LMFDB - Embedded newform 847.2.n.h.81.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.5
Character	$\chi$	$=$	847.81
Dual form			847.2.n.h.366.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.275074 - 2.61716i) q^{2} +(-1.48109 - 1.64492i) q^{3} +(-4.81754 - 1.02400i) q^{4} +(-1.07466 - 0.478467i) q^{5} +(-4.71241 + 3.42377i) q^{6} +(-2.62673 - 0.316648i) q^{7} +(-2.37875 + 7.32103i) q^{8} +(-0.198538 + 1.88897i) q^{9} +O(q^{10})$	\(q+(0.275074 - 2.61716i) q^{2} +(-1.48109 - 1.64492i) q^{3} +(-4.81754 - 1.02400i) q^{4} +(-1.07466 - 0.478467i) q^{5} +(-4.71241 + 3.42377i) q^{6} +(-2.62673 - 0.316648i) q^{7} +(-2.37875 + 7.32103i) q^{8} +(-0.198538 + 1.88897i) q^{9} +(-1.54783 + 2.68093i) q^{10} +(5.45081 + 9.44109i) q^{12} +(0.0294854 + 0.0214224i) q^{13} +(-1.55126 + 6.78747i) q^{14} +(0.804622 + 2.47637i) q^{15} +(9.50722 + 4.23289i) q^{16} +(-0.636436 - 6.05528i) q^{17} +(4.88911 + 1.03921i) q^{18} +(1.88405 - 0.400466i) q^{19} +(4.68725 + 3.40548i) q^{20} +(3.36957 + 4.78974i) q^{21} +(-1.02155 - 1.76938i) q^{23} +(15.5656 - 6.93026i) q^{24} +(-2.41970 - 2.68735i) q^{25} +(0.0641765 - 0.0712752i) q^{26} +(-1.97092 + 1.43196i) q^{27} +(12.3302 + 4.21524i) q^{28} +(1.53843 + 4.73482i) q^{29} +(6.70238 - 1.42463i) q^{30} +(2.58732 - 1.15195i) q^{31} +(5.99553 - 10.3846i) q^{32} -16.0227 q^{34} +(2.67133 + 1.59709i) q^{35} +(2.89077 - 8.89688i) q^{36} +(-1.78148 + 1.97854i) q^{37} +(-0.529830 - 5.04100i) q^{38} +(-0.00843247 - 0.0802296i) q^{39} +(6.05921 - 6.72944i) q^{40} +(2.52670 - 7.77639i) q^{41} +(13.4624 - 7.50115i) q^{42} +2.96835 q^{43} +(1.11717 - 1.93499i) q^{45} +(-4.91174 + 2.18685i) q^{46} +(-3.12419 + 0.664066i) q^{47} +(-7.11830 - 21.9079i) q^{48} +(6.79947 + 1.66350i) q^{49} +(-7.69881 + 5.59351i) q^{50} +(-9.01781 + 10.0153i) q^{51} +(-0.120111 - 0.133397i) q^{52} +(-9.05672 + 4.03231i) q^{53} +(3.20550 + 5.55209i) q^{54} +(8.56653 - 18.4772i) q^{56} +(-3.44917 - 2.50597i) q^{57} +(12.8149 - 2.72390i) q^{58} +(-3.97101 - 0.844065i) q^{59} +(-1.34049 - 12.7540i) q^{60} +(7.92827 + 3.52989i) q^{61} +(-2.30312 - 7.08829i) q^{62} +(1.11965 - 4.89895i) q^{63} +(-8.68998 - 6.31364i) q^{64} +(-0.0214368 - 0.0371295i) q^{65} +(-1.12669 + 1.95148i) q^{67} +(-3.13455 + 29.8233i) q^{68} +(-1.39747 + 4.30097i) q^{69} +(4.91466 - 6.55196i) q^{70} +(-3.43968 + 2.49907i) q^{71} +(-13.3569 - 5.94688i) q^{72} +(4.19875 + 0.892472i) q^{73} +(4.68811 + 5.20667i) q^{74} +(-0.836672 + 7.96040i) q^{75} -9.48655 q^{76} -0.212293 q^{78} +(-0.324478 + 3.08720i) q^{79} +(-8.19169 - 9.09779i) q^{80} +(10.8481 + 2.30584i) q^{81} +(-19.6570 - 8.75186i) q^{82} +(4.91092 - 3.56800i) q^{83} +(-11.3283 - 26.5252i) q^{84} +(-2.21331 + 6.81186i) q^{85} +(0.816517 - 7.76864i) q^{86} +(5.50981 - 9.54328i) q^{87} +(-2.16161 - 3.74402i) q^{89} +(-4.75688 - 3.45607i) q^{90} +(-0.0706670 - 0.0656075i) q^{91} +(3.10952 + 9.57012i) q^{92} +(-5.72691 - 2.54978i) q^{93} +(0.878582 + 8.35915i) q^{94} +(-2.21631 - 0.471091i) q^{95} +(-25.9616 + 5.51831i) q^{96} +(-3.75055 - 2.72494i) q^{97} +(6.22400 - 17.3377i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9} - 14 q^{10} - 18 q^{12} + 4 q^{13} + 22 q^{14} + 16 q^{15} + 20 q^{16} + 12 q^{17} + 41 q^{18} + 24 q^{19} + 40 q^{20} + 2 q^{21} - 14 q^{23} + 7 q^{24} - 29 q^{25} - 5 q^{26} + 4 q^{27} + 24 q^{28} + 30 q^{29} - 6 q^{30} + 3 q^{31} + 30 q^{32} + 48 q^{34} - 6 q^{35} - 46 q^{36} - 11 q^{37} + 12 q^{38} + 32 q^{39} + 20 q^{40} - 10 q^{41} + 45 q^{42} + 72 q^{43} - 16 q^{45} + 17 q^{46} + 3 q^{47} - 62 q^{48} + 35 q^{49} - 6 q^{50} - 28 q^{51} - 2 q^{52} - 42 q^{53} - 34 q^{54} + 24 q^{56} + 36 q^{57} + 8 q^{58} - 9 q^{59} + 27 q^{60} + 20 q^{61} - 128 q^{62} + 36 q^{63} - 36 q^{64} + 40 q^{65} - 38 q^{67} + 33 q^{68} + 106 q^{69} - 18 q^{70} - 50 q^{71} - 42 q^{72} + 14 q^{73} + q^{74} - 16 q^{75} + 96 q^{76} - 100 q^{78} - 11 q^{79} - 18 q^{80} + 12 q^{81} - 24 q^{82} - 104 q^{83} + 44 q^{84} - 32 q^{85} + 2 q^{86} - 48 q^{87} - 10 q^{89} - 42 q^{90} - 14 q^{91} + 80 q^{92} - 13 q^{93} + 18 q^{94} + 8 q^{95} - 7 q^{96} + 46 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9 - 14 * q^10 - 18 * q^12 + 4 * q^13 + 22 * q^14 + 16 * q^15 + 20 * q^16 + 12 * q^17 + 41 * q^18 + 24 * q^19 + 40 * q^20 + 2 * q^21 - 14 * q^23 + 7 * q^24 - 29 * q^25 - 5 * q^26 + 4 * q^27 + 24 * q^28 + 30 * q^29 - 6 * q^30 + 3 * q^31 + 30 * q^32 + 48 * q^34 - 6 * q^35 - 46 * q^36 - 11 * q^37 + 12 * q^38 + 32 * q^39 + 20 * q^40 - 10 * q^41 + 45 * q^42 + 72 * q^43 - 16 * q^45 + 17 * q^46 + 3 * q^47 - 62 * q^48 + 35 * q^49 - 6 * q^50 - 28 * q^51 - 2 * q^52 - 42 * q^53 - 34 * q^54 + 24 * q^56 + 36 * q^57 + 8 * q^58 - 9 * q^59 + 27 * q^60 + 20 * q^61 - 128 * q^62 + 36 * q^63 - 36 * q^64 + 40 * q^65 - 38 * q^67 + 33 * q^68 + 106 * q^69 - 18 * q^70 - 50 * q^71 - 42 * q^72 + 14 * q^73 + q^74 - 16 * q^75 + 96 * q^76 - 100 * q^78 - 11 * q^79 - 18 * q^80 + 12 * q^81 - 24 * q^82 - 104 * q^83 + 44 * q^84 - 32 * q^85 + 2 * q^86 - 48 * q^87 - 10 * q^89 - 42 * q^90 - 14 * q^91 + 80 * q^92 - 13 * q^93 + 18 * q^94 + 8 * q^95 - 7 * q^96 + 46 * q^97 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.275074	−	2.61716i	0.194507	−	1.85061i	−0.267282	−	0.963618i	$-0.586125\pi$
$2$	0.275074	−	2.61716i	0.194507	−	1.85061i	0.461789	−	0.886990i	$-0.347208\pi$
$3$	−1.48109	−	1.64492i	−0.855107	−	0.949693i	0.144098	−	0.989563i	$-0.453972\pi$
$3$	−1.48109	−	1.64492i	−0.855107	−	0.949693i	−0.999205	+	0.0398709i	$0.987305\pi$
$4$	−4.81754	−	1.02400i	−2.40877	−	0.512000i
$5$	−1.07466	−	0.478467i	−0.480601	−	0.213977i	0.152113	−	0.988363i	$-0.451392\pi$
$5$	−1.07466	−	0.478467i	−0.480601	−	0.213977i	−0.632713	+	0.774386i	$0.718059\pi$
$6$	−4.71241	+	3.42377i	−1.92383	+	1.39775i
$7$	−2.62673	−	0.316648i	−0.992812	−	0.119682i
$7$	−2.62673	−	0.316648i	−0.992812	−	0.119682i
$8$	−2.37875	+	7.32103i	−0.841014	+	2.58838i
$9$	−0.198538	+	1.88897i	−0.0661795	+	0.629656i
$10$	−1.54783	+	2.68093i	−0.489468	+	0.847783i
$11$		0			0
$11$		0			0
$12$	5.45081	+	9.44109i	1.57351	+	2.72541i
$13$	0.0294854	+	0.0214224i	0.00817779	+	0.00594151i	0.591867	−	0.806036i	$-0.298391\pi$
$13$	0.0294854	+	0.0214224i	0.00817779	+	0.00594151i	−0.583689	+	0.811977i	$0.698391\pi$
$14$	−1.55126	+	6.78747i	−0.414593	+	1.81403i
$15$	0.804622	+	2.47637i	0.207752	+	0.639396i
$16$	9.50722	+	4.23289i	2.37681	+	1.05822i
$17$	−0.636436	−	6.05528i	−0.154358	−	1.46862i	−0.747896	−	0.663816i	$-0.768936\pi$
$17$	−0.636436	−	6.05528i	−0.154358	−	1.46862i	0.593538	−	0.804806i	$-0.297731\pi$
$18$	4.88911	+	1.03921i	1.15237	+	0.244945i
$19$	1.88405	−	0.400466i	0.432230	−	0.0918733i	0.0133413	−	0.999911i	$-0.495753\pi$
$19$	1.88405	−	0.400466i	0.432230	−	0.0918733i	0.418888	+	0.908038i	$0.362420\pi$
$20$	4.68725	+	3.40548i	1.04810	+	0.761489i
$21$	3.36957	+	4.78974i	0.735300	+	1.04521i
$22$		0			0
$23$	−1.02155	−	1.76938i	−0.213008	−	0.368941i	0.739647	−	0.672996i	$-0.234993\pi$
$23$	−1.02155	−	1.76938i	−0.213008	−	0.368941i	−0.952655	+	0.304055i	$0.901659\pi$
$24$	15.5656	−	6.93026i	3.17732	−	1.41463i
$25$	−2.41970	−	2.68735i	−0.483940	−	0.537470i
$26$	0.0641765	−	0.0712752i	0.0125860	−	0.0139782i
$27$	−1.97092	+	1.43196i	−0.379303	+	0.275580i
$28$	12.3302	+	4.21524i	2.33018	+	0.796606i
$29$	1.53843	+	4.73482i	0.285680	+	0.879233i	0.986194	+	0.165594i	$0.0529542\pi$
$29$	1.53843	+	4.73482i	0.285680	+	0.879233i	−0.700514	+	0.713639i	$0.747046\pi$
$30$	6.70238	−	1.42463i	1.22368	−	0.260101i
$31$	2.58732	−	1.15195i	0.464696	−	0.206896i	−0.161013	−	0.986952i	$-0.551476\pi$
$31$	2.58732	−	1.15195i	0.464696	−	0.206896i	0.625710	+	0.780056i	$0.284810\pi$
$32$	5.99553	−	10.3846i	1.05987	−	1.83575i
$33$		0			0
$34$	−16.0227			−2.74787
$35$	2.67133	+	1.59709i	0.451537	+	0.269958i
$36$	2.89077	−	8.89688i	0.481795	−	1.48281i
$37$	−1.78148	+	1.97854i	−0.292874	+	0.325270i	−0.871568	−	0.490275i	$-0.836896\pi$
$37$	−1.78148	+	1.97854i	−0.292874	+	0.325270i	0.578693	+	0.815545i	$0.303563\pi$
$38$	−0.529830	−	5.04100i	−0.0859498	−	0.817758i
$39$	−0.00843247	−	0.0802296i	−0.00135028	−	0.0128470i
$40$	6.05921	−	6.72944i	0.958045	−	1.06402i
$41$	2.52670	−	7.77639i	0.394605	−	1.21447i	−0.534664	−	0.845065i	$-0.679562\pi$
$41$	2.52670	−	7.77639i	0.394605	−	1.21447i	0.929269	−	0.369404i	$-0.120438\pi$
$42$	13.4624	−	7.50115i	2.07729	−	1.15745i
$43$	2.96835			0.452669			0.226335	−	0.974050i	$-0.427326\pi$
$43$	2.96835			0.452669			0.226335	+	0.974050i	$0.427326\pi$
$44$		0			0
$45$	1.11717	−	1.93499i	0.166538	−	0.288452i
$46$	−4.91174	+	2.18685i	−0.724196	+	0.322433i
$47$	−3.12419	+	0.664066i	−0.455710	+	0.0968640i	−0.430047	−	0.902807i	$-0.641503\pi$
$47$	−3.12419	+	0.664066i	−0.455710	+	0.0968640i	−0.0256627	+	0.999671i	$0.508170\pi$
$48$	−7.11830	−	21.9079i	−1.02744	−	3.16213i
$49$	6.79947	+	1.66350i	0.971353	+	0.237643i
$50$	−7.69881	+	5.59351i	−1.08878	+	0.791042i
$51$	−9.01781	+	10.0153i	−1.26275	+	1.40242i
$52$	−0.120111	−	0.133397i	−0.0166564	−	0.0184988i
$53$	−9.05672	+	4.03231i	−1.24404	+	0.553881i	−0.919909	−	0.392133i	$-0.871737\pi$
$53$	−9.05672	+	4.03231i	−1.24404	+	0.553881i	−0.324128	+	0.946013i	$0.605071\pi$
$54$	3.20550	+	5.55209i	0.436213	+	0.755544i
$55$		0			0
$56$	8.56653	−	18.4772i	1.14475	−	2.46912i
$57$	−3.44917	−	2.50597i	−0.456854	−	0.331924i
$58$	12.8149	−	2.72390i	1.68268	−	0.357665i
$59$	−3.97101	−	0.844065i	−0.516982	−	0.109888i	−0.0579704	−	0.998318i	$-0.518463\pi$
$59$	−3.97101	−	0.844065i	−0.516982	−	0.109888i	−0.459011	+	0.888430i	$0.651796\pi$
$60$	−1.34049	−	12.7540i	−0.173057	−	1.64653i
