LMFDB - Embedded newform 225.4.k.d.49.12

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			49.12
Character	$\chi$	$=$	225.49
Dual form			225.4.k.d.124.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.69081 - 2.13089i) q^{2} +(-2.76977 + 4.39640i) q^{3} +(5.08138 - 8.80120i) q^{4} +(-0.854448 + 22.1284i) q^{6} +(-26.6423 + 15.3820i) q^{7} -9.21718i q^{8} +(-11.6567 - 24.3541i) q^{9} +O(q^{10})$	\(q+(3.69081 - 2.13089i) q^{2} +(-2.76977 + 4.39640i) q^{3} +(5.08138 - 8.80120i) q^{4} +(-0.854448 + 22.1284i) q^{6} +(-26.6423 + 15.3820i) q^{7} -9.21718i q^{8} +(-11.6567 - 24.3541i) q^{9} +(-20.3573 - 35.2599i) q^{11} +(24.6194 + 46.7171i) q^{12} +(-54.7482 - 31.6089i) q^{13} +(-65.5545 + 113.544i) q^{14} +(21.0102 + 36.3908i) q^{16} +6.58990i q^{17} +(-94.9186 - 65.0470i) q^{18} -75.3803 q^{19} +(6.16789 - 159.735i) q^{21} +(-150.270 - 86.7584i) q^{22} +(54.0077 + 31.1814i) q^{23} +(40.5225 + 25.5295i) q^{24} -269.420 q^{26} +(139.357 + 16.2075i) q^{27} +312.646i q^{28} +(24.8042 + 42.9621i) q^{29} +(-51.5021 + 89.2043i) q^{31} +(218.948 + 126.410i) q^{32} +(211.402 + 8.16291i) q^{33} +(14.0423 + 24.3221i) q^{34} +(-273.577 - 21.1590i) q^{36} +282.029i q^{37} +(-278.214 + 160.627i) q^{38} +(290.606 - 153.146i) q^{39} +(78.7700 - 136.434i) q^{41} +(-317.613 - 602.695i) q^{42} +(-292.555 + 168.907i) q^{43} -413.773 q^{44} +265.776 q^{46} +(-38.5518 + 22.2579i) q^{47} +(-218.182 - 8.42472i) q^{48} +(301.710 - 522.577i) q^{49} +(-28.9719 - 18.2525i) q^{51} +(-556.393 + 321.234i) q^{52} +26.2752i q^{53} +(548.876 - 237.135i) q^{54} +(141.778 + 245.567i) q^{56} +(208.786 - 331.402i) q^{57} +(183.095 + 105.710i) q^{58} +(-212.963 + 368.863i) q^{59} +(-425.297 - 736.637i) q^{61} +438.981i q^{62} +(685.176 + 469.546i) q^{63} +741.296 q^{64} +(797.638 - 420.346i) q^{66} +(83.4048 + 48.1538i) q^{67} +(57.9990 + 33.4858i) q^{68} +(-286.675 + 151.075i) q^{69} +952.164 q^{71} +(-224.476 + 107.442i) q^{72} -50.8558i q^{73} +(600.973 + 1040.92i) q^{74} +(-383.036 + 663.437i) q^{76} +(1084.73 + 626.271i) q^{77} +(746.233 - 1184.48i) q^{78} +(-98.6395 - 170.849i) q^{79} +(-457.241 + 567.778i) q^{81} -671.400i q^{82} +(-171.247 + 98.8693i) q^{83} +(-1374.52 - 865.959i) q^{84} +(-719.844 + 1246.81i) q^{86} +(-257.581 - 9.94603i) q^{87} +(-324.997 + 187.637i) q^{88} -1364.54 q^{89} +1944.83 q^{91} +(548.868 - 316.889i) q^{92} +(-249.529 - 473.499i) q^{93} +(-94.8583 + 164.299i) q^{94} +(-1162.18 + 612.458i) q^{96} +(1239.42 - 715.579i) q^{97} -2571.64i q^{98} +(-621.422 + 906.799i) 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 $

$2$	3.69081	−	2.13089i	1.30490	−	0.753383i	0.323658	−	0.946174i	$-0.395087\pi$
$2$	3.69081	−	2.13089i	1.30490	−	0.753383i	0.981240	+	0.192791i	$0.0617539\pi$
$3$	−2.76977	+	4.39640i	−0.533043	+	0.846088i
$3$	−2.76977	+	4.39640i	−0.533043	+	0.846088i
$4$	5.08138	−	8.80120i	0.635172	−	1.10015i
$5$		0			0
$5$		0			0
$6$	−0.854448	+	22.1284i	−0.0581378	+	1.50564i
$7$	−26.6423	+	15.3820i	−1.43855	+	0.830548i	−0.997749	−	0.0670561i	$-0.978639\pi$
$7$	−26.6423	+	15.3820i	−1.43855	+	0.830548i	−0.440802	+	0.897604i	$0.645306\pi$
$8$		−	9.21718i		−	0.407346i
$9$	−11.6567	−	24.3541i	−0.431731	−	0.902003i
$10$		0			0
$11$	−20.3573	−	35.2599i	−0.557996	−	0.966478i	−0.997664	−	0.0683175i	$-0.978237\pi$
$11$	−20.3573	−	35.2599i	−0.557996	−	0.966478i	0.439667	−	0.898161i	$-0.355096\pi$
$12$	24.6194	+	46.7171i	0.592250	+	1.12384i
$13$	−54.7482	−	31.6089i	−1.16803	−	0.674364i	−0.214817	−	0.976654i	$-0.568915\pi$
$13$	−54.7482	−	31.6089i	−1.16803	−	0.674364i	−0.953216	+	0.302290i	$0.902249\pi$
$14$	−65.5545	+	113.544i	−1.25144	+	2.16756i
$15$		0			0
$16$	21.0102	+	36.3908i	0.328285	+	0.568606i
$17$			6.58990i			0.0940168i	0.998894	+	0.0470084i	$0.0149687\pi$
$17$			6.58990i			0.0940168i	−0.998894	+	0.0470084i	$0.985031\pi$
$18$	−94.9186	−	65.0470i	−1.24292	−	0.851763i
$19$	−75.3803			−0.910180			−0.455090	−	0.890445i	$-0.650393\pi$
$19$	−75.3803			−0.910180			−0.455090	+	0.890445i	$0.650393\pi$
$20$		0			0
$21$	6.16789	−	159.735i	0.0640926	−	1.65986i
$22$	−150.270	−	86.7584i	−1.45626	−	0.840770i
$23$	54.0077	+	31.1814i	0.489626	+	0.282686i	0.724419	−	0.689360i	$-0.242108\pi$
$23$	54.0077	+	31.1814i	0.489626	+	0.282686i	−0.234793	+	0.972045i	$0.575441\pi$
$24$	40.5225	+	25.5295i	0.344651	+	0.217133i
$25$		0			0
$26$	−269.420			−2.03222
$27$	139.357	+	16.2075i	0.993305	+	0.115524i
$28$			312.646i			2.11016i
$29$	24.8042	+	42.9621i	0.158828	+	0.275099i	0.934446	−	0.356104i	$-0.115895\pi$
$29$	24.8042	+	42.9621i	0.158828	+	0.275099i	−0.775618	+	0.631202i	$0.782562\pi$
$30$		0			0
$31$	−51.5021	+	89.2043i	−0.298389	+	0.516824i	−0.975767	−	0.218810i	$-0.929783\pi$
$31$	−51.5021	+	89.2043i	−0.298389	+	0.516824i	0.677379	+	0.735634i	$0.263116\pi$
$32$	218.948	+	126.410i	1.20953	+	0.698321i
$33$	211.402	+	8.16291i	1.11516	+	0.0430600i
$34$	14.0423	+	24.3221i	0.0708306	+	0.122682i
$35$		0			0
$36$	−273.577	−	21.1590i	−1.26656	−	0.0979582i
$37$			282.029i			1.25312i	0.779374	+	0.626559i	$0.215537\pi$
$37$			282.029i			1.25312i	−0.779374	+	0.626559i	$0.784463\pi$
$38$	−278.214	+	160.627i	−1.18769	+	0.685714i
$39$	290.606	−	153.146i	1.19318	−	0.628794i
$40$		0			0
$41$	78.7700	−	136.434i	0.300044	−	0.519692i	−0.676102	−	0.736808i	$-0.736332\pi$
$41$	78.7700	−	136.434i	0.300044	−	0.519692i	0.976146	+	0.217117i	$0.0696653\pi$
$42$	−317.613	−	602.695i	−1.16688	−	2.21423i
$43$	−292.555	+	168.907i	−1.03754	+	0.599025i	−0.919136	−	0.393940i	$-0.871112\pi$
$43$	−292.555	+	168.907i	−1.03754	+	0.599025i	−0.118406	+	0.992965i	$0.537778\pi$
$44$	−413.773			−1.41770
$45$		0			0
$46$	265.776			0.851882
$47$	−38.5518	+	22.2579i	−0.119646	+	0.0690777i	−0.558629	−	0.829418i	$-0.688672\pi$
$47$	−38.5518	+	22.2579i	−0.119646	+	0.0690777i	0.438983	+	0.898496i	$0.355339\pi$
$48$	−218.182	−	8.42472i	−0.656081	−	0.0253334i
$49$	301.710	−	522.577i	0.879620	−	1.52355i
$50$		0			0
$51$	−28.9719	−	18.2525i	−0.0795465	−	0.0501150i
$52$	−556.393	+	321.234i	−1.48380	+	0.856675i
$53$			26.2752i			0.0680978i	0.999420	+	0.0340489i	$0.0108402\pi$
$53$			26.2752i			0.0680978i	−0.999420	+	0.0340489i	$0.989160\pi$
$54$	548.876	−	237.135i	1.38319	−	0.597592i
$55$		0			0
$56$	141.778	+	245.567i	0.338320	+	0.585988i
$57$	208.786	−	331.402i	0.485165	−	0.770093i
$58$	183.095	+	105.710i	0.414509	+	0.239317i
$59$	−212.963	+	368.863i	−0.469923	+	0.813930i	−0.999409	−	0.0343889i	$-0.989052\pi$
$59$	−212.963	+	368.863i	−0.469923	+	0.813930i	0.529486	+	0.848319i	$0.322385\pi$
$60$		0			0
$61$	−425.297	−	736.637i	−0.892684	−	1.54617i	−0.836644	−	0.547746i	$-0.815486\pi$
$61$	−425.297	−	736.637i	−0.892684	−	1.54617i	−0.0560400	−	0.998429i	$-0.517847\pi$
$62$			438.981i			0.899204i
$63$	685.176	+	469.546i	1.37022	+	0.939004i
$64$	741.296			1.44784
$65$		0			0
$66$	797.638	−	420.346i	1.48761	−	0.783955i
$67$	83.4048	+	48.1538i	0.152082	+	0.0878048i	0.574110	−	0.818778i	$-0.305348\pi$
$67$	83.4048	+	48.1538i	0.152082	+	0.0878048i	−0.422028	+	0.906583i	$0.638681\pi$
$68$	57.9990	+	33.4858i	0.103433	+	0.0597168i
$69$	−286.675	+	151.075i	−0.500169	+	0.263583i
$70$		0			0
$71$	952.164			1.59156			0.795782	−	0.605583i	$-0.207060\pi$
$71$	952.164			1.59156			0.795782	+	0.605583i	$0.207060\pi$
$72$	−224.476	+	107.442i	−0.367427	+	0.175864i
$73$		−	50.8558i		−	0.0815373i	−0.999169	−	0.0407686i	$-0.987019\pi$
$73$		−	50.8558i		−	0.0815373i	0.999169	−	0.0407686i	$-0.0129807\pi$
$74$	600.973	+	1040.92i	0.944077	+	1.63519i
$75$		0			0
$76$	−383.036	+	663.437i	−0.578121	+	1.00134i
$77$	1084.73	+	626.271i	1.60541	+	0.926886i
$78$	746.233	−	1184.48i	1.08326	−	1.71944i
$79$	−98.6395	−	170.849i	−0.140479	−	0.243316i	0.787198	−	0.616700i	$-0.211531\pi$
$79$	−98.6395	−	170.849i	−0.140479	−	0.243316i	−0.927677	+	0.373384i	$0.878197\pi$
