LMFDB - Embedded newform 225.4.k.b.49.1

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			49.1
Root			$-0.396143 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	225.49
Dual form			225.4.k.b.124.1

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−3.78651	+	2.18614i	−1.33873	+	0.772917i	−0.986619	−	0.163040i	$-0.947870\pi$
$2$	−3.78651	+	2.18614i	−1.33873	+	0.772917i	−0.352113	+	0.935958i	$0.614537\pi$
$3$	−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	$-0.772746\pi$
$7$	−10.4935	+	6.05842i	−0.566595	+	0.327124i	0.189193	+	0.981940i	$0.439413\pi$
$8$			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	0.789144	−	0.614209i	$-0.210525\pi$
$11$	−5.01087	−	8.67909i	−0.137349	−	0.237895i	−0.926492	+	0.376314i	$0.877191\pi$
$12$	13.2116	+	56.2337i	0.317822	+	1.35277i
$13$	42.0752	+	24.2921i	0.897658	+	0.518263i	0.876440	−	0.481512i	$-0.159912\pi$
$13$	42.0752	+	24.2921i	0.897658	+	0.518263i	0.0212183	+	0.999775i	$0.493246\pi$
$14$	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	$-0.278122\pi$
$23$	32.9725	+	19.0367i	0.298923	+	0.172584i	−0.343036	+	0.939322i	$0.611455\pi$
$24$	−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	0.827527	−	0.561426i	$-0.189747\pi$
$29$	−11.3139	−	19.5962i	−0.0724459	−	0.125480i	−0.899973	+	0.435946i	$0.856414\pi$
$30$		0			0
$31$	−15.0584	+	26.0820i	−0.0872443	+	0.151112i	−0.906345	−	0.422538i	$-0.861139\pi$
$31$	−15.0584	+	26.0820i	−0.0872443	+	0.151112i	0.819101	+	0.573649i	$0.194473\pi$
$32$	−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	0.318339	+	0.947977i	$0.396875\pi$
$41$	−173.742	+	300.930i	−0.661803	+	1.14628i	−0.980142	+	0.198299i	$0.936458\pi$
$42$	62.9610	+	267.986i	0.231312	+	0.984552i
$43$	23.1803	−	13.3832i	0.0822085	−	0.0474631i	−0.458332	−	0.888781i	$-0.651553\pi$
$43$	23.1803	−	13.3832i	0.0822085	−	0.0474631i	0.540541	+	0.841318i	$0.318220\pi$
$44$	−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	$-0.920317\pi$
$47$	−399.132	+	230.439i	−1.23871	+	0.715169i	−0.269879	+	0.962894i	$0.586984\pi$
$48$	−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	−0.861371	−	0.507976i	$-0.830394\pi$
$59$	4.18487	−	7.24841i	0.00923430	−	0.0159943i	0.870606	+	0.491982i	$0.163727\pi$
$60$		0			0
$61$	41.0448	+	71.0916i	0.0861515	+	0.149219i	0.905881	−	0.423532i	$-0.139210\pi$
$61$	41.0448	+	71.0916i	0.0861515	+	0.149219i	−0.819730	+	0.572750i	$0.805876\pi$
$62$		−	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	$-0.119158\pi$
$67$	591.989	+	341.785i	1.07945	+	0.623220i	0.148701	+	0.988882i	$0.452491\pi$
$68$	−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	0.985552	−	0.169371i	$-0.0541737\pi$
$79$	243.017	+	420.919i	0.346096	+	0.599456i	−0.639456	+	0.768828i	$0.720840\pi$
$80$		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	$-0.645780\pi$
$83$	85.8802	−	49.5829i	0.113573	−	0.0655715i	0.555711	+	0.831376i	$0.312446\pi$
$84$	−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	$-0.779105\pi$
$97$	−572.419	+	330.486i	−0.599179	+	0.345936i	0.169540	+	0.985523i	$0.445772\pi$
