LMFDB - Embedded newform 380.2.bb.a.59.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.9
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24529 - 0.670264i) q^{2} +(0.497064 - 0.592377i) q^{3} +(1.10149 + 1.66935i) q^{4} +(-1.92300 + 1.14109i) q^{5} +(-1.01604 + 0.404518i) q^{6} +(-0.647033 - 1.12069i) q^{7} +(-0.252775 - 2.81711i) q^{8} +(0.417106 + 2.36552i) q^{9} +O(q^{10})$	\(q+(-1.24529 - 0.670264i) q^{2} +(0.497064 - 0.592377i) q^{3} +(1.10149 + 1.66935i) q^{4} +(-1.92300 + 1.14109i) q^{5} +(-1.01604 + 0.404518i) q^{6} +(-0.647033 - 1.12069i) q^{7} +(-0.252775 - 2.81711i) q^{8} +(0.417106 + 2.36552i) q^{9} +(3.15952 - 0.132067i) q^{10} +(-3.51998 - 2.03226i) q^{11} +(1.53639 + 0.177272i) q^{12} +(0.500232 - 0.419744i) q^{13} +(0.0545826 + 1.82927i) q^{14} +(-0.279898 + 1.70633i) q^{15} +(-1.57343 + 3.67754i) q^{16} +(-6.09239 - 1.07425i) q^{17} +(1.06611 - 3.22533i) q^{18} +(-4.32757 + 0.521627i) q^{19} +(-4.02304 - 1.95325i) q^{20} +(-0.985491 - 0.173769i) q^{21} +(3.02125 + 4.89007i) q^{22} +(-3.27900 - 1.19346i) q^{23} +(-1.79444 - 1.25054i) q^{24} +(2.39584 - 4.38862i) q^{25} +(-0.904273 + 0.187416i) q^{26} +(3.61769 + 2.08867i) q^{27} +(1.15812 - 2.31456i) q^{28} +(0.235148 - 0.0414630i) q^{29} +(1.49225 - 1.93727i) q^{30} +(2.17265 + 3.76314i) q^{31} +(4.42430 - 3.52499i) q^{32} +(-2.95352 + 1.07499i) q^{33} +(6.86676 + 5.42127i) q^{34} +(2.52305 + 1.41677i) q^{35} +(-3.48944 + 3.30190i) q^{36} -11.3618 q^{37} +(5.73871 + 2.25104i) q^{38} -0.504966i q^{39} +(3.70065 + 5.12886i) q^{40} +(-3.07574 + 3.66552i) q^{41} +(1.11075 + 0.876932i) q^{42} +(-1.67175 + 0.608467i) q^{43} +(-0.484684 - 8.11459i) q^{44} +(-3.50136 - 4.07294i) q^{45} +(3.28337 + 3.68399i) q^{46} +(2.14370 + 12.1575i) q^{47} +(1.39640 + 2.76004i) q^{48} +(2.66270 - 4.61192i) q^{49} +(-5.92505 + 3.85925i) q^{50} +(-3.66467 + 3.07502i) q^{51} +(1.25170 + 0.372715i) q^{52} +(-1.04851 - 0.381626i) q^{53} +(-3.10511 - 5.02581i) q^{54} +(9.08791 - 0.108569i) q^{55} +(-2.99357 + 2.10605i) q^{56} +(-1.84208 + 2.82284i) q^{57} +(-0.320619 - 0.105978i) q^{58} +(1.57571 - 8.93630i) q^{59} +(-3.15677 + 1.41227i) q^{60} +(7.73764 + 2.81627i) q^{61} +(-0.183281 - 6.14244i) q^{62} +(2.38115 - 1.99802i) q^{63} +(-7.87221 + 1.42419i) q^{64} +(-0.482980 + 1.37798i) q^{65} +(4.39852 + 0.640961i) q^{66} +(-8.22648 + 1.45055i) q^{67} +(-4.91742 - 11.3536i) q^{68} +(-2.33685 + 1.34918i) q^{69} +(-2.19232 - 3.45540i) q^{70} +(-2.30080 + 0.837424i) q^{71} +(6.55851 - 1.77298i) q^{72} +(7.87401 - 9.38388i) q^{73} +(14.1487 + 7.61539i) q^{74} +(-1.40883 - 3.60066i) q^{75} +(-5.63757 - 6.64965i) q^{76} +5.25977i q^{77} +(-0.338460 + 0.628829i) q^{78} +(10.3968 + 8.72395i) q^{79} +(-1.17069 - 8.86733i) q^{80} +(-3.73597 + 1.35978i) q^{81} +(6.28705 - 2.50308i) q^{82} +(-5.50091 - 9.52786i) q^{83} +(-0.795431 - 1.83653i) q^{84} +(12.9415 - 4.88616i) q^{85} +(2.48965 + 0.362796i) q^{86} +(0.0923220 - 0.159906i) q^{87} +(-4.83535 + 10.4299i) q^{88} +(-9.55984 - 11.3930i) q^{89} +(1.63026 + 7.41883i) q^{90} +(-0.794072 - 0.289019i) q^{91} +(-1.61950 - 6.78836i) q^{92} +(3.30914 + 0.583491i) q^{93} +(5.47923 - 16.5765i) q^{94} +(7.72670 - 5.94123i) q^{95} +(0.111033 - 4.37300i) q^{96} +(0.139455 - 0.790887i) q^{97} +(-6.40703 + 3.95847i) q^{98} +(3.33916 - 9.17427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$

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 $

$2$	−1.24529	−	0.670264i	−0.880553	−	0.473948i
$2$	−1.24529	−	0.670264i	−0.880553	−	0.473948i
$3$	0.497064	−	0.592377i	0.286980	−	0.342009i	−0.603224	−	0.797572i	$-0.706117\pi$
$3$	0.497064	−	0.592377i	0.286980	−	0.342009i	0.890204	+	0.455563i	$0.150562\pi$
$4$	1.10149	+	1.66935i	0.550746	+	0.834673i
$5$	−1.92300	+	1.14109i	−0.859991	+	0.510310i
$5$	−1.92300	+	1.14109i	−0.859991	+	0.510310i
$6$	−1.01604	+	0.404518i	−0.414796	+	0.165144i
$7$	−0.647033	−	1.12069i	−0.244556	−	0.423583i	0.717451	−	0.696609i	$-0.245309\pi$
$7$	−0.647033	−	1.12069i	−0.244556	−	0.423583i	−0.962007	+	0.273026i	$0.911975\pi$
$8$	−0.252775	−	2.81711i	−0.0893693	−	0.995999i
$9$	0.417106	+	2.36552i	0.139035	+	0.788508i
$10$	3.15952	−	0.132067i	0.999128	−	0.0417634i
$11$	−3.51998	−	2.03226i	−1.06131	−	0.612750i	−0.135519	−	0.990775i	$-0.543270\pi$
$11$	−3.51998	−	2.03226i	−1.06131	−	0.612750i	−0.925796	+	0.378024i	$0.876604\pi$
$12$	1.53639	+	0.177272i	0.443519	+	0.0511740i
$13$	0.500232	−	0.419744i	0.138739	−	0.116416i	−0.570777	−	0.821105i	$-0.693358\pi$
$13$	0.500232	−	0.419744i	0.138739	−	0.116416i	0.709516	+	0.704689i	$0.248913\pi$
$14$	0.0545826	+	1.82927i	0.0145878	+	0.488894i
$15$	−0.279898	+	1.70633i	−0.0722694	+	0.440573i
$16$	−1.57343	+	3.67754i	−0.393357	+	0.919386i
$17$	−6.09239	−	1.07425i	−1.47762	−	0.260545i	−0.623995	−	0.781428i	$-0.714491\pi$
$17$	−6.09239	−	1.07425i	−1.47762	−	0.260545i	−0.853628	+	0.520884i	$0.825602\pi$
$18$	1.06611	−	3.22533i	0.251284	−	0.760219i
$19$	−4.32757	+	0.521627i	−0.992814	+	0.119669i
$19$	−4.32757	+	0.521627i	−0.992814	+	0.119669i
$20$	−4.02304	−	1.95325i	−0.899578	−	0.436760i
$21$	−0.985491	−	0.173769i	−0.215052	−	0.0379194i
$22$	3.02125	+	4.89007i	0.644132	+	1.04257i
$23$	−3.27900	−	1.19346i	−0.683718	−	0.248853i	−0.0232748	−	0.999729i	$-0.507409\pi$
$23$	−3.27900	−	1.19346i	−0.683718	−	0.248853i	−0.660443	+	0.750876i	$0.729631\pi$
$24$	−1.79444	−	1.25054i	−0.366288	−	0.255266i
$25$	2.39584	−	4.38862i	0.479168	−	0.877723i
$26$	−0.904273	+	0.187416i	−0.177343	+	0.0367553i
$27$	3.61769	+	2.08867i	0.696224	+	0.401965i
$28$	1.15812	−	2.31456i	0.218865	−	0.437411i
$29$	0.235148	−	0.0414630i	0.0436660	−	0.00769949i	−0.151773	−	0.988415i	$-0.548498\pi$
$29$	0.235148	−	0.0414630i	0.0436660	−	0.00769949i	0.195438	+	0.980716i	$0.437387\pi$
$30$	1.49225	−	1.93727i	0.272446	−	0.353696i
$31$	2.17265	+	3.76314i	0.390219	+	0.675880i	0.992478	−	0.122421i	$-0.0390659\pi$
$31$	2.17265	+	3.76314i	0.390219	+	0.675880i	−0.602259	+	0.798301i	$0.705733\pi$
$32$	4.42430	−	3.52499i	0.782113	−	0.623136i
$33$	−2.95352	+	1.07499i	−0.514142	+	0.187132i
$34$	6.86676	+	5.42127i	1.17764	+	0.929740i
$35$	2.52305	+	1.41677i	0.426474	+	0.239478i
$36$	−3.48944	+	3.30190i	−0.581573	+	0.550317i
$37$	−11.3618			−1.86787			−0.933933	−	0.357449i	$-0.883647\pi$
$37$	−11.3618			−1.86787			−0.933933	+	0.357449i	$0.883647\pi$
$38$	5.73871	+	2.25104i	0.930942	+	0.365167i
$39$		−	0.504966i		−	0.0808592i
$40$	3.70065	+	5.12886i	0.585124	+	0.810944i
$41$	−3.07574	+	3.66552i	−0.480349	+	0.572458i	−0.950736	−	0.310003i	$-0.899670\pi$
$41$	−3.07574	+	3.66552i	−0.480349	+	0.572458i	0.470386	+	0.882461i	$0.344115\pi$
$42$	1.11075	+	0.876932i	0.171393	+	0.135313i
$43$	−1.67175	+	0.608467i	−0.254939	+	0.0927904i	−0.466328	−	0.884612i	$-0.654424\pi$
$43$	−1.67175	+	0.608467i	−0.254939	+	0.0927904i	0.211389	+	0.977402i	$0.432201\pi$
$44$	−0.484684	−	8.11459i	−0.0730689	−	1.22332i
$45$	−3.50136	−	4.07294i	−0.521952	−	0.607159i
$46$	3.28337	+	3.68399i	0.484106	+	0.543175i
$47$	2.14370	+	12.1575i	0.312691	+	1.77336i	0.584886	+	0.811115i	$0.301139\pi$
$47$	2.14370	+	12.1575i	0.312691	+	1.77336i	−0.272195	+	0.962242i	$0.587750\pi$
$48$	1.39640	+	2.76004i	0.201553	+	0.398377i
$49$	2.66270	−	4.61192i	0.380385	−	0.658846i
$50$	−5.92505	+	3.85925i	−0.837928	+	0.545780i
$51$	−3.66467	+	3.07502i	−0.513157	+	0.430590i
$52$	1.25170	+	0.372715i	0.173580	+	0.0516862i
$53$	−1.04851	−	0.381626i	−0.144024	−	0.0524203i	0.269003	−	0.963139i	$-0.413306\pi$
$53$	−1.04851	−	0.381626i	−0.144024	−	0.0524203i	−0.413026	+	0.910719i	$0.635528\pi$
$54$	−3.10511	−	5.02581i	−0.422552	−	0.683926i
$55$	9.08791	−	0.108569i	1.22541	−	0.0146394i
$56$	−2.99357	+	2.10605i	−0.400032	+	0.281432i
$57$	−1.84208	+	2.82284i	−0.243990	+	0.373894i
$58$	−0.320619	−	0.105978i	−0.0420993	−	0.0139156i
$59$	1.57571	−	8.93630i	0.205140	−	1.16341i	−0.692079	−	0.721822i	$-0.743305\pi$
$59$	1.57571	−	8.93630i	0.205140	−	1.16341i	0.897219	−	0.441586i	$-0.145584\pi$
$60$	−3.15677	+	1.41227i	−0.407537	+	0.182323i
$61$	7.73764	+	2.81627i	0.990703	+	0.360586i	0.785992	−	0.618236i	$-0.212152\pi$
$61$	7.73764	+	2.81627i	0.990703	+	0.360586i	0.204711	+	0.978823i	$0.434375\pi$
$62$	−0.183281	−	6.14244i	−0.0232767	−	0.780091i
$63$	2.38115	−	1.99802i	0.299997	−	0.251727i
$64$	−7.87221	+	1.42419i	−0.984026	+	0.178023i
$65$	−0.482980	+	1.37798i	−0.0599063	+	0.170917i
$66$	4.39852	+	0.640961i	0.541421	+	0.0788968i
$67$	−8.22648	+	1.45055i	−1.00502	+	0.177213i	−0.651853	−	0.758346i	$-0.726008\pi$
$67$	−8.22648	+	1.45055i	−1.00502	+	0.177213i	−0.353172	+	0.935559i	$0.614897\pi$
$68$	−4.91742	−	11.3536i	−0.596325	−	1.37683i
$69$	−2.33685	+	1.34918i	−0.281323	+	0.162422i
$70$	−2.19232	−	3.45540i	−0.262033	−	0.413000i
$71$	−2.30080	+	0.837424i	−0.273055	+	0.0993840i	−0.474919	−	0.880030i	$-0.657523\pi$
$71$	−2.30080	+	0.837424i	−0.273055	+	0.0993840i	0.201863	+	0.979414i	$0.435300\pi$
$72$	6.55851	−	1.77298i	0.772928	−	0.208947i
$73$	7.87401	−	9.38388i	0.921583	−	1.09830i	−0.0733041	−	0.997310i	$-0.523354\pi$
$73$	7.87401	−	9.38388i	0.921583	−	1.09830i	0.994887	−	0.100991i	$-0.0322012\pi$
$74$	14.1487	+	7.61539i	1.64475	+	0.885272i
$75$	−1.40883	−	3.60066i	−0.162678	−	0.415769i
$76$	−5.63757	−	6.64965i	−0.646673	−	0.762767i
$77$			5.25977i			0.599406i
$78$	−0.338460	+	0.628829i	−0.0383231	+	0.0712008i
