LMFDB - Embedded newform 225.4.k.d.124.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,4,Mod(49,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.49"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.5
Character	$\chi$	$=$	225.124
Dual form			225.4.k.d.49.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.90044 - 1.09722i) q^{2} +(-5.19206 + 0.206141i) q^{3} +(-1.59221 - 2.75778i) q^{4} +(10.0934 + 5.30509i) q^{6} +(2.39547 + 1.38302i) q^{7} +24.5436i q^{8} +(26.9150 - 2.14059i) q^{9} +(26.3295 - 45.6040i) q^{11} +(8.83533 + 13.9904i) q^{12} +(17.7132 - 10.2267i) q^{13} +(-3.03497 - 5.25672i) q^{14} +(14.1921 - 24.5814i) q^{16} -3.66084i q^{17} +(-53.4992 - 25.4637i) q^{18} +95.6705 q^{19} +(-12.7225 - 6.68694i) q^{21} +(-100.075 + 57.7786i) q^{22} +(-77.8047 + 44.9206i) q^{23} +(-5.05943 - 127.432i) q^{24} -44.8840 q^{26} +(-139.303 + 16.6623i) q^{27} -8.80825i q^{28} +(-113.890 + 197.264i) q^{29} +(-139.569 - 241.741i) q^{31} +(116.100 - 67.0306i) q^{32} +(-127.303 + 242.206i) q^{33} +(-4.01675 + 6.95722i) q^{34} +(-48.7576 - 70.8175i) q^{36} -273.725i q^{37} +(-181.816 - 104.972i) q^{38} +(-89.8599 + 56.7492i) q^{39} +(-32.4323 - 56.1744i) q^{41} +(16.8414 + 26.6676i) q^{42} +(-362.658 - 209.381i) q^{43} -167.688 q^{44} +197.151 q^{46} +(120.125 + 69.3544i) q^{47} +(-68.6190 + 130.554i) q^{48} +(-167.674 - 290.421i) q^{49} +(0.754647 + 19.0073i) q^{51} +(-56.4062 - 32.5661i) q^{52} -197.063i q^{53} +(283.020 + 121.181i) q^{54} +(-33.9444 + 58.7934i) q^{56} +(-496.727 + 19.7216i) q^{57} +(432.884 - 249.926i) q^{58} +(370.552 + 641.814i) q^{59} +(-244.234 + 423.026i) q^{61} +612.554i q^{62} +(67.4346 + 32.0964i) q^{63} -521.263 q^{64} +(507.687 - 320.620i) q^{66} +(356.341 - 205.734i) q^{67} +(-10.0958 + 5.82882i) q^{68} +(394.707 - 249.269i) q^{69} -310.343 q^{71} +(52.5377 + 660.591i) q^{72} -51.0260i q^{73} +(-300.338 + 520.200i) q^{74} +(-152.327 - 263.839i) q^{76} +(126.143 - 72.8286i) q^{77} +(233.040 - 9.25240i) q^{78} +(603.999 - 1046.16i) q^{79} +(719.836 - 115.228i) q^{81} +142.342i q^{82} +(-783.945 - 452.611i) q^{83} +(1.81574 + 45.7330i) q^{84} +(459.475 + 795.833i) q^{86} +(550.661 - 1047.68i) q^{87} +(1119.29 + 646.220i) q^{88} -663.633 q^{89} +56.5752 q^{91} +(247.763 + 143.046i) q^{92} +(774.485 + 1226.36i) q^{93} +(-152.194 - 263.608i) q^{94} +(-588.982 + 371.960i) q^{96} +(-628.159 - 362.668i) q^{97} +735.905i q^{98} +(611.039 - 1283.79i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41}+ \cdots - 4640 q^{99}+O(q^{100}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.90044	−	1.09722i	−0.671909	−	0.387927i	0.124891	−	0.992170i	$-0.460142\pi$
$2$	−1.90044	−	1.09722i	−0.671909	−	0.387927i	−0.796799	+	0.604244i	$0.793475\pi$
$3$	−5.19206	+	0.206141i	−0.999213	+	0.0396718i
$3$	−5.19206	+	0.206141i	−0.999213	+	0.0396718i
$4$	−1.59221	−	2.75778i	−0.199026	−	0.344723i
$5$		0			0
$5$		0			0
$6$	10.0934	+	5.30509i	0.686769	+	0.360965i
$7$	2.39547	+	1.38302i	0.129343	+	0.0746763i	0.563275	−	0.826269i	$-0.309541\pi$
$7$	2.39547	+	1.38302i	0.129343	+	0.0746763i	−0.433932	+	0.900945i	$0.642874\pi$
$8$			24.5436i			1.08468i
$9$	26.9150	−	2.14059i	0.996852	−	0.0792811i
$10$		0			0
$11$	26.3295	−	45.6040i	0.721694	−	1.25001i	−0.238626	−	0.971112i	$-0.576697\pi$
$11$	26.3295	−	45.6040i	0.721694	−	1.25001i	0.960320	−	0.278900i	$-0.0899698\pi$
$12$	8.83533	+	13.9904i	0.212545	+	0.336556i
$13$	17.7132	−	10.2267i	0.377905	−	0.218183i	−0.299002	−	0.954253i	$-0.596654\pi$
$13$	17.7132	−	10.2267i	0.377905	−	0.218183i	0.676906	+	0.736069i	$0.263320\pi$
$14$	−3.03497	−	5.25672i	−0.0579378	−	0.100351i
$15$		0			0
$16$	14.1921	−	24.5814i	0.221751	−	0.384085i
$17$		−	3.66084i		−	0.0522285i	−0.999659	−	0.0261142i	$-0.991687\pi$
$17$		−	3.66084i		−	0.0522285i	0.999659	−	0.0261142i	$-0.00831336\pi$
$18$	−53.4992	−	25.4637i	−0.700549	−	0.333436i
$19$	95.6705			1.15517			0.577587	−	0.816329i	$-0.303994\pi$
$19$	95.6705			1.15517			0.577587	+	0.816329i	$0.303994\pi$
$20$		0			0
$21$	−12.7225	−	6.68694i	−0.132204	−	0.0694862i
$22$	−100.075	+	57.7786i	−0.969825	+	0.559929i
$23$	−77.8047	+	44.9206i	−0.705365	+	0.407243i	−0.809343	−	0.587337i	$-0.800176\pi$
$23$	−77.8047	+	44.9206i	−0.705365	+	0.407243i	0.103977	+	0.994580i	$0.466843\pi$
$24$	−5.05943	−	127.432i	−0.0430313	−	1.08383i
$25$		0			0
$26$	−44.8840			−0.338556
$27$	−139.303	+	16.6623i	−0.992922	+	0.118766i
$28$		−	8.80825i		−	0.0594501i
$29$	−113.890	+	197.264i	−0.729272	+	1.26314i	0.227919	+	0.973680i	$0.426808\pi$
$29$	−113.890	+	197.264i	−0.729272	+	1.26314i	−0.957191	+	0.289456i	$0.906526\pi$
$30$		0			0
$31$	−139.569	−	241.741i	−0.808625	−	1.40058i	−0.913816	−	0.406128i	$-0.866879\pi$
$31$	−139.569	−	241.741i	−0.808625	−	1.40058i	0.105191	−	0.994452i	$-0.466455\pi$
$32$	116.100	−	67.0306i	0.641370	−	0.370295i
$33$	−127.303	+	242.206i	−0.671536	+	1.27766i
$34$	−4.01675	+	6.95722i	−0.0202608	+	0.0350928i
$35$		0			0
$36$	−48.7576	−	70.8175i	−0.225730	−	0.327859i
$37$		−	273.725i		−	1.21622i	−0.793852	−	0.608110i	$-0.791928\pi$
$37$		−	273.725i		−	1.21622i	0.793852	−	0.608110i	$-0.208072\pi$
$38$	−181.816	−	104.972i	−0.776172	−	0.448123i
$39$	−89.8599	+	56.7492i	−0.368951	+	0.233004i
$40$		0			0
$41$	−32.4323	−	56.1744i	−0.123539	−	0.213975i	0.797622	−	0.603157i	$-0.206091\pi$
$41$	−32.4323	−	56.1744i	−0.123539	−	0.213975i	−0.921161	+	0.389182i	$0.872758\pi$
$42$	16.8414	+	26.6676i	0.0618733	+	0.0979738i
$43$	−362.658	−	209.381i	−1.28616	−	0.742565i	−0.308193	−	0.951324i	$-0.599724\pi$
$43$	−362.658	−	209.381i	−1.28616	−	0.742565i	−0.977967	+	0.208759i	$0.933057\pi$
$44$	−167.688			−0.574544
$45$		0			0
$46$	197.151			0.631921
$47$	120.125	+	69.3544i	0.372810	+	0.215242i	0.674685	−	0.738105i	$-0.264279\pi$
$47$	120.125	+	69.3544i	0.372810	+	0.215242i	−0.301875	+	0.953347i	$0.597613\pi$
$48$	−68.6190	+	130.554i	−0.206339	+	0.392580i
$49$	−167.674	−	290.421i	−0.488847	−	0.846708i
$50$		0			0
$51$	0.754647	+	19.0073i	0.00207200	+	0.0521874i
$52$	−56.4062	−	32.5661i	−0.150426	−	0.0868483i
$53$		−	197.063i		−	0.510730i	−0.966845	−	0.255365i	$-0.917804\pi$
$53$		−	197.063i		−	0.510730i	0.966845	−	0.255365i	$-0.0821957\pi$
$54$	283.020	+	121.181i	0.713225	+	0.305381i
$55$		0			0
$56$	−33.9444	+	58.7934i	−0.0810001	+	0.140296i
$57$	−496.727	+	19.7216i	−1.15427	+	0.0458278i
$58$	432.884	−	249.926i	0.980008	−	0.565808i
$59$	370.552	+	641.814i	0.817656	+	1.41622i	0.907405	+	0.420257i	$0.138060\pi$
$59$	370.552	+	641.814i	0.817656	+	1.41622i	−0.0897490	+	0.995964i	$0.528606\pi$
$60$		0			0
$61$	−244.234	+	423.026i	−0.512639	+	0.887916i	0.487254	+	0.873260i	$0.337999\pi$
$61$	−244.234	+	423.026i	−0.512639	+	0.887916i	−0.999893	+	0.0146560i	$0.995335\pi$
$62$			612.554i			1.25475i
$63$	67.4346	+	32.0964i	0.134856	+	0.0641868i
$64$	−521.263			−1.01809
$65$		0			0
$66$	507.687	−	320.620i	0.946848	−	0.597963i
$67$	356.341	−	205.734i	0.649762	−	0.375140i	−0.138603	−	0.990348i	$-0.544261\pi$
$67$	356.341	−	205.734i	0.649762	−	0.375140i	0.788365	+	0.615208i	$0.210928\pi$
$68$	−10.0958	+	5.82882i	−0.0180044	+	0.0103948i
$69$	394.707	−	249.269i	0.688654	−	0.434905i
$70$		0			0
$71$	−310.343			−0.518746			−0.259373	−	0.965777i	$-0.583516\pi$
$71$	−310.343			−0.518746			−0.259373	+	0.965777i	$0.583516\pi$
$72$	52.5377	+	660.591i	0.0859948	+	1.08127i
$73$		−	51.0260i		−	0.0818101i	−0.999163	−	0.0409051i	$-0.986976\pi$
$73$		−	51.0260i		−	0.0818101i	0.999163	−	0.0409051i	$-0.0130241\pi$
$74$	−300.338	+	520.200i	−0.471804	+	0.817189i
$75$		0			0
$76$	−152.327	−	263.839i	−0.229910	−	0.398215i
$77$	126.143	−	72.8286i	0.186692	−	0.107787i
$78$	233.040	−	9.25240i	0.338290	−	0.0134311i
$79$	603.999	−	1046.16i	0.860193	−	1.48990i	−0.0115496	−	0.999933i	$-0.503676\pi$
$79$	603.999	−	1046.16i	0.860193	−	1.48990i	0.871742	−	0.489964i	$-0.162990\pi$
