LMFDB - Embedded newform 847.2.n.d.81.3

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	847.81
Dual form			847.2.n.d.366.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.191731 - 1.82420i) q^{2} +(-1.47121 - 1.63395i) q^{3} +(-1.33463 - 0.283685i) q^{4} +(-0.580606 - 0.258502i) q^{5} +(-3.26271 + 2.37050i) q^{6} +(2.39985 - 1.11389i) q^{7} +(0.360239 - 1.10870i) q^{8} +(-0.191731 + 1.82420i) q^{9} +O(q^{10})$	\(q+(0.191731 - 1.82420i) q^{2} +(-1.47121 - 1.63395i) q^{3} +(-1.33463 - 0.283685i) q^{4} +(-0.580606 - 0.258502i) q^{5} +(-3.26271 + 2.37050i) q^{6} +(2.39985 - 1.11389i) q^{7} +(0.360239 - 1.10870i) q^{8} +(-0.191731 + 1.82420i) q^{9} +(-0.582878 + 1.00958i) q^{10} +(1.50000 + 2.59808i) q^{12} +(-1.45729 - 1.05878i) q^{13} +(-1.57182 - 4.59135i) q^{14} +(0.431815 + 1.32899i) q^{15} +(-4.44639 - 1.97966i) q^{16} +(-0.296259 - 2.81872i) q^{17} +(3.29093 + 0.699508i) q^{18} +(-5.44157 + 1.15664i) q^{19} +(0.701561 + 0.509714i) q^{20} +(-5.35071 - 2.28245i) q^{21} +(-1.08288 - 1.87560i) q^{23} +(-2.34154 + 1.04252i) q^{24} +(-3.07537 - 3.41555i) q^{25} +(-2.21083 + 2.45538i) q^{26} +(-2.07362 + 1.50658i) q^{27} +(-3.51890 + 0.805829i) q^{28} +(3.22315 + 9.91982i) q^{29} +(2.50713 - 0.532907i) q^{30} +(5.87439 - 2.61545i) q^{31} +(-3.29804 + 5.71237i) q^{32} -5.19869 q^{34} +(-1.68131 + 0.0263633i) q^{35} +(0.773386 - 2.38024i) q^{36} +(4.05886 - 4.50782i) q^{37} +(1.06662 + 10.1483i) q^{38} +(0.413987 + 3.93883i) q^{39} +(-0.495758 + 0.550595i) q^{40} +(-2.32865 + 7.16684i) q^{41} +(-5.18954 + 9.32312i) q^{42} +4.86718 q^{43} +(0.582878 - 1.00958i) q^{45} +(-3.62908 + 1.61577i) q^{46} +(2.77231 - 0.589272i) q^{47} +(3.30692 + 10.1777i) q^{48} +(4.51851 - 5.34631i) q^{49} +(-6.82027 + 4.95522i) q^{50} +(-4.16977 + 4.63100i) q^{51} +(1.64458 + 1.82650i) q^{52} +(6.82400 - 3.03824i) q^{53} +(2.35071 + 4.07155i) q^{54} +(-0.370450 - 3.06197i) q^{56} +(9.89559 + 7.18957i) q^{57} +(18.7137 - 3.97771i) q^{58} +(-11.5488 - 2.45477i) q^{59} +(-0.199300 - 1.89621i) q^{60} +(3.95703 + 1.76179i) q^{61} +(-3.64478 - 11.2175i) q^{62} +(1.57182 + 4.59135i) q^{63} +(1.91288 + 1.38979i) q^{64} +(0.572413 + 0.991448i) q^{65} +(0.801309 - 1.38791i) q^{67} +(-0.404230 + 3.84599i) q^{68} +(-1.47149 + 4.52877i) q^{69} +(-0.274266 + 3.07208i) q^{70} +(-3.47233 + 2.52280i) q^{71} +(1.95342 + 0.869717i) q^{72} +(-15.6440 - 3.32523i) q^{73} +(-7.44493 - 8.26844i) q^{74} +(-1.05630 + 10.0500i) q^{75} +7.59061 q^{76} +7.26456 q^{78} +(0.497747 - 4.73574i) q^{79} +(2.06985 + 2.29880i) q^{80} +(10.8949 + 2.31578i) q^{81} +(12.6272 + 5.62201i) q^{82} +(-7.46854 + 5.42621i) q^{83} +(6.49373 + 4.56415i) q^{84} +(-0.556635 + 1.71315i) q^{85} +(0.933187 - 8.87868i) q^{86} +(11.4665 - 19.8606i) q^{87} +(-0.182224 - 0.315621i) q^{89} +(-1.72991 - 1.25685i) q^{90} +(-4.67663 - 0.917660i) q^{91} +(0.913165 + 2.81043i) q^{92} +(-12.9160 - 5.75056i) q^{93} +(-0.543411 - 5.17021i) q^{94} +(3.45840 + 0.735106i) q^{95} +(14.1858 - 3.01529i) q^{96} +(2.10027 + 1.52593i) q^{97} +(-8.88637 - 9.26770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8}+O(q^{10}) $ 24 * q - q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8} - 36 q^{10} + 36 q^{12} - 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} - 28 q^{20} - 40 q^{21} - 48 q^{23} - 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} + 13 q^{28} - 18 q^{29} - 2 q^{30} - 3 q^{31} - 12 q^{32} - 80 q^{34} + 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} + 5 q^{39} + 3 q^{40} - 10 q^{41} + 2 q^{42} - 16 q^{43} + 36 q^{45} + 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} - 6 q^{50} - 2 q^{51} + 7 q^{52} + 17 q^{53} - 32 q^{54} + 12 q^{56} + 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} + 24 q^{61} + 26 q^{62} + 12 q^{63} + 14 q^{64} + 60 q^{65} + 64 q^{67} - 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} - 10 q^{72} + 20 q^{73} - 22 q^{74} + 25 q^{75} + 312 q^{76} - 48 q^{78} - 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} - 22 q^{83} + 12 q^{84} + 22 q^{85} - 21 q^{86} + 120 q^{87} - 4 q^{89} + 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} + 10 q^{94} + 17 q^{95} - 27 q^{96} - 18 q^{97} + 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8 - 36 * q^10 + 36 * q^12 - 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 + 3 * q^17 - 10 * q^18 + 11 * q^19 - 28 * q^20 - 40 * q^21 - 48 * q^23 - 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 + 13 * q^28 - 18 * q^29 - 2 * q^30 - 3 * q^31 - 12 * q^32 - 80 * q^34 + 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 + 5 * q^39 + 3 * q^40 - 10 * q^41 + 2 * q^42 - 16 * q^43 + 36 * q^45 + 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 - 6 * q^50 - 2 * q^51 + 7 * q^52 + 17 * q^53 - 32 * q^54 + 12 * q^56 + 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 + 24 * q^61 + 26 * q^62 + 12 * q^63 + 14 * q^64 + 60 * q^65 + 64 * q^67 - 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 - 10 * q^72 + 20 * q^73 - 22 * q^74 + 25 * q^75 + 312 * q^76 - 48 * q^78 - 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 - 22 * q^83 + 12 * q^84 + 22 * q^85 - 21 * q^86 + 120 * q^87 - 4 * q^89 + 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 + 10 * q^94 + 17 * q^95 - 27 * q^96 - 18 * q^97 + 96 * 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 $

$2$	0.191731	−	1.82420i	0.135574	−	1.28990i	−0.689255	−	0.724519i	$-0.742062\pi$
$2$	0.191731	−	1.82420i	0.135574	−	1.28990i	0.824829	−	0.565382i	$-0.191271\pi$
$3$	−1.47121	−	1.63395i	−0.849404	−	0.943359i	0.149565	−	0.988752i	$-0.452213\pi$
$3$	−1.47121	−	1.63395i	−0.849404	−	0.943359i	−0.998969	+	0.0453928i	$0.985546\pi$
$4$	−1.33463	−	0.283685i	−0.667316	−	0.141842i
$5$	−0.580606	−	0.258502i	−0.259655	−	0.115606i	0.272781	−	0.962076i	$-0.412057\pi$
$5$	−0.580606	−	0.258502i	−0.259655	−	0.115606i	−0.532436	+	0.846470i	$0.678723\pi$
$6$	−3.26271	+	2.37050i	−1.33200	+	0.967752i
$7$	2.39985	−	1.11389i	0.907056	−	0.421009i
$7$	2.39985	−	1.11389i	0.907056	−	0.421009i
$8$	0.360239	−	1.10870i	0.127364	−	0.391985i
$9$	−0.191731	+	1.82420i	−0.0639102	+	0.608065i
$10$	−0.582878	+	1.00958i	−0.184322	+	0.319256i
$11$		0			0
$11$		0			0
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$	−1.45729	−	1.05878i	−0.404179	−	0.293653i	0.367062	−	0.930197i	$-0.380364\pi$
$13$	−1.45729	−	1.05878i	−0.404179	−	0.293653i	−0.771241	+	0.636543i	$0.780364\pi$
$14$	−1.57182	−	4.59135i	−0.420087	−	1.22709i
$15$	0.431815	+	1.32899i	0.111494	+	0.343144i
$16$	−4.44639	−	1.97966i	−1.11160	−	0.494915i
$17$	−0.296259	−	2.81872i	−0.0718534	−	0.683639i	−0.969861	−	0.243659i	$-0.921652\pi$
$17$	−0.296259	−	2.81872i	−0.0718534	−	0.683639i	0.898008	−	0.439980i	$-0.145014\pi$
$18$	3.29093	+	0.699508i	0.775679	+	0.164876i
$19$	−5.44157	+	1.15664i	−1.24838	+	0.265352i	−0.784267	−	0.620423i	$-0.786961\pi$
$19$	−5.44157	+	1.15664i	−1.24838	+	0.265352i	−0.464115	+	0.885775i	$0.653628\pi$
$20$	0.701561	+	0.509714i	0.156874	+	0.113976i
$21$	−5.35071	−	2.28245i	−1.16762	−	0.498073i
$22$		0			0
$23$	−1.08288	−	1.87560i	−0.225796	−	0.391090i	0.730762	−	0.682632i	$-0.239165\pi$
$23$	−1.08288	−	1.87560i	−0.225796	−	0.391090i	−0.956558	+	0.291542i	$0.905832\pi$
$24$	−2.34154	+	1.04252i	−0.477966	+	0.212804i
$25$	−3.07537	−	3.41555i	−0.615075	−	0.683110i
$26$	−2.21083	+	2.45538i	−0.433580	+	0.481539i
$27$	−2.07362	+	1.50658i	−0.399069	+	0.289941i
$28$	−3.51890	+	0.805829i	−0.665010	+	0.152287i
$29$	3.22315	+	9.91982i	0.598523	+	1.84206i	0.536344	+	0.843999i	$0.319805\pi$
$29$	3.22315	+	9.91982i	0.598523	+	1.84206i	0.0621790	+	0.998065i	$0.480195\pi$
$30$	2.50713	−	0.532907i	0.457737	−	0.0972950i
$31$	5.87439	−	2.61545i	1.05507	−	0.469748i	0.195468	−	0.980710i	$-0.437377\pi$
$31$	5.87439	−	2.61545i	1.05507	−	0.469748i	0.859603	+	0.510962i	$0.170711\pi$
$32$	−3.29804	+	5.71237i	−0.583016	+	1.00981i
$33$		0			0
$34$	−5.19869			−0.891568
$35$	−1.68131	+	0.0263633i	−0.284193	+	0.00445620i
$36$	0.773386	−	2.38024i	0.128898	−	0.396706i
$37$	4.05886	−	4.50782i	0.667272	−	0.741081i	−0.310541	−	0.950560i	$-0.600510\pi$
$37$	4.05886	−	4.50782i	0.667272	−	0.741081i	0.977813	+	0.209479i	$0.0671768\pi$
$38$	1.06662	+	10.1483i	0.173029	+	1.64626i
$39$	0.413987	+	3.93883i	0.0662910	+	0.630717i
$40$	−0.495758	+	0.550595i	−0.0783863	+	0.0870568i
$41$	−2.32865	+	7.16684i	−0.363674	+	1.11927i	0.587134	+	0.809490i	$0.300256\pi$
$41$	−2.32865	+	7.16684i	−0.363674	+	1.11927i	−0.950807	+	0.309783i	$0.899744\pi$
$42$	−5.18954	+	9.32312i	−0.800763	+	1.43859i
$43$	4.86718			0.742238			0.371119	−	0.928585i	$-0.378974\pi$
$43$	4.86718			0.742238			0.371119	+	0.928585i	$0.378974\pi$
$44$		0			0
$45$	0.582878	−	1.00958i	0.0868904	−	0.150499i
$46$	−3.62908	+	1.61577i	−0.535079	+	0.238232i
$47$	2.77231	−	0.589272i	0.404383	−	0.0859542i	−0.00122998	−	0.999999i	$-0.500392\pi$
$47$	2.77231	−	0.589272i	0.404383	−	0.0859542i	0.405613	+	0.914045i	$0.367058\pi$
$48$	3.30692	+	10.1777i	0.477313	+	1.46902i
$49$	4.51851	−	5.34631i	0.645502	−	0.763759i
$50$	−6.82027	+	4.95522i	−0.964532	+	0.700773i
$51$	−4.16977	+	4.63100i	−0.583885	+	0.648470i
$52$	1.64458	+	1.82650i	0.228063	+	0.253289i
$53$	6.82400	−	3.03824i	0.937348	−	0.417334i	0.119543	−	0.992829i	$-0.461857\pi$
$53$	6.82400	−	3.03824i	0.937348	−	0.417334i	0.817805	+	0.575495i	$0.195190\pi$
$54$	2.35071	+	4.07155i	0.319891	+	0.554068i
$55$		0			0
$56$	−0.370450	−	3.06197i	−0.0495034	−	0.409174i
$57$	9.89559	+	7.18957i	1.31070	+	0.952282i
$58$	18.7137	−	3.97771i	2.45722	−	0.522299i
