LMFDB - Embedded newform 966.2.q.c.85.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	966.85
Dual form			966.2.q.c.841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.817178 + 1.78937i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.817178 + 1.78937i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(1.88745 + 0.554206i) q^{10} +(0.898983 + 1.03748i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(5.03158 + 1.47740i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(1.65486 + 1.06351i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.490593 - 3.41215i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(-0.545886 - 3.79672i) q^{19} +(1.65486 - 1.06351i) q^{20} +(-0.654861 + 0.755750i) q^{21} +1.37279 q^{22} +(3.99987 + 2.64594i) q^{23} -1.00000 q^{24} +(0.740237 - 0.854279i) q^{25} +(4.41153 - 2.83512i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.415415 + 0.909632i) q^{28} +(-0.413293 + 2.87451i) q^{29} +(1.88745 - 0.554206i) q^{30} +(6.33807 + 4.07323i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(1.31718 + 0.386758i) q^{33} +(-2.25746 - 2.60525i) q^{34} +(-1.28820 - 1.48666i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.60504 - 5.70423i) q^{37} +(-3.22685 - 2.07377i) q^{38} +(5.03158 - 1.47740i) q^{39} +(0.279953 - 1.94711i) q^{40} +(-0.924635 - 2.02467i) q^{41} +(0.142315 + 0.989821i) q^{42} +(-3.99751 + 2.56904i) q^{43} +(0.898983 - 1.03748i) q^{44} +1.96714 q^{45} +(4.61903 - 1.29018i) q^{46} -6.48010 q^{47} +(-0.654861 + 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.160869 - 1.11887i) q^{50} +(-1.43203 - 3.13572i) q^{51} +(0.746298 - 5.19062i) q^{52} +(9.57256 - 2.81076i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-1.12181 + 2.45642i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-2.51189 - 2.89887i) q^{57} +(1.90176 + 2.19475i) q^{58} +(-4.98689 - 1.46428i) q^{59} +(0.817178 - 1.78937i) q^{60} +(-6.67787 - 4.29160i) q^{61} +(7.22889 - 2.12259i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.46807 + 10.2107i) q^{65} +(1.15486 - 0.742184i) q^{66} +(-10.0196 + 11.5632i) q^{67} -3.44724 q^{68} +(4.79541 + 0.0634158i) q^{69} -1.96714 q^{70} +(-2.16342 + 2.49672i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(1.08203 + 7.52569i) q^{73} +(-2.60504 - 5.70423i) q^{74} +(0.160869 - 1.11887i) q^{75} +(-3.68038 + 1.08066i) q^{76} +(-1.15486 - 0.742184i) q^{77} +(2.17843 - 4.77011i) q^{78} +(3.45960 + 1.01583i) q^{79} +(-1.28820 - 1.48666i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-2.13565 - 0.627083i) q^{82} +(-3.28615 + 7.19567i) q^{83} +(0.841254 + 0.540641i) q^{84} +(6.50650 - 1.91048i) q^{85} +(-0.676259 + 4.70348i) q^{86} +(1.20640 + 2.64164i) q^{87} +(-0.195368 - 1.35881i) q^{88} +(-9.33108 + 5.99672i) q^{89} +(1.28820 - 1.48666i) q^{90} -5.24399 q^{91} +(2.04977 - 4.33572i) q^{92} +7.53408 q^{93} +(-4.24356 + 4.89733i) q^{94} +(6.34765 - 4.07939i) q^{95} +(0.142315 + 0.989821i) q^{96} +(-7.70763 - 16.8773i) q^{97} +(0.142315 - 0.989821i) q^{98} +(1.31718 - 0.386758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 - q^3 - q^4 + q^6 - q^7 + q^8 - q^9	$ 10 q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} + q^{8} - q^{9} - 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 11 q^{15} - q^{16} - 5 q^{17} + q^{18} + 31 q^{19} + 11 q^{20} - q^{21} + 6 q^{22} - q^{23} - 10 q^{24} - 17 q^{25} + 24 q^{26} - q^{27} - q^{28} - 5 q^{29} + 3 q^{31} + q^{32} + 5 q^{33} + 16 q^{34} - q^{36} + 14 q^{37} - 9 q^{38} - 2 q^{39} + 11 q^{40} - 28 q^{41} + q^{42} + 9 q^{43} - 6 q^{44} + 23 q^{46} - 44 q^{47} - q^{48} - q^{49} - 5 q^{50} - 5 q^{51} + 20 q^{52} + q^{53} + q^{54} + q^{56} - 2 q^{57} + 16 q^{58} - 11 q^{59} - 41 q^{61} + 30 q^{62} - q^{63} - q^{64} + 11 q^{65} + 6 q^{66} - 12 q^{67} + 6 q^{68} + 21 q^{69} - 22 q^{71} + q^{72} + 19 q^{73} - 14 q^{74} + 5 q^{75} - 24 q^{76} - 6 q^{77} + 2 q^{78} + 3 q^{79} - q^{81} + 6 q^{82} - 39 q^{83} - q^{84} + 22 q^{85} + 35 q^{86} + 6 q^{87} - 5 q^{88} - 17 q^{89} - 2 q^{91} - q^{92} - 8 q^{93} + 11 q^{94} + q^{96} - 12 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) $ 10 * q + q^2 - q^3 - q^4 + q^6 - q^7 + q^8 - q^9 - 6 * q^11 - q^12 - 2 * q^13 + q^14 + 11 * q^15 - q^16 - 5 * q^17 + q^18 + 31 * q^19 + 11 * q^20 - q^21 + 6 * q^22 - q^23 - 10 * q^24 - 17 * q^25 + 24 * q^26 - q^27 - q^28 - 5 * q^29 + 3 * q^31 + q^32 + 5 * q^33 + 16 * q^34 - q^36 + 14 * q^37 - 9 * q^38 - 2 * q^39 + 11 * q^40 - 28 * q^41 + q^42 + 9 * q^43 - 6 * q^44 + 23 * q^46 - 44 * q^47 - q^48 - q^49 - 5 * q^50 - 5 * q^51 + 20 * q^52 + q^53 + q^54 + q^56 - 2 * q^57 + 16 * q^58 - 11 * q^59 - 41 * q^61 + 30 * q^62 - q^63 - q^64 + 11 * q^65 + 6 * q^66 - 12 * q^67 + 6 * q^68 + 21 * q^69 - 22 * q^71 + q^72 + 19 * q^73 - 14 * q^74 + 5 * q^75 - 24 * q^76 - 6 * q^77 + 2 * q^78 + 3 * q^79 - q^81 + 6 * q^82 - 39 * q^83 - q^84 + 22 * q^85 + 35 * q^86 + 6 * q^87 - 5 * q^88 - 17 * q^89 - 2 * q^91 - q^92 - 8 * q^93 + 11 * q^94 + q^96 - 12 * q^97 + q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.817178	+	1.78937i	0.365453	+	0.800231i	0.999634	+	0.0270462i	$0.00861013\pi$
$5$	0.817178	+	1.78937i	0.365453	+	0.800231i	−0.634181	+	0.773185i	$0.718663\pi$
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	1.88745	+	0.554206i	0.596865	+	0.175255i
$11$	0.898983	+	1.03748i	0.271054	+	0.312813i	0.874915	−	0.484277i	$-0.160917\pi$
$11$	0.898983	+	1.03748i	0.271054	+	0.312813i	−0.603861	+	0.797090i	$0.706372\pi$
$12$	−0.654861	−	0.755750i	−0.189042	−	0.218166i
$13$	5.03158	+	1.47740i	1.39551	+	0.409758i	0.891139	−	0.453730i	$-0.149907\pi$
$13$	5.03158	+	1.47740i	1.39551	+	0.409758i	0.504369	+	0.863488i	$0.331725\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	1.65486	+	1.06351i	0.427283	+	0.274598i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.490593	−	3.41215i	0.118986	−	0.827568i	−0.839690	−	0.543067i	$-0.817263\pi$
$17$	0.490593	−	3.41215i	0.118986	−	0.827568i	0.958676	−	0.284501i	$-0.0918279\pi$
$18$	−0.415415	−	0.909632i	−0.0979143	−	0.214402i
$19$	−0.545886	−	3.79672i	−0.125235	−	0.871027i	−0.951479	−	0.307714i	$-0.900436\pi$
$19$	−0.545886	−	3.79672i	−0.125235	−	0.871027i	0.826244	−	0.563312i	$-0.190473\pi$
$20$	1.65486	−	1.06351i	0.370038	−	0.237809i
$21$	−0.654861	+	0.755750i	−0.142902	+	0.164918i
$22$	1.37279			0.292679
$23$	3.99987	+	2.64594i	0.834031	+	0.551718i
$23$	3.99987	+	2.64594i	0.834031	+	0.551718i
$24$	−1.00000			−0.204124
$25$	0.740237	−	0.854279i	0.148047	−	0.170856i
$26$	4.41153	−	2.83512i	0.865172	−	0.556012i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	0.415415	+	0.909632i	0.0785061	+	0.171904i
$29$	−0.413293	+	2.87451i	−0.0767465	+	0.533784i	0.914787	+	0.403936i	$0.132358\pi$
$29$	−0.413293	+	2.87451i	−0.0767465	+	0.533784i	−0.991534	+	0.129848i	$0.958551\pi$
$30$	1.88745	−	0.554206i	0.344600	−	0.101184i
$31$	6.33807	+	4.07323i	1.13835	+	0.731574i	0.967287	−	0.253686i	$-0.0816431\pi$
$31$	6.33807	+	4.07323i	1.13835	+	0.731574i	0.171064	+	0.985260i	$0.445279\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	1.31718	+	0.386758i	0.229291	+	0.0673260i
$34$	−2.25746	−	2.60525i	−0.387151	−	0.446796i
$35$	−1.28820	−	1.48666i	−0.217746	−	0.251292i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	2.60504	−	5.70423i	0.428265	−	0.937770i	−0.565340	−	0.824858i	$-0.691255\pi$
$37$	2.60504	−	5.70423i	0.428265	−	0.937770i	0.993605	−	0.112912i	$-0.0360178\pi$
$38$	−3.22685	−	2.07377i	−0.523464	−	0.336410i
$39$	5.03158	−	1.47740i	0.805697	−	0.236574i
$40$	0.279953	−	1.94711i	0.0442644	−	0.307866i
$41$	−0.924635	−	2.02467i	−0.144404	−	0.316200i	0.823585	−	0.567192i	$-0.191970\pi$
$41$	−0.924635	−	2.02467i	−0.144404	−	0.316200i	−0.967989	+	0.250992i	$0.919243\pi$
$42$	0.142315	+	0.989821i	0.0219597	+	0.152733i
$43$	−3.99751	+	2.56904i	−0.609614	+	0.391775i	−0.808712	−	0.588204i	$-0.799835\pi$
$43$	−3.99751	+	2.56904i	−0.609614	+	0.391775i	0.199098	+	0.979980i	$0.436199\pi$
$44$	0.898983	−	1.03748i	0.135527	−	0.156406i
$45$	1.96714			0.293243
$46$	4.61903	−	1.29018i	0.681039	−	0.190226i
$47$	−6.48010			−0.945220			−0.472610	−	0.881272i	$-0.656688\pi$
$47$	−6.48010			−0.945220			−0.472610	+	0.881272i	$0.656688\pi$
$48$	−0.654861	+	0.755750i	−0.0945210	+	0.109083i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−0.160869	−	1.11887i	−0.0227503	−	0.158232i
$51$	−1.43203	−	3.13572i	−0.200525	−	0.439088i
$52$	0.746298	−	5.19062i	0.103493	−	0.719809i
$53$	9.57256	−	2.81076i	1.31489	−	0.386087i	0.452245	−	0.891894i	$-0.350623\pi$
$53$	9.57256	−	2.81076i	1.31489	−	0.386087i	0.862647	+	0.505806i	$0.168805\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	−1.12181	+	2.45642i	−0.151265	+	0.331224i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	−2.51189	−	2.89887i	−0.332708	−	0.383965i
$58$	1.90176	+	2.19475i	0.249714	+	0.288185i
$59$	−4.98689	−	1.46428i	−0.649238	−	0.190634i	−0.0595004	−	0.998228i	$-0.518951\pi$
$59$	−4.98689	−	1.46428i	−0.649238	−	0.190634i	−0.589738	+	0.807595i	$0.700769\pi$
$60$	0.817178	−	1.78937i	0.105497	−	0.231007i
$61$	−6.67787	−	4.29160i	−0.855013	−	0.549484i	0.0381214	−	0.999273i	$-0.487863\pi$
$61$	−6.67787	−	4.29160i	−0.855013	−	0.549484i	−0.893135	+	0.449790i	$0.851499\pi$
$62$	7.22889	−	2.12259i	0.918071	−	0.269570i
$63$	−0.142315	+	0.989821i	−0.0179300	+	0.124706i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	1.46807	+	10.2107i	0.182092	+	1.26648i
$66$	1.15486	−	0.742184i	0.142154	−	0.0913565i
