LMFDB - Embedded newform 690.2.m.c.601.2

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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			601.2
Root			$-0.248715 - 1.72985i$ of defining polynomial
Character	$\chi$	$=$	690.601
Dual form			690.2.m.c.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.959493 + 0.281733i) q^{6} +(1.99973 - 1.28515i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(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} +(1.99973 - 1.28515i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.841254 + 0.540641i) q^{10} +(-0.0482085 + 0.335298i) q^{11} +(0.142315 - 0.989821i) q^{12} +(-3.00886 - 1.93368i) q^{13} +(-1.55666 - 1.79648i) q^{14} +(-0.415415 - 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(5.91702 + 1.73739i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(3.66689 - 1.07670i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.338294 + 2.35288i) q^{21} +0.338745 q^{22} +(-0.240622 + 4.78979i) q^{23} -1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-1.48579 + 3.25342i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-1.55666 + 1.79648i) q^{28} +(8.33098 + 2.44620i) q^{29} +(-0.841254 + 0.540641i) q^{30} +(2.08334 + 4.56187i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-0.284971 - 0.183140i) q^{33} +(0.877630 - 6.10405i) q^{34} +(-0.338294 + 2.35288i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-0.647773 - 0.747570i) q^{37} +(-1.58759 - 3.47634i) q^{38} +(3.00886 - 1.93368i) q^{39} +(-0.959493 - 0.281733i) q^{40} +(0.803707 - 0.927527i) q^{41} +(2.28079 - 0.669701i) q^{42} +(2.71815 - 5.95192i) q^{43} +(-0.0482085 - 0.335298i) q^{44} +1.00000 q^{45} +(4.77528 - 0.443486i) q^{46} +9.10661 q^{47} +(0.142315 + 0.989821i) q^{48} +(-0.560599 + 1.22754i) q^{49} +(-0.959493 + 0.281733i) q^{50} +(-4.03841 + 4.66057i) q^{51} +(3.43176 + 1.00766i) q^{52} +(5.84714 - 3.75773i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-0.221831 - 0.256007i) q^{55} +(1.99973 + 1.28515i) q^{56} +(-0.543884 + 3.78279i) q^{57} +(1.23568 - 8.59432i) q^{58} +(1.65530 + 1.06380i) q^{59} +(0.654861 + 0.755750i) q^{60} +(0.831520 + 1.82078i) q^{61} +(4.21895 - 2.71135i) q^{62} +(-2.28079 - 0.669701i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(3.43176 - 1.00766i) q^{65} +(-0.140720 + 0.308134i) q^{66} +(-1.28144 - 8.91260i) q^{67} -6.16682 q^{68} +(-4.25699 - 2.20863i) q^{69} +2.37708 q^{70} +(0.857788 + 5.96605i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-4.05924 + 1.19190i) q^{73} +(-0.647773 + 0.747570i) q^{74} +(0.959493 + 0.281733i) q^{75} +(-3.21501 + 2.06616i) q^{76} +(0.334503 + 0.732458i) q^{77} +(-2.34220 - 2.70304i) q^{78} +(-6.04715 - 3.88627i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-1.03247 - 0.663526i) q^{82} +(-3.14370 - 3.62802i) q^{83} +(-0.987475 - 2.16227i) q^{84} +(-5.18786 + 3.33403i) q^{85} +(-6.27817 - 1.84344i) q^{86} +(-5.68595 + 6.56194i) q^{87} +(-0.325024 + 0.0954356i) q^{88} +(-5.32572 + 11.6617i) q^{89} +(-0.142315 - 0.989821i) q^{90} -8.50195 q^{91} +(-1.11857 - 4.66356i) q^{92} -5.01508 q^{93} +(-1.29601 - 9.01391i) q^{94} +(-1.58759 + 3.47634i) q^{95} +(0.959493 - 0.281733i) q^{96} +(2.50300 - 2.88861i) q^{97} +(1.29483 + 0.380196i) q^{98} +(0.284971 - 0.183140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

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
$7$	1.99973	−	1.28515i	0.755826	−	0.485740i	−0.105106	−	0.994461i	$-0.533518\pi$
$7$	1.99973	−	1.28515i	0.755826	−	0.485740i	0.860931	+	0.508721i	$0.169882\pi$
$8$	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
$11$	−0.0482085	+	0.335298i	−0.0145354	+	0.101096i	−0.995798	−	0.0915811i	$-0.970808\pi$
$11$	−0.0482085	+	0.335298i	−0.0145354	+	0.101096i	0.981262	+	0.192677i	$0.0617170\pi$
$12$	0.142315	−	0.989821i	0.0410828	−	0.285737i
$13$	−3.00886	−	1.93368i	−0.834507	−	0.536305i	0.0521998	−	0.998637i	$-0.483377\pi$
$13$	−3.00886	−	1.93368i	−0.834507	−	0.536305i	−0.886707	+	0.462331i	$0.847013\pi$
$14$	−1.55666	−	1.79648i	−0.416034	−	0.480129i
$15$	−0.415415	−	0.909632i	−0.107260	−	0.234866i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	5.91702	+	1.73739i	1.43509	+	0.421380i	0.904581	−	0.426301i	$-0.140184\pi$
$17$	5.91702	+	1.73739i	1.43509	+	0.421380i	0.530506	+	0.847681i	$0.322002\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	3.66689	−	1.07670i	0.841242	−	0.247011i	0.167402	−	0.985889i	$-0.446462\pi$
$19$	3.66689	−	1.07670i	0.841242	−	0.247011i	0.673840	+	0.738878i	$0.264644\pi$
$20$	0.415415	−	0.909632i	0.0928896	−	0.203400i
$21$	0.338294	+	2.35288i	0.0738217	+	0.513441i
$22$	0.338745			0.0722208
$23$	−0.240622	+	4.78979i	−0.0501731	+	0.998741i
$23$	−0.240622	+	4.78979i	−0.0501731	+	0.998741i
$24$	−1.00000			−0.204124
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−1.48579	+	3.25342i	−0.291387	+	0.638049i
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$	−1.55666	+	1.79648i	−0.294180	+	0.339502i
$29$	8.33098	+	2.44620i	1.54702	+	0.454247i	0.940210	−	0.340596i	$-0.110629\pi$
$29$	8.33098	+	2.44620i	1.54702	+	0.454247i	0.606815	+	0.794843i	$0.292447\pi$
$30$	−0.841254	+	0.540641i	−0.153591	+	0.0987071i
$31$	2.08334	+	4.56187i	0.374178	+	0.819337i	0.999248	+	0.0387677i	$0.0123432\pi$
$31$	2.08334	+	4.56187i	0.374178	+	0.819337i	−0.625070	+	0.780569i	$0.714930\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−0.284971	−	0.183140i	−0.0496071	−	0.0318805i
$34$	0.877630	−	6.10405i	0.150512	−	1.04684i
$35$	−0.338294	+	2.35288i	−0.0571821	+	0.397710i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−0.647773	−	0.747570i	−0.106493	−	0.122900i	0.700001	−	0.714142i	$-0.253183\pi$
$37$	−0.647773	−	0.747570i	−0.106493	−	0.122900i	−0.806494	+	0.591243i	$0.798638\pi$
$38$	−1.58759	−	3.47634i	−0.257541	−	0.563936i
$39$	3.00886	−	1.93368i	0.481803	−	0.309636i
$40$	−0.959493	−	0.281733i	−0.151709	−	0.0445458i
$41$	0.803707	−	0.927527i	0.125518	−	0.144855i	−0.689512	−	0.724274i	$-0.742175\pi$
$41$	0.803707	−	0.927527i	0.125518	−	0.144855i	0.815030	+	0.579419i	$0.196720\pi$
$42$	2.28079	−	0.669701i	0.351934	−	0.103337i
$43$	2.71815	−	5.95192i	0.414514	−	0.907659i	−0.581076	−	0.813849i	$-0.697368\pi$
$43$	2.71815	−	5.95192i	0.414514	−	0.907659i	0.995590	−	0.0938098i	$-0.0299046\pi$
$44$	−0.0482085	−	0.335298i	−0.00726771	−	0.0505480i
$45$	1.00000			0.149071
$46$	4.77528	−	0.443486i	0.704077	−	0.0653884i
$47$	9.10661			1.32834			0.664168	−	0.747584i	$-0.268786\pi$
$47$	9.10661			1.32834			0.664168	+	0.747584i	$0.268786\pi$
$48$	0.142315	+	0.989821i	0.0205414	+	0.142868i
$49$	−0.560599	+	1.22754i	−0.0800856	+	0.175363i
$50$	−0.959493	+	0.281733i	−0.135693	+	0.0398430i
$51$	−4.03841	+	4.66057i	−0.565490	+	0.652610i
$52$	3.43176	+	1.00766i	0.475899	+	0.139737i
$53$	5.84714	−	3.75773i	0.803166	−	0.516164i	−0.0734815	−	0.997297i	$-0.523411\pi$
$53$	5.84714	−	3.75773i	0.803166	−	0.516164i	0.876648	+	0.481133i	$0.159775\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	−0.221831	−	0.256007i	−0.0299117	−	0.0345199i
$56$	1.99973	+	1.28515i	0.267225	+	0.171735i
$57$	−0.543884	+	3.78279i	−0.0720392	+	0.501043i
$58$	1.23568	−	8.59432i	0.162252	−	1.12849i
$59$	1.65530	+	1.06380i	0.215502	+	0.138495i	0.643939	−	0.765077i	$-0.277299\pi$
$59$	1.65530	+	1.06380i	0.215502	+	0.138495i	−0.428437	+	0.903572i	$0.640935\pi$
$60$	0.654861	+	0.755750i	0.0845422	+	0.0975669i
$61$	0.831520	+	1.82078i	0.106465	+	0.233126i	0.955365	−	0.295427i	$-0.0954619\pi$
$61$	0.831520	+	1.82078i	0.106465	+	0.233126i	−0.848900	+	0.528553i	$0.822735\pi$
$62$	4.21895	−	2.71135i	0.535807	−	0.344342i
$63$	−2.28079	−	0.669701i	−0.287353	−	0.0843744i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	3.43176	−	1.00766i	0.425657	−	0.124984i
$66$	−0.140720	+	0.308134i	−0.0173214	+	0.0379286i
$67$	−1.28144	−	8.91260i	−0.156553	−	1.08885i	−0.904926	−	0.425569i	$-0.860074\pi$
$67$	−1.28144	−	8.91260i	−0.156553	−	1.08885i	0.748373	−	0.663278i	$-0.230835\pi$
$68$	−6.16682			−0.747836
$69$	−4.25699	−	2.20863i	−0.512481	−	0.265888i
$70$	2.37708			0.284115
$71$	0.857788	+	5.96605i	0.101801	+	0.708039i	0.975247	+	0.221119i	$0.0709708\pi$
$71$	0.857788	+	5.96605i	0.101801	+	0.708039i	−0.873446	+	0.486921i	$0.838120\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	−4.05924	+	1.19190i	−0.475098	+	0.139501i	−0.510511	−	0.859871i	$-0.670544\pi$
$73$	−4.05924	+	1.19190i	−0.475098	+	0.139501i	0.0354127	+	0.999373i	$0.488725\pi$
$74$	−0.647773	+	0.747570i	−0.0753021	+	0.0869033i
$75$	0.959493	+	0.281733i	0.110793	+	0.0325317i
$76$	−3.21501	+	2.06616i	−0.368787	+	0.237005i
$77$	0.334503	+	0.732458i	0.0381201	+	0.0834714i
$78$	−2.34220	−	2.70304i	−0.265202	−	0.306059i
$79$	−6.04715	−	3.88627i	−0.680357	−	0.437239i	0.154289	−	0.988026i	$-0.450691\pi$
$79$	−6.04715	−	3.88627i	−0.680357	−	0.437239i	−0.834646	+	0.550787i	$0.814328\pi$
$80$	−0.142315	+	0.989821i	−0.0159113	+	0.110665i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−1.03247	−	0.663526i	−0.114017	−	0.0732741i
$83$	−3.14370	−	3.62802i	−0.345066	−	0.398227i	0.556515	−	0.830837i	$-0.312138\pi$
