LMFDB - Embedded newform 225.4.p.b.32.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.6
Character	$\chi$	$=$	225.32
Dual form			225.4.p.b.218.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43923 - 0.385641i) q^{2} +(2.38802 + 4.61491i) q^{3} +(-5.00553 - 2.88994i) q^{4} +(-1.65722 - 7.56285i) q^{6} +(-6.62758 + 24.7344i) q^{7} +(14.5184 + 14.5184i) q^{8} +(-15.5947 + 22.0410i) q^{9} +O(q^{10})$	\(q+(-1.43923 - 0.385641i) q^{2} +(2.38802 + 4.61491i) q^{3} +(-5.00553 - 2.88994i) q^{4} +(-1.65722 - 7.56285i) q^{6} +(-6.62758 + 24.7344i) q^{7} +(14.5184 + 14.5184i) q^{8} +(-15.5947 + 22.0410i) q^{9} +(11.8937 - 6.86683i) q^{11} +(1.38352 - 30.0013i) q^{12} +(-21.6449 - 80.7799i) q^{13} +(19.0773 - 33.0428i) q^{14} +(7.82311 + 13.5500i) q^{16} +(-19.6420 + 19.6420i) q^{17} +(30.9444 - 25.7081i) q^{18} +23.7249i q^{19} +(-129.974 + 28.4807i) q^{21} +(-19.7659 + 5.29627i) q^{22} +(-74.1658 + 19.8727i) q^{23} +(-32.3308 + 101.671i) q^{24} +124.608i q^{26} +(-138.958 - 19.3339i) q^{27} +(104.656 - 104.656i) q^{28} +(-103.697 - 179.609i) q^{29} +(-16.4679 + 28.5232i) q^{31} +(-48.5466 - 181.178i) q^{32} +(60.0922 + 38.4902i) q^{33} +(35.8441 - 20.6946i) q^{34} +(141.757 - 65.2589i) q^{36} +(-156.441 - 156.441i) q^{37} +(9.14932 - 34.1457i) q^{38} +(321.103 - 292.793i) q^{39} +(-247.106 - 142.667i) q^{41} +(198.046 + 9.13295i) q^{42} +(122.522 + 32.8295i) q^{43} -79.3790 q^{44} +114.406 q^{46} +(-332.652 - 89.1338i) q^{47} +(-43.8503 + 68.4606i) q^{48} +(-270.821 - 156.359i) q^{49} +(-137.551 - 43.7404i) q^{51} +(-125.105 + 466.899i) q^{52} +(-169.925 - 169.925i) q^{53} +(192.536 + 81.4138i) q^{54} +(-455.326 + 262.882i) q^{56} +(-109.488 + 56.6556i) q^{57} +(79.9798 + 298.489i) q^{58} +(-219.565 + 380.298i) q^{59} +(138.080 + 239.161i) q^{61} +(34.7009 - 34.7009i) q^{62} +(-441.816 - 531.805i) q^{63} +154.310i q^{64} +(-71.6433 - 78.5704i) q^{66} +(912.635 - 244.540i) q^{67} +(155.083 - 41.5543i) q^{68} +(-268.820 - 294.812i) q^{69} +112.676i q^{71} +(-546.409 + 93.5891i) q^{72} +(474.023 - 474.023i) q^{73} +(164.825 + 285.485i) q^{74} +(68.5637 - 118.756i) q^{76} +(91.0209 + 339.695i) q^{77} +(-575.056 + 297.567i) q^{78} +(-286.620 + 165.480i) q^{79} +(-242.609 - 687.446i) q^{81} +(300.625 + 300.625i) q^{82} +(-388.308 + 1449.19i) q^{83} +(732.896 + 233.056i) q^{84} +(-163.677 - 94.4988i) q^{86} +(581.246 - 907.461i) q^{87} +(272.373 + 72.9820i) q^{88} -598.425 q^{89} +2141.50 q^{91} +(428.670 + 114.862i) q^{92} +(-170.958 - 7.88376i) q^{93} +(444.390 + 256.569i) q^{94} +(720.191 - 656.695i) q^{96} +(-77.4097 + 288.897i) q^{97} +(329.477 + 329.477i) q^{98} +(-34.1273 + 369.235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.43923	−	0.385641i	−0.508846	−	0.136345i	−0.00474347	−	0.999989i	$-0.501510\pi$
$2$	−1.43923	−	0.385641i	−0.508846	−	0.136345i	−0.504102	+	0.863644i	$0.668177\pi$
$3$	2.38802	+	4.61491i	0.459575	+	0.888139i
$3$	2.38802	+	4.61491i	0.459575	+	0.888139i
$4$	−5.00553	−	2.88994i	−0.625691	−	0.361243i
$5$		0			0
$5$		0			0
$6$	−1.65722	−	7.56285i	−0.112759	−	0.514587i
$7$	−6.62758	+	24.7344i	−0.357855	+	1.33553i	0.518997	+	0.854776i	$0.326305\pi$
$7$	−6.62758	+	24.7344i	−0.357855	+	1.33553i	−0.876853	+	0.480759i	$0.840361\pi$
$8$	14.5184	+	14.5184i	0.641628	+	0.641628i
$9$	−15.5947	+	22.0410i	−0.577582	+	0.816332i
$10$		0			0
$11$	11.8937	−	6.86683i	0.326008	−	0.188221i	−0.328059	−	0.944657i	$-0.606395\pi$
$11$	11.8937	−	6.86683i	0.326008	−	0.188221i	0.654067	+	0.756436i	$0.273061\pi$
$12$	1.38352	−	30.0013i	0.0332823	−	0.721719i
$13$	−21.6449	−	80.7799i	−0.461786	−	1.72341i	−0.667331	−	0.744761i	$-0.732563\pi$
$13$	−21.6449	−	80.7799i	−0.461786	−	1.72341i	0.205545	−	0.978648i	$-0.434103\pi$
$14$	19.0773	−	33.0428i	0.364186	−	0.630789i
$15$		0			0
$16$	7.82311	+	13.5500i	0.122236	+	0.211719i
$17$	−19.6420	+	19.6420i	−0.280228	+	0.280228i	−0.833200	−	0.552972i	$-0.813494\pi$
$17$	−19.6420	+	19.6420i	−0.280228	+	0.280228i	0.552972	+	0.833200i	$0.313494\pi$
$18$	30.9444	−	25.7081i	0.405203	−	0.336637i
$19$			23.7249i			0.286467i	0.989689	+	0.143233i	$0.0457500\pi$
$19$			23.7249i			0.286467i	−0.989689	+	0.143233i	$0.954250\pi$
$20$		0			0
$21$	−129.974	+	28.4807i	−1.35060	+	0.295952i
$22$	−19.7659	+	5.29627i	−0.191551	+	0.0513258i
$23$	−74.1658	+	19.8727i	−0.672375	+	0.180162i	−0.578825	−	0.815452i	$-0.696488\pi$
$23$	−74.1658	+	19.8727i	−0.672375	+	0.180162i	−0.0935508	+	0.995615i	$0.529822\pi$
$24$	−32.3308	+	101.671i	−0.274979	+	0.864731i
$25$		0			0
$26$			124.608i			0.939911i
$27$	−138.958	−	19.3339i	−0.990459	−	0.137808i
$28$	104.656	−	104.656i	0.706360	−	0.706360i
$29$	−103.697	−	179.609i	−0.664002	−	1.15009i	−0.979555	−	0.201178i	$-0.935523\pi$
$29$	−103.697	−	179.609i	−0.664002	−	1.15009i	0.315552	−	0.948908i	$-0.397810\pi$
$30$		0			0
$31$	−16.4679	+	28.5232i	−0.0954104	+	0.165256i	−0.909780	−	0.415091i	$-0.863750\pi$
$31$	−16.4679	+	28.5232i	−0.0954104	+	0.165256i	0.814369	+	0.580347i	$0.197083\pi$
$32$	−48.5466	−	181.178i	−0.268185	−	1.00088i
$33$	60.0922	+	38.4902i	0.316991	+	0.203039i
$34$	35.8441	−	20.6946i	0.180800	−	0.104385i
$35$		0			0
$36$	141.757	−	65.2589i	0.656283	−	0.302124i
$37$	−156.441	−	156.441i	−0.695101	−	0.695101i	0.268249	−	0.963350i	$-0.413555\pi$
$37$	−156.441	−	156.441i	−0.695101	−	0.695101i	−0.963350	+	0.268249i	$0.913555\pi$
$38$	9.14932	−	34.1457i	0.0390583	−	0.145768i
$39$	321.103	−	292.793i	1.31840	−	1.20216i
$40$		0			0
$41$	−247.106	−	142.667i	−0.941255	−	0.543434i	−0.0509015	−	0.998704i	$-0.516209\pi$
$41$	−247.106	−	142.667i	−0.941255	−	0.543434i	−0.890354	+	0.455270i	$0.849543\pi$
$42$	198.046	+	9.13295i	0.727600	+	0.0335535i
$43$	122.522	+	32.8295i	0.434520	+	0.116429i	0.469447	−	0.882961i	$-0.344453\pi$
$43$	122.522	+	32.8295i	0.434520	+	0.116429i	−0.0349271	+	0.999390i	$0.511120\pi$
$44$	−79.3790			−0.271974
$45$		0			0
$46$	114.406			0.366700
$47$	−332.652	−	89.1338i	−1.03239	−	0.276628i	−0.297433	−	0.954743i	$-0.596130\pi$
$47$	−332.652	−	89.1338i	−1.03239	−	0.276628i	−0.734956	+	0.678115i	$0.762797\pi$
$48$	−43.8503	+	68.4606i	−0.131859	+	0.205863i
$49$	−270.821	−	156.359i	−0.789567	−	0.455857i
$50$		0			0
$51$	−137.551	−	43.7404i	−0.377667	−	0.120096i
$52$	−125.105	+	466.899i	−0.333634	+	1.24514i
$53$	−169.925	−	169.925i	−0.440397	−	0.440397i	0.451748	−	0.892145i	$-0.350800\pi$
$53$	−169.925	−	169.925i	−0.440397	−	0.440397i	−0.892145	+	0.451748i	$0.850800\pi$
$54$	192.536	+	81.4138i	0.485201	+	0.205167i
$55$		0			0
$56$	−455.326	+	262.882i	−1.08653	+	0.627306i
$57$	−109.488	+	56.6556i	−0.254423	+	0.131653i
$58$	79.9798	+	298.489i	0.181067	+	0.675750i
$59$	−219.565	+	380.298i	−0.484491	+	0.839162i	−0.999841	−	0.0178172i	$-0.994328\pi$
$59$	−219.565	+	380.298i	−0.484491	+	0.839162i	0.515351	+	0.856979i	$0.327662\pi$
$60$		0			0
$61$	138.080	+	239.161i	0.289824	+	0.501990i	0.973768	−	0.227545i	$-0.0730698\pi$
$61$	138.080	+	239.161i	0.289824	+	0.501990i	−0.683943	+	0.729535i	$0.739736\pi$
$62$	34.7009	−	34.7009i	0.0710810	−	0.0710810i
$63$	−441.816	−	531.805i	−0.883549	−	1.06351i
$64$			154.310i			0.301386i
$65$		0			0
$66$	−71.6433	−	78.5704i	−0.133616	−	0.146536i
$67$	912.635	−	244.540i	1.66412	−	0.445900i	0.700605	−	0.713549i	$-0.252913\pi$
$67$	912.635	−	244.540i	1.66412	−	0.445900i	0.963516	+	0.267649i	$0.0862468\pi$
$68$	155.083	−	41.5543i	0.276567	−	0.0741058i
$69$	−268.820	−	294.812i	−0.469016	−	0.514365i
$70$		0			0
$71$			112.676i			0.188341i	0.995556	+	0.0941705i	$0.0300199\pi$
$71$			112.676i			0.188341i	−0.995556	+	0.0941705i	$0.969980\pi$
$72$	−546.409	+	93.5891i	−0.894374	+	0.153189i
$73$	474.023	−	474.023i	0.760002	−	0.760002i	−0.216320	−	0.976322i	$-0.569405\pi$
$73$	474.023	−	474.023i	0.760002	−	0.760002i	0.976322	+	0.216320i	$0.0694055\pi$
$74$	164.825	+	285.485i	0.258926	+	0.448473i
$75$		0			0
$76$	68.5637	−	118.756i	0.103484	−	0.179240i
$77$	91.0209	+	339.695i	0.134712	+	0.502751i
$78$	−575.056	+	297.567i	−0.834772	+	0.431959i
$79$	−286.620	+	165.480i	−0.408194	+	0.235671i	−0.690013	−	0.723797i	$-0.742395\pi$
$79$	−286.620	+	165.480i	−0.408194	+	0.235671i	0.281820	+	0.959467i	$0.409062\pi$
