LMFDB - Embedded newform 108.4.h.a.71.2

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			71.2
Root			$-2.14417 + 1.84460i$ of defining polynomial
Character	$\chi$	$=$	108.71
Dual form			108.4.h.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.525382 + 2.77920i) q^{2} +(-7.44795 - 2.92028i) q^{4} +(-4.30507 - 2.48553i) q^{5} +(-3.07102 + 1.77306i) q^{7} +(12.0291 - 19.1651i) q^{8} +O(q^{10})$	\(q+(-0.525382 + 2.77920i) q^{2} +(-7.44795 - 2.92028i) q^{4} +(-4.30507 - 2.48553i) q^{5} +(-3.07102 + 1.77306i) q^{7} +(12.0291 - 19.1651i) q^{8} +(9.16960 - 10.6588i) q^{10} +(-22.1867 - 38.4285i) q^{11} +(30.6949 - 53.1652i) q^{13} +(-3.31423 - 9.46654i) q^{14} +(46.9439 + 43.5003i) q^{16} -99.9210i q^{17} +85.6058i q^{19} +(24.8055 + 31.0841i) q^{20} +(118.457 - 41.4718i) q^{22} +(-41.3024 + 71.5379i) q^{23} +(-50.1443 - 86.8524i) q^{25} +(131.630 + 113.239i) q^{26} +(28.0507 - 4.23737i) q^{28} +(152.983 - 88.3250i) q^{29} +(-171.407 - 98.9620i) q^{31} +(-145.560 + 107.612i) q^{32} +(277.701 + 52.4967i) q^{34} +17.6280 q^{35} -172.780 q^{37} +(-237.916 - 44.9757i) q^{38} +(-99.4215 + 52.6084i) q^{40} +(-38.2467 - 22.0817i) q^{41} +(-67.7220 + 39.0993i) q^{43} +(53.0233 + 351.005i) q^{44} +(-177.119 - 152.373i) q^{46} +(-229.919 - 398.231i) q^{47} +(-165.213 + 286.157i) q^{49} +(267.725 - 93.7305i) q^{50} +(-383.872 + 306.334i) q^{52} +290.321i q^{53} +220.583i q^{55} +(-2.96079 + 80.1848i) q^{56} +(165.099 + 471.577i) q^{58} +(-147.857 + 256.096i) q^{59} +(-247.340 - 428.406i) q^{61} +(365.090 - 424.383i) q^{62} +(-222.602 - 461.077i) q^{64} +(-264.287 + 152.586i) q^{65} +(19.4994 + 11.2580i) q^{67} +(-291.798 + 744.207i) q^{68} +(-9.26140 + 48.9917i) q^{70} +304.326 q^{71} +1163.14 q^{73} +(90.7753 - 480.190i) q^{74} +(249.993 - 637.588i) q^{76} +(136.272 + 78.6767i) q^{77} +(964.094 - 556.620i) q^{79} +(-93.9752 - 303.952i) q^{80} +(81.4637 - 94.6940i) q^{82} +(400.836 + 694.268i) q^{83} +(-248.357 + 430.167i) q^{85} +(-73.0851 - 208.755i) q^{86} +(-1003.37 - 37.0491i) q^{88} -346.372i q^{89} +217.695i q^{91} +(516.530 - 412.196i) q^{92} +(1227.56 - 429.768i) q^{94} +(212.776 - 368.539i) q^{95} +(291.434 + 504.778i) q^{97} +(-708.488 - 609.501i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.525382	+	2.77920i	−0.185750	+	0.982597i
$2$	−0.525382	+	2.77920i	−0.185750	+	0.982597i
$3$		0			0
$3$		0			0
$4$	−7.44795	−	2.92028i	−0.930994	−	0.365036i
$5$	−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	−0.580613	−	0.814179i	$-0.697187\pi$
$7$	−3.07102	+	1.77306i	−0.165820	+	0.0957361i	0.414794	+	0.909916i	$0.363854\pi$
$8$	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	$-0.958582\pi$
$11$	−22.1867	−	38.4285i	−0.608141	−	1.05333i	0.383406	−	0.923580i	$-0.374751\pi$
$12$		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	$-0.0606078\pi$
$14$	−3.31423	−	9.46654i	−0.0632689	−	0.180717i
$15$		0			0
$16$	46.9439	+	43.5003i	0.733498	+	0.679692i
$17$		−	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	$0.172886\pi$
$19$			85.6058i			1.03365i	−0.856091	+	0.516824i	$0.827114\pi$
$20$	24.8055	+	31.0841i	0.277333	+	0.347531i
$21$		0			0
$22$	118.457	−	41.4718i	1.14796	−	0.401901i
$23$	−41.3024	+	71.5379i	−0.374441	+	0.648552i	−0.990243	−	0.139349i	$-0.955499\pi$
$23$	−41.3024	+	71.5379i	−0.374441	+	0.648552i	0.615802	+	0.787901i	$0.288832\pi$
$24$		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	−0.0868904	−	0.996218i	$-0.527693\pi$
$31$	−171.407	−	98.9620i	−0.993086	−	0.573358i	−0.906195	+	0.422860i	$0.861026\pi$
$32$	−145.560	+	107.612i	−0.804110	+	0.594480i
$33$		0			0
$34$	277.701	+	52.4967i	1.40074	+	0.264797i
$35$	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	$0.625402\pi$
$38$	−237.916	−	44.9757i	−1.01566	−	0.192001i
$39$		0			0
$40$	−99.4215	+	52.6084i	−0.392998	+	0.207953i
$41$	−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	−0.615257	−	0.788327i	$-0.710948\pi$
$43$	−67.7220	+	39.0993i	−0.240175	+	0.138665i	0.375082	+	0.926992i	$0.377614\pi$
$44$	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	$-0.913751\pi$
$47$	−229.919	−	398.231i	−0.713555	−	1.23591i	0.249960	−	0.968256i	$-0.419583\pi$
$48$		0			0
$49$	−165.213	+	286.157i	−0.481669	+	0.834276i
$50$	267.725	−	93.7305i	0.757242	−	0.265110i
$51$		0			0
$52$	−383.872	+	306.334i	−1.02372	+	0.816939i
$53$			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
$56$	−2.96079	+	80.1848i	−0.00706521	+	0.191342i
$57$		0			0
$58$	165.099	+	471.577i	0.373767	+	1.06760i
$59$	−147.857	+	256.096i	−0.326260	+	0.565098i	−0.981766	−	0.190091i	$-0.939122\pi$
$59$	−147.857	+	256.096i	−0.326260	+	0.565098i	0.655507	+	0.755189i	$0.272455\pi$