$67$	−10.0196	+	11.5632i	−1.22409	+	1.41267i	−0.343254	+	0.939243i	$0.611529\pi$
$67$	−10.0196	+	11.5632i	−1.22409	+	1.41267i	−0.880833	+	0.473428i	$0.843016\pi$
$68$	−3.44724			−0.418039
$69$	4.79541	+	0.0634158i	0.577300	+	0.00763437i
$70$	−1.96714			−0.235118
$71$	−2.16342	+	2.49672i	−0.256751	+	0.296307i	−0.869461	−	0.494001i	$-0.835534\pi$
$71$	−2.16342	+	2.49672i	−0.256751	+	0.296307i	0.612710	+	0.790308i	$0.290079\pi$
$72$	−0.841254	+	0.540641i	−0.0991427	+	0.0637151i
$73$	1.08203	+	7.52569i	0.126642	+	0.880815i	0.949768	+	0.312956i	$0.101319\pi$
$73$	1.08203	+	7.52569i	0.126642	+	0.880815i	−0.823126	+	0.567859i	$0.807772\pi$
$74$	−2.60504	−	5.70423i	−0.302829	−	0.663104i
$75$	0.160869	−	1.11887i	0.0185755	−	0.129196i
$76$	−3.68038	+	1.08066i	−0.422169	+	0.123960i
$77$	−1.15486	−	0.742184i	−0.131609	−	0.0845797i
$78$	2.17843	−	4.77011i	0.246659	−	0.540108i
$79$	3.45960	+	1.01583i	0.389235	+	0.114290i	0.470494	−	0.882403i	$-0.344076\pi$
$79$	3.45960	+	1.01583i	0.389235	+	0.114290i	−0.0812588	+	0.996693i	$0.525894\pi$
$80$	−1.28820	−	1.48666i	−0.144025	−	0.166214i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−2.13565	−	0.627083i	−0.235843	−	0.0692498i
$83$	−3.28615	+	7.19567i	−0.360702	+	0.789827i	0.639084	+	0.769137i	$0.279314\pi$
$83$	−3.28615	+	7.19567i	−0.360702	+	0.789827i	−0.999786	+	0.0206904i	$0.993414\pi$
$84$	0.841254	+	0.540641i	0.0917883	+	0.0589887i
$85$	6.50650	−	1.91048i	0.705729	−	0.207221i
$86$	−0.676259	+	4.70348i	−0.0729228	+	0.507189i
$87$	1.20640	+	2.64164i	0.129339	+	0.283213i
$88$	−0.195368	−	1.35881i	−0.0208263	−	0.144850i
$89$	−9.33108	+	5.99672i	−0.989093	+	0.635651i	−0.931901	−	0.362712i	$-0.881851\pi$
$89$	−9.33108	+	5.99672i	−0.989093	+	0.635651i	−0.0571913	+	0.998363i	$0.518215\pi$
$90$	1.28820	−	1.48666i	0.135788	−	0.156708i
$91$	−5.24399			−0.549720
$92$	2.04977	−	4.33572i	0.213703	−	0.452030i
$93$	7.53408			0.781247
$94$	−4.24356	+	4.89733i	−0.437690	+	0.505121i
$95$	6.34765	−	4.07939i	0.651255	−	0.418536i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	−7.70763	−	16.8773i	−0.782591	−	1.71364i	−0.696736	−	0.717327i	$-0.745365\pi$
$97$	−7.70763	−	16.8773i	−0.782591	−	1.71364i	−0.0858547	−	0.996308i	$-0.527362\pi$
$98$	0.142315	−	0.989821i	0.0143760	−	0.0999871i
$99$	1.31718	−	0.386758i	0.132381	−	0.0388707i
$100$	−0.950930	−	0.611126i	−0.0950930	−	0.0611126i
$101$	−5.34176	+	11.6968i	−0.531525	+	1.16388i	0.433364	+	0.901219i	$0.357326\pi$
$101$	−5.34176	+	11.6968i	−0.531525	+	1.16388i	−0.964889	+	0.262658i	$0.915401\pi$
$102$	−3.30760	−	0.971199i	−0.327501	−	0.0961630i
$103$	−10.4527	−	12.0631i	−1.02994	−	1.18861i	−0.981828	−	0.189772i	$-0.939225\pi$
$103$	−10.4527	−	12.0631i	−1.02994	−	1.18861i	−0.0481112	−	0.998842i	$-0.515320\pi$
$104$	−3.43409	−	3.96315i	−0.336740	−	0.388619i
$105$	−1.88745	−	0.554206i	−0.184197	−	0.0540850i
$106$	4.14446	−	9.07511i	0.402546	−	0.881453i
$107$	6.32451	+	4.06451i	0.611413	+	0.392931i	0.809387	−	0.587276i	$-0.199800\pi$
$107$	6.32451	+	4.06451i	0.611413	+	0.392931i	−0.197974	+	0.980207i	$0.563436\pi$
$108$	−0.959493	+	0.281733i	−0.0923273	+	0.0271097i
$109$	2.50607	−	17.4301i	0.240038	−	1.66950i	−0.411899	−	0.911229i	$-0.635134\pi$
$109$	2.50607	−	17.4301i	0.240038	−	1.66950i	0.651937	−	0.758273i	$-0.273956\pi$
$110$	1.12181	+	2.45642i	0.106960	+	0.234211i
$111$	−0.892446	−	6.20710i	−0.0847072	−	0.589151i
$112$	0.841254	−	0.540641i	0.0794910	−	0.0510858i
$113$	−6.56474	+	7.57612i	−0.617559	+	0.712701i	−0.975242	−	0.221142i	$-0.929022\pi$
$113$	−6.56474	+	7.57612i	−0.617559	+	0.712701i	0.357682	+	0.933843i	$0.383567\pi$
$114$	−3.83576			−0.359252
$115$	−1.46597	+	9.31946i	−0.136702	+	0.869044i
$116$	2.90407			0.269636
$117$	3.43409	−	3.96315i	0.317481	−	0.366393i
$118$	−4.37235	+	2.80994i	−0.402508	+	0.258676i
$119$	0.490593	+	3.41215i	0.0449726	+	0.312791i
$120$	−0.817178	−	1.78937i	−0.0745978	−	0.163346i
$121$	1.29727	−	9.02268i	0.117933	−	0.820243i
$122$	−7.61645	+	2.23639i	−0.689561	+	0.202473i
$123$	−1.87247	−	1.20336i	−0.168835	−	0.108504i
$124$	3.12977	−	6.85324i	0.281062	−	0.615439i
$125$	11.5708	+	3.39749i	1.03492	+	0.303881i
$126$	0.654861	+	0.755750i	0.0583396	+	0.0673275i
$127$	−2.88732	−	3.33214i	−0.256208	−	0.295680i	0.613044	−	0.790049i	$-0.289945\pi$
$127$	−2.88732	−	3.33214i	−0.256208	−	0.295680i	−0.869252	+	0.494369i	$0.835399\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	−1.97399	+	4.32243i	−0.173800	+	0.380569i
$130$	8.67808	+	5.57706i	0.761118	+	0.489141i
$131$	11.3587	−	3.33523i	0.992418	−	0.291400i	0.255077	−	0.966921i	$-0.417899\pi$
$131$	11.3587	−	3.33523i	0.992418	−	0.291400i	0.737341	+	0.675521i	$0.236081\pi$
$132$	0.195368	−	1.35881i	0.0170046	−	0.118269i
$133$	1.59343	+	3.48913i	0.138168	+	0.302546i
$134$	2.17746	+	15.1446i	0.188104	+	1.30829i
$135$	1.65486	−	1.06351i	0.142428	−	0.0915327i
$136$	−2.25746	+	2.60525i	−0.193576	+	0.223398i
$137$	−10.3407			−0.883465			−0.441733	−	0.897147i	$-0.645636\pi$
$137$	−10.3407			−0.883465			−0.441733	+	0.897147i	$0.645636\pi$
$138$	3.18825	−	3.58260i	0.271402	−	0.304971i
$139$	4.85447			0.411751			0.205875	−	0.978578i	$-0.433996\pi$
$139$	4.85447			0.411751			0.205875	+	0.978578i	$0.433996\pi$
$140$	−1.28820	+	1.48666i	−0.108873	+	0.125646i
$141$	−5.45141	+	3.50341i	−0.459091	+	0.295040i
$142$	0.470157	+	3.27001i	0.0394547	+	0.274413i
$143$	2.99052	+	6.54833i	0.250080	+	0.547599i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−5.48130	+	1.60946i	−0.455197	+	0.133658i
$146$	6.39611	+	4.11053i	0.529346	+	0.340190i
$147$	0.415415	−	0.909632i	0.0342629	−	0.0750252i
$148$	−6.01691	−	1.76672i	−0.494587	−	0.145224i
$149$	−10.4500	−	12.0599i	−0.856094	−	0.987985i	0.143905	−	0.989592i	$-0.454034\pi$
$149$	−10.4500	−	12.0599i	−0.856094	−	0.987985i	−0.999999	+	0.00160648i	$0.999489\pi$
$150$	−0.740237	−	0.854279i	−0.0604401	−	0.0697516i
$151$	−4.67481	−	1.37265i	−0.380430	−	0.111704i	0.0859257	−	0.996302i	$-0.472615\pi$
$151$	−4.67481	−	1.37265i	−0.380430	−	0.111704i	−0.466356	+	0.884597i	$0.654433\pi$
$152$	−1.59343	+	3.48913i	−0.129244	+	0.283006i
$153$	−2.90000	−	1.86372i	−0.234451	−	0.150673i
$154$	−1.31718	+	0.386758i	−0.106141	+	0.0311659i
$155$	−2.10919	+	14.6697i	−0.169414	+	1.17830i
$156$	−2.17843	−	4.77011i	−0.174414	−	0.381914i
$157$	−0.0575229	−	0.400081i	−0.00459083	−	0.0319299i	0.987397	−	0.158261i	$-0.0505888\pi$
$157$	−0.0575229	−	0.400081i	−0.00459083	−	0.0319299i	−0.991988	+	0.126331i	$0.959680\pi$
$158$	3.03327	−	1.94936i	0.241314	−	0.155083i
$159$	6.53334	−	7.53988i	0.518128	−	0.597951i
$160$	−1.96714			−0.155516
$161$	−4.58330	−	1.41187i	−0.361214	−	0.111271i
$162$	−1.00000			−0.0785674
$163$	−0.0869524	+	0.100348i	−0.00681064	+	0.00785990i	−0.759145	−	0.650922i	$-0.774383\pi$
$163$	−0.0869524	+	0.100348i	−0.00681064	+	0.00785990i	0.752334	+	0.658782i	$0.228928\pi$
$164$	−1.87247	+	1.20336i	−0.146215	+	0.0939669i
$165$	0.384315	+	2.67297i	0.0299189	+	0.208090i
$166$	3.28615	+	7.19567i	0.255055	+	0.558492i
$167$	−3.25052	+	22.6078i	−0.251533	+	1.74945i	0.337488	+	0.941330i	$0.390423\pi$
$167$	−3.25052	+	22.6078i	−0.251533	+	1.74945i	−0.589021	+	0.808118i	$0.700486\pi$
$168$	0.959493	−	0.281733i	0.0740265	−	0.0217361i
$169$	12.1977	+	7.83901i	0.938288	+	0.603001i
$170$	2.81701	−	6.16838i	0.216055	−	0.473093i
$171$	−3.68038	−	1.08066i	−0.281446	−	0.0826400i
$172$	3.11180	+	3.59121i	0.237272	+	0.273827i
$173$	12.5556	+	14.4900i	0.954586	+	1.10165i	0.994737	+	0.102458i	$0.0326707\pi$
$173$	12.5556	+	14.4900i	0.954586	+	1.10165i	−0.0401509	+	0.999194i	$0.512784\pi$
$174$	2.78644	+	0.818172i	0.211239	+	0.0620254i
$175$	−0.469574	+	1.02822i	−0.0354965	+	0.0777264i
$176$	−1.15486	−	0.742184i	−0.0870509	−	0.0559442i
$177$	−4.98689	+	1.46428i	−0.374838	+	0.110062i
$178$	−1.57854	+	10.9790i	−0.118316	+	0.822909i
$179$	2.01355	+	4.40905i	0.150499	+	0.329548i	0.969833	−	0.243769i	$-0.0783838\pi$
$179$	2.01355	+	4.40905i	0.150499	+	0.329548i	−0.819334	+	0.573317i	$0.805657\pi$
$180$	−0.279953	−	1.94711i	−0.0208664	−	0.145129i
$181$	−17.8167	+	11.4501i	−1.32430	+	0.851078i	−0.995632	−	0.0933660i	$-0.970237\pi$
$181$	−17.8167	+	11.4501i	−1.32430	+	0.851078i	−0.328672	+	0.944444i	$0.606601\pi$
$182$	−3.43409	+	3.96315i	−0.254551	+	0.293768i
$183$	−7.93800			−0.586793
$184$	−1.93440	−	4.38840i	−0.142606	−	0.323517i
$185$	12.3358			0.906944
$186$	4.93377	−	5.69388i	0.361762	−	0.417495i
$187$	3.98108	−	2.55848i	0.291125	−	0.187095i
$188$	0.922214	+	6.41414i	0.0672594	+	0.467799i
$189$	0.415415	+	0.909632i	0.0302170	+	0.0661660i
$190$	1.07383	−	7.46866i	0.0779039	−	0.541834i
$191$	−4.51002	+	1.32426i	−0.326334	+	0.0958203i	−0.440796	−	0.897607i	$-0.645304\pi$
$191$	−4.51002	+	1.32426i	−0.326334	+	0.0958203i	0.114462	+	0.993428i	$0.463486\pi$
$192$	0.841254	+	0.540641i	0.0607122	+	0.0390174i
$193$	6.68352	−	14.6349i	0.481090	−	1.05344i	−0.501072	−	0.865405i	$-0.667061\pi$
$193$	6.68352	−	14.6349i	0.481090	−	1.05344i	0.982162	−	0.188035i	$-0.0602118\pi$
$194$	−17.8025	−	5.22728i	−1.27814	−	0.375297i
$195$	6.75532	+	7.79605i	0.483758	+	0.558287i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	12.3129	+	3.61540i	0.877260	+	0.257587i	0.689200	−	0.724571i	$-0.257962\pi$
$197$	12.3129	+	3.61540i	0.877260	+	0.257587i	0.188060	+	0.982158i	$0.439780\pi$
$198$	0.570276	−	1.24873i	0.0405277	−	0.0887434i
$199$	−8.13384	−	5.22730i	−0.576593	−	0.370554i	0.219606	−	0.975589i	$-0.429523\pi$
$199$	−8.13384	−	5.22730i	−0.576593	−	0.370554i	−0.796199	+	0.605035i	$0.793159\pi$
