LMFDB - Embedded newform 225.4.k.d.49.3

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			49.3
Character	$\chi$	$=$	225.49
Dual form			225.4.k.d.124.3

$q$-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	−0.981240	−	0.192791i	$-0.938246\pi$
$2$	−3.69081	+	2.13089i	−1.30490	+	0.753383i	−0.323658	+	0.946174i	$0.604913\pi$
$3$	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	0.440802	−	0.897604i	$-0.354694\pi$
$7$	26.6423	−	15.3820i	1.43855	−	0.830548i	0.997749	+	0.0670561i	$0.0213606\pi$
$8$			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	0.953216	−	0.302290i	$-0.0977512\pi$
$13$	54.7482	+	31.6089i	1.16803	+	0.674364i	0.214817	+	0.976654i	$0.431085\pi$
$14$	−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	$-0.985031\pi$
$17$		−	6.58990i		−	0.0940168i	0.998894	−	0.0470084i	$-0.0149687\pi$
$18$	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	0.234793	−	0.972045i	$-0.424559\pi$
$23$	−54.0077	−	31.1814i	−0.489626	−	0.282686i	−0.724419	+	0.689360i	$0.757892\pi$
$24$	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	$-0.784463\pi$
$37$		−	282.029i		−	1.25312i	0.779374	−	0.626559i	$-0.215537\pi$
$38$	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	0.118406	−	0.992965i	$-0.462222\pi$
$43$	292.555	−	168.907i	1.03754	−	0.599025i	0.919136	+	0.393940i	$0.128888\pi$
$44$	−413.773			−1.41770
$45$		0			0
$46$	265.776			0.851882
$47$	38.5518	−	22.2579i	0.119646	−	0.0690777i	−0.438983	−	0.898496i	$-0.644661\pi$
$47$	38.5518	−	22.2579i	0.119646	−	0.0690777i	0.558629	+	0.829418i	$0.311328\pi$
$48$	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	$-0.989160\pi$
$53$		−	26.2752i		−	0.0680978i	0.999420	−	0.0340489i	$-0.0108402\pi$
$54$	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	0.422028	−	0.906583i	$-0.361319\pi$
$67$	−83.4048	−	48.1538i	−0.152082	−	0.0878048i	−0.574110	+	0.818778i	$0.694652\pi$
$68$	−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	$0.0129807\pi$
$73$			50.8558i			0.0815373i	−0.999169	+	0.0407686i	$0.987019\pi$
$74$	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	−0.382474	−	0.923966i	$-0.624928\pi$
$83$	171.247	−	98.8693i	0.226467	−	0.130751i	0.608941	+	0.793215i	$0.291595\pi$
$84$	−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	−0.979947	−	0.199256i	$-0.936147\pi$
$97$	−1239.42	+	715.579i	−1.29736	+	0.749031i	−0.317413	+	0.948288i	$0.602814\pi$
$98$			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	0.702814	−	0.711373i	$-0.251926\pi$
$103$	458.018	+	264.437i	0.438154	+	0.252969i	−0.264660	+	0.964342i	$0.585260\pi$
$104$	−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	$0.0711823\pi$
$107$			490.910i			0.443533i	−0.975100	+	0.221766i	$0.928818\pi$
$108$	−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	0.975113	−	0.221710i	$-0.0711637\pi$
$113$	1526.33	+	881.226i	1.27066	+	0.733618i	0.295550	+	0.955327i	$0.404497\pi$
$114$	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	$-0.823628\pi$
$127$		−	1506.12i		−	1.05234i	0.850380	−	0.526169i	$-0.176372\pi$
$128$	−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	−0.0581150	−	0.998310i	$-0.518509\pi$
$137$	1246.58	−	719.712i	0.777389	−	0.448826i	0.835504	+	0.549484i	$0.185176\pi$
$138$	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	0.459468	−	0.888194i	$-0.348040\pi$