$98$		−	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	0.970981	−	0.239156i	$-0.0768708\pi$
$101$	282.561	+	489.410i	0.278375	+	0.482160i	−0.692606	+	0.721316i	$0.743537\pi$
$102$	−1639.01	−	494.181i	−1.59104	−	0.479717i
$103$	841.068	+	485.591i	0.804592	+	0.464531i	0.845074	−	0.534649i	$-0.179556\pi$
$103$	841.068	+	485.591i	0.804592	+	0.464531i	−0.0404826	+	0.999180i	$0.512890\pi$
$104$	−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	$-0.240458\pi$
$113$	598.478	+	345.531i	0.498231	+	0.287654i	−0.229752	+	0.973249i	$0.573791\pi$
$114$	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	0.446288	+	0.894889i	$0.352746\pi$
$131$	−827.428	+	1433.15i	−0.551853	+	0.955837i	−0.998141	+	0.0609476i	$0.980588\pi$
$132$	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	$-0.356919\pi$
$137$	2295.91	−	1325.55i	1.43177	−	0.826635i	0.997256	+	0.0740277i	$0.0235853\pi$
$138$	630.330	−	592.361i	0.388821	−	0.365400i
$139$	317.084	−	549.206i	0.193487	−	0.335130i	−0.752916	−	0.658116i	$-0.771354\pi$
$139$	317.084	−	549.206i	0.193487	−	0.335130i	0.946404	+	0.322986i	$0.104687\pi$
$140$		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	−0.164372	+	0.986398i	$0.552560\pi$
$149$	−1703.16	+	2949.96i	−0.936432	+	1.62195i	−0.772060	+	0.635550i	$0.780773\pi$
$150$		0			0
$151$	875.159	+	1515.82i	0.471652	+	0.816925i	0.999474	−	0.0324302i	$-0.0103247\pi$
$151$	875.159	+	1515.82i	0.471652	+	0.816925i	−0.527822	+	0.849355i	$0.676991\pi$
$152$			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	$-0.146540\pi$
$157$	1886.70	+	1089.29i	0.959076	+	0.553723i	0.0631876	+	0.998002i	$0.479873\pi$
$158$	−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	$-0.186511\pi$
$167$	1663.67	+	960.520i	0.770890	+	0.445074i	−0.0623020	+	0.998057i	$0.519844\pi$
$168$	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	$-0.421395\pi$
$173$	2745.15	−	1584.91i	1.20642	−	0.696525i	0.961974	+	0.273139i	$0.0880620\pi$
$174$	−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	0.998693	−	0.0511008i	$-0.0162730\pi$
$191$	1201.29	+	2080.70i	0.455092	+	0.788243i	−0.543601	+	0.839344i	$0.682940\pi$
$192$	−3040.41	+	2857.27i	−1.14283	+	1.07399i
$193$	1156.20	+	667.535i	0.431220	+	0.248965i	0.699866	−	0.714274i	$-0.253243\pi$
$193$	1156.20	+	667.535i	0.431220	+	0.248965i	−0.268646	+	0.963239i	$0.586576\pi$
$194$	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	−0.544361	−	0.838851i	$-0.683228\pi$
$211$	1392.36	−	2411.65i	0.454286	−	0.786847i	0.998647	+	0.0520047i	$0.0165611\pi$
$212$	−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	$-0.668725\pi$
$223$	−37.2890	+	21.5288i	−0.0111976	+	0.00646491i	0.494391	+	0.869240i	$0.335391\pi$
$224$	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	$-0.698515\pi$
$227$	−591.721	+	341.630i	−0.173013	+	0.0998889i	0.410993	+	0.911639i	$0.365182\pi$
$228$	1533.23	+	6526.01i	0.445353	+	1.89559i
$229$	2147.15	−	3718.98i	0.619598	−	1.07317i	−0.369962	−	0.929047i	$-0.620629\pi$
