LMFDB - Embedded newform 51.4.e.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,4,Mod(4,51)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("51.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	51.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.00909741029$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 88 x^{14} + 3086 x^{12} + 54880 x^{10} + 516641 x^{8} + 2403800 x^{6} + 4378064 x^{4} + \cdots + 295936 $ x^16 + 88x^14 + 3086x^12 + 54880x^10 + 516641x^8 + 2403800x^6 + 4378064x^4 + 2140928*x^2 + 295936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.5
Root			$0.496675i$ of defining polynomial
Character	$\chi$	$=$	51.13
Dual form			51.4.e.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.49668i q^{2} +(2.12132 + 2.12132i) q^{3} +5.75996 q^{4} +(0.574777 + 0.574777i) q^{5} +(-3.17493 + 3.17493i) q^{6} +(2.73692 - 2.73692i) q^{7} +20.5942i q^{8} +9.00000i q^{9} +(-0.860255 + 0.860255i) q^{10} +(-14.2363 + 14.2363i) q^{11} +(12.2187 + 12.2187i) q^{12} +20.0363 q^{13} +(4.09628 + 4.09628i) q^{14} +2.43857i q^{15} +15.2569 q^{16} +(-58.0925 - 39.2207i) q^{17} -13.4701 q^{18} -123.098i q^{19} +(3.31070 + 3.31070i) q^{20} +11.6118 q^{21} +(-21.3072 - 21.3072i) q^{22} +(29.6574 - 29.6574i) q^{23} +(-43.6869 + 43.6869i) q^{24} -124.339i q^{25} +29.9879i q^{26} +(-19.0919 + 19.0919i) q^{27} +(15.7646 - 15.7646i) q^{28} +(-17.6364 - 17.6364i) q^{29} -3.64975 q^{30} +(-54.0799 - 54.0799i) q^{31} +187.588i q^{32} -60.3996 q^{33} +(58.7006 - 86.9456i) q^{34} +3.14624 q^{35} +51.8397i q^{36} +(22.3384 + 22.3384i) q^{37} +184.238 q^{38} +(42.5035 + 42.5035i) q^{39} +(-11.8371 + 11.8371i) q^{40} +(-76.6455 + 76.6455i) q^{41} +17.3791i q^{42} +233.202i q^{43} +(-82.0007 + 82.0007i) q^{44} +(-5.17299 + 5.17299i) q^{45} +(44.3874 + 44.3874i) q^{46} +51.1712 q^{47} +(32.3648 + 32.3648i) q^{48} +328.019i q^{49} +186.095 q^{50} +(-40.0331 - 206.432i) q^{51} +115.409 q^{52} -1.55884i q^{53} +(-28.5743 - 28.5743i) q^{54} -16.3654 q^{55} +(56.3647 + 56.3647i) q^{56} +(261.131 - 261.131i) q^{57} +(26.3960 - 26.3960i) q^{58} -588.603i q^{59} +14.0461i q^{60} +(-513.681 + 513.681i) q^{61} +(80.9401 - 80.9401i) q^{62} +(24.6323 + 24.6323i) q^{63} -158.703 q^{64} +(11.5164 + 11.5164i) q^{65} -90.3986i q^{66} +266.752 q^{67} +(-334.611 - 225.910i) q^{68} +125.826 q^{69} +4.70890i q^{70} +(-621.733 - 621.733i) q^{71} -185.348 q^{72} +(236.509 + 236.509i) q^{73} +(-33.4333 + 33.4333i) q^{74} +(263.763 - 263.763i) q^{75} -709.043i q^{76} +77.9274i q^{77} +(-63.6139 + 63.6139i) q^{78} +(-582.906 + 582.906i) q^{79} +(8.76932 + 8.76932i) q^{80} -81.0000 q^{81} +(-114.713 - 114.713i) q^{82} +224.694i q^{83} +66.8834 q^{84} +(-10.8471 - 55.9334i) q^{85} -349.028 q^{86} -74.8250i q^{87} +(-293.186 - 293.186i) q^{88} +561.132 q^{89} +(-7.74229 - 7.74229i) q^{90} +(54.8379 - 54.8379i) q^{91} +(170.825 - 170.825i) q^{92} -229.442i q^{93} +76.5866i q^{94} +(70.7542 - 70.7542i) q^{95} +(-397.935 + 397.935i) q^{96} +(1257.15 + 1257.15i) q^{97} -490.937 q^{98} +(-128.127 - 128.127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 48 q^{4} - 32 q^{5} + 12 q^{6} - 8 q^{7} - 20 q^{10} + 96 q^{11} + 120 q^{13} - 288 q^{14} - 200 q^{16} + 16 q^{17} - 72 q^{18} + 384 q^{20} + 168 q^{21} + 4 q^{22} + 208 q^{23} + 312 q^{24} + 904 q^{28}+ \cdots + 864 q^{99}+O(q^{100}) $ 16 * q - 48 * q^4 - 32 * q^5 + 12 * q^6 - 8 * q^7 - 20 * q^10 + 96 * q^11 + 120 * q^13 - 288 * q^14 - 200 * q^16 + 16 * q^17 - 72 * q^18 + 384 * q^20 + 168 * q^21 + 4 * q^22 + 208 * q^23 + 312 * q^24 + 904 * q^28 + 320 * q^29 - 432 * q^30 - 624 * q^31 - 72 * q^33 - 788 * q^34 - 1184 * q^35 + 256 * q^37 - 168 * q^38 - 24 * q^39 - 664 * q^40 + 800 * q^41 + 128 * q^44 + 288 * q^45 + 572 * q^46 + 368 * q^47 + 96 * q^48 - 720 * q^50 - 120 * q^51 - 3160 * q^52 + 108 * q^54 + 4296 * q^55 + 576 * q^56 - 1080 * q^57 + 1368 * q^58 - 1296 * q^61 + 536 * q^62 - 72 * q^63 + 1752 * q^64 - 4288 * q^65 - 1248 * q^67 - 240 * q^68 + 576 * q^69 + 1488 * q^71 + 864 * q^72 - 1208 * q^73 + 2272 * q^74 + 1200 * q^75 + 564 * q^78 - 1256 * q^79 + 384 * q^80 - 1296 * q^81 + 3564 * q^82 - 2088 * q^84 + 3216 * q^85 + 3224 * q^86 - 1296 * q^88 - 2608 * q^89 - 180 * q^90 - 56 * q^91 - 5072 * q^92 + 160 * q^95 - 408 * q^96 - 4456 * q^97 - 1208 * q^98 + 864 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			1.49668i			0.529155i	0.964364	+	0.264577i	$0.0852324\pi$
$2$			1.49668i			0.529155i	−0.964364	+	0.264577i	$0.914768\pi$
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$4$	5.75996			0.719995
$5$	0.574777	+	0.574777i	0.0514096	+	0.0514096i	0.732344	−	0.680935i	$-0.238426\pi$
$5$	0.574777	+	0.574777i	0.0514096	+	0.0514096i	−0.680935	+	0.732344i	$0.738426\pi$
$6$	−3.17493	+	3.17493i	−0.216026	+	0.216026i
$7$	2.73692	−	2.73692i	0.147780	−	0.147780i	−0.629346	−	0.777126i	$-0.716677\pi$
$7$	2.73692	−	2.73692i	0.147780	−	0.147780i	0.777126	+	0.629346i	$0.216677\pi$
$8$			20.5942i			0.910143i
$9$			9.00000i			0.333333i
$10$	−0.860255	+	0.860255i	−0.0272036	+	0.0272036i
$11$	−14.2363	+	14.2363i	−0.390219	+	0.390219i	−0.874766	−	0.484546i	$-0.838985\pi$
$11$	−14.2363	+	14.2363i	−0.390219	+	0.390219i	0.484546	+	0.874766i	$0.338985\pi$
$12$	12.2187	+	12.2187i	0.293937	+	0.293937i
$13$	20.0363			0.427468			0.213734	−	0.976892i	$-0.431437\pi$
$13$	20.0363			0.427468			0.213734	+	0.976892i	$0.431437\pi$
$14$	4.09628	+	4.09628i	0.0781984	+	0.0781984i
$15$			2.43857i			0.0419758i
$16$	15.2569			0.238389
$17$	−58.0925	−	39.2207i	−0.828794	−	0.559554i
$17$	−58.0925	−	39.2207i	−0.828794	−	0.559554i
$18$	−13.4701			−0.176385
$19$		−	123.098i		−	1.48635i	−0.669095	−	0.743177i	$-0.733318\pi$
$19$		−	123.098i		−	1.48635i	0.669095	−	0.743177i	$-0.266682\pi$
$20$	3.31070	+	3.31070i	0.0370147	+	0.0370147i
$21$	11.6118			0.120662
$22$	−21.3072	−	21.3072i	−0.206486	−	0.206486i
$23$	29.6574	−	29.6574i	0.268869	−	0.268869i	−0.559775	−	0.828644i	$-0.689113\pi$
$23$	29.6574	−	29.6574i	0.268869	−	0.268869i	0.828644	+	0.559775i	$0.189113\pi$
$24$	−43.6869	+	43.6869i	−0.371564	+	0.371564i
$25$		−	124.339i		−	0.994714i
$26$			29.9879i			0.226196i
$27$	−19.0919	+	19.0919i	−0.136083	+	0.136083i
$28$	15.7646	−	15.7646i	0.106401	−	0.106401i
$29$	−17.6364	−	17.6364i	−0.112931	−	0.112931i	0.648383	−	0.761314i	$-0.275445\pi$
$29$	−17.6364	−	17.6364i	−0.112931	−	0.112931i	−0.761314	+	0.648383i	$0.775445\pi$
$30$	−3.64975			−0.0222117
$31$	−54.0799	−	54.0799i	−0.313324	−	0.313324i	0.532872	−	0.846196i	$-0.321113\pi$
$31$	−54.0799	−	54.0799i	−0.313324	−	0.313324i	−0.846196	+	0.532872i	$0.821113\pi$
$32$			187.588i			1.03629i
$33$	−60.3996			−0.318613
$34$	58.7006	−	86.9456i	0.296090	−	0.438560i
$35$	3.14624			0.0151946
$36$			51.8397i			0.239998i
$37$	22.3384	+	22.3384i	0.0992543	+	0.0992543i	0.754990	−	0.655736i	$-0.227642\pi$
$37$	22.3384	+	22.3384i	0.0992543	+	0.0992543i	−0.655736	+	0.754990i	$0.727642\pi$
$38$	184.238			0.786511
$39$	42.5035	+	42.5035i	0.174513	+	0.174513i
$40$	−11.8371	+	11.8371i	−0.0467901	+	0.0467901i
$41$	−76.6455	+	76.6455i	−0.291952	+	0.291952i	−0.837851	−	0.545899i	$-0.816188\pi$
$41$	−76.6455	+	76.6455i	−0.291952	+	0.291952i	0.545899	+	0.837851i	$0.316188\pi$
$42$			17.3791i			0.0638487i
$43$			233.202i			0.827047i	0.910493	+	0.413524i	$0.135702\pi$
$43$			233.202i			0.827047i	−0.910493	+	0.413524i	$0.864298\pi$
$44$	−82.0007	+	82.0007i	−0.280956	+	0.280956i
$45$	−5.17299	+	5.17299i	−0.0171365	+	0.0171365i
$46$	44.3874	+	44.3874i	0.142273	+	0.142273i
$47$	51.1712			0.158810			0.0794052	−	0.996842i	$-0.474698\pi$
$47$	51.1712			0.158810			0.0794052	+	0.996842i	$0.474698\pi$
$48$	32.3648	+	32.3648i	0.0973219	+	0.0973219i
$49$			328.019i			0.956322i
$50$	186.095			0.526357
$51$	−40.0331	−	206.432i	−0.109917	−	0.566791i
$52$	115.409			0.307775
$53$		−	1.55884i		−	0.00404007i	−0.999998	−	0.00202003i	$-0.999357\pi$
$53$		−	1.55884i		−	0.00404007i	0.999998	−	0.00202003i	$-0.000642997\pi$
$54$	−28.5743	−	28.5743i	−0.0720088	−	0.0720088i
$55$	−16.3654			−0.0401221
$56$	56.3647	+	56.3647i	0.134501	+	0.134501i
$57$	261.131	−	261.131i	0.606801	−	0.606801i
$58$	26.3960	−	26.3960i	0.0597580	−	0.0597580i
$59$		−	588.603i		−	1.29881i	−0.760445	−	0.649403i	$-0.775019\pi$
$59$		−	588.603i		−	1.29881i	0.760445	−	0.649403i	$-0.224981\pi$