$200$	−1.08458	+	0.318463i	−0.0766917	+	0.0225187i
$201$	−2.17746	+	15.1446i	−0.153586	+	1.06822i
$202$	5.34176	+	11.6968i	0.375845	+	0.822986i
$203$	−0.413293	−	2.87451i	−0.0290075	−	0.201751i
$204$	−2.90000	+	1.86372i	−0.203041	+	0.130486i
$205$	2.86729	−	3.30903i	0.200260	−	0.231113i
$206$	−15.9618			−1.11211
$207$	4.06844	−	2.53925i	0.282776	−	0.176490i
$208$	−5.24399			−0.363606
$209$	3.44828	−	3.97953i	0.238523	−	0.275270i
$210$	−1.65486	+	1.06351i	−0.114196	+	0.0733895i
$211$	2.46132	+	17.1188i	0.169444	+	1.17851i	0.880037	+	0.474905i	$0.157518\pi$
$211$	2.46132	+	17.1188i	0.169444	+	1.17851i	−0.710593	+	0.703603i	$0.751573\pi$
$212$	−4.14446	−	9.07511i	−0.284643	−	0.623281i
$213$	−0.470157	+	3.27001i	−0.0322146	+	0.224058i
$214$	7.21343	−	2.11805i	0.493100	−	0.144787i
$215$	−7.86365	−	5.05366i	−0.536296	−	0.344657i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	−7.22889	−	2.12259i	−0.490729	−	0.144091i
$218$	−11.5317	−	13.3083i	−0.781024	−	0.901349i
$219$	4.97896	+	5.74602i	0.336447	+	0.388280i
$220$	2.59107	+	0.760807i	0.174690	+	0.0512936i
$221$	7.50958	−	16.4437i	0.505149	−	1.10612i
$222$	−5.27544	−	3.39032i	−0.354064	−	0.227543i
$223$	−13.5417	+	3.97619i	−0.906818	+	0.266266i	−0.701701	−	0.712472i	$-0.747576\pi$
$223$	−13.5417	+	3.97619i	−0.906818	+	0.266266i	−0.205117	+	0.978737i	$0.565757\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	−0.469574	−	1.02822i	−0.0313049	−	0.0685482i
$226$	1.42666	+	9.92261i	0.0948997	+	0.660042i
$227$	2.91955	−	1.87628i	0.193777	−	0.124533i	−0.440155	−	0.897922i	$-0.645076\pi$
$227$	2.91955	−	1.87628i	0.193777	−	0.124533i	0.633932	+	0.773389i	$0.281440\pi$
$228$	−2.51189	+	2.89887i	−0.166354	+	0.191983i
$229$	6.46389			0.427146			0.213573	−	0.976927i	$-0.431490\pi$
$229$	6.46389			0.427146			0.213573	+	0.976927i	$0.431490\pi$
$230$	6.08318	+	7.21085i	0.401113	+	0.475470i
$231$	−1.37279			−0.0903227
$232$	1.90176	−	2.19475i	0.124857	−	0.144093i
$233$	4.07012	−	2.61571i	0.266643	−	0.171361i	−0.400487	−	0.916302i	$-0.631159\pi$
$233$	4.07012	−	2.61571i	0.266643	−	0.171361i	0.667130	+	0.744942i	$0.267523\pi$
$234$	−0.746298	−	5.19062i	−0.0487870	−	0.339321i
$235$	−5.29540	−	11.5953i	−0.345434	−	0.756394i
$236$	−0.739671	+	5.14452i	−0.0481485	+	0.334880i
$237$	3.45960	−	1.01583i	0.224725	−	0.0659852i
$238$	2.90000	+	1.86372i	0.187979	+	0.120807i
$239$	−5.07604	+	11.1150i	−0.328342	+	0.718968i	−0.999755	−	0.0221145i	$-0.992960\pi$
$239$	−5.07604	+	11.1150i	−0.328342	+	0.718968i	0.671414	+	0.741083i	$0.265687\pi$
$240$	−1.88745	−	0.554206i	−0.121835	−	0.0357739i
$241$	−3.91370	−	4.51665i	−0.252104	−	0.290943i	0.615565	−	0.788086i	$-0.288928\pi$
$241$	−3.91370	−	4.51665i	−0.252104	−	0.290943i	−0.867669	+	0.497143i	$0.834382\pi$
$242$	−5.96936	−	6.88900i	−0.383725	−	0.442842i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	−3.29756	+	7.22065i	−0.211105	+	0.462255i
$245$	1.65486	+	1.06351i	0.105725	+	0.0679454i
$246$	−2.13565	+	0.627083i	−0.136164	+	0.0399814i
$247$	2.86262	−	19.9100i	0.182144	−	1.26684i
$248$	−3.12977	−	6.85324i	−0.198741	−	0.435181i
$249$	1.12579	+	7.83001i	0.0713438	+	0.496207i
$250$	10.1449	−	6.51974i	0.641621	−	0.412345i
$251$	−4.43921	+	5.12312i	−0.280201	+	0.323369i	−0.878352	−	0.478014i	$-0.841357\pi$
$251$	−4.43921	+	5.12312i	−0.280201	+	0.323369i	0.598151	+	0.801383i	$0.295902\pi$
$252$	1.00000			0.0629941
$253$	0.850699	+	6.52846i	0.0534830	+	0.410441i
$254$	−4.40906			−0.276649
$255$	4.44073	−	5.12488i	0.278089	−	0.320932i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	1.68434	+	11.7148i	0.105066	+	0.730752i	0.972450	+	0.233112i	$0.0748908\pi$
$257$	1.68434	+	11.7148i	0.105066	+	0.730752i	−0.867384	+	0.497640i	$0.834200\pi$
$258$	1.97399	+	4.32243i	0.122895	+	0.269103i
$259$	−0.892446	+	6.20710i	−0.0554539	+	0.385690i
$260$	9.89780	−	2.90626i	0.613835	−	0.180238i
$261$	2.44306	+	1.57006i	0.151222	+	0.0971843i
$262$	4.91780	−	10.7685i	0.303822	−	0.665278i
$263$	−1.23963	−	0.363989i	−0.0764390	−	0.0224445i	0.243289	−	0.969954i	$-0.421774\pi$
$263$	−1.23963	−	0.363989i	−0.0764390	−	0.0224445i	−0.319728	+	0.947509i	$0.603592\pi$
$264$	−0.898983	−	1.03748i	−0.0553286	−	0.0638526i
$265$	12.8520	+	14.8320i	0.789490	+	0.911120i
$266$	3.68038	+	1.08066i	0.225659	+	0.0662594i
$267$	−4.60773	+	10.0895i	−0.281989	+	0.617469i
$268$	12.8714	+	8.27198i	0.786249	+	0.505291i
$269$	−28.7134	+	8.43102i	−1.75069	+	0.514048i	−0.990721	−	0.135914i	$-0.956603\pi$
$269$	−28.7134	+	8.43102i	−1.75069	+	0.514048i	−0.759966	+	0.649962i	$0.774785\pi$
$270$	0.279953	−	1.94711i	0.0170374	−	0.118498i
$271$	−4.38675	−	9.60565i	−0.266476	−	0.583502i	0.728337	−	0.685219i	$-0.240294\pi$
$271$	−4.38675	−	9.60565i	−0.266476	−	0.583502i	−0.994813	+	0.101717i	$0.967566\pi$
$272$	0.490593	+	3.41215i	0.0297466	+	0.206892i
$273$	−4.41153	+	2.83512i	−0.266998	+	0.171589i
$274$	−6.77172	+	7.81498i	−0.409094	+	0.472120i
$275$	1.55176			0.0935746
$276$	−0.619688	−	4.75563i	−0.0373008	−	0.286255i
$277$	15.2744			0.917750			0.458875	−	0.888501i	$-0.348253\pi$
$277$	15.2744			0.917750			0.458875	+	0.888501i	$0.348253\pi$
$278$	3.17900	−	3.66876i	0.190664	−	0.220038i
$279$	6.33807	−	4.07323i	0.379450	−	0.243858i
$280$	0.279953	+	1.94711i	0.0167304	+	0.116362i
$281$	5.74018	+	12.5692i	0.342431	+	0.749819i	0.999994	−	0.00358109i	$-0.00113990\pi$
$281$	5.74018	+	12.5692i	0.342431	+	0.749819i	−0.657563	+	0.753400i	$0.728413\pi$
$282$	−0.922214	+	6.41414i	−0.0549171	+	0.381957i
$283$	−12.7039	+	3.73020i	−0.755169	+	0.221738i	−0.636585	−	0.771207i	$-0.719654\pi$
$283$	−12.7039	+	3.73020i	−0.755169	+	0.221738i	−0.118584	+	0.992944i	$0.537835\pi$
$284$	2.77920	+	1.78608i	0.164915	+	0.105984i
$285$	3.13450	−	6.86360i	0.185672	−	0.406564i
$286$	6.90728	+	2.02816i	0.408436	+	0.119928i
$287$	1.45760	+	1.68216i	0.0860392	+	0.0992945i
$288$	0.654861	+	0.755750i	0.0385880	+	0.0445330i
$289$	4.90930	+	1.44150i	0.288783	+	0.0847942i
$290$	−2.37314	+	5.19646i	−0.139356	+	0.305147i
$291$	−15.6087	−	10.0311i	−0.914995	−	0.588032i
$292$	7.29510	−	2.14203i	0.426913	−	0.125353i
$293$	2.07694	−	14.4455i	0.121336	−	0.843912i	−0.834709	−	0.550692i	$-0.814364\pi$
$293$	2.07694	−	14.4455i	0.121336	−	0.843912i	0.956045	−	0.293220i	$-0.0947270\pi$
$294$	−0.415415	−	0.909632i	−0.0242275	−	0.0530508i
$295$	−1.45503	−	10.1200i	−0.0847153	−	0.589208i
$296$	−5.27544	+	3.39032i	−0.306629	+	0.197058i
$297$	0.898983	−	1.03748i	0.0521643	−	0.0602008i
$298$	−15.9575			−0.924395
$299$	16.2165	+	19.2227i	0.937826	+	1.11168i
$300$	−1.13037			−0.0652621
$301$	3.11180	−	3.59121i	0.179361	−	0.206994i
$302$	−4.09872	+	2.63409i	−0.235855	+	0.151575i
$303$	1.83001	+	12.7280i	0.105131	+	0.731203i
$304$	1.59343	+	3.48913i	0.0913896	+	0.200115i
$305$	2.22226	−	15.4562i	0.127246	−	0.885018i
$306$	−3.30760	+	0.971199i	−0.189083	+	0.0555197i
$307$	−24.7368	−	15.8974i	−1.41181	−	0.907312i	−0.411814	−	0.911268i	$-0.635105\pi$
$307$	−24.7368	−	15.8974i	−1.41181	−	0.907312i	−0.999992	+	0.00395560i	$0.998741\pi$
$308$	−0.570276	+	1.24873i	−0.0324945	+	0.0711530i
$309$	−15.3152	−	4.49695i	−0.871252	−	0.255823i
$310$	9.70540	+	11.2006i	0.551230	+	0.636153i
$311$	−4.37090	−	5.04428i	−0.247851	−	0.286035i	0.618168	−	0.786046i	$-0.287875\pi$
$311$	−4.37090	−	5.04428i	−0.247851	−	0.286035i	−0.866019	+	0.500010i	$0.833329\pi$
$312$	−5.03158	−	1.47740i	−0.284857	−	0.0836415i
$313$	4.84910	−	10.6180i	0.274087	−	0.600167i	−0.721665	−	0.692243i	$-0.756623\pi$
$313$	4.84910	−	10.6180i	0.274087	−	0.600167i	0.995752	+	0.0920754i	$0.0293501\pi$
$314$	−0.340030	−	0.218524i	−0.0191890	−	0.0123320i
$315$	−1.88745	+	0.554206i	−0.106346	+	0.0312260i
$316$	0.513137	−	3.56895i	0.0288662	−	0.200769i
$317$	−14.0311	−	30.7239i	−0.788068	−	1.72563i	−0.682101	−	0.731258i	$-0.738934\pi$
$317$	−14.0311	−	30.7239i	−0.788068	−	1.72563i	−0.105967	−	0.994370i	$-0.533794\pi$
$318$	−1.41983	−	9.87514i	−0.0796201	−	0.553770i
$319$	−3.35380	+	2.15536i	−0.187777	+	0.120677i
$320$	−1.28820	+	1.48666i	−0.0720126	+	0.0831070i
$321$	7.51796			0.419611
$322$	−4.06844	+	2.53925i	−0.226725	+	0.141507i
$323$	−13.2228			−0.735735
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	4.98667	−	3.20474i	0.276611	−	0.177767i
$326$	0.0188966	+	0.131429i	0.00104658	+	0.00727915i
$327$	−7.31519	−	16.0180i	−0.404531	−	0.885799i
$328$	−0.316766	+	2.20315i	−0.0174905	+	0.121649i
$329$	6.21761	−	1.82566i	0.342788	−	0.100652i
$330$	2.27177	+	1.45998i	0.125057	+	0.0803691i
$331$	12.7755	−	27.9745i	0.702207	−	1.53762i	−0.135067	−	0.990836i	$-0.543125\pi$
$331$	12.7755	−	27.9745i	0.702207	−	1.53762i	0.837274	−	0.546783i	$-0.184148\pi$
$332$	7.59010	+	2.22865i	0.416561	+	0.122313i
$333$	−4.10658	−	4.73925i	−0.225039	−	0.259709i
$334$	14.9572	+	17.2616i	0.818423	+	0.944511i
$335$	−28.8786	−	8.47953i	−1.57781	−	0.463286i
$336$	0.415415	−	0.909632i	0.0226627	−	0.0496245i
$337$	7.09749	+	4.56128i	0.386625	+	0.248469i	0.719486	−	0.694507i	$-0.244378\pi$
$337$	7.09749	+	4.56128i	0.386625	+	0.248469i	−0.332861	+	0.942976i	$0.608014\pi$
$338$	13.9122	−	4.08498i	0.756721	−	0.222193i
$339$	−1.42666	+	9.92261i	−0.0774853	+	0.538922i
$340$	−2.81701	−	6.16838i	−0.152774	−	0.334528i
$341$	1.47192	+	10.2374i	0.0797087	+	0.554386i
$342$	−3.22685	+	2.07377i	−0.174488	+	0.112137i
$343$	−0.654861	+	0.755750i	−0.0353592	+	0.0408066i
$344$	4.75185			0.256203
$345$	3.80523	+	8.63259i	0.204867	+	0.464763i
$346$	19.1730			1.03075
