LMFDB - Embedded newform 804.2.e.a.535.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.22
Character	$\chi$	$=$	804.535
Dual form			804.2.e.a.535.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.530406 + 1.31098i) q^{2} -1.00000 q^{3} +(-1.43734 + 1.39070i) q^{4} -2.85552i q^{5} +(-0.530406 - 1.31098i) q^{6} -4.91599 q^{7} +(-2.58556 - 1.14669i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.530406 + 1.31098i) q^{2} -1.00000 q^{3} +(-1.43734 + 1.39070i) q^{4} -2.85552i q^{5} +(-0.530406 - 1.31098i) q^{6} -4.91599 q^{7} +(-2.58556 - 1.14669i) q^{8} +1.00000 q^{9} +(3.74353 - 1.51458i) q^{10} +6.48515 q^{11} +(1.43734 - 1.39070i) q^{12} +2.89216i q^{13} +(-2.60747 - 6.44477i) q^{14} +2.85552i q^{15} +(0.131892 - 3.99782i) q^{16} +4.14913 q^{17} +(0.530406 + 1.31098i) q^{18} +4.77723i q^{19} +(3.97118 + 4.10435i) q^{20} +4.91599 q^{21} +(3.43976 + 8.50190i) q^{22} +6.27256i q^{23} +(2.58556 + 1.14669i) q^{24} -3.15398 q^{25} +(-3.79156 + 1.53402i) q^{26} -1.00000 q^{27} +(7.06595 - 6.83668i) q^{28} +4.52052 q^{29} +(-3.74353 + 1.51458i) q^{30} -0.791471 q^{31} +(5.31103 - 1.94756i) q^{32} -6.48515 q^{33} +(2.20072 + 5.43943i) q^{34} +14.0377i q^{35} +(-1.43734 + 1.39070i) q^{36} +2.50822 q^{37} +(-6.26285 + 2.53387i) q^{38} -2.89216i q^{39} +(-3.27439 + 7.38311i) q^{40} -7.22384i q^{41} +(2.60747 + 6.44477i) q^{42} +4.34535 q^{43} +(-9.32136 + 9.01892i) q^{44} -2.85552i q^{45} +(-8.22320 + 3.32700i) q^{46} +1.23363i q^{47} +(-0.131892 + 3.99782i) q^{48} +17.1670 q^{49} +(-1.67289 - 4.13481i) q^{50} -4.14913 q^{51} +(-4.02213 - 4.15701i) q^{52} +0.123360i q^{53} +(-0.530406 - 1.31098i) q^{54} -18.5185i q^{55} +(12.7106 + 5.63711i) q^{56} -4.77723i q^{57} +(2.39771 + 5.92632i) q^{58} +2.67952i q^{59} +(-3.97118 - 4.10435i) q^{60} +4.75980i q^{61} +(-0.419800 - 1.03760i) q^{62} -4.91599 q^{63} +(5.37021 + 5.92966i) q^{64} +8.25860 q^{65} +(-3.43976 - 8.50190i) q^{66} +(6.66494 - 4.75169i) q^{67} +(-5.96371 + 5.77021i) q^{68} -6.27256i q^{69} +(-18.4032 + 7.44567i) q^{70} -15.6852i q^{71} +(-2.58556 - 1.14669i) q^{72} -1.84732 q^{73} +(1.33037 + 3.28823i) q^{74} +3.15398 q^{75} +(-6.64371 - 6.86650i) q^{76} -31.8809 q^{77} +(3.79156 - 1.53402i) q^{78} -0.728927 q^{79} +(-11.4159 - 0.376619i) q^{80} +1.00000 q^{81} +(9.47032 - 3.83157i) q^{82} +13.8943i q^{83} +(-7.06595 + 6.83668i) q^{84} -11.8479i q^{85} +(2.30480 + 5.69667i) q^{86} -4.52052 q^{87} +(-16.7677 - 7.43644i) q^{88} +0.704907 q^{89} +(3.74353 - 1.51458i) q^{90} -14.2178i q^{91} +(-8.72326 - 9.01580i) q^{92} +0.791471 q^{93} +(-1.61727 + 0.654326i) q^{94} +13.6415 q^{95} +(-5.31103 + 1.94756i) q^{96} +9.89044i q^{97} +(9.10545 + 22.5056i) q^{98} +6.48515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.530406	+	1.31098i	0.375053	+	0.927003i
$2$	0.530406	+	1.31098i	0.375053	+	0.927003i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.43734	+	1.39070i	−0.718670	+	0.695351i
$5$		−	2.85552i		−	1.27703i	−0.769611	−	0.638513i	$-0.779550\pi$
$5$		−	2.85552i		−	1.27703i	0.769611	−	0.638513i	$-0.220450\pi$
$6$	−0.530406	−	1.31098i	−0.216537	−	0.535206i
$7$	−4.91599			−1.85807			−0.929035	−	0.369992i	$-0.879360\pi$
$7$	−4.91599			−1.85807			−0.929035	+	0.369992i	$0.879360\pi$
$8$	−2.58556	−	1.14669i	−0.914133	−	0.405415i
$9$	1.00000			0.333333
$10$	3.74353	−	1.51458i	1.18381	−	0.478953i
$11$	6.48515			1.95535			0.977673	−	0.210132i	$-0.0673893\pi$
$11$	6.48515			1.95535			0.977673	+	0.210132i	$0.0673893\pi$
$12$	1.43734	−	1.39070i	0.414924	−	0.401461i
$13$			2.89216i			0.802140i	0.916047	+	0.401070i	$0.131362\pi$
$13$			2.89216i			0.802140i	−0.916047	+	0.401070i	$0.868638\pi$
$14$	−2.60747	−	6.44477i	−0.696875	−	1.72244i
$15$			2.85552i			0.737292i
$16$	0.131892	−	3.99782i	0.0329729	−	0.999456i
$17$	4.14913			1.00631			0.503156	−	0.864196i	$-0.332172\pi$
$17$	4.14913			1.00631			0.503156	+	0.864196i	$0.332172\pi$
$18$	0.530406	+	1.31098i	0.125018	+	0.309001i
$19$			4.77723i			1.09597i	0.836488	+	0.547986i	$0.184605\pi$
$19$			4.77723i			1.09597i	−0.836488	+	0.547986i	$0.815395\pi$
$20$	3.97118	+	4.10435i	0.887982	+	0.917761i
$21$	4.91599			1.07276
$22$	3.43976	+	8.50190i	0.733359	+	1.81261i
$23$			6.27256i			1.30792i	0.756530	+	0.653959i	$0.226893\pi$
$23$			6.27256i			1.30792i	−0.756530	+	0.653959i	$0.773107\pi$
$24$	2.58556	+	1.14669i	0.527775	+	0.234067i
$25$	−3.15398			−0.630797
$26$	−3.79156	+	1.53402i	−0.743586	+	0.300845i
$27$	−1.00000			−0.192450
$28$	7.06595	−	6.83668i	1.33534	−	1.29201i
$29$	4.52052			0.839440			0.419720	−	0.907654i	$-0.362128\pi$
$29$	4.52052			0.839440			0.419720	+	0.907654i	$0.362128\pi$
$30$	−3.74353	+	1.51458i	−0.683472	+	0.276524i
$31$	−0.791471			−0.142152			−0.0710762	−	0.997471i	$-0.522643\pi$
$31$	−0.791471			−0.142152			−0.0710762	+	0.997471i	$0.522643\pi$
$32$	5.31103	−	1.94756i	0.938866	−	0.344283i
$33$	−6.48515			−1.12892
$34$	2.20072	+	5.43943i	0.377421	+	0.932854i
$35$			14.0377i			2.37280i
$36$	−1.43734	+	1.39070i	−0.239557	+	0.231784i
$37$	2.50822			0.412349			0.206174	−	0.978515i	$-0.433899\pi$
$37$	2.50822			0.412349			0.206174	+	0.978515i	$0.433899\pi$
$38$	−6.26285	+	2.53387i	−1.01597	+	0.411048i
$39$		−	2.89216i		−	0.463116i
$40$	−3.27439	+	7.38311i	−0.517726	+	1.16737i
$41$		−	7.22384i		−	1.12817i	−0.825715	−	0.564087i	$-0.809228\pi$
$41$		−	7.22384i		−	1.12817i	0.825715	−	0.564087i	$-0.190772\pi$
$42$	2.60747	+	6.44477i	0.402341	+	0.994449i
$43$	4.34535			0.662659			0.331330	−	0.943515i	$-0.392503\pi$
$43$	4.34535			0.662659			0.331330	+	0.943515i	$0.392503\pi$
$44$	−9.32136	+	9.01892i	−1.40525	+	1.35965i
$45$		−	2.85552i		−	0.425675i
$46$	−8.22320	+	3.32700i	−1.21244	+	0.490539i
$47$			1.23363i			0.179944i	0.995944	+	0.0899720i	$0.0286778\pi$
$47$			1.23363i			0.179944i	−0.995944	+	0.0899720i	$0.971322\pi$
$48$	−0.131892	+	3.99782i	−0.0190369	+	0.577036i
$49$	17.1670			2.45242
$50$	−1.67289	−	4.13481i	−0.236582	−	0.584750i
$51$	−4.14913			−0.580995
$52$	−4.02213	−	4.15701i	−0.557769	−	0.576474i
$53$			0.123360i			0.0169447i	0.999964	+	0.00847237i	$0.00269687\pi$
$53$			0.123360i			0.0169447i	−0.999964	+	0.00847237i	$0.997303\pi$
$54$	−0.530406	−	1.31098i	−0.0721791	−	0.178402i
$55$		−	18.5185i		−	2.49703i
$56$	12.7106	+	5.63711i	1.69852	+	0.753290i
$57$		−	4.77723i		−	0.632759i
$58$	2.39771	+	5.92632i	0.314835	+	0.778163i
$59$			2.67952i			0.348844i	0.984671	+	0.174422i	$0.0558058\pi$
$59$			2.67952i			0.348844i	−0.984671	+	0.174422i	$0.944194\pi$
$60$	−3.97118	−	4.10435i	−0.512677	−	0.529869i
$61$			4.75980i			0.609430i	0.952444	+	0.304715i	$0.0985613\pi$
$61$			4.75980i			0.609430i	−0.952444	+	0.304715i	$0.901439\pi$
$62$	−0.419800	−	1.03760i	−0.0533147	−	0.131776i
$63$	−4.91599			−0.619357
$64$	5.37021	+	5.92966i	0.671277	+	0.741207i
$65$	8.25860			1.02435
$66$	−3.43976	−	8.50190i	−0.423405	−	1.04651i
$67$	6.66494	−	4.75169i	0.814252	−	0.580511i
$67$	6.66494	−	4.75169i	0.814252	−	0.580511i
$68$	−5.96371	+	5.77021i	−0.723206	+	0.699740i
$69$		−	6.27256i		−	0.755127i
$70$	−18.4032	+	7.44567i	−2.19960	+	0.889928i
$71$		−	15.6852i		−	1.86149i	−0.365666	−	0.930746i	$-0.619159\pi$
$71$		−	15.6852i		−	1.86149i	0.365666	−	0.930746i	$-0.380841\pi$
$72$	−2.58556	−	1.14669i	−0.304711	−	0.135138i
$73$	−1.84732			−0.216212			−0.108106	−	0.994139i	$-0.534479\pi$
$73$	−1.84732			−0.216212			−0.108106	+	0.994139i	$0.534479\pi$
$74$	1.33037	+	3.28823i	0.154653	+	0.382249i
$75$	3.15398			0.364191
$76$	−6.64371	−	6.86650i	−0.762085	−	0.787642i
$77$	−31.8809			−3.63317
$78$	3.79156	−	1.53402i	0.429310	−	0.173693i
$79$	−0.728927			−0.0820107			−0.0410053	−	0.999159i	$-0.513056\pi$