$80$		0			0
$81$	−242.609	−	687.446i	−0.332797	−	0.942998i
$82$	300.625	+	300.625i	0.404859	+	0.404859i
$83$	−388.308	+	1449.19i	−0.513523	+	1.91649i	−0.135202	+	0.990818i	$0.543168\pi$
$83$	−388.308	+	1449.19i	−0.513523	+	1.91649i	−0.378321	+	0.925674i	$0.623498\pi$
$84$	732.896	+	233.056i	0.951971	+	0.302721i
$85$		0			0
$86$	−163.677	−	94.4988i	−0.205229	−	0.118489i
$87$	581.246	−	907.461i	0.716278	−	1.11828i
$88$	272.373	+	72.9820i	0.329943	+	0.0884080i
$89$	−598.425			−0.712730			−0.356365	−	0.934347i	$-0.615984\pi$
$89$	−598.425			−0.712730			−0.356365	+	0.934347i	$0.615984\pi$
$90$		0			0
$91$	2141.50			2.46692
$92$	428.670	+	114.862i	0.485782	+	0.130165i
$93$	−170.958	−	7.88376i	−0.190618	−	0.00879041i
$94$	444.390	+	256.569i	0.487610	+	0.281522i
$95$		0			0
$96$	720.191	−	656.695i	0.765669	−	0.698164i
$97$	−77.4097	+	288.897i	−0.0810285	+	0.302402i	−0.994533	−	0.104427i	$-0.966699\pi$
$97$	−77.4097	+	288.897i	−0.0810285	+	0.302402i	0.913504	+	0.406830i	$0.133366\pi$
$98$	329.477	+	329.477i	0.339614	+	0.339614i
$99$	−34.1273	+	369.235i	−0.0346457	+	0.374844i
$100$		0			0
$101$	−72.2861	+	41.7344i	−0.0712152	+	0.0411161i	−0.535185	−	0.844735i	$-0.679758\pi$
$101$	−72.2861	+	41.7344i	−0.0712152	+	0.0411161i	0.463970	+	0.885851i	$0.346425\pi$
$102$	181.100	+	115.998i	0.175800	+	0.112603i
$103$	−67.7920	−	253.003i	−0.0648519	−	0.242031i	0.925889	−	0.377795i	$-0.123318\pi$
$103$	−67.7920	−	253.003i	−0.0648519	−	0.242031i	−0.990741	+	0.135764i	$0.956651\pi$
$104$	858.544	−	1487.04i	0.809492	−	1.40208i
$105$		0			0
$106$	179.032	+	310.092i	0.164048	+	0.284140i
$107$	−278.425	+	278.425i	−0.251555	+	0.251555i	−0.821608	−	0.570053i	$-0.806923\pi$
$107$	−278.425	+	278.425i	−0.251555	+	0.251555i	0.570053	+	0.821608i	$0.306923\pi$
$108$	639.682	+	498.356i	0.569939	+	0.444022i
$109$			1231.78i			1.08242i	0.840889	+	0.541208i	$0.182033\pi$
$109$			1231.78i			1.08242i	−0.840889	+	0.541208i	$0.817967\pi$
$110$		0			0
$111$	348.376	−	1095.54i	0.297896	−	0.936797i
$112$	−387.000	+	103.696i	−0.326501	+	0.0874857i
$113$	90.0361	−	24.1251i	0.0749547	−	0.0200841i	−0.221147	−	0.975241i	$-0.570980\pi$
$113$	90.0361	−	24.1251i	0.0749547	−	0.0200841i	0.296102	+	0.955156i	$0.404313\pi$
$114$	179.428	−	39.3174i	0.147412	−	0.0323019i
$115$		0			0
$116$			1198.72i			0.959465i
$117$	2118.01	+	782.665i	1.67359	+	0.618440i
$118$	462.664	−	462.664i	0.360946	−	0.360946i
$119$	−355.654	−	616.012i	−0.273973	−	0.474535i
$120$		0			0
$121$	−571.193	+	989.336i	−0.429146	+	0.743303i
$122$	−106.498	−	397.457i	−0.0790321	−	0.294952i
$123$	68.2995	−	1481.06i	0.0500680	−	1.08571i
$124$	164.861	−	95.1827i	0.119395	−	0.0689327i
$125$		0			0
$126$	430.790	+	935.774i	0.304586	+	0.661630i
$127$	394.695	+	394.695i	0.275776	+	0.275776i	0.831420	−	0.555644i	$-0.187528\pi$
$127$	394.695	+	394.695i	0.275776	+	0.275776i	−0.555644	+	0.831420i	$0.687528\pi$
$128$	−328.864	+	1227.34i	−0.227092	+	0.847519i
$129$	141.079	+	643.823i	0.0962889	+	0.439422i
$130$		0			0
$131$	566.164	+	326.875i	0.377603	+	0.218009i	0.676775	−	0.736190i	$-0.263377\pi$
$131$	566.164	+	326.875i	0.377603	+	0.218009i	−0.299172	+	0.954199i	$0.596710\pi$
$132$	−189.559	−	366.327i	−0.124992	−	0.241550i
$133$	−586.823	−	157.239i	−0.382587	−	0.102514i
$134$	−1407.80			−0.907577
$135$		0			0
$136$	−570.339			−0.359604
$137$	9.89738	+	2.65200i	0.00617219	+	0.00165383i	0.261904	−	0.965094i	$-0.415650\pi$
$137$	9.89738	+	2.65200i	0.00617219	+	0.00165383i	−0.255732	+	0.966748i	$0.582316\pi$
$138$	273.203	+	527.971i	0.168526	+	0.325680i
$139$	1435.50	+	828.789i	0.875956	+	0.505734i	0.869323	−	0.494244i	$-0.164555\pi$
$139$	1435.50	+	828.789i	0.875956	+	0.505734i	0.00663323	+	0.999978i	$0.497889\pi$
$140$		0			0
$141$	−383.035	−	1748.01i	−0.228776	−	1.04404i
$142$	43.4526	−	162.167i	0.0256793	−	0.0958366i
$143$	−812.140	−	812.140i	−0.474927	−	0.474927i
$144$	−420.655	−	38.8799i	−0.243435	−	0.0224999i
$145$		0			0
$146$	−865.032	+	499.427i	−0.490346	+	0.283102i
$147$	74.8545	−	1623.20i	0.0419993	−	0.910745i
$148$	330.964	+	1235.18i	0.183818	+	0.686019i
$149$	763.694	−	1322.76i	0.419894	−	0.727278i	−0.576034	−	0.817426i	$-0.695400\pi$
$149$	763.694	−	1322.76i	0.419894	−	0.727278i	0.995928	+	0.0901473i	$0.0287338\pi$
$150$		0			0
$151$	−219.184	−	379.637i	−0.118125	−	0.204599i	0.800900	−	0.598799i	$-0.204355\pi$
$151$	−219.184	−	379.637i	−0.118125	−	0.204599i	−0.919025	+	0.394200i	$0.871022\pi$
$152$	−344.448	+	344.448i	−0.183805	+	0.183805i
$153$	−126.617	−	739.239i	−0.0669044	−	0.390614i
$154$		−	524.001i		−	0.274190i
$155$		0			0
$156$	−2453.45	+	537.615i	−1.25919	+	0.275921i
$157$	−1472.31	+	394.505i	−0.748430	+	0.200541i	−0.612821	−	0.790221i	$-0.709965\pi$
$157$	−1472.31	+	394.505i	−0.748430	+	0.200541i	−0.135608	+	0.990763i	$0.543299\pi$
$158$	476.330	−	127.632i	0.239840	−	0.0642650i
$159$	378.405	−	1189.97i	0.188739	−	0.593529i
$160$		0			0
$161$		−	1966.16i		−	0.962453i
$162$	84.0636	+	1082.96i	0.0407695	+	0.525216i
$163$	−1347.15	+	1347.15i	−0.647345	+	0.647345i	−0.952350	−	0.305006i	$-0.901342\pi$
$163$	−1347.15	+	1347.15i	−0.647345	+	0.647345i	0.305006	+	0.952350i	$0.401342\pi$
$164$	824.597	+	1428.24i	0.392623	+	0.680044i
$165$		0			0
$166$	1117.73	−	1935.97i	0.522608	−	0.905183i
$167$	30.5750	+	114.108i	0.0141675	+	0.0528737i	0.972648	−	0.232285i	$-0.0746203\pi$
$167$	30.5750	+	114.108i	0.0141675	+	0.0528737i	−0.958480	+	0.285159i	$0.907954\pi$
$168$	−2300.50	−	1473.52i	−1.05647	−	0.676692i
$169$	−4154.23	+	2398.45i	−1.89087	+	1.09169i
$170$		0			0
$171$	−522.921	−	369.984i	−0.233852	−	0.165458i
$172$	−518.410	−	518.410i	−0.229816	−	0.229816i
$173$	127.211	−	474.757i	0.0559056	−	0.208642i	−0.932323	−	0.361626i	$-0.882222\pi$
$173$	127.211	−	474.757i	0.0559056	−	0.208642i	0.988229	+	0.152984i	$0.0488883\pi$
$174$	−1186.50	+	1081.90i	−0.516946	+	0.471370i
$175$		0			0
$176$	186.091	+	107.440i	0.0796998	+	0.0460147i
$177$	−2279.37	−	105.114i	−0.967952	−	0.0446374i
$178$	861.274	+	230.778i	0.362670	+	0.0971770i
$179$	−641.856			−0.268015			−0.134007	−	0.990980i	$-0.542785\pi$
$179$	−641.856			−0.268015			−0.134007	+	0.990980i	$0.542785\pi$
$180$		0			0
$181$	−1243.05			−0.510470			−0.255235	−	0.966879i	$-0.582153\pi$
$181$	−1243.05			−0.510470			−0.255235	+	0.966879i	$0.582153\pi$
$182$	−3082.12	−	825.851i	−1.25528	−	0.336352i
$183$	−773.968	+	1208.35i	−0.312641	+	0.488106i
$184$	−1365.29	−	788.248i	−0.547012	−	0.315817i
$185$		0			0
$186$	243.008	+	77.2750i	0.0957968	+	0.0304628i
$187$	−98.7376	+	368.494i	−0.0386118	+	0.144101i
$188$	1407.51	+	1407.51i	0.546027	+	0.546027i
$189$	1399.17	−	3308.90i	0.538488	−	1.27348i
$190$		0			0
$191$	−3517.42	+	2030.79i	−1.33252	+	0.769332i	−0.985686	−	0.168593i	$-0.946078\pi$
$191$	−3517.42	+	2030.79i	−1.33252	+	0.769332i	−0.346837	+	0.937925i	$0.612744\pi$
$192$	−712.125	+	368.495i	−0.267673	+	0.138509i
$193$	−661.892	−	2470.21i	−0.246860	−	0.921295i	−0.972439	−	0.233156i	$-0.925095\pi$
$193$	−661.892	−	2470.21i	−0.246860	−	0.921295i	0.725579	−	0.688139i	$-0.241572\pi$
$194$	222.821	−	385.938i	0.0824620	−	0.142828i
$195$		0			0
$196$	903.736	+	1565.32i	0.329350	+	0.570451i
$197$	1350.59	−	1350.59i	0.488454	−	0.488454i	−0.419364	−	0.907818i	$-0.637747\pi$
$197$	1350.59	−	1350.59i	0.488454	−	0.488454i	0.907818	+	0.419364i	$0.137747\pi$
$198$	191.510	−	518.255i	0.0687373	−	0.186014i
$199$		−	4890.58i		−	1.74213i	−0.491167	−	0.871065i	$-0.663430\pi$
$199$		−	4890.58i		−	1.74213i	0.491167	−	0.871065i	$-0.336570\pi$
$200$		0			0
$201$	3307.92	+	3627.76i	1.16081	+	1.27305i
$202$	120.131	−	32.1890i	0.0418435	−	0.0112119i
$203$	5129.78	−	1374.52i	1.77360	−	0.475234i
$204$	562.109	+	616.459i	0.192919	+	0.211572i
$205$		0			0
$206$			390.274i			0.131999i
$207$	718.582	−	1944.59i	0.241280	−	0.652941i
$208$	925.239	−	925.239i	0.308432	−	0.308432i
$209$	162.915	+	282.177i	0.0539190	+	0.0933905i
$210$		0			0
$211$	−1481.97	+	2566.85i	−0.483522	+	0.837484i	−0.999821	−	0.0189240i	$-0.993976\pi$
$211$	−1481.97	+	2566.85i	−0.483522	+	0.837484i	0.516299	+	0.856408i	$0.327309\pi$