$80$		0			0
$81$	719.836	−	115.228i	0.987429	−	0.158063i
$82$			142.342i			0.191695i
$83$	−783.945	−	452.611i	−1.03674	−	0.598560i	−0.117829	−	0.993034i	$-0.537594\pi$
$83$	−783.945	−	452.611i	−1.03674	−	0.598560i	−0.918907	+	0.394474i	$0.870927\pi$
$84$	1.81574	+	45.7330i	0.00235849	+	0.0594033i
$85$		0			0
$86$	459.475	+	795.833i	0.576121	+	0.997871i
$87$	550.661	−	1047.68i	0.678587	−	1.29107i
$88$	1119.29	+	646.220i	1.35587	+	0.782810i
$89$	−663.633			−0.790393			−0.395197	−	0.918597i	$-0.629324\pi$
$89$	−663.633			−0.790393			−0.395197	+	0.918597i	$0.629324\pi$
$90$		0			0
$91$	56.5752			0.0651725
$92$	247.763	+	143.046i	0.280772	+	0.162104i
$93$	774.485	+	1226.36i	0.863552	+	1.36740i
$94$	−152.194	−	263.608i	−0.166996	−	0.289246i
$95$		0			0
$96$	−588.982	+	371.960i	−0.626175	+	0.395448i
$97$	−628.159	−	362.668i	−0.657525	−	0.379622i	0.133809	−	0.991007i	$-0.457279\pi$
$97$	−628.159	−	362.668i	−0.657525	−	0.379622i	−0.791333	+	0.611385i	$0.790613\pi$
$98$			735.905i			0.758547i
$99$	611.039	−	1283.79i	0.620321	−	1.30329i
$100$		0			0
$101$	−488.891	+	846.784i	−0.481648	+	0.834239i	−0.999778	−	0.0210629i	$-0.993295\pi$
$101$	−488.891	+	846.784i	−0.481648	+	0.834239i	0.518130	+	0.855302i	$0.326628\pi$
$102$	19.4211	−	36.9503i	0.0188527	−	0.0358689i
$103$	1374.99	−	793.852i	1.31536	−	0.759423i	0.332381	−	0.943145i	$-0.392148\pi$
$103$	1374.99	−	793.852i	1.31536	−	0.759423i	0.982978	+	0.183722i	$0.0588147\pi$
$104$	251.000	+	434.745i	0.236660	+	0.409907i
$105$		0			0
$106$	−216.222	+	374.507i	−0.198126	+	0.343164i
$107$		−	897.731i		−	0.811093i	−0.914074	−	0.405546i	$-0.867081\pi$
$107$		−	897.731i		−	0.811093i	0.914074	−	0.405546i	$-0.132919\pi$
$108$	267.751	+	357.638i	0.238559	+	0.318646i
$109$	−855.492			−0.751754			−0.375877	−	0.926669i	$-0.622659\pi$
$109$	−855.492			−0.751754			−0.375877	+	0.926669i	$0.622659\pi$
$110$		0			0
$111$	56.4259	+	1421.20i	0.0482496	+	1.21526i
$112$	67.9934	−	39.2560i	0.0573640	−	0.0331191i
$113$	788.292	−	455.121i	0.656250	−	0.378886i	−0.134597	−	0.990900i	$-0.542974\pi$
$113$	788.292	−	455.121i	0.656250	−	0.378886i	0.790847	+	0.612014i	$0.209641\pi$
$114$	965.641	+	507.540i	0.793339	+	0.416978i
$115$		0			0
$116$	725.348			0.580576
$117$	454.860	−	313.169i	0.359417	−	0.247457i
$118$		−	1626.31i		−	1.26876i
$119$	5.06303	−	8.76943i	0.00390023	−	0.00675539i
$120$		0			0
$121$	−720.984	−	1248.78i	−0.541686	−	0.938227i
$122$	928.306	−	535.958i	0.688893	−	0.397732i
$123$	179.971	+	284.976i	0.131930	+	0.208906i
$124$	−444.447	+	769.804i	−0.321875	+	0.557504i
$125$		0			0
$126$	−92.9387	−	134.988i	−0.0657114	−	0.0954420i
$127$			2038.25i			1.42414i	0.702111	+	0.712068i	$0.252241\pi$
$127$			2038.25i			1.42414i	−0.702111	+	0.712068i	$0.747759\pi$
$128$	61.8287	+	35.6968i	0.0426948	+	0.0246499i
$129$	1926.11	+	1012.36i	1.31461	+	0.690956i
$130$		0			0
$131$	−117.823	−	204.075i	−0.0785817	−	0.136108i	0.824057	−	0.566508i	$-0.191706\pi$
$131$	−117.823	−	204.075i	−0.0785817	−	0.136108i	−0.902638	+	0.430400i	$0.858372\pi$
$132$	870.647	−	34.5673i	0.574091	−	0.0227932i
$133$	229.176	+	132.315i	0.149414	+	0.0862642i
$134$	−902.942			−0.582107
$135$		0			0
$136$	89.8501			0.0566513
$137$	−2574.60	−	1486.45i	−1.60557	−	0.926975i	−0.990345	−	0.138621i	$-0.955733\pi$
$137$	−2574.60	−	1486.45i	−1.60557	−	0.926975i	−0.615222	−	0.788354i	$-0.710934\pi$
$138$	−1023.62	+	40.6409i	−0.631424	+	0.0250694i
$139$	−1047.32	−	1814.00i	−0.639080	−	1.10692i	−0.985635	−	0.168890i	$-0.945982\pi$
$139$	−1047.32	−	1814.00i	−0.639080	−	1.10692i	0.346555	−	0.938030i	$-0.387352\pi$
$140$		0			0
$141$	−637.995	−	335.330i	−0.381056	−	0.200283i
$142$	589.790	+	340.515i	0.348550	+	0.201235i
$143$		−	1077.06i		−	0.629847i
$144$	329.362	−	691.989i	0.190603	−	0.400456i
$145$		0			0
$146$	−55.9868	+	96.9720i	−0.0317363	+	0.0549689i
$147$	930.444	+	1473.32i	0.522052	+	0.826648i
$148$	−754.876	+	435.828i	−0.419259	+	0.242060i
$149$	136.969	+	237.237i	0.0753081	+	0.130437i	0.901220	−	0.433361i	$-0.142673\pi$
$149$	136.969	+	237.237i	0.0753081	+	0.130437i	−0.825912	+	0.563799i	$0.809339\pi$
$150$		0			0
$151$	468.422	−	811.331i	0.252448	−	0.437253i	−0.711751	−	0.702432i	$-0.752098\pi$
$151$	468.422	−	811.331i	0.252448	−	0.437253i	0.964199	+	0.265179i	$0.0854310\pi$
$152$			2348.10i			1.25300i
$153$	−7.83635	−	98.5315i	−0.00414073	−	0.0520641i
$154$	−319.637			−0.167254
$155$		0			0
$156$	299.578	+	157.458i	0.153753	+	0.0808123i
$157$	−345.055	+	199.218i	−0.175404	+	0.101269i	−0.585131	−	0.810938i	$-0.698957\pi$
$157$	−345.055	+	199.218i	−0.175404	+	0.101269i	0.409728	+	0.912208i	$0.365624\pi$
$158$	−2295.73	+	1325.44i	−1.15594	+	0.667383i
$159$	40.6227	+	1023.16i	0.0202616	+	0.510328i
$160$		0			0
$161$	−248.505			−0.121646
$162$	−1494.44	−	570.835i	−0.724779	−	0.276846i
$163$			478.154i			0.229766i	0.993379	+	0.114883i	$0.0366493\pi$
$163$			478.154i			0.229766i	−0.993379	+	0.114883i	$0.963351\pi$
$164$	−103.278	+	178.883i	−0.0491747	+	0.0851732i
$165$		0			0
$166$	993.229	+	1720.32i	0.464395	+	0.804355i
$167$	294.763	−	170.181i	0.136583	−	0.0788564i	−0.430151	−	0.902757i	$-0.641540\pi$
$167$	294.763	−	170.181i	0.136583	−	0.0788564i	0.566735	+	0.823900i	$0.308206\pi$
$168$	164.122	−	312.256i	0.0753705	−	0.143399i
$169$	−889.328	+	1540.36i	−0.404792	+	0.701120i
$170$		0			0
$171$	2574.97	−	204.791i	1.15154	−	0.0915835i
$172$			1333.51i			0.591159i
$173$	−3270.17	−	1888.03i	−1.43715	−	0.829738i	−0.439497	−	0.898244i	$-0.644843\pi$
$173$	−3270.17	−	1888.03i	−1.43715	−	0.829738i	−0.997651	+	0.0685065i	$0.978177\pi$
$174$	−2196.04	+	1386.87i	−0.956790	+	0.604241i
$175$		0			0
$176$	−747.341	−	1294.43i	−0.320073	−	0.554384i
$177$	−2056.23	−	3255.95i	−0.873196	−	1.38267i
$178$	1261.20	+	728.153i	0.531072	+	0.306615i
$179$	−186.652			−0.0779385			−0.0389693	−	0.999240i	$-0.512407\pi$
$179$	−186.652			−0.0779385			−0.0389693	+	0.999240i	$0.512407\pi$
$180$		0			0
$181$	1438.75			0.590837			0.295418	−	0.955368i	$-0.404541\pi$
$181$	1438.75			0.590837			0.295418	+	0.955368i	$0.404541\pi$
$182$	−107.518	−	62.0756i	−0.0437900	−	0.0252821i
$183$	1180.88	−	2246.72i	0.477010	−	0.907555i
$184$	−1102.51	−	1909.61i	−0.441729	−	0.765098i
$185$		0			0
$186$	−126.272	−	3180.42i	−0.0497781	−	1.25376i
$187$	−166.949	−	96.3880i	−0.0652862	−	0.0376930i
$188$		−	441.706i		−	0.171355i
$189$	−356.741	−	152.746i	−0.137297	−	0.0587863i
$190$		0			0
$191$	195.218	−	338.127i	0.0739552	−	0.128094i	−0.826676	−	0.562678i	$-0.809771\pi$
$191$	195.218	−	338.127i	0.0739552	−	0.128094i	0.900631	+	0.434584i	$0.143104\pi$
$192$	2706.43	−	107.453i	1.01729	−	0.0403895i
$193$	−3390.53	+	1957.52i	−1.26454	+	0.730081i	−0.973949	−	0.226767i	$-0.927184\pi$
$193$	−3390.53	+	1957.52i	−1.26454	+	0.730081i	−0.290588	+	0.956848i	$0.593851\pi$
$194$	795.854	+	1378.46i	0.294531	+	0.510143i
$195$		0			0
$196$	−533.945	+	924.820i	−0.194586	+	0.337034i
$197$			892.680i			0.322847i	0.986885	+	0.161423i	$0.0516085\pi$
$197$			892.680i			0.322847i	−0.986885	+	0.161423i	$0.948392\pi$
$198$	−2569.85	+	1769.33i	−0.922381	+	0.635055i
$199$	2770.50			0.986913			0.493457	−	0.869770i	$-0.335733\pi$
$199$	2770.50			0.986913			0.493457	+	0.869770i	$0.335733\pi$
$200$		0			0
$201$	−1807.74	+	1141.64i	−0.634368	+	0.400622i
$202$	1858.22	−	1072.84i	0.647247	−	0.373688i
$203$	−545.641	+	315.026i	−0.188653	+	0.108919i
$204$	51.2165	−	32.3447i	0.0175778	−	0.0111009i
$205$		0			0
$206$	−3484.13			−1.17840
$207$	−1997.96	+	1375.59i	−0.670859	+	0.461883i
$208$		−	580.554i		−	0.193530i
$209$	2518.96	−	4362.96i	0.833683	−	1.44398i
$210$		0			0
$211$	−2291.25	−	3968.57i	−0.747566	−	1.29482i	−0.948986	−	0.315318i	$-0.897889\pi$
$211$	−2291.25	−	3968.57i	−0.747566	−	1.29482i	0.201420	−	0.979505i	$-0.435444\pi$
$212$	−543.458	+	313.765i	−0.176060	+	0.101649i