$59$	−11.5488	−	2.45477i	−1.50352	−	0.319583i	−0.618742	−	0.785594i	$-0.712357\pi$
$59$	−11.5488	−	2.45477i	−1.50352	−	0.319583i	−0.884779	+	0.466011i	$0.845691\pi$
$60$	−0.199300	−	1.89621i	−0.0257295	−	0.244800i
$61$	3.95703	+	1.76179i	0.506646	+	0.225573i	0.644109	−	0.764933i	$-0.277228\pi$
$61$	3.95703	+	1.76179i	0.506646	+	0.225573i	−0.137463	+	0.990507i	$0.543895\pi$
$62$	−3.64478	−	11.2175i	−0.462888	−	1.42462i
$63$	1.57182	+	4.59135i	0.198031	+	0.578456i
$64$	1.91288	+	1.38979i	0.239110	+	0.173723i
$65$	0.572413	+	0.991448i	0.0709990	+	0.122974i
$66$		0			0
$67$	0.801309	−	1.38791i	0.0978954	−	0.169560i	−0.812918	−	0.582378i	$-0.802122\pi$
$67$	0.801309	−	1.38791i	0.0978954	−	0.169560i	0.910813	+	0.412818i	$0.135456\pi$
$68$	−0.404230	+	3.84599i	−0.0490201	+	0.466395i
$69$	−1.47149	+	4.52877i	−0.177146	+	0.545200i
$70$	−0.274266	+	3.07208i	−0.0327811	+	0.367184i
$71$	−3.47233	+	2.52280i	−0.412090	+	0.299401i	−0.774447	−	0.632638i	$-0.781972\pi$
$71$	−3.47233	+	2.52280i	−0.412090	+	0.299401i	0.362358	+	0.932039i	$0.381972\pi$
$72$	1.95342	+	0.869717i	0.230212	+	0.102497i
$73$	−15.6440	−	3.32523i	−1.83099	−	0.389188i	−0.842279	−	0.539042i	$-0.818786\pi$
$73$	−15.6440	−	3.32523i	−1.83099	−	0.389188i	−0.988708	+	0.149854i	$0.952120\pi$
$74$	−7.44493	−	8.26844i	−0.865456	−	0.961186i
$75$	−1.05630	+	10.0500i	−0.121971	+	1.16047i
$76$	7.59061			0.870703
$77$		0			0
$78$	7.26456			0.822549
$79$	0.497747	−	4.73574i	0.0560009	−	0.532813i	−0.930176	−	0.367115i	$-0.880346\pi$
$79$	0.497747	−	4.73574i	0.0560009	−	0.532813i	0.986177	−	0.165698i	$-0.0529877\pi$
$80$	2.06985	+	2.29880i	0.231416	+	0.257014i
$81$	10.8949	+	2.31578i	1.21054	+	0.257309i
$82$	12.6272	+	5.62201i	1.39445	+	0.620847i
$83$	−7.46854	+	5.42621i	−0.819779	+	0.595604i	−0.916649	−	0.399693i	$-0.869117\pi$
$83$	−7.46854	+	5.42621i	−0.819779	+	0.595604i	0.0968702	+	0.995297i	$0.469117\pi$
$84$	6.49373	+	4.56415i	0.708524	+	0.497990i
$85$	−0.556635	+	1.71315i	−0.0603755	+	0.185817i
$86$	0.933187	−	8.87868i	0.100628	−	0.957413i
$87$	11.4665	−	19.8606i	1.22934	−	2.12928i
$88$		0			0
$89$	−0.182224	−	0.315621i	−0.0193157	−	0.0334558i	0.856206	−	0.516635i	$-0.172815\pi$
$89$	−0.182224	−	0.315621i	−0.0193157	−	0.0334558i	−0.875522	+	0.483179i	$0.839482\pi$
$90$	−1.72991	−	1.25685i	−0.182348	−	0.132484i
$91$	−4.67663	−	0.917660i	−0.490244	−	0.0961969i
$92$	0.913165	+	2.81043i	0.0952040	+	0.293008i
$93$	−12.9160	−	5.75056i	−1.33932	−	0.596305i
$94$	−0.543411	−	5.17021i	−0.0560486	−	0.533267i
$95$	3.45840	+	0.735106i	0.354824	+	0.0754203i
$96$	14.1858	−	3.01529i	1.44783	−	0.307746i
$97$	2.10027	+	1.52593i	0.213250	+	0.154935i	0.689283	−	0.724492i	$-0.257926\pi$
$97$	2.10027	+	1.52593i	0.213250	+	0.154935i	−0.476033	+	0.879427i	$0.657926\pi$
$98$	−8.88637	−	9.26770i	−0.897659	−	0.936179i
$99$		0			0
$100$	3.13555	+	5.43094i	0.313555	+	0.543094i
$101$	9.04420	−	4.02674i	0.899932	−	0.400675i	0.0959892	−	0.995382i	$-0.469399\pi$
$101$	9.04420	−	4.02674i	0.899932	−	0.400675i	0.803943	+	0.594707i	$0.202732\pi$
$102$	7.64837	+	8.49438i	0.757302	+	0.841069i
$103$	4.16977	−	4.63100i	0.410860	−	0.456306i	−0.501826	−	0.864969i	$-0.667338\pi$
$103$	4.16977	−	4.63100i	0.410860	−	0.456306i	0.912685	+	0.408663i	$0.134005\pi$
$104$	−1.69885	+	1.23428i	−0.166585	+	0.121031i
$105$	2.51663	+	2.70838i	0.245598	+	0.264311i
$106$	−4.23397	−	13.0308i	−0.411240	−	1.26567i
$107$	10.8563	−	2.30757i	1.04952	−	0.223081i	0.349298	−	0.937012i	$-0.386420\pi$
$107$	10.8563	−	2.30757i	1.04952	−	0.223081i	0.700217	+	0.713930i	$0.253087\pi$
$108$	3.19492	−	1.42247i	0.307431	−	0.136877i
$109$	−7.15202	+	12.3877i	−0.685039	+	1.18652i	0.288385	+	0.957514i	$0.406882\pi$
$109$	−7.15202	+	12.3877i	−0.685039	+	1.18652i	−0.973424	+	0.229008i	$0.926452\pi$
$110$		0			0
$111$	−13.3370			−1.26589
$112$	−12.8758	+	0.201895i	−1.21664	+	0.0190773i
$113$	−2.68518	+	8.26413i	−0.252600	+	0.777424i	0.741693	+	0.670740i	$0.234023\pi$
$113$	−2.68518	+	8.26413i	−0.252600	+	0.777424i	−0.994293	+	0.106684i	$0.965977\pi$
$114$	15.0125	−	16.6730i	1.40605	−	1.56157i
$115$	0.143878	+	1.36891i	0.0134167	+	0.127652i
$116$	−1.48761	−	14.1537i	−0.138121	−	1.31413i
$117$	2.21083	−	2.45538i	0.204392	−	0.227000i
$118$	−6.69222	+	20.5965i	−0.616069	+	1.89607i
$119$	−3.85071	−	6.43449i	−0.352994	−	0.589848i
$120$	1.62901			0.148707
$121$		0			0
$122$	3.97252	−	6.88061i	0.359655	−	0.622942i
$123$	15.1362	−	6.73906i	1.36478	−	0.607640i
$124$	−8.58210	+	1.82418i	−0.770696	+	0.163816i
$125$	1.88463	+	5.80031i	0.168567	+	0.518795i
$126$	8.67689	−	1.98701i	0.772999	−	0.177017i
$127$	16.9885	−	12.3429i	1.50748	−	1.09525i	0.540206	−	0.841533i	$-0.318346\pi$
$127$	16.9885	−	12.3429i	1.50748	−	1.09525i	0.967278	−	0.253718i	$-0.0816535\pi$
$128$	−5.92527	+	6.58068i	−0.523725	+	0.581655i
$129$	−7.16065	−	7.95271i	−0.630460	−	0.700197i
$130$	1.91834	−	0.854101i	0.168250	−	0.0749096i
$131$	−6.85071	−	11.8658i	−0.598549	−	1.03672i	−0.993035	−	0.117816i	$-0.962411\pi$
$131$	−6.85071	−	11.8658i	−0.598549	−	1.03672i	0.394486	−	0.918902i	$-0.370923\pi$
$132$		0			0
$133$	−11.7706	+	8.83705i	−1.02064	+	0.766270i
$134$	−2.37818	−	1.72785i	−0.205443	−	0.149263i
$135$	1.59341	−	0.338690i	0.137139	−	0.0291498i
$136$	−3.23184	−	0.686948i	−0.277128	−	0.0589053i
$137$	−0.759353	−	7.22476i	−0.0648759	−	0.617253i	−0.977860	−	0.209259i	$-0.932895\pi$
$137$	−0.759353	−	7.22476i	−0.0648759	−	0.617253i	0.912984	−	0.407995i	$-0.133772\pi$
$138$	7.97923	+	3.55258i	0.679237	+	0.302416i
$139$	0.804253	+	2.47524i	0.0682159	+	0.209947i	0.979353	−	0.202155i	$-0.0647946\pi$
$139$	0.804253	+	2.47524i	0.0682159	+	0.209947i	−0.911138	+	0.412102i	$0.864795\pi$
$140$	2.25140	+	0.441775i	0.190278	+	0.0373368i
$141$	−5.04149	−	3.66286i	−0.424570	−	0.308468i
$142$	3.93632	+	6.81790i	0.330328	+	0.572146i
$143$		0			0
$144$	4.46379	−	7.73152i	0.371983	−	0.644293i
$145$	0.692920	−	6.59269i	0.0575439	−	0.547493i
$146$	−9.06529	+	27.9001i	−0.750249	+	2.30903i
$147$	−15.3833	+	0.482545i	−1.26879	+	0.0397996i
$148$	−6.69588	+	4.86484i	−0.550398	+	0.399888i
$149$	0.913545	+	0.406737i	0.0748406	+	0.0333212i	0.443816	−	0.896118i	$-0.353625\pi$
$149$	0.913545	+	0.406737i	0.0748406	+	0.0333212i	−0.368975	+	0.929439i	$0.620291\pi$
$150$	18.1306	+	3.85378i	1.48036	+	0.314660i
$151$	−1.16124	−	1.28968i	−0.0945000	−	0.104953i	0.694040	−	0.719937i	$-0.255829\pi$
$151$	−1.16124	−	1.28968i	−0.0945000	−	0.104953i	−0.788540	+	0.614984i	$0.789163\pi$
$152$	−0.677895	+	6.44974i	−0.0549845	+	0.523143i
$153$	5.19869			0.420289
$154$		0			0
$155$	−4.08680			−0.328260
$156$	0.564864	−	5.37432i	0.0452253	−	0.430290i
$157$	−5.31262	−	5.90027i	−0.423993	−	0.470892i	0.492864	−	0.870106i	$-0.335950\pi$
$157$	−5.31262	−	5.90027i	−0.423993	−	0.470892i	−0.916858	+	0.399214i	$0.869283\pi$
$158$	−8.54349	−	1.81597i	−0.679683	−	0.144471i
$159$	−15.0039	−	6.68015i	−1.18988	−	0.529770i
$160$	3.39152	−	2.46408i	0.268123	−	0.194803i
$161$	−4.68795	−	3.29495i	−0.369462	−	0.259678i
$162$	6.31332	−	19.4304i	0.496021	−	1.52660i
$163$	1.67303	−	15.9178i	0.131042	−	1.24678i	−0.709373	−	0.704833i	$-0.751022\pi$
$163$	1.67303	−	15.9178i	0.131042	−	1.24678i	0.840415	−	0.541944i	$-0.182311\pi$
$164$	5.14101	−	8.90449i	0.401446	−	0.695324i
$165$		0			0
$166$	8.46652	+	14.6644i	0.657130	+	1.13818i
$167$	0.937823	+	0.681368i	0.0725709	+	0.0527259i	0.623479	−	0.781840i	$-0.285719\pi$
$167$	0.937823	+	0.681368i	0.0725709	+	0.0527259i	−0.550908	+	0.834566i	$0.685719\pi$
$168$	−4.45809	+	5.11011i	−0.343949	+	0.394253i
$169$	−3.01455	−	9.27783i	−0.231888	−	0.713679i
$170$	3.01839	+	1.34387i	0.231500	+	0.103070i
$171$	−1.06662	−	10.1483i	−0.0815668	−	0.776056i
$172$	−6.49589	−	1.38074i	−0.495307	−	0.105281i
$173$	−0.971747	+	0.206551i	−0.0738805	+	0.0157038i	−0.244704	−	0.969598i	$-0.578691\pi$
$173$	−0.971747	+	0.206551i	−0.0738805	+	0.0157038i	0.170823	+	0.985302i	$0.445357\pi$
$174$	−34.0311	−	24.7251i	−2.57989	−	1.87440i
$175$	−11.1850	−	4.77117i	−0.845503	−	0.360667i
$176$		0			0
$177$	12.9797	+	22.4815i	0.975615	+	1.68982i
$178$	−0.610693	+	0.271898i	−0.0457734	+	0.0203796i
$179$	−13.1564	−	14.6117i	−0.983356	−	1.09213i	−0.995740	−	0.0922042i	$-0.970609\pi$
$179$	−13.1564	−	14.6117i	−0.983356	−	1.09213i	0.0123840	−	0.999923i	$-0.496058\pi$
$180$	−1.06433	+	1.18206i	−0.0793304	+	0.0881053i
$181$	19.3134	−	14.0320i	1.43555	−	1.04299i	0.446602	−	0.894732i	$-0.352634\pi$
$181$	19.3134	−	14.0320i	1.43555	−	1.04299i	0.988949	−	0.148257i	$-0.0473662\pi$
$182$	−2.57064	+	8.35515i	−0.190549	+	0.619325i
$183$	−2.94297	−	9.05754i	−0.217551	−	0.669553i
$184$	−2.46957	+	0.524924i	−0.182059	+	0.0386979i
$185$	−3.52188	+	1.56804i	−0.258934	+	0.115285i
$186$	−12.9665	+	22.4587i	−0.950752	+	1.64675i
$187$		0			0
$188$	−3.86718			−0.282043
$189$	−3.29822	+	5.92533i	−0.239910	+	0.431004i
$190$	2.00406	−	6.16786i	0.145390	−	0.447463i
$191$	−7.44859	+	8.27249i	−0.538961	+	0.598577i	−0.949694	−	0.313179i	$-0.898606\pi$
$191$	−7.44859	+	8.27249i	−0.538961	+	0.598577i	0.410733	+	0.911756i	$0.365273\pi$
$192$	−0.543411	−	5.17021i	−0.0392173	−	0.373128i
$193$	0.377831	+	3.59482i	0.0271969	+	0.258761i	0.999669	+	0.0257402i	$0.00819427\pi$
$193$	0.377831	+	3.59482i	0.0271969	+	0.258761i	−0.972472	+	0.233021i	$0.925139\pi$
$194$	3.18629	−	3.53873i	0.228762	−	0.254066i
$195$	0.777832	−	2.39392i	0.0557017	−	0.171432i
$196$	−7.54722	+	5.85352i	−0.539087	+	0.418109i
$197$	−2.41831			−0.172298			−0.0861489	−	0.996282i	$-0.527456\pi$
$197$	−2.41831			−0.172298			−0.0861489	+	0.996282i	$0.527456\pi$
$198$		0			0