$79$	−0.728927			−0.0820107			−0.0410053	+	0.999159i	$0.513056\pi$
$80$	−11.4159	−	0.376619i	−1.27633	−	0.0421073i
$81$	1.00000			0.111111
$82$	9.47032	−	3.83157i	1.04582	−	0.423126i
$83$			13.8943i			1.52509i	0.646933	+	0.762547i	$0.276051\pi$
$83$			13.8943i			1.52509i	−0.646933	+	0.762547i	$0.723949\pi$
$84$	−7.06595	+	6.83668i	−0.770958	+	0.745943i
$85$		−	11.8479i		−	1.28509i
$86$	2.30480	+	5.69667i	0.248533	+	0.614287i
$87$	−4.52052			−0.484651
$88$	−16.7677	−	7.43644i	−1.78745	−	0.792728i
$89$	0.704907			0.0747200			0.0373600	−	0.999302i	$-0.488105\pi$
$89$	0.704907			0.0747200			0.0373600	+	0.999302i	$0.488105\pi$
$90$	3.74353	−	1.51458i	0.394603	−	0.159651i
$91$		−	14.2178i		−	1.49043i
$92$	−8.72326	−	9.01580i	−0.909463	−	0.939962i
$93$	0.791471			0.0820717
$94$	−1.61727	+	0.654326i	−0.166809	+	0.0674886i
$95$	13.6415			1.39958
$96$	−5.31103	+	1.94756i	−0.542054	+	0.198772i
$97$			9.89044i			1.00422i	0.864803	+	0.502111i	$0.167443\pi$
$97$			9.89044i			1.00422i	−0.864803	+	0.502111i	$0.832557\pi$
$98$	9.10545	+	22.5056i	0.919790	+	2.27340i
$99$	6.48515			0.651782
$100$	4.53335	−	4.38625i	0.453335	−	0.438625i
$101$			15.2447i			1.51690i	0.651731	+	0.758450i	$0.274043\pi$
$101$			15.2447i			1.51690i	−0.651731	+	0.758450i	$0.725957\pi$
$102$	−2.20072	−	5.43943i	−0.217904	−	0.538584i
$103$			14.6917i			1.44762i	0.689999	+	0.723810i	$0.257611\pi$
$103$			14.6917i			1.44762i	−0.689999	+	0.723810i	$0.742389\pi$
$104$	3.31640	−	7.47784i	0.325200	−	0.733262i
$105$		−	14.0377i		−	1.36994i
$106$	−0.161722	+	0.0654306i	−0.0157078	+	0.00635518i
$107$		−	6.16728i		−	0.596213i	−0.954533	−	0.298107i	$-0.903645\pi$
$107$		−	6.16728i		−	0.596213i	0.954533	−	0.298107i	$-0.0963551\pi$
$108$	1.43734	−	1.39070i	0.138308	−	0.133820i
$109$		−	7.52989i		−	0.721233i	−0.932714	−	0.360616i	$-0.882566\pi$
$109$		−	7.52989i		−	0.721233i	0.932714	−	0.360616i	$-0.117434\pi$
$110$	24.2773	−	9.82230i	2.31475	−	0.936519i
$111$	−2.50822			−0.238070
$112$	−0.648378	+	19.6533i	−0.0612660	+	1.85706i
$113$			18.4438i			1.73505i	0.497398	+	0.867523i	$0.334289\pi$
$113$			18.4438i			1.73505i	−0.497398	+	0.867523i	$0.665711\pi$
$114$	6.26285	−	2.53387i	0.586570	−	0.237319i
$115$	17.9114			1.67025
$116$	−6.49753	+	6.28670i	−0.603280	+	0.583706i
$117$			2.89216i			0.267380i
$118$	−3.51280	+	1.42123i	−0.323380	+	0.130835i
$119$	−20.3971			−1.86980
$120$	3.27439	−	7.38311i	0.298909	−	0.673982i
$121$	31.0572			2.82338
$122$	−6.24001	+	2.52463i	−0.564944	+	0.228569i
$123$			7.22384i			0.651352i
$124$	1.13761	−	1.10070i	0.102161	−	0.0988458i
$125$		−	5.27134i		−	0.471483i
$126$	−2.60747	−	6.44477i	−0.232292	−	0.574146i
$127$			5.11884i			0.454223i	0.973869	+	0.227112i	$0.0729282\pi$
$127$			5.11884i			0.454223i	−0.973869	+	0.227112i	$0.927072\pi$
$128$	−4.92527	+	10.1854i	−0.435337	+	0.900268i
$129$	−4.34535			−0.382587
$130$	4.38041	+	10.8269i	0.384187	+	0.949579i
$131$		−	4.64485i		−	0.405822i	−0.979197	−	0.202911i	$-0.934960\pi$
$131$		−	4.64485i		−	0.405822i	0.979197	−	0.202911i	$-0.0650402\pi$
$132$	9.32136	−	9.01892i	0.811321	−	0.784996i
$133$		−	23.4848i		−	2.03639i
$134$	9.76449	+	6.21729i	0.843524	+	0.537092i
$135$			2.85552i			0.245764i
$136$	−10.7278	−	4.75776i	−0.919903	−	0.407974i
$137$			5.36190i			0.458098i	0.973415	+	0.229049i	$0.0735616\pi$
$137$			5.36190i			0.458098i	−0.973415	+	0.229049i	$0.926438\pi$
$138$	8.22320	−	3.32700i	0.700005	−	0.283213i
$139$	−14.8346			−1.25826			−0.629129	−	0.777301i	$-0.716588\pi$
$139$	−14.8346			−1.25826			−0.629129	+	0.777301i	$0.716588\pi$
$140$	−19.5223	−	20.1769i	−1.64993	−	1.70526i
$141$		−	1.23363i		−	0.103891i
$142$	20.5630	−	8.31953i	1.72561	−	0.698159i
$143$			18.7561i			1.56846i
$144$	0.131892	−	3.99782i	0.0109910	−	0.333152i
$145$		−	12.9084i		−	1.07199i
$146$	−0.979827	−	2.42180i	−0.0810911	−	0.200429i
$147$	−17.1670			−1.41591
$148$	−3.60516	+	3.48819i	−0.296343	+	0.286727i
$149$	−17.9068			−1.46698			−0.733490	−	0.679700i	$-0.762110\pi$
$149$	−17.9068			−1.46698			−0.733490	+	0.679700i	$0.762110\pi$
$150$	1.67289	+	4.13481i	0.136591	+	0.337606i
$151$		−	15.3988i		−	1.25314i	−0.779365	−	0.626570i	$-0.784458\pi$
$151$		−	15.3988i		−	1.25314i	0.779365	−	0.626570i	$-0.215542\pi$
$152$	5.47799	−	12.3518i	0.444324	−	1.00186i
$153$	4.14913			0.335437
$154$	−16.9098	−	41.7953i	−1.36263	−	3.36796i
$155$			2.26006i			0.181532i
$156$	4.02213	+	4.15701i	0.322028	+	0.332827i
$157$	−0.211856			−0.0169080			−0.00845399	−	0.999964i	$-0.502691\pi$
$157$	−0.211856			−0.0169080			−0.00845399	+	0.999964i	$0.502691\pi$
$158$	−0.386627	−	0.955609i	−0.0307584	−	0.0760241i
$159$		−	0.123360i		−	0.00978305i
$160$	−5.56130	−	15.1657i	−0.439659	−	1.19896i
$161$		−	30.8358i		−	2.43020i
$162$	0.530406	+	1.31098i	0.0416726	+	0.103000i
$163$		−	14.5738i		−	1.14151i	−0.821121	−	0.570754i	$-0.806651\pi$
$163$		−	14.5738i		−	1.14151i	0.821121	−	0.570754i	$-0.193349\pi$
$164$	10.0462	+	10.3831i	0.784478	+	0.810785i
$165$			18.5185i			1.44166i
$166$	−18.2151	+	7.36959i	−1.41377	+	0.571991i
$167$		−	7.04225i		−	0.544945i	−0.962164	−	0.272473i	$-0.912159\pi$
$167$		−	7.04225i		−	0.544945i	0.962164	−	0.272473i	$-0.0878415\pi$
$168$	−12.7106	−	5.63711i	−0.980642	−	0.434912i
$169$	4.63543			0.356572
$170$	15.5324	−	6.28420i	1.19128	−	0.481976i
$171$			4.77723i			0.365324i
$172$	−6.24574	+	6.04309i	−0.476233	+	0.460781i
$173$	13.3693			1.01645			0.508223	−	0.861225i	$-0.330302\pi$
$173$	13.3693			1.01645			0.508223	+	0.861225i	$0.330302\pi$
$174$	−2.39771	−	5.92632i	−0.181770	−	0.449273i
$175$	15.5049			1.17206
$176$	0.855338	−	25.9265i	0.0644735	−	1.95428i
$177$		−	2.67952i		−	0.201405i
$178$	0.373887	+	0.924120i	0.0280240	+	0.0692657i
$179$	10.9481			0.818302			0.409151	−	0.912467i	$-0.365825\pi$
$179$	10.9481			0.818302			0.409151	+	0.912467i	$0.365825\pi$
$180$	3.97118	+	4.10435i	0.295994	+	0.305920i
$181$	9.89701			0.735639			0.367819	−	0.929897i	$-0.380104\pi$
$181$	9.89701			0.735639			0.367819	+	0.929897i	$0.380104\pi$
$182$	18.6393	−	7.54121i	1.38164	−	0.558992i
$183$		−	4.75980i		−	0.351855i
$184$	7.19267	−	16.2181i	0.530250	−	1.19561i
$185$		−	7.16226i		−	0.526580i
$186$	0.419800	+	1.03760i	0.0307813	+	0.0760807i
$187$	26.9077			1.96769
$188$	−1.71562	−	1.77315i	−0.125124	−	0.129320i
$189$	4.91599			0.357586
$190$	7.23551	+	17.8837i	0.524919	+	1.29742i
$191$	15.8927			1.14996			0.574979	−	0.818168i	$-0.305010\pi$
$191$	15.8927			1.14996			0.574979	+	0.818168i	$0.305010\pi$
$192$	−5.37021	−	5.92966i	−0.387562	−	0.427936i
$193$	−18.8963			−1.36019			−0.680094	−	0.733125i	$-0.738061\pi$
$193$	−18.8963			−1.36019			−0.680094	+	0.733125i	$0.738061\pi$
$194$	−12.9662	+	5.24594i	−0.930917	+	0.376637i
$195$	−8.25860			−0.591411
$196$	−24.6748	+	23.8741i	−1.76248	+	1.70530i
$197$			5.67643i			0.404429i	0.979341	+	0.202214i	$0.0648138\pi$
$197$			5.67643i			0.404429i	−0.979341	+	0.202214i	$0.935186\pi$
$198$	3.43976	+	8.50190i	0.244453	+	0.604204i
$199$			7.38387i			0.523428i	0.965145	+	0.261714i	$0.0842878\pi$
$199$			7.38387i			0.523428i	−0.965145	+	0.261714i	$0.915712\pi$
$200$	8.15480	+	3.61663i	0.576632	+	0.255735i
$201$	−6.66494	+	4.75169i	−0.470109	+	0.335158i
$202$	−19.9855	+	8.08585i	−1.40617	+	0.568919i
$203$	−22.2228			−1.55974
$204$	5.96371	−	5.77021i	0.417543	−	0.403995i
$205$	−20.6278			−1.44071
$206$	−19.2606	+	7.79258i	−1.34195	+	0.542935i
$207$			6.27256i			0.435973i
$208$	11.5623	+	0.381452i	0.801704	+	0.0264489i
$209$			30.9810i			2.14300i
$210$	18.4032	−	7.44567i	1.26994	−	0.513800i
$211$		−	19.0362i		−	1.31050i	−0.755411	−	0.655252i	$-0.772563\pi$