$83$	−3.14370	−	3.62802i	−0.345066	−	0.398227i	−0.901581	+	0.432610i	$0.857593\pi$
$84$	−0.987475	−	2.16227i	−0.107742	−	0.235923i
$85$	−5.18786	+	3.33403i	−0.562702	+	0.361627i
$86$	−6.27817	−	1.84344i	−0.676992	−	0.198783i
$87$	−5.68595	+	6.56194i	−0.609598	+	0.703514i
$88$	−0.325024	+	0.0954356i	−0.0346477	+	0.0101735i
$89$	−5.32572	+	11.6617i	−0.564526	+	1.23614i	0.385136	+	0.922860i	$0.374155\pi$
$89$	−5.32572	+	11.6617i	−0.564526	+	1.23614i	−0.949661	+	0.313279i	$0.898573\pi$
$90$	−0.142315	−	0.989821i	−0.0150013	−	0.104336i
$91$	−8.50195			−0.891247
$92$	−1.11857	−	4.66356i	−0.116618	−	0.486210i
$93$	−5.01508			−0.520039
$94$	−1.29601	−	9.01391i	−0.133673	−	0.929714i
$95$	−1.58759	+	3.47634i	−0.162883	+	0.356664i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	2.50300	−	2.88861i	0.254141	−	0.293294i	−0.614315	−	0.789061i	$-0.710568\pi$
$97$	2.50300	−	2.88861i	0.254141	−	0.293294i	0.868456	+	0.495767i	$0.165113\pi$
$98$	1.29483	+	0.380196i	0.130797	+	0.0384056i
$99$	0.284971	−	0.183140i	0.0286406	−	0.0184062i
$100$	0.415415	+	0.909632i	0.0415415	+	0.0909632i
$101$	−0.783869	−	0.904633i	−0.0779979	−	0.0900144i	0.715409	−	0.698706i	$-0.246240\pi$
$101$	−0.783869	−	0.904633i	−0.0779979	−	0.0900144i	−0.793407	+	0.608691i	$0.791695\pi$
$102$	5.18786	+	3.33403i	0.513674	+	0.330118i
$103$	0.618961	−	4.30497i	0.0609881	−	0.424181i	−0.936338	−	0.351100i	$-0.885808\pi$
$103$	0.618961	−	4.30497i	0.0609881	−	0.424181i	0.997326	−	0.0730812i	$-0.0232832\pi$
$104$	0.509009	−	3.54023i	0.0499124	−	0.347148i
$105$	−1.99973	−	1.28515i	−0.195153	−	0.125417i
$106$	−4.55161	−	5.25284i	−0.442092	−	0.510201i
$107$	−7.74108	−	16.9506i	−0.748359	−	1.63868i	−0.769293	−	0.638896i	$-0.779391\pi$
$107$	−7.74108	−	16.9506i	−0.748359	−	1.63868i	0.0209343	−	0.999781i	$-0.493336\pi$
$108$	−0.841254	+	0.540641i	−0.0809497	+	0.0520232i
$109$	3.65017	+	1.07179i	0.349622	+	0.102658i	0.451828	−	0.892105i	$-0.350772\pi$
$109$	3.65017	+	1.07179i	0.349622	+	0.102658i	−0.102206	+	0.994763i	$0.532590\pi$
$110$	−0.221831	+	0.256007i	−0.0211508	+	0.0244093i
$111$	0.949109	−	0.278683i	0.0900854	−	0.0264515i
$112$	0.987475	−	2.16227i	0.0933076	−	0.204315i
$113$	2.54546	+	17.7041i	0.239457	+	1.66546i	0.654804	+	0.755798i	$0.272751\pi$
$113$	2.54546	+	17.7041i	0.239457	+	1.66546i	−0.415347	+	0.909663i	$0.636340\pi$
$114$	3.82169			0.357934
$115$	−3.46231	−	3.31850i	−0.322862	−	0.309451i
$116$	−8.68269			−0.806168
$117$	0.509009	+	3.54023i	0.0470579	+	0.327295i
$118$	0.817397	−	1.78985i	0.0752475	−	0.164769i
$119$	14.0652	−	4.12992i	1.28936	−	0.378589i
$120$	0.654861	−	0.755750i	0.0597803	−	0.0689902i
$121$	10.4443	+	3.06673i	0.949484	+	0.278794i
$122$	1.68390	−	1.08218i	0.152454	−	0.0979760i
$123$	0.509837	+	1.11639i	0.0459704	+	0.100661i
$124$	−3.28418	−	3.79014i	−0.294928	−	0.340365i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	−0.338294	+	2.35288i	−0.0301376	+	0.209612i
$127$	0.606695	−	4.21966i	0.0538355	−	0.374434i	−0.945037	−	0.326963i	$-0.893975\pi$
$127$	0.606695	−	4.21966i	0.0538355	−	0.374434i	0.998873	−	0.0474711i	$-0.0151162\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	4.28489	+	4.94503i	0.377264	+	0.435386i
$130$	−1.48579	−	3.25342i	−0.130312	−	0.285344i
$131$	−14.7633	+	9.48781i	−1.28988	+	0.828954i	−0.992072	−	0.125673i	$-0.959891\pi$
$131$	−14.7633	+	9.48781i	−1.28988	+	0.828954i	−0.297805	+	0.954627i	$0.596255\pi$
$132$	0.325024	+	0.0954356i	0.0282897	+	0.00830660i
$133$	5.94906	−	6.86559i	0.515849	−	0.595322i
$134$	−8.63951	+	2.53679i	−0.746340	+	0.219145i
$135$	−0.415415	+	0.909632i	−0.0357532	+	0.0782887i
$136$	0.877630	+	6.10405i	0.0752561	+	0.523418i
$137$	−15.9474			−1.36248			−0.681238	−	0.732062i	$-0.738558\pi$
$137$	−15.9474			−1.36248			−0.681238	+	0.732062i	$0.738558\pi$
$138$	−1.58031	+	4.52798i	−0.134525	+	0.385447i
$139$	−16.2181			−1.37560			−0.687800	−	0.725900i	$-0.741423\pi$
$139$	−16.2181			−1.37560			−0.687800	+	0.725900i	$0.741423\pi$
$140$	−0.338294	−	2.35288i	−0.0285910	−	0.198855i
$141$	−3.78302	+	8.28366i	−0.318588	+	0.697610i
$142$	5.78324	−	1.69811i	0.485319	−	0.142503i
$143$	0.793410	−	0.915643i	0.0663482	−	0.0765700i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	−7.30435	+	4.69422i	−0.606593	+	0.389834i
$146$	1.75746	+	3.84830i	0.145448	+	0.318487i
$147$	−0.883729	−	1.01988i	−0.0728888	−	0.0841181i
$148$	0.832149	+	0.534790i	0.0684022	+	0.0439594i
$149$	−2.21343	+	15.3948i	−0.181332	+	1.26119i	0.672287	+	0.740291i	$0.265312\pi$
$149$	−2.21343	+	15.3948i	−0.181332	+	1.26119i	−0.853619	+	0.520899i	$0.825597\pi$
$150$	0.142315	−	0.989821i	0.0116200	−	0.0808186i
$151$	5.68150	+	3.65128i	0.462354	+	0.297137i	0.751004	−	0.660298i	$-0.229570\pi$
$151$	5.68150	+	3.65128i	0.462354	+	0.297137i	−0.288650	+	0.957435i	$0.593206\pi$
$152$	2.50268	+	2.88824i	0.202994	+	0.234267i
$153$	−2.56179	−	5.60953i	−0.207108	−	0.453504i
$154$	0.677398	−	0.435337i	0.0545863	−	0.0350805i
$155$	−4.81193	−	1.41291i	−0.386503	−	0.113488i
$156$	−2.34220	+	2.70304i	−0.187526	+	0.216417i
$157$	20.8784	−	6.13046i	1.66628	−	0.489264i	0.693396	−	0.720556i	$-0.256114\pi$
$157$	20.8784	−	6.13046i	1.66628	−	0.489264i	0.972884	+	0.231292i	$0.0742954\pi$
$158$	−2.98611	+	6.53867i	−0.237562	+	0.520189i
$159$	0.989160	+	6.87976i	0.0784455	+	0.545600i
$160$	1.00000			0.0790569
$161$	5.67441	+	9.88751i	0.447206	+	0.779245i
$162$	1.00000			0.0785674
$163$	−1.55033	−	10.7828i	−0.121431	−	0.844573i	−0.955937	−	0.293573i	$-0.905156\pi$
$163$	−1.55033	−	10.7828i	−0.121431	−	0.844573i	0.834505	−	0.551000i	$-0.185753\pi$
$164$	−0.509837	+	1.11639i	−0.0398115	+	0.0871751i
$165$	0.325024	−	0.0954356i	0.0253031	−	0.00742965i
$166$	−3.14370	+	3.62802i	−0.243998	+	0.281589i
$167$	−19.2199	−	5.64348i	−1.48728	−	0.436706i	−0.565610	−	0.824673i	$-0.691359\pi$
$167$	−19.2199	−	5.64348i	−1.48728	−	0.436706i	−0.921673	+	0.387967i	$0.873177\pi$
$168$	−1.99973	+	1.28515i	−0.154282	+	0.0991512i
$169$	−0.0862646	−	0.188893i	−0.00663574	−	0.0145302i
$170$	4.03841	+	4.66057i	0.309732	+	0.357449i
$171$	−3.21501	−	2.06616i	−0.245858	−	0.158003i
$172$	−0.931197	+	6.47662i	−0.0710031	+	0.493837i
$173$	0.801682	−	5.57582i	0.0609508	−	0.423922i	−0.936385	−	0.350975i	$-0.885850\pi$
$173$	0.801682	−	5.57582i	0.0609508	−	0.423922i	0.997336	−	0.0729474i	$-0.0232405\pi$
$174$	7.30435	+	4.69422i	0.553741	+	0.355868i
$175$	−1.55666	−	1.79648i	−0.117672	−	0.135801i
$176$	0.140720	+	0.308134i	0.0106072	+	0.0232265i
$177$	−1.65530	+	1.06380i	−0.124420	+	0.0799600i
$178$	12.3009	+	3.61188i	0.921994	+	0.270722i
$179$	12.0352	−	13.8894i	0.899557	−	1.03814i	−0.0995137	−	0.995036i	$-0.531729\pi$
$179$	12.0352	−	13.8894i	0.899557	−	1.03814i	0.999070	−	0.0431076i	$-0.0137258\pi$
$180$	−0.959493	+	0.281733i	−0.0715164	+	0.0209991i
$181$	−1.62721	+	3.56310i	−0.120950	+	0.264843i	−0.960416	−	0.278568i	$-0.910140\pi$
$181$	−1.62721	+	3.56310i	−0.120950	+	0.264843i	0.839467	+	0.543411i	$0.182867\pi$
$182$	1.20995	+	8.41542i	0.0896878	+	0.623792i
$183$	−2.00166			−0.147967
$184$	−4.45691	+	1.77087i	−0.328567	+	0.130551i
$185$	0.989177			0.0727258
$186$	0.713720	+	4.96403i	0.0523325	+	0.363980i
$187$	−0.867794	+	1.90020i	−0.0634594	+	0.138957i
$188$	−8.73773	+	2.56563i	−0.637264	+	0.187118i
$189$	1.55666	−	1.79648i	0.113230	−	0.130674i
$190$	3.66689	+	1.07670i	0.266024	+	0.0781117i
$191$	4.83636	−	3.10814i	0.349947	−	0.224897i	−0.353844	−	0.935304i	$-0.615126\pi$
$191$	4.83636	−	3.10814i	0.349947	−	0.224897i	0.703791	+	0.710407i	$0.251489\pi$
$192$	−0.415415	−	0.909632i	−0.0299800	−	0.0656470i
$193$	−2.00093	−	2.30919i	−0.144030	−	0.166219i	0.679151	−	0.733999i	$-0.262348\pi$
$193$	−2.00093	−	2.30919i	−0.144030	−	0.166219i	−0.823181	+	0.567779i	$0.807803\pi$
$194$	−3.21542	−	2.06643i	−0.230854	−	0.148361i
$195$	−0.509009	+	3.54023i	−0.0364509	+	0.253521i
$196$	0.192053	−	1.33576i	0.0137181	−	0.0954111i
$197$	−11.8181	−	7.59506i	−0.842008	−	0.541126i	0.0470646	−	0.998892i	$-0.485013\pi$
$197$	−11.8181	−	7.59506i	−0.842008	−	0.541126i	−0.889073	+	0.457766i	$0.848650\pi$
$198$	−0.221831	−	0.256007i	−0.0157648	−	0.0181936i
$199$	−0.893491	−	1.95647i	−0.0633379	−	0.138691i	0.875316	−	0.483551i	$-0.160653\pi$
$199$	−0.893491	−	1.95647i	−0.0633379	−	0.138691i	−0.938654	+	0.344861i	$0.887926\pi$
$200$	0.841254	−	0.540641i	0.0594856	−	0.0382291i
$201$	8.63951	+	2.53679i	0.609384	+	0.178931i
$202$	−0.783869	+	0.904633i	−0.0551528	+	0.0636498i
$203$	19.8034	−	5.81481i	1.38993	−	0.408119i
$204$	2.56179	−	5.60953i	0.179361	−	0.392746i
$205$	0.174662	+	1.21480i	0.0121989	+	0.0848455i
$206$	−4.34924			−0.303026
$207$	3.77746	−	2.95480i	0.262551	−	0.205373i
$208$	−3.57664			−0.247995
$209$	0.184238	+	1.28140i	0.0127440	+	0.0886366i
$210$	−0.987475	+	2.16227i	−0.0681422	+	0.149211i
$211$	−15.6640	+	4.59938i	−1.07836	+	0.316634i	−0.772221	−	0.635353i	$-0.780854\pi$
$211$	−15.6640	+	4.59938i	−1.07836	+	0.316634i	−0.306136	+	0.951988i	$0.599036\pi$
$212$	−4.55161	+	5.25284i	−0.312606	+	0.360767i
$213$	−5.78324	−	1.69811i	−0.396261	−	0.116353i
$214$	−15.6764	+	10.0746i	−1.07162	+	0.688686i