$79$	10.3968	+	8.72395i	1.16973	+	0.981521i	0.999992	−	0.00396763i	$-0.00126294\pi$
$79$	10.3968	+	8.72395i	1.16973	+	0.981521i	0.169739	+	0.985489i	$0.445707\pi$
$80$	−1.17069	−	8.86733i	−0.130888	−	0.991397i
$81$	−3.73597	+	1.35978i	−0.415107	+	0.151087i
$82$	6.28705	−	2.50308i	0.694288	−	0.276419i
$83$	−5.50091	−	9.52786i	−0.603804	−	1.04582i	−0.992239	−	0.124343i	$-0.960318\pi$
$83$	−5.50091	−	9.52786i	−0.603804	−	1.04582i	0.388436	−	0.921476i	$-0.373016\pi$
$84$	−0.795431	−	1.83653i	−0.0867886	−	0.200382i
$85$	12.9415	−	4.88616i	1.40370	−	0.529979i
$86$	2.48965	+	0.362796i	0.268465	+	0.0391213i
$87$	0.0923220	−	0.159906i	0.00989796	−	0.0171438i
$88$	−4.83535	+	10.4299i	−0.515450	+	1.11183i
$89$	−9.55984	−	11.3930i	−1.01334	−	1.20765i	−0.978070	−	0.208275i	$-0.933215\pi$
$89$	−9.55984	−	11.3930i	−1.01334	−	1.20765i	−0.0352707	−	0.999378i	$-0.511229\pi$
$90$	1.63026	+	7.41883i	0.171845	+	0.782014i
$91$	−0.794072	−	0.289019i	−0.0832414	−	0.0302974i
$92$	−1.61950	−	6.78836i	−0.168844	−	0.707735i
$93$	3.30914	+	0.583491i	0.343142	+	0.0605052i
$94$	5.47923	−	16.5765i	0.565139	−	1.70973i
$95$	7.72670	−	5.94123i	0.792742	−	0.609557i
$96$	0.111033	−	4.37300i	0.0113323	−	0.446318i
$97$	0.139455	−	0.790887i	0.0141595	−	0.0803024i	−0.976909	−	0.213655i	$-0.931463\pi$
$97$	0.139455	−	0.790887i	0.0141595	−	0.0803024i	0.991069	+	0.133353i	$0.0425743\pi$
$98$	−6.40703	+	3.95847i	−0.647208	+	0.399866i
$99$	3.33916	−	9.17427i	0.335599	−	0.922049i
$100$	9.96512	−	0.834539i	0.996512	−	0.0834539i
$101$	5.84992	−	4.90866i	0.582089	−	0.488430i	−0.303544	−	0.952818i	$-0.598170\pi$
$101$	5.84992	−	4.90866i	0.582089	−	0.488430i	0.885632	+	0.464387i	$0.153725\pi$
$102$	6.62465	−	1.37300i	0.655939	−	0.135947i
$103$	7.03711	+	4.06287i	0.693387	+	0.400327i	0.804880	−	0.593438i	$-0.202230\pi$
$103$	7.03711	+	4.06287i	0.693387	+	0.400327i	−0.111493	+	0.993765i	$0.535563\pi$
$104$	−1.30891	−	1.30311i	−0.128349	−	0.127780i
$105$	2.09338	−	0.790374i	0.204293	−	0.0771326i
$106$	1.04991	+	1.17801i	0.101976	+	0.114419i
$107$	8.75169	−	5.05279i	0.846058	−	0.488472i	−0.0132607	−	0.999912i	$-0.504221\pi$
$107$	8.75169	−	5.05279i	0.846058	−	0.488472i	0.859319	+	0.511440i	$0.170888\pi$
$108$	0.498138	+	8.33983i	0.0479333	+	0.802500i
$109$	0.476234	+	1.30844i	0.0456150	+	0.125326i	0.960408	−	0.278596i	$-0.0898690\pi$
$109$	0.476234	+	1.30844i	0.0456150	+	0.125326i	−0.914793	+	0.403922i	$0.867647\pi$
$110$	−11.3898	−	5.95610i	−1.08598	−	0.567892i
$111$	−5.64753	+	6.73046i	−0.536040	+	0.638827i
$112$	5.13946	−	0.616159i	0.485634	−	0.0582215i
$113$	7.44050			0.699943			0.349972	−	0.936760i	$-0.386191\pi$
$113$	7.44050			0.699943			0.349972	+	0.936760i	$0.386191\pi$
$114$	4.18597	−	2.28057i	0.392052	−	0.213595i
$115$	7.66734	−	1.44660i	0.714983	−	0.134897i
$116$	0.328230	+	0.346873i	0.0304754	+	0.0322063i
$117$	1.20157	+	1.00823i	0.111085	+	0.0932112i
$118$	−7.95190	+	10.0721i	−0.732032	+	0.927216i
$119$	2.73807	+	7.52279i	0.250999	+	0.689613i
$120$	4.87768	+	0.357186i	0.445269	+	0.0326065i
$121$	2.76019	+	4.78078i	0.250926	+	0.434617i
$122$	−7.74796	−	8.69333i	−0.701467	−	0.787057i
$123$	0.642534	+	3.64399i	0.0579354	+	0.328568i
$124$	−3.88882	+	7.77197i	−0.349227	+	0.697943i
$125$	0.400594	+	11.1732i	0.0358302	+	0.999358i
$126$	−4.30442	+	0.892117i	−0.383469	+	0.0794761i
$127$	−6.29024	−	7.49641i	−0.558168	−	0.665199i	0.410989	−	0.911640i	$-0.365183\pi$
$127$	−6.29024	−	7.49641i	−0.558168	−	0.665199i	−0.969158	+	0.246441i	$0.920739\pi$
$128$	10.7578	+	3.50293i	0.950861	+	0.309619i
$129$	−0.470524	+	1.29275i	−0.0414273	+	0.113821i
$130$	1.52506	−	1.39225i	0.133756	−	0.122109i
$131$	−0.592416	−	0.104459i	−0.0517597	−	0.00912662i	0.147708	−	0.989031i	$-0.452810\pi$
$131$	−0.592416	−	0.104459i	−0.0517597	−	0.00912662i	−0.199468	+	0.979904i	$0.563921\pi$
$132$	−5.04782	−	3.74635i	−0.439356	−	0.326078i
$133$	3.38467	+	4.51238i	0.293488	+	0.391273i
$134$	11.2166	+	3.70756i	0.968967	+	0.320284i
$135$	−9.34016	+	0.111583i	−0.803873	+	0.00960350i
$136$	−1.48629	+	17.4345i	−0.127448	+	1.49499i
$137$	−4.81932	+	13.2410i	−0.411742	+	1.13125i	0.544522	+	0.838747i	$0.316711\pi$
$137$	−4.81932	+	13.2410i	−0.411742	+	1.13125i	−0.956264	+	0.292505i	$0.905511\pi$
$138$	3.81436	−	0.113814i	0.324700	−	0.00968852i
$139$	−10.1432	−	12.0882i	−0.860334	−	1.02531i	−0.999387	−	0.0350210i	$-0.988850\pi$
$139$	−10.1432	−	12.0882i	−0.860334	−	1.02531i	0.139053	−	0.990285i	$-0.455594\pi$
$140$	0.414042	+	5.77241i	0.0349929	+	0.487858i
$141$	8.26740	+	4.77319i	0.696241	+	0.401975i
$142$	3.42646	+	0.499311i	0.287542	+	0.0419012i
$143$	−2.61384	+	0.460890i	−0.218580	+	0.0385416i
$144$	−9.35560	−	2.18806i	−0.779634	−	0.182339i
$145$	−0.404877	+	0.348058i	−0.0336232	+	0.0289046i
$146$	−16.0951	+	6.40798i	−1.33204	+	0.530328i
$147$	−1.40847	−	3.86974i	−0.116169	−	0.319171i
$148$	−12.5149	−	18.9667i	−1.02872	−	1.55906i
$149$	−0.818404	−	0.686722i	−0.0670462	−	0.0562585i	0.608649	−	0.793440i	$-0.291712\pi$
$149$	−0.818404	−	0.686722i	−0.0670462	−	0.0562585i	−0.675695	+	0.737181i	$0.736156\pi$
$150$	−0.658993	+	5.42816i	−0.0538065	+	0.443207i
$151$	−1.10953			−0.0902925			−0.0451463	−	0.998980i	$-0.514375\pi$
$151$	−1.10953			−0.0902925			−0.0451463	+	0.998980i	$0.514375\pi$
$152$	2.56338	+	12.0594i	0.207918	+	0.978146i
$153$		−	14.8598i		−	1.20134i
$154$	3.52543	−	6.54994i	0.284088	−	0.527809i
$155$	−8.47207	−	4.75733i	−0.680493	−	0.382118i
$156$	0.842962	−	0.556216i	0.0674910	−	0.0445329i
$157$	−3.04036	−	8.35332i	−0.242647	−	0.666668i	−0.999908	−	0.0135552i	$-0.995685\pi$
$157$	−3.04036	−	8.35332i	−0.242647	−	0.666668i	0.757261	−	0.653112i	$-0.226537\pi$
$158$	−7.09968	−	17.8324i	−0.564820	−	1.41867i
$159$	−0.747242	+	0.431420i	−0.0592601	+	0.0342138i
$160$	−4.48560	+	11.8271i	−0.354618	+	0.935011i
$161$	0.784119	+	4.44696i	0.0617972	+	0.350469i
$162$	5.56377	+	0.810764i	0.437131	+	0.0636996i
$163$	−1.43302	+	2.48207i	−0.112243	+	0.194411i	−0.916674	−	0.399635i	$-0.869137\pi$
$163$	−1.43302	+	2.48207i	−0.112243	+	0.194411i	0.804431	+	0.594046i	$0.202470\pi$
$164$	−9.50692	−	1.09693i	−0.742366	−	0.0856555i
$165$	4.45296	−	5.43744i	0.346662	−	0.423304i
$166$	0.464047	+	15.5520i	0.0360171	+	1.20707i
$167$	−1.48086	+	4.06863i	−0.114592	+	0.314840i	−0.983709	−	0.179767i	$-0.942466\pi$
$167$	−1.48086	+	4.06863i	−0.114592	+	0.314840i	0.869117	+	0.494607i	$0.164688\pi$
$168$	−0.240418	+	2.82016i	−0.0185487	+	0.217580i
$169$	−2.18338	+	12.3826i	−0.167952	+	0.952505i
$170$	−19.3909	−	2.58952i	−1.48721	−	0.198607i
$171$	−3.03898	−	10.0194i	−0.232396	−	0.766204i
$172$	−2.85716	−	2.12051i	−0.217857	−	0.161687i
$173$	−2.36685	+	13.4231i	−0.179948	+	1.02054i	0.752327	+	0.658789i	$0.228931\pi$
$173$	−2.36685	+	13.4231i	−0.179948	+	1.02054i	−0.932276	+	0.361749i	$0.882180\pi$
$174$	−0.222147	+	0.137250i	−0.0168409	+	0.0104049i
$175$	−6.46849	+	0.154574i	−0.488972	+	0.0116847i
$176$	13.0122	−	9.74726i	0.980830	−	0.734728i
$177$	−4.51044	−	5.37533i	−0.339025	−	0.404034i
$178$	4.26847	+	20.5952i	0.319935	+	1.54367i
$179$	−6.60254	+	11.4359i	−0.493497	+	0.854762i	−0.999972	−	0.00749289i	$-0.997615\pi$
$179$	−6.60254	+	11.4359i	−0.493497	+	0.854762i	0.506475	+	0.862255i	$0.330948\pi$
$180$	2.94243	−	10.3313i	0.219316	−	0.770050i
$181$	−12.6495	+	2.23045i	−0.940230	+	0.165788i	−0.622700	−	0.782460i	$-0.713964\pi$
$181$	−12.6495	+	2.23045i	−0.940230	+	0.165788i	−0.317530	+	0.948248i	$0.602853\pi$
$182$	0.795131	+	0.892150i	0.0589390	+	0.0661306i
$183$	5.51439	−	3.18374i	0.407636	−	0.235349i
$184$	−2.53325	+	9.53896i	−0.186754	+	0.703222i
$185$	21.8487	−	12.9648i	1.60635	−	0.953190i
$186$	−3.72975	−	2.94462i	−0.273478	−	0.215910i
$187$	19.2620	+	16.1627i	1.40857	+	1.18193i
$188$	−17.9338	+	16.9700i	−1.30796	+	1.23766i
$189$		−	5.40577i		−	0.393212i
$190$	−13.6042	+	2.21962i	−0.986950	+	0.161028i
$191$		−	1.96817i		−	0.142412i	−0.997462	−	0.0712059i	$-0.977315\pi$
$191$		−	1.96817i		−	0.142412i	0.997462	−	0.0712059i	$-0.0226847\pi$
$192$	−3.06933	+	5.37123i	−0.221510	+	0.387635i
$193$	9.09531	+	7.63187i	0.654695	+	0.549354i	0.908491	−	0.417904i	$-0.137235\pi$
$193$	9.09531	+	7.63187i	0.654695	+	0.549354i	−0.253797	+	0.967258i	$0.581679\pi$
$194$	−0.703764	+	0.891412i	−0.0505273	+	0.0639996i
$195$	0.576210	+	0.971048i	0.0412632	+	0.0695382i
$196$	10.6318	−	0.635039i	0.759417	−	0.0453600i
$197$	−9.40767	+	5.43152i	−0.670269	+	0.386980i	−0.796179	−	0.605062i	$-0.793148\pi$
$197$	−9.40767	+	5.43152i	−0.670269	+	0.386980i	0.125910	+	0.992042i	$0.459815\pi$
$198$	−10.3074	+	9.18651i	−0.732516	+	0.652857i
$199$	−0.987286	+	0.174085i	−0.0699869	+	0.0123406i	−0.208532	−	0.978016i	$-0.566869\pi$
$199$	−0.987286	+	0.174085i	−0.0699869	+	0.0123406i	0.138545	+	0.990356i	$0.455757\pi$
$200$	−12.9688	−	5.64002i	−0.917034	−	0.398809i
$201$	−3.22981	+	5.59420i	−0.227813	+	0.394584i
$202$	−10.5749	+	2.19172i	−0.744051	+	0.154209i
$203$	−0.198616	−	0.236702i	−0.0139401	−	0.0166132i
$204$	−9.16988	−	2.73049i	−0.642020	−	0.191172i
$205$	1.73196	−	10.5585i	0.120965	−	0.737435i
$206$	−6.04004	−	9.77617i	−0.420829	−	0.681138i
$207$	1.45546	−	8.25434i	0.101162	−	0.573716i
$208$	0.756548	+	2.50006i	0.0524572	+	0.173348i
$209$	16.2931	+	6.95865i	1.12702	+	0.481340i
$210$	−3.13663	−	0.418874i	−0.216448	−	0.0289051i
$211$	−4.26511	+	24.1886i	−0.293622	+	1.66521i	0.379128	+	0.925344i	$0.376224\pi$
