LMFDB - Embedded newform 108.4.h.b.71.12

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			71.12
Character	$\chi$	$=$	108.71
Dual form			108.4.h.b.35.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.81402 - 0.285097i) q^{2} +(7.83744 - 1.60454i) q^{4} +(14.4924 + 8.36717i) q^{5} +(-16.7175 + 9.65186i) q^{7} +(21.5973 - 6.74964i) q^{8} +O(q^{10})$	\(q+(2.81402 - 0.285097i) q^{2} +(7.83744 - 1.60454i) q^{4} +(14.4924 + 8.36717i) q^{5} +(-16.7175 + 9.65186i) q^{7} +(21.5973 - 6.74964i) q^{8} +(43.1673 + 19.4137i) q^{10} +(-2.44092 - 4.22780i) q^{11} +(6.03848 - 10.4590i) q^{13} +(-44.2917 + 31.9267i) q^{14} +(58.8509 - 25.1509i) q^{16} -71.2528i q^{17} +68.3003i q^{19} +(127.009 + 42.3237i) q^{20} +(-8.07414 - 11.2012i) q^{22} +(68.0491 - 117.865i) q^{23} +(77.5192 + 134.267i) q^{25} +(14.0106 - 31.1533i) q^{26} +(-115.536 + 102.470i) q^{28} +(-190.237 + 109.833i) q^{29} +(-285.221 - 164.672i) q^{31} +(158.437 - 87.5535i) q^{32} +(-20.3140 - 200.507i) q^{34} -323.035 q^{35} -133.618 q^{37} +(19.4722 + 192.199i) q^{38} +(369.471 + 82.8899i) q^{40} +(29.5326 + 17.0507i) q^{41} +(-0.558209 + 0.322282i) q^{43} +(-25.9142 - 29.2186i) q^{44} +(157.889 - 351.074i) q^{46} +(-93.4753 - 161.904i) q^{47} +(14.8169 - 25.6636i) q^{49} +(256.420 + 355.730i) q^{50} +(30.5444 - 91.6604i) q^{52} +266.453i q^{53} -81.6944i q^{55} +(-295.906 + 321.291i) q^{56} +(-504.018 + 363.309i) q^{58} +(104.347 - 180.734i) q^{59} +(0.801886 + 1.38891i) q^{61} +(-849.565 - 382.076i) q^{62} +(420.885 - 291.548i) q^{64} +(175.024 - 101.050i) q^{65} +(371.407 + 214.432i) q^{67} +(-114.328 - 558.440i) q^{68} +(-909.028 + 92.0964i) q^{70} +386.365 q^{71} -776.832 q^{73} +(-376.004 + 38.0941i) q^{74} +(109.591 + 535.300i) q^{76} +(81.6122 + 47.1188i) q^{77} +(68.5000 - 39.5485i) q^{79} +(1063.33 + 127.919i) q^{80} +(87.9665 + 39.5613i) q^{82} +(462.668 + 801.365i) q^{83} +(596.185 - 1032.62i) q^{85} +(-1.47893 + 1.06605i) q^{86} +(-81.2533 - 74.8336i) q^{88} -1044.26i q^{89} +233.130i q^{91} +(344.213 - 1032.94i) q^{92} +(-309.200 - 428.952i) q^{94} +(-571.481 + 989.834i) q^{95} +(733.184 + 1269.91i) q^{97} +(34.3784 - 76.4422i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	2.81402	−	0.285097i	0.994907	−	0.100797i
$2$	2.81402	−	0.285097i	0.994907	−	0.100797i
$3$		0			0
$3$		0			0
$4$	7.83744	−	1.60454i	0.979680	−	0.200567i
$5$	14.4924	+	8.36717i	1.29624	+	0.748383i	0.979752	−	0.200215i	$-0.0641640\pi$
$5$	14.4924	+	8.36717i	1.29624	+	0.748383i	0.316485	+	0.948598i	$0.397497\pi$
$6$		0			0
$7$	−16.7175	+	9.65186i	−0.902661	+	0.521152i	−0.878063	−	0.478546i	$-0.841164\pi$
$7$	−16.7175	+	9.65186i	−0.902661	+	0.521152i	−0.0245984	+	0.999697i	$0.507831\pi$
$8$	21.5973	−	6.74964i	0.954474	−	0.298295i
$9$		0			0
$10$	43.1673	+	19.4137i	1.36507	+	0.613915i
$11$	−2.44092	−	4.22780i	−0.0669059	−	0.115884i	0.830632	−	0.556822i	$-0.187979\pi$
$11$	−2.44092	−	4.22780i	−0.0669059	−	0.115884i	−0.897538	+	0.440937i	$0.854646\pi$
$12$		0			0
$13$	6.03848	−	10.4590i	0.128829	−	0.223138i	−0.794394	−	0.607402i	$-0.792212\pi$
$13$	6.03848	−	10.4590i	0.128829	−	0.223138i	0.923223	+	0.384264i	$0.125545\pi$
$14$	−44.2917	+	31.9267i	−0.845533	+	0.609483i
$15$		0			0
$16$	58.8509	−	25.1509i	0.919546	−	0.392984i
$17$		−	71.2528i		−	1.01655i	−0.861195	−	0.508275i	$-0.830283\pi$
$17$		−	71.2528i		−	1.01655i	0.861195	−	0.508275i	$-0.169717\pi$
$18$		0			0
$19$			68.3003i			0.824693i	0.911027	+	0.412347i	$0.135291\pi$
$19$			68.3003i			0.824693i	−0.911027	+	0.412347i	$0.864709\pi$
$20$	127.009	+	42.3237i	1.42000	+	0.473193i
$21$		0			0
$22$	−8.07414	−	11.2012i	−0.0782460	−	0.108550i
$23$	68.0491	−	117.865i	0.616923	−	1.06854i	−0.373121	−	0.927783i	$-0.621712\pi$
$23$	68.0491	−	117.865i	0.616923	−	1.06854i	0.990044	−	0.140759i	$-0.0449543\pi$
$24$		0			0
$25$	77.5192	+	134.267i	0.620154	+	1.07414i
$26$	14.0106	−	31.1533i	0.105681	−	0.234987i
$27$		0			0
$28$	−115.536	+	102.470i	−0.779793	+	0.691606i
$29$	−190.237	+	109.833i	−1.21814	+	0.703295i	−0.964520	−	0.264009i	$-0.914955\pi$
$29$	−190.237	+	109.833i	−1.21814	+	0.703295i	−0.253622	+	0.967303i	$0.581622\pi$
$30$		0			0
$31$	−285.221	−	164.672i	−1.65249	−	0.954065i	−0.976044	−	0.217571i	$-0.930187\pi$
$31$	−285.221	−	164.672i	−1.65249	−	0.954065i	−0.676444	−	0.736494i	$-0.736480\pi$
$32$	158.437	−	87.5535i	0.875251	−	0.483669i
$33$		0			0
$34$	−20.3140	−	200.507i	−0.102465	−	1.01137i
$35$	−323.035			−1.56008
$36$		0			0
$37$	−133.618			−0.593693			−0.296847	−	0.954925i	$-0.595935\pi$
$37$	−133.618			−0.593693			−0.296847	+	0.954925i	$0.595935\pi$
$38$	19.4722	+	192.199i	0.0831266	+	0.820493i
$39$		0			0
$40$	369.471	+	82.8899i	1.46046	+	0.327651i
$41$	29.5326	+	17.0507i	0.112493	+	0.0649480i	0.555191	−	0.831723i	$-0.312645\pi$
$41$	29.5326	+	17.0507i	0.112493	+	0.0649480i	−0.442698	+	0.896671i	$0.645979\pi$
$42$		0			0
$43$	−0.558209	+	0.322282i	−0.00197967	+	0.00114297i	−0.500990	−	0.865453i	$-0.667030\pi$
$43$	−0.558209	+	0.322282i	−0.00197967	+	0.00114297i	0.499010	+	0.866596i	$0.333697\pi$
$44$	−25.9142	−	29.2186i	−0.0887890	−	0.100111i
$45$		0			0
$46$	157.889	−	351.074i	0.506075	−	1.12528i
$47$	−93.4753	−	161.904i	−0.290102	−	0.502471i	0.683732	−	0.729733i	$-0.260356\pi$
$47$	−93.4753	−	161.904i	−0.290102	−	0.502471i	−0.973834	+	0.227263i	$0.927022\pi$
$48$		0			0
$49$	14.8169	−	25.6636i	0.0431979	−	0.0748210i
$50$	256.420	+	355.730i	0.725265	+	1.00616i
$51$		0			0
$52$	30.5444	−	91.6604i	0.0814568	−	0.244443i
$53$			266.453i			0.690569i	0.938498	+	0.345284i	$0.112218\pi$
$53$			266.453i			0.690569i	−0.938498	+	0.345284i	$0.887782\pi$
$54$		0			0
$55$		−	81.6944i		−	0.200285i
$56$	−295.906	+	321.291i	−0.706110	+	0.766684i
$57$		0			0
$58$	−504.018	+	363.309i	−1.14105	+	0.822498i
$59$	104.347	−	180.734i	0.230251	−	0.398806i	−0.727631	−	0.685969i	$-0.759379\pi$
$59$	104.347	−	180.734i	0.230251	−	0.398806i	0.957882	+	0.287163i	$0.0927120\pi$
$60$		0			0
$61$	0.801886	+	1.38891i	0.00168313	+	0.00291527i	0.866866	−	0.498542i	$-0.166131\pi$
$61$	0.801886	+	1.38891i	0.00168313	+	0.00291527i	−0.865183	+	0.501457i	$0.832798\pi$
$62$	−849.565	−	382.076i	−1.74024	−	0.782640i
$63$		0			0
$64$	420.885	−	291.548i	0.822041	−	0.569429i
$65$	175.024	−	101.050i	0.333985	−	0.192826i
$66$		0			0
$67$	371.407	+	214.432i	0.677233	+	0.391001i	0.798812	−	0.601581i	$-0.205462\pi$
$67$	371.407	+	214.432i	0.677233	+	0.391001i	−0.121579	+	0.992582i	$0.538796\pi$
$68$	−114.328	−	558.440i	−0.203887	−	0.995893i
$69$		0			0
$70$	−909.028	+	92.0964i	−1.55214	+	0.157252i
$71$	386.365			0.645817			0.322909	−	0.946430i	$-0.395339\pi$
$71$	386.365			0.645817			0.322909	+	0.946430i	$0.395339\pi$
$72$		0			0
$73$	−776.832			−1.24550			−0.622749	−	0.782422i	$-0.713984\pi$
$73$	−776.832			−1.24550			−0.622749	+	0.782422i	$0.713984\pi$
$74$	−376.004	+	38.0941i	−0.590670	+	0.0598425i
$75$		0			0
$76$	109.591	+	535.300i	0.165407	+	0.807935i
$77$	81.6122	+	47.1188i	0.120787	+	0.0697362i
$78$		0			0
$79$	68.5000	−	39.5485i	0.0975551	−	0.0563235i	−0.450429	−	0.892812i	$-0.648729\pi$
$79$	68.5000	−	39.5485i	0.0975551	−	0.0563235i	0.547984	+	0.836489i	$0.315396\pi$
$80$	1063.33	+	127.919i	1.48605	+	0.178772i
$81$		0			0
$82$	87.9665	+	39.5613i	0.118467	+	0.0532782i
