LMFDB - Embedded newform 225.4.k.d.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

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")

//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: 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:	$28$
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			49.5
Character	$\chi$	$=$	225.49
Dual form			225.4.k.d.124.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90044 + 1.09722i) q^{2} +(-5.19206 - 0.206141i) q^{3} +(-1.59221 + 2.75778i) q^{4} +(10.0934 - 5.30509i) q^{6} +(2.39547 - 1.38302i) q^{7} -24.5436i q^{8} +(26.9150 + 2.14059i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.796799	−	0.604244i	$-0.793475\pi$
$2$	−1.90044	+	1.09722i	−0.671909	+	0.387927i	0.124891	+	0.992170i	$0.460142\pi$
$3$	−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	−0.433932	−	0.900945i	$-0.642874\pi$
$7$	2.39547	−	1.38302i	0.129343	−	0.0746763i	0.563275	+	0.826269i	$0.309541\pi$
$8$		−	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	0.960320	+	0.278900i	$0.0899698\pi$
$11$	26.3295	+	45.6040i	0.721694	+	1.25001i	−0.238626	+	0.971112i	$0.576697\pi$
$12$	8.83533	−	13.9904i	0.212545	−	0.336556i
$13$	17.7132	+	10.2267i	0.377905	+	0.218183i	0.676906	−	0.736069i	$-0.263320\pi$
$13$	17.7132	+	10.2267i	0.377905	+	0.218183i	−0.299002	+	0.954253i	$0.596654\pi$
$14$	−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	$0.00831336\pi$
$17$			3.66084i			0.0522285i	−0.999659	+	0.0261142i	$0.991687\pi$
$18$	−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	0.103977	−	0.994580i	$-0.466843\pi$
$23$	−77.8047	−	44.9206i	−0.705365	−	0.407243i	−0.809343	+	0.587337i	$0.800176\pi$
$24$	−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	−0.957191	−	0.289456i	$-0.906526\pi$
$29$	−113.890	−	197.264i	−0.729272	−	1.26314i	0.227919	−	0.973680i	$-0.426808\pi$
$30$		0			0
$31$	−139.569	+	241.741i	−0.808625	+	1.40058i	0.105191	+	0.994452i	$0.466455\pi$
$31$	−139.569	+	241.741i	−0.808625	+	1.40058i	−0.913816	+	0.406128i	$0.866879\pi$
$32$	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	$0.208072\pi$
$37$			273.725i			1.21622i	−0.793852	+	0.608110i	$0.791928\pi$
$38$	−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	−0.921161	−	0.389182i	$-0.872758\pi$
$41$	−32.4323	+	56.1744i	−0.123539	+	0.213975i	0.797622	+	0.603157i	$0.206091\pi$
$42$	16.8414	−	26.6676i	0.0618733	−	0.0979738i
$43$	−362.658	+	209.381i	−1.28616	+	0.742565i	−0.977967	−	0.208759i	$-0.933057\pi$
$43$	−362.658	+	209.381i	−1.28616	+	0.742565i	−0.308193	+	0.951324i	$0.599724\pi$
$44$	−167.688			−0.574544
$45$		0			0
$46$	197.151			0.631921
$47$	120.125	−	69.3544i	0.372810	−	0.215242i	−0.301875	−	0.953347i	$-0.597613\pi$
$47$	120.125	−	69.3544i	0.372810	−	0.215242i	0.674685	+	0.738105i	$0.264279\pi$
$48$	−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	$0.0821957\pi$
$53$			197.063i			0.510730i	−0.966845	+	0.255365i	$0.917804\pi$
$54$	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	−0.0897490	−	0.995964i	$-0.528606\pi$
$59$	370.552	−	641.814i	0.817656	−	1.41622i	0.907405	−	0.420257i	$-0.138060\pi$
$60$		0			0
$61$	−244.234	−	423.026i	−0.512639	−	0.887916i	−0.999893	−	0.0146560i	$-0.995335\pi$
$61$	−244.234	−	423.026i	−0.512639	−	0.887916i	0.487254	−	0.873260i	$-0.337999\pi$
$62$		−	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	0.788365	−	0.615208i	$-0.210928\pi$