$347$	16.6239	−	19.1850i	0.892416	−	1.02990i	−0.106949	−	0.994265i	$-0.534108\pi$
$347$	16.6239	−	19.1850i	0.892416	−	1.02990i	0.999365	−	0.0356386i	$-0.0113465\pi$
$348$	2.44306	−	1.57006i	0.130962	−	0.0841641i
$349$	3.68620	+	25.6381i	0.197318	+	1.37238i	0.812026	+	0.583622i	$0.198365\pi$
$349$	3.68620	+	25.6381i	0.197318	+	1.37238i	−0.614708	+	0.788755i	$0.710726\pi$
$350$	0.469574	+	1.02822i	0.0250998	+	0.0549609i
$351$	0.746298	−	5.19062i	0.0398345	−	0.277055i
$352$	−1.31718	+	0.386758i	−0.0702058	+	0.0206143i
$353$	−7.77992	−	4.99985i	−0.414084	−	0.266115i	0.316970	−	0.948436i	$-0.397335\pi$
$353$	−7.77992	−	4.99985i	−0.414084	−	0.266115i	−0.731053	+	0.682320i	$0.760971\pi$
$354$	−2.15909	+	4.72775i	−0.114754	+	0.251277i
$355$	−6.23547	−	1.83090i	−0.330944	−	0.0971740i
$356$	7.26364	+	8.38268i	0.384972	+	0.444281i
$357$	2.25746	+	2.60525i	0.119477	+	0.137884i
$358$	4.65073	+	1.36558i	0.245799	+	0.0721730i
$359$	−3.40564	+	7.45732i	−0.179743	+	0.393582i	−0.977961	−	0.208786i	$-0.933049\pi$
$359$	−3.40564	+	7.45732i	−0.179743	+	0.393582i	0.798218	+	0.602368i	$0.205776\pi$
$360$	−1.65486	−	1.06351i	−0.0872188	−	0.0560521i
$361$	4.11329	−	1.20777i	0.216489	−	0.0635670i
$362$	−3.01405	+	20.9632i	−0.158415	+	1.10180i
$363$	−3.78670	−	8.29171i	−0.198750	−	0.435202i
$364$	0.746298	+	5.19062i	0.0391167	+	0.272062i
$365$	−12.5820	+	8.08598i	−0.658574	+	0.423240i
$366$	−5.19828	+	5.99914i	−0.271719	+	0.313580i
$367$	−27.0158			−1.41021			−0.705106	−	0.709102i	$-0.749100\pi$
$367$	−27.0158			−1.41021			−0.705106	+	0.709102i	$0.749100\pi$
$368$	−4.58330	−	1.41187i	−0.238921	−	0.0735989i
$369$	−2.22581			−0.115871
$370$	8.07821	−	9.32275i	0.419966	−	0.484667i
$371$	−8.39292	+	5.39380i	−0.435739	+	0.280032i
$372$	−1.07221	−	7.45739i	−0.0555916	−	0.386648i
$373$	11.1311	+	24.3738i	0.576349	+	1.26203i	0.943348	+	0.331806i	$0.107658\pi$
$373$	11.1311	+	24.3738i	0.576349	+	1.26203i	−0.366999	+	0.930221i	$0.619615\pi$
$374$	0.673479	−	4.68415i	0.0348248	−	0.242212i
$375$	11.5708	−	3.39749i	0.597513	−	0.175446i
$376$	5.45141	+	3.50341i	0.281135	+	0.180674i
$377$	−6.32633	+	13.8527i	−0.325823	+	0.713452i
$378$	0.959493	+	0.281733i	0.0493510	+	0.0144908i
$379$	10.9824	+	12.6744i	0.564130	+	0.651040i	0.964116	−	0.265481i	$-0.0855306\pi$
$379$	10.9824	+	12.6744i	0.564130	+	0.651040i	−0.399986	+	0.916521i	$0.630985\pi$
$380$	−4.94123	−	5.70248i	−0.253480	−	0.292531i
$381$	−4.23046	−	1.24218i	−0.216733	−	0.0636386i
$382$	−1.95263	+	4.27566i	−0.0999051	+	0.218762i
$383$	2.66090	+	1.71006i	0.135966	+	0.0873800i	0.606856	−	0.794812i	$-0.292431\pi$
$383$	2.66090	+	1.71006i	0.135966	+	0.0873800i	−0.470890	+	0.882192i	$0.656067\pi$
$384$	0.959493	−	0.281733i	0.0489639	−	0.0143771i
$385$	0.384315	−	2.67297i	0.0195865	−	0.136227i
$386$	−6.68352	−	14.6349i	−0.340182	−	0.744895i
$387$	0.676259	+	4.70348i	0.0343762	+	0.239091i
$388$	−15.6087	+	10.0311i	−0.792409	+	0.509250i
$389$	0.200387	−	0.231259i	0.0101600	−	0.0117253i	−0.750647	−	0.660704i	$-0.770258\pi$
$389$	0.200387	−	0.231259i	0.0101600	−	0.0117253i	0.760807	+	0.648978i	$0.224803\pi$
$390$	10.3157			0.522354
$391$	10.9907	−	12.3501i	0.555822	−	0.624570i
$392$	−1.00000			−0.0505076
$393$	7.75242	−	8.94677i	0.391058	−	0.451305i
$394$	10.7956	−	6.93791i	0.543874	−	0.349527i
$395$	1.00941	+	7.02061i	0.0507890	+	0.353245i
$396$	−0.570276	−	1.24873i	−0.0286574	−	0.0627510i
$397$	3.06198	−	21.2966i	0.153677	−	1.06884i	−0.756312	−	0.654211i	$-0.773001\pi$
$397$	3.06198	−	21.2966i	0.153677	−	1.06884i	0.909989	−	0.414633i	$-0.136090\pi$
$398$	−9.27706	+	2.72399i	−0.465017	+	0.136541i
$399$	3.22685	+	2.07377i	0.161544	+	0.103818i
$400$	−0.469574	+	1.02822i	−0.0234787	+	0.0514112i
$401$	−14.1239	−	4.14716i	−0.705315	−	0.207099i	−0.0906449	−	0.995883i	$-0.528893\pi$
$401$	−14.1239	−	4.14716i	−0.705315	−	0.207099i	−0.614670	+	0.788784i	$0.710711\pi$
$402$	10.0196	+	11.5632i	0.499731	+	0.576720i
$403$	25.8727	+	29.8587i	1.28881	+	1.48737i
$404$	12.3380	+	3.62276i	0.613837	+	0.180239i
$405$	0.817178	−	1.78937i	0.0406059	−	0.0889145i
$406$	−2.44306	−	1.57006i	−0.121247	−	0.0779208i
$407$	8.25992	−	2.42533i	0.409429	−	0.120219i
$408$	−0.490593	+	3.41215i	−0.0242880	+	0.168927i
$409$	−0.732619	−	1.60421i	−0.0362257	−	0.0793232i	0.890654	−	0.454682i	$-0.150247\pi$
$409$	−0.732619	−	1.60421i	−0.0362257	−	0.0793232i	−0.926880	+	0.375358i	$0.877520\pi$
$410$	−0.623122	−	4.33391i	−0.0307738	−	0.214036i
$411$	−8.69915	+	5.59060i	−0.429097	+	0.275764i
$412$	−10.4527	+	12.0631i	−0.514970	+	0.594307i
$413$	5.19743			0.255749
$414$	0.745229	−	4.73758i	0.0366260	−	0.232839i
$415$	−15.5611			−0.763864
$416$	−3.43409	+	3.96315i	−0.168370	+	0.194309i
$417$	4.08384	−	2.62452i	0.199986	−	0.128523i
$418$	−0.749384	−	5.21208i	−0.0366536	−	0.254931i
$419$	−7.04242	−	15.4208i	−0.344045	−	0.753353i	0.655954	−	0.754801i	$-0.272266\pi$
$419$	−7.04242	−	15.4208i	−0.344045	−	0.753353i	−0.999999	+	0.00144770i	$0.999539\pi$
$420$	−0.279953	+	1.94711i	−0.0136603	+	0.0950094i
$421$	23.9612	−	7.03565i	1.16780	−	0.342897i	0.360340	−	0.932821i	$-0.382661\pi$
$421$	23.9612	−	7.03565i	1.16780	−	0.342897i	0.807459	+	0.589924i	$0.200842\pi$
$422$	14.5494	+	9.35031i	0.708252	+	0.455166i
$423$	−2.69193	+	5.89451i	−0.130886	+	0.286601i
$424$	−9.57256	−	2.81076i	−0.464885	−	0.136502i
$425$	−2.55177	−	2.94490i	−0.123779	−	0.142849i
$426$	2.16342	+	2.49672i	0.104818	+	0.120967i
$427$	7.61645	+	2.23639i	0.368586	+	0.108227i
$428$	3.12307	−	6.83857i	0.150959	−	0.330555i
$429$	6.05608	+	3.89201i	0.292390	+	0.187908i
$430$	−8.96890	+	2.63351i	−0.432519	+	0.126999i
$431$	3.48426	−	24.2336i	0.167831	−	1.16729i	−0.715525	−	0.698587i	$-0.753812\pi$
$431$	3.48426	−	24.2336i	0.167831	−	1.16729i	0.883356	−	0.468703i	$-0.155279\pi$
$432$	0.415415	+	0.909632i	0.0199867	+	0.0437647i
$433$	2.29514	+	15.9631i	0.110298	+	0.767136i	0.967630	+	0.252373i	$0.0812111\pi$
$433$	2.29514	+	15.9631i	0.110298	+	0.767136i	−0.857332	+	0.514763i	$0.827880\pi$
$434$	−6.33807	+	4.07323i	−0.304237	+	0.195521i
$435$	−3.74103	+	4.31738i	−0.179369	+	0.207002i
$436$	−17.6094			−0.843335
$437$	7.86243	−	16.6308i	0.376111	−	0.795558i
$438$	7.60308			0.363289
$439$	8.54485	−	9.86128i	0.407823	−	0.470653i	−0.514266	−	0.857631i	$-0.671936\pi$
$439$	8.54485	−	9.86128i	0.407823	−	0.470653i	0.922089	+	0.386978i	$0.126481\pi$
$440$	2.27177	−	1.45998i	0.108302	−	0.0696017i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	−7.50958	−	16.4437i	−0.357194	−	0.782146i
$443$	3.54606	−	24.6634i	0.168478	−	1.17179i	−0.713552	−	0.700602i	$-0.752915\pi$
$443$	3.54606	−	24.6634i	0.168478	−	1.17179i	0.882031	−	0.471192i	$-0.156176\pi$
$444$	−6.01691	+	1.76672i	−0.285550	+	0.0838450i
$445$	−18.3555	−	11.7964i	−0.870135	−	0.559202i
$446$	−5.86290	+	12.8380i	−0.277617	+	0.607895i
$447$	−15.3111	−	4.49576i	−0.724192	−	0.212642i
$448$	−0.654861	−	0.755750i	−0.0309393	−	0.0357058i
$449$	13.5184	+	15.6011i	0.637973	+	0.736260i	0.979015	−	0.203788i	$-0.0653253\pi$
$449$	13.5184	+	15.6011i	0.637973	+	0.736260i	−0.341042	+	0.940048i	$0.610780\pi$
$450$	−1.08458	−	0.318463i	−0.0511278	−	0.0150125i
$451$	1.26933	−	2.77944i	0.0597702	−	0.130879i
$452$	8.43326	+	5.41973i	0.396667	+	0.254923i
$453$	−4.67481	+	1.37265i	−0.219642	+	0.0644926i
$454$	0.493900	−	3.43515i	0.0231799	−	0.161220i
$455$	−4.28528	−	9.38345i	−0.200897	−	0.439903i
$456$	0.545886	+	3.79672i	0.0255634	+	0.177798i
$457$	10.5207	−	6.76123i	0.492137	−	0.316277i	−0.270928	−	0.962600i	$-0.587330\pi$
$457$	10.5207	−	6.76123i	0.492137	−	0.316277i	0.763064	+	0.646323i	$0.223694\pi$
$458$	4.23295	−	4.88508i	0.197793	−	0.228265i
$459$	−3.44724			−0.160903
$460$	9.43323	+	0.124748i	0.439827	+	0.00581639i
$461$	12.3853			0.576842			0.288421	−	0.957504i	$-0.406870\pi$
$461$	12.3853			0.576842			0.288421	+	0.957504i	$0.406870\pi$
$462$	−0.898983	+	1.03748i	−0.0418245	+	0.0482680i
$463$	1.97284	−	1.26787i	0.0916855	−	0.0589227i	−0.493995	−	0.869465i	$-0.664464\pi$
$463$	1.97284	−	1.26787i	0.0916855	−	0.0589227i	0.585680	+	0.810542i	$0.300827\pi$
$464$	−0.413293	−	2.87451i	−0.0191866	−	0.133446i
$465$	6.15668	+	13.4813i	0.285509	+	0.625178i
$466$	0.688543	−	4.78892i	0.0318961	−	0.221842i
$467$	−6.12836	+	1.79945i	−0.283587	+	0.0832685i	−0.420433	−	0.907324i	$-0.638122\pi$
$467$	−6.12836	+	1.79945i	−0.283587	+	0.0832685i	0.136846	+	0.990592i	$0.456303\pi$
$468$	−4.41153	−	2.83512i	−0.203923	−	0.131053i
$469$	6.35598	−	13.9177i	0.293492	−	0.642658i
$470$	−12.2309	−	3.59131i	−0.564169	−	0.165655i
$471$	−0.264691	−	0.305470i	−0.0121963	−	0.0140753i
$472$	3.40359	+	3.92795i	0.156663	+	0.180799i
$473$	−6.25903	−	1.83782i	−0.287791	−	0.0845029i
$474$	1.49784	−	3.27981i	0.0687981	−	0.150647i
$475$	−3.64754	−	2.34413i	−0.167361	−	0.107556i
$476$	3.30760	−	0.971199i	0.151604	−	0.0445148i
$477$	1.41983	−	9.87514i	0.0650096	−	0.452151i
$478$	5.07604	+	11.1150i	0.232173	+	0.508387i
$479$	1.52932	+	10.6367i	0.0698764	+	0.486001i	0.994468	+	0.105041i	$0.0334974\pi$
$479$	1.52932	+	10.6367i	0.0698764	+	0.486001i	−0.924592	+	0.380960i	$0.875594\pi$
$480$	−1.65486	+	1.06351i	−0.0755337	+	0.0485426i
$481$	21.5349	−	24.8526i	0.981907	−	1.13318i
$482$	−5.97638			−0.272217
$483$	−4.61903	+	1.29018i	−0.210173	+	0.0587051i
$484$	−9.11546			−0.414339
$485$	23.9013	−	27.5836i	1.08530	−	1.25251i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−1.03883	−	7.22525i	−0.0470741	−	0.327407i	−0.999727	−	0.0233488i	$-0.992567\pi$
$487$	−1.03883	−	7.22525i	−0.0470741	−	0.327407i	0.952653	−	0.304059i	$-0.0983419\pi$