$80$		0			0
$81$	−457.241	+	567.778i	−0.627217	+	0.778844i
$82$		−	671.400i		−	0.904192i
$83$	−171.247	+	98.8693i	−0.226467	+	0.130751i	−0.608941	−	0.793215i	$-0.708405\pi$
$83$	−171.247	+	98.8693i	−0.226467	+	0.130751i	0.382474	+	0.923966i	$0.375072\pi$
$84$	−1374.52	−	865.959i	−1.78539	−	1.12481i
$85$		0			0
$86$	−719.844	+	1246.81i	−0.902590	+	1.56333i
$87$	−257.581	−	9.94603i	−0.317420	−	0.0122566i
$88$	−324.997	+	187.637i	−0.393691	+	0.227298i
$89$	−1364.54			−1.62519			−0.812593	−	0.582832i	$-0.801944\pi$
$89$	−1364.54			−1.62519			−0.812593	+	0.582832i	$0.801944\pi$
$90$		0			0
$91$	1944.83			2.24037
$92$	548.868	−	316.889i	0.621993	−	0.359108i
$93$	−249.529	−	473.499i	−0.278225	−	0.527953i
$94$	−94.8583	+	164.299i	−0.104084	+	0.180279i
$95$		0			0
$96$	−1162.18	+	612.458i	−1.23557	+	0.651132i
$97$	1239.42	−	715.579i	1.29736	−	0.749031i	0.317413	−	0.948288i	$-0.397186\pi$
$97$	1239.42	−	715.579i	1.29736	−	0.749031i	0.979947	+	0.199256i	$0.0638527\pi$
$98$		−	2571.64i		−	2.65076i
$99$	−621.422	+	906.799i	−0.630862	+	0.920573i
$100$		0			0
$101$	−553.808	−	959.224i	−0.545604	−	0.945013i	−0.998569	−	0.0534851i	$-0.982967\pi$
$101$	−553.808	−	959.224i	−0.545604	−	0.945013i	0.452965	−	0.891528i	$-0.350366\pi$
$102$	−145.824	−	5.63073i	−0.141556	−	0.00546593i
$103$	−458.018	−	264.437i	−0.438154	−	0.252969i	0.264660	−	0.964342i	$-0.414740\pi$
$103$	−458.018	−	264.437i	−0.438154	−	0.252969i	−0.702814	+	0.711373i	$0.748074\pi$
$104$	−291.345	+	504.624i	−0.274699	+	0.475793i
$105$		0			0
$106$	55.9896	+	96.9769i	0.0513037	+	0.0888607i
$107$		−	490.910i		−	0.443533i	−0.975100	−	0.221766i	$-0.928818\pi$
$107$		−	490.910i		−	0.443533i	0.975100	−	0.221766i	$-0.0711823\pi$
$108$	850.770	−	1144.15i	0.758013	−	1.01941i
$109$	351.634			0.308994			0.154497	−	0.987993i	$-0.450624\pi$
$109$	351.634			0.308994			0.154497	+	0.987993i	$0.450624\pi$
$110$		0			0
$111$	−1239.91	−	781.157i	−1.06025	−	0.667965i
$112$	−1119.52	−	646.357i	−0.944509	−	0.545313i
$113$	−1526.33	−	881.226i	−1.27066	−	0.733618i	−0.295550	−	0.955327i	$-0.595503\pi$
$113$	−1526.33	−	881.226i	−1.27066	−	0.733618i	−0.975113	+	0.221710i	$0.928836\pi$
$114$	64.4085	−	1668.04i	0.0529159	−	1.37041i
$115$		0			0
$116$	504.158			0.403533
$117$	−131.620	+	1701.80i	−0.104002	+	1.34471i
$118$			1815.20i			1.41613i
$119$	−101.366	−	175.570i	−0.0780854	−	0.135248i
$120$		0			0
$121$	−163.340	+	282.914i	−0.122720	+	0.212557i
$122$	−3139.38	−	1812.52i	−2.32972	−	1.34507i
$123$	381.642	+	724.195i	0.279769	+	0.530882i
$124$	523.403	+	906.561i	0.379056	+	0.656545i
$125$		0			0
$126$	3529.40	+	272.971i	2.49543	+	0.193001i
$127$			1506.12i			1.05234i	0.850380	+	0.526169i	$0.176372\pi$
$127$			1506.12i			1.05234i	−0.850380	+	0.526169i	$0.823628\pi$
$128$	984.399	−	568.343i	0.679761	−	0.392460i
$129$	67.7286	−	1754.03i	0.0462262	−	1.19716i
$130$		0			0
$131$	−637.562	+	1104.29i	−0.425222	+	0.736506i	−0.996441	−	0.0842915i	$-0.973137\pi$
$131$	−637.562	+	1104.29i	−0.425222	+	0.736506i	0.571219	+	0.820798i	$0.306471\pi$
$132$	1146.06	−	1819.11i	0.755692	−	1.19950i
$133$	2008.31	−	1159.50i	1.30934	−	0.755948i
$134$	410.441			0.264603
$135$		0			0
$136$	60.7403			0.0382973
$137$	−1246.58	+	719.712i	−0.777389	+	0.448826i	−0.835504	−	0.549484i	$-0.814824\pi$
$137$	−1246.58	+	719.712i	−0.777389	+	0.448826i	0.0581150	+	0.998310i	$0.481491\pi$
$138$	−736.140	+	1168.46i	−0.454090	+	0.720768i
$139$	−1269.75	+	2199.27i	−0.774811	+	1.34201i	0.160090	+	0.987102i	$0.448822\pi$
$139$	−1269.75	+	2199.27i	−0.774811	+	1.34201i	−0.934901	+	0.354909i	$0.884512\pi$
$140$		0			0
$141$	8.92502	−	231.139i	0.00533065	−	0.138052i
$142$	3514.25	−	2028.96i	2.07683	−	1.19906i
$143$			2573.89i			1.50517i
$144$	641.353	−	935.882i	0.371153	−	0.541598i
$145$		0			0
$146$	−108.368	−	187.699i	−0.0614288	−	0.106398i
$147$	1461.79	+	2773.86i	0.820180	+	1.55635i
$148$	2482.20	+	1433.10i	1.37862	+	0.795945i
$149$	46.8796	−	81.1979i	0.0257754	−	0.0446442i	−0.852850	−	0.522156i	$-0.825128\pi$
$149$	46.8796	−	81.1979i	0.0257754	−	0.0446442i	0.878625	+	0.477512i	$0.158461\pi$
$150$		0			0
$151$	534.065	+	925.027i	0.287825	+	0.498527i	0.973290	−	0.229578i	$-0.0737345\pi$
$151$	534.065	+	925.027i	0.287825	+	0.498527i	−0.685465	+	0.728105i	$0.740401\pi$
$152$			694.794i			0.370758i
$153$	160.491	−	76.8166i	0.0848034	−	0.0405899i
$154$	5338.06			2.79320
$155$		0			0
$156$	128.809	−	3335.87i	0.0661087	−	1.71207i
$157$	157.370	+	90.8574i	0.0799966	+	0.0461861i	0.539465	−	0.842008i	$-0.318627\pi$
$157$	157.370	+	90.8574i	0.0799966	+	0.0461861i	−0.459468	+	0.888194i	$0.651960\pi$
$158$	−728.119	−	420.380i	−0.366621	−	0.211668i
$159$	−115.517	−	72.7764i	−0.0576167	−	0.0362990i
$160$		0			0
$161$	−1918.52			−0.939136
$162$	−477.719	+	3069.89i	−0.231686	+	1.48885i
$163$		−	1103.07i		−	0.530056i	−0.964241	−	0.265028i	$-0.914619\pi$
$163$		−	1103.07i		−	0.530056i	0.964241	−	0.265028i	$-0.0853813\pi$
$164$	−800.520	−	1386.54i	−0.381159	−	0.660187i
$165$		0			0
$166$	−421.359	+	729.816i	−0.197011	+	0.341233i
$167$	−3500.22	−	2020.85i	−1.62189	−	0.936396i	−0.986415	−	0.164270i	$-0.947473\pi$
$167$	−3500.22	−	2020.85i	−1.62189	−	0.936396i	−0.635470	−	0.772126i	$-0.719194\pi$
$168$	−1472.31	−	56.8506i	−0.676137	−	0.0261078i
$169$	899.745	+	1558.40i	0.409534	+	0.709333i
$170$		0			0
$171$	878.687	+	1835.82i	0.392953	+	0.820985i
$172$			3433.12i			1.52194i
$173$	−2379.63	+	1373.88i	−1.04578	+	0.603780i	−0.921465	−	0.388463i	$-0.873006\pi$
$173$	−2379.63	+	1373.88i	−1.04578	+	0.603780i	−0.124314	+	0.992243i	$0.539673\pi$
$174$	−971.875	+	512.167i	−0.423435	+	0.223145i
$175$		0			0
$176$	855.423	−	1481.64i	0.366363	−	0.634560i
$177$	−1031.81	−	1957.94i	−0.438168	−	0.831456i
$178$	−5036.27	+	2907.69i	−2.12070	+	1.22439i
$179$	2838.32			1.18517			0.592587	−	0.805506i	$-0.298107\pi$
$179$	2838.32			1.18517			0.592587	+	0.805506i	$0.298107\pi$
$180$		0			0
$181$	3442.25			1.41359			0.706796	−	0.707417i	$-0.250140\pi$
$181$	3442.25			1.41359			0.706796	+	0.707417i	$0.250140\pi$
$182$	7177.99	−	4144.21i	2.92345	−	1.68785i
$183$	4416.53	+	170.537i	1.78404	+	0.0688876i
$184$	287.405	−	497.799i	0.115151	−	0.199447i
$185$		0			0
$186$	−1929.94	−	1215.88i	−0.760806	−	0.479314i
$187$	232.359	−	134.153i	0.0908652	−	0.0524610i
$188$			452.403i			0.175505i
$189$	−3962.10	+	1711.77i	−1.52487	+	0.658801i
$190$		0			0
$191$	373.148	+	646.311i	0.141361	+	0.244845i	0.928010	−	0.372557i	$-0.121519\pi$
$191$	373.148	+	646.311i	0.141361	+	0.244845i	−0.786648	+	0.617402i	$0.788185\pi$
$192$	−2053.22	+	3259.04i	−0.771763	+	1.22500i
$193$	−93.4506	−	53.9538i	−0.0348535	−	0.0201227i	0.482472	−	0.875911i	$-0.339739\pi$
$193$	−93.4506	−	53.9538i	−0.0348535	−	0.0201227i	−0.517326	+	0.855789i	$0.673072\pi$
$194$	3049.64	−	5282.13i	1.12861	−	1.95482i
$195$		0			0
$196$	−3066.20	−	5310.82i	−1.11742	−	1.93543i
$197$			3361.02i			1.21555i	0.794110	+	0.607774i	$0.207937\pi$
$197$			3361.02i			1.21555i	−0.794110	+	0.607774i	$0.792063\pi$
$198$	−361.264	+	4671.00i	−0.129666	+	1.67653i
$199$	−1368.99			−0.487663			−0.243831	−	0.969818i	$-0.578404\pi$
$199$	−1368.99			−0.487663			−0.243831	+	0.969818i	$0.578404\pi$
$200$		0			0
$201$	−442.716	+	233.306i	−0.155357	+	0.0818714i
$202$	−4088.00	−	2360.21i	−1.42391	−	0.822097i
$203$	−1321.68	−	763.074i	−0.456965	−	0.263829i
$204$	−307.861	+	162.239i	−0.105660	+	0.0556815i
$205$		0			0
$206$	−2253.94			−0.762329
$207$	129.840	−	1678.78i	0.0435966	−	0.563688i
$208$		−	2656.44i		−	0.885534i
$209$	1534.54	+	2657.90i	0.507877	+	0.879669i
$210$		0			0
$211$	−1251.27	+	2167.27i	−0.408252	+	0.707114i	−0.994694	−	0.102878i	$-0.967195\pi$
$211$	−1251.27	+	2167.27i	−0.408252	+	0.707114i	0.586442	+	0.809991i	$0.300528\pi$
$212$	231.254	+	133.514i	0.0749178	+	0.0432538i