$211$		−	19.0362i		−	1.31050i	0.755411	−	0.655252i	$-0.227437\pi$
$212$	−0.171557	−	0.177310i	−0.0117826	−	0.0121777i
$213$			15.6852i			1.07473i
$214$	8.08518	−	3.27116i	0.552692	−	0.223612i
$215$		−	12.4082i		−	0.846234i
$216$	2.58556	+	1.14669i	0.175925	+	0.0780222i
$217$	3.89086			0.264129
$218$	9.87154	−	3.99390i	0.668585	−	0.270501i
$219$	1.84732			0.124830
$220$	25.7537	+	26.6173i	1.73631	+	1.79454i
$221$			11.9999i			0.807203i
$222$	−1.33037	−	3.28823i	−0.0892888	−	0.220691i
$223$			17.7433i			1.18818i	0.804400	+	0.594088i	$0.202487\pi$
$223$			17.7433i			1.18818i	−0.804400	+	0.594088i	$0.797513\pi$
$224$	−26.1090	+	9.57419i	−1.74448	+	0.639703i
$225$	−3.15398			−0.210266
$226$	−24.1794	+	9.78269i	−1.60839	+	0.650735i
$227$		−	15.8446i		−	1.05164i	−0.850596	−	0.525820i	$-0.823758\pi$
$227$		−	15.8446i		−	1.05164i	0.850596	−	0.525820i	$-0.176242\pi$
$228$	6.64371	+	6.86650i	0.439990	+	0.454745i
$229$			16.2266i			1.07228i	0.844128	+	0.536141i	$0.180119\pi$
$229$			16.2266i			1.07228i	−0.844128	+	0.536141i	$0.819881\pi$
$230$	9.50030	+	23.4815i	0.626432	+	1.54832i
$231$	31.8809			2.09761
$232$	−11.6881	−	5.18363i	−0.767359	−	0.340322i
$233$		−	5.40768i		−	0.354269i	−0.984187	−	0.177135i	$-0.943317\pi$
$233$		−	5.40768i		−	0.354269i	0.984187	−	0.177135i	$-0.0566828\pi$
$234$	−3.79156	+	1.53402i	−0.247862	+	0.100282i
$235$	3.52266			0.229793
$236$	−3.72642	−	3.85139i	−0.242569	−	0.250704i
$237$	0.728927			0.0473489
$238$	−10.8187	−	26.7402i	−0.701274	−	1.73331i
$239$	24.3789			1.57694			0.788471	−	0.615072i	$-0.210873\pi$
$239$	24.3789			1.57694			0.788471	+	0.615072i	$0.210873\pi$
$240$	11.4159	+	0.376619i	0.736891	+	0.0243107i
$241$	−17.7424			−1.14289			−0.571444	−	0.820641i	$-0.693617\pi$
$241$	−17.7424			−1.14289			−0.571444	+	0.820641i	$0.693617\pi$
$242$	16.4729	+	40.7153i	1.05892	+	2.61728i
$243$	−1.00000			−0.0641500
$244$	−6.61947	−	6.84145i	−0.423768	−	0.437979i
$245$		−	49.0206i		−	3.13181i
$246$	−9.47032	+	3.83157i	−0.603806	+	0.244292i
$247$	−13.8165			−0.879123
$248$	2.04639	+	0.907570i	0.129946	+	0.0576308i
$249$		−	13.8943i		−	0.880513i
$250$	6.91062	−	2.79595i	0.437066	−	0.176831i
$251$	−4.05323			−0.255838			−0.127919	−	0.991785i	$-0.540830\pi$
$251$	−4.05323			−0.255838			−0.127919	+	0.991785i	$0.540830\pi$
$252$	7.06595	−	6.83668i	0.445113	−	0.430670i
$253$			40.6785i			2.55743i
$254$	−6.71070	+	2.71506i	−0.421066	+	0.170358i
$255$			11.8479i			0.741945i
$256$	−15.9652	−	1.05456i	−0.997826	−	0.0659100i
$257$	16.7288			1.04351			0.521755	−	0.853095i	$-0.325277\pi$
$257$	16.7288			1.04351			0.521755	+	0.853095i	$0.325277\pi$
$258$	−2.30480	−	5.69667i	−0.143490	−	0.354659i
$259$	−12.3304			−0.766173
$260$	−11.8704	+	11.4853i	−0.736172	+	0.712286i
$261$	4.52052			0.279813
$262$	6.08930	−	2.46365i	0.376198	−	0.152205i
$263$		−	5.59576i		−	0.345049i	−0.985005	−	0.172525i	$-0.944808\pi$
$263$		−	5.59576i		−	0.345049i	0.985005	−	0.172525i	$-0.0551924\pi$
$264$	16.7677	+	7.43644i	1.03198	+	0.457681i
$265$	0.352256			0.0216389
$266$	30.7881	−	12.4565i	1.88774	−	0.763756i
$267$	−0.704907			−0.0431396
$268$	−2.97160	+	16.0987i	−0.181520	+	0.983387i
$269$	2.92544			0.178367			0.0891837	−	0.996015i	$-0.471574\pi$
$269$	2.92544			0.178367			0.0891837	+	0.996015i	$0.471574\pi$
$270$	−3.74353	+	1.51458i	−0.227824	+	0.0921746i
$271$	−2.01844			−0.122611			−0.0613057	−	0.998119i	$-0.519526\pi$
$271$	−2.01844			−0.122611			−0.0613057	+	0.998119i	$0.519526\pi$
$272$	0.547236	−	16.5875i	0.0331811	−	1.00576i
$273$			14.2178i			0.860501i
$274$	−7.02934	+	2.84398i	−0.424658	+	0.171811i
$275$	−20.4541			−1.23343
$276$	8.72326	+	9.01580i	0.525079	+	0.542687i
$277$	−14.1610			−0.850854			−0.425427	−	0.904993i	$-0.639876\pi$
$277$	−14.1610			−0.850854			−0.425427	+	0.904993i	$0.639876\pi$
$278$	−7.86838	−	19.4479i	−0.471914	−	1.16641i
$279$	−0.791471			−0.0473841
$280$	16.0969	−	36.2953i	0.961972	−	2.16906i
$281$			5.14672i			0.307028i	0.988146	+	0.153514i	$0.0490590\pi$
$281$			5.14672i			0.307028i	−0.988146	+	0.153514i	$0.950941\pi$
$282$	1.61727	−	0.654326i	0.0963070	−	0.0389646i
$283$		−	17.8958i		−	1.06379i	−0.846809	−	0.531897i	$-0.821479\pi$
$283$		−	17.8958i		−	1.06379i	0.846809	−	0.531897i	$-0.178521\pi$
$284$	21.8135	+	22.5450i	1.29439	+	1.33780i
$285$	−13.6415			−0.808051
$286$	−24.5888	+	9.94832i	−1.45397	+	0.588257i
$287$			35.5124i			2.09623i
$288$	5.31103	−	1.94756i	0.312955	−	0.114761i
$289$	0.215286			0.0126639
$290$	16.9227	−	6.84670i	0.993735	−	0.402052i
$291$		−	9.89044i		−	0.579788i
$292$	2.65522	−	2.56907i	0.155385	−	0.150343i
$293$	−12.5828			−0.735098			−0.367549	−	0.930004i	$-0.619803\pi$
$293$	−12.5828			−0.735098			−0.367549	+	0.930004i	$0.619803\pi$
$294$	−9.10545	−	22.5056i	−0.531041	−	1.31255i
$295$	7.65143			0.445484
$296$	−6.48514	−	2.87614i	−0.376941	−	0.167173i
$297$	−6.48515			−0.376307
$298$	−9.49786	−	23.4754i	−0.550196	−	1.35990i
$299$	−18.1412			−1.04913
$300$	−4.53335	+	4.38625i	−0.261733	+	0.253240i
$301$	−21.3617			−1.23127
$302$	20.1876	−	8.16763i	1.16166	−	0.469994i
$303$		−	15.2447i		−	0.875783i
$304$	19.0985	+	0.630077i	1.09538	+	0.0361374i
$305$	13.5917			0.778259
$306$	2.20072	+	5.43943i	0.125807	+	0.310951i
$307$			8.63603i			0.492885i	0.969157	+	0.246442i	$0.0792616\pi$
$307$			8.63603i			0.492885i	−0.969157	+	0.246442i	$0.920738\pi$
$308$	45.8237	−	44.3369i	2.61105	−	2.52633i
$309$		−	14.6917i		−	0.835784i
$310$	−2.96289	+	1.19875i	−0.168281	+	0.0680843i
$311$	−12.4339			−0.705061			−0.352531	−	0.935800i	$-0.614679\pi$
$311$	−12.4339			−0.705061			−0.352531	+	0.935800i	$0.614679\pi$
$312$	−3.31640	+	7.47784i	−0.187754	+	0.423349i
$313$		−	2.51221i		−	0.141998i	−0.997476	−	0.0709991i	$-0.977381\pi$
$313$		−	2.51221i		−	0.141998i	0.997476	−	0.0709991i	$-0.0226188\pi$
$314$	−0.112370	−	0.277740i	−0.00634139	−	0.0156738i
$315$			14.0377i			0.790935i
$316$	1.04772	−	1.01372i	0.0589386	−	0.0570262i
$317$	−10.6688			−0.599218			−0.299609	−	0.954062i	$-0.596856\pi$
$317$	−10.6688			−0.599218			−0.299609	+	0.954062i	$0.596856\pi$
$318$	0.161722	−	0.0654306i	0.00906892	−	0.00366917i
$319$	29.3163			1.64140
$320$	16.9322	−	15.3347i	0.946541	−	0.857238i
$321$			6.16728i			0.344224i
$322$	40.4252	−	16.3555i	2.25281	−	0.911456i
$323$			19.8213i			1.10289i
$324$	−1.43734	+	1.39070i	−0.0798522	+	0.0772613i
$325$		−	9.12181i		−	0.505987i
$326$	19.1060	−	7.73002i	1.05818	−	0.428126i
$327$			7.52989i			0.416404i
$328$	−8.28350	+	18.6777i	−0.457380	+	1.03130i
$329$		−	6.06453i		−	0.334348i
$330$	−24.2773	+	9.82230i	−1.33642	+	0.540700i
$331$	−5.92505			−0.325670			−0.162835	−	0.986653i	$-0.552064\pi$
$331$	−5.92505			−0.325670			−0.162835	+	0.986653i	$0.552064\pi$
$332$	−19.3228	−	19.9708i	−1.06048	−	1.09604i
$333$	2.50822			0.137450
$334$	9.23225	−	3.73525i	0.505166	−	0.204384i
$335$	−13.5685	−	19.0319i	−0.741328	−	1.03982i
$336$	0.648378	−	19.6533i	0.0353719	−	1.07217i
$337$		−	5.04413i		−	0.274771i	−0.990518	−	0.137386i	$-0.956130\pi$
$337$		−	5.04413i		−	0.274771i	0.990518	−	0.137386i	$-0.0438700\pi$
$338$	2.45866	+	6.07696i	0.133733	+	0.330543i
$339$		−	18.4438i		−	1.00173i
$340$	16.4769	+	17.0295i	0.893587	+	0.923553i
$341$	−5.13281			−0.277957
$342$	−6.26285	+	2.53387i	−0.338656	+	0.137016i
$343$	−49.9807			−2.69870
$344$	−11.2351	−	4.98276i	−0.605759	−	0.268652i
$345$	−17.9114			−0.964317
$346$	7.09113	+	17.5268i	0.381222	+	0.942249i
$347$	−1.82049			−0.0977288			−0.0488644	−	0.998805i	$-0.515560\pi$
$347$	−1.82049			−0.0977288			−0.0488644	+	0.998805i	$0.515560\pi$
$348$	6.49753	−	6.28670i	0.348304	−	0.337003i
$349$	−14.8552			−0.795178			−0.397589	−	0.917564i	$-0.630153\pi$
