LMFDB - Embedded newform 345.2.m.a.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			151.3
Character	$\chi$	$=$	345.151
Dual form			345.2.m.a.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996473 + 1.14999i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.0448918 + 0.312230i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.216554 - 1.50617i) q^{6} +(2.33660 + 0.686088i) q^{7} +(2.15640 - 1.38584i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.996473 + 1.14999i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.0448918 + 0.312230i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.216554 - 1.50617i) q^{6} +(2.33660 + 0.686088i) q^{7} +(2.15640 - 1.38584i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.46002 + 0.428700i) q^{10} +(-0.103138 + 0.119028i) q^{11} +(0.206570 - 0.238394i) q^{12} +(3.49167 - 1.02525i) q^{13} +(1.53937 + 3.37074i) q^{14} +(0.841254 - 0.540641i) q^{15} +(4.34783 + 1.27664i) q^{16} +(0.383225 + 2.66539i) q^{17} +(-0.632119 + 1.38415i) q^{18} +(-0.505144 + 3.51336i) q^{19} +(-0.265365 - 0.170540i) q^{20} +(-1.59475 - 1.84044i) q^{21} -0.239655 q^{22} +(-4.67624 - 1.06432i) q^{23} -2.56332 q^{24} +(-0.654861 - 0.755750i) q^{25} +(4.65838 + 2.99376i) q^{26} +(0.142315 - 0.989821i) q^{27} +(-0.319111 + 0.698756i) q^{28} +(0.390343 + 2.71489i) q^{29} +(1.46002 + 0.428700i) q^{30} +(7.10391 - 4.56540i) q^{31} +(0.734686 + 1.60874i) q^{32} +(0.151117 - 0.0443718i) q^{33} +(-2.68330 + 3.09670i) q^{34} +(-1.59475 + 1.84044i) q^{35} +(-0.302663 + 0.0888698i) q^{36} +(-1.34983 - 2.95571i) q^{37} +(-4.54369 + 2.92005i) q^{38} +(-3.49167 - 1.02525i) q^{39} +(0.364799 + 2.53723i) q^{40} +(1.58078 - 3.46143i) q^{41} +(0.527363 - 3.66789i) q^{42} +(-3.95474 - 2.54156i) q^{43} +(-0.0325339 - 0.0375462i) q^{44} -1.00000 q^{45} +(-3.43579 - 6.43821i) q^{46} -12.7257 q^{47} +(-2.96742 - 3.42459i) q^{48} +(-0.899789 - 0.578259i) q^{49} +(0.216554 - 1.50617i) q^{50} +(1.11863 - 2.44946i) q^{51} +(0.163365 + 1.13623i) q^{52} +(-7.09172 - 2.08232i) q^{53} +(1.28010 - 0.822670i) q^{54} +(-0.0654263 - 0.143264i) q^{55} +(5.98946 - 1.75866i) q^{56} +(2.32442 - 2.68252i) q^{57} +(-2.73314 + 3.15421i) q^{58} +(-0.00668115 + 0.00196176i) q^{59} +(0.131039 + 0.286935i) q^{60} +(-4.24856 + 2.73038i) q^{61} +(12.3290 + 3.62013i) q^{62} +(0.346572 + 2.41046i) q^{63} +(2.64686 - 5.79583i) q^{64} +(-0.517895 + 3.60204i) q^{65} +(0.201611 + 0.129567i) q^{66} +(-5.27776 - 6.09086i) q^{67} -0.849417 q^{68} +(3.35849 + 3.42353i) q^{69} -3.70561 q^{70} +(-0.115126 - 0.132862i) q^{71} +(2.15640 + 1.38584i) q^{72} +(-0.529955 + 3.68592i) q^{73} +(2.05398 - 4.49758i) q^{74} +(0.142315 + 0.989821i) q^{75} +(-1.07430 - 0.315442i) q^{76} +(-0.322656 + 0.207358i) q^{77} +(-2.30033 - 5.03702i) q^{78} +(-8.25044 + 2.42255i) q^{79} +(-2.96742 + 3.42459i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(5.55582 - 1.63134i) q^{82} +(2.96614 + 6.49495i) q^{83} +(0.646230 - 0.415307i) q^{84} +(-2.58372 - 0.758649i) q^{85} +(-1.01802 - 7.08051i) q^{86} +(1.13941 - 2.49495i) q^{87} +(-0.0574544 + 0.399604i) q^{88} +(14.0852 + 9.05201i) q^{89} +(-0.996473 - 1.14999i) q^{90} +8.86204 q^{91} +(0.542238 - 1.41228i) q^{92} -8.44443 q^{93} +(-12.6808 - 14.6344i) q^{94} +(-2.98602 - 1.91900i) q^{95} +(0.251692 - 1.75056i) q^{96} +(5.84431 - 12.7972i) q^{97} +(-0.231623 - 1.61097i) q^{98} +(-0.151117 - 0.0443718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.996473	+	1.14999i	0.704613	+	0.813167i	0.989368	−	0.145433i	$-0.0464577\pi$
$2$	0.996473	+	1.14999i	0.704613	+	0.813167i	−0.284755	+	0.958600i	$0.591912\pi$
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$	−0.0448918	+	0.312230i	−0.0224459	+	0.156115i
$5$	−0.415415	+	0.909632i	−0.185779	+	0.406800i
$5$	−0.415415	+	0.909632i	−0.185779	+	0.406800i
$6$	−0.216554	−	1.50617i	−0.0884080	−	0.614891i
$7$	2.33660	+	0.686088i	0.883152	+	0.259317i	0.691700	−	0.722185i	$-0.256862\pi$
$7$	2.33660	+	0.686088i	0.883152	+	0.259317i	0.191452	+	0.981502i	$0.438680\pi$
$8$	2.15640	−	1.38584i	0.762404	−	0.489967i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−1.46002	+	0.428700i	−0.461699	+	0.135567i
$11$	−0.103138	+	0.119028i	−0.0310973	+	0.0358882i	−0.771085	−	0.636732i	$-0.780286\pi$
$11$	−0.103138	+	0.119028i	−0.0310973	+	0.0358882i	0.739988	+	0.672620i	$0.234831\pi$
$12$	0.206570	−	0.238394i	0.0596315	−	0.0688184i
$13$	3.49167	−	1.02525i	0.968414	−	0.284352i	0.240981	−	0.970530i	$-0.422531\pi$
$13$	3.49167	−	1.02525i	0.968414	−	0.284352i	0.727434	+	0.686178i	$0.240713\pi$
$14$	1.53937	+	3.37074i	0.411413	+	0.900868i
$15$	0.841254	−	0.540641i	0.217211	−	0.139593i
$16$	4.34783	+	1.27664i	1.08696	+	0.319159i
$17$	0.383225	+	2.66539i	0.0929458	+	0.646452i	0.982032	+	0.188713i	$0.0604315\pi$
$17$	0.383225	+	2.66539i	0.0929458	+	0.646452i	−0.889087	+	0.457739i	$0.848659\pi$
$18$	−0.632119	+	1.38415i	−0.148992	+	0.326247i
$19$	−0.505144	+	3.51336i	−0.115888	+	0.806019i	0.846119	+	0.532994i	$0.178933\pi$
$19$	−0.505144	+	3.51336i	−0.115888	+	0.806019i	−0.962007	+	0.273025i	$0.911976\pi$
$20$	−0.265365	−	0.170540i	−0.0593375	−	0.0381339i
$21$	−1.59475	−	1.84044i	−0.348002	−	0.401616i
$22$	−0.239655			−0.0510947
$23$	−4.67624	−	1.06432i	−0.975063	−	0.221927i
$23$	−4.67624	−	1.06432i	−0.975063	−	0.221927i
$24$	−2.56332			−0.523236
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	4.65838	+	2.99376i	0.913583	+	0.587124i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	−0.319111	+	0.698756i	−0.0603064	+	0.132053i
$29$	0.390343	+	2.71489i	0.0724849	+	0.504143i	0.993429	+	0.114449i	$0.0365102\pi$
$29$	0.390343	+	2.71489i	0.0724849	+	0.504143i	−0.920944	+	0.389694i	$0.872581\pi$
$30$	1.46002	+	0.428700i	0.266562	+	0.0782696i
$31$	7.10391	−	4.56540i	1.27590	−	0.819971i	0.285523	−	0.958372i	$-0.407833\pi$
$31$	7.10391	−	4.56540i	1.27590	−	0.819971i	0.990376	+	0.138401i	$0.0441964\pi$
$32$	0.734686	+	1.60874i	0.129875	+	0.284387i
$33$	0.151117	−	0.0443718i	0.0263060	−	0.00772414i
$34$	−2.68330	+	3.09670i	−0.460183	+	0.531079i
$35$	−1.59475	+	1.84044i	−0.269561	+	0.311090i
$36$	−0.302663	+	0.0888698i	−0.0504438	+	0.0148116i
$37$	−1.34983	−	2.95571i	−0.221910	−	0.485916i	0.765630	−	0.643281i	$-0.222427\pi$
$37$	−1.34983	−	2.95571i	−0.221910	−	0.485916i	−0.987540	+	0.157365i	$0.949700\pi$