$199$	9.24809	−	16.0182i	0.655580	−	1.13550i	−0.326168	−	0.945312i	$-0.605758\pi$
$199$	9.24809	−	16.0182i	0.655580	−	1.13550i	0.981748	−	0.190186i	$-0.0609091\pi$
$200$	−4.89469	+	2.17926i	−0.346107	+	0.154097i
$201$	−3.44666	+	0.732610i	−0.243109	+	0.0516743i
$202$	−5.61151	−	17.2704i	−0.394824	−	1.21514i
$203$	18.7846	+	20.2158i	1.31842	+	1.41887i
$204$	6.87885	−	4.99778i	0.481616	−	0.349915i
$205$	3.20467	−	3.55915i	0.223824	−	0.248582i
$206$	−7.64837	−	8.49438i	−0.532888	−	0.591832i
$207$	3.62908	−	1.61577i	0.252239	−	0.112304i
$208$	4.38364	+	7.59270i	0.303951	+	0.526459i
$209$		0			0
$210$	5.42312	−	4.07155i	0.374231	−	0.280964i
$211$	−6.35497	−	4.61716i	−0.437494	−	0.317858i	0.347144	−	0.937812i	$-0.387151\pi$
$211$	−6.35497	−	4.61716i	−0.437494	−	0.317858i	−0.784638	+	0.619954i	$0.787151\pi$
$212$	−9.96942	+	2.11907i	−0.684703	+	0.145538i
$213$	9.23064	+	1.96203i	0.632473	+	0.134436i
$214$	−2.12798	−	20.2464i	−0.145466	−	1.38401i
$215$	−2.82591	−	1.25818i	−0.192725	−	0.0858069i
$216$	0.923342	+	2.84175i	0.0628255	+	0.193357i
$217$	11.1843	−	12.8201i	0.759240	−	0.870283i
$218$	21.2262	+	15.4218i	1.43762	+	1.04449i
$219$	17.5823	+	30.4535i	1.18810	+	2.05786i
$220$		0			0
$221$	−2.55267	+	4.42136i	−0.171711	+	0.297413i
$222$	−2.55711	+	24.3292i	−0.171622	+	1.63287i
$223$	6.28447	−	19.3416i	0.420839	−	1.29521i	−0.486083	−	0.873913i	$-0.661575\pi$
$223$	6.28447	−	19.3416i	0.420839	−	1.29521i	0.906922	−	0.421298i	$-0.138425\pi$
$224$	−1.55185	+	17.3824i	−0.103687	+	1.16141i
$225$	6.82027	−	4.95522i	0.454685	−	0.330348i
$226$	14.5605	+	6.48277i	0.968553	+	0.431228i
$227$	7.06186	+	1.50104i	0.468712	+	0.0996278i	0.436212	−	0.899844i	$-0.356320\pi$
$227$	7.06186	+	1.50104i	0.468712	+	0.0996278i	0.0324999	+	0.999472i	$0.489653\pi$
$228$	−11.1674	−	12.4027i	−0.739579	−	0.821386i
$229$	−1.26180	+	12.0052i	−0.0833819	+	0.793326i	0.870303	+	0.492517i	$0.163923\pi$
$229$	−1.26180	+	12.0052i	−0.0833819	+	0.793326i	−0.953685	+	0.300809i	$0.902743\pi$
$230$	2.52475			0.166477
$231$		0			0
$232$	12.1592			0.798291
$233$	−0.788375	+	7.50089i	−0.0516482	+	0.491400i	0.937870	+	0.346988i	$0.112796\pi$
$233$	−0.788375	+	7.50089i	−0.0516482	+	0.491400i	−0.989518	+	0.144412i	$0.953871\pi$
$234$	−4.05521	−	4.50376i	−0.265097	−	0.294420i
$235$	−1.76195	−	0.374513i	−0.114937	−	0.0244305i
$236$	14.7170	+	6.55241i	0.957993	+	0.426526i
$237$	−8.47024	+	6.15399i	−0.550201	+	0.399745i
$238$	−12.4761	+	5.79075i	−0.808702	+	0.375359i
$239$	3.04266	−	9.36434i	0.196813	−	0.605729i	−0.803138	−	0.595794i	$-0.796838\pi$
$239$	3.04266	−	9.36434i	0.196813	−	0.605729i	0.999951	−	0.00993486i	$-0.00316242\pi$
$240$	0.710930	−	6.76405i	0.0458904	−	0.436618i
$241$	−0.837515	+	1.45062i	−0.0539491	+	0.0934426i	−0.891739	−	0.452551i	$-0.850514\pi$
$241$	−0.837515	+	1.45062i	−0.0539491	+	0.0934426i	0.837790	+	0.545993i	$0.183848\pi$
$242$		0			0
$243$	−8.40011	−	14.5494i	−0.538867	−	0.933346i
$244$	−4.78139	−	3.47388i	−0.306097	−	0.222393i
$245$	−4.00551	+	1.93605i	−0.255903	+	0.123690i
$246$	−9.39129	−	28.9034i	−0.598767	−	1.84281i
$247$	9.15458	+	4.07588i	0.582492	+	0.259342i
$248$	−0.783565	−	7.45512i	−0.0497564	−	0.473401i
$249$	19.8539	+	4.22009i	1.25819	+	0.267437i
$250$	10.9422	−	2.32584i	0.692048	−	0.147099i
$251$	−15.9974	−	11.6228i	−1.00974	−	0.733623i	−0.0455893	−	0.998960i	$-0.514517\pi$
$251$	−15.9974	−	11.6228i	−1.00974	−	0.733623i	−0.964156	+	0.265338i	$0.914517\pi$
$252$	−0.795307	−	6.57367i	−0.0500997	−	0.414102i
$253$		0			0
$254$	−19.2586	−	33.3568i	−1.20839	−	2.09299i
$255$	3.61812	−	1.61089i	0.226575	−	0.100878i
$256$	14.0326	+	15.5848i	0.877040	+	0.974051i
$257$	1.82001	−	2.02133i	0.113529	−	0.126087i	−0.683701	−	0.729762i	$-0.739631\pi$
$257$	1.82001	−	2.02133i	0.113529	−	0.126087i	0.797231	+	0.603675i	$0.206298\pi$
$258$	−15.8802	+	11.5376i	−0.988658	+	0.718302i
$259$	4.71943	−	15.3392i	0.293251	−	0.953130i
$260$	−0.482701	−	1.48560i	−0.0299359	−	0.0921331i
$261$	−18.7137	+	3.97771i	−1.15835	+	0.246214i
$262$	−22.9590	+	10.2220i	−1.41841	+	0.631517i
$263$	6.34744	−	10.9941i	0.391400	−	0.677924i	−0.601235	−	0.799073i	$-0.705324\pi$
$263$	6.34744	−	10.9941i	0.391400	−	0.677924i	0.992634	+	0.121148i	$0.0386576\pi$
$264$		0			0
$265$	−4.74744			−0.291633
$266$	13.8637	+	23.1661i	0.850040	+	1.42041i
$267$	−0.247618	+	0.762090i	−0.0151540	+	0.0466391i
$268$	−1.46318	+	1.62503i	−0.0893780	+	0.0992643i
$269$	0.741456	+	7.05449i	0.0452074	+	0.430120i	0.993594	+	0.113005i	$0.0360475\pi$
$269$	0.741456	+	7.05449i	0.0452074	+	0.430120i	−0.948387	+	0.317115i	$0.897286\pi$
$270$	−0.312331	−	2.97163i	−0.0190078	−	0.180848i
$271$	12.1890	−	13.5372i	0.740428	−	0.822329i	−0.248824	−	0.968549i	$-0.580044\pi$
$271$	12.1890	−	13.5372i	0.740428	−	0.822329i	0.989252	+	0.146220i	$0.0467107\pi$
$272$	−4.26282	+	13.1196i	−0.258471	+	0.795493i
$273$	5.38091	+	8.99144i	0.325667	+	0.544187i
$274$	−13.3250			−0.804991
$275$		0			0
$276$	3.24864	−	5.62680i	0.195545	−	0.338694i
$277$	−12.6514	+	5.63275i	−0.760146	+	0.338439i	−0.749937	−	0.661509i	$-0.769916\pi$
$277$	−12.6514	+	5.63275i	−0.760146	+	0.338439i	−0.0102090	+	0.999948i	$0.503250\pi$
$278$	4.66951	−	0.992536i	0.280059	−	0.0595283i
$279$	3.64478	+	11.2175i	0.218207	+	0.671573i
$280$	−0.576442	+	1.87356i	−0.0344490	+	0.111967i
$281$	17.0160	−	12.3628i	1.01509	−	0.737506i	0.0498191	−	0.998758i	$-0.484136\pi$
$281$	17.0160	−	12.3628i	1.01509	−	0.737506i	0.965270	+	0.261253i	$0.0841355\pi$
$282$	−7.64837	+	8.49438i	−0.455454	+	0.505833i
$283$	−0.235832	−	0.261918i	−0.0140187	−	0.0155694i	0.736095	−	0.676879i	$-0.236668\pi$
$283$	−0.235832	−	0.261918i	−0.0140187	−	0.0155694i	−0.750113	+	0.661309i	$0.770001\pi$
$284$	5.34996	−	2.38196i	0.317462	−	0.141343i
$285$	−3.88692	−	6.73234i	−0.230241	−	0.398789i
$286$		0			0
$287$	2.39465	+	19.7932i	0.141352	+	1.16835i
$288$	−9.78814	−	7.11150i	−0.576772	−	0.419049i
$289$	8.77111	−	1.86436i	0.515948	−	0.109668i
$290$	−11.8935	−	2.52804i	−0.698411	−	0.148452i
$291$	−0.596645	−	5.67670i	−0.0349759	−	0.332774i
$292$	19.9356	+	8.87590i	1.16664	+	0.519423i
$293$	1.07020	+	3.29375i	0.0625220	+	0.192423i	0.977438	−	0.211220i	$-0.0677437\pi$
$293$	1.07020	+	3.29375i	0.0625220	+	0.192423i	−0.914917	+	0.403643i	$0.867744\pi$
$294$	−2.06919	+	28.1546i	−0.120678	+	1.64201i
$295$	6.07071	+	4.41063i	0.353451	+	0.256797i
$296$	−3.53566	−	6.12395i	−0.205506	−	0.355947i
$297$		0			0
$298$	0.917122	−	1.58850i	0.0531274	−	0.0920194i
$299$	−0.407786	+	3.87983i	−0.0235829	+	0.224376i
$300$	4.26079	−	13.1134i	0.245997	−	0.757101i
$301$	11.6805	−	5.42148i	0.673251	−	0.312489i
$302$	−2.57528	+	1.87105i	−0.148191	+	0.107667i
$303$	−19.8854	−	8.85355i	−1.14239	−	0.508623i
$304$	26.4851	+	5.62958i	1.51902	+	0.322879i
$305$	−1.84205	−	2.04580i	−0.105476	−	0.117142i
$306$	0.996748	−	9.48343i	0.0569803	−	0.542131i
$307$	6.51473			0.371815			0.185908	−	0.982567i	$-0.440477\pi$
$307$	6.51473			0.371815			0.185908	+	0.982567i	$0.440477\pi$
$308$		0			0
$309$	−13.7014			−0.779447
$310$	−0.783565	+	7.45512i	−0.0445035	+	0.423422i
$311$	7.78205	+	8.64284i	0.441280	+	0.490091i	0.922222	−	0.386662i	$-0.126372\pi$
$311$	7.78205	+	8.64284i	0.441280	+	0.490091i	−0.480942	+	0.876752i	$0.659705\pi$
$312$	4.51611	+	0.959929i	0.255675	+	0.0543453i
$313$	−24.7550	−	11.0216i	−1.39924	−	0.622980i	−0.438067	−	0.898942i	$-0.644337\pi$
$313$	−24.7550	−	11.0216i	−1.39924	−	0.622980i	−0.961168	+	0.275963i	$0.911003\pi$
$314$	−11.7818	+	8.56000i	−0.664887	+	0.483069i
$315$	0.274266	−	3.07208i	0.0154531	−	0.173092i
$316$	−2.00777	+	6.17927i	−0.112946	+	0.347611i
$317$	−0.403660	+	3.84056i	−0.0226718	+	0.215708i	0.977320	+	0.211766i	$0.0679214\pi$
$317$	−0.403660	+	3.84056i	−0.0226718	+	0.215708i	−0.999992	+	0.00394180i	$0.998745\pi$
$318$	−15.0626	+	26.0892i	−0.844668	+	1.46301i
$319$		0			0
$320$	−0.751365	−	1.30140i	−0.0420026	−	0.0727506i
$321$	−19.7423	−	14.3436i	−1.10191	−	0.800583i
$322$	−6.90945	+	7.91999i	−0.385049	+	0.441364i
$323$	4.87236	+	14.9956i	0.271105	+	0.834377i
$324$	−13.8837	−	6.18142i	−0.771317	−	0.343412i
$325$	0.865386	+	8.23359i	0.0480030	+	0.456718i
$326$	−28.7164	−	6.10385i	−1.59045	−	0.338061i
$327$	30.7629	−	6.53886i	1.70119	−	0.361600i
$328$	7.10701	+	5.16355i	0.392419	+	0.285109i
$329$	5.99673	−	4.50220i	0.330610	−	0.248214i
$330$		0			0
$331$	−3.07514	−	5.32630i	−0.169025	−	0.292760i	0.769052	−	0.639186i	$-0.220729\pi$
$331$	−3.07514	−	5.32630i	−0.169025	−	0.292760i	−0.938077	+	0.346426i	$0.887395\pi$
$332$	11.5071	−	5.12328i	0.631533	−	0.281177i
$333$	7.44493	+	8.26844i	0.407980	+	0.453108i
$334$	1.42276	−	1.58013i	0.0778499	−	0.0864610i
$335$	−0.824022	+	0.598687i	−0.0450211	+	0.0327097i
$336$	19.2729	+	20.7413i	1.05142	+	1.13153i
$337$	3.63427	+	11.1851i	0.197971	+	0.609293i	0.999929	+	0.0119123i	$0.00379189\pi$
$337$	3.63427	+	11.1851i	0.197971	+	0.609293i	−0.801958	+	0.597381i	$0.796208\pi$
$338$	−17.5026	+	3.72028i	−0.952013	+	0.202357i
$339$	17.4536	−	7.77084i	0.947950	−	0.422054i
$340$	1.22890	−	2.12851i	0.0666462	−	0.115435i
$341$		0			0
$342$	−18.7169			−1.01209
$343$	4.88855	−	17.8634i	0.263957	−	0.964534i
$344$	1.75335	−	5.39624i	0.0945341	−	0.290946i
$345$	2.02505	−	2.24905i	0.109025	−	0.121085i
$346$	0.190476	+	1.81226i	0.0102401	+	0.0974276i
$347$	−0.0878862	−	0.836181i	−0.00471798	−	0.0448886i	0.991910	−	0.126946i	$-0.0405175\pi$
$347$	−0.0878862	−	0.836181i	−0.00471798	−	0.0448886i	−0.996628	+	0.0820576i	$0.973851\pi$
$348$	−20.9377	+	23.2537i	−1.12238	+	1.24653i
$349$	−2.82186	+	8.68480i	−0.151051	+	0.464887i	−0.997739	−	0.0672022i	$-0.978593\pi$
