LMFDB - Embedded newform 966.2.q.g.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			673.1
Character	$\chi$	$=$	966.673
Dual form			966.2.q.g.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-2.54794 + 1.63746i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.142315 - 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-2.54794 + 1.63746i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.142315 - 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.431035 - 2.99791i) q^{10} +(1.48774 + 3.25770i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.0270409 + 0.188073i) q^{13} +(0.841254 + 0.540641i) q^{14} +(-2.90606 + 0.853295i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.17640 + 1.35764i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(0.336450 + 0.388284i) q^{19} +(2.90606 + 0.853295i) q^{20} +(0.415415 - 0.909632i) q^{21} -3.58134 q^{22} +(-4.76027 - 0.582923i) q^{23} +1.00000 q^{24} +(1.73364 - 3.79614i) q^{25} +(-0.182311 - 0.0535312i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-4.35185 + 5.02231i) q^{29} +(0.431035 - 2.99791i) q^{30} +(-1.36329 + 0.400298i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.509678 + 3.54489i) q^{33} +(-0.746256 - 1.63407i) q^{34} +(1.25818 + 2.75504i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-6.45350 - 4.14741i) q^{37} +(-0.492962 + 0.144747i) q^{38} +(-0.0270409 + 0.188073i) q^{39} +(-1.98340 + 2.28897i) q^{40} +(-5.70368 + 3.66553i) q^{41} +(0.654861 + 0.755750i) q^{42} +(-7.31409 - 2.14761i) q^{43} +(1.48774 - 3.25770i) q^{44} -3.02874 q^{45} +(2.50773 - 4.08794i) q^{46} +2.51907 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(2.73291 + 3.15395i) q^{50} +(-1.51124 + 0.971213i) q^{51} +(0.124428 - 0.143598i) q^{52} +(1.71439 - 11.9238i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-9.12504 - 5.86431i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(0.213429 + 0.467345i) q^{57} +(-2.76063 - 6.04493i) q^{58} +(0.778932 + 5.41759i) q^{59} +(2.54794 + 1.63746i) q^{60} +(-11.3146 + 3.32225i) q^{61} +(0.202207 - 1.40638i) q^{62} +(0.654861 - 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.376861 - 0.434921i) q^{65} +(-3.43627 - 1.00898i) q^{66} +(5.13699 - 11.2484i) q^{67} +1.79641 q^{68} +(-4.40322 - 1.90043i) q^{69} -3.02874 q^{70} +(-2.92492 + 6.40468i) q^{71} +(0.959493 + 0.281733i) q^{72} +(9.36817 + 10.8114i) q^{73} +(6.45350 - 4.14741i) q^{74} +(2.73291 - 3.15395i) q^{75} +(0.0731176 - 0.508544i) q^{76} +(3.43627 - 1.00898i) q^{77} +(-0.159844 - 0.102726i) q^{78} +(2.08075 + 14.4719i) q^{79} +(-1.25818 - 2.75504i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.964892 - 6.71097i) q^{82} +(11.7111 + 7.52625i) q^{83} +(-0.959493 + 0.281733i) q^{84} +(0.774316 - 5.38548i) q^{85} +(4.99191 - 5.76098i) q^{86} +(-5.59052 + 3.59281i) q^{87} +(2.34528 + 2.70660i) q^{88} +(-10.2775 - 3.01775i) q^{89} +(1.25818 - 2.75504i) q^{90} +0.190007 q^{91} +(2.67677 + 3.97931i) q^{92} -1.42084 q^{93} +(-1.04646 + 2.29143i) q^{94} +(-1.49305 - 0.438400i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(-4.85431 + 3.11967i) q^{97} +(0.654861 - 0.755750i) q^{98} +(-0.509678 + 3.54489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 10 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 10 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 10 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9} + 10 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} - 3 q^{14} - q^{15} - 3 q^{16} + 5 q^{17} + 3 q^{18} + 18 q^{19} + q^{20} - 3 q^{21} + 2 q^{22} + 21 q^{23} + 30 q^{24} + 13 q^{25} - 10 q^{26} + 3 q^{27} + 3 q^{28} + 17 q^{29} - 10 q^{30} + 12 q^{31} + 3 q^{32} + 13 q^{33} + 17 q^{34} - q^{35} - 3 q^{36} + 16 q^{37} + 15 q^{38} + 12 q^{39} - 12 q^{40} + 10 q^{41} + 3 q^{42} - 35 q^{43} + 9 q^{44} + 12 q^{45} + q^{46} - 8 q^{47} + 3 q^{48} - 3 q^{49} - 2 q^{50} + 6 q^{51} - q^{52} + 42 q^{53} - 3 q^{54} + 49 q^{55} - 3 q^{56} + 15 q^{57} + 5 q^{58} - 6 q^{59} + 10 q^{60} - 18 q^{61} - 34 q^{62} + 3 q^{63} - 3 q^{64} + 34 q^{65} - 2 q^{66} + 72 q^{67} - 6 q^{68} - 10 q^{69} + 12 q^{70} + 17 q^{71} + 3 q^{72} + 9 q^{73} - 16 q^{74} - 2 q^{75} + 18 q^{76} + 2 q^{77} + 10 q^{78} - 56 q^{79} + q^{80} - 3 q^{81} + 12 q^{82} + 52 q^{83} - 3 q^{84} - 53 q^{85} - 31 q^{86} + 5 q^{87} + 13 q^{88} - 104 q^{89} - q^{90} + 34 q^{91} - 12 q^{92} + 32 q^{93} - 14 q^{94} - 92 q^{95} - 3 q^{96} - 82 q^{97} + 3 q^{98} - 13 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 10 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9 + 10 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 - 3 * q^14 - q^15 - 3 * q^16 + 5 * q^17 + 3 * q^18 + 18 * q^19 + q^20 - 3 * q^21 + 2 * q^22 + 21 * q^23 + 30 * q^24 + 13 * q^25 - 10 * q^26 + 3 * q^27 + 3 * q^28 + 17 * q^29 - 10 * q^30 + 12 * q^31 + 3 * q^32 + 13 * q^33 + 17 * q^34 - q^35 - 3 * q^36 + 16 * q^37 + 15 * q^38 + 12 * q^39 - 12 * q^40 + 10 * q^41 + 3 * q^42 - 35 * q^43 + 9 * q^44 + 12 * q^45 + q^46 - 8 * q^47 + 3 * q^48 - 3 * q^49 - 2 * q^50 + 6 * q^51 - q^52 + 42 * q^53 - 3 * q^54 + 49 * q^55 - 3 * q^56 + 15 * q^57 + 5 * q^58 - 6 * q^59 + 10 * q^60 - 18 * q^61 - 34 * q^62 + 3 * q^63 - 3 * q^64 + 34 * q^65 - 2 * q^66 + 72 * q^67 - 6 * q^68 - 10 * q^69 + 12 * q^70 + 17 * q^71 + 3 * q^72 + 9 * q^73 - 16 * q^74 - 2 * q^75 + 18 * q^76 + 2 * q^77 + 10 * q^78 - 56 * q^79 + q^80 - 3 * q^81 + 12 * q^82 + 52 * q^83 - 3 * q^84 - 53 * q^85 - 31 * q^86 + 5 * q^87 + 13 * q^88 - 104 * q^89 - q^90 + 34 * q^91 - 12 * q^92 + 32 * q^93 - 14 * q^94 - 92 * q^95 - 3 * q^96 - 82 * q^97 + 3 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−2.54794	+	1.63746i	−1.13947	+	0.732295i	−0.967516	−	0.252810i	$-0.918645\pi$
$5$	−2.54794	+	1.63746i	−1.13947	+	0.732295i	−0.171957	+	0.985104i	$0.555009\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.431035	−	2.99791i	−0.136305	−	0.948023i
$11$	1.48774	+	3.25770i	0.448572	+	0.982235i	0.989945	+	0.141453i	$0.0451773\pi$
$11$	1.48774	+	3.25770i	0.448572	+	0.982235i	−0.541373	+	0.840782i	$0.682095\pi$
$12$	−0.415415	−	0.909632i	−0.119920	−	0.262588i
$13$	0.0270409	+	0.188073i	0.00749978	+	0.0521621i	0.993228	−	0.116184i	$-0.0370663\pi$
$13$	0.0270409	+	0.188073i	0.00749978	+	0.0521621i	−0.985728	+	0.168346i	$0.946157\pi$
$14$	0.841254	+	0.540641i	0.224834	+	0.144492i
$15$	−2.90606	+	0.853295i	−0.750340	+	0.220320i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−1.17640	+	1.35764i	−0.285319	+	0.329275i	−0.880258	−	0.474495i	$-0.842631\pi$
$17$	−1.17640	+	1.35764i	−0.285319	+	0.329275i	0.594939	+	0.803771i	$0.297176\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	0.336450	+	0.388284i	0.0771869	+	0.0890785i	0.793029	−	0.609183i	$-0.208503\pi$
$19$	0.336450	+	0.388284i	0.0771869	+	0.0890785i	−0.715843	+	0.698262i	$0.753957\pi$
$20$	2.90606	+	0.853295i	0.649814	+	0.190803i
$21$	0.415415	−	0.909632i	0.0906510	−	0.198498i
$22$	−3.58134			−0.763545
$23$	−4.76027	−	0.582923i	−0.992586	−	0.121548i
$23$	−4.76027	−	0.582923i	−0.992586	−	0.121548i
$24$	1.00000			0.204124
$25$	1.73364	−	3.79614i	0.346728	−	0.759228i
$26$	−0.182311	−	0.0535312i	−0.0357541	−	0.0104983i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	−0.841254	+	0.540641i	−0.158982	+	0.102172i
$29$	−4.35185	+	5.02231i	−0.808119	+	0.932619i	−0.998797	−	0.0490337i	$-0.984386\pi$
$29$	−4.35185	+	5.02231i	−0.808119	+	0.932619i	0.190678	+	0.981653i	$0.438931\pi$
$30$	0.431035	−	2.99791i	0.0786958	−	0.547341i
$31$	−1.36329	+	0.400298i	−0.244854	+	0.0718957i	−0.401857	−	0.915703i	$-0.631635\pi$
$31$	−1.36329	+	0.400298i	−0.244854	+	0.0718957i	0.157003	+	0.987598i	$0.449817\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	0.509678	+	3.54489i	0.0887236	+	0.617086i
$34$	−0.746256	−	1.63407i	−0.127982	−	0.280241i
$35$	1.25818	+	2.75504i	0.212672	+	0.465687i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−6.45350	−	4.14741i	−1.06095	−	0.681830i	−0.110868	−	0.993835i	$-0.535363\pi$
$37$	−6.45350	−	4.14741i	−1.06095	−	0.681830i	−0.950080	+	0.312005i	$0.898999\pi$
$38$	−0.492962	+	0.144747i	−0.0799690	+	0.0234810i
$39$	−0.0270409	+	0.188073i	−0.00433000	+	0.0301158i
$40$	−1.98340	+	2.28897i	−0.313604	+	0.361918i
$41$	−5.70368	+	3.66553i	−0.890766	+	0.572460i	−0.904038	−	0.427452i	$-0.859411\pi$
$41$	−5.70368	+	3.66553i	−0.890766	+	0.572460i	0.0132727	+	0.999912i	$0.495775\pi$
$42$	0.654861	+	0.755750i	0.101047	+	0.116615i
$43$	−7.31409	−	2.14761i	−1.11539	−	0.327507i	−0.328439	−	0.944525i	$-0.606522\pi$
$43$	−7.31409	−	2.14761i	−1.11539	−	0.327507i	−0.786949	+	0.617018i	$0.788341\pi$
$44$	1.48774	−	3.25770i	0.224286	−	0.491117i
$45$	−3.02874			−0.451498
$46$	2.50773	−	4.08794i	0.369745	−	0.602734i
$47$	2.51907			0.367444			0.183722	−	0.982978i	$-0.441185\pi$
$47$	2.51907			0.367444			0.183722	+	0.982978i	$0.441185\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	2.73291	+	3.15395i	0.386492	+	0.446035i
$51$	−1.51124	+	0.971213i	−0.211616	+	0.135997i
$52$	0.124428	−	0.143598i	0.0172551	−	0.0199134i
$53$	1.71439	−	11.9238i	0.235489	−	1.63786i	−0.438220	−	0.898868i	$-0.644391\pi$
$53$	1.71439	−	11.9238i	0.235489	−	1.63786i	0.673709	−	0.738997i	$-0.264700\pi$
$54$	−0.959493	+	0.281733i	−0.130570	+	0.0383389i
$55$	−9.12504	−	5.86431i	−1.23042	−	0.790743i
$56$	−0.142315	−	0.989821i	−0.0190176	−	0.132270i
$57$	0.213429	+	0.467345i	0.0282694	+	0.0619013i
$58$	−2.76063	−	6.04493i	−0.362488	−	0.793738i
$59$	0.778932	+	5.41759i	0.101408	+	0.705310i	0.975572	+	0.219679i	$0.0705011\pi$
$59$	0.778932	+	5.41759i	0.101408	+	0.705310i	−0.874164	+	0.485631i	$0.838590\pi$
$60$	2.54794	+	1.63746i	0.328937	+	0.211395i