$38$	−4.54369	+	2.92005i	−0.737084	+	0.473695i
$39$	−3.49167	−	1.02525i	−0.559114	−	0.164171i
$40$	0.364799	+	2.53723i	0.0576798	+	0.401171i
$41$	1.58078	−	3.46143i	0.246877	−	0.540584i	−0.745108	−	0.666944i	$-0.767602\pi$
$41$	1.58078	−	3.46143i	0.246877	−	0.540584i	0.991984	+	0.126360i	$0.0403293\pi$
$42$	0.527363	−	3.66789i	0.0813739	−	0.565968i
$43$	−3.95474	−	2.54156i	−0.603092	−	0.387584i	0.203169	−	0.979144i	$-0.434876\pi$
$43$	−3.95474	−	2.54156i	−0.603092	−	0.387584i	−0.806261	+	0.591560i	$0.798512\pi$
$44$	−0.0325339	−	0.0375462i	−0.00490467	−	0.00566030i
$45$	−1.00000			−0.149071
$46$	−3.43579	−	6.43821i	−0.506579	−	0.949262i
$47$	−12.7257			−1.85623			−0.928116	−	0.372292i	$-0.878572\pi$
$47$	−12.7257			−1.85623			−0.928116	+	0.372292i	$0.878572\pi$
$48$	−2.96742	−	3.42459i	−0.428310	−	0.494297i
$49$	−0.899789	−	0.578259i	−0.128541	−	0.0826085i
$50$	0.216554	−	1.50617i	0.0306254	−	0.213004i
$51$	1.11863	−	2.44946i	0.156639	−	0.342992i
$52$	0.163365	+	1.13623i	0.0226546	+	0.157566i
$53$	−7.09172	−	2.08232i	−0.974122	−	0.286028i	−0.244326	−	0.969693i	$-0.578567\pi$
$53$	−7.09172	−	2.08232i	−0.974122	−	0.286028i	−0.729796	+	0.683665i	$0.760385\pi$
$54$	1.28010	−	0.822670i	0.174199	−	0.111951i
$55$	−0.0654263	−	0.143264i	−0.00882208	−	0.0193177i
$56$	5.98946	−	1.75866i	0.800375	−	0.235011i
$57$	2.32442	−	2.68252i	0.307877	−	0.355309i
$58$	−2.73314	+	3.15421i	−0.358879	+	0.414168i
$59$	−0.00668115	+	0.00196176i	−0.000869811	+	0.000255400i	−0.282167	−	0.959365i	$-0.591053\pi$
$59$	−0.00668115	+	0.00196176i	−0.000869811	+	0.000255400i	0.281298	+	0.959621i	$0.409235\pi$
$60$	0.131039	+	0.286935i	0.0169170	+	0.0370431i
$61$	−4.24856	+	2.73038i	−0.543972	+	0.349589i	−0.783591	−	0.621278i	$-0.786614\pi$
$61$	−4.24856	+	2.73038i	−0.543972	+	0.349589i	0.239619	+	0.970867i	$0.422978\pi$
$62$	12.3290	+	3.62013i	1.56579	+	0.459757i
$63$	0.346572	+	2.41046i	0.0436639	+	0.303689i
$64$	2.64686	−	5.79583i	0.330858	−	0.724478i
$65$	−0.517895	+	3.60204i	−0.0642369	+	0.446778i
$66$	0.201611	+	0.129567i	0.0248166	+	0.0159487i
$67$	−5.27776	−	6.09086i	−0.644781	−	0.744117i	0.335432	−	0.942065i	$-0.391118\pi$
$67$	−5.27776	−	6.09086i	−0.644781	−	0.744117i	−0.980213	+	0.197948i	$0.936572\pi$
$68$	−0.849417			−0.103007
$69$	3.35849	+	3.42353i	0.404314	+	0.412145i
$70$	−3.70561			−0.442905
$71$	−0.115126	−	0.132862i	−0.0136629	−	0.0157678i	0.748877	−	0.662709i	$-0.230593\pi$
$71$	−0.115126	−	0.132862i	−0.0136629	−	0.0157678i	−0.762540	+	0.646941i	$0.776048\pi$
$72$	2.15640	+	1.38584i	0.254135	+	0.163322i
$73$	−0.529955	+	3.68592i	−0.0620266	+	0.431404i	0.935019	+	0.354597i	$0.115382\pi$
$73$	−0.529955	+	3.68592i	−0.0620266	+	0.431404i	−0.997046	+	0.0768077i	$0.975527\pi$
$74$	2.05398	−	4.49758i	0.238770	−	0.522833i
$75$	0.142315	+	0.989821i	0.0164331	+	0.114295i
$76$	−1.07430	−	0.315442i	−0.123230	−	0.0361837i
$77$	−0.322656	+	0.207358i	−0.0367701	+	0.0236307i
$78$	−2.30033	−	5.03702i	−0.260461	−	0.570330i
$79$	−8.25044	+	2.42255i	−0.928247	+	0.272558i	−0.710703	−	0.703493i	$-0.751623\pi$
$79$	−8.25044	+	2.42255i	−0.928247	+	0.272558i	−0.217544	+	0.976050i	$0.569805\pi$
$80$	−2.96742	+	3.42459i	−0.331768	+	0.382880i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	5.55582	−	1.63134i	0.613538	−	0.180151i
$83$	2.96614	+	6.49495i	0.325577	+	0.712913i	0.999669	−	0.0257338i	$-0.00819223\pi$
$83$	2.96614	+	6.49495i	0.325577	+	0.712913i	−0.674092	+	0.738647i	$0.735465\pi$
$84$	0.646230	−	0.415307i	0.0705094	−	0.0453137i
$85$	−2.58372	−	0.758649i	−0.280244	−	0.0822870i
$86$	−1.01802	−	7.08051i	−0.109776	−	0.763511i
$87$	1.13941	−	2.49495i	0.122157	−	0.267487i
$88$	−0.0574544	+	0.399604i	−0.00612466	+	0.0425980i
$89$	14.0852	+	9.05201i	1.49303	+	0.959512i	0.995767	+	0.0919111i	$0.0292976\pi$
$89$	14.0852	+	9.05201i	1.49303	+	0.959512i	0.497262	+	0.867600i	$0.334339\pi$
$90$	−0.996473	−	1.14999i	−0.105038	−	0.121220i
$91$	8.86204			0.928994
$92$	0.542238	−	1.41228i	0.0565322	−	0.147240i
$93$	−8.44443			−0.875646
$94$	−12.6808	−	14.6344i	−1.30792	−	1.50943i
$95$	−2.98602	−	1.91900i	−0.306359	−	0.196885i
$96$	0.251692	−	1.75056i	0.0256882	−	0.178666i
$97$	5.84431	−	12.7972i	0.593399	−	1.29936i	−0.339967	−	0.940437i	$-0.610416\pi$
$97$	5.84431	−	12.7972i	0.593399	−	1.29936i	0.933366	−	0.358926i	$-0.116857\pi$
$98$	−0.231623	−	1.61097i	−0.0233974	−	0.162733i
$99$	−0.151117	−	0.0443718i	−0.0151878	−	0.00445954i
$100$	0.265365	−	0.170540i	0.0265365	−	0.0170540i
$101$	1.95257	+	4.27554i	0.194288	+	0.425432i	0.981555	−	0.191181i	$-0.0612317\pi$
$101$	1.95257	+	4.27554i	0.194288	+	0.425432i	−0.787266	+	0.616613i	$0.788504\pi$
$102$	3.93154	−	1.15440i	0.389280	−	0.114303i
$103$	3.18716	−	3.67818i	0.314040	−	0.362422i	−0.576683	−	0.816968i	$-0.695653\pi$
$103$	3.18716	−	3.67818i	0.314040	−	0.362422i	0.890723	+	0.454546i	$0.150199\pi$
$104$	6.10862	−	7.04973i	0.599000	−	0.691283i
$105$	2.33660	−	0.686088i	0.228029	−	0.0669553i
$106$	−4.67206	−	10.2304i	−0.453791	−	0.993663i
$107$	−12.4593	+	8.00713i	−1.20449	+	0.774079i	−0.979727	−	0.200335i	$-0.935797\pi$
$107$	−12.4593	+	8.00713i	−1.20449	+	0.774079i	−0.224762	+	0.974414i	$0.572161\pi$
$108$	0.302663	+	0.0888698i	0.0291237	+	0.00855150i
$109$	0.709337	+	4.93355i	0.0679422	+	0.472548i	0.995179	+	0.0980734i	$0.0312680\pi$
$109$	0.709337	+	4.93355i	0.0679422	+	0.472548i	−0.927237	+	0.374475i	$0.877823\pi$
$110$	0.0995564	−	0.217998i	0.00949233	−	0.0207853i
$111$	−0.462430	+	3.21627i	−0.0438920	+	0.305275i
$112$	9.28325	+	5.96598i	0.877184	+	0.563732i
$113$	−0.0192078	−	0.0221670i	−0.00180692	−	0.00208530i	0.754845	−	0.655903i	$-0.227712\pi$
$113$	−0.0192078	−	0.0221670i	−0.00180692	−	0.00208530i	−0.756652	+	0.653817i	$0.773166\pi$
$114$	5.40110			0.505859
$115$	2.91072	−	3.81152i	0.271426	−	0.355426i
$116$	−0.865194			−0.0803312
$117$	2.38309	+	2.75023i	0.220317	+	0.254259i
$118$	−0.00891360	−	0.00572842i	−0.000820563	−	0.000527344i
$119$	−0.933247	+	6.49088i	−0.0855506	+	0.595018i
$120$	1.06484	−	2.33168i	0.0972064	−	0.212852i
$121$	1.56193	+	10.8635i	0.141994	+	0.987589i
$122$	−7.37349	−	2.16505i	−0.667564	−	0.196015i
$123$	−3.20123	+	2.05730i	−0.288645	+	0.185501i
$124$	1.10655	+	2.42300i	0.0993708	+	0.217592i
$125$	0.959493	−	0.281733i	0.0858197	−	0.0251989i