$67$	356.341	+	205.734i	0.649762	+	0.375140i	−0.138603	+	0.990348i	$0.544261\pi$
$68$	−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	$0.0130241\pi$
$73$			51.0260i			0.0818101i	−0.999163	+	0.0409051i	$0.986976\pi$
$74$	−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	0.871742	+	0.489964i	$0.162990\pi$
$79$	603.999	+	1046.16i	0.860193	+	1.48990i	−0.0115496	+	0.999933i	$0.503676\pi$
$80$		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	−0.918907	−	0.394474i	$-0.870927\pi$
$83$	−783.945	+	452.611i	−1.03674	+	0.598560i	−0.117829	+	0.993034i	$0.537594\pi$
$84$	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	−0.791333	−	0.611385i	$-0.790613\pi$
$97$	−628.159	+	362.668i	−0.657525	+	0.379622i	0.133809	+	0.991007i	$0.457279\pi$
$98$		−	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	0.518130	−	0.855302i	$-0.326628\pi$
$101$	−488.891	−	846.784i	−0.481648	−	0.834239i	−0.999778	+	0.0210629i	$0.993295\pi$
$102$	19.4211	+	36.9503i	0.0188527	+	0.0358689i
$103$	1374.99	+	793.852i	1.31536	+	0.759423i	0.982978	−	0.183722i	$-0.0588147\pi$
$103$	1374.99	+	793.852i	1.31536	+	0.759423i	0.332381	+	0.943145i	$0.392148\pi$
$104$	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	$0.132919\pi$
$107$			897.731i			0.811093i	−0.914074	+	0.405546i	$0.867081\pi$
$108$	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	0.790847	−	0.612014i	$-0.209641\pi$
$113$	788.292	+	455.121i	0.656250	+	0.378886i	−0.134597	+	0.990900i	$0.542974\pi$
$114$	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	$-0.747759\pi$
$127$		−	2038.25i		−	1.42414i	0.702111	−	0.712068i	$-0.252241\pi$
$128$	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	−0.902638	−	0.430400i	$-0.858372\pi$
$131$	−117.823	+	204.075i	−0.0785817	+	0.136108i	0.824057	+	0.566508i	$0.191706\pi$
$132$	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	−0.615222	+	0.788354i	$0.710934\pi$
$137$	−2574.60	+	1486.45i	−1.60557	+	0.926975i	−0.990345	+	0.138621i	$0.955733\pi$
$138$	−1023.62	−	40.6409i	−0.631424	−	0.0250694i
$139$	−1047.32	+	1814.00i	−0.639080	+	1.10692i	0.346555	+	0.938030i	$0.387352\pi$
$139$	−1047.32	+	1814.00i	−0.639080	+	1.10692i	−0.985635	+	0.168890i	$0.945982\pi$
$140$		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	−0.825912	−	0.563799i	$-0.809339\pi$
$149$	136.969	−	237.237i	0.0753081	−	0.130437i	0.901220	+	0.433361i	$0.142673\pi$
$150$		0			0
$151$	468.422	+	811.331i	0.252448	+	0.437253i	0.964199	−	0.265179i	$-0.0854310\pi$
$151$	468.422	+	811.331i	0.252448	+	0.437253i	−0.711751	+	0.702432i	$0.752098\pi$
$152$		−	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	0.409728	−	0.912208i	$-0.365624\pi$
$157$	−345.055	−	199.218i	−0.175404	−	0.101269i	−0.585131	+	0.810938i	$0.698957\pi$
$158$	−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	$-0.963351\pi$
$163$		−	478.154i		−	0.229766i	0.993379	−	0.114883i	$-0.0366493\pi$
$164$	−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	0.566735	−	0.823900i	$-0.308206\pi$
$167$	294.763	+	170.181i	0.136583	+	0.0788564i	−0.430151	+	0.902757i	$0.641540\pi$
$168$	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	−0.997651	−	0.0685065i	$-0.978177\pi$
$173$	−3270.17	+	1888.03i	−1.43715	+	0.829738i	−0.439497	+	0.898244i	$0.644843\pi$
$174$	−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	0.900631	−	0.434584i	$-0.143104\pi$
