LMFDB - Embedded newform 690.2.m.h.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	690.31
Dual form			690.2.m.h.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-3.23498 - 2.07900i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-3.23498 - 2.07900i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(-0.436188 - 3.03376i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(5.09384 - 3.27361i) q^{13} +(-2.51822 + 2.90618i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(4.68281 - 1.37500i) q^{17} +(0.654861 + 0.755750i) q^{18} +(-5.19533 - 1.52549i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(0.547262 - 3.80629i) q^{21} -3.06495 q^{22} +(-4.47873 - 1.71493i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-2.51536 - 5.50788i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(2.51822 + 2.90618i) q^{28} +(7.16153 - 2.10282i) q^{29} +(0.841254 + 0.540641i) q^{30} +(3.85885 - 8.44970i) q^{31} +(0.654861 - 0.755750i) q^{32} +(2.57840 - 1.65704i) q^{33} +(-0.694568 - 4.83083i) q^{34} +(-0.547262 - 3.80629i) q^{35} +(0.841254 - 0.540641i) q^{36} +(0.683485 - 0.788784i) q^{37} +(-2.24933 + 4.92535i) q^{38} +(5.09384 + 3.27361i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(-3.48638 - 4.02350i) q^{41} +(-3.68966 - 1.08338i) q^{42} +(4.81952 + 10.5533i) q^{43} +(-0.436188 + 3.03376i) q^{44} -1.00000 q^{45} +(-2.33486 + 4.18908i) q^{46} -3.07419 q^{47} +(-0.142315 + 0.989821i) q^{48} +(3.23498 + 7.08362i) q^{49} +(0.959493 + 0.281733i) q^{50} +(3.19605 + 3.68844i) q^{51} +(-5.80979 + 1.70591i) q^{52} +(-2.28501 - 1.46849i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(2.00712 - 2.31634i) q^{55} +(3.23498 - 2.07900i) q^{56} +(-0.770587 - 5.35955i) q^{57} +(-1.06222 - 7.38790i) q^{58} +(5.57026 - 3.57979i) q^{59} +(0.654861 - 0.755750i) q^{60} +(-2.39017 + 5.23375i) q^{61} +(-7.81453 - 5.02209i) q^{62} +(3.68966 - 1.08338i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.80979 + 1.70591i) q^{65} +(-1.27323 - 2.78798i) q^{66} +(-1.58527 + 11.0258i) q^{67} -4.88050 q^{68} +(-0.300576 - 4.78640i) q^{69} -3.84543 q^{70} +(1.89820 - 13.2023i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(-14.7827 - 4.34058i) q^{73} +(-0.683485 - 0.788784i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(4.55510 + 2.92739i) q^{76} +(-4.89611 + 10.7210i) q^{77} +(3.96522 - 4.57611i) q^{78} +(-8.79705 + 5.65352i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-4.47871 + 2.87829i) q^{82} +(4.49111 - 5.18302i) q^{83} +(-1.59745 + 3.49793i) q^{84} +(4.10574 + 2.63860i) q^{85} +(11.1317 - 3.26857i) q^{86} +(4.88780 + 5.64082i) q^{87} +(2.94080 + 0.863497i) q^{88} +(1.42517 + 3.12069i) q^{89} +(-0.142315 + 0.989821i) q^{90} -23.2843 q^{91} +(3.81416 + 2.90727i) q^{92} +9.28914 q^{93} +(-0.437503 + 3.04290i) q^{94} +(-2.24933 - 4.92535i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-0.929335 - 1.07251i) q^{97} +(7.47190 - 2.19395i) q^{98} +(2.57840 + 1.65704i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	−3.23498	−	2.07900i	−1.22271	−	0.785787i	−0.239969	−	0.970781i	$-0.577137\pi$
$7$	−3.23498	−	2.07900i	−1.22271	−	0.785787i	−0.982740	+	0.184993i	$0.940774\pi$
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	0.841254	−	0.540641i	0.266028	−	0.170966i
$11$	−0.436188	−	3.03376i	−0.131516	−	0.914712i	−0.943580	−	0.331144i	$-0.892565\pi$
$11$	−0.436188	−	3.03376i	−0.131516	−	0.914712i	0.812065	−	0.583568i	$-0.198344\pi$
$12$	−0.142315	−	0.989821i	−0.0410828	−	0.285737i
$13$	5.09384	−	3.27361i	1.41278	−	0.907937i	0.412781	−	0.910830i	$-0.364557\pi$
$13$	5.09384	−	3.27361i	1.41278	−	0.907937i	0.999996	+	0.00289349i	$0.000921028\pi$
$14$	−2.51822	+	2.90618i	−0.673023	+	0.776710i
$15$	−0.415415	+	0.909632i	−0.107260	+	0.234866i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	4.68281	−	1.37500i	1.13575	−	0.333486i	0.340784	−	0.940142i	$-0.389308\pi$
$17$	4.68281	−	1.37500i	1.13575	−	0.333486i	0.794964	+	0.606656i	$0.207489\pi$
$18$	0.654861	+	0.755750i	0.154352	+	0.178132i
$19$	−5.19533	−	1.52549i	−1.19189	−	0.349971i	−0.375144	−	0.926967i	$-0.622407\pi$
$19$	−5.19533	−	1.52549i	−1.19189	−	0.349971i	−0.816747	+	0.576996i	$0.804225\pi$
$20$	−0.415415	−	0.909632i	−0.0928896	−	0.203400i
$21$	0.547262	−	3.80629i	0.119422	−	0.830601i
$22$	−3.06495			−0.653450
$23$	−4.47873	−	1.71493i	−0.933880	−	0.357588i
$23$	−4.47873	−	1.71493i	−0.933880	−	0.357588i
$24$	−1.00000			−0.204124
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	−2.51536	−	5.50788i	−0.493303	−	1.08018i
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$	2.51822	+	2.90618i	0.475899	+	0.549217i
$29$	7.16153	−	2.10282i	1.32986	−	0.390483i	0.461821	−	0.886973i	$-0.347196\pi$
$29$	7.16153	−	2.10282i	1.32986	−	0.390483i	0.868042	+	0.496490i	$0.165378\pi$
$30$	0.841254	+	0.540641i	0.153591	+	0.0987071i
$31$	3.85885	−	8.44970i	0.693070	−	1.51761i	−0.155107	−	0.987898i	$-0.549572\pi$
$31$	3.85885	−	8.44970i	0.693070	−	1.51761i	0.848176	−	0.529714i	$-0.177701\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$	2.57840	−	1.65704i	0.448842	−	0.288453i
$34$	−0.694568	−	4.83083i	−0.119117	−	0.828480i
$35$	−0.547262	−	3.80629i	−0.0925042	−	0.643381i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	0.683485	−	0.788784i	0.112364	−	0.129675i	−0.696781	−	0.717284i	$-0.745385\pi$
$37$	0.683485	−	0.788784i	0.112364	−	0.129675i	0.809145	+	0.587609i	$0.199931\pi$
$38$	−2.24933	+	4.92535i	−0.364890	+	0.798997i
$39$	5.09384	+	3.27361i	0.815667	+	0.524197i
$40$	−0.959493	+	0.281733i	−0.151709	+	0.0445458i
$41$	−3.48638	−	4.02350i	−0.544482	−	0.628365i	0.415107	−	0.909773i	$-0.363744\pi$
$41$	−3.48638	−	4.02350i	−0.544482	−	0.628365i	−0.959588	+	0.281407i	$0.909199\pi$
$42$	−3.68966	−	1.08338i	−0.569328	−	0.167170i
$43$	4.81952	+	10.5533i	0.734969	+	1.60936i	0.791657	+	0.610966i	$0.209219\pi$
$43$	4.81952	+	10.5533i	0.734969	+	1.60936i	−0.0566873	+	0.998392i	$0.518054\pi$
$44$	−0.436188	+	3.03376i	−0.0657578	+	0.457356i
$45$	−1.00000			−0.149071
$46$	−2.33486	+	4.18908i	−0.344257	+	0.617646i
$47$	−3.07419			−0.448417			−0.224208	−	0.974541i	$-0.571980\pi$
$47$	−3.07419			−0.448417			−0.224208	+	0.974541i	$0.571980\pi$
$48$	−0.142315	+	0.989821i	−0.0205414	+	0.142868i
$49$	3.23498	+	7.08362i	0.462140	+	1.01195i
$50$	0.959493	+	0.281733i	0.135693	+	0.0398430i
$51$	3.19605	+	3.68844i	0.447537	+	0.516485i
$52$	−5.80979	+	1.70591i	−0.805673	+	0.236567i
$53$	−2.28501	−	1.46849i	−0.313870	−	0.201712i	0.374215	−	0.927342i	$-0.377912\pi$
$53$	−2.28501	−	1.46849i	−0.313870	−	0.201712i	−0.688085	+	0.725630i	$0.741549\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	2.00712	−	2.31634i	0.270640	−	0.312335i
$56$	3.23498	−	2.07900i	0.432293	−	0.277818i
$57$	−0.770587	−	5.35955i	−0.102067	−	0.709890i
$58$	−1.06222	−	7.38790i	−0.139476	−	0.970079i
$59$	5.57026	−	3.57979i	0.725186	−	0.466048i	−0.125252	−	0.992125i	$-0.539974\pi$
$59$	5.57026	−	3.57979i	0.725186	−	0.466048i	0.850437	+	0.526077i	$0.176337\pi$
$60$	0.654861	−	0.755750i	0.0845422	−	0.0975669i
$61$	−2.39017	+	5.23375i	−0.306030	+	0.670112i	−0.998691	−	0.0511510i	$-0.983711\pi$
$61$	−2.39017	+	5.23375i	−0.306030	+	0.670112i	0.692661	+	0.721263i	$0.256438\pi$
$62$	−7.81453	−	5.02209i	−0.992446	−	0.637806i
$63$	3.68966	−	1.08338i	0.464854	−	0.136493i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	5.80979	+	1.70591i	0.720615	+	0.211592i
$66$	−1.27323	−	2.78798i	−0.156723	−	0.343176i
$67$	−1.58527	+	11.0258i	−0.193671	+	1.34701i	0.628517	+	0.777796i	$0.283662\pi$
$67$	−1.58527	+	11.0258i	−0.193671	+	1.34701i	−0.822188	+	0.569216i	$0.807247\pi$
$68$	−4.88050			−0.591848
$69$	−0.300576	−	4.78640i	−0.0361851	−	0.576215i
$70$	−3.84543			−0.459617
$71$	1.89820	−	13.2023i	0.225275	−	1.56682i	−0.492352	−	0.870396i	$-0.663863\pi$
$71$	1.89820	−	13.2023i	0.225275	−	1.56682i	0.717627	−	0.696428i	$-0.245228\pi$
$72$	−0.415415	−	0.909632i	−0.0489571	−	0.107201i
$73$	−14.7827	−	4.34058i	−1.73018	−	0.508026i	−0.743227	−	0.669040i	$-0.766706\pi$
$73$	−14.7827	−	4.34058i	−1.73018	−	0.508026i	−0.986952	+	0.161013i	$0.948524\pi$
$74$	−0.683485	−	0.788784i	−0.0794535	−	0.0916943i
$75$	−0.959493	+	0.281733i	−0.110793	+	0.0325317i
$76$	4.55510	+	2.92739i	0.522506	+	0.335794i
$77$	−4.89611	+	10.7210i	−0.557963	+	1.22177i
$78$	3.96522	−	4.57611i	0.448973	−	0.518142i
$79$	−8.79705	+	5.65352i	−0.989745	+	0.636071i	−0.932075	−	0.362265i	$-0.882004\pi$
$79$	−8.79705	+	5.65352i	−0.989745	+	0.636071i	−0.0576702	+	0.998336i	$0.518367\pi$
$80$	0.142315	+	0.989821i	0.0159113	+	0.110665i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−4.47871	+	2.87829i	−0.494591	+	0.317854i
$83$	4.49111	−	5.18302i	0.492963	−	0.568910i	−0.453692	−	0.891159i	$-0.649893\pi$
$83$	4.49111	−	5.18302i	0.492963	−	0.568910i	0.946655	+	0.322249i	$0.104439\pi$
$84$	−1.59745	+	3.49793i	−0.174296	+	0.381655i
$85$	4.10574	+	2.63860i	0.445330	+	0.286196i
$86$	11.1317	−	3.26857i	1.20037	−	0.352459i
