LMFDB - Embedded newform 108.4.h.b.35.4

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.4
Character	$\chi$	$=$	108.35
Dual form			108.4.h.b.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44536 + 2.43124i) q^{2} +(-3.82189 - 7.02803i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(3.08966 + 1.78382i) q^{7} +(22.6108 + 0.866066i) q^{8} +O(q^{10})$	\(q+(-1.44536 + 2.43124i) q^{2} +(-3.82189 - 7.02803i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(3.08966 + 1.78382i) q^{7} +(22.6108 + 0.866066i) q^{8} +(0.610574 - 47.8425i) q^{10} +(25.0688 - 43.4205i) q^{11} +(-18.9966 - 32.9032i) q^{13} +(-8.80255 + 4.93346i) q^{14} +(-34.7863 + 53.7207i) q^{16} -84.3819i q^{17} -62.9237i q^{19} +(115.434 + 70.6340i) q^{20} +(69.3323 + 123.706i) q^{22} +(37.6066 + 65.1366i) q^{23} +(80.5801 - 139.569i) q^{25} +(107.453 + 1.37133i) q^{26} +(0.728372 - 28.5317i) q^{28} +(-105.644 - 60.9938i) q^{29} +(17.2800 - 9.97659i) q^{31} +(-80.3294 - 162.220i) q^{32} +(205.153 + 121.962i) q^{34} -60.3510 q^{35} +17.7622 q^{37} +(152.983 + 90.9472i) q^{38} +(-338.572 + 178.558i) q^{40} +(-299.072 + 172.670i) q^{41} +(-113.206 - 65.3596i) q^{43} +(-400.970 - 10.2362i) q^{44} +(-212.718 - 2.71474i) q^{46} +(-153.083 + 265.147i) q^{47} +(-165.136 - 286.024i) q^{49} +(222.859 + 397.636i) q^{50} +(-158.641 + 259.261i) q^{52} -479.464i q^{53} +848.142i q^{55} +(68.3149 + 43.0094i) q^{56} +(300.984 - 168.689i) q^{58} +(-245.774 - 425.693i) q^{59} +(-49.9168 + 86.4585i) q^{61} +(-0.720188 + 56.4315i) q^{62} +(510.500 + 39.1649i) q^{64} +(556.599 + 321.352i) q^{65} +(536.669 - 309.846i) q^{67} +(-593.039 + 322.498i) q^{68} +(87.2287 - 146.728i) q^{70} +254.455 q^{71} +100.485 q^{73} +(-25.6727 + 43.1841i) q^{74} +(-442.230 + 240.488i) q^{76} +(154.908 - 89.4363i) q^{77} +(-856.295 - 494.382i) q^{79} +(55.2404 - 1081.23i) q^{80} +(12.4646 - 976.687i) q^{82} +(251.755 - 436.053i) q^{83} +(713.714 + 1236.19i) q^{85} +(322.528 - 180.764i) q^{86} +(604.432 - 960.062i) q^{88} +1019.86i q^{89} -135.546i q^{91} +(314.053 - 513.245i) q^{92} +(-423.378 - 755.413i) q^{94} +(532.217 + 921.828i) q^{95} +(-503.589 + 872.242i) q^{97} +(934.074 + 11.9208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) $ 24 * q - 12 * q^4 + 72 * q^5	$ 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.44536	+	2.43124i	−0.511011	+	0.859574i
$2$	−1.44536	+	2.43124i	−0.511011	+	0.859574i
$3$		0			0
$3$		0			0
$4$	−3.82189	−	7.02803i	−0.477736	−	0.878503i
$5$	−14.6499	+	8.45813i	−1.31033	+	0.756519i	−0.982150	−	0.188097i	$-0.939768\pi$
$5$	−14.6499	+	8.45813i	−1.31033	+	0.756519i	−0.328178	+	0.944616i	$0.606435\pi$
$6$		0			0
$7$	3.08966	+	1.78382i	0.166826	+	0.0963170i	0.581088	−	0.813841i	$-0.302627\pi$
$7$	3.08966	+	1.78382i	0.166826	+	0.0963170i	−0.414262	+	0.910157i	$0.635960\pi$
$8$	22.6108	+	0.866066i	0.999267	+	0.0382750i
$9$		0			0
$10$	0.610574	−	47.8425i	0.0193080	−	1.51291i
$11$	25.0688	−	43.4205i	0.687139	−	1.19016i	−0.285620	−	0.958343i	$-0.592199\pi$
$11$	25.0688	−	43.4205i	0.687139	−	1.19016i	0.972759	−	0.231817i	$-0.0744672\pi$
$12$		0			0
$13$	−18.9966	−	32.9032i	−0.405286	−	0.701977i	0.589068	−	0.808083i	$-0.299495\pi$
$13$	−18.9966	−	32.9032i	−0.405286	−	0.701977i	−0.994355	+	0.106107i	$0.966162\pi$
$14$	−8.80255	+	4.93346i	−0.168041	+	0.0941802i
$15$		0			0
$16$	−34.7863	+	53.7207i	−0.543537	+	0.839386i
$17$		−	84.3819i		−	1.20386i	−0.798549	−	0.601930i	$-0.794399\pi$
$17$		−	84.3819i		−	1.20386i	0.798549	−	0.601930i	$-0.205601\pi$
$18$		0			0
$19$		−	62.9237i		−	0.759773i	−0.925033	−	0.379887i	$-0.875963\pi$
$19$		−	62.9237i		−	0.759773i	0.925033	−	0.379887i	$-0.124037\pi$
$20$	115.434	+	70.6340i	1.29060	+	0.789712i
$21$		0			0
$22$	69.3323	+	123.706i	0.671896	+	1.19883i
$23$	37.6066	+	65.1366i	0.340936	+	0.590518i	0.984607	−	0.174784i	$-0.0559227\pi$
$23$	37.6066	+	65.1366i	0.340936	+	0.590518i	−0.643671	+	0.765302i	$0.722589\pi$
$24$		0			0
$25$	80.5801	−	139.569i	0.644641	−	1.11655i
$26$	107.453	+	1.37133i	0.810507	+	0.0103438i
$27$		0			0
$28$	0.728372	−	28.5317i	0.00491605	−	0.192571i
$29$	−105.644	−	60.9938i	−0.676471	−	0.390561i	0.122053	−	0.992524i	$-0.461052\pi$
$29$	−105.644	−	60.9938i	−0.676471	−	0.390561i	−0.798524	+	0.601963i	$0.794386\pi$
$30$		0			0
$31$	17.2800	−	9.97659i	0.100115	−	0.0578016i	−0.449106	−	0.893478i	$-0.648258\pi$
$31$	17.2800	−	9.97659i	0.100115	−	0.0578016i	0.549222	+	0.835677i	$0.314924\pi$
$32$	−80.3294	−	162.220i	−0.443761	−	0.896145i
$33$		0			0
$34$	205.153	+	121.962i	1.03481	+	0.615186i
$35$	−60.3510			−0.291462
$36$		0			0
$37$	17.7622			0.0789211			0.0394606	−	0.999221i	$-0.487436\pi$
$37$	17.7622			0.0789211			0.0394606	+	0.999221i	$0.487436\pi$
$38$	152.983	+	90.9472i	0.653082	+	0.388252i
$39$		0			0
$40$	−338.572	+	178.558i	−1.33832	+	0.705811i
$41$	−299.072	+	172.670i	−1.13920	+	0.657718i	−0.946233	−	0.323486i	$-0.895145\pi$
$41$	−299.072	+	172.670i	−1.13920	+	0.657718i	−0.192969	+	0.981205i	$0.561812\pi$
$42$		0			0
$43$	−113.206	−	65.3596i	−0.401483	−	0.231796i	0.285641	−	0.958337i	$-0.407794\pi$
$43$	−113.206	−	65.3596i	−0.401483	−	0.231796i	−0.687124	+	0.726540i	$0.741127\pi$
$44$	−400.970	−	10.2362i	−1.37383	−	0.0350718i
$45$		0			0
$46$	−212.718	−	2.71474i	−0.681816	−	0.00870145i
$47$	−153.083	+	265.147i	−0.475094	+	0.822887i	−0.999593	−	0.0285243i	$-0.990919\pi$
$47$	−153.083	+	265.147i	−0.475094	+	0.822887i	0.524499	+	0.851411i	$0.324253\pi$
$48$		0			0
$49$	−165.136	−	286.024i	−0.481446	−	0.833889i
$50$	222.859	+	397.636i	0.630340	+	1.12469i
$51$		0			0
$52$	−158.641	+	259.261i	−0.423069	+	0.691405i
$53$		−	479.464i		−	1.24263i	−0.783561	−	0.621315i	$-0.786599\pi$
$53$		−	479.464i		−	1.24263i	0.783561	−	0.621315i	$-0.213401\pi$
$54$		0			0
$55$			848.142i			2.07933i
$56$	68.3149	+	43.0094i	0.163017	+	0.102632i
$57$		0			0
$58$	300.984	−	168.689i	0.681400	−	0.381896i
$59$	−245.774	−	425.693i	−0.542323	−	0.939330i	−0.998770	−	0.0495801i	$-0.984212\pi$
$59$	−245.774	−	425.693i	−0.542323	−	0.939330i	0.456447	−	0.889750i	$-0.349122\pi$
$60$		0			0
$61$	−49.9168	+	86.4585i	−0.104774	+	0.181473i	−0.913646	−	0.406511i	$-0.866745\pi$
$61$	−49.9168	+	86.4585i	−0.104774	+	0.181473i	0.808872	+	0.587985i	$0.200079\pi$
$62$	−0.720188	+	56.4315i	−0.00147523	+	0.115594i
$63$		0			0
$64$	510.500	+	39.1649i	0.997070	+	0.0764940i
$65$	556.599	+	321.352i	1.06212	+	0.613213i
$66$		0			0
$67$	536.669	−	309.846i	0.978575	−	0.564980i	0.0767351	−	0.997052i	$-0.475550\pi$
$67$	536.669	−	309.846i	0.978575	−	0.564980i	0.901839	+	0.432071i	$0.142217\pi$
$68$	−593.039	+	322.498i	−1.05760	+	0.575127i
$69$		0			0
$70$	87.2287	−	146.728i	0.148940	−	0.250534i
$71$	254.455			0.425327			0.212663	−	0.977125i	$-0.431786\pi$
$71$	254.455			0.425327			0.212663	+	0.977125i	$0.431786\pi$
$72$		0			0
$73$	100.485			0.161108			0.0805541	−	0.996750i	$-0.474331\pi$
$73$	100.485			0.161108			0.0805541	+	0.996750i	$0.474331\pi$
$74$	−25.6727	+	43.1841i	−0.0403295	+	0.0678386i
$75$		0			0
$76$	−442.230	+	240.488i	−0.667464	+	0.362971i
$77$	154.908	−	89.4363i	0.229265	−	0.132366i
$78$		0			0
$79$	−856.295	−	494.382i	−1.21950	−	0.704080i	−0.254691	−	0.967022i	$-0.581974\pi$
$79$	−856.295	−	494.382i	−1.21950	−	0.704080i	−0.964812	+	0.262942i	$0.915307\pi$
$80$	55.2404	−	1081.23i	0.0772008	−	1.51107i