$212$	359.492	+	1341.64i	0.116462	+	0.434643i
$213$	−519.991	+	269.073i	−0.167273	+	0.0865568i
$214$	508.090	−	293.346i	0.162301	−	0.0937043i
$215$		0			0
$216$	−1736.74	−	2298.14i	−0.547085	−	0.723927i
$217$	−596.365	−	596.365i	−0.186562	−	0.186562i
$218$	475.026	−	1772.82i	0.147582	−	0.550782i
$219$	3319.55	+	1055.60i	1.02427	+	0.325710i
$220$		0			0
$221$	2011.82	+	1161.53i	0.612353	+	0.353542i
$222$	−923.882	+	1442.40i	−0.279310	+	0.436069i
$223$	2259.54	+	605.443i	0.678521	+	0.181809i	0.581590	−	0.813482i	$-0.302431\pi$
$223$	2259.54	+	605.443i	0.678521	+	0.181809i	0.0969311	+	0.995291i	$0.469097\pi$
$224$	4803.09			1.43268
$225$		0			0
$226$	−138.887			−0.0408787
$227$	−1979.99	−	530.537i	−0.578928	−	0.155123i	−0.0425397	−	0.999095i	$-0.513545\pi$
$227$	−1979.99	−	530.537i	−0.578928	−	0.155123i	−0.536388	+	0.843972i	$0.680212\pi$
$228$	711.779	+	32.8239i	0.206749	+	0.00953427i
$229$	3464.76	+	2000.38i	0.999815	+	0.577244i	0.908194	−	0.418550i	$-0.137462\pi$
$229$	3464.76	+	2000.38i	0.999815	+	0.577244i	0.0916215	+	0.995794i	$0.470795\pi$
$230$		0			0
$231$	−1350.30	+	1231.25i	−0.384602	+	0.350694i
$232$	1102.11	−	4113.14i	0.311885	−	1.16397i
$233$	−4906.70	−	4906.70i	−1.37961	−	1.37961i	−0.845271	−	0.534337i	$-0.820561\pi$
$233$	−4906.70	−	4906.70i	−1.37961	−	1.37961i	−0.534337	−	0.845271i	$-0.679439\pi$
$234$	−2746.49	−	1943.23i	−0.767280	−	0.542876i
$235$		0			0
$236$	2198.08	−	1269.06i	0.606283	−	0.350038i
$237$	−1448.13	−	927.556i	−0.396904	−	0.254225i
$238$	274.310	+	1023.74i	0.0747096	+	0.278820i
$239$	−2501.24	+	4332.28i	−0.676954	+	1.17252i	0.298939	+	0.954272i	$0.403367\pi$
$239$	−2501.24	+	4332.28i	−0.676954	+	1.17252i	−0.975894	+	0.218247i	$0.929966\pi$
$240$		0			0
$241$	−1825.14	−	3161.24i	−0.487834	−	0.844952i	0.512069	−	0.858945i	$-0.328879\pi$
$241$	−1825.14	−	3161.24i	−0.487834	−	0.844952i	−0.999902	+	0.0139921i	$0.995546\pi$
$242$	1203.61	−	1203.61i	0.319715	−	0.319715i
$243$	2593.14	−	2761.25i	0.684569	−	0.728948i
$244$		−	1596.17i		−	0.418788i
$245$		0			0
$246$	−669.458	+	2105.25i	−0.173508	+	0.545634i
$247$	1916.50	−	513.524i	0.493700	−	0.132286i
$248$	−653.199	+	175.024i	−0.167251	+	0.0448147i
$249$	−7615.15	+	1668.68i	−1.93811	+	0.424692i
$250$		0			0
$251$		−	3563.08i		−	0.896013i	−0.894030	−	0.448007i	$-0.852134\pi$
$251$		−	3563.08i		−	0.896013i	0.894030	−	0.448007i	$-0.147866\pi$
$252$	674.637	+	3938.79i	0.168643	+	0.984605i
$253$	−745.643	+	745.643i	−0.185289	+	0.185289i
$254$	−415.847	−	720.268i	−0.102727	−	0.177928i
$255$		0			0
$256$	1563.86	−	2708.69i	0.381803	−	0.661302i
$257$	1785.37	+	6663.08i	0.433339	+	1.61724i	0.745010	+	0.667053i	$0.232444\pi$
$257$	1785.37	+	6663.08i	0.433339	+	1.61724i	−0.311672	+	0.950190i	$0.600889\pi$
$258$	45.2399	−	981.017i	0.0109167	−	0.236727i
$259$	4906.30	−	2832.66i	1.17708	−	0.679586i
$260$		0			0
$261$	5575.88	+	515.362i	1.32237	+	0.122223i
$262$	−688.785	−	688.785i	−0.162417	−	0.162417i
$263$	−1321.88	+	4933.33i	−0.309927	+	1.15666i	0.618694	+	0.785632i	$0.287662\pi$
$263$	−1321.88	+	4933.33i	−0.309927	+	1.15666i	−0.928621	+	0.371030i	$0.879005\pi$
$264$	313.626	+	1431.26i	0.0731149	+	0.333666i
$265$		0			0
$266$	783.937	+	452.607i	0.180700	+	0.104327i
$267$	−1429.05	−	2761.68i	−0.327553	−	0.633003i
$268$	−5274.93	−	1413.41i	−1.20230	−	0.322157i
$269$	−6950.52			−1.57539			−0.787696	−	0.616064i	$-0.788726\pi$
$269$	−6950.52			−1.57539			−0.787696	+	0.616064i	$0.788726\pi$
$270$		0			0
$271$	−5694.64			−1.27648			−0.638238	−	0.769839i	$-0.720336\pi$
$271$	−5694.64			−1.27648			−0.638238	+	0.769839i	$0.720336\pi$
$272$	−419.810	−	112.488i	−0.0935836	−	0.0250756i
$273$	5113.94	+	9882.82i	1.13374	+	2.19097i
$274$	−13.2219	−	7.63368i	−0.00291520	−	0.00168309i
$275$		0			0
$276$	493.596	+	2252.56i	0.107648	+	0.491262i
$277$	−742.484	+	2770.99i	−0.161052	+	0.601056i	0.837458	+	0.546501i	$0.184041\pi$
$277$	−742.484	+	2770.99i	−0.161052	+	0.601056i	−0.998511	+	0.0545548i	$0.982626\pi$
$278$	−1746.41	−	1746.41i	−0.376772	−	0.376772i
$279$	−371.868	−	807.781i	−0.0797962	−	0.173335i
$280$		0			0
$281$	5092.45	−	2940.13i	1.08110	−	0.624176i	0.149910	−	0.988700i	$-0.452102\pi$
$281$	5092.45	−	2940.13i	1.08110	−	0.624176i	0.931194	+	0.364524i	$0.118768\pi$
$282$	−122.828	+	2663.51i	−0.0259373	+	0.562446i
$283$	470.532	+	1756.05i	0.0988348	+	0.368856i	0.997573	−	0.0696293i	$-0.0221817\pi$
$283$	470.532	+	1756.05i	0.0988348	+	0.368856i	−0.898738	+	0.438486i	$0.855515\pi$
$284$	325.628	−	564.005i	0.0680369	−	0.117843i
$285$		0			0
$286$	855.664	+	1482.05i	0.176911	+	0.306418i
$287$	5166.49	−	5166.49i	1.06261	−	1.06261i
$288$	4750.42	+	1755.41i	0.971948	+	0.359162i
$289$			4141.39i			0.842945i
$290$		0			0
$291$	−1518.09	+	332.653i	−0.305814	+	0.0670119i
$292$	−3742.63	+	1002.84i	−0.750072	+	0.200981i
$293$	−6655.60	+	1783.36i	−1.32705	+	0.355581i	−0.851613	−	0.524172i	$-0.824375\pi$
$293$	−6655.60	+	1783.36i	−1.32705	+	0.355581i	−0.475432	+	0.879752i	$0.657708\pi$
$294$	−733.707	+	2307.30i	−0.145547	+	0.457703i
$295$		0			0
$296$		−	4542.54i		−	0.891992i
$297$	−1785.48	+	724.246i	−0.348836	+	0.141498i
$298$	−1609.24	+	1609.24i	−0.312822	+	0.312822i
$299$	3210.62	+	5560.96i	0.620987	+	1.07558i
$300$		0			0
$301$	−1624.04	+	2812.92i	−0.310991	+	0.538652i
$302$	169.052	+	630.912i	0.0322115	+	0.120215i
$303$	−365.221	−	233.931i	−0.0692455	−	0.0443531i
$304$	−321.473	+	185.603i	−0.0606505	+	0.0350166i
$305$		0			0
$306$	−102.850	+	1112.77i	−0.0192141	+	0.207884i
$307$	1580.63	+	1580.63i	0.293848	+	0.293848i	0.838598	−	0.544750i	$-0.183376\pi$
$307$	1580.63	+	1580.63i	0.293848	+	0.293848i	−0.544750	+	0.838598i	$0.683376\pi$
$308$	526.091	−	1963.40i	0.0973273	−	0.363230i
$309$	1005.70	−	917.031i	0.185153	−	0.168829i
$310$		0			0
$311$	−1301.03	−	751.148i	−0.237217	−	0.136957i	0.376680	−	0.926343i	$-0.377066\pi$
$311$	−1301.03	−	751.148i	−0.237217	−	0.136957i	−0.613897	+	0.789386i	$0.710399\pi$
$312$	8912.78	+	411.015i	1.61727	+	0.0745806i
$313$	−3778.34	−	1012.40i	−0.682314	−	0.182825i	−0.0990184	−	0.995086i	$-0.531570\pi$
$313$	−3778.34	−	1012.40i	−0.682314	−	0.182825i	−0.583295	+	0.812260i	$0.698237\pi$
$314$	2271.14			0.408178
$315$		0			0
$316$	1912.92			0.340538
$317$	3726.04	+	998.390i	0.660175	+	0.176893i	0.573325	−	0.819328i	$-0.305653\pi$
$317$	3726.04	+	998.390i	0.660175	+	0.176893i	0.0868500	+	0.996221i	$0.472320\pi$
$318$	−1003.52	+	1566.72i	−0.176963	+	0.276281i
$319$	−2466.68	−	1424.14i	−0.432940	−	0.249958i
$320$		0			0
$321$	−1949.79	−	620.020i	−0.339024	−	0.107807i
$322$	−758.232	+	2829.76i	−0.131225	+	0.489740i
$323$	−466.004	−	466.004i	−0.0802761	−	0.0802761i
$324$	−772.293	+	4142.16i	−0.132423	+	0.710247i
$325$		0			0
$326$	2458.39	−	1419.35i	0.417661	−	0.241136i
$327$	−5684.56	+	2941.52i	−0.961335	+	0.497451i
$328$	−1516.29	−	5658.87i	−0.255253	−	0.952618i
$329$	4409.35	−	7637.22i	0.738892	−	1.27980i
$330$		0			0
$331$	−3448.09	−	5972.26i	−0.572580	−	0.991738i	−0.996300	−	0.0859446i	$-0.972609\pi$
$331$	−3448.09	−	5972.26i	−0.572580	−	0.991738i	0.423720	−	0.905793i	$-0.360724\pi$
$332$	6131.76	−	6131.76i	1.01363	−	1.01363i
$333$	5887.76	−	1008.46i	0.968912	−	0.165955i
$334$		−	176.018i		−	0.0288362i
$335$		0			0
$336$	−1402.71	−	1538.34i	−0.227751	−	0.249772i
$337$	6614.22	−	1772.28i	1.06914	−	0.286475i	0.318999	−	0.947755i	$-0.396653\pi$
$337$	6614.22	−	1772.28i	1.06914	−	0.286475i	0.750139	+	0.661280i	$0.229987\pi$
$338$	6903.85	−	1849.88i	1.11101	−	0.297693i
$339$	326.343	+	357.897i	0.0522847	+	0.0573401i
$340$		0			0
$341$			452.329i			0.0718329i
$342$	609.924	+	734.153i	0.0964354	+	0.116077i
$343$	−548.319	+	548.319i	−0.0863162	+	0.0863162i
$344$	1302.18	+	2255.45i	0.204096	+	0.353504i
$345$		0			0
$346$	−366.172	+	634.229i	−0.0568946	+	0.0985444i
$347$	69.6922	+	260.095i	0.0107818	+	0.0402381i	0.971107	−	0.238644i	$-0.0767029\pi$
$347$	69.6922	+	260.095i	0.0107818	+	0.0402381i	−0.960325	+	0.278882i	$0.910036\pi$
$348$	−5531.96	+	2862.56i	−0.852138	+	0.440946i
$349$	8184.76	−	4725.48i	1.25536	−	0.724782i	0.283190	−	0.959064i	$-0.408607\pi$
$349$	8184.76	−	4725.48i	1.25536	−	0.724782i	0.972169	+	0.234282i	$0.0752738\pi$
