264.3i			1.09439i
$630$		0			0
$631$		−	12601.8i		−	0.795041i	−0.917593	−	0.397521i	$-0.869871\pi$
$631$		−	12601.8i		−	0.795041i	0.917593	−	0.397521i	$-0.130129\pi$
$632$	22264.8	+	11781.3i	1.40134	+	0.741513i
$633$		0			0
$634$	10693.4	−	2021.49i	0.669860	−	0.126630i
$635$	119.858	−	207.600i	0.00749040	−	0.0129738i
$636$		0			0
$637$	10142.4	+	17567.1i	0.630856	+	1.09268i
$638$	−14459.0	−	16807.2i	−0.897237	−	1.04295i
$639$		0			0
$640$	−6955.71	+	1855.22i	−0.429607	+	0.114584i
$641$	−26029.5	+	15028.1i	−1.60390	+	0.926014i	−0.613206	+	0.789923i	$0.710121\pi$
$641$	−26029.5	+	15028.1i	−1.60390	+	0.926014i	−0.990696	+	0.136091i	$0.956546\pi$
$642$		0			0
$643$	14262.2	+	8234.26i	0.874719	+	0.505020i	0.868914	−	0.494964i	$-0.164819\pi$
$643$	14262.2	+	8234.26i	0.874719	+	0.505020i	0.00580579	+	0.999983i	$0.498152\pi$
$644$	1461.69	−	1831.67i	0.0894391	−	0.112078i
$645$		0			0
$646$	22834.9	+	7994.47i	1.39075	+	0.486901i
$647$	−31904.7			−1.93864			−0.969321	−	0.245797i	$-0.920950\pi$
$647$	−31904.7			−1.93864			−0.969321	+	0.245797i	$0.920950\pi$
$648$		0			0
$649$	13121.8			0.793648
$650$	16435.6	+	5754.10i	0.991782	+	0.347222i
$651$		0			0
$652$	17899.2	−	22429.8i	1.07514	−	1.34727i
$653$	−10949.7	−	6321.81i	−0.656195	−	0.378854i	0.134631	−	0.990896i	$-0.457015\pi$
$653$	−10949.7	−	6321.81i	−0.656195	−	0.378854i	−0.790825	+	0.612042i	$0.790348\pi$
$654$		0			0
$655$	1708.07	−	986.156i	0.101893	−	0.0588279i
$656$	834.886	−	2700.34i	0.0496903	−	0.160717i
$657$		0			0
$658$	−3007.86	−	3496.36i	−0.178205	−	0.207146i
$659$	14222.5	+	24634.1i	0.840715	+	1.45616i	0.889292	+	0.457341i	$0.151198\pi$
$659$	14222.5	+	24634.1i	0.840715	+	1.45616i	−0.0485770	+	0.998819i	$0.515469\pi$
$660$		0			0
$661$	4409.41	−	7637.33i	0.259465	−	0.449406i	−0.706634	−	0.707579i	$-0.749787\pi$
$661$	4409.41	−	7637.33i	0.259465	−	0.449406i	0.966099	+	0.258173i	$0.0831205\pi$
$662$	−13151.0	+	2486.07i	−0.772096	+	0.145957i
$663$		0			0
$664$	−8484.03	+	16033.5i	−0.495850	+	0.937077i
$665$			1509.06i			0.0879980i
$666$		0			0
$667$		−	14592.2i		−	0.847092i
$668$	−10161.4	+	3984.22i	−0.588560	+	0.230770i
$669$		0			0
$670$	−58.8050	−	311.071i	−0.00339080	−	0.0179369i
$671$	10975.3	−	19009.9i	0.631443	−	1.09369i
$672$		0			0
$673$	−8056.85	−	13954.9i	−0.461469	−	0.799288i	0.537565	−	0.843222i	$-0.319344\pi$
$673$	−8056.85	−	13954.9i	−0.461469	−	0.799288i	−0.999034	+	0.0439342i	$0.986011\pi$
$674$	7024.00	−	6042.63i	0.401416	−	0.345332i
$675$		0			0
$676$	1878.10	−	12432.7i	0.106856	−	0.707366i
$677$	11118.5	−	6419.28i	0.631196	−	0.364421i	−0.150019	−	0.988683i	$-0.547934\pi$
$677$	11118.5	−	6419.28i	0.631196	−	0.364421i	0.781215	+	0.624262i	$0.214600\pi$
$678$		0			0
$679$	1790.00	+	1033.46i	0.101169	+	0.0584101i
$680$	11231.7	−	414.725i	0.633405	−	0.0233882i
$681$		0			0
$682$	8208.27	−	23445.5i	0.460866	−	1.31639i
