LMFDB - Embedded newform 966.2.q.c.211.1

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			211.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	966.211
Dual form			966.2.q.c.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.512546 - 0.329393i) q^{5} +(0.654861 + 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.512546 - 0.329393i) 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} +(-0.0867074 + 0.603063i) q^{10} +(0.0366213 - 0.0801894i) q^{11} +(0.415415 - 0.909632i) q^{12} +(-0.291654 + 2.02850i) q^{13} +(-0.841254 + 0.540641i) q^{14} +(0.584585 + 0.171650i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.448396 + 0.517476i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(4.55875 - 5.26107i) q^{19} +(0.584585 - 0.171650i) q^{20} +(0.415415 + 0.909632i) q^{21} -0.0881559 q^{22} +(-3.50140 + 3.27723i) q^{23} -1.00000 q^{24} +(-1.92287 - 4.21050i) q^{25} +(1.96635 - 0.577371i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{28} +(0.230471 + 0.265977i) q^{29} +(-0.0867074 - 0.603063i) q^{30} +(-5.95954 - 1.74988i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-0.0125459 + 0.0872586i) q^{33} +(0.284443 - 0.622842i) q^{34} +(-0.253098 + 0.554206i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(7.13423 - 4.58489i) q^{37} +(-6.67941 - 1.96125i) q^{38} +(-0.291654 - 2.02850i) q^{39} +(-0.398983 - 0.460451i) q^{40} +(-3.96272 - 2.54669i) q^{41} +(0.654861 - 0.755750i) q^{42} +(-1.36255 + 0.400081i) q^{43} +(0.0366213 + 0.0801894i) q^{44} -0.609264 q^{45} +(4.43560 + 1.82357i) q^{46} -6.29398 q^{47} +(0.415415 + 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(-3.03122 + 3.49821i) q^{50} +(-0.576022 - 0.370187i) q^{51} +(-1.34204 - 1.54880i) q^{52} +(-1.03170 - 7.17566i) q^{53} +(0.959493 + 0.281733i) q^{54} +(-0.0451840 + 0.0290380i) q^{55} +(0.142315 - 0.989821i) q^{56} +(-2.89187 + 6.33231i) q^{57} +(0.146201 - 0.320135i) q^{58} +(0.496376 - 3.45237i) q^{59} +(-0.512546 + 0.329393i) q^{60} +(-11.1970 - 3.28775i) q^{61} +(0.883936 + 6.14791i) q^{62} +(-0.654861 - 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.817660 - 0.943630i) q^{65} +(0.0845850 - 0.0248364i) q^{66} +(-2.97730 - 6.51937i) q^{67} -0.684719 q^{68} +(2.43626 - 4.13094i) q^{69} +0.609264 q^{70} +(-5.66820 - 12.4116i) q^{71} +(0.959493 - 0.281733i) q^{72} +(0.0217659 - 0.0251192i) q^{73} +(-7.13423 - 4.58489i) q^{74} +(3.03122 + 3.49821i) q^{75} +(0.990710 + 6.89054i) q^{76} +(-0.0845850 - 0.0248364i) q^{77} +(-1.72403 + 1.10797i) q^{78} +(1.68431 - 11.7146i) q^{79} +(-0.253098 + 0.554206i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.670373 + 4.66255i) q^{82} +(-12.0486 + 7.74315i) q^{83} +(-0.959493 - 0.281733i) q^{84} +(-0.0593702 - 0.412929i) q^{85} +(0.929949 + 1.07322i) q^{86} +(-0.296070 - 0.190272i) q^{87} +(0.0577299 - 0.0666238i) q^{88} +(-5.61217 + 1.64788i) q^{89} +(0.253098 + 0.554206i) q^{90} +2.04936 q^{91} +(-0.183838 - 4.79231i) q^{92} +6.21113 q^{93} +(2.61462 + 5.72521i) q^{94} +(-4.06953 + 1.19492i) q^{95} +(0.654861 - 0.755750i) q^{96} +(10.8847 + 6.99520i) q^{97} +(0.654861 + 0.755750i) q^{98} +(-0.0125459 - 0.0872586i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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
$5$	−0.512546	−	0.329393i	−0.229217	−	0.147309i	0.420991	−	0.907065i	$-0.361682\pi$
$5$	−0.512546	−	0.329393i	−0.229217	−	0.147309i	−0.650209	+	0.759755i	$0.725319\pi$
$6$	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
$10$	−0.0867074	+	0.603063i	−0.0274193	+	0.190705i
$11$	0.0366213	−	0.0801894i	0.0110417	−	0.0241780i	−0.904031	−	0.427467i	$-0.859406\pi$
$11$	0.0366213	−	0.0801894i	0.0110417	−	0.0241780i	0.915073	+	0.403289i	$0.132133\pi$
$12$	0.415415	−	0.909632i	0.119920	−	0.262588i
$13$	−0.291654	+	2.02850i	−0.0808903	+	0.562605i	0.908562	+	0.417749i	$0.137181\pi$
$13$	−0.291654	+	2.02850i	−0.0808903	+	0.562605i	−0.989453	+	0.144856i	$0.953728\pi$
$14$	−0.841254	+	0.540641i	−0.224834	+	0.144492i
$15$	0.584585	+	0.171650i	0.150939	+	0.0443197i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	0.448396	+	0.517476i	0.108752	+	0.125506i	0.807516	−	0.589846i	$-0.200812\pi$
$17$	0.448396	+	0.517476i	0.108752	+	0.125506i	−0.698764	+	0.715352i	$0.746266\pi$
$18$	−0.841254	−	0.540641i	−0.198285	−	0.127430i
$19$	4.55875	−	5.26107i	1.04585	−	1.20697i	0.0679939	−	0.997686i	$-0.478340\pi$
$19$	4.55875	−	5.26107i	1.04585	−	1.20697i	0.977854	−	0.209287i	$-0.0671144\pi$
$20$	0.584585	−	0.171650i	0.130717	−	0.0383820i
$21$	0.415415	+	0.909632i	0.0906510	+	0.198498i
$22$	−0.0881559			−0.0187949
$23$	−3.50140	+	3.27723i	−0.730091	+	0.683350i
$23$	−3.50140	+	3.27723i	−0.730091	+	0.683350i
$24$	−1.00000			−0.204124
$25$	−1.92287	−	4.21050i	−0.384574	−	0.842100i
$26$	1.96635	−	0.577371i	0.385632	−	0.113232i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	0.841254	+	0.540641i	0.158982	+	0.102172i
$29$	0.230471	+	0.265977i	0.0427973	+	0.0493908i	0.776745	−	0.629816i	$-0.216870\pi$
$29$	0.230471	+	0.265977i	0.0427973	+	0.0493908i	−0.733947	+	0.679206i	$0.762324\pi$
$30$	−0.0867074	−	0.603063i	−0.0158305	−	0.110104i
$31$	−5.95954	−	1.74988i	−1.07036	−	0.314287i	−0.301347	−	0.953515i	$-0.597436\pi$
$31$	−5.95954	−	1.74988i	−1.07036	−	0.314287i	−0.769018	+	0.639227i	$0.779254\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	−0.0125459	+	0.0872586i	−0.00218396	+	0.0151898i
$34$	0.284443	−	0.622842i	0.0487815	−	0.106817i
$35$	−0.253098	+	0.554206i	−0.0427813	+	0.0936780i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	7.13423	−	4.58489i	1.17286	−	0.753751i	0.198800	−	0.980040i	$-0.436296\pi$
$37$	7.13423	−	4.58489i	1.17286	−	0.753751i	0.974060	+	0.226289i	$0.0726593\pi$
$38$	−6.67941	−	1.96125i	−1.08354	−	0.318157i
$39$	−0.291654	−	2.02850i	−0.0467020	−	0.324820i
$40$	−0.398983	−	0.460451i	−0.0630848	−	0.0728038i
$41$	−3.96272	−	2.54669i	−0.618873	−	0.397726i	0.193302	−	0.981139i	$-0.438080\pi$
$41$	−3.96272	−	2.54669i	−0.618873	−	0.397726i	−0.812175	+	0.583414i	$0.801717\pi$
$42$	0.654861	−	0.755750i	0.101047	−	0.116615i
$43$	−1.36255	+	0.400081i	−0.207787	+	0.0610117i	−0.383970	−	0.923346i	$-0.625443\pi$
$43$	−1.36255	+	0.400081i	−0.207787	+	0.0610117i	0.176183	+	0.984357i	$0.443625\pi$
$44$	0.0366213	+	0.0801894i	0.00552087	+	0.0120890i
$45$	−0.609264			−0.0908238
$46$	4.43560	+	1.82357i	0.653994	+	0.268871i
$47$	−6.29398			−0.918072			−0.459036	−	0.888418i	$-0.651805\pi$
$47$	−6.29398			−0.918072			−0.459036	+	0.888418i	$0.651805\pi$
$48$	0.415415	+	0.909632i	0.0599600	+	0.131294i
$49$	−0.959493	+	0.281733i	−0.137070	+	0.0402475i
$50$	−3.03122	+	3.49821i	−0.428679	+	0.494722i
$51$	−0.576022	−	0.370187i	−0.0806593	−	0.0518366i
$52$	−1.34204	−	1.54880i	−0.186108	−	0.214780i
$53$	−1.03170	−	7.17566i	−0.141715	−	0.985653i	−0.929268	−	0.369405i	$-0.879561\pi$
$53$	−1.03170	−	7.17566i	−0.141715	−	0.985653i	0.787553	−	0.616247i	$-0.211348\pi$
$54$	0.959493	+	0.281733i	0.130570	+	0.0383389i
$55$	−0.0451840	+	0.0290380i	−0.00609260	+	0.00391548i
$56$	0.142315	−	0.989821i	0.0190176	−	0.132270i
$57$	−2.89187	+	6.33231i	−0.383037	+	0.838735i
$58$	0.146201	−	0.320135i	0.0191971	−	0.0420357i
$59$	0.496376	−	3.45237i	0.0646226	−	0.449460i	−0.931661	−	0.363328i	$-0.881640\pi$
$59$	0.496376	−	3.45237i	0.0646226	−	0.449460i	0.996284	−	0.0861318i	$-0.0274506\pi$
$60$	−0.512546	+	0.329393i	−0.0661694	+	0.0425245i
$61$	−11.1970	−	3.28775i	−1.43364	−	0.420953i	−0.529540	−	0.848285i	$-0.677635\pi$
$61$	−11.1970	−	3.28775i	−1.43364	−	0.420953i	−0.904095	+	0.427332i	$0.859454\pi$
$62$	0.883936	+	6.14791i	0.112260	+	0.780786i
$63$	−0.654861	−	0.755750i	−0.0825047	−	0.0952155i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	0.817660	−	0.943630i	0.101418	−	0.117043i
$66$	0.0845850	−	0.0248364i	0.0104117	−	0.00305715i
$67$	−2.97730	−	6.51937i	−0.363735	−	0.796468i	−0.999694	−	0.0247454i	$-0.992122\pi$
$67$	−2.97730	−	6.51937i	−0.363735	−	0.796468i	0.635959	−	0.771723i	$-0.280605\pi$
$68$	−0.684719			−0.0830344
$69$	2.43626	−	4.13094i	0.293291	−	0.497306i
$70$	0.609264			0.0728210
$71$	−5.66820	−	12.4116i	−0.672691	−	1.47299i	−0.870206	−	0.492689i	$-0.836014\pi$
$71$	−5.66820	−	12.4116i	−0.672691	−	1.47299i	0.197514	−	0.980300i	$-0.436713\pi$
$72$	0.959493	−	0.281733i	0.113077	−	0.0332025i
$73$	0.0217659	−	0.0251192i	0.00254751	−	0.00293998i	−0.754474	−	0.656329i	$-0.772108\pi$
$73$	0.0217659	−	0.0251192i	0.00254751	−	0.00293998i	0.757022	+	0.653390i	$0.226654\pi$
$74$	−7.13423	−	4.58489i	−0.829337	−	0.532983i
$75$	3.03122	+	3.49821i	0.350015	+	0.403939i
$76$	0.990710	+	6.89054i	0.113642	+	0.790399i
$77$	−0.0845850	−	0.0248364i	−0.00963935	−	0.00283037i
$78$	−1.72403	+	1.10797i	−0.195208	+	0.125453i
$79$	1.68431	−	11.7146i	0.189499	−	1.31800i	−0.643808	−	0.765187i	$-0.722647\pi$
$79$	1.68431	−	11.7146i	0.189499	−	1.31800i	0.833307	−	0.552810i	$-0.186444\pi$
$80$	−0.253098	+	0.554206i	−0.0282972	+	0.0619622i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−0.670373	+	4.66255i	−0.0740304	+	0.514892i
$83$	−12.0486	+	7.74315i	−1.32250	+	0.849921i	−0.995469	−	0.0950915i	$-0.969686\pi$
$83$	−12.0486	+	7.74315i	−1.32250	+	0.849921i	−0.327034	+	0.945012i	$0.606049\pi$