$60$			14.0461i			0.0302224i
$61$	−513.681	+	513.681i	−1.07820	+	1.07820i	−0.0815267	+	0.996671i	$0.525980\pi$
$61$	−513.681	+	513.681i	−1.07820	+	1.07820i	−0.996671	+	0.0815267i	$0.974020\pi$
$62$	80.9401	−	80.9401i	0.165797	−	0.165797i
$63$	24.6323	+	24.6323i	0.0492600	+	0.0492600i
$64$	−158.703			−0.309967
$65$	11.5164	+	11.5164i	0.0219760	+	0.0219760i
$66$		−	90.3986i		−	0.168595i
$67$	266.752			0.486403			0.243201	−	0.969976i	$-0.421802\pi$
$67$	266.752			0.486403			0.243201	+	0.969976i	$0.421802\pi$
$68$	−334.611	−	225.910i	−0.596728	−	0.402876i
$69$	125.826			0.219531
$70$			4.70890i			0.00804030i
$71$	−621.733	−	621.733i	−1.03924	−	1.03924i	−0.999198	−	0.0400429i	$-0.987251\pi$
$71$	−621.733	−	621.733i	−1.03924	−	1.03924i	−0.0400429	−	0.999198i	$-0.512749\pi$
$72$	−185.348			−0.303381
$73$	236.509	+	236.509i	0.379195	+	0.379195i	0.870812	−	0.491617i	$-0.163594\pi$
$73$	236.509	+	236.509i	0.379195	+	0.379195i	−0.491617	+	0.870812i	$0.663594\pi$
$74$	−33.4333	+	33.4333i	−0.0525209	+	0.0525209i
$75$	263.763	−	263.763i	0.406090	−	0.406090i
$76$		−	709.043i		−	1.07017i
$77$			77.9274i			0.115333i
$78$	−63.6139	+	63.6139i	−0.0923443	+	0.0923443i
$79$	−582.906	+	582.906i	−0.830153	+	0.830153i	−0.987537	−	0.157384i	$-0.949694\pi$
$79$	−582.906	+	582.906i	−0.830153	+	0.830153i	0.157384	+	0.987537i	$0.449694\pi$
$80$	8.76932	+	8.76932i	0.0122555	+	0.0122555i
$81$	−81.0000			−0.111111
$82$	−114.713	−	114.713i	−0.154488	−	0.154488i
$83$			224.694i			0.297149i	0.988901	+	0.148574i	$0.0474684\pi$
$83$			224.694i			0.297149i	−0.988901	+	0.148574i	$0.952532\pi$
$84$	66.8834			0.0868760
$85$	−10.8471	−	55.9334i	−0.0138415	−	0.0713745i
$86$	−349.028			−0.437636
$87$		−	74.8250i		−	0.0922078i
$88$	−293.186	−	293.186i	−0.355156	−	0.355156i
$89$	561.132			0.668313			0.334157	−	0.942518i	$-0.391549\pi$
$89$	561.132			0.668313			0.334157	+	0.942518i	$0.391549\pi$
$90$	−7.74229	−	7.74229i	−0.00906788	−	0.00906788i
$91$	54.8379	−	54.8379i	0.0631711	−	0.0631711i
$92$	170.825	−	170.825i	0.193584	−	0.193584i
$93$		−	229.442i		−	0.255828i
$94$			76.5866i			0.0840352i
$95$	70.7542	−	70.7542i	0.0764129	−	0.0764129i
$96$	−397.935	+	397.935i	−0.423063	+	0.423063i
$97$	1257.15	+	1257.15i	1.31592	+	1.31592i	0.916978	+	0.398938i	$0.130621\pi$
$97$	1257.15	+	1257.15i	1.31592	+	1.31592i	0.398938	+	0.916978i	$0.369379\pi$
$98$	−490.937			−0.506042
$99$	−128.127	−	128.127i	−0.130073	−	0.130073i
$100$		−	716.190i		−	0.716190i
$101$	1943.41			1.91462			0.957310	−	0.289064i	$-0.0933441\pi$
$101$	1943.41			1.91462			0.957310	+	0.289064i	$0.0933441\pi$
$102$	308.962	−	59.9166i	0.299920	−	0.0581630i
$103$	−197.134			−0.188585			−0.0942923	−	0.995545i	$-0.530059\pi$
$103$	−197.134			−0.188585			−0.0942923	+	0.995545i	$0.530059\pi$
$104$			412.632i			0.389057i
$105$	6.67419	+	6.67419i	0.00620318	+	0.00620318i
$106$	2.33308			0.00213782
$107$	1071.43	+	1071.43i	0.968033	+	0.968033i	0.999505	−	0.0314720i	$-0.0100195\pi$
$107$	1071.43	+	1071.43i	0.968033	+	0.968033i	−0.0314720	+	0.999505i	$0.510019\pi$
$108$	−109.969	+	109.969i	−0.0979790	+	0.0979790i
$109$	−564.212	+	564.212i	−0.495795	+	0.495795i	−0.910126	−	0.414331i	$-0.864016\pi$
$109$	−564.212	+	564.212i	−0.495795	+	0.495795i	0.414331	+	0.910126i	$0.364016\pi$
$110$		−	24.4937i		−	0.0212308i
$111$			94.7738i			0.0810408i
$112$	41.7569	−	41.7569i	0.0352291	−	0.0352291i
$113$	−1134.32	+	1134.32i	−0.944317	+	0.944317i	−0.998529	−	0.0542129i	$-0.982735\pi$
$113$	−1134.32	+	1134.32i	−0.944317	+	0.944317i	0.0542129	+	0.998529i	$0.482735\pi$
$114$	390.829	+	390.829i	0.321092	+	0.321092i
$115$	34.0927			0.0276449
$116$	−101.585	−	101.585i	−0.0813098	−	0.0813098i
$117$			180.327i			0.142489i
$118$	880.947			0.687269
$119$	−266.339	+	51.6506i	−0.205170	+	0.0397883i
$120$	−50.2204			−0.0382040
$121$			925.654i			0.695458i
$122$	−768.813	−	768.813i	−0.570533	−	0.570533i
$123$	−325.179			−0.238377
$124$	−311.499	−	311.499i	−0.225592	−	0.225592i
$125$	143.315	−	143.315i	0.102548	−	0.102548i
$126$	−36.8666	+	36.8666i	−0.0260661	+	0.0260661i
$127$		−	2315.35i		−	1.61775i	−0.587980	−	0.808876i	$-0.700077\pi$
$127$		−	2315.35i		−	1.61775i	0.587980	−	0.808876i	$-0.299923\pi$
$128$			1263.18i			0.872267i
$129$	−494.697	+	494.697i	−0.337641	+	0.337641i
$130$	−17.2363	+	17.2363i	−0.0116287	+	0.0116287i
$131$	−1255.78	−	1255.78i	−0.837541	−	0.837541i	0.150994	−	0.988535i	$-0.451753\pi$
$131$	−1255.78	−	1255.78i	−0.837541	−	0.837541i	−0.988535	+	0.150994i	$0.951753\pi$
$132$	−347.900			−0.229400
$133$	−336.911	−	336.911i	−0.219653	−	0.219653i
$134$			399.242i			0.257382i
$135$	−21.9472			−0.0139919
$136$	807.719	−	1196.37i	0.509274	−	0.754321i
$137$	1489.27			0.928736			0.464368	−	0.885642i	$-0.346281\pi$
$137$	1489.27			0.928736			0.464368	+	0.885642i	$0.346281\pi$
$138$			188.320i			0.116166i
$139$	−1739.62	−	1739.62i	−1.06153	−	1.06153i	−0.997979	−	0.0635492i	$-0.979758\pi$
$139$	−1739.62	−	1739.62i	−1.06153	−	1.06153i	−0.0635492	−	0.997979i	$-0.520242\pi$
$140$	18.1222			0.0109401
$141$	108.550	+	108.550i	0.0648340	+	0.0648340i
$142$	930.532	−	930.532i	0.549919	−	0.549919i
$143$	−285.244	+	285.244i	−0.166806	+	0.166806i
$144$			137.312i			0.0794630i
$145$		−	20.2740i		−	0.0116115i
$146$	−353.977	+	353.977i	−0.200653	+	0.200653i
$147$	−695.832	+	695.832i	−0.390417	+	0.390417i
$148$	128.668	+	128.668i	0.0714627	+	0.0714627i
$149$	−1981.35			−1.08938			−0.544692	−	0.838636i	$-0.683353\pi$
$149$	−1981.35			−1.08938			−0.544692	+	0.838636i	$0.683353\pi$
$150$	394.768	+	394.768i	0.214885	+	0.214885i
$151$		−	1293.87i		−	0.697306i	−0.937252	−	0.348653i	$-0.886639\pi$
$151$		−	1293.87i		−	0.697306i	0.937252	−	0.348653i	$-0.113361\pi$
$152$	2535.11			1.35280
$153$	352.986	−	522.832i	0.186518	−	0.276265i
$154$	−116.632			−0.0610291
$155$		−	62.1678i		−	0.0322157i
$156$	244.818	+	244.818i	0.125649	+	0.125649i
$157$	3212.58			1.63307			0.816535	−	0.577296i	$-0.195892\pi$
$157$	3212.58			1.63307			0.816535	+	0.577296i	$0.195892\pi$
$158$	−872.421	−	872.421i	−0.439279	−	0.439279i
$159$	3.30681	−	3.30681i	0.00164935	−	0.00164935i
$160$	−107.821	+	107.821i	−0.0532752	+	0.0532752i
$161$		−	162.340i		−	0.0794669i
$162$		−	121.231i		−	0.0587949i
$163$	442.905	−	442.905i	0.212828	−	0.212828i	−0.592640	−	0.805468i	$-0.701914\pi$
$163$	442.905	−	442.905i	0.212828	−	0.212828i	0.805468	+	0.592640i	$0.201914\pi$
$164$	−441.475	+	441.475i	−0.210204	+	0.210204i
$165$	−34.7163	−	34.7163i	−0.0163798	−	0.0163798i
$166$	−336.293			−0.157238
$167$	−2645.12	−	2645.12i	−1.22566	−	1.22566i	−0.965589	−	0.260072i	$-0.916254\pi$
$167$	−2645.12	−	2645.12i	−1.22566	−	1.22566i	−0.260072	−	0.965589i	$-0.583746\pi$
$168$			239.135i			0.109820i
$169$	−1795.55			−0.817271
$170$	83.7141	−	16.2346i	0.0377681	−	0.00732431i
$171$	1107.89			0.495451
$172$			1343.24i			0.595470i
$173$	−70.5192	−	70.5192i	−0.0309912	−	0.0309912i	0.691441	−	0.722433i	$-0.256976\pi$
$173$	−70.5192	−	70.5192i	−0.0309912	−	0.0309912i	−0.722433	+	0.691441i	$0.756976\pi$
$174$	111.989			0.0487922
$175$	−340.307	−	340.307i	−0.146999	−	0.146999i
$176$	−217.202	+	217.202i	−0.0930240	+	0.0930240i
$177$	1248.61	−	1248.61i	0.530235	−	0.530235i
$178$			839.832i			0.353641i
$179$			2170.40i			0.906275i	0.891441	+	0.453138i	$0.149695\pi$
$179$			2170.40i			0.906275i	−0.891441	+	0.453138i	$0.850305\pi$
$180$	−29.7963	+	29.7963i	−0.0123382	+	0.0123382i
$181$	−1974.50	+	1974.50i	−0.810848	+	0.810848i	−0.984761	−	0.173913i	$-0.944359\pi$
$181$	−1974.50	+	1974.50i	−0.810848	+	0.810848i	0.173913	+	0.984761i	$0.444359\pi$
$182$	82.0745	+	82.0745i	0.0334273	+	0.0334273i
$183$	−2179.36			−0.880345
$184$	610.769	+	610.769i	0.244709	+	0.244709i
$185$			25.6792i			0.0102053i
$186$	343.400			0.135373
$187$	1385.38	−	268.665i	0.541760	−	0.105063i
$188$	294.744			0.114343
$189$			104.506i			0.0402206i
$190$	105.896	+	105.896i	0.0404342	+	0.0404342i
$191$	3351.18			1.26955			0.634773	−	0.772699i	$-0.281094\pi$
$191$	3351.18			1.26955			0.634773	+	0.772699i	$0.281094\pi$
$192$	−336.661	−	336.661i	−0.126544	−	0.126544i
$193$	−1979.89	+	1979.89i	−0.738423	+	0.738423i	−0.972273	−	0.233850i	$-0.924868\pi$
$193$	−1979.89	+	1979.89i	−0.738423	+	0.738423i	0.233850	+	0.972273i	$0.424868\pi$
$194$	−1881.54	+	1881.54i	−0.696323	+	0.696323i
$195$			48.8601i			0.0179433i