$215$	2.71815	+	5.95192i	0.185376	+	0.405917i
$216$	0.654861	+	0.755750i	0.0445576	+	0.0514222i
$217$	10.0288	+	6.44511i	0.680798	+	0.437522i
$218$	0.541403	−	3.76554i	0.0366685	−	0.255035i
$219$	0.602078	−	4.18755i	0.0406847	−	0.282968i
$220$	0.284971	+	0.183140i	0.0192127	+	0.0123473i
$221$	−14.4439	−	16.6692i	−0.971603	−	1.12129i
$222$	−0.410919	−	0.899787i	−0.0275791	−	0.0603898i
$223$	−8.19870	+	5.26898i	−0.549025	+	0.352837i	−0.785560	−	0.618786i	$-0.787625\pi$
$223$	−8.19870	+	5.26898i	−0.549025	+	0.352837i	0.236534	+	0.971623i	$0.423988\pi$
$224$	−2.28079	−	0.669701i	−0.152392	−	0.0447463i
$225$	−0.654861	+	0.755750i	−0.0436574	+	0.0503833i
$226$	17.1616	−	5.03911i	1.14158	−	0.335197i
$227$	1.19892	−	2.62526i	0.0795749	−	0.174245i	−0.865663	−	0.500628i	$-0.833103\pi$
$227$	1.19892	−	2.62526i	0.0795749	−	0.174245i	0.945238	+	0.326383i	$0.105830\pi$
$228$	−0.543884	−	3.78279i	−0.0360196	−	0.250522i
$229$	15.4090			1.01826			0.509129	−	0.860690i	$-0.329968\pi$
$229$	15.4090			1.01826			0.509129	+	0.860690i	$0.329968\pi$
$230$	−2.79198	+	3.89934i	−0.184098	+	0.257115i
$231$	−0.805225			−0.0529799
$232$	1.23568	+	8.59432i	0.0811261	+	0.564244i
$233$	−11.8953	+	26.0470i	−0.779284	+	1.70639i	−0.0742285	+	0.997241i	$0.523649\pi$
$233$	−11.8953	+	26.0470i	−0.779284	+	1.70639i	−0.705055	+	0.709152i	$0.749078\pi$
$234$	3.43176	−	1.00766i	0.224341	−	0.0658725i
$235$	−5.96356	+	6.88231i	−0.389020	+	0.448953i
$236$	−1.88796	−	0.554355i	−0.122896	−	0.0360854i
$237$	6.04715	−	3.88627i	0.392805	−	0.252440i
$238$	−6.08958	−	13.3343i	−0.394729	−	0.864335i
$239$	−12.0102	−	13.8605i	−0.776877	−	0.896564i	0.220003	−	0.975499i	$-0.429393\pi$
$239$	−12.0102	−	13.8605i	−0.776877	−	0.896564i	−0.996880	+	0.0789356i	$0.974848\pi$
$240$	−0.841254	−	0.540641i	−0.0543027	−	0.0348982i
$241$	−3.75426	+	26.1115i	−0.241833	+	1.68199i	0.401077	+	0.916045i	$0.368636\pi$
$241$	−3.75426	+	26.1115i	−0.241833	+	1.68199i	−0.642910	+	0.765942i	$0.722273\pi$
$242$	1.54913	−	10.7745i	0.0995820	−	0.692608i
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$	−1.31081	−	1.51275i	−0.0839160	−	0.0968442i
$245$	−0.560599	−	1.22754i	−0.0358154	−	0.0784247i
$246$	1.03247	−	0.663526i	0.0658276	−	0.0423048i
$247$	−13.1151	−	3.85095i	−0.834496	−	0.245030i
$248$	−3.28418	+	3.79014i	−0.208545	+	0.240674i
$249$	4.60611	−	1.35247i	0.291900	−	0.0857096i
$250$	0.415415	−	0.909632i	0.0262732	−	0.0575302i
$251$	1.36530	+	9.49588i	0.0861771	+	0.599375i	0.986452	+	0.164052i	$0.0524566\pi$
$251$	1.36530	+	9.49588i	0.0861771	+	0.599375i	−0.900275	+	0.435323i	$0.856634\pi$
$252$	2.37708			0.149742
$253$	−1.59441	−	0.311589i	−0.100239	−	0.0195894i
$254$	−4.26305			−0.267488
$255$	−0.877630	−	6.10405i	−0.0549593	−	0.382250i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	12.6338	−	3.70961i	0.788072	−	0.231399i	0.137157	−	0.990549i	$-0.456204\pi$
$257$	12.6338	−	3.70961i	0.788072	−	0.231399i	0.650915	+	0.759151i	$0.274385\pi$
$258$	4.28489	−	4.94503i	0.266766	−	0.307864i
$259$	−2.25611	−	0.662453i	−0.140188	−	0.0411628i
$260$	−3.00886	+	1.93368i	−0.186602	+	0.119922i
$261$	−3.60692	−	7.89806i	−0.223263	−	0.488877i
$262$	11.4923	+	13.2628i	0.709995	+	0.819378i
$263$	13.4416	+	8.63842i	0.828847	+	0.532668i	0.884911	−	0.465759i	$-0.154219\pi$
$263$	13.4416	+	8.63842i	0.828847	+	0.532668i	−0.0560643	+	0.998427i	$0.517855\pi$
$264$	0.0482085	−	0.335298i	0.00296703	−	0.0206361i
$265$	−0.989160	+	6.87976i	−0.0607636	+	0.422620i
$266$	−7.64234	−	4.91144i	−0.468582	−	0.301139i
$267$	−8.39548	−	9.68890i	−0.513795	−	0.592951i
$268$	3.74050	+	8.19055i	0.228487	+	0.500318i
$269$	6.80184	−	4.37128i	0.414716	−	0.266522i	−0.316602	−	0.948558i	$-0.602542\pi$
$269$	6.80184	−	4.37128i	0.414716	−	0.266522i	0.731318	+	0.682037i	$0.238906\pi$
$270$	0.959493	+	0.281733i	0.0583929	+	0.0171457i
$271$	7.80061	−	9.00239i	0.473853	−	0.546856i	−0.467626	−	0.883926i	$-0.654891\pi$
$271$	7.80061	−	9.00239i	0.473853	−	0.546856i	0.941479	+	0.337070i	$0.109436\pi$
$272$	5.91702	−	1.73739i	0.358772	−	0.105345i
$273$	3.53184	−	7.73365i	0.213757	−	0.468062i
$274$	2.26955	+	15.7850i	0.137108	+	0.953609i
$275$	0.338745			0.0204271
$276$	4.70679	+	0.919831i	0.283316	+	0.0553673i
$277$	−27.2008			−1.63434			−0.817170	−	0.576397i	$-0.804458\pi$
$277$	−27.2008			−1.63434			−0.817170	+	0.576397i	$0.804458\pi$
$278$	2.30807	+	16.0530i	0.138429	+	0.962795i
$279$	2.08334	−	4.56187i	0.124726	−	0.273112i
$280$	−2.28079	+	0.669701i	−0.136303	+	0.0400223i
$281$	−5.53712	+	6.39017i	−0.330317	+	0.381206i	−0.896478	−	0.443089i	$-0.853883\pi$
$281$	−5.53712	+	6.39017i	−0.330317	+	0.381206i	0.566161	+	0.824295i	$0.308428\pi$
$282$	8.73773	+	2.56563i	0.520324	+	0.152781i
$283$	18.4878	−	11.8814i	1.09899	−	0.706276i	0.140121	−	0.990134i	$-0.455251\pi$
$283$	18.4878	−	11.8814i	1.09899	−	0.706276i	0.958866	+	0.283858i	$0.0916146\pi$
$284$	−2.50387	−	5.48271i	−0.148577	−	0.325339i
$285$	−2.50268	−	2.88824i	−0.148246	−	0.171085i
$286$	−1.01924	−	0.655024i	−0.0602688	−	0.0387324i
$287$	0.415186	−	2.88768i	0.0245077	−	0.170454i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	17.6913	+	11.3695i	1.04066	+	0.668793i
$290$	5.68595	+	6.56194i	0.333891	+	0.385330i
$291$	1.58779	+	3.47678i	0.0930780	+	0.203812i
$292$	3.55901	−	2.28724i	0.208276	−	0.133851i
$293$	3.41227	+	1.00193i	0.199347	+	0.0585336i	0.379882	−	0.925035i	$-0.375965\pi$
$293$	3.41227	+	1.00193i	0.199347	+	0.0585336i	−0.180535	+	0.983569i	$0.557783\pi$
$294$	−0.883729	+	1.01988i	−0.0515401	+	0.0594805i
$295$	−1.88796	+	0.554355i	−0.109921	+	0.0322758i
$296$	0.410919	−	0.899787i	0.0238842	−	0.0522991i
$297$	0.0482085	+	0.335298i	0.00279734	+	0.0194559i
$298$	15.5531			0.900966
$299$	9.98590	−	13.9465i	0.577500	−	0.806548i
$300$	−1.00000			−0.0577350
$301$	−2.21353	−	15.3954i	−0.127586	−	0.887378i
$302$	2.80555	−	6.14330i	0.161441	−	0.353507i
$303$	1.14851	−	0.337234i	0.0659804	−	0.0193736i
$304$	2.50268	−	2.88824i	0.143538	−	0.165652i
$305$	−1.92058	−	0.563933i	−0.109972	−	0.0322907i
$306$	−5.18786	+	3.33403i	−0.296570	+	0.190594i
$307$	−10.4699	−	22.9260i	−0.597551	−	1.30845i	−0.930770	−	0.365605i	$-0.880862\pi$
$307$	−10.4699	−	22.9260i	−0.597551	−	1.30845i	0.333219	−	0.942850i	$-0.391865\pi$
$308$	−0.527310	−	0.608548i	−0.0300463	−	0.0346753i
$309$	3.65881	+	2.35138i	0.208143	+	0.133765i
$310$	−0.713720	+	4.96403i	−0.0405365	+	0.281938i
$311$	4.82310	−	33.5454i	0.273493	−	1.90218i	−0.137428	−	0.990512i	$-0.543883\pi$
$311$	4.82310	−	33.5454i	0.273493	−	1.90218i	0.410920	−	0.911671i	$-0.365207\pi$
$312$	3.00886	+	1.93368i	0.170343	+	0.109473i
$313$	−6.62545	−	7.64617i	−0.374492	−	0.432187i	0.536951	−	0.843614i	$-0.319576\pi$
$313$	−6.62545	−	7.64617i	−0.374492	−	0.432187i	−0.911443	+	0.411426i	$0.865031\pi$
$314$	−9.03937	−	19.7935i	−0.510121	−	1.11701i
$315$	1.99973	−	1.28515i	0.112672	−	0.0724098i
$316$	6.89709	+	2.02517i	0.387991	+	0.113925i
$317$	12.5630	−	14.4985i	0.705608	−	0.814315i	−0.283891	−	0.958857i	$-0.591625\pi$
$317$	12.5630	−	14.4985i	0.705608	−	0.814315i	0.989499	+	0.144542i	$0.0461707\pi$
$318$	6.66896	−	1.95818i	0.373977	−	0.109809i
$319$	−1.22183	+	2.67543i	−0.0684092	+	0.149795i
$320$	−0.142315	−	0.989821i	−0.00795564	−	0.0553327i
$321$	18.6346			1.04008
$322$	8.97932	−	7.02379i	0.500398	−	0.391420i
$323$	23.5677			1.31134
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−1.48579	+	3.25342i	−0.0824168	+	0.180468i
$326$	−10.4524	+	3.06910i	−0.578905	+	0.169982i
$327$	−2.49126	+	2.87507i	−0.137767	+	0.158992i
$328$	1.17758	+	0.345769i	0.0650210	+	0.0190919i
$329$	18.2107	−	11.7033i	1.00399	−	0.645225i
$330$	−0.140720	−	0.308134i	−0.00774638	−	0.0169622i
$331$	2.36796	+	2.73277i	0.130155	+	0.150207i	0.817086	−	0.576516i	$-0.195588\pi$
$331$	2.36796	+	2.73277i	0.130155	+	0.150207i	−0.686931	+	0.726722i	$0.741043\pi$
$332$	4.03849	+	2.59538i	0.221641	+	0.142440i
$333$	−0.140775	+	0.979109i	−0.00771440	+	0.0536548i
$334$	−2.85076	+	19.8274i	−0.155986	+	1.08491i
$335$	7.57485	+	4.86806i	0.413859	+	0.265971i
$336$	1.55666	+	1.79648i	0.0849226	+	0.0980059i
$337$	−8.81317	−	19.2981i	−0.480084	−	1.05124i	−0.982440	−	0.186577i	$-0.940261\pi$
$337$	−8.81317	−	19.2981i	−0.480084	−	1.05124i	0.502356	−	0.864661i	$-0.332467\pi$
$338$	−0.174694	+	0.112269i	−0.00950208	+	0.00610662i
$339$	−17.1616	−	5.03911i	−0.932092	−	0.273687i
$340$	4.03841	−	4.66057i	0.219013	−	0.252755i
$341$	−1.63002	+	0.478617i	−0.0882705	+	0.0259186i
$342$	−1.58759	+	3.47634i	−0.0858470	+	0.187979i
$343$	2.82458	+	19.6454i	0.152513	+	1.06075i
$344$	6.54322			0.352787
$345$	4.45691	−	1.77087i	0.239952	−	0.0953407i
$346$	−5.63316			−0.302841
$347$	0.326582	+	2.27143i	0.0175318	+	0.121937i	0.996708	−	0.0810763i	$-0.0258357\pi$
$347$	0.326582	+	2.27143i	0.0175318	+	0.121937i	−0.979176	+	0.203013i	$0.934927\pi$
$348$	3.60692	−	7.89806i	0.193351	−	0.423380i
$349$	21.7899	−	6.39810i	1.16639	−	0.342482i	0.359476	−	0.933154i	$-0.382955\pi$
$349$	21.7899	−	6.39810i	1.16639	−	0.342482i	0.806912	+	0.590672i	$0.201137\pi$
$350$	−1.55666	+	1.79648i	−0.0832068	+	0.0960257i