$84$	−0.959493	−	0.281733i	−0.104689	−	0.0307395i
$85$	−0.0593702	−	0.412929i	−0.00643960	−	0.0447884i
$86$	0.929949	+	1.07322i	0.100279	+	0.115728i
$87$	−0.296070	−	0.190272i	−0.0317420	−	0.0203993i
$88$	0.0577299	−	0.0666238i	0.00615402	−	0.00710212i
$89$	−5.61217	+	1.64788i	−0.594889	+	0.174675i	−0.565298	−	0.824887i	$-0.691239\pi$
$89$	−5.61217	+	1.64788i	−0.594889	+	0.174675i	−0.0295913	+	0.999562i	$0.509421\pi$
$90$	0.253098	+	0.554206i	0.0266788	+	0.0584185i
$91$	2.04936			0.214831
$92$	−0.183838	−	4.79231i	−0.0191665	−	0.499633i
$93$	6.21113			0.644064
$94$	2.61462	+	5.72521i	0.269677	+	0.590510i
$95$	−4.06953	+	1.19492i	−0.417525	+	0.122596i
$96$	0.654861	−	0.755750i	0.0668364	−	0.0771334i
$97$	10.8847	+	6.99520i	1.10518	+	0.710255i	0.960237	−	0.279185i	$-0.0900643\pi$
$97$	10.8847	+	6.99520i	1.10518	+	0.710255i	0.144941	+	0.989440i	$0.453701\pi$
$98$	0.654861	+	0.755750i	0.0661509	+	0.0763422i
$99$	−0.0125459	−	0.0872586i	−0.00126091	−	0.00876982i
$100$	4.44130	+	1.30408i	0.444130	+	0.130408i
$101$	−13.9730	+	8.97988i	−1.39036	+	0.893531i	−0.999636	−	0.0269758i	$-0.991412\pi$
$101$	−13.9730	+	8.97988i	−1.39036	+	0.893531i	−0.390726	+	0.920507i	$0.627776\pi$
$102$	−0.0974457	+	0.677750i	−0.00964856	+	0.0671072i
$103$	5.50656	−	12.0577i	0.542577	−	1.18808i	−0.417585	−	0.908638i	$-0.637124\pi$
$103$	5.50656	−	12.0577i	0.542577	−	1.18808i	0.960163	−	0.279441i	$-0.0901492\pi$
$104$	−0.851334	+	1.86416i	−0.0834802	+	0.182796i
$105$	0.0867074	−	0.603063i	0.00846177	−	0.0588529i
$106$	−6.09862	+	3.91935i	−0.592351	+	0.380681i
$107$	−1.69566	−	0.497890i	−0.163925	−	0.0481328i	0.198740	−	0.980052i	$-0.436315\pi$
$107$	−1.69566	−	0.497890i	−0.163925	−	0.0481328i	−0.362665	+	0.931919i	$0.618133\pi$
$108$	−0.142315	−	0.989821i	−0.0136943	−	0.0952456i
$109$	4.44616	+	5.13114i	0.425865	+	0.491475i	0.927615	−	0.373538i	$-0.121856\pi$
$109$	4.44616	+	5.13114i	0.425865	+	0.491475i	−0.501750	+	0.865013i	$0.667310\pi$
$110$	0.0451840	+	0.0290380i	0.00430812	+	0.00276866i
$111$	−5.55353	+	6.40911i	−0.527118	+	0.608326i
$112$	−0.959493	+	0.281733i	−0.0906636	+	0.0266212i
$113$	4.11853	+	9.01832i	0.387439	+	0.848372i	0.998391	+	0.0567048i	$0.0180594\pi$
$113$	4.11853	+	9.01832i	0.387439	+	0.848372i	−0.610952	+	0.791667i	$0.709213\pi$
$114$	6.96140			0.651995
$115$	2.87412	−	0.526394i	0.268013	−	0.0490865i
$116$	−0.351939			−0.0326767
$117$	0.851334	+	1.86416i	0.0787059	+	0.172342i
$118$	−3.34659	+	0.982647i	−0.308078	+	0.0904600i
$119$	0.448396	−	0.517476i	0.0411044	−	0.0474370i
$120$	0.512546	+	0.329393i	0.0467888	+	0.0300694i
$121$	7.19838	+	8.30737i	0.654398	+	0.755216i
$122$	1.66078	+	11.5510i	0.150360	+	1.04578i
$123$	4.51969	+	1.32710i	0.407527	+	0.119661i
$124$	5.22514	−	3.35799i	0.469231	−	0.301557i
$125$	−0.834888	+	5.80677i	−0.0746746	+	0.519373i
$126$	−0.415415	+	0.909632i	−0.0370081	+	0.0810365i
$127$	−0.117351	+	0.256962i	−0.0104132	+	0.0228017i	−0.914767	−	0.403982i	$-0.867626\pi$
$127$	−0.117351	+	0.256962i	−0.0104132	+	0.0228017i	0.904354	+	0.426783i	$0.140353\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	1.19464	−	0.767749i	0.105182	−	0.0675965i
$130$	−1.19802	−	0.351772i	−0.105074	−	0.0308524i
$131$	−2.30834	−	16.0548i	−0.201680	−	1.40272i	−0.799297	−	0.600936i	$-0.794794\pi$
$131$	−2.30834	−	16.0548i	−0.201680	−	1.40272i	0.597616	−	0.801782i	$-0.296115\pi$
$132$	−0.0577299	−	0.0666238i	−0.00502474	−	0.00579886i
$133$	−5.85630	−	3.76362i	−0.507806	−	0.326347i
$134$	−4.69342	+	5.41649i	−0.405450	+	0.467914i
$135$	0.584585	−	0.171650i	0.0503131	−	0.0147732i
$136$	0.284443	+	0.622842i	0.0243907	+	0.0534083i
$137$	18.8108			1.60711			0.803556	−	0.595230i	$-0.202939\pi$
$137$	18.8108			1.60711			0.803556	+	0.595230i	$0.202939\pi$
$138$	−4.76969	−	0.500049i	−0.406023	−	0.0425670i
$139$	0.873421			0.0740826			0.0370413	−	0.999314i	$-0.488207\pi$
$139$	0.873421			0.0740826			0.0370413	+	0.999314i	$0.488207\pi$
$140$	−0.253098	−	0.554206i	−0.0213907	−	0.0468390i
$141$	6.03903	−	1.77322i	0.508578	−	0.149332i
$142$	−8.93535	+	10.3119i	−0.749838	+	0.865359i
$143$	0.151983	+	0.0976739i	0.0127095	+	0.00816790i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	−0.0305157	−	0.212241i	−0.00253419	−	0.0176257i
$146$	−0.0318911	−	0.00936407i	−0.00263933	−	0.000774976i
$147$	0.841254	−	0.540641i	0.0693854	−	0.0445913i
$148$	−1.20690	+	8.39415i	−0.0992063	+	0.689995i
$149$	−2.08932	+	4.57496i	−0.171163	+	0.374795i	−0.975701	−	0.219106i	$-0.929686\pi$
$149$	−2.08932	+	4.57496i	−0.171163	+	0.374795i	0.804538	+	0.593902i	$0.202413\pi$
$150$	1.92287	−	4.21050i	0.157002	−	0.343786i
$151$	1.87239	−	13.0228i	0.152373	−	1.05978i	−0.759855	−	0.650093i	$-0.774730\pi$
$151$	1.87239	−	13.0228i	0.152373	−	1.05978i	0.912228	−	0.409684i	$-0.134361\pi$
$152$	5.85630	−	3.76362i	0.475009	−	0.305270i
$153$	0.656983	+	0.192908i	0.0531139	+	0.0155957i
$154$	0.0125459	+	0.0872586i	0.00101098	+	0.00703150i
$155$	2.47814	+	2.85992i	0.199049	+	0.229715i
$156$	1.72403	+	1.10797i	0.138033	+	0.0887084i
$157$	0.0965433	−	0.111417i	0.00770499	−	0.00889204i	−0.751884	−	0.659295i	$-0.770855\pi$
$157$	0.0965433	−	0.111417i	0.00770499	−	0.00889204i	0.759589	+	0.650403i	$0.225400\pi$
$158$	−11.3557	+	3.33433i	−0.903409	+	0.265265i
$159$	3.01153	+	6.59433i	0.238830	+	0.522964i
$160$	0.609264			0.0481666
$161$	3.74217	+	2.99936i	0.294924	+	0.236383i
$162$	−1.00000			−0.0785674
$163$	−2.86559	−	6.27477i	−0.224450	−	0.491478i	0.763585	−	0.645708i	$-0.223438\pi$
$163$	−2.86559	−	6.27477i	−0.224450	−	0.491478i	−0.988035	+	0.154230i	$0.950710\pi$
$164$	4.51969	−	1.32710i	0.352928	−	0.103629i
$165$	0.0351727	−	0.0405915i	0.00273819	−	0.00316005i
$166$	12.0486	+	7.74315i	0.935151	+	0.600985i
$167$	5.15800	+	5.95265i	0.399138	+	0.460630i	0.919369	−	0.393396i	$-0.128700\pi$
$167$	5.15800	+	5.95265i	0.399138	+	0.460630i	−0.520231	+	0.854025i	$0.674154\pi$
$168$	0.142315	+	0.989821i	0.0109798	+	0.0763664i
$169$	8.44366	+	2.47928i	0.649512	+	0.190714i
$170$	−0.350950	+	0.225542i	−0.0269166	+	0.0172983i
$171$	0.990710	−	6.89054i	0.0757615	−	0.526933i
$172$	0.589919	−	1.29174i	0.0449809	−	0.0984945i
$173$	7.08427	−	15.5124i	0.538607	−	1.17939i	−0.423295	−	0.905992i	$-0.639127\pi$
$173$	7.08427	−	15.5124i	0.538607	−	1.17939i	0.961902	−	0.273393i	$-0.0881461\pi$
$174$	−0.0500861	+	0.348356i	−0.00379702	+	0.0264088i
$175$	−3.89399	+	2.50252i	−0.294358	+	0.189172i
$176$	−0.0845850	−	0.0248364i	−0.00637583	−	0.00187211i
$177$	0.496376	+	3.45237i	0.0373099	+	0.259496i
$178$	3.83035	+	4.42046i	0.287097	+	0.331327i
$179$	−8.42610	−	5.41512i	−0.629796	−	0.404745i	0.186438	−	0.982467i	$-0.440306\pi$
$179$	−8.42610	−	5.41512i	−0.629796	−	0.404745i	−0.816234	+	0.577721i	$0.803942\pi$
$180$	0.398983	−	0.460451i	0.0297385	−	0.0343200i
$181$	−7.42033	+	2.17881i	−0.551549	+	0.161949i	−0.545619	−	0.838033i	$-0.683706\pi$
$181$	−7.42033	+	2.17881i	−0.551549	+	0.161949i	−0.00592946	+	0.999982i	$0.501887\pi$
$182$	−0.851334	−	1.86416i	−0.0631051	−	0.138181i
$183$	11.6698			0.862653
$184$	−4.28287	+	2.15802i	−0.315737	+	0.159091i
$185$	−5.16685			−0.379874
$186$	−2.58020	−	5.64984i	−0.189189	−	0.414267i
$187$	0.0579170	−	0.0170060i	0.00423531	−	0.00124360i
$188$	4.12168	−	4.75668i	0.300605	−	0.346916i
$189$	0.841254	+	0.540641i	0.0611922	+	0.0393258i
$190$	2.77748	+	3.20539i	0.201500	+	0.232543i
$191$	1.46168	+	10.1662i	0.105763	+	0.735599i	0.971832	+	0.235674i	$0.0757299\pi$
$191$	1.46168	+	10.1662i	0.105763	+	0.735599i	−0.866069	+	0.499925i	$0.833361\pi$
$192$	−0.959493	−	0.281733i	−0.0692454	−	0.0203323i
$193$	15.8751	−	10.2023i	1.14272	−	0.734380i	0.174541	−	0.984650i	$-0.444156\pi$
$193$	15.8751	−	10.2023i	1.14272	−	0.734380i	0.968176	+	0.250270i	$0.0805193\pi$
$194$	1.84137	−	12.8070i	0.132203	−	0.919491i
$195$	−0.518688	+	1.13577i	−0.0371440	+	0.0813340i
$196$	0.415415	−	0.909632i	0.0296725	−	0.0649737i
$197$	−0.158634	+	1.10332i	−0.0113022	+	0.0786085i	−0.994692	−	0.102898i	$-0.967188\pi$
$197$	−0.158634	+	1.10332i	−0.0113022	+	0.0786085i	0.983390	+	0.181507i	$0.0580974\pi$
$198$	−0.0741615	+	0.0476607i	−0.00527043	+	0.00338710i
$199$	17.8252	+	5.23396i	1.26360	+	0.371025i	0.843832	−	0.536608i	$-0.180294\pi$
$199$	17.8252	+	5.23396i	1.26360	+	0.371025i	0.419764	+	0.907633i	$0.362113\pi$
$200$	−0.658746	−	4.58168i	−0.0465804	−	0.323974i
$201$	4.69342	+	5.41649i	0.331048	+	0.382050i
$202$	13.9730	+	8.97988i	0.983134	+	0.631822i
$203$	0.230471	−	0.265977i	0.0161759	−	0.0186680i
$204$	0.656983	−	0.192908i	0.0459980	−	0.0135062i
$205$	1.19222	+	2.61059i	0.0832679	+	0.182331i
$206$	−13.2556			−0.923559
$207$	−1.17376	+	4.64998i	−0.0815818	+	0.323196i
$208$	2.04936			0.142097
$209$	−0.254935	−	0.558231i	−0.0176343	−	0.0386136i
$210$	−0.584585	+	0.171650i	−0.0403402	+	0.0118450i
$211$	−6.62576	+	7.64653i	−0.456136	+	0.526409i	−0.936504	−	0.350658i	$-0.885958\pi$
$211$	−6.62576	+	7.64653i	−0.456136	+	0.526409i	0.480367	+	0.877067i	$0.340503\pi$
$212$	6.09862	+	3.91935i	0.418855	+	0.269182i
$213$	8.93535	+	10.3119i	0.612240	+	0.706563i
$214$	0.251505	+	1.74925i	0.0171925	+	0.119577i
$215$	0.830153	+	0.243755i	0.0566160	+	0.0166239i
