LMFDB - Embedded newform 536.2.c.a.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [536,2,Mod(269,536)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(536, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("536.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 536 = 2^{3} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	536.c (of order $2$, degree $1$, 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:	$4.27998154834$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			269.1
Character	$\chi$	$=$	536.269
Dual form			536.2.c.a.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41318 - 0.0539790i) q^{2} +0.637598i q^{3} +(1.99417 + 0.152564i) q^{4} +3.76727i q^{5} +(0.0344169 - 0.901042i) q^{6} +3.61196 q^{7} +(-2.80990 - 0.323245i) q^{8} +2.59347 q^{9} +O(q^{10})$	\(q+(-1.41318 - 0.0539790i) q^{2} +0.637598i q^{3} +(1.99417 + 0.152564i) q^{4} +3.76727i q^{5} +(0.0344169 - 0.901042i) q^{6} +3.61196 q^{7} +(-2.80990 - 0.323245i) q^{8} +2.59347 q^{9} +(0.203353 - 5.32384i) q^{10} +2.97019i q^{11} +(-0.0972747 + 1.27148i) q^{12} -0.741673i q^{13} +(-5.10436 - 0.194970i) q^{14} -2.40200 q^{15} +(3.95345 + 0.608479i) q^{16} +6.44337 q^{17} +(-3.66505 - 0.139993i) q^{18} -5.81462i q^{19} +(-0.574751 + 7.51259i) q^{20} +2.30298i q^{21} +(0.160328 - 4.19742i) q^{22} -4.96502 q^{23} +(0.206100 - 1.79158i) q^{24} -9.19234 q^{25} +(-0.0400347 + 1.04812i) q^{26} +3.56638i q^{27} +(7.20287 + 0.551056i) q^{28} -5.34206i q^{29} +(3.39447 + 0.129658i) q^{30} -1.06469 q^{31} +(-5.55410 - 1.07330i) q^{32} -1.89379 q^{33} +(-9.10565 - 0.347806i) q^{34} +13.6072i q^{35} +(5.17182 + 0.395671i) q^{36} +6.66760i q^{37} +(-0.313867 + 8.21712i) q^{38} +0.472889 q^{39} +(1.21775 - 10.5856i) q^{40} -2.07194 q^{41} +(0.124312 - 3.25453i) q^{42} -8.81268i q^{43} +(-0.453145 + 5.92307i) q^{44} +9.77030i q^{45} +(7.01649 + 0.268007i) q^{46} +5.03520 q^{47} +(-0.387965 + 2.52071i) q^{48} +6.04627 q^{49} +(12.9905 + 0.496193i) q^{50} +4.10828i q^{51} +(0.113153 - 1.47902i) q^{52} +9.77188i q^{53} +(0.192510 - 5.03995i) q^{54} -11.1895 q^{55} +(-10.1492 - 1.16755i) q^{56} +3.70739 q^{57} +(-0.288359 + 7.54931i) q^{58} -10.2586i q^{59} +(-4.79001 - 0.366460i) q^{60} +10.1557i q^{61} +(1.50460 + 0.0574708i) q^{62} +9.36751 q^{63} +(7.79103 + 1.81657i) q^{64} +2.79408 q^{65} +(2.67627 + 0.102225i) q^{66} -1.00000i q^{67} +(12.8492 + 0.983028i) q^{68} -3.16569i q^{69} +(0.734505 - 19.2295i) q^{70} -6.60715 q^{71} +(-7.28738 - 0.838325i) q^{72} -6.68651 q^{73} +(0.359910 - 9.42255i) q^{74} -5.86101i q^{75} +(0.887103 - 11.5954i) q^{76} +10.7282i q^{77} +(-0.668279 - 0.0255261i) q^{78} +1.93675 q^{79} +(-2.29231 + 14.8937i) q^{80} +5.50649 q^{81} +(2.92804 + 0.111841i) q^{82} +2.24564i q^{83} +(-0.351352 + 4.59254i) q^{84} +24.2739i q^{85} +(-0.475699 + 12.4539i) q^{86} +3.40609 q^{87} +(0.960098 - 8.34592i) q^{88} -17.4282 q^{89} +(0.527391 - 13.8072i) q^{90} -2.67890i q^{91} +(-9.90111 - 0.757485i) q^{92} -0.678843i q^{93} +(-7.11566 - 0.271795i) q^{94} +21.9053 q^{95} +(0.684331 - 3.54128i) q^{96} -12.2295 q^{97} +(-8.54448 - 0.326371i) q^{98} +7.70310i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 4 q^{4} + 2 q^{6} - 6 q^{8} - 66 q^{9}+O(q^{10}) $ 66 * q - 4 * q^4 + 2 * q^6 - 6 * q^8 - 66 * q^9	$ 66 q - 4 q^{4} + 2 q^{6} - 6 q^{8} - 66 q^{9} - 4 q^{10} + 4 q^{12} - 2 q^{14} + 8 q^{15} - 12 q^{16} - 4 q^{17} - 10 q^{18} + 22 q^{20} + 8 q^{22} - 12 q^{23} - 62 q^{25} - 24 q^{26} + 10 q^{28} + 22 q^{30} - 16 q^{31} + 10 q^{32} - 10 q^{34} + 2 q^{36} + 8 q^{38} + 8 q^{39} - 18 q^{40} + 4 q^{41} + 28 q^{42} + 34 q^{44} + 18 q^{46} + 20 q^{47} - 38 q^{48} + 66 q^{49} - 32 q^{50} - 6 q^{52} + 38 q^{54} + 16 q^{55} - 30 q^{56} + 2 q^{58} + 18 q^{60} + 22 q^{62} - 40 q^{63} + 26 q^{64} + 16 q^{65} - 34 q^{66} + 26 q^{68} - 18 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{73} - 4 q^{74} - 30 q^{76} - 36 q^{78} + 16 q^{79} - 32 q^{80} + 66 q^{81} + 16 q^{82} - 6 q^{84} + 2 q^{86} + 32 q^{87} + 22 q^{88} - 20 q^{89} - 18 q^{90} + 8 q^{92} - 16 q^{94} - 64 q^{96} + 12 q^{97} - 46 q^{98}+O(q^{100}) $ 66 * q - 4 * q^4 + 2 * q^6 - 6 * q^8 - 66 * q^9 - 4 * q^10 + 4 * q^12 - 2 * q^14 + 8 * q^15 - 12 * q^16 - 4 * q^17 - 10 * q^18 + 22 * q^20 + 8 * q^22 - 12 * q^23 - 62 * q^25 - 24 * q^26 + 10 * q^28 + 22 * q^30 - 16 * q^31 + 10 * q^32 - 10 * q^34 + 2 * q^36 + 8 * q^38 + 8 * q^39 - 18 * q^40 + 4 * q^41 + 28 * q^42 + 34 * q^44 + 18 * q^46 + 20 * q^47 - 38 * q^48 + 66 * q^49 - 32 * q^50 - 6 * q^52 + 38 * q^54 + 16 * q^55 - 30 * q^56 + 2 * q^58 + 18 * q^60 + 22 * q^62 - 40 * q^63 + 26 * q^64 + 16 * q^65 - 34 * q^66 + 26 * q^68 - 18 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^73 - 4 * q^74 - 30 * q^76 - 36 * q^78 + 16 * q^79 - 32 * q^80 + 66 * q^81 + 16 * q^82 - 6 * q^84 + 2 * q^86 + 32 * q^87 + 22 * q^88 - 20 * q^89 - 18 * q^90 + 8 * q^92 - 16 * q^94 - 64 * q^96 + 12 * q^97 - 46 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$.

$n$	$135$	$269$	$337$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.41318	−	0.0539790i	−0.999271	−	0.0381689i
$2$	−1.41318	−	0.0539790i	−0.999271	−	0.0381689i
$3$			0.637598i			0.368117i	0.982915	+	0.184059i	$0.0589236\pi$
$3$			0.637598i			0.368117i	−0.982915	+	0.184059i	$0.941076\pi$
$4$	1.99417	+	0.152564i	0.997086	+	0.0762822i
$5$			3.76727i			1.68478i	0.538872	+	0.842388i	$0.318851\pi$
$5$			3.76727i			1.68478i	−0.538872	+	0.842388i	$0.681149\pi$
$6$	0.0344169	−	0.901042i	0.0140506	−	0.367849i
$7$	3.61196			1.36519			0.682597	−	0.730795i	$-0.260851\pi$
$7$	3.61196			1.36519			0.682597	+	0.730795i	$0.260851\pi$
$8$	−2.80990	−	0.323245i	−0.993448	−	0.114284i
$9$	2.59347			0.864490
$10$	0.203353	−	5.32384i	0.0643060	−	1.68355i
$11$			2.97019i			0.895546i	0.894147	+	0.447773i	$0.147783\pi$
$11$			2.97019i			0.895546i	−0.894147	+	0.447773i	$0.852217\pi$
$12$	−0.0972747	+	1.27148i	−0.0280808	+	0.367045i
$13$		−	0.741673i		−	0.205703i	−0.994697	−	0.102852i	$-0.967203\pi$
$13$		−	0.741673i		−	0.205703i	0.994697	−	0.102852i	$-0.0327967\pi$
$14$	−5.10436	−	0.194970i	−1.36420	−	0.0521079i
$15$	−2.40200			−0.620195
$16$	3.95345	+	0.608479i	0.988362	+	0.152120i
$17$	6.44337			1.56275			0.781373	−	0.624065i	$-0.214520\pi$
$17$	6.44337			1.56275			0.781373	+	0.624065i	$0.214520\pi$
$18$	−3.66505	−	0.139993i	−0.863860	−	0.0329966i
$19$		−	5.81462i		−	1.33397i	−0.745073	−	0.666983i	$-0.767586\pi$
$19$		−	5.81462i		−	1.33397i	0.745073	−	0.666983i	$-0.232414\pi$
$20$	−0.574751	+	7.51259i	−0.128518	+	1.67987i
$21$			2.30298i			0.502551i
$22$	0.160328	−	4.19742i	0.0341820	−	0.894893i
$23$	−4.96502			−1.03528			−0.517639	−	0.855599i	$-0.673189\pi$
$23$	−4.96502			−1.03528			−0.517639	+	0.855599i	$0.673189\pi$
$24$	0.206100	−	1.79158i	0.0420700	−	0.365705i
$25$	−9.19234			−1.83847
$26$	−0.0400347	+	1.04812i	−0.00785146	+	0.205553i
$27$			3.56638i			0.686351i
$28$	7.20287	+	0.551056i	1.36122	+	0.104140i
$29$		−	5.34206i		−	0.991996i	−0.868324	−	0.495998i	$-0.834802\pi$
$29$		−	5.34206i		−	0.991996i	0.868324	−	0.495998i	$-0.165198\pi$
$30$	3.39447	+	0.129658i	0.619743	+	0.0236722i
$31$	−1.06469			−0.191224			−0.0956119	−	0.995419i	$-0.530481\pi$
$31$	−1.06469			−0.191224			−0.0956119	+	0.995419i	$0.530481\pi$
$32$	−5.55410	−	1.07330i	−0.981836	−	0.189734i
$33$	−1.89379			−0.329666
$34$	−9.10565	−	0.347806i	−1.56161	−	0.0596483i
$35$			13.6072i			2.30004i
$36$	5.17182	+	0.395671i	0.861971	+	0.0659451i
$37$			6.66760i			1.09615i	0.836430	+	0.548074i	$0.184639\pi$
$37$			6.66760i			1.09615i	−0.836430	+	0.548074i	$0.815361\pi$
$38$	−0.313867	+	8.21712i	−0.0509160	+	1.33299i
$39$	0.472889			0.0757229
$40$	1.21775	−	10.5856i	0.192543	−	1.67374i
$41$	−2.07194			−0.323583			−0.161792	−	0.986825i	$-0.551727\pi$
$41$	−2.07194			−0.323583			−0.161792	+	0.986825i	$0.551727\pi$
$42$	0.124312	−	3.25453i	0.0191818	−	0.502185i
$43$		−	8.81268i		−	1.34392i	−0.740587	−	0.671961i	$-0.765452\pi$
$43$		−	8.81268i		−	1.34392i	0.740587	−	0.671961i	$-0.234548\pi$
$44$	−0.453145	+	5.92307i	−0.0683142	+	0.892937i
$45$			9.77030i			1.45647i
$46$	7.01649	+	0.268007i	1.03452	+	0.0395154i
$47$	5.03520			0.734460			0.367230	−	0.930130i	$-0.380306\pi$
