LMFDB - Embedded newform 225.4.e.d.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, 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:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.3
Root			$1.09722 + 1.90044i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.d.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09722 + 1.90044i) q^{2} +(-0.206141 - 5.19206i) q^{3} +(1.59221 + 2.75778i) q^{4} +(10.0934 + 5.30509i) q^{6} +(1.38302 - 2.39547i) q^{7} -24.5436 q^{8} +(-26.9150 + 2.14059i) q^{9} +O(q^{10})$	\(q+(-1.09722 + 1.90044i) q^{2} +(-0.206141 - 5.19206i) q^{3} +(1.59221 + 2.75778i) q^{4} +(10.0934 + 5.30509i) q^{6} +(1.38302 - 2.39547i) q^{7} -24.5436 q^{8} +(-26.9150 + 2.14059i) q^{9} +(26.3295 - 45.6040i) q^{11} +(13.9904 - 8.83533i) q^{12} +(10.2267 + 17.7132i) q^{13} +(3.03497 + 5.25672i) q^{14} +(14.1921 - 24.5814i) q^{16} -3.66084 q^{17} +(25.4637 - 53.4992i) q^{18} -95.6705 q^{19} +(-12.7225 - 6.68694i) q^{21} +(57.7786 + 100.075i) q^{22} +(-44.9206 - 77.8047i) q^{23} +(5.05943 + 127.432i) q^{24} -44.8840 q^{26} +(16.6623 + 139.303i) q^{27} +8.80825 q^{28} +(113.890 - 197.264i) q^{29} +(-139.569 - 241.741i) q^{31} +(-67.0306 - 116.100i) q^{32} +(-242.206 - 127.303i) q^{33} +(4.01675 - 6.95722i) q^{34} +(-48.7576 - 70.8175i) q^{36} -273.725 q^{37} +(104.972 - 181.816i) q^{38} +(89.8599 - 56.7492i) q^{39} +(-32.4323 - 56.1744i) q^{41} +(26.6676 - 16.8414i) q^{42} +(209.381 - 362.658i) q^{43} +167.688 q^{44} +197.151 q^{46} +(69.3544 - 120.125i) q^{47} +(-130.554 - 68.6190i) q^{48} +(167.674 + 290.421i) q^{49} +(0.754647 + 19.0073i) q^{51} +(-32.5661 + 56.4062i) q^{52} +197.063 q^{53} +(-283.020 - 121.181i) q^{54} +(-33.9444 + 58.7934i) q^{56} +(19.7216 + 496.727i) q^{57} +(249.926 + 432.884i) q^{58} +(-370.552 - 641.814i) q^{59} +(-244.234 + 423.026i) q^{61} +612.554 q^{62} +(-32.0964 + 67.4346i) q^{63} +521.263 q^{64} +(507.687 - 320.620i) q^{66} +(-205.734 - 356.341i) q^{67} +(-5.82882 - 10.0958i) q^{68} +(-394.707 + 249.269i) q^{69} -310.343 q^{71} +(660.591 - 52.5377i) q^{72} +51.0260 q^{73} +(300.338 - 520.200i) q^{74} +(-152.327 - 263.839i) q^{76} +(-72.8286 - 126.143i) q^{77} +(9.25240 + 233.040i) q^{78} +(-603.999 + 1046.16i) q^{79} +(719.836 - 115.228i) q^{81} +142.342 q^{82} +(452.611 - 783.945i) q^{83} +(-1.81574 - 45.7330i) q^{84} +(459.475 + 795.833i) q^{86} +(-1047.68 - 550.661i) q^{87} +(-646.220 + 1119.29i) q^{88} +663.633 q^{89} +56.5752 q^{91} +(143.046 - 247.763i) q^{92} +(-1226.36 + 774.485i) q^{93} +(152.194 + 263.608i) q^{94} +(-588.982 + 371.960i) q^{96} +(-362.668 + 628.159i) q^{97} -735.905 q^{98} +(-611.039 + 1283.79i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9 + 23 * q^11 - 287 * q^12 + 96 * q^13 - 21 * q^14 - 324 * q^16 + 322 * q^17 + 89 * q^18 + 558 * q^19 + 180 * q^21 + 311 * q^22 - 96 * q^23 + 48 * q^24 + 716 * q^26 + 470 * q^27 - 674 * q^28 - 296 * q^29 - 244 * q^31 + 314 * q^32 + 211 * q^33 - 125 * q^34 - 2399 * q^36 - 808 * q^37 - 305 * q^38 + 634 * q^39 - 47 * q^41 - 1941 * q^42 + 525 * q^43 - 110 * q^44 + 1434 * q^46 - 164 * q^47 - 2051 * q^48 - 1225 * q^49 + 1517 * q^51 + 1682 * q^52 + 1012 * q^53 - 4066 * q^54 - 981 * q^56 - 337 * q^57 + 1183 * q^58 - 85 * q^59 - 828 * q^61 - 1572 * q^62 + 828 * q^63 + 4472 * q^64 + 4930 * q^66 + 1093 * q^67 - 2473 * q^68 - 822 * q^69 - 656 * q^71 + 4626 * q^72 - 4170 * q^73 - 1316 * q^74 - 2789 * q^76 - 24 * q^77 + 5314 * q^78 - 2110 * q^79 - 2167 * q^81 + 124 * q^82 - 1290 * q^83 + 5775 * q^84 - 2569 * q^86 - 3604 * q^87 + 2271 * q^88 + 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 696 * q^93 + 517 * q^94 - 593 * q^96 + 1787 * q^97 + 2558 * q^98 + 2320 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.09722	+	1.90044i	−0.387927	+	0.671909i	−0.992170	−	0.124891i	$-0.960142\pi$
$2$	−1.09722	+	1.90044i	−0.387927	+	0.671909i	0.604244	+	0.796799i	$0.293475\pi$
$3$	−0.206141	−	5.19206i	−0.0396718	−	0.999213i
$3$	−0.206141	−	5.19206i	−0.0396718	−	0.999213i
$4$	1.59221	+	2.75778i	0.199026	+	0.344723i
$5$		0			0
$5$		0			0
$6$	10.0934	+	5.30509i	0.686769	+	0.360965i
$7$	1.38302	−	2.39547i	0.0746763	−	0.129343i	−0.826269	−	0.563275i	$-0.809541\pi$
$7$	1.38302	−	2.39547i	0.0746763	−	0.129343i	0.900945	+	0.433932i	$0.142874\pi$
$8$	−24.5436			−1.08468
$9$	−26.9150	+	2.14059i	−0.996852	+	0.0792811i
$10$		0			0
$11$	26.3295	−	45.6040i	0.721694	−	1.25001i	−0.238626	−	0.971112i	$-0.576697\pi$
$11$	26.3295	−	45.6040i	0.721694	−	1.25001i	0.960320	−	0.278900i	$-0.0899698\pi$
$12$	13.9904	−	8.83533i	0.336556	−	0.212545i
$13$	10.2267	+	17.7132i	0.218183	+	0.377905i	0.954253	−	0.299002i	$-0.0966536\pi$
$13$	10.2267	+	17.7132i	0.218183	+	0.377905i	−0.736069	+	0.676906i	$0.763320\pi$
$14$	3.03497	+	5.25672i	0.0579378	+	0.100351i
$15$		0			0
$16$	14.1921	−	24.5814i	0.221751	−	0.384085i
$17$	−3.66084			−0.0522285			−0.0261142	−	0.999659i	$-0.508313\pi$
$17$	−3.66084			−0.0522285			−0.0261142	+	0.999659i	$0.508313\pi$
$18$	25.4637	−	53.4992i	0.333436	−	0.700549i
$19$	−95.6705			−1.15517			−0.577587	−	0.816329i	$-0.696006\pi$
$19$	−95.6705			−1.15517			−0.577587	+	0.816329i	$0.696006\pi$
$20$		0			0
$21$	−12.7225	−	6.68694i	−0.132204	−	0.0694862i
$22$	57.7786	+	100.075i	0.559929	+	0.969825i
$23$	−44.9206	−	77.8047i	−0.407243	−	0.705365i	0.587337	−	0.809343i	$-0.300176\pi$
$23$	−44.9206	−	77.8047i	−0.407243	−	0.705365i	−0.994580	+	0.103977i	$0.966843\pi$
$24$	5.05943	+	127.432i	0.0430313	+	1.08383i
$25$		0			0
$26$	−44.8840			−0.338556
$27$	16.6623	+	139.303i	0.118766	+	0.992922i
$28$	8.80825			0.0594501
$29$	113.890	−	197.264i	0.729272	−	1.26314i	−0.227919	−	0.973680i	$-0.573192\pi$
$29$	113.890	−	197.264i	0.729272	−	1.26314i	0.957191	−	0.289456i	$-0.0934744\pi$
$30$		0			0
$31$	−139.569	−	241.741i	−0.808625	−	1.40058i	−0.913816	−	0.406128i	$-0.866879\pi$
$31$	−139.569	−	241.741i	−0.808625	−	1.40058i	0.105191	−	0.994452i	$-0.466455\pi$
$32$	−67.0306	−	116.100i	−0.370295	−	0.641370i
$33$	−242.206	−	127.303i	−1.27766	−	0.671536i
$34$	4.01675	−	6.95722i	0.0202608	−	0.0350928i
$35$		0			0
$36$	−48.7576	−	70.8175i	−0.225730	−	0.327859i
$37$	−273.725			−1.21622			−0.608110	−	0.793852i	$-0.708072\pi$
$37$	−273.725			−1.21622			−0.608110	+	0.793852i	$0.708072\pi$
$38$	104.972	−	181.816i	0.448123	−	0.776172i
$39$	89.8599	−	56.7492i	0.368951	−	0.233004i
$40$		0			0
$41$	−32.4323	−	56.1744i	−0.123539	−	0.213975i	0.797622	−	0.603157i	$-0.206091\pi$
$41$	−32.4323	−	56.1744i	−0.123539	−	0.213975i	−0.921161	+	0.389182i	$0.872758\pi$
$42$	26.6676	−	16.8414i	0.0979738	−	0.0618733i
$43$	209.381	−	362.658i	0.742565	−	1.28616i	−0.208759	−	0.977967i	$-0.566943\pi$
$43$	209.381	−	362.658i	0.742565	−	1.28616i	0.951324	−	0.308193i	$-0.0997241\pi$
$44$	167.688			0.574544
$45$		0			0
$46$	197.151			0.631921
$47$	69.3544	−	120.125i	0.215242	−	0.372810i	−0.738105	−	0.674685i	$-0.764279\pi$
$47$	69.3544	−	120.125i	0.215242	−	0.372810i	0.953347	+	0.301875i	$0.0976126\pi$
$48$	−130.554	−	68.6190i	−0.392580	−	0.206339i
$49$	167.674	+	290.421i	0.488847	+	0.846708i
$50$		0			0
$51$	0.754647	+	19.0073i	0.00207200	+	0.0521874i
$52$	−32.5661	+	56.4062i	−0.0868483	+	0.150426i
$53$	197.063			0.510730			0.255365	−	0.966845i	$-0.417804\pi$
$53$	197.063			0.510730			0.255365	+	0.966845i	$0.417804\pi$
$54$	−283.020	−	121.181i	−0.713225	−	0.305381i
$55$		0			0
$56$	−33.9444	+	58.7934i	−0.0810001	+	0.140296i
$57$	19.7216	+	496.727i	0.0458278	+	1.15427i
$58$	249.926	+	432.884i	0.565808	+	0.980008i
$59$	−370.552	−	641.814i	−0.817656	−	1.41622i	−0.907405	−	0.420257i	$-0.861940\pi$
$59$	−370.552	−	641.814i	−0.817656	−	1.41622i	0.0897490	−	0.995964i	$-0.471394\pi$
$60$		0			0
$61$	−244.234	+	423.026i	−0.512639	+	0.887916i	0.487254	+	0.873260i	$0.337999\pi$
$61$	−244.234	+	423.026i	−0.512639	+	0.887916i	−0.999893	+	0.0146560i	$0.995335\pi$
$62$	612.554			1.25475
$63$	−32.0964	+	67.4346i	−0.0641868	+	0.134856i
$64$	521.263			1.01809
$65$		0			0
$66$	507.687	−	320.620i	0.946848	−	0.597963i