$216$	−0.841254	+	0.540641i	−0.0572401	+	0.0367859i
$217$	−0.883936	+	6.14791i	−0.0600055	+	0.417347i
$218$	2.82045	−	6.17593i	0.191025	−	0.418286i
$219$	−0.0138073	+	0.0302339i	−0.000933014	+	0.00204301i
$220$	0.00764377	−	0.0531636i	0.000515343	−	0.00358429i
$221$	−1.18048	+	0.758646i	−0.0794074	+	0.0510321i
$222$	8.13696	+	2.38923i	0.546117	+	0.160354i
$223$	1.66237	+	11.5621i	0.111321	+	0.774252i	0.966638	+	0.256147i	$0.0824532\pi$
$223$	1.66237	+	11.5621i	0.111321	+	0.774252i	−0.855317	+	0.518105i	$0.826638\pi$
$224$	0.654861	+	0.755750i	0.0437547	+	0.0504956i
$225$	−3.89399	−	2.50252i	−0.259599	−	0.166834i
$226$	6.49245	−	7.49269i	0.431872	−	0.498406i
$227$	−15.2072	+	4.46525i	−1.00934	+	0.296369i	−0.744283	−	0.667864i	$-0.767209\pi$
$227$	−15.2072	+	4.46525i	−1.00934	+	0.296369i	−0.265056	+	0.964233i	$0.585391\pi$
$228$	−2.89187	−	6.33231i	−0.191519	−	0.419368i
$229$	−22.3938			−1.47982			−0.739910	−	0.672705i	$-0.765132\pi$
$229$	−22.3938			−1.47982			−0.739910	+	0.672705i	$0.765132\pi$
$230$	−1.67278	−	2.39572i	−0.110300	−	0.157969i
$231$	0.0881559			0.00580023
$232$	0.146201	+	0.320135i	0.00959854	+	0.0210179i
$233$	15.8204	−	4.64530i	1.03643	−	0.304324i	0.281108	−	0.959676i	$-0.409298\pi$
$233$	15.8204	−	4.64530i	1.03643	−	0.304324i	0.755323	+	0.655352i	$0.227480\pi$
$234$	1.34204	−	1.54880i	0.0877322	−	0.101248i
$235$	3.22596	+	2.07320i	0.210438	+	0.135240i
$236$	2.28407	+	2.63596i	0.148680	+	0.171586i
$237$	1.68431	+	11.7146i	0.109407	+	0.760946i
$238$	−0.656983	−	0.192908i	−0.0425859	−	0.0125043i
$239$	14.0473	−	9.02763i	0.908642	−	0.583949i	−0.000699438	−	1.00000i	$-0.500223\pi$
$239$	14.0473	−	9.02763i	0.908642	−	0.583949i	0.909341	+	0.416051i	$0.136586\pi$
$240$	0.0867074	−	0.603063i	0.00559694	−	0.0389276i
$241$	5.62462	−	12.3162i	0.362313	−	0.793356i	−0.637426	−	0.770512i	$-0.720001\pi$
$241$	5.62462	−	12.3162i	0.362313	−	0.793356i	0.999739	−	0.0228439i	$-0.00727208\pi$
$242$	4.56634	−	9.99888i	0.293535	−	0.642753i
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$	9.81722	−	6.30915i	0.628483	−	0.403902i
$245$	0.584585	+	0.171650i	0.0373478	+	0.0109663i
$246$	−0.670373	−	4.66255i	−0.0427415	−	0.297273i
$247$	9.34251	+	10.7818i	0.594450	+	0.686031i
$248$	−5.22514	−	3.35799i	−0.331796	−	0.213233i
$249$	9.37903	−	10.8240i	0.594372	−	0.685941i
$250$	5.62885	−	1.65278i	0.356000	−	0.104531i
$251$	−9.28751	−	20.3368i	−0.586223	−	1.28365i	−0.937698	−	0.347451i	$-0.887047\pi$
$251$	−9.28751	−	20.3368i	−0.586223	−	1.28365i	0.351475	−	0.936197i	$-0.385680\pi$
$252$	1.00000			0.0629941
$253$	0.134574	+	0.400791i	0.00846057	+	0.0251975i
$254$	0.282490			0.0177250
$255$	0.173301	+	0.379476i	0.0108525	+	0.0237637i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	2.68061	−	3.09359i	0.167212	−	0.192973i	−0.665959	−	0.745988i	$-0.731978\pi$
$257$	2.68061	−	3.09359i	0.167212	−	0.192973i	0.833171	+	0.553015i	$0.186523\pi$
$258$	−1.19464	−	0.767749i	−0.0743751	−	0.0477980i
$259$	−5.55353	−	6.40911i	−0.345080	−	0.398243i
$260$	0.177695	+	1.23589i	0.0110201	+	0.0766468i
$261$	0.337683	+	0.0991526i	0.0209020	+	0.00613739i
$262$	−13.6451	+	8.76916i	−0.842996	+	0.541761i
$263$	2.82653	−	19.6590i	0.174291	−	1.21222i	−0.695398	−	0.718625i	$-0.744772\pi$
$263$	2.82653	−	19.6590i	0.174291	−	1.21222i	0.869690	−	0.493599i	$-0.164319\pi$
$264$	−0.0366213	+	0.0801894i	−0.00225388	+	0.00493532i
$265$	−1.83482	+	4.01769i	−0.112712	+	0.246805i
$266$	−0.990710	+	6.89054i	−0.0607443	+	0.422486i
$267$	4.92058	−	3.16226i	0.301135	−	0.193527i
$268$	6.87673	+	2.01919i	0.420063	+	0.123342i
$269$	1.48414	+	10.3224i	0.0904896	+	0.629369i	0.983712	+	0.179753i	$0.0575300\pi$
$269$	1.48414	+	10.3224i	0.0904896	+	0.629369i	−0.893222	+	0.449616i	$0.851561\pi$
$270$	−0.398983	−	0.460451i	−0.0242814	−	0.0280222i
$271$	−10.0384	−	6.45131i	−0.609791	−	0.391889i	0.198988	−	0.980002i	$-0.436235\pi$
$271$	−10.0384	−	6.45131i	−0.609791	−	0.391889i	−0.808779	+	0.588113i	$0.799871\pi$
$272$	0.448396	−	0.517476i	0.0271880	−	0.0313766i
$273$	−1.96635	+	0.577371i	−0.119009	+	0.0349441i
$274$	−7.81427	−	17.1109i	−0.472077	−	1.03371i
$275$	−0.408056			−0.0246067
$276$	1.52654	+	4.54639i	0.0918869	+	0.273661i
$277$	4.16803			0.250433			0.125216	−	0.992129i	$-0.460037\pi$
$277$	4.16803			0.250433			0.125216	+	0.992129i	$0.460037\pi$
$278$	−0.362832	−	0.794492i	−0.0217612	−	0.0476505i
$279$	−5.95954	+	1.74988i	−0.356788	+	0.104762i
$280$	−0.398983	+	0.460451i	−0.0238438	+	0.0275172i
$281$	6.44293	+	4.14062i	0.384353	+	0.247009i	0.718522	−	0.695505i	$-0.244819\pi$
$281$	6.44293	+	4.14062i	0.384353	+	0.247009i	−0.334168	+	0.942513i	$0.608455\pi$
$282$	−4.12168	−	4.75668i	−0.245443	−	0.283256i
$283$	2.00401	+	13.9382i	0.119126	+	0.828538i	0.958522	+	0.285018i	$0.0919996\pi$
$283$	2.00401	+	13.9382i	0.119126	+	0.828538i	−0.839396	+	0.543520i	$0.817091\pi$
$284$	13.0920	+	3.84415i	0.776865	+	0.228108i
$285$	3.56804	−	2.29304i	0.211352	−	0.135828i
$286$	0.0257110	−	0.178824i	0.00152033	−	0.0105741i
$287$	−1.95681	+	4.28482i	−0.115507	+	0.252925i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	2.35263	−	16.3629i	0.138390	−	0.962523i
$290$	−0.180385	+	0.115926i	−0.0105926	+	0.00680742i
$291$	−12.4146	−	3.64526i	−0.727758	−	0.213689i
$292$	0.00473018	+	0.0328992i	0.000276813	+	0.00192528i
$293$	13.9808	+	16.1347i	0.816768	+	0.942600i	0.999175	−	0.0406230i	$-0.0129343\pi$
$293$	13.9808	+	16.1347i	0.816768	+	0.942600i	−0.182407	+	0.983223i	$0.558389\pi$
$294$	−0.841254	−	0.540641i	−0.0490629	−	0.0315308i
$295$	−1.39160	+	1.60600i	−0.0810222	+	0.0935046i
$296$	8.13696	−	2.38923i	0.472951	−	0.138871i
$297$	0.0366213	+	0.0801894i	0.00212498	+	0.00465306i
$298$	5.02946			0.291349
$299$	−5.62666	−	8.05840i	−0.325398	−	0.466029i
$300$	−4.62880			−0.267244
$301$	0.589919	+	1.29174i	0.0340024	+	0.0744548i
$302$	−12.6237	+	3.70666i	−0.726414	+	0.213294i
$303$	10.8770	−	12.5528i	0.624869	−	0.721138i
$304$	−5.85630	−	3.76362i	−0.335882	−	0.215858i
$305$	4.65604	+	5.37335i	0.266604	+	0.307677i
$306$	−0.0974457	−	0.677750i	−0.00557060	−	0.0387444i
$307$	13.8856	+	4.07717i	0.792492	+	0.232697i	0.652832	−	0.757503i	$-0.273581\pi$
$307$	13.8856	+	4.07717i	0.792492	+	0.232697i	0.139660	+	0.990200i	$0.455399\pi$
$308$	0.0741615	−	0.0476607i	0.00422574	−	0.00271572i
$309$	−1.88646	+	13.1206i	−0.107317	+	0.746407i
$310$	1.57202	−	3.44225i	0.0892849	−	0.195507i
$311$	−10.4603	+	22.9049i	−0.593151	+	1.29882i	0.340368	+	0.940292i	$0.389448\pi$
$311$	−10.4603	+	22.9049i	−0.593151	+	1.29882i	−0.933519	+	0.358527i	$0.883279\pi$
$312$	0.291654	−	2.02850i	0.0165117	−	0.114841i
$313$	−8.69788	+	5.58979i	−0.491633	+	0.315953i	−0.762862	−	0.646562i	$-0.776206\pi$
$313$	−8.69788	+	5.58979i	−0.491633	+	0.315953i	0.271229	+	0.962515i	$0.412570\pi$
$314$	−0.141454	−	0.0415346i	−0.00798271	−	0.00234393i
$315$	0.0867074	+	0.603063i	0.00488541	+	0.0339788i
$316$	7.75033	+	8.94435i	0.435990	+	0.503159i
$317$	11.1415	+	7.16022i	0.625770	+	0.402158i	0.814741	−	0.579825i	$-0.196879\pi$
$317$	11.1415	+	7.16022i	0.625770	+	0.402158i	−0.188971	+	0.981983i	$0.560515\pi$
$318$	4.74738	−	5.47877i	0.266220	−	0.307234i
$319$	0.0297687	−	0.00874089i	0.00166673	−	0.000489396i
$320$	−0.253098	−	0.554206i	−0.0141486	−	0.0309811i
$321$	1.76724			0.0986379
$322$	1.17376	−	4.64998i	0.0654109	−	0.259133i
$323$	4.76660			0.265221
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	9.10181	−	2.67253i	0.504878	−	0.148245i
$326$	−4.51732	+	5.21327i	−0.250191	+	0.288736i
$327$	−5.71167	−	3.67067i	−0.315856	−	0.202988i
$328$	−3.08472	−	3.55996i	−0.170325	−	0.196566i
$329$	0.895727	+	6.22992i	0.0493830	+	0.343467i
$330$	−0.0515346	−	0.0151319i	−0.00283689	−	0.000832985i
$331$	−16.3712	+	10.5211i	−0.899843	+	0.578294i	−0.906744	−	0.421682i	$-0.861440\pi$
$331$	−16.3712	+	10.5211i	−0.899843	+	0.578294i	0.00690082	+	0.999976i	$0.497803\pi$
$332$	2.03826	−	14.1764i	0.111864	−	0.778030i
$333$	3.52292	−	7.71411i	0.193055	−	0.422731i
$334$	3.27201	−	7.16470i	0.179036	−	0.392035i
$335$	−0.621436	+	4.32218i	−0.0339527	+	0.236146i
$336$	0.841254	−	0.540641i	0.0458941	−	0.0294944i
$337$	4.35701	+	1.27933i	0.237342	+	0.0696898i	0.398240	−	0.917281i	$-0.369621\pi$
$337$	4.35701	+	1.27933i	0.237342	+	0.0696898i	−0.160899	+	0.986971i	$0.551439\pi$
$338$	−1.25239	−	8.71056i	−0.0681210	−	0.473792i
$339$	−6.49245	−	7.49269i	−0.352622	−	0.406947i
$340$	0.350950	+	0.225542i	0.0190329	+	0.0122317i
$341$	−0.358568	+	0.413809i	−0.0194175	+	0.0224090i
$342$	−6.67941	+	1.96125i	−0.361181	+	0.106052i
$343$	0.415415	+	0.909632i	0.0224303	+	0.0491155i
$344$	−1.42007			−0.0765652
$345$	−2.60940	+	1.31481i	−0.140485	+	0.0707868i
$346$	−17.0535			−0.916801
$347$	−1.66723	−	3.65073i	−0.0895018	−	0.195982i	0.859588	−	0.510988i	$-0.170720\pi$
$347$	−1.66723	−	3.65073i	−0.0895018	−	0.195982i	−0.949089	+	0.315007i	$0.897993\pi$
$348$	0.337683	−	0.0991526i	0.0181017	−	0.00531513i
$349$	−22.8296	+	26.3468i	−1.22204	+	1.41031i	−0.339151	+	0.940732i	$0.610140\pi$
$349$	−22.8296	+	26.3468i	−1.22204	+	1.41031i	−0.882891	+	0.469579i	$0.844406\pi$
$350$	3.89399	+	2.50252i	0.208143	+	0.133765i
$351$	−1.34204	−	1.54880i	−0.0716330	−	0.0826689i