$349$	−2.82186	+	8.68480i	−0.151051	+	0.464887i	0.846689	+	0.532089i	$0.178593\pi$
$350$	−10.8480	+	19.4888i	−0.579852	+	1.04172i
$351$	4.61701			0.246438
$352$		0			0
$353$	−11.3639	+	19.6829i	−0.604840	+	1.04761i	0.387237	+	0.921980i	$0.373429\pi$
$353$	−11.3639	+	19.6829i	−0.604840	+	1.04761i	−0.992077	+	0.125633i	$0.959904\pi$
$354$	43.4993	−	19.3671i	2.31196	−	1.02935i
$355$	2.66820	−	0.567144i	0.141613	−	0.0301009i
$356$	0.153665	+	0.472932i	0.00814423	+	0.0250654i
$357$	−4.84840	+	15.7583i	−0.256604	+	0.834020i
$358$	−29.1770	+	21.1983i	−1.54205	+	1.12037i
$359$	17.5436	−	19.4842i	0.925917	−	1.02834i	−0.0736007	−	0.997288i	$-0.523449\pi$
$359$	17.5436	−	19.4842i	0.925917	−	1.02834i	0.999518	−	0.0310474i	$-0.00988429\pi$
$360$	−0.909341	−	1.00993i	−0.0479265	−	0.0532278i
$361$	10.9155	−	4.85990i	0.574501	−	0.255784i
$362$	−21.8941	−	37.9217i	−1.15073	−	1.99312i
$363$		0			0
$364$	5.98126	+	2.55143i	0.313503	+	0.133731i
$365$	8.22339	+	5.97464i	0.430432	+	0.312727i
$366$	−17.0870	+	3.63195i	−0.893151	+	0.189845i
$367$	3.73872	+	0.794688i	0.195159	+	0.0414824i	0.304454	−	0.952527i	$-0.401526\pi$
$367$	3.73872	+	0.794688i	0.195159	+	0.0414824i	−0.109295	+	0.994009i	$0.534859\pi$
$368$	1.10185	+	10.4834i	0.0574378	+	0.546484i
$369$	−12.6272	−	5.62201i	−0.657348	−	0.292670i
$370$	2.18516	+	6.72523i	0.113601	+	0.349628i
$371$	12.9923	−	14.8925i	0.674526	−	0.773178i
$372$	15.6067	+	11.3389i	0.809170	+	0.587896i
$373$	7.55387	+	13.0837i	0.391124	+	0.677447i	0.992598	−	0.121445i	$-0.0387529\pi$
$373$	7.55387	+	13.0837i	0.391124	+	0.677447i	−0.601474	+	0.798893i	$0.705420\pi$
$374$		0			0
$375$	6.70469	−	11.6129i	0.346229	−	0.599686i
$376$	0.345366	−	3.28594i	0.0178109	−	0.169459i
$377$	5.80588	−	17.8687i	0.299018	−	0.920283i
$378$	10.1766	+	7.15267i	0.523427	+	0.367893i
$379$	9.20374	−	6.68691i	0.472764	−	0.343483i	−0.325753	−	0.945455i	$-0.605618\pi$
$379$	9.20374	−	6.68691i	0.472764	−	0.343483i	0.798518	+	0.601971i	$0.205618\pi$
$380$	−4.40715	−	1.96219i	−0.226082	−	0.100658i
$381$	−45.1612	−	9.59931i	−2.31368	−	0.491788i
$382$	13.6625	+	15.1738i	0.699035	+	0.776357i
$383$	−0.928811	+	8.83705i	−0.0474600	+	0.451552i	0.944825	+	0.327575i	$0.106231\pi$
$383$	−0.928811	+	8.83705i	−0.0474600	+	0.451552i	−0.992285	+	0.123977i	$0.960435\pi$
$384$	19.4698			0.993564
$385$		0			0
$386$	6.63009			0.337463
$387$	−0.933187	+	8.87868i	−0.0474366	+	0.451329i
$388$	−2.37020	−	2.63237i	−0.120329	−	0.133639i
$389$	19.4642	+	4.13724i	0.986873	+	0.209766i	0.672955	−	0.739684i	$-0.265025\pi$
$389$	19.4642	+	4.13724i	0.986873	+	0.209766i	0.313919	+	0.949450i	$0.398358\pi$
$390$	−4.21784	−	1.87791i	−0.213579	−	0.0950914i
$391$	−4.96597	+	3.60799i	−0.251140	+	0.182464i
$392$	−4.29971	−	6.93563i	−0.217168	−	0.350302i
$393$	−9.30920	+	28.6508i	−0.469587	+	1.44524i
$394$	−0.463665	+	4.41148i	−0.0233591	+	0.222247i
$395$	−1.51320	+	2.62093i	−0.0761371	+	0.131873i
$396$		0			0
$397$	17.4303	+	30.1902i	0.874803	+	1.51520i	0.856973	+	0.515361i	$0.172342\pi$
$397$	17.4303	+	30.1902i	0.874803	+	1.51520i	0.0178296	+	0.999841i	$0.494324\pi$
$398$	−27.4471	−	19.9415i	−1.37580	−	0.999577i
$399$	31.7563	+	6.23129i	1.58980	+	0.311955i
$400$	6.91268	+	21.2750i	0.345634	+	1.06375i
$401$	10.4110	+	4.63529i	0.519902	+	0.231475i	0.649874	−	0.760042i	$-0.274822\pi$
$401$	10.4110	+	4.63529i	0.519902	+	0.231475i	−0.129971	+	0.991518i	$0.541489\pi$
$402$	0.675594	+	6.42784i	0.0336956	+	0.320592i
$403$	−11.3299	−	2.40824i	−0.564381	−	0.119963i
$404$	−13.2130	+	2.80851i	−0.657371	+	0.139729i
$405$	−5.72700	−	4.16091i	−0.284577	−	0.206757i
$406$	40.4792	−	30.3908i	2.00895	−	1.50827i
$407$		0			0
$408$	3.63228	+	6.29129i	0.179825	+	0.311465i
$409$	3.73447	−	1.66269i	0.184658	−	0.0822149i	−0.312325	−	0.949975i	$-0.601108\pi$
$409$	3.73447	−	1.66269i	0.184658	−	0.0822149i	0.496983	+	0.867760i	$0.334441\pi$
$410$	−5.87815	−	6.52834i	−0.290301	−	0.322412i
$411$	−10.6877	+	11.8699i	−0.527186	+	0.585499i
$412$	−6.87885	+	4.99778i	−0.338897	+	0.246223i
$413$	−30.4496	+	6.97295i	−1.49833	+	0.343117i
$414$	−2.25168	−	6.92995i	−0.110664	−	0.340588i
$415$	5.73897	−	1.21985i	0.281715	−	0.0598803i
$416$	10.8544	−	4.83267i	0.532178	−	0.236941i
$417$	2.86118	−	4.95570i	0.140112	−	0.242682i
$418$		0			0
$419$	32.8002			1.60240			0.801198	−	0.598399i	$-0.204196\pi$
$419$	32.8002			1.60240			0.801198	+	0.598399i	$0.204196\pi$
$420$	−2.59045	−	4.32862i	−0.126401	−	0.211215i
$421$	−2.63322	+	8.10422i	−0.128335	+	0.394975i	−0.994494	−	0.104794i	$-0.966582\pi$
$421$	−2.63322	+	8.10422i	−0.128335	+	0.394975i	0.866159	+	0.499769i	$0.166582\pi$
$422$	−9.64103	+	10.7075i	−0.469318	+	0.521231i
$423$	0.543411	+	5.17021i	0.0264216	+	0.251384i
$424$	−0.910230	−	8.66026i	−0.0442047	−	0.420579i
$425$	−8.71636	+	9.68049i	−0.422805	+	0.469573i
$426$	5.34893	−	16.4623i	0.259156	−	0.797602i
$427$	11.4587	−	0.179675i	0.554525	−	0.00869508i
$428$	−15.1437			−0.732000
$429$		0			0
$430$	−2.83697	+	4.91378i	−0.136811	+	0.236964i
$431$	15.2876	−	6.80648i	0.736378	−	0.327856i	−0.00405075	−	0.999992i	$-0.501289\pi$
$431$	15.2876	−	6.80648i	0.736378	−	0.327856i	0.740428	+	0.672135i	$0.234623\pi$
$432$	12.2026	−	2.59375i	0.587100	−	0.124792i
$433$	−7.99306	−	24.6001i	−0.384122	−	1.18221i	−0.937115	−	0.349020i	$-0.886514\pi$
$433$	−7.99306	−	24.6001i	−0.384122	−	1.18221i	0.552993	−	0.833186i	$-0.313486\pi$
$434$	−21.2419	−	22.8604i	−1.01964	−	1.09733i
$435$	−11.7915	+	8.56705i	−0.565361	+	0.410759i
$436$	13.0595	−	14.5040i	0.625437	−	0.694618i
$437$	8.06196	+	8.95371i	0.385656	+	0.428314i
$438$	58.9242	−	26.2347i	2.81551	−	1.25354i
$439$	−4.78430	−	8.28665i	−0.228342	−	0.395500i	0.728975	−	0.684541i	$-0.239997\pi$
$439$	−4.78430	−	8.28665i	−0.228342	−	0.395500i	−0.957317	+	0.289040i	$0.906664\pi$
$440$		0			0
$441$	8.88637	+	9.26770i	0.423161	+	0.441319i
$442$	7.57600	+	5.50428i	0.360353	+	0.261812i
$443$	−18.6170	+	3.95717i	−0.884521	+	0.188011i	−0.627707	−	0.778450i	$-0.716006\pi$
$443$	−18.6170	+	3.95717i	−0.884521	+	0.188011i	−0.256815	+	0.966461i	$0.582673\pi$
$444$	17.7999	+	3.78350i	0.844748	+	0.179557i
$445$	0.0242115	+	0.230357i	0.00114773	+	0.0109200i
$446$	−34.0779	−	15.1725i	−1.61364	−	0.718438i
$447$	−0.679433	−	2.09108i	−0.0321361	−	0.0989047i
$448$	6.13868	+	1.20455i	0.290025	+	0.0569094i
$449$	−26.9746	−	19.5982i	−1.27301	−	0.924896i	−0.273692	−	0.961817i	$-0.588245\pi$
$449$	−26.9746	−	19.5982i	−1.27301	−	0.924896i	−0.999318	+	0.0369217i	$0.988245\pi$
$450$	−7.73163	−	13.3916i	−0.364472	−	0.631285i
$451$		0			0
$452$	5.92813	−	10.2678i	0.278836	−	0.482958i
$453$	−0.398849	+	3.79479i	−0.0187396	+	0.178295i
$454$	4.09217	−	12.5944i	0.192055	−	0.591085i
$455$	2.47806	+	1.74172i	0.116173	+	0.0816530i
$456$	11.5359	−	8.38129i	0.540216	−	0.392490i
$457$	−10.9265	−	4.86478i	−0.511119	−	0.227565i	0.134938	−	0.990854i	$-0.456917\pi$
$457$	−10.9265	−	4.86478i	−0.511119	−	0.227565i	−0.646057	+	0.763289i	$0.723583\pi$
$458$	21.6579	+	4.60353i	1.01201	+	0.215109i
$459$	4.86094	+	5.39862i	0.226889	+	0.251986i
$460$	0.196314	−	1.86781i	0.00915321	−	0.0870870i
$461$	−12.4896			−0.581701			−0.290850	−	0.956769i	$-0.593938\pi$
$461$	−12.4896			−0.581701			−0.290850	+	0.956769i	$0.593938\pi$
$462$		0			0
$463$	12.3095			0.572071			0.286035	−	0.958219i	$-0.407662\pi$
$463$	12.3095			0.572071			0.286035	+	0.958219i	$0.407662\pi$
$464$	5.30651	−	50.4881i	0.246349	−	2.34385i
$465$	6.01255	+	6.67761i	0.278825	+	0.309667i
$466$	13.5319	+	2.87630i	0.626855	+	0.133242i
$467$	29.9284	+	13.3250i	1.38492	+	0.616607i	0.957760	−	0.287568i	$-0.0928466\pi$
$467$	29.9284	+	13.3250i	1.38492	+	0.616607i	0.427162	+	0.904175i	$0.359513\pi$
$468$	−3.64720	+	2.64985i	−0.168592	+	0.122489i
$469$	0.377046	−	4.22333i	0.0174104	−	0.195015i
$470$	−1.02100	+	3.14233i	−0.0470954	+	0.144945i
$471$	−1.82472	+	17.3611i	−0.0840788	+	0.799956i
$472$	−6.88191	+	11.9198i	−0.316766	+	0.548654i
$473$		0			0
$474$	9.60208	+	16.6313i	0.441038	+	0.763900i
$475$	20.6854	+	15.0288i	0.949113	+	0.689571i
$476$	3.31391	+	9.68005i	0.151893	+	0.443685i
$477$	4.23397	+	13.0308i	0.193860	+	0.596641i
$478$	−16.4990	−	7.34583i	−0.754647	−	0.335990i
$479$	2.71544	+	25.8357i	0.124072	+	1.18046i	0.862474	+	0.506102i	$0.168914\pi$
$479$	2.71544	+	25.8357i	0.124072	+	1.18046i	−0.738402	+	0.674360i	$0.764419\pi$
$480$	−9.01582	−	1.91637i	−0.411514	−	0.0874700i
$481$	−10.6877	+	2.27175i	−0.487319	+	0.103583i
$482$	2.48563	+	1.80592i	0.113218	+	0.0822573i
$483$	1.51320	+	12.5074i	0.0688528	+	0.569107i
$484$		0			0
$485$	−0.824970	−	1.42889i	−0.0374600	−	0.0648825i
$486$	−28.1515	+	12.5339i	−1.27698	+	0.568548i
$487$	9.72626	+	10.8021i	0.440739	+	0.489490i	0.922056	−	0.387056i	$-0.126508\pi$
$487$	9.72626	+	10.8021i	0.440739	+	0.489490i	−0.481317	+	0.876546i	$0.659841\pi$
$488$	3.37877	−	3.75250i	0.152950	−	0.169868i
$489$	−28.4702	+	20.6848i	−1.28747	+	0.935398i
$490$	2.76376	+	7.67803i	0.124854	+	0.346858i
$491$	12.1738	+	37.4671i	0.549395	+	1.69087i	0.710303	+	0.703896i	$0.248558\pi$
$491$	12.1738	+	37.4671i	0.549395	+	1.69087i	−0.160908	+	0.986969i	$0.551442\pi$
$492$	−22.1130	+	4.70026i	−0.996930	+	0.211904i
$493$	27.0063	−	12.0240i	1.21630	−	0.541532i
$494$	9.19041	−	15.9183i	0.413496	−	0.716196i
$495$		0			0
$496$	−31.2975			−1.40530
$497$	−5.52295	+	9.92210i	−0.247738	+	0.445067i
$498$	11.5049	−	35.4083i	0.515546	−	1.58669i
$499$	−17.5517	+	19.4931i	−0.785720	+	0.872631i	−0.994436	−	0.105346i	$-0.966405\pi$
$499$	−17.5517	+	19.4931i	−0.785720	+	0.872631i	0.208716	+	0.977976i	$0.433072\pi$
