LMFDB - Embedded newform 136.2.s.c.107.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(3,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 8, 1]))

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

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

chi := DirichletCharacter("136.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.s (of order $16$, degree $8$, 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:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.14
Character	$\chi$	$=$	136.107
Dual form			136.2.s.c.75.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40738 + 0.138902i) q^{2} +(-0.456483 - 0.683175i) q^{3} +(1.96141 + 0.390973i) q^{4} +(1.61884 + 0.322007i) q^{5} +(-0.547549 - 1.02489i) q^{6} +(-4.21158 + 0.837735i) q^{7} +(2.70614 + 0.822690i) q^{8} +(0.889699 - 2.14792i) q^{9} +O(q^{10})$	\(q+(1.40738 + 0.138902i) q^{2} +(-0.456483 - 0.683175i) q^{3} +(1.96141 + 0.390973i) q^{4} +(1.61884 + 0.322007i) q^{5} +(-0.547549 - 1.02489i) q^{6} +(-4.21158 + 0.837735i) q^{7} +(2.70614 + 0.822690i) q^{8} +(0.889699 - 2.14792i) q^{9} +(2.23359 + 0.678044i) q^{10} +(-0.106698 - 0.0712931i) q^{11} +(-0.628249 - 1.51846i) q^{12} +(-2.31804 + 2.31804i) q^{13} +(-6.04364 + 0.594013i) q^{14} +(-0.518985 - 1.25294i) q^{15} +(3.69428 + 1.53372i) q^{16} +(-2.89543 - 2.93539i) q^{17} +(1.55049 - 2.89935i) q^{18} +(1.68438 + 4.06645i) q^{19} +(3.04931 + 1.26451i) q^{20} +(2.49484 + 2.49484i) q^{21} +(-0.140261 - 0.115157i) q^{22} +(-2.14808 - 1.43530i) q^{23} +(-0.673265 - 2.22431i) q^{24} +(-2.10245 - 0.870864i) q^{25} +(-3.58433 + 2.94037i) q^{26} +(-4.29112 + 0.853557i) q^{27} +(-8.58818 - 0.00347072i) q^{28} +(-0.908461 + 4.56714i) q^{29} +(-0.556371 - 1.83545i) q^{30} +(-2.02231 - 3.02660i) q^{31} +(4.98620 + 2.67166i) q^{32} +0.105437i q^{33} +(-3.66723 - 4.53337i) q^{34} -7.08762 q^{35} +(2.58485 - 3.86511i) q^{36} +(7.00926 - 4.68344i) q^{37} +(1.80572 + 5.95698i) q^{38} +(2.64177 + 0.525481i) q^{39} +(4.11589 + 2.20320i) q^{40} +(2.02785 + 10.1947i) q^{41} +(3.16463 + 3.85771i) q^{42} +(3.26274 - 7.87696i) q^{43} +(-0.181405 - 0.181551i) q^{44} +(2.13192 - 3.19065i) q^{45} +(-2.82379 - 2.31838i) q^{46} +(4.90893 - 4.90893i) q^{47} +(-0.638577 - 3.22396i) q^{48} +(10.5684 - 4.37759i) q^{49} +(-2.83798 - 1.51767i) q^{50} +(-0.683670 + 3.31804i) q^{51} +(-5.45291 + 3.64033i) q^{52} +(-1.32699 + 0.549659i) q^{53} +(-6.15778 + 0.605232i) q^{54} +(-0.149769 - 0.149769i) q^{55} +(-12.0863 - 1.19780i) q^{56} +(2.00921 - 3.00699i) q^{57} +(-1.91293 + 6.30150i) q^{58} +(12.6911 + 5.25683i) q^{59} +(-0.528077 - 2.66044i) q^{60} +(-0.813692 - 4.09070i) q^{61} +(-2.42575 - 4.54046i) q^{62} +(-1.94765 + 9.79148i) q^{63} +(6.64636 + 4.45262i) q^{64} +(-4.49895 + 3.00610i) q^{65} +(-0.0146454 + 0.148390i) q^{66} +3.72469i q^{67} +(-4.53147 - 6.88954i) q^{68} +2.12271i q^{69} +(-9.97494 - 0.984481i) q^{70} +(0.759116 - 0.507225i) q^{71} +(4.17472 - 5.08063i) q^{72} +(-0.631605 + 3.17529i) q^{73} +(10.5152 - 5.61776i) q^{74} +(0.364781 + 1.83388i) q^{75} +(1.71389 + 8.63453i) q^{76} +(0.509091 + 0.210872i) q^{77} +(3.64497 + 1.10649i) q^{78} +(6.49126 - 9.71485i) q^{79} +(5.48657 + 3.67243i) q^{80} +(-2.38989 - 2.38989i) q^{81} +(1.43789 + 14.6294i) q^{82} +(-4.75872 + 1.97112i) q^{83} +(3.91799 + 5.86882i) q^{84} +(-3.74201 - 5.68426i) q^{85} +(5.68603 - 10.6326i) q^{86} +(3.53486 - 1.46419i) q^{87} +(-0.230087 - 0.280708i) q^{88} +(-0.886097 + 0.886097i) q^{89} +(3.44360 - 4.19431i) q^{90} +(7.82069 - 11.7045i) q^{91} +(-3.65211 - 3.65506i) q^{92} +(-1.14455 + 2.76318i) q^{93} +(7.59057 - 6.22685i) q^{94} +(1.41731 + 7.12530i) q^{95} +(-0.450905 - 4.62602i) q^{96} +(-8.67498 - 1.72556i) q^{97} +(15.4818 - 4.69294i) q^{98} +(-0.248061 + 0.165749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	1.40738	+	0.138902i	0.995165	+	0.0982182i
$2$	1.40738	+	0.138902i	0.995165	+	0.0982182i
$3$	−0.456483	−	0.683175i	−0.263551	−	0.394431i	0.675967	−	0.736932i	$-0.263726\pi$
$3$	−0.456483	−	0.683175i	−0.263551	−	0.394431i	−0.939518	+	0.342500i	$0.888726\pi$
$4$	1.96141	+	0.390973i	0.980706	+	0.195487i
$5$	1.61884	+	0.322007i	0.723966	+	0.144006i	0.543300	−	0.839539i	$-0.317175\pi$
$5$	1.61884	+	0.322007i	0.723966	+	0.144006i	0.180666	+	0.983544i	$0.442175\pi$
$6$	−0.547549	−	1.02489i	−0.223536	−	0.418410i
$7$	−4.21158	+	0.837735i	−1.59183	+	0.316634i	−0.909913	−	0.414798i	$-0.863852\pi$
$7$	−4.21158	+	0.837735i	−1.59183	+	0.316634i	−0.681914	+	0.731432i	$0.738852\pi$
$8$	2.70614	+	0.822690i	0.956764	+	0.290865i
$9$	0.889699	−	2.14792i	0.296566	−	0.715974i
$10$	2.23359	+	0.678044i	0.706322	+	0.214416i
$11$	−0.106698	−	0.0712931i	−0.0321706	−	0.0214957i	0.539381	−	0.842062i	$-0.318658\pi$
$11$	−0.106698	−	0.0712931i	−0.0321706	−	0.0214957i	−0.571552	+	0.820566i	$0.693658\pi$
$12$	−0.628249	−	1.51846i	−0.181360	−	0.438342i
$13$	−2.31804	+	2.31804i	−0.642907	+	0.642907i	−0.951269	−	0.308362i	$-0.900219\pi$
$13$	−2.31804	+	2.31804i	−0.642907	+	0.642907i	0.308362	+	0.951269i	$0.400219\pi$
$14$	−6.04364	+	0.594013i	−1.61523	+	0.158757i
$15$	−0.518985	−	1.25294i	−0.134001	−	0.323508i
$16$	3.69428	+	1.53372i	0.923570	+	0.383430i
$17$	−2.89543	−	2.93539i	−0.702244	−	0.711936i
$17$	−2.89543	−	2.93539i	−0.702244	−	0.711936i
$18$	1.55049	−	2.89935i	0.365454	−	0.683384i
$19$	1.68438	+	4.06645i	0.386423	+	0.932907i	0.990691	+	0.136127i	$0.0434654\pi$
$19$	1.68438	+	4.06645i	0.386423	+	0.932907i	−0.604269	+	0.796781i	$0.706535\pi$
$20$	3.04931	+	1.26451i	0.681847	+	0.282753i
$21$	2.49484	+	2.49484i	0.544418	+	0.544418i
$22$	−0.140261	−	0.115157i	−0.0299038	−	0.0245515i
$23$	−2.14808	−	1.43530i	−0.447906	−	0.299281i	0.311085	−	0.950382i	$-0.399308\pi$
$23$	−2.14808	−	1.43530i	−0.447906	−	0.299281i	−0.758991	+	0.651101i	$0.774308\pi$
$24$	−0.673265	−	2.22431i	−0.137430	−	0.454036i
$25$	−2.10245	−	0.870864i	−0.420490	−	0.174173i
$26$	−3.58433	+	2.94037i	−0.702944	+	0.576654i
$27$	−4.29112	+	0.853557i	−0.825827	+	0.164267i
$28$	−8.58818	−	0.00347072i	−1.62301	−	0.000655905i
$29$	−0.908461	+	4.56714i	−0.168697	+	0.848097i	0.800028	+	0.599962i	$0.204818\pi$
$29$	−0.908461	+	4.56714i	−0.168697	+	0.848097i	−0.968725	+	0.248135i	$0.920182\pi$
$30$	−0.556371	−	1.83545i	−0.101579	−	0.335105i
$31$	−2.02231	−	3.02660i	−0.363217	−	0.543593i	0.604183	−	0.796845i	$-0.293500\pi$
$31$	−2.02231	−	3.02660i	−0.363217	−	0.543593i	−0.967400	+	0.253253i	$0.918500\pi$
$32$	4.98620	+	2.67166i	0.881445	+	0.472288i
$33$			0.105437i			0.0183543i
$34$	−3.66723	−	4.53337i	−0.628924	−	0.777467i
$35$	−7.08762			−1.19803
$36$	2.58485	−	3.86511i	0.430808	−	0.644186i
$37$	7.00926	−	4.68344i	1.15231	−	0.769952i	0.175593	−	0.984463i	$-0.443816\pi$
$37$	7.00926	−	4.68344i	1.15231	−	0.769952i	0.976722	+	0.214511i	$0.0688157\pi$
$38$	1.80572	+	5.95698i	0.292926	+	0.966350i
$39$	2.64177	+	0.525481i	0.423022	+	0.0841442i
$40$	4.11589	+	2.20320i	0.650779	+	0.348356i
$41$	2.02785	+	10.1947i	0.316696	+	1.59214i	0.731246	+	0.682114i	$0.238939\pi$
$41$	2.02785	+	10.1947i	0.316696	+	1.59214i	−0.414550	+	0.910027i	$0.636061\pi$
$42$	3.16463	+	3.85771i	0.488314	+	0.595257i
$43$	3.26274	−	7.87696i	0.497564	−	1.20122i	−0.453228	−	0.891394i	$-0.649728\pi$
$43$	3.26274	−	7.87696i	0.497564	−	1.20122i	0.950792	−	0.309830i	$-0.100272\pi$
$44$	−0.181405	−	0.181551i	−0.0273478	−	0.0273699i
$45$	2.13192	−	3.19065i	0.317808	−	0.475634i
$46$	−2.82379	−	2.31838i	−0.416346	−	0.341827i
$47$	4.90893	−	4.90893i	0.716041	−	0.716041i	−0.251751	−	0.967792i	$-0.581006\pi$
$47$	4.90893	−	4.90893i	0.716041	−	0.716041i	0.967792	+	0.251751i	$0.0810064\pi$
$48$	−0.638577	−	3.22396i	−0.0921706	−	0.465338i
$49$	10.5684	−	4.37759i	1.50978	−	0.625370i
$50$	−2.83798	−	1.51767i	−0.401350	−	0.214630i
$51$	−0.683670	+	3.31804i	−0.0957329	+	0.464619i
$52$	−5.45291	+	3.64033i	−0.756183	+	0.504824i
$53$	−1.32699	+	0.549659i	−0.182277	+	0.0755015i	−0.471955	−	0.881623i	$-0.656452\pi$
$53$	−1.32699	+	0.549659i	−0.182277	+	0.0755015i	0.289679	+	0.957124i	$0.406452\pi$
$54$	−6.15778	+	0.605232i	−0.837968	+	0.0823617i
$55$	−0.149769	−	0.149769i	−0.0201949	−	0.0201949i
$56$	−12.0863	−	1.19780i	−1.61510	−	0.160062i
$57$	2.00921	−	3.00699i	0.266126	−	0.398286i
$58$	−1.91293	+	6.30150i	−0.251180	+	0.827427i
$59$	12.6911	+	5.25683i	1.65224	+	0.684381i	0.997446	−	0.0714255i	$-0.0227548\pi$
$59$	12.6911	+	5.25683i	1.65224	+	0.684381i	0.654795	+	0.755806i	$0.272755\pi$
$60$	−0.528077	−	2.66044i	−0.0681745	−	0.343462i
$61$	−0.813692	−	4.09070i	−0.104183	−	0.523761i	−0.997268	−	0.0738732i	$-0.976464\pi$
$61$	−0.813692	−	4.09070i	−0.104183	−	0.523761i	0.893085	−	0.449888i	$-0.148536\pi$
$62$	−2.42575	−	4.54046i	−0.308070	−	0.576639i
$63$	−1.94765	+	9.79148i	−0.245380	+	1.23361i
$64$	6.64636	+	4.45262i	0.830795	+	0.556578i
$65$	−4.49895	+	3.00610i	−0.558026	+	0.372861i
$66$	−0.0146454	+	0.148390i	−0.00180273	+	0.0182655i
$67$			3.72469i			0.455044i	0.973773	+	0.227522i	$0.0730623\pi$
$67$			3.72469i			0.455044i	−0.973773	+	0.227522i	$0.926938\pi$
$68$	−4.53147	−	6.88954i	−0.549522	−	0.835479i
$69$			2.12271i			0.255544i
$70$	−9.97494	−	0.984481i	−1.19223	−	0.117668i
$71$	0.759116	−	0.507225i	0.0900904	−	0.0601965i	−0.509709	−	0.860347i	$-0.670247\pi$
$71$	0.759116	−	0.507225i	0.0900904	−	0.0601965i	0.599800	+	0.800150i	$0.295247\pi$
