LMFDB - Embedded newform 975.2.bc.l.751.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (of order $6$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 150x^{8} + 520x^{6} + 825x^{4} + 512x^{2} + 100 $ x^12 + 20x^10 + 150x^8 + 520x^6 + 825x^4 + 512*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.3
Root			$0.834094i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.l.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.722346 + 0.417047i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.652144 + 1.12955i) q^{4} +(-0.722346 - 0.417047i) q^{6} +(2.05120 + 1.18426i) q^{7} -2.75609i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.722346 + 0.417047i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.652144 + 1.12955i) q^{4} +(-0.722346 - 0.417047i) q^{6} +(2.05120 + 1.18426i) q^{7} -2.75609i q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.18031 - 2.41350i) q^{11} -1.30429 q^{12} +(-1.05393 + 3.44808i) q^{13} -1.97557 q^{14} +(-0.154871 - 0.268245i) q^{16} +(1.61191 - 2.79192i) q^{17} -0.834094i q^{18} +(5.78949 + 3.34257i) q^{19} +2.36852i q^{21} +(-2.01309 + 3.48677i) q^{22} +(3.81798 + 6.61294i) q^{23} +(2.38684 - 1.37804i) q^{24} +(-0.676709 - 2.93024i) q^{26} -1.00000 q^{27} +(-2.67535 + 1.54462i) q^{28} +(-0.192985 - 0.334259i) q^{29} -9.05365i q^{31} +(4.99742 + 2.88526i) q^{32} +(4.18031 + 2.41350i) q^{33} +2.68897i q^{34} +(-0.652144 - 1.12955i) q^{36} +(-9.12360 + 5.26752i) q^{37} -5.57603 q^{38} +(-3.51309 + 0.811311i) q^{39} +(6.41426 - 3.70327i) q^{41} +(-0.987784 - 1.71089i) q^{42} +(1.19160 - 2.06392i) q^{43} +6.29580i q^{44} +(-5.51581 - 3.18456i) q^{46} +9.84986i q^{47} +(0.154871 - 0.268245i) q^{48} +(-0.695053 - 1.20387i) q^{49} +3.22383 q^{51} +(-3.20745 - 3.43910i) q^{52} -12.8269 q^{53} +(0.722346 - 0.417047i) q^{54} +(3.26392 - 5.65328i) q^{56} +6.68513i q^{57} +(0.278804 + 0.160967i) q^{58} +(-2.07875 - 1.20017i) q^{59} +(-6.13735 + 10.6302i) q^{61} +(3.77580 + 6.53987i) q^{62} +(-2.05120 + 1.18426i) q^{63} -4.19367 q^{64} -4.02617 q^{66} +(4.35671 - 2.51535i) q^{67} +(2.10240 + 3.64146i) q^{68} +(-3.81798 + 6.61294i) q^{69} +(3.99077 + 2.30407i) q^{71} +(2.38684 + 1.37804i) q^{72} -0.0638636i q^{73} +(4.39360 - 7.60994i) q^{74} +(-7.55117 + 4.35967i) q^{76} +11.4329 q^{77} +(2.19931 - 2.05117i) q^{78} -5.13133 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.08888 + 5.35009i) q^{82} -0.431363i q^{83} +(-2.67535 - 1.54462i) q^{84} +1.98782i q^{86} +(0.192985 - 0.334259i) q^{87} +(-6.65182 - 11.5213i) q^{88} +(-0.578954 + 0.334259i) q^{89} +(-6.24524 + 5.82457i) q^{91} -9.95950 q^{92} +(7.84069 - 4.52683i) q^{93} +(-4.10785 - 7.11501i) q^{94} +5.77053i q^{96} +(-4.60647 - 2.65955i) q^{97} +(1.00414 + 0.579740i) q^{98} +4.82700i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9} + 9 q^{11} + 16 q^{12} - 3 q^{13} + 10 q^{14} - 4 q^{16} - 9 q^{19} + 15 q^{22} + q^{23} - 5 q^{26} - 12 q^{27} - 39 q^{28} - 16 q^{29} + 30 q^{32} + 9 q^{33} + 8 q^{36} - 15 q^{37} + 30 q^{38} - 3 q^{39} + 18 q^{41} + 5 q^{42} + q^{43} - 45 q^{46} + 4 q^{48} + 31 q^{49} - 40 q^{52} - 16 q^{53} + 25 q^{56} - 30 q^{58} + 54 q^{59} - 11 q^{61} - 20 q^{62} + 3 q^{63} + 16 q^{64} + 30 q^{66} + 45 q^{67} - 30 q^{68} - q^{69} - 33 q^{71} + 5 q^{74} - 27 q^{76} - 28 q^{77} + 20 q^{78} + 18 q^{79} - 6 q^{81} - 20 q^{82} - 39 q^{84} + 16 q^{87} - 5 q^{88} - 48 q^{89} - 29 q^{91} + 46 q^{92} - 12 q^{93} - 30 q^{94} - 9 q^{97} + 105 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9 + 9 * q^11 + 16 * q^12 - 3 * q^13 + 10 * q^14 - 4 * q^16 - 9 * q^19 + 15 * q^22 + q^23 - 5 * q^26 - 12 * q^27 - 39 * q^28 - 16 * q^29 + 30 * q^32 + 9 * q^33 + 8 * q^36 - 15 * q^37 + 30 * q^38 - 3 * q^39 + 18 * q^41 + 5 * q^42 + q^43 - 45 * q^46 + 4 * q^48 + 31 * q^49 - 40 * q^52 - 16 * q^53 + 25 * q^56 - 30 * q^58 + 54 * q^59 - 11 * q^61 - 20 * q^62 + 3 * q^63 + 16 * q^64 + 30 * q^66 + 45 * q^67 - 30 * q^68 - q^69 - 33 * q^71 + 5 * q^74 - 27 * q^76 - 28 * q^77 + 20 * q^78 + 18 * q^79 - 6 * q^81 - 20 * q^82 - 39 * q^84 + 16 * q^87 - 5 * q^88 - 48 * q^89 - 29 * q^91 + 46 * q^92 - 12 * q^93 - 30 * q^94 - 9 * q^97 + 105 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−0.722346	+	0.417047i	−0.510776	+	0.294897i	−0.733153	−	0.680064i	$-0.761952\pi$
$2$	−0.722346	+	0.417047i	−0.510776	+	0.294897i	0.222377	+	0.974961i	$0.428619\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.652144	+	1.12955i	−0.326072	+	0.564773i
$5$		0			0
$5$		0			0
$6$	−0.722346	−	0.417047i	−0.294897	−	0.170259i
$7$	2.05120	+	1.18426i	0.775281	+	0.447608i	0.834755	−	0.550621i	$-0.185609\pi$
$7$	2.05120	+	1.18426i	0.775281	+	0.447608i	−0.0594745	+	0.998230i	$0.518943\pi$
$8$		−	2.75609i		−	0.974423i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	4.18031	−	2.41350i	1.26041	−	0.727698i	0.287256	−	0.957854i	$-0.407257\pi$
$11$	4.18031	−	2.41350i	1.26041	−	0.727698i	0.973154	+	0.230156i	$0.0739235\pi$
$12$	−1.30429			−0.376515
$13$	−1.05393	+	3.44808i	−0.292307	+	0.956325i
$13$	−1.05393	+	3.44808i	−0.292307	+	0.956325i
$14$	−1.97557			−0.527993
$15$		0			0
$16$	−0.154871	−	0.268245i	−0.0387178	−	0.0670612i
$17$	1.61191	−	2.79192i	0.390946	−	0.677139i	−0.601628	−	0.798776i	$-0.705481\pi$
$17$	1.61191	−	2.79192i	0.390946	−	0.677139i	0.992575	+	0.121637i	$0.0388144\pi$
$18$		−	0.834094i		−	0.196598i
$19$	5.78949	+	3.34257i	1.32820	+	0.766837i	0.985021	−	0.172433i	$-0.0551627\pi$
$19$	5.78949	+	3.34257i	1.32820	+	0.766837i	0.343180	+	0.939270i	$0.388496\pi$
$20$		0			0
$21$			2.36852i			0.516854i
$22$	−2.01309	+	3.48677i	−0.429191	+	0.743381i
$23$	3.81798	+	6.61294i	0.796105	+	1.37889i	0.922135	+	0.386868i	$0.126443\pi$
$23$	3.81798	+	6.61294i	0.796105	+	1.37889i	−0.126030	+	0.992026i	$0.540224\pi$
$24$	2.38684	−	1.37804i	0.487212	−	0.281292i
$25$		0			0
$26$	−0.676709	−	2.93024i	−0.132714	−	0.574668i
$27$	−1.00000			−0.192450
$28$	−2.67535	+	1.54462i	−0.505595	+	0.291905i
$29$	−0.192985	−	0.334259i	−0.0358364	−	0.0620704i	0.847551	−	0.530714i	$-0.178076\pi$
$29$	−0.192985	−	0.334259i	−0.0358364	−	0.0620704i	−0.883387	+	0.468644i	$0.844743\pi$
$30$		0			0
$31$		−	9.05365i		−	1.62608i	−0.582205	−	0.813042i	$-0.697810\pi$
$31$		−	9.05365i		−	1.62608i	0.582205	−	0.813042i	$-0.302190\pi$
$32$	4.99742	+	2.88526i	0.883428	+	0.510047i
$33$	4.18031	+	2.41350i	0.727698	+	0.420137i
$34$			2.68897i			0.461155i
$35$		0			0
$36$	−0.652144	−	1.12955i	−0.108691	−	0.188258i
$37$	−9.12360	+	5.26752i	−1.49991	+	0.865974i	−1.00000		0.000102359i	$-0.999967\pi$
$37$	−9.12360	+	5.26752i	−1.49991	+	0.865974i	−0.499911	+	0.866077i	$0.666634\pi$
$38$	−5.57603			−0.904551
$39$	−3.51309	+	0.811311i	−0.562544	+	0.129914i
$40$		0			0
$41$	6.41426	−	3.70327i	1.00174	−	0.578354i	0.0929766	−	0.995668i	$-0.470362\pi$
$41$	6.41426	−	3.70327i	1.00174	−	0.578354i	0.908762	+	0.417314i	$0.137028\pi$
$42$	−0.987784	−	1.71089i	−0.152418	−	0.263996i
$43$	1.19160	−	2.06392i	0.181718	−	0.314745i	−0.760748	−	0.649048i	$-0.775168\pi$
$43$	1.19160	−	2.06392i	0.181718	−	0.314745i	0.942466	+	0.334303i	$0.108501\pi$
$44$			6.29580i			0.949128i
$45$		0			0
$46$	−5.51581	−	3.18456i	−0.813262	−	0.469537i
$47$			9.84986i			1.43675i	0.695656	+	0.718375i	$0.255114\pi$
$47$			9.84986i			1.43675i	−0.695656	+	0.718375i	$0.744886\pi$
$48$	0.154871	−	0.268245i	0.0223537	−	0.0387178i
$49$	−0.695053	−	1.20387i	−0.0992933	−	0.171981i
$50$		0			0
$51$	3.22383			0.451426
$52$	−3.20745	−	3.43910i	−0.444793	−	0.476918i
$53$	−12.8269			−1.76192			−0.880958	−	0.473194i	$-0.843101\pi$
$53$	−12.8269			−1.76192			−0.880958	+	0.473194i	$0.843101\pi$
$54$	0.722346	−	0.417047i	0.0982989	−	0.0567529i
$55$		0			0
$56$	3.26392	−	5.65328i	0.436160	−	0.755451i
$57$			6.68513i			0.885467i
$58$	0.278804	+	0.160967i	0.0366087	+	0.0211361i
$59$	−2.07875	−	1.20017i	−0.270631	−	0.156249i	0.358544	−	0.933513i	$-0.383273\pi$
$59$	−2.07875	−	1.20017i	−0.270631	−	0.156249i	−0.629174	+	0.777264i	$0.716607\pi$
$60$		0			0
$61$	−6.13735	+	10.6302i	−0.785807	+	1.36106i	0.142709	+	0.989765i	$0.454419\pi$