$349$	−14.8552			−0.795178			−0.397589	+	0.917564i	$0.630153\pi$
$350$	8.22391	+	20.3267i	0.439587	+	1.08651i
$351$		−	2.89216i		−	0.154372i
$352$	34.4428	−	12.6302i	1.83581	−	0.673193i
$353$			3.34439i			0.178004i	0.996031	+	0.0890020i	$0.0283678\pi$
$353$			3.34439i			0.178004i	−0.996031	+	0.0890020i	$0.971632\pi$
$354$	3.51280	−	1.42123i	0.186703	−	0.0755378i
$355$	−44.7894			−2.37718
$356$	−1.01319	+	0.980316i	−0.0536990	+	0.0519567i
$357$	20.3971			1.07953
$358$	5.80695	+	14.3528i	0.306907	+	0.758569i
$359$		−	1.21464i		−	0.0641061i	−0.999486	−	0.0320531i	$-0.989795\pi$
$359$		−	1.21464i		−	0.0641061i	0.999486	−	0.0320531i	$-0.0102046\pi$
$360$	−3.27439	+	7.38311i	−0.172575	+	0.389124i
$361$	−3.82192			−0.201154
$362$	5.24943	+	12.9748i	0.275904	+	0.681940i
$363$	−31.0572			−1.63008
$364$	19.7728	+	20.4358i	1.03637	+	1.07113i
$365$			5.27505i			0.276109i
$366$	6.24001	−	2.52463i	0.326170	−	0.131964i
$367$	28.6573			1.49590			0.747950	−	0.663755i	$-0.231038\pi$
$367$	28.6573			1.49590			0.747950	+	0.663755i	$0.231038\pi$
$368$	25.0766	+	0.827298i	1.30721	+	0.0431259i
$369$		−	7.22384i		−	0.376058i
$370$	9.38959	−	3.79890i	0.488141	−	0.197496i
$371$		−	0.606435i		−	0.0314845i
$372$	−1.13761	+	1.10070i	−0.0589825	+	0.0570687i
$373$		−	17.6187i		−	0.912262i	−0.889913	−	0.456131i	$-0.849235\pi$
$373$		−	17.6187i		−	0.912262i	0.889913	−	0.456131i	$-0.150765\pi$
$374$	14.2720	+	35.2755i	0.737988	+	1.82405i
$375$			5.27134i			0.272211i
$376$	1.41459	−	3.18963i	0.0729521	−	0.164493i
$377$			13.0741i			0.673348i
$378$	2.60747	+	6.44477i	0.134114	+	0.331483i
$379$	−0.501202			−0.0257450			−0.0128725	−	0.999917i	$-0.504098\pi$
$379$	−0.501202			−0.0257450			−0.0128725	+	0.999917i	$0.504098\pi$
$380$	−19.6074	+	18.9712i	−1.00584	+	0.973203i
$381$		−	5.11884i		−	0.262246i
$382$	8.42959	+	20.8351i	0.431296	+	1.06601i
$383$	−14.3173			−0.731579			−0.365790	−	0.930698i	$-0.619201\pi$
$383$	−14.3173			−0.731579			−0.365790	+	0.930698i	$0.619201\pi$
$384$	4.92527	−	10.1854i	0.251342	−	0.519770i
$385$			91.0366i			4.63965i
$386$	−10.0227	−	24.7727i	−0.510143	−	1.26090i
$387$	4.34535			0.220886
$388$	−13.7547	−	14.2159i	−0.698287	−	0.721704i
$389$	0.947612			0.0480458			0.0240229	−	0.999711i	$-0.492353\pi$
$389$	0.947612			0.0480458			0.0240229	+	0.999711i	$0.492353\pi$
$390$	−4.38041	−	10.8269i	−0.221811	−	0.548240i
$391$			26.0257i			1.31617i
$392$	−44.3862	−	19.6852i	−2.24184	−	0.994250i
$393$			4.64485i			0.234302i
$394$	−7.44169	+	3.01081i	−0.374907	+	0.151682i
$395$			2.08146i			0.104730i
$396$	−9.32136	+	9.01892i	−0.468416	+	0.453218i
$397$	−1.94768			−0.0977515			−0.0488757	−	0.998805i	$-0.515564\pi$
$397$	−1.94768			−0.0977515			−0.0488757	+	0.998805i	$0.515564\pi$
$398$	−9.68010	+	3.91644i	−0.485220	+	0.196314i
$399$			23.4848i			1.17571i
$400$	−0.415984	+	12.6091i	−0.0207992	+	0.630454i
$401$			30.3290i			1.51456i	0.653090	+	0.757280i	$0.273472\pi$
$401$			30.3290i			1.51456i	−0.653090	+	0.757280i	$0.726528\pi$
$402$	−9.76449	−	6.21729i	−0.487009	−	0.310090i
$403$		−	2.28906i		−	0.114026i
$404$	−21.2008	−	21.9118i	−1.05478	−	1.09015i
$405$		−	2.85552i		−	0.141892i
$406$	−11.7871	−	29.1337i	−0.584985	−	1.44588i
$407$	16.2662			0.806284
$408$	10.7278	+	4.75776i	0.531106	+	0.235544i
$409$			6.20520i			0.306827i	0.988162	+	0.153414i	$0.0490267\pi$
$409$			6.20520i			0.306827i	−0.988162	+	0.153414i	$0.950973\pi$
$410$	−10.9411	−	27.0427i	−0.540343	−	1.33554i
$411$		−	5.36190i		−	0.264483i
$412$	−20.4318	−	21.1170i	−1.00660	−	1.04036i
$413$		−	13.1725i		−	0.648177i
$414$	−8.22320	+	3.32700i	−0.404148	+	0.163513i
$415$	39.6753			1.94758
$416$	5.63265	+	15.3603i	0.276163	+	0.753102i
$417$	14.8346			0.726456
$418$	−40.6155	+	16.4325i	−1.98657	+	0.803741i
$419$			39.0213i			1.90632i	0.302470	+	0.953159i	$0.402189\pi$
$419$			39.0213i			1.90632i	−0.302470	+	0.953159i	$0.597811\pi$
$420$	19.5223	+	20.1769i	0.952589	+	0.984534i
$421$	29.9711			1.46070			0.730350	−	0.683073i	$-0.239357\pi$
$421$	29.9711			1.46070			0.730350	+	0.683073i	$0.239357\pi$
$422$	24.9560	−	10.0969i	1.21484	−	0.491509i
$423$			1.23363i			0.0599813i
$424$	0.141455	−	0.318953i	0.00686966	−	0.0154897i
$425$	−13.0863			−0.634778
$426$	−20.5630	+	8.31953i	−0.996281	+	0.403082i
$427$		−	23.3991i		−	1.13236i
$428$	8.57685	+	8.86448i	0.414578	+	0.428481i
$429$		−	18.7561i		−	0.905551i
$430$	16.2669	−	6.58139i	0.784461	−	0.317383i
$431$		−	21.7828i		−	1.04924i	−0.851336	−	0.524620i	$-0.824207\pi$
$431$		−	21.7828i		−	1.04924i	0.851336	−	0.524620i	$-0.175793\pi$
$432$	−0.131892	+	3.99782i	−0.00634564	+	0.192345i
$433$		−	7.29826i		−	0.350732i	−0.984503	−	0.175366i	$-0.943889\pi$
$433$		−	7.29826i		−	0.350732i	0.984503	−	0.175366i	$-0.0561109\pi$
$434$	2.06374	+	5.10085i	0.0990625	+	0.244848i
$435$			12.9084i			0.618912i
$436$	10.4718	+	10.8230i	0.501510	+	0.518328i
$437$	−29.9654			−1.43344
$438$	0.979827	+	2.42180i	0.0468180	+	0.115718i
$439$			7.82313i			0.373378i	0.982419	+	0.186689i	$0.0597756\pi$
$439$			7.82313i			0.373378i	−0.982419	+	0.186689i	$0.940224\pi$
$440$	−21.2349	+	47.8805i	−1.01233	+	2.28262i
$441$	17.1670			0.817474
$442$	−15.7317	+	6.36483i	−0.748280	+	0.302744i
$443$	−24.7893			−1.17778			−0.588889	−	0.808214i	$-0.700434\pi$
$443$	−24.7893			−1.17778			−0.588889	+	0.808214i	$0.700434\pi$
$444$	3.60516	−	3.48819i	0.171093	−	0.165542i
$445$		−	2.01287i		−	0.0954194i
$446$	−23.2611	+	9.41112i	−1.10144	+	0.445629i
$447$	17.9068			0.846962
$448$	−26.3999	−	29.1501i	−1.24728	−	1.37721i
$449$	42.3589			1.99904			0.999521	−	0.0309436i	$-0.00985122\pi$
$449$	42.3589			1.99904			0.999521	+	0.0309436i	$0.00985122\pi$
$450$	−1.67289	−	4.13481i	−0.0788608	−	0.194917i
$451$		−	46.8477i		−	2.20597i
$452$	−25.6498	−	26.5100i	−1.20647	−	1.24692i
$453$			15.3988i			0.723500i
$454$	20.7719	−	8.40404i	0.974874	−	0.394421i
$455$	−40.5992			−1.90332
$456$	−5.47799	+	12.3518i	−0.256530	+	0.578426i
$457$	13.6330			0.637727			0.318863	−	0.947801i	$-0.396699\pi$
$457$	13.6330			0.637727			0.318863	+	0.947801i	$0.396699\pi$
$458$	−21.2727	+	8.60667i	−0.994009	+	0.402163i
$459$	−4.14913			−0.193665
$460$	−25.7448	+	24.9094i	−1.20036	+	1.16141i
$461$	−29.4296			−1.37067			−0.685336	−	0.728227i	$-0.740345\pi$
$461$	−29.4296			−1.37067			−0.685336	+	0.728227i	$0.740345\pi$
$462$	16.9098	+	41.7953i	0.786716	+	1.94449i
$463$	11.7817			0.547542			0.273771	−	0.961795i	$-0.411729\pi$
$463$	11.7817			0.547542			0.273771	+	0.961795i	$0.411729\pi$
$464$	0.596219	−	18.0723i	0.0276788	−	0.838983i
$465$		−	2.26006i		−	0.104808i
$466$	7.08937	−	2.86826i	0.328409	−	0.132870i
$467$		−	32.3532i		−	1.49713i	−0.663063	−	0.748564i	$-0.730744\pi$
$467$		−	32.3532i		−	1.49713i	0.663063	−	0.748564i	$-0.269256\pi$
$468$	−4.02213	−	4.15701i	−0.185923	−	0.192158i
$469$	−32.7648	+	23.3593i	−1.51294	+	1.07863i
$470$	1.86844	+	4.61814i	0.0861847	+	0.213019i
$471$	0.211856			0.00976183
$472$	3.07258	−	6.92806i	0.141427	−	0.318890i
$473$	28.1802			1.29573
$474$	0.386627	+	0.955609i	0.0177584	+	0.0438926i
$475$		−	15.0673i		−	0.691335i
$476$	29.3175	−	28.3663i	1.34377	−	1.30017i
$477$			0.123360i			0.00564825i
$478$	12.9307	+	31.9603i	0.591437	+	1.46183i
$479$		−	23.8652i		−	1.09043i	−0.838297	−	0.545214i	$-0.816448\pi$
$479$		−	23.8652i		−	1.09043i	0.838297	−	0.545214i	$-0.183552\pi$
$480$	5.56130	+	15.1657i	0.253837	+	0.692218i
$481$			7.25416i			0.330761i
$482$	−9.41066	−	23.2599i	−0.428644	−	1.05946i
$483$			30.8358i			1.40308i
$484$	−44.6397	+	43.1913i	−2.02908	+	1.96324i
$485$	28.2423			1.28242
$486$	−0.530406	−	1.31098i	−0.0240597	−	0.0594673i