$72$	4.17472	−	5.08063i	0.491996	−	0.598758i
$73$	−0.631605	+	3.17529i	−0.0739238	+	0.371640i	−0.999984	−	0.00573683i	$-0.998174\pi$
$73$	−0.631605	+	3.17529i	−0.0739238	+	0.371640i	0.926060	+	0.377377i	$0.123174\pi$
$74$	10.5152	−	5.61776i	1.22237	−	0.653051i
$75$	0.364781	+	1.83388i	0.0421213	+	0.211758i
$76$	1.71389	+	8.63453i	0.196596	+	0.990448i
$77$	0.509091	+	0.210872i	0.0580163	+	0.0240311i
$78$	3.64497	+	1.10649i	0.412712	+	0.125286i
$79$	6.49126	−	9.71485i	0.730323	−	1.09301i	−0.261477	−	0.965210i	$-0.584210\pi$
$79$	6.49126	−	9.71485i	0.730323	−	1.09301i	0.991800	−	0.127796i	$-0.0407904\pi$
$80$	5.48657	+	3.67243i	0.613417	+	0.410590i
$81$	−2.38989	−	2.38989i	−0.265544	−	0.265544i
$82$	1.43789	+	14.6294i	0.158788	+	1.61555i
$83$	−4.75872	+	1.97112i	−0.522337	+	0.216359i	−0.628243	−	0.778017i	$-0.716226\pi$
$83$	−4.75872	+	1.97112i	−0.522337	+	0.216359i	0.105906	+	0.994376i	$0.466226\pi$
$84$	3.91799	+	5.86882i	0.427487	+	0.640340i
$85$	−3.74201	−	5.68426i	−0.405878	−	0.616545i
$86$	5.68603	−	10.6326i	0.613140	−	1.14655i
$87$	3.53486	−	1.46419i	0.378976	−	0.156977i
$88$	−0.230087	−	0.280708i	−0.0245273	−	0.0299236i
$89$	−0.886097	+	0.886097i	−0.0939261	+	0.0939261i	−0.752509	−	0.658582i	$-0.771156\pi$
$89$	−0.886097	+	0.886097i	−0.0939261	+	0.0939261i	0.658582	+	0.752509i	$0.271156\pi$
$90$	3.44360	−	4.19431i	0.362988	−	0.442119i
$91$	7.82069	−	11.7045i	0.819831	−	1.22696i
$92$	−3.65211	−	3.65506i	−0.380759	−	0.381067i
$93$	−1.14455	+	2.76318i	−0.118684	+	0.286528i
$94$	7.59057	−	6.22685i	0.782907	−	0.642251i
$95$	1.41731	+	7.12530i	0.145413	+	0.731040i
$96$	−0.450905	−	4.62602i	−0.0460203	−	0.472141i
$97$	−8.67498	−	1.72556i	−0.880811	−	0.175204i	−0.266089	−	0.963948i	$-0.585732\pi$
$97$	−8.67498	−	1.72556i	−0.880811	−	0.175204i	−0.614721	+	0.788744i	$0.710732\pi$
$98$	15.4818	−	4.69294i	1.56390	−	0.474059i
$99$	−0.248061	+	0.165749i	−0.0249311	+	0.0166584i
$100$	−3.78329	−	2.53013i	−0.378329	−	0.253013i
$101$	−12.7602			−1.26968			−0.634842	−	0.772642i	$-0.718935\pi$
$101$	−12.7602			−1.26968			−0.634842	+	0.772642i	$0.718935\pi$
$102$	−1.42306	+	4.57477i	−0.140904	+	0.452969i
$103$			8.51240i			0.838752i	0.907813	+	0.419376i	$0.137751\pi$
$103$			8.51240i			0.838752i	−0.907813	+	0.419376i	$0.862249\pi$
$104$	−8.17995	+	4.36590i	−0.802110	+	0.428112i
$105$	3.23538	+	4.84209i	0.315741	+	0.472539i
$106$	−1.94393	+	0.589255i	−0.188811	+	0.0572335i
$107$	0.542503	−	2.72735i	0.0524457	−	0.263662i	−0.945662	−	0.325151i	$-0.894585\pi$
$107$	0.542503	−	2.72735i	0.0524457	−	0.263662i	0.998108	+	0.0614887i	$0.0195848\pi$
$108$	−8.75038	−	0.00353627i	−0.842005	−	0.000340278i
$109$	13.8733	−	2.75956i	1.32882	−	0.264318i	0.520902	−	0.853617i	$-0.325596\pi$
$109$	13.8733	−	2.75956i	1.32882	−	0.264318i	0.807915	+	0.589298i	$0.200596\pi$
$110$	−0.189979	−	0.231585i	−0.0181137	−	0.0220808i
$111$	−6.39922	−	2.65064i	−0.607387	−	0.251588i
$112$	−16.8436	−	3.36456i	−1.59157	−	0.317921i
$113$	6.43022	+	4.29653i	0.604904	+	0.404184i	0.819962	−	0.572417i	$-0.193994\pi$
$113$	6.43022	+	4.29653i	0.604904	+	0.404184i	−0.215059	+	0.976601i	$0.568994\pi$
$114$	3.24538	−	3.95288i	0.303958	−	0.370221i
$115$	−3.01522	−	3.01522i	−0.281171	−	0.281171i
$116$	−3.56750	+	8.60287i	−0.331234	+	0.798756i
$117$	2.91661	+	7.04131i	0.269640	+	0.650970i
$118$	17.1310	+	9.16115i	1.57703	+	0.843352i
$119$	14.6534	+	9.93701i	1.34328	+	0.910924i
$120$	−0.373664	−	3.81759i	−0.0341107	−	0.348497i
$121$	−4.20322	−	10.1475i	−0.382111	−	0.922496i
$122$	−0.576965	−	5.87018i	−0.0522359	−	0.531461i
$123$	6.03907	−	6.03907i	0.544525	−	0.544525i
$124$	−2.78326	−	6.72707i	−0.249944	−	0.604109i
$125$	−9.98502	−	6.67178i	−0.893088	−	0.596742i
$126$	−4.10112	+	13.5098i	−0.365357	+	1.20354i
$127$	−4.46964	+	10.7907i	−0.396616	+	0.957516i	0.591846	+	0.806051i	$0.298399\pi$
$127$	−4.46964	+	10.7907i	−0.396616	+	0.957516i	−0.988463	+	0.151465i	$0.951601\pi$
$128$	8.73545	+	7.18970i	0.772112	+	0.635486i
$129$	−6.87073	+	1.36667i	−0.604934	+	0.120329i
$130$	−6.74926	+	3.60580i	−0.591949	+	0.316250i
$131$	−18.8074	−	3.74102i	−1.64321	−	0.326855i	−0.715060	−	0.699063i	$-0.753601\pi$
$131$	−18.8074	−	3.74102i	−1.64321	−	0.326855i	−0.928149	+	0.372208i	$0.878601\pi$
$132$	−0.0412232	+	0.206806i	−0.00358802	+	0.0180002i
$133$	−10.5005	−	15.7151i	−0.910509	−	1.36267i
$134$	−0.517366	+	5.24204i	−0.0446936	+	0.452844i
$135$	−7.22148			−0.621526
$136$	−5.42052	−	10.3256i	−0.464805	−	0.885413i
$137$	−8.21097			−0.701511			−0.350755	−	0.936467i	$-0.614075\pi$
$137$	−8.21097			−0.701511			−0.350755	+	0.936467i	$0.614075\pi$
$138$	−0.294848	+	2.98745i	−0.0250991	+	0.254309i
$139$	6.37970	+	9.54790i	0.541119	+	0.809842i	0.996769	−	0.0803166i	$-0.0255931\pi$
$139$	6.37970	+	9.54790i	0.541119	+	0.809842i	−0.455650	+	0.890159i	$0.650593\pi$
$140$	−13.9017	−	2.77107i	−1.17491	−	0.234198i
$141$	−5.59450	−	1.11282i	−0.471142	−	0.0937160i
$142$	1.13882	−	0.608413i	0.0955672	−	0.0510569i
$143$	0.412589	−	0.0820691i	0.0345024	−	0.00686296i
$144$	6.58111	−	6.57048i	0.548426	−	0.547540i
$145$	−2.94130	+	7.10093i	−0.244262	+	0.589700i
$146$	−1.32996	+	4.38110i	−0.110068	+	0.362583i
$147$	−7.81498	−	5.22180i	−0.644568	−	0.430687i
$148$	15.5791	−	6.44572i	1.28060	−	0.529835i
$149$	−15.9196	+	15.9196i	−1.30418	+	1.30418i	−0.378635	+	0.925546i	$0.623606\pi$
$149$	−15.9196	+	15.9196i	−1.30418	+	1.30418i	−0.925546	+	0.378635i	$0.876394\pi$
$150$	0.258655	+	2.63162i	0.0211191	+	0.214871i
$151$	−6.91534	−	16.6951i	−0.562762	−	1.35863i	−0.907549	−	0.419947i	$-0.862049\pi$
$151$	−6.91534	−	16.6951i	−0.562762	−	1.35863i	0.344786	−	0.938681i	$-0.387951\pi$
$152$	1.21273	+	12.3901i	0.0983657	+	1.00497i
$153$	−8.88104	+	3.60755i	−0.717990	+	0.291653i
$154$	0.687191	+	0.367490i	0.0553754	+	0.0296132i
$155$	−2.29920	−	5.55076i	−0.184676	−	0.445848i
$156$	4.97615	+	2.06355i	0.398411	+	0.165216i
$157$	−4.46396	−	4.46396i	−0.356263	−	0.356263i	0.506170	−	0.862433i	$-0.331061\pi$
$157$	−4.46396	−	4.46396i	−0.356263	−	0.356263i	−0.862433	+	0.506170i	$0.831061\pi$
$158$	10.4850	−	12.7708i	0.834145	−	1.01599i
$159$	0.981264	+	0.655660i	0.0778193	+	0.0519972i
$160$	7.21156	+	5.93058i	0.570124	+	0.468853i
$161$	10.2492	+	4.24537i	0.807752	+	0.334582i
$162$	−3.03152	−	3.69544i	−0.238178	−	0.290341i
$163$	2.19822	−	0.437254i	0.172178	−	0.0342484i	−0.108248	−	0.994124i	$-0.534524\pi$
$163$	2.19822	−	0.437254i	0.172178	−	0.0342484i	0.280426	+	0.959876i	$0.409524\pi$
$164$	−0.00840134	+	20.7888i	−0.000656034	+	1.62333i
$165$	−0.0339515	+	0.170686i	−0.00264312	+	0.0132879i
$166$	−6.97109	+	2.11312i	−0.541062	+	0.164010i
$167$	3.16809	+	4.74138i	0.245154	+	0.366899i	0.933557	−	0.358430i	$-0.116688\pi$
$167$	3.16809	+	4.74138i	0.245154	+	0.366899i	−0.688403	+	0.725329i	$0.741688\pi$
$168$	4.69889	+	8.80384i	0.362527	+	0.679231i
$169$			2.25342i			0.173340i
$170$	−4.47687	−	8.51966i	−0.343360	−	0.653428i
$171$	10.2330			0.782537
$172$	9.47927	−	14.1743i	0.722787	−	1.08078i
$173$	0.701217	−	0.468538i	0.0533125	−	0.0356223i	−0.528628	−	0.848853i	$-0.677293\pi$
$173$	0.701217	−	0.468538i	0.0533125	−	0.0356223i	0.581941	+	0.813231i	$0.302293\pi$
$174$	5.17825	−	1.56966i	0.392562	−	0.118996i
$175$	9.58419	+	1.90641i	0.724497	+	0.144111i
$176$	−0.284827	−	0.427021i	−0.0214697	−	0.0321879i
$177$	−2.20194	−	11.0699i	−0.165508	−	0.832065i
$178$	−1.37015	+	1.12399i	−0.102697	+	0.0842467i
$179$	−1.92271	+	4.64184i	−0.143710	+	0.346947i	−0.979302	−	0.202403i	$-0.935125\pi$
$179$	−1.92271	+	4.64184i	−0.143710	+	0.346947i	0.835592	+	0.549351i	$0.185125\pi$
$180$	5.42904	−	5.42465i	0.404657	−	0.404330i
$181$	−2.50824	+	3.75385i	−0.186436	+	0.279022i	−0.912900	−	0.408183i	$-0.866162\pi$
$181$	−2.50824	+	3.75385i	−0.186436	+	0.279022i	0.726464	+	0.687205i	$0.241162\pi$
$182$	12.6324	−	15.3863i	0.936377	−	1.14051i
$183$	−2.42323	+	2.42323i	−0.179130	+	0.179130i
$184$	−4.63220	−	5.65133i	−0.341490	−	0.416622i
$185$	12.8549	−	5.32469i	0.945114	−	0.391479i
$186$	−1.99462	+	3.72985i	−0.146252	+	0.273486i
$187$	0.0996626	+	0.519623i	0.00728805	+	0.0379986i
$188$	11.5477	−	7.70918i	0.842202	−	0.562249i
$189$	17.3573	−	7.18965i	1.26256	−	0.522970i
$190$	1.00497	+	10.2248i	0.0729084	+	0.741788i
$191$	7.24027	+	7.24027i	0.523888	+	0.523888i	0.918743	−	0.394856i	$-0.129205\pi$
$191$	7.24027	+	7.24027i	0.523888	+	0.523888i	−0.394856	+	0.918743i	$0.629205\pi$
$192$	0.00796922	−	6.57318i	0.000575129	−	0.474378i
$193$	6.38433	−	9.55482i	0.459554	−	0.687771i	−0.527246	−	0.849712i	$-0.676775\pi$
$193$	6.38433	−	9.55482i	0.459554	−	0.687771i	0.986800	+	0.161941i	$0.0517755\pi$
$194$	−11.9693	−	3.63348i	−0.859344	−	0.260869i
$195$	4.10739	+	1.70134i	0.294136	+	0.121835i
$196$	22.4406	−	4.45428i	1.60290	−	0.318163i
$197$	3.26593	+	16.4189i	0.232688	+	1.16980i	0.903637	+	0.428298i	$0.140887\pi$
$197$	3.26593	+	16.4189i	0.232688	+	1.16980i	−0.670949	+	0.741503i	$0.734113\pi$
$198$	−0.372138	+	0.198815i	−0.0264467	+	0.0141292i
$199$	1.30692	−	6.57032i	0.0926450	−	0.465758i	−0.906414	−	0.422390i	$-0.861191\pi$
$199$	1.30692	−	6.57032i	0.0926450	−	0.465758i	0.999059	−	0.0433677i	$-0.0138087\pi$
$200$	−4.97307	−	4.08634i	−0.351649	−	0.288948i
$201$	2.54462	−	1.70026i	0.179484	−	0.119927i
$202$	−17.9584	−	1.77241i	−1.26355	−	0.124706i
$203$		−	19.9959i		−	1.40344i
$204$	−2.63822	+	6.24075i	−0.184713	+	0.436940i