$61$	7.92827	+	3.52989i	1.01511	+	0.451956i	0.845739	−	0.533596i	$-0.179160\pi$
$61$	7.92827	+	3.52989i	1.01511	+	0.451956i	0.169371	+	0.985552i	$0.445826\pi$
$62$	−2.30312	−	7.08829i	−0.292497	−	0.900214i
$63$	1.11965	−	4.89895i	0.141062	−	0.617209i
$64$	−8.68998	−	6.31364i	−1.08625	−	0.789205i
$65$	−0.0214368	−	0.0371295i	−0.00265890	−	0.00460535i
$66$		0			0
$67$	−1.12669	+	1.95148i	−0.137647	+	0.238411i	−0.926605	−	0.376035i	$-0.877287\pi$
$67$	−1.12669	+	1.95148i	−0.137647	+	0.238411i	0.788959	+	0.614446i	$0.210621\pi$
$68$	−3.13455	+	29.8233i	−0.380121	+	3.61661i
$69$	−1.39747	+	4.30097i	−0.168236	+	0.517776i
$70$	4.91466	−	6.55196i	0.587414	−	0.783109i
$71$	−3.43968	+	2.49907i	−0.408215	+	0.296586i	−0.772879	−	0.634554i	$-0.781184\pi$
$71$	−3.43968	+	2.49907i	−0.408215	+	0.296586i	0.364664	+	0.931139i	$0.381184\pi$
$72$	−13.3569	−	5.94688i	−1.57413	−	0.700847i
$73$	4.19875	+	0.892472i	0.491427	+	0.104456i	0.446958	−	0.894555i	$-0.352507\pi$
$73$	4.19875	+	0.892472i	0.491427	+	0.104456i	0.0444685	+	0.999011i	$0.485841\pi$
$74$	4.68811	+	5.20667i	0.544981	+	0.605263i
$75$	−0.836672	+	7.96040i	−0.0966106	+	0.919188i
$76$	−9.48655			−1.08818
$77$		0			0
$78$	−0.212293			−0.0240374
$79$	−0.324478	+	3.08720i	−0.0365067	+	0.347338i	0.960988	+	0.276591i	$0.0892048\pi$
$79$	−0.324478	+	3.08720i	−0.0365067	+	0.347338i	−0.997494	+	0.0707465i	$0.977462\pi$
$80$	−8.19169	−	9.09779i	−0.915859	−	1.01716i
$81$	10.8481	+	2.30584i	1.20535	+	0.256205i
$82$	−19.6570	−	8.75186i	−2.17075	−	0.966481i
$83$	4.91092	−	3.56800i	0.539044	−	0.391638i	−0.284686	−	0.958621i	$-0.591889\pi$
$83$	4.91092	−	3.56800i	0.539044	−	0.391638i	0.823730	+	0.566983i	$0.191889\pi$
$84$	−11.3283	−	26.5252i	−1.23602	−	2.89414i
$85$	−2.21331	+	6.81186i	−0.240067	+	0.738850i
$86$	0.816517	−	7.76864i	0.0880473	−	0.837714i
$87$	5.50981	−	9.54328i	0.590714	−	1.02315i
$88$		0			0
$89$	−2.16161	−	3.74402i	−0.229130	−	0.396866i	0.728420	−	0.685131i	$-0.240255\pi$
$89$	−2.16161	−	3.74402i	−0.229130	−	0.396866i	−0.957551	+	0.288265i	$0.906922\pi$
$90$	−4.75688	−	3.45607i	−0.501419	−	0.364302i
$91$	−0.0706670	−	0.0656075i	−0.00740792	−	0.00687754i
$92$	3.10952	+	9.57012i	0.324190	+	0.997754i
$93$	−5.72691	−	2.54978i	−0.593853	−	0.264400i
$94$	0.878582	+	8.35915i	0.0906188	+	0.862181i
$95$	−2.21631	−	0.471091i	−0.227389	−	0.0483329i
$96$	−25.9616	+	5.51831i	−2.64970	+	0.563211i
$97$	−3.75055	−	2.72494i	−0.380811	−	0.276675i	0.380869	−	0.924629i	$-0.375625\pi$
$97$	−3.75055	−	2.72494i	−0.380811	−	0.276675i	−0.761680	+	0.647954i	$0.775625\pi$
$98$	6.22400	−	17.3377i	0.628719	−	1.75137i
$99$		0			0
$100$	8.90516	+	15.4242i	0.890516	+	1.54242i
$101$	15.5407	−	6.91918i	1.54636	−	0.688484i	0.556542	−	0.830819i	$-0.312128\pi$
$101$	15.5407	−	6.91918i	1.54636	−	0.688484i	0.989819	+	0.142335i	$0.0454611\pi$
$102$	23.7310	+	26.3560i	2.34972	+	2.60963i
$103$	−11.2761	+	12.5234i	−1.11107	+	1.23396i	−0.141290	+	0.989968i	$0.545125\pi$
$103$	−11.2761	+	12.5234i	−1.11107	+	1.23396i	−0.969776	+	0.243995i	$0.921542\pi$
$104$	−0.226973	+	0.164905i	−0.0222565	+	0.0161703i
$105$	−1.32939	−	6.75955i	−0.129735	−	0.659664i
$106$	8.06192	+	24.8120i	0.783043	+	2.40996i
$107$	−0.912252	+	0.193905i	−0.0881907	+	0.0187455i	−0.251796	−	0.967780i	$-0.581021\pi$
$107$	−0.912252	+	0.193905i	−0.0881907	+	0.0187455i	0.163605	+	0.986526i	$0.447688\pi$
$108$	10.9613	−	4.88028i	1.05475	−	0.469606i
$109$	0.811795	−	1.40607i	0.0777558	−	0.134677i	−0.824526	−	0.565825i	$-0.808558\pi$
$109$	0.811795	−	1.40607i	0.0777558	−	0.134677i	0.902281	+	0.431148i	$0.141891\pi$
$110$		0			0
$111$	5.89307			0.559345
$112$	−23.6326	−	14.1291i	−2.23307	−	1.33508i
$113$	1.09361	−	3.36578i	0.102878	−	0.316626i	−0.886348	−	0.463019i	$-0.846766\pi$
$113$	1.09361	−	3.36578i	0.102878	−	0.316626i	0.989227	+	0.146392i	$0.0467662\pi$
$114$	−7.50729	+	8.33769i	−0.703122	+	0.780896i
$115$	0.251225	+	2.39025i	0.0234269	+	0.222892i
$116$	−2.56302	−	24.3855i	−0.237971	−	2.26414i
$117$	−0.0463203	+	0.0514439i	−0.00428231	+	0.00475599i
$118$	−3.30137	+	10.1606i	−0.303916	+	0.935357i
$119$	−0.245646	+	16.1071i	−0.0225183	+	1.47654i
$120$	−20.0436			−1.82972
$121$		0			0
$122$	11.4191	−	19.7785i	1.03384	−	1.79066i
$123$	−16.5338	+	7.36131i	−1.49080	+	0.663747i
$124$	−13.6441	+	2.90015i	−1.22528	+	0.260441i
$125$	3.13211	+	9.63963i	0.280144	+	0.862195i
$126$	−12.5133	−	4.27786i	−1.11478	−	0.381102i
$127$	−15.9472	+	11.5864i	−1.41509	+	1.02812i	−0.422532	+	0.906348i	$0.638858\pi$
$127$	−15.9472	+	11.5864i	−1.41509	+	1.02812i	−0.992558	+	0.121774i	$0.961142\pi$
$128$	−2.86701	+	3.18414i	−0.253411	+	0.281441i
$129$	−4.39639	−	4.88269i	−0.387081	−	0.429897i
$130$	−0.103070	+	0.0458899i	−0.00903988	+	0.00402481i
$131$	−8.09187	−	14.0155i	−0.706990	−	1.22454i	−0.965969	−	0.258659i	$-0.916719\pi$
$131$	−8.09187	−	14.0155i	−0.706990	−	1.22454i	0.258979	−	0.965883i	$-0.416614\pi$
$132$		0			0
$133$	−5.07569	+	0.455339i	−0.440119	+	0.0394829i
$134$	4.79740	+	3.48551i	0.414432	+	0.301103i
$135$	2.80320	−	0.595839i	0.241261	−	0.0512816i
$136$	45.8449	+	9.74463i	3.93116	+	0.835595i
$137$	1.77451	+	16.8834i	0.151607	+	1.44244i	0.760576	+	0.649249i	$0.224917\pi$
$137$	1.77451	+	16.8834i	0.151607	+	1.44244i	−0.608969	+	0.793194i	$0.708417\pi$
$138$	10.8719	+	4.84048i	0.925477	+	0.412049i
$139$	2.27033	+	6.98735i	0.192567	+	0.592659i	0.999996	+	0.00269552i	$0.000858011\pi$
$139$	2.27033	+	6.98735i	0.192567	+	0.592659i	−0.807430	+	0.589964i	$0.799142\pi$
$140$	−11.2338	−	10.4295i	−0.949430	−	0.881455i
$141$	5.71953	+	4.15548i	0.481671	+	0.349955i
$142$	5.59430	+	9.68961i	0.469463	+	0.813134i
$143$		0			0
$144$	−9.88334	+	17.1184i	−0.823611	+	1.42654i
$145$	0.612168	−	5.82439i	0.0508378	−	0.483689i
$146$	3.49071	−	10.7433i	0.288893	−	0.889121i
$147$	−7.33430	−	13.6483i	−0.604923	−	1.12570i
$148$	10.6084	−	7.70746i	0.872005	−	0.633549i
$149$	4.58685	+	2.04220i	0.375770	+	0.167303i	0.585926	−	0.810364i	$-0.300731\pi$
$149$	4.58685	+	2.04220i	0.375770	+	0.167303i	−0.210157	+	0.977668i	$0.567397\pi$
$150$	20.6035	+	4.37940i	1.68227	+	0.357577i
$151$	−5.61931	−	6.24088i	−0.457293	−	0.507875i	0.469766	−	0.882791i	$-0.344338\pi$
$151$	−5.61931	−	6.24088i	−0.457293	−	0.507875i	−0.927059	+	0.374916i	$0.877672\pi$
$152$	−1.54984	+	14.7458i	−0.125709	+	1.19604i
$153$	11.5646			0.934942
$154$		0			0
$155$	−3.33165			−0.267604
$156$	−0.0415313	+	0.395144i	−0.00332517	+	0.0316369i
$157$	−10.0013	−	11.1076i	−0.798191	−	0.886481i	0.197396	−	0.980324i	$-0.436752\pi$
$157$	−10.0013	−	11.1076i	−0.798191	−	0.886481i	−0.995587	+	0.0938428i	$0.970085\pi$
$158$	7.99044	+	1.69842i	0.635685	+	0.135119i
$159$	20.0466	+	8.92533i	1.58980	+	0.707825i
$160$	−11.4118	+	8.29115i	−0.902182	+	0.655473i
$161$	2.12307	+	4.97116i	0.167321	+	0.391782i
$162$	9.01880	−	27.7570i	0.708584	−	2.18080i
$163$	−0.260132	+	2.47499i	−0.0203751	+	0.193856i	−0.999975	−	0.00710270i	$-0.997739\pi$
$163$	−0.260132	+	2.47499i	−0.0203751	+	0.193856i	0.979600	+	0.200959i	$0.0644058\pi$
$164$	−20.1355	+	34.8758i	−1.57232	+	2.72334i
$165$		0			0
$166$	−7.98713	−	13.8341i	−0.619921	−	1.07374i
$167$	−9.95537	−	7.23300i	−0.770370	−	0.559706i	0.131704	−	0.991289i	$-0.457955\pi$
$167$	−9.95537	−	7.23300i	−0.770370	−	0.559706i	−0.902073	+	0.431583i	$0.857955\pi$
$168$	−43.0812	+	13.2751i	−3.32379	+	1.02420i
$169$	−4.01681	−	12.3625i	−0.308985	−	0.950959i
$170$	17.2189	+	7.66633i	1.32063	+	0.587981i
$171$	0.382412	+	3.63841i	0.0292438	+	0.278236i
$172$	−14.3002	−	3.03959i	−1.09038	−	0.231767i
$173$	11.9383	−	2.53757i	0.907654	−	0.192928i	0.269648	−	0.962959i	$-0.413093\pi$
$173$	11.9383	−	2.53757i	0.907654	−	0.192928i	0.638006	+	0.770031i	$0.279759\pi$
$174$	−23.4606	−	17.0451i	−1.77855	−	1.29219i
$175$	5.50497	+	7.82515i	0.416136	+	0.591525i
$176$		0			0
$177$	4.49301	+	7.78211i	0.337715	+	0.584940i
$178$	−10.3933	+	4.62739i	−0.779010	+	0.346838i
$179$	2.55201	+	2.83430i	0.190746	+	0.211845i	0.830931	−	0.556376i	$-0.187809\pi$
$179$	2.55201	+	2.83430i	0.190746	+	0.211845i	−0.640184	+	0.768221i	$0.721142\pi$
$180$	−7.36345	+	8.17794i	−0.548839	+	0.609547i
$181$	−5.69860	+	4.14027i	−0.423574	+	0.307744i	−0.779074	−	0.626932i	$-0.784310\pi$
$181$	−5.69860	+	4.14027i	−0.423574	+	0.307744i	0.355501	+	0.934676i	$0.384310\pi$
$182$	−0.191144	+	0.166900i	−0.0141685	+	0.0123714i
$183$	−5.93609	−	18.2694i	−0.438809	−	1.35051i
$184$	15.3837	−	3.26990i	1.13410	−	0.241060i
$185$	2.86115	−	1.27387i	0.210356	−	0.0936565i
$186$	−8.24851	+	14.2868i	−0.604810	+	1.04756i
$187$		0			0
$188$	15.7309			1.14729
$189$	5.63050	−	3.13728i	0.409559	−	0.228203i
$190$	−1.84257	+	5.67084i	−0.133674	+	0.411406i
$191$	−10.6566	+	11.8353i	−0.771083	+	0.856375i	−0.992929	−	0.118707i	$-0.962125\pi$
$191$	−10.6566	+	11.8353i	−0.771083	+	0.856375i	0.221846	+	0.975082i	$0.428792\pi$
$192$	2.48523	+	23.6454i	0.179356	+	1.70646i
$193$	1.54679	+	14.7167i	0.111340	+	1.05933i	0.897412	+	0.441194i	$0.145445\pi$
$193$	1.54679	+	14.7167i	0.111340	+	1.05933i	−0.786072	+	0.618135i	$0.787888\pi$
$194$	−8.16326	+	9.06622i	−0.586088	+	0.650917i
$195$	−0.0293252	+	0.0902538i	−0.00210002	+	0.00646321i
$196$	−31.0533	−	14.9766i	−2.21809	−	1.06976i
$197$	−8.28808			−0.590501			−0.295251	−	0.955420i	$-0.595403\pi$
$197$	−8.28808			−0.590501			−0.295251	+	0.955420i	$0.595403\pi$
$198$		0			0
$199$	−9.14220	+	15.8348i	−0.648073	+	1.12250i	0.335509	+	0.942037i	$0.391092\pi$
$199$	−9.14220	+	15.8348i	−0.648073	+	1.12250i	−0.983582	+	0.180459i	$0.942242\pi$