$87$	4.88780	+	5.64082i	0.524027	+	0.604759i
$88$	2.94080	+	0.863497i	0.313490	+	0.0920491i
$89$	1.42517	+	3.12069i	0.151068	+	0.330793i	0.970003	−	0.243094i	$-0.0781623\pi$
$89$	1.42517	+	3.12069i	0.151068	+	0.330793i	−0.818935	+	0.573886i	$0.805435\pi$
$90$	−0.142315	+	0.989821i	−0.0150013	+	0.104336i
$91$	−23.2843			−2.44086
$92$	3.81416	+	2.90727i	0.397653	+	0.303104i
$93$	9.28914			0.963239
$94$	−0.437503	+	3.04290i	−0.0451250	+	0.313851i
$95$	−2.24933	−	4.92535i	−0.230777	−	0.505330i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	−0.929335	−	1.07251i	−0.0943596	−	0.108897i	0.706606	−	0.707607i	$-0.250225\pi$
$97$	−0.929335	−	1.07251i	−0.0943596	−	0.108897i	−0.800965	+	0.598711i	$0.795680\pi$
$98$	7.47190	−	2.19395i	0.754776	−	0.221622i
$99$	2.57840	+	1.65704i	0.259139	+	0.166539i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	−2.31941	+	2.67675i	−0.230790	+	0.266346i	−0.859319	−	0.511440i	$-0.829112\pi$
$101$	−2.31941	+	2.67675i	−0.230790	+	0.266346i	0.628528	+	0.777787i	$0.283658\pi$
$102$	4.10574	−	2.63860i	0.406529	−	0.261260i
$103$	2.52848	+	17.5860i	0.249138	+	1.73280i	0.603214	+	0.797579i	$0.293886\pi$
$103$	2.52848	+	17.5860i	0.249138	+	1.73280i	−0.354076	+	0.935217i	$0.615205\pi$
$104$	0.861725	+	5.99343i	0.0844991	+	0.587704i
$105$	3.23498	−	2.07900i	0.315702	−	0.202889i
$106$	−1.77873	+	2.05277i	−0.172766	+	0.199382i
$107$	1.02524	−	2.24495i	0.0991133	−	0.217028i	−0.853580	−	0.520962i	$-0.825573\pi$
$107$	1.02524	−	2.24495i	0.0991133	−	0.217028i	0.952693	+	0.303935i	$0.0983004\pi$
$108$	0.841254	+	0.540641i	0.0809497	+	0.0520232i
$109$	−3.44988	+	1.01298i	−0.330439	+	0.0970255i	−0.442744	−	0.896648i	$-0.645995\pi$
$109$	−3.44988	+	1.01298i	−0.330439	+	0.0970255i	0.112305	+	0.993674i	$0.464177\pi$
$110$	−2.00712	−	2.31634i	−0.191371	−	0.220854i
$111$	1.00143	+	0.294047i	0.0950518	+	0.0279097i
$112$	−1.59745	−	3.49793i	−0.150945	−	0.330523i
$113$	0.101466	−	0.705711i	0.00954511	−	0.0663877i	−0.984492	−	0.175429i	$-0.943869\pi$
$113$	0.101466	−	0.705711i	0.00954511	−	0.0663877i	0.994037	+	0.109041i	$0.0347780\pi$
$114$	−5.41466			−0.507130
$115$	−1.63689	−	4.50784i	−0.152640	−	0.420358i
$116$	−7.46387			−0.693003
$117$	−0.861725	+	5.99343i	−0.0796665	+	0.554093i
$118$	−2.75062	−	6.02302i	−0.253215	−	0.554464i
$119$	−18.0074	−	5.28746i	−1.65074	−	0.484700i
$120$	−0.654861	−	0.755750i	−0.0597803	−	0.0689902i
$121$	1.54101	−	0.452482i	0.140092	−	0.0411347i
$122$	4.84032	+	3.11068i	0.438222	+	0.281628i
$123$	2.21161	−	4.84275i	0.199414	−	0.436656i
$124$	−6.08310	+	7.02027i	−0.546278	+	0.630439i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	−0.547262	−	3.80629i	−0.0487540	−	0.339091i
$127$	2.37429	+	16.5136i	0.210684	+	1.46534i	0.770879	+	0.636981i	$0.219817\pi$
$127$	2.37429	+	16.5136i	0.210684	+	1.46534i	−0.560195	+	0.828361i	$0.689274\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$	−7.59749	+	8.76797i	−0.668922	+	0.771977i
$130$	2.51536	−	5.50788i	0.220612	−	0.483073i
$131$	16.3366	+	10.4989i	1.42733	+	0.917292i	0.999912	+	0.0132390i	$0.00421423\pi$
$131$	16.3366	+	10.4989i	1.42733	+	0.917292i	0.427421	+	0.904053i	$0.359422\pi$
$132$	−2.94080	+	0.863497i	−0.255964	+	0.0751577i
$133$	13.6353	+	15.7360i	1.18233	+	1.36448i
$134$	10.6879	+	3.13826i	0.923296	+	0.271104i
$135$	−0.415415	−	0.909632i	−0.0357532	−	0.0782887i
$136$	−0.694568	+	4.83083i	−0.0595587	+	0.414240i
$137$	−0.482154			−0.0411932			−0.0205966	−	0.999788i	$-0.506557\pi$
$137$	−0.482154			−0.0411932			−0.0205966	+	0.999788i	$0.506557\pi$
$138$	−4.78046	−	0.383660i	−0.406940	−	0.0326593i
$139$	−2.20181			−0.186755			−0.0933777	−	0.995631i	$-0.529766\pi$
$139$	−2.20181			−0.186755			−0.0933777	+	0.995631i	$0.529766\pi$
$140$	−0.547262	+	3.80629i	−0.0462521	+	0.321690i
$141$	−1.27707	−	2.79638i	−0.107548	−	0.235498i
$142$	−12.7978	−	3.75776i	−1.07397	−	0.315345i
$143$	−12.1532	−	14.0256i	−1.01630	−	1.17288i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	6.27901	+	4.03527i	0.521443	+	0.335111i
$146$	−6.40019	+	14.0145i	−0.529684	+	1.15985i
$147$	−5.09963	+	5.88528i	−0.420610	+	0.485410i
$148$	−0.878025	+	0.564273i	−0.0721732	+	0.0463829i
$149$	0.370985	+	2.58026i	0.0303923	+	0.211383i	0.999359	−	0.0358097i	$-0.0114010\pi$
$149$	0.370985	+	2.58026i	0.0303923	+	0.211383i	−0.968966	+	0.247193i	$0.920492\pi$
$150$	0.142315	+	0.989821i	0.0116200	+	0.0808186i
$151$	16.6099	−	10.6746i	1.35170	−	0.868683i	0.353917	−	0.935277i	$-0.384849\pi$
$151$	16.6099	−	10.6746i	1.35170	−	0.868683i	0.997780	+	0.0665934i	$0.0212130\pi$
$152$	3.54585	−	4.09213i	0.287606	−	0.331915i
$153$	−2.02743	+	4.43946i	−0.163908	+	0.358909i
$154$	9.91507	+	6.37203i	0.798979	+	0.513473i
$155$	8.91287	−	2.61705i	0.715899	−	0.210207i
$156$	−3.96522	−	4.57611i	−0.317472	−	0.366382i
$157$	16.3839	+	4.81074i	1.30758	+	0.383939i	0.859994	−	0.510304i	$-0.170467\pi$
$157$	16.3839	+	4.81074i	1.30758	+	0.383939i	0.447582	+	0.894243i	$0.352285\pi$
$158$	4.34402	+	9.51209i	0.345592	+	0.756741i
$159$	0.386555	−	2.68855i	0.0306558	−	0.213216i
$160$	1.00000			0.0790569
$161$	10.9233	+	14.8590i	0.860875	+	1.17106i
$162$	−1.00000			−0.0785674
$163$	0.676572	−	4.70566i	0.0529932	−	0.368576i	−0.946018	−	0.324114i	$-0.894934\pi$
$163$	0.676572	−	4.70566i	0.0529932	−	0.368576i	0.999011	−	0.0444615i	$-0.0141572\pi$
$164$	2.21161	+	4.84275i	0.172698	+	0.378155i
$165$	2.94080	+	0.863497i	0.228941	+	0.0672231i
$166$	−4.49111	−	5.18302i	−0.348578	−	0.402280i
$167$	2.96972	−	0.871988i	0.229804	−	0.0674764i	−0.164803	−	0.986326i	$-0.552699\pi$
$167$	2.96972	−	0.871988i	0.229804	−	0.0674764i	0.394607	+	0.918850i	$0.370881\pi$
$168$	3.23498	+	2.07900i	0.249584	+	0.160398i
$169$	9.83028	−	21.5253i	0.756175	−	1.65579i
$170$	3.19605	−	3.68844i	0.245126	−	0.282890i
$171$	4.55510	−	2.92739i	0.348338	−	0.223863i
$172$	−1.65109	−	11.4836i	−0.125895	−	0.875616i
$173$	2.38730	+	16.6040i	0.181503	+	1.26238i	0.853211	+	0.521565i	$0.174652\pi$
$173$	2.38730	+	16.6040i	0.181503	+	1.26238i	−0.671709	+	0.740816i	$0.734439\pi$
$174$	6.27901	−	4.03527i	0.476010	−	0.305913i
$175$	2.51822	−	2.90618i	0.190360	−	0.219687i
$176$	1.27323	−	2.78798i	0.0959731	−	0.210152i
$177$	5.57026	+	3.57979i	0.418686	+	0.269073i
$178$	3.29175	−	0.966545i	0.246727	−	0.0724456i
$179$	−14.1915	−	16.3779i	−1.06073	−	1.22414i	−0.973675	−	0.227939i	$-0.926801\pi$
$179$	−14.1915	−	16.3779i	−1.06073	−	1.22414i	−0.0870502	−	0.996204i	$-0.527744\pi$
$180$	0.959493	+	0.281733i	0.0715164	+	0.0209991i
$181$	−6.65219	−	14.5663i	−0.494453	−	1.08270i	−0.978233	−	0.207511i	$-0.933464\pi$
$181$	−6.65219	−	14.5663i	−0.494453	−	1.08270i	0.483780	−	0.875190i	$-0.339264\pi$
$182$	−3.31370	+	23.0473i	−0.245628	+	1.70838i
$183$	−5.75370			−0.425325
$184$	3.42049	−	3.36159i	0.252162	−	0.247820i
$185$	1.04371			0.0767351
$186$	1.32198	−	9.19459i	0.0969325	−	0.674180i
$187$	−6.21399	−	13.6067i	−0.454412	−	0.995023i
$188$	2.94967	+	0.866100i	0.215126	+	0.0631668i
$189$	2.51822	+	2.90618i	0.183174	+	0.211394i
$190$	−5.19533	+	1.52549i	−0.376909	+	0.110670i
$191$	16.5791	+	10.6547i	1.19962	+	0.770949i	0.978890	−	0.204386i	$-0.0655197\pi$
$191$	16.5791	+	10.6547i	1.19962	+	0.770949i	0.220730	+	0.975335i	$0.429156\pi$
$192$	0.415415	−	0.909632i	0.0299800	−	0.0656470i
$193$	−15.8062	+	18.2414i	−1.13776	+	1.31304i	−0.194531	+	0.980896i	$0.562318\pi$
$193$	−15.8062	+	18.2414i	−1.13776	+	1.31304i	−0.943228	+	0.332147i	$0.892227\pi$
$194$	−1.19385	+	0.767241i	−0.0857135	+	0.0550847i
$195$	0.861725	+	5.99343i	0.0617094	+	0.429198i
$196$	−1.10825	−	7.70808i	−0.0791611	−	0.550577i
$197$	8.58077	−	5.51452i	0.611354	−	0.392894i	−0.198010	−	0.980200i	$-0.563448\pi$
$197$	8.58077	−	5.51452i	0.611354	−	0.392894i	0.809365	+	0.587306i	$0.199812\pi$
$198$	2.00712	−	2.31634i	0.142640	−	0.164615i
$199$	2.23053	−	4.88418i	0.158118	−	0.346230i	−0.813948	−	0.580938i	$-0.802686\pi$
$199$	2.23053	−	4.88418i	0.158118	−	0.346230i	0.972066	+	0.234707i	$0.0754132\pi$
$200$	−0.841254	−	0.540641i	−0.0594856	−	0.0382291i
$201$	−10.6879	+	3.13826i	−0.753868	+	0.221356i
$202$	2.31941	+	2.67675i	0.163193	+	0.188335i
$203$	−27.5392	−	8.08624i	−1.93287	−	0.567542i
$204$	−2.02743	−	4.43946i	−0.141949	−	0.310825i
$205$	0.757664	−	5.26967i	0.0529175	−	0.368049i
$206$	17.7668			1.23787
$207$	4.22900	−	2.26176i	0.293936	−	0.157203i
$208$	6.05506			0.419843
$209$	−2.36181	+	16.4268i	−0.163370	+	1.13626i
$210$	−1.59745	−	3.49793i	−0.110235	−	0.241380i
$211$	15.5100	+	4.55414i	1.06775	+	0.313520i	0.767968	−	0.640488i	$-0.221268\pi$
$211$	15.5100	+	4.55414i	1.06775	+	0.313520i	0.299782	+	0.954008i	$0.403086\pi$
$212$	1.77873	+	2.05277i	0.122164	+	0.140985i
$213$	12.7978	−	3.75776i	0.876889	−	0.257478i
$214$	−2.07620	−	1.33429i	−0.141926	−	0.0912102i
$215$	−4.81952	+	10.5533i	−0.328688	+	0.719727i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	−30.0502	+	19.3121i	−2.03994	+	1.31099i
$218$	0.511697	+	3.55893i	0.0346565	+	0.241041i
$219$	−2.19261	−	15.2499i	−0.148163	−	1.03049i