$350$		0			0
$351$	1445.93	+	11643.5i	0.219881	+	1.77060i
$352$	−1821.52	−	1821.52i	−0.275816	−	0.275816i
$353$	−91.7954	+	342.585i	−0.0138407	+	0.0516543i	−0.972501	−	0.232899i	$-0.925179\pi$
$353$	−91.7954	+	342.585i	−0.0138407	+	0.0516543i	0.958660	+	0.284554i	$0.0918454\pi$
$354$	3240.00	+	1030.30i	0.486452	+	0.154689i
$355$		0			0
$356$	2995.44	+	1729.42i	0.445949	+	0.257469i
$357$	1993.53	−	3112.36i	0.295542	−	0.461411i
$358$	923.781	+	247.526i	0.136378	+	0.0365424i
$359$	−2385.59			−0.350715			−0.175358	−	0.984505i	$-0.556108\pi$
$359$	−2385.59			−0.350715			−0.175358	+	0.984505i	$0.556108\pi$
$360$		0			0
$361$	6296.13			0.917937
$362$	1789.04	+	479.371i	0.259750	+	0.0695999i
$363$	−5929.71	−	273.450i	−0.857381	−	0.0395383i
$364$	−10719.3	−	6188.81i	−1.54353	−	0.891159i
$365$		0			0
$366$	1579.91	−	1440.62i	0.225637	−	0.205744i
$367$	859.169	−	3206.46i	0.122202	−	0.456065i	−0.877522	−	0.479536i	$-0.840805\pi$
$367$	859.169	−	3206.46i	0.122202	−	0.456065i	0.999725	+	0.0234708i	$0.00747167\pi$
$368$	−849.482	−	849.482i	−0.120332	−	0.120332i
$369$	6998.06	−	3221.61i	0.987275	−	0.454499i
$370$		0			0
$371$	5329.20	−	3076.82i	0.745764	−	0.430567i
$372$	832.951	+	533.521i	0.116093	+	0.0743596i
$373$	2837.71	+	10590.5i	0.393917	+	1.47012i	0.823618	+	0.567145i	$0.191952\pi$
$373$	2837.71	+	10590.5i	0.393917	+	1.47012i	−0.429701	+	0.902971i	$0.641381\pi$
$374$	284.213	−	492.271i	0.0392949	−	0.0680608i
$375$		0			0
$376$	−3535.49	−	6123.65i	−0.484917	−	0.839901i
$377$	−12264.3	+	12264.3i	−1.67544	+	1.67544i
$378$	−3289.77	+	4222.70i	−0.447640	+	0.574583i
$379$			1340.48i			0.181677i	0.995866	+	0.0908385i	$0.0289547\pi$
$379$			1340.48i			0.181677i	−0.995866	+	0.0908385i	$0.971045\pi$
$380$		0			0
$381$	−878.940	+	2764.02i	−0.118188	+	0.371666i
$382$	5845.55	−	1566.31i	0.782943	−	0.209789i
$383$	13746.2	−	3683.28i	1.83394	−	0.491401i	0.835614	−	0.549318i	$-0.185112\pi$
$383$	13746.2	−	3683.28i	1.83394	−	0.491401i	0.998321	+	0.0579162i	$0.0184456\pi$
$384$	−6449.39	+	1413.23i	−0.857081	+	0.187809i
$385$		0			0
$386$			3810.47i			0.502455i
$387$	−2634.28	+	2188.53i	−0.346016	+	0.287465i
$388$	1222.37	−	1222.37i	0.159940	−	0.159940i
$389$	5939.24	+	10287.1i	0.774116	+	1.34081i	0.935290	+	0.353883i	$0.115139\pi$
$389$	5939.24	+	10287.1i	0.774116	+	1.34081i	−0.161174	+	0.986926i	$0.551528\pi$
$390$		0			0
$391$	1066.42	−	1847.10i	0.137932	−	0.238905i
$392$	−1661.81	−	6201.96i	−0.214118	−	0.799098i
$393$	−156.486	+	3393.38i	−0.0200857	+	0.435555i
$394$	−2464.66	+	1422.97i	−0.315146	+	0.181950i
$395$		0			0
$396$	1237.89	−	1749.59i	0.157087	−	0.222021i
$397$	−1019.37	−	1019.37i	−0.128869	−	0.128869i	0.639731	−	0.768599i	$-0.279046\pi$
$397$	−1019.37	−	1019.37i	−0.128869	−	0.128869i	−0.768599	+	0.639731i	$0.779046\pi$
$398$	−1886.01	+	7038.68i	−0.237530	+	0.886476i
$399$	−675.703	−	3083.62i	−0.0847806	−	0.386903i
$400$		0			0
$401$	8126.77	+	4691.99i	1.01205	+	0.584306i	0.911791	−	0.410655i	$-0.134700\pi$
$401$	8126.77	+	4691.99i	1.01205	+	0.584306i	0.100257	+	0.994962i	$0.468033\pi$
$402$	−3361.85	−	6496.86i	−0.417100	−	0.806055i
$403$	2660.55	+	712.893i	0.328862	+	0.0881184i
$404$	482.440			0.0594116
$405$		0			0
$406$	−7913.02			−0.967283
$407$	−2934.92	−	786.408i	−0.357441	−	0.0957760i
$408$	−1361.98	−	2632.06i	−0.165265	−	0.319378i
$409$	−2717.07	−	1568.70i	−0.328485	−	0.189651i	0.326683	−	0.945134i	$-0.394069\pi$
$409$	−2717.07	−	1568.70i	−0.328485	−	0.189651i	−0.655168	+	0.755483i	$0.727402\pi$
$410$		0			0
$411$	11.3964	+	52.0085i	0.00136775	+	0.00624183i
$412$	−391.830	+	1462.33i	−0.0468546	+	0.174864i
$413$	−7951.27	−	7951.27i	−0.947353	−	0.947353i
$414$	−1784.12	+	2521.61i	−0.211799	+	0.299349i
$415$		0			0
$416$	−13584.8	+	7843.18i	−1.60108	+	0.924383i
$417$	−396.770	+	8603.88i	−0.0465946	+	1.01039i
$418$	−125.654	−	468.946i	−0.0147032	−	0.0548729i
$419$	−1590.40	+	2754.66i	−0.185433	+	0.321179i	−0.943722	−	0.330739i	$-0.892702\pi$
$419$	−1590.40	+	2754.66i	−0.185433	+	0.321179i	0.758290	+	0.651918i	$0.226035\pi$
$420$		0			0
$421$	1402.60	+	2429.37i	0.162372	+	0.281236i	0.935719	−	0.352747i	$-0.114752\pi$
$421$	1402.60	+	2429.37i	0.162372	+	0.281236i	−0.773347	+	0.633983i	$0.781419\pi$
$422$	3122.79	−	3122.79i	0.360225	−	0.360225i
$423$	7152.21	−	5941.96i	0.822110	−	0.682997i
$424$		−	4934.08i		−	0.565142i
$425$		0			0
$426$	852.154	−	186.729i	0.0969178	−	0.0212372i
$427$	−6830.64	+	1830.27i	−0.774141	+	0.207430i
$428$	2198.30	−	589.032i	0.248268	−	0.0665232i
$429$	1808.54	−	5687.36i	0.203537	−	0.640066i
$430$		0			0
$431$		−	14909.0i		−	1.66623i	−0.553103	−	0.833113i	$-0.686556\pi$
$431$		−	14909.0i		−	1.66623i	0.553103	−	0.833113i	$-0.313444\pi$
$432$	−825.105	−	2034.13i	−0.0918932	−	0.226544i
$433$	−3778.79	+	3778.79i	−0.419393	+	0.419393i	−0.884994	−	0.465602i	$-0.845838\pi$
$433$	−3778.79	+	3778.79i	−0.419393	+	0.419393i	0.465602	+	0.884994i	$0.345838\pi$
$434$	628.325	+	1088.29i	0.0694944	+	0.120368i
$435$		0			0
$436$	3559.78	−	6165.72i	0.391015	−	0.677258i
$437$	−471.478	−	1759.58i	−0.0516106	−	0.192613i
$438$	−4370.52	−	2799.40i	−0.476784	−	0.305390i
$439$	−1424.98	+	822.711i	−0.154921	+	0.0894438i	−0.575457	−	0.817832i	$-0.695176\pi$
$439$	−1424.98	+	822.711i	−0.154921	+	0.0894438i	0.420535	+	0.907276i	$0.361842\pi$
$440$		0			0
$441$	7669.69	−	3530.80i	0.828170	−	0.381254i
$442$	−2447.55	−	2447.55i	−0.263389	−	0.263389i
$443$	1770.56	−	6607.83i	0.189891	−	0.708685i	−0.803639	−	0.595117i	$-0.797106\pi$
$443$	1770.56	−	6607.83i	0.189891	−	0.708685i	0.993530	−	0.113567i	$-0.0362277\pi$
$444$	−4909.87	+	4476.99i	−0.524802	+	0.478533i
$445$		0			0
$446$	−3018.53	−	1742.75i	−0.320474	−	0.185026i
$447$	7928.12	+	365.607i	0.838897	+	0.0386860i
$448$	−3816.77	−	1022.70i	−0.402512	−	0.107853i
$449$	−7775.18			−0.817224			−0.408612	−	0.912708i	$-0.633987\pi$
$449$	−7775.18			−0.817224			−0.408612	+	0.912708i	$0.633987\pi$
$450$		0			0
$451$	−3918.67			−0.409142
$452$	−520.399	−	139.440i	−0.0541537	−	0.0145104i
$453$	1228.57	−	1918.09i	0.127425	−	0.198940i
$454$	2645.07	+	1527.13i	0.273435	+	0.157868i
$455$		0			0
$456$	−2412.14	−	767.046i	−0.247717	−	0.0787724i
$457$	616.297	−	2300.05i	0.0630834	−	0.235431i	−0.927184	−	0.374605i	$-0.877778\pi$
$457$	616.297	−	2300.05i	0.0630834	−	0.235431i	0.990268	+	0.139175i	$0.0444449\pi$
$458$	−4215.17	−	4215.17i	−0.430048	−	0.430048i
$459$	3109.15	−	2349.64i	0.316172	−	0.238937i
$460$		0			0
$461$	−7507.21	+	4334.29i	−0.758451	+	0.437892i	−0.828739	−	0.559635i	$-0.810941\pi$
$461$	−7507.21	+	4334.29i	−0.758451	+	0.437892i	0.0702886	+	0.997527i	$0.477608\pi$
$462$	2418.22	−	1251.33i	0.243519	−	0.126011i
$463$	−1323.45	−	4939.17i	−0.132842	−	0.495772i	0.867156	−	0.498037i	$-0.165946\pi$
$463$	−1323.45	−	4939.17i	−0.132842	−	0.495772i	−0.999997	+	0.00226497i	$0.999279\pi$
$464$	1622.47	−	2810.20i	0.162330	−	0.281164i
$465$		0			0
$466$	5169.66	+	8954.12i	0.513906	+	0.890111i
$467$	−4104.76	+	4104.76i	−0.406736	+	0.406736i	−0.880599	−	0.473863i	$-0.842859\pi$
$467$	−4104.76	+	4104.76i	−0.406736	+	0.406736i	0.473863	+	0.880599i	$0.342859\pi$
$468$	−8339.92	−	10038.6i	−0.823746	−	0.991526i
$469$			24194.2i			2.38206i
$470$		0			0
$471$	−5336.52	−	5852.50i	−0.522068	−	0.572546i
$472$	−8709.04	+	2333.58i	−0.849292	+	0.227567i
$473$	1682.67	−	450.870i	0.163571	−	0.0438288i
$474$	1726.49	+	1893.43i	0.167301	+	0.183477i
$475$		0			0
$476$			4111.29i			0.395883i
$477$	6395.26	−	1095.38i	0.613876	−	0.105145i
$478$	5270.58	−	5270.58i	0.504332	−	0.504332i
$479$	−7608.37	−	13178.1i	−0.725752	−	1.25704i	−0.958664	−	0.284541i	$-0.908159\pi$
$479$	−7608.37	−	13178.1i	−0.725752	−	1.25704i	0.232912	−	0.972498i	$-0.425175\pi$
$480$		0			0
$481$	−9251.13	+	16023.4i	−0.876955	+	1.51893i
$482$	1407.70	+	5253.62i	0.133027	+	0.496464i
$483$	9073.63	−	4695.22i	0.854792	−	0.442319i
$484$	5718.25	−	3301.43i	0.537026	−	0.310052i
$485$		0			0
$486$	−4796.99	+	2974.06i	−0.447728	+	0.277585i
$487$	−1399.75	−	1399.75i	−0.130244	−	0.130244i	0.638980	−	0.769223i	$-0.279357\pi$
$487$	−1399.75	−	1399.75i	−0.130244	−	0.130244i	−0.769223	+	0.638980i	$0.779357\pi$