$191$	195.218	+	338.127i	0.0739552	+	0.128094i	−0.826676	+	0.562678i	$0.809771\pi$
$192$	2706.43	+	107.453i	1.01729	+	0.0403895i
$193$	−3390.53	−	1957.52i	−1.26454	−	0.730081i	−0.290588	−	0.956848i	$-0.593851\pi$
$193$	−3390.53	−	1957.52i	−1.26454	−	0.730081i	−0.973949	+	0.226767i	$0.927184\pi$
$194$	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	$-0.948392\pi$
$197$		−	892.680i		−	0.322847i	0.986885	−	0.161423i	$-0.0516085\pi$
$198$	−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	0.201420	+	0.979505i	$0.435444\pi$
$211$	−2291.25	+	3968.57i	−0.747566	+	1.29482i	−0.948986	+	0.315318i	$0.897889\pi$
$212$	−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	−0.926820	−	0.375506i	$-0.877469\pi$
$223$	−3546.66	+	2047.67i	−1.06503	+	0.614897i	−0.138212	+	0.990403i	$0.544136\pi$
$224$	370.820			0.110609
$225$		0			0
$226$	−1997.47			−0.587920
$227$	−3350.96	+	1934.68i	−0.979784	+	0.565678i	−0.902205	−	0.431308i	$-0.858052\pi$
$227$	−3350.96	+	1934.68i	−0.979784	+	0.565678i	−0.0775789	+	0.996986i	$0.524719\pi$
$228$	845.281	−	1338.47i	0.245527	−	0.388781i
$229$	618.006	−	1070.42i	0.178336	−	0.308887i	−0.762975	−	0.646429i	$-0.776262\pi$
$229$	618.006	−	1070.42i	0.178336	−	0.308887i	0.941311	+	0.337541i	$0.109595\pi$
$230$		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	$-0.899579\pi$
$233$		−	2207.05i		−	0.620552i	0.950647	−	0.310276i	$-0.100421\pi$
$234$	−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	−0.800594	−	0.599207i	$-0.795483\pi$
$239$	438.324	−	759.199i	0.118631	−	0.205475i	0.919225	+	0.393732i	$0.128816\pi$
$240$		0			0
$241$	238.931	+	413.840i	0.0638626	+	0.110613i	0.896189	−	0.443673i	$-0.146325\pi$
$241$	238.931	+	413.840i	0.0638626	+	0.110613i	−0.832326	+	0.554286i	$0.812991\pi$
$242$		−	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	0.999548	+	0.0300589i	$0.00956949\pi$
$257$	6284.49	+	3628.35i	1.52535	+	0.880664i	0.525806	+	0.850605i	$0.323764\pi$
$258$	−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	0.305409	−	0.952221i	$-0.401207\pi$
$263$	5471.16	−	3158.78i	1.28276	−	0.740603i	0.977352	+	0.211618i	$0.0678733\pi$
$264$	−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	−0.265372	−	0.964146i	$-0.585495\pi$
$277$	2014.27	−	1162.94i	0.436917	−	0.252254i	0.702289	+	0.711892i	$0.252161\pi$
$278$		−	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	0.637461	−	0.770483i	$-0.279985\pi$
$281$	−1641.71	−	2843.52i	−0.348527	−	0.603667i	−0.985988	+	0.166816i	$0.946652\pi$
$282$	844.543	−	1337.30i	0.178340	−	0.282393i
$283$	1744.36	+	1007.11i	0.366400	+	0.211541i	0.671885	−	0.740656i	$-0.265485\pi$
$283$	1744.36	+	1007.11i	0.366400	+	0.211541i	−0.305484	+	0.952197i	$0.598818\pi$
$284$	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	0.540928	−	0.841069i	$-0.318073\pi$
$293$	416.295	+	240.348i	0.0830042	+	0.0479225i	−0.457923	+	0.888992i	$0.651407\pi$
$294$	−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	$0.0968242\pi$
$307$			3222.21i			0.599026i	−0.954092	+	0.299513i	$0.903176\pi$
$308$	−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	−0.954830	−	0.297152i	$-0.903963\pi$
$311$	−1207.00	+	2090.59i	−0.220074	+	0.381179i	0.734757	+	0.678331i	$0.237296\pi$
$312$	−1392.83	+	2205.48i	−0.252735	+	0.400195i
$313$	2171.07	−	1253.47i	0.392065	−	0.226359i	−0.290990	−	0.956726i	$-0.593985\pi$