$196$			1889.37i			0.688548i
$197$	1794.75	−	1794.75i	0.649088	−	0.649088i	−0.303685	−	0.952773i	$-0.598217\pi$
$197$	1794.75	−	1794.75i	0.649088	−	0.649088i	0.952773	+	0.303685i	$0.0982169\pi$
$198$	191.764	−	191.764i	0.0688288	−	0.0688288i
$199$	1926.29	+	1926.29i	0.686186	+	0.686186i	0.961387	−	0.275201i	$-0.0887444\pi$
$199$	1926.29	+	1926.29i	0.686186	+	0.686186i	−0.275201	+	0.961387i	$0.588744\pi$
$200$	2560.67			0.905332
$201$	565.867	+	565.867i	0.198573	+	0.198573i
$202$			2908.65i			1.01313i
$203$	−96.5390			−0.0333779
$204$	−230.589	−	1189.04i	−0.0791396	−	0.408087i
$205$	−88.1082			−0.0300183
$206$		−	295.046i		−	0.0997904i
$207$	266.916	+	266.916i	0.0896230	+	0.0896230i
$208$	305.692			0.101904
$209$	1752.47	+	1752.47i	0.580004	+	0.580004i
$210$	−9.98909	+	9.98909i	−0.00328244	+	0.00328244i
$211$	295.026	−	295.026i	0.0962581	−	0.0962581i	−0.657338	−	0.753596i	$-0.728318\pi$
$211$	295.026	−	295.026i	0.0962581	−	0.0962581i	0.753596	+	0.657338i	$0.228318\pi$
$212$		−	8.97888i		−	0.00290883i
$213$		−	2637.79i		−	0.848537i
$214$	−1603.59	+	1603.59i	−0.512239	+	0.512239i
$215$	−134.039	+	134.039i	−0.0425182	+	0.0425182i
$216$	−393.182	−	393.182i	−0.123855	−	0.123855i
$217$	−296.025			−0.0926060
$218$	−844.442	−	844.442i	−0.262352	−	0.262352i
$219$			1003.42i			0.309612i
$220$	−94.2643			−0.0288877
$221$	−1163.96	−	785.839i	−0.354283	−	0.239191i
$222$	−141.846			−0.0428831
$223$		−	1074.81i		−	0.322757i	−0.986893	−	0.161379i	$-0.948406\pi$
$223$		−	1074.81i		−	0.322757i	0.986893	−	0.161379i	$-0.0515940\pi$
$224$	513.414	+	513.414i	0.153143	+	0.153143i
$225$	1119.05			0.331571
$226$	−1697.71	−	1697.71i	−0.499689	−	0.499689i
$227$	2386.83	−	2386.83i	0.697884	−	0.697884i	−0.266070	−	0.963954i	$-0.585725\pi$
$227$	2386.83	−	2386.83i	0.697884	−	0.697884i	0.963954	+	0.266070i	$0.0857251\pi$
$228$	1504.11	−	1504.11i	0.436894	−	0.436894i
$229$		−	2565.82i		−	0.740410i	−0.928950	−	0.370205i	$-0.879287\pi$
$229$		−	2565.82i		−	0.740410i	0.928950	−	0.370205i	$-0.120713\pi$
$230$			51.0258i			0.0146284i
$231$	−165.309	+	165.309i	−0.0470846	+	0.0470846i
$232$	363.208	−	363.208i	0.102783	−	0.102783i
$233$	−150.071	−	150.071i	−0.0421952	−	0.0421952i	0.685694	−	0.727890i	$-0.259499\pi$
$233$	−150.071	−	150.071i	−0.0421952	−	0.0421952i	−0.727890	+	0.685694i	$0.759499\pi$
$234$	−269.891			−0.0753988
$235$	29.4120	+	29.4120i	0.00816438	+	0.00816438i
$236$		−	3390.33i		−	0.935134i
$237$	−2473.06			−0.677817
$238$	−77.3042	−	398.622i	−0.0210542	−	0.108567i
$239$	−4285.84			−1.15995			−0.579975	−	0.814634i	$-0.696938\pi$
$239$	−4285.84			−1.15995			−0.579975	+	0.814634i	$0.696938\pi$
$240$			37.2051i			0.0100066i
$241$	781.219	+	781.219i	0.208808	+	0.208808i	0.803761	−	0.594953i	$-0.202829\pi$
$241$	781.219	+	781.219i	0.208808	+	0.208808i	−0.594953	+	0.803761i	$0.702829\pi$
$242$	−1385.40			−0.368005
$243$	−171.827	−	171.827i	−0.0453609	−	0.0453609i
$244$	−2958.78	+	2958.78i	−0.776298	+	0.776298i
$245$	−188.538	+	188.538i	−0.0491642	+	0.0491642i
$246$		−	486.688i		−	0.126139i
$247$		−	2466.44i		−	0.635368i
$248$	1113.73	−	1113.73i	0.285170	−	0.285170i
$249$	−476.647	+	476.647i	−0.121310	+	0.121310i
$250$	214.495	+	214.495i	0.0542635	+	0.0542635i
$251$	−480.822			−0.120913			−0.0604566	−	0.998171i	$-0.519256\pi$
$251$	−480.822			−0.120913			−0.0604566	+	0.998171i	$0.519256\pi$
$252$	141.881	+	141.881i	0.0354670	+	0.0354670i
$253$			844.424i			0.209836i
$254$	3465.33			0.856040
$255$	95.6425	−	141.663i	0.0234877	−	0.0347893i
$256$	−3160.19			−0.771532
$257$		−	4146.30i		−	1.00638i	−0.864176	−	0.503189i	$-0.832160\pi$
$257$		−	4146.30i		−	1.00638i	0.864176	−	0.503189i	$-0.167840\pi$
$258$	−740.401	−	740.401i	−0.178664	−	0.178664i
$259$	122.277			0.0293356
$260$	66.3342	+	66.3342i	0.0158226	+	0.0158226i
$261$	158.728	−	158.728i	0.0376437	−	0.0376437i
$262$	1879.49	−	1879.49i	0.443188	−	0.443188i
$263$			8011.72i			1.87842i	0.343346	+	0.939209i	$0.388440\pi$
$263$			8011.72i			1.87842i	−0.343346	+	0.939209i	$0.611560\pi$
$264$		−	1243.88i		−	0.289983i
$265$	0.895988	−	0.895988i	0.000207698	−	0.000207698i
$266$	504.246	−	504.246i	0.116231	−	0.116231i
$267$	1190.34	+	1190.34i	0.272838	+	0.272838i
$268$	1536.48			0.350208
$269$	−3943.92	−	3943.92i	−0.893922	−	0.893922i	0.100968	−	0.994890i	$-0.467806\pi$
$269$	−3943.92	−	3943.92i	−0.893922	−	0.893922i	−0.994890	+	0.100968i	$0.967806\pi$
$270$		−	32.8478i		−	0.00740389i
$271$	−3089.50			−0.692524			−0.346262	−	0.938138i	$-0.612549\pi$
$271$	−3089.50			−0.692524			−0.346262	+	0.938138i	$0.612549\pi$
$272$	−886.311	−	598.386i	−0.197575	−	0.133391i
$273$	232.657			0.0515790
$274$			2228.95i			0.491445i
$275$	1770.13	+	1770.13i	0.388157	+	0.388157i
$276$	724.750			0.158061
$277$	−414.012	−	414.012i	−0.0898036	−	0.0898036i	0.660778	−	0.750581i	$-0.270227\pi$
$277$	−414.012	−	414.012i	−0.0898036	−	0.0898036i	−0.750581	+	0.660778i	$0.770227\pi$
$278$	2603.64	−	2603.64i	0.561712	−	0.561712i
$279$	486.720	−	486.720i	0.104441	−	0.104441i
$280$			64.7943i			0.0138293i
$281$			6399.58i			1.35860i	0.733860	+	0.679301i	$0.237717\pi$
$281$			6399.58i			1.35860i	−0.733860	+	0.679301i	$0.762283\pi$
$282$	−162.465	+	162.465i	−0.0343072	+	0.0343072i
$283$	4267.26	−	4267.26i	0.896333	−	0.896333i	−0.0987768	−	0.995110i	$-0.531493\pi$
$283$	4267.26	−	4267.26i	0.896333	−	0.896333i	0.995110	+	0.0987768i	$0.0314930\pi$
$284$	−3581.16	−	3581.16i	−0.748249	−	0.748249i
$285$	300.185			0.0623909
$286$	−426.917	−	426.917i	−0.0882662	−	0.0882662i
$287$			419.546i			0.0862892i
$288$	−1688.29			−0.345429
$289$	1836.47	+	4556.86i	0.373799	+	0.927510i
$290$	30.3436			0.00614427
$291$			5333.62i			1.07444i
$292$	1362.28	+	1362.28i	0.273019	+	0.273019i
$293$	−7539.51			−1.50329			−0.751643	−	0.659570i	$-0.770738\pi$
$293$	−7539.51			−1.50329			−0.751643	+	0.659570i	$0.770738\pi$
$294$	−1041.43	−	1041.43i	−0.206591	−	0.206591i
$295$	338.315	−	338.315i	0.0667711	−	0.0667711i
$296$	−460.041	+	460.041i	−0.0903357	+	0.0903357i
$297$		−	543.597i		−	0.106204i
$298$		−	2965.43i		−	0.576453i
$299$	594.225	−	594.225i	0.114933	−	0.114933i
$300$	1519.27	−	1519.27i	0.292383	−	0.292383i
$301$	638.257	+	638.257i	0.122221	+	0.122221i
$302$	1936.50			0.368983
$303$	4122.60	+	4122.60i	0.781640	+	0.781640i
$304$		−	1878.10i		−	0.354330i
$305$	−590.504			−0.110860
$306$	782.510	+	528.306i	0.146187	+	0.0986968i
$307$	5367.77			0.997899			0.498950	−	0.866631i	$-0.333719\pi$
$307$	5367.77			0.997899			0.498950	+	0.866631i	$0.333719\pi$
$308$			448.859i			0.0830394i
$309$	−418.185	−	418.185i	−0.0769893	−	0.0769893i
$310$	93.0450			0.0170471
$311$	6862.87	+	6862.87i	1.25131	+	1.25131i	0.955133	+	0.296178i	$0.0957123\pi$
$311$	6862.87	+	6862.87i	1.25131	+	1.25131i	0.296178	+	0.955133i	$0.404288\pi$
$312$	−875.325	+	875.325i	−0.158832	+	0.158832i
$313$	2021.32	−	2021.32i	0.365022	−	0.365022i	−0.500636	−	0.865658i	$-0.666901\pi$
$313$	2021.32	−	2021.32i	0.365022	−	0.365022i	0.865658	+	0.500636i	$0.166901\pi$
$314$			4808.19i			0.864146i
$315$			28.3162i			0.00506487i
$316$	−3357.52	+	3357.52i	−0.597707	+	0.597707i
$317$	4064.38	−	4064.38i	0.720121	−	0.720121i	−0.248509	−	0.968630i	$-0.579941\pi$
$317$	4064.38	−	4064.38i	0.720121	−	0.720121i	0.968630	+	0.248509i	$0.0799405\pi$
$318$	4.94921	+	4.94921i	0.000872762	+	0.000872762i
$319$	502.155			0.0881357
$320$	−91.2191	−	91.2191i	−0.0159353	−	0.0159353i
$321$			4545.71i			0.790395i
$322$	242.970			0.0420503
$323$	−4828.01	+	7151.10i	−0.831695	+	1.23188i
$324$	−466.557			−0.0799995
$325$		−	2491.30i		−	0.425208i
$326$	662.885	+	662.885i	0.112619	+	0.112619i
$327$	−2393.75			−0.404815
$328$	−1578.45	−	1578.45i	−0.265718	−	0.265718i
$329$	140.052	−	140.052i	0.0234690	−	0.0234690i
$330$	51.9590	−	51.9590i	0.00866743	−	0.00866743i
$331$		−	5525.96i		−	0.917626i	−0.888533	−	0.458813i	$-0.848275\pi$
$331$		−	5525.96i		−	0.917626i	0.888533	−	0.458813i	$-0.151725\pi$
$332$			1294.23i			0.213946i
$333$	−201.046	+	201.046i	−0.0330848	+	0.0330848i
$334$	3958.88	−	3958.88i	0.648564	−	0.648564i
$335$	153.323	+	153.323i	0.0250058	+	0.0250058i
$336$	177.160			0.0287644
$337$	3165.98	+	3165.98i	0.511757	+	0.511757i	0.915065	−	0.403307i	$-0.132139\pi$
$337$	3165.98	+	3165.98i	0.511757	+	0.511757i	−0.403307	+	0.915065i	$0.632139\pi$