$229$	2147.15	−	3718.98i	0.619598	−	1.07317i	0.989559	−	0.144127i	$-0.0460375\pi$
$230$		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	−0.177261	−	0.984164i	$-0.556724\pi$
$239$	2821.69	−	4887.30i	0.763681	−	1.32273i	0.940941	−	0.338570i	$-0.109943\pi$
$240$		0			0
$241$	−3294.71	−	5706.61i	−0.880627	−	1.52529i	−0.850645	−	0.525741i	$-0.823788\pi$
$241$	−3294.71	−	5706.61i	−0.880627	−	1.52529i	−0.0299825	−	0.999550i	$-0.509545\pi$
$242$			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	$-0.466375\pi$
$257$	−2896.53	−	1672.31i	−0.703036	−	0.405898i	−0.808477	+	0.588527i	$0.799708\pi$
$258$	−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	$-0.389647\pi$
$263$	5647.78	−	3260.75i	1.32417	−	0.764511i	0.984391	+	0.175994i	$0.0563139\pi$
$264$	−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	0.577610	−	0.816313i	$-0.303985\pi$
$277$	7253.51	−	4187.82i	1.57336	−	0.908381i	0.995753	−	0.0920685i	$-0.0293479\pi$
$278$			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	0.998290	+	0.0584616i	$0.0186195\pi$
$281$	2589.67	+	4485.43i	0.549774	+	0.952237i	−0.448516	+	0.893775i	$0.648047\pi$
$282$	2394.79	+	10193.2i	0.505701	+	2.15246i
$283$	2667.42	+	1540.03i	0.560288	+	0.323482i	0.753261	−	0.657722i	$-0.228480\pi$
$283$	2667.42	+	1540.03i	0.560288	+	0.323482i	−0.192973	+	0.981204i	$0.561813\pi$
$284$	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	$-0.451845\pi$
$293$	−3160.04	−	1824.45i	−0.630073	−	0.363773i	−0.780780	+	0.624806i	$0.785178\pi$
$294$	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	0.327968	+	0.944689i	$0.393636\pi$
$311$	−3587.66	+	6214.02i	−0.654141	+	1.13301i	−0.982108	+	0.188316i	$0.939697\pi$
$312$	−786.850	−	3349.14i	−0.142778	−	0.607717i
$313$	−4206.54	+	2428.65i	−0.759642	+	0.438579i	−0.829167	−	0.559001i	$-0.811185\pi$
$313$	−4206.54	+	2428.65i	−0.759642	+	0.438579i	0.0695253	+	0.997580i	$0.477852\pi$
$314$	−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	$-0.899801\pi$
$317$	−6536.70	+	3773.97i	−1.15816	+	0.668666i	−0.207300	+	0.978277i	$0.566468\pi$
$318$	−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	0.966203	−	0.257782i	$-0.0829915\pi$
$331$	1564.86	+	2710.41i	0.259856	+	0.450084i	−0.706347	+	0.707866i	$0.749658\pi$
$332$		−	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	$-0.601351\pi$
$337$	−7993.39	−	4614.99i	−1.29207	−	0.745978i	−0.979021	+	0.203759i	$0.934684\pi$
$338$	−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	$-0.549009\pi$
$347$	−7018.61	−	4052.20i	−1.08582	−	0.626897i	−0.932460	+	0.361273i	$0.882342\pi$
$348$	952.491	−	895.117i	0.146721	−	0.137883i
$349$	1538.21	+	2664.26i	0.235927	+	0.408638i	0.959542	−	0.281566i	$-0.0908540\pi$
$349$	1538.21	+	2664.26i	0.235927	+	0.408638i	−0.723615	+	0.690204i	$0.757521\pi$
$350$		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	$-0.820127\pi$
$353$	−5326.13	+	3075.04i	−0.803063	+	0.463649i	0.0414780	+	0.999139i	$0.486793\pi$
$354$	−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	$-0.733930\pi$