$351$	−3.43176	−	1.00766i	−0.183174	−	0.0537847i
$352$	0.284971	−	0.183140i	0.0151890	−	0.00976137i
$353$	0.419536	+	0.918656i	0.0223297	+	0.0488951i	0.920468	−	0.390817i	$-0.127808\pi$
$353$	0.419536	+	0.918656i	0.0223297	+	0.0488951i	−0.898139	+	0.439713i	$0.855080\pi$
$354$	1.28855	+	1.48706i	0.0684854	+	0.0790364i
$355$	−5.07057	−	3.25866i	−0.269118	−	0.172952i
$356$	1.82451	−	12.6898i	0.0966989	−	0.672556i
$357$	−2.08620	+	14.5098i	−0.110413	+	0.767940i
$358$	−15.4608	−	9.93608i	−0.817131	−	0.525138i
$359$	−7.77255	−	8.97000i	−0.410220	−	0.473419i	0.512613	−	0.858620i	$-0.328678\pi$
$359$	−7.77255	−	8.97000i	−0.410220	−	0.473419i	−0.922833	+	0.385201i	$0.874132\pi$
$360$	0.415415	+	0.909632i	0.0218943	+	0.0479418i
$361$	−3.69702	+	2.37593i	−0.194580	+	0.125049i
$362$	3.75841	+	1.10357i	0.197537	+	0.0580022i
$363$	−7.12832	+	8.22652i	−0.374140	+	0.431781i
$364$	8.15757	−	2.39528i	0.427573	−	0.125547i
$365$	1.75746	−	3.84830i	0.0919896	−	0.201429i
$366$	0.284866	+	1.98129i	0.0148902	+	0.103564i
$367$	1.10887			0.0578826			0.0289413	−	0.999581i	$-0.490786\pi$
$367$	1.10887			0.0578826			0.0289413	+	0.999581i	$0.490786\pi$
$368$	2.38713	+	4.15952i	0.124438	+	0.216830i
$369$	−1.22729			−0.0638904
$370$	−0.140775	−	0.979109i	−0.00731852	−	0.0509014i
$371$	6.86345	−	15.0289i	0.356332	−	0.780259i
$372$	4.81193	−	1.41291i	0.249487	−	0.0732560i
$373$	−10.0709	+	11.6225i	−0.521454	+	0.601789i	−0.953994	−	0.299825i	$-0.903072\pi$
$373$	−10.0709	+	11.6225i	−0.521454	+	0.601789i	0.432541	+	0.901614i	$0.357617\pi$
$374$	2.00436	+	0.588534i	0.103643	+	0.0304324i
$375$	−0.841254	+	0.540641i	−0.0434421	+	0.0279186i
$376$	3.78302	+	8.28366i	0.195094	+	0.427197i
$377$	−20.3366	−	23.4697i	−1.04739	−	1.20875i
$378$	−1.99973	−	1.28515i	−0.102855	−	0.0661008i
$379$	−3.48556	+	24.2426i	−0.179041	+	1.24526i	0.679947	+	0.733261i	$0.262003\pi$
$379$	−3.48556	+	24.2426i	−0.179041	+	1.24526i	−0.858988	+	0.511996i	$0.828906\pi$
$380$	0.543884	−	3.78279i	0.0279006	−	0.194053i
$381$	3.58631	+	2.30478i	0.183732	+	0.118077i
$382$	−3.76479	−	4.34480i	−0.192623	−	0.222299i
$383$	7.56292	+	16.5605i	0.386447	+	0.846201i	0.998467	+	0.0553582i	$0.0176301\pi$
$383$	7.56292	+	16.5605i	0.386447	+	0.846201i	−0.612020	+	0.790843i	$0.709643\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	−0.772608	−	0.226858i	−0.0393757	−	0.0115618i
$386$	−2.00093	+	2.30919i	−0.101845	+	0.117535i
$387$	−6.27817	+	1.84344i	−0.319137	+	0.0937072i
$388$	−1.58779	+	3.47678i	−0.0806079	+	0.176507i
$389$	−0.911898	−	6.34239i	−0.0462351	−	0.321572i	−0.999793	−	0.0203613i	$-0.993518\pi$
$389$	−0.911898	−	6.34239i	−0.0462351	−	0.321572i	0.953558	−	0.301211i	$-0.0973908\pi$
$390$	3.57664			0.181110
$391$	−9.74551	+	27.9232i	−0.492852	+	1.41214i
$392$	−1.34949			−0.0681596
$393$	−2.49751	−	17.3706i	−0.125983	−	0.876229i
$394$	−5.83586	+	12.7787i	−0.294006	+	0.643784i
$395$	6.89709	−	2.02517i	0.347030	−	0.101897i
$396$	−0.221831	+	0.256007i	−0.0111474	+	0.0128648i
$397$	16.1056	+	4.72902i	0.808315	+	0.237343i	0.659677	−	0.751549i	$-0.270693\pi$
$397$	16.1056	+	4.72902i	0.808315	+	0.237343i	0.148638	+	0.988892i	$0.452511\pi$
$398$	−1.80940	+	1.16283i	−0.0906971	+	0.0582875i
$399$	3.77383	+	8.26353i	0.188928	+	0.413694i
$400$	−0.654861	−	0.755750i	−0.0327430	−	0.0377875i
$401$	−8.36334	−	5.37480i	−0.417646	−	0.268404i	0.314897	−	0.949126i	$-0.398030\pi$
$401$	−8.36334	−	5.37480i	−0.417646	−	0.268404i	−0.732542	+	0.680721i	$0.761666\pi$
$402$	1.28144	−	8.91260i	0.0639123	−	0.444520i
$403$	2.55272	−	17.7545i	0.127160	−	0.884416i
$404$	1.00698	+	0.647148i	0.0500992	+	0.0321968i
$405$	−0.654861	−	0.755750i	−0.0325403	−	0.0375535i
$406$	−8.57394	−	18.7743i	−0.425517	−	0.931753i
$407$	0.281887	−	0.181158i	0.0139726	−	0.00897965i
$408$	−5.91702	−	1.73739i	−0.292936	−	0.0860138i
$409$	21.3270	−	24.6127i	1.05455	−	1.21702i	0.0790867	−	0.996868i	$-0.474800\pi$
$409$	21.3270	−	24.6127i	1.05455	−	1.21702i	0.975466	−	0.220151i	$-0.0706549\pi$
$410$	1.17758	−	0.345769i	0.0581566	−	0.0170763i
$411$	6.62477	−	14.5062i	0.326776	−	0.715540i
$412$	0.618961	+	4.30497i	0.0304940	+	0.212091i
$413$	4.67729			0.230155
$414$	−3.46231	−	3.31850i	−0.170163	−	0.163095i
$415$	4.80056			0.235650
$416$	0.509009	+	3.54023i	0.0249562	+	0.173574i
$417$	6.73724	−	14.7525i	0.329924	−	0.722433i
$418$	1.24214	−	0.364726i	0.0607551	−	0.0178393i
$419$	−3.00235	+	3.46490i	−0.146674	+	0.169271i	−0.824333	−	0.566106i	$-0.808449\pi$
$419$	−3.00235	+	3.46490i	−0.146674	+	0.169271i	0.677658	+	0.735377i	$0.262995\pi$
$420$	2.28079	+	0.669701i	0.111291	+	0.0326781i
$421$	2.99584	−	1.92531i	0.146008	−	0.0938337i	−0.465597	−	0.884997i	$-0.654160\pi$
$421$	2.99584	−	1.92531i	0.146008	−	0.0938337i	0.611605	+	0.791163i	$0.290524\pi$
$422$	6.78179	+	14.8500i	0.330132	+	0.722889i
$423$	−5.96356	−	6.88231i	−0.289958	−	0.334630i
$424$	5.84714	+	3.75773i	0.283962	+	0.182491i
$425$	0.877630	−	6.10405i	0.0425713	−	0.296090i
$426$	−0.857788	+	5.96605i	−0.0415600	+	0.289056i
$427$	4.00278	+	2.57243i	0.193708	+	0.124489i
$428$	12.2031	+	14.0831i	0.589857	+	0.680731i
$429$	0.503304	+	1.10208i	0.0242998	+	0.0532091i
$430$	5.50450	−	3.53753i	0.265451	−	0.170595i
$431$	−32.4670	−	9.53318i	−1.56388	−	0.459197i	−0.618669	−	0.785652i	$-0.712328\pi$
$431$	−32.4670	−	9.53318i	−1.56388	−	0.459197i	−0.945213	+	0.326454i	$0.894146\pi$
$432$	0.654861	−	0.755750i	0.0315070	−	0.0363610i
$433$	20.9832	−	6.16123i	1.00839	−	0.296090i	0.264495	−	0.964387i	$-0.414795\pi$
$433$	20.9832	−	6.16123i	1.00839	−	0.296090i	0.743894	+	0.668297i	$0.232977\pi$
$434$	4.95226	−	10.8439i	0.237716	−	0.520526i
$435$	−1.23568	−	8.59432i	−0.0592461	−	0.412066i
$436$	−3.80426			−0.182191
$437$	4.27481	+	17.8227i	0.204492	+	0.852576i
$438$	−4.23061			−0.202146
$439$	0.979191	+	6.81042i	0.0467342	+	0.325044i	0.999755	+	0.0221385i	$0.00704750\pi$
$439$	0.979191	+	6.81042i	0.0467342	+	0.325044i	−0.953021	+	0.302905i	$0.902043\pi$
$440$	0.140720	−	0.308134i	0.00670856	−	0.0146897i
$441$	1.29483	−	0.380196i	0.0616585	−	0.0181046i
$442$	−14.4439	+	16.6692i	−0.687027	+	0.792872i
$443$	35.7986	+	10.5114i	1.70084	+	0.499413i	0.980882	−	0.194602i	$-0.0623415\pi$
$443$	35.7986	+	10.5114i	1.70084	+	0.499413i	0.719961	+	0.694015i	$0.244160\pi$
$444$	−0.832149	+	0.534790i	−0.0394920	+	0.0253800i
$445$	−5.32572	−	11.6617i	−0.252464	−	0.552818i
$446$	6.38215	+	7.36539i	0.302203	+	0.348761i
$447$	−13.0841	−	8.40863i	−0.618856	−	0.397715i
$448$	−0.338294	+	2.35288i	−0.0159829	+	0.111163i
$449$	−1.90025	+	13.2166i	−0.0896785	+	0.623728i	0.894569	+	0.446930i	$0.147483\pi$
$449$	−1.90025	+	13.2166i	−0.0896785	+	0.623728i	−0.984247	+	0.176797i	$0.943426\pi$
$450$	0.841254	+	0.540641i	0.0396571	+	0.0254861i
$451$	0.272252	+	0.314196i	0.0128199	+	0.0147949i
$452$	−7.43018	−	16.2698i	−0.349486	−	0.765268i
$453$	−5.68150	+	3.65128i	−0.266940	+	0.171552i
$454$	−2.76916	−	0.813100i	−0.129963	−	0.0381607i
$455$	5.56760	−	6.42535i	0.261013	−	0.301225i
$456$	−3.66689	+	1.07670i	−0.171718	+	0.0504209i
$457$	−17.0715	+	37.3813i	−0.798569	+	1.74862i	−0.148266	+	0.988948i	$0.547369\pi$
$457$	−17.0715	+	37.3813i	−0.798569	+	1.74862i	−0.650303	+	0.759675i	$0.725358\pi$
$458$	−2.19293	−	15.2522i	−0.102469	−	0.712688i
$459$	6.16682			0.287842
$460$	4.25699	+	2.20863i	0.198483	+	0.102978i
$461$	17.2886			0.805212			0.402606	−	0.915373i	$-0.368104\pi$
$461$	17.2886			0.805212			0.402606	+	0.915373i	$0.368104\pi$
$462$	0.114595	+	0.797029i	0.00533146	+	0.0370811i
$463$	3.81097	−	8.34486i	0.177111	−	0.387819i	−0.800168	−	0.599776i	$-0.795256\pi$
$463$	3.81097	−	8.34486i	0.177111	−	0.387819i	0.977279	+	0.211957i	$0.0679837\pi$
$464$	8.33098	−	2.44620i	0.386756	−	0.113562i
$465$	3.28418	−	3.79014i	0.152300	−	0.175764i
$466$	27.4747	+	8.06730i	1.27274	+	0.373711i
$467$	−30.3754	+	19.5211i	−1.40561	+	0.903328i	−0.999943	−	0.0106952i	$-0.996596\pi$
$467$	−30.3754	+	19.5211i	−1.40561	+	0.903328i	−0.405663	+	0.914023i	$0.632959\pi$
$468$	−1.48579	−	3.25342i	−0.0686806	−	0.150390i
$469$	−14.0165	−	16.1759i	−0.647223	−	0.746935i
$470$	7.66097	+	4.92340i	0.353374	+	0.227100i
$471$	−3.09675	+	21.5384i	−0.142691	+	0.992436i
$472$	−0.280028	+	1.94764i	−0.0128893	+	0.0896472i
$473$	1.86463	+	1.19832i	0.0857356	+	0.0550989i
$474$	−4.70731	−	5.43252i	−0.216214	−	0.249524i
$475$	−1.58759	−	3.47634i	−0.0728436	−	0.159505i
$476$	−12.3319	+	7.92526i	−0.565234	+	0.363254i
$477$	−6.66896	−	1.95818i	−0.305351	−	0.0896591i
$478$	−12.0102	+	13.8605i	−0.549335	+	0.633966i
$479$	1.53187	−	0.449796i	0.0699928	−	0.0205517i	−0.246549	−	0.969130i	$-0.579297\pi$
$479$	1.53187	−	0.449796i	0.0699928	−	0.0205517i	0.316541	+	0.948579i	$0.397478\pi$
$480$	−0.415415	+	0.909632i	−0.0189610	+	0.0415188i
$481$	0.503500	+	3.50192i	0.0229576	+	0.159674i
$482$	26.3800			1.20157
$483$	−11.3512	+	1.05420i	−0.516499	+	0.0479678i
$484$	−10.8853			−0.494784
$485$	0.543953	+	3.78328i	0.0246996	+	0.171790i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	18.0563	−	5.30181i	0.818210	−	0.240248i	0.154265	−	0.988030i	$-0.450699\pi$