$338$		−	2687.35i		−	0.432463i
$339$	−4812.51			−0.771031
$340$	−62.4788	−	322.174i	−0.00996585	−	0.0513893i
$341$	1539.80			0.244530
$342$			1658.15i			0.262170i
$343$	1836.53	+	1836.53i	0.289105	+	0.289105i
$344$	−4802.62			−0.752732
$345$	72.3216	+	72.3216i	0.0112860	+	0.0112860i
$346$	105.544	−	105.544i	0.0163991	−	0.0163991i
$347$	−6954.35	+	6954.35i	−1.07588	+	1.07588i	−0.0790022	+	0.996874i	$0.525173\pi$
$347$	−6954.35	+	6954.35i	−1.07588	+	1.07588i	−0.996874	+	0.0790022i	$0.974827\pi$
$348$		−	430.989i		−	0.0663892i
$349$		−	9155.23i		−	1.40421i	−0.712075	−	0.702104i	$-0.752244\pi$
$349$		−	9155.23i		−	1.40421i	0.712075	−	0.702104i	$-0.247756\pi$
$350$	509.329	−	509.329i	0.0777851	−	0.0777851i
$351$	−382.531	+	382.531i	−0.0581710	+	0.0581710i
$352$	−2670.57	−	2670.57i	−0.404380	−	0.404380i
$353$	7025.07			1.05923			0.529613	−	0.848239i	$-0.322337\pi$
$353$	7025.07			1.05923			0.529613	+	0.848239i	$0.322337\pi$
$354$	1868.77	+	1868.77i	0.280576	+	0.280576i
$355$		−	714.716i		−	0.106854i
$356$	3232.10			0.481182
$357$	−674.557	−	455.422i	−0.100004	−	0.0675168i
$358$	−3248.38			−0.479560
$359$		−	8370.77i		−	1.23062i	−0.788285	−	0.615310i	$-0.789031\pi$
$359$		−	8370.77i		−	1.23062i	0.788285	−	0.615310i	$-0.210969\pi$
$360$	−106.534	−	106.534i	−0.0155967	−	0.0155967i
$361$	−8294.23			−1.20925
$362$	−2955.19	−	2955.19i	−0.429064	−	0.429064i
$363$	−1963.61	+	1963.61i	−0.283919	+	0.283919i
$364$	315.864	−	315.864i	0.0454829	−	0.0454829i
$365$			271.880i			0.0389886i
$366$		−	3261.80i		−	0.465838i
$367$	4661.47	−	4661.47i	0.663015	−	0.663015i	−0.293074	−	0.956090i	$-0.594678\pi$
$367$	4661.47	−	4661.47i	0.663015	−	0.663015i	0.956090	+	0.293074i	$0.0946783\pi$
$368$	452.479	−	452.479i	0.0640954	−	0.0640954i
$369$	−689.809	−	689.809i	−0.0973172	−	0.0973172i
$370$	−38.4334			−0.00540016
$371$	−4.26643	−	4.26643i	−0.000597041	−	0.000597041i
$372$		−	1321.58i		−	0.184195i
$373$	−10437.4			−1.44886			−0.724432	−	0.689347i	$-0.757898\pi$
$373$	−10437.4			−1.44886			−0.724432	+	0.689347i	$0.757898\pi$
$374$	402.104	+	2073.47i	0.0555944	+	0.286675i
$375$	608.032			0.0837297
$376$			1053.83i			0.144540i
$377$	−353.369	−	353.369i	−0.0482743	−	0.0482743i
$378$	−156.412			−0.0212829
$379$	−1234.49	−	1234.49i	−0.167313	−	0.167313i	0.618484	−	0.785797i	$-0.287747\pi$
$379$	−1234.49	−	1234.49i	−0.167313	−	0.167313i	−0.785797	+	0.618484i	$0.787747\pi$
$380$	407.542	−	407.542i	0.0550169	−	0.0550169i
$381$	4911.61	−	4911.61i	0.660444	−	0.660444i
$382$			5015.63i			0.671786i
$383$			1031.82i			0.137660i	0.997628	+	0.0688298i	$0.0219266\pi$
$383$			1031.82i			0.137660i	−0.997628	+	0.0688298i	$0.978073\pi$
$384$	−2679.61	+	2679.61i	−0.356102	+	0.356102i
$385$	−44.7909	+	44.7909i	−0.00592924	+	0.00592924i
$386$	−2963.25	−	2963.25i	−0.390740	−	0.390740i
$387$	−2098.82			−0.275682
$388$	7241.12	+	7241.12i	0.947453	+	0.947453i
$389$		−	7514.99i		−	0.979499i	−0.871863	−	0.489750i	$-0.837088\pi$
$389$		−	7514.99i		−	0.979499i	0.871863	−	0.489750i	$-0.162912\pi$
$390$	−73.1276			−0.00949477
$391$	−2886.05	+	559.688i	−0.373284	+	0.0723903i
$392$	−6755.28			−0.870390
$393$		−	5327.81i		−	0.683849i
$394$	2686.15	+	2686.15i	0.343468	+	0.343468i
$395$	−670.083			−0.0853557
$396$	−738.006	−	738.006i	−0.0936521	−	0.0936521i
$397$	−2133.89	+	2133.89i	−0.269766	+	0.269766i	−0.829006	−	0.559240i	$-0.811093\pi$
$397$	−2133.89	+	2133.89i	−0.269766	+	0.269766i	0.559240	+	0.829006i	$0.311093\pi$
$398$	−2883.03	+	2883.03i	−0.363098	+	0.363098i
$399$		−	1429.39i		−	0.179346i
$400$		−	1897.03i		−	0.237129i
$401$	10503.3	−	10503.3i	1.30800	−	1.30800i	0.385146	−	0.922856i	$-0.374151\pi$
$401$	10503.3	−	10503.3i	1.30800	−	1.30800i	0.922856	−	0.385146i	$-0.125849\pi$
$402$	−846.919	+	846.919i	−0.105076	+	0.105076i
$403$	−1083.56	−	1083.56i	−0.133936	−	0.133936i
$404$	11194.0			1.37852
$405$	−46.5570	−	46.5570i	−0.00571218	−	0.00571218i
$406$		−	144.487i		−	0.0176621i
$407$	−636.033			−0.0774619
$408$	4251.31	−	824.450i	0.515861	−	0.100040i
$409$	5721.53			0.691714			0.345857	−	0.938287i	$-0.387588\pi$
$409$	5721.53			0.691714			0.345857	+	0.938287i	$0.387588\pi$
$410$		−	131.869i		−	0.0158843i
$411$	3159.22	+	3159.22i	0.379155	+	0.379155i
$412$	−1135.49			−0.135780
$413$	−1610.96	−	1610.96i	−0.191937	−	0.191937i
$414$	−399.487	+	399.487i	−0.0474244	+	0.0474244i
$415$	−129.149	+	129.149i	−0.0152763	+	0.0152763i
$416$			3758.58i			0.442980i
$417$		−	7380.57i		−	0.866734i
$418$	−2622.88	+	2622.88i	−0.306912	+	0.306912i
$419$	4335.25	−	4335.25i	0.505467	−	0.505467i	−0.407665	−	0.913132i	$-0.633657\pi$
$419$	4335.25	−	4335.25i	0.505467	−	0.505467i	0.913132	+	0.407665i	$0.133657\pi$
$420$	38.4431	+	38.4431i	0.00446626	+	0.00446626i
$421$	−6388.31			−0.739542			−0.369771	−	0.929123i	$-0.620564\pi$
$421$	−6388.31			−0.739542			−0.369771	+	0.929123i	$0.620564\pi$
$422$	441.559	+	441.559i	0.0509354	+	0.0509354i
$423$			460.541i			0.0529368i
$424$	32.1031			0.00367704
$425$	−4876.67	+	7223.18i	−0.556596	+	0.824413i
$426$	3947.91			0.449007
$427$			2811.81i			0.318672i
$428$	6171.42	+	6171.42i	0.696979	+	0.696979i
$429$	−1210.19			−0.136197
$430$	−200.613	−	200.613i	−0.0224987	−	0.0224987i
$431$	−604.177	+	604.177i	−0.0675224	+	0.0675224i	−0.740062	−	0.672539i	$-0.765204\pi$
$431$	−604.177	+	604.177i	−0.0675224	+	0.0675224i	0.672539	+	0.740062i	$0.265204\pi$
$432$	−291.283	+	291.283i	−0.0324406	+	0.0324406i
$433$			10107.4i			1.12178i	0.827889	+	0.560892i	$0.189542\pi$
$433$			10107.4i			1.12178i	−0.827889	+	0.560892i	$0.810458\pi$
$434$		−	443.054i		−	0.0490029i
$435$	43.0077	−	43.0077i	0.00474037	−	0.00474037i
$436$	−3249.84	+	3249.84i	−0.356970	+	0.356970i
$437$	−3650.77	−	3650.77i	−0.399634	−	0.399634i
$438$	−1501.80			−0.163832
$439$	11609.5	+	11609.5i	1.26217	+	1.26217i	0.950041	+	0.312125i	$0.101041\pi$
$439$	11609.5	+	11609.5i	1.26217	+	1.26217i	0.312125	+	0.950041i	$0.398959\pi$
$440$		−	337.033i		−	0.0365168i
$441$	−2952.17			−0.318774
$442$	1176.15	−	1742.07i	0.126569	−	0.187470i
$443$	5106.09			0.547625			0.273812	−	0.961783i	$-0.411715\pi$
$443$	5106.09			0.547625			0.273812	+	0.961783i	$0.411715\pi$
$444$			545.894i			0.0583490i
$445$	322.526	+	322.526i	0.0343577	+	0.0343577i
$446$	1608.65			0.170788
$447$	−4203.07	−	4203.07i	−0.444739	−	0.444739i
$448$	−434.359	+	434.359i	−0.0458070	+	0.0458070i
$449$	−7972.68	+	7972.68i	−0.837982	+	0.837982i	−0.988593	−	0.150611i	$-0.951876\pi$
$449$	−7972.68	+	7972.68i	−0.837982	+	0.837982i	0.150611	+	0.988593i	$0.451876\pi$
$450$			1674.86i			0.175452i
$451$		−	2182.30i		−	0.227850i
$452$	−6533.64	+	6533.64i	−0.679904	+	0.679904i
$453$	2744.70	−	2744.70i	0.284674	−	0.284674i
$454$	3572.31	+	3572.31i	0.369289	+	0.369289i
$455$	63.0391			0.00649521
$456$	5377.79	+	5377.79i	0.552276	+	0.552276i
$457$			13048.0i			1.33557i	0.744352	+	0.667787i	$0.232758\pi$
$457$			13048.0i			1.33557i	−0.744352	+	0.667787i	$0.767242\pi$
$458$	3840.19			0.391791
$459$	1857.89	−	360.298i	0.188930	−	0.0366389i
$460$	196.373			0.0199042
$461$		−	14147.2i		−	1.42929i	−0.699487	−	0.714645i	$-0.746588\pi$
$461$		−	14147.2i		−	1.42929i	0.699487	−	0.714645i	$-0.253412\pi$
$462$	−247.414	−	247.414i	−0.0249150	−	0.0249150i
$463$	−7778.27			−0.780749			−0.390375	−	0.920656i	$-0.627655\pi$
$463$	−7778.27			−0.780749			−0.390375	+	0.920656i	$0.627655\pi$
$464$	−269.077	−	269.077i	−0.0269215	−	0.0269215i
$465$	131.878	−	131.878i	0.0131520	−	0.0131520i
$466$	224.608	−	224.608i	0.0223278	−	0.0223278i
$467$			3546.16i			0.351384i	0.984445	+	0.175692i	$0.0562163\pi$
$467$			3546.16i			0.351384i	−0.984445	+	0.175692i	$0.943784\pi$
$468$			1038.68i			0.102592i
$469$	730.081	−	730.081i	0.0718806	−	0.0718806i
$470$	−44.0203	+	44.0203i	−0.00432022	+	0.00432022i
$471$	6814.91	+	6814.91i	0.666698	+	0.666698i
$472$	12121.8			1.18210
$473$	−3319.95	−	3319.95i	−0.322730	−	0.322730i
$474$		−	3701.37i		−	0.358670i
$475$	−15306.0			−1.47850
$476$	−1534.10	+	297.506i	−0.147721	+	0.0286474i
$477$	14.0296			0.00134669
$478$		−	6414.51i		−	0.613793i
$479$	−1653.30	−	1653.30i	−0.157706	−	0.157706i	0.623843	−	0.781550i	$-0.285570\pi$
$479$	−1653.30	−	1653.30i	−0.157706	−	0.157706i	−0.781550	+	0.623843i	$0.785570\pi$
$480$	−457.447			−0.0434990
$481$	447.579	+	447.579i	0.0424280	+	0.0424280i
