LMFDB - Embedded newform 975.2.bc.i.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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.3
Root			$0.500000 - 0.564882i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.i.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.260797 + 0.150571i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.954656 + 1.65351i) q^{4} +(-0.260797 - 0.150571i) q^{6} +(-2.97125 - 1.71545i) q^{7} -1.17726i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.260797 + 0.150571i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.954656 + 1.65351i) q^{4} +(-0.260797 - 0.150571i) q^{6} +(-2.97125 - 1.71545i) q^{7} -1.17726i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.28749 - 1.32068i) q^{11} -1.90931 q^{12} +(-0.572034 - 3.55988i) q^{13} +1.03319 q^{14} +(-1.73205 - 3.00000i) q^{16} +(-0.0403455 + 0.0698805i) q^{17} -0.301143i q^{18} +(0.824892 + 0.476251i) q^{19} -3.43091i q^{21} +(-0.397714 + 0.688861i) q^{22} +(-0.110226 - 0.190917i) q^{23} +(1.01954 - 0.588631i) q^{24} +(0.685202 + 0.842277i) q^{26} -1.00000 q^{27} +(5.67305 - 3.27534i) q^{28} +(-4.82362 - 8.35476i) q^{29} +1.57498i q^{31} +(2.94251 + 1.69886i) q^{32} +(2.28749 + 1.32068i) q^{33} -0.0242995i q^{34} +(-0.954656 - 1.65351i) q^{36} +(2.47841 - 1.43091i) q^{37} -0.286840 q^{38} +(2.79693 - 2.27534i) q^{39} +(6.89590 - 3.98135i) q^{41} +(0.516597 + 0.894772i) q^{42} +(4.46704 - 7.73715i) q^{43} +5.04319i q^{44} +(0.0574933 + 0.0331938i) q^{46} +8.52159i q^{47} +(1.73205 - 3.00000i) q^{48} +(2.38556 + 4.13192i) q^{49} -0.0806910 q^{51} +(6.43241 + 2.45260i) q^{52} -5.28273 q^{53} +(0.260797 - 0.150571i) q^{54} +(-2.01954 + 3.49794i) q^{56} +0.952503i q^{57} +(2.51598 + 1.45260i) q^{58} +(-8.37841 - 4.83728i) q^{59} +(6.49373 - 11.2475i) q^{61} +(-0.237147 - 0.410750i) q^{62} +(2.97125 - 1.71545i) q^{63} +5.90501 q^{64} -0.795428 q^{66} +(-2.17001 + 1.25286i) q^{67} +(-0.0770322 - 0.133424i) q^{68} +(0.110226 - 0.190917i) q^{69} +(4.58363 + 2.64636i) q^{71} +(1.01954 + 0.588631i) q^{72} +14.3591i q^{73} +(-0.430908 + 0.746354i) q^{74} +(-1.57498 + 0.909313i) q^{76} -9.06228 q^{77} +(-0.386832 + 1.01454i) q^{78} +11.8661 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.19895 + 2.07665i) q^{82} -9.58956i q^{83} +(5.67305 + 3.27534i) q^{84} +2.69044i q^{86} +(4.82362 - 8.35476i) q^{87} +(-1.55479 - 2.69297i) q^{88} +(-9.17319 + 5.29614i) q^{89} +(-4.40716 + 11.5586i) q^{91} +0.420912 q^{92} +(-1.36397 + 0.787488i) q^{93} +(-1.28311 - 2.22241i) q^{94} +3.39771i q^{96} +(4.05202 + 2.33943i) q^{97} +(-1.24430 - 0.718396i) q^{98} +2.64136i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} + 4 q^{3} + 4 q^{4} - 6 q^{6} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 + 4 * q^3 + 4 * q^4 - 6 * q^6 - 6 * q^7 - 4 * q^9	$ 8 q - 6 q^{2} + 4 q^{3} + 4 q^{4} - 6 q^{6} - 6 q^{7} - 4 q^{9} + 12 q^{11} + 8 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{17} + 12 q^{19} - 4 q^{23} - 12 q^{24} - 4 q^{26} - 8 q^{27} + 12 q^{28} - 6 q^{29} - 12 q^{32} + 12 q^{33} + 4 q^{36} + 12 q^{37} + 16 q^{38} - 30 q^{41} - 2 q^{42} - 6 q^{43} + 36 q^{46} - 8 q^{49} + 4 q^{51} + 20 q^{52} + 32 q^{53} + 6 q^{54} + 4 q^{56} - 12 q^{58} - 30 q^{59} + 30 q^{62} + 6 q^{63} + 32 q^{64} - 30 q^{67} - 16 q^{68} + 4 q^{69} + 18 q^{71} - 12 q^{72} + 12 q^{74} + 8 q^{77} - 14 q^{78} + 56 q^{79} - 4 q^{81} + 24 q^{82} + 12 q^{84} + 6 q^{87} - 8 q^{88} - 18 q^{89} - 16 q^{91} - 40 q^{92} + 24 q^{93} - 16 q^{94} + 6 q^{97} + 12 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 + 4 * q^3 + 4 * q^4 - 6 * q^6 - 6 * q^7 - 4 * q^9 + 12 * q^11 + 8 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^17 + 12 * q^19 - 4 * q^23 - 12 * q^24 - 4 * q^26 - 8 * q^27 + 12 * q^28 - 6 * q^29 - 12 * q^32 + 12 * q^33 + 4 * q^36 + 12 * q^37 + 16 * q^38 - 30 * q^41 - 2 * q^42 - 6 * q^43 + 36 * q^46 - 8 * q^49 + 4 * q^51 + 20 * q^52 + 32 * q^53 + 6 * q^54 + 4 * q^56 - 12 * q^58 - 30 * q^59 + 30 * q^62 + 6 * q^63 + 32 * q^64 - 30 * q^67 - 16 * q^68 + 4 * q^69 + 18 * q^71 - 12 * q^72 + 12 * q^74 + 8 * q^77 - 14 * q^78 + 56 * q^79 - 4 * q^81 + 24 * q^82 + 12 * q^84 + 6 * q^87 - 8 * q^88 - 18 * q^89 - 16 * q^91 - 40 * q^92 + 24 * q^93 - 16 * q^94 + 6 * q^97 + 12 * 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 $

$2$	−0.260797	+	0.150571i	−0.184412	+	0.106470i	−0.589364	−	0.807868i	$-0.700622\pi$
$2$	−0.260797	+	0.150571i	−0.184412	+	0.106470i	0.404952	+	0.914338i	$0.367288\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.954656	+	1.65351i	−0.477328	+	0.826757i
$5$		0			0
$5$		0			0
$6$	−0.260797	−	0.150571i	−0.106470	−	0.0614706i
$7$	−2.97125	−	1.71545i	−1.12303	−	0.648381i	−0.180856	−	0.983510i	$-0.557887\pi$
$7$	−2.97125	−	1.71545i	−1.12303	−	0.648381i	−0.942172	+	0.335129i	$0.891220\pi$
$8$		−	1.17726i		−	0.416225i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.28749	−	1.32068i	0.689704	−	0.398201i	−0.113797	−	0.993504i	$-0.536301\pi$
$11$	2.28749	−	1.32068i	0.689704	−	0.398201i	0.803501	+	0.595303i	$0.202968\pi$
$12$	−1.90931			−0.551171
$13$	−0.572034	−	3.55988i	−0.158654	−	0.987334i
$13$	−0.572034	−	3.55988i	−0.158654	−	0.987334i
$14$	1.03319			0.276133
$15$		0			0
$16$	−1.73205	−	3.00000i	−0.433013	−	0.750000i
$17$	−0.0403455	+	0.0698805i	−0.00978522	+	0.0169485i	−0.870877	−	0.491502i	$-0.836448\pi$
$17$	−0.0403455	+	0.0698805i	−0.00978522	+	0.0169485i	0.861091	+	0.508450i	$0.169781\pi$
$18$		−	0.301143i		−	0.0709801i
$19$	0.824892	+	0.476251i	0.189243	+	0.109260i	0.591628	−	0.806211i	$-0.298485\pi$
$19$	0.824892	+	0.476251i	0.189243	+	0.109260i	−0.402385	+	0.915471i	$0.631819\pi$
$20$		0			0
$21$		−	3.43091i		−	0.748685i
$22$	−0.397714	+	0.688861i	−0.0847929	+	0.146866i
$23$	−0.110226	−	0.190917i	−0.0229837	−	0.0398089i	0.854305	−	0.519772i	$-0.173983\pi$
$23$	−0.110226	−	0.190917i	−0.0229837	−	0.0398089i	−0.877288	+	0.479963i	$0.840650\pi$
$24$	1.01954	−	0.588631i	0.208113	−	0.120154i
$25$		0			0
$26$	0.685202	+	0.842277i	0.134379	+	0.165184i
$27$	−1.00000			−0.192450
$28$	5.67305	−	3.27534i	1.07211	−	0.618981i
$29$	−4.82362	−	8.35476i	−0.895724	−	1.55144i	−0.832905	−	0.553415i	$-0.813324\pi$
$29$	−4.82362	−	8.35476i	−0.895724	−	1.55144i	−0.0628190	−	0.998025i	$-0.520009\pi$
$30$		0			0
$31$			1.57498i			0.282874i	0.989947	+	0.141437i	$0.0451723\pi$
$31$			1.57498i			0.282874i	−0.989947	+	0.141437i	$0.954828\pi$
$32$	2.94251	+	1.69886i	0.520167	+	0.300318i
$33$	2.28749	+	1.32068i	0.398201	+	0.229901i
$34$		−	0.0242995i		−	0.00416734i
$35$		0			0
$36$	−0.954656	−	1.65351i	−0.159109	−	0.275586i
$37$	2.47841	−	1.43091i	0.407447	−	0.235240i	−0.282245	−	0.959342i	$-0.591079\pi$
$37$	2.47841	−	1.43091i	0.407447	−	0.235240i	0.689692	+	0.724103i	$0.257746\pi$
$38$	−0.286840			−0.0465315
$39$	2.79693	−	2.27534i	0.447868	−	0.364346i
$40$		0			0
$41$	6.89590	−	3.98135i	1.07696	−	0.621782i	0.146884	−	0.989154i	$-0.453076\pi$
$41$	6.89590	−	3.98135i	1.07696	−	0.621782i	0.930074	+	0.367372i	$0.119742\pi$
$42$	0.516597	+	0.894772i	0.0797126	+	0.138066i
$43$	4.46704	−	7.73715i	0.681218	−	1.17990i	−0.293392	−	0.955992i	$-0.594784\pi$
$43$	4.46704	−	7.73715i	0.681218	−	1.17990i	0.974609	−	0.223911i	$-0.0718826\pi$
$44$			5.04319i			0.760289i
$45$		0			0
$46$	0.0574933	+	0.0331938i	0.00847693	+	0.00489416i
$47$			8.52159i			1.24300i	0.783413	+	0.621501i	$0.213477\pi$
$47$			8.52159i			1.24300i	−0.783413	+	0.621501i	$0.786523\pi$
$48$	1.73205	−	3.00000i	0.250000	−	0.433013i
$49$	2.38556	+	4.13192i	0.340795	+	0.590274i
$50$		0			0
$51$	−0.0806910			−0.0112990
$52$	6.43241	+	2.45260i	0.892015	+	0.340114i
$53$	−5.28273			−0.725638			−0.362819	−	0.931860i	$-0.618186\pi$
$53$	−5.28273			−0.725638			−0.362819	+	0.931860i	$0.618186\pi$
$54$	0.260797	−	0.150571i	0.0354900	−	0.0204902i
$55$		0			0
$56$	−2.01954	+	3.49794i	−0.269872	+	0.467432i
$57$			0.952503i			0.126162i
$58$	2.51598	+	1.45260i	0.330364	+	0.190736i
$59$	−8.37841	−	4.83728i	−1.09078	−	0.629760i	−0.156993	−	0.987600i	$-0.550180\pi$
$59$	−8.37841	−	4.83728i	−1.09078	−	0.629760i	−0.933783	+	0.357840i	$0.883513\pi$
$60$		0			0
