LMFDB - Embedded newform 975.2.bc.m.751.2

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 269x^{12} + 1420x^{10} + 4080x^{8} + 6272x^{6} + 4672x^{4} + 1308x^{2} + 100 $ x^16 + 26x^14 + 269x^12 + 1420x^10 + 4080x^8 + 6272x^6 + 4672x^4 + 1308*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.2
Root			$-2.01123i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.m.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74177 + 1.00561i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.02251 - 1.77105i) q^{4} +(1.74177 + 1.00561i) q^{6} +(-1.92561 - 1.11175i) q^{7} +0.0905636i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.74177 + 1.00561i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.02251 - 1.77105i) q^{4} +(1.74177 + 1.00561i) q^{6} +(-1.92561 - 1.11175i) q^{7} +0.0905636i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.40935 + 2.54574i) q^{11} -2.04503 q^{12} +(-3.38998 - 1.22803i) q^{13} +4.47196 q^{14} +(1.95396 + 3.38435i) q^{16} +(-1.15676 + 2.00356i) q^{17} -2.01123i q^{18} +(6.07004 + 3.50454i) q^{19} +2.22350i q^{21} +(5.12006 - 8.86820i) q^{22} +(2.75574 + 4.77307i) q^{23} +(0.0784304 - 0.0452818i) q^{24} +(7.13949 - 1.27006i) q^{26} +1.00000 q^{27} +(-3.93792 + 2.27356i) q^{28} +(-0.503549 - 0.872172i) q^{29} -9.55876i q^{31} +(-6.96356 - 4.02041i) q^{32} +(4.40935 + 2.54574i) q^{33} -4.65300i q^{34} +(1.02251 + 1.77105i) q^{36} +(-1.00423 + 0.579795i) q^{37} -14.0968 q^{38} +(0.631485 + 3.54982i) q^{39} +(1.42586 - 0.823222i) q^{41} +(-2.23598 - 3.87283i) q^{42} +(4.60635 - 7.97844i) q^{43} +10.4122i q^{44} +(-9.59973 - 5.54241i) q^{46} +1.34816i q^{47} +(1.95396 - 3.38435i) q^{48} +(-1.02803 - 1.78060i) q^{49} +2.31351 q^{51} +(-5.64120 + 4.74813i) q^{52} +9.36564 q^{53} +(-1.74177 + 1.00561i) q^{54} +(0.100684 - 0.174390i) q^{56} -7.00908i q^{57} +(1.75413 + 1.01275i) q^{58} +(-0.894540 - 0.516463i) q^{59} +(5.32768 - 9.22782i) q^{61} +(9.61241 + 16.6492i) q^{62} +(1.92561 - 1.11175i) q^{63} +8.35609 q^{64} -10.2401 q^{66} +(2.88530 - 1.66583i) q^{67} +(2.36560 + 4.09734i) q^{68} +(2.75574 - 4.77307i) q^{69} +(1.54037 + 0.889333i) q^{71} +(-0.0784304 - 0.0452818i) q^{72} +4.49399i q^{73} +(1.16610 - 2.01974i) q^{74} +(12.4134 - 7.16688i) q^{76} +11.3209 q^{77} +(-4.66965 - 5.54795i) q^{78} +7.05606 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.65568 + 2.86773i) q^{82} -2.25488i q^{83} +(3.93792 + 2.27356i) q^{84} +18.5288i q^{86} +(-0.503549 + 0.872172i) q^{87} +(-0.230551 - 0.399327i) q^{88} +(7.03934 - 4.06416i) q^{89} +(5.16250 + 6.13350i) q^{91} +11.2711 q^{92} +(-8.27813 + 4.77938i) q^{93} +(-1.35573 - 2.34819i) q^{94} +8.04083i q^{96} +(-5.22710 - 3.01787i) q^{97} +(3.58118 + 2.06760i) q^{98} -5.09148i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 10 q^{4} - 6 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 10 * q^4 - 6 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 10 q^{4} - 6 q^{7} - 8 q^{9} - 6 q^{11} - 20 q^{12} - 4 q^{14} - 14 q^{16} + 10 q^{17} - 2 q^{22} + 12 q^{23} + 26 q^{26} + 16 q^{27} - 24 q^{28} + 12 q^{29} - 30 q^{32} + 6 q^{33} + 10 q^{36} - 6 q^{37} + 16 q^{38} - 18 q^{41} + 2 q^{42} + 16 q^{43} - 24 q^{46} - 14 q^{48} + 14 q^{49} - 20 q^{51} - 24 q^{52} + 40 q^{53} - 28 q^{56} - 72 q^{58} - 42 q^{59} - 16 q^{61} + 34 q^{62} + 6 q^{63} - 68 q^{64} + 4 q^{66} + 18 q^{67} - 28 q^{68} + 12 q^{69} + 6 q^{71} - 20 q^{74} + 24 q^{76} - 48 q^{77} - 16 q^{78} + 52 q^{79} - 8 q^{81} + 28 q^{82} + 24 q^{84} + 12 q^{87} + 68 q^{88} + 24 q^{89} + 6 q^{91} + 108 q^{92} - 6 q^{93} + 4 q^{94} + 24 q^{98}+O(q^{100}) $ 16 * q - 8 * q^3 + 10 * q^4 - 6 * q^7 - 8 * q^9 - 6 * q^11 - 20 * q^12 - 4 * q^14 - 14 * q^16 + 10 * q^17 - 2 * q^22 + 12 * q^23 + 26 * q^26 + 16 * q^27 - 24 * q^28 + 12 * q^29 - 30 * q^32 + 6 * q^33 + 10 * q^36 - 6 * q^37 + 16 * q^38 - 18 * q^41 + 2 * q^42 + 16 * q^43 - 24 * q^46 - 14 * q^48 + 14 * q^49 - 20 * q^51 - 24 * q^52 + 40 * q^53 - 28 * q^56 - 72 * q^58 - 42 * q^59 - 16 * q^61 + 34 * q^62 + 6 * q^63 - 68 * q^64 + 4 * q^66 + 18 * q^67 - 28 * q^68 + 12 * q^69 + 6 * q^71 - 20 * q^74 + 24 * q^76 - 48 * q^77 - 16 * q^78 + 52 * q^79 - 8 * q^81 + 28 * q^82 + 24 * q^84 + 12 * q^87 + 68 * q^88 + 24 * q^89 + 6 * q^91 + 108 * q^92 - 6 * q^93 + 4 * q^94 + 24 * 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 $

$2$	−1.74177	+	1.00561i	−1.23162	+	0.711076i	−0.967367	−	0.253378i	$-0.918458\pi$
$2$	−1.74177	+	1.00561i	−1.23162	+	0.711076i	−0.264252	+	0.964454i	$0.585125\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.02251	−	1.77105i	0.511257	−	0.885524i
$5$		0			0
$5$		0			0
$6$	1.74177	+	1.00561i	0.711076	+	0.410540i
$7$	−1.92561	−	1.11175i	−0.727811	−	0.420202i	0.0898101	−	0.995959i	$-0.471374\pi$
$7$	−1.92561	−	1.11175i	−0.727811	−	0.420202i	−0.817621	+	0.575757i	$0.804707\pi$
$8$			0.0905636i			0.0320191i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−4.40935	+	2.54574i	−1.32947	+	0.767569i	−0.985217	−	0.171308i	$-0.945201\pi$
$11$	−4.40935	+	2.54574i	−1.32947	+	0.767569i	−0.344251	+	0.938877i	$0.611867\pi$
$12$	−2.04503			−0.590349
$13$	−3.38998	−	1.22803i	−0.940211	−	0.340594i
$13$	−3.38998	−	1.22803i	−0.940211	−	0.340594i
$14$	4.47196			1.19518
$15$		0			0
$16$	1.95396	+	3.38435i	0.488489	+	0.846088i
$17$	−1.15676	+	2.00356i	−0.280555	+	0.485935i	−0.971521	−	0.236952i	$-0.923852\pi$
$17$	−1.15676	+	2.00356i	−0.280555	+	0.485935i	0.690967	+	0.722886i	$0.257185\pi$
$18$		−	2.01123i		−	0.474050i
$19$	6.07004	+	3.50454i	1.39256	+	0.803996i	0.993598	−	0.112970i	$-0.0360364\pi$
$19$	6.07004	+	3.50454i	1.39256	+	0.803996i	0.398964	+	0.916967i	$0.369370\pi$
$20$		0			0
$21$			2.22350i			0.485207i
$22$	5.12006	−	8.86820i	1.09160	−	1.89071i
$23$	2.75574	+	4.77307i	0.574611	+	0.995255i	0.996084	+	0.0884139i	$0.0281798\pi$
$23$	2.75574	+	4.77307i	0.574611	+	0.995255i	−0.421473	+	0.906841i	$0.638487\pi$
$24$	0.0784304	−	0.0452818i	0.0160095	−	0.00924311i
$25$		0			0
$26$	7.13949	−	1.27006i	1.40017	−	0.249079i
$27$	1.00000			0.192450
$28$	−3.93792	+	2.27356i	−0.744197	+	0.429662i
$29$	−0.503549	−	0.872172i	−0.0935066	−	0.161958i	0.815478	−	0.578788i	$-0.196474\pi$
$29$	−0.503549	−	0.872172i	−0.0935066	−	0.161958i	−0.908984	+	0.416830i	$0.863141\pi$
$30$		0			0
$31$		−	9.55876i		−	1.71680i	−0.512977	−	0.858402i	$-0.671458\pi$
$31$		−	9.55876i		−	1.71680i	0.512977	−	0.858402i	$-0.328542\pi$
$32$	−6.96356	−	4.02041i	−1.23099	−	0.710715i
$33$	4.40935	+	2.54574i	0.767569	+	0.443156i
$34$		−	4.65300i		−	0.797982i
$35$		0			0
$36$	1.02251	+	1.77105i	0.170419	+	0.295175i
$37$	−1.00423	+	0.579795i	−0.165095	+	0.0953178i	−0.580271	−	0.814423i	$-0.697053\pi$
$37$	−1.00423	+	0.579795i	−0.165095	+	0.0953178i	0.415176	+	0.909741i	$0.363720\pi$
$38$	−14.0968			−2.28681
$39$	0.631485	+	3.54982i	0.101118	+	0.568426i
$40$		0			0
$41$	1.42586	−	0.823222i	0.222682	−	0.128566i	−0.384509	−	0.923121i	$-0.625629\pi$
$41$	1.42586	−	0.823222i	0.222682	−	0.128566i	0.607192	+	0.794555i	$0.292296\pi$
$42$	−2.23598	−	3.87283i	−0.345019	−	0.597590i
$43$	4.60635	−	7.97844i	0.702462	−	1.21670i	−0.265137	−	0.964211i	$-0.585417\pi$
$43$	4.60635	−	7.97844i	0.702462	−	1.21670i	0.967600	−	0.252490i	$-0.0812494\pi$
$44$			10.4122i			1.56970i
$45$		0			0
$46$	−9.59973	−	5.54241i	−1.41540	−	0.817183i
$47$			1.34816i			0.196649i	0.995154	+	0.0983246i	$0.0313484\pi$
$47$			1.34816i			0.196649i	−0.995154	+	0.0983246i	$0.968652\pi$
$48$	1.95396	−	3.38435i	0.282029	−	0.488489i
$49$	−1.02803	−	1.78060i	−0.146861	−	0.254371i
$50$		0			0
$51$	2.31351			0.323956
$52$	−5.64120	+	4.74813i	−0.782293	+	0.658447i
$53$	9.36564			1.28647			0.643235	−	0.765669i	$-0.277592\pi$
$53$	9.36564			1.28647			0.643235	+	0.765669i	$0.277592\pi$
$54$	−1.74177	+	1.00561i	−0.237025	+	0.136847i
$55$		0			0
$56$	0.100684	−	0.174390i	0.0134545	−	0.0233038i
$57$		−	7.00908i		−	0.928375i
$58$	1.75413	+	1.01275i	0.230329	+	0.132981i
$59$	−0.894540	−	0.516463i	−0.116459	−	0.0672377i	0.440639	−	0.897684i	$-0.354752\pi$
$59$	−0.894540	−	0.516463i	−0.116459	−	0.0672377i	−0.557098	+	0.830447i	$0.688085\pi$