$482$	−1169.23	+	1169.23i	−0.110492	+	0.110492i
$483$	344.375	−	344.375i	0.0324422	−	0.0324422i
$484$			5331.73i			0.500726i
$485$			1445.16i			0.135302i
$486$	257.169	−	257.169i	0.0240029	−	0.0240029i
$487$	−2352.91	+	2352.91i	−0.218934	+	0.218934i	−0.808049	−	0.589115i	$-0.799476\pi$
$487$	−2352.91	+	2352.91i	−0.218934	+	0.218934i	0.589115	+	0.808049i	$0.299476\pi$
$488$	−10578.8	−	10578.8i	−0.981315	−	0.981315i
$489$	1879.09			0.173773
$490$	−282.179	−	282.179i	−0.0260154	−	0.0260154i
$491$			5511.23i			0.506554i	0.967394	+	0.253277i	$0.0815085\pi$
$491$			5511.23i			0.506554i	−0.967394	+	0.253277i	$0.918492\pi$
$492$	−1873.02			−0.171631
$493$	332.831	+	1716.26i	0.0304056	+	0.156788i
$494$	3691.46			0.336208
$495$		−	147.289i		−	0.0133740i
$496$	−825.092	−	825.092i	−0.0746930	−	0.0746930i
$497$	−3403.27			−0.307158
$498$	−713.386	−	713.386i	−0.0641919	−	0.0641919i
$499$	10717.0	−	10717.0i	0.961438	−	0.961438i	−0.0378459	−	0.999284i	$-0.512050\pi$
$499$	10717.0	−	10717.0i	0.961438	−	0.961438i	0.999284	+	0.0378459i	$0.0120496\pi$
$500$	825.486	−	825.486i	0.0738338	−	0.0738338i
$501$		−	11222.3i		−	1.00075i
$502$		−	719.634i		−	0.0639817i
$503$	7580.21	−	7580.21i	0.671938	−	0.671938i	−0.286225	−	0.958163i	$-0.592400\pi$
$503$	7580.21	−	7580.21i	0.671938	−	0.671938i	0.958163	+	0.286225i	$0.0924003\pi$
$504$	−507.282	+	507.282i	−0.0448336	+	0.0448336i
$505$	1117.03	+	1117.03i	0.0984299	+	0.0984299i
$506$	−1263.83			−0.111036
$507$	−3808.93	−	3808.93i	−0.333650	−	0.333650i
$508$		−	13336.4i		−	1.16477i
$509$	12724.1			1.10803			0.554013	−	0.832508i	$-0.313096\pi$
$509$	12724.1			1.10803			0.554013	+	0.832508i	$0.313096\pi$
$510$	212.023	+	143.146i	0.0184089	+	0.0124286i
$511$	1294.61			0.112075
$512$			5375.64i			0.464008i
$513$	2350.18	+	2350.18i	0.202267	+	0.202267i
$514$	6205.67			0.532530
$515$	−113.308	−	113.308i	−0.00969506	−	0.00969506i
$516$	−2849.44	+	2849.44i	−0.243100	+	0.243100i
$517$	−728.490	+	728.490i	−0.0619709	+	0.0619709i
$518$			183.009i			0.0155231i
$519$		−	299.188i		−	0.0253042i
$520$	−237.172	+	237.172i	−0.0200013	+	0.0200013i
$521$	9567.51	−	9567.51i	0.804530	−	0.804530i	−0.179270	−	0.983800i	$-0.557374\pi$
$521$	9567.51	−	9567.51i	0.804530	−	0.804530i	0.983800	+	0.179270i	$0.0573735\pi$
$522$	237.564	+	237.564i	0.0199193	+	0.0199193i
$523$	−7104.82			−0.594019			−0.297010	−	0.954875i	$-0.595989\pi$
$523$	−7104.82			−0.594019			−0.297010	+	0.954875i	$0.595989\pi$
$524$	−7233.24	−	7233.24i	−0.603026	−	0.603026i
$525$		−	1443.80i		−	0.120024i
$526$	−11990.9			−0.993973
$527$	1020.59	+	5262.69i	0.0843594	+	0.435003i
$528$	−921.511			−0.0759538
$529$			10407.9i			0.855419i
$530$	1.34100	+	1.34100i	0.000109905	+	0.000109905i
$531$	5297.42			0.432935
$532$	−1940.59	−	1940.59i	−0.158149	−	0.158149i
$533$	−1535.69	+	1535.69i	−0.124800	+	0.124800i
$534$	−1781.55	+	1781.55i	−0.144373	+	0.144373i
$535$			1231.67i			0.0995324i
$536$			5493.55i			0.442696i
$537$	−4604.11	+	4604.11i	−0.369985	+	0.369985i
$538$	5902.76	−	5902.76i	0.473023	−	0.473023i
$539$	−4669.78	−	4669.78i	−0.373175	−	0.373175i
$540$	−126.415			−0.0100741
$541$	−11677.6	−	11677.6i	−0.928023	−	0.928023i	0.0695555	−	0.997578i	$-0.477842\pi$
$541$	−11677.6	−	11677.6i	−0.928023	−	0.928023i	−0.997578	+	0.0695555i	$0.977842\pi$
$542$		−	4623.98i		−	0.366452i
$543$	−8377.10			−0.662055
$544$	7357.34	−	10897.5i	0.579859	−	0.858869i
$545$	−648.592			−0.0509773
$546$			348.213i			0.0272933i
$547$	548.342	+	548.342i	0.0428618	+	0.0428618i	0.728213	−	0.685351i	$-0.240351\pi$
$547$	548.342	+	548.342i	0.0428618	+	0.0428618i	−0.685351	+	0.728213i	$0.740351\pi$
$548$	8578.14			0.668686
$549$	−4623.13	−	4623.13i	−0.359399	−	0.359399i
$550$	−2649.32	+	2649.32i	−0.205395	+	0.205395i
$551$	−2171.01	+	2171.01i	−0.167855	+	0.167855i
$552$			2591.27i			0.199804i
$553$			3190.74i			0.245360i
$554$	619.642	−	619.642i	0.0475200	−	0.0475200i
$555$	−54.4738	+	54.4738i	−0.00416628	+	0.00416628i
$556$	−10020.1	−	10020.1i	−0.764295	−	0.764295i
$557$	−14283.2			−1.08653			−0.543267	−	0.839560i	$-0.682813\pi$
$557$	−14283.2			−1.08653			−0.543267	+	0.839560i	$0.682813\pi$
$558$	728.461	+	728.461i	0.0552656	+	0.0552656i
$559$			4672.52i			0.353536i
$560$	48.0019			0.00362223
$561$	3508.76	+	2368.91i	0.264064	+	0.178281i
$562$	−9578.10			−0.718910
$563$			7158.60i			0.535877i	0.963436	+	0.267939i	$0.0863424\pi$
$563$			7158.60i			0.535877i	−0.963436	+	0.267939i	$0.913658\pi$
$564$	625.247	+	625.247i	0.0466802	+	0.0466802i
$565$	−1303.96			−0.0970939
$566$	6386.70	+	6386.70i	0.474299	+	0.474299i
$567$	−221.691	+	221.691i	−0.0164200	+	0.0164200i
$568$	12804.1	−	12804.1i	0.945858	−	0.945858i
$569$			4328.74i			0.318929i	0.987204	+	0.159464i	$0.0509767\pi$
$569$			4328.74i			0.318929i	−0.987204	+	0.159464i	$0.949023\pi$
$570$			449.279i			0.0330144i
$571$	9148.34	−	9148.34i	0.670483	−	0.670483i	−0.287344	−	0.957827i	$-0.592772\pi$
$571$	9148.34	−	9148.34i	0.670483	−	0.670483i	0.957827	+	0.287344i	$0.0927723\pi$
$572$	−1642.99	+	1642.99i	−0.120100	+	0.120100i
$573$	7108.94	+	7108.94i	0.518290	+	0.518290i
$574$	−627.923			−0.0456603
$575$	−3687.57	−	3687.57i	−0.267448	−	0.267448i
$576$		−	1428.33i		−	0.103322i
$577$	14654.1			1.05729			0.528645	−	0.848843i	$-0.322700\pi$
$577$	14654.1			1.05729			0.528645	+	0.848843i	$0.322700\pi$
$578$	−6820.13	+	2748.61i	−0.490796	+	0.197797i
$579$	−8399.97			−0.602920
$580$		−	116.778i		−	0.00836022i
$581$	614.969	+	614.969i	0.0439126	+	0.0439126i
$582$	−7982.69			−0.568545
$583$	22.1922	+	22.1922i	0.00157651	+	0.00157651i
$584$	−4870.71	+	4870.71i	−0.345122	+	0.345122i
$585$	−103.648	+	103.648i	−0.00732532	+	0.00732532i
$586$		−	11284.2i		−	0.795471i
$587$			12094.6i			0.850419i	0.905095	+	0.425209i	$0.139799\pi$
$587$			12094.6i			0.850419i	−0.905095	+	0.425209i	$0.860201\pi$
$588$	−4007.97	+	4007.97i	−0.281098	+	0.281098i
$589$	−6657.16	+	6657.16i	−0.465710	+	0.465710i
$590$	506.348	+	506.348i	0.0353322	+	0.0353322i
$591$	7614.46			0.529978
$592$	340.815	+	340.815i	0.0236611	+	0.0236611i
$593$			8913.39i			0.617249i	0.951184	+	0.308625i	$0.0998687\pi$
$593$			8913.39i			0.617249i	−0.951184	+	0.308625i	$0.900131\pi$
$594$	813.587			0.0561985
$595$	−182.773	−	123.398i	−0.0125932	−	0.00850221i
$596$	−11412.5			−0.784352
$597$			8172.55i			0.560268i
$598$	889.361	+	889.361i	0.0608172	+	0.0608172i
$599$	17664.7			1.20494			0.602470	−	0.798142i	$-0.294183\pi$
$599$	17664.7			1.20494			0.602470	+	0.798142i	$0.294183\pi$
$600$	5431.99	+	5431.99i	0.369600	+	0.369600i
$601$	−2346.22	+	2346.22i	−0.159242	+	0.159242i	−0.782231	−	0.622989i	$-0.785918\pi$
$601$	−2346.22	+	2346.22i	−0.159242	+	0.159242i	0.622989	+	0.782231i	$0.285918\pi$
$602$	−955.263	+	955.263i	−0.0646738	+	0.0646738i
$603$			2400.77i			0.162134i
$604$		−	7452.62i		−	0.502057i
$605$	−532.045	+	532.045i	−0.0357532	+	0.0357532i
$606$	−6170.19	+	6170.19i	−0.413608	+	0.413608i
$607$	10813.0	+	10813.0i	0.723042	+	0.723042i	0.969224	−	0.246182i	$-0.0791761\pi$
$607$	10813.0	+	10813.0i	0.723042	+	0.723042i	−0.246182	+	0.969224i	$0.579176\pi$
$608$	23091.8			1.54029
$609$	−204.790	−	204.790i	−0.0136265	−	0.0136265i
$610$		−	883.792i		−	0.0586618i
$611$	1025.28			0.0678863
$612$	2033.19	−	3011.50i	0.134292	−	0.198909i
$613$	13570.8			0.894160			0.447080	−	0.894494i	$-0.352464\pi$
$613$	13570.8			0.894160			0.447080	+	0.894494i	$0.352464\pi$
$614$			8033.81i			0.528043i
$615$	−186.906	−	186.906i	−0.0122549	−	0.0122549i
$616$	−1604.85			−0.104970
$617$	12451.6	+	12451.6i	0.812450	+	0.812450i	0.985001	−	0.172551i	$-0.0552009\pi$
$617$	12451.6	+	12451.6i	0.812450	+	0.812450i	−0.172551	+	0.985001i	$0.555201\pi$
$618$	625.887	−	625.887i	0.0407393	−	0.0407393i
$619$	14955.7	−	14955.7i	0.971116	−	0.971116i	−0.0284784	−	0.999594i	$-0.509066\pi$
$619$	14955.7	−	14955.7i	0.971116	−	0.971116i	0.999594	+	0.0284784i	$0.00906618\pi$
$620$		−	358.084i		−	0.0231952i
$621$			1132.43i			0.0731769i
$622$	−10271.5	+	10271.5i	−0.662137	+	0.662137i
$623$	1535.77	−	1535.77i	0.0987633	−	0.0987633i
$624$	648.471	+	648.471i	0.0416020	+	0.0416020i
$625$	−15377.7			−0.984170
$626$	3025.26	+	3025.26i	0.193153	+	0.193153i
$627$			7435.10i			0.473571i
$628$	18504.4			1.17580
$629$	−421.566	−	2173.82i	−0.0267232	−	0.137800i
$630$	−42.3801			−0.00268010