$61$	6.49373	−	11.2475i	0.831437	−	1.44009i	−0.0654609	−	0.997855i	$-0.520852\pi$
$61$	6.49373	−	11.2475i	0.831437	−	1.44009i	0.896898	−	0.442237i	$-0.145815\pi$
$62$	−0.237147	−	0.410750i	−0.0301176	−	0.0521653i
$63$	2.97125	−	1.71545i	0.374343	−	0.216127i
$64$	5.90501			0.738126
$65$		0			0
$66$	−0.795428			−0.0979104
$67$	−2.17001	+	1.25286i	−0.265109	+	0.153061i	−0.626663	−	0.779290i	$-0.715580\pi$
$67$	−2.17001	+	1.25286i	−0.265109	+	0.153061i	0.361554	+	0.932351i	$0.382246\pi$
$68$	−0.0770322	−	0.133424i	−0.00934153	−	0.0161800i
$69$	0.110226	−	0.190917i	0.0132696	−	0.0229837i
$70$		0			0
$71$	4.58363	+	2.64636i	0.543977	+	0.314065i	0.746689	−	0.665173i	$-0.231642\pi$
$71$	4.58363	+	2.64636i	0.543977	+	0.314065i	−0.202712	+	0.979238i	$0.564976\pi$
$72$	1.01954	+	0.588631i	0.120154	+	0.0693708i
$73$			14.3591i			1.68061i	0.542116	+	0.840303i	$0.317623\pi$
$73$			14.3591i			1.68061i	−0.542116	+	0.840303i	$0.682377\pi$
$74$	−0.430908	+	0.746354i	−0.0500920	+	0.0867619i
$75$		0			0
$76$	−1.57498	+	0.909313i	−0.180662	+	0.104305i
$77$	−9.06228			−1.03274
$78$	−0.386832	+	1.01454i	−0.0438001	+	0.114874i
$79$	11.8661			1.33504			0.667522	−	0.744590i	$-0.267355\pi$
$79$	11.8661			1.33504			0.667522	+	0.744590i	$0.267355\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.19895	+	2.07665i	−0.132402	+	0.229328i
$83$		−	9.58956i		−	1.05259i	−0.850302	−	0.526295i	$-0.823581\pi$
$83$		−	9.58956i		−	1.05259i	0.850302	−	0.526295i	$-0.176419\pi$
$84$	5.67305	+	3.27534i	0.618981	+	0.357369i
$85$		0			0
$86$			2.69044i			0.290117i
$87$	4.82362	−	8.35476i	0.517147	−	0.895724i
$88$	−1.55479	−	2.69297i	−0.165741	−	0.287072i
$89$	−9.17319	+	5.29614i	−0.972356	+	0.561390i	−0.899954	−	0.435985i	$-0.856400\pi$
$89$	−9.17319	+	5.29614i	−0.972356	+	0.561390i	−0.0724026	+	0.997375i	$0.523067\pi$
$90$		0			0
$91$	−4.40716	+	11.5586i	−0.461996	+	1.21167i
$92$	0.420912			0.0438831
$93$	−1.36397	+	0.787488i	−0.141437	+	0.0816587i
$94$	−1.28311	−	2.22241i	−0.132343	−	0.229224i
$95$		0			0
$96$			3.39771i			0.346778i
$97$	4.05202	+	2.33943i	0.411420	+	0.237533i	0.691400	−	0.722473i	$-0.256994\pi$
$97$	4.05202	+	2.33943i	0.411420	+	0.237533i	−0.279980	+	0.960006i	$0.590328\pi$
$98$	−1.24430	−	0.718396i	−0.125693	−	0.0725689i
$99$			2.64136i			0.265467i
$100$		0			0
$101$	−3.40137	−	5.89135i	−0.338449	−	0.586211i	0.645692	−	0.763598i	$-0.276569\pi$
$101$	−3.40137	−	5.89135i	−0.338449	−	0.586211i	−0.984141	+	0.177387i	$0.943236\pi$
$102$	0.0210440	−	0.0121498i	0.00208367	−	0.00120301i
$103$	−4.67456			−0.460598			−0.230299	−	0.973120i	$-0.573970\pi$
$103$	−4.67456			−0.460598			−0.230299	+	0.973120i	$0.573970\pi$
$104$	−4.19092	+	0.673434i	−0.410953	+	0.0660357i
$105$		0			0
$106$	1.37772	−	0.795428i	0.133816	−	0.0772588i
$107$	−6.66217	−	11.5392i	−0.644056	−	1.11554i	−0.984519	−	0.175280i	$-0.943917\pi$
$107$	−6.66217	−	11.5392i	−0.644056	−	1.11554i	0.340462	−	0.940258i	$-0.389416\pi$
$108$	0.954656	−	1.65351i	0.0918619	−	0.159109i
$109$		−	5.12976i		−	0.491342i	−0.969353	−	0.245671i	$-0.920992\pi$
$109$		−	5.12976i		−	0.491342i	0.969353	−	0.245671i	$-0.0790083\pi$
$110$		0			0
$111$	2.47841	+	1.43091i	0.235240	+	0.135816i
$112$			11.8850i			1.12303i
$113$	4.08658	−	7.07816i	0.384433	−	0.665857i	−0.607258	−	0.794505i	$-0.707730\pi$
$113$	4.08658	−	7.07816i	0.384433	−	0.665857i	0.991690	+	0.128648i	$0.0410638\pi$
$114$	−0.143420	−	0.248410i	−0.0134325	−	0.0232658i
$115$		0			0
$116$	18.4196			1.71022
$117$	3.36897	+	1.28455i	0.311461	+	0.118756i
$118$	2.91342			0.268203
$119$	0.239753	−	0.138422i	0.0219782	−	0.0126891i
$120$		0			0
$121$	−2.01160	+	3.48419i	−0.182873	+	0.316745i
$122$			3.91108i			0.354093i
$123$	6.89590	+	3.98135i	0.621782	+	0.358986i
$124$	−2.60424	−	1.50356i	−0.233868	−	0.135024i
$125$		0			0
$126$	−0.516597	+	0.894772i	−0.0460221	+	0.0797126i
$127$	−10.4744	−	18.1422i	−0.929456	−	1.60986i	−0.784234	−	0.620465i	$-0.786944\pi$
$127$	−10.4744	−	18.1422i	−0.929456	−	1.60986i	−0.145222	−	0.989399i	$-0.546390\pi$
$128$	−7.42502	+	4.28684i	−0.656286	+	0.378907i
$129$	8.93409			0.786603
$130$		0			0
$131$	−17.0250			−1.48748			−0.743739	−	0.668470i	$-0.766950\pi$
$131$	−17.0250			−1.48748			−0.743739	+	0.668470i	$0.766950\pi$
$132$	−4.36753	+	2.52159i	−0.380145	+	0.219477i
$133$	−1.63397	−	2.83013i	−0.141684	−	0.245403i
$134$	0.377289	−	0.653484i	0.0325928	−	0.0564524i
$135$		0			0
$136$	0.0822676	+	0.0474972i	0.00705439	+	0.00407285i
$137$	−12.9233	−	7.46126i	−1.10411	−	0.637458i	−0.166813	−	0.985989i	$-0.553347\pi$
$137$	−12.9233	−	7.46126i	−1.10411	−	0.637458i	−0.937297	+	0.348530i	$0.886681\pi$
$138$			0.0663876i			0.00565128i
$139$	4.05479	−	7.02310i	0.343923	−	0.595692i	−0.641235	−	0.767345i	$-0.721578\pi$
$139$	4.05479	−	7.02310i	0.343923	−	0.595692i	0.985157	+	0.171653i	$0.0549109\pi$
$140$		0			0
$141$	−7.37992	+	4.26080i	−0.621501	+	0.358824i
$142$	−1.59387			−0.133754
$143$	−6.01000	−	7.38772i	−0.502581	−	0.617792i
$144$	3.46410			0.288675
$145$		0			0
$146$	−2.16207	−	3.74482i	−0.178934	−	0.309923i
$147$	−2.38556	+	4.13192i	−0.196758	+	0.340795i
$148$			5.46410i			0.449146i
$149$	−18.8471	−	10.8814i	−1.54401	−	0.891435i	−0.998580	−	0.0532800i	$-0.983032\pi$
$149$	−18.8471	−	10.8814i	−1.54401	−	0.891435i	−0.545432	−	0.838155i	$-0.683634\pi$
$150$		0			0
$151$		−	14.1688i		−	1.15304i	−0.817082	−	0.576522i	$-0.804409\pi$
$151$		−	14.1688i		−	1.15304i	0.817082	−	0.576522i	$-0.195591\pi$
$152$	0.560673	−	0.971114i	0.0454766	−	0.0787677i
$153$	−0.0403455	−	0.0698805i	−0.00326174	−	0.00564950i
$154$	2.36342	−	1.36452i	0.190450	−	0.109956i
$155$		0			0
$156$	1.09219	+	6.79693i	0.0874454	+	0.544190i
$157$	6.03449			0.481605			0.240802	−	0.970574i	$-0.422589\pi$
$157$	6.03449			0.481605			0.240802	+	0.970574i	$0.422589\pi$
$158$	−3.09465	+	1.78670i	−0.246198	+	0.142142i
$159$	−2.64136	−	4.57498i	−0.209474	−	0.362819i
$160$		0			0
$161$			0.756350i			0.0596088i
$162$	0.260797	+	0.150571i	0.0204902	+	0.0118300i
$163$	17.7138	+	10.2271i	1.38745	+	0.801045i	0.993027	−	0.117885i	$-0.0376113\pi$
$163$	17.7138	+	10.2271i	1.38745	+	0.801045i	0.394423	+	0.918929i	$0.370945\pi$
$164$			15.2033i			1.18718i
$165$		0			0
$166$	1.44391	+	2.50093i	0.112069	+	0.194110i
$167$	14.6704	−	8.46999i	1.13523	−	0.655427i	0.189987	−	0.981787i	$-0.439155\pi$
$167$	14.6704	−	8.46999i	1.13523	−	0.655427i	0.945246	+	0.326359i	$0.105822\pi$
$168$	−4.03908			−0.311622
$169$	−12.3456	+	4.07275i	−0.949658	+	0.313289i
$170$		0			0
$171$	−0.824892	+	0.476251i	−0.0630810	+	0.0364199i
$172$	8.52898	+	14.7726i	0.650329	+	1.12640i
$173$	−9.40534	+	16.2905i	−0.715075	+	1.23855i	0.247856	+	0.968797i	$0.420274\pi$
$173$	−9.40534	+	16.2905i	−0.715075	+	1.23855i	−0.962931	+	0.269749i	$0.913059\pi$
$174$			2.90520i			0.220243i
$175$		0			0
$176$	−7.92409	−	4.57498i	−0.597301	−	0.344852i
$177$		−	9.67456i		−	0.727184i
$178$	1.59490	−	2.76244i	0.119543	−	0.207054i
$179$	5.13842	+	8.90001i	0.384064	+	0.665218i	0.991639	−	0.129044i	$-0.0411910\pi$
$179$	5.13842	+	8.90001i	0.384064	+	0.665218i	−0.607575	+	0.794262i	$0.707858\pi$
$180$		0			0
$181$	−15.0970			−1.12215			−0.561077	−	0.827763i	$-0.689613\pi$
$181$	−15.0970			−1.12215			−0.561077	+	0.827763i	$0.689613\pi$
$182$	−0.591022	−	3.67805i	−0.0438095	−	0.272635i
$183$	12.9875			0.960061
$184$	−0.224759	+	0.129765i	−0.0165695	+	0.00956639i
$185$		0			0
$186$	0.237147	−	0.410750i	0.0173884	−	0.0301176i
$187$			0.213134i			0.0155859i
$188$	−14.0906	−	8.13520i	−1.02766	−	0.593320i
$189$	2.97125	+	1.71545i	0.216127	+	0.124781i
$190$		0			0
$191$	−5.75659	+	9.97070i	−0.416532	+	0.721455i	−0.995588	−	0.0938332i	$-0.970088\pi$
$191$	−5.75659	+	9.97070i	−0.416532	+	0.721455i	0.579056	+	0.815288i	$0.303421\pi$
$192$	2.95250	+	5.11388i	0.213079	+	0.369063i
$193$	−14.6819	+	8.47659i	−1.05682	+	0.610158i	−0.924552	−	0.381055i	$-0.875561\pi$
$193$	−14.6819	+	8.47659i	−1.05682	+	0.610158i	−0.132273	+	0.991213i	$0.542227\pi$
$194$	−1.40901			−0.101161
$195$		0			0
$196$	−9.10958			−0.650684
$197$	10.1868	−	5.88135i	0.725780	−	0.419029i	−0.0910965	−	0.995842i	$-0.529037\pi$