$61$	−11.3146	+	3.32225i	−1.44868	+	0.425371i	−0.909105	−	0.416567i	$-0.863233\pi$
$61$	−11.3146	+	3.32225i	−1.44868	+	0.425371i	−0.539575	+	0.841937i	$0.681415\pi$
$62$	0.202207	−	1.40638i	0.0256803	−	0.178611i
$63$	0.654861	−	0.755750i	0.0825047	−	0.0952155i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.376861	−	0.434921i	−0.0467439	−	0.0539453i
$66$	−3.43627	−	1.00898i	−0.422976	−	0.124197i
$67$	5.13699	−	11.2484i	0.627584	−	1.37422i	−0.282289	−	0.959329i	$-0.591094\pi$
$67$	5.13699	−	11.2484i	0.627584	−	1.37422i	0.909873	−	0.414887i	$-0.136179\pi$
$68$	1.79641			0.217847
$69$	−4.40322	−	1.90043i	−0.530085	−	0.228785i
$70$	−3.02874			−0.362004
$71$	−2.92492	+	6.40468i	−0.347124	+	0.760096i	0.652872	+	0.757468i	$0.273564\pi$
$71$	−2.92492	+	6.40468i	−0.347124	+	0.760096i	−0.999997	+	0.00262790i	$0.999164\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	9.36817	+	10.8114i	1.09646	+	1.26538i	0.961581	+	0.274522i	$0.0885196\pi$
$73$	9.36817	+	10.8114i	1.09646	+	1.26538i	0.134881	+	0.990862i	$0.456935\pi$
$74$	6.45350	−	4.14741i	0.750204	−	0.482127i
$75$	2.73291	−	3.15395i	0.315569	−	0.364186i
$76$	0.0731176	−	0.508544i	0.00838716	−	0.0583340i
$77$	3.43627	−	1.00898i	0.391600	−	0.114984i
$78$	−0.159844	−	0.102726i	−0.0180988	−	0.0116314i
$79$	2.08075	+	14.4719i	0.234103	+	1.62822i	0.680053	+	0.733163i	$0.261957\pi$
$79$	2.08075	+	14.4719i	0.234103	+	1.62822i	−0.445951	+	0.895058i	$0.647134\pi$
$80$	−1.25818	−	2.75504i	−0.140669	−	0.308023i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.964892	−	6.71097i	−0.106554	−	0.741103i
$83$	11.7111	+	7.52625i	1.28546	+	0.826114i	0.991551	−	0.129720i	$-0.0414079\pi$
$83$	11.7111	+	7.52625i	1.28546	+	0.826114i	0.293907	+	0.955834i	$0.405044\pi$
$84$	−0.959493	+	0.281733i	−0.104689	+	0.0307395i
$85$	0.774316	−	5.38548i	0.0839863	−	0.584138i
$86$	4.99191	−	5.76098i	0.538292	−	0.621222i
$87$	−5.59052	+	3.59281i	−0.599367	+	0.385190i
$88$	2.34528	+	2.70660i	0.250008	+	0.288524i
$89$	−10.2775	−	3.01775i	−1.08941	−	0.319881i	−0.312776	−	0.949827i	$-0.601259\pi$
$89$	−10.2775	−	3.01775i	−1.08941	−	0.319881i	−0.776639	+	0.629946i	$0.783077\pi$
$90$	1.25818	−	2.75504i	0.132624	−	0.290407i
$91$	0.190007			0.0199182
$92$	2.67677	+	3.97931i	0.279073	+	0.414872i
$93$	−1.42084			−0.147335
$94$	−1.04646	+	2.29143i	−0.107934	+	0.236343i
$95$	−1.49305	−	0.438400i	−0.153184	−	0.0449789i
$96$	−0.654861	−	0.755750i	−0.0668364	−	0.0771334i
$97$	−4.85431	+	3.11967i	−0.492880	+	0.316755i	−0.763363	−	0.645970i	$-0.776453\pi$
$97$	−4.85431	+	3.11967i	−0.492880	+	0.316755i	0.270483	+	0.962725i	$0.412817\pi$
$98$	0.654861	−	0.755750i	0.0661509	−	0.0763422i
$99$	−0.509678	+	3.54489i	−0.0512246	+	0.356275i
$100$	−4.00422	+	1.17575i	−0.400422	+	0.117575i
$101$	5.41455	+	3.47972i	0.538767	+	0.346245i	0.781557	−	0.623834i	$-0.214426\pi$
$101$	5.41455	+	3.47972i	0.538767	+	0.346245i	−0.242789	+	0.970079i	$0.578062\pi$
$102$	−0.255656	−	1.77813i	−0.0253137	−	0.176061i
$103$	2.37127	+	5.19237i	0.233649	+	0.511619i	0.989746	−	0.142840i	$-0.0456236\pi$
$103$	2.37127	+	5.19237i	0.233649	+	0.511619i	−0.756097	+	0.654459i	$0.772896\pi$
$104$	0.0789319	+	0.172837i	0.00773991	+	0.0169480i
$105$	0.431035	+	2.99791i	0.0420647	+	0.292566i
$106$	10.1341	+	6.51280i	0.984313	+	0.632579i
$107$	5.86722	−	1.72277i	0.567205	−	0.166547i	0.0144582	−	0.999895i	$-0.495398\pi$
$107$	5.86722	−	1.72277i	0.567205	−	0.166547i	0.552747	+	0.833349i	$0.313579\pi$
$108$	0.142315	−	0.989821i	0.0136943	−	0.0952456i
$109$	9.59507	−	11.0733i	0.919041	−	1.06063i	−0.0789254	−	0.996881i	$-0.525149\pi$
$109$	9.59507	−	11.0733i	0.919041	−	1.06063i	0.997966	−	0.0637489i	$-0.0203057\pi$
$110$	9.12504	−	5.86431i	0.870039	−	0.559140i
$111$	−5.02363	−	5.79757i	−0.476821	−	0.550281i
$112$	0.959493	+	0.281733i	0.0906636	+	0.0266212i
$113$	−5.06254	+	11.0854i	−0.476243	+	1.04283i	0.507236	+	0.861807i	$0.330667\pi$
$113$	−5.06254	+	11.0854i	−0.476243	+	1.04283i	−0.983479	+	0.181020i	$0.942060\pi$
$114$	−0.513773			−0.0481193
$115$	13.0834	−	6.30951i	1.22003	−	0.588365i
$116$	6.64546			0.617016
$117$	−0.0789319	+	0.172837i	−0.00729725	+	0.0159788i
$118$	−5.25159	−	1.54201i	−0.483448	−	0.141953i
$119$	1.17640	+	1.35764i	0.107840	+	0.124454i
$120$	−2.54794	+	1.63746i	−0.232594	+	0.149479i
$121$	−1.19579	+	1.38001i	−0.108708	+	0.125456i
$122$	1.67821	−	11.6722i	0.151938	−	1.05675i
$123$	−6.50534	+	1.91014i	−0.586567	+	0.172232i
$124$	1.19529	+	0.768166i	0.107340	+	0.0689834i
$125$	−0.356350	−	2.47847i	−0.0318729	−	0.221681i
$126$	0.415415	+	0.909632i	0.0370081	+	0.0810365i
$127$	−1.94683	−	4.26297i	−0.172754	−	0.378278i	0.803374	−	0.595474i	$-0.203036\pi$
$127$	−1.94683	−	4.26297i	−0.172754	−	0.378278i	−0.976128	+	0.217197i	$0.930309\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	−6.41276	−	4.12123i	−0.564612	−	0.362854i
$130$	0.552172	−	0.162132i	0.0484287	−	0.0142199i
$131$	−0.715875	+	4.97902i	−0.0625463	+	0.435019i	0.934354	+	0.356346i	$0.115977\pi$
$131$	−0.715875	+	4.97902i	−0.0625463	+	0.435019i	−0.996900	+	0.0786731i	$0.974932\pi$
$132$	2.34528	−	2.70660i	0.204131	−	0.235579i
$133$	0.432214	−	0.277767i	0.0374777	−	0.0240854i
$134$	8.09796	+	9.34555i	0.699558	+	0.807332i
$135$	−2.90606	−	0.853295i	−0.250113	−	0.0734399i
$136$	−0.746256	+	1.63407i	−0.0639909	+	0.140121i
$137$	1.33042			0.113666			0.0568329	−	0.998384i	$-0.481900\pi$
$137$	1.33042			0.113666			0.0568329	+	0.998384i	$0.481900\pi$
$138$	3.55786	−	3.21584i	0.302865	−	0.273751i
$139$	−6.39029			−0.542017			−0.271009	−	0.962577i	$-0.587357\pi$
$139$	−6.39029			−0.542017			−0.271009	+	0.962577i	$0.587357\pi$
$140$	1.25818	−	2.75504i	0.106336	−	0.232843i
$141$	2.41703	+	0.709704i	0.203551	+	0.0597679i
$142$	−4.61085	−	5.32120i	−0.386934	−	0.446545i
$143$	−0.572457	+	0.367896i	−0.0478713	+	0.0307650i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	2.86443	−	19.9225i	0.237878	−	1.65448i
$146$	−13.7261	+	4.03035i	−1.13598	+	0.333554i
$147$	−0.841254	−	0.540641i	−0.0693854	−	0.0445913i
$148$	1.09174	+	7.59321i	0.0897403	+	0.624158i
$149$	−1.98786	−	4.35282i	−0.162852	−	0.356597i	0.810560	−	0.585655i	$-0.199163\pi$
$149$	−1.98786	−	4.35282i	−0.162852	−	0.356597i	−0.973413	+	0.229058i	$0.926435\pi$
$150$	1.73364	+	3.79614i	0.141551	+	0.309953i
$151$	−1.26319	−	8.78571i	−0.102797	−	0.714971i	−0.974410	−	0.224776i	$-0.927835\pi$
$151$	−1.26319	−	8.78571i	−0.102797	−	0.714971i	0.871613	−	0.490194i	$-0.163074\pi$
$152$	0.432214	+	0.277767i	0.0350572	+	0.0225299i
$153$	−1.72364	+	0.506108i	−0.139348	+	0.0409164i
$154$	−0.509678	+	3.54489i	−0.0410710	+	0.285655i
$155$	2.81811	−	3.25227i	0.226356	−	0.261229i
$156$	0.159844	−	0.102726i	0.0127978	−	0.00822464i
$157$	4.46956	+	5.15815i	0.356710	+	0.411665i	0.905535	−	0.424272i	$-0.139470\pi$
$157$	4.46956	+	5.15815i	0.356710	+	0.411665i	−0.548825	+	0.835937i	$0.684925\pi$
$158$	−14.0285	−	4.11914i	−1.11605	−	0.327701i
$159$	5.00428	−	10.9578i	0.396865	−	0.869013i
$160$	3.02874			0.239443
$161$	−1.25445	+	4.62886i	−0.0988643	+	0.364805i
$162$	−1.00000			−0.0785674
$163$	−7.09615	+	15.5384i	−0.555813	+	1.21706i	0.398201	+	0.917298i	$0.369635\pi$
$163$	−7.09615	+	15.5384i	−0.555813	+	1.21706i	−0.954014	+	0.299763i	$0.903093\pi$
$164$	6.50534	+	1.91014i	0.507982	+	0.149157i
$165$	−7.10325	−	8.19759i	−0.552987	−	0.638181i
$166$	−11.7111	+	7.52625i	−0.908956	+	0.584151i
$167$	−1.45816	+	1.68281i	−0.112836	+	0.130219i	−0.809358	−	0.587316i	$-0.800184\pi$
$167$	−1.45816	+	1.68281i	−0.112836	+	0.130219i	0.696522	+	0.717536i	$0.254730\pi$
$168$	0.142315	−	0.989821i	0.0109798	−	0.0763664i
$169$	12.4388	−	3.65235i	0.956828	−	0.280950i
$170$	4.57715	+	2.94155i	0.351051	+	0.225607i
$171$	0.0731176	+	0.508544i	0.00559144	+	0.0388893i
$172$	3.16665	+	6.93400i	0.241455	+	0.528713i
$173$	4.96255	+	10.8665i	0.377295	+	0.826162i	0.999076	+	0.0429705i	$0.0136822\pi$
$173$	4.96255	+	10.8665i	0.377295	+	0.826162i	−0.621781	+	0.783191i	$0.713591\pi$
$174$	−0.945748	−	6.57782i	−0.0716970	−	0.498663i
$175$	−3.51078	−	2.25624i	−0.265390	−	0.170556i
$176$	−3.43627	+	1.00898i	−0.259019	+	0.0760548i
$177$	−0.778932	+	5.41759i	−0.0585481	+	0.407211i
$178$	7.01448	−	8.09514i	0.525757	−	0.606756i
$179$	13.8518	−	8.90204i	1.03534	−	0.665370i	0.0915064	−	0.995804i	$-0.470832\pi$
$179$	13.8518	−	8.90204i	1.03534	−	0.665370i	0.943829	+	0.330435i	$0.107195\pi$
$180$	1.98340	+	2.28897i	0.147834	+	0.170610i
$181$	−0.924593	−	0.271485i	−0.0687244	−	0.0201793i	0.247190	−	0.968967i	$-0.420493\pi$
$181$	−0.924593	−	0.271485i	−0.0687244	−	0.0201793i	−0.315914	+	0.948788i	$0.602311\pi$
$182$	−0.0789319	+	0.172837i	−0.00585082	+	0.0128115i
$183$	−11.7922			−0.871706
$184$	−4.73168	+	0.781813i	−0.348824	+	0.0576360i
$185$	23.2343			1.70822
$186$	0.590240	−	1.29245i	0.0432785	−	0.0947667i
$187$	−6.17296	−	1.81254i	−0.451412	−	0.132546i
$188$	−1.64964	−	1.90379i	−0.120312	−	0.138848i
$189$	0.841254	−	0.540641i	0.0611922	−	0.0393258i
$190$	1.01902	−	1.17601i	0.0739275	−	0.0853168i
$191$	0.000368617	−	0.00256379i	2.66722e−5	−	0.000185509i	−0.989808	−	0.142408i	$-0.954516\pi$
$191$	0.000368617	−	0.00256379i	2.66722e−5	−	0.000185509i	0.989835	+	0.142222i	$0.0454247\pi$
$192$	0.959493	−	0.281733i	0.0692454	−	0.0203323i
$193$	7.66151	+	4.92375i	0.551487	+	0.354419i	0.786517	−	0.617569i	$-0.211882\pi$
$193$	7.66151	+	4.92375i	0.551487	+	0.354419i	−0.235029	+	0.971988i	$0.575519\pi$
$194$	−0.821203	−	5.71159i	−0.0589589	−	0.410069i
$195$	−0.239064	−	0.523477i	−0.0171197	−	0.0374870i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	0.180704	+	1.25682i	0.0128746	+	0.0895448i	0.995246	−	0.0973968i	$-0.0310516\pi$
$197$	0.180704	+	1.25682i	0.0128746	+	0.0895448i	−0.982371	+	0.186942i	$0.940142\pi$