$47$	5.03520			0.734460			0.367230	+	0.930130i	$0.380306\pi$
$48$	−0.387965	+	2.52071i	−0.0559979	+	0.363833i
$49$	6.04627			0.863752
$50$	12.9905	+	0.496193i	1.83713	+	0.0701723i
$51$			4.10828i			0.575274i
$52$	0.113153	−	1.47902i	0.0156915	−	0.205104i
$53$			9.77188i			1.34227i	0.741335	+	0.671135i	$0.234193\pi$
$53$			9.77188i			1.34227i	−0.741335	+	0.671135i	$0.765807\pi$
$54$	0.192510	−	5.03995i	0.0261973	−	0.685851i
$55$	−11.1895			−1.50879
$56$	−10.1492	−	1.16755i	−1.35625	−	0.156020i
$57$	3.70739			0.491056
$58$	−0.288359	+	7.54931i	−0.0378634	+	0.991273i
$59$		−	10.2586i		−	1.33555i	−0.744361	−	0.667777i	$-0.767246\pi$
$59$		−	10.2586i		−	1.33555i	0.744361	−	0.667777i	$-0.232754\pi$
$60$	−4.79001	−	0.366460i	−0.618388	−	0.0473098i
$61$			10.1557i			1.30031i	0.759802	+	0.650154i	$0.225296\pi$
$61$			10.1557i			1.30031i	−0.759802	+	0.650154i	$0.774704\pi$
$62$	1.50460	+	0.0574708i	0.191084	+	0.00729880i
$63$	9.36751			1.18020
$64$	7.79103	+	1.81657i	0.973878	+	0.227071i
$65$	2.79408			0.346564
$66$	2.67627	+	0.102225i	0.329426	+	0.0125830i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$	12.8492	+	0.983028i	1.55819	+	0.119210i
$69$		−	3.16569i		−	0.381104i
$70$	0.734505	−	19.2295i	0.0877901	−	2.29837i
$71$	−6.60715			−0.784124			−0.392062	−	0.919939i	$-0.628238\pi$
$71$	−6.60715			−0.784124			−0.392062	+	0.919939i	$0.628238\pi$
$72$	−7.28738	−	0.838325i	−0.858826	−	0.0987975i
$73$	−6.68651			−0.782597			−0.391298	−	0.920264i	$-0.627974\pi$
$73$	−6.68651			−0.782597			−0.391298	+	0.920264i	$0.627974\pi$
$74$	0.359910	−	9.42255i	0.0418387	−	1.09535i
$75$		−	5.86101i		−	0.676772i
$76$	0.887103	−	11.5954i	0.101758	−	1.33008i
$77$			10.7282i			1.22259i
$78$	−0.668279	−	0.0255261i	−0.0756677	−	0.00289026i
$79$	1.93675			0.217901			0.108951	−	0.994047i	$-0.465251\pi$
$79$	1.93675			0.217901			0.108951	+	0.994047i	$0.465251\pi$
$80$	−2.29231	+	14.8937i	−0.256288	+	1.66517i
$81$	5.50649			0.611832
$82$	2.92804	+	0.111841i	0.323348	+	0.0123508i
$83$			2.24564i			0.246491i	0.992376	+	0.123246i	$0.0393303\pi$
$83$			2.24564i			0.246491i	−0.992376	+	0.123246i	$0.960670\pi$
$84$	−0.351352	+	4.59254i	−0.0383357	+	0.501087i
$85$			24.2739i			2.63288i
$86$	−0.475699	+	12.4539i	−0.0512960	+	1.34294i
$87$	3.40609			0.365171
$88$	0.960098	−	8.34592i	0.102347	−	0.889678i
$89$	−17.4282			−1.84739			−0.923694	−	0.383131i	$-0.874846\pi$
$89$	−17.4282			−1.84739			−0.923694	+	0.383131i	$0.874846\pi$
$90$	0.527391	−	13.8072i	0.0555919	−	1.45541i
$91$		−	2.67890i		−	0.280825i
$92$	−9.90111	−	0.757485i	−1.03226	−	0.0789733i
$93$		−	0.678843i		−	0.0703928i
$94$	−7.11566	−	0.271795i	−0.733925	−	0.0280335i
$95$	21.9053			2.24743
$96$	0.684331	−	3.54128i	0.0698442	−	0.361431i
$97$	−12.2295			−1.24172			−0.620861	−	0.783921i	$-0.713217\pi$
$97$	−12.2295			−1.24172			−0.620861	+	0.783921i	$0.713217\pi$
$98$	−8.54448	−	0.326371i	−0.863123	−	0.0329685i
$99$			7.70310i			0.774190i
$100$	−18.3311	−	1.40242i	−1.83311	−	0.140242i
$101$		−	12.3179i		−	1.22568i	−0.790207	−	0.612840i	$-0.790027\pi$
$101$		−	12.3179i		−	1.22568i	0.790207	−	0.612840i	$-0.209973\pi$
$102$	0.221760	−	5.80575i	0.0219576	−	0.574854i
$103$	3.40928			0.335926			0.167963	−	0.985793i	$-0.446281\pi$
$103$	3.40928			0.335926			0.167963	+	0.985793i	$0.446281\pi$
$104$	−0.239742	+	2.08402i	−0.0235086	+	0.204355i
$105$	−8.67595			−0.846686
$106$	0.527476	−	13.8095i	0.0512330	−	1.34129i
$107$		−	12.7084i		−	1.22857i	−0.789084	−	0.614285i	$-0.789445\pi$
$107$		−	12.7084i		−	1.22857i	0.789084	−	0.614285i	$-0.210555\pi$
$108$	−0.544103	+	7.11198i	−0.0523563	+	0.684351i
$109$		−	9.98627i		−	0.956512i	−0.878221	−	0.478256i	$-0.841269\pi$
$109$		−	9.98627i		−	0.956512i	0.878221	−	0.478256i	$-0.158731\pi$
$110$	15.8128	+	0.603998i	1.50769	+	0.0575890i
$111$	−4.25125			−0.403511
$112$	14.2797	+	2.19780i	1.34931	+	0.207673i
$113$	−1.47437			−0.138697			−0.0693484	−	0.997593i	$-0.522092\pi$
$113$	−1.47437			−0.138697			−0.0693484	+	0.997593i	$0.522092\pi$
$114$	−5.23922	−	0.200121i	−0.490698	−	0.0187430i
$115$		−	18.7046i		−	1.74421i
$116$	0.815008	−	10.6530i	0.0756716	−	0.989106i
$117$		−	1.92351i		−	0.177828i
$118$	−0.553748	+	14.4973i	−0.0509766	+	1.33458i
$119$	23.2732			2.13345
$120$	6.74938	+	0.776435i	0.616131	+	0.0708785i
$121$	2.17797			0.197997
$122$	0.548196	−	14.3519i	0.0496313	−	1.29936i
$123$		−	1.32107i		−	0.119117i
$124$	−2.12317	−	0.162433i	−0.190667	−	0.0145870i
$125$		−	15.7937i		−	1.41263i
$126$	−13.2380	−	0.505648i	−1.17934	−	0.0450467i
$127$	−16.2239			−1.43964			−0.719819	−	0.694162i	$-0.755775\pi$
$127$	−16.2239			−1.43964			−0.719819	+	0.694162i	$0.755775\pi$
$128$	−10.9121	−	2.98769i	−0.964502	−	0.264077i
$129$	5.61895			0.494721
$130$	−3.94855	−	0.150822i	−0.346311	−	0.0132279i
$131$		−	21.2434i		−	1.85605i	−0.372521	−	0.928024i	$-0.621507\pi$
$131$		−	21.2434i		−	1.85605i	0.372521	−	0.928024i	$-0.378493\pi$
$132$	−3.77654	−	0.288924i	−0.328705	−	0.0251476i
$133$		−	21.0022i		−	1.82112i
$134$	−0.0539790	+	1.41318i	−0.00466307	+	0.122080i
$135$	−13.4355			−1.15635
$136$	−18.1052	−	2.08278i	−1.55251	−	0.178597i
$137$	10.6352			0.908623			0.454312	−	0.890843i	$-0.349885\pi$
$137$	10.6352			0.908623			0.454312	+	0.890843i	$0.349885\pi$
$138$	−0.170881	+	4.47370i	−0.0145463	+	0.380826i
$139$		−	1.15592i		−	0.0980442i	−0.998798	−	0.0490221i	$-0.984390\pi$
$139$		−	1.15592i		−	0.0980442i	0.998798	−	0.0490221i	$-0.0156105\pi$
$140$	−2.07598	+	27.1352i	−0.175452	+	2.29334i
$141$			3.21043i			0.270367i
$142$	9.33711	+	0.356647i	0.783553	+	0.0299291i
$143$	2.20291			0.184217
$144$	10.2531	+	1.57807i	0.854429	+	0.131506i
$145$	20.1250			1.67129
$146$	9.44926	+	0.360931i	0.782027	+	0.0298709i
$147$			3.85509i			0.317962i
$148$	−1.01724	+	13.2964i	−0.0836165	+	1.09295i
$149$		−	3.95863i		−	0.324303i	−0.986766	−	0.162152i	$-0.948157\pi$
$149$		−	3.95863i		−	0.324303i	0.986766	−	0.162152i	$-0.0518434\pi$
$150$	−0.316372	+	8.28269i	−0.0258316	+	0.676279i
$151$	12.7029			1.03375			0.516874	−	0.856062i	$-0.327096\pi$
$151$	12.7029			1.03375			0.516874	+	0.856062i	$0.327096\pi$
$152$	−1.87954	+	16.3385i	−0.152451	+	1.32523i
$153$	16.7107			1.35098
$154$	0.579098	−	15.1609i	0.0466650	−	1.22170i
$155$		−	4.01097i		−	0.322169i
$156$	0.943023	+	0.0721460i	0.0755022	+	0.00577630i
$157$		−	1.94708i		−	0.155394i	−0.996977	−	0.0776970i	$-0.975243\pi$
$157$		−	1.94708i		−	0.155394i	0.996977	−	0.0776970i	$-0.0247567\pi$
$158$	−2.73698	−	0.104544i	−0.217742	−	0.00831704i
$159$	−6.23053			−0.494113
$160$	4.04340	−	20.9238i	0.319658	−	1.65417i
$161$	−17.9335			−1.41336
$162$	−7.78168	−	0.297235i	−0.611386	−	0.0233530i
$163$			13.1473i			1.02978i	0.857257	+	0.514888i	$0.172167\pi$
$163$			13.1473i			1.02978i	−0.857257	+	0.514888i	$0.827833\pi$
$164$	−4.13181	−	0.316105i	−0.322641	−	0.0246836i
$165$		−	7.13441i		−	0.555413i
$166$	0.121218	−	3.17351i	0.00940831	−	0.246312i
$167$	−12.1550			−0.940579			−0.470289	−	0.882512i	$-0.655850\pi$
$167$	−12.1550			−0.940579			−0.470289	+	0.882512i	$0.655850\pi$
$168$	0.744426	−	6.47113i	0.0574337	−	0.499259i
$169$	12.4499			0.957686
$170$	1.31028	−	34.3035i	0.100494	−	2.63096i
$171$		−	15.0800i		−	1.15320i
$172$	1.34450	−	17.5740i	0.102517	−	1.34001i
$173$			14.9124i			1.13377i	0.823796	+	0.566886i	$0.191852\pi$
$173$			14.9124i			1.13377i	−0.823796	+	0.566886i	$0.808148\pi$
$174$	−4.81343	−	0.183857i	−0.364905	−	0.0139382i
$175$	−33.2024			−2.50986
$176$	−1.80730	+	11.7425i	−0.136230	+	0.885124i
$177$	6.54085			0.491641
$178$	24.6293	+	0.940757i	1.84604	+	0.0705127i
$179$		−	2.65803i		−	0.198670i	−0.995054	−	0.0993352i	$-0.968328\pi$
$179$		−	2.65803i		−	0.198670i	0.995054	−	0.0993352i	$-0.0316716\pi$
$180$	−1.49060	+	19.4837i	−0.111103	+	1.45223i
$181$		−	5.76766i		−	0.428707i	−0.976756	−	0.214353i	$-0.931236\pi$
$181$		−	5.76766i		−	0.428707i	0.976756	−	0.214353i	$-0.0687644\pi$
$182$	−0.144604	+	3.78577i	−0.0107188	+	0.280620i
$183$	−6.47527			−0.478666
$184$	13.9512	+	1.60492i	1.02850	+	0.118316i
$185$	−25.1187			−1.84676
$186$	−0.0366433	+	0.959330i	−0.00268681	+	0.0703415i
$187$			19.1380i			1.39951i
$188$	10.0411	+	0.768192i	0.732320	+	0.0560262i
$189$			12.8816i			0.937002i