$197$	10.1868	−	5.88135i	0.725780	−	0.419029i	0.816876	+	0.576813i	$0.195704\pi$
$198$	−0.397714	−	0.688861i	−0.0282643	−	0.0489552i
$199$	4.15724	−	7.20056i	0.294699	−	0.510434i	−0.680216	−	0.733012i	$-0.738114\pi$
$199$	4.15724	−	7.20056i	0.294699	−	0.510434i	0.974915	+	0.222578i	$0.0714472\pi$
$200$		0			0
$201$	−2.17001	−	1.25286i	−0.153061	−	0.0883697i
$202$	1.77414	+	1.02430i	0.124828	+	0.0720695i
$203$			33.0988i			2.32308i
$204$	0.0770322	−	0.133424i	0.00539333	−	0.00934153i
$205$		0			0
$206$	1.21911	−	0.703855i	0.0849396	−	0.0490399i
$207$	0.220452			0.0153225
$208$	−9.68886	+	7.88200i	−0.671802	+	0.546519i
$209$	2.51591			0.174029
$210$		0			0
$211$	8.21775	+	14.2336i	0.565733	+	0.979878i	0.996981	+	0.0776450i	$0.0247401\pi$
$211$	8.21775	+	14.2336i	0.565733	+	0.979878i	−0.431248	+	0.902233i	$0.641927\pi$
$212$	5.04319	−	8.73506i	0.346368	−	0.599926i
$213$			5.29272i			0.362651i
$214$	3.47495	+	2.00627i	0.237543	+	0.137146i
$215$		0			0
$216$			1.17726i			0.0801025i
$217$	2.70180	−	4.67965i	0.183410	−	0.317676i
$218$	0.772396	+	1.33783i	0.0523133	+	0.0906093i
$219$	−12.4354	+	7.17956i	−0.840303	+	0.485149i
$220$		0			0
$221$	0.271845	+	0.103651i	0.0182863	+	0.00697234i
$222$	−0.861816			−0.0578413
$223$	1.97139	−	1.13818i	0.132014	−	0.0762185i	−0.432538	−	0.901615i	$-0.642382\pi$
$223$	1.97139	−	1.13818i	0.132014	−	0.0762185i	0.564553	+	0.825397i	$0.309049\pi$
$224$	−5.82862	−	10.0955i	−0.389441	−	0.674532i
$225$		0			0
$226$			2.46129i			0.163722i
$227$	17.0113	+	9.82147i	1.12908	+	0.651874i	0.943703	−	0.330794i	$-0.107316\pi$
$227$	17.0113	+	9.82147i	1.12908	+	0.651874i	0.185376	+	0.982668i	$0.440650\pi$
$228$	−1.57498	−	0.909313i	−0.104305	−	0.0602207i
$229$			6.38800i			0.422131i	0.977472	+	0.211065i	$0.0676933\pi$
$229$			6.38800i			0.422131i	−0.977472	+	0.211065i	$0.932307\pi$
$230$		0			0
$231$	−4.53114	−	7.84816i	−0.298127	−	0.516371i
$232$	−9.83574	+	5.67867i	−0.645748	+	0.372823i
$233$	−20.0391			−1.31280			−0.656402	−	0.754411i	$-0.727922\pi$
$233$	−20.0391			−1.31280			−0.656402	+	0.754411i	$0.727922\pi$
$234$	−1.07203	+	0.172264i	−0.0700811	+	0.0112613i
$235$		0			0
$236$	15.9970	−	9.23588i	1.04132	−	0.601204i
$237$	5.93306	+	10.2764i	0.385394	+	0.667522i
$238$	−0.0416847	+	0.0722001i	−0.00270202	+	0.00468004i
$239$			4.47998i			0.289786i	0.989447	+	0.144893i	$0.0462838\pi$
$239$			4.47998i			0.289786i	−0.989447	+	0.144893i	$0.953716\pi$
$240$		0			0
$241$	−0.535517	−	0.309181i	−0.0344957	−	0.0199161i	0.482653	−	0.875812i	$-0.339673\pi$
$241$	−0.535517	−	0.309181i	−0.0344957	−	0.0199161i	−0.517149	+	0.855896i	$0.673007\pi$
$242$		−	1.21156i		−	0.0778819i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	12.3986	+	21.4750i	0.793737	+	1.37479i
$245$		0			0
$246$	−2.39791			−0.152885
$247$	1.22353	−	3.20895i	0.0778516	−	0.204181i
$248$	1.85416			0.117739
$249$	8.30480	−	4.79478i	0.526295	−	0.303857i
$250$		0			0
$251$	−9.01543	+	15.6152i	−0.569049	+	0.985621i	0.427612	+	0.903963i	$0.359355\pi$
$251$	−9.01543	+	15.6152i	−0.569049	+	0.985621i	−0.996660	+	0.0816587i	$0.973978\pi$
$252$			6.55068i			0.412654i
$253$	−0.504281	−	0.291147i	−0.0317039	−	0.0183042i
$254$	5.46341	+	3.15430i	0.342805	+	0.197918i
$255$		0			0
$256$	−4.61405	+	7.99178i	−0.288378	+	0.499486i
$257$	3.80193	+	6.58514i	0.237158	+	0.410770i	0.959898	−	0.280351i	$-0.0904508\pi$
$257$	3.80193	+	6.58514i	0.237158	+	0.410770i	−0.722740	+	0.691120i	$0.757117\pi$
$258$	−2.32999	+	1.34522i	−0.145059	+	0.0837497i
$259$	−9.81863			−0.610100
$260$		0			0
$261$	9.64725			0.597150
$262$	4.44007	−	2.56347i	0.274308	−	0.158372i
$263$	1.48713	+	2.57579i	0.0917006	+	0.158830i	0.908227	−	0.418478i	$-0.137436\pi$
$263$	1.48713	+	2.57579i	0.0917006	+	0.158830i	−0.816526	+	0.577308i	$0.804103\pi$
$264$	1.55479	−	2.69297i	0.0956906	−	0.165741i
$265$		0			0
$266$	0.852273	+	0.492060i	0.0522562	+	0.0301701i
$267$	−9.17319	−	5.29614i	−0.561390	−	0.324119i
$268$		−	4.78419i		−	0.292241i
$269$	14.0536	−	24.3416i	0.856864	−	1.48413i	−0.0180404	−	0.999837i	$-0.505743\pi$
$269$	14.0536	−	24.3416i	0.856864	−	1.48413i	0.874905	−	0.484295i	$-0.160924\pi$
$270$		0			0
$271$	16.3350	−	9.43101i	0.992279	−	0.572893i	0.0863245	−	0.996267i	$-0.472488\pi$
$271$	16.3350	−	9.43101i	0.992279	−	0.572893i	0.905955	+	0.423374i	$0.139154\pi$
$272$	0.279522			0.0169485
$273$	−12.2136	+	1.96260i	−0.739203	+	0.118782i
$274$	4.49381			0.271481
$275$		0			0
$276$	0.210456	+	0.364520i	0.0126680	+	0.0219415i
$277$	10.7668	−	18.6487i	0.646916	−	1.12049i	−0.336940	−	0.941526i	$-0.609392\pi$
$277$	10.7668	−	18.6487i	0.646916	−	1.12049i	0.983856	−	0.178965i	$-0.0572747\pi$
$278$			2.44214i			0.146470i
$279$	−1.36397	−	0.787488i	−0.0816587	−	0.0471457i
$280$		0			0
$281$			18.5104i			1.10424i	0.833766	+	0.552118i	$0.186180\pi$
$281$			18.5104i			1.10424i	−0.833766	+	0.552118i	$0.813820\pi$
$282$	1.28311	−	2.22241i	0.0764080	−	0.132343i
$283$	−5.07672	−	8.79313i	−0.301780	−	0.522698i	0.674760	−	0.738038i	$-0.264247\pi$
$283$	−5.07672	−	8.79313i	−0.301780	−	0.522698i	−0.976539	+	0.215340i	$0.930914\pi$
$284$	−8.75159	+	5.05273i	−0.519311	+	0.299825i
$285$		0			0
$286$	2.67977	+	1.02176i	0.158458	+	0.0604182i
$287$	−27.3193			−1.61261
$288$	−2.94251	+	1.69886i	−0.173389	+	0.100106i
$289$	8.49674	+	14.7168i	0.499808	+	0.865694i
$290$		0			0
$291$			4.67886i			0.274280i
$292$	−23.7430	−	13.7080i	−1.38945	−	0.802201i
$293$	−14.6080	−	8.43395i	−0.853410	−	0.492716i	0.00838997	−	0.999965i	$-0.497329\pi$
$293$	−14.6080	−	8.43395i	−0.853410	−	0.492716i	−0.861800	+	0.507248i	$0.830663\pi$
$294$		−	1.43679i		−	0.0837954i
$295$		0			0
$296$	−1.68455	−	2.91773i	−0.0979127	−	0.169590i
$297$	−2.28749	+	1.32068i	−0.132734	+	0.0766337i
$298$	6.55369			0.379645
$299$	−0.616589	+	0.501603i	−0.0356583	+	0.0290084i
$300$		0			0
$301$	−26.5454	+	15.3260i	−1.53005	+	0.883377i
$302$	2.13342	+	3.69520i	0.122765	+	0.212635i
$303$	3.40137	−	5.89135i	0.195404	−	0.338449i
$304$		−	3.29957i		−	0.189243i
$305$		0			0
$306$	0.0210440	+	0.0121498i	0.00120301	+	0.000694556i
$307$		−	6.94155i		−	0.396175i	−0.980184	−	0.198088i	$-0.936527\pi$
$307$		−	6.94155i		−	0.396175i	0.980184	−	0.198088i	$-0.0634730\pi$
$308$	8.65136	−	14.9846i	0.492957	−	0.853827i
$309$	−2.33728	−	4.04829i	−0.132963	−	0.230299i
$310$		0			0
$311$	13.9341			0.790130			0.395065	−	0.918653i	$-0.370722\pi$
$311$	13.9341			0.790130			0.395065	+	0.918653i	$0.370722\pi$
$312$	−2.67867	−	3.29272i	−0.151650	−	0.186414i
$313$	9.02908			0.510354			0.255177	−	0.966894i	$-0.417866\pi$
$313$	9.02908			0.510354			0.255177	+	0.966894i	$0.417866\pi$
$314$	−1.57378	+	0.908622i	−0.0888135	+	0.0512765i
$315$		0			0
$316$	−11.3281	+	19.6208i	−0.637254	+	1.10376i
$317$		−	0.496821i		−	0.0279042i	−0.999903	−	0.0139521i	$-0.995559\pi$
$317$		−	0.496821i		−	0.0279042i	0.999903	−	0.0139521i	$-0.00444124\pi$
$318$	1.37772	+	0.795428i	0.0772588	+	0.0446054i
$319$	−22.0680	−	12.7409i	−1.23557	−	0.713356i
$320$		0			0
$321$	6.66217	−	11.5392i	0.371846	−	0.644056i
$322$	−0.113885	−	0.197254i	−0.00634655	−	0.0109925i
$323$	−0.0665613	+	0.0384292i	−0.00370357	+	0.00213826i
$324$	1.90931			0.106073
$325$		0			0
$326$	−6.15961			−0.341149
$327$	4.44251	−	2.56488i	0.245671	−	0.141838i
$328$	−4.68709	−	8.11828i	−0.258801	−	0.448257i
$329$	14.6184	−	25.3198i	0.805939	−	1.39593i
$330$		0			0
$331$	22.5350	+	13.0106i	1.23863	+	0.715126i	0.968815	−	0.247786i	$-0.0797028\pi$
$331$	22.5350	+	13.0106i	1.23863	+	0.715126i	0.269819	+	0.962911i	$0.413036\pi$
$332$	15.8565	+	9.15473i	0.870237	+	0.502431i
$333$			2.86182i			0.156827i
$334$	−2.55068	+	4.41790i	−0.139567	+	0.241737i
$335$		0			0
$336$	−10.2927	+	5.94251i	−0.561514	+	0.324190i
$337$	1.60276			0.0873079			0.0436540	−	0.999047i	$-0.486100\pi$
$337$	1.60276			0.0873079			0.0436540	+	0.999047i	$0.486100\pi$
$338$	2.60645	−	2.92105i	0.141772	−	0.158884i
$339$	8.17315			0.443905
$340$		0			0
$341$	2.08004	+	3.60274i	0.112641	+	0.195099i
$342$	0.143420	−	0.248410i	0.00775525	−	0.0134325i
$343$			7.64705i			0.412902i
$344$	−9.10865	−	5.25888i	−0.491105	−	0.283540i
$345$		0			0
$346$		−	5.66470i		−	0.304536i