$198$	−3.01282	−	1.93622i	−0.214112	−	0.137601i
$199$	−17.8362	+	5.23717i	−1.26437	+	0.371253i	−0.844120	−	0.536154i	$-0.819876\pi$
$199$	−17.8362	+	5.23717i	−1.26437	+	0.371253i	−0.420252	+	0.907407i	$0.638058\pi$
$200$	0.593918	−	4.13079i	0.0419964	−	0.292091i
$201$	8.09796	−	9.34555i	0.571186	−	0.659184i
$202$	−5.41455	+	3.47972i	−0.380966	+	0.244832i
$203$	4.35185	+	5.02231i	0.305440	+	0.352497i
$204$	1.72364	+	0.506108i	0.120679	+	0.0354346i
$205$	8.53046	−	18.6791i	0.595794	−	1.30461i
$206$	−5.70820			−0.397709
$207$	−3.68944	−	3.06398i	−0.256434	−	0.212962i
$208$	−0.190007			−0.0131746
$209$	−0.764363	+	1.67372i	−0.0528721	+	0.115774i
$210$	−2.90606	−	0.853295i	−0.200537	−	0.0588829i
$211$	3.46875	+	4.00315i	0.238799	+	0.275588i	0.862481	−	0.506090i	$-0.168910\pi$
$211$	3.46875	+	4.00315i	0.238799	+	0.275588i	−0.623682	+	0.781678i	$0.714364\pi$
$212$	−10.1341	+	6.51280i	−0.696014	+	0.447301i
$213$	−4.61085	+	5.32120i	−0.315930	+	0.364603i
$214$	−0.870243	+	6.05268i	−0.0594886	+	0.413752i
$215$	22.1525	−	6.50455i	1.51079	−	0.443607i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	0.202207	+	1.40638i	0.0137267	+	0.0954714i
$218$	6.08669	+	13.3280i	0.412243	+	0.902686i
$219$	5.94276	+	13.0128i	0.401574	+	0.879325i
$220$	1.54368	+	10.7366i	0.104075	+	0.723858i
$221$	−0.287146	−	0.184538i	−0.0193155	−	0.0124133i
$222$	7.36055	−	2.16125i	0.494008	−	0.145054i
$223$	−0.658925	+	4.58292i	−0.0441249	+	0.306895i	0.955793	+	0.294042i	$0.0950005\pi$
$223$	−0.658925	+	4.58292i	−0.0441249	+	0.306895i	−0.999917	+	0.0128533i	$0.995909\pi$
$224$	−0.654861	+	0.755750i	−0.0437547	+	0.0504956i
$225$	3.51078	−	2.25624i	0.234052	−	0.150416i
$226$	−7.98059	−	9.21009i	−0.530861	−	0.612646i
$227$	−18.5810	−	5.45588i	−1.23327	−	0.362119i	−0.400784	−	0.916172i	$-0.631262\pi$
$227$	−18.5810	−	5.45588i	−1.23327	−	0.362119i	−0.832481	+	0.554053i	$0.813081\pi$
$228$	0.213429	−	0.467345i	0.0141347	−	0.0309507i
$229$	24.2920			1.60526			0.802629	−	0.596479i	$-0.203434\pi$
$229$	24.2920			1.60526			0.802629	+	0.596479i	$0.203434\pi$
$230$	0.304290	+	14.5221i	0.0200643	+	0.957562i
$231$	3.58134			0.235635
$232$	−2.76063	+	6.04493i	−0.181244	+	0.396869i
$233$	8.78044	+	2.57817i	0.575226	+	0.168902i	0.556390	−	0.830921i	$-0.312186\pi$
$233$	8.78044	+	2.57817i	0.575226	+	0.168902i	0.0188356	+	0.999823i	$0.494004\pi$
$234$	−0.124428	−	0.143598i	−0.00813413	−	0.00938729i
$235$	−6.41844	+	4.12488i	−0.418693	+	0.269077i
$236$	3.58425	−	4.13645i	0.233315	−	0.269260i
$237$	−2.08075	+	14.4719i	−0.135159	+	0.940053i
$238$	−1.72364	+	0.506108i	−0.111727	+	0.0328061i
$239$	−4.45762	−	2.86474i	−0.288340	−	0.185305i	0.388473	−	0.921460i	$-0.373003\pi$
$239$	−4.45762	−	2.86474i	−0.288340	−	0.185305i	−0.676812	+	0.736156i	$0.736639\pi$
$240$	−0.431035	−	2.99791i	−0.0278232	−	0.193514i
$241$	7.27617	+	15.9326i	0.468700	+	1.02631i	0.985418	+	0.170153i	$0.0544263\pi$
$241$	7.27617	+	15.9326i	0.468700	+	1.02631i	−0.516718	+	0.856156i	$0.672846\pi$
$242$	−0.758556	−	1.66101i	−0.0487618	−	0.106774i
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$	9.92025	+	6.37536i	0.635079	+	0.408140i
$245$	2.90606	−	0.853295i	0.185661	−	0.0545150i
$246$	0.964892	−	6.71097i	0.0615193	−	0.427876i
$247$	−0.0639279	+	0.0737768i	−0.00406764	+	0.00469430i
$248$	−1.19529	+	0.768166i	−0.0759010	+	0.0487786i
$249$	9.11631	+	10.5208i	0.577723	+	0.666727i
$250$	2.40252	+	0.705445i	0.151949	+	0.0446162i
$251$	6.54449	−	14.3304i	0.413085	−	0.904530i	−0.582689	−	0.812695i	$-0.698000\pi$
$251$	6.54449	−	14.3304i	0.413085	−	0.904530i	0.995774	−	0.0918346i	$-0.0292731\pi$
$252$	−1.00000			−0.0629941
$253$	−5.18307	−	16.3748i	−0.325857	−	1.02948i
$254$	4.68648			0.294056
$255$	2.26022	−	4.94918i	0.141540	−	0.309930i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	17.8901	+	20.6462i	1.11595	+	1.28788i	0.953578	+	0.301148i	$0.0973697\pi$
$257$	17.8901	+	20.6462i	1.11595	+	1.28788i	0.162374	+	0.986729i	$0.448085\pi$
$258$	6.41276	−	4.12123i	0.399241	−	0.256577i
$259$	−5.02363	+	5.79757i	−0.312153	+	0.360244i
$260$	−0.0818997	+	0.569625i	−0.00507921	+	0.0353266i
$261$	−6.37628	+	1.87224i	−0.394682	+	0.115889i
$262$	−4.23169	−	2.71954i	−0.261435	−	0.168014i
$263$	1.65308	+	11.4974i	0.101934	+	0.708963i	0.975136	+	0.221606i	$0.0711299\pi$
$263$	1.65308	+	11.4974i	0.101934	+	0.708963i	−0.873203	+	0.487357i	$0.837961\pi$
$264$	1.48774	+	3.25770i	0.0915643	+	0.200498i
$265$	15.1567	+	33.1884i	0.931066	+	2.03875i
$266$	0.0731176	+	0.508544i	0.00448313	+	0.0311808i
$267$	−9.01101	−	5.79102i	−0.551465	−	0.354405i
$268$	−11.8650	+	3.48389i	−0.724772	+	0.212812i
$269$	0.288902	−	2.00936i	0.0176147	−	0.122513i	−0.979117	−	0.203298i	$-0.934834\pi$
$269$	0.288902	−	2.00936i	0.0176147	−	0.122513i	0.996731	+	0.0807857i	$0.0257429\pi$
$270$	1.98340	−	2.28897i	0.120706	−	0.139302i
$271$	−1.45257	+	0.933512i	−0.0882375	+	0.0567068i	−0.584016	−	0.811742i	$-0.698519\pi$
$271$	−1.45257	+	0.933512i	−0.0882375	+	0.0567068i	0.495778	+	0.868449i	$0.334883\pi$
$272$	−1.17640	−	1.35764i	−0.0713297	−	0.0823188i
$273$	0.182311	+	0.0535312i	0.0110339	+	0.00323986i
$274$	−0.552678	+	1.21020i	−0.0333885	+	0.0731106i
$275$	14.9459			0.901272
$276$	1.44724	+	4.57225i	0.0871138	+	0.275217i
$277$	3.11698			0.187281			0.0936406	−	0.995606i	$-0.470150\pi$
$277$	3.11698			0.187281			0.0936406	+	0.995606i	$0.470150\pi$
$278$	2.65462	−	5.81281i	0.159214	−	0.348629i
$279$	−1.36329	−	0.400298i	−0.0816180	−	0.0239652i
$280$	1.98340	+	2.28897i	0.118531	+	0.136792i
$281$	−10.1515	+	6.52395i	−0.605585	+	0.389186i	−0.807199	−	0.590279i	$-0.799018\pi$
$281$	−10.1515	+	6.52395i	−0.605585	+	0.389186i	0.201614	+	0.979465i	$0.435381\pi$
$282$	−1.64964	+	1.90379i	−0.0982347	+	0.113369i
$283$	0.196417	−	1.36611i	0.0116758	−	0.0812067i	−0.983150	−	0.182798i	$-0.941484\pi$
$283$	0.196417	−	1.36611i	0.0116758	−	0.0812067i	0.994826	+	0.101592i	$0.0323935\pi$
$284$	6.75575	−	1.98367i	0.400880	−	0.117709i
$285$	−1.30906	−	0.841284i	−0.0775422	−	0.0498333i
$286$	−0.0968426	−	0.673555i	−0.00572642	−	0.0398281i
$287$	2.81651	+	6.16729i	0.166253	+	0.364043i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	1.96009	+	13.6327i	0.115299	+	0.801925i
$290$	16.9322	+	10.8817i	0.994295	+	0.638995i
$291$	−5.53659	+	1.62569i	−0.324561	+	0.0952996i
$292$	2.03590	−	14.1600i	0.119142	−	0.828650i
$293$	2.56509	−	2.96027i	0.149854	−	0.172941i	−0.675859	−	0.737031i	$-0.736227\pi$
$293$	2.56509	−	2.96027i	0.149854	−	0.172941i	0.825713	+	0.564090i	$0.190773\pi$
$294$	0.841254	−	0.540641i	0.0490629	−	0.0315308i
$295$	−10.8558	−	12.5282i	−0.632047	−	0.729421i
$296$	−7.36055	−	2.16125i	−0.427823	−	0.125620i
$297$	−1.48774	+	3.25770i	−0.0863276	+	0.189031i
$298$	4.78525			0.277202
$299$	−0.0190895	−	0.911043i	−0.00110398	−	0.0526870i
$300$	−4.17327			−0.240944
$301$	−3.16665	+	6.93400i	−0.182523	+	0.399669i
$302$	8.51651	+	2.50067i	0.490070	+	0.143898i
$303$	4.21487	+	4.86422i	0.242138	+	0.279442i
$304$	−0.432214	+	0.277767i	−0.0247892	+	0.0159310i
$305$	23.3887	−	26.9920i	1.33923	−	1.54556i
$306$	0.255656	−	1.77813i	0.0146149	−	0.101649i
$307$	26.1756	−	7.68585i	1.49392	−	0.438655i	0.570131	−	0.821554i	$-0.306893\pi$
$307$	26.1756	−	7.68585i	1.49392	−	0.438655i	0.923790	+	0.382899i	$0.125074\pi$
$308$	−3.01282	−	1.93622i	−0.171671	−	0.110326i
$309$	0.812362	+	5.65010i	0.0462137	+	0.321423i
$310$	1.78768	+	3.91448i	0.101534	+	0.222328i
$311$	10.7327	+	23.5013i	0.608594	+	1.33263i	0.923532	+	0.383522i	$0.125289\pi$
$311$	10.7327	+	23.5013i	0.608594	+	1.33263i	−0.314938	+	0.949112i	$0.601984\pi$
$312$	0.0270409	+	0.188073i	0.00153089	+	0.0106476i
$313$	8.40469	+	5.40137i	0.475061	+	0.305303i	0.756173	−	0.654372i	$-0.227067\pi$
$313$	8.40469	+	5.40137i	0.475061	+	0.305303i	−0.281112	+	0.959675i	$0.590703\pi$
$314$	−6.54874	+	1.92288i	−0.369567	+	0.108515i
$315$	−0.431035	+	2.99791i	−0.0242861	+	0.168913i
$316$	9.57456	−	11.0496i	0.538611	−	0.621590i
$317$	19.5108	−	12.5389i	1.09584	−	0.704252i	0.137675	−	0.990477i	$-0.456037\pi$
$317$	19.5108	−	12.5389i	1.09584	−	0.704252i	0.958162	+	0.286225i	$0.0924006\pi$
$318$	7.88875	+	9.10410i	0.442379	+	0.510533i
$319$	−22.8356	−	6.70515i	−1.27855	−	0.375416i
$320$	−1.25818	+	2.75504i	−0.0703346	+	0.154011i
$321$	6.11492			0.341301
$322$	−3.68944	−	3.06398i	−0.205605	−	0.170749i
$323$	−0.922948			−0.0513542
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	0.760831	+	0.223400i	0.0422033	+	0.0123920i
$326$	−11.1864	−	12.9098i	−0.619556	−	0.715006i
$327$	12.3261	−	7.92151i	0.681635	−	0.438060i
$328$	−4.43994	+	5.12397i	−0.245155	+	0.282924i
$329$	0.358501	−	2.49343i	0.0197648	−	0.137467i
$330$	10.4076	−	3.05594i	0.572919	−	0.168224i
$331$	−11.7588	−	7.55691i	−0.646321	−	0.415365i	0.175999	−	0.984390i	$-0.443684\pi$
$331$	−11.7588	−	7.55691i	−0.646321	−	0.415365i	−0.822320	+	0.569025i	$0.807321\pi$
$332$	−1.98116	−	13.7793i	−0.108730	−	0.756237i
$333$	−3.18677	−	6.97805i	−0.174634	−	0.382395i
$334$	−0.924992	−	2.02545i	−0.0506133	−	0.110828i
$335$	5.33015	+	37.0720i	0.291217	+	2.02546i
$336$	0.841254	+	0.540641i	0.0458941	+	0.0294944i
$337$	16.6955	−	4.90223i	0.909460	−	0.267041i	0.206646	−	0.978416i	$-0.433745\pi$
$337$	16.6955	−	4.90223i	0.909460	−	0.267041i	0.702813	+	0.711374i	$0.251927\pi$
$338$	−1.84495	+	12.8319i	−0.100352	+	0.697966i
$339$	−7.98059	+	9.21009i	−0.433446	+	0.500223i
$340$	−4.57715	+	2.94155i	−0.248231	+	0.159528i
$341$	−3.33228	−	3.84565i	−0.180453	−	0.208254i
$342$	−0.492962	−	0.144747i	−0.0266563	−	0.00782700i
$343$	−0.415415	+	0.909632i	−0.0224303	+	0.0491155i
$344$	−7.62286			−0.410997
$345$	14.3310	−	2.36791i	0.771556	−	0.127484i