$157$	−157.370	−	90.8574i	−0.0799966	−	0.0461861i	−0.539465	+	0.842008i	$0.681373\pi$
$158$	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	$0.0853813\pi$
$163$			1103.07i			0.530056i	−0.964241	+	0.265028i	$0.914619\pi$
$164$	−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	$0.0525269\pi$
$167$	3500.22	+	2020.85i	1.62189	+	0.936396i	0.635470	+	0.772126i	$0.280806\pi$
$168$	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	0.124314	−	0.992243i	$-0.460327\pi$
$173$	2379.63	−	1373.88i	1.04578	−	0.603780i	0.921465	+	0.388463i	$0.126994\pi$
$174$	−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	0.517326	−	0.855789i	$-0.326928\pi$
$193$	93.4506	+	53.9538i	0.0348535	+	0.0201227i	−0.482472	+	0.875911i	$0.660261\pi$
$194$	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	$-0.792063\pi$
$197$		−	3361.02i		−	1.21555i	0.794110	−	0.607774i	$-0.207937\pi$
$198$	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	−0.723532	−	0.690291i	$-0.757483\pi$
$223$	−1623.39	+	937.263i	−0.487489	+	0.281452i	0.236043	+	0.971743i	$0.424149\pi$
$224$	−7777.72			−2.31996
$225$		0			0
$226$	−7511.18			−2.21078
$227$	4398.32	−	2539.37i	1.28602	−	0.742484i	0.308078	−	0.951361i	$-0.400314\pi$
$227$	4398.32	−	2539.37i	1.28602	−	0.742484i	0.977942	+	0.208877i	$0.0669808\pi$
$228$	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	$-0.948670\pi$
$233$		−	1142.10i		−	0.321122i	0.987026	−	0.160561i	$-0.0513304\pi$
$234$	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	0.243052	−	0.970013i	$-0.421851\pi$
$257$	−1958.98	−	1131.02i	−0.475478	−	0.274517i	−0.718530	+	0.695496i	$0.755185\pi$
$258$	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	−0.999699	−	0.0245245i	$-0.992193\pi$
$263$	−6305.20	+	3640.31i	−1.47831	+	0.853503i	−0.478611	+	0.878027i	$0.658859\pi$
$264$	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	−0.158064	−	0.987429i	$-0.550525\pi$
$277$	2849.30	−	1645.04i	0.618042	−	0.356827i	0.776106	+	0.630602i	$0.217192\pi$
$278$		−	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	0.717452	−	0.696608i	$-0.245308\pi$
$283$	2251.37	+	1299.83i	0.472898	+	0.273028i	−0.244554	+	0.969636i	$0.578642\pi$
$284$	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	0.515297	−	0.857012i	$-0.327682\pi$
$293$	154.227	+	89.0427i	0.0307509	+	0.0177540i	−0.484546	+	0.874766i	$0.661015\pi$
$294$	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	$0.0456505\pi$
$307$			1537.60i			0.285848i	−0.989734	+	0.142924i	$0.954349\pi$
$308$	−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	−0.647160	−	0.762354i	$-0.724043\pi$
$313$	−1719.52	+	992.767i	−0.310521	+	0.179280i	0.336638	+	0.941634i	$0.390710\pi$
$314$	774.428			0.139183
$315$		0			0
$316$	−2004.90			−0.356913
$317$	−4488.81	+	2591.62i	−0.795321	+	0.459179i	−0.841833	−	0.539739i	$-0.818523\pi$
$317$	−4488.81	+	2591.62i	−0.795321	+	0.459179i	0.0465112	+	0.998918i	$0.485190\pi$
$318$	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	0.935942	−	0.352155i	$-0.114551\pi$
$337$	6798.57	+	3925.16i	1.09894	+	0.634472i	0.162995	+	0.986627i	$0.447884\pi$
$338$	−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	0.972232	−	0.234018i	$-0.0751875\pi$
$347$	8116.60	+	4686.12i	1.25568	+	0.724969i	0.283451	+	0.958987i	$0.408521\pi$