$683$	−30770.7			−1.72388			−0.861938	−	0.507014i	$-0.830749\pi$
$683$	−30770.7			−1.72388			−0.861938	+	0.507014i	$0.830749\pi$
$684$		0			0
$685$	3264.23			0.182073
$686$	2231.88	−	6375.00i	0.124218	−	0.354809i
$687$		0			0
$688$	3401.66	+	3670.95i	0.188499	+	0.203421i
$689$	15435.0	+	8911.37i	0.853447	+	0.492738i
$690$		0			0
$691$	−16101.2	+	9296.02i	−0.886422	+	0.511776i	−0.872770	−	0.488131i	$-0.837679\pi$
$691$	−16101.2	+	9296.02i	−0.886422	+	0.511776i	−0.0136514	+	0.999907i	$0.504346\pi$
$692$	1432.66	+	216.419i	0.0787014	+	0.0118887i
$693$		0			0
$694$	−8055.37	+	6929.91i	−0.440602	+	0.379043i
$695$	−1442.54	−	2498.55i	−0.0787317	−	0.136367i
$696$		0			0
$697$	−2206.43	+	3821.65i	−0.119906	+	0.207683i
$698$	−2529.05	−	13378.4i	−0.137143	−	0.725472i
$699$		0			0
$700$	−1038.55	−	2648.75i	−0.0560767	−	0.143019i
$701$		−	21732.5i		−	1.17093i	−0.810697	−	0.585466i	$-0.800912\pi$
$701$		−	21732.5i		−	1.17093i	0.810697	−	0.585466i	$-0.199088\pi$
$702$		0			0
$703$			14791.0i			0.793530i
$704$	−22657.3	+	1675.51i	−1.21297	+	0.0896990i
$705$		0			0
$706$	−8104.12	+	1532.01i	−0.432015	+	0.0816683i
$707$	−126.108	+	218.426i	−0.00670832	+	0.0116191i
$708$		0			0
$709$	3222.28	+	5581.15i	0.170684	+	0.295634i	0.938659	−	0.344846i	$-0.112069\pi$
$709$	3222.28	+	5581.15i	0.170684	+	0.295634i	−0.767975	+	0.640480i	$0.778735\pi$
$710$	−2790.55	−	3243.75i	−0.147503	−	0.171459i
$711$		0			0
$712$	−6638.26	+	4166.54i	−0.349409	+	0.219308i
$713$	14159.1	−	8174.75i	0.743705	−	0.429378i
$714$		0			0
$715$	−11727.4	−	6770.79i	−0.613396	−	0.354144i
$716$	8943.42	+	7136.94i	0.466803	+	0.372514i
$717$		0			0
$718$	−6091.95	−	2132.79i	−0.316643	−	0.110856i
$719$	11526.9			0.597885			0.298943	−	0.954271i	$-0.403366\pi$
$719$	11526.9			0.597885			0.298943	+	0.954271i	$0.403366\pi$
$720$		0			0
$721$	2673.73			0.138107
$722$	1252.98	+	438.668i	0.0645860	+	0.0226115i
$723$		0			0
$724$	−12648.9	−	10094.0i	−0.649301	−	0.518149i
$725$	−15342.5	−	8857.99i	−0.785939	−	0.453762i
$726$		0			0
$727$	20341.7	−	11744.3i	1.03773	−	0.599135i	0.118543	−	0.992949i	$-0.462178\pi$
$727$	20341.7	−	11744.3i	1.03773	−	0.599135i	0.919190	+	0.393814i	$0.128844\pi$
$728$	−4172.16	+	2618.68i	−0.212404	+	0.133317i
$729$		0			0
$730$	10665.5	+	12397.7i	0.540751	+	0.628573i
$731$	−3906.85	−	6766.86i	−0.197674	−	0.342382i
$732$		0			0
$733$	−8909.30	+	15431.4i	−0.448939	+	0.777586i	−0.998317	−	0.0579884i	$-0.981531\pi$
$733$	−8909.30	+	15431.4i	−0.448939	+	0.777586i	0.549378	+	0.835574i	$0.314865\pi$
$734$	31219.3	−	5901.71i	1.56993	−	0.296779i
$735$		0			0
$736$	−12023.9	−	8889.31i	−0.602185	−	0.445196i
$737$		−	999.111i		−	0.0499358i
$738$		0			0
$739$			29721.7i			1.47947i	0.672896	+	0.739737i	$0.265050\pi$
$739$			29721.7i			1.47947i	−0.672896	+	0.739737i	$0.734950\pi$
$740$	2508.23	+	6397.03i	0.124600	+	0.317783i