$60$		0			0
$61$	5.32768	−	9.22782i	0.682140	−	1.18150i	−0.292187	−	0.956361i	$-0.594383\pi$
$61$	5.32768	−	9.22782i	0.682140	−	1.18150i	0.974327	−	0.225140i	$-0.0722838\pi$
$62$	9.61241	+	16.6492i	1.22078	+	2.11445i
$63$	1.92561	−	1.11175i	0.242604	−	0.140067i
$64$	8.35609			1.04451
$65$		0			0
$66$	−10.2401			−1.26047
$67$	2.88530	−	1.66583i	0.352495	−	0.203513i	−0.313288	−	0.949658i	$-0.601431\pi$
$67$	2.88530	−	1.66583i	0.352495	−	0.203513i	0.665784	+	0.746145i	$0.268097\pi$
$68$	2.36560	+	4.09734i	0.286871	+	0.496875i
$69$	2.75574	−	4.77307i	0.331752	−	0.574611i
$70$		0			0
$71$	1.54037	+	0.889333i	0.182808	+	0.105544i	0.588611	−	0.808416i	$-0.299675\pi$
$71$	1.54037	+	0.889333i	0.182808	+	0.105544i	−0.405803	+	0.913961i	$0.633008\pi$
$72$	−0.0784304	−	0.0452818i	−0.00924311	−	0.00533651i
$73$			4.49399i			0.525982i	0.964798	+	0.262991i	$0.0847089\pi$
$73$			4.49399i			0.525982i	−0.964798	+	0.262991i	$0.915291\pi$
$74$	1.16610	−	2.01974i	0.135556	−	0.234790i
$75$		0			0
$76$	12.4134	−	7.16688i	1.42392	−	0.822098i
$77$	11.3209			1.29014
$78$	−4.66965	−	5.54795i	−0.528734	−	0.628182i
$79$	7.05606			0.793868			0.396934	−	0.917847i	$-0.370074\pi$
$79$	7.05606			0.793868			0.396934	+	0.917847i	$0.370074\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.65568	+	2.86773i	−0.182840	+	0.316688i
$83$		−	2.25488i		−	0.247505i	−0.992313	−	0.123752i	$-0.960507\pi$
$83$		−	2.25488i		−	0.247505i	0.992313	−	0.123752i	$-0.0394928\pi$
$84$	3.93792	+	2.27356i	0.429662	+	0.248066i
$85$		0			0
$86$			18.5288i			1.99802i
$87$	−0.503549	+	0.872172i	−0.0539861	+	0.0935066i
$88$	−0.230551	−	0.399327i	−0.0245769	−	0.0425684i
$89$	7.03934	−	4.06416i	0.746168	−	0.430800i	−0.0781395	−	0.996942i	$-0.524898\pi$
$89$	7.03934	−	4.06416i	0.746168	−	0.430800i	0.824308	+	0.566142i	$0.191565\pi$
$90$		0			0
$91$	5.16250	+	6.13350i	0.541177	+	0.642966i
$92$	11.2711			1.17510
$93$	−8.27813	+	4.77938i	−0.858402	+	0.495599i
$94$	−1.35573	−	2.34819i	−0.139833	−	0.242197i
$95$		0			0
$96$			8.04083i			0.820663i
$97$	−5.22710	−	3.01787i	−0.530731	−	0.306418i	0.210583	−	0.977576i	$-0.432464\pi$
$97$	−5.22710	−	3.01787i	−0.530731	−	0.306418i	−0.741314	+	0.671158i	$0.765797\pi$
$98$	3.58118	+	2.06760i	0.361754	+	0.208859i
$99$		−	5.09148i		−	0.511713i
$100$		0			0
$101$	4.13627	+	7.16422i	0.411574	+	0.712867i	0.995062	−	0.0992549i	$-0.0316459\pi$
$101$	4.13627	+	7.16422i	0.411574	+	0.712867i	−0.583488	+	0.812122i	$0.698313\pi$
$102$	−4.02961	+	2.32650i	−0.398991	+	0.230358i
$103$	12.4746			1.22916			0.614581	−	0.788854i	$-0.289325\pi$
$103$	12.4746			1.22916			0.614581	+	0.788854i	$0.289325\pi$
$104$	0.111215	−	0.307009i	0.0109055	−	0.0301047i
$105$		0			0
$106$	−16.3128	+	9.41821i	−1.58444	+	0.914777i
$107$	3.54477	+	6.13972i	0.342686	+	0.593549i	0.984931	−	0.172951i	$-0.0553301\pi$
$107$	3.54477	+	6.13972i	0.342686	+	0.593549i	−0.642245	+	0.766500i	$0.721997\pi$
$108$	1.02251	−	1.77105i	0.0983915	−	0.170419i
$109$		−	8.37275i		−	0.801964i	−0.916086	−	0.400982i	$-0.868669\pi$
$109$		−	8.37275i		−	0.801964i	0.916086	−	0.400982i	$-0.131331\pi$
$110$		0			0
$111$	1.00423	+	0.579795i	0.0953178	+	0.0550317i
$112$		−	8.68924i		−	0.821056i
$113$	−1.28611	+	2.22760i	−0.120987	+	0.209555i	−0.920157	−	0.391549i	$-0.871939\pi$
$113$	−1.28611	+	2.22760i	−0.120987	+	0.209555i	0.799170	+	0.601105i	$0.205273\pi$
$114$	7.04842	+	12.2082i	0.660145	+	1.14340i
$115$		0			0
$116$	−2.05954			−0.191224
$117$	2.75849	−	2.32179i	0.255023	−	0.214650i
$118$	2.07745			0.191244
$119$	4.45491	−	2.57204i	0.408381	−	0.235779i
$120$		0			0
$121$	7.46158	−	12.9238i	0.678325	−	1.17489i
$122$			21.4303i			1.94021i
$123$	−1.42586	−	0.823222i	−0.128566	−	0.0742274i
$124$	−16.9290	−	9.77397i	−1.52027	−	0.877729i
$125$		0			0
$126$	−2.23598	+	3.87283i	−0.199197	+	0.345019i
$127$	10.2212	+	17.7037i	0.906986	+	1.57095i	0.818229	+	0.574892i	$0.194956\pi$
$127$	10.2212	+	17.7037i	0.906986	+	1.57095i	0.0887562	+	0.996053i	$0.471711\pi$
$128$	−0.627284	+	0.362163i	−0.0554446	+	0.0320110i
$129$	−9.21271			−0.811134
$130$		0			0
$131$	−3.75523			−0.328096			−0.164048	−	0.986452i	$-0.552455\pi$
$131$	−3.75523			−0.328096			−0.164048	+	0.986452i	$0.552455\pi$
$132$	9.01725	−	5.20611i	0.784851	−	0.453134i
$133$	−7.79234	−	13.4967i	−0.675681	−	1.17031i
$134$	−3.35036	+	5.80299i	−0.289427	+	0.501302i
$135$		0			0
$136$	−0.181450	−	0.104760i	−0.0155592	−	0.00898310i
$137$	−1.79746	−	1.03777i	−0.153568	−	0.0886623i	0.421247	−	0.906946i	$-0.361593\pi$
$137$	−1.79746	−	1.03777i	−0.153568	−	0.0886623i	−0.574815	+	0.818284i	$0.694926\pi$
$138$			11.0848i			0.943602i
$139$	−10.7917	+	18.6917i	−0.915337	+	1.58541i	−0.108931	+	0.994049i	$0.534743\pi$
$139$	−10.7917	+	18.6917i	−0.915337	+	1.58541i	−0.806406	+	0.591362i	$0.798591\pi$
$140$		0			0
$141$	1.16754	−	0.674080i	0.0983246	−	0.0567678i
$142$	−3.57730			−0.300200
$143$	18.0738	−	3.21519i	1.51141	−	0.268868i
$144$	−3.90791			−0.325660
$145$		0			0
$146$	−4.51921	−	7.82751i	−0.374013	−	0.647809i
$147$	−1.02803	+	1.78060i	−0.0847904	+	0.146861i
$148$			2.37140i			0.194928i
$149$	−16.1862	−	9.34512i	−1.32603	−	0.765582i	−0.341344	−	0.939938i	$-0.610882\pi$
$149$	−16.1862	−	9.34512i	−1.32603	−	0.765582i	−0.984683	+	0.174357i	$0.944215\pi$
$150$		0			0
$151$			1.70343i			0.138623i	0.997595	+	0.0693117i	$0.0220803\pi$
$151$			1.70343i			0.138623i	−0.997595	+	0.0693117i	$0.977920\pi$
$152$	−0.317384	+	0.549725i	−0.0257432	+	0.0445886i
$153$	−1.15676	−	2.00356i	−0.0935182	−	0.161978i
$154$	−19.7184	+	11.3844i	−1.58896	+	0.917384i
$155$		0			0
$156$	6.93260	+	2.51135i	0.555052	+	0.201069i
$157$	9.10906			0.726982			0.363491	−	0.931598i	$-0.381585\pi$
$157$	9.10906			0.726982			0.363491	+	0.931598i	$0.381585\pi$
$158$	−12.2900	+	7.09566i	−0.977744	+	0.564501i
$159$	−4.68282	−	8.11088i	−0.371372	−	0.643235i
$160$		0			0
$161$		−	12.2547i		−	0.965809i
$162$	1.74177	+	1.00561i	0.136847	+	0.0790084i
$163$	7.06916	+	4.08138i	0.553700	+	0.319679i	0.750613	−	0.660742i	$-0.229758\pi$
$163$	7.06916	+	4.08138i	0.553700	+	0.319679i	−0.196913	+	0.980421i	$0.563092\pi$
$164$		−	3.36702i		−	0.262920i
$165$		0			0
$166$	2.26753	+	3.92748i	0.175995	+	0.304832i
$167$	−2.11365	+	1.22032i	−0.163559	+	0.0944309i	−0.579545	−	0.814940i	$-0.696770\pi$
$167$	−2.11365	+	1.22032i	−0.163559	+	0.0944309i	0.415986	+	0.909371i	$0.363436\pi$
$168$	−0.201368			−0.0155359
$169$	9.98389	+	8.32598i	0.767992	+	0.640460i
$170$		0			0
$171$	−6.07004	+	3.50454i	−0.464188	+	0.267999i
$172$	−9.42013	−	16.3161i	−0.718278	−	1.24409i
$173$	4.54317	−	7.86899i	0.345411	−	0.598269i	−0.640018	−	0.768360i	$-0.721073\pi$
$173$	4.54317	−	7.86899i	0.345411	−	0.598269i	0.985428	+	0.170092i	$0.0544063\pi$
$174$		−	2.02550i		−	0.153553i
$175$		0			0
$176$	−17.2314	−	9.94853i	−1.29886	−	0.749899i
$177$			1.03293i			0.0776394i
$178$	−8.17395	+	14.1577i	−0.612663	+	1.06116i
$179$	9.86590	+	17.0882i	0.737412	+	1.27724i	0.953657	+	0.300896i	$0.0972858\pi$
$179$	9.86590	+	17.0882i	0.737412	+	1.27724i	−0.216245	+	0.976339i	$0.569381\pi$
$180$		0			0
$181$	5.17994			0.385022			0.192511	−	0.981295i	$-0.438337\pi$
$181$	5.17994			0.385022			0.192511	+	0.981295i	$0.438337\pi$
$182$	−15.1598	−	5.49169i	−1.12372	−	0.407071i
$183$	−10.6554			−0.787667
$184$	−0.432267	+	0.249569i	−0.0318671	+	0.0183985i
$185$		0			0
$186$	9.61241	−	16.6492i	0.704816	−	1.22078i
$187$		−	11.7792i		−	0.861380i
$188$	2.38765	+	1.37851i	0.174138	+	0.100538i
$189$	−1.92561	−	1.11175i	−0.140067	−	0.0808678i
$190$		0			0
$191$	0.477649	−	0.827312i	0.0345614	−	0.0598622i	−0.848227	−	0.529632i	$-0.822330\pi$
$191$	0.477649	−	0.827312i	0.0345614	−	0.0598622i	0.882789	+	0.469770i	$0.155663\pi$
$192$	−4.17804	−	7.23658i	−0.301524	−	0.522255i
$193$	−8.53580	+	4.92814i	−0.614420	+	0.354736i	−0.774693	−	0.632337i	$-0.782096\pi$
$193$	−8.53580	+	4.92814i	−0.614420	+	0.354736i	0.160273	+	0.987073i	$0.448762\pi$
$194$	12.1392			0.871545
$195$		0			0
$196$	−4.20470			−0.300335
$197$	2.77281	−	1.60088i	0.197554	−	0.114058i	−0.397960	−	0.917403i	$-0.630282\pi$