$220$	−2.57840	+	1.65704i	−0.173836	+	0.111717i
$221$	19.3523	−	22.3337i	1.30178	−	1.50233i
$222$	0.433573	−	0.949393i	0.0290995	−	0.0637191i
$223$	10.1096	+	6.49704i	0.676988	+	0.435074i	0.833439	−	0.552612i	$-0.186369\pi$
$223$	10.1096	+	6.49704i	0.676988	+	0.435074i	−0.156451	+	0.987686i	$0.550005\pi$
$224$	−3.68966	+	1.08338i	−0.246526	+	0.0723866i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	−0.684087	−	0.200866i	−0.0455048	−	0.0133614i
$227$	4.60031	+	10.0733i	0.305333	+	0.668586i	0.998644	−	0.0520520i	$-0.0165761\pi$
$227$	4.60031	+	10.0733i	0.305333	+	0.668586i	−0.693311	+	0.720638i	$0.743849\pi$
$228$	−0.770587	+	5.35955i	−0.0510334	+	0.354945i
$229$	4.56808			0.301868			0.150934	−	0.988544i	$-0.451772\pi$
$229$	4.56808			0.301868			0.150934	+	0.988544i	$0.451772\pi$
$230$	−4.69491	+	0.978693i	−0.309573	+	0.0645331i
$231$	−11.7861			−0.775466
$232$	−1.06222	+	7.38790i	−0.0697382	+	0.485039i
$233$	−11.7984	−	25.8348i	−0.772936	−	1.69249i	−0.720079	−	0.693892i	$-0.755895\pi$
$233$	−11.7984	−	25.8348i	−0.772936	−	1.69249i	−0.0528566	−	0.998602i	$-0.516833\pi$
$234$	5.80979	+	1.70591i	0.379798	+	0.111519i
$235$	−2.01317	−	2.32332i	−0.131325	−	0.151557i
$236$	−6.35316	+	1.86546i	−0.413556	+	0.121431i
$237$	−8.79705	−	5.65352i	−0.571430	−	0.367236i
$238$	−7.79636	+	17.0717i	−0.505363	+	1.10659i
$239$	1.13581	−	1.31079i	0.0734694	−	0.0847882i	−0.717825	−	0.696224i	$-0.754862\pi$
$239$	1.13581	−	1.31079i	0.0734694	−	0.0847882i	0.791294	+	0.611435i	$0.209408\pi$
$240$	−0.841254	+	0.540641i	−0.0543027	+	0.0348982i
$241$	0.00632836	+	0.0440147i	0.000407645	+	0.00283524i	0.990024	−	0.140897i	$-0.0449987\pi$
$241$	0.00632836	+	0.0440147i	0.000407645	+	0.00283524i	−0.989617	+	0.143732i	$0.954090\pi$
$242$	−0.228567	−	1.58972i	−0.0146929	−	0.102191i
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$	3.76787	−	4.34835i	0.241213	−	0.278375i
$245$	−3.23498	+	7.08362i	−0.206675	+	0.452556i
$246$	−4.47871	−	2.87829i	−0.285552	−	0.183513i
$247$	−31.4580	+	9.23691i	−2.00163	+	0.587731i
$248$	6.08310	+	7.02027i	0.386277	+	0.445787i
$249$	6.58031	+	1.93215i	0.417010	+	0.122445i
$250$	0.415415	+	0.909632i	0.0262732	+	0.0575302i
$251$	1.45531	−	10.1219i	0.0918584	−	0.638889i	−0.890928	−	0.454144i	$-0.849945\pi$
$251$	1.45531	−	10.1219i	0.0918584	−	0.638889i	0.982786	−	0.184745i	$-0.0591459\pi$
$252$	−3.84543			−0.242239
$253$	−3.24911	+	14.3354i	−0.204270	+	0.901259i
$254$	16.6834			1.04681
$255$	−0.694568	+	4.83083i	−0.0434955	+	0.302518i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−4.61249	−	1.35435i	−0.287719	−	0.0844819i	0.134688	−	0.990888i	$-0.456997\pi$
$257$	−4.61249	−	1.35435i	−0.287719	−	0.0844819i	−0.422407	+	0.906406i	$0.638815\pi$
$258$	7.59749	+	8.76797i	0.472999	+	0.545870i
$259$	−3.85094	+	1.13074i	−0.239286	+	0.0702607i
$260$	−5.09384	−	3.27361i	−0.315907	−	0.203021i
$261$	−3.10060	+	6.78938i	−0.191923	+	0.420252i
$262$	12.7170	−	14.6762i	0.785656	−	0.906696i
$263$	0.978902	−	0.629102i	0.0603617	−	0.0387921i	−0.510112	−	0.860108i	$-0.670396\pi$
$263$	0.978902	−	0.629102i	0.0603617	−	0.0387921i	0.570474	+	0.821316i	$0.306760\pi$
$264$	0.436188	+	3.03376i	0.0268455	+	0.186715i
$265$	−0.386555	−	2.68855i	−0.0237459	−	0.165156i
$266$	17.5163	−	11.2571i	1.07400	−	0.690215i
$267$	−2.24664	+	2.59276i	−0.137492	+	0.158675i
$268$	4.62737	−	10.1325i	0.282661	−	0.618942i
$269$	7.14425	+	4.59133i	0.435593	+	0.279938i	0.740004	−	0.672602i	$-0.234823\pi$
$269$	7.14425	+	4.59133i	0.435593	+	0.279938i	−0.304412	+	0.952541i	$0.598460\pi$
$270$	−0.959493	+	0.281733i	−0.0583929	+	0.0171457i
$271$	−0.229496	−	0.264853i	−0.0139409	−	0.0160887i	0.748736	−	0.662868i	$-0.230661\pi$
$271$	−0.229496	−	0.264853i	−0.0139409	−	0.0160887i	−0.762677	+	0.646779i	$0.776115\pi$
$272$	4.68281	+	1.37500i	0.283937	+	0.0833714i
$273$	−9.67266	−	21.1802i	−0.585416	−	1.28188i
$274$	−0.0686177	+	0.477246i	−0.00414535	+	0.0288315i
$275$	3.06495			0.184824
$276$	−1.06009	+	4.67720i	−0.0638096	+	0.281534i
$277$	22.3494			1.34285			0.671424	−	0.741074i	$-0.265683\pi$
$277$	22.3494			1.34285			0.671424	+	0.741074i	$0.265683\pi$
$278$	−0.313351	+	2.17940i	−0.0187935	+	0.130712i
$279$	3.85885	+	8.44970i	0.231023	+	0.505871i
$280$	3.68966	+	1.08338i	0.220500	+	0.0647445i
$281$	−3.02162	−	3.48714i	−0.180255	−	0.208025i	0.658430	−	0.752642i	$-0.271221\pi$
$281$	−3.02162	−	3.48714i	−0.180255	−	0.208025i	−0.838685	+	0.544616i	$0.816675\pi$
$282$	−2.94967	+	0.866100i	−0.175650	+	0.0515755i
$283$	−7.78762	−	5.00480i	−0.462926	−	0.297504i	0.288311	−	0.957537i	$-0.406906\pi$
$283$	−7.78762	−	5.00480i	−0.462926	−	0.297504i	−0.751237	+	0.660032i	$0.770543\pi$
$284$	−5.54083	+	12.1327i	−0.328788	+	0.719945i
$285$	3.54585	−	4.09213i	0.210038	−	0.242397i
$286$	−15.6124	+	10.0335i	−0.923179	+	0.593291i
$287$	2.91354	+	20.2641i	0.171981	+	1.19615i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	5.73678	−	3.68681i	0.337458	−	0.216871i
$290$	4.88780	−	5.64082i	0.287021	−	0.331240i
$291$	0.589529	−	1.29089i	0.0345588	−	0.0756732i
$292$	12.9610	+	8.32951i	0.758484	+	0.487448i
$293$	5.74181	−	1.68595i	0.335440	−	0.0984941i	−0.109675	−	0.993968i	$-0.534981\pi$
$293$	5.74181	−	1.68595i	0.335440	−	0.0984941i	0.445115	+	0.895473i	$0.353163\pi$
$294$	5.09963	+	5.88528i	0.297416	+	0.343237i
$295$	6.35316	+	1.86546i	0.369896	+	0.108611i
$296$	0.433573	+	0.949393i	0.0252009	+	0.0551823i
$297$	−0.436188	+	3.03376i	−0.0253102	+	0.176036i
$298$	2.60679			0.151007
$299$	−28.4279	+	5.92604i	−1.64403	+	0.342712i
$300$	1.00000			0.0577350
$301$	6.34916	−	44.1594i	0.365960	−	2.54531i
$302$	−8.20207	−	17.9600i	−0.471976	−	1.03348i
$303$	−3.39837	−	0.997853i	−0.195232	−	0.0573251i
$304$	−3.54585	−	4.09213i	−0.203368	−	0.234700i
$305$	−5.52063	+	1.62100i	−0.316110	+	0.0928184i
$306$	4.10574	+	2.63860i	0.234710	+	0.150839i
$307$	−8.41931	+	18.4357i	−0.480516	+	1.05218i	0.501806	+	0.864980i	$0.332669\pi$
$307$	−8.41931	+	18.4357i	−0.480516	+	1.05218i	−0.982321	+	0.187202i	$0.940058\pi$
$308$	7.71823	−	8.90731i	0.439787	−	0.507541i
$309$	−14.9464	+	9.60546i	−0.850270	+	0.546435i
$310$	−1.32198	−	9.19459i	−0.0750836	−	0.522218i
$311$	−1.26760	−	8.81632i	−0.0718788	−	0.499928i	−0.993679	−	0.112262i	$-0.964190\pi$
$311$	−1.26760	−	8.81632i	−0.0718788	−	0.499928i	0.921800	−	0.387666i	$-0.126719\pi$
$312$	−5.09384	+	3.27361i	−0.288382	+	0.185332i
$313$	13.1429	−	15.1677i	0.742881	−	0.857330i	−0.250977	−	0.967993i	$-0.580752\pi$
$313$	13.1429	−	15.1677i	0.742881	−	0.857330i	0.993858	+	0.110663i	$0.0352973\pi$
$314$	7.09345	−	15.5325i	0.400306	−	0.876549i
$315$	3.23498	+	2.07900i	0.182271	+	0.117138i
$316$	10.0335	−	2.94610i	0.564428	−	0.165731i
$317$	10.1232	+	11.6828i	0.568577	+	0.656173i	0.965109	−	0.261848i	$-0.0843319\pi$
$317$	10.1232	+	11.6828i	0.568577	+	0.656173i	−0.396532	+	0.918021i	$0.629786\pi$
$318$	−2.60617	−	0.765242i	−0.146147	−	0.0429126i
$319$	−9.50321	−	20.8091i	−0.532077	−	1.16509i
$320$	0.142315	−	0.989821i	0.00795564	−	0.0553327i
$321$	2.46798			0.137749
$322$	16.2623	−	8.69743i	0.906265	−	0.484689i
$323$	−26.4263			−1.47040
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	2.51536	+	5.50788i	0.139527	+	0.305522i
$326$	−4.56148	−	1.33937i	−0.252637	−	0.0741809i
$327$	−2.35457	−	2.71732i	−0.130208	−	0.150268i
$328$	5.10820	−	1.49990i	0.282053	−	0.0828183i
$329$	9.94496	+	6.39124i	0.548283	+	0.352360i
$330$	1.27323	−	2.78798i	0.0700888	−	0.153473i
$331$	−4.81080	+	5.55196i	−0.264425	+	0.305163i	−0.872399	−	0.488794i	$-0.837437\pi$
$331$	−4.81080	+	5.55196i	−0.264425	+	0.305163i	0.607974	+	0.793957i	$0.291983\pi$
$332$	−5.76941	+	3.70778i	−0.316638	+	0.203491i
$333$	0.148536	+	1.03309i	0.00813970	+	0.0566128i
$334$	−0.440477	−	3.06359i	−0.0241018	−	0.167632i
$335$	−9.37084	+	6.02228i	−0.511984	+	0.329032i
$336$	2.51822	−	2.90618i	0.137380	−	0.158545i
$337$	−5.56352	+	12.1824i	−0.303064	+	0.663618i	−0.998487	−	0.0549828i	$-0.982490\pi$
$337$	−5.56352	+	12.1824i	−0.303064	+	0.663618i	0.695423	+	0.718600i	$0.255217\pi$
$338$	−19.9072	−	12.7936i	−1.08281	−	0.695879i
$339$	0.684087	−	0.200866i	0.0371545	−	0.0109096i
$340$	−3.19605	−	3.68844i	−0.173330	−	0.200034i
$341$	−27.3175	−	8.02115i	−1.47933	−	0.434369i
$342$	−2.24933	−	4.92535i	−0.121630	−	0.266332i
$343$	0.430884	−	2.99686i	0.0232656	−	0.161815i
$344$	−11.6017			−0.625521
$345$	3.42049	−	3.36159i	0.184153	−	0.180982i
$346$	16.7748			0.901817
$347$	0.609118	−	4.23651i	0.0326992	−	0.227428i	−0.966918	−	0.255086i	$-0.917896\pi$
$347$	0.609118	−	4.23651i	0.0326992	−	0.227428i	0.999617	+	0.0276587i	$0.00880516\pi$
$348$	−3.10060	−	6.78938i	−0.166210	−	0.363949i
$349$	−26.4639	−	7.77050i	−1.41658	−	0.415945i	−0.518235	−	0.855238i	$-0.673411\pi$
$349$	−26.4639	−	7.77050i	−1.41658	−	0.415945i	−0.898344	+	0.439293i	$0.855229\pi$
$350$	−2.51822	−	2.90618i	−0.134605	−	0.155342i
$351$	−5.80979	+	1.70591i	−0.310103	+	0.0910546i
$352$	−2.57840	−	1.65704i	−0.137429	−	0.0883204i