$190$	−30.9561	−	1.18242i	−2.24579	−	0.0857820i
$191$	−6.73297			−0.487180			−0.243590	−	0.969878i	$-0.578325\pi$
$191$	−6.73297			−0.487180			−0.243590	+	0.969878i	$0.578325\pi$
$192$	−1.15824	+	4.96754i	−0.0835887	+	0.358501i
$193$	12.9420			0.931584			0.465792	−	0.884894i	$-0.345770\pi$
$193$	12.9420			0.931584			0.465792	+	0.884894i	$0.345770\pi$
$194$	17.2826	+	0.660138i	1.24082	+	0.0473951i
$195$			1.78150i			0.127576i
$196$	12.0573	+	0.922444i	0.861236	+	0.0658889i
$197$			19.2905i			1.37439i	0.726472	+	0.687196i	$0.241159\pi$
$197$			19.2905i			1.37439i	−0.726472	+	0.687196i	$0.758841\pi$
$198$	0.415805	−	10.8859i	0.0295500	−	0.773626i
$199$	1.07015			0.0758608			0.0379304	−	0.999280i	$-0.487923\pi$
$199$	1.07015			0.0758608			0.0379304	+	0.999280i	$0.487923\pi$
$200$	25.8295	+	2.97137i	1.82642	+	0.210108i
$201$	0.637598			0.0449727
$202$	−0.664909	+	17.4075i	−0.0467828	+	1.22479i
$203$		−	19.2953i		−	1.35427i
$204$	−0.626776	+	8.19261i	−0.0438831	+	0.573597i
$205$		−	7.80558i		−	0.545165i
$206$	−4.81794	−	0.184029i	−0.335682	−	0.0128219i
$207$	−12.8766			−0.894988
$208$	0.451293	−	2.93217i	0.0312915	−	0.203309i
$209$	17.2705			1.19463
$210$	12.2607	+	0.468319i	0.846069	+	0.0323171i
$211$		−	16.0024i		−	1.10165i	−0.834620	−	0.550827i	$-0.814312\pi$
$211$		−	16.0024i		−	1.10165i	0.834620	−	0.550827i	$-0.185688\pi$
$212$	−1.49084	+	19.4868i	−0.102391	+	1.33836i
$213$		−	4.21270i		−	0.288650i
$214$	−0.685988	+	17.9593i	−0.0468931	+	1.22767i
$215$	33.1998			2.26421
$216$	1.15281	−	10.0212i	0.0784391	−	0.681854i
$217$	−3.84561			−0.261057
$218$	−0.539049	+	14.1124i	−0.0365090	+	0.955815i
$219$		−	4.26330i		−	0.288087i
$220$	−22.3138	−	1.70712i	−1.50440	−	0.115094i
$221$		−	4.77887i		−	0.321462i
$222$	6.00779	+	0.229478i	0.403217	+	0.0154016i
$223$	6.51096			0.436006			0.218003	−	0.975948i	$-0.430046\pi$
$223$	6.51096			0.436006			0.218003	+	0.975948i	$0.430046\pi$
$224$	−20.0612	−	3.87670i	−1.34040	−	0.259023i
$225$	−23.8400			−1.58934
$226$	2.08355	+	0.0795848i	0.138596	+	0.00529390i
$227$			22.8466i			1.51638i	0.652032	+	0.758191i	$0.273917\pi$
$227$			22.8466i			1.51638i	−0.652032	+	0.758191i	$0.726083\pi$
$228$	7.39317	+	0.565615i	0.489625	+	0.0374588i
$229$		−	9.40845i		−	0.621728i	−0.950454	−	0.310864i	$-0.899382\pi$
$229$		−	9.40845i		−	0.621728i	0.950454	−	0.310864i	$-0.100618\pi$
$230$	−1.00965	+	26.4330i	−0.0665746	+	1.74294i
$231$	−6.84028			−0.450058
$232$	−1.72679	+	15.0106i	−0.113370	+	0.985497i
$233$	−1.76238			−0.115457			−0.0577285	−	0.998332i	$-0.518386\pi$
$233$	−1.76238			−0.115457			−0.0577285	+	0.998332i	$0.518386\pi$
$234$	−0.103829	+	2.71827i	−0.00678751	+	0.177699i
$235$			18.9690i			1.23740i
$236$	1.56509	−	20.4574i	0.101879	−	1.33166i
$237$			1.23487i			0.0802132i
$238$	−32.8893	−	1.25626i	−2.13190	−	0.0814314i
$239$	−10.1937			−0.659378			−0.329689	−	0.944090i	$-0.606944\pi$
$239$	−10.1937			−0.659378			−0.329689	+	0.944090i	$0.606944\pi$
$240$	−9.49620	−	1.46157i	−0.612977	−	0.0943439i
$241$	7.33845			0.472711			0.236356	−	0.971667i	$-0.424047\pi$
$241$	7.33845			0.472711			0.236356	+	0.971667i	$0.424047\pi$
$242$	−3.07787	−	0.117565i	−0.197853	−	0.00755734i
$243$			14.2101i			0.911577i
$244$	−1.54940	+	20.2523i	−0.0991903	+	1.29652i
$245$			22.7779i			1.45523i
$246$	−0.0713098	+	1.86691i	−0.00454655	+	0.119030i
$247$	−4.31255			−0.274401
$248$	2.99166	+	0.344155i	0.189971	+	0.0218539i
$249$	−1.43182			−0.0907378
$250$	−0.852526	+	22.3194i	−0.0539185	+	1.41160i
$251$			16.2761i			1.02734i	0.857988	+	0.513670i	$0.171715\pi$
$251$			16.2761i			1.02734i	−0.857988	+	0.513670i	$0.828285\pi$
$252$	18.6804	+	1.42915i	1.17676	+	0.0900278i
$253$		−	14.7471i		−	0.927140i
$254$	22.9273	+	0.875749i	1.43859	+	0.0549494i
$255$	−15.4770			−0.969207
$256$	15.2595	+	4.81118i	0.953719	+	0.300699i
$257$	28.4552			1.77499			0.887493	−	0.460821i	$-0.152445\pi$
$257$	28.4552			1.77499			0.887493	+	0.460821i	$0.152445\pi$
$258$	−7.94060	−	0.303305i	−0.494360	−	0.0188829i
$259$			24.0831i			1.49645i
$260$	5.57189	+	0.426278i	0.345554	+	0.0264366i
$261$		−	13.8545i		−	0.857571i
$262$	−1.14670	+	30.0209i	−0.0708433	+	1.85469i
$263$	−7.58696			−0.467832			−0.233916	−	0.972257i	$-0.575154\pi$
$263$	−7.58696			−0.467832			−0.233916	+	0.972257i	$0.575154\pi$
$264$	5.32134	+	0.612156i	0.327506	+	0.0376756i
$265$	−36.8133			−2.26142
$266$	−1.13368	+	29.6799i	−0.0695101	+	1.81979i
$267$		−	11.1122i		−	0.680055i
$268$	0.152564	−	1.99417i	0.00931935	−	0.121813i
$269$		−	6.92827i		−	0.422424i	−0.977440	−	0.211212i	$-0.932259\pi$
$269$		−	6.92827i		−	0.422424i	0.977440	−	0.211212i	$-0.0677411\pi$
$270$	18.9869	+	0.725236i	1.15550	+	0.0441365i
$271$	1.53326			0.0931391			0.0465695	−	0.998915i	$-0.485171\pi$
$271$	1.53326			0.0931391			0.0465695	+	0.998915i	$0.485171\pi$
$272$	25.4735	+	3.92065i	1.54456	+	0.237725i
$273$	1.70806			0.103376
$274$	−15.0294	−	0.574075i	−0.907961	−	0.0346811i
$275$		−	27.3030i		−	1.64643i
$276$	0.482971	−	6.31293i	0.0290714	−	0.379994i
$277$			1.42714i			0.0857484i	0.999080	+	0.0428742i	$0.0136515\pi$
$277$			1.42714i			0.0857484i	−0.999080	+	0.0428742i	$0.986349\pi$
$278$	−0.0623956	+	1.63353i	−0.00374224	+	0.0979728i
$279$	−2.76124			−0.165311
$280$	4.39847	−	38.2349i	0.262859	−	2.28497i
$281$	21.9847			1.31150			0.655750	−	0.754978i	$-0.272353\pi$
$281$	21.9847			1.31150			0.655750	+	0.754978i	$0.272353\pi$
$282$	0.173296	−	4.53693i	0.0103196	−	0.270170i
$283$		−	23.4215i		−	1.39226i	−0.717914	−	0.696132i	$-0.754903\pi$
$283$		−	23.4215i		−	1.39226i	0.717914	−	0.696132i	$-0.245097\pi$
$284$	−13.1758	−	1.00801i	−0.781839	−	0.0598147i
$285$			13.9667i			0.827318i
$286$	−3.11312	−	0.118911i	−0.184082	−	0.00703134i
$287$	−7.48378			−0.441754
$288$	−14.4044	−	2.78356i	−0.848787	−	0.164023i
$289$	24.5170			1.44217
$290$	−28.4403	−	1.08633i	−1.67007	−	0.0637913i
$291$		−	7.79753i		−	0.457099i
$292$	−13.3341	−	1.02012i	−0.780317	−	0.0596982i
$293$			31.5165i			1.84121i	0.390494	+	0.920605i	$0.372304\pi$
$293$			31.5165i			1.84121i	−0.390494	+	0.920605i	$0.627696\pi$
$294$	0.208094	−	5.44794i	0.0121363	−	0.317730i
$295$	38.6469			2.25011
$296$	2.15527	−	18.7353i	0.125272	−	1.08897i
$297$	−10.5928			−0.614659
$298$	−0.213683	+	5.59426i	−0.0123783	+	0.324067i
$299$			3.68242i			0.212960i
$300$	0.894182	−	11.6879i	0.0516256	−	0.674800i
$301$		−	31.8311i		−	1.83471i
$302$	−17.9515	−	0.685690i	−1.03299	−	0.0394570i
$303$	7.85388			0.451194
$304$	3.53807	−	22.9878i	0.202922	−	1.31844i
$305$	−38.2594			−2.19073
$306$	−23.6152	−	0.902025i	−1.34999	−	0.0515653i
$307$			8.14759i			0.465007i	0.972596	+	0.232504i	$0.0746918\pi$
$307$			8.14759i			0.465007i	−0.972596	+	0.232504i	$0.925308\pi$
$308$	−1.63674	+	21.3939i	−0.0932620	+	1.21903i
$309$			2.17375i			0.123660i
$310$	−0.216508	+	5.66824i	−0.0122968	+	0.321934i
$311$	29.5984			1.67837			0.839184	−	0.543847i	$-0.183033\pi$
$311$	29.5984			1.67837			0.839184	+	0.543847i	$0.183033\pi$
$312$	−1.32877	−	0.152859i	−0.0752267	−	0.00865393i
$313$	−2.81708			−0.159231			−0.0796155	−	0.996826i	$-0.525369\pi$
$313$	−2.81708			−0.159231			−0.0796155	+	0.996826i	$0.525369\pi$
$314$	−0.105101	+	2.75158i	−0.00593121	+	0.155281i
$315$			35.2900i			1.98836i
$316$	3.86221	+	0.295479i	0.217266	+	0.0166220i
$317$		−	34.7621i		−	1.95243i	−0.216797	−	0.976217i	$-0.569561\pi$
$317$		−	34.7621i		−	1.95243i	0.216797	−	0.976217i	$-0.430439\pi$
$318$	8.80488	+	0.336317i	0.493753	+	0.0188597i
$319$	15.8669			0.888378
$320$	−6.84350	+	29.3509i	−0.382563	+	1.64077i
$321$	8.10286			0.452258
$322$	25.3433	+	0.968030i	1.41233	+	0.0539462i
$323$		−	37.4657i		−	2.08465i
$324$	10.9809	+	0.840094i	0.610049	+	0.0466719i
$325$			6.81771i			0.378179i
$326$	0.709678	−	18.5795i	0.0393054	−	1.02903i
$327$	6.36723			0.352108
$328$	5.82195	+	0.669745i	0.321463	+	0.0369805i
$329$	18.1870			1.00268
$330$	−0.385108	+	10.0822i	−0.0211995	+	0.555008i
$331$		−	6.41424i		−	0.352559i	−0.984340	−	0.176279i	$-0.943594\pi$
$331$		−	6.41424i		−	0.352559i	0.984340	−	0.176279i	$-0.0564062\pi$
$332$	−0.342605	+	4.47820i	−0.0188029	+	0.245773i
$333$			17.2922i			0.947608i
$334$	17.1772	+	0.656112i	0.939893	+	0.0359008i
$335$	3.76727			0.205828