$205$			17.1565i			1.19826i
$206$	−1.18239	+	11.9802i	−0.0823807	+	0.834697i
$207$	−4.99407	+	3.33693i	−0.347112	+	0.231933i
$208$	−12.1187	+	5.00825i	−0.840280	+	0.347260i
$209$	0.110191	−	0.553965i	0.00762204	−	0.0383186i
$210$	3.88082	+	7.26403i	0.267802	+	0.501266i
$211$	4.19940	+	21.1118i	0.289099	+	1.45340i	0.803221	+	0.595681i	$0.203118\pi$
$211$	4.19940	+	21.1118i	0.289099	+	1.45340i	−0.514122	+	0.857717i	$0.671882\pi$
$212$	−2.81769	+	0.559289i	−0.193519	+	0.0384121i
$213$	−0.693047	−	0.287069i	−0.0474868	−	0.0196697i
$214$	1.14234	−	3.76304i	0.0780886	−	0.257236i
$215$	7.81828	−	11.7009i	0.533203	−	0.797994i
$216$	−12.3146	−	1.22042i	−0.837901	−	0.0830389i
$217$	11.0526	+	11.0526i	0.750299	+	0.750299i
$218$	19.9082	−	1.95672i	1.34835	−	0.132526i
$219$	2.45760	−	1.01797i	0.166069	−	0.0687881i
$220$	−0.235204	−	0.352315i	−0.0158574	−	0.0237531i
$221$	13.5160	+	0.0926259i	0.909187	+	0.00623069i
$222$	−8.63792	−	4.61931i	−0.579739	−	0.310028i
$223$	−10.8572	+	4.49720i	−0.727051	+	0.301154i	−0.715340	−	0.698777i	$-0.753728\pi$
$223$	−10.8572	+	4.49720i	−0.727051	+	0.301154i	−0.0117116	+	0.999931i	$0.503728\pi$
$224$	−23.2379	−	7.07480i	−1.55265	−	0.472705i
$225$	−3.74110	+	3.74110i	−0.249406	+	0.249406i
$226$	8.45293	+	6.94000i	0.562281	+	0.461642i
$227$	1.55096	−	2.32117i	0.102941	−	0.154062i	−0.776423	−	0.630212i	$-0.782968\pi$
$227$	1.55096	−	2.32117i	0.102941	−	0.154062i	0.879364	+	0.476150i	$0.157968\pi$
$228$	5.11654	−	5.11240i	0.338851	−	0.338577i
$229$	11.3819	−	27.4784i	0.752138	−	1.81582i	0.205037	−	0.978754i	$-0.434269\pi$
$229$	11.3819	−	27.4784i	0.752138	−	1.81582i	0.547101	−	0.837067i	$-0.315731\pi$
$230$	−3.82473	−	4.66236i	−0.252195	−	0.307427i
$231$	−0.0883286	−	0.444058i	−0.00581159	−	0.0292169i
$232$	−6.21576	+	11.6119i	−0.408085	+	0.762361i
$233$	−6.35323	−	1.26374i	−0.416214	−	0.0827901i	−0.0174590	−	0.999848i	$-0.505558\pi$
$233$	−6.35323	−	1.26374i	−0.416214	−	0.0827901i	−0.398755	+	0.917057i	$0.630558\pi$
$234$	3.12671	+	10.3149i	0.204400	+	0.674306i
$235$	9.52747	−	6.36605i	0.621503	−	0.415275i
$236$	22.8372	+	15.2727i	1.48658	+	0.994168i
$237$	−9.60010			−0.623593
$238$	19.2426	+	16.0205i	1.24731	+	1.03845i
$239$		−	12.7854i		−	0.827016i	−0.910500	−	0.413508i	$-0.864303\pi$
$239$		−	12.7854i		−	0.827016i	0.910500	−	0.413508i	$-0.135697\pi$
$240$	0.00438454	−	5.42469i	0.000283021	−	0.350162i
$241$	1.59519	+	2.38736i	0.102755	+	0.153784i	0.879284	−	0.476298i	$-0.158022\pi$
$241$	1.59519	+	2.38736i	0.102755	+	0.153784i	−0.776529	+	0.630081i	$0.783022\pi$
$242$	−4.50601	−	14.8651i	−0.289657	−	0.955566i
$243$	−3.10244	+	15.5970i	−0.199022	+	1.00055i
$244$	0.00337111	−	8.34169i	0.000215813	−	0.534022i
$245$	18.5182	−	3.68350i	1.18308	−	0.235330i
$246$	9.33808	−	7.66041i	0.595374	−	0.488410i
$247$	−13.3306	−	5.52172i	−0.848207	−	0.351339i
$248$	−2.98269	−	9.85412i	−0.189401	−	0.625737i
$249$	3.51890	+	2.35125i	0.223001	+	0.149005i
$250$	−13.1260	−	10.7766i	−0.830159	−	0.681574i
$251$	−4.86266	−	4.86266i	−0.306928	−	0.306928i	0.536789	−	0.843717i	$-0.319637\pi$
$251$	−4.86266	−	4.86266i	−0.306928	−	0.306928i	−0.843717	+	0.536789i	$0.819637\pi$
$252$	−7.64834	+	18.4436i	−0.481800	+	1.16184i
$253$	0.126868	+	0.306287i	0.00797614	+	0.0192561i
$254$	−7.78930	+	14.5657i	−0.488744	+	0.913931i
$255$	−2.17518	+	5.15122i	−0.136215	+	0.322582i
$256$	11.2954	+	11.3320i	0.705963	+	0.708249i
$257$	3.21534	+	7.76252i	0.200567	+	0.484213i	0.991877	−	0.127204i	$-0.0406001\pi$
$257$	3.21534	+	7.76252i	0.200567	+	0.484213i	−0.791309	+	0.611416i	$0.790600\pi$
$258$	−9.85953	+	0.969068i	−0.613828	+	0.0603315i
$259$	−25.5966	+	25.5966i	−1.59049	+	1.59049i
$260$	−9.99959	+	4.13723i	−0.620149	+	0.256580i
$261$	9.00161	+	6.01468i	0.557186	+	0.372300i
$262$	−25.9494	−	7.87740i	−1.60316	−	0.486667i
$263$	4.88181	−	11.7857i	0.301025	−	0.726739i	−0.698908	−	0.715211i	$-0.746330\pi$
$263$	4.88181	−	11.7857i	0.301025	−	0.726739i	0.999934	−	0.0115280i	$-0.00366955\pi$
$264$	−0.0867422	+	0.285328i	−0.00533862	+	0.0175607i
$265$	−2.32518	+	0.462507i	−0.142835	+	0.0284116i
$266$	−12.5953	−	23.5756i	−0.772267	−	1.44551i
$267$	1.00985	+	0.200871i	0.0618017	+	0.0122931i
$268$	−1.45626	+	7.30566i	−0.0889550	+	0.446264i
$269$	−5.07304	−	7.59234i	−0.309309	−	0.462913i	0.643950	−	0.765067i	$-0.277294\pi$
$269$	−5.07304	−	7.59234i	−0.309309	−	0.462913i	−0.953259	+	0.302154i	$0.902294\pi$
$270$	−10.1633	−	1.00307i	−0.618521	−	0.0610452i
$271$	−12.5928			−0.764955			−0.382478	−	0.923965i	$-0.624929\pi$
$271$	−12.5928			−0.764955			−0.382478	+	0.923965i	$0.624929\pi$
$272$	−6.19446	−	15.2849i	−0.375594	−	0.926784i
$273$	−11.5662			−0.700020
$274$	−11.5559	−	1.14052i	−0.698119	−	0.0689011i
$275$	0.162240	+	0.242810i	0.00978345	+	0.0146420i
$276$	−0.829923	+	4.16351i	−0.0499555	+	0.250614i
$277$	25.2468	+	5.02190i	1.51693	+	0.301737i	0.882155	−	0.470959i	$-0.156092\pi$
$277$	25.2468	+	5.02190i	1.51693	+	0.301737i	0.634777	+	0.772695i	$0.281092\pi$
$278$	7.65242	+	14.3236i	0.458962	+	0.859075i
$279$	−8.30014	+	1.65100i	−0.496916	+	0.0988428i
$280$	−19.1801	−	5.83091i	−1.14623	−	0.348464i
$281$	12.5687	−	30.3435i	0.749784	−	1.81014i	0.189414	−	0.981897i	$-0.439341\pi$
$281$	12.5687	−	30.3435i	0.749784	−	1.81014i	0.560370	−	0.828242i	$-0.310659\pi$
$282$	−7.71900	−	2.34324i	−0.459660	−	0.139538i
$283$	15.7022	+	10.4918i	0.933396	+	0.623675i	0.926497	−	0.376301i	$-0.122804\pi$
$283$	15.7022	+	10.4918i	0.933396	+	0.623675i	0.00689850	+	0.999976i	$0.497804\pi$
$284$	1.68725	−	0.698083i	0.100120	−	0.0414236i
$285$	4.22085	−	4.22085i	0.250022	−	0.250022i
$286$	0.592067	−	0.0581928i	0.0350097	−	0.00344101i
$287$	−17.0809	−	41.2369i	−1.00825	−	2.43414i
$288$	10.1747	−	8.33300i	0.599552	−	0.491027i
$289$	−0.232992	+	16.9984i	−0.0137054	+	0.999906i
$290$	−5.12585	+	9.58513i	−0.301000	+	0.562858i
$291$	2.78112	+	6.71422i	0.163032	+	0.393595i
$292$	−2.48029	+	5.98112i	−0.145148	+	0.350019i
$293$	−2.94002	−	2.94002i	−0.171758	−	0.171758i	0.615994	−	0.787751i	$-0.288755\pi$
$293$	−2.94002	−	2.94002i	−0.171758	−	0.171758i	−0.787751	+	0.615994i	$0.788755\pi$
$294$	−10.2733	−	8.43455i	−0.599151	−	0.491913i
$295$	18.8521	+	12.5966i	1.09761	+	0.733401i
$296$	22.8210	−	6.90758i	1.32645	−	0.401495i
$297$	0.518706	+	0.214855i	0.0300983	+	0.0124671i
$298$	−24.6161	+	20.1935i	−1.42597	+	1.16978i
$299$	8.30642	−	1.65225i	0.480372	−	0.0955520i
$300$	−0.00151128	+	3.73961i	−8.72539e−5	+	0.215907i
$301$	−7.14249	+	35.9077i	−0.411687	+	2.06969i
$302$	−7.41350	−	24.4568i	−0.426599	−	1.40733i
$303$	5.82480	+	8.71743i	0.334626	+	0.500804i
$304$	−0.0142301	+	17.6060i	−0.000816154	+	1.00977i
$305$		−	6.88420i		−	0.394188i
$306$	−13.0001	+	3.84358i	−0.743164	+	0.219723i
$307$	−17.5822			−1.00347			−0.501734	−	0.865022i	$-0.667304\pi$
$307$	−17.5822			−1.00347			−0.501734	+	0.865022i	$0.667304\pi$
$308$	0.916091	+	0.612648i	0.0521991	+	0.0349089i
$309$	5.81546	−	3.88577i	0.330830	−	0.221054i
$310$	−2.46483	−	8.13137i	−0.139993	−	0.461831i
$311$	12.9719	+	2.58028i	0.735571	+	0.146314i	0.548640	−	0.836059i	$-0.315146\pi$
$311$	12.9719	+	2.58028i	0.735571	+	0.146314i	0.186931	+	0.982373i	$0.440146\pi$
$312$	6.71668	+	3.59538i	0.380257	+	0.203548i
$313$	−6.19591	−	31.1489i	−0.350213	−	1.76064i	−0.607513	−	0.794310i	$-0.707833\pi$
$313$	−6.19591	−	31.1489i	−0.350213	−	1.76064i	0.257299	−	0.966332i	$-0.417167\pi$
$314$	−5.66242	−	6.90252i	−0.319549	−	0.389532i
$315$	−6.30584	+	15.2237i	−0.355294	+	0.857756i
$316$	16.5303	−	16.5169i	0.929901	−	0.929150i
$317$	−10.3583	+	15.5022i	−0.581778	+	0.870693i	−0.999278	−	0.0379839i	$-0.987906\pi$
$317$	−10.3583	+	15.5022i	−0.581778	+	0.870693i	0.417500	+	0.908677i	$0.362906\pi$
$318$	1.28994	+	1.05906i	0.0723360	+	0.0593891i
$319$	0.422537	−	0.422537i	0.0236575	−	0.0236575i
$320$	9.32561	+	9.34825i	0.521317	+	0.522583i
$321$	−2.11090	+	0.874363i	−0.117819	+	0.0488022i
$322$	13.8348	+	7.39846i	0.770984	+	0.412300i
$323$	7.05960	−	16.7184i	0.392807	−	0.930237i
$324$	−3.75318	−	5.62195i	−0.208510	−	0.312330i
$325$	6.89225	−	2.85486i	0.382313	−	0.158359i
$326$	3.15446	−	0.310044i	0.174709	−	0.0171717i
$327$	−8.21818	−	8.21818i	−0.454466	−	0.454466i
$328$	−2.89942	+	29.2565i	−0.160094	+	1.61542i
$329$	−16.5620	+	24.7867i	−0.913091	+	1.36654i
$330$	−0.0714911	+	0.235503i	−0.00393546	+	0.0129640i
$331$	−28.8044	−	11.9312i	−1.58323	−	0.655796i	−0.594311	−	0.804235i	$-0.702575\pi$
$331$	−28.8044	−	11.9312i	−1.58323	−	0.655796i	−0.988922	+	0.148439i	$0.952575\pi$
$332$	−10.1045	+	2.00566i	−0.554555	+	0.110075i
$333$	−3.82353	−	19.2222i	−0.209528	−	1.05337i
$334$	3.80011	+	7.11296i	0.207933	+	0.389204i
$335$	−1.19938	+	6.02967i	−0.0655290	+	0.329436i
$336$	5.39024	+	13.0430i	0.294062	+	0.711554i
$337$	11.8732	−	7.93343i	0.646775	−	0.432161i	−0.188440	−	0.982085i	$-0.560343\pi$
$337$	11.8732	−	7.93343i	0.646775	−	0.432161i	0.835215	+	0.549923i	$0.185343\pi$
$338$	−0.313004	+	3.17141i	−0.0170252	+	0.172502i
$339$		−	6.35426i		−	0.345116i
$340$	−5.11724	−	12.6122i	−0.277521	−	0.683993i
$341$			0.467107i			0.0252953i
$342$	14.4017	+	1.42138i	0.778754	+	0.0768594i
$343$	−15.8497	+	10.5904i	−0.855805	+	0.571831i
$344$	15.3097	−	18.6319i	0.825445	−	1.00457i
$345$	−0.683527	+	3.43632i	−0.0367998	+	0.185005i
$346$	1.05196	−	0.562009i	0.0565535	−	0.0302138i