$213$	1611.32	−	63.9743i	0.518338	−	0.0205796i
$214$	−985.010	+	1706.09i	−0.314644	+	0.544980i
$215$		0			0
$216$	−408.953	−	3419.00i	−0.128823	−	1.07701i
$217$		−	772.111i		−	0.241541i
$218$	1625.81	+	938.664i	0.505110	+	0.291626i
$219$	10.5185	+	264.930i	0.00324555	+	0.0817457i
$220$		0			0
$221$	−37.4384	−	64.8452i	−0.0113954	−	0.0197374i
$222$	1452.14	−	2762.82i	0.439014	−	0.835263i
$223$	−3546.66	−	2047.67i	−1.06503	−	0.614897i	−0.138212	−	0.990403i	$-0.544136\pi$
$223$	−3546.66	−	2047.67i	−1.06503	−	0.614897i	−0.926820	+	0.375506i	$0.877469\pi$
$224$	370.820			0.110609
$225$		0			0
$226$	−1997.47			−0.587920
$227$	−3350.96	−	1934.68i	−0.979784	−	0.565678i	−0.0775789	−	0.996986i	$-0.524719\pi$
$227$	−3350.96	−	1934.68i	−0.979784	−	0.565678i	−0.902205	+	0.431308i	$0.858052\pi$
$228$	845.281	+	1338.47i	0.245527	+	0.388781i
$229$	618.006	+	1070.42i	0.178336	+	0.308887i	0.941311	−	0.337541i	$-0.109595\pi$
$229$	618.006	+	1070.42i	0.178336	+	0.308887i	−0.762975	+	0.646429i	$0.776262\pi$
$230$		0			0
$231$	−639.929	+	404.134i	−0.182269	+	0.115109i
$232$	−4841.56	−	2795.27i	−1.37010	−	0.791029i
$233$			2207.05i			0.620552i	0.950647	+	0.310276i	$0.100421\pi$
$233$			2207.05i			0.620552i	−0.950647	+	0.310276i	$0.899579\pi$
$234$	−1208.05	+	96.0781i	−0.337491	+	0.0268411i
$235$		0			0
$236$	1179.99	−	2043.80i	0.325470	−	0.563730i
$237$	−2920.35	+	5556.22i	−0.800409	+	1.52285i
$238$	−19.2440	+	11.1105i	−0.00524119	+	0.00302600i
$239$	438.324	+	759.199i	0.118631	+	0.205475i	0.919225	−	0.393732i	$-0.128816\pi$
$239$	438.324	+	759.199i	0.118631	+	0.205475i	−0.800594	+	0.599207i	$0.795483\pi$
$240$		0			0
$241$	238.931	−	413.840i	0.0638626	−	0.110613i	−0.832326	−	0.554286i	$-0.812991\pi$
$241$	238.931	−	413.840i	0.0638626	−	0.110613i	0.896189	+	0.443673i	$0.146325\pi$
$242$			3164.32i			0.840537i
$243$	−3713.68	+	746.658i	−0.980381	+	0.197112i
$244$	1555.49			0.408114
$245$		0			0
$246$	−29.3424	−	739.048i	−0.00760490	−	0.191545i
$247$	1694.63	−	978.396i	0.436546	−	0.252040i
$248$	5933.19	−	3425.53i	1.51919	−	0.877102i
$249$	4163.59	+	2188.38i	1.05967	+	0.556960i
$250$		0			0
$251$	6892.28			1.73322			0.866608	−	0.498990i	$-0.166296\pi$
$251$	6892.28			1.73322			0.866608	+	0.498990i	$0.166296\pi$
$252$	−18.8548	−	237.074i	−0.00471327	−	0.0592630i
$253$			4730.94i			1.17562i
$254$	2236.41	−	3873.57i	0.552460	−	0.956889i
$255$		0			0
$256$	2006.72	+	3475.74i	0.489921	+	0.848568i
$257$	6284.49	−	3628.35i	1.52535	−	0.880664i	0.525806	−	0.850605i	$-0.323764\pi$
$257$	6284.49	−	3628.35i	1.52535	−	0.880664i	0.999548	−	0.0300589i	$-0.00956949\pi$
$258$	−2549.67	−	4037.30i	−0.615255	−	0.974230i
$259$	378.569	−	655.701i	0.0908229	−	0.157310i
$260$		0			0
$261$	−2643.10	+	5553.15i	−0.626834	+	1.31698i
$262$			517.110i			0.121936i
$263$	5471.16	+	3158.78i	1.28276	+	0.740603i	0.977352	−	0.211618i	$-0.0678733\pi$
$263$	5471.16	+	3158.78i	1.28276	+	0.740603i	0.305409	+	0.952221i	$0.401207\pi$
$264$	−5944.61	−	3124.48i	−1.38585	−	0.728404i
$265$		0			0
$266$	−290.357	−	502.913i	−0.0669283	−	0.115923i
$267$	3445.63	−	136.802i	0.789771	−	0.0313563i
$268$	−1134.74	−	655.142i	−0.258639	−	0.149325i
$269$	−5746.22			−1.30243			−0.651214	−	0.758894i	$-0.725740\pi$
$269$	−5746.22			−1.30243			−0.651214	+	0.758894i	$0.725740\pi$
$270$		0			0
$271$	4925.20			1.10400			0.552001	−	0.833844i	$-0.313865\pi$
$271$	4925.20			1.10400			0.552001	+	0.833844i	$0.313865\pi$
$272$	−89.9886	−	51.9550i	−0.0200602	−	0.0115817i
$273$	−293.742	+	11.6625i	−0.0651212	+	0.00258551i
$274$	3261.92	+	5649.81i	0.719196	+	1.24568i
$275$		0			0
$276$	−1315.89	−	691.629i	−0.286982	−	0.150837i
$277$	2014.27	+	1162.94i	0.436917	+	0.252254i	0.702289	−	0.711892i	$-0.252161\pi$
$277$	2014.27	+	1162.94i	0.436917	+	0.252254i	−0.265372	+	0.964146i	$0.585495\pi$
$278$			4596.55i			0.991665i
$279$	−4273.98	−	6207.70i	−0.917119	−	1.33206i
$280$		0			0
$281$	−1641.71	+	2843.52i	−0.348527	+	0.603667i	−0.985988	−	0.166816i	$-0.946652\pi$
$281$	−1641.71	+	2843.52i	−0.348527	+	0.603667i	0.637461	+	0.770483i	$0.279985\pi$
$282$	844.543	+	1337.30i	0.178340	+	0.282393i
$283$	1744.36	−	1007.11i	0.366400	−	0.211541i	−0.305484	−	0.952197i	$-0.598818\pi$
$283$	1744.36	−	1007.11i	0.366400	−	0.211541i	0.671885	+	0.740656i	$0.265485\pi$
$284$	494.131	+	855.860i	0.103244	+	0.178824i
$285$		0			0
$286$	−1181.77	+	2046.89i	−0.244334	+	0.423199i
$287$		−	179.419i		−	0.0369016i
$288$	2981.36	−	2052.65i	0.609994	−	0.419978i
$289$	4899.60			0.997272
$290$		0			0
$291$	3336.20	+	1753.50i	0.672067	+	0.353238i
$292$	−140.719	+	81.2440i	−0.0282018	+	0.0162823i
$293$	416.295	−	240.348i	0.0830042	−	0.0479225i	−0.457923	−	0.888992i	$-0.651407\pi$
$293$	416.295	−	240.348i	0.0830042	−	0.0479225i	0.540928	+	0.841069i	$0.318073\pi$
$294$	−151.700	−	3820.86i	−0.0300929	−	0.757950i
$295$		0			0
$296$	6718.20			1.31921
$297$	−2907.91	+	6791.49i	−0.568128	+	1.32688i
$298$		−	601.140i		−	0.116856i
$299$	−918.781	+	1591.37i	−0.177707	+	0.307798i
$300$		0			0
$301$	−579.158	−	1003.13i	−0.110904	−	0.192091i
$302$	−1780.42	+	1027.93i	−0.339244	+	0.195863i
$303$	2363.79	−	4497.33i	0.448173	−	0.852690i
$304$	1357.76	−	2351.72i	0.256162	−	0.443685i
$305$		0			0
$306$	−93.2184	+	195.852i	−0.0174148	+	0.0365886i
$307$		−	3222.21i		−	0.599026i	−0.954092	−	0.299513i	$-0.903176\pi$
$307$		−	3222.21i		−	0.599026i	0.954092	−	0.299513i	$-0.0968242\pi$
$308$	−401.691	−	231.917i	−0.0743133	−	0.0429048i
$309$	−6975.40	+	4405.17i	−1.28420	+	0.811008i
$310$		0			0
$311$	−1207.00	−	2090.59i	−0.220074	−	0.381179i	0.734757	−	0.678331i	$-0.237296\pi$
$311$	−1207.00	−	2090.59i	−0.220074	−	0.381179i	−0.954830	+	0.297152i	$0.903963\pi$
$312$	−1392.83	−	2205.48i	−0.252735	−	0.400195i
$313$	2171.07	+	1253.47i	0.392065	+	0.226359i	0.683054	−	0.730368i	$-0.260651\pi$
$313$	2171.07	+	1253.47i	0.392065	+	0.226359i	−0.290990	+	0.956726i	$0.593985\pi$
$314$	874.344			0.157140
$315$		0			0
$316$	−3846.77			−0.684803
$317$	3210.46	+	1853.56i	0.568825	+	0.328411i	0.756680	−	0.653786i	$-0.226820\pi$
$317$	3210.46	+	1853.56i	0.568825	+	0.328411i	−0.187855	+	0.982197i	$0.560154\pi$
$318$	1045.44	−	1989.04i	0.184356	−	0.350754i
$319$	5997.34	+	10387.7i	1.05262	+	1.82320i
$320$		0			0
$321$	185.059	+	4661.07i	0.0321775	+	0.810454i
$322$	472.270	+	272.665i	0.0817347	+	0.0471895i
$323$		−	350.234i		−	0.0603330i
$324$	−1463.90	−	1801.69i	−0.251012	−	0.308931i
$325$		0			0
$326$	524.641	−	908.704i	0.0891324	−	0.154382i
$327$	4441.77	−	176.352i	0.751163	−	0.0298234i
$328$	1378.72	−	796.005i	0.232095	−	0.134000i
$329$	191.838	+	332.272i	0.0321470	+	0.0556802i
$330$		0			0
$331$	−1276.72	+	2211.35i	−0.212009	+	0.367211i	−0.952343	−	0.305029i	$-0.901334\pi$
$331$	−1276.72	+	2211.35i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$332$			2882.60i			0.476516i
$333$	−585.933	−	7367.32i	−0.0964233	−	1.21239i
$334$	−746.906			−0.122362
$335$		0			0
$336$	−344.934	+	217.836i	−0.0560050	+	0.0353688i
$337$	−3076.89	+	1776.44i	−0.497356	+	0.287148i	−0.727621	−	0.685979i	$-0.759374\pi$
$337$	−3076.89	+	1776.44i	−0.497356	+	0.287148i	0.230265	+	0.973128i	$0.426041\pi$
$338$	3380.24	−	1951.58i	0.543966	−	0.314059i
$339$	−3999.04	+	2525.51i	−0.640702	+	0.404623i
$340$		0			0
$341$	−14699.2			−2.33432
$342$	−5118.29	−	2436.12i	−0.809256	−	0.385177i
$343$		−	1876.35i		−	0.295374i
$344$	5138.95	−	8900.93i	0.805447	−	1.39508i
$345$		0			0
$346$	4143.19	+	7176.21i	0.643754	+	1.11502i
$347$	6727.30	−	3884.01i	1.04075	−	0.600878i	0.120705	−	0.992688i	$-0.461485\pi$
$347$	6727.30	−	3884.01i	1.04075	−	0.600878i	0.920046	+	0.391811i	$0.128151\pi$
$348$	−3766.05	+	149.524i	−0.580119	+	0.0230325i
$349$	348.003	−	602.760i	0.0533759	−	0.0924498i	−0.838103	−	0.545512i	$-0.816335\pi$
$349$	348.003	−	602.760i	0.0533759	−	0.0924498i	0.891479	+	0.453062i	$0.149669\pi$
$350$		0			0