$313$	2171.07	−	1253.47i	0.392065	−	0.226359i	0.683054	+	0.730368i	$0.260651\pi$
$314$	874.344			0.157140
$315$		0			0
$316$	−3846.77			−0.684803
$317$	3210.46	−	1853.56i	0.568825	−	0.328411i	−0.187855	−	0.982197i	$-0.560154\pi$
$317$	3210.46	−	1853.56i	0.568825	−	0.328411i	0.756680	+	0.653786i	$0.226820\pi$
$318$	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	0.740334	−	0.672239i	$-0.234667\pi$
$331$	−1276.72	−	2211.35i	−0.212009	−	0.367211i	−0.952343	+	0.305029i	$0.901334\pi$
$332$		−	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	0.230265	−	0.973128i	$-0.426041\pi$
$337$	−3076.89	−	1776.44i	−0.497356	−	0.287148i	−0.727621	+	0.685979i	$0.759374\pi$
$338$	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	0.920046	−	0.391811i	$-0.128151\pi$
$347$	6727.30	+	3884.01i	1.04075	+	0.600878i	0.120705	+	0.992688i	$0.461485\pi$
$348$	−3766.05	−	149.524i	−0.580119	−	0.0230325i
$349$	348.003	+	602.760i	0.0533759	+	0.0924498i	0.891479	−	0.453062i	$-0.149669\pi$
$349$	348.003	+	602.760i	0.0533759	+	0.0924498i	−0.838103	+	0.545512i	$0.816335\pi$
$350$		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	−0.0998692	−	0.995001i	$-0.531842\pi$
$353$	4721.46	−	2725.94i	0.711892	−	0.411011i	0.811761	+	0.583990i	$0.198509\pi$
$354$	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	0.391817	−	0.920043i	$-0.371847\pi$
$367$	9734.06	−	5619.96i	1.38451	−	0.799345i	0.992689	+	0.120698i	$0.0385134\pi$
$368$		−	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	0.0693853	−	0.997590i	$-0.477896\pi$
$373$	−5473.90	−	3160.36i	−0.759860	−	0.438706i	−0.829246	+	0.558884i	$0.811230\pi$
$374$	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	0.978305	−	0.207170i	$-0.0664254\pi$
$383$	9654.47	+	5574.01i	1.28804	+	0.743652i	0.309738	+	0.950822i	$0.399759\pi$
$384$	−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	0.996715	−	0.0809902i	$-0.0258082\pi$
$389$	3285.41	+	5690.49i	0.428218	+	0.741695i	−0.568497	+	0.822685i	$0.692475\pi$
$390$		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	$0.0807266\pi$
$397$			3969.33i			0.501800i	−0.968013	+	0.250900i	$0.919273\pi$
$398$	−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	−0.969475	−	0.245190i	$-0.921150\pi$
$401$	−2187.35	+	3788.60i	−0.272396	+	0.471804i	0.697079	+	0.716995i	$0.254483\pi$
$402$	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	0.462780	+	0.886473i	$0.346852\pi$
$409$	−4436.16	+	7683.66i	−0.536318	+	0.928930i	−0.999098	+	0.0424573i	$0.986481\pi$
$410$		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	−0.894072	−	0.447923i	$-0.852164\pi$
$419$	−507.087	+	878.300i	−0.0591236	+	0.102405i	0.834949	+	0.550328i	$0.185497\pi$
$420$		0			0
$421$	7446.57	+	12897.8i	0.862051	+	1.49312i	0.869946	+	0.493147i	$0.164154\pi$
$421$	7446.57	+	12897.8i	0.862051	+	1.49312i	−0.00789511	+	0.999969i	$0.502513\pi$
$422$		−	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	$-0.827356\pi$
$433$		−	9301.59i		−	1.03235i	0.856484	−	0.516173i	$-0.172644\pi$
$434$	−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	0.904381	−	0.426727i	$-0.140333\pi$
$439$	760.076	+	1316.49i	0.0826343	+	0.143127i	−0.821746	+	0.569853i	$0.807000\pi$
$440$		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	−0.692712	−	0.721214i	$-0.743584\pi$
$443$	−3864.62	+	2231.24i	−0.414478	+	0.239299i	0.278234	+	0.960513i	$0.410251\pi$