$347$	−15.4789	+	26.8102i	−0.830950	+	1.43925i	0.0663361	+	0.997797i	$0.478869\pi$
$347$	−15.4789	+	26.8102i	−0.830950	+	1.43925i	−0.897286	+	0.441450i	$0.854464\pi$
$348$	9.20981	+	15.9519i	0.493697	+	0.855109i
$349$	−14.1851	+	8.18979i	−0.759313	+	0.438389i	−0.829049	−	0.559176i	$-0.811118\pi$
$349$	−14.1851	+	8.18979i	−0.759313	+	0.438389i	0.0697363	+	0.997565i	$0.477784\pi$
$350$		0			0
$351$	0.572034	+	3.55988i	0.0305329	+	0.190013i
$352$	8.97460			0.478348
$353$	17.6768	−	10.2057i	0.940840	−	0.543194i	0.0506166	−	0.998718i	$-0.483881\pi$
$353$	17.6768	−	10.2057i	0.940840	−	0.543194i	0.890224	+	0.455524i	$0.150548\pi$
$354$	1.45671	+	2.52310i	0.0774234	+	0.134101i
$355$		0			0
$356$		−	20.2240i		−	1.07187i
$357$	0.239753	+	0.138422i	0.0126891	+	0.00732605i
$358$	−2.68017	−	1.54740i	−0.141652	−	0.0817826i
$359$			27.7823i			1.46629i	0.680071	+	0.733146i	$0.261949\pi$
$359$			27.7823i			1.46629i	−0.680071	+	0.733146i	$0.738051\pi$
$360$		0			0
$361$	−9.04637	−	15.6688i	−0.476125	−	0.824672i
$362$	3.93727	−	2.27318i	0.206938	−	0.119476i
$363$	−4.02320			−0.211163
$364$	−14.9050	−	18.3218i	−0.781235	−	0.960324i
$365$		0			0
$366$	−3.38710	+	1.95554i	−0.177046	+	0.102218i
$367$	2.83998	+	4.91900i	0.148246	+	0.256769i	0.930579	−	0.366091i	$-0.119304\pi$
$367$	2.83998	+	4.91900i	0.148246	+	0.256769i	−0.782333	+	0.622860i	$0.785971\pi$
$368$	−0.381834	+	0.661356i	−0.0199045	+	0.0344756i
$369$			7.96269i			0.414521i
$370$		0			0
$371$	15.6963	+	9.06228i	0.814912	+	0.470490i
$372$		−	3.00712i		−	0.155912i
$373$	−1.99014	+	3.44703i	−0.103046	+	0.178480i	−0.912938	−	0.408098i	$-0.866192\pi$
$373$	−1.99014	+	3.44703i	−0.103046	+	0.178480i	0.809892	+	0.586579i	$0.199525\pi$
$374$	−0.0320920	−	0.0555849i	−0.00165944	−	0.00287423i
$375$		0			0
$376$	10.0322			0.517369
$377$	−26.9827	+	21.9508i	−1.38968	+	1.13052i
$378$	−1.03319			−0.0531418
$379$	23.5846	−	13.6166i	1.21146	−	0.699437i	0.248383	−	0.968662i	$-0.420101\pi$
$379$	23.5846	−	13.6166i	1.21146	−	0.699437i	0.963077	+	0.269225i	$0.0867675\pi$
$380$		0			0
$381$	10.4744	−	18.1422i	0.536621	−	0.929456i
$382$		−	3.46711i		−	0.177393i
$383$	10.4776	+	6.04924i	0.535380	+	0.309102i	0.743204	−	0.669064i	$-0.233305\pi$
$383$	10.4776	+	6.04924i	0.535380	+	0.309102i	−0.207825	+	0.978166i	$0.566638\pi$
$384$	−7.42502	−	4.28684i	−0.378907	−	0.218762i
$385$		0			0
$386$	2.55266	−	4.42134i	0.129927	−	0.225041i
$387$	4.46704	+	7.73715i	0.227073	+	0.393301i
$388$	−7.73657	+	4.46671i	−0.392765	+	0.226763i
$389$	−38.7373			−1.96406			−0.982030	−	0.188726i	$-0.939564\pi$
$389$	−38.7373			−1.96406			−0.982030	+	0.188726i	$0.939564\pi$
$390$		0			0
$391$	0.0177885			0.000899603
$392$	4.86435	−	2.80843i	0.245687	−	0.141847i
$393$	−8.51248	−	14.7441i	−0.429398	−	0.743739i
$394$	−1.77113	+	3.06768i	−0.0892282	+	0.154548i
$395$		0			0
$396$	−4.36753	−	2.52159i	−0.219477	−	0.126715i
$397$	−2.32709	−	1.34354i	−0.116793	−	0.0674306i	0.440465	−	0.897770i	$-0.354813\pi$
$397$	−2.32709	−	1.34354i	−0.116793	−	0.0674306i	−0.557259	+	0.830339i	$0.688147\pi$
$398$			2.50385i			0.125507i
$399$	1.63397	−	2.83013i	0.0818010	−	0.141684i
$400$		0			0
$401$	−5.93978	+	3.42933i	−0.296618	+	0.171253i	−0.640923	−	0.767605i	$-0.721448\pi$
$401$	−5.93978	+	3.42933i	−0.296618	+	0.171253i	0.344304	+	0.938858i	$0.388115\pi$
$402$	0.754578			0.0376350
$403$	5.60673	−	0.900940i	0.279291	−	0.0448790i
$404$	12.9886			0.646206
$405$		0			0
$406$	−4.98374	−	8.63209i	−0.247339	−	0.428403i
$407$	3.77955	−	6.54637i	0.187345	−	0.324491i
$408$			0.0949945i			0.00470293i
$409$	0.360959	+	0.208400i	0.0178483	+	0.0103047i	0.508898	−	0.860827i	$-0.330053\pi$
$409$	0.360959	+	0.208400i	0.0178483	+	0.0103047i	−0.491049	+	0.871132i	$0.663387\pi$
$410$		0			0
$411$		−	14.9225i		−	0.736073i
$412$	4.46260	−	7.72944i	0.219856	−	0.380802i
$413$	16.5963	+	28.7456i	0.816648	+	1.41448i
$414$	−0.0574933	+	0.0331938i	−0.00282564	+	0.00163139i
$415$		0			0
$416$	4.36452	−	11.4468i	0.213988	−	0.561225i
$417$	8.10958			0.397128
$418$	−0.656142	+	0.378824i	−0.0320930	+	0.0185289i
$419$	5.31726	+	9.20977i	0.259765	+	0.449926i	0.966179	−	0.257873i	$-0.0830215\pi$
$419$	5.31726	+	9.20977i	0.259765	+	0.449926i	−0.706414	+	0.707799i	$0.749688\pi$
$420$		0			0
$421$		−	26.1373i		−	1.27385i	−0.770925	−	0.636926i	$-0.780205\pi$
$421$		−	26.1373i		−	1.27385i	0.770925	−	0.636926i	$-0.219795\pi$
$422$	−4.28634	−	2.47472i	−0.208656	−	0.120467i
$423$	−7.37992	−	4.26080i	−0.358824	−	0.207167i
$424$			6.21915i			0.302029i
$425$		0			0
$426$	−0.796933	−	1.38033i	−0.0386115	−	0.0668772i
$427$	−38.5891	+	22.2794i	−1.86746	+	1.07818i
$428$	25.4403			1.22971
$429$	3.39295	−	8.89867i	0.163813	−	0.429632i
$430$		0			0
$431$	−14.6870	+	8.47953i	−0.707447	+	0.408445i	−0.810115	−	0.586271i	$-0.800595\pi$
$431$	−14.6870	+	8.47953i	−0.707447	+	0.408445i	0.102668	+	0.994716i	$0.467262\pi$
$432$	1.73205	+	3.00000i	0.0833333	+	0.144338i
$433$	17.9671	−	31.1200i	0.863446	−	1.49553i	−0.00513654	−	0.999987i	$-0.501635\pi$
$433$	17.9671	−	31.1200i	0.863446	−	1.49553i	0.868582	−	0.495545i	$-0.165032\pi$
$434$			1.62726i			0.0781108i
$435$		0			0
$436$	8.48214	+	4.89716i	0.406221	+	0.234532i
$437$		−	0.209981i		−	0.0100448i
$438$	2.16207	−	3.74482i	0.103308	−	0.178934i
$439$	1.89125	+	3.27575i	0.0902646	+	0.156343i	0.907622	−	0.419787i	$-0.137895\pi$
$439$	1.89125	+	3.27575i	0.0902646	+	0.156343i	−0.817358	+	0.576130i	$0.804562\pi$
$440$		0			0
$441$	−4.77113			−0.227197
$442$	−0.0865035	+	0.0139002i	−0.00411455	+	0.000661163i
$443$	33.5683			1.59488			0.797440	−	0.603399i	$-0.206187\pi$
$443$	33.5683			1.59488			0.797440	+	0.603399i	$0.206187\pi$
$444$	−4.73205	+	2.73205i	−0.224573	+	0.129657i
$445$		0			0
$446$	−0.342756	+	0.593671i	−0.0162300	+	0.0281111i
$447$		−	21.7627i		−	1.02934i
$448$	−17.5453	−	10.1298i	−0.828936	−	0.478586i
$449$	15.2743	+	8.81863i	0.720839	+	0.416177i	0.815061	−	0.579374i	$-0.196703\pi$
$449$	15.2743	+	8.81863i	0.720839	+	0.416177i	−0.0942223	+	0.995551i	$0.530036\pi$
$450$		0			0
$451$	10.5162	−	18.2146i	0.495188	−	0.857691i
$452$	7.80255	+	13.5144i	0.367001	+	0.635665i
$453$	12.2706	−	7.08442i	0.576522	−	0.332855i
$454$	−5.91533			−0.277620
$455$		0			0
$456$	1.12135			0.0525118
$457$	18.2930	−	10.5615i	0.855710	−	0.494044i	−0.00686344	−	0.999976i	$-0.502185\pi$
$457$	18.2930	−	10.5615i	0.855710	−	0.494044i	0.862573	+	0.505932i	$0.168851\pi$
$458$	−0.961850	−	1.66597i	−0.0449443	−	0.0778458i
$459$	0.0403455	−	0.0698805i	0.00188317	−	0.00326174i
$460$		0			0
$461$	−20.8786	−	12.0543i	−0.972413	−	0.561423i	−0.0724423	−	0.997373i	$-0.523079\pi$
$461$	−20.8786	−	12.0543i	−0.972413	−	0.561423i	−0.899971	+	0.435949i	$0.856413\pi$
$462$	2.36342	+	1.36452i	0.109956	+	0.0634832i
$463$			19.0861i			0.887006i	0.896273	+	0.443503i	$0.146264\pi$
$463$			19.0861i			0.887006i	−0.896273	+	0.443503i	$0.853736\pi$
$464$	−16.7095	+	28.9417i	−0.775720	+	1.34359i
$465$		0			0
$466$	5.22614	−	3.01731i	0.242096	−	0.139774i
$467$	13.7080			0.634332			0.317166	−	0.948370i	$-0.397269\pi$
$467$	13.7080			0.634332			0.317166	+	0.948370i	$0.397269\pi$
$468$	−5.34022	+	4.34433i	−0.246852	+	0.200817i
$469$	8.59688			0.396967
$470$		0			0
$471$	3.01725	+	5.22602i	0.139027	+	0.240802i
$472$	−5.69474	+	9.86359i	−0.262122	+	0.454008i
$473$		−	23.5982i		−	1.08505i
$474$	−3.09465	−	1.78670i	−0.142142	−	0.0820658i
$475$		0			0
$476$			0.528581i			0.0242275i
$477$	2.64136	−	4.57498i	0.120940	−	0.209474i
$478$	−0.674557	−	1.16837i	−0.0308535	−	0.0534399i
$479$	30.3652	−	17.5314i	1.38742	−	0.801029i	0.394399	−	0.918939i	$-0.370953\pi$
$479$	30.3652	−	17.5314i	1.38742	−	0.801029i	0.993024	+	0.117910i	$0.0376196\pi$
$480$		0			0
$481$	−6.51160	−	8.00431i	−0.296903	−	0.364965i
$482$	0.186215			0.00848187
$483$	−0.655019	+	0.378175i	−0.0298044	+	0.0172076i
$484$	−3.84077	−	6.65241i	−0.174581	−	0.302382i
$485$		0			0
$486$			0.301143i			0.0136601i
$487$	2.61331	+	1.50880i	0.118420	+	0.0683701i	0.558040	−	0.829814i	$-0.311553\pi$
$487$	2.61331	+	1.50880i	0.118420	+	0.0683701i	−0.439620	+	0.898184i	$0.644887\pi$
$488$	−13.2412	−	7.64483i	−0.599402	−	0.346065i
$489$			20.4541i			0.924967i