$126$	−2.42666	+	2.80051i	−0.216184	+	0.249489i
$127$	9.09037	−	10.4908i	0.806640	−	0.930912i	−0.192086	−	0.981378i	$-0.561525\pi$
$127$	9.09037	−	10.4908i	0.806640	−	0.930912i	0.998726	+	0.0504662i	$0.0160707\pi$
$128$	12.6965	−	3.72804i	1.12222	−	0.329515i
$129$	1.95287	+	4.27619i	0.171941	+	0.376497i
$130$	−4.65838	+	2.99376i	−0.408567	+	0.262570i
$131$	5.67287	+	1.66571i	0.495641	+	0.145533i	0.519994	−	0.854170i	$-0.325934\pi$
$131$	5.67287	+	1.66571i	0.495641	+	0.145533i	−0.0243525	+	0.999703i	$0.507752\pi$
$132$	0.00707030	+	0.0491750i	0.000615390	+	0.00428013i
$133$	−3.59079	+	7.86273i	−0.311361	+	0.681786i
$134$	1.74529	−	12.1388i	0.150770	−	1.04863i
$135$	0.841254	+	0.540641i	0.0724036	+	0.0465310i
$136$	4.52018	+	5.21657i	0.387602	+	0.447317i
$137$	−0.000207022	0		−1.76871e−5	0		−8.84354e−6	−	1.00000i	$-0.500003\pi$
$137$	−0.000207022	0		−1.76871e−5	0		−8.84354e−6		1.00000i	$0.500003\pi$
$138$	−0.590389	+	7.27369i	−0.0502572	+	0.619178i
$139$	−21.1954			−1.79777			−0.898886	−	0.438182i	$-0.855622\pi$
$139$	−21.1954			−1.79777			−0.898886	+	0.438182i	$0.855622\pi$
$140$	−0.503047	−	0.580548i	−0.0425153	−	0.0490652i
$141$	10.7055	+	6.88002i	0.901568	+	0.579402i
$142$	0.0380706	−	0.264787i	0.00319482	−	0.0222204i
$143$	−0.238091	+	0.521347i	−0.0199102	+	0.0435973i
$144$	0.644882	+	4.48526i	0.0537402	+	0.373771i
$145$	−2.63171	−	0.772740i	−0.218552	−	0.0641725i
$146$	−4.76686	+	3.06348i	−0.394509	+	0.253535i
$147$	0.444320	+	0.972926i	0.0366469	+	0.0802455i
$148$	0.983457	−	0.288769i	0.0808397	−	0.0237367i
$149$	5.34035	−	6.16309i	0.437499	−	0.504900i	−0.493589	−	0.869695i	$-0.664315\pi$
$149$	5.34035	−	6.16309i	0.437499	−	0.504900i	0.931088	+	0.364795i	$0.118861\pi$
$150$	−0.996473	+	1.14999i	−0.0813617	+	0.0938964i
$151$	0.282936	−	0.0830777i	0.0230250	−	0.00676076i	−0.270200	−	0.962804i	$-0.587090\pi$
$151$	0.282936	−	0.0830777i	0.0230250	−	0.00676076i	0.293225	+	0.956044i	$0.405272\pi$
$152$	3.77964	+	8.27626i	0.306569	+	0.671293i
$153$	−2.26533	+	1.45584i	−0.183141	+	0.117697i
$154$	−0.559979	−	0.164425i	−0.0451244	−	0.0132497i
$155$	1.20177	+	8.35848i	0.0965283	+	0.671369i
$156$	0.476860	−	1.04418i	0.0381793	−	0.0836011i
$157$	−2.60395	+	18.1109i	−0.207818	+	1.44541i	0.572438	+	0.819948i	$0.305998\pi$
$157$	−2.60395	+	18.1109i	−0.207818	+	1.44541i	−0.780257	+	0.625460i	$0.784912\pi$
$158$	−11.0073	−	7.07393i	−0.875690	−	0.562772i
$159$	4.84015	+	5.58583i	0.383849	+	0.442985i
$160$	−1.76856			−0.139817
$161$	−10.1963	−	5.69521i	−0.803580	−	0.448845i
$162$	−1.52166			−0.119553
$163$	−12.0608	−	13.9189i	−0.944675	−	1.09021i	−0.995803	−	0.0915213i	$-0.970827\pi$
$163$	−12.0608	−	13.9189i	−0.944675	−	1.09021i	0.0511278	−	0.998692i	$-0.483718\pi$
$164$	1.00980	+	0.648957i	0.0788518	+	0.0506750i
$165$	−0.0224141	+	0.155893i	−0.00174493	+	0.0121363i
$166$	−4.51345	+	9.88309i	−0.350312	+	0.767076i
$167$	−2.80097	−	19.4812i	−0.216746	−	1.50750i	−0.749939	−	0.661507i	$-0.769917\pi$
$167$	−2.80097	−	19.4812i	−0.216746	−	1.50750i	0.533194	−	0.845993i	$-0.320992\pi$
$168$	−5.98946	−	1.75866i	−0.462097	−	0.135684i
$169$	0.204320	−	0.131308i	0.0157169	−	0.0101006i
$170$	−1.70217	−	3.72723i	−0.130550	−	0.285866i
$171$	−3.40570	+	1.00001i	−0.260441	+	0.0764723i
$172$	0.971085	−	1.12069i	0.0740445	−	0.0854519i
$173$	−12.9533	+	14.9489i	−0.984819	+	1.13654i	0.00581266	+	0.999983i	$0.498150\pi$
$173$	−12.9533	+	14.9489i	−0.984819	+	1.13654i	−0.990632	+	0.136559i	$0.956396\pi$
$174$	4.00456	−	1.17584i	0.303585	−	0.0891405i
$175$	−1.01164	−	2.21518i	−0.0764726	−	0.167452i
$176$	−0.600382	+	0.385842i	−0.0452555	+	0.0290839i
$177$	0.00668115	+	0.00196176i	0.000502186	+	0.000147455i
$178$	3.62580	+	25.2180i	0.271765	+	1.89017i
$179$	10.6834	−	23.3933i	0.798511	−	1.74850i	0.148016	−	0.988985i	$-0.452711\pi$
$179$	10.6834	−	23.3933i	0.798511	−	1.74850i	0.650495	−	0.759511i	$-0.274562\pi$
$180$	0.0448918	−	0.312230i	0.00334604	−	0.0232722i
$181$	18.9274	+	12.1639i	1.40686	+	0.904135i	0.999956	−	0.00933508i	$-0.00297149\pi$
$181$	18.9274	+	12.1639i	1.40686	+	0.904135i	0.406905	+	0.913470i	$0.366608\pi$
$182$	8.83079	+	10.1913i	0.654582	+	0.755428i
$183$	5.05027			0.373327
$184$	−11.5588	+	4.18540i	−0.852129	+	0.308551i
$185$	3.24935			0.238897
$186$	−8.41465	−	9.71102i	−0.616992	−	0.712047i
$187$	−0.356780	−	0.229289i	−0.0260904	−	0.0167673i
$188$	0.571279	−	3.97333i	0.0416648	−	0.289785i
$189$	1.01164	−	2.21518i	0.0735858	−	0.161130i
$190$	−0.768656	−	5.34612i	−0.0557642	−	0.387848i
$191$	−13.4565	−	3.95119i	−0.973679	−	0.285898i	−0.244066	−	0.969759i	$-0.578481\pi$
$191$	−13.4565	−	3.95119i	−0.973679	−	0.285898i	−0.729613	+	0.683861i	$0.760300\pi$
$192$	−5.36014	+	3.44476i	−0.386835	+	0.248604i
$193$	2.19353	+	4.80315i	0.157894	+	0.345739i	0.972001	−	0.234975i	$-0.0755009\pi$
$193$	2.19353	+	4.80315i	0.157894	+	0.345739i	−0.814108	+	0.580714i	$0.802774\pi$
$194$	20.5404	−	6.03121i	1.47472	−	0.433016i
$195$	2.38309	−	2.75023i	0.170656	−	0.196948i
$196$	0.220943	−	0.254982i	0.0157816	−	0.0182130i
$197$	−12.4272	+	3.64895i	−0.885400	+	0.259977i	−0.692653	−	0.721271i	$-0.743558\pi$
$197$	−12.4272	+	3.64895i	−0.885400	+	0.259977i	−0.192748	+	0.981248i	$0.561740\pi$
$198$	−0.0995564	−	0.217998i	−0.00707517	−	0.0154925i
$199$	0.784100	−	0.503910i	0.0555833	−	0.0357212i	−0.512554	−	0.858655i	$-0.671301\pi$
$199$	0.784100	−	0.503910i	0.0555833	−	0.0357212i	0.568137	+	0.822934i	$0.307664\pi$
$200$	−2.45949	−	0.722171i	−0.173912	−	0.0510652i
$201$	1.14697	+	7.97733i	0.0809008	+	0.562677i
$202$	−2.97115	+	6.50591i	−0.209049	+	0.457754i
$203$	−0.950581	+	6.61143i	−0.0667177	+	0.464032i
$204$	0.714575	+	0.459230i	0.0500303	+	0.0321525i
$205$	2.49195	+	2.87586i	0.174045	+	0.200859i
$206$	7.40580			0.515986
$207$	−0.974439	−	4.69579i	−0.0677282	−	0.326380i
$208$	16.4900			1.14338
$209$	−0.366087	−	0.422487i	−0.0253228	−	0.0292240i
$210$	3.11736	+	2.00340i	0.215118	+	0.138248i
$211$	−1.09032	+	7.58337i	−0.0750610	+	0.522061i	0.917252	+	0.398307i	$0.130402\pi$
$211$	−1.09032	+	7.58337i	−0.0750610	+	0.522061i	−0.992313	+	0.123753i	$0.960507\pi$
$212$	0.968521	−	2.12076i	0.0665183	−	0.145655i
$213$	0.0250192	+	0.174012i	0.00171429	+	0.0119231i
$214$	−21.6235	−	6.34924i	−1.47815	−	0.434025i
$215$	3.95474	−	2.54156i	0.269711	−	0.173333i
$216$	−1.06484	−	2.33168i	−0.0724534	−	0.158651i