$60$		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	0.517672	−	0.855579i	$-0.326799\pi$
$67$	19.4994	+	11.2580i	0.0355557	+	0.0205281i	−0.482117	+	0.876107i	$0.660132\pi$
$68$	−291.798	+	744.207i	−0.520378	+	1.32718i
$69$		0			0
$70$	−9.26140	+	48.9917i	−0.0158136	+	0.0836518i
$71$	304.326			0.508688			0.254344	−	0.967114i	$-0.418141\pi$
$71$	304.326			0.508688			0.254344	+	0.967114i	$0.418141\pi$
$72$		0			0
$73$	1163.14			1.86486			0.932432	−	0.361345i	$-0.117682\pi$
$73$	1163.14			1.86486			0.932432	+	0.361345i	$0.117682\pi$
$74$	90.7753	−	480.190i	0.142600	−	0.754337i
$75$		0			0
$76$	249.993	−	637.588i	0.377319	−	0.962320i
$77$	136.272	+	78.6767i	0.201684	+	0.116442i
$78$		0			0
$79$	964.094	−	556.620i	1.37303	−	0.792717i	0.381718	−	0.924279i	$-0.375333\pi$
$79$	964.094	−	556.620i	1.37303	−	0.792717i	0.991308	+	0.131562i	$0.0419993\pi$
$80$	−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	$0.0111751\pi$
$83$	400.836	+	694.268i	0.530090	+	0.918142i	−0.469294	+	0.883042i	$0.655492\pi$
$84$		0			0
$85$	−248.357	+	430.167i	−0.316919	+	0.548919i
$86$	−73.0851	−	208.755i	−0.0916392	−	0.261752i
$87$		0			0
$88$	−1003.37	−	37.0491i	−1.21545	−	0.0448801i
$89$		−	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
$92$	516.530	−	412.196i	0.585347	−	0.467113i
$93$		0			0
$94$	1227.56	−	429.768i	1.34695	−	0.471565i
$95$	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	0.154024	−	0.988067i	$-0.450777\pi$
$103$	−652.974	−	376.995i	−0.624655	−	0.360645i	−0.778679	+	0.627422i	$0.784110\pi$
$104$	−649.684	−	1227.80i	−0.612565	−	1.15765i
$105$		0			0
$106$	−806.860	−	152.529i	−0.739332	−	0.139764i
$107$	883.464			0.798203			0.399102	−	0.916907i	$-0.369322\pi$
$107$	883.464			0.798203			0.399102	+	0.916907i	$0.369322\pi$
$108$		0			0
$109$	627.057			0.551020			0.275510	−	0.961298i	$-0.411153\pi$
$109$	627.057			0.551020			0.275510	+	0.961298i	$0.411153\pi$
$110$	−613.046	−	115.890i	−0.531378	−	0.100452i
$111$		0			0
$112$	−221.294	−	50.3562i	−0.186699	−	0.0424841i
$113$	−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
$122$	1320.58	−	462.332i	0.979994	−	0.343095i
$123$		0			0
$124$	987.635	+	1237.62i	0.715260	+	0.896304i
$125$			1119.92i			0.801352i
$126$		0			0
$127$		−	48.2222i		−	0.0336931i	−0.999858	−	0.0168466i	$-0.994637\pi$
$127$		−	48.2222i		−	0.0336931i	0.999858	−	0.0168466i	$-0.00536268\pi$
$128$	1398.38	−	376.416i	0.965628	−	0.259928i
$129$		0			0
$130$	−285.217	−	814.675i	−0.192425	−	0.549629i
$131$	198.379	−	343.603i	0.132309	−	0.229166i	−0.792257	−	0.610187i	$-0.791094\pi$
$131$	198.379	−	343.603i	0.132309	−	0.229166i	0.924566	+	0.381021i	$0.124428\pi$
$132$		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	0.338748	−	0.940877i	$-0.389997\pi$
$139$	−502.618	−	290.187i	−0.306702	−	0.177074i	−0.645450	+	0.763803i	$0.723330\pi$
$140$	−131.292	−	51.4786i	−0.0792586	−	0.0310767i
$141$		0			0
$142$	−159.887	+	845.783i	−0.0944890	+	0.499835i
$143$	−2724.08			−1.59300
$144$		0			0
$145$	−878.139			−0.502934
$146$	−611.092	+	3232.60i	−0.346399	+	1.83241i
$147$		0			0
$148$	1286.85	+	504.566i	0.714722	+	0.280237i
$149$	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	−0.0664908	−	0.997787i	$-0.521180\pi$
$151$	1418.31	−	818.861i	0.764373	−	0.441311i	0.830864	+	0.556476i	$0.187847\pi$
$152$	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	$0.128849\pi$
$158$	1040.44	+	2971.85i	0.523881	+	1.49638i
$159$		0			0
$160$	894.117	−	101.486i	0.441789	−	0.0501446i
$161$		−	292.926i		−	0.143390i
$162$		0			0
$163$			3587.04i			1.72367i	0.507185	+	0.861837i	$0.330686\pi$
$163$			3587.04i			1.72367i	−0.507185	+	0.861837i	$0.669314\pi$
$164$	220.374	+	276.155i	0.104929	+	0.131488i
$165$		0			0
$166$	−2140.10	+	749.249i	−1.00063	+	0.350319i
$167$	682.164	−	1181.54i	0.316092	−	0.547488i	−0.663577	−	0.748108i	$-0.730962\pi$
$167$	682.164	−	1181.54i	0.316092	−	0.547488i	0.979669	+	0.200620i	$0.0642958\pi$
$168$		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
$176$	630.121	−	2769.11i	0.269870	−	1.18596i
$177$		0			0
$178$	962.638	+	181.977i	0.405353	+	0.0766280i
$179$	−1430.26			−0.597220			−0.298610	−	0.954375i	$-0.596523\pi$
$179$	−1430.26			−0.597220			−0.298610	+	0.954375i	$0.596523\pi$
$180$		0			0
$181$	−2022.85			−0.830705			−0.415352	−	0.909661i	$-0.636342\pi$
$181$	−2022.85			−0.830705			−0.415352	+	0.909661i	$0.636342\pi$
$182$	−605.020	−	114.373i	−0.246412	−	0.0465819i
$183$		0			0
$184$	874.201	+	1652.10i	0.350255	+	0.661927i
$185$	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	$-0.994827\pi$