$352$	0.0125459	+	0.0872586i	0.000668698	+	0.00465090i
$353$	29.7138	+	8.72476i	1.58151	+	0.464372i	0.950324	−	0.311263i	$-0.100752\pi$
$353$	29.7138	+	8.72476i	1.58151	+	0.464372i	0.631182	+	0.775635i	$0.282570\pi$
$354$	2.93418	−	1.88569i	0.155950	−	0.100223i
$355$	−1.18309	+	8.22859i	−0.0627921	+	0.436728i
$356$	2.42981	−	5.32053i	0.128779	−	0.281988i
$357$	−0.284443	+	0.622842i	−0.0150543	+	0.0329643i
$358$	−1.42544	+	9.91417i	−0.0753370	+	0.523980i
$359$	−15.8031	+	10.1560i	−0.834055	+	0.536014i	−0.886564	−	0.462606i	$-0.846914\pi$
$359$	−15.8031	+	10.1560i	−0.834055	+	0.536014i	0.0525092	+	0.998620i	$0.483278\pi$
$360$	−0.584585	−	0.171650i	−0.0308103	−	0.00904673i
$361$	−4.19275	−	29.1612i	−0.220671	−	1.53480i
$362$	5.06443	+	5.84466i	0.266180	+	0.307189i
$363$	−9.24725	−	5.94285i	−0.485355	−	0.311919i
$364$	−1.34204	+	1.54880i	−0.0703423	+	0.0811793i
$365$	−0.0194301	+	0.00570520i	−0.00101702	+	0.000298624i
$366$	−4.84779	−	10.6152i	−0.253398	−	0.554864i
$367$	17.3965			0.908091			0.454045	−	0.890979i	$-0.349980\pi$
$367$	17.3965			0.908091			0.454045	+	0.890979i	$0.349980\pi$
$368$	3.74217	+	2.99936i	0.195074	+	0.156352i
$369$	−4.71050			−0.245219
$370$	2.14639	+	4.69993i	0.111585	+	0.244338i
$371$	−6.95579	+	2.04241i	−0.361127	+	0.106036i
$372$	−4.06743	+	4.69406i	−0.210886	+	0.243376i
$373$	−29.1258	−	18.7180i	−1.50808	−	0.969183i	−0.993755	−	0.111586i	$-0.964407\pi$
$373$	−29.1258	−	18.7180i	−1.50808	−	0.969183i	−0.514323	−	0.857597i	$-0.671957\pi$
$374$	−0.0395287	−	0.0456186i	−0.00204398	−	0.00235888i
$375$	−0.834888	−	5.80677i	−0.0431134	−	0.299860i
$376$	−6.03903	−	1.77322i	−0.311439	−	0.0914468i
$377$	−0.606753	+	0.389936i	−0.0312494	+	0.0200827i
$378$	0.142315	−	0.989821i	0.00731989	−	0.0509109i
$379$	6.25291	−	13.6920i	0.321191	−	0.703309i	−0.678314	−	0.734772i	$-0.737289\pi$
$379$	6.25291	−	13.6920i	0.321191	−	0.703309i	0.999505	+	0.0314626i	$0.0100165\pi$
$380$	1.76191	−	3.85805i	0.0903842	−	0.197914i
$381$	0.0402026	−	0.279615i	0.00205964	−	0.0143251i
$382$	8.64028	−	5.55277i	0.442075	−	0.284105i
$383$	−21.7817	−	6.39569i	−1.11299	−	0.326805i	−0.326991	−	0.945027i	$-0.606035\pi$
$383$	−21.7817	−	6.39569i	−1.11299	−	0.326805i	−0.786003	+	0.618223i	$0.787853\pi$
$384$	0.142315	+	0.989821i	0.00726247	+	0.0505116i
$385$	0.0351727	+	0.0405915i	0.00179257	+	0.00206874i
$386$	−15.8751	−	10.2023i	−0.808023	−	0.519285i
$387$	−0.929949	+	1.07322i	−0.0472720	+	0.0545548i
$388$	−12.4146	+	3.64526i	−0.630257	+	0.185060i
$389$	−5.24270	−	11.4799i	−0.265816	−	0.582055i	0.728912	−	0.684607i	$-0.240026\pi$
$389$	−5.24270	−	11.4799i	−0.265816	−	0.582055i	−0.994728	+	0.102553i	$0.967299\pi$
$390$	1.24860			0.0632254
$391$	−3.26590	−	0.342393i	−0.165164	−	0.0173156i
$392$	−1.00000			−0.0505076
$393$	6.73801	+	14.7542i	0.339888	+	0.744250i
$394$	1.06952	−	0.314038i	0.0538814	−	0.0158210i
$395$	−4.72200	+	5.44948i	−0.237590	+	0.274193i
$396$	0.0741615	+	0.0476607i	0.00372675	+	0.00239504i
$397$	8.43675	+	9.73653i	0.423428	+	0.488662i	0.926878	−	0.375362i	$-0.122482\pi$
$397$	8.43675	+	9.73653i	0.423428	+	0.488662i	−0.503450	+	0.864024i	$0.667936\pi$
$398$	−2.64389	−	18.3887i	−0.132526	−	0.921740i
$399$	6.67941	+	1.96125i	0.334389	+	0.0981854i
$400$	−3.89399	+	2.50252i	−0.194700	+	0.125126i
$401$	−5.11427	+	35.5705i	−0.255394	+	1.77631i	0.309258	+	0.950978i	$0.399919\pi$
$401$	−5.11427	+	35.5705i	−0.255394	+	1.77631i	−0.564652	+	0.825329i	$0.690990\pi$
$402$	2.97730	−	6.51937i	0.148494	−	0.325157i
$403$	5.28775	−	11.5786i	0.263402	−	0.576769i
$404$	2.36381	−	16.4406i	0.117604	−	0.817952i
$405$	−0.512546	+	0.329393i	−0.0254686	+	0.0163677i
$406$	−0.337683	−	0.0991526i	−0.0167589	−	0.00492086i
$407$	−0.106395	−	0.739994i	−0.00527381	−	0.0366802i
$408$	−0.448396	−	0.517476i	−0.0221989	−	0.0256189i
$409$	−2.77974	−	1.78643i	−0.137449	−	0.0883333i	0.470109	−	0.882608i	$-0.344215\pi$
$409$	−2.77974	−	1.78643i	−0.137449	−	0.0883333i	−0.607558	+	0.794275i	$0.707851\pi$
$410$	1.87941	−	2.16895i	0.0928174	−	0.107117i
$411$	−18.0488	+	5.29960i	−0.890281	+	0.261410i
$412$	5.50656	+	12.0577i	0.271289	+	0.594039i
$413$	−3.48787			−0.171627
$414$	4.71737	−	0.863983i	0.231846	−	0.0424625i
$415$	8.72599			0.428342
$416$	−0.851334	−	1.86416i	−0.0417401	−	0.0913981i
$417$	−0.838042	+	0.246071i	−0.0410391	+	0.0120502i
$418$	−0.401880	+	0.463795i	−0.0196566	+	0.0226849i
$419$	−11.1107	−	7.14039i	−0.542791	−	0.348831i	0.240339	−	0.970689i	$-0.422742\pi$
$419$	−11.1107	−	7.14039i	−0.542791	−	0.348831i	−0.783130	+	0.621858i	$0.786378\pi$
$420$	0.398983	+	0.460451i	0.0194684	+	0.0224677i
$421$	1.70985	+	11.8923i	0.0833331	+	0.579595i	0.988115	+	0.153719i	$0.0491250\pi$
$421$	1.70985	+	11.8923i	0.0833331	+	0.579595i	−0.904782	+	0.425876i	$0.859966\pi$
$422$	9.70797	+	2.85052i	0.472577	+	0.138761i
$423$	−5.29484	+	3.40278i	−0.257444	+	0.165449i
$424$	1.03170	−	7.17566i	0.0501040	−	0.348481i
$425$	1.31663	−	2.88301i	0.0638658	−	0.139847i
$426$	5.66820	−	12.4116i	0.274625	−	0.601345i
$427$	−1.66078	+	11.5510i	−0.0803707	+	0.558991i
$428$	1.48670	−	0.955444i	0.0718623	−	0.0461831i
$429$	−0.173345	−	0.0508987i	−0.00836918	−	0.00245741i
$430$	−0.123131	−	0.856393i	−0.00593789	−	0.0412989i
$431$	20.6284	+	23.8065i	0.993637	+	1.14672i	0.989177	+	0.146729i	$0.0468744\pi$
$431$	20.6284	+	23.8065i	0.993637	+	1.14672i	0.00446049	+	0.999990i	$0.498580\pi$
$432$	0.841254	+	0.540641i	0.0404748	+	0.0260116i
$433$	3.85275	−	4.44631i	0.185151	−	0.213676i	−0.655584	−	0.755122i	$-0.727578\pi$
$433$	3.85275	−	4.44631i	0.185151	−	0.213676i	0.840735	+	0.541446i	$0.182123\pi$
$434$	5.95954	−	1.74988i	0.286067	−	0.0839968i
$435$	0.0890748	+	0.195047i	0.00427081	+	0.00935177i
$436$	−6.78948			−0.325157
$437$	1.27977	+	33.3612i	0.0612198	+	1.59588i
$438$	0.0332375			0.00158815
$439$	−4.82424	−	10.5636i	−0.230248	−	0.504174i	0.758879	−	0.651231i	$-0.225747\pi$
$439$	−4.82424	−	10.5636i	−0.230248	−	0.504174i	−0.989128	+	0.147057i	$0.953020\pi$
$440$	−0.0515346	+	0.0151319i	−0.00245682	+	0.000721387i
$441$	−0.654861	+	0.755750i	−0.0311838	+	0.0359881i
$442$	1.18048	+	0.758646i	0.0561495	+	0.0360851i
$443$	8.35045	+	9.63693i	0.396742	+	0.457864i	0.918612	−	0.395160i	$-0.129311\pi$
$443$	8.35045	+	9.63693i	0.396742	+	0.457864i	−0.521870	+	0.853025i	$0.674766\pi$
$444$	−1.20690	−	8.39415i	−0.0572768	−	0.398369i
$445$	3.41930	+	1.00400i	0.162090	+	0.0475940i
$446$	9.82664	−	6.31520i	0.465305	−	0.299033i
$447$	0.715767	−	4.97827i	0.0338546	−	0.235464i
$448$	0.415415	−	0.909632i	0.0196265	−	0.0429761i
$449$	1.99238	−	4.36271i	0.0940263	−	0.205889i	−0.856775	−	0.515691i	$-0.827535\pi$
$449$	1.99238	−	4.36271i	0.0940263	−	0.205889i	0.950801	+	0.309802i	$0.100263\pi$
$450$	−0.658746	+	4.58168i	−0.0310536	+	0.215983i
$451$	−0.349337	+	0.224505i	−0.0164497	+	0.0105716i
$452$	−9.51265	−	2.79317i	−0.447438	−	0.131380i
$453$	1.87239	+	13.0228i	0.0879725	+	0.611863i
$454$	10.3790	+	11.9781i	0.487113	+	0.562158i
$455$	−1.05039	−	0.675045i	−0.0492431	−	0.0316466i
$456$	−4.55875	+	5.26107i	−0.213483	+	0.246372i
$457$	−40.4655	+	11.8818i	−1.89290	+	0.555805i	−0.900152	+	0.435577i	$0.856544\pi$
$457$	−40.4655	+	11.8818i	−1.89290	+	0.555805i	−0.992746	+	0.120228i	$0.961637\pi$
$458$	9.30270	+	20.3701i	0.434687	+	0.951831i
$459$	−0.684719			−0.0319599
$460$	−1.48433	+	2.51683i	−0.0692071	+	0.117348i
$461$	−21.3110			−0.992553			−0.496277	−	0.868165i	$-0.665300\pi$
$461$	−21.3110			−0.992553			−0.496277	+	0.868165i	$0.665300\pi$
$462$	−0.0366213	−	0.0801894i	−0.00170378	−	0.00373075i
$463$	−27.6524	+	8.11947i	−1.28512	+	0.377344i	−0.851785	−	0.523892i	$-0.824480\pi$
$463$	−27.6524	+	8.11947i	−1.28512	+	0.377344i	−0.433330	+	0.901235i	$0.642662\pi$
$464$	0.230471	−	0.265977i	0.0106993	−	0.0123477i
$465$	−3.18349	−	2.04590i	−0.147631	−	0.0948766i
$466$	−10.7976	−	12.4611i	−0.500187	−	0.577247i
$467$	−1.82546	−	12.6964i	−0.0844723	−	0.587518i	−0.987462	−	0.157856i	$-0.949542\pi$
$467$	−1.82546	−	12.6964i	−0.0844723	−	0.587518i	0.902990	−	0.429662i	$-0.141367\pi$
$468$	−1.96635	−	0.577371i	−0.0908944	−	0.0266890i
$469$	−6.02930	+	3.87480i	−0.278407	+	0.178922i
$470$	0.545735	−	3.79567i	0.0251729	−	0.175081i
$471$	−0.0612428	+	0.134103i	−0.00282192	+	0.00617914i
$472$	1.44891	−	3.17268i	0.0666917	−	0.146034i
$473$	−0.0178161	+	0.123914i	−0.000819184	+	0.00569755i
$474$	9.95630	−	6.39852i	0.457308	−	0.293894i
$475$	−30.9176	−	9.07824i	−1.41860	−	0.416538i
$476$	0.0974457	+	0.677750i	0.00446642	+	0.0310646i
$477$	−4.74738	−	5.47877i	−0.217368	−	0.250856i
$478$	−14.0473	−	9.02763i	−0.642507	−	0.412914i
$479$	20.9079	−	24.1290i	0.955305	−	1.10248i	−0.0393499	−	0.999225i	$-0.512529\pi$
$479$	20.9079	−	24.1290i	0.955305	−	1.10248i	0.994655	−	0.103255i	$-0.0329259\pi$
$480$	−0.584585	+	0.171650i	−0.0266825	+	0.00783470i
$481$	7.21972	+	15.8090i	0.329191	+	0.720828i
$482$	−13.5398			−0.616719
$483$	−4.43560	−	1.82357i	−0.201827	−	0.0829754i
$484$	−10.9922			−0.499647
$485$	−3.27476	−	7.17072i	−0.148699	−	0.325606i
$486$	0.959493	−	0.281733i	0.0435235	−	0.0127796i
$487$	−17.0839	+	19.7159i	−0.774146	+	0.893412i	−0.996672	−	0.0815143i	$-0.974024\pi$