$217$	19.7313	−	5.79362i	1.33944	−	0.393297i
$218$	−4.96671	+	5.73188i	−0.336388	+	0.388212i
$219$	2.43859	−	2.81428i	0.164784	−	0.190171i
$220$	0.0476683	−	0.0139967i	0.00321379	−	0.000943655i
$221$	4.07078	+	8.91376i	0.273830	+	0.599604i
$222$	−4.15949	+	2.67314i	−0.279167	+	0.179409i
$223$	24.0413	+	7.05917i	1.60993	+	0.472717i	0.958286	−	0.285812i	$-0.0922633\pi$
$223$	24.0413	+	7.05917i	1.60993	+	0.472717i	0.651640	+	0.758529i	$0.274081\pi$
$224$	0.612932	+	4.26304i	0.0409533	+	0.284836i
$225$	0.415415	−	0.909632i	0.0276943	−	0.0606421i
$226$	0.00635179	−	0.0441776i	0.000422515	−	0.00293865i
$227$	−12.5684	−	8.07719i	−0.834191	−	0.536102i	0.0524161	−	0.998625i	$-0.483308\pi$
$227$	−12.5684	−	8.07719i	−0.834191	−	0.536102i	−0.886607	+	0.462523i	$0.846944\pi$
$228$	0.733215	+	0.846175i	0.0485584	+	0.0560393i
$229$	15.4474			1.02079			0.510397	−	0.859939i	$-0.329498\pi$
$229$	15.4474			1.02079			0.510397	+	0.859939i	$0.329498\pi$
$230$	7.28368	−	0.450775i	0.480271	−	0.0297232i
$231$	0.383542			0.0252352
$232$	4.60414	+	5.31346i	0.302276	+	0.348846i
$233$	9.60483	+	6.17265i	0.629233	+	0.404384i	0.816026	−	0.578016i	$-0.196173\pi$
$233$	9.60483	+	6.17265i	0.629233	+	0.404384i	−0.186792	+	0.982399i	$0.559809\pi$
$234$	−0.788058	+	5.48106i	−0.0515170	+	0.358308i
$235$	5.28644	−	11.5757i	0.344849	−	0.755114i
$236$	−0.000312591	−	0.00217412i	−2.03480e−5	−	0.000141523i
$237$	8.25044	+	2.42255i	0.535924	+	0.157361i
$238$	−8.39441	+	5.39476i	−0.544129	+	0.349690i
$239$	−2.69071	−	5.89183i	−0.174048	−	0.381111i	0.802425	−	0.596753i	$-0.203543\pi$
$239$	−2.69071	−	5.89183i	−0.174048	−	0.381111i	−0.976472	+	0.215642i	$0.930816\pi$
$240$	4.34783	−	1.27664i	0.280651	−	0.0824065i
$241$	5.77643	−	6.66636i	0.372093	−	0.429418i	−0.538562	−	0.842586i	$-0.681032\pi$
$241$	5.77643	−	6.66636i	0.372093	−	0.429418i	0.910655	+	0.413168i	$0.135578\pi$
$242$	−10.9365	+	12.6214i	−0.703024	+	0.811333i
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$	−0.661780	−	1.44910i	−0.0423661	−	0.0927689i
$245$	0.899789	−	0.578259i	0.0574854	−	0.0369436i
$246$	−5.55582	−	1.63134i	−0.354226	−	0.104010i
$247$	1.83826	+	12.7854i	0.116966	+	0.813513i
$248$	8.99199	−	19.6897i	0.570992	−	1.25030i
$249$	1.01616	−	7.06752i	0.0643963	−	0.447886i
$250$	1.28010	+	0.822670i	0.0809606	+	0.0520302i
$251$	−4.54187	−	5.24159i	−0.286680	−	0.330846i	0.594083	−	0.804404i	$-0.297515\pi$
$251$	−4.54187	−	5.24159i	−0.286680	−	0.330846i	−0.880763	+	0.473557i	$0.842970\pi$
$252$	−0.768175			−0.0483904
$253$	0.608982	−	0.446830i	0.0382864	−	0.0280920i
$254$	21.1227			1.32536
$255$	1.76341	+	2.03508i	0.110429	+	0.127442i
$256$	6.21867	+	3.99650i	0.388667	+	0.249781i
$257$	3.22549	−	22.4337i	0.201200	−	1.39938i	−0.599529	−	0.800353i	$-0.704646\pi$
$257$	3.22549	−	22.4337i	0.201200	−	1.39938i	0.800730	−	0.599026i	$-0.204445\pi$
$258$	−2.97160	+	6.50689i	−0.185004	+	0.405101i
$259$	−1.12613	−	7.83242i	−0.0699744	−	0.486683i
$260$	−1.10141	−	0.323404i	−0.0683067	−	0.0200567i
$261$	−2.30740	+	1.48288i	−0.142825	+	0.0917877i
$262$	3.73732	+	8.18359i	0.230892	+	0.505584i
$263$	9.47605	−	2.78242i	0.584318	−	0.171571i	0.0238047	−	0.999717i	$-0.492422\pi$
$263$	9.47605	−	2.78242i	0.584318	−	0.171571i	0.560513	+	0.828145i	$0.310604\pi$
$264$	0.264376	−	0.305106i	0.0162712	−	0.0187780i
$265$	4.84015	−	5.58583i	0.297328	−	0.343135i
$266$	−12.6202	+	3.70563i	−0.773795	+	0.227207i
$267$	−6.95534	−	15.2301i	−0.425660	−	0.932066i
$268$	2.13868	−	1.37444i	0.130640	−	0.0839575i
$269$	−6.80693	−	1.99870i	−0.415026	−	0.121863i	0.0675517	−	0.997716i	$-0.478481\pi$
$269$	−6.80693	−	1.99870i	−0.415026	−	0.121863i	−0.482578	+	0.875853i	$0.660299\pi$
$270$	0.216554	+	1.50617i	0.0131791	+	0.0916625i
$271$	5.90629	−	12.9330i	0.358781	−	0.785621i	−0.641054	−	0.767495i	$-0.721503\pi$
$271$	5.90629	−	12.9330i	0.358781	−	0.785621i	0.999836	−	0.0181260i	$-0.00577001\pi$
$272$	−1.73654	+	12.0779i	−0.105293	+	0.732330i
$273$	−7.45522	−	4.79118i	−0.451211	−	0.289976i
$274$	−0.000206292	0	0.000238074i	−1.24626e−5	0	1.43826e-5i
$275$	0.157496			0.00949738
$276$	−1.21970	+	0.894931i	−0.0734171	+	0.0538685i
$277$	−16.7847			−1.00849			−0.504246	−	0.863560i	$-0.668230\pi$
$277$	−16.7847			−1.00849			−0.504246	+	0.863560i	$0.668230\pi$
$278$	−21.1207	−	24.3746i	−1.26673	−	1.46189i
$279$	7.10391	+	4.56540i	0.425300	+	0.273324i
$280$	−0.888374	+	6.17878i	−0.0530905	+	0.369253i
$281$	−0.252366	+	0.552605i	−0.0150549	+	0.0329656i	−0.917010	−	0.398864i	$-0.869405\pi$
$281$	−0.252366	+	0.552605i	−0.0150549	+	0.0329656i	0.901955	+	0.431830i	$0.142132\pi$
$282$	2.75580	+	19.1670i	0.164106	+	1.14138i
$283$	20.3943	+	5.98829i	1.21231	+	0.355967i	0.824548	−	0.565792i	$-0.191429\pi$
$283$	20.3943	+	5.98829i	1.21231	+	0.355967i	0.387764	+	0.921759i	$0.373247\pi$
$284$	0.0466517	−	0.0299812i	0.00276827	−	0.00177906i
$285$	1.47451	+	3.22872i	0.0873424	+	0.191253i
$286$	−0.836797	+	0.245706i	−0.0494808	+	0.0145289i
$287$	6.06850	−	7.00342i	0.358212	−	0.413399i
$288$	−1.15816	+	1.33659i	−0.0682452	+	0.0787592i
$289$	9.35394	−	2.74656i	0.550232	−	0.161563i
$290$	−1.73378	−	3.79646i	−0.101811	−	0.222936i
$291$	−11.8353	+	7.60606i	−0.693795	+	0.445875i
$292$	−1.12706	−	0.330936i	−0.0659564	−	0.0193665i
$293$	−0.0884562	−	0.615226i	−0.00516766	−	0.0359419i	0.987074	−	0.160262i	$-0.0512340\pi$
$293$	−0.0884562	−	0.615226i	−0.00516766	−	0.0359419i	−0.992242	+	0.124320i	$0.960325\pi$
$294$	−0.676103	+	1.48046i	−0.0394311	+	0.0863421i
$295$	0.000990968	−	0.00689233i	5.76964e−5	−	0.000401287i
$296$	−7.00691	−	4.50307i	−0.407268	−	0.261735i
$297$	0.103138	+	0.119028i	0.00598468	+	0.00690669i
$298$	12.4090			0.718836
$299$	−17.4191	+	1.07804i	−1.00737	+	0.0623445i
$300$	−0.315440			−0.0182120
$301$	−7.49691	−	8.65190i	−0.432115	−	0.498687i
$302$	0.377477	+	0.242590i	0.0217214	+	0.0139595i
$303$	0.668922	−	4.65245i	0.0384286	−	0.267277i
$304$	−6.68156	+	14.6306i	−0.383214	+	0.839121i
$305$	−0.718728	−	4.99886i	−0.0411543	−	0.286234i
$306$	−3.93154	−	1.15440i	−0.224751	−	0.0659929i
$307$	−9.33878	+	6.00167i	−0.532992	+	0.342533i	−0.779293	−	0.626660i	$-0.784421\pi$
$307$	−9.33878	+	6.00167i	−0.532992	+	0.342533i	0.246300	+	0.969194i	$0.420785\pi$
$308$	−0.0502588	−	0.110051i	−0.00286376	−	0.00627077i
$309$	−4.66978	+	1.37117i	−0.265655	+	0.0780033i