$487$	−13.9001			−0.629875			−0.314938	−	0.949112i	$-0.601984\pi$
$487$	−13.9001			−0.629875			−0.314938	+	0.949112i	$0.601984\pi$
$488$	5.45801	−	12.3067i	0.247072	−	0.557100i
$489$			14.5738i			0.659050i
$490$	64.2650	−	26.0008i	2.90320	−	1.17460i
$491$			12.8500i			0.579914i	0.957040	+	0.289957i	$0.0936410\pi$
$491$			12.8500i			0.579914i	−0.957040	+	0.289957i	$0.906359\pi$
$492$	−10.0462	−	10.3831i	−0.452919	−	0.468107i
$493$	18.7562			0.844738
$494$	−7.32835	−	18.1132i	−0.329718	−	0.814949i
$495$		−	18.5185i		−	0.832343i
$496$	−0.104388	+	3.16416i	−0.00468718	+	0.142075i
$497$			77.1084i			3.45878i
$498$	18.2151	−	7.36959i	0.816238	−	0.330239i
$499$	−2.61774			−0.117186			−0.0585931	−	0.998282i	$-0.518661\pi$
$499$	−2.61774			−0.117186			−0.0585931	+	0.998282i	$0.518661\pi$
$500$	7.33086	+	7.57670i	0.327846	+	0.338840i
$501$			7.04225i			0.314624i
$502$	−2.14986	−	5.31371i	−0.0959528	−	0.237162i
$503$	−28.5414			−1.27260			−0.636298	−	0.771443i	$-0.719535\pi$
$503$	−28.5414			−1.27260			−0.636298	+	0.771443i	$0.719535\pi$
$504$	12.7106	+	5.63711i	0.566174	+	0.251097i
$505$	43.5314			1.93712
$506$	−53.3287	+	21.5761i	−2.37075	+	0.959174i
$507$	−4.63543			−0.205867
$508$	−7.11878	−	7.35751i	−0.315845	−	0.326437i
$509$	19.0491			0.844338			0.422169	−	0.906517i	$-0.361269\pi$
$509$	19.0491			0.844338			0.422169	+	0.906517i	$0.361269\pi$
$510$	−15.5324	+	6.28420i	−0.687786	+	0.278269i
$511$	9.08139			0.401737
$512$	−7.08553	−	21.4894i	−0.313139	−	0.949707i
$513$		−	4.77723i		−	0.210920i
$514$	8.87302	+	21.9311i	0.391372	+	0.967338i
$515$	41.9525			1.84865
$516$	6.24574	−	6.04309i	0.274954	−	0.266032i
$517$			8.00030i			0.351853i
$518$	−6.54010	−	16.1649i	−0.287356	−	0.710244i
$519$	−13.3693			−0.586846
$520$	−21.3531	−	9.47004i	−0.936395	−	0.415289i
$521$			4.18847i			0.183500i	0.995782	+	0.0917500i	$0.0292461\pi$
$521$			4.18847i			0.183500i	−0.995782	+	0.0917500i	$0.970754\pi$
$522$	2.39771	+	5.92632i	0.104945	+	0.259388i
$523$		−	19.8355i		−	0.867345i	−0.901071	−	0.433673i	$-0.857217\pi$
$523$		−	19.8355i		−	0.867345i	0.901071	−	0.433673i	$-0.142783\pi$
$524$	6.45960	+	6.67622i	0.282189	+	0.291652i
$525$	−15.5049			−0.676691
$526$	7.33593	−	2.96802i	0.319862	−	0.129412i
$527$	−3.28392			−0.143050
$528$	−0.855338	+	25.9265i	−0.0372238	+	1.12831i
$529$	−16.3450			−0.710651
$530$	0.186838	+	0.461800i	0.00811574	+	0.0200593i
$531$			2.67952i			0.116281i
$532$	32.6604	+	33.7557i	1.41601	+	1.46349i
$533$	20.8925			0.904954
$534$	−0.373887	−	0.924120i	−0.0161797	−	0.0399906i
$535$	−17.6108			−0.761380
$536$	−22.6813	+	4.64315i	−0.979683	+	0.200554i
$537$	−10.9481			−0.472447
$538$	1.55167	+	3.83520i	0.0668973	+	0.165347i
$539$	111.330			4.79534
$540$	−3.97118	−	4.10435i	−0.170892	−	0.176623i
$541$		−	25.5904i		−	1.10022i	−0.835093	−	0.550109i	$-0.814586\pi$
$541$		−	25.5904i		−	1.10022i	0.835093	−	0.550109i	$-0.185414\pi$
$542$	−1.07059	−	2.64613i	−0.0459858	−	0.113661i
$543$	−9.89701			−0.424721
$544$	22.0361	−	8.08069i	0.944792	−	0.346457i
$545$	−21.5017			−0.921033
$546$	−18.6393	+	7.54121i	−0.797687	+	0.322734i
$547$	−5.52707			−0.236320			−0.118160	−	0.992995i	$-0.537700\pi$
$547$	−5.52707			−0.236320			−0.118160	+	0.992995i	$0.537700\pi$
$548$	−7.45680	−	7.70687i	−0.318539	−	0.329221i
$549$			4.75980i			0.203143i
$550$	−10.8489	−	26.8149i	−0.462600	−	1.14339i
$551$			21.5956i			0.920002i
$552$	−7.19267	+	16.2181i	−0.306140	+	0.690286i
$553$	3.58340			0.152382
$554$	−7.51109	−	18.5648i	−0.319116	−	0.788745i
$555$			7.16226i			0.304021i
$556$	21.3224	−	20.6306i	0.904272	−	0.874932i
$557$	−29.2234			−1.23824			−0.619118	−	0.785298i	$-0.712510\pi$
$557$	−29.2234			−1.23824			−0.619118	+	0.785298i	$0.712510\pi$
$558$	−0.419800	−	1.03760i	−0.0177716	−	0.0439252i
$559$			12.5674i			0.531546i
$560$	56.1203	+	1.85146i	2.37151	+	0.0782383i
$561$	−26.9077			−1.13605
$562$	−6.74725	+	2.72985i	−0.284616	+	0.115152i
$563$	15.0136			0.632747			0.316374	−	0.948635i	$-0.397535\pi$
$563$	15.0136			0.632747			0.316374	+	0.948635i	$0.397535\pi$
$564$	1.71562	+	1.77315i	0.0722405	+	0.0746631i
$565$	52.6666			2.21570
$566$	23.4610	−	9.49203i	0.986141	−	0.398980i
$567$	−4.91599			−0.206452
$568$	−17.9860	+	40.5550i	−0.754678	+	1.70165i
$569$	−8.86391			−0.371595			−0.185797	−	0.982588i	$-0.559487\pi$
$569$	−8.86391			−0.371595			−0.185797	+	0.982588i	$0.559487\pi$
$570$	−7.23551	−	17.8837i	−0.303062	−	0.749066i
$571$			16.2972i			0.682015i	0.940061	+	0.341007i	$0.110768\pi$
$571$			16.2972i			0.682015i	−0.940061	+	0.341007i	$0.889232\pi$
$572$	−26.0841	−	26.9588i	−1.09063	−	1.12721i
$573$	−15.8927			−0.663928
$574$	−46.5560	+	18.8359i	−1.94321	+	0.786197i
$575$		−	19.7835i		−	0.825030i
$576$	5.37021	+	5.92966i	0.223759	+	0.247069i
$577$		−	38.2988i		−	1.59440i	−0.603715	−	0.797200i	$-0.706314\pi$
$577$		−	38.2988i		−	1.59440i	0.603715	−	0.797200i	$-0.293686\pi$
$578$	0.114189	+	0.282236i	0.00474963	+	0.0117395i
$579$	18.8963			0.785305
$580$	17.9518	+	18.5538i	0.745407	+	0.770405i
$581$		−	68.3041i		−	2.83373i
$582$	12.9662	−	5.24594i	0.537465	−	0.217451i
$583$			0.800006i			0.0331328i
$584$	4.77634	+	2.11830i	0.197647	+	0.0876557i
$585$	8.25860			0.341451
$586$	−6.67401	−	16.4959i	−0.275701	−	0.681438i
$587$	−35.5641			−1.46789			−0.733943	−	0.679211i	$-0.762322\pi$
$587$	−35.5641			−1.46789			−0.733943	+	0.679211i	$0.762322\pi$
$588$	24.6748	−	23.8741i	1.01757	−	0.984553i
$589$		−	3.78104i		−	0.155795i
$590$	4.05836	+	10.0309i	0.167080	+	0.412965i
$591$		−	5.67643i		−	0.233497i
$592$	0.330813	−	10.0274i	0.0135963	−	0.412124i
$593$		−	20.1922i		−	0.829196i	−0.910005	−	0.414598i	$-0.863922\pi$
$593$		−	20.1922i		−	0.829196i	0.910005	−	0.414598i	$-0.136078\pi$
$594$	−3.43976	−	8.50190i	−0.141135	−	0.348837i
$595$			58.2442i			2.38778i
$596$	25.7381	−	24.9030i	1.05427	−	1.02007i
$597$		−	7.38387i		−	0.302201i
$598$	−9.62220	−	23.7828i	−0.393481	−	0.972550i
$599$	−2.28406			−0.0933243			−0.0466622	−	0.998911i	$-0.514858\pi$
$599$	−2.28406			−0.0933243			−0.0466622	+	0.998911i	$0.514858\pi$
$600$	−8.15480	−	3.61663i	−0.332918	−	0.147648i
$601$	18.6583			0.761086			0.380543	−	0.924763i	$-0.375737\pi$
$601$	18.6583			0.761086			0.380543	+	0.924763i	$0.375737\pi$
$602$	−11.3304	−	28.0048i	−0.461791	−	1.14139i
$603$	6.66494	−	4.75169i	0.271417	−	0.193504i
$604$	21.4152	+	22.1334i	0.871372	+	0.900594i
$605$		−	88.6843i		−	3.60553i
$606$	19.9855	−	8.08585i	0.811853	−	0.328465i
$607$			12.3425i			0.500967i	0.968121	+	0.250484i	$0.0805896\pi$
$607$			12.3425i			0.500967i	−0.968121	+	0.250484i	$0.919410\pi$
$608$	9.30395	+	25.3720i	0.377325	+	1.02897i
$609$	22.2228			0.900515
$610$	7.20911	+	17.8185i	0.291889	+	0.721448i
$611$	−3.56786			−0.144340
$612$	−5.96371	+	5.77021i	−0.241069	+	0.233247i
$613$	10.9193			0.441028			0.220514	−	0.975384i	$-0.429227\pi$
$613$	10.9193			0.441028			0.220514	+	0.975384i	$0.429227\pi$
$614$	−11.3217	+	4.58060i	−0.456906	+	0.184858i
$615$	20.6278			0.831794
$616$	82.4300	+	36.5575i	3.32120	+	1.47294i
$617$	−20.0559			−0.807421			−0.403710	−	0.914887i	$-0.632280\pi$
$617$	−20.0559			−0.807421			−0.403710	+	0.914887i	$0.632280\pi$
$618$	19.2606	−	7.79258i	0.774774	−	0.313463i
$619$			11.3753i			0.457211i	0.973519	+	0.228606i	$0.0734167\pi$
$619$			11.3753i			0.457211i	−0.973519	+	0.228606i	$0.926583\pi$
$620$	−3.14307	−	3.24847i	−0.126229	−	0.130462i
$621$		−	6.27256i		−	0.251709i
$622$	−6.59501	−	16.3006i	−0.264436	−	0.653594i
$623$	−3.46532			−0.138835
$624$	−11.5623	−	0.381452i	−0.462864	−	0.0152703i
$625$	−30.8223			−1.23289
$626$	3.29345	−	1.33249i	0.131633	−	0.0532569i