$61$	−6.13735	+	10.6302i	−0.785807	+	1.36106i	−0.928516	+	0.371293i	$0.878915\pi$
$62$	3.77580	+	6.53987i	0.479527	+	0.830565i
$63$	−2.05120	+	1.18426i	−0.258427	+	0.149203i
$64$	−4.19367			−0.524209
$65$		0			0
$66$	−4.02617			−0.495588
$67$	4.35671	−	2.51535i	0.532257	−	0.307299i	−0.209678	−	0.977770i	$-0.567242\pi$
$67$	4.35671	−	2.51535i	0.532257	−	0.307299i	0.741935	+	0.670472i	$0.233908\pi$
$68$	2.10240	+	3.64146i	0.254953	+	0.441592i
$69$	−3.81798	+	6.61294i	−0.459631	+	0.796105i
$70$		0			0
$71$	3.99077	+	2.30407i	0.473617	+	0.273443i	0.717753	−	0.696298i	$-0.245171\pi$
$71$	3.99077	+	2.30407i	0.473617	+	0.273443i	−0.244135	+	0.969741i	$0.578504\pi$
$72$	2.38684	+	1.37804i	0.281292	+	0.162404i
$73$		−	0.0638636i		−	0.00747467i	−0.999993	−	0.00373733i	$-0.998810\pi$
$73$		−	0.0638636i		−	0.00747467i	0.999993	−	0.00373733i	$-0.00118963\pi$
$74$	4.39360	−	7.60994i	0.510746	−	0.884638i
$75$		0			0
$76$	−7.55117	+	4.35967i	−0.866178	+	0.500088i
$77$	11.4329			1.30290
$78$	2.19931	−	2.05117i	0.249023	−	0.232249i
$79$	−5.13133			−0.577320			−0.288660	−	0.957432i	$-0.593210\pi$
$79$	−5.13133			−0.577320			−0.288660	+	0.957432i	$0.593210\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.08888	+	5.35009i	−0.341109	+	0.590819i
$83$		−	0.431363i		−	0.0473483i	−0.999720	−	0.0236741i	$-0.992464\pi$
$83$		−	0.431363i		−	0.0473483i	0.999720	−	0.0236741i	$-0.00753641\pi$
$84$	−2.67535	−	1.54462i	−0.291905	−	0.168532i
$85$		0			0
$86$			1.98782i			0.214352i
$87$	0.192985	−	0.334259i	0.0206901	−	0.0358364i
$88$	−6.65182	−	11.5213i	−0.709086	−	1.22817i
$89$	−0.578954	+	0.334259i	−0.0613690	+	0.0354314i	−0.530371	−	0.847766i	$-0.677947\pi$
$89$	−0.578954	+	0.334259i	−0.0613690	+	0.0354314i	0.469002	+	0.883197i	$0.344614\pi$
$90$		0			0
$91$	−6.24524	+	5.82457i	−0.654679	+	0.610581i
$92$	−9.95950			−1.03835
$93$	7.84069	−	4.52683i	0.813042	−	0.469410i
$94$	−4.10785	−	7.11501i	−0.423693	−	0.733857i
$95$		0			0
$96$			5.77053i			0.588952i
$97$	−4.60647	−	2.65955i	−0.467717	−	0.270036i	0.247567	−	0.968871i	$-0.420369\pi$
$97$	−4.60647	−	2.65955i	−0.467717	−	0.270036i	−0.715283	+	0.698835i	$0.753702\pi$
$98$	1.00414	+	0.579740i	0.101433	+	0.0585625i
$99$			4.82700i			0.485132i
$100$		0			0
$101$	0.890814	+	1.54293i	0.0886393	+	0.153528i	0.906936	−	0.421268i	$-0.138415\pi$
$101$	0.890814	+	1.54293i	0.0886393	+	0.153528i	−0.818297	+	0.574796i	$0.805081\pi$
$102$	−2.32872	+	1.34449i	−0.230578	+	0.133124i
$103$	7.41214			0.730340			0.365170	−	0.930941i	$-0.381011\pi$
$103$	7.41214			0.730340			0.365170	+	0.930941i	$0.381011\pi$
$104$	9.50320	+	2.90471i	0.931865	+	0.284831i
$105$		0			0
$106$	9.26550	−	5.34944i	0.899945	−	0.519583i
$107$	−3.66449	−	6.34709i	−0.354260	−	0.613596i	0.632731	−	0.774372i	$-0.281934\pi$
$107$	−3.66449	−	6.34709i	−0.354260	−	0.613596i	−0.986991	+	0.160775i	$0.948601\pi$
$108$	0.652144	−	1.12955i	0.0627526	−	0.108691i
$109$			8.94422i			0.856701i	0.903613	+	0.428351i	$0.140905\pi$
$109$			8.94422i			0.856701i	−0.903613	+	0.428351i	$0.859095\pi$
$110$		0			0
$111$	−9.12360	−	5.26752i	−0.865974	−	0.499970i
$112$		−	0.733632i		−	0.0693217i
$113$	2.91620	−	5.05101i	0.274333	−	0.475159i	−0.695634	−	0.718397i	$-0.744876\pi$
$113$	2.91620	−	5.05101i	0.274333	−	0.475159i	0.969967	+	0.243238i	$0.0782096\pi$
$114$	−2.78801	−	4.82898i	−0.261121	−	0.452275i
$115$		0			0
$116$	0.503415			0.0467409
$117$	−2.45916	−	2.63677i	−0.227349	−	0.243769i
$118$	2.00211			0.184309
$119$	6.61271	−	3.81785i	0.606186	−	0.349982i
$120$		0			0
$121$	6.14998	−	10.6521i	0.559089	−	0.968371i
$122$		−	10.2382i		−	0.926927i
$123$	6.41426	+	3.70327i	0.578354	+	0.333913i
$124$	10.2265	+	5.90428i	0.918369	+	0.530220i
$125$		0			0
$126$	0.987784	−	1.71089i	0.0879988	−	0.152418i
$127$	2.84102	+	4.92079i	0.252100	+	0.436650i	0.964104	−	0.265526i	$-0.0855455\pi$
$127$	2.84102	+	4.92079i	0.252100	+	0.436650i	−0.712004	+	0.702175i	$0.752212\pi$
$128$	−6.96556	+	4.02157i	−0.615674	+	0.355460i
$129$	2.38321			0.209830
$130$		0			0
$131$	19.1656			1.67451			0.837254	−	0.546814i	$-0.184159\pi$
$131$	19.1656			1.67451			0.837254	+	0.546814i	$0.184159\pi$
$132$	−5.45232	+	3.14790i	−0.474564	+	0.273990i
$133$	7.91694	+	13.7125i	0.686486	+	1.18903i
$134$	−2.09803	+	3.63390i	−0.181243	+	0.313921i
$135$		0			0
$136$	−7.69476	−	4.44257i	−0.659820	−	0.380947i
$137$	2.70128	+	1.55958i	0.230786	+	0.133244i	0.610935	−	0.791681i	$-0.290794\pi$
$137$	2.70128	+	1.55958i	0.230786	+	0.133244i	−0.380149	+	0.924925i	$0.624127\pi$
$138$		−	6.36911i		−	0.542175i
$139$	1.76755	−	3.06149i	0.149922	−	0.259673i	−0.781276	−	0.624185i	$-0.785431\pi$
$139$	1.76755	−	3.06149i	0.149922	−	0.259673i	0.931198	+	0.364513i	$0.118764\pi$
$140$		0			0
$141$	−8.53023	+	4.92493i	−0.718375	+	0.414754i
$142$	−3.84363			−0.322550
$143$	3.91620	+	16.9577i	0.327489	+	1.41807i
$144$	0.309743			0.0258119
$145$		0			0
$146$	0.0266341	+	0.0461316i	0.00220425	+	0.00381788i
$147$	0.695053	−	1.20387i	0.0573270	−	0.0992933i
$148$		−	13.7407i		−	1.12948i
$149$	−9.82074	−	5.67001i	−0.804546	−	0.464505i	0.0405122	−	0.999179i	$-0.487101\pi$
$149$	−9.82074	−	5.67001i	−0.804546	−	0.464505i	−0.845058	+	0.534674i	$0.820434\pi$
$150$		0			0
$151$			19.4198i			1.58036i	0.612873	+	0.790181i	$0.290014\pi$
$151$			19.4198i			1.58036i	−0.612873	+	0.790181i	$0.709986\pi$
$152$	9.21240	−	15.9563i	0.747224	−	1.29423i
$153$	1.61191	+	2.79192i	0.130315	+	0.225713i
$154$	−8.25848	+	4.76804i	−0.665488	+	0.384219i
$155$		0			0
$156$	1.37462	−	4.49729i	0.110058	−	0.360071i
$157$	6.63751			0.529731			0.264865	−	0.964285i	$-0.414672\pi$
$157$	6.63751			0.529731			0.264865	+	0.964285i	$0.414672\pi$
$158$	3.70660	−	2.14001i	0.294881	−	0.170250i
$159$	−6.41347	−	11.1085i	−0.508622	−	0.880958i
$160$		0			0
$161$			18.0860i			1.42537i
$162$	0.722346	+	0.417047i	0.0567529	+	0.0327663i
$163$	−9.84605	−	5.68462i	−0.771202	−	0.445254i	0.0621011	−	0.998070i	$-0.480220\pi$
$163$	−9.84605	−	5.68462i	−0.771202	−	0.445254i	−0.833303	+	0.552816i	$0.813553\pi$
$164$			9.66027i			0.754340i
$165$		0			0
$166$	0.179899	+	0.311594i	0.0139628	+	0.0241844i
$167$	−2.87497	+	1.65986i	−0.222472	+	0.128444i	−0.607094	−	0.794630i	$-0.707665\pi$
$167$	−2.87497	+	1.65986i	−0.222472	+	0.128444i	0.384623	+	0.923074i	$0.374332\pi$
$168$	6.52785			0.503634
$169$	−10.7785	−	7.26804i	−0.829114	−	0.559080i
$170$		0			0
$171$	−5.78949	+	3.34257i	−0.442734	+	0.255612i
$172$	1.55419	+	2.69194i	0.118506	+	0.205259i
$173$	4.69428	−	8.13074i	0.356900	−	0.618169i	−0.630541	−	0.776156i	$-0.717167\pi$
$173$	4.69428	−	8.13074i	0.356900	−	0.618169i	0.987441	+	0.157987i	$0.0505004\pi$
$174$			0.321935i			0.0244058i
$175$		0			0
$176$	−1.29482	−	0.747564i	−0.0976007	−	0.0563498i
$177$		−	2.40034i		−	0.180420i
$178$	0.278804	−	0.482902i	0.0208972	−	0.0361950i
$179$	−2.84587	−	4.92918i	−0.212710	−	0.368424i	0.739852	−	0.672770i	$-0.234896\pi$
$179$	−2.84587	−	4.92918i	−0.212710	−	0.368424i	−0.952562	+	0.304345i	$0.901562\pi$
$180$		0			0
$181$	−21.7754			−1.61855			−0.809277	−	0.587427i	$-0.800141\pi$
$181$	−21.7754			−1.61855			−0.809277	+	0.587427i	$0.800141\pi$
$182$	2.08210	−	6.81191i	0.154336	−	0.504933i
$183$	−12.2747			−0.907372
$184$	18.2258	−	10.5227i	1.34363	−	0.775743i
$185$		0			0
$186$	−3.77580	+	6.53987i	−0.276855	+	0.479527i
$187$		−	15.5614i		−	1.13796i
$188$	−11.1259	−	6.42353i	−0.811438	−	0.468484i
$189$	−2.05120	−	1.18426i	−0.149203	−	0.0861423i
$190$		0			0
$191$	11.2044	−	19.4065i	0.810719	−	1.40421i	−0.101642	−	0.994821i	$-0.532410\pi$
$191$	11.2044	−	19.4065i	0.810719	−	1.40421i	0.912361	−	0.409386i	$-0.134257\pi$
$192$	−2.09684	−	3.63183i	−0.151326	−	0.262105i
$193$	10.8117	−	6.24211i	0.778240	−	0.449317i	−0.0575662	−	0.998342i	$-0.518334\pi$
$193$	10.8117	−	6.24211i	0.778240	−	0.449317i	0.835806	+	0.549025i	$0.185001\pi$
$194$	4.43663			0.318531
$195$		0			0
$196$	1.81310			0.129507
$197$	13.1877	−	7.61391i	0.939583	−	0.542468i	0.0497532	−	0.998762i	$-0.484157\pi$