$490$		0			0
$491$	1.10047	+	1.90607i	0.0496634	+	0.0860195i	0.889788	−	0.456373i	$-0.150852\pi$
$491$	1.10047	+	1.90607i	0.0496634	+	0.0860195i	−0.840125	+	0.542393i	$0.817518\pi$
$492$	−13.1664	+	7.60164i	−0.593588	+	0.342708i
$493$	0.778446			0.0350595
$494$	0.164082	+	1.02112i	0.00738240	+	0.0459422i
$495$		0			0
$496$	4.72493	−	2.72794i	0.212156	−	0.122488i
$497$	−9.07942	−	15.7260i	−0.407268	−	0.705409i
$498$	−1.44391	+	2.50093i	−0.0647033	+	0.112069i
$499$		−	8.68475i		−	0.388783i	−0.980924	−	0.194391i	$-0.937727\pi$
$499$		−	8.68475i		−	0.388783i	0.980924	−	0.194391i	$-0.0622732\pi$
$500$		0			0
$501$	14.6704	+	8.46999i	0.655427	+	0.378411i
$502$		−	5.42986i		−	0.242347i
$503$	7.93251	−	13.7395i	0.353693	−	0.612615i	−0.633200	−	0.773988i	$-0.718259\pi$
$503$	7.93251	−	13.7395i	0.353693	−	0.612615i	0.986893	+	0.161373i	$0.0515924\pi$
$504$	−2.01954	−	3.49794i	−0.0899574	−	0.155811i
$505$		0			0
$506$	0.175354			0.00779542
$507$	−9.69988	−	8.65519i	−0.430787	−	0.384390i
$508$	39.9979			1.77462
$509$	36.9324	−	21.3229i	1.63700	−	0.945122i	0.655141	−	0.755506i	$-0.272609\pi$
$509$	36.9324	−	21.3229i	1.63700	−	0.945122i	0.981858	−	0.189616i	$-0.0607242\pi$
$510$		0			0
$511$	24.6324	−	42.6646i	1.08967	−	1.88737i
$512$		−	19.9263i		−	0.880628i
$513$	−0.824892	−	0.476251i	−0.0364199	−	0.0210270i
$514$	−1.98307	−	1.14492i	−0.0874694	−	0.0505005i
$515$		0			0
$516$	−8.52898	+	14.7726i	−0.375468	+	0.650329i
$517$	11.2543	+	19.4930i	0.494964	+	0.857303i
$518$	2.56067	−	1.47841i	0.112509	−	0.0649574i
$519$	−18.8107			−0.825697
$520$		0			0
$521$	−5.40996			−0.237015			−0.118507	−	0.992953i	$-0.537811\pi$
$521$	−5.40996			−0.237015			−0.118507	+	0.992953i	$0.537811\pi$
$522$	−2.51598	+	1.45260i	−0.110121	+	0.0635786i
$523$	−8.80021	−	15.2424i	−0.384806	−	0.666504i	0.606936	−	0.794751i	$-0.292398\pi$
$523$	−8.80021	−	15.2424i	−0.384806	−	0.666504i	−0.991742	+	0.128247i	$0.959065\pi$
$524$	16.2530	−	28.1510i	0.710015	−	1.22978i
$525$		0			0
$526$	−0.775681	−	0.447840i	−0.0338213	−	0.0195267i
$527$	−0.110060	−	0.0635432i	−0.00479429	−	0.00276799i
$528$		−	9.14995i		−	0.398201i
$529$	11.4757	−	19.8765i	0.498943	−	0.864195i
$530$		0			0
$531$	8.37841	−	4.83728i	0.363592	−	0.209920i
$532$	6.23954			0.270518
$533$	−18.1178	−	22.2711i	−0.784770	−	0.964669i
$534$	3.18979			0.138036
$535$		0			0
$536$	1.47494	+	2.55467i	0.0637078	+	0.110345i
$537$	−5.13842	+	8.90001i	−0.221739	+	0.384064i
$538$			8.46430i			0.364922i
$539$	10.9139	+	6.30114i	0.470095	+	0.271409i
$540$		0			0
$541$		−	2.26288i		−	0.0972887i	−0.998816	−	0.0486444i	$-0.984510\pi$
$541$		−	2.26288i		−	0.0972887i	0.998816	−	0.0486444i	$-0.0154901\pi$
$542$	−2.84008	+	4.91916i	−0.121992	+	0.211296i
$543$	−7.54852	−	13.0744i	−0.323938	−	0.561077i
$544$	−0.237434	+	0.137082i	−0.0101799	+	0.00587736i
$545$		0			0
$546$	2.88977	−	2.35087i	0.123671	−	0.100608i
$547$	−0.320033			−0.0136836			−0.00684182	−	0.999977i	$-0.502178\pi$
$547$	−0.320033			−0.0136836			−0.00684182	+	0.999977i	$0.502178\pi$
$548$	24.6746	−	14.2459i	1.05405	−	0.608554i
$549$	6.49373	+	11.2475i	0.277146	+	0.480031i
$550$		0			0
$551$		−	9.18903i		−	0.391466i
$552$	−0.224759	−	0.129765i	−0.00956639	−	0.00552316i
$553$	−35.2573	−	20.3558i	−1.49929	−	0.865616i
$554$			6.48471i			0.275509i
$555$		0			0
$556$	7.74186	+	13.4093i	0.328328	+	0.568681i
$557$	13.8305	−	7.98505i	0.586017	−	0.338337i	−0.177504	−	0.984120i	$-0.556802\pi$
$557$	13.8305	−	7.98505i	0.586017	−	0.338337i	0.763521	+	0.645783i	$0.223469\pi$
$558$	0.474293			0.0200784
$559$	−30.0986	−	11.4762i	−1.27304	−	0.485394i
$560$		0			0
$561$	−0.184580	+	0.106567i	−0.00779296	+	0.00449927i
$562$	−2.78713	−	4.82746i	−0.117568	−	0.203634i
$563$	−6.15426	+	10.6595i	−0.259371	+	0.449244i	−0.966074	−	0.258267i	$-0.916849\pi$
$563$	−6.15426	+	10.6595i	−0.259371	+	0.449244i	0.706702	+	0.707511i	$0.250182\pi$
$564$		−	16.2704i		−	0.685107i
$565$		0			0
$566$	2.64799	+	1.52882i	0.111303	+	0.0642610i
$567$			3.43091i			0.144085i
$568$	3.11546	−	5.39614i	0.130722	−	0.226417i
$569$	13.8416	+	23.9743i	0.580269	+	1.00506i	0.995447	+	0.0953158i	$0.0303861\pi$
$569$	13.8416	+	23.9743i	0.580269	+	1.00506i	−0.415178	+	0.909740i	$0.636281\pi$
$570$		0			0
$571$	−19.9502			−0.834892			−0.417446	−	0.908702i	$-0.637075\pi$
$571$	−19.9502			−0.834892			−0.417446	+	0.908702i	$0.637075\pi$
$572$	17.9532	−	2.88488i	0.750660	−	0.120623i
$573$	−11.5132			−0.480970
$574$	7.12480	−	4.11350i	0.297383	−	0.171694i
$575$		0			0
$576$	−2.95250	+	5.11388i	−0.123021	+	0.213079i
$577$			24.1623i			1.00589i	0.864318	+	0.502946i	$0.167750\pi$
$577$			24.1623i			1.00589i	−0.864318	+	0.502946i	$0.832250\pi$
$578$	−4.43186	−	2.55873i	−0.184341	−	0.106429i
$579$	−14.6819	−	8.47659i	−0.610158	−	0.352275i
$580$		0			0
$581$	−16.4504	+	28.4930i	−0.682480	+	1.18209i
$582$	−0.704504	−	1.22024i	−0.0292026	−	0.0505804i
$583$	−12.0842	+	6.97680i	−0.500475	+	0.288950i
$584$	16.9044			0.699511
$585$		0			0
$586$	5.07965			0.209838
$587$	−9.55436	+	5.51622i	−0.394351	+	0.227679i	−0.684044	−	0.729441i	$-0.739780\pi$
$587$	−9.55436	+	5.51622i	−0.394351	+	0.227679i	0.289693	+	0.957120i	$0.406447\pi$
$588$	−4.55479	−	7.88913i	−0.187836	−	0.325342i
$589$	−0.750085	+	1.29918i	−0.0309067	+	0.0535320i
$590$		0			0
$591$	10.1868	+	5.88135i	0.419029	+	0.241927i
$592$	−8.58545	−	4.95681i	−0.352860	−	0.203724i
$593$		−	1.72909i		−	0.0710053i	−0.999370	−	0.0355027i	$-0.988697\pi$
$593$		−	1.72909i		−	0.0710053i	0.999370	−	0.0355027i	$-0.0113032\pi$
$594$	0.397714	−	0.688861i	0.0163184	−	0.0282643i
$595$		0			0
$596$	35.9849	−	20.7759i	1.47400	−	0.851014i
$597$	8.31449			0.340289
$598$	0.0852779	−	0.223658i	0.00348727	−	0.00914604i
$599$	15.5218			0.634203			0.317102	−	0.948392i	$-0.397290\pi$
$599$	15.5218			0.634203			0.317102	+	0.948392i	$0.397290\pi$
$600$		0			0
$601$	7.39125	+	12.8020i	0.301495	+	0.522206i	0.976475	−	0.215631i	$-0.0691808\pi$
$601$	7.39125	+	12.8020i	0.301495	+	0.522206i	−0.674979	+	0.737837i	$0.735848\pi$
$602$	4.61532	−	7.99397i	0.188106	−	0.325810i
$603$		−	2.50571i		−	0.102041i
$604$	23.4284	+	13.5264i	0.953287	+	0.550380i
$605$		0			0
$606$			2.04860i			0.0832186i
$607$	−12.4674	+	21.5941i	−0.506035	+	0.876479i	0.493940	+	0.869496i	$0.335556\pi$
$607$	−12.4674	+	21.5941i	−0.506035	+	0.876479i	−0.999976	+	0.00698303i	$0.997777\pi$
$608$	1.61817	+	2.80275i	0.0656253	+	0.113666i
$609$	−28.6644	+	16.5494i	−1.16154	+	0.670616i
$610$		0			0
$611$	30.3359	−	4.87464i	1.22726	−	0.197207i
$612$	0.154064			0.00622768
$613$	25.5334	−	14.7417i	1.03129	−	0.595413i	0.113933	−	0.993488i	$-0.463655\pi$
$613$	25.5334	−	14.7417i	1.03129	−	0.595413i	0.917353	+	0.398075i	$0.130322\pi$
$614$	1.04520	+	1.81034i	0.0421808	+	0.0730593i
$615$		0			0
$616$			10.6687i			0.429853i
$617$	−14.0182	−	8.09339i	−0.564350	−	0.325827i	0.190540	−	0.981679i	$-0.438976\pi$
$617$	−14.0182	−	8.09339i	−0.564350	−	0.325827i	−0.754890	+	0.655852i	$0.772310\pi$
$618$	1.21911	+	0.703855i	0.0490399	+	0.0283132i
$619$			39.3442i			1.58138i	0.612218	+	0.790689i	$0.290278\pi$
$619$			39.3442i			1.58138i	−0.612218	+	0.790689i	$0.709722\pi$
$620$		0			0
$621$	0.110226	+	0.190917i	0.00442322	+	0.00766124i
$622$	−3.63397	+	2.09808i	−0.145709	+	0.0841252i
$623$	36.3412			1.45598
$624$	−11.6704	−	4.44980i	−0.467192	−	0.178134i
$625$		0			0
$626$	−2.35476	+	1.35952i	−0.0941152	+	0.0543374i
$627$	1.25795	+	2.17884i	0.0502378	+	0.0870144i
$628$	−5.76087	+	9.97811i	−0.229884	+	0.398170i
$629$			0.230923i			0.00920750i
$630$		0			0
$631$	18.1035	+	10.4520i	0.720688	+	0.416090i	0.815006	−	0.579453i	$-0.196734\pi$
$631$	18.1035	+	10.4520i	0.720688	+	0.416090i	−0.0943177	+	0.995542i	$0.530067\pi$
$632$		−	13.9695i		−	0.555678i
$633$	−8.21775	+	14.2336i	−0.326626	+	0.565733i
$634$	0.0748070	+	0.129570i	0.00297097	+	0.00514586i
$635$		0			0
$636$	10.0864			0.399951
$637$	13.3445	−	10.8559i	0.528729	−	0.430128i
$638$	7.67369			0.303804
$639$	−4.58363	+	2.64636i	−0.181326	+	0.104688i
$640$		0			0
$641$	6.91708	−	11.9807i	0.273208	−	0.473211i	−0.696473	−	0.717583i	$-0.745248\pi$