$351$	−2297.10	+	1719.76i	−0.349317	+	0.261521i
$352$		−	7059.52i		−	1.06896i
$353$	4721.46	+	2725.94i	0.711892	+	0.411011i	0.811761	−	0.583990i	$-0.198509\pi$
$353$	4721.46	+	2725.94i	0.711892	+	0.411011i	−0.0998692	+	0.995001i	$0.531842\pi$
$354$	335.248	+	8443.90i	0.0503340	+	1.26776i
$355$		0			0
$356$	1056.64	+	1830.16i	0.157309	+	0.272467i
$357$	−24.4798	+	46.5751i	−0.00362916	+	0.00690481i
$358$	354.721	+	204.798i	0.0523675	+	0.0302344i
$359$	−4036.41			−0.593408			−0.296704	−	0.954969i	$-0.595887\pi$
$359$	−4036.41			−0.593408			−0.296704	+	0.954969i	$0.595887\pi$
$360$		0			0
$361$	2293.85			0.334429
$362$	−2734.26	−	1578.63i	−0.396988	−	0.229201i
$363$	4000.82	+	6335.12i	0.578481	+	0.915999i
$364$	−90.0795	−	156.022i	−0.0129710	−	0.0224665i
$365$		0			0
$366$	−4709.34	+	2974.09i	−0.672572	+	0.424749i
$367$	9734.06	+	5619.96i	1.38451	+	0.799345i	0.992689	−	0.120698i	$-0.0385134\pi$
$367$	9734.06	+	5619.96i	1.38451	+	0.799345i	0.391817	+	0.920043i	$0.371847\pi$
$368$			2550.07i			0.361227i
$369$	−993.163	−	1442.51i	−0.140114	−	0.203507i
$370$		0			0
$371$	272.543	−	472.059i	0.0381394	−	0.0660595i
$372$	2148.91	−	4088.49i	0.299504	−	0.569834i
$373$	−5473.90	+	3160.36i	−0.759860	+	0.438706i	−0.829246	−	0.558884i	$-0.811230\pi$
$373$	−5473.90	+	3160.36i	−0.759860	+	0.438706i	0.0693853	+	0.997590i	$0.477896\pi$
$374$	211.518	+	366.360i	0.0292442	+	0.0506525i
$375$		0			0
$376$	−1702.20	+	2948.30i	−0.233469	+	0.404381i
$377$			4658.90i			0.636460i
$378$	510.370	+	681.708i	0.0694460	+	0.0927600i
$379$	−9325.49			−1.26390			−0.631950	−	0.775009i	$-0.717745\pi$
$379$	−9325.49			−1.26390			−0.631950	+	0.775009i	$0.717745\pi$
$380$		0			0
$381$	−420.165	−	10582.7i	−0.0564980	−	1.42301i
$382$	−742.000	+	428.394i	−0.0993823	+	0.0573784i
$383$	9654.47	−	5574.01i	1.28804	−	0.743652i	0.309738	−	0.950822i	$-0.399759\pi$
$383$	9654.47	−	5574.01i	1.28804	−	0.743652i	0.978305	+	0.207170i	$0.0664254\pi$
$384$	−328.377	−	172.595i	−0.0436391	−	0.0229367i
$385$		0			0
$386$	8591.35			1.13287
$387$	−10209.1	−	4859.19i	−1.34098	−	0.638259i
$388$			2309.77i			0.302219i
$389$	3285.41	−	5690.49i	0.428218	−	0.741695i	−0.568497	−	0.822685i	$-0.692475\pi$
$389$	3285.41	−	5690.49i	0.428218	−	0.741695i	0.996715	+	0.0809902i	$0.0258082\pi$
$390$		0			0
$391$	164.447	+	284.831i	0.0212697	+	0.0368402i
$392$	7127.96	−	4115.33i	0.918409	−	0.530244i
$393$	653.810	+	1035.28i	0.0839195	+	0.132883i
$394$	979.469	−	1696.49i	0.125241	−	0.216924i
$395$		0			0
$396$	−4513.33	+	358.951i	−0.572735	+	0.0455504i
$397$		−	3969.33i		−	0.501800i	−0.968013	−	0.250900i	$-0.919273\pi$
$397$		−	3969.33i		−	0.501800i	0.968013	−	0.250900i	$-0.0807266\pi$
$398$	−5265.19	−	3039.86i	−0.663115	−	0.382850i
$399$	−1217.17	−	639.743i	−0.152719	−	0.0802687i
$400$		0			0
$401$	−2187.35	−	3788.60i	−0.272396	−	0.471804i	0.697079	−	0.716995i	$-0.254483\pi$
$401$	−2187.35	−	3788.60i	−0.272396	−	0.471804i	−0.969475	+	0.245190i	$0.921150\pi$
$402$	4688.13	−	186.133i	0.581649	−	0.0230932i
$403$	−4944.44	−	2854.67i	−0.611166	−	0.352857i
$404$	3113.66			0.383442
$405$		0			0
$406$	1382.61			0.169010
$407$	−12483.0	−	7207.05i	−1.52029	−	0.877740i
$408$	−466.507	+	18.5217i	−0.0566067	+	0.00224746i
$409$	−4436.16	−	7683.66i	−0.536318	−	0.928930i	−0.999098	−	0.0424573i	$-0.986481\pi$
$409$	−4436.16	−	7683.66i	−0.536318	−	0.928930i	0.462780	−	0.886473i	$-0.346852\pi$
$410$		0			0
$411$	13673.9	+	7186.99i	1.64108	+	0.862550i
$412$	−4378.55	−	2527.95i	−0.523581	−	0.302290i
$413$			2049.93i			0.244238i
$414$	5306.33	−	422.020i	0.629932	−	0.0500994i
$415$		0			0
$416$	1371.01	−	2374.65i	0.161584	−	0.279872i
$417$	5811.67	+	9202.53i	0.682491	+	1.08069i
$418$	−9574.27	+	5527.71i	−1.12032	+	0.646816i
$419$	−507.087	−	878.300i	−0.0591236	−	0.102405i	0.834949	−	0.550328i	$-0.185497\pi$
$419$	−507.087	−	878.300i	−0.0591236	−	0.102405i	−0.894072	+	0.447923i	$0.852164\pi$
$420$		0			0
$421$	7446.57	−	12897.8i	0.862051	−	1.49312i	−0.00789511	−	0.999969i	$-0.502513\pi$
$421$	7446.57	−	12897.8i	0.862051	−	1.49312i	0.869946	−	0.493147i	$-0.164154\pi$
$422$			10056.1i			1.16000i
$423$	3381.63	+	1609.54i	0.388701	+	0.185008i
$424$	4836.63			0.553980
$425$		0			0
$426$	−3132.42	−	1646.40i	−0.356259	−	0.187249i
$427$	−1170.11	+	675.563i	−0.132613	+	0.0765639i
$428$	−2475.75	+	1429.37i	−0.279602	+	0.161429i
$429$	222.025	+	5592.15i	0.0249871	+	0.629351i
$430$		0			0
$431$	−4363.90			−0.487707			−0.243853	−	0.969812i	$-0.578412\pi$
$431$	−4363.90			−0.487707			−0.243853	+	0.969812i	$0.578412\pi$
$432$	−1567.42	+	3660.74i	−0.174566	+	0.407703i
$433$			9301.59i			1.03235i	0.856484	+	0.516173i	$0.172644\pi$
$433$			9301.59i			1.03235i	−0.856484	+	0.516173i	$0.827356\pi$
$434$	−847.177	+	1467.35i	−0.0937000	+	0.162293i
$435$		0			0
$436$	1362.12	+	2359.26i	0.149619	+	0.259147i
$437$	−7443.62	+	4297.57i	−0.814820	+	0.470437i
$438$	270.697	−	515.026i	0.0295306	−	0.0561847i
$439$	760.076	−	1316.49i	0.0826343	−	0.143127i	−0.821746	−	0.569853i	$-0.807000\pi$
$439$	760.076	−	1316.49i	0.0826343	−	0.143127i	0.904381	+	0.426727i	$0.140333\pi$
$440$		0			0
$441$	−5134.63	−	7457.76i	−0.554436	−	0.805286i
$442$			164.313i			0.0176823i
$443$	−3864.62	−	2231.24i	−0.414478	−	0.239299i	0.278234	−	0.960513i	$-0.410251\pi$
$443$	−3864.62	−	2231.24i	−0.414478	−	0.239299i	−0.692712	+	0.721214i	$0.743584\pi$
$444$	3829.52	−	2418.45i	0.409326	−	0.258502i
$445$		0			0
$446$	4493.49	+	7782.96i	0.477070	+	0.826309i
$447$	−760.053	−	1203.51i	−0.0804235	−	0.127347i
$448$	−1248.67	−	720.919i	−0.131683	−	0.0760273i
$449$	5371.66			0.564598			0.282299	−	0.959326i	$-0.408903\pi$
$449$	5371.66			0.564598			0.282299	+	0.959326i	$0.408903\pi$
$450$		0			0
$451$	−3415.71			−0.356628
$452$	−2510.25	−	1449.29i	−0.261222	−	0.150816i
$453$	−2264.83	+	4309.04i	−0.234903	+	0.446923i
$454$	4245.54	+	7353.49i	0.438883	+	0.760168i
$455$		0			0
$456$	−484.038	−	12191.5i	−0.0497087	−	1.25201i
$457$	13445.4	+	7762.71i	1.37626	+	0.794583i	0.991707	−	0.128520i	$-0.0410228\pi$
$457$	13445.4	+	7762.71i	1.37626	+	0.794583i	0.384551	+	0.923104i	$0.374356\pi$
$458$		−	2712.36i		−	0.276725i
$459$	60.9982	+	509.966i	0.00620294	+	0.0518588i
$460$		0			0
$461$	28.2090	−	48.8594i	0.00284994	−	0.00493624i	−0.864597	−	0.502466i	$-0.832426\pi$
$461$	28.2090	−	48.8594i	0.00284994	−	0.00493624i	0.867447	+	0.497530i	$0.165760\pi$
$462$	1659.57	−	65.8901i	0.167122	−	0.00663525i
$463$	11582.0	−	6686.89i	1.16255	−	0.671201i	0.210640	−	0.977564i	$-0.432445\pi$
$463$	11582.0	−	6686.89i	1.16255	−	0.671201i	0.951915	+	0.306363i	$0.0991120\pi$
$464$	3232.68	+	5599.17i	0.323434	+	0.560204i
$465$		0			0
$466$	2421.62	−	4194.37i	0.240729	−	0.416954i
$467$		−	2677.46i		−	0.265306i	−0.991163	−	0.132653i	$-0.957650\pi$
$467$		−	2677.46i		−	0.265306i	0.991163	−	0.132653i	$-0.0423496\pi$
$468$	−1587.88	−	755.776i	−0.156838	−	0.0746490i
$469$	1138.14			0.112056
$470$		0			0
$471$	1750.48	−	1105.48i	0.171248	−	0.108148i
$472$	−15752.4	+	9094.66i	−1.53615	+	0.886898i
$473$	−19097.2	+	11025.8i	−1.85643	+	1.07181i
$474$	11646.4	−	7355.02i	1.12856	−	0.712716i
$475$		0			0
$476$	−32.2456			−0.00310499
$477$	−421.831	−	5303.96i	−0.0404912	−	0.509123i
$478$		−	1923.75i		−	0.184080i
$479$	−1734.96	+	3005.05i	−0.165496	+	0.286647i	−0.936831	−	0.349782i	$-0.886256\pi$
$479$	−1734.96	+	3005.05i	−0.165496	+	0.286647i	0.771335	+	0.636429i	$0.219589\pi$
$480$		0			0
$481$	−2799.31	−	4848.55i	−0.265359	−	0.459616i
$482$	−908.149	+	524.320i	−0.0858196	+	0.0495480i
$483$	1290.25	−	51.2270i	0.121550	−	0.00482589i
$484$	−2295.91	+	3976.64i	−0.215619	+	0.373463i
$485$		0			0
$486$	7876.89	+	2655.75i	0.735191	+	0.247875i
$487$			14040.6i			1.30645i	0.757165	+	0.653224i	$0.226584\pi$
$487$			14040.6i			1.30645i	−0.757165	+	0.653224i	$0.773416\pi$
$488$	−10382.6	−	5994.38i	−0.963108	−	0.556051i