$488$	−1467.54	+	5476.92i	−0.136132	+	0.508050i
$489$	−9434.01	−	2999.96i	−0.872435	−	0.277429i
$490$		0			0
$491$	−10186.1	−	5880.94i	−0.936235	−	0.540536i	−0.0474571	−	0.998873i	$-0.515112\pi$
$491$	−10186.1	−	5880.94i	−0.936235	−	0.540536i	−0.888778	+	0.458338i	$0.848445\pi$
$492$	−4622.06	+	7216.12i	−0.423534	+	0.661235i
$493$	5564.68	+	1491.05i	0.508358	+	0.136214i
$494$	−2956.32			−0.269254
$495$		0			0
$496$	−515.321			−0.0466504
$497$	−2786.99	−	746.771i	−0.251536	−	0.0673989i
$498$	11603.5	+	535.098i	1.04411	+	0.0481492i
$499$	13118.8	+	7574.16i	1.17691	+	0.679491i	0.955298	−	0.295644i	$-0.0955342\pi$
$499$	13118.8	+	7574.16i	1.17691	+	0.679491i	0.221614	+	0.975134i	$0.428867\pi$
$500$		0			0
$501$	−453.582	+	413.592i	−0.0404482	+	0.0368821i
$502$	−1374.07	+	5128.10i	−0.122167	+	0.455933i
$503$	10418.9	+	10418.9i	0.923572	+	0.923572i	0.997280	−	0.0737075i	$-0.0234831\pi$
$503$	10418.9	+	10418.9i	0.923572	+	0.923572i	−0.0737075	+	0.997280i	$0.523483\pi$
$504$	1306.49	−	14135.4i	0.115468	−	1.24929i
$505$		0			0
$506$	1360.71	−	785.604i	0.119547	−	0.0690205i
$507$	−20989.0	−	13443.9i	−1.83857	−	1.17764i
$508$	−835.011	−	3116.30i	−0.0729284	−	0.272172i
$509$	5758.26	−	9973.60i	0.501435	−	0.868511i	−0.498564	−	0.866853i	$-0.666139\pi$
$509$	5758.26	−	9973.60i	0.501435	−	0.868511i	0.999999	−	0.00165784i	$-0.000527706\pi$
$510$		0			0
$511$	8583.07	+	14866.3i	0.743038	+	1.28698i
$512$	3892.45	−	3892.45i	0.335983	−	0.335983i
$513$	458.696	−	3296.76i	0.0394774	−	0.283734i
$514$		−	10278.2i		−	0.882011i
$515$		0			0
$516$	1154.44	−	3630.38i	0.0984910	−	0.309726i
$517$	−4568.53	+	1224.13i	−0.388634	+	0.104134i
$518$	−8153.71	+	2184.78i	−0.691609	+	0.185316i
$519$	2494.74	−	546.664i	0.210996	−	0.0462348i
$520$		0			0
$521$			17652.9i			1.48443i	0.670162	+	0.742215i	$0.266225\pi$
$521$			17652.9i			1.48443i	−0.670162	+	0.742215i	$0.733775\pi$
$522$	−7826.24	−	2892.02i	−0.656217	−	0.242491i
$523$	−3650.39	+	3650.39i	−0.305202	+	0.305202i	−0.843045	−	0.537843i	$-0.819239\pi$
$523$	−3650.39	+	3650.39i	−0.305202	+	0.305202i	0.537843	+	0.843045i	$0.319239\pi$
$524$	−1889.30	−	3272.36i	−0.157508	−	0.272813i
$525$		0			0
$526$	3804.99	−	6590.44i	0.315410	−	0.546306i
$527$	−236.791	−	883.714i	−0.0195726	−	0.0730459i
$528$	−51.4353	+	1115.36i	−0.00423946	+	0.0919317i
$529$	−5431.29	+	3135.76i	−0.446395	+	0.257726i
$530$		0			0
$531$	−4958.08	−	10770.1i	−0.405202	−	0.880191i
$532$	2482.95	+	2482.95i	0.202349	+	0.202349i
$533$	−6176.01	+	23049.2i	−0.501900	+	1.87312i
$534$	991.721	+	4525.80i	0.0803670	+	0.366761i
$535$		0			0
$536$	16800.3	+	9699.66i	1.35385	+	0.781645i
$537$	−1532.77	−	2962.11i	−0.123173	−	0.238034i
$538$	10003.4	+	2680.41i	0.801632	+	0.214797i
$539$	−4294.76			−0.343207
$540$		0			0
$541$	572.214			0.0454739			0.0227370	−	0.999741i	$-0.492762\pi$
$541$	572.214			0.0454739			0.0227370	+	0.999741i	$0.492762\pi$
$542$	8195.92	+	2196.09i	0.649529	+	0.174041i
$543$	−2968.42	−	5736.55i	−0.234599	−	0.453368i
$544$	4512.25	+	2605.15i	0.355627	+	0.205321i
$545$		0			0
$546$	−3548.93	−	16195.8i	−0.278169	−	1.26945i
$547$	5037.74	−	18801.1i	0.393781	−	1.46961i	−0.430066	−	0.902797i	$-0.641510\pi$
$547$	5037.74	−	18801.1i	0.393781	−	1.46961i	0.823847	−	0.566812i	$-0.191823\pi$
$548$	−41.8775	−	41.8775i	−0.00326445	−	0.00326445i
$549$	−7424.65	−	686.239i	−0.577188	−	0.0533478i
$550$		0			0
$551$	4261.20	−	2460.21i	0.329462	−	0.190215i
$552$	377.362	−	8183.02i	0.0290971	−	0.630964i
$553$	−2193.47	−	8186.13i	−0.168672	−	0.629493i
$554$	2137.22	−	3701.77i	0.163902	−	0.283886i
$555$		0			0
$556$	−4790.31	−	8297.06i	−0.365385	−	0.632866i
$557$	−7665.26	+	7665.26i	−0.583101	+	0.583101i	−0.935754	−	0.352653i	$-0.885280\pi$
$557$	−7665.26	+	7665.26i	−0.583101	+	0.583101i	0.352653	+	0.935754i	$0.385280\pi$
$558$	223.691	+	1305.99i	0.0169706	+	0.0990808i
$559$		−	10607.9i		−	0.802621i
$560$		0			0
$561$	−1936.35	+	424.305i	−0.145727	+	0.0319326i
$562$	−8463.06	+	2267.67i	−0.635218	+	0.170206i
$563$	−6711.58	+	1798.36i	−0.502415	+	0.134622i	−0.501121	−	0.865378i	$-0.667079\pi$
$563$	−6711.58	+	1798.36i	−0.502415	+	0.134622i	−0.00129433	+	0.999999i	$0.500412\pi$
$564$	−3134.36	+	9856.67i	−0.234008	+	0.735888i
$565$		0			0
$566$		−	2708.82i		−	0.201167i
$567$	18611.5	−	1444.70i	1.37850	−	0.107005i
$568$	−1635.88	+	1635.88i	−0.120845	+	0.120845i
$569$	−1142.29	−	1978.50i	−0.0841603	−	0.145770i	0.820873	−	0.571111i	$-0.193487\pi$
$569$	−1142.29	−	1978.50i	−0.0841603	−	0.145770i	−0.905033	+	0.425341i	$0.860154\pi$
$570$		0			0
$571$	9342.12	−	16181.0i	0.684686	−	1.18591i	−0.288850	−	0.957375i	$-0.593273\pi$
$571$	9342.12	−	16181.0i	0.684686	−	1.18591i	0.973535	−	0.228536i	$-0.0733939\pi$
$572$	1718.15	+	6412.23i	0.125594	+	0.468722i
$573$	−17771.6	−	11383.0i	−1.29567	−	0.829900i
$574$	−9428.20	+	5443.38i	−0.685585	+	0.395823i
$575$		0			0
$576$	−3401.14	−	2406.42i	−0.246031	−	0.174075i
$577$	17462.0	+	17462.0i	1.25989	+	1.25989i	0.951146	+	0.308740i	$0.0999073\pi$
$577$	17462.0	+	17462.0i	1.25989	+	1.25989i	0.308740	+	0.951146i	$0.400093\pi$
$578$	1597.09	−	5960.42i	0.114931	−	0.428929i
$579$	9819.20	−	8953.49i	0.704787	−	0.642650i
$580$		0			0
$581$	−33271.3	−	19209.2i	−2.37578	−	1.37165i
$582$	2313.17	+	106.672i	0.164749	+	0.00759744i
$583$	−3187.89	−	854.193i	−0.226465	−	0.0606810i
$584$	13764.1			0.975277
$585$		0			0
$586$	10266.7			0.723743
$587$	−22383.6	−	5997.68i	−1.57389	−	0.421722i	−0.636860	−	0.770980i	$-0.719767\pi$
$587$	−22383.6	−	5997.68i	−1.57389	−	0.421722i	−0.937027	+	0.349258i	$0.886434\pi$
$588$	−5065.65	+	7908.67i	−0.355279	+	0.554673i
$589$	−676.712	−	390.700i	−0.0473403	−	0.0273319i
$590$		0			0
$591$	9458.08	+	3007.61i	0.658297	+	0.209334i
$592$	895.924	−	3343.63i	0.0621997	−	0.232133i
$593$	13119.3	+	13119.3i	0.908505	+	0.908505i	0.996152	−	0.0876470i	$-0.0279347\pi$
$593$	13119.3	+	13119.3i	0.908505	+	0.908505i	−0.0876470	+	0.996152i	$0.527935\pi$
$594$	2849.03	−	353.804i	0.196796	−	0.0244389i
$595$		0			0
$596$	−7645.39	+	4414.07i	−0.525449	+	0.303368i
$597$	22569.6	−	11678.8i	1.54725	−	0.800639i
$598$	−2476.30	−	9241.67i	−0.169337	−	0.631973i
$599$	−3451.75	+	5978.61i	−0.235450	+	0.407812i	−0.959403	−	0.282037i	$-0.908990\pi$
$599$	−3451.75	+	5978.61i	−0.235450	+	0.407812i	0.723953	+	0.689849i	$0.242323\pi$
$600$		0			0
$601$	9078.32	+	15724.1i	0.616161	+	1.06722i	0.990180	+	0.139801i	$0.0446462\pi$
$601$	9078.32	+	15724.1i	0.616161	+	1.06722i	−0.374019	+	0.927421i	$0.622021\pi$
$602$	3422.15	−	3422.15i	0.231689	−	0.231689i
$603$	−8842.40	+	23928.9i	−0.597165	+	1.61602i
$604$			2533.71i			0.170688i
$605$		0			0
$606$	435.425	+	477.526i	0.0291880	+	0.0320102i
$607$	7416.77	−	1987.32i	0.495943	−	0.132888i	−0.00217355	−	0.999998i	$-0.500692\pi$
$607$	7416.77	−	1987.32i	0.495943	−	0.132888i	0.498116	+	0.867110i	$0.334025\pi$
$608$	4298.44	−	1151.76i	0.286719	−	0.0768260i
$609$	18593.3	+	20391.1i	1.23717	+	1.35679i
$610$		0			0
$611$			28800.9i			1.90697i
$612$	−1502.57	+	4066.20i	−0.0992450	+	0.268572i
$613$	13352.5	−	13352.5i	0.879776	−	0.879776i	−0.113735	−	0.993511i	$-0.536282\pi$
$613$	13352.5	−	13352.5i	0.879776	−	0.879776i	0.993511	+	0.113735i	$0.0362816\pi$
$614$	−1665.34	−	2884.45i	−0.109459	−	0.189588i
$615$		0			0
$616$	−3610.34	+	6253.29i	−0.236144	+	0.409013i
$617$	−3067.84	−	11449.3i	−0.200172	−	0.747054i	−0.990867	−	0.134843i	$-0.956947\pi$
$617$	−3067.84	−	11449.3i	−0.200172	−	0.747054i	0.790695	−	0.612211i	$-0.209720\pi$
$618$	−1801.08	+	931.983i	−0.117233	+	0.0606632i
$619$	−6467.28	+	3733.89i	−0.419939	+	0.242452i	−0.695051	−	0.718960i	$-0.744618\pi$
$619$	−6467.28	+	3733.89i	−0.419939	+	0.242452i	0.275112	+	0.961412i	$0.411285\pi$
$620$		0			0
$621$	10690.1	−	1327.54i	0.690788	−	0.0857849i
$622$	1582.81	+	1582.81i	0.102033	+	0.102033i
$623$	3966.11	−	14801.7i	0.255054	−	0.951875i
$624$	6479.38	+	2060.40i	0.415677	+	0.132183i
$625$		0			0
$626$	5047.48	+	2914.17i	0.322265	+	0.186060i
$627$	−913.177	+	1425.68i	−0.0581639	+	0.0908075i
$628$	8509.81	+	2280.20i	0.540730	+	0.144888i
$629$	6145.61			0.389573