$500$	−0.869834	−	8.27591i	−0.0389001	−	0.370110i
$501$	−0.266417	−	2.53479i	−0.0119026	−	0.113246i
$502$	−24.2694	+	26.9539i	−1.08320	+	1.20301i
$503$	−1.21942	+	3.75300i	−0.0543714	+	0.167338i	−0.974555	−	0.224150i	$-0.928039\pi$
$503$	−1.21942	+	3.75300i	−0.0543714	+	0.167338i	0.920183	+	0.391488i	$0.128039\pi$
$504$	5.65667	−	0.0886978i	0.251968	−	0.00395091i
$505$	−6.29204			−0.279992
$506$		0			0
$507$	−10.7244	+	18.5753i	−0.476289	+	0.824956i
$508$	−26.1748	+	11.6538i	−1.16132	+	0.517053i
$509$	−16.5361	+	3.51487i	−0.732952	+	0.155794i	−0.559243	−	0.829003i	$-0.688908\pi$
$509$	−16.5361	+	3.51487i	−0.732952	+	0.155794i	−0.173708	+	0.984797i	$0.555575\pi$
$510$	−2.24487	−	6.90901i	−0.0994046	−	0.305936i
$511$	−41.2470	+	9.44557i	−1.82466	+	0.417847i
$512$	16.7923	−	12.2003i	0.742120	−	0.539182i
$513$	9.54120	−	10.5966i	0.421254	−	0.467850i
$514$	−3.33835	−	3.70761i	−0.147248	−	0.163536i
$515$	−3.61812	+	1.61089i	−0.159433	+	0.0709843i
$516$	7.30077	+	12.6453i	0.321398	+	0.556678i
$517$		0			0
$518$	−27.0768	−	11.5502i	−1.18969	−	0.507485i
$519$	1.76714	+	1.28390i	0.0775688	+	0.0563570i
$520$	1.30542	−	0.277476i	0.0572466	−	0.0121681i
$521$	−1.52364	−	0.323860i	−0.0667519	−	0.0141886i	0.174415	−	0.984672i	$-0.444197\pi$
$521$	−1.52364	−	0.323860i	−0.0667519	−	0.0141886i	−0.241167	+	0.970484i	$0.577530\pi$
$522$	3.66814	+	34.9000i	0.160550	+	1.52753i
$523$	11.4218	+	5.08532i	0.499441	+	0.222365i	0.640966	−	0.767569i	$-0.278534\pi$
$523$	11.4218	+	5.08532i	0.499441	+	0.222365i	−0.141525	+	0.989935i	$0.545201\pi$
$524$	5.77703	+	17.7799i	0.252371	+	0.776718i
$525$	8.65960	+	25.2950i	0.377936	+	1.10396i
$526$	−18.8384	−	13.6869i	−0.821391	−	0.596776i
$527$	−9.11254	−	15.7834i	−0.396949	−	0.687535i
$528$		0			0
$529$	9.15475	−	15.8565i	0.398033	−	0.689413i
$530$	−0.910230	+	8.66026i	−0.0395379	+	0.376178i
$531$	6.69222	−	20.5965i	0.290418	−	0.893814i
$532$	18.2163	−	8.45508i	0.789777	−	0.366574i
$533$	10.9816	−	7.97863i	0.475668	−	0.345593i
$534$	1.34272	+	0.597820i	0.0581054	+	0.0258702i
$535$	−6.89972	−	1.46658i	−0.298301	−	0.0634058i
$536$	−1.25011	−	1.38839i	−0.0539966	−	0.0599693i
$537$	−4.51882	+	42.9937i	−0.195002	+	1.85532i
$538$	13.0109			0.560941
$539$		0			0
$540$	−2.22270			−0.0956497
$541$	−1.73121	+	16.4713i	−0.0744304	+	0.708158i	0.892141	+	0.451758i	$0.149203\pi$
$541$	−1.73121	+	16.4713i	−0.0744304	+	0.708158i	−0.966571	+	0.256400i	$0.917464\pi$
$542$	−22.3576	−	24.8306i	−0.960340	−	1.06657i
$543$	−51.3416	−	10.9130i	−2.20328	−	0.468321i
$544$	17.0786	+	7.60389i	0.732240	+	0.326014i
$545$	7.35474	−	5.34353i	0.315042	−	0.228892i
$546$	17.4338	−	8.09189i	0.746099	−	0.346301i
$547$	2.05326	−	6.31928i	0.0877909	−	0.270193i	−0.897517	−	0.440980i	$-0.854631\pi$
$547$	2.05326	−	6.31928i	0.0877909	−	0.270193i	0.985308	+	0.170787i	$0.0546310\pi$
$548$	−1.03610	+	9.85782i	−0.0442599	+	0.421105i
$549$	−3.97252	+	6.88061i	−0.169543	+	0.293657i
$550$		0			0
$551$	−29.0127	−	50.2514i	−1.23598	−	2.14078i
$552$	4.49096	+	3.26288i	0.191148	+	0.138877i
$553$	−4.08057	−	11.9195i	−0.173523	−	0.506868i
$554$	7.84957	+	24.1585i	0.333496	+	1.02640i
$555$	7.74352	+	3.44764i	0.328694	+	0.146344i
$556$	−0.371195	−	3.53168i	−0.0157422	−	0.149777i
$557$	12.8254	+	2.72612i	0.543428	+	0.115509i	0.471443	−	0.881896i	$-0.343733\pi$
$557$	12.8254	+	2.72612i	0.543428	+	0.115509i	0.0719851	+	0.997406i	$0.477067\pi$
$558$	21.1617	−	4.49806i	0.895846	−	0.190418i
$559$	−7.09289	−	5.15328i	−0.299997	−	0.217961i
$560$	7.52793	+	3.21119i	0.318113	+	0.135698i
$561$		0			0
$562$	−19.2898	−	33.4108i	−0.813689	−	1.40935i
$563$	−27.8527	+	12.4008i	−1.17385	+	0.522632i	−0.898612	−	0.438744i	$-0.855423\pi$
$563$	−27.8527	+	12.4008i	−1.17385	+	0.522632i	−0.275239	+	0.961376i	$0.588757\pi$
$564$	5.68944	+	6.31876i	0.239568	+	0.266068i
$565$	3.69532	−	4.10407i	0.155463	−	0.172660i
$566$	−0.523005	+	0.379986i	−0.0219836	+	0.0159720i
$567$	28.7255	−	6.57815i	1.20636	−	0.276256i
$568$	1.54616	+	4.75858i	0.0648753	+	0.199666i
$569$	−34.5852	+	7.35132i	−1.44989	+	0.308183i	−0.864526	−	0.502588i	$-0.832381\pi$
$569$	−34.5852	+	7.35132i	−1.44989	+	0.308183i	−0.585363	+	0.810771i	$0.699048\pi$
$570$	−13.0263	+	5.79970i	−0.545613	+	0.242923i
$571$	−20.6422	+	35.7533i	−0.863849	+	1.49623i	0.00433587	+	0.999991i	$0.498620\pi$
$571$	−20.6422	+	35.7533i	−0.863849	+	1.49623i	−0.868185	+	0.496240i	$0.834713\pi$
$572$		0			0
$573$	24.4753			1.02247
$574$	36.5657	−	0.573359i	1.52622	−	0.0239315i
$575$	−3.07595	+	9.46680i	−0.128276	+	0.394793i
$576$	−2.90200	+	3.22300i	−0.120917	+	0.134292i
$577$	−0.909660	−	8.65483i	−0.0378696	−	0.360305i	−0.997004	−	0.0773535i	$-0.975353\pi$
$577$	−0.909660	−	8.65483i	−0.0378696	−	0.360305i	0.959134	−	0.282952i	$-0.0913137\pi$
$578$	−1.71926	−	16.3577i	−0.0715118	−	0.680390i
$579$	5.31787	−	5.90609i	0.221003	−	0.245449i
$580$	−2.79504	+	8.60225i	−0.116058	+	0.357189i
$581$	−11.8792	+	21.3412i	−0.492831	+	0.885381i
$582$	−10.4698			−0.433987
$583$		0			0
$584$	−9.32224	+	16.1466i	−0.385757	+	0.668151i
$585$	−1.91834	+	0.854101i	−0.0793137	+	0.0353127i
$586$	6.21363	−	1.32075i	0.256683	−	0.0545596i
$587$	−7.12404	−	21.9255i	−0.294040	−	0.904963i	−0.983542	−	0.180679i	$-0.942170\pi$
$587$	−7.12404	−	21.9255i	−0.294040	−	0.904963i	0.689502	−	0.724284i	$-0.257830\pi$
$588$	20.6679	+	3.71998i	0.852329	+	0.153409i
$589$	−28.9408	+	21.0267i	−1.19248	+	0.866390i
$590$	9.20979	−	10.2285i	0.379161	−	0.421101i
$591$	3.55785	+	3.95139i	0.146350	+	0.162539i
$592$	−26.9712	+	12.0084i	−1.10851	+	0.493540i
$593$	15.0494	+	26.0663i	0.618005	+	1.07042i	0.989849	+	0.142121i	$0.0453921\pi$
$593$	15.0494	+	26.0663i	0.618005	+	1.07042i	−0.371844	+	0.928295i	$0.621275\pi$
$594$		0			0
$595$	0.572413	+	4.73131i	0.0234666	+	0.193965i
$596$	−1.10386	−	0.802002i	−0.0452159	−	0.0328513i
$597$	−39.7787	+	8.45523i	−1.62803	+	0.346049i
$598$	6.99937	+	1.48776i	0.286226	+	0.0608391i
$599$	−3.05761	−	29.0912i	−0.124931	−	1.18864i	−0.859874	−	0.510507i	$-0.829458\pi$
$599$	−3.05761	−	29.0912i	−0.124931	−	1.18864i	0.734943	−	0.678129i	$-0.237209\pi$
$600$	10.7619	+	4.79151i	0.439353	+	0.195613i
$601$	8.28853	+	25.5095i	0.338096	+	1.04055i	0.965177	+	0.261599i	$0.0842496\pi$
$601$	8.28853	+	25.5095i	0.338096	+	1.04055i	−0.627081	+	0.778954i	$0.715750\pi$
$602$	−7.65034	−	22.3469i	−0.311804	−	0.910793i
$603$	2.37818	+	1.72785i	0.0968469	+	0.0703634i
$604$	1.18396	+	2.05068i	0.0481746	+	0.0834409i
$605$		0			0
$606$	−19.9633	+	34.5774i	−0.810952	+	1.40461i
$607$	3.36682	−	32.0332i	0.136655	−	1.30019i	−0.684303	−	0.729198i	$-0.739893\pi$
$607$	3.36682	−	32.0332i	0.136655	−	1.30019i	0.820958	−	0.570988i	$-0.193440\pi$
$608$	11.3393	−	34.8989i	0.459871	−	1.41534i
$609$	5.39543	−	60.4348i	0.218634	−	2.44894i
$610$	−4.08512	+	2.96802i	−0.165402	+	0.120171i
$611$	−4.66397	−	2.07653i	−0.188684	−	0.0840075i
$612$	−6.93834	−	1.47479i	−0.280466	−	0.0596148i
$613$	−29.8399	−	33.1405i	−1.20522	−	1.33853i	−0.925637	−	0.378412i	$-0.876470\pi$
$613$	−29.8399	−	33.1405i	−1.20522	−	1.33853i	−0.279584	−	0.960121i	$-0.590197\pi$
$614$	1.24907	−	11.8841i	0.0504085	−	0.479605i
$615$	−10.5302			−0.424619
$616$		0			0
$617$	−0.531290			−0.0213889			−0.0106945	−	0.999943i	$-0.503404\pi$
$617$	−0.531290			−0.0213889			−0.0106945	+	0.999943i	$0.503404\pi$
$618$	−2.62698	+	24.9941i	−0.105673	+	1.00541i
$619$	27.9330	+	31.0228i	1.12272	+	1.24691i	0.965797	+	0.259301i	$0.0834921\pi$
$619$	27.9330	+	31.0228i	1.12272	+	1.24691i	0.156927	+	0.987610i	$0.449841\pi$
$620$	5.45437	+	1.15936i	0.219053	+	0.0465611i
$621$	5.07122	+	2.25785i	0.203501	+	0.0906044i
$622$	17.2583	−	12.5389i	0.691994	−	0.502763i
$623$	−0.788876	−	0.554465i	−0.0316056	−	0.0222142i
$624$	5.95679	−	18.3331i	0.238462	−	0.733911i
$625$	−1.99694	+	18.9996i	−0.0798776	+	0.759984i
$626$	−24.8519	+	43.0448i	−0.993282	+	1.72041i
$627$		0			0
$628$	5.41658	+	9.38179i	0.216145	+	0.374374i
$629$	−13.9087	−	10.1053i	−0.554578	−	0.402924i
$630$	−5.55150	−	1.08933i	−0.221177	−	0.0433998i
$631$	−0.0671302	−	0.206606i	−0.00267241	−	0.00822484i	0.949711	−	0.313127i	$-0.101376\pi$
$631$	−0.0671302	−	0.206606i	−0.00267241	−	0.00822484i	−0.952384	+	0.304902i	$0.901376\pi$
$632$	−5.07122	−	2.25785i	−0.201722	−	0.0898125i
$633$	1.80532	+	17.1765i	0.0717551	+	0.682704i
$634$	6.92854	+	1.47271i	0.275168	+	0.0584887i
$635$	−13.0543	+	2.77477i	−0.518043	+	0.110113i
$636$	18.1296	+	13.1719i	0.718884	+	0.522300i
$637$	−12.2454	+	3.00700i	−0.485179	+	0.119142i
$638$		0			0
$639$	−3.93632	−	6.81790i	−0.155718	−	0.269712i
$640$	5.14136	−	2.28908i	0.203230	−	0.0904839i
$641$	−6.48421	−	7.20145i	−0.256111	−	0.284440i	0.601354	−	0.798983i	$-0.294628\pi$
$641$	−6.48421	−	7.20145i	−0.256111	−	0.284440i	−0.857465	+	0.514543i	$0.827962\pi$
$642$	−29.9508	+	33.2637i	−1.18206	+	1.31281i
$643$	−13.3191	+	9.67686i	−0.525252	+	0.381618i	−0.818579	−	0.574394i	$-0.805238\pi$
$643$	−13.3191	+	9.67686i	−0.525252	+	0.381618i	0.293327	+	0.956012i	$0.405238\pi$
$644$	5.32196	+	5.72744i	0.209714	+	0.225693i
$645$	2.10172	+	6.46843i	0.0827551	+	0.254694i
$646$	28.2890	−	6.01302i	1.11302	−	0.236579i
$647$	0.798184	−	0.355375i	0.0313799	−	0.0139712i	−0.390987	−	0.920396i	$-0.627866\pi$
$647$	0.798184	−	0.355375i	0.0313799	−	0.0139712i	0.422367	+	0.906425i	$0.361199\pi$
$648$	6.49226	−	11.2449i	0.255040	−	0.441743i
$649$		0			0
$650$	15.1856			0.595628
$651$	−37.4018	+	0.586468i	−1.46589	+	0.0229855i
$652$	−6.74850	+	20.7698i	−0.264292	+	0.813407i
$653$	−26.7204	+	29.6760i	−1.04565	+	1.16131i	−0.0590343	+	0.998256i	$0.518802\pi$