$487$	−17.0839	+	19.7159i	−0.774146	+	0.893412i	0.222526	+	0.974927i	$0.428570\pi$
$488$	−9.81722	−	6.30915i	−0.444405	−	0.285602i
$489$	4.51732	+	5.21327i	0.204280	+	0.235752i
$490$	−0.0867074	−	0.603063i	−0.00391704	−	0.0272436i
$491$	21.6152	+	6.34681i	0.975483	+	0.286428i	0.730358	−	0.683064i	$-0.239353\pi$
$491$	21.6152	+	6.34681i	0.975483	+	0.286428i	0.245124	+	0.969492i	$0.421171\pi$
$492$	−3.96272	+	2.54669i	−0.178653	+	0.114813i
$493$	−0.0342949	+	0.238526i	−0.00154456	+	0.0107427i
$494$	5.92648	−	12.9772i	0.266645	−	0.583871i
$495$	−0.0223121	+	0.0488566i	−0.00100285	+	0.00219594i
$496$	−0.883936	+	6.14791i	−0.0396899	+	0.276049i
$497$	−11.4786	+	7.37686i	−0.514887	+	0.330897i
$498$	−13.7420	−	4.03502i	−0.615795	−	0.180814i
$499$	−5.08154	−	35.3429i	−0.227481	−	1.58216i	−0.708666	−	0.705544i	$-0.750703\pi$
$499$	−5.08154	−	35.3429i	−0.227481	−	1.58216i	0.481185	−	0.876619i	$-0.340207\pi$
$500$	−3.84173	−	4.43359i	−0.171807	−	0.198276i
$501$	−6.62612	−	4.25835i	−0.296033	−	0.190249i
$502$	−14.6408	+	16.8964i	−0.653453	+	0.754125i
$503$	−8.45400	+	2.48232i	−0.376945	+	0.110681i	−0.464716	−	0.885460i	$-0.653844\pi$
$503$	−8.45400	+	2.48232i	−0.376945	+	0.110681i	0.0877712	+	0.996141i	$0.472026\pi$
$504$	−0.415415	−	0.909632i	−0.0185041	−	0.0405182i
$505$	10.1197			0.450321
$506$	0.308669	−	0.288907i	0.0137220	−	0.0128435i
$507$	−8.80013			−0.390827
$508$	−0.117351	−	0.256962i	−0.00520660	−	0.0114009i
$509$	29.9522	−	8.79476i	1.32761	−	0.389821i	0.460375	−	0.887724i	$-0.347715\pi$
$509$	29.9522	−	8.79476i	1.32761	−	0.389821i	0.867232	+	0.497904i	$0.165897\pi$
$510$	0.273192	−	0.315280i	0.0120971	−	0.0139608i
$511$	−0.0279611	−	0.0179695i	−0.00123693	−	0.000794925i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	0.990710	+	6.89054i	0.0437409	+	0.304225i
$514$	−3.92759	−	1.15325i	−0.173239	−	0.0508675i
$515$	−6.79408	+	4.36629i	−0.299383	+	0.192402i
$516$	−0.202097	+	1.40562i	−0.00889684	+	0.0618789i
$517$	−0.230494	+	0.504711i	−0.0101371	+	0.0221972i
$518$	−3.52292	+	7.71411i	−0.154788	+	0.338939i
$519$	−2.42696	+	16.8799i	−0.106532	+	0.740945i
$520$	1.05039	−	0.675045i	0.0460627	−	0.0296027i
$521$	−16.9106	−	4.96539i	−0.740865	−	0.217538i	−0.110543	−	0.993871i	$-0.535259\pi$
$521$	−16.9106	−	4.96539i	−0.740865	−	0.217538i	−0.630322	+	0.776334i	$0.717077\pi$
$522$	−0.0500861	−	0.348356i	−0.00219221	−	0.0152471i
$523$	6.58694	+	7.60174i	0.288027	+	0.332401i	0.881262	−	0.472629i	$-0.156695\pi$
$523$	6.58694	+	7.60174i	0.288027	+	0.332401i	−0.593235	+	0.805030i	$0.702149\pi$
$524$	13.6451	+	8.76916i	0.596088	+	0.383083i
$525$	3.03122	−	3.49821i	0.132293	−	0.152674i
$526$	−19.0566	+	5.59552i	−0.830907	+	0.243976i
$527$	−1.76671	−	3.86856i	−0.0769591	−	0.168517i
$528$	0.0881559			0.00383649
$529$	1.51954	−	22.9497i	0.0660669	−	0.997815i
$530$	4.41683			0.191855
$531$	−1.44891	−	3.17268i	−0.0628775	−	0.137683i
$532$	6.67941	−	1.96125i	0.289589	−	0.0850311i
$533$	6.32170	−	7.29563i	0.273823	−	0.316009i
$534$	−4.92058	−	3.16226i	−0.212934	−	0.136845i
$535$	0.705101	+	0.813729i	0.0304842	+	0.0351806i
$536$	−1.01998	−	7.09410i	−0.0440563	−	0.306418i
$537$	9.61040	+	2.82187i	0.414719	+	0.121773i
$538$	8.77307	−	5.63811i	0.378234	−	0.243076i
$539$	−0.0125459	+	0.0872586i	−0.000540390	+	0.00375849i
$540$	−0.253098	+	0.554206i	−0.0108916	+	0.0238492i
$541$	16.0842	−	35.2194i	0.691512	−	1.51420i	−0.158456	−	0.987366i	$-0.550652\pi$
$541$	16.0842	−	35.2194i	0.691512	−	1.51420i	0.849968	−	0.526834i	$-0.176621\pi$
$542$	−1.69820	+	11.8112i	−0.0729440	+	0.507336i
$543$	6.50592	−	4.18110i	0.279196	−	0.179428i
$544$	−0.656983	−	0.192908i	−0.0281679	−	0.00827085i
$545$	−0.588698	−	4.09448i	−0.0252170	−	0.175388i
$546$	1.34204	+	1.54880i	0.0574342	+	0.0662826i
$547$	−7.15239	−	4.59656i	−0.305814	−	0.196535i	0.378728	−	0.925508i	$-0.376361\pi$
$547$	−7.15239	−	4.59656i	−0.305814	−	0.196535i	−0.684542	+	0.728973i	$0.739998\pi$
$548$	−12.3184	+	14.2162i	−0.526217	+	0.607287i
$549$	−11.1970	+	3.28775i	−0.477878	+	0.140318i
$550$	0.169513	+	0.371181i	0.00722804	+	0.0158272i
$551$	2.44998			0.104373
$552$	3.50140	−	3.27723i	0.149029	−	0.139488i
$553$	−11.8351			−0.503279
$554$	−1.73146	−	3.79138i	−0.0735629	−	0.161080i
$555$	4.95756	−	1.45567i	0.210437	−	0.0617898i
$556$	−0.571969	+	0.660088i	−0.0242569	+	0.0279940i
$557$	7.52202	+	4.83411i	0.318718	+	0.204828i	0.690211	−	0.723608i	$-0.257518\pi$
$557$	7.52202	+	4.83411i	0.318718	+	0.204828i	−0.371493	+	0.928436i	$0.621154\pi$
$558$	4.06743	+	4.69406i	0.172188	+	0.198715i
$559$	−0.414170	−	2.88062i	−0.0175175	−	0.121837i
$560$	0.584585	+	0.171650i	0.0247032	+	0.00725352i
$561$	−0.0507798	+	0.0326342i	−0.00214392	+	0.00137782i
$562$	1.08995	−	7.58078i	0.0459768	−	0.319776i
$563$	3.48542	−	7.63201i	0.146893	−	0.321651i	−0.821855	−	0.569696i	$-0.807061\pi$
$563$	3.48542	−	7.63201i	0.146893	−	0.321651i	0.968748	+	0.248045i	$0.0797882\pi$
$564$	−2.61462	+	5.72521i	−0.110095	+	0.241075i
$565$	0.859639	−	5.97892i	0.0361653	−	0.251535i
$566$	11.8461	−	7.61303i	0.497929	−	0.320000i
$567$	−0.959493	−	0.281733i	−0.0402949	−	0.0118317i
$568$	−1.94184	−	13.5058i	−0.0814777	−	0.566690i
$569$	−4.45869	−	5.14561i	−0.186918	−	0.215715i	0.654554	−	0.756015i	$-0.272856\pi$
$569$	−4.45869	−	5.14561i	−0.186918	−	0.215715i	−0.841473	+	0.540300i	$0.818311\pi$
$570$	−3.56804	−	2.29304i	−0.149449	−	0.0960448i
$571$	−1.00813	+	1.16344i	−0.0421889	+	0.0486886i	−0.776452	−	0.630177i	$-0.782982\pi$
$571$	−1.00813	+	1.16344i	−0.0421889	+	0.0486886i	0.734263	+	0.678865i	$0.237528\pi$
$572$	−0.173345	+	0.0508987i	−0.00724792	+	0.00212818i
$573$	−4.26661	−	9.34258i	−0.178240	−	0.390292i
$574$	4.71050			0.196612
$575$	20.5315	+	8.44094i	0.856223	+	0.352012i
$576$	1.00000			0.0416667
$577$	7.29746	+	15.9792i	0.303797	+	0.665223i	0.998539	−	0.0540363i	$-0.0172087\pi$
$577$	7.29746	+	15.9792i	0.303797	+	0.665223i	−0.694742	+	0.719259i	$0.744481\pi$
$578$	−15.8615	+	4.65737i	−0.659753	+	0.193721i
$579$	−12.3578	+	14.2616i	−0.513571	+	0.592692i
$580$	0.180385	+	0.115926i	0.00749007	+	0.00481357i
$581$	9.37903	+	10.8240i	0.389108	+	0.449054i
$582$	1.84137	+	12.8070i	0.0763273	+	0.530868i
$583$	−0.613194	−	0.180050i	−0.0253959	−	0.00745691i
$584$	0.0279611	−	0.0179695i	0.00115704	−	0.000743584i
$585$	0.177695	−	1.23589i	0.00734677	−	0.0510979i
$586$	8.86881	−	19.4200i	0.366367	−	0.802233i
$587$	−2.29444	+	5.02411i	−0.0947015	+	0.207367i	−0.951054	−	0.309024i	$-0.899998\pi$
$587$	−2.29444	+	5.02411i	−0.0947015	+	0.207367i	0.856353	+	0.516391i	$0.172725\pi$
$588$	−0.142315	+	0.989821i	−0.00586897	+	0.0408195i
$589$	−36.3743	+	23.3763i	−1.49878	+	0.963204i
$590$	2.03896	+	0.598692i	0.0839425	+	0.0246478i
$591$	−0.158634	−	1.10332i	−0.00652532	−	0.0453846i
$592$	−5.55353	−	6.40911i	−0.228249	−	0.263413i
$593$	−18.4431	−	11.8527i	−0.757368	−	0.486731i	0.104085	−	0.994568i	$-0.466809\pi$
$593$	−18.4431	−	11.8527i	−0.757368	−	0.486731i	−0.861453	+	0.507838i	$0.830445\pi$
$594$	0.0577299	−	0.0666238i	0.00236868	−	0.00273361i
$595$	−0.400276	+	0.117532i	−0.0164097	+	0.00481833i
$596$	−2.08932	−	4.57496i	−0.0855817	−	0.187398i
$597$	−18.5777			−0.760337
$598$	−4.99278	+	8.46577i	−0.204170	+	0.346191i
$599$	5.57631			0.227842			0.113921	−	0.993490i	$-0.463659\pi$
$599$	5.57631			0.227842			0.113921	+	0.993490i	$0.463659\pi$
$600$	1.92287	+	4.21050i	0.0785009	+	0.171893i
$601$	22.4304	−	6.58616i	0.914955	−	0.268655i	0.209830	−	0.977738i	$-0.432709\pi$
$601$	22.4304	−	6.58616i	0.914955	−	0.268655i	0.705125	+	0.709083i	$0.250891\pi$
$602$	0.929949	−	1.07322i	0.0379019	−	0.0437411i
$603$	−6.02930	−	3.87480i	−0.245532	−	0.157794i
$604$	8.61579	+	9.94315i	0.350571	+	0.404581i
$605$	−0.953107	−	6.62901i	−0.0387493	−	0.269507i
$606$	−15.9369	−	4.67949i	−0.647392	−	0.190091i
$607$	−33.0740	+	21.2554i	−1.34243	+	0.862729i	−0.997126	−	0.0757610i	$-0.975861\pi$
$607$	−33.0740	+	21.2554i	−1.34243	+	0.862729i	−0.345306	+	0.938490i	$0.612225\pi$
$608$	−0.990710	+	6.89054i	−0.0401786	+	0.279448i
$609$	−0.146201	+	0.320135i	−0.00592435	+	0.0129725i
$610$	2.95359	−	6.46745i	0.119587	−	0.261860i
$611$	1.83567	−	12.7673i	0.0742631	−	0.516511i
$612$	−0.576022	+	0.370187i	−0.0232843	+	0.0149639i
$613$	8.47747	+	2.48921i	0.342402	+	0.100538i	0.448412	−	0.893827i	$-0.351990\pi$
$613$	8.47747	+	2.48921i	0.342402	+	0.100538i	−0.106011	+	0.994365i	$0.533808\pi$
$614$	−2.05955	−	14.3245i	−0.0831167	−	0.578089i
$615$	−1.87941	−	2.16895i	−0.0757851	−	0.0874607i
$616$	−0.0741615	−	0.0476607i	−0.00298805	−	0.00192030i
$617$	23.5549	−	27.1838i	0.948285	−	1.09438i	−0.0471454	−	0.998888i	$-0.515012\pi$
$617$	23.5549	−	27.1838i	0.948285	−	1.09438i	0.995430	−	0.0954911i	$-0.0304421\pi$
$618$	12.7186	−	3.73452i	0.511618	−	0.150225i
$619$	4.35896	+	9.54479i	0.175201	+	0.383637i	0.976778	−	0.214255i	$-0.0687323\pi$
$619$	4.35896	+	9.54479i	0.175201	+	0.383637i	−0.801576	+	0.597892i	$0.796005\pi$
$620$	−3.78422			−0.151978
$621$	−0.183838	−	4.79231i	−0.00737718	−	0.192309i
$622$	25.1804			1.00964
$623$	2.42981	+	5.32053i	0.0973481	+	0.213163i
$624$	−1.96635	+	0.577371i	−0.0787168	+	0.0231133i
$625$	−12.8155	+	14.7898i	−0.512618	+	0.591593i