$741$		0			0
$742$	−540.886	−	2861.22i	−0.0267608	−	0.141562i
$743$	11863.8	−	20548.7i	0.585788	−	1.01461i	−0.408989	−	0.912540i	$-0.634118\pi$
$743$	11863.8	−	20548.7i	0.585788	−	1.01461i	0.994777	−	0.102075i	$-0.0325483\pi$
$744$		0			0
$745$	−3853.90	−	6675.15i	−0.189525	−	0.328266i
$746$	−4275.81	+	3678.41i	−0.209851	+	0.180531i
$747$		0			0
$748$	35072.8	+	5298.15i	1.71442	+	0.258983i
$749$	−2713.14	+	1566.43i	−0.132358	+	0.0764168i
$750$		0			0
$751$	9826.00	+	5673.05i	0.477438	+	0.275649i	0.719348	−	0.694650i	$-0.244441\pi$
$751$	9826.00	+	5673.05i	0.477438	+	0.275649i	−0.241910	+	0.970299i	$0.577774\pi$
$752$	−21586.5	+	20003.0i	−1.04678	+	0.969994i
$753$		0			0
$754$	−10135.4	+	28950.0i	−0.489534	+	1.39827i
$755$	8141.21			0.392436
$756$		0			0
$757$	−17117.6			−0.821860			−0.410930	−	0.911667i	$-0.634796\pi$
$757$	−17117.6			−0.821860			−0.410930	+	0.911667i	$0.634796\pi$
$758$	−7200.67	+	20567.5i	−0.345039	+	0.985548i
$759$		0			0
$760$	9622.58	−	355.310i	0.459273	−	0.0169585i
$761$	28863.1	+	16664.1i	1.37488	+	0.793788i	0.991538	−	0.129817i	$-0.0414391\pi$
$761$	28863.1	+	16664.1i	1.37488	+	0.793788i	0.383344	+	0.923606i	$0.374772\pi$
$762$		0			0
$763$	1925.71	−	1111.81i	0.0913700	−	0.0527525i
$764$	−3242.60	+	21465.5i	−0.153551	+	1.01648i
$765$		0			0
$766$	14025.0	−	12065.4i	0.661543	−	0.569115i
$767$	−9076.91	−	15721.7i	−0.427312	−	0.740126i
$768$		0			0
$769$	4673.17	−	8094.17i	0.219140	−	0.379562i	−0.735405	−	0.677628i	$-0.763008\pi$
$769$	4673.17	−	8094.17i	0.219140	−	0.379562i	0.954545	+	0.298066i	$0.0963414\pi$
$770$	410.960	+	2173.93i	0.0192337	+	0.101744i
$771$		0			0
$772$	5331.68	−	2090.51i	0.248564	−	0.0974600i
$773$			22674.0i			1.05502i	0.849549	+	0.527509i	$0.176874\pi$
$773$			22674.0i			1.05502i	−0.849549	+	0.527509i	$0.823126\pi$
$774$		0			0
$775$		−	19849.5i		−	0.920020i
$776$	6168.45	−	11657.4i	0.285354	−	0.539273i
$777$		0			0
$778$	−38987.8	+	7370.26i	−1.79663	+	0.339636i
$779$	−1890.32	+	3274.14i	−0.0869421	+	0.150588i
$780$		0			0
$781$	−6752.00	−	11694.8i	−0.309354	−	0.535817i
$782$	15225.2	+	17697.9i	0.696231	+	0.809304i
$783$		0			0
$784$	−20203.6	−	6246.51i	−0.920353	−	0.284553i
$785$	−2007.61	+	1159.10i	−0.0912799	+	0.0527005i
$786$		0			0
$787$	−9647.46	−	5569.96i	−0.436969	−	0.252284i	0.265342	−	0.964154i	$-0.414515\pi$
$787$	−9647.46	−	5569.96i	−0.436969	−	0.252284i	−0.702311	+	0.711870i	$0.747849\pi$
$788$	20260.5	−	25388.8i	0.915928	−	1.14776i
$789$		0			0
$790$	−14773.3	−	5172.11i	−0.665328	−	0.232931i
$791$	−2416.36			−0.108617
$792$		0			0
$793$	−30368.4			−1.35991
$794$	−14399.0	−	5041.08i	−0.643579	−	0.225317i
$795$		0			0
$796$	−25353.0	+	31770.2i	−1.12891	+	1.41466i
$797$	−17390.1	−	10040.2i	−0.772883	−	0.446224i	0.0610191	−	0.998137i	$-0.480565\pi$
$797$	−17390.1	−	10040.2i	−0.772883	−	0.446224i	−0.833902	+	0.551912i	$0.813898\pi$