$310$	−8.41465	+	9.71102i	−0.477920	+	0.551549i
$311$	1.21051	−	1.39701i	0.0686420	−	0.0792171i	−0.720390	−	0.693569i	$-0.756037\pi$
$311$	1.21051	−	1.39701i	0.0686420	−	0.0792171i	0.789032	+	0.614352i	$0.210583\pi$
$312$	−8.95027	+	2.62804i	−0.506709	+	0.148783i
$313$	5.36695	+	11.7520i	0.303358	+	0.664262i	0.998508	−	0.0546031i	$-0.0173894\pi$
$313$	5.36695	+	11.7520i	0.303358	+	0.664262i	−0.695150	+	0.718865i	$0.744662\pi$
$314$	−23.4222	+	15.0525i	−1.32179	+	0.849462i
$315$	−2.33660	−	0.686088i	−0.131653	−	0.0386567i
$316$	−0.386014	−	2.68478i	−0.0217150	−	0.151031i
$317$	10.0430	−	21.9910i	0.564068	−	1.23514i	−0.385827	−	0.922571i	$-0.626084\pi$
$317$	10.0430	−	21.9910i	0.564068	−	1.23514i	0.949896	−	0.312567i	$-0.101189\pi$
$318$	−1.60058	+	11.1323i	−0.0897559	+	0.624266i
$319$	−0.363407	−	0.233547i	−0.0203469	−	0.0130761i
$320$	4.17252	+	4.81535i	0.233251	+	0.269186i
$321$	14.8104			0.826639
$322$	−3.61089	−	17.4008i	−0.201227	−	0.969707i
$323$	−9.55804			−0.531824
$324$	−0.206570	−	0.238394i	−0.0114761	−	0.0132441i
$325$	−3.06139	−	1.96743i	−0.169815	−	0.109134i
$326$	3.98836	−	27.7397i	0.220895	−	1.53636i
$327$	2.07055	−	4.53386i	0.114501	−	0.250723i
$328$	−1.38817	−	9.65494i	−0.0766489	−	0.533105i
$329$	−29.7348	−	8.73093i	−1.63933	−	0.481352i
$330$	−0.201611	+	0.129567i	−0.0110983	+	0.00713245i
$331$	−3.91271	−	8.56764i	−0.215062	−	0.470920i	0.771098	−	0.636716i	$-0.219708\pi$
$331$	−3.91271	−	8.56764i	−0.215062	−	0.470920i	−0.986160	+	0.165796i	$0.946981\pi$
$332$	−2.16107	+	0.634548i	−0.118604	+	0.0348253i
$333$	2.12787	−	2.45569i	0.116607	−	0.134571i
$334$	19.6121	−	22.6336i	1.07313	−	1.23845i
$335$	7.73290	−	2.27058i	0.422494	−	0.124055i
$336$	−4.58411	−	10.0378i	−0.250084	−	0.547607i
$337$	−24.4854	+	15.7358i	−1.33381	+	0.857186i	−0.996450	−	0.0841908i	$-0.973169\pi$
$337$	−24.4854	+	15.7358i	−1.33381	+	0.857186i	−0.337358	+	0.941377i	$0.609533\pi$
$338$	0.354603	+	0.104121i	0.0192879	+	0.00566343i
$339$	0.00417426	+	0.0290326i	0.000226714	+	0.00157683i
$340$	0.352861	−	0.772657i	0.0191366	−	0.0419032i
$341$	−0.189274	+	1.31643i	−0.0102498	+	0.0712886i
$342$	−4.54369	−	2.92005i	−0.245695	−	0.157898i
$343$	−12.8689	−	14.8515i	−0.694857	−	0.801908i
$344$	−12.0502			−0.649703
$345$	−4.50932	+	1.63280i	−0.242774	+	0.0879071i
$346$	−30.0987			−1.61812
$347$	−8.29742	−	9.57574i	−0.445429	−	0.514052i	0.487986	−	0.872852i	$-0.337732\pi$
$347$	−8.29742	−	9.57574i	−0.445429	−	0.514052i	−0.933415	+	0.358799i	$0.883186\pi$
$348$	0.727847	+	0.467759i	0.0390167	+	0.0250745i
$349$	−0.579004	+	4.02706i	−0.0309934	+	0.215564i	−0.999432	−	0.0336867i	$-0.989275\pi$
$349$	−0.579004	+	4.02706i	−0.0309934	+	0.215564i	0.968439	+	0.249250i	$0.0801842\pi$
$350$	1.53937	−	3.37074i	0.0822825	−	0.180174i
$351$	−0.517895	−	3.60204i	−0.0276432	−	0.192262i
$352$	−0.267259	−	0.0784742i	−0.0142449	−	0.00418269i
$353$	8.42894	−	5.41695i	0.448627	−	0.288315i	−0.296754	−	0.954954i	$-0.595904\pi$
$353$	8.42894	−	5.41695i	0.448627	−	0.288315i	0.745381	+	0.666639i	$0.232268\pi$
$354$	0.00440158	+	0.00963811i	0.000233941	+	0.000512260i
$355$	0.168681	−	0.0495291i	0.00895264	−	0.00262873i
$356$	−3.45862	+	3.99146i	−0.183306	+	0.211547i
$357$	4.29433	−	4.95592i	0.227280	−	0.262295i
$358$	37.5478	−	11.0250i	1.98446	−	0.582690i
$359$	15.0884	+	33.0390i	0.796336	+	1.74373i	0.657550	+	0.753411i	$0.271593\pi$
$359$	15.0884	+	33.0390i	0.796336	+	1.74373i	0.138786	+	0.990322i	$0.455680\pi$
$360$	−2.15640	+	1.38584i	−0.113652	+	0.0730400i
$361$	6.14187	+	1.80342i	0.323256	+	0.0949167i
$362$	4.87226	+	33.8873i	0.256081	+	1.78108i
$363$	4.55926	−	9.98339i	0.239299	−	0.523992i
$364$	−0.397833	+	2.76699i	−0.0208521	+	0.145030i
$365$	−3.13268	−	2.01325i	−0.163972	−	0.105378i
$366$	5.03246	+	5.80777i	0.263051	+	0.303577i
$367$	3.48523			0.181927			0.0909637	−	0.995854i	$-0.471005\pi$
$367$	3.48523			0.181927			0.0909637	+	0.995854i	$0.471005\pi$
$368$	−18.9727	−	10.5973i	−0.989021	−	0.552425i
$369$	3.80531			0.198096
$370$	3.23789	+	3.73672i	0.168330	+	0.194263i
$371$	−15.1419	−	9.73108i	−0.786126	−	0.505213i
$372$	0.379086	−	2.63660i	0.0196547	−	0.136701i
$373$	−2.80648	+	6.14534i	−0.145314	+	0.318193i	−0.968268	−	0.249915i	$-0.919597\pi$
$373$	−2.80648	+	6.14534i	−0.145314	+	0.318193i	0.822954	+	0.568108i	$0.192325\pi$
$374$	−0.0918420	−	0.638775i	−0.00474903	−	0.0330303i
$375$	−0.959493	−	0.281733i	−0.0495480	−	0.0145486i
$376$	−27.4417	+	17.6357i	−1.41520	+	0.909492i
$377$	4.14638	+	9.07931i	0.213550	+	0.467608i
$378$	3.55550	−	1.04399i	0.182875	−	0.0536971i
$379$	−15.9069	+	18.3576i	−0.817084	+	0.942965i	−0.999187	−	0.0403147i	$-0.987164\pi$
$379$	−15.9069	+	18.3576i	−0.817084	+	0.942965i	0.182103	+	0.983279i	$0.441709\pi$
$380$	0.733215	−	0.846175i	0.0376131	−	0.0434079i
$381$	−13.3191	+	3.91084i	−0.682357	+	0.200358i
$382$	−8.86522	−	19.4121i	−0.453584	−	0.993211i
$383$	29.7253	−	19.1033i	1.51889	−	0.976133i	0.526887	−	0.849936i	$-0.323359\pi$
$383$	29.7253	−	19.1033i	1.51889	−	0.976133i	0.992005	−	0.126197i	$-0.0402771\pi$
$384$	−12.6965	−	3.72804i	−0.647917	−	0.190245i
$385$	−0.0545837	−	0.379638i	−0.00278184	−	0.0193481i
$386$	−3.33780	+	7.30875i	−0.169889	+	0.372006i
$387$	0.669023	−	4.65316i	0.0340084	−	0.236533i
$388$	3.73332	+	2.39926i	0.189530	+	0.121804i
$389$	0.0874399	+	0.100911i	0.00443338	+	0.00511639i	0.757962	−	0.652299i	$-0.226195\pi$
$389$	0.0874399	+	0.100911i	0.00443338	+	0.00511639i	−0.753529	+	0.657415i	$0.771650\pi$
$390$	5.53743			0.280398
$391$	1.04478	−	12.8719i	0.0528368	−	0.650959i
$392$	−2.74168			−0.138476
$393$	−3.87178	−	4.46827i	−0.195305	−	0.225394i
$394$	−16.5796	−	10.6551i	−0.835269	−	0.536795i
$395$	1.22373	−	8.51123i	0.0615725	−	0.428246i
$396$	0.0206381	−	0.0451911i	0.00103710	−	0.00227094i
$397$	0.0567723	+	0.394860i	0.00284932	+	0.0198175i	0.991197	−	0.132399i	$-0.0422680\pi$
$397$	0.0567723	+	0.394860i	0.00284932	+	0.0198175i	−0.988347	+	0.152216i	$0.951359\pi$
$398$	1.36083	+	0.399575i	0.0682121	+	0.0200289i
$399$	7.27168	−	4.67323i	0.364039	−	0.233954i
$400$	−1.88240	−	4.12189i	−0.0941201	−	0.206094i
$401$	−2.85252	+	0.837576i	−0.142448	+	0.0418266i	−0.352179	−	0.935933i	$-0.614559\pi$
$401$	−2.85252	+	0.837576i	−0.142448	+	0.0418266i	0.209731	+	0.977759i	$0.432741\pi$
