LMFDB - Embedded newform 225.4.k.b.124.4

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.4
Root			$0.396143 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.4.k.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.78651 + 2.18614i) q^{2} +(3.78651 + 3.55842i) q^{3} +(5.55842 + 9.62747i) q^{4} +(6.55842 + 21.7518i) q^{6} +(10.4935 + 6.05842i) q^{7} +13.6277i q^{8} +(1.67527 + 26.9480i) q^{9} +O(q^{10})$	\(q+(3.78651 + 2.18614i) q^{2} +(3.78651 + 3.55842i) q^{3} +(5.55842 + 9.62747i) q^{4} +(6.55842 + 21.7518i) q^{6} +(10.4935 + 6.05842i) q^{7} +13.6277i q^{8} +(1.67527 + 26.9480i) q^{9} +(-5.01087 + 8.67909i) q^{11} +(-13.2116 + 56.2337i) q^{12} +(-42.0752 + 24.2921i) q^{13} +(26.4891 + 45.8805i) q^{14} +(14.6753 - 25.4183i) q^{16} -75.3505i q^{17} +(-52.5687 + 105.701i) q^{18} +116.052 q^{19} +(18.1753 + 60.2805i) q^{21} +(-37.9474 + 21.9090i) q^{22} +(-32.9725 + 19.0367i) q^{23} +(-48.4932 + 51.6014i) q^{24} -212.424 q^{26} +(-89.5489 + 108.000i) q^{27} +134.701i q^{28} +(-11.3139 + 19.5962i) q^{29} +(-15.0584 - 26.0820i) q^{31} +(205.552 - 118.675i) q^{32} +(-49.8576 + 15.0326i) q^{33} +(164.727 - 285.315i) q^{34} +(-250.129 + 165.917i) q^{36} -130.103i q^{37} +(439.430 + 253.705i) q^{38} +(-245.759 - 57.7390i) q^{39} +(-173.742 - 300.930i) q^{41} +(-62.9610 + 267.986i) q^{42} +(-23.1803 - 13.3832i) q^{43} -111.410 q^{44} -166.467 q^{46} +(399.132 + 230.439i) q^{47} +(146.017 - 44.0258i) q^{48} +(-98.0910 - 169.899i) q^{49} +(268.129 - 285.315i) q^{51} +(-467.743 - 270.052i) q^{52} -438.310i q^{53} +(-575.181 + 213.176i) q^{54} +(-82.5625 + 143.002i) q^{56} +(439.430 + 412.961i) q^{57} +(-85.6800 + 49.4674i) q^{58} +(4.18487 + 7.24841i) q^{59} +(41.0448 - 71.0916i) q^{61} -131.679i q^{62} +(-145.683 + 292.928i) q^{63} +802.959 q^{64} +(-221.649 - 52.0745i) q^{66} +(-591.989 + 341.785i) q^{67} +(725.435 - 418.830i) q^{68} +(-192.591 - 45.2475i) q^{69} +1097.61 q^{71} +(-367.239 + 22.8301i) q^{72} +470.464i q^{73} +(284.424 - 492.637i) q^{74} +(645.064 + 1117.28i) q^{76} +(-105.163 + 60.7160i) q^{77} +(-804.344 - 755.894i) q^{78} +(243.017 - 420.919i) q^{79} +(-723.387 + 90.2901i) q^{81} -1519.30i q^{82} +(-85.8802 - 49.5829i) q^{83} +(-479.323 + 510.046i) q^{84} +(-58.5149 - 101.351i) q^{86} +(-112.571 + 33.9416i) q^{87} +(-118.276 - 68.2868i) q^{88} -8.80426 q^{89} -588.687 q^{91} +(-366.550 - 211.628i) q^{92} +(35.7918 - 152.344i) q^{93} +(1007.54 + 1745.12i) q^{94} +(1200.62 + 282.075i) q^{96} +(572.419 + 330.486i) q^{97} -857.763i q^{98} +(-242.278 - 120.493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9}+O(q^{10}) $ 8 * q + 10 * q^4 + 18 * q^6 - 90 * q^9	$ 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9} - 132 q^{11} + 120 q^{14} + 14 q^{16} + 308 q^{19} + 42 q^{21} + 198 q^{24} - 1056 q^{26} - 102 q^{29} - 86 q^{31} + 594 q^{34} - 450 q^{36} - 1518 q^{39} - 264 q^{41} + 924 q^{44} - 1056 q^{46} - 1026 q^{49} + 594 q^{51} - 2430 q^{54} - 132 q^{56} + 1596 q^{59} - 878 q^{61} + 2908 q^{64} - 1980 q^{66} - 1782 q^{69} + 5472 q^{71} + 1632 q^{74} + 3058 q^{76} - 1606 q^{79} - 1134 q^{81} - 1284 q^{84} - 66 q^{86} + 1584 q^{89} - 3124 q^{91} + 4200 q^{94} + 2160 q^{96} - 594 q^{99}+O(q^{100}) $ 8 * q + 10 * q^4 + 18 * q^6 - 90 * q^9 - 132 * q^11 + 120 * q^14 + 14 * q^16 + 308 * q^19 + 42 * q^21 + 198 * q^24 - 1056 * q^26 - 102 * q^29 - 86 * q^31 + 594 * q^34 - 450 * q^36 - 1518 * q^39 - 264 * q^41 + 924 * q^44 - 1056 * q^46 - 1026 * q^49 + 594 * q^51 - 2430 * q^54 - 132 * q^56 + 1596 * q^59 - 878 * q^61 + 2908 * q^64 - 1980 * q^66 - 1782 * q^69 + 5472 * q^71 + 1632 * q^74 + 3058 * q^76 - 1606 * q^79 - 1134 * q^81 - 1284 * q^84 - 66 * q^86 + 1584 * q^89 - 3124 * q^91 + 4200 * q^94 + 2160 * q^96 - 594 * 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 $

$2$	3.78651	+	2.18614i	1.33873	+	0.772917i	0.986619	−	0.163040i	$-0.0521300\pi$
$2$	3.78651	+	2.18614i	1.33873	+	0.772917i	0.352113	+	0.935958i	$0.385463\pi$
$3$	3.78651	+	3.55842i	0.728714	+	0.684819i
$3$	3.78651	+	3.55842i	0.728714	+	0.684819i
$4$	5.55842	+	9.62747i	0.694803	+	1.20343i
$5$		0			0
$5$		0			0
$6$	6.55842	+	21.7518i	0.446244	+	1.48002i
$7$	10.4935	+	6.05842i	0.566595	+	0.327124i	0.755788	−	0.654816i	$-0.227254\pi$
$7$	10.4935	+	6.05842i	0.566595	+	0.327124i	−0.189193	+	0.981940i	$0.560587\pi$
$8$			13.6277i			0.602266i
$9$	1.67527	+	26.9480i	0.0620469	+	0.998073i
$10$		0			0
$11$	−5.01087	+	8.67909i	−0.137349	+	0.237895i	−0.926492	−	0.376314i	$-0.877191\pi$
$11$	−5.01087	+	8.67909i	−0.137349	+	0.237895i	0.789144	+	0.614209i	$0.210525\pi$
$12$	−13.2116	+	56.2337i	−0.317822	+	1.35277i
$13$	−42.0752	+	24.2921i	−0.897658	+	0.518263i	−0.876440	−	0.481512i	$-0.840088\pi$
$13$	−42.0752	+	24.2921i	−0.897658	+	0.518263i	−0.0212183	+	0.999775i	$0.506754\pi$
$14$	26.4891	+	45.8805i	0.505680	+	0.875863i
$15$		0			0
$16$	14.6753	−	25.4183i	0.229301	−	0.397161i
$17$		−	75.3505i		−	1.07501i	−0.843260	−	0.537506i	$-0.819367\pi$
$17$		−	75.3505i		−	1.07501i	0.843260	−	0.537506i	$-0.180633\pi$
$18$	−52.5687	+	105.701i	−0.688364	+	1.38411i
$19$	116.052			1.40127			0.700633	−	0.713522i	$-0.252901\pi$
$19$	116.052			1.40127			0.700633	+	0.713522i	$0.252901\pi$
$20$		0			0
$21$	18.1753	+	60.2805i	0.188865	+	0.626395i
$22$	−37.9474	+	21.9090i	−0.367746	+	0.212318i
$23$	−32.9725	+	19.0367i	−0.298923	+	0.172584i	−0.641959	−	0.766739i	$-0.721878\pi$
$23$	−32.9725	+	19.0367i	−0.298923	+	0.172584i	0.343036	+	0.939322i	$0.388545\pi$
$24$	−48.4932	+	51.6014i	−0.412443	+	0.438879i
$25$		0			0
$26$	−212.424			−1.60230
$27$	−89.5489	+	108.000i	−0.638285	+	0.769800i
$28$			134.701i			0.909147i
$29$	−11.3139	+	19.5962i	−0.0724459	+	0.125480i	−0.899973	−	0.435946i	$-0.856414\pi$
$29$	−11.3139	+	19.5962i	−0.0724459	+	0.125480i	0.827527	+	0.561426i	$0.189747\pi$
$30$		0			0
$31$	−15.0584	−	26.0820i	−0.0872443	−	0.151112i	0.819101	−	0.573649i	$-0.194473\pi$
$31$	−15.0584	−	26.0820i	−0.0872443	−	0.151112i	−0.906345	+	0.422538i	$0.861139\pi$
$32$	205.552	−	118.675i	1.13552	−	0.655594i
$33$	−49.8576	+	15.0326i	−0.263003	+	0.0792983i
$34$	164.727	−	285.315i	0.830895	−	1.43915i
$35$		0			0
$36$	−250.129	+	165.917i	−1.15800	+	0.768133i
$37$		−	130.103i		−	0.578077i	−0.957318	−	0.289038i	$-0.906665\pi$
$37$		−	130.103i		−	0.578077i	0.957318	−	0.289038i	$-0.0933355\pi$
$38$	439.430	+	253.705i	1.87592	+	1.08306i
$39$	−245.759	−	57.7390i	−1.00905	−	0.237068i
$40$		0			0
$41$	−173.742	−	300.930i	−0.661803	−	1.14628i	−0.980142	−	0.198299i	$-0.936458\pi$
$41$	−173.742	−	300.930i	−0.661803	−	1.14628i	0.318339	−	0.947977i	$-0.396875\pi$
$42$	−62.9610	+	267.986i	−0.231312	+	0.984552i
$43$	−23.1803	−	13.3832i	−0.0822085	−	0.0474631i	0.458332	−	0.888781i	$-0.348447\pi$
$43$	−23.1803	−	13.3832i	−0.0822085	−	0.0474631i	−0.540541	+	0.841318i	$0.681780\pi$
$44$	−111.410			−0.381721
$45$		0			0
$46$	−166.467			−0.533571
$47$	399.132	+	230.439i	1.23871	+	0.715169i	0.968830	−	0.247725i	$-0.0796829\pi$
$47$	399.132	+	230.439i	1.23871	+	0.715169i	0.269879	+	0.962894i	$0.413016\pi$
$48$	146.017	−	44.0258i	0.439078	−	0.132387i
$49$	−98.0910	−	169.899i	−0.285980	−	0.495331i
$50$		0			0
$51$	268.129	−	285.315i	0.736188	−	0.783375i
$52$	−467.743	−	270.052i	−1.24739	−	0.720181i
$53$		−	438.310i		−	1.13597i	−0.823039	−	0.567985i	$-0.807723\pi$
$53$		−	438.310i		−	1.13597i	0.823039	−	0.567985i	$-0.192277\pi$
$54$	−575.181	+	213.176i	−1.44948	+	0.537215i
$55$		0			0
$56$	−82.5625	+	143.002i	−0.197016	+	0.341241i
$57$	439.430	+	412.961i	1.02112	+	0.959613i
$58$	−85.6800	+	49.4674i	−0.193971	+	0.111989i
$59$	4.18487	+	7.24841i	0.00923430	+	0.0159943i	0.870606	−	0.491982i	$-0.163727\pi$
$59$	4.18487	+	7.24841i	0.00923430	+	0.0159943i	−0.861371	+	0.507976i	$0.830394\pi$
$60$		0			0
$61$	41.0448	−	71.0916i	0.0861515	−	0.149219i	−0.819730	−	0.572750i	$-0.805876\pi$
$61$	41.0448	−	71.0916i	0.0861515	−	0.149219i	0.905881	+	0.423532i	$0.139210\pi$
$62$		−	131.679i		−	0.269730i
$63$	−145.683	+	292.928i	−0.291338	+	0.585801i
$64$	802.959			1.56828
$65$		0			0
$66$	−221.649	−	52.0745i	−0.413381	−	0.0971202i
$67$	−591.989	+	341.785i	−1.07945	+	0.623220i	−0.930747	−	0.365663i	$-0.880842\pi$