$197$	13.1877	−	7.61391i	0.939583	−	0.542468i	0.889829	+	0.456293i	$0.150823\pi$
$198$	−2.01309	−	3.48677i	−0.143064	−	0.247794i
$199$	4.03222	−	6.98401i	0.285837	−	0.495084i	−0.686975	−	0.726681i	$-0.741062\pi$
$199$	4.03222	−	6.98401i	0.285837	−	0.495084i	0.972812	+	0.231597i	$0.0743952\pi$
$200$		0			0
$201$	4.35671	+	2.51535i	0.307299	+	0.177419i
$202$	−1.28695	−	0.743022i	−0.0905496	−	0.0522789i
$203$		−	0.914177i		−	0.0641627i
$204$	−2.10240	+	3.64146i	−0.147197	+	0.254953i
$205$		0			0
$206$	−5.35413	+	3.09121i	−0.373040	+	0.215375i
$207$	−7.63597			−0.530737
$208$	1.08815	−	0.251298i	0.0754498	−	0.0174244i
$209$	32.2691			2.23210
$210$		0			0
$211$	13.2528	+	22.9546i	0.912363	+	1.58026i	0.810717	+	0.585438i	$0.199077\pi$
$211$	13.2528	+	22.9546i	0.912363	+	1.58026i	0.101646	+	0.994821i	$0.467589\pi$
$212$	8.36502	−	14.4886i	0.574512	−	0.995083i
$213$			4.60815i			0.315745i
$214$	5.29407	+	3.05653i	0.361895	+	0.208940i
$215$		0			0
$216$			2.75609i			0.187528i
$217$	10.7219	−	18.5708i	0.727849	−	1.26067i
$218$	−3.73016	−	6.46083i	−0.252638	−	0.437582i
$219$	0.0553075	−	0.0319318i	0.00373733	−	0.00215775i
$220$		0			0
$221$	7.92790	+	8.50048i	0.533289	+	0.571804i
$222$	8.78720			0.589758
$223$	−11.9760	+	6.91433i	−0.801970	+	0.463018i	−0.844160	−	0.536092i	$-0.819900\pi$
$223$	−11.9760	+	6.91433i	−0.801970	+	0.463018i	0.0421893	+	0.999110i	$0.486567\pi$
$224$	6.83381	+	11.8365i	0.456603	+	0.790859i
$225$		0			0
$226$			4.86477i			0.323600i
$227$	−10.4522	−	6.03455i	−0.693734	−	0.400527i	0.111275	−	0.993790i	$-0.464506\pi$
$227$	−10.4522	−	6.03455i	−0.693734	−	0.400527i	−0.805009	+	0.593262i	$0.797840\pi$
$228$	−7.55117	−	4.35967i	−0.500088	−	0.288726i
$229$		−	0.346351i		−	0.0228875i	−0.999935	−	0.0114438i	$-0.996357\pi$
$229$		−	0.346351i		−	0.0228875i	0.999935	−	0.0114438i	$-0.00364274\pi$
$230$		0			0
$231$	5.71643	+	9.90115i	0.376113	+	0.651448i
$232$	−0.921248	+	0.531883i	−0.0604829	+	0.0349198i
$233$	9.38189			0.614628			0.307314	−	0.951608i	$-0.400570\pi$
$233$	9.38189			0.614628			0.307314	+	0.951608i	$0.400570\pi$
$234$	2.87602	+	0.879074i	0.188011	+	0.0574668i
$235$		0			0
$236$	2.71129	−	1.56536i	0.176490	−	0.101897i
$237$	−2.56567	−	4.44386i	−0.166658	−	0.288660i
$238$	−3.18445	+	5.51562i	−0.206417	+	0.357525i
$239$		−	20.5413i		−	1.32871i	−0.747419	−	0.664353i	$-0.768707\pi$
$239$		−	20.5413i		−	1.32871i	0.747419	−	0.664353i	$-0.231293\pi$
$240$		0			0
$241$	−9.73089	−	5.61813i	−0.626822	−	0.361896i	0.152698	−	0.988273i	$-0.451204\pi$
$241$	−9.73089	−	5.61813i	−0.626822	−	0.361896i	−0.779520	+	0.626377i	$0.784537\pi$
$242$			10.2593i			0.659494i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−8.00487	−	13.8648i	−0.512459	−	0.887606i
$245$		0			0
$246$	−6.17775			−0.393879
$247$	−17.6271	+	16.4398i	−1.12159	+	1.04604i
$248$	−24.9526			−1.58449
$249$	0.373572	−	0.215682i	0.0236741	−	0.0136683i
$250$		0			0
$251$	11.1189	−	19.2586i	0.701821	−	1.21559i	−0.266006	−	0.963971i	$-0.585704\pi$
$251$	11.1189	−	19.2586i	0.701821	−	1.21559i	0.967827	−	0.251618i	$-0.0809627\pi$
$252$		−	3.08923i		−	0.194603i
$253$	31.9207	+	18.4294i	2.00684	+	1.15865i
$254$	−4.10440	−	2.36968i	−0.257533	−	0.148687i
$255$		0			0
$256$	7.54804	−	13.0736i	0.471752	−	0.817099i
$257$	1.17173	+	2.02950i	0.0730908	+	0.126597i	0.900254	−	0.435364i	$-0.143380\pi$
$257$	1.17173	+	2.02950i	0.0730908	+	0.126597i	−0.827164	+	0.561961i	$0.810047\pi$
$258$	−1.72150	+	0.993909i	−0.107176	+	0.0618781i
$259$	−24.9524			−1.55047
$260$		0			0
$261$	0.385970			0.0238909
$262$	−13.8442	+	7.99296i	−0.855299	+	0.493807i
$263$	−5.67625	−	9.83155i	−0.350012	−	0.606239i	0.636239	−	0.771492i	$-0.280489\pi$
$263$	−5.67625	−	9.83155i	−0.350012	−	0.606239i	−0.986251	+	0.165253i	$0.947156\pi$
$264$	6.65182	−	11.5213i	0.409391	−	0.709086i
$265$		0			0
$266$	−11.4375	−	6.60347i	−0.701281	−	0.404885i
$267$	−0.578954	−	0.334259i	−0.0354314	−	0.0204563i
$268$			6.56147i			0.400806i
$269$	14.7694	−	25.5814i	0.900507	−	1.55972i	0.0736705	−	0.997283i	$-0.476529\pi$
$269$	14.7694	−	25.5814i	0.900507	−	1.55972i	0.826837	−	0.562442i	$-0.190138\pi$
$270$		0			0
$271$	−2.54465	+	1.46916i	−0.154577	+	0.0892448i	−0.575293	−	0.817947i	$-0.695112\pi$
$271$	−2.54465	+	1.46916i	−0.154577	+	0.0892448i	0.420717	+	0.907192i	$0.361779\pi$
$272$	−0.998556			−0.0605464
$273$	−8.16684	−	2.49625i	−0.494280	−	0.151080i
$274$	−2.60168			−0.157173
$275$		0			0
$276$	−4.97975	−	8.62518i	−0.299746	−	0.519175i
$277$	16.4475	−	28.4878i	0.988232	−	1.71167i	0.361644	−	0.932316i	$-0.382215\pi$
$277$	16.4475	−	28.4878i	0.988232	−	1.71167i	0.626587	−	0.779351i	$-0.284451\pi$
$278$			2.94861i			0.176846i
$279$	7.84069	+	4.52683i	0.469410	+	0.271014i
$280$		0			0
$281$			18.0686i			1.07788i	0.842344	+	0.538941i	$0.181175\pi$
$281$			18.0686i			1.07788i	−0.842344	+	0.538941i	$0.818825\pi$
$282$	4.10785	−	7.11501i	0.244619	−	0.423693i
$283$	−4.56599	−	7.90853i	−0.271420	−	0.470114i	0.697806	−	0.716287i	$-0.254160\pi$
$283$	−4.56599	−	7.90853i	−0.271420	−	0.470114i	−0.969226	+	0.246174i	$0.920827\pi$
$284$	−5.20511	+	3.00517i	−0.308867	+	0.178324i
$285$		0			0
$286$	−9.90100	−	10.6161i	−0.585458	−	0.627742i
$287$	17.5426			1.03550
$288$	−4.99742	+	2.88526i	−0.294476	+	0.170016i
$289$	3.30347	+	5.72178i	0.194322	+	0.336575i
$290$		0			0
$291$		−	5.31910i		−	0.311811i
$292$	0.0721369	+	0.0416483i	0.00422149	+	0.00243728i
$293$	−0.686712	−	0.396473i	−0.0401181	−	0.0231622i	0.479807	−	0.877374i	$-0.340707\pi$
$293$	−0.686712	−	0.396473i	−0.0401181	−	0.0231622i	−0.519925	+	0.854212i	$0.674040\pi$
$294$			1.15948i			0.0676222i
$295$		0			0
$296$	14.5177	+	25.1454i	0.843825	+	1.46155i
$297$	−4.18031	+	2.41350i	−0.242566	+	0.140046i
$298$	9.45863			0.547924
$299$	−26.8258	+	6.19515i	−1.55138	+	0.358275i
$300$		0			0
$301$	4.88844	−	2.82234i	0.281765	−	0.162677i
$302$	−8.09898	−	14.0278i	−0.466044	−	0.807211i
$303$	−0.890814	+	1.54293i	−0.0511759	+	0.0886393i
$304$		−	2.07067i		−	0.118761i
$305$		0			0
$306$	−2.32872	−	1.34449i	−0.133124	−	0.0768592i
$307$			5.98810i			0.341759i	0.985292	+	0.170879i	$0.0546608\pi$
$307$			5.98810i			0.341759i	−0.985292	+	0.170879i	$0.945339\pi$
$308$	−7.45587	+	12.9139i	−0.424838	+	0.735840i
$309$	3.70607	+	6.41910i	0.210831	+	0.365170i
$310$		0			0
$311$	−10.6267			−0.602585			−0.301292	−	0.953532i	$-0.597418\pi$
$311$	−10.6267			−0.602585			−0.301292	+	0.953532i	$0.597418\pi$
$312$	2.23604	+	9.68237i	0.126591	+	0.548156i
$313$	0.304950			0.0172368			0.00861839	−	0.999963i	$-0.497257\pi$
$313$	0.304950			0.0172368			0.00861839	+	0.999963i	$0.497257\pi$
$314$	−4.79458	+	2.76815i	−0.270574	+	0.156216i
$315$		0			0
$316$	3.34637	−	5.79608i	0.188248	−	0.326055i
$317$			1.13093i			0.0635192i	0.999496	+	0.0317596i	$0.0101111\pi$
$317$			1.13093i			0.0635192i	−0.999496	+	0.0317596i	$0.989889\pi$
$318$	9.26550	+	5.34944i	0.519583	+	0.299982i
$319$	−1.61347	−	0.931538i	−0.0903371	−	0.0521561i
$320$		0			0
$321$	3.66449	−	6.34709i	0.204532	−	0.354260i
$322$	−7.54269	−	13.0643i	−0.420338	−	0.728046i
$323$	18.6643	−	10.7759i	1.03851	−	0.599585i
$324$	1.30429			0.0724604
$325$		0			0
$326$	9.48301			0.525215
$327$	−7.74593	+	4.47211i	−0.428351	+	0.247308i
$328$	−10.2065	−	17.6782i	−0.563562	−	0.976118i
$329$	−11.6648	+	20.2040i	−0.643102	+	1.11388i
$330$		0			0
$331$	−0.376428	−	0.217331i	−0.0206903	−	0.0119456i	0.489619	−	0.871936i	$-0.337136\pi$
$331$	−0.376428	−	0.217331i	−0.0206903	−	0.0119456i	−0.510309	+	0.859991i	$0.670469\pi$
$332$	0.487245	+	0.281311i	0.0267410	+	0.0154389i
$333$		−	10.5350i		−	0.577316i
$334$	1.38448	−	2.39799i	0.0757554	−	0.131212i
$335$		0			0
$336$	0.635344	−	0.366816i	0.0346608	−	0.0200115i
$337$	26.5846			1.44815			0.724077	−	0.689719i	$-0.242266\pi$
$337$	26.5846			1.44815			0.724077	+	0.689719i	$0.242266\pi$
$338$	10.8169	+	0.754915i	0.588362	+	0.0410620i
$339$	5.83240			0.316773
$340$		0			0
$341$	−21.8510	−	37.8470i	−1.18330	−	2.04953i
$342$	2.78801	−	4.82898i	0.150758	−	0.261121i