$627$		−	30.9810i		−	1.23726i
$628$	0.304510	−	0.294629i	0.0121513	−	0.0117570i
$629$	10.4069			0.414951
$630$	−18.4032	+	7.44567i	−0.733199	+	0.296643i
$631$	38.3525			1.52679			0.763395	−	0.645932i	$-0.223531\pi$
$631$	38.3525			1.52679			0.763395	+	0.645932i	$0.223531\pi$
$632$	1.88468	+	0.835851i	0.0749686	+	0.0332484i
$633$			19.0362i			0.756619i
$634$	−5.65878	−	13.9866i	−0.224739	−	0.555477i
$635$	14.6169			0.580055
$636$	0.171557	+	0.177310i	0.00680266	+	0.00703079i
$637$			49.6495i			1.96719i
$638$	15.5495	+	38.4330i	0.615611	+	1.52158i
$639$		−	15.6852i		−	0.620497i
$640$	29.0845	+	14.0642i	1.14967	+	0.555936i
$641$			5.63089i			0.222407i	0.993798	+	0.111203i	$0.0354705\pi$
$641$			5.63089i			0.222407i	−0.993798	+	0.111203i	$0.964530\pi$
$642$	−8.08518	+	3.27116i	−0.319097	+	0.129102i
$643$		−	21.1619i		−	0.834543i	−0.908782	−	0.417272i	$-0.862986\pi$
$643$		−	21.1619i		−	0.834543i	0.908782	−	0.417272i	$-0.137014\pi$
$644$	42.8835	+	44.3216i	1.68985	+	1.74651i
$645$			12.4082i			0.488573i
$646$	−25.9854	+	10.5134i	−1.02238	+	0.413642i
$647$	16.6498			0.654572			0.327286	−	0.944925i	$-0.393866\pi$
$647$	16.6498			0.654572			0.327286	+	0.944925i	$0.393866\pi$
$648$	−2.58556	−	1.14669i	−0.101570	−	0.0450462i
$649$			17.3771i			0.682112i
$650$	11.9585	−	4.83826i	0.469052	−	0.189772i
$651$	−3.89086			−0.152495
$652$	20.2678	+	20.9475i	0.793749	+	0.820367i
$653$			31.2845i			1.22426i	0.790758	+	0.612128i	$0.209686\pi$
$653$			31.2845i			1.22426i	−0.790758	+	0.612128i	$0.790314\pi$
$654$	−9.87154	+	3.99390i	−0.386008	+	0.156174i
$655$	−13.2634			−0.518246
$656$	−28.8797	−	0.952765i	−1.12756	−	0.0371992i
$657$	−1.84732			−0.0720707
$658$	7.95048	−	3.21666i	0.309942	−	0.125399i
$659$			40.3816i			1.57304i	0.617563	+	0.786521i	$0.288120\pi$
$659$			40.3816i			1.57304i	−0.617563	+	0.786521i	$0.711880\pi$
$660$	−25.7537	−	26.6173i	−1.00246	−	1.03608i
$661$		−	28.1687i		−	1.09563i	−0.836598	−	0.547817i	$-0.815459\pi$
$661$		−	28.1687i		−	1.09563i	0.836598	−	0.547817i	$-0.184541\pi$
$662$	−3.14268	−	7.76762i	−0.122144	−	0.301897i
$663$		−	11.9999i		−	0.466039i
$664$	15.9324	−	35.9244i	0.618296	−	1.39414i
$665$	−67.0613			−2.60053
$666$	1.33037	+	3.28823i	0.0515509	+	0.127416i
$667$			28.3552i			1.09792i
$668$	9.79367	+	10.1221i	0.378929	+	0.391636i
$669$		−	17.7433i		−	0.685994i
$670$	17.7536	−	27.8827i	0.685881	−	1.07720i
$671$			30.8680i			1.19165i
$672$	26.1090	−	9.57419i	1.00717	−	0.369332i
$673$		−	34.3235i		−	1.32307i	−0.749913	−	0.661537i	$-0.769905\pi$
$673$		−	34.3235i		−	1.32307i	0.749913	−	0.661537i	$-0.230095\pi$
$674$	6.61276	−	2.67544i	0.254714	−	0.103054i
$675$	3.15398			0.121397
$676$	−6.66269	+	6.44651i	−0.256257	+	0.247943i
$677$		−	37.3316i		−	1.43477i	−0.696678	−	0.717384i	$-0.745339\pi$
$677$		−	37.3316i		−	1.43477i	0.696678	−	0.717384i	$-0.254661\pi$
$678$	24.1794	−	9.78269i	0.928606	−	0.375702i
$679$		−	48.6213i		−	1.86591i
$680$	−13.5859	+	30.6335i	−0.520994	+	1.17474i
$681$			15.8446i			0.607165i
$682$	−2.72247	−	6.72901i	−0.104249	−	0.257667i
$683$	−34.3656			−1.31496			−0.657481	−	0.753471i	$-0.728378\pi$
$683$	−34.3656			−1.31496			−0.657481	+	0.753471i	$0.728378\pi$
$684$	−6.64371	−	6.86650i	−0.254028	−	0.262547i
$685$	15.3110			0.585003
$686$	−26.5100	−	65.5237i	−1.01216	−	2.50171i
$687$		−	16.2266i		−	0.619082i
$688$	0.573116	−	17.3719i	0.0218498	−	0.662299i
$689$	−0.356775			−0.0135921
$690$	−9.50030	−	23.4815i	−0.361670	−	0.893925i
$691$			29.4379i			1.11987i	0.828536	+	0.559936i	$0.189174\pi$
$691$			29.4379i			1.11987i	−0.828536	+	0.559936i	$0.810826\pi$
$692$	−19.2162	+	18.5927i	−0.730490	+	0.706787i
$693$	−31.8809			−1.21106
$694$	−0.965596	−	2.38662i	−0.0366535	−	0.0905949i
$695$			42.3606i			1.60683i
$696$	11.6881	+	5.18363i	0.443035	+	0.196485i
$697$		−	29.9727i		−	1.13530i
$698$	−7.87925	−	19.4748i	−0.298234	−	0.737133i
$699$			5.40768i			0.204537i
$700$	−22.2859	+	21.5628i	−0.842327	+	0.814996i
$701$			25.3710i			0.958250i	0.877747	+	0.479125i	$0.159046\pi$
$701$			25.3710i			0.958250i	−0.877747	+	0.479125i	$0.840954\pi$
$702$	3.79156	−	1.53402i	0.143103	−	0.0578977i
$703$			11.9823i			0.451922i
$704$	34.8266	+	38.4547i	1.31258	+	1.44932i
$705$	−3.52266			−0.132671
$706$	−4.38443	+	1.77388i	−0.165010	+	0.0667610i
$707$		−	74.9426i		−	2.81851i
$708$	3.72642	+	3.85139i	0.140048	+	0.144744i
$709$	−25.7636			−0.967572			−0.483786	−	0.875186i	$-0.660739\pi$
$709$	−25.7636			−0.967572			−0.483786	+	0.875186i	$0.660739\pi$
$710$	−23.7566	−	58.7180i	−0.891568	−	2.20365i
$711$	−0.728927			−0.0273369
$712$	−1.82258	−	0.808309i	−0.0683040	−	0.0302926i
$713$		−	4.96454i		−	0.185924i
$714$	10.8187	+	26.7402i	0.404881	+	1.00073i
$715$	53.5583			2.00297
$716$	−15.7362	+	15.2256i	−0.588089	+	0.569008i
$717$	−24.3789			−0.910448
$718$	1.59237	−	0.644251i	0.0594266	−	0.0240432i
$719$		−	18.5554i		−	0.692001i	−0.938234	−	0.346000i	$-0.887540\pi$
$719$		−	18.5554i		−	0.692001i	0.938234	−	0.346000i	$-0.112460\pi$
$720$	−11.4159	−	0.376619i	−0.425444	−	0.0140358i
$721$		−	72.2244i		−	2.68978i
$722$	−2.02717	−	5.01046i	−0.0754434	−	0.186470i
$723$	17.7424			0.659847
$724$	−14.2254	+	13.7638i	−0.528682	+	0.511528i
$725$	−14.2576			−0.529516
$726$	−16.4729	−	40.7153i	−0.611366	−	1.51109i
$727$	−5.08959			−0.188762			−0.0943812	−	0.995536i	$-0.530087\pi$
$727$	−5.08959			−0.188762			−0.0943812	+	0.995536i	$0.530087\pi$
$728$	−16.3034	+	36.7610i	−0.604244	+	1.36245i
$729$	1.00000			0.0370370
$730$	−6.91548	+	2.79791i	−0.255954	+	0.103555i
$731$	18.0294			0.666842
$732$	6.61947	+	6.84145i	0.244663	+	0.252867i
$733$			14.2486i			0.526284i	0.964757	+	0.263142i	$0.0847588\pi$
$733$			14.2486i			0.526284i	−0.964757	+	0.263142i	$0.915241\pi$
$734$	15.2000	+	37.5692i	0.561042	+	1.38670i
$735$			49.0206i			1.80815i
$736$	12.2162	+	33.3137i	0.450295	+	1.22796i
$737$	43.2232	−	30.8154i	1.59215	−	1.13510i
$738$	9.47032	−	3.83157i	0.348607	−	0.141042i
$739$	10.5314			0.387405			0.193702	−	0.981060i	$-0.437950\pi$
$739$	10.5314			0.387405			0.193702	+	0.981060i	$0.437950\pi$
$740$	9.96058	+	10.2946i	0.366158	+	0.378437i
$741$	13.8165			0.507562
$742$	0.795024	−	0.321656i	0.0291863	−	0.0118084i
$743$		−	35.6194i		−	1.30675i	−0.757035	−	0.653375i	$-0.773353\pi$
$743$		−	35.6194i		−	1.30675i	0.757035	−	0.653375i	$-0.226647\pi$
$744$	−2.04639	−	0.907570i	−0.0750244	−	0.0332731i
$745$			51.1331i			1.87337i
$746$	23.0978	−	9.34506i	0.845670	−	0.342147i
$747$			13.8943i			0.508364i
$748$	−38.6756	+	37.4207i	−1.41412	+	1.36823i
$749$			30.3183i			1.10781i
$750$	−6.91062	+	2.79595i	−0.252340	+	0.102094i
$751$			12.8419i			0.468607i	0.972164	+	0.234303i	$0.0752809\pi$
$751$			12.8419i			0.468607i	−0.972164	+	0.234303i	$0.924719\pi$
$752$	4.93185	+	0.162706i	0.179846	+	0.00593328i
$753$	4.05323			0.147708
$754$	−17.1398	+	6.93455i	−0.624196	+	0.252541i
$755$	−43.9717			−1.60029
$756$	−7.06595	+	6.83668i	−0.256986	+	0.248648i
$757$		−	9.91210i		−	0.360261i	−0.983643	−	0.180131i	$-0.942348\pi$
$757$		−	9.91210i		−	0.360261i	0.983643	−	0.180131i	$-0.0576521\pi$
$758$	−0.265840	−	0.657066i	−0.00965575	−	0.0238657i
$759$		−	40.6785i		−	1.47653i
$760$	−35.2708	−	15.6425i	−1.27941	−	0.567413i
$761$	30.5324			1.10680			0.553399	−	0.832916i	$-0.313331\pi$
$761$	30.5324			1.10680			0.553399	+	0.832916i	$0.313331\pi$
$762$	6.71070	−	2.71506i	0.243103	−	0.0983562i
$763$			37.0169i			1.34010i
$764$	−22.8433	+	22.1021i	−0.826440	+	0.799625i
$765$		−	11.8479i		−	0.428362i
$766$	−7.59397	−	18.7697i	−0.274381	−	0.678176i
$767$	−7.74960			−0.279822
$768$	15.9652	+	1.05456i	0.576095	+	0.0380532i