$67$	−591.989	+	341.785i	−1.07945	+	0.623220i	−0.148701	+	0.988882i	$0.547509\pi$
$68$	725.435	−	418.830i	1.29370	−	0.746921i
$69$	−192.591	−	45.2475i	−0.336018	−	0.0789444i
$70$		0			0
$71$	1097.61			1.83468			0.917339	−	0.398107i	$-0.130333\pi$
$71$	1097.61			1.83468			0.917339	+	0.398107i	$0.130333\pi$
$72$	−367.239	+	22.8301i	−0.601105	+	0.0373687i
$73$			470.464i			0.754297i	0.926153	+	0.377149i	$0.123095\pi$
$73$			470.464i			0.754297i	−0.926153	+	0.377149i	$0.876905\pi$
$74$	284.424	−	492.637i	0.446805	−	0.773890i
$75$		0			0
$76$	645.064	+	1117.28i	0.973604	+	1.68633i
$77$	−105.163	+	60.7160i	−0.155642	+	0.0898601i
$78$	−804.344	−	755.894i	−1.16762	−	1.09728i
$79$	243.017	−	420.919i	0.346096	−	0.599456i	−0.639456	−	0.768828i	$-0.720840\pi$
$79$	243.017	−	420.919i	0.346096	−	0.599456i	0.985552	+	0.169371i	$0.0541737\pi$
$80$		0			0
$81$	−723.387	+	90.2901i	−0.992300	+	0.123855i
$82$		−	1519.30i		−	2.04608i
$83$	−85.8802	−	49.5829i	−0.113573	−	0.0655715i	0.442137	−	0.896947i	$-0.354220\pi$
$83$	−85.8802	−	49.5829i	−0.113573	−	0.0655715i	−0.555711	+	0.831376i	$0.687554\pi$
$84$	−479.323	+	510.046i	−0.622601	+	0.662508i
$85$		0			0
$86$	−58.5149	−	101.351i	−0.0733701	−	0.127081i
$87$	−112.571	+	33.9416i	−0.138723	+	0.0418267i
$88$	−118.276	−	68.2868i	−0.143276	−	0.0827204i
$89$	−8.80426			−0.0104859			−0.00524297	−	0.999986i	$-0.501669\pi$
$89$	−8.80426			−0.0104859			−0.00524297	+	0.999986i	$0.501669\pi$
$90$		0			0
$91$	−588.687			−0.678145
$92$	−366.550	−	211.628i	−0.415386	−	0.239823i
$93$	35.7918	−	152.344i	0.0399079	−	0.169864i
$94$	1007.54	+	1745.12i	1.10553	+	1.91484i
$95$		0			0
$96$	1200.62	+	282.075i	1.27643	+	0.299887i
$97$	572.419	+	330.486i	0.599179	+	0.345936i	0.768719	−	0.639587i	$-0.220895\pi$
$97$	572.419	+	330.486i	0.599179	+	0.345936i	−0.169540	+	0.985523i	$0.554228\pi$
$98$		−	857.763i		−	0.884155i
$99$	−242.278	−	120.493i	−0.245959	−	0.122323i
$100$		0			0
$101$	282.561	−	489.410i	0.278375	−	0.482160i	−0.692606	−	0.721316i	$-0.743537\pi$
$101$	282.561	−	489.410i	0.278375	−	0.482160i	0.970981	+	0.239156i	$0.0768708\pi$
$102$	1639.01	−	494.181i	1.59104	−	0.479717i
$103$	−841.068	+	485.591i	−0.804592	+	0.464531i	−0.845074	−	0.534649i	$-0.820444\pi$
$103$	−841.068	+	485.591i	−0.804592	+	0.464531i	0.0404826	+	0.999180i	$0.487110\pi$
$104$	−331.046	−	573.389i	−0.312132	−	0.540629i
$105$		0			0
$106$	958.206	−	1659.66i	0.878012	−	1.52076i
$107$			563.845i			0.509430i	0.967016	+	0.254715i	$0.0819816\pi$
$107$			563.845i			0.509430i	−0.967016	+	0.254715i	$0.918018\pi$
$108$	−1537.52	−	261.819i	−1.36989	−	0.233274i
$109$	−225.484			−0.198142			−0.0990709	−	0.995080i	$-0.531587\pi$
$109$	−225.484			−0.198142			−0.0990709	+	0.995080i	$0.531587\pi$
$110$		0			0
$111$	462.962	−	492.637i	0.395878	−	0.421252i
$112$	307.990	−	177.818i	0.259842	−	0.150020i
$113$	−598.478	+	345.531i	−0.498231	+	0.287654i	−0.727983	−	0.685596i	$-0.759542\pi$
$113$	−598.478	+	345.531i	−0.498231	+	0.287654i	0.229752	+	0.973249i	$0.426209\pi$
$114$	761.115	+	2524.33i	0.625307	+	2.07391i
$115$		0			0
$116$	−251.549			−0.201342
$117$	−725.110	−	1093.14i	−0.572961	−	0.863772i
$118$			36.5949i			0.0285494i
$119$	456.505	−	790.690i	0.351662	−	0.609096i
$120$		0			0
$121$	615.282	+	1065.70i	0.462271	+	0.800676i
$122$	310.833	−	179.459i	0.230668	−	0.133176i
$123$	412.960	−	1757.72i	0.302726	−	1.28852i
$124$	167.402	−	289.949i	0.121235	−	0.209985i
$125$		0			0
$126$	−1192.01	+	790.690i	−0.842800	+	0.559050i
$127$			895.897i			0.625968i	0.949758	+	0.312984i	$0.101329\pi$
$127$			895.897i			0.625968i	−0.949758	+	0.312984i	$0.898671\pi$
$128$	1396.00	+	805.979i	0.963983	+	0.556556i
$129$	−40.1495	−	133.161i	−0.0274028	−	0.0908849i
$130$		0			0
$131$	−827.428	−	1433.15i	−0.551853	−	0.955837i	−0.998141	−	0.0609476i	$-0.980588\pi$
$131$	−827.428	−	1433.15i	−0.551853	−	0.955837i	0.446288	−	0.894889i	$-0.352746\pi$
$132$	−421.856	−	396.445i	−0.278165	−	0.261410i
$133$	1217.79	+	703.090i	0.793951	+	0.458388i
$134$	−2988.76			−1.92679
$135$		0			0
$136$	1026.86			0.647442
$137$	−2295.91	−	1325.55i	−1.43177	−	0.826635i	−0.434518	−	0.900663i	$-0.643081\pi$
$137$	−2295.91	−	1325.55i	−1.43177	−	0.826635i	−0.997256	+	0.0740277i	$0.976415\pi$
$138$	−630.330	−	592.361i	−0.388821	−	0.365400i
$139$	317.084	+	549.206i	0.193487	+	0.335130i	0.946404	−	0.322986i	$-0.104687\pi$
$139$	317.084	+	549.206i	0.193487	+	0.335130i	−0.752916	+	0.658116i	$0.771354\pi$
$140$		0			0
$141$	691.316	+	2292.84i	0.412903	+	1.36944i
$142$	4156.10	+	2399.53i	2.45614	+	1.41805i
$143$		−	486.899i		−	0.284731i
$144$	709.557	+	352.886i	0.410623	+	0.204217i
$145$		0			0
$146$	−1028.50	+	1781.42i	−0.583009	+	1.00980i
$147$	233.149	−	992.372i	0.130815	−	0.556799i
$148$	1252.56	−	723.168i	0.695677	−	0.401649i
$149$	−1703.16	−	2949.96i	−0.936432	−	1.62195i	−0.772060	−	0.635550i	$-0.780773\pi$
$149$	−1703.16	−	2949.96i	−0.936432	−	1.62195i	−0.164372	−	0.986398i	$-0.552560\pi$
$150$		0			0
$151$	875.159	−	1515.82i	0.471652	−	0.816925i	−0.527822	−	0.849355i	$-0.676991\pi$
$151$	875.159	−	1515.82i	0.471652	−	0.816925i	0.999474	+	0.0324302i	$0.0103247\pi$
$152$			1581.52i			0.843935i
$153$	2030.54	−	126.232i	1.07294	−	0.0667011i
$154$	−530.935			−0.277818
$155$		0			0
$156$	−810.155	−	2686.98i	−0.415797	−	1.37904i
$157$	−1886.70	+	1089.29i	−0.959076	+	0.553723i	−0.895889	−	0.444279i	$-0.853460\pi$
$157$	−1886.70	+	1089.29i	−0.959076	+	0.553723i	−0.0631876	+	0.998002i	$0.520127\pi$
$158$	1840.37	−	1062.54i	0.926660	−	0.535008i
$159$	1559.69	−	1659.66i	0.777934	−	0.827797i
$160$		0			0
$161$	−461.329			−0.225825
$162$	−2936.50	−	1239.54i	−1.42415	−	0.601158i
$163$			2188.41i			1.05159i	0.850610	+	0.525797i	$0.176233\pi$
$163$			2188.41i			1.05159i	−0.850610	+	0.525797i	$0.823767\pi$
$164$	1931.46	−	3345.39i	0.919645	−	1.59287i
$165$		0			0
$166$	−216.791	−	375.492i	−0.101363	−	0.175565i
$167$	−1663.67	+	960.520i	−0.770890	+	0.445074i	−0.833192	−	0.552984i	$-0.813489\pi$
$167$	−1663.67	+	960.520i	−0.770890	+	0.445074i	0.0623020	+	0.998057i	$0.480156\pi$
$168$	−821.486	+	247.687i	−0.377256	+	0.113747i
$169$	81.7132	−	141.531i	0.0371931	−	0.0644203i
$170$		0			0
$171$	194.417	+	3127.36i	0.0869442	+	1.39857i
$172$		−	297.557i		−	0.131910i
$173$	−2745.15	−	1584.91i	−1.20642	−	0.696525i	−0.244442	−	0.969664i	$-0.578605\pi$
$173$	−2745.15	−	1584.91i	−1.20642	−	0.696525i	−0.961974	+	0.273139i	$0.911938\pi$
$174$	−500.454	−	117.577i	−0.218042	−	0.0512270i
$175$		0			0
$176$	147.072	+	254.736i	0.0629884	+	0.109099i
$177$	−9.94685	+	42.3377i	−0.00422402	+	0.0179791i
$178$	−33.3374	−	19.2473i	−0.0140379	−	0.00810477i
$179$	−1368.78			−0.571551			−0.285776	−	0.958297i	$-0.592251\pi$
$179$	−1368.78			−0.571551			−0.285776	+	0.958297i	$0.592251\pi$
$180$		0			0
$181$	−3951.44			−1.62270			−0.811350	−	0.584561i	$-0.801267\pi$
$181$	−3951.44			−1.62270			−0.811350	+	0.584561i	$0.801267\pi$
$182$	−2229.07	−	1286.95i	−0.907855	−	0.524150i
$183$	408.390	−	123.134i	0.164968	−	0.0497396i
$184$	−259.426	−	449.340i	−0.103941	−	0.180031i
$185$		0			0
$186$	468.571	−	498.605i	0.184716	−	0.196556i
$187$	653.974	+	377.572i	0.255740	+	0.147651i
$188$			5123.50i			1.98761i
$189$	−1593.99	+	590.773i	−0.613469	+	0.227367i
$190$		0			0
$191$	1201.29	−	2080.70i	0.455092	−	0.788243i	−0.543601	−	0.839344i	$-0.682940\pi$
$191$	1201.29	−	2080.70i	0.455092	−	0.788243i	0.998693	+	0.0511008i	$0.0162730\pi$
$192$	3040.41	+	2857.27i	1.14283	+	1.07399i
$193$	−1156.20	+	667.535i	−0.431220	+	0.248965i	−0.699866	−	0.714274i	$-0.746757\pi$
$193$	−1156.20	+	667.535i	−0.431220	+	0.248965i	0.268646	+	0.963239i	$0.413424\pi$
$194$	1444.98	+	2502.78i	0.534760	+	0.926232i
$195$		0			0
$196$	1090.46	−	1888.74i	0.397399	−	0.688315i
$197$			2630.89i			0.951487i	0.879584	+	0.475743i	$0.157821\pi$
$197$			2630.89i			0.951487i	−0.879584	+	0.475743i	$0.842179\pi$
$198$	−653.974	−	985.903i	−0.234727	−	0.353864i
$199$	−2477.34			−0.882483			−0.441241	−	0.897388i	$-0.645462\pi$
$199$	−2477.34			−0.882483			−0.441241	+	0.897388i	$0.645462\pi$
$200$		0			0
$201$	−3457.79	−	812.376i	−1.21340	−	0.285078i