$81$		0			0
$82$	12.4646	−	976.687i	0.0167864	−	1.31533i
$83$	251.755	−	436.053i	0.332936	−	0.576663i	−0.650150	−	0.759806i	$-0.725294\pi$
$83$	251.755	−	436.053i	0.332936	−	0.576663i	0.983086	+	0.183143i	$0.0586272\pi$
$84$		0			0
$85$	713.714	+	1236.19i	0.910743	+	1.57745i
$86$	322.528	−	180.764i	0.404408	−	0.226654i
$87$		0			0
$88$	604.432	−	960.062i	0.732189	−	1.16299i
$89$			1019.86i			1.21467i	0.794448	+	0.607333i	$0.207761\pi$
$89$			1019.86i			1.21467i	−0.794448	+	0.607333i	$0.792239\pi$
$90$		0			0
$91$		−	135.546i		−	0.156144i
$92$	314.053	−	513.245i	0.355895	−	0.581625i
$93$		0			0
$94$	−423.378	−	755.413i	−0.464554	−	0.828882i
$95$	532.217	+	921.828i	0.574783	+	0.995553i
$96$		0			0
$97$	−503.589	+	872.242i	−0.527131	+	0.913018i	0.472369	+	0.881401i	$0.343399\pi$
$97$	−503.589	+	872.242i	−0.527131	+	0.913018i	−0.999500	+	0.0316171i	$0.989934\pi$
$98$	934.074	+	11.9208i	0.962814	+	0.0122876i
$99$		0			0
$100$	−1288.86	−	32.9027i	−1.28886	−	0.0329027i
$101$	364.582	+	210.492i	0.359181	+	0.207373i	0.668721	−	0.743513i	$-0.266842\pi$
$101$	364.582	+	210.492i	0.359181	+	0.207373i	−0.309540	+	0.950886i	$0.600175\pi$
$102$		0			0
$103$	1496.60	−	864.065i	1.43170	−	0.826591i	0.434447	−	0.900697i	$-0.356944\pi$
$103$	1496.60	−	864.065i	1.43170	−	0.826591i	0.997250	+	0.0741066i	$0.0236105\pi$
$104$	−401.034	−	760.420i	−0.378121	−	0.716975i
$105$		0			0
$106$	1165.69	+	692.996i	1.06813	+	0.634998i
$107$	63.1607			0.0570652			0.0285326	−	0.999593i	$-0.490917\pi$
$107$	63.1607			0.0570652			0.0285326	+	0.999593i	$0.490917\pi$
$108$		0			0
$109$	−835.373			−0.734076			−0.367038	−	0.930206i	$-0.619628\pi$
$109$	−835.373			−0.734076			−0.367038	+	0.930206i	$0.619628\pi$
$110$	−2062.04	−	1225.87i	−1.78734	−	1.06256i
$111$		0			0
$112$	−203.306	+	103.926i	−0.171523	+	0.0876794i
$113$	891.915	−	514.947i	0.742516	−	0.428692i	−0.0804674	−	0.996757i	$-0.525641\pi$
$113$	891.915	−	514.947i	0.742516	−	0.428692i	0.822983	+	0.568065i	$0.192308\pi$
$114$		0			0
$115$	−1101.87	−	636.164i	−0.893476	−	0.515849i
$116$	−24.9051	+	975.583i	−0.0199343	+	0.780867i
$117$		0			0
$118$	1390.19	+	17.7419i	1.08456	+	0.0138413i
$119$	150.522	−	260.711i	0.115952	−	0.200835i
$120$		0			0
$121$	−591.391	−	1024.32i	−0.444321	−	0.769587i
$122$	−138.054	−	246.323i	−0.102449	−	0.182796i
$123$		0			0
$124$	−136.158	−	83.3146i	−0.0986075	−	0.0603377i
$125$			611.695i			0.437693i
$126$		0			0
$127$			794.523i			0.555138i	0.960706	+	0.277569i	$0.0895287\pi$
$127$			794.523i			0.555138i	−0.960706	+	0.277569i	$0.910471\pi$
$128$	−833.074	+	1184.54i	−0.575266	+	0.817967i
$129$		0			0
$130$	−1585.77	+	888.758i	−1.06986	+	0.599610i
$131$	−111.039	−	192.325i	−0.0740575	−	0.128271i	0.826619	−	0.562763i	$-0.190262\pi$
$131$	−111.039	−	192.325i	−0.0740575	−	0.128271i	−0.900676	+	0.434491i	$0.856928\pi$
$132$		0			0
$133$	112.244	−	194.413i	0.0731791	−	0.126750i
$134$	−22.3671	+	1752.61i	−0.0144196	+	1.12987i
$135$		0			0
$136$	73.0803	−	1907.95i	0.0460778	−	1.20298i
$137$	−1054.28	−	608.690i	−0.657470	−	0.379591i	0.133842	−	0.991003i	$-0.457268\pi$
$137$	−1054.28	−	608.690i	−0.657470	−	0.379591i	−0.791312	+	0.611412i	$0.790602\pi$
$138$		0			0
$139$	−1909.09	+	1102.21i	−1.16494	+	0.672578i	−0.952483	−	0.304592i	$-0.901480\pi$
$139$	−1909.09	+	1102.21i	−1.16494	+	0.672578i	−0.212457	+	0.977170i	$0.568146\pi$
$140$	230.655	+	424.148i	0.139242	+	0.256051i
$141$		0			0
$142$	−367.778	+	618.641i	−0.217347	+	0.365600i
$143$	−1904.89			−1.11395
$144$		0			0
$145$	2063.57			1.18187
$146$	−145.237	+	244.304i	−0.0823280	+	0.138485i
$147$		0			0
$148$	−67.8850	−	124.833i	−0.0377035	−	0.0693325i
$149$	352.120	−	203.297i	0.193603	−	0.111777i	−0.400065	−	0.916487i	$-0.631013\pi$
$149$	352.120	−	203.297i	0.193603	−	0.111777i	0.593668	+	0.804710i	$0.297679\pi$
$150$		0			0
$151$	2990.17	+	1726.37i	1.61150	+	0.930399i	0.989023	+	0.147759i	$0.0472060\pi$
$151$	2990.17	+	1726.37i	1.61150	+	0.930399i	0.622475	+	0.782640i	$0.286127\pi$
$152$	54.4961	−	1422.76i	0.0290804	−	0.759217i
$153$		0			0
$154$	−6.45621	+	505.887i	−0.00337829	+	0.264711i
$155$	−168.767	+	292.312i	−0.0874559	+	0.151478i
$156$		0			0
$157$	440.287	+	762.599i	0.223813	+	0.387656i	0.955963	−	0.293488i	$-0.0948160\pi$
$157$	440.287	+	762.599i	0.223813	+	0.387656i	−0.732149	+	0.681144i	$0.761483\pi$
$158$	2439.62	−	1367.30i	1.22839	−	0.688461i
$159$		0			0
$160$	2548.89	+	1697.07i	1.25942	+	0.838531i
$161$			268.333i			0.131352i
$162$		0			0
$163$			1693.56i			0.813802i	0.913472	+	0.406901i	$0.133391\pi$
$163$			1693.56i			0.813802i	−0.913472	+	0.406901i	$0.866609\pi$
$164$	2356.55	+	1441.97i	1.12205	+	0.686577i
$165$		0			0
$166$	696.274	+	1242.33i	0.325550	+	0.580864i
$167$	−820.051	−	1420.37i	−0.379985	−	0.658153i	0.611075	−	0.791573i	$-0.290737\pi$
$167$	−820.051	−	1420.37i	−0.379985	−	0.658153i	−0.991060	+	0.133420i	$0.957404\pi$
$168$		0			0
$169$	376.755	−	652.558i	0.171486	−	0.297022i
$170$	−4037.05	−	51.5214i	−1.82134	−	0.0232442i
$171$		0			0
$172$	−26.6878	+	1045.41i	−0.0118310	+	0.463442i
$173$	−1889.17	−	1090.71i	−0.830234	−	0.479336i	0.0236985	−	0.999719i	$-0.492456\pi$
$173$	−1889.17	−	1090.71i	−0.830234	−	0.479336i	−0.853933	+	0.520383i	$0.825789\pi$
$174$		0			0
$175$	497.930	−	287.480i	0.215085	−	0.124180i
$176$	1460.52	+	2857.15i	0.625518	+	1.22367i
$177$		0			0
$178$	−2479.53	−	1474.07i	−1.04410	−	0.620707i
$179$	2350.24			0.981370			0.490685	−	0.871337i	$-0.336747\pi$
$179$	2350.24			0.981370			0.490685	+	0.871337i	$0.336747\pi$
$180$		0			0
$181$	−2280.14			−0.936362			−0.468181	−	0.883633i	$-0.655090\pi$
$181$	−2280.14			−0.936362			−0.468181	+	0.883633i	$0.655090\pi$
$182$	329.545	+	195.912i	0.134217	+	0.0797912i
$183$		0			0
$184$	793.905	+	1505.36i	0.318084	+	0.603135i
$185$	−260.214	+	150.235i	−0.103413	+	0.0597053i
$186$		0			0
$187$	−3663.90	−	2115.36i	−1.43279	−	0.827220i
$188$	2448.53	+	62.5071i	0.949878	+	0.0242489i
$189$		0			0
$190$	−3010.43	−	38.4196i	−1.14947	−	0.0146697i
$191$	−1966.48	+	3406.04i	−0.744970	+	1.29033i	0.205239	+	0.978712i	$0.434203\pi$
$191$	−1966.48	+	3406.04i	−0.744970	+	1.29033i	−0.950209	+	0.311614i	$0.899130\pi$
$192$		0			0
$193$	−1356.60	−	2349.69i	−0.505958	−	0.876346i	−0.999976	−	0.00689392i	$-0.997806\pi$
$193$	−1356.60	−	2349.69i	−0.505958	−	0.876346i	0.494018	−	0.869452i	$-0.335528\pi$
$194$	−1392.77	−	2485.05i	−0.515437	−	0.919671i
$195$		0			0
$196$	−1379.05	+	2253.73i	−0.502570	+	0.821331i
$197$		−	1997.91i		−	0.722565i	−0.932456	−	0.361282i	$-0.882339\pi$
$197$		−	1997.91i		−	0.722565i	0.932456	−	0.361282i	$-0.117661\pi$
$198$		0			0
$199$		−	2409.09i		−	0.858170i	−0.903264	−	0.429085i	$-0.858836\pi$
$199$		−	2409.09i		−	0.858170i	0.903264	−	0.429085i	$-0.141164\pi$
$200$	1942.86	−	3085.98i	0.686904	−	1.09106i
$201$		0			0
$202$	−1038.71	+	582.153i	−0.361798	+	0.202773i
$203$	−217.603	−	376.900i	−0.0752353	−	0.130311i
$204$		0			0
$205$	2920.92	−	5059.19i	0.995152	−	1.72365i
$206$	−62.3750	+	4887.49i	−0.0210965	+	1.65305i
$207$		0			0
$208$	2428.40	+	124.068i	0.809517	+	0.0413584i
$209$	−2732.18	−	1577.42i	−0.904252	−	0.522070i
$210$		0			0
$211$	1575.68	−	909.717i	0.514095	−	0.296813i	−0.220420	−	0.975405i	$-0.570743\pi$
$211$	1575.68	−	909.717i	0.514095	−	0.296813i	0.734515	+	0.678592i	$0.237410\pi$