$488$	3.29756	+	7.22065i	0.149274	+	0.326864i
$489$	−0.0188966	+	0.131429i	−0.000854532	+	0.00594340i
$490$	1.88745	−	0.554206i	0.0852665	−	0.0250365i
$491$	−13.3866	−	8.60306i	−0.604130	−	0.388250i	0.202522	−	0.979278i	$-0.435086\pi$
$491$	−13.3866	−	8.60306i	−0.604130	−	0.388250i	−0.806652	+	0.591027i	$0.798723\pi$
$492$	−0.924635	+	2.02467i	−0.0416858	+	0.0912791i
$493$	9.60551	+	2.82043i	0.432610	+	0.127026i
$494$	−13.1723	−	15.2017i	−0.592651	−	0.683956i
$495$	1.76842	+	2.04087i	0.0794847	+	0.0917302i
$496$	−7.22889	−	2.12259i	−0.324587	−	0.0953073i
$497$	1.37238	−	3.00510i	0.0615597	−	0.134797i
$498$	6.65476	+	4.27676i	0.298207	+	0.191646i
$499$	−20.7064	+	6.07995i	−0.926946	+	0.272176i	−0.710158	−	0.704043i	$-0.751376\pi$
$499$	−20.7064	+	6.07995i	−0.926946	+	0.272176i	−0.216789	+	0.976219i	$0.569558\pi$
$500$	1.71621	−	11.9365i	0.0767515	−	0.533818i
$501$	9.48822	+	20.7763i	0.423902	+	0.928216i
$502$	0.964733	+	6.70987i	0.0430581	+	0.299476i
$503$	3.73809	−	2.40232i	0.166673	−	0.107114i	−0.454645	−	0.890673i	$-0.650234\pi$
$503$	3.73809	−	2.40232i	0.166673	−	0.107114i	0.621318	+	0.783558i	$0.286597\pi$
$504$	0.654861	−	0.755750i	0.0291698	−	0.0336638i
$505$	−25.2951			−1.12562
$506$	5.49097	+	3.63231i	0.244103	+	0.161476i
$507$	14.4995			0.643945
$508$	−2.88732	+	3.33214i	−0.128104	+	0.147840i
$509$	10.5019	−	6.74916i	0.465489	−	0.299151i	−0.286794	−	0.957992i	$-0.592589\pi$
$509$	10.5019	−	6.74916i	0.465489	−	0.299151i	0.752282	+	0.658841i	$0.228953\pi$
$510$	−0.965063	−	6.71216i	−0.0427337	−	0.297220i
$511$	−3.15843	−	6.91600i	−0.139721	−	0.305946i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−3.68038	+	1.08066i	−0.162493	+	0.0477122i
$514$	9.95650	+	6.39865i	0.439162	+	0.282232i
$515$	13.0436	−	28.5615i	0.574771	−	1.25857i
$516$	4.55937	+	1.33875i	0.200715	+	0.0589352i
$517$	−5.82550	−	6.72299i	−0.256205	−	0.295677i
$518$	4.10658	+	4.73925i	0.180433	+	0.208231i
$519$	18.3963	+	5.40165i	0.807509	+	0.237106i
$520$	4.28528	−	9.38345i	0.187922	−	0.411492i
$521$	29.3980	+	18.8930i	1.28795	+	0.827716i	0.991846	−	0.127440i	$-0.0406759\pi$
$521$	29.3980	+	18.8930i	1.28795	+	0.827716i	0.296105	+	0.955156i	$0.404312\pi$
$522$	2.78644	−	0.818172i	0.121959	−	0.0358104i
$523$	2.39365	−	16.6482i	0.104667	−	0.727976i	−0.868133	−	0.496331i	$-0.834680\pi$
$523$	2.39365	−	16.6482i	0.104667	−	0.727976i	0.972800	−	0.231645i	$-0.0744108\pi$
$524$	−4.91780	−	10.7685i	−0.214835	−	0.470423i
$525$	0.160869	+	1.11887i	0.00702089	+	0.0488314i
$526$	−1.08687	+	0.698490i	−0.0473898	+	0.0304556i
$527$	17.0079	−	19.6281i	0.740875	−	0.855015i
$528$	−1.37279			−0.0597428
$529$	8.99796	+	21.1669i	0.391216	+	0.920299i
$530$	19.6255			0.852477
$531$	−3.40359	+	3.92795i	−0.147703	+	0.170459i
$532$	3.22685	−	2.07377i	0.139902	−	0.0899093i
$533$	−1.66112	−	11.5533i	−0.0719510	−	0.500430i
$534$	4.60773	+	10.0895i	0.199396	+	0.436617i
$535$	−2.10467	+	14.6383i	−0.0909929	+	0.632870i
$536$	14.6805	−	4.31060i	0.634103	−	0.186189i
$537$	4.07762	+	2.62052i	0.175962	+	0.113084i
$538$	−12.4315	+	27.2213i	−0.535962	+	1.17359i
$539$	1.31718	+	0.386758i	0.0567349	+	0.0166589i
$540$	−1.28820	−	1.48666i	−0.0554353	−	0.0639758i
$541$	−23.2932	−	26.8818i	−1.00145	−	1.15574i	−0.987784	−	0.155832i	$-0.950194\pi$
$541$	−23.2932	−	26.8818i	−1.00145	−	1.15574i	−0.0136699	−	0.999907i	$-0.504351\pi$
$542$	−10.1322	−	2.97508i	−0.435214	−	0.127790i
$543$	−8.79796	+	19.2649i	−0.377557	+	0.826734i
$544$	2.90000	+	1.86372i	0.124336	+	0.0799062i
$545$	33.2368	−	9.75922i	1.42371	−	0.418039i
$546$	−0.746298	+	5.19062i	−0.0319386	+	0.222138i
$547$	−13.5800	−	29.7360i	−0.580637	−	1.27142i	−0.940937	−	0.338582i	$-0.890053\pi$
$547$	−13.5800	−	29.7360i	−0.580637	−	1.27142i	0.360300	−	0.932837i	$-0.382674\pi$
$548$	1.47163	+	10.2354i	0.0628651	+	0.437236i
$549$	−6.67787	+	4.29160i	−0.285004	+	0.183161i
$550$	1.01619	−	1.17274i	0.0433303	−	0.0500059i
$551$	11.1393			0.474551
$552$	−3.99987	−	2.64594i	−0.170246	−	0.112619i
$553$	−3.60565			−0.153328
$554$	10.0026	−	11.5436i	0.424970	−	0.490441i
$555$	10.3775	−	6.66922i	0.440501	−	0.283093i
$556$	−0.690863	−	4.80506i	−0.0292991	−	0.203780i
$557$	−14.4740	−	31.6935i	−0.613281	−	1.34290i	−0.920307	−	0.391197i	$-0.872061\pi$
$557$	−14.4740	−	31.6935i	−0.613281	−	1.34290i	0.307026	−	0.951701i	$-0.400666\pi$
$558$	1.07221	−	7.45739i	0.0453903	−	0.315697i
$559$	−23.9093	+	7.02040i	−1.01126	+	0.296931i
$560$	1.65486	+	1.06351i	0.0699306	+	0.0449417i
$561$	1.96588	−	4.30467i	0.0829993	−	0.181743i
$562$	13.2582	+	3.89297i	0.559264	+	0.164215i
$563$	−13.1341	−	15.1576i	−0.553538	−	0.638817i	0.408166	−	0.912908i	$-0.366169\pi$
$563$	−13.1341	−	15.1576i	−0.553538	−	0.638817i	−0.961704	+	0.274091i	$0.911623\pi$
$564$	4.24356	+	4.89733i	0.178686	+	0.206215i
$565$	−18.9210	−	5.55572i	−0.796014	−	0.233731i
$566$	−5.50019	+	12.0437i	−0.231190	+	0.506236i
$567$	0.841254	+	0.540641i	0.0353293	+	0.0227048i
$568$	3.16982	−	0.930743i	0.133003	−	0.0390531i
$569$	−0.912828	+	6.34886i	−0.0382677	+	0.266158i	−0.999968	−	0.00794373i	$-0.997471\pi$
$569$	−0.912828	+	6.34886i	−0.0382677	+	0.266158i	0.961701	+	0.274102i	$0.0883805\pi$
$570$	−3.13450	−	6.86360i	−0.131290	−	0.287484i
$571$	−1.86707	−	12.9858i	−0.0781345	−	0.543437i	−0.990863	−	0.134871i	$-0.956938\pi$
$571$	−1.86707	−	12.9858i	−0.0781345	−	0.543437i	0.912729	−	0.408566i	$-0.133971\pi$
$572$	6.05608	−	3.89201i	0.253218	−	0.162733i
$573$	−3.07812	+	3.55234i	−0.128590	+	0.148401i
$574$	2.22581			0.0929035
$575$	5.22123	−	1.45838i	0.217740	−	0.0608187i
$576$	1.00000			0.0416667
$577$	−5.11390	+	5.90175i	−0.212894	+	0.245693i	−0.852146	−	0.523305i	$-0.824699\pi$
$577$	−5.11390	+	5.90175i	−0.212894	+	0.245693i	0.639251	+	0.768998i	$0.279244\pi$
$578$	4.30433	−	2.76622i	0.179036	−	0.115060i
$579$	−2.28967	−	15.9250i	−0.0951555	−	0.661821i
$580$	2.37314	+	5.19646i	0.0985395	+	0.215771i
$581$	1.12579	−	7.83001i	0.0467055	−	0.324844i
$582$	−17.8025	+	5.22728i	−0.737936	+	0.216678i
$583$	11.5217	+	7.40454i	0.477179	+	0.306665i
$584$	3.15843	−	6.91600i	0.130697	−	0.286186i
$585$	9.89780	+	2.90626i	0.409224	+	0.120159i
$586$	−9.55704	−	11.0294i	−0.394798	−	0.455621i
$587$	21.4390	+	24.7419i	0.884880	+	1.02121i	0.999613	+	0.0278099i	$0.00885331\pi$
$587$	21.4390	+	24.7419i	0.884880	+	1.02121i	−0.114733	+	0.993396i	$0.536601\pi$
$588$	−0.959493	−	0.281733i	−0.0395688	−	0.0116185i
$589$	12.0050	−	26.2874i	0.494659	−	1.08315i
$590$	−8.60102	−	5.52754i	−0.354098	−	0.227565i
$591$	12.3129	−	3.61540i	0.506486	−	0.148718i
$592$	−0.892446	+	6.20710i	−0.0366793	+	0.255110i
$593$	−15.3774	−	33.6719i	−0.631475	−	1.38274i	−0.906871	−	0.421407i	$-0.861536\pi$
$593$	−15.3774	−	33.6719i	−0.631475	−	1.38274i	0.275396	−	0.961331i	$-0.411191\pi$
$594$	−0.195368	−	1.35881i	−0.00801604	−	0.0557528i
$595$	−5.70470	+	3.66619i	−0.233870	+	0.150299i
$596$	−10.4500	+	12.0599i	−0.428047	+	0.493993i
$597$	−9.66871			−0.395714
$598$	25.1471	+	0.332552i	1.02834	+	0.0135991i
$599$	11.6979			0.477964			0.238982	−	0.971024i	$-0.423186\pi$
$599$	11.6979			0.477964			0.238982	+	0.971024i	$0.423186\pi$
$600$	−0.740237	+	0.854279i	−0.0302200	+	0.0348758i
$601$	−0.217446	+	0.139744i	−0.00886981	+	0.00570028i	−0.545068	−	0.838392i	$-0.683496\pi$
$601$	−0.217446	+	0.139744i	−0.00886981	+	0.00570028i	0.536198	+	0.844092i	$0.319860\pi$
$602$	−0.676259	−	4.70348i	−0.0275622	−	0.191700i
$603$	6.35598	+	13.9177i	0.258836	+	0.566771i
$604$	−0.693381	+	4.82257i	−0.0282133	+	0.196228i
$605$	17.2050	−	5.05185i	0.699483	−	0.205387i
$606$	10.8176	+	6.95202i	0.439433	+	0.282407i
$607$	−2.28705	+	5.00794i	−0.0928285	+	0.203266i	−0.950351	−	0.311181i	$-0.899276\pi$
$607$	−2.28705	+	5.00794i	−0.0928285	+	0.203266i	0.857522	+	0.514447i	$0.172003\pi$
$608$	3.68038	+	1.08066i	0.149259	+	0.0438265i
$609$	−1.90176	−	2.19475i	−0.0770633	−	0.0889358i
$610$	−10.2257	−	11.8011i	−0.414028	−	0.477813i
$611$	−32.6051	−	9.57373i	−1.31906	−	0.387311i
$612$	−1.43203	+	3.13572i	−0.0578865	+	0.126754i
$613$	29.7284	+	19.1053i	1.20072	+	0.771654i	0.979080	−	0.203475i	$-0.0652237\pi$
$613$	29.7284	+	19.1053i	1.20072	+	0.771654i	0.221637	+	0.975129i	$0.428860\pi$
$614$	−28.2136	+	8.28427i	−1.13861	+	0.334326i
$615$	0.623122	−	4.33391i	0.0251267	−	0.174760i
$616$	0.570276	+	1.24873i	0.0229771	+	0.0503128i
$617$	5.59393	+	38.9066i	0.225203	+	1.56632i	0.717916	+	0.696129i	$0.245096\pi$
$617$	5.59393	+	38.9066i	0.225203	+	1.56632i	−0.492714	+	0.870192i	$0.663995\pi$
$618$	−13.4279	+	8.62959i	−0.540150	+	0.347133i
$619$	−20.2645	+	23.3865i	−0.814500	+	0.939983i	−0.999082	−	0.0428344i	$-0.986361\pi$
$619$	−20.2645	+	23.3865i	−0.814500	+	0.939983i	0.184583	+	0.982817i	$0.440907\pi$
$620$	14.8206			0.595208
$621$	2.04977	−	4.33572i	0.0822545	−	0.173986i
$622$	−6.67455			−0.267625
$623$	7.26364	−	8.38268i	0.291011	−	0.335845i
$624$	−4.41153	+	2.83512i	−0.176603	+	0.113496i
$625$	2.57168	+	17.8865i	0.102867	+	0.715458i
$626$	−4.84910	−	10.6180i	−0.193809	−	0.424382i
$627$	0.749384	−	5.21208i	0.0299275	−	0.208150i
$628$	−0.387822	+	0.113875i	−0.0154758	+	0.00454410i
$629$	−18.1857	−	11.6872i	−0.725111	−	0.466000i
$630$	−0.817178	+	1.78937i	−0.0325572	+	0.0712902i
$631$	18.5696	+	5.45253i	0.739245	+	0.217062i	0.629611	−	0.776910i	$-0.283214\pi$
$631$	18.5696	+	5.45253i	0.739245	+	0.217062i	0.109633	+	0.993972i	$0.465032\pi$
$632$	−2.36120	−	2.72497i	−0.0939234	−	0.108393i
$633$	11.3257	+	13.0706i	0.450157	+	0.519509i