$202$	2139.84	−	1235.44i	0.745340	−	0.430322i
$203$	−237.444	+	137.088i	−0.0820950	+	0.0473976i
$204$	4237.24	+	995.501i	1.45425	+	0.341662i
$205$		0			0
$206$	−4246.28			−1.43618
$207$	−568.238	−	856.650i	−0.190798	−	0.287639i
$208$			1425.97i			0.475353i
$209$	−581.520	+	1007.22i	−0.192462	+	0.333354i
$210$		0			0
$211$	1392.36	+	2411.65i	0.454286	+	0.786847i	0.998647	−	0.0520047i	$-0.0165611\pi$
$211$	1392.36	+	2411.65i	0.454286	+	0.786847i	−0.544361	+	0.838851i	$0.683228\pi$
$212$	4219.81	−	2436.31i	1.36707	−	0.789276i
$213$	4156.10	+	3905.75i	1.33696	+	1.25642i
$214$	−1232.64	+	2135.00i	−0.393747	+	0.681990i
$215$		0			0
$216$	−1471.79	−	1220.35i	−0.463624	−	0.384417i
$217$		−	364.921i		−	0.114159i
$218$	−853.797	−	492.940i	−0.265259	−	0.153147i
$219$	−1674.11	+	1781.42i	−0.516557	+	0.549667i
$220$		0			0
$221$	1830.42	+	3170.39i	0.557138	+	0.964992i
$222$	2829.98	−	853.272i	0.855567	−	0.257963i
$223$	37.2890	+	21.5288i	0.0111976	+	0.00646491i	0.505588	−	0.862775i	$-0.331275\pi$
$223$	37.2890	+	21.5288i	0.0111976	+	0.00646491i	−0.494391	+	0.869240i	$0.664609\pi$
$224$	2875.94			0.857843
$225$		0			0
$226$	−3021.52			−0.889330
$227$	591.721	+	341.630i	0.173013	+	0.0998889i	0.584006	−	0.811750i	$-0.301485\pi$
$227$	591.721	+	341.630i	0.173013	+	0.0998889i	−0.410993	+	0.911639i	$0.634818\pi$
$228$	−1533.23	+	6526.01i	−0.445353	+	1.89559i
$229$	2147.15	+	3718.98i	0.619598	+	1.07317i	0.989559	+	0.144127i	$0.0460375\pi$
$229$	2147.15	+	3718.98i	0.619598	+	1.07317i	−0.369962	+	0.929047i	$0.620629\pi$
$230$		0			0
$231$	−614.254	−	144.313i	−0.174957	−	0.0411045i
$232$	−267.051	−	154.182i	−0.0755723	−	0.0436317i
$233$			3466.34i			0.974625i	0.873228	+	0.487313i	$0.162023\pi$
$233$			3466.34i			0.974625i	−0.873228	+	0.487313i	$0.837977\pi$
$234$	−355.866	−	5724.39i	−0.0994176	−	1.59921i
$235$		0			0
$236$	−46.5225	+	80.5794i	−0.0128320	+	0.0222257i
$237$	2417.99	−	729.052i	0.662724	−	0.199819i
$238$	3457.12	−	1995.97i	0.941562	−	0.543611i
$239$	2821.69	+	4887.30i	0.763681	+	1.32273i	0.940941	+	0.338570i	$0.109943\pi$
$239$	2821.69	+	4887.30i	0.763681	+	1.32273i	−0.177261	+	0.984164i	$0.556724\pi$
$240$		0			0
$241$	−3294.71	+	5706.61i	−0.880627	+	1.52529i	−0.0299825	+	0.999550i	$0.509545\pi$
$241$	−3294.71	+	5706.61i	−0.880627	+	1.52529i	−0.850645	+	0.525741i	$0.823788\pi$
$242$			5380.37i			1.42919i
$243$	−3060.40	−	2232.23i	−0.807921	−	0.589291i
$244$	912.577			0.239433
$245$		0			0
$246$	5406.30	−	5752.82i	1.40119	−	1.49100i
$247$	−4882.89	+	2819.14i	−1.25786	+	0.726225i
$248$	355.438	−	205.212i	0.0910093	−	0.0525442i
$249$	−148.749	−	493.344i	−0.0378577	−	0.125560i
$250$		0			0
$251$	4135.47			1.03996			0.519978	−	0.854180i	$-0.325940\pi$
$251$	4135.47			1.03996			0.519978	+	0.854180i	$0.325940\pi$
$252$	−3629.92	+	225.660i	−0.907395	+	0.0564097i
$253$		−	381.562i		−	0.0948165i
$254$	−1958.56	+	3392.32i	−0.483822	+	0.838004i
$255$		0			0
$256$	312.132	+	540.628i	0.0762041	+	0.131989i
$257$	2896.53	−	1672.31i	0.703036	−	0.405898i	−0.105441	−	0.994426i	$-0.533625\pi$
$257$	2896.53	−	1672.31i	0.703036	−	0.405898i	0.808477	+	0.588527i	$0.200292\pi$
$258$	139.082	−	591.986i	0.0335615	−	0.142851i
$259$	788.220	−	1365.24i	0.189103	−	0.327536i
$260$		0			0
$261$	−547.031	−	272.057i	−0.129733	−	0.0645207i
$262$		−	7235.49i		−	1.70615i
$263$	−5647.78	−	3260.75i	−1.32417	−	0.764511i	−0.339780	−	0.940505i	$-0.610353\pi$
$263$	−5647.78	−	3260.75i	−1.32417	−	0.764511i	−0.984391	+	0.175994i	$0.943686\pi$
$264$	−204.860	−	679.445i	−0.0477587	−	0.158398i
$265$		0			0
$266$	3074.11	+	5324.51i	0.708592	+	1.22732i
$267$	−33.3374	−	31.3293i	−0.00764125	−	0.00718097i
$268$	−6581.05	−	3799.57i	−1.50001	−	0.866029i
$269$	2904.99			0.658441			0.329220	−	0.944253i	$-0.393214\pi$
$269$	2904.99			0.658441			0.329220	+	0.944253i	$0.393214\pi$
$270$		0			0
$271$	−1335.38			−0.299331			−0.149665	−	0.988737i	$-0.547820\pi$
$271$	−1335.38			−0.299331			−0.149665	+	0.988737i	$0.547820\pi$
$272$	−1915.28	−	1105.79i	−0.426953	−	0.246501i
$273$	−2229.07	−	2094.80i	−0.494174	−	0.464406i
$274$	−5795.66	−	10038.4i	−1.27784	−	2.21329i
$275$		0			0
$276$	−634.883	−	2105.67i	−0.138462	−	0.459226i
$277$	−7253.51	−	4187.82i	−1.57336	−	0.908381i	−0.995753	−	0.0920685i	$-0.970652\pi$
$277$	−7253.51	−	4187.82i	−1.57336	−	0.908381i	−0.577610	−	0.816313i	$-0.696015\pi$
$278$			2772.76i			0.598199i
$279$	677.629	−	449.488i	0.145407	−	0.0964522i
$280$		0			0
$281$	2589.67	−	4485.43i	0.549774	−	0.952237i	−0.448516	−	0.893775i	$-0.648047\pi$
$281$	2589.67	−	4485.43i	0.549774	−	0.952237i	0.998290	−	0.0584616i	$-0.0186195\pi$
$282$	−2394.79	+	10193.2i	−0.505701	+	2.15246i
$283$	−2667.42	+	1540.03i	−0.560288	+	0.323482i	−0.753261	−	0.657722i	$-0.771520\pi$
$283$	−2667.42	+	1540.03i	−0.560288	+	0.323482i	0.192973	+	0.981204i	$0.438187\pi$
$284$	6100.97	+	10567.2i	1.27474	+	2.20791i
$285$		0			0
$286$	1064.43	−	1843.65i	0.220074	−	0.381179i
$287$		−	4210.40i		−	0.865966i
$288$	3542.41	+	5340.39i	0.724787	+	1.09266i
$289$	−764.703			−0.155649
$290$		0			0
$291$	991.459	+	3288.30i	0.199726	+	0.662417i
$292$	−4529.38	+	2615.04i	−0.907747	+	0.524088i
$293$	3160.04	−	1824.45i	0.630073	−	0.363773i	−0.150708	−	0.988578i	$-0.548155\pi$
$293$	3160.04	−	1824.45i	0.630073	−	0.363773i	0.780780	+	0.624806i	$0.214822\pi$
$294$	3052.28	−	3247.93i	0.605486	−	0.644296i
$295$		0			0
$296$	1773.01			0.348156
$297$	−488.624	−	1318.38i	−0.0954640	−	0.257576i
$298$		−	14893.4i		−	2.89514i
$299$	924.882	−	1601.94i	0.178887	−	0.309842i
$300$		0			0
$301$	−162.162	−	280.872i	−0.0310526	−	0.0537847i
$302$	6627.59	−	3826.44i	1.26283	−	0.729096i
$303$	2811.45	−	847.684i	0.533048	−	0.160720i
$304$	1703.09	−	2949.84i	0.321312	−	0.556528i
$305$		0			0
$306$	7964.63	+	3961.08i	1.48793	+	0.739999i
$307$			3439.25i			0.639376i	0.947523	+	0.319688i	$0.103578\pi$
$307$			3439.25i			0.639376i	−0.947523	+	0.319688i	$0.896422\pi$
$308$	−1169.08	−	674.970i	−0.216281	−	0.124870i
$309$	−4912.65	−	1154.18i	−0.904436	−	0.212489i
$310$		0			0
$311$	−3587.66	−	6214.02i	−0.654141	−	1.13301i	−0.982108	−	0.188316i	$-0.939697\pi$
$311$	−3587.66	−	6214.02i	−0.654141	−	1.13301i	0.327968	−	0.944689i	$-0.393636\pi$
$312$	786.850	−	3349.14i	0.142778	−	0.607717i
$313$	4206.54	+	2428.65i	0.759642	+	0.438579i	0.829167	−	0.559001i	$-0.188815\pi$
$313$	4206.54	+	2428.65i	0.759642	+	0.438579i	−0.0695253	+	0.997580i	$0.522148\pi$
$314$	−9525.33			−1.71193
$315$		0			0
$316$	5403.17			0.961874
$317$	6536.70	+	3773.97i	1.15816	+	0.668666i	0.950863	−	0.309611i	$-0.100199\pi$
$317$	6536.70	+	3773.97i	1.15816	+	0.668666i	0.207300	+	0.978277i	$0.433532\pi$
$318$	9534.03	−	2874.62i	1.68126	−	0.506920i
$319$	−113.385	−	196.388i	−0.0199007	−	0.0344690i
$320$		0			0
$321$	−2006.40	+	2135.00i	−0.348867	+	0.371228i
$322$	−1746.82	−	1008.53i	−0.302319	−	0.174544i
$323$		−	8744.55i		−	1.50638i
$324$	−4890.15	−	6462.52i	−0.838504	−	1.10811i
$325$		0			0
$326$	−4784.18	+	8286.44i	−0.812795	+	1.40780i
$327$	−853.797	−	802.367i	−0.144389	−	0.135691i
$328$	4100.98	−	2367.70i	0.690363	−	0.398581i
$329$	2792.19	+	4836.22i	0.467898	+	0.810423i
$330$		0			0
$331$	1564.86	−	2710.41i	0.259856	−	0.450084i	−0.706347	−	0.707866i	$-0.749658\pi$
$331$	1564.86	−	2710.41i	0.259856	−	0.450084i	0.966203	+	0.257782i	$0.0829915\pi$
$332$		−	1102.41i		−	0.182237i
$333$	3506.02	−	217.957i	0.576963	−	0.0358679i
$334$	−8399.33			−1.37602
$335$		0			0
$336$	1798.96	+	422.648i	0.292087	+	0.0686231i
$337$	7993.39	−	4614.99i	1.29207	−	0.745978i	0.313050	−	0.949737i	$-0.398649\pi$
$337$	7993.39	−	4614.99i	1.29207	−	0.745978i	0.979021	+	0.203759i	$0.0653159\pi$
$338$	618.815	−	357.273i	0.0995832	−	0.0574944i
$339$	−3495.69	−	821.280i	−0.560058	−	0.131581i
$340$		0			0
$341$	301.823			0.0479315
$342$	−6100.68	+	12266.8i	−0.964581	+	1.93951i
$343$		−	6533.19i		−	1.02845i
$344$	182.382	−	315.895i	0.0285854	−	0.0495113i
$345$		0			0
$346$	−6929.69	−	12002.6i	−1.07671	−	1.86492i
$347$	7018.61	−	4052.20i	1.08582	−	0.626897i	0.153358	−	0.988171i	$-0.450991\pi$
$347$	7018.61	−	4052.20i	1.08582	−	0.626897i	0.932460	+	0.361273i	$0.117658\pi$