$197$	2.77281	−	1.60088i	0.197554	−	0.114058i	0.595514	+	0.803345i	$0.296948\pi$
$198$	5.12006	+	8.86820i	0.363867	+	0.630235i
$199$	9.62676	−	16.6740i	0.682423	−	1.18199i	−0.291816	−	0.956474i	$-0.594260\pi$
$199$	9.62676	−	16.6740i	0.682423	−	1.18199i	0.974239	−	0.225517i	$-0.0724070\pi$
$200$		0			0
$201$	−2.88530	−	1.66583i	−0.203513	−	0.117498i
$202$	−14.4089	−	8.31896i	−1.01380	−	0.585320i
$203$			2.23928i			0.157167i
$204$	2.36560	−	4.09734i	0.165625	−	0.286871i
$205$		0			0
$206$	−21.7280	+	12.5446i	−1.51386	+	0.874027i
$207$	−5.51147			−0.383074
$208$	−2.46779	−	13.8724i	−0.171110	−	0.961878i
$209$	−35.6866			−2.46849
$210$		0			0
$211$	7.58883	+	13.1442i	0.522436	+	0.904887i	0.999659	+	0.0261042i	$0.00831015\pi$
$211$	7.58883	+	13.1442i	0.522436	+	0.904887i	−0.477223	+	0.878782i	$0.658357\pi$
$212$	9.57650	−	16.5870i	0.657717	−	1.13920i
$213$		−	1.77867i		−	0.121872i
$214$	−12.3484	−	7.12933i	−0.844116	−	0.487351i
$215$		0			0
$216$			0.0905636i			0.00616207i
$217$	−10.6269	+	18.4064i	−0.721404	+	1.24951i
$218$	8.41975	+	14.5834i	0.570257	+	0.987714i
$219$	3.89191	−	2.24699i	0.262991	−	0.151838i
$220$		0			0
$221$	6.38181	−	5.37149i	0.429287	−	0.361326i
$222$	−2.33220			−0.156527
$223$	0.965676	−	0.557533i	0.0646665	−	0.0373352i	−0.467318	−	0.884089i	$-0.654780\pi$
$223$	0.965676	−	0.557533i	0.0646665	−	0.0373352i	0.531985	+	0.846754i	$0.321446\pi$
$224$	8.93938	+	15.4835i	0.597287	+	1.03453i
$225$		0			0
$226$		−	5.17330i		−	0.344123i
$227$	13.2569	+	7.65390i	0.879894	+	0.508007i	0.870623	−	0.491950i	$-0.163716\pi$
$227$	13.2569	+	7.65390i	0.879894	+	0.508007i	0.00927048	+	0.999957i	$0.497049\pi$
$228$	−12.4134	−	7.16688i	−0.822098	−	0.474638i
$229$			9.57447i			0.632699i	0.948643	+	0.316349i	$0.102457\pi$
$229$			9.57447i			0.632699i	−0.948643	+	0.316349i	$0.897543\pi$
$230$		0			0
$231$	−5.66045	−	9.80418i	−0.372430	−	0.645068i
$232$	0.0789870	−	0.0456032i	0.00518575	−	0.00299400i
$233$	−22.9693			−1.50477			−0.752384	−	0.658724i	$-0.771096\pi$
$233$	−22.9693			−1.50477			−0.752384	+	0.658724i	$0.771096\pi$
$234$	−2.46984	+	6.81801i	−0.161459	+	0.445707i
$235$		0			0
$236$	−1.82936	+	1.05618i	−0.119081	+	0.0687516i
$237$	−3.52803	−	6.11072i	−0.229170	−	0.396934i
$238$	−5.17296	+	8.95983i	−0.335313	+	0.580780i
$239$		−	11.5257i		−	0.745538i	−0.927924	−	0.372769i	$-0.878408\pi$
$239$		−	11.5257i		−	0.745538i	0.927924	−	0.372769i	$-0.121592\pi$
$240$		0			0
$241$	−13.2207	−	7.63297i	−0.851620	−	0.491683i	0.00957728	−	0.999954i	$-0.496951\pi$
$241$	−13.2207	−	7.63297i	−0.851620	−	0.491683i	−0.861197	+	0.508271i	$0.830285\pi$
$242$			30.0138i			1.92936i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−10.8953	−	18.8712i	−0.697498	−	1.20810i
$245$		0			0
$246$	3.31137			0.211125
$247$	−16.2736	−	19.3345i	−1.03547	−	1.23022i
$248$	0.865676			0.0549705
$249$	−1.95278	+	1.12744i	−0.123752	+	0.0714485i
$250$		0			0
$251$	14.6941	−	25.4509i	0.927483	−	1.60645i	0.139965	−	0.990157i	$-0.455301\pi$
$251$	14.6941	−	25.4509i	0.927483	−	1.60645i	0.787518	−	0.616291i	$-0.211366\pi$
$252$		−	4.54712i		−	0.286442i
$253$	−24.3020	−	14.0308i	−1.52785	−	0.882107i
$254$	−35.6060	−	20.5572i	−2.23412	−	1.28987i
$255$		0			0
$256$	−7.62770	+	13.2116i	−0.476731	+	0.825722i
$257$	−15.6066	−	27.0314i	−0.973513	−	1.68617i	−0.684757	−	0.728772i	$-0.740092\pi$
$257$	−15.6066	−	27.0314i	−0.973513	−	1.68617i	−0.288756	−	0.957403i	$-0.593242\pi$
$258$	16.0464	−	9.26442i	0.999008	−	0.576777i
$259$	2.57835			0.160211
$260$		0			0
$261$	1.00710			0.0623378
$262$	6.54075	−	3.77630i	0.404089	−	0.233301i
$263$	2.79159	+	4.83518i	0.172137	+	0.298150i	0.939167	−	0.343462i	$-0.111600\pi$
$263$	2.79159	+	4.83518i	0.172137	+	0.298150i	−0.767030	+	0.641611i	$0.778266\pi$
$264$	−0.230551	+	0.399327i	−0.0141895	+	0.0245769i
$265$		0			0
$266$	27.1450	+	15.6721i	1.66436	+	0.960921i
$267$	−7.03934	−	4.06416i	−0.430800	−	0.248723i
$268$		−	6.81333i		−	0.416191i
$269$	8.99744	−	15.5840i	0.548584	−	0.950175i	−0.449788	−	0.893135i	$-0.648501\pi$
$269$	8.99744	−	15.5840i	0.548584	−	0.950175i	0.998372	−	0.0570394i	$-0.0181661\pi$
$270$		0			0
$271$	−14.1527	+	8.17105i	−0.859714	+	0.496356i	−0.863916	−	0.503635i	$-0.831996\pi$
$271$	−14.1527	+	8.17105i	−0.859714	+	0.496356i	0.00420268	+	0.999991i	$0.498662\pi$
$272$	−9.04101			−0.548192
$273$	2.73052	−	7.53761i	0.165259	−	0.456197i
$274$	4.17436			0.252182
$275$		0			0
$276$	−5.63556	−	9.76108i	−0.339221	−	0.587548i
$277$	−0.0478916	+	0.0829507i	−0.00287753	+	0.00498402i	−0.867461	−	0.497506i	$-0.834249\pi$
$277$	−0.0478916	+	0.0829507i	−0.00287753	+	0.00498402i	0.864583	+	0.502490i	$0.167583\pi$
$278$		−	43.4090i		−	2.60350i
$279$	8.27813	+	4.77938i	0.495599	+	0.286134i
$280$		0			0
$281$		−	29.8592i		−	1.78125i	−0.454735	−	0.890627i	$-0.650266\pi$
$281$		−	29.8592i		−	1.78125i	0.454735	−	0.890627i	$-0.349734\pi$
$282$	−1.35573	+	2.34819i	−0.0807324	+	0.139833i
$283$	1.05939	+	1.83492i	0.0629744	+	0.109075i	0.895794	−	0.444470i	$-0.146608\pi$
$283$	1.05939	+	1.83492i	0.0629744	+	0.109075i	−0.832819	+	0.553545i	$0.813275\pi$
$284$	3.15010	−	1.81871i	0.186924	−	0.107921i
$285$		0			0
$286$	−28.2473	+	23.7754i	−1.67030	+	1.40587i
$287$	−3.66086			−0.216094
$288$	6.96356	−	4.02041i	0.410332	−	0.236905i
$289$	5.82383	+	10.0872i	0.342578	+	0.593363i
$290$		0			0
$291$			6.03573i			0.353821i
$292$	7.95907	+	4.59517i	0.465769	+	0.268912i
$293$	16.0653	+	9.27529i	0.938544	+	0.541868i	0.889503	−	0.456928i	$-0.151050\pi$
$293$	16.0653	+	9.27529i	0.938544	+	0.541868i	0.0490402	+	0.998797i	$0.484384\pi$
$294$		−	4.13519i		−	0.241169i
$295$		0			0
$296$	−0.0525084	−	0.0909471i	−0.00305199	−	0.00528620i
$297$	−4.40935	+	2.54574i	−0.255856	+	0.147719i
$298$	37.5903			2.17755
$299$	−3.48041	−	19.5647i	−0.201277	−	1.13146i
$300$		0			0
$301$	−17.7400	+	10.2422i	−1.02252	+	0.590352i
$302$	−1.71299	−	2.96699i	−0.0985718	−	0.170731i
$303$	4.13627	−	7.16422i	0.237622	−	0.411574i
$304$			27.3909i			1.57097i
$305$		0			0
$306$	4.02961	+	2.32650i	0.230358	+	0.132997i
$307$			2.19278i			0.125148i	0.998040	+	0.0625742i	$0.0199310\pi$
$307$			2.19278i			0.125148i	−0.998040	+	0.0625742i	$0.980069\pi$
$308$	11.5758	−	20.0498i	0.659591	−	1.14245i
$309$	−6.23732	−	10.8033i	−0.354828	−	0.614581i
$310$		0			0
$311$	6.95530			0.394399			0.197199	−	0.980363i	$-0.436815\pi$
$311$	6.95530			0.394399			0.197199	+	0.980363i	$0.436815\pi$
$312$	−0.321485	+	0.0571895i	−0.0182005	+	0.00323772i
$313$	6.01866			0.340195			0.170097	−	0.985427i	$-0.445592\pi$
$313$	6.01866			0.340195			0.170097	+	0.985427i	$0.445592\pi$
$314$	−15.8659	+	9.16019i	−0.895366	+	0.516940i
$315$		0			0
$316$	7.21492	−	12.4966i	0.405871	−	0.702989i
$317$			11.8288i			0.664373i	0.943214	+	0.332187i	$0.107786\pi$
$317$			11.8288i			0.664373i	−0.943214	+	0.332187i	$0.892214\pi$
$318$	16.3128	+	9.41821i	0.914777	+	0.528147i
$319$	4.44064	+	2.56381i	0.248628	+	0.143546i
$320$		0			0
$321$	3.54477	−	6.13972i	0.197850	−	0.342686i
$322$	12.3235	+	21.3450i	0.686763	+	1.18951i
$323$	−14.0431	+	8.10779i	−0.781380	+	0.451130i
$324$	−2.04503			−0.113613
$325$		0			0
$326$	−16.4172			−0.909263
$327$	−7.25101	+	4.18638i	−0.400982	+	0.231507i
$328$	0.0745539	+	0.129131i	0.00411655	+	0.00713008i
$329$	1.49882	−	2.59602i	0.0826324	−	0.143123i
$330$		0			0
$331$	30.1726	+	17.4202i	1.65844	+	0.957499i	0.973437	+	0.228956i	$0.0735313\pi$
$331$	30.1726	+	17.4202i	1.65844	+	0.957499i	0.685000	+	0.728543i	$0.259802\pi$
$332$	−3.99349	−	2.30564i	−0.219171	−	0.126539i
$333$		−	1.15959i		−	0.0635452i
$334$	2.45433	−	4.25103i	0.134295	−	0.232606i
$335$		0			0
$336$	−7.52510	+	4.34462i	−0.410528	+	0.237018i
$337$	6.74322			0.367327			0.183663	−	0.982989i	$-0.441204\pi$
$337$	6.74322			0.367327			0.183663	+	0.982989i	$0.441204\pi$
$338$	−25.7624	−	4.46203i	−1.40129	−	0.242703i
$339$	2.57221			0.139703
$340$		0			0
$341$	24.3341	+	42.1479i	1.31777	+	2.28244i
$342$	7.04842	−	12.2082i	0.381135	−	0.660145i
$343$			20.1361i			1.08725i
$344$	0.722556	+	0.417168i	0.0389576	+	0.0224922i