$212$	−3369.69	+	1832.46i	−1.09166	+	0.593650i
$213$		0			0
$214$	−91.2897	+	153.559i	−0.0291609	+	0.0490518i
$215$	2211.28			0.701433
$216$		0			0
$217$	71.1856			0.0222691
$218$	1207.41	−	2031.00i	0.375120	−	0.630992i
$219$		0			0
$220$	5960.76	−	3241.50i	1.82670	−	0.993373i
$221$	−2776.43	+	1602.97i	−0.845082	+	0.487908i
$222$		0			0
$223$	2316.13	+	1337.22i	0.695514	+	0.401555i	0.805674	−	0.592359i	$-0.201803\pi$
$223$	2316.13	+	1337.22i	0.695514	+	0.401555i	−0.110160	+	0.993914i	$0.535136\pi$
$224$	41.1795	−	644.496i	0.0122831	−	0.192242i
$225$		0			0
$226$	−37.1729	+	2912.74i	−0.0109412	+	0.857314i
$227$	2949.58	−	5108.82i	0.862425	−	1.49376i	−0.00715576	−	0.999974i	$-0.502278\pi$
$227$	2949.58	−	5108.82i	0.862425	−	1.49376i	0.869581	−	0.493790i	$-0.164389\pi$
$228$		0			0
$229$	−1516.38	−	2626.44i	−0.437576	−	0.757904i	0.559926	−	0.828543i	$-0.310830\pi$
$229$	−1516.38	−	2626.44i	−0.437576	−	0.757904i	−0.997502	+	0.0706386i	$0.977496\pi$
$230$	3139.26	−	1759.43i	0.899986	−	0.504405i
$231$		0			0
$232$	−2335.88	−	1470.62i	−0.661027	−	0.416167i
$233$		−	1294.13i		−	0.363867i	−0.983311	−	0.181934i	$-0.941764\pi$
$233$		−	1294.13i		−	0.363867i	0.983311	−	0.181934i	$-0.0582356\pi$
$234$		0			0
$235$		−	5179.18i		−	1.43767i
$236$	−2052.46	+	3354.26i	−0.566118	+	0.925184i
$237$		0			0
$238$	416.295	+	742.776i	0.113380	+	0.202298i
$239$	2875.14	+	4979.89i	0.778149	+	1.34779i	0.933008	+	0.359856i	$0.117174\pi$
$239$	2875.14	+	4979.89i	0.778149	+	1.34779i	−0.154859	+	0.987937i	$0.549492\pi$
$240$		0			0
$241$	−3008.82	+	5211.43i	−0.804212	+	1.39294i	0.112611	+	0.993639i	$0.464079\pi$
$241$	−3008.82	+	5211.43i	−0.804212	+	1.39294i	−0.916822	+	0.399296i	$0.869255\pi$
$242$	3345.14	+	42.6912i	0.888570	+	0.0113401i
$243$		0			0
$244$	798.409	+	20.3822i	0.209479	+	0.00534769i
$245$	4838.46	+	2793.49i	1.26171	+	0.728446i
$246$		0			0
$247$	−2070.39	+	1195.34i	−0.533343	+	0.307926i
$248$	399.355	−	210.613i	0.102254	−	0.0539273i
$249$		0			0
$250$	−1487.18	−	884.117i	−0.376230	−	0.223666i
$251$	−3207.28			−0.806541			−0.403270	−	0.915081i	$-0.632127\pi$
$251$	−3207.28			−0.806541			−0.403270	+	0.915081i	$0.632127\pi$
$252$		0			0
$253$	3771.02			0.937082
$254$	−1931.68	−	1148.37i	−0.477182	−	0.283681i
$255$		0			0
$256$	−1675.82	−	3737.49i	−0.409136	−	0.912473i
$257$	2518.27	−	1453.92i	0.611226	−	0.352892i	−0.162219	−	0.986755i	$-0.551865\pi$
$257$	2518.27	−	1453.92i	0.611226	−	0.352892i	0.773445	+	0.633863i	$0.218532\pi$
$258$		0			0
$259$	54.8790	+	31.6844i	0.0131661	+	0.00760144i
$260$	131.215	−	5139.96i	0.0312986	−	1.22603i
$261$		0			0
$262$	628.081	+	8.01567i	0.148103	+	0.00189011i
$263$	−156.053	+	270.292i	−0.0365880	+	0.0633723i	−0.883740	−	0.467979i	$-0.844982\pi$
$263$	−156.053	+	270.292i	−0.0365880	+	0.0633723i	0.847152	+	0.531351i	$0.178316\pi$
$264$		0			0
$265$	4055.37	+	7024.11i	0.940073	+	1.62825i
$266$	310.432	+	553.889i	0.0715556	+	0.127673i
$267$		0			0
$268$	−4228.69	−	2587.53i	−0.963838	−	0.589770i
$269$			1826.27i			0.413939i	0.978347	+	0.206969i	$0.0663600\pi$
$269$			1826.27i			0.413939i	−0.978347	+	0.206969i	$0.933640\pi$
$270$		0			0
$271$			4987.26i			1.11791i	0.829197	+	0.558956i	$0.188798\pi$
$271$			4987.26i			1.11791i	−0.829197	+	0.558956i	$0.811202\pi$
$272$	4533.05	+	2935.34i	1.01050	+	0.654342i
$273$		0			0
$274$	3003.69	−	1683.44i	0.662261	−	0.371170i
$275$	−4040.09	−	6997.65i	−0.885916	−	1.53445i
$276$		0			0
$277$	−2125.92	+	3682.20i	−0.461134	+	0.798708i	−0.999018	−	0.0443112i	$-0.985891\pi$
$277$	−2125.92	+	3682.20i	−0.461134	+	0.798708i	0.537884	+	0.843019i	$0.319224\pi$
$278$	79.5662	−	6234.54i	0.0171657	−	1.34505i
$279$		0			0
$280$	−1364.59	−	52.2679i	−0.291249	−	0.0111557i
$281$	2541.67	+	1467.43i	0.539585	+	0.311529i	0.744911	−	0.667164i	$-0.232492\pi$
$281$	2541.67	+	1467.43i	0.539585	+	0.311529i	−0.205326	+	0.978694i	$0.565825\pi$
$282$		0			0
$283$	−3467.24	+	2001.81i	−0.728289	+	0.420478i	−0.817796	−	0.575508i	$-0.804804\pi$
$283$	−3467.24	+	2001.81i	−0.728289	+	0.420478i	0.0895066	+	0.995986i	$0.471471\pi$
$284$	−972.497	−	1788.31i	−0.203194	−	0.373651i
$285$		0			0
$286$	2753.25	−	4631.26i	0.569242	−	0.957525i
$287$	−1232.04			−0.253398
$288$		0			0
$289$	−2207.31			−0.449280
$290$	−2982.60	+	5017.05i	−0.603946	+	1.01590i
$291$		0			0
$292$	−384.043	−	706.213i	−0.0769672	−	0.141534i
$293$	−2334.26	+	1347.69i	−0.465423	+	0.268712i	−0.714322	−	0.699817i	$-0.753265\pi$
$293$	−2334.26	+	1347.69i	−0.465423	+	0.268712i	0.248899	+	0.968530i	$0.419931\pi$
$294$		0			0
$295$	7201.14	+	4157.58i	1.42124	+	0.820554i
$296$	401.617	+	15.3832i	0.0788633	+	0.00302071i
$297$		0			0
$298$	−14.6755	+	1149.93i	−0.00285279	+	0.223535i
$299$	1428.80	−	2474.75i	0.276353	−	0.478658i
$300$		0			0
$301$	−233.179	−	403.878i	−0.0446518	−	0.0773393i
$302$	−8519.09	+	4774.60i	−1.62324	+	0.909759i
$303$		0			0
$304$	3380.31	+	2188.89i	0.637743	+	0.412965i
$305$		−	1688.81i		−	0.317053i
$306$		0			0
$307$		−	4575.16i		−	0.850547i	−0.905065	−	0.425274i	$-0.860178\pi$
$307$		−	4575.16i		−	0.850547i	0.905065	−	0.425274i	$-0.139822\pi$
$308$	−1220.60	−	746.883i	−0.225813	−	0.138174i
$309$		0			0
$310$	−466.755	−	832.809i	−0.0855158	−	0.152582i
$311$	4119.46	+	7135.11i	0.751103	+	1.30095i	0.947289	+	0.320381i	$0.103811\pi$
$311$	4119.46	+	7135.11i	0.751103	+	1.30095i	−0.196186	+	0.980567i	$0.562856\pi$
$312$		0			0
$313$	2659.91	−	4607.09i	0.480341	−	0.831975i	−0.519405	−	0.854528i	$-0.673846\pi$
$313$	2659.91	−	4607.09i	0.480341	−	0.831975i	0.999746	+	0.0225534i	$0.00717958\pi$
$314$	−2490.44	−	31.7833i	−0.447591	−	0.00571222i
$315$		0			0
$316$	−201.867	+	7907.54i	−0.0359365	+	1.40770i
$317$	7641.35	+	4411.73i	1.35388	+	0.781665i	0.988791	−	0.149307i	$-0.0477042\pi$
$317$	7641.35	+	4411.73i	1.35388	+	0.781665i	0.365092	+	0.930971i	$0.381038\pi$
$318$		0			0
$319$	−5296.76	+	3058.08i	−0.929660	+	0.536739i
$320$	−7810.04	+	3744.11i	−1.36436	+	0.654070i
$321$		0			0
$322$	−652.383	−	387.837i	−0.112907	−	0.0671221i
$323$	−5309.63			−0.914661
$324$		0			0
$325$	−6123.01			−1.04506
$326$	−4117.45	−	2447.80i	−0.699523	−	0.415862i
$327$		0			0
$328$	−6911.82	+	3645.19i	−1.16354	+	0.613633i
$329$	−945.947	+	546.143i	−0.158516	+	0.0915192i
$330$		0			0
$331$	2056.23	+	1187.17i	0.341452	+	0.197138i	0.660914	−	0.750462i	$-0.270169\pi$
$331$	2056.23	+	1187.17i	0.341452	+	0.197138i	−0.319462	+	0.947599i	$0.603502\pi$
$332$	−4026.77	−	102.797i	−0.665656	−	0.0169932i
$333$		0			0
$334$	4638.53	+	59.1977i	0.759908	+	0.00969806i
$335$	−5241.43	+	9078.43i	−0.854836	+	1.48062i
$336$		0			0
$337$	321.888	+	557.527i	0.0520308	+	0.0901199i	0.890868	−	0.454263i	$-0.150097\pi$
$337$	321.888	+	557.527i	0.0520308	+	0.0901199i	−0.838837	+	0.544383i	$0.816764\pi$
$338$	1041.98	+	1859.16i	0.167682	+	0.299187i
$339$		0			0
$340$	5960.23	−	9740.57i	0.950703	−	1.55370i
$341$		−	1000.41i		−	0.158871i
$342$		0			0
$343$		−	2401.99i		−	0.378120i
$344$	−2503.08	−	1575.88i	−0.392317	−	0.246993i
$345$		0			0
$346$	5382.30	−	3016.56i	0.836284	−	0.468702i
$347$	−768.265	−	1330.67i	−0.118855	−	0.205863i	0.800459	−	0.599387i	$-0.204589\pi$
$347$	−768.265	−	1330.67i	−0.118855	−	0.205863i	−0.919314	+	0.393525i	$0.871256\pi$
$348$		0			0
$349$	−3432.65	+	5945.53i	−0.526492	+	0.911910i	0.473032	+	0.881045i	$0.343160\pi$