$200$	25.4300	−	11.3222i	1.79817	−	0.800599i
$201$	4.87874	−	1.03701i	0.344120	−	0.0731449i
$202$	−13.8337	−	42.5758i	−0.973337	−	2.99562i
$203$	−2.54179	−	12.9242i	−0.178399	−	0.907104i
$204$	53.6994	−	39.0149i	3.75971	−	2.73159i
$205$	−6.43609	+	7.14800i	−0.449516	+	0.499238i
$206$	29.6738	+	32.9561i	2.06747	+	2.29616i
$207$	3.54511	−	1.57839i	0.246402	−	0.109705i
$208$	0.189646	+	0.328476i	0.0131496	+	0.0227757i
$209$		0			0
$210$	−18.0565	+	1.61984i	−1.24602	+	0.111780i
$211$	19.0962	+	13.8742i	1.31464	+	0.955138i	0.999982	+	0.00593136i	$0.00188802\pi$
$211$	19.0962	+	13.8742i	1.31464	+	0.955138i	0.314653	+	0.949207i	$0.398112\pi$
$212$	47.7602	−	10.1517i	3.28019	−	0.697225i
$213$	9.20524	+	1.95663i	0.630733	+	0.134066i
$214$	0.256543	+	2.44084i	0.0175369	+	0.166853i
$215$	−3.18996	−	1.42026i	−0.217553	−	0.0968609i
$216$	−5.79508	−	17.8354i	−0.394305	−	1.21355i
$217$	−7.16096	+	2.20659i	−0.486118	+	0.149793i
$218$	−3.45660	−	2.51137i	−0.234110	−	0.170091i
$219$	−4.75068	−	8.22842i	−0.321021	−	0.556025i
$220$		0			0
$221$	0.110953	−	0.192177i	0.00746352	−	0.0129272i
$222$	1.62103	−	15.4231i	0.108796	−	1.03513i
$223$	−3.73166	+	11.4849i	−0.249891	+	0.769084i	0.744903	+	0.667173i	$0.232496\pi$
$223$	−3.73166	+	11.4849i	−0.249891	+	0.769084i	−0.994793	+	0.101911i	$0.967504\pi$
$224$	−19.0369	+	25.3790i	−1.27196	+	1.69571i
$225$	5.55672	−	4.03719i	0.370448	−	0.269146i
$226$	−8.50796	−	3.78799i	−0.565941	−	0.251973i
$227$	−10.1016	−	2.14717i	−0.670469	−	0.142513i	−0.139915	−	0.990164i	$-0.544683\pi$
$227$	−10.1016	−	2.14717i	−0.670469	−	0.142513i	−0.530554	+	0.847651i	$0.678016\pi$
$228$	14.0504	+	15.6046i	0.930512	+	1.03344i
$229$	2.88086	−	27.4095i	0.190372	−	1.81127i	−0.315785	−	0.948831i	$-0.602268\pi$
$229$	2.88086	−	27.4095i	0.190372	−	1.81127i	0.506157	−	0.862441i	$-0.331065\pi$
$230$	6.32476			0.417042
$231$		0			0
$232$	−38.3233			−2.51605
$233$	0.418134	−	3.97828i	0.0273929	−	0.260626i	−0.972251	−	0.233940i	$-0.924838\pi$
$233$	0.418134	−	3.97828i	0.0273929	−	0.260626i	0.999644	−	0.0266856i	$-0.00849530\pi$
$234$	0.121895	+	0.135378i	0.00796853	+	0.00884995i
$235$	3.67516	+	0.781179i	0.239741	+	0.0509585i
$236$	18.2662	+	8.13263i	1.18903	+	0.529389i
$237$	5.55877	−	4.03869i	0.361081	−	0.262341i
$238$	42.0873	+	5.07355i	2.72812	+	0.328870i
$239$	−6.55854	+	20.1851i	−0.424237	+	1.30567i	0.479487	+	0.877549i	$0.340823\pi$
$239$	−6.55854	+	20.1851i	−0.424237	+	1.30567i	−0.903723	+	0.428117i	$0.859177\pi$
$240$	−2.83248	+	26.9493i	−0.182836	+	1.73957i
$241$	−6.80326	+	11.7836i	−0.438237	+	0.759048i	−0.997554	−	0.0699056i	$-0.977730\pi$
$241$	−6.80326	+	11.7836i	−0.438237	+	0.759048i	0.559317	+	0.828954i	$0.311064\pi$
$242$		0			0
$243$	−8.61987	−	14.9301i	−0.552965	−	0.957763i
$244$	−34.5801	−	25.1239i	−2.21377	−	1.60840i
$245$	−6.51115	−	5.04101i	−0.415982	−	0.322059i
$246$	14.7177	+	45.2964i	0.938366	+	2.88799i
$247$	0.0641309	+	0.0285529i	0.00408055	+	0.00181678i
$248$	2.27888	+	21.6821i	0.144709	+	1.37681i
$249$	−13.1426	−	2.79354i	−0.832876	−	0.177033i
$250$	26.0900	−	5.54560i	1.65007	−	0.350734i
$251$	13.3601	+	9.70665i	0.843279	+	0.612678i	0.923285	−	0.384116i	$-0.125494\pi$
$251$	13.3601	+	9.70665i	0.843279	+	0.612678i	−0.0800054	+	0.996794i	$0.525494\pi$
$252$	−10.4105	+	22.4544i	−0.655798	+	1.41449i
$253$		0			0
$254$	25.9366	+	44.9235i	1.62741	+	2.81875i
$255$	14.4830	−	6.44826i	0.906963	−	0.403806i
$256$	−6.83006	−	7.58555i	−0.426879	−	0.474097i
$257$	19.5743	−	21.7395i	1.22101	−	1.35607i	0.306318	−	0.951929i	$-0.400903\pi$
$257$	19.5743	−	21.7395i	1.22101	−	1.35607i	0.914695	−	0.404144i	$-0.132430\pi$
$258$	−13.9881	+	10.1629i	−0.870861	+	0.632717i
$259$	5.30599	−	4.63299i	0.329698	−	0.287880i
$260$	0.0652518	+	0.200824i	0.00404674	+	0.0124546i
$261$	−9.24935	+	1.96601i	−0.572520	+	0.121693i
$262$	−38.9067	+	17.3224i	−2.40366	+	1.07018i
$263$	−9.96601	+	17.2616i	−0.614530	+	1.06440i	0.375936	+	0.926646i	$0.377321\pi$
$263$	−9.96601	+	17.2616i	−0.614530	+	1.06440i	−0.990467	+	0.137752i	$0.956012\pi$
$264$		0			0
$265$	11.6622			0.716402
$266$	−0.204499	+	13.4091i	−0.0125386	+	0.822167i
$267$	−2.95706	+	9.10090i	−0.180969	+	0.556966i
$268$	7.42617	−	8.24760i	0.453626	−	0.503802i
$269$	−0.0646715	−	0.615308i	−0.00394309	−	0.0375160i	0.992373	−	0.123268i	$-0.0393374\pi$
$269$	−0.0646715	−	0.615308i	−0.00394309	−	0.0375160i	−0.996317	+	0.0857519i	$0.972671\pi$
$270$	−0.788315	−	7.50031i	−0.0479753	−	0.456454i
$271$	0.0774894	−	0.0860607i	0.00470715	−	0.00522782i	−0.740787	−	0.671740i	$-0.765547\pi$
$271$	0.0774894	−	0.0860607i	0.00470715	−	0.00522782i	0.745494	+	0.666513i	$0.232214\pi$
$272$	19.5806	−	60.2629i	1.18725	−	3.65397i
$273$	−0.00325469	+	0.213412i	−0.000196983	+	0.0129163i
$274$	44.6745			2.69889
$275$		0			0
$276$	11.1366	−	19.2891i	0.670342	−	1.16107i
$277$	−8.82821	+	3.93057i	−0.530436	+	0.236165i	−0.654436	−	0.756117i	$-0.727094\pi$
$277$	−8.82821	+	3.93057i	−0.530436	+	0.236165i	0.124001	+	0.992282i	$0.460427\pi$
$278$	18.9115	−	4.01976i	1.13424	−	0.241089i
$279$	1.66231	+	5.11607i	0.0995200	+	0.306291i
$280$	−18.0468	+	15.7578i	−1.07850	+	0.941709i
$281$	−2.80199	+	2.03576i	−0.167153	+	0.121443i	−0.668217	−	0.743967i	$-0.732942\pi$
$281$	−2.80199	+	2.03576i	−0.167153	+	0.121443i	0.501064	+	0.865410i	$0.332942\pi$
$282$	12.4488	−	13.8258i	0.741318	−	0.823317i
$283$	−17.6245	−	19.5740i	−1.04767	−	1.16356i	−0.986219	−	0.165446i	$-0.947094\pi$
$283$	−17.6245	−	19.5740i	−1.04767	−	1.16356i	−0.0614514	−	0.998110i	$-0.519573\pi$
$284$	19.1299	−	8.51716i	1.13515	−	0.505401i
$285$	2.50765	+	4.34337i	0.148540	+	0.257279i
$286$		0			0
$287$	−9.09936	+	19.6264i	−0.537118	+	1.15851i
$288$	18.4257	+	13.3871i	1.08575	+	0.788842i
$289$	−19.6329	+	4.17310i	−1.15488	+	0.245477i
$290$	−15.0749	−	3.20428i	−0.885230	−	0.188162i
$291$	1.07261	+	10.2052i	0.0628776	+	0.598241i
$292$	−19.3138	−	8.59905i	−1.13025	−	0.503221i
$293$	−4.72493	−	14.5418i	−0.276033	−	0.849543i	−0.988944	−	0.148288i	$-0.952624\pi$
$293$	−4.72493	−	14.5418i	−0.276033	−	0.849543i	0.712911	−	0.701254i	$-0.247376\pi$
$294$	−37.7373	+	15.4407i	−2.20088	+	0.900519i
$295$	3.86361	+	2.80708i	0.224948	+	0.163434i
$296$	−10.2473	−	17.7488i	−0.595609	−	1.03163i
$297$		0			0
$298$	6.60648	−	11.4428i	0.382703	−	0.662861i
$299$	0.00778349	−	0.0740549i	0.000450131	−	0.00428271i
$300$	12.1822	−	37.4928i	0.703337	−	2.16465i
$301$	−7.79707	−	0.939923i	−0.449416	−	0.0541763i
$302$	−17.8791	+	12.9899i	−1.02883	+	0.747485i
$303$	−34.3987	−	15.3153i	−1.97615	−	0.879840i
$304$	19.6072	+	4.16763i	1.12455	+	0.239030i
$305$	−6.83122	−	7.58683i	−0.391154	−	0.434421i
$306$	3.18112	−	30.2663i	0.181852	−	1.73021i
$307$	−32.1611			−1.83553			−0.917766	−	0.397123i	$-0.870009\pi$
$307$	−32.1611			−1.83553			−0.917766	+	0.397123i	$0.870009\pi$
$308$		0			0
$309$	37.3008			2.12197
$310$	−0.916450	+	8.71944i	−0.0520509	+	0.495231i
$311$	1.41739	+	1.57417i	0.0803730	+	0.0892632i	0.781990	−	0.623291i	$-0.214205\pi$
$311$	1.41739	+	1.57417i	0.0803730	+	0.0892632i	−0.701617	+	0.712554i	$0.747538\pi$
$312$	0.607422	+	0.129112i	0.0343885	+	0.00730950i
$313$	−5.60776	−	2.49673i	−0.316969	−	0.141124i	0.242085	−	0.970255i	$-0.422169\pi$
$313$	−5.60776	−	2.49673i	−0.316969	−	0.141124i	−0.559054	+	0.829131i	$0.688835\pi$
$314$	−31.8214	+	23.1196i	−1.79578	+	1.30471i
$315$	−3.54722	+	4.72897i	−0.199863	+	0.266447i
$316$	4.72449	−	14.5405i	0.265773	−	0.817966i
$317$	1.85788	−	17.6765i	0.104349	−	0.992814i	−0.809599	−	0.586983i	$-0.800316\pi$
$317$	1.85788	−	17.6765i	0.104349	−	0.992814i	0.913948	−	0.405831i	$-0.133018\pi$
$318$	28.8733	−	50.0100i	1.61913	−	2.80442i
$319$		0			0
$320$	6.31787	+	10.9429i	0.353179	+	0.611725i
$321$	1.67008	+	1.21339i	0.0932150	+	0.0677246i
$322$	13.5943	−	4.18897i	0.757580	−	0.233442i
$323$	−3.62401	−	11.1536i	−0.201645	−	0.620601i
$324$	−49.9002	−	22.2170i	−2.77223	−	1.23428i
$325$	−0.0137764	−	0.131073i	−0.000764176	−	0.00727065i
$326$	6.40588	+	1.36161i	0.354789	+	0.0754127i
$327$	−3.51521	+	0.747180i	−0.194391	+	0.0413192i
$328$	50.9208	+	36.9962i	2.81163	+	2.04277i
$329$	8.41668	−	0.755058i	0.464027	−	0.0416277i
$330$		0			0
$331$	−9.78286	−	16.9444i	−0.537714	−	0.931349i	−0.999027	−	0.0441108i	$-0.985955\pi$
$331$	−9.78286	−	16.9444i	−0.537714	−	0.931349i	0.461312	−	0.887238i	$-0.347379\pi$
$332$	−27.3122	+	12.1602i	−1.49895	+	0.667377i
$333$	−3.38370	−	3.75798i	−0.185426	−	0.205936i
$334$	−21.6684	+	24.0651i	−1.18564	+	1.31679i
$335$	2.14452	−	1.55808i	0.117168	−	0.0851272i
$336$	11.7608	+	59.8001i	0.641604	+	3.26236i
$337$	−7.12726	−	21.9355i	−0.388247	−	1.19490i	−0.934097	−	0.357018i	$-0.883793\pi$
$337$	−7.12726	−	21.9355i	−0.388247	−	1.19490i	0.545851	−	0.837882i	$-0.316207\pi$
$338$	−33.4594	+	7.11202i	−1.81995	+	0.386843i
$339$	−7.15616	+	3.18613i	−0.388670	+	0.173047i
$340$	17.6380	−	30.5500i	0.956557	−	1.65681i
$341$		0			0
$342$	9.62747			0.520594
$343$	−17.3337	−	6.52261i	−0.935929	−	0.352188i
$344$	−7.06096	+	21.7314i	−0.380702	+	1.17168i
$345$	3.55967	−	3.95342i	0.191646	−	0.212845i
$346$	−3.35729	−	31.9425i	−0.180489	−	1.71724i
$347$	−2.61753	−	24.9041i	−0.140516	−	1.33692i	−0.806623	−	0.591067i	$-0.798707\pi$
$347$	−2.61753	−	24.9041i	−0.140516	−	1.33692i	0.666107	−	0.745857i	$-0.267960\pi$
$348$	−36.3161	+	40.3331i	−1.94675	+	2.16208i
$349$	−6.04728	+	18.6116i	−0.323703	+	0.996257i	0.648319	+	0.761369i	$0.275472\pi$
$349$	−6.04728	+	18.6116i	−0.323703	+	0.996257i	−0.972022	+	0.234888i	$0.924528\pi$
$350$	21.9939	−	12.2549i	1.17562	−	0.655050i