$343$		−	19.8721i		−	1.07300i
$344$	−5.68834	−	3.28416i	−0.306695	−	0.177070i
$345$		0			0
$346$			7.83094i			0.420994i
$347$	−10.0079	+	17.3342i	−0.537254	+	0.930551i	0.461797	+	0.886986i	$0.347205\pi$
$347$	−10.0079	+	17.3342i	−0.537254	+	0.930551i	−0.999051	+	0.0435651i	$0.986128\pi$
$348$	0.251708	+	0.435971i	0.0134929	+	0.0233705i
$349$	15.8345	−	9.14208i	0.847604	−	0.489364i	−0.0122378	−	0.999925i	$-0.503896\pi$
$349$	15.8345	−	9.14208i	0.847604	−	0.489364i	0.859842	+	0.510561i	$0.170562\pi$
$350$		0			0
$351$	1.05393	−	3.44808i	0.0562545	−	0.184045i
$352$	27.8543			1.48464
$353$	−19.5239	+	11.2721i	−1.03915	+	0.599955i	−0.919593	−	0.392872i	$-0.871482\pi$
$353$	−19.5239	+	11.2721i	−1.03915	+	0.599955i	−0.119560	+	0.992827i	$0.538148\pi$
$354$	1.00105	+	1.73387i	0.0532053	+	0.0921544i
$355$		0			0
$356$		−	0.871941i		−	0.0462128i
$357$	6.61271	+	3.81785i	0.349982	+	0.202062i
$358$	4.11140	+	2.37372i	0.217294	+	0.125455i
$359$		−	31.5554i		−	1.66543i	−0.553702	−	0.832715i	$-0.686786\pi$
$359$		−	31.5554i		−	1.66543i	0.553702	−	0.832715i	$-0.313214\pi$
$360$		0			0
$361$	12.8455	+	22.2490i	0.676078	+	1.17100i
$362$	15.7294	−	9.08137i	0.826719	−	0.477306i
$363$	12.3000			0.645580
$364$	−2.50633	−	10.8527i	−0.131367	−	0.568838i
$365$		0			0
$366$	8.86658	−	5.11912i	0.463464	−	0.267581i
$367$	1.44262	+	2.49870i	0.0753044	+	0.130431i	0.901219	−	0.433365i	$-0.142674\pi$
$367$	1.44262	+	2.49870i	0.0753044	+	0.130431i	−0.825914	+	0.563796i	$0.809340\pi$
$368$	1.18259	−	2.04831i	0.0616469	−	0.106776i
$369$			7.40655i			0.385569i
$370$		0			0
$371$	−26.3106	−	15.1905i	−1.36598	−	0.788649i
$372$			11.8086i			0.612246i
$373$	−3.89840	+	6.75222i	−0.201851	+	0.349617i	−0.949125	−	0.314900i	$-0.898029\pi$
$373$	−3.89840	+	6.75222i	−0.201851	+	0.349617i	0.747274	+	0.664516i	$0.231362\pi$
$374$	6.48984	+	11.2407i	0.335582	+	0.581245i
$375$		0			0
$376$	27.1471			1.40000
$377$	1.35594	−	0.313141i	0.0698347	−	0.0161276i
$378$	1.97557			0.101612
$379$	−13.3750	+	7.72208i	−0.687029	+	0.396657i	−0.802498	−	0.596654i	$-0.796496\pi$
$379$	−13.3750	+	7.72208i	−0.687029	+	0.396657i	0.115469	+	0.993311i	$0.463163\pi$
$380$		0			0
$381$	−2.84102	+	4.92079i	−0.145550	+	0.252100i
$382$			18.6910i			0.956313i
$383$	−8.67070	−	5.00603i	−0.443052	−	0.255796i	0.261839	−	0.965111i	$-0.415671\pi$
$383$	−8.67070	−	5.00603i	−0.443052	−	0.255796i	−0.704891	+	0.709315i	$0.749004\pi$
$384$	−6.96556	−	4.02157i	−0.355460	−	0.205225i
$385$		0			0
$386$	−5.20651	+	9.01793i	−0.265004	+	0.459001i
$387$	1.19160	+	2.06392i	0.0605726	+	0.104915i
$388$	6.00817	−	3.46882i	0.305018	−	0.176103i
$389$	−8.27602			−0.419611			−0.209805	−	0.977743i	$-0.567283\pi$
$389$	−8.27602			−0.419611			−0.209805	+	0.977743i	$0.567283\pi$
$390$		0			0
$391$	24.6170			1.24494
$392$	−3.31796	+	1.91563i	−0.167582	+	0.0967537i
$393$	9.58281	+	16.5979i	0.483389	+	0.837254i
$394$	−6.35071	+	10.9998i	−0.319944	+	0.554159i
$395$		0			0
$396$	−5.45232	−	3.14790i	−0.273990	−	0.158188i
$397$	−15.2007	−	8.77614i	−0.762902	−	0.440462i	0.0674344	−	0.997724i	$-0.478519\pi$
$397$	−15.2007	−	8.77614i	−0.762902	−	0.440462i	−0.830337	+	0.557262i	$0.811852\pi$
$398$			6.72650i			0.337169i
$399$	−7.91694	+	13.7125i	−0.396343	+	0.686486i
$400$		0			0
$401$	−18.4012	+	10.6239i	−0.918910	+	0.530533i	−0.883287	−	0.468833i	$-0.844675\pi$
$401$	−18.4012	+	10.6239i	−0.918910	+	0.530533i	−0.0356227	+	0.999365i	$0.511341\pi$
$402$	−4.19607			−0.209281
$403$	31.2177	+	9.54189i	1.55506	+	0.475315i
$404$	−2.32376			−0.115611
$405$		0			0
$406$	0.381255	+	0.660352i	0.0189214	+	0.0327727i
$407$	−25.4263	+	44.0397i	−1.26034	+	2.18297i
$408$		−	8.88514i		−	0.439880i
$409$	−7.70687	−	4.44956i	−0.381080	−	0.220017i	0.297208	−	0.954813i	$-0.403945\pi$
$409$	−7.70687	−	4.44956i	−0.381080	−	0.220017i	−0.678288	+	0.734796i	$0.737278\pi$
$410$		0			0
$411$			3.11917i			0.153857i
$412$	−4.83378	+	8.37236i	−0.238143	+	0.412476i
$413$	−2.84262	−	4.92357i	−0.139876	−	0.242273i
$414$	5.51581	−	3.18456i	0.271087	−	0.156512i
$415$		0			0
$416$	−15.2155	+	14.1906i	−0.746003	+	0.695753i
$417$	3.53511			0.173115
$418$	−23.3095	+	13.4577i	−1.14010	+	0.658240i
$419$	1.40039	+	2.42554i	0.0684134	+	0.118496i	0.898203	−	0.439581i	$-0.144873\pi$
$419$	1.40039	+	2.42554i	0.0684134	+	0.118496i	−0.829790	+	0.558076i	$0.811540\pi$
$420$		0			0
$421$			15.7467i			0.767450i	0.923448	+	0.383725i	$0.125359\pi$
$421$			15.7467i			0.767450i	−0.923448	+	0.383725i	$0.874641\pi$
$422$	−19.1463	−	11.0541i	−0.932026	−	0.538105i
$423$	−8.53023	−	4.92493i	−0.414754	−	0.239458i
$424$			35.3522i			1.71685i
$425$		0			0
$426$	−1.92181	−	3.32868i	−0.0931121	−	0.161275i
$427$	−25.1779	+	14.5364i	−1.21844	+	0.703468i
$428$	9.55911			0.462057
$429$	−12.7277	+	11.8704i	−0.614498	+	0.573107i
$430$		0			0
$431$	−4.28969	+	2.47666i	−0.206627	+	0.119296i	−0.599743	−	0.800193i	$-0.704731\pi$
$431$	−4.28969	+	2.47666i	−0.206627	+	0.119296i	0.393116	+	0.919489i	$0.371397\pi$
$432$	0.154871	+	0.268245i	0.00745125	+	0.0129059i
$433$	−2.32843	+	4.03295i	−0.111897	+	0.193811i	−0.916535	−	0.399954i	$-0.869026\pi$
$433$	−2.32843	+	4.03295i	−0.111897	+	0.193811i	0.804638	+	0.593766i	$0.202359\pi$
$434$			17.8861i			0.858561i
$435$		0			0
$436$	−10.1029	−	5.83292i	−0.483842	−	0.279346i
$437$			51.0475i			2.44193i
$438$	−0.0266341	+	0.0461316i	−0.00127263	+	0.00220425i
$439$	9.90442	+	17.1550i	0.472712	+	0.818761i	0.999512	−	0.0312279i	$-0.00994176\pi$
$439$	9.90442	+	17.1550i	0.472712	+	0.818761i	−0.526800	+	0.849989i	$0.676608\pi$
$440$		0			0
$441$	1.39011			0.0661956
$442$	−9.27179	−	2.83398i	−0.441014	−	0.134799i
$443$	−0.446940			−0.0212348			−0.0106174	−	0.999944i	$-0.503380\pi$
$443$	−0.446940			−0.0212348			−0.0106174	+	0.999944i	$0.503380\pi$
$444$	11.8998	−	6.87036i	0.564740	−	0.326053i
$445$		0			0
$446$	5.76720	−	9.98908i	0.273085	−	0.472997i
$447$		−	11.3400i		−	0.536364i
$448$	−8.60206	−	4.96640i	−0.406409	−	0.234640i
$449$	21.0406	+	12.1478i	0.992966	+	0.573289i	0.906160	−	0.422936i	$-0.139001\pi$
$449$	21.0406	+	12.1478i	0.992966	+	0.573289i	0.0868064	+	0.996225i	$0.472334\pi$
$450$		0			0
$451$	17.8757	−	30.9616i	0.841735	−	1.45793i
$452$	3.80357	+	6.58797i	0.178905	+	0.309872i
$453$	−16.8181	+	9.70991i	−0.790181	+	0.456211i
$454$	10.0668			0.472457
$455$		0			0
$456$	18.4248			0.862820
$457$	21.5574	−	12.4462i	1.00841	−	0.582207i	0.0976863	−	0.995217i	$-0.468856\pi$
$457$	21.5574	−	12.4462i	1.00841	−	0.582207i	0.910727	+	0.413010i	$0.135522\pi$
$458$	0.144445	+	0.250185i	0.00674945	+	0.0116904i
$459$	−1.61191	+	2.79192i	−0.0752377	+	0.130315i
$460$		0			0
$461$	16.7973	+	9.69792i	0.782328	+	0.451677i	0.837255	−	0.546813i	$-0.184159\pi$
$461$	16.7973	+	9.69792i	0.782328	+	0.451677i	−0.0549268	+	0.998490i	$0.517493\pi$
$462$	−8.25848	−	4.76804i	−0.384219	−	0.221829i
$463$		−	16.2478i		−	0.755098i	−0.925990	−	0.377549i	$-0.876767\pi$
$463$		−	16.2478i		−	0.755098i	0.925990	−	0.377549i	$-0.123233\pi$
$464$	−0.0597756	+	0.103534i	−0.00277501	+	0.00480646i
$465$		0			0
$466$	−6.77697	+	3.91269i	−0.313937	+	0.181252i
$467$	−31.9803			−1.47987			−0.739935	−	0.672679i	$-0.765144\pi$
$467$	−31.9803			−1.47987			−0.739935	+	0.672679i	$0.765144\pi$
$468$	4.58208	−	1.05818i	0.211807	−	0.0489145i
$469$	11.9153			0.550198
$470$		0			0
$471$	3.31875	+	5.74825i	0.152920	+	0.264865i
$472$	−3.30777	+	5.72922i	−0.152252	+	0.263709i
$473$		−	11.5038i		−	0.528943i
$474$	3.70660	+	2.14001i	0.170250	+	0.0982937i
$475$		0			0
$476$			9.95915i			0.456477i
$477$	6.41347	−	11.1085i	0.293653	−	0.508622i
$478$	8.56669	+	14.8379i	0.391831	+	0.678671i
$479$	−31.8274	+	18.3755i	−1.45423	+	0.839600i	−0.998717	−	0.0506303i	$-0.983877\pi$
$479$	−31.8274	+	18.3755i	−1.45423	+	0.839600i	−0.455512	+	0.890230i	$0.650544\pi$
$480$		0			0
$481$	−8.54719	−	37.0105i	−0.389718	−	1.68753i
$482$	9.37210			0.426887
$483$	−15.6629	+	9.04298i	−0.712686	+	0.411470i
$484$	8.02134	+	13.8934i	0.364606	+	0.631517i
$485$		0			0
$486$			0.834094i			0.0378353i