$191$	−1356.81	−	2350.07i	−0.514008	−	0.890288i	0.485860	−	0.874037i	$-0.338506\pi$
$192$		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	$0.124047\pi$
$194$	−1556.00	+	544.753i	−0.575845	+	0.201603i
$195$		0			0
$196$	2066.15	−	1648.81i	0.752971	−	0.600879i
$197$		−	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	$-0.639913\pi$
$199$		−	5080.79i		−	1.80989i	0.425532	−	0.904944i	$-0.360087\pi$
$200$	−2267.73	−	83.7347i	−0.801762	−	0.0296047i
$201$		0			0
$202$	−66.4737	−	189.871i	−0.0231538	−	0.0661350i
$203$	−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	0.160933	−	0.986965i	$-0.448550\pi$
$211$	−1879.85	−	1085.33i	−0.613337	−	0.354110i	−0.774270	+	0.632855i	$0.781883\pi$
$212$	847.819	−	2162.29i	0.274663	−	0.700504i
$213$		0			0
$214$	−464.156	+	2455.33i	−0.148267	+	0.784312i
$215$	388.731			0.123308
$216$		0			0
$217$	701.861			0.219564
$218$	−329.444	+	1742.72i	−0.102352	+	0.541431i
$219$		0			0
$220$	644.166	−	1642.89i	0.197408	−	0.503472i
$221$	−5312.32	−	3067.07i	−1.61695	−	0.933545i
$222$		0			0
$223$	−1500.22	+	866.150i	−0.450502	+	0.260097i	−0.708042	−	0.706170i	$-0.750421\pi$
$223$	−1500.22	+	866.150i	−0.450502	+	0.260097i	0.257540	+	0.966268i	$0.417088\pi$
$224$	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	0.999750	−	0.0223459i	$-0.00711350\pi$
$227$	1643.44	+	2846.52i	0.480523	+	0.832290i	−0.519227	+	0.854636i	$0.673780\pi$
$228$		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	$0.103020\pi$
$230$	383.782	+	1096.21i	0.110025	+	0.314269i
$231$		0			0
$232$	147.492	−	3994.41i	0.0417384	−	1.13037i
$233$			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
$236$	1849.10	−	1475.60i	0.510027	−	0.407007i
$237$		0			0
$238$	−945.906	+	331.161i	−0.257622	+	0.0901932i
$239$	−433.303	+	750.502i	−0.117272	+	0.203121i	−0.918686	−	0.394989i	$-0.870748\pi$
$239$	−433.303	+	750.502i	−0.117272	+	0.203121i	0.801414	+	0.598110i	$0.204082\pi$
$240$		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
$248$	−3958.49	+	2094.62i	−1.01357	+	0.536324i
$249$		0			0
$250$	−3112.50	−	588.387i	−0.787406	−	0.148851i
$251$	4161.12			1.04641			0.523203	−	0.852208i	$-0.324737\pi$
$251$	4161.12			1.04641			0.523203	+	0.852208i	$0.324737\pi$
$252$		0			0
$253$	3665.46			0.910853
$254$	134.019	+	25.3350i	0.0331067	+	0.00625851i
$255$		0			0
$256$	311.455	+	4084.14i	0.0760387	+	0.997105i
$257$	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	$-0.785397\pi$
$263$	−3971.86	−	6879.47i	−0.931238	−	1.61295i	−0.150028	−	0.988682i	$-0.547936\pi$
$264$		0			0
$265$	721.601	−	1249.85i	0.167274	−	0.289727i
$266$	810.391	−	283.717i	0.186798	−	0.0653978i
$267$		0			0
$268$	−112.354	−	140.793i	−0.0256086	−	0.0320906i
$269$			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	$-0.846772\pi$
$271$		−	4131.13i		−	0.926007i	0.886356	−	0.463004i	$-0.153228\pi$
$272$	4346.59	−	4690.68i	0.968937	−	1.04564i
$273$		0			0
$274$	−613.706	−	1752.95i	−0.135312	−	0.386495i
$275$	−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	$0.0196219\pi$
$283$	7381.63	+	4261.78i	1.55050	+	0.895183i	0.552402	+	0.833578i	$0.313711\pi$
$284$	−2266.60	−	888.718i	−0.473585	−	0.185689i
$285$		0			0
$286$	1431.18	−	7570.78i	0.295901	−	1.56528i
$287$	156.609			0.0322102
$288$		0			0
$289$	−5071.21			−1.03220
$290$	461.358	−	2440.53i	0.0934202	−	0.494182i
$291$		0			0
$292$	−8663.00	−	3396.70i	−1.73618	−	0.680742i
$293$	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
$302$	1530.63	+	4371.98i	0.291648	+	0.833044i
$303$		0			0
$304$	−3723.88	+	4018.67i	−0.702562	+	0.758179i
$305$			2459.09i			0.461662i
$306$		0			0
$307$		−	4979.02i		−	0.925628i	−0.886456	−	0.462814i	$-0.846840\pi$
$307$		−	4979.02i		−	0.925628i	0.886456	−	0.462814i	$-0.153160\pi$
$308$	−785.189	−	983.933i	−0.145261	−	0.182029i
$309$		0			0
$310$	−2626.55	+	919.554i	−0.481220	+	0.168475i
$311$	829.382	−	1436.53i	0.151222	−	0.261924i	−0.780455	−	0.625212i	$-0.785013\pi$
$311$	829.382	−	1436.53i	0.151222	−	0.261924i	0.931677	+	0.363288i	$0.118346\pi$
$312$		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
$320$	−187.704	+	2538.25i	−0.0327905	+	0.443415i
$321$		0			0
$322$	814.102	+	153.898i	0.140895	+	0.0266348i
$323$	8553.82			1.47352
$324$		0			0
$325$	−6156.70			−1.05081
$326$	−9969.12	−	1884.57i	−1.69368	−	0.320173i
$327$		0			0
$328$	−883.271	+	467.379i	−0.148690	+	0.0786789i
$329$	1412.17	+	815.317i	0.236643	+	0.136626i
$330$		0			0
$331$	−4097.97	+	2365.96i	−0.680497	+	0.392885i	−0.800042	−	0.599943i	$-0.795190\pi$
$331$	−4097.97	+	2365.96i	−0.680497	+	0.392885i	0.119545	+	0.992829i	$0.461856\pi$