$213$	−2637.28	+	4186.10i	−0.848372	+	1.34660i
$214$	−1046.07	−	1811.85i	−0.334150	−	0.578765i
$215$		0			0
$216$	149.388	−	1284.48i	0.0470581	−	0.404619i
$217$		−	3168.81i		−	0.991305i
$218$	1297.81	−	749.292i	0.403206	−	0.232791i
$219$	223.583	+	140.859i	0.0689877	+	0.0434629i
$220$		0			0
$221$	208.299	−	360.785i	0.0634015	−	0.109815i
$222$	−6240.85	−	240.979i	−1.88675	−	0.0728535i
$223$	1623.39	−	937.263i	0.487489	−	0.281452i	−0.236043	−	0.971743i	$-0.575851\pi$
$223$	1623.39	−	937.263i	0.487489	−	0.281452i	0.723532	+	0.690291i	$0.242517\pi$
$224$	−7777.72			−2.31996
$225$		0			0
$226$	−7511.18			−2.21078
$227$	−4398.32	+	2539.37i	−1.28602	+	0.742484i	−0.977942	−	0.208877i	$-0.933019\pi$
$227$	−4398.32	+	2539.37i	−1.28602	+	0.742484i	−0.308078	+	0.951361i	$0.599686\pi$
$228$	−1855.82	−	3521.55i	−0.539055	−	1.02290i
$229$	432.933	−	749.861i	0.124930	−	0.216385i	−0.796776	−	0.604275i	$-0.793463\pi$
$229$	432.933	−	749.861i	0.124930	−	0.216385i	0.921706	+	0.387890i	$0.126796\pi$
$230$		0			0
$231$	−5757.80	+	3034.30i	−1.63998	+	0.864252i
$232$	395.990	−	228.625i	0.112060	−	0.0646981i
$233$			1142.10i			0.321122i	0.987026	+	0.160561i	$0.0513304\pi$
$233$			1142.10i			0.321122i	−0.987026	+	0.160561i	$0.948670\pi$
$234$	3140.56	+	6561.48i	0.877371	+	1.83307i
$235$		0			0
$236$	2164.29	+	3748.66i	0.596964	+	1.03397i
$237$	1024.33	+	39.5527i	0.280748	+	0.0108406i
$238$	−748.242	−	431.998i	−0.203787	−	0.117657i
$239$	−1574.68	+	2727.43i	−0.426183	+	0.738171i	−0.996530	−	0.0832330i	$-0.973475\pi$
$239$	−1574.68	+	2727.43i	−0.426183	+	0.738171i	0.570347	+	0.821404i	$0.306809\pi$
$240$		0			0
$241$	−2252.18	−	3900.90i	−0.601975	−	1.04265i	−0.992522	−	0.122068i	$-0.961047\pi$
$241$	−2252.18	−	3900.90i	−0.601975	−	1.04265i	0.390547	−	0.920583i	$-0.372286\pi$
$242$			1392.24i			0.369821i
$243$	−1229.72	−	3582.83i	−0.324637	−	0.945839i
$244$	−8644.39			−2.26803
$245$		0			0
$246$	2951.75	+	1859.63i	0.765027	+	0.481973i
$247$	4126.94	+	2382.69i	1.06312	+	0.613793i
$248$	822.212	+	474.704i	0.210526	+	0.121547i
$249$	39.6448	−	1026.72i	0.0100899	−	0.261307i
$250$		0			0
$251$	886.861			0.223021			0.111510	−	0.993763i	$-0.464431\pi$
$251$	886.861			0.223021			0.111510	+	0.993763i	$0.464431\pi$
$252$	7614.21	−	3644.43i	1.90337	−	0.911023i
$253$		−	2539.08i		−	0.630950i
$254$	3209.38	+	5558.81i	0.792813	+	1.37319i
$255$		0			0
$256$	−543.033	+	940.561i	−0.132576	+	0.229629i
$257$	1958.98	+	1131.02i	0.475478	+	0.274517i	0.718530	−	0.695496i	$-0.244815\pi$
$257$	1958.98	+	1131.02i	0.475478	+	0.274517i	−0.243052	+	0.970013i	$0.578149\pi$
$258$	−3487.66	−	6618.09i	−0.841598	−	1.59699i
$259$	−4338.17	−	7513.92i	−1.04077	−	1.80267i
$260$		0			0
$261$	757.166	−	1104.88i	0.179569	−	0.262032i
$262$			5434.30i			1.28142i
$263$	6305.20	−	3640.31i	1.47831	−	0.853503i	0.478611	−	0.878027i	$-0.341141\pi$
$263$	6305.20	−	3640.31i	1.47831	−	0.853503i	0.999699	+	0.0245245i	$0.00780717\pi$
$264$	75.2391	−	1948.53i	0.0175403	−	0.454257i
$265$		0			0
$266$	4941.52	−	8558.96i	1.13904	−	1.97287i
$267$	3779.48	−	5999.09i	0.866293	−	1.37505i
$268$	847.622	−	489.375i	0.193197	−	0.111542i
$269$	106.781			0.0242028			0.0121014	−	0.999927i	$-0.496148\pi$
$269$	106.781			0.0242028			0.0121014	+	0.999927i	$0.496148\pi$
$270$		0			0
$271$	5908.85			1.32449			0.662246	−	0.749287i	$-0.269603\pi$
$271$	5908.85			1.32449			0.662246	+	0.749287i	$0.269603\pi$
$272$	−239.811	+	138.455i	−0.0534585	+	0.0308643i
$273$	−5386.73	+	8550.25i	−1.19421	+	1.89555i
$274$	−3067.25	+	5312.64i	−0.676276	+	1.17134i
$275$		0			0
$276$	−127.067	+	3290.75i	−0.0277120	+	0.717681i
$277$	−2849.30	+	1645.04i	−0.618042	+	0.356827i	−0.776106	−	0.630602i	$-0.782808\pi$
$277$	−2849.30	+	1645.04i	−0.618042	+	0.356827i	0.158064	+	0.987429i	$0.449475\pi$
$278$			10822.8i			2.33492i
$279$	2772.83	+	214.456i	0.595000	+	0.0460184i
$280$		0			0
$281$	−169.861	−	294.209i	−0.0360608	−	0.0624591i	0.847432	−	0.530904i	$-0.178148\pi$
$281$	−169.861	−	294.209i	−0.0360608	−	0.0624591i	−0.883493	+	0.468445i	$0.844814\pi$
$282$	−459.590	−	872.107i	−0.0970504	−	0.184160i
$283$	−2251.37	−	1299.83i	−0.472898	−	0.273028i	0.244554	−	0.969636i	$-0.421358\pi$
$283$	−2251.37	−	1299.83i	−0.472898	−	0.273028i	−0.717452	+	0.696608i	$0.754692\pi$
$284$	4838.30	−	8380.19i	1.01092	−	1.75096i
$285$		0			0
$286$	5484.67	+	9499.73i	1.13397	+	1.96409i
$287$			4846.55i			0.996804i
$288$	526.373	−	6805.80i	0.107697	−	1.39248i
$289$	4869.57			0.991161
$290$		0			0
$291$	−286.934	+	7430.98i	−0.0578020	+	1.49695i
$292$	−447.592	−	258.418i	−0.0897033	−	0.0517902i
$293$	−154.227	−	89.0427i	−0.0307509	−	0.0177540i	0.484546	−	0.874766i	$-0.338985\pi$
$293$	−154.227	−	89.0427i	−0.0307509	−	0.0177540i	−0.515297	+	0.857012i	$0.672318\pi$
$294$	11306.0	+	7122.86i	2.24278	+	1.41297i
$295$		0			0
$296$	2599.52			0.510452
$297$	−2265.45	−	5243.65i	−0.442609	−	1.02447i
$298$		−	399.581i		−	0.0776749i
$299$	−1971.22	−	3414.25i	−0.381266	−	0.660372i
$300$		0			0
$301$	5196.24	−	9000.16i	0.995038	−	1.72346i
$302$	3942.26	+	2276.07i	0.751164	+	0.433685i
$303$	5751.06	+	222.067i	1.09039	+	0.0421037i
$304$	−1583.76	−	2743.15i	−0.298798	−	0.517534i
$305$		0			0
$306$	428.653	−	625.504i	0.0800800	−	0.116855i
$307$		−	1537.60i		−	0.285848i	−0.989734	−	0.142924i	$-0.954349\pi$
$307$		−	1537.60i		−	0.285848i	0.989734	−	0.142924i	$-0.0456505\pi$
$308$	11023.9	−	6364.64i	2.03943	−	1.17746i
$309$	2431.18	−	1281.20i	0.447589	−	0.235874i
$310$		0			0
$311$	−472.662	+	818.674i	−0.0861807	+	0.149269i	−0.905894	−	0.423505i	$-0.860800\pi$
$311$	−472.662	+	818.674i	−0.0861807	+	0.149269i	0.819713	+	0.572774i	$0.194133\pi$
$312$	−1411.57	−	2678.57i	−0.256137	−	0.486038i
$313$	1719.52	−	992.767i	0.310521	−	0.179280i	−0.336638	−	0.941634i	$-0.609290\pi$
$313$	1719.52	−	992.767i	0.310521	−	0.179280i	0.647160	+	0.762354i	$0.275957\pi$
$314$	774.428			0.139183
$315$		0			0
$316$	−2004.90			−0.356913
$317$	4488.81	−	2591.62i	0.795321	−	0.459179i	−0.0465112	−	0.998918i	$-0.514810\pi$
$317$	4488.81	−	2591.62i	0.795321	−	0.459179i	0.841833	+	0.539739i	$0.181477\pi$
$318$	−581.428	−	22.4508i	−0.102531	−	0.00395906i
$319$	1009.89	−	1749.19i	0.177251	−	0.307008i
$320$		0			0
$321$	2158.24	+	1359.71i	0.375268	+	0.236422i
$322$	−7080.91	+	4088.16i	−1.22548	+	0.707529i
$323$		−	496.748i		−	0.0855722i
$324$	2673.71	+	6909.37i	0.458455	+	1.18473i
$325$		0			0
$326$	−2350.52	−	4071.22i	−0.399336	−	0.691670i
$327$	−973.945	+	1545.92i	−0.164707	+	0.261437i
$328$	−1257.53	−	726.037i	−0.211694	−	0.122222i
$329$	684.741	−	1186.01i	0.114745	−	0.198744i
$330$		0			0
$331$	1086.68	+	1882.19i	0.180451	+	0.312551i	0.942034	−	0.335517i	$-0.108911\pi$
$331$	1086.68	+	1882.19i	0.180451	+	0.312551i	−0.761583	+	0.648067i	$0.775578\pi$
$332$			2009.57i			0.332197i
$333$	6868.56	−	3287.54i	1.13032	−	0.541009i
$334$	−17224.8			−2.82186
$335$		0			0
$336$	5942.47	−	3131.61i	0.964846	−	0.508463i
$337$	−6798.57	−	3925.16i	−1.09894	−	0.634472i	−0.162995	−	0.986627i	$-0.552116\pi$
$337$	−6798.57	−	3925.16i	−1.09894	−	0.634472i	−0.935942	+	0.352155i	$0.885449\pi$
$338$	6641.58	+	3834.52i	1.06880	+	0.617071i
$339$	8101.81	−	4269.56i	1.29802	−	0.684043i
$340$		0			0
$341$	4193.78			0.665999
$342$	7154.99	+	4903.26i	1.13128	+	0.775257i
$343$			8011.53i			1.26117i
$344$	1556.85	+	2696.54i	0.244010	+	0.422638i
$345$		0			0
$346$	−5855.16	+	10141.4i	−0.909756	+	1.57574i
$347$	−8116.60	−	4686.12i	−1.25568	−	0.724969i	−0.283451	−	0.958987i	$-0.591479\pi$
$347$	−8116.60	−	4686.12i	−1.25568	−	0.724969i	−0.972232	+	0.234018i	$0.924813\pi$
$348$	−1396.40	+	2216.48i	−0.215101	+	0.341425i
$349$	−588.952	−	1020.10i	−0.0903321	−	0.156460i	0.817319	−	0.576186i	$-0.195460\pi$
$349$	−588.952	−	1020.10i	−0.0903321	−	0.156460i	−0.907651	+	0.419726i	$0.862126\pi$
$350$		0			0