$487$	2.28393	+	1.31863i	0.103495	+	0.0597528i	0.550854	−	0.834602i	$-0.314302\pi$
$487$	2.28393	+	1.31863i	0.103495	+	0.0597528i	−0.447359	+	0.894354i	$0.647635\pi$
$488$	29.2977	+	16.9151i	1.32625	+	0.765709i
$489$		−	11.3692i		−	0.514135i
$490$		0			0
$491$	0.129983	+	0.225137i	0.00586605	+	0.0101603i	0.868944	−	0.494911i	$-0.164799\pi$
$491$	0.129983	+	0.225137i	0.00586605	+	0.0101603i	−0.863077	+	0.505072i	$0.831466\pi$
$492$	−8.36604	+	4.83014i	−0.377170	+	0.217759i
$493$	−1.24430			−0.0560404
$494$	5.87672	−	19.2266i	0.264406	−	0.865044i
$495$		0			0
$496$	−2.42860	+	1.40215i	−0.109047	+	0.0629584i
$497$	5.45725	+	9.45223i	0.244791	+	0.423990i
$498$	−0.179899	+	0.311594i	−0.00806145	+	0.0139628i
$499$		−	17.9707i		−	0.804480i	−0.915534	−	0.402240i	$-0.868232\pi$
$499$		−	17.9707i		−	0.804480i	0.915534	−	0.402240i	$-0.131768\pi$
$500$		0			0
$501$	−2.87497	−	1.65986i	−0.128444	−	0.0741572i
$502$			18.5485i			0.827858i
$503$	7.36268	−	12.7525i	0.328286	−	0.568607i	−0.653886	−	0.756593i	$-0.726862\pi$
$503$	7.36268	−	12.7525i	0.328286	−	0.568607i	0.982172	+	0.187986i	$0.0601958\pi$
$504$	3.26392	+	5.65328i	0.145387	+	0.251817i
$505$		0			0
$506$	−30.7437			−1.36673
$507$	0.905073	−	12.9685i	0.0401957	−	0.575949i
$508$	−7.41102			−0.328811
$509$	20.7919	−	12.0042i	0.921586	−	0.532078i	0.0374455	−	0.999299i	$-0.488078\pi$
$509$	20.7919	−	12.0042i	0.921586	−	0.532078i	0.884141	+	0.467221i	$0.154745\pi$
$510$		0			0
$511$	0.0756312	−	0.130997i	0.00334573	−	0.00579497i
$512$		−	3.49473i		−	0.154447i
$513$	−5.78949	−	3.34257i	−0.255612	−	0.147578i
$514$	−1.69280	−	0.977336i	−0.0746660	−	0.0431084i
$515$		0			0
$516$	−1.55419	+	2.69194i	−0.0684196	+	0.118506i
$517$	23.7727	+	41.1755i	1.04552	+	1.81089i
$518$	18.0243	−	10.4063i	0.791943	−	0.457228i
$519$	9.38857			0.412112
$520$		0			0
$521$	−15.7803			−0.691348			−0.345674	−	0.938355i	$-0.612350\pi$
$521$	−15.7803			−0.691348			−0.345674	+	0.938355i	$0.612350\pi$
$522$	−0.278804	+	0.160967i	−0.0122029	+	0.00704535i
$523$	14.6174	+	25.3181i	0.639174	+	1.10708i	0.985614	+	0.169010i	$0.0540570\pi$
$523$	14.6174	+	25.3181i	0.639174	+	1.10708i	−0.346440	+	0.938072i	$0.612610\pi$
$524$	−12.4987	+	21.6485i	−0.546010	+	0.945717i
$525$		0			0
$526$	8.20043	+	4.73452i	0.357556	+	0.206435i
$527$	−25.2770	−	14.5937i	−1.10109	−	0.635712i
$528$		−	1.49513i		−	0.0650671i
$529$	−17.6540	+	30.5776i	−0.767566	+	1.32946i
$530$		0			0
$531$	2.07875	−	1.20017i	0.0902102	−	0.0520829i
$532$	−20.6519			−0.895375
$533$	6.00902	+	26.0198i	0.260279	+	1.12704i
$534$	0.557607			0.0241300
$535$		0			0
$536$	−6.93251	−	12.0075i	−0.299439	−	0.518643i
$537$	2.84587	−	4.92918i	0.122808	−	0.212710i
$538$			24.6382i			1.06223i
$539$	−5.81107	−	3.35502i	−0.250301	−	0.144511i
$540$		0			0
$541$			17.7559i			0.763387i	0.924289	+	0.381694i	$0.124659\pi$
$541$			17.7559i			0.763387i	−0.924289	+	0.381694i	$0.875341\pi$
$542$	1.22541	−	2.12248i	0.0526360	−	0.0911682i
$543$	−10.8877	−	18.8581i	−0.467236	−	0.809277i
$544$	16.1108	−	9.30159i	0.690746	−	0.398802i
$545$		0			0
$546$	6.94034	−	1.60280i	0.297019	−	0.0685935i
$547$	−18.6461			−0.797251			−0.398625	−	0.917114i	$-0.630513\pi$
$547$	−18.6461			−0.797251			−0.398625	+	0.917114i	$0.630513\pi$
$548$	−3.52324	+	2.03415i	−0.150506	+	0.0868944i
$549$	−6.13735	−	10.6302i	−0.261936	−	0.453686i
$550$		0			0
$551$		−	2.58026i		−	0.109923i
$552$	18.2258	+	10.5227i	0.775743	+	0.447875i
$553$	−10.5254	−	6.07684i	−0.447585	−	0.258413i
$554$			27.4374i			1.16570i
$555$		0			0
$556$	2.30540	+	3.99307i	0.0977708	+	0.169344i
$557$	−1.19310	+	0.688834i	−0.0505531	+	0.0291868i	−0.525064	−	0.851063i	$-0.675958\pi$
$557$	−1.19310	+	0.688834i	−0.0505531	+	0.0291868i	0.474510	+	0.880250i	$0.342625\pi$
$558$	−7.55159			−0.319684
$559$	5.86069	+	6.28396i	0.247881	+	0.265783i
$560$		0			0
$561$	13.4766	−	7.78071i	0.568982	−	0.328502i
$562$	−7.53545	−	13.0518i	−0.317864	−	0.550556i
$563$	−4.69819	+	8.13750i	−0.198005	+	0.342955i	−0.947881	−	0.318623i	$-0.896780\pi$
$563$	−4.69819	+	8.13750i	−0.198005	+	0.342955i	0.749877	+	0.661578i	$0.230113\pi$
$564$		−	12.8471i		−	0.540959i
$565$		0			0
$566$	6.59646	+	3.80847i	0.277270	+	0.160082i
$567$		−	2.36852i		−	0.0994685i
$568$	6.35022	−	10.9989i	0.266449	−	0.461504i
$569$	−3.74102	−	6.47963i	−0.156832	−	0.271640i	0.776893	−	0.629633i	$-0.216795\pi$
$569$	−3.74102	−	6.47963i	−0.156832	−	0.271640i	−0.933724	+	0.357993i	$0.883461\pi$
$570$		0			0
$571$	−14.5630			−0.609441			−0.304720	−	0.952442i	$-0.598563\pi$
$571$	−14.5630			−0.609441			−0.304720	+	0.952442i	$0.598563\pi$
$572$	−21.7084	−	6.63531i	−0.907674	−	0.277436i
$573$	22.4087			0.936138
$574$	−12.6718	+	7.31607i	−0.528911	+	0.305367i
$575$		0			0
$576$	2.09684	−	3.63183i	0.0873682	−	0.151326i
$577$			19.6811i			0.819333i	0.912235	+	0.409667i	$0.134355\pi$
$577$			19.6811i			0.819333i	−0.912235	+	0.409667i	$0.865645\pi$
$578$	−4.77250	−	2.75540i	−0.198510	−	0.114610i
$579$	10.8117	+	6.24211i	0.449317	+	0.259413i
$580$		0			0
$581$	0.510846	−	0.884812i	0.0211935	−	0.0367082i
$582$	2.21831	+	3.84223i	0.0919520	+	0.159266i
$583$	−53.6206	+	30.9579i	−2.22074	+	1.28214i
$584$	−0.176014			−0.00728349
$585$		0			0
$586$	0.661392			0.0273218
$587$	21.9715	−	12.6853i	0.906863	−	0.523578i	0.0274424	−	0.999623i	$-0.491264\pi$
$587$	21.9715	−	12.6853i	0.906863	−	0.523578i	0.879420	+	0.476046i	$0.157930\pi$
$588$	0.906550	+	1.57019i	0.0373855	+	0.0647535i
$589$	30.2624	−	52.4161i	1.24694	−	2.15977i
$590$		0			0
$591$	13.1877	+	7.61391i	0.542468	+	0.313194i
$592$	2.82597	+	1.63157i	0.116147	+	0.0670573i
$593$		−	34.6838i		−	1.42429i	−0.702032	−	0.712146i	$-0.747724\pi$
$593$		−	34.6838i		−	1.42429i	0.702032	−	0.712146i	$-0.252276\pi$
$594$	2.01309	−	3.48677i	0.0825979	−	0.143064i
$595$		0			0
$596$	12.8091	−	7.39532i	0.524680	−	0.302924i
$597$	8.06445			0.330056
$598$	16.7939	−	15.6627i	0.686752	−	0.640494i
$599$	−4.13726			−0.169044			−0.0845218	−	0.996422i	$-0.526936\pi$
$599$	−4.13726			−0.169044			−0.0845218	+	0.996422i	$0.526936\pi$
$600$		0			0
$601$	−21.0650	−	36.4856i	−0.859258	−	1.48828i	−0.872637	−	0.488369i	$-0.837592\pi$
$601$	−21.0650	−	36.4856i	−0.859258	−	1.48828i	0.0133791	−	0.999910i	$-0.495741\pi$
$602$	−2.35410	+	4.07741i	−0.0959458	+	0.166183i
$603$			5.03069i			0.204866i
$604$	−21.9356	−	12.6645i	−0.892547	−	0.515312i
$605$		0			0
$606$		−	1.48604i		−	0.0603664i
$607$	−0.923773	+	1.60002i	−0.0374948	+	0.0649429i	−0.884164	−	0.467177i	$-0.845271\pi$
$607$	−0.923773	+	1.60002i	−0.0374948	+	0.0649429i	0.846669	+	0.532120i	$0.178604\pi$
$608$	19.2884	+	33.4084i	0.782246	+	1.35489i
$609$	0.791701	−	0.457089i	0.0320813	−	0.0185222i
$610$		0			0
$611$	−33.9631	−	10.3810i	−1.37400	−	0.419972i
$612$	−4.20480			−0.169969
$613$	−3.70023	+	2.13633i	−0.149451	+	0.0862855i	−0.572861	−	0.819653i	$-0.694166\pi$
$613$	−3.70023	+	2.13633i	−0.149451	+	0.0862855i	0.423410	+	0.905938i	$0.360833\pi$
$614$	−2.49732	−	4.32548i	−0.100783	−	0.174562i
$615$		0			0
$616$		−	31.5099i		−	1.26957i
$617$	5.61384	+	3.24115i	0.226005	+	0.130484i	0.608728	−	0.793379i	$-0.291680\pi$
$617$	5.61384	+	3.24115i	0.226005	+	0.130484i	−0.382723	+	0.923863i	$0.625014\pi$
$618$	−5.35413	−	3.09121i	−0.215375	−	0.124347i
$619$			45.5600i			1.83121i	0.402078	+	0.915605i	$0.368288\pi$
$619$			45.5600i			1.83121i	−0.402078	+	0.915605i	$0.631712\pi$
$620$		0			0
$621$	−3.81798	−	6.61294i	−0.153210	−	0.265368i
$622$	7.67615	−	4.43183i	0.307786	−	0.177700i
$623$	−1.58340			−0.0634376
$624$	0.761706	+	0.816719i	0.0304927	+	0.0326949i
$625$		0			0
$626$	−0.220279	+	0.127178i	−0.00880413	+	0.00508307i
$627$	16.1346	+	27.9459i	0.644353	+	1.11605i
$628$	−4.32861	+	7.49737i	−0.172730	+	0.299178i
$629$			33.9631i			1.35420i
$630$		0			0
$631$	−6.58330	−	3.80087i	−0.262077	−	0.151310i	0.363205	−	0.931709i	$-0.381683\pi$
$631$	−6.58330	−	3.80087i	−0.262077	−	0.151310i	−0.625282	+	0.780399i	$0.715016\pi$
$632$			14.1424i			0.562554i
$633$	−13.2528	+	22.9546i	−0.526753	+	0.912363i