$348$	−952.491	−	895.117i	−0.146721	−	0.137883i
$349$	1538.21	−	2664.26i	0.235927	−	0.408638i	−0.723615	−	0.690204i	$-0.757521\pi$
$349$	1538.21	−	2664.26i	0.235927	−	0.408638i	0.959542	+	0.281566i	$0.0908540\pi$
$350$		0			0
$351$	1144.24	−	6719.45i	0.174002	−	1.02182i
$352$			2378.67i			0.360180i
$353$	5326.13	+	3075.04i	0.803063	+	0.463649i	0.844541	−	0.535491i	$-0.179873\pi$
$353$	5326.13	+	3075.04i	0.803063	+	0.463649i	−0.0414780	+	0.999139i	$0.513207\pi$
$354$	−130.220	+	138.567i	−0.0195512	+	0.0208043i
$355$		0			0
$356$	−48.9378	−	84.7627i	−0.00728566	−	0.0126191i
$357$	4542.17	−	1369.52i	0.673381	−	0.203032i
$358$	−5182.91	−	2992.35i	−0.765154	−	0.441762i
$359$	−3307.94			−0.486313			−0.243156	−	0.969987i	$-0.578183\pi$
$359$	−3307.94			−0.486313			−0.243156	+	0.969987i	$0.578183\pi$
$360$		0			0
$361$	6608.97			0.963548
$362$	−14962.2	−	8638.41i	−2.17236	−	1.25421i
$363$	−1462.44	+	6224.71i	−0.211455	+	0.900035i
$364$	−3272.17	−	5667.57i	−0.471177	−	0.816103i
$365$		0			0
$366$	1815.56	+	426.550i	0.259292	+	0.0609183i
$367$	2554.16	+	1474.65i	0.363287	+	0.209744i	0.670522	−	0.741890i	$-0.266070\pi$
$367$	2554.16	+	1474.65i	0.363287	+	0.209744i	−0.307235	+	0.951634i	$0.599404\pi$
$368$			1117.47i			0.158294i
$369$	7818.38	−	5186.13i	1.10300	−	0.731650i
$370$		0			0
$371$	2655.46	−	4599.40i	0.371603	−	0.643636i
$372$	1665.63	−	502.206i	0.232148	−	0.0699951i
$373$	1007.69	−	581.790i	0.139883	−	0.0807612i	−0.428425	−	0.903577i	$-0.640932\pi$
$373$	1007.69	−	581.790i	0.139883	−	0.0807612i	0.568308	+	0.822816i	$0.307598\pi$
$374$	1650.85	+	2859.36i	0.228245	+	0.395331i
$375$		0			0
$376$	−3140.36	+	5439.25i	−0.430722	+	0.746032i
$377$		−	1099.35i		−	0.150184i
$378$	−7327.17	−	1247.72i	−0.997007	−	0.169778i
$379$	4016.67			0.544387			0.272193	−	0.962243i	$-0.412251\pi$
$379$	4016.67			0.544387			0.272193	+	0.962243i	$0.412251\pi$
$380$		0			0
$381$	−3187.98	+	3392.32i	−0.428675	+	0.456152i
$382$	9097.42	−	5252.40i	1.21849	−	0.703497i
$383$	−9355.93	+	5401.65i	−1.24821	+	0.720656i	−0.970753	−	0.240081i	$-0.922826\pi$
$383$	−9355.93	+	5401.65i	−1.24821	+	0.720656i	−0.277460	+	0.960737i	$0.589493\pi$
$384$	2417.94	+	8019.39i	0.321328	+	1.06572i
$385$		0			0
$386$	−5837.30			−0.769717
$387$	321.816	−	647.083i	0.0422708	−	0.0849950i
$388$			7347.93i			0.961429i
$389$	1032.29	−	1787.99i	0.134549	−	0.233045i	−0.790876	−	0.611976i	$-0.790375\pi$
$389$	1032.29	−	1787.99i	0.134549	−	0.233045i	0.925425	+	0.378931i	$0.123708\pi$
$390$		0			0
$391$	1434.42	+	2484.49i	0.185529	+	0.321346i
$392$	2315.33	−	1336.76i	0.298321	−	0.172236i
$393$	1966.68	−	8370.96i	0.252432	−	1.07445i
$394$	−5751.49	+	9961.87i	−0.735421	+	1.27379i
$395$		0			0
$396$	−186.642	−	3002.28i	−0.0236846	−	0.380985i
$397$			7937.61i			1.00347i	0.865022	+	0.501735i	$0.167305\pi$
$397$			7937.61i			1.00347i	−0.865022	+	0.501735i	$0.832695\pi$
$398$	−9380.47	−	5415.82i	−1.18141	−	0.682086i
$399$	2109.27	+	6995.65i	0.264650	+	0.877746i
$400$		0			0
$401$	−1289.10	−	2232.79i	−0.160536	−	0.278056i	0.774525	−	0.632543i	$-0.217989\pi$
$401$	−1289.10	−	2232.79i	−0.160536	−	0.278056i	−0.935061	+	0.354487i	$0.884656\pi$
$402$	−11317.0	−	10635.3i	−1.40408	−	1.31950i
$403$	1267.17	+	731.602i	0.156631	+	0.0904310i
$404$	6282.38			0.773663
$405$		0			0
$406$	−1198.78			−0.146538
$407$	1129.18	+	651.931i	0.137521	+	0.0793981i
$408$	3888.20	+	3653.99i	0.471800	+	0.443381i
$409$	2922.88	+	5062.57i	0.353367	+	0.612049i	0.986837	−	0.161718i	$-0.0517034\pi$
$409$	2922.88	+	5062.57i	0.353367	+	0.612049i	−0.633470	+	0.773767i	$0.718370\pi$
$410$		0			0
$411$	−3976.64	−	13189.0i	−0.477258	−	1.58289i
$412$	−9350.03	−	5398.24i	−1.11806	−	0.645515i
$413$			101.415i			0.0120830i
$414$	−278.877	−	4485.96i	−0.0331064	−	0.532543i
$415$		0			0
$416$	−5765.75	+	9986.56i	−0.679541	+	1.17700i
$417$	−753.665	+	3207.89i	−0.0885063	+	0.376717i
$418$	−4403.86	+	2542.57i	−0.515310	+	0.297515i
$419$	−4370.66	−	7570.20i	−0.509596	−	0.882646i	−0.999938	−	0.0111158i	$-0.996462\pi$
$419$	−4370.66	−	7570.20i	−0.509596	−	0.882646i	0.490343	−	0.871530i	$-0.336872\pi$
$420$		0			0
$421$	−528.254	+	914.963i	−0.0611533	+	0.105921i	−0.894981	−	0.446104i	$-0.852811\pi$
$421$	−528.254	+	914.963i	−0.0611533	+	0.105921i	0.833828	+	0.552024i	$0.186145\pi$
$422$			12175.6i			1.40450i
$423$	−5541.21	+	11141.8i	−0.636933	+	1.28070i
$424$	5973.16			0.684156
$425$		0			0
$426$	7198.58	+	23875.0i	0.818714	+	2.71537i
$427$	861.406	−	497.333i	0.0976261	−	0.0563645i
$428$	−5428.40	+	3134.09i	−0.613065	+	0.353953i
$429$	1732.59	−	1843.65i	0.194989	−	0.207487i
$430$		0			0
$431$	9868.64			1.10291			0.551457	−	0.834203i	$-0.314072\pi$
$431$	9868.64			1.10291			0.551457	+	0.834203i	$0.314072\pi$
$432$	1431.02	+	3861.11i	0.159375	+	0.430018i
$433$			477.948i			0.0530456i	0.999648	+	0.0265228i	$0.00844346\pi$
$433$			477.948i			0.0530456i	−0.999648	+	0.0265228i	$0.991557\pi$
$434$	797.769	−	1381.78i	0.0882353	−	0.152828i
$435$		0			0
$436$	−1253.34	−	2170.84i	−0.137669	−	0.238450i
$437$	−3826.51	+	2209.24i	−0.418871	+	0.241835i
$438$	−10233.5	+	3085.50i	−1.11638	+	0.336601i
$439$	−526.239	+	911.473i	−0.0572119	+	0.0990939i	−0.893213	−	0.449634i	$-0.851554\pi$
$439$	−526.239	+	911.473i	−0.0572119	+	0.0990939i	0.836001	+	0.548728i	$0.184888\pi$
$440$		0			0
$441$	4414.10	−	2927.98i	0.476633	−	0.316162i
$442$			16006.3i			1.72249i
$443$	9092.14	+	5249.35i	0.975126	+	0.562989i	0.900795	−	0.434245i	$-0.142985\pi$
$443$	9092.14	+	5249.35i	0.975126	+	0.562989i	0.0743307	+	0.997234i	$0.476318\pi$
$444$	7316.18	+	1718.87i	0.782006	+	0.183725i
$445$		0			0
$446$	94.1300	+	163.038i	0.00999369	+	0.0173096i
$447$	4048.18	−	17230.6i	0.428349	−	1.82322i
$448$	8425.85	+	4864.66i	0.888580	+	0.513022i
$449$	7329.40			0.770369			0.385184	−	0.922840i	$-0.374138\pi$
$449$	7329.40			0.770369			0.385184	+	0.922840i	$0.374138\pi$
$450$		0			0
$451$	3482.39			0.363591
$452$	−6653.18	−	3841.22i	−0.692344	−	0.399725i
$453$	8707.72	−	2625.48i	0.903144	−	0.272308i
$454$	1493.70	+	2587.17i	0.154412	+	0.267449i
$455$		0			0
$456$	−5627.71	+	5988.43i	−0.577942	+	0.614987i
$457$	6187.23	+	3572.20i	0.633318	+	0.365646i	0.782036	−	0.623233i	$-0.214181\pi$
$457$	6187.23	+	3572.20i	0.633318	+	0.365646i	−0.148718	+	0.988880i	$0.547515\pi$
$458$			18775.9i			1.91559i
$459$	8137.86	+	6747.55i	0.827544	+	0.686163i
$460$		0			0
$461$	−2859.34	+	4952.53i	−0.288878	+	0.500352i	−0.973542	−	0.228507i	$-0.926616\pi$
$461$	−2859.34	+	4952.53i	−0.288878	+	0.500352i	0.684664	+	0.728859i	$0.259949\pi$
$462$	−2010.39	−	1889.29i	−0.202450	−	0.190255i
$463$	682.831	−	394.233i	0.0685397	−	0.0395714i	−0.465339	−	0.885133i	$-0.654067\pi$
$463$	682.831	−	394.233i	0.0685397	−	0.0395714i	0.533878	+	0.845561i	$0.320734\pi$
$464$	332.068	+	575.158i	0.0332238	+	0.0575454i
$465$		0			0
$466$	−7577.91	+	13125.3i	−0.753305	+	1.30476i
$467$			17068.0i			1.69125i	0.533776	+	0.845626i	$0.320772\pi$
$467$			17068.0i			1.69125i	−0.533776	+	0.845626i	$0.679228\pi$
$468$	6493.75	−	13057.1i	0.641397	−	1.28967i
$469$	−8282.72			−0.815481
$470$		0			0
$471$	−11020.1	−	2589.08i	−1.07809	−	0.253288i
$472$	−98.7793	+	57.0302i	−0.00963280	+	0.00556150i
$473$	232.307	−	134.123i	0.0225824	−	0.0130380i
$474$	10749.6	+	2525.51i	1.04165	+	0.244727i
$475$		0			0
$476$	10149.8			0.977343
$477$	11811.6	−	734.285i	1.13378	−	0.0704834i
$478$			24674.4i			2.36105i
$479$	758.994	−	1314.62i	0.0723994	−	0.125399i	−0.827553	−	0.561388i	$-0.810268\pi$
$479$	758.994	−	1314.62i	0.0723994	−	0.125399i	0.899952	+	0.435988i	$0.143601\pi$
$480$		0			0
$481$	3160.48	+	5474.11i	0.299596	+	0.518915i
$482$	−24950.9	+	14405.4i	−2.35785	+	1.36130i
$483$	−1746.82	−	1641.60i	−0.164562	−	0.154649i
$484$	−6840.00	+	11847.2i	−0.642374	+	1.11262i
$485$		0			0
$486$	−6708.25	−	15142.8i	−0.626116	−	1.41336i
$487$		−	12737.3i		−	1.18518i	−0.805503	−	0.592591i	$-0.798105\pi$
$487$		−	12737.3i		−	1.18518i	0.805503	−	0.592591i	$-0.201895\pi$
$488$	968.817	+	559.347i	0.0898694	+	0.0518861i
$489$	−7787.30	+	8286.44i	−0.720151	+	0.766310i
$490$		0			0
$491$	−2823.85	−	4891.05i	−0.259549	−	0.449552i	0.706572	−	0.707641i	$-0.250241\pi$