$444$	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	0.384551	−	0.923104i	$-0.374356\pi$
$457$	13445.4	−	7762.71i	1.37626	−	0.794583i	0.991707	+	0.128520i	$0.0410228\pi$
$458$			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	0.867447	−	0.497530i	$-0.165760\pi$
$461$	28.2090	+	48.8594i	0.00284994	+	0.00493624i	−0.864597	+	0.502466i	$0.832426\pi$
$462$	1659.57	+	65.8901i	0.167122	+	0.00663525i
$463$	11582.0	+	6686.89i	1.16255	+	0.671201i	0.951915	−	0.306363i	$-0.0991120\pi$
$463$	11582.0	+	6686.89i	1.16255	+	0.671201i	0.210640	+	0.977564i	$0.432445\pi$
$464$	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	$0.0423496\pi$
$467$			2677.46i			0.265306i	−0.991163	+	0.132653i	$0.957650\pi$
$468$	−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	0.771335	−	0.636429i	$-0.219589\pi$
$479$	−1734.96	−	3005.05i	−0.165496	−	0.286647i	−0.936831	+	0.349782i	$0.886256\pi$
$480$		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	$-0.773416\pi$
$487$		−	14040.6i		−	1.30645i	0.757165	−	0.653224i	$-0.226584\pi$
$488$	−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	−0.998454	−	0.0555902i	$-0.982296\pi$
$491$	−4907.72	+	8500.42i	−0.451084	+	0.781301i	0.547369	+	0.836891i	$0.315629\pi$
$492$	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	0.458267	+	0.888815i	$0.348470\pi$
$499$	−6026.00	+	10437.3i	−0.540603	+	0.936351i	−0.998869	+	0.0475367i	$0.984863\pi$
$500$		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	$0.0667264\pi$
$503$			4695.09i			0.416191i	−0.978109	+	0.208095i	$0.933274\pi$
$504$	−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	−0.883321	−	0.468769i	$-0.844698\pi$
$509$	−409.907	+	709.979i	−0.0356951	+	0.0618257i	0.847626	+	0.530594i	$0.178031\pi$
$510$		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	$0.148629\pi$
$523$			10768.1i			0.900300i	−0.892953	+	0.450150i	$0.851371\pi$
$524$	−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	−0.429037	−	0.903287i	$-0.641147\pi$
$547$	1774.59	−	1024.56i	0.138713	−	0.0800862i	0.567751	+	0.823201i	$0.307814\pi$
$548$		−	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	$0.0442614\pi$
$557$			3644.07i			0.277207i	−0.990348	+	0.138603i	$0.955739\pi$
$558$	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	0.511326	−	0.859387i	$-0.329155\pi$
$563$	303.746	+	175.368i	0.0227378	+	0.0131277i	−0.488588	+	0.872515i	$0.662488\pi$
$564$	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	−0.962394	−	0.271658i	$-0.912428\pi$
$569$	−9724.34	−	16843.1i	−0.716460	−	1.24095i	0.245934	−	0.969287i	$-0.420905\pi$
$570$		0			0
$571$	7572.97	−	13116.8i	0.555024	−	0.961330i	−0.442877	−	0.896582i	$-0.646042\pi$
$571$	7572.97	−	13116.8i	0.555024	−	0.961330i	0.997902	−	0.0647480i	$-0.0206244\pi$
$572$	−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	$-0.926251\pi$
$577$		−	6365.11i		−	0.459243i	0.973280	−	0.229621i	$-0.0737488\pi$
$578$	−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	−0.153046	−	0.988219i	$-0.548908\pi$
$587$	8906.52	−	5142.18i	0.626254	−	0.361568i	0.779300	+	0.626651i	$0.215575\pi$
$588$	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	$-0.992653\pi$
$593$		−	666.566i		−	0.0461595i	0.999734	−	0.0230798i	$-0.00734717\pi$
$594$	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	−0.0120807	−	0.999927i	$-0.503845\pi$