$634$	−0.471649	−	0.816921i	−0.0187316	−	0.0324441i
$635$		0			0
$636$	16.7300			0.663389
$637$	4.88356	−	1.12781i	0.193494	−	0.0446854i
$638$	1.55398			0.0615227
$639$	−3.99077	+	2.30407i	−0.157872	+	0.0911477i
$640$		0			0
$641$	13.8305	−	23.9551i	0.546272	−	0.946170i	−0.452254	−	0.891889i	$-0.649380\pi$
$641$	13.8305	−	23.9551i	0.546272	−	0.946170i	0.998526	−	0.0542811i	$-0.0172867\pi$
$642$			6.11306i			0.241263i
$643$	1.30843	+	0.755420i	0.0515993	+	0.0297909i	0.525578	−	0.850746i	$-0.323849\pi$
$643$	1.30843	+	0.755420i	0.0515993	+	0.0297909i	−0.473978	+	0.880536i	$0.657183\pi$
$644$	−20.4289	−	11.7946i	−0.805012	−	0.464774i
$645$		0			0
$646$	−8.98807	+	15.5678i	−0.353631	+	0.612507i
$647$	6.69989	+	11.6046i	0.263400	+	0.456222i	0.967143	−	0.254232i	$-0.0818228\pi$
$647$	6.69989	+	11.6046i	0.263400	+	0.456222i	−0.703743	+	0.710454i	$0.748489\pi$
$648$	−2.38684	+	1.37804i	−0.0937639	+	0.0541346i
$649$	−11.5864			−0.454807
$650$		0			0
$651$	21.4438			0.840448
$652$	12.8421	−	7.41438i	0.502935	−	0.290370i
$653$	−17.1312	−	29.6722i	−0.670397	−	1.16116i	−0.977792	−	0.209580i	$-0.932790\pi$
$653$	−17.1312	−	29.6722i	−0.670397	−	1.16116i	0.307395	−	0.951582i	$-0.400543\pi$
$654$	3.73016	−	6.46083i	0.145861	−	0.252638i
$655$		0			0
$656$	−1.98677	−	1.14706i	−0.0775703	−	0.0447852i
$657$	0.0553075	+	0.0319318i	0.00215775	+	0.00124578i
$658$		−	19.4591i		−	0.758594i
$659$	−22.0211	+	38.1416i	−0.857819	+	1.48579i	0.0161854	+	0.999869i	$0.494848\pi$
$659$	−22.0211	+	38.1416i	−0.857819	+	1.48579i	−0.874005	+	0.485918i	$0.838486\pi$
$660$		0			0
$661$	−15.9737	+	9.22243i	−0.621305	+	0.358711i	−0.777377	−	0.629035i	$-0.783450\pi$
$661$	−15.9737	+	9.22243i	−0.621305	+	0.358711i	0.156072	+	0.987746i	$0.450117\pi$
$662$	0.362548			0.0140908
$663$	−3.39768	+	11.1160i	−0.131955	+	0.431710i
$664$	−1.18887			−0.0461373
$665$		0			0
$666$	4.39360	+	7.60994i	0.170249	+	0.294879i
$667$	1.47363	−	2.55239i	0.0570590	−	0.0988291i
$668$		−	4.32988i		−	0.167528i
$669$	−11.9760	−	6.91433i	−0.463018	−	0.267323i
$670$		0			0
$671$			59.2500i			2.28732i
$672$	−6.83381	+	11.8365i	−0.263620	+	0.456603i
$673$	−23.1033	−	40.0161i	−0.890568	−	1.54251i	−0.839196	−	0.543829i	$-0.816974\pi$
$673$	−23.1033	−	40.0161i	−0.890568	−	1.54251i	−0.0513714	−	0.998680i	$-0.516359\pi$
$674$	−19.2033	+	11.0870i	−0.739683	+	0.427056i
$675$		0			0
$676$	15.2387	−	7.43498i	0.586104	−	0.285961i
$677$	−42.6645			−1.63973			−0.819865	−	0.572556i	$-0.805952\pi$
$677$	−42.6645			−1.63973			−0.819865	+	0.572556i	$0.805952\pi$
$678$	−4.21301	+	2.43238i	−0.161800	+	0.0934152i
$679$	−6.29920	−	10.9105i	−0.241741	−	0.418708i
$680$		0			0
$681$		−	12.0691i		−	0.462489i
$682$	31.5680	+	18.2258i	1.20880	+	0.697901i
$683$	17.2022	+	9.93167i	0.658222	+	0.380025i	0.791599	−	0.611041i	$-0.209249\pi$
$683$	17.2022	+	9.93167i	0.658222	+	0.380025i	−0.133377	+	0.991065i	$0.542582\pi$
$684$		−	8.71934i		−	0.333392i
$685$		0			0
$686$	8.28762	+	14.3546i	0.316423	+	0.548060i
$687$	0.299949	−	0.173175i	0.0114438	−	0.00660706i
$688$	−0.738181			−0.0281429
$689$	13.5187	−	44.2283i	0.515020	−	1.68496i
$690$		0			0
$691$	36.6818	−	21.1782i	1.39544	−	0.805659i	0.401531	−	0.915846i	$-0.368478\pi$
$691$	36.6818	−	21.1782i	1.39544	−	0.805659i	0.993911	+	0.110187i	$0.0351450\pi$
$692$	6.12270	+	10.6048i	0.232750	+	0.403135i
$693$	−5.71643	+	9.90115i	−0.217149	+	0.376113i
$694$		−	16.6951i		−	0.633737i
$695$		0			0
$696$	−0.921248	−	0.531883i	−0.0349198	−	0.0201610i
$697$		−	23.8774i		−	0.904422i
$698$	−7.62535	+	13.2075i	−0.288624	+	0.499911i
$699$	4.69095	+	8.12496i	0.177428	+	0.307314i
$700$		0			0
$701$	3.47802			0.131363			0.0656816	−	0.997841i	$-0.479078\pi$
$701$	3.47802			0.131363			0.0656816	+	0.997841i	$0.479078\pi$
$702$	0.676709	+	2.93024i	0.0255408	+	0.110595i
$703$	−70.4281			−2.65624
$704$	−17.5308	+	10.1214i	−0.660718	+	0.381466i
$705$		0			0
$706$	9.40202	−	16.2848i	0.353850	−	0.612885i
$707$			4.21982i			0.158703i
$708$	2.71129	+	1.56536i	0.101897	+	0.0588300i
$709$	22.8509	+	13.1930i	0.858185	+	0.495473i	0.863404	−	0.504513i	$-0.168328\pi$
$709$	22.8509	+	13.1930i	0.858185	+	0.495473i	−0.00521905	+	0.999986i	$0.501661\pi$
$710$		0			0
$711$	2.56567	−	4.44386i	0.0962200	−	0.166658i
$712$	0.921248	+	1.59565i	0.0345252	+	0.0597994i
$713$	59.8713	−	34.5667i	2.24220	−	1.29453i
$714$	−6.36889			−0.238350
$715$		0			0
$716$	7.42365			0.277435
$717$	17.7893	−	10.2707i	0.664353	−	0.383565i
$718$	13.1601	+	22.7939i	0.491129	+	0.850661i
$719$	14.9869	−	25.9582i	0.558919	−	0.968076i	−0.438668	−	0.898649i	$-0.644550\pi$
$719$	14.9869	−	25.9582i	0.558919	−	0.968076i	0.997587	−	0.0694267i	$-0.0221170\pi$
$720$		0			0
$721$	15.2038	+	8.77791i	0.566218	+	0.326906i
$722$	−18.5578	−	10.7143i	−0.690649	−	0.398746i
$723$		−	11.2363i		−	0.417881i
$724$	14.2007	−	24.5963i	0.527765	−	0.914116i
$725$		0			0
$726$	−8.88483	+	5.12966i	−0.329747	+	0.190379i
$727$	3.96270			0.146968			0.0734842	−	0.997296i	$-0.476588\pi$
$727$	3.96270			0.146968			0.0734842	+	0.997296i	$0.476588\pi$
$728$	16.0530	+	17.2124i	0.594964	+	0.637934i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.84153	−	6.65372i	−0.142084	−	0.246097i
$732$	8.00487	−	13.8648i	0.295869	−	0.512459i
$733$			0.557302i			0.0205844i	0.999947	+	0.0102922i	$0.00327617\pi$
$733$			0.557302i			0.0205844i	−0.999947	+	0.0102922i	$0.996724\pi$
$734$	−2.08415	−	1.20328i	−0.0769273	−	0.0444140i
$735$		0			0
$736$			44.0635i			1.62420i
$737$	12.1416	−	21.0298i	0.447241	−	0.774644i
$738$	−3.08888	−	5.35009i	−0.113703	−	0.196940i
$739$	5.07077	−	2.92761i	0.186531	−	0.107694i	−0.403826	−	0.914836i	$-0.632320\pi$
$739$	5.07077	−	2.92761i	0.186531	−	0.107694i	0.590358	+	0.807142i	$0.298987\pi$
$740$		0			0
$741$	−23.0508	−	7.04564i	−0.846794	−	0.258828i
$742$	25.3405			0.930280
$743$	29.2071	−	16.8627i	1.07150	−	0.618633i	0.142912	−	0.989735i	$-0.454354\pi$
$743$	29.2071	−	16.8627i	1.07150	−	0.618633i	0.928592	+	0.371103i	$0.121020\pi$
$744$	−12.4763	−	21.6096i	−0.457404	−	0.792247i
$745$		0			0
$746$		−	6.50326i		−	0.238101i
$747$	0.373572	+	0.215682i	0.0136683	+	0.00789138i
$748$	17.5773	+	10.1483i	0.642692	+	0.371058i
$749$		−	17.3589i		−	0.634279i
$750$		0			0
$751$	−1.63968	−	2.84001i	−0.0598329	−	0.103634i	0.834557	−	0.550921i	$-0.185723\pi$
$751$	−1.63968	−	2.84001i	−0.0598329	−	0.103634i	−0.894390	+	0.447287i	$0.852390\pi$
$752$	2.64218	−	1.52546i	0.0963502	−	0.0556278i
$753$	22.2379			0.810393
$754$	−0.848867	+	0.791689i	−0.0309139	+	0.0288316i
$755$		0			0
$756$	2.67535	−	1.54462i	0.0973017	−	0.0561772i
$757$	−22.0038	−	38.1116i	−0.799740	−	1.38519i	−0.919785	−	0.392422i	$-0.871637\pi$
$757$	−22.0038	−	38.1116i	−0.799740	−	1.38519i	0.120045	−	0.992768i	$-0.461696\pi$
$758$	6.44094	−	11.1560i	0.233945	−	0.405205i
$759$			36.8588i			1.33789i
$760$		0			0
$761$	−6.30621	−	3.64089i	−0.228600	−	0.131982i	0.381326	−	0.924441i	$-0.375468\pi$
$761$	−6.30621	−	3.64089i	−0.228600	−	0.131982i	−0.609926	+	0.792458i	$0.708801\pi$
$762$		−	4.73935i		−	0.171689i
$763$	−10.5923	+	18.3464i	−0.383467	+	0.664184i
$764$	14.6137	+	25.3117i	0.528706	+	0.915745i
$765$		0			0
$766$	8.35099			0.301734
$767$	6.32913	−	5.90281i	0.228532	−	0.213138i
$768$	15.0961			0.544733
$769$	1.50534	−	0.869107i	0.0542839	−	0.0313408i	−0.472612	−	0.881270i	$-0.656689\pi$
$769$	1.50534	−	0.869107i	0.0542839	−	0.0313408i	0.526896	+	0.849930i	$0.323356\pi$
$770$		0			0
$771$	−1.17173	+	2.02950i	−0.0421990	+	0.0730908i
$772$			16.2830i			0.586039i
$773$	−7.04969	−	4.07014i	−0.253560	−	0.146393i	0.367833	−	0.929892i	$-0.380100\pi$
$773$	−7.04969	−	4.07014i	−0.253560	−	0.146393i	−0.621393	+	0.783499i	$0.713433\pi$
$774$	−1.72150	−	0.993909i	−0.0618781	−	0.0357253i
$775$		0			0
$776$	−7.32994	+	12.6958i	−0.263130	+	0.455754i
$777$	−12.4762	−	21.6095i	−0.447582	−	0.775235i
$778$	5.97815	−	3.45149i	0.214327	−	0.123742i
$779$	49.5137			1.77401
$780$		0			0
$781$	22.2435			0.795936
$782$	−17.7820	+	10.2665i	−0.635884	+	0.367128i