$211$	−4.26511	+	24.1886i	−0.293622	+	1.66521i	−0.672750	+	0.739870i	$0.734887\pi$
$212$	−0.517858	−	2.17068i	−0.0355667	−	0.149083i
$213$	−0.647575	+	1.77920i	−0.0443711	+	0.121909i
$214$	−14.2851	+	0.426245i	−0.976509	+	0.0291375i
$215$	2.52046	−	3.07769i	0.171894	−	0.209897i
$216$	4.96956	−	10.7194i	0.338136	−	0.729362i
$217$	2.81155	−	4.86975i	0.190861	−	0.330580i
$218$	0.283953	−	1.94859i	0.0192317	−	0.131975i
$219$	−1.64491	−	9.32877i	−0.111153	−	0.630380i
$220$	10.1915	+	15.0513i	0.687111	+	1.01476i
$221$	−3.49852	+	2.01987i	−0.235336	+	0.135871i
$222$	11.5440	−	4.59604i	0.774782	−	0.308466i
$223$	1.95990	+	5.38479i	0.131245	+	0.360592i	0.987856	−	0.155370i	$-0.0496569\pi$
$223$	1.95990	+	5.38479i	0.131245	+	0.360592i	−0.856612	+	0.515962i	$0.827435\pi$
$224$	−6.81311	−	2.67750i	−0.455220	−	0.178898i
$225$	11.3807	+	3.83690i	0.758713	+	0.255794i
$226$	−9.26558	−	4.98710i	−0.616337	−	0.331737i
$227$		−	14.8537i		−	0.985873i	−0.870065	−	0.492936i	$-0.835924\pi$
$227$		−	14.8537i		−	0.985873i	0.870065	−	0.492936i	$-0.164076\pi$
$228$	−6.74133	+	0.0342673i	−0.446456	+	0.00226941i
$229$	8.14498			0.538235			0.269118	−	0.963107i	$-0.413268\pi$
$229$	8.14498			0.538235			0.269118	+	0.963107i	$0.413268\pi$
$230$	−10.5177	−	3.33770i	−0.693514	−	0.220081i
$231$	3.11577	+	2.61444i	0.205003	+	0.172018i
$232$	−0.176245	−	0.651958i	−0.0115711	−	0.0428031i
$233$	2.99173	+	8.21972i	0.195995	+	0.538492i	0.998291	−	0.0584342i	$-0.0186108\pi$
$233$	2.99173	+	8.21972i	0.195995	+	0.538492i	−0.802296	+	0.596926i	$0.796389\pi$
$234$	−0.820514	−	2.06091i	−0.0536387	−	0.134726i
$235$	−17.9951	−	20.9327i	−1.17387	−	1.36550i
$236$	16.6534	−	7.21286i	1.08404	−	0.469517i
$237$	10.3357	−	1.82247i	0.671379	−	0.118382i
$238$	1.63256	−	11.2033i	0.105823	−	0.726201i
$239$	13.1030	+	7.56501i	0.847562	+	0.489340i	0.859827	−	0.510585i	$-0.170571\pi$
$239$	13.1030	+	7.56501i	0.847562	+	0.489340i	−0.0122657	+	0.999925i	$0.503904\pi$
$240$	−5.83471	−	3.71413i	−0.376629	−	0.239746i
$241$	−8.84218	−	10.5377i	−0.569575	−	0.678793i	0.401969	−	0.915653i	$-0.368326\pi$
$241$	−8.84218	−	10.5377i	−0.569575	−	0.678793i	−0.971544	+	0.236861i	$0.923882\pi$
$242$	−0.232844	−	7.80351i	−0.0149678	−	0.501629i
$243$	−5.33772	+	14.6653i	−0.342415	+	0.940777i
$244$	3.82162	+	16.0189i	0.244654	+	1.02550i
$245$	0.142248	+	11.9071i	0.00908792	+	0.760716i
$246$	1.64230	−	4.96850i	0.104709	−	0.316780i
$247$	−1.94584	+	2.07741i	−0.123811	+	0.132182i
$248$	10.0520	−	7.07181i	0.638301	−	0.449061i
$249$	−8.37840	−	1.47734i	−0.530959	−	0.0936224i
$250$	6.99011	−	14.1823i	0.442094	−	0.896969i
$251$	4.13506	−	11.3610i	0.261003	−	0.717100i	−0.738098	−	0.674694i	$-0.764276\pi$
$251$	4.13506	−	11.3610i	0.261003	−	0.717100i	0.999100	−	0.0424057i	$-0.0135022\pi$
$252$	5.95821	+	1.77416i	0.375332	+	0.111761i
$253$	9.11659	+	10.8647i	0.573155	+	0.683060i
$254$	2.80859	+	13.5513i	0.176227	+	0.850286i
$255$	3.53828	−	10.0950i	0.221576	−	0.632172i
$256$	−11.0486	−	11.5727i	−0.690540	−	0.723294i
$257$	4.04349	+	22.9318i	0.252226	+	1.43044i	0.803094	+	0.595852i	$0.203186\pi$
$257$	4.04349	+	22.9318i	0.252226	+	1.43044i	−0.550868	+	0.834592i	$0.685703\pi$
$258$	1.45242	−	1.29448i	0.0904240	−	0.0805907i
$259$	7.35145	+	12.7331i	0.456797	+	0.791196i
$260$	−2.83232	+	0.711569i	−0.175653	+	0.0441296i
$261$	0.196164	+	0.538955i	0.0121422	+	0.0333605i
$262$	0.667715	+	0.527157i	0.0412516	+	0.0325679i
$263$	5.40776	+	4.53765i	0.333457	+	0.279803i	0.794107	−	0.607778i	$-0.207939\pi$
$263$	5.40776	+	4.53765i	0.333457	+	0.279803i	−0.460650	+	0.887582i	$0.652384\pi$
$264$	3.77495	+	8.04867i	0.232332	+	0.495361i
$265$	2.45175	−	0.462573i	0.150610	−	0.0284157i
$266$	−1.19041	−	7.88784i	−0.0729886	−	0.483635i
$267$	−11.5008			−0.703837
$268$	−11.4829	−	12.1351i	−0.701428	−	0.741267i
$269$	−12.2528	+	14.6023i	−0.747068	+	0.890321i	−0.996957	−	0.0779535i	$-0.975161\pi$
$269$	−12.2528	+	14.6023i	−0.747068	+	0.890321i	0.249889	+	0.968274i	$0.419606\pi$
$270$	11.7060	+	6.12142i	0.712404	+	0.372538i
$271$	−5.50726	−	15.1311i	−0.334542	−	0.919147i	−0.986914	−	0.161248i	$-0.948448\pi$
$271$	−5.50726	−	15.1311i	−0.334542	−	0.919147i	0.652372	−	0.757899i	$-0.273774\pi$
$272$	13.5366	−	20.7148i	0.820775	−	1.25602i
$273$	−0.565913	+	0.326730i	−0.0342506	+	0.0197746i
$274$	14.8764	−	13.2586i	0.898716	−	0.800983i
$275$	−17.3521	+	10.5789i	−1.04637	+	0.637930i
$276$	−4.82626	−	2.41489i	−0.290507	−	0.145360i
$277$	−21.3155	−	12.3065i	−1.28072	−	0.739425i	−0.303741	−	0.952755i	$-0.598236\pi$
$277$	−21.3155	−	12.3065i	−1.28072	−	0.739425i	−0.976980	+	0.213329i	$0.931569\pi$
$278$	4.52893	+	21.8519i	0.271627	+	1.31059i
$279$	−7.99557	+	6.70908i	−0.478682	+	0.401662i
$280$	3.35344	−	7.46584i	0.200406	−	0.446170i
$281$	4.50045	−	12.3649i	0.268474	−	0.737627i	−0.730054	−	0.683390i	$-0.760505\pi$
$281$	4.50045	−	12.3649i	0.268474	−	0.737627i	0.998528	−	0.0542372i	$-0.0172727\pi$
$282$	−7.09601	−	11.4853i	−0.422561	−	0.683942i
$283$	4.45275	−	25.2528i	0.264689	−	1.50112i	−0.505231	−	0.862984i	$-0.668593\pi$
$283$	4.45275	−	25.2528i	0.264689	−	1.50112i	0.769920	−	0.638140i	$-0.220296\pi$
$284$	−3.93227	−	2.91842i	−0.233337	−	0.173176i
$285$	0.321211	−	7.53029i	0.0190269	−	0.446056i
$286$	3.56390	+	1.17802i	0.210738	+	0.0696578i
$287$	6.09803	+	1.07525i	0.359956	+	0.0634699i
$288$	10.1839	+	8.99550i	0.600090	+	0.530065i
$289$	19.9885	+	7.27520i	1.17579	+	0.427953i
$290$	0.737480	−	0.162059i	0.0433063	−	0.00951641i
$291$	−0.399186	−	0.475731i	−0.0234007	−	0.0278878i
$292$	24.3381	+	2.80817i	1.42428	+	0.164336i
$293$	5.19491	−	8.99785i	0.303490	−	0.525660i	−0.673434	−	0.739247i	$-0.735181\pi$
$293$	5.19491	−	8.99785i	0.303490	−	0.525660i	0.976924	+	0.213587i	$0.0685147\pi$
$294$	−0.839794	+	5.76299i	−0.0489778	+	0.336105i
$295$	7.16701	+	18.9825i	0.417279	+	1.10520i
$296$	2.87197	+	32.0074i	0.166930	+	1.86039i
$297$	−8.48947	−	14.7042i	−0.492609	−	0.853224i
$298$	0.558864	+	1.40371i	0.0323741	+	0.0813150i
$299$	−2.14120	+	0.779335i	−0.123829	+	0.0450701i
$300$	4.45894	−	6.31793i	0.257437	−	0.364766i
$301$	1.76358	+	1.47982i	0.101651	+	0.0852956i
$302$	1.38169	+	0.743680i	0.0795073	+	0.0427940i
$303$		−	5.90528i		−	0.339249i
$304$	4.89083	−	16.7356i	0.280508	−	0.959852i
$305$	−18.0931	+	3.41364i	−1.03601	+	0.195464i
$306$	−9.95998	+	18.5047i	−0.569374	+	1.05785i
$307$	−20.8203	+	24.8127i	−1.18828	+	1.41613i	−0.301794	+	0.953373i	$0.597585\pi$
$307$	−20.8203	+	24.8127i	−1.18828	+	1.41613i	−0.886483	+	0.462760i	$0.846859\pi$
$308$	−8.78037	+	5.79360i	−0.500308	+	0.330121i
$309$	5.90465	−	2.14912i	0.335904	−	0.122259i
$310$	7.36151	+	11.6028i	0.418106	+	0.658993i
$311$	21.3810	−	12.3443i	1.21240	−	0.699982i	0.249122	−	0.968472i	$-0.419858\pi$
$311$	21.3810	−	12.3443i	1.21240	−	0.699982i	0.963282	+	0.268490i	$0.0865247\pi$
$312$	−1.42254	+	0.127642i	−0.0805357	+	0.00722633i
$313$	−21.1754	+	3.73380i	−1.19691	+	0.211047i	−0.736361	−	0.676589i	$-0.763458\pi$
$313$	−21.1754	+	3.73380i	−1.19691	+	0.211047i	−0.460546	+	0.887636i	$0.652346\pi$
$314$	−1.81280	+	12.4401i	−0.102302	+	0.702038i
$315$	−2.29903	+	6.55929i	−0.129536	+	0.369574i
$316$	−3.11130	+	26.9652i	−0.175024	+	1.51691i
$317$	−4.65198	+	3.90347i	−0.261281	+	0.219241i	−0.764012	−	0.645202i	$-0.776773\pi$
$317$	−4.65198	+	3.90347i	−0.261281	+	0.219241i	0.502731	+	0.864443i	$0.332329\pi$
$318$	1.21970	−	0.0363938i	0.0683973	−	0.00204087i
$319$	−0.911982	−	0.331934i	−0.0510612	−	0.0185848i
$320$	13.5131	−	11.7216i	0.755406	−	0.655256i
$321$	1.35699	−	7.69587i	0.0757397	−	0.429541i
$322$	2.00418	−	6.06332i	0.111689	−	0.337896i
$323$	26.9256	+	1.47095i	1.49818	+	0.0818461i
$324$	−6.38508	−	4.73883i	−0.354727	−	0.263268i
$325$	−0.643620	−	3.20097i	−0.0357016	−	0.177558i
$326$	3.44817	−	2.13039i	0.190976	−	0.117991i
$327$	1.01181	+	0.368269i	0.0559533	+	0.0203653i
$328$	11.1036	+	7.73814i	0.613096	+	0.427267i
$329$	12.2378	−	10.2688i	0.674693	−	0.566135i
$330$	−9.18974	+	3.78653i	−0.505878	+	0.208442i
$331$	14.1358	−	24.4840i	0.776975	−	1.34576i	−0.156703	−	0.987646i	$-0.550086\pi$
$331$	14.1358	−	24.4840i	0.776975	−	1.34576i	0.933678	−	0.358115i	$-0.116580\pi$
$332$	9.84608	−	19.6778i	0.540374	−	1.07996i
$333$	−4.73907	−	26.8766i	−0.259699	−	1.47283i
$334$	4.57116	−	4.07406i	0.250123	−	0.222922i
$335$	14.1643	−	12.1765i	0.773878	−	0.665275i
$336$	2.18964	−	3.35077i	0.119455	−	0.182800i
$337$	−19.6601	+	7.15567i	−1.07095	+	0.389794i	−0.816532	−	0.577300i	$-0.804106\pi$
$337$	−19.6601	+	7.15567i	−1.07095	+	0.389794i	−0.254419	+	0.967094i	$0.581884\pi$
$338$	11.0185	−	13.9564i	0.599329	−	0.759130i
$339$	3.69840	−	4.40758i	0.200870	−	0.239387i
$340$	22.4116	+	16.2217i	1.21544	+	0.879746i
$341$		−	17.6616i		−	0.956428i
$342$	−2.93124	+	14.5140i	−0.158503	+	0.784826i
$343$	−15.9499			−0.861213
$344$	2.13669	+	4.55570i	0.115203	+	0.245627i
$345$	2.95422	−	5.26101i	0.159050	−	0.283243i
$346$	11.9444	−	15.1292i	0.642136	−	0.813351i
$347$	−1.61068	+	0.586241i	−0.0864660	+	0.0314711i	−0.384891	−	0.922962i	$-0.625761\pi$
$347$	−1.61068	+	0.586241i	−0.0864660	+	0.0314711i	0.298425	+	0.954433i	$0.403539\pi$
$348$	0.368631	−	0.0220183i	0.0197607	−	0.00118031i
$349$	−13.4455	−	23.2883i	−0.719722	−	1.24660i	−0.961110	−	0.276166i	$-0.910936\pi$
$349$	−13.4455	−	23.2883i	−0.719722	−	1.24660i	0.241388	−	0.970429i	$-0.422397\pi$