$346$	−11.9460			−0.642221
$347$	1.82783	−	4.00240i	0.0981233	−	0.214860i	−0.854204	−	0.519938i	$-0.825955\pi$
$347$	1.82783	−	4.00240i	0.0981233	−	0.214860i	0.952327	+	0.305078i	$0.0986824\pi$
$348$	6.37628	+	1.87224i	0.341804	+	0.100363i
$349$	−0.392313	−	0.452754i	−0.0210000	−	0.0242353i	0.745152	−	0.666894i	$-0.232377\pi$
$349$	−0.392313	−	0.452754i	−0.0210000	−	0.0242353i	−0.766152	+	0.642659i	$0.777831\pi$
$350$	3.51078	−	2.25624i	0.187659	−	0.120601i
$351$	−0.124428	+	0.143598i	−0.00664149	+	0.00766469i
$352$	0.509678	−	3.54489i	0.0271659	−	0.188943i
$353$	−28.5518	+	8.38356i	−1.51966	+	0.446212i	−0.931867	−	0.362801i	$-0.881820\pi$
$353$	−28.5518	+	8.38356i	−1.51966	+	0.446212i	−0.587791	+	0.809013i	$0.700002\pi$
$354$	−4.60443	−	2.95909i	−0.244723	−	0.157274i
$355$	−3.03490	−	21.1082i	−0.161076	−	1.12031i
$356$	4.44968	+	9.74343i	0.235832	+	0.516401i
$357$	0.746256	+	1.63407i	0.0394961	+	0.0864843i
$358$	2.34332	+	16.2981i	0.123848	+	0.861382i
$359$	−14.7616	−	9.48674i	−0.779090	−	0.500691i	0.0896415	−	0.995974i	$-0.471428\pi$
$359$	−14.7616	−	9.48674i	−0.779090	−	0.500691i	−0.868731	+	0.495283i	$0.835064\pi$
$360$	−2.90606	+	0.853295i	−0.153163	+	0.0449726i
$361$	2.66642	−	18.5453i	0.140338	−	0.976070i
$362$	0.631041	−	0.728260i	0.0331668	−	0.0382765i
$363$	−1.53615	+	0.987221i	−0.0806267	+	0.0518157i
$364$	−0.124428	−	0.143598i	−0.00652181	−	0.00752657i
$365$	−41.5728	−	12.2069i	−2.17602	−	0.638938i
$366$	4.89867	−	10.7266i	0.256057	−	0.560687i
$367$	11.6525			0.608254			0.304127	−	0.952632i	$-0.401635\pi$
$367$	11.6525			0.608254			0.304127	+	0.952632i	$0.401635\pi$
$368$	1.25445	−	4.62886i	0.0653926	−	0.241296i
$369$	−6.77998			−0.352952
$370$	−9.65189	+	21.1347i	−0.501778	+	1.09874i
$371$	−11.5585	−	3.39388i	−0.600087	−	0.176201i
$372$	0.930455	+	1.07380i	0.0482418	+	0.0556741i
$373$	3.35119	−	2.15368i	0.173518	−	0.111513i	−0.450999	−	0.892524i	$-0.648932\pi$
$373$	3.35119	−	2.15368i	0.173518	−	0.111513i	0.624517	+	0.781011i	$0.285296\pi$
$374$	4.21309	−	4.86216i	0.217854	−	0.251417i
$375$	0.356350	−	2.47847i	0.0184018	−	0.127987i
$376$	2.41703	−	0.709704i	0.124649	−	0.0366002i
$377$	−1.06224	−	0.682660i	−0.0547081	−	0.0351588i
$378$	0.142315	+	0.989821i	0.00731989	+	0.0509109i
$379$	−13.5407	−	29.6500i	−0.695540	−	1.52302i	−0.845297	−	0.534297i	$-0.820577\pi$
$379$	−13.5407	−	29.6500i	−0.695540	−	1.52302i	0.149757	−	0.988723i	$-0.452151\pi$
$380$	0.646422	+	1.41547i	0.0331607	+	0.0726119i
$381$	−0.666956	−	4.63878i	−0.0341692	−	0.237652i
$382$	0.00217898	+	0.00140034i	0.000111486	+	7.16478e-5i
$383$	−22.0278	+	6.46795i	−1.12557	+	0.330497i	−0.790964	−	0.611862i	$-0.790421\pi$
$383$	−22.0278	+	6.46795i	−1.12557	+	0.330497i	−0.334604	+	0.942359i	$0.608602\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−7.10325	+	8.19759i	−0.362015	+	0.417788i
$386$	−7.66151	+	4.92375i	−0.389960	+	0.250612i
$387$	−4.99191	−	5.76098i	−0.253753	−	0.292847i
$388$	5.53659	+	1.62569i	0.281078	+	0.0825319i
$389$	2.79483	−	6.11981i	0.141703	−	0.310287i	−0.825452	−	0.564472i	$-0.809080\pi$
$389$	2.79483	−	6.11981i	0.141703	−	0.310287i	0.967156	+	0.254185i	$0.0818072\pi$
$390$	0.575483			0.0291407
$391$	6.39138	−	5.77697i	0.323226	−	0.292154i
$392$	−1.00000			−0.0505076
$393$	−2.08963	+	4.57565i	−0.105408	+	0.230811i
$394$	−1.21831	−	0.357729i	−0.0613777	−	0.0180221i
$395$	−28.9989	−	33.4665i	−1.45909	−	1.68388i
$396$	3.01282	−	1.93622i	0.151400	−	0.0972987i
$397$	6.38691	−	7.37089i	0.320550	−	0.369934i	−0.572490	−	0.819912i	$-0.694022\pi$
$397$	6.38691	−	7.37089i	0.320550	−	0.369934i	0.893040	+	0.449977i	$0.148568\pi$
$398$	2.64551	−	18.3999i	0.132608	−	0.922306i
$399$	0.492962	−	0.144747i	0.0246790	−	0.00724640i
$400$	3.51078	+	2.25624i	0.175539	+	0.112812i
$401$	−5.17648	−	36.0032i	−0.258501	−	1.79791i	−0.543525	−	0.839393i	$-0.682911\pi$
$401$	−5.17648	−	36.0032i	−0.258501	−	1.79791i	0.285024	−	0.958520i	$-0.407998\pi$
$402$	5.13699	+	11.2484i	0.256210	+	0.561022i
$403$	−0.112150	−	0.245574i	−0.00558658	−	0.0122329i
$404$	−0.915979	−	6.37077i	−0.0455716	−	0.316958i
$405$	−2.54794	−	1.63746i	−0.126608	−	0.0813661i
$406$	−6.37628	+	1.87224i	−0.316449	+	0.0929179i
$407$	3.90989	−	27.1939i	0.193806	−	1.34795i
$408$	−1.17640	+	1.35764i	−0.0582404	+	0.0672131i
$409$	9.33296	−	5.99793i	0.461485	−	0.296578i	−0.289164	−	0.957280i	$-0.593377\pi$
$409$	9.33296	−	5.99793i	0.461485	−	0.296578i	0.750649	+	0.660701i	$0.229741\pi$
$410$	13.4474	+	15.5192i	0.664121	+	0.766437i
$411$	1.27653	+	0.374824i	0.0629667	+	0.0184887i
$412$	2.37127	−	5.19237i	0.116824	−	0.255810i
$413$	5.47330			0.269324
$414$	4.31975	−	2.08321i	0.212304	−	0.102384i
$415$	−42.1631			−2.06970
$416$	0.0789319	−	0.172837i	0.00386995	−	0.00847402i
$417$	−6.13144	−	1.80035i	−0.300258	−	0.0881636i
$418$	−1.20494	−	1.39058i	−0.0589357	−	0.0680154i
$419$	−29.0294	+	18.6560i	−1.41818	+	0.911408i	−0.418183	+	0.908363i	$0.637333\pi$
$419$	−29.0294	+	18.6560i	−1.41818	+	0.911408i	−0.999995	+	0.00304456i	$0.999031\pi$
$420$	1.98340	−	2.28897i	0.0967802	−	0.111690i
$421$	−3.78105	+	26.2978i	−0.184277	+	1.28167i	0.662232	+	0.749299i	$0.269609\pi$
$421$	−3.78105	+	26.2978i	−0.184277	+	1.28167i	−0.846509	+	0.532375i	$0.821300\pi$
$422$	−5.08236	+	1.49232i	−0.247406	+	0.0726448i
$423$	2.11918	+	1.36191i	0.103038	+	0.0662184i
$424$	−1.71439	−	11.9238i	−0.0832581	−	0.579073i
$425$	3.11433	+	6.81943i	0.151067	+	0.330791i
$426$	−2.92492	−	6.40468i	−0.141713	−	0.310308i
$427$	1.67821	+	11.6722i	0.0812142	+	0.564857i
$428$	−5.14420	−	3.30597i	−0.248654	−	0.159800i
$429$	−0.652917	+	0.191714i	−0.0315231	+	0.00925602i
$430$	−3.28572	+	22.8527i	−0.158451	+	1.10205i
$431$	−20.5933	+	23.7659i	−0.991945	+	1.14477i	−0.00247892	+	0.999997i	$0.500789\pi$
$431$	−20.5933	+	23.7659i	−0.991945	+	1.14477i	−0.989466	+	0.144768i	$0.953756\pi$
$432$	−0.841254	+	0.540641i	−0.0404748	+	0.0260116i
$433$	22.4020	+	25.8533i	1.07657	+	1.24243i	0.968691	+	0.248268i	$0.0798613\pi$
$433$	22.4020	+	25.8533i	1.07657	+	1.24243i	0.107882	+	0.994164i	$0.465593\pi$
$434$	−1.36329	−	0.400298i	−0.0654400	−	0.0192149i
$435$	8.36122	−	18.3085i	0.400890	−	0.877826i
$436$	−14.6521			−0.701707
$437$	−1.37525	−	2.04446i	−0.0657873	−	0.0977999i
$438$	−14.3056			−0.683548
$439$	12.9370	−	28.3281i	0.617450	−	1.35203i	−0.299910	−	0.953968i	$-0.596957\pi$
$439$	12.9370	−	28.3281i	0.617450	−	1.35203i	0.917360	−	0.398059i	$-0.130316\pi$
$440$	−10.4076	−	3.05594i	−0.496162	−	0.145686i
$441$	−0.654861	−	0.755750i	−0.0311838	−	0.0359881i
$442$	0.287146	−	0.184538i	0.0136581	−	0.00877756i
$443$	−1.49032	+	1.71992i	−0.0708071	+	0.0817157i	−0.790048	−	0.613045i	$-0.789944\pi$
$443$	−1.49032	+	1.71992i	−0.0708071	+	0.0817157i	0.719241	+	0.694761i	$0.244490\pi$
$444$	−1.09174	+	7.59321i	−0.0518116	+	0.360358i
$445$	31.1279	−	9.13998i	1.47561	−	0.433277i
$446$	−3.89505	−	2.50319i	−0.184436	−	0.118530i
$447$	−0.681012	−	4.73654i	−0.0322108	−	0.224031i
$448$	−0.415415	−	0.909632i	−0.0196265	−	0.0429761i
$449$	6.71132	+	14.6957i	0.316727	+	0.693535i	0.999305	−	0.0372775i	$-0.0118685\pi$
$449$	6.71132	+	14.6957i	0.316727	+	0.693535i	−0.682578	+	0.730813i	$0.739141\pi$
$450$	0.593918	+	4.13079i	0.0279976	+	0.194727i
$451$	−20.4268	−	13.1275i	−0.961863	−	0.618152i
$452$	11.6930	−	3.43339i	0.549995	−	0.161493i
$453$	1.26319	−	8.78571i	0.0593500	−	0.412789i
$454$	12.6817	−	14.6354i	0.595181	−	0.686875i
$455$	−0.484127	+	0.311129i	−0.0226962	+	0.0145860i
$456$	0.336450	+	0.388284i	0.0157557	+	0.0181831i
$457$	6.75518	+	1.98350i	0.315994	+	0.0927843i	0.435884	−	0.900003i	$-0.356436\pi$
$457$	6.75518	+	1.98350i	0.315994	+	0.0927843i	−0.119890	+	0.992787i	$0.538254\pi$
$458$	−10.0912	+	22.0967i	−0.471533	+	1.03251i
$459$	−1.79641			−0.0838493
$460$	−13.3362	−	5.75592i	−0.621804	−	0.268371i
$461$	−3.84693			−0.179170			−0.0895848	−	0.995979i	$-0.528554\pi$
$461$	−3.84693			−0.179170			−0.0895848	+	0.995979i	$0.528554\pi$
$462$	−1.48774	+	3.25770i	−0.0692161	+	0.151562i
$463$	9.22839	+	2.70970i	0.428879	+	0.125930i	0.489046	−	0.872258i	$-0.337345\pi$
$463$	9.22839	+	2.70970i	0.428879	+	0.125930i	−0.0601666	+	0.998188i	$0.519163\pi$
$464$	−4.35185	−	5.02231i	−0.202030	−	0.233155i
$465$	3.62022	−	2.32658i	0.167884	−	0.107892i
$466$	−5.99271	+	6.91596i	−0.277607	+	0.320376i
$467$	−1.63786	+	11.3916i	−0.0757913	+	0.527140i	0.916189	+	0.400747i	$0.131249\pi$
$467$	−1.63786	+	11.3916i	−0.0757913	+	0.527140i	−0.991980	+	0.126393i	$0.959660\pi$
$468$	0.182311	−	0.0535312i	0.00842731	−	0.00247448i
$469$	−10.4029	−	6.68553i	−0.480361	−	0.308709i
$470$	−1.08581	−	7.55195i	−0.0500845	−	0.348346i
$471$	2.83529	+	6.20843i	0.130643	+	0.286069i
$472$	2.27369	+	4.97869i	0.104655	+	0.229163i
$473$	−3.88521	−	27.0222i	−0.178642	−	1.24248i
$474$	−12.2998	−	7.90458i	−0.564947	−	0.363069i
$475$	2.05726	−	0.604067i	0.0943937	−	0.0277165i
$476$	0.255656	−	1.77813i	0.0117180	−	0.0815003i
$477$	7.88875	−	9.10410i	0.361201	−	0.416848i
$478$	4.45762	−	2.86474i	0.203887	−	0.131030i
$479$	−20.5280	−	23.6906i	−0.937950	−	1.08245i	−0.996452	−	0.0841644i	$-0.973178\pi$
$479$	−20.5280	−	23.6906i	−0.937950	−	1.08245i	0.0585022	−	0.998287i	$-0.481368\pi$
$480$	2.90606	+	0.853295i	0.132643	+	0.0389474i
$481$	0.605509	−	1.32588i	0.0276088	−	0.0604549i
$482$	−17.5154			−0.797806
$483$	−2.50773	+	4.08794i	−0.114106	+	0.186008i
$484$	1.82602			0.0830009
$485$	7.26013	−	15.8975i	0.329666	−	0.721867i
$486$	−0.959493	−	0.281733i	−0.0435235	−	0.0127796i
$487$	−4.65293	−	5.36977i	−0.210845	−	0.243328i	0.640470	−	0.767983i	$-0.278740\pi$
$487$	−4.65293	−	5.36977i	−0.210845	−	0.243328i	−0.851315	+	0.524656i	$0.824194\pi$