$353$	−6.66261	+	14.5891i	−0.354615	+	0.776498i	0.645306	+	0.763924i	$0.276730\pi$
$353$	−6.66261	+	14.5891i	−0.354615	+	0.776498i	−0.999921	+	0.0125742i	$0.995997\pi$
$354$	4.33608	−	5.00410i	0.230460	−	0.265965i
$355$	11.2207	−	7.21110i	0.595532	−	0.382725i
$356$	−0.488242	−	3.39580i	−0.0258768	−	0.179977i
$357$	−2.67091	−	18.5766i	−0.141360	−	0.983179i
$358$	−18.2309	+	11.7163i	−0.963532	+	0.619224i
$359$	−16.6495	+	19.2146i	−0.878729	+	1.01411i	0.121040	+	0.992648i	$0.461377\pi$
$359$	−16.6495	+	19.2146i	−0.878729	+	1.01411i	−0.999770	+	0.0214603i	$0.993168\pi$
$360$	0.415415	−	0.909632i	0.0218943	−	0.0479418i
$361$	8.68053	+	5.57864i	0.456870	+	0.293613i
$362$	−15.3647	+	4.51148i	−0.807551	+	0.237118i
$363$	1.05175	+	1.21379i	0.0552026	+	0.0637072i
$364$	22.3411	+	6.55995i	1.17099	+	0.343835i
$365$	−6.40019	−	14.0145i	−0.335001	−	0.733550i
$366$	−0.818836	+	5.69513i	−0.0428013	+	0.297689i
$367$	4.86933			0.254177			0.127089	−	0.991891i	$-0.459437\pi$
$367$	4.86933			0.254177			0.127089	+	0.991891i	$0.459437\pi$
$368$	−2.84059	−	3.86407i	−0.148076	−	0.201429i
$369$	5.32386			0.277149
$370$	0.148536	−	1.03309i	0.00772199	−	0.0537076i
$371$	4.33899	+	9.50107i	0.225269	+	0.493271i
$372$	−8.91287	−	2.61705i	−0.462111	−	0.135688i
$373$	−6.03879	−	6.96913i	−0.312676	−	0.360848i	0.577559	−	0.816349i	$-0.304005\pi$
$373$	−6.03879	−	6.96913i	−0.312676	−	0.360848i	−0.890235	+	0.455501i	$0.849460\pi$
$374$	−14.3526	+	4.21430i	−0.742155	+	0.217916i
$375$	−0.841254	−	0.540641i	−0.0434421	−	0.0279186i
$376$	1.27707	−	2.79638i	0.0658596	−	0.144212i
$377$	29.5959	−	34.1555i	1.52427	−	1.75910i
$378$	3.23498	−	2.07900i	0.166390	−	0.106932i
$379$	−2.59669	−	18.0604i	−0.133383	−	0.927699i	−0.941100	−	0.338128i	$-0.890206\pi$
$379$	−2.59669	−	18.0604i	−0.133383	−	0.927699i	0.807717	−	0.589570i	$-0.200703\pi$
$380$	0.770587	+	5.35955i	0.0395303	+	0.274939i
$381$	−14.0350	+	9.01972i	−0.719032	+	0.462094i
$382$	12.9057	−	14.8940i	0.660315	−	0.762044i
$383$	8.19442	−	17.9433i	0.418715	−	0.916858i	−0.576310	−	0.817231i	$-0.695508\pi$
$383$	8.19442	−	17.9433i	0.418715	−	0.916858i	0.995025	−	0.0996268i	$-0.0317649\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	−11.3086	+	3.32052i	−0.576342	+	0.169229i
$386$	15.8062	+	18.2414i	0.804517	+	0.928462i
$387$	−11.1317	−	3.26857i	−0.565858	−	0.166151i
$388$	0.589529	+	1.29089i	0.0299288	+	0.0655350i
$389$	3.32009	−	23.0917i	0.168335	−	1.17080i	−0.713989	−	0.700157i	$-0.753113\pi$
$389$	3.32009	−	23.0917i	0.168335	−	1.17080i	0.882325	−	0.470641i	$-0.155977\pi$
$390$	6.05506			0.306610
$391$	−23.3311	−	1.87245i	−1.17990	−	0.0946940i
$392$	−7.78735			−0.393320
$393$	−2.76366	+	19.2217i	−0.139408	+	0.969605i
$394$	−4.23722	−	9.27823i	−0.213468	−	0.467430i
$395$	−10.0335	−	2.94610i	−0.504840	−	0.148234i
$396$	−2.00712	−	2.31634i	−0.100861	−	0.116400i
$397$	13.9787	−	4.10452i	0.701572	−	0.206000i	0.0885565	−	0.996071i	$-0.471775\pi$
$397$	13.9787	−	4.10452i	0.701572	−	0.206000i	0.613015	+	0.790071i	$0.289956\pi$
$398$	−4.51703	−	2.90292i	−0.226418	−	0.145510i
$399$	−8.64965	+	18.9401i	−0.433024	+	0.948191i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	−9.33830	+	6.00136i	−0.466333	+	0.299694i	−0.752626	−	0.658448i	$-0.771213\pi$
$401$	−9.33830	+	6.00136i	−0.466333	+	0.299694i	0.286293	+	0.958142i	$0.407577\pi$
$402$	1.58527	+	11.0258i	0.0790658	+	0.549915i
$403$	−8.00469	−	55.6738i	−0.398742	−	2.77331i
$404$	2.97959	−	1.91487i	0.148240	−	0.0952681i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	−11.9232	+	26.1081i	−0.591737	+	1.29572i
$407$	−2.69111	−	1.72947i	−0.133393	−	0.0857266i
$408$	−4.68281	+	1.37500i	−0.231834	+	0.0680725i
$409$	−13.4845	−	15.5620i	−0.666767	−	0.769490i	0.317100	−	0.948392i	$-0.397291\pi$
$409$	−13.4845	−	15.5620i	−0.666767	−	0.769490i	−0.983867	+	0.178902i	$0.942746\pi$
$410$	−5.10820	−	1.49990i	−0.252276	−	0.0740749i
$411$	−0.200294	−	0.438583i	−0.00987978	−	0.0216337i
$412$	2.52848	−	17.5860i	0.124569	−	0.866398i
$413$	−25.4621			−1.25291
$414$	−1.63689	−	4.50784i	−0.0804486	−	0.221548i
$415$	6.85811			0.336652
$416$	0.861725	−	5.99343i	0.0422495	−	0.293852i
$417$	−0.914666	−	2.00284i	−0.0447914	−	0.0980795i
$418$	15.9234	+	4.67554i	0.778841	+	0.228688i
$419$	−19.3576	−	22.3398i	−0.945679	−	1.09137i	−0.995701	−	0.0926235i	$-0.970475\pi$
$419$	−19.3576	−	22.3398i	−0.945679	−	1.09137i	0.0500224	−	0.998748i	$-0.484071\pi$
$420$	−3.68966	+	1.08338i	−0.180037	+	0.0528637i
$421$	6.42699	+	4.13038i	0.313232	+	0.201302i	0.687805	−	0.725895i	$-0.258574\pi$
$421$	6.42699	+	4.13038i	0.313232	+	0.201302i	−0.374573	+	0.927197i	$0.622211\pi$
$422$	6.71508	−	14.7040i	0.326885	−	0.715778i
$423$	2.01317	−	2.32332i	0.0978836	−	0.112964i
$424$	2.28501	−	1.46849i	0.110970	−	0.0713161i
$425$	0.694568	+	4.83083i	0.0336915	+	0.234330i
$426$	−1.89820	−	13.2023i	−0.0919683	−	0.639653i
$427$	18.6131	−	11.9619i	0.900751	−	0.578878i
$428$	−1.61618	+	1.86517i	−0.0781211	+	0.0901566i
$429$	7.70947	−	16.8814i	0.372217	−	0.815040i
$430$	9.75996	+	6.27235i	0.470667	+	0.302479i
$431$	32.2552	−	9.47097i	1.55368	−	0.456201i	0.611480	−	0.791260i	$-0.290574\pi$
$431$	32.2552	−	9.47097i	1.55368	−	0.456201i	0.942197	+	0.335059i	$0.108756\pi$
$432$	−0.654861	−	0.755750i	−0.0315070	−	0.0363610i
$433$	5.58923	+	1.64115i	0.268601	+	0.0788684i	0.413260	−	0.910613i	$-0.364390\pi$
$433$	5.58923	+	1.64115i	0.268601	+	0.0788684i	−0.144658	+	0.989482i	$0.546208\pi$
$434$	14.8389	+	32.4928i	0.712292	+	1.55970i
$435$	−1.06222	+	7.38790i	−0.0509295	+	0.354223i
$436$	3.59552			0.172194
$437$	20.6524	+	15.7419i	0.987937	+	0.753036i
$438$	−15.4067			−0.736162
$439$	−3.76775	+	26.2053i	−0.179825	+	1.25071i	0.677341	+	0.735669i	$0.263132\pi$
$439$	−3.76775	+	26.2053i	−0.179825	+	1.25071i	−0.857166	+	0.515040i	$0.827777\pi$
$440$	1.27323	+	2.78798i	0.0606987	+	0.132912i
$441$	−7.47190	−	2.19395i	−0.355805	−	0.104474i
$442$	−19.3523	−	22.3337i	−0.920494	−	1.06231i
$443$	−3.03802	+	0.892042i	−0.144341	+	0.0423822i	−0.353105	−	0.935584i	$-0.614874\pi$
$443$	−3.03802	+	0.892042i	−0.144341	+	0.0423822i	0.208764	+	0.977966i	$0.433056\pi$
$444$	−0.878025	−	0.564273i	−0.0416692	−	0.0267792i
$445$	−1.42517	+	3.12069i	−0.0675596	+	0.147935i
$446$	7.86965	−	9.08206i	0.372639	−	0.430048i
$447$	−2.19297	+	1.40934i	−0.103724	+	0.0666594i
$448$	0.547262	+	3.80629i	0.0258557	+	0.179830i
$449$	1.06967	+	7.43975i	0.0504811	+	0.351103i	0.999370	+	0.0354931i	$0.0113002\pi$
$449$	1.06967	+	7.43975i	0.0504811	+	0.351103i	−0.948889	+	0.315610i	$0.897791\pi$
$450$	−0.841254	+	0.540641i	−0.0396571	+	0.0254861i
$451$	−10.6856	+	12.3318i	−0.503165	+	0.580684i
$452$	−0.296177	+	0.648538i	−0.0139310	+	0.0305047i
$453$	16.6099	+	10.6746i	0.780403	+	0.501535i
$454$	10.6254	−	3.11991i	0.498676	−	0.146425i
$455$	−15.2480	−	17.5971i	−0.714837	−	0.824965i
$456$	5.19533	+	1.52549i	0.243294	+	0.0714375i
$457$	9.70564	+	21.2524i	0.454010	+	0.994144i	0.988812	+	0.149167i	$0.0476591\pi$
$457$	9.70564	+	21.2524i	0.454010	+	0.994144i	−0.534802	+	0.844978i	$0.679614\pi$
$458$	0.650106	−	4.52159i	0.0303775	−	0.211280i
$459$	−4.88050			−0.227802
$460$	0.300576	+	4.78640i	0.0140144	+	0.223167i
$461$	34.3912			1.60176			0.800879	−	0.598826i	$-0.204366\pi$
$461$	34.3912			1.60176			0.800879	+	0.598826i	$0.204366\pi$
$462$	−1.67733	+	11.6661i	−0.0780365	+	0.542756i
$463$	3.32011	+	7.27003i	0.154299	+	0.337867i	0.970957	−	0.239255i	$-0.0769031\pi$
$463$	3.32011	+	7.27003i	0.154299	+	0.337867i	−0.816658	+	0.577122i	$0.804176\pi$
$464$	7.16153	+	2.10282i	0.332466	+	0.0976208i
$465$	6.08310	+	7.02027i	0.282097	+	0.325557i
$466$	−27.2509	+	8.00159i	−1.26237	+	0.370667i
$467$	16.4693	+	10.5842i	0.762108	+	0.489777i	0.863052	−	0.505115i	$-0.168550\pi$
$467$	16.4693	+	10.5842i	0.762108	+	0.489777i	−0.100944	+	0.994892i	$0.532186\pi$
$468$	2.51536	−	5.50788i	0.116273	−	0.254602i
$469$	28.0508	−	32.3724i	1.29527	−	1.49482i
$470$	−2.58617	+	1.66203i	−0.119291	+	0.0766639i
$471$	2.43011	+	16.9018i	0.111973	+	0.778792i
$472$	0.942320	+	6.55398i	0.0433738	+	0.301671i
$473$	29.9138	−	19.2244i	1.37544	−	0.883941i
$474$	−6.84793	+	7.90293i	−0.314536	+	0.362993i
$475$	2.24933	−	4.92535i	0.103206	−	0.225991i
$476$	15.7883	+	10.1466i	0.723658	+	0.465067i
$477$	2.60617	−	0.765242i	0.119328	−	0.0350380i
$478$	−1.13581	−	1.31079i	−0.0519507	−	0.0599543i
$479$	6.71320	+	1.97117i	0.306734	+	0.0900652i	0.431477	−	0.902124i	$-0.357993\pi$
$479$	6.71320	+	1.97117i	0.306734	+	0.0900652i	−0.124743	+	0.992189i	$0.539811\pi$
$480$	0.415415	+	0.909632i	0.0189610	+	0.0415188i
$481$	0.899391	−	6.25540i	0.0410087	−	0.285222i
$482$	0.0444673			0.00202543
$483$	−8.97856	+	16.1088i	−0.408539	+	0.732977i
$484$	−1.60607			−0.0730031
$485$	0.201964	−	1.40469i	0.00917070	−	0.0637836i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	14.7121	+	4.31987i	0.666670	+	0.195752i	0.597519	−	0.801854i	$-0.296153\pi$
$487$	14.7121	+	4.31987i	0.666670	+	0.195752i	0.0691501	+	0.997606i	$0.477971\pi$