$351$	−7117.23	−	5292.25i	−1.08231	−	0.804784i
$352$		−	10293.4i		−	1.55864i
$353$	−6289.19	+	3631.06i	−0.948271	+	0.547484i	−0.892543	−	0.450962i	$-0.851081\pi$
$353$	−6289.19	+	3631.06i	−0.948271	+	0.547484i	−0.0557274	+	0.998446i	$0.517748\pi$
$354$	−7980.37	−	5027.70i	−1.19817	−	0.754856i
$355$		0			0
$356$	−6933.77	+	12009.6i	−1.03227	+	1.78795i
$357$	1052.64	+	40.6458i	0.156055	+	0.00602578i
$358$	10475.7	−	6048.15i	1.54653	−	0.892890i
$359$	1939.95			0.285199			0.142600	−	0.989780i	$-0.454454\pi$
$359$	1939.95			0.285199			0.142600	+	0.989780i	$0.454454\pi$
$360$		0			0
$361$	−1176.81			−0.171572
$362$	12704.7	−	7335.05i	1.84459	−	1.06498i
$363$	−791.388	−	1501.72i	−0.114427	−	0.217134i
$364$	9882.41	−	17116.8i	1.42302	−	2.46474i
$365$		0			0
$366$	16664.0	−	8781.72i	2.37989	−	1.25417i
$367$	−5630.85	+	3250.97i	−0.800893	+	0.462396i	−0.843783	−	0.536684i	$-0.819677\pi$
$367$	−5630.85	+	3250.97i	−0.800893	+	0.462396i	0.0428901	+	0.999080i	$0.486343\pi$
$368$			2620.51i			0.371205i
$369$	−4240.91	−	328.000i	−0.598301	−	0.0462737i
$370$		0			0
$371$	−404.165	−	700.034i	−0.0565585	−	0.0979622i
$372$	−5435.32	−	209.875i	−0.757548	−	0.0292514i
$373$	−11533.8	−	6659.02i	−1.60106	−	0.924372i	−0.991276	−	0.131805i	$-0.957923\pi$
$373$	−11533.8	−	6659.02i	−1.60106	−	0.924372i	−0.609784	−	0.792568i	$-0.708744\pi$
$374$	571.729	−	990.263i	0.0790465	−	0.136913i
$375$		0			0
$376$	205.155	+	355.339i	0.0281385	+	0.0487373i
$377$		−	3136.13i		−	0.428432i
$378$	−10975.7	+	14760.6i	−1.49347	+	2.00848i
$379$	3198.42			0.433488			0.216744	−	0.976228i	$-0.430456\pi$
$379$	3198.42			0.433488			0.216744	+	0.976228i	$0.430456\pi$
$380$		0			0
$381$	−6621.53	−	4171.62i	−0.890370	−	0.560941i
$382$	2754.43	+	1590.27i	0.368924	+	0.212999i
$383$	2026.93	+	1170.25i	0.270422	+	0.156128i	0.629079	−	0.777341i	$-0.283432\pi$
$383$	2026.93	+	1170.25i	0.270422	+	0.156128i	−0.358658	+	0.933469i	$0.616765\pi$
$384$	−227.895	+	5902.00i	−0.0302858	+	0.784336i
$385$		0			0
$386$	−459.878			−0.0606403
$387$	7523.81	+	5156.01i	0.988261	+	0.677248i
$388$		−	14544.5i		−	1.90305i
$389$	1995.97	+	3457.12i	0.260153	+	0.450599i	0.966282	−	0.257484i	$-0.0828936\pi$
$389$	1995.97	+	3457.12i	0.260153	+	0.450599i	−0.706129	+	0.708083i	$0.749560\pi$
$390$		0			0
$391$	−205.482	+	355.906i	−0.0265772	+	0.0460330i
$392$	−4816.69	−	2780.91i	−0.620611	−	0.358310i
$393$	−3089.00	−	5861.61i	−0.396488	−	0.752365i
$394$	7161.96	+	12404.9i	0.915773	+	1.58616i
$395$		0			0
$396$	4823.24	+	10077.1i	0.612063	+	1.27876i
$397$			4960.90i			0.627155i	0.949563	+	0.313577i	$0.101528\pi$
$397$			4960.90i			0.627155i	−0.949563	+	0.313577i	$0.898472\pi$
$398$	−5052.66	+	2917.16i	−0.636350	+	0.367397i
$399$	−464.937	+	12040.9i	−0.0583358	+	1.51077i
$400$		0			0
$401$	−413.811	+	716.742i	−0.0515330	+	0.0892578i	−0.890641	−	0.454707i	$-0.849744\pi$
$401$	−413.811	+	716.742i	−0.0515330	+	0.0892578i	0.839108	+	0.543965i	$0.183077\pi$
$402$	−1136.83	+	1804.47i	−0.141044	+	0.223877i
$403$	5639.30	−	3255.85i	0.697056	−	0.402445i
$404$	−11256.4			−1.38621
$405$		0			0
$406$	−6504.11			−0.795058
$407$	9944.33	−	5741.36i	1.21111	−	0.699235i
$408$	−168.237	+	267.039i	−0.0204141	+	0.0324029i
$409$	−4183.82	+	7246.59i	−0.505811	+	0.876090i	0.494167	+	0.869367i	$0.335473\pi$
$409$	−4183.82	+	7246.59i	−0.505811	+	0.876090i	−0.999977	+	0.00672263i	$0.997860\pi$
$410$		0			0
$411$	288.592	−	7473.90i	0.0346354	−	0.896983i
$412$	−4654.73	+	2687.41i	−0.556607	+	0.321357i
$413$		−	13103.2i		−	1.56117i
$414$	−3098.08	−	6472.74i	−0.367784	−	0.768400i
$415$		0			0
$416$	−7991.34	−	13841.4i	−0.941845	−	1.63132i
$417$	−6151.96	−	11673.8i	−0.722453	−	1.37091i
$418$	11327.4	+	6539.87i	1.32546	+	0.765252i
$419$	2100.36	−	3637.93i	0.244891	−	0.424163i	−0.717210	−	0.696857i	$-0.754581\pi$
$419$	2100.36	−	3637.93i	0.244891	−	0.424163i	0.962101	+	0.272694i	$0.0879145\pi$
$420$		0			0
$421$	−3469.38	−	6009.14i	−0.401632	−	0.695648i	0.592291	−	0.805724i	$-0.298224\pi$
$421$	−3469.38	−	6009.14i	−0.401632	−	0.695648i	−0.993923	+	0.110077i	$0.964890\pi$
$422$			10665.3i			1.23028i
$423$	991.459	+	679.440i	0.113963	+	0.0780981i
$424$	242.184			0.0277394
$425$		0			0
$426$	−813.575	+	21069.8i	−0.0925301	+	2.39633i
$427$	22661.8	+	13083.8i	2.56835	+	1.48283i
$428$	−4320.60	−	2494.50i	−0.487953	−	0.281720i
$429$	−11315.9	−	7129.09i	−1.27351	−	0.802321i
$430$		0			0
$431$	6827.09			0.762991			0.381496	−	0.924371i	$-0.375409\pi$
$431$	6827.09			0.762991			0.381496	+	0.924371i	$0.375409\pi$
$432$	2338.11	+	5411.83i	0.260399	+	0.602724i
$433$		−	2199.59i		−	0.244124i	−0.992522	−	0.122062i	$-0.961049\pi$
$433$		−	2199.59i		−	0.244124i	0.992522	−	0.122062i	$-0.0389507\pi$
$434$	−6752.39	−	11695.5i	−0.746832	−	1.29355i
$435$		0			0
$436$	1786.78	−	3094.80i	0.196265	−	0.339940i
$437$	−4071.12	−	2350.46i	−0.445648	−	0.257295i
$438$	1125.36	+	43.4536i	0.122766	+	0.00474040i
$439$	4162.16	+	7209.07i	0.452504	+	0.783759i	0.998541	−	0.0540018i	$-0.0171977\pi$
$439$	4162.16	+	7209.07i	0.452504	+	0.783759i	−0.546037	+	0.837761i	$0.683864\pi$
$440$		0			0
$441$	−16243.8	−	1256.33i	−1.75400	−	0.135658i
$442$		−	1775.45i		−	0.191063i
$443$	−9410.93	+	5433.41i	−1.00932	+	0.582729i	−0.910991	−	0.412426i	$-0.864682\pi$
$443$	−9410.93	+	5433.41i	−1.00932	+	0.582729i	−0.0983247	+	0.995154i	$0.531348\pi$
$444$	−13175.6	+	6943.39i	−1.40830	+	0.742159i
$445$		0			0
$446$	3994.41	−	6918.51i	0.424082	−	0.734532i
$447$	227.133	+	431.001i	0.0240336	+	0.0456055i
$448$	−19749.9	+	11402.6i	−2.08280	+	1.20250i
$449$	4947.73			0.520040			0.260020	−	0.965603i	$-0.416271\pi$
$449$	4947.73			0.520040			0.260020	+	0.965603i	$0.416271\pi$
$450$		0			0
$451$	−6414.18			−0.669694
$452$	−15511.7	+	8955.69i	−1.61418	+	0.931947i
$453$	−5546.03	−	214.150i	−0.575221	−	0.0222112i
$454$	−10822.2	+	18744.7i	−1.11875	+	1.93773i
$455$		0			0
$456$	−3054.59	−	1924.42i	−0.313694	−	0.197630i
$457$	12295.6	−	7098.85i	1.25856	−	0.726630i	0.285766	−	0.958299i	$-0.407752\pi$
$457$	12295.6	−	7098.85i	1.25856	−	0.726630i	0.972795	+	0.231669i	$0.0744186\pi$
$458$		−	3690.13i		−	0.376481i
$459$	−106.806	+	918.347i	−0.0108612	+	0.0933873i
$460$		0			0
$461$	9114.02	+	15785.9i	0.920786	+	1.59485i	0.798202	+	0.602390i	$0.205785\pi$
$461$	9114.02	+	15785.9i	0.920786	+	1.59485i	0.122584	+	0.992458i	$0.460882\pi$
$462$	−14785.2	+	23468.3i	−1.48890	+	2.36329i
$463$	−3759.58	−	2170.59i	−0.377370	−	0.217875i	0.299303	−	0.954158i	$-0.403246\pi$
$463$	−3759.58	−	2170.59i	−0.377370	−	0.217875i	−0.676674	+	0.736283i	$0.736579\pi$
$464$	−1042.28	+	1805.29i	−0.104282	+	0.180621i
$465$		0			0
$466$	2433.69	+	4215.28i	0.241928	+	0.419032i
$467$		−	4919.63i		−	0.487481i	−0.969841	−	0.243740i	$-0.921626\pi$
$467$		−	4919.63i		−	0.487481i	0.969841	−	0.243740i	$-0.0783744\pi$
$468$	14309.1	+	9805.90i	1.41333	+	0.968542i
$469$	−2962.80			−0.291704
$470$		0			0
$471$	−835.324	+	440.206i	−0.0817191	+	0.0430650i
$472$	3399.88	+	1962.92i	0.331551	+	0.191421i
$473$	11911.3	+	6876.98i	1.15789	+	0.668508i
$474$	3864.88	−	2036.75i	0.374515	−	0.197365i
$475$		0			0
$476$	−2060.31			−0.198391
$477$	639.909	−	306.283i	0.0614244	−	0.0293999i
$478$			13421.9i			1.28432i
$479$	2286.41	+	3960.19i	0.218098	+	0.377757i	0.954226	−	0.299085i	$-0.0966814\pi$
$479$	2286.41	+	3960.19i	0.218098	+	0.377757i	−0.736128	+	0.676842i	$0.763348\pi$
$480$		0			0
$481$	8914.64	−	15440.6i	0.845057	−	1.46368i
$482$	−16624.8	−	9598.31i	−1.57103	−	0.907035i
$483$	5313.87	−	8434.61i	0.500600	−	0.794592i
$484$	1659.99	+	2875.19i	0.155897	+	0.270021i
$485$		0			0
$486$	−12173.3	−	10603.1i	−1.13620	−	0.989646i
$487$		−	15751.5i		−	1.46564i	−0.680421	−	0.732822i	$-0.738203\pi$
$487$		−	15751.5i		−	1.46564i	0.680421	−	0.732822i	$-0.261797\pi$
$488$	−6789.72	+	3920.04i	−0.629828	+	0.363631i