$351$	−0.0887893			−0.00473922
$352$		0			0
$353$	−10.1136	+	17.5172i	−0.538292	+	0.932349i	0.460704	+	0.887554i	$0.347597\pi$
$353$	−10.1136	+	17.5172i	−0.538292	+	0.932349i	−0.998996	+	0.0447952i	$0.985736\pi$
$354$	21.6029	−	9.61824i	1.14818	−	0.511203i
$355$	4.89220	−	1.03987i	0.259651	−	0.0551905i
$356$	6.57978	+	20.2505i	0.348728	+	1.07327i
$357$	26.8587	−	23.4521i	1.42151	−	1.24121i
$358$	8.11979	−	5.89937i	0.429144	−	0.311792i
$359$	16.6769	−	18.5216i	0.880174	−	0.977532i	−0.119709	−	0.992809i	$-0.538196\pi$
$359$	16.6769	−	18.5216i	0.880174	−	0.977532i	0.999883	+	0.0152768i	$0.00486294\pi$
$360$	11.5087	+	12.7817i	0.606562	+	0.673655i
$361$	−13.9681	+	6.21900i	−0.735164	+	0.327316i
$362$	9.26821	+	16.0530i	0.487126	+	0.843727i
$363$		0			0
$364$	0.273259	+	0.388430i	0.0143227	+	0.0203593i
$365$	−4.08519	−	2.96807i	−0.213829	−	0.155356i
$366$	−49.4468	+	10.5102i	−2.58462	+	0.549379i
$367$	−7.32584	−	1.55715i	−0.382406	−	0.0812828i	0.0126981	−	0.999919i	$-0.495958\pi$
$367$	−7.32584	−	1.55715i	−0.382406	−	0.0812828i	−0.395104	+	0.918637i	$0.629291\pi$
$368$	−2.22253	−	21.1460i	−0.115857	−	1.10231i
$369$	14.1877	+	6.31677i	0.738582	+	0.328838i
$370$	−2.54688	−	7.83848i	−0.132406	−	0.407503i
$371$	25.0664	−	7.72402i	1.30138	−	0.401011i
$372$	24.9786	+	18.1480i	1.29508	+	0.940933i
$373$	−0.802488	−	1.38995i	−0.0415513	−	0.0719689i	0.844502	−	0.535553i	$-0.179897\pi$
$373$	−0.802488	−	1.38995i	−0.0415513	−	0.0719689i	−0.886053	+	0.463584i	$0.846563\pi$
$374$		0			0
$375$	11.2175	−	19.4292i	0.579267	−	1.00332i
$376$	2.57000	−	24.4519i	0.132538	−	1.26101i
$377$	−0.0560698	+	0.172565i	−0.00288774	+	0.00888756i
$378$	−6.66194	−	15.5989i	−0.342653	−	0.802320i
$379$	−13.7907	+	10.0195i	−0.708380	+	0.514668i	−0.882651	−	0.470030i	$-0.844243\pi$
$379$	−13.7907	+	10.0195i	−0.708380	+	0.514668i	0.174271	+	0.984698i	$0.444243\pi$
$380$	10.1948	+	4.53900i	0.522981	+	0.232846i
$381$	42.6779	+	9.07146i	2.18645	+	0.464745i
$382$	28.0436	+	31.1455i	1.43483	+	1.59354i
$383$	1.82110	−	17.3266i	0.0930540	−	0.885350i	−0.844042	−	0.536277i	$-0.819830\pi$
$383$	1.82110	−	17.3266i	0.0930540	−	0.885350i	0.937096	−	0.349072i	$-0.113503\pi$
$384$	9.48395			0.483976
$385$		0			0
$386$	38.9413			1.98206
$387$	−0.589332	+	5.60712i	−0.0299574	+	0.285026i
$388$	15.2781	+	16.9681i	0.775629	+	0.861423i
$389$	10.9901	+	2.33601i	0.557219	+	0.118441i	0.477909	−	0.878409i	$-0.341395\pi$
$389$	10.9901	+	2.33601i	0.557219	+	0.118441i	0.0793100	+	0.996850i	$0.474728\pi$
$390$	0.228142	+	0.101575i	0.0115524	+	0.00514346i
$391$	−10.0639	+	7.31187i	−0.508955	+	0.369777i
$392$	−28.3528	+	45.8221i	−1.43203	+	2.31436i
$393$	−11.0696	+	34.0687i	−0.558387	+	1.71854i
$394$	−2.27984	+	21.6912i	−0.114857	+	1.09279i
$395$	1.82583	−	3.16243i	0.0918674	−	0.159119i
$396$		0			0
$397$	−9.85421	−	17.0680i	−0.494568	−	0.856618i	0.505412	−	0.862878i	$-0.331341\pi$
$397$	−9.85421	−	17.0680i	−0.494568	−	0.856618i	−0.999980	+	0.00626047i	$0.998007\pi$
$398$	38.9272	+	28.2823i	1.95125	+	1.41766i
$399$	8.26655	+	7.67469i	0.413845	+	0.384215i
$400$	−11.6294	−	35.7915i	−0.581469	−	1.78958i
$401$	−11.4543	−	5.09977i	−0.571999	−	0.254670i	0.100291	−	0.994958i	$-0.468023\pi$
$401$	−11.4543	−	5.09977i	−0.571999	−	0.254670i	−0.672290	+	0.740288i	$0.734689\pi$
$402$	−1.37200	−	13.0537i	−0.0684290	−	0.651058i
$403$	0.100966	+	0.0214609i	0.00502946	+	0.00106905i
$404$	−81.9534	+	17.4197i	−4.07733	+	0.866664i
$405$	−10.5547	−	7.66847i	−0.524470	−	0.381050i
$406$	−34.5239	+	3.09713i	−1.71339	+	0.153708i
$407$		0			0
$408$	−51.8712	−	89.8436i	−2.56801	−	4.44792i
$409$	−14.2565	+	6.34742i	−0.704940	+	0.313860i	−0.727714	−	0.685881i	$-0.759417\pi$
$409$	−14.2565	+	6.34742i	−0.704940	+	0.313860i	0.0227734	+	0.999741i	$0.492750\pi$
$410$	16.9370	+	18.8105i	0.836460	+	0.928983i
$411$	25.1435	−	27.9247i	1.24024	−	1.37742i
$412$	67.1470	−	48.7851i	3.30809	−	2.40347i
$413$	10.1635	+	3.47455i	0.500114	+	0.170971i
$414$	−3.15571	−	9.71228i	−0.155095	−	0.477333i
$415$	−6.98472	+	1.48465i	−0.342866	+	0.0728785i
$416$	0.399243	−	0.177754i	0.0195745	−	0.00871513i
$417$	8.13105	−	14.0834i	0.398179	−	0.689666i
$418$		0			0
$419$	−31.8183			−1.55443			−0.777213	−	0.629238i	$-0.783367\pi$
$419$	−31.8183			−1.55443			−0.777213	+	0.629238i	$0.783367\pi$
$420$	−0.517391	+	33.9257i	−0.0252461	+	1.65541i
$421$	7.37972	−	22.7125i	0.359666	−	1.10694i	−0.593589	−	0.804769i	$-0.702289\pi$
$421$	7.37972	−	22.7125i	0.359666	−	1.10694i	0.953254	−	0.302169i	$-0.0977106\pi$
$422$	41.5638	−	46.1612i	2.02329	−	2.24709i
$423$	−0.634128	−	6.03333i	−0.0308324	−	0.293351i
$424$	−7.97703	−	75.8964i	−0.387399	−	3.68586i
$425$	−14.7327	+	16.3623i	−0.714640	+	0.793688i
$426$	7.65294	−	23.5533i	0.370786	−	1.14116i
$427$	−19.7077	−	11.7826i	−0.953723	−	0.570198i
$428$	4.59337			0.222029
$429$		0			0
$430$	−4.59452	+	7.95793i	−0.221567	+	0.383766i
$431$	7.62250	−	3.39376i	0.367163	−	0.163471i	−0.214858	−	0.976645i	$-0.568929\pi$
$431$	7.62250	−	3.39376i	0.367163	−	0.163471i	0.582021	+	0.813174i	$0.302262\pi$
$432$	−24.7993	+	5.27124i	−1.19315	+	0.253613i
$433$	3.96670	+	12.2082i	0.190627	+	0.586691i	1.00000		0.000604904i	$-0.000192547\pi$
$433$	3.96670	+	12.2082i	0.190627	+	0.586691i	−0.809372	+	0.587296i	$0.800193\pi$
$434$	3.80520	+	19.3483i	0.182656	+	0.928750i
$435$	−10.4873	+	7.61947i	−0.502827	+	0.365326i
$436$	−5.35067	+	5.94252i	−0.256251	+	0.284595i
$437$	−2.63322	−	2.92449i	−0.125964	−	0.139897i
$438$	−22.8419	+	10.1698i	−1.09143	+	0.485934i
$439$	−12.2991	−	21.3026i	−0.587002	−	1.01672i	−0.994623	−	0.103566i	$-0.966975\pi$
$439$	−12.2991	−	21.3026i	−0.587002	−	1.01672i	0.407620	−	0.913151i	$-0.366359\pi$
$440$		0			0
$441$	−4.49225	+	12.5137i	−0.213917	+	0.595891i
$442$	−0.472436	−	0.343245i	−0.0224715	−	0.0163265i
$443$	15.7746	−	3.35300i	0.749474	−	0.159306i	0.182689	−	0.983171i	$-0.441520\pi$
$443$	15.7746	−	3.35300i	0.749474	−	0.159306i	0.566786	+	0.823865i	$0.308187\pi$
$444$	−28.3901	−	6.03450i	−1.34733	−	0.286385i
$445$	0.531596	+	5.05779i	0.0252000	+	0.239762i
$446$	29.0312	+	12.9255i	1.37467	+	0.612042i
$447$	−3.43429	−	10.5697i	−0.162436	−	0.499928i
$448$	20.8271	+	19.3359i	0.983987	+	0.913537i
$449$	−27.8811	−	20.2568i	−1.31579	−	0.955979i	−0.999974	−	0.00715956i	$-0.997721\pi$
$449$	−27.8811	−	20.2568i	−1.31579	−	0.955979i	−0.315818	−	0.948820i	$-0.602279\pi$
$450$	−9.03745	−	15.6533i	−0.426029	−	0.737905i
$451$		0			0
$452$	−8.71507	+	15.0950i	−0.409923	+	0.710007i
$453$	−1.94302	+	18.4866i	−0.0912910	+	0.868576i
$454$	−8.39818	+	25.8469i	−0.394146	+	1.21306i
$455$	0.0445517	+	0.104317i	0.00208861	+	0.00489047i
$456$	26.5510	−	19.2904i	1.24336	−	0.903357i
$457$	29.6428	+	13.1978i	1.38663	+	0.617369i	0.958172	−	0.286191i	$-0.0923893\pi$
$457$	29.6428	+	13.1978i	1.38663	+	0.617369i	0.428461	+	0.903560i	$0.359056\pi$
$458$	−70.9425	−	15.0793i	−3.31493	−	0.704609i
$459$	9.92526	+	11.0231i	0.463271	+	0.514515i
$460$	1.23733	−	11.7724i	0.0576907	−	0.548890i
$461$	29.4973			1.37383			0.686914	−	0.726739i	$-0.258965\pi$
$461$	29.4973			1.37383			0.686914	+	0.726739i	$0.258965\pi$
$462$		0			0
$463$	22.2588			1.03445			0.517227	−	0.855848i	$-0.326964\pi$
$463$	22.2588			1.03445			0.517227	+	0.855848i	$0.326964\pi$
$464$	−5.41570	+	51.5270i	−0.251418	+	2.39208i
$465$	4.93447	+	5.48028i	0.228830	+	0.254142i
$466$	−10.2968	−	2.18864i	−0.476988	−	0.101387i
$467$	21.6127	+	9.62258i	1.00012	+	0.445280i	0.840449	−	0.541891i	$-0.182292\pi$
$467$	21.6127	+	9.62258i	1.00012	+	0.445280i	0.159666	+	0.987171i	$0.448958\pi$
$468$	0.275828	−	0.200401i	0.0127502	−	0.00926354i
$469$	3.57744	−	4.76925i	0.165191	−	0.220224i
$470$	3.05541	−	9.40358i	0.140935	−	0.433755i
$471$	−3.45820	+	32.9026i	−0.159346	+	1.51607i
$472$	15.6255	−	27.0641i	0.719220	−	1.24573i
$473$		0			0
$474$	−9.04079	−	15.6591i	−0.415257	−	0.719247i
$475$	−5.63502	−	4.09408i	−0.258552	−	0.187849i
$476$	17.6771	−	77.3453i	0.810230	−	3.54512i
$477$	−5.81880	−	17.9084i	−0.266424	−	0.819970i
$478$	51.0235	+	22.7171i	2.33376	+	1.03906i
$479$	−1.20777	−	11.4911i	−0.0551843	−	0.525044i	−0.986840	−	0.161701i	$-0.948302\pi$
$479$	−1.20777	−	11.4911i	−0.0551843	−	0.525044i	0.931655	−	0.363343i	$-0.118365\pi$
$480$	30.5401	+	6.49151i	1.39396	+	0.296295i
$481$	−0.0949130	+	0.0201744i	−0.00432766	+	0.000919872i
$482$	28.9681	+	21.0466i	1.31946	+	0.958645i
$483$	5.03268	−	10.8550i	0.228995	−	0.493919i
$484$		0			0
$485$	2.72676	+	4.72289i	0.123816	+	0.214455i
$486$	−41.4454	+	18.4527i	−1.88000	+	0.837030i
$487$	0.0881648	+	0.0979170i	0.00399513	+	0.00443704i	0.745139	−	0.666909i	$-0.232383\pi$
$487$	0.0881648	+	0.0979170i	0.00399513	+	0.00443704i	−0.741144	+	0.671346i	$0.765716\pi$
$488$	−44.7018	+	49.6464i	−2.02356	+	2.24739i
$489$	4.45643	−	3.23779i	0.201527	−	0.146418i
$490$	−14.9842	+	15.6541i	−0.676916	+	0.707178i
$491$	0.00689282	+	0.0212139i	0.000311069	+	0.000957370i	0.951212	−	0.308538i	$-0.0998398\pi$
$491$	0.00689282	+	0.0212139i	0.000311069	+	0.000957370i	−0.950901	+	0.309496i	$0.899840\pi$
$492$	87.1902	−	18.5328i	3.93084	−	0.835525i
$493$	27.6915	−	12.3291i	1.24716	−	0.555273i
$494$	0.0923681	−	0.159986i	0.00415584	−	0.00719812i
$495$		0			0
$496$	29.4743			1.32343
$497$	9.82645	−	5.47524i	0.440777	−	0.245598i
$498$	−10.9263	+	33.6277i	−0.489619	+	1.50689i
$499$	−4.63648	+	5.14933i	−0.207557	+	0.230516i	−0.837931	−	0.545776i	$-0.816235\pi$
$499$	−4.63648	+	5.14933i	−0.207557	+	0.230516i	0.630374	+	0.776292i	$0.282902\pi$
$500$	−5.21807	−	49.6466i	−0.233359	−	2.22026i