$653$	−26.7204	+	29.6760i	−1.04565	+	1.16131i	−0.986617	+	0.163057i	$0.947865\pi$
$654$	−6.02996	−	57.3712i	−0.235790	−	2.24339i
$655$	0.910230	+	8.66026i	0.0355656	+	0.338384i
$656$	24.5420	−	27.2566i	0.958203	−	1.06419i
$657$	9.06529	−	27.9001i	0.353671	−	1.08849i
$658$	−7.06313	−	11.8024i	−0.275350	−	0.460106i
$659$	6.89465			0.268578			0.134289	−	0.990942i	$-0.457125\pi$
$659$	6.89465			0.268578			0.134289	+	0.990942i	$0.457125\pi$
$660$		0			0
$661$	20.0072	−	34.6535i	0.778190	−	1.34786i	−0.154795	−	0.987947i	$-0.549472\pi$
$661$	20.0072	−	34.6535i	0.778190	−	1.34786i	0.932984	−	0.359917i	$-0.117195\pi$
$662$	−10.3058	+	4.58844i	−0.400547	+	0.178335i
$663$	10.9798	−	2.33383i	0.426420	−	0.0906383i
$664$	3.32559	+	10.2351i	0.129058	+	0.397199i
$665$	9.11845	−	2.08813i	0.353598	−	0.0809740i
$666$	16.5107	−	11.9957i	0.639775	−	0.464824i
$667$	15.1153	−	16.7873i	0.585269	−	0.650007i
$668$	−1.05835	−	1.17542i	−0.0409490	−	0.0454784i
$669$	−40.8489	+	18.1871i	−1.57931	+	0.703155i
$670$	0.934131	+	1.61796i	0.0360886	+	0.0625073i
$671$		0			0
$672$	30.6851	−	23.0376i	1.18370	−	0.888695i
$673$	25.3860	+	18.4440i	0.978559	+	0.710965i	0.957386	−	0.288811i	$-0.0932600\pi$
$673$	25.3860	+	18.4440i	0.978559	+	0.710965i	0.0211728	+	0.999776i	$0.493260\pi$
$674$	21.1007	−	4.48509i	0.812767	−	0.172759i
$675$	11.5229	+	2.44928i	0.443518	+	0.0942728i
$676$	1.39133	+	13.2377i	0.0535129	+	0.509141i
$677$	33.3732	+	14.8587i	1.28264	+	0.571066i	0.930982	−	0.365064i	$-0.118953\pi$
$677$	33.3732	+	14.8587i	1.28264	+	0.571066i	0.351653	+	0.936130i	$0.385620\pi$
$678$	−10.8291	−	33.3287i	−0.415891	−	1.27998i
$679$	6.74003	+	1.32255i	0.258659	+	0.0507546i
$680$	1.69885	+	1.23428i	0.0651477	+	0.0473326i
$681$	−7.93686	−	13.7470i	−0.304141	−	0.526788i
$682$		0			0
$683$	7.63501	−	13.2242i	0.292146	−	0.506011i	−0.682171	−	0.731192i	$-0.738964\pi$
$683$	7.63501	−	13.2242i	0.292146	−	0.506011i	0.974317	+	0.225181i	$0.0722975\pi$
$684$	−1.45535	+	13.8468i	−0.0556468	+	0.529444i
$685$	−1.42673	+	4.39103i	−0.0545127	+	0.167773i
$686$	−31.6491	−	12.3426i	−1.20837	−	0.471244i
$687$	21.4722	−	15.6005i	0.819216	−	0.595195i
$688$	−21.6414	−	9.63535i	−0.825069	−	0.367344i
$689$	−13.1614	−	2.79754i	−0.501408	−	0.106578i
$690$	−3.71444	−	4.12530i	−0.141406	−	0.157047i
$691$	4.01225	−	38.1740i	0.152633	−	1.45221i	−0.603276	−	0.797532i	$-0.706138\pi$
$691$	4.01225	−	38.1740i	0.152633	−	1.45221i	0.755910	−	0.654676i	$-0.227195\pi$
$692$	1.35552			0.0515291
$693$		0			0
$694$	−1.54221			−0.0585414
$695$	0.172900	−	1.64504i	0.00655849	−	0.0623998i
$696$	−17.8888	−	19.8675i	−0.678072	−	0.753076i
$697$	20.8912	+	4.44056i	0.791310	+	0.168198i
$698$	15.3017	+	6.81277i	0.579179	+	0.257867i
$699$	13.4159	−	9.74723i	0.507437	−	0.368674i
$700$	13.5743	+	9.54076i	0.513060	+	0.360607i
$701$	−5.53313	+	17.0292i	−0.208983	+	0.643184i	0.790543	+	0.612407i	$0.209798\pi$
$701$	−5.53313	+	17.0292i	−0.208983	+	0.643184i	−0.999526	+	0.0307778i	$0.990202\pi$
$702$	0.885221	−	8.42232i	0.0334105	−	0.317880i
$703$	−16.8726	+	29.2243i	−0.636364	+	1.10221i
$704$		0			0
$705$	1.98026	+	3.42991i	0.0745809	+	0.129178i
$706$	33.7266	+	24.5038i	1.26932	+	0.922212i
$707$	17.2194	−	19.7378i	0.647601	−	0.742315i
$708$	−10.9455	−	33.6867i	−0.411356	−	1.26602i
$709$	31.4254	+	13.9915i	1.18021	+	0.525461i	0.900598	−	0.434653i	$-0.143129\pi$
$709$	31.4254	+	13.9915i	1.18021	+	0.525461i	0.279607	+	0.960114i	$0.409796\pi$
$710$	−0.523005	−	4.97606i	−0.0196280	−	0.186748i
$711$	8.54349	+	1.81597i	0.320406	+	0.0681044i
$712$	−0.415574	+	0.0883329i	−0.0155743	+	0.00331042i
$713$	−11.2668	−	8.18579i	−0.421944	−	0.306560i
$714$	27.8167	+	11.8658i	1.04101	+	0.444066i
$715$		0			0
$716$	13.4138	+	23.2335i	0.501299	+	0.868276i
$717$	−19.7772	+	8.80538i	−0.738594	+	0.328843i
$718$	−32.1793	−	35.7387i	−1.20092	−	1.33376i
$719$	33.0666	−	36.7242i	1.23318	−	1.36958i	0.327924	−	0.944704i	$-0.393651\pi$
$719$	33.0666	−	36.7242i	1.23318	−	1.36958i	0.905252	−	0.424876i	$-0.139682\pi$
$720$	−4.59032	+	3.33506i	−0.171071	+	0.124290i
$721$	4.84840	−	15.7583i	0.180564	−	0.586871i
$722$	−6.77257	−	20.8438i	−0.252049	−	0.775727i
$723$	3.60239	−	0.765713i	0.133974	−	0.0284772i
$724$	−29.7569	+	13.2486i	−1.10591	+	0.492381i
$725$	23.9693	−	41.5160i	0.890196	−	1.54186i
$726$		0			0
$727$	−19.8201			−0.735086			−0.367543	−	0.930007i	$-0.619801\pi$
$727$	−19.8201			−0.735086			−0.367543	+	0.930007i	$0.619801\pi$
$728$	−2.70211	+	4.85441i	−0.100147	+	0.179916i
$729$	−1.08887	+	3.35120i	−0.0403286	+	0.124119i
$730$	12.4756	−	13.8555i	0.461742	−	0.512817i
$731$	−1.44195	−	13.7192i	−0.0533323	−	0.507423i
$732$	1.35830	+	12.9234i	0.0502042	+	0.477661i
$733$	20.5072	−	22.7756i	0.757451	−	0.841235i	−0.233929	−	0.972254i	$-0.575158\pi$
$733$	20.5072	−	22.7756i	0.757451	−	0.841235i	0.991380	+	0.131019i	$0.0418248\pi$
$734$	2.16649	−	6.66778i	0.0799667	−	0.246112i
$735$	9.05635	+	3.69644i	0.334049	+	0.136345i
$736$	14.2855			0.526570
$737$		0			0
$738$	−12.6767	+	21.9566i	−0.466635	+	0.808235i
$739$	−15.6233	+	6.95596i	−0.574714	+	0.255879i	−0.673448	−	0.739235i	$-0.735187\pi$
$739$	−15.6233	+	6.95596i	−0.574714	+	0.255879i	0.0987339	+	0.995114i	$0.468521\pi$
$740$	5.14524	−	1.09365i	0.189143	−	0.0402035i
$741$	−6.80855	−	20.9546i	−0.250118	−	0.769785i
$742$	−24.6757	−	26.5558i	−0.905875	−	0.974894i
$743$	−5.64089	+	4.09835i	−0.206944	+	0.150354i	−0.686430	−	0.727196i	$-0.740823\pi$
$743$	−5.64089	+	4.09835i	−0.206944	+	0.150354i	0.479486	+	0.877550i	$0.340823\pi$
$744$	−11.0285	+	12.2484i	−0.404324	+	0.449047i
$745$	−0.425267	−	0.472307i	−0.0155806	−	0.0173040i
$746$	25.3155	−	11.2712i	0.926866	−	0.412667i
$747$	−8.46652	−	14.6644i	−0.309774	−	0.536544i
$748$		0			0
$749$	23.4830	−	17.6305i	0.858050	−	0.644203i
$750$	−19.8986	−	14.4572i	−0.726596	−	0.527903i
$751$	−14.8998	+	3.16706i	−0.543703	+	0.115568i	−0.471572	−	0.881828i	$-0.656313\pi$
$751$	−14.8998	+	3.16706i	−0.543703	+	0.115568i	−0.0721309	+	0.997395i	$0.522980\pi$
$752$	−13.4933	−	2.86809i	−0.492051	−	0.104589i
$753$	4.54454	+	43.2384i	0.165612	+	1.57569i
$754$	−31.4828	−	14.0170i	−1.14653	−	0.510470i
$755$	0.340834	+	1.04898i	0.0124042	+	0.0381763i
$756$	6.08283	−	6.97248i	0.221231	−	0.253587i
$757$	11.7571	+	8.54204i	0.427320	+	0.310466i	0.780576	−	0.625061i	$-0.214926\pi$
$757$	11.7571	+	8.54204i	0.427320	+	0.310466i	−0.353257	+	0.935526i	$0.614926\pi$
$758$	−10.4336	−	18.0715i	−0.378965	−	0.656387i
$759$		0			0
$760$	2.06086	−	3.56952i	0.0747553	−	0.129480i
$761$	−0.179102	+	1.70404i	−0.00649243	+	0.0617713i	−0.997288	−	0.0735924i	$-0.976554\pi$
$761$	−0.179102	+	1.70404i	−0.00649243	+	0.0617713i	0.990796	+	0.135364i	$0.0432203\pi$
$762$	−26.1698	+	80.5424i	−0.948032	+	2.91774i
$763$	−3.36529	+	37.6950i	−0.121832	+	1.36465i
$764$	12.2879	−	8.92768i	0.444561	−	0.322992i
$765$	−3.01839	−	1.34387i	−0.109130	−	0.0485878i
$766$	15.9424	+	3.38867i	0.576023	+	0.122437i
$767$	14.2308	+	15.8049i	0.513845	+	0.570683i
$768$	4.81978	−	45.8571i	0.173919	−	1.65473i
$769$	36.5874			1.31937			0.659687	−	0.751540i	$-0.270689\pi$
$769$	36.5874			1.31937			0.659687	+	0.751540i	$0.270689\pi$
$770$		0			0
$771$	−5.98037			−0.215378
$772$	0.515530	−	4.90494i	0.0185543	−	0.176533i
$773$	17.9469	+	19.9320i	0.645504	+	0.716904i	0.973733	−	0.227694i	$-0.0731185\pi$
$773$	17.9469	+	19.9320i	0.645504	+	0.716904i	−0.328229	+	0.944598i	$0.606452\pi$
$774$	16.0175	+	3.40463i	0.575738	+	0.122377i
$775$	−26.9991	−	12.0208i	−0.969837	−	0.431799i
$776$	2.44840	−	1.77887i	0.0878925	−	0.0638576i
$777$	−32.0067	+	14.8559i	−1.14823	+	0.532951i
$778$	11.2790	−	34.7132i	0.404372	−	1.24453i
$779$	4.38204	−	41.6923i	0.157003	−	1.49378i
$780$	−1.71724	+	2.97434i	−0.0614870	+	0.106499i
$781$		0			0
$782$	5.62955	+	9.75067i	0.201312	+	0.348683i
$783$	−21.6285	−	15.7141i	−0.772941	−	0.561575i
$784$	−30.6749	+	14.8266i	−1.09553	+	0.529523i
$785$	1.55931	+	4.79905i	0.0556540	+	0.171286i
$786$	50.4797	+	22.4750i	1.80055	+	0.801657i
$787$	0.517582	+	4.92447i	0.0184498	+	0.175538i	0.999866	−	0.0163514i	$-0.00520506\pi$
$787$	0.517582	+	4.92447i	0.0184498	+	0.175538i	−0.981416	+	0.191890i	$0.938538\pi$
$788$	3.22756	+	0.686039i	0.114977	+	0.0244391i
$789$	−27.3022	+	5.80326i	−0.971983	+	0.206601i
$790$	4.49096	+	3.26288i	0.159781	+	0.116088i
$791$	2.76129	+	22.8236i	0.0981801	+	0.811514i
$792$		0			0
$793$	−3.90120	−	6.75707i	−0.138536	−	0.239951i
$794$	58.4147	−	26.0079i	2.07306	−	0.922986i
$795$	6.98449	+	7.75707i	0.247714	+	0.275115i
$796$	−16.8869	+	18.7548i	−0.598541	+	0.664747i
$797$	21.5860	−	15.6832i	0.764616	−	0.555526i	−0.135707	−	0.990749i	$-0.543330\pi$
$797$	21.5860	−	15.6832i	0.764616	−	0.555526i	0.900323	+	0.435223i	$0.143330\pi$
$798$	17.4557	−	56.7349i	0.617926	−	2.00839i
$799$	−2.48231	−	7.63977i	−0.0878179	−	0.270276i
$800$	29.6536	−	6.30306i	1.04841	−	0.222847i
$801$	0.610693	−	0.271898i	0.0215778	−	0.00960704i
$802$	10.4518	−	18.1030i	0.369066	−	0.639240i
$803$		0			0
$804$	4.80785			0.169560
$805$	1.87010	+	3.12491i	0.0659122	+	0.110139i
$806$	−6.56538	+	20.2062i	−0.231256	+	0.711732i
$807$	10.4358	−	11.5901i	0.367358	−	0.407992i
$808$	−1.20638	−	11.4779i	−0.0424402	−	0.403791i
$809$	−4.13306	−	39.3234i	−0.145311	−	1.38254i	−0.787652	−	0.616120i	$-0.788704\pi$
$809$	−4.13306	−	39.3234i	−0.145311	−	1.38254i	0.642342	−	0.766418i	$-0.277963\pi$
$810$	−8.68834	+	9.64938i	−0.305277	+	0.339045i
$811$	10.3380	−	31.8170i	0.363015	−	1.11724i	−0.588200	−	0.808715i	$-0.700163\pi$
$811$	10.3380	−	31.8170i	0.363015	−	1.11724i	0.951215	−	0.308529i	$-0.0998367\pi$