$350$	8.15875	+	4.14311i	0.436103	+	0.221458i
$351$	2.68639	−	0.473683i	0.143389	−	0.0252833i
$352$	−22.7372	+	3.41657i	−1.21190	+	0.182104i
$353$	−11.3732	−	6.56633i	−0.605335	−	0.349491i	0.165802	−	0.986159i	$-0.446979\pi$
$353$	−11.3732	−	6.56633i	−0.605335	−	0.349491i	−0.771138	+	0.636669i	$0.780312\pi$
$354$	2.01391	+	9.71702i	0.107038	+	0.516454i
$355$	3.46887	−	4.23578i	0.184108	−	0.224812i
$356$	8.48872	−	28.5079i	0.449901	−	1.51092i
$357$	5.81733	+	2.11733i	0.307886	+	0.112061i
$358$	15.8872	−	9.81560i	0.839663	−	0.518771i
$359$	24.2269	+	4.27185i	1.27865	+	0.225460i	0.771405	−	0.636345i	$-0.219554\pi$
$359$	24.2269	+	4.27185i	1.27865	+	0.225460i	0.507241	+	0.861804i	$0.330666\pi$
$360$	−10.5889	+	10.8933i	−0.558083	+	0.574125i
$361$	18.4558	−	4.51476i	0.971358	−	0.237619i
$362$	17.2473	+	5.70095i	0.906497	+	0.299635i
$363$	4.20402	+	0.741282i	0.220654	+	0.0389072i
$364$	−0.392192	−	1.64393i	−0.0205565	−	0.0861655i
$365$	−4.43388	+	27.0301i	−0.232080	+	1.41482i
$366$	−9.00096	+	0.268574i	−0.470488	+	0.0140386i
$367$	−22.8093	+	19.1393i	−1.19064	+	0.999064i	−0.190790	+	0.981631i	$0.561105\pi$
$367$	−22.8093	+	19.1393i	−1.19064	+	0.999064i	−0.999848	+	0.0174328i	$0.994451\pi$
$368$	9.54826	−	10.1808i	0.497737	−	0.530712i
$369$	−9.95378	−	5.74682i	−0.518173	−	0.299168i
$370$	−35.8978	+	1.50052i	−1.86624	+	0.0780084i
$371$	0.250734	+	1.42198i	0.0130175	+	0.0738256i
$372$	2.67095	+	6.16681i	0.138482	+	0.319734i
$373$	−6.12009	−	10.6003i	−0.316886	−	0.548863i	0.662950	−	0.748663i	$-0.269304\pi$
$373$	−6.12009	−	10.6003i	−0.316886	−	0.548863i	−0.979837	+	0.199800i	$0.935971\pi$
$374$	−13.1534	−	33.0378i	−0.680148	−	1.70835i
$375$	6.81785	+	5.31647i	0.352072	+	0.274541i
$376$	33.7072	−	9.11215i	1.73832	−	0.469923i
$377$	0.100225	−	0.119443i	0.00516184	−	0.00615164i
$378$	−3.62329	+	6.73174i	−0.186362	+	0.346244i
$379$	−25.3592			−1.30262			−0.651308	−	0.758813i	$-0.725780\pi$
$379$	−25.3592			−1.30262			−0.651308	+	0.758813i	$0.725780\pi$
$380$	18.4289	+	6.35431i	0.945380	+	0.325969i
$381$	−7.56736			−0.387687
$382$	−1.31919	+	2.45094i	−0.0674958	+	0.125401i
$383$	−7.88693	+	9.39927i	−0.403003	+	0.480280i	−0.928933	−	0.370247i	$-0.879273\pi$
$383$	−7.88693	+	9.39927i	−0.403003	+	0.480280i	0.525930	+	0.850528i	$0.323717\pi$
$384$	7.42235	−	4.63147i	0.378770	−	0.236349i
$385$	−6.00185	−	10.1145i	−0.305883	−	0.515484i
$386$	−6.21093	−	15.6001i	−0.316128	−	0.794027i
$387$	−2.13664	−	3.70077i	−0.108612	−	0.188121i
$388$	1.47387	−	0.638358i	0.0748245	−	0.0324077i
$389$	−0.548095	−	3.10840i	−0.0277895	−	0.157602i	0.967755	−	0.251893i	$-0.0810529\pi$
$389$	−0.548095	−	3.10840i	−0.0277895	−	0.157602i	−0.995545	+	0.0942902i	$0.969942\pi$
$390$	−0.0666895	−	1.59545i	−0.00337695	−	0.0807887i
$391$	18.6949	+	10.7935i	0.945439	+	0.545850i
$392$	−13.6654	−	6.33533i	−0.690205	−	0.319982i
$393$	−0.356348	+	0.299011i	−0.0179754	+	0.0150831i
$394$	15.3558	−	0.458194i	0.773616	−	0.0230835i
$395$	−29.9478	−	4.91249i	−1.50684	−	0.247174i
$396$	18.9931	−	4.53118i	0.954439	−	0.227700i
$397$	−23.3841	−	4.12325i	−1.17362	−	0.206940i	−0.447353	−	0.894358i	$-0.647633\pi$
$397$	−23.3841	−	4.12325i	−1.17362	−	0.206940i	−0.726262	+	0.687418i	$0.758744\pi$
$398$	1.34614	+	0.444956i	0.0674759	+	0.0223036i
$399$	4.35543	+	0.237938i	0.218044	+	0.0119118i
$400$	12.3696	+	15.7160i	0.618482	+	0.785799i
$401$	−37.3671	−	6.58883i	−1.86602	−	0.329030i	−0.877439	−	0.479689i	$-0.840750\pi$
$401$	−37.3671	−	6.58883i	−1.86602	−	0.329030i	−0.988586	+	0.150658i	$0.951861\pi$
$402$	7.77164	−	4.80157i	0.387614	−	0.239480i
$403$	2.66638	+	0.970484i	0.132822	+	0.0483433i
$404$	14.6379	+	4.35868i	0.728263	+	0.216852i
$405$	5.63263	−	6.87792i	0.279888	−	0.341767i
$406$	0.0886822	+	0.427887i	0.00440122	+	0.0212357i
$407$	39.9933	+	23.0901i	1.98239	+	1.14454i
$408$	9.58901	+	9.54649i	0.474727	+	0.472622i
$409$	−13.6552	+	2.40777i	−0.675204	+	0.119057i	−0.500728	−	0.865605i	$-0.666934\pi$
$409$	−13.6552	+	2.40777i	−0.675204	+	0.119057i	−0.174476	+	0.984661i	$0.555823\pi$
$410$	−9.23375	+	11.9875i	−0.456022	+	0.592020i
$411$	5.44814	+	9.43646i	0.268737	+	0.465466i
$412$	0.968975	+	16.2226i	0.0477380	+	0.799230i
$413$	−11.0344	+	4.01620i	−0.542968	+	0.197624i
$414$	−7.34506	+	9.30350i	−0.360990	+	0.457242i
$415$	21.4504	+	12.0450i	1.05296	+	0.591268i
$416$	0.733580	−	3.62039i	0.0359667	−	0.177504i
$417$	−12.2026			−0.597563
$418$	−15.6255	−	19.5862i	−0.764266	−	0.957992i
$419$			8.75463i			0.427692i	0.976867	+	0.213846i	$0.0685990\pi$
$419$			8.75463i			0.427692i	−0.976867	+	0.213846i	$0.931401\pi$
$420$	3.62525	+	2.62399i	0.176894	+	0.128038i
$421$	2.42433	−	2.88920i	0.118154	−	0.140811i	−0.703725	−	0.710473i	$-0.748481\pi$
$421$	2.42433	−	2.88920i	0.118154	−	0.140811i	0.821879	+	0.569662i	$0.192926\pi$
$422$	21.5241	−	27.2631i	1.04777	−	1.32715i
$423$	−27.8648	+	10.1419i	−1.35483	+	0.493118i
$424$	−0.810045	+	3.05023i	−0.0393393	+	0.148132i
$425$	−19.3109	+	24.1634i	−0.936716	+	1.17210i
$426$	1.99895	−	1.78157i	0.0968495	−	0.0863173i
$427$	−1.85033	−	10.4938i	−0.0895438	−	0.507828i
$428$	18.0748	+	9.04399i	0.873677	+	0.437158i
$429$	−1.02622	+	1.77747i	−0.0495465	+	0.0858171i
$430$	−5.20157	+	2.14325i	−0.250842	+	0.103357i
$431$	−17.6866	+	14.8408i	−0.851933	+	0.714857i	−0.960215	−	0.279263i	$-0.909910\pi$
$431$	−17.6866	+	14.8408i	−0.851933	+	0.714857i	0.108281	+	0.994120i	$0.465465\pi$
$432$	−13.3734	+	10.0178i	−0.643426	+	0.481983i
$433$	20.1855	+	7.34691i	0.970052	+	0.353070i	0.777965	−	0.628308i	$-0.216252\pi$
$433$	20.1855	+	7.34691i	0.970052	+	0.353070i	0.192087	+	0.981378i	$0.438474\pi$
$434$	−6.76522	+	4.17977i	−0.324741	+	0.200635i
$435$	0.00493209	+	0.412847i	0.000236476	+	0.0197945i
$436$	−1.65968	+	2.23624i	−0.0794840	+	0.107096i
$437$	14.8126	+	3.45436i	0.708584	+	0.165244i
$438$	−4.20435	+	12.7196i	−0.200891	+	0.607764i
$439$	1.77851	−	10.0864i	0.0848837	−	0.481399i	−0.912498	−	0.409081i	$-0.865849\pi$
$439$	1.77851	−	10.0864i	0.0848837	−	0.481399i	0.997382	−	0.0723180i	$-0.0230396\pi$
$440$	−2.60304	−	25.5742i	−0.124095	−	1.21920i
$441$	12.0202	+	4.37501i	0.572393	+	0.208334i
$442$	5.71052	−	0.170393i	0.271622	−	0.00810476i
$443$	−21.4279	+	17.9801i	−1.01807	+	0.854262i	−0.989384	−	0.145326i	$-0.953577\pi$
$443$	−21.4279	+	17.9801i	−1.01807	+	0.854262i	−0.0286863	+	0.999588i	$0.509132\pi$
$444$	−17.4562	−	2.01413i	−0.828434	−	0.0955862i
$445$	31.3839	+	11.0001i	1.48774	+	0.521453i
$446$	1.16858	−	8.01927i	0.0553340	−	0.379723i
$447$	−0.813598	+	0.143459i	−0.0384818	+	0.00678539i
$448$	6.68966	+	7.90085i	0.316057	+	0.373280i
$449$	0.167174	−	0.0965178i	0.00788941	−	0.00455496i	−0.496050	−	0.868294i	$-0.665217\pi$
$449$	0.167174	−	0.0965178i	0.00788941	−	0.00455496i	0.503940	+	0.863739i	$0.331883\pi$
$450$	−11.6005	−	12.4061i	−0.546854	−	0.584831i
$451$	18.2758	−	6.65186i	0.860576	−	0.313224i
$452$	8.19565	+	12.4208i	0.385491	+	0.584224i
$453$	−0.551509	+	0.657262i	−0.0259121	+	0.0308809i
$454$	−9.95588	+	18.4971i	−0.467253	+	0.868113i
$455$	1.85679	−	0.350323i	0.0870479	−	0.0164234i
$456$	8.41788	+	4.47580i	0.394203	+	0.209599i
$457$			24.4488i			1.14367i	0.820370	+	0.571833i	$0.193768\pi$
$457$			24.4488i			1.14367i	−0.820370	+	0.571833i	$0.806232\pi$
$458$	−10.1429	−	5.45928i	−0.473944	−	0.255096i
$459$	−19.7966	−	16.6113i	−0.924027	−	0.775351i
$460$	10.8604	+	11.2060i	0.506369	+	0.522483i
$461$	1.98574	−	0.722750i	0.0924850	−	0.0336618i	−0.295363	−	0.955385i	$-0.595441\pi$
$461$	1.98574	−	0.722750i	0.0924850	−	0.0336618i	0.387848	+	0.921723i	$0.373218\pi$
$462$	−2.12767	−	5.34412i	−0.0989881	−	0.248631i
$463$	−9.67820	−	16.7631i	−0.449784	−	0.779049i	0.548588	−	0.836093i	$-0.315166\pi$
$463$	−9.67820	−	16.7631i	−0.449784	−	0.779049i	−0.998372	+	0.0570444i	$0.981832\pi$
$464$	−0.217507	+	0.930007i	−0.0100975	+	0.0431745i
$465$	−7.02929	+	2.65397i	−0.325975	+	0.123075i
$466$	1.78381	−	12.2412i	0.0826333	−	0.567062i
$467$	16.5808	−	28.7187i	0.767266	−	1.32894i	−0.171774	−	0.985136i	$-0.554950\pi$
$467$	16.5808	−	28.7187i	0.767266	−	1.32894i	0.939040	−	0.343808i	$-0.111717\pi$
$468$	−0.359574	+	3.11639i	−0.0166213	+	0.144055i
$469$	6.94843	+	8.28082i	0.320849	+	0.382373i
$470$	8.37867	+	38.1288i	0.386479	+	1.75875i
$471$	−6.45957	−	2.35109i	−0.297641	−	0.108333i
$472$	−25.5728	−	2.18008i	−1.17709	−	0.100346i
$473$	7.12110	+	1.25564i	0.327428	+	0.0577345i
$474$	−14.0925	−	4.65817i	−0.647291	−	0.213957i
$475$	−8.07896	+	20.2418i	−0.370688	+	0.928757i
$476$	−9.54217	+	12.8571i	−0.437365	+	0.589304i
$477$	0.465406	−	2.63945i	0.0213095	−	0.120852i
$478$	−11.2465	−	18.2031i	−0.514401	−	0.832590i
$479$	3.31652	−	9.11207i	0.151536	−	0.416341i	−0.840577	−	0.541693i	$-0.817784\pi$
$479$	3.31652	−	9.11207i	0.151536	−	0.416341i	0.992112	+	0.125352i	$0.0400059\pi$
$480$	4.77646	+	8.53597i	0.218014	+	0.389612i
$481$	−5.68353	+	4.76904i	−0.259146	+	0.217450i
$482$	3.94803	+	19.0491i	0.179828	+	0.867662i
$483$	3.02404	+	1.74593i	0.137598	+	0.0794425i
$484$	−4.94046	+	9.87370i	−0.224566	+	0.448805i
$485$	0.634300	+	1.68000i	0.0288021	+	0.0762850i
$486$	16.4766	−	14.6848i	0.747394	−	0.666117i
$487$	12.5324	−	7.23557i	0.567896	−	0.327875i	−0.188412	−	0.982090i	$-0.560334\pi$
$487$	12.5324	−	7.23557i	0.567896	−	0.327875i	0.756309	+	0.654215i	$0.227001\pi$