$501$	2.84711	+	27.0885i	0.127200	+	1.21022i
$502$	29.0788	−	32.2953i	1.29785	−	1.44141i
$503$	2.59431	−	7.98448i	0.115675	−	0.356010i	−0.876412	−	0.481561i	$-0.840070\pi$
$503$	2.59431	−	7.98448i	0.115675	−	0.356010i	0.992087	+	0.125551i	$0.0400699\pi$
$504$	33.2020	+	19.8503i	1.47894	+	0.884204i
$505$	−20.0115			−0.890502
$506$		0			0
$507$	−14.3860	+	24.9172i	−0.638903	+	1.10661i
$508$	88.6910	−	39.4878i	3.93503	−	1.75199i
$509$	1.21275	−	0.257779i	0.0537543	−	0.0114258i	−0.180956	−	0.983491i	$-0.557919\pi$
$509$	1.21275	−	0.257779i	0.0537543	−	0.0114258i	0.234710	+	0.972065i	$0.424586\pi$
$510$	−12.8922	−	39.6781i	−0.570876	−	1.75698i
$511$	−10.7464	−	3.67381i	−0.475393	−	0.162520i
$512$	−28.6641	+	20.8257i	−1.26679	+	0.920374i
$513$	−3.13985	+	3.48715i	−0.138628	+	0.153962i
$514$	−51.5113	−	57.2091i	−2.27206	−	2.52338i
$515$	18.1099	−	8.06306i	0.798019	−	0.355301i
$516$	16.1799	+	28.0245i	0.712282	+	1.23371i
$517$		0			0
$518$	−10.6657	−	15.1610i	−0.468625	−	0.666137i
$519$	−21.8558	−	15.8792i	−0.959364	−	0.697018i
$520$	0.322819	−	0.0686174i	0.0141566	−	0.00300907i
$521$	−42.7902	−	9.09533i	−1.87467	−	0.398474i	−0.877906	−	0.478834i	$-0.841060\pi$
$521$	−42.7902	−	9.09533i	−1.87467	−	0.398474i	−0.996766	+	0.0803600i	$0.974393\pi$
$522$	2.60110	+	24.7478i	0.113847	+	1.08318i
$523$	27.8731	+	12.4099i	1.21881	+	0.542648i	0.912418	−	0.409259i	$-0.134213\pi$
$523$	27.8731	+	12.4099i	1.21881	+	0.542648i	0.306389	+	0.951907i	$0.400879\pi$
$524$	24.6310	+	75.8064i	1.07601	+	3.31162i
$525$	4.71836	−	20.6449i	0.205926	−	0.901019i
$526$	42.4350	+	30.8308i	1.85025	+	1.34429i
$527$	−8.62204	−	14.9338i	−0.375582	−	0.650527i
$528$		0			0
$529$	9.41287	−	16.3036i	0.409255	−	0.708851i
$530$	3.20796	−	30.5217i	0.139345	−	1.32578i
$531$	2.38281	−	7.33353i	0.103405	−	0.318248i
$532$	24.9186	+	3.00390i	1.08036	+	0.130235i
$533$	0.241090	−	0.175162i	0.0104428	−	0.00758712i
$534$	23.0051	+	10.2425i	0.995526	+	0.443237i
$535$	1.07313	+	0.228102i	0.0463956	+	0.00986169i
$536$	−11.6067	−	12.8906i	−0.501335	−	0.556788i
$537$	0.882423	−	8.39569i	0.0380794	−	0.362301i
$538$	−1.62815			−0.0701944
$539$		0			0
$540$	−14.1147			−0.607399
$541$	0.0296740	−	0.282330i	0.00127579	−	0.0121383i	−0.993865	−	0.110596i	$-0.964724\pi$
$541$	0.0296740	−	0.282330i	0.00127579	−	0.0121383i	0.995141	+	0.0984574i	$0.0313908\pi$
$542$	−0.203919	−	0.226475i	−0.00875907	−	0.00972793i
$543$	15.2505	+	3.24160i	0.654463	+	0.139110i
$544$	−66.6972	−	29.6955i	−2.85962	−	1.27318i
$545$	−1.54516	+	1.12262i	−0.0661873	+	0.0480879i
$546$	0.557637	+	0.0672221i	0.0238647	+	0.00287684i
$547$	−3.32791	+	10.2422i	−0.142291	+	0.437927i	−0.996653	−	0.0817521i	$-0.973948\pi$
$547$	−3.32791	+	10.2422i	−0.142291	+	0.437927i	0.854362	+	0.519679i	$0.173948\pi$
$548$	8.73978	−	83.1534i	0.373345	−	3.55214i
$549$	−8.24192	+	14.2754i	−0.351756	+	0.609260i
$550$		0			0
$551$	4.79461	+	8.30452i	0.204257	+	0.353784i
$552$	−28.1633	−	20.4618i	−1.19871	−	0.870914i
$553$	1.82988	−	8.00652i	0.0778142	−	0.340472i
$554$	7.85850	+	24.1860i	0.333876	+	1.02756i
$555$	−6.33302	−	2.81964i	−0.268822	−	0.119687i
$556$	−3.78235	−	35.9867i	−0.160407	−	1.52617i
$557$	39.0790	+	8.30649i	1.65583	+	0.351957i	0.938634	−	0.344916i	$-0.112092\pi$
$557$	39.0790	+	8.30649i	1.65583	+	0.351957i	0.717195	+	0.696873i	$0.245426\pi$
$558$	13.8468	−	2.94323i	0.586182	−	0.124597i
$559$	0.0875232	+	0.0635893i	0.00370184	+	0.00268954i
$560$	18.6366	+	26.4914i	0.787540	+	1.11946i
$561$		0			0
$562$	4.55716	+	7.89323i	0.192232	+	0.332956i
$563$	10.9104	−	4.85763i	0.459819	−	0.204725i	−0.163736	−	0.986504i	$-0.552354\pi$
$563$	10.9104	−	4.85763i	0.459819	−	0.204725i	0.623555	+	0.781779i	$0.285688\pi$
$564$	−23.2989	−	25.8760i	−0.981059	−	1.08958i
$565$	−2.78567	+	3.09380i	−0.117194	+	0.130157i
$566$	−56.0764	+	40.7419i	−2.35707	+	1.71251i
$567$	−27.7651	−	9.49189i	−1.16602	−	0.398622i
$568$	−10.1137	−	31.1267i	−0.424360	−	1.30605i
$569$	−10.7357	+	2.28193i	−0.450062	+	0.0956636i	−0.427366	−	0.904079i	$-0.640558\pi$
$569$	−10.7357	+	2.28193i	−0.450062	+	0.0956636i	−0.0226962	+	0.999742i	$0.507225\pi$
$570$	12.0571	−	5.36815i	0.505015	−	0.224847i
$571$	3.74628	−	6.48874i	0.156777	−	0.271545i	−0.776928	−	0.629590i	$-0.783223\pi$
$571$	3.74628	−	6.48874i	0.156777	−	0.271545i	0.933705	+	0.358044i	$0.116556\pi$
$572$		0			0
$573$	35.2515			1.47265
$574$	48.8625	+	29.2132i	2.03948	+	1.21933i
$575$	−2.28309	+	7.02662i	−0.0952114	+	0.293030i
$576$	13.6516	−	15.1616i	0.568815	−	0.631733i
$577$	3.74663	+	35.6468i	0.155974	+	1.48400i	0.740190	+	0.672398i	$0.234736\pi$
$577$	3.74663	+	35.6468i	0.155974	+	1.48400i	−0.584216	+	0.811598i	$0.698598\pi$
$578$	5.52115	+	52.5303i	0.229650	+	2.18497i
$579$	21.9168	−	24.3410i	0.910830	−	1.01158i
$580$	−8.91332	+	27.4324i	−0.370105	+	1.13907i
$581$	−14.0295	+	7.81714i	−0.582041	+	0.324310i
$582$	27.0037			1.11934
$583$		0			0
$584$	−16.5216	+	28.6162i	−0.683668	+	1.18415i
$585$	0.0743925	−	0.0331217i	0.00307575	−	0.00136941i
$586$	−39.3579	+	8.36579i	−1.62586	+	0.345587i
$587$	3.10017	+	9.54133i	0.127958	+	0.393813i	0.994428	−	0.105415i	$-0.0336171\pi$
$587$	3.10017	+	9.54133i	0.127958	+	0.393813i	−0.866471	+	0.499228i	$0.833617\pi$
$588$	21.3574	+	73.2618i	0.880763	+	3.02127i
$589$	4.41331	−	3.20646i	0.181847	−	0.132120i
$590$	8.40934	−	9.33952i	0.346207	−	0.384502i
$591$	12.2754	+	13.6332i	0.504942	+	0.560795i
$592$	−25.3119	+	11.2696i	−1.04031	+	0.463177i
$593$	14.1715	+	24.5458i	0.581954	+	1.00797i	0.995248	+	0.0973765i	$0.0310451\pi$
$593$	14.1715	+	24.5458i	0.581954	+	1.00797i	−0.413293	+	0.910598i	$0.635622\pi$
$594$		0			0
$595$	7.97073	−	17.1921i	0.326768	−	0.704807i
$596$	−20.0061	−	14.5353i	−0.819484	−	0.595390i
$597$	39.5872	−	8.41453i	1.62020	−	0.344384i
$598$	−0.191672	−	0.0407412i	−0.00783806	−	0.00166603i
$599$	−3.48978	−	33.2030i	−0.142589	−	1.35664i	−0.798588	−	0.601878i	$-0.794419\pi$
$599$	−3.48978	−	33.2030i	−0.142589	−	1.35664i	0.655999	−	0.754761i	$-0.272247\pi$
$600$	−56.2882	−	25.0611i	−2.29795	−	1.02312i
$601$	0.545054	+	1.67750i	0.0222332	+	0.0684269i	0.961558	−	0.274604i	$-0.0885466\pi$
$601$	0.545054	+	1.67750i	0.0222332	+	0.0684269i	−0.939324	+	0.343030i	$0.888547\pi$
$602$	−4.60470	+	20.1476i	−0.187673	+	0.821155i
$603$	−3.46259	−	2.51572i	−0.141007	−	0.102448i
$604$	20.6806	+	35.8199i	0.841482	+	1.45749i
$605$		0			0
$606$	−49.5446	+	85.8138i	−2.01261	+	3.48595i
$607$	−1.49541	+	14.2279i	−0.0606970	+	0.577494i	0.921334	+	0.388773i	$0.127101\pi$
$607$	−1.49541	+	14.2279i	−0.0606970	+	0.577494i	−0.982031	+	0.188721i	$0.939566\pi$
$608$	7.13718	−	21.9660i	0.289451	−	0.890838i
$609$	−17.4947	+	23.3230i	−0.708920	+	0.945095i
$610$	−21.7350	+	15.7914i	−0.880025	+	0.639376i
$611$	−0.106344	−	0.0473474i	−0.00430222	−	0.00191547i
$612$	−55.7129	−	11.8421i	−2.25206	−	0.478690i
$613$	3.81386	+	4.23572i	0.154040	+	0.171079i	0.815226	−	0.579144i	$-0.196613\pi$
$613$	3.81386	+	4.23572i	0.154040	+	0.171079i	−0.661185	+	0.750223i	$0.729946\pi$
$614$	−8.84669	+	84.1706i	−0.357023	+	3.39685i
$615$	21.2903			0.858506
$616$		0			0
$617$	17.9653			0.723257			0.361628	−	0.932322i	$-0.382221\pi$
$617$	17.9653			0.723257			0.361628	+	0.932322i	$0.382221\pi$
$618$	10.2605	−	97.6219i	0.412737	−	3.92693i
$619$	4.07697	+	4.52794i	0.163867	+	0.181993i	0.819486	−	0.573099i	$-0.194259\pi$
$619$	4.07697	+	4.52794i	0.163867	+	0.181993i	−0.655619	+	0.755092i	$0.727592\pi$
$620$	16.0504	+	3.41161i	0.644598	+	0.137013i
$621$	4.54706	+	2.02448i	0.182467	+	0.0812396i
$622$	4.50975	−	3.27652i	0.180824	−	0.131377i
$623$	4.49244	+	10.5190i	0.179986	+	0.421436i
$624$	0.259433	−	0.798454i	0.0103857	−	0.0319637i
$625$	−0.643656	+	6.12398i	−0.0257463	+	0.244959i
$626$	−8.07689	+	13.9896i	−0.322817	+	0.559136i
$627$		0			0
$628$	36.8076	+	63.7526i	1.46878	+	2.54400i
$629$	13.1144	+	9.52818i	0.522906	+	0.379914i
$630$	11.4007	+	10.5844i	0.454215	+	0.421694i
$631$	13.6845	+	42.1164i	0.544770	+	1.67663i	0.721536	+	0.692377i	$0.243436\pi$
$631$	13.6845	+	42.1164i	0.544770	+	1.67663i	−0.176766	+	0.984253i	$0.556564\pi$
$632$	−21.8297	−	9.71920i	−0.868338	−	0.386609i
$633$	−5.46127	−	51.9605i	−0.217066	−	2.06524i
$634$	−45.7512	−	9.72472i	−1.81701	−	0.386218i
$635$	22.6815	−	4.82110i	0.900087	−	0.191319i
$636$	−87.4359	−	63.5259i	−3.46706	−	2.51897i
$637$	0.164849	+	0.194710i	0.00653156	+	0.00771470i
$638$		0			0
$639$	−4.03776	−	6.99361i	−0.159731	−	0.276663i
$640$	4.60456	−	2.05008i	0.182011	−	0.0810366i
$641$	25.6289	+	28.4638i	1.01228	+	1.12425i	0.992225	+	0.124454i	$0.0397180\pi$
$641$	25.6289	+	28.4638i	1.01228	+	1.12425i	0.0200566	+	0.999799i	$0.493615\pi$
$642$	3.63502	−	4.03710i	0.143463	−	0.159332i
$643$	23.2361	−	16.8820i	0.916341	−	0.665760i	−0.0262698	−	0.999655i	$-0.508363\pi$
$643$	23.2361	−	16.8820i	0.916341	−	0.665760i	0.942610	+	0.333894i	$0.108363\pi$
$644$	−5.13752	−	26.1228i	−0.202447	−	1.02938i
$645$	2.38840	+	7.35074i	0.0940432	+	0.289435i
$646$	−30.1875	+	6.41654i	−1.18771	+	0.252456i
$647$	−18.6972	+	8.32451i	−0.735061	+	0.327270i	−0.739899	−	0.672718i	$-0.765127\pi$
$647$	−18.6972	+	8.32451i	−0.735061	+	0.327270i	0.00483790	+	0.999988i	$0.498460\pi$
$648$	−42.6862	+	73.9346i	−1.67687	+	2.90443i
$649$		0			0
$650$	−0.346829			−0.0136038
$651$	14.2357	+	8.51102i	0.557941	+	0.333573i
$652$	3.78759	−	11.6570i	0.148333	−	0.456523i
$653$	18.9086	−	21.0001i	0.739949	−	0.821797i	−0.249240	−	0.968442i	$-0.580181\pi$
$653$	18.9086	−	21.0001i	0.739949	−	0.821797i	0.989189	+	0.146645i	$0.0468474\pi$