$489$	4849.55	+	3055.26i	0.448475	+	0.282543i
$490$		0			0
$491$	−7654.18	+	13257.4i	−0.703520	+	1.21853i	0.263703	+	0.964604i	$0.415056\pi$
$491$	−7654.18	+	13257.4i	−0.703520	+	1.21853i	−0.967223	+	0.253928i	$0.918277\pi$
$492$	8313.05	+	320.994i	0.761751	+	0.0294137i
$493$	−283.116	+	163.457i	−0.0258639	+	0.0149325i
$494$	20309.0			1.84968
$495$		0			0
$496$	−4328.28			−0.391826
$497$	−25367.9	+	14646.2i	−2.28955	+	1.32187i
$498$	−2041.49	−	3873.89i	−0.183698	−	0.348580i
$499$	8866.05	−	15356.5i	0.795389	−	1.37765i	−0.127203	−	0.991877i	$-0.540600\pi$
$499$	8866.05	−	15356.5i	0.795389	−	1.37765i	0.922592	−	0.385777i	$-0.126067\pi$
$500$		0			0
$501$	18579.3	−	9791.07i	1.65681	−	0.873119i
$502$	3273.23	−	1889.80i	0.291019	−	0.168020i
$503$		−	10511.5i		−	0.931775i	−0.884844	−	0.465887i	$-0.845735\pi$
$503$		−	10511.5i		−	0.931775i	0.884844	−	0.465887i	$-0.154265\pi$
$504$	4327.89	−	6315.39i	0.382499	−	0.558155i
$505$		0			0
$506$	−5410.49	−	9371.25i	−0.475347	−	0.823326i
$507$	−9343.47	−	360.782i	−0.818457	−	0.0316033i
$508$	13255.7	+	7653.18i	1.15773	+	0.668416i
$509$	9815.42	−	17000.8i	0.854737	−	1.48045i	−0.0221524	−	0.999755i	$-0.507052\pi$
$509$	9815.42	−	17000.8i	0.854737	−	1.48045i	0.876889	−	0.480693i	$-0.159615\pi$
$510$		0			0
$511$	782.262	+	1354.92i	0.0677206	+	0.117296i
$512$			13722.1i			1.18444i
$513$	−10504.8	−	1221.73i	−0.904086	−	0.105147i
$514$	9640.30			0.827267
$515$		0			0
$516$	−15093.4	−	9508.96i	−1.28769	−	0.811257i
$517$	1569.62	+	906.223i	0.133524	+	0.0770902i
$518$	−32022.7	−	18488.3i	−2.71621	−	1.56820i
$519$	550.900	−	14267.1i	0.0465931	−	1.20666i
$520$		0			0
$521$	88.4336			0.00743636			0.00371818	−	0.999993i	$-0.498816\pi$
$521$	88.4336			0.00743636			0.00371818	+	0.999993i	$0.498816\pi$
$522$	440.179	−	5691.34i	0.0369082	−	0.477209i
$523$			21346.4i			1.78473i	0.451317	+	0.892363i	$0.350954\pi$
$523$			21346.4i			1.78473i	−0.451317	+	0.892363i	$0.649046\pi$
$524$	6479.39	+	11222.6i	0.540178	+	0.935616i
$525$		0			0
$526$	15514.2	−	26871.4i	1.28603	−	2.22747i
$527$	−587.847	−	339.394i	−0.0485902	−	0.0280535i
$528$	4144.55	+	7864.58i	0.341606	+	0.648224i
$529$	−4138.94	−	7168.86i	−0.340178	−	0.589205i
$530$		0			0
$531$	11465.8	+	886.783i	0.937047	+	0.0724729i
$532$		−	23567.4i		−	1.92063i
$533$	−8625.03	+	4979.67i	−0.700923	+	0.404678i
$534$	1165.93	−	30195.1i	0.0944847	−	2.44695i
$535$		0			0
$536$	443.842	−	768.757i	0.0357669	−	0.0619501i
$537$	−7861.51	+	12478.4i	−0.631749	+	1.00276i
$538$	394.108	−	227.538i	0.0315821	−	0.0182340i
$539$	−24568.0			−1.96330
$540$		0			0
$541$	−14432.6			−1.14696			−0.573480	−	0.819220i	$-0.694407\pi$
$541$	−14432.6			−1.14696			−0.573480	+	0.819220i	$0.694407\pi$
$542$	21808.4	−	12591.1i	1.72833	−	0.997850i
$543$	−9534.24	+	15133.5i	−0.753505	+	1.19602i
$544$	−833.027	+	1442.84i	−0.0656539	+	0.113716i
$545$		0			0
$546$	−1661.75	+	43035.9i	−0.130250	+	3.37320i
$547$	14349.7	−	8284.80i	1.12166	−	0.647592i	0.179837	−	0.983696i	$-0.442443\pi$
$547$	14349.7	−	8284.80i	1.12166	−	0.647592i	0.941825	+	0.336105i	$0.109110\pi$
$548$			14628.5i			1.14033i
$549$	−12982.5	+	18944.5i	−1.00925	+	1.47273i
$550$		0			0
$551$	−1869.75	−	3238.50i	−0.144562	−	0.250389i
$552$	1392.48	+	2642.34i	0.107369	+	0.203742i
$553$	5255.98	+	3034.54i	0.404172	+	0.233349i
$554$	−7010.80	+	12143.1i	−0.537654	+	0.931245i
$555$		0			0
$556$	12904.1	+	22350.6i	0.984277	+	1.70482i
$557$		−	11597.0i		−	0.882191i	−0.897460	−	0.441096i	$-0.854590\pi$
$557$		−	11597.0i		−	0.882191i	0.897460	−	0.441096i	$-0.145410\pi$
$558$	10691.0	−	5117.08i	0.811084	−	0.388214i
$559$	21355.9			1.61584
$560$		0			0
$561$	−53.7928	+	1393.12i	−0.00404836	+	0.104844i
$562$	−1253.85	−	723.912i	−0.0941113	−	0.0543352i
$563$	19961.3	+	11524.6i	1.49426	+	0.862709i	0.999978	−	0.00659429i	$-0.00209904\pi$
$563$	19961.3	+	11524.6i	1.49426	+	0.862709i	0.494278	+	0.869304i	$0.335432\pi$
$564$	−1988.95	−	1253.05i	−0.148493	−	0.0935516i
$565$		0			0
$566$	−11079.2			−0.822778
$567$	3448.45	−	22160.2i	0.255417	−	1.64134i
$568$		−	8776.27i		−	0.648317i
$569$	7366.96	+	12759.9i	0.542775	+	0.940114i	0.998743	+	0.0501179i	$0.0159597\pi$
$569$	7366.96	+	12759.9i	0.542775	+	0.940114i	−0.455968	+	0.889996i	$0.650707\pi$
$570$		0			0
$571$	−7555.94	+	13087.3i	−0.553776	+	0.959169i	0.444221	+	0.895917i	$0.353480\pi$
$571$	−7555.94	+	13087.3i	−0.553776	+	0.959169i	−0.997998	+	0.0632515i	$0.979853\pi$
$572$	22653.3	+	13078.9i	1.65591	+	0.956043i
$573$	−3874.98	−	149.625i	−0.282512	−	0.0109087i
$574$	10327.5	+	17887.7i	0.750975	+	1.30073i
$575$		0			0
$576$	−8641.09	−	18053.6i	−0.625079	−	1.30596i
$577$			26150.5i			1.88676i	0.331715	+	0.943380i	$0.392373\pi$
$577$			26150.5i			1.88676i	−0.331715	+	0.943380i	$0.607627\pi$
$578$	17972.7	−	10376.5i	1.29336	−	0.746724i
$579$	496.039	−	261.407i	0.0356040	−	0.0187629i
$580$		0			0
$581$	3041.61	−	5268.22i	0.217190	−	0.376184i
$582$	14775.6	+	28037.7i	1.05235	+	1.99691i
$583$	926.463	−	534.894i	0.0658150	−	0.0379983i
$584$	−468.747			−0.0332139
$585$		0			0
$586$	−758.961			−0.0535023
$587$	−1811.33	+	1045.77i	−0.127362	+	0.0735326i	−0.562327	−	0.826915i	$-0.690094\pi$
$587$	−1811.33	+	1045.77i	−0.127362	+	0.0735326i	0.434965	+	0.900447i	$0.356761\pi$
$588$	31841.2	+	1229.49i	2.23318	+	0.0862303i
$589$	3882.24	−	6724.24i	0.271587	−	0.470403i
$590$		0			0
$591$	−14776.4	−	9309.26i	−1.02846	−	0.647939i
$592$	−10263.3	+	5925.50i	−0.712530	+	0.411379i
$593$			3260.34i			0.225778i	0.993608	+	0.112889i	$0.0360104\pi$
$593$			3260.34i			0.225778i	−0.993608	+	0.112889i	$0.963990\pi$
$594$	−19535.0	−	14525.9i	−1.34938	−	1.00337i
$595$		0			0
$596$	−476.426	−	825.194i	−0.0327436	−	0.0567135i
$597$	3791.78	−	6018.61i	0.259945	−	0.412606i
$598$	−14550.8	−	8400.90i	−0.995026	−	0.574479i
$599$	−11499.6	+	19917.9i	−0.784410	+	1.35864i	0.144941	+	0.989440i	$0.453701\pi$
$599$	−11499.6	+	19917.9i	−0.784410	+	1.35864i	−0.929351	+	0.369197i	$0.879633\pi$
$600$		0			0
$601$	7146.93	+	12378.9i	0.485074	+	0.840173i	0.999853	−	0.0171500i	$-0.00545928\pi$
$601$	7146.93	+	12378.9i	0.485074	+	0.840173i	−0.514779	+	0.857323i	$0.672126\pi$
$602$		−	44290.5i		−	2.99858i
$603$	200.513	−	2592.56i	0.0135415	−	0.175087i
$604$	10855.1			0.731274
$605$		0			0
$606$	21699.3	−	11435.3i	1.45457	−	0.766544i
$607$	−14232.3	−	8217.04i	−0.951685	−	0.549455i	−0.0580809	−	0.998312i	$-0.518498\pi$
$607$	−14232.3	−	8217.04i	−0.951685	−	0.549455i	−0.893604	+	0.448856i	$0.851831\pi$
$608$	−16504.4	−	9528.80i	−1.10089	−	0.635598i
$609$	7015.54	−	3697.11i	0.466805	−	0.246001i
$610$		0			0
$611$	2814.19			0.186334
$612$	139.435	−	1802.85i	0.00920971	−	0.119078i
$613$			3674.45i			0.242104i	0.992646	+	0.121052i	$0.0386267\pi$
$613$			3674.45i			0.242104i	−0.992646	+	0.121052i	$0.961373\pi$
$614$	−3276.45	−	5674.99i	−0.215353	−	0.373003i
$615$		0			0
$616$	5772.46	−	9998.19i	0.377563	−	0.653958i
$617$	7471.69	+	4313.78i	0.487519	+	0.281469i	0.723544	−	0.690278i	$-0.242512\pi$
$617$	7471.69	+	4313.78i	0.487519	+	0.281469i	−0.236026	+	0.971747i	$0.575845\pi$
$618$	6242.91	−	9909.25i	0.406354	−	0.644998i
$619$	−654.905	−	1134.33i	−0.0425248	−	0.0736551i	0.843980	−	0.536375i	$-0.180207\pi$
$619$	−654.905	−	1134.33i	−0.0425248	−	0.0736551i	−0.886504	+	0.462720i	$0.846873\pi$
$620$		0			0
$621$	7020.97	+	5220.67i	0.453691	+	0.337356i
$622$			4028.76i			0.259708i
$623$	36354.7	−	20989.4i	2.33791	−	1.34979i
$624$	11678.8	+	7357.73i	0.749240	+	0.472027i
$625$		0			0
$626$	4230.95	−	7328.23i	0.270132	−	0.467883i
$627$	−15935.5	−	615.323i	−1.01500	−	0.0391924i
$628$	1599.31	−	923.362i	0.101623	−	0.0586722i
$629$	−1858.54			−0.117814
$630$		0			0
$631$	14447.2			0.911463			0.455731	−	0.890117i	$-0.349378\pi$
$631$	14447.2			0.911463			0.455731	+	0.890117i	$0.349378\pi$