$641$	6.91708	−	11.9807i	0.273208	−	0.473211i	0.969682	+	0.244372i	$0.0785818\pi$
$642$			4.01253i			0.158362i
$643$	−0.133542	−	0.0771004i	−0.00526638	−	0.00304054i	0.497364	−	0.867542i	$-0.334301\pi$
$643$	−0.133542	−	0.0771004i	−0.00526638	−	0.00304054i	−0.502631	+	0.864501i	$0.667635\pi$
$644$	−1.25064	−	0.722055i	−0.0492819	−	0.0284529i
$645$		0			0
$646$	0.0115727	−	0.0200445i	0.000455321	−	0.000788640i
$647$	6.69998	+	11.6047i	0.263403	+	0.456228i	0.967144	−	0.254229i	$-0.0818216\pi$
$647$	6.69998	+	11.6047i	0.263403	+	0.456228i	−0.703741	+	0.710457i	$0.748488\pi$
$648$	−1.01954	+	0.588631i	−0.0400513	+	0.0231236i
$649$	−25.5540			−1.00308
$650$		0			0
$651$	5.40360			0.211784
$652$	−33.8211	+	19.5266i	−1.32454	+	0.764722i
$653$	−2.67870	−	4.63964i	−0.104826	−	0.181563i	0.808841	−	0.588027i	$-0.200095\pi$
$653$	−2.67870	−	4.63964i	−0.104826	−	0.181563i	−0.913667	+	0.406464i	$0.866762\pi$
$654$	−0.772396	+	1.33783i	−0.0302031	+	0.0523133i
$655$		0			0
$656$	−23.8881	−	13.7918i	−0.932673	−	0.538479i
$657$	−12.4354	−	7.17956i	−0.485149	−	0.280101i
$658$			8.80446i			0.343234i
$659$	6.44138	−	11.1568i	0.250920	−	0.434607i	−0.712859	−	0.701307i	$-0.752600\pi$
$659$	6.44138	−	11.1568i	0.250920	−	0.434607i	0.963780	+	0.266700i	$0.0859334\pi$
$660$		0			0
$661$	−5.28132	+	3.04917i	−0.205420	+	0.118599i	−0.599181	−	0.800614i	$-0.704507\pi$
$661$	−5.28132	+	3.04917i	−0.205420	+	0.118599i	0.393761	+	0.919213i	$0.371174\pi$
$662$	−7.83608			−0.304558
$663$	0.0461580	+	0.287251i	0.00179263	+	0.0111559i
$664$	−11.2894			−0.438115
$665$		0			0
$666$	−0.430908	−	0.746354i	−0.0166973	−	0.0289206i
$667$	−1.06338	+	1.84182i	−0.0411741	+	0.0713157i
$668$			32.3437i			1.25142i
$669$	1.97139	+	1.13818i	0.0762185	+	0.0440047i
$670$		0			0
$671$		−	34.3046i		−	1.32432i
$672$	5.82862	−	10.0955i	0.224844	−	0.389441i
$673$	10.3388	+	17.9073i	0.398531	+	0.690276i	0.993545	−	0.113440i	$-0.0361869\pi$
$673$	10.3388	+	17.9073i	0.398531	+	0.690276i	−0.595014	+	0.803715i	$0.702854\pi$
$674$	−0.417996	+	0.241330i	−0.0161006	+	0.00929569i
$675$		0			0
$676$	5.05141	−	24.3016i	0.194285	−	0.934678i
$677$	25.5159			0.980656			0.490328	−	0.871538i	$-0.336877\pi$
$677$	25.5159			0.980656			0.490328	+	0.871538i	$0.336877\pi$
$678$	−2.13154	+	1.23064i	−0.0818612	+	0.0472626i
$679$	−8.02638	−	13.9021i	−0.308024	−	0.533513i
$680$		0			0
$681$			19.6429i			0.752719i
$682$	−1.08494	−	0.626390i	−0.0415445	−	0.0239857i
$683$	1.38625	+	0.800355i	0.0530436	+	0.0306247i	0.526287	−	0.850307i	$-0.323584\pi$
$683$	1.38625	+	0.800355i	0.0530436	+	0.0306247i	−0.473244	+	0.880932i	$0.656917\pi$
$684$		−	1.81863i		−	0.0695369i
$685$		0			0
$686$	−1.15143	−	1.99433i	−0.0439617	−	0.0761439i
$687$	−5.53217	+	3.19400i	−0.211065	+	0.121859i
$688$	−30.9486			−1.17990
$689$	3.02190	+	18.8059i	0.115125	+	0.716448i
$690$		0			0
$691$	−22.8052	+	13.1666i	−0.867551	+	0.500881i	−0.866534	−	0.499119i	$-0.833657\pi$
$691$	−22.8052	+	13.1666i	−0.867551	+	0.500881i	−0.00101729	+	0.999999i	$0.500324\pi$
$692$	−17.9577	−	31.1037i	−0.682651	−	1.18239i
$693$	4.53114	−	7.84816i	0.172124	−	0.298127i
$694$		−	9.32271i		−	0.353885i
$695$		0			0
$696$	−9.83574	−	5.67867i	−0.372823	−	0.215249i
$697$			0.642518i			0.0243371i
$698$	2.46630	−	4.27175i	0.0933507	−	0.161688i
$699$	−10.0195	−	17.3544i	−0.378974	−	0.656402i
$700$		0			0
$701$	−39.3777			−1.48728			−0.743638	−	0.668582i	$-0.766901\pi$
$701$	−39.3777			−1.48728			−0.743638	+	0.668582i	$0.766901\pi$
$702$	−0.685202	−	0.842277i	−0.0258613	−	0.0317897i
$703$	2.72589			0.102809
$704$	13.5076	−	7.79863i	0.509088	−	0.293922i
$705$		0			0
$706$	−3.07337	+	5.32324i	−0.115668	+	0.200343i
$707$			23.3396i			0.877776i
$708$	15.9970	+	9.23588i	0.601204	+	0.347106i
$709$	−15.5842	−	8.99756i	−0.585278	−	0.337911i	0.177950	−	0.984040i	$-0.443053\pi$
$709$	−15.5842	−	8.99756i	−0.585278	−	0.337911i	−0.763228	+	0.646129i	$0.776387\pi$
$710$		0			0
$711$	−5.93306	+	10.2764i	−0.222507	+	0.385394i
$712$	6.23495	+	10.7993i	0.233665	+	0.404719i
$713$	0.300690	−	0.173603i	0.0112609	−	0.00650149i
$714$	−0.0833695			−0.00312002
$715$		0			0
$716$	−19.6217			−0.733298
$717$	−3.87978	+	2.23999i	−0.144893	+	0.0836540i
$718$	−4.18322	−	7.24555i	−0.156116	−	0.270401i
$719$	−10.1016	+	17.4964i	−0.376725	+	0.652507i	−0.990584	−	0.136909i	$-0.956283\pi$
$719$	−10.1016	+	17.4964i	−0.376725	+	0.652507i	0.613859	+	0.789416i	$0.289616\pi$
$720$		0			0
$721$	13.8893	+	8.01899i	0.517264	+	0.298643i
$722$	4.71854	+	2.72425i	0.175606	+	0.101386i
$723$		−	0.618361i		−	0.0229971i
$724$	14.4125	−	24.9632i	0.535636	−	0.927749i
$725$		0			0
$726$	1.04924	−	0.605779i	0.0389409	−	0.0224826i
$727$	21.8795			0.811466			0.405733	−	0.913992i	$-0.367016\pi$
$727$	21.8795			0.811466			0.405733	+	0.913992i	$0.367016\pi$
$728$	13.6075	+	5.18838i	0.504328	+	0.192294i
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.360450	+	0.624318i	0.0133317	+	0.0230912i
$732$	−12.3986	+	21.4750i	−0.458264	+	0.793737i
$733$			26.2697i			0.970294i	0.874433	+	0.485147i	$0.161234\pi$
$733$			26.2697i			0.970294i	−0.874433	+	0.485147i	$0.838766\pi$
$734$	−1.48132	−	0.855241i	−0.0546766	−	0.0315675i
$735$		0			0
$736$		−	0.749033i		−	0.0276097i
$737$	−3.30925	+	5.73179i	−0.121898	+	0.211133i
$738$	−1.19895	−	2.07665i	−0.0441341	−	0.0764426i
$739$	−36.1172	+	20.8523i	−1.32859	+	0.767064i	−0.985082	−	0.172084i	$-0.944950\pi$
$739$	−36.1172	+	20.8523i	−1.32859	+	0.767064i	−0.343512	+	0.939148i	$0.611617\pi$
$740$		0			0
$741$	3.39080	−	0.544864i	0.124564	−	0.0200161i
$742$	−5.45808			−0.200372
$743$	9.06081	−	5.23126i	0.332409	−	0.191916i	−0.324501	−	0.945885i	$-0.605196\pi$
$743$	9.06081	−	5.23126i	0.332409	−	0.191916i	0.656910	+	0.753969i	$0.271863\pi$
$744$	0.927080	+	1.60575i	0.0339884	+	0.0588696i
$745$		0			0
$746$		−	1.19864i		−	0.0438852i
$747$	8.30480	+	4.79478i	0.303857	+	0.175432i
$748$	−0.352420	−	0.203470i	−0.0128858	−	0.00743960i
$749$			45.7146i			1.67037i
$750$		0			0
$751$	14.3155	+	24.7952i	0.522381	+	0.904791i	0.999661	+	0.0260396i	$0.00828961\pi$
$751$	14.3155	+	24.7952i	0.522381	+	0.904791i	−0.477279	+	0.878752i	$0.658377\pi$
$752$	25.5648	−	14.7598i	0.932252	−	0.538236i
$753$	−18.0309			−0.657081
$754$	3.73186	−	9.78753i	0.135906	−	0.356441i
$755$		0			0
$756$	−5.67305	+	3.27534i	−0.206327	+	0.119123i
$757$	−4.66717	−	8.08377i	−0.169631	−	0.293810i	0.768659	−	0.639659i	$-0.220924\pi$
$757$	−4.66717	−	8.08377i	−0.169631	−	0.293810i	−0.938290	+	0.345849i	$0.887591\pi$
$758$	−4.10054	+	7.10234i	−0.148938	+	0.257969i
$759$		−	0.582294i		−	0.0211359i
$760$		0			0
$761$	0.754600	+	0.435668i	0.0273542	+	0.0157930i	0.513615	−	0.858021i	$-0.328306\pi$
$761$	0.754600	+	0.435668i	0.0273542	+	0.0157930i	−0.486261	+	0.873814i	$0.661639\pi$
$762$			6.30860i			0.228537i
$763$	−8.79988	+	15.2418i	−0.318577	+	0.551791i
$764$	−10.9911	−	19.0372i	−0.397645	−	0.688741i
$765$		0			0
$766$	−3.64337			−0.131640
$767$	−12.4274	+	32.5933i	−0.448728	+	1.17687i
$768$	−9.22811			−0.332991
$769$	−30.0008	+	17.3209i	−1.08186	+	0.624609i	−0.931396	−	0.364007i	$-0.881408\pi$
$769$	−30.0008	+	17.3209i	−1.08186	+	0.624609i	−0.150459	+	0.988616i	$0.548075\pi$
$770$		0			0
$771$	−3.80193	+	6.58514i	−0.136923	+	0.237158i
$772$		−	32.3689i		−	1.16498i
$773$	−23.3874	−	13.5027i	−0.841187	−	0.485659i	0.0164808	−	0.999864i	$-0.494754\pi$
$773$	−23.3874	−	13.5027i	−0.841187	−	0.485659i	−0.857667	+	0.514205i	$0.828087\pi$
$774$	−2.32999	−	1.34522i	−0.0837497	−	0.0483529i
$775$		0			0
$776$	2.75413	−	4.77028i	0.0988673	−	0.171243i
$777$	−4.90931	−	8.50318i	−0.176121	−	0.305050i
$778$	10.1026	−	5.83273i	0.362195	−	0.209114i
$779$	7.58449			0.271742
$780$		0			0
$781$	13.9800			0.500244
$782$	−0.00463919	+	0.00267844i	−0.000165897	+	9.57808e-5i
$783$	4.82362	+	8.35476i	0.172382	+	0.298575i
$784$	8.26384	−	14.3134i	0.295137	−	0.511192i
$785$		0			0
$786$	4.44007	+	2.56347i	0.158372	+	0.0914361i
$787$	21.0283	+	12.1407i	0.749577	+	0.432768i	0.825541	−	0.564342i	$-0.190870\pi$
$787$	21.0283	+	12.1407i	0.749577	+	0.432768i	−0.0759643	+	0.997111i	$0.524204\pi$
$788$			22.4587i			0.800058i