$630$		0			0
$631$	2875.59			0.181419			0.0907094	−	0.995877i	$-0.471087\pi$
$631$	2875.59			0.181419			0.0907094	+	0.995877i	$0.471087\pi$
$632$	−6563.77	−	1758.76i	−0.413121	−	0.110696i
$633$	−15384.7	−	709.472i	−0.966017	−	0.0445481i
$634$	−4977.63	−	2873.83i	−0.311809	−	0.180023i
$635$		0			0
$636$	−5333.08	+	4862.89i	−0.332500	+	0.303185i
$637$	−6768.74	+	25261.3i	−0.421016	+	1.57125i
$638$	3000.93	+	3000.93i	0.186219	+	0.186219i
$639$	−2483.50	−	1757.16i	−0.153749	−	0.108782i
$640$		0			0
$641$	3459.55	−	1997.37i	0.213173	−	0.123076i	−0.389612	−	0.920979i	$-0.627391\pi$
$641$	3459.55	−	1997.37i	0.213173	−	0.123076i	0.602785	+	0.797903i	$0.294058\pi$
$642$	2567.09	+	1644.27i	0.157812	+	0.101081i
$643$	4499.32	+	16791.7i	0.275950	+	1.02986i	0.955202	+	0.295955i	$0.0956377\pi$
$643$	4499.32	+	16791.7i	0.275950	+	1.02986i	−0.679252	+	0.733905i	$0.737696\pi$
$644$	−5682.08	+	9841.66i	−0.347679	+	0.602198i
$645$		0			0
$646$	490.978	+	850.399i	0.0299029	+	0.0517934i
$647$	7322.01	−	7322.01i	0.444912	−	0.444912i	−0.448747	−	0.893659i	$-0.648130\pi$
$647$	7322.01	−	7322.01i	0.444912	−	0.444912i	0.893659	+	0.448747i	$0.148130\pi$
$648$	6458.31	−	13502.9i	0.391522	−	0.818586i
$649$			6030.87i			0.364765i
$650$		0			0
$651$	1328.04	−	4176.30i	0.0799537	−	0.251432i
$652$	10636.4	−	2850.02i	0.638887	−	0.171189i
$653$	−8188.49	+	2194.10i	−0.490720	+	0.131488i	−0.495690	−	0.868499i	$-0.665085\pi$
$653$	−8188.49	+	2194.10i	−0.490720	+	0.131488i	0.00496957	+	0.999988i	$0.498418\pi$
$654$	9315.77	−	2041.33i	0.556996	−	0.122053i
$655$		0			0
$656$		−	4464.39i		−	0.265709i
$657$	3055.67	+	17840.2i	0.181451	+	1.05938i
$658$	−9291.31	+	9291.31i	−0.550476	+	0.550476i
$659$	−4605.68	−	7977.27i	−0.272249	−	0.471548i	0.697189	−	0.716888i	$-0.254434\pi$
$659$	−4605.68	−	7977.27i	−0.272249	−	0.471548i	−0.969437	+	0.245339i	$0.921101\pi$
$660$		0			0
$661$	7007.31	−	12137.0i	0.412334	−	0.714183i	−0.582811	−	0.812608i	$-0.698047\pi$
$661$	7007.31	−	12137.0i	0.412334	−	0.714183i	0.995145	+	0.0984247i	$0.0313804\pi$
$662$	2659.45	+	9925.20i	0.156137	+	0.582710i
$663$	−556.064	+	12058.1i	−0.0325727	+	0.706333i
$664$	−26677.4	+	15402.2i	−1.55917	+	0.900184i
$665$		0			0
$666$	−8862.77	−	819.160i	−0.515654	−	0.0476604i
$667$	11260.1	+	11260.1i	0.653661	+	0.653661i
$668$	176.720	−	659.529i	0.0102358	−	0.0382005i
$669$	2601.77	+	11873.4i	0.150359	+	0.686176i
$670$		0			0
$671$	3284.55	+	1896.34i	0.188970	+	0.109102i
$672$	11469.9	+	22165.8i	0.658423	+	1.27242i
$673$	14115.8	+	3782.31i	0.808503	+	0.216638i	0.639314	−	0.768946i	$-0.279218\pi$
$673$	14115.8	+	3782.31i	0.808503	+	0.216638i	0.169189	+	0.985584i	$0.445885\pi$
$674$	−10202.9			−0.583086
$675$		0			0
$676$	27725.5			1.57746
$677$	17159.0	+	4597.75i	0.974113	+	0.261013i	0.710564	−	0.703633i	$-0.248440\pi$
$677$	17159.0	+	4597.75i	0.974113	+	0.261013i	0.263550	+	0.964646i	$0.415107\pi$
$678$	−331.664	−	640.949i	−0.0187868	−	0.0363060i
$679$	−6632.67	−	3829.37i	−0.374872	−	0.216433i
$680$		0			0
$681$	−2279.88	−	10404.4i	−0.128289	−	0.585459i
$682$	174.437	−	651.007i	0.00979404	−	0.0365519i
$683$	−15195.5	−	15195.5i	−0.851301	−	0.851301i	0.138993	−	0.990293i	$-0.455614\pi$
$683$	−15195.5	−	15195.5i	−0.851301	−	0.851301i	−0.990293	+	0.138993i	$0.955614\pi$
$684$	1548.26	+	3363.18i	0.0865487	+	0.188003i
$685$		0			0
$686$	1000.61	−	577.705i	0.0556904	−	0.0321529i
$687$	−957.652	+	20766.5i	−0.0531830	+	1.15326i
$688$	513.658	+	1917.00i	0.0284637	+	0.106228i
$689$	−10048.5	+	17404.6i	−0.555615	+	0.962353i
$690$		0			0
$691$	−10015.8	−	17347.9i	−0.551404	−	0.955060i	−0.998174	−	0.0604108i	$-0.980759\pi$
$691$	−10015.8	−	17347.9i	−0.551404	−	0.955060i	0.446770	−	0.894649i	$-0.352574\pi$
$692$	−2008.78	+	2008.78i	−0.110350	+	0.110350i
$693$	−8906.65	−	3291.25i	−0.488219	−	0.180410i
$694$		−	401.213i		−	0.0219450i
$695$		0			0
$696$	21613.6	−	4736.11i	1.17710	−	0.257934i
$697$	7655.90	−	2051.39i	0.416051	−	0.111481i
$698$	−13602.1	+	3644.68i	−0.737605	+	0.197641i
$699$	10926.7	−	34361.3i	0.591251	−	1.85932i
$700$		0			0
$701$		−	16064.1i		−	0.865523i	−0.901508	−	0.432762i	$-0.857539\pi$
$701$		−	16064.1i		−	0.865523i	0.901508	−	0.432762i	$-0.142461\pi$
$702$	2409.17	−	17315.3i	0.129527	−	0.930944i
$703$	3711.55	−	3711.55i	0.199123	−	0.199123i
$704$	1059.62	+	1835.31i	0.0567271	+	0.0982543i
$705$		0			0
$706$	264.230	−	457.660i	0.0140856	−	0.0243970i
$707$	−553.196	−	2064.55i	−0.0294273	−	0.109824i
$708$	11105.7	+	7113.39i	0.589514	+	0.377595i
$709$	15927.0	−	9195.47i	0.843656	−	0.487085i	−0.0148496	−	0.999890i	$-0.504727\pi$
$709$	15927.0	−	9195.47i	0.843656	−	0.487085i	0.858505	+	0.512805i	$0.171394\pi$
$710$		0			0
$711$	822.417	−	8898.01i	0.0433798	−	0.469341i
$712$	−8688.16	−	8688.16i	−0.457307	−	0.457307i
$713$	654.522	−	2442.71i	0.0343788	−	0.128303i
$714$	−4069.40	+	3710.63i	−0.213296	+	0.194491i
$715$		0			0
$716$	3212.83	+	1854.93i	0.167694	+	0.0968184i
$717$	−25966.1	−	1197.43i	−1.35247	−	0.0623696i
$718$	3433.42	+	919.983i	0.178460	+	0.0478182i
$719$	−4922.15			−0.255306			−0.127653	−	0.991819i	$-0.540744\pi$
$719$	−4922.15			−0.255306			−0.127653	+	0.991819i	$0.540744\pi$
$720$		0			0
$721$	6707.20			0.346448
$722$	−9061.60	−	2428.05i	−0.467088	−	0.125156i
$723$	10230.4	−	15972.0i	0.526239	−	0.821583i
$724$	6222.11	+	3592.34i	0.319396	+	0.184404i
$725$		0			0
$726$	8428.79	+	2680.30i	0.430884	+	0.137018i
$727$	3460.69	−	12915.5i	0.176547	−	0.658884i	−0.819736	−	0.572742i	$-0.805880\pi$
$727$	3460.69	−	12915.5i	0.176547	−	0.658884i	0.996283	−	0.0861414i	$-0.0274537\pi$
$728$	31091.1	+	31091.1i	1.58285	+	1.58285i
$729$	18935.4	+	5373.19i	0.962018	+	0.272986i
$730$		0			0
$731$	−3051.40	+	1761.73i	−0.154391	+	0.0891379i
$732$	7366.17	−	3811.68i	0.371942	−	0.192464i
$733$	5253.09	+	19604.8i	0.264703	+	0.987886i	0.962432	+	0.271524i	$0.0875275\pi$
$733$	5253.09	+	19604.8i	0.264703	+	0.987886i	−0.697729	+	0.716362i	$0.745806\pi$
$734$	−2473.09	+	4283.51i	−0.124364	+	0.215405i
$735$		0			0
$736$	7200.99	+	12472.5i	0.360641	+	0.624649i
$737$	9175.40	−	9175.40i	0.458589	−	0.458589i
$738$	−11314.2	+	1937.90i	−0.564339	+	0.0966602i
$739$			21111.0i			1.05085i	0.850839	+	0.525427i	$0.176094\pi$
$739$			21111.0i			1.05085i	−0.850839	+	0.525427i	$0.823906\pi$
$740$		0			0
$741$	6946.50	+	7618.15i	0.344381	+	0.377679i
$742$	−8856.51	+	2373.10i	−0.438184	+	0.117411i
$743$	−17034.6	+	4564.40i	−0.841101	+	0.225372i	−0.653551	−	0.756883i	$-0.726721\pi$
$743$	−17034.6	+	4564.40i	−0.841101	+	0.225372i	−0.187550	+	0.982255i	$0.560055\pi$
$744$	−2367.57	−	2596.49i	−0.116666	−	0.127946i
$745$		0			0
$746$		−	16336.5i		−	0.801771i
$747$	−25885.9	−	31158.4i	−1.26789	−	1.52614i
$748$	1559.16	−	1559.16i	0.0762146	−	0.0762146i
$749$	−5041.40	−	8731.96i	−0.245940	−	0.425980i
$750$		0			0
$751$	−1012.62	+	1753.91i	−0.0492023	+	0.0852210i	−0.889578	−	0.456784i	$-0.849001\pi$
$751$	−1012.62	+	1753.91i	−0.0492023	+	0.0852210i	0.840375	+	0.542005i	$0.182335\pi$
$752$	−1394.61	−	5204.74i	−0.0676278	−	0.252390i
$753$	16443.3	−	8508.69i	0.795785	−	0.411785i
$754$	22380.7	−	12921.5i	1.08098	−	0.624103i
$755$		0			0
$756$	−16566.1	+	12519.3i	−0.796962	+	0.602278i
$757$	−314.843	−	314.843i	−0.0151164	−	0.0151164i	0.699508	−	0.714625i	$-0.253402\pi$
$757$	−314.843	−	314.843i	−0.0151164	−	0.0151164i	−0.714625	+	0.699508i	$0.753402\pi$
$758$	516.943	−	1929.26i	0.0247707	−	0.0924456i
$759$	−5221.69	−	1660.46i	−0.249717	−	0.0794085i
$760$		0			0
$761$	8783.13	+	5070.94i	0.418381	+	0.241553i	0.694385	−	0.719604i	$-0.255677\pi$
$761$	8783.13	+	5070.94i	0.418381	+	0.241553i	−0.276003	+	0.961157i	$0.589010\pi$
$762$	2330.92	−	3639.11i	0.110814	−	0.173007i
$763$	−30467.4	−	8163.72i	−1.44560	−	0.387348i
$764$	23475.4			1.11166
$765$		0			0
$766$	−21204.4			−1.00019
$767$	35472.9	+	9504.93i	1.66995	+	0.447462i
$768$	16234.9	+	748.677i	0.762795	+	0.0351765i
$769$	−11311.9	−	6530.95i	−0.530454	−	0.306258i	0.210748	−	0.977541i	$-0.432410\pi$
$769$	−11311.9	−	6530.95i	−0.530454	−	0.306258i	−0.741201	+	0.671283i	$0.765744\pi$
$770$		0			0
$771$	−26486.0	+	24150.9i	−1.23719	+	1.12811i