$487$	18.0563	−	5.30181i	0.818210	−	0.240248i	0.663945	+	0.747781i	$0.268881\pi$
$488$	−1.31081	+	1.51275i	−0.0593376	+	0.0684792i
$489$	10.4524	+	3.06910i	0.472674	+	0.138790i
$490$	−1.13526	+	0.729590i	−0.0512860	+	0.0329595i
$491$	−4.35731	−	9.54117i	−0.196643	−	0.430587i	0.785466	−	0.618905i	$-0.212424\pi$
$491$	−4.35731	−	9.54117i	−0.196643	−	0.430587i	−0.982108	+	0.188318i	$0.939696\pi$
$492$	−0.803707	−	0.927527i	−0.0362339	−	0.0418162i
$493$	45.0446	+	28.9484i	2.02871	+	1.30377i
$494$	−1.94528	+	13.5297i	−0.0875221	+	0.608729i
$495$	−0.0482085	+	0.335298i	−0.00216681	+	0.0150705i
$496$	4.21895	+	2.71135i	0.189436	+	0.121743i
$497$	9.38258	+	10.8281i	0.420866	+	0.485706i
$498$	−1.99423	−	4.36674i	−0.0893634	−	0.195679i
$499$	−30.6977	+	19.7282i	−1.37422	+	0.883156i	−0.999040	−	0.0437974i	$-0.986054\pi$
$499$	−30.6977	+	19.7282i	−1.37422	+	0.883156i	−0.375177	+	0.926953i	$0.622418\pi$
$500$	−0.959493	−	0.281733i	−0.0429098	−	0.0125995i
$501$	13.1177	−	15.1387i	0.586057	−	0.676346i
$502$	9.20493	−	2.70281i	0.410836	−	0.120632i
$503$	−6.67557	+	14.6175i	−0.297649	+	0.651760i	−0.998079	−	0.0619614i	$-0.980264\pi$
$503$	−6.67557	+	14.6175i	−0.297649	+	0.651760i	0.700430	+	0.713721i	$0.252992\pi$
$504$	−0.338294	−	2.35288i	−0.0150688	−	0.104806i
$505$	1.19700			0.0532659
$506$	−0.0815095	+	1.62252i	−0.00362354	+	0.0721298i
$507$	0.207659			0.00922245
$508$	0.606695	+	4.21966i	0.0269178	+	0.187217i
$509$	−8.11017	+	17.7588i	−0.359477	+	0.787145i	0.640342	+	0.768090i	$0.278793\pi$
$509$	−8.11017	+	17.7588i	−0.359477	+	0.787145i	−0.999818	+	0.0190543i	$0.993934\pi$
$510$	−5.91702	+	1.73739i	−0.262010	+	0.0769331i
$511$	−6.58560	+	7.60019i	−0.291330	+	0.336213i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	3.21501	−	2.06616i	0.141946	−	0.0912234i
$514$	−5.46982	−	11.9772i	−0.241263	−	0.528293i
$515$	2.84815	+	3.28694i	0.125504	+	0.144840i
$516$	−5.50450	−	3.53753i	−0.242322	−	0.155731i
$517$	−0.439016	+	3.05342i	−0.0193079	+	0.134289i
$518$	−0.334632	+	2.32742i	−0.0147029	+	0.102261i
$519$	4.73892	+	3.04552i	0.208015	+	0.133683i
$520$	2.34220	+	2.70304i	0.102712	+	0.118536i
$521$	−12.6135	−	27.6198i	−0.552608	−	1.21004i	−0.955553	−	0.294819i	$-0.904741\pi$
$521$	−12.6135	−	27.6198i	−0.552608	−	1.21004i	0.402945	−	0.915224i	$-0.367987\pi$
$522$	−7.30435	+	4.69422i	−0.319703	+	0.205460i
$523$	−30.4956	−	8.95432i	−1.33348	−	0.391545i	−0.464141	−	0.885761i	$-0.653637\pi$
$523$	−30.4956	−	8.95432i	−1.33348	−	0.391545i	−0.869339	+	0.494217i	$0.835455\pi$
$524$	11.4923	−	13.2628i	0.502042	−	0.579388i
$525$	2.28079	−	0.669701i	0.0995419	−	0.0292281i
$526$	6.63755	−	14.5342i	0.289411	−	0.633721i
$527$	4.40138	+	30.6123i	0.191727	+	1.33349i
$528$	−0.338745			−0.0147420
$529$	−22.8842	−	2.30506i	−0.994965	−	0.100220i
$530$	6.95051			0.301911
$531$	−0.280028	−	1.94764i	−0.0121522	−	0.0845202i
$532$	−3.77383	+	8.26353i	−0.163616	+	0.358269i
$533$	−4.21178	+	1.23669i	−0.182432	+	0.0535670i
$534$	−8.39548	+	9.68890i	−0.363308	+	0.419280i
$535$	17.8797	+	5.24997i	0.773009	+	0.226976i
$536$	7.57485	−	4.86806i	0.327184	−	0.210268i
$537$	7.63464	+	16.7175i	0.329459	+	0.721414i
$538$	−5.29479	−	6.11051i	−0.228275	−	0.263443i
$539$	−0.384566	−	0.247145i	−0.0165644	−	0.0106453i
$540$	0.142315	−	0.989821i	0.00612426	−	0.0425951i
$541$	−4.13093	+	28.7313i	−0.177603	+	1.23525i	0.684687	+	0.728837i	$0.259939\pi$
$541$	−4.13093	+	28.7313i	−0.177603	+	1.23525i	−0.862289	+	0.506416i	$0.830970\pi$
$542$	−10.0209	−	6.44004i	−0.430434	−	0.276623i
$543$	−2.56514	−	2.96033i	−0.110081	−	0.127040i
$544$	−2.56179	−	5.60953i	−0.109836	−	0.240507i
$545$	−3.20035	+	2.05674i	−0.137088	+	0.0881011i
$546$	−8.15757	−	2.39528i	−0.349112	−	0.102508i
$547$	−2.61840	+	3.02179i	−0.111955	+	0.129202i	−0.808961	−	0.587863i	$-0.799970\pi$
$547$	−2.61840	+	3.02179i	−0.111955	+	0.129202i	0.697006	+	0.717065i	$0.254515\pi$
$548$	15.3014	−	4.49289i	0.653643	−	0.191927i
$549$	0.831520	−	1.82078i	0.0354884	−	0.0777088i
$550$	−0.0482085	−	0.335298i	−0.00205562	−	0.0142971i
$551$	33.1826			1.41363
$552$	0.240622	−	4.78979i	0.0102415	−	0.203867i
$553$	−17.0871			−0.726616
$554$	3.87108	+	26.9240i	0.164466	+	1.14389i
$555$	−0.410919	+	0.899787i	−0.0174425	+	0.0381938i
$556$	15.5611	−	4.56916i	0.659939	−	0.193776i
$557$	−7.96532	+	9.19247i	−0.337501	+	0.389497i	−0.898977	−	0.437996i	$-0.855688\pi$
$557$	−7.96532	+	9.19247i	−0.337501	+	0.389497i	0.561476	+	0.827493i	$0.310234\pi$
$558$	−4.81193	−	1.41291i	−0.203705	−	0.0598132i
$559$	−19.6876	+	12.6525i	−0.832697	+	0.535142i
$560$	0.987475	+	2.16227i	0.0417284	+	0.0913725i
$561$	−1.36799	−	1.57875i	−0.0577567	−	0.0666547i
$562$	7.11314	+	4.57134i	0.300050	+	0.192830i
$563$	0.436521	−	3.03607i	0.0183972	−	0.127955i	−0.978553	−	0.205995i	$-0.933957\pi$
$563$	0.436521	−	3.03607i	0.0183972	−	0.127955i	0.996950	+	0.0780398i	$0.0248661\pi$
$564$	1.29601	−	9.01391i	0.0545717	−	0.379554i
$565$	−15.0468	−	9.66998i	−0.633023	−	0.406819i
$566$	−14.3916	−	16.6087i	−0.604922	−	0.698117i
$567$	0.987475	+	2.16227i	0.0414700	+	0.0908067i
$568$	−5.07057	+	3.25866i	−0.212756	+	0.136730i
$569$	5.29119	+	1.55363i	0.221818	+	0.0651316i	0.390753	−	0.920496i	$-0.372215\pi$
$569$	5.29119	+	1.55363i	0.221818	+	0.0651316i	−0.168935	+	0.985627i	$0.554033\pi$
$570$	−2.50268	+	2.88824i	−0.104826	+	0.120975i
$571$	−30.9417	+	9.08531i	−1.29487	+	0.380208i	−0.855362	−	0.518030i	$-0.826666\pi$
$571$	−30.9417	+	9.08531i	−1.29487	+	0.380208i	−0.439509	+	0.898238i	$0.644847\pi$
$572$	−0.503304	+	1.10208i	−0.0210442	+	0.0460804i
$573$	0.818167	+	5.69048i	0.0341794	+	0.237723i
$574$	−2.91738			−0.121769
$575$	4.77528	−	0.443486i	0.199143	−	0.0184946i
$576$	1.00000			0.0416667
$577$	3.27571	+	22.7830i	0.136369	+	0.948470i	0.937004	+	0.349318i	$0.113587\pi$
$577$	3.27571	+	22.7830i	0.136369	+	0.948470i	−0.800635	+	0.599153i	$0.795504\pi$
$578$	8.73602	−	19.1292i	0.363371	−	0.795671i
$579$	2.93173	−	0.860835i	0.121839	−	0.0357751i
$580$	5.68595	−	6.56194i	0.236096	−	0.272470i
$581$	−10.9491	−	3.21494i	−0.454244	−	0.133378i
$582$	3.21542	−	2.06643i	0.133284	−	0.0856562i
$583$	0.978075	+	2.14169i	0.0405077	+	0.0886995i
$584$	−2.77046	−	3.19728i	−0.114642	−	0.132304i
$585$	−3.00886	−	1.93368i	−0.124401	−	0.0799477i
$586$	0.506118	−	3.52013i	0.0209075	−	0.145415i
$587$	3.90147	−	27.1353i	0.161031	−	1.12000i	−0.735664	−	0.677347i	$-0.763130\pi$
$587$	3.90147	−	27.1353i	0.161031	−	1.12000i	0.896695	−	0.442649i	$-0.145961\pi$
$588$	1.13526	+	0.729590i	0.0468175	+	0.0300878i
$589$	12.5511	+	14.4848i	0.517160	+	0.596834i
$590$	0.817397	+	1.78985i	0.0336517	+	0.0736869i
$591$	11.8181	−	7.59506i	0.486134	−	0.312419i
$592$	−0.949109	−	0.278683i	−0.0390081	−	0.0114538i
$593$	−20.7985	+	24.0028i	−0.854093	+	0.985675i	−0.999993	−	0.00362387i	$-0.998846\pi$
$593$	−20.7985	+	24.0028i	−0.854093	+	0.985675i	0.145901	+	0.989299i	$0.453392\pi$
$594$	0.325024	−	0.0954356i	0.0133359	−	0.00391577i
$595$	−6.08958	+	13.3343i	−0.249648	+	0.546653i
$596$	−2.21343	−	15.3948i	−0.0906658	−	0.630595i
$597$	2.15084			0.0880280
$598$	−15.2257	−	7.89946i	−0.622626	−	0.323033i
$599$	5.01613			0.204953			0.102477	−	0.994735i	$-0.467323\pi$
$599$	5.01613			0.204953			0.102477	+	0.994735i	$0.467323\pi$
$600$	0.142315	+	0.989821i	0.00580998	+	0.0404093i
$601$	18.9402	−	41.4733i	0.772587	−	1.69173i	0.0517142	−	0.998662i	$-0.483532\pi$
$601$	18.9402	−	41.4733i	0.772587	−	1.69173i	0.720873	−	0.693067i	$-0.243741\pi$
$602$	−14.9237	+	4.38200i	−0.608245	+	0.178597i
$603$	−5.89653	+	6.80496i	−0.240125	+	0.277119i
$604$	−6.48004	−	1.90271i	−0.263669	−	0.0774202i
$605$	−9.15726	+	5.88501i	−0.372295	+	0.239260i
$606$	−0.497252	−	1.08883i	−0.0201995	−	0.0442307i
$607$	4.42738	+	5.10947i	0.179702	+	0.207387i	0.838453	−	0.544974i	$-0.183460\pi$
$607$	4.42738	+	5.10947i	0.179702	+	0.207387i	−0.658751	+	0.752361i	$0.728915\pi$
$608$	−3.21501	−	2.06616i	−0.130386	−	0.0837940i
$609$	−2.93730	+	20.4294i	−0.119025	+	0.827840i
$610$	−0.284866	+	1.98129i	−0.0115339	+	0.0802200i
$611$	−27.4005	−	17.6092i	−1.10851	−	0.712393i
$612$	4.03841	+	4.66057i	0.163243	+	0.188392i
$613$	4.25996	+	9.32802i	0.172058	+	0.376755i	0.975942	−	0.218032i	$-0.0699636\pi$
$613$	4.25996	+	9.32802i	0.172058	+	0.376755i	−0.803883	+	0.594787i	$0.797236\pi$
$614$	−21.2026	+	13.6261i	−0.855667	+	0.549904i
$615$	−1.17758	−	0.345769i	−0.0474846	−	0.0139427i
$616$	−0.527310	+	0.608548i	−0.0212459	+	0.0245191i
$617$	−15.2621	+	4.48135i	−0.614428	+	0.180412i	−0.574115	−	0.818775i	$-0.694654\pi$
$617$	−15.2621	+	4.48135i	−0.614428	+	0.180412i	−0.0403129	+	0.999187i	$0.512835\pi$
$618$	1.80674	−	3.95621i	0.0726777	−	0.159142i
$619$	−0.708506	−	4.92777i	−0.0284773	−	0.198064i	0.970616	−	0.240633i	$-0.0773549\pi$
$619$	−0.708506	−	4.92777i	−0.0284773	−	0.198064i	−0.999094	+	0.0425689i	$0.986446\pi$
$620$	5.01508			0.201410
$621$	1.11857	+	4.66356i	0.0448865	+	0.187142i
$622$	−33.8903			−1.35888
$623$	4.33701	+	30.1646i	0.173759	+	1.20852i
$624$	1.48579	−	3.25342i	0.0594792	−	0.130241i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	−6.62545	+	7.64617i	−0.264806	+	0.305603i