$631$		−	5652.30i		−	0.356600i	−0.983976	−	0.178300i	$-0.942940\pi$
$631$		−	5652.30i		−	0.356600i	0.983976	−	0.178300i	$-0.0570598\pi$
$632$	−12004.5	−	12004.5i	−0.755558	−	0.755558i
$633$	1251.69			0.0785944
$634$	6083.05	+	6083.05i	0.381055	+	0.381055i
$635$	1330.81	−	1330.81i	0.0831680	−	0.0831680i
$636$	19.0471	−	19.0471i	0.00118753	−	0.00118753i
$637$			6572.29i			0.408797i
$638$			751.563i			0.0466374i
$639$	5595.59	−	5595.59i	0.346414	−	0.346414i
$640$	−726.046	+	726.046i	−0.0448429	+	0.0448429i
$641$	15125.0	+	15125.0i	0.931982	+	0.931982i	0.997830	−	0.0658478i	$-0.0209752\pi$
$641$	15125.0	+	15125.0i	0.931982	+	0.931982i	−0.0658478	+	0.997830i	$0.520975\pi$
$642$	−6803.45			−0.418241
$643$	−4112.50	−	4112.50i	−0.252226	−	0.252226i	0.569657	−	0.821883i	$-0.307076\pi$
$643$	−4112.50	−	4112.50i	−0.252226	−	0.252226i	−0.821883	+	0.569657i	$0.807076\pi$
$644$		−	935.071i		−	0.0572158i
$645$	−568.681			−0.0347160
$646$	−10702.9	−	7225.96i	−0.651855	−	0.440095i
$647$	−24007.9			−1.45881			−0.729404	−	0.684084i	$-0.760202\pi$
$647$	−24007.9			−1.45881			−0.729404	+	0.684084i	$0.760202\pi$
$648$		−	1668.13i		−	0.101127i
$649$	8379.54	+	8379.54i	0.506819	+	0.506819i
$650$	3728.67			0.225001
$651$	−627.964	−	627.964i	−0.0378062	−	0.0378062i
$652$	2551.12	−	2551.12i	0.153235	−	0.153235i
$653$	756.860	−	756.860i	0.0453572	−	0.0453572i	−0.684064	−	0.729422i	$-0.739789\pi$
$653$	756.860	−	756.860i	0.0453572	−	0.0453572i	0.729422	+	0.684064i	$0.239789\pi$
$654$		−	3582.66i		−	0.214210i
$655$		−	1443.59i		−	0.0861153i
$656$	−1169.37	+	1169.37i	−0.0695981	+	0.0695981i
$657$	−2128.58	+	2128.58i	−0.126398	+	0.126398i
$658$	209.612	+	209.612i	0.0124187	+	0.0124187i
$659$	−12742.8			−0.753245			−0.376623	−	0.926367i	$-0.622915\pi$
$659$	−12742.8			−0.753245			−0.376623	+	0.926367i	$0.622915\pi$
$660$	−199.965	−	199.965i	−0.0117934	−	0.0117934i
$661$		−	1443.34i		−	0.0849312i	−0.999098	−	0.0424656i	$-0.986479\pi$
$661$		−	1443.34i		−	0.0849312i	0.999098	−	0.0424656i	$-0.0135213\pi$
$662$	8270.57			0.485566
$663$	−802.117	−	4136.15i	−0.0469859	−	0.242285i
$664$	−4627.38			−0.270448
$665$		−	387.297i		−	0.0225846i
$666$	−300.900	−	300.900i	−0.0175070	−	0.0175070i
$667$	−1046.10			−0.0607273
$668$	−15235.8	−	15235.8i	−0.882471	−	0.882471i
$669$	2280.02	−	2280.02i	0.131765	−	0.131765i
$670$	−229.475	+	229.475i	−0.0132319	+	0.0132319i
$671$		−	14625.9i		−	0.841467i
$672$			2178.23i			0.125040i
$673$	−3389.13	+	3389.13i	−0.194118	+	0.194118i	−0.797473	−	0.603355i	$-0.793830\pi$
$673$	−3389.13	+	3389.13i	−0.194118	+	0.194118i	0.603355	+	0.797473i	$0.293830\pi$
$674$	−4738.45	+	4738.45i	−0.270799	+	0.270799i
$675$	2373.87	+	2373.87i	0.135363	+	0.135363i
$676$	−10342.3			−0.588432
$677$	−15674.7	−	15674.7i	−0.889846	−	0.889846i	0.104662	−	0.994508i	$-0.466624\pi$
$677$	−15674.7	−	15674.7i	−0.889846	−	0.889846i	−0.994508	+	0.104662i	$0.966624\pi$
$678$		−	7202.76i		−	0.407995i
$679$	6881.42			0.388932
$680$	1151.90	−	223.387i	0.0649610	−	0.0125978i
$681$	10126.5			0.569820
$682$			2304.58i			0.129394i
$683$	−21436.1	−	21436.1i	−1.20092	−	1.20092i	−0.973887	−	0.227034i	$-0.927097\pi$
$683$	−21436.1	−	21436.1i	−1.20092	−	1.20092i	−0.227034	−	0.973887i	$-0.572903\pi$
$684$	6381.38			0.356723
$685$	855.998	+	855.998i	0.0477460	+	0.0477460i
$686$	−2748.68	+	2748.68i	−0.152981	+	0.152981i
$687$	5442.92	−	5442.92i	0.302271	−	0.302271i
$688$			3557.94i			0.197159i
$689$		−	31.2335i		−	0.00172700i
$690$	−108.242	+	108.242i	−0.00597203	+	0.00597203i
$691$	−18537.6	+	18537.6i	−1.02056	+	1.02056i	−0.0207713	+	0.999784i	$0.506612\pi$
$691$	−18537.6	+	18537.6i	−1.02056	+	1.02056i	−0.999784	+	0.0207713i	$0.993388\pi$
$692$	−406.188	−	406.188i	−0.0223135	−	0.0223135i
$693$	−701.347			−0.0384444
$694$	−10408.4	−	10408.4i	−0.569305	−	0.569305i
$695$		−	1999.78i		−	0.109146i
$696$	1540.96			0.0839223
$697$	7458.62	−	1446.44i	0.405330	−	0.0786051i
$698$	13702.4			0.743043
$699$		−	636.698i		−	0.0344522i
$700$	−1960.16	−	1960.16i	−0.105838	−	0.105838i
$701$	10843.2			0.584228			0.292114	−	0.956384i	$-0.405641\pi$
$701$	10843.2			0.584228			0.292114	+	0.956384i	$0.405641\pi$
$702$	−572.525	−	572.525i	−0.0307814	−	0.0307814i
$703$	2749.82	−	2749.82i	0.147527	−	0.147527i
$704$	2259.35	−	2259.35i	0.120955	−	0.120955i
$705$			124.785i			0.00666619i
$706$			10514.3i			0.560494i
$707$	5318.96	−	5318.96i	0.282942	−	0.282942i
$708$	7191.98	−	7191.98i	0.381767	−	0.381767i
$709$	3788.77	+	3788.77i	0.200691	+	0.200691i	0.800296	−	0.599605i	$-0.204676\pi$
$709$	3788.77	+	3788.77i	0.200691	+	0.200691i	−0.599605	+	0.800296i	$0.704676\pi$
$710$	1069.70			0.0565423
$711$	−5246.16	−	5246.16i	−0.276718	−	0.276718i
$712$			11556.1i			0.608261i
$713$	−3207.74			−0.168486
$714$	681.619	−	1009.59i	0.0357268	−	0.0529175i
$715$	−327.903			−0.0171509
$716$			12501.4i			0.652514i
$717$	−9091.65	−	9091.65i	−0.473548	−	0.473548i
$718$	12528.3			0.651188
$719$	−5780.09	−	5780.09i	−0.299806	−	0.299806i	0.541132	−	0.840938i	$-0.317996\pi$
$719$	−5780.09	−	5780.09i	−0.299806	−	0.299806i	−0.840938	+	0.541132i	$0.817996\pi$
$720$	−78.9238	+	78.9238i	−0.00408516	+	0.00408516i
$721$	−539.541	+	539.541i	−0.0278690	+	0.0278690i
$722$		−	12413.8i		−	0.639879i
$723$			3314.43i			0.170491i
$724$	−11373.1	+	11373.1i	−0.583807	+	0.583807i
$725$	−2192.90	+	2192.90i	−0.112334	+	0.112334i
$726$	−2938.88	−	2938.88i	−0.150237	−	0.150237i
$727$	−22324.8			−1.13890			−0.569451	−	0.822026i	$-0.692844\pi$
$727$	−22324.8			−1.13890			−0.569451	+	0.822026i	$0.692844\pi$
$728$	1129.34	+	1129.34i	0.0574948	+	0.0574948i
$729$		−	729.000i		−	0.0370370i
$730$	−406.915			−0.0206310
$731$	9146.36	−	13547.3i	0.462778	−	0.685452i
$732$	−12553.0			−0.633844
$733$			7293.42i			0.367515i	0.982972	+	0.183758i	$0.0588261\pi$
$733$			7293.42i			0.367515i	−0.982972	+	0.183758i	$0.941174\pi$
$734$	6976.70	+	6976.70i	0.350838	+	0.350838i
$735$	−799.897			−0.0401424
$736$	5563.37	+	5563.37i	0.278626	+	0.278626i
$737$	−3797.57	+	3797.57i	−0.189804	+	0.189804i
$738$	1032.42	−	1032.42i	0.0514958	−	0.0514958i
$739$		−	12956.5i		−	0.644945i	−0.946579	−	0.322472i	$-0.895486\pi$
$739$		−	12956.5i		−	0.644945i	0.946579	−	0.322472i	$-0.104514\pi$
$740$			147.911i			0.00734774i
$741$	5232.11	−	5232.11i	0.259388	−	0.259388i
$742$	6.38547	−	6.38547i	0.000315927	−	0.000315927i
$743$	10116.8	+	10116.8i	0.499528	+	0.499528i	0.911291	−	0.411763i	$-0.135087\pi$
$743$	10116.8	+	10116.8i	0.499528	+	0.499528i	−0.411763	+	0.911291i	$0.635087\pi$
$744$	4725.17			0.232840
$745$	−1138.83	−	1138.83i	−0.0560048	−	0.0560048i
$746$		−	15621.3i		−	0.766673i
$747$	−2022.24			−0.0990495
$748$	7979.75	−	1547.50i	0.390065	−	0.0756447i
$749$	5864.87			0.286112
$750$			910.026i			0.0443059i
$751$	−16468.4	−	16468.4i	−0.800189	−	0.800189i	0.182936	−	0.983125i	$-0.441440\pi$
$751$	−16468.4	−	16468.4i	−0.800189	−	0.800189i	−0.983125	+	0.182936i	$0.941440\pi$
$752$	780.713			0.0378586
$753$	−1019.98	−	1019.98i	−0.0493626	−	0.0493626i
$754$	528.878	−	528.878i	0.0255446	−	0.0255446i
$755$	743.684	−	743.684i	0.0358483	−	0.0358483i
$756$			601.951i			0.0289587i
$757$		−	615.306i		−	0.0295425i	−0.999891	−	0.0147712i	$-0.995298\pi$
$757$		−	615.306i		−	0.0295425i	0.999891	−	0.0147712i	$-0.00470201\pi$
$758$	1847.63	−	1847.63i	0.0885343	−	0.0885343i
$759$	−1791.29	+	1791.29i	−0.0856651	+	0.0856651i
$760$	1457.13	+	1457.13i	0.0695467	+	0.0695467i
$761$	−2678.42			−0.127586			−0.0637928	−	0.997963i	$-0.520320\pi$
$761$	−2678.42			−0.127586			−0.0637928	+	0.997963i	$0.520320\pi$
$762$	7351.08	+	7351.08i	0.349477	+	0.349477i
$763$			3088.41i			0.146537i
$764$	19302.7			0.914067
$765$	503.401	−	97.6237i	0.0237915	−	0.00461385i
$766$	−1544.30			−0.0728432
$767$		−	11793.4i		−	0.555197i
$768$	−6703.78	−	6703.78i	−0.314976	−	0.314976i
$769$	8111.73			0.380385			0.190193	−	0.981747i	$-0.439089\pi$
$769$	8111.73			0.380385			0.190193	+	0.981747i	$0.439089\pi$
$770$	−67.0374	−	67.0374i	−0.00313748	−	0.00313748i
$771$	8795.64	−	8795.64i	0.410852	−	0.410852i
$772$	−11404.1	+	11404.1i	−0.531661	+	0.531661i
$773$		−	14345.3i		−	0.667481i	−0.942665	−	0.333740i	$-0.891689\pi$
$773$		−	14345.3i		−	0.667481i	0.942665	−	0.333740i	$-0.108311\pi$
$774$		−	3141.25i		−	0.145879i
$775$	−6724.26	+	6724.26i	−0.311668	+	0.311668i