$489$	−98.5669	−	2482.60i	−0.00911523	−	0.229585i
$490$		0			0
$491$	−4907.72	−	8500.42i	−0.451084	−	0.781301i	0.547369	−	0.836891i	$-0.315629\pi$
$491$	−4907.72	−	8500.42i	−0.451084	−	0.781301i	−0.998454	+	0.0555902i	$0.982296\pi$
$492$	499.351	−	950.060i	0.0457571	−	0.0870570i
$493$	722.151	+	416.934i	0.0659717	+	0.0380888i
$494$	−4294.07			−0.391092
$495$		0			0
$496$	−7923.12			−0.717255
$497$	−743.418	−	429.212i	−0.0670962	−	0.0387380i
$498$	−5511.53	−	8727.28i	−0.495939	−	0.785299i
$499$	−6026.00	−	10437.3i	−0.540603	−	0.936351i	−0.998869	−	0.0475367i	$-0.984863\pi$
$499$	−6026.00	−	10437.3i	−0.540603	−	0.936351i	0.458267	−	0.888815i	$-0.348470\pi$
$500$		0			0
$501$	−1495.34	+	944.354i	−0.133347	+	0.0842128i
$502$	−13098.4	−	7562.36i	−1.16456	−	0.672360i
$503$		−	4695.09i		−	0.416191i	−0.978109	−	0.208095i	$-0.933274\pi$
$503$		−	4695.09i		−	0.416191i	0.978109	−	0.208095i	$-0.0667264\pi$
$504$	−787.760	+	1655.08i	−0.0696223	+	0.146276i
$505$		0			0
$506$	5190.89	−	8990.89i	0.456054	−	0.789909i
$507$	4299.92	−	8180.98i	0.376659	−	0.716627i
$508$	5621.05	−	3245.31i	0.490932	−	0.283440i
$509$	−409.907	−	709.979i	−0.0356951	−	0.0618257i	0.847626	−	0.530594i	$-0.178031\pi$
$509$	−409.907	−	709.979i	−0.0356951	−	0.0618257i	−0.883321	+	0.468769i	$0.844698\pi$
$510$		0			0
$511$	70.5702	−	122.231i	0.00610928	−	0.0105816i
$512$		−	9378.41i		−	0.809514i
$513$	−13327.2	+	1594.09i	−1.14700	+	0.137195i
$514$	−15924.4			−1.36653
$515$		0			0
$516$	−274.891	−	6923.67i	−0.0234523	−	0.590693i
$517$	6325.68	−	3652.13i	0.538110	−	0.310678i
$518$	−1438.90	+	830.748i	−0.122049	+	0.0704652i
$519$	17368.1	+	9128.68i	1.46893	+	0.772070i
$520$		0			0
$521$	3282.80			0.276050			0.138025	−	0.990429i	$-0.455925\pi$
$521$	3282.80			0.276050			0.138025	+	0.990429i	$0.455925\pi$
$522$	11116.1	−	7653.38i	0.932066	−	0.641723i
$523$		−	10768.1i		−	0.900300i	−0.892953	−	0.450150i	$-0.851371\pi$
$523$		−	10768.1i		−	0.900300i	0.892953	−	0.450150i	$-0.148629\pi$
$524$	−375.196	+	649.859i	−0.0312796	+	0.0541779i
$525$		0			0
$526$	−6931.76	−	12006.2i	−0.574599	−	0.995235i
$527$	−884.975	+	510.941i	−0.0731502	+	0.0422333i
$528$	4147.07	+	6566.71i	0.341815	+	0.541249i
$529$	−2047.78	+	3546.87i	−0.168306	+	0.291515i
$530$		0			0
$531$	11347.3	+	16481.2i	0.927362	+	1.34694i
$532$		−	842.690i		−	0.0686752i
$533$	−1148.96	−	663.353i	−0.0933716	−	0.0539081i
$534$	−6698.32	−	3520.63i	−0.542818	−	0.285305i
$535$		0			0
$536$	5049.44	+	8745.89i	0.406908	+	0.704785i
$537$	969.106	−	38.4765i	0.0778771	−	0.00309196i
$538$	10920.4	+	6304.88i	0.875113	+	0.505247i
$539$	−17659.1			−1.41119
$540$		0			0
$541$	−16037.9			−1.27453			−0.637266	−	0.770644i	$-0.719935\pi$
$541$	−16037.9			−1.27453			−0.637266	+	0.770644i	$0.719935\pi$
$542$	−9360.06	−	5404.04i	−0.741788	−	0.428272i
$543$	−7470.08	+	296.585i	−0.590372	+	0.0234395i
$544$	−245.388	−	425.025i	−0.0193399	−	0.0334978i
$545$		0			0
$546$	571.037	+	300.137i	0.0447585	+	0.0235250i
$547$	1774.59	+	1024.56i	0.138713	+	0.0800862i	0.567751	−	0.823201i	$-0.307814\pi$
$547$	1774.59	+	1024.56i	0.138713	+	0.0800862i	−0.429037	+	0.903287i	$0.641147\pi$
$548$			9466.92i			0.737968i
$549$	−5668.04	+	11908.5i	−0.440630	+	0.925764i
$550$		0			0
$551$	−10895.9	+	18872.3i	−0.842437	+	1.45914i
$552$	6117.95	+	9687.52i	0.471734	+	0.746971i
$553$	2893.72	−	1670.69i	0.222520	−	0.128472i
$554$	−2552.01	−	4420.21i	−0.195712	−	0.338983i
$555$		0			0
$556$	−3335.09	+	5776.54i	−0.254387	+	0.440611i
$557$		−	3644.07i		−	0.277207i	−0.990348	−	0.138603i	$-0.955739\pi$
$557$		−	3644.07i		−	0.277207i	0.990348	−	0.138603i	$-0.0442614\pi$
$558$	1311.23	+	16486.9i	0.0994778	+	1.25080i
$559$	−8565.12			−0.648061
$560$		0			0
$561$	886.679	+	466.038i	0.0667301	+	0.0350733i
$562$	6239.96	−	3602.64i	0.468357	−	0.270406i
$563$	303.746	−	175.368i	0.0227378	−	0.0131277i	−0.488588	−	0.872515i	$-0.662488\pi$
$563$	303.746	−	175.368i	0.0227378	−	0.0131277i	0.511326	+	0.859387i	$0.329155\pi$
$564$	91.0536	+	2293.37i	0.00679796	+	0.171220i
$565$		0			0
$566$	−4420.07			−0.328250
$567$	1883.71	+	719.525i	0.139521	+	0.0532932i
$568$		−	7616.93i		−	0.562675i
$569$	−9724.34	+	16843.1i	−0.716460	+	1.24095i	0.245934	+	0.969287i	$0.420905\pi$
$569$	−9724.34	+	16843.1i	−0.716460	+	1.24095i	−0.962394	+	0.271658i	$0.912428\pi$
$570$		0			0
$571$	7572.97	+	13116.8i	0.555024	+	0.961330i	0.997902	+	0.0647480i	$0.0206244\pi$
$571$	7572.97	+	13116.8i	0.555024	+	0.961330i	−0.442877	+	0.896582i	$0.646042\pi$
$572$	−2970.29	+	1714.90i	−0.217123	+	0.125356i
$573$	−943.880	+	1795.82i	−0.0688153	+	0.130927i
$574$	−196.862	+	340.975i	−0.0143151	+	0.0247945i
$575$		0			0
$576$	−14029.8	+	1115.81i	−1.01489	+	0.0807154i
$577$			6365.11i			0.459243i	0.973280	+	0.229621i	$0.0737488\pi$
$577$			6365.11i			0.459243i	−0.973280	+	0.229621i	$0.926251\pi$
$578$	−9311.41	−	5375.95i	−0.670076	−	0.386868i
$579$	17200.3	−	10862.5i	1.23458	−	0.779673i
$580$		0			0
$581$	−1251.94	−	2168.43i	−0.0893965	−	0.154839i
$582$	−4416.28	−	6992.99i	−0.314537	−	0.498056i
$583$	−8986.87	−	5188.57i	−0.638419	−	0.368591i
$584$	1252.36			0.0887381
$585$		0			0
$586$	−1054.86			−0.0743617
$587$	8906.52	+	5142.18i	0.626254	+	0.361568i	0.779300	−	0.626651i	$-0.215575\pi$
$587$	8906.52	+	5142.18i	0.626254	+	0.361568i	−0.153046	+	0.988219i	$0.548908\pi$
$588$	2581.63	−	4911.79i	0.181063	−	0.344488i
$589$	−13352.7	−	23127.5i	−0.934103	−	1.61791i
$590$		0			0
$591$	−184.018	−	4634.85i	−0.0128079	−	0.322593i
$592$	−6728.56	−	3884.73i	−0.467132	−	0.269699i
$593$			666.566i			0.0461595i	0.999734	+	0.0230798i	$0.00734717\pi$
$593$			666.566i			0.0461595i	−0.999734	+	0.0230798i	$0.992653\pi$
$594$	12978.1	−	9716.23i	0.896461	−	0.671148i
$595$		0			0
$596$	436.165	−	755.460i	0.0299765	−	0.0519209i
$597$	−14384.6	+	571.113i	−0.986136	+	0.0391526i
$598$	3492.18	−	2016.21i	0.238806	−	0.137875i
$599$	12606.6	+	21835.3i	0.859922	+	1.48943i	0.872003	+	0.489501i	$0.162821\pi$
$599$	12606.6	+	21835.3i	0.859922	+	1.48943i	−0.0120807	+	0.999927i	$0.503845\pi$
$600$		0			0
$601$	10309.3	−	17856.3i	0.699712	−	1.21194i	−0.268855	−	0.963181i	$-0.586645\pi$
$601$	10309.3	−	17856.3i	0.699712	−	1.21194i	0.968566	−	0.248755i	$-0.0800215\pi$
$602$			2541.86i			0.172090i
$603$	9150.54	−	6300.11i	0.617975	−	0.425473i
$604$	−2983.30			−0.200975
$605$		0			0
$606$	−9426.83	+	5953.32i	−0.631912	+	0.399071i
$607$	4402.45	−	2541.76i	0.294382	−	0.169962i	−0.345534	−	0.938406i	$-0.612302\pi$
$607$	4402.45	−	2541.76i	0.294382	−	0.169962i	0.639916	+	0.768444i	$0.278969\pi$
$608$	11107.4	−	6412.85i	0.740894	−	0.427755i
$609$	2768.06	−	1748.11i	0.184183	−	0.116317i
$610$		0			0
$611$	2837.07			0.187849
$612$	−259.252	+	178.494i	−0.0171236	+	0.0117895i
$613$			2625.18i			0.172969i	0.996253	+	0.0864845i	$0.0275633\pi$
$613$			2625.18i			0.172969i	−0.996253	+	0.0864845i	$0.972437\pi$
$614$	−3535.47	+	6123.62i	−0.232378	+	0.402491i
$615$		0			0
$616$	1787.48	+	3096.00i	0.116915	+	0.202502i
$617$	1412.76	−	815.659i	0.0921811	−	0.0532208i	−0.453201	−	0.891408i	$-0.649718\pi$
$617$	1412.76	−	815.659i	0.0921811	−	0.0532208i	0.545382	+	0.838188i	$0.316385\pi$
$618$	18089.8	−	718.220i	1.17747	−	0.0467493i
$619$	1592.33	−	2758.00i	0.103395	−	0.179085i	−0.809687	−	0.586863i	$-0.800363\pi$
$619$	1592.33	−	2758.00i	0.103395	−	0.179085i	0.913081	+	0.407778i	$0.133696\pi$
$620$		0			0
$621$	10090.0	−	7553.99i	0.652007	−	0.488134i
$622$			5297.40i			0.341489i
$623$	−1589.71	−	917.821i	−0.102232	−	0.0590236i
$624$	119.676	+	3014.27i	0.00767767	+	0.193377i
$625$		0			0
$626$	−2750.67	−	4764.29i	−0.175621	−	0.304184i
$627$	−12179.2	+	23172.0i	−0.775742	+	1.47592i
$628$	1098.80	+	634.392i	0.0698199	+	0.0403105i
$629$	−1002.06			−0.0635214
$630$		0			0
$631$	10436.7			0.658447			0.329223	−	0.944252i	$-0.393213\pi$