$83$	462.668	+	801.365i	0.611861	+	1.05977i	0.990927	+	0.134404i	$0.0429121\pi$
$83$	462.668	+	801.365i	0.611861	+	1.05977i	−0.379066	+	0.925370i	$0.623755\pi$
$84$		0			0
$85$	596.185	−	1032.62i	0.760768	−	1.31769i
$86$	−1.47893	+	1.06605i	−0.00185438	+	0.00133669i
$87$		0			0
$88$	−81.2533	−	74.8336i	−0.0984277	−	0.0906510i
$89$		−	1044.26i		−	1.24372i	−0.783128	−	0.621861i	$-0.786377\pi$
$89$		−	1044.26i		−	1.24372i	0.783128	−	0.621861i	$-0.213623\pi$
$90$		0			0
$91$			233.130i			0.268557i
$92$	344.213	−	1032.94i	0.390072	−	1.17056i
$93$		0			0
$94$	−309.200	−	428.952i	−0.339272	−	0.470670i
$95$	−571.481	+	989.834i	−0.617186	+	1.06900i
$96$		0			0
$97$	733.184	+	1269.91i	0.767460	+	1.32928i	0.938936	+	0.344091i	$0.111813\pi$
$97$	733.184	+	1269.91i	0.767460	+	1.32928i	−0.171477	+	0.985188i	$0.554854\pi$
$98$	34.3784	−	76.4422i	0.0354362	−	0.0787941i
$99$		0			0
$100$	822.989	+	927.929i	0.822989	+	0.927929i
$101$	314.302	−	181.462i	0.309646	−	0.178774i	−0.337122	−	0.941461i	$-0.609454\pi$
$101$	314.302	−	181.462i	0.309646	−	0.178774i	0.646768	+	0.762687i	$0.276120\pi$
$102$		0			0
$103$	466.128	+	269.119i	0.445912	+	0.257447i	0.706102	−	0.708110i	$-0.250452\pi$
$103$	466.128	+	269.119i	0.445912	+	0.257447i	−0.260190	+	0.965557i	$0.583785\pi$
$104$	59.8206	−	266.643i	0.0564028	−	0.251408i
$105$		0			0
$106$	75.9650	+	749.805i	0.0696073	+	0.687052i
$107$	430.456			0.388914			0.194457	−	0.980911i	$-0.437706\pi$
$107$	430.456			0.388914			0.194457	+	0.980911i	$0.437706\pi$
$108$		0			0
$109$	899.324			0.790272			0.395136	−	0.918623i	$-0.370697\pi$
$109$	899.324			0.790272			0.395136	+	0.918623i	$0.370697\pi$
$110$	−23.2908	−	229.890i	−0.0201881	−	0.199265i
$111$		0			0
$112$	−741.088	+	988.482i	−0.625234	+	0.833953i
$113$	330.860	+	191.022i	0.275440	+	0.159025i	0.631357	−	0.775492i	$-0.282498\pi$
$113$	330.860	+	191.022i	0.275440	+	0.159025i	−0.355917	+	0.934517i	$0.615832\pi$
$114$		0			0
$115$	1972.39	−	1138.76i	1.59936	−	0.923389i
$116$	−1314.74	+	1166.05i	−1.05233	+	0.933323i
$117$		0			0
$118$	242.107	−	538.338i	0.188880	−	0.419983i
$119$	687.722	+	1191.17i	0.529776	+	0.917600i
$120$		0			0
$121$	653.584	−	1132.04i	0.491047	−	0.850519i
$122$	2.65250	+	3.67980i	0.00196841	+	0.00273077i
$123$		0			0
$124$	−2499.62	−	832.961i	−1.81026	−	0.603243i
$125$			502.674i			0.359684i
$126$		0			0
$127$			1677.92i			1.17237i	0.810177	+	0.586186i	$0.199371\pi$
$127$			1677.92i			1.17237i	−0.810177	+	0.586186i	$0.800629\pi$
$128$	1101.26	−	940.414i	0.760457	−	0.649388i
$129$		0			0
$130$	463.712	−	334.256i	0.312848	−	0.225509i
$131$	712.418	−	1233.94i	0.475147	−	0.822979i	−0.524448	−	0.851443i	$-0.675728\pi$
$131$	712.418	−	1233.94i	0.475147	−	0.822979i	0.999595	+	0.0284637i	$0.00906150\pi$
$132$		0			0
$133$	−659.225	−	1141.81i	−0.429790	−	0.744418i
$134$	1106.28	+	497.529i	0.713196	+	0.320746i
$135$		0			0
$136$	−480.931	−	1538.87i	−0.303231	−	0.970270i
$137$	−23.2295	+	13.4116i	−0.0144864	+	0.00836370i	−0.507226	−	0.861813i	$-0.669329\pi$
$137$	−23.2295	+	13.4116i	−0.0144864	+	0.00836370i	0.492739	+	0.870177i	$0.335996\pi$
$138$		0			0
$139$	−1434.57	−	828.252i	−0.875388	−	0.505406i	−0.00625321	−	0.999980i	$-0.501990\pi$
$139$	−1434.57	−	828.252i	−0.875388	−	0.505406i	−0.869135	+	0.494575i	$0.835324\pi$
$140$	−2531.77	+	518.322i	−1.52838	+	0.312902i
$141$		0			0
$142$	1087.24	−	110.151i	0.642528	−	0.0650965i
$143$	−58.9578			−0.0344776
$144$		0			0
$145$	−3675.98			−2.10533
$146$	−2186.02	+	221.473i	−1.23915	+	0.125542i
$147$		0			0
$148$	−1047.22	+	214.395i	−0.581629	+	0.119075i
$149$	−738.285	−	426.249i	−0.405924	−	0.234360i	0.283113	−	0.959087i	$-0.408633\pi$
$149$	−738.285	−	426.249i	−0.405924	−	0.234360i	−0.689037	+	0.724726i	$0.741966\pi$
$150$		0			0
$151$	−1272.06	+	734.422i	−0.685553	+	0.395804i	−0.801944	−	0.597399i	$-0.796201\pi$
$151$	−1272.06	+	734.422i	−0.685553	+	0.395804i	0.116391	+	0.993203i	$0.462867\pi$
$152$	461.002	+	1475.10i	0.246002	+	0.787148i
$153$		0			0
$154$	243.092	+	109.326i	0.127201	+	0.0572061i
$155$	−2755.68	−	4772.98i	−1.42801	−	2.47339i
$156$		0			0
$157$	−1344.52	+	2328.78i	−0.683469	+	1.18380i	0.290446	+	0.956891i	$0.406196\pi$
$157$	−1344.52	+	2328.78i	−0.683469	+	1.18380i	−0.973915	+	0.226912i	$0.927137\pi$
$158$	181.485	−	130.820i	0.0913811	−	0.0658699i
$159$		0			0
$160$	3028.71	+	56.8143i	1.49650	+	0.0280723i
$161$			2627.20i			1.28604i
$162$		0			0
$163$		−	2186.50i		−	1.05067i	−0.850895	−	0.525336i	$-0.823940\pi$
$163$		−	2186.50i		−	1.05067i	0.850895	−	0.525336i	$-0.176060\pi$
$164$	258.819	+	86.2473i	0.123234	+	0.0410658i
$165$		0			0
$166$	1530.43	+	2123.15i	0.715567	+	0.992703i
$167$	−1790.65	+	3101.49i	−0.829726	+	1.43713i	0.0685268	+	0.997649i	$0.478170\pi$
$167$	−1790.65	+	3101.49i	−0.829726	+	1.43713i	−0.898253	+	0.439479i	$0.855163\pi$
$168$		0			0
$169$	1025.57	+	1776.35i	0.466806	+	0.808532i
$170$	1383.28	−	3075.79i	0.624075	−	1.38766i
$171$		0			0
$172$	−3.85781	+	3.42153i	−0.00171021	+	0.00151680i
$173$	94.5051	−	54.5625i	0.0415323	−	0.0239787i	−0.479090	−	0.877766i	$-0.659033\pi$
$173$	94.5051	−	54.5625i	0.0415323	−	0.0239787i	0.520622	+	0.853787i	$0.325700\pi$
$174$		0			0
$175$	−2591.86	−	1496.41i	−1.11958	−	0.646388i
$176$	−249.983	−	187.418i	−0.107064	−	0.0802681i
$177$		0			0
$178$	−297.715	−	2938.57i	−0.125363	−	1.23739i
$179$	268.397			0.112072			0.0560361	−	0.998429i	$-0.482154\pi$
$179$	268.397			0.112072			0.0560361	+	0.998429i	$0.482154\pi$
$180$		0			0
$181$	898.582			0.369011			0.184506	−	0.982831i	$-0.440932\pi$
$181$	898.582			0.369011			0.184506	+	0.982831i	$0.440932\pi$
$182$	66.4648	+	656.034i	0.0270698	+	0.267189i
$183$		0			0
$184$	674.133	−	3004.86i	0.270096	−	1.20392i
$185$	−1936.44	−	1118.00i	−0.769567	−	0.444310i
$186$		0			0
$187$	−301.242	+	173.922i	−0.117802	+	0.0680132i
$188$	−992.388	−	1118.93i	−0.384986	−	0.434076i
$189$		0			0
$190$	−1325.96	+	2948.34i	−0.506291	+	1.12576i
$191$	−257.331	−	445.711i	−0.0974860	−	0.168851i	0.813157	−	0.582044i	$-0.197747\pi$
$191$	−257.331	−	445.711i	−0.0974860	−	0.168851i	−0.910643	+	0.413193i	$0.864413\pi$
$192$		0			0
$193$	1229.66	−	2129.83i	0.458616	−	0.794346i	−0.540272	−	0.841490i	$-0.681679\pi$
$193$	1229.66	−	2129.83i	0.458616	−	0.794346i	0.998888	+	0.0471443i	$0.0150121\pi$
$194$	2425.24	+	3364.53i	0.897538	+	1.24515i
$195$		0			0
$196$	74.9482	−	224.911i	0.0273135	−	0.0819647i
$197$			646.506i			0.233815i	0.993143	+	0.116908i	$0.0372982\pi$
$197$			646.506i			0.233815i	−0.993143	+	0.116908i	$0.962702\pi$
$198$		0			0
$199$			1742.98i			0.620886i	0.950592	+	0.310443i	$0.100477\pi$
$199$			1742.98i			0.620886i	−0.950592	+	0.310443i	$0.899523\pi$
$200$	2580.46	+	2376.58i	0.912330	+	0.840248i
$201$		0			0
$202$	832.719	−	600.246i	0.290049	−	0.209075i
$203$	2120.19	−	3672.28i	0.733046	−	1.26967i
$204$		0			0
$205$	285.332	+	494.209i	0.0972119	+	0.168376i
$206$	1388.42	+	624.415i	0.469591	+	0.211190i
$207$		0			0
$208$	92.3175	−	767.393i	0.0307744	−	0.255813i
$209$	288.760	−	166.716i	0.0955691	−	0.0551769i
$210$		0			0
$211$	3648.27	+	2106.33i	1.19032	+	0.687231i	0.958379	−	0.285499i	$-0.0921593\pi$
$211$	3648.27	+	2106.33i	1.19032	+	0.687231i	0.231940	+	0.972730i	$0.425493\pi$
$212$	427.534	+	2088.31i	0.138506	+	0.676537i
$213$		0			0
$214$	1211.31	−	122.722i	0.386933	−	0.0392013i