$348$	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	0.0557274	−	0.998446i	$-0.482252\pi$
$353$	6289.19	−	3631.06i	0.948271	−	0.547484i	0.892543	+	0.450962i	$0.148919\pi$
$354$	−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	−0.0428901	−	0.999080i	$-0.513657\pi$
$367$	5630.85	−	3250.97i	0.800893	−	0.462396i	0.843783	+	0.536684i	$0.180323\pi$
$368$		−	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	$0.0420772\pi$
$373$	11533.8	+	6659.02i	1.60106	+	0.924372i	0.609784	+	0.792568i	$0.291256\pi$
$374$	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	0.358658	−	0.933469i	$-0.383235\pi$
$383$	−2026.93	−	1170.25i	−0.270422	−	0.156128i	−0.629079	+	0.777341i	$0.716568\pi$
$384$	−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	$-0.898472\pi$
$397$		−	4960.90i		−	0.627155i	0.949563	−	0.313577i	$-0.101528\pi$
$398$	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	$0.0389507\pi$
$433$			2199.59i			0.244124i	−0.992522	+	0.122062i	$0.961049\pi$
$434$	−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	0.0983247	−	0.995154i	$-0.468652\pi$
$443$	9410.93	−	5433.41i	1.00932	−	0.582729i	0.910991	+	0.412426i	$0.135318\pi$
$444$	−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	−0.972795	−	0.231669i	$-0.925581\pi$
$457$	−12295.6	+	7098.85i	−1.25856	+	0.726630i	−0.285766	+	0.958299i	$0.592248\pi$
$458$			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	0.676674	−	0.736283i	$-0.263421\pi$
$463$	3759.58	+	2170.59i	0.377370	+	0.217875i	−0.299303	+	0.954158i	$0.596754\pi$
$464$	−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	$0.0783744\pi$
$467$			4919.63i			0.487481i	−0.969841	+	0.243740i	$0.921626\pi$
$468$	−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	$0.261797\pi$
$487$			15751.5i			1.46564i	−0.680421	+	0.732822i	$0.738203\pi$
$488$	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	$0.154265\pi$
$503$			10511.5i			0.931775i	−0.884844	+	0.465887i	$0.845735\pi$
$504$	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	$-0.649046\pi$
$523$		−	21346.4i		−	1.78473i	0.451317	−	0.892363i	$-0.350954\pi$
$524$	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	−0.941825	−	0.336105i	$-0.890890\pi$
$547$	−14349.7	+	8284.80i	−1.12166	+	0.647592i	−0.179837	+	0.983696i	$0.557557\pi$
$548$		−	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	$0.145410\pi$
$557$			11597.0i			0.882191i	−0.897460	+	0.441096i	$0.854590\pi$
$558$	−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	−0.494278	−	0.869304i	$-0.664568\pi$
$563$	−19961.3	−	11524.6i	−1.49426	−	0.862709i	−0.999978	+	0.00659429i	$0.997901\pi$
$564$	−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	$-0.607627\pi$
$577$		−	26150.5i		−	1.88676i	0.331715	−	0.943380i	$-0.392373\pi$
$578$	−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	−0.434965	−	0.900447i	$-0.643239\pi$
$587$	1811.33	−	1045.77i	0.127362	−	0.0735326i	0.562327	+	0.826915i	$0.309906\pi$
$588$	−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	$-0.963990\pi$
$593$		−	3260.34i		−	0.225778i	0.993608	−	0.112889i	$-0.0360104\pi$
$594$	−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	0.893604	−	0.448856i	$-0.148169\pi$
$607$	14232.3	+	8217.04i	0.951685	+	0.549455i	0.0580809	+	0.998312i	$0.481502\pi$
$608$	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	$-0.961373\pi$