$783$	0.192985	+	0.334259i	0.00689671	+	0.0119455i
$784$	−0.215288	+	0.372889i	−0.00768884	+	0.0133175i
$785$		0			0
$786$	−13.8442	−	7.99296i	−0.493807	−	0.285100i
$787$	−30.8197	−	17.7937i	−1.09860	−	0.634278i	−0.162749	−	0.986668i	$-0.552036\pi$
$787$	−30.8197	−	17.7937i	−1.09860	−	0.634278i	−0.935854	+	0.352389i	$0.885369\pi$
$788$			19.8614i			0.707535i
$789$	5.67625	−	9.83155i	0.202080	−	0.350012i
$790$		0			0
$791$	11.9634	−	6.90709i	0.425370	−	0.245588i
$792$	13.3036			0.472724
$793$	−30.1854	−	32.3655i	−1.07192	−	1.14933i
$794$	14.6402			0.519563
$795$		0			0
$796$	5.25918	+	9.10917i	0.186407	+	0.322866i
$797$	24.9553	−	43.2239i	0.883962	−	1.53107i	0.0370643	−	0.999313i	$-0.488199\pi$
$797$	24.9553	−	43.2239i	0.883962	−	1.53107i	0.846898	−	0.531755i	$-0.178467\pi$
$798$		−	13.2069i		−	0.467520i
$799$	27.5000	+	15.8771i	0.972880	+	0.561692i
$800$		0			0
$801$		−	0.668519i		−	0.0236210i
$802$	8.86134	−	15.3483i	0.312905	−	0.541967i
$803$	−0.154135	−	0.266969i	−0.00543930	−	0.00942115i
$804$	−5.68240	+	3.28074i	−0.200403	+	0.115703i
$805$		0			0
$806$	−26.5294	+	6.12669i	−0.934458	+	0.215804i
$807$	29.5388			1.03982
$808$	4.25246	−	2.45516i	0.149601	−	0.0863722i
$809$	−10.2363	−	17.7298i	−0.359889	−	0.623345i	0.628053	−	0.778170i	$-0.283852\pi$
$809$	−10.2363	−	17.7298i	−0.359889	−	0.623345i	−0.987942	+	0.154825i	$0.950519\pi$
$810$		0			0
$811$			5.35182i			0.187928i	0.995576	+	0.0939638i	$0.0299538\pi$
$811$			5.35182i			0.187928i	−0.995576	+	0.0939638i	$0.970046\pi$
$812$	1.03261	+	0.596175i	0.0362374	+	0.0209216i
$813$	−2.54465	−	1.46916i	−0.0892448	−	0.0515255i
$814$		−	42.4158i		−	1.48667i
$815$		0			0
$816$	−0.499278	−	0.864775i	−0.0174782	−	0.0302732i
$817$	13.7976	−	7.96603i	0.482716	−	0.278696i
$818$	7.42270			0.259529
$819$	−1.92161	−	8.32082i	−0.0671464	−	0.290753i
$820$		0			0
$821$	15.6448	−	9.03251i	0.546006	−	0.315237i	−0.201503	−	0.979488i	$-0.564583\pi$
$821$	15.6448	−	9.03251i	0.546006	−	0.315237i	0.747510	+	0.664251i	$0.231249\pi$
$822$	−1.30084	−	2.25312i	−0.0453720	−	0.0785865i
$823$	25.3347	−	43.8810i	0.883112	−	1.52960i	0.0352505	−	0.999379i	$-0.488777\pi$
$823$	25.3347	−	43.8810i	0.883112	−	1.52960i	0.847862	−	0.530217i	$-0.177890\pi$
$824$		−	20.4285i		−	0.711660i
$825$		0			0
$826$	4.10672	+	2.37101i	0.142891	+	0.0824981i
$827$		−	22.6359i		−	0.787127i	−0.919297	−	0.393563i	$-0.871242\pi$
$827$		−	22.6359i		−	0.787127i	0.919297	−	0.393563i	$-0.128758\pi$
$828$	4.97975	−	8.62518i	0.173058	−	0.299746i
$829$	5.46126	+	9.45918i	0.189677	+	0.328531i	0.945143	−	0.326658i	$-0.105922\pi$
$829$	5.46126	+	9.45918i	0.189677	+	0.328531i	−0.755465	+	0.655189i	$0.772589\pi$
$830$		0			0
$831$	32.8949			1.14111
$832$	4.41982	−	14.4601i	0.153230	−	0.501314i
$833$	−4.48146			−0.155274
$834$	−2.55357	+	1.47431i	−0.0884230	+	0.0510510i
$835$		0			0
$836$	−21.0441	+	36.4495i	−0.727826	+	1.26063i
$837$			9.05365i			0.312940i
$838$	−2.02313	−	1.16805i	−0.0698879	−	0.0403498i
$839$	−47.2584	−	27.2846i	−1.63154	−	0.941970i	−0.983619	−	0.180263i	$-0.942305\pi$
$839$	−47.2584	−	27.2846i	−1.63154	−	0.941970i	−0.647921	−	0.761707i	$-0.724361\pi$
$840$		0			0
$841$	14.4255	−	24.9857i	0.497432	−	0.861577i
$842$	−6.56713	−	11.3746i	−0.226318	−	0.391995i
$843$	−15.6479	+	9.03430i	−0.538941	+	0.311158i
$844$	−34.5710			−1.18998
$845$		0			0
$846$	8.21571			0.282462
$847$	25.2297	−	14.5664i	0.866902	−	0.500506i
$848$	1.98653	+	3.44076i	0.0682176	+	0.118156i
$849$	4.56599	−	7.90853i	0.156705	−	0.271420i
$850$		0			0
$851$	−69.6676	−	40.2226i	−2.38817	−	1.37881i
$852$	−5.20511	−	3.00517i	−0.178324	−	0.102956i
$853$		−	4.25275i		−	0.145611i	−0.997346	−	0.0728057i	$-0.976805\pi$
$853$		−	4.25275i		−	0.145611i	0.997346	−	0.0728057i	$-0.0231953\pi$
$854$	12.1248	−	21.0007i	0.414901	−	0.718629i
$855$		0			0
$856$	−17.4931	+	10.0997i	−0.597903	+	0.345199i
$857$	−42.6525			−1.45698			−0.728490	−	0.685056i	$-0.759778\pi$
$857$	−42.6525			−1.45698			−0.728490	+	0.685056i	$0.759778\pi$
$858$	4.24329	−	13.8826i	0.144864	−	0.473943i
$859$	35.0427			1.19564			0.597820	−	0.801630i	$-0.296034\pi$
$859$	35.0427			1.19564			0.597820	+	0.801630i	$0.296034\pi$
$860$		0			0
$861$	8.77128	+	15.1923i	0.298925	+	0.517752i
$862$	2.06576	−	3.57801i	0.0703602	−	0.121867i
$863$			20.6468i			0.702827i	0.936220	+	0.351413i	$0.114299\pi$
$863$			20.6468i			0.702827i	−0.936220	+	0.351413i	$0.885701\pi$
$864$	−4.99742	−	2.88526i	−0.170016	−	0.0981586i
$865$		0			0
$866$		−	3.88425i		−	0.131992i
$867$	−3.30347	+	5.72178i	−0.112192	+	0.194322i
$868$	13.9844	+	24.2217i	0.474662	+	0.822139i
$869$	−21.4505	+	12.3845i	−0.727660	+	0.420115i
$870$		0			0
$871$	4.08146	+	17.6733i	0.138295	+	0.598836i
$872$	24.6510			0.834790
$873$	4.60647	−	2.65955i	0.155906	−	0.0900121i
$874$	−21.2892	−	36.8739i	−0.720117	−	1.24728i
$875$		0			0
$876$			0.0832965i			0.00281433i
$877$	−9.68193	−	5.58987i	−0.326936	−	0.188756i	0.327544	−	0.944836i	$-0.393779\pi$
$877$	−9.68193	−	5.58987i	−0.326936	−	0.188756i	−0.654480	+	0.756080i	$0.727112\pi$
$878$	−14.3088	−	8.26121i	−0.482900	−	0.278802i
$879$		−	0.792946i		−	0.0267454i
$880$		0			0
$881$	−2.82282	−	4.88927i	−0.0951033	−	0.164724i	0.814548	−	0.580096i	$-0.196985\pi$
$881$	−2.82282	−	4.88927i	−0.0951033	−	0.164724i	−0.909652	+	0.415372i	$0.863651\pi$
$882$	−1.00414	+	0.579740i	−0.0338111	+	0.0195208i
$883$	−49.4552			−1.66430			−0.832149	−	0.554551i	$-0.812890\pi$
$883$	−49.4552			−1.66430			−0.832149	+	0.554551i	$0.812890\pi$
$884$	−14.7718	+	3.41140i	−0.496830	+	0.114738i
$885$		0			0
$886$	0.322845	−	0.186395i	0.0108462	−	0.00626206i
$887$	−4.25593	−	7.37149i	−0.142900	−	0.247510i	0.785687	−	0.618624i	$-0.212309\pi$
$887$	−4.25593	−	7.37149i	−0.142900	−	0.247510i	−0.928588	+	0.371113i	$0.878976\pi$
$888$	−14.5177	+	25.1454i	−0.487183	+	0.843825i
$889$			13.4580i			0.451368i
$890$		0			0
$891$	−4.18031	−	2.41350i	−0.140046	−	0.0808553i
$892$		−	18.0366i		−	0.603908i
$893$	−32.9238	+	57.0257i	−1.10175	+	1.90829i
$894$	4.72932	+	8.19141i	0.158172	+	0.273962i
$895$		0			0
$896$	−19.0503			−0.636427
$897$	−18.7781	−	20.1343i	−0.626981	−	0.672264i
$898$	−20.2648			−0.676244
$899$	−3.02627	+	1.74722i	−0.100932	+	0.0582730i
$900$		0			0
$901$	−20.6759	+	35.8118i	−0.688815	+	1.19306i
$902$			29.8200i			0.992899i
$903$	4.88844	+	2.82234i	0.162677	+	0.0939216i
$904$	−13.9210	−	8.03730i	−0.463006	−	0.267317i
$905$		0			0
$906$	8.09898	−	14.0278i	0.269070	−	0.466044i
$907$	−12.6022	−	21.8276i	−0.418449	−	0.724775i	0.577335	−	0.816508i	$-0.304093\pi$
$907$	−12.6022	−	21.8276i	−0.418449	−	0.724775i	−0.995784	+	0.0917326i	$0.970760\pi$
$908$	13.6326	−	7.87080i	0.452414	−	0.261202i
$909$	−1.78163			−0.0590929
$910$		0			0
$911$	29.3382			0.972017			0.486008	−	0.873954i	$-0.338452\pi$
$911$	29.3382			0.972017			0.486008	+	0.873954i	$0.338452\pi$
$912$	1.79325	−	1.03533i	0.0593805	−	0.0342834i
$913$	−1.04110	−	1.80323i	−0.0344552	−	0.0596782i
$914$	−10.3813	+	17.9809i	−0.343382	+	0.594755i
$915$		0			0
$916$	0.391220	+	0.225871i	0.0129263	+	0.00746298i
$917$	39.3125	+	22.6971i	1.29821	+	0.749524i
$918$		−	2.68897i		−	0.0887494i
$919$	3.92444	−	6.79734i	0.129455	−	0.224223i	−0.794010	−	0.607904i	$-0.792010\pi$
$919$	3.92444	−	6.79734i	0.129455	−	0.224223i	0.923466	+	0.383681i	$0.125344\pi$
$920$		0			0
$921$	−5.18584	+	2.99405i	−0.170879	+	0.0986572i
$922$	−16.1779			−0.532792
$923$	−12.1506	+	11.3322i	−0.399942	+	0.373003i
$924$	−14.9117			−0.490560
$925$		0			0
$926$	6.77608	+	11.7365i	0.222676	+	0.385686i
$927$	−3.70607	+	6.41910i	−0.121723	+	0.210831i
$928$		−	2.22725i		−	0.0731130i
$929$	42.3758	+	24.4657i	1.39031	+	0.802693i	0.993349	−	0.115144i	$-0.0367331\pi$
$929$	42.3758	+	24.4657i	1.39031	+	0.802693i	0.396956	+	0.917837i	$0.370066\pi$
$930$		0			0
$931$		−	9.29305i		−	0.304567i
$932$	−6.11834	+	10.5973i	−0.200413	+	0.347125i
$933$	−5.31335	−	9.20299i	−0.173951	−	0.301292i
$934$	23.1008	−	13.3373i	0.755882	−	0.436409i
$935$		0			0