$332$	−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	$0.251959\pi$
$338$	4195.78	−	1468.94i	0.675208	−	0.236390i
$339$		0			0
$340$	3105.96	−	2478.59i	0.495424	−	0.395354i
$341$			8782.58i			1.39473i
$342$		0			0
$343$		−	2388.04i		−	0.375925i
$344$	−65.2911	+	1768.23i	−0.0102333	+	0.277141i
$345$		0			0
$346$	169.270	+	483.492i	0.0263007	+	0.0751235i
$347$	−1878.44	+	3253.55i	−0.290604	+	0.503342i	−0.973953	−	0.226751i	$-0.927190\pi$
$347$	−1878.44	+	3253.55i	−0.290604	+	0.503342i	0.683348	+	0.730092i	$0.260523\pi$
$348$		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
$356$	−1011.50	+	2579.76i	−0.150589	+	0.384065i
$357$		0			0
$358$	751.430	−	3974.97i	0.110934	−	0.586827i
$359$	−2282.01			−0.335487			−0.167744	−	0.985831i	$-0.553648\pi$
$359$	−2282.01			−0.335487			−0.167744	+	0.985831i	$0.553648\pi$
$360$		0			0
$361$	−469.360			−0.0684298
$362$	1062.77	−	5621.92i	0.154304	−	0.816248i
$363$		0			0
$364$	635.733	−	1621.38i	0.0915424	−	0.233472i
$365$	−5007.39	−	2891.02i	−0.718079	−	0.414583i
$366$		0			0
$367$	9728.22	−	5616.59i	1.38368	−	0.798866i	0.391083	−	0.920355i	$-0.372101\pi$
$367$	9728.22	−	5616.59i	1.38368	−	0.798866i	0.992593	+	0.121490i	$0.0387672\pi$
$368$	−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	$0.122468\pi$
$374$	−4143.90	−	11836.4i	−0.572931	−	1.63648i
$375$		0			0
$376$	−10397.8	−	383.936i	−1.42614	−	0.0526595i
$377$		−	10844.5i		−	1.48149i
$378$		0			0
$379$			7704.47i			1.04420i	0.852884	+	0.522101i	$0.174851\pi$
$379$			7704.47i			1.04420i	−0.852884	+	0.522101i	$0.825149\pi$
$380$	−2660.98	+	2123.49i	−0.359225	+	0.286665i
$381$		0			0
$382$	7244.16	−	2536.18i	0.970271	−	0.339691i
$383$	3270.48	−	5664.65i	0.436329	−	0.755744i	−0.561074	−	0.827766i	$-0.689612\pi$
$383$	3270.48	−	5664.65i	0.436329	−	0.755744i	0.997403	+	0.0720217i	$0.0229451\pi$
$384$		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
$392$	3496.86	+	6608.52i	0.450557	+	0.851481i
$393$		0			0
$394$	11284.3	+	2133.18i	1.44287	+	0.272761i
$395$	−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	$0.389255\pi$
$398$	14120.5	+	2669.35i	1.77839	+	0.336187i
$399$		0			0
$400$	1424.14	−	6258.48i	0.178017	−	0.782310i
$401$	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	$-0.143349\pi$
$410$	−586.072	+	205.183i	−0.0705951	+	0.0247153i
$411$		0			0
$412$	3762.39	+	4714.71i	0.449902	+	0.563779i
$413$		−	1048.63i		−	0.124939i
$414$		0			0
$415$		−	3985.16i		−	0.471383i
$416$	1253.29	+	11041.9i	0.147711	+	1.30137i
$417$		0			0
$418$	3550.23	+	10140.6i	0.415424	+	1.18659i
$419$	621.302	−	1076.13i	0.0724406	−	0.125471i	−0.827530	−	0.561422i	$-0.810255\pi$
$419$	621.302	−	1076.13i	0.0724406	−	0.125471i	0.899970	+	0.435951i	$0.143588\pi$
$420$		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
$428$	−6580.00	−	2579.97i	−0.743122	−	0.291373i
$429$		0			0
$430$	−204.232	+	1080.36i	−0.0229045	+	0.121162i
$431$	−9018.30			−1.00788			−0.503940	−	0.863739i	$-0.668117\pi$
$431$	−9018.30			−1.00788			−0.503940	+	0.863739i	$0.668117\pi$
$432$		0			0
$433$	3108.94			0.345048			0.172524	−	0.985005i	$-0.444808\pi$
$433$	3108.94			0.345048			0.172524	+	0.985005i	$0.444808\pi$
$434$	−368.745	+	1950.62i	−0.0407842	+	0.215743i
$435$		0			0
$436$	−4670.29	−	1831.19i	−0.512996	−	0.201142i
$437$	−6124.06	−	3535.73i	−0.670375	−	0.387041i
$438$		0			0
$439$	−6391.17	+	3689.94i	−0.694838	+	0.401165i	−0.805422	−	0.592702i	$-0.798061\pi$
$439$	−6391.17	+	3689.94i	−0.694838	+	0.401165i	0.110584	+	0.993867i	$0.464728\pi$
$440$	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	0.783879	−	0.620914i	$-0.213238\pi$
$443$	−1359.33	−	2354.44i	−0.145788	−	0.252512i	−0.929667	+	0.368402i	$0.879905\pi$
$444$		0			0
$445$	−860.918	+	1491.15i	−0.0917111	+	0.158848i
$446$	−1619.02	−	4624.47i	−0.171890	−	0.490975i
$447$		0			0
$448$	1501.13	+	1021.29i	0.158308	+	0.107704i
$449$		−	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
$452$	3400.21	+	4260.86i	0.353833	+	0.443394i
$453$		0			0
$454$	−8774.48	+	3071.94i	−0.907063	+	0.317562i
$455$	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	−0.0362966	−	0.999341i	$-0.511556\pi$
$463$	−9164.57	−	5291.16i	−0.919900	−	0.531104i	−0.883603	+	0.468237i	$0.844889\pi$
$464$	11023.8	+	2508.50i	1.10295	+	0.250979i
$465$		0			0
$466$	−1795.66	−	339.451i	−0.178502	−	0.0337442i
$467$	−11595.9			−1.14902			−0.574511	−	0.818497i	$-0.694808\pi$
$467$	−11595.9			−1.14902			−0.574511	+	0.818497i	$0.694808\pi$
$468$		0			0
$469$	−79.8441			−0.00786111
$470$	−6352.92	−	1200.96i	−0.623486	−	0.117864i
$471$		0			0
$472$	3129.52	+	5914.29i	0.305186	+	0.576752i
$473$	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	$-0.996029\pi$