$349$	−3432.65	+	5945.53i	−0.526492	+	0.911910i	−0.999524	+	0.0308650i	$0.990174\pi$
$350$	−20.7525	+	1626.10i	−0.00316934	+	0.248339i
$351$		0			0
$352$	−9057.41	−	578.715i	−1.37148	−	0.0876296i
$353$	−107.968	−	62.3355i	−0.0162792	−	0.00939881i	0.491838	−	0.870687i	$-0.336325\pi$
$353$	−107.968	−	62.3355i	−0.0162792	−	0.00939881i	−0.508118	+	0.861288i	$0.669658\pi$
$354$		0			0
$355$	−3727.74	+	2152.21i	−0.557318	+	0.321768i
$356$	7167.62	−	3897.80i	1.06709	−	0.580289i
$357$		0			0
$358$	−3396.94	+	5714.01i	−0.501491	+	0.843560i
$359$	4489.49			0.660017			0.330009	−	0.943978i	$-0.392948\pi$
$359$	4489.49			0.660017			0.330009	+	0.943978i	$0.392948\pi$
$360$		0			0
$361$	2899.60			0.422744
$362$	3295.61	−	5543.57i	0.478491	−	0.804872i
$363$		0			0
$364$	−952.621	+	518.042i	−0.137173	+	0.0745955i
$365$	−1472.10	+	849.917i	−0.211105	+	0.121881i
$366$		0			0
$367$	750.997	+	433.589i	0.106817	+	0.0616707i	0.552457	−	0.833542i	$-0.313690\pi$
$367$	750.997	+	433.589i	0.106817	+	0.0616707i	−0.445640	+	0.895212i	$0.647024\pi$
$368$	−4807.38	−	245.610i	−0.680984	−	0.0347916i
$369$		0			0
$370$	10.8451	−	849.787i	0.00152381	−	0.119401i
$371$	855.275	−	1481.38i	0.119686	−	0.207303i
$372$		0			0
$373$	2169.58	+	3757.82i	0.301170	+	0.521642i	0.976401	−	0.215964i	$-0.0692895\pi$
$373$	2169.58	+	3757.82i	0.301170	+	0.521642i	−0.675231	+	0.737606i	$0.735956\pi$
$374$	10438.6	−	5850.40i	1.44323	−	0.808869i
$375$		0			0
$376$	−3690.96	+	5862.62i	−0.506242	+	0.804099i
$377$			4634.71i			0.633156i
$378$		0			0
$379$		−	14096.9i		−	1.91058i	−0.295677	−	0.955288i	$-0.595545\pi$
$379$		−	14096.9i		−	1.91058i	0.295677	−	0.955288i	$-0.404455\pi$
$380$	4444.55	−	7263.56i	0.600002	−	0.980560i
$381$		0			0
$382$	−5438.65	−	9703.92i	−0.728443	−	1.29973i
$383$	−4134.45	−	7161.08i	−0.551594	−	0.955390i	−0.998160	−	0.0606386i	$-0.980686\pi$
$383$	−4134.45	−	7161.08i	−0.551594	−	0.955390i	0.446565	−	0.894751i	$-0.352647\pi$
$384$		0			0
$385$	−1512.93	+	2620.47i	−0.200275	+	0.346887i
$386$	7673.45	+	97.9297i	1.01183	+	0.0129132i
$387$		0			0
$388$	8054.80	+	205.627i	1.05392	+	0.0269050i
$389$	−4972.96	−	2871.14i	−0.648173	−	0.374223i	0.139583	−	0.990210i	$-0.455424\pi$
$389$	−4972.96	−	2871.14i	−0.648173	−	0.374223i	−0.787756	+	0.615987i	$0.788757\pi$
$390$		0			0
$391$	5496.35	−	3173.32i	0.710902	−	0.410439i
$392$	−3486.15	−	6610.26i	−0.449176	−	0.851705i
$393$		0			0
$394$	4857.41	+	2887.69i	0.621098	+	0.369238i
$395$	16726.2			2.13060
$396$		0			0
$397$	10494.4			1.32670			0.663349	−	0.748310i	$-0.269134\pi$
$397$	10494.4			1.32670			0.663349	+	0.748310i	$0.269134\pi$
$398$	5857.08	+	3481.99i	0.737661	+	0.438534i
$399$		0			0
$400$	4694.64	+	9183.90i	0.586830	+	1.14799i
$401$	7070.19	−	4081.97i	0.880469	−	0.508339i	0.00965631	−	0.999953i	$-0.496926\pi$
$401$	7070.19	−	4081.97i	0.880469	−	0.508339i	0.870813	+	0.491614i	$0.163593\pi$
$402$		0			0
$403$	−656.523	−	379.044i	−0.0811507	−	0.0468524i
$404$	85.9485	−	3366.77i	0.0105844	−	0.414611i
$405$		0			0
$406$	1230.85	+	15.7083i	0.150458	+	0.00192017i
$407$	445.277	−	771.242i	0.0542298	−	0.0939288i
$408$		0			0
$409$	−2037.43	−	3528.93i	−0.246319	−	0.426637i	0.716183	−	0.697913i	$-0.245888\pi$
$409$	−2037.43	−	3528.93i	−0.246319	−	0.426637i	−0.962502	+	0.271276i	$0.912554\pi$
$410$	8078.34	+	14413.8i	0.973076	+	1.73621i
$411$		0			0
$412$	−11792.5	−	7215.82i	−1.41014	−	0.862859i
$413$		−	1753.66i		−	0.208940i
$414$		0			0
$415$			8517.52i			1.00749i
$416$	−3811.55	+	5724.72i	−0.449222	+	0.674705i
$417$		0			0
$418$	7784.07	−	4362.65i	0.910841	−	0.510489i
$419$	346.536	+	600.219i	0.0404043	+	0.0699823i	0.885520	−	0.464601i	$-0.153802\pi$
$419$	346.536	+	600.219i	0.0404043	+	0.0699823i	−0.845116	+	0.534583i	$0.820469\pi$
$420$		0			0
$421$	5362.68	−	9288.44i	0.620810	−	1.07527i	−0.368525	−	0.929618i	$-0.620137\pi$
$421$	5362.68	−	9288.44i	0.620810	−	1.07527i	0.989335	−	0.145657i	$-0.0465296\pi$
$422$	−65.6705	+	5145.72i	−0.00757533	+	0.593577i
$423$		0			0
$424$	415.247	−	10841.1i	0.0475618	−	1.24172i
$425$	−11777.1	−	6799.50i	−1.34417	−	0.776057i
$426$		0			0
$427$	−308.452	+	178.085i	−0.0349579	+	0.0201830i
$428$	−241.393	−	443.895i	−0.0272621	−	0.0501319i
$429$		0			0
$430$	−3196.09	+	5376.16i	−0.358440	+	0.602934i
$431$	−10013.8			−1.11914			−0.559569	−	0.828784i	$-0.689033\pi$
$431$	−10013.8			−1.11914			−0.559569	+	0.828784i	$0.689033\pi$
$432$		0			0
$433$	−9726.02			−1.07945			−0.539726	−	0.841841i	$-0.681472\pi$
$433$	−9726.02			−1.07945			−0.539726	+	0.841841i	$0.681472\pi$
$434$	−102.889	+	173.069i	−0.0113797	+	0.0191419i
$435$		0			0
$436$	3192.70	+	5871.03i	0.350694	+	0.644888i
$437$	4098.64	−	2366.35i	0.448660	−	0.259034i
$438$		0			0
$439$	−5675.95	−	3277.01i	−0.617080	−	0.356271i	0.158651	−	0.987335i	$-0.449285\pi$
$439$	−5675.95	−	3277.01i	−0.617080	−	0.356271i	−0.775731	+	0.631063i	$0.782619\pi$
$440$	−734.546	+	19177.2i	−0.0795866	+	2.07781i
$441$		0			0
$442$	115.715	−	9067.05i	0.0124525	−	0.975737i
$443$	2939.61	−	5091.55i	0.315271	−	0.546065i	−0.664224	−	0.747533i	$-0.731238\pi$
$443$	2939.61	−	5091.55i	0.315271	−	0.546065i	0.979495	+	0.201468i	$0.0645713\pi$
$444$		0			0
$445$	−8626.14	−	14940.9i	−0.918917	−	1.59161i
$446$	−6598.74	+	3698.32i	−0.700582	+	0.392647i
$447$		0			0
$448$	1507.41	+	1031.64i	0.158969	+	0.108796i
$449$			6761.00i			0.710627i	0.934747	+	0.355313i	$0.115626\pi$
$449$			6761.00i			0.710627i	−0.934747	+	0.355313i	$0.884374\pi$
$450$		0			0
$451$			17314.5i			1.80778i
$452$	−7027.86	−	4300.33i	−0.731334	−	0.447501i
$453$		0			0
$454$	8157.60	+	14555.2i	0.843293	+	1.50465i
$455$	1146.47	+	1985.74i	0.118126	+	0.204600i
$456$		0			0
$457$	7620.16	−	13198.5i	0.779992	−	1.35099i	−0.151954	−	0.988388i	$-0.548557\pi$
$457$	7620.16	−	13198.5i	0.779992	−	1.35099i	0.931946	−	0.362598i	$-0.118110\pi$
$458$	8577.22	+	109.464i	0.875081	+	0.0111679i
$459$		0			0
$460$	−259.760	+	10175.3i	−0.0263291	+	1.03136i
$461$	−11900.4	−	6870.68i	−1.20229	−	0.694142i	−0.241226	−	0.970469i	$-0.577550\pi$
$461$	−11900.4	−	6870.68i	−1.20229	−	0.694142i	−0.961064	+	0.276327i	$0.910883\pi$
$462$		0			0
$463$	15291.7	−	8828.66i	1.53491	−	0.886183i	0.535789	−	0.844352i	$-0.320014\pi$
$463$	15291.7	−	8828.66i	1.53491	−	0.886183i	0.999125	−	0.0418305i	$-0.0133190\pi$
$464$	6951.61	−	3553.53i	0.695518	−	0.355536i
$465$		0			0
$466$	3146.34	+	1870.48i	0.312771	+	0.185940i
$467$	−6165.12			−0.610895			−0.305447	−	0.952209i	$-0.598806\pi$
$467$	−6165.12			−0.610895			−0.305447	+	0.952209i	$0.598806\pi$
$468$		0			0
$469$	2210.83			0.217669
$470$	12591.8	+	7485.76i	1.23578	+	0.734664i
$471$		0			0
$472$	−5188.48	−	9838.13i	−0.505972	−	0.959400i
$473$	−5675.89	+	3276.98i	−0.551750	+	0.318553i
$474$		0			0
$475$	−8782.19	−	5070.40i	−0.848325	−	0.489781i
$476$	−2407.56	−	61.4614i	−0.231829	−	0.00591824i
$477$		0			0
$478$	−16262.9	−	207.550i	−1.55617	−	0.0198601i
$479$	8659.06	−	14997.9i	0.825976	−	1.43063i	−0.0751944	−	0.997169i	$-0.523958\pi$
$479$	8659.06	−	14997.9i	0.825976	−	1.43063i	0.901171	−	0.433464i	$-0.142709\pi$
$480$		0			0
$481$	−337.422	−	584.431i	−0.0319857	−	0.0554008i
$482$	−8321.43	−	14847.5i	−0.786371	−	1.40308i
$483$		0			0
$484$	−4938.72	+	8071.15i	−0.463816	+	0.757997i
$485$		−	17037.7i		−	1.59514i
$486$		0			0
$487$		−	7352.14i		−	0.684101i	−0.939682	−	0.342050i	$-0.888879\pi$