$631$	10436.7			0.658447			0.329223	+	0.944252i	$0.393213\pi$
$632$	25676.4	+	14824.3i	1.61607	+	0.933037i
$633$	12714.4	+	20132.7i	0.798346	+	1.26415i
$634$	−4067.54	−	7045.18i	−0.254799	−	0.441325i
$635$		0			0
$636$	2756.99	−	1741.12i	0.171889	−	0.108553i
$637$	−5940.11	−	3429.52i	−0.369475	−	0.213316i
$638$		−	26321.7i		−	1.63336i
$639$	−8352.89	+	664.317i	−0.517113	+	0.0411267i
$640$		0			0
$641$	−4541.73	+	7866.50i	−0.279856	+	0.484724i	−0.971349	−	0.237659i	$-0.923620\pi$
$641$	−4541.73	+	7866.50i	−0.279856	+	0.484724i	0.691493	+	0.722383i	$0.256953\pi$
$642$	4762.54	−	9061.16i	0.292776	−	0.557034i
$643$	14884.9	−	8593.81i	0.912914	−	0.527071i	0.0315465	−	0.999502i	$-0.489957\pi$
$643$	14884.9	−	8593.81i	0.912914	−	0.527071i	0.881368	+	0.472431i	$0.156623\pi$
$644$	395.672	+	685.323i	0.0242106	+	0.0419340i
$645$		0			0
$646$	−384.285	+	665.601i	−0.0234048	+	0.0405383i
$647$		−	2359.17i		−	0.143352i	−0.997428	−	0.0716758i	$-0.977165\pi$
$647$		−	2359.17i		−	0.143352i	0.997428	−	0.0716758i	$-0.0228347\pi$
$648$	2828.11	+	17667.3i	0.171448	+	1.07105i
$649$	39025.7			2.36039
$650$		0			0
$651$	159.163	+	4008.85i	0.00958234	+	0.241350i
$652$	1318.64	−	761.320i	0.0792057	−	0.0457294i
$653$	4707.81	−	2718.06i	0.282130	−	0.162888i	−0.352257	−	0.935903i	$-0.614586\pi$
$653$	4707.81	−	2718.06i	0.282130	−	0.162888i	0.634387	+	0.773015i	$0.281252\pi$
$654$	−8634.82	−	4538.46i	−0.516282	−	0.271357i
$655$		0			0
$656$	−1841.13			−0.109579
$657$	−109.226	−	1373.36i	−0.00648599	−	0.0815526i
$658$		−	841.954i		−	0.0498826i
$659$	1544.45	−	2675.07i	0.0912950	−	0.158128i	−0.816761	−	0.576976i	$-0.804233\pi$
$659$	1544.45	−	2675.07i	0.0912950	−	0.158128i	0.908056	+	0.418848i	$0.137566\pi$
$660$		0			0
$661$	9526.94	+	16501.2i	0.560598	+	0.970984i	0.997444	+	0.0714479i	$0.0227620\pi$
$661$	9526.94	+	16501.2i	0.560598	+	0.970984i	−0.436846	+	0.899536i	$0.643905\pi$
$662$	4852.68	−	2801.70i	0.284902	−	0.164488i
$663$	207.750	+	328.963i	0.0121694	+	0.0192698i
$664$	11108.7	−	19240.8i	0.649248	−	1.12453i
$665$		0			0
$666$	−6970.05	+	14644.1i	−0.405532	+	0.852022i
$667$		−	20464.1i		−	1.18796i
$668$	−938.646	−	541.928i	−0.0543672	−	0.0313889i
$669$	18836.6	+	9900.51i	1.08859	+	0.572161i
$670$		0			0
$671$	12861.1	+	22276.1i	0.739937	+	1.28161i
$672$	−1925.32	+	76.4409i	−0.110522	+	0.00438806i
$673$	25320.4	+	14618.7i	1.45027	+	0.837312i	0.998496	−	0.0548215i	$-0.0174590\pi$
$673$	25320.4	+	14618.7i	1.45027	+	0.837312i	0.451771	+	0.892134i	$0.350792\pi$
$674$	7796.61			0.445570
$675$		0			0
$676$	5663.98			0.322257
$677$	12532.5	+	7235.62i	0.711465	+	0.410764i	0.811603	−	0.584209i	$-0.198595\pi$
$677$	12532.5	+	7235.62i	0.711465	+	0.410764i	−0.100138	+	0.994974i	$0.531929\pi$
$678$	10371.0	−	411.760i	0.587457	−	0.0233238i
$679$	−1003.16	−	1737.52i	−0.0566975	−	0.0982030i
$680$		0			0
$681$	17797.2	+	9354.19i	1.00145	+	0.526363i
$682$	27934.9	+	16128.2i	1.56845	+	0.905545i
$683$			5782.94i			0.323980i	0.986792	+	0.161990i	$0.0517912\pi$
$683$			5782.94i			0.323980i	−0.986792	+	0.161990i	$0.948209\pi$
$684$	−4664.66	−	6775.15i	−0.260757	−	0.378734i
$685$		0			0
$686$	−2058.77	+	3565.89i	−0.114583	+	0.198464i
$687$	−3429.38	−	5430.28i	−0.190450	−	0.301569i
$688$	−10293.8	+	5943.10i	−0.570415	+	0.329329i
$689$	−2015.31	−	3490.62i	−0.111433	−	0.193007i
$690$		0			0
$691$	−5527.56	+	9574.01i	−0.304310	+	0.527080i	−0.977107	−	0.212746i	$-0.931759\pi$
$691$	−5527.56	+	9574.01i	−0.304310	+	0.527080i	0.672797	+	0.739827i	$0.265093\pi$
$692$			12024.6i			0.660557i
$693$	3239.24	−	2230.20i	0.177559	−	0.122249i
$694$	−17046.5			−0.932386
$695$		0			0
$696$	25713.9	+	13515.2i	1.40041	+	0.736052i
$697$	−205.646	+	118.730i	−0.0111756	+	0.00645223i
$698$	−1322.72	+	763.674i	−0.0717275	+	0.0414119i
$699$	−454.962	−	11459.1i	−0.0246184	−	0.620064i
$700$		0			0
$701$	−13554.2			−0.730294			−0.365147	−	0.930950i	$-0.618981\pi$
$701$	−13554.2			−0.730294			−0.365147	+	0.930950i	$0.618981\pi$
$702$	6252.48	−	747.872i	0.336160	−	0.0402088i
$703$		−	26187.4i		−	1.40495i
$704$	−13724.6	+	23771.7i	−0.734751	+	1.27263i
$705$		0			0
$706$	−5981.91	−	10361.0i	−0.318884	−	0.552324i
$707$	−2342.25	+	1352.30i	−0.124596	+	0.0719354i
$708$	−5705.27	+	10854.8i	−0.302849	+	0.576198i
$709$	−4694.58	+	8131.26i	−0.248672	+	0.430713i	−0.963158	−	0.268937i	$-0.913328\pi$
$709$	−4694.58	+	8131.26i	−0.248672	+	0.430713i	0.714485	+	0.699650i	$0.246661\pi$
$710$		0			0
$711$	14017.3	−	29450.3i	0.739365	−	1.55340i
$712$		−	16287.9i		−	0.857326i
$713$	21718.3	+	12539.1i	1.14075	+	0.658614i
$714$	97.6258	−	61.6536i	0.00511702	−	0.00323155i
$715$		0			0
$716$	297.188	+	514.745i	0.0155118	+	0.0268672i
$717$	−2432.31	−	3851.45i	−0.126689	−	0.200607i
$718$	7670.97	+	4428.84i	0.398716	+	0.230199i
$719$	26301.8			1.36424			0.682122	−	0.731238i	$-0.261057\pi$
$719$	26301.8			1.36424			0.682122	+	0.731238i	$0.261057\pi$
$720$		0			0
$721$	4391.67			0.226844
$722$	−4359.33	−	2516.86i	−0.224705	−	0.129734i
$723$	−1155.23	+	2197.94i	−0.0594241	+	0.113060i
$724$	−2290.79	−	3967.76i	−0.117592	−	0.203675i
$725$		0			0
$726$	−652.294	−	16429.3i	−0.0333456	−	0.839876i
$727$	−22117.1	−	12769.3i	−1.12830	−	0.651427i	−0.184797	−	0.982777i	$-0.559163\pi$
$727$	−22117.1	−	12769.3i	−1.12830	−	0.651427i	−0.943508	+	0.331350i	$0.892496\pi$
$728$			1388.56i			0.0706915i
$729$	19127.7	−	4642.23i	0.971789	−	0.235850i
$730$		0			0
$731$	−766.510	+	1327.63i	−0.0387830	+	0.0671742i
$732$	−8076.18	+	320.649i	−0.407792	+	0.0161906i
$733$	6046.70	−	3491.06i	0.304693	−	0.175914i	−0.339856	−	0.940477i	$-0.610378\pi$
$733$	6046.70	−	3491.06i	0.304693	−	0.175914i	0.644549	+	0.764563i	$0.277045\pi$
$734$	−12332.7	−	21360.8i	−0.620174	−	1.07417i
$735$		0			0
$736$	−6022.10	+	10430.6i	−0.301600	+	0.522387i
$737$		−	21667.5i		−	1.08295i
$738$	304.695	+	3831.13i	0.0151978	+	0.191092i
$739$	−8863.91			−0.441224			−0.220612	−	0.975362i	$-0.570805\pi$
$739$	−8863.91			−0.441224			−0.220612	+	0.975362i	$0.570805\pi$
$740$		0			0
$741$	−8596.94	+	5429.22i	−0.426203	+	0.269160i
$742$	−1035.91	+	598.081i	−0.0512524	+	0.0295906i
$743$	−33727.3	+	19472.4i	−1.66532	+	0.961473i	−0.695211	+	0.718806i	$0.744689\pi$
$743$	−33727.3	+	19472.4i	−1.66532	+	0.961473i	−0.970110	+	0.242668i	$0.921978\pi$
$744$	−30099.3	+	19008.6i	−1.48319	+	0.936680i
$745$		0			0
$746$	13870.5			0.680742
$747$	−22068.7	−	10503.9i	−1.08093	−	0.514482i
$748$			613.879i			0.0300075i
$749$	1241.58	−	2150.49i	0.0605694	−	0.104909i
$750$		0			0
$751$	−8795.16	−	15233.7i	−0.427350	−	0.740192i	0.569287	−	0.822139i	$-0.307220\pi$
$751$	−8795.16	−	15233.7i	−0.427350	−	0.740192i	−0.996637	+	0.0819470i	$0.973886\pi$
$752$	3409.66	−	1968.57i	0.165342	−	0.0954604i
$753$	−35785.2	+	1420.78i	−1.73185	+	0.0687597i
$754$	5111.84	−	8853.97i	0.246900	−	0.427643i
$755$		0			0
$756$	146.766	+	1227.02i	0.00706062	+	0.0590293i
$757$			4075.85i			0.195693i	0.995202	+	0.0978463i	$0.0311954\pi$
$757$			4075.85i			0.195693i	−0.995202	+	0.0978463i	$0.968805\pi$
$758$	17722.6	+	10232.1i	0.849225	+	0.490300i
$759$	−975.239	−	24563.3i	−0.0466389	−	1.17469i
$760$		0			0
$761$	−20268.5	−	35106.1i	−0.965483	−	1.67227i	−0.708312	−	0.705899i	$-0.750543\pi$
$761$	−20268.5	−	35106.1i	−0.965483	−	1.67227i	−0.257171	−	0.966366i	$-0.582790\pi$
$762$	−10813.1	+	20572.9i	−0.514064	+	0.978052i
$763$	−2049.30	−	1183.17i	−0.0972343	−	0.0561382i
$764$	−1243.31			−0.0588761
$765$		0			0
$766$	−24463.7			−1.15393
$767$	13127.3	+	7579.06i	0.617992	+	0.356798i
$768$	−11135.5	−	17632.6i	−0.523200	−	0.828464i
$769$	12016.3	+	20812.9i	0.563485	+	0.975985i	0.997189	+	0.0749293i	$0.0238731\pi$
$769$	12016.3	+	20812.9i	0.563485	+	0.975985i	−0.433704	+	0.901056i	$0.642794\pi$
$770$		0			0
$771$	−31881.5	+	20134.1i	−1.48922	+	0.940484i
$772$	10796.9	+	6233.57i	0.503351	+	0.290610i