$632$	−1574.74	+	909.179i	−0.0991138	+	0.0572234i
$633$	−6062.45	−	11503.9i	−0.380665	−	0.722339i
$634$	11044.9	−	19130.3i	0.691875	−	1.19836i
$635$		0			0
$636$	−1227.50	+	646.881i	−0.0765310	+	0.0403309i
$637$	−33036.2	+	19073.4i	−2.05485	+	1.18637i
$638$		−	8607.88i		−	0.534152i
$639$	−11099.1	−	23189.1i	−0.687127	−	1.43560i
$640$		0			0
$641$	10036.6	+	17383.8i	0.618440	+	1.07117i	0.989770	+	0.142669i	$0.0455685\pi$
$641$	10036.6	+	17383.8i	0.618440	+	1.07117i	−0.371330	+	0.928501i	$0.621098\pi$
$642$	10863.0	+	419.457i	0.667803	+	0.0257860i
$643$	15359.8	+	8867.96i	0.942037	+	0.543885i	0.890598	−	0.454791i	$-0.150286\pi$
$643$	15359.8	+	8867.96i	0.942037	+	0.543885i	0.0514386	+	0.998676i	$0.483619\pi$
$644$	−9748.75	+	16885.3i	−0.596513	+	1.03319i
$645$		0			0
$646$	−1058.52	−	1833.40i	−0.0644686	−	0.111663i
$647$			11456.8i			0.696158i	0.937465	+	0.348079i	$0.113166\pi$
$647$			11456.8i			0.696158i	−0.937465	+	0.348079i	$0.886834\pi$
$648$	5233.31	+	4214.48i	0.317259	+	0.255494i
$649$	17341.4			1.04886
$650$		0			0
$651$	13931.4	+	8776.89i	0.838731	+	0.528408i
$652$	−9708.36	−	5605.12i	−0.583142	−	0.336677i
$653$	−25177.0	−	14536.0i	−1.50881	−	0.871113i	−0.999947	−	0.0102660i	$-0.996732\pi$
$653$	−25177.0	−	14536.0i	−1.50881	−	0.871113i	−0.508864	−	0.860847i	$-0.669935\pi$
$654$	−300.453	+	7781.08i	−0.0179643	+	0.465236i
$655$		0			0
$656$	6619.90			0.393999
$657$	−1238.55	+	592.812i	−0.0735468	+	0.0352021i
$658$		−	5836.43i		−	0.345787i
$659$	−2177.54	−	3771.62i	−0.128718	−	0.222946i	0.794462	−	0.607314i	$-0.207753\pi$
$659$	−2177.54	−	3771.62i	−0.128718	−	0.222946i	−0.923180	+	0.384368i	$0.874419\pi$
$660$		0			0
$661$	−13647.7	+	23638.5i	−0.803075	+	1.39097i	0.114508	+	0.993422i	$0.463471\pi$
$661$	−13647.7	+	23638.5i	−0.803075	+	1.39097i	−0.917583	+	0.397545i	$0.869862\pi$
$662$	8021.46	+	4631.19i	0.470941	+	0.271898i
$663$	1009.22	+	1915.06i	0.0591172	+	0.112179i
$664$	911.297	+	1578.41i	0.0532608	+	0.0922504i
$665$		0			0
$666$	18345.2	−	26769.8i	1.06736	−	1.55752i
$667$			3093.72i			0.179594i
$668$	−35571.8	+	20537.4i	−2.06035	+	1.18955i
$669$	−375.825	+	9733.06i	−0.0217194	+	0.562484i
$670$		0			0
$671$	−17315.8	+	29991.9i	−0.996230	+	1.72552i
$672$	21542.5	−	34194.0i	1.23664	−	1.96289i
$673$	−15380.6	+	8880.01i	−0.880951	+	0.508617i	−0.870972	−	0.491333i	$-0.836510\pi$
$673$	−15380.6	+	8880.01i	−0.880951	+	0.508617i	−0.00997909	+	0.999950i	$0.503176\pi$
$674$	−33456.3			−1.91200
$675$		0			0
$676$	18287.8			1.04050
$677$	−1677.78	+	968.667i	−0.0952472	+	0.0549910i	−0.546867	−	0.837219i	$-0.684180\pi$
$677$	−1677.78	+	968.667i	−0.0952472	+	0.0549910i	0.451620	+	0.892210i	$0.350846\pi$
$678$	20804.3	−	33022.2i	1.17844	−	1.87052i
$679$	−22014.0	+	38129.4i	−1.24421	+	2.15504i
$680$		0			0
$681$	1018.24	−	26370.3i	0.0572968	−	1.48386i
$682$	15478.4	−	8936.48i	0.869061	−	0.501753i
$683$		−	2125.71i		−	0.119090i	−0.998226	−	0.0595448i	$-0.981035\pi$
$683$		−	2125.71i		−	0.119090i	0.998226	−	0.0595448i	$-0.0189649\pi$
$684$	20622.3	+	1594.97i	1.15280	+	0.0891596i
$685$		0			0
$686$	17071.7	+	29569.0i	0.950146	+	1.64570i
$687$	2097.57	+	3980.29i	0.116488	+	0.221045i
$688$	−12293.3	−	7097.55i	−0.681218	−	0.393301i
$689$	830.532	−	1438.52i	0.0459227	−	0.0795405i
$690$		0			0
$691$	−6913.13	−	11973.9i	−0.380590	−	0.659201i	0.610557	−	0.791973i	$-0.290946\pi$
$691$	−6913.13	−	11973.9i	−0.380590	−	0.659201i	−0.991147	+	0.132771i	$0.957612\pi$
$692$			27924.8i			1.53402i
$693$	2607.81	−	33717.9i	0.142947	−	1.84825i
$694$	−39942.4			−2.18472
$695$		0			0
$696$	−91.6744	+	2374.17i	−0.00499268	+	0.129300i
$697$	899.084	+	519.086i	0.0488597	+	0.0282092i
$698$	−4347.42	−	2509.98i	−0.235748	−	0.136109i
$699$	−5021.14	−	3163.36i	−0.271698	−	0.171172i
$700$		0			0
$701$	−24464.0			−1.31810			−0.659052	−	0.752097i	$-0.729042\pi$
$701$	−24464.0			−1.31810			−0.659052	+	0.752097i	$0.729042\pi$
$702$	−37545.5	−	4366.64i	−2.01861	−	0.234769i
$703$		−	21259.5i		−	1.14056i
$704$	−15090.8	−	26138.0i	−0.807892	−	1.39931i
$705$		0			0
$706$	−15474.8	+	26803.1i	−0.824931	+	1.42882i
$707$	29509.5	+	17037.3i	1.56976	+	0.906300i
$708$	−22475.2	−	867.842i	−1.19304	−	0.0460671i
$709$	−14749.1	−	25546.2i	−0.781263	−	1.35319i	−0.931206	−	0.364492i	$-0.881243\pi$
$709$	−14749.1	−	25546.2i	−0.781263	−	1.35319i	0.149944	−	0.988695i	$-0.452091\pi$
$710$		0			0
$711$	−3011.05	+	4393.81i	−0.158823	+	0.231759i
$712$			12577.3i			0.662012i
$713$	−5563.02	+	3211.81i	−0.292198	+	0.168700i
$714$	3971.70	−	2093.04i	0.208175	−	0.109706i
$715$		0			0
$716$	14422.6	−	24980.7i	0.752790	−	1.30387i
$717$	−7629.38	−	14477.3i	−0.397384	−	0.754065i
$718$	7159.98	−	4133.81i	0.372156	−	0.214864i
$719$	3857.66			0.200093			0.100046	−	0.994983i	$-0.468101\pi$
$719$	3857.66			0.200093			0.100046	+	0.994983i	$0.468101\pi$
$720$		0			0
$721$	16270.2			0.840410
$722$	−4343.39	+	2507.66i	−0.223884	+	0.129260i
$723$	23387.9	+	903.085i	1.20305	+	0.0464538i
$724$	17491.4	−	30295.9i	0.897874	−	1.55516i
$725$		0			0
$726$	−6120.86	−	3856.19i	−0.312901	−	0.197130i
$727$	−7573.48	+	4372.55i	−0.386361	+	0.223066i	−0.680582	−	0.732672i	$-0.738273\pi$
$727$	−7573.48	+	4372.55i	−0.386361	+	0.223066i	0.294221	+	0.955737i	$0.404940\pi$
$728$		−	17925.8i		−	0.912604i
$729$	19157.6	+	4517.26i	0.973309	+	0.229501i
$730$		0			0
$731$	−1113.08	−	1927.91i	−0.0563184	−	0.0975463i
$732$	23943.0	−	38004.2i	1.20896	−	1.91896i
$733$	8156.58	+	4709.20i	0.411010	+	0.237296i	0.691223	−	0.722641i	$-0.257072\pi$
$733$	8156.58	+	4709.20i	0.411010	+	0.237296i	−0.280214	+	0.959938i	$0.590405\pi$
$734$	−13854.9	+	23997.4i	−0.696723	+	1.20676i
$735$		0			0
$736$	7883.26	+	13654.2i	0.394811	+	0.683832i
$737$		−	3921.13i		−	0.195979i
$738$	−16351.3	+	7826.33i	−0.815584	+	0.390368i
$739$	−6219.42			−0.309587			−0.154794	−	0.987947i	$-0.549471\pi$
$739$	−6219.42			−0.309587			−0.154794	+	0.987947i	$0.549471\pi$
$740$		0			0
$741$	−21905.9	+	11544.2i	−1.08601	+	0.572316i
$742$	−2983.39	−	1722.46i	−0.147606	−	0.0852204i
$743$	25450.3	+	14693.7i	1.25663	+	0.725518i	0.972419	−	0.233242i	$-0.0749334\pi$
$743$	25450.3	+	14693.7i	1.25663	+	0.725518i	0.284216	+	0.958760i	$0.408267\pi$
$744$	−4364.33	+	2299.95i	−0.215059	+	0.113334i
$745$		0			0
$746$	−56758.5			−2.78563
$747$	4404.05	+	3018.06i	0.215710	+	0.147825i
$748$		−	2726.72i		−	0.133287i
$749$	7551.15	+	13079.0i	0.368375	+	0.638045i
$750$		0			0
$751$	10823.6	−	18747.0i	0.525909	−	0.910901i	−0.473636	−	0.880721i	$-0.657059\pi$
$751$	10823.6	−	18747.0i	0.525909	−	0.910901i	0.999544	−	0.0301801i	$-0.00960808\pi$
$752$	−1619.97	−	935.287i	−0.0785559	−	0.0453543i
$753$	−2456.40	+	3899.00i	−0.118880	+	0.188695i
$754$	−6682.75	−	11574.9i	−0.322774	−	0.559061i
$755$		0			0
$756$	−5067.23	+	43569.4i	−0.243774	+	2.09604i
$757$			13907.2i			0.667722i	0.942622	+	0.333861i	$0.108352\pi$
$757$			13907.2i			0.667722i	−0.942622	+	0.333861i	$0.891648\pi$
$758$	11804.8	−	6815.48i	0.565657	−	0.326582i
$759$	11162.8	+	7032.66i	0.533840	+	0.336324i
$760$		0			0
$761$	11953.0	−	20703.3i	0.569379	−	0.986193i	−0.427249	−	0.904134i	$-0.640517\pi$
$761$	11953.0	−	20703.3i	0.569379	−	0.986193i	0.996628	−	0.0820585i	$-0.0261494\pi$
$762$	−33328.0	−	1286.90i	−1.58445	−	0.0611806i
$763$	−9368.35	+	5408.82i	−0.444504	+	0.256635i
$764$	7584.42			0.359155
$765$		0			0
$766$	9974.70			0.470497
$767$	23318.7	−	13463.1i	1.09777	−	0.633798i
$768$	−2631.01	−	4992.53i	−0.123618	−	0.234573i
$769$	−12555.8	+	21747.3i	−0.588783	+	1.01980i	0.405609	+	0.914047i	$0.367059\pi$
$769$	−12555.8	+	21747.3i	−0.588783	+	1.01980i	−0.994392	+	0.105755i	$0.966274\pi$
$770$		0			0
$771$	−10398.3	+	5479.81i	−0.485716	+	0.255967i
$772$	−949.716	+	548.319i	−0.0442759	+	0.0255627i
$773$			14909.4i			0.693729i	0.937915	+	0.346865i	$0.112754\pi$