$798$		0			0
$799$	39791.6	−	22973.7i	1.76186	−	1.01721i
$800$	−16645.4	+	7246.06i	−0.735628	+	0.320233i
$801$		0			0
$802$	−5351.37	−	6220.47i	−0.235615	−	0.273881i
$803$	25806.2	+	44697.7i	1.13410	+	1.96432i
$804$		0			0
$805$	−728.078	+	1261.07i	−0.0318775	+	0.0552134i
$806$	−33768.8	+	6383.67i	−1.47575	+	0.278976i
$807$		0			0
$808$	1422.50	+	752.707i	0.0619347	+	0.0327724i
$809$		−	28192.5i		−	1.22521i	−0.790389	−	0.612605i	$-0.790122\pi$
$809$		−	28192.5i		−	1.22521i	0.790389	−	0.612605i	$-0.209878\pi$
$810$		0			0
$811$		−	2957.47i		−	0.128053i	−0.997948	−	0.0640264i	$-0.979606\pi$
$811$		−	2957.47i		−	0.128053i	0.997948	−	0.0640264i	$-0.0203942\pi$
$812$	4665.55	−	1829.33i	0.201637	−	0.0790602i
$813$		0			0
$814$	4028.01	+	21307.7i	0.173442	+	0.917487i
$815$	−8915.71	+	15442.5i	−0.383195	+	0.663713i
$816$		0			0
$817$	−3347.13	−	5797.40i	−0.143331	−	0.248256i
$818$	−29338.4	+	25239.4i	−1.25403	+	1.07882i
$819$		0			0
$820$	−262.335	+	1736.61i	−0.0111721	+	0.0739575i
$821$	20324.9	−	11734.6i	0.863999	−	0.498830i	−0.00135045	−	0.999999i	$-0.500430\pi$
$821$	20324.9	−	11734.6i	0.863999	−	0.498830i	0.865349	+	0.501169i	$0.167097\pi$
$822$		0			0
$823$	−5653.95	−	3264.31i	−0.239471	−	0.138258i	0.375463	−	0.926837i	$-0.377484\pi$
$823$	−5653.95	−	3264.31i	−0.239471	−	0.138258i	−0.614933	+	0.788579i	$0.710817\pi$
$824$	−629.535	−	17049.2i	−0.0266151	−	0.720798i
$825$		0			0
$826$	−980.062	+	2799.38i	−0.0412842	+	0.117921i
$827$	28855.8			1.21332			0.606659	−	0.794962i	$-0.292509\pi$
$827$	28855.8			1.21332			0.606659	+	0.794962i	$0.292509\pi$
$828$		0			0
$829$	−6475.24			−0.271284			−0.135642	−	0.990758i	$-0.543310\pi$
$829$	−6475.24			−0.271284			−0.135642	+	0.990758i	$0.543310\pi$
$830$	3724.56	−	10638.6i	0.155761	−	0.444905i
$831$		0			0
$832$	17680.5	+	25987.4i	0.736732	+	1.08288i
$833$	28593.0	+	16508.2i	1.18930	+	0.686645i
$834$		0			0
$835$	5873.52	−	3391.08i	0.243427	−	0.140543i
$836$	30048.1	+	4539.11i	1.24310	+	0.187785i
$837$		0			0
$838$	2664.36	−	2292.10i	0.109831	−	0.0944862i
$839$	−3490.55	−	6045.81i	−0.143632	−	0.248778i	0.785230	−	0.619205i	$-0.212545\pi$
$839$	−3490.55	−	6045.81i	−0.143632	−	0.248778i	−0.928862	+	0.370427i	$0.879211\pi$
$840$		0			0
$841$	3408.13	−	5903.05i	0.139740	−	0.242037i
$842$	8673.70	+	45882.8i	0.355006	+	1.87794i
$843$		0			0
$844$	6338.95	+	16167.0i	0.258526	+	0.659349i
$845$			7813.10i			0.318081i
$846$		0			0
$847$			2262.44i			0.0917807i
$848$	−18117.4	+	4122.67i	−0.733671	+	0.166949i
$849$		0			0
$850$	27850.2	−	5264.81i	1.12383	−	0.212449i
$851$	−7136.22	+	12360.3i	−0.287458	+	0.497892i
$852$		0			0
$853$	305.664	+	529.425i	0.0122693	+	0.0212511i	0.872095	−	0.489337i	$-0.162761\pi$
$853$	305.664	+	529.425i	0.0122693	+	0.0212511i	−0.859826	+	0.510588i	$0.829428\pi$
$854$	3235.78	+	3761.29i	0.129656	+	0.150713i