$67$	−205.734	−	356.341i	−0.375140	−	0.649762i	0.615208	−	0.788365i	$-0.289072\pi$
$67$	−205.734	−	356.341i	−0.375140	−	0.649762i	−0.990348	+	0.138603i	$0.955739\pi$
$68$	−5.82882	−	10.0958i	−0.0103948	−	0.0180044i
$69$	−394.707	+	249.269i	−0.688654	+	0.434905i
$70$		0			0
$71$	−310.343			−0.518746			−0.259373	−	0.965777i	$-0.583516\pi$
$71$	−310.343			−0.518746			−0.259373	+	0.965777i	$0.583516\pi$
$72$	660.591	−	52.5377i	1.08127	−	0.0859948i
$73$	51.0260			0.0818101			0.0409051	−	0.999163i	$-0.486976\pi$
$73$	51.0260			0.0818101			0.0409051	+	0.999163i	$0.486976\pi$
$74$	300.338	−	520.200i	0.471804	−	0.817189i
$75$		0			0
$76$	−152.327	−	263.839i	−0.229910	−	0.398215i
$77$	−72.8286	−	126.143i	−0.107787	−	0.186692i
$78$	9.25240	+	233.040i	0.0134311	+	0.338290i
$79$	−603.999	+	1046.16i	−0.860193	+	1.48990i	0.0115496	+	0.999933i	$0.496324\pi$
$79$	−603.999	+	1046.16i	−0.860193	+	1.48990i	−0.871742	+	0.489964i	$0.837010\pi$
$80$		0			0
$81$	719.836	−	115.228i	0.987429	−	0.158063i
$82$	142.342			0.191695
$83$	452.611	−	783.945i	0.598560	−	1.03674i	−0.394474	−	0.918907i	$-0.629073\pi$
$83$	452.611	−	783.945i	0.598560	−	1.03674i	0.993034	−	0.117829i	$-0.0375935\pi$
$84$	−1.81574	−	45.7330i	−0.00235849	−	0.0594033i
$85$		0			0
$86$	459.475	+	795.833i	0.576121	+	0.997871i
$87$	−1047.68	−	550.661i	−1.29107	−	0.678587i
$88$	−646.220	+	1119.29i	−0.782810	+	1.35587i
$89$	663.633			0.790393			0.395197	−	0.918597i	$-0.370676\pi$
$89$	663.633			0.790393			0.395197	+	0.918597i	$0.370676\pi$
$90$		0			0
$91$	56.5752			0.0651725
$92$	143.046	−	247.763i	0.162104	−	0.280772i
$93$	−1226.36	+	774.485i	−1.36740	+	0.863552i
$94$	152.194	+	263.608i	0.166996	+	0.289246i
$95$		0			0
$96$	−588.982	+	371.960i	−0.626175	+	0.395448i
$97$	−362.668	+	628.159i	−0.379622	+	0.657525i	−0.991007	−	0.133809i	$-0.957279\pi$
$97$	−362.668	+	628.159i	−0.379622	+	0.657525i	0.611385	+	0.791333i	$0.290613\pi$
$98$	−735.905			−0.758547
$99$	−611.039	+	1283.79i	−0.620321	+	1.30329i
$100$		0			0
$101$	−488.891	+	846.784i	−0.481648	+	0.834239i	−0.999778	−	0.0210629i	$-0.993295\pi$
$101$	−488.891	+	846.784i	−0.481648	+	0.834239i	0.518130	+	0.855302i	$0.326628\pi$
$102$	−36.9503	−	19.4211i	−0.0358689	−	0.0188527i
$103$	793.852	+	1374.99i	0.759423	+	1.31536i	0.943145	+	0.332381i	$0.107852\pi$
$103$	793.852	+	1374.99i	0.759423	+	1.31536i	−0.183722	+	0.982978i	$0.558815\pi$
$104$	−251.000	−	434.745i	−0.236660	−	0.409907i
$105$		0			0
$106$	−216.222	+	374.507i	−0.198126	+	0.343164i
$107$	−897.731			−0.811093			−0.405546	−	0.914074i	$-0.632919\pi$
$107$	−897.731			−0.811093			−0.405546	+	0.914074i	$0.632919\pi$
$108$	−357.638	+	267.751i	−0.318646	+	0.238559i
$109$	855.492			0.751754			0.375877	−	0.926669i	$-0.377341\pi$
$109$	855.492			0.751754			0.375877	+	0.926669i	$0.377341\pi$
$110$		0			0
$111$	56.4259	+	1421.20i	0.0482496	+	1.21526i
$112$	−39.2560	−	67.9934i	−0.0331191	−	0.0573640i
$113$	455.121	+	788.292i	0.378886	+	0.656250i	0.990900	−	0.134597i	$-0.0429738\pi$
$113$	455.121	+	788.292i	0.378886	+	0.656250i	−0.612014	+	0.790847i	$0.709641\pi$
$114$	−965.641	−	507.540i	−0.793339	−	0.416978i
$115$		0			0
$116$	725.348			0.580576
$117$	−313.169	−	454.860i	−0.247457	−	0.359417i
$118$	1626.31			1.26876
$119$	−5.06303	+	8.76943i	−0.00390023	+	0.00675539i
$120$		0			0
$121$	−720.984	−	1248.78i	−0.541686	−	0.938227i
$122$	−535.958	−	928.306i	−0.397732	−	0.688893i
$123$	−284.976	+	179.971i	−0.208906	+	0.131930i
$124$	444.447	−	769.804i	0.321875	−	0.557504i
$125$		0			0
$126$	−92.9387	−	134.988i	−0.0657114	−	0.0954420i
$127$	2038.25			1.42414			0.712068	−	0.702111i	$-0.247759\pi$
$127$	2038.25			1.42414			0.712068	+	0.702111i	$0.247759\pi$
$128$	−35.6968	+	61.8287i	−0.0246499	+	0.0426948i
$129$	−1926.11	−	1012.36i	−1.31461	−	0.690956i
$130$		0			0
$131$	−117.823	−	204.075i	−0.0785817	−	0.136108i	0.824057	−	0.566508i	$-0.191706\pi$
$131$	−117.823	−	204.075i	−0.0785817	−	0.136108i	−0.902638	+	0.430400i	$0.858372\pi$
$132$	−34.5673	−	870.647i	−0.0227932	−	0.574091i
$133$	−132.315	+	229.176i	−0.0862642	+	0.149414i
$134$	902.942			0.582107
$135$		0			0
$136$	89.8501			0.0566513
$137$	−1486.45	+	2574.60i	−0.926975	+	1.60557i	−0.138621	+	0.990345i	$0.544267\pi$
$137$	−1486.45	+	2574.60i	−0.926975	+	1.60557i	−0.788354	+	0.615222i	$0.789066\pi$
$138$	−40.6409	−	1023.62i	−0.0250694	−	0.631424i
$139$	1047.32	+	1814.00i	0.639080	+	1.10692i	0.985635	+	0.168890i	$0.0540182\pi$
$139$	1047.32	+	1814.00i	0.639080	+	1.10692i	−0.346555	+	0.938030i	$0.612648\pi$
$140$		0			0
$141$	−637.995	−	335.330i	−0.381056	−	0.200283i
$142$	340.515	−	589.790i	0.201235	−	0.348550i
$143$	1077.06			0.629847
$144$	−329.362	+	691.989i	−0.190603	+	0.400456i
$145$		0			0
$146$	−55.9868	+	96.9720i	−0.0317363	+	0.0549689i
$147$	1473.32	−	930.444i	0.826648	−	0.522052i
$148$	−435.828	−	754.876i	−0.242060	−	0.419259i
$149$	−136.969	−	237.237i	−0.0753081	−	0.130437i	0.825912	−	0.563799i	$-0.190661\pi$
$149$	−136.969	−	237.237i	−0.0753081	−	0.130437i	−0.901220	+	0.433361i	$0.857327\pi$
$150$		0			0
$151$	468.422	−	811.331i	0.252448	−	0.437253i	−0.711751	−	0.702432i	$-0.752098\pi$
$151$	468.422	−	811.331i	0.252448	−	0.437253i	0.964199	+	0.265179i	$0.0854310\pi$
$152$	2348.10			1.25300
$153$	98.5315	−	7.83635i	0.0520641	−	0.00414073i
$154$	319.637			0.167254
$155$		0			0
$156$	299.578	+	157.458i	0.153753	+	0.0808123i
$157$	199.218	+	345.055i	0.101269	+	0.175404i	0.912208	−	0.409728i	$-0.134376\pi$
$157$	199.218	+	345.055i	0.101269	+	0.175404i	−0.810938	+	0.585131i	$0.801043\pi$
$158$	−1325.44	−	2295.73i	−0.667383	−	1.15594i
$159$	−40.6227	−	1023.16i	−0.0202616	−	0.510328i
$160$		0			0
$161$	−248.505			−0.121646
$162$	−570.835	+	1494.44i	−0.276846	+	0.724779i
$163$	−478.154			−0.229766			−0.114883	−	0.993379i	$-0.536649\pi$
$163$	−478.154			−0.229766			−0.114883	+	0.993379i	$0.536649\pi$
$164$	103.278	−	178.883i	0.0491747	−	0.0851732i
$165$		0			0
$166$	993.229	+	1720.32i	0.464395	+	0.804355i
$167$	−170.181	−	294.763i	−0.0788564	−	0.136583i	0.823900	−	0.566735i	$-0.191794\pi$
$167$	−170.181	−	294.763i	−0.0788564	−	0.136583i	−0.902757	+	0.430151i	$0.858460\pi$
$168$	312.256	+	164.122i	0.143399	+	0.0753705i
$169$	889.328	−	1540.36i	0.404792	−	0.701120i
$170$		0			0
$171$	2574.97	−	204.791i	1.15154	−	0.0915835i
$172$	1333.51			0.591159
$173$	1888.03	−	3270.17i	0.829738	−	1.43715i	−0.0685065	−	0.997651i	$-0.521823\pi$
$173$	1888.03	−	3270.17i	0.829738	−	1.43715i	0.898244	−	0.439497i	$-0.144843\pi$
$174$	2196.04	−	1386.87i	0.956790	−	0.604241i
$175$		0			0
$176$	−747.341	−	1294.43i	−0.320073	−	0.554384i
$177$	−3255.95	+	2056.23i	−1.38267	+	0.873196i
$178$	−728.153	+	1261.20i	−0.306615	+	0.531072i
$179$	186.652			0.0779385			0.0389693	−	0.999240i	$-0.487593\pi$
$179$	186.652			0.0779385			0.0389693	+	0.999240i	$0.487593\pi$
$180$		0			0
$181$	1438.75			0.590837			0.295418	−	0.955368i	$-0.404541\pi$
$181$	1438.75			0.590837			0.295418	+	0.955368i	$0.404541\pi$
$182$	−62.0756	+	107.518i	−0.0252821	+	0.0437900i
$183$	2246.72	+	1180.88i	0.907555	+	0.477010i
$184$	1102.51	+	1909.61i	0.441729	+	0.765098i
$185$		0			0
$186$	−126.272	−	3180.42i	−0.0497781	−	1.25376i
$187$	−96.3880	+	166.949i	−0.0376930	+	0.0652862i
$188$	441.706			0.171355
$189$	356.741	+	152.746i	0.137297	+	0.0587863i
$190$		0			0
$191$	195.218	−	338.127i	0.0739552	−	0.128094i	−0.826676	−	0.562678i	$-0.809771\pi$
$191$	195.218	−	338.127i	0.0739552	−	0.128094i	0.900631	+	0.434584i	$0.143104\pi$
$192$	−107.453	−	2706.43i	−0.0403895	−	1.01729i
$193$	−1957.52	−	3390.53i	−0.730081	−	1.26454i	−0.956848	−	0.290588i	$-0.906149\pi$
$193$	−1957.52	−	3390.53i	−0.730081	−	1.26454i	0.226767	−	0.973949i	$-0.427184\pi$
$194$	−795.854	−	1378.46i	−0.294531	−	0.510143i
$195$		0			0
$196$	−533.945	+	924.820i	−0.194586	+	0.337034i
$197$	892.680			0.322847			0.161423	−	0.986885i	$-0.448392\pi$
$197$	892.680			0.322847			0.161423	+	0.986885i	$0.448392\pi$
$198$	−1769.33	−	2569.85i	−0.635055	−	0.922381i