$367$	−2554.16	+	1474.65i	−0.363287	+	0.209744i	0.307235	+	0.951634i	$0.400596\pi$
$368$			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	$-0.359068\pi$
$373$	−1007.69	−	581.790i	−0.139883	−	0.0807612i	−0.568308	+	0.822816i	$0.692402\pi$
$374$	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	$-0.0771741\pi$
$383$	9355.93	+	5401.65i	1.24821	+	0.720656i	0.277460	+	0.960737i	$0.410507\pi$
$384$	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	0.925425	−	0.378931i	$-0.123708\pi$
$389$	1032.29	+	1787.99i	0.134549	+	0.233045i	−0.790876	+	0.611976i	$0.790375\pi$
$390$		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	−0.935061	−	0.354487i	$-0.884656\pi$
$401$	−1289.10	+	2232.79i	−0.160536	+	0.278056i	0.774525	+	0.632543i	$0.217989\pi$
$402$	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	−0.633470	−	0.773767i	$-0.718370\pi$
$409$	2922.88	−	5062.57i	0.353367	−	0.612049i	0.986837	+	0.161718i	$0.0517034\pi$
$410$		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	0.490343	+	0.871530i	$0.336872\pi$
$419$	−4370.66	+	7570.20i	−0.509596	+	0.882646i	−0.999938	+	0.0111158i	$0.996462\pi$
$420$		0			0
$421$	−528.254	−	914.963i	−0.0611533	−	0.105921i	0.833828	−	0.552024i	$-0.186145\pi$
$421$	−528.254	−	914.963i	−0.0611533	−	0.105921i	−0.894981	+	0.446104i	$0.852811\pi$
$422$			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	0.836001	−	0.548728i	$-0.184888\pi$
$439$	−526.239	−	911.473i	−0.0572119	−	0.0990939i	−0.893213	+	0.449634i	$0.851554\pi$
$440$		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	$-0.857015\pi$
$443$	−9092.14	+	5249.35i	−0.975126	+	0.562989i	−0.0743307	+	0.997234i	$0.523682\pi$
$444$	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	$-0.785819\pi$
$457$	−6187.23	+	3572.20i	−0.633318	+	0.365646i	0.148718	+	0.988880i	$0.452485\pi$
$458$			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	0.684664	−	0.728859i	$-0.259949\pi$
$461$	−2859.34	−	4952.53i	−0.288878	−	0.500352i	−0.973542	+	0.228507i	$0.926616\pi$
$462$	2010.39	−	1889.29i	0.202450	−	0.190255i
$463$	−682.831	−	394.233i	−0.0685397	−	0.0395714i	0.465339	−	0.885133i	$-0.345933\pi$
$463$	−682.831	−	394.233i	−0.0685397	−	0.0395714i	−0.533878	+	0.845561i	$0.679266\pi$
$464$	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	0.899952	−	0.435988i	$-0.143601\pi$
$479$	758.994	+	1314.62i	0.0723994	+	0.125399i	−0.827553	+	0.561388i	$0.810268\pi$
$480$		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	−0.966121	−	0.258089i	$-0.916907\pi$
$491$	−2823.85	+	4891.05i	−0.259549	+	0.449552i	0.706572	+	0.707641i	$0.250241\pi$
$492$	−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	−0.513361	−	0.858173i	$-0.671600\pi$
$499$	5423.14	−	9393.15i	0.486519	−	0.842676i	0.999880	+	0.0154970i	$0.00493306\pi$
$500$		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	−0.965357	−	0.260933i	$-0.915970\pi$
$509$	−2947.87	+	5105.87i	−0.256704	+	0.444624i	0.708653	+	0.705557i	$0.249303\pi$
$510$		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	0.644863	−	0.764298i	$-0.276914\pi$