$773$			14909.4i			0.693729i	−0.937915	+	0.346865i	$0.887246\pi$
$774$	38755.8	+	2997.45i	1.79981	+	0.139200i
$775$		0			0
$776$	−6595.62	−	11424.0i	−0.305115	−	0.528474i
$777$	45050.0	+	1739.53i	2.08000	+	0.0803155i
$778$	14733.5	+	8506.37i	0.678947	+	0.391990i
$779$	−5937.70	+	10284.4i	−0.273094	+	0.473013i
$780$		0			0
$781$	−19383.5	−	33573.2i	−0.888087	−	1.53821i
$782$			1751.44i			0.0800912i
$783$	2760.32	+	6389.08i	0.125984	+	0.291605i
$784$	25356.0			1.15506
$785$		0			0
$786$	−23891.4	−	15051.8i	−1.08419	−	0.683052i
$787$	−2302.56	−	1329.38i	−0.104292	−	0.0602128i	0.446947	−	0.894560i	$-0.352511\pi$
$787$	−2302.56	−	1329.38i	−0.104292	−	0.0602128i	−0.551239	+	0.834348i	$0.685845\pi$
$788$	29581.0	+	17078.6i	1.33728	+	0.772082i
$789$	−1459.70	+	37803.1i	−0.0658640	+	1.70573i
$790$		0			0
$791$	54220.0			2.43722
$792$	8358.13	+	5727.76i	0.374991	+	0.256979i
$793$			53772.7i			2.40798i
$794$	10571.1	+	18309.7i	0.472488	+	0.818373i
$795$		0			0
$796$	−6956.33	+	12048.7i	−0.309750	+	0.536502i
$797$	−12273.5	−	7086.11i	−0.545483	−	0.314935i	0.201815	−	0.979424i	$-0.435316\pi$
$797$	−12273.5	−	7086.11i	−0.545483	−	0.314935i	−0.747298	+	0.664489i	$0.768649\pi$
$798$	23941.8	+	45431.3i	1.06207	+	2.01535i
$799$	−146.677	−	254.053i	−0.00649446	−	0.0112487i
$800$		0			0
$801$	15906.1	+	33232.2i	0.701642	+	1.46592i
$802$			3527.14i			0.155296i
$803$	−1793.17	+	1035.29i	−0.0788040	+	0.0454975i
$804$	−196.231	+	5081.95i	−0.00860761	+	0.222918i
$805$		0			0
$806$	13875.7	−	24033.4i	0.606391	−	1.05030i
$807$	−295.759	+	469.452i	−0.0129011	+	0.0204777i
$808$	−8841.34	+	5104.55i	−0.384947	+	0.222249i
$809$	21077.7			0.916012			0.458006	−	0.888949i	$-0.348564\pi$
$809$	21077.7			0.916012			0.458006	+	0.888949i	$0.348564\pi$
$810$		0			0
$811$	−11937.4			−0.516868			−0.258434	−	0.966029i	$-0.583206\pi$
$811$	−11937.4			−0.516868			−0.258434	+	0.966029i	$0.583206\pi$
$812$	−13431.9	+	7754.94i	−0.580503	+	0.335154i
$813$	−16366.2	+	25977.7i	−0.706011	+	1.12064i
$814$	24468.4	−	42380.5i	1.05358	−	1.82486i
$815$		0			0
$816$	55.5180	−	1437.80i	0.00238176	−	0.0616826i
$817$	22052.9	−	12732.3i	0.944350	−	0.545221i
$818$			35661.0i			1.52428i
$819$	−22670.3	−	47364.5i	−0.967235	−	2.02082i
$820$		0			0
$821$	−7400.25	−	12817.6i	−0.314580	−	0.544869i	0.664768	−	0.747050i	$-0.268530\pi$
$821$	−7400.25	−	12817.6i	−0.314580	−	0.544869i	−0.979348	+	0.202181i	$0.935197\pi$
$822$	−14860.9	−	28199.7i	−0.630576	−	1.19657i
$823$	−28731.8	−	16588.3i	−1.21692	−	0.702591i	−0.252665	−	0.967554i	$-0.581307\pi$
$823$	−28731.8	−	16588.3i	−1.21692	−	0.702591i	−0.964259	+	0.264963i	$0.914640\pi$
$824$	−2437.37	+	4221.64i	−0.103046	+	0.178480i
$825$		0			0
$826$	−27921.4	−	48361.3i	−1.17616	−	2.03717i
$827$			29001.3i			1.21944i	0.792619	+	0.609718i	$0.208717\pi$
$827$			29001.3i			1.21944i	−0.792619	+	0.609718i	$0.791283\pi$
$828$	−14115.5	−	9673.27i	−0.592450	−	0.406002i
$829$	−13221.1			−0.553904			−0.276952	−	0.960884i	$-0.589324\pi$
$829$	−13221.1			−0.553904			−0.276952	+	0.960884i	$0.589324\pi$
$830$		0			0
$831$	659.632	−	17083.0i	0.0275360	−	0.713122i
$832$	−40584.7	−	23431.6i	−1.69113	−	0.976374i
$833$	3443.73	+	1988.24i	0.143239	+	0.0826991i
$834$	−47581.3	−	29976.6i	−1.97555	−	1.24461i
$835$		0			0
$836$	31190.3			1.29036
$837$	−8622.95	+	11596.5i	−0.356096	+	0.478893i
$838$		−	17902.5i		−	0.737987i
$839$	−21062.0	−	36480.4i	−0.866675	−	1.50112i	−0.865375	−	0.501125i	$-0.832920\pi$
$839$	−21062.0	−	36480.4i	−0.866675	−	1.50112i	−0.00129985	−	0.999999i	$-0.500414\pi$
$840$		0			0
$841$	10964.0	−	18990.2i	0.449547	−	0.778638i
$842$	−25609.6	−	14785.7i	−1.04818	−	0.605166i
$843$	1763.94	+	68.1114i	0.0720679	+	0.00278278i
$844$	12716.4	+	22025.4i	0.518621	+	0.898278i
$845$		0			0
$846$	5107.10	+	394.992i	0.207548	+	0.0160521i
$847$		−	10050.0i		−	0.407700i
$848$	−956.177	+	552.049i	−0.0387208	+	0.0223555i
$849$	11950.4	−	6297.71i	0.483081	−	0.254578i
$850$		0			0
$851$	−8794.07	+	15231.8i	−0.354238	+	0.613559i
$852$	23441.7	+	44482.4i	0.942605	+	1.78866i
$853$	12498.2	−	7215.84i	0.501677	−	0.289643i	−0.227729	−	0.973725i	$-0.573130\pi$
$853$	12498.2	−	7215.84i	0.501677	−	0.289643i	0.729406	+	0.684081i	$0.239797\pi$
$854$	111521.			4.46857
$855$		0			0
$856$	−4524.80			−0.180671
$857$	−13954.6	+	8056.71i	−0.556220	+	0.321134i	−0.751627	−	0.659588i	$-0.770731\pi$
$857$	−13954.6	+	8056.71i	−0.556220	+	0.321134i	0.195407	+	0.980722i	$0.437397\pi$
$858$	−56956.0	−	2199.25i	−2.26625	−	0.0875074i
$859$	−11250.2	+	19485.9i	−0.446858	+	0.773982i	−0.998180	−	0.0603115i	$-0.980791\pi$
$859$	−11250.2	+	19485.9i	−0.446858	+	0.773982i	0.551321	+	0.834293i	$0.314124\pi$
$860$		0			0
$861$	−21307.4	−	13423.8i	−0.843384	−	0.531339i
$862$	25197.5	−	14547.8i	0.995626	−	0.574825i
$863$		−	43396.8i		−	1.71175i	−0.517180	−	0.855877i	$-0.673018\pi$
$863$		−	43396.8i		−	1.71175i	0.517180	−	0.855877i	$-0.326982\pi$
$864$	28463.1	+	21164.6i	1.12076	+	0.833375i
$865$		0			0
$866$	−4687.09	−	8118.28i	−0.183919	−	0.318557i
$867$	−13487.6	+	21408.6i	−0.528331	+	0.838610i
$868$	−27889.4	−	16101.9i	−1.09058	−	0.629649i
$869$	−4016.07	+	6956.04i	−0.156773	+	0.271539i
$870$		0			0
$871$	−3044.18	−	5272.67i	−0.118425	−	0.205118i
$872$		−	3241.07i		−	0.125868i
$873$	−31874.8	−	21843.6i	−1.23574	−	0.846842i
$874$	−20034.3			−0.775366
$875$		0			0
$876$	2375.84	−	1252.04i	0.0916348	−	0.0482905i
$877$	−2135.21	−	1232.77i	−0.0822133	−	0.0474659i	0.458330	−	0.888782i	$-0.348448\pi$
$877$	−2135.21	−	1232.77i	−0.0822133	−	0.0474659i	−0.540543	+	0.841316i	$0.681781\pi$
$878$	30723.5	+	17738.2i	1.18094	+	0.681817i
$879$	818.640	−	431.414i	0.0314130	−	0.0165543i
$880$		0			0
$881$	24512.9			0.937412			0.468706	−	0.883354i	$-0.344720\pi$
$881$	24512.9			0.937412			0.468706	+	0.883354i	$0.344720\pi$
$882$	−62629.9	+	29976.9i	−2.39100	+	1.14442i
$883$			24236.1i			0.923679i	0.886963	+	0.461840i	$0.152810\pi$
$883$			24236.1i			0.923679i	−0.886963	+	0.461840i	$0.847190\pi$
$884$	−2116.90	−	3666.57i	−0.0805418	−	0.139502i
$885$		0			0
$886$	−23156.0	+	40107.3i	−0.878036	+	1.52080i
$887$	21822.7	+	12599.3i	0.826082	+	0.476939i	0.852509	−	0.522712i	$-0.175080\pi$
$887$	21822.7	+	12599.3i	0.826082	+	0.476939i	−0.0264274	+	0.999651i	$0.508413\pi$
$888$	−7200.07	+	11428.5i	−0.272093	+	0.431888i
$889$	−23167.1	−	40126.7i	−0.874017	−	1.51384i
$890$		0			0
$891$	29328.0	+	4563.86i	1.10272	+	0.171599i
$892$		−	19050.3i		−	0.715081i
$893$	2906.05	−	1677.81i	0.108899	−	0.0628731i
$894$	1756.72	+	1106.75i	0.0657198	+	0.0414040i
$895$		0			0
$896$	−17484.5	+	30284.0i	−0.651914	+	1.12915i
$897$	20470.3	+	790.423i	0.761964	+	0.0294219i
$898$	18261.1	−	10543.1i	0.678599	−	0.391789i
$899$	−5109.87			−0.189570
$900$		0			0
$901$	−173.151			−0.00640233
$902$	−23673.5	+	13667.9i	−0.873882	+	0.504536i
$903$	25175.9	+	47773.2i	0.927798	+	1.76057i
$904$	−8122.42	+	14068.5i	−0.298836	+	0.517599i
$905$		0			0
$906$	−20925.7	+	11027.6i	−0.767338	+	0.404379i
$907$	−23043.3	+	13304.0i	−0.843594	+	0.487049i	−0.858484	−	0.512840i	$-0.828593\pi$
$907$	−23043.3	+	13304.0i	−0.843594	+	0.487049i	0.0148906	+	0.999889i	$0.495260\pi$
$908$			51614.0i			1.88642i
$909$	−16905.4	+	24668.9i	−0.616851	+	0.900127i
$910$		0			0
$911$	−12416.1	−	21505.2i	−0.451550	−	0.782108i	0.546932	−	0.837177i	$-0.315796\pi$
$911$	−12416.1	−	21505.2i	−0.451550	−	0.782108i	−0.998483	+	0.0550686i	$0.982462\pi$
$912$	16446.6	+	635.058i	0.597151	+	0.0230580i
$913$	6972.25	+	4025.43i	0.252736	+	0.145917i
$914$	30253.7	−	52401.0i	1.09486	−	1.89636i
$915$		0			0
$916$	−4399.79	−	7620.66i	−0.158704	−	0.274884i
$917$		−	39227.8i		−	1.41267i
$918$	1562.70	+	3617.03i	0.0561837	+	0.130043i
$919$	26107.2			0.937102			0.468551	−	0.883436i	$-0.344776\pi$
$919$	26107.2			0.937102			0.468551	+	0.883436i	$0.344776\pi$