$789$	−1.48713	+	2.57579i	−0.0529434	+	0.0917006i
$790$		0			0
$791$	−24.2845	+	14.0207i	−0.863457	+	0.498517i
$792$	3.10958			0.110494
$793$	−43.7544	−	16.6830i	−1.55376	−	0.592431i
$794$	0.809198			0.0287174
$795$		0			0
$796$	7.93748	+	13.7481i	0.281336	+	0.487289i
$797$	5.49209	−	9.51258i	0.194540	−	0.336953i	−0.752210	−	0.658924i	$-0.771012\pi$
$797$	5.49209	−	9.51258i	0.194540	−	0.336953i	0.946750	+	0.321971i	$0.104345\pi$
$798$			0.984120i			0.0348375i
$799$	−0.595493	−	0.343808i	−0.0210670	−	0.0121631i
$800$		0			0
$801$		−	10.5923i		−	0.374260i
$802$	1.03272	−	1.78872i	0.0364666	−	0.0631620i
$803$	18.9638	+	32.8463i	0.669219	+	1.15912i
$804$	4.14323	−	2.39210i	0.146121	−	0.0843628i
$805$		0			0
$806$	−1.32657	+	1.07918i	−0.0467263	+	0.0380124i
$807$	28.1072			0.989422
$808$	−6.93566	+	4.00431i	−0.243996	+	0.140871i
$809$	−25.3218	−	43.8587i	−0.890267	−	1.54199i	−0.839555	−	0.543275i	$-0.817184\pi$
$809$	−25.3218	−	43.8587i	−0.890267	−	1.54199i	−0.0507123	−	0.998713i	$-0.516149\pi$
$810$		0			0
$811$		−	7.67073i		−	0.269356i	−0.990889	−	0.134678i	$-0.957000\pi$
$811$		−	7.67073i		−	0.269356i	0.990889	−	0.134678i	$-0.0430000\pi$
$812$	−54.7293	−	31.5980i	−1.92062	−	1.10887i
$813$	16.3350	+	9.43101i	0.572893	+	0.330760i
$814$			2.27637i			0.0797867i
$815$		0			0
$816$	0.139761	+	0.242073i	0.00489261	+	0.00847425i
$817$	7.36965	−	4.25487i	0.257832	−	0.148859i
$818$	−0.125516			−0.00438857
$819$	−7.80648	−	9.59602i	−0.272780	−	0.335312i
$820$		0			0
$821$	−30.3041	+	17.4961i	−1.05762	+	0.610617i	−0.924773	−	0.380520i	$-0.875745\pi$
$821$	−30.3041	+	17.4961i	−1.05762	+	0.610617i	−0.132846	+	0.991137i	$0.542412\pi$
$822$	2.24691	+	3.89175i	0.0783698	+	0.135741i
$823$	8.10657	−	14.0410i	0.282577	−	0.489438i	−0.689442	−	0.724341i	$-0.742144\pi$
$823$	8.10657	−	14.0410i	0.282577	−	0.489438i	0.972019	+	0.234903i	$0.0754773\pi$
$824$			5.50318i			0.191712i
$825$		0			0
$826$	−8.65652	−	4.99785i	−0.301199	−	0.173897i
$827$			26.9634i			0.937611i	0.883301	+	0.468805i	$0.155315\pi$
$827$			26.9634i			0.937611i	−0.883301	+	0.468805i	$0.844685\pi$
$828$	−0.210456	+	0.364520i	−0.00731385	+	0.0126680i
$829$	1.08254	+	1.87501i	0.0375981	+	0.0651219i	0.884212	−	0.467086i	$-0.154696\pi$
$829$	1.08254	+	1.87501i	0.0375981	+	0.0651219i	−0.846614	+	0.532207i	$0.821363\pi$
$830$		0			0
$831$	21.5336			0.746994
$832$	−3.37786	−	21.0211i	−0.117106	−	0.728777i
$833$	−0.384987			−0.0133390
$834$	−2.11496	+	1.22107i	−0.0732350	+	0.0422822i
$835$		0			0
$836$	−2.40183	+	4.16008i	−0.0830689	+	0.143880i
$837$		−	1.57498i		−	0.0544391i
$838$	−2.77346	−	1.60126i	−0.0958074	−	0.0553145i
$839$	−6.71524	−	3.87705i	−0.231836	−	0.133851i	0.379583	−	0.925158i	$-0.376068\pi$
$839$	−6.71524	−	3.87705i	−0.231836	−	0.133851i	−0.611419	+	0.791307i	$0.709401\pi$
$840$		0			0
$841$	−32.0347	+	55.4857i	−1.10464	+	1.91330i
$842$	3.93553	+	6.81654i	0.135627	+	0.234913i
$843$	−16.0304	+	9.25518i	−0.552118	+	0.318765i
$844$	−31.3805			−1.08016
$845$		0			0
$846$	2.56622			0.0882284
$847$	11.9539	−	6.90161i	0.410742	−	0.237142i
$848$	9.14995	+	15.8482i	0.314211	+	0.544229i
$849$	5.07672	−	8.79313i	0.174233	−	0.301780i
$850$		0			0
$851$	−0.546369	−	0.315446i	−0.0187293	−	0.0108134i
$852$	−8.75159	−	5.05273i	−0.299825	−	0.173104i
$853$			14.4459i			0.494618i	0.968937	+	0.247309i	$0.0795462\pi$
$853$			14.4459i			0.494618i	−0.968937	+	0.247309i	$0.920454\pi$
$854$	6.70929	−	11.6208i	0.229587	−	0.397656i
$855$		0			0
$856$	−13.5847	+	7.84312i	−0.464315	+	0.268072i
$857$	−1.52830			−0.0522058			−0.0261029	−	0.999659i	$-0.508310\pi$
$857$	−1.52830			−0.0522058			−0.0261029	+	0.999659i	$0.508310\pi$
$858$	0.455012	+	2.83163i	0.0155339	+	0.0966703i
$859$	49.1152			1.67579			0.837894	−	0.545833i	$-0.183787\pi$
$859$	49.1152			1.67579			0.837894	+	0.545833i	$0.183787\pi$
$860$		0			0
$861$	−13.6596	−	23.6592i	−0.465519	−	0.806303i
$862$	2.55355	−	4.42288i	0.0869743	−	0.150644i
$863$			9.73540i			0.331397i	0.986176	+	0.165698i	$0.0529878\pi$
$863$			9.73540i			0.331397i	−0.986176	+	0.165698i	$0.947012\pi$
$864$	−2.94251	−	1.69886i	−0.100106	−	0.0577963i
$865$		0			0
$866$			10.8214i			0.367725i
$867$	−8.49674	+	14.7168i	−0.288565	+	0.499808i
$868$	5.15858	+	8.93492i	0.175094	+	0.303271i
$869$	27.1436	−	15.6714i	0.920784	−	0.531615i
$870$		0			0
$871$	5.70135	+	7.00832i	0.193183	+	0.237468i
$872$	−6.03908			−0.204509
$873$	−4.05202	+	2.33943i	−0.137140	+	0.0791778i
$874$	0.0316172	+	0.0547625i	0.00106947	+	0.00185237i
$875$		0			0
$876$		−	27.4160i		−	0.926302i
$877$	42.3637	+	24.4587i	1.43052	+	0.825911i	0.997160	−	0.0753094i	$-0.0239945\pi$
$877$	42.3637	+	24.4587i	1.43052	+	0.825911i	0.433360	+	0.901221i	$0.357328\pi$
$878$	−0.986468	−	0.569538i	−0.0332917	−	0.0192210i
$879$		−	16.8679i		−	0.568940i
$880$		0			0
$881$	0.353227	+	0.611807i	0.0119005	+	0.0206123i	0.871914	−	0.489658i	$-0.162879\pi$
$881$	0.353227	+	0.611807i	0.0119005	+	0.0206123i	−0.860014	+	0.510271i	$0.829545\pi$
$882$	1.24430	−	0.718396i	0.0418977	−	0.0241896i
$883$	−6.46965			−0.217721			−0.108860	−	0.994057i	$-0.534720\pi$
$883$	−6.46965			−0.217721			−0.108860	+	0.994057i	$0.534720\pi$
$884$	−0.430908	+	0.350549i	−0.0144930	+	0.0117902i
$885$		0			0
$886$	−8.75453	+	5.05443i	−0.294114	+	0.169807i
$887$	−20.8317	−	36.0815i	−0.699459	−	1.21150i	−0.968654	−	0.248413i	$-0.920091\pi$
$887$	−20.8317	−	36.0815i	−0.699459	−	1.21150i	0.269196	−	0.963086i	$-0.413242\pi$
$888$	1.68455	−	2.91773i	0.0565299	−	0.0979127i
$889$			71.8736i			2.41056i
$890$		0			0
$891$	−2.28749	−	1.32068i	−0.0766337	−	0.0442445i
$892$			4.34630i			0.145525i
$893$	−4.05842	+	7.02939i	−0.135810	+	0.235230i
$894$	3.27684	+	5.67566i	0.109594	+	0.189822i
$895$		0			0
$896$	29.4155			0.982703
$897$	−0.742695	−	0.283181i	−0.0247979	−	0.00945513i
$898$	−5.31133			−0.177242
$899$	13.1586	−	7.59709i	0.438862	−	0.253377i
$900$		0			0
$901$	0.213134	−	0.369159i	0.00710053	−	0.0122985i
$902$			6.33375i			0.210891i
$903$	−26.5454	−	15.3260i	−0.883377	−	0.510018i
$904$	−8.33284	−	4.81097i	−0.277146	−	0.160010i
$905$		0			0
$906$	−2.13342	+	3.69520i	−0.0708783	+	0.122765i
$907$	−25.1044	−	43.4822i	−0.833579	−	1.44380i	−0.895182	−	0.445701i	$-0.852955\pi$
$907$	−25.1044	−	43.4822i	−0.833579	−	1.44380i	0.0616030	−	0.998101i	$-0.480379\pi$
$908$	−32.4799	+	18.7523i	−1.07788	+	0.622316i
$909$	6.80275			0.225633
$910$		0			0
$911$	6.06993			0.201106			0.100553	−	0.994932i	$-0.467939\pi$
$911$	6.06993			0.201106			0.100553	+	0.994932i	$0.467939\pi$
$912$	2.85751	−	1.64978i	0.0946216	−	0.0546298i
$913$	−12.6648	−	21.9360i	−0.419142	−	0.725976i
$914$	−3.18051	+	5.50880i	−0.105202	+	0.182215i
$915$		0			0
$916$	−10.5626	−	6.09834i	−0.348999	−	0.201495i
$917$	50.5855	+	29.2056i	1.67048	+	0.964452i
$918$			0.0242995i			0.000802004i
$919$	9.61032	−	16.6456i	0.317015	−	0.549087i	−0.662849	−	0.748754i	$-0.730653\pi$
$919$	9.61032	−	16.6456i	0.317015	−	0.549087i	0.979864	+	0.199667i	$0.0639860\pi$
$920$		0			0
$921$	6.01156	−	3.47077i	0.198088	−	0.114366i
$922$	7.26012			0.239099
$923$	6.79875	−	17.8310i	0.223783	−	0.586915i
$924$	17.3027			0.569218
$925$		0			0
$926$	−2.87382	−	4.97760i	−0.0944396	−	0.163574i
$927$	2.33728	−	4.04829i	0.0767663	−	0.132963i
$928$		−	32.7786i		−	1.07601i
$929$	−5.33864	−	3.08227i	−0.175155	−	0.101126i	0.409859	−	0.912149i	$-0.365578\pi$
$929$	−5.33864	−	3.08227i	−0.175155	−	0.101126i	−0.585014	+	0.811023i	$0.698911\pi$
$930$		0			0
$931$			4.54451i			0.148940i
$932$	19.1304	−	33.1349i	0.626638	−	1.08537i
$933$	6.96704	+	12.0673i	0.228091	+	0.395065i
$934$	−3.57502	+	2.06404i	−0.116978	+	0.0675374i
$935$		0			0
$936$	1.51225	−	3.96616i	0.0494294	−	0.129638i
$937$	−7.89678			−0.257977			−0.128988	−	0.991646i	$-0.541173\pi$
$937$	−7.89678			−0.257977			−0.128988	+	0.991646i	$0.541173\pi$
$938$	−2.24204	+	1.29444i	−0.0732053	+	0.0422651i
$939$	4.51454	+	7.81941i	0.147326	+	0.255177i
$940$		0			0
$941$			38.9659i			1.27025i	0.772409	+	0.635126i	$0.219052\pi$
$941$			38.9659i			1.27025i	−0.772409	+	0.635126i	$0.780948\pi$
$942$	−1.57378	−	0.908622i	−0.0512765	−	0.0296045i
$943$	−1.52021	−	0.877696i	−0.0495050	−	0.0285817i