$347$	3.56365	+	17.9157i	0.191307	+	0.961765i	0.950459	+	0.310851i	$0.100614\pi$
$347$	3.56365	+	17.9157i	0.191307	+	0.961765i	−0.759152	+	0.650914i	$0.774386\pi$
$348$	7.50577	−	1.48984i	0.402352	−	0.0798637i
$349$	18.5330	+	7.67664i	0.992051	+	0.410921i	0.818876	−	0.573970i	$-0.194597\pi$
$349$	18.5330	+	7.67664i	0.992051	+	0.410921i	0.173175	+	0.984891i	$0.444597\pi$
$350$	13.2238	+	4.01430i	0.706840	+	0.214573i
$351$	7.96840	−	11.9255i	0.425322	−	0.636539i
$352$	−0.341545	−	0.640542i	−0.0182044	−	0.0341410i
$353$	4.65183	+	4.65183i	0.247592	+	0.247592i	0.819982	−	0.572390i	$-0.193984\pi$
$353$	4.65183	+	4.65183i	0.247592	+	0.247592i	−0.572390	+	0.819982i	$0.693984\pi$
$354$	−1.56133	−	15.8854i	−0.0829838	−	0.844298i
$355$	1.39221	−	0.576674i	0.0738911	−	0.0306067i
$356$	−2.08444	+	1.39156i	−0.110475	+	0.0737526i
$357$	0.0996905	−	14.5469i	0.00527618	−	0.769905i
$358$	−3.35074	+	6.26574i	−0.177092	+	0.331155i
$359$	−17.9010	+	7.41484i	−0.944779	+	0.391340i	−0.801266	−	0.598308i	$-0.795840\pi$
$359$	−17.9010	+	7.41484i	−0.944779	+	0.391340i	−0.143513	+	0.989648i	$0.545840\pi$
$360$	8.39419	−	6.88042i	0.442413	−	0.362630i
$361$	−0.263841	+	0.263841i	−0.0138864	+	0.0138864i
$362$	−4.05146	+	4.93468i	−0.212940	+	0.259361i
$363$	−5.01380	+	7.50368i	−0.263156	+	0.393841i
$364$	19.9157	−	19.8997i	1.04387	−	1.04303i
$365$	−2.04493	+	4.93690i	−0.107037	+	0.258409i
$366$	−3.74699	+	3.07381i	−0.195858	+	0.160670i
$367$	0.558331	+	2.80692i	0.0291446	+	0.146520i	0.992618	−	0.121285i	$-0.0387016\pi$
$367$	0.558331	+	2.80692i	0.0291446	+	0.146520i	−0.963473	+	0.267805i	$0.913702\pi$
$368$	−5.73427	−	8.59697i	−0.298919	−	0.448148i
$369$	23.7015	+	4.71453i	1.23385	+	0.245429i
$370$	18.8313	−	5.70827i	0.978995	−	0.296759i
$371$	5.12827	−	3.42660i	0.266247	−	0.177900i
$372$	−3.32526	+	4.97225i	−0.172407	+	0.257799i
$373$	−18.3339			−0.949292			−0.474646	−	0.880177i	$-0.657424\pi$
$373$	−18.3339			−0.949292			−0.474646	+	0.880177i	$0.657424\pi$
$374$	0.0680863	+	0.745148i	0.00352066	+	0.0385307i
$375$			9.86708i			0.509534i
$376$	17.3228	−	9.24571i	0.893353	−	0.476811i
$377$	−8.48095	−	12.6926i	−0.436791	−	0.653704i
$378$	25.4270	−	7.70757i	1.30782	−	0.396435i
$379$	6.92319	−	34.8052i	0.355620	−	1.78782i	−0.225750	−	0.974185i	$-0.572483\pi$
$379$	6.92319	−	34.8052i	0.355620	−	1.78782i	0.581371	−	0.813639i	$-0.302517\pi$
$380$	−0.00587189	+	14.5298i	−0.000301222	+	0.745362i
$381$	9.41222	−	1.87221i	0.482203	−	0.0959161i
$382$	9.18410	+	11.1955i	0.469899	+	0.572810i
$383$	13.2592	+	5.49215i	0.677515	+	0.280636i	0.694787	−	0.719215i	$-0.255498\pi$
$383$	13.2592	+	5.49215i	0.677515	+	0.280636i	−0.0172729	+	0.999851i	$0.505498\pi$
$384$	0.924241	−	9.24983i	0.0471650	−	0.472028i
$385$	0.756233	+	0.505298i	0.0385412	+	0.0257524i
$386$	10.3123	−	12.5604i	0.524884	−	0.639309i
$387$	−14.0162	−	14.0162i	−0.712485	−	0.712485i
$388$	−16.3406	−	6.77622i	−0.829566	−	0.344011i
$389$	12.8699	+	31.0706i	0.652529	+	1.57534i	0.809096	+	0.587676i	$0.199957\pi$
$389$	12.8699	+	31.0706i	0.652529	+	1.57534i	−0.156567	+	0.987667i	$0.550043\pi$
$390$	5.54432	+	2.96494i	0.280747	+	0.150136i
$391$	2.00645	+	10.4613i	0.101471	+	0.529049i
$392$	32.2011	−	3.15182i	1.62640	−	0.159191i
$393$	6.02948	+	14.5565i	0.304147	+	0.734276i
$394$	2.31578	+	23.5613i	0.116667	+	1.18700i
$395$	13.6365	−	13.6365i	0.686129	−	0.686129i
$396$	−0.551353	+	0.228117i	−0.0277065	+	0.0114633i
$397$	−14.3219	−	9.56956i	−0.718794	−	0.480283i	0.141593	−	0.989925i	$-0.454778\pi$
$397$	−14.3219	−	9.56956i	−0.718794	−	0.480283i	−0.860386	+	0.509642i	$0.829778\pi$
$398$	2.75195	−	9.06538i	0.137943	−	0.454406i
$399$	−5.94287	+	14.3474i	−0.297516	+	0.718266i
$400$	−6.43138	−	6.44179i	−0.321569	−	0.322089i
$401$	−14.9183	+	2.96743i	−0.744984	+	0.148187i	−0.552965	−	0.833205i	$-0.686504\pi$
$401$	−14.9183	+	2.96743i	−0.744984	+	0.148187i	−0.192019	+	0.981391i	$0.561504\pi$
$402$	3.81740	−	2.03945i	0.190395	−	0.101719i
$403$	11.7035	+	2.32798i	0.582995	+	0.115965i
$404$	−25.0280	−	4.98889i	−1.24519	−	0.248206i
$405$	−3.09929	−	4.63841i	−0.154005	−	0.230484i
$406$	2.77747	−	28.1418i	0.137843	−	1.39665i
$407$	−1.08177			−0.0536213
$408$	−4.57982	+	8.41663i	−0.226735	+	0.416685i
$409$	18.7470			0.926980			0.463490	−	0.886102i	$-0.346597\pi$
$409$	18.7470			0.926980			0.463490	+	0.886102i	$0.346597\pi$
$410$	−2.38306	+	24.1456i	−0.117691	+	1.19247i
$411$	3.74817	+	5.60953i	0.184884	+	0.276698i
$412$	−3.32812	+	16.6963i	−0.163965	+	0.822569i
$413$	−57.8534	−	11.5078i	−2.84678	−	0.566260i
$414$	−7.49203	+	4.00263i	−0.368213	+	0.196718i
$415$	−8.33830	+	1.65859i	−0.409311	+	0.0814171i
$416$	−17.7512	+	5.36519i	−0.870324	+	0.263050i
$417$	3.61066	−	8.71691i	0.176815	−	0.426869i
$418$	0.232026	−	0.764332i	0.0113488	−	0.0373847i
$419$	−10.2065	−	6.81973i	−0.498618	−	0.333166i	0.280699	−	0.959796i	$-0.409434\pi$
$419$	−10.2065	−	6.81973i	−0.498618	−	0.333166i	−0.779317	+	0.626630i	$0.784434\pi$
$420$	4.45279	+	10.7623i	0.217274	+	0.525145i
$421$	−19.1632	+	19.1632i	−0.933956	+	0.933956i	−0.997950	−	0.0639943i	$-0.979616\pi$
$421$	−19.1632	+	19.1632i	−0.933956	+	0.933956i	0.0639943	+	0.997950i	$0.479616\pi$
$422$	2.97767	+	30.2956i	0.144951	+	1.47477i
$423$	−6.17653	−	14.9115i	−0.300313	−	0.725020i
$424$	−4.04323	+	0.395749i	−0.196357	+	0.0192193i
$425$	3.53117	+	8.69303i	0.171287	+	0.421674i
$426$	−0.935503	−	0.500280i	−0.0453253	−	0.0242386i
$427$	6.85385	+	16.5467i	0.331681	+	0.800749i
$428$	2.13039	−	5.13735i	0.102976	−	0.248323i
$429$	−0.244408	−	0.244408i	−0.0118001	−	0.0118001i
$430$	12.6285	−	15.3816i	0.609002	−	0.741765i
$431$	−18.4061	−	12.2986i	−0.886591	−	0.592401i	0.0267298	−	0.999643i	$-0.491491\pi$
$431$	−18.4061	−	12.2986i	−0.886591	−	0.592401i	−0.913320	+	0.407242i	$0.866491\pi$
$432$	−17.1617	−	3.42810i	−0.825694	−	0.164935i
$433$	−28.9741	−	12.0015i	−1.39241	−	0.576754i	−0.444638	−	0.895710i	$-0.646668\pi$
$433$	−28.9741	−	12.0015i	−1.39241	−	0.576754i	−0.947770	+	0.318956i	$0.896668\pi$
$434$	14.0199	+	17.0904i	0.672978	+	0.820364i
$435$	6.19384	−	1.23203i	0.296972	−	0.0590713i
$436$	28.2901	+	0.0114328i	1.35485	+	0.000547533i
$437$	2.21840	−	11.1527i	0.106121	−	0.533504i
$438$	3.60017	−	1.09130i	0.172023	−	0.0521445i
$439$	−3.06257	−	4.58346i	−0.146168	−	0.218756i	0.751160	−	0.660120i	$-0.229495\pi$
$439$	−3.06257	−	4.58346i	−0.146168	−	0.218756i	−0.897328	+	0.441364i	$0.854495\pi$
$440$	−0.282083	−	0.528510i	−0.0134478	−	0.0251957i
$441$		−	26.5949i		−	1.26643i
$442$	19.0093	+	2.00776i	0.904179	+	0.0954993i
$443$	7.96439			0.378399			0.189200	−	0.981939i	$-0.439411\pi$
$443$	7.96439			0.378399			0.189200	+	0.981939i	$0.439411\pi$
$444$	−11.5152	−	7.70093i	−0.546486	−	0.365470i
$445$	−1.71978	+	1.14912i	−0.0815252	+	0.0544734i
$446$	−15.9048	+	4.82116i	−0.753115	+	0.228289i
$447$	18.1429	+	3.60884i	0.858128	+	0.170692i
$448$	−31.7218	−	13.1847i	−1.49871	−	0.622918i
$449$	1.14085	+	5.73542i	0.0538398	+	0.270671i	0.998323	−	0.0578886i	$-0.0184368\pi$
$449$	1.14085	+	5.73542i	0.0538398	+	0.270671i	−0.944483	+	0.328560i	$0.893437\pi$
$450$	−5.78477	+	4.74548i	−0.272697	+	0.223704i
$451$	0.510444	−	1.23232i	0.0240359	−	0.0580277i
$452$	10.9325	+	10.9413i	0.514220	+	0.514636i
$453$	−8.24895	+	12.3454i	−0.387569	+	0.580039i
$454$	2.50519	−	3.05133i	0.117575	−	0.143206i
$455$	16.4294	−	16.4294i	0.770220	−	0.770220i
$456$	7.91101	−	6.48438i	0.370467	−	0.303659i
$457$	−9.51504	+	3.94126i	−0.445095	+	0.184364i	−0.593962	−	0.804493i	$-0.702437\pi$
$457$	−9.51504	+	3.94126i	−0.445095	+	0.184364i	0.148868	+	0.988857i	$0.452437\pi$
$458$	19.8354	−	37.0914i	0.926848	−	1.73317i
$459$	14.9302	+	10.1247i	0.696880	+	0.472580i
$460$	−4.73522	−	7.09296i	−0.220781	−	0.330711i
$461$	7.51342	−	3.11216i	0.349935	−	0.144948i	−0.200791	−	0.979634i	$-0.564351\pi$
$461$	7.51342	−	3.11216i	0.349935	−	0.144948i	0.550725	+	0.834686i	$0.314351\pi$
$462$	−0.0626312	−	0.637225i	−0.00291387	−	0.0296464i
$463$	26.0197	+	26.0197i	1.20924	+	1.20924i	0.971274	+	0.237964i	$0.0764802\pi$
$463$	26.0197	+	26.0197i	1.20924	+	1.20924i	0.237964	+	0.971274i	$0.423520\pi$
$464$	−10.3608	+	15.4790i	−0.480989	+	0.718593i
$465$	−2.74260	+	4.10459i	−0.127185	+	0.190346i
$466$	−8.76585	−	2.66103i	−0.406070	−	0.123270i
$467$	0.560574	+	0.232198i	0.0259403	+	0.0107448i	0.395616	−	0.918416i	$-0.370531\pi$
$467$	0.560574	+	0.232198i	0.0259403	+	0.0107448i	−0.369676	+	0.929161i	$0.620531\pi$
$468$	2.96771	+	14.9512i	0.137182	+	0.691121i
$469$	−3.12031	−	15.6868i	−0.144082	−	0.724351i
$470$	14.2930	−	7.63604i	0.659286	−	0.352224i
$471$	−1.01195	+	5.08739i	−0.0466280	+	0.234415i
$472$	30.0191	+	24.6665i	1.38174	+	1.13537i
$473$	−0.909700	+	0.607842i	−0.0418281	+	0.0279486i
$474$	−13.5109	−	1.33347i	−0.620578	−	0.0612482i
$475$		−	10.0164i		−	0.459583i
$476$	24.8563	+	25.2197i	1.13928	+	1.15594i
$477$			3.33931i			0.152897i
$478$	1.77591	−	17.9938i	0.0812280	−	0.823017i
$479$	26.8598	−	17.9471i	1.22725	−	0.820025i	0.238730	−	0.971086i	$-0.423269\pi$
$479$	26.8598	−	17.9471i	1.22725	−	0.820025i	0.988524	+	0.151061i	$0.0482690\pi$
$480$	0.759669	−	7.63397i	0.0346740	−	0.348441i
$481$	−5.39134	+	27.1041i	−0.245824	+	1.23584i
$482$	1.91342	+	3.58149i	0.0871538	+	0.163132i
$483$	−1.77827	−	8.93996i	−0.0809140	−	0.406782i
$484$	−4.27685	−	21.5467i	−0.194402	−	0.979396i