$491$	−2823.85	−	4891.05i	−0.259549	−	0.449552i	−0.966121	+	0.258089i	$0.916907\pi$
$492$	19217.8	−	5794.38i	1.76099	−	0.530957i
$493$	1476.58	+	852.505i	0.134892	+	0.0778801i
$494$	−24652.1			−2.24525
$495$		0			0
$496$	−883.945			−0.0800208
$497$	11517.7	+	6649.78i	1.03952	+	0.600167i
$498$	515.281	−	2193.24i	0.0463661	−	0.197352i
$499$	5423.14	+	9393.15i	0.486519	+	0.842676i	0.999880	−	0.0154970i	$-0.00493306\pi$
$499$	5423.14	+	9393.15i	0.486519	+	0.842676i	−0.513361	+	0.858173i	$0.671600\pi$
$500$		0			0
$501$	−9717.43	−	2283.02i	−0.866553	−	0.203589i
$502$	15659.0	+	9040.73i	1.39222	+	0.803800i
$503$		−	12345.7i		−	1.09437i	−0.837011	−	0.547186i	$-0.815699\pi$
$503$		−	12345.7i		−	1.09437i	0.837011	−	0.547186i	$-0.184301\pi$
$504$	−3991.94	−	1985.32i	−0.352808	−	0.175463i
$505$		0			0
$506$	834.147	−	1444.79i	0.0732853	−	0.126934i
$507$	813.036	−	245.140i	0.0712193	−	0.0214734i
$508$	−8625.22	+	4979.77i	−0.753311	+	0.434925i
$509$	−2947.87	−	5105.87i	−0.256704	−	0.444624i	0.708653	−	0.705557i	$-0.249303\pi$
$509$	−2947.87	−	5105.87i	−0.256704	−	0.444624i	−0.965357	+	0.260933i	$0.915970\pi$
$510$		0			0
$511$	−2850.27	+	4936.82i	−0.246749	+	0.427381i
$512$		−	10166.2i		−	0.877514i
$513$	−10392.3	+	12533.6i	−0.894407	+	1.07870i
$514$	14623.6			1.25490
$515$		0			0
$516$	1058.83	−	1126.70i	0.0903344	−	0.0961245i
$517$	−4000.00	+	2309.40i	−0.340270	+	0.196455i
$518$	5969.20	−	3446.32i	0.506316	−	0.292322i
$519$	−4754.74	−	15769.7i	−0.402139	−	1.33374i
$520$		0			0
$521$	5211.51			0.438235			0.219118	−	0.975698i	$-0.429682\pi$
$521$	5211.51			0.438235			0.219118	+	0.975698i	$0.429682\pi$
$522$	−1476.58	−	2226.03i	−0.123809	−	0.186649i
$523$		−	9809.86i		−	0.820182i	−0.912045	−	0.410091i	$-0.865497\pi$
$523$		−	9809.86i		−	0.820182i	0.912045	−	0.410091i	$-0.134503\pi$
$524$	9198.38	−	15932.1i	0.766857	−	1.32824i
$525$		0			0
$526$	−14256.9	−	24693.7i	−1.18181	−	2.04695i
$527$	−1965.29	+	1134.66i	−0.162447	+	0.0937886i
$528$	−349.569	+	1487.90i	−0.0288126	+	0.122638i
$529$	−5358.71	+	9281.56i	−0.440430	+	0.762847i
$530$		0			0
$531$	−188.319	+	124.917i	−0.0153905	+	0.0102089i
$532$			15632.3i			1.27396i
$533$	14620.4	+	8441.11i	1.18814	+	0.685976i
$534$	−57.7420	−	191.509i	−0.00467929	−	0.0155195i
$535$		0			0
$536$	−4657.75	−	8067.47i	−0.375344	−	0.650115i
$537$	−5182.91	−	4870.71i	−0.416497	−	0.391409i
$538$	10999.8	+	6350.72i	0.881476	+	0.508920i
$539$	1966.09			0.157116
$540$		0			0
$541$	8084.25			0.642456			0.321228	−	0.947002i	$-0.395904\pi$
$541$	8084.25			0.642456			0.321228	+	0.947002i	$0.395904\pi$
$542$	−5056.43	−	2919.33i	−0.400724	−	0.231358i
$543$	−14962.2	−	14060.9i	−1.18248	−	1.11125i
$544$	−8942.24	−	15488.4i	−0.704771	−	1.22070i
$545$		0			0
$546$	−3860.86	−	12805.0i	−0.302618	−	1.00367i
$547$	−20842.7	−	12033.6i	−1.62920	−	0.940617i	−0.984333	−	0.176319i	$-0.943581\pi$
$547$	−20842.7	−	12033.6i	−1.62920	−	0.940617i	−0.644863	−	0.764298i	$-0.723086\pi$
$548$		−	29471.8i		−	2.29739i
$549$	1984.54	+	986.976i	0.154277	+	0.0767270i
$550$		0			0
$551$	−1312.99	+	2274.17i	−0.101516	+	0.175831i
$552$	616.621	−	2624.58i	0.0475455	−	0.202372i
$553$	5100.20	−	2944.60i	0.392193	−	0.226433i
$554$	−18310.3	−	31714.4i	−1.40421	−	2.43216i
$555$		0			0
$556$	−3524.98	+	6105.44i	−0.268871	+	0.465698i
$557$		−	4582.37i		−	0.348584i	−0.984694	−	0.174292i	$-0.944236\pi$
$557$		−	4582.37i		−	0.348584i	0.984694	−	0.174292i	$-0.0557637\pi$
$558$	3548.49	−	220.598i	0.269211	−	0.0167359i
$559$	1300.42			0.0983934
$560$		0			0
$561$	1132.72	+	3756.79i	0.0852466	+	0.282731i
$562$	19611.6	−	11322.7i	1.47200	−	0.849860i
$563$	−2680.62	+	1547.66i	−0.200666	+	0.115854i	−0.596966	−	0.802267i	$-0.703627\pi$
$563$	−2680.62	+	1547.66i	−0.200666	+	0.115854i	0.396300	+	0.918121i	$0.370294\pi$
$564$	−18231.6	+	19400.2i	−1.36115	+	1.44840i
$565$		0			0
$566$	−13466.9			−1.00010
$567$	−8137.87	−	3435.13i	−0.602749	−	0.254430i
$568$			14957.9i			1.10496i
$569$	10282.5	−	17809.9i	0.757586	−	1.31218i	−0.186492	−	0.982456i	$-0.559712\pi$
$569$	10282.5	−	17809.9i	0.757586	−	1.31218i	0.944078	−	0.329721i	$-0.106955\pi$
$570$		0			0
$571$	584.992	+	1013.24i	0.0428742	+	0.0742602i	0.886666	−	0.462410i	$-0.153015\pi$
$571$	584.992	+	1013.24i	0.0428742	+	0.0742602i	−0.843792	+	0.536670i	$0.819682\pi$
$572$	4687.60	−	2706.39i	0.342655	−	0.197832i
$573$	11952.7	−	3603.88i	0.871435	−	0.262748i
$574$	9204.54	−	15942.7i	0.669320	−	1.15930i
$575$		0			0
$576$	1345.17	+	21638.1i	0.0973069	+	1.56526i
$577$			13073.0i			0.943214i	0.881809	+	0.471607i	$0.156326\pi$
$577$			13073.0i			0.943214i	−0.881809	+	0.471607i	$0.843674\pi$
$578$	−2895.55	−	1671.75i	−0.208372	−	0.120304i
$579$	−6753.35	−	1586.64i	−0.484731	−	0.113883i
$580$		0			0
$581$	−600.789	−	1040.60i	−0.0429000	−	0.0743050i
$582$	−3434.51	+	14618.6i	−0.244614	+	1.04117i
$583$	3804.13	+	2196.31i	0.270242	+	0.156024i
$584$	−6411.36			−0.454287
$585$		0			0
$586$	15954.0			1.12466
$587$	−12598.8	−	7273.91i	−0.885873	−	0.511459i	−0.0132825	−	0.999912i	$-0.504228\pi$
$587$	−12598.8	−	7273.91i	−0.885873	−	0.511459i	−0.872590	+	0.488453i	$0.837561\pi$
$588$	10850.0	−	3271.39i	0.760961	−	0.229438i
$589$	−1747.55	−	3026.85i	−0.122252	−	0.211747i
$590$		0			0
$591$	−9361.80	+	9961.87i	−0.651596	+	0.693361i
$592$	−3307.00	−	1909.30i	−0.229589	−	0.132554i
$593$			19018.0i			1.31699i	0.752586	+	0.658494i	$0.228806\pi$
$593$			19018.0i			1.31699i	−0.752586	+	0.658494i	$0.771194\pi$
$594$	1031.98	−	6060.24i	0.0712840	−	0.418611i
$595$		0			0
$596$	18933.8	−	32794.3i	1.30127	−	2.25387i
$597$	−9380.47	−	8815.43i	−0.643077	−	0.604341i
$598$	7004.14	−	4043.84i	0.478964	−	0.276530i
$599$	5587.20	+	9677.32i	0.381113	+	0.660108i	0.991222	−	0.132210i	$-0.0422074\pi$
$599$	5587.20	+	9677.32i	0.381113	+	0.660108i	−0.610108	+	0.792318i	$0.708874\pi$
$600$		0			0
$601$	−2294.27	+	3973.79i	−0.155716	+	0.269708i	−0.933319	−	0.359047i	$-0.883102\pi$
$601$	−2294.27	+	3973.79i	−0.155716	+	0.269708i	0.777604	+	0.628755i	$0.216435\pi$
$602$		−	1418.03i		−	0.0960045i
$603$	−10202.2	−	15380.3i	−0.688995	−	1.03870i
$604$	19458.0			1.31082
$605$		0			0
$606$	12498.7	+	2936.46i	0.837832	+	0.196841i
$607$	9950.61	−	5744.99i	0.665375	−	0.384155i	−0.128947	−	0.991652i	$-0.541160\pi$
$607$	9950.61	−	5744.99i	0.665375	−	0.384155i	0.794322	+	0.607497i	$0.207826\pi$
$608$	23854.6	−	13772.5i	1.59117	−	0.918662i
$609$	−1386.90	−	325.840i	−0.0922825	−	0.0216809i
$610$		0			0
$611$	−22391.4			−1.48258
$612$	12501.9	+	18847.4i	0.825752	+	1.24487i
$613$		−	22966.9i		−	1.51326i	−0.653846	−	0.756628i	$-0.726846\pi$
$613$		−	22966.9i		−	1.51326i	0.653846	−	0.756628i	$-0.273154\pi$
$614$	−7518.69	+	13022.7i	−0.494185	+	0.855953i
$615$		0			0
$616$	−827.420	−	1433.13i	−0.0541197	−	0.0937380i
$617$	7358.29	−	4248.31i	0.480120	−	0.277197i	−0.240347	−	0.970687i	$-0.577261\pi$
$617$	7358.29	−	4248.31i	0.480120	−	0.277197i	0.720466	+	0.693490i	$0.243928\pi$
$618$	−16078.6	−	15110.1i	−1.04656	−	0.983521i
$619$	7169.94	−	12418.7i	0.465564	−	0.806381i	−0.533662	−	0.845698i	$-0.679185\pi$
$619$	7169.94	−	12418.7i	0.465564	−	0.806381i	0.999227	+	0.0393163i	$0.0125180\pi$
$620$		0			0
$621$	896.688	−	5265.74i	0.0579434	−	0.340269i
$622$		−	31372.6i		−	2.02239i
$623$	−92.3874	−	53.3399i	−0.00594129	−	0.00343021i
$624$	−5074.21	+	5399.46i	−0.325531	+	0.346396i
$625$		0			0
$626$	10618.7	+	18392.2i	0.677971	+	1.17428i
$627$	−5786.05	+	1744.56i	−0.368537	+	0.111118i
$628$	−20974.1	−	12109.4i	−1.33274	−	0.769456i
$629$	−9803.34			−0.621439
$630$		0			0
$631$	17834.3			1.12516			0.562578	−	0.826744i	$-0.309810\pi$
$631$	17834.3			1.12516			0.562578	+	0.826744i	$0.309810\pi$
$632$	5736.16	+	3311.77i	0.361032	+	0.208442i
$633$	−3309.46	+	14086.3i	−0.207803	+	0.884489i
$634$	16500.8	+	28580.3i	1.03365	+	1.79033i
$635$		0			0
$636$	24647.8	+	5790.77i	1.53671	+	0.361036i
$637$	8254.39	+	4765.68i	0.513424	+	0.296425i
$638$		−	991.499i		−	0.0615264i
$639$	1838.79	+	29578.3i	0.113836	+	1.83114i
$640$		0			0
$641$	−13173.0	+	22816.3i	−0.811705	+	1.40591i	0.0999654	+	0.994991i	$0.468127\pi$