$199$	−2770.50			−0.986913			−0.493457	−	0.869770i	$-0.664267\pi$
$199$	−2770.50			−0.986913			−0.493457	+	0.869770i	$0.664267\pi$
$200$		0			0
$201$	−1807.74	+	1141.64i	−0.634368	+	0.400622i
$202$	−1072.84	−	1858.22i	−0.373688	−	0.647247i
$203$	−315.026	−	545.641i	−0.108919	−	0.188653i
$204$	−51.2165	+	32.3447i	−0.0175778	+	0.0111009i
$205$		0			0
$206$	−3484.13			−1.17840
$207$	1375.59	+	1997.96i	0.461883	+	0.670859i
$208$	580.554			0.193530
$209$	−2518.96	+	4362.96i	−0.833683	+	1.44398i
$210$		0			0
$211$	−2291.25	−	3968.57i	−0.747566	−	1.29482i	−0.948986	−	0.315318i	$-0.897889\pi$
$211$	−2291.25	−	3968.57i	−0.747566	−	1.29482i	0.201420	−	0.979505i	$-0.435444\pi$
$212$	313.765	+	543.458i	0.101649	+	0.176060i
$213$	63.9743	+	1611.32i	0.0205796	+	0.518338i
$214$	985.010	−	1706.09i	0.314644	−	0.544980i
$215$		0			0
$216$	−408.953	−	3419.00i	−0.128823	−	1.07701i
$217$	−772.111			−0.241541
$218$	−938.664	+	1625.81i	−0.291626	+	0.505110i
$219$	−10.5185	−	264.930i	−0.00324555	−	0.0817457i
$220$		0			0
$221$	−37.4384	−	64.8452i	−0.0113954	−	0.0197374i
$222$	−2762.82	−	1452.14i	−0.835263	−	0.439014i
$223$	2047.67	−	3546.66i	0.614897	−	1.06503i	−0.375506	−	0.926820i	$-0.622531\pi$
$223$	2047.67	−	3546.66i	0.614897	−	1.06503i	0.990403	−	0.138212i	$-0.0441356\pi$
$224$	−370.820			−0.110609
$225$		0			0
$226$	−1997.47			−0.587920
$227$	−1934.68	+	3350.96i	−0.565678	+	0.979784i	0.431308	+	0.902205i	$0.358052\pi$
$227$	−1934.68	+	3350.96i	−0.565678	+	0.979784i	−0.996986	+	0.0775789i	$0.975281\pi$
$228$	−1338.47	+	845.281i	−0.388781	+	0.245527i
$229$	−618.006	−	1070.42i	−0.178336	−	0.308887i	0.762975	−	0.646429i	$-0.223738\pi$
$229$	−618.006	−	1070.42i	−0.178336	−	0.308887i	−0.941311	+	0.337541i	$0.890405\pi$
$230$		0			0
$231$	−639.929	+	404.134i	−0.182269	+	0.115109i
$232$	−2795.27	+	4841.56i	−0.791029	+	1.37010i
$233$	−2207.05			−0.620552			−0.310276	−	0.950647i	$-0.600421\pi$
$233$	−2207.05			−0.620552			−0.310276	+	0.950647i	$0.600421\pi$
$234$	1208.05	−	96.0781i	0.337491	−	0.0268411i
$235$		0			0
$236$	1179.99	−	2043.80i	0.325470	−	0.563730i
$237$	5556.22	+	2920.35i	1.52285	+	0.800409i
$238$	−11.1105	−	19.2440i	−0.00302600	−	0.00524119i
$239$	−438.324	−	759.199i	−0.118631	−	0.205475i	0.800594	−	0.599207i	$-0.204517\pi$
$239$	−438.324	−	759.199i	−0.118631	−	0.205475i	−0.919225	+	0.393732i	$0.871184\pi$
$240$		0			0
$241$	238.931	−	413.840i	0.0638626	−	0.110613i	−0.832326	−	0.554286i	$-0.812991\pi$
$241$	238.931	−	413.840i	0.0638626	−	0.110613i	0.896189	+	0.443673i	$0.146325\pi$
$242$	3164.32			0.840537
$243$	−746.658	−	3713.68i	−0.197112	−	0.980381i
$244$	−1555.49			−0.408114
$245$		0			0
$246$	−29.3424	−	739.048i	−0.00760490	−	0.191545i
$247$	−978.396	−	1694.63i	−0.252040	−	0.436546i
$248$	3425.53	+	5933.19i	0.877102	+	1.51919i
$249$	−4163.59	−	2188.38i	−1.05967	−	0.556960i
$250$		0			0
$251$	6892.28			1.73322			0.866608	−	0.498990i	$-0.166296\pi$
$251$	6892.28			1.73322			0.866608	+	0.498990i	$0.166296\pi$
$252$	−237.074	+	18.8548i	−0.0592630	+	0.00471327i
$253$	−4730.94			−1.17562
$254$	−2236.41	+	3873.57i	−0.552460	+	0.956889i
$255$		0			0
$256$	2006.72	+	3475.74i	0.489921	+	0.848568i
$257$	−3628.35	−	6284.49i	−0.880664	−	1.52535i	−0.850605	−	0.525806i	$-0.823764\pi$
$257$	−3628.35	−	6284.49i	−0.880664	−	1.52535i	−0.0300589	−	0.999548i	$-0.509569\pi$
$258$	4037.30	−	2549.67i	0.974230	−	0.615255i
$259$	−378.569	+	655.701i	−0.0908229	+	0.157310i
$260$		0			0
$261$	−2643.10	+	5553.15i	−0.626834	+	1.31698i
$262$	517.110			0.121936
$263$	−3158.78	+	5471.16i	−0.740603	+	1.28276i	0.211618	+	0.977352i	$0.432127\pi$
$263$	−3158.78	+	5471.16i	−0.740603	+	1.28276i	−0.952221	+	0.305409i	$0.901207\pi$
$264$	5944.61	+	3124.48i	1.38585	+	0.728404i
$265$		0			0
$266$	−290.357	−	502.913i	−0.0669283	−	0.115923i
$267$	−136.802	−	3445.63i	−0.0313563	−	0.789771i
$268$	655.142	−	1134.74i	0.149325	−	0.258639i
$269$	5746.22			1.30243			0.651214	−	0.758894i	$-0.274260\pi$
$269$	5746.22			1.30243			0.651214	+	0.758894i	$0.274260\pi$
$270$		0			0
$271$	4925.20			1.10400			0.552001	−	0.833844i	$-0.313865\pi$
$271$	4925.20			1.10400			0.552001	+	0.833844i	$0.313865\pi$
$272$	−51.9550	+	89.9886i	−0.0115817	+	0.0200602i
$273$	−11.6625	−	293.742i	−0.00258551	−	0.0651212i
$274$	−3261.92	−	5649.81i	−0.719196	−	1.24568i
$275$		0			0
$276$	−1315.89	−	691.629i	−0.286982	−	0.150837i
$277$	1162.94	−	2014.27i	0.252254	−	0.436917i	−0.711892	−	0.702289i	$-0.752161\pi$
$277$	1162.94	−	2014.27i	0.252254	−	0.436917i	0.964146	+	0.265372i	$0.0854948\pi$
$278$	−4596.55			−0.991665
$279$	4273.98	+	6207.70i	0.917119	+	1.33206i
$280$		0			0
$281$	−1641.71	+	2843.52i	−0.348527	+	0.603667i	−0.985988	−	0.166816i	$-0.946652\pi$
$281$	−1641.71	+	2843.52i	−0.348527	+	0.603667i	0.637461	+	0.770483i	$0.279985\pi$
$282$	1337.30	−	844.543i	0.282393	−	0.178340i
$283$	1007.11	+	1744.36i	0.211541	+	0.366400i	0.952197	−	0.305484i	$-0.0988184\pi$
$283$	1007.11	+	1744.36i	0.211541	+	0.366400i	−0.740656	+	0.671885i	$0.765485\pi$
$284$	−494.131	−	855.860i	−0.103244	−	0.178824i
$285$		0			0
$286$	−1181.77	+	2046.89i	−0.244334	+	0.423199i
$287$	−179.419			−0.0369016
$288$	2052.65	+	2981.36i	0.419978	+	0.609994i
$289$	−4899.60			−0.997272
$290$		0			0
$291$	3336.20	+	1753.50i	0.672067	+	0.353238i
$292$	81.2440	+	140.719i	0.0162823	+	0.0282018i
$293$	240.348	+	416.295i	0.0479225	+	0.0830042i	0.888992	−	0.457923i	$-0.151407\pi$
$293$	240.348	+	416.295i	0.0479225	+	0.0830042i	−0.841069	+	0.540928i	$0.818073\pi$
$294$	151.700	+	3820.86i	0.0300929	+	0.757950i
$295$		0			0
$296$	6718.20			1.31921
$297$	6791.49	+	2907.91i	1.32688	+	0.568128i
$298$	601.140			0.116856
$299$	918.781	−	1591.37i	0.177707	−	0.307798i
$300$		0			0
$301$	−579.158	−	1003.13i	−0.110904	−	0.192091i
$302$	1027.93	+	1780.42i	0.195863	+	0.339244i
$303$	4497.33	+	2363.79i	0.852690	+	0.448173i
$304$	−1357.76	+	2351.72i	−0.256162	+	0.443685i
$305$		0			0
$306$	−93.2184	+	195.852i	−0.0174148	+	0.0365886i
$307$	−3222.21			−0.599026			−0.299513	−	0.954092i	$-0.596824\pi$
$307$	−3222.21			−0.599026			−0.299513	+	0.954092i	$0.596824\pi$
$308$	231.917	−	401.691i	0.0429048	−	0.0743133i
$309$	6975.40	−	4405.17i	1.28420	−	0.811008i
$310$		0			0
$311$	−1207.00	−	2090.59i	−0.220074	−	0.381179i	0.734757	−	0.678331i	$-0.237296\pi$
$311$	−1207.00	−	2090.59i	−0.220074	−	0.381179i	−0.954830	+	0.297152i	$0.903963\pi$
$312$	−2205.48	+	1392.83i	−0.400195	+	0.252735i
$313$	−1253.47	+	2171.07i	−0.226359	+	0.392065i	−0.956726	−	0.290990i	$-0.906015\pi$
$313$	−1253.47	+	2171.07i	−0.226359	+	0.392065i	0.730368	+	0.683054i	$0.239349\pi$
$314$	−874.344			−0.157140
$315$		0			0
$316$	−3846.77			−0.684803
$317$	1853.56	−	3210.46i	0.328411	−	0.568825i	−0.653786	−	0.756680i	$-0.726820\pi$
$317$	1853.56	−	3210.46i	0.328411	−	0.568825i	0.982197	+	0.187855i	$0.0601535\pi$
$318$	1989.04	+	1045.44i	0.350754	+	0.184356i
$319$	−5997.34	−	10387.7i	−1.05262	−	1.82320i
$320$		0			0
$321$	185.059	+	4661.07i	0.0321775	+	0.810454i
$322$	272.665	−	472.270i	0.0471895	−	0.0817347i
$323$	350.234			0.0603330
$324$	1463.90	+	1801.69i	0.251012	+	0.308931i
$325$		0			0
$326$	524.641	−	908.704i	0.0891324	−	0.154382i
$327$	−176.352	−	4441.77i	−0.0298234	−	0.751163i
$328$	796.005	+	1378.72i	0.134000	+	0.232095i
$329$	−191.838	−	332.272i	−0.0321470	−	0.0556802i
$330$		0			0
$331$	−1276.72	+	2211.35i	−0.212009	+	0.367211i	−0.952343	−	0.305029i	$-0.901334\pi$
$331$	−1276.72	+	2211.35i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$332$	2882.60			0.476516
$333$	7367.32	−	585.933i	1.21239	−	0.0964233i
$334$	746.906			0.122362
$335$		0			0
$336$	−344.934	+	217.836i	−0.0560050	+	0.0353688i
$337$	1776.44	+	3076.89i	0.287148	+	0.497356i	0.973128	−	0.230265i	$-0.0739594\pi$
$337$	1776.44	+	3076.89i	0.287148	+	0.497356i	−0.685979	+	0.727621i	$0.740626\pi$
$338$	1951.58	+	3380.24i	0.314059	+	0.543966i
$339$	3999.04	−	2525.51i	0.640702	−	0.404623i
$340$		0			0
$341$	−14699.2			−2.33432