$485$	−13.4877	−	5.58680i	−0.612447	−	0.253684i
$486$	−6.53275	+	21.5199i	−0.296332	+	0.976164i
$487$	−3.03440	+	4.54130i	−0.137502	+	0.205786i	−0.893830	−	0.448407i	$-0.851992\pi$
$487$	−3.03440	+	4.54130i	−0.137502	+	0.205786i	0.756328	+	0.654193i	$0.226992\pi$
$488$	1.16342	−	11.7394i	0.0526655	−	0.531419i
$489$	−1.30217	−	1.30217i	−0.0588863	−	0.0588863i
$490$	26.5737	−	2.61186i	1.20048	−	0.117992i
$491$	−11.2995	+	4.68043i	−0.509941	+	0.211225i	−0.622792	−	0.782387i	$-0.714002\pi$
$491$	−11.2995	+	4.68043i	−0.509941	+	0.211225i	0.112851	+	0.993612i	$0.464002\pi$
$492$	14.2062	−	9.48400i	0.640466	−	0.427572i
$493$	16.0367	−	10.5571i	0.722257	−	0.475470i
$494$	−17.9942	−	9.62278i	−0.809598	−	0.432949i
$495$	−0.454943	+	0.188443i	−0.0204481	+	0.00846990i
$496$	−2.82902	−	14.2827i	−0.127027	−	0.641314i
$497$	−2.77215	+	2.77215i	−0.124348	+	0.124348i
$498$	4.62582	+	3.79788i	0.207288	+	0.170187i
$499$	−6.26864	+	9.38168i	−0.280623	+	0.419982i	−0.944827	−	0.327569i	$-0.893770\pi$
$499$	−6.26864	+	9.38168i	−0.280623	+	0.419982i	0.664204	+	0.747551i	$0.268770\pi$
$500$	−16.9763	−	16.9900i	−0.759202	−	0.759815i
$501$	1.79301	−	4.32872i	0.0801060	−	0.193393i
$502$	−6.16816	−	7.51902i	−0.275298	−	0.335590i
$503$	8.11441	+	40.7939i	0.361804	+	1.81891i	0.548095	+	0.836416i	$0.315353\pi$
$503$	8.11441	+	40.7939i	0.361804	+	1.81891i	−0.186291	+	0.982495i	$0.559647\pi$
$504$	−13.3259	+	24.8948i	−0.593585	+	1.10890i
$505$	−20.6566	−	4.10886i	−0.919208	−	0.182842i
$506$	0.136008	+	0.448683i	0.00604627	+	0.0199464i
$507$	1.53948	−	1.02865i	0.0683708	−	0.0456839i
$508$	−12.9857	+	19.4174i	−0.576146	+	0.861509i
$509$	32.7742			1.45269			0.726345	−	0.687330i	$-0.241217\pi$
$509$	32.7742			1.45269			0.726345	+	0.687330i	$0.241217\pi$
$510$	−3.77681	+	6.94757i	−0.167240	+	0.307643i
$511$		−	13.9021i		−	0.614994i
$512$	14.3228	+	17.5173i	0.632986	+	0.774163i
$513$	−10.6988	−	16.0119i	−0.472364	−	0.706943i
$514$	3.44697	+	11.3714i	0.152039	+	0.501571i
$515$	−2.74105	+	13.7802i	−0.120785	+	0.607228i
$516$	−14.0107	−	0.00566211i	−0.616785	−	0.000249260i
$517$	−0.873745	+	0.173799i	−0.0384272	+	0.00764365i
$518$	−39.5794	+	32.4686i	−1.73902	+	1.42659i
$519$	−0.640187	−	0.265174i	−0.0281011	−	0.0116399i
$520$	−14.6479	+	4.43368i	−0.642351	+	0.194430i
$521$	18.0123	+	12.0354i	0.789133	+	0.527282i	0.883598	−	0.468246i	$-0.155114\pi$
$521$	18.0123	+	12.0354i	0.789133	+	0.527282i	−0.0944646	+	0.995528i	$0.530114\pi$
$522$	11.8332	+	9.71526i	0.517925	+	0.425225i
$523$	−7.97077	−	7.97077i	−0.348537	−	0.348537i	0.511027	−	0.859565i	$-0.329265\pi$
$523$	−7.97077	−	7.97077i	−0.348537	−	0.348537i	−0.859565	+	0.511027i	$0.829265\pi$
$524$	−35.4264	−	14.6909i	−1.54761	−	0.641774i
$525$	−3.07261	−	7.41793i	−0.134100	−	0.323745i
$526$	8.50760	−	15.9089i	0.370949	−	0.693659i
$527$	−3.02879	+	14.6995i	−0.131936	+	0.640322i
$528$	−0.161711	+	0.389515i	−0.00703759	+	0.0169515i
$529$	−6.24755	−	15.0829i	−0.271633	−	0.655780i
$530$	−3.33665	+	0.327950i	−0.144935	+	0.0142453i
$531$	22.5825	−	22.5825i	0.979998	−	0.979998i
$532$	−14.4516	−	34.9292i	−0.626557	−	1.51437i
$533$	−28.3322	−	18.9310i	−1.22721	−	0.819992i
$534$	1.39333	+	0.422971i	0.0602955	+	0.0183037i
$535$	1.75645	−	4.24044i	0.0759378	−	0.183330i
$536$	−3.06427	+	10.0795i	−0.132356	+	0.435370i
$537$	4.04888	−	0.805372i	0.174722	−	0.0347544i
$538$	−6.08509	−	11.3899i	−0.262347	−	0.491055i
$539$	−1.43972	−	0.286378i	−0.0620132	−	0.0123352i
$540$	−14.1643	−	2.82341i	−0.609534	−	0.121500i
$541$	1.41516	+	2.11794i	0.0608425	+	0.0910573i	0.860643	−	0.509208i	$-0.170062\pi$
$541$	1.41516	+	2.11794i	0.0608425	+	0.0910573i	−0.799801	+	0.600265i	$0.795062\pi$
$542$	−17.7227	−	1.74915i	−0.761256	−	0.0751325i
$543$	3.70951			0.159190
$544$	−6.59483	−	22.3720i	−0.282751	−	0.959193i
$545$	23.3471			1.00008
$546$	−16.2780	−	1.60657i	−0.696636	−	0.0687548i
$547$	−5.58404	−	8.35711i	−0.238756	−	0.357324i	0.692670	−	0.721255i	$-0.256434\pi$
$547$	−5.58404	−	8.35711i	−0.238756	−	0.357324i	−0.931426	+	0.363931i	$0.881434\pi$
$548$	−16.1051	−	3.21027i	−0.687976	−	0.137136i
$549$	−9.51046	−	1.89175i	−0.405896	−	0.0807378i
$550$	0.194606	+	0.364260i	0.00829804	+	0.0155321i
$551$	−20.1022	+	3.99858i	−0.856384	+	0.170345i
$552$	−1.74633	+	5.74434i	−0.0743288	+	0.244495i
$553$	−19.2000	+	46.3528i	−0.816466	+	1.97112i
$554$	34.8342	+	10.5745i	1.47996	+	0.449268i
$555$	−9.50577	−	6.35155i	−0.403497	−	0.269608i
$556$	8.78026	+	21.2217i	0.372366	+	0.899999i
$557$	8.39351	−	8.39351i	0.355644	−	0.355644i	−0.506560	−	0.862205i	$-0.669083\pi$
$557$	8.39351	−	8.39351i	0.355644	−	0.355644i	0.862205	+	0.506560i	$0.169083\pi$
$558$	−11.9107	+	1.17068i	−0.504222	+	0.0495586i
$559$	10.6959	+	25.8222i	0.452389	+	1.09216i
$560$	−26.1836	−	10.8704i	−1.10646	−	0.459359i
$561$	0.309499	−	0.305286i	0.0130671	−	0.0128892i
$562$	21.9036	−	40.9589i	0.923948	−	1.72774i
$563$	−3.70762	−	8.95099i	−0.156258	−	0.377239i	0.826291	−	0.563243i	$-0.190446\pi$
$563$	−3.70762	−	8.95099i	−0.156258	−	0.377239i	−0.982549	+	0.186003i	$0.940446\pi$
$564$	−10.5380	−	4.36999i	−0.443732	−	0.184010i
$565$	9.02596	+	9.02596i	0.379725	+	0.379725i
$566$	20.6415	+	16.9470i	0.867627	+	0.712336i
$567$	12.0673	+	8.06312i	0.506780	+	0.338619i
$568$	2.47156	−	0.748104i	0.103704	−	0.0313897i
$569$	3.81051	+	1.57837i	0.159745	+	0.0661685i	0.461123	−	0.887336i	$-0.347447\pi$
$569$	3.81051	+	1.57837i	0.159745	+	0.0661685i	−0.301378	+	0.953505i	$0.597447\pi$
$570$	6.52661	−	5.35404i	0.273369	−	0.224256i
$571$	−15.3808	+	3.05943i	−0.643667	+	0.128033i	−0.506122	−	0.862462i	$-0.668921\pi$
$571$	−15.3808	+	3.05943i	−0.643667	+	0.128033i	−0.137545	+	0.990495i	$0.543921\pi$
$572$	0.841344		0.000340011i	0.0351784		1.42166e-5i
$573$	1.64131	−	8.25144i	0.0685668	−	0.344709i
$574$	−18.3113	−	60.4083i	−0.764301	−	2.52140i
$575$	3.26629	+	4.88834i	0.136214	+	0.203858i
$576$	15.4771	−	10.3144i	0.644881	−	0.429766i
$577$			14.5403i			0.605319i	0.953099	+	0.302660i	$0.0978746\pi$
$577$			14.5403i			0.605319i	−0.953099	+	0.302660i	$0.902125\pi$
$578$	−2.68901	+	23.8908i	−0.111848	+	0.993725i
$579$	−9.44196			−0.392394
$580$	−8.54538	+	12.7779i	−0.354828	+	0.530573i
$581$	18.3904	−	12.2881i	0.762964	−	0.509796i
$582$	2.98147	+	9.83573i	0.123586	+	0.407704i
$583$	0.180774	+	0.0359582i	0.00748690	+	0.00148924i
$584$	−4.32149	+	8.07317i	−0.178825	+	0.334070i
$585$	2.45416	+	12.3379i	0.101467	+	0.510110i
$586$	−3.72934	−	4.54608i	−0.154058	−	0.187797i
$587$	−9.18052	+	22.1637i	−0.378921	+	0.914795i	0.613248	+	0.789890i	$0.289863\pi$
$587$	−9.18052	+	22.1637i	−0.378921	+	0.914795i	−0.992169	+	0.124905i	$0.960137\pi$
$588$	−13.2868	−	13.2976i	−0.547939	−	0.548382i
$589$	8.90117	−	13.3215i	0.366766	−	0.548904i
$590$	24.7823	+	20.3467i	1.02027	+	0.837660i
$591$	9.72618	−	9.72618i	0.400082	−	0.400082i
$592$	33.0772	−	6.55168i	1.35947	−	0.269273i
$593$	12.4965	−	5.17620i	0.513168	−	0.212561i	−0.111045	−	0.993815i	$-0.535420\pi$
$593$	12.4965	−	5.17620i	0.513168	−	0.212561i	0.624213	+	0.781254i	$0.285420\pi$
$594$	0.700170	+	0.374431i	0.0287283	+	0.0153631i
$595$	20.5217	+	20.8049i	0.841307	+	0.852918i
$596$	−37.4490	+	25.0007i	−1.53397	+	1.02407i
$597$	−5.08527	+	2.10639i	−0.208126	+	0.0862087i
$598$	11.9197	−	1.17156i	0.487435	−	0.0479087i
$599$	−7.44471	−	7.44471i	−0.304183	−	0.304183i	0.538465	−	0.842648i	$-0.319004\pi$
$599$	−7.44471	−	7.44471i	−0.304183	−	0.304183i	−0.842648	+	0.538465i	$0.819004\pi$
$600$	−0.521565	+	5.26283i	−0.0212928	+	0.214854i
$601$	1.02713	−	1.53720i	0.0418974	−	0.0627039i	−0.809930	−	0.586527i	$-0.800495\pi$
$601$	1.02713	−	1.53720i	0.0418974	−	0.0627039i	0.851827	+	0.523823i	$0.175495\pi$
$602$	−15.0398	+	49.5436i	−0.612977	+	2.01925i
$603$	8.00035	+	3.31386i	0.325800	+	0.134951i
$604$	−7.03649	−	35.4497i	−0.286311	−	1.44243i
$605$	−3.53677	−	17.7806i	−0.143790	−	0.722882i
$606$	6.98682	+	13.0778i	0.283820	+	0.531248i
$607$	7.66107	−	38.5148i	0.310953	−	1.56327i	−0.436966	−	0.899478i	$-0.643947\pi$
$607$	7.66107	−	38.5148i	0.310953	−	1.56327i	0.747919	−	0.663790i	$-0.231053\pi$
$608$	−2.46552	+	24.7762i	−0.0999901	+	1.00481i
$609$	−13.6607	+	9.12781i	−0.553561	+	0.369877i
$610$	0.956226	−	9.68865i	0.0387165	−	0.392282i
$611$			22.7581i			0.920696i
$612$	−18.8298	+	3.60363i	−0.761151	+	0.145668i
$613$		−	8.51336i		−	0.343852i	−0.985110	−	0.171926i	$-0.945001\pi$
$613$		−	8.51336i		−	0.343852i	0.985110	−	0.171926i	$-0.0549989\pi$
$614$	−24.7447	−	2.44219i	−0.998616	−	0.0985589i
$615$	11.7209	−	7.83165i	0.472632	−	0.315803i
$616$	1.20419	+	0.989473i	0.0485181	+	0.0398670i
$617$	−3.79851	+	19.0964i	−0.152922	+	0.768791i	0.825858	+	0.563878i	$0.190691\pi$
$617$	−3.79851	+	19.0964i	−0.152922	+	0.768791i	−0.978780	+	0.204913i	$0.934309\pi$
$618$	8.72428	−	4.66096i	0.350942	−	0.187491i
$619$	−3.33048	−	16.7435i	−0.133863	−	0.672977i	−0.988189	−	0.153239i	$-0.951030\pi$
$619$	−3.33048	−	16.7435i	−0.133863	−	0.672977i	0.854326	−	0.519738i	$-0.173970\pi$
$620$	−2.33948	−	11.7863i	−0.0939559	−	0.473348i
$621$	10.4428	+	4.32555i	0.419055	+	0.173578i
$622$	17.8980	+	5.43325i	0.717644	+	0.217853i
$623$	2.98955	−	4.47418i	0.119774	−	0.179254i
$624$	8.95349	+	5.99301i	0.358427	+	0.239912i
$625$	−5.97004	−	5.97004i	−0.238801	−	0.238801i
$626$	−4.39334	−	44.6989i	−0.175593	−	1.78653i