$855$		0			0
$856$	10627.3	+	16931.7i	0.424337	+	0.676067i
$857$	−36414.7	+	21024.1i	−1.45146	+	0.838003i	−0.998565	−	0.0535593i	$-0.982943\pi$
$857$	−36414.7	+	21024.1i	−1.45146	+	0.838003i	−0.452899	+	0.891562i	$0.649610\pi$
$858$		0			0
$859$	−7116.46	−	4108.69i	−0.282666	−	0.163197i	0.351964	−	0.936014i	$-0.385514\pi$
$859$	−7116.46	−	4108.69i	−0.282666	−	0.163197i	−0.634630	+	0.772816i	$0.718847\pi$
$860$	−2430.74	−	1939.75i	−0.0963808	−	0.0769129i
$861$		0			0
$862$	−24074.8	−	8428.57i	−0.951266	−	0.333038i
$863$	13435.6			0.529956			0.264978	−	0.964254i	$-0.414635\pi$
$863$	13435.6			0.529956			0.264978	+	0.964254i	$0.414635\pi$
$864$		0			0
$865$	−900.328			−0.0353897
$866$	−8299.47	−	2905.64i	−0.325667	−	0.114016i
$867$		0			0
$868$	4388.75	+	3502.27i	0.171617	+	0.136952i
$869$	−42780.2	−	24699.2i	−1.66999	−	0.964167i
$870$		0			0
$871$	−1197.06	+	691.126i	−0.0465683	+	0.0268862i
$872$	−7542.92	−	12017.6i	−0.292931	−	0.466706i
$873$		0			0
$874$	13044.0	+	15162.4i	0.504828	+	0.586815i
$875$	1985.69	+	3439.31i	0.0767183	+	0.132880i
$876$		0			0
$877$	−2392.91	+	4144.64i	−0.0921354	+	0.159583i	−0.908409	−	0.418082i	$-0.862703\pi$
$877$	−2392.91	+	4144.64i	−0.0921354	+	0.159583i	0.816274	+	0.577665i	$0.196036\pi$
$878$	−20510.2	+	3877.26i	−0.788367	+	0.149033i
$879$		0			0
$880$	13765.4	−	3132.37i	0.527310	−	0.119991i
$881$		−	4711.22i		−	0.180165i	−0.995934	−	0.0900823i	$-0.971287\pi$
$881$		−	4711.22i		−	0.180165i	0.995934	−	0.0900823i	$-0.0287130\pi$
$882$		0			0
$883$			41957.5i			1.59907i	0.600617	+	0.799537i	$0.294922\pi$
$883$			41957.5i			1.59907i	−0.600617	+	0.799537i	$0.705078\pi$
$884$	−17913.4	−	45686.7i	−0.681554	−	1.73825i
$885$		0			0
$886$	−1428.34	−	7555.73i	−0.0541602	−	0.286501i
$887$	951.789	−	1648.55i	0.0360292	−	0.0624045i	−0.847449	−	0.530878i	$-0.821862\pi$
$887$	951.789	−	1648.55i	0.0360292	−	0.0624045i	0.883478	+	0.468473i	$0.155196\pi$
$888$		0			0
$889$	85.5006	+	148.091i	0.00322565	+	0.00558698i
$890$	3691.91	−	3176.09i	0.139048	−	0.119621i
$891$		0			0
$892$	13702.9	+	2069.98i	0.514359	+	0.0776998i
$893$	34090.9	−	19682.4i	1.27750	−	0.737565i
$894$		0			0
$895$	−6157.35	−	3554.95i	−0.229964	−	0.132770i
$896$	1334.81	−	4958.81i	0.0497690	−	0.184891i
$897$		0			0
$898$	−10115.1	+	28892.2i	−0.375887	+	1.07366i
$899$	34963.3			1.29710
$900$		0			0
$901$	29009.1			1.07262
$902$	−1831.54	+	5231.48i	−0.0676093	+	0.193115i
$903$		0			0
$904$	568.935	+	15408.0i	0.0209320	+	0.566885i
$905$	8708.52	+	5027.87i	0.319869	+	0.184676i
$906$		0			0
$907$	2730.67	−	1576.55i	0.0999672	−	0.0577161i	−0.449183	−	0.893440i	$-0.648285\pi$
$907$	2730.67	−	1576.55i	0.0999672	−	0.0577161i	0.549150	+	0.835724i	$0.314952\pi$
$908$	3927.60	−	26000.0i	0.143548	−	0.950265i
$909$		0			0
$910$	2320.37	−	1996.18i	0.0845271	−	0.0727173i