$599$	12606.6	−	21835.3i	0.859922	−	1.48943i	0.872003	−	0.489501i	$-0.162821\pi$
$600$		0			0
$601$	10309.3	+	17856.3i	0.699712	+	1.21194i	0.968566	+	0.248755i	$0.0800215\pi$
$601$	10309.3	+	17856.3i	0.699712	+	1.21194i	−0.268855	+	0.963181i	$0.586645\pi$
$602$		−	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	0.639916	−	0.768444i	$-0.278969\pi$
$607$	4402.45	+	2541.76i	0.294382	+	0.169962i	−0.345534	+	0.938406i	$0.612302\pi$
$608$	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	$-0.972437\pi$
$613$		−	2625.18i		−	0.172969i	0.996253	−	0.0864845i	$-0.0275633\pi$
$614$	−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	0.545382	−	0.838188i	$-0.316385\pi$
$617$	1412.76	+	815.659i	0.0921811	+	0.0532208i	−0.453201	+	0.891408i	$0.649718\pi$
$618$	18089.8	+	718.220i	1.17747	+	0.0467493i
$619$	1592.33	+	2758.00i	0.103395	+	0.179085i	0.913081	−	0.407778i	$-0.133696\pi$
$619$	1592.33	+	2758.00i	0.103395	+	0.179085i	−0.809687	+	0.586863i	$0.800363\pi$
$620$		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	0.691493	−	0.722383i	$-0.256953\pi$
$641$	−4541.73	−	7866.50i	−0.279856	−	0.484724i	−0.971349	+	0.237659i	$0.923620\pi$
$642$	4762.54	+	9061.16i	0.292776	+	0.557034i
$643$	14884.9	+	8593.81i	0.912914	+	0.527071i	0.881368	−	0.472431i	$-0.156623\pi$
$643$	14884.9	+	8593.81i	0.912914	+	0.527071i	0.0315465	+	0.999502i	$0.489957\pi$
$644$	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	$0.0228347\pi$
$647$			2359.17i			0.143352i	−0.997428	+	0.0716758i	$0.977165\pi$
$648$	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	0.634387	−	0.773015i	$-0.281252\pi$
$653$	4707.81	+	2718.06i	0.282130	+	0.162888i	−0.352257	+	0.935903i	$0.614586\pi$
$654$	−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	0.908056	−	0.418848i	$-0.137566\pi$
$659$	1544.45	+	2675.07i	0.0912950	+	0.158128i	−0.816761	+	0.576976i	$0.804233\pi$
$660$		0			0
$661$	9526.94	−	16501.2i	0.560598	−	0.970984i	−0.436846	−	0.899536i	$-0.643905\pi$
$661$	9526.94	−	16501.2i	0.560598	−	0.970984i	0.997444	−	0.0714479i	$-0.0227620\pi$
$662$	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	0.451771	−	0.892134i	$-0.350792\pi$
$673$	25320.4	−	14618.7i	1.45027	−	0.837312i	0.998496	+	0.0548215i	$0.0174590\pi$
$674$	7796.61			0.445570
$675$		0			0
$676$	5663.98			0.322257
$677$	12532.5	−	7235.62i	0.711465	−	0.410764i	−0.100138	−	0.994974i	$-0.531929\pi$
$677$	12532.5	−	7235.62i	0.711465	−	0.410764i	0.811603	+	0.584209i	$0.198595\pi$
$678$	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	$-0.948209\pi$
$683$		−	5782.94i		−	0.323980i	0.986792	−	0.161990i	$-0.0517912\pi$
$684$	−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	0.672797	−	0.739827i	$-0.265093\pi$
$691$	−5527.56	−	9574.01i	−0.304310	−	0.527080i	−0.977107	+	0.212746i	$0.931759\pi$
$692$		−	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	0.714485	−	0.699650i	$-0.246661\pi$
$709$	−4694.58	−	8131.26i	−0.248672	−	0.430713i	−0.963158	+	0.268937i	$0.913328\pi$
$710$		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	−0.943508	−	0.331350i	$-0.892496\pi$
$727$	−22117.1	+	12769.3i	−1.12830	+	0.651427i	−0.184797	+	0.982777i	$0.559163\pi$
$728$		−	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	0.644549	−	0.764563i	$-0.277045\pi$
$733$	6046.70	+	3491.06i	0.304693	+	0.175914i	−0.339856	+	0.940477i	$0.610378\pi$