$215$	−10.7864			−0.00342150
$216$		0			0
$217$	6357.58			1.98885
$218$	2530.72	−	256.395i	0.786247	−	0.0796570i
$219$		0			0
$220$	−131.082	−	640.275i	−0.0401706	−	0.196215i
$221$	−745.230	−	430.259i	−0.226831	−	0.130961i
$222$		0			0
$223$	−5558.55	+	3209.23i	−1.66918	+	0.963703i	−0.701103	+	0.713060i	$0.747309\pi$
$223$	−5558.55	+	3209.23i	−1.66918	+	0.963703i	−0.968080	+	0.250643i	$0.919358\pi$
$224$	−1803.62	+	2992.89i	−0.537990	+	0.892728i
$225$		0			0
$226$	985.507	+	443.213i	0.290066	+	0.130452i
$227$	1124.83	+	1948.27i	0.328889	+	0.569653i	0.982292	−	0.187358i	$-0.0599924\pi$
$227$	1124.83	+	1948.27i	0.328889	+	0.569653i	−0.653403	+	0.757011i	$0.726659\pi$
$228$		0			0
$229$	−1735.36	+	3005.74i	−0.500769	+	0.867357i	0.499231	+	0.866469i	$0.333616\pi$
$229$	−1735.36	+	3005.74i	−0.500769	+	0.867357i	−1.00000		0.000888202i	$0.999717\pi$
$230$	5225.68	−	3766.81i	1.49814	−	1.07990i
$231$		0			0
$232$	−3367.27	+	3656.13i	−0.952896	+	1.03464i
$233$		−	3852.67i		−	1.08325i	−0.840621	−	0.541624i	$-0.817810\pi$
$233$		−	3852.67i		−	1.08325i	0.840621	−	0.541624i	$-0.182190\pi$
$234$		0			0
$235$		−	3128.50i		−	0.868428i
$236$	527.817	−	1583.92i	0.145585	−	0.436883i
$237$		0			0
$238$	2274.86	+	3155.91i	0.619570	+	0.859527i
$239$	−19.9334	+	34.5257i	−0.00539491	+	0.00934426i	−0.868710	−	0.495321i	$-0.835051\pi$
$239$	−19.9334	+	34.5257i	−0.00539491	+	0.00934426i	0.863315	+	0.504665i	$0.168384\pi$
$240$		0			0
$241$	−1729.18	−	2995.03i	−0.462184	−	0.800527i	0.536885	−	0.843655i	$-0.319601\pi$
$241$	−1729.18	−	2995.03i	−0.462184	−	0.800527i	−0.999070	+	0.0431286i	$0.986267\pi$
$242$	1516.46	−	3371.92i	0.402817	−	0.895683i
$243$		0			0
$244$	8.51329	+	9.59882i	0.00223364	+	0.00251845i
$245$	429.464	−	247.951i	0.111989	−	0.0646572i
$246$		0			0
$247$	714.350	+	412.430i	0.184020	+	0.106244i
$248$	−7271.47	−	1631.34i	−1.86185	−	0.417701i
$249$		0			0
$250$	143.311	+	1414.53i	0.0362551	+	0.357852i
$251$	−2977.61			−0.748786			−0.374393	−	0.927270i	$-0.622149\pi$
$251$	−2977.61			−0.748786			−0.374393	+	0.927270i	$0.622149\pi$
$252$		0			0
$253$	−664.410			−0.165103
$254$	478.369	+	4721.70i	0.118172	+	1.16640i
$255$		0			0
$256$	2830.86	−	2960.31i	0.691128	−	0.722732i
$257$	5593.28	+	3229.28i	1.35758	+	0.783802i	0.989298	−	0.145910i	$-0.0466111\pi$
$257$	5593.28	+	3229.28i	1.35758	+	0.783802i	0.368287	+	0.929712i	$0.379944\pi$
$258$		0			0
$259$	2233.76	−	1289.66i	0.535904	−	0.309404i
$260$	1209.60	−	1072.81i	0.288524	−	0.255895i
$261$		0			0
$262$	1652.97	−	3675.46i	0.389773	−	0.866681i
$263$	2940.99	+	5093.94i	0.689540	+	1.19432i	0.971987	+	0.235036i	$0.0755207\pi$
$263$	2940.99	+	5093.94i	0.689540	+	1.19432i	−0.282447	+	0.959283i	$0.591146\pi$
$264$		0			0
$265$	−2229.46	+	3861.54i	−0.516810	+	0.895141i
$266$	−2180.60	−	3025.14i	−0.502636	−	0.697306i
$267$		0			0
$268$	3254.95	+	1084.66i	0.741894	+	0.247225i
$269$		−	2967.07i		−	0.672510i	−0.941771	−	0.336255i	$-0.890840\pi$
$269$		−	2967.07i		−	0.672510i	0.941771	−	0.336255i	$-0.109160\pi$
$270$		0			0
$271$		−	1985.78i		−	0.445121i	−0.974919	−	0.222561i	$-0.928559\pi$
$271$		−	1985.78i		−	0.445121i	0.974919	−	0.222561i	$-0.0714415\pi$
$272$	−1792.08	−	4193.29i	−0.399487	−	0.934764i
$273$		0			0
$274$	−61.5447	+	44.3631i	−0.0135695	+	0.00978128i
$275$	378.436	−	655.471i	0.0829839	−	0.143732i
$276$		0			0
$277$	−2171.48	−	3761.12i	−0.471017	−	0.815825i	0.528433	−	0.848975i	$-0.322780\pi$
$277$	−2171.48	−	3761.12i	−0.471017	−	0.815825i	−0.999450	+	0.0331494i	$0.989446\pi$
$278$	−4273.05	−	1921.73i	−0.921873	−	0.414595i
$279$		0			0
$280$	−6976.68	+	2180.37i	−1.48906	+	0.465365i
$281$	−6752.10	+	3898.33i	−1.43344	+	0.827597i	−0.997381	−	0.0723220i	$-0.976959\pi$
$281$	−6752.10	+	3898.33i	−1.43344	+	0.827597i	−0.436058	+	0.899919i	$0.643626\pi$
$282$		0			0
$283$	1771.47	+	1022.76i	0.372094	+	0.214829i	0.674373	−	0.738391i	$-0.264414\pi$
$283$	1771.47	+	1022.76i	0.372094	+	0.214829i	−0.302279	+	0.953220i	$0.597747\pi$
$284$	3028.11	−	619.937i	0.632694	−	0.129530i
$285$		0			0
$286$	−165.909	+	16.8087i	−0.0343020	+	0.00347524i
$287$	−658.283			−0.135391
$288$		0			0
$289$	−163.963			−0.0333732
$290$	−10344.3	+	1048.01i	−2.09461	+	0.212211i
$291$		0			0
$292$	−6088.38	+	1246.46i	−1.22019	+	0.249806i
$293$	2041.60	+	1178.72i	0.407070	+	0.235022i	0.689530	−	0.724257i	$-0.257817\pi$
$293$	2041.60	+	1178.72i	0.407070	+	0.235022i	−0.282460	+	0.959279i	$0.591151\pi$
$294$		0			0
$295$	3024.46	−	1746.18i	0.596919	−	0.344631i
$296$	−2885.78	+	901.873i	−0.566665	+	0.177096i
$297$		0			0
$298$	−2199.07	−	988.991i	−0.427479	−	0.192251i
$299$	−821.827	−	1423.45i	−0.158955	−	0.275318i
$300$		0			0
$301$	6.22124	−	10.7755i	0.00119132	−	0.00206342i
$302$	−3370.21	+	2429.34i	−0.642165	+	0.462890i
$303$		0			0
$304$	1717.82	+	4019.54i	0.324091	+	0.758343i
$305$			26.8381i			0.00503851i
$306$		0			0
$307$			5521.27i			1.02643i	0.858259	+	0.513217i	$0.171546\pi$
$307$			5521.27i			1.02643i	−0.858259	+	0.513217i	$0.828454\pi$
$308$	715.235	+	238.341i	0.132319	+	0.0440933i
$309$		0			0
$310$	−9115.32	−	12645.6i	−1.67005	−	2.31685i
$311$	767.330	−	1329.05i	0.139908	−	0.242327i	−0.787554	−	0.616246i	$-0.788653\pi$
$311$	767.330	−	1329.05i	0.139908	−	0.242327i	0.927461	+	0.373919i	$0.121986\pi$
$312$		0			0
$313$	−4383.28	−	7592.06i	−0.791557	−	1.37102i	−0.925003	−	0.379961i	$-0.875937\pi$
$313$	−4383.28	−	7592.06i	−0.791557	−	1.37102i	0.133446	−	0.991056i	$-0.457396\pi$
$314$	−3119.59	+	6936.57i	−0.560664	+	1.24667i
$315$		0			0
$316$	473.408	−	419.870i	0.0842762	−	0.0747454i
$317$	6074.45	−	3507.08i	1.07626	−	0.621380i	0.146376	−	0.989229i	$-0.453239\pi$
$317$	6074.45	−	3507.08i	1.07626	−	0.621380i	0.929886	+	0.367849i	$0.119906\pi$
$318$		0			0
$319$	928.706	+	536.189i	0.163002	+	0.0941091i
$320$	8539.05	−	703.599i	1.49171	−	0.122914i
$321$		0			0
$322$	749.008	+	7393.01i	0.129629	+	1.27949i
$323$	4866.59			0.838342
$324$		0			0
$325$	1872.39			0.319574
$326$	−623.363	−	6152.85i	−0.105905	−	1.04532i
$327$		0			0
$328$	752.910	+	168.914i	0.126745	+	0.0284350i
$329$	3125.35	+	1804.42i	0.523727	+	0.302374i
$330$		0			0
$331$	8563.21	−	4943.97i	1.42198	−	0.820982i	0.425515	−	0.904951i	$-0.360093\pi$
$331$	8563.21	−	4943.97i	1.42198	−	0.820982i	0.996468	+	0.0839692i	$0.0267597\pi$
$332$	4911.96	+	5538.28i	0.811984	+	0.915520i
$333$		0			0
$334$	−4154.69	+	9238.16i	−0.680642	+	1.51344i
$335$	3588.38	+	6215.26i	0.585236	+	1.01366i
$336$		0			0
$337$	2504.10	−	4337.22i	0.404768	−	0.701079i	−0.589527	−	0.807749i	$-0.700686\pi$
$337$	2504.10	−	4337.22i	0.404768	−	0.701079i	0.994294	+	0.106670i	$0.0340190\pi$
$338$	3392.42	+	4706.29i	0.545927	+	0.757362i
$339$		0			0
$340$	3015.68	−	9049.71i	0.481024	−	1.44350i
$341$			1607.81i			0.255330i
$342$		0			0
$343$		−	6049.14i		−	0.952252i
$344$	−9.88050	+	10.7281i	−0.00154861	+	0.00168146i
$345$		0			0
$346$	250.384	−	180.483i	0.0389038	−	0.0280429i
$347$	−3897.53	+	6750.72i	−0.602969	+	1.04437i	0.389399	+	0.921069i	$0.372683\pi$
$347$	−3897.53	+	6750.72i	−0.602969	+	1.04437i	−0.992369	+	0.123305i	$0.960651\pi$
$348$		0			0
$349$	4540.81	+	7864.91i	0.696458	+	1.20630i	0.969687	+	0.244352i	$0.0785753\pi$
$349$	4540.81	+	7864.91i	0.696458	+	1.20630i	−0.273228	+	0.961949i	$0.588091\pi$
$350$	−7720.17	−	3472.00i	−1.17903	−	0.530246i