$772$	−3825.66	+	14277.6i	−0.178353	+	0.665623i
$773$	−17678.7	−	17678.7i	−0.822587	−	0.822587i	0.163891	−	0.986478i	$-0.447595\pi$
$773$	−17678.7	−	17678.7i	−0.822587	−	0.822587i	−0.986478	+	0.163891i	$0.947595\pi$
$774$	4635.34	−	2133.91i	0.215263	−	0.0990980i
$775$		0			0
$776$	−5318.18	+	3070.45i	−0.246020	+	0.142040i
$777$	24788.8	+	15877.7i	1.14452	+	0.733088i
$778$	−4580.83	−	17095.9i	−0.211093	−	0.787812i
$779$	3384.76	−	5862.57i	0.155676	−	0.269638i
$780$		0			0
$781$	773.729	+	1340.14i	0.0354497	+	0.0614007i
$782$	−2247.15	+	2247.15i	−0.102759	+	0.102759i
$783$	10937.0	+	26962.8i	0.499176	+	1.23062i
$784$		−	4892.85i		−	0.222888i
$785$		0			0
$786$	1533.85	−	4823.51i	0.0696062	−	0.218892i
$787$	−1860.23	+	498.448i	−0.0842568	+	0.0225766i	−0.300701	−	0.953718i	$-0.597221\pi$
$787$	−1860.23	+	498.448i	−0.0842568	+	0.0225766i	0.216444	+	0.976295i	$0.430554\pi$
$788$	−10663.5	+	2857.29i	−0.482072	+	0.129171i
$789$	−25923.5	+	5680.53i	−1.16971	+	0.256314i
$790$		0			0
$791$			2386.88i			0.107292i
$792$	−5856.17	+	4865.22i	−0.262740	+	0.218280i
$793$	16330.7	−	16330.7i	0.731298	−	0.731298i
$794$	1074.00	+	1860.23i	0.0480037	+	0.0831449i
$795$		0			0
$796$	−14133.5	+	24479.9i	−0.629332	+	1.09004i
$797$	−4788.55	−	17871.1i	−0.212822	−	0.794263i	−0.986922	−	0.161199i	$-0.948464\pi$
$797$	−4788.55	−	17871.1i	−0.212822	−	0.794263i	0.774100	−	0.633064i	$-0.218203\pi$
$798$	−216.679	+	4698.63i	−0.00961196	+	0.208433i
$799$	8284.70	−	4783.17i	0.366823	−	0.211785i
$800$		0			0
$801$	9332.28	−	13189.9i	0.411660	−	0.581824i
$802$	−9886.89	−	9886.89i	−0.435309	−	0.435309i
$803$	2382.85	−	8892.92i	0.104719	−	0.390815i
$804$	−6073.87	−	27718.6i	−0.266429	−	1.21587i
$805$		0			0
$806$	−3554.23	−	2052.04i	−0.155326	−	0.0896773i
$807$	−16598.0	−	32076.0i	−0.724010	−	1.39917i
$808$	−1655.39	−	443.561i	−0.0720749	−	0.0193124i
$809$	−3636.86			−0.158054			−0.0790268	−	0.996872i	$-0.525181\pi$
$809$	−3636.86			−0.158054			−0.0790268	+	0.996872i	$0.525181\pi$
$810$		0			0
$811$	−5975.99			−0.258749			−0.129374	−	0.991596i	$-0.541297\pi$
$811$	−5975.99			−0.258749			−0.129374	+	0.991596i	$0.541297\pi$
$812$	−29649.6	−	7944.58i	−1.28140	−	0.343350i
$813$	−13598.9	−	26280.2i	−0.586636	−	1.13369i
$814$	3920.76	+	2263.65i	0.168824	+	0.0974704i
$815$		0			0
$816$	−483.394	−	2206.01i	−0.0207380	−	0.0946394i
$817$	−778.879	+	2906.82i	−0.0333531	+	0.124476i
$818$	3305.54	+	3305.54i	0.141290	+	0.141290i
$819$	−33396.1	+	47200.7i	−1.42485	+	2.01383i
$820$		0			0
$821$	−17908.5	+	10339.5i	−0.761279	+	0.439525i	−0.829755	−	0.558128i	$-0.811520\pi$
$821$	−17908.5	+	10339.5i	−0.761279	+	0.439525i	0.0684756	+	0.997653i	$0.478186\pi$
$822$	3.65451	−	79.2473i	0.000155068	−	0.00336261i
$823$	−5978.81	−	22313.2i	−0.253230	−	0.945066i	−0.969067	−	0.246799i	$-0.920621\pi$
$823$	−5978.81	−	22313.2i	−0.253230	−	0.945066i	0.715837	−	0.698268i	$-0.246045\pi$
$824$	2688.97	−	4657.43i	0.113683	−	0.196904i
$825$		0			0
$826$	8377.40	+	14510.1i	0.352890	+	0.611223i
$827$	−21798.8	+	21798.8i	−0.916590	+	0.916590i	−0.996780	−	0.0801900i	$-0.974447\pi$
$827$	−21798.8	+	21798.8i	−0.916590	+	0.916590i	0.0801900	+	0.996780i	$0.474447\pi$
$828$	−9216.65	+	7657.07i	−0.386837	+	0.321379i
$829$		−	39148.0i		−	1.64013i	−0.572270	−	0.820065i	$-0.693937\pi$
$829$		−	39148.0i		−	1.64013i	0.572270	−	0.820065i	$-0.306063\pi$
$830$		0			0
$831$	−14560.9	+	3190.68i	−0.607837	+	0.133193i
$832$	12465.1	−	3340.02i	0.519412	−	0.139176i
$833$	8390.66	−	2248.27i	0.349002	−	0.0935149i
$834$	3889.06	−	12230.0i	0.161471	−	0.507781i
$835$		0			0
$836$		−	1883.26i		−	0.0779115i
$837$	2839.81	−	3645.13i	0.117274	−	0.150531i
$838$	3351.27	−	3351.27i	0.138148	−	0.138148i
$839$	−8171.00	−	14152.6i	−0.336227	−	0.582362i	0.647493	−	0.762071i	$-0.275817\pi$
$839$	−8171.00	−	14152.6i	−0.336227	−	0.582362i	−0.983720	+	0.179710i	$0.942484\pi$
$840$		0			0
$841$	−9311.67	+	16128.3i	−0.381798	+	0.661294i
$842$	−1081.80	−	4037.34i	−0.0442771	−	0.165244i
$843$	25729.3	+	16480.1i	1.05120	+	0.673316i
$844$	14836.1	−	8565.63i	0.605071	−	0.349338i
$845$		0			0
$846$	−12585.2	+	5793.67i	−0.511450	+	0.235450i
$847$	−20685.0	−	20685.0i	−0.839134	−	0.839134i
$848$	973.148	−	3631.84i	0.0394080	−	0.147073i
$849$	−6980.37	+	6364.94i	−0.282174	+	0.257296i
$850$		0			0
$851$	14711.5	+	8493.67i	0.592600	+	0.342138i
$852$	3380.44	+	155.890i	0.135929	+	0.00626842i
$853$	−30664.8	−	8216.62i	−1.23088	−	0.329814i	−0.415960	−	0.909383i	$-0.636555\pi$
$853$	−30664.8	−	8216.62i	−1.23088	−	0.329814i	−0.814924	+	0.579568i	$0.803221\pi$
$854$	10536.7			0.422200
$855$		0			0
$856$	−8084.55			−0.322809
$857$	16805.2	+	4502.95i	0.669843	+	0.179484i	0.577684	−	0.816260i	$-0.303957\pi$
$857$	16805.2	+	4502.95i	0.669843	+	0.179484i	0.0921589	+	0.995744i	$0.470623\pi$
$858$	−4796.20	+	7487.98i	−0.190839	+	0.297944i
$859$	20096.3	+	11602.6i	0.798226	+	0.460856i	0.842850	−	0.538148i	$-0.180876\pi$
$859$	20096.3	+	11602.6i	0.798226	+	0.460856i	−0.0446246	+	0.999004i	$0.514209\pi$
$860$		0			0
$861$	36180.6	+	11505.2i	1.43209	+	0.455396i
$862$	−5749.54	+	21457.6i	−0.227181	+	0.847852i
$863$	3319.49	+	3319.49i	0.130935	+	0.130935i	0.769537	−	0.638602i	$-0.220487\pi$
$863$	3319.49	+	3319.49i	0.130935	+	0.130935i	−0.638602	+	0.769537i	$0.720487\pi$
$864$	3243.03	+	26114.7i	0.127697	+	1.02829i
$865$		0			0
$866$	6895.81	−	3981.30i	0.270588	−	0.156224i
$867$	−19112.1	+	9889.71i	−0.748652	+	0.387396i
$868$	1261.66	+	4708.58i	0.0493359	+	0.184124i
$869$	−2272.65	+	3936.35i	−0.0887162	+	0.153661i
$870$		0			0
$871$	−39507.8	−	68429.5i	−1.53694	−	2.66205i
$872$	−17883.5	+	17883.5i	−0.694508	+	0.694508i
$873$	−5160.39	−	6211.45i	−0.200060	−	0.240809i
$874$			2714.26i			0.105047i
$875$		0			0
$876$	−13565.5	−	14877.1i	−0.523214	−	0.573803i
$877$	11623.6	−	3114.52i	0.447548	−	0.119920i	−0.0280039	−	0.999608i	$-0.508915\pi$
$877$	11623.6	−	3114.52i	0.447548	−	0.119920i	0.475552	+	0.879688i	$0.342248\pi$
$878$	2368.15	−	634.543i	0.0910262	−	0.0243904i
$879$	−24123.8	−	26456.3i	−0.925681	−	1.01518i
$880$		0			0
$881$		−	4720.28i		−	0.180511i	−0.995919	−	0.0902556i	$-0.971232\pi$
$881$		−	4720.28i		−	0.180511i	0.995919	−	0.0902556i	$-0.0287684\pi$
$882$	−12400.1	+	2123.89i	−0.473393	+	0.0810829i
$883$	7647.30	−	7647.30i	0.291452	−	0.291452i	−0.546202	−	0.837654i	$-0.683927\pi$
$883$	7647.30	−	7647.30i	0.291452	−	0.291452i	0.837654	+	0.546202i	$0.183927\pi$
$884$	−6713.50	−	11628.1i	−0.255429	−	0.442416i
$885$		0			0
$886$	−5096.50	+	8827.40i	−0.193251	+	0.334720i
$887$	−2598.74	−	9698.64i	−0.0983735	−	0.367135i	0.899136	−	0.437670i	$-0.144196\pi$
$887$	−2598.74	−	9698.64i	−0.0983735	−	0.367135i	−0.997509	+	0.0705349i	$0.977529\pi$
$888$	20963.4	−	10847.7i	0.792213	−	0.409937i
$889$	−12378.4	+	7146.69i	−0.466996	+	0.269620i
$890$		0			0
$891$	−7606.10	−	6510.32i	−0.285986	−	0.244786i
$892$	−9560.52	−	9560.52i	−0.358868	−	0.358868i
$893$	2114.69	−	7892.14i	0.0792447	−	0.295745i
$894$	−11269.4	−	3583.60i	−0.421595	−	0.134064i
$895$		0			0
$896$	−28178.0	−	16268.6i	−1.05063	−	0.606579i
$897$	−17996.3	+	28096.4i	−0.669876	+	1.04583i
$898$	11190.3	+	2998.43i	0.415841	+	0.111424i
$899$	6830.70			0.253411
$900$		0			0
$901$	6675.33			0.246823
$902$	5639.88	+	1511.20i	0.208190	+	0.0557844i
$903$	−16859.6	−	777.486i	−0.621321	−	0.0286524i
$904$	1657.44	+	956.921i	0.0609795	+	0.0352065i
$905$		0			0
$906$	−2507.90	+	2286.79i	−0.0919641	+	0.0838561i
$907$	7160.88	−	26724.8i	0.262153	−	0.978369i	−0.701817	−	0.712358i	$-0.747627\pi$
$907$	7160.88	−	26724.8i	0.262153	−	0.978369i	0.963970	−	0.266012i	$-0.0857059\pi$
$908$	8377.68	+	8377.68i	0.306193	+	0.306193i
$909$	207.415	−	2244.09i	0.00756823	−	0.0818832i
$910$		0			0
$911$	40788.9	−	23549.5i	1.48342	−	0.856453i	0.483598	−	0.875290i	$-0.339330\pi$
$911$	40788.9	−	23549.5i	1.48342	−	0.856453i	0.999823	+	0.0188372i	$0.00599642\pi$
$912$	−1624.22	−	1040.35i	−0.0589730	−	0.0377734i
$913$	5332.90	+	19902.6i	0.193311	+	0.721447i
$914$	−1773.99	+	3072.64i	−0.0641995	+	0.111197i
$915$		0			0
$916$	−11562.0	−	20025.9i	−0.417050	−	0.722352i