$776$	−25889.9	+	25889.9i	−1.19767	+	1.19767i
$777$	259.389	+	259.389i	0.0119762	+	0.0119762i
$778$	11247.5			0.518307
$779$	9434.94	+	9434.94i	0.433943	+	0.433943i
$780$			281.432i			0.0129191i
$781$	17702.4			0.811064
$782$	−837.670	−	4319.48i	−0.0383057	−	0.197525i
$783$	673.425			0.0307359
$784$			5004.54i			0.227977i
$785$	1846.52	+	1846.52i	0.0839555	+	0.0839555i
$786$	7974.01			0.361862
$787$	−3820.33	−	3820.33i	−0.173037	−	0.173037i	0.615275	−	0.788312i	$-0.289045\pi$
$787$	−3820.33	−	3820.33i	−0.173037	−	0.173037i	−0.788312	+	0.615275i	$0.789045\pi$
$788$	10337.7	−	10337.7i	0.467340	−	0.467340i
$789$	−16995.4	+	16995.4i	−0.766861	+	0.766861i
$790$		−	1002.90i		−	0.0451664i
$791$			6209.09i			0.279102i
$792$	2638.67	−	2638.67i	0.118385	−	0.118385i
$793$	−10292.3	+	10292.3i	−0.460895	+	0.460895i
$794$	−3193.74	−	3193.74i	−0.142748	−	0.142748i
$795$	3.80135			0.000169585
$796$	11095.4	+	11095.4i	0.494051	+	0.494051i
$797$			24962.7i			1.10944i	0.832038	+	0.554719i	$0.187174\pi$
$797$			24962.7i			1.10944i	−0.832038	+	0.554719i	$0.812826\pi$
$798$	2139.34			0.0949018
$799$	−2972.66	−	2006.97i	−0.131621	−	0.0888629i
$800$	23324.6			1.03081
$801$			5050.19i			0.222771i
$802$	15720.0	+	15720.0i	0.692135	+	0.692135i
$803$	−6734.03			−0.295939
$804$	3259.37	+	3259.37i	0.142972	+	0.142972i
$805$	93.3092	−	93.3092i	0.00408536	−	0.00408536i
$806$	1621.74	−	1621.74i	0.0708728	−	0.0708728i
$807$		−	16732.6i		−	0.729884i
$808$			40023.0i			1.74258i
$809$	−22875.2	+	22875.2i	−0.994126	+	0.994126i	−0.999983	−	0.00585676i	$-0.998136\pi$
$809$	−22875.2	+	22875.2i	−0.994126	+	0.994126i	0.00585676	+	0.999983i	$0.498136\pi$
$810$	69.6806	−	69.6806i	0.00302263	−	0.00302263i
$811$	−12837.7	−	12837.7i	−0.555848	−	0.555848i	0.372275	−	0.928123i	$-0.378578\pi$
$811$	−12837.7	−	12837.7i	−0.555848	−	0.555848i	−0.928123	+	0.372275i	$0.878578\pi$
$812$	−556.061			−0.0240319
$813$	−6553.83	−	6553.83i	−0.282722	−	0.282722i
$814$		−	951.935i		−	0.0409893i
$815$	509.143			0.0218828
$816$	−610.781	−	3149.52i	−0.0262030	−	0.135117i
$817$	28706.9			1.22928
$818$			8563.26i			0.366024i
$819$	493.541	+	493.541i	0.0210570	+	0.0210570i
$820$	−507.500			−0.0216130
$821$	22482.6	+	22482.6i	0.955721	+	0.955721i	0.999060	−	0.0433397i	$-0.0137998\pi$
$821$	22482.6	+	22482.6i	0.955721	+	0.955721i	−0.0433397	+	0.999060i	$0.513800\pi$
$822$	−4728.32	+	4728.32i	−0.200632	+	0.200632i
$823$	−23777.0	+	23777.0i	−1.00707	+	1.00707i	−0.00709128	+	0.999975i	$0.502257\pi$
$823$	−23777.0	+	23777.0i	−1.00707	+	1.00707i	−0.999975	+	0.00709128i	$0.997743\pi$
$824$		−	4059.82i		−	0.171639i
$825$			7510.04i			0.316929i
$826$	2411.08	−	2411.08i	0.101565	−	0.101565i
$827$	−3394.68	+	3394.68i	−0.142738	+	0.142738i	−0.774865	−	0.632127i	$-0.782182\pi$
$827$	−3394.68	+	3394.68i	−0.142738	+	0.142738i	0.632127	+	0.774865i	$0.282182\pi$
$828$	1537.43	+	1537.43i	0.0645281	+	0.0645281i
$829$	4599.00			0.192678			0.0963389	−	0.995349i	$-0.469287\pi$
$829$	4599.00			0.192678			0.0963389	+	0.995349i	$0.469287\pi$
$830$	−193.294	−	193.294i	−0.00808352	−	0.00808352i
$831$		−	1756.51i		−	0.0733243i
$832$	−3179.83			−0.132501
$833$	12865.1	−	19055.4i	0.535114	−	0.792594i
$834$	11046.3			0.458636
$835$		−	3040.71i		−	0.126022i
$836$	10094.2	+	10094.2i	0.417600	+	0.417600i
$837$	2064.98			0.0852760
$838$	6488.45	+	6488.45i	0.267470	+	0.267470i
$839$	21296.4	−	21296.4i	0.876321	−	0.876321i	−0.116831	−	0.993152i	$-0.537274\pi$
$839$	21296.4	−	21296.4i	0.876321	−	0.876321i	0.993152	+	0.116831i	$0.0372737\pi$
$840$	−137.449	+	137.449i	−0.00564578	+	0.00564578i
$841$		−	23766.9i		−	0.974493i
$842$		−	9561.23i		−	0.391332i
$843$	−13575.6	+	13575.6i	−0.554647	+	0.554647i
$844$	1699.34	−	1699.34i	0.0693054	−	0.0693054i
$845$	−1032.04	−	1032.04i	−0.0420156	−	0.0420156i
$846$	−689.280			−0.0280117
$847$	2533.44	+	2533.44i	0.102775	+	0.102775i
$848$		−	23.7831i		−	0.000963108i
$849$	18104.4			0.731853
$850$	−10810.7	−	7298.79i	−0.436242	−	0.294525i
$851$	1325.00			0.0533728
$852$		−	15193.6i		−	0.610943i
$853$	−30470.1	−	30470.1i	−1.22307	−	1.22307i	−0.966536	−	0.256531i	$-0.917421\pi$
$853$	−30470.1	−	30470.1i	−1.22307	−	1.22307i	−0.256531	−	0.966536i	$-0.582579\pi$
$854$	−4208.36			−0.168627
$855$	636.788	+	636.788i	0.0254710	+	0.0254710i
$856$	−22065.3	+	22065.3i	−0.881049	+	0.881049i
$857$	−8446.07	+	8446.07i	−0.336654	+	0.336654i	−0.855106	−	0.518453i	$-0.826508\pi$
$857$	−8446.07	+	8446.07i	−0.336654	+	0.336654i	0.518453	+	0.855106i	$0.326508\pi$
$858$		−	1811.26i		−	0.0720691i
$859$		−	11237.0i		−	0.446335i	−0.974780	−	0.223168i	$-0.928360\pi$
$859$		−	11237.0i		−	0.446335i	0.974780	−	0.223168i	$-0.0716397\pi$
$860$	−772.062	+	772.062i	−0.0306129	+	0.0306129i
$861$	−889.991	+	889.991i	−0.0352274	+	0.0352274i
$862$	−904.256	−	904.256i	−0.0357298	−	0.0357298i
$863$	−22755.7			−0.897583			−0.448791	−	0.893637i	$-0.648145\pi$
$863$	−22755.7			−0.897583			−0.448791	+	0.893637i	$0.648145\pi$
$864$	−3581.41	−	3581.41i	−0.141021	−	0.141021i
$865$		−	81.0656i		−	0.00318649i
$866$	−15127.5			−0.593597
$867$	−5770.80	+	13562.3i	−0.226051	+	0.531257i
$868$	−1705.09			−0.0666759
$869$		−	16596.9i		−	0.647884i
$870$	64.3685	+	64.3685i	0.00250839	+	0.00250839i
$871$	5344.74			0.207921
$872$	−11619.5	−	11619.5i	−0.451245	−	0.451245i
$873$	−11314.3	+	11314.3i	−0.438639	+	0.438639i
$874$	5464.02	−	5464.02i	0.211468	−	0.211468i
$875$		−	784.481i		−	0.0303089i
$876$			5779.67i			0.222919i
$877$	25825.6	−	25825.6i	0.994378	−	0.994378i	−0.00560613	−	0.999984i	$-0.501784\pi$
$877$	25825.6	−	25825.6i	0.994378	−	0.994378i	0.999984	+	0.00560613i	$0.00178450\pi$
$878$	−17375.6	+	17375.6i	−0.667881	+	0.667881i
$879$	−15993.7	−	15993.7i	−0.613714	−	0.613714i
$880$	−249.686			−0.00956466
$881$	13415.9	+	13415.9i	0.513045	+	0.513045i	0.915458	−	0.402413i	$-0.131829\pi$
$881$	13415.9	+	13415.9i	0.513045	+	0.513045i	−0.402413	+	0.915458i	$0.631829\pi$
$882$		−	4418.43i		−	0.168681i
$883$	28154.1			1.07300			0.536501	−	0.843899i	$-0.319746\pi$
$883$	28154.1			1.07300			0.536501	+	0.843899i	$0.319746\pi$
$884$	−6704.37	−	4526.40i	−0.255082	−	0.172217i
$885$	1435.35			0.0545184
$886$			7642.16i			0.289778i
$887$	−10563.8	−	10563.8i	−0.399884	−	0.399884i	0.478308	−	0.878192i	$-0.341250\pi$
$887$	−10563.8	−	10563.8i	−0.399884	−	0.399884i	−0.878192	+	0.478308i	$0.841250\pi$
$888$	−1951.79			−0.0737588
$889$	−6336.94	−	6336.94i	−0.239071	−	0.239071i
$890$	−482.716	+	482.716i	−0.0181805	+	0.0181805i
$891$	1153.14	−	1153.14i	0.0433577	−	0.0433577i
$892$		−	6190.89i		−	0.232384i
$893$		−	6299.09i		−	0.236048i
$894$	6290.63	−	6290.63i	0.235336	−	0.235336i
$895$	−1247.50	+	1247.50i	−0.0465913	+	0.0465913i
$896$	3457.22	+	3457.22i	0.128904	+	0.128904i
$897$	2521.08			0.0938422
$898$	−11932.5	−	11932.5i	−0.443422	−	0.443422i
$899$			1907.55i			0.0707680i
$900$	6445.71			0.238730
$901$	−61.1389	+	90.5571i	−0.00226064	+	0.00334838i
$902$	3266.19			0.120568
$903$			2707.89i			0.0997930i
$904$	−23360.4	−	23360.4i	−0.859463	−	0.859463i
$905$	−2269.80			−0.0833708
$906$	4107.93	+	4107.93i	0.150637	+	0.150637i
$907$	36144.8	−	36144.8i	1.32323	−	1.32323i	0.412080	−	0.911148i	$-0.364802\pi$
$907$	36144.8	−	36144.8i	1.32323	−	1.32323i	0.911148	−	0.412080i	$-0.135198\pi$
$908$	13748.1	−	13748.1i	0.502474	−	0.502474i
$909$			17490.7i			0.638206i
$910$			94.3491i			0.00343697i
$911$	−7029.06	+	7029.06i	−0.255634	+	0.255634i	−0.823276	−	0.567641i	$-0.807856\pi$
$911$	−7029.06	+	7029.06i	−0.255634	+	0.255634i	0.567641	+	0.823276i	$0.307856\pi$
$912$	3984.05	−	3984.05i	0.144655	−	0.144655i
$913$	−3198.81	−	3198.81i	−0.115953	−	0.115953i
$914$	−19528.5			−0.706725
$915$	−1252.65	−	1252.65i	−0.0452582	−	0.0452582i
$916$		−	14779.0i		−	0.533092i
$917$	−6873.93			−0.247543
$918$	539.249	+	2780.66i	0.0193877	+	0.0999733i
$919$	−20224.2			−0.725937			−0.362968	−	0.931801i	$-0.618237\pi$
$919$	−20224.2			−0.725937			−0.362968	+	0.931801i	$0.618237\pi$
$920$			702.113i			0.0251608i
$921$	11386.8	+	11386.8i	0.407391	+	0.407391i
$922$	21173.8			0.756315
$923$	−12457.2	−	12457.2i	−0.444242	−	0.444242i
$924$	−952.174	+	952.174i	−0.0339007	+	0.0339007i
$925$	2777.54	−	2777.54i	0.0987297	−	0.0987297i
$926$		−	11641.5i		−	0.413137i
$927$		−	1774.21i		−	0.0628615i
$928$	3308.38	−	3308.38i	0.117029	−	0.117029i