$634$	−32.4080	−	9.51586i	−1.28709	−	0.377923i
$635$	3.60299	−	7.88944i	0.142980	−	0.313083i
$636$	−8.39292	−	5.39380i	−0.332801	−	0.213878i
$637$	5.03158	−	1.47740i	0.199358	−	0.0585369i
$638$	−0.567362	+	3.94609i	−0.0224621	+	0.156227i
$639$	1.37238	+	3.00510i	0.0542906	+	0.118880i
$640$	0.279953	+	1.94711i	0.0110661	+	0.0769664i
$641$	10.2256	−	6.57162i	0.403889	−	0.259563i	−0.322888	−	0.946437i	$-0.604654\pi$
$641$	10.2256	−	6.57162i	0.403889	−	0.259563i	0.726777	+	0.686874i	$0.241017\pi$
$642$	4.92321	−	5.68169i	0.194304	−	0.224239i
$643$	−28.8265			−1.13680			−0.568402	−	0.822751i	$-0.692438\pi$
$643$	−28.8265			−1.13680			−0.568402	+	0.822751i	$0.692438\pi$
$644$	−0.745229	+	4.73758i	−0.0293661	+	0.186687i
$645$	−9.34754			−0.368059
$646$	−8.65907	+	9.99310i	−0.340687	+	0.393173i
$647$	−15.1571	+	9.74089i	−0.595888	+	0.382954i	−0.803542	−	0.595249i	$-0.797054\pi$
$647$	−15.1571	+	9.74089i	−0.595888	+	0.382954i	0.207654	+	0.978202i	$0.433417\pi$
$648$	0.142315	+	0.989821i	0.00559065	+	0.0388839i
$649$	−2.96397	−	6.49018i	−0.116346	−	0.254762i
$650$	0.843595	−	5.86734i	0.0330885	−	0.230136i
$651$	−7.22889	+	2.12259i	−0.283323	+	0.0831911i
$652$	0.111702	+	0.0717863i	0.00437457	+	0.00281137i
$653$	−15.4970	+	33.9337i	−0.606445	+	1.32793i	0.318535	+	0.947911i	$0.396809\pi$
$653$	−15.4970	+	33.9337i	−0.606445	+	1.32793i	−0.924979	+	0.380017i	$0.875918\pi$
$654$	−16.8961	−	4.96113i	−0.660688	−	0.193995i
$655$	15.2501	+	17.5995i	0.595870	+	0.687670i
$656$	1.45760	+	1.68216i	0.0569096	+	0.0656771i
$657$	7.29510	+	2.14203i	0.284609	+	0.0835687i
$658$	2.69193	−	5.89451i	0.104942	−	0.229792i
$659$	14.6503	+	9.41521i	0.570696	+	0.366764i	0.793938	−	0.607999i	$-0.208027\pi$
$659$	14.6503	+	9.41521i	0.570696	+	0.366764i	−0.223241	+	0.974763i	$0.571664\pi$
$660$	2.59107	−	0.760807i	0.100857	−	0.0296144i
$661$	2.62695	−	18.2709i	0.102177	−	0.710654i	−0.872757	−	0.488156i	$-0.837670\pi$
$661$	2.62695	−	18.2709i	0.102177	−	0.710654i	0.974933	−	0.222498i	$-0.0714211\pi$
$662$	−12.7755	−	27.9745i	−0.496536	−	1.08726i
$663$	−2.57267	−	17.8933i	−0.0999141	−	0.694918i
$664$	6.65476	−	4.27676i	0.258255	−	0.165970i
$665$	−4.94123	+	5.70248i	−0.191613	+	0.221133i
$666$	−6.27092			−0.242993
$667$	−9.25892	+	10.4041i	−0.358507	+	0.402850i
$668$	22.8403			0.883719
$669$	−9.24229	+	10.6662i	−0.357328	+	0.412378i
$670$	−25.3199	+	16.2721i	−0.978193	+	0.628646i
$671$	−1.55083	−	10.7862i	−0.0598691	−	0.416398i
$672$	−0.415415	−	0.909632i	−0.0160250	−	0.0350898i
$673$	−2.01907	+	14.0430i	−0.0778296	+	0.541317i	0.913183	+	0.407549i	$0.133617\pi$
$673$	−2.01907	+	14.0430i	−0.0778296	+	0.541317i	−0.991013	+	0.133767i	$0.957293\pi$
$674$	8.09505	−	2.37692i	0.311810	−	0.0915556i
$675$	−0.950930	−	0.611126i	−0.0366013	−	0.0235222i
$676$	6.02330	−	13.1892i	0.231665	−	0.507277i
$677$	8.72412	+	2.56163i	0.335295	+	0.0984515i	0.445046	−	0.895508i	$-0.353187\pi$
$677$	8.72412	+	2.56163i	0.335295	+	0.0984515i	−0.109751	+	0.993959i	$0.535005\pi$
$678$	6.56474	+	7.57612i	0.252117	+	0.290959i
$679$	12.1503	+	14.0222i	0.466286	+	0.538123i
$680$	−6.50650	−	1.91048i	−0.249513	−	0.0732636i
$681$	1.44169	−	3.15685i	0.0552456	−	0.120971i
$682$	8.70081	+	5.59167i	0.333171	+	0.214116i
$683$	−10.1378	+	2.97673i	−0.387913	+	0.113902i	−0.469873	−	0.882734i	$-0.655700\pi$
$683$	−10.1378	+	2.97673i	−0.387913	+	0.113902i	0.0819599	+	0.996636i	$0.473882\pi$
$684$	−0.545886	+	3.79672i	−0.0208725	+	0.145171i
$685$	−8.45019	−	18.5033i	−0.322865	−	0.706976i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	5.43777	−	3.49464i	0.207464	−	0.133329i
$688$	3.11180	−	3.59121i	0.118636	−	0.136914i
$689$	52.3177			1.99315
$690$	9.01597	+	2.77734i	0.343232	+	0.105732i
$691$	25.0391			0.952532			0.476266	−	0.879301i	$-0.341990\pi$
$691$	25.0391			0.952532			0.476266	+	0.879301i	$0.341990\pi$
$692$	12.5556	−	14.4900i	0.477293	−	0.550826i
$693$	−1.15486	+	0.742184i	−0.0438695	+	0.0281932i
$694$	−3.61271	−	25.1270i	−0.137137	−	0.953807i
$695$	3.96696	+	8.68644i	0.150476	+	0.329495i
$696$	0.413293	−	2.87451i	0.0156658	−	0.108958i
$697$	−7.36209	+	2.16170i	−0.278859	+	0.0818804i
$698$	21.7899	+	14.0035i	0.824761	+	0.530042i
$699$	2.00985	−	4.40095i	0.0760194	−	0.166459i
$700$	1.08458	+	0.318463i	0.0409935	+	0.0120368i
$701$	8.83790	+	10.1995i	0.333803	+	0.385229i	0.897694	−	0.440620i	$-0.145241\pi$
$701$	8.83790	+	10.1995i	0.333803	+	0.385229i	−0.563891	+	0.825850i	$0.690696\pi$
$702$	−3.43409	−	3.96315i	−0.129611	−	0.149579i
$703$	−23.0794	−	6.77673i	−0.870457	−	0.255589i
$704$	−0.570276	+	1.24873i	−0.0214931	+	0.0470633i
$705$	−10.7237	−	6.89168i	−0.403876	−	0.259556i
$706$	−8.87340	+	2.60547i	−0.333955	+	0.0980580i
$707$	1.83001	−	12.7280i	0.0688244	−	0.478684i
$708$	2.15909	+	4.72775i	0.0811435	+	0.177680i
$709$	−3.05674	−	21.2601i	−0.114798	−	0.798440i	−0.963142	−	0.268994i	$-0.913309\pi$
$709$	−3.05674	−	21.2601i	−0.114798	−	0.798440i	0.848344	−	0.529446i	$-0.177600\pi$
$710$	−5.46706	+	3.51347i	−0.205175	+	0.131858i
$711$	2.36120	−	2.72497i	0.0885518	−	0.102194i
$712$	11.0919			0.415686
$713$	14.5739	+	33.0626i	0.545798	+	1.23820i
$714$	3.44724			0.129010
$715$	−9.27360	+	10.7023i	−0.346813	+	0.400244i
$716$	4.07762	−	2.62052i	0.152388	−	0.0979336i
$717$	1.73897	+	12.0948i	0.0649432	+	0.451690i
$718$	3.40564	+	7.45732i	0.127097	+	0.278305i
$719$	7.08284	−	49.2622i	0.264145	−	1.83717i	−0.236636	−	0.971598i	$-0.576045\pi$
$719$	7.08284	−	49.2622i	0.264145	−	1.83717i	0.500782	−	0.865574i	$-0.333046\pi$
$720$	−1.88745	+	0.554206i	−0.0703413	+	0.0206541i
$721$	13.4279	+	8.62959i	0.500081	+	0.321383i
$722$	1.78086	−	3.89954i	0.0662768	−	0.145126i
$723$	−5.73430	−	1.68374i	−0.213261	−	0.0626190i
$724$	13.8691	+	16.0058i	0.515442	+	0.594852i
$725$	2.14970	+	2.48089i	0.0798379	+	0.0921379i
$726$	−8.74622	−	2.56812i	−0.324603	−	0.0953119i
$727$	−11.6241	+	25.4531i	−0.431112	+	0.944005i	0.562033	+	0.827115i	$0.310020\pi$
$727$	−11.6241	+	25.4531i	−0.431112	+	0.944005i	−0.993145	+	0.116889i	$0.962708\pi$
$728$	4.41153	+	2.83512i	0.163502	+	0.105076i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−2.12850	+	14.8041i	−0.0787794	+	0.547923i
$731$	6.80481	+	14.9005i	0.251685	+	0.551113i
$732$	1.12969	+	7.85720i	0.0417547	+	0.290410i
$733$	−6.82445	+	4.38581i	−0.252067	+	0.161993i	−0.660572	−	0.750762i	$-0.729686\pi$
$733$	−6.82445	+	4.38581i	−0.252067	+	0.161993i	0.408506	+	0.912756i	$0.366050\pi$
$734$	−17.6916	+	20.4172i	−0.653008	+	0.753611i
$735$	1.96714			0.0725589
$736$	−4.06844	+	2.53925i	−0.149965	+	0.0935979i
$737$	−21.0041			−0.773694
$738$	−1.45760	+	1.68216i	−0.0536548	+	0.0619210i
$739$	−36.2130	+	23.2727i	−1.33212	+	0.856100i	−0.996310	−	0.0858312i	$-0.972645\pi$
$739$	−36.2130	+	23.2727i	−1.33212	+	0.856100i	−0.335807	+	0.941931i	$0.609009\pi$
$740$	−1.75556	−	12.2102i	−0.0645358	−	0.448856i
$741$	−8.35595	−	18.2970i	−0.306964	−	0.672156i
$742$	−1.41983	+	9.87514i	−0.0521236	+	0.362528i
$743$	−35.5316	+	10.4330i	−1.30353	+	0.382750i	−0.858522	−	0.512777i	$-0.828617\pi$
$743$	−35.5316	+	10.4330i	−1.30353	+	0.382750i	−0.445006	+	0.895527i	$0.646799\pi$
$744$	−6.33807	−	4.07323i	−0.232365	−	0.149332i
$745$	13.0401	−	28.5539i	0.477754	−	1.04614i
$746$	25.7098	+	7.54909i	0.941304	+	0.276392i
$747$	5.18030	+	5.97838i	0.189537	+	0.218737i
$748$	−3.09901	−	3.57645i	−0.113311	−	0.130768i
$749$	−7.21343	−	2.11805i	−0.263573	−	0.0773920i
$750$	5.00961	−	10.9695i	0.182925	−	0.400550i
$751$	43.6732	+	28.0670i	1.59366	+	1.02418i	0.970195	+	0.242326i	$0.0779104\pi$
$751$	43.6732	+	28.0670i	1.59366	+	1.02418i	0.623461	+	0.781854i	$0.285726\pi$
$752$	6.21761	−	1.82566i	0.226733	−	0.0665748i
$753$	−0.964733	+	6.70987i	−0.0351568	+	0.244521i
$754$	6.32633	+	13.8527i	0.230391	+	0.504487i
$755$	−1.36398	−	9.48666i	−0.0496401	−	0.345255i
$756$	0.841254	−	0.540641i	0.0305961	−	0.0196629i
$757$	−14.4838	+	16.7152i	−0.526424	+	0.607526i	−0.955228	−	0.295872i	$-0.904390\pi$
$757$	−14.4838	+	16.7152i	−0.526424	+	0.607526i	0.428804	+	0.903398i	$0.358935\pi$
$758$	16.7706			0.609137
$759$	4.24520	+	5.03216i	0.154091	+	0.182656i
$760$	−7.54546			−0.273703
$761$	−7.90374	+	9.12140i	−0.286510	+	0.330650i	−0.880700	−	0.473674i	$-0.842927\pi$
$761$	−7.90374	+	9.12140i	−0.286510	+	0.330650i	0.594190	+	0.804325i	$0.297473\pi$
$762$	−3.70914	+	2.38372i	−0.134368	+	0.0863530i
$763$	2.50607	+	17.4301i	0.0907259	+	0.631013i
$764$	1.95263	+	4.27566i	0.0706436	+	0.154688i
$765$	0.965063	−	6.71216i	0.0348919	−	0.242679i
$766$	3.03490	−	0.891127i	0.109655	−	0.0321977i
$767$	−22.9286	−	14.7353i	−0.827904	−	0.532061i
$768$	0.415415	−	0.909632i	0.0149900	−	0.0328235i
$769$	29.4695	+	8.65303i	1.06270	+	0.312036i	0.765937	−	0.642916i	$-0.222275\pi$
$769$	29.4695	+	8.65303i	1.06270	+	0.312036i	0.296761	+	0.954952i	$0.404094\pi$
$770$	−1.76842	−	2.04087i	−0.0637296	−	0.0735478i
$771$	7.75048	+	8.94453i	0.279127	+	0.322129i
$772$	−15.4371	−	4.53273i	−0.555592	−	0.163137i
$773$	7.32369	−	16.0366i	0.263415	−	0.576798i	−0.730995	−	0.682382i	$-0.760944\pi$
$773$	7.32369	−	16.0366i	0.263415	−	0.576798i	0.994410	+	0.105584i	$0.0336712\pi$
$774$	3.99751	+	2.56904i	0.143688	+	0.0923424i
$775$	8.17135	−	2.39932i	0.293523	−	0.0861863i
$776$	−2.64052	+	18.3652i	−0.0947890	+	0.659272i
$777$	2.60504	+	5.70423i	0.0934552	+	0.204638i
$778$	−0.0435483	−	0.302885i	−0.00156128	−	0.0108590i
$779$	−7.18235	+	4.61582i	−0.257334	+	0.165379i
$780$	6.75532	−	7.79605i	0.241879	−	0.279143i
$781$	−4.53519			−0.162282