$769$			7.68551i			0.277147i	0.990352	+	0.138573i	$0.0442516\pi$
$769$			7.68551i			0.277147i	−0.990352	+	0.138573i	$0.955748\pi$
$770$	−119.347	+	48.2863i	−4.30097	+	1.74012i
$771$	−16.7288			−0.602471
$772$	27.1605	−	26.2792i	0.977527	−	0.945809i
$773$	26.4942			0.952929			0.476464	−	0.879194i	$-0.341918\pi$
$773$	26.4942			0.952929			0.476464	+	0.879194i	$0.341918\pi$
$774$	2.30480	+	5.69667i	0.0828442	+	0.204762i
$775$	2.49629			0.0896692
$776$	11.3412	−	25.5723i	0.407127	−	0.917992i
$777$	12.3304			0.442350
$778$	0.502619	+	1.24230i	0.0180198	+	0.0445387i
$779$	34.5100			1.23645
$780$	11.8704	−	11.4853i	0.425029	−	0.411238i
$781$		−	101.721i		−	3.63986i
$782$	−34.1191	+	13.8042i	−1.22010	+	0.493636i
$783$	−4.52052			−0.161550
$784$	2.26418	−	68.6305i	0.0808636	−	2.45109i
$785$			0.604960i			0.0215919i
$786$	−6.08930	+	2.46365i	−0.217198	+	0.0878756i
$787$	48.5740			1.73148			0.865738	−	0.500497i	$-0.166849\pi$
$787$	48.5740			1.73148			0.865738	+	0.500497i	$0.166849\pi$
$788$	−7.89423	−	8.15896i	−0.281220	−	0.290651i
$789$			5.59576i			0.199214i
$790$	−2.72876	+	1.10402i	−0.0970848	+	0.0392793i
$791$		−	90.6695i		−	3.22384i
$792$	−16.7677	−	7.43644i	−0.595815	−	0.264243i
$793$	−13.7661			−0.488848
$794$	−1.03306	−	2.55338i	−0.0366620	−	0.0906159i
$795$	−0.352256			−0.0124932
$796$	−10.2688	−	10.6131i	−0.363967	−	0.376172i
$797$	−27.4280			−0.971551			−0.485775	−	0.874084i	$-0.661463\pi$
$797$	−27.4280			−0.971551			−0.485775	+	0.874084i	$0.661463\pi$
$798$	−30.7881	+	12.4565i	−1.08989	+	0.440954i
$799$			5.11851i			0.181080i
$800$	−16.7509	+	6.14257i	−0.592233	+	0.217173i
$801$	0.704907			0.0249067
$802$	−39.7608	+	16.0867i	−1.40400	+	0.568041i
$803$	−11.9801			−0.422770
$804$	2.97160	−	16.0987i	0.104800	−	0.567759i
$805$	−88.0523			−3.10343
$806$	3.00091	−	1.21413i	0.105703	−	0.0427659i
$807$	−2.92544			−0.102981
$808$	17.4809	−	39.4159i	0.614975	−	1.38665i
$809$			13.9260i			0.489612i	0.969572	+	0.244806i	$0.0787242\pi$
$809$			13.9260i			0.489612i	−0.969572	+	0.244806i	$0.921276\pi$
$810$	3.74353	−	1.51458i	0.131534	−	0.0532170i
$811$	−43.8769			−1.54072			−0.770362	−	0.637606i	$-0.779925\pi$
$811$	−43.8769			−1.54072			−0.770362	+	0.637606i	$0.779925\pi$
$812$	31.9418	−	30.9054i	1.12094	−	1.08457i
$813$	2.01844			0.0707898
$814$	8.62767	+	21.3246i	0.302400	+	0.747428i
$815$	−41.6157			−1.45774
$816$	−0.547236	+	16.5875i	−0.0191571	+	0.580679i
$817$			20.7587i			0.726256i
$818$	−8.13490	+	3.29127i	−0.284430	+	0.115077i
$819$		−	14.2178i		−	0.496811i
$820$	29.6492	−	28.6872i	1.03539	−	1.00180i
$821$	46.0911			1.60859			0.804295	−	0.594230i	$-0.202543\pi$
$821$	46.0911			1.60859			0.804295	+	0.594230i	$0.202543\pi$
$822$	7.02934	−	2.84398i	0.245176	−	0.0991952i
$823$		−	26.6569i		−	0.929201i	−0.885520	−	0.464601i	$-0.846198\pi$
$823$		−	26.6569i		−	0.929201i	0.885520	−	0.464601i	$-0.153802\pi$
$824$	16.8468	−	37.9863i	0.586887	−	1.32332i
$825$	20.4541			0.712119
$826$	17.2689	−	6.98678i	0.600862	−	0.243101i
$827$			43.0483i			1.49694i	0.663171	+	0.748468i	$0.269210\pi$
$827$			43.0483i			1.49694i	−0.663171	+	0.748468i	$0.730790\pi$
$828$	−8.72326	−	9.01580i	−0.303154	−	0.313321i
$829$	−14.1747			−0.492308			−0.246154	−	0.969231i	$-0.579167\pi$
$829$	−14.1747			−0.492308			−0.246154	+	0.969231i	$0.579167\pi$
$830$	21.0440	+	52.0136i	0.730448	+	1.80542i
$831$	14.1610			0.491241
$832$	−17.1495	+	15.5315i	−0.594552	+	0.538458i
$833$	71.2280			2.46790
$834$	7.86838	+	19.4479i	0.272460	+	0.673427i
$835$	−20.1093			−0.695910
$836$	−43.0854	−	44.5303i	−1.49014	−	1.54011i
$837$	0.791471			0.0273572
$838$	−51.1562	+	20.6971i	−1.76716	+	0.714971i
$839$			45.8812i			1.58399i	0.610525	+	0.791997i	$0.290959\pi$
$839$			45.8812i			1.58399i	−0.610525	+	0.791997i	$0.709041\pi$
$840$	−16.0969	+	36.2953i	−0.555395	+	1.25231i
$841$	−8.56489			−0.295341
$842$	15.8968	+	39.2915i	0.547841	+	1.35407i
$843$		−	5.14672i		−	0.177263i
$844$	26.4736	+	27.3614i	0.911260	+	0.941819i
$845$		−	13.2366i		−	0.455351i
$846$	−1.61727	+	0.654326i	−0.0556029	+	0.0224962i
$847$	−152.677			−5.24603
$848$	0.493170	+	0.0162701i	0.0169355	+	0.000558718i
$849$			17.8958i			0.614182i
$850$	−6.94104	−	17.1559i	−0.238076	−	0.588441i
$851$			15.7329i			0.539318i
$852$	−21.8135	−	22.5450i	−0.747317	−	0.772378i
$853$	−13.7259			−0.469967			−0.234984	−	0.971999i	$-0.575504\pi$
$853$	−13.7259			−0.469967			−0.234984	+	0.971999i	$0.575504\pi$
$854$	30.6758	−	12.4110i	1.04971	−	0.424697i
$855$	13.6415			0.466528
$856$	−7.07195	+	15.9459i	−0.241714	+	0.545018i
$857$		−	20.8193i		−	0.711175i	−0.934643	−	0.355587i	$-0.884281\pi$
$857$		−	20.8193i		−	0.711175i	0.934643	−	0.355587i	$-0.115719\pi$
$858$	24.5888	−	9.94832i	0.839449	−	0.339630i
$859$		−	34.4614i		−	1.17581i	−0.808931	−	0.587903i	$-0.799954\pi$
$859$		−	34.4614i		−	1.17581i	0.808931	−	0.587903i	$-0.200046\pi$
$860$	17.2561	+	17.8348i	0.588430	+	0.608163i
$861$		−	35.5124i		−	1.21026i
$862$	28.5568	−	11.5537i	0.972649	−	0.393521i
$863$		−	19.3715i		−	0.659415i	−0.944083	−	0.329707i	$-0.893050\pi$
$863$		−	19.3715i		−	0.659415i	0.944083	−	0.329707i	$-0.106950\pi$
$864$	−5.31103	+	1.94756i	−0.180685	+	0.0662574i
$865$		−	38.1762i		−	1.29803i
$866$	9.56788	−	3.87104i	0.325130	−	0.131543i
$867$	−0.215286			−0.00731149
$868$	−5.59249	+	5.41103i	−0.189822	+	0.183662i
$869$	−4.72720			−0.160359
$870$	−16.9227	+	6.84670i	−0.573733	+	0.232125i
$871$	13.7426	+	19.2761i	0.465651	+	0.653144i
$872$	−8.63443	+	19.4690i	−0.292399	+	0.659302i
$873$			9.89044i			0.334741i
$874$	−15.8938	−	39.2841i	−0.537617	−	1.32880i
$875$			25.9138i			0.876048i
$876$	−2.65522	+	2.56907i	−0.0897117	+	0.0868008i
$877$	45.1084			1.52320			0.761601	−	0.648046i	$-0.224414\pi$
$877$	45.1084			1.52320			0.761601	+	0.648046i	$0.224414\pi$
$878$	−10.2560	+	4.14943i	−0.346122	+	0.140037i
$879$	12.5828			0.424409
$880$	−74.0336	−	2.44243i	−2.49567	−	0.0823344i
$881$	17.1631			0.578240			0.289120	−	0.957293i	$-0.406637\pi$
$881$	17.1631			0.578240			0.289120	+	0.957293i	$0.406637\pi$
$882$	9.10545	+	22.5056i	0.306597	+	0.757801i
$883$	23.7712			0.799964			0.399982	−	0.916523i	$-0.369016\pi$
$883$	23.7712			0.799964			0.399982	+	0.916523i	$0.369016\pi$
$884$	−16.6883	−	17.2480i	−0.561290	−	0.580113i
$885$	−7.65143			−0.257200
$886$	−13.1484	−	32.4983i	−0.441729	−	1.09180i
$887$		−	32.1414i		−	1.07920i	−0.841921	−	0.539600i	$-0.818575\pi$
$887$		−	32.1414i		−	1.07920i	0.841921	−	0.539600i	$-0.181425\pi$
$888$	6.48514	+	2.87614i	0.217627	+	0.0965171i
$889$		−	25.1642i		−	0.843979i
$890$	2.63884	−	1.06764i	0.0884541	−	0.0357874i
$891$	6.48515			0.217261
$892$	−24.6756	−	25.5031i	−0.826200	−	0.853906i
$893$	−5.89335			−0.197213
$894$	9.49786	+	23.4754i	0.317656	+	0.785136i
$895$		−	31.2626i		−	1.04499i
$896$	24.2126	−	50.0712i	0.808886	−	1.67276i
$897$	18.1412			0.605718
$898$	22.4674	+	55.5318i	0.749748	+	1.85312i
$899$	−3.57786			−0.119328
$900$	4.53335	−	4.38625i	0.151112	−	0.146208i
$901$			0.511835i			0.0170517i
$902$	61.4164	−	24.8483i	2.04494	−	0.827357i
$903$	21.3617			0.710873
$904$	21.1493	−	47.6875i	0.703414	−	1.58606i
$905$		−	28.2611i		−	0.939430i
$906$	−20.1876	+	8.16763i	−0.670687	+	0.271351i
$907$		−	3.16640i		−	0.105139i	−0.998617	−	0.0525693i	$-0.983259\pi$
$907$		−	3.16640i		−	0.105139i	0.998617	−	0.0525693i	$-0.0167411\pi$
$908$	22.0351	+	22.7740i	0.731260	+	0.755782i
$909$			15.2447i			0.505633i
$910$	−21.5341	−	53.2248i	−0.713847	−	1.76438i
$911$			43.1547i			1.42978i	0.699238	+	0.714889i	$0.253523\pi$
$911$			43.1547i			1.42978i	−0.699238	+	0.714889i	$0.746477\pi$