$342$	−2436.12	+	5118.29i	−0.385177	+	0.809256i
$343$	1876.35			0.295374
$344$	−5138.95	+	8900.93i	−0.805447	+	1.39508i
$345$		0			0
$346$	4143.19	+	7176.21i	0.643754	+	1.11502i
$347$	−3884.01	−	6727.30i	−0.600878	−	1.04075i	−0.992688	−	0.120705i	$-0.961485\pi$
$347$	−3884.01	−	6727.30i	−0.600878	−	1.04075i	0.391811	−	0.920046i	$-0.371849\pi$
$348$	−149.524	−	3766.05i	−0.0230325	−	0.580119i
$349$	−348.003	+	602.760i	−0.0533759	+	0.0924498i	−0.891479	−	0.453062i	$-0.850331\pi$
$349$	−348.003	+	602.760i	−0.0533759	+	0.0924498i	0.838103	+	0.545512i	$0.183665\pi$
$350$		0			0
$351$	−2297.10	+	1719.76i	−0.349317	+	0.261521i
$352$	−7059.52			−1.06896
$353$	−2725.94	+	4721.46i	−0.411011	+	0.711892i	−0.995001	−	0.0998692i	$-0.968158\pi$
$353$	−2725.94	+	4721.46i	−0.411011	+	0.711892i	0.583990	+	0.811761i	$0.301491\pi$
$354$	−335.248	−	8443.90i	−0.0503340	−	1.26776i
$355$		0			0
$356$	1056.64	+	1830.16i	0.157309	+	0.272467i
$357$	46.5751	+	24.4798i	0.00690481	+	0.00362916i
$358$	−204.798	+	354.721i	−0.0302344	+	0.0523675i
$359$	4036.41			0.593408			0.296704	−	0.954969i	$-0.404113\pi$
$359$	4036.41			0.593408			0.296704	+	0.954969i	$0.404113\pi$
$360$		0			0
$361$	2293.85			0.334429
$362$	−1578.63	+	2734.26i	−0.229201	+	0.396988i
$363$	−6335.12	+	4000.82i	−0.915999	+	0.578481i
$364$	90.0795	+	156.022i	0.0129710	+	0.0224665i
$365$		0			0
$366$	−4709.34	+	2974.09i	−0.672572	+	0.424749i
$367$	5619.96	−	9734.06i	0.799345	−	1.38451i	−0.120698	−	0.992689i	$-0.538513\pi$
$367$	5619.96	−	9734.06i	0.799345	−	1.38451i	0.920043	−	0.391817i	$-0.128153\pi$
$368$	−2550.07			−0.361227
$369$	993.163	+	1442.51i	0.140114	+	0.203507i
$370$		0			0
$371$	272.543	−	472.059i	0.0381394	−	0.0660595i
$372$	−4088.49	−	2148.91i	−0.569834	−	0.299504i
$373$	−3160.36	−	5473.90i	−0.438706	−	0.759860i	0.558884	−	0.829246i	$-0.311230\pi$
$373$	−3160.36	−	5473.90i	−0.438706	−	0.759860i	−0.997590	+	0.0693853i	$0.977896\pi$
$374$	−211.518	−	366.360i	−0.0292442	−	0.0506525i
$375$		0			0
$376$	−1702.20	+	2948.30i	−0.233469	+	0.404381i
$377$	4658.90			0.636460
$378$	−681.708	+	510.370i	−0.0927600	+	0.0694460i
$379$	9325.49			1.26390			0.631950	−	0.775009i	$-0.282255\pi$
$379$	9325.49			1.26390			0.631950	+	0.775009i	$0.282255\pi$
$380$		0			0
$381$	−420.165	−	10582.7i	−0.0564980	−	1.42301i
$382$	428.394	+	742.000i	0.0573784	+	0.0993823i
$383$	5574.01	+	9654.47i	0.743652	+	1.28804i	0.950822	+	0.309738i	$0.100241\pi$
$383$	5574.01	+	9654.47i	0.743652	+	1.28804i	−0.207170	+	0.978305i	$0.566425\pi$
$384$	328.377	+	172.595i	0.0436391	+	0.0229367i
$385$		0			0
$386$	8591.35			1.13287
$387$	−4859.19	+	10209.1i	−0.638259	+	1.34098i
$388$	−2309.77			−0.302219
$389$	−3285.41	+	5690.49i	−0.428218	+	0.741695i	−0.996715	−	0.0809902i	$-0.974192\pi$
$389$	−3285.41	+	5690.49i	−0.428218	+	0.741695i	0.568497	+	0.822685i	$0.307525\pi$
$390$		0			0
$391$	164.447	+	284.831i	0.0212697	+	0.0368402i
$392$	−4115.33	−	7127.96i	−0.530244	−	0.918409i
$393$	−1035.28	+	653.810i	−0.132883	+	0.0839195i
$394$	−979.469	+	1696.49i	−0.125241	+	0.216924i
$395$		0			0
$396$	−4513.33	+	358.951i	−0.572735	+	0.0455504i
$397$	−3969.33			−0.501800			−0.250900	−	0.968013i	$-0.580727\pi$
$397$	−3969.33			−0.501800			−0.250900	+	0.968013i	$0.580727\pi$
$398$	3039.86	−	5265.19i	0.382850	−	0.663115i
$399$	1217.17	+	639.743i	0.152719	+	0.0802687i
$400$		0			0
$401$	−2187.35	−	3788.60i	−0.272396	−	0.471804i	0.697079	−	0.716995i	$-0.254483\pi$
$401$	−2187.35	−	3788.60i	−0.272396	−	0.471804i	−0.969475	+	0.245190i	$0.921150\pi$
$402$	−186.133	−	4688.13i	−0.0230932	−	0.581649i
$403$	2854.67	−	4944.44i	0.352857	−	0.611166i
$404$	−3113.66			−0.383442
$405$		0			0
$406$	1382.61			0.169010
$407$	−7207.05	+	12483.0i	−0.877740	+	1.52029i
$408$	−18.5217	−	466.507i	−0.00224746	−	0.0566067i
$409$	4436.16	+	7683.66i	0.536318	+	0.928930i	0.999098	+	0.0424573i	$0.0135186\pi$
$409$	4436.16	+	7683.66i	0.536318	+	0.928930i	−0.462780	+	0.886473i	$0.653148\pi$
$410$		0			0
$411$	13673.9	+	7186.99i	1.64108	+	0.862550i
$412$	−2527.95	+	4378.55i	−0.302290	+	0.523581i
$413$	−2049.93			−0.244238
$414$	−5306.33	+	422.020i	−0.629932	+	0.0500994i
$415$		0			0
$416$	1371.01	−	2374.65i	0.161584	−	0.279872i
$417$	9202.53	−	5811.67i	1.08069	−	0.682491i
$418$	−5527.71	−	9574.27i	−0.646816	−	1.12032i
$419$	507.087	+	878.300i	0.0591236	+	0.102405i	0.894072	−	0.447923i	$-0.147836\pi$
$419$	507.087	+	878.300i	0.0591236	+	0.102405i	−0.834949	+	0.550328i	$0.814503\pi$
$420$		0			0
$421$	7446.57	−	12897.8i	0.862051	−	1.49312i	−0.00789511	−	0.999969i	$-0.502513\pi$
$421$	7446.57	−	12897.8i	0.862051	−	1.49312i	0.869946	−	0.493147i	$-0.164154\pi$
$422$	10056.1			1.16000
$423$	−1609.54	+	3381.63i	−0.185008	+	0.388701i
$424$	−4836.63			−0.553980
$425$		0			0
$426$	−3132.42	−	1646.40i	−0.356259	−	0.187249i
$427$	675.563	+	1170.11i	0.0765639	+	0.132613i
$428$	−1429.37	−	2475.75i	−0.161429	−	0.279602i
$429$	−222.025	−	5592.15i	−0.0249871	−	0.629351i
$430$		0			0
$431$	−4363.90			−0.487707			−0.243853	−	0.969812i	$-0.578412\pi$
$431$	−4363.90			−0.487707			−0.243853	+	0.969812i	$0.578412\pi$
$432$	3660.74	+	1567.42i	0.407703	+	0.174566i
$433$	−9301.59			−1.03235			−0.516173	−	0.856484i	$-0.672644\pi$
$433$	−9301.59			−1.03235			−0.516173	+	0.856484i	$0.672644\pi$
$434$	847.177	−	1467.35i	0.0937000	−	0.162293i
$435$		0			0
$436$	1362.12	+	2359.26i	0.149619	+	0.259147i
$437$	4297.57	+	7443.62i	0.470437	+	0.814820i
$438$	515.026	+	270.697i	0.0561847	+	0.0295306i
$439$	−760.076	+	1316.49i	−0.0826343	+	0.143127i	−0.904381	−	0.426727i	$-0.859667\pi$
$439$	−760.076	+	1316.49i	−0.0826343	+	0.143127i	0.821746	+	0.569853i	$0.193000\pi$
$440$		0			0
$441$	−5134.63	−	7457.76i	−0.554436	−	0.805286i
$442$	164.313			0.0176823
$443$	2231.24	−	3864.62i	0.239299	−	0.414478i	−0.721214	−	0.692712i	$-0.756416\pi$
$443$	2231.24	−	3864.62i	0.239299	−	0.414478i	0.960513	+	0.278234i	$0.0897490\pi$
$444$	−3829.52	+	2418.45i	−0.409326	+	0.258502i
$445$		0			0
$446$	4493.49	+	7782.96i	0.477070	+	0.826309i
$447$	−1203.51	+	760.053i	−0.127347	+	0.0804235i
$448$	720.919	−	1248.67i	0.0760273	−	0.131683i
$449$	−5371.66			−0.564598			−0.282299	−	0.959326i	$-0.591097\pi$
$449$	−5371.66			−0.564598			−0.282299	+	0.959326i	$0.591097\pi$
$450$		0			0
$451$	−3415.71			−0.356628
$452$	−1449.29	+	2510.25i	−0.150816	+	0.261222i
$453$	−4309.04	−	2264.83i	−0.446923	−	0.234903i
$454$	−4245.54	−	7353.49i	−0.438883	−	0.760168i
$455$		0			0
$456$	−484.038	−	12191.5i	−0.0497087	−	1.25201i
$457$	7762.71	−	13445.4i	0.794583	−	1.37626i	−0.128520	−	0.991707i	$-0.541023\pi$
$457$	7762.71	−	13445.4i	0.794583	−	1.37626i	0.923104	−	0.384551i	$-0.125644\pi$
$458$	2712.36			0.276725
$459$	−60.9982	−	509.966i	−0.00620294	−	0.0518588i
$460$		0			0
$461$	28.2090	−	48.8594i	0.00284994	−	0.00493624i	−0.864597	−	0.502466i	$-0.832426\pi$
$461$	28.2090	−	48.8594i	0.00284994	−	0.00493624i	0.867447	+	0.497530i	$0.165760\pi$
$462$	−65.8901	−	1659.57i	−0.00663525	−	0.167122i
$463$	6686.89	+	11582.0i	0.671201	+	1.16255i	0.977564	+	0.210640i	$0.0675547\pi$
$463$	6686.89	+	11582.0i	0.671201	+	1.16255i	−0.306363	+	0.951915i	$0.599112\pi$
$464$	−3232.68	−	5599.17i	−0.323434	−	0.560204i
$465$		0			0
$466$	2421.62	−	4194.37i	0.240729	−	0.416954i
$467$	−2677.46			−0.265306			−0.132653	−	0.991163i	$-0.542350\pi$
$467$	−2677.46			−0.265306			−0.132653	+	0.991163i	$0.542350\pi$
$468$	755.776	−	1587.88i	0.0746490	−	0.156838i
$469$	−1138.14			−0.112056
$470$		0			0
$471$	1750.48	−	1105.48i	0.171248	−	0.108148i
$472$	9094.66	+	15752.4i	0.886898	+	1.53615i
$473$	−11025.8	−	19097.2i	−1.07181	−	1.85643i
$474$	−11646.4	+	7355.02i	−1.12856	+	0.712716i
$475$		0			0
$476$	−32.2456			−0.00310499
$477$	−5303.96	+	421.831i	−0.509123	+	0.0404912i
$478$	1923.75			0.184080
$479$	1734.96	−	3005.05i	0.165496	−	0.286647i	−0.771335	−	0.636429i	$-0.780411\pi$
$479$	1734.96	−	3005.05i	0.165496	−	0.286647i	0.936831	+	0.349782i	$0.113744\pi$
$480$		0			0
$481$	−2799.31	−	4848.55i	−0.265359	−	0.459616i