$488$	5.97786	−	22.5097i	0.270605	−	1.01896i
$489$	0.758018	+	2.08264i	0.0342787	+	0.0941801i
$490$	7.80375	−	14.9231i	0.352538	−	0.674158i
$491$	0.0406164	−	0.0484047i	0.00183299	−	0.00218448i	−0.765127	−	0.643879i	$-0.777324\pi$
$491$	0.0406164	−	0.0484047i	0.00183299	−	0.00218448i	0.766960	+	0.641695i	$0.221768\pi$
$492$	−5.37534	+	5.08644i	−0.242339	+	0.229315i
$493$	−1.47716			−0.0665279
$494$	3.81555	−	1.28275i	0.171670	−	0.0577136i
$495$	4.04744	+	21.4524i	0.181919	+	0.964213i
$496$	−17.2576	+	2.06898i	−0.774890	+	0.0928997i
$497$	2.42719	+	2.03666i	0.108875	+	0.0913566i
$498$	9.44332	+	7.45545i	0.423165	+	0.334087i
$499$	−2.50810	−	6.89095i	−0.112278	−	0.308481i	0.870809	−	0.491622i	$-0.163596\pi$
$499$	−2.50810	−	6.89095i	−0.112278	−	0.308481i	−0.983087	+	0.183141i	$0.941374\pi$
$500$	−18.2106	+	12.9759i	−0.814403	+	0.580299i
$501$	1.67408	+	2.89960i	0.0747925	+	0.129544i
$502$	−12.7642	+	11.3761i	−0.569695	+	0.507742i
$503$	−6.42035	−	36.4116i	−0.286269	−	1.62351i	−0.700717	−	0.713440i	$-0.747136\pi$
$503$	−6.42035	−	36.4116i	−0.286269	−	1.62351i	0.414448	−	0.910073i	$-0.363975\pi$
$504$	−6.23054	−	6.20291i	−0.277530	−	0.276300i
$505$	−5.64817	+	16.1146i	−0.251340	+	0.717091i
$506$	−4.07056	−	19.6403i	−0.180958	−	0.873116i
$507$	6.24987	+	7.44831i	0.277567	+	0.330791i
$508$	5.58546	−	18.7578i	0.247815	−	0.832244i
$509$	−2.03894	+	5.60194i	−0.0903743	+	0.248301i	−0.976642	−	0.214871i	$-0.931067\pi$
$509$	−2.03894	+	5.60194i	−0.0903743	+	0.248301i	0.886268	+	0.463173i	$0.153289\pi$
$510$	−11.1725	+	10.1996i	−0.494726	+	0.451645i
$511$	−15.6112	−	2.75268i	−0.690600	−	0.121771i
$512$	6.00198	+	21.8169i	0.265253	+	0.964179i
$513$	−16.7453	−	7.15181i	−0.739324	−	0.315760i
$514$	10.3350	−	31.2669i	0.455858	−	1.37912i
$515$	−18.1684	+	0.217050i	−0.800597	+	0.00956436i
$516$	−2.67633	+	0.638491i	−0.117819	+	0.0281080i
$517$	17.1615	−	47.1508i	0.754762	−	2.07369i
$518$	−0.620156	−	20.7838i	−0.0272481	−	0.913188i
$519$	6.77506	+	8.07420i	0.297392	+	0.354418i
$520$	4.00399	+	1.01229i	0.175587	+	0.0443919i
$521$	5.64764	+	3.26066i	0.247427	+	0.142852i	0.618586	−	0.785717i	$-0.287706\pi$
$521$	5.64764	+	3.26066i	0.247427	+	0.142852i	−0.371158	+	0.928570i	$0.621039\pi$
$522$	0.116962	−	0.802636i	0.00511927	−	0.0351304i
$523$	32.5138	−	5.73306i	1.42173	−	0.250689i	0.590688	−	0.806900i	$-0.298856\pi$
$523$	32.5138	−	5.73306i	1.42173	−	0.250689i	0.831041	+	0.556211i	$0.187745\pi$
$524$	−0.478164	−	1.10401i	−0.0208887	−	0.0482288i
$525$	−3.12368	+	3.90862i	−0.136329	+	0.170586i
$526$	−3.69280	−	9.27532i	−0.161014	−	0.404423i
$527$	−9.19407	−	25.2605i	−0.400500	−	1.10036i
$528$	0.693823	−	12.5531i	0.0301948	−	0.546305i
$529$	−8.29155	−	6.95744i	−0.360502	−	0.302497i
$530$	−3.36318	−	1.06728i	−0.146087	−	0.0463597i
$531$	21.7963			0.945878
$532$	−3.80453	+	10.6205i	−0.164948	+	0.460459i
$533$			3.12463i			0.135343i
$534$	14.3218	+	7.70857i	0.619766	+	0.333582i
$535$	−11.0638	+	19.7030i	−0.478330	+	0.851833i
$536$	6.16580	+	22.8082i	0.266322	+	0.985165i
$537$	3.49251	+	9.59558i	0.150713	+	0.414080i
$538$	25.0457	−	9.97153i	1.07980	−	0.429903i
$539$	−18.7453	+	10.8226i	−0.807417	+	0.466162i
$540$	−10.4744	−	15.4691i	−0.450746	−	0.665682i
$541$	−4.15660	−	23.5732i	−0.178706	−	1.01349i	−0.933779	−	0.357851i	$-0.883509\pi$
$541$	−4.15660	−	23.5732i	−0.178706	−	1.01349i	0.755072	−	0.655641i	$-0.227602\pi$
$542$	−3.28368	+	22.5339i	−0.141046	+	0.967913i
$543$	−4.96634	+	8.60196i	−0.213126	+	0.369145i
$544$	−30.7413	+	16.7228i	−1.31802	+	0.716985i
$545$	−2.40884	−	1.97271i	−0.103184	−	0.0845015i
$546$	0.923720	−	0.0275623i	0.0395316	−	0.00117956i
$547$	−9.83267	+	27.0150i	−0.420414	+	1.15508i	0.531055	+	0.847337i	$0.321796\pi$
$547$	−9.83267	+	27.0150i	−0.420414	+	1.15508i	−0.951470	+	0.307742i	$0.900427\pi$
$548$	−27.4122	+	6.53972i	−1.17099	+	0.279363i
$549$	−3.43454	+	19.4783i	−0.146583	+	0.831312i
$550$	28.6991	−	1.54324i	1.22373	−	0.0658041i
$551$	−0.995994	+	0.302094i	−0.0424308	+	0.0128696i
$552$	4.39148	+	6.24211i	0.186914	+	0.265682i
$553$	3.04981	−	17.2963i	0.129691	−	0.735515i
$554$	18.2953	+	29.6121i	0.777294	+	1.25810i
$555$	3.18014	−	19.3870i	0.134990	−	0.822932i
$556$	9.00671	−	30.2475i	0.381969	−	1.28278i
$557$	9.06492	+	10.8032i	0.384093	+	0.457744i	0.923102	−	0.384556i	$-0.125645\pi$
$557$	9.06492	+	10.8032i	0.384093	+	0.457744i	−0.539009	+	0.842300i	$0.681201\pi$
$558$	14.4537	−	2.99560i	0.611872	−	0.126814i
$559$	−0.580862	+	1.00608i	−0.0245678	+	0.0425527i
$560$	−9.18009	+	7.04945i	−0.387930	+	0.297894i
$561$	19.1488	−	3.37646i	0.808465	−	0.142554i
$562$	−13.8921	+	12.3814i	−0.586003	+	0.522276i
$563$	11.4131	−	6.58938i	0.481007	−	0.277709i	−0.239829	−	0.970815i	$-0.577091\pi$
$563$	11.4131	−	6.58938i	0.481007	−	0.277709i	0.720836	+	0.693106i	$0.243758\pi$
$564$	1.13838	+	19.0588i	0.0479345	+	0.802519i
$565$	−14.3081	+	8.49026i	−0.601945	+	0.357188i
$566$	−22.4710	+	28.4626i	−0.944528	+	1.19637i
$567$	3.94120	+	3.30706i	0.165515	+	0.138883i
$568$	2.94070	+	6.26994i	0.123389	+	0.263081i
$569$		−	0.00913241i		−	0.000382850i	−1.00000		0.000191425i	$-0.999939\pi$
$569$		−	0.00913241i		−	0.000382850i	1.00000		0.000191425i	$-6.09325e-5\pi$
$570$	−5.44728	+	9.16209i	−0.228162	+	0.383758i
$571$		−	0.969575i		−	0.0405754i	−0.999794	−	0.0202877i	$-0.993542\pi$
$571$		−	0.969575i		−	0.0405754i	0.999794	−	0.0202877i	$-0.00645822\pi$
$572$	−3.64851	−	3.85573i	−0.152552	−	0.161216i
$573$	−1.16590	−	0.978306i	−0.0487062	−	0.0408693i
$574$	−6.87312	−	5.42629i	−0.286878	−	0.226489i
$575$	−13.0936	+	11.5309i	−0.546040	+	0.480872i
$576$	−6.65249	−	18.0279i	−0.277187	−	0.751161i
$577$	36.1447	−	20.8681i	1.50472	−	0.868752i	0.504738	−	0.863273i	$-0.331589\pi$
$577$	36.1447	−	20.8681i	1.50472	−	0.868752i	0.999985	−	0.00547920i	$-0.00174409\pi$
$578$	−20.0151	−	22.4573i	−0.832519	−	0.934100i
$579$	9.04190	−	1.59433i	0.375768	−	0.0662581i
$580$	−1.02700	−	0.292496i	−0.0426438	−	0.0121452i
$581$	−7.11855	+	12.3297i	−0.295327	+	0.511522i
$582$	0.178236	+	0.859983i	0.00738814	+	0.0356474i
$583$	2.91517	+	3.47416i	0.120734	+	0.143885i
$584$	−28.4258	−	19.8099i	−1.17627	−	0.819741i
$585$	−3.46109	−	0.567739i	−0.143098	−	0.0234731i
$586$	−12.5001	+	7.72297i	−0.516375	+	0.319033i
$587$	1.74429	−	9.89239i	0.0719948	−	0.408303i	−0.927418	−	0.374027i	$-0.877977\pi$
$587$	1.74429	−	9.89239i	0.0719948	−	0.408303i	0.999412	−	0.0342752i	$-0.0109123\pi$
$588$	4.90852	−	6.61371i	0.202424	−	0.272745i
$589$	−11.3653	−	15.1519i	−0.468297	−	0.624325i
$590$	3.79830	−	28.4425i	0.156373	−	1.17096i
$591$	−1.45870	+	8.27271i	−0.0600030	+	0.340294i
$592$	17.8770	−	41.7834i	0.734739	−	1.71729i
$593$	1.36514	−	3.75070i	0.0560598	−	0.154023i	−0.908502	−	0.417881i	$-0.862773\pi$
$593$	1.36514	−	3.75070i	0.0560598	−	0.154023i	0.964561	+	0.263858i	$0.0849951\pi$
$594$	0.716156	+	24.0012i	0.0293843	+	0.984779i
$595$	−13.8495	−	11.3419i	−0.567773	−	0.464974i
$596$	0.244911	−	2.12262i	0.0100320	−	0.0869458i
$597$	−0.387620	+	0.671377i	−0.0158642	+	0.0274776i
$598$	3.18878	+	0.464675i	0.130399	+	0.0190020i
$599$	3.74301	+	21.2276i	0.152935	+	0.867338i	0.960649	+	0.277764i	$0.0895932\pi$
$599$	3.74301	+	21.2276i	0.152935	+	0.867338i	−0.807714	+	0.589574i	$0.799296\pi$
$600$	−9.78735	+	4.87899i	−0.399567	+	0.199184i
$601$	4.39412	−	2.53694i	0.179240	−	0.103484i	−0.407696	−	0.913118i	$-0.633668\pi$
$601$	4.39412	−	2.53694i	0.179240	−	0.103484i	0.586935	+	0.809634i	$0.300334\pi$
$602$	−1.20430	−	3.02488i	−0.0490836	−	0.123285i
$603$	−6.86262	−	18.8549i	−0.279468	−	0.767831i
$604$	−1.22214	−	1.85219i	−0.0497283	−	0.0753647i
$605$	−10.7631	−	6.04382i	−0.437583	−	0.245716i
$606$	−3.95810	+	7.35378i	−0.160787	+	0.298727i
$607$		−	27.7036i		−	1.12445i	−0.826983	−	0.562227i	$-0.809945\pi$
$607$		−	27.7036i		−	1.12445i	0.826983	−	0.562227i	$-0.190055\pi$
$608$	−17.3078	+	17.5625i	−0.701922	+	0.712254i
$609$	−0.238942			−0.00968240
$610$	24.8192	+	7.87617i	1.00490	+	0.318897i
$611$	6.17540	+	5.18178i	0.249830	+	0.209632i
$612$	24.8061	−	16.3679i	1.00273	−	0.661635i
$613$	11.6155	+	31.9133i	0.469145	+	1.28897i	0.918432	+	0.395579i	$0.129456\pi$
$613$	11.6155	+	31.9133i	0.469145	+	1.28897i	−0.449287	+	0.893388i	$0.648322\pi$
$614$	42.5583	−	16.9439i	1.71751	−	0.683798i
$615$	−5.39371	−	6.27420i	−0.217495	−	0.253000i
$616$	14.8173	−	1.32954i	0.597008	−	0.0535685i
$617$	11.0655	−	1.95114i	0.445479	−	0.0785500i	0.0535911	−	0.998563i	$-0.482933\pi$
$617$	11.0655	−	1.95114i	0.445479	−	0.0785500i	0.391888	+	0.920013i	$0.371822\pi$
$618$	−8.79347	−	1.28140i	−0.353725	−	0.0515455i
$619$	−35.8033	−	20.6710i	−1.43906	−	0.830839i	−0.441271	−	0.897374i	$-0.645472\pi$
$619$	−35.8033	−	20.6710i	−1.43906	−	0.830839i	−0.997784	+	0.0665345i	$0.978806\pi$
$620$	−1.39030	−	19.3830i	−0.0558356	−	0.778439i
$621$	−9.36964	−	11.1663i	−0.375991	−	0.448088i
$622$	−34.8995	+	1.04134i	−1.39934	+	0.0417541i
$623$	−6.58251	+	18.0853i	−0.263723	+	0.724572i
$624$	1.85703	+	0.794528i	0.0743408	+	0.0318066i
$625$	−13.5199	−	21.0289i	−0.540796	−	0.841154i
$626$	28.8722	+	9.54348i	1.15397	+	0.381434i
$627$	12.2208	−	6.19276i	0.488054	−	0.247315i
$628$	10.5956	−	14.2765i	0.422812	−	0.569696i
$629$	69.2204	+	12.2054i	2.76000	+	0.486662i
$630$	7.25941	−	6.62726i	0.289222	−	0.264036i
$631$	−3.57194	+	9.81382i	−0.142197	+	0.390682i	−0.990263	−	0.139208i	$-0.955544\pi$