$654$	0.988544	+	9.40537i	0.0386551	+	0.367779i
$655$	1.99000	+	18.9336i	0.0777556	+	0.739795i
$656$	56.9385	−	63.2366i	2.22308	−	2.46898i
$657$	−2.51946	+	7.75411i	−0.0982937	+	0.302517i
$658$	0.339107	−	22.2355i	0.0132198	−	0.866829i
$659$	−25.1666			−0.980350			−0.490175	−	0.871624i	$-0.663067\pi$
$659$	−25.1666			−0.980350			−0.490175	+	0.871624i	$0.663067\pi$
$660$		0			0
$661$	−10.3561	+	17.9373i	−0.402805	+	0.697679i	−0.994063	−	0.108803i	$-0.965298\pi$
$661$	−10.3561	+	17.9373i	−0.402805	+	0.697679i	0.591258	+	0.806483i	$0.298632\pi$
$662$	−47.0371	+	20.9423i	−1.82815	+	0.813945i
$663$	−0.480446	+	0.102122i	−0.0186590	+	0.00396609i
$664$	14.4396	+	44.4404i	0.560364	+	1.72462i
$665$	5.67249	+	1.93922i	0.219970	+	0.0751998i
$666$	−10.7660	+	7.82195i	−0.417174	+	0.303095i
$667$	6.80609	−	7.55892i	0.263533	−	0.292683i
$668$	40.5538	+	45.0396i	1.56907	+	1.74263i
$669$	24.4186	−	10.8718i	0.944077	−	0.420330i
$670$	−3.48785	−	6.04113i	−0.134747	−	0.233389i
$671$		0			0
$672$	69.9417	−	6.27445i	2.69806	−	0.242042i
$673$	−15.8762	−	11.5347i	−0.611983	−	0.444632i	0.238129	−	0.971234i	$-0.423466\pi$
$673$	−15.8762	−	11.5347i	−0.611983	−	0.444632i	−0.850112	+	0.526602i	$0.823466\pi$
$674$	−59.3690	+	12.6193i	−2.28681	+	0.486076i
$675$	8.61719	+	1.83164i	0.331676	+	0.0704999i
$676$	6.69198	+	63.6699i	0.257384	+	2.44884i
$677$	−20.8247	−	9.27175i	−0.800358	−	0.356342i	−0.0345427	−	0.999403i	$-0.510997\pi$
$677$	−20.8247	−	9.27175i	−0.800358	−	0.356342i	−0.765815	+	0.643061i	$0.777664\pi$
$678$	6.37012	+	19.6052i	0.244643	+	0.752934i
$679$	8.98886	+	8.34529i	0.344961	+	0.320263i
$680$	−44.6049	−	32.4074i	−1.71052	−	1.24277i
$681$	11.4295	+	19.7965i	0.437980	+	0.758603i
$682$		0			0
$683$	11.9753	−	20.7418i	0.458222	−	0.793664i	−0.540645	−	0.841251i	$-0.681820\pi$
$683$	11.9753	−	20.7418i	0.458222	−	0.793664i	0.998867	+	0.0475871i	$0.0151532\pi$
$684$	1.88344	−	17.9198i	0.0720153	−	0.685180i
$685$	6.17115	−	18.9928i	0.235788	−	0.725679i
$686$	−21.8387	+	43.5707i	−0.833807	+	1.66354i
$687$	−49.3532	+	35.8572i	−1.88294	+	1.36804i
$688$	28.2208	+	12.5647i	1.07591	+	0.479025i
$689$	−0.353423	−	0.0751224i	−0.0134644	−	0.00286194i
$690$	−9.36753	−	10.4037i	−0.356616	−	0.396062i
$691$	−4.27922	+	40.7141i	−0.162789	+	1.54884i	0.542584	+	0.840001i	$0.317446\pi$
$691$	−4.27922	+	40.7141i	−0.162789	+	1.54884i	−0.705373	+	0.708836i	$0.749221\pi$
$692$	−60.1119			−2.28511
$693$		0			0
$694$	−65.8980			−2.50145
$695$	0.903400	−	8.59527i	0.0342679	−	0.326037i
$696$	56.7602	+	63.0386i	2.15149	+	2.38947i
$697$	−48.6963	−	10.3507i	−1.84451	−	0.392062i
$698$	47.0460	+	20.9462i	1.78072	+	0.792827i
$699$	−7.16323	+	5.20439i	−0.270938	+	0.196848i
$700$	−18.5075	−	43.3351i	−0.699516	−	1.63791i
$701$	−3.07782	+	9.47255i	−0.116248	+	0.357773i	−0.992205	−	0.124615i	$-0.960231\pi$
$701$	−3.07782	+	9.47255i	−0.116248	+	0.357773i	0.875958	+	0.482388i	$0.160231\pi$
$702$	−0.0244236	+	0.232375i	−0.000921811	+	0.00877044i
$703$	−2.56406	+	4.44108i	−0.0967054	+	0.167499i
$704$		0			0
$705$	−4.15826	−	7.20232i	−0.156609	−	0.271255i
$706$	43.0634	+	31.2874i	1.62071	+	1.17752i
$707$	−43.0123	+	13.2539i	−1.61764	+	0.498464i
$708$	−13.6764	−	42.0915i	−0.513989	−	1.58190i
$709$	−43.4104	−	19.3275i	−1.63031	−	0.725861i	−0.631535	−	0.775347i	$-0.717575\pi$
$709$	−43.4104	−	19.3275i	−1.63031	−	0.725861i	−0.998775	+	0.0494861i	$0.984242\pi$
$710$	−1.37578	−	13.0897i	−0.0516321	−	0.491247i
$711$	−5.76721	−	1.22586i	−0.216287	−	0.0459733i
$712$	32.5520	−	6.91915i	1.21994	−	0.259306i
$713$	−4.68131	−	3.40117i	−0.175316	−	0.127375i
$714$	−53.9895	−	76.7445i	−2.02051	−	2.87209i
$715$		0			0
$716$	−9.39211	−	16.2676i	−0.351000	−	0.607949i
$717$	42.9166	−	19.1077i	1.60275	−	0.713590i
$718$	−43.8865	−	48.7409i	−1.63783	−	1.81899i
$719$	13.2116	−	14.6729i	0.492708	−	0.547208i	−0.444591	−	0.895734i	$-0.646651\pi$
$719$	13.2116	−	14.6729i	0.492708	−	0.547208i	0.937299	+	0.348526i	$0.113318\pi$
$720$	18.8118	−	13.6676i	0.701074	−	0.509360i
$721$	33.5848	−	29.3250i	1.25076	−	1.09212i
$722$	12.4338	+	38.2674i	0.462739	+	1.42417i
$723$	29.4593	−	6.26176i	1.09560	−	0.232877i
$724$	31.6929	−	14.1106i	1.17786	−	0.524416i
$725$	9.00155	−	15.5911i	0.334309	−	0.579040i
$726$		0			0
$727$	38.0241			1.41024			0.705118	−	0.709090i	$-0.250894\pi$
$727$	38.0241			1.41024			0.705118	+	0.709090i	$0.250894\pi$
$728$	0.648414	−	0.361292i	0.0240318	−	0.0133904i
$729$	−1.51042	+	4.64861i	−0.0559416	+	0.172171i
$730$	−8.89162	+	9.87515i	−0.329094	+	0.365496i
$731$	−1.88917	−	17.9742i	−0.0698733	−	0.664800i
$732$	9.88949	+	94.0922i	0.365526	+	3.47775i
$733$	−19.1463	+	21.2641i	−0.707184	+	0.785408i	−0.984502	−	0.175371i	$-0.943888\pi$
$733$	−19.1463	+	21.2641i	−0.707184	+	0.785408i	0.277318	+	0.960778i	$0.410554\pi$
$734$	−6.09046	+	18.7445i	−0.224803	+	0.691873i
$735$	1.35155	+	18.1765i	0.0498528	+	0.670450i
$736$	−24.4989			−0.903042
$737$		0			0
$738$	20.4346	−	35.3938i	0.752210	−	1.30287i
$739$	−8.27485	+	3.68420i	−0.304395	+	0.135526i	−0.553250	−	0.833015i	$-0.686613\pi$
$739$	−8.27485	+	3.68420i	−0.304395	+	0.135526i	0.248855	+	0.968541i	$0.419946\pi$
$740$	−15.0881	+	3.20708i	−0.554651	+	0.117895i
$741$	−0.0480164	−	0.147779i	−0.00176393	−	0.00542881i
$742$	−13.3198	−	67.7274i	−0.488986	−	2.48635i
$743$	6.75393	−	4.90702i	0.247778	−	0.180021i	−0.456964	−	0.889485i	$-0.651063\pi$
$743$	6.75393	−	4.90702i	0.247778	−	0.180021i	0.704741	+	0.709464i	$0.251063\pi$
$744$	32.2899	−	35.8616i	1.18381	−	1.31475i
$745$	−3.95216	−	4.38932i	−0.144796	−	0.160812i
$746$	−3.85846	+	1.71790i	−0.141268	+	0.0628967i
$747$	5.76482	+	9.98496i	0.210924	+	0.365331i
$748$		0			0
$749$	2.45764	−	0.220474i	0.0898003	−	0.00805596i
$750$	−47.7636	−	34.7023i	−1.74408	−	1.26715i
$751$	−48.1405	+	10.2326i	−1.75667	+	0.373392i	−0.969834	−	0.243766i	$-0.921617\pi$
$751$	−48.1405	+	10.2326i	−1.75667	+	0.373392i	−0.786839	+	0.617159i	$0.788284\pi$
$752$	−32.5133	−	6.91091i	−1.18564	−	0.252015i
$753$	−3.82081	−	36.3526i	−0.139238	−	1.32476i
$754$	0.436206	+	0.194212i	0.0158857	+	0.00707277i
$755$	3.05277	+	9.39545i	0.111102	+	0.341935i
$756$	−30.3378	+	9.34834i	−1.10337	+	0.339996i
$757$	−18.1226	−	13.1668i	−0.658676	−	0.478556i	0.207539	−	0.978227i	$-0.433454\pi$
$757$	−18.1226	−	13.1668i	−0.658676	−	0.478556i	−0.866216	+	0.499670i	$0.833454\pi$
$758$	22.4292	+	38.8485i	0.814665	+	1.41104i
$759$		0			0
$760$	8.72092	−	15.1051i	0.316341	−	0.547919i
$761$	−2.65358	+	25.2471i	−0.0961922	+	0.915208i	0.834894	+	0.550410i	$0.185529\pi$
$761$	−2.65358	+	25.2471i	−0.0961922	+	0.915208i	−0.931087	+	0.364798i	$0.881138\pi$
$762$	35.4810	−	109.199i	1.28534	−	3.95587i
$763$	−2.57760	+	3.43632i	−0.0933153	+	0.124403i
$764$	63.4579	−	46.1049i	2.29583	−	1.66802i
$765$	−12.4279	−	5.53328i	−0.449333	−	0.200056i
$766$	−44.8456	−	9.53222i	−1.62034	−	0.344413i
$767$	−0.0990051	−	0.109956i	−0.00357487	−	0.00397029i
$768$	−2.36167	+	22.4697i	−0.0852193	+	0.810807i
$769$	44.5582			1.60681			0.803406	−	0.595432i	$-0.203019\pi$
$769$	44.5582			1.60681			0.803406	+	0.595432i	$0.203019\pi$
$770$		0			0
$771$	−64.7510			−2.33195
$772$	7.61818	−	72.4821i	0.274184	−	2.60869i
$773$	22.1079	+	24.5533i	0.795167	+	0.883122i	0.995319	−	0.0966426i	$-0.0308104\pi$
$773$	22.1079	+	24.5533i	0.795167	+	0.883122i	−0.200152	+	0.979765i	$0.564144\pi$
$774$	14.5126	+	3.08475i	0.521644	+	0.110879i
$775$	−9.35623	−	4.16566i	−0.336086	−	0.149635i
$776$	28.8710	−	20.9760i	1.03641	−	0.752994i
$777$	−15.4795	−	1.86603i	−0.555325	−	0.0669434i
$778$	9.13679	−	28.1202i	0.327570	−	1.00816i
$779$	1.64624	−	15.6629i	0.0589827	−	0.561183i
$780$	0.233696	−	0.404772i	0.00836764	−	0.0144932i
$781$		0			0
$782$	16.3680	+	28.3502i	0.585318	+	1.01380i
$783$	−9.81217	−	7.12896i	−0.350658	−	0.254768i
$784$	57.6026	+	44.5967i	2.05724	+	1.59274i
$785$	5.43334	+	16.7221i	0.193924	+	0.596838i
$786$	86.1181	+	38.3422i	3.07173	+	1.36762i
$787$	4.51332	+	42.9414i	0.160883	+	1.53070i	0.715513	+	0.698599i	$0.246193\pi$
$787$	4.51332	+	42.9414i	0.160883	+	1.53070i	−0.554631	+	0.832097i	$0.687140\pi$
$788$	39.9282	+	8.48700i	1.42238	+	0.302337i
$789$	43.1545	−	9.17277i	1.53634	−	0.326559i
$790$	−7.77433	−	5.64838i	−0.276598	−	0.200960i
$791$	−3.93839	+	8.49473i	−0.140033	+	0.302038i
$792$		0			0
$793$	0.158150	+	0.273923i	0.00561606	+	0.00972729i
$794$	−47.3802	+	21.0950i	−1.68146	+	0.748635i
$795$	−17.2727	−	19.1833i	−0.612601	−	0.680362i
$796$	60.2577	−	66.9230i	2.13578	−	2.37202i
$797$	8.67461	−	6.30247i	0.307270	−	0.223245i	−0.423454	−	0.905918i	$-0.639182\pi$
$797$	8.67461	−	6.30247i	0.307270	−	0.223245i	0.730724	+	0.682673i	$0.239182\pi$
$798$	22.3598	−	19.5237i	0.791528	−	0.691133i
$799$	6.00946	+	18.4952i	0.212599	+	0.654313i
$800$	−42.4143	+	9.01544i	−1.49957	+	0.318744i
$801$	7.50150	−	3.33988i	0.265052	−	0.118009i
$802$	−16.4977	+	28.5748i	−0.582553	+	1.00901i
$803$		0			0
$804$	−24.5654			−0.866356
$805$	0.0969656	−	6.35810i	0.00341759	−	0.224094i
$806$	0.0839397	−	0.258340i	0.00295665	−	0.00909963i
$807$	−0.916346	+	1.01771i	−0.0322569	+	0.0358249i
$808$	13.6881	+	130.233i	0.481544	+	4.58159i
$809$	−0.120271	−	1.14430i	−0.00422849	−	0.0402314i	0.992204	−	0.124623i	$-0.0397721\pi$
$809$	−0.120271	−	1.14430i	−0.00422849	−	0.0402314i	−0.996433	+	0.0843914i	$0.973105\pi$
$810$	−22.9729	+	25.5140i	−0.807186	+	0.896471i
$811$	10.9601	−	33.7316i	0.384860	−	1.18448i	−0.551722	−	0.834028i	$-0.686029\pi$
$811$	10.9601	−	33.7316i	0.384860	−	1.18448i	0.936582	−	0.350449i	$-0.113971\pi$
$812$	−0.989251	+	64.8659i	−0.0347159	+	2.27635i