$929$	−840.813	+	840.813i	−0.0296945	+	0.0296945i	−0.721798	−	0.692104i	$-0.756684\pi$
$929$	−840.813	+	840.813i	−0.0296945	+	0.0296945i	0.692104	+	0.721798i	$0.256684\pi$
$930$	197.378	+	197.378i	0.00695945	+	0.00695945i
$931$	40378.6			1.42143
$932$	−864.404	−	864.404i	−0.0303804	−	0.0303804i
$933$			29116.7i			1.02169i
$934$	−5307.44			−0.185937
$935$	950.709	+	641.863i	0.0332529	+	0.0224505i
$936$	−3713.69			−0.129686
$937$		−	37390.7i		−	1.30363i	−0.758378	−	0.651815i	$-0.774008\pi$
$937$		−	37390.7i		−	1.30363i	0.758378	−	0.651815i	$-0.225992\pi$
$938$	1092.69	+	1092.69i	0.0380359	+	0.0380359i
$939$	8575.73			0.298039
$940$	169.412	+	169.412i	0.00587832	+	0.00587832i
$941$	−26248.6	+	26248.6i	−0.909331	+	0.909331i	−0.996218	−	0.0868875i	$-0.972308\pi$
$941$	−26248.6	+	26248.6i	−0.909331	+	0.909331i	0.0868875	+	0.996218i	$0.472308\pi$
$942$	−10199.7	+	10199.7i	−0.352786	+	0.352786i
$943$			4546.21i			0.156993i
$944$		−	8980.25i		−	0.309621i
$945$	−60.0677	+	60.0677i	−0.00206773	+	0.00206773i
$946$	4968.88	−	4968.88i	0.170774	−	0.170774i
$947$	36161.1	+	36161.1i	1.24084	+	1.24084i	0.959651	+	0.281192i	$0.0907299\pi$
$947$	36161.1	+	36161.1i	1.24084	+	1.24084i	0.281192	+	0.959651i	$0.409270\pi$
$948$	−14244.8			−0.488025
$949$	4738.77	+	4738.77i	0.162094	+	0.162094i
$950$		−	22908.1i		−	0.782353i
$951$	17243.7			0.587976
$952$	−1063.70	−	5485.03i	−0.0362131	−	0.186734i
$953$	−1138.42			−0.0386958			−0.0193479	−	0.999813i	$-0.506159\pi$
$953$	−1138.42			−0.0386958			−0.0193479	+	0.999813i	$0.506159\pi$
$954$			20.9977i			0.000712607i
$955$	1926.18	+	1926.18i	0.0652669	+	0.0652669i
$956$	−24686.3			−0.835159
$957$	1065.23	+	1065.23i	0.0359813	+	0.0359813i
$958$	2474.46	−	2474.46i	0.0834510	−	0.0834510i
$959$	4076.02	−	4076.02i	0.137249	−	0.137249i
$960$		−	387.010i		−	0.0130111i
$961$		−	23941.7i		−	0.803656i
$962$	−669.881	+	669.881i	−0.0224510	+	0.0224510i
$963$	−9642.91	+	9642.91i	−0.322678	+	0.322678i
$964$	4499.80	+	4499.80i	0.150341	+	0.150341i
$965$	−2275.99			−0.0759241
$966$	515.417	+	515.417i	0.0171669	+	0.0171669i
$967$			4270.42i			0.142014i	0.997476	+	0.0710070i	$0.0226213\pi$
$967$			4270.42i			0.142014i	−0.997476	+	0.0710070i	$0.977379\pi$
$968$	−19063.1			−0.632966
$969$	−25411.5	+	4928.02i	−0.842451	+	0.163375i
$970$	−2162.93			−0.0715954
$971$			8703.18i			0.287640i	0.989604	+	0.143820i	$0.0459386\pi$
$971$			8703.18i			0.287640i	−0.989604	+	0.143820i	$0.954061\pi$
$972$	−989.717	−	989.717i	−0.0326597	−	0.0326597i
$973$	−9522.39			−0.313745
$974$	−3521.55	−	3521.55i	−0.115850	−	0.115850i
$975$	5284.85	−	5284.85i	0.173590	−	0.173590i
$976$	−7837.17	+	7837.17i	−0.257031	+	0.257031i
$977$			10690.5i			0.350072i	0.984562	+	0.175036i	$0.0560041\pi$
$977$			10690.5i			0.350072i	−0.984562	+	0.175036i	$0.943996\pi$
$978$			2812.38i			0.0919530i
$979$	−7988.46	+	7988.46i	−0.260789	+	0.260789i
$980$	−1085.97	+	1085.97i	−0.0353980	+	0.0353980i
$981$	−5077.91	−	5077.91i	−0.165265	−	0.165265i
$982$	−8248.51			−0.268045
$983$	31067.0	+	31067.0i	1.00802	+	1.00802i	0.999968	+	0.00805257i	$0.00256324\pi$
$983$	31067.0	+	31067.0i	1.00802	+	1.00802i	0.00805257	+	0.999968i	$0.497437\pi$
$984$		−	6696.81i		−	0.216958i
$985$	2063.16			0.0667387
$986$	−2568.68	+	498.139i	−0.0829648	+	0.0160892i
$987$	594.189			0.0191623
$988$		−	14206.6i		−	0.457462i
$989$	6916.17	+	6916.17i	0.222367	+	0.222367i
$990$	220.444			0.00707693
$991$	11977.7	+	11977.7i	0.383939	+	0.383939i	0.872519	−	0.488580i	$-0.162485\pi$
$991$	11977.7	+	11977.7i	0.383939	+	0.383939i	−0.488580	+	0.872519i	$0.662485\pi$
$992$	10144.8	−	10144.8i	0.324694	−	0.324694i
$993$	11722.3	−	11722.3i	0.374619	−	0.374619i
$994$		−	5093.59i		−	0.162534i
$995$			2214.37i			0.0705531i
$996$	−2745.47	+	2745.47i	−0.0873429	+	0.0873429i
$997$	7884.24	−	7884.24i	0.250448	−	0.250448i	−0.570706	−	0.821154i	$-0.693331\pi$
$997$	7884.24	−	7884.24i	0.250448	−	0.250448i	0.821154	+	0.570706i	$0.193331\pi$
$998$	16039.8	+	16039.8i	0.508749	+	0.508749i
$999$	−852.964			−0.0270136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.4.e.a.13.5	yes	16
3.2	odd	2		153.4.f.b.64.4		16
17.2	even	8		867.4.a.q.1.4		8
17.4	even	4	inner	51.4.e.a.4.4	✓	16
17.15	even	8		867.4.a.p.1.4		8
51.38	odd	4		153.4.f.b.55.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.e.a.4.4	✓	16	17.4	even	4	inner
51.4.e.a.13.5	yes	16	1.1	even	1	trivial
153.4.f.b.55.5		16	51.38	odd	4
153.4.f.b.64.4		16	3.2	odd	2
867.4.a.p.1.4		8	17.15	even	8
867.4.a.q.1.4		8	17.2	even	8

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	51.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.49668i q^{2} +(2.12132 + 2.12132i) q^{3} +5.75996 q^{4} +(0.574777 + 0.574777i) q^{5} +(-3.17493 + 3.17493i) q^{6} +(2.73692 - 2.73692i) q^{7} +20.5942i q^{8} +9.00000i q^{9} +(-0.860255 + 0.860255i) q^{10} +(-14.2363 + 14.2363i) q^{11} +(12.2187 + 12.2187i) q^{12} +20.0363 q^{13} +(4.09628 + 4.09628i) q^{14} +2.43857i q^{15} +15.2569 q^{16} +(-58.0925 - 39.2207i) q^{17} -13.4701 q^{18} -123.098i q^{19} +(3.31070 + 3.31070i) q^{20} +11.6118 q^{21} +(-21.3072 - 21.3072i) q^{22} +(29.6574 - 29.6574i) q^{23} +(-43.6869 + 43.6869i) q^{24} -124.339i q^{25} +29.9879i q^{26} +(-19.0919 + 19.0919i) q^{27} +(15.7646 - 15.7646i) q^{28} +(-17.6364 - 17.6364i) q^{29} -3.64975 q^{30} +(-54.0799 - 54.0799i) q^{31} +187.588i q^{32} -60.3996 q^{33} +(58.7006 - 86.9456i) q^{34} +3.14624 q^{35} +51.8397i q^{36} +(22.3384 + 22.3384i) q^{37} +184.238 q^{38} +(42.5035 + 42.5035i) q^{39} +(-11.8371 + 11.8371i) q^{40} +(-76.6455 + 76.6455i) q^{41} +17.3791i q^{42} +233.202i q^{43} +(-82.0007 + 82.0007i) q^{44} +(-5.17299 + 5.17299i) q^{45} +(44.3874 + 44.3874i) q^{46} +51.1712 q^{47} +(32.3648 + 32.3648i) q^{48} +328.019i q^{49} +186.095 q^{50} +(-40.0331 - 206.432i) q^{51} +115.409 q^{52} -1.55884i q^{53} +(-28.5743 - 28.5743i) q^{54} -16.3654 q^{55} +(56.3647 + 56.3647i) q^{56} +(261.131 - 261.131i) q^{57} +(26.3960 - 26.3960i) q^{58} -588.603i q^{59} +14.0461i q^{60} +(-513.681 + 513.681i) q^{61} +(80.9401 - 80.9401i) q^{62} +(24.6323 + 24.6323i) q^{63} -158.703 q^{64} +(11.5164 + 11.5164i) q^{65} -90.3986i q^{66} +266.752 q^{67} +(-334.611 - 225.910i) q^{68} +125.826 q^{69} +4.70890i q^{70} +(-621.733 - 621.733i) q^{71} -185.348 q^{72} +(236.509 + 236.509i) q^{73} +(-33.4333 + 33.4333i) q^{74} +(263.763 - 263.763i) q^{75} -709.043i q^{76} +77.9274i q^{77} +(-63.6139 + 63.6139i) q^{78} +(-582.906 + 582.906i) q^{79} +(8.76932 + 8.76932i) q^{80} -81.0000 q^{81} +(-114.713 - 114.713i) q^{82} +224.694i q^{83} +66.8834 q^{84} +(-10.8471 - 55.9334i) q^{85} -349.028 q^{86} -74.8250i q^{87} +(-293.186 - 293.186i) q^{88} +561.132 q^{89} +(-7.74229 - 7.74229i) q^{90} +(54.8379 - 54.8379i) q^{91} +(170.825 - 170.825i) q^{92} -229.442i q^{93} +76.5866i q^{94} +(70.7542 - 70.7542i) q^{95} +(-397.935 + 397.935i) q^{96} +(1257.15 + 1257.15i) q^{97} -490.937 q^{98} +(-128.127 - 128.127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 48 q^{4} - 32 q^{5} + 12 q^{6} - 8 q^{7} - 20 q^{10} + 96 q^{11} + 120 q^{13} - 288 q^{14} - 200 q^{16} + 16 q^{17} - 72 q^{18} + 384 q^{20} + 168 q^{21} + 4 q^{22} + 208 q^{23} + 312 q^{24} + 904 q^{28}+ \cdots + 864 q^{99}+O(q^{100}) \) 16 * q - 48 * q^4 - 32 * q^5 + 12 * q^6 - 8 * q^7 - 20 * q^10 + 96 * q^11 + 120 * q^13 - 288 * q^14 - 200 * q^16 + 16 * q^17 - 72 * q^18 + 384 * q^20 + 168 * q^21 + 4 * q^22 + 208 * q^23 + 312 * q^24 + 904 * q^28 + 320 * q^29 - 432 * q^30 - 624 * q^31 - 72 * q^33 - 788 * q^34 - 1184 * q^35 + 256 * q^37 - 168 * q^38 - 24 * q^39 - 664 * q^40 + 800 * q^41 + 128 * q^44 + 288 * q^45 + 572 * q^46 + 368 * q^47 + 96 * q^48 - 720 * q^50 - 120 * q^51 - 3160 * q^52 + 108 * q^54 + 4296 * q^55 + 576 * q^56 - 1080 * q^57 + 1368 * q^58 - 1296 * q^61 + 536 * q^62 - 72 * q^63 + 1752 * q^64 - 4288 * q^65 - 1248 * q^67 - 240 * q^68 + 576 * q^69 + 1488 * q^71 + 864 * q^72 - 1208 * q^73 + 2272 * q^74 + 1200 * q^75 + 564 * q^78 - 1256 * q^79 + 384 * q^80 - 1296 * q^81 + 3564 * q^82 - 2088 * q^84 + 3216 * q^85 + 3224 * q^86 - 1296 * q^88 - 2608 * q^89 - 180 * q^90 - 56 * q^91 - 5072 * q^92 + 160 * q^95 - 408 * q^96 - 4456 * q^97 - 1208 * q^98 + 864 * q^99

Introduction

L-functions

Modular forms

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