$912$	−19.0985	−	0.630077i	−0.632415	−	0.0208639i
$913$			90.1064i			2.98209i
$914$	7.23104	+	17.8726i	0.239181	+	0.591175i
$915$	−13.5917			−0.449328
$916$	−22.5663	−	23.3231i	−0.745613	−	0.770617i
$917$			22.8340i			0.754046i
$918$	−2.20072	−	5.43943i	−0.0726347	−	0.179528i
$919$	8.67211			0.286067			0.143033	−	0.989718i	$-0.454314\pi$
$919$	8.67211			0.286067			0.143033	+	0.989718i	$0.454314\pi$
$920$	−46.3109	−	20.5388i	−1.52683	−	0.677144i
$921$		−	8.63603i		−	0.284567i
$922$	−15.6096	−	38.5816i	−0.514075	−	1.27062i
$923$	45.3641			1.49318
$924$	−45.8237	+	44.3369i	−1.50749	+	1.45858i
$925$	−7.91088			−0.260108
$926$	6.24907	+	15.4456i	0.205357	+	0.507573i
$927$			14.6917i			0.482540i
$928$	24.0086	−	8.80399i	0.788121	−	0.289005i
$929$		−	2.36461i		−	0.0775804i	−0.999247	−	0.0387902i	$-0.987650\pi$
$929$		−	2.36461i		−	0.0775804i	0.999247	−	0.0387902i	$-0.0123504\pi$
$930$	2.96289	−	1.19875i	0.0971571	−	0.0393085i
$931$			82.0105i			2.68779i
$932$	7.52048	+	7.77268i	0.246341	+	0.254603i
$933$	12.4339			0.407067
$934$	42.4144	−	17.1603i	1.38784	−	0.561503i
$935$		−	76.8355i		−	2.51279i
$936$	3.31640	−	7.47784i	0.108400	−	0.244421i
$937$			14.4846i			0.473192i	0.971608	+	0.236596i	$0.0760318\pi$
$937$			14.4846i			0.473192i	−0.971608	+	0.236596i	$0.923968\pi$
$938$	−48.0022	−	30.5641i	−1.56733	−	0.997954i
$939$			2.51221i			0.0819828i
$940$	−5.06326	+	4.89898i	−0.165145	+	0.159787i
$941$		−	20.4179i		−	0.665605i	−0.942997	−	0.332803i	$-0.892006\pi$
$941$		−	20.4179i		−	0.665605i	0.942997	−	0.332803i	$-0.107994\pi$
$942$	0.112370	+	0.277740i	0.00366121	+	0.00904924i
$943$	45.3120			1.47556
$944$	10.7123	+	0.353407i	0.348655	+	0.0115024i
$945$		−	14.0377i		−	0.456646i
$946$	14.9470	+	36.9437i	0.485967	+	1.20114i
$947$		−	12.3163i		−	0.400226i	−0.979773	−	0.200113i	$-0.935869\pi$
$947$		−	12.3163i		−	0.400226i	0.979773	−	0.200113i	$-0.0641309\pi$
$948$	−1.04772	+	1.01372i	−0.0340282	+	0.0329241i
$949$		−	5.34273i		−	0.173432i
$950$	19.7529	−	7.99178i	0.640870	−	0.259288i
$951$	10.6688			0.345959
$952$	52.7378	+	23.3891i	1.70924	+	0.758045i
$953$	15.7894			0.511470			0.255735	−	0.966747i	$-0.417683\pi$
$953$	15.7894			0.511470			0.255735	+	0.966747i	$0.417683\pi$
$954$	−0.161722	+	0.0654306i	−0.00523595	+	0.00211839i
$955$		−	45.3820i		−	1.46853i
$956$	−35.0408	+	33.9038i	−1.13330	+	1.09653i
$957$	−29.3163			−0.947660
$958$	31.2868	−	12.6582i	1.01083	−	0.408969i
$959$		−	26.3590i		−	0.851178i
$960$	−16.9322	+	15.3347i	−0.546486	+	0.494927i
$961$	−30.3736			−0.979793
$962$	−9.51006	+	3.84765i	−0.306617	+	0.124053i
$963$		−	6.16728i		−	0.198738i
$964$	25.5018	−	24.6744i	0.821359	−	0.794709i
$965$			53.9589i			1.73700i
$966$	−40.4252	+	16.3555i	−1.30066	+	0.526229i
$967$			53.6220i			1.72437i	0.506596	+	0.862184i	$0.330904\pi$
$967$			53.6220i			1.72437i	−0.506596	+	0.862184i	$0.669096\pi$
$968$	−80.3001	−	35.6129i	−2.58094	−	1.14464i
$969$		−	19.8213i		−	0.636753i
$970$	14.9799	+	37.0251i	0.480975	+	1.18881i
$971$		−	39.4081i		−	1.26467i	−0.774696	−	0.632334i	$-0.782097\pi$
$971$		−	39.4081i		−	1.26467i	0.774696	−	0.632334i	$-0.217903\pi$
$972$	1.43734	−	1.39070i	0.0461027	−	0.0446068i
$973$	72.9270			2.33793
$974$	−7.37271	−	18.2228i	−0.236237	−	0.583897i
$975$			9.12181i			0.292132i
$976$	19.0289	+	0.627779i	0.609099	+	0.0200947i
$977$	−30.8985			−0.988529			−0.494265	−	0.869312i	$-0.664563\pi$
$977$	−30.8985			−0.988529			−0.494265	+	0.869312i	$0.664563\pi$
$978$	−19.1060	+	7.73002i	−0.610941	+	0.247179i
$979$	4.57143			0.146103
$980$	68.1730	+	70.4592i	2.17771	+	2.25074i
$981$		−	7.52989i		−	0.240411i
$982$	−16.8462	+	6.81573i	−0.537582	+	0.217499i
$983$	6.34031			0.202224			0.101112	−	0.994875i	$-0.467760\pi$
$983$	6.34031			0.202224			0.101112	+	0.994875i	$0.467760\pi$
$984$	8.28350	−	18.6777i	0.264068	−	0.595422i
$985$	16.2091			0.516466
$986$	9.94841	+	24.5891i	0.316822	+	0.783075i
$987$			6.06453i			0.193036i
$988$	19.8590	−	19.2146i	0.631799	−	0.611299i
$989$			27.2564i			0.866705i
$990$	24.2773	−	9.82230i	0.771585	−	0.312173i
$991$	47.6876			1.51485			0.757424	−	0.652924i	$-0.226458\pi$
$991$	47.6876			1.51485			0.757424	+	0.652924i	$0.226458\pi$
$992$	−4.20352	+	1.54144i	−0.133462	+	0.0489407i
$993$	5.92505			0.188026
$994$	−101.088	+	40.8987i	−3.20630	+	1.29723i
$995$	21.0848			0.668432
$996$	19.3228	+	19.9708i	0.612266	+	0.632798i
$997$	−11.3226			−0.358591			−0.179296	−	0.983795i	$-0.557382\pi$
$997$	−11.3226			−0.358591			−0.179296	+	0.983795i	$0.557382\pi$
$998$	−1.38846	−	3.43181i	−0.0439511	−	0.108632i
$999$	−2.50822			−0.0793565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.a.535.22	yes	34
4.3	odd	2		804.2.e.b.535.14	yes	34
67.66	odd	2		804.2.e.b.535.13	yes	34
268.267	even	2	inner	804.2.e.a.535.21	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.21	✓	34	268.267	even	2	inner
804.2.e.a.535.22	yes	34	1.1	even	1	trivial
804.2.e.b.535.13	yes	34	67.66	odd	2
804.2.e.b.535.14	yes	34	4.3	odd	2

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.530406 + 1.31098i) q^{2} -1.00000 q^{3} +(-1.43734 + 1.39070i) q^{4} -2.85552i q^{5} +(-0.530406 - 1.31098i) q^{6} -4.91599 q^{7} +(-2.58556 - 1.14669i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.530406 + 1.31098i) q^{2} -1.00000 q^{3} +(-1.43734 + 1.39070i) q^{4} -2.85552i q^{5} +(-0.530406 - 1.31098i) q^{6} -4.91599 q^{7} +(-2.58556 - 1.14669i) q^{8} +1.00000 q^{9} +(3.74353 - 1.51458i) q^{10} +6.48515 q^{11} +(1.43734 - 1.39070i) q^{12} +2.89216i q^{13} +(-2.60747 - 6.44477i) q^{14} +2.85552i q^{15} +(0.131892 - 3.99782i) q^{16} +4.14913 q^{17} +(0.530406 + 1.31098i) q^{18} +4.77723i q^{19} +(3.97118 + 4.10435i) q^{20} +4.91599 q^{21} +(3.43976 + 8.50190i) q^{22} +6.27256i q^{23} +(2.58556 + 1.14669i) q^{24} -3.15398 q^{25} +(-3.79156 + 1.53402i) q^{26} -1.00000 q^{27} +(7.06595 - 6.83668i) q^{28} +4.52052 q^{29} +(-3.74353 + 1.51458i) q^{30} -0.791471 q^{31} +(5.31103 - 1.94756i) q^{32} -6.48515 q^{33} +(2.20072 + 5.43943i) q^{34} +14.0377i q^{35} +(-1.43734 + 1.39070i) q^{36} +2.50822 q^{37} +(-6.26285 + 2.53387i) q^{38} -2.89216i q^{39} +(-3.27439 + 7.38311i) q^{40} -7.22384i q^{41} +(2.60747 + 6.44477i) q^{42} +4.34535 q^{43} +(-9.32136 + 9.01892i) q^{44} -2.85552i q^{45} +(-8.22320 + 3.32700i) q^{46} +1.23363i q^{47} +(-0.131892 + 3.99782i) q^{48} +17.1670 q^{49} +(-1.67289 - 4.13481i) q^{50} -4.14913 q^{51} +(-4.02213 - 4.15701i) q^{52} +0.123360i q^{53} +(-0.530406 - 1.31098i) q^{54} -18.5185i q^{55} +(12.7106 + 5.63711i) q^{56} -4.77723i q^{57} +(2.39771 + 5.92632i) q^{58} +2.67952i q^{59} +(-3.97118 - 4.10435i) q^{60} +4.75980i q^{61} +(-0.419800 - 1.03760i) q^{62} -4.91599 q^{63} +(5.37021 + 5.92966i) q^{64} +8.25860 q^{65} +(-3.43976 - 8.50190i) q^{66} +(6.66494 - 4.75169i) q^{67} +(-5.96371 + 5.77021i) q^{68} -6.27256i q^{69} +(-18.4032 + 7.44567i) q^{70} -15.6852i q^{71} +(-2.58556 - 1.14669i) q^{72} -1.84732 q^{73} +(1.33037 + 3.28823i) q^{74} +3.15398 q^{75} +(-6.64371 - 6.86650i) q^{76} -31.8809 q^{77} +(3.79156 - 1.53402i) q^{78} -0.728927 q^{79} +(-11.4159 - 0.376619i) q^{80} +1.00000 q^{81} +(9.47032 - 3.83157i) q^{82} +13.8943i q^{83} +(-7.06595 + 6.83668i) q^{84} -11.8479i q^{85} +(2.30480 + 5.69667i) q^{86} -4.52052 q^{87} +(-16.7677 - 7.43644i) q^{88} +0.704907 q^{89} +(3.74353 - 1.51458i) q^{90} -14.2178i q^{91} +(-8.72326 - 9.01580i) q^{92} +0.791471 q^{93} +(-1.61727 + 0.654326i) q^{94} +13.6415 q^{95} +(-5.31103 + 1.94756i) q^{96} +9.89044i q^{97} +(9.10545 + 22.5056i) q^{98} +6.48515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

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