$488$	−3.76787	−	4.34835i	−0.170563	−	0.196841i
$489$	4.56148	−	1.33937i	0.206277	−	0.0605685i
$490$	6.55113	+	4.21016i	0.295950	+	0.190195i
$491$	−14.9584	+	32.7544i	−0.675065	+	1.47819i	0.192723	+	0.981253i	$0.438268\pi$
$491$	−14.9584	+	32.7544i	−0.675065	+	1.47819i	−0.867789	+	0.496934i	$0.834459\pi$
$492$	−3.48638	+	4.02350i	−0.157178	+	0.181393i
$493$	30.6447	−	19.6942i	1.38017	−	0.886981i
$494$	4.66595	+	32.4524i	0.209931	+	1.46010i
$495$	0.436188	+	3.03376i	0.0196052	+	0.136357i
$496$	7.81453	−	5.02209i	0.350883	−	0.225499i
$497$	−33.5882	+	38.7628i	−1.50664	+	1.73875i
$498$	2.84896	−	6.23836i	0.127665	−	0.279548i
$499$	2.44744	+	1.57287i	0.109562	+	0.0704115i	0.594275	−	0.804262i	$-0.297439\pi$
$499$	2.44744	+	1.57287i	0.109562	+	0.0704115i	−0.484712	+	0.874674i	$0.661076\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	2.02685	+	2.33911i	0.0905531	+	0.104504i
$502$	−9.81177	−	2.88100i	−0.437921	−	0.128585i
$503$	−9.00933	−	19.7277i	−0.401706	−	0.879614i	−0.997094	−	0.0761760i	$-0.975729\pi$
$503$	−9.00933	−	19.7277i	−0.401706	−	0.879614i	0.595388	−	0.803438i	$-0.296998\pi$
$504$	−0.547262	+	3.80629i	−0.0243770	+	0.169546i
$505$	−3.54184			−0.157610
$506$	13.7271	+	5.25618i	0.610244	+	0.233666i
$507$	23.6637			1.05094
$508$	2.37429	−	16.5136i	0.105342	−	0.732671i
$509$	9.09940	+	19.9249i	0.403324	+	0.883156i	0.996922	+	0.0783947i	$0.0249794\pi$
$509$	9.09940	+	19.9249i	0.403324	+	0.883156i	−0.593599	+	0.804761i	$0.702293\pi$
$510$	4.68281	+	1.37500i	0.207358	+	0.0608859i
$511$	38.7976	+	44.7748i	1.71630	+	1.98072i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	4.55510	+	2.92739i	0.201113	+	0.129247i
$514$	−1.99699	+	4.37279i	−0.0880834	+	0.192876i
$515$	−11.6348	+	13.4272i	−0.512690	+	0.591675i
$516$	9.75996	−	6.27235i	0.429658	−	0.276125i
$517$	1.34093	+	9.32635i	0.0589739	+	0.410172i
$518$	0.571183	+	3.97267i	0.0250963	+	0.174549i
$519$	−14.1118	+	9.06912i	−0.619441	+	0.398090i
$520$	−3.96522	+	4.57611i	−0.173886	+	0.200676i
$521$	−4.19311	+	9.18164i	−0.183704	+	0.402255i	−0.978970	−	0.204006i	$-0.934604\pi$
$521$	−4.19311	+	9.18164i	−0.183704	+	0.402255i	0.795266	+	0.606261i	$0.207331\pi$
$522$	6.27901	+	4.03527i	0.274825	+	0.176619i
$523$	−30.2327	+	8.87712i	−1.32198	+	0.388169i	−0.865208	−	0.501413i	$-0.832814\pi$
$523$	−30.2327	+	8.87712i	−1.32198	+	0.388169i	−0.456775	+	0.889582i	$0.650996\pi$
$524$	−12.7170	−	14.6762i	−0.555543	−	0.641131i
$525$	3.68966	+	1.08338i	0.161030	+	0.0472827i
$526$	−0.483386	−	1.05847i	−0.0210766	−	0.0461514i
$527$	6.45194	−	44.8743i	0.281051	−	1.95475i
$528$	3.06495			0.133385
$529$	17.1180	+	15.3614i	0.744262	+	0.667888i
$530$	−2.71620			−0.117984
$531$	−0.942320	+	6.55398i	−0.0408932	+	0.284419i
$532$	−8.64965	−	18.9401i	−0.375010	−	0.821157i
$533$	−30.9305	−	9.08200i	−1.33975	−	0.393385i
$534$	2.24664	+	2.59276i	0.0972217	+	0.112200i
$535$	2.36801	−	0.695310i	0.102378	−	0.0300609i
$536$	−9.37084	−	6.02228i	−0.404759	−	0.260123i
$537$	9.00249	−	19.7127i	0.388486	−	0.850666i
$538$	5.56133	−	6.41812i	0.239766	−	0.276705i
$539$	20.0789	−	12.9039i	0.864860	−	0.555812i
$540$	0.142315	+	0.989821i	0.00612426	+	0.0425951i
$541$	−0.770902	−	5.36174i	−0.0331437	−	0.230519i	0.966516	−	0.256606i	$-0.0826044\pi$
$541$	−0.770902	−	5.36174i	−0.0331437	−	0.230519i	−0.999660	+	0.0260871i	$0.991695\pi$
$542$	−0.294818	+	0.189468i	−0.0126635	+	0.00813834i
$543$	10.4865	−	12.1021i	0.450019	−	0.519350i
$544$	2.02743	−	4.43946i	0.0869256	−	0.190340i
$545$	−3.02475	−	1.94389i	−0.129566	−	0.0832670i
$546$	−22.3411	+	6.55995i	−0.956113	+	0.280740i
$547$	−10.7400	−	12.3946i	−0.459208	−	0.529954i	0.478170	−	0.878267i	$-0.341300\pi$
$547$	−10.7400	−	12.3946i	−0.459208	−	0.529954i	−0.937378	+	0.348313i	$0.886755\pi$
$548$	0.462624	+	0.135839i	0.0197623	+	0.00580273i
$549$	−2.39017	−	5.23375i	−0.102010	−	0.223371i
$550$	0.436188	−	3.03376i	0.0185991	−	0.129360i
$551$	−40.4144			−1.72171
$552$	4.47873	+	1.71493i	0.190627	+	0.0729923i
$553$	40.2120			1.70999
$554$	3.18066	−	22.1219i	0.135133	−	0.939871i
$555$	0.433573	+	0.949393i	0.0184042	+	0.0402995i
$556$	2.11262	+	0.620323i	0.0895952	+	0.0263075i
$557$	3.13883	+	3.62241i	0.132997	+	0.153486i	0.818341	−	0.574732i	$-0.194894\pi$
$557$	3.13883	+	3.62241i	0.132997	+	0.153486i	−0.685345	+	0.728219i	$0.740348\pi$
$558$	8.91287	−	2.61705i	0.377312	−	0.110789i
$559$	59.0972	+	37.9794i	2.49954	+	1.60636i
$560$	1.59745	−	3.49793i	0.0675046	−	0.147814i
$561$	9.79574	−	11.3049i	0.413577	−	0.477293i
$562$	−3.88167	+	2.49460i	−0.163738	+	0.105228i
$563$	−0.450218	−	3.13134i	−0.0189744	−	0.131970i	0.978132	−	0.207983i	$-0.0666900\pi$
$563$	−0.450218	−	3.13134i	−0.0189744	−	0.131970i	−0.997107	+	0.0760132i	$0.975781\pi$
$564$	0.437503	+	3.04290i	0.0184222	+	0.128129i
$565$	0.599787	−	0.385459i	0.0252332	−	0.0162164i
$566$	−6.06215	+	6.99609i	−0.254811	+	0.294068i
$567$	−1.59745	+	3.49793i	−0.0670866	+	0.146899i
$568$	11.2207	+	7.21110i	0.470810	+	0.302571i
$569$	1.22787	−	0.360535i	0.0514750	−	0.0151144i	−0.255894	−	0.966705i	$-0.582370\pi$
$569$	1.22787	−	0.360535i	0.0514750	−	0.0151144i	0.307369	+	0.951591i	$0.400552\pi$
$570$	−3.54585	−	4.09213i	−0.148519	−	0.171400i
$571$	−0.392300	−	0.115190i	−0.0164172	−	0.00482054i	0.273514	−	0.961868i	$-0.411814\pi$
$571$	−0.392300	−	0.115190i	−0.0164172	−	0.00482054i	−0.289931	+	0.957048i	$0.593632\pi$
$572$	7.70947	+	16.8814i	0.322349	+	0.705846i
$573$	−2.80468	+	19.5070i	−0.117167	+	0.814917i
$574$	20.4725			0.854507
$575$	2.33486	−	4.18908i	0.0973706	−	0.174697i
$576$	1.00000			0.0416667
$577$	4.09206	−	28.4609i	0.170355	−	1.18484i	−0.707782	−	0.706431i	$-0.750304\pi$
$577$	4.09206	−	28.4609i	0.170355	−	1.18484i	0.878136	−	0.478411i	$-0.158787\pi$
$578$	−2.83285	−	6.20308i	−0.117831	−	0.258014i
$579$	−23.1591	−	6.80012i	−0.962459	−	0.282603i
$580$	−4.88780	−	5.64082i	−0.202955	−	0.234222i
$581$	−25.3041	+	7.42997i	−1.04979	+	0.308247i
$582$	−1.19385	−	0.767241i	−0.0494867	−	0.0318032i
$583$	−3.45834	+	7.57270i	−0.143230	+	0.313629i
$584$	10.0893	−	11.6436i	0.417497	−	0.481817i
$585$	−5.09384	+	3.27361i	−0.210604	+	0.135347i
$586$	−0.851642	−	5.92330i	−0.0351810	−	0.244689i
$587$	−4.92725	−	34.2698i	−0.203369	−	1.41447i	−0.794193	−	0.607665i	$-0.792106\pi$
$587$	−4.92725	−	34.2698i	−0.203369	−	1.41447i	0.590824	−	0.806800i	$-0.298803\pi$
$588$	6.55113	−	4.21016i	0.270164	−	0.173624i
$589$	−32.9379	+	38.0124i	−1.35718	+	1.56627i
$590$	2.75062	−	6.02302i	0.113241	−	0.247964i
$591$	8.58077	+	5.51452i	0.352966	+	0.226837i
$592$	1.00143	−	0.294047i	0.0411586	−	0.0120853i
$593$	22.6874	+	26.1826i	0.931658	+	1.07519i	0.997006	+	0.0773280i	$0.0246389\pi$
$593$	22.6874	+	26.1826i	0.931658	+	1.07519i	−0.0653478	+	0.997863i	$0.520816\pi$
$594$	2.94080	+	0.863497i	0.120662	+	0.0354297i
$595$	−7.79636	−	17.0717i	−0.319620	−	0.699870i
$596$	0.370985	−	2.58026i	0.0151961	−	0.105691i
$597$	5.36940			0.219755
$598$	1.82001	+	28.9820i	0.0744256	+	1.18516i
$599$	18.3410			0.749392			0.374696	−	0.927148i	$-0.377747\pi$
$599$	18.3410			0.749392			0.374696	+	0.927148i	$0.377747\pi$
$600$	0.142315	−	0.989821i	0.00580998	−	0.0404093i
$601$	4.97210	+	10.8874i	0.202816	+	0.444106i	0.983521	−	0.180795i	$-0.0578669\pi$
$601$	4.97210	+	10.8874i	0.202816	+	0.444106i	−0.780705	+	0.624900i	$0.785140\pi$
$602$	−42.8063	−	12.5691i	−1.74466	−	0.512277i
$603$	−7.29459	−	8.41840i	−0.297059	−	0.342824i
$604$	−18.9445	+	5.56260i	−0.770840	+	0.226339i
$605$	1.35111	+	0.868306i	0.0549305	+	0.0353017i
$606$	−1.47134	+	3.22177i	−0.0597689	+	0.130876i
$607$	19.5656	−	22.5799i	0.794143	−	0.916490i	−0.203902	−	0.978991i	$-0.565362\pi$
$607$	19.5656	−	22.5799i	0.794143	−	0.916490i	0.998045	+	0.0625016i	$0.0199079\pi$
$608$	−4.55510	+	2.92739i	−0.184734	+	0.118721i
$609$	−4.08469	−	28.4097i	−0.165520	−	1.15122i
$610$	0.818836	+	5.69513i	0.0331537	+	0.230589i
$611$	−15.6594	+	10.0637i	−0.633513	+	0.407134i
$612$	3.19605	−	3.68844i	0.129193	−	0.149096i
$613$	4.45461	−	9.75422i	0.179920	−	0.393969i	−0.798087	−	0.602542i	$-0.794155\pi$
$613$	4.45461	−	9.75422i	0.179920	−	0.393969i	0.978007	+	0.208573i	$0.0668818\pi$
$614$	17.0499	+	10.9573i	0.688077	+	0.442200i
$615$	5.10820	−	1.49990i	0.205983	−	0.0604819i
$616$	−7.71823	−	8.90731i	−0.310976	−	0.358886i
$617$	−31.6401	−	9.29037i	−1.27378	−	0.374016i	−0.426176	−	0.904640i	$-0.640139\pi$
$617$	−31.6401	−	9.29037i	−1.27378	−	0.374016i	−0.847607	+	0.530624i	$0.821958\pi$
$618$	7.38059	+	16.1612i	0.296891	+	0.650101i
$619$	−3.60712	+	25.0881i	−0.144982	+	1.00837i	0.779296	+	0.626656i	$0.215577\pi$
$619$	−3.60712	+	25.0881i	−0.144982	+	1.00837i	−0.924278	+	0.381719i	$0.875332\pi$
$620$	−9.28914			−0.373061
$621$	3.81416	+	2.90727i	0.153057	+	0.116665i
$622$	−8.90698			−0.357137
$623$	1.87750	−	13.0583i	0.0752205	−	0.523170i
$624$	2.51536	+	5.50788i	0.100695	+	0.220491i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	−13.1429	−	15.1677i	−0.525296	−	0.606224i