$488$	−9.92025	+	6.37536i	−0.449069	+	0.288599i
$489$	−11.1864	+	12.9098i	−0.505865	+	0.583800i
$490$	−0.431035	+	2.99791i	−0.0194722	+	0.135432i
$491$	14.0665	−	4.13029i	0.634811	−	0.186397i	0.0515346	−	0.998671i	$-0.483589\pi$
$491$	14.0665	−	4.13029i	0.634811	−	0.186397i	0.583276	+	0.812274i	$0.301771\pi$
$492$	5.70368	+	3.66553i	0.257142	+	0.165255i
$493$	−1.69895	−	11.8165i	−0.0765170	−	0.532187i
$494$	−0.0405531	−	0.0887989i	−0.00182457	−	0.00399525i
$495$	−4.50599	−	9.86674i	−0.202529	−	0.443477i
$496$	−0.202207	−	1.40638i	−0.00907937	−	0.0631484i
$497$	5.92323	+	3.80663i	0.265693	+	0.170751i
$498$	−13.3571	+	3.92200i	−0.598546	+	0.175749i
$499$	−4.15039	+	28.8666i	−0.185797	+	1.29225i	0.656949	+	0.753935i	$0.271847\pi$
$499$	−4.15039	+	28.8666i	−0.185797	+	1.29225i	−0.842746	+	0.538312i	$0.819062\pi$
$500$	−1.63974	+	1.89236i	−0.0733314	+	0.0846289i
$501$	−1.87319	+	1.20383i	−0.0836882	+	0.0537831i
$502$	10.3167	+	11.9062i	0.460459	+	0.531398i
$503$	−35.5603	−	10.4415i	−1.58556	−	0.465561i	−0.634076	−	0.773271i	$-0.718619\pi$
$503$	−35.5603	−	10.4415i	−1.58556	−	0.465561i	−0.951480	+	0.307709i	$0.900438\pi$
$504$	0.415415	−	0.909632i	0.0185041	−	0.0405182i
$505$	−19.4938			−0.867464
$506$	17.0482	+	2.08765i	0.757884	+	0.0928073i
$507$	12.9639			0.575747
$508$	−1.94683	+	4.26297i	−0.0863768	+	0.189139i
$509$	−21.4786	−	6.30668i	−0.952022	−	0.279539i	−0.231393	−	0.972860i	$-0.574328\pi$
$509$	−21.4786	−	6.30668i	−0.952022	−	0.279539i	−0.720628	+	0.693322i	$0.756147\pi$
$510$	3.56301	+	4.11193i	0.157773	+	0.182079i
$511$	12.0346	−	7.73419i	0.532381	−	0.342140i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−0.0731176	+	0.508544i	−0.00322822	+	0.0224528i
$514$	−26.2123	+	7.69662i	−1.15617	+	0.339483i
$515$	−14.5442	−	9.34696i	−0.640892	−	0.411876i
$516$	1.08485	+	7.54528i	0.0477577	+	0.332162i
$517$	3.74773	+	8.20639i	0.164825	+	0.360917i
$518$	−3.18677	−	6.97805i	−0.140019	−	0.306598i
$519$	1.70009	+	11.8244i	0.0746258	+	0.519034i
$520$	−0.484127	−	0.311129i	−0.0212304	−	0.0136439i
$521$	−10.6062	+	3.11425i	−0.464664	+	0.136438i	−0.505681	−	0.862721i	$-0.668759\pi$
$521$	−10.6062	+	3.11425i	−0.464664	+	0.136438i	0.0410163	+	0.999158i	$0.486940\pi$
$522$	0.945748	−	6.57782i	0.0413943	−	0.287903i
$523$	−10.5137	+	12.1335i	−0.459732	+	0.530559i	−0.937527	−	0.347912i	$-0.886891\pi$
$523$	−10.5137	+	12.1335i	−0.459732	+	0.530559i	0.477795	+	0.878471i	$0.341436\pi$
$524$	4.23169	−	2.71954i	0.184862	−	0.118804i
$525$	−2.73291	−	3.15395i	−0.119274	−	0.137650i
$526$	−11.1452	−	3.27252i	−0.485952	−	0.142688i
$527$	1.06031	−	2.32176i	0.0461880	−	0.101138i
$528$	−3.58134			−0.155858
$529$	22.3204	+	5.54975i	0.970452	+	0.241293i
$530$	−36.4856			−1.58483
$531$	−2.27369	+	4.97869i	−0.0986698	+	0.216057i
$532$	−0.492962	−	0.144747i	−0.0213726	−	0.00627556i
$533$	−0.843621	−	0.973591i	−0.0365413	−	0.0421709i
$534$	9.01101	−	5.79102i	0.389944	−	0.250602i
$535$	−12.1283	+	13.9969i	−0.524354	+	0.605137i
$536$	1.75986	−	12.2401i	0.0760142	−	0.528690i
$537$	15.7987	−	4.63893i	0.681766	−	0.200185i
$538$	1.70776	+	1.09751i	0.0736268	+	0.0473171i
$539$	−0.509678	−	3.54489i	−0.0219534	−	0.152689i
$540$	1.25818	+	2.75504i	0.0541436	+	0.118558i
$541$	−2.17497	−	4.76251i	−0.0935091	−	0.204756i	0.857098	−	0.515154i	$-0.172265\pi$
$541$	−2.17497	−	4.76251i	−0.0935091	−	0.204756i	−0.950607	+	0.310397i	$0.899538\pi$
$542$	−0.245732	−	1.70910i	−0.0105551	−	0.0734122i
$543$	−0.810654	−	0.520976i	−0.0347885	−	0.0223572i
$544$	1.72364	−	0.506108i	0.0739006	−	0.0216992i
$545$	−6.31555	+	43.9256i	−0.270528	+	1.88157i
$546$	−0.124428	+	0.143598i	−0.00532504	+	0.00614542i
$547$	−38.7042	+	24.8737i	−1.65487	+	1.06352i	−0.729852	+	0.683605i	$0.760411\pi$
$547$	−38.7042	+	24.8737i	−1.65487	+	1.06352i	−0.925020	+	0.379917i	$0.875952\pi$
$548$	−0.871242	−	1.00547i	−0.0372176	−	0.0429514i
$549$	−11.3146	−	3.32225i	−0.482893	−	0.141790i
$550$	−6.20876	+	13.5953i	−0.264742	+	0.579705i
$551$	−3.41426			−0.145452
$552$	−4.76027	−	0.582923i	−0.202611	−	0.0248109i
$553$	14.6208			0.621738
$554$	−1.29484	+	2.83530i	−0.0550125	+	0.120461i
$555$	22.2932	+	6.54587i	0.946293	+	0.277857i
$556$	4.18475	+	4.82946i	0.177473	+	0.204815i
$557$	24.3021	−	15.6180i	1.02971	−	0.661756i	0.0872905	−	0.996183i	$-0.472179\pi$
$557$	24.3021	−	15.6180i	1.02971	−	0.661756i	0.942422	+	0.334427i	$0.108543\pi$
$558$	0.930455	−	1.07380i	0.0393893	−	0.0454577i
$559$	0.206129	−	1.43366i	0.00871832	−	0.0606372i
$560$	−2.90606	+	0.853295i	−0.122803	+	0.0360583i
$561$	−5.41226	−	3.47825i	−0.228506	−	0.146852i
$562$	−1.71732	−	11.9442i	−0.0724409	−	0.503837i
$563$	3.49156	+	7.64545i	0.147152	+	0.322217i	0.968827	−	0.247739i	$-0.0796875\pi$
$563$	3.49156	+	7.64545i	0.147152	+	0.322217i	−0.821675	+	0.569956i	$0.806960\pi$
$564$	−1.04646	−	2.29143i	−0.0440639	−	0.0964865i
$565$	−5.25289	−	36.5346i	−0.220991	−	1.53702i
$566$	1.16106	+	0.746169i	0.0488031	+	0.0313638i
$567$	0.959493	−	0.281733i	0.0402949	−	0.0118317i
$568$	−1.00203	+	6.96929i	−0.0420444	+	0.292425i
$569$	28.1639	−	32.5029i	1.18069	−	1.36259i	0.263251	−	0.964727i	$-0.415205\pi$
$569$	28.1639	−	32.5029i	1.18069	−	1.36259i	0.917443	−	0.397866i	$-0.130249\pi$
$570$	1.30906	−	0.841284i	0.0548306	−	0.0352375i
$571$	17.5349	+	20.2364i	0.733813	+	0.846865i	0.992895	−	0.118990i	$-0.0379656\pi$
$571$	17.5349	+	20.2364i	0.733813	+	0.846865i	−0.259082	+	0.965855i	$0.583420\pi$
$572$	0.652917	+	0.191714i	0.0272998	+	0.00801595i
$573$	0.00107599	−	0.00235609i	4.49501e−5	−	9.84270e-5i
$574$	−6.77998			−0.282991
$575$	−10.4655	+	17.0601i	−0.436440	+	0.711455i
$576$	1.00000			0.0416667
$577$	9.07851	−	19.8792i	0.377943	−	0.827580i	−0.621095	−	0.783735i	$-0.713312\pi$
$577$	9.07851	−	19.8792i	0.377943	−	0.827580i	0.999038	−	0.0438450i	$-0.0139608\pi$
$578$	−13.2150	−	3.88028i	−0.549672	−	0.161398i
$579$	5.96398	+	6.88280i	0.247855	+	0.286039i
$580$	−16.9322	+	10.8817i	−0.703073	+	0.451837i
$581$	9.11631	−	10.5208i	0.378208	−	0.436476i
$582$	0.821203	−	5.71159i	0.0340400	−	0.236753i
$583$	41.3949	−	12.1546i	1.71440	−	0.503394i
$584$	12.0346	+	7.73419i	0.497997	+	0.320043i
$585$	−0.0818997	−	0.569625i	−0.00338614	−	0.0235511i
$586$	1.62718	+	3.56303i	0.0672182	+	0.147187i
$587$	−7.43995	−	16.2912i	−0.307080	−	0.672411i	0.691680	−	0.722204i	$-0.256871\pi$
$587$	−7.43995	−	16.2912i	−0.307080	−	0.672411i	−0.998760	+	0.0497935i	$0.984144\pi$
$588$	0.142315	+	0.989821i	0.00586897	+	0.0408195i
$589$	−0.614108	−	0.394663i	−0.0253039	−	0.0162618i
$590$	15.9057	−	4.67034i	0.654828	−	0.192275i
$591$	−0.180704	+	1.25682i	−0.00743316	+	0.0516987i
$592$	5.02363	−	5.79757i	0.206470	−	0.238279i
$593$	−27.5815	+	17.7256i	−1.13264	+	0.727902i	−0.966109	−	0.258135i	$-0.916892\pi$
$593$	−27.5815	+	17.7256i	−1.13264	+	0.727902i	−0.166529	+	0.986037i	$0.553256\pi$
$594$	−2.34528	−	2.70660i	−0.0962280	−	0.111053i
$595$	−5.22047	−	1.53287i	−0.214018	−	0.0628415i
$596$	−1.98786	+	4.35282i	−0.0814261	+	0.178298i
$597$	−18.5892			−0.760803
$598$	0.836644	+	0.361096i	0.0342129	+	0.0147663i
$599$	9.85920			0.402836			0.201418	−	0.979505i	$-0.435445\pi$
$599$	9.85920			0.402836			0.201418	+	0.979505i	$0.435445\pi$
$600$	1.73364	−	3.79614i	0.0707755	−	0.154977i
$601$	14.2697	+	4.18997i	0.582075	+	0.170913i	0.559497	−	0.828833i	$-0.310994\pi$
$601$	14.2697	+	4.18997i	0.582075	+	0.170913i	0.0225780	+	0.999745i	$0.492813\pi$
$602$	−4.99191	−	5.76098i	−0.203455	−	0.234800i
$603$	10.4029	−	6.68553i	0.423638	−	0.272256i
$604$	−5.81258	+	6.70807i	−0.236510	+	0.272948i
$605$	0.787078	−	5.47425i	0.0319993	−	0.222560i
$606$	−6.17557	+	1.81331i	−0.250865	+	0.0736607i
$607$	21.3900	+	13.7465i	0.868192	+	0.557953i	0.897199	−	0.441626i	$-0.145598\pi$
$607$	21.3900	+	13.7465i	0.868192	+	0.557953i	−0.0290072	+	0.999579i	$0.509235\pi$
$608$	−0.0731176	−	0.508544i	−0.00296531	−	0.0206242i
$609$	2.76063	+	6.04493i	0.111866	+	0.244953i
$610$	14.8368	+	32.4880i	0.600724	+	1.31540i
$611$	0.0681178	+	0.473770i	0.00275575	+	0.0191667i
$612$	1.51124	+	0.971213i	0.0610881	+	0.0392590i
$613$	−11.9329	+	3.50383i	−0.481967	+	0.141518i	−0.513686	−	0.857979i	$-0.671720\pi$
$613$	−11.9329	+	3.50383i	−0.481967	+	0.141518i	0.0317184	+	0.999497i	$0.489902\pi$
$614$	−3.88244	+	27.0030i	−0.156683	+	1.08975i
$615$	13.4474	−	15.5192i	0.542253	−	0.625793i
$616$	3.01282	−	1.93622i	0.121390	−	0.0780125i
$617$	20.1674	+	23.2744i	0.811907	+	0.936991i	0.998971	−	0.0453568i	$-0.0144425\pi$
$617$	20.1674	+	23.2744i	0.811907	+	0.936991i	−0.187063	+	0.982348i	$0.559897\pi$
$618$	−5.47698	−	1.60819i	−0.220317	−	0.0646908i
$619$	−14.0825	+	30.8363i	−0.566022	+	1.23942i	0.382866	+	0.923804i	$0.374937\pi$
$619$	−14.0825	+	30.8363i	−0.566022	+	1.23942i	−0.948888	+	0.315612i	$0.897790\pi$
$620$	−4.30337			−0.172827
$621$	−2.67677	−	3.97931i	−0.107415	−	0.159684i
$622$	−25.8360			−1.03593
$623$	−4.44968	+	9.74343i	−0.178273	+	0.390362i
$624$	−0.182311	−	0.0535312i	−0.00729827	−	0.00214296i
$625$	18.6309	+	21.5012i	0.745236	+	0.860048i
$626$	−8.40469	+	5.40137i	−0.335919	+	0.215882i
$627$	−1.20494	+	1.39058i	−0.0481208	+	0.0555343i
$628$	0.971328	−	6.75574i	0.0387602	−	0.269583i
$629$	13.2226	−	3.88250i	0.527218	−	0.154805i
$630$	−2.54794	−	1.63746i	−0.101512	−	0.0652380i
$631$	−1.49249	−	10.3805i	−0.0594150	−	0.413240i	−0.997723	−	0.0674404i	$-0.978517\pi$
$631$	−1.49249	−	10.3805i	−0.0594150	−	0.413240i	0.938308	−	0.345800i	$-0.112392\pi$
$632$	6.07368	+	13.2995i	0.241598	+	0.529026i
$633$	2.20042	+	4.81825i	0.0874590	+	0.191508i
$634$	3.30065	+	22.9565i	0.131085	+	0.911719i
$635$	11.9409	+	7.67393i	0.473859	+	0.304530i
$636$	−11.5585	+	3.39388i	−0.458324	+	0.134576i