$402$	−8.03094	+	9.26820i	−0.400547	+	0.462256i
$403$	20.1238	−	23.2241i	1.00244	−	1.15688i
$404$	−1.42261	+	0.417715i	−0.0707772	+	0.0207821i
$405$	−0.415415	−	0.909632i	−0.0206421	−	0.0452000i
$406$	−8.55032	+	5.49496i	−0.424345	+	0.272710i
$407$	0.491030	+	0.144180i	0.0243395	+	0.00714671i
$408$	−0.982330	−	6.83225i	−0.0486326	−	0.338247i
$409$	−15.0543	+	32.9644i	−0.744388	+	1.62998i	0.0318102	+	0.999494i	$0.489873\pi$
$409$	−15.0543	+	32.9644i	−0.744388	+	1.62998i	−0.776198	+	0.630489i	$0.782854\pi$
$410$	−0.824056	+	5.73143i	−0.0406972	+	0.283055i
$411$	0.000174158	0	0.000111925i	8.59058e−6	0	5.52083e-6i
$412$	1.00536	+	1.16025i	0.0495305	+	0.0571612i
$413$	−0.0169571			−0.000834405
$414$	4.42912	−	5.79983i	0.217679	−	0.285046i
$415$	−7.14020			−0.350498
$416$	4.21463	+	4.86395i	0.206639	+	0.238475i
$417$	17.8307	+	11.4591i	0.873174	+	0.561155i
$418$	0.121061	−	0.841994i	0.00592126	−	0.0411833i
$419$	−7.43868	+	16.2884i	−0.363403	+	0.795742i	0.636301	+	0.771440i	$0.280463\pi$
$419$	−7.43868	+	16.2884i	−0.363403	+	0.795742i	−0.999705	+	0.0243015i	$0.992264\pi$
$420$	0.109323	+	0.760356i	0.00533440	+	0.0371016i
$421$	10.3459	+	3.03782i	0.504226	+	0.148054i	0.523946	−	0.851751i	$-0.324459\pi$
$421$	10.3459	+	3.03782i	0.504226	+	0.148054i	−0.0197201	+	0.999806i	$0.506278\pi$
$422$	−9.80730	+	6.30277i	−0.477412	+	0.306814i
$423$	−5.28644	−	11.5757i	−0.257035	−	0.562829i
$424$	−18.1784	+	5.33765i	−0.882819	+	0.259219i
$425$	1.76341	−	2.03508i	0.0855379	−	0.0987159i
$426$	−0.175182	+	0.202171i	−0.00848759	+	0.00979520i
$427$	−11.8005	+	3.46493i	−0.571064	+	0.167680i
$428$	−1.94074	−	4.24963i	−0.0938093	−	0.205414i
$429$	0.482157	−	0.309863i	0.0232788	−	0.0149603i
$430$	6.86356	+	2.01532i	0.330990	+	0.0971875i
$431$	3.62660	+	25.2235i	0.174687	+	1.21498i	0.868820	+	0.495128i	$0.164879\pi$
$431$	3.62660	+	25.2235i	0.174687	+	1.21498i	−0.694133	+	0.719847i	$0.744212\pi$
$432$	1.88240	−	4.12189i	0.0905671	−	0.198314i
$433$	4.22440	−	29.3813i	0.203012	−	1.41198i	−0.592271	−	0.805739i	$-0.701769\pi$
$433$	4.22440	−	29.3813i	0.203012	−	1.41198i	0.795283	−	0.606238i	$-0.207322\pi$
$434$	26.3243	+	16.9176i	1.26361	+	0.812070i
$435$	1.79616	+	2.07288i	0.0861193	+	0.0993870i
$436$	−1.57224			−0.0752968
$437$	6.10152	−	15.8917i	0.291875	−	0.760201i
$438$	5.66638			0.270750
$439$	7.16726	+	8.27146i	0.342075	+	0.394775i	0.900555	−	0.434743i	$-0.143161\pi$
$439$	7.16726	+	8.27146i	0.342075	+	0.394775i	−0.558480	+	0.829518i	$0.688615\pi$
$440$	−0.339626	−	0.218264i	−0.0161910	−	0.0104053i
$441$	0.152217	−	1.05869i	0.00724844	−	0.0504140i
$442$	−6.19432	+	13.5637i	−0.294634	+	0.645158i
$443$	2.12556	+	14.7836i	0.100988	+	0.702389i	0.975918	+	0.218139i	$0.0699985\pi$
$443$	2.12556	+	14.7836i	0.100988	+	0.702389i	−0.874929	+	0.484250i	$0.839092\pi$
$444$	−0.983457	−	0.288769i	−0.0466728	−	0.0137044i
$445$	−14.0852	+	9.05201i	−0.667703	+	0.429107i
$446$	15.8385	+	34.6816i	0.749977	+	1.64222i
$447$	−7.82461	+	2.29751i	−0.370091	+	0.108669i
$448$	10.1611	−	11.7265i	0.480067	−	0.554027i
$449$	18.5376	−	21.3935i	0.874843	−	1.00962i	−0.125004	−	0.992156i	$-0.539894\pi$
$449$	18.5376	−	21.3935i	0.874843	−	1.00962i	0.999847	−	0.0174668i	$-0.00556015\pi$
$450$	1.46002	−	0.428700i	0.0688260	−	0.0202091i
$451$	0.248967	+	0.545162i	0.0117234	+	0.0256707i
$452$	0.00778347	−	0.00500213i	0.000366104	−	0.000235280i
$453$	−0.282936	−	0.0830777i	−0.0132935	−	0.00390333i
$454$	−3.23533	−	22.5022i	−0.151842	−	1.05608i
$455$	−3.68143	+	8.06120i	−0.172588	+	0.377915i
$456$	1.29485	−	9.00586i	0.0606368	−	0.421738i
$457$	−19.4758	−	12.5164i	−0.911041	−	0.585490i	−0.000995595	−	1.00000i	$-0.500317\pi$
$457$	−19.4758	−	12.5164i	−0.911041	−	0.585490i	−0.910045	+	0.414509i	$0.863953\pi$
$458$	15.3930	+	17.7644i	0.719265	+	0.830076i
$459$	2.69280			0.125689
$460$	1.05940	+	1.07992i	0.0493949	+	0.0503515i
$461$	−7.63289			−0.355499			−0.177749	−	0.984076i	$-0.556882\pi$
$461$	−7.63289			−0.355499			−0.177749	+	0.984076i	$0.556882\pi$
$462$	0.382189	+	0.441070i	0.0177811	+	0.0205204i
$463$	20.5374	+	13.1986i	0.954454	+	0.613390i	0.922458	−	0.386098i	$-0.126177\pi$
$463$	20.5374	+	13.1986i	0.954454	+	0.613390i	0.0319962	+	0.999488i	$0.489814\pi$
$464$	−1.76879	+	12.3022i	−0.0821141	+	0.571116i
$465$	3.50794	−	7.68132i	0.162677	−	0.356213i
$466$	2.47246	+	17.1964i	0.114535	+	0.796606i
$467$	36.6442	+	10.7597i	1.69569	+	0.497900i	0.979744	−	0.200254i	$-0.0641768\pi$
$467$	36.6442	+	10.7597i	1.69569	+	0.497900i	0.715948	+	0.698154i	$0.245995\pi$
$468$	−0.965685	+	0.620608i	−0.0446388	+	0.0286876i
$469$	−8.15315	−	17.8529i	−0.376478	−	0.824371i
$470$	18.5797	−	5.45550i	0.857019	−	0.251644i
$471$	11.9821	−	13.8281i	0.552105	−	0.637163i
$472$	−0.0116886	+	0.0134893i	−0.000538010	+	0.000620897i
$473$	0.710400	−	0.208592i	0.0326642	−	0.00959108i
$474$	5.43543	+	11.9019i	0.249658	+	0.546674i
$475$	2.98602	−	1.91900i	0.137008	−	0.0880496i
$476$	−1.98475	−	0.582775i	−0.0909708	−	0.0267114i
$477$	−1.05186	−	7.31588i	−0.0481616	−	0.334971i
$478$	4.09434	−	8.96535i	0.187271	−	0.410066i
$479$	−4.90353	+	34.1048i	−0.224048	+	1.55829i	0.498451	+	0.866918i	$0.333902\pi$
$479$	−4.90353	+	34.1048i	−0.224048	+	1.55829i	−0.722500	+	0.691371i	$0.757007\pi$
$480$	1.48781	+	0.956155i	0.0679088	+	0.0436423i
$481$	−7.74348	−	8.93646i	−0.353072	−	0.407467i
$482$	13.4223			0.611370
$483$	5.49860	+	10.3036i	0.250195	+	0.468832i
$484$	−3.46202			−0.157365
$485$	9.21297	+	10.6323i	0.418339	+	0.482789i
$486$	1.28010	+	0.822670i	0.0580665	+	0.0373171i
$487$	4.52984	−	31.5057i	0.205267	−	1.42766i	−0.583073	−	0.812420i	$-0.698150\pi$
$487$	4.52984	−	31.5057i	0.205267	−	1.42766i	0.788339	−	0.615241i	$-0.210941\pi$
$488$	−5.37774	+	11.7756i	−0.243439	+	0.533057i
$489$	2.62106	+	18.2299i	0.118529	+	0.824385i
$490$	1.56161	+	0.458530i	0.0705463	+	0.0207143i
$491$	3.09550	−	1.98936i	0.139698	−	0.0897784i	−0.468925	−	0.883238i	$-0.655359\pi$
$491$	3.09550	−	1.98936i	0.139698	−	0.0897784i	0.608623	+	0.793460i	$0.291722\pi$
$492$	−0.498642	−	1.09187i	−0.0224805	−	0.0492255i
$493$	−7.08666	+	2.08083i	−0.319167	+	0.0937159i
$494$	−12.8713	+	14.8543i	−0.579107	+	0.668325i
$495$	0.103138	−	0.119028i	0.00463571	−	0.00534990i
$496$	36.7149	−	10.7805i	1.64855	−	0.484057i
$497$	−0.177848	−	0.389432i	−0.00797756	−	0.0174684i