$911$	−2770.16	−	4798.05i	−0.100746	−	0.174497i	0.811246	−	0.584704i	$-0.198790\pi$
$911$	−2770.16	−	4798.05i	−0.100746	−	0.174497i	−0.911992	+	0.410208i	$0.865456\pi$
$912$		0			0
$913$	17786.5	−	30807.1i	0.644739	−	1.11672i
$914$	−583.449	−	3086.37i	−0.0211146	−	0.111694i
$915$		0			0
$916$	10252.9	−	4020.08i	0.369831	−	0.145008i
$917$			1406.95i			0.0506670i
$918$		0			0
$919$		−	34750.8i		−	1.24736i	−0.781680	−	0.623679i	$-0.785637\pi$
$919$		−	34750.8i		−	1.24736i	0.781680	−	0.623679i	$-0.214363\pi$
$920$	8212.70	+	4345.71i	0.294309	+	0.155732i
$921$		0			0
$922$	−13763.6	+	2601.87i	−0.491626	+	0.0929371i
$923$	−9341.26	+	16179.5i	−0.333122	+	0.576984i
$924$		0			0
$925$	8663.91	+	15006.3i	0.307965	+	0.533411i
$926$	−19520.1	−	22690.3i	−0.692733	−	0.805238i
$927$		0			0
$928$	−12763.3	−	29319.5i	−0.451484	−	1.03713i
$929$	4915.63	−	2838.04i	0.173602	−	0.100229i	−0.410681	−	0.911779i	$-0.634709\pi$
$929$	4915.63	−	2838.04i	0.173602	−	0.100229i	0.584283	+	0.811550i	$0.301376\pi$
$930$		0			0
$931$	24496.7	+	14143.2i	0.862348	+	0.497877i
$932$	−3224.04	+	4040.10i	−0.113312	+	0.141993i
$933$		0			0
$934$	−30955.8	−	10837.6i	−1.08448	−	0.379676i
$935$	−22040.9			−0.770925
$936$		0			0
$937$	−42080.2			−1.46713			−0.733564	−	0.679620i	$-0.762145\pi$
$937$	−42080.2			−1.46713			−0.733564	+	0.679620i	$0.762145\pi$
$938$	213.148	+	74.6230i	0.00741954	+	0.00259758i
$939$		0			0
$940$	11406.5	−	14293.6i	0.395785	−	0.495965i
$941$	15154.5	+	8749.47i	0.524998	+	0.303108i	0.738977	−	0.673730i	$-0.235309\pi$
$941$	15154.5	+	8749.47i	0.524998	+	0.303108i	−0.213979	+	0.976838i	$0.568642\pi$
$942$		0			0
$943$	−3159.36	+	1824.06i	−0.109102	+	0.0629899i
$944$	18081.2	+	5590.31i	0.623403	+	0.192743i
$945$		0			0
$946$	−6400.65	−	7440.16i	−0.219982	−	0.255709i
$947$	−24011.6	−	41589.3i	−0.823941	−	1.42711i	−0.902726	−	0.430215i	$-0.858438\pi$
$947$	−24011.6	−	41589.3i	−0.823941	−	1.42711i	0.0787856	−	0.996892i	$-0.474896\pi$
$948$		0			0
$949$	35702.5	−	61838.5i	1.22123	−	2.11524i
$950$	23860.3	−	4510.55i	0.814873	−	0.154044i
$951$		0			0
$952$	−3749.86	+	7086.64i	−0.127661	+	0.241260i
$953$		−	26540.6i		−	0.902136i	−0.892490	−	0.451068i	$-0.851043\pi$
$953$		−	26540.6i		−	0.902136i	0.892490	−	0.451068i	$-0.148957\pi$
$954$		0			0
$955$		−	13489.6i		−	0.457082i
$956$	6454.43	−	2530.73i	0.218359	−	0.0856169i
$957$		0			0
$958$	−5626.38	−	29762.9i	−0.189750	−	1.00375i
$959$	−1164.27	+	2016.57i	−0.0392036	+	0.0679026i
$960$		0			0
$961$	4691.47	+	8125.86i	0.157479	+	0.272762i
$962$	22743.1	−	19565.5i	0.762230	−	0.655735i
$963$		0			0
$964$	3194.84	−	21149.3i	0.106741	−	0.706610i
$965$	−3081.82	+	1779.29i	−0.102805	+	0.0593548i
$966$		0			0
$967$	−49733.6	−	28713.7i	−1.65390	−	0.954882i	−0.975445	−	0.220244i	$-0.929315\pi$
$967$	−49733.6	−	28713.7i	−1.65390	−	0.954882i	−0.678460	−	0.734638i	$-0.737352\pi$
$968$	14426.6	−	532.694i	0.479016	−	0.0176874i