$631$	−3.57194	+	9.81382i	−0.142197	+	0.390682i	0.848067	+	0.529890i	$0.177767\pi$
$632$	21.9483	−	31.4941i	0.873056	−	1.25277i
$633$	12.2088	+	14.5498i	0.485255	+	0.578304i
$634$	8.40942	−	1.74290i	0.333981	−	0.0692195i
$635$	20.6502	+	7.23788i	0.819477	+	0.287226i
$636$	−1.54327	−	0.772199i	−0.0611947	−	0.0306197i
$637$	−0.603864	−	3.42468i	−0.0239260	−	0.135691i
$638$	0.913198	+	1.02462i	0.0361539	+	0.0405652i
$639$	−2.94063	−	5.09331i	−0.116329	−	0.201488i
$640$	−24.6843	+	5.53941i	−0.975733	+	0.218964i
$641$	7.26275	+	19.9542i	0.286861	+	0.788145i	0.996501	+	0.0835804i	$0.0266355\pi$
$641$	7.26275	+	19.9542i	0.286861	+	0.788145i	−0.709640	+	0.704565i	$0.751142\pi$
$642$	−6.84811	+	8.67404i	−0.270273	+	0.342337i
$643$	−18.3969	−	15.4368i	−0.725503	−	0.608769i	0.203399	−	0.979096i	$-0.434801\pi$
$643$	−18.3969	−	15.4368i	−0.725503	−	0.608769i	−0.928901	+	0.370327i	$0.879246\pi$
$644$	−6.55981	+	6.20726i	−0.258493	+	0.244600i
$645$	−0.570328	−	3.02287i	−0.0224566	−	0.119025i
$646$	−32.5443	−	19.8791i	−1.28044	−	0.782131i
$647$	−39.6665			−1.55945			−0.779726	−	0.626121i	$-0.784642\pi$
$647$	−39.6665			−1.55945			−0.779726	+	0.626121i	$0.784642\pi$
$648$	4.77501	+	10.1809i	0.187580	+	0.399944i
$649$	−23.7074	+	28.2534i	−0.930597	+	1.10904i
$650$	−1.34400	+	4.41753i	−0.0527160	+	0.173270i
$651$	−1.48721	−	4.08608i	−0.0582884	−	0.160146i
$652$	−5.72189	+	0.341769i	−0.224087	+	0.0133847i
$653$	−1.47393	+	0.850973i	−0.0576793	+	0.0333012i	−0.528562	−	0.848894i	$-0.677269\pi$
$653$	−1.47393	+	0.850973i	−0.0576793	+	0.0333012i	0.470883	+	0.882196i	$0.343935\pi$
$654$	−1.01316	−	1.13678i	−0.0396177	−	0.0444517i
$655$	1.25841	−	0.475124i	0.0491702	−	0.0185646i
$656$	−8.64065	−	17.0786i	−0.337361	−	0.666807i
$657$	25.4821	+	14.7121i	0.994151	+	0.573974i
$658$	−22.1224	+	4.58500i	−0.862422	+	0.178742i
$659$	−7.63985	+	6.41060i	−0.297606	+	0.249721i	−0.779347	−	0.626592i	$-0.784449\pi$
$659$	−7.63985	+	6.41060i	−0.297606	+	0.249721i	0.481741	+	0.876314i	$0.340005\pi$
$660$	13.9819	+	1.44423i	0.544243	+	0.0562164i
$661$	−8.25775	+	22.6880i	−0.321189	+	0.882460i	0.669067	+	0.743202i	$0.266694\pi$
$661$	−8.25775	+	22.6880i	−0.321189	+	0.882460i	−0.990256	+	0.139258i	$0.955528\pi$
$662$	−34.0139	+	21.0149i	−1.32199	+	0.816767i
$663$	−0.542461	+	3.07645i	−0.0210674	+	0.119479i
$664$	−25.4505	+	17.9051i	−0.987672	+	0.694852i
$665$	−11.6577	−	4.81510i	−0.452068	−	0.186721i
$666$	−12.1129	+	36.6455i	−0.469365	+	1.41999i
$667$	−0.820535	−	0.144682i	−0.0317712	−	0.00560213i
$668$	−8.42311	+	2.00950i	−0.325900	+	0.0777498i
$669$	4.16402	+	1.51558i	0.160990	+	0.0585957i
$670$	−25.8001	+	5.66949i	−0.996746	+	0.219031i
$671$	−21.5130	−	25.6381i	−0.830498	−	0.989749i
$672$	−4.97264	+	2.70504i	−0.191824	+	0.104349i
$673$	−7.12247	+	12.3365i	−0.274551	+	0.475536i	−0.970022	−	0.243018i	$-0.921863\pi$
$673$	−7.12247	+	12.3365i	−0.274551	+	0.475536i	0.695471	+	0.718554i	$0.255196\pi$
$674$	29.2787	+	4.26654i	1.12777	+	0.164341i
$675$	17.8338	−	10.8725i	0.686423	−	0.418483i
$676$	−23.0758	+	9.99448i	−0.887529	+	0.384403i
$677$	9.95159	+	17.2367i	0.382471	+	0.662458i	0.991415	−	0.130755i	$-0.0417400\pi$
$677$	9.95159	+	17.2367i	0.382471	+	0.662458i	−0.608944	+	0.793213i	$0.708407\pi$
$678$	−7.55983	+	3.00981i	−0.290333	+	0.115591i
$679$	−0.976575	+	0.355444i	−0.0374775	+	0.0136407i
$680$	−17.0361	−	35.2225i	−0.653306	−	1.35072i
$681$	−8.79898	−	7.38322i	−0.337178	−	0.282926i
$682$	−11.8379	+	21.9938i	−0.453297	+	0.842185i
$683$			25.1586i			0.962667i	0.876537	+	0.481334i	$0.159847\pi$
$683$			25.1586i			0.962667i	−0.876537	+	0.481334i	$0.840153\pi$
$684$	13.3784	−	16.1094i	0.511538	−	0.615959i
$685$	−5.84156	−	30.9616i	−0.223194	−	1.18298i
$686$	19.8622	+	10.6906i	0.758343	+	0.408170i
$687$	4.04857	−	4.82490i	0.154463	−	0.184081i
$688$	0.392717	−	7.10531i	0.0149722	−	0.270887i
$689$	−0.684682	+	0.249204i	−0.0260843	+	0.00949392i
$690$	−7.20513	+	4.57138i	−0.274294	+	0.174029i
$691$	3.80733	−	2.19816i	0.144837	−	0.0836220i	−0.425830	−	0.904803i	$-0.640018\pi$
$691$	3.80733	−	2.19816i	0.144837	−	0.0836220i	0.570668	+	0.821181i	$0.306685\pi$
$692$	−25.0148	+	10.8343i	−0.950921	+	0.411859i
$693$	−12.4421	+	2.19388i	−0.472637	+	0.0833386i
$694$	2.39870	+	0.349544i	0.0910535	+	0.0132685i
$695$	33.2990	+	11.6713i	1.26310	+	0.442717i
$696$	−0.473810	−	0.219661i	−0.0179597	−	0.00832622i
$697$	22.6763	−	19.0277i	0.858926	−	0.720724i
$698$	1.13424	+	38.0127i	0.0429316	+	1.43880i
$699$	6.35626	+	2.31349i	0.240416	+	0.0875042i
$700$	−7.38303	−	10.6279i	−0.279052	−	0.401696i
$701$	−3.85596	+	21.8682i	−0.145637	+	0.825951i	0.821216	+	0.570618i	$0.193296\pi$
$701$	−3.85596	+	21.8682i	−0.145637	+	0.825951i	−0.966853	+	0.255333i	$0.917815\pi$
$702$	−3.66283	−	1.21072i	−0.138245	−	0.0456956i
$703$	49.1690	−	5.92661i	1.85444	−	0.223526i
$704$	30.6044	+	10.9853i	1.15345	+	0.414024i
$705$	−21.3448	+	0.254997i	−0.803892	+	0.00960373i
$706$	9.76177	+	15.8000i	0.367389	+	0.594642i
$707$	−9.28621	−	3.37990i	−0.349244	−	0.127114i
$708$	4.00507	−	13.4504i	0.150520	−	0.505495i
$709$	−6.43156	+	5.39672i	−0.241542	+	0.202678i	−0.755520	−	0.655125i	$-0.772616\pi$
$709$	−6.43156	+	5.39672i	−0.241542	+	0.202678i	0.513978	+	0.857803i	$0.328171\pi$
$710$	−7.15884	+	2.94972i	−0.268666	+	0.110701i
$711$	−16.3002	+	28.2327i	−0.611304	+	1.05881i
$712$	−29.6788	+	29.8110i	−1.11226	+	1.11721i
$713$	−2.63296	−	14.9323i	−0.0986052	−	0.559218i
$714$	−5.82509	−	6.53584i	−0.217998	−	0.244598i
$715$	4.50049	−	3.86891i	0.168309	−	0.144689i
$716$	−26.3632	+	1.57467i	−0.985238	+	0.0588483i
$717$	10.9944	−	4.00162i	0.410592	−	0.149443i
$718$	−27.3062	−	21.5581i	−1.01906	−	0.804541i
$719$	−18.8665	+	22.4842i	−0.703601	+	0.838519i	−0.992929	−	0.118711i	$-0.962124\pi$
$719$	−18.8665	+	22.4842i	−0.703601	+	0.838519i	0.289328	+	0.957230i	$0.406568\pi$
$720$	20.4876	−	6.46792i	0.763527	−	0.241045i
$721$		−	10.5153i		−	0.391609i
$722$	−26.0089	−	6.74808i	−0.967951	−	0.251138i
$723$	−10.6374			−0.395610
$724$	−17.6567	−	18.6596i	−0.656207	−	0.693478i
$725$	0.381413	−	1.13131i	0.0141653	−	0.0420160i
$726$	−4.73836	−	3.74091i	−0.175857	−	0.138838i
$727$	−14.7991	+	5.38642i	−0.548867	+	0.199771i	−0.601543	−	0.798840i	$-0.705447\pi$
$727$	−14.7991	+	5.38642i	−0.548867	+	0.199771i	0.0526759	+	0.998612i	$0.483225\pi$
$728$	−0.613476	+	2.31004i	−0.0227369	+	0.0856160i
$729$	0.0705855	+	0.122258i	0.00261428	+	0.00452806i
$730$	23.6388	−	30.6884i	0.874911	−	1.13583i
$731$	10.8386	−	1.91114i	0.400880	−	0.0706860i
$732$	11.3888	+	5.69857i	0.420943	+	0.210625i
$733$	30.2310	+	17.4538i	1.11661	+	0.644673i	0.940532	−	0.339704i	$-0.110327\pi$
$733$	30.2310	+	17.4538i	1.11661	+	0.644673i	0.176073	+	0.984377i	$0.443660\pi$
$734$	41.2326	−	8.54570i	1.52192	−	0.315428i
$735$	7.12420	+	5.83432i	0.262780	+	0.215202i
$736$	−18.7142	+	6.27822i	−0.689814	+	0.231418i
$737$	31.9050	+	11.6125i	1.17523	+	0.427750i
$738$	8.54346	+	13.8281i	0.314489	+	0.509020i
$739$	22.5797	+	3.98141i	0.830607	+	0.146458i	0.572755	−	0.819726i	$-0.305874\pi$
$739$	22.5797	+	3.98141i	0.830607	+	0.146458i	0.257851	+	0.966185i	$0.416986\pi$
$740$	45.7089	+	22.1924i	1.68029	+	0.815809i
$741$	0.263404	+	2.18528i	0.00967638	+	0.0802782i
$742$	0.640867	−	1.93884i	0.0235270	−	0.0711770i
$743$	37.5947	+	6.62895i	1.37921	+	0.243193i	0.813575	−	0.581460i	$-0.197518\pi$
$743$	37.5947	+	6.62895i	1.37921	+	0.243193i	0.565639	+	0.824653i	$0.308629\pi$
$744$	0.807291	−	9.46971i	0.0295967	−	0.347176i
$745$	2.35740	+	0.386696i	0.0863684	+	0.0141674i
$746$	0.516280	+	17.3025i	0.0189024	+	0.633491i
$747$	20.2439	−	16.9867i	0.740687	−	0.621510i
$748$	−5.76424	+	49.9579i	−0.210761	+	1.82664i
$749$	−11.3253	−	6.53865i	−0.413817	−	0.238917i
$750$	−4.92676	−	11.1903i	−0.179900	−	0.408612i
$751$	−5.27030	−	29.8894i	−0.192316	−	1.09068i	−0.916189	−	0.400746i	$-0.868751\pi$
$751$	−5.27030	−	29.8894i	−0.192316	−	1.09068i	0.723873	−	0.689933i	$-0.242360\pi$
$752$	−48.0828	−	11.2455i	−1.75340	−	0.410080i
$753$	−4.67461	−	8.09666i	−0.170352	−	0.295059i
$754$	−0.204868	+	0.0815644i	−0.00746084	+	0.00297040i
$755$	2.13363	−	1.26607i	0.0776507	−	0.0460771i
$756$	9.02409	−	5.95441i	0.328203	−	0.216560i
$757$	15.3178	−	18.2551i	0.556736	−	0.663492i	−0.412116	−	0.911131i	$-0.635210\pi$
$757$	15.3178	−	18.2551i	0.556736	−	0.663492i	0.968852	+	0.247639i	$0.0796547\pi$
$758$	31.5796	+	16.9974i	1.14702	+	0.617373i
$759$	10.9675			0.398097
$760$	−18.6902	−	20.2652i	−0.677965	−	0.735094i
$761$	23.3418			0.846140			0.423070	−	0.906097i	$-0.360952\pi$
$761$	23.3418			0.846140			0.423070	+	0.906097i	$0.360952\pi$
$762$	9.42355	+	5.07213i	0.341379	+	0.183744i
$763$	1.15823	−	1.38032i	0.0419306	−	0.0499709i
$764$	3.28556	−	2.16792i	0.118867	−	0.0784327i
$765$	16.9563	+	28.5753i	0.613056	+	1.03314i
$766$	16.1215	−	6.41849i	0.582494	−	0.231910i
$767$	−2.96274	−	5.13162i	−0.106978	−	0.185292i
$768$	−12.3473	+	0.792591i	−0.445544	+	0.0286002i
$769$	3.46242	+	19.6364i	0.124858	+	0.708106i	0.981392	+	0.192015i	$0.0615023\pi$
$769$	3.46242	+	19.6364i	0.124858	+	0.708106i	−0.856534	+	0.516091i	$0.827387\pi$
$770$	0.694644	+	16.6183i	0.0250332	+	0.598883i
$771$	15.5941	+	9.00328i	0.561609	+	0.324245i
$772$	−2.72182	+	23.5897i	−0.0979603	+	0.849010i