$637$	0.0270409	−	0.188073i	0.00107140	−	0.00745173i
$638$	15.5855	−	17.9866i	0.617035	−	0.712096i
$639$	−5.92323	+	3.80663i	−0.234319	+	0.150588i
$640$	−1.98340	−	2.28897i	−0.0784009	−	0.0904795i
$641$	−42.9359	−	12.6071i	−1.69586	−	0.497951i	−0.716082	−	0.698016i	$-0.754066\pi$
$641$	−42.9359	−	12.6071i	−1.69586	−	0.497951i	−0.979783	+	0.200065i	$0.935885\pi$
$642$	−2.54023	+	5.56232i	−0.100255	+	0.219527i
$643$	21.4043			0.844103			0.422052	−	0.906572i	$-0.361310\pi$
$643$	21.4043			0.844103			0.422052	+	0.906572i	$0.361310\pi$
$644$	4.31975	−	2.08321i	0.170222	−	0.0820900i
$645$	23.0877			0.909077
$646$	0.383407	−	0.839543i	0.0150849	−	0.0330314i
$647$	17.8649	+	5.24561i	0.702342	+	0.206226i	0.613356	−	0.789807i	$-0.289819\pi$
$647$	17.8649	+	5.24561i	0.702342	+	0.206226i	0.0889862	+	0.996033i	$0.471637\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	−16.4901	+	10.5975i	−0.647292	+	0.415989i
$650$	−0.519273	+	0.599273i	−0.0203676	+	0.0235054i
$651$	−0.202207	+	1.40638i	−0.00792513	+	0.0551205i
$652$	16.3901	−	4.81257i	0.641887	−	0.188475i
$653$	−40.3352	−	25.9218i	−1.57844	−	1.01440i	−0.976410	−	0.215925i	$-0.930723\pi$
$653$	−40.3352	−	25.9218i	−1.57844	−	1.01440i	−0.602028	−	0.798475i	$-0.705640\pi$
$654$	2.08521	+	14.5029i	0.0815380	+	0.567110i
$655$	−6.32894	−	13.8584i	−0.247292	−	0.541494i
$656$	−2.81651	−	6.16729i	−0.109966	−	0.240792i
$657$	2.03590	+	14.1600i	0.0794279	+	0.552434i
$658$	2.11918	+	1.36191i	0.0826141	+	0.0530929i
$659$	−20.1219	+	5.90833i	−0.783839	+	0.230156i	−0.649078	−	0.760722i	$-0.724845\pi$
$659$	−20.1219	+	5.90833i	−0.783839	+	0.230156i	−0.134762	+	0.990878i	$0.543027\pi$
$660$	−1.54368	+	10.7366i	−0.0600878	+	0.417920i
$661$	4.34924	−	5.01929i	0.169166	−	0.195228i	−0.664836	−	0.746989i	$-0.731499\pi$
$661$	4.34924	−	5.01929i	0.169166	−	0.195228i	0.834002	+	0.551761i	$0.186044\pi$
$662$	11.7588	−	7.55691i	0.457018	−	0.293707i
$663$	−0.223524	−	0.257961i	−0.00868097	−	0.0100184i
$664$	13.3571	+	3.92200i	0.518356	+	0.152203i
$665$	−0.646422	+	1.41547i	−0.0250672	+	0.0548894i
$666$	7.67129			0.297256
$667$	23.6436	−	21.3708i	0.915485	−	0.827479i
$668$	2.22667			0.0861525
$669$	−1.92339	+	4.21164i	−0.0743626	+	0.162831i
$670$	−35.9361	−	10.5518i	−1.38833	−	0.407651i
$671$	−27.6561	−	31.9168i	−1.06765	−	1.23213i
$672$	−0.841254	+	0.540641i	−0.0324521	+	0.0208557i
$673$	9.74801	−	11.2498i	0.375758	−	0.433648i	−0.536099	−	0.844155i	$-0.680103\pi$
$673$	9.74801	−	11.2498i	0.375758	−	0.433648i	0.911858	+	0.410507i	$0.134648\pi$
$674$	−2.47632	+	17.2232i	−0.0953843	+	0.663412i
$675$	4.00422	−	1.17575i	0.154123	−	0.0452545i
$676$	−10.9059	−	7.00881i	−0.419459	−	0.269570i
$677$	−3.81871	−	26.5597i	−0.146765	−	1.02077i	−0.921470	−	0.388450i	$-0.873011\pi$
$677$	−3.81871	−	26.5597i	−0.146765	−	1.02077i	0.774705	−	0.632323i	$-0.217898\pi$
$678$	−5.06254	−	11.0854i	−0.194425	−	0.425732i
$679$	2.39708	+	5.24887i	0.0919915	+	0.201433i
$680$	−0.774316	−	5.38548i	−0.0296936	−	0.206524i
$681$	−16.2913	−	10.4698i	−0.624282	−	0.401202i
$682$	4.88241	−	1.43360i	0.186957	−	0.0548956i
$683$	0.599297	−	4.16821i	0.0229315	−	0.159492i	−0.975138	−	0.221598i	$-0.928873\pi$
$683$	0.599297	−	4.16821i	0.0229315	−	0.159492i	0.998070	+	0.0621062i	$0.0197818\pi$
$684$	0.336450	−	0.388284i	0.0128645	−	0.0148464i
$685$	−3.38984	+	2.17852i	−0.129519	+	0.0832368i
$686$	−0.654861	−	0.755750i	−0.0250027	−	0.0288547i
$687$	23.3080	+	6.84383i	0.889254	+	0.261109i
$688$	3.16665	−	6.93400i	0.120727	−	0.264356i
$689$	2.28891			0.0872006
$690$	−3.79940	+	14.0196i	−0.144641	+	0.533718i
$691$	−13.1626			−0.500729			−0.250365	−	0.968152i	$-0.580550\pi$
$691$	−13.1626			−0.500729			−0.250365	+	0.968152i	$0.580550\pi$
$692$	4.96255	−	10.8665i	0.188648	−	0.413081i
$693$	3.43627	+	1.00898i	0.130533	+	0.0383280i
$694$	2.88140	+	3.32531i	0.109376	+	0.126227i
$695$	16.2821	−	10.4638i	0.617614	−	0.396916i
$696$	−4.35185	+	5.02231i	−0.164957	+	0.190370i
$697$	1.73334	−	12.0557i	0.0656550	−	0.456641i
$698$	0.574812	−	0.168780i	0.0217570	−	0.00638842i
$699$	7.69842	+	4.94747i	0.291181	+	0.187131i
$700$	0.593918	+	4.13079i	0.0224480	+	0.156129i
$701$	−9.54555	−	20.9018i	−0.360530	−	0.789452i	−0.999791	−	0.0204611i	$-0.993487\pi$
$701$	−9.54555	−	20.9018i	−0.360530	−	0.789452i	0.639260	−	0.768991i	$-0.279241\pi$
$702$	−0.0789319	−	0.172837i	−0.00297909	−	0.00652330i
$703$	−0.560906	−	3.90119i	−0.0211550	−	0.147136i
$704$	3.01282	+	1.93622i	0.113550	+	0.0729741i
$705$	−7.32056	+	2.14951i	−0.275708	+	0.0809552i
$706$	4.23488	−	29.4543i	0.159382	−	1.10853i
$707$	4.21487	−	4.86422i	0.158516	−	0.182938i
$708$	4.60443	−	2.95909i	0.173045	−	0.111209i
$709$	11.2523	+	12.9858i	0.422588	+	0.487692i	0.926623	−	0.375991i	$-0.122698\pi$
$709$	11.2523	+	12.9858i	0.422588	+	0.487692i	−0.504036	+	0.863683i	$0.668152\pi$
$710$	20.4614	+	6.00801i	0.767903	+	0.225477i
$711$	−6.07368	+	13.2995i	−0.227781	+	0.498771i
$712$	−10.7114			−0.401427
$713$	6.72298	−	1.11083i	0.251777	−	0.0416011i
$714$	−1.79641			−0.0672290
$715$	0.856171	−	1.87475i	0.0320190	−	0.0701118i
$716$	−15.7987	−	4.63893i	−0.590427	−	0.173365i
$717$	−3.46997	−	4.00456i	−0.129588	−	0.149553i
$718$	14.7616	−	9.48674i	0.550900	−	0.354042i
$719$	−5.16276	+	5.95814i	−0.192538	+	0.222201i	−0.843808	−	0.536645i	$-0.819691\pi$
$719$	−5.16276	+	5.95814i	−0.192538	+	0.222201i	0.651270	+	0.758847i	$0.274237\pi$
$720$	0.431035	−	2.99791i	0.0160637	−	0.111726i
$721$	5.47698	−	1.60819i	0.203973	−	0.0598920i
$722$	15.7618	+	10.1295i	0.586592	+	0.376980i
$723$	2.49271	+	17.3372i	0.0927047	+	0.644776i
$724$	0.400305	+	0.876545i	0.0148772	+	0.0325765i
$725$	11.5208	+	25.2271i	0.427873	+	0.936911i
$726$	−0.259870	−	1.80743i	−0.00964467	−	0.0670802i
$727$	−8.74253	−	5.61848i	−0.324243	−	0.208378i	0.368385	−	0.929673i	$-0.379911\pi$
$727$	−8.74253	−	5.61848i	−0.324243	−	0.208378i	−0.692628	+	0.721295i	$0.743547\pi$
$728$	0.182311	−	0.0535312i	0.00675688	−	0.00198400i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	28.3738	−	32.7451i	1.05016	−	1.21195i
$731$	11.5200	−	7.40343i	0.426081	−	0.273826i
$732$	7.72226	+	8.91197i	0.285423	+	0.329396i
$733$	26.4975	+	7.78036i	0.978706	+	0.287374i	0.731690	−	0.681637i	$-0.238732\pi$
$733$	26.4975	+	7.78036i	0.978706	+	0.287374i	0.247016	+	0.969011i	$0.420550\pi$
$734$	−4.84061	+	10.5995i	−0.178670	+	0.391233i
$735$	3.02874			0.111717
$736$	3.68944	+	3.06398i	0.135995	+	0.112940i
$737$	44.2866			1.63132
$738$	2.81651	−	6.16729i	0.103677	−	0.227021i
$739$	−9.96643	−	2.92641i	−0.366621	−	0.107650i	0.0932326	−	0.995644i	$-0.470280\pi$
$739$	−9.96643	−	2.92641i	−0.366621	−	0.107650i	−0.459854	+	0.887995i	$0.652098\pi$
$740$	−15.2153	−	17.5593i	−0.559324	−	0.645494i
$741$	−0.0821237	+	0.0527777i	−0.00301689	+	0.00193884i
$742$	7.88875	−	9.10410i	0.289605	−	0.334222i
$743$	−2.39925	+	16.6871i	−0.0880199	+	0.612192i	0.897293	+	0.441435i	$0.145530\pi$
$743$	−2.39925	+	16.6871i	−0.0880199	+	0.612192i	−0.985313	+	0.170757i	$0.945379\pi$
$744$	−1.36329	+	0.400298i	−0.0499806	+	0.0146756i
$745$	12.1925	+	7.83566i	0.446700	+	0.287076i
$746$	0.566921	+	3.94302i	0.0207565	+	0.144364i
$747$	5.78299	+	12.6630i	0.211588	+	0.463314i
$748$	2.67260	+	5.85218i	0.0977199	+	0.213977i
$749$	−0.870243	−	6.05268i	−0.0317980	−	0.221160i
$750$	2.10646	+	1.35374i	0.0769170	+	0.0494315i
$751$	−20.9253	+	6.14422i	−0.763575	+	0.224206i	−0.640257	−	0.768161i	$-0.721172\pi$
$751$	−20.9253	+	6.14422i	−0.763575	+	0.224206i	−0.123319	+	0.992367i	$0.539354\pi$
$752$	−0.358501	+	2.49343i	−0.0130732	+	0.0909260i
$753$	10.3167	−	11.9062i	0.375963	−	0.433885i
$754$	1.06224	−	0.682660i	0.0386845	−	0.0248610i
$755$	17.6048	+	20.3170i	0.640704	+	0.739412i
$756$	−0.959493	−	0.281733i	−0.0348964	−	0.0102465i
$757$	12.4148	−	27.1845i	0.451222	−	0.988038i	−0.538179	−	0.842830i	$-0.680888\pi$
$757$	12.4148	−	27.1845i	0.451222	−	0.988038i	0.989401	−	0.145208i	$-0.0463851\pi$
$758$	32.5956			1.18393
$759$	−0.359809	−	17.1717i	−0.0130602	−	0.623295i
$760$	−1.55609			−0.0564452
$761$	−21.6046	+	47.3074i	−0.783165	+	1.71489i	−0.0879101	+	0.996128i	$0.528019\pi$
$761$	−21.6046	+	47.3074i	−0.783165	+	1.71489i	−0.695255	+	0.718763i	$0.744708\pi$
$762$	4.49664	+	1.32033i	0.162896	+	0.0478306i
$763$	−9.59507	−	11.0733i	−0.347365	−	0.400880i
$764$	−0.00217898	+	0.00140034i	−7.88326e−5	+	5.06626e-5i
$765$	3.56301	−	4.11193i	0.128821	−	0.148667i
$766$	3.26723	−	22.7241i	0.118050	−	0.821054i
$767$	−0.997841	+	0.292993i	−0.0360300	+	0.0105793i
$768$	−0.841254	−	0.540641i	−0.0303561	−	0.0195087i
$769$	0.539711	+	3.75377i	0.0194625	+	0.135365i	0.997236	−	0.0742995i	$-0.0236721\pi$
$769$	0.539711	+	3.75377i	0.0194625	+	0.135365i	−0.977773	+	0.209664i	$0.932763\pi$
$770$	−4.50599	−	9.86674i	−0.162385	−	0.355573i
$771$	11.3487	+	24.8501i	0.408713	+	0.894956i
$772$	−1.29610	−	9.01455i	−0.0466476	−	0.324441i
$773$	−23.2560	−	14.9457i	−0.836459	−	0.537560i	0.0508650	−	0.998706i	$-0.483802\pi$
$773$	−23.2560	−	14.9457i	−0.836459	−	0.537560i	−0.887324	+	0.461146i	$0.847439\pi$
$774$	7.31409	−	2.14761i	0.262899	−	0.0771942i
$775$	−0.843865	+	5.86921i	−0.0303125	+	0.210828i
$776$	−3.77876	+	4.36092i	−0.135650	+	0.156548i
$777$	−6.45350	+	4.14741i	−0.231518	+	0.148788i
$778$	4.40577	+	5.08453i	0.157954	+	0.182289i
$779$	−3.34227	−	0.981380i	−0.119749	−	0.0351616i
$780$	−0.239064	+	0.523477i	−0.00855987	+	0.0187435i
$781$	−25.2161			−0.902303
$782$	2.59984	+	8.21364i	0.0929702	+	0.293719i
$783$	−6.64546			−0.237489
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	−19.8344	−	5.82391i	−0.707921	−	0.207864i
$786$	−3.29409	−	3.80158i	−0.117496	−	0.135598i