$641$	−13173.0	+	22816.3i	−0.811705	+	1.40591i	−0.911670	+	0.410923i	$0.865207\pi$
$642$	−12264.7	+	3697.93i	−0.753968	+	0.227330i
$643$	−18675.9	+	10782.5i	−1.14542	+	0.661309i	−0.947767	−	0.318963i	$-0.896665\pi$
$643$	−18675.9	+	10782.5i	−1.14542	+	0.661309i	−0.197653	+	0.980272i	$0.563332\pi$
$644$	−2564.26	−	4441.43i	−0.156904	−	0.271765i
$645$		0			0
$646$	19116.8	−	33111.3i	1.16431	−	2.01664i
$647$		−	4186.32i		−	0.254376i	−0.991879	−	0.127188i	$-0.959405\pi$
$647$		−	4186.32i		−	0.254376i	0.991879	−	0.127188i	$-0.0405952\pi$
$648$	−1230.45	−	9858.11i	−0.0745934	−	0.597629i
$649$	−83.8794			−0.00507328
$650$		0			0
$651$	1298.54	−	1381.78i	0.0781781	−	0.0831891i
$652$	−21068.9	+	12164.1i	−1.26552	+	0.730650i
$653$	2429.33	−	1402.57i	0.145585	−	0.0840534i	−0.425438	−	0.904987i	$-0.639880\pi$
$653$	2429.33	−	1402.57i	0.145585	−	0.0840534i	0.571023	+	0.820934i	$0.306547\pi$
$654$	−1478.82	−	4904.69i	−0.0884196	−	0.293255i
$655$		0			0
$656$	−10198.8			−0.607008
$657$	−12678.1	+	788.153i	−0.752844	+	0.0468018i
$658$			24416.5i			1.44659i
$659$	−9536.15	+	16517.1i	−0.563696	+	0.976350i	0.433474	+	0.901166i	$0.357288\pi$
$659$	−9536.15	+	16517.1i	−0.563696	+	0.976350i	−0.997170	+	0.0751839i	$0.976046\pi$
$660$		0			0
$661$	12256.5	+	21228.9i	0.721216	+	1.24918i	0.960513	+	0.278237i	$0.0897500\pi$
$661$	12256.5	+	21228.9i	0.721216	+	1.24918i	−0.239296	+	0.970947i	$0.576917\pi$
$662$	11850.7	−	6842.00i	0.695756	−	0.401695i
$663$	−4350.66	+	18518.1i	−0.254850	+	1.08474i
$664$	675.702	−	1170.35i	0.0394915	−	0.0684012i
$665$		0			0
$666$	13752.0	+	6839.35i	0.800122	+	0.397927i
$667$		−	861.513i		−	0.0500119i
$668$	−18494.8	−	10678.0i	−1.07123	−	0.618477i
$669$	64.5864	+	214.209i	0.00373252	+	0.0123794i
$670$		0			0
$671$	411.340	+	712.462i	0.0236656	+	0.0409900i
$672$	10889.8	+	10233.8i	0.625122	+	0.587467i
$673$	3071.49	+	1773.32i	0.175924	+	0.101570i	0.585376	−	0.810762i	$-0.300947\pi$
$673$	3071.49	+	1773.32i	0.175924	+	0.101570i	−0.409452	+	0.912332i	$0.634280\pi$
$674$	40356.1			2.30632
$675$		0			0
$676$	1816.79			0.103367
$677$	15480.2	+	8937.50i	0.878807	+	0.507380i	0.870265	−	0.492584i	$-0.163948\pi$
$677$	15480.2	+	8937.50i	0.878807	+	0.507380i	0.00854232	+	0.999964i	$0.497281\pi$
$678$	−11441.0	−	10751.8i	−0.648067	−	0.609030i
$679$	4004.45	+	6935.91i	0.226328	+	0.392012i
$680$		0			0
$681$	1024.89	+	3399.18i	0.0576709	+	0.191273i
$682$	1142.86	+	659.829i	0.0641675	+	0.0370471i
$683$			2857.23i			0.160072i	0.996792	+	0.0800358i	$0.0255034\pi$
$683$			2857.23i			0.160072i	−0.996792	+	0.0800358i	$0.974497\pi$
$684$	−29027.9	+	19254.9i	−1.62267	+	1.07636i
$685$		0			0
$686$	14282.5	−	24737.9i	0.794908	−	1.37682i
$687$	−5103.48	+	21722.4i	−0.283421	+	1.20635i
$688$	−680.354	+	392.803i	−0.0377010	+	0.0217667i
$689$	10647.5	+	18441.9i	0.588732	+	1.01971i
$690$		0			0
$691$	7813.79	−	13533.9i	0.430175	−	0.745084i	−0.566714	−	0.823915i	$-0.691785\pi$
$691$	7813.79	−	13533.9i	0.430175	−	0.745084i	0.996888	+	0.0788308i	$0.0251187\pi$
$692$		−	35238.5i		−	1.93579i
$693$	−1812.35	−	2732.22i	−0.0993441	−	0.149767i
$694$	35434.7			1.93816
$695$		0			0
$696$	−462.546	−	1534.09i	−0.0251908	−	0.0835483i
$697$	−22675.2	+	13091.5i	−1.23226	+	0.711445i
$698$	11648.9	−	6725.49i	0.631687	−	0.364704i
$699$	−12334.7	+	13125.3i	−0.667442	+	0.710223i
$700$		0			0
$701$	17562.6			0.946264			0.473132	−	0.880992i	$-0.343123\pi$
$701$	17562.6			0.946264			0.473132	+	0.880992i	$0.343123\pi$
$702$	19022.3	−	22941.8i	1.02272	−	1.23345i
$703$		−	15098.7i		−	0.810039i
$704$	−4023.53	+	6968.95i	−0.215401	+	0.373086i
$705$		0			0
$706$	13445.0	+	23287.3i	0.716724	+	1.24140i
$707$	5930.11	−	3423.75i	0.315452	−	0.182126i
$708$	−462.893	+	139.568i	−0.0245715	+	0.00740858i
$709$	10001.8	−	17323.6i	0.529795	−	0.917632i	−0.469601	−	0.882879i	$-0.655602\pi$
$709$	10001.8	−	17323.6i	0.529795	−	0.917632i	0.999396	−	0.0347532i	$-0.0110645\pi$
$710$		0			0
$711$	11750.0	+	5843.68i	0.619775	+	0.308235i
$712$		−	119.982i		−	0.00631533i
$713$	993.027	+	573.324i	0.0521587	+	0.0301138i
$714$	20192.9	+	4744.14i	1.05840	+	0.248663i
$715$		0			0
$716$	−7608.27	−	13177.9i	−0.397115	−	0.687824i
$717$	−6706.75	+	28546.6i	−0.349328	+	1.48688i
$718$	−12525.5	−	7231.62i	−0.651043	−	0.375880i
$719$	−25504.1			−1.32287			−0.661435	−	0.750002i	$-0.730052\pi$
$719$	−25504.1			−1.32287			−0.661435	+	0.750002i	$0.730052\pi$
$720$		0			0
$721$	−11767.7			−0.607837
$722$	25024.9	+	14448.1i	1.28993	+	0.744743i
$723$	−32782.0	+	9884.14i	−1.68627	+	0.508430i
$724$	−21963.8	−	38042.4i	−1.12746	−	1.95281i
$725$		0			0
$726$	−19145.6	+	20372.8i	−0.978735	+	1.04147i
$727$	−20706.5	−	11954.9i	−1.05634	−	0.609879i	−0.131924	−	0.991260i	$-0.542115\pi$
$727$	−20706.5	−	11954.9i	−1.05634	−	0.609879i	−0.924418	+	0.381380i	$0.875449\pi$
$728$		−	8022.47i		−	0.408424i
$729$	−3645.00	−	19342.6i	−0.185185	−	0.982704i
$730$		0			0
$731$	−1008.43	+	1746.65i	−0.0510233	+	0.0883750i
$732$	3455.48	+	3247.33i	0.174478	+	0.163968i
$733$	−7366.02	+	4252.77i	−0.371173	+	0.214297i	−0.673971	−	0.738758i	$-0.735413\pi$
$733$	−7366.02	+	4252.77i	−0.371173	+	0.214297i	0.302798	+	0.953055i	$0.402079\pi$
$734$	6447.57	+	11167.5i	0.324229	+	0.561581i
$735$		0			0
$736$	−4518.36	+	7826.04i	−0.226290	+	0.391945i
$737$		−	6850.57i		−	0.342394i
$738$	40942.0	−	2545.22i	2.04213	−	0.126953i
$739$	−25802.5			−1.28438			−0.642192	−	0.766544i	$-0.721975\pi$
$739$	−25802.5			−1.28438			−0.642192	+	0.766544i	$0.721975\pi$
$740$		0			0
$741$	−28520.8	−	6700.70i	−1.41395	−	0.332195i
$742$	20109.9	−	11610.4i	0.994955	−	0.574437i
$743$	23675.0	−	13668.8i	1.16898	−	0.674911i	0.215541	−	0.976495i	$-0.430849\pi$
$743$	23675.0	−	13668.8i	1.16898	−	0.674911i	0.953440	+	0.301584i	$0.0975152\pi$
$744$	2076.10	+	487.760i	0.102303	+	0.0240352i
$745$		0			0
$746$	5087.50			0.249687
$747$	1192.29	−	2397.36i	0.0583983	−	0.117423i
$748$			8394.82i			0.410354i
$749$	−3416.01	+	5916.71i	−0.166647	+	0.288641i
$750$		0			0
$751$	−1668.32	−	2889.61i	−0.0810623	−	0.140404i	0.822644	−	0.568557i	$-0.192498\pi$
$751$	−1668.32	−	2889.61i	−0.0810623	−	0.140404i	−0.903706	+	0.428153i	$0.859165\pi$
$752$	11714.7	−	6763.50i	0.568075	−	0.327978i
$753$	15659.0	+	14715.8i	0.757830	+	0.712181i
$754$	2403.33	−	4162.70i	0.116080	−	0.201056i
$755$		0			0
$756$	−14547.7	−	12062.3i	−0.699861	−	0.580294i
$757$		−	33149.5i		−	1.59160i	−0.605562	−	0.795798i	$-0.707052\pi$
$757$		−	33149.5i		−	1.59160i	0.605562	−	0.795798i	$-0.292948\pi$
$758$	15209.2	+	8781.01i	0.728788	+	0.420766i
$759$	1357.76	−	1444.79i	0.0649321	−	0.0690940i
$760$		0			0
$761$	5498.42	+	9523.54i	0.261915	+	0.453651i	0.966751	−	0.255720i	$-0.0823125\pi$
$761$	5498.42	+	9523.54i	0.261915	+	0.453651i	−0.704836	+	0.709371i	$0.748979\pi$
$762$	−19487.4	+	5875.67i	−0.926448	+	0.279335i
$763$	−2366.12	−	1366.08i	−0.112266	−	0.0648169i
$764$	26709.2			1.26480
$765$		0			0
$766$	−47235.0			−2.22803
$767$	−352.158	−	203.319i	−0.0165785	−	0.00957159i
$768$	−741.894	+	3157.79i	−0.0348578	+	0.148368i
$769$	16642.5	+	28825.6i	0.780420	+	1.35173i	0.931697	+	0.363236i	$0.118328\pi$
$769$	16642.5	+	28825.6i	0.780420	+	1.35173i	−0.151277	+	0.988491i	$0.548339\pi$
$770$		0			0
$771$	16918.5	+	3974.85i	0.790279	+	0.185669i
$772$	−12853.3	−	7420.88i	−0.599225	−	0.345963i
$773$		−	7242.46i		−	0.336990i	−0.985703	−	0.168495i	$-0.946109\pi$
$773$		−	7242.46i		−	0.336990i	0.985703	−	0.168495i	$-0.0538907\pi$
$774$	2633.17	−	1746.65i	0.122283	−	0.0811137i
$775$		0			0
$776$	−4503.77	+	7800.77i	−0.208345	+	0.360865i
$777$	7842.69	−	2364.66i	0.362104	−	0.109179i
$778$	7817.58	−	4513.48i	0.360249	−	0.207990i
$779$	−20163.0	−	34923.4i	−0.927362	−	1.60624i
$780$		0			0
$781$	−5499.98	+	9526.24i	−0.251991	+	0.436461i
$782$			12543.4i			0.573595i
$783$	−1103.24	−	2976.71i	−0.0503534	−	0.135861i
$784$	−5758.05			−0.262302
$785$		0			0
$786$	25746.9	−	27397.2i	1.16840	−	1.24329i
$787$	−15081.2	+	8707.15i	−0.683084	+	0.394379i	−0.801016	−	0.598643i	$-0.795707\pi$
$787$	−15081.2	+	8707.15i	−0.683084	+	0.394379i	0.117932	+	0.993022i	$0.462374\pi$
$788$	−25328.8	+	14623.6i	−1.14505	+	0.661096i