$345$		0			0
$346$			18.2747i			0.982452i
$347$	10.7893	−	18.6877i	0.579202	−	1.00321i	−0.416369	−	0.909196i	$-0.636698\pi$
$347$	10.7893	−	18.6877i	0.579202	−	1.00321i	0.995571	−	0.0940118i	$-0.0299691\pi$
$348$	1.02977	+	1.78362i	0.0552016	+	0.0956119i
$349$	1.11343	−	0.642839i	0.0596005	−	0.0344104i	−0.469904	−	0.882718i	$-0.655711\pi$
$349$	1.11343	−	0.642839i	0.0596005	−	0.0344104i	0.529504	+	0.848307i	$0.322378\pi$
$350$		0			0
$351$	−3.38998	−	1.22803i	−0.180944	−	0.0655473i
$352$	40.9397			2.18209
$353$	1.40021	−	0.808410i	0.0745255	−	0.0430273i	−0.462274	−	0.886737i	$-0.652966\pi$
$353$	1.40021	−	0.808410i	0.0745255	−	0.0430273i	0.536800	+	0.843710i	$0.319633\pi$
$354$	−1.03872	−	1.79912i	−0.0552075	−	0.0956222i
$355$		0			0
$356$		−	16.6227i		−	0.880999i
$357$	−4.45491	−	2.57204i	−0.235779	−	0.136127i
$358$	−34.3683	−	19.8426i	−1.81642	−	1.04871i
$359$			22.7418i			1.20026i	0.799901	+	0.600132i	$0.204885\pi$
$359$			22.7418i			1.20026i	−0.799901	+	0.600132i	$0.795115\pi$
$360$		0			0
$361$	15.0636	+	26.0909i	0.792820	+	1.37321i
$362$	−9.02228	+	5.20902i	−0.474201	+	0.273780i
$363$	−14.9232			−0.783262
$364$	16.1415	−	2.87143i	0.846042	−	0.150504i
$365$		0			0
$366$	18.5592	−	10.7152i	0.970106	−	0.560091i
$367$	−13.4253	−	23.2533i	−0.700795	−	1.21381i	−0.968188	−	0.250225i	$-0.919495\pi$
$367$	−13.4253	−	23.2533i	−0.700795	−	1.21381i	0.267393	−	0.963588i	$-0.413838\pi$
$368$	−10.7692	+	18.6528i	−0.561382	+	0.972343i
$369$			1.64644i			0.0857104i
$370$		0			0
$371$	−18.0345	−	10.4122i	−0.936306	−	0.540577i
$372$			19.5479i			1.01351i
$373$	1.42558	−	2.46918i	0.0738138	−	0.127849i	−0.826756	−	0.562561i	$-0.809816\pi$
$373$	1.42558	−	2.46918i	0.0738138	−	0.127849i	0.900570	+	0.434711i	$0.143150\pi$
$374$	11.8453	+	20.5167i	0.612507	+	1.06089i
$375$		0			0
$376$	−0.122094			−0.00629653
$377$	0.635966	+	3.57502i	0.0327539	+	0.184123i
$378$	4.47196			0.230013
$379$	2.73248	−	1.57760i	0.140358	−	0.0810357i	−0.428177	−	0.903695i	$-0.640844\pi$
$379$	2.73248	−	1.57760i	0.140358	−	0.0810357i	0.568535	+	0.822659i	$0.307511\pi$
$380$		0			0
$381$	10.2212	−	17.7037i	0.523648	−	0.906986i
$382$			1.92132i			0.0983032i
$383$	3.05495	+	1.76378i	0.156101	+	0.0901248i	0.576016	−	0.817439i	$-0.304607\pi$
$383$	3.05495	+	1.76378i	0.156101	+	0.0901248i	−0.419915	+	0.907563i	$0.637940\pi$
$384$	0.627284	+	0.362163i	0.0320110	+	0.0184815i
$385$		0			0
$386$	9.91161	−	17.1674i	0.504488	−	0.873798i
$387$	4.60635	+	7.97844i	0.234154	+	0.405567i
$388$	−10.6896	+	6.17163i	−0.542681	+	0.313317i
$389$	10.2877			0.521608			0.260804	−	0.965392i	$-0.416012\pi$
$389$	10.2877			0.521608			0.260804	+	0.965392i	$0.416012\pi$
$390$		0			0
$391$	−12.7509			−0.644838
$392$	0.161257	−	0.0931020i	0.00814473	−	0.00470236i
$393$	1.87761	+	3.25212i	0.0947130	+	0.164048i
$394$	−3.21973	+	5.57674i	−0.162208	+	0.280952i
$395$		0			0
$396$	−9.01725	−	5.20611i	−0.453134	−	0.261617i
$397$	−7.68204	−	4.43523i	−0.385550	−	0.222598i	0.294680	−	0.955596i	$-0.404787\pi$
$397$	−7.68204	−	4.43523i	−0.385550	−	0.222598i	−0.680230	+	0.732998i	$0.738120\pi$
$398$			38.7232i			1.94102i
$399$	−7.79234	+	13.4967i	−0.390105	+	0.675681i
$400$		0			0
$401$	−18.1333	+	10.4693i	−0.905533	+	0.522810i	−0.878991	−	0.476838i	$-0.841783\pi$
$401$	−18.1333	+	10.4693i	−0.905533	+	0.522810i	−0.0265418	+	0.999648i	$0.508450\pi$
$402$	6.70071			0.334201
$403$	−11.7384	+	32.4040i	−0.584733	+	1.61416i
$404$	16.9176			0.841680
$405$		0			0
$406$	−2.25185	−	3.90031i	−0.111757	−	0.193569i
$407$	2.95202	−	5.11304i	0.146326	−	0.253444i
$408$			0.209520i			0.0103728i
$409$	5.25909	+	3.03634i	0.260045	+	0.150137i	0.624355	−	0.781141i	$-0.285362\pi$
$409$	5.25909	+	3.03634i	0.260045	+	0.150137i	−0.364310	+	0.931278i	$0.618695\pi$
$410$		0			0
$411$			2.07553i			0.102378i
$412$	12.7555	−	22.0932i	0.628418	−	1.08845i
$413$	1.14835	+	1.98901i	0.0565068	+	0.0978727i
$414$	9.59973	−	5.54241i	0.471801	−	0.272394i
$415$		0			0
$416$	18.6691	+	22.1806i	0.915329	+	1.08749i
$417$	21.5833			1.05694
$418$	62.1579	−	35.8869i	3.04024	−	1.75528i
$419$	14.1532	+	24.5140i	0.691428	+	1.19759i	0.971370	+	0.237571i	$0.0763514\pi$
$419$	14.1532	+	24.5140i	0.691428	+	1.19759i	−0.279942	+	0.960017i	$0.590315\pi$
$420$		0			0
$421$		−	6.60307i		−	0.321814i	−0.986970	−	0.160907i	$-0.948558\pi$
$421$		−	6.60307i		−	0.321814i	0.986970	−	0.160907i	$-0.0514419\pi$
$422$	−26.4360	−	15.2628i	−1.28689	−	0.742984i
$423$	−1.16754	−	0.674080i	−0.0567678	−	0.0327749i
$424$			0.848186i			0.0411916i
$425$		0			0
$426$	1.78865	+	3.09803i	0.0866604	+	0.150100i
$427$	−20.5180	+	11.8461i	−0.992937	+	0.573273i
$428$	14.4983			0.700802
$429$	−11.8214	−	14.0448i	−0.570740	−	0.678090i
$430$		0			0
$431$	0.428160	−	0.247198i	0.0206238	−	0.0119071i	−0.489653	−	0.871918i	$-0.662876\pi$
$431$	0.428160	−	0.247198i	0.0206238	−	0.0119071i	0.510276	+	0.860010i	$0.329543\pi$
$432$	1.95396	+	3.38435i	0.0940098	+	0.162830i
$433$	−10.5406	+	18.2568i	−0.506547	+	0.877366i	0.493424	+	0.869789i	$0.335745\pi$
$433$	−10.5406	+	18.2568i	−0.506547	+	0.877366i	−0.999971	+	0.00757691i	$0.997588\pi$
$434$		−	42.7464i		−	2.05189i
$435$		0			0
$436$	−14.8285	−	8.56126i	−0.710158	−	0.410010i
$437$			38.6303i			1.84794i
$438$	−4.51921	+	7.82751i	−0.215936	+	0.374013i
$439$	10.9328	+	18.9362i	0.521794	+	0.903774i	0.999679	+	0.0253511i	$0.00807037\pi$
$439$	10.9328	+	18.9362i	0.521794	+	0.903774i	−0.477885	+	0.878423i	$0.658596\pi$
$440$		0			0
$441$	2.05606			0.0979075
$442$	−5.71401	+	15.7735i	−0.271788	+	0.750271i
$443$	8.83792			0.419902			0.209951	−	0.977712i	$-0.432669\pi$
$443$	8.83792			0.419902			0.209951	+	0.977712i	$0.432669\pi$
$444$	2.05369	−	1.18570i	0.0974638	−	0.0562707i
$445$		0			0
$446$	−1.12133	+	1.94219i	−0.0530963	+	0.0919655i
$447$			18.6902i			0.884018i
$448$	−16.0905	−	9.28987i	−0.760206	−	0.438905i
$449$	14.9282	+	8.61882i	0.704507	+	0.406747i	0.809024	−	0.587776i	$-0.199996\pi$
$449$	14.9282	+	8.61882i	0.704507	+	0.406747i	−0.104517	+	0.994523i	$0.533330\pi$
$450$		0			0
$451$	−4.19142	+	7.25975i	−0.197366	+	0.341848i
$452$	2.63013	+	4.55551i	0.123711	+	0.214273i
$453$	1.47522	−	0.851717i	0.0693117	−	0.0400171i
$454$	−30.7874			−1.44493
$455$		0			0
$456$	0.634767			0.0297257
$457$	27.5826	−	15.9248i	1.29026	−	0.744933i	0.311561	−	0.950226i	$-0.399148\pi$
$457$	27.5826	−	15.9248i	1.29026	−	0.744933i	0.978700	+	0.205294i	$0.0658149\pi$
$458$	−9.62821	−	16.6766i	−0.449897	−	0.779244i
$459$	−1.15676	+	2.00356i	−0.0539927	+	0.0935182i
$460$		0			0
$461$	−30.9451	−	17.8662i	−1.44126	−	0.832110i	−0.443324	−	0.896362i	$-0.646201\pi$
$461$	−30.9451	−	17.8662i	−1.44126	−	0.832110i	−0.997934	+	0.0642514i	$0.979534\pi$
$462$	19.7184	+	11.3844i	0.917384	+	0.529652i
$463$		−	27.4133i		−	1.27401i	−0.770862	−	0.637003i	$-0.780174\pi$
$463$		−	27.4133i		−	1.27401i	0.770862	−	0.637003i	$-0.219826\pi$
$464$	1.96783	−	3.40837i	0.0913540	−	0.158230i
$465$		0			0
$466$	40.0073	−	23.0982i	1.85330	−	1.07000i
$467$	−13.6947			−0.633716			−0.316858	−	0.948473i	$-0.602628\pi$
$467$	−13.6947			−0.633716			−0.316858	+	0.948473i	$0.602628\pi$
$468$	−1.29140	−	7.25949i	−0.0596952	−	0.335570i
$469$	−7.40793			−0.342066
$470$		0			0
$471$	−4.55453	−	7.88868i	−0.209862	−	0.363491i
$472$	0.0467727	−	0.0810128i	0.00215289	−	0.00372891i
$473$			46.9063i			2.15675i
$474$	12.2900	+	7.09566i	0.564501	+	0.325915i
$475$		0			0
$476$		−	10.5198i		−	0.482175i
$477$	−4.68282	+	8.11088i	−0.214412	+	0.371372i
$478$	11.5904	+	20.0752i	0.530134	+	0.918219i
$479$	−11.1837	+	6.45690i	−0.510996	+	0.295023i	−0.733243	−	0.679967i	$-0.761994\pi$
$479$	−11.1837	+	6.45690i	−0.510996	+	0.295023i	0.222247	+	0.974990i	$0.428661\pi$
$480$		0			0
$481$	4.11634	−	0.732263i	0.187689	−	0.0333883i
$482$	30.7033			1.39850
$483$	−10.6129	+	6.12737i	−0.482905	+	0.278805i
$484$	−15.2591	−	26.4296i	−0.693597	−	1.20135i
$485$		0			0
$486$		−	2.01123i		−	0.0912311i
$487$	31.3965	+	18.1268i	1.42271	+	0.821403i	0.996530	−	0.0832337i	$-0.0265248\pi$