$773$	3.42115	−	2.87068i	0.123050	−	0.103251i	−0.579186	−	0.815195i	$-0.696630\pi$
$773$	3.42115	−	2.87068i	0.123050	−	0.103251i	0.702236	+	0.711944i	$0.252185\pi$
$774$	0.180243	+	6.04064i	0.00647871	+	0.217126i
$775$	21.7203	−	0.519038i	0.780216	−	0.0186444i
$776$	−2.26327	−	0.192943i	−0.0812465	−	0.00692625i
$777$	11.1969	+	1.97432i	0.401688	+	0.0708284i
$778$	−1.40091	+	4.23823i	−0.0502252	+	0.151948i
$779$	11.3984	−	17.4672i	0.408392	−	0.625827i
$780$	−0.986324	+	2.03150i	−0.0353161	+	0.0727392i
$781$	9.80066	+	1.72812i	0.350695	+	0.0618370i
$782$	−16.0460	−	25.9715i	−0.573805	−	0.928739i
$783$	0.937296	+	0.341148i	0.0334962	+	0.0121916i
$784$	12.7710	+	17.0487i	0.456106	+	0.608883i
$785$	15.3785	+	12.5941i	0.548881	+	0.449503i
$786$	0.644173	−	0.133509i	0.0229769	−	0.00476209i
$787$	−2.18867	−	1.26363i	−0.0780176	−	0.0450435i	0.460484	−	0.887668i	$-0.347676\pi$
$787$	−2.18867	−	1.26363i	−0.0780176	−	0.0450435i	−0.538501	+	0.842625i	$0.681009\pi$
$788$	−19.4296	−	9.72188i	−0.692150	−	0.346328i
$789$	5.37600	−	0.947934i	0.191391	−	0.0337474i
$790$	34.0010	+	26.1904i	1.20970	+	0.931813i
$791$	−4.81425	−	8.33853i	−0.171175	−	0.296484i
$792$	−26.6890	−	7.08776i	−0.948352	−	0.251853i
$793$	5.05273	−	1.83904i	0.179428	−	0.0653063i
$794$	26.3563	+	20.8082i	0.935351	+	0.738454i
$795$	0.944656	−	1.68229i	0.0335035	−	0.0596646i
$796$	−1.37810	−	1.45637i	−0.0488453	−	0.0516196i
$797$	34.3778			1.21773			0.608863	−	0.793275i	$-0.291626\pi$
$797$	34.3778			1.21773			0.608863	+	0.793275i	$0.291626\pi$
$798$	−5.26429	−	3.21559i	−0.186354	−	0.113831i
$799$		−	76.3713i		−	2.70182i
$800$	−4.86991	−	27.8619i	−0.172177	−	0.985066i
$801$	22.9629	−	27.3661i	0.811354	−	0.966934i
$802$	42.1166	+	33.2508i	1.48719	+	1.17413i
$803$	−46.7869	+	17.0290i	−1.65107	+	0.600942i
$804$	−12.8963	+	0.770293i	−0.454816	+	0.0271662i
$805$	−6.58223	−	7.65675i	−0.231993	−	0.269865i
$806$	−2.66994	−	2.99572i	−0.0940446	−	0.105520i
$807$	2.55967	+	14.5166i	0.0901046	+	0.511008i
$808$	−15.3070	−	15.2391i	−0.538497	−	0.536109i
$809$	19.8927	−	34.4551i	0.699389	−	1.21138i	−0.269289	−	0.963059i	$-0.586789\pi$
$809$	19.8927	−	34.4551i	0.699389	−	1.21138i	0.968678	−	0.248319i	$-0.0798780\pi$
$810$	−11.6243	+	4.78965i	−0.408435	+	0.168291i
$811$	4.58998	−	3.85145i	0.161176	−	0.135243i	−0.558633	−	0.829415i	$-0.688674\pi$
$811$	4.58998	−	3.85145i	0.161176	−	0.135243i	0.719809	+	0.694172i	$0.244229\pi$
$812$	0.176363	−	0.592284i	0.00618911	−	0.0207851i
$813$	−11.7008	−	4.25873i	−0.410364	−	0.149360i
$814$	−34.3267	−	55.5600i	−1.20315	−	1.94738i
$815$	−0.0765560	−	6.40822i	−0.00268164	−	0.224470i
$816$	−5.54243	−	18.3153i	−0.194024	−	0.641164i
$817$	6.91723	−	3.50522i	0.242003	−	0.122632i
$818$	18.6185	+	6.15419i	0.650980	+	0.215176i
$819$	0.352469	−	1.99895i	0.0123162	−	0.0698489i
$820$	19.5335	−	8.73884i	0.682138	−	0.305173i
$821$	−47.0952	−	17.1413i	−1.64363	−	0.598234i	−0.655965	−	0.754791i	$-0.727738\pi$
$821$	−47.0952	−	17.1413i	−1.64363	−	0.598234i	−0.987669	+	0.156557i	$0.949960\pi$
$822$	−0.459596	−	15.4028i	−0.0160302	−	0.537235i
$823$	−21.2658	+	17.8441i	−0.741277	+	0.622006i	−0.933180	−	0.359408i	$-0.882979\pi$
$823$	−21.2658	+	17.8441i	−0.741277	+	0.622006i	0.191903	+	0.981414i	$0.438534\pi$
$824$	9.66676	−	20.8513i	0.336758	−	0.726389i
$825$	−2.35843	+	15.5374i	−0.0821102	+	0.540943i
$826$	16.4329	+	2.39464i	0.571775	+	0.0833202i
$827$	−30.4274	+	5.36517i	−1.05806	+	0.186565i	−0.675497	−	0.737363i	$-0.736071\pi$
$827$	−30.4274	+	5.36517i	−1.05806	+	0.186565i	−0.382567	+	0.923928i	$0.624960\pi$
$828$	15.3825	−	6.66242i	0.534580	−	0.231535i
$829$	−27.5592	+	15.9113i	−0.957171	+	0.552623i	−0.895301	−	0.445461i	$-0.853040\pi$
$829$	−27.5592	+	15.9113i	−0.957171	+	0.552623i	−0.0618700	+	0.998084i	$0.519706\pi$
$830$	−18.6386	−	29.3770i	−0.646954	−	1.01969i
$831$	−17.8852	+	6.50969i	−0.620432	+	0.225819i
$832$	−3.34014	+	4.01674i	−0.115798	+	0.139255i
$833$	−21.1766	+	25.2372i	−0.733724	+	0.874419i
$834$	15.1957	+	8.17895i	0.526185	+	0.283214i
$835$	−1.79497	−	9.51376i	−0.0621175	−	0.329237i
$836$	6.33030	+	34.8637i	0.218938	+	1.20579i
$837$			18.1518i			0.627418i
$838$	5.86791	−	10.9020i	0.202704	−	0.376605i
$839$	36.0356	+	30.2374i	1.24409	+	1.04391i	0.997193	+	0.0748690i	$0.0238539\pi$
$839$	36.0356	+	30.2374i	1.24409	+	1.04391i	0.246892	+	0.969043i	$0.420591\pi$
$840$	−2.75572	−	5.69750i	−0.0950815	−	0.196582i
$841$	−27.1975	+	9.89908i	−0.937845	+	0.341348i
$842$	−4.95552	+	1.97295i	−0.170778	+	0.0679924i
$843$	−5.08767	−	8.81210i	−0.175229	−	0.303505i
$844$	−45.0772	+	19.5236i	−1.55162	+	0.672032i
$845$	−9.93094	−	26.3031i	−0.341635	−	0.904853i
$846$	41.4975	+	6.04709i	1.42671	+	0.207903i
$847$	3.57187	−	6.18665i	0.122731	−	0.212576i
$848$	3.05320	−	3.25547i	0.104847	−	0.111793i
$849$	−12.7459	−	15.1900i	−0.437438	−	0.521319i
$850$	40.2435	−	17.1471i	1.38034	−	0.588140i
$851$	37.2552	+	13.5598i	1.27709	+	0.464824i
$852$	−3.68339	+	0.878746i	−0.126191	+	0.0301053i
$853$	−5.73790	−	1.01175i	−0.196462	−	0.0346415i	0.0745512	−	0.997217i	$-0.476248\pi$
$853$	−5.73790	−	1.01175i	−0.196462	−	0.0346415i	−0.271013	+	0.962576i	$0.587359\pi$
$854$	−4.72939	+	14.3080i	−0.161836	+	0.489609i
$855$	17.2770	+	15.7996i	0.590860	+	0.540334i
$856$	−16.4465	−	23.3773i	−0.562129	−	0.799018i
$857$	4.16460	−	23.6186i	0.142260	−	0.806797i	−0.827266	−	0.561810i	$-0.810105\pi$
$857$	4.16460	−	23.6186i	0.142260	−	0.806797i	0.969526	−	0.244987i	$-0.0787837\pi$
$858$	2.46932	−	1.52563i	0.0843012	−	0.0520840i
$859$	−3.90903	+	10.7400i	−0.133374	+	0.366443i	−0.988344	−	0.152235i	$-0.951353\pi$
$859$	−3.90903	+	10.7400i	−0.133374	+	0.366443i	0.854970	+	0.518677i	$0.173575\pi$
$860$	7.91400	+	0.817459i	0.269865	+	0.0278751i
$861$	3.66806	−	3.07787i	0.125007	−	0.104894i
$862$	31.9722	−	6.62642i	1.08898	−	0.225697i
$863$	47.4026	+	27.3679i	1.61360	+	0.931613i	0.988526	+	0.151049i	$0.0482652\pi$
$863$	47.4026	+	27.3679i	1.61360	+	0.931613i	0.625076	+	0.780564i	$0.285068\pi$
$864$	23.3683	−	3.51141i	0.795005	−	0.119460i
$865$	−10.7655	−	28.5133i	−0.366036	−	0.969483i
$866$	−20.2124	−	22.6786i	−0.686845	−	0.770651i
$867$	14.2452	−	8.22447i	0.483793	−	0.279318i
$868$	11.2262	−	0.670541i	0.381042	−	0.0227597i
$869$	−18.8672	−	51.8372i	−0.640026	−	1.75846i
$870$	0.270575	−	0.517420i	0.00917334	−	0.0175422i
$871$	−3.50629	+	4.17863i	−0.118806	+	0.141587i
$872$	3.56565	−	1.67235i	0.120748	−	0.0566328i
$873$	1.92903			0.0652878
$874$	−16.1307	−	14.2301i	−0.545629	−	0.481339i
$875$	12.2625	−	7.67835i	0.414548	−	0.259576i
$876$	13.7611	−	13.0215i	0.464944	−	0.439956i
$877$	5.64798	+	4.73922i	0.190719	+	0.160032i	0.733147	−	0.680070i	$-0.238051\pi$
$877$	5.64798	+	4.73922i	0.190719	+	0.160032i	−0.542429	+	0.840102i	$0.682495\pi$
$878$	−8.97533	+	11.3685i	−0.302903	+	0.383667i
$879$	−2.74792	−	7.54986i	−0.0926851	−	0.254650i
$880$	−13.8999	+	33.5920i	−0.468566	+	1.13239i
$881$	15.3647	+	26.6124i	0.517650	+	0.896596i	0.999790	+	0.0205019i	$0.00652641\pi$
$881$	15.3647	+	26.6124i	0.517650	+	0.896596i	−0.482140	+	0.876094i	$0.660140\pi$
$882$	−12.0363	−	13.5049i	−0.405282	−	0.454733i
$883$	−4.79890	−	27.2159i	−0.161496	−	0.915888i	−0.952604	−	0.304212i	$-0.901607\pi$
$883$	−4.79890	−	27.2159i	−0.161496	−	0.915888i	0.791108	−	0.611676i	$-0.209504\pi$
$884$	−7.22546	−	3.61537i	−0.243018	−	0.121598i
$885$	14.8073	+	5.18995i	0.497741	+	0.174458i
$886$	38.7354	−	8.02813i	1.30134	−	0.269710i
$887$	−3.29939	−	3.93206i	−0.110783	−	0.132026i	0.707803	−	0.706409i	$-0.249686\pi$
$887$	−3.29939	−	3.93206i	−0.110783	−	0.132026i	−0.818586	+	0.574384i	$0.805242\pi$
$888$	20.3880	+	14.2084i	0.684177	+	0.476803i
$889$	−4.33120	+	11.8999i	−0.145264	+	0.399109i
$890$	−31.7091	−	34.7338i	−1.06289	−	1.16428i
$891$	15.9140	+	2.80606i	0.533138	+	0.0940066i
$892$	−6.83025	+	9.20305i	−0.228694	+	0.308141i
$893$	−15.6187	−	51.4944i	−0.522660	−	1.72319i
$894$	1.10932	+	0.366677i	0.0371012	+	0.0122635i
$895$	−0.352726	−	29.5253i	−0.0117903	−	0.986923i
$896$	−3.03491	−	14.3227i	−0.101389	−	0.478487i
$897$	−0.602655	+	1.65578i	−0.0201221	+	0.0552849i
$898$	−0.272872	+	0.00814207i	−0.00910586	+	0.000271704i
$899$	0.666926	+	0.794811i	0.0222432	+	0.0265084i
$900$	6.13063	+	23.2246i	0.204354	+	0.774155i
$901$	5.97796	+	3.45138i	0.199155	+	0.114982i
$902$	−27.2172	−	3.96614i	−0.906234	−	0.132058i
$903$	1.75323	−	0.309141i	0.0583438	−	0.0102876i
$904$	−1.88077	−	20.9607i	−0.0625534	−	0.697143i
$905$	21.7798	−	18.7233i	0.723986	−	0.622385i
$906$	1.12733	−	0.448826i	0.0374529	−	0.0149112i
$907$	0.108807	+	0.298944i	0.00361287	+	0.00992628i	0.941486	−	0.337052i	$-0.109430\pi$
$907$	0.108807	+	0.298944i	0.00361287	+	0.00992628i	−0.937873	+	0.346979i	$0.887208\pi$
$908$	24.7959	−	16.3612i	0.822881	−	0.542966i
$909$	14.0516	+	11.7907i	0.466062	+	0.391073i
$910$	−2.54706	−	0.808289i	−0.0844341	−	0.0267945i
$911$	−45.4335			−1.50528			−0.752639	−	0.658434i	$-0.771219\pi$
$911$	−45.4335			−1.50528			−0.752639	+	0.658434i	$0.771219\pi$
$912$	−7.48273	−	11.2159i	−0.247778	−	0.371395i
$913$			44.7172i			1.47992i
$914$	16.3872	−	30.4458i	0.542039	−	1.00706i
$915$	−6.97125	+	12.4147i	−0.230462	+	0.410418i
$916$	8.97163	+	13.5968i	0.296431	+	0.449250i
$917$	0.266247	+	0.731506i	0.00879224	+	0.0241565i
$918$	13.5185	+	33.9549i	0.446178	+	1.12068i
$919$	8.37263	−	4.83394i	0.276188	−	0.159457i	−0.355509	−	0.934673i	$-0.615692\pi$