$789$	−9782.25	−	32444.0i	−0.441391	−	1.46393i
$790$		0			0
$791$	−8373.50			−0.376394
$792$	1642.05	−	3301.70i	0.0736712	−	0.148132i
$793$			3988.26i			0.178597i
$794$	−17352.7	+	30055.8i	−0.775599	+	1.34338i
$795$		0			0
$796$	−13770.1	−	23850.5i	−0.613151	−	1.06201i
$797$	−25229.9	+	14566.5i	−1.12131	+	0.647391i	−0.941736	−	0.336353i	$-0.890807\pi$
$797$	−25229.9	+	14566.5i	−1.12131	+	0.647391i	−0.179578	+	0.983744i	$0.557473\pi$
$798$	−7306.72	+	31100.2i	−0.324129	+	1.37962i
$799$	17363.7	−	30074.8i	0.768815	−	1.33163i
$800$		0			0
$801$	−14.7495	−	237.257i	−0.000650620	−	0.0104657i
$802$		−	11272.7i		−	0.496323i
$803$	−4083.20	−	2357.44i	−0.179443	−	0.103602i
$804$	−11398.7	−	37805.3i	−0.500002	−	1.65832i
$805$		0			0
$806$	3198.77	+	5540.43i	0.139791	+	0.242126i
$807$	10999.8	+	10337.2i	0.479815	+	0.450912i
$808$	6669.55	+	3850.66i	0.290388	+	0.167656i
$809$	36440.1			1.58364			0.791820	−	0.610754i	$-0.209134\pi$
$809$	36440.1			1.58364			0.791820	+	0.610754i	$0.209134\pi$
$810$		0			0
$811$	−18922.0			−0.819286			−0.409643	−	0.912246i	$-0.634347\pi$
$811$	−18922.0			−0.819286			−0.409643	+	0.912246i	$0.634347\pi$
$812$	−2639.63	−	1523.99i	−0.114080	−	0.0658639i
$813$	−5056.43	−	4751.85i	−0.218126	−	0.204987i
$814$	2850.42	+	4937.08i	0.122736	+	0.212585i
$815$		0			0
$816$	−3317.37	−	11002.5i	−0.142318	−	0.472014i
$817$	−2690.11	−	1553.14i	−0.115196	−	0.0665084i
$818$			25559.3i			1.09249i
$819$	−986.208	−	15863.9i	−0.0420768	−	0.676839i
$820$		0			0
$821$	8955.36	−	15511.1i	0.380687	−	0.659369i	−0.610474	−	0.792037i	$-0.709021\pi$
$821$	8955.36	−	15511.1i	0.380687	−	0.659369i	0.991161	+	0.132667i	$0.0423542\pi$
$822$	13775.5	−	58633.8i	0.584519	−	2.48794i
$823$	15176.6	−	8762.22i	0.642799	−	0.371120i	−0.142893	−	0.989738i	$-0.545640\pi$
$823$	15176.6	−	8762.22i	0.642799	−	0.371120i	0.785692	+	0.618618i	$0.212307\pi$
$824$	−6617.50	−	11461.8i	−0.279771	−	0.484578i
$825$		0			0
$826$	−221.707	+	384.008i	−0.00933920	+	0.0161760i
$827$			17643.9i			0.741885i	0.928656	+	0.370943i	$0.120965\pi$
$827$			17643.9i			0.741885i	−0.928656	+	0.370943i	$0.879035\pi$
$828$	5088.87	−	10232.3i	0.213588	−	0.429466i
$829$	−45178.6			−1.89278			−0.946391	−	0.323023i	$-0.895301\pi$
$829$	−45178.6			−1.89278			−0.946391	+	0.323023i	$0.895301\pi$
$830$		0			0
$831$	−12563.5	−	41668.3i	−0.524454	−	1.73942i
$832$	−33784.6	+	19505.6i	−1.40778	+	0.812781i
$833$	−12802.0	+	7391.21i	−0.532487	+	0.307431i
$834$	−9866.66	+	10499.1i	−0.409658	+	0.435916i
$835$		0			0
$836$	−12929.3			−0.534893
$837$	4165.32	+	709.300i	0.172012	+	0.0292915i
$838$		−	38219.5i		−	1.57550i
$839$	13388.0	−	23188.7i	0.550901	−	0.954188i	−0.447309	−	0.894379i	$-0.647618\pi$
$839$	13388.0	−	23188.7i	0.550901	−	0.954188i	0.998210	−	0.0598087i	$-0.0190491\pi$
$840$		0			0
$841$	11938.5	+	20678.1i	0.489503	+	0.847844i
$842$	−4000.48	+	2309.68i	−0.163736	+	0.0945329i
$843$	25766.9	−	7769.00i	1.05274	−	0.317412i
$844$	−15478.7	+	26809.9i	−0.631278	+	1.09341i
$845$		0			0
$846$	−45339.4	+	30074.8i	−1.84256	+	1.22221i
$847$			14910.6i			0.604879i
$848$	−11141.1	−	6432.31i	−0.451163	−	0.260479i
$849$	−15580.3	−	3660.45i	−0.629816	−	0.147970i
$850$		0			0
$851$	2476.73	+	4289.83i	0.0997665	+	0.172801i
$852$	−14501.2	+	61722.6i	−0.583100	+	2.48190i
$853$	6851.78	+	3955.88i	0.275030	+	0.158789i	0.631171	−	0.775644i	$-0.282575\pi$
$853$	6851.78	+	3955.88i	0.275030	+	0.158789i	−0.356141	+	0.934432i	$0.615908\pi$
$854$	4348.96			0.174260
$855$		0			0
$856$	−7683.92			−0.306812
$857$	1600.67	+	924.149i	0.0638016	+	0.0368359i	0.531561	−	0.847020i	$-0.321605\pi$
$857$	1600.67	+	924.149i	0.0638016	+	0.0368359i	−0.467760	+	0.883856i	$0.654939\pi$
$858$	10590.9	−	3193.29i	0.421409	−	0.127060i
$859$	−9427.10	−	16328.2i	−0.374445	−	0.648558i	0.615799	−	0.787904i	$-0.288833\pi$
$859$	−9427.10	−	16328.2i	−0.374445	−	0.648558i	−0.990244	+	0.139345i	$0.955500\pi$
$860$		0			0
$861$	14982.4	−	15942.7i	0.593030	−	0.631041i
$862$	37367.7	+	21574.2i	1.47651	+	0.852461i
$863$			2086.03i			0.0822821i	0.999153	+	0.0411410i	$0.0130993\pi$
$863$			2086.03i			0.0822821i	−0.999153	+	0.0411410i	$0.986901\pi$
$864$	−5589.98	+	32826.8i	−0.220110	+	1.29258i
$865$		0			0
$866$	−1044.86	+	1809.75i	−0.0409999	+	0.0710138i
$867$	−2895.55	−	2721.13i	−0.113423	−	0.106591i
$868$	3513.27	−	2028.39i	0.137383	−	0.0793178i
$869$	2435.46	+	4218.34i	0.0950717	+	0.164669i
$870$		0			0
$871$	16605.4	−	28761.3i	0.645983	−	1.11888i
$872$		−	3072.83i		−	0.119334i
$873$	−7946.98	+	15979.2i	−0.308092	+	0.619489i
$874$	−19318.8			−0.747675
$875$		0			0
$876$	−26455.9	−	6215.59i	−1.02039	−	0.239732i
$877$	21457.7	−	12388.6i	0.826197	−	0.477005i	−0.0263520	−	0.999653i	$-0.508389\pi$
$877$	21457.7	−	12388.6i	0.826197	−	0.477005i	0.852549	+	0.522648i	$0.175056\pi$
$878$	−3985.21	+	2300.86i	−0.153183	+	0.0884401i
$879$	18457.6	+	4336.46i	0.708261	+	0.166399i
$880$		0			0
$881$	3741.26			0.143072			0.0715359	−	0.997438i	$-0.477210\pi$
$881$	3741.26			0.143072			0.0715359	+	0.997438i	$0.477210\pi$
$882$	23115.0	−	1436.98i	0.882451	−	0.0548591i
$883$			14131.6i			0.538580i	0.963059	+	0.269290i	$0.0867890\pi$
$883$			14131.6i			0.538580i	−0.963059	+	0.269290i	$0.913211\pi$
$884$	−20348.5	+	35244.7i	−0.774203	+	1.34096i
$885$		0			0
$886$	22951.6	+	39753.4i	0.870288	+	1.50738i
$887$	−23055.8	+	13311.3i	−0.872759	+	0.503888i	−0.868264	−	0.496102i	$-0.834764\pi$
$887$	−23055.8	+	13311.3i	−0.872759	+	0.503888i	−0.00449496	+	0.999990i	$0.501431\pi$
$888$	6713.51	+	6309.12i	0.253706	+	0.238424i
$889$	−5427.72	+	9401.09i	−0.204769	+	0.354671i
$890$		0			0
$891$	2841.17	−	6730.77i	0.106827	−	0.253074i
$892$			478.665i			0.0179674i
$893$	46319.9	+	26742.8i	1.73576	+	1.00214i
$894$	52997.0	−	56394.0i	1.98265	−	2.10973i
$895$		0			0
$896$	9765.93	+	16915.1i	0.364126	+	0.630684i
$897$	9202.46	−	2774.65i	0.342543	−	0.103281i
$898$	27752.8	+	16023.1i	1.03132	+	0.595431i
$899$	681.475			0.0252820
$900$		0			0
$901$	−33026.9			−1.22118
$902$	13186.1	+	7613.00i	0.486751	+	0.281026i
$903$	385.436	−	1640.56i	0.0142043	−	0.0604591i
$904$	−4708.80	−	8155.89i	−0.173244	−	0.300067i
$905$		0			0
$906$	38711.5	+	9094.91i	1.41954	+	0.333508i
$907$	45569.7	+	26309.7i	1.66827	+	0.963174i	0.968572	+	0.248731i	$0.0800137\pi$
$907$	45569.7	+	26309.7i	1.66827	+	0.963174i	0.699694	+	0.714443i	$0.253320\pi$
$908$			7595.70i			0.277612i
$909$	13662.0	+	6794.56i	0.498503	+	0.247922i
$910$		0			0
$911$	−5090.22	+	8816.52i	−0.185122	+	0.320641i	−0.943618	−	0.331037i	$-0.892601\pi$
$911$	−5090.22	+	8816.52i	−0.185122	+	0.320641i	0.758495	+	0.651678i	$0.225935\pi$
$912$	16945.5	−	5109.26i	0.615265	−	0.185509i
$913$	860.670	−	496.908i	0.0311983	−	0.0180123i
$914$	15618.7	+	27052.3i	0.565229	+	0.979005i
$915$		0			0
$916$	−23869.6	+	41343.3i	−0.860996	+	1.49129i
$917$		−	20051.6i		−	0.722097i
$918$	16062.9	+	43340.2i	0.577512	+	1.55821i
$919$	45618.2			1.63744			0.818718	−	0.574195i	$-0.194685\pi$
$919$	45618.2			1.63744			0.818718	+	0.574195i	$0.194685\pi$
$920$		0			0
$921$	−12238.3	+	13022.7i	−0.437857	+	0.465922i
$922$	−21653.9	+	12501.9i	−0.773462	+	0.446558i
$923$	−46182.1	+	26663.2i	−1.64691	+	0.950846i
$924$	−2024.91	−	6715.87i	−0.0720938	−	0.239108i
$925$		0			0
$926$	3447.39			0.122342
$927$	−14494.7	−	21851.6i	−0.513558	−	0.774219i
$928$			5370.70i			0.189980i
$929$	−6600.20	+	11431.9i	−0.233095	+	0.403733i	−0.958717	−	0.284361i	$-0.908219\pi$
$929$	−6600.20	+	11431.9i	−0.233095	+	0.403733i	0.725622	+	0.688093i	$0.241552\pi$
$930$		0			0
$931$	−11383.6	−	19717.0i	−0.400734	−	0.694091i
$932$	−33372.1	+	19267.4i	−1.17290	+	0.677172i
$933$	8527.38	−	36295.8i	0.299222	−	1.27360i
$934$	−37313.1	+	64628.2i	−1.30720	+	2.26413i
$935$		0			0
$936$	14897.1	−	9881.60i	0.520220	−	0.345075i
$937$			13468.1i			0.469565i	0.972048	+	0.234783i	$0.0754378\pi$
$937$			13468.1i			0.469565i	−0.972048	+	0.234783i	$0.924562\pi$
$938$	−31362.6	−	18107.2i	−1.09171	−	0.630299i
$939$	7285.95	+	24164.8i	0.253214	+	0.839816i
$940$		0			0
$941$	−6942.05	−	12024.0i	−0.240493	−	0.416547i	0.720362	−	0.693599i	$-0.243976\pi$