$351$		0			0
$352$	−756.891	−	456.130i	−0.114609	−	0.0690676i
$353$	−3944.55	+	2277.39i	−0.594752	+	0.343380i	−0.766974	−	0.641678i	$-0.778239\pi$
$353$	−3944.55	+	2277.39i	−0.594752	+	0.343380i	0.172222	+	0.985058i	$0.444905\pi$
$354$		0			0
$355$	5599.34	+	3232.78i	0.837133	+	0.483319i
$356$	−1675.55	−	8184.32i	−0.249450	−	1.21845i
$357$		0			0
$358$	755.275	−	76.5192i	0.111501	−	0.0112965i
$359$	−5415.10			−0.796095			−0.398047	−	0.917365i	$-0.630312\pi$
$359$	−5415.10			−0.796095			−0.398047	+	0.917365i	$0.630312\pi$
$360$		0			0
$361$	2194.06			0.319881
$362$	2528.63	−	256.183i	0.367132	−	0.0371953i
$363$		0			0
$364$	374.067	+	1827.15i	0.0538638	+	0.263100i
$365$	−11258.1	−	6499.89i	−1.61446	−	0.932109i
$366$		0			0
$367$	−9228.51	+	5328.08i	−1.31260	+	0.757830i	−0.982526	−	0.186125i	$-0.940407\pi$
$367$	−9228.51	+	5328.08i	−1.31260	+	0.757830i	−0.330074	+	0.943955i	$0.607074\pi$
$368$	1040.35	−	8647.94i	0.147369	−	1.22501i
$369$		0			0
$370$	−5767.93	−	2594.02i	−0.810433	−	0.364477i
$371$	−2571.77	−	4454.43i	−0.359891	−	0.623350i
$372$		0			0
$373$	−1354.99	+	2346.91i	−0.188093	+	0.325786i	−0.944614	−	0.328183i	$-0.893564\pi$
$373$	−1354.99	+	2346.91i	−0.188093	+	0.325786i	0.756522	+	0.653969i	$0.226897\pi$
$374$	−798.118	+	575.305i	−0.110347	+	0.0795409i
$375$		0			0
$376$	−3111.61	−	2865.76i	−0.426779	−	0.393059i
$377$			2652.91i			0.362418i
$378$		0			0
$379$		−	6395.35i		−	0.866774i	−0.901208	−	0.433387i	$-0.857318\pi$
$379$		−	6395.35i		−	0.866774i	0.901208	−	0.433387i	$-0.142682\pi$
$380$	−2890.72	+	8674.73i	−0.390239	+	1.17106i
$381$		0			0
$382$	−851.206	−	1180.88i	−0.114009	−	0.158164i
$383$	682.579	−	1182.26i	0.0910656	−	0.157730i	−0.816894	−	0.576788i	$-0.804306\pi$
$383$	682.579	−	1182.26i	0.0910656	−	0.157730i	0.907960	+	0.419057i	$0.137639\pi$
$384$		0			0
$385$	788.503	+	1365.73i	0.104379	+	0.180789i
$386$	2853.08	−	6343.97i	0.376212	−	0.836528i
$387$		0			0
$388$	7783.91	+	8776.44i	1.01847	+	1.14834i
$389$	5380.83	−	3106.62i	0.701333	−	0.404915i	−0.106510	−	0.994312i	$-0.533968\pi$
$389$	5380.83	−	3106.62i	0.701333	−	0.404915i	0.807844	+	0.589397i	$0.200634\pi$
$390$		0			0
$391$	−8398.18	−	4848.69i	−1.08623	−	0.627133i
$392$	146.784	−	654.272i	0.0189126	−	0.0843004i
$393$		0			0
$394$	184.317	+	1819.28i	0.0235679	+	0.232625i
$395$	1323.64			0.168606
$396$		0			0
$397$	3291.69			0.416134			0.208067	−	0.978115i	$-0.433283\pi$
$397$	3291.69			0.416134			0.208067	+	0.978115i	$0.433283\pi$
$398$	496.917	+	4904.77i	0.0625834	+	0.617723i
$399$		0			0
$400$	7939.02	+	5952.07i	0.992378	+	0.744008i
$401$	−3529.51	−	2037.76i	−0.439539	−	0.253768i	0.263863	−	0.964560i	$-0.415003\pi$
$401$	−3529.51	−	2037.76i	−0.439539	−	0.253768i	−0.703402	+	0.710792i	$0.748337\pi$
$402$		0			0
$403$	−3444.60	+	1988.74i	−0.425776	+	0.245822i
$404$	2172.16	−	1926.51i	0.267498	−	0.237246i
$405$		0			0
$406$	4919.31	−	10938.3i	0.601333	−	1.33710i
$407$	326.151	+	564.910i	0.0397216	+	0.0687998i
$408$		0			0
$409$	−7054.78	+	12219.2i	−0.852900	+	1.47727i	0.0256787	+	0.999670i	$0.491825\pi$
$409$	−7054.78	+	12219.2i	−0.852900	+	1.47727i	−0.878579	+	0.477597i	$0.841508\pi$
$410$	943.828	+	1309.37i	0.113689	+	0.157720i
$411$		0			0
$412$	4085.06	+	1361.28i	0.488487	+	0.162781i
$413$			4028.56i			0.479982i
$414$		0			0
$415$			15484.9i			1.83162i
$416$	41.0022	−	2185.78i	0.00483244	−	0.257612i
$417$		0			0
$418$	765.047	−	551.466i	0.0895207	−	0.0645289i
$419$	3184.20	−	5515.19i	0.371261	−	0.643042i	−0.618499	−	0.785786i	$-0.712259\pi$
$419$	3184.20	−	5515.19i	0.371261	−	0.643042i	0.989760	+	0.142743i	$0.0455923\pi$
$420$		0			0
$421$	−5406.24	−	9363.89i	−0.625853	−	1.08401i	−0.988375	−	0.152034i	$-0.951418\pi$
$421$	−5406.24	−	9363.89i	−0.625853	−	1.08401i	0.362522	−	0.931975i	$-0.381916\pi$
$422$	10866.8	+	4887.15i	1.25353	+	0.563750i
$423$		0			0
$424$	1798.46	+	5754.66i	0.205993	+	0.659130i
$425$	9566.92	−	5523.46i	1.09191	−	0.630417i
$426$		0			0
$427$	−26.8111	−	15.4794i	−0.00303859	−	0.00175433i
$428$	3373.67	−	690.683i	0.381011	−	0.0780034i
$429$		0			0
$430$	−30.3530	+	3.07516i	−0.00340408	+	0.000344877i
$431$	10968.4			1.22583			0.612913	−	0.790150i	$-0.289998\pi$
$431$	10968.4			1.22583			0.612913	+	0.790150i	$0.289998\pi$
$432$		0			0
$433$	−1491.10			−0.165491			−0.0827457	−	0.996571i	$-0.526369\pi$
$433$	−1491.10			−0.165491			−0.0827457	+	0.996571i	$0.526369\pi$
$434$	17890.4	−	1812.53i	1.97872	−	0.200470i
$435$		0			0
$436$	7048.40	−	1443.00i	0.774213	−	0.158503i
$437$	8050.19	+	4647.78i	0.881219	+	0.508772i
$438$		0			0
$439$	−1927.62	+	1112.91i	−0.209567	+	0.120994i	−0.601110	−	0.799166i	$-0.705275\pi$
$439$	−1927.62	+	1112.91i	−0.209567	+	0.120994i	0.391543	+	0.920160i	$0.371941\pi$
$440$	−551.408	−	1764.38i	−0.0597439	−	0.191167i
$441$		0			0
$442$	−2219.76	−	998.295i	−0.238876	−	0.107430i
$443$	−7938.74	−	13750.3i	−0.851425	−	1.47471i	−0.879923	−	0.475117i	$-0.842406\pi$
$443$	−7938.74	−	13750.3i	−0.851425	−	1.47471i	0.0284982	−	0.999594i	$-0.490927\pi$
$444$		0			0
$445$	8737.50	−	15133.8i	0.930780	−	1.61216i
$446$	−14726.9	+	10615.6i	−1.56354	+	1.12704i
$447$		0			0
$448$	−4222.17	+	8936.27i	−0.445265	+	0.942409i
$449$		−	11558.7i		−	1.21490i	−0.794358	−	0.607450i	$-0.792193\pi$
$449$		−	11558.7i		−	1.21490i	0.794358	−	0.607450i	$-0.207807\pi$
$450$		0			0
$451$		−	166.477i		−	0.0173816i
$452$	2899.60	+	966.246i	0.301738	+	0.100550i
$453$		0			0
$454$	3720.75	+	5161.78i	0.384633	+	0.533600i
$455$	−1950.64	+	3378.61i	−0.200984	+	0.348114i
$456$		0			0
$457$	5444.85	+	9430.75i	0.557329	+	0.965322i	0.997718	+	0.0675148i	$0.0215070\pi$
$457$	5444.85	+	9430.75i	0.557329	+	0.965322i	−0.440390	+	0.897807i	$0.645160\pi$
$458$	−4026.43	+	8952.96i	−0.410792	+	0.913416i
$459$		0			0
$460$	13631.3	−	12089.7i	1.38166	−	1.22540i
$461$	−10197.5	+	5887.54i	−1.03025	+	0.594816i	−0.917057	−	0.398757i	$-0.869442\pi$
$461$	−10197.5	+	5887.54i	−1.03025	+	0.594816i	−0.113195	+	0.993573i	$0.536108\pi$
$462$		0			0
$463$	2303.58	+	1329.97i	0.231223	+	0.133497i	0.611136	−	0.791525i	$-0.290713\pi$
$463$	2303.58	+	1329.97i	0.231223	+	0.133497i	−0.379913	+	0.925022i	$0.624046\pi$
$464$	−8433.21	+	11248.4i	−0.843754	+	1.12542i
$465$		0			0
$466$	−1098.39	−	10841.5i	−0.109188	−	1.07773i
$467$	−32.9750			−0.00326746			−0.00163373	−	0.999999i	$-0.500520\pi$
$467$	−32.9750			−0.00326746			−0.00163373	+	0.999999i	$0.500520\pi$
$468$		0			0
$469$	−8278.68			−0.815083
$470$	−891.925	−	8803.66i	−0.0875350	−	0.864006i
$471$		0			0
$472$	1033.72	−	4607.66i	0.100807	−	0.449332i
$473$	2.72509	+	1.57333i	0.000264904	+	0.000152942i
$474$		0			0
$475$	−9170.50	+	5294.59i	−0.885834	+	0.511437i
$476$	7301.26	+	8232.25i	0.703052	+	0.792698i
$477$		0			0
$478$	−46.2499	+	102.839i	−0.00442556	+	0.00984046i
$479$	−4069.08	−	7047.85i	−0.388144	−	0.672284i	0.604056	−	0.796942i	$-0.293550\pi$
$479$	−4069.08	−	7047.85i	−0.388144	−	0.672284i	−0.992200	+	0.124657i	$0.960217\pi$
$480$		0			0
$481$	−806.850	+	1397.50i	−0.0764848	+	0.132476i
$482$	−5719.83	−	7935.10i	−0.540521	−	0.749863i
$483$		0			0
$484$	3306.02	−	9921.00i	0.310483	−	0.931724i
$485$			24538.7i			2.29741i
$486$		0			0
$487$		−	1992.29i		−	0.185378i	−0.995695	−	0.0926891i	$-0.970454\pi$
$487$		−	1992.29i		−	0.185378i	0.995695	−	0.0926891i	$-0.0295463\pi$