$487$		−	7352.14i		−	0.684101i	0.939682	−	0.342050i	$-0.111121\pi$
$488$	−1203.54	+	1911.67i	−0.111643	+	0.177330i
$489$		0			0
$490$	−13784.9	+	7725.89i	−1.27090	+	0.712286i
$491$	4221.27	+	7311.46i	0.387991	+	0.672019i	0.992179	−	0.124822i	$-0.0398360\pi$
$491$	4221.27	+	7311.46i	0.387991	+	0.672019i	−0.604189	+	0.796841i	$0.706503\pi$
$492$		0			0
$493$	−5146.77	+	8914.47i	−0.470181	+	0.814377i
$494$	86.2890	−	6761.31i	0.00785896	−	0.615801i
$495$		0			0
$496$	−65.1574	+	1275.34i	−0.00589850	+	0.115453i
$497$	786.178	+	453.900i	0.0709555	+	0.0409662i
$498$		0			0
$499$	−6542.34	+	3777.22i	−0.586924	+	0.338861i	−0.763880	−	0.645358i	$-0.776708\pi$
$499$	−6542.34	+	3777.22i	−0.586924	+	0.338861i	0.176956	+	0.984219i	$0.443375\pi$
$500$	4299.01	−	2337.83i	0.384515	−	0.209102i
$501$		0			0
$502$	4635.66	−	7797.68i	0.412151	−	0.693282i
$503$	−604.632			−0.0535968			−0.0267984	−	0.999641i	$-0.508531\pi$
$503$	−604.632			−0.0535968			−0.0267984	+	0.999641i	$0.508531\pi$
$504$		0			0
$505$	−7121.47			−0.627527
$506$	−5450.46	+	9168.26i	−0.478859	+	0.805492i
$507$		0			0
$508$	5583.93	−	3036.58i	0.487691	−	0.265209i
$509$	−8861.66	+	5116.28i	−0.771682	+	0.445531i	−0.833474	−	0.552558i	$-0.813652\pi$
$509$	−8861.66	+	5116.28i	−0.771682	+	0.445531i	0.0617925	+	0.998089i	$0.480318\pi$
$510$		0			0
$511$	310.465	+	179.247i	0.0268770	+	0.0155175i
$512$	11508.9	+	1327.68i	0.993412	+	0.114601i
$513$		0			0
$514$	−104.955	+	8223.96i	−0.00900659	+	0.705726i
$515$	−14616.8	+	25317.0i	−1.25066	+	2.16621i
$516$		0			0
$517$	7675.21	+	13293.8i	0.652911	+	1.13088i
$518$	−156.352	+	87.6290i	−0.0132620	+	0.00743281i
$519$		0			0
$520$	12306.9	+	7748.10i	1.03787	+	0.653416i
$521$			18465.3i			1.55274i	0.630276	+	0.776371i	$0.282942\pi$
$521$			18465.3i			1.55274i	−0.630276	+	0.776371i	$0.717058\pi$
$522$		0			0
$523$			15941.5i			1.33284i	0.745579	+	0.666418i	$0.232173\pi$
$523$			15941.5i			1.33284i	−0.745579	+	0.666418i	$0.767827\pi$
$524$	−927.289	+	1515.43i	−0.0773069	+	0.126340i
$525$		0			0
$526$	−431.593	−	770.072i	−0.0357764	−	0.0638341i
$527$	−841.844	−	1458.12i	−0.0695850	−	0.120525i
$528$		0			0
$529$	3254.98	−	5637.79i	0.267525	−	0.463368i
$530$	−22938.8	−	292.748i	−1.87999	−	0.0239928i
$531$		0			0
$532$	−1795.32	−	45.8319i	−0.146310	−	0.00373508i
$533$	11362.7	+	6560.29i	0.923406	+	0.533129i
$534$		0			0
$535$	−925.299	+	534.221i	−0.0747741	+	0.0431709i
$536$	12402.9	−	6541.08i	0.999482	−	0.527111i
$537$		0			0
$538$	−4440.10	−	2639.61i	−0.355811	−	0.211527i
$539$	−16559.1			−1.32328
$540$		0			0
$541$	7256.04			0.576638			0.288319	−	0.957534i	$-0.406904\pi$
$541$	7256.04			0.576638			0.288319	+	0.957534i	$0.406904\pi$
$542$	−12125.2	−	7208.37i	−0.960929	−	0.571265i
$543$		0			0
$544$	−13688.4	+	6778.35i	−1.07883	+	0.534227i
$545$	12238.1	−	7065.70i	0.961880	−	0.555342i
$546$		0			0
$547$	374.999	+	216.506i	0.0293122	+	0.0169234i	0.514585	−	0.857440i	$-0.327946\pi$
$547$	374.999	+	216.506i	0.0293122	+	0.0169234i	−0.485272	+	0.874363i	$0.661280\pi$
$548$	−248.542	+	9735.87i	−0.0193744	+	0.758934i
$549$		0			0
$550$	22852.4	+	291.646i	1.77169	+	0.0226106i
$551$	−3837.96	+	6647.54i	−0.296738	+	0.513965i
$552$		0			0
$553$	−1763.77	−	3054.94i	−0.135630	−	0.234918i
$554$	−5879.62	−	10490.7i	−0.450904	−	0.804527i
$555$		0			0
$556$	15042.7	+	9204.58i	1.14740	+	0.702089i
$557$		−	9185.88i		−	0.698776i	−0.936978	−	0.349388i	$-0.886390\pi$
$557$		−	9185.88i		−	0.698776i	0.936978	−	0.349388i	$-0.113610\pi$
$558$		0			0
$559$			4966.45i			0.375776i
$560$	2099.39	−	3242.10i	0.158420	−	0.244649i
$561$		0			0
$562$	−7241.31	+	4058.45i	−0.543516	+	0.304618i
$563$	6499.11	+	11256.8i	0.486510	+	0.842659i	0.999880	−	0.0155079i	$-0.00493650\pi$
$563$	6499.11	+	11256.8i	0.486510	+	0.842659i	−0.513370	+	0.858167i	$0.671603\pi$
$564$		0			0
$565$	−8710.99	+	15087.9i	−0.648627	+	1.12345i
$566$	144.506	−	11323.0i	0.0107315	−	0.840888i
$567$		0			0
$568$	5753.43	+	220.374i	0.425015	+	0.0162794i
$569$	−5424.42	−	3131.79i	−0.399655	−	0.230741i	0.286680	−	0.958026i	$-0.407448\pi$
$569$	−5424.42	−	3131.79i	−0.399655	−	0.230741i	−0.686335	+	0.727286i	$0.740782\pi$
$570$		0			0
$571$	21837.8	−	12608.1i	1.60050	−	0.924047i	0.609109	−	0.793086i	$-0.291527\pi$
$571$	21837.8	−	12608.1i	1.60050	−	0.924047i	0.991388	−	0.130961i	$-0.0418063\pi$
$572$	7280.29	+	13387.6i	0.532175	+	0.978611i
$573$		0			0
$574$	1780.74	−	2995.39i	0.129489	−	0.217814i
$575$	12121.4			0.879125
$576$		0			0
$577$	18112.2			1.30680			0.653398	−	0.757014i	$-0.273343\pi$
$577$	18112.2			1.30680			0.653398	+	0.757014i	$0.273343\pi$
$578$	3190.35	−	5366.51i	0.229587	−	0.386189i
$579$		0			0
$580$	−7886.75	−	14502.9i	−0.564620	−	1.03827i
$581$	1555.67	−	898.169i	0.111085	−	0.0641348i
$582$		0			0
$583$	−20818.6	−	12019.6i	−1.47893	−	0.853861i
$584$	2272.05	+	87.0268i	0.160990	+	0.00616643i
$585$		0			0
$586$	97.2865	−	7623.04i	0.00685813	−	0.537380i
$587$	13172.1	−	22814.8i	0.926189	−	1.60421i	0.136551	−	0.990633i	$-0.456398\pi$
$587$	13172.1	−	22814.8i	0.926189	−	1.60421i	0.789638	−	0.613573i	$-0.210268\pi$
$588$		0			0
$589$	−627.764	−	1087.32i	−0.0439161	−	0.0760649i
$590$	−20516.3	+	11498.5i	−1.43160	+	0.802351i
$591$		0			0
$592$	−617.881	+	954.195i	−0.0428965	+	0.0662453i
$593$			11633.4i			0.805609i	0.915286	+	0.402804i	$0.131965\pi$
$593$			11633.4i			0.805609i	−0.915286	+	0.402804i	$0.868035\pi$
$594$		0			0
$595$			5092.53i			0.350880i
$596$	−2774.54	−	1697.73i	−0.190687	−	0.116681i
$597$		0			0
$598$	3951.60	+	7050.66i	0.270223	+	0.482146i
$599$	−11060.5	−	19157.3i	−0.754454	−	1.30675i	−0.945645	−	0.325200i	$-0.894568\pi$
$599$	−11060.5	−	19157.3i	−0.754454	−	1.30675i	0.191191	−	0.981553i	$-0.438765\pi$
$600$		0			0
$601$	846.923	−	1466.91i	0.0574820	−	0.0995618i	−0.835852	−	0.548954i	$-0.815026\pi$
$601$	846.923	−	1466.91i	0.0574820	−	0.0995618i	0.893334	+	0.449392i	$0.148359\pi$
$602$	1318.95	+	16.8327i	0.0892964	+	0.00113962i
$603$		0			0
$604$	704.917	−	27613.0i	0.0474879	−	1.86019i
$605$	17327.7	+	10004.1i	1.16441	+	0.672274i
$606$		0			0
$607$	−11418.4	+	6592.43i	−0.763525	+	0.440821i	−0.830560	−	0.556929i	$-0.811979\pi$
$607$	−11418.4	+	6592.43i	−0.763525	+	0.440821i	0.0670351	+	0.997751i	$0.478646\pi$
$608$	−10207.5	+	5054.62i	−0.680867	+	0.337158i
$609$		0			0
$610$	4105.92	+	2440.94i	0.272531	+	0.162018i
$611$	11632.2			0.770196
$612$		0			0
$613$	−18052.3			−1.18944			−0.594719	−	0.803934i	$-0.702737\pi$
$613$	−18052.3			−1.18944			−0.594719	+	0.803934i	$0.702737\pi$
$614$	11123.3	+	6612.73i	0.731108	+	0.434639i
$615$		0			0
$616$	3580.06	−	1888.07i	0.234164	−	0.123494i
$617$	18897.2	−	10910.3i	1.23302	−	0.711884i	0.265361	−	0.964149i	$-0.414509\pi$
$617$	18897.2	−	10910.3i	1.23302	−	0.711884i	0.967658	+	0.252266i	$0.0811756\pi$
$618$		0			0
$619$	15640.0	+	9029.74i	1.01555	+	0.586326i	0.912811	−	0.408382i	$-0.133907\pi$
$619$	15640.0	+	9029.74i	1.01555	+	0.586326i	0.102736	+	0.994709i	$0.467240\pi$
$620$	2699.39	+	68.9112i	0.174855	+	0.00446378i
$621$		0			0
$622$	−23301.3	−	297.374i	−1.50208	−	0.0191698i
$623$	−1819.25	+	3151.03i	−0.116993	+	0.202638i
$624$		0			0
$625$	4898.71	+	8484.82i	0.313518	+	0.543028i
$626$	7356.45	+	13125.8i	0.469685	+	0.838037i
$627$		0			0
$628$	3676.84	−	6008.92i	0.233634	−	0.381818i