$613$		−	3674.45i		−	0.242104i	0.992646	−	0.121052i	$-0.0386267\pi$
$614$	−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	0.236026	−	0.971747i	$-0.424155\pi$
$617$	−7471.69	−	4313.78i	−0.487519	−	0.281469i	−0.723544	+	0.690278i	$0.757488\pi$
$618$	−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	−0.0514386	−	0.998676i	$-0.516381\pi$
$643$	−15359.8	−	8867.96i	−0.942037	−	0.543885i	−0.890598	+	0.454791i	$0.849714\pi$
$644$	−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	$-0.886834\pi$
$647$		−	11456.8i		−	0.696158i	0.937465	−	0.348079i	$-0.113166\pi$
$648$	−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	$0.00326784\pi$
$653$	25177.0	+	14536.0i	1.50881	+	0.871113i	0.508864	+	0.860847i	$0.330065\pi$
$654$	−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	0.00997909	−	0.999950i	$-0.496824\pi$
$673$	15380.6	−	8880.01i	0.880951	−	0.508617i	0.870972	+	0.491333i	$0.163490\pi$
$674$	−33456.3			−1.91200
$675$		0			0
$676$	18287.8			1.04050
$677$	1677.78	−	968.667i	0.0952472	−	0.0549910i	−0.451620	−	0.892210i	$-0.649154\pi$
$677$	1677.78	−	968.667i	0.0952472	−	0.0549910i	0.546867	+	0.837219i	$0.315820\pi$
$678$	−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	$0.0189649\pi$
$683$			2125.71i			0.119090i	−0.998226	+	0.0595448i	$0.981035\pi$
$684$	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	−0.294221	−	0.955737i	$-0.595060\pi$
$727$	7573.48	−	4372.55i	0.386361	−	0.223066i	0.680582	+	0.732672i	$0.261727\pi$
$728$			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	0.280214	−	0.959938i	$-0.409595\pi$
$733$	−8156.58	−	4709.20i	−0.411010	−	0.237296i	−0.691223	+	0.722641i	$0.742928\pi$
$734$	−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	−0.284216	−	0.958760i	$-0.591733\pi$
$743$	−25450.3	−	14693.7i	−1.25663	−	0.725518i	−0.972419	+	0.233242i	$0.925067\pi$
$744$	−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	$-0.891648\pi$
$757$		−	13907.2i		−	0.667722i	0.942622	−	0.333861i	$-0.108352\pi$
$758$	−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	$-0.887246\pi$
$773$		−	14909.4i		−	0.693729i	0.937915	−	0.346865i	$-0.112754\pi$
$774$	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	0.551239	−	0.834348i	$-0.314155\pi$
$787$	2302.56	+	1329.38i	0.104292	+	0.0602128i	−0.446947	+	0.894560i	$0.647489\pi$
$788$	−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	0.747298	−	0.664489i	$-0.231351\pi$
$797$	12273.5	+	7086.11i	0.545483	+	0.314935i	−0.201815	+	0.979424i	$0.564684\pi$
$798$	−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	0.964259	−	0.264963i	$-0.0853596\pi$
$823$	28731.8	+	16588.3i	1.21692	+	0.702591i	0.252665	+	0.967554i	$0.418693\pi$
$824$	−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	$-0.791283\pi$
$827$		−	29001.3i		−	1.21944i	0.792619	−	0.609718i	$-0.208717\pi$
$828$	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	−0.729406	−	0.684081i	$-0.760203\pi$
$853$	−12498.2	+	7215.84i	−0.501677	+	0.289643i	0.227729	+	0.973725i	$0.426870\pi$
$854$	111521.			4.46857
$855$		0			0
$856$	−4524.80			−0.180671
$857$	13954.6	−	8056.71i	0.556220	−	0.321134i	−0.195407	−	0.980722i	$-0.562603\pi$
$857$	13954.6	−	8056.71i	0.556220	−	0.321134i	0.751627	+	0.659588i	$0.229269\pi$
$858$	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	$0.326982\pi$