$487$	31.3965	+	18.1268i	1.42271	+	0.821403i	0.426183	+	0.904637i	$0.359858\pi$
$488$	0.835705	+	0.482494i	0.0378306	+	0.0218415i
$489$		−	8.16277i		−	0.369133i
$490$		0			0
$491$	−1.60516	−	2.78022i	−0.0724400	−	0.125470i	0.827530	−	0.561421i	$-0.189745\pi$
$491$	−1.60516	−	2.78022i	−0.0724400	−	0.125470i	−0.899970	+	0.435952i	$0.856412\pi$
$492$	−2.91593	+	1.68351i	−0.131460	+	0.0758986i
$493$	2.32993			0.104935
$494$	47.7880	+	17.3113i	2.15008	+	0.778873i
$495$		0			0
$496$	32.3502	−	18.6774i	1.45257	−	0.838640i
$497$	−1.97743	−	3.42501i	−0.0886999	−	0.153633i
$498$	2.26753	−	3.92748i	0.101611	−	0.175995i
$499$		−	13.6867i		−	0.612703i	−0.951918	−	0.306351i	$-0.900892\pi$
$499$		−	13.6867i		−	0.612703i	0.951918	−	0.306351i	$-0.0991083\pi$
$500$		0			0
$501$	2.11365	+	1.22032i	0.0944309	+	0.0545197i
$502$			59.1063i			2.63804i
$503$	12.6120	−	21.8447i	0.562343	−	0.974006i	−0.434949	−	0.900455i	$-0.643233\pi$
$503$	12.6120	−	21.8447i	0.562343	−	0.974006i	0.997291	−	0.0735511i	$-0.0234332\pi$
$504$	0.100684	+	0.174390i	0.00448482	+	0.00776794i
$505$		0			0
$506$	56.4381			2.50898
$507$	2.21856	−	12.8093i	0.0985299	−	0.568881i
$508$	41.8053			1.85481
$509$	29.1852	−	16.8501i	1.29361	−	0.746866i	0.314318	−	0.949318i	$-0.398224\pi$
$509$	29.1852	−	16.8501i	1.29361	−	0.746866i	0.979292	+	0.202452i	$0.0648910\pi$
$510$		0			0
$511$	4.99619	−	8.65365i	0.221018	−	0.382815i
$512$		−	32.1307i		−	1.41999i
$513$	6.07004	+	3.50454i	0.267999	+	0.154729i
$514$	54.3663	+	31.3884i	2.39799	+	1.38448i
$515$		0			0
$516$	−9.42013	+	16.3161i	−0.414698	+	0.718278i
$517$	−3.43206	−	5.94451i	−0.150942	−	0.261439i
$518$	−4.49089	+	2.59282i	−0.197319	+	0.113922i
$519$	−9.08633			−0.398846
$520$		0			0
$521$	−2.79900			−0.122627			−0.0613133	−	0.998119i	$-0.519529\pi$
$521$	−2.79900			−0.122627			−0.0613133	+	0.998119i	$0.519529\pi$
$522$	−1.75413	+	1.01275i	−0.0767764	+	0.0443269i
$523$	−14.0813	−	24.3895i	−0.615731	−	1.06648i	−0.990256	−	0.139260i	$-0.955527\pi$
$523$	−14.0813	−	24.3895i	−0.615731	−	1.06648i	0.374525	−	0.927217i	$-0.377806\pi$
$524$	−3.83977	+	6.65068i	−0.167741	+	0.290536i
$525$		0			0
$526$	−9.72463	−	5.61452i	−0.424014	−	0.244805i
$527$	19.1516	+	11.0572i	0.834255	+	0.481657i
$528$			19.8971i			0.865908i
$529$	−3.68816	+	6.38808i	−0.160355	+	0.277743i
$530$		0			0
$531$	0.894540	−	0.516463i	0.0388197	−	0.0224126i
$532$	−31.8711			−1.38179
$533$	−5.84458	+	1.03970i	−0.253157	+	0.0450346i
$534$	16.3479			0.707443
$535$		0			0
$536$	0.150863	+	0.261303i	0.00651631	+	0.0112866i
$537$	9.86590	−	17.0882i	0.425745	−	0.737412i
$538$			36.1918i			1.56034i
$539$	9.06587	+	5.23418i	0.390495	+	0.225452i
$540$		0			0
$541$		−	5.41109i		−	0.232641i	−0.993212	−	0.116320i	$-0.962890\pi$
$541$		−	5.41109i		−	0.232641i	0.993212	−	0.116320i	$-0.0371100\pi$
$542$	16.4338	−	28.4642i	0.705893	−	1.22264i
$543$	−2.58997	−	4.48596i	−0.111146	−	0.192511i
$544$	16.1103	−	9.30127i	0.690722	−	0.398789i
$545$		0			0
$546$	2.82397	+	15.8746i	0.120855	+	0.679372i
$547$	−41.1838			−1.76089			−0.880446	−	0.474147i	$-0.842757\pi$
$547$	−41.1838			−1.76089			−0.880446	+	0.474147i	$0.842757\pi$
$548$	−3.67586	+	2.12226i	−0.157025	+	0.0906585i
$549$	5.32768	+	9.22782i	0.227380	+	0.393834i
$550$		0			0
$551$		−	7.05882i		−	0.300716i
$552$	0.432267	+	0.249569i	0.0183985	+	0.0106224i
$553$	−13.5872	−	7.84456i	−0.577786	−	0.333585i
$554$		−	0.192642i		−	0.00818456i
$555$		0			0
$556$	22.0693	+	38.2251i	0.935946	+	1.62111i
$557$	−28.0070	+	16.1698i	−1.18669	+	0.685137i	−0.957553	−	0.288256i	$-0.906924\pi$
$557$	−28.0070	+	16.1698i	−1.18669	+	0.685137i	−0.229139	+	0.973394i	$0.573591\pi$
$558$	−19.2248			−0.813852
$559$	−25.4132	+	21.3900i	−1.07486	+	0.904700i
$560$		0			0
$561$	−10.2011	+	5.88960i	−0.430690	+	0.248659i
$562$	30.0268	+	52.0080i	1.26661	+	2.19383i
$563$	22.4655	−	38.9114i	0.946809	−	1.63992i	0.194722	−	0.980858i	$-0.437619\pi$
$563$	22.4655	−	38.9114i	0.946809	−	1.63992i	0.752087	−	0.659064i	$-0.229047\pi$
$564$		−	2.75703i		−	0.116092i
$565$		0			0
$566$	−3.69044	−	2.13068i	−0.155121	−	0.0895591i
$567$			2.22350i			0.0933781i
$568$	−0.0805412	+	0.139501i	−0.00337943	+	0.00585335i
$569$	−14.5891	−	25.2691i	−0.611608	−	1.05934i	−0.990969	−	0.134088i	$-0.957190\pi$
$569$	−14.5891	−	25.2691i	−0.611608	−	1.05934i	0.379362	−	0.925249i	$-0.376144\pi$
$570$		0			0
$571$	−8.45655			−0.353895			−0.176948	−	0.984220i	$-0.556622\pi$
$571$	−8.45655			−0.353895			−0.176948	+	0.984220i	$0.556622\pi$
$572$	12.7865	−	35.2972i	0.534631	−	1.47585i
$573$	−0.955297			−0.0399081
$574$	6.37639	−	3.68141i	0.266145	−	0.153659i
$575$		0			0
$576$	−4.17804	+	7.23658i	−0.174085	+	0.301524i
$577$			27.2027i			1.13246i	0.824246	+	0.566232i	$0.191599\pi$
$577$			27.2027i			1.13246i	−0.824246	+	0.566232i	$0.808401\pi$
$578$	−20.2876	−	11.7130i	−0.843852	−	0.487198i
$579$	8.53580	+	4.92814i	0.354736	+	0.204807i
$580$		0			0
$581$	−2.50686	+	4.34200i	−0.104002	+	0.180137i
$582$	−6.06961	−	10.5129i	−0.251594	−	0.435773i
$583$	−41.2964	+	23.8425i	−1.71032	+	0.987454i
$584$	−0.406992			−0.0168414
$585$		0			0
$586$	−37.3094			−1.54124
$587$	26.7561	−	15.4477i	1.10434	−	0.637593i	0.166986	−	0.985959i	$-0.446597\pi$
$587$	26.7561	−	15.4477i	1.10434	−	0.637593i	0.937359	+	0.348366i	$0.113263\pi$
$588$	2.10235	+	3.64137i	0.0866994	+	0.150168i
$589$	33.4991	−	58.0221i	1.38030	−	2.39076i
$590$		0			0
$591$	−2.77281	−	1.60088i	−0.114058	−	0.0658515i
$592$	−3.92446	−	2.26579i	−0.161294	−	0.0931234i
$593$		−	14.6049i		−	0.599750i	−0.953979	−	0.299875i	$-0.903055\pi$
$593$		−	14.6049i		−	0.599750i	0.953979	−	0.299875i	$-0.0969450\pi$
$594$	5.12006	−	8.86820i	0.210078	−	0.363867i
$595$		0			0
$596$	−33.1013	+	19.1110i	−1.35588	+	0.782819i
$597$	−19.2535			−0.787994
$598$	25.7366	+	30.5774i	1.05245	+	1.25040i
$599$	−21.9911			−0.898532			−0.449266	−	0.893398i	$-0.648314\pi$
$599$	−21.9911			−0.898532			−0.449266	+	0.893398i	$0.648314\pi$
$600$		0			0
$601$	−22.3908	−	38.7820i	−0.913339	−	1.58195i	−0.809314	−	0.587376i	$-0.800161\pi$
$601$	−22.3908	−	38.7820i	−0.913339	−	1.58195i	−0.104025	−	0.994575i	$-0.533172\pi$
$602$	20.5994	−	35.6792i	0.839569	−	1.45418i
$603$			3.33166i			0.135676i
$604$	3.01686	+	1.74179i	0.122754	+	0.0708723i
$605$		0			0
$606$			16.6379i			0.675870i
$607$	6.56151	−	11.3649i	0.266323	−	0.461285i	−0.701586	−	0.712585i	$-0.747524\pi$
$607$	6.56151	−	11.3649i	0.266323	−	0.461285i	0.967909	+	0.251299i	$0.0808578\pi$
$608$	−28.1794	−	48.8081i	−1.14282	−	1.97943i
$609$	1.93927	−	1.11964i	0.0785833	−	0.0453701i
$610$		0			0
$611$	1.65558	−	4.57023i	0.0669775	−	0.184892i
$612$	−4.73120			−0.191247
$613$	14.9801	−	8.64874i	0.605039	−	0.349320i	−0.165982	−	0.986129i	$-0.553079\pi$
$613$	14.9801	−	8.64874i	0.605039	−	0.349320i	0.771021	+	0.636809i	$0.219746\pi$
$614$	−2.20508	−	3.81932i	−0.0889900	−	0.154135i
$615$		0			0
$616$			1.02526i			0.0413089i
$617$	−14.0281	−	8.09910i	−0.564748	−	0.326058i	0.190301	−	0.981726i	$-0.439054\pi$
$617$	−14.0281	−	8.09910i	−0.564748	−	0.326058i	−0.755049	+	0.655668i	$0.772387\pi$
$618$	21.7280	+	12.5446i	0.874027	+	0.504620i
$619$			10.8858i			0.437539i	0.975777	+	0.218770i	$0.0702043\pi$
$619$			10.8858i			0.437539i	−0.975777	+	0.218770i	$0.929796\pi$
$620$		0			0
$621$	2.75574	+	4.77307i	0.110584	+	0.191537i
$622$	−12.1145	+	6.99434i	−0.485749	+	0.280447i
$623$	−18.0733			−0.724092
$624$	−10.7800	+	9.07336i	−0.431543	+	0.363225i
$625$		0			0
$626$	−10.4831	+	6.05244i	−0.418990	+	0.241904i
$627$	17.8433	+	30.9055i	0.712592	+	1.23425i
$628$	9.31415	−	16.1326i	0.371675	−	0.643760i
$629$		−	2.68273i		−	0.106967i
$630$		0			0
$631$	29.1425	+	16.8254i	1.16014	+	0.669810i	0.951339	−	0.308147i	$-0.0997090\pi$
$631$	29.1425	+	16.8254i	1.16014	+	0.669810i	0.208806	+	0.977957i	$0.433042\pi$
$632$			0.639022i			0.0254189i
$633$	7.58883	−	13.1442i	0.301629	−	0.522436i
$634$	−11.8952	−	20.6031i	−0.472420	−	0.818255i
$635$		0			0
$636$	−19.1530			−0.759466
$637$	1.29837	+	7.29863i	0.0514432	+	0.289182i
$638$	−10.3128			−0.408287
$639$	−1.54037	+	0.889333i	−0.0609361	+	0.0351815i