$787$	−27.8442	+	17.8944i	−0.992537	+	0.637865i	−0.932817	−	0.360350i	$-0.882657\pi$
$787$	−27.8442	+	17.8944i	−0.992537	+	0.637865i	−0.0597201	+	0.998215i	$0.519021\pi$
$788$	0.831507	−	0.959610i	0.0296212	−	0.0341847i
$789$	−1.65308	+	11.4974i	−0.0588513	+	0.409320i
$790$	42.4887	−	12.4758i	1.51168	−	0.443870i
$791$	10.2521	+	6.58862i	0.364523	+	0.234264i
$792$	0.509678	+	3.54489i	0.0181106	+	0.125962i
$793$	−0.930782	−	2.03813i	−0.0330530	−	0.0723761i
$794$	4.05158	+	8.87172i	0.143785	+	0.314846i
$795$	5.19244	+	36.1142i	0.184157	+	1.28084i
$796$	15.6382	+	10.0501i	0.554281	+	0.356215i
$797$	18.8815	−	5.54409i	0.668815	−	0.196382i	0.0703399	−	0.997523i	$-0.477592\pi$
$797$	18.8815	−	5.54409i	0.668815	−	0.196382i	0.598475	+	0.801141i	$0.295773\pi$
$798$	−0.0731176	+	0.508544i	−0.00258833	+	0.0180023i
$799$	−2.96343	+	3.41998i	−0.104839	+	0.120990i
$800$	−3.51078	+	2.25624i	−0.124125	+	0.0797701i
$801$	−7.01448	−	8.09514i	−0.247844	−	0.286028i
$802$	34.9000	+	10.2476i	1.23236	+	0.361854i
$803$	−21.2831	+	46.6034i	−0.751063	+	1.64460i
$804$	−12.3659			−0.436113
$805$	−4.38332	−	13.8482i	−0.154492	−	0.488084i
$806$	0.269971			0.00950931
$807$	0.843301	−	1.84657i	0.0296856	−	0.0650024i
$808$	6.17557	+	1.81331i	0.217256	+	0.0637920i
$809$	−5.37456	−	6.20258i	−0.188960	−	0.218071i	0.653363	−	0.757045i	$-0.273358\pi$
$809$	−5.37456	−	6.20258i	−0.188960	−	0.218071i	−0.842322	+	0.538974i	$0.818812\pi$
$810$	2.54794	−	1.63746i	0.0895254	−	0.0575345i
$811$	29.4184	−	33.9506i	1.03302	−	1.19217i	0.0519215	−	0.998651i	$-0.483465\pi$
$811$	29.4184	−	33.9506i	1.03302	−	1.19217i	0.981097	−	0.193516i	$-0.0619891\pi$
$812$	0.945748	−	6.57782i	0.0331893	−	0.230836i
$813$	−1.65673	+	0.486461i	−0.0581042	+	0.0170609i
$814$	23.1122	+	14.8533i	0.810082	+	0.520608i
$815$	−7.36296	−	51.2105i	−0.257913	−	1.79383i
$816$	−0.746256	−	1.63407i	−0.0261242	−	0.0572040i
$817$	−1.62694	−	3.56251i	−0.0569195	−	0.124636i
$818$	1.57886	+	10.9812i	0.0552034	+	0.383948i
$819$	0.159844	+	0.102726i	0.00558541	+	0.00358953i
$820$	−19.7030	+	5.78532i	−0.688059	+	0.202032i
$821$	−7.06139	+	49.1130i	−0.246444	+	1.71406i	0.372004	+	0.928231i	$0.378671\pi$
$821$	−7.06139	+	49.1130i	−0.246444	+	1.71406i	−0.618448	+	0.785825i	$0.712238\pi$
$822$	−0.871242	+	1.00547i	−0.0303881	+	0.0350697i
$823$	−22.7162	+	14.5988i	−0.791837	+	0.508883i	−0.872943	−	0.487823i	$-0.837791\pi$
$823$	−22.7162	+	14.5988i	−0.791837	+	0.508883i	0.0811059	+	0.996705i	$0.474155\pi$
$824$	3.73808	+	4.31397i	0.130222	+	0.150284i
$825$	14.3405	+	4.21075i	0.499272	+	0.146599i
$826$	−2.27369	+	4.97869i	−0.0791119	+	0.173231i
$827$	37.1626			1.29227			0.646135	−	0.763223i	$-0.276384\pi$
$827$	37.1626			1.29227			0.646135	+	0.763223i	$0.276384\pi$
$828$	0.100467	+	4.79478i	0.00349149	+	0.166630i
$829$	−7.10894			−0.246904			−0.123452	−	0.992351i	$-0.539396\pi$
$829$	−7.10894			−0.246904			−0.123452	+	0.992351i	$0.539396\pi$
$830$	17.5152	−	38.3529i	0.607960	−	1.33125i
$831$	2.99072	+	0.878155i	0.103747	+	0.0304628i
$832$	0.124428	+	0.143598i	0.00431377	+	0.00497836i
$833$	1.51124	−	0.971213i	0.0523613	−	0.0336505i
$834$	4.18475	−	4.82946i	0.144906	−	0.167230i
$835$	0.959772	−	6.67536i	0.0332143	−	0.231010i
$836$	1.76547	−	0.518388i	0.0610599	−	0.0179288i
$837$	−1.19529	−	0.768166i	−0.0413153	−	0.0265517i
$838$	−4.91090	−	34.1561i	−0.169644	−	1.17990i
$839$	5.89037	+	12.8981i	0.203358	+	0.445292i	0.983642	−	0.180133i	$-0.0576528\pi$
$839$	5.89037	+	12.8981i	0.203358	+	0.445292i	−0.780284	+	0.625425i	$0.784926\pi$
$840$	1.25818	+	2.75504i	0.0434115	+	0.0950579i
$841$	−2.15780	−	15.0079i	−0.0744070	−	0.517512i
$842$	−22.3506	−	14.3638i	−0.770252	−	0.495011i
$843$	−11.5783	+	3.39968i	−0.398777	+	0.117091i
$844$	0.753831	−	5.24301i	0.0259479	−	0.180472i
$845$	−25.7126	+	29.6740i	−0.884542	+	1.02082i
$846$	−2.11918	+	1.36191i	−0.0728588	+	0.0468235i
$847$	1.19579	+	1.38001i	0.0410878	+	0.0474178i
$848$	11.5585	+	3.39388i	0.396920	+	0.116546i
$849$	0.573338	−	1.25543i	0.0196769	−	0.0430864i
$850$	−7.49691			−0.257142
$851$	28.3028	+	23.5047i	0.970207	+	0.805731i
$852$	7.04096			0.241219
$853$	−1.51148	+	3.30969i	−0.0517522	+	0.113322i	−0.933742	−	0.357948i	$-0.883477\pi$
$853$	−1.51148	+	3.30969i	−0.0517522	+	0.113322i	0.881989	+	0.471269i	$0.156204\pi$
$854$	−11.3146	−	3.32225i	−0.387176	−	0.113685i
$855$	−1.01902	−	1.17601i	−0.0348497	−	0.0402187i
$856$	5.14420	−	3.30597i	0.175825	−	0.112996i
$857$	29.5582	−	34.1119i	1.00969	−	1.16524i	0.0234809	−	0.999724i	$-0.492525\pi$
$857$	29.5582	−	34.1119i	1.00969	−	1.16524i	0.986207	−	0.165517i	$-0.0529294\pi$
$858$	0.0968426	−	0.673555i	0.00330615	−	0.0229948i
$859$	29.4093	−	8.63534i	1.00343	−	0.294634i	0.261568	−	0.965185i	$-0.415760\pi$
$859$	29.4093	−	8.63534i	1.00343	−	0.294634i	0.741864	+	0.670551i	$0.233942\pi$
$860$	−19.4226	−	12.4821i	−0.662305	−	0.425638i
$861$	0.964892	+	6.71097i	0.0328834	+	0.228709i
$862$	−13.0635	−	28.6051i	−0.444944	−	0.974292i
$863$	12.1735	+	26.6563i	0.414392	+	0.907393i	0.995606	+	0.0936417i	$0.0298508\pi$
$863$	12.1735	+	26.6563i	0.414392	+	0.907393i	−0.581214	+	0.813751i	$0.697422\pi$
$864$	−0.142315	−	0.989821i	−0.00484165	−	0.0336744i
$865$	−30.4377	−	19.5611i	−1.03491	−	0.665097i
$866$	−32.8232	+	9.63775i	−1.11538	+	0.327504i
$867$	−1.96009	+	13.6327i	−0.0665681	+	0.462991i
$868$	0.930455	−	1.07380i	0.0315817	−	0.0364472i
$869$	−44.0497	+	28.3090i	−1.49428	+	0.960317i
$870$	13.1806	+	15.2113i	0.446865	+	0.515710i
$871$	2.25444	+	0.661964i	0.0763888	+	0.0224298i
$872$	6.08669	−	13.3280i	0.206121	−	0.451343i
$873$	−5.77033			−0.195296
$874$	2.43101	−	0.401675i	0.0822301	−	0.0135868i
$875$	−2.50395			−0.0846490
$876$	5.94276	−	13.0128i	0.200787	−	0.439663i
$877$	13.8221	+	4.05853i	0.466738	+	0.137047i	0.506642	−	0.862157i	$-0.330887\pi$
$877$	13.8221	+	4.05853i	0.466738	+	0.137047i	−0.0399032	+	0.999204i	$0.512705\pi$
$878$	20.3939	+	23.5358i	0.688262	+	0.794296i
$879$	3.29519	−	2.11769i	0.111144	−	0.0714279i
$880$	7.10325	−	8.19759i	0.239450	−	0.276341i
$881$	−2.07932	+	14.4620i	−0.0700541	+	0.487237i	0.924346	+	0.381556i	$0.124612\pi$
$881$	−2.07932	+	14.4620i	−0.0700541	+	0.487237i	−0.994400	+	0.105682i	$0.966298\pi$
$882$	0.959493	−	0.281733i	0.0323078	−	0.00948643i
$883$	−28.3651	−	18.2291i	−0.954561	−	0.613459i	−0.0320734	−	0.999486i	$-0.510211\pi$
$883$	−28.3651	−	18.2291i	−0.954561	−	0.613459i	−0.922488	+	0.386026i	$0.873847\pi$
$884$	0.0485765	+	0.337857i	0.00163380	+	0.0113634i
$885$	−6.88642	−	15.0792i	−0.231485	−	0.506880i
$886$	−0.945392	−	2.07012i	−0.0317611	−	0.0695470i
$887$	1.23026	+	8.55663i	0.0413080	+	0.287304i	0.999996	+	0.00284371i	$0.000905181\pi$
$887$	1.23026	+	8.55663i	0.0413080	+	0.287304i	−0.958688	+	0.284460i	$0.908186\pi$
$888$	−6.45350	−	4.14741i	−0.216565	−	0.139178i
$889$	−4.49664	+	1.32033i	−0.150813	+	0.0442826i
$890$	−4.61699	+	32.1118i	−0.154762	+	1.07639i
$891$	−2.34528	+	2.70660i	−0.0785699	+	0.0906745i
$892$	3.89505	−	2.50319i	0.130416	−	0.0838131i
$893$	0.847541	+	0.978115i	0.0283619	+	0.0327314i
$894$	4.59141	+	1.34816i	0.153560	+	0.0450892i
$895$	−20.7169	+	45.3637i	−0.692490	+	1.51634i
$896$	1.00000			0.0334077
$897$	0.238354	−	0.879517i	0.00795841	−	0.0293662i
$898$	−16.1557			−0.539123
$899$	3.92242	−	8.58890i	0.130820	−	0.286456i
$900$	−4.00422	−	1.17575i	−0.133474	−	0.0391915i
$901$	14.1714	+	16.3547i	0.472119	+	0.544854i
$902$	20.4268	−	13.1275i	0.680140	−	0.437099i
$903$	−4.99191	+	5.76098i	−0.166121	+	0.191713i
$904$	−1.73435	+	12.0626i	−0.0576835	+	0.401198i
$905$	2.80035	−	0.822257i	0.0930868	−	0.0273328i
$906$	7.46701	+	4.79876i	0.248075	+	0.159428i
$907$	5.56567	+	38.7101i	0.184805	+	1.28535i	0.845208	+	0.534437i	$0.179476\pi$
$907$	5.56567	+	38.7101i	0.184805	+	1.28535i	−0.660403	+	0.750911i	$0.729615\pi$
$908$	8.04470	+	17.6154i	0.266973	+	0.584589i
$909$	2.67373	+	5.85465i	0.0886820	+	0.194186i
$910$	−0.0818997	−	0.569625i	−0.00271495	−	0.0188829i
$911$	23.9884	+	15.4164i	0.794773	+	0.510769i	0.873906	−	0.486095i	$-0.161579\pi$
$911$	23.9884	+	15.4164i	0.794773	+	0.510769i	−0.0791335	+	0.996864i	$0.525215\pi$
$912$	−0.492962	+	0.144747i	−0.0163236	+	0.00479304i
$913$	−7.09523	+	49.3484i	−0.234818	+	1.63319i
$914$	−4.61046	+	5.32076i	−0.152501	+	0.175995i
$915$	30.0459	−	19.3093i	0.993286	−	0.638346i
$916$	−15.9078	−	18.3586i	−0.525610	−	0.606586i
$917$	4.82646	+	1.41718i	0.159384	+	0.0467993i
$918$	0.746256	−	1.63407i	0.0246301	−	0.0539325i
$919$	15.6966			0.517784			0.258892	−	0.965906i	$-0.416643\pi$
$919$	15.6966			0.517784			0.258892	+	0.965906i	$0.416643\pi$
$920$	10.7758	−	9.73995i	0.355269	−	0.321117i
$921$	27.2807			0.898929
$922$	1.59807	−	3.49929i	0.0526298	−	0.115243i
$923$	−1.28364	−	0.376911i	−0.0422516	−	0.0124062i
$924$	−2.34528	−	2.70660i	−0.0771541	−	0.0890406i
$925$	−26.9322	+	17.3083i	−0.885525	+	0.569092i
$926$	−6.29844	+	7.26879i	−0.206980	+	0.238867i
$927$	−0.812362	+	5.65010i	−0.0266815	+	0.185574i
$928$	6.37628	−	1.87224i	0.209312	−	0.0614594i
$929$	−8.63174	−	5.54728i	−0.283198	−	0.182000i	0.391328	−	0.920251i	$-0.372016\pi$
$929$	−8.63174	−	5.54728i	−0.283198	−	0.182000i	−0.674526	+	0.738251i	$0.735652\pi$
$930$	0.612433	+	4.25957i	0.0200825	+	0.139677i
$931$	−0.213429	−	0.467345i	−0.00699486	−	0.0153166i
$932$	−3.80152	−	8.32416i	−0.124523	−	0.272667i
$933$	3.67685	+	25.5730i	0.120375	+	0.837224i
$934$	−9.68176	−	6.22209i	−0.316797	−	0.203593i
$935$	18.6963	−	5.48973i	0.611434	−	0.179533i
$936$	−0.0270409	+	0.188073i	−0.000883858	+	0.00614737i
$937$	29.9899	−	34.6101i	0.979726	−	1.13066i	−0.0116917	−	0.999932i	$-0.503722\pi$
$937$	29.9899	−	34.6101i	0.979726	−	1.13066i	0.991418	−	0.130732i	$-0.0417329\pi$