$498$	9.14016	−	5.87402i	0.409580	−	0.263221i
$499$	−3.26130	−	0.957603i	−0.145996	−	0.0428682i	0.207918	−	0.978146i	$-0.433331\pi$
$499$	−3.26130	−	0.957603i	−0.145996	−	0.0428682i	−0.353914	+	0.935278i	$0.615149\pi$
$500$	0.0448918	+	0.312230i	0.00200762	+	0.0139633i
$501$	−8.17600	+	17.9029i	−0.365277	+	0.799844i
$502$	1.50194	−	10.4462i	0.0670348	−	0.466238i
$503$	0.670661	+	0.431008i	0.0299033	+	0.0192177i	0.555507	−	0.831512i	$-0.312524\pi$
$503$	0.670661	+	0.431008i	0.0299033	+	0.0192177i	−0.525604	+	0.850730i	$0.676161\pi$
$504$	4.08785	+	4.71763i	0.182087	+	0.210140i
$505$	−4.70030			−0.209160
$506$	1.12069	+	0.255070i	0.0498206	+	0.0113393i
$507$	−0.242876			−0.0107865
$508$	2.86747	+	3.30924i	0.127223	+	0.146824i
$509$	13.9644	+	8.97436i	0.618960	+	0.397782i	0.812208	−	0.583368i	$-0.198266\pi$
$509$	13.9644	+	8.97436i	0.618960	+	0.397782i	−0.193247	+	0.981150i	$0.561902\pi$
$510$	−0.583137	+	4.05581i	−0.0258218	+	0.179594i
$511$	−3.76716	+	8.24893i	−0.166649	+	0.364911i
$512$	−2.16557	−	15.0619i	−0.0957056	−	0.665647i
$513$	3.40570	+	1.00001i	0.150366	+	0.0441513i
$514$	29.0127	−	18.6454i	1.27970	−	0.822411i
$515$	2.02180	+	4.42711i	0.0890910	+	0.195082i
$516$	−1.42282	+	0.417778i	−0.0626362	+	0.0183916i
$517$	1.31250	−	1.51471i	0.0577238	−	0.0666168i
$518$	7.88505	−	9.09984i	0.346449	−	0.399824i
$519$	18.9790	−	5.57273i	0.833084	−	0.244616i
$520$	3.87504	+	8.48516i	0.169932	+	0.372099i
$521$	23.5219	−	15.1166i	1.03051	−	0.662271i	0.0878909	−	0.996130i	$-0.471987\pi$
$521$	23.5219	−	15.1166i	1.03051	−	0.662271i	0.942623	+	0.333859i	$0.108351\pi$
$522$	−4.00456	−	1.17584i	−0.175275	−	0.0514653i
$523$	3.04182	+	21.1563i	0.133009	+	0.925101i	0.941601	+	0.336730i	$0.109321\pi$
$523$	3.04182	+	21.1563i	0.133009	+	0.925101i	−0.808592	+	0.588370i	$0.799770\pi$
$524$	−0.774749	+	1.69646i	−0.0338450	+	0.0741103i
$525$	−0.346572	+	2.41046i	−0.0151256	+	0.105201i
$526$	12.6424	+	8.12477i	0.551234	+	0.354257i
$527$	14.8910	+	17.1851i	0.648661	+	0.748595i
$528$	0.713675			0.0310587
$529$	20.7344	+	9.95405i	0.901497	+	0.432785i
$530$	11.2467			0.488527
$531$	−0.00455993	−	0.00526244i	−0.000197884	−	0.000228370i
$532$	−2.29378	−	1.47412i	−0.0994480	−	0.0639114i
$533$	1.97075	−	13.7068i	0.0853625	−	0.593710i
$534$	10.5836	−	23.1750i	0.457999	−	1.00288i
$535$	−2.10775	−	14.6597i	−0.0911258	−	0.633794i
$536$	−19.8219	−	5.82024i	−0.856176	−	0.251396i
$537$	−21.6348	+	13.9038i	−0.933609	+	0.599994i
$538$	−4.48444	−	9.81956i	−0.193338	−	0.423351i
$539$	0.161631	−	0.0474593i	0.00696196	−	0.00204422i
$540$	−0.206570	+	0.238394i	−0.00888934	+	0.0102588i
$541$	6.28125	−	7.24895i	0.270052	−	0.311657i	−0.604484	−	0.796617i	$-0.706621\pi$
$541$	6.28125	−	7.24895i	0.270052	−	0.311657i	0.874536	+	0.484961i	$0.161166\pi$
$542$	20.7583	−	6.09517i	0.891643	−	0.261810i
$543$	−9.34644	−	20.4658i	−0.401094	−	0.878273i
$544$	−4.00636	+	2.57473i	−0.171771	+	0.110391i
$545$	−4.78238	−	1.40423i	−0.204855	−	0.0601508i
$546$	−1.91911	−	13.3477i	−0.0821305	−	0.571230i
$547$	−16.9219	+	37.0537i	−0.723527	+	1.58430i	0.0853679	+	0.996349i	$0.472793\pi$
$547$	−16.9219	+	37.0537i	−0.723527	+	1.58430i	−0.808895	+	0.587953i	$0.799934\pi$
$548$	9.29360e−6	0	6.46384e-5i	3.97003e−7	0	2.76122e-6i
$549$	−4.24856	−	2.73038i	−0.181324	−	0.116530i
$550$	0.156941	+	0.181119i	0.00669198	+	0.00772296i
$551$	−9.73557			−0.414749
$552$	11.9867	+	2.72820i	0.510188	+	0.116120i
$553$	−20.9401			−0.890462
$554$	−16.7255	−	19.3022i	−0.710597	−	0.820073i
$555$	−2.73353	−	1.75673i	−0.116032	−	0.0745690i
$556$	0.951502	−	6.61784i	0.0403527	−	0.280659i
$557$	17.6291	−	38.6022i	0.746967	−	1.63563i	−0.0247743	−	0.999693i	$-0.507887\pi$
$557$	17.6291	−	38.6022i	0.746967	−	1.63563i	0.771741	−	0.635937i	$-0.219386\pi$
$558$	1.82868	+	12.7187i	0.0774141	+	0.538427i
$559$	−16.4144	−	4.81969i	−0.694253	−	0.203851i
$560$	−9.28325	+	5.96598i	−0.392289	+	0.252109i
$561$	0.176180	+	0.385780i	0.00743832	+	0.0162876i
$562$	−0.886967	+	0.260437i	−0.0374145	+	0.0109859i
$563$	−20.5473	+	23.7129i	−0.865967	+	0.999379i	0.133998	+	0.990982i	$0.457218\pi$
$563$	−20.5473	+	23.7129i	−0.865967	+	0.999379i	−0.999965	+	0.00839740i	$0.997327\pi$
$564$	−2.62874	+	3.03372i	−0.110690	+	0.127743i
$565$	0.0281430	−	0.00826354i	0.00118399	−	0.000347650i
$566$	13.4358	+	29.4204i	0.564751	+	1.23663i
$567$	−2.04866	+	1.31659i	−0.0860356	+	0.0552917i
$568$	−0.432383	−	0.126959i	−0.0181424	−	0.00532708i
$569$	1.82396	+	12.6859i	0.0764644	+	0.531822i	0.991667	+	0.128828i	$0.0411214\pi$
$569$	1.82396	+	12.6859i	0.0764644	+	0.531822i	−0.915203	+	0.402994i	$0.867969\pi$
$570$	−2.24370	+	4.91301i	−0.0939781	+	0.205783i
$571$	0.930485	−	6.47167i	0.0389396	−	0.270831i	−0.961045	−	0.276392i	$-0.910861\pi$
$571$	0.930485	−	6.47167i	0.0389396	−	0.270831i	0.999985	+	0.00556128i	$0.00177022\pi$
$572$	−0.152092	−	0.0977434i	−0.00635927	−	0.00408686i
$573$	9.18416	+	10.5991i	0.383674	+	0.442783i
$574$	14.1010			0.588563
$575$	2.25792	+	4.23105i	0.0941620	+	0.176447i
$576$	6.37162			0.265484
$577$	30.8750	+	35.6316i	1.28534	+	1.48336i	0.787809	+	0.615919i	$0.211215\pi$
$577$	30.8750	+	35.6316i	1.28534	+	1.48336i	0.497533	+	0.867445i	$0.334239\pi$
$578$	12.4795	+	8.02007i	0.519078	+	0.333591i
$579$	0.751469	−	5.22658i	0.0312300	−	0.217209i
$580$	0.359414	−	0.787008i	0.0149239	−	0.0326787i
$581$	2.47459	+	17.2111i	0.102663	+	0.714038i
$582$	−20.5404	−	6.03121i	−0.851428	−	0.250002i
$583$	0.979280	−	0.629345i	0.0405576	−	0.0260648i
$584$	3.96529	+	8.68276i	0.164085	+	0.359295i
$585$	−3.49167	+	1.02525i	−0.144363	+	0.0423887i
$586$	0.619361	−	0.714780i	0.0255856	−	0.0295273i
$587$	−14.5740	+	16.8193i	−0.601534	+	0.694208i	−0.972092	−	0.234602i	$-0.924621\pi$
$587$	−14.5740	+	16.8193i	−0.601534	+	0.694208i	0.370557	+	0.928810i	$0.379167\pi$
$588$	−0.323723	+	0.0950535i	−0.0133501	+	0.00391994i
$589$	12.4514	+	27.2647i	0.513050	+	1.12342i
$590$	0.00891360	−	0.00572842i	0.000366967	−	0.000235835i
$591$	12.4272	+	3.64895i	0.511186	+	0.150098i
$592$	−2.09545	−	14.5742i	−0.0861223	−	0.598994i
$593$	−5.07151	+	11.1051i	−0.208262	+	0.456030i	−0.984721	−	0.174137i	$-0.944286\pi$
$593$	−5.07151	+	11.1051i	−0.208262	+	0.456030i	0.776460	+	0.630167i	$0.217014\pi$
$594$	−0.0341065	+	0.237216i	−0.00139941	+	0.00973309i
$595$	−5.51662	−	3.54532i	−0.226160	−	0.145344i