$627$	−15.9234	+	4.67554i	−0.635921	+	0.186723i
$628$	−14.3649	−	9.23175i	−0.573221	−	0.368387i
$629$	2.11606	−	4.63351i	0.0843726	−	0.184750i
$630$	2.51822	−	2.90618i	0.100328	−	0.115785i
$631$	−19.3925	+	12.4628i	−0.772002	+	0.496136i	−0.866371	−	0.499402i	$-0.833553\pi$
$631$	−19.3925	+	12.4628i	−0.772002	+	0.496136i	0.0943685	+	0.995537i	$0.469917\pi$
$632$	−1.48820	−	10.3506i	−0.0591973	−	0.411726i
$633$	2.30048	+	16.0002i	0.0914360	+	0.635951i
$634$	13.0046	−	8.35755i	0.516479	−	0.331921i
$635$	−10.9253	+	12.6085i	−0.433557	+	0.500351i
$636$	−1.12835	+	2.47074i	−0.0447420	+	0.0979712i
$637$	39.6675	+	25.4927i	1.57168	+	1.01006i
$638$	−21.9498	+	6.44503i	−0.868999	+	0.255161i
$639$	8.73457	+	10.0802i	0.345534	+	0.398768i
$640$	−0.959493	−	0.281733i	−0.0379273	−	0.0111365i
$641$	17.0034	+	37.2324i	0.671596	+	1.47059i	0.871309	+	0.490735i	$0.163272\pi$
$641$	17.0034	+	37.2324i	0.671596	+	1.47059i	−0.199713	+	0.979854i	$0.564001\pi$
$642$	0.351230	−	2.44286i	0.0138619	−	0.0964119i
$643$	27.6361			1.08986			0.544930	−	0.838481i	$-0.316556\pi$
$643$	27.6361			1.08986			0.544930	+	0.838481i	$0.316556\pi$
$644$	−6.29453	−	17.3346i	−0.248039	−	0.683078i
$645$	−11.6017			−0.456816
$646$	−3.76085	+	26.1573i	−0.147969	+	1.02915i
$647$	20.3398	+	44.5379i	0.799640	+	1.75097i	0.646719	+	0.762729i	$0.276141\pi$
$647$	20.3398	+	44.5379i	0.799640	+	1.75097i	0.152921	+	0.988238i	$0.451132\pi$
$648$	0.959493	+	0.281733i	0.0376924	+	0.0110675i
$649$	−13.2899	−	15.3373i	−0.521673	−	0.602043i
$650$	5.80979	−	1.70591i	0.227879	−	0.0669112i
$651$	−30.0502	−	19.3121i	−1.17776	−	0.756901i
$652$	−1.97490	+	4.32444i	−0.0773432	+	0.169358i
$653$	−29.4183	+	33.9505i	−1.15123	+	1.32859i	−0.215237	+	0.976562i	$0.569053\pi$
$653$	−29.4183	+	33.9505i	−1.15123	+	1.32859i	−0.935990	+	0.352026i	$0.885493\pi$
$654$	−3.02475	+	1.94389i	−0.118277	+	0.0760120i
$655$	2.76366	+	19.2217i	0.107985	+	0.751053i
$656$	−0.757664	−	5.26967i	−0.0295818	−	0.205746i
$657$	12.9610	−	8.32951i	0.505656	−	0.324965i
$658$	7.74150	−	8.93416i	0.301795	−	0.348290i
$659$	18.0413	−	39.5050i	0.702791	−	1.53890i	−0.133763	−	0.991013i	$-0.542706\pi$
$659$	18.0413	−	39.5050i	0.702791	−	1.53890i	0.836554	−	0.547885i	$-0.184567\pi$
$660$	−2.57840	−	1.65704i	−0.100364	−	0.0645001i
$661$	−31.6985	+	9.30753i	−1.23293	+	0.362021i	−0.832355	−	0.554243i	$-0.813008\pi$
$661$	−31.6985	+	9.30753i	−1.23293	+	0.362021i	−0.400575	+	0.916264i	$0.631190\pi$
$662$	4.81080	+	5.55196i	0.186977	+	0.215783i
$663$	28.3547	+	8.32569i	1.10120	+	0.323343i
$664$	2.84896	+	6.23836i	0.110561	+	0.242095i
$665$	−2.96324	+	20.6098i	−0.114909	+	0.799213i
$666$	1.04371			0.0404430
$667$	−35.6808	−	2.86359i	−1.38156	−	0.110879i
$668$	−3.09509			−0.119753
$669$	−1.71024	+	11.8950i	−0.0661217	+	0.459886i
$670$	4.62737	+	10.1325i	0.178771	+	0.391453i
$671$	16.9205	+	4.96830i	0.653207	+	0.191799i
$672$	−2.51822	−	2.90618i	−0.0971425	−	0.112108i
$673$	6.34127	−	1.86197i	0.244438	−	0.0717735i	−0.157219	−	0.987564i	$-0.550253\pi$
$673$	6.34127	−	1.86197i	0.244438	−	0.0717735i	0.401657	+	0.915790i	$0.368435\pi$
$674$	11.2666	+	7.24062i	0.433974	+	0.278898i
$675$	0.415415	−	0.909632i	0.0159893	−	0.0350118i
$676$	−15.4965	+	17.8839i	−0.596018	+	0.687841i
$677$	−2.08538	+	1.34020i	−0.0801479	+	0.0515079i	−0.580101	−	0.814545i	$-0.696987\pi$
$677$	−2.08538	+	1.34020i	−0.0801479	+	0.0515079i	0.499953	+	0.866052i	$0.333351\pi$
$678$	−0.101466	−	0.705711i	−0.00389677	−	0.0271027i
$679$	0.776638	+	5.40163i	0.0298046	+	0.207296i
$680$	−4.10574	+	2.63860i	−0.157448	+	0.101186i
$681$	−7.25193	+	8.36917i	−0.277895	+	0.320707i
$682$	−11.8272	+	25.8979i	−0.452887	+	0.991683i
$683$	16.1015	+	10.3478i	0.616108	+	0.395949i	0.811143	−	0.584848i	$-0.198846\pi$
$683$	16.1015	+	10.3478i	0.616108	+	0.395949i	−0.195035	+	0.980796i	$0.562482\pi$
$684$	−5.19533	+	1.52549i	−0.198648	+	0.0583284i
$685$	−0.315744	−	0.364388i	−0.0120640	−	0.0139225i
$686$	−2.90504	−	0.852997i	−0.110915	−	0.0325676i
$687$	1.89765	+	4.15528i	0.0723999	+	0.158534i
$688$	−1.65109	+	11.4836i	−0.0629473	+	0.437808i
$689$	−16.4467			−0.626571
$690$	−2.84059	−	3.86407i	−0.108139	−	0.147103i
$691$	−45.9941			−1.74970			−0.874848	−	0.484397i	$-0.839039\pi$
$691$	−45.9941			−1.74970			−0.874848	+	0.484397i	$0.839039\pi$
$692$	2.38730	−	16.6040i	0.0907515	−	0.631190i
$693$	−4.89611	−	10.7210i	−0.185988	−	0.407256i
$694$	−4.10670	−	1.20584i	−0.155888	−	0.0457729i
$695$	−1.44188	−	1.66402i	−0.0546937	−	0.0631199i
$696$	−7.16153	+	2.10282i	−0.271457	+	0.0797070i
$697$	−21.8584	−	14.0475i	−0.827945	−	0.532088i
$698$	−11.4576	+	25.0887i	−0.433677	+	0.949620i
$699$	18.5989	−	21.4643i	0.703477	−	0.811855i
$700$	−3.23498	+	2.07900i	−0.122271	+	0.0785787i
$701$	−3.63951	−	25.3134i	−0.137463	−	0.956073i	−0.935465	−	0.353419i	$-0.885019\pi$
$701$	−3.63951	−	25.3134i	−0.137463	−	0.956073i	0.798003	−	0.602654i	$-0.205890\pi$
$702$	0.861725	+	5.99343i	0.0325237	+	0.226207i
$703$	−4.75421	+	3.05535i	−0.179308	+	0.115235i
$704$	−2.00712	+	2.31634i	−0.0756461	+	0.0873002i
$705$	1.27707	−	2.79638i	0.0480971	−	0.105318i
$706$	13.4924	+	8.67104i	0.507793	+	0.326339i
$707$	13.0682	−	3.83717i	0.491481	−	0.144312i
$708$	−4.33608	−	5.00410i	−0.162960	−	0.188066i
$709$	−27.9383	−	8.20342i	−1.04924	−	0.308086i	−0.288732	−	0.957410i	$-0.593234\pi$
$709$	−27.9383	−	8.20342i	−1.04924	−	0.308086i	−0.760512	+	0.649324i	$0.775052\pi$
$710$	−5.54083	−	12.1327i	−0.207944	−	0.455333i
$711$	1.48820	−	10.3506i	0.0558117	−	0.388179i
$712$	−3.43072			−0.128572
$713$	−31.7734	+	31.2263i	−1.18992	+	1.16943i
$714$	−18.7676			−0.702362
$715$	2.64115	−	18.3696i	0.0987732	−	0.686983i
$716$	9.00249	+	19.7127i	0.336439	+	0.736699i
$717$	1.66417	+	0.488645i	0.0621497	+	0.0182488i
$718$	16.6495	+	19.2146i	0.621356	+	0.717083i
$719$	36.6066	−	10.7487i	1.36520	−	0.400858i	0.484604	−	0.874733i	$-0.338964\pi$
$719$	36.6066	−	10.7487i	1.36520	−	0.400858i	0.880592	+	0.473876i	$0.157145\pi$
$720$	−0.841254	−	0.540641i	−0.0313517	−	0.0201485i
$721$	28.3816	−	62.1470i	1.05698	−	2.31447i
$722$	6.75723	−	7.79826i	0.251478	−	0.290221i
$723$	−0.0374083	+	0.0240408i	−0.00139123	+	0.000894089i
$724$	2.27894	+	15.8504i	0.0846960	+	0.589074i
$725$	1.06222	+	7.38790i	0.0394499	+	0.274380i
$726$	1.35111	−	0.868306i	0.0501444	−	0.0322259i
$727$	17.1593	−	19.8029i	0.636402	−	0.734447i	−0.342332	−	0.939579i	$-0.611217\pi$
$727$	17.1593	−	19.8029i	0.636402	−	0.734447i	0.978734	+	0.205132i	$0.0657623\pi$
$728$	9.67266	−	21.1802i	0.358492	−	0.784989i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−14.7827	+	4.34058i	−0.547131	+	0.160652i
$731$	37.0796	+	42.7921i	1.37144	+	1.58272i
$732$	5.52063	+	1.62100i	0.204048	+	0.0599140i
$733$	−0.732875	−	1.60477i	−0.0270694	−	0.0592736i	0.895614	−	0.444831i	$-0.146736\pi$
$733$	−0.732875	−	1.60477i	−0.0270694	−	0.0592736i	−0.922684	+	0.385558i	$0.874009\pi$
$734$	0.692978	−	4.81977i	0.0255783	−	0.177901i
$735$	−7.78735			−0.287241
$736$	−4.22900	+	2.26176i	−0.155883	+	0.0833695i
$737$	34.1409			1.25760
$738$	0.757664	−	5.26967i	0.0278900	−	0.193979i
$739$	0.100690	+	0.220480i	0.00370394	+	0.00811049i	0.911475	−	0.411356i	$-0.134945\pi$
$739$	0.100690	+	0.220480i	0.00370394	+	0.00811049i	−0.907771	+	0.419466i	$0.862217\pi$
$740$	−1.00143	−	0.294047i	−0.0368134	−	0.0108094i
$741$	−21.4703	−	24.7781i	−0.788732	−	0.910246i
$742$	10.0219	−	2.94268i	0.367914	−	0.108029i
$743$	17.0647	+	10.9668i	0.626043	+	0.402333i	0.814842	−	0.579682i	$-0.196823\pi$
$743$	17.0647	+	10.9668i	0.626043	+	0.402333i	−0.188800	+	0.982016i	$0.560460\pi$
$744$	−3.85885	+	8.44970i	−0.141472	+	0.309781i
$745$	−1.70708	+	1.97008i	−0.0625428	+	0.0721782i
$746$	−7.75760	+	4.98551i	−0.284026	+	0.182532i
$747$	0.976011	+	6.78831i	0.0357104	+	0.248371i
$748$	2.12882	+	14.8063i	0.0778373	+	0.541370i
$749$	−7.98387	+	5.13092i	−0.291724	+	0.187480i
$750$	−0.654861	+	0.755750i	−0.0239121	+	0.0275961i
$751$	17.0584	−	37.3527i	0.622469	−	1.36302i	−0.291240	−	0.956650i	$-0.594068\pi$
$751$	17.0584	−	37.3527i	0.622469	−	1.36302i	0.913710	−	0.406368i	$-0.133205\pi$
$752$	−2.58617	−	1.66203i	−0.0943081	−	0.0606081i
$753$	9.81177	−	2.88100i	0.357561	−	0.104989i
$754$	−29.5959	−	34.1555i	−1.07782	−	1.24387i
$755$	18.9445	+	5.56260i	0.689461	+	0.202444i
$756$	−1.59745	−	3.49793i	−0.0580987	−	0.127218i
$757$	−1.40841	+	9.79570i	−0.0511895	+	0.356031i	0.948087	+	0.318010i	$0.103014\pi$
$757$	−1.40841	+	9.79570i	−0.0511895	+	0.356031i	−0.999277	+	0.0380210i	$0.987895\pi$
$758$	−18.2461			−0.662728
$759$	−14.3897	+	2.99965i	−0.522312	+	0.108880i
$760$	5.41466			0.196410
$761$	−0.302349	+	2.10289i	−0.0109602	+	0.0762296i	−0.994567	−	0.104095i	$-0.966806\pi$
$761$	−0.302349	+	2.10289i	−0.0109602	+	0.0762296i	0.983607	+	0.180324i	$0.0577146\pi$
$762$	6.93053	+	15.1757i	0.251066	+	0.549759i
$763$	13.2663	+	3.89533i	0.480272	+	0.141020i
$764$	−12.9057	−	14.8940i	−0.466913	−	0.538846i
$765$	−4.68281	+	1.37500i	−0.169307	+	0.0497131i