$627$	−1.24214	−	0.364726i	−0.0496064	−	0.0145657i
$628$	−18.3056	+	11.7643i	−0.730471	+	0.469446i
$629$	−2.53406	−	5.54882i	−0.101040	−	0.221246i
$630$	−1.55666	−	1.79648i	−0.0620187	−	0.0715734i
$631$	18.1965	+	11.6942i	0.724391	+	0.465538i	0.850162	−	0.526522i	$-0.176504\pi$
$631$	18.1965	+	11.6942i	0.724391	+	0.465538i	−0.125771	+	0.992059i	$0.540140\pi$
$632$	1.02300	−	7.11509i	0.0406926	−	0.283023i
$633$	2.32334	−	16.1592i	0.0923444	−	0.642269i
$634$	−16.1388	−	10.3718i	−0.640953	−	0.411916i
$635$	2.79170	+	3.22180i	0.110785	+	0.127853i
$636$	−2.88734	−	6.32240i	−0.114491	−	0.250700i
$637$	4.06043	−	2.60948i	0.160880	−	0.103391i
$638$	2.82208	+	0.828638i	0.111727	+	0.0328061i
$639$	3.94711	−	4.55520i	0.156145	−	0.180201i
$640$	−0.959493	+	0.281733i	−0.0379273	+	0.0111365i
$641$	14.8879	−	32.5999i	0.588036	−	1.28762i	−0.348585	−	0.937277i	$-0.613338\pi$
$641$	14.8879	−	32.5999i	0.588036	−	1.28762i	0.936621	−	0.350343i	$-0.113935\pi$
$642$	−2.65198	−	18.4449i	−0.104665	−	0.727962i
$643$	28.4779			1.12306			0.561529	−	0.827457i	$-0.310213\pi$
$643$	28.4779			1.12306			0.561529	+	0.827457i	$0.310213\pi$
$644$	−8.23018	−	7.88833i	−0.324315	−	0.310844i
$645$	−6.54322			−0.257639
$646$	−3.35403	−	23.3278i	−0.131963	−	0.917820i
$647$	−0.461866	+	1.01135i	−0.0181578	+	0.0397601i	−0.918494	−	0.395436i	$-0.870594\pi$
$647$	−0.461866	+	1.01135i	−0.0181578	+	0.0397601i	0.900336	+	0.435196i	$0.143321\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	−0.436489	+	0.503735i	−0.0171337	+	0.0197733i
$650$	3.43176	+	1.00766i	0.134605	+	0.0395235i
$651$	−10.0288	+	6.44511i	−0.393059	+	0.252604i
$652$	4.52539	+	9.90923i	0.177228	+	0.388075i
$653$	−17.3170	−	19.9849i	−0.677668	−	0.782070i	0.307888	−	0.951423i	$-0.400378\pi$
$653$	−17.3170	−	19.9849i	−0.677668	−	0.782070i	−0.985556	+	0.169352i	$0.945832\pi$
$654$	3.20035	+	2.05674i	0.125144	+	0.0804249i
$655$	2.49751	−	17.3706i	0.0975858	−	0.678724i
$656$	0.174662	−	1.21480i	0.00681941	−	0.0474301i
$657$	3.55901	+	2.28724i	0.138850	+	0.0892337i
$658$	−14.1759	−	16.3598i	−0.552632	−	0.637772i
$659$	−1.88494	−	4.12745i	−0.0734269	−	0.160783i	0.869359	−	0.494181i	$-0.164532\pi$
$659$	−1.88494	−	4.12745i	−0.0734269	−	0.160783i	−0.942786	+	0.333398i	$0.891805\pi$
$660$	−0.284971	+	0.183140i	−0.0110925	+	0.00712870i
$661$	2.14378	+	0.629471i	0.0833834	+	0.0244836i	0.323158	−	0.946345i	$-0.395255\pi$
$661$	2.14378	+	0.629471i	0.0833834	+	0.0244836i	−0.239775	+	0.970829i	$0.577074\pi$
$662$	2.36796	−	2.73277i	0.0920333	−	0.106212i
$663$	21.1630	−	6.21403i	0.821904	−	0.241333i
$664$	1.99423	−	4.36674i	0.0773910	−	0.169463i
$665$	1.29286	+	8.99200i	0.0501348	+	0.348695i
$666$	0.989177			0.0383298
$667$	−13.7214	+	39.3151i	−0.531294	+	1.52229i
$668$	20.0313			0.775036
$669$	−1.38697	−	9.64661i	−0.0536235	−	0.372959i
$670$	3.74050	−	8.19055i	0.144508	−	0.316429i
$671$	−0.650588	+	0.191030i	−0.0251157	+	0.00737462i
$672$	1.55666	−	1.79648i	0.0600493	−	0.0693006i
$673$	−38.3470	−	11.2597i	−1.47817	−	0.434029i	−0.559423	−	0.828882i	$-0.688977\pi$
$673$	−38.3470	−	11.2597i	−1.47817	−	0.434029i	−0.918744	+	0.394854i	$0.870795\pi$
$674$	−17.8475	+	11.4699i	−0.687459	+	0.441803i
$675$	−0.415415	−	0.909632i	−0.0159893	−	0.0350118i
$676$	0.135988	+	0.156938i	0.00523029	+	0.00603608i
$677$	23.8771	+	15.3449i	0.917672	+	0.589752i	0.911981	−	0.410232i	$-0.134552\pi$
$677$	23.8771	+	15.3449i	0.917672	+	0.589752i	0.00569075	+	0.999984i	$0.498189\pi$
$678$	−2.54546	+	17.7041i	−0.0977580	+	0.679922i
$679$	1.29302	−	8.99315i	0.0496216	−	0.345125i
$680$	−5.18786	−	3.33403i	−0.198945	−	0.127854i
$681$	1.88997	+	2.18115i	0.0724240	+	0.0835817i
$682$	0.705721	+	1.54531i	0.0270235	+	0.0591731i
$683$	−36.0791	+	23.1866i	−1.38053	+	0.887211i	−0.999305	−	0.0372728i	$-0.988133\pi$
$683$	−36.0791	+	23.1866i	−1.38053	+	0.887211i	−0.381222	+	0.924484i	$0.624497\pi$
$684$	3.66689	+	1.07670i	0.140207	+	0.0411685i
$685$	10.4433	−	12.0522i	0.399018	−	0.460491i
$686$	19.0434	−	5.59166i	0.727082	−	0.213491i
$687$	−6.40114	+	14.0165i	−0.244219	+	0.534765i
$688$	−0.931197	−	6.47662i	−0.0355015	−	0.246919i
$689$	−24.8594			−0.947069
$690$	−2.38713	−	4.15952i	−0.0908766	−	0.158350i
$691$	−2.44328			−0.0929468			−0.0464734	−	0.998920i	$-0.514798\pi$
$691$	−2.44328			−0.0929468			−0.0464734	+	0.998920i	$0.514798\pi$
$692$	0.801682	+	5.57582i	0.0304754	+	0.211961i
$693$	0.334503	−	0.732458i	0.0127067	−	0.0278238i
$694$	2.20183	−	0.646516i	0.0835803	−	0.0245414i
$695$	10.6206	−	12.2568i	0.402862	−	0.464927i
$696$	−8.33098	−	2.44620i	−0.315785	−	0.0927229i
$697$	6.36703	−	4.09184i	0.241168	−	0.154990i
$698$	−9.43401	−	20.6576i	−0.357082	−	0.781901i
$699$	−18.7517	−	21.6406i	−0.709254	−	0.818523i
$700$	1.99973	+	1.28515i	0.0755826	+	0.0485740i
$701$	2.25087	−	15.6551i	0.0850142	−	0.591287i	−0.902131	−	0.431462i	$-0.857998\pi$
$701$	2.25087	−	15.6551i	0.0850142	−	0.591287i	0.987145	−	0.159825i	$-0.0510930\pi$
$702$	−0.509009	+	3.54023i	−0.0192113	+	0.133617i
$703$	−3.18022	−	2.04380i	−0.119944	−	0.0770835i
$704$	−0.221831	−	0.256007i	−0.00836057	−	0.00964862i
$705$	−3.78302	−	8.28366i	−0.142477	−	0.311981i
$706$	0.849600	−	0.546004i	0.0319751	−	0.0205492i
$707$	−2.73011	−	0.801633i	−0.102676	−	0.0301485i
$708$	1.28855	−	1.48706i	0.0484265	−	0.0558872i
$709$	−25.1308	+	7.37907i	−0.943808	+	0.277127i	−0.717206	−	0.696861i	$-0.754580\pi$
$709$	−25.1308	+	7.37907i	−0.943808	+	0.277127i	−0.226601	+	0.973988i	$0.572761\pi$
$710$	−2.50387	+	5.48271i	−0.0939686	+	0.205763i
$711$	1.02300	+	7.11509i	0.0383654	+	0.266837i
$712$	−12.8202			−0.480459
$713$	−22.3517	+	8.88107i	−0.837078	+	0.332599i
$714$	14.6590			0.548600
$715$	0.172424	+	1.19924i	0.00644831	+	0.0448490i
$716$	−7.63464	+	16.7175i	−0.285320	+	0.624763i
$717$	17.5972	−	5.16701i	0.657180	−	0.192965i
$718$	−7.77255	+	8.97000i	−0.290069	+	0.334757i
$719$	31.8728	+	9.35870i	1.18865	+	0.349021i	0.815505	−	0.578750i	$-0.196459\pi$
$719$	31.8728	+	9.35870i	1.18865	+	0.349021i	0.373150	+	0.927771i	$0.378278\pi$
$720$	0.841254	−	0.540641i	0.0313517	−	0.0201485i
$721$	−4.29476	−	9.40422i	−0.159945	−	0.350231i
$722$	2.87789	+	3.32126i	0.107104	+	0.123604i
$723$	−22.1922	−	14.2621i	−0.825338	−	0.530413i
$724$	0.557458	−	3.87721i	0.0207178	−	0.144095i
$725$	1.23568	−	8.59432i	0.0458919	−	0.319185i
$726$	9.15726	+	5.88501i	0.339858	+	0.218413i
$727$	−11.5252	−	13.3007i	−0.427444	−	0.493297i	0.500646	−	0.865652i	$-0.333096\pi$
$727$	−11.5252	−	13.3007i	−0.427444	−	0.493297i	−0.928090	+	0.372355i	$0.878550\pi$
$728$	−3.53184	−	7.73365i	−0.130899	−	0.286628i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−4.05924	−	1.19190i	−0.150239	−	0.0441142i
$731$	26.4242	−	30.4951i	0.977333	−	1.12790i
$732$	1.92058	−	0.563933i	0.0709867	−	0.0208436i
$733$	−21.4036	+	46.8675i	−0.790562	+	1.73109i	−0.115525	+	0.993305i	$0.536855\pi$
$733$	−21.4036	+	46.8675i	−0.790562	+	1.73109i	−0.675036	+	0.737784i	$0.735872\pi$
$734$	−0.157809	−	1.09758i	−0.00582483	−	0.0405126i
$735$	1.34949			0.0497768
$736$	3.77746	−	2.95480i	0.139239	−	0.108915i
$737$	3.05015			0.112354
$738$	0.174662	+	1.21480i	0.00642941	+	0.0447175i
$739$	9.85253	−	21.5740i	0.362431	−	0.793614i	−0.637304	−	0.770612i	$-0.719951\pi$
$739$	9.85253	−	21.5740i	0.362431	−	0.793614i	0.999735	−	0.0230014i	$-0.00732222\pi$
$740$	−0.949109	+	0.278683i	−0.0348899	+	0.0102446i
$741$	8.95117	−	10.3302i	0.328830	−	0.379489i
$742$	−15.8527	−	4.65476i	−0.581969	−	0.170882i
$743$	15.8498	−	10.1860i	0.581473	−	0.373690i	−0.216591	−	0.976262i	$-0.569494\pi$
$743$	15.8498	−	10.1860i	0.581473	−	0.373690i	0.798064	+	0.602572i	$0.205858\pi$
$744$	−2.08334	−	4.56187i	−0.0763789	−	0.167246i
$745$	−10.1851	−	11.7542i	−0.373153	−	0.430642i
$746$	12.9374	+	8.31438i	0.473673	+	0.304411i
$747$	−0.683191	+	4.75170i	−0.0249967	+	0.173856i
$748$	0.297293	−	2.06772i	0.0108701	−	0.0756033i
$749$	−37.2641	−	23.9482i	−1.36160	−	0.875047i
$750$	0.654861	+	0.755750i	0.0239121	+	0.0275961i
$751$	−0.802276	−	1.75674i	−0.0292755	−	0.0641043i	0.894429	−	0.447209i	$-0.147582\pi$
$751$	−0.802276	−	1.75674i	−0.0292755	−	0.0641043i	−0.923705	+	0.383105i	$0.874855\pi$
$752$	7.66097	−	4.92340i	0.279367	−	0.179538i
$753$	−9.20493	−	2.70281i	−0.335446	−	0.0984959i
$754$	−20.3366	+	23.4697i	−0.740615	+	0.854716i
$755$	−6.48004	+	1.90271i	−0.235833	+	0.0692468i
$756$	−0.987475	+	2.16227i	−0.0359141	+	0.0786409i
$757$	3.78042	+	26.2934i	0.137402	+	0.955650i	0.935551	+	0.353191i	$0.114903\pi$
$757$	3.78042	+	26.2934i	0.137402	+	0.955650i	−0.798150	+	0.602459i	$0.794188\pi$
$758$	24.4919			0.889585
$759$	0.945771	−	1.32088i	0.0343293	−	0.0479450i
$760$	−3.82169			−0.138627
$761$	2.79486	+	19.4387i	0.101314	+	0.704653i	0.975650	+	0.219332i	$0.0703879\pi$
$761$	2.79486	+	19.4387i	0.101314	+	0.704653i	−0.874336	+	0.485320i	$0.838703\pi$
$762$	1.77094	−	3.87781i	0.0641542	−	0.140478i
$763$	8.67673	−	2.54772i	0.314119	−	0.0922336i
$764$	−3.76479	+	4.34480i	−0.136205	+	0.157189i
$765$	5.91702	+	1.73739i	0.213930	+	0.0628156i
$766$	15.3156	−	9.84274i	0.553375	−	0.355633i