$627$	−0.428756	+	0.177596i	−0.0171228	+	0.00709252i
$628$	−7.01038	−	10.5010i	−0.279745	−	0.419034i
$629$	−34.0425	−	7.01433i	−1.35736	−	0.279680i
$630$	−10.9893	+	20.5495i	−0.437823	+	0.818712i
$631$	6.51453	−	2.69841i	0.259339	−	0.107422i	−0.249226	−	0.968445i	$-0.580176\pi$
$631$	6.51453	−	2.69841i	0.259339	−	0.107422i	0.508565	+	0.861024i	$0.330176\pi$
$632$	25.5585	−	20.9494i	1.01666	−	0.833324i
$633$	12.5061	−	12.5061i	0.497074	−	0.497074i
$634$	−16.7313	+	20.3787i	−0.664483	+	0.809342i
$635$	−10.7103	+	16.0291i	−0.425024	+	0.636094i
$636$	1.66832	+	1.66967i	0.0661531	+	0.0662066i
$637$	−14.3506	+	34.6454i	−0.568592	+	1.37270i
$638$	0.653359	−	0.535977i	0.0258667	−	0.0212195i
$639$	−0.414095	−	2.08180i	−0.0163814	−	0.0823547i
$640$	11.8261	+	14.4518i	0.467469	+	0.571259i
$641$	19.0576	+	3.79080i	0.752730	+	0.149727i	0.556520	−	0.830834i	$-0.312136\pi$
$641$	19.0576	+	3.79080i	0.752730	+	0.149727i	0.196211	+	0.980562i	$0.437136\pi$
$642$	−3.09228	+	0.937350i	−0.122042	+	0.0369942i
$643$	39.0244	−	26.0753i	1.53897	−	1.02831i	0.559000	−	0.829168i	$-0.311185\pi$
$643$	39.0244	−	26.0753i	1.53897	−	1.02831i	0.979971	−	0.199140i	$-0.0638149\pi$
$644$	18.4431	+	12.3341i	0.726761	+	0.486031i
$645$	−11.5627			−0.455280
$646$	12.2577	−	22.5485i	0.482274	−	0.887159i
$647$			6.68386i			0.262770i	0.991331	+	0.131385i	$0.0419424\pi$
$647$			6.68386i			0.262770i	−0.991331	+	0.131385i	$0.958058\pi$
$648$	−4.50124	−	8.43352i	−0.176825	−	0.331300i
$649$	−0.979336	−	1.46568i	−0.0384423	−	0.0575330i
$650$	10.0965	−	3.06052i	0.396019	−	0.120044i
$651$	2.50554	−	12.5962i	0.0981997	−	0.493683i
$652$	4.48258	+	0.00181154i	0.175551	+	7.09452e-5i
$653$	35.9272	−	7.14636i	1.40594	−	0.279659i	0.566926	−	0.823769i	$-0.308133\pi$
$653$	35.9272	−	7.14636i	1.40594	−	0.279659i	0.839014	+	0.544110i	$0.183133\pi$
$654$	−10.4245	−	12.7076i	−0.407632	−	0.496906i
$655$	−29.2415	−	12.1122i	−1.14256	−	0.473263i
$656$	−8.14434	+	40.7721i	−0.317983	+	1.59188i
$657$	6.25835	+	4.18169i	0.244161	+	0.163143i
$658$	−26.7518	+	32.5838i	−1.04289	+	1.27025i
$659$	7.78629	+	7.78629i	0.303311	+	0.303311i	0.842308	−	0.538997i	$-0.181197\pi$
$659$	7.78629	+	7.78629i	0.303311	+	0.303311i	−0.538997	+	0.842308i	$0.681197\pi$
$660$	−0.133327	+	0.321511i	−0.00518973	+	0.0125148i
$661$	13.9674	+	33.7202i	0.543267	+	1.31156i	0.922405	+	0.386223i	$0.126220\pi$
$661$	13.9674	+	33.7202i	0.543267	+	1.31156i	−0.379138	+	0.925340i	$0.623780\pi$
$662$	−38.8813	−	20.7926i	−1.51117	−	0.808128i
$663$	−6.10656	−	9.27611i	−0.237159	−	0.360254i
$664$	−14.4994	+	1.41919i	−0.562685	+	0.0550752i
$665$	−11.9382	−	28.8214i	−0.462945	−	1.11765i
$666$	−2.71115	−	27.5839i	−0.105055	−	1.06886i
$667$	8.50668	−	8.50668i	0.329380	−	0.329380i
$668$	4.36018	+	10.5384i	0.168700	+	0.407745i
$669$	8.02850	+	5.36447i	0.310400	+	0.207402i
$670$	−2.52550	+	8.31942i	−0.0975688	+	0.321407i
$671$	−0.204820	+	0.494479i	−0.00790699	+	0.0190892i
$672$	5.77440	+	19.1051i	0.222752	+	0.736996i
$673$	18.9914	−	3.77763i	0.732066	−	0.145617i	0.185038	−	0.982731i	$-0.440759\pi$
$673$	18.9914	−	3.77763i	0.732066	−	0.145617i	0.547028	+	0.837114i	$0.315759\pi$
$674$	17.8120	−	9.51611i	0.686094	−	0.366547i
$675$	9.76521	+	1.94242i	0.375863	+	0.0747638i
$676$	−0.881028	+	4.41989i	−0.0338857	+	0.169996i
$677$	8.13684	+	12.1776i	0.312724	+	0.468025i	0.954222	−	0.299100i	$-0.0966865\pi$
$677$	8.13684	+	12.1776i	0.312724	+	0.468025i	−0.641497	+	0.767125i	$0.721687\pi$
$678$	0.882617	−	8.94283i	0.0338967	−	0.343447i
$679$	37.9809			1.45757
$680$	−5.45002	−	18.4609i	−0.208999	−	0.707944i
$681$	−2.29375			−0.0878968
$682$	−0.0648819	+	0.657396i	−0.00248446	+	0.0251730i
$683$	8.74789	+	13.0921i	0.334729	+	0.500957i	0.960209	−	0.279283i	$-0.0900968\pi$
$683$	8.74789	+	13.0921i	0.334729	+	0.500957i	−0.625480	+	0.780240i	$0.715097\pi$
$684$	20.0711	+	4.00083i	0.767439	+	0.152976i
$685$	−13.2922	−	2.64399i	−0.507870	−	0.101022i
$686$	−23.7776	+	12.7032i	−0.907831	+	0.485010i
$687$	−23.9682	+	4.76757i	−0.914443	+	0.181894i
$688$	24.1345	−	24.0956i	0.920120	−	0.918634i
$689$	1.80189	−	4.35015i	0.0686466	−	0.165728i
$690$	−1.43929	+	4.74125i	−0.0547928	+	0.180496i
$691$	5.11972	+	3.42089i	0.194763	+	0.130137i	0.649128	−	0.760679i	$-0.275134\pi$
$691$	5.11972	+	3.42089i	0.194763	+	0.130137i	−0.454365	+	0.890816i	$0.650134\pi$
$692$	1.55856	−	0.644839i	0.0592476	−	0.0245131i
$693$	0.905874	−	0.905874i	0.0344113	−	0.0344113i
$694$	2.52688	+	25.7091i	0.0959191	+	0.975905i
$695$	7.25321	+	17.5108i	0.275130	+	0.664223i
$696$	10.7704	−	1.05420i	0.408250	−	0.0399593i
$697$	24.0538	−	35.4705i	0.911104	−	1.34354i
$698$	25.0167	+	13.3782i	0.946894	+	0.506372i
$699$	2.03679	+	4.91725i	0.0770385	+	0.185987i
$700$	18.0532	+	7.48643i	0.682347	+	0.282960i
$701$	−3.72512	−	3.72512i	−0.140696	−	0.140696i	0.633251	−	0.773947i	$-0.281720\pi$
$701$	−3.72512	−	3.72512i	−0.140696	−	0.140696i	−0.773947	+	0.633251i	$0.781720\pi$
$702$	12.8710	−	15.6769i	0.485785	−	0.591687i
$703$	30.8512	+	20.6141i	1.16357	+	0.777476i
$704$	−0.391710	−	0.948925i	−0.0147631	−	0.0357639i
$705$	−8.69826	−	3.60294i	−0.327595	−	0.135694i
$706$	5.90073	+	7.19302i	0.222077	+	0.270713i
$707$	53.7405	−	10.6896i	2.02112	−	0.402025i
$708$	0.00912261	−	22.5736i	0.000342849	−	0.848366i
$709$	−2.64917	+	13.3183i	−0.0994916	+	0.500178i	0.898619	+	0.438731i	$0.144572\pi$
$709$	−2.64917	+	13.3183i	−0.0994916	+	0.500178i	−0.998110	+	0.0614477i	$0.980428\pi$
$710$	2.03947	−	0.618216i	0.0765399	−	0.0232012i
$711$	−15.0915	−	22.5860i	−0.565975	−	0.847041i
$712$	−3.12688	+	1.66892i	−0.117185	+	0.0625454i
$713$			9.40400i			0.352183i
$714$	2.16089	−	20.4591i	0.0808694	−	0.765664i
$715$	0.694341			0.0259669
$716$	−5.58607	+	8.35283i	−0.208761	+	0.312160i
$717$	−8.73464	+	5.83630i	−0.326201	+	0.217961i
$718$	−26.2234	+	7.94899i	−0.978648	+	0.296654i
$719$	−1.34159	−	0.266860i	−0.0500330	−	0.00995218i	0.170010	−	0.985442i	$-0.445620\pi$
$719$	−1.34159	−	0.266860i	−0.0500330	−	0.00995218i	−0.220043	+	0.975490i	$0.570620\pi$
$720$	12.7695	−	8.51737i	0.475890	−	0.317424i
$721$	−7.13114	−	35.8507i	−0.265578	−	1.33515i
$722$	−0.407971	+	0.334676i	−0.0151831	+	0.0124553i
$723$	0.902813	−	2.17958i	0.0335760	−	0.0810596i
$724$	−6.38736	+	6.38220i	−0.237384	+	0.237192i
$725$	5.88736	−	8.81105i	0.218651	−	0.327234i
$726$	−8.09857	+	9.86407i	−0.300566	+	0.366090i
$727$	24.5142	−	24.5142i	0.909180	−	0.909180i	−0.0870256	−	0.996206i	$-0.527736\pi$
$727$	24.5142	−	24.5142i	0.909180	−	0.909180i	0.996206	+	0.0870256i	$0.0277362\pi$
$728$	30.7930	−	25.2400i	1.14127	−	0.935455i
$729$	2.70408	−	1.12007i	0.100151	−	0.0414840i
$730$	−3.56373	+	6.66404i	−0.131900	+	0.246647i
$731$	−32.5690	+	13.2298i	−1.20461	+	0.489320i
$732$	−5.70038	+	3.80554i	−0.210692	+	0.140657i
$733$	11.7341	−	4.86043i	0.433409	−	0.179524i	−0.155303	−	0.987867i	$-0.549635\pi$
$733$	11.7341	−	4.86043i	0.433409	−	0.179524i	0.588712	+	0.808343i	$0.299635\pi$
$734$	0.395896	+	4.02794i	0.0146128	+	0.148674i
$735$	−10.9697	−	10.9697i	−0.404624	−	0.404624i
$736$	−6.87613	−	12.8957i	−0.253458	−	0.475340i
$737$	0.265545	−	0.397416i	0.00978148	−	0.0146390i
$738$	32.7021	+	9.92730i	1.20378	+	0.365429i
$739$	−17.2497	−	7.14505i	−0.634540	−	0.262835i	0.0421407	−	0.999112i	$-0.486582\pi$
$739$	−17.2497	−	7.14505i	−0.634540	−	0.262835i	−0.676681	+	0.736277i	$0.736582\pi$
$740$	27.2957	−	5.41798i	1.00341	−	0.199169i
$741$	2.31290	+	11.6277i	0.0849664	+	0.427155i
$742$	7.69337	−	4.11019i	0.282432	−	0.150890i
$743$	1.83763	−	9.23837i	0.0674159	−	0.338923i	−0.932326	−	0.361618i	$-0.882225\pi$
$743$	1.83763	−	9.23837i	0.0674159	−	0.338923i	0.999742	+	0.0226948i	$0.00722459\pi$
$744$	−5.37054	+	6.53594i	−0.196894	+	0.239619i
$745$	−30.8974	+	20.6450i	−1.13199	+	0.756373i
$746$	−25.8027	−	2.54660i	−0.944702	−	0.0932378i
$747$			11.9751i			0.438145i
$748$	−0.00767927	+	1.05816i	−0.000280782	+	0.0386902i
$749$			11.9409i			0.436311i
$750$	−1.37055	+	13.8867i	−0.0500455	+	0.507070i
$751$	−39.0008	+	26.0595i	−1.42316	+	0.950925i	−0.424189	+	0.905574i	$0.639441\pi$
$751$	−39.0008	+	26.0595i	−1.42316	+	0.950925i	−0.998971	+	0.0453512i	$0.985559\pi$
$752$	25.6639	−	10.6060i	0.935866	−	0.386762i
$753$	−1.10233	+	5.54177i	−0.0401710	+	0.201953i
$754$	−10.1729	−	19.0413i	−0.370474	−	0.693445i
$755$	−5.81887	−	29.2534i	−0.211770	−	1.06464i
$756$	36.8559	−	7.31561i	1.34043	−	0.266066i
$757$	7.19106	+	2.97863i	0.261363	+	0.108260i	0.509517	−	0.860460i	$-0.329824\pi$
$757$	7.19106	+	2.97863i	0.261363	+	0.108260i	−0.248154	+	0.968721i	$0.579824\pi$
$758$	14.5780	−	48.0224i	0.529498	−	1.74425i
$759$	0.151335	−	0.226488i	0.00549310	−	0.00822100i
$760$	−2.02647	+	20.4480i	−0.0735079	+	0.741729i
$761$	−6.55025	−	6.55025i	−0.237446	−	0.237446i	0.578346	−	0.815792i	$-0.303699\pi$
$761$	−6.55025	−	6.55025i	−0.237446	−	0.237446i	−0.815792	+	0.578346i	$0.803699\pi$
$762$	13.5066	−	1.32753i	0.489292	−	0.0480912i
$763$	−56.1165	+	23.2442i	−2.03156	+	0.841498i
$764$	11.3704	+	17.0319i	0.411367	+	0.616193i
$765$	−15.5386	+	2.98027i	−0.561800	+	0.107752i
$766$	17.8978	+	9.57124i	0.646675	+	0.345823i
$767$	−41.6040	+	17.2329i	−1.50223	+	0.622245i
$768$	2.58557	−	12.8896i	0.0932987	−	0.465113i
$769$	−16.3062	+	16.3062i	−0.588016	+	0.588016i	−0.937094	−	0.349078i	$-0.886495\pi$
$769$	−16.3062	+	16.3062i	−0.588016	+	0.588016i	0.349078	+	0.937094i	$0.386495\pi$