$488$	26.6932	+	24.5842i	0.00247611	+	0.00228048i
$489$		0			0
$490$	1137.83	−	820.178i	0.104902	−	0.0756161i
$491$	4407.34	−	7633.75i	0.405093	−	0.701642i	−0.589239	−	0.807959i	$-0.700572\pi$
$491$	4407.34	−	7633.75i	0.405093	−	0.701642i	0.994332	+	0.106317i	$0.0339058\pi$
$492$		0			0
$493$	7825.94	+	13554.9i	0.714934	+	1.23830i
$494$	2127.78	+	956.929i	0.193792	+	0.0871544i
$495$		0			0
$496$	−20927.2	−	2517.54i	−1.89447	−	0.227905i
$497$	−6459.06	+	3729.14i	−0.582954	+	0.336569i
$498$		0			0
$499$	−18252.9	−	10538.3i	−1.63750	−	0.945409i	−0.981691	−	0.190479i	$-0.938996\pi$
$499$	−18252.9	−	10538.3i	−1.63750	−	0.945409i	−0.655806	−	0.754930i	$-0.727671\pi$
$500$	806.559	+	3939.67i	0.0721408	+	0.352375i
$501$		0			0
$502$	−8379.07	+	848.909i	−0.744973	+	0.0754754i
$503$	−19011.6			−1.68526			−0.842629	−	0.538494i	$-0.818994\pi$
$503$	−19011.6			−1.68526			−0.842629	+	0.538494i	$0.818994\pi$
$504$		0			0
$505$	6073.31			0.535166
$506$	−1869.66	+	189.421i	−0.164262	+	0.0166419i
$507$		0			0
$508$	2692.28	+	13150.6i	0.235139	+	1.14855i
$509$	−11096.0	−	6406.27i	−0.966250	−	0.557865i	−0.0681588	−	0.997674i	$-0.521712\pi$
$509$	−11096.0	−	6406.27i	−0.966250	−	0.557865i	−0.898091	+	0.439810i	$0.855046\pi$
$510$		0			0
$511$	12986.7	−	7497.88i	1.12426	−	0.649093i
$512$	7122.13	−	9137.45i	0.614759	−	0.788715i
$513$		0			0
$514$	16660.3	+	7492.64i	1.42968	+	0.642970i
$515$	4503.53	+	7800.35i	0.385339	+	0.667426i
$516$		0			0
$517$	−456.332	+	790.390i	−0.0388190	+	0.0672365i
$518$	5918.17	−	4265.98i	0.501987	−	0.361846i
$519$		0			0
$520$	3097.99	−	3363.75i	0.261261	−	0.283674i
$521$		−	14455.7i		−	1.21558i	−0.794100	−	0.607788i	$-0.792057\pi$
$521$		−	14455.7i		−	1.21558i	0.794100	−	0.607788i	$-0.207943\pi$
$522$		0			0
$523$		−	15232.9i		−	1.27359i	−0.771032	−	0.636796i	$-0.780259\pi$
$523$		−	15232.9i		−	1.27359i	0.771032	−	0.636796i	$-0.219741\pi$
$524$	3603.62	−	10814.1i	0.300429	−	0.901555i
$525$		0			0
$526$	9728.27	+	13496.0i	0.806412	+	1.11873i
$527$	−11733.4	+	20322.8i	−0.969854	+	1.67984i
$528$		0			0
$529$	−3177.87	−	5504.23i	−0.261187	−	0.452390i
$530$	−5172.84	+	11502.1i	−0.423950	+	0.942675i
$531$		0			0
$532$	−6998.72	−	7891.13i	−0.570363	−	0.643090i
$533$	356.664	−	205.920i	0.0289847	−	0.0167343i
$534$		0			0
$535$	6238.33	+	3601.70i	0.504124	+	0.291056i
$536$	9468.72	+	2124.29i	0.763035	+	0.171185i
$537$		0			0
$538$	−845.902	−	8349.39i	−0.0677870	−	0.669085i
$539$	−144.667			−0.0115608
$540$		0			0
$541$	−23075.7			−1.83383			−0.916915	−	0.399083i	$-0.869328\pi$
$541$	−23075.7			−1.83383			−0.916915	+	0.399083i	$0.869328\pi$
$542$	−566.141	−	5588.04i	−0.0448669	−	0.442854i
$543$		0			0
$544$	−6238.43	−	11289.1i	−0.491674	−	0.889736i
$545$	13033.3	+	7524.80i	1.02438	+	0.591426i
$546$		0			0
$547$	−317.151	+	183.107i	−0.0247905	+	0.0143128i	−0.512344	−	0.858780i	$-0.671223\pi$
$547$	−317.151	+	183.107i	−0.0247905	+	0.0143128i	0.487554	+	0.873093i	$0.337889\pi$
$548$	−160.540	+	142.385i	−0.0125145	+	0.0110992i
$549$		0			0
$550$	878.056	−	1952.40i	0.0680735	−	0.151365i
$551$	−7501.66	−	12993.2i	−0.580002	−	1.00459i
$552$		0			0
$553$	−763.434	+	1322.31i	−0.0587061	+	0.101682i
$554$	−7182.88	−	9964.78i	−0.550851	−	0.764193i
$555$		0			0
$556$	−12572.3	−	4189.54i	−0.958968	−	0.319562i
$557$		−	3402.66i		−	0.258842i	−0.991590	−	0.129421i	$-0.958688\pi$
$557$		−	3402.66i		−	0.258842i	0.991590	−	0.129421i	$-0.0413119\pi$
$558$		0			0
$559$			7.78437i			0.000588987i
$560$	−19010.9	+	8124.64i	−1.43457	+	0.613087i
$561$		0			0
$562$	−17889.2	+	12895.0i	−1.34272	+	0.967868i
$563$	2461.45	−	4263.36i	0.184259	−	0.319146i	−0.759068	−	0.651012i	$-0.774345\pi$
$563$	2461.45	−	4263.36i	0.184259	−	0.319146i	0.943327	+	0.331866i	$0.107678\pi$
$564$		0			0
$565$	3196.63	+	5536.73i	0.238023	+	0.412269i
$566$	5276.53	+	2373.02i	0.391854	+	0.176229i
$567$		0			0
$568$	8344.42	−	2607.82i	0.616416	−	0.192644i
$569$	−10423.8	+	6018.16i	−0.767990	+	0.443399i	−0.832157	−	0.554540i	$-0.812894\pi$
$569$	−10423.8	+	6018.16i	−0.767990	+	0.443399i	0.0641669	+	0.997939i	$0.479561\pi$
$570$		0			0
$571$	522.706	+	301.784i	0.0383092	+	0.0221178i	0.519032	−	0.854755i	$-0.326292\pi$
$571$	522.706	+	301.784i	0.0383092	+	0.0221178i	−0.480723	+	0.876872i	$0.659626\pi$
$572$	−462.078	+	94.6001i	−0.0337770	+	0.00691508i
$573$		0			0
$574$	−1852.42	+	187.674i	−0.134701	+	0.0136470i
$575$	21100.5			1.53035
$576$		0			0
$577$	−6971.52			−0.502995			−0.251497	−	0.967858i	$-0.580923\pi$
$577$	−6971.52			−0.502995			−0.251497	+	0.967858i	$0.580923\pi$
$578$	−461.395	+	46.7453i	−0.0332033	+	0.00336392i
$579$		0			0
$580$	−28810.3	+	5898.25i	−2.06255	+	0.422261i
$581$	−15469.3	−	8931.22i	−1.10461	−	0.637745i
$582$		0			0
$583$	1126.51	−	650.391i	0.0800262	−	0.0462032i
$584$	−16777.5	+	5243.34i	−1.18880	+	0.371525i
$585$		0			0
$586$	6081.15	+	2734.88i	0.428686	+	0.192793i
$587$	10334.9	+	17900.6i	0.726691	+	1.25867i	0.958274	+	0.285851i	$0.0922762\pi$
$587$	10334.9	+	17900.6i	0.726691	+	1.25867i	−0.231583	+	0.972815i	$0.574390\pi$
$588$		0			0
$589$	11247.2	−	19480.7i	0.786811	−	1.36280i
$590$	8013.08	−	5776.04i	0.559141	−	0.403044i
$591$		0			0
$592$	−7863.54	+	3360.62i	−0.545928	+	0.233312i
$593$			2417.22i			0.167392i	0.996491	+	0.0836958i	$0.0266724\pi$
$593$			2417.22i			0.167392i	−0.996491	+	0.0836958i	$0.973328\pi$
$594$		0			0
$595$			23017.2i			1.58590i
$596$	−6470.19	−	2156.09i	−0.444680	−	0.148183i
$597$		0			0
$598$	−2718.46	−	3771.31i	−0.185896	−	0.257893i
$599$	14467.5	−	25058.4i	0.986852	−	1.70928i	0.353452	−	0.935453i	$-0.385008\pi$
$599$	14467.5	−	25058.4i	0.986852	−	1.70928i	0.633400	−	0.773825i	$-0.281659\pi$
$600$		0			0
$601$	−318.246	−	551.219i	−0.0215999	−	0.0374121i	0.855023	−	0.518589i	$-0.173543\pi$
$601$	−318.246	−	551.219i	−0.0215999	−	0.0374121i	−0.876623	+	0.481177i	$0.840209\pi$
$602$	14.4346	−	32.0962i	0.000977263	−	0.00217299i
$603$		0			0
$604$	−8791.25	+	7797.05i	−0.592237	+	0.525261i
$605$	18944.0	−	10937.3i	1.27303	−	0.734983i
$606$		0			0
$607$	16616.3	+	9593.41i	1.11109	+	0.641490i	0.939112	−	0.343610i	$-0.111650\pi$
$607$	16616.3	+	9593.41i	1.11109	+	0.641490i	0.171981	+	0.985100i	$0.444983\pi$
$608$	5979.94	+	10821.3i	0.398879	+	0.721813i
$609$		0			0
$610$	7.65146	+	75.5230i	0.000507866	+	0.00501284i
$611$	−2257.80			−0.149494
$612$		0			0
$613$	6429.22			0.423612			0.211806	−	0.977312i	$-0.432066\pi$
$613$	6429.22			0.423612			0.211806	+	0.977312i	$0.432066\pi$
$614$	1574.10	+	15537.0i	0.103462	+	1.02121i
$615$		0			0
$616$	2080.64	+	466.786i	0.136090	+	0.0305314i
$617$	6024.79	+	3478.41i	0.393110	+	0.226962i	0.683507	−	0.729944i	$-0.260454\pi$
$617$	6024.79	+	3478.41i	0.393110	+	0.226962i	−0.290397	+	0.956906i	$0.593787\pi$
$618$		0			0
$619$	19227.5	−	11101.0i	1.24850	−	0.720819i	0.277686	−	0.960672i	$-0.410433\pi$
$619$	19227.5	−	11101.0i	1.24850	−	0.720819i	0.970809	+	0.239853i	$0.0770992\pi$
$620$	−29255.9	−	32986.4i	−1.89508	−	2.13672i
$621$		0			0
$622$	1780.37	−	3958.75i	0.114769	−	0.255195i
$623$	10079.0	+	17457.4i	0.648168	+	1.12266i
$624$		0			0
$625$	5483.94	−	9498.47i	0.350972	−	0.607902i
$626$	−14499.1	−	20114.6i	−0.925720	−	1.28425i
$627$		0			0
$628$	−6801.00	+	20409.0i	−0.432149	+	1.29683i
$629$			9520.65i			0.603519i