$547$	20842.7	−	12033.6i	1.62920	−	0.940617i	0.984333	−	0.176319i	$-0.0564191\pi$
$548$		−	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	$-0.296373\pi$
$563$	2680.62	+	1547.66i	0.200666	+	0.115854i	−0.396300	+	0.918121i	$0.629706\pi$
$564$	−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	0.944078	+	0.329721i	$0.106955\pi$
$569$	10282.5	+	17809.9i	0.757586	+	1.31218i	−0.186492	+	0.982456i	$0.559712\pi$
$570$		0			0
$571$	584.992	−	1013.24i	0.0428742	−	0.0742602i	−0.843792	−	0.536670i	$-0.819682\pi$
$571$	584.992	−	1013.24i	0.0428742	−	0.0742602i	0.886666	+	0.462410i	$0.153015\pi$
$572$	−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	$-0.495772\pi$
$587$	12598.8	−	7273.91i	0.885873	−	0.511459i	0.872590	+	0.488453i	$0.162439\pi$
$588$	−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	−0.610108	−	0.792318i	$-0.708874\pi$
$599$	5587.20	−	9677.32i	0.381113	−	0.660108i	0.991222	+	0.132210i	$0.0422074\pi$
$600$		0			0
$601$	−2294.27	−	3973.79i	−0.155716	−	0.269708i	0.777604	−	0.628755i	$-0.216435\pi$
$601$	−2294.27	−	3973.79i	−0.155716	−	0.269708i	−0.933319	+	0.359047i	$0.883102\pi$
$602$		−	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	$-0.458840\pi$
$607$	−9950.61	−	5744.99i	−0.665375	−	0.384155i	−0.794322	+	0.607497i	$0.792174\pi$
$608$	−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	$-0.422739\pi$
$617$	−7358.29	−	4248.31i	−0.480120	−	0.277197i	−0.720466	+	0.693490i	$0.756072\pi$
$618$	16078.6	−	15110.1i	1.04656	−	0.983521i
$619$	7169.94	+	12418.7i	0.465564	+	0.806381i	0.999227	−	0.0393163i	$-0.0125180\pi$
$619$	7169.94	+	12418.7i	0.465564	+	0.806381i	−0.533662	+	0.845698i	$0.679185\pi$
$620$		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	−0.911670	−	0.410923i	$-0.865207\pi$
$641$	−13173.0	−	22816.3i	−0.811705	−	1.40591i	0.0999654	−	0.994991i	$-0.468127\pi$
$642$	12264.7	+	3697.93i	0.753968	+	0.227330i
$643$	18675.9	+	10782.5i	1.14542	+	0.661309i	0.947767	−	0.318963i	$-0.103335\pi$
$643$	18675.9	+	10782.5i	1.14542	+	0.661309i	0.197653	+	0.980272i	$0.436668\pi$
$644$	−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	$-0.360120\pi$
$653$	−2429.33	−	1402.57i	−0.145585	−	0.0840534i	−0.571023	+	0.820934i	$0.693453\pi$
$654$	−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	−0.997170	−	0.0751839i	$-0.976046\pi$
$659$	−9536.15	−	16517.1i	−0.563696	−	0.976350i	0.433474	−	0.901166i	$-0.357288\pi$
$660$		0			0
$661$	12256.5	−	21228.9i	0.721216	−	1.24918i	−0.239296	−	0.970947i	$-0.576917\pi$
$661$	12256.5	−	21228.9i	0.721216	−	1.24918i	0.960513	−	0.278237i	$-0.0897500\pi$
$662$	−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	$-0.699053\pi$
$673$	−3071.49	+	1773.32i	−0.175924	+	0.101570i	0.409452	+	0.912332i	$0.365720\pi$
$674$	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	$-0.836052\pi$
$677$	−15480.2	+	8937.50i	−0.878807	+	0.507380i	−0.00854232	+	0.999964i	$0.502719\pi$
$678$	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	0.996888	−	0.0788308i	$-0.0251187\pi$