$479$	−5354.57	−	9274.39i	−0.510765	−	0.884671i	0.489157	−	0.872196i	$-0.337304\pi$
$480$		0			0
$481$	−5303.46	+	9185.87i	−0.502738	+	0.870768i
$482$	7137.45	−	2498.82i	0.674486	−	0.236137i
$483$		0			0
$484$	3989.45	−	3183.62i	0.374667	−	0.298988i
$485$		−	2897.47i		−	0.271273i
$486$		0			0
$487$			15654.6i			1.45663i	0.685243	+	0.728314i	$0.259696\pi$
$487$			15654.6i			1.45663i	−0.685243	+	0.728314i	$0.740304\pi$
$488$	−11185.7	−	413.028i	−1.03761	−	0.0383133i
$489$		0			0
$490$	1535.15	+	4384.91i	0.141533	+	0.404265i
$491$	8454.61	−	14643.8i	0.777090	−	1.34596i	−0.156523	−	0.987674i	$-0.550028\pi$
$491$	8454.61	−	14643.8i	0.777090	−	1.34596i	0.933613	−	0.358284i	$-0.116638\pi$
$492$		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	0.193522	−	0.981096i	$-0.438009\pi$
$499$	−6235.20	−	3599.90i	−0.559371	−	0.322953i	−0.752893	+	0.658143i	$0.771342\pi$
$500$	3270.50	−	8341.13i	0.292522	−	0.746054i
$501$		0			0
$502$	−2186.18	+	11564.6i	−0.194370	+	1.02820i
$503$	747.770			0.0662852			0.0331426	−	0.999451i	$-0.489448\pi$
$503$	747.770			0.0662852			0.0331426	+	0.999451i	$0.489448\pi$
$504$		0			0
$505$	353.565			0.0311553
$506$	−1925.77	+	10187.1i	−0.169191	+	0.895001i
$507$		0			0
$508$	−140.822	+	359.156i	−0.0122992	+	0.0313681i
$509$	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
$518$	572.631	+	1635.63i	0.0485714	+	0.138736i
$519$		0			0
$520$	−254.800	+	6900.57i	−0.0214880	+	0.581942i
$521$			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	$-0.882949\pi$
$523$		−	8599.53i		−	0.718989i	0.933147	−	0.359495i	$-0.117051\pi$
$524$	−2480.94	+	1979.81i	−0.206833	+	0.165054i
$525$		0			0
$526$	21206.2	−	7424.27i	1.75786	−	0.615425i
$527$	−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
$536$	450.320	−	238.285i	0.0362889	−	0.0192021i
$537$		0			0
$538$	−8870.72	−	1676.92i	−0.710862	−	0.134382i
$539$	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	$0.558240\pi$
$542$	11481.2	+	2170.42i	0.909892	+	0.172006i
$543$		0			0
$544$	10752.7	+	14544.5i	0.847463	+	1.14630i
$545$	−2699.52	−	1558.57i	−0.212174	−	0.122499i
$546$		0			0
$547$	8822.88	−	5093.89i	0.689651	−	0.398170i	−0.113830	−	0.993500i	$-0.536312\pi$
$547$	8822.88	−	5093.89i	0.689651	−	0.398170i	0.803481	+	0.595330i	$0.202979\pi$
$548$	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
$554$	−20749.0	+	7264.20i	−1.59123	+	0.557088i
$555$		0			0
$556$	2896.05	+	3629.08i	0.220899	+	0.276812i
$557$			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
$560$	827.524	+	766.821i	0.0624452	+	0.0578644i
$561$		0			0
$562$	−7941.97	−	22684.9i	−0.596107	−	1.70268i
$563$	−4860.90	+	8419.32i	−0.363876	+	0.630252i	−0.988595	−	0.150598i	$-0.951880\pi$
$563$	−4860.90	+	8419.32i	−0.363876	+	0.630252i	0.624719	+	0.780850i	$0.285214\pi$
$564$		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	0.358207	−	0.933642i	$-0.383388\pi$
$571$	−3701.00	−	2136.77i	−0.271247	−	0.156605i	−0.629454	+	0.777038i	$0.716722\pi$
$572$	20288.8	+	7955.09i	1.48307	+	0.581502i
$573$		0			0
$574$	−82.2793	+	435.247i	−0.00598305	+	0.0316496i
$575$	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	$0.427321\pi$
$578$	2664.32	−	14093.9i	0.191732	−	1.01424i
$579$		0			0
$580$	6540.33	+	2564.42i	0.468228	+	0.183589i
$581$	−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	0.906550	−	0.422099i	$-0.138707\pi$
$587$	1247.63	+	2160.97i	0.0877263	+	0.151946i	−0.818823	+	0.574046i	$0.805373\pi$
$588$		0			0
$589$	8471.73	−	14673.5i	0.592651	−	1.02650i
$590$	1373.88	+	3924.27i	0.0958677	+	0.273830i
$591$		0			0
$592$	−8110.95	−	7515.96i	−0.563105	−	0.521798i
$593$		−	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
$596$	−7737.11	−	9695.50i	−0.531752	−	0.666348i
$597$		0			0
$598$	−13537.6	+	4739.49i	−0.925740	+	0.324101i
$599$	11725.3	−	20308.7i	0.799801	−	1.38530i	−0.119944	−	0.992781i	$-0.538271\pi$
$599$	11725.3	−	20308.7i	0.799801	−	1.38530i	0.919745	−	0.392516i	$-0.128395\pi$
$600$		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	0.826643	−	0.562726i	$-0.190248\pi$
$607$	11255.5	+	6498.36i	0.752630	+	0.434531i	−0.0740137	+	0.997257i	$0.523581\pi$
$608$	−9212.25	−	12460.7i	−0.614483	−	0.831168i
$609$		0			0
$610$	−6834.31	−	1291.96i	−0.453628	−	0.0857539i
$611$	−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	$0.369110\pi$
$614$	13837.7	+	2615.88i	0.909519	+	0.171936i
$615$		0			0
$616$	3147.07	−	1665.26i	0.205843	−	0.108921i
$617$	−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	0.0850450	−	0.996377i	$-0.472897\pi$
$619$	15253.5	−	8806.64i	0.990455	−	0.571840i	0.905410	+	0.424537i	$0.139563\pi$