$630$		0			0
$631$		−	529.250i		−	0.0333901i	−0.999861	−	0.0166950i	$-0.994686\pi$
$631$		−	529.250i		−	0.0333901i	0.999861	−	0.0166950i	$-0.00531444\pi$
$632$	1212.48	−	1316.49i	0.0763128	−	0.0828595i
$633$		0			0
$634$	16093.8	−	11600.8i	1.00815	−	0.726699i
$635$	−14039.4	+	24317.0i	−0.877383	+	1.51967i
$636$		0			0
$637$	−178.943	−	309.938i	−0.0111303	−	0.0192782i
$638$	2766.27	+	1244.08i	0.171658	+	0.0771997i
$639$		0			0
$640$	23828.5	−	4414.40i	1.47172	−	0.272648i
$641$	19866.3	−	11469.8i	1.22414	−	0.706755i	0.258339	−	0.966054i	$-0.416825\pi$
$641$	19866.3	−	11469.8i	1.22414	−	0.706755i	0.965797	+	0.259299i	$0.0834915\pi$
$642$		0			0
$643$	2182.17	+	1259.88i	0.133836	+	0.0772702i	0.565423	−	0.824801i	$-0.308713\pi$
$643$	2182.17	+	1259.88i	0.133836	+	0.0772702i	−0.431587	+	0.902071i	$0.642046\pi$
$644$	4215.45	+	20590.5i	0.257938	+	1.25991i
$645$		0			0
$646$	13694.7	−	1387.45i	0.834072	−	0.0845023i
$647$	−5938.61			−0.360851			−0.180426	−	0.983589i	$-0.557748\pi$
$647$	−5938.61			−0.360851			−0.180426	+	0.983589i	$0.557748\pi$
$648$		0			0
$649$	−1018.81			−0.0616205
$650$	5268.96	−	533.814i	0.317947	−	0.0322122i
$651$		0			0
$652$	−3508.32	−	17136.5i	−0.210731	−	1.02932i
$653$	22562.1	+	13026.3i	1.35210	+	0.780638i	0.988544	−	0.150933i	$-0.0482277\pi$
$653$	22562.1	+	13026.3i	1.35210	+	0.780638i	0.363561	+	0.931571i	$0.381561\pi$
$654$		0			0
$655$	20649.3	−	11921.9i	1.23181	−	0.711184i
$656$	2166.86	+	260.674i	0.128966	+	0.0155146i
$657$		0			0
$658$	9309.24	+	4186.66i	0.551538	+	0.248044i
$659$	14176.7	+	24554.8i	0.838008	+	1.45147i	0.891558	+	0.452907i	$0.149613\pi$
$659$	14176.7	+	24554.8i	0.838008	+	1.45147i	−0.0535504	+	0.998565i	$0.517054\pi$
$660$		0			0
$661$	5168.04	−	8951.31i	0.304105	−	0.526725i	−0.672957	−	0.739682i	$-0.734976\pi$
$661$	5168.04	−	8951.31i	0.304105	−	0.526725i	0.977062	+	0.212957i	$0.0683093\pi$
$662$	22687.5	−	16353.8i	1.33199	−	0.960133i
$663$		0			0
$664$	15401.3	+	14184.5i	0.900130	+	0.829012i
$665$		−	22063.4i		−	1.28659i
$666$		0			0
$667$			29896.3i			1.73551i
$668$	−9057.62	+	27180.9i	−0.524625	+	1.57434i
$669$		0			0
$670$	11869.7	+	16466.8i	0.684430	+	0.949507i
$671$	3.91468	−	6.78042i	0.000225223	−	0.000390097i
$672$		0			0
$673$	7541.97	+	13063.1i	0.431979	+	0.748209i	0.997044	−	0.0768374i	$-0.0244822\pi$
$673$	7541.97	+	13063.1i	0.431979	+	0.748209i	−0.565065	+	0.825046i	$0.691149\pi$
$674$	5810.05	−	12918.9i	0.332040	−	0.738307i
$675$		0			0
$676$	10888.1	+	12276.4i	0.619486	+	0.698477i
$677$	11873.7	−	6855.26i	0.674065	−	0.389172i	−0.123550	−	0.992338i	$-0.539428\pi$
$677$	11873.7	−	6855.26i	0.674065	−	0.389172i	0.797615	+	0.603167i	$0.206095\pi$
$678$		0			0
$679$	−24514.0	−	14153.2i	−1.38551	−	0.799925i
$680$	5906.14	−	26325.9i	0.333074	−	1.48463i
$681$		0			0
$682$	458.381	+	4524.41i	0.0257365	+	0.254030i
$683$	807.274			0.0452262			0.0226131	−	0.999744i	$-0.492801\pi$
$683$	807.274			0.0452262			0.0226131	+	0.999744i	$0.492801\pi$
$684$		0			0
$685$	−448.867			−0.0250370
$686$	−1724.59	−	17022.4i	−0.0959842	−	0.947403i
$687$		0			0
$688$	−24.7454	+	33.0061i	−0.00137123	+	0.00182899i
$689$	2786.82	+	1608.97i	0.154092	+	0.0889651i
$690$		0			0
$691$	−19006.4	+	10973.4i	−1.04636	+	0.604119i	−0.921629	−	0.388072i	$-0.873141\pi$
$691$	−19006.4	+	10973.4i	−1.04636	+	0.604119i	−0.124735	+	0.992190i	$0.539808\pi$
$692$	653.130	−	579.268i	0.0358790	−	0.0318215i
$693$		0			0
$694$	−9043.13	+	20107.9i	−0.494629	+	1.09983i
$695$	−13860.3	−	24006.7i	−0.756474	−	1.31025i
$696$		0			0
$697$	1214.91	−	2104.28i	0.0660228	−	0.114355i
$698$	15020.2	+	20837.5i	0.814503	+	1.12996i
$699$		0			0
$700$	−22714.6	−	7569.28i	−1.22647	−	0.408703i
$701$			3170.45i			0.170822i	0.996346	+	0.0854110i	$0.0272203\pi$
$701$			3170.45i			0.170822i	−0.996346	+	0.0854110i	$0.972780\pi$
$702$		0			0
$703$		−	9126.15i		−	0.489615i
$704$	−2259.95	−	1067.77i	−0.120987	−	0.0571636i
$705$		0			0
$706$	−10450.8	+	7533.20i	−0.557111	+	0.401580i
$707$	−3502.90	+	6067.20i	−0.186337	+	0.322745i
$708$		0			0
$709$	−1413.03	−	2447.45i	−0.0748485	−	0.129641i	0.826172	−	0.563418i	$-0.190514\pi$
$709$	−1413.03	−	2447.45i	−0.0748485	−	0.129641i	−0.901020	+	0.433777i	$0.857181\pi$
$710$	16678.3	+	7500.76i	0.881586	+	0.396477i
$711$		0			0
$712$	−7048.37	−	22553.2i	−0.370996	−	1.18710i
$713$	−38818.0	+	22411.6i	−2.03892	+	1.17717i
$714$		0			0
$715$	−854.438	−	493.310i	−0.0446912	−	0.0258025i
$716$	2103.54	−	430.653i	0.109795	−	0.0224780i
$717$		0			0
$718$	−15238.2	+	1543.83i	−0.792040	+	0.0802440i
$719$	15469.9			0.802408			0.401204	−	0.915989i	$-0.368592\pi$
$719$	15469.9			0.802408			0.401204	+	0.915989i	$0.368592\pi$
$720$		0			0
$721$	−10390.0			−0.536677
$722$	6174.14	−	625.521i	0.318252	−	0.0322430i
$723$		0			0
$724$	7042.58	−	1441.81i	0.361513	−	0.0740116i
$725$	−29494.0	−	17028.4i	−1.51087	−	0.872301i
$726$		0			0
$727$	6900.11	−	3983.78i	0.352009	−	0.203233i	−0.313561	−	0.949568i	$-0.601522\pi$
$727$	6900.11	−	3983.78i	0.352009	−	0.203233i	0.665570	+	0.746336i	$0.268189\pi$
$728$	1573.55	+	5034.98i	0.0801092	+	0.256331i
$729$		0			0
$730$	−33533.8	−	15081.2i	−1.70019	−	0.764629i
$731$	22.9635	+	39.7739i	0.00116188	+	0.00201244i
$732$		0			0
$733$	−12334.6	+	21364.2i	−0.621542	+	1.07654i	0.367656	+	0.929962i	$0.380160\pi$
$733$	−12334.6	+	21364.2i	−0.621542	+	1.07654i	−0.989199	+	0.146581i	$0.953173\pi$
$734$	−24450.2	+	17624.4i	−1.22953	+	0.886277i
$735$		0			0
$736$	462.063	−	24632.1i	0.0231411	−	1.23363i
$737$		−	2093.65i		−	0.104641i
$738$		0			0
$739$		−	1182.09i		−	0.0588414i	−0.999567	−	0.0294207i	$-0.990634\pi$
$739$		−	1182.09i		−	0.0588414i	0.999567	−	0.0294207i	$-0.00936624\pi$
$740$	−16970.6	−	5655.20i	−0.843044	−	0.280931i
$741$		0			0
$742$	−8506.96	−	11801.7i	−0.420890	−	0.583899i
$743$	13616.4	−	23584.4i	0.672327	−	1.16450i	−0.304916	−	0.952379i	$-0.598628\pi$
$743$	13616.4	−	23584.4i	0.672327	−	1.16450i	0.977243	−	0.212125i	$-0.0680383\pi$
$744$		0			0
$745$	−7133.00	−	12354.7i	−0.350782	−	0.607573i
$746$	−3143.87	+	6990.55i	−0.154296	+	0.343086i
$747$		0			0
$748$	−2081.90	+	1846.46i	−0.101767	+	0.0902584i
$749$	−7196.16	+	4154.70i	−0.351057	+	0.202683i
$750$		0			0
$751$	12287.2	+	7093.99i	0.597024	+	0.344692i	0.767870	−	0.640606i	$-0.221317\pi$
$751$	12287.2	+	7093.99i	0.597024	+	0.344692i	−0.170846	+	0.985298i	$0.554650\pi$
$752$	−9573.15	−	7177.21i	−0.464224	−	0.348040i
$753$		0			0
$754$	756.336	+	7465.34i	0.0365307	+	0.360572i
$755$	−24580.1			−1.18485
$756$		0			0
$757$	30482.1			1.46353			0.731764	−	0.681559i	$-0.238698\pi$
$757$	30482.1			1.46353			0.731764	+	0.681559i	$0.238698\pi$
$758$	−1823.30	−	17996.7i	−0.0873682	−	0.862359i
$759$		0			0
$760$	−5661.41	+	25235.0i	−0.270212	+	1.20443i
$761$	19985.7	+	11538.8i	0.952013	+	0.549645i	0.893706	−	0.448654i	$-0.148096\pi$
$761$	19985.7	+	11538.8i	0.952013	+	0.549645i	0.0583074	+	0.998299i	$0.481430\pi$
$762$		0			0
$763$	−15034.5	+	8680.15i	−0.713348	+	0.411851i
$764$	−2731.98	−	3080.33i	−0.129371	−	0.145867i
$765$		0			0
$766$	1583.73	−	3521.51i	0.0747031	−	0.166106i
$767$	−1260.19	−	2182.72i	−0.0593258	−	0.102755i
$768$		0			0
$769$	−1035.31	+	1793.21i	−0.0485491	+	0.0840895i	−0.889279	−	0.457366i	$-0.848793\pi$
$769$	−1035.31	+	1793.21i	−0.0485491	+	0.0840895i	0.840730	+	0.541455i	$0.182126\pi$