$640$		0			0
$641$	−14.7514	+	25.5501i	−0.582643	+	1.00917i	0.412521	+	0.910948i	$0.364648\pi$
$641$	−14.7514	+	25.5501i	−0.582643	+	1.00917i	−0.995165	+	0.0982199i	$0.968685\pi$
$642$			14.2587i			0.562744i
$643$	22.0327	+	12.7206i	0.868885	+	0.501651i	0.866978	−	0.498347i	$-0.166059\pi$
$643$	22.0327	+	12.7206i	0.868885	+	0.501651i	0.00190769	+	0.999998i	$0.499393\pi$
$644$	−21.7037	−	12.5307i	−0.855247	−	0.493777i
$645$		0			0
$646$	16.3066	−	28.2439i	0.641575	−	1.11124i
$647$	−2.47042	−	4.27889i	−0.0971222	−	0.168221i	0.813370	−	0.581747i	$-0.197630\pi$
$647$	−2.47042	−	4.27889i	−0.0971222	−	0.168221i	−0.910492	+	0.413526i	$0.864297\pi$
$648$	0.0784304	−	0.0452818i	0.00308104	−	0.00177884i
$649$	5.25912			0.206438
$650$		0			0
$651$	21.2539			0.833005
$652$	14.4566	−	8.34655i	0.566166	−	0.326876i
$653$	7.27351	+	12.5981i	0.284634	+	0.493001i	0.972520	−	0.232818i	$-0.0747945\pi$
$653$	7.27351	+	12.5981i	0.284634	+	0.493001i	−0.687886	+	0.725819i	$0.741461\pi$
$654$	8.41975	−	14.5834i	0.329238	−	0.570257i
$655$		0			0
$656$	5.57215	+	3.21708i	0.217556	+	0.125606i
$657$	−3.89191	−	2.24699i	−0.151838	−	0.0876636i
$658$			6.02891i			0.235031i
$659$	−4.47698	+	7.75435i	−0.174398	+	0.302067i	−0.939953	−	0.341304i	$-0.889131\pi$
$659$	−4.47698	+	7.75435i	−0.174398	+	0.302067i	0.765555	+	0.643371i	$0.222465\pi$
$660$		0			0
$661$	−10.3161	+	5.95599i	−0.401249	+	0.231661i	−0.687023	−	0.726636i	$-0.741083\pi$
$661$	−10.3161	+	5.95599i	−0.401249	+	0.231661i	0.285774	+	0.958297i	$0.407749\pi$
$662$	−70.0718			−2.72342
$663$	−7.84275	−	2.84106i	−0.304587	−	0.110338i
$664$	0.204210			0.00792487
$665$		0			0
$666$	1.16610	+	2.01974i	0.0451854	+	0.0782635i
$667$	2.77529	−	4.80695i	0.107460	−	0.186126i
$668$			4.99116i			0.193114i
$669$	−0.965676	−	0.557533i	−0.0373352	−	0.0215555i
$670$		0			0
$671$			54.2516i			2.09436i
$672$	8.93938	−	15.4835i	0.344844	−	0.597287i
$673$	−1.30236	−	2.25576i	−0.0502025	−	0.0869532i	0.839832	−	0.542846i	$-0.182653\pi$
$673$	−1.30236	−	2.25576i	−0.0502025	−	0.0869532i	−0.890035	+	0.455893i	$0.849320\pi$
$674$	−11.7452	+	6.78107i	−0.452407	+	0.261197i
$675$		0			0
$676$	24.9544	−	9.16851i	0.959784	−	0.352635i
$677$	15.6343			0.600877			0.300438	−	0.953801i	$-0.402867\pi$
$677$	15.6343			0.600877			0.300438	+	0.953801i	$0.402867\pi$
$678$	−4.48021	+	2.58665i	−0.172061	+	0.0993397i
$679$	6.71022	+	11.6224i	0.257515	+	0.446028i
$680$		0			0
$681$		−	15.3078i		−	0.586596i
$682$	−84.7690	−	48.9414i	−3.24597	−	1.87406i
$683$	−28.9520	−	16.7155i	−1.10782	−	0.639599i	−0.169555	−	0.985521i	$-0.554233\pi$
$683$	−28.9520	−	16.7155i	−1.10782	−	0.639599i	−0.938264	+	0.345921i	$0.887566\pi$
$684$			14.3338i			0.548065i
$685$		0			0
$686$	−20.2491	−	35.0725i	−0.773116	−	1.33908i
$687$	8.29173	−	4.78724i	0.316349	−	0.182644i
$688$	36.0025			1.37258
$689$	−31.7493	−	11.5013i	−1.20955	−	0.438164i
$690$		0			0
$691$	23.4855	−	13.5594i	0.893431	−	0.515823i	0.0183678	−	0.999831i	$-0.494153\pi$
$691$	23.4855	−	13.5594i	0.893431	−	0.515823i	0.875063	+	0.484009i	$0.160820\pi$
$692$	−9.29091	−	16.0923i	−0.353187	−	0.611738i
$693$	−5.66045	+	9.80418i	−0.215023	+	0.372430i
$694$			43.3996i			1.64743i
$695$		0			0
$696$	−0.0789870	−	0.0456032i	−0.00299400	−	0.00172858i
$697$			3.80907i			0.144279i
$698$	−1.29289	+	2.23936i	−0.0489368	+	0.0847610i
$699$	11.4846	+	19.8920i	0.434389	+	0.752384i
$700$		0			0
$701$	31.5261			1.19072			0.595362	−	0.803457i	$-0.297008\pi$
$701$	31.5261			1.19072			0.595362	+	0.803457i	$0.297008\pi$
$702$	7.13949	−	1.27006i	0.269463	−	0.0479352i
$703$	−8.12766			−0.306541
$704$	−36.8449	+	21.2724i	−1.38864	+	0.801734i
$705$		0			0
$706$	−1.62590	+	2.81613i	−0.0611914	+	0.105987i
$707$		−	18.3940i		−	0.691776i
$708$	1.82936	+	1.05618i	0.0687516	+	0.0396937i
$709$	−16.0354	−	9.25806i	−0.602223	−	0.347694i	0.167692	−	0.985839i	$-0.446368\pi$
$709$	−16.0354	−	9.25806i	−0.602223	−	0.347694i	−0.769916	+	0.638146i	$0.779702\pi$
$710$		0			0
$711$	−3.52803	+	6.11072i	−0.132311	+	0.229170i
$712$	0.368065	+	0.637508i	0.0137938	+	0.0238916i
$713$	45.6247	−	26.3414i	1.70866	−	0.986494i
$714$	10.3459			0.387187
$715$		0			0
$716$	40.3521			1.50803
$717$	−9.98158	+	5.76287i	−0.372769	+	0.215218i
$718$	−22.8694	−	39.6110i	−0.853479	−	1.47827i
$719$	−8.35147	+	14.4652i	−0.311457	+	0.539460i	−0.978678	−	0.205400i	$-0.934150\pi$
$719$	−8.35147	+	14.4652i	−0.311457	+	0.539460i	0.667221	+	0.744860i	$0.267484\pi$
$720$		0			0
$721$	−24.0212	−	13.8687i	−0.894597	−	0.516496i
$722$	−52.4747	−	30.2963i	−1.95291	−	1.12751i
$723$			15.2659i			0.567747i
$724$	5.29657	−	9.17392i	0.196845	−	0.340946i
$725$		0			0
$726$	25.9927	−	15.0069i	0.964681	−	0.556959i
$727$	9.38173			0.347949			0.173974	−	0.984750i	$-0.444339\pi$
$727$	9.38173			0.347949			0.173974	+	0.984750i	$0.444339\pi$
$728$	−0.555472	+	0.467535i	−0.0205872	+	0.0173280i
$729$	1.00000			0.0370370
$730$		0			0
$731$	10.6569	+	18.4582i	0.394158	+	0.682702i
$732$	−10.8953	+	18.8712i	−0.402701	+	0.697498i
$733$		−	8.06377i		−	0.297842i	−0.988849	−	0.148921i	$-0.952420\pi$
$733$		−	8.06377i		−	0.297842i	0.988849	−	0.148921i	$-0.0475800\pi$
$734$	46.7676	+	27.0013i	1.72623	+	0.996637i
$735$		0			0
$736$		−	44.3168i		−	1.63354i
$737$	−8.48153	+	14.6904i	−0.312421	+	0.541129i
$738$	−1.65568	−	2.86773i	−0.0609466	−	0.105563i
$739$	−8.05917	+	4.65297i	−0.296461	+	0.171162i	−0.640852	−	0.767664i	$-0.721419\pi$
$739$	−8.05917	+	4.65297i	−0.296461	+	0.171162i	0.344391	+	0.938826i	$0.388086\pi$
$740$		0			0
$741$	−8.60735	+	23.7606i	−0.316199	+	0.872868i
$742$	41.8827			1.53756
$743$	29.8641	−	17.2420i	1.09561	−	0.632549i	0.160543	−	0.987029i	$-0.448676\pi$
$743$	29.8641	−	17.2420i	1.09561	−	0.632549i	0.935064	+	0.354480i	$0.115342\pi$
$744$	−0.432838	−	0.749697i	−0.0158686	−	0.0274852i
$745$		0			0
$746$			5.73433i			0.209949i
$747$	1.95278	+	1.12744i	0.0714485	+	0.0412508i
$748$	−20.8615	−	12.0444i	−0.762772	−	0.440387i
$749$		−	15.7636i		−	0.575988i
$750$		0			0
$751$	13.5823	+	23.5253i	0.495626	+	0.858450i	0.999987	−	0.00504305i	$-0.00160526\pi$
$751$	13.5823	+	23.5253i	0.495626	+	0.858450i	−0.504361	+	0.863493i	$0.668272\pi$
$752$	−4.56265	+	2.63425i	−0.166383	+	0.0960611i
$753$	−29.3882			−1.07097
$754$	−4.70279	−	5.58733i	−0.171266	−	0.203478i
$755$		0			0
$756$	−3.93792	+	2.27356i	−0.143221	+	0.0826885i
$757$	−16.7147	−	28.9507i	−0.607506	−	1.05223i	−0.991650	−	0.128958i	$-0.958837\pi$
$757$	−16.7147	−	28.9507i	−0.607506	−	1.05223i	0.384144	−	0.923273i	$-0.374497\pi$
$758$	−3.17290	+	5.49563i	−0.115245	+	0.199610i
$759$			28.0615i			1.01857i
$760$		0			0
$761$	−6.95046	−	4.01285i	−0.251954	−	0.145466i	0.368705	−	0.929547i	$-0.379801\pi$
$761$	−6.95046	−	4.01285i	−0.251954	−	0.145466i	−0.620659	+	0.784081i	$0.713135\pi$
$762$			41.1143i			1.48941i
$763$	−9.30840	+	16.1226i	−0.336987	+	0.583678i
$764$	−0.976805	−	1.69188i	−0.0353396	−	0.0612099i
$765$		0			0
$766$	−7.09471			−0.256342
$767$	2.39824	+	2.84932i	0.0865954	+	0.102883i
$768$	15.2554			0.550481
$769$	−16.7658	+	9.67974i	−0.604590	+	0.349060i	−0.770845	−	0.637022i	$-0.780166\pi$
$769$	−16.7658	+	9.67974i	−0.604590	+	0.349060i	0.166255	+	0.986083i	$0.446833\pi$
$770$		0			0
$771$	−15.6066	+	27.0314i	−0.562058	+	0.973513i
$772$			20.1564i			0.725445i
$773$	40.3109	+	23.2735i	1.44988	+	0.837090i	0.998474	−	0.0552265i	$-0.0175881\pi$
$773$	40.3109	+	23.2735i	1.44988	+	0.837090i	0.451409	+	0.892317i	$0.350921\pi$
$774$	−16.0464	−	9.26442i	−0.576777	−	0.333003i
$775$		0			0
$776$	0.273309	−	0.473385i	0.00981122	−	0.0169935i
$777$	−1.28917	−	2.23291i	−0.0462488	−	0.0801053i
$778$	−17.9189	+	10.3455i	−0.642423	+	0.370903i
$779$	11.5401			0.413465
$780$		0			0
$781$	−9.05604			−0.324051
$782$	22.2091	−	12.8224i	0.794195	−	0.458529i
$783$	−0.503549	−	0.872172i	−0.0179954	−	0.0311689i
$784$	4.01745	−	6.95842i	0.143480	−	0.248515i
$785$		0			0
$786$	−6.54075	−	3.77630i	−0.233301	−	0.134696i
$787$	−18.7915	−	10.8493i	−0.669845	−	0.386735i	0.126173	−	0.992008i	$-0.459731\pi$