$938$	10.4029	−	6.68553i	0.339666	−	0.218290i
$939$	6.54250	+	7.55045i	0.213506	+	0.246400i
$940$	7.32056	+	2.14951i	0.238770	+	0.0701093i
$941$	−9.06673	+	19.8534i	−0.295567	+	0.647202i	−0.997909	−	0.0646383i	$-0.979411\pi$
$941$	−9.06673	+	19.8534i	−0.295567	+	0.647202i	0.702342	+	0.711840i	$0.252138\pi$
$942$	−6.82521			−0.222377
$943$	29.2878	−	14.1241i	0.953742	−	0.459945i
$944$	−5.47330			−0.178141
$945$	−1.25818	+	2.75504i	−0.0409287	+	0.0896214i
$946$	26.1943	+	7.69133i	0.851649	+	0.250067i
$947$	−19.5399	−	22.5502i	−0.634961	−	0.732784i	0.343515	−	0.939147i	$-0.388382\pi$
$947$	−19.5399	−	22.5502i	−0.634961	−	0.732784i	−0.978475	+	0.206364i	$0.933837\pi$
$948$	12.2998	−	7.90458i	0.399478	−	0.256729i
$949$	−1.78002	+	2.05425i	−0.0577819	+	0.0666839i
$950$	−0.305139	+	2.12229i	−0.00990003	+	0.0688562i
$951$	22.2531	−	6.53410i	0.721607	−	0.211883i
$952$	1.51124	+	0.971213i	0.0489795	+	0.0314772i
$953$	5.18567	+	36.0672i	0.167980	+	1.16833i	0.883051	+	0.469277i	$0.155486\pi$
$953$	5.18567	+	36.0672i	0.167980	+	1.16833i	−0.715070	+	0.699053i	$0.753605\pi$
$954$	5.00428	+	10.9578i	0.162019	+	0.354773i
$955$	0.00325889	+	0.00713598i	0.000105455	+	0.000230915i
$956$	0.754096	+	5.24485i	0.0243892	+	0.169631i
$957$	−20.0216	−	12.8671i	−0.647205	−	0.415934i
$958$	30.0774	−	8.83152i	0.971756	−	0.285333i
$959$	0.189339	−	1.31688i	0.00611407	−	0.0425243i
$960$	−1.98340	+	2.28897i	−0.0640141	+	0.0738762i
$961$	−24.3805	+	15.6684i	−0.786469	+	0.505433i
$962$	0.954525	+	1.10158i	0.0307751	+	0.0355164i
$963$	5.86722	+	1.72277i	0.189068	+	0.0555155i
$964$	7.27617	−	15.9326i	0.234350	−	0.513154i
$965$	−27.5835			−0.887944
$966$	−2.67677	−	3.97931i	−0.0861237	−	0.128032i
$967$	−33.0172			−1.06176			−0.530880	−	0.847447i	$-0.678139\pi$
$967$	−33.0172			−1.06176			−0.530880	+	0.847447i	$0.678139\pi$
$968$	−0.758556	+	1.66101i	−0.0243809	+	0.0533868i
$969$	−0.885562	−	0.260025i	−0.0284484	−	0.00835319i
$970$	11.4449	+	13.2081i	0.367473	+	0.424087i
$971$	−36.6322	+	23.5421i	−1.17558	+	0.755502i	−0.974569	−	0.224086i	$-0.928060\pi$
$971$	−36.6322	+	23.5421i	−1.17558	+	0.755502i	−0.201015	+	0.979588i	$0.564424\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−0.909433	+	6.32524i	−0.0291551	+	0.202778i
$974$	6.81742	−	2.00177i	0.218444	−	0.0641410i
$975$	0.667073	+	0.428702i	0.0213634	+	0.0137294i
$976$	−1.67821	−	11.6722i	−0.0537181	−	0.373618i
$977$	−13.6370	−	29.8609i	−0.436286	−	0.955333i	−0.992265	−	0.124137i	$-0.960384\pi$
$977$	−13.6370	−	29.8609i	−0.436286	−	0.955333i	0.555979	−	0.831196i	$-0.312343\pi$
$978$	−7.09615	−	15.5384i	−0.226910	−	0.496863i
$979$	−5.45937	−	37.9707i	−0.174482	−	1.21355i
$980$	−2.54794	−	1.63746i	−0.0813909	−	0.0523068i
$981$	14.0586	−	4.12797i	0.448855	−	0.131796i
$982$	−2.08638	+	14.5111i	−0.0665791	+	0.463068i
$983$	31.8929	−	36.8064i	1.01723	−	1.17394i	0.0325631	−	0.999470i	$-0.489633\pi$
$983$	31.8929	−	36.8064i	1.01723	−	1.17394i	0.984662	−	0.174471i	$-0.0558215\pi$
$984$	−5.70368	+	3.66553i	−0.181827	+	0.116853i
$985$	−2.51842	−	2.90641i	−0.0802435	−	0.0926059i
$986$	11.4544	+	3.36332i	0.364783	+	0.107110i
$987$	1.04646	−	2.29143i	0.0333092	−	0.0729369i
$988$	0.0976207			0.00310573
$989$	33.5652	+	14.4868i	1.06731	+	0.460652i
$990$	10.8470			0.344739
$991$	−11.4470	+	25.0654i	−0.363626	+	0.796230i	0.636071	+	0.771630i	$0.280558\pi$
$991$	−11.4470	+	25.0654i	−0.363626	+	0.796230i	−0.999697	+	0.0245998i	$0.992169\pi$
$992$	1.36329	+	0.400298i	0.0432845	+	0.0127095i
$993$	−9.15343	−	10.5636i	−0.290475	−	0.335227i
$994$	−5.92323	+	3.80663i	−0.187873	+	0.120739i
$995$	36.8698	−	42.5500i	1.16885	−	1.34893i
$996$	1.98116	−	13.7793i	0.0627756	−	0.436614i
$997$	6.74463	−	1.98040i	0.213604	−	0.0627199i	−0.173180	−	0.984890i	$-0.555404\pi$
$997$	6.74463	−	1.98040i	0.213604	−	0.0627199i	0.386784	+	0.922170i	$0.373586\pi$
$998$	−24.5339	−	15.7670i	−0.776606	−	0.499094i
$999$	−1.09174	−	7.59321i	−0.0345411	−	0.240238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.g.673.1	yes	30
23.4	even	11	inner	966.2.q.g.211.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.g.211.1	✓	30	23.4	even	11	inner
966.2.q.g.673.1	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-2.54794 + 1.63746i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.142315 - 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-2.54794 + 1.63746i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.142315 - 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.431035 - 2.99791i) q^{10} +(1.48774 + 3.25770i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.0270409 + 0.188073i) q^{13} +(0.841254 + 0.540641i) q^{14} +(-2.90606 + 0.853295i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.17640 + 1.35764i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(0.336450 + 0.388284i) q^{19} +(2.90606 + 0.853295i) q^{20} +(0.415415 - 0.909632i) q^{21} -3.58134 q^{22} +(-4.76027 - 0.582923i) q^{23} +1.00000 q^{24} +(1.73364 - 3.79614i) q^{25} +(-0.182311 - 0.0535312i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-4.35185 + 5.02231i) q^{29} +(0.431035 - 2.99791i) q^{30} +(-1.36329 + 0.400298i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.509678 + 3.54489i) q^{33} +(-0.746256 - 1.63407i) q^{34} +(1.25818 + 2.75504i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-6.45350 - 4.14741i) q^{37} +(-0.492962 + 0.144747i) q^{38} +(-0.0270409 + 0.188073i) q^{39} +(-1.98340 + 2.28897i) q^{40} +(-5.70368 + 3.66553i) q^{41} +(0.654861 + 0.755750i) q^{42} +(-7.31409 - 2.14761i) q^{43} +(1.48774 - 3.25770i) q^{44} -3.02874 q^{45} +(2.50773 - 4.08794i) q^{46} +2.51907 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(2.73291 + 3.15395i) q^{50} +(-1.51124 + 0.971213i) q^{51} +(0.124428 - 0.143598i) q^{52} +(1.71439 - 11.9238i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-9.12504 - 5.86431i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(0.213429 + 0.467345i) q^{57} +(-2.76063 - 6.04493i) q^{58} +(0.778932 + 5.41759i) q^{59} +(2.54794 + 1.63746i) q^{60} +(-11.3146 + 3.32225i) q^{61} +(0.202207 - 1.40638i) q^{62} +(0.654861 - 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.376861 - 0.434921i) q^{65} +(-3.43627 - 1.00898i) q^{66} +(5.13699 - 11.2484i) q^{67} +1.79641 q^{68} +(-4.40322 - 1.90043i) q^{69} -3.02874 q^{70} +(-2.92492 + 6.40468i) q^{71} +(0.959493 + 0.281733i) q^{72} +(9.36817 + 10.8114i) q^{73} +(6.45350 - 4.14741i) q^{74} +(2.73291 - 3.15395i) q^{75} +(0.0731176 - 0.508544i) q^{76} +(3.43627 - 1.00898i) q^{77} +(-0.159844 - 0.102726i) q^{78} +(2.08075 + 14.4719i) q^{79} +(-1.25818 - 2.75504i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.964892 - 6.71097i) q^{82} +(11.7111 + 7.52625i) q^{83} +(-0.959493 + 0.281733i) q^{84} +(0.774316 - 5.38548i) q^{85} +(4.99191 - 5.76098i) q^{86} +(-5.59052 + 3.59281i) q^{87} +(2.34528 + 2.70660i) q^{88} +(-10.2775 - 3.01775i) q^{89} +(1.25818 - 2.75504i) q^{90} +0.190007 q^{91} +(2.67677 + 3.97931i) q^{92} -1.42084 q^{93} +(-1.04646 + 2.29143i) q^{94} +(-1.49305 - 0.438400i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(-4.85431 + 3.11967i) q^{97} +(0.654861 - 0.755750i) q^{98} +(-0.509678 + 3.54489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 10 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 10 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 10 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9} + 10 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} - 3 q^{14} - q^{15} - 3 q^{16} + 5 q^{17} + 3 q^{18} + 18 q^{19} + q^{20} - 3 q^{21} + 2 q^{22} + 21 q^{23} + 30 q^{24} + 13 q^{25} - 10 q^{26} + 3 q^{27} + 3 q^{28} + 17 q^{29} - 10 q^{30} + 12 q^{31} + 3 q^{32} + 13 q^{33} + 17 q^{34} - q^{35} - 3 q^{36} + 16 q^{37} + 15 q^{38} + 12 q^{39} - 12 q^{40} + 10 q^{41} + 3 q^{42} - 35 q^{43} + 9 q^{44} + 12 q^{45} + q^{46} - 8 q^{47} + 3 q^{48} - 3 q^{49} - 2 q^{50} + 6 q^{51} - q^{52} + 42 q^{53} - 3 q^{54} + 49 q^{55} - 3 q^{56} + 15 q^{57} + 5 q^{58} - 6 q^{59} + 10 q^{60} - 18 q^{61} - 34 q^{62} + 3 q^{63} - 3 q^{64} + 34 q^{65} - 2 q^{66} + 72 q^{67} - 6 q^{68} - 10 q^{69} + 12 q^{70} + 17 q^{71} + 3 q^{72} + 9 q^{73} - 16 q^{74} - 2 q^{75} + 18 q^{76} + 2 q^{77} + 10 q^{78} - 56 q^{79} + q^{80} - 3 q^{81} + 12 q^{82} + 52 q^{83} - 3 q^{84} - 53 q^{85} - 31 q^{86} + 5 q^{87} + 13 q^{88} - 104 q^{89} - q^{90} + 34 q^{91} - 12 q^{92} + 32 q^{93} - 14 q^{94} - 92 q^{95} - 3 q^{96} - 82 q^{97} + 3 q^{98} - 13 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 10 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9 + 10 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 - 3 * q^14 - q^15 - 3 * q^16 + 5 * q^17 + 3 * q^18 + 18 * q^19 + q^20 - 3 * q^21 + 2 * q^22 + 21 * q^23 + 30 * q^24 + 13 * q^25 - 10 * q^26 + 3 * q^27 + 3 * q^28 + 17 * q^29 - 10 * q^30 + 12 * q^31 + 3 * q^32 + 13 * q^33 + 17 * q^34 - q^35 - 3 * q^36 + 16 * q^37 + 15 * q^38 + 12 * q^39 - 12 * q^40 + 10 * q^41 + 3 * q^42 - 35 * q^43 + 9 * q^44 + 12 * q^45 + q^46 - 8 * q^47 + 3 * q^48 - 3 * q^49 - 2 * q^50 + 6 * q^51 - q^52 + 42 * q^53 - 3 * q^54 + 49 * q^55 - 3 * q^56 + 15 * q^57 + 5 * q^58 - 6 * q^59 + 10 * q^60 - 18 * q^61 - 34 * q^62 + 3 * q^63 - 3 * q^64 + 34 * q^65 - 2 * q^66 + 72 * q^67 - 6 * q^68 - 10 * q^69 + 12 * q^70 + 17 * q^71 + 3 * q^72 + 9 * q^73 - 16 * q^74 - 2 * q^75 + 18 * q^76 + 2 * q^77 + 10 * q^78 - 56 * q^79 + q^80 - 3 * q^81 + 12 * q^82 + 52 * q^83 - 3 * q^84 - 53 * q^85 - 31 * q^86 + 5 * q^87 + 13 * q^88 - 104 * q^89 - q^90 + 34 * q^91 - 12 * q^92 + 32 * q^93 - 14 * q^94 - 92 * q^95 - 3 * q^96 - 82 * q^97 + 3 * q^98 - 13 * q^99

Introduction

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