$734$	−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	−0.970110	−	0.242668i	$-0.921978\pi$
$743$	−33727.3	−	19472.4i	−1.66532	−	0.961473i	−0.695211	−	0.718806i	$-0.744689\pi$
$744$	−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	−0.996637	−	0.0819470i	$-0.973886\pi$
$751$	−8795.16	+	15233.7i	−0.427350	+	0.740192i	0.569287	+	0.822139i	$0.307220\pi$
$752$	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	$-0.968805\pi$
$757$		−	4075.85i		−	0.195693i	0.995202	−	0.0978463i	$-0.0311954\pi$
$758$	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	−0.257171	+	0.966366i	$0.582790\pi$
$761$	−20268.5	+	35106.1i	−0.965483	+	1.67227i	−0.708312	+	0.705899i	$0.750543\pi$
$762$	−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	−0.433704	−	0.901056i	$-0.642794\pi$
$769$	12016.3	−	20812.9i	0.563485	−	0.975985i	0.997189	−	0.0749293i	$-0.0238731\pi$
$770$		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	$0.161474\pi$
$773$			20881.5i			0.971611i	−0.874067	+	0.485805i	$0.838526\pi$
$774$	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	0.597345	−	0.801985i	$-0.296223\pi$
$787$	4448.25	+	2568.20i	0.201478	+	0.116323i	−0.395867	+	0.918308i	$0.629556\pi$
$788$	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	0.0128922	−	0.999917i	$-0.495896\pi$
$797$	−19049.1	−	10998.0i	−0.846615	−	0.488794i	−0.859507	+	0.511123i	$0.829230\pi$
$798$	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	0.901354	−	0.433083i	$-0.142574\pi$
$821$	1778.81	+	3080.99i	0.0756162	+	0.130971i	−0.825738	+	0.564054i	$0.809241\pi$
$822$	−18100.7	+	28661.8i	−0.768049	+	1.21617i
$823$	5325.52	+	3074.69i	0.225560	+	0.130227i	0.608522	−	0.793537i	$-0.291763\pi$
$823$	5325.52	+	3074.69i	0.225560	+	0.130227i	−0.382962	+	0.923764i	$0.625096\pi$
$824$	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	$0.146694\pi$
$827$			21152.8i			0.889425i	−0.895673	+	0.444713i	$0.853306\pi$
$828$	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	0.617986	−	0.786189i	$-0.287949\pi$
$839$	−9037.12	−	15652.8i	−0.371867	−	0.644092i	−0.989853	+	0.142097i	$0.954615\pi$
$840$		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	−0.996126	−	0.0879416i	$-0.971971\pi$
$853$	−35327.2	+	20396.1i	−1.41803	+	0.818699i	−0.421903	+	0.906641i	$0.638638\pi$
$854$	2964.97			0.118805
$855$		0			0
$856$	22033.5			0.879778
$857$	−9576.39	+	5528.93i	−0.381707	+	0.220379i	−0.678561	−	0.734544i	$-0.737396\pi$
$857$	−9576.39	+	5528.93i	−0.381707	+	0.220379i	0.296854	+	0.954923i	$0.404063\pi$
$858$	5713.88	+	10871.2i	0.227353	+	0.432559i
$859$	−876.815	+	1518.69i	−0.0348272	+	0.0603224i	−0.882914	−	0.469535i	$-0.844421\pi$
$859$	−876.815	+	1518.69i	−0.0348272	+	0.0603224i	0.848086	+	0.529858i	$0.177755\pi$
$860$		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	$0.123525\pi$
$863$			19186.5i			0.756796i	−0.925643	+	0.378398i	$0.876475\pi$
$864$	−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	0.635197	−	0.772350i	$-0.280919\pi$
$877$	7373.86	+	4257.30i	0.283920	+	0.163921i	−0.351277	+	0.936272i	$0.614252\pi$
$878$	−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	$-0.787098\pi$
$883$		−	32540.4i		−	1.24017i	0.784533	−	0.620086i	$-0.212902\pi$
$884$	−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	0.464074	−	0.885796i	$-0.346387\pi$
$887$	−1875.90	−	1083.05i	−0.0710106	−	0.0409980i	−0.535085	+	0.844798i	$0.679720\pi$