$620$	−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
$626$	−15922.7	+	5574.52i	−1.01661	+	0.355915i
$627$		0			0
$628$	−2916.01	+	2327.01i	−0.185289	+	0.147863i
$629$			17264.3i			1.09439i
$630$		0			0
$631$			12601.8i			0.795041i	0.917593	+	0.397521i	$0.130129\pi$
$631$			12601.8i			0.795041i	−0.917593	+	0.397521i	$0.869871\pi$
$632$	929.486	−	25172.6i	0.0585016	−	1.58435i
$633$		0			0
$634$	−3596.06	−	10271.5i	−0.225265	−	0.643431i
$635$	−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	−0.00580579	−	0.999983i	$-0.501848\pi$
$643$	−14262.2	−	8234.26i	−0.874719	−	0.505020i	−0.868914	+	0.494964i	$0.835181\pi$
$644$	−855.428	+	2181.70i	−0.0523425	+	0.133495i
$645$		0			0
$646$	−4494.02	+	23772.8i	−0.273707	+	1.44788i
$647$	31904.7			1.93864			0.969321	−	0.245797i	$-0.0790498\pi$
$647$	31904.7			1.93864			0.969321	+	0.245797i	$0.0790498\pi$
$648$		0			0
$649$	13121.8			0.793648
$650$	3234.62	−	17110.7i	0.195188	−	1.03252i
$651$		0			0
$652$	10475.2	−	26716.1i	0.629202	−	1.60473i
$653$	−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	$-0.848802\pi$
$659$	−14222.5	−	24634.1i	−0.840715	−	1.45616i	0.0485770	−	0.998819i	$-0.484531\pi$
$660$		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	$0.0831205\pi$
$662$	−4422.50	−	12632.1i	−0.259645	−	0.741633i
$663$		0			0
$664$	18127.4	+	669.346i	1.05946	+	0.0391200i
$665$			1509.06i			0.0879980i
$666$		0			0
$667$			14592.2i			0.847092i
$668$	−8531.16	+	6807.95i	−0.494132	+	0.394323i
$669$		0			0
$670$	298.798	−	104.609i	0.0172292	−	0.00603194i
$671$	−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
$680$	5256.68	+	9934.29i	0.296448	+	0.560239i
$681$		0			0
$682$	−24408.6	−	4614.20i	−1.37046	−	0.259072i
$683$	30770.7			1.72388			0.861938	−	0.507014i	$-0.169251\pi$
$683$	30770.7			1.72388			0.861938	+	0.507014i	$0.169251\pi$
$684$		0			0
$685$	3264.23			0.182073
$686$	6636.86	+	1254.63i	0.369382	+	0.0698282i
$687$		0			0
$688$	−4879.97	−	1110.45i	−0.270417	−	0.0615343i
$689$	15435.0	+	8911.37i	0.853447	+	0.492738i
$690$		0			0
$691$	16101.2	−	9296.02i	0.886422	−	0.511776i	0.0136514	−	0.999907i	$-0.495654\pi$
$691$	16101.2	−	9296.02i	0.886422	−	0.511776i	0.872770	+	0.488131i	$0.162321\pi$
$692$	−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
$698$	−12850.5	+	4498.97i	−0.696849	+	0.243966i
$699$		0			0
$700$	−1774.61	−	2223.79i	−0.0958197	−	0.120073i
$701$		−	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
$704$	−12779.7	+	18784.1i	−0.684167	+	1.00561i
$705$		0			0
$706$	2725.31	+	7784.38i	0.145281	+	0.414970i
$707$	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
$716$	10652.5	+	4176.76i	0.556008	+	0.218007i
$717$		0			0
$718$	1198.93	−	6342.17i	0.0623169	−	0.329649i
$719$	−11526.9			−0.597885			−0.298943	−	0.954271i	$-0.596634\pi$
$719$	−11526.9			−0.597885			−0.298943	+	0.954271i	$0.596634\pi$
$720$		0			0
$721$	2673.73			0.138107
$722$	246.593	−	1304.45i	0.0127109	−	0.0672389i
$723$		0			0
$724$	15066.1	+	5907.31i	0.773381	+	0.303237i
$725$	−15342.5	−	8857.99i	−0.785939	−	0.453762i
$726$		0			0
$727$	−20341.7	+	11744.3i	−1.03773	+	0.599135i	−0.919190	−	0.393814i	$-0.871156\pi$
$727$	−20341.7	+	11744.3i	−1.03773	+	0.599135i	−0.118543	+	0.992949i	$0.537822\pi$
$728$	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	$0.314865\pi$
$734$	10498.6	+	29987.6i	0.527945	+	1.50799i
$735$		0			0
$736$	−1686.40	−	14857.7i	−0.0844586	−	0.744105i
$737$		−	999.111i		−	0.0499358i
$738$		0			0
$739$		−	29721.7i		−	1.47947i	−0.672896	−	0.739737i	$-0.734950\pi$
$739$		−	29721.7i		−	1.47947i	0.672896	−	0.739737i	$-0.265050\pi$
$740$	−4285.88	−	5370.71i	−0.212908	−	0.266799i
$741$		0			0
$742$	2748.33	−	962.189i	0.135976	−	0.0476052i
$743$	−11863.8	+	20548.7i	−0.585788	+	1.01461i	0.408989	+	0.912540i	$0.365882\pi$
$743$	−11863.8	+	20548.7i	−0.585788	+	1.01461i	−0.994777	+	0.102075i	$0.967452\pi$
$744$		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	0.241910	−	0.970299i	$-0.422226\pi$
$751$	−9826.00	−	5673.05i	−0.477438	−	0.275649i	−0.719348	+	0.694650i	$0.755559\pi$
$752$	6529.87	−	28696.0i	0.316649	−	1.39154i
$753$		0			0
$754$	30139.1	+	5697.51i	1.45571	+	0.275187i
$755$	−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	$0.634796\pi$
$758$	−21412.3	−	4047.79i	−1.02603	−	0.193961i
$759$		0			0
$760$	−4503.59	−	8511.06i	−0.214950	−	0.406222i
$761$	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	$0.0963414\pi$
$770$	2088.16	−	731.063i	0.0977299	−	0.0342152i
$771$		0			0
$772$	−4476.28	+	3572.11i	−0.208685	+	0.166533i
$773$			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