$336$	−1.40131	+	9.10471i	−0.0764480	+	0.496703i
$337$	35.0843			1.91116			0.955582	−	0.294726i	$-0.0952285\pi$
$337$	35.0843			1.91116			0.955582	+	0.294726i	$0.0952285\pi$
$338$	−17.5940	−	0.672034i	−0.956988	−	0.0365538i
$339$		−	0.940053i		−	0.0510567i
$340$	−3.70333	+	48.4064i	−0.200841	+	2.62520i
$341$		−	3.16233i		−	0.171250i
$342$	−0.814005	+	21.3108i	−0.0440163	+	1.15236i
$343$	−3.44485			−0.186004
$344$	−2.84865	+	24.7627i	−0.153589	+	1.33512i
$345$	11.9260			0.642075
$346$	0.804958	−	21.0740i	0.0432748	−	1.13295i
$347$			0.659693i			0.0354142i	0.999843	+	0.0177071i	$0.00563664\pi$
$347$			0.659693i			0.0354142i	−0.999843	+	0.0177071i	$0.994363\pi$
$348$	6.79233	+	0.519647i	0.364107	+	0.0278560i
$349$		−	5.46164i		−	0.292355i	−0.989258	−	0.146177i	$-0.953303\pi$
$349$		−	5.46164i		−	0.292355i	0.989258	−	0.146177i	$-0.0466970\pi$
$350$	46.9210	+	1.79223i	2.50803	+	0.0957987i
$351$	2.64509			0.141185
$352$	3.18789	−	16.4967i	0.169915	−	0.879279i
$353$	−18.3119			−0.974644			−0.487322	−	0.873222i	$-0.662026\pi$
$353$	−18.3119			−0.974644			−0.487322	+	0.873222i	$0.662026\pi$
$354$	−9.24342	−	0.353069i	−0.491282	−	0.0187654i
$355$		−	24.8909i		−	1.32107i
$356$	−34.7549	−	2.65892i	−1.84201	−	0.140923i
$357$			14.8389i			0.785360i
$358$	−0.143478	+	3.75628i	−0.00758303	+	0.198526i
$359$	−33.6128			−1.77401			−0.887007	−	0.461756i	$-0.847220\pi$
$359$	−33.6128			−1.77401			−0.887007	+	0.461756i	$0.847220\pi$
$360$	3.15820	−	27.4535i	0.166452	−	1.44693i
$361$	−14.8098			−0.779463
$362$	−0.311332	+	8.15076i	−0.0163633	+	0.428394i
$363$			1.38867i			0.0728863i
$364$	0.408704	−	5.34218i	0.0214219	−	0.280006i
$365$		−	25.1899i		−	1.31850i
$366$	9.15075	+	0.349529i	0.478317	+	0.0182702i
$367$	19.6977			1.02821			0.514107	−	0.857726i	$-0.328124\pi$
$367$	19.6977			1.02821			0.514107	+	0.857726i	$0.328124\pi$
$368$	−19.6290	−	3.02111i	−1.02323	−	0.157486i
$369$	−5.37352			−0.279734
$370$	35.4973	+	1.35588i	1.84542	+	0.0704889i
$371$			35.2957i			1.83246i
$372$	0.103567	−	1.35373i	0.00536971	−	0.0701877i
$373$			8.35290i			0.432497i	0.976338	+	0.216248i	$0.0693821\pi$
$373$			8.35290i			0.432497i	−0.976338	+	0.216248i	$0.930618\pi$
$374$	1.03305	−	27.0455i	0.0534178	−	1.39849i
$375$	10.0700			0.520013
$376$	−14.1484	−	1.62760i	−0.729648	−	0.0839372i
$377$	−3.96207			−0.204057
$378$	0.695338	−	18.2041i	0.0357643	−	0.936319i
$379$			14.4316i			0.741302i	0.928772	+	0.370651i	$0.120865\pi$
$379$			14.4316i			0.741302i	−0.928772	+	0.370651i	$0.879135\pi$
$380$	43.6829	+	3.34196i	2.24088	+	0.171439i
$381$		−	10.3443i		−	0.529955i
$382$	9.51492	+	0.363439i	0.486825	+	0.0185951i
$383$	−1.89070			−0.0966105			−0.0483052	−	0.998833i	$-0.515382\pi$
$383$	−1.89070			−0.0966105			−0.0483052	+	0.998833i	$0.515382\pi$
$384$	1.90495	−	6.95752i	0.0972114	−	0.355050i
$385$	−40.4161			−2.05979
$386$	−18.2894	−	0.698594i	−0.930905	−	0.0355575i
$387$		−	22.8554i		−	1.16181i
$388$	−24.3878	−	1.86579i	−1.23810	−	0.0947212i
$389$		−	16.3922i		−	0.831120i	−0.909566	−	0.415560i	$-0.863586\pi$
$389$		−	16.3922i		−	0.831120i	0.909566	−	0.415560i	$-0.136414\pi$
$390$	0.0961636	−	2.51759i	0.00486944	−	0.127483i
$391$	−31.9915			−1.61788
$392$	−16.9894	−	1.95442i	−0.858093	−	0.0987133i
$393$	13.5448			0.683243
$394$	1.04128	−	27.2610i	0.0524590	−	1.37339i
$395$			7.29626i			0.367114i
$396$	−1.17522	+	15.3613i	−0.0590569	+	0.771934i
$397$			16.9960i			0.853006i	0.904486	+	0.426503i	$0.140255\pi$
$397$			16.9960i			0.853006i	−0.904486	+	0.426503i	$0.859745\pi$
$398$	−1.51231	−	0.0577655i	−0.0758055	−	0.00289552i
$399$	13.3909			0.670386
$400$	−36.3414	−	5.59335i	−1.81707	−	0.279667i
$401$	−6.11225			−0.305231			−0.152616	−	0.988286i	$-0.548770\pi$
$401$	−6.11225			−0.305231			−0.152616	+	0.988286i	$0.548770\pi$
$402$	−0.901042	−	0.0344169i	−0.0449399	−	0.00171656i
$403$			0.789651i			0.0393353i
$404$	1.87928	−	24.5641i	0.0934974	−	1.22211i
$405$			20.7444i			1.03080i
$406$	−1.04154	+	27.2678i	−0.0516908	+	1.35328i
$407$	−19.8041			−0.981650
$408$	1.32798	−	11.5438i	0.0657447	−	0.571505i
$409$	−29.7848			−1.47276			−0.736382	−	0.676566i	$-0.763467\pi$
$409$	−29.7848			−1.47276			−0.736382	+	0.676566i	$0.763467\pi$
$410$	−0.421337	+	11.0307i	−0.0208084	+	0.544768i
$411$			6.78096i			0.334480i
$412$	6.79869	+	0.520134i	0.334948	+	0.0256252i
$413$		−	37.0536i		−	1.82329i
$414$	18.1970	+	0.695067i	0.894336	+	0.0341607i
$415$	−8.45995			−0.415283
$416$	−0.796034	+	4.11933i	−0.0390288	+	0.201967i
$417$	0.737015			0.0360918
$418$	−24.4064	−	0.932245i	−1.19376	−	0.0455976i
$419$			36.0287i			1.76012i	0.474866	+	0.880058i	$0.342496\pi$
$419$			36.0287i			1.76012i	−0.474866	+	0.880058i	$0.657504\pi$
$420$	−17.3013	−	1.32364i	−0.844219	−	0.0645870i
$421$			13.3139i			0.648880i	0.945906	+	0.324440i	$0.105176\pi$
$421$			13.3139i			0.648880i	−0.945906	+	0.324440i	$0.894824\pi$
$422$	−0.863795	+	22.6144i	−0.0420489	+	1.10085i
$423$	13.0586			0.634933
$424$	3.15871	−	27.4580i	0.153400	−	1.33348i
$425$	−59.2296			−2.87306
$426$	−0.227397	+	5.95332i	−0.0110174	+	0.288439i
$427$			36.6821i			1.77517i
$428$	1.93885	−	25.3428i	0.0937180	−	1.22499i
$429$			1.40457i			0.0678133i
$430$	−46.9173	−	1.79209i	−2.26256	−	0.0864222i
$431$	26.0268			1.25367			0.626834	−	0.779153i	$-0.284350\pi$
$431$	26.0268			1.25367			0.626834	+	0.779153i	$0.284350\pi$
$432$	−2.17007	+	14.0995i	−0.104408	+	0.678363i
$433$	−9.67776			−0.465084			−0.232542	−	0.972586i	$-0.574704\pi$
$433$	−9.67776			−0.465084			−0.232542	+	0.972586i	$0.574704\pi$
$434$	5.43456	+	0.207582i	0.260867	+	0.00996427i
$435$			12.8317i			0.615231i
$436$	1.52355	−	19.9144i	0.0729648	−	0.953725i
$437$			28.8697i			1.38103i
$438$	−0.230129	+	6.02483i	−0.0109960	+	0.287878i
$439$	−14.2932			−0.682176			−0.341088	−	0.940031i	$-0.610795\pi$
$439$	−14.2932			−0.682176			−0.341088	+	0.940031i	$0.610795\pi$
$440$	31.4414	+	3.61695i	1.49891	+	0.172431i
$441$	15.6808			0.746705
$442$	−0.257959	+	6.75342i	−0.0122698	+	0.321227i
$443$		−	27.1121i		−	1.28814i	−0.764968	−	0.644068i	$-0.777245\pi$
$443$		−	27.1121i		−	1.28814i	0.764968	−	0.644068i	$-0.222755\pi$
$444$	−8.47773	−	0.648589i	−0.402335	−	0.0307807i
$445$		−	65.6569i		−	3.11243i
$446$	−9.20118	−	0.351455i	−0.435689	−	0.0166419i
$447$	2.52401			0.119382
$448$	28.1409	+	6.56137i	1.32953	+	0.309996i
$449$	−39.2801			−1.85374			−0.926870	−	0.375382i	$-0.877512\pi$
$449$	−39.2801			−1.85374			−0.926870	+	0.375382i	$0.877512\pi$
$450$	33.6903	+	1.28686i	1.58818	+	0.0606632i
$451$		−	6.15407i		−	0.289784i
$452$	−2.94014	−	0.224936i	−0.138293	−	0.0105801i
$453$			8.09935i			0.380540i
$454$	1.23324	−	32.2864i	0.0578786	−	1.51528i
$455$	10.0921			0.473126
$456$	−10.4174	−	1.19839i	−0.487838	−	0.0561199i
$457$	24.1176			1.12817			0.564086	−	0.825716i	$-0.309229\pi$
$457$	24.1176			1.12817			0.564086	+	0.825716i	$0.309229\pi$
$458$	−0.507859	+	13.2959i	−0.0237307	+	0.621275i
$459$			22.9795i			1.07259i
$460$	2.85365	−	37.3002i	0.133052	−	1.73913i
$461$		−	14.3210i		−	0.666995i	−0.942751	−	0.333497i	$-0.891771\pi$
$461$		−	14.3210i		−	0.666995i	0.942751	−	0.333497i	$-0.108229\pi$
$462$	9.66657	+	0.369231i	0.449730	+	0.0171782i
$463$	20.6496			0.959667			0.479833	−	0.877360i	$-0.340697\pi$
$463$	20.6496			0.959667			0.479833	+	0.877360i	$0.340697\pi$
$464$	3.25053	−	21.1196i	0.150902	−	0.980451i
$465$	2.55739			0.118596
$466$	2.49056	+	0.0951312i	0.115373	+	0.00440687i
$467$		−	2.33197i		−	0.107911i	−0.998543	−	0.0539553i	$-0.982817\pi$
$467$		−	2.33197i		−	0.107911i	0.998543	−	0.0539553i	$-0.0171828\pi$
$468$	0.293458	−	3.83580i	0.0135651	−	0.177310i
$469$		−	3.61196i		−	0.166785i
$470$	1.02393	−	26.8066i	0.0472302	−	1.23650i
$471$	1.24145			0.0572032
$472$	−3.31603	+	28.8256i	−0.152633	+	1.32680i
$473$	26.1753			1.20354
$474$	0.0666568	−	1.74509i	0.00306165	−	0.0801547i
$475$			53.4499i			2.45245i
$476$	46.4108	+	3.55066i	2.12723	+	0.162744i
$477$			25.3431i			1.16038i
$478$	14.4056	+	0.550247i	0.658898	+	0.0251677i
$479$	6.65588			0.304115			0.152057	−	0.988372i	$-0.451410\pi$
$479$	6.65588			0.304115			0.152057	+	0.988372i	$0.451410\pi$
$480$	13.3410	+	2.57806i	0.608929	+	0.117672i
$481$	4.94518			0.225481