$770$	2608.23	+	3618.39i	0.122070	+	0.169348i
$771$		0			0
$772$	6219.99	−	18665.5i	0.289977	−	0.870188i
$773$		−	35103.0i		−	1.63333i	−0.577110	−	0.816666i	$-0.695820\pi$
$773$		−	35103.0i		−	1.63333i	0.577110	−	0.816666i	$-0.304180\pi$
$774$		0			0
$775$		−	51061.1i		−	2.36667i
$776$	24406.2	+	22477.9i	1.12904	+	1.03983i
$777$		0			0
$778$	14256.1	−	10276.2i	0.656947	−	0.473545i
$779$	−1164.57	+	2017.09i	−0.0535622	+	0.0927724i
$780$		0			0
$781$	−943.085	−	1633.47i	−0.0432090	−	0.0748402i
$782$	−25015.0	−	11250.0i	−1.14391	−	0.514450i
$783$		0			0
$784$	226.523	−	1882.98i	0.0103190	−	0.0857774i
$785$	−38970.7	+	22499.7i	−1.77188	+	1.02299i
$786$		0			0
$787$	20621.0	+	11905.5i	0.934000	+	0.539245i	0.888074	−	0.459700i	$-0.152043\pi$
$787$	20621.0	+	11905.5i	0.934000	+	0.539245i	0.0459253	+	0.998945i	$0.485376\pi$
$788$	1037.34	+	5066.95i	0.0468957	+	0.229064i
$789$		0			0
$790$	3724.74	−	377.365i	0.167747	−	0.0169950i
$791$	−7374.87			−0.331505
$792$		0			0
$793$	19.3687			0.000867343
$794$	9262.90	−	938.452i	0.414015	−	0.0419451i
$795$		0			0
$796$	2796.67	+	13660.5i	0.124529	+	0.608269i
$797$	2079.48	+	1200.59i	0.0924202	+	0.0533588i	0.545498	−	0.838112i	$-0.316341\pi$
$797$	2079.48	+	1200.59i	0.0924202	+	0.0533588i	−0.453078	+	0.891471i	$0.649674\pi$
$798$		0			0
$799$	−11536.1	+	6660.38i	−0.510787	+	0.294903i
$800$	24037.5	+	14485.9i	1.06232	+	0.640190i
$801$		0			0
$802$	−10513.1	−	4728.06i	−0.462880	−	0.208171i
$803$	1896.19	+	3284.29i	0.0833312	+	0.144334i
$804$		0			0
$805$	−21982.3	+	38074.4i	−0.962451	+	1.66701i
$806$	−9126.20	+	6578.41i	−0.398830	+	0.287487i
$807$		0			0
$808$	5563.27	−	6040.52i	0.242222	−	0.263001i
$809$			29338.0i			1.27499i	0.770453	+	0.637497i	$0.220030\pi$
$809$			29338.0i			1.27499i	−0.770453	+	0.637497i	$0.779970\pi$
$810$		0			0
$811$		−	30884.9i		−	1.33726i	−0.743597	−	0.668629i	$-0.766882\pi$
$811$		−	30884.9i		−	1.33726i	0.743597	−	0.668629i	$-0.233118\pi$
$812$	10724.6	−	32183.2i	0.463496	−	1.39090i
$813$		0			0
$814$	1078.85	+	1496.68i	0.0464541	+	0.0644456i
$815$	18294.8	−	31687.5i	0.786305	−	1.36192i
$816$		0			0
$817$	−22.0120	−	38.1258i	−0.000942596	−	0.00163262i
$818$	−16368.6	+	36396.5i	−0.699653	+	1.55571i
$819$		0			0
$820$	3029.25	+	3415.51i	0.129007	+	0.145457i
$821$	17356.7	−	10020.9i	0.737824	−	0.425983i	−0.0834539	−	0.996512i	$-0.526595\pi$
$821$	17356.7	−	10020.9i	0.737824	−	0.425983i	0.821277	+	0.570529i	$0.193262\pi$
$822$		0			0
$823$	−5398.43	−	3116.78i	−0.228648	−	0.132010i	0.381300	−	0.924451i	$-0.375476\pi$
$823$	−5398.43	−	3116.78i	−0.228648	−	0.132010i	−0.609948	+	0.792441i	$0.708810\pi$
$824$	11883.5	+	2666.05i	0.502407	+	0.112714i
$825$		0			0
$826$	1148.53	+	11336.5i	0.0483808	+	0.477538i
$827$	−43288.8			−1.82019			−0.910096	−	0.414397i	$-0.863993\pi$
$827$	−43288.8			−1.82019			−0.910096	+	0.414397i	$0.863993\pi$
$828$		0			0
$829$	−15655.6			−0.655902			−0.327951	−	0.944695i	$-0.606358\pi$
$829$	−15655.6			−0.655902			−0.327951	+	0.944695i	$0.606358\pi$
$830$	4414.70	+	43574.9i	0.184622	+	1.82230i
$831$		0			0
$832$	−507.778	−	6162.52i	−0.0211587	−	0.256787i
$833$	−1828.60	−	1055.74i	−0.0760592	−	0.0439128i
$834$		0			0
$835$	−51901.4	+	29965.3i	−2.15104	+	1.24191i
$836$	1995.64	−	1769.95i	0.0825605	−	0.0732237i
$837$		0			0
$838$	7388.04	−	16427.7i	0.304553	−	0.677189i
$839$	−22793.5	−	39479.4i	−0.937924	−	1.62453i	−0.769336	−	0.638845i	$-0.779413\pi$
$839$	−22793.5	−	39479.4i	−0.937924	−	1.62453i	−0.168588	−	0.985687i	$-0.553921\pi$
$840$		0			0
$841$	11932.2	−	20667.2i	0.489247	−	0.847400i
$842$	−17882.9	−	24808.9i	−0.731931	−	1.01540i
$843$		0			0
$844$	31972.8	+	10654.4i	1.30397	+	0.434527i
$845$			34324.6i			1.39740i
$846$		0			0
$847$			25233.2i			1.02364i
$848$	6701.55	+	15681.0i	0.271382	+	0.635010i
$849$		0			0
$850$	25346.8	−	18270.6i	1.02281	−	0.737268i
$851$	−9092.58	+	15748.8i	−0.366263	+	0.634386i
$852$		0			0
$853$	−1318.98	−	2284.55i	−0.0529439	−	0.0917016i	0.838339	−	0.545150i	$-0.183527\pi$
$853$	−1318.98	−	2284.55i	−0.0529439	−	0.0917016i	−0.891283	+	0.453448i	$0.850194\pi$
$854$	−79.8601	−	35.9156i	−0.00319995	−	0.00143912i
$855$		0			0
$856$	9296.68	−	2905.42i	0.371208	−	0.116011i
$857$	21068.1	−	12163.7i	0.839759	−	0.484835i	−0.0174233	−	0.999848i	$-0.505546\pi$
$857$	21068.1	−	12163.7i	0.839759	−	0.484835i	0.857182	+	0.515013i	$0.172213\pi$
$858$		0			0
$859$	−38889.0	−	22452.6i	−1.54468	−	0.891819i	−0.998534	−	0.0541273i	$-0.982762\pi$
$859$	−38889.0	−	22452.6i	−1.54468	−	0.891819i	−0.546143	−	0.837692i	$-0.683904\pi$
$860$	−84.5374	+	17.3071i	−0.00335198	+	0.000686242i
$861$		0			0
$862$	30865.4	−	3127.07i	1.21958	−	0.123560i
$863$	−3830.25			−0.151081			−0.0755406	−	0.997143i	$-0.524068\pi$
$863$	−3830.25			−0.151081			−0.0755406	+	0.997143i	$0.524068\pi$
$864$		0			0
$865$	1826.14			0.0717809
$866$	−4195.99	+	425.109i	−0.164649	+	0.0166810i
$867$		0			0
$868$	49827.1	−	10201.0i	1.94844	−	0.398898i
$869$	−334.406	−	193.070i	−0.0130540	−	0.00753675i
$870$		0			0
$871$	4485.47	−	2589.69i	0.174494	−	0.100744i
$872$	19423.0	−	6070.11i	0.754294	−	0.235734i
$873$		0			0
$874$	23978.5	+	10783.9i	0.928014	+	0.417357i
$875$	−4851.74	−	8403.45i	−0.187450	−	0.324673i
$876$		0			0
$877$	−12549.7	+	21736.6i	−0.483206	+	0.836938i	−0.999814	−	0.0192844i	$-0.993861\pi$
$877$	−12549.7	+	21736.6i	−0.483206	+	0.836938i	0.516608	+	0.856222i	$0.327195\pi$
$878$	−5107.07	+	3681.31i	−0.196304	+	0.141501i
$879$		0			0
$880$	−2054.69	−	4807.79i	−0.0787087	−	0.184171i
$881$		−	3336.88i		−	0.127608i	−0.997962	−	0.0638038i	$-0.979677\pi$
$881$		−	3336.88i		−	0.127608i	0.997962	−	0.0638038i	$-0.0203232\pi$
$882$		0			0
$883$			26792.8i			1.02112i	0.859841	+	0.510561i	$0.170562\pi$
$883$			26792.8i			1.02112i	−0.859841	+	0.510561i	$0.829438\pi$
$884$	−6531.06	−	2176.38i	−0.248488	−	0.0828048i
$885$		0			0
$886$	−26260.0	−	36430.4i	−0.995735	−	1.38138i
$887$	−13004.9	+	22525.1i	−0.492290	+	0.852672i	−0.999961	−	0.00887981i	$-0.997173\pi$
$887$	−13004.9	+	22525.1i	−0.492290	+	0.852672i	0.507670	+	0.861551i	$0.330507\pi$
$888$		0			0
$889$	−16195.0	−	28050.6i	−0.610983	−	1.05825i
$890$	20272.9	−	45077.9i	0.763539	−	1.69777i
$891$		0			0
$892$	−38415.4	+	34071.0i	−1.44198	+	1.27890i
$893$	11058.1	−	6384.40i	0.414384	−	0.239245i
$894$		0			0
$895$	3889.71	+	2245.72i	0.145272	+	0.0838729i
$896$	−9333.58	+	26350.6i	−0.348006	+	0.982491i
$897$		0			0
$898$	−3295.36	−	32526.5i	−0.122458	−	1.20871i
$899$	72346.0			2.68395
$900$		0			0
$901$	18985.5			0.701998
$902$	−47.4622	−	468.471i	−0.00175201	−	0.0172931i
$903$		0			0
$904$	8435.00	+	1892.37i	0.310336	+	0.0696232i
$905$	13022.6	+	7518.59i	0.478326	+	0.276162i
$906$		0			0
$907$	23690.0	−	13677.4i	0.867269	−	0.500718i	0.000829418	−	1.00000i	$-0.499736\pi$
$907$	23690.0	−	13677.4i	0.867269	−	0.500718i	0.866440	+	0.499282i	$0.166403\pi$
$908$	11941.9	+	13464.6i	0.436460	+	0.492113i
$909$		0			0
$910$	−4525.92	+	10063.6i	−0.164871	+	0.366599i
$911$	−2661.94	−	4610.61i	−0.0968100	−	0.167680i	0.813553	−	0.581491i	$-0.197531\pi$
$911$	−2661.94	−	4610.61i	−0.0968100	−	0.167680i	−0.910363	+	0.413812i	$0.864197\pi$
$912$		0			0
$913$	2258.67	−	3912.14i	0.0818742	−	0.141810i
$914$	18010.6	+	24986.0i	0.651792	+	0.904228i
$915$		0			0