$766$	−16.5944	−	10.6646i	−0.599582	−	0.385328i
$767$	16.6552	−	36.4697i	0.601383	−	1.31685i
$768$	−0.654861	+	0.755750i	−0.0236303	+	0.0272708i
$769$	−6.35159	+	4.08192i	−0.229044	+	0.147198i	−0.650130	−	0.759823i	$-0.725286\pi$
$769$	−6.35159	+	4.08192i	−0.229044	+	0.147198i	0.421086	+	0.907021i	$0.361649\pi$
$770$	1.67733	+	11.6661i	0.0604468	+	0.420417i
$771$	−0.684137	−	4.75828i	−0.0246386	−	0.171365i
$772$	20.3052	−	13.0493i	0.730799	−	0.469656i
$773$	0.278771	−	0.321719i	0.0100267	−	0.0115714i	−0.750714	−	0.660627i	$-0.770290\pi$
$773$	0.278771	−	0.321719i	0.0100267	−	0.0115714i	0.760741	+	0.649056i	$0.224836\pi$
$774$	−4.81952	+	10.5533i	−0.173234	+	0.379329i
$775$	7.81453	+	5.02209i	0.280706	+	0.180399i
$776$	1.36165	−	0.399816i	0.0488803	−	0.0143526i
$777$	−2.62830	−	3.03321i	−0.0942896	−	0.108816i
$778$	−22.3842	−	6.57260i	−0.802513	−	0.235639i
$779$	11.9751	+	26.2219i	0.429053	+	0.939495i
$780$	0.861725	−	5.99343i	0.0308547	−	0.214599i
$781$	−40.8805			−1.46282
$782$	−5.17375	+	22.8271i	−0.185013	+	0.816296i
$783$	−7.46387			−0.266737
$784$	−1.10825	+	7.70808i	−0.0395805	+	0.275289i
$785$	7.09345	+	15.5325i	0.253176	+	0.554378i
$786$	18.6327	+	5.47106i	0.664607	+	0.195146i
$787$	22.6411	+	26.1293i	0.807069	+	0.931408i	0.998747	−	0.0500502i	$-0.0159381\pi$
$787$	22.6411	+	26.1293i	0.807069	+	0.931408i	−0.191677	+	0.981458i	$0.561393\pi$
$788$	−9.78681	+	2.87367i	−0.348641	+	0.102370i
$789$	0.978902	+	0.629102i	0.0348498	+	0.0223966i
$790$	−4.34402	+	9.51209i	−0.154553	+	0.338425i
$791$	−1.79541	+	2.07201i	−0.0638375	+	0.0736724i
$792$	−2.57840	+	1.65704i	−0.0916195	+	0.0588803i
$793$	4.95810	+	34.4844i	0.176067	+	1.22458i
$794$	−2.07336	−	14.4206i	−0.0735810	−	0.511767i
$795$	2.28501	−	1.46849i	0.0810410	−	0.0520819i
$796$	−3.51621	+	4.05792i	−0.124629	+	0.143829i
$797$	19.9690	−	43.7260i	0.707339	−	1.54886i	−0.123501	−	0.992344i	$-0.539412\pi$
$797$	19.9690	−	43.7260i	0.707339	−	1.54886i	0.830840	−	0.556512i	$-0.187860\pi$
$798$	17.5163	+	11.2571i	0.620072	+	0.398496i
$799$	−14.3959	+	4.22700i	−0.509289	+	0.149541i
$800$	0.654861	+	0.755750i	0.0231528	+	0.0267198i
$801$	−3.29175	−	0.966545i	−0.116308	−	0.0341512i
$802$	4.61130	+	10.0973i	0.162831	+	0.356549i
$803$	−6.72024	+	46.7403i	−0.237152	+	1.64943i
$804$	11.1391			0.392847
$805$	−4.07648	+	17.9859i	−0.143677	+	0.633918i
$806$	−56.2463			−1.98119
$807$	−1.20859	+	8.40595i	−0.0425445	+	0.295903i
$808$	−1.47134	−	3.22177i	−0.0517614	−	0.113342i
$809$	−0.859161	−	0.252272i	−0.0302065	−	0.00886943i	0.266594	−	0.963809i	$-0.414102\pi$
$809$	−0.859161	−	0.252272i	−0.0302065	−	0.00886943i	−0.296801	+	0.954939i	$0.595920\pi$
$810$	−0.654861	−	0.755750i	−0.0230095	−	0.0265543i
$811$	17.2097	−	5.05322i	0.604314	−	0.177443i	0.0347587	−	0.999396i	$-0.488934\pi$
$811$	17.2097	−	5.05322i	0.604314	−	0.177443i	0.569555	+	0.821953i	$0.307116\pi$
$812$	24.1455	+	15.5174i	0.847341	+	0.544553i
$813$	0.145582	−	0.318781i	0.00510580	−	0.0111801i
$814$	−2.09485	+	2.41758i	−0.0734244	+	0.0847363i
$815$	3.99936	−	2.57023i	0.140092	−	0.0900314i
$816$	0.694568	+	4.83083i	0.0243148	+	0.169113i
$817$	−8.94011	−	62.1798i	−0.312775	−	2.17540i
$818$	−17.3226	+	11.1326i	−0.605671	+	0.389241i
$819$	15.2480	−	17.5971i	0.532808	−	0.614893i
$820$	−2.21161	+	4.84275i	−0.0772328	+	0.169116i
$821$	−6.20130	−	3.98534i	−0.216427	−	0.139089i	0.427936	−	0.903809i	$-0.359241\pi$
$821$	−6.20130	−	3.98534i	−0.216427	−	0.139089i	−0.644363	+	0.764720i	$0.722877\pi$
$822$	−0.462624	+	0.135839i	−0.0161358	+	0.00473791i
$823$	−17.1138	−	19.7504i	−0.596551	−	0.688457i	0.374528	−	0.927216i	$-0.377805\pi$
$823$	−17.1138	−	19.7504i	−0.596551	−	0.688457i	−0.971079	+	0.238759i	$0.923259\pi$
$824$	−17.0471	−	5.00549i	−0.593864	−	0.174374i
$825$	1.27323	+	2.78798i	0.0443281	+	0.0970650i
$826$	−3.62363	+	25.2029i	−0.126082	+	0.876920i
$827$	−43.5869			−1.51566			−0.757832	−	0.652449i	$-0.773741\pi$
$827$	−43.5869			−1.51566			−0.757832	+	0.652449i	$0.773741\pi$
$828$	−4.69491	+	0.978693i	−0.163159	+	0.0340119i
$829$	11.1991			0.388959			0.194480	−	0.980907i	$-0.437698\pi$
$829$	11.1991			0.388959			0.194480	+	0.980907i	$0.437698\pi$
$830$	0.976011	−	6.78831i	0.0338779	−	0.235626i
$831$	9.28429	+	20.3298i	0.322068	+	0.705231i
$832$	−5.80979	−	1.70591i	−0.201418	−	0.0591417i
$833$	24.8888	+	28.7231i	0.862344	+	0.995198i
$834$	−2.11262	+	0.620323i	−0.0731542	+	0.0214800i
$835$	2.60376	+	1.67333i	0.0901067	+	0.0579081i
$836$	6.89410	−	15.0960i	0.238437	−	0.522105i
$837$	−6.08310	+	7.02027i	−0.210263	+	0.242656i
$838$	−24.8673	+	15.9812i	−0.859027	+	0.552063i
$839$	5.57864	+	38.8003i	0.192596	+	1.33953i	0.825104	+	0.564980i	$0.191116\pi$
$839$	5.57864	+	38.8003i	0.192596	+	1.33953i	−0.632508	+	0.774553i	$0.717975\pi$
$840$	0.547262	+	3.80629i	0.0188823	+	0.131330i
$841$	22.4694	−	14.4402i	0.774806	−	0.497938i
$842$	5.00299	−	5.77376i	0.172414	−	0.198977i
$843$	1.91679	−	4.19718i	0.0660176	−	0.144558i
$844$	−13.5987	−	8.73932i	−0.468085	−	0.300820i
$845$	22.7052	−	6.66685i	0.781083	−	0.229347i
$846$	−2.01317	−	2.32332i	−0.0692141	−	0.0798774i
$847$	−5.92586	−	1.73999i	−0.203615	−	0.0597867i
$848$	−1.12835	−	2.47074i	−0.0387477	−	0.0848456i
$849$	1.31743	−	9.16293i	0.0452141	−	0.314471i
$850$	4.88050			0.167400
$851$	−4.41385	+	2.36062i	−0.151305	+	0.0809210i
$852$	−13.3381			−0.456954
$853$	−3.90833	+	27.1830i	−0.133819	+	0.930729i	0.806694	+	0.590970i	$0.201255\pi$
$853$	−3.90833	+	27.1830i	−0.133819	+	0.930729i	−0.940512	+	0.339759i	$0.889654\pi$
$854$	−9.19124	−	20.1260i	−0.314518	−	0.688698i
$855$	5.19533	+	1.52549i	0.177677	+	0.0521705i
$856$	1.61618	+	1.86517i	0.0552400	+	0.0637503i
$857$	16.3471	−	4.79993i	0.558405	−	0.163962i	0.00966148	−	0.999953i	$-0.496925\pi$
$857$	16.3471	−	4.79993i	0.558405	−	0.163962i	0.548743	+	0.835991i	$0.315106\pi$
$858$	−15.6124	−	10.0335i	−0.532998	−	0.342537i
$859$	−7.44719	+	16.3071i	−0.254095	+	0.556390i	−0.993095	−	0.117315i	$-0.962571\pi$
$859$	−7.44719	+	16.3071i	−0.254095	+	0.556390i	0.739000	+	0.673706i	$0.235298\pi$
$860$	7.59749	−	8.76797i	0.259072	−	0.298985i
$861$	−17.2226	+	11.0683i	−0.586944	+	0.377206i
$862$	−4.78418	−	33.2747i	−0.162950	−	1.13334i
$863$	−5.48478	−	38.1475i	−0.186704	−	1.29855i	−0.840470	−	0.541858i	$-0.817721\pi$
$863$	−5.48478	−	38.1475i	−0.186704	−	1.29855i	0.653766	−	0.756697i	$-0.273188\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	−10.9851	+	12.6775i	−0.373506	+	0.431049i
$866$	2.41987	−	5.29878i	0.0822306	−	0.180060i
$867$	5.73678	+	3.68681i	0.194831	+	0.125210i
$868$	34.2738	−	10.0637i	1.16333	−	0.341584i
$869$	20.9886	+	24.2221i	0.711988	+	0.821678i
$870$	7.16153	+	2.10282i	0.242799	+	0.0712921i
$871$	28.0190	+	61.3530i	0.949387	+	2.07887i
$872$	0.511697	−	3.55893i	0.0173282	−	0.120520i
$873$	1.41913			0.0480304
$874$	18.5208	−	18.2019i	0.626475	−	0.615687i
$875$	3.84543			0.129999
$876$	−2.19261	+	15.2499i	−0.0740813	+	0.515247i
$877$	1.51664	+	3.32097i	0.0512132	+	0.112141i	0.933509	−	0.358554i	$-0.116730\pi$
$877$	1.51664	+	3.32097i	0.0512132	+	0.112141i	−0.882296	+	0.470696i	$0.844003\pi$
$878$	25.4023	+	7.45880i	0.857287	+	0.251722i
$879$	3.91883	+	4.52257i	0.132179	+	0.152542i
$880$	2.94080	−	0.863497i	0.0991343	−	0.0291085i
$881$	18.9009	+	12.1469i	0.636787	+	0.409238i	0.818817	−	0.574055i	$-0.194630\pi$
$881$	18.9009	+	12.1469i	0.636787	+	0.409238i	−0.182030	+	0.983293i	$0.558267\pi$
$882$	−3.23498	+	7.08362i	−0.108927	+	0.238518i
$883$	−1.76206	+	2.03352i	−0.0592980	+	0.0684335i	−0.784624	−	0.619972i	$-0.787144\pi$
$883$	−1.76206	+	2.03352i	−0.0592980	+	0.0684335i	0.725326	+	0.688406i	$0.241689\pi$
$884$	−24.8605	+	15.9769i	−0.836149	+	0.537361i
$885$	0.942320	+	6.55398i	0.0316757	+	0.220310i
$886$	0.450608	+	3.13405i	0.0151385	+	0.105290i
$887$	−38.6888	+	24.8638i	−1.29904	+	0.834844i	−0.993107	−	0.117208i	$-0.962606\pi$
$887$	−38.6888	+	24.8638i	−1.29904	+	0.834844i	−0.305935	+	0.952052i	$0.598969\pi$
$888$	−0.683485	+	0.788784i	−0.0229363	+	0.0264699i
$889$	26.6509	−	58.3573i	0.893841	−	1.95724i
$890$	2.88610	+	1.85479i	0.0967424	+	0.0621726i
$891$	−2.94080	+	0.863497i	−0.0985205	+	0.0289282i
$892$	−7.86965	−	9.08206i	−0.263495	−	0.304090i
$893$	15.9714	+	4.68964i	0.534464	+	0.156933i
$894$	1.08290	+	2.37122i	0.0362176	+	0.0793055i
$895$	3.08412	−	21.4505i	0.103091	−	0.717011i
$896$	3.84543			0.128467
$897$	−17.1999	−	23.3972i	−0.574288	−	0.781210i
$898$	7.51625			0.250821
$899$	9.86711	−	68.6273i	0.329087	−	2.28885i
$900$	0.415415	+	0.909632i	0.0138472	+	0.0303211i
$901$	−12.7194	−	3.73476i	−0.423746	−	0.124423i
$902$	10.6856	+	12.3318i	0.355792	+	0.410605i
$903$	42.8063	−	12.5691i	1.42451	−	0.418273i
$904$	0.599787	+	0.385459i	0.0199486	+	0.0128202i
$905$	6.65219	−	14.5663i	0.221126	−	0.484199i
$906$	12.9297	−	14.9217i	0.429562	−	0.495741i
$907$	11.2921	−	7.25697i	0.374947	−	0.240964i	−0.339572	−	0.940580i	$-0.610282\pi$
$907$	11.2921	−	7.25697i	0.374947	−	0.240964i	0.714519	+	0.699616i	$0.246646\pi$