$767$	−2.92353	−	6.40164i	−0.105563	−	0.231150i
$768$	0.654861	+	0.755750i	0.0236303	+	0.0272708i
$769$	28.5439	+	18.3440i	1.02932	+	0.661503i	0.942323	−	0.334706i	$-0.108637\pi$
$769$	28.5439	+	18.3440i	1.02932	+	0.661503i	0.0869959	+	0.996209i	$0.472273\pi$
$770$	−0.114595	+	0.797029i	−0.00412973	+	0.0287229i
$771$	−1.87388	+	13.0331i	−0.0674860	+	0.469375i
$772$	2.57045	+	1.65193i	0.0925126	+	0.0594542i
$773$	−13.1903	−	15.2224i	−0.474422	−	0.547513i	0.467214	−	0.884144i	$-0.345258\pi$
$773$	−13.1903	−	15.2224i	−0.474422	−	0.547513i	−0.941636	+	0.336632i	$0.890712\pi$
$774$	2.71815	+	5.95192i	0.0977019	+	0.213937i
$775$	4.21895	−	2.71135i	0.151549	−	0.0973947i
$776$	3.66736	+	1.07683i	0.131650	+	0.0386560i
$777$	1.53981	−	1.77703i	0.0552403	−	0.0637508i
$778$	−6.14806	+	1.80523i	−0.220419	+	0.0647207i
$779$	1.94844	−	4.26649i	0.0698101	−	0.152863i
$780$	−0.509009	−	3.54023i	−0.0182254	−	0.126761i
$781$	−2.04175			−0.0730597
$782$	29.0259	+	5.67243i	1.03797	+	0.202846i
$783$	8.68269			0.310294
$784$	0.192053	+	1.33576i	0.00685903	+	0.0477056i
$785$	−9.03937	+	19.7935i	−0.322629	+	0.706459i
$786$	−16.8383	+	4.94418i	−0.600603	+	0.176353i
$787$	18.9205	−	21.8354i	0.674441	−	0.778347i	−0.310623	−	0.950533i	$-0.600538\pi$
$787$	18.9205	−	21.8354i	0.674441	−	0.778347i	0.985064	+	0.172186i	$0.0550831\pi$
$788$	13.4792	+	3.95785i	0.480177	+	0.140993i
$789$	−13.4416	+	8.63842i	−0.478535	+	0.307536i
$790$	−2.98611	−	6.53867i	−0.106241	−	0.232635i
$791$	27.8426	+	32.1321i	0.989968	+	1.14248i
$792$	0.284971	+	0.183140i	0.0101260	+	0.00650758i
$793$	1.01886	−	7.08635i	0.0361809	−	0.251644i
$794$	2.38883	−	16.6146i	0.0847762	−	0.589632i
$795$	−5.84714	−	3.75773i	−0.207377	−	0.133273i
$796$	1.40850	+	1.62550i	0.0499230	+	0.0576142i
$797$	−0.299131	−	0.655006i	−0.0105958	−	0.0232015i	0.904260	−	0.426982i	$-0.140423\pi$
$797$	−0.299131	−	0.655006i	−0.0105958	−	0.0232015i	−0.914856	+	0.403780i	$0.867696\pi$
$798$	7.64234	−	4.91144i	0.270536	−	0.173863i
$799$	53.8840	+	15.8218i	1.90628	+	0.559733i
$800$	−0.654861	+	0.755750i	−0.0231528	+	0.0267198i
$801$	12.3009	−	3.61188i	0.434632	−	0.127620i
$802$	−4.12986	+	9.04313i	−0.145830	+	0.319324i
$803$	−0.203951	−	1.41851i	−0.00719728	−	0.0500582i
$804$	−9.00425			−0.317555
$805$	−11.1884	−	2.18651i	−0.394340	−	0.0770644i
$806$	−17.9371			−0.631808
$807$	1.15067	+	8.00307i	0.0405054	+	0.281721i
$808$	0.497252	−	1.08883i	0.0174933	−	0.0383049i
$809$	−51.3707	+	15.0838i	−1.80610	+	0.530318i	−0.998253	−	0.0590801i	$-0.981183\pi$
$809$	−51.3707	+	15.0838i	−1.80610	+	0.530318i	−0.807843	+	0.589398i	$0.799365\pi$
$810$	−0.654861	+	0.755750i	−0.0230095	+	0.0265543i
$811$	−11.0871	−	3.25545i	−0.389319	−	0.114314i	0.0812140	−	0.996697i	$-0.474120\pi$
$811$	−11.0871	−	3.25545i	−0.389319	−	0.114314i	−0.470533	+	0.882382i	$0.655938\pi$
$812$	−17.3630	+	11.1585i	−0.609322	+	0.391588i
$813$	4.94837	+	10.8354i	0.173547	+	0.380015i
$814$	−0.219430	−	0.253236i	−0.00769103	−	0.00887592i
$815$	9.16433	+	5.88956i	0.321013	+	0.206302i
$816$	−0.877630	+	6.10405i	−0.0307232	+	0.213684i
$817$	3.55875	−	24.7516i	0.124505	−	0.865950i
$818$	−27.3973	−	17.6072i	−0.957924	−	0.615621i
$819$	5.56760	+	6.42535i	0.194548	+	0.224520i
$820$	−0.509837	−	1.11639i	−0.0178043	−	0.0389859i
$821$	7.36041	−	4.73025i	0.256880	−	0.165087i	−0.405862	−	0.913934i	$-0.633029\pi$
$821$	7.36041	−	4.73025i	0.256880	−	0.165087i	0.662742	+	0.748847i	$0.269392\pi$
$822$	−15.3014	−	4.49289i	−0.533697	−	0.156708i
$823$	−0.103001	+	0.118869i	−0.00359039	+	0.00414353i	−0.757542	−	0.652787i	$-0.773600\pi$
$823$	−0.103001	+	0.118869i	−0.00359039	+	0.00414353i	0.753952	+	0.656930i	$0.228145\pi$
$824$	4.17307	−	1.22532i	0.145376	−	0.0426861i
$825$	−0.140720	+	0.308134i	−0.00489924	+	0.0107278i
$826$	−0.665648	−	4.62968i	−0.0231609	−	0.161087i
$827$	−55.8586			−1.94239			−0.971197	−	0.238278i	$-0.923417\pi$
$827$	−55.8586			−1.94239			−0.971197	+	0.238278i	$0.923417\pi$
$828$	−2.79198	+	3.89934i	−0.0970280	+	0.135511i
$829$	−5.13050			−0.178190			−0.0890948	−	0.996023i	$-0.528397\pi$
$829$	−5.13050			−0.178190			−0.0890948	+	0.996023i	$0.528397\pi$
$830$	−0.683191	−	4.75170i	−0.0237139	−	0.164934i
$831$	11.2996	−	24.7427i	0.391980	−	0.858316i
$832$	3.43176	−	1.00766i	0.118975	−	0.0349342i
$833$	−5.44980	+	6.28940i	−0.188824	+	0.217915i
$834$	−15.5611	−	4.56916i	−0.538838	−	0.158217i
$835$	16.8514	−	10.8298i	0.583168	−	0.374779i
$836$	−0.537789	−	1.17759i	−0.0185998	−	0.0407279i
$837$	3.28418	+	3.79014i	0.113518	+	0.131006i
$838$	3.85691	+	2.47868i	0.133235	+	0.0856248i
$839$	−5.41336	+	37.6507i	−0.186890	+	1.29985i	0.653111	+	0.757262i	$0.273464\pi$
$839$	−5.41336	+	37.6507i	−0.186890	+	1.29985i	−0.840001	+	0.542585i	$0.817446\pi$
$840$	0.338294	−	2.35288i	0.0116722	−	0.0811822i
$841$	39.0250	+	25.0799i	1.34569	+	0.864823i
$842$	−2.33206	−	2.69134i	−0.0803682	−	0.0927498i
$843$	−3.51250	−	7.69131i	−0.120977	−	0.264903i
$844$	13.7337	−	8.82614i	0.472735	−	0.303808i
$845$	0.199247	+	0.0585042i	0.00685431	+	0.00201261i
$846$	−5.96356	+	6.88231i	−0.205031	+	0.236619i
$847$	24.8270	−	7.28986i	0.853065	−	0.250483i
$848$	2.88734	−	6.32240i	0.0991518	−	0.217112i
$849$	3.12758	+	21.7528i	0.107338	+	0.746555i
$850$	−6.16682			−0.211520
$851$	3.73657	−	2.92282i	0.128088	−	0.100193i
$852$	6.02740			0.206495
$853$	−5.54443	−	38.5623i	−0.189838	−	1.32035i	−0.832425	−	0.554137i	$-0.813048\pi$
$853$	−5.54443	−	38.5623i	−0.189838	−	1.32035i	0.642588	−	0.766212i	$-0.277861\pi$
$854$	1.97659	−	4.32813i	0.0676375	−	0.148105i
$855$	3.66689	−	1.07670i	0.125405	−	0.0368222i
$856$	12.2031	−	14.0831i	0.417092	−	0.481350i
$857$	−35.7921	−	10.5095i	−1.22263	−	0.358998i	−0.394169	−	0.919038i	$-0.628968\pi$
$857$	−35.7921	−	10.5095i	−1.22263	−	0.358998i	−0.828466	+	0.560040i	$0.810786\pi$
$858$	1.01924	−	0.655024i	0.0347962	−	0.0223622i
$859$	12.7905	+	28.0074i	0.436408	+	0.955599i	0.992244	+	0.124308i	$0.0396709\pi$
$859$	12.7905	+	28.0074i	0.436408	+	0.955599i	−0.555836	+	0.831292i	$0.687602\pi$
$860$	−4.28489	−	4.94503i	−0.146114	−	0.168624i
$861$	2.45425	+	1.57725i	0.0836407	+	0.0537526i
$862$	−4.81561	+	33.4933i	−0.164020	+	1.14079i
$863$	6.18047	−	42.9861i	0.210386	−	1.46327i	−0.561486	−	0.827486i	$-0.689770\pi$
$863$	6.18047	−	42.9861i	0.210386	−	1.46327i	0.771871	−	0.635779i	$-0.219321\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	3.68894	+	4.25726i	0.125428	+	0.144751i
$866$	−9.08474	−	19.8928i	−0.308712	−	0.675985i
$867$	−17.6913	+	11.3695i	−0.600826	+	0.386128i
$868$	−11.4383	−	3.35860i	−0.388243	−	0.113998i
$869$	1.59458	−	1.84024i	0.0540924	−	0.0624260i
$870$	−8.33098	+	2.44620i	−0.282447	+	0.0829339i
$871$	−13.3784	+	29.2946i	−0.453310	+	0.992611i
$872$	0.541403	+	3.76554i	0.0183342	+	0.127517i
$873$	−3.82218			−0.129361
$874$	17.0329	−	6.76774i	0.576147	−	0.228922i
$875$	2.37708			0.0803600
$876$	0.602078	+	4.18755i	0.0203423	+	0.141484i
$877$	13.4368	−	29.4225i	0.453729	−	0.993529i	−0.535143	−	0.844762i	$-0.679742\pi$
$877$	13.4368	−	29.4225i	0.453729	−	0.993529i	0.988872	−	0.148767i	$-0.0475305\pi$
$878$	6.60175	−	1.93845i	0.222798	−	0.0654195i
$879$	−2.32890	+	2.68769i	−0.0785518	+	0.0906536i
$880$	−0.325024	−	0.0954356i	−0.0109566	−	0.00321713i
$881$	29.1350	−	18.7239i	0.981583	−	0.630825i	0.0516929	−	0.998663i	$-0.483538\pi$
$881$	29.1350	−	18.7239i	0.981583	−	0.630825i	0.929890	+	0.367838i	$0.119902\pi$
$882$	−0.560599	−	1.22754i	−0.0188764	−	0.0413335i
$883$	−21.5228	−	24.8386i	−0.724298	−	0.835885i	0.267519	−	0.963553i	$-0.413796\pi$
$883$	−21.5228	−	24.8386i	−0.724298	−	0.835885i	−0.991817	+	0.127668i	$0.959251\pi$
$884$	18.5551	+	11.9246i	0.624075	+	0.401069i
$885$	0.280028	−	1.94764i	0.00941303	−	0.0654690i
$886$	5.30976	−	36.9302i	0.178385	−	1.24069i
$887$	28.5241	+	18.3313i	0.957745	+	0.615505i	0.923373	−	0.383904i	$-0.125421\pi$
$887$	28.5241	+	18.3313i	0.957745	+	0.615505i	0.0343716	+	0.999409i	$0.489057\pi$
$888$	0.647773	+	0.747570i	0.0217379	+	0.0250868i
$889$	−4.20965	−	9.21786i	−0.141187	−	0.309157i
$890$	−10.7851	+	6.93115i	−0.361517	+	0.232333i
$891$	−0.325024	−	0.0954356i	−0.0108887	−	0.00319721i
$892$	6.38215	−	7.36539i	0.213690	−	0.246612i
$893$	33.3929	−	9.80504i	1.11745	−	0.328113i
$894$	−6.46098	+	14.1476i	−0.216088	+	0.473166i
$895$	2.61551	+	18.1913i	0.0874268	+	0.608067i
$896$	2.37708			0.0794127
$897$	8.53791	+	14.8771i	0.285073	+	0.496732i
$898$	13.3525			0.445577
$899$	6.19701	+	43.1011i	0.206682	+	1.43750i
$900$	0.415415	−	0.909632i	0.0138472	−	0.0303211i
$901$	41.1263	−	12.0758i	1.37011	−	0.402302i
$902$	0.272252	−	0.314196i	0.00906500	−	0.0104616i
$903$	14.9237	+	4.38200i	0.496630	+	0.145824i
$904$	−15.0468	+	9.66998i	−0.500449	+	0.321619i
$905$	−1.62721	−	3.56310i	−0.0540904	−	0.118441i
$906$	4.42267	+	5.10404i	0.146934	+	0.169570i
$907$	−44.1472	−	28.3717i	−1.46589	−	0.942067i	−0.998310	−	0.0581138i	$-0.981491\pi$
$907$	−44.1472	−	28.3717i	−1.46589	−	0.942067i	−0.467575	−	0.883953i	$-0.654872\pi$
$908$	−0.410731	+	2.85670i	−0.0136306	+	0.0948028i
$909$	−0.170351	+	1.18482i	−0.00565019	+	0.0392979i