$773$		−	20881.5i		−	0.971611i	−0.874067	−	0.485805i	$-0.838526\pi$
$773$		−	20881.5i		−	0.971611i	0.874067	−	0.485805i	$-0.161474\pi$
$774$	14070.3	+	20436.3i	0.653420	+	0.949055i
$775$		0			0
$776$	8901.16	−	15417.3i	0.411770	−	0.713206i
$777$	−1830.39	+	3482.48i	−0.0845106	+	0.160789i
$778$	−12487.5	+	7209.64i	−0.575446	+	0.332234i
$779$	−3102.82	−	5374.24i	−0.142709	−	0.247179i
$780$		0			0
$781$	−8171.18	+	14152.9i	−0.374376	+	0.648439i
$782$		−	721.740i		−	0.0330043i
$783$	12578.4	−	29377.1i	0.574093	−	1.34081i
$784$	−9518.60			−0.433610
$785$		0			0
$786$	−106.597	−	2684.87i	−0.00483741	−	0.121840i
$787$	4448.25	−	2568.20i	0.201478	−	0.116323i	−0.395867	−	0.918308i	$-0.629556\pi$
$787$	4448.25	−	2568.20i	0.201478	−	0.116323i	0.597345	+	0.801985i	$0.296223\pi$
$788$	2461.82	−	1421.33i	0.111293	−	0.0642549i
$789$	−29057.8	−	15272.7i	−1.31113	−	0.689130i
$790$		0			0
$791$	2517.77			0.113175
$792$	31508.9	+	14997.1i	1.41366	+	0.672851i
$793$			9990.86i			0.447397i
$794$	−4355.23	+	7543.48i	−0.194662	+	0.337164i
$795$		0			0
$796$	−4411.22	−	7640.45i	−0.196421	−	0.340212i
$797$	−19049.1	+	10998.0i	−0.846615	+	0.488794i	−0.859507	−	0.511123i	$-0.829230\pi$
$797$	−19049.1	+	10998.0i	−0.846615	+	0.488794i	0.0128922	+	0.999917i	$0.495896\pi$
$798$	1611.22	+	2551.30i	0.0714745	+	0.113177i
$799$	253.895	−	439.760i	0.0112418	−	0.0194713i
$800$		0			0
$801$	−17861.7	+	1420.57i	−0.787905	+	0.0626632i
$802$			9600.03i			0.422679i
$803$	−2326.99	−	1343.49i	−0.102264	−	0.0590419i
$804$	6026.69	+	3167.62i	0.264359	+	0.138947i
$805$		0			0
$806$	6264.42	+	10850.3i	0.273765	+	0.474175i
$807$	29834.7	−	1184.53i	1.30140	−	0.0516696i
$808$	−20783.1	−	11999.1i	−0.904885	−	0.522435i
$809$	−31094.2			−1.35132			−0.675658	−	0.737215i	$-0.736140\pi$
$809$	−31094.2			−1.35132			−0.675658	+	0.737215i	$0.736140\pi$
$810$		0			0
$811$	19130.6			0.828320			0.414160	−	0.910204i	$-0.364075\pi$
$811$	19130.6			0.828320			0.414160	+	0.910204i	$0.364075\pi$
$812$	1737.55	+	1003.17i	0.0750936	+	0.0433553i
$813$	−25571.9	+	1015.28i	−1.10313	+	0.0437977i
$814$	15815.5	+	27393.2i	0.680997	+	1.17952i
$815$		0			0
$816$	477.937	+	251.203i	0.0205038	+	0.0107768i
$817$	−34695.7	−	20031.6i	−1.48574	−	0.857792i
$818$			19469.8i			0.832208i
$819$	1522.72	−	121.104i	0.0649674	−	0.00516694i
$820$		0			0
$821$	1778.81	−	3080.99i	0.0756162	−	0.130971i	−0.825738	−	0.564054i	$-0.809241\pi$
$821$	1778.81	−	3080.99i	0.0756162	−	0.130971i	0.901354	+	0.433083i	$0.142574\pi$
$822$	−18100.7	−	28661.8i	−0.768049	−	1.21617i
$823$	5325.52	−	3074.69i	0.225560	−	0.130227i	−0.382962	−	0.923764i	$-0.625096\pi$
$823$	5325.52	−	3074.69i	0.225560	−	0.130227i	0.608522	+	0.793537i	$0.291763\pi$
$824$	19484.0	+	33747.2i	0.823733	+	1.42675i
$825$		0			0
$826$	2249.23	−	3895.77i	0.0947464	−	0.164106i
$827$		−	21152.8i		−	0.889425i	−0.895673	−	0.444713i	$-0.853306\pi$
$827$		−	21152.8i		−	0.889425i	0.895673	−	0.444713i	$-0.146694\pi$
$828$	6974.73	+	3319.72i	0.292740	+	0.139334i
$829$	17402.4			0.729083			0.364541	−	0.931187i	$-0.381226\pi$
$829$	17402.4			0.729083			0.364541	+	0.931187i	$0.381226\pi$
$830$		0			0
$831$	−10698.0	−	5622.84i	−0.446580	−	0.234722i
$832$	−9233.24	+	5330.81i	−0.384742	+	0.222131i
$833$	−1063.18	+	613.829i	−0.0442222	+	0.0255317i
$834$	−947.536	−	23865.6i	−0.0393411	−	0.990884i
$835$		0			0
$836$	−16042.8			−0.663698
$837$	23470.4	+	31349.7i	0.969243	+	1.29463i
$838$			2225.55i			0.0917425i
$839$	−9037.12	+	15652.8i	−0.371867	+	0.644092i	−0.989853	−	0.142097i	$-0.954615\pi$
$839$	−9037.12	+	15652.8i	−0.371867	+	0.644092i	0.617986	+	0.786189i	$0.287949\pi$
$840$		0			0
$841$	−13747.5	−	23811.3i	−0.563675	−	0.976314i
$842$	−28303.6	+	16341.1i	−1.15844	+	0.668825i
$843$	7937.69	−	15102.2i	0.324304	−	0.617019i
$844$	−7296.31	+	12637.6i	−0.297570	+	0.515407i
$845$		0			0
$846$	−4660.59	−	6769.23i	−0.189402	−	0.275096i
$847$		−	3988.55i		−	0.161804i
$848$	−4844.09	−	2796.74i	−0.196164	−	0.113255i
$849$	−8849.21	+	5588.54i	−0.357720	+	0.225911i
$850$		0			0
$851$	12295.9	+	21297.1i	0.495297	+	0.857880i
$852$	−2741.99	−	4341.82i	−0.110257	−	0.174587i
$853$	−35327.2	−	20396.1i	−1.41803	−	0.818699i	−0.421903	−	0.906641i	$-0.638638\pi$
$853$	−35327.2	−	20396.1i	−1.41803	−	0.818699i	−0.996126	+	0.0879416i	$0.971971\pi$
$854$	2964.97			0.118805
$855$		0			0
$856$	22033.5			0.879778
$857$	−9576.39	−	5528.93i	−0.381707	−	0.220379i	0.296854	−	0.954923i	$-0.404063\pi$
$857$	−9576.39	−	5528.93i	−0.381707	−	0.220379i	−0.678561	+	0.734544i	$0.737396\pi$
$858$	5713.88	−	10871.2i	0.227353	−	0.432559i
$859$	−876.815	−	1518.69i	−0.0348272	−	0.0603224i	0.848086	−	0.529858i	$-0.177755\pi$
$859$	−876.815	−	1518.69i	−0.0348272	−	0.0603224i	−0.882914	+	0.469535i	$0.844421\pi$
$860$		0			0
$861$	36.9855	+	931.554i	0.00146395	+	0.0368725i
$862$	8293.35	+	4788.17i	0.327694	+	0.189194i
$863$		−	19186.5i		−	0.756796i	−0.925643	−	0.378398i	$-0.876475\pi$
$863$		−	19186.5i		−	0.756796i	0.925643	−	0.378398i	$-0.123525\pi$
$864$	−15056.3	+	11272.1i	−0.592852	+	0.443847i
$865$		0			0
$866$	10205.9	−	17677.2i	0.400475	−	0.693642i
$867$	−25439.0	+	1010.01i	−0.996487	+	0.0395635i
$868$	−2129.32	+	1229.36i	−0.0832646	+	0.0480728i
$869$	−31806.0	−	55089.6i	−1.24159	−	2.15050i
$870$		0			0
$871$	4207.97	−	7288.41i	0.163699	−	0.283534i
$872$		−	20996.8i		−	0.815415i
$873$	−17683.2	−	8416.58i	−0.685552	−	0.326298i
$874$	18861.6			0.729980
$875$		0			0
$876$	713.872	−	450.831i	0.0275337	−	0.0173883i
$877$	7373.86	−	4257.30i	0.283920	−	0.163921i	−0.351277	−	0.936272i	$-0.614252\pi$
$877$	7373.86	−	4257.30i	0.283920	−	0.163921i	0.635197	+	0.772350i	$0.280919\pi$
$878$	−2888.96	+	1667.94i	−0.111045	+	0.0641121i
$879$	−2111.89	+	1333.72i	−0.0810377	+	0.0511777i
$880$		0			0
$881$	41177.0			1.57467			0.787337	−	0.616522i	$-0.211459\pi$
$881$	41177.0			1.57467			0.787337	+	0.616522i	$0.211459\pi$
$882$	1575.27	+	19806.9i	0.0601384	+	0.756159i
$883$			32540.4i			1.24017i	0.784533	+	0.620086i	$0.212902\pi$
$883$			32540.4i			1.24017i	−0.784533	+	0.620086i	$0.787098\pi$
$884$	−119.219	+	206.494i	−0.00453595	+	0.00785650i
$885$		0			0
$886$	4896.34	+	8480.70i	0.185661	+	0.321574i
$887$	−1875.90	+	1083.05i	−0.0710106	+	0.0409980i	−0.535085	−	0.844798i	$-0.679720\pi$
$887$	−1875.90	+	1083.05i	−0.0710106	+	0.0409980i	0.464074	+	0.885796i	$0.346387\pi$
$888$	−34881.3	+	1384.89i	−1.31818	+	0.0523356i
$889$	−2818.95	+	4882.56i	−0.106349	+	0.184202i
$890$		0			0
$891$	13698.1	−	35861.3i	0.515041	−	1.34837i
$892$			13041.2i			0.489522i
$893$	11492.4	+	6635.17i	0.430661	+	0.248642i
$894$	123.919	+	3121.15i	0.00463588	+	0.116764i
$895$		0			0
$896$	98.7391	+	171.021i	0.00368152	+	0.00637658i
$897$	4442.32	−	8451.92i	0.165356	−	0.314606i
$898$	−10208.5	−	5893.91i	−0.379358	−	0.219023i
$899$	63582.3			2.35883
$900$		0			0
$901$	−721.416			−0.0266747
$902$	6491.36	+	3747.79i	0.239622	+	0.138346i
$903$	3213.81	+	5088.93i	0.118437	+	0.187540i
$904$	11170.3	+	19347.5i	0.410971	+	0.711823i
$905$		0			0
$906$	9032.15	−	5704.07i	0.331207	−	0.209167i
$907$	−611.468	−	353.031i	−0.0223853	−	0.0129241i	0.488766	−	0.872415i	$-0.337447\pi$
$907$	−611.468	−	353.031i	−0.0223853	−	0.0129241i	−0.511151	+	0.859491i	$0.670781\pi$
$908$			12321.6i			0.450339i
$909$	−11345.9	+	23837.7i	−0.413993	+	0.869799i
$910$		0			0
$911$	247.743	−	429.103i	0.00900997	−	0.0156057i	−0.861485	−	0.507783i	$-0.830465\pi$
$911$	247.743	−	429.103i	0.00900997	−	0.0156057i	0.870495	+	0.492177i	$0.163799\pi$
$912$	−6564.81	+	12490.1i	−0.238358	+	0.453498i
$913$	−41281.7	+	23834.0i	−1.49641	+	0.863955i
$914$	−17034.8	−	29505.2i	−0.616480	−	1.06777i
$915$		0			0
$916$	1967.99	−	3408.66i	0.0709871	−	0.122953i
$917$		−	651.806i		−	0.0234728i
$918$	443.623	−	1036.09i	0.0159496	−	0.0372507i
$919$	−20473.6			−0.734889			−0.367445	−	0.930045i	$-0.619767\pi$