$916$	−8777.99	+	26341.8i	−0.316630	+	0.950170i
$917$			27504.7i			0.990495i
$918$		0			0
$919$			3951.52i			0.141837i	0.997482	+	0.0709187i	$0.0225931\pi$
$919$			3951.52i			0.141837i	−0.997482	+	0.0709187i	$0.977407\pi$
$920$	34912.0	−	37907.0i	1.25110	−	1.35843i
$921$		0			0
$922$	−27017.5	+	19475.0i	−0.965049	+	0.695633i
$923$	2333.06	−	4040.97i	0.0831999	−	0.144106i
$924$		0			0
$925$	−10358.0	−	17940.5i	−0.368181	−	0.637708i
$926$	6861.49	+	3085.82i	0.243502	+	0.109510i
$927$		0			0
$928$	−20524.3	+	34057.6i	−0.726017	+	1.20474i
$929$	−2705.24	+	1561.87i	−0.0955394	+	0.0551597i	−0.547008	−	0.837127i	$-0.684233\pi$
$929$	−2705.24	+	1561.87i	−0.0955394	+	0.0551597i	0.451469	+	0.892287i	$0.350900\pi$
$930$		0			0
$931$	1752.83	+	1012.00i	0.0617044	+	0.0356250i
$932$	−6181.76	−	30195.1i	−0.217264	−	1.06124i
$933$		0			0
$934$	−92.7925	+	9.40108i	−0.00325082	+	0.000329350i
$935$	−5820.96			−0.203600
$936$		0			0
$937$	24002.2			0.836838			0.418419	−	0.908254i	$-0.362584\pi$
$937$	24002.2			0.836838			0.418419	+	0.908254i	$0.362584\pi$
$938$	−23296.4	+	2360.23i	−0.810931	+	0.0821579i
$939$		0			0
$940$	−5019.79	−	24519.4i	−0.174178	−	0.850782i
$941$	−42104.3	−	24308.9i	−1.45862	−	0.842135i	−0.459676	−	0.888086i	$-0.652035\pi$
$941$	−42104.3	−	24308.9i	−1.45862	−	0.842135i	−0.998944	+	0.0459518i	$0.985368\pi$
$942$		0			0
$943$	4019.34	−	2320.57i	0.138799	−	0.0801358i
$944$	1595.27	−	13260.8i	0.0550019	−	0.457205i
$945$		0			0
$946$	8.11700	+	3.65047i	0.000278971	+	0.000125462i
$947$	9870.34	+	17095.9i	0.338694	+	0.586635i	0.984187	−	0.177131i	$-0.0566816\pi$
$947$	9870.34	+	17095.9i	0.338694	+	0.586635i	−0.645493	+	0.763766i	$0.723348\pi$
$948$		0			0
$949$	−4690.89	+	8124.86i	−0.160456	+	0.277918i
$950$	−24296.5	+	17513.6i	−0.829771	+	0.598121i
$951$		0			0
$952$	22892.9	+	21084.2i	0.779373	+	0.717795i
$953$		−	47895.5i		−	1.62800i	−0.580863	−	0.814002i	$-0.697285\pi$
$953$		−	47895.5i		−	1.62800i	0.580863	−	0.814002i	$-0.302715\pi$
$954$		0			0
$955$		−	8612.54i		−	0.291827i
$956$	−100.829	+	302.577i	−0.00341113	+	0.0102364i
$957$		0			0
$958$	−13459.8	−	18672.7i	−0.453931	−	0.629737i
$959$	258.893	−	448.416i	0.00871751	−	0.0150992i
$960$		0			0
$961$	39338.4	+	68136.1i	1.32048	+	2.28714i
$962$	−1872.07	+	4162.64i	−0.0627421	+	0.139510i
$963$		0			0
$964$	−18358.0	−	20698.8i	−0.613352	−	0.691561i
$965$	35641.4	−	20577.6i	1.18895	−	0.686441i
$966$		0			0
$967$	39942.4	+	23060.8i	1.32830	+	0.766892i	0.985036	−	0.172349i	$-0.0551356\pi$
$967$	39942.4	+	23060.8i	1.32830	+	0.766892i	0.343259	+	0.939241i	$0.388469\pi$
$968$	6474.77	−	28860.4i	0.214987	−	0.958275i
$969$		0			0
$970$	6995.91	+	69052.5i	0.231572	+	2.28571i
$971$	51058.5			1.68748			0.843741	−	0.536751i	$-0.180349\pi$
$971$	51058.5			1.68748			0.843741	+	0.536751i	$0.180349\pi$
$972$		0			0
$973$	31976.7			1.05357
$974$	−567.995	−	5606.34i	−0.0186856	−	0.184434i
$975$		0			0
$976$	82.1241	+	61.5703i	0.00269337	+	0.00201928i
$977$	−19394.5	−	11197.4i	−0.635093	−	0.366671i	0.147629	−	0.989043i	$-0.452836\pi$
$977$	−19394.5	−	11197.4i	−0.635093	−	0.366671i	−0.782722	+	0.622372i	$0.786169\pi$
$978$		0			0
$979$	−4414.92	+	2548.95i	−0.144128	+	0.0832124i
$980$	2968.05	−	2632.39i	0.0967457	−	0.0858047i
$981$		0			0
$982$	10226.0	−	22738.0i	0.332307	−	0.738900i
$983$	6698.78	+	11602.6i	0.217353	+	0.376466i	0.953998	−	0.299813i	$-0.0969244\pi$
$983$	6698.78	+	11602.6i	0.217353	+	0.376466i	−0.736645	+	0.676280i	$0.763591\pi$
$984$		0			0
$985$	−5409.43	+	9369.40i	−0.174983	+	0.303080i
$986$	25886.8	+	35912.7i	0.836110	+	1.15993i
$987$		0			0
$988$	6260.44	+	2086.20i	0.201590	+	0.0671768i
$989$			87.7240i			0.00282049i
$990$		0			0
$991$			24672.3i			0.790858i	0.918496	+	0.395429i	$0.129404\pi$
$991$			24672.3i			0.790858i	−0.918496	+	0.395429i	$0.870596\pi$
$992$	−59607.2	−	1118.15i	−1.90779	−	0.0357875i
$993$		0			0
$994$	−17112.8	+	12335.3i	−0.546060	+	0.393615i
$995$	−14583.8	+	25259.8i	−0.464660	+	0.804815i
$996$		0			0
$997$	−29032.1	−	50285.1i	−0.922223	−	1.59734i	−0.795968	−	0.605339i	$-0.793038\pi$
$997$	−29032.1	−	50285.1i	−0.922223	−	1.59734i	−0.126255	−	0.991998i	$-0.540296\pi$
$998$	−54368.4	−	24451.2i	−1.72445	−	0.775539i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.h.b.71.12		24
3.2	odd	2		36.4.h.b.23.1	yes	24
4.3	odd	2	inner	108.4.h.b.71.9		24
9.2	odd	6	inner	108.4.h.b.35.9		24
9.4	even	3		324.4.b.c.323.10		24
9.5	odd	6		324.4.b.c.323.15		24
9.7	even	3		36.4.h.b.11.4	yes	24
12.11	even	2		36.4.h.b.23.4	yes	24
36.7	odd	6		36.4.h.b.11.1	✓	24
36.11	even	6	inner	108.4.h.b.35.12		24
36.23	even	6		324.4.b.c.323.9		24
36.31	odd	6		324.4.b.c.323.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.1	✓	24	36.7	odd	6
36.4.h.b.11.4	yes	24	9.7	even	3
36.4.h.b.23.1	yes	24	3.2	odd	2
36.4.h.b.23.4	yes	24	12.11	even	2
108.4.h.b.35.9		24	9.2	odd	6	inner
108.4.h.b.35.12		24	36.11	even	6	inner
108.4.h.b.71.9		24	4.3	odd	2	inner
108.4.h.b.71.12		24	1.1	even	1	trivial
324.4.b.c.323.9		24	36.23	even	6
324.4.b.c.323.10		24	9.4	even	3
324.4.b.c.323.15		24	9.5	odd	6
324.4.b.c.323.16		24	36.31	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)

\(f(q)\)	\(=\)	\(q+(2.81402 - 0.285097i) q^{2} +(7.83744 - 1.60454i) q^{4} +(14.4924 + 8.36717i) q^{5} +(-16.7175 + 9.65186i) q^{7} +(21.5973 - 6.74964i) q^{8} +O(q^{10})\)	\(q+(2.81402 - 0.285097i) q^{2} +(7.83744 - 1.60454i) q^{4} +(14.4924 + 8.36717i) q^{5} +(-16.7175 + 9.65186i) q^{7} +(21.5973 - 6.74964i) q^{8} +(43.1673 + 19.4137i) q^{10} +(-2.44092 - 4.22780i) q^{11} +(6.03848 - 10.4590i) q^{13} +(-44.2917 + 31.9267i) q^{14} +(58.8509 - 25.1509i) q^{16} -71.2528i q^{17} +68.3003i q^{19} +(127.009 + 42.3237i) q^{20} +(-8.07414 - 11.2012i) q^{22} +(68.0491 - 117.865i) q^{23} +(77.5192 + 134.267i) q^{25} +(14.0106 - 31.1533i) q^{26} +(-115.536 + 102.470i) q^{28} +(-190.237 + 109.833i) q^{29} +(-285.221 - 164.672i) q^{31} +(158.437 - 87.5535i) q^{32} +(-20.3140 - 200.507i) q^{34} -323.035 q^{35} -133.618 q^{37} +(19.4722 + 192.199i) q^{38} +(369.471 + 82.8899i) q^{40} +(29.5326 + 17.0507i) q^{41} +(-0.558209 + 0.322282i) q^{43} +(-25.9142 - 29.2186i) q^{44} +(157.889 - 351.074i) q^{46} +(-93.4753 - 161.904i) q^{47} +(14.8169 - 25.6636i) q^{49} +(256.420 + 355.730i) q^{50} +(30.5444 - 91.6604i) q^{52} +266.453i q^{53} -81.6944i q^{55} +(-295.906 + 321.291i) q^{56} +(-504.018 + 363.309i) q^{58} +(104.347 - 180.734i) q^{59} +(0.801886 + 1.38891i) q^{61} +(-849.565 - 382.076i) q^{62} +(420.885 - 291.548i) q^{64} +(175.024 - 101.050i) q^{65} +(371.407 + 214.432i) q^{67} +(-114.328 - 558.440i) q^{68} +(-909.028 + 92.0964i) q^{70} +386.365 q^{71} -776.832 q^{73} +(-376.004 + 38.0941i) q^{74} +(109.591 + 535.300i) q^{76} +(81.6122 + 47.1188i) q^{77} +(68.5000 - 39.5485i) q^{79} +(1063.33 + 127.919i) q^{80} +(87.9665 + 39.5613i) q^{82} +(462.668 + 801.365i) q^{83} +(596.185 - 1032.62i) q^{85} +(-1.47893 + 1.06605i) q^{86} +(-81.2533 - 74.8336i) q^{88} -1044.26i q^{89} +233.130i q^{91} +(344.213 - 1032.94i) q^{92} +(-309.200 - 428.952i) q^{94} +(-571.481 + 989.834i) q^{95} +(733.184 + 1269.91i) q^{97} +(34.3784 - 76.4422i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 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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