$482$	524.320	+	908.149i	0.0495480	+	0.0858196i
$483$	51.2270	+	1290.25i	0.00482589	+	0.121550i
$484$	2295.91	−	3976.64i	0.215619	−	0.373463i
$485$		0			0
$486$	7876.89	+	2655.75i	0.735191	+	0.247875i
$487$	14040.6			1.30645			0.653224	−	0.757165i	$-0.273416\pi$
$487$	14040.6			1.30645			0.653224	+	0.757165i	$0.273416\pi$
$488$	5994.38	−	10382.6i	0.556051	−	0.963108i
$489$	98.5669	+	2482.60i	0.00911523	+	0.229585i
$490$		0			0
$491$	−4907.72	−	8500.42i	−0.451084	−	0.781301i	0.547369	−	0.836891i	$-0.315629\pi$
$491$	−4907.72	−	8500.42i	−0.451084	−	0.781301i	−0.998454	+	0.0555902i	$0.982296\pi$
$492$	−950.060	−	499.351i	−0.0870570	−	0.0457571i
$493$	−416.934	+	722.151i	−0.0380888	+	0.0659717i
$494$	4294.07			0.391092
$495$		0			0
$496$	−7923.12			−0.717255
$497$	−429.212	+	743.418i	−0.0387380	+	0.0670962i
$498$	8727.28	−	5511.53i	0.785299	−	0.495939i
$499$	6026.00	+	10437.3i	0.540603	+	0.936351i	0.998869	+	0.0475367i	$0.0151371\pi$
$499$	6026.00	+	10437.3i	0.540603	+	0.936351i	−0.458267	+	0.888815i	$0.651530\pi$
$500$		0			0
$501$	−1495.34	+	944.354i	−0.133347	+	0.0842128i
$502$	−7562.36	+	13098.4i	−0.672360	+	1.16456i
$503$	4695.09			0.416191			0.208095	−	0.978109i	$-0.433274\pi$
$503$	4695.09			0.416191			0.208095	+	0.978109i	$0.433274\pi$
$504$	787.760	−	1655.08i	0.0696223	−	0.146276i
$505$		0			0
$506$	5190.89	−	8990.89i	0.456054	−	0.789909i
$507$	−8180.98	−	4299.92i	−0.716627	−	0.376659i
$508$	3245.31	+	5621.05i	0.283440	+	0.490932i
$509$	409.907	+	709.979i	0.0356951	+	0.0618257i	0.883321	−	0.468769i	$-0.155302\pi$
$509$	409.907	+	709.979i	0.0356951	+	0.0618257i	−0.847626	+	0.530594i	$0.821969\pi$
$510$		0			0
$511$	70.5702	−	122.231i	0.00610928	−	0.0105816i
$512$	−9378.41			−0.809514
$513$	−1594.09	−	13327.2i	−0.137195	−	1.14700i
$514$	15924.4			1.36653
$515$		0			0
$516$	−274.891	−	6923.67i	−0.0234523	−	0.590693i
$517$	−3652.13	−	6325.68i	−0.310678	−	0.538110i
$518$	−830.748	−	1438.90i	−0.0704652	−	0.122049i
$519$	−17368.1	−	9128.68i	−1.46893	−	0.772070i
$520$		0			0
$521$	3282.80			0.276050			0.138025	−	0.990429i	$-0.455925\pi$
$521$	3282.80			0.276050			0.138025	+	0.990429i	$0.455925\pi$
$522$	−7653.38	−	11116.1i	−0.641723	−	0.932066i
$523$	10768.1			0.900300			0.450150	−	0.892953i	$-0.351371\pi$
$523$	10768.1			0.900300			0.450150	+	0.892953i	$0.351371\pi$
$524$	375.196	−	649.859i	0.0312796	−	0.0541779i
$525$		0			0
$526$	−6931.76	−	12006.2i	−0.574599	−	0.995235i
$527$	510.941	+	884.975i	0.0422333	+	0.0731502i
$528$	−6566.71	+	4147.07i	−0.541249	+	0.341815i
$529$	2047.78	−	3546.87i	0.168306	−	0.291515i
$530$		0			0
$531$	11347.3	+	16481.2i	0.927362	+	1.34694i
$532$	−842.690			−0.0686752
$533$	663.353	−	1148.96i	0.0539081	−	0.0933716i
$534$	6698.32	+	3520.63i	0.542818	+	0.285305i
$535$		0			0
$536$	5049.44	+	8745.89i	0.406908	+	0.704785i
$537$	−38.4765	−	969.106i	−0.00309196	−	0.0778771i
$538$	−6304.88	+	10920.4i	−0.505247	+	0.875113i
$539$	17659.1			1.41119
$540$		0			0
$541$	−16037.9			−1.27453			−0.637266	−	0.770644i	$-0.719935\pi$
$541$	−16037.9			−1.27453			−0.637266	+	0.770644i	$0.719935\pi$
$542$	−5404.04	+	9360.06i	−0.428272	+	0.741788i
$543$	−296.585	−	7470.08i	−0.0234395	−	0.590372i
$544$	245.388	+	425.025i	0.0193399	+	0.0334978i
$545$		0			0
$546$	571.037	+	300.137i	0.0447585	+	0.0235250i
$547$	1024.56	−	1774.59i	0.0800862	−	0.138713i	−0.823201	−	0.567751i	$-0.807814\pi$
$547$	1024.56	−	1774.59i	0.0800862	−	0.138713i	0.903287	+	0.429037i	$0.141147\pi$
$548$	−9466.92			−0.737968
$549$	5668.04	−	11908.5i	0.440630	−	0.925764i
$550$		0			0
$551$	−10895.9	+	18872.3i	−0.842437	+	1.45914i
$552$	9687.52	−	6117.95i	0.746971	−	0.471734i
$553$	1670.69	+	2893.72i	0.128472	+	0.222520i
$554$	2552.01	+	4420.21i	0.195712	+	0.338983i
$555$		0			0
$556$	−3335.09	+	5776.54i	−0.254387	+	0.440611i
$557$	−3644.07			−0.277207			−0.138603	−	0.990348i	$-0.544261\pi$
$557$	−3644.07			−0.277207			−0.138603	+	0.990348i	$0.544261\pi$
$558$	−16486.9	+	1311.23i	−1.25080	+	0.0994778i
$559$	8565.12			0.648061
$560$		0			0
$561$	886.679	+	466.038i	0.0667301	+	0.0350733i
$562$	−3602.64	−	6239.96i	−0.270406	−	0.468357i
$563$	175.368	+	303.746i	0.0131277	+	0.0227378i	0.872515	−	0.488588i	$-0.162488\pi$
$563$	175.368	+	303.746i	0.0131277	+	0.0227378i	−0.859387	+	0.511326i	$0.829155\pi$
$564$	−91.0536	−	2293.37i	−0.00679796	−	0.171220i
$565$		0			0
$566$	−4420.07			−0.328250
$567$	719.525	−	1883.71i	0.0532932	−	0.139521i
$568$	7616.93			0.562675
$569$	9724.34	−	16843.1i	0.716460	−	1.24095i	−0.245934	−	0.969287i	$-0.579095\pi$
$569$	9724.34	−	16843.1i	0.716460	−	1.24095i	0.962394	−	0.271658i	$-0.0875721\pi$
$570$		0			0
$571$	7572.97	+	13116.8i	0.555024	+	0.961330i	0.997902	+	0.0647480i	$0.0206244\pi$
$571$	7572.97	+	13116.8i	0.555024	+	0.961330i	−0.442877	+	0.896582i	$0.646042\pi$
$572$	1714.90	+	2970.29i	0.125356	+	0.217123i
$573$	−1795.82	−	943.880i	−0.130927	−	0.0688153i
$574$	196.862	−	340.975i	0.0143151	−	0.0247945i
$575$		0			0
$576$	−14029.8	+	1115.81i	−1.01489	+	0.0807154i
$577$	6365.11			0.459243			0.229621	−	0.973280i	$-0.426251\pi$
$577$	6365.11			0.459243			0.229621	+	0.973280i	$0.426251\pi$
$578$	5375.95	−	9311.41i	0.386868	−	0.670076i
$579$	−17200.3	+	10862.5i	−1.23458	+	0.779673i
$580$		0			0
$581$	−1251.94	−	2168.43i	−0.0893965	−	0.154839i
$582$	−6992.99	+	4416.28i	−0.498056	+	0.314537i
$583$	5188.57	−	8986.87i	0.368591	−	0.638419i
$584$	−1252.36			−0.0887381
$585$		0			0
$586$	−1054.86			−0.0743617
$587$	5142.18	−	8906.52i	0.361568	−	0.626254i	−0.626651	−	0.779300i	$-0.715575\pi$
$587$	5142.18	−	8906.52i	0.361568	−	0.626254i	0.988219	+	0.153046i	$0.0489081\pi$
$588$	4911.79	+	2581.63i	0.344488	+	0.181063i
$589$	13352.7	+	23127.5i	0.934103	+	1.61791i
$590$		0			0
$591$	−184.018	−	4634.85i	−0.0128079	−	0.322593i
$592$	−3884.73	+	6728.56i	−0.269699	+	0.467132i
$593$	−666.566			−0.0461595			−0.0230798	−	0.999734i	$-0.507347\pi$
$593$	−666.566			−0.0461595			−0.0230798	+	0.999734i	$0.507347\pi$
$594$	−12978.1	+	9716.23i	−0.896461	+	0.671148i
$595$		0			0
$596$	436.165	−	755.460i	0.0299765	−	0.0519209i
$597$	571.113	+	14384.6i	0.0391526	+	0.986136i
$598$	2016.21	+	3492.18i	0.137875	+	0.238806i
$599$	−12606.6	−	21835.3i	−0.859922	−	1.48943i	−0.872003	−	0.489501i	$-0.837179\pi$
$599$	−12606.6	−	21835.3i	−0.859922	−	1.48943i	0.0120807	−	0.999927i	$-0.496155\pi$
$600$		0			0
$601$	10309.3	−	17856.3i	0.699712	−	1.21194i	−0.268855	−	0.963181i	$-0.586645\pi$
$601$	10309.3	−	17856.3i	0.699712	−	1.21194i	0.968566	−	0.248755i	$-0.0800215\pi$
$602$	2541.86			0.172090
$603$	6300.11	+	9150.54i	0.425473	+	0.617975i
$604$	2983.30			0.200975
$605$		0			0
$606$	−9426.83	+	5953.32i	−0.631912	+	0.399071i
$607$	−2541.76	−	4402.45i	−0.169962	−	0.294382i	0.768444	−	0.639916i	$-0.221031\pi$
$607$	−2541.76	−	4402.45i	−0.169962	−	0.294382i	−0.938406	+	0.345534i	$0.887698\pi$
$608$	6412.85	+	11107.4i	0.427755	+	0.740894i
$609$	−2768.06	+	1748.11i	−0.184183	+	0.116317i
$610$		0			0
$611$	2837.07			0.187849
$612$	178.494	+	259.252i	0.0117895	+	0.0171236i
$613$	−2625.18			−0.172969			−0.0864845	−	0.996253i	$-0.527563\pi$
$613$	−2625.18			−0.172969			−0.0864845	+	0.996253i	$0.527563\pi$
$614$	3535.47	−	6123.62i	0.232378	−	0.402491i
$615$		0			0
$616$	1787.48	+	3096.00i	0.116915	+	0.202502i
$617$	−815.659	−	1412.76i	−0.0532208	−	0.0921811i	0.838188	−	0.545382i	$-0.183615\pi$
$617$	−815.659	−	1412.76i	−0.0532208	−	0.0921811i	−0.891408	+	0.453201i	$0.850282\pi$
$618$	718.220	+	18089.8i	0.0467493	+	1.17747i
$619$	−1592.33	+	2758.00i	−0.103395	+	0.179085i	−0.913081	−	0.407778i	$-0.866304\pi$
$619$	−1592.33	+	2758.00i	−0.103395	+	0.179085i	0.809687	+	0.586863i	$0.199637\pi$
$620$		0			0
$621$	10090.0	−	7553.99i	0.652007	−	0.488134i
$622$	5297.40			0.341489
$623$	917.821	−	1589.71i	0.0590236	−	0.102232i
$624$	−119.676	−	3014.27i	−0.00767767	−	0.193377i
$625$		0			0
$626$	−2750.67	−	4764.29i	−0.175621	−	0.304184i
$627$	23172.0	+	12179.2i	1.47592	+	0.775742i