$629$		−	1498.81i		−	0.0950100i
$630$		0			0
$631$		−	7301.94i		−	0.460674i	−0.973111	−	0.230337i	$-0.926017\pi$
$631$		−	7301.94i		−	0.460674i	0.973111	−	0.230337i	$-0.0739829\pi$
$632$	−18933.4	−	11920.0i	−1.19166	−	0.750241i
$633$		0			0
$634$	−21770.5	+	12201.4i	−1.36375	+	0.764324i
$635$	−6720.18	−	11639.7i	−0.419972	−	0.727413i
$636$		0			0
$637$	−6274.06	+	10867.0i	−0.390247	+	0.675928i
$638$	220.756	−	17297.7i	0.0136988	−	1.07339i
$639$		0			0
$640$	2185.45	−	24399.7i	0.134980	−	1.50700i
$641$	−735.990	−	424.924i	−0.0453508	−	0.0261833i	0.477153	−	0.878820i	$-0.341669\pi$
$641$	−735.990	−	424.924i	−0.0453508	−	0.0261833i	−0.522504	+	0.852637i	$0.675002\pi$
$642$		0			0
$643$	984.538	−	568.423i	0.0603832	−	0.0348622i	−0.469504	−	0.882930i	$-0.655567\pi$
$643$	984.538	−	568.423i	0.0603832	−	0.0348622i	0.529888	+	0.848068i	$0.322234\pi$
$644$	1885.85	−	1025.54i	0.115393	−	0.0627514i
$645$		0			0
$646$	7674.30	−	12909.0i	0.467402	−	0.786219i
$647$	995.889			0.0605138			0.0302569	−	0.999542i	$-0.490367\pi$
$647$	995.889			0.0605138			0.0302569	+	0.999542i	$0.490367\pi$
$648$		0			0
$649$	−24645.0			−1.49061
$650$	8849.93	−	14886.5i	0.534035	−	0.898303i
$651$		0			0
$652$	11902.4	−	6472.59i	0.714928	−	0.388783i
$653$	−24496.2	+	14142.9i	−1.46801	+	0.847557i	−0.999358	−	0.0358245i	$-0.988594\pi$
$653$	−24496.2	+	14142.9i	−1.46801	+	0.847557i	−0.468654	+	0.883382i	$0.655261\pi$
$654$		0			0
$655$	3253.43	+	1878.37i	0.194079	+	0.112052i
$656$	1127.71	−	22072.9i	0.0671185	−	1.31372i
$657$		0			0
$658$	39.4248	−	3089.20i	0.00233577	−	0.183023i
$659$	−12722.0	+	22035.1i	−0.752014	+	1.30253i	0.194831	+	0.980837i	$0.437584\pi$
$659$	−12722.0	+	22035.1i	−0.752014	+	1.30253i	−0.946845	+	0.321690i	$0.895749\pi$
$660$		0			0
$661$	2109.30	+	3653.42i	0.124119	+	0.214980i	0.921388	−	0.388644i	$-0.127056\pi$
$661$	2109.30	+	3653.42i	0.124119	+	0.214980i	−0.797269	+	0.603624i	$0.793723\pi$
$662$	−5858.28	+	3283.32i	−0.343940	+	0.192764i
$663$		0			0
$664$	6070.04	−	9641.48i	0.354764	−	0.563497i
$665$			3797.51i			0.221445i
$666$		0			0
$667$		−	9175.09i		−	0.532625i
$668$	−6848.26	+	11191.8i	−0.396657	+	0.648241i
$669$		0			0
$670$	−14496.1	−	25864.8i	−0.835872	−	1.49141i
$671$	2502.71	+	4334.83i	0.143988	+	0.249395i
$672$		0			0
$673$	−7212.87	+	12493.0i	−0.413129	+	0.715560i	−0.995230	−	0.0975565i	$-0.968897\pi$
$673$	−7212.87	+	12493.0i	−0.413129	+	0.715560i	0.582101	+	0.813116i	$0.302231\pi$
$674$	−1820.73	−	23.2364i	−0.104053	−	0.00132794i
$675$		0			0
$676$	−6026.11	−	153.837i	−0.342860	−	0.00875270i
$677$	27870.5	+	16091.1i	1.58220	+	0.913486i	0.994537	+	0.104382i	$0.0332865\pi$
$677$	27870.5	+	16091.1i	1.58220	+	0.913486i	0.587666	+	0.809103i	$0.300047\pi$
$678$		0			0
$679$	−3111.84	+	1796.62i	−0.175878	+	0.101543i
$680$	15067.0	+	28569.4i	0.849698	+	1.61116i
$681$		0			0
$682$	2432.23	+	1445.94i	0.136561	+	0.0811847i
$683$	28383.3			1.59012			0.795062	−	0.606528i	$-0.207438\pi$
$683$	28383.3			1.59012			0.795062	+	0.606528i	$0.207438\pi$
$684$		0			0
$685$	20593.5			1.14867
$686$	5839.81	+	3471.73i	0.325022	+	0.193223i
$687$		0			0
$688$	7449.19	−	3807.89i	0.412787	−	0.211009i
$689$	−15775.9	+	9108.21i	−0.872298	+	0.503621i
$690$		0			0
$691$	−4592.61	−	2651.54i	−0.252838	−	0.145976i	0.368225	−	0.929737i	$-0.379966\pi$
$691$	−4592.61	−	2651.54i	−0.252838	−	0.145976i	−0.621063	+	0.783761i	$0.713299\pi$
$692$	−445.362	+	17445.7i	−0.0244655	+	0.958360i
$693$		0			0
$694$	4345.61	+	55.4594i	0.237690	+	0.00303344i
$695$	18645.3	−	32294.6i	1.01764	−	1.76260i
$696$		0			0
$697$	14570.2	+	25236.3i	0.791801	+	1.37144i
$698$	−9493.61	−	16939.0i	−0.514812	−	0.918555i
$699$		0			0
$700$	−3923.45	−	2400.75i	−0.211846	−	0.129628i
$701$		−	10087.7i		−	0.543519i	−0.962365	−	0.271760i	$-0.912394\pi$
$701$		−	10087.7i		−	0.543519i	0.962365	−	0.271760i	$-0.0876056\pi$
$702$		0			0
$703$		−	1117.66i		−	0.0599622i
$704$	14498.2	−	21184.3i	0.776166	−	1.13411i
$705$		0			0
$706$	307.605	−	172.400i	0.0163978	−	0.00919031i
$707$	750.956	+	1300.69i	0.0399471	+	0.0691905i
$708$		0			0
$709$	12869.6	−	22290.9i	0.681706	−	1.18075i	−0.292754	−	0.956188i	$-0.594572\pi$
$709$	12869.6	−	22290.9i	0.681706	−	1.18075i	0.974460	−	0.224561i	$-0.0720949\pi$
$710$	155.363	−	12173.8i	0.00821223	−	0.643483i
$711$		0			0
$712$	−883.268	+	23059.9i	−0.0464914	+	1.21378i
$713$	1299.68	+	750.372i	0.0682658	+	0.0394133i
$714$		0			0
$715$	27906.5	−	16111.9i	1.45964	−	0.842726i
$716$	−8982.36	−	16517.6i	−0.468836	−	0.862137i
$717$		0			0
$718$	−6488.92	+	10915.0i	−0.337276	+	0.567334i
$719$	−7178.86			−0.372359			−0.186180	−	0.982516i	$-0.559611\pi$
$719$	−7178.86			−0.372359			−0.186180	+	0.982516i	$0.559611\pi$
$720$		0			0
$721$	6165.33			0.318459
$722$	−4190.96	+	7049.64i	−0.216027	+	0.363380i
$723$		0			0
$724$	8714.44	+	16024.9i	0.447334	+	0.822597i
$725$	−17025.7	+	9829.77i	−0.872161	+	0.503543i
$726$		0			0
$727$	−18250.7	−	10537.0i	−0.931061	−	0.537548i	−0.0439138	−	0.999035i	$-0.513983\pi$
$727$	−18250.7	−	10537.0i	−0.931061	−	0.537548i	−0.887147	+	0.461487i	$0.847316\pi$
$728$	117.392	−	3064.81i	0.00597641	−	0.156029i
$729$		0			0
$730$	61.3537	−	4807.47i	0.00311069	−	0.243743i
$731$	−5515.17	+	9552.55i	−0.279050	+	0.483330i
$732$		0			0
$733$	−10114.0	−	17518.0i	−0.509645	−	0.882730i	−0.999938	−	0.0111727i	$-0.996444\pi$
$733$	−10114.0	−	17518.0i	−0.509645	−	0.882730i	0.490293	−	0.871558i	$-0.336890\pi$
$734$	−2139.62	+	1199.17i	−0.107595	+	0.0603026i
$735$		0			0
$736$	7545.52	−	11332.9i	0.377896	−	0.567577i
$737$		−	31069.9i		−	1.55288i
$738$		0			0
$739$			8782.55i			0.437173i	0.975818	+	0.218587i	$0.0701447\pi$
$739$			8782.55i			0.437173i	−0.975818	+	0.218587i	$0.929855\pi$
$740$	2050.36	+	1254.61i	0.101855	+	0.0623250i
$741$		0			0
$742$	2365.42	+	4220.50i	0.117031	+	0.208813i
$743$	11676.8	+	20224.8i	0.576553	+	0.998620i	0.995871	+	0.0907800i	$0.0289360\pi$
$743$	11676.8	+	20224.8i	0.576553	+	0.998620i	−0.419318	+	0.907840i	$0.637731\pi$
$744$		0			0
$745$	−3439.02	+	5956.56i	−0.169122	+	0.292928i
$746$	−12272.0	−	156.617i	−0.602291	−	0.00768654i
$747$		0			0
$748$	−863.747	+	33834.7i	−0.0422216	+	1.65390i
$749$	195.145	+	112.667i	0.00951995	+	0.00549634i
$750$		0			0
$751$	−14625.3	+	8443.94i	−0.710634	+	0.410285i	−0.811296	−	0.584636i	$-0.801237\pi$
$751$	−14625.3	+	8443.94i	−0.710634	+	0.410285i	0.100662	+	0.994921i	$0.467904\pi$
$752$	−8918.69	−	17447.2i	−0.432488	−	0.846056i
$753$		0			0
$754$	−11268.1	−	6698.81i	−0.544244	−	0.323549i
$755$	−58407.6			−2.81546
$756$		0			0
$757$	6838.01			0.328311			0.164156	−	0.986434i	$-0.447510\pi$
$757$	6838.01			0.328311			0.164156	+	0.986434i	$0.447510\pi$
$758$	34272.9	+	20375.0i	1.64228	+	0.976325i
$759$		0			0
$760$	11235.5	+	21304.2i	0.536257	+	1.01682i
$761$	20503.9	−	11837.9i	0.976696	−	0.563896i	0.0754248	−	0.997151i	$-0.475969\pi$
$761$	20503.9	−	11837.9i	0.976696	−	0.563896i	0.901271	+	0.433256i	$0.142635\pi$
$762$		0			0
$763$	−2581.02	−	1490.15i	−0.122463	−	0.0707039i
$764$	31453.4	+	802.957i	1.48945	+	0.0380235i
$765$		0			0
$766$	23386.1	+	298.457i	1.10310	+	0.0140779i
$767$	−9337.76	+	16173.5i	−0.439592	+	0.761396i
$768$		0			0
$769$	−18418.7	−	31902.0i	−0.863711	−	1.49599i	−0.868322	−	0.496002i	$-0.834801\pi$