$919$	−20473.6			−0.734889			−0.367445	+	0.930045i	$0.619767\pi$
$920$		0			0
$921$	664.227	+	16729.9i	0.0237644	+	0.598554i
$922$	−107.219	+	61.9030i	−0.00382980	+	0.00221114i
$923$	−5497.17	+	3173.80i	−0.196037	+	0.113182i
$924$	2133.41	+	1121.32i	0.0759569	+	0.0399229i
$925$		0			0
$926$	−29348.0			−1.04151
$927$	35308.6	−	24309.8i	1.25101	−	0.861316i
$928$			30536.5i			1.08018i
$929$	24857.7	−	43054.7i	0.877883	−	1.52054i	0.0242231	−	0.999707i	$-0.492289\pi$
$929$	24857.7	−	43054.7i	0.877883	−	1.52054i	0.853660	−	0.520831i	$-0.174378\pi$
$930$		0			0
$931$	−16041.5	−	27784.7i	−0.564704	−	0.978095i
$932$	6086.57	−	3514.08i	0.213919	−	0.123506i
$933$	6697.79	+	10605.7i	0.235022	+	0.372148i
$934$	−2937.77	+	5088.36i	−0.102919	+	0.178261i
$935$		0			0
$936$	7686.29	+	11163.9i	0.268413	+	0.389854i
$937$			31524.9i			1.09912i	0.835454	+	0.549560i	$0.185204\pi$
$937$			31524.9i			1.09912i	−0.835454	+	0.549560i	$0.814796\pi$
$938$	−2162.97	−	1248.79i	−0.0752916	−	0.0434696i
$939$	−11530.7	−	6060.54i	−0.400736	−	0.210626i
$940$		0			0
$941$	−18764.2	−	32500.6i	−0.650050	−	1.12592i	−0.983110	−	0.183014i	$-0.941415\pi$
$941$	−18764.2	−	32500.6i	−0.650050	−	1.12592i	0.333060	−	0.942905i	$-0.391919\pi$
$942$	−4539.65	+	180.238i	−0.157017	+	0.00623404i
$943$	5046.78	+	2913.76i	0.174280	+	0.100620i
$944$	21035.6			0.725265
$945$		0			0
$946$	48390.9			1.66313
$947$	22398.3	+	12931.7i	0.768582	+	0.443741i	0.832369	−	0.554222i	$-0.186984\pi$
$947$	22398.3	+	12931.7i	0.768582	+	0.443741i	−0.0637862	+	0.997964i	$0.520318\pi$
$948$	19972.7	−	792.975i	0.684264	−	0.0271673i
$949$	−521.829	−	903.834i	−0.0178496	−	0.0309164i
$950$		0			0
$951$	−17051.0	−	8962.00i	−0.581406	−	0.305586i
$952$	215.233	+	124.265i	0.00732746	+	0.00423051i
$953$			1060.03i			0.0360312i	0.999838	+	0.0180156i	$0.00573485\pi$
$953$			1060.03i			0.0360312i	−0.999838	+	0.0180156i	$0.994265\pi$
$954$	−5017.95	+	10542.7i	−0.170296	+	0.357791i
$955$		0			0
$956$	1395.81	−	2417.61i	0.0472213	−	0.0817897i
$957$	−33279.9	−	52697.3i	−1.12412	−	1.78000i
$958$	6594.40	−	3807.28i	0.222396	−	0.128400i
$959$	−4111.58	−	7121.46i	−0.138446	−	0.239796i
$960$		0			0
$961$	−24063.7	+	41679.5i	−0.807750	+	1.39906i
$962$			12285.9i			0.411759i
$963$	−1921.67	−	24162.4i	−0.0643043	−	0.808540i
$964$	−1521.71			−0.0508412
$965$		0			0
$966$	−2508.26	−	1318.34i	−0.0835424	−	0.0439098i
$967$	4490.35	−	2592.51i	0.149328	−	0.0862145i	−0.423474	−	0.905908i	$-0.639190\pi$
$967$	4490.35	−	2592.51i	0.149328	−	0.0862145i	0.572802	+	0.819694i	$0.305856\pi$
$968$	30649.5	−	17695.5i	1.01768	−	0.587557i
$969$	72.1975	+	1818.44i	0.00239352	+	0.0602855i
$970$		0			0
$971$	28314.9			0.935805			0.467903	−	0.883780i	$-0.345010\pi$
$971$	28314.9			0.935805			0.467903	+	0.883780i	$0.345010\pi$
$972$	7972.07	+	9052.69i	0.263070	+	0.298730i
$973$		−	5793.85i		−	0.190897i
$974$	15405.6	−	26683.4i	0.506806	−	0.877813i
$975$		0			0
$976$	6932.38	+	12007.2i	0.227357	+	0.393793i
$977$	−38881.6	+	22448.3i	−1.27322	+	0.735093i	−0.975592	−	0.219590i	$-0.929528\pi$
$977$	−38881.6	+	22448.3i	−1.27322	+	0.735093i	−0.297626	+	0.954683i	$0.596195\pi$
$978$	−2536.65	+	4826.20i	−0.0829376	+	0.157796i
$979$	−17473.1	+	30264.3i	−0.570422	+	0.988001i
$980$		0			0
$981$	−23025.6	+	1831.26i	−0.749388	+	0.0595999i
$982$			21539.4i			0.699950i
$983$	12620.4	+	7286.40i	0.409490	+	0.236419i	0.690571	−	0.723265i	$-0.257360\pi$
$983$	12620.4	+	7286.40i	0.409490	+	0.236419i	−0.281081	+	0.959684i	$0.590693\pi$
$984$	−6994.32	+	4417.12i	−0.226596	+	0.143102i
$985$		0			0
$986$	−914.938	−	1584.72i	−0.0295513	−	0.0511843i
$987$	−1064.53	−	1685.63i	−0.0343306	−	0.0543610i
$988$	−5396.41	−	3115.62i	−0.173768	−	0.100325i
$989$	37622.0			1.20962
$990$		0			0
$991$	10602.1			0.339844			0.169922	−	0.985457i	$-0.445648\pi$
$991$	10602.1			0.339844			0.169922	+	0.985457i	$0.445648\pi$
$992$	−32408.1	−	18710.8i	−1.03726	−	0.598860i
$993$	6172.98	−	11744.6i	0.197274	−	0.375332i
$994$	941.882	+	1631.39i	0.0300550	+	0.0520568i
$995$		0			0
$996$	−594.221	−	14966.6i	−0.0189042	−	0.476141i
$997$	24159.5	+	13948.5i	0.767441	+	0.443082i	0.831961	−	0.554834i	$-0.187218\pi$
$997$	24159.5	+	13948.5i	0.767441	+	0.443082i	−0.0645202	+	0.997916i	$0.520552\pi$
$998$			26447.4i			0.838857i
$999$	4560.91	+	38130.8i	0.144445	+	1.20761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.d.124.5		28
5.2	odd	4		45.4.e.c.16.5	✓	14
5.3	odd	4		225.4.e.d.151.3		14
5.4	even	2	inner	225.4.k.d.124.10		28
9.4	even	3	inner	225.4.k.d.49.10		28
15.2	even	4		135.4.e.c.46.3		14
45.2	even	12		405.4.a.n.1.5		7
45.4	even	6	inner	225.4.k.d.49.5		28
45.7	odd	12		405.4.a.m.1.3		7
45.13	odd	12		225.4.e.d.76.3		14
45.22	odd	12		45.4.e.c.31.5	yes	14
45.32	even	12		135.4.e.c.91.3		14
45.38	even	12		2025.4.a.ba.1.3		7
45.43	odd	12		2025.4.a.bb.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.5	✓	14	5.2	odd	4
45.4.e.c.31.5	yes	14	45.22	odd	12
135.4.e.c.46.3		14	15.2	even	4
135.4.e.c.91.3		14	45.32	even	12
225.4.e.d.76.3		14	45.13	odd	12
225.4.e.d.151.3		14	5.3	odd	4
225.4.k.d.49.5		28	45.4	even	6	inner
225.4.k.d.49.10		28	9.4	even	3	inner
225.4.k.d.124.5		28	1.1	even	1	trivial
225.4.k.d.124.10		28	5.4	even	2	inner
405.4.a.m.1.3		7	45.7	odd	12
405.4.a.n.1.5		7	45.2	even	12
2025.4.a.ba.1.3		7	45.38	even	12
2025.4.a.bb.1.5		7	45.43	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.90044 - 1.09722i) q^{2} +(-5.19206 + 0.206141i) q^{3} +(-1.59221 - 2.75778i) q^{4} +(10.0934 + 5.30509i) q^{6} +(2.39547 + 1.38302i) q^{7} +24.5436i q^{8} +(26.9150 - 2.14059i) q^{9} +(26.3295 - 45.6040i) q^{11} +(8.83533 + 13.9904i) q^{12} +(17.7132 - 10.2267i) q^{13} +(-3.03497 - 5.25672i) q^{14} +(14.1921 - 24.5814i) q^{16} -3.66084i q^{17} +(-53.4992 - 25.4637i) q^{18} +95.6705 q^{19} +(-12.7225 - 6.68694i) q^{21} +(-100.075 + 57.7786i) q^{22} +(-77.8047 + 44.9206i) q^{23} +(-5.05943 - 127.432i) q^{24} -44.8840 q^{26} +(-139.303 + 16.6623i) q^{27} -8.80825i q^{28} +(-113.890 + 197.264i) q^{29} +(-139.569 - 241.741i) q^{31} +(116.100 - 67.0306i) q^{32} +(-127.303 + 242.206i) q^{33} +(-4.01675 + 6.95722i) q^{34} +(-48.7576 - 70.8175i) q^{36} -273.725i q^{37} +(-181.816 - 104.972i) q^{38} +(-89.8599 + 56.7492i) q^{39} +(-32.4323 - 56.1744i) q^{41} +(16.8414 + 26.6676i) q^{42} +(-362.658 - 209.381i) q^{43} -167.688 q^{44} +197.151 q^{46} +(120.125 + 69.3544i) q^{47} +(-68.6190 + 130.554i) q^{48} +(-167.674 - 290.421i) q^{49} +(0.754647 + 19.0073i) q^{51} +(-56.4062 - 32.5661i) q^{52} -197.063i q^{53} +(283.020 + 121.181i) q^{54} +(-33.9444 + 58.7934i) q^{56} +(-496.727 + 19.7216i) q^{57} +(432.884 - 249.926i) q^{58} +(370.552 + 641.814i) q^{59} +(-244.234 + 423.026i) q^{61} +612.554i q^{62} +(67.4346 + 32.0964i) q^{63} -521.263 q^{64} +(507.687 - 320.620i) q^{66} +(356.341 - 205.734i) q^{67} +(-10.0958 + 5.82882i) q^{68} +(394.707 - 249.269i) q^{69} -310.343 q^{71} +(52.5377 + 660.591i) q^{72} -51.0260i q^{73} +(-300.338 + 520.200i) q^{74} +(-152.327 - 263.839i) q^{76} +(126.143 - 72.8286i) q^{77} +(233.040 - 9.25240i) q^{78} +(603.999 - 1046.16i) q^{79} +(719.836 - 115.228i) q^{81} +142.342i q^{82} +(-783.945 - 452.611i) q^{83} +(1.81574 + 45.7330i) q^{84} +(459.475 + 795.833i) q^{86} +(550.661 - 1047.68i) q^{87} +(1119.29 + 646.220i) q^{88} -663.633 q^{89} +56.5752 q^{91} +(247.763 + 143.046i) q^{92} +(774.485 + 1226.36i) q^{93} +(-152.194 - 263.608i) q^{94} +(-588.982 + 371.960i) q^{96} +(-628.159 - 362.668i) q^{97} +735.905i q^{98} +(611.039 - 1283.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41}+ \cdots - 4640 q^{99}+O(q^{100}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Introduction

L-functions

Modular forms

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Database

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