$482$	−10.3706	−	0.396122i	−0.472367	−	0.0180429i
$483$		−	11.4343i		−	0.520281i
$484$	4.34325	+	0.332281i	0.197421	+	0.0151037i
$485$		−	46.0720i		−	2.09202i
$486$	0.767045	−	20.0814i	0.0347939	−	0.910913i
$487$	12.2525			0.555215			0.277607	−	0.960695i	$-0.410459\pi$
$487$	12.2525			0.555215			0.277607	+	0.960695i	$0.410459\pi$
$488$	3.28279	−	28.5366i	0.148605	−	1.29179i
$489$	−8.38269			−0.379079
$490$	1.22953	−	32.1894i	0.0555445	−	1.45417i
$491$		−	7.67576i		−	0.346402i	−0.984886	−	0.173201i	$-0.944589\pi$
$491$		−	7.67576i		−	0.346402i	0.984886	−	0.173201i	$-0.0554111\pi$
$492$	0.201548	−	2.63444i	0.00908647	−	0.118770i
$493$		−	34.4209i		−	1.55024i
$494$	6.09442	+	0.232787i	0.274201	+	0.0104736i
$495$	−29.0197			−1.30434
$496$	−4.20919	−	0.647841i	−0.188998	−	0.0290889i
$497$	−23.8648			−1.07048
$498$	2.02342	+	0.0772880i	0.0906716	+	0.00346336i
$499$			3.82552i			0.171254i	0.996327	+	0.0856270i	$0.0272893\pi$
$499$			3.82552i			0.171254i	−0.996327	+	0.0856270i	$0.972711\pi$
$500$	2.40955	−	31.4953i	0.107758	−	1.40851i
$501$		−	7.74997i		−	0.346243i
$502$	0.878569	−	23.0012i	0.0392125	−	1.02659i
$503$	−1.60323			−0.0714847			−0.0357423	−	0.999361i	$-0.511380\pi$
$503$	−1.60323			−0.0714847			−0.0357423	+	0.999361i	$0.511380\pi$
$504$	−26.3217	−	3.02800i	−1.17246	−	0.134878i
$505$	46.4050			2.06499
$506$	−0.796031	+	20.8403i	−0.0353879	+	0.926464i
$507$			7.93804i			0.352541i
$508$	−32.3532	−	2.47519i	−1.43544	−	0.109819i
$509$		−	24.9782i		−	1.10714i	−0.832804	−	0.553569i	$-0.813266\pi$
$509$		−	24.9782i		−	1.10714i	0.832804	−	0.553569i	$-0.186734\pi$
$510$	21.8718	+	0.835432i	0.968501	+	0.0369935i
$511$	−24.1514			−1.06840
$512$	−21.3048	−	7.62277i	−0.941547	−	0.336882i
$513$	20.7372			0.915568
$514$	−40.2124	−	1.53598i	−1.77369	−	0.0677493i
$515$			12.8437i			0.565960i
$516$	11.2051	+	0.857251i	0.493279	+	0.0377384i
$517$			14.9555i			0.657743i
$518$	1.29998	−	34.0339i	0.0571180	−	1.49536i
$519$	−9.50814			−0.417361
$520$	−7.85109	−	0.903173i	−0.344293	−	0.0396068i
$521$	6.09101			0.266852			0.133426	−	0.991059i	$-0.457402\pi$
$521$	6.09101			0.266852			0.133426	+	0.991059i	$0.457402\pi$
$522$	−0.747850	+	19.5789i	−0.0327325	+	0.856946i
$523$			14.2769i			0.624286i	0.950035	+	0.312143i	$0.101047\pi$
$523$			14.2769i			0.624286i	−0.950035	+	0.312143i	$0.898953\pi$
$524$	3.24099	−	42.3631i	0.141583	−	1.85064i
$525$		−	21.1698i		−	0.923924i
$526$	10.7218	+	0.409536i	0.467491	+	0.0178566i
$527$	−6.86018			−0.298834
$528$	−7.48699	−	1.15233i	−0.325829	−	0.0501487i
$529$	1.65146			0.0718024
$530$	52.0240	+	1.98715i	2.25978	+	0.0863161i
$531$		−	26.6053i		−	1.15457i
$532$	3.20418	−	41.8820i	0.138919	−	1.81581i
$533$			1.53671i			0.0665621i
$534$	−0.599825	+	15.7036i	−0.0259570	+	0.679560i
$535$	47.8761			2.06986
$536$	−0.323245	+	2.80990i	−0.0139620	+	0.121369i
$537$	1.69475			0.0731340
$538$	−0.373981	+	9.79092i	−0.0161235	+	0.422117i
$539$			17.9586i			0.773530i
$540$	−26.7928	−	2.04978i	−1.15298	−	0.0882086i
$541$		−	13.1195i		−	0.564049i	−0.959407	−	0.282025i	$-0.908994\pi$
$541$		−	13.1195i		−	0.564049i	0.959407	−	0.282025i	$-0.0910060\pi$
$542$	−2.16678	−	0.0827640i	−0.0930712	−	0.00355502i
$543$	3.67745			0.157814
$544$	−35.7871	−	6.91563i	−1.53436	−	0.296505i
$545$	37.6210			1.61151
$546$	−2.41380	−	0.0921992i	−0.103301	−	0.00394576i
$547$			3.51707i			0.150379i	0.997169	+	0.0751895i	$0.0239562\pi$
$547$			3.51707i			0.150379i	−0.997169	+	0.0751895i	$0.976044\pi$
$548$	21.2083	+	1.62255i	0.905976	+	0.0693117i
$549$			26.3386i			1.12410i
$550$	−1.47379	+	38.5841i	−0.0628425	+	1.64523i
$551$	−31.0621			−1.32329
$552$	−1.02329	+	8.89525i	−0.0435542	+	0.378607i
$553$	6.99546			0.297477
$554$	0.0770355	−	2.01681i	0.00327292	−	0.0856860i
$555$		−	16.0156i		−	0.679825i
$556$	0.176353	−	2.30511i	0.00747902	−	0.0977585i
$557$			35.8252i			1.51796i	0.651112	+	0.758982i	$0.274303\pi$
$557$			35.8252i			1.51796i	−0.651112	+	0.758982i	$0.725697\pi$
$558$	3.90213	+	0.149049i	0.165190	+	0.00630974i
$559$	−6.53613			−0.276449
$560$	−8.27972	+	53.7955i	−0.349882	+	2.27328i
$561$	−12.2024			−0.515184
$562$	−31.0685	−	1.18671i	−1.31054	−	0.0500585i
$563$		−	34.0201i		−	1.43377i	−0.697189	−	0.716887i	$-0.745566\pi$
$563$		−	34.0201i		−	1.43377i	0.697189	−	0.716887i	$-0.254434\pi$
$564$	−0.489798	+	6.40216i	−0.0206242	+	0.269580i
$565$		−	5.55434i		−	0.233673i
$566$	−1.26427	+	33.0989i	−0.0531411	+	1.39125i
$567$	19.8892			0.835269
$568$	18.5654	+	2.13572i	0.778987	+	0.0896130i
$569$	13.8324			0.579883			0.289941	−	0.957044i	$-0.406364\pi$
$569$	13.8324			0.579883			0.289941	+	0.957044i	$0.406364\pi$
$570$	0.753910	−	19.7376i	0.0315778	−	0.826715i
$571$			28.1585i			1.17840i	0.807988	+	0.589199i	$0.200556\pi$
$571$			28.1585i			1.17840i	−0.807988	+	0.589199i	$0.799444\pi$
$572$	4.39298	+	0.336085i	0.183680	+	0.0140524i
$573$		−	4.29293i		−	0.179340i
$574$	10.5760	+	0.403967i	0.441432	+	0.0168613i
$575$	45.6402			1.90333
$576$	20.2058	+	4.71121i	0.841908	+	0.196300i
$577$	2.29012			0.0953390			0.0476695	−	0.998863i	$-0.484821\pi$
$577$	2.29012			0.0953390			0.0476695	+	0.998863i	$0.484821\pi$
$578$	−34.6469	−	1.32340i	−1.44112	−	0.0550462i
$579$			8.25177i			0.342932i
$580$	40.1327	+	3.07036i	1.66642	+	0.127490i
$581$			8.11118i			0.336508i
$582$	−0.420903	+	11.0193i	−0.0174470	+	0.456766i
$583$	−29.0243			−1.20207
$584$	18.7884	+	2.16138i	0.777469	+	0.0894385i
$585$	7.24637			0.299601
$586$	1.70123	−	44.5385i	0.0702770	−	1.83987i
$587$			3.10343i			0.128092i	0.997947	+	0.0640462i	$0.0204005\pi$
$587$			3.10343i			0.128092i	−0.997947	+	0.0640462i	$0.979599\pi$
$588$	−0.588149	+	7.68771i	−0.0242548	+	0.317036i
$589$			6.19076i			0.255086i
$590$	−54.6151	−	2.08612i	−2.24847	−	0.0858842i
$591$	−12.2996			−0.505937
$592$	−4.05710	+	26.3600i	−0.166746	+	1.08339i
$593$	−41.3482			−1.69797			−0.848983	−	0.528421i	$-0.822784\pi$
$593$	−41.3482			−1.69797			−0.848983	+	0.528421i	$0.822784\pi$
$594$	14.9696	+	0.571790i	0.614211	+	0.0234608i
$595$			87.6764i			3.59438i
$596$	0.603945	−	7.89418i	0.0247386	−	0.323358i
$597$			0.682324i			0.0279257i
$598$	0.198773	−	5.20394i	0.00812845	−	0.212805i
$599$	1.94432			0.0794428			0.0397214	−	0.999211i	$-0.487353\pi$
$599$	1.94432			0.0794428			0.0397214	+	0.999211i	$0.487353\pi$
$600$	−1.89454	+	16.4688i	−0.0773443	+	0.672338i
$601$	−33.5774			−1.36965			−0.684825	−	0.728708i	$-0.740121\pi$
$601$	−33.5774			−1.36965			−0.684825	+	0.728708i	$0.740121\pi$
$602$	−1.71821	+	44.9831i	−0.0700289	+	1.83338i
$603$		−	2.59347i		−	0.105614i
$604$	25.3318	+	1.93801i	1.03074	+	0.0788565i
$605$			8.20501i			0.333581i
$606$	−11.0990	−	0.423944i	−0.450865	−	0.0172216i
$607$	−2.11809			−0.0859708			−0.0429854	−	0.999076i	$-0.513687\pi$
$607$	−2.11809			−0.0859708			−0.0429854	+	0.999076i	$0.513687\pi$
$608$	−6.24080	+	32.2950i	−0.253098	+	1.30973i
$609$	12.3027			0.498529
$610$	54.0676	+	2.06520i	2.18913	+	0.0836176i
$611$		−	3.73448i		−	0.151081i
$612$	33.3240	+	2.54945i	1.34704	+	0.103055i
$613$			7.70844i			0.311341i	0.987809	+	0.155671i	$0.0497538\pi$
$613$			7.70844i			0.311341i	−0.987809	+	0.155671i	$0.950246\pi$
$614$	0.439798	−	11.5140i	0.0177488	−	0.464669i
$615$	4.97682			0.200685
$616$	3.46784	−	30.1452i	0.139723	−	1.21458i
$617$	10.5836			0.426081			0.213041	−	0.977043i	$-0.431663\pi$
$617$	10.5836			0.426081			0.213041	+	0.977043i	$0.431663\pi$
$618$	0.117337	−	3.07191i	0.00471998	−	0.123570i
$619$			22.9947i			0.924234i	0.886819	+	0.462117i	$0.152910\pi$
$619$			22.9947i			0.924234i	−0.886819	+	0.462117i	$0.847090\pi$
$620$	0.611931	−	7.99857i	0.0245757	−	0.321230i
$621$		−	17.7072i		−	0.710565i
$622$	−41.8279	−	1.59769i	−1.67715	−	0.0640615i
$623$	−62.9501			−2.52204
$624$	1.86954	+	0.287743i	0.0748416	+	0.0115189i
$625$	13.5374			0.541496
$626$	3.98106	+	0.152063i	0.159115	+	0.00607767i
$627$			11.0116i			0.439763i
$628$	0.297055	−	3.88281i	0.0118538	−	0.154941i
$629$			42.9618i			1.71300i
$630$	1.90492	−	49.8712i	0.0758936	−	1.98692i
$631$	19.8316			0.789485			0.394743	−	0.918792i	$-0.370834\pi$
$631$	19.8316			0.789485			0.394743	+	0.918792i	$0.370834\pi$
$632$	−5.44206	−	0.626043i	−0.216473	−	0.0249027i