$691$	7813.79	+	13533.9i	0.430175	+	0.745084i	−0.566714	+	0.823915i	$0.691785\pi$
$692$		−	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	0.999396	+	0.0347532i	$0.0110645\pi$
$709$	10001.8	+	17323.6i	0.529795	+	0.917632i	−0.469601	+	0.882879i	$0.655602\pi$
$710$		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	$-0.457885\pi$
$727$	20706.5	−	11954.9i	1.05634	−	0.609879i	0.924418	+	0.381380i	$0.124551\pi$
$728$		−	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	$-0.264587\pi$
$733$	7366.02	+	4252.77i	0.371173	+	0.214297i	−0.302798	+	0.953055i	$0.597921\pi$
$734$	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	$-0.569151\pi$
$743$	−23675.0	−	13668.8i	−1.16898	−	0.674911i	−0.953440	+	0.301584i	$0.902485\pi$
$744$	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	−0.903706	−	0.428153i	$-0.859165\pi$
$751$	−1668.32	+	2889.61i	−0.0810623	+	0.140404i	0.822644	+	0.568557i	$0.192498\pi$
$752$	−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	−0.704836	−	0.709371i	$-0.748979\pi$
$761$	5498.42	−	9523.54i	0.261915	−	0.453651i	0.966751	+	0.255720i	$0.0823125\pi$
$762$	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	−0.151277	−	0.988491i	$-0.548339\pi$
$769$	16642.5	−	28825.6i	0.780420	−	1.35173i	0.931697	−	0.363236i	$-0.118328\pi$
$770$		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	$-0.204293\pi$
$787$	15081.2	+	8707.15i	0.683084	+	0.394379i	−0.117932	+	0.993022i	$0.537626\pi$
$788$	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	$-0.109193\pi$
$797$	25229.9	+	14566.5i	1.12131	+	0.647391i	0.179578	+	0.983744i	$0.442527\pi$
$798$	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	0.991161	−	0.132667i	$-0.0423542\pi$
$821$	8955.36	+	15511.1i	0.380687	+	0.659369i	−0.610474	+	0.792037i	$0.709021\pi$
$822$	−13775.5	−	58633.8i	−0.584519	−	2.48794i
$823$	−15176.6	−	8762.22i	−0.642799	−	0.371120i	0.142893	−	0.989738i	$-0.454360\pi$
$823$	−15176.6	−	8762.22i	−0.642799	−	0.371120i	−0.785692	+	0.618618i	$0.787693\pi$
$824$	−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	0.998210	+	0.0598087i	$0.0190491\pi$
$839$	13388.0	+	23188.7i	0.550901	+	0.954188i	−0.447309	+	0.894379i	$0.647618\pi$
$840$		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	$-0.717425\pi$
$853$	−6851.78	+	3955.88i	−0.275030	+	0.158789i	0.356141	+	0.934432i	$0.384092\pi$
$854$	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	$-0.678395\pi$
$857$	−1600.67	+	924.149i	−0.0638016	+	0.0368359i	0.467760	+	0.883856i	$0.345061\pi$
$858$	−10590.9	−	3193.29i	−0.421409	−	0.127060i
$859$	−9427.10	+	16328.2i	−0.374445	+	0.648558i	−0.990244	−	0.139345i	$-0.955500\pi$
$859$	−9427.10	+	16328.2i	−0.374445	+	0.648558i	0.615799	+	0.787904i	$0.288833\pi$
$860$		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	$-0.491611\pi$
$877$	−21457.7	−	12388.6i	−0.826197	−	0.477005i	−0.852549	+	0.522648i	$0.824944\pi$
$878$	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	$-0.165236\pi$
$887$	23055.8	+	13311.3i	0.872759	+	0.503888i	0.00449496	+	0.999990i	$0.498569\pi$