$812$	−19.3356	−	32.3096i	−0.678547	−	1.13384i
$813$	−40.0517			−1.40467
$814$		0			0
$815$	−5.08615	+	8.80947i	−0.178160	+	0.308582i
$816$	27.7082	−	12.3365i	0.969982	−	0.431864i
$817$	−26.4851	+	5.62958i	−0.926596	+	0.196954i
$818$	−2.31706	−	7.13119i	−0.0810142	−	0.249336i
$819$	2.57064	−	8.35515i	0.0898256	−	0.291952i
$820$	−5.28673	+	3.84104i	−0.184621	+	0.134135i
$821$	−38.0481	+	42.2567i	−1.32789	+	1.47477i	−0.571588	+	0.820541i	$0.693672\pi$
$821$	−38.0481	+	42.2567i	−1.32789	+	1.47477i	−0.756299	+	0.654226i	$0.772994\pi$
$822$	19.6039	+	21.7723i	0.683763	+	0.759396i
$823$	−36.7022	+	16.3409i	−1.27936	+	0.569607i	−0.930061	−	0.367404i	$-0.880247\pi$
$823$	−36.7022	+	16.3409i	−1.27936	+	0.569607i	−0.349298	+	0.937012i	$0.613580\pi$
$824$	−3.63228	−	6.29129i	−0.126536	−	0.219168i
$825$		0			0
$826$	6.88191	+	56.8829i	0.239452	+	1.97921i
$827$	−4.64007	−	3.37121i	−0.161351	−	0.117228i	0.504180	−	0.863599i	$-0.331795\pi$
$827$	−4.64007	−	3.37121i	−0.161351	−	0.117228i	−0.665531	+	0.746370i	$0.731795\pi$
$828$	−5.30186	+	1.12694i	−0.184252	+	0.0391640i
$829$	34.8182	+	7.40084i	1.20929	+	0.257042i	0.768074	−	0.640361i	$-0.221215\pi$
$829$	34.8182	+	7.40084i	1.20929	+	0.257042i	0.441212	+	0.897403i	$0.354549\pi$
$830$	−1.12492	−	10.7029i	−0.0390465	−	0.371502i
$831$	27.8164	+	12.3847i	0.964941	+	0.429619i
$832$	−1.31613	−	4.05065i	−0.0456288	−	0.140431i
$833$	−16.4084	−	11.1525i	−0.568517	−	0.386412i
$834$	−8.49159	−	6.16950i	−0.294040	−	0.213632i
$835$	−0.368370	−	0.638036i	−0.0127480	−	0.0220801i
$836$		0			0
$837$	−8.24090	+	14.2737i	−0.284847	+	0.493370i
$838$	6.28881	−	59.8340i	0.217243	−	2.06693i
$839$	−12.9085	+	39.7282i	−0.445651	+	1.37157i	0.436118	+	0.899889i	$0.356353\pi$
$839$	−12.9085	+	39.7282i	−0.445651	+	1.37157i	−0.881769	+	0.471682i	$0.843647\pi$
$840$	3.90937	−	1.81453i	0.134886	−	0.0626072i
$841$	−64.5527	+	46.9003i	−2.22595	+	1.61725i
$842$	14.2788	+	6.35733i	0.492080	+	0.219088i
$843$	−45.2344	−	9.61486i	−1.55795	−	0.331153i
$844$	7.17173	+	7.96501i	0.246861	+	0.274167i
$845$	−0.648076	+	6.16603i	−0.0222945	+	0.212118i
$846$	9.53566			0.327843
$847$		0			0
$848$	−36.3568			−1.24850
$849$	−0.0810010	+	0.770673i	−0.00277995	+	0.0264494i
$850$	15.9879	+	17.7564i	0.548381	+	0.609039i
$851$	−12.8501	−	2.73138i	−0.440496	−	0.0936304i
$852$	−11.7629	−	5.23718i	−0.402991	−	0.179423i
$853$	40.2786	−	29.2641i	1.37911	−	1.00199i	0.382152	−	0.924099i	$-0.375183\pi$
$853$	40.2786	−	29.2641i	1.37911	−	1.00199i	0.996962	−	0.0778858i	$-0.0248169\pi$
$854$	1.86922	−	20.9374i	0.0639634	−	0.716461i
$855$	−2.00406	+	6.16786i	−0.0685373	+	0.210936i
$856$	1.35244	−	12.8676i	0.0462255	−	0.439806i
$857$	12.7394	−	22.0652i	0.435168	−	0.753734i	−0.562141	−	0.827041i	$-0.690022\pi$
$857$	12.7394	−	22.0652i	0.435168	−	0.753734i	0.997309	+	0.0733077i	$0.0233555\pi$
$858$		0			0
$859$	−8.08080	−	13.9964i	−0.275713	−	0.477549i	0.694602	−	0.719395i	$-0.255581\pi$
$859$	−8.08080	−	13.9964i	−0.275713	−	0.477549i	−0.970315	+	0.241845i	$0.922247\pi$
$860$	3.41462	+	2.48087i	0.116438	+	0.0845970i
$861$	28.8179	−	33.0327i	0.982112	−	1.12575i
$862$	−9.48524	−	29.1926i	−0.323069	−	0.994303i
$863$	2.64839	+	1.17914i	0.0901524	+	0.0401384i	0.451317	−	0.892363i	$-0.350954\pi$
$863$	2.64839	+	1.17914i	0.0901524	+	0.0401384i	−0.361165	+	0.932502i	$0.617621\pi$
$864$	−1.76723	−	16.8140i	−0.0601223	−	0.572025i
$865$	0.617596	+	0.131274i	0.0209989	+	0.00446345i
$866$	−46.4079	+	9.86431i	−1.57701	+	0.335203i
$867$	−15.9504	−	11.5887i	−0.541705	−	0.393572i
$868$	−18.5638	+	13.9372i	−0.630096	+	0.473061i
$869$		0			0
$870$	13.3672	+	23.1526i	0.453190	+	0.784948i
$871$	−2.63723	+	1.17417i	−0.0893592	+	0.0397853i
$872$	11.1578	+	12.3920i	0.377850	+	0.419645i
$873$	−3.18629	+	3.53873i	−0.107839	+	0.119768i
$874$	17.8790	−	12.9899i	0.604768	−	0.439389i
$875$	10.9837	+	11.8206i	0.371317	+	0.399608i
$876$	−14.8267	−	45.6320i	−0.500949	−	1.54176i
$877$	−8.23096	+	1.74954i	−0.277940	+	0.0590779i	−0.344773	−	0.938686i	$-0.612044\pi$
$877$	−8.23096	+	1.74954i	−0.277940	+	0.0590779i	0.0668327	+	0.997764i	$0.478711\pi$
$878$	−16.0338	+	7.13869i	−0.541113	+	0.240919i
$879$	3.80731	−	6.59445i	0.128417	−	0.222425i
$880$		0			0
$881$	41.5335			1.39930			0.699649	−	0.714486i	$-0.253340\pi$
$881$	41.5335			1.39930			0.699649	+	0.714486i	$0.253340\pi$
$882$	18.6099	−	14.4336i	0.626627	−	0.486004i
$883$	−17.4518	+	53.7112i	−0.587300	+	1.80752i	0.00252951	+	0.999997i	$0.499195\pi$
$883$	−17.4518	+	53.7112i	−0.587300	+	1.80752i	−0.589830	+	0.807528i	$0.700805\pi$
$884$	4.66115	−	5.17673i	0.156771	−	0.174112i
$885$	−1.72457	−	16.4082i	−0.0579708	−	0.551555i
$886$	3.64920	+	34.7198i	0.122597	+	1.16643i
$887$	23.1382	−	25.6976i	0.776905	−	0.862841i	−0.216643	−	0.976251i	$-0.569511\pi$
$887$	23.1382	−	25.6976i	0.776905	−	0.862841i	0.993548	+	0.113410i	$0.0361775\pi$
$888$	−4.80449	+	14.7867i	−0.161228	+	0.496209i
$889$	27.0212	−	48.5442i	0.906261	−	1.62812i
$890$	0.424858			0.0142413
$891$		0			0
$892$	−13.8744	+	24.0311i	−0.464548	+	0.804621i
$893$	−14.4041	+	6.41313i	−0.482016	+	0.214607i
$894$	−3.94481	+	0.838494i	−0.131934	+	0.0280434i
$895$	3.86153	+	11.8846i	0.129077	+	0.397258i
$896$	−6.88960	+	22.3927i	−0.230165	+	0.748087i
$897$	6.93937	−	5.04174i	0.231699	−	0.168339i
$898$	−40.9228	+	45.4493i	−1.36561	+	1.51666i
$899$	44.8788	+	49.8429i	1.49679	+	1.66235i
$900$	−10.5083	+	4.67858i	−0.350276	+	0.155953i
$901$	−10.5856	−	18.3348i	−0.352658	−	0.610821i
$902$		0			0
$903$	−26.0429	−	11.1091i	−0.866652	−	0.369688i
$904$	8.19514	+	5.95412i	0.272566	+	0.198031i
$905$	−14.8407	+	3.15450i	−0.493323	+	0.104859i
$906$	6.84597	+	1.45516i	0.227442	+	0.0483443i
$907$	−0.878336	−	8.35681i	−0.0291647	−	0.277483i	−0.999379	−	0.0352354i	$-0.988782\pi$
$907$	−0.878336	−	8.35681i	−0.0291647	−	0.277483i	0.970214	−	0.242248i	$-0.0778848\pi$
$908$	−8.99915	−	4.00668i	−0.298647	−	0.132966i
$909$	5.61151	+	17.2704i	0.186122	+	0.572824i
$910$	3.65235	−	4.18653i	0.121074	−	0.138782i
$911$	0.480304	+	0.348962i	0.0159132	+	0.0115616i	0.595713	−	0.803197i	$-0.296869\pi$
$911$	0.480304	+	0.348962i	0.0159132	+	0.0115616i	−0.579800	+	0.814759i	$0.696869\pi$
$912$	−29.7667	−	51.5575i	−0.985675	−	1.70724i
$913$		0			0
$914$	−10.9693	+	18.9993i	−0.362831	+	0.628441i
$915$	−0.632688	+	6.01962i	−0.0209160	+	0.199003i
$916$	5.08973	−	15.6646i	0.168169	−	0.517572i
$917$	−29.6578	−	20.8451i	−0.979386	−	0.688366i
$918$	10.7801	−	7.83222i	0.355797	−	0.258502i
$919$	14.9246	+	6.64485i	0.492316	+	0.219193i	0.637851	−	0.770160i	$-0.279824\pi$
$919$	14.9246	+	6.64485i	0.492316	+	0.219193i	−0.145535	+	0.989353i	$0.546490\pi$
$920$	1.56954	+	0.333617i	0.0517463	+	0.0109990i
$921$	−9.58455	−	10.6447i	−0.315822	−	0.350755i
$922$	−2.39465	+	22.7835i	−0.0788635	+	0.750336i
$923$	7.73128			0.254478
$924$		0			0
$925$	−27.8792			−0.916662
$926$	2.36011	−	22.4549i	0.0775579	−	0.737915i
$927$	7.64837	+	8.49438i	0.251206	+	0.278992i
$928$	−67.2957	−	14.3041i	−2.20909	−	0.469557i
$929$	8.13165	+	3.62044i	0.266791	+	0.118783i	0.535772	−	0.844362i	$-0.320020\pi$
$929$	8.13165	+	3.62044i	0.266791	+	0.118783i	−0.268982	+	0.963145i	$0.586687\pi$
$930$	13.3341	−	9.68776i	0.437241	−	0.317674i
$931$	−18.4041	+	34.3186i	−0.603168	+	1.12475i
$932$	3.18008	−	9.78728i	0.104167	−	0.320593i
$933$	2.67290	−	25.4309i	0.0875067	−	0.832570i
$934$	30.0456	−	52.0405i	0.983122	−	1.70282i
$935$		0			0
$936$	−1.92585	−	3.33567i	−0.0629485	−	0.109030i
$937$	36.5967	+	26.5891i	1.19556	+	0.868627i	0.993841	−	0.110817i	$-0.0353466\pi$
$937$	36.5967	+	26.5891i	1.19556	+	0.868627i	0.201721	+	0.979443i	$0.435347\pi$
$938$	−7.63189	−	1.49755i	−0.249190	−	0.0488966i
$939$	18.4111	+	56.6635i	0.600823	+	1.84914i
$940$	2.24530	+	0.999674i	0.0732338	+	0.0326058i
$941$	−0.724701	−	6.89507i	−0.0236246	−	0.224773i	−0.999964	−	0.00852748i	$-0.997286\pi$
$941$	−0.724701	−	6.89507i	−0.0236246	−	0.224773i	0.976339	−	0.216245i	$-0.0693811\pi$
$942$	31.3201	+	6.65730i	1.02047	+	0.216907i
$943$	15.9638	−	3.39321i	0.519852	−	0.110498i
$944$	46.4907	+	33.7775i	1.51314	+	1.09936i
$945$	3.44668	−	2.58768i	0.112120	−	0.0841773i
$946$		0			0
$947$	−10.3716	−	17.9642i	−0.337033	−	0.583758i	0.646840	−	0.762626i	$-0.276090\pi$
$947$	−10.3716	−	17.9642i	−0.337033	−	0.583758i	−0.983873	+	0.178867i	$0.942757\pi$
$948$	13.0504	−	5.81043i	0.423859	−	0.188714i
$949$	19.2771	+	21.4094i	0.625761	+	0.694978i
$950$	31.3816	−	34.8528i	1.01815	−	1.13077i
$951$	6.86914	−	4.99072i	0.222747	−	0.161835i
$952$	−8.52109	+	1.95133i	−0.276170	+	0.0632430i
$953$	−6.24450	−	19.2186i	−0.202279	−	0.622551i	−0.999814	−	0.0192785i	$-0.993863\pi$
$953$	−6.24450	−	19.2186i	−0.202279	−	0.622551i	0.797535	−	0.603273i	$-0.206137\pi$
$954$	24.5825	−	5.22518i	0.795889	−	0.169172i
$955$	6.46315	−	2.87758i	0.209143	−	0.0931163i
$956$	−6.71735	+	11.6348i	−0.217254	+	0.376296i
$957$		0			0
$958$	47.6499			1.53950
$959$	−9.86990	−	16.4925i	−0.318716	−	0.532570i
$960$	−1.02100	+	3.14233i	−0.0329528	+	0.101418i
$961$	6.92482	−	7.69079i	0.223381	−	0.248090i
$962$	2.09495	+	19.9321i	0.0675437	+	0.642636i
$963$	2.12798	+	20.2464i	0.0685732	+	0.652431i
$964$	1.52929	−	1.69845i	0.0492552	−	0.0547034i
$965$	0.709898	−	2.18484i	0.0228524	−	0.0703326i
$966$	23.1061	−	0.362309i	0.743426	−	0.0116571i
$967$	7.98254			0.256701			0.128351	−	0.991729i	$-0.459032\pi$
$967$	7.98254			0.256701			0.128351	+	0.991729i	$0.459032\pi$
$968$		0			0
$969$	17.3337	−	30.0229i	0.556839	−	0.964473i
$970$	−2.76475	+	1.23094i	−0.0887706	+	0.0395232i