$782$	−2.13621	−	16.3938i	−0.0763907	−	0.586240i
$783$	2.90407			0.103783
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	0.668886	−	0.429867i	0.0238736	−	0.0153426i
$786$	−1.68476	−	11.7178i	−0.0600935	−	0.417959i
$787$	3.49719	+	7.65778i	0.124661	+	0.272970i	0.961665	−	0.274227i	$-0.0884220\pi$
$787$	3.49719	+	7.65778i	0.124661	+	0.272970i	−0.837004	+	0.547197i	$0.815695\pi$
$788$	1.82629	−	12.7021i	0.0650589	−	0.452495i
$789$	−1.23963	+	0.363989i	−0.0441321	+	0.0129584i
$790$	5.96685	+	3.83466i	0.212291	+	0.136431i
$791$	4.16439	−	9.11873i	0.148069	−	0.324225i
$792$	−1.31718	−	0.386758i	−0.0468039	−	0.0137429i
$793$	−27.2598	−	31.4594i	−0.968023	−	1.11716i
$794$	−14.0897	−	16.2604i	−0.500025	−	0.577059i
$795$	18.8305	+	5.52914i	0.667850	+	0.196099i
$796$	−4.01653	+	8.79497i	−0.142362	+	0.311729i
$797$	−33.0948	−	21.2687i	−1.17228	−	0.753377i	−0.198326	−	0.980136i	$-0.563551\pi$
$797$	−33.0948	−	21.2687i	−1.17228	−	0.753377i	−0.973951	+	0.226759i	$0.927187\pi$
$798$	3.68038	−	1.08066i	0.130284	−	0.0382549i
$799$	−3.17909	+	22.1111i	−0.112468	+	0.782233i
$800$	0.469574	+	1.02822i	0.0166019	+	0.0363532i
$801$	1.57854	+	10.9790i	0.0557749	+	0.387923i
$802$	−12.3834	+	7.95834i	−0.437274	+	0.281019i
$803$	−6.83504	+	7.88805i	−0.241203	+	0.278363i
$804$	15.3003			0.539601
$805$	−1.21901	−	9.35497i	−0.0429645	−	0.329719i
$806$	39.5087			1.39163
$807$	−19.5971	+	22.6163i	−0.689851	+	0.796130i
$808$	10.8176	−	6.95202i	0.380560	−	0.244571i
$809$	6.51889	+	45.3398i	0.229192	+	1.59406i	0.701526	+	0.712644i	$0.252503\pi$
$809$	6.51889	+	45.3398i	0.229192	+	1.59406i	−0.472334	+	0.881420i	$0.656588\pi$
$810$	−0.817178	−	1.78937i	−0.0287127	−	0.0628721i
$811$	−5.29570	+	36.8324i	−0.185957	+	1.29336i	0.656388	+	0.754423i	$0.272083\pi$
$811$	−5.29570	+	36.8324i	−0.185957	+	1.29336i	−0.842345	+	0.538938i	$0.818826\pi$
$812$	−2.78644	+	0.818172i	−0.0977848	+	0.0287122i
$813$	−8.88358	−	5.70913i	−0.311561	−	0.200228i
$814$	3.57616	−	7.83069i	0.125344	−	0.274466i
$815$	−0.250616	−	0.0735875i	−0.00877870	−	0.00257766i
$816$	2.25746	+	2.60525i	0.0790269	+	0.0912019i
$817$	11.9361	+	13.7750i	0.417592	+	0.481927i
$818$	−1.69215	−	0.496859i	−0.0591645	−	0.0173723i
$819$	−2.17843	+	4.77011i	−0.0761207	+	0.166681i
$820$	−3.68341	−	2.36718i	−0.128630	−	0.0826656i
$821$	36.6216	−	10.7531i	1.27810	−	0.375285i	0.428900	−	0.903352i	$-0.358901\pi$
$821$	36.6216	−	10.7531i	1.27810	−	0.375285i	0.849203	+	0.528067i	$0.177083\pi$
$822$	−1.47163	+	10.2354i	−0.0513291	+	0.357002i
$823$	18.7863	+	41.1363i	0.654850	+	1.43392i	0.887244	+	0.461300i	$0.152617\pi$
$823$	18.7863	+	41.1363i	0.654850	+	1.43392i	−0.232394	+	0.972622i	$0.574656\pi$
$824$	2.27160	+	15.7993i	0.0791349	+	0.550395i
$825$	1.30542	−	0.838945i	0.0454490	−	0.0292083i
$826$	3.40359	−	3.92795i	0.118426	−	0.136671i
$827$	13.2229			0.459807			0.229903	−	0.973213i	$-0.426159\pi$
$827$	13.2229			0.459807			0.229903	+	0.973213i	$0.426159\pi$
$828$	−3.09240	−	3.66566i	−0.107468	−	0.127390i
$829$	44.5059			1.54575			0.772877	−	0.634555i	$-0.218817\pi$
$829$	44.5059			1.54575			0.772877	+	0.634555i	$0.218817\pi$
$830$	−10.1903	+	11.7603i	−0.353712	+	0.408206i
$831$	12.8496	−	8.25796i	0.445749	−	0.286466i
$832$	0.746298	+	5.19062i	0.0258732	+	0.179952i
$833$	−1.43203	−	3.13572i	−0.0496170	−	0.108646i
$834$	0.690863	−	4.80506i	0.0239226	−	0.166385i
$835$	−43.1101	+	12.6583i	−1.49189	+	0.438057i
$836$	−4.42977	−	2.84684i	−0.153207	−	0.0984600i
$837$	3.12977	−	6.85324i	0.108181	−	0.236883i
$838$	−16.2660	−	4.77614i	−0.561901	−	0.164989i
$839$	−19.0362	−	21.9689i	−0.657202	−	0.758451i	0.325116	−	0.945674i	$-0.394597\pi$
$839$	−19.0362	−	21.9689i	−0.657202	−	0.758451i	−0.982317	+	0.187223i	$0.940051\pi$
$840$	1.28820	+	1.48666i	0.0444471	+	0.0512947i
$841$	19.7333	+	5.79421i	0.680458	+	0.199800i
$842$	10.3741	−	22.7161i	0.357514	−	0.782847i
$843$	11.6244	+	7.47055i	0.400366	+	0.257299i
$844$	16.5943	−	4.87253i	0.571199	−	0.167719i
$845$	−4.05917	+	28.2321i	−0.139640	+	0.971215i
$846$	2.69193	+	5.89451i	0.0925505	+	0.202657i
$847$	1.29727	+	9.02268i	0.0445746	+	0.310023i
$848$	−8.39292	+	5.39380i	−0.288214	+	0.185224i
$849$	−8.67050	+	10.0063i	−0.297571	+	0.343415i
$850$	−3.89666			−0.133654
$851$	25.5129	−	15.9234i	0.874571	−	0.545848i
$852$	3.30364			0.113181
$853$	13.3186	−	15.3705i	0.456020	−	0.526275i	−0.480450	−	0.877022i	$-0.659527\pi$
$853$	13.3186	−	15.3705i	0.456020	−	0.526275i	0.936470	+	0.350747i	$0.114072\pi$
$854$	6.67787	−	4.29160i	0.228512	−	0.146856i
$855$	−1.07383	−	7.46866i	−0.0367243	−	0.255423i
$856$	−3.12307	−	6.83857i	−0.106744	−	0.233738i
$857$	5.37165	−	37.3607i	0.183492	−	1.27622i	−0.664934	−	0.746902i	$-0.731540\pi$
$857$	5.37165	−	37.3607i	0.183492	−	1.27622i	0.848426	−	0.529314i	$-0.177551\pi$
$858$	6.90728	−	2.02816i	0.235810	−	0.0692402i
$859$	−9.29098	−	5.97095i	−0.317004	−	0.203726i	0.372456	−	0.928050i	$-0.378516\pi$
$859$	−9.29098	−	5.97095i	−0.317004	−	0.203726i	−0.689460	+	0.724324i	$0.742152\pi$
$860$	−3.88311	+	8.50282i	−0.132413	+	0.289944i
$861$	2.13565	+	0.627083i	0.0727827	+	0.0213709i
$862$	−16.0328	−	18.5029i	−0.546080	−	0.630210i
$863$	6.77971	+	7.82421i	0.230784	+	0.266339i	0.859316	−	0.511444i	$-0.170889\pi$
$863$	6.77971	+	7.82421i	0.230784	+	0.266339i	−0.628532	+	0.777784i	$0.716344\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	−15.6677	+	34.3075i	−0.532719	+	1.16649i
$866$	13.5671	+	8.71904i	0.461028	+	0.296285i
$867$	4.90930	−	1.44150i	0.166729	−	0.0489560i
$868$	−1.07221	+	7.45739i	−0.0363932	+	0.253120i
$869$	2.05621	+	4.50248i	0.0697523	+	0.152736i
$870$	0.813003	+	5.65456i	0.0275634	+	0.191708i
$871$	−67.4978	+	43.3782i	−2.28708	+	1.46981i
$872$	−11.5317	+	13.3083i	−0.390512	+	0.450675i
$873$	−18.5540			−0.627959
$874$	−7.41990	−	16.8329i	−0.250982	−	0.569380i
$875$	−12.0593			−0.407678
$876$	4.97896	−	5.74602i	0.168223	−	0.194140i
$877$	−31.1379	+	20.0111i	−1.05145	+	0.675727i	−0.947793	−	0.318886i	$-0.896691\pi$
$877$	−31.1379	+	20.0111i	−1.05145	+	0.675727i	−0.103659	+	0.994613i	$0.533055\pi$
$878$	−1.85697	−	12.9155i	−0.0626698	−	0.435878i
$879$	−6.06257	−	13.2752i	−0.204485	−	0.447760i
$880$	0.384315	−	2.67297i	0.0129553	−	0.0901058i
$881$	−37.3341	+	10.9623i	−1.25782	+	0.369329i	−0.841682	−	0.539973i	$-0.818434\pi$
$881$	−37.3341	+	10.9623i	−1.25782	+	0.369329i	−0.416137	+	0.909302i	$0.636616\pi$
$882$	−0.841254	−	0.540641i	−0.0283265	−	0.0182043i
$883$	3.04590	−	6.66958i	0.102503	−	0.224449i	−0.851431	−	0.524466i	$-0.824265\pi$
$883$	3.04590	−	6.66958i	0.102503	−	0.224449i	0.953934	+	0.300017i	$0.0969923\pi$
$884$	−17.3450	−	5.09296i	−0.583377	−	0.171295i
$885$	−6.69533	−	7.72682i	−0.225061	−	0.259734i
$886$	−16.3172	−	18.8310i	−0.548186	−	0.632641i
$887$	−8.05297	−	2.36456i	−0.270392	−	0.0793943i	0.143726	−	0.989618i	$-0.454092\pi$
$887$	−8.05297	−	2.36456i	−0.270392	−	0.0793943i	−0.414118	+	0.910223i	$0.635910\pi$
$888$	−2.60504	+	5.70423i	−0.0874193	+	0.191422i
$889$	3.70914	+	2.38372i	0.124400	+	0.0799473i
$890$	−20.9354	+	6.14719i	−0.701756	+	0.206054i
$891$	0.195368	−	1.35881i	0.00654507	−	0.0455219i
$892$	5.86290	+	12.8380i	0.196305	+	0.429847i
$893$	3.53739	+	24.6031i	0.118374	+	0.823312i
$894$	−13.4243	+	8.62729i	−0.448977	+	0.288540i
$895$	−6.24400	+	7.20596i	−0.208714	+	0.240869i
$896$	−1.00000			−0.0334077
$897$	24.0348	+	7.40384i	0.802498	+	0.247207i
$898$	20.6432			0.688872
$899$	−14.3280	+	16.5354i	−0.477867	+	0.551487i
$900$	−0.950930	+	0.611126i	−0.0316977	+	0.0203709i
$901$	−4.89449	−	34.0419i	−0.163059	−	1.13410i
$902$	−1.26933	−	2.77944i	−0.0422639	−	0.0925451i
$903$	0.676259	−	4.70348i	0.0225045	−	0.156522i
$904$	9.61857	−	2.82427i	0.319909	−	0.0939338i
$905$	−35.0479	−	22.5239i	−1.16503	−	0.748719i
$906$	−2.02397	+	4.43187i	−0.0672419	+	0.147239i
$907$	−9.17749	−	2.69475i	−0.304733	−	0.0894778i	0.125791	−	0.992057i	$-0.459853\pi$
$907$	−9.17749	−	2.69475i	−0.304733	−	0.0894778i	−0.430524	+	0.902579i	$0.641671\pi$
$908$	−2.27268	−	2.62281i	−0.0754215	−	0.0870410i
$909$	8.42076	+	9.71807i	0.279299	+	0.322328i
$910$	−9.89780	−	2.90626i	−0.328109	−	0.0963414i
$911$	4.89007	−	10.7078i	0.162015	−	0.354764i	−0.811162	−	0.584822i	$-0.801164\pi$
$911$	4.89007	−	10.7078i	0.162015	−	0.354764i	0.973177	+	0.230058i	$0.0738916\pi$
$912$	3.22685	+	2.07377i	0.106852	+	0.0686693i
$913$	−10.4196	+	3.05946i	−0.344838	+	0.101253i
$914$	1.77978	−	12.3787i	0.0588700	−	0.409450i
$915$	−6.48676	−	14.2040i	−0.214446	−	0.469570i
$916$	−0.919907	−	6.39809i	−0.0303946	−	0.211399i
$917$	−9.95899	+	6.40025i	−0.328875	+	0.211355i
$918$	−2.25746	+	2.60525i	−0.0745073	+	0.0859860i
$919$	40.5254			1.33681			0.668405	−	0.743797i	$-0.266977\pi$
$919$	40.5254			1.33681			0.668405	+	0.743797i	$0.266977\pi$
$920$	6.27173	−	7.04747i	0.206773	−	0.232348i
$921$	−29.4047			−0.968919
$922$	8.11066	−	9.36020i	0.267110	−	0.308262i
$923$	−14.5741	+	9.36621i	−0.479712	+	0.308292i
$924$	0.195368	+	1.35881i	0.00642713	+	0.0447017i
$925$	−2.94466	−	6.44791i	−0.0968199	−	0.212006i
$926$	0.333745	−	2.32125i	0.0109675	−	0.0762809i
$927$	−15.3152	+	4.49695i	−0.503018	+	0.147699i
$928$	−2.44306	−	1.57006i	−0.0801974	−	0.0515398i
$929$	−14.7932	+	32.3927i	−0.485350	+	1.06277i	0.495607	+	0.868547i	$0.334946\pi$
$929$	−14.7932	+	32.3927i	−0.485350	+	1.06277i	−0.980958	+	0.194222i	$0.937782\pi$
$930$	14.2202	+	4.17543i	0.466300	+	0.136918i
$931$	−2.51189	−	2.89887i	−0.0823238	−	0.0950068i
$932$	−3.16833	−	3.65644i	−0.103782	−	0.119771i