$936$	−7.26715	+	6.77765i	−0.237534	+	0.221535i
$937$	10.6173			0.346851			0.173425	−	0.984847i	$-0.444516\pi$
$937$	10.6173			0.346851			0.173425	+	0.984847i	$0.444516\pi$
$938$	−8.60698	+	4.96924i	−0.281028	+	0.162251i
$939$	0.152475	+	0.264094i	0.00497583	+	0.00861839i
$940$		0			0
$941$			32.1160i			1.04695i	0.852040	+	0.523476i	$0.175365\pi$
$941$			32.1160i			1.04695i	−0.852040	+	0.523476i	$0.824635\pi$
$942$	−4.79458	−	2.76815i	−0.156216	−	0.0901913i
$943$	48.9791	+	28.2781i	1.59498	+	0.920861i
$944$			0.743486i			0.0241984i
$945$		0			0
$946$	4.79760	+	8.30969i	0.155984	+	0.270171i
$947$	−23.7176	+	13.6934i	−0.770718	+	0.444974i	−0.833131	−	0.553076i	$-0.813454\pi$
$947$	−23.7176	+	13.6934i	−0.770718	+	0.444974i	0.0624128	+	0.998050i	$0.480120\pi$
$948$	6.69273			0.217370
$949$	0.220207	+	0.0673076i	0.00714821	+	0.00218490i
$950$		0			0
$951$	−0.979411	+	0.565463i	−0.0317596	+	0.0183364i
$952$	−10.5223	−	18.2252i	−0.341031	−	0.590682i
$953$	20.1081	−	34.8282i	0.651365	−	1.12820i	−0.331427	−	0.943481i	$-0.607530\pi$
$953$	20.1081	−	34.8282i	0.651365	−	1.12820i	0.982792	−	0.184716i	$-0.0591367\pi$
$954$			10.6989i			0.346389i
$955$		0			0
$956$	23.2024	+	13.3959i	0.750418	+	0.433254i
$957$		−	1.86308i		−	0.0602247i
$958$	15.3269	−	26.5470i	0.495190	−	0.857694i
$959$	3.69391	+	6.39803i	0.119282	+	0.206603i
$960$		0			0
$961$	−50.9686			−1.64415
$962$	21.6091	+	23.1698i	0.696706	+	0.747024i
$963$	7.32899			0.236173
$964$	12.6919	−	7.32766i	0.408778	−	0.236008i
$965$		0			0
$966$	7.54269	−	13.0643i	0.242682	−	0.420338i
$967$			12.1127i			0.389518i	0.980851	+	0.194759i	$0.0623924\pi$
$967$			12.1127i			0.389518i	−0.980851	+	0.194759i	$0.937608\pi$
$968$	−29.3580	−	16.9499i	−0.943603	−	0.544789i
$969$	18.6643	+	10.7759i	0.599585	+	0.346170i
$970$		0			0
$971$	−27.2888	+	47.2656i	−0.875740	+	1.51683i	−0.0197681	+	0.999805i	$0.506293\pi$
$971$	−27.2888	+	47.2656i	−0.875740	+	1.51683i	−0.855972	+	0.517022i	$0.827041\pi$
$972$	0.652144	+	1.12955i	0.0209175	+	0.0362302i
$973$	7.25122	−	4.18649i	0.232463	−	0.134213i
$974$	−2.19972			−0.0704836
$975$		0			0
$976$	3.80200			0.121699
$977$	36.3036	−	20.9599i	1.16146	−	0.670567i	0.209804	−	0.977743i	$-0.432717\pi$
$977$	36.3036	−	20.9599i	1.16146	−	0.670567i	0.951653	+	0.307176i	$0.0993841\pi$
$978$	4.74151	+	8.21253i	0.151617	+	0.262608i
$979$	−1.61347	+	2.79461i	−0.0515668	+	0.0893163i
$980$		0			0
$981$	−7.74593	−	4.47211i	−0.247308	−	0.142784i
$982$	−0.187785	−	0.108418i	−0.00599247	−	0.00345976i
$983$		−	24.7811i		−	0.790396i	−0.918596	−	0.395198i	$-0.870676\pi$
$983$		−	24.7811i		−	0.790396i	0.918596	−	0.395198i	$-0.129324\pi$
$984$	10.2065	−	17.6782i	0.325373	−	0.563562i
$985$		0			0
$986$	0.898815	−	0.518931i	0.0286241	−	0.0165261i
$987$	−23.3296			−0.742590
$988$	−7.07409	−	30.6318i	−0.225057	−	0.974527i
$989$	18.1981			0.578666
$990$		0			0
$991$	−6.35945	−	11.0149i	−0.202015	−	0.349899i	0.747163	−	0.664641i	$-0.231415\pi$
$991$	−6.35945	−	11.0149i	−0.202015	−	0.349899i	−0.949177	+	0.314742i	$0.898082\pi$
$992$	26.1222	−	45.2449i	0.829380	−	1.43653i
$993$		−	0.434661i		−	0.0137936i
$994$	−7.88404	−	4.55185i	−0.250067	−	0.144376i
$995$		0			0
$996$			0.562622i			0.0178274i
$997$	5.29376	−	9.16906i	0.167655	−	0.290387i	−0.769940	−	0.638116i	$-0.779714\pi$
$997$	5.29376	−	9.16906i	0.167655	−	0.290387i	0.937595	+	0.347729i	$0.113047\pi$
$998$	7.49463	+	12.9811i	0.237238	+	0.410909i
$999$	9.12360	−	5.26752i	0.288658	−	0.166657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.l.751.3	yes	12
5.2	odd	4		975.2.w.k.49.5		24
5.3	odd	4		975.2.w.k.49.8		24
5.4	even	2		975.2.bc.k.751.4	✓	12
13.4	even	6	inner	975.2.bc.l.901.3	yes	12
65.4	even	6		975.2.bc.k.901.4	yes	12
65.17	odd	12		975.2.w.k.199.8		24
65.43	odd	12		975.2.w.k.199.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.w.k.49.5		24	5.2	odd	4
975.2.w.k.49.8		24	5.3	odd	4
975.2.w.k.199.5		24	65.43	odd	12
975.2.w.k.199.8		24	65.17	odd	12
975.2.bc.k.751.4	✓	12	5.4	even	2
975.2.bc.k.901.4	yes	12	65.4	even	6
975.2.bc.l.751.3	yes	12	1.1	even	1	trivial
975.2.bc.l.901.3	yes	12	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.722346 + 0.417047i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.652144 + 1.12955i) q^{4} +(-0.722346 - 0.417047i) q^{6} +(2.05120 + 1.18426i) q^{7} -2.75609i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.722346 + 0.417047i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.652144 + 1.12955i) q^{4} +(-0.722346 - 0.417047i) q^{6} +(2.05120 + 1.18426i) q^{7} -2.75609i q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.18031 - 2.41350i) q^{11} -1.30429 q^{12} +(-1.05393 + 3.44808i) q^{13} -1.97557 q^{14} +(-0.154871 - 0.268245i) q^{16} +(1.61191 - 2.79192i) q^{17} -0.834094i q^{18} +(5.78949 + 3.34257i) q^{19} +2.36852i q^{21} +(-2.01309 + 3.48677i) q^{22} +(3.81798 + 6.61294i) q^{23} +(2.38684 - 1.37804i) q^{24} +(-0.676709 - 2.93024i) q^{26} -1.00000 q^{27} +(-2.67535 + 1.54462i) q^{28} +(-0.192985 - 0.334259i) q^{29} -9.05365i q^{31} +(4.99742 + 2.88526i) q^{32} +(4.18031 + 2.41350i) q^{33} +2.68897i q^{34} +(-0.652144 - 1.12955i) q^{36} +(-9.12360 + 5.26752i) q^{37} -5.57603 q^{38} +(-3.51309 + 0.811311i) q^{39} +(6.41426 - 3.70327i) q^{41} +(-0.987784 - 1.71089i) q^{42} +(1.19160 - 2.06392i) q^{43} +6.29580i q^{44} +(-5.51581 - 3.18456i) q^{46} +9.84986i q^{47} +(0.154871 - 0.268245i) q^{48} +(-0.695053 - 1.20387i) q^{49} +3.22383 q^{51} +(-3.20745 - 3.43910i) q^{52} -12.8269 q^{53} +(0.722346 - 0.417047i) q^{54} +(3.26392 - 5.65328i) q^{56} +6.68513i q^{57} +(0.278804 + 0.160967i) q^{58} +(-2.07875 - 1.20017i) q^{59} +(-6.13735 + 10.6302i) q^{61} +(3.77580 + 6.53987i) q^{62} +(-2.05120 + 1.18426i) q^{63} -4.19367 q^{64} -4.02617 q^{66} +(4.35671 - 2.51535i) q^{67} +(2.10240 + 3.64146i) q^{68} +(-3.81798 + 6.61294i) q^{69} +(3.99077 + 2.30407i) q^{71} +(2.38684 + 1.37804i) q^{72} -0.0638636i q^{73} +(4.39360 - 7.60994i) q^{74} +(-7.55117 + 4.35967i) q^{76} +11.4329 q^{77} +(2.19931 - 2.05117i) q^{78} -5.13133 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.08888 + 5.35009i) q^{82} -0.431363i q^{83} +(-2.67535 - 1.54462i) q^{84} +1.98782i q^{86} +(0.192985 - 0.334259i) q^{87} +(-6.65182 - 11.5213i) q^{88} +(-0.578954 + 0.334259i) q^{89} +(-6.24524 + 5.82457i) q^{91} -9.95950 q^{92} +(7.84069 - 4.52683i) q^{93} +(-4.10785 - 7.11501i) q^{94} +5.77053i q^{96} +(-4.60647 - 2.65955i) q^{97} +(1.00414 + 0.579740i) q^{98} +4.82700i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9} + 9 q^{11} + 16 q^{12} - 3 q^{13} + 10 q^{14} - 4 q^{16} - 9 q^{19} + 15 q^{22} + q^{23} - 5 q^{26} - 12 q^{27} - 39 q^{28} - 16 q^{29} + 30 q^{32} + 9 q^{33} + 8 q^{36} - 15 q^{37} + 30 q^{38} - 3 q^{39} + 18 q^{41} + 5 q^{42} + q^{43} - 45 q^{46} + 4 q^{48} + 31 q^{49} - 40 q^{52} - 16 q^{53} + 25 q^{56} - 30 q^{58} + 54 q^{59} - 11 q^{61} - 20 q^{62} + 3 q^{63} + 16 q^{64} + 30 q^{66} + 45 q^{67} - 30 q^{68} - q^{69} - 33 q^{71} + 5 q^{74} - 27 q^{76} - 28 q^{77} + 20 q^{78} + 18 q^{79} - 6 q^{81} - 20 q^{82} - 39 q^{84} + 16 q^{87} - 5 q^{88} - 48 q^{89} - 29 q^{91} + 46 q^{92} - 12 q^{93} - 30 q^{94} - 9 q^{97} + 105 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9 + 9 * q^11 + 16 * q^12 - 3 * q^13 + 10 * q^14 - 4 * q^16 - 9 * q^19 + 15 * q^22 + q^23 - 5 * q^26 - 12 * q^27 - 39 * q^28 - 16 * q^29 + 30 * q^32 + 9 * q^33 + 8 * q^36 - 15 * q^37 + 30 * q^38 - 3 * q^39 + 18 * q^41 + 5 * q^42 + q^43 - 45 * q^46 + 4 * q^48 + 31 * q^49 - 40 * q^52 - 16 * q^53 + 25 * q^56 - 30 * q^58 + 54 * q^59 - 11 * q^61 - 20 * q^62 + 3 * q^63 + 16 * q^64 + 30 * q^66 + 45 * q^67 - 30 * q^68 - q^69 - 33 * q^71 + 5 * q^74 - 27 * q^76 - 28 * q^77 + 20 * q^78 + 18 * q^79 - 6 * q^81 - 20 * q^82 - 39 * q^84 + 16 * q^87 - 5 * q^88 - 48 * q^89 - 29 * q^91 + 46 * q^92 - 12 * q^93 - 30 * q^94 - 9 * q^97 + 105 * q^98

Introduction

L-functions

Modular forms

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Database

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