$633$	10.2031			0.405538
$634$	−1.87642	+	49.1252i	−0.0745222	+	1.95101i
$635$		−	61.1198i		−	2.42547i
$636$	−12.4247	−	0.950556i	−0.492673	−	0.0376920i
$637$		−	4.48435i		−	0.177677i
$638$	−22.4229	−	0.856481i	−0.887731	−	0.0339084i
$639$	−17.1354			−0.677867
$640$	11.2555	−	41.1088i	0.444911	−	1.62497i
$641$	9.61156			0.379634			0.189817	−	0.981820i	$-0.439211\pi$
$641$	9.61156			0.379634			0.189817	+	0.981820i	$0.439211\pi$
$642$	−11.4508	−	0.437384i	−0.451928	−	0.0172622i
$643$		−	26.3018i		−	1.03724i	−0.855004	−	0.518621i	$-0.826446\pi$
$643$		−	26.3018i		−	1.03724i	0.855004	−	0.518621i	$-0.173554\pi$
$644$	−35.7624	−	2.73601i	−1.40924	−	0.107814i
$645$			21.1681i			0.833493i
$646$	−2.02236	+	52.9459i	−0.0795687	+	2.08313i
$647$	−25.3714			−0.997452			−0.498726	−	0.866760i	$-0.666199\pi$
$647$	−25.3714			−0.997452			−0.498726	+	0.866760i	$0.666199\pi$
$648$	−15.4727	−	1.77994i	−0.607823	−	0.0699228i
$649$	30.4700			1.19605
$650$	0.368013	−	9.63467i	0.0144347	−	0.377903i
$651$		−	2.45196i		−	0.0960997i
$652$	−2.00581	+	26.2180i	−0.0785536	+	1.02678i
$653$		−	20.1518i		−	0.788601i	−0.918982	−	0.394300i	$-0.870987\pi$
$653$		−	20.1518i		−	0.788601i	0.918982	−	0.394300i	$-0.129013\pi$
$654$	−8.99806	−	0.343696i	−0.351852	−	0.0134396i
$655$	80.0298			3.12702
$656$	−8.19132	−	1.26073i	−0.319818	−	0.0492234i
$657$	−17.3413			−0.676547
$658$	−25.7015	−	0.981713i	−1.00195	−	0.0382712i
$659$			19.4823i			0.758922i	0.925208	+	0.379461i	$0.123891\pi$
$659$			19.4823i			0.758922i	−0.925208	+	0.379461i	$0.876109\pi$
$660$	1.08846	−	14.2272i	0.0423681	−	0.553795i
$661$			32.0473i			1.24650i	0.782024	+	0.623248i	$0.214187\pi$
$661$			32.0473i			1.24650i	−0.782024	+	0.623248i	$0.785813\pi$
$662$	−0.346234	+	9.06450i	−0.0134568	+	0.352302i
$663$	3.04700			0.118336
$664$	0.725892	−	6.31003i	0.0281701	−	0.244876i
$665$	79.1209			3.06818
$666$	0.933416	−	24.4371i	0.0361692	−	0.946918i
$667$			26.5235i			1.02699i
$668$	−24.2391	−	1.85441i	−0.937838	−	0.0717494i
$669$			4.15138i			0.160501i
$670$	−5.32384	−	0.203353i	−0.205678	−	0.00785623i
$671$	−30.1645			−1.16449
$672$	2.47178	−	12.7910i	0.0953509	−	0.493423i
$673$	−1.20544			−0.0464663			−0.0232331	−	0.999730i	$-0.507396\pi$
$673$	−1.20544			−0.0464663			−0.0232331	+	0.999730i	$0.507396\pi$
$674$	−49.5805	−	1.89381i	−1.90977	−	0.0729470i
$675$		−	32.7834i		−	1.26183i
$676$	24.8273	+	1.89941i	0.954896	+	0.0730544i
$677$		−	14.8140i		−	0.569349i	−0.958624	−	0.284675i	$-0.908114\pi$
$677$		−	14.8140i		−	0.569349i	0.958624	−	0.284675i	$-0.0918856\pi$
$678$	−0.0507431	+	1.32847i	−0.00194878	+	0.0510195i
$679$	−44.1726			−1.69519
$680$	7.84641	−	68.2072i	0.300896	−	2.61562i
$681$	−14.5669			−0.558206
$682$	−0.170699	+	4.46895i	−0.00653641	+	0.171125i
$683$		−	37.2170i		−	1.42407i	−0.702144	−	0.712035i	$-0.747774\pi$
$683$		−	37.2170i		−	1.42407i	0.702144	−	0.712035i	$-0.252226\pi$
$684$	2.30068	−	30.0722i	0.0879685	−	1.14984i
$685$			40.0655i			1.53083i
$686$	4.86820	+	0.185949i	0.185869	+	0.00709958i
$687$	5.99881			0.228869
$688$	5.36233	−	34.8405i	0.204437	−	1.32828i
$689$	7.24754			0.276109
$690$	−16.8536	−	0.643754i	−0.641607	−	0.0245073i
$691$			30.9342i			1.17679i	0.808572	+	0.588397i	$0.200241\pi$
$691$			30.9342i			1.17679i	−0.808572	+	0.588397i	$0.799759\pi$
$692$	−2.27511	+	29.7380i	−0.0864866	+	1.13047i
$693$			27.8233i			1.05692i
$694$	0.0356096	−	0.932267i	0.00135172	−	0.0353884i
$695$	4.35468			0.165182
$696$	−9.57075	−	1.10100i	−0.362778	−	0.0417333i
$697$	−13.3503			−0.505678
$698$	−0.294813	+	7.71829i	−0.0111589	+	0.292142i
$699$		−	1.12369i		−	0.0425018i
$700$	−66.2113	−	5.06550i	−2.50255	−	0.191458i
$701$		−	14.6774i		−	0.554359i	−0.960818	−	0.277179i	$-0.910600\pi$
$701$		−	14.6774i		−	0.554359i	0.960818	−	0.277179i	$-0.0893997\pi$
$702$	−3.73800	−	0.142779i	−0.141082	−	0.00538886i
$703$	38.7696			1.46222
$704$	−5.39555	+	23.1408i	−0.203352	+	0.872153i
$705$	−12.0946			−0.455508
$706$	25.8781	+	0.988458i	0.973934	+	0.0372011i
$707$		−	44.4919i		−	1.67329i
$708$	13.0436	+	0.997901i	0.490208	+	0.0375034i
$709$		−	9.55778i		−	0.358950i	−0.983763	−	0.179475i	$-0.942560\pi$
$709$		−	9.55778i		−	0.358950i	0.983763	−	0.179475i	$-0.0574399\pi$
$710$	−1.34359	+	35.1754i	−0.0504239	+	1.32011i
$711$	5.02290			0.188373
$712$	48.9715	+	5.63358i	1.83528	+	0.211127i
$713$	5.28620			0.197970
$714$	0.800990	−	20.9701i	0.0299763	−	0.784787i
$715$			8.29896i			0.310364i
$716$	0.405520	−	5.30057i	0.0151550	−	0.198092i
$717$		−	6.49950i		−	0.242728i
$718$	47.5010	+	1.81438i	1.77272	+	0.0677121i
$719$	−38.6166			−1.44016			−0.720079	−	0.693892i	$-0.755894\pi$
$719$	−38.6166			−1.44016			−0.720079	+	0.693892i	$0.755894\pi$
$720$	−5.94503	+	38.6264i	−0.221558	+	1.43952i
$721$	12.3142			0.458604
$722$	20.9290	+	0.799418i	0.778895	+	0.0297512i
$723$			4.67898i			0.174013i
$724$	0.879939	−	11.5017i	0.0327027	−	0.427458i
$725$			49.1061i			1.82375i
$726$	0.0749590	−	1.96245i	0.00278199	−	0.0728332i
$727$	−0.784740			−0.0291044			−0.0145522	−	0.999894i	$-0.504632\pi$
$727$	−0.784740			−0.0291044			−0.0145522	+	0.999894i	$0.504632\pi$
$728$	−0.865938	+	7.52742i	−0.0320938	+	0.278985i
$729$	7.45915			0.276265
$730$	−1.35972	+	35.5979i	−0.0503257	+	1.31754i
$731$		−	56.7833i		−	2.10021i
$732$	−12.9128	−	0.987896i	−0.477271	−	0.0365137i
$733$			46.2176i			1.70709i	0.521022	+	0.853543i	$0.325551\pi$
$733$			46.2176i			1.70709i	−0.521022	+	0.853543i	$0.674449\pi$
$734$	−27.8365	−	1.06326i	−1.02746	−	0.0392458i
$735$	−14.5232			−0.535695
$736$	27.5762	+	5.32894i	1.01647	+	0.196427i
$737$	2.97019			0.109408
$738$	7.59377	+	0.290057i	0.279531	+	0.0106772i
$739$			4.53390i			0.166782i	0.996517	+	0.0833910i	$0.0265750\pi$
$739$			4.53390i			0.166782i	−0.996517	+	0.0833910i	$0.973425\pi$
$740$	−50.0910	−	3.83221i	−1.84138	−	0.140875i
$741$		−	2.74967i		−	0.101012i
$742$	1.90522	−	49.8792i	0.0699429	−	1.83112i
$743$	−2.57128			−0.0943311			−0.0471655	−	0.998887i	$-0.515019\pi$
$743$	−2.57128			−0.0943311			−0.0471655	+	0.998887i	$0.515019\pi$
$744$	−0.219432	+	1.90748i	−0.00804478	+	0.0699316i
$745$	14.9132			0.546378
$746$	0.450881	−	11.8042i	0.0165079	−	0.432181i
$747$			5.82401i			0.213089i
$748$	−2.91978	+	38.1645i	−0.106758	+	1.39543i
$749$		−	45.9023i		−	1.67724i
$750$	−14.2308	−	0.543569i	−0.519634	−	0.0198483i
$751$	−49.7600			−1.81577			−0.907884	−	0.419221i	$-0.862303\pi$
$751$	−49.7600			−1.81577			−0.907884	+	0.419221i	$0.862303\pi$
$752$	19.9064	+	3.06382i	0.725912	+	0.111726i
$753$	−10.3776			−0.378182
$754$	5.59912	+	0.213868i	0.203908	+	0.00778862i
$755$			47.8553i			1.74163i
$756$	−1.96528	+	25.6882i	−0.0714765	+	0.934271i
$757$		−	50.4225i		−	1.83264i	−0.400451	−	0.916318i	$-0.631147\pi$
$757$		−	50.4225i		−	1.83264i	0.400451	−	0.916318i	$-0.368853\pi$
$758$	0.779004	−	20.3945i	0.0282947	−	0.740762i
$759$	9.40269			0.341296
$760$	−61.5515	−	7.08076i	−2.23271	−	0.256846i
$761$	2.60997			0.0946113			0.0473056	−	0.998880i	$-0.484937\pi$
$761$	2.60997			0.0946113			0.0473056	+	0.998880i	$0.484937\pi$
$762$	−0.558375	+	14.6184i	−0.0202278	+	0.529569i
$763$		−	36.0700i		−	1.30582i
$764$	−13.4267	−	1.02721i	−0.485761	−	0.0371632i
$765$			62.9536i			2.27609i
$766$	2.67191	+	0.102058i	0.0965401	+	0.00368751i
$767$	−7.60852			−0.274728
$768$	−3.06760	+	9.72943i	−0.110692	+	0.351080i
$769$	−21.0646			−0.759610			−0.379805	−	0.925067i	$-0.624009\pi$
$769$	−21.0646			−0.759610			−0.379805	+	0.925067i	$0.624009\pi$
$770$	57.1153	+	2.18162i	2.05829	+	0.0786201i
$771$			18.1430i			0.653403i
$772$	25.8085	+	1.97448i	0.928869	+	0.0710632i
$773$		−	13.1448i		−	0.472784i	−0.971658	−	0.236392i	$-0.924035\pi$
$773$		−	13.1448i		−	0.472784i	0.971658	−	0.236392i	$-0.0759650\pi$
$774$	−1.23371	+	32.2989i	−0.0443449	+	1.16096i
$775$	9.78698			0.351559
$776$	34.3637	+	3.95313i	1.23359	+	0.141909i
$777$	−15.3554			−0.550870
$778$	−0.884836	+	23.1652i	−0.0317229	+	0.830514i
$779$			12.0476i			0.431649i
$780$	−0.271794	+	3.55262i	−0.00973177	+	0.127204i
$781$		−	19.6245i		−	0.702219i
$782$	45.2098	+	1.72687i	1.61670	+	0.0617526i
$783$	19.0518			0.680857
$784$	23.9036	+	3.67903i	0.853700	+	0.131394i
$785$	7.33518			0.261804