$626$	8.69788	+	5.58979i	0.347637	+	0.223413i
$627$	0.401880	+	0.463795i	0.0160496	+	0.0185222i
$628$	0.0209809	+	0.145925i	0.000837227	+	0.00582304i
$629$	5.57153	+	1.63595i	0.222151	+	0.0652295i
$630$	0.512546	−	0.329393i	0.0204203	−	0.0131233i
$631$	−0.396629	+	2.75861i	−0.0157895	+	0.109819i	−0.996192	−	0.0871864i	$-0.972212\pi$
$631$	−0.396629	+	2.75861i	−0.0157895	+	0.109819i	0.980402	+	0.197005i	$0.0631215\pi$
$632$	4.91647	−	10.7656i	0.195567	−	0.428231i
$633$	4.20309	−	9.20349i	0.167058	−	0.365806i
$634$	1.88481	−	13.1091i	0.0748554	−	0.520631i
$635$	0.144789	−	0.0930504i	0.00574579	−	0.00369259i
$636$	−6.95579	−	2.04241i	−0.275815	−	0.0809866i
$637$	−0.291654	−	2.02850i	−0.0115558	−	0.0803721i
$638$	−0.0203174	−	0.0234475i	−0.000804372	−	0.000928295i
$639$	−11.4786	−	7.37686i	−0.454087	−	0.291824i
$640$	−0.398983	+	0.460451i	−0.0157712	+	0.0182009i
$641$	29.5134	−	8.66591i	1.16571	−	0.342283i	0.359060	−	0.933315i	$-0.383097\pi$
$641$	29.5134	−	8.66591i	1.16571	−	0.342283i	0.806648	+	0.591032i	$0.201279\pi$
$642$	−0.734139	−	1.60754i	−0.0289742	−	0.0634446i
$643$	17.4407			0.687796			0.343898	−	0.939007i	$-0.388253\pi$
$643$	17.4407			0.687796			0.343898	+	0.939007i	$0.388253\pi$
$644$	−4.71737	+	0.863983i	−0.185890	+	0.0340457i
$645$	−0.865199			−0.0340672
$646$	−1.98012	−	4.33585i	−0.0779067	−	0.170592i
$647$	4.33236	−	1.27210i	0.170323	−	0.0500113i	−0.195459	−	0.980712i	$-0.562620\pi$
$647$	4.33236	−	1.27210i	0.170323	−	0.0500113i	0.365782	+	0.930701i	$0.380802\pi$
$648$	0.654861	−	0.755750i	0.0257254	−	0.0296886i
$649$	−0.258666	−	0.166234i	−0.0101535	−	0.00652527i
$650$	−6.21205	−	7.16909i	−0.243657	−	0.281195i
$651$	−0.883936	−	6.14791i	−0.0346442	−	0.240956i
$652$	6.61872	+	1.94343i	0.259209	+	0.0761106i
$653$	−21.7829	+	13.9990i	−0.852429	+	0.547823i	−0.892331	−	0.451381i	$-0.850932\pi$
$653$	−21.7829	+	13.9990i	−0.852429	+	0.547823i	0.0399025	+	0.999204i	$0.487295\pi$
$654$	−0.966243	+	6.72037i	−0.0377831	+	0.262787i
$655$	−4.10523	+	8.98920i	−0.160405	+	0.351237i
$656$	−1.95681	+	4.28482i	−0.0764006	+	0.167294i
$657$	0.00473018	−	0.0328992i	0.000184542	−	0.00128352i
$658$	5.29484	−	3.40278i	0.206414	−	0.132654i
$659$	−10.6557	−	3.12880i	−0.415088	−	0.121881i	0.0675187	−	0.997718i	$-0.478492\pi$
$659$	−10.6557	−	3.12880i	−0.415088	−	0.121881i	−0.482607	+	0.875837i	$0.660310\pi$
$660$	0.00764377	+	0.0531636i	0.000297533	+	0.00206939i
$661$	−21.9941	−	25.3825i	−0.855471	−	0.987266i	0.144526	−	0.989501i	$-0.453834\pi$
$661$	−21.9941	−	25.3825i	−0.855471	−	0.987266i	−0.999998	+	0.00223454i	$0.999289\pi$
$662$	16.3712	+	10.5211i	0.636285	+	0.408916i
$663$	0.918924	−	1.06049i	0.0356880	−	0.0411862i
$664$	−13.7420	+	4.03502i	−0.533294	+	0.156589i
$665$	1.76191	+	3.85805i	0.0683241	+	0.149609i
$666$	−8.48047			−0.328612
$667$	−1.67864	−	0.175987i	−0.0649971	−	0.00681423i
$668$	−7.87648			−0.304750
$669$	−4.85244	−	10.6254i	−0.187606	−	0.410800i
$670$	4.18975	−	1.23022i	0.161864	−	0.0475276i
$671$	−0.673693	+	0.777483i	−0.0260076	+	0.0300144i
$672$	−0.841254	−	0.540641i	−0.0324521	−	0.0208557i
$673$	4.11046	+	4.74373i	0.158447	+	0.182857i	0.829422	−	0.558622i	$-0.188670\pi$
$673$	4.11046	+	4.74373i	0.158447	+	0.182857i	−0.670975	+	0.741480i	$0.734124\pi$
$674$	−0.646245	−	4.49473i	−0.0248924	−	0.173131i
$675$	4.44130	+	1.30408i	0.170946	+	0.0501942i
$676$	−7.40314	+	4.75771i	−0.284736	+	0.182989i
$677$	2.48960	−	17.3155i	0.0956830	−	0.665490i	−0.884375	−	0.466777i	$-0.845415\pi$
$677$	2.48960	−	17.3155i	0.0956830	−	0.665490i	0.980058	−	0.198712i	$-0.0636760\pi$
$678$	−4.11853	+	9.01832i	−0.158171	+	0.346346i
$679$	5.37494	−	11.7695i	0.206271	−	0.451671i
$680$	0.0593702	−	0.412929i	0.00227674	−	0.0158351i
$681$	13.3332	−	8.56875i	0.510931	−	0.328355i
$682$	0.525368	+	0.154262i	0.0201174	+	0.00590700i
$683$	2.62635	+	18.2666i	0.100494	+	0.698954i	0.976321	+	0.216328i	$0.0694079\pi$
$683$	2.62635	+	18.2666i	0.100494	+	0.698954i	−0.875826	+	0.482626i	$0.839683\pi$
$684$	4.55875	+	5.26107i	0.174308	+	0.201162i
$685$	−9.64138	−	6.19614i	−0.368378	−	0.236742i
$686$	0.654861	−	0.755750i	0.0250027	−	0.0288547i
$687$	21.4866	−	6.30905i	0.819767	−	0.240705i
$688$	0.589919	+	1.29174i	0.0224905	+	0.0492472i
$689$	14.8567			0.565996
$690$	2.27997	+	1.82740i	0.0867971	+	0.0695680i
$691$	34.6050			1.31644			0.658218	−	0.752827i	$-0.271310\pi$
$691$	34.6050			1.31644			0.658218	+	0.752827i	$0.271310\pi$
$692$	7.08427	+	15.5124i	0.269304	+	0.589693i
$693$	−0.0845850	+	0.0248364i	−0.00321312	+	0.000943457i
$694$	−2.62823	+	3.03314i	−0.0997662	+	0.115136i
$695$	−0.447669	−	0.287699i	−0.0169810	−	0.0109130i
$696$	−0.230471	−	0.265977i	−0.00873597	−	0.0100818i
$697$	−0.459017	−	3.19254i	−0.0173865	−	0.120926i
$698$	33.4496	+	9.82170i	1.26609	+	0.371757i
$699$	−13.8709	+	8.91427i	−0.524644	+	0.337169i
$700$	0.658746	−	4.58168i	0.0248983	−	0.173171i
$701$	2.77285	−	6.07169i	0.104729	−	0.229325i	−0.850012	−	0.526764i	$-0.823405\pi$
$701$	2.77285	−	6.07169i	0.104729	−	0.229325i	0.954741	+	0.297439i	$0.0961326\pi$
$702$	−0.851334	+	1.86416i	−0.0321315	+	0.0703583i
$703$	8.40169	−	58.4351i	0.316876	−	2.20392i
$704$	0.0741615	−	0.0476607i	0.00279507	−	0.00179628i
$705$	−3.67937	−	1.08036i	−0.138573	−	0.0406887i
$706$	−4.40724	−	30.6530i	−0.165869	−	1.15364i
$707$	10.8770	+	12.5528i	0.409073	+	0.472095i
$708$	−2.93418	−	1.88569i	−0.110273	−	0.0708684i
$709$	18.9799	−	21.9040i	0.712804	−	0.822620i	−0.277618	−	0.960692i	$-0.589545\pi$
$709$	18.9799	−	21.9040i	0.712804	−	0.822620i	0.990422	+	0.138071i	$0.0440904\pi$
$710$	7.97647	−	2.34210i	0.299351	−	0.0878975i
$711$	−4.91647	−	10.7656i	−0.184382	−	0.403740i
$712$	−5.84910			−0.219204
$713$	26.6014	−	13.4038i	0.996232	−	0.501975i
$714$	0.684719			0.0256250
$715$	−0.0457254	−	0.100125i	−0.00171003	−	0.00374445i
$716$	9.61040	−	2.82187i	0.359157	−	0.105458i
$717$	−10.9349	+	12.6195i	−0.408370	+	0.471284i
$718$	15.8031	+	10.1560i	0.589766	+	0.379019i
$719$	−2.98425	−	3.44401i	−0.111294	−	0.128440i	0.697369	−	0.716712i	$-0.254354\pi$
$719$	−2.98425	−	3.44401i	−0.111294	−	0.128440i	−0.808663	+	0.588272i	$0.799808\pi$
$720$	0.0867074	+	0.603063i	0.00323139	+	0.0224748i
$721$	−12.7186	−	3.73452i	−0.473666	−	0.139081i
$722$	−24.7842	+	15.9279i	−0.922373	+	0.592773i
$723$	−1.92691	+	13.4019i	−0.0716625	+	0.498424i
$724$	3.21265	−	7.03473i	0.119397	−	0.261444i
$725$	0.676733	−	1.48184i	0.0251332	−	0.0550341i
$726$	−1.56436	+	10.8803i	−0.0580587	+	0.403807i
$727$	−10.1157	+	6.50094i	−0.375169	+	0.241107i	−0.714613	−	0.699520i	$-0.753397\pi$
$727$	−10.1157	+	6.50094i	−0.375169	+	0.241107i	0.339444	+	0.940626i	$0.389761\pi$
$728$	1.96635	+	0.577371i	0.0728776	+	0.0213988i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	0.0132612	+	0.0153042i	0.000490819	+	0.000566435i
$731$	−0.817993	−	0.525692i	−0.0302546	−	0.0194434i
$732$	−7.64206	+	8.81941i	−0.282459	+	0.325975i
$733$	2.62673	−	0.771279i	0.0970206	−	0.0284878i	−0.232862	−	0.972510i	$-0.574809\pi$
$733$	2.62673	−	0.771279i	0.0970206	−	0.0284878i	0.329883	+	0.944022i	$0.392991\pi$
$734$	−7.22677	−	15.8244i	−0.266745	−	0.584090i
$735$	−0.609264			−0.0224731
$736$	1.17376	−	4.64998i	0.0432653	−	0.171400i
$737$	−0.631818			−0.0232733
$738$	1.95681	+	4.28482i	0.0720312	+	0.157726i
$739$	31.4328	−	9.22951i	1.15627	−	0.339513i	0.353291	−	0.935514i	$-0.385063\pi$
$739$	31.4328	−	9.22951i	1.15627	−	0.339513i	0.802984	+	0.596001i	$0.203244\pi$
$740$	3.38357	−	3.90485i	0.124382	−	0.143545i
$741$	−12.0017	−	7.71300i	−0.440892	−	0.283344i
$742$	4.74738	+	5.47877i	0.174282	+	0.201132i
$743$	0.333629	+	2.32044i	0.0122397	+	0.0851288i	0.995026	−	0.0996188i	$-0.0317623\pi$
$743$	0.333629	+	2.32044i	0.0122397	+	0.0851288i	−0.982786	+	0.184748i	$0.940853\pi$
$744$	5.95954	+	1.74988i	0.218487	+	0.0641536i
$745$	2.57783	−	1.65667i	0.0944444	−	0.0606958i
$746$	−4.92721	+	34.2695i	−0.180398	+	1.25470i
$747$	−5.94964	+	13.0279i	−0.217686	+	0.476666i
$748$	−0.0250753	+	0.0549072i	−0.000916844	+	0.00200761i
$749$	−0.251505	+	1.74925i	−0.00918979	+	0.0639164i
$750$	−4.93520	+	3.17166i	−0.180208	+	0.115813i
$751$	−20.9790	−	6.16000i	−0.765536	−	0.224782i	−0.124424	−	0.992229i	$-0.539708\pi$
$751$	−20.9790	−	6.16000i	−0.765536	−	0.224782i	−0.641112	+	0.767447i	$0.721527\pi$
$752$	0.895727	+	6.22992i	0.0326638	+	0.227182i
$753$	14.6408	+	16.8964i	0.533542	+	0.615740i
$754$	0.606753	+	0.389936i	0.0220966	+	0.0142006i
$755$	−5.24929	+	6.05801i	−0.191041	+	0.220473i
$756$	−0.959493	+	0.281733i	−0.0348964	+	0.0102465i
$757$	13.5681	+	29.7101i	0.493143	+	1.07983i	0.978638	+	0.205593i	$0.0659122\pi$
$757$	13.5681	+	29.7101i	0.493143	+	1.07983i	−0.485495	+	0.874239i	$0.661361\pi$
$758$	−15.0522			−0.546721
$759$	−0.242038	−	0.346643i	−0.00878544	−	0.0125823i
$760$	−4.24133			−0.153849
$761$	3.94599	+	8.64052i	0.143042	+	0.313218i	0.967570	−	0.252603i	$-0.0812865\pi$
$761$	3.94599	+	8.64052i	0.143042	+	0.313218i	−0.824528	+	0.565821i	$0.808559\pi$
$762$	−0.271048	+	0.0795867i	−0.00981902	+	0.00288312i
$763$	4.44616	−	5.13114i	0.160962	−	0.185760i
$764$	−8.64028	−	5.55277i	−0.312594	−	0.200892i
$765$	−0.273192	−	0.315280i	−0.00987726	−	0.0113990i