$941$	−6942.05	−	12024.0i	−0.240493	−	0.416547i	−0.960855	+	0.277052i	$0.910643\pi$
$942$	−36067.7	−	33895.1i	−1.24751	−	1.17236i
$943$	11457.4	+	6614.93i	0.395657	+	0.228432i
$944$	245.656			0.00846974
$945$		0			0
$946$	1172.84			0.0403091
$947$	4569.70	+	2638.32i	0.156806	+	0.0905320i	0.576350	−	0.817203i	$-0.304477\pi$
$947$	4569.70	+	2638.32i	0.156806	+	0.0905320i	−0.419544	+	0.907735i	$0.637810\pi$
$948$	20459.2	+	19226.8i	0.700931	+	0.658710i
$949$	−11428.6	−	19794.9i	−0.390924	−	0.677101i
$950$		0			0
$951$	11321.9	+	37550.5i	0.386054	+	1.28040i
$952$	10775.3	+	6221.13i	0.366838	+	0.211794i
$953$		−	26131.4i		−	0.888225i	−0.895971	−	0.444112i	$-0.853519\pi$
$953$		−	26131.4i		−	0.888225i	0.895971	−	0.444112i	$-0.146481\pi$
$954$	46329.8	+	23041.3i	1.57231	+	0.781961i
$955$		0			0
$956$	−31368.2	+	54331.4i	−1.06121	+	1.83808i
$957$	269.500	−	1147.09i	0.00910312	−	0.0387464i
$958$	5747.87	−	3318.54i	0.193847	−	0.111918i
$959$	−16061.4	−	27819.2i	−0.540825	−	0.936736i
$960$		0			0
$961$	14442.0	−	25014.3i	0.484777	−	0.839658i
$962$			27637.0i			0.926251i
$963$	−15194.5	+	944.591i	−0.508448	+	0.0316085i
$964$	−73253.6			−2.44745
$965$		0			0
$966$	−3025.59	−	10034.7i	−0.100773	−	0.334226i
$967$	3461.96	−	1998.77i	0.115128	−	0.0664695i	−0.441330	−	0.897345i	$-0.645493\pi$
$967$	3461.96	−	1998.77i	0.115128	−	0.0664695i	0.556458	+	0.830875i	$0.312160\pi$
$968$	−14523.1	+	8384.89i	−0.482220	+	0.278410i
$969$	31116.8	−	33111.3i	1.03159	−	1.09772i
$970$		0			0
$971$	41785.1			1.38100			0.690499	−	0.723334i	$-0.257391\pi$
$971$	41785.1			1.38100			0.690499	+	0.723334i	$0.257391\pi$
$972$	4479.75	−	41871.6i	0.147827	−	1.38172i
$973$			7684.12i			0.253177i
$974$	27845.6	−	48230.0i	0.916048	−	1.58664i
$975$		0			0
$976$	−1204.69	−	2086.58i	−0.0395093	−	0.0684321i
$977$	−10604.6	+	6122.55i	−0.347257	+	0.200489i	−0.663476	−	0.748197i	$-0.730920\pi$
$977$	−10604.6	+	6122.55i	−0.347257	+	0.200489i	0.316220	+	0.948686i	$0.397586\pi$
$978$	−47602.0	+	14352.5i	−1.55638	+	0.469267i
$979$	44.1170	−	76.4129i	0.00144023	−	0.00249455i
$980$		0			0
$981$	−377.746	−	6076.34i	−0.0122941	−	0.197760i
$982$		−	24693.3i		−	0.802439i
$983$	−37917.3	−	21891.5i	−1.23029	−	0.710307i	−0.263198	−	0.964742i	$-0.584777\pi$
$983$	−37917.3	−	21891.5i	−1.23029	−	0.710307i	−0.967090	+	0.254435i	$0.918111\pi$
$984$	23953.7	+	5627.70i	0.776032	+	0.182322i
$985$		0			0
$986$	3727.39	+	6456.03i	0.120390	+	0.208521i
$987$	−6636.65	+	28248.2i	−0.214029	+	0.910992i
$988$	−54282.3	−	31339.9i	−1.74793	−	1.00917i
$989$	1019.08			0.0327654
$990$		0			0
$991$	5178.38			0.165991			0.0829953	−	0.996550i	$-0.473551\pi$
$991$	5178.38			0.165991			0.0829953	+	0.996550i	$0.473551\pi$
$992$	−6190.57	−	3574.12i	−0.198136	−	0.114394i
$993$	15570.1	−	4694.57i	0.497587	−	0.150028i
$994$	29074.7	+	50358.8i	0.927760	+	1.60693i
$995$		0			0
$996$	3922.85	−	4174.29i	0.124799	−	0.132799i
$997$	22275.0	+	12860.5i	0.707578	+	0.408520i	0.810164	−	0.586204i	$-0.199378\pi$
$997$	22275.0	+	12860.5i	0.707578	+	0.408520i	−0.102586	+	0.994724i	$0.532712\pi$
$998$			47423.0i			1.50416i
$999$	14051.1	+	11650.6i	0.445004	+	0.368977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.b.124.4		8
5.2	odd	4		9.4.c.a.7.1	yes	4
5.3	odd	4		225.4.e.b.151.2		4
5.4	even	2	inner	225.4.k.b.124.1		8
9.4	even	3	inner	225.4.k.b.49.1		8
15.2	even	4		27.4.c.a.19.2		4
20.7	even	4		144.4.i.c.97.1		4
45.2	even	12		81.4.a.a.1.1		2
45.4	even	6	inner	225.4.k.b.49.4		8
45.7	odd	12		81.4.a.d.1.2		2
45.13	odd	12		225.4.e.b.76.2		4
45.22	odd	12		9.4.c.a.4.1	✓	4
45.32	even	12		27.4.c.a.10.2		4
45.38	even	12		2025.4.a.n.1.2		2
45.43	odd	12		2025.4.a.g.1.1		2
60.47	odd	4		432.4.i.c.289.1		4
180.7	even	12		1296.4.a.u.1.1		2
180.47	odd	12		1296.4.a.i.1.2		2
180.67	even	12		144.4.i.c.49.1		4
180.167	odd	12		432.4.i.c.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.1	✓	4	45.22	odd	12
9.4.c.a.7.1	yes	4	5.2	odd	4
27.4.c.a.10.2		4	45.32	even	12
27.4.c.a.19.2		4	15.2	even	4
81.4.a.a.1.1		2	45.2	even	12
81.4.a.d.1.2		2	45.7	odd	12
144.4.i.c.49.1		4	180.67	even	12
144.4.i.c.97.1		4	20.7	even	4
225.4.e.b.76.2		4	45.13	odd	12
225.4.e.b.151.2		4	5.3	odd	4
225.4.k.b.49.1		8	9.4	even	3	inner
225.4.k.b.49.4		8	45.4	even	6	inner
225.4.k.b.124.1		8	5.4	even	2	inner
225.4.k.b.124.4		8	1.1	even	1	trivial
432.4.i.c.145.1		4	180.167	odd	12
432.4.i.c.289.1		4	60.47	odd	4
1296.4.a.i.1.2		2	180.47	odd	12
1296.4.a.u.1.1		2	180.7	even	12
2025.4.a.g.1.1		2	45.43	odd	12
2025.4.a.n.1.2		2	45.38	even	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)

\(f(q)\)	\(=\)	\(q+(3.78651 + 2.18614i) q^{2} +(3.78651 + 3.55842i) q^{3} +(5.55842 + 9.62747i) q^{4} +(6.55842 + 21.7518i) q^{6} +(10.4935 + 6.05842i) q^{7} +13.6277i q^{8} +(1.67527 + 26.9480i) q^{9} +O(q^{10})\)	\(q+(3.78651 + 2.18614i) q^{2} +(3.78651 + 3.55842i) q^{3} +(5.55842 + 9.62747i) q^{4} +(6.55842 + 21.7518i) q^{6} +(10.4935 + 6.05842i) q^{7} +13.6277i q^{8} +(1.67527 + 26.9480i) q^{9} +(-5.01087 + 8.67909i) q^{11} +(-13.2116 + 56.2337i) q^{12} +(-42.0752 + 24.2921i) q^{13} +(26.4891 + 45.8805i) q^{14} +(14.6753 - 25.4183i) q^{16} -75.3505i q^{17} +(-52.5687 + 105.701i) q^{18} +116.052 q^{19} +(18.1753 + 60.2805i) q^{21} +(-37.9474 + 21.9090i) q^{22} +(-32.9725 + 19.0367i) q^{23} +(-48.4932 + 51.6014i) q^{24} -212.424 q^{26} +(-89.5489 + 108.000i) q^{27} +134.701i q^{28} +(-11.3139 + 19.5962i) q^{29} +(-15.0584 - 26.0820i) q^{31} +(205.552 - 118.675i) q^{32} +(-49.8576 + 15.0326i) q^{33} +(164.727 - 285.315i) q^{34} +(-250.129 + 165.917i) q^{36} -130.103i q^{37} +(439.430 + 253.705i) q^{38} +(-245.759 - 57.7390i) q^{39} +(-173.742 - 300.930i) q^{41} +(-62.9610 + 267.986i) q^{42} +(-23.1803 - 13.3832i) q^{43} -111.410 q^{44} -166.467 q^{46} +(399.132 + 230.439i) q^{47} +(146.017 - 44.0258i) q^{48} +(-98.0910 - 169.899i) q^{49} +(268.129 - 285.315i) q^{51} +(-467.743 - 270.052i) q^{52} -438.310i q^{53} +(-575.181 + 213.176i) q^{54} +(-82.5625 + 143.002i) q^{56} +(439.430 + 412.961i) q^{57} +(-85.6800 + 49.4674i) q^{58} +(4.18487 + 7.24841i) q^{59} +(41.0448 - 71.0916i) q^{61} -131.679i q^{62} +(-145.683 + 292.928i) q^{63} +802.959 q^{64} +(-221.649 - 52.0745i) q^{66} +(-591.989 + 341.785i) q^{67} +(725.435 - 418.830i) q^{68} +(-192.591 - 45.2475i) q^{69} +1097.61 q^{71} +(-367.239 + 22.8301i) q^{72} +470.464i q^{73} +(284.424 - 492.637i) q^{74} +(645.064 + 1117.28i) q^{76} +(-105.163 + 60.7160i) q^{77} +(-804.344 - 755.894i) q^{78} +(243.017 - 420.919i) q^{79} +(-723.387 + 90.2901i) q^{81} -1519.30i q^{82} +(-85.8802 - 49.5829i) q^{83} +(-479.323 + 510.046i) q^{84} +(-58.5149 - 101.351i) q^{86} +(-112.571 + 33.9416i) q^{87} +(-118.276 - 68.2868i) q^{88} -8.80426 q^{89} -588.687 q^{91} +(-366.550 - 211.628i) q^{92} +(35.7918 - 152.344i) q^{93} +(1007.54 + 1745.12i) q^{94} +(1200.62 + 282.075i) q^{96} +(572.419 + 330.486i) q^{97} -857.763i q^{98} +(-242.278 - 120.493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9}+O(q^{10}) \) 8 * q + 10 * q^4 + 18 * q^6 - 90 * q^9	\( 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9} - 132 q^{11} + 120 q^{14} + 14 q^{16} + 308 q^{19} + 42 q^{21} + 198 q^{24} - 1056 q^{26} - 102 q^{29} - 86 q^{31} + 594 q^{34} - 450 q^{36} - 1518 q^{39} - 264 q^{41} + 924 q^{44} - 1056 q^{46} - 1026 q^{49} + 594 q^{51} - 2430 q^{54} - 132 q^{56} + 1596 q^{59} - 878 q^{61} + 2908 q^{64} - 1980 q^{66} - 1782 q^{69} + 5472 q^{71} + 1632 q^{74} + 3058 q^{76} - 1606 q^{79} - 1134 q^{81} - 1284 q^{84} - 66 q^{86} + 1584 q^{89} - 3124 q^{91} + 4200 q^{94} + 2160 q^{96} - 594 q^{99}+O(q^{100}) \) 8 * q + 10 * q^4 + 18 * q^6 - 90 * q^9 - 132 * q^11 + 120 * q^14 + 14 * q^16 + 308 * q^19 + 42 * q^21 + 198 * q^24 - 1056 * q^26 - 102 * q^29 - 86 * q^31 + 594 * q^34 - 450 * q^36 - 1518 * q^39 - 264 * q^41 + 924 * q^44 - 1056 * q^46 - 1026 * q^49 + 594 * q^51 - 2430 * q^54 - 132 * q^56 + 1596 * q^59 - 878 * q^61 + 2908 * q^64 - 1980 * q^66 - 1782 * q^69 + 5472 * q^71 + 1632 * q^74 + 3058 * q^76 - 1606 * q^79 - 1134 * q^81 - 1284 * q^84 - 66 * q^86 + 1584 * q^89 - 3124 * q^91 + 4200 * q^94 + 2160 * q^96 - 594 * q^99

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