$628$	−634.392	+	1098.80i	−0.0403105	+	0.0698199i
$629$	1002.06			0.0635214
$630$		0			0
$631$	10436.7			0.658447			0.329223	−	0.944252i	$-0.393213\pi$
$631$	10436.7			0.658447			0.329223	+	0.944252i	$0.393213\pi$
$632$	14824.3	−	25676.4i	0.933037	−	1.61607i
$633$	−20132.7	+	12714.4i	−1.26415	+	0.798346i
$634$	4067.54	+	7045.18i	0.254799	+	0.441325i
$635$		0			0
$636$	2756.99	−	1741.12i	0.171889	−	0.108553i
$637$	−3429.52	+	5940.11i	−0.213316	+	0.369475i
$638$	26321.7			1.63336
$639$	8352.89	−	664.317i	0.517113	−	0.0411267i
$640$		0			0
$641$	−4541.73	+	7866.50i	−0.279856	+	0.484724i	−0.971349	−	0.237659i	$-0.923620\pi$
$641$	−4541.73	+	7866.50i	−0.279856	+	0.484724i	0.691493	+	0.722383i	$0.256953\pi$
$642$	−9061.16	−	4762.54i	−0.557034	−	0.292776i
$643$	8593.81	+	14884.9i	0.527071	+	0.912914i	0.999502	+	0.0315465i	$0.0100432\pi$
$643$	8593.81	+	14884.9i	0.527071	+	0.912914i	−0.472431	+	0.881368i	$0.656623\pi$
$644$	−395.672	−	685.323i	−0.0242106	−	0.0419340i
$645$		0			0
$646$	−384.285	+	665.601i	−0.0234048	+	0.0405383i
$647$	−2359.17			−0.143352			−0.0716758	−	0.997428i	$-0.522835\pi$
$647$	−2359.17			−0.143352			−0.0716758	+	0.997428i	$0.522835\pi$
$648$	−17667.3	+	2828.11i	−1.07105	+	0.171448i
$649$	−39025.7			−2.36039
$650$		0			0
$651$	159.163	+	4008.85i	0.00958234	+	0.241350i
$652$	−761.320	−	1318.64i	−0.0457294	−	0.0792057i
$653$	2718.06	+	4707.81i	0.162888	+	0.282130i	0.935903	−	0.352257i	$-0.114586\pi$
$653$	2718.06	+	4707.81i	0.162888	+	0.282130i	−0.773015	+	0.634387i	$0.781252\pi$
$654$	8634.82	+	4538.46i	0.516282	+	0.271357i
$655$		0			0
$656$	−1841.13			−0.109579
$657$	−1373.36	+	109.226i	−0.0815526	+	0.00648599i
$658$	841.954			0.0498826
$659$	−1544.45	+	2675.07i	−0.0912950	+	0.158128i	−0.908056	−	0.418848i	$-0.862434\pi$
$659$	−1544.45	+	2675.07i	−0.0912950	+	0.158128i	0.816761	+	0.576976i	$0.195767\pi$
$660$		0			0
$661$	9526.94	+	16501.2i	0.560598	+	0.970984i	0.997444	+	0.0714479i	$0.0227620\pi$
$661$	9526.94	+	16501.2i	0.560598	+	0.970984i	−0.436846	+	0.899536i	$0.643905\pi$
$662$	−2801.70	−	4852.68i	−0.164488	−	0.284902i
$663$	−328.963	+	207.750i	−0.0192698	+	0.0121694i
$664$	−11108.7	+	19240.8i	−0.649248	+	1.12453i
$665$		0			0
$666$	−6970.05	+	14644.1i	−0.405532	+	0.852022i
$667$	−20464.1			−1.18796
$668$	541.928	−	938.646i	0.0313889	−	0.0543672i
$669$	−18836.6	−	9900.51i	−1.08859	−	0.572161i
$670$		0			0
$671$	12861.1	+	22276.1i	0.739937	+	1.28161i
$672$	76.4409	+	1925.32i	0.00438806	+	0.110522i
$673$	−14618.7	+	25320.4i	−0.837312	+	1.45027i	0.0548215	+	0.998496i	$0.482541\pi$
$673$	−14618.7	+	25320.4i	−0.837312	+	1.45027i	−0.892134	+	0.451771i	$0.850792\pi$
$674$	−7796.61			−0.445570
$675$		0			0
$676$	5663.98			0.322257
$677$	7235.62	−	12532.5i	0.410764	−	0.711465i	−0.584209	−	0.811603i	$-0.698595\pi$
$677$	7235.62	−	12532.5i	0.410764	−	0.711465i	0.994974	+	0.100138i	$0.0319285\pi$
$678$	411.760	+	10371.0i	0.0233238	+	0.587457i
$679$	1003.16	+	1737.52i	0.0566975	+	0.0982030i
$680$		0			0
$681$	17797.2	+	9354.19i	1.00145	+	0.526363i
$682$	16128.2	−	27934.9i	0.905545	−	1.56845i
$683$	−5782.94			−0.323980			−0.161990	−	0.986792i	$-0.551791\pi$
$683$	−5782.94			−0.323980			−0.161990	+	0.986792i	$0.551791\pi$
$684$	4664.66	+	6775.15i	0.260757	+	0.378734i
$685$		0			0
$686$	−2058.77	+	3565.89i	−0.114583	+	0.198464i
$687$	−5430.28	+	3429.38i	−0.301569	+	0.190450i
$688$	−5943.10	−	10293.8i	−0.329329	−	0.570415i
$689$	2015.31	+	3490.62i	0.111433	+	0.193007i
$690$		0			0
$691$	−5527.56	+	9574.01i	−0.304310	+	0.527080i	−0.977107	−	0.212746i	$-0.931759\pi$
$691$	−5527.56	+	9574.01i	−0.304310	+	0.527080i	0.672797	+	0.739827i	$0.265093\pi$
$692$	12024.6			0.660557
$693$	2230.20	+	3239.24i	0.122249	+	0.177559i
$694$	17046.5			0.932386
$695$		0			0
$696$	25713.9	+	13515.2i	1.40041	+	0.736052i
$697$	118.730	+	205.646i	0.00645223	+	0.0111756i
$698$	−763.674	−	1322.72i	−0.0414119	−	0.0717275i
$699$	454.962	+	11459.1i	0.0246184	+	0.620064i
$700$		0			0
$701$	−13554.2			−0.730294			−0.365147	−	0.930950i	$-0.618981\pi$
$701$	−13554.2			−0.730294			−0.365147	+	0.930950i	$0.618981\pi$
$702$	−747.872	−	6252.48i	−0.0402088	−	0.336160i
$703$	26187.4			1.40495
$704$	13724.6	−	23771.7i	0.734751	−	1.27263i
$705$		0			0
$706$	−5981.91	−	10361.0i	−0.318884	−	0.552324i
$707$	1352.30	+	2342.25i	0.0719354	+	0.124596i
$708$	−10854.8	−	5705.27i	−0.576198	−	0.302849i
$709$	4694.58	−	8131.26i	0.248672	−	0.430713i	−0.714485	−	0.699650i	$-0.753339\pi$
$709$	4694.58	−	8131.26i	0.248672	−	0.430713i	0.963158	+	0.268937i	$0.0866724\pi$
$710$		0			0
$711$	14017.3	−	29450.3i	0.739365	−	1.55340i
$712$	−16287.9			−0.857326
$713$	−12539.1	+	21718.3i	−0.658614	+	1.14075i
$714$	−97.6258	+	61.6536i	−0.00511702	+	0.00323155i
$715$		0			0
$716$	297.188	+	514.745i	0.0155118	+	0.0268672i
$717$	−3851.45	+	2432.31i	−0.200607	+	0.126689i
$718$	−4428.84	+	7670.97i	−0.230199	+	0.398716i
$719$	−26301.8			−1.36424			−0.682122	−	0.731238i	$-0.738943\pi$
$719$	−26301.8			−1.36424			−0.682122	+	0.731238i	$0.738943\pi$
$720$		0			0
$721$	4391.67			0.226844
$722$	−2516.86	+	4359.33i	−0.129734	+	0.224705i
$723$	−2197.94	−	1155.23i	−0.113060	−	0.0594241i
$724$	2290.79	+	3967.76i	0.117592	+	0.203675i
$725$		0			0
$726$	−652.294	−	16429.3i	−0.0333456	−	0.839876i
$727$	−12769.3	+	22117.1i	−0.651427	+	1.12830i	0.331350	+	0.943508i	$0.392496\pi$
$727$	−12769.3	+	22117.1i	−0.651427	+	1.12830i	−0.982777	+	0.184797i	$0.940837\pi$
$728$	−1388.56			−0.0706915
$729$	−19127.7	+	4642.23i	−0.971789	+	0.235850i
$730$		0			0
$731$	−766.510	+	1327.63i	−0.0387830	+	0.0671742i
$732$	320.649	+	8076.18i	0.0161906	+	0.407792i
$733$	3491.06	+	6046.70i	0.175914	+	0.304693i	0.940477	−	0.339856i	$-0.110378\pi$
$733$	3491.06	+	6046.70i	0.175914	+	0.304693i	−0.764563	+	0.644549i	$0.777045\pi$
$734$	12332.7	+	21360.8i	0.620174	+	1.07417i
$735$		0			0
$736$	−6022.10	+	10430.6i	−0.301600	+	0.522387i
$737$	−21667.5			−1.08295
$738$	−3831.13	+	304.695i	−0.191092	+	0.0151978i
$739$	8863.91			0.441224			0.220612	−	0.975362i	$-0.429195\pi$
$739$	8863.91			0.441224			0.220612	+	0.975362i	$0.429195\pi$
$740$		0			0
$741$	−8596.94	+	5429.22i	−0.426203	+	0.269160i
$742$	598.081	+	1035.91i	0.0295906	+	0.0512524i
$743$	−19472.4	−	33727.3i	−0.961473	−	1.66532i	−0.718806	−	0.695211i	$-0.755311\pi$
$743$	−19472.4	−	33727.3i	−0.961473	−	1.66532i	−0.242668	−	0.970110i	$-0.578022\pi$
$744$	30099.3	−	19008.6i	1.48319	−	0.936680i
$745$		0			0
$746$	13870.5			0.680742
$747$	−10503.9	+	22068.7i	−0.514482	+	1.08093i
$748$	−613.879			−0.0300075
$749$	−1241.58	+	2150.49i	−0.0605694	+	0.104909i
$750$		0			0
$751$	−8795.16	−	15233.7i	−0.427350	−	0.740192i	0.569287	−	0.822139i	$-0.307220\pi$
$751$	−8795.16	−	15233.7i	−0.427350	−	0.740192i	−0.996637	+	0.0819470i	$0.973886\pi$
$752$	−1968.57	−	3409.66i	−0.0954604	−	0.165342i
$753$	−1420.78	−	35785.2i	−0.0687597	−	1.73185i
$754$	−5111.84	+	8853.97i	−0.246900	+	0.427643i
$755$		0			0
$756$	146.766	+	1227.02i	0.00706062	+	0.0590293i
$757$	4075.85			0.195693			0.0978463	−	0.995202i	$-0.468805\pi$
$757$	4075.85			0.195693			0.0978463	+	0.995202i	$0.468805\pi$
$758$	−10232.1	+	17722.6i	−0.490300	+	0.849225i
$759$	975.239	+	24563.3i	0.0466389	+	1.17469i
$760$		0			0
$761$	−20268.5	−	35106.1i	−0.965483	−	1.67227i	−0.708312	−	0.705899i	$-0.750543\pi$
$761$	−20268.5	−	35106.1i	−0.965483	−	1.67227i	−0.257171	−	0.966366i	$-0.582790\pi$
$762$	20572.9	+	10813.1i	0.978052	+	0.514064i
$763$	1183.17	−	2049.30i	0.0561382	−	0.0972343i
$764$	1243.31			0.0588761
$765$		0			0
$766$	−24463.7			−1.15393
$767$	7579.06	−	13127.3i	0.356798	−	0.617992i
$768$	17632.6	−	11135.5i	0.828464	−	0.523200i
$769$	−12016.3	−	20812.9i	−0.563485	−	0.975985i	−0.997189	−	0.0749293i	$-0.976127\pi$
$769$	−12016.3	−	20812.9i	−0.563485	−	0.975985i	0.433704	−	0.901056i	$-0.357206\pi$
$770$		0			0
$771$	−31881.5	+	20134.1i	−1.48922	+	0.940484i
$772$	6233.57	−	10796.9i	0.290610	−	0.503351i
$773$	20881.5			0.971611			0.485805	−	0.874067i	$-0.338526\pi$