$813$	−0.256331			−0.00898993
$814$		0			0
$815$	1.46375	−	2.53530i	0.0512731	−	0.0888076i
$816$	−128.128	+	57.0463i	−4.48538	+	1.99702i
$817$	5.59251	−	1.18872i	0.195657	−	0.0415882i
$818$	12.6906	+	39.0576i	0.443716	+	1.36562i
$819$	0.137961	−	0.120462i	0.00482073	−	0.00420929i
$820$	38.3257	−	27.8452i	1.33839	−	0.972397i
$821$	−13.1966	+	14.6564i	−0.460566	+	0.511511i	−0.928032	−	0.372501i	$-0.878500\pi$
$821$	−13.1966	+	14.6564i	−0.460566	+	0.511511i	0.467466	+	0.884011i	$0.345167\pi$
$822$	−66.1669	−	73.4858i	−2.30784	−	2.56311i
$823$	37.2966	−	16.6055i	1.30008	−	0.578832i	0.364253	−	0.931300i	$-0.381324\pi$
$823$	37.2966	−	16.6055i	1.30008	−	0.578832i	0.935824	+	0.352468i	$0.114658\pi$
$824$	−64.8610	−	112.343i	−2.25954	−	3.91364i
$825$		0			0
$826$	11.8892	−	25.6438i	0.413676	−	0.892260i
$827$	−0.758333	−	0.550961i	−0.0263698	−	0.0191588i	0.574522	−	0.818489i	$-0.305188\pi$
$827$	−0.758333	−	0.550961i	−0.0263698	−	0.0191588i	−0.600892	+	0.799330i	$0.705188\pi$
$828$	−18.6950	+	3.97374i	−0.649696	+	0.138097i
$829$	14.9613	+	3.18013i	0.519629	+	0.110451i	0.460258	−	0.887785i	$-0.347757\pi$
$829$	14.9613	+	3.18013i	0.519629	+	0.110451i	0.0593714	+	0.998236i	$0.481090\pi$
$830$	1.96424	+	18.6885i	0.0681797	+	0.648687i
$831$	19.5408	+	8.70013i	0.677863	+	0.301804i
$832$	−0.120974	−	0.372321i	−0.00419403	−	0.0129079i
$833$	5.74554	−	42.2314i	0.199071	−	1.46323i
$834$	−34.6218	−	25.1542i	−1.19885	−	0.871018i
$835$	7.23784	+	12.5363i	0.250476	+	0.433837i
$836$		0			0
$837$	−3.44985	+	5.97532i	−0.119244	+	0.206537i
$838$	−8.75239	+	83.2734i	−0.302346	+	2.87663i
$839$	4.33906	−	13.3543i	0.149801	−	0.461040i	−0.847796	−	0.530322i	$-0.822071\pi$
$839$	4.33906	−	13.3543i	0.149801	−	0.461040i	0.997597	+	0.0692823i	$0.0220709\pi$
$840$	52.6492	+	6.34676i	1.81657	+	0.218984i
$841$	3.40980	−	2.47736i	0.117579	−	0.0854263i
$842$	−57.4121	−	25.5615i	−1.97855	−	0.880907i
$843$	7.49865	+	1.59389i	0.258267	+	0.0548964i
$844$	−77.7895	−	86.3940i	−2.67762	−	2.97380i
$845$	−1.59835	+	15.2073i	−0.0549850	+	0.523147i
$846$	−15.9646			−0.548874
$847$		0			0
$848$	−103.173			−3.54296
$849$	−6.09413	+	57.9818i	−0.209150	+	1.98993i
$850$	38.7701	+	43.0585i	1.32980	+	1.47690i
$851$	5.32066	+	1.13094i	0.182390	+	0.0387682i
$852$	−42.3430	−	18.8523i	−1.45065	−	0.645870i
$853$	2.96428	−	2.15368i	0.101495	−	0.0737405i	−0.535880	−	0.844294i	$-0.680020\pi$
$853$	2.96428	−	2.15368i	0.101495	−	0.0737405i	0.637375	+	0.770554i	$0.280020\pi$
$854$	−36.2579	+	48.3371i	−1.24072	+	1.65406i
$855$	1.32990	−	4.09301i	0.0454816	−	0.139978i
$856$	0.750431	−	7.13988i	0.0256492	−	0.244036i
$857$	2.52090	−	4.36633i	0.0861124	−	0.149151i	−0.819752	−	0.572718i	$-0.805889\pi$
$857$	2.52090	−	4.36633i	0.0861124	−	0.149151i	0.905865	+	0.423567i	$0.139222\pi$
$858$		0			0
$859$	−26.8888	−	46.5728i	−0.917434	−	1.58904i	−0.803298	−	0.595578i	$-0.796923\pi$
$859$	−26.8888	−	46.5728i	−0.917434	−	1.58904i	−0.114137	−	0.993465i	$-0.536410\pi$
$860$	13.9134	+	10.1087i	0.474443	+	0.344703i
$861$	45.7608	−	14.1008i	1.55952	−	0.480555i
$862$	−6.78523	−	20.8828i	−0.231106	−	0.711271i
$863$	−30.3976	−	13.5339i	−1.03475	−	0.460699i	−0.182151	−	0.983271i	$-0.558306\pi$
$863$	−30.3976	−	13.5339i	−1.03475	−	0.460699i	−0.852595	+	0.522572i	$0.824973\pi$
$864$	3.05353	+	29.0524i	0.103883	+	0.988383i
$865$	−14.0437	−	2.98509i	−0.477501	−	0.101496i
$866$	33.0420	−	7.02330i	1.12281	−	0.238661i
$867$	35.9425	+	26.1137i	1.22067	+	0.886869i
$868$	36.7578	−	3.29753i	1.24764	−	0.111926i
$869$		0			0
$870$	17.0565	+	29.5428i	0.578271	+	1.00160i
$871$	−0.0750262	+	0.0334038i	−0.00254217	+	0.00113185i
$872$	8.36283	+	9.28786i	0.283201	+	0.314527i
$873$	5.89195	−	6.54367i	0.199412	−	0.221470i
$874$	−8.37818	+	6.08710i	−0.283396	+	0.205899i
$875$	−5.17484	−	26.3125i	−0.174942	−	0.889526i
$876$	14.4607	+	44.5055i	0.488582	+	1.50370i
$877$	−12.8789	+	2.73750i	−0.434891	+	0.0924389i	−0.420155	−	0.907452i	$-0.638024\pi$
$877$	−12.8789	+	2.73750i	−0.434891	+	0.0924389i	−0.0147363	+	0.999891i	$0.504691\pi$
$878$	−59.1354	+	26.3288i	−1.99572	+	0.888553i
$879$	−16.9220	+	29.3098i	−0.570766	+	0.988596i
$880$		0			0
$881$	−33.1960			−1.11840			−0.559201	−	0.829032i	$-0.688892\pi$
$881$	−33.1960			−1.11840			−0.559201	+	0.829032i	$0.688892\pi$
$882$	31.5146	+	15.1991i	1.06115	+	0.511781i
$883$	−9.62662	+	29.6277i	−0.323962	+	0.997052i	0.647945	+	0.761687i	$0.275628\pi$
$883$	−9.62662	+	29.6277i	−0.323962	+	0.997052i	−0.971907	+	0.235365i	$0.924372\pi$
$884$	−0.731311	+	0.812203i	−0.0245967	+	0.0273173i
$885$	−1.10494	−	10.5128i	−0.0371423	−	0.353386i
$886$	−4.43613	−	42.2069i	−0.149035	−	1.41797i
$887$	22.1703	−	24.6226i	0.744406	−	0.826746i	−0.245363	−	0.969431i	$-0.578907\pi$
$887$	22.1703	−	24.6226i	0.744406	−	0.826746i	0.989768	+	0.142685i	$0.0455737\pi$
$888$	−14.0181	+	43.1434i	−0.470417	+	1.44780i
$889$	45.5580	−	25.3846i	1.52797	−	0.851372i
$890$	13.3833			0.448608
$891$		0			0
$892$	29.7380	−	51.5076i	0.995700	−	1.72460i
$893$	−5.62017	+	2.50226i	−0.188072	+	0.0837350i
$894$	−28.6071	+	6.08064i	−0.956766	+	0.203367i
$895$	−1.38642	−	4.26695i	−0.0463428	−	0.142628i
$896$	8.53914	−	7.45606i	0.285273	−	0.249089i
$897$	−0.133342	+	0.0968788i	−0.00445217	+	0.00323469i
$898$	−60.6847	+	67.3972i	−2.02507	+	2.24907i
$899$	9.43469	+	10.4783i	0.314664	+	0.349470i
$900$	−30.9038	+	13.7593i	−1.03013	+	0.458642i
$901$	30.1808	+	52.2747i	1.00547	+	1.74152i
$902$		0			0
$903$	10.0021	+	14.2176i	0.332848	+	0.473133i
$904$	22.0396	+	16.0127i	0.733026	+	0.532575i
$905$	8.10502	−	1.72277i	0.269420	−	0.0572670i
$906$	47.8478	+	10.1704i	1.58964	+	0.337888i
$907$	−1.18551	−	11.2794i	−0.0393643	−	0.374526i	−0.996415	−	0.0846044i	$-0.973037\pi$
$907$	−1.18551	−	11.2794i	−0.0393643	−	0.374526i	0.957050	−	0.289922i	$-0.0936293\pi$
$908$	46.4664	+	20.6882i	1.54204	+	0.686561i
$909$	9.98467	+	30.7297i	0.331171	+	1.01924i
$910$	0.285270	−	0.0879036i	0.00945660	−	0.00291398i
$911$	23.6200	+	17.1609i	0.782564	+	0.568566i	0.905747	−	0.423818i	$-0.139310\pi$
$911$	23.6200	+	17.1609i	0.782564	+	0.568566i	−0.123183	+	0.992384i	$0.539310\pi$
$912$	−22.1846	−	38.4248i	−0.734604	−	1.27237i
$913$		0			0
$914$	42.6948	−	73.9495i	1.41222	−	2.44603i
$915$	−2.36207	+	22.4736i	−0.0780875	+	0.742953i
$916$	−41.9460	+	129.096i	−1.38593	+	4.26547i
$917$	16.8172	+	39.3773i	0.555353	+	1.30035i
$918$	31.5794	−	22.9438i	1.04228	−	0.757257i
$919$	−13.2967	−	5.92005i	−0.438616	−	0.195285i	0.175535	−	0.984473i	$-0.443835\pi$
$919$	−13.2967	−	5.92005i	−0.438616	−	0.195285i	−0.614151	+	0.789189i	$0.710501\pi$
$920$	−18.0967	−	3.84657i	−0.596630	−	0.126818i
$921$	47.6335	+	52.9023i	1.56958	+	1.74319i
$922$	8.11395	−	77.1991i	0.267219	−	2.54242i
$923$	−0.154957			−0.00510046
$924$		0			0
$925$	9.62768			0.316556
$926$	6.12282	−	58.2548i	0.201208	−	1.91437i
$927$	−21.4175	−	23.7865i	−0.703443	−	0.781252i
$928$	58.3927	+	12.4117i	1.91683	+	0.407436i
$929$	−6.00905	−	2.67540i	−0.197151	−	0.0877771i	0.305786	−	0.952100i	$-0.401081\pi$
$929$	−6.00905	−	2.67540i	−0.197151	−	0.0877771i	−0.502937	+	0.864323i	$0.667747\pi$
$930$	15.7001	−	11.4068i	0.514826	−	0.374043i
$931$	13.4767	+	0.411154i	0.441680	+	0.0134750i
$932$	−6.08814	+	18.7374i	−0.199424	+	0.613763i
$933$	0.490099	−	4.66298i	0.0160451	−	0.152659i
$934$	31.1289	−	53.9168i	1.01857	−	1.76421i
$935$		0			0
$936$	−0.266438	−	0.461484i	−0.00870880	−	0.0150841i
$937$	−24.5499	−	17.8365i	−0.802009	−	0.582694i	0.109494	−	0.993987i	$-0.465077\pi$
$937$	−24.5499	−	17.8365i	−0.802009	−	0.582694i	−0.911503	+	0.411294i	$0.865077\pi$
$938$	−11.4978	−	10.6746i	−0.375417	−	0.348538i
$939$	4.19867	+	12.9222i	0.137018	+	0.421699i
$940$	−16.9053	−	7.52673i	−0.551390	−	0.245495i
$941$	−1.59366	−	15.1626i	−0.0519517	−	0.494287i	−0.989300	−	0.145894i	$-0.953394\pi$
$941$	−1.59366	−	15.1626i	−0.0519517	−	0.494287i	0.937348	−	0.348393i	$-0.113273\pi$
$942$	85.1600	+	18.1013i	2.77466	+	0.589773i
$943$	−16.3405	+	3.47329i	−0.532121	+	0.113106i
$944$	−34.1805	−	24.8336i	−1.11248	−	0.808263i
$945$	−7.55193	+	0.677482i	−0.245664	+	0.0220385i
$946$		0			0
$947$	−15.6044	−	27.0276i	−0.507075	−	0.878280i	−0.999966	−	0.00818941i	$-0.997393\pi$
$947$	−15.6044	−	27.0276i	−0.507075	−	0.878280i	0.492891	−	0.870091i	$-0.335940\pi$
$948$	−30.9152	+	13.7644i	−1.00408	+	0.447045i
$949$	0.104683	+	0.116262i	0.00339816	+	0.00377404i
$950$	−12.2649	+	13.6215i	−0.397926	+	0.441941i
$951$	−31.8281	+	23.1245i	−1.03210	+	0.749863i
$952$	−117.337	−	40.1132i	−3.80290	−	1.30008i
$953$	−6.67805	−	20.5529i	−0.216323	−	0.665775i	−0.999057	−	0.0434178i	$-0.986175\pi$
$953$	−6.67805	−	20.5529i	−0.216323	−	0.665775i	0.782734	−	0.622357i	$-0.213825\pi$
$954$	−48.4697	+	10.3026i	−1.56926	+	0.333558i
$955$	17.1150	−	7.62008i	0.553828	−	0.246580i
$956$	52.2656	−	90.5266i	1.69039	−	2.92784i
$957$		0			0
$958$	−30.4063			−0.982384
$959$	0.684910	−	44.9100i	0.0221169	−	1.45022i
$960$	8.64277	−	26.5997i	0.278944	−	0.858502i
$961$	−15.3758	+	17.0766i	−0.495994	+	0.550857i
$962$	0.0266914	+	0.253951i	0.000860564	+	0.00818772i
$963$	−0.185163	−	1.76171i	−0.00596680	−	0.0567704i
$964$	44.8414	−	49.8014i	1.44424	−	1.60400i
$965$	5.37919	−	16.5554i	0.173162	−	0.532939i
$966$	−27.0249	−	16.1572i	−0.869511	−	0.519850i
$967$	−5.74025			−0.184594			−0.0922970	−	0.995732i	$-0.529421\pi$
$967$	−5.74025			−0.184594			−0.0922970	+	0.995732i	$0.529421\pi$
$968$		0			0
$969$	−12.9792	+	22.4806i	−0.416951	+	0.722181i
$970$	13.1106	−	5.83721i	0.420956	−	0.187422i