$787$	−18.7915	−	10.8493i	−0.669845	−	0.386735i	−0.796018	+	0.605273i	$0.793064\pi$
$788$		−	6.54770i		−	0.233252i
$789$	2.79159	−	4.83518i	0.0993833	−	0.172137i
$790$		0			0
$791$	4.95307	−	2.85965i	0.176111	−	0.101678i
$792$	0.461103			0.0163846
$793$	−29.3927	+	24.7395i	−1.04377	+	0.878527i
$794$	17.8405			0.633135
$795$		0			0
$796$	−19.6870	−	34.0989i	−0.697787	−	1.20860i
$797$	−1.70634	+	2.95547i	−0.0604418	+	0.104688i	−0.894663	−	0.446742i	$-0.852584\pi$
$797$	−1.70634	+	2.95547i	−0.0604418	+	0.104688i	0.834221	+	0.551430i	$0.185918\pi$
$798$		−	31.3443i		−	1.10958i
$799$	−2.70112	−	1.55949i	−0.0955587	−	0.0551709i
$800$		0			0
$801$			8.12833i			0.287200i
$802$	21.0560	−	36.4701i	0.743515	−	1.28780i
$803$	−11.4405	−	19.8156i	−0.403727	−	0.699276i
$804$	−5.90052	+	3.40667i	−0.208095	+	0.120144i
$805$		0			0
$806$	−12.1402	−	68.2447i	−0.427620	−	2.40382i
$807$	−17.9949			−0.633450
$808$	−0.648818	+	0.374595i	−0.0228253	+	0.0131782i
$809$	9.89881	+	17.1452i	0.348024	+	0.602795i	0.985898	−	0.167345i	$-0.0535195\pi$
$809$	9.89881	+	17.1452i	0.348024	+	0.602795i	−0.637875	+	0.770140i	$0.720186\pi$
$810$		0			0
$811$			6.24712i			0.219366i	0.993967	+	0.109683i	$0.0349836\pi$
$811$			6.24712i			0.219366i	−0.993967	+	0.109683i	$0.965016\pi$
$812$	3.96587	+	2.28970i	0.139175	+	0.0803526i
$813$	14.1527	+	8.17105i	0.496356	+	0.286571i
$814$			11.8743i			0.416195i
$815$		0			0
$816$	4.52050	+	7.82974i	0.158249	+	0.274096i
$817$	55.9215	−	32.2863i	1.95645	−	1.12955i
$818$	−12.2135			−0.427036
$819$	−7.89302	+	1.40410i	−0.275804	+	0.0490634i
$820$		0			0
$821$	−17.2097	+	9.93601i	−0.600622	+	0.346769i	−0.769286	−	0.638904i	$-0.779388\pi$
$821$	−17.2097	+	9.93601i	−0.600622	+	0.346769i	0.168664	+	0.985674i	$0.446055\pi$
$822$	−2.08718	−	3.61510i	−0.0727988	−	0.126091i
$823$	−13.8832	+	24.0465i	−0.483939	+	0.838207i	−0.999830	−	0.0184475i	$-0.994128\pi$
$823$	−13.8832	+	24.0465i	−0.483939	+	0.838207i	0.515891	+	0.856654i	$0.327461\pi$
$824$			1.12975i			0.0393566i
$825$		0			0
$826$	−4.00034	−	2.30960i	−0.139190	−	0.0803612i
$827$		−	24.0957i		−	0.837889i	−0.908012	−	0.418944i	$-0.862400\pi$
$827$		−	24.0957i		−	0.837889i	0.908012	−	0.418944i	$-0.137600\pi$
$828$	−5.63556	+	9.76108i	−0.195849	+	0.339221i
$829$	−18.5805	−	32.1824i	−0.645329	−	1.11774i	−0.984225	−	0.176919i	$-0.943387\pi$
$829$	−18.5805	−	32.1824i	−0.645329	−	1.11774i	0.338896	−	0.940824i	$-0.389946\pi$
$830$		0			0
$831$	0.0957832			0.00332268
$832$	−28.3269	−	10.2615i	−0.982060	−	0.355754i
$833$	4.75671			0.164810
$834$	−37.5933	+	21.7045i	−1.30175	+	0.751565i
$835$		0			0
$836$	−36.4900	+	63.2026i	−1.26203	+	2.18591i
$837$		−	9.55876i		−	0.330399i
$838$	−49.3032	−	28.4652i	−1.70315	−	0.983315i
$839$	27.2829	+	15.7518i	0.941912	+	0.543813i	0.890559	−	0.454867i	$-0.150313\pi$
$839$	27.2829	+	15.7518i	0.941912	+	0.543813i	0.0513528	+	0.998681i	$0.483647\pi$
$840$		0			0
$841$	13.9929	−	24.2364i	0.482513	−	0.835737i
$842$	6.64014	+	11.5011i	0.228834	+	0.396353i
$843$	−25.8589	+	14.9296i	−0.890627	+	0.514204i
$844$	31.0387			1.06840
$845$		0			0
$846$	2.71145			0.0932217
$847$	−28.7361	+	16.5908i	−0.987384	+	0.570067i
$848$	18.3001	+	31.6966i	0.628427	+	1.08847i
$849$	1.05939	−	1.83492i	0.0363583	−	0.0629744i
$850$		0			0
$851$	−5.53481	−	3.19553i	−0.189731	−	0.109541i
$852$	−3.15010	−	1.81871i	−0.107921	−	0.0623080i
$853$		−	50.8047i		−	1.73952i	−0.493474	−	0.869760i	$-0.664273\pi$
$853$		−	50.8047i		−	1.73952i	0.493474	−	0.869760i	$-0.335727\pi$
$854$	23.8252	−	41.2664i	0.815280	−	1.41211i
$855$		0			0
$856$	−0.556035	+	0.321027i	−0.0190049	+	0.0109725i
$857$	−9.65725			−0.329885			−0.164943	−	0.986303i	$-0.552744\pi$
$857$	−9.65725			−0.329885			−0.164943	+	0.986303i	$0.552744\pi$
$858$	34.7137	+	12.5752i	1.18511	+	0.429309i
$859$	−8.60606			−0.293635			−0.146817	−	0.989164i	$-0.546903\pi$
$859$	−8.60606			−0.293635			−0.146817	+	0.989164i	$0.546903\pi$
$860$		0			0
$861$	1.83043	+	3.17040i	0.0623810	+	0.108047i
$862$	−0.497172	+	0.861127i	−0.0169337	+	0.0293301i
$863$			40.2071i			1.36866i	0.729170	+	0.684332i	$0.239906\pi$
$863$			40.2071i			1.36866i	−0.729170	+	0.684332i	$0.760094\pi$
$864$	−6.96356	−	4.02041i	−0.236905	−	0.136777i
$865$		0			0
$866$		−	42.3989i		−	1.44077i
$867$	5.82383	−	10.0872i	0.197788	−	0.342578i
$868$	21.7324	+	37.6416i	0.737646	+	1.27764i
$869$	−31.1126	+	17.9629i	−1.05542	+	0.609349i
$870$		0			0
$871$	−11.8268	+	2.10389i	−0.400735	+	0.0712876i
$872$	0.758267			0.0256781
$873$	5.22710	−	3.01787i	0.176910	−	0.102139i
$874$	−38.8472	−	67.2853i	−1.31402	−	2.27596i
$875$		0			0
$876$		−	9.19034i		−	0.310513i
$877$	29.4421	+	16.9984i	0.994189	+	0.573995i	0.906524	−	0.422155i	$-0.138726\pi$
$877$	29.4421	+	16.9984i	0.994189	+	0.573995i	0.0876652	+	0.996150i	$0.472059\pi$
$878$	−38.0849	−	21.9883i	−1.28530	−	0.742070i
$879$		−	18.5506i		−	0.625696i
$880$		0			0
$881$	−1.29166	−	2.23722i	−0.0435172	−	0.0753740i	0.843446	−	0.537213i	$-0.180523\pi$
$881$	−1.29166	−	2.23722i	−0.0435172	−	0.0753740i	−0.886964	+	0.461839i	$0.847190\pi$
$882$	−3.58118	+	2.06760i	−0.120585	+	0.0696196i
$883$	41.6034			1.40007			0.700034	−	0.714110i	$-0.253168\pi$
$883$	41.6034			1.40007			0.700034	+	0.714110i	$0.253168\pi$
$884$	−2.98768	−	16.7949i	−0.100487	−	0.564874i
$885$		0			0
$886$	−15.3937	+	8.88753i	−0.517160	+	0.298582i
$887$	−20.8873	−	36.1779i	−0.701328	−	1.21473i	−0.968001	−	0.250948i	$-0.919258\pi$
$887$	−20.8873	−	36.1779i	−0.701328	−	1.21473i	0.266673	−	0.963787i	$-0.414076\pi$
$888$	−0.0525084	+	0.0909471i	−0.00176207	+	0.00305199i
$889$		−	45.4537i		−	1.52447i
$890$		0			0
$891$	4.40935	+	2.54574i	0.147719	+	0.0852855i
$892$		−	2.28034i		−	0.0763516i
$893$	−4.72468	+	8.18338i	−0.158105	+	0.273846i
$894$	−18.7951	−	32.5541i	−0.628604	−	1.08877i
$895$		0			0
$896$	1.61054			0.0538042
$897$	−15.2034	+	12.7965i	−0.507625	+	0.427262i
$898$	−34.6688			−1.15691
$899$	−8.33688	+	4.81330i	−0.278051	+	0.160533i
$900$		0			0
$901$	−10.8338	+	18.7646i	−0.360925	+	0.625140i
$902$		−	16.8598i		−	0.561369i
$903$	17.7400	+	10.2422i	0.590352	+	0.340840i
$904$	−0.201740	−	0.116474i	−0.00670976	−	0.00387388i
$905$		0			0
$906$	−1.71299	+	2.96699i	−0.0569104	+	0.0985718i
$907$	22.7675	+	39.4345i	0.755984	+	1.30940i	0.944884	+	0.327406i	$0.106174\pi$
$907$	22.7675	+	39.4345i	0.755984	+	1.30940i	−0.188900	+	0.981996i	$0.560492\pi$
$908$	27.1108	−	15.6524i	0.899704	−	0.519445i
$909$	−8.27253			−0.274383
$910$		0			0
$911$	11.6856			0.387163			0.193581	−	0.981084i	$-0.437990\pi$
$911$	11.6856			0.387163			0.193581	+	0.981084i	$0.437990\pi$
$912$	23.7212	−	13.6954i	0.785487	−	0.453501i
$913$	5.74032	+	9.94253i	0.189977	+	0.329050i
$914$	−32.0285	+	55.4749i	−1.05941	+	1.83495i
$915$		0			0
$916$	16.9568	+	9.79004i	0.560270	+	0.323472i
$917$	7.23108	+	4.17487i	0.238791	+	0.137866i
$918$		−	4.65300i		−	0.153572i
$919$	−12.0274	+	20.8320i	−0.396747	+	0.687186i	−0.993322	−	0.115371i	$-0.963194\pi$
$919$	−12.0274	+	20.8320i	−0.396747	+	0.687186i	0.596576	+	0.802557i	$0.296528\pi$
$920$		0			0
$921$	1.89900	−	1.09639i	0.0625742	−	0.0361272i
$922$	71.8658			2.36677
$923$	−4.12969	−	4.90644i	−0.135931	−	0.161497i
$924$	−23.1516			−0.761630
$925$		0			0
$926$	27.5672	+	47.7478i	0.905914	+	1.56909i
$927$	−6.23732	+	10.8033i	−0.204860	+	0.354828i
$928$			8.09789i			0.265826i
$929$	−37.6020	−	21.7095i	−1.23368	−	0.712266i	−0.265886	−	0.964004i	$-0.585664\pi$
$929$	−37.6020	−	21.7095i	−1.23368	−	0.712266i	−0.967795	+	0.251738i	$0.918998\pi$
$930$		0			0
$931$		−	14.4111i		−	0.472304i
$932$	−23.4864	+	40.6797i	−0.769324	+	1.33251i
$933$	−3.47765	−	6.02346i	−0.113853	−	0.197199i
$934$	23.8531	−	13.7716i	0.780497	−	0.450620i
$935$		0			0
$936$	0.210270	+	0.249819i	0.00687289	+	0.00816559i
$937$	16.9942			0.555177			0.277588	−	0.960700i	$-0.410465\pi$
$937$	16.9942			0.555177			0.277588	+	0.960700i	$0.410465\pi$
$938$	12.9029	−	7.44951i	0.421296	−	0.243235i
$939$	−3.00933	−	5.21231i	−0.0982057	−	0.170097i
$940$		0			0
$941$			33.1512i			1.08070i	0.841440	+	0.540350i	$0.181708\pi$