$766$	3.23073	+	22.4702i	0.116731	+	0.811882i
$767$	6.85836	+	2.01380i	0.247641	+	0.0727140i
$768$	0.841254	−	0.540641i	0.0303561	−	0.0195087i
$769$	0.810328	−	5.63596i	0.0292212	−	0.203238i	−0.969981	−	0.243182i	$-0.921809\pi$
$769$	0.810328	−	5.63596i	0.0292212	−	0.203238i	0.999202	+	0.0399440i	$0.0127179\pi$
$770$	0.0223121	−	0.0488566i	0.000804071	−	0.00176067i
$771$	−1.70046	+	3.72349i	−0.0612406	+	0.134098i
$772$	−2.68560	+	18.6787i	−0.0966567	+	0.672262i
$773$	2.58163	−	1.65911i	0.0928547	−	0.0596741i	−0.493390	−	0.869808i	$-0.664242\pi$
$773$	2.58163	−	1.65911i	0.0928547	−	0.0596741i	0.586244	+	0.810134i	$0.300606\pi$
$774$	1.36255	+	0.400081i	0.0489758	+	0.0143806i
$775$	4.09156	+	28.4574i	0.146973	+	1.02222i
$776$	8.47306	+	9.77843i	0.304165	+	0.351025i
$777$	7.13423	+	4.58489i	0.255939	+	0.164482i
$778$	−8.26460	+	9.53786i	−0.296300	+	0.341949i
$779$	−31.4633	+	9.23847i	−1.12729	+	0.331003i
$780$	−0.518688	−	1.13577i	−0.0185720	−	0.0406670i
$781$	−1.20286			−0.0430416
$782$	1.04525	+	3.11300i	0.0373781	+	0.111321i
$783$	−0.351939			−0.0125773
$784$	0.415415	+	0.909632i	0.0148363	+	0.0324869i
$785$	−0.0861828	+	0.0253056i	−0.00307600	+	0.000903194i
$786$	10.6218	−	12.2582i	0.378867	−	0.437236i
$787$	20.4214	+	13.1240i	0.727944	+	0.467821i	0.851392	−	0.524530i	$-0.175759\pi$
$787$	20.4214	+	13.1240i	0.727944	+	0.467821i	−0.123448	+	0.992351i	$0.539395\pi$
$788$	−0.729952	−	0.842410i	−0.0260035	−	0.0300096i
$789$	2.82653	+	19.6590i	0.100627	+	0.699878i
$790$	6.91861	+	2.03149i	0.246153	+	0.0722770i
$791$	8.34040	−	5.36005i	0.296550	−	0.190581i
$792$	0.0125459	−	0.0872586i	0.000445799	−	0.00310060i
$793$	9.93486	−	21.7543i	0.352797	−	0.772519i
$794$	5.35190	−	11.7190i	0.189932	−	0.415893i
$795$	0.628581	−	4.37187i	0.0222935	−	0.155054i
$796$	−15.6286	+	10.0439i	−0.553941	+	0.355996i
$797$	−28.3151	−	8.31407i	−1.00297	−	0.294499i	−0.261297	−	0.965258i	$-0.584150\pi$
$797$	−28.3151	−	8.31407i	−1.00297	−	0.294499i	−0.741675	+	0.670759i	$0.765968\pi$
$798$	−0.990710	−	6.89054i	−0.0350708	−	0.243923i
$799$	−2.82219	−	3.25699i	−0.0998421	−	0.115224i
$800$	3.89399	+	2.50252i	0.137673	+	0.0884773i
$801$	−3.83035	+	4.42046i	−0.135339	+	0.156189i
$802$	34.4806	−	10.1244i	1.21755	−	0.357506i
$803$	−0.00121720	−	0.00266529i	−4.29540e−5	−	9.40562e-5i
$804$	−7.16705			−0.252762
$805$	−0.930067	−	2.76995i	−0.0327805	−	0.0976281i
$806$	−12.7288			−0.448354
$807$	−4.33218	−	9.48616i	−0.152500	−	0.333929i
$808$	−15.9369	+	4.67949i	−0.560658	+	0.164624i
$809$	27.1845	−	31.3726i	0.955757	−	1.10300i	−0.0388452	−	0.999245i	$-0.512368\pi$
$809$	27.1845	−	31.3726i	0.955757	−	1.10300i	0.994603	−	0.103758i	$-0.0330866\pi$
$810$	0.512546	+	0.329393i	0.0180090	+	0.0115737i
$811$	17.6023	+	20.3142i	0.618101	+	0.713326i	0.975345	−	0.220685i	$-0.0708291\pi$
$811$	17.6023	+	20.3142i	0.618101	+	0.713326i	−0.357244	+	0.934011i	$0.616284\pi$
$812$	0.0500861	+	0.348356i	0.00175768	+	0.0122249i
$813$	11.4493	+	3.36183i	0.401546	+	0.117905i
$814$	−0.628924	+	0.404185i	−0.0220438	+	0.0141667i
$815$	−0.598120	+	4.16001i	−0.0209512	+	0.145719i
$816$	−0.284443	+	0.622842i	−0.00995748	+	0.0218038i
$817$	−4.10666	+	8.99234i	−0.143674	+	0.314602i
$818$	−0.470249	+	3.27065i	−0.0164419	+	0.114356i
$819$	1.72403	−	1.10797i	0.0602425	−	0.0387155i
$820$	−2.75369	−	0.808555i	−0.0961629	−	0.0282360i
$821$	4.03091	+	28.0356i	0.140680	+	0.978450i	0.930808	+	0.365508i	$0.119105\pi$
$821$	4.03091	+	28.0356i	0.140680	+	0.978450i	−0.790128	+	0.612942i	$0.789986\pi$
$822$	12.3184	+	14.2162i	0.429654	+	0.495848i
$823$	−23.4588	−	15.0760i	−0.817722	−	0.525518i	0.0636325	−	0.997973i	$-0.479731\pi$
$823$	−23.4588	−	15.0760i	−0.817722	−	0.525518i	−0.881355	+	0.472455i	$0.843368\pi$
$824$	8.68055	−	10.0179i	0.302401	−	0.348990i
$825$	0.391527	−	0.114963i	0.0136312	−	0.00400248i
$826$	1.44891	+	3.17268i	0.0504142	+	0.110392i
$827$	19.6985			0.684983			0.342491	−	0.939521i	$-0.388729\pi$
$827$	19.6985			0.684983			0.342491	+	0.939521i	$0.388729\pi$
$828$	−2.74557	−	3.93215i	−0.0954152	−	0.136652i
$829$	12.8687			0.446948			0.223474	−	0.974710i	$-0.428260\pi$
$829$	12.8687			0.446948			0.223474	+	0.974710i	$0.428260\pi$
$830$	−3.62491	−	7.93744i	−0.125822	−	0.275512i
$831$	−3.99920	+	1.17427i	−0.138731	+	0.0407350i
$832$	−1.34204	+	1.54880i	−0.0465270	+	0.0536951i
$833$	−0.576022	−	0.370187i	−0.0199580	−	0.0128262i
$834$	0.571969	+	0.660088i	0.0198057	+	0.0228570i
$835$	−0.682949	−	4.75002i	−0.0236344	−	0.164381i
$836$	0.588830	+	0.172896i	0.0203651	+	0.00597973i
$837$	5.22514	−	3.35799i	0.180607	−	0.116069i
$838$	−1.87959	+	13.0728i	−0.0649293	+	0.451594i
$839$	23.3827	−	51.2009i	0.807260	−	1.76765i	0.188498	−	0.982074i	$-0.439638\pi$
$839$	23.3827	−	51.2009i	0.807260	−	1.76765i	0.618762	−	0.785578i	$-0.287634\pi$
$840$	0.253098	−	0.554206i	0.00873270	−	0.0191219i
$841$	4.10950	−	28.5822i	0.141707	−	0.985594i
$842$	10.1073	−	6.49557i	0.348321	−	0.223852i
$843$	−7.34850	−	2.15771i	−0.253096	−	0.0743156i
$844$	−1.43992	−	10.0148i	−0.0495639	−	0.344725i
$845$	−3.51110	−	4.05203i	−0.120786	−	0.139394i
$846$	5.29484	+	3.40278i	0.182040	+	0.116990i
$847$	7.19838	−	8.30737i	0.247339	−	0.285445i
$848$	−6.95579	+	2.04241i	−0.238863	+	0.0701365i
$849$	−5.84966	−	12.8090i	−0.200760	−	0.439603i
$850$	−3.16943			−0.108710
$851$	−9.95402	+	39.4340i	−0.341219	+	1.35178i
$852$	−13.6447			−0.467458
$853$	0.399703	+	0.875227i	0.0136856	+	0.0299672i	0.916351	−	0.400375i	$-0.131120\pi$
$853$	0.399703	+	0.875227i	0.0136856	+	0.0299672i	−0.902666	+	0.430342i	$0.858393\pi$
$854$	11.1970	−	3.28775i	0.383155	−	0.112504i
$855$	−2.77748	+	3.20539i	−0.0949879	+	0.109622i
$856$	−1.48670	−	0.955444i	−0.0508143	−	0.0326564i
$857$	18.2543	+	21.0666i	0.623555	+	0.719621i	0.976378	−	0.216069i	$-0.0693237\pi$
$857$	18.2543	+	21.0666i	0.623555	+	0.719621i	−0.352823	+	0.935690i	$0.614778\pi$
$858$	0.0257110	+	0.178824i	0.000877761	+	0.00610496i
$859$	16.1958	+	4.75553i	0.552595	+	0.162257i	0.546096	−	0.837722i	$-0.316113\pi$
$859$	16.1958	+	4.75553i	0.552595	+	0.162257i	0.00649860	+	0.999979i	$0.497931\pi$
$860$	−0.727852	+	0.467762i	−0.0248196	+	0.0159506i
$861$	0.670373	−	4.66255i	0.0228463	−	0.158899i
$862$	13.0858	−	28.6539i	0.445704	−	0.975955i
$863$	−2.73956	+	5.99879i	−0.0932556	+	0.204201i	−0.950512	−	0.310689i	$-0.899440\pi$
$863$	−2.73956	+	5.99879i	−0.0932556	+	0.204201i	0.857256	+	0.514891i	$0.172167\pi$
$864$	0.142315	−	0.989821i	0.00484165	−	0.0336744i
$865$	−8.74069	+	5.61730i	−0.297192	+	0.190994i
$866$	−5.64499	−	1.65752i	−0.191825	−	0.0563248i
$867$	2.35263	+	16.3629i	0.0798995	+	0.555713i
$868$	−4.06743	−	4.69406i	−0.138057	−	0.159327i
$869$	−0.877707	−	0.564068i	−0.0297742	−	0.0191347i
$870$	0.140418	−	0.162051i	0.00476060	−	0.00549403i
$871$	14.0929	−	4.13805i	0.477519	−	0.140212i
$872$	2.82045	+	6.17593i	0.0955125	+	0.209143i
$873$	12.9387			0.437909
$874$	29.8147	−	15.0228i	1.00850	−	0.508155i
$875$	5.86648			0.198323
$876$	−0.0138073	−	0.0302339i	−0.000466507	−	0.00102151i
$877$	−41.2970	+	12.1259i	−1.39450	+	0.409463i	−0.890792	−	0.454410i	$-0.849850\pi$
$877$	−41.2970	+	12.1259i	−1.39450	+	0.409463i	−0.503709	+	0.863873i	$0.668032\pi$
$878$	−7.60494	+	8.77657i	−0.256654	+	0.296195i
$879$	−17.9602	−	11.5423i	−0.605781	−	0.389312i
$880$	0.0351727	+	0.0405915i	0.00118567	+	0.00136834i
$881$	1.45871	+	10.1455i	0.0491450	+	0.341811i	0.999528	+	0.0307282i	$0.00978263\pi$
$881$	1.45871	+	10.1455i	0.0491450	+	0.341811i	−0.950383	+	0.311083i	$0.899308\pi$
$882$	0.959493	+	0.281733i	0.0323078	+	0.00948643i
$883$	30.1617	−	19.3837i	1.01502	−	0.652315i	0.0763335	−	0.997082i	$-0.475679\pi$
$883$	30.1617	−	19.3837i	1.01502	−	0.652315i	0.938688	+	0.344768i	$0.112042\pi$
$884$	0.199701	−	1.38895i	0.00671668	−	0.0467155i
$885$	0.882772	−	1.93300i	0.0296741	−	0.0649771i
$886$	5.29716	−	11.5992i	0.177962	−	0.389681i
$887$	3.37728	−	23.4895i	0.113398	−	0.788700i	−0.851175	−	0.524883i	$-0.824109\pi$
$887$	3.37728	−	23.4895i	0.113398	−	0.788700i	0.964573	−	0.263818i	$-0.0849817\pi$
$888$	−7.13423	+	4.58489i	−0.239409	+	0.153859i
$889$	0.271048	+	0.0795867i	0.00909064	+	0.00266925i
$890$	−0.507160	−	3.52738i	−0.0170001	−	0.118238i
$891$	−0.0577299	−	0.0666238i	−0.00193402	−	0.00223198i
$892$	−9.82664	−	6.31520i	−0.329020	−	0.211448i
$893$	−28.6927	+	33.1131i	−0.960164	+	1.10809i
$894$	−4.82574	+	1.41696i	−0.161397	+	0.0473904i
$895$	2.53506	+	5.55100i	0.0847376	+	0.185549i
$896$	−1.00000			−0.0334077
$897$	7.66905	+	6.14676i	0.256062	+	0.205234i
$898$	−4.79612			−0.160049
$899$	−0.908071	−	1.98840i	−0.0302859	−	0.0663168i
$900$	4.44130	−	1.30408i	0.148043	−	0.0434694i
$901$	3.25062	−	3.75142i	0.108294	−	0.124978i
$902$	0.349337	+	0.224505i	0.0116317	+	0.00747521i
$903$	−0.929949	−	1.07322i	−0.0309468	−	0.0357145i
$904$	1.41095	+	9.81334i	0.0469273	+	0.326387i
$905$	4.52094	+	1.32747i	0.150281	+	0.0441266i
$906$	11.0681	−	7.11303i	0.367713	−	0.236315i
$907$	−7.75731	+	53.9533i	−0.257577	+	1.79149i	0.292385	+	0.956301i	$0.405551\pi$
$907$	−7.75731	+	53.9533i	−0.257577	+	1.79149i	−0.549963	+	0.835189i	$0.685358\pi$
$908$	6.58401	−	14.4170i	0.218498	−	0.478444i