$971$	6.71188	−	1.42665i	0.215394	−	0.0457835i	−0.0989504	−	0.995092i	$-0.531549\pi$
$971$	6.71188	−	1.42665i	0.215394	−	0.0457835i	0.314345	+	0.949309i	$0.398215\pi$
$972$	26.2382	+	80.7529i	0.841591	+	2.59015i
$973$	−3.75102	−	19.0728i	−0.120252	−	0.611446i
$974$	0.280516	−	0.203807i	0.00898831	−	0.00653039i
$975$	−0.195201	+	0.216792i	−0.00625143	+	0.00694292i
$976$	60.4342	+	67.1189i	1.93445	+	2.14842i
$977$	−9.51447	+	4.23611i	−0.304395	+	0.135525i	−0.553250	−	0.833015i	$-0.686612\pi$
$977$	−9.51447	+	4.23611i	−0.304395	+	0.135525i	0.248855	+	0.968541i	$0.419946\pi$
$978$	−7.24794	−	12.5538i	−0.231764	−	0.401426i
$979$		0			0
$980$	26.2058	+	30.9527i	0.837112	+	0.988748i
$981$	2.49485	+	1.81261i	0.0796543	+	0.0578723i
$982$	0.0574161	−	0.0122042i	0.00183222	−	0.000389451i
$983$	−15.4076	−	3.27498i	−0.491425	−	0.104456i	−0.0444675	−	0.999011i	$-0.514159\pi$
$983$	−15.4076	−	3.27498i	−0.491425	−	0.104456i	−0.446957	+	0.894555i	$0.647492\pi$
$984$	−14.5627	−	138.555i	−0.464243	−	4.41698i
$985$	8.90683	+	3.96558i	0.283795	+	0.126354i
$986$	−24.6499	−	75.8645i	−0.785011	−	2.41602i
$987$	−13.7079	−	12.7264i	−0.436326	−	0.405087i
$988$	−0.279715	−	0.203225i	−0.00889892	−	0.00646544i
$989$	−3.03232	−	5.25213i	−0.0964222	−	0.167008i
$990$		0			0
$991$	−4.05884	+	7.03011i	−0.128933	+	0.223319i	−0.923264	−	0.384167i	$-0.874489\pi$
$991$	−4.05884	+	7.03011i	−0.128933	+	0.223319i	0.794330	+	0.607486i	$0.207822\pi$
$992$	3.54986	−	33.7747i	0.112708	−	1.07235i
$993$	−13.3828	+	41.1881i	−0.424692	+	1.30707i
$994$	−11.6265	−	27.2235i	−0.368771	−	0.863476i
$995$	17.4011	−	12.6427i	0.551653	−	0.400799i
$996$	60.4543	+	26.9160i	1.91557	+	0.852865i
$997$	−40.3531	−	8.57731i	−1.27799	−	0.271646i	−0.481582	−	0.876401i	$-0.659938\pi$
$997$	−40.3531	−	8.57731i	−1.27799	−	0.271646i	−0.796412	+	0.604755i	$0.793271\pi$
$998$	12.2012	+	13.5508i	0.386223	+	0.428944i
$999$	0.677979	−	6.45054i	0.0214503	−	0.204086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.h.81.5		40
7.2	even	3	inner	847.2.n.h.807.1		40
11.2	odd	10		77.2.m.b.60.5	yes	40
11.3	even	5	inner	847.2.n.h.487.1		40
11.4	even	5		847.2.n.j.130.5		40
11.5	even	5		847.2.e.h.606.10		20
11.6	odd	10		847.2.e.i.606.1		20
11.7	odd	10		77.2.m.b.53.1	yes	40
11.8	odd	10		847.2.n.i.487.5		40
11.9	even	5		847.2.n.j.753.1		40
11.10	odd	2		847.2.n.i.81.1		40
33.2	even	10		693.2.by.b.676.1		40
33.29	even	10		693.2.by.b.361.5		40
77.2	odd	30		77.2.m.b.16.1	yes	40
77.9	even	15		847.2.n.j.632.5		40
77.13	even	10		539.2.q.h.214.5		40
77.16	even	15		847.2.e.h.485.10		20
77.17	even	30		5929.2.a.bx.1.10		10
77.18	odd	30		539.2.f.h.295.5		20
77.24	even	30		539.2.f.g.148.5		20
77.30	odd	30		847.2.n.i.366.1		40
77.37	even	15		847.2.n.j.9.1		40
77.38	odd	30		5929.2.a.bz.1.1		10
77.39	odd	30		5929.2.a.bw.1.10		10
77.40	even	30		539.2.q.h.471.5		40
77.46	odd	30		539.2.f.h.148.5		20
77.51	odd	30		77.2.m.b.9.5	✓	40
77.58	even	15	inner	847.2.n.h.366.5		40
77.60	even	15		5929.2.a.by.1.1		10
77.62	even	10		539.2.q.h.361.1		40
77.65	odd	6		847.2.n.i.807.5		40
77.68	even	30		539.2.q.h.324.1		40
77.72	odd	30		847.2.e.i.485.1		20
77.73	even	30		539.2.f.g.295.5		20
231.2	even	30		693.2.by.b.478.5		40
231.128	even	30		693.2.by.b.163.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.5	✓	40	77.51	odd	30
77.2.m.b.16.1	yes	40	77.2	odd	30
77.2.m.b.53.1	yes	40	11.7	odd	10
77.2.m.b.60.5	yes	40	11.2	odd	10
539.2.f.g.148.5		20	77.24	even	30
539.2.f.g.295.5		20	77.73	even	30
539.2.f.h.148.5		20	77.46	odd	30
539.2.f.h.295.5		20	77.18	odd	30
539.2.q.h.214.5		40	77.13	even	10
539.2.q.h.324.1		40	77.68	even	30
539.2.q.h.361.1		40	77.62	even	10
539.2.q.h.471.5		40	77.40	even	30
693.2.by.b.163.1		40	231.128	even	30
693.2.by.b.361.5		40	33.29	even	10
693.2.by.b.478.5		40	231.2	even	30
693.2.by.b.676.1		40	33.2	even	10
847.2.e.h.485.10		20	77.16	even	15
847.2.e.h.606.10		20	11.5	even	5
847.2.e.i.485.1		20	77.72	odd	30
847.2.e.i.606.1		20	11.6	odd	10
847.2.n.h.81.5		40	1.1	even	1	trivial
847.2.n.h.366.5		40	77.58	even	15	inner
847.2.n.h.487.1		40	11.3	even	5	inner
847.2.n.h.807.1		40	7.2	even	3	inner
847.2.n.i.81.1		40	11.10	odd	2
847.2.n.i.366.1		40	77.30	odd	30
847.2.n.i.487.5		40	11.8	odd	10
847.2.n.i.807.5		40	77.65	odd	6
847.2.n.j.9.1		40	77.37	even	15
847.2.n.j.130.5		40	11.4	even	5
847.2.n.j.632.5		40	77.9	even	15
847.2.n.j.753.1		40	11.9	even	5
5929.2.a.bw.1.10		10	77.39	odd	30
5929.2.a.bx.1.10		10	77.17	even	30
5929.2.a.by.1.1		10	77.60	even	15
5929.2.a.bz.1.1		10	77.38	odd	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.275074 - 2.61716i) q^{2} +(-1.48109 - 1.64492i) q^{3} +(-4.81754 - 1.02400i) q^{4} +(-1.07466 - 0.478467i) q^{5} +(-4.71241 + 3.42377i) q^{6} +(-2.62673 - 0.316648i) q^{7} +(-2.37875 + 7.32103i) q^{8} +(-0.198538 + 1.88897i) q^{9} +O(q^{10})\)	\(q+(0.275074 - 2.61716i) q^{2} +(-1.48109 - 1.64492i) q^{3} +(-4.81754 - 1.02400i) q^{4} +(-1.07466 - 0.478467i) q^{5} +(-4.71241 + 3.42377i) q^{6} +(-2.62673 - 0.316648i) q^{7} +(-2.37875 + 7.32103i) q^{8} +(-0.198538 + 1.88897i) q^{9} +(-1.54783 + 2.68093i) q^{10} +(5.45081 + 9.44109i) q^{12} +(0.0294854 + 0.0214224i) q^{13} +(-1.55126 + 6.78747i) q^{14} +(0.804622 + 2.47637i) q^{15} +(9.50722 + 4.23289i) q^{16} +(-0.636436 - 6.05528i) q^{17} +(4.88911 + 1.03921i) q^{18} +(1.88405 - 0.400466i) q^{19} +(4.68725 + 3.40548i) q^{20} +(3.36957 + 4.78974i) q^{21} +(-1.02155 - 1.76938i) q^{23} +(15.5656 - 6.93026i) q^{24} +(-2.41970 - 2.68735i) q^{25} +(0.0641765 - 0.0712752i) q^{26} +(-1.97092 + 1.43196i) q^{27} +(12.3302 + 4.21524i) q^{28} +(1.53843 + 4.73482i) q^{29} +(6.70238 - 1.42463i) q^{30} +(2.58732 - 1.15195i) q^{31} +(5.99553 - 10.3846i) q^{32} -16.0227 q^{34} +(2.67133 + 1.59709i) q^{35} +(2.89077 - 8.89688i) q^{36} +(-1.78148 + 1.97854i) q^{37} +(-0.529830 - 5.04100i) q^{38} +(-0.00843247 - 0.0802296i) q^{39} +(6.05921 - 6.72944i) q^{40} +(2.52670 - 7.77639i) q^{41} +(13.4624 - 7.50115i) q^{42} +2.96835 q^{43} +(1.11717 - 1.93499i) q^{45} +(-4.91174 + 2.18685i) q^{46} +(-3.12419 + 0.664066i) q^{47} +(-7.11830 - 21.9079i) q^{48} +(6.79947 + 1.66350i) q^{49} +(-7.69881 + 5.59351i) q^{50} +(-9.01781 + 10.0153i) q^{51} +(-0.120111 - 0.133397i) q^{52} +(-9.05672 + 4.03231i) q^{53} +(3.20550 + 5.55209i) q^{54} +(8.56653 - 18.4772i) q^{56} +(-3.44917 - 2.50597i) q^{57} +(12.8149 - 2.72390i) q^{58} +(-3.97101 - 0.844065i) q^{59} +(-1.34049 - 12.7540i) q^{60} +(7.92827 + 3.52989i) q^{61} +(-2.30312 - 7.08829i) q^{62} +(1.11965 - 4.89895i) q^{63} +(-8.68998 - 6.31364i) q^{64} +(-0.0214368 - 0.0371295i) q^{65} +(-1.12669 + 1.95148i) q^{67} +(-3.13455 + 29.8233i) q^{68} +(-1.39747 + 4.30097i) q^{69} +(4.91466 - 6.55196i) q^{70} +(-3.43968 + 2.49907i) q^{71} +(-13.3569 - 5.94688i) q^{72} +(4.19875 + 0.892472i) q^{73} +(4.68811 + 5.20667i) q^{74} +(-0.836672 + 7.96040i) q^{75} -9.48655 q^{76} -0.212293 q^{78} +(-0.324478 + 3.08720i) q^{79} +(-8.19169 - 9.09779i) q^{80} +(10.8481 + 2.30584i) q^{81} +(-19.6570 - 8.75186i) q^{82} +(4.91092 - 3.56800i) q^{83} +(-11.3283 - 26.5252i) q^{84} +(-2.21331 + 6.81186i) q^{85} +(0.816517 - 7.76864i) q^{86} +(5.50981 - 9.54328i) q^{87} +(-2.16161 - 3.74402i) q^{89} +(-4.75688 - 3.45607i) q^{90} +(-0.0706670 - 0.0656075i) q^{91} +(3.10952 + 9.57012i) q^{92} +(-5.72691 - 2.54978i) q^{93} +(0.878582 + 8.35915i) q^{94} +(-2.21631 - 0.471091i) q^{95} +(-25.9616 + 5.51831i) q^{96} +(-3.75055 - 2.72494i) q^{97} +(6.22400 - 17.3377i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9} - 14 q^{10} - 18 q^{12} + 4 q^{13} + 22 q^{14} + 16 q^{15} + 20 q^{16} + 12 q^{17} + 41 q^{18} + 24 q^{19} + 40 q^{20} + 2 q^{21} - 14 q^{23} + 7 q^{24} - 29 q^{25} - 5 q^{26} + 4 q^{27} + 24 q^{28} + 30 q^{29} - 6 q^{30} + 3 q^{31} + 30 q^{32} + 48 q^{34} - 6 q^{35} - 46 q^{36} - 11 q^{37} + 12 q^{38} + 32 q^{39} + 20 q^{40} - 10 q^{41} + 45 q^{42} + 72 q^{43} - 16 q^{45} + 17 q^{46} + 3 q^{47} - 62 q^{48} + 35 q^{49} - 6 q^{50} - 28 q^{51} - 2 q^{52} - 42 q^{53} - 34 q^{54} + 24 q^{56} + 36 q^{57} + 8 q^{58} - 9 q^{59} + 27 q^{60} + 20 q^{61} - 128 q^{62} + 36 q^{63} - 36 q^{64} + 40 q^{65} - 38 q^{67} + 33 q^{68} + 106 q^{69} - 18 q^{70} - 50 q^{71} - 42 q^{72} + 14 q^{73} + q^{74} - 16 q^{75} + 96 q^{76} - 100 q^{78} - 11 q^{79} - 18 q^{80} + 12 q^{81} - 24 q^{82} - 104 q^{83} + 44 q^{84} - 32 q^{85} + 2 q^{86} - 48 q^{87} - 10 q^{89} - 42 q^{90} - 14 q^{91} + 80 q^{92} - 13 q^{93} + 18 q^{94} + 8 q^{95} - 7 q^{96} + 46 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9 - 14 * q^10 - 18 * q^12 + 4 * q^13 + 22 * q^14 + 16 * q^15 + 20 * q^16 + 12 * q^17 + 41 * q^18 + 24 * q^19 + 40 * q^20 + 2 * q^21 - 14 * q^23 + 7 * q^24 - 29 * q^25 - 5 * q^26 + 4 * q^27 + 24 * q^28 + 30 * q^29 - 6 * q^30 + 3 * q^31 + 30 * q^32 + 48 * q^34 - 6 * q^35 - 46 * q^36 - 11 * q^37 + 12 * q^38 + 32 * q^39 + 20 * q^40 - 10 * q^41 + 45 * q^42 + 72 * q^43 - 16 * q^45 + 17 * q^46 + 3 * q^47 - 62 * q^48 + 35 * q^49 - 6 * q^50 - 28 * q^51 - 2 * q^52 - 42 * q^53 - 34 * q^54 + 24 * q^56 + 36 * q^57 + 8 * q^58 - 9 * q^59 + 27 * q^60 + 20 * q^61 - 128 * q^62 + 36 * q^63 - 36 * q^64 + 40 * q^65 - 38 * q^67 + 33 * q^68 + 106 * q^69 - 18 * q^70 - 50 * q^71 - 42 * q^72 + 14 * q^73 + q^74 - 16 * q^75 + 96 * q^76 - 100 * q^78 - 11 * q^79 - 18 * q^80 + 12 * q^81 - 24 * q^82 - 104 * q^83 + 44 * q^84 - 32 * q^85 + 2 * q^86 - 48 * q^87 - 10 * q^89 - 42 * q^90 - 14 * q^91 + 80 * q^92 - 13 * q^93 + 18 * q^94 + 8 * q^95 - 7 * q^96 + 46 * q^97 - 116 * q^98

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