$920$		0			0
$921$	6759.91	+	4258.80i	0.241853	+	0.152369i
$922$	67276.2	+	38841.9i	2.40306	+	1.38741i
$923$	−52129.3	−	30096.9i	−1.85900	−	1.07329i
$924$	−2552.11	+	66094.0i	−0.0908637	+	2.35317i
$925$		0			0
$926$	−18501.2			−0.656573
$927$	−1101.12	+	14237.1i	−0.0390136	+	0.504431i
$928$			12542.0i			0.443653i
$929$	−11680.8	−	20231.7i	−0.412523	−	0.714511i	0.582642	−	0.812729i	$-0.302019\pi$
$929$	−11680.8	−	20231.7i	−0.412523	−	0.714511i	−0.995165	+	0.0982184i	$0.968686\pi$
$930$		0			0
$931$	−22743.0	+	39392.0i	−0.800613	+	1.38670i
$932$	10051.9	+	5803.45i	0.353283	+	0.203968i
$933$	−2290.06	−	4345.55i	−0.0803570	−	0.152483i
$934$	−10483.2	−	18157.4i	−0.367260	−	0.636112i
$935$		0			0
$936$	15685.8	+	1213.17i	0.547763	+	0.0423650i
$937$		−	10548.5i		−	0.367775i	−0.982947	−	0.183888i	$-0.941132\pi$
$937$		−	10548.5i		−	0.367775i	0.982947	−	0.183888i	$-0.0588682\pi$
$938$	−10935.1	+	6313.40i	−0.380644	+	0.219765i
$939$	−398.082	+	10309.5i	−0.0138348	+	0.358292i
$940$		0			0
$941$	3245.07	−	5620.62i	0.112419	−	0.194715i	−0.804326	−	0.594188i	$-0.797473\pi$
$941$	3245.07	−	5620.62i	0.112419	−	0.194715i	0.916745	+	0.399473i	$0.130807\pi$
$942$	−2144.99	+	3404.70i	−0.0741906	+	0.117761i
$943$	8508.38	−	4912.32i	0.293819	−	0.169636i
$944$	−17897.6			−0.617074
$945$		0			0
$946$	58616.4			2.01457
$947$	−20356.8	+	11753.0i	−0.698528	+	0.403295i	−0.806799	−	0.590826i	$-0.798802\pi$
$947$	−20356.8	+	11753.0i	−0.698528	+	0.403295i	0.108271	+	0.994121i	$0.465469\pi$
$948$	5553.11	−	8814.34i	0.190250	−	0.301979i
$949$	−1607.50	+	2784.26i	−0.0549858	+	0.0952382i
$950$		0			0
$951$	−1039.19	+	26912.8i	−0.0354344	+	0.917674i
$952$	−1618.26	+	934.305i	−0.0550927	+	0.0318078i
$953$			6740.26i			0.229106i	0.993417	+	0.114553i	$0.0365437\pi$
$953$			6740.26i			0.229106i	−0.993417	+	0.114553i	$0.963456\pi$
$954$	1709.13	−	2494.01i	0.0580032	−	0.0846400i
$955$		0			0
$956$	16003.1	+	27718.2i	0.541399	+	0.937731i
$957$	4892.95	+	9284.74i	0.165274	+	0.313619i
$958$	16877.4	+	9744.19i	0.569191	+	0.328623i
$959$	22141.2	−	38349.6i	0.745543	−	1.29132i
$960$		0			0
$961$	9590.57	+	16611.4i	0.321928	+	0.557596i
$962$		−	75984.4i		−	2.54661i
$963$	−11955.6	+	5722.40i	−0.400068	+	0.191487i
$964$	−45776.8			−1.52943
$965$		0			0
$966$	1639.28	−	42453.8i	0.0545993	−	1.41400i
$967$	14534.1	+	8391.27i	0.483336	+	0.279054i	0.721806	−	0.692096i	$-0.243312\pi$
$967$	14534.1	+	8391.27i	0.483336	+	0.279054i	−0.238470	+	0.971150i	$0.576646\pi$
$968$	2607.67	+	1505.54i	0.0865844	+	0.0499895i
$969$	2183.91	+	1375.88i	0.0724016	+	0.0456136i
$970$		0			0
$971$	−46282.7			−1.52964			−0.764822	−	0.644242i	$-0.777173\pi$
$971$	−46282.7			−1.52964			−0.764822	+	0.644242i	$0.777173\pi$
$972$	−37781.9	−	7382.66i	−1.24677	−	0.243620i
$973$		−	78124.9i		−	2.57407i
$974$	−33564.7	−	58135.8i	−1.10419	−	1.91252i
$975$		0			0
$976$	17871.2	−	30953.8i	0.586109	−	1.01517i
$977$	5861.22	+	3383.98i	0.191931	+	0.110812i	0.592886	−	0.805286i	$-0.297988\pi$
$977$	5861.22	+	3383.98i	0.191931	+	0.110812i	−0.400955	+	0.916098i	$0.631322\pi$
$978$	24409.2	+	942.517i	0.798076	+	0.0308163i
$979$	27778.5	+	48113.7i	0.906848	+	1.57071i
$980$		0			0
$981$	−4098.90	−	8563.71i	−0.133402	−	0.278714i
$982$			65240.8i			2.12008i
$983$	−43366.1	+	25037.4i	−1.40708	+	0.812381i	−0.995106	−	0.0988128i	$-0.968496\pi$
$983$	−43366.1	+	25037.4i	−1.40708	+	0.812381i	−0.411979	+	0.911194i	$0.635162\pi$
$984$	6675.04	−	3517.67i	0.216252	−	0.113963i
$985$		0			0
$986$	−696.618	+	1206.58i	−0.0224998	+	0.0389708i
$987$	3317.58	+	6295.36i	0.106991	+	0.203023i
$988$	41941.0	−	24214.7i	1.35053	−	0.779728i
$989$	−21067.0			−0.677343
$990$		0			0
$991$	−2658.60			−0.0852200			−0.0426100	−	0.999092i	$-0.513567\pi$
$991$	−2658.60			−0.0852200			−0.0426100	+	0.999092i	$0.513567\pi$
$992$	−22552.6	+	13020.7i	−0.721819	+	0.416742i
$993$	−11284.7	−	435.739i	−0.360634	−	0.0139252i
$994$	−62418.7	+	108112.i	−1.99175	+	3.44981i
$995$		0			0
$996$	−8834.88	−	5566.05i	−0.281068	−	0.177075i
$997$	52498.5	−	30310.0i	1.66765	−	0.962817i	0.698748	−	0.715368i	$-0.253741\pi$
$997$	52498.5	−	30310.0i	1.66765	−	0.962817i	0.968901	−	0.247449i	$-0.0795923\pi$
$998$		−	75570.3i		−	2.39693i
$999$	−4571.00	+	39302.7i	−0.144765	+	1.24473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.d.49.12		28
5.2	odd	4		45.4.e.c.31.6	yes	14
5.3	odd	4		225.4.e.d.76.2		14
5.4	even	2	inner	225.4.k.d.49.3		28
9.7	even	3	inner	225.4.k.d.124.3		28
15.2	even	4		135.4.e.c.91.2		14
45.2	even	12		135.4.e.c.46.2		14
45.7	odd	12		45.4.e.c.16.6	✓	14
45.13	odd	12		2025.4.a.bb.1.6		7
45.22	odd	12		405.4.a.m.1.2		7
45.23	even	12		2025.4.a.ba.1.2		7
45.32	even	12		405.4.a.n.1.6		7
45.34	even	6	inner	225.4.k.d.124.12		28
45.43	odd	12		225.4.e.d.151.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.6	✓	14	45.7	odd	12
45.4.e.c.31.6	yes	14	5.2	odd	4
135.4.e.c.46.2		14	45.2	even	12
135.4.e.c.91.2		14	15.2	even	4
225.4.e.d.76.2		14	5.3	odd	4
225.4.e.d.151.2		14	45.43	odd	12
225.4.k.d.49.3		28	5.4	even	2	inner
225.4.k.d.49.12		28	1.1	even	1	trivial
225.4.k.d.124.3		28	9.7	even	3	inner
225.4.k.d.124.12		28	45.34	even	6	inner
405.4.a.m.1.2		7	45.22	odd	12
405.4.a.n.1.6		7	45.32	even	12
2025.4.a.ba.1.2		7	45.23	even	12
2025.4.a.bb.1.6		7	45.13	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)

\(f(q)\)	\(=\)	\(q+(3.69081 - 2.13089i) q^{2} +(-2.76977 + 4.39640i) q^{3} +(5.08138 - 8.80120i) q^{4} +(-0.854448 + 22.1284i) q^{6} +(-26.6423 + 15.3820i) q^{7} -9.21718i q^{8} +(-11.6567 - 24.3541i) q^{9} +O(q^{10})\)	\(q+(3.69081 - 2.13089i) q^{2} +(-2.76977 + 4.39640i) q^{3} +(5.08138 - 8.80120i) q^{4} +(-0.854448 + 22.1284i) q^{6} +(-26.6423 + 15.3820i) q^{7} -9.21718i q^{8} +(-11.6567 - 24.3541i) q^{9} +(-20.3573 - 35.2599i) q^{11} +(24.6194 + 46.7171i) q^{12} +(-54.7482 - 31.6089i) q^{13} +(-65.5545 + 113.544i) q^{14} +(21.0102 + 36.3908i) q^{16} +6.58990i q^{17} +(-94.9186 - 65.0470i) q^{18} -75.3803 q^{19} +(6.16789 - 159.735i) q^{21} +(-150.270 - 86.7584i) q^{22} +(54.0077 + 31.1814i) q^{23} +(40.5225 + 25.5295i) q^{24} -269.420 q^{26} +(139.357 + 16.2075i) q^{27} +312.646i q^{28} +(24.8042 + 42.9621i) q^{29} +(-51.5021 + 89.2043i) q^{31} +(218.948 + 126.410i) q^{32} +(211.402 + 8.16291i) q^{33} +(14.0423 + 24.3221i) q^{34} +(-273.577 - 21.1590i) q^{36} +282.029i q^{37} +(-278.214 + 160.627i) q^{38} +(290.606 - 153.146i) q^{39} +(78.7700 - 136.434i) q^{41} +(-317.613 - 602.695i) q^{42} +(-292.555 + 168.907i) q^{43} -413.773 q^{44} +265.776 q^{46} +(-38.5518 + 22.2579i) q^{47} +(-218.182 - 8.42472i) q^{48} +(301.710 - 522.577i) q^{49} +(-28.9719 - 18.2525i) q^{51} +(-556.393 + 321.234i) q^{52} +26.2752i q^{53} +(548.876 - 237.135i) q^{54} +(141.778 + 245.567i) q^{56} +(208.786 - 331.402i) q^{57} +(183.095 + 105.710i) q^{58} +(-212.963 + 368.863i) q^{59} +(-425.297 - 736.637i) q^{61} +438.981i q^{62} +(685.176 + 469.546i) q^{63} +741.296 q^{64} +(797.638 - 420.346i) q^{66} +(83.4048 + 48.1538i) q^{67} +(57.9990 + 33.4858i) q^{68} +(-286.675 + 151.075i) q^{69} +952.164 q^{71} +(-224.476 + 107.442i) q^{72} -50.8558i q^{73} +(600.973 + 1040.92i) q^{74} +(-383.036 + 663.437i) q^{76} +(1084.73 + 626.271i) q^{77} +(746.233 - 1184.48i) q^{78} +(-98.6395 - 170.849i) q^{79} +(-457.241 + 567.778i) q^{81} -671.400i q^{82} +(-171.247 + 98.8693i) q^{83} +(-1374.52 - 865.959i) q^{84} +(-719.844 + 1246.81i) q^{86} +(-257.581 - 9.94603i) q^{87} +(-324.997 + 187.637i) q^{88} -1364.54 q^{89} +1944.83 q^{91} +(548.868 - 316.889i) q^{92} +(-249.529 - 473.499i) q^{93} +(-94.8583 + 164.299i) q^{94} +(-1162.18 + 612.458i) q^{96} +(1239.42 - 715.579i) q^{97} -2571.64i q^{98} +(-621.422 + 906.799i) 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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