$776$	13179.8	+	486.659i	0.609701	+	0.0225129i
$777$		0			0
$778$	13111.1	+	37449.5i	0.604182	+	1.72575i
$779$	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	0.702311	−	0.711870i	$-0.252151\pi$
$787$	9647.46	+	5569.96i	0.436969	+	0.252284i	−0.265342	+	0.964154i	$0.585485\pi$
$788$	−11857.1	+	30240.5i	−0.536029	+	1.36710i
$789$		0			0
$790$	2907.45	−	15380.1i	0.130940	−	0.692656i
$791$	2416.36			0.108617
$792$		0			0
$793$	−30368.4			−1.35991
$794$	−2833.80	+	14990.5i	−0.126660	+	0.670014i
$795$		0			0
$796$	−14837.3	+	37841.5i	−0.660673	+	1.68499i
$797$	−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
$806$	−11356.0	−	32436.5i	−0.496275	−	1.41753i
$807$		0			0
$808$	−59.3847	+	1608.27i	−0.00258558	+	0.0700232i
$809$		−	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	$0.0203942\pi$
$811$			2957.47i			0.128053i	−0.997948	+	0.0640264i	$0.979606\pi$
$812$	3917.02	−	3125.82i	0.169286	−	0.135092i
$813$		0			0
$814$	−20467.0	+	7165.49i	−0.881288	+	0.308538i
$815$	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	0.614933	−	0.788579i	$-0.289183\pi$
$823$	5653.95	+	3264.31i	0.239471	+	0.138258i	−0.375463	+	0.926837i	$0.622516\pi$
$824$	−15079.8	+	7979.42i	−0.637537	+	0.337350i
$825$		0			0
$826$	2914.37	+	550.933i	0.122765	+	0.0232075i
$827$	−28855.8			−1.21332			−0.606659	−	0.794962i	$-0.707491\pi$
$827$	−28855.8			−1.21332			−0.606659	+	0.794962i	$0.707491\pi$
$828$		0			0
$829$	−6475.24			−0.271284			−0.135642	−	0.990758i	$-0.543310\pi$
$829$	−6475.24			−0.271284			−0.135642	+	0.990758i	$0.543310\pi$
$830$	11075.6	+	2093.73i	0.463179	+	0.0875595i
$831$		0			0
$832$	−31346.0	−	2318.04i	−1.30616	−	0.0965907i
$833$	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	0.928862	−	0.370427i	$-0.120789\pi$
$839$	3490.55	+	6045.81i	0.143632	+	0.248778i	−0.785230	+	0.619205i	$0.787455\pi$
$840$		0			0
$841$	3408.13	−	5903.05i	0.139740	−	0.242037i
$842$	44072.5	−	15429.8i	1.80385	−	0.631525i
$843$		0			0
$844$	10831.5	+	13573.2i	0.441750	+	0.553564i
$845$			7813.10i			0.318081i
$846$		0			0
$847$		−	2262.44i		−	0.0917807i
$848$	−12629.0	+	13628.8i	−0.511418	+	0.551903i
$849$		0			0
$850$	−9365.65	−	26751.4i	−0.377928	−	1.07949i
$851$	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	0.634630	−	0.772816i	$-0.281153\pi$
$859$	7116.46	+	4108.69i	0.282666	+	0.163197i	−0.351964	+	0.936014i	$0.614486\pi$
$860$	−2895.24	−	1135.20i	−0.114799	−	0.0450118i
$861$		0			0
$862$	4738.05	−	25063.7i	0.187214	−	0.990339i
$863$	−13435.6			−0.529956			−0.264978	−	0.964254i	$-0.585365\pi$
$863$	−13435.6			−0.529956			−0.264978	+	0.964254i	$0.585365\pi$
$864$		0			0
$865$	−900.328			−0.0353897
$866$	−1633.38	+	8640.37i	−0.0640929	+	0.339044i
$867$		0			0
$868$	−5227.43	−	2049.63i	−0.204413	−	0.0801488i
$869$	−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	$0.196036\pi$
$878$	−6897.31	−	19701.0i	−0.265117	−	0.757263i
$879$		0			0
$880$	−9595.43	+	10355.0i	−0.367570	+	0.396668i
$881$		−	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	$-0.705078\pi$
$883$		−	41957.5i		−	1.59907i	0.600617	−	0.799537i	$-0.294922\pi$
$884$	30609.2	+	38356.9i	1.16459	+	1.45937i
$885$		0			0
$886$	7257.62	−	2540.89i	0.275197	−	0.0963463i
$887$	−951.789	+	1648.55i	−0.0360292	+	0.0624045i	−0.883478	−	0.468473i	$-0.844804\pi$
$887$	−951.789	+	1648.55i	−0.0360292	+	0.0624045i	0.847449	+	0.530878i	$0.178138\pi$
$888$		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
$896$	−3627.05	+	3635.39i	−0.135236	+	0.135547i
$897$		0			0
$898$	30078.9	+	5686.13i	1.11776	+	0.211301i
$899$	−34963.3			−1.29710
$900$		0			0
$901$	29009.1			1.07262
$902$	−5446.37	−	1029.58i	−0.201047	−	0.0380059i
$903$		0			0
$904$	−13628.2	+	7211.31i	−0.501402	+	0.265315i
$905$	8708.52	+	5027.87i	0.319869	+	0.184676i
$906$		0			0
$907$	−2730.67	+	1576.55i	−0.0999672	+	0.0577161i	−0.549150	−	0.835724i	$-0.685048\pi$
$907$	−2730.67	+	1576.55i	−0.0999672	+	0.0577161i	0.449183	+	0.893440i	$0.351715\pi$
$908$	−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	0.911992	−	0.410208i	$-0.134544\pi$
$911$	2770.16	+	4798.05i	0.100746	+	0.174497i	−0.811246	+	0.584704i	$0.801210\pi$
$912$		0			0
$913$	17786.5	−	30807.1i	0.644739	−	1.11672i
$914$	−2964.60	+	1037.91i	−0.107287	+	0.0375611i
$915$		0			0
$916$	−8607.94	+	6869.22i	−0.310496	+	0.247779i
$917$			1406.95i			0.0506670i
$918$		0			0
$919$			34750.8i			1.24736i	0.781680	+	0.623679i	$0.214363\pi$
$919$			34750.8i			1.24736i	−0.781680	+	0.623679i	$0.785637\pi$
$920$	342.854	−	9285.26i	0.0122865	−	0.332746i
$921$		0			0
$922$	4628.50	+	13220.5i	0.165327	+	0.472229i
$923$	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