$888$	−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	−0.511151	−	0.859491i	$-0.670781\pi$
$907$	−611.468	+	353.031i	−0.0223853	+	0.0129241i	0.488766	+	0.872415i	$0.337447\pi$
$908$		−	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	0.870495	−	0.492177i	$-0.163799\pi$
$911$	247.743	+	429.103i	0.00900997	+	0.0156057i	−0.861485	+	0.507783i	$0.830465\pi$
$912$	−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	0.853660	+	0.520831i	$0.174378\pi$
$929$	24857.7	+	43054.7i	0.877883	+	1.52054i	0.0242231	+	0.999707i	$0.492289\pi$
$930$		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	$-0.814796\pi$
$937$		−	31524.9i		−	1.09912i	0.835454	−	0.549560i	$-0.185204\pi$
$938$	−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	0.333060	+	0.942905i	$0.391919\pi$
$941$	−18764.2	+	32500.6i	−0.650050	+	1.12592i	−0.983110	+	0.183014i	$0.941415\pi$
$942$	−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	−0.0637862	−	0.997964i	$-0.520318\pi$
$947$	22398.3	−	12931.7i	0.768582	−	0.443741i	0.832369	+	0.554222i	$0.186984\pi$
$948$	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	$-0.994265\pi$
$953$		−	1060.03i		−	0.0360312i	0.999838	−	0.0180156i	$-0.00573485\pi$
$954$	−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	0.572802	−	0.819694i	$-0.305856\pi$
$967$	4490.35	+	2592.51i	0.149328	+	0.0862145i	−0.423474	+	0.905908i	$0.639190\pi$
$968$	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	−0.297626	−	0.954683i	$-0.596195\pi$
$977$	−38881.6	−	22448.3i	−1.27322	−	0.735093i	−0.975592	+	0.219590i	$0.929528\pi$
$978$	−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	−0.281081	−	0.959684i	$-0.590693\pi$
$983$	12620.4	−	7286.40i	0.409490	−	0.236419i	0.690571	+	0.723265i	$0.257360\pi$
$984$	−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	−0.0645202	−	0.997916i	$-0.520552\pi$
$997$	24159.5	−	13948.5i	0.767441	−	0.443082i	0.831961	+	0.554834i	$0.187218\pi$
$998$		−	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.49.5		28
5.2	odd	4		225.4.e.d.76.3		14
5.3	odd	4		45.4.e.c.31.5	yes	14
5.4	even	2	inner	225.4.k.d.49.10		28
9.7	even	3	inner	225.4.k.d.124.10		28
15.8	even	4		135.4.e.c.91.3		14
45.7	odd	12		225.4.e.d.151.3		14
45.13	odd	12		405.4.a.m.1.3		7
45.22	odd	12		2025.4.a.bb.1.5		7
45.23	even	12		405.4.a.n.1.5		7
45.32	even	12		2025.4.a.ba.1.3		7
45.34	even	6	inner	225.4.k.d.124.5		28
45.38	even	12		135.4.e.c.46.3		14
45.43	odd	12		45.4.e.c.16.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.5	✓	14	45.43	odd	12
45.4.e.c.31.5	yes	14	5.3	odd	4
135.4.e.c.46.3		14	45.38	even	12
135.4.e.c.91.3		14	15.8	even	4
225.4.e.d.76.3		14	5.2	odd	4
225.4.e.d.151.3		14	45.7	odd	12
225.4.k.d.49.5		28	1.1	even	1	trivial
225.4.k.d.49.10		28	5.4	even	2	inner
225.4.k.d.124.5		28	45.34	even	6	inner
225.4.k.d.124.10		28	9.7	even	3	inner
405.4.a.m.1.3		7	45.13	odd	12
405.4.a.n.1.5		7	45.23	even	12
2025.4.a.ba.1.3		7	45.32	even	12
2025.4.a.bb.1.5		7	45.22	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.90044 + 1.09722i) q^{2} +(-5.19206 - 0.206141i) q^{3} +(-1.59221 + 2.75778i) q^{4} +(10.0934 - 5.30509i) q^{6} +(2.39547 - 1.38302i) q^{7} -24.5436i q^{8} +(26.9150 + 2.14059i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) \) 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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