$969$		0			0
$970$	−2708.00	+	7734.95i	−0.0896378	+	0.256035i
$971$	−31999.3			−1.05758			−0.528788	−	0.848754i	$-0.677354\pi$
$971$	−31999.3			−1.05758			−0.528788	+	0.848754i	$0.677354\pi$
$972$		0			0
$973$	2058.07			0.0678096
$974$	−14630.9	+	41790.8i	−0.481319	+	1.37481i
$975$		0			0
$976$	23222.2	−	21518.7i	0.761604	−	0.705736i
$977$	−34383.9	−	19851.6i	−1.12594	−	0.650059i	−0.183026	−	0.983108i	$-0.558589\pi$
$977$	−34383.9	−	19851.6i	−1.12594	−	0.650059i	−0.942909	+	0.333049i	$0.891922\pi$
$978$		0			0
$979$	13310.6	−	7684.86i	0.434533	−	0.250878i
$980$	12993.1	+	1962.75i	0.423520	+	0.0639774i
$981$		0			0
$982$	36256.2	−	31190.7i	1.17819	−	1.01358i
$983$	−17766.5	−	30772.5i	−0.576464	−	0.998466i	−0.995881	−	0.0906717i	$-0.971099\pi$
$983$	−17766.5	−	30772.5i	−0.576464	−	0.998466i	0.419416	−	0.907794i	$-0.362235\pi$
$984$		0			0
$985$	−10091.9	+	17479.6i	−0.326451	+	0.565429i
$986$	9273.54	+	49055.9i	0.299523	+	1.58444i
$987$		0			0
$988$	−15347.1	−	39141.4i	−0.494185	−	1.26038i
$989$		−	6459.59i		−	0.207688i
$990$		0			0
$991$			32646.5i			1.04647i	0.852189	+	0.523235i	$0.175275\pi$
$991$			32646.5i			1.04647i	−0.852189	+	0.523235i	$0.824725\pi$
$992$	21299.1	−	28809.7i	0.681700	−	0.922087i
$993$		0			0
$994$	2999.24	−	566.978i	0.0957045	−	0.0180920i
$995$	12628.5	−	21873.1i	0.402361	−	0.696909i
$996$		0			0
$997$	25515.5	+	44194.2i	0.810516	+	1.40386i	0.912503	+	0.409070i	$0.134147\pi$
$997$	25515.5	+	44194.2i	0.810516	+	1.40386i	−0.101987	+	0.994786i	$0.532520\pi$
$998$	−13280.7	−	15437.6i	−0.421236	−	0.489647i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.h.a.71.1		8
3.2	odd	2		36.4.h.a.23.4	yes	8
4.3	odd	2	inner	108.4.h.a.71.2		8
9.2	odd	6	inner	108.4.h.a.35.2		8
9.4	even	3		324.4.b.b.323.7		8
9.5	odd	6		324.4.b.b.323.2		8
9.7	even	3		36.4.h.a.11.3	✓	8
12.11	even	2		36.4.h.a.23.3	yes	8
36.7	odd	6		36.4.h.a.11.4	yes	8
36.11	even	6	inner	108.4.h.a.35.1		8
36.23	even	6		324.4.b.b.323.8		8
36.31	odd	6		324.4.b.b.323.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.a.11.3	✓	8	9.7	even	3
36.4.h.a.11.4	yes	8	36.7	odd	6
36.4.h.a.23.3	yes	8	12.11	even	2
36.4.h.a.23.4	yes	8	3.2	odd	2
108.4.h.a.35.1		8	36.11	even	6	inner
108.4.h.a.35.2		8	9.2	odd	6	inner
108.4.h.a.71.1		8	1.1	even	1	trivial
108.4.h.a.71.2		8	4.3	odd	2	inner
324.4.b.b.323.1		8	36.31	odd	6
324.4.b.b.323.2		8	9.5	odd	6
324.4.b.b.323.7		8	9.4	even	3
324.4.b.b.323.8		8	36.23	even	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.66955 - 0.934608i) q^{2} +(6.25302 + 4.98997i) q^{4} +(-4.30507 - 2.48553i) q^{5} +(3.07102 - 1.77306i) q^{7} +(-12.0291 - 19.1651i) q^{8} +O(q^{10})\)	\(q+(-2.66955 - 0.934608i) q^{2} +(6.25302 + 4.98997i) q^{4} +(-4.30507 - 2.48553i) q^{5} +(3.07102 - 1.77306i) q^{7} +(-12.0291 - 19.1651i) q^{8} +(9.16960 + 10.6588i) q^{10} +(22.1867 + 38.4285i) q^{11} +(30.6949 - 53.1652i) q^{13} +(-9.85537 + 1.86306i) q^{14} +(14.2004 + 62.4047i) q^{16} -99.9210i q^{17} -85.6058i q^{19} +(-14.5169 - 37.0242i) q^{20} +(-23.3130 - 123.323i) q^{22} +(41.3024 - 71.5379i) q^{23} +(-50.1443 - 86.8524i) q^{25} +(-131.630 + 113.239i) q^{26} +(28.0507 + 4.23737i) q^{28} +(152.983 - 88.3250i) q^{29} +(171.407 + 98.9620i) q^{31} +(20.4153 - 179.864i) q^{32} +(-93.3870 + 266.744i) q^{34} -17.6280 q^{35} -172.780 q^{37} +(-80.0079 + 228.529i) q^{38} +(4.15053 + 112.406i) q^{40} +(-38.2467 - 22.0817i) q^{41} +(67.7220 - 39.0993i) q^{43} +(-53.0233 + 351.005i) q^{44} +(-177.119 + 152.373i) q^{46} +(229.919 + 398.231i) q^{47} +(-165.213 + 286.157i) q^{49} +(52.6897 + 278.722i) q^{50} +(457.229 - 179.276i) q^{52} +290.321i q^{53} -220.583i q^{55} +(-70.9224 - 37.5283i) q^{56} +(-490.947 + 92.8087i) q^{58} +(147.857 - 256.096i) q^{59} +(-247.340 - 428.406i) q^{61} +(-365.090 - 424.383i) q^{62} +(-222.602 + 461.077i) q^{64} +(-264.287 + 152.586i) q^{65} +(-19.4994 - 11.2580i) q^{67} +(498.603 - 624.808i) q^{68} +(47.0587 + 16.4752i) q^{70} -304.326 q^{71} +1163.14 q^{73} +(461.244 + 161.481i) q^{74} +(427.171 - 535.295i) q^{76} +(136.272 + 78.6767i) q^{77} +(-964.094 + 556.620i) q^{79} +(93.9752 - 303.952i) q^{80} +(81.4637 + 94.6940i) q^{82} +(-400.836 - 694.268i) q^{83} +(-248.357 + 430.167i) q^{85} +(-217.330 + 41.0841i) q^{86} +(469.601 - 887.471i) q^{88} -346.372i q^{89} -217.695i q^{91} +(615.237 - 241.230i) q^{92} +(-241.590 - 1277.98i) q^{94} +(-212.776 + 368.539i) q^{95} +(291.434 + 504.778i) q^{97} +(708.488 - 609.501i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 11 q^{4} - 66 q^{5}+O(q^{10}) \) 8 * q + 3 * q^2 + 11 * q^4 - 66 * q^5	\( 8 q + 3 q^{2} + 11 q^{4} - 66 q^{5} - 116 q^{10} + 214 q^{13} + 42 q^{14} + 71 q^{16} - 306 q^{20} + 207 q^{22} - 54 q^{25} + 540 q^{28} + 498 q^{29} - 327 q^{32} + 469 q^{34} - 1256 q^{37} - 1035 q^{38} - 602 q^{40} + 1272 q^{41} - 912 q^{46} - 154 q^{49} + 1329 q^{50} - 464 q^{52} + 1314 q^{56} - 830 q^{58} + 262 q^{61} - 550 q^{64} - 3282 q^{65} + 843 q^{68} - 480 q^{70} + 3940 q^{73} - 222 q^{74} + 105 q^{76} - 330 q^{77} + 4786 q^{82} - 472 q^{85} - 1209 q^{86} - 1425 q^{88} + 1308 q^{92} + 1356 q^{94} - 572 q^{97}+O(q^{100}) \) 8 * q + 3 * q^2 + 11 * q^4 - 66 * q^5 - 116 * q^10 + 214 * q^13 + 42 * q^14 + 71 * q^16 - 306 * q^20 + 207 * q^22 - 54 * q^25 + 540 * q^28 + 498 * q^29 - 327 * q^32 + 469 * q^34 - 1256 * q^37 - 1035 * q^38 - 602 * q^40 + 1272 * q^41 - 912 * q^46 - 154 * q^49 + 1329 * q^50 - 464 * q^52 + 1314 * q^56 - 830 * q^58 + 262 * q^61 - 550 * q^64 - 3282 * q^65 + 843 * q^68 - 480 * q^70 + 3940 * q^73 - 222 * q^74 + 105 * q^76 - 330 * q^77 + 4786 * q^82 - 472 * q^85 - 1209 * q^86 - 1425 * q^88 + 1308 * q^92 + 1356 * q^94 - 572 * q^97

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