$769$	−18418.7	−	31902.0i	−0.863711	−	1.49599i	0.00461075	−	0.999989i	$-0.498532\pi$
$770$	−4184.28	−	7465.81i	−0.195832	−	0.349414i
$771$		0			0
$772$	−11329.0	+	18514.5i	−0.528158	+	0.863148i
$773$		−	7505.51i		−	0.349230i	−0.984637	−	0.174615i	$-0.944132\pi$
$773$		−	7505.51i		−	0.349230i	0.984637	−	0.174615i	$-0.0558680\pi$
$774$		0			0
$775$		−	3215.66i		−	0.149045i
$776$	−12142.0	+	19286.0i	−0.561691	+	0.892173i
$777$		0			0
$778$	14168.2	−	7940.66i	0.652896	−	0.365921i
$779$	10865.0	+	18818.8i	0.499717	+	0.865535i
$780$		0			0
$781$	6378.88	−	11048.5i	0.292259	−	0.506207i
$782$	−229.075	+	17949.6i	−0.0104753	+	0.820812i
$783$		0			0
$784$	21109.9	+	1078.51i	0.961638	+	0.0491303i
$785$	−12900.3	−	7448.01i	−0.586538	−	0.338638i
$786$		0			0
$787$	−16864.0	+	9736.41i	−0.763832	+	0.440998i	−0.830670	−	0.556765i	$-0.812042\pi$
$787$	−16864.0	+	9736.41i	−0.763832	+	0.440998i	0.0668382	+	0.997764i	$0.478709\pi$
$788$	−14041.4	+	7635.79i	−0.634775	+	0.345195i
$789$		0			0
$790$	−24175.3	+	40665.5i	−1.08876	+	1.83141i
$791$	3674.28			0.165161
$792$		0			0
$793$	3793.01			0.169853
$794$	−15168.2	+	25514.5i	−0.677957	+	1.14040i
$795$		0			0
$796$	−16931.2	+	9207.27i	−0.753906	+	0.409979i
$797$	30984.0	−	17888.6i	1.37705	−	0.795040i	0.385247	−	0.922814i	$-0.374116\pi$
$797$	30984.0	−	17888.6i	1.37705	−	0.795040i	0.991803	+	0.127773i	$0.0407830\pi$
$798$		0			0
$799$	22373.6	+	12917.4i	0.990640	+	0.571947i
$800$	−29113.7	−	1860.20i	−1.28666	−	0.0822098i
$801$		0			0
$802$	−294.669	+	23089.3i	−0.0129740	+	1.01660i
$803$	2519.04	−	4363.11i	0.110704	−	0.191745i
$804$		0			0
$805$	−2269.60	−	3931.06i	−0.0993700	−	0.172114i
$806$	1870.46	−	1048.31i	0.0817420	−	0.0458130i
$807$		0			0
$808$	8061.21	+	5075.14i	0.350981	+	0.220969i
$809$			16519.8i			0.717932i	0.933351	+	0.358966i	$0.116871\pi$
$809$			16519.8i			0.717932i	−0.933351	+	0.358966i	$0.883129\pi$
$810$		0			0
$811$			18594.4i			0.805103i	0.915397	+	0.402552i	$0.131877\pi$
$811$			18594.4i			0.805103i	−0.915397	+	0.402552i	$0.868123\pi$
$812$	−1817.21	+	2969.79i	−0.0785363	+	0.128349i
$813$		0			0
$814$	1231.49	+	2197.29i	0.0530268	+	0.0946132i
$815$	−14324.3	−	24810.5i	−0.615656	−	1.06635i
$816$		0			0
$817$	−4112.67	+	7123.35i	−0.176113	+	0.305036i
$818$	11524.5	+	147.078i	0.492598	+	0.00628661i
$819$		0			0
$820$	−46719.6	−	1192.68i	−1.98966	−	0.0507929i
$821$	−35701.8	−	20612.4i	−1.51766	−	0.876222i	−0.999784	−	0.0207677i	$-0.993389\pi$
$821$	−35701.8	−	20612.4i	−1.51766	−	0.876222i	−0.517878	−	0.855455i	$-0.673278\pi$
$822$		0			0
$823$	−3713.28	+	2143.86i	−0.157274	+	0.0908025i	−0.576572	−	0.817047i	$-0.695610\pi$
$823$	−3713.28	+	2143.86i	−0.157274	+	0.0908025i	0.419297	+	0.907849i	$0.362277\pi$
$824$	34587.8	−	18241.1i	1.46229	−	0.771187i
$825$		0			0
$826$	4263.58	+	2534.67i	0.179599	+	0.106770i
$827$	24944.4			1.04885			0.524426	−	0.851456i	$-0.324280\pi$
$827$	24944.4			1.04885			0.524426	+	0.851456i	$0.324280\pi$
$828$		0			0
$829$	−31040.8			−1.30047			−0.650235	−	0.759733i	$-0.725330\pi$
$829$	−31040.8			−1.30047			−0.650235	+	0.759733i	$0.725330\pi$
$830$	−20708.2	−	12310.8i	−0.866013	−	0.514838i
$831$		0			0
$832$	−8409.14	−	17541.1i	−0.350402	−	0.730922i
$833$	−24135.3	+	13934.5i	−1.00389	+	0.579594i
$834$		0			0
$835$	24027.4	+	13872.2i	0.995810	+	0.574931i
$836$	−644.098	+	25230.6i	−0.0266466	+	1.04380i
$837$		0			0
$838$	−1960.15	−	25.0157i	−0.0808021	−	0.00103121i
$839$	6393.60	−	11074.0i	0.263089	−	0.455683i	−0.703972	−	0.710228i	$-0.748592\pi$
$839$	6393.60	−	11074.0i	0.263089	−	0.455683i	0.967061	+	0.254544i	$0.0819254\pi$
$840$		0			0
$841$	−4754.02	−	8234.20i	−0.194925	−	0.337619i
$842$	14831.5	+	26463.1i	0.607038	+	1.08311i
$843$		0			0
$844$	−12415.6	−	7597.06i	−0.506353	−	0.309836i
$845$			12746.6i			0.518929i
$846$		0			0
$847$		−	4219.73i		−	0.171183i
$848$	25757.1	+	16678.8i	1.04305	+	0.675415i
$849$		0			0
$850$	33553.3	−	18805.3i	1.35396	−	0.758841i
$851$	667.975	+	1156.97i	0.0269070	+	0.0466044i
$852$		0			0
$853$	23491.5	−	40688.4i	0.942946	−	1.63323i	0.183132	−	0.983088i	$-0.441376\pi$
$853$	23491.5	−	40688.4i	0.942946	−	1.63323i	0.759813	−	0.650141i	$-0.225290\pi$
$854$	12.8556	−	1007.32i	0.000515115	−	0.0403627i
$855$		0			0
$856$	1428.12	+	54.7013i	0.0570234	+	0.00218417i
$857$	−39991.4	−	23089.0i	−1.59402	−	0.920310i	−0.992607	−	0.121375i	$-0.961269\pi$
$857$	−39991.4	−	23089.0i	−1.59402	−	0.920310i	−0.601418	−	0.798935i	$-0.705397\pi$
$858$		0			0
$859$	5670.77	−	3274.02i	0.225244	−	0.130045i	−0.383132	−	0.923694i	$-0.625155\pi$
$859$	5670.77	−	3274.02i	0.225244	−	0.130045i	0.608376	+	0.793649i	$0.291821\pi$
$860$	−8451.27	−	15540.9i	−0.335100	−	0.616211i
$861$		0			0
$862$	14473.5	−	24346.0i	0.571892	−	0.961983i
$863$	−29442.2			−1.16133			−0.580663	−	0.814144i	$-0.697207\pi$
$863$	−29442.2			−1.16133			−0.580663	+	0.814144i	$0.697207\pi$
$864$		0			0
$865$	36901.5			1.45051
$866$	14057.6	−	23646.3i	0.551611	−	0.927869i
$867$		0			0
$868$	−272.063	−	500.294i	−0.0106387	−	0.0195635i
$869$	−42932.6	+	24787.2i	−1.67594	+	0.967603i
$870$		0			0
$871$	−20389.8	−	11772.1i	−0.793206	−	0.457958i
$872$	−18888.5	−	723.488i	−0.733538	−	0.0280968i
$873$		0			0
$874$	−170.822	+	13385.0i	−0.00661113	+	0.518026i
$875$	−1091.15	+	1889.93i	−0.0421573	+	0.0730186i
$876$		0			0
$877$	16384.3	+	28378.4i	0.630853	+	1.09267i	0.987378	+	0.158383i	$0.0506282\pi$
$877$	16384.3	+	28378.4i	0.630853	+	1.09267i	−0.356525	+	0.934286i	$0.616039\pi$
$878$	16171.0	−	9063.16i	0.621576	−	0.348368i
$879$		0			0
$880$	−45562.7	−	29503.7i	−1.74536	−	1.13019i
$881$			15082.2i			0.576769i	0.957515	+	0.288384i	$0.0931181\pi$
$881$			15082.2i			0.576769i	−0.957515	+	0.288384i	$0.906882\pi$
$882$		0			0
$883$		−	425.340i		−	0.0162105i	−0.999967	−	0.00810523i	$-0.997420\pi$
$883$		−	425.340i		−	0.0162105i	0.999967	−	0.00810523i	$-0.00258000\pi$
$884$	21877.0	+	13386.5i	0.832355	+	0.509316i
$885$		0			0
$886$	8130.01	+	14506.0i	0.308277	+	0.550044i
$887$	−6078.41	−	10528.1i	−0.230094	−	0.398534i	0.727742	−	0.685851i	$-0.240570\pi$
$887$	−6078.41	−	10528.1i	−0.230094	−	0.398534i	−0.957835	+	0.287317i	$0.907237\pi$
$888$		0			0
$889$	−1417.28	+	2454.80i	−0.0534692	+	0.0926114i
$890$	48792.8	+	622.702i	1.83768	+	0.0234528i
$891$		0			0
$892$	546.017	−	21388.5i	0.0204955	−	0.802849i
$893$	16684.0	+	9632.54i	0.625207	+	0.360964i
$894$		0			0
$895$	−34430.8	+	19878.7i	−1.28592	+	0.742425i
$896$	−4686.92	+	2173.78i	−0.174753	+	0.0810501i
$897$		0			0
$898$	−16437.6	−	9772.06i	−0.610836	−	0.363138i
$899$	−2434.04			−0.0903001
$900$		0			0
$901$	−40458.1			−1.49595
$902$	−42095.7	−	25025.6i	−1.55392	−	0.923793i
$903$		0			0
$904$	20612.9	−	10870.9i	0.758380	−	0.399958i
$905$	33403.9	−	19285.7i	1.22694	−	0.708375i
$906$		0			0
$907$	39674.6	+	22906.2i	1.45245	+	0.838574i	0.998620	−	0.0525131i	$-0.0167231\pi$
$907$	39674.6	+	22906.2i	1.45245	+	0.838574i	0.453832	+	0.891087i	$0.350056\pi$
$908$	−47177.9	−	1204.38i	−1.72429	−	0.0440185i
$909$		0			0
$910$	−6484.87	−	82.7609i	−0.236232	−	0.00301483i
$911$	14411.9	−	24962.1i	0.524134	−	0.907827i	−0.475471	−	0.879732i	$-0.657722\pi$
$911$	14411.9	−	24962.1i	0.524134	−	0.907827i	0.999605	−	0.0280960i	$-0.00894440\pi$
$912$		0			0
$913$	−12622.4	−	21862.7i	−0.457547	−	0.792495i
$914$	21074.9	+	37603.0i	0.762688	+	1.36083i
$915$		0			0