$941$			33.1512i			1.08070i	−0.841440	+	0.540350i	$0.818292\pi$
$942$	15.8659	+	9.16019i	0.516940	+	0.298455i
$943$	7.85860	+	4.53716i	0.255911	+	0.147750i
$944$		−	4.03659i		−	0.131380i
$945$		0			0
$946$	−47.1696	−	81.7001i	−1.53362	−	2.65630i
$947$	14.1951	−	8.19555i	0.461279	−	0.266319i	−0.251303	−	0.967908i	$-0.580859\pi$
$947$	14.1951	−	8.19555i	0.461279	−	0.266319i	0.712582	+	0.701589i	$0.247526\pi$
$948$	−14.4298			−0.468659
$949$	5.51875	−	15.2345i	0.179146	−	0.494533i
$950$		0			0
$951$	10.2441	−	5.91442i	0.332187	−	0.191788i
$952$	0.232934	+	0.403453i	0.00754942	+	0.0130760i
$953$	16.9461	−	29.3515i	0.548938	−	0.950788i	−0.449410	−	0.893326i	$-0.648366\pi$
$953$	16.9461	−	29.3515i	0.548938	−	0.950788i	0.998348	−	0.0574626i	$-0.0183010\pi$
$954$		−	18.8364i		−	0.609851i
$955$		0			0
$956$	−20.4126	−	11.7852i	−0.660191	−	0.381162i
$957$		−	5.12761i		−	0.165752i
$958$	12.9863	−	22.4929i	0.419568	−	0.726713i
$959$	2.30747	+	3.99666i	0.0745121	+	0.129059i
$960$		0			0
$961$	−60.3699			−1.94742
$962$	−6.43335	+	5.41488i	−0.207420	+	0.174583i
$963$	−7.08954			−0.228457
$964$	−27.0367	+	15.6096i	−0.870794	+	0.502753i
$965$		0			0
$966$	12.3235	−	21.3450i	0.396503	−	0.686763i
$967$			39.0470i			1.25567i	0.778348	+	0.627833i	$0.216058\pi$
$967$			39.0470i			1.25567i	−0.778348	+	0.627833i	$0.783942\pi$
$968$	1.17043	+	0.675747i	0.0376190	+	0.0217193i
$969$	14.0431	+	8.10779i	0.451130	+	0.260460i
$970$		0			0
$971$	−13.5561	+	23.4799i	−0.435037	+	0.753506i	−0.997299	−	0.0734533i	$-0.976598\pi$
$971$	−13.5561	+	23.4799i	−0.435037	+	0.753506i	0.562262	+	0.826959i	$0.309931\pi$
$972$	1.02251	+	1.77105i	0.0327972	+	0.0568064i
$973$	41.5610	−	23.9953i	1.33238	−	0.769253i
$974$	−72.9142			−2.33632
$975$		0			0
$976$	41.6403			1.33287
$977$	−15.4819	+	8.93848i	−0.495310	+	0.285967i	−0.726775	−	0.686876i	$-0.758982\pi$
$977$	−15.4819	+	8.93848i	−0.495310	+	0.285967i	0.231465	+	0.972843i	$0.425648\pi$
$978$	8.20858	+	14.2177i	0.262482	+	0.454631i
$979$	−20.6926	+	35.8406i	−0.661338	+	1.14547i
$980$		0			0
$981$	7.25101	+	4.18638i	0.231507	+	0.133661i
$982$	5.59166	+	3.22834i	0.178437	+	0.103021i
$983$			18.6955i			0.596293i	0.954520	+	0.298146i	$0.0963684\pi$
$983$			18.6955i			0.596293i	−0.954520	+	0.298146i	$0.903632\pi$
$984$	0.0745539	−	0.129131i	0.00237669	−	0.00411655i
$985$		0			0
$986$	−4.05821	+	2.34301i	−0.129240	+	0.0746166i
$987$	−2.99763			−0.0954156
$988$	−50.8823	+	9.05155i	−1.61878	+	0.287968i
$989$	50.7756			1.61457
$990$		0			0
$991$	−13.5235	−	23.4234i	−0.429588	−	0.744068i	0.567248	−	0.823547i	$-0.308008\pi$
$991$	−13.5235	−	23.4234i	−0.429588	−	0.744068i	−0.996837	+	0.0794782i	$0.974675\pi$
$992$	−38.4302	+	66.5630i	−1.22016	+	2.11338i
$993$		−	34.8403i		−	1.10562i
$994$	6.88847	+	3.97706i	0.218489	+	0.126145i
$995$		0			0
$996$			4.61129i			0.146114i
$997$	−14.2044	+	24.6028i	−0.449859	+	0.779179i	−0.998376	−	0.0569605i	$-0.981859\pi$
$997$	−14.2044	+	24.6028i	−0.449859	+	0.779179i	0.548517	+	0.836139i	$0.315192\pi$
$998$	13.7636	+	23.8392i	0.435678	+	0.754617i
$999$	−1.00423	+	0.579795i	−0.0317726	+	0.0183439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.m.751.2		16
5.2	odd	4		195.2.v.a.49.3	yes	32
5.3	odd	4		195.2.v.a.49.14	yes	32
5.4	even	2		975.2.bc.n.751.7		16
13.4	even	6	inner	975.2.bc.m.901.2		16
15.2	even	4		585.2.bf.c.244.14		32
15.8	even	4		585.2.bf.c.244.3		32
65.4	even	6		975.2.bc.n.901.7		16
65.17	odd	12		195.2.v.a.4.14	yes	32
65.43	odd	12		195.2.v.a.4.3	✓	32
195.17	even	12		585.2.bf.c.199.3		32
195.173	even	12		585.2.bf.c.199.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.3	✓	32	65.43	odd	12
195.2.v.a.4.14	yes	32	65.17	odd	12
195.2.v.a.49.3	yes	32	5.2	odd	4
195.2.v.a.49.14	yes	32	5.3	odd	4
585.2.bf.c.199.3		32	195.17	even	12
585.2.bf.c.199.14		32	195.173	even	12
585.2.bf.c.244.3		32	15.8	even	4
585.2.bf.c.244.14		32	15.2	even	4
975.2.bc.m.751.2		16	1.1	even	1	trivial
975.2.bc.m.901.2		16	13.4	even	6	inner
975.2.bc.n.751.7		16	5.4	even	2
975.2.bc.n.901.7		16	65.4	even	6

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)

\(f(q)\)	\(=\)	\(q+(-1.74177 + 1.00561i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.02251 - 1.77105i) q^{4} +(1.74177 + 1.00561i) q^{6} +(-1.92561 - 1.11175i) q^{7} +0.0905636i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.74177 + 1.00561i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.02251 - 1.77105i) q^{4} +(1.74177 + 1.00561i) q^{6} +(-1.92561 - 1.11175i) q^{7} +0.0905636i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.40935 + 2.54574i) q^{11} -2.04503 q^{12} +(-3.38998 - 1.22803i) q^{13} +4.47196 q^{14} +(1.95396 + 3.38435i) q^{16} +(-1.15676 + 2.00356i) q^{17} -2.01123i q^{18} +(6.07004 + 3.50454i) q^{19} +2.22350i q^{21} +(5.12006 - 8.86820i) q^{22} +(2.75574 + 4.77307i) q^{23} +(0.0784304 - 0.0452818i) q^{24} +(7.13949 - 1.27006i) q^{26} +1.00000 q^{27} +(-3.93792 + 2.27356i) q^{28} +(-0.503549 - 0.872172i) q^{29} -9.55876i q^{31} +(-6.96356 - 4.02041i) q^{32} +(4.40935 + 2.54574i) q^{33} -4.65300i q^{34} +(1.02251 + 1.77105i) q^{36} +(-1.00423 + 0.579795i) q^{37} -14.0968 q^{38} +(0.631485 + 3.54982i) q^{39} +(1.42586 - 0.823222i) q^{41} +(-2.23598 - 3.87283i) q^{42} +(4.60635 - 7.97844i) q^{43} +10.4122i q^{44} +(-9.59973 - 5.54241i) q^{46} +1.34816i q^{47} +(1.95396 - 3.38435i) q^{48} +(-1.02803 - 1.78060i) q^{49} +2.31351 q^{51} +(-5.64120 + 4.74813i) q^{52} +9.36564 q^{53} +(-1.74177 + 1.00561i) q^{54} +(0.100684 - 0.174390i) q^{56} -7.00908i q^{57} +(1.75413 + 1.01275i) q^{58} +(-0.894540 - 0.516463i) q^{59} +(5.32768 - 9.22782i) q^{61} +(9.61241 + 16.6492i) q^{62} +(1.92561 - 1.11175i) q^{63} +8.35609 q^{64} -10.2401 q^{66} +(2.88530 - 1.66583i) q^{67} +(2.36560 + 4.09734i) q^{68} +(2.75574 - 4.77307i) q^{69} +(1.54037 + 0.889333i) q^{71} +(-0.0784304 - 0.0452818i) q^{72} +4.49399i q^{73} +(1.16610 - 2.01974i) q^{74} +(12.4134 - 7.16688i) q^{76} +11.3209 q^{77} +(-4.66965 - 5.54795i) q^{78} +7.05606 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.65568 + 2.86773i) q^{82} -2.25488i q^{83} +(3.93792 + 2.27356i) q^{84} +18.5288i q^{86} +(-0.503549 + 0.872172i) q^{87} +(-0.230551 - 0.399327i) q^{88} +(7.03934 - 4.06416i) q^{89} +(5.16250 + 6.13350i) q^{91} +11.2711 q^{92} +(-8.27813 + 4.77938i) q^{93} +(-1.35573 - 2.34819i) q^{94} +8.04083i q^{96} +(-5.22710 - 3.01787i) q^{97} +(3.58118 + 2.06760i) q^{98} -5.09148i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 10 q^{4} - 6 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 10 * q^4 - 6 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 10 q^{4} - 6 q^{7} - 8 q^{9} - 6 q^{11} - 20 q^{12} - 4 q^{14} - 14 q^{16} + 10 q^{17} - 2 q^{22} + 12 q^{23} + 26 q^{26} + 16 q^{27} - 24 q^{28} + 12 q^{29} - 30 q^{32} + 6 q^{33} + 10 q^{36} - 6 q^{37} + 16 q^{38} - 18 q^{41} + 2 q^{42} + 16 q^{43} - 24 q^{46} - 14 q^{48} + 14 q^{49} - 20 q^{51} - 24 q^{52} + 40 q^{53} - 28 q^{56} - 72 q^{58} - 42 q^{59} - 16 q^{61} + 34 q^{62} + 6 q^{63} - 68 q^{64} + 4 q^{66} + 18 q^{67} - 28 q^{68} + 12 q^{69} + 6 q^{71} - 20 q^{74} + 24 q^{76} - 48 q^{77} - 16 q^{78} + 52 q^{79} - 8 q^{81} + 28 q^{82} + 24 q^{84} + 12 q^{87} + 68 q^{88} + 24 q^{89} + 6 q^{91} + 108 q^{92} - 6 q^{93} + 4 q^{94} + 24 q^{98}+O(q^{100}) \) 16 * q - 8 * q^3 + 10 * q^4 - 6 * q^7 - 8 * q^9 - 6 * q^11 - 20 * q^12 - 4 * q^14 - 14 * q^16 + 10 * q^17 - 2 * q^22 + 12 * q^23 + 26 * q^26 + 16 * q^27 - 24 * q^28 + 12 * q^29 - 30 * q^32 + 6 * q^33 + 10 * q^36 - 6 * q^37 + 16 * q^38 - 18 * q^41 + 2 * q^42 + 16 * q^43 - 24 * q^46 - 14 * q^48 + 14 * q^49 - 20 * q^51 - 24 * q^52 + 40 * q^53 - 28 * q^56 - 72 * q^58 - 42 * q^59 - 16 * q^61 + 34 * q^62 + 6 * q^63 - 68 * q^64 + 4 * q^66 + 18 * q^67 - 28 * q^68 + 12 * q^69 + 6 * q^71 - 20 * q^74 + 24 * q^76 - 48 * q^77 - 16 * q^78 + 52 * q^79 - 8 * q^81 + 28 * q^82 + 24 * q^84 + 12 * q^87 + 68 * q^88 + 24 * q^89 + 6 * q^91 + 108 * q^92 - 6 * q^93 + 4 * q^94 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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