$888$	−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	−0.699694	+	0.714443i	$0.746680\pi$
$907$	−45569.7	+	26309.7i	−1.66827	+	0.963174i	−0.968572	+	0.248731i	$0.919986\pi$
$908$			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	0.758495	−	0.651678i	$-0.225935\pi$
$911$	−5090.22	−	8816.52i	−0.185122	−	0.320641i	−0.943618	+	0.331037i	$0.892601\pi$
$912$	−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	0.725622	−	0.688093i	$-0.241552\pi$
$929$	−6600.20	−	11431.9i	−0.233095	−	0.403733i	−0.958717	+	0.284361i	$0.908219\pi$
$930$		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	−0.960855	−	0.277052i	$-0.910643\pi$
$941$	−6942.05	+	12024.0i	−0.240493	+	0.416547i	0.720362	+	0.693599i	$0.243976\pi$
$942$	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	$-0.695523\pi$
$947$	−4569.70	+	2638.32i	−0.156806	+	0.0905320i	0.419544	+	0.907735i	$0.362190\pi$
$948$	−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	$-0.354507\pi$
$967$	−3461.96	−	1998.77i	−0.115128	−	0.0664695i	−0.556458	+	0.830875i	$0.687840\pi$
$968$	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	$-0.269080\pi$
$977$	10604.6	+	6122.55i	0.347257	+	0.200489i	−0.316220	+	0.948686i	$0.602414\pi$
$978$	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	$-0.415223\pi$
$983$	37917.3	−	21891.5i	1.23029	−	0.710307i	0.967090	+	0.254435i	$0.0818893\pi$
$984$	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	$-0.800622\pi$
$997$	−22275.0	+	12860.5i	−0.707578	+	0.408520i	0.102586	+	0.994724i	$0.467288\pi$
$998$			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.49.1		8
5.2	odd	4		9.4.c.a.4.1	✓	4
5.3	odd	4		225.4.e.b.76.2		4
5.4	even	2	inner	225.4.k.b.49.4		8
9.7	even	3	inner	225.4.k.b.124.4		8
15.2	even	4		27.4.c.a.10.2		4
20.7	even	4		144.4.i.c.49.1		4
45.2	even	12		27.4.c.a.19.2		4
45.7	odd	12		9.4.c.a.7.1	yes	4
45.13	odd	12		2025.4.a.g.1.1		2
45.22	odd	12		81.4.a.d.1.2		2
45.23	even	12		2025.4.a.n.1.2		2
45.32	even	12		81.4.a.a.1.1		2
45.34	even	6	inner	225.4.k.b.124.1		8
45.43	odd	12		225.4.e.b.151.2		4
60.47	odd	4		432.4.i.c.145.1		4
180.7	even	12		144.4.i.c.97.1		4
180.47	odd	12		432.4.i.c.289.1		4
180.67	even	12		1296.4.a.u.1.1		2
180.167	odd	12		1296.4.a.i.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.1	✓	4	5.2	odd	4
9.4.c.a.7.1	yes	4	45.7	odd	12
27.4.c.a.10.2		4	15.2	even	4
27.4.c.a.19.2		4	45.2	even	12
81.4.a.a.1.1		2	45.32	even	12
81.4.a.d.1.2		2	45.22	odd	12
144.4.i.c.49.1		4	20.7	even	4
144.4.i.c.97.1		4	180.7	even	12
225.4.e.b.76.2		4	5.3	odd	4
225.4.e.b.151.2		4	45.43	odd	12
225.4.k.b.49.1		8	1.1	even	1	trivial
225.4.k.b.49.4		8	5.4	even	2	inner
225.4.k.b.124.1		8	45.34	even	6	inner
225.4.k.b.124.4		8	9.7	even	3	inner
432.4.i.c.145.1		4	60.47	odd	4
432.4.i.c.289.1		4	180.47	odd	12
1296.4.a.i.1.2		2	180.167	odd	12
1296.4.a.u.1.1		2	180.67	even	12
2025.4.a.g.1.1		2	45.13	odd	12
2025.4.a.n.1.2		2	45.23	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

Introduction

L-functions

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