$917$	−11837.4	+	11837.4i	−0.426286	+	0.426286i
$918$	−5380.92	+	2182.67i	−0.193461	+	0.0784735i
$919$			2547.69i			0.0914479i	0.998954	+	0.0457239i	$0.0145595\pi$
$919$			2547.69i			0.0914479i	−0.998954	+	0.0457239i	$0.985441\pi$
$920$		0			0
$921$	−3519.88	+	11069.0i	−0.125933	+	0.396023i
$922$	12476.1	−	3342.96i	0.445639	−	0.119409i
$923$	9101.98	−	2438.87i	0.324589	−	0.0869733i
$924$	10317.2	−	2260.77i	0.367328	−	0.0804912i
$925$		0			0
$926$			7618.99i			0.270384i
$927$	6633.64	+	2451.31i	0.235035	+	0.0868519i
$928$	−27507.1	+	27507.1i	−0.973021	+	0.973021i
$929$	25014.8	+	43327.0i	0.883434	+	1.53015i	0.847498	+	0.530799i	$0.178108\pi$
$929$	25014.8	+	43327.0i	0.883434	+	1.53015i	0.0359367	+	0.999354i	$0.488559\pi$
$930$		0			0
$931$	3709.60	−	6425.22i	0.130588	−	0.226185i
$932$	10380.6	+	38740.7i	0.364835	+	1.36158i
$933$	359.601	−	7797.87i	0.0126182	−	0.273623i
$934$	7490.67	−	4324.74i	0.262422	−	0.151510i
$935$		0			0
$936$	19387.1	+	42113.2i	0.677016	+	1.47063i
$937$	−33647.3	−	33647.3i	−1.17312	−	1.17312i	−0.981462	−	0.191655i	$-0.938615\pi$
$937$	−33647.3	−	33647.3i	−1.17312	−	1.17312i	−0.191655	−	0.981462i	$-0.561385\pi$
$938$	9330.30	−	34821.1i	0.324782	−	1.21210i
$939$	−4350.60	−	19854.3i	−0.151200	−	0.690011i
$940$		0			0
$941$	5692.71	+	3286.68i	0.197212	+	0.113861i	0.595355	−	0.803463i	$-0.297012\pi$
$941$	5692.71	+	3286.68i	0.197212	+	0.113861i	−0.398142	+	0.917324i	$0.630345\pi$
$942$	5423.53	+	10481.1i	0.187588	+	0.362519i
$943$	21162.0	+	5670.33i	0.730783	+	0.195813i
$944$	−6870.73			−0.236889
$945$		0			0
$946$	−2595.63			−0.0892084
$947$	35416.4	+	9489.79i	1.21529	+	0.325636i	0.808835	−	0.588036i	$-0.200099\pi$
$947$	35416.4	+	9489.79i	1.21529	+	0.325636i	0.406453	+	0.913671i	$0.366765\pi$
$948$	4568.08	+	8827.93i	0.156502	+	0.302445i
$949$	−48551.7	−	28031.3i	−1.66075	−	0.958836i
$950$		0			0
$951$	4290.39	+	19579.5i	0.146294	+	0.667623i
$952$	3779.96	−	14107.0i	0.128686	−	0.480264i
$953$	6706.27	+	6706.27i	0.227951	+	0.227951i	0.811836	−	0.583885i	$-0.198468\pi$
$953$	6706.27	+	6706.27i	0.227951	+	0.227951i	−0.583885	+	0.811836i	$0.698468\pi$
$954$	−9626.69	−	889.767i	−0.326704	−	0.0301963i
$955$		0			0
$956$	25040.1	−	14456.9i	0.847129	−	0.489090i
$957$	681.786	−	14784.4i	0.0230293	−	0.499385i
$958$	5868.20	+	21900.4i	0.197905	+	0.738592i
$959$	−131.191	+	227.230i	−0.00441751	+	0.00765134i
$960$		0			0
$961$	14353.1	+	24860.3i	0.481794	+	0.834491i
$962$	19493.8	−	19493.8i	0.653333	−	0.653333i
$963$	−1794.80	−	10478.7i	−0.0600587	−	0.350646i
$964$			21098.3i			0.704906i
$965$		0			0
$966$	−14869.7	+	3258.35i	−0.495265	+	0.108526i
$967$	−32473.0	+	8701.12i	−1.07990	+	0.289358i	−0.754554	−	0.656237i	$-0.772147\pi$
$967$	−32473.0	+	8701.12i	−1.07990	+	0.289358i	−0.325345	+	0.945596i	$0.605480\pi$
$968$	−22656.3	+	6070.75i	−0.752275	+	0.201572i
$969$	1037.74	−	3263.39i	0.0344035	−	0.108189i
$970$		0			0
$971$			34772.8i			1.14924i	0.818421	+	0.574620i	$0.194850\pi$
$971$			34772.8i			1.14924i	−0.818421	+	0.574620i	$0.805150\pi$
$972$	−20959.9	+	6327.50i	−0.691656	+	0.208801i
$973$	−30013.6	+	30013.6i	−0.988890	+	0.988890i
$974$	1474.76	+	2554.37i	0.0485159	+	0.0840320i
$975$		0			0
$976$	−2160.42	+	3741.96i	−0.0708539	+	0.122723i
$977$	−11480.2	−	42844.6i	−0.375930	−	1.40299i	−0.851982	−	0.523571i	$-0.824599\pi$
$977$	−11480.2	−	42844.6i	−0.375930	−	1.40299i	0.476052	−	0.879417i	$-0.342067\pi$
$978$	12420.8	+	7955.78i	0.406109	+	0.260121i
$979$	−7117.49	+	4109.29i	−0.232356	+	0.134151i
$980$		0			0
$981$	−27149.7	−	19209.3i	−0.883611	−	0.625184i
$982$	12392.2	+	12392.2i	0.402700	+	0.402700i
$983$	14642.2	−	54645.5i	0.475091	−	1.77306i	−0.145956	−	0.989291i	$-0.546626\pi$
$983$	14642.2	−	54645.5i	0.475091	−	1.77306i	0.621048	−	0.783773i	$-0.286707\pi$
$984$	22494.2	−	20511.0i	0.728749	−	0.664499i
$985$		0			0
$986$	−7433.86	−	4291.94i	−0.240104	−	0.138624i
$987$	45774.7	+	2110.91i	1.47621	+	0.0680760i
$988$	−11077.1	−	2968.11i	−0.356691	−	0.0955751i
$989$	−9739.32			−0.313137
$990$		0			0
$991$	−45374.8			−1.45447			−0.727234	−	0.686390i	$-0.759195\pi$
$991$	−45374.8			−1.45447			−0.727234	+	0.686390i	$0.759195\pi$
$992$	5967.26	+	1598.92i	0.190988	+	0.0511752i
$993$	19327.3	−	30174.5i	0.617658	−	0.964308i
$994$	3723.14	+	2149.55i	0.118804	+	0.0685913i
$995$		0			0
$996$	42940.2	+	13654.7i	1.36608	+	0.434404i
$997$	−12347.7	+	46082.2i	−0.392232	+	1.46383i	0.434212	+	0.900811i	$0.357027\pi$
$997$	−12347.7	+	46082.2i	−0.392232	+	1.46383i	−0.826444	+	0.563019i	$0.809640\pi$
$998$	−15960.1	−	15960.1i	−0.506222	−	0.506222i
$999$	18714.0	+	24763.3i	0.592679	+	0.784259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.32.6		64
5.2	odd	4		45.4.l.a.23.11	yes	64
5.3	odd	4	inner	225.4.p.b.68.6		64
5.4	even	2		45.4.l.a.32.11	yes	64
9.2	odd	6	inner	225.4.p.b.182.6		64
15.2	even	4		135.4.m.a.98.6		64
15.14	odd	2		135.4.m.a.17.6		64
45.2	even	12		45.4.l.a.38.11	yes	64
45.7	odd	12		135.4.m.a.8.6		64
45.29	odd	6		45.4.l.a.2.11	✓	64
45.34	even	6		135.4.m.a.62.6		64
45.38	even	12	inner	225.4.p.b.218.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.11	✓	64	45.29	odd	6
45.4.l.a.23.11	yes	64	5.2	odd	4
45.4.l.a.32.11	yes	64	5.4	even	2
45.4.l.a.38.11	yes	64	45.2	even	12
135.4.m.a.8.6		64	45.7	odd	12
135.4.m.a.17.6		64	15.14	odd	2
135.4.m.a.62.6		64	45.34	even	6
135.4.m.a.98.6		64	15.2	even	4
225.4.p.b.32.6		64	1.1	even	1	trivial
225.4.p.b.68.6		64	5.3	odd	4	inner
225.4.p.b.182.6		64	9.2	odd	6	inner
225.4.p.b.218.6		64	45.38	even	12	inner

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43923 - 0.385641i) q^{2} +(2.38802 + 4.61491i) q^{3} +(-5.00553 - 2.88994i) q^{4} +(-1.65722 - 7.56285i) q^{6} +(-6.62758 + 24.7344i) q^{7} +(14.5184 + 14.5184i) q^{8} +(-15.5947 + 22.0410i) q^{9} +O(q^{10})\)	\(q+(-1.43923 - 0.385641i) q^{2} +(2.38802 + 4.61491i) q^{3} +(-5.00553 - 2.88994i) q^{4} +(-1.65722 - 7.56285i) q^{6} +(-6.62758 + 24.7344i) q^{7} +(14.5184 + 14.5184i) q^{8} +(-15.5947 + 22.0410i) q^{9} +(11.8937 - 6.86683i) q^{11} +(1.38352 - 30.0013i) q^{12} +(-21.6449 - 80.7799i) q^{13} +(19.0773 - 33.0428i) q^{14} +(7.82311 + 13.5500i) q^{16} +(-19.6420 + 19.6420i) q^{17} +(30.9444 - 25.7081i) q^{18} +23.7249i q^{19} +(-129.974 + 28.4807i) q^{21} +(-19.7659 + 5.29627i) q^{22} +(-74.1658 + 19.8727i) q^{23} +(-32.3308 + 101.671i) q^{24} +124.608i q^{26} +(-138.958 - 19.3339i) q^{27} +(104.656 - 104.656i) q^{28} +(-103.697 - 179.609i) q^{29} +(-16.4679 + 28.5232i) q^{31} +(-48.5466 - 181.178i) q^{32} +(60.0922 + 38.4902i) q^{33} +(35.8441 - 20.6946i) q^{34} +(141.757 - 65.2589i) q^{36} +(-156.441 - 156.441i) q^{37} +(9.14932 - 34.1457i) q^{38} +(321.103 - 292.793i) q^{39} +(-247.106 - 142.667i) q^{41} +(198.046 + 9.13295i) q^{42} +(122.522 + 32.8295i) q^{43} -79.3790 q^{44} +114.406 q^{46} +(-332.652 - 89.1338i) q^{47} +(-43.8503 + 68.4606i) q^{48} +(-270.821 - 156.359i) q^{49} +(-137.551 - 43.7404i) q^{51} +(-125.105 + 466.899i) q^{52} +(-169.925 - 169.925i) q^{53} +(192.536 + 81.4138i) q^{54} +(-455.326 + 262.882i) q^{56} +(-109.488 + 56.6556i) q^{57} +(79.9798 + 298.489i) q^{58} +(-219.565 + 380.298i) q^{59} +(138.080 + 239.161i) q^{61} +(34.7009 - 34.7009i) q^{62} +(-441.816 - 531.805i) q^{63} +154.310i q^{64} +(-71.6433 - 78.5704i) q^{66} +(912.635 - 244.540i) q^{67} +(155.083 - 41.5543i) q^{68} +(-268.820 - 294.812i) q^{69} +112.676i q^{71} +(-546.409 + 93.5891i) q^{72} +(474.023 - 474.023i) q^{73} +(164.825 + 285.485i) q^{74} +(68.5637 - 118.756i) q^{76} +(91.0209 + 339.695i) q^{77} +(-575.056 + 297.567i) q^{78} +(-286.620 + 165.480i) q^{79} +(-242.609 - 687.446i) q^{81} +(300.625 + 300.625i) q^{82} +(-388.308 + 1449.19i) q^{83} +(732.896 + 233.056i) q^{84} +(-163.677 - 94.4988i) q^{86} +(581.246 - 907.461i) q^{87} +(272.373 + 72.9820i) q^{88} -598.425 q^{89} +2141.50 q^{91} +(428.670 + 114.862i) q^{92} +(-170.958 - 7.88376i) q^{93} +(444.390 + 256.569i) q^{94} +(720.191 - 656.695i) q^{96} +(-77.4097 + 288.897i) q^{97} +(329.477 + 329.477i) q^{98} +(-34.1273 + 369.235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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