$910$	−7.15230	−	4.59650i	−0.237096	−	0.152373i
$911$	−24.3783	−	28.1341i	−0.807690	−	0.932124i	0.191086	−	0.981573i	$-0.438799\pi$
$911$	−24.3783	−	28.1341i	−0.807690	−	0.932124i	−0.998777	+	0.0494489i	$0.984254\pi$
$912$	1.58759	+	3.47634i	0.0525703	+	0.115113i
$913$	1.36802	−	0.879173i	0.0452749	−	0.0290964i
$914$	39.4303	+	11.5778i	1.30424	+	0.382959i
$915$	1.31081	−	1.51275i	0.0433340	−	0.0500101i
$916$	−14.7849	+	4.34123i	−0.488505	+	0.143438i
$917$	−17.3294	+	37.9460i	−0.572266	+	1.25309i
$918$	−0.877630	−	6.10405i	−0.0289661	−	0.201464i
$919$	3.53036			0.116456			0.0582279	−	0.998303i	$-0.481455\pi$
$919$	3.53036			0.116456			0.0582279	+	0.998303i	$0.481455\pi$
$920$	1.58031	−	4.52798i	0.0521014	−	0.149283i
$921$	25.2036			0.830486
$922$	−2.46043	−	17.1127i	−0.0810299	−	0.563575i
$923$	8.95544	−	19.6097i	0.294772	−	0.645460i
$924$	0.772608	−	0.226858i	0.0254169	−	0.00746308i
$925$	−0.647773	+	0.747570i	−0.0212987	+	0.0245800i
$926$	−8.80228	−	2.58458i	−0.289261	−	0.0849347i
$927$	−3.65881	+	2.35138i	−0.120171	+	0.0772293i
$928$	−3.60692	−	7.89806i	−0.118403	−	0.259266i
$929$	−23.0522	−	26.6037i	−0.756318	−	0.872838i	0.238846	−	0.971057i	$-0.423231\pi$
$929$	−23.0522	−	26.6037i	−0.756318	−	0.872838i	−0.995165	+	0.0982194i	$0.968685\pi$
$930$	−4.21895	−	2.71135i	−0.138345	−	0.0889088i
$931$	−0.733967	+	5.10485i	−0.0240548	+	0.167305i
$932$	4.07513	−	28.3432i	0.133485	−	0.928411i
$933$	28.5104	+	18.3225i	0.933387	+	0.599851i
$934$	23.6452	+	27.2881i	0.773696	+	0.892893i
$935$	−0.867794	−	1.90020i	−0.0283799	−	0.0621433i
$936$	−3.00886	+	1.93368i	−0.0983477	+	0.0632042i
$937$	20.6232	+	6.05551i	0.673729	+	0.197825i	0.600663	−	0.799502i	$-0.294903\pi$
$937$	20.6232	+	6.05551i	0.673729	+	0.197825i	0.0730664	+	0.997327i	$0.476722\pi$
$938$	−14.0165	+	16.1759i	−0.457655	+	0.528163i
$939$	9.70752	−	2.85038i	0.316793	−	0.0930188i
$940$	3.78302	−	8.28366i	0.123389	−	0.270183i
$941$	6.11230	+	42.5120i	0.199255	+	1.38585i	0.806452	+	0.591299i	$0.201385\pi$
$941$	6.11230	+	42.5120i	0.199255	+	1.38585i	−0.607197	+	0.794551i	$0.707706\pi$
$942$	21.7599			0.708975
$943$	4.24927	+	4.07277i	0.138375	+	0.132628i
$944$	1.96766			0.0640420
$945$	0.338294	+	2.35288i	0.0110047	+	0.0765393i
$946$	0.920761	−	2.01619i	0.0299365	−	0.0655518i
$947$	−11.1490	+	3.27364i	−0.362293	+	0.106379i	−0.457813	−	0.889049i	$-0.651367\pi$
$947$	−11.1490	+	3.27364i	−0.362293	+	0.106379i	0.0955194	+	0.995428i	$0.469549\pi$
$948$	−4.70731	+	5.43252i	−0.152886	+	0.176440i
$949$	14.5184	+	4.26300i	0.471288	+	0.138383i
$950$	−3.21501	+	2.06616i	−0.104309	+	0.0670352i
$951$	7.96941	+	17.4506i	0.258426	+	0.565874i
$952$	9.59961	+	11.0785i	0.311125	+	0.359058i
$953$	−15.3996	−	9.89675i	−0.498843	−	0.320587i	0.266910	−	0.963721i	$-0.413997\pi$
$953$	−15.3996	−	9.89675i	−0.498843	−	0.320587i	−0.765753	+	0.643134i	$0.777634\pi$
$954$	−0.989160	+	6.87976i	−0.0320252	+	0.222740i
$955$	−0.818167	+	5.69048i	−0.0264753	+	0.184139i
$956$	15.4287	+	9.91542i	0.498999	+	0.320687i
$957$	−1.92609	−	2.22283i	−0.0622617	−	0.0718538i
$958$	−0.663225	−	1.45226i	−0.0214278	−	0.0469204i
$959$	−31.8904	+	20.4947i	−1.02979	+	0.661808i
$960$	0.959493	+	0.281733i	0.0309675	+	0.00909288i
$961$	3.83030	−	4.42040i	0.123558	−	0.142593i
$962$	3.39462	−	0.996750i	0.109447	−	0.0321365i
$963$	−7.74108	+	16.9506i	−0.249453	+	0.546226i
$964$	−3.75426	−	26.1115i	−0.120917	−	0.840993i
$965$	3.05550			0.0983601
$966$	2.65892	+	11.0857i	0.0855493	+	0.356675i
$967$	19.5673			0.629242			0.314621	−	0.949217i	$-0.398123\pi$
$967$	19.5673			0.629242			0.314621	+	0.949217i	$0.398123\pi$
$968$	1.54913	+	10.7745i	0.0497910	+	0.346304i
$969$	−9.79037	+	21.4379i	−0.314512	+	0.688685i
$970$	3.66736	−	1.07683i	0.117752	−	0.0345750i
$971$	18.0289	−	20.8064i	0.578574	−	0.667710i	−0.388724	−	0.921354i	$-0.627084\pi$
$971$	18.0289	−	20.8064i	0.578574	−	0.667710i	0.967297	+	0.253645i	$0.0816294\pi$
$972$	0.959493	+	0.281733i	0.0307758	+	0.00903658i
$973$	−32.4317	+	20.8426i	−1.03971	+	0.668184i
$974$	−7.81753	−	17.1180i	−0.250490	−	0.548496i
$975$	−2.34220	−	2.70304i	−0.0750104	−	0.0865667i
$976$	1.68390	+	1.08218i	0.0539005	+	0.0346397i
$977$	−5.24885	+	36.5065i	−0.167925	+	1.16795i	0.715238	+	0.698881i	$0.246318\pi$
$977$	−5.24885	+	36.5065i	−0.167925	+	1.16795i	−0.883163	+	0.469066i	$0.844591\pi$
$978$	1.55033	−	10.7828i	0.0495741	−	0.344795i
$979$	−3.65340	−	2.34790i	−0.116763	−	0.0750391i
$980$	0.883729	+	1.01988i	0.0282297	+	0.0325788i
$981$	−1.58035	−	3.46048i	−0.0504566	−	0.110485i
$982$	−8.82395	+	5.67081i	−0.281583	+	0.180963i
$983$	44.6957	+	13.1238i	1.42557	+	0.418586i	0.901385	−	0.433018i	$-0.142551\pi$
$983$	44.6957	+	13.1238i	1.42557	+	0.418586i	0.524186	+	0.851604i	$0.324370\pi$
$984$	−0.803707	+	0.927527i	−0.0256212	+	0.0295685i
$985$	13.4792	−	3.95785i	0.429483	−	0.126108i
$986$	22.2432	−	48.7059i	0.708369	−	1.55111i
$987$	3.08071	+	21.4268i	0.0980600	+	0.682022i
$988$	13.6688			0.434863
$989$	27.8544	+	14.4515i	0.885718	+	0.459532i
$990$	0.338745			0.0107660
$991$	−6.54154	−	45.4974i	−0.207799	−	1.44527i	−0.780319	−	0.625382i	$-0.784943\pi$
$991$	−6.54154	−	45.4974i	−0.207799	−	1.44527i	0.572520	−	0.819891i	$-0.305966\pi$
$992$	2.08334	−	4.56187i	0.0661460	−	0.144840i
$993$	−3.46950	+	1.01874i	−0.110101	+	0.0323286i
$994$	9.38258	−	10.8281i	0.297597	−	0.343446i
$995$	2.06371	+	0.605961i	0.0654242	+	0.0192103i
$996$	−4.03849	+	2.59538i	−0.127964	+	0.0822378i
$997$	0.577212	+	1.26392i	0.0182805	+	0.0400287i	0.918552	−	0.395300i	$-0.129359\pi$
$997$	0.577212	+	1.26392i	0.0182805	+	0.0400287i	−0.900272	+	0.435329i	$0.856632\pi$
$998$	23.8961	+	27.5776i	0.756419	+	0.872954i
$999$	−0.832149	−	0.534790i	−0.0263280	−	0.0169200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.c.601.2	yes	20
23.8	even	11	inner	690.2.m.c.31.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.c.31.2	✓	20	23.8	even	11	inner
690.2.m.c.601.2	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.959493 + 0.281733i) q^{6} +(1.99973 - 1.28515i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(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} +(1.99973 - 1.28515i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.841254 + 0.540641i) q^{10} +(-0.0482085 + 0.335298i) q^{11} +(0.142315 - 0.989821i) q^{12} +(-3.00886 - 1.93368i) q^{13} +(-1.55666 - 1.79648i) q^{14} +(-0.415415 - 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(5.91702 + 1.73739i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(3.66689 - 1.07670i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.338294 + 2.35288i) q^{21} +0.338745 q^{22} +(-0.240622 + 4.78979i) q^{23} -1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-1.48579 + 3.25342i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-1.55666 + 1.79648i) q^{28} +(8.33098 + 2.44620i) q^{29} +(-0.841254 + 0.540641i) q^{30} +(2.08334 + 4.56187i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-0.284971 - 0.183140i) q^{33} +(0.877630 - 6.10405i) q^{34} +(-0.338294 + 2.35288i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-0.647773 - 0.747570i) q^{37} +(-1.58759 - 3.47634i) q^{38} +(3.00886 - 1.93368i) q^{39} +(-0.959493 - 0.281733i) q^{40} +(0.803707 - 0.927527i) q^{41} +(2.28079 - 0.669701i) q^{42} +(2.71815 - 5.95192i) q^{43} +(-0.0482085 - 0.335298i) q^{44} +1.00000 q^{45} +(4.77528 - 0.443486i) q^{46} +9.10661 q^{47} +(0.142315 + 0.989821i) q^{48} +(-0.560599 + 1.22754i) q^{49} +(-0.959493 + 0.281733i) q^{50} +(-4.03841 + 4.66057i) q^{51} +(3.43176 + 1.00766i) q^{52} +(5.84714 - 3.75773i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-0.221831 - 0.256007i) q^{55} +(1.99973 + 1.28515i) q^{56} +(-0.543884 + 3.78279i) q^{57} +(1.23568 - 8.59432i) q^{58} +(1.65530 + 1.06380i) q^{59} +(0.654861 + 0.755750i) q^{60} +(0.831520 + 1.82078i) q^{61} +(4.21895 - 2.71135i) q^{62} +(-2.28079 - 0.669701i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(3.43176 - 1.00766i) q^{65} +(-0.140720 + 0.308134i) q^{66} +(-1.28144 - 8.91260i) q^{67} -6.16682 q^{68} +(-4.25699 - 2.20863i) q^{69} +2.37708 q^{70} +(0.857788 + 5.96605i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-4.05924 + 1.19190i) q^{73} +(-0.647773 + 0.747570i) q^{74} +(0.959493 + 0.281733i) q^{75} +(-3.21501 + 2.06616i) q^{76} +(0.334503 + 0.732458i) q^{77} +(-2.34220 - 2.70304i) q^{78} +(-6.04715 - 3.88627i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-1.03247 - 0.663526i) q^{82} +(-3.14370 - 3.62802i) q^{83} +(-0.987475 - 2.16227i) q^{84} +(-5.18786 + 3.33403i) q^{85} +(-6.27817 - 1.84344i) q^{86} +(-5.68595 + 6.56194i) q^{87} +(-0.325024 + 0.0954356i) q^{88} +(-5.32572 + 11.6617i) q^{89} +(-0.142315 - 0.989821i) q^{90} -8.50195 q^{91} +(-1.11857 - 4.66356i) q^{92} -5.01508 q^{93} +(-1.29601 - 9.01391i) q^{94} +(-1.58759 + 3.47634i) q^{95} +(0.959493 - 0.281733i) q^{96} +(2.50300 - 2.88861i) q^{97} +(1.29483 + 0.380196i) q^{98} +(0.284971 - 0.183140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

L-functions

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