$770$	0.994117	+	0.816187i	0.0358255	+	0.0294133i
$771$	3.83541	−	5.74010i	0.138129	−	0.206725i
$772$	16.2580	−	16.2449i	0.585138	−	0.584665i
$773$	5.81873	−	14.0477i	0.209285	−	0.505259i	−0.784026	−	0.620728i	$-0.786837\pi$
$773$	5.81873	−	14.0477i	0.209285	−	0.505259i	0.993311	+	0.115469i	$0.0368370\pi$
$774$	−17.7792	−	21.6730i	−0.639061	−	0.779019i
$775$	1.61605	+	8.12442i	0.0580502	+	0.291838i
$776$	−22.0561	−	11.8064i	−0.791767	−	0.423826i
$777$	29.1713	+	5.80254i	1.04652	+	0.208165i
$778$	13.7970	+	45.5157i	0.494646	+	1.63182i
$779$	−38.0404	+	25.4178i	−1.36294	+	0.910688i
$780$	7.39110	+	4.94290i	0.264644	+	0.176984i
$781$	−0.117158			−0.00419223
$782$	1.37074	+	15.0016i	0.0490176	+	0.536457i
$783$		−	20.3736i		−	0.728093i
$784$	45.7568	+	0.0369832i	1.63417	+	0.00132083i
$785$	−5.78900	−	8.66386i	−0.206618	−	0.309226i
$786$	6.46383	+	21.3239i	0.230557	+	0.760599i
$787$	1.24633	−	6.26575i	0.0444270	−	0.223350i	−0.952193	−	0.305496i	$-0.901178\pi$
$787$	1.24633	−	6.26575i	0.0444270	−	0.223350i	0.996620	+	0.0821467i	$0.0261776\pi$
$788$	−0.0135307	+	33.4812i	−0.000482011	+	1.19272i
$789$	−10.2802	+	2.04486i	−0.365984	+	0.0727988i
$790$	21.0859	−	17.2976i	0.750201	−	0.615421i
$791$	−30.6807	−	12.7084i	−1.09088	−	0.451858i
$792$	−0.807647	+	0.244463i	−0.0286985	+	0.00868660i
$793$	11.3686	+	7.59623i	0.403710	+	0.269750i
$794$	−18.8270	−	15.4573i	−0.668146	−	0.548559i
$795$	1.37738	+	1.37738i	0.0488506	+	0.0488506i
$796$	5.13223	−	12.3761i	0.181907	−	0.438661i
$797$	−0.792947	−	1.91434i	−0.0280876	−	0.0678095i	0.909213	−	0.416330i	$-0.136684\pi$
$797$	−0.792947	−	1.91434i	−0.0280876	−	0.0678095i	−0.937301	+	0.348521i	$0.886684\pi$
$798$	−10.3567	+	19.3667i	−0.366624	+	0.685572i
$799$	−28.6231	−	0.196155i	−1.01261	−	0.00693946i
$800$	−8.15660	−	9.95934i	−0.288379	−	0.352116i
$801$	1.11491	+	2.69163i	0.0393934	+	0.0951040i
$802$	−21.4078	+	2.10412i	−0.755936	+	0.0742990i
$803$	0.293768	−	0.293768i	0.0103668	−	0.0103668i
$804$	5.65581	−	2.34003i	0.199465	−	0.0825266i
$805$	15.2248	+	10.1729i	0.536603	+	0.358547i
$806$	16.1479	+	4.90198i	0.568786	+	0.172665i
$807$	−2.87114	+	6.93156i	−0.101069	+	0.244002i
$808$	−34.5308	−	10.4977i	−1.21479	−	0.369306i
$809$	−2.74562	+	0.546138i	−0.0965310	+	0.0192012i	−0.243119	−	0.969996i	$-0.578171\pi$
$809$	−2.74562	+	0.546138i	−0.0965310	+	0.0192012i	0.146588	+	0.989198i	$0.453171\pi$
$810$	−3.71758	−	6.95848i	−0.130622	−	0.244496i
$811$	−29.0513	−	5.77867i	−1.02013	−	0.202917i	−0.343433	−	0.939177i	$-0.611590\pi$
$811$	−29.0513	−	5.77867i	−1.02013	−	0.202917i	−0.676698	+	0.736261i	$0.736590\pi$
$812$	7.81788	−	39.2203i	0.274354	−	1.37636i
$813$	5.74838	+	8.60306i	0.201604	+	0.301722i
$814$	−1.52245	−	0.150259i	−0.0533620	−	0.00526659i
$815$	3.69936			0.129583
$816$	−7.61461	+	11.2092i	−0.266565	+	0.392401i
$817$	37.5269			1.31290
$818$	26.3841	+	2.60399i	0.922498	+	0.0910463i
$819$	−18.1823	−	27.2117i	−0.635340	−	0.950854i
$820$	−6.70773	+	33.6510i	−0.234244	+	1.17514i
$821$	14.8916	+	2.96213i	0.519722	+	0.103379i	0.447979	−	0.894044i	$-0.352144\pi$
$821$	14.8916	+	2.96213i	0.519722	+	0.103379i	0.0717428	+	0.997423i	$0.477144\pi$
$822$	4.49591	+	8.41535i	0.156813	+	0.293519i
$823$	−48.5611	+	9.65941i	−1.69274	+	0.336706i	−0.944945	−	0.327229i	$-0.893885\pi$
$823$	−48.5611	+	9.65941i	−1.69274	+	0.336706i	−0.747790	+	0.663935i	$0.768885\pi$
$824$	−7.00307	+	23.0357i	−0.243963	+	0.802488i
$825$	0.0918216	−	0.221677i	0.00319682	−	0.00771780i
$826$	−79.8231	−	24.2317i	−2.77740	−	0.843128i
$827$	−22.3231	−	14.9158i	−0.776252	−	0.518675i	0.103201	−	0.994660i	$-0.467091\pi$
$827$	−22.3231	−	14.9158i	−0.776252	−	0.518675i	−0.879453	+	0.475986i	$0.842091\pi$
$828$	−11.1001	+	4.59255i	−0.385754	+	0.159602i
$829$	−5.46751	+	5.46751i	−0.189894	+	0.189894i	−0.795650	−	0.605756i	$-0.792871\pi$
$829$	−5.46751	+	5.46751i	−0.189894	+	0.189894i	0.605756	+	0.795650i	$0.292871\pi$
$830$	−11.9655	+	1.17606i	−0.415329	+	0.0408216i
$831$	−8.09389	−	19.5404i	−0.280774	−	0.677849i
$832$	−25.7278	+	5.08517i	−0.891953	+	0.176296i
$833$	−43.4501	−	18.3475i	−1.50546	−	0.635702i
$834$	6.29235	−	11.7664i	0.217886	−	0.407439i
$835$	3.60186	+	8.69567i	0.124648	+	0.300926i
$836$	0.432715	−	1.04347i	0.0149658	−	0.0360893i
$837$	11.2613	+	11.2613i	0.389249	+	0.389249i
$838$	−13.4170	−	11.0156i	−0.463484	−	0.380528i
$839$	−21.4706	−	14.3462i	−0.741247	−	0.495285i	0.126701	−	0.991941i	$-0.459561\pi$
$839$	−21.4706	−	14.3462i	−0.741247	−	0.495285i	−0.867948	+	0.496656i	$0.834561\pi$
$840$	4.77185	+	15.7651i	0.164644	+	0.543946i
$841$	6.75902	+	2.79968i	0.233070	+	0.0965406i
$842$	−29.6316	+	24.3080i	−1.02117	+	0.837709i
$843$	−26.4673	+	5.26467i	−0.911582	+	0.181325i
$844$	−0.0173981	+	43.0509i	−0.000598866	+	1.48187i
$845$	−0.725617	+	3.64792i	−0.0249620	+	0.125492i
$846$	−6.62148	−	21.8440i	−0.227651	−	0.751011i
$847$	26.2031	+	39.2157i	0.900348	+	1.34747i
$848$	−5.74531	−	0.00464368i	−0.197295	−	0.000159465i
$849$		−	15.5167i		−	0.532531i
$850$	3.76221	+	12.7248i	0.129043	+	0.436459i
$851$	−21.7786			−0.746561
$852$	−1.24711	−	0.834025i	−0.0427254	−	0.0285732i
$853$	−8.10721	+	5.41706i	−0.277585	+	0.185477i	−0.686568	−	0.727065i	$-0.740884\pi$
$853$	−8.10721	+	5.41706i	−0.277585	+	0.185477i	0.408983	+	0.912542i	$0.365884\pi$
$854$	7.34759	+	24.2394i	0.251429	+	0.829455i
$855$	16.5656	+	3.29510i	0.566530	+	0.112690i
$856$	3.71185	−	6.93426i	0.126868	−	0.237008i
$857$	2.51232	+	12.6303i	0.0858192	+	0.431442i	0.999677	+	0.0254083i	$0.00808857\pi$
$857$	2.51232	+	12.6303i	0.0858192	+	0.431442i	−0.913858	+	0.406034i	$0.866911\pi$
$858$	−0.310025	−	0.377922i	−0.0105841	−	0.0129020i
$859$	8.15299	−	19.6831i	0.278177	−	0.671578i	−0.721609	−	0.692301i	$-0.756597\pi$
$859$	8.15299	−	19.6831i	0.278177	−	0.671578i	0.999785	+	0.0207235i	$0.00659697\pi$
$860$	19.9096	−	19.8935i	0.678912	−	0.678364i
$861$	−20.3749	+	30.4932i	−0.694374	+	1.03920i
$862$	−24.1960	−	19.8653i	−0.824119	−	0.676616i
$863$	−22.6525	+	22.6525i	−0.771101	+	0.771101i	−0.978299	−	0.207198i	$-0.933566\pi$
$863$	−22.6525	+	22.6525i	−0.771101	+	0.771101i	0.207198	+	0.978299i	$0.433566\pi$
$864$	−23.6768	−	7.20841i	−0.805502	−	0.245235i
$865$	1.28603	−	0.532690i	0.0437263	−	0.0181120i
$866$	−39.1105	−	20.9151i	−1.32903	−	0.710725i
$867$	11.7192	−	7.60031i	0.398007	−	0.258120i
$868$	17.3574	+	26.0000i	0.589149	+	0.882496i
$869$	−1.38520	+	0.573770i	−0.0469898	+	0.0194638i
$870$	8.88818	−	0.873596i	0.301338	−	0.0296177i
$871$	−8.63397	−	8.63397i	−0.292551	−	0.292551i
$872$	39.8132	+	3.94563i	1.34825	+	0.133616i
$873$	−11.4245	+	17.0980i	−0.386660	+	0.578678i
$874$	4.67125	−	15.3878i	0.158007	−	0.520502i
$875$	47.6419	+	19.7339i	1.61059	+	0.667128i
$876$	5.21837	−	1.03581i	0.176312	−	0.0349966i
$877$	−4.17129	−	20.9705i	−0.140855	−	0.708124i	−0.985075	−	0.172127i	$-0.944936\pi$
$877$	−4.17129	−	20.9705i	−0.140855	−	0.708124i	0.844220	−	0.535996i	$-0.180064\pi$
$878$	−3.67353	−	6.87604i	−0.123976	−	0.232055i
$879$	−0.666479	+	3.35062i	−0.0224798	+	0.113014i
$880$	−0.323586	−	0.782994i	−0.0109081	−	0.0263947i
$881$	18.4972	−	12.3594i	0.623187	−	0.416400i	−0.203490	−	0.979077i	$-0.565228\pi$
$881$	18.4972	−	12.3594i	0.623187	−	0.416400i	0.826677	+	0.562677i	$0.190228\pi$
$882$	3.69408	−	37.4291i	0.124386	−	1.26030i
$883$			13.4575i			0.452881i	0.974025	+	0.226440i	$0.0727088\pi$
$883$			13.4575i			0.452881i	−0.974025	+	0.226440i	$0.927291\pi$
$884$	26.4743	+	5.46609i	0.890427	+	0.183844i
$885$		−	18.6294i		−	0.626221i
$886$	11.2089	+	1.10627i	0.376570	+	0.0371657i
$887$	−9.75945	+	6.52106i	−0.327690	+	0.218956i	−0.708522	−	0.705689i	$-0.750638\pi$
$887$	−9.75945	+	6.52106i	−0.327690	+	0.218956i	0.380832	+	0.924644i	$0.375638\pi$
$888$	−15.1365	−	12.4376i	−0.507948	−	0.417378i
$889$	9.78451	−	49.1901i	0.328162	−	1.64978i
$890$	−2.57999	+	1.37836i	−0.0864813	+	0.0462028i
$891$	0.0846131	+	0.425379i	0.00283465	+	0.0142507i
$892$	−23.0537	+	4.57598i	−0.771895	+	0.153215i
$893$	28.2304	+	11.6934i	0.944694	+	0.391305i
$894$	25.0326	+	7.59907i	0.837214	+	0.254151i
$895$	−4.60726	+	6.89526i	−0.154004	+	0.230483i
$896$	−42.8131	−	22.9620i	−1.43029	−	0.767107i
$897$	−4.92051	−	4.92051i	−0.164291	−	0.164291i
$898$	0.808940	+	8.23035i	0.0269947	+	0.274650i
$899$	15.6601	−	6.48662i	0.522293	−	0.216341i
$900$	−8.80050	+	5.87517i	−0.293350	+	0.195839i
$901$	5.45568	+	2.30374i	0.181755	+	0.0767488i
$902$	0.889557	−	1.66344i	0.0296190	−	0.0553863i
$903$	27.7917	−	11.5117i	0.924850	−	0.383086i
$904$	13.8663	+	16.9171i	0.461188	+	0.562654i
$905$	−5.26920	+	5.26920i	−0.175154	+	0.175154i
$906$	−13.3242	+	16.2289i	−0.442666	+	0.539168i
$907$	0.826092	−	1.23633i	0.0274299	−	0.0410518i	−0.817501	−	0.575927i	$-0.804641\pi$
$907$	0.826092	−	1.23633i	0.0274299	−	0.0410518i	0.844931	+	0.534875i	$0.179641\pi$
$908$	3.94958	−	3.94639i	0.131072	−	0.130966i
$909$	−11.3527	+	27.4079i	−0.376545	+	0.909061i
$910$	25.4043	−	20.8402i	0.842145	−	0.690846i
$911$	−7.64631	−	38.4406i	−0.253334	−	1.27359i	−0.872609	−	0.488420i	$-0.837573\pi$
$911$	−7.64631	−	38.4406i	−0.253334	−	1.27359i	0.619275	−	0.785174i	$-0.287427\pi$
$912$	12.0345	−	8.02710i	0.398501	−	0.265804i
$913$	0.648272	+	0.128949i	0.0214547	+	0.00426760i
$914$	−13.9387	+	4.22518i	−0.461051	+	0.139756i
$915$	−4.70311	+	3.14252i	−0.155480	+	0.103889i