$786$	−19.1412	−	0.731132i	−0.682745	−	0.0260786i
$787$			14.3189i			0.510413i	0.966887	+	0.255206i	$0.0821434\pi$
$787$			14.3189i			0.510413i	−0.966887	+	0.255206i	$0.917857\pi$
$788$	−2.94304	+	38.4686i	−0.104842	+	1.37039i
$789$		−	4.83743i		−	0.172217i
$790$	0.393844	−	10.3109i	0.0140124	−	0.366847i
$791$	−5.32536			−0.189348
$792$	2.48998	−	21.6449i	0.0884777	−	0.769118i
$793$	7.53224			0.267478
$794$	0.917427	−	24.0185i	0.0325583	−	0.852384i
$795$		−	23.4721i		−	0.832469i
$796$	2.13406	+	0.163266i	0.0756397	+	0.00578682i
$797$			48.0574i			1.70228i	0.524939	+	0.851140i	$0.324088\pi$
$797$			48.0574i			1.70228i	−0.524939	+	0.851140i	$0.675912\pi$
$798$	−18.9239	−	0.722829i	−0.669897	−	0.0255879i
$799$	32.4437			1.14777
$800$	51.0552	+	9.86609i	1.80507	+	0.348819i
$801$	−45.1996			−1.59705
$802$	8.63773	+	0.329933i	0.305009	+	0.0116503i
$803$		−	19.8602i		−	0.700852i
$804$	1.27148	+	0.0972747i	0.0448416	+	0.00343061i
$805$		−	67.5603i		−	2.38119i
$806$	0.0426245	−	1.11592i	0.00150139	−	0.0393067i
$807$	4.41745			0.155502
$808$	−3.98170	+	34.6121i	−0.140076	+	1.21765i
$809$	16.7651			0.589431			0.294715	−	0.955585i	$-0.404775\pi$
$809$	16.7651			0.589431			0.294715	+	0.955585i	$0.404775\pi$
$810$	1.11976	−	29.3157i	0.0393445	−	1.03005i
$811$			38.7425i			1.36043i	0.733011	+	0.680217i	$0.238115\pi$
$811$			38.7425i			1.36043i	−0.733011	+	0.680217i	$0.761885\pi$
$812$	2.94378	−	38.4782i	0.103306	−	1.35032i
$813$			0.977605i			0.0342861i
$814$	27.9867	+	1.06900i	0.980935	+	0.0374685i
$815$	−49.5295			−1.73494
$816$	−2.49980	+	16.2419i	−0.0875105	+	0.568579i
$817$	−51.2424			−1.79274
$818$	42.0914	+	1.60775i	1.47169	+	0.0562137i
$819$		−	6.94763i		−	0.242770i
$820$	1.19085	−	15.5657i	0.0415864	−	0.543577i
$821$		−	45.0588i		−	1.57256i	−0.617868	−	0.786282i	$-0.712003\pi$
$821$		−	45.0588i		−	1.57256i	0.617868	−	0.786282i	$-0.287997\pi$
$822$	0.366029	−	9.58273i	0.0127667	−	0.334236i
$823$	−48.4990			−1.69057			−0.845285	−	0.534316i	$-0.820569\pi$
$823$	−48.4990			−1.69057			−0.845285	+	0.534316i	$0.820569\pi$
$824$	−9.57972	−	1.10203i	−0.333725	−	0.0383911i
$825$	17.4083			0.606080
$826$	−2.00012	+	52.3636i	−0.0695930	+	1.82196i
$827$			53.1095i			1.84680i	0.383842	+	0.923399i	$0.374601\pi$
$827$			53.1095i			1.84680i	−0.383842	+	0.923399i	$0.625399\pi$
$828$	−25.6782	−	1.96451i	−0.892380	−	0.0682716i
$829$		−	10.4651i		−	0.363467i	−0.983348	−	0.181733i	$-0.941829\pi$
$829$		−	10.4651i		−	0.363467i	0.983348	−	0.181733i	$-0.0581708\pi$
$830$	11.9555	+	0.456659i	0.414980	+	0.0158509i
$831$	−0.909940			−0.0315655
$832$	1.34730	−	5.77839i	0.0467092	−	0.200330i
$833$	38.9583			1.34983
$834$	−1.04154	−	0.0397833i	−0.0360655	−	0.00137758i
$835$		−	45.7910i		−	1.58466i
$836$	34.4404	+	2.63487i	1.19115	+	0.0911287i
$837$		−	3.79709i		−	0.131247i
$838$	1.94479	−	50.9151i	0.0671817	−	1.75883i
$839$	21.4740			0.741365			0.370682	−	0.928760i	$-0.379124\pi$
$839$	21.4740			0.741365			0.370682	+	0.928760i	$0.379124\pi$
$840$	24.3785	+	2.80445i	0.841138	+	0.0967628i
$841$	0.462360			0.0159434
$842$	0.718670	−	18.8150i	0.0247670	−	0.648407i
$843$			14.0174i			0.482786i
$844$	2.44140	−	31.9116i	0.0840365	−	1.09844i
$845$			46.9022i			1.61349i
$846$	−18.4543	−	0.704892i	−0.634470	−	0.0242347i
$847$	7.86675			0.270305
$848$	−5.94598	+	38.6326i	−0.204186	+	1.32665i
$849$	14.9335			0.512516
$850$	83.7023	+	3.19715i	2.87096	+	0.109661i
$851$		−	33.1048i		−	1.13482i
$852$	0.642708	−	8.40086i	0.0220188	−	0.287809i
$853$			44.0380i			1.50783i	0.656971	+	0.753916i	$0.271838\pi$
$853$			44.0380i			1.50783i	−0.656971	+	0.753916i	$0.728162\pi$
$854$	1.98006	−	51.8386i	0.0677564	−	1.77388i
$855$	56.8106			1.94288
$856$	−4.10793	+	35.7093i	−0.140406	+	1.22052i
$857$	−17.0234			−0.581507			−0.290753	−	0.956798i	$-0.593906\pi$
$857$	−17.0234			−0.581507			−0.290753	+	0.956798i	$0.593906\pi$
$858$	0.0758173	−	1.98492i	0.00258836	−	0.0677639i
$859$			39.6246i			1.35198i	0.736913	+	0.675988i	$0.236283\pi$
$859$			39.6246i			1.35198i	−0.736913	+	0.675988i	$0.763717\pi$
$860$	66.2061	+	5.06510i	2.25761	+	0.172718i
$861$		−	4.77164i		−	0.162617i
$862$	−36.7807	−	1.40490i	−1.25275	−	0.0478511i
$863$	15.6571			0.532975			0.266488	−	0.963838i	$-0.414137\pi$
$863$	15.6571			0.532975			0.266488	+	0.963838i	$0.414137\pi$
$864$	3.82778	−	19.8081i	0.130224	−	0.673884i
$865$	−56.1792			−1.91015
$866$	13.6764	+	0.522396i	0.464745	+	0.0177517i
$867$			15.6320i			0.530889i
$868$	−7.66882	−	0.586704i	−0.260297	−	0.0199140i
$869$			5.75251i			0.195140i
$870$	0.692640	−	18.1335i	0.0234827	−	0.614783i
$871$	−0.741673			−0.0251306
$872$	−3.22801	+	28.0604i	−0.109314	+	0.950245i
$873$	−31.7169			−1.07346
$874$	1.55836	−	40.7982i	0.0527122	−	1.38002i
$875$		−	57.0462i		−	1.92851i
$876$	0.650428	−	8.50177i	0.0219759	−	0.287248i
$877$		−	38.9944i		−	1.31675i	−0.752691	−	0.658374i	$-0.771244\pi$
$877$		−	38.9944i		−	1.31675i	0.752691	−	0.658374i	$-0.228756\pi$
$878$	20.1989	+	0.771531i	0.681679	+	0.0260379i
$879$	−20.0948			−0.677781
$880$	−44.2372	−	6.80858i	−1.49123	−	0.229517i
$881$	52.0977			1.75522			0.877608	−	0.479380i	$-0.159138\pi$
$881$	52.0977			1.75522			0.877608	+	0.479380i	$0.159138\pi$
$882$	−22.1598	−	0.846434i	−0.746161	−	0.0285009i
$883$			50.4549i			1.69794i	0.528438	+	0.848972i	$0.322778\pi$
$883$			50.4549i			1.69794i	−0.528438	+	0.848972i	$0.677222\pi$
$884$	0.729085	−	9.52989i	0.0245218	−	0.320525i
$885$			24.6412i			0.828304i
$886$	−1.46348	+	38.3144i	−0.0491667	+	1.28720i
$887$	36.1709			1.21450			0.607250	−	0.794511i	$-0.292273\pi$
$887$	36.1709			1.21450			0.607250	+	0.794511i	$0.292273\pi$
$888$	11.9456	+	1.37419i	0.400867	+	0.0461149i
$889$	−58.6001			−1.96538
$890$	−3.54409	+	92.7852i	−0.118798	+	3.11017i
$891$			16.3553i			0.547924i
$892$	12.9840	+	0.993340i	0.434736	+	0.0332595i
$893$		−	29.2778i		−	0.979744i
$894$	−3.56689	−	0.136244i	−0.119295	−	0.00455667i
$895$	10.0135			0.334715
$896$	−39.4140	−	10.7914i	−1.31673	−	0.360517i
$897$	−2.34791			−0.0783943
$898$	55.5099	+	2.12030i	1.85239	+	0.0707552i
$899$			5.68763i			0.189693i
$900$	−47.5412	−	3.63714i	−1.58471	−	0.121238i
$901$			62.9638i			2.09763i
$902$	−0.332190	+	8.69682i	−0.0110607	+	0.289573i
$903$	20.2954			0.675389
$904$	4.14282	+	0.476581i	0.137788	+	0.0158509i
$905$	21.7283			0.722275
$906$	0.437194	−	11.4459i	0.0145248	−	0.380263i
$907$			2.37898i			0.0789928i	0.999220	+	0.0394964i	$0.0125754\pi$
$907$			2.37898i			0.0789928i	−0.999220	+	0.0394964i	$0.987425\pi$
$908$	−3.48558	+	45.5601i	−0.115673	+	1.51196i
$909$		−	31.9461i		−	1.05959i
$910$	−14.2620	−	0.544763i	−0.472781	−	0.0180587i
$911$	34.1939			1.13289			0.566447	−	0.824098i	$-0.308318\pi$
$911$	34.1939			1.13289			0.566447	+	0.824098i	$0.308318\pi$
$912$	14.6570	+	2.25587i	0.485341	+	0.0746993i
$913$	−6.66999			−0.220744
$914$	−34.0825	−	1.30184i	−1.12735	−	0.0430611i
$915$		−	24.3941i		−	0.806445i
$916$	1.43539	−	18.7621i	0.0474268	−	0.619917i
$917$		−	76.7305i		−	2.53386i
$918$	1.24041	−	32.4743i	0.0409396	−	1.07181i
$919$	−38.8818			−1.28259			−0.641296	−	0.767293i	$-0.721603\pi$
$919$	−38.8818			−1.28259			−0.641296	+	0.767293i	$0.721603\pi$
$920$	−6.04616	+	52.5580i	−0.199336	+	1.73278i
$921$	−5.19488			−0.171177
$922$	−0.773032	+	20.2382i	−0.0254584	+	0.666509i
$923$			4.90034i			0.161297i
$924$	−13.6407	−	1.04358i	−0.448746	−	0.0343314i
$925$		−	61.2909i		−	2.01523i
$926$	−29.1816	−	1.11464i	−0.958967	−	0.0366294i
$927$	8.84186			0.290405
$928$	−5.73361	+	29.6704i	−0.188215	+	0.973977i
$929$	−10.7657			−0.353212			−0.176606	−	0.984282i	$-0.556512\pi$
$929$	−10.7657			−0.353212			−0.176606	+	0.984282i	$0.556512\pi$
$930$	−3.61406	−	0.138045i	−0.118510	−	0.00452668i
$931$		−	35.1567i		−	1.15222i
$932$	−3.51448	−	0.268876i	−0.115121	−	0.00880732i
$933$			18.8718i			0.617836i
$934$	−0.125877	+	3.29550i	−0.00411883	+	0.107832i
$935$	−72.0981			−2.35786
$936$	−0.621763	+	5.40485i	−0.0203230	+	0.176663i
$937$	20.8760			0.681988			0.340994	−	0.940065i	$-0.389236\pi$
$937$	20.8760			0.681988			0.340994	+	0.940065i	$0.389236\pi$
$938$	−0.194970	+	5.10436i	−0.00636599	+	0.166663i
$939$		−	1.79617i		−	0.0586157i
$940$	−2.89399	+	37.8274i	−0.0943915	+	1.23379i