$863$			43396.8i			1.71175i	−0.517180	+	0.855877i	$0.673018\pi$
$864$	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	0.540543	−	0.841316i	$-0.318219\pi$
$877$	2135.21	+	1232.77i	0.0822133	+	0.0474659i	−0.458330	+	0.888782i	$0.651552\pi$
$878$	−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	$-0.847190\pi$
$883$		−	24236.1i		−	0.923679i	0.886963	−	0.461840i	$-0.152810\pi$
$884$	−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	0.0264274	−	0.999651i	$-0.491587\pi$
$887$	−21822.7	−	12599.3i	−0.826082	−	0.476939i	−0.852509	+	0.522712i	$0.824920\pi$
$888$	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	−0.0148906	−	0.999889i	$-0.504740\pi$
$907$	23043.3	−	13304.0i	0.843594	−	0.487049i	0.858484	+	0.512840i	$0.171407\pi$
$908$		−	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	$0.0588682\pi$
$937$			10548.5i			0.367775i	−0.982947	+	0.183888i	$0.941132\pi$
$938$	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	−0.108271	−	0.994121i	$-0.534531\pi$
$947$	20356.8	−	11753.0i	0.698528	−	0.403295i	0.806799	+	0.590826i	$0.201198\pi$
$948$	−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	$-0.963456\pi$
$953$		−	6740.26i		−	0.229106i	0.993417	−	0.114553i	$-0.0365437\pi$
$954$	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	0.238470	−	0.971150i	$-0.423354\pi$
$967$	−14534.1	−	8391.27i	−0.483336	−	0.279054i	−0.721806	+	0.692096i	$0.756688\pi$
$968$	−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	0.400955	−	0.916098i	$-0.368678\pi$
$977$	−5861.22	−	3383.98i	−0.191931	−	0.110812i	−0.592886	+	0.805286i	$0.702012\pi$
$978$	−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	0.411979	−	0.911194i	$-0.364838\pi$
$983$	43366.1	−	25037.4i	1.40708	−	0.812381i	0.995106	+	0.0988128i	$0.0315045\pi$
$984$	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	$0.746259\pi$
$997$	−52498.5	+	30310.0i	−1.66765	+	0.962817i	−0.968901	+	0.247449i	$0.920408\pi$
$998$			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.49.3		28
5.2	odd	4		225.4.e.d.76.2		14
5.3	odd	4		45.4.e.c.31.6	yes	14
5.4	even	2	inner	225.4.k.d.49.12		28
9.7	even	3	inner	225.4.k.d.124.12		28
15.8	even	4		135.4.e.c.91.2		14
45.7	odd	12		225.4.e.d.151.2		14
45.13	odd	12		405.4.a.m.1.2		7
45.22	odd	12		2025.4.a.bb.1.6		7
45.23	even	12		405.4.a.n.1.6		7
45.32	even	12		2025.4.a.ba.1.2		7
45.34	even	6	inner	225.4.k.d.124.3		28
45.38	even	12		135.4.e.c.46.2		14
45.43	odd	12		45.4.e.c.16.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.6	✓	14	45.43	odd	12
45.4.e.c.31.6	yes	14	5.3	odd	4
135.4.e.c.46.2		14	45.38	even	12
135.4.e.c.91.2		14	15.8	even	4
225.4.e.d.76.2		14	5.2	odd	4
225.4.e.d.151.2		14	45.7	odd	12
225.4.k.d.49.3		28	1.1	even	1	trivial
225.4.k.d.49.12		28	5.4	even	2	inner
225.4.k.d.124.3		28	45.34	even	6	inner
225.4.k.d.124.12		28	9.7	even	3	inner
405.4.a.m.1.2		7	45.13	odd	12
405.4.a.n.1.6		7	45.23	even	12
2025.4.a.ba.1.2		7	45.32	even	12
2025.4.a.bb.1.6		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)

\(f(q)\)	\(=\)	\(q+(-3.69081 + 2.13089i) q^{2} +(2.76977 - 4.39640i) q^{3} +(5.08138 - 8.80120i) q^{4} +(-0.854448 + 22.1284i) q^{6} +(26.6423 - 15.3820i) q^{7} +9.21718i q^{8} +(-11.6567 - 24.3541i) q^{9} +O(q^{10})\)	\(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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