$933$	−6.40418	−	1.88044i	−0.209663	−	0.0615627i
$934$	−2.65329	+	5.80989i	−0.0868182	+	0.190105i
$935$	7.83132	+	5.03289i	0.256112	+	0.164593i
$936$	−5.03158	+	1.47740i	−0.164462	+	0.0482905i
$937$	2.91263	−	20.2578i	0.0951515	−	0.661793i	−0.885298	−	0.465023i	$-0.846046\pi$
$937$	2.91263	−	20.2578i	0.0951515	−	0.661793i	0.980450	−	0.196769i	$-0.0630450\pi$
$938$	−6.35598	−	13.9177i	−0.207530	−	0.454428i
$939$	−1.66123	−	11.5541i	−0.0542121	−	0.377053i
$940$	−10.7237	+	6.89168i	−0.349767	+	0.224782i
$941$	15.5166	−	17.9071i	0.505827	−	0.583755i	−0.444198	−	0.895928i	$-0.646512\pi$
$941$	15.5166	−	17.9071i	0.505827	−	0.583755i	0.950025	+	0.312173i	$0.101057\pi$
$942$	−0.404195			−0.0131694
$943$	1.65874	−	10.5449i	0.0540159	−	0.343391i
$944$	5.19743			0.169162
$945$	−1.28820	+	1.48666i	−0.0419052	+	0.0483611i
$946$	−5.48772	+	3.52675i	−0.178421	+	0.114664i
$947$	−0.553350	−	3.84863i	−0.0179815	−	0.125064i	0.978854	−	0.204562i	$-0.0655772\pi$
$947$	−0.553350	−	3.84863i	−0.0179815	−	0.125064i	−0.996835	+	0.0794986i	$0.974668\pi$
$948$	−1.49784	−	3.27981i	−0.0486476	−	0.106523i
$949$	−5.67416	+	39.4647i	−0.184191	+	1.28108i
$950$	−4.16021	+	1.22155i	−0.134975	+	0.0396322i
$951$	−28.4144	−	18.2608i	−0.921399	−	0.592147i
$952$	1.43203	−	3.13572i	0.0464125	−	0.101629i
$953$	5.48722	+	1.61119i	0.177748	+	0.0521917i	0.369396	−	0.929272i	$-0.379565\pi$
$953$	5.48722	+	1.61119i	0.177748	+	0.0521917i	−0.191647	+	0.981464i	$0.561383\pi$
$954$	−6.53334	−	7.53988i	−0.211525	−	0.244112i
$955$	−6.05509	−	6.98795i	−0.195938	−	0.226125i
$956$	11.7242	+	3.44255i	0.379189	+	0.111340i
$957$	−1.65612	+	3.62640i	−0.0535348	+	0.117225i
$958$	9.04014	+	5.80974i	0.292074	+	0.187704i
$959$	9.92183	−	2.91331i	0.320392	−	0.0940757i
$960$	−0.279953	+	1.94711i	−0.00903544	+	0.0628428i
$961$	10.7021	+	23.4342i	0.345228	+	0.755943i
$962$	−4.67998	−	32.5500i	−0.150889	−	1.04945i
$963$	6.32451	−	4.06451i	0.203804	−	0.130977i
$964$	−3.91370	+	4.51665i	−0.126052	+	0.145471i
$965$	31.6488			1.01881
$966$	−2.04977	+	4.33572i	−0.0659503	+	0.139499i
$967$	28.0478			0.901958			0.450979	−	0.892535i	$-0.351075\pi$
$967$	28.0478			0.901958			0.450979	+	0.892535i	$0.351075\pi$
$968$	−5.96936	+	6.88900i	−0.191862	+	0.221421i
$969$	−11.1237	+	7.14877i	−0.357345	+	0.229652i
$970$	−5.19425	−	36.1268i	−0.166777	−	1.15996i
$971$	24.4954	+	53.6373i	0.786093	+	1.72130i	0.687509	+	0.726175i	$0.258704\pi$
$971$	24.4954	+	53.6373i	0.786093	+	1.72130i	0.0985839	+	0.995129i	$0.468569\pi$
$972$	−0.142315	+	0.989821i	−0.00456475	+	0.0317485i
$973$	−4.65783	+	1.36766i	−0.149323	+	0.0438452i
$974$	−6.14077	−	3.94644i	−0.196763	−	0.126452i
$975$	2.46244	−	5.39200i	0.0788613	−	0.172682i
$976$	7.61645	+	2.23639i	0.243797	+	0.0715852i
$977$	−18.7737	−	21.6660i	−0.600624	−	0.693157i	0.371284	−	0.928519i	$-0.378918\pi$
$977$	−18.7737	−	21.6660i	−0.600624	−	0.693157i	−0.971908	+	0.235363i	$0.924372\pi$
$978$	0.0869524	+	0.100348i	0.00278043	+	0.00320879i
$979$	−14.6100	−	4.28988i	−0.466937	−	0.137105i
$980$	0.817178	−	1.78937i	0.0261038	−	0.0571593i
$981$	−14.8139	−	9.52033i	−0.472972	−	0.303961i
$982$	−15.2681	+	4.48313i	−0.487225	+	0.143062i
$983$	5.22154	−	36.3166i	0.166541	−	1.15832i	−0.719425	−	0.694570i	$-0.755595\pi$
$983$	5.22154	−	36.3166i	0.166541	−	1.15832i	0.885966	−	0.463750i	$-0.153496\pi$
$984$	0.924635	+	2.02467i	0.0294763	+	0.0645441i
$985$	3.59256	+	24.9868i	0.114469	+	0.796146i
$986$	8.42181	−	5.41237i	0.268205	−	0.172365i
$987$	4.24356	−	4.89733i	0.135074	−	0.155884i
$988$	−20.1147			−0.639934
$989$	−22.7871	−	0.301342i	−0.724587	−	0.00958213i
$990$	2.70046			0.0858262
$991$	22.4820	−	25.9457i	0.714166	−	0.824191i	−0.276427	−	0.961035i	$-0.589150\pi$
$991$	22.4820	−	25.9457i	0.714166	−	0.824191i	0.990593	+	0.136844i	$0.0436959\pi$
$992$	−6.33807	+	4.07323i	−0.201234	+	0.129325i
$993$	−4.37671	−	30.4407i	−0.138891	−	0.966005i
$994$	−1.37238	−	3.00510i	−0.0435293	−	0.0953158i
$995$	2.70678	−	18.8261i	0.0858108	−	0.596827i
$996$	7.59010	−	2.22865i	0.240501	−	0.0706176i
$997$	−20.4108	−	13.1172i	−0.646416	−	0.415426i	0.175939	−	0.984401i	$-0.443704\pi$
$997$	−20.4108	−	13.1172i	−0.646416	−	0.415426i	−0.822355	+	0.568975i	$0.807340\pi$
$998$	−8.96490	+	19.6304i	−0.283779	+	0.621389i
$999$	−6.01691	−	1.76672i	−0.190367	−	0.0558967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.c.85.1	✓	10
23.13	even	11	inner	966.2.q.c.841.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.c.85.1	✓	10	1.1	even	1	trivial
966.2.q.c.841.1	yes	10	23.13	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.817178 + 1.78937i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.817178 + 1.78937i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(1.88745 + 0.554206i) q^{10} +(0.898983 + 1.03748i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(5.03158 + 1.47740i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(1.65486 + 1.06351i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.490593 - 3.41215i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(-0.545886 - 3.79672i) q^{19} +(1.65486 - 1.06351i) q^{20} +(-0.654861 + 0.755750i) q^{21} +1.37279 q^{22} +(3.99987 + 2.64594i) q^{23} -1.00000 q^{24} +(0.740237 - 0.854279i) q^{25} +(4.41153 - 2.83512i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.415415 + 0.909632i) q^{28} +(-0.413293 + 2.87451i) q^{29} +(1.88745 - 0.554206i) q^{30} +(6.33807 + 4.07323i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(1.31718 + 0.386758i) q^{33} +(-2.25746 - 2.60525i) q^{34} +(-1.28820 - 1.48666i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.60504 - 5.70423i) q^{37} +(-3.22685 - 2.07377i) q^{38} +(5.03158 - 1.47740i) q^{39} +(0.279953 - 1.94711i) q^{40} +(-0.924635 - 2.02467i) q^{41} +(0.142315 + 0.989821i) q^{42} +(-3.99751 + 2.56904i) q^{43} +(0.898983 - 1.03748i) q^{44} +1.96714 q^{45} +(4.61903 - 1.29018i) q^{46} -6.48010 q^{47} +(-0.654861 + 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.160869 - 1.11887i) q^{50} +(-1.43203 - 3.13572i) q^{51} +(0.746298 - 5.19062i) q^{52} +(9.57256 - 2.81076i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-1.12181 + 2.45642i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-2.51189 - 2.89887i) q^{57} +(1.90176 + 2.19475i) q^{58} +(-4.98689 - 1.46428i) q^{59} +(0.817178 - 1.78937i) q^{60} +(-6.67787 - 4.29160i) q^{61} +(7.22889 - 2.12259i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.46807 + 10.2107i) q^{65} +(1.15486 - 0.742184i) q^{66} +(-10.0196 + 11.5632i) q^{67} -3.44724 q^{68} +(4.79541 + 0.0634158i) q^{69} -1.96714 q^{70} +(-2.16342 + 2.49672i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(1.08203 + 7.52569i) q^{73} +(-2.60504 - 5.70423i) q^{74} +(0.160869 - 1.11887i) q^{75} +(-3.68038 + 1.08066i) q^{76} +(-1.15486 - 0.742184i) q^{77} +(2.17843 - 4.77011i) q^{78} +(3.45960 + 1.01583i) q^{79} +(-1.28820 - 1.48666i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-2.13565 - 0.627083i) q^{82} +(-3.28615 + 7.19567i) q^{83} +(0.841254 + 0.540641i) q^{84} +(6.50650 - 1.91048i) q^{85} +(-0.676259 + 4.70348i) q^{86} +(1.20640 + 2.64164i) q^{87} +(-0.195368 - 1.35881i) q^{88} +(-9.33108 + 5.99672i) q^{89} +(1.28820 - 1.48666i) q^{90} -5.24399 q^{91} +(2.04977 - 4.33572i) q^{92} +7.53408 q^{93} +(-4.24356 + 4.89733i) q^{94} +(6.34765 - 4.07939i) q^{95} +(0.142315 + 0.989821i) q^{96} +(-7.70763 - 16.8773i) q^{97} +(0.142315 - 0.989821i) q^{98} +(1.31718 - 0.386758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 - q^3 - q^4 + q^6 - q^7 + q^8 - q^9	\( 10 q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} + q^{8} - q^{9} - 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 11 q^{15} - q^{16} - 5 q^{17} + q^{18} + 31 q^{19} + 11 q^{20} - q^{21} + 6 q^{22} - q^{23} - 10 q^{24} - 17 q^{25} + 24 q^{26} - q^{27} - q^{28} - 5 q^{29} + 3 q^{31} + q^{32} + 5 q^{33} + 16 q^{34} - q^{36} + 14 q^{37} - 9 q^{38} - 2 q^{39} + 11 q^{40} - 28 q^{41} + q^{42} + 9 q^{43} - 6 q^{44} + 23 q^{46} - 44 q^{47} - q^{48} - q^{49} - 5 q^{50} - 5 q^{51} + 20 q^{52} + q^{53} + q^{54} + q^{56} - 2 q^{57} + 16 q^{58} - 11 q^{59} - 41 q^{61} + 30 q^{62} - q^{63} - q^{64} + 11 q^{65} + 6 q^{66} - 12 q^{67} + 6 q^{68} + 21 q^{69} - 22 q^{71} + q^{72} + 19 q^{73} - 14 q^{74} + 5 q^{75} - 24 q^{76} - 6 q^{77} + 2 q^{78} + 3 q^{79} - q^{81} + 6 q^{82} - 39 q^{83} - q^{84} + 22 q^{85} + 35 q^{86} + 6 q^{87} - 5 q^{88} - 17 q^{89} - 2 q^{91} - q^{92} - 8 q^{93} + 11 q^{94} + q^{96} - 12 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) \) 10 * q + q^2 - q^3 - q^4 + q^6 - q^7 + q^8 - q^9 - 6 * q^11 - q^12 - 2 * q^13 + q^14 + 11 * q^15 - q^16 - 5 * q^17 + q^18 + 31 * q^19 + 11 * q^20 - q^21 + 6 * q^22 - q^23 - 10 * q^24 - 17 * q^25 + 24 * q^26 - q^27 - q^28 - 5 * q^29 + 3 * q^31 + q^32 + 5 * q^33 + 16 * q^34 - q^36 + 14 * q^37 - 9 * q^38 - 2 * q^39 + 11 * q^40 - 28 * q^41 + q^42 + 9 * q^43 - 6 * q^44 + 23 * q^46 - 44 * q^47 - q^48 - q^49 - 5 * q^50 - 5 * q^51 + 20 * q^52 + q^53 + q^54 + q^56 - 2 * q^57 + 16 * q^58 - 11 * q^59 - 41 * q^61 + 30 * q^62 - q^63 - q^64 + 11 * q^65 + 6 * q^66 - 12 * q^67 + 6 * q^68 + 21 * q^69 - 22 * q^71 + q^72 + 19 * q^73 - 14 * q^74 + 5 * q^75 - 24 * q^76 - 6 * q^77 + 2 * q^78 + 3 * q^79 - q^81 + 6 * q^82 - 39 * q^83 - q^84 + 22 * q^85 + 35 * q^86 + 6 * q^87 - 5 * q^88 - 17 * q^89 - 2 * q^91 - q^92 - 8 * q^93 + 11 * q^94 + q^96 - 12 * q^97 + q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more