$919$	8.37263	−	4.83394i	0.276188	−	0.159457i	0.631696	+	0.775216i	$0.282359\pi$
$920$	−6.01335	−	21.2341i	−0.198254	−	0.700066i
$921$	4.34945	+	24.6670i	0.143319	+	0.812804i
$922$	−2.95725	−	0.430936i	−0.0973919	−	0.0141921i
$923$	−0.799431	+	1.38466i	−0.0263136	+	0.0455765i
$924$	−0.932409	+	8.08108i	−0.0306740	+	0.265848i
$925$	−27.2210	+	49.8625i	−0.895022	+	1.63947i
$926$	0.816435	+	27.3619i	0.0268297	+	0.899168i
$927$	−6.67561	+	18.3411i	−0.219256	+	0.602401i
$928$	0.894210	−	1.01234i	0.0293539	−	0.0332317i
$929$	−0.676084	+	3.83427i	−0.0221816	+	0.125798i	−0.993888	−	0.110395i	$-0.964789\pi$
$929$	−0.676084	+	3.83427i	−0.0221816	+	0.125798i	0.971706	+	0.236193i	$0.0758997\pi$
$930$	10.5324	+	1.40652i	0.345370	+	0.0461217i
$931$	−9.11731	+	21.3474i	−0.298808	+	0.699632i
$932$	−10.4262	+	14.0482i	−0.341521	+	0.460164i
$933$	3.31522	−	18.8015i	0.108535	−	0.615534i
$934$	−39.8970	+	24.6496i	−1.30547	+	0.806561i
$935$	−55.4837	−	9.10127i	−1.81451	−	0.297643i
$936$	2.53658	−	3.63980i	0.0829106	−	0.118970i
$937$	−4.40008	−	5.24381i	−0.143744	−	0.171308i	0.689369	−	0.724411i	$-0.257888\pi$
$937$	−4.40008	−	5.24381i	−0.143744	−	0.171308i	−0.833113	+	0.553103i	$0.813444\pi$
$938$	−3.10247	−	14.9693i	−0.101299	−	0.488765i
$939$	−8.31373	+	14.3998i	−0.271308	+	0.469920i
$940$	15.1225	−	53.0973i	0.493242	−	1.73184i
$941$	5.66886	−	0.999573i	0.184799	−	0.0325851i	−0.0804824	−	0.996756i	$-0.525646\pi$
$941$	5.66886	−	0.999573i	0.184799	−	0.0325851i	0.265282	+	0.964171i	$0.414535\pi$
$942$	6.46819	+	7.25741i	0.210745	+	0.236459i
$943$	14.4600	−	8.34846i	0.470881	−	0.271863i
$944$	30.3844	+	19.8554i	0.988927	+	0.646238i
$945$	6.16845	+	10.3953i	0.200660	+	0.338158i
$946$	−8.02622	−	6.33665i	−0.260955	−	0.206022i
$947$	16.0665	+	13.4814i	0.522091	+	0.438086i	0.865360	−	0.501151i	$-0.167090\pi$
$947$	16.0665	+	13.4814i	0.522091	+	0.438086i	−0.343269	+	0.939237i	$0.611534\pi$
$948$	14.4271	+	15.2465i	0.468570	+	0.495183i
$949$		−	7.99919i		−	0.259665i
$950$	23.6280	−	19.7919i	0.766593	−	0.642133i
$951$			4.69600i			0.152278i
$952$	20.5004	−	9.61502i	0.664422	−	0.311625i
$953$	−22.4062	−	18.8010i	−0.725807	−	0.609024i	0.203178	−	0.979142i	$-0.434873\pi$
$953$	−22.4062	−	18.8010i	−0.725807	−	0.609024i	−0.928985	+	0.370118i	$0.879317\pi$
$954$	−2.34869	+	2.97493i	−0.0760418	+	0.0963170i
$955$	2.24585	+	3.78479i	0.0726741	+	0.122473i
$956$	1.80422	+	30.2062i	0.0583526	+	0.976939i
$957$	−0.649944	+	0.375245i	−0.0210097	+	0.0121300i
$958$	−10.2375	+	9.12422i	−0.330759	+	0.294790i
$959$	17.9573	−	3.16636i	0.579873	−	0.102247i
$960$	−0.226720	−	13.8312i	−0.00731735	−	0.446401i
$961$	6.05919	−	10.4948i	0.195458	−	0.338543i
$962$	10.2742	−	2.12938i	0.331252	−	0.0686539i
$963$	15.6029	+	18.5948i	0.502796	+	0.599209i
$964$	7.85147	−	26.3678i	0.252879	−	0.849251i
$965$	−26.1989	−	4.29753i	−0.843372	−	0.138342i
$966$	−2.59557	−	4.20109i	−0.0835110	−	0.135168i
$967$	10.1872	−	57.7745i	0.327599	−	1.85790i	−0.163149	−	0.986601i	$-0.552165\pi$
$967$	10.1872	−	57.7745i	0.327599	−	1.85790i	0.490747	−	0.871302i	$-0.336724\pi$
$968$	12.7703	−	8.98421i	0.410453	−	0.288763i
$969$	14.2551	−	15.2190i	0.457941	−	0.488904i
$970$	0.336159	−	2.51724i	0.0107934	−	0.0808237i
$971$	0.530315	−	3.00756i	0.0170186	−	0.0965173i	−0.975115	−	0.221698i	$-0.928840\pi$
$971$	0.530315	−	3.00756i	0.0170186	−	0.0965173i	0.992134	+	0.125181i	$0.0399511\pi$
$972$	−30.3609	+	7.24318i	−0.973825	+	0.232325i
$973$	−6.98418	+	19.1889i	−0.223902	+	0.615167i
$974$	−20.4562	+	0.610380i	−0.655458	+	0.0195578i
$975$	−2.21610	−	1.20982i	−0.0709720	−	0.0387452i
$976$	−22.5316	+	24.0243i	−0.721218	+	0.768999i
$977$	30.5570	−	52.9262i	0.977603	−	1.69326i	0.306542	−	0.951857i	$-0.400828\pi$
$977$	30.5570	−	52.9262i	0.977603	−	1.69326i	0.671061	−	0.741402i	$-0.265839\pi$
$978$	0.451965	−	3.10156i	0.0144522	−	0.0991769i
$979$	10.4970	+	59.5312i	0.335484	+	1.90262i
$980$	−19.7204	+	13.3530i	−0.629944	+	0.426547i
$981$	−2.89651	+	1.67230i	−0.0924786	+	0.0533925i
$982$	−0.0830231	+	0.0330542i	−0.00264937	+	0.00105480i
$983$	−9.08348	−	24.9567i	−0.289718	−	0.795994i	−0.996106	−	0.0881686i	$-0.971899\pi$
$983$	−9.08348	−	24.9567i	−0.289718	−	0.795994i	0.706387	−	0.707825i	$-0.250324\pi$
$984$	10.1031	−	2.73120i	0.322075	−	0.0870674i
$985$	11.8931	−	21.1798i	0.378946	−	0.674844i
$986$	1.83949	+	0.990086i	0.0585813	+	0.0315308i
$987$		−	12.3536i		−	0.393221i
$988$	−5.61124	−	0.960030i	−0.178517	−	0.0305426i
$989$	6.20784			0.197398
$990$	9.33853	−	29.4273i	0.296798	−	0.935261i
$991$	−43.4663	−	36.4726i	−1.38075	−	1.15859i	−0.968933	−	0.247325i	$-0.920449\pi$
$991$	−43.4663	−	36.4726i	−1.38075	−	1.15859i	−0.411821	−	0.911265i	$-0.635107\pi$
$992$	22.8775	+	8.99068i	0.726361	+	0.285454i
$993$	−7.47734	−	20.5438i	−0.237286	−	0.651939i
$994$	−1.65746	−	4.16309i	−0.0525715	−	0.132045i
$995$	1.69990	−	1.46134i	0.0538905	−	0.0463277i
$996$	−6.76255	−	15.6137i	−0.214280	−	0.494739i
$997$	−20.4025	+	3.59751i	−0.646154	+	0.113934i	−0.487115	−	0.873338i	$-0.661951\pi$
$997$	−20.4025	+	3.59751i	−0.646154	+	0.113934i	−0.159039	+	0.987272i	$0.550840\pi$
$998$	−1.49544	+	10.2623i	−0.0473374	+	0.324848i
$999$	−41.1034	−	23.7311i	−1.30045	−	0.750817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.59.9	yes	336
4.3	odd	2	inner	380.2.bb.a.59.54	yes	336
5.4	even	2	inner	380.2.bb.a.59.48	yes	336
19.10	odd	18	inner	380.2.bb.a.219.3	yes	336
20.19	odd	2	inner	380.2.bb.a.59.3	✓	336
76.67	even	18	inner	380.2.bb.a.219.48	yes	336
95.29	odd	18	inner	380.2.bb.a.219.54	yes	336
380.219	even	18	inner	380.2.bb.a.219.9	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.3	✓	336	20.19	odd	2	inner
380.2.bb.a.59.9	yes	336	1.1	even	1	trivial
380.2.bb.a.59.48	yes	336	5.4	even	2	inner
380.2.bb.a.59.54	yes	336	4.3	odd	2	inner
380.2.bb.a.219.3	yes	336	19.10	odd	18	inner
380.2.bb.a.219.9	yes	336	380.219	even	18	inner
380.2.bb.a.219.48	yes	336	76.67	even	18	inner
380.2.bb.a.219.54	yes	336	95.29	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24529 - 0.670264i) q^{2} +(0.497064 - 0.592377i) q^{3} +(1.10149 + 1.66935i) q^{4} +(-1.92300 + 1.14109i) q^{5} +(-1.01604 + 0.404518i) q^{6} +(-0.647033 - 1.12069i) q^{7} +(-0.252775 - 2.81711i) q^{8} +(0.417106 + 2.36552i) q^{9} +O(q^{10})\)	\(q+(-1.24529 - 0.670264i) q^{2} +(0.497064 - 0.592377i) q^{3} +(1.10149 + 1.66935i) q^{4} +(-1.92300 + 1.14109i) q^{5} +(-1.01604 + 0.404518i) q^{6} +(-0.647033 - 1.12069i) q^{7} +(-0.252775 - 2.81711i) q^{8} +(0.417106 + 2.36552i) q^{9} +(3.15952 - 0.132067i) q^{10} +(-3.51998 - 2.03226i) q^{11} +(1.53639 + 0.177272i) q^{12} +(0.500232 - 0.419744i) q^{13} +(0.0545826 + 1.82927i) q^{14} +(-0.279898 + 1.70633i) q^{15} +(-1.57343 + 3.67754i) q^{16} +(-6.09239 - 1.07425i) q^{17} +(1.06611 - 3.22533i) q^{18} +(-4.32757 + 0.521627i) q^{19} +(-4.02304 - 1.95325i) q^{20} +(-0.985491 - 0.173769i) q^{21} +(3.02125 + 4.89007i) q^{22} +(-3.27900 - 1.19346i) q^{23} +(-1.79444 - 1.25054i) q^{24} +(2.39584 - 4.38862i) q^{25} +(-0.904273 + 0.187416i) q^{26} +(3.61769 + 2.08867i) q^{27} +(1.15812 - 2.31456i) q^{28} +(0.235148 - 0.0414630i) q^{29} +(1.49225 - 1.93727i) q^{30} +(2.17265 + 3.76314i) q^{31} +(4.42430 - 3.52499i) q^{32} +(-2.95352 + 1.07499i) q^{33} +(6.86676 + 5.42127i) q^{34} +(2.52305 + 1.41677i) q^{35} +(-3.48944 + 3.30190i) q^{36} -11.3618 q^{37} +(5.73871 + 2.25104i) q^{38} -0.504966i q^{39} +(3.70065 + 5.12886i) q^{40} +(-3.07574 + 3.66552i) q^{41} +(1.11075 + 0.876932i) q^{42} +(-1.67175 + 0.608467i) q^{43} +(-0.484684 - 8.11459i) q^{44} +(-3.50136 - 4.07294i) q^{45} +(3.28337 + 3.68399i) q^{46} +(2.14370 + 12.1575i) q^{47} +(1.39640 + 2.76004i) q^{48} +(2.66270 - 4.61192i) q^{49} +(-5.92505 + 3.85925i) q^{50} +(-3.66467 + 3.07502i) q^{51} +(1.25170 + 0.372715i) q^{52} +(-1.04851 - 0.381626i) q^{53} +(-3.10511 - 5.02581i) q^{54} +(9.08791 - 0.108569i) q^{55} +(-2.99357 + 2.10605i) q^{56} +(-1.84208 + 2.82284i) q^{57} +(-0.320619 - 0.105978i) q^{58} +(1.57571 - 8.93630i) q^{59} +(-3.15677 + 1.41227i) q^{60} +(7.73764 + 2.81627i) q^{61} +(-0.183281 - 6.14244i) q^{62} +(2.38115 - 1.99802i) q^{63} +(-7.87221 + 1.42419i) q^{64} +(-0.482980 + 1.37798i) q^{65} +(4.39852 + 0.640961i) q^{66} +(-8.22648 + 1.45055i) q^{67} +(-4.91742 - 11.3536i) q^{68} +(-2.33685 + 1.34918i) q^{69} +(-2.19232 - 3.45540i) q^{70} +(-2.30080 + 0.837424i) q^{71} +(6.55851 - 1.77298i) q^{72} +(7.87401 - 9.38388i) q^{73} +(14.1487 + 7.61539i) q^{74} +(-1.40883 - 3.60066i) q^{75} +(-5.63757 - 6.64965i) q^{76} +5.25977i q^{77} +(-0.338460 + 0.628829i) q^{78} +(10.3968 + 8.72395i) q^{79} +(-1.17069 - 8.86733i) q^{80} +(-3.73597 + 1.35978i) q^{81} +(6.28705 - 2.50308i) q^{82} +(-5.50091 - 9.52786i) q^{83} +(-0.795431 - 1.83653i) q^{84} +(12.9415 - 4.88616i) q^{85} +(2.48965 + 0.362796i) q^{86} +(0.0923220 - 0.159906i) q^{87} +(-4.83535 + 10.4299i) q^{88} +(-9.55984 - 11.3930i) q^{89} +(1.63026 + 7.41883i) q^{90} +(-0.794072 - 0.289019i) q^{91} +(-1.61950 - 6.78836i) q^{92} +(3.30914 + 0.583491i) q^{93} +(5.47923 - 16.5765i) q^{94} +(7.72670 - 5.94123i) q^{95} +(0.111033 - 4.37300i) q^{96} +(0.139455 - 0.790887i) q^{97} +(-6.40703 + 3.95847i) q^{98} +(3.33916 - 9.17427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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