$971$	13.4782	−	2.86488i	0.432535	−	0.0919382i	0.0135016	−	0.999909i	$-0.495702\pi$
$971$	13.4782	−	2.86488i	0.432535	−	0.0919382i	0.419034	+	0.907971i	$0.362369\pi$
$972$	7.08361	+	21.8011i	0.227207	+	0.699271i
$973$	4.68721	+	5.04434i	0.150265	+	0.161714i
$974$	21.5700	−	15.6715i	0.691146	−	0.502147i
$975$	12.1801	−	13.5274i	0.390075	−	0.433222i
$976$	−14.1068	−	15.6672i	−0.451547	−	0.501494i
$977$	10.9817	−	4.88935i	0.351335	−	0.156424i	−0.223479	−	0.974709i	$-0.571741\pi$
$977$	10.9817	−	4.88935i	0.351335	−	0.156424i	0.574813	+	0.818285i	$0.305075\pi$
$978$	32.2745	+	55.9010i	1.03202	+	1.78752i
$979$		0			0
$980$	5.89511	−	1.44761i	0.188312	−	0.0462423i
$981$	−21.2262	−	15.4218i	−0.677702	−	0.492379i
$982$	70.6813	−	15.0238i	2.25553	−	0.479428i
$983$	43.6785	+	9.28415i	1.39313	+	0.296119i	0.842529	−	0.538651i	$-0.181066\pi$
$983$	43.6785	+	9.28415i	1.39313	+	0.296119i	0.550599	+	0.834770i	$0.314399\pi$
$984$	−2.01896	−	19.2091i	−0.0643622	−	0.612365i
$985$	1.40409	+	0.625140i	0.0447379	+	0.0199186i
$986$	−16.7561	−	51.5701i	−0.533624	−	1.64233i
$987$	−16.1788	−	3.17464i	−0.514977	−	0.101050i
$988$	−11.0617	−	8.03681i	−0.351920	−	0.255685i
$989$	−5.27056	−	9.12888i	−0.167594	−	0.290282i
$990$		0			0
$991$	11.4830	−	19.8891i	0.364769	−	0.631799i	−0.623970	−	0.781448i	$-0.714481\pi$
$991$	11.4830	−	19.8891i	0.364769	−	0.631799i	0.988739	+	0.149650i	$0.0478146\pi$
$992$	−4.43356	+	42.1825i	−0.140766	+	1.33930i
$993$	−4.17871	+	12.8607i	−0.132607	+	0.408123i
$994$	17.0409	+	11.9773i	0.540505	+	0.379897i
$995$	−9.51023	+	6.90958i	−0.301494	+	0.219049i
$996$	−25.3005	−	11.2645i	−0.801678	−	0.356930i
$997$	1.31950	+	0.280468i	0.0417889	+	0.00888250i	0.228759	−	0.973483i	$-0.426533\pi$
$997$	1.31950	+	0.280468i	0.0417889	+	0.00888250i	−0.186970	+	0.982366i	$0.559867\pi$
$998$	32.1940	+	35.7551i	1.01908	+	1.13181i
$999$	−1.62517	+	15.4625i	−0.0514182	+	0.489212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.d.81.3		24
7.2	even	3	inner	847.2.n.d.807.1		24
11.2	odd	10		847.2.n.e.753.3		24
11.3	even	5	inner	847.2.n.d.487.1		24
11.4	even	5	inner	847.2.n.d.130.3		24
11.5	even	5		847.2.e.d.606.3		6
11.6	odd	10		77.2.e.b.67.1	yes	6
11.7	odd	10		847.2.n.e.130.1		24
11.8	odd	10		847.2.n.e.487.3		24
11.9	even	5	inner	847.2.n.d.753.1		24
11.10	odd	2		847.2.n.e.81.1		24
33.17	even	10		693.2.i.g.298.3		6
44.39	even	10		1232.2.q.k.529.1		6
77.2	odd	30		847.2.n.e.632.1		24
77.6	even	10		539.2.e.l.67.1		6
77.9	even	15	inner	847.2.n.d.632.3		24
77.16	even	15		847.2.e.d.485.3		6
77.17	even	30		539.2.a.i.1.3		3
77.30	odd	30		847.2.n.e.366.1		24
77.37	even	15	inner	847.2.n.d.9.1		24
77.38	odd	30		5929.2.a.w.1.1		3
77.39	odd	30		539.2.a.h.1.3		3
77.51	odd	30		847.2.n.e.9.3		24
77.58	even	15	inner	847.2.n.d.366.3		24
77.60	even	15		5929.2.a.v.1.1		3
77.61	even	30		539.2.e.l.177.1		6
77.65	odd	6		847.2.n.e.807.3		24
77.72	odd	30		77.2.e.b.23.1	✓	6
231.17	odd	30		4851.2.a.bn.1.1		3
231.116	even	30		4851.2.a.bo.1.1		3
231.149	even	30		693.2.i.g.100.3		6
308.39	even	30		8624.2.a.cl.1.3		3
308.171	odd	30		8624.2.a.ck.1.1		3
308.303	even	30		1232.2.q.k.177.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	77.72	odd	30
77.2.e.b.67.1	yes	6	11.6	odd	10
539.2.a.h.1.3		3	77.39	odd	30
539.2.a.i.1.3		3	77.17	even	30
539.2.e.l.67.1		6	77.6	even	10
539.2.e.l.177.1		6	77.61	even	30
693.2.i.g.100.3		6	231.149	even	30
693.2.i.g.298.3		6	33.17	even	10
847.2.e.d.485.3		6	77.16	even	15
847.2.e.d.606.3		6	11.5	even	5
847.2.n.d.9.1		24	77.37	even	15	inner
847.2.n.d.81.3		24	1.1	even	1	trivial
847.2.n.d.130.3		24	11.4	even	5	inner
847.2.n.d.366.3		24	77.58	even	15	inner
847.2.n.d.487.1		24	11.3	even	5	inner
847.2.n.d.632.3		24	77.9	even	15	inner
847.2.n.d.753.1		24	11.9	even	5	inner
847.2.n.d.807.1		24	7.2	even	3	inner
847.2.n.e.9.3		24	77.51	odd	30
847.2.n.e.81.1		24	11.10	odd	2
847.2.n.e.130.1		24	11.7	odd	10
847.2.n.e.366.1		24	77.30	odd	30
847.2.n.e.487.3		24	11.8	odd	10
847.2.n.e.632.1		24	77.2	odd	30
847.2.n.e.753.3		24	11.2	odd	10
847.2.n.e.807.3		24	77.65	odd	6
1232.2.q.k.177.1		6	308.303	even	30
1232.2.q.k.529.1		6	44.39	even	10
4851.2.a.bn.1.1		3	231.17	odd	30
4851.2.a.bo.1.1		3	231.116	even	30
5929.2.a.v.1.1		3	77.60	even	15
5929.2.a.w.1.1		3	77.38	odd	30
8624.2.a.ck.1.1		3	308.171	odd	30
8624.2.a.cl.1.3		3	308.39	even	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)

\(f(q)\)	\(=\)	\(q+(0.191731 - 1.82420i) q^{2} +(-1.47121 - 1.63395i) q^{3} +(-1.33463 - 0.283685i) q^{4} +(-0.580606 - 0.258502i) q^{5} +(-3.26271 + 2.37050i) q^{6} +(2.39985 - 1.11389i) q^{7} +(0.360239 - 1.10870i) q^{8} +(-0.191731 + 1.82420i) q^{9} +O(q^{10})\)	\(q+(0.191731 - 1.82420i) q^{2} +(-1.47121 - 1.63395i) q^{3} +(-1.33463 - 0.283685i) q^{4} +(-0.580606 - 0.258502i) q^{5} +(-3.26271 + 2.37050i) q^{6} +(2.39985 - 1.11389i) q^{7} +(0.360239 - 1.10870i) q^{8} +(-0.191731 + 1.82420i) q^{9} +(-0.582878 + 1.00958i) q^{10} +(1.50000 + 2.59808i) q^{12} +(-1.45729 - 1.05878i) q^{13} +(-1.57182 - 4.59135i) q^{14} +(0.431815 + 1.32899i) q^{15} +(-4.44639 - 1.97966i) q^{16} +(-0.296259 - 2.81872i) q^{17} +(3.29093 + 0.699508i) q^{18} +(-5.44157 + 1.15664i) q^{19} +(0.701561 + 0.509714i) q^{20} +(-5.35071 - 2.28245i) q^{21} +(-1.08288 - 1.87560i) q^{23} +(-2.34154 + 1.04252i) q^{24} +(-3.07537 - 3.41555i) q^{25} +(-2.21083 + 2.45538i) q^{26} +(-2.07362 + 1.50658i) q^{27} +(-3.51890 + 0.805829i) q^{28} +(3.22315 + 9.91982i) q^{29} +(2.50713 - 0.532907i) q^{30} +(5.87439 - 2.61545i) q^{31} +(-3.29804 + 5.71237i) q^{32} -5.19869 q^{34} +(-1.68131 + 0.0263633i) q^{35} +(0.773386 - 2.38024i) q^{36} +(4.05886 - 4.50782i) q^{37} +(1.06662 + 10.1483i) q^{38} +(0.413987 + 3.93883i) q^{39} +(-0.495758 + 0.550595i) q^{40} +(-2.32865 + 7.16684i) q^{41} +(-5.18954 + 9.32312i) q^{42} +4.86718 q^{43} +(0.582878 - 1.00958i) q^{45} +(-3.62908 + 1.61577i) q^{46} +(2.77231 - 0.589272i) q^{47} +(3.30692 + 10.1777i) q^{48} +(4.51851 - 5.34631i) q^{49} +(-6.82027 + 4.95522i) q^{50} +(-4.16977 + 4.63100i) q^{51} +(1.64458 + 1.82650i) q^{52} +(6.82400 - 3.03824i) q^{53} +(2.35071 + 4.07155i) q^{54} +(-0.370450 - 3.06197i) q^{56} +(9.89559 + 7.18957i) q^{57} +(18.7137 - 3.97771i) q^{58} +(-11.5488 - 2.45477i) q^{59} +(-0.199300 - 1.89621i) q^{60} +(3.95703 + 1.76179i) q^{61} +(-3.64478 - 11.2175i) q^{62} +(1.57182 + 4.59135i) q^{63} +(1.91288 + 1.38979i) q^{64} +(0.572413 + 0.991448i) q^{65} +(0.801309 - 1.38791i) q^{67} +(-0.404230 + 3.84599i) q^{68} +(-1.47149 + 4.52877i) q^{69} +(-0.274266 + 3.07208i) q^{70} +(-3.47233 + 2.52280i) q^{71} +(1.95342 + 0.869717i) q^{72} +(-15.6440 - 3.32523i) q^{73} +(-7.44493 - 8.26844i) q^{74} +(-1.05630 + 10.0500i) q^{75} +7.59061 q^{76} +7.26456 q^{78} +(0.497747 - 4.73574i) q^{79} +(2.06985 + 2.29880i) q^{80} +(10.8949 + 2.31578i) q^{81} +(12.6272 + 5.62201i) q^{82} +(-7.46854 + 5.42621i) q^{83} +(6.49373 + 4.56415i) q^{84} +(-0.556635 + 1.71315i) q^{85} +(0.933187 - 8.87868i) q^{86} +(11.4665 - 19.8606i) q^{87} +(-0.182224 - 0.315621i) q^{89} +(-1.72991 - 1.25685i) q^{90} +(-4.67663 - 0.917660i) q^{91} +(0.913165 + 2.81043i) q^{92} +(-12.9160 - 5.75056i) q^{93} +(-0.543411 - 5.17021i) q^{94} +(3.45840 + 0.735106i) q^{95} +(14.1858 - 3.01529i) q^{96} +(2.10027 + 1.52593i) q^{97} +(-8.88637 - 9.26770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8}+O(q^{10}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8} - 36 q^{10} + 36 q^{12} - 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} - 28 q^{20} - 40 q^{21} - 48 q^{23} - 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} + 13 q^{28} - 18 q^{29} - 2 q^{30} - 3 q^{31} - 12 q^{32} - 80 q^{34} + 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} + 5 q^{39} + 3 q^{40} - 10 q^{41} + 2 q^{42} - 16 q^{43} + 36 q^{45} + 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} - 6 q^{50} - 2 q^{51} + 7 q^{52} + 17 q^{53} - 32 q^{54} + 12 q^{56} + 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} + 24 q^{61} + 26 q^{62} + 12 q^{63} + 14 q^{64} + 60 q^{65} + 64 q^{67} - 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} - 10 q^{72} + 20 q^{73} - 22 q^{74} + 25 q^{75} + 312 q^{76} - 48 q^{78} - 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} - 22 q^{83} + 12 q^{84} + 22 q^{85} - 21 q^{86} + 120 q^{87} - 4 q^{89} + 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} + 10 q^{94} + 17 q^{95} - 27 q^{96} - 18 q^{97} + 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8 - 36 * q^10 + 36 * q^12 - 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 + 3 * q^17 - 10 * q^18 + 11 * q^19 - 28 * q^20 - 40 * q^21 - 48 * q^23 - 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 + 13 * q^28 - 18 * q^29 - 2 * q^30 - 3 * q^31 - 12 * q^32 - 80 * q^34 + 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 + 5 * q^39 + 3 * q^40 - 10 * q^41 + 2 * q^42 - 16 * q^43 + 36 * q^45 + 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 - 6 * q^50 - 2 * q^51 + 7 * q^52 + 17 * q^53 - 32 * q^54 + 12 * q^56 + 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 + 24 * q^61 + 26 * q^62 + 12 * q^63 + 14 * q^64 + 60 * q^65 + 64 * q^67 - 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 - 10 * q^72 + 20 * q^73 - 22 * q^74 + 25 * q^75 + 312 * q^76 - 48 * q^78 - 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 - 22 * q^83 + 12 * q^84 + 22 * q^85 - 21 * q^86 + 120 * q^87 - 4 * q^89 + 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 + 10 * q^94 + 17 * q^95 - 27 * q^96 - 18 * q^97 + 96 * q^98

Introduction

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