$932$	1886.81	−	4812.15i	0.0663138	−	0.169128i
$933$		0			0
$934$	6092.26	−	32227.3i	0.213431	−	1.12903i
$935$	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	$0.762145\pi$
$938$	41.9486	−	221.903i	0.00146020	−	0.00772430i
$939$		0			0
$940$	6675.42	−	17025.1i	0.231626	−	0.590742i
$941$	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	$0.141562\pi$
$947$	24011.6	+	41589.3i	0.823941	+	1.42711i	−0.0787856	+	0.996892i	$0.525104\pi$
$948$		0			0
$949$	35702.5	−	61838.5i	1.22123	−	2.11524i
$950$	8023.88	+	22918.9i	0.274030	+	0.782722i
$951$		0			0
$952$	8012.14	+	295.845i	0.272768	+	0.0100718i
$953$		−	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
$956$	5418.90	−	4324.33i	0.183326	−	0.146296i
$957$		0			0
$958$	28588.6	−	10008.8i	0.964150	−	0.337548i
$959$	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	$0.0706855\pi$
$967$	49733.6	+	28713.7i	1.65390	+	0.954882i	0.678460	+	0.734638i	$0.262648\pi$
$968$	6751.95	+	12760.1i	0.224190	+	0.423683i
$969$		0			0
$970$	8052.67	+	1522.28i	0.266552	+	0.0503891i
$971$	31999.3			1.05758			0.528788	−	0.848754i	$-0.322646\pi$
$971$	31999.3			1.05758			0.528788	+	0.848754i	$0.322646\pi$
$972$		0			0
$973$	2058.07			0.0678096
$974$	−43507.3	−	8224.64i	−1.43128	−	0.270569i
$975$		0			0
$976$	7024.66	−	30870.4i	0.230383	−	1.01244i
$977$	−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	$0.0289014\pi$
$983$	17766.5	+	30772.5i	0.576464	+	0.998466i	−0.419416	+	0.907794i	$0.637765\pi$
$984$		0			0
$985$	−10091.9	+	17479.6i	−0.326451	+	0.565429i
$986$	47120.4	−	16496.8i	1.52193	−	0.532825i
$987$		0			0
$988$	−26223.9	−	32861.7i	−0.844428	−	1.05817i
$989$		−	6459.59i		−	0.207688i
$990$		0			0
$991$		−	32646.5i		−	1.04647i	−0.852189	−	0.523235i	$-0.824725\pi$
$991$		−	32646.5i		−	1.04647i	0.852189	−	0.523235i	$-0.175275\pi$
$992$	35599.5	−	4040.67i	1.13940	−	0.129326i
$993$		0			0
$994$	−1008.60	−	2880.91i	−0.0321841	−	0.0919285i
$995$	−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.71.2		8
3.2	odd	2		36.4.h.a.23.3	yes	8
4.3	odd	2	inner	108.4.h.a.71.1		8
9.2	odd	6	inner	108.4.h.a.35.1		8
9.4	even	3		324.4.b.b.323.1		8
9.5	odd	6		324.4.b.b.323.8		8
9.7	even	3		36.4.h.a.11.4	yes	8
12.11	even	2		36.4.h.a.23.4	yes	8
36.7	odd	6		36.4.h.a.11.3	✓	8
36.11	even	6	inner	108.4.h.a.35.2		8
36.23	even	6		324.4.b.b.323.2		8
36.31	odd	6		324.4.b.b.323.7		8

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

\(f(q)\)	\(=\)	\(q+(-0.525382 + 2.77920i) q^{2} +(-7.44795 - 2.92028i) q^{4} +(-4.30507 - 2.48553i) q^{5} +(-3.07102 + 1.77306i) q^{7} +(12.0291 - 19.1651i) q^{8} +O(q^{10})\)	\(q+(-0.525382 + 2.77920i) q^{2} +(-7.44795 - 2.92028i) q^{4} +(-4.30507 - 2.48553i) q^{5} +(-3.07102 + 1.77306i) q^{7} +(12.0291 - 19.1651i) q^{8} +(9.16960 - 10.6588i) q^{10} +(-22.1867 - 38.4285i) q^{11} +(30.6949 - 53.1652i) q^{13} +(-3.31423 - 9.46654i) q^{14} +(46.9439 + 43.5003i) q^{16} -99.9210i q^{17} +85.6058i q^{19} +(24.8055 + 31.0841i) q^{20} +(118.457 - 41.4718i) q^{22} +(-41.3024 + 71.5379i) q^{23} +(-50.1443 - 86.8524i) q^{25} +(131.630 + 113.239i) q^{26} +(28.0507 - 4.23737i) q^{28} +(152.983 - 88.3250i) q^{29} +(-171.407 - 98.9620i) q^{31} +(-145.560 + 107.612i) q^{32} +(277.701 + 52.4967i) q^{34} +17.6280 q^{35} -172.780 q^{37} +(-237.916 - 44.9757i) q^{38} +(-99.4215 + 52.6084i) q^{40} +(-38.2467 - 22.0817i) q^{41} +(-67.7220 + 39.0993i) q^{43} +(53.0233 + 351.005i) q^{44} +(-177.119 - 152.373i) q^{46} +(-229.919 - 398.231i) q^{47} +(-165.213 + 286.157i) q^{49} +(267.725 - 93.7305i) q^{50} +(-383.872 + 306.334i) q^{52} +290.321i q^{53} +220.583i q^{55} +(-2.96079 + 80.1848i) q^{56} +(165.099 + 471.577i) q^{58} +(-147.857 + 256.096i) q^{59} +(-247.340 - 428.406i) q^{61} +(365.090 - 424.383i) q^{62} +(-222.602 - 461.077i) q^{64} +(-264.287 + 152.586i) q^{65} +(19.4994 + 11.2580i) q^{67} +(-291.798 + 744.207i) q^{68} +(-9.26140 + 48.9917i) q^{70} +304.326 q^{71} +1163.14 q^{73} +(90.7753 - 480.190i) q^{74} +(249.993 - 637.588i) q^{76} +(136.272 + 78.6767i) q^{77} +(964.094 - 556.620i) q^{79} +(-93.9752 - 303.952i) q^{80} +(81.4637 - 94.6940i) q^{82} +(400.836 + 694.268i) q^{83} +(-248.357 + 430.167i) q^{85} +(-73.0851 - 208.755i) q^{86} +(-1003.37 - 37.0491i) q^{88} -346.372i q^{89} +217.695i q^{91} +(516.530 - 412.196i) q^{92} +(1227.56 - 429.768i) q^{94} +(212.776 - 368.539i) q^{95} +(291.434 + 504.778i) q^{97} +(-708.488 - 609.501i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 11 q^{4} - 66 q^{5}+O(q^{10}) \) 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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