$773$	20881.5			0.971611			0.485805	+	0.874067i	$0.338526\pi$
$774$	−14070.3	−	20436.3i	−0.653420	−	0.949055i
$775$		0			0
$776$	8901.16	−	15417.3i	0.411770	−	0.713206i
$777$	3482.48	+	1830.39i	0.160789	+	0.0845106i
$778$	−7209.64	−	12487.5i	−0.332234	−	0.575446i
$779$	3102.82	+	5374.24i	0.142709	+	0.247179i
$780$		0			0
$781$	−8171.18	+	14152.9i	−0.374376	+	0.648439i
$782$	−721.740			−0.0330043
$783$	29377.1	+	12578.4i	1.34081	+	0.574093i
$784$	9518.60			0.433610
$785$		0			0
$786$	−106.597	−	2684.87i	−0.00483741	−	0.121840i
$787$	−2568.20	−	4448.25i	−0.116323	−	0.201478i	0.801985	−	0.597345i	$-0.203777\pi$
$787$	−2568.20	−	4448.25i	−0.116323	−	0.201478i	−0.918308	+	0.395867i	$0.870444\pi$
$788$	1421.33	+	2461.82i	0.0642549	+	0.111293i
$789$	29057.8	+	15272.7i	1.31113	+	0.689130i
$790$		0			0
$791$	2517.77			0.113175
$792$	14997.1	−	31508.9i	0.672851	−	1.41366i
$793$	−9990.86			−0.447397
$794$	4355.23	−	7543.48i	0.194662	−	0.337164i
$795$		0			0
$796$	−4411.22	−	7640.45i	−0.196421	−	0.340212i
$797$	10998.0	+	19049.1i	0.488794	+	0.846615i	0.999917	−	0.0128922i	$-0.00410382\pi$
$797$	10998.0	+	19049.1i	0.488794	+	0.846615i	−0.511123	+	0.859507i	$0.670770\pi$
$798$	−2551.30	+	1611.22i	−0.113177	+	0.0714745i
$799$	−253.895	+	439.760i	−0.0112418	+	0.0194713i
$800$		0			0
$801$	−17861.7	+	1420.57i	−0.787905	+	0.0626632i
$802$	9600.03			0.422679
$803$	1343.49	−	2326.99i	0.0590419	−	0.102264i
$804$	−6026.69	−	3167.62i	−0.264359	−	0.138947i
$805$		0			0
$806$	6264.42	+	10850.3i	0.273765	+	0.474175i
$807$	−1184.53	−	29834.7i	−0.0516696	−	1.30140i
$808$	11999.1	−	20783.1i	0.522435	−	0.904885i
$809$	31094.2			1.35132			0.675658	−	0.737215i	$-0.263860\pi$
$809$	31094.2			1.35132			0.675658	+	0.737215i	$0.263860\pi$
$810$		0			0
$811$	19130.6			0.828320			0.414160	−	0.910204i	$-0.364075\pi$
$811$	19130.6			0.828320			0.414160	+	0.910204i	$0.364075\pi$
$812$	1003.17	−	1737.55i	0.0433553	−	0.0750936i
$813$	−1015.28	−	25571.9i	−0.0437977	−	1.10313i
$814$	−15815.5	−	27393.2i	−0.680997	−	1.17952i
$815$		0			0
$816$	477.937	+	251.203i	0.0205038	+	0.0107768i
$817$	−20031.6	+	34695.7i	−0.857792	+	1.48574i
$818$	−19469.8			−0.832208
$819$	−1522.72	+	121.104i	−0.0649674	+	0.00516694i
$820$		0			0
$821$	1778.81	−	3080.99i	0.0756162	−	0.130971i	−0.825738	−	0.564054i	$-0.809241\pi$
$821$	1778.81	−	3080.99i	0.0756162	−	0.130971i	0.901354	+	0.433083i	$0.142574\pi$
$822$	−28661.8	+	18100.7i	−1.21617	+	0.768049i
$823$	3074.69	+	5325.52i	0.130227	+	0.225560i	0.923764	−	0.382962i	$-0.125096\pi$
$823$	3074.69	+	5325.52i	0.130227	+	0.225560i	−0.793537	+	0.608522i	$0.791763\pi$
$824$	−19484.0	−	33747.2i	−0.823733	−	1.42675i
$825$		0			0
$826$	2249.23	−	3895.77i	0.0947464	−	0.164106i
$827$	−21152.8			−0.889425			−0.444713	−	0.895673i	$-0.646694\pi$
$827$	−21152.8			−0.889425			−0.444713	+	0.895673i	$0.646694\pi$
$828$	−3319.72	+	6974.73i	−0.139334	+	0.292740i
$829$	−17402.4			−0.729083			−0.364541	−	0.931187i	$-0.618774\pi$
$829$	−17402.4			−0.729083			−0.364541	+	0.931187i	$0.618774\pi$
$830$		0			0
$831$	−10698.0	−	5622.84i	−0.446580	−	0.234722i
$832$	5330.81	+	9233.24i	0.222131	+	0.384742i
$833$	−613.829	−	1063.18i	−0.0255317	−	0.0442222i
$834$	947.536	+	23865.6i	0.0393411	+	0.990884i
$835$		0			0
$836$	−16042.8			−0.663698
$837$	31349.7	−	23470.4i	1.29463	−	0.969243i
$838$	−2225.55			−0.0917425
$839$	9037.12	−	15652.8i	0.371867	−	0.644092i	−0.617986	−	0.786189i	$-0.712051\pi$
$839$	9037.12	−	15652.8i	0.371867	−	0.644092i	0.989853	+	0.142097i	$0.0453845\pi$
$840$		0			0
$841$	−13747.5	−	23811.3i	−0.563675	−	0.976314i
$842$	16341.1	+	28303.6i	0.668825	+	1.15844i
$843$	15102.2	+	7937.69i	0.617019	+	0.324304i
$844$	7296.31	−	12637.6i	0.297570	−	0.515407i
$845$		0			0
$846$	−4660.59	−	6769.23i	−0.189402	−	0.275096i
$847$	−3988.55			−0.161804
$848$	2796.74	−	4844.09i	0.113255	−	0.196164i
$849$	8849.21	−	5588.54i	0.357720	−	0.225911i
$850$		0			0
$851$	12295.9	+	21297.1i	0.495297	+	0.857880i
$852$	−4341.82	+	2741.99i	−0.174587	+	0.110257i
$853$	20396.1	−	35327.2i	0.818699	−	1.41803i	−0.0879416	−	0.996126i	$-0.528029\pi$
$853$	20396.1	−	35327.2i	0.818699	−	1.41803i	0.906641	−	0.421903i	$-0.138638\pi$
$854$	−2964.97			−0.118805
$855$		0			0
$856$	22033.5			0.879778
$857$	−5528.93	+	9576.39i	−0.220379	+	0.381707i	−0.954923	−	0.296854i	$-0.904063\pi$
$857$	−5528.93	+	9576.39i	−0.220379	+	0.381707i	0.734544	+	0.678561i	$0.237396\pi$
$858$	10871.2	+	5713.88i	0.432559	+	0.227353i
$859$	876.815	+	1518.69i	0.0348272	+	0.0603224i	0.882914	−	0.469535i	$-0.155579\pi$
$859$	876.815	+	1518.69i	0.0348272	+	0.0603224i	−0.848086	+	0.529858i	$0.822245\pi$
$860$		0			0
$861$	36.9855	+	931.554i	0.00146395	+	0.0368725i
$862$	4788.17	−	8293.35i	0.189194	−	0.327694i
$863$	19186.5			0.756796			0.378398	−	0.925643i	$-0.376475\pi$
$863$	19186.5			0.756796			0.378398	+	0.925643i	$0.376475\pi$
$864$	15056.3	−	11272.1i	0.592852	−	0.443847i
$865$		0			0
$866$	10205.9	−	17677.2i	0.400475	−	0.693642i
$867$	1010.01	+	25439.0i	0.0395635	+	0.996487i
$868$	−1229.36	−	2129.32i	−0.0480728	−	0.0832646i
$869$	31806.0	+	55089.6i	1.24159	+	2.15050i
$870$		0			0
$871$	4207.97	−	7288.41i	0.163699	−	0.283534i
$872$	−20996.8			−0.815415
$873$	8416.58	−	17683.2i	0.326298	−	0.685552i
$874$	−18861.6			−0.729980
$875$		0			0
$876$	713.872	−	450.831i	0.0275337	−	0.0173883i
$877$	−4257.30	−	7373.86i	−0.163921	−	0.283920i	0.772350	−	0.635197i	$-0.219081\pi$
$877$	−4257.30	−	7373.86i	−0.163921	−	0.283920i	−0.936272	+	0.351277i	$0.885748\pi$
$878$	−1667.94	−	2888.96i	−0.0641121	−	0.111045i
$879$	2111.89	−	1333.72i	0.0810377	−	0.0511777i
$880$		0			0
$881$	41177.0			1.57467			0.787337	−	0.616522i	$-0.211459\pi$
$881$	41177.0			1.57467			0.787337	+	0.616522i	$0.211459\pi$
$882$	19806.9	−	1575.27i	0.756159	−	0.0601384i
$883$	−32540.4			−1.24017			−0.620086	−	0.784533i	$-0.712902\pi$
$883$	−32540.4			−1.24017			−0.620086	+	0.784533i	$0.712902\pi$
$884$	119.219	−	206.494i	0.00453595	−	0.00785650i
$885$		0			0
$886$	4896.34	+	8480.70i	0.185661	+	0.321574i
$887$	1083.05	+	1875.90i	0.0409980	+	0.0710106i	0.885796	−	0.464074i	$-0.153613\pi$
$887$	1083.05	+	1875.90i	0.0409980	+	0.0710106i	−0.844798	+	0.535085i	$0.820280\pi$
$888$	−1384.89	−	34881.3i	−0.0523356	−	1.31818i
$889$	2818.95	−	4882.56i	0.106349	−	0.184202i
$890$		0			0
$891$	13698.1	−	35861.3i	0.515041	−	1.34837i
$892$	13041.2			0.489522
$893$	−6635.17	+	11492.4i	−0.248642	+	0.430661i
$894$	−123.919	−	3121.15i	−0.00463588	−	0.116764i
$895$		0			0
$896$	98.7391	+	171.021i	0.00368152	+	0.00637658i
$897$	−8451.92	−	4442.32i	−0.314606	−	0.165356i
$898$	5893.91	−	10208.5i	0.219023	−	0.379358i
$899$	−63582.3			−2.35883
$900$		0			0
$901$	−721.416			−0.0266747
$902$	3747.79	−	6491.36i	0.138346	−	0.239622i
$903$	−5088.93	+	3213.81i	−0.187540	+	0.118437i
$904$	−11170.3	−	19347.5i	−0.410971	−	0.711823i
$905$		0			0
$906$	9032.15	−	5704.07i	0.331207	−	0.209167i
$907$	−353.031	+	611.468i	−0.0129241	+	0.0223853i	−0.872415	−	0.488766i	$-0.837447\pi$
$907$	−353.031	+	611.468i	−0.0129241	+	0.0223853i	0.859491	+	0.511151i	$0.170781\pi$
$908$	−12321.6			−0.450339
$909$	11345.9	−	23837.7i	0.413993	−	0.869799i
$910$		0			0
$911$	247.743	−	429.103i	0.00900997	−	0.0156057i	−0.861485	−	0.507783i	$-0.830465\pi$
$911$	247.743	−	429.103i	0.00900997	−	0.0156057i	0.870495	+	0.492177i	$0.163799\pi$
$912$	12490.1	+	6564.81i	0.453498	+	0.238358i
$913$	−23834.0	−	41281.7i	−0.863955	−	1.49641i
$914$	17034.8	+	29505.2i	0.616480	+	1.06777i
$915$		0			0
$916$	1967.99	−	3408.66i	0.0709871	−	0.122953i
$917$	−651.806			−0.0234728
$918$	1036.09	+	443.623i	0.0372507	+	0.0159496i
$919$	20473.6			0.734889			0.367445	−	0.930045i	$-0.380233\pi$
$919$	20473.6			0.734889			0.367445	+	0.930045i	$0.380233\pi$
$920$		0			0
$921$	664.227	+	16729.9i	0.0237644	+	0.598554i
$922$	61.9030	+	107.219i	0.00221114	+	0.00382980i
$923$	−3173.80	−	5497.17i	−0.113182	−	0.196037i
$924$	−2133.41	−	1121.32i	−0.0759569	−	0.0399229i