$944$			33.5137i			1.09078i
$945$		0			0
$946$	3.55321	+	6.15434i	0.115525	+	0.200095i
$947$	17.5175	−	10.1137i	0.569243	−	0.328652i	−0.187604	−	0.982245i	$-0.560072\pi$
$947$	17.5175	−	10.1137i	0.569243	−	0.328652i	0.756847	+	0.653592i	$0.226739\pi$
$948$	−22.6561			−0.735837
$949$	51.1168	−	8.21390i	1.65932	−	0.266635i
$950$		0			0
$951$	0.430259	−	0.248410i	0.0139521	−	0.00805526i
$952$	−0.162959	−	0.282253i	−0.00528152	−	0.00914786i
$953$	7.18379	−	12.4427i	0.232706	−	0.403059i	−0.725898	−	0.687803i	$-0.758575\pi$
$953$	7.18379	−	12.4427i	0.232706	−	0.403059i	0.958604	+	0.284744i	$0.0919087\pi$
$954$			1.59086i			0.0515059i
$955$		0			0
$956$	−7.40771	−	4.27684i	−0.239582	−	0.138323i
$957$		−	25.4819i		−	0.823713i
$958$	−5.27945	+	9.14428i	−0.170571	+	0.295438i
$959$	25.5989	+	44.3386i	0.826631	+	1.43177i
$960$		0			0
$961$	28.5195			0.919982
$962$	2.90343	+	1.10704i	0.0936103	+	0.0356925i
$963$	13.3243			0.429371
$964$	1.02247	−	0.590323i	0.0329315	−	0.0190130i
$965$		0			0
$966$	0.113885	−	0.197254i	0.00366418	−	0.00634655i
$967$			3.30779i			0.106371i	0.998585	+	0.0531857i	$0.0169375\pi$
$967$			3.30779i			0.106371i	−0.998585	+	0.0531857i	$0.983062\pi$
$968$	4.10181	+	2.36818i	0.131837	+	0.0761162i
$969$	−0.0665613	−	0.0384292i	−0.00213826	−	0.00123452i
$970$		0			0
$971$	14.6341	−	25.3469i	0.469630	−	0.813422i	−0.529767	−	0.848143i	$-0.677721\pi$
$971$	14.6341	−	25.3469i	0.469630	−	0.813422i	0.999397	+	0.0347206i	$0.0110541\pi$
$972$	0.954656	+	1.65351i	0.0306206	+	0.0530365i
$973$	−24.0956	+	13.9116i	−0.772470	+	0.445986i
$974$	−0.908727			−0.0291175
$975$		0			0
$976$	−44.9899			−1.44009
$977$	−43.8512	+	25.3175i	−1.40292	+	0.809979i	−0.994692	−	0.102900i	$-0.967188\pi$
$977$	−43.8512	+	25.3175i	−1.40292	+	0.809979i	−0.408232	+	0.912878i	$0.633855\pi$
$978$	−3.07981	−	5.33438i	−0.0984813	−	0.170575i
$979$	−13.9890	+	24.2297i	−0.447092	+	0.774386i
$980$		0			0
$981$	4.44251	+	2.56488i	0.141838	+	0.0818904i
$982$	−0.573998	−	0.331398i	−0.0183170	−	0.0105753i
$983$		−	29.1032i		−	0.928248i	−0.885770	−	0.464124i	$-0.846369\pi$
$983$		−	29.1032i		−	0.928248i	0.885770	−	0.464124i	$-0.153631\pi$
$984$	4.68709	−	8.11828i	0.149419	−	0.258801i
$985$		0			0
$986$	−0.203017	+	0.117212i	−0.00646537	+	0.00373278i
$987$	29.2368			0.930618
$988$	4.13799	+	5.08658i	0.131647	+	0.161826i
$989$	−1.96954			−0.0626276
$990$		0			0
$991$	−9.67671	−	16.7606i	−0.307391	−	0.532417i	0.670400	−	0.742000i	$-0.266123\pi$
$991$	−9.67671	−	16.7606i	−0.307391	−	0.532417i	−0.977791	+	0.209583i	$0.932789\pi$
$992$	−2.67566	+	4.63438i	−0.0849523	+	0.147142i
$993$			26.0211i			0.825756i
$994$	4.73578	+	2.73420i	0.150210	+	0.0867237i
$995$		0			0
$996$			18.3095i			0.580158i
$997$	30.8483	−	53.4309i	0.976976	−	1.69217i	0.303723	−	0.952760i	$-0.401770\pi$
$997$	30.8483	−	53.4309i	0.976976	−	1.69217i	0.673253	−	0.739412i	$-0.264896\pi$
$998$	1.30768	+	2.26496i	0.0413937	+	0.0716961i
$999$	−2.47841	+	1.43091i	−0.0784133	+	0.0452719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.i.751.3		8
5.2	odd	4		975.2.w.g.49.3		8
5.3	odd	4		975.2.w.j.49.2		8
5.4	even	2		195.2.bb.c.166.2	yes	8
13.4	even	6	inner	975.2.bc.i.901.3		8
15.14	odd	2		585.2.bu.b.361.3		8
65.4	even	6		195.2.bb.c.121.2	✓	8
65.17	odd	12		975.2.w.j.199.2		8
65.24	odd	12		2535.2.a.bi.1.3		4
65.43	odd	12		975.2.w.g.199.3		8
65.54	odd	12		2535.2.a.bl.1.2		4
195.89	even	12		7605.2.a.ck.1.2		4
195.119	even	12		7605.2.a.cg.1.3		4
195.134	odd	6		585.2.bu.b.316.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.c.121.2	✓	8	65.4	even	6
195.2.bb.c.166.2	yes	8	5.4	even	2
585.2.bu.b.316.3		8	195.134	odd	6
585.2.bu.b.361.3		8	15.14	odd	2
975.2.w.g.49.3		8	5.2	odd	4
975.2.w.g.199.3		8	65.43	odd	12
975.2.w.j.49.2		8	5.3	odd	4
975.2.w.j.199.2		8	65.17	odd	12
975.2.bc.i.751.3		8	1.1	even	1	trivial
975.2.bc.i.901.3		8	13.4	even	6	inner
2535.2.a.bi.1.3		4	65.24	odd	12
2535.2.a.bl.1.2		4	65.54	odd	12
7605.2.a.cg.1.3		4	195.119	even	12
7605.2.a.ck.1.2		4	195.89	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.260797 + 0.150571i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.954656 + 1.65351i) q^{4} +(-0.260797 - 0.150571i) q^{6} +(-2.97125 - 1.71545i) q^{7} -1.17726i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.260797 + 0.150571i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.954656 + 1.65351i) q^{4} +(-0.260797 - 0.150571i) q^{6} +(-2.97125 - 1.71545i) q^{7} -1.17726i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.28749 - 1.32068i) q^{11} -1.90931 q^{12} +(-0.572034 - 3.55988i) q^{13} +1.03319 q^{14} +(-1.73205 - 3.00000i) q^{16} +(-0.0403455 + 0.0698805i) q^{17} -0.301143i q^{18} +(0.824892 + 0.476251i) q^{19} -3.43091i q^{21} +(-0.397714 + 0.688861i) q^{22} +(-0.110226 - 0.190917i) q^{23} +(1.01954 - 0.588631i) q^{24} +(0.685202 + 0.842277i) q^{26} -1.00000 q^{27} +(5.67305 - 3.27534i) q^{28} +(-4.82362 - 8.35476i) q^{29} +1.57498i q^{31} +(2.94251 + 1.69886i) q^{32} +(2.28749 + 1.32068i) q^{33} -0.0242995i q^{34} +(-0.954656 - 1.65351i) q^{36} +(2.47841 - 1.43091i) q^{37} -0.286840 q^{38} +(2.79693 - 2.27534i) q^{39} +(6.89590 - 3.98135i) q^{41} +(0.516597 + 0.894772i) q^{42} +(4.46704 - 7.73715i) q^{43} +5.04319i q^{44} +(0.0574933 + 0.0331938i) q^{46} +8.52159i q^{47} +(1.73205 - 3.00000i) q^{48} +(2.38556 + 4.13192i) q^{49} -0.0806910 q^{51} +(6.43241 + 2.45260i) q^{52} -5.28273 q^{53} +(0.260797 - 0.150571i) q^{54} +(-2.01954 + 3.49794i) q^{56} +0.952503i q^{57} +(2.51598 + 1.45260i) q^{58} +(-8.37841 - 4.83728i) q^{59} +(6.49373 - 11.2475i) q^{61} +(-0.237147 - 0.410750i) q^{62} +(2.97125 - 1.71545i) q^{63} +5.90501 q^{64} -0.795428 q^{66} +(-2.17001 + 1.25286i) q^{67} +(-0.0770322 - 0.133424i) q^{68} +(0.110226 - 0.190917i) q^{69} +(4.58363 + 2.64636i) q^{71} +(1.01954 + 0.588631i) q^{72} +14.3591i q^{73} +(-0.430908 + 0.746354i) q^{74} +(-1.57498 + 0.909313i) q^{76} -9.06228 q^{77} +(-0.386832 + 1.01454i) q^{78} +11.8661 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.19895 + 2.07665i) q^{82} -9.58956i q^{83} +(5.67305 + 3.27534i) q^{84} +2.69044i q^{86} +(4.82362 - 8.35476i) q^{87} +(-1.55479 - 2.69297i) q^{88} +(-9.17319 + 5.29614i) q^{89} +(-4.40716 + 11.5586i) q^{91} +0.420912 q^{92} +(-1.36397 + 0.787488i) q^{93} +(-1.28311 - 2.22241i) q^{94} +3.39771i q^{96} +(4.05202 + 2.33943i) q^{97} +(-1.24430 - 0.718396i) q^{98} +2.64136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + 4 q^{3} + 4 q^{4} - 6 q^{6} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 + 4 * q^3 + 4 * q^4 - 6 * q^6 - 6 * q^7 - 4 * q^9	\( 8 q - 6 q^{2} + 4 q^{3} + 4 q^{4} - 6 q^{6} - 6 q^{7} - 4 q^{9} + 12 q^{11} + 8 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{17} + 12 q^{19} - 4 q^{23} - 12 q^{24} - 4 q^{26} - 8 q^{27} + 12 q^{28} - 6 q^{29} - 12 q^{32} + 12 q^{33} + 4 q^{36} + 12 q^{37} + 16 q^{38} - 30 q^{41} - 2 q^{42} - 6 q^{43} + 36 q^{46} - 8 q^{49} + 4 q^{51} + 20 q^{52} + 32 q^{53} + 6 q^{54} + 4 q^{56} - 12 q^{58} - 30 q^{59} + 30 q^{62} + 6 q^{63} + 32 q^{64} - 30 q^{67} - 16 q^{68} + 4 q^{69} + 18 q^{71} - 12 q^{72} + 12 q^{74} + 8 q^{77} - 14 q^{78} + 56 q^{79} - 4 q^{81} + 24 q^{82} + 12 q^{84} + 6 q^{87} - 8 q^{88} - 18 q^{89} - 16 q^{91} - 40 q^{92} + 24 q^{93} - 16 q^{94} + 6 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 + 4 * q^3 + 4 * q^4 - 6 * q^6 - 6 * q^7 - 4 * q^9 + 12 * q^11 + 8 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^17 + 12 * q^19 - 4 * q^23 - 12 * q^24 - 4 * q^26 - 8 * q^27 + 12 * q^28 - 6 * q^29 - 12 * q^32 + 12 * q^33 + 4 * q^36 + 12 * q^37 + 16 * q^38 - 30 * q^41 - 2 * q^42 - 6 * q^43 + 36 * q^46 - 8 * q^49 + 4 * q^51 + 20 * q^52 + 32 * q^53 + 6 * q^54 + 4 * q^56 - 12 * q^58 - 30 * q^59 + 30 * q^62 + 6 * q^63 + 32 * q^64 - 30 * q^67 - 16 * q^68 + 4 * q^69 + 18 * q^71 - 12 * q^72 + 12 * q^74 + 8 * q^77 - 14 * q^78 + 56 * q^79 - 4 * q^81 + 24 * q^82 + 12 * q^84 + 6 * q^87 - 8 * q^88 - 18 * q^89 - 16 * q^91 - 40 * q^92 + 24 * q^93 - 16 * q^94 + 6 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

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