$916$	33.0679	−	49.4464i	1.09259	−	1.63375i
$917$	82.3428			2.71920
$918$	19.6060	+	16.3231i	0.647094	+	0.538741i
$919$		−	34.1022i		−	1.12493i	−0.826821	−	0.562465i	$-0.809853\pi$
$919$		−	34.1022i		−	1.12493i	0.826821	−	0.562465i	$-0.190147\pi$
$920$	−5.67901	−	10.6402i	−0.187231	−	0.350797i
$921$	8.02597	+	12.0117i	0.264465	+	0.395800i
$922$	11.0065	−	3.33635i	0.362479	−	0.109877i
$923$	−0.583892	+	2.93542i	−0.0192190	+	0.0966206i
$924$	0.000365944	−	0.905515i	1.20387e−5	−	0.0297892i
$925$	−18.8153	+	3.74259i	−0.618642	+	0.123056i
$926$	33.0053	+	40.2337i	1.08462	+	1.32216i
$927$	18.2840	+	7.57347i	0.600525	+	0.248746i
$928$	−16.7316	+	20.3456i	−0.549243	+	0.667877i
$929$	−39.0848	−	26.1156i	−1.28233	−	0.856826i	−0.287441	−	0.957798i	$-0.592805\pi$
$929$	−39.0848	−	26.1156i	−1.28233	−	0.856826i	−0.994889	+	0.100972i	$0.967805\pi$
$930$	−4.43000	+	5.39575i	−0.145265	+	0.176933i
$931$	35.6025	+	35.6025i	1.16682	+	1.16682i
$932$	−11.9672	−	4.96265i	−0.391999	−	0.162557i
$933$	−4.15869	−	10.0400i	−0.136149	−	0.328694i
$934$	0.756686	+	0.404654i	0.0247595	+	0.0132407i
$935$	−0.00598460	+	0.873277i	−0.000195717	+	0.0285592i
$936$	2.09993	+	21.4542i	0.0686382	+	0.701253i
$937$	−5.85996	−	14.1472i	−0.191437	−	0.462169i	0.798795	−	0.601604i	$-0.205471\pi$
$937$	−5.85996	−	14.1472i	−0.191437	−	0.462169i	−0.990231	+	0.139435i	$0.955471\pi$
$938$	−2.21252	−	22.5107i	−0.0722413	−	0.735000i
$939$	−18.4519	+	18.4519i	−0.602154	+	0.602154i
$940$	21.1763	−	8.76147i	0.690693	−	0.285768i
$941$	4.36730	+	2.91814i	0.142370	+	0.0951286i	0.624715	−	0.780852i	$-0.285215\pi$
$941$	4.36730	+	2.91814i	0.142370	+	0.0951286i	−0.482345	+	0.875981i	$0.660215\pi$
$942$	−2.13083	+	7.01931i	−0.0694263	+	0.228702i
$943$	10.2765	−	24.8096i	0.334648	−	0.807911i
$944$	38.8220	+	38.8848i	1.26355	+	1.26559i
$945$	30.4138	−	6.04969i	0.989362	−	0.196796i
$946$	−1.36472	+	0.729104i	−0.0443709	+	0.0237052i
$947$	40.3489	+	8.02589i	1.31116	+	0.260806i	0.800685	−	0.599085i	$-0.204469\pi$
$947$	40.3489	+	8.02589i	1.31116	+	0.260806i	0.510477	+	0.859892i	$0.329469\pi$
$948$	−18.8298	−	3.75338i	−0.611562	−	0.121904i
$949$	−5.89636	−	8.82453i	−0.191404	−	0.286456i
$950$	1.39129	−	14.0968i	0.0451394	−	0.457361i
$951$	15.3191			0.496757
$952$	31.4790	+	38.9461i	1.02024	+	1.26225i
$953$	−39.1075			−1.26682			−0.633408	−	0.773818i	$-0.718345\pi$
$953$	−39.1075			−1.26682			−0.633408	+	0.773818i	$0.718345\pi$
$954$	−0.463836	+	4.69967i	−0.0150172	+	0.152157i
$955$	9.38941	+	14.0522i	0.303834	+	0.454720i
$956$	4.99873	−	25.0774i	0.161671	−	0.811060i
$957$	−0.481547	−	0.0957857i	−0.0155662	−	0.00309631i
$958$	40.2947	−	21.5275i	1.30186	−	0.695521i
$959$	34.5812	−	6.87862i	1.11668	−	0.222122i
$960$	2.12951	−	10.6383i	0.0687296	−	0.343351i
$961$	6.79263	−	16.3989i	0.219117	−	0.528995i
$962$	−11.3524	+	37.3968i	−0.366017	+	1.20572i
$963$	−5.37546	−	3.59177i	−0.173222	−	0.115743i
$964$	2.19542	+	5.30628i	0.0707098	+	0.170904i
$965$	13.4119	−	13.4119i	0.431745	−	0.431745i
$966$	−1.26092	−	12.8289i	−0.0405693	−	0.412762i
$967$	3.78282	+	9.13255i	0.121647	+	0.293683i	0.972959	−	0.230977i	$-0.0741923\pi$
$967$	3.78282	+	9.13255i	0.121647	+	0.293683i	−0.851312	+	0.524660i	$0.824192\pi$
$968$	−3.02627	−	30.9184i	−0.0972680	−	0.993754i
$969$	−14.6442	+	2.80873i	−0.470439	+	0.0902293i
$970$	−18.2063	−	9.73620i	−0.584569	−	0.312611i
$971$	12.6614	+	30.5674i	0.406324	+	0.980954i	0.986096	+	0.166175i	$0.0531416\pi$
$971$	12.6614	+	30.5674i	0.406324	+	0.980954i	−0.579772	+	0.814779i	$0.696858\pi$
$972$	−12.1832	+	29.3792i	−0.390776	+	0.942339i
$973$	−34.8672	−	34.8672i	−1.11779	−	1.11779i
$974$	−4.90133	+	5.96983i	−0.157049	+	0.191286i
$975$	−5.09657	−	3.40542i	−0.163221	−	0.109061i
$976$	3.26799	−	16.3602i	0.104606	−	0.523677i
$977$	0.554837	+	0.229821i	0.0177508	+	0.00735263i	0.391541	−	0.920161i	$-0.371942\pi$
$977$	0.554837	+	0.229821i	0.0177508	+	0.00735263i	−0.373790	+	0.927513i	$0.621942\pi$
$978$	−1.65177	−	2.01352i	−0.0528179	−	0.0643853i
$979$	0.157717	−	0.0313719i	0.00504066	−	0.00100265i
$980$	37.7620	+	0.0152607i	1.20626	+	0.000487484i
$981$	6.41569	−	32.2539i	0.204837	−	1.02979i
$982$	−16.5528	+	5.01759i	−0.528222	+	0.160118i
$983$	16.9723	+	25.4009i	0.541333	+	0.810162i	0.996787	−	0.0800974i	$-0.0255231\pi$
$983$	16.9723	+	25.4009i	0.541333	+	0.810162i	−0.455454	+	0.890259i	$0.650523\pi$
$984$	21.3108	−	11.3743i	0.679365	−	0.362599i
$985$			27.6313i			0.880405i
$986$	24.0361	−	12.6303i	0.765465	−	0.402232i
$987$	24.4939			0.779651
$988$	−23.9880	−	16.0423i	−0.763160	−	0.510373i
$989$	−18.3145	+	12.2373i	−0.582366	+	0.389125i
$990$	−0.666450	+	0.202018i	−0.0211812	+	0.00642057i
$991$	−19.2840	−	3.83582i	−0.612576	−	0.121849i	−0.120955	−	0.992658i	$-0.538596\pi$
$991$	−19.2840	−	3.83582i	−0.612576	−	0.121849i	−0.491621	+	0.870809i	$0.663596\pi$
$992$	−1.99759	−	20.4941i	−0.0634236	−	0.650690i
$993$	4.99764	+	25.1248i	0.158595	+	0.797312i
$994$	−4.28652	+	3.51641i	−0.135960	+	0.111534i
$995$	4.23137	−	10.2154i	0.134144	−	0.323851i
$996$	5.98273	+	5.98757i	0.189570	+	0.189723i
$997$	−12.9291	+	19.3497i	−0.409468	+	0.612813i	−0.977688	−	0.210065i	$-0.932633\pi$
$997$	−12.9291	+	19.3497i	−0.409468	+	0.612813i	0.568219	+	0.822877i	$0.307633\pi$
$998$	−10.1255	+	12.3328i	−0.320516	+	0.390389i
$999$	−26.0800	+	26.0800i	−0.825134	+	0.825134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.s.c.107.14	yes	112
4.3	odd	2		544.2.cc.c.175.8		112
8.3	odd	2	inner	136.2.s.c.107.5	yes	112
8.5	even	2		544.2.cc.c.175.7		112
17.7	odd	16	inner	136.2.s.c.75.5	✓	112
68.7	even	16		544.2.cc.c.143.7		112
136.75	even	16	inner	136.2.s.c.75.14	yes	112
136.109	odd	16		544.2.cc.c.143.8		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.75.5	✓	112	17.7	odd	16	inner
136.2.s.c.75.14	yes	112	136.75	even	16	inner
136.2.s.c.107.5	yes	112	8.3	odd	2	inner
136.2.s.c.107.14	yes	112	1.1	even	1	trivial
544.2.cc.c.143.7		112	68.7	even	16
544.2.cc.c.143.8		112	136.109	odd	16
544.2.cc.c.175.7		112	8.5	even	2
544.2.cc.c.175.8		112	4.3	odd	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40738 + 0.138902i) q^{2} +(-0.456483 - 0.683175i) q^{3} +(1.96141 + 0.390973i) q^{4} +(1.61884 + 0.322007i) q^{5} +(-0.547549 - 1.02489i) q^{6} +(-4.21158 + 0.837735i) q^{7} +(2.70614 + 0.822690i) q^{8} +(0.889699 - 2.14792i) q^{9} +O(q^{10})\)	\(q+(1.40738 + 0.138902i) q^{2} +(-0.456483 - 0.683175i) q^{3} +(1.96141 + 0.390973i) q^{4} +(1.61884 + 0.322007i) q^{5} +(-0.547549 - 1.02489i) q^{6} +(-4.21158 + 0.837735i) q^{7} +(2.70614 + 0.822690i) q^{8} +(0.889699 - 2.14792i) q^{9} +(2.23359 + 0.678044i) q^{10} +(-0.106698 - 0.0712931i) q^{11} +(-0.628249 - 1.51846i) q^{12} +(-2.31804 + 2.31804i) q^{13} +(-6.04364 + 0.594013i) q^{14} +(-0.518985 - 1.25294i) q^{15} +(3.69428 + 1.53372i) q^{16} +(-2.89543 - 2.93539i) q^{17} +(1.55049 - 2.89935i) q^{18} +(1.68438 + 4.06645i) q^{19} +(3.04931 + 1.26451i) q^{20} +(2.49484 + 2.49484i) q^{21} +(-0.140261 - 0.115157i) q^{22} +(-2.14808 - 1.43530i) q^{23} +(-0.673265 - 2.22431i) q^{24} +(-2.10245 - 0.870864i) q^{25} +(-3.58433 + 2.94037i) q^{26} +(-4.29112 + 0.853557i) q^{27} +(-8.58818 - 0.00347072i) q^{28} +(-0.908461 + 4.56714i) q^{29} +(-0.556371 - 1.83545i) q^{30} +(-2.02231 - 3.02660i) q^{31} +(4.98620 + 2.67166i) q^{32} +0.105437i q^{33} +(-3.66723 - 4.53337i) q^{34} -7.08762 q^{35} +(2.58485 - 3.86511i) q^{36} +(7.00926 - 4.68344i) q^{37} +(1.80572 + 5.95698i) q^{38} +(2.64177 + 0.525481i) q^{39} +(4.11589 + 2.20320i) q^{40} +(2.02785 + 10.1947i) q^{41} +(3.16463 + 3.85771i) q^{42} +(3.26274 - 7.87696i) q^{43} +(-0.181405 - 0.181551i) q^{44} +(2.13192 - 3.19065i) q^{45} +(-2.82379 - 2.31838i) q^{46} +(4.90893 - 4.90893i) q^{47} +(-0.638577 - 3.22396i) q^{48} +(10.5684 - 4.37759i) q^{49} +(-2.83798 - 1.51767i) q^{50} +(-0.683670 + 3.31804i) q^{51} +(-5.45291 + 3.64033i) q^{52} +(-1.32699 + 0.549659i) q^{53} +(-6.15778 + 0.605232i) q^{54} +(-0.149769 - 0.149769i) q^{55} +(-12.0863 - 1.19780i) q^{56} +(2.00921 - 3.00699i) q^{57} +(-1.91293 + 6.30150i) q^{58} +(12.6911 + 5.25683i) q^{59} +(-0.528077 - 2.66044i) q^{60} +(-0.813692 - 4.09070i) q^{61} +(-2.42575 - 4.54046i) q^{62} +(-1.94765 + 9.79148i) q^{63} +(6.64636 + 4.45262i) q^{64} +(-4.49895 + 3.00610i) q^{65} +(-0.0146454 + 0.148390i) q^{66} +3.72469i q^{67} +(-4.53147 - 6.88954i) q^{68} +2.12271i q^{69} +(-9.97494 - 0.984481i) q^{70} +(0.759116 - 0.507225i) q^{71} +(4.17472 - 5.08063i) q^{72} +(-0.631605 + 3.17529i) q^{73} +(10.5152 - 5.61776i) q^{74} +(0.364781 + 1.83388i) q^{75} +(1.71389 + 8.63453i) q^{76} +(0.509091 + 0.210872i) q^{77} +(3.64497 + 1.10649i) q^{78} +(6.49126 - 9.71485i) q^{79} +(5.48657 + 3.67243i) q^{80} +(-2.38989 - 2.38989i) q^{81} +(1.43789 + 14.6294i) q^{82} +(-4.75872 + 1.97112i) q^{83} +(3.91799 + 5.86882i) q^{84} +(-3.74201 - 5.68426i) q^{85} +(5.68603 - 10.6326i) q^{86} +(3.53486 - 1.46419i) q^{87} +(-0.230087 - 0.280708i) q^{88} +(-0.886097 + 0.886097i) q^{89} +(3.44360 - 4.19431i) q^{90} +(7.82069 - 11.7045i) q^{91} +(-3.65211 - 3.65506i) q^{92} +(-1.14455 + 2.76318i) q^{93} +(7.59057 - 6.22685i) q^{94} +(1.41731 + 7.12530i) q^{95} +(-0.450905 - 4.62602i) q^{96} +(-8.67498 - 1.72556i) q^{97} +(15.4818 - 4.69294i) q^{98} +(-0.248061 + 0.165749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more