$925$		0			0
$926$	−29348.0			−1.04151
$927$	−24309.8	−	35308.6i	−0.861316	−	1.25101i
$928$	−30536.5			−1.08018
$929$	−24857.7	+	43054.7i	−0.877883	+	1.52054i	−0.0242231	+	0.999707i	$0.507711\pi$
$929$	−24857.7	+	43054.7i	−0.877883	+	1.52054i	−0.853660	+	0.520831i	$0.825622\pi$
$930$		0			0
$931$	−16041.5	−	27784.7i	−0.564704	−	0.978095i
$932$	−3514.08	−	6086.57i	−0.123506	−	0.213919i
$933$	−10605.7	+	6697.79i	−0.372148	+	0.235022i
$934$	2937.77	−	5088.36i	0.102919	−	0.178261i
$935$		0			0
$936$	7686.29	+	11163.9i	0.268413	+	0.389854i
$937$	31524.9			1.09912			0.549560	−	0.835454i	$-0.314796\pi$
$937$	31524.9			1.09912			0.549560	+	0.835454i	$0.314796\pi$
$938$	1248.79	−	2162.97i	0.0434696	−	0.0752916i
$939$	11530.7	+	6060.54i	0.400736	+	0.210626i
$940$		0			0
$941$	−18764.2	−	32500.6i	−0.650050	−	1.12592i	−0.983110	−	0.183014i	$-0.941415\pi$
$941$	−18764.2	−	32500.6i	−0.650050	−	1.12592i	0.333060	−	0.942905i	$-0.391919\pi$
$942$	180.238	+	4539.65i	0.00623404	+	0.157017i
$943$	−2913.76	+	5046.78i	−0.100620	+	0.174280i
$944$	−21035.6			−0.725265
$945$		0			0
$946$	48390.9			1.66313
$947$	12931.7	−	22398.3i	0.443741	−	0.768582i	−0.554222	−	0.832369i	$-0.686984\pi$
$947$	12931.7	−	22398.3i	0.443741	−	0.768582i	0.997964	+	0.0637862i	$0.0203176\pi$
$948$	792.975	+	19972.7i	0.0271673	+	0.684264i
$949$	521.829	+	903.834i	0.0178496	+	0.0309164i
$950$		0			0
$951$	−17051.0	−	8962.00i	−0.581406	−	0.305586i
$952$	124.265	−	215.233i	0.00423051	−	0.00732746i
$953$	−1060.03			−0.0360312			−0.0180156	−	0.999838i	$-0.505735\pi$
$953$	−1060.03			−0.0360312			−0.0180156	+	0.999838i	$0.505735\pi$
$954$	5017.95	−	10542.7i	0.170296	−	0.357791i
$955$		0			0
$956$	1395.81	−	2417.61i	0.0472213	−	0.0817897i
$957$	−52697.3	+	33279.9i	−1.78000	+	1.12412i
$958$	3807.28	+	6594.40i	0.128400	+	0.222396i
$959$	4111.58	+	7121.46i	0.138446	+	0.239796i
$960$		0			0
$961$	−24063.7	+	41679.5i	−0.807750	+	1.39906i
$962$	12285.9			0.411759
$963$	24162.4	−	1921.67i	0.808540	−	0.0643043i
$964$	1521.71			0.0508412
$965$		0			0
$966$	−2508.26	−	1318.34i	−0.0835424	−	0.0439098i
$967$	−2592.51	−	4490.35i	−0.0862145	−	0.149328i	0.819694	−	0.572802i	$-0.194144\pi$
$967$	−2592.51	−	4490.35i	−0.0862145	−	0.149328i	−0.905908	+	0.423474i	$0.860810\pi$
$968$	17695.5	+	30649.5i	0.587557	+	1.01768i
$969$	−72.1975	−	1818.44i	−0.00239352	−	0.0602855i
$970$		0			0
$971$	28314.9			0.935805			0.467903	−	0.883780i	$-0.345010\pi$
$971$	28314.9			0.935805			0.467903	+	0.883780i	$0.345010\pi$
$972$	9052.69	−	7972.07i	0.298730	−	0.263070i
$973$	5793.85			0.190897
$974$	−15405.6	+	26683.4i	−0.506806	+	0.877813i
$975$		0			0
$976$	6932.38	+	12007.2i	0.227357	+	0.393793i
$977$	22448.3	+	38881.6i	0.735093	+	1.27322i	0.954683	+	0.297626i	$0.0961948\pi$
$977$	22448.3	+	38881.6i	0.735093	+	1.27322i	−0.219590	+	0.975592i	$0.570472\pi$
$978$	−4826.20	−	2536.65i	−0.157796	−	0.0829376i
$979$	17473.1	−	30264.3i	0.570422	−	0.988001i
$980$		0			0
$981$	−23025.6	+	1831.26i	−0.749388	+	0.0595999i
$982$	21539.4			0.699950
$983$	−7286.40	+	12620.4i	−0.236419	+	0.409490i	−0.959684	−	0.281081i	$-0.909307\pi$
$983$	−7286.40	+	12620.4i	−0.236419	+	0.409490i	0.723265	+	0.690571i	$0.242640\pi$
$984$	6994.32	−	4417.12i	0.226596	−	0.143102i
$985$		0			0
$986$	−914.938	−	1584.72i	−0.0295513	−	0.0511843i
$987$	−1685.63	+	1064.53i	−0.0543610	+	0.0343306i
$988$	3115.62	−	5396.41i	0.100325	−	0.173768i
$989$	−37622.0			−1.20962
$990$		0			0
$991$	10602.1			0.339844			0.169922	−	0.985457i	$-0.445648\pi$
$991$	10602.1			0.339844			0.169922	+	0.985457i	$0.445648\pi$
$992$	−18710.8	+	32408.1i	−0.598860	+	1.03726i
$993$	11744.6	+	6172.98i	0.375332	+	0.197274i
$994$	−941.882	−	1631.39i	−0.0300550	−	0.0520568i
$995$		0			0
$996$	−594.221	−	14966.6i	−0.0189042	−	0.476141i
$997$	13948.5	−	24159.5i	0.443082	−	0.767441i	−0.554834	−	0.831961i	$-0.687218\pi$
$997$	13948.5	−	24159.5i	0.443082	−	0.767441i	0.997916	+	0.0645202i	$0.0205517\pi$
$998$	−26447.4			−0.838857
$999$	−4560.91	−	38130.8i	−0.144445	−	1.20761i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.5	✓	14	5.4	even	2
45.4.e.c.31.5	yes	14	45.4	even	6
135.4.e.c.46.3		14	15.14	odd	2
135.4.e.c.91.3		14	45.14	odd	6
225.4.e.d.76.3		14	9.4	even	3	inner
225.4.e.d.151.3		14	1.1	even	1	trivial
225.4.k.d.49.5		28	45.13	odd	12
225.4.k.d.49.10		28	45.22	odd	12
225.4.k.d.124.5		28	5.2	odd	4
225.4.k.d.124.10		28	5.3	odd	4
405.4.a.m.1.3		7	45.34	even	6
405.4.a.n.1.5		7	45.29	odd	6
2025.4.a.ba.1.3		7	9.2	odd	6
2025.4.a.bb.1.5		7	9.7	even	3

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09722 + 1.90044i) q^{2} +(-0.206141 - 5.19206i) q^{3} +(1.59221 + 2.75778i) q^{4} +(10.0934 + 5.30509i) q^{6} +(1.38302 - 2.39547i) q^{7} -24.5436 q^{8} +(-26.9150 + 2.14059i) q^{9} +O(q^{10})\)	\(q+(-1.09722 + 1.90044i) q^{2} +(-0.206141 - 5.19206i) q^{3} +(1.59221 + 2.75778i) q^{4} +(10.0934 + 5.30509i) q^{6} +(1.38302 - 2.39547i) q^{7} -24.5436 q^{8} +(-26.9150 + 2.14059i) q^{9} +(26.3295 - 45.6040i) q^{11} +(13.9904 - 8.83533i) q^{12} +(10.2267 + 17.7132i) q^{13} +(3.03497 + 5.25672i) q^{14} +(14.1921 - 24.5814i) q^{16} -3.66084 q^{17} +(25.4637 - 53.4992i) q^{18} -95.6705 q^{19} +(-12.7225 - 6.68694i) q^{21} +(57.7786 + 100.075i) q^{22} +(-44.9206 - 77.8047i) q^{23} +(5.05943 + 127.432i) q^{24} -44.8840 q^{26} +(16.6623 + 139.303i) q^{27} +8.80825 q^{28} +(113.890 - 197.264i) q^{29} +(-139.569 - 241.741i) q^{31} +(-67.0306 - 116.100i) q^{32} +(-242.206 - 127.303i) q^{33} +(4.01675 - 6.95722i) q^{34} +(-48.7576 - 70.8175i) q^{36} -273.725 q^{37} +(104.972 - 181.816i) q^{38} +(89.8599 - 56.7492i) q^{39} +(-32.4323 - 56.1744i) q^{41} +(26.6676 - 16.8414i) q^{42} +(209.381 - 362.658i) q^{43} +167.688 q^{44} +197.151 q^{46} +(69.3544 - 120.125i) q^{47} +(-130.554 - 68.6190i) q^{48} +(167.674 + 290.421i) q^{49} +(0.754647 + 19.0073i) q^{51} +(-32.5661 + 56.4062i) q^{52} +197.063 q^{53} +(-283.020 - 121.181i) q^{54} +(-33.9444 + 58.7934i) q^{56} +(19.7216 + 496.727i) q^{57} +(249.926 + 432.884i) q^{58} +(-370.552 - 641.814i) q^{59} +(-244.234 + 423.026i) q^{61} +612.554 q^{62} +(-32.0964 + 67.4346i) q^{63} +521.263 q^{64} +(507.687 - 320.620i) q^{66} +(-205.734 - 356.341i) q^{67} +(-5.82882 - 10.0958i) q^{68} +(-394.707 + 249.269i) q^{69} -310.343 q^{71} +(660.591 - 52.5377i) q^{72} +51.0260 q^{73} +(300.338 - 520.200i) q^{74} +(-152.327 - 263.839i) q^{76} +(-72.8286 - 126.143i) q^{77} +(9.25240 + 233.040i) q^{78} +(-603.999 + 1046.16i) q^{79} +(719.836 - 115.228i) q^{81} +142.342 q^{82} +(452.611 - 783.945i) q^{83} +(-1.81574 - 45.7330i) q^{84} +(459.475 + 795.833i) q^{86} +(-1047.68 - 550.661i) q^{87} +(-646.220 + 1119.29i) q^{88} +663.633 q^{89} +56.5752 q^{91} +(143.046 - 247.763i) q^{92} +(-1226.36 + 774.485i) q^{93} +(152.194 + 263.608i) q^{94} +(-588.982 + 371.960i) q^{96} +(-362.668 + 628.159i) q^{97} -735.905 q^{98} +(-611.039 + 1283.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9 + 23 * q^11 - 287 * q^12 + 96 * q^13 - 21 * q^14 - 324 * q^16 + 322 * q^17 + 89 * q^18 + 558 * q^19 + 180 * q^21 + 311 * q^22 - 96 * q^23 + 48 * q^24 + 716 * q^26 + 470 * q^27 - 674 * q^28 - 296 * q^29 - 244 * q^31 + 314 * q^32 + 211 * q^33 - 125 * q^34 - 2399 * q^36 - 808 * q^37 - 305 * q^38 + 634 * q^39 - 47 * q^41 - 1941 * q^42 + 525 * q^43 - 110 * q^44 + 1434 * q^46 - 164 * q^47 - 2051 * q^48 - 1225 * q^49 + 1517 * q^51 + 1682 * q^52 + 1012 * q^53 - 4066 * q^54 - 981 * q^56 - 337 * q^57 + 1183 * q^58 - 85 * q^59 - 828 * q^61 - 1572 * q^62 + 828 * q^63 + 4472 * q^64 + 4930 * q^66 + 1093 * q^67 - 2473 * q^68 - 822 * q^69 - 656 * q^71 + 4626 * q^72 - 4170 * q^73 - 1316 * q^74 - 2789 * q^76 - 24 * q^77 + 5314 * q^78 - 2110 * q^79 - 2167 * q^81 + 124 * q^82 - 1290 * q^83 + 5775 * q^84 - 2569 * q^86 - 3604 * q^87 + 2271 * q^88 + 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 696 * q^93 + 517 * q^94 - 593 * q^96 + 1787 * q^97 + 2558 * q^98 + 2320 * q^99

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