$916$	−12663.3	+	20695.1i	−0.456775	+	0.746490i
$917$		−	792.293i		−	0.0285320i
$918$		0			0
$919$		−	41488.4i		−	1.48920i	−0.667511	−	0.744600i	$-0.732640\pi$
$919$		−	41488.4i		−	1.48920i	0.667511	−	0.744600i	$-0.267360\pi$
$920$	−24363.2	−	15338.5i	−0.873077	−	0.549669i
$921$		0			0
$922$	33904.6	−	19002.1i	1.21105	−	0.678743i
$923$	−4833.79	−	8372.36i	−0.172379	−	0.298570i
$924$		0			0
$925$	1431.28	−	2479.04i	0.0508758	−	0.0881194i
$926$	−637.321	+	49938.4i	−0.0226174	+	1.77222i
$927$		0			0
$928$	−1408.04	+	22037.2i	−0.0498075	+	0.779532i
$929$	−3659.97	−	2113.09i	−0.129257	−	0.0746266i	0.433977	−	0.900924i	$-0.357110\pi$
$929$	−3659.97	−	2113.09i	−0.129257	−	0.0746266i	−0.563234	+	0.826297i	$0.690443\pi$
$930$		0			0
$931$	−17997.7	+	10391.0i	−0.633567	+	0.365790i
$932$	−9095.16	+	4946.01i	−0.319659	+	0.173833i
$933$		0			0
$934$	8910.80	−	14988.9i	0.312174	−	0.525109i
$935$	71567.8			2.50323
$936$		0			0
$937$	31514.2			1.09875			0.549373	−	0.835577i	$-0.314867\pi$
$937$	31514.2			1.09875			0.549373	+	0.835577i	$0.314867\pi$
$938$	−3195.44	+	5375.07i	−0.111231	+	0.187102i
$939$		0			0
$940$	−36399.4	+	19794.2i	−1.26300	+	0.686826i
$941$	23040.3	−	13302.3i	0.798185	−	0.460832i	−0.0446514	−	0.999003i	$-0.514218\pi$
$941$	23040.3	−	13302.3i	0.798185	−	0.460832i	0.842836	+	0.538171i	$0.180884\pi$
$942$		0			0
$943$	−22494.2	−	12987.0i	−0.776790	−	0.448480i
$944$	31418.1	+	1605.16i	1.08323	+	0.0553426i
$945$		0			0
$946$	236.558	−	18535.9i	0.00813018	−	0.637054i
$947$	−25814.6	+	44712.3i	−0.885811	+	1.53427i	−0.0410299	+	0.999158i	$0.513064\pi$
$947$	−25814.6	+	44712.3i	−0.885811	+	1.53427i	−0.844781	+	0.535112i	$0.820269\pi$
$948$		0			0
$949$	−1908.88	−	3306.28i	−0.0652950	−	0.113094i
$950$	25020.8	−	14023.1i	0.854506	−	0.478915i
$951$		0			0
$952$	3629.22	−	5764.54i	0.123554	−	0.196250i
$953$		−	25766.7i		−	0.875829i	−0.899017	−	0.437915i	$-0.855717\pi$
$953$		−	25766.7i		−	0.875829i	0.899017	−	0.437915i	$-0.144283\pi$
$954$		0			0
$955$		−	66530.9i		−	2.25433i
$956$	24010.4	−	39239.2i	0.812291	−	1.32750i
$957$		0			0
$958$	23948.2	+	42729.7i	0.807653	+	1.44106i
$959$	−2171.58	−	3761.29i	−0.0731220	−	0.126651i
$960$		0			0
$961$	−14696.4	+	25455.0i	−0.493318	+	0.854452i
$962$	1908.59	+	24.3577i	0.0639661	+	0.000816346i
$963$		0			0
$964$	48125.4	+	1228.57i	1.60790	+	0.0410472i
$965$	39748.1	+	22948.6i	1.32594	+	0.765534i
$966$		0			0
$967$	39828.3	−	22994.9i	1.32450	−	0.764700i	0.340056	−	0.940405i	$-0.389554\pi$
$967$	39828.3	−	22994.9i	1.32450	−	0.764700i	0.984443	+	0.175705i	$0.0562205\pi$
$968$	−12484.7	−	23672.9i	−0.414540	−	0.786029i
$969$		0			0
$970$	41422.8	+	24625.6i	1.37114	+	0.815133i
$971$	22109.4			0.730714			0.365357	−	0.930867i	$-0.380947\pi$
$971$	22109.4			0.730714			0.365357	+	0.930867i	$0.380947\pi$
$972$		0			0
$973$	−7864.57			−0.259123
$974$	17874.8	+	10626.5i	0.588036	+	0.349583i
$975$		0			0
$976$	−2908.19	−	5689.14i	−0.0953778	−	0.186583i
$977$	43850.9	−	25317.3i	1.43594	−	0.829040i	0.438375	−	0.898792i	$-0.355554\pi$
$977$	43850.9	−	25317.3i	1.43594	−	0.829040i	0.997564	+	0.0697519i	$0.0222208\pi$
$978$		0			0
$979$	44282.9	+	25566.8i	1.44565	+	0.834645i
$980$	1140.64	−	44681.2i	0.0371801	−	1.45642i
$981$		0			0
$982$	−23877.2	−	304.724i	−0.775918	−	0.00990239i
$983$	6989.79	−	12106.7i	0.226795	−	0.392821i	−0.730061	−	0.683382i	$-0.760509\pi$
$983$	6989.79	−	12106.7i	0.226795	−	0.392821i	0.956856	+	0.290561i	$0.0938419\pi$
$984$		0			0
$985$	16898.6	+	29269.2i	0.546633	+	0.946797i
$986$	−14234.3	−	25397.7i	−0.459750	−	0.820310i
$987$		0			0
$988$	16313.7	+	9982.30i	0.525311	+	0.321437i
$989$		−	9831.82i		−	0.316111i
$990$		0			0
$991$		−	29526.4i		−	0.946456i	−0.880940	−	0.473228i	$-0.843089\pi$
$991$		−	29526.4i		−	0.946456i	0.880940	−	0.473228i	$-0.156911\pi$
$992$	−3006.49	−	2001.73i	−0.0962258	−	0.0640677i
$993$		0			0
$994$	−2239.85	+	1255.34i	−0.0714725	+	0.0400574i
$995$	20376.4	+	35293.0i	0.649222	+	1.12448i
$996$		0			0
$997$	−2513.86	+	4354.14i	−0.0798545	+	0.138312i	−0.903187	−	0.429247i	$-0.858779\pi$
$997$	−2513.86	+	4354.14i	−0.0798545	+	0.138312i	0.823333	+	0.567559i	$0.192112\pi$
$998$	272.669	−	21365.4i	0.00864849	−	0.677667i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.h.b.35.4		24
3.2	odd	2		36.4.h.b.11.9	yes	24
4.3	odd	2	inner	108.4.h.b.35.8		24
9.2	odd	6		324.4.b.c.323.1		24
9.4	even	3		36.4.h.b.23.5	yes	24
9.5	odd	6	inner	108.4.h.b.71.8		24
9.7	even	3		324.4.b.c.323.24		24
12.11	even	2		36.4.h.b.11.5	✓	24
36.7	odd	6		324.4.b.c.323.2		24
36.11	even	6		324.4.b.c.323.23		24
36.23	even	6	inner	108.4.h.b.71.4		24
36.31	odd	6		36.4.h.b.23.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.5	✓	24	12.11	even	2
36.4.h.b.11.9	yes	24	3.2	odd	2
36.4.h.b.23.5	yes	24	9.4	even	3
36.4.h.b.23.9	yes	24	36.31	odd	6
108.4.h.b.35.4		24	1.1	even	1	trivial
108.4.h.b.35.8		24	4.3	odd	2	inner
108.4.h.b.71.4		24	36.23	even	6	inner
108.4.h.b.71.8		24	9.5	odd	6	inner
324.4.b.c.323.1		24	9.2	odd	6
324.4.b.c.323.2		24	36.7	odd	6
324.4.b.c.323.23		24	36.11	even	6
324.4.b.c.323.24		24	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.44536 + 2.43124i) q^{2} +(-3.82189 - 7.02803i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(3.08966 + 1.78382i) q^{7} +(22.6108 + 0.866066i) q^{8} +O(q^{10})\)	\(q+(-1.44536 + 2.43124i) q^{2} +(-3.82189 - 7.02803i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(3.08966 + 1.78382i) q^{7} +(22.6108 + 0.866066i) q^{8} +(0.610574 - 47.8425i) q^{10} +(25.0688 - 43.4205i) q^{11} +(-18.9966 - 32.9032i) q^{13} +(-8.80255 + 4.93346i) q^{14} +(-34.7863 + 53.7207i) q^{16} -84.3819i q^{17} -62.9237i q^{19} +(115.434 + 70.6340i) q^{20} +(69.3323 + 123.706i) q^{22} +(37.6066 + 65.1366i) q^{23} +(80.5801 - 139.569i) q^{25} +(107.453 + 1.37133i) q^{26} +(0.728372 - 28.5317i) q^{28} +(-105.644 - 60.9938i) q^{29} +(17.2800 - 9.97659i) q^{31} +(-80.3294 - 162.220i) q^{32} +(205.153 + 121.962i) q^{34} -60.3510 q^{35} +17.7622 q^{37} +(152.983 + 90.9472i) q^{38} +(-338.572 + 178.558i) q^{40} +(-299.072 + 172.670i) q^{41} +(-113.206 - 65.3596i) q^{43} +(-400.970 - 10.2362i) q^{44} +(-212.718 - 2.71474i) q^{46} +(-153.083 + 265.147i) q^{47} +(-165.136 - 286.024i) q^{49} +(222.859 + 397.636i) q^{50} +(-158.641 + 259.261i) q^{52} -479.464i q^{53} +848.142i q^{55} +(68.3149 + 43.0094i) q^{56} +(300.984 - 168.689i) q^{58} +(-245.774 - 425.693i) q^{59} +(-49.9168 + 86.4585i) q^{61} +(-0.720188 + 56.4315i) q^{62} +(510.500 + 39.1649i) q^{64} +(556.599 + 321.352i) q^{65} +(536.669 - 309.846i) q^{67} +(-593.039 + 322.498i) q^{68} +(87.2287 - 146.728i) q^{70} +254.455 q^{71} +100.485 q^{73} +(-25.6727 + 43.1841i) q^{74} +(-442.230 + 240.488i) q^{76} +(154.908 - 89.4363i) q^{77} +(-856.295 - 494.382i) q^{79} +(55.2404 - 1081.23i) q^{80} +(12.4646 - 976.687i) q^{82} +(251.755 - 436.053i) q^{83} +(713.714 + 1236.19i) q^{85} +(322.528 - 180.764i) q^{86} +(604.432 - 960.062i) q^{88} +1019.86i q^{89} -135.546i q^{91} +(314.053 - 513.245i) q^{92} +(-423.378 - 755.413i) q^{94} +(532.217 + 921.828i) q^{95} +(-503.589 + 872.242i) q^{97} +(934.074 + 11.9208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 24 * q - 12 * q^4 + 72 * q^5	\( 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

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