$908$	−1.57600	−	10.9613i	−0.0523012	−	0.363763i
$909$	−0.504057	−	3.50579i	−0.0167185	−	0.116280i
$910$	−19.5880	+	12.5885i	−0.649336	+	0.417303i
$911$	12.0045	−	13.8539i	0.397726	−	0.459000i	−0.521198	−	0.853436i	$-0.674515\pi$
$911$	12.0045	−	13.8539i	0.397726	−	0.459000i	0.918923	+	0.394436i	$0.129060\pi$
$912$	2.24933	−	4.92535i	0.0744828	−	0.163095i
$913$	−17.6830	−	11.3642i	−0.585221	−	0.376099i
$914$	22.4173	−	6.58232i	0.741499	−	0.217724i
$915$	−3.76787	−	4.34835i	−0.124562	−	0.143752i
$916$	−4.38305	−	1.28698i	−0.144820	−	0.0425230i
$917$	−31.0214	−	67.9274i	−1.02442	−	2.24316i
$918$	−0.694568	+	4.83083i	−0.0229242	+	0.159441i
$919$	13.4210			0.442716			0.221358	−	0.975193i	$-0.428951\pi$
$919$	13.4210			0.442716			0.221358	+	0.975193i	$0.428951\pi$
$920$	4.78046	+	0.383660i	0.157607	+	0.0126489i
$921$	−20.2672			−0.667828
$922$	4.89438	−	34.0411i	0.161188	−	1.12109i
$923$	−33.5500	−	73.4644i	−1.10431	−	2.41811i
$924$	11.3086	+	3.32052i	0.372027	+	0.109237i
$925$	0.683485	+	0.788784i	0.0224729	+	0.0259351i
$926$	7.66854	−	2.25169i	0.252004	−	0.0739950i
$927$	−14.9464	−	9.60546i	−0.490904	−	0.315485i
$928$	3.10060	−	6.78938i	0.101782	−	0.222872i
$929$	−4.80221	+	5.54205i	−0.157556	+	0.181829i	−0.829039	−	0.559191i	$-0.811112\pi$
$929$	−4.80221	+	5.54205i	−0.157556	+	0.181829i	0.671484	+	0.741019i	$0.265657\pi$
$930$	7.81453	−	5.02209i	0.256248	−	0.164681i
$931$	−6.00083	−	41.7367i	−0.196669	−	1.36786i
$932$	4.04194	+	28.1123i	0.132398	+	0.920849i
$933$	7.49303	−	4.81548i	0.245311	−	0.157652i
$934$	12.8203	−	14.7954i	0.419492	−	0.484120i
$935$	6.21399	−	13.6067i	0.203219	−	0.444988i
$936$	−5.09384	−	3.27361i	−0.166497	−	0.107001i
$937$	−27.2017	+	7.98713i	−0.888639	+	0.260928i	−0.694024	−	0.719952i	$-0.744164\pi$
$937$	−27.2017	+	7.98713i	−0.888639	+	0.260928i	−0.194615	+	0.980880i	$0.562346\pi$
$938$	−28.0508	−	32.3724i	−0.915892	−	1.05700i
$939$	19.2568	+	5.65431i	0.628422	+	0.184521i
$940$	1.27707	+	2.79638i	0.0416533	+	0.0912080i
$941$	−6.55754	+	45.6087i	−0.213770	+	1.48680i	0.546646	+	0.837364i	$0.315904\pi$
$941$	−6.55754	+	45.6087i	−0.213770	+	1.48680i	−0.760415	+	0.649437i	$0.775005\pi$
$942$	17.0756			0.556352
$943$	8.71454	+	23.9991i	0.283785	+	0.781517i
$944$	6.62138			0.215507
$945$	−0.547262	+	3.80629i	−0.0178024	+	0.123819i
$946$	−14.7716	−	32.3453i	−0.480266	−	1.05164i
$947$	23.5447	+	6.91336i	0.765101	+	0.224654i	0.640922	−	0.767606i	$-0.278552\pi$
$947$	23.5447	+	6.91336i	0.765101	+	0.224654i	0.124179	+	0.992260i	$0.460370\pi$
$948$	6.84793	+	7.90293i	0.222410	+	0.256675i
$949$	−89.5099	+	26.2825i	−2.90561	+	0.853165i
$950$	−4.55510	−	2.92739i	−0.147787	−	0.0949770i
$951$	−6.42173	+	14.0616i	−0.208239	+	0.455980i
$952$	12.2902	−	14.1836i	0.398328	−	0.459694i
$953$	−24.9663	+	16.0448i	−0.808737	+	0.519744i	−0.878456	−	0.477823i	$-0.841426\pi$
$953$	−24.9663	+	16.0448i	−0.808737	+	0.519744i	0.0697194	+	0.997567i	$0.477790\pi$
$954$	−0.386555	−	2.68855i	−0.0125152	−	0.0870451i
$955$	2.80468	+	19.5070i	0.0907574	+	0.631232i
$956$	−1.45909	+	0.937703i	−0.0471905	+	0.0303275i
$957$	14.9809	−	17.2888i	0.484263	−	0.558869i
$958$	2.90650	−	6.36434i	0.0939046	−	0.205622i
$959$	1.55976	+	1.00240i	0.0503673	+	0.0323691i
$960$	0.959493	−	0.281733i	0.0309675	−	0.00909288i
$961$	−36.2061	−	41.7840i	−1.16794	−	1.34787i
$962$	−6.06374	−	1.78047i	−0.195503	−	0.0574048i
$963$	1.02524	+	2.24495i	0.0330378	+	0.0723426i
$964$	0.00632836	−	0.0440147i	0.000203823	−	0.00141762i
$965$	−24.1368			−0.776991
$966$	14.6671	+	11.1797i	0.471906	+	0.359701i
$967$	25.1900			0.810057			0.405028	−	0.914304i	$-0.367262\pi$
$967$	25.1900			0.810057			0.405028	+	0.914304i	$0.367262\pi$
$968$	−0.228567	+	1.58972i	−0.00734644	+	0.0510956i
$969$	−10.9779	−	24.0382i	−0.352660	−	0.772218i
$970$	−1.36165	−	0.399816i	−0.0437199	−	0.0128373i
$971$	6.58404	+	7.59839i	0.211292	+	0.243844i	0.851496	−	0.524361i	$-0.175696\pi$
$971$	6.58404	+	7.59839i	0.211292	+	0.243844i	−0.640204	+	0.768205i	$0.721150\pi$
$972$	−0.959493	+	0.281733i	−0.0307758	+	0.00903658i
$973$	7.12283	+	4.57756i	0.228347	+	0.146750i
$974$	6.36965	−	13.9476i	0.204097	−	0.446909i
$975$	−3.96522	+	4.57611i	−0.126989	+	0.146553i
$976$	−4.84032	+	3.11068i	−0.154935	+	0.0995705i
$977$	5.83700	+	40.5972i	0.186742	+	1.29882i	0.840373	+	0.542008i	$0.182336\pi$
$977$	5.83700	+	40.5972i	0.186742	+	1.29882i	−0.653631	+	0.756813i	$0.726755\pi$
$978$	−0.676572	−	4.70566i	−0.0216344	−	0.150471i
$979$	8.84577	−	5.68483i	0.282712	−	0.181688i
$980$	5.09963	−	5.88528i	0.162902	−	0.187998i
$981$	1.49363	−	3.27060i	0.0476881	−	0.104422i
$982$	30.2922	+	19.4676i	0.966664	+	0.621237i
$983$	33.4596	−	9.82462i	1.06719	−	0.313357i	0.299450	−	0.954112i	$-0.403197\pi$
$983$	33.4596	−	9.82462i	1.06719	−	0.313357i	0.767745	+	0.640755i	$0.221379\pi$
$984$	3.48638	+	4.02350i	0.111142	+	0.128265i
$985$	9.78681	+	2.87367i	0.311834	+	0.0915626i
$986$	−15.1325	−	33.1356i	−0.481917	−	1.05525i
$987$	−1.68239	+	11.7013i	−0.0535510	+	0.372455i
$988$	32.7861			1.04306
$989$	−3.48719	−	55.5304i	−0.110886	−	1.76576i
$990$	3.06495			0.0974106
$991$	−5.74644	+	39.9674i	−0.182542	+	1.26961i	0.668184	+	0.743996i	$0.267072\pi$
$991$	−5.74644	+	39.9674i	−0.182542	+	1.26961i	−0.850726	+	0.525610i	$0.823837\pi$
$992$	−3.85885	−	8.44970i	−0.122519	−	0.268278i
$993$	−7.04872	−	2.06969i	−0.223684	−	0.0656796i
$994$	33.5882	+	38.7628i	1.06535	+	1.22948i
$995$	5.15190	−	1.51274i	0.163326	−	0.0479569i
$996$	−5.76941	−	3.70778i	−0.182811	−	0.117485i
$997$	−10.0327	+	21.9684i	−0.317737	+	0.695748i	−0.999353	−	0.0359626i	$-0.988550\pi$
$997$	−10.0327	+	21.9684i	−0.317737	+	0.695748i	0.681616	+	0.731710i	$0.261278\pi$
$998$	1.90517	−	2.19868i	0.0603071	−	0.0695982i
$999$	−0.878025	+	0.564273i	−0.0277795	+	0.0178528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.31.1	✓	30
23.3	even	11	inner	690.2.m.h.601.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.31.1	✓	30	1.1	even	1	trivial
690.2.m.h.601.1	yes	30	23.3	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-3.23498 - 2.07900i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-3.23498 - 2.07900i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(-0.436188 - 3.03376i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(5.09384 - 3.27361i) q^{13} +(-2.51822 + 2.90618i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(4.68281 - 1.37500i) q^{17} +(0.654861 + 0.755750i) q^{18} +(-5.19533 - 1.52549i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(0.547262 - 3.80629i) q^{21} -3.06495 q^{22} +(-4.47873 - 1.71493i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-2.51536 - 5.50788i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(2.51822 + 2.90618i) q^{28} +(7.16153 - 2.10282i) q^{29} +(0.841254 + 0.540641i) q^{30} +(3.85885 - 8.44970i) q^{31} +(0.654861 - 0.755750i) q^{32} +(2.57840 - 1.65704i) q^{33} +(-0.694568 - 4.83083i) q^{34} +(-0.547262 - 3.80629i) q^{35} +(0.841254 - 0.540641i) q^{36} +(0.683485 - 0.788784i) q^{37} +(-2.24933 + 4.92535i) q^{38} +(5.09384 + 3.27361i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(-3.48638 - 4.02350i) q^{41} +(-3.68966 - 1.08338i) q^{42} +(4.81952 + 10.5533i) q^{43} +(-0.436188 + 3.03376i) q^{44} -1.00000 q^{45} +(-2.33486 + 4.18908i) q^{46} -3.07419 q^{47} +(-0.142315 + 0.989821i) q^{48} +(3.23498 + 7.08362i) q^{49} +(0.959493 + 0.281733i) q^{50} +(3.19605 + 3.68844i) q^{51} +(-5.80979 + 1.70591i) q^{52} +(-2.28501 - 1.46849i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(2.00712 - 2.31634i) q^{55} +(3.23498 - 2.07900i) q^{56} +(-0.770587 - 5.35955i) q^{57} +(-1.06222 - 7.38790i) q^{58} +(5.57026 - 3.57979i) q^{59} +(0.654861 - 0.755750i) q^{60} +(-2.39017 + 5.23375i) q^{61} +(-7.81453 - 5.02209i) q^{62} +(3.68966 - 1.08338i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.80979 + 1.70591i) q^{65} +(-1.27323 - 2.78798i) q^{66} +(-1.58527 + 11.0258i) q^{67} -4.88050 q^{68} +(-0.300576 - 4.78640i) q^{69} -3.84543 q^{70} +(1.89820 - 13.2023i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(-14.7827 - 4.34058i) q^{73} +(-0.683485 - 0.788784i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(4.55510 + 2.92739i) q^{76} +(-4.89611 + 10.7210i) q^{77} +(3.96522 - 4.57611i) q^{78} +(-8.79705 + 5.65352i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-4.47871 + 2.87829i) q^{82} +(4.49111 - 5.18302i) q^{83} +(-1.59745 + 3.49793i) q^{84} +(4.10574 + 2.63860i) q^{85} +(11.1317 - 3.26857i) q^{86} +(4.88780 + 5.64082i) q^{87} +(2.94080 + 0.863497i) q^{88} +(1.42517 + 3.12069i) q^{89} +(-0.142315 + 0.989821i) q^{90} -23.2843 q^{91} +(3.81416 + 2.90727i) q^{92} +9.28914 q^{93} +(-0.437503 + 3.04290i) q^{94} +(-2.24933 - 4.92535i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-0.929335 - 1.07251i) q^{97} +(7.47190 - 2.19395i) q^{98} +(2.57840 + 1.65704i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

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