$941$		−	20.5326i		−	0.669343i	−0.942335	−	0.334672i	$-0.891375\pi$
$941$		−	20.5326i		−	0.669343i	0.942335	−	0.334672i	$-0.108625\pi$
$942$	−1.75440	−	0.0670124i	−0.0571615	−	0.00218338i
$943$	10.2873			0.334999
$944$	6.24214	−	40.5568i	0.203164	−	1.32001i
$945$	−48.5286			−1.57864
$946$	−36.9905	−	1.41292i	−1.20267	−	0.0459379i
$947$		−	24.8690i		−	0.808135i	−0.914729	−	0.404067i	$-0.867596\pi$
$947$		−	24.8690i		−	0.808135i	0.914729	−	0.404067i	$-0.132404\pi$
$948$	−0.188396	+	2.46254i	−0.00611883	+	0.0799795i
$949$			4.95921i			0.160983i
$950$	2.88517	−	75.5346i	0.0936074	−	2.45066i
$951$	22.1642			0.718724
$952$	−65.3952	−	7.52293i	−2.11947	−	0.243820i
$953$	−27.8110			−0.900888			−0.450444	−	0.892805i	$-0.648734\pi$
$953$	−27.8110			−0.900888			−0.450444	+	0.892805i	$0.648734\pi$
$954$	1.36799	−	35.8144i	0.0442904	−	1.15953i
$955$		−	25.3649i		−	0.820790i
$956$	−20.3281	−	1.55520i	−0.657457	−	0.0502988i
$957$			10.1167i			0.327027i
$958$	−9.40598	−	0.359278i	−0.303893	−	0.0116077i
$959$	38.4138			1.24045
$960$	−18.7141	−	4.36340i	−0.603994	−	0.140828i
$961$	−29.8664			−0.963433
$962$	−6.98845	−	0.266936i	−0.225317	−	0.00860636i
$963$		−	32.9589i		−	1.06209i
$964$	14.6341	+	1.11959i	0.471334	+	0.0360594i
$965$			48.7559i			1.56951i
$966$	−0.617214	+	16.1588i	−0.0198585	+	0.519902i
$967$	−48.6296			−1.56382			−0.781912	−	0.623389i	$-0.785755\pi$
$967$	−48.6296			−1.56382			−0.781912	+	0.623389i	$0.785755\pi$
$968$	−6.11987	−	0.704018i	−0.196700	−	0.0226280i
$969$	23.8881			0.767395
$970$	−2.48692	+	65.1082i	−0.0798502	+	2.09050i
$971$			17.2232i			0.552718i	0.961054	+	0.276359i	$0.0891279\pi$
$971$			17.2232i			0.552718i	−0.961054	+	0.276359i	$0.910872\pi$
$972$	−2.16795	+	28.3373i	−0.0695370	+	0.908921i
$973$		−	4.17515i		−	0.133849i
$974$	−17.3151	−	0.661379i	−0.554810	−	0.0211919i
$975$	−4.34696			−0.139214
$976$	−6.17955	+	40.1502i	−0.197803	+	1.28518i
$977$	−16.4861			−0.527436			−0.263718	−	0.964600i	$-0.584949\pi$
$977$	−16.4861			−0.527436			−0.263718	+	0.964600i	$0.584949\pi$
$978$	11.8463	+	0.452489i	0.378802	+	0.0144690i
$979$		−	51.7651i		−	1.65442i
$980$	−3.47510	+	45.4231i	−0.111008	+	1.45099i
$981$		−	25.8991i		−	0.826894i
$982$	−0.414330	+	10.8473i	−0.0132218	+	0.346150i
$983$	−17.8258			−0.568553			−0.284277	−	0.958742i	$-0.591753\pi$
$983$	−17.8258			−0.568553			−0.284277	+	0.958742i	$0.591753\pi$
$984$	−0.427028	+	3.71206i	−0.0136132	+	0.118336i
$985$	−72.6726			−2.31554
$986$	−1.85800	+	48.6430i	−0.0591709	+	1.54911i
$987$			11.5960i			0.369104i
$988$	−8.59996	−	0.657941i	−0.273601	−	0.0209319i
$989$			43.7552i			1.39133i
$990$	41.0101	+	1.56645i	1.30339	+	0.0497851i
$991$	33.2278			1.05552			0.527758	−	0.849395i	$-0.323033\pi$
$991$	33.2278			1.05552			0.527758	+	0.849395i	$0.323033\pi$
$992$	5.91339	+	1.14273i	0.187750	+	0.0362816i
$993$	4.08971			0.129783
$994$	33.7253	+	1.28820i	1.06970	+	0.0408591i
$995$			4.03154i			0.127808i
$996$	−2.85529	−	0.218444i	−0.0904734	−	0.00692167i
$997$		−	42.0393i		−	1.33140i	−0.746221	−	0.665699i	$-0.768134\pi$
$997$		−	42.0393i		−	1.33140i	0.746221	−	0.665699i	$-0.231866\pi$
$998$	0.206498	−	5.40616i	0.00653657	−	0.171129i
$999$	−23.7792			−0.752342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	536.2.c.a.269.1	✓	66
4.3	odd	2		2144.2.c.a.1073.26		66
8.3	odd	2		2144.2.c.a.1073.41		66
8.5	even	2	inner	536.2.c.a.269.2	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
536.2.c.a.269.1	✓	66	1.1	even	1	trivial
536.2.c.a.269.2	yes	66	8.5	even	2	inner
2144.2.c.a.1073.26		66	4.3	odd	2
2144.2.c.a.1073.41		66	8.3	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:	\( N \)	\(=\)	\( 536 = 2^{3} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	536.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41318 - 0.0539790i) q^{2} +0.637598i q^{3} +(1.99417 + 0.152564i) q^{4} +3.76727i q^{5} +(0.0344169 - 0.901042i) q^{6} +3.61196 q^{7} +(-2.80990 - 0.323245i) q^{8} +2.59347 q^{9} +O(q^{10})\)	\(q+(-1.41318 - 0.0539790i) q^{2} +0.637598i q^{3} +(1.99417 + 0.152564i) q^{4} +3.76727i q^{5} +(0.0344169 - 0.901042i) q^{6} +3.61196 q^{7} +(-2.80990 - 0.323245i) q^{8} +2.59347 q^{9} +(0.203353 - 5.32384i) q^{10} +2.97019i q^{11} +(-0.0972747 + 1.27148i) q^{12} -0.741673i q^{13} +(-5.10436 - 0.194970i) q^{14} -2.40200 q^{15} +(3.95345 + 0.608479i) q^{16} +6.44337 q^{17} +(-3.66505 - 0.139993i) q^{18} -5.81462i q^{19} +(-0.574751 + 7.51259i) q^{20} +2.30298i q^{21} +(0.160328 - 4.19742i) q^{22} -4.96502 q^{23} +(0.206100 - 1.79158i) q^{24} -9.19234 q^{25} +(-0.0400347 + 1.04812i) q^{26} +3.56638i q^{27} +(7.20287 + 0.551056i) q^{28} -5.34206i q^{29} +(3.39447 + 0.129658i) q^{30} -1.06469 q^{31} +(-5.55410 - 1.07330i) q^{32} -1.89379 q^{33} +(-9.10565 - 0.347806i) q^{34} +13.6072i q^{35} +(5.17182 + 0.395671i) q^{36} +6.66760i q^{37} +(-0.313867 + 8.21712i) q^{38} +0.472889 q^{39} +(1.21775 - 10.5856i) q^{40} -2.07194 q^{41} +(0.124312 - 3.25453i) q^{42} -8.81268i q^{43} +(-0.453145 + 5.92307i) q^{44} +9.77030i q^{45} +(7.01649 + 0.268007i) q^{46} +5.03520 q^{47} +(-0.387965 + 2.52071i) q^{48} +6.04627 q^{49} +(12.9905 + 0.496193i) q^{50} +4.10828i q^{51} +(0.113153 - 1.47902i) q^{52} +9.77188i q^{53} +(0.192510 - 5.03995i) q^{54} -11.1895 q^{55} +(-10.1492 - 1.16755i) q^{56} +3.70739 q^{57} +(-0.288359 + 7.54931i) q^{58} -10.2586i q^{59} +(-4.79001 - 0.366460i) q^{60} +10.1557i q^{61} +(1.50460 + 0.0574708i) q^{62} +9.36751 q^{63} +(7.79103 + 1.81657i) q^{64} +2.79408 q^{65} +(2.67627 + 0.102225i) q^{66} -1.00000i q^{67} +(12.8492 + 0.983028i) q^{68} -3.16569i q^{69} +(0.734505 - 19.2295i) q^{70} -6.60715 q^{71} +(-7.28738 - 0.838325i) q^{72} -6.68651 q^{73} +(0.359910 - 9.42255i) q^{74} -5.86101i q^{75} +(0.887103 - 11.5954i) q^{76} +10.7282i q^{77} +(-0.668279 - 0.0255261i) q^{78} +1.93675 q^{79} +(-2.29231 + 14.8937i) q^{80} +5.50649 q^{81} +(2.92804 + 0.111841i) q^{82} +2.24564i q^{83} +(-0.351352 + 4.59254i) q^{84} +24.2739i q^{85} +(-0.475699 + 12.4539i) q^{86} +3.40609 q^{87} +(0.960098 - 8.34592i) q^{88} -17.4282 q^{89} +(0.527391 - 13.8072i) q^{90} -2.67890i q^{91} +(-9.90111 - 0.757485i) q^{92} -0.678843i q^{93} +(-7.11566 - 0.271795i) q^{94} +21.9053 q^{95} +(0.684331 - 3.54128i) q^{96} -12.2295 q^{97} +(-8.54448 - 0.326371i) q^{98} +7.70310i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 4 q^{4} + 2 q^{6} - 6 q^{8} - 66 q^{9}+O(q^{10}) \) 66 * q - 4 * q^4 + 2 * q^6 - 6 * q^8 - 66 * q^9	\( 66 q - 4 q^{4} + 2 q^{6} - 6 q^{8} - 66 q^{9} - 4 q^{10} + 4 q^{12} - 2 q^{14} + 8 q^{15} - 12 q^{16} - 4 q^{17} - 10 q^{18} + 22 q^{20} + 8 q^{22} - 12 q^{23} - 62 q^{25} - 24 q^{26} + 10 q^{28} + 22 q^{30} - 16 q^{31} + 10 q^{32} - 10 q^{34} + 2 q^{36} + 8 q^{38} + 8 q^{39} - 18 q^{40} + 4 q^{41} + 28 q^{42} + 34 q^{44} + 18 q^{46} + 20 q^{47} - 38 q^{48} + 66 q^{49} - 32 q^{50} - 6 q^{52} + 38 q^{54} + 16 q^{55} - 30 q^{56} + 2 q^{58} + 18 q^{60} + 22 q^{62} - 40 q^{63} + 26 q^{64} + 16 q^{65} - 34 q^{66} + 26 q^{68} - 18 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{73} - 4 q^{74} - 30 q^{76} - 36 q^{78} + 16 q^{79} - 32 q^{80} + 66 q^{81} + 16 q^{82} - 6 q^{84} + 2 q^{86} + 32 q^{87} + 22 q^{88} - 20 q^{89} - 18 q^{90} + 8 q^{92} - 16 q^{94} - 64 q^{96} + 12 q^{97} - 46 q^{98}+O(q^{100}) \) 66 * q - 4 * q^4 + 2 * q^6 - 6 * q^8 - 66 * q^9 - 4 * q^10 + 4 * q^12 - 2 * q^14 + 8 * q^15 - 12 * q^16 - 4 * q^17 - 10 * q^18 + 22 * q^20 + 8 * q^22 - 12 * q^23 - 62 * q^25 - 24 * q^26 + 10 * q^28 + 22 * q^30 - 16 * q^31 + 10 * q^32 - 10 * q^34 + 2 * q^36 + 8 * q^38 + 8 * q^39 - 18 * q^40 + 4 * q^41 + 28 * q^42 + 34 * q^44 + 18 * q^46 + 20 * q^47 - 38 * q^48 + 66 * q^49 - 32 * q^50 - 6 * q^52 + 38 * q^54 + 16 * q^55 - 30 * q^56 + 2 * q^58 + 18 * q^60 + 22 * q^62 - 40 * q^63 + 26 * q^64 + 16 * q^65 - 34 * q^66 + 26 * q^68 - 18 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^73 - 4 * q^74 - 30 * q^76 - 36 * q^78 + 16 * q^79 - 32 * q^80 + 66 * q^81 + 16 * q^82 - 6 * q^84 + 2 * q^86 + 32 * q^87 + 22 * q^88 - 20 * q^89 - 18 * q^90 + 8 * q^92 - 16 * q^94 - 64 * q^96 + 12 * q^97 - 46 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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