$909$	−6.89992	+	15.1087i	−0.228856	+	0.501124i
$910$	−0.177695	+	1.23589i	−0.00589052	+	0.0409694i
$911$	4.04950	−	2.60246i	0.134166	−	0.0862232i	−0.471836	−	0.881686i	$-0.656409\pi$
$911$	4.04950	−	2.60246i	0.134166	−	0.0862232i	0.606002	+	0.795463i	$0.292772\pi$
$912$	6.67941	+	1.96125i	0.221177	+	0.0649436i
$913$	0.179684	+	1.24973i	0.00594669	+	0.0413601i
$914$	27.6180	+	31.8729i	0.913523	+	1.05426i
$915$	−5.98128	−	3.84394i	−0.197735	−	0.127077i
$916$	14.6648	−	16.9241i	0.484538	−	0.559187i
$917$	−15.5629	+	4.56969i	−0.513933	+	0.150904i
$918$	0.284443	+	0.622842i	0.00938800	+	0.0205569i
$919$	29.7364			0.980914			0.490457	−	0.871465i	$-0.336830\pi$
$919$	29.7364			0.980914			0.490457	+	0.871465i	$0.336830\pi$
$920$	2.90600	+	0.304662i	0.0958081	+	0.0100444i
$921$	−14.4718			−0.476862
$922$	8.85292	+	19.3852i	0.291555	+	0.638417i
$923$	26.8301	−	7.87803i	0.883124	−	0.259309i
$924$	−0.0577299	+	0.0666238i	−0.00189917	+	0.00219176i
$925$	−33.0229	−	21.2225i	−1.08579	−	0.697792i
$926$	18.8729	+	21.7805i	0.620203	+	0.715753i
$927$	−1.88646	−	13.1206i	−0.0619596	−	0.430938i
$928$	−0.337683	−	0.0991526i	−0.0110850	−	0.00325484i
$929$	39.6833	−	25.5029i	1.30197	−	0.836723i	0.308541	−	0.951211i	$-0.400159\pi$
$929$	39.6833	−	25.5029i	1.30197	−	0.836723i	0.993425	+	0.114488i	$0.0365228\pi$
$930$	−0.538551	+	3.74570i	−0.0176598	+	0.122826i
$931$	−2.89187	+	6.33231i	−0.0947772	+	0.207533i
$932$	−6.84950	+	14.9983i	−0.224363	+	0.491286i
$933$	3.58355	−	24.9241i	0.117320	−	0.815979i
$934$	−10.7907	+	6.93476i	−0.353082	+	0.226912i
$935$	−0.0352867	−	0.0103611i	−0.00115400	−	0.000338845i
$936$	0.291654	+	2.02850i	0.00953302	+	0.0663036i
$937$	3.72270	+	4.29622i	0.121615	+	0.140351i	0.813292	−	0.581856i	$-0.197673\pi$
$937$	3.72270	+	4.29622i	0.121615	+	0.140351i	−0.691677	+	0.722207i	$0.743128\pi$
$938$	6.02930	+	3.87480i	0.196864	+	0.126517i
$939$	6.77073	−	7.81384i	0.220954	−	0.254995i
$940$	−3.67937	+	1.08036i	−0.120008	+	0.0352375i
$941$	−0.930088	−	2.03661i	−0.0303200	−	0.0663915i	0.893866	−	0.448334i	$-0.147982\pi$
$941$	−0.930088	−	2.03661i	−0.0303200	−	0.0663915i	−0.924186	+	0.381943i	$0.875255\pi$
$942$	0.147426			0.00480339
$943$	22.2211	−	4.06979i	0.723620	−	0.132531i
$944$	−3.48787			−0.113521
$945$	−0.253098	−	0.554206i	−0.00823327	−	0.0180283i
$946$	0.120117	−	0.0352695i	0.00390533	−	0.00114671i
$947$	19.2282	−	22.1905i	0.624832	−	0.721095i	−0.351785	−	0.936081i	$-0.614425\pi$
$947$	19.2282	−	22.1905i	0.624832	−	0.721095i	0.976617	+	0.214986i	$0.0689706\pi$
$948$	−9.95630	−	6.39852i	−0.323366	−	0.207814i
$949$	0.0446062	+	0.0514783i	0.00144798	+	0.00167105i
$950$	4.58580	+	31.8949i	0.148783	+	1.03481i
$951$	−12.7075	−	3.73125i	−0.412068	−	0.120994i
$952$	0.576022	−	0.370187i	0.0186690	−	0.0119978i
$953$	−4.26999	+	29.6985i	−0.138319	+	0.962027i	0.795926	+	0.605394i	$0.206985\pi$
$953$	−4.26999	+	29.6985i	−0.138319	+	0.962027i	−0.934244	+	0.356633i	$0.883925\pi$
$954$	−3.01153	+	6.59433i	−0.0975019	+	0.213499i
$955$	2.59950	−	5.69210i	0.0841177	−	0.184192i
$956$	−2.37637	+	16.5280i	−0.0768575	+	0.534555i
$957$	−0.0261003	+	0.0167736i	−0.000843702	+	0.000542215i
$958$	−30.6339	−	8.99493i	−0.989737	−	0.290613i
$959$	−2.67705	−	18.6193i	−0.0864464	−	0.601248i
$960$	0.398983	+	0.460451i	0.0128771	+	0.0148610i
$961$	6.37515	+	4.09706i	0.205650	+	0.132163i
$962$	11.3812	−	13.1346i	0.366944	−	0.423476i
$963$	−1.69566	+	0.497890i	−0.0546418	+	0.0160443i
$964$	5.62462	+	12.3162i	0.181157	+	0.396678i
$965$	−11.4973			−0.370112
$966$	0.183838	+	4.79231i	0.00591490	+	0.154190i
$967$	42.3015			1.36033			0.680163	−	0.733061i	$-0.261909\pi$
$967$	42.3015			1.36033			0.680163	+	0.733061i	$0.261909\pi$
$968$	4.56634	+	9.99888i	0.146768	+	0.321376i
$969$	−4.57352	+	1.34291i	−0.146923	+	0.0431404i
$970$	−5.16234	+	5.95765i	−0.165753	+	0.191289i
$971$	−22.5269	−	14.4772i	−0.722923	−	0.464595i	0.126729	−	0.991937i	$-0.459552\pi$
$971$	−22.5269	−	14.4772i	−0.722923	−	0.464595i	−0.849653	+	0.527343i	$0.823188\pi$
$972$	−0.654861	−	0.755750i	−0.0210047	−	0.0242407i
$973$	−0.124301	−	0.864531i	−0.00398490	−	0.0277156i
$974$	25.0311	+	7.34980i	0.802049	+	0.235503i
$975$	−7.98019	+	5.12855i	−0.255571	+	0.164245i
$976$	−1.66078	+	11.5510i	−0.0531602	+	0.369738i
$977$	−15.2932	+	33.4874i	−0.489272	+	1.07136i	0.490537	+	0.871420i	$0.336801\pi$
$977$	−15.2932	+	33.4874i	−0.489272	+	1.07136i	−0.979809	+	0.199936i	$0.935927\pi$
$978$	2.86559	−	6.27477i	0.0916315	−	0.200645i
$979$	−0.0733822	+	0.510385i	−0.00234531	+	0.0163120i
$980$	−0.512546	+	0.329393i	−0.0163727	+	0.0105221i
$981$	6.51446	+	1.91282i	0.207991	+	0.0610715i
$982$	−3.20604	−	22.2985i	−0.102309	−	0.711573i
$983$	38.5332	+	44.4697i	1.22902	+	1.41836i	0.875696	+	0.482862i	$0.160403\pi$
$983$	38.5332	+	44.4697i	1.22902	+	1.41836i	0.353323	+	0.935502i	$0.385052\pi$
$984$	3.96272	+	2.54669i	0.126327	+	0.0811854i
$985$	0.444734	−	0.513250i	0.0141704	−	0.0163535i
$986$	0.231218	−	0.0678916i	0.00736347	−	0.00216211i
$987$	−2.61462	−	5.72521i	−0.0832241	−	0.182235i
$988$	−14.2664			−0.453875
$989$	3.45967	−	5.86623i	0.110011	−	0.186535i
$990$	0.0537103			0.00170702
$991$	23.8066	+	52.1293i	0.756243	+	1.65594i	0.754812	+	0.655942i	$0.227728\pi$
$991$	23.8066	+	52.1293i	0.756243	+	1.65594i	0.00143117	+	0.999999i	$0.499544\pi$
$992$	5.95954	−	1.74988i	0.189215	−	0.0555587i
$993$	12.7439	−	14.7073i	0.404416	−	0.466721i
$994$	11.4786	+	7.37686i	0.364080	+	0.233980i
$995$	−7.41221	−	8.55415i	−0.234983	−	0.271185i
$996$	2.03826	+	14.1764i	0.0645846	+	0.449196i
$997$	25.9653	+	7.62410i	0.822329	+	0.241458i	0.665719	−	0.746203i	$-0.268125\pi$
$997$	25.9653	+	7.62410i	0.822329	+	0.241458i	0.156611	+	0.987660i	$0.449943\pi$
$998$	−30.0380	+	19.3043i	−0.950838	+	0.611066i
$999$	−1.20690	+	8.39415i	−0.0381845	+	0.265579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.c.211.1	✓	10
23.6	even	11	inner	966.2.q.c.673.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.c.211.1	✓	10	1.1	even	1	trivial
966.2.q.c.673.1	yes	10	23.6	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)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.512546 - 0.329393i) q^{5} +(0.654861 + 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.512546 - 0.329393i) 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} +(-0.0867074 + 0.603063i) q^{10} +(0.0366213 - 0.0801894i) q^{11} +(0.415415 - 0.909632i) q^{12} +(-0.291654 + 2.02850i) q^{13} +(-0.841254 + 0.540641i) q^{14} +(0.584585 + 0.171650i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.448396 + 0.517476i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(4.55875 - 5.26107i) q^{19} +(0.584585 - 0.171650i) q^{20} +(0.415415 + 0.909632i) q^{21} -0.0881559 q^{22} +(-3.50140 + 3.27723i) q^{23} -1.00000 q^{24} +(-1.92287 - 4.21050i) q^{25} +(1.96635 - 0.577371i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{28} +(0.230471 + 0.265977i) q^{29} +(-0.0867074 - 0.603063i) q^{30} +(-5.95954 - 1.74988i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-0.0125459 + 0.0872586i) q^{33} +(0.284443 - 0.622842i) q^{34} +(-0.253098 + 0.554206i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(7.13423 - 4.58489i) q^{37} +(-6.67941 - 1.96125i) q^{38} +(-0.291654 - 2.02850i) q^{39} +(-0.398983 - 0.460451i) q^{40} +(-3.96272 - 2.54669i) q^{41} +(0.654861 - 0.755750i) q^{42} +(-1.36255 + 0.400081i) q^{43} +(0.0366213 + 0.0801894i) q^{44} -0.609264 q^{45} +(4.43560 + 1.82357i) q^{46} -6.29398 q^{47} +(0.415415 + 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(-3.03122 + 3.49821i) q^{50} +(-0.576022 - 0.370187i) q^{51} +(-1.34204 - 1.54880i) q^{52} +(-1.03170 - 7.17566i) q^{53} +(0.959493 + 0.281733i) q^{54} +(-0.0451840 + 0.0290380i) q^{55} +(0.142315 - 0.989821i) q^{56} +(-2.89187 + 6.33231i) q^{57} +(0.146201 - 0.320135i) q^{58} +(0.496376 - 3.45237i) q^{59} +(-0.512546 + 0.329393i) q^{60} +(-11.1970 - 3.28775i) q^{61} +(0.883936 + 6.14791i) q^{62} +(-0.654861 - 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.817660 - 0.943630i) q^{65} +(0.0845850 - 0.0248364i) q^{66} +(-2.97730 - 6.51937i) q^{67} -0.684719 q^{68} +(2.43626 - 4.13094i) q^{69} +0.609264 q^{70} +(-5.66820 - 12.4116i) q^{71} +(0.959493 - 0.281733i) q^{72} +(0.0217659 - 0.0251192i) q^{73} +(-7.13423 - 4.58489i) q^{74} +(3.03122 + 3.49821i) q^{75} +(0.990710 + 6.89054i) q^{76} +(-0.0845850 - 0.0248364i) q^{77} +(-1.72403 + 1.10797i) q^{78} +(1.68431 - 11.7146i) q^{79} +(-0.253098 + 0.554206i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.670373 + 4.66255i) q^{82} +(-12.0486 + 7.74315i) q^{83} +(-0.959493 - 0.281733i) q^{84} +(-0.0593702 - 0.412929i) q^{85} +(0.929949 + 1.07322i) q^{86} +(-0.296070 - 0.190272i) q^{87} +(0.0577299 - 0.0666238i) q^{88} +(-5.61217 + 1.64788i) q^{89} +(0.253098 + 0.554206i) q^{90} +2.04936 q^{91} +(-0.183838 - 4.79231i) q^{92} +6.21113 q^{93} +(2.61462 + 5.72521i) q^{94} +(-4.06953 + 1.19492i) q^{95} +(0.654861 - 0.755750i) q^{96} +(10.8847 + 6.99520i) q^{97} +(0.654861 + 0.755750i) q^{98} +(-0.0125459 - 0.0872586i) 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

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