$596$	1.68456	+	1.94409i	0.0690024	+	0.0796330i
$597$	−0.932061			−0.0381467
$598$	−18.5974	−	18.9575i	−0.760503	−	0.775232i
$599$	−18.0130			−0.735993			−0.367996	−	0.929827i	$-0.619956\pi$
$599$	−18.0130			−0.735993			−0.367996	+	0.929827i	$0.619956\pi$
$600$	1.67862	+	1.93723i	0.0685293	+	0.0790871i
$601$	−36.7010	−	23.5863i	−1.49707	−	0.962106i	−0.995273	−	0.0971178i	$-0.969038\pi$
$601$	−36.7010	−	23.5863i	−1.49707	−	0.962106i	−0.501793	−	0.864988i	$-0.667326\pi$
$602$	2.47914	−	17.2428i	0.101042	−	0.702763i
$603$	3.34798	−	7.33105i	0.136340	−	0.298544i
$604$	0.0132378	+	0.0920707i	0.000538637	+	0.00374630i
$605$	−10.5306	−	3.09207i	−0.428131	−	0.125711i
$606$	6.01685	−	3.86679i	0.244418	−	0.157078i
$607$	9.31529	+	20.3976i	0.378096	+	0.827915i	0.999029	+	0.0440513i	$0.0140265\pi$
$607$	9.31529	+	20.3976i	0.378096	+	0.827915i	−0.620933	+	0.783863i	$0.713246\pi$
$608$	−6.02319	+	1.76857i	−0.244273	+	0.0717249i
$609$	4.37409	−	5.04797i	0.177247	−	0.204554i
$610$	5.03246	−	5.80777i	0.203758	−	0.235150i
$611$	−44.4338	+	13.0470i	−1.79760	+	0.527823i
$612$	−0.352861	−	0.772657i	−0.0142635	−	0.0312328i
$613$	6.04217	−	3.88307i	0.244041	−	0.156836i	−0.412903	−	0.910775i	$-0.635485\pi$
$613$	6.04217	−	3.88307i	0.244041	−	0.156836i	0.656944	+	0.753939i	$0.271849\pi$
$614$	−16.2077	−	4.75901i	−0.654090	−	0.192058i
$615$	−0.541552	−	3.76657i	−0.0218375	−	0.151883i
$616$	−0.408412	+	0.894297i	−0.0164554	+	0.0360323i
$617$	−1.10220	+	7.66597i	−0.0443729	+	0.308621i	0.955533	+	0.294885i	$0.0952814\pi$
$617$	−1.10220	+	7.66597i	−0.0443729	+	0.308621i	−0.999906	+	0.0137355i	$0.995628\pi$
$618$	−6.23015	−	4.00388i	−0.250614	−	0.161060i
$619$	−26.5573	−	30.6488i	−1.06743	−	1.23188i	−0.971637	−	0.236477i	$-0.924007\pi$
$619$	−26.5573	−	30.6488i	−1.06743	−	1.23188i	−0.0957912	−	0.995401i	$-0.530538\pi$
$620$	−2.66371			−0.106977
$621$	−1.71899	+	4.47717i	−0.0689806	+	0.179663i
$622$	2.81279			0.112783
$623$	26.7010	+	30.8146i	1.06975	+	1.23456i
$624$	−13.8723	−	8.91518i	−0.555336	−	0.356893i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−8.16666	+	17.8825i	−0.326405	+	0.714728i
$627$	0.0795583	+	0.553340i	0.00317725	+	0.0220983i
$628$	−5.53786	−	1.62606i	−0.220985	−	0.0648870i
$629$	7.36083	−	4.73052i	0.293496	−	0.188618i
$630$	−1.53937	−	3.37074i	−0.0613298	−	0.134293i
$631$	−8.10361	+	2.37943i	−0.322600	+	0.0947238i	−0.439023	−	0.898476i	$-0.644675\pi$
$631$	−8.10361	+	2.37943i	−0.322600	+	0.0947238i	0.116423	+	0.993200i	$0.462857\pi$
$632$	−14.4340	+	16.6578i	−0.574155	+	0.662610i
$633$	5.01712	−	5.79007i	0.199413	−	0.230134i
$634$	35.2970	−	10.3641i	1.40182	−	0.411612i
$635$	5.76653	+	12.6269i	0.228838	+	0.501085i
$636$	−1.96134	+	1.26048i	−0.0777723	+	0.0499812i
$637$	−3.73462	−	1.09658i	−0.147971	−	0.0434483i
$638$	−0.0935477	−	0.650639i	−0.00370359	−	0.0257590i
$639$	0.0730307	−	0.159915i	0.00288905	−	0.00632614i
$640$	−1.88319	+	13.0978i	−0.0744395	+	0.517738i
$641$	−37.1651	−	23.8846i	−1.46793	−	0.943384i	−0.998162	−	0.0605960i	$-0.980700\pi$
$641$	−37.1651	−	23.8846i	−1.46793	−	0.943384i	−0.469772	−	0.882788i	$-0.655664\pi$
$642$	14.7582	+	17.0319i	0.582460	+	0.672195i
$643$	−42.6078			−1.68029			−0.840144	−	0.542363i	$-0.817530\pi$
$643$	−42.6078			−1.68029			−0.840144	+	0.542363i	$0.817530\pi$
$644$	2.23594	−	2.92791i	0.0881085	−	0.115376i
$645$	−4.70101			−0.185102
$646$	−9.52434	−	10.9917i	−0.374730	−	0.432462i
$647$	−20.4858	−	13.1654i	−0.805378	−	0.517585i	0.0719886	−	0.997405i	$-0.477065\pi$
$647$	−20.4858	−	13.1654i	−0.805378	−	0.517585i	−0.877367	+	0.479820i	$0.840702\pi$
$648$	−0.364799	+	2.53723i	−0.0143306	+	0.0996719i
$649$	0.000455577	0	0.000997574i	1.78830e−5	0	3.91582e-5i
$650$	−0.788058	−	5.48106i	−0.0309102	−	0.214985i
$651$	−19.7313	−	5.79362i	−0.773329	−	0.227070i
$652$	4.88733	−	3.14090i	0.191403	−	0.123007i
$653$	6.74732	+	14.7746i	0.264043	+	0.578174i	0.994494	−	0.104791i	$-0.0334174\pi$
$653$	6.74732	+	14.7746i	0.264043	+	0.578174i	−0.730451	+	0.682965i	$0.760690\pi$
$654$	7.27715	−	2.13676i	0.284559	−	0.0835541i
$655$	−3.87178	+	4.46827i	−0.151283	+	0.174590i
$656$	11.2919	−	13.0316i	0.440876	−	0.508799i
$657$	−3.57298	+	1.04912i	−0.139395	+	0.0409302i
$658$	−19.5895	−	42.8949i	−0.763677	−	1.67222i
$659$	27.9502	−	17.9625i	1.08878	−	0.699719i	0.132214	−	0.991221i	$-0.457791\pi$
$659$	27.9502	−	17.9625i	1.08878	−	0.699719i	0.956570	+	0.291502i	$0.0941550\pi$
$660$	−0.0476683	−	0.0139967i	−0.00185548	−	0.000544819i
$661$	6.02230	+	41.8860i	0.234240	+	1.62918i	0.679430	+	0.733741i	$0.262227\pi$
$661$	6.02230	+	41.8860i	0.234240	+	1.62918i	−0.445189	+	0.895436i	$0.646864\pi$
$662$	5.95380	−	13.0370i	0.231401	−	0.506698i
$663$	1.39459	−	9.69956i	0.0541612	−	0.376700i
$664$	15.3971	+	9.89514i	0.597525	+	0.384006i
$665$	−5.66053	−	6.53260i	−0.219506	−	0.253323i
$666$	4.94439			0.191591
$667$	1.06419	−	13.1109i	0.0412054	−	0.507658i
$668$	6.20835			0.240208
$669$	−16.4084	−	18.9363i	−0.634384	−	0.732118i
$670$	10.3168	+	6.63020i	0.398572	+	0.256147i
$671$	0.113197	−	0.787302i	0.00436992	−	0.0303935i
$672$	1.78914	−	3.91767i	0.0690176	−	0.151127i
$673$	5.97541	+	41.5599i	0.230335	+	1.60201i	0.696660	+	0.717401i	$0.254669\pi$
$673$	5.97541	+	41.5599i	0.230335	+	1.60201i	−0.466325	+	0.884613i	$0.654422\pi$
$674$	−42.4952	−	12.4777i	−1.63685	−	0.480623i
$675$	−0.841254	+	0.540641i	−0.0323799	+	0.0208093i
$676$	0.0318261	+	0.0696894i	0.00122408	+	0.00268036i
$677$	39.8821	−	11.7104i	1.53279	−	0.450069i	0.596889	−	0.802324i	$-0.296403\pi$
$677$	39.8821	−	11.7104i	1.53279	−	0.450069i	0.935904	+	0.352255i	$0.114585\pi$
$678$	−0.0292277	+	0.0337306i	−0.00112248	+	0.00129541i
$679$	22.4358	−	25.8923i	0.861009	−	0.993657i
$680$	−6.62291	+	1.94466i	−0.253977	+	0.0745744i
$681$	6.20631	+	13.5899i	0.237826	+	0.520767i
$682$	−1.70249	+	1.09412i	−0.0651917	+	0.0418961i
$683$	49.4453	+	14.5184i	1.89197	+	0.555533i	0.993092	+	0.117336i	$0.0374354\pi$
$683$	49.4453	+	14.5184i	1.89197	+	0.555533i	0.898879	+	0.438197i	$0.144383\pi$
$684$	−0.159343	−	1.10825i	−0.00609263	−	0.0423752i
$685$	8.60001e−5	0	0.000188314i	3.28589e−6	0	7.19510e-6i
$686$	4.25560	−	29.5983i	0.162480	−	1.13007i
$687$	−12.9952	−	8.35151i	−0.495798	−	0.318630i
$688$	−13.9499	−	16.0990i	−0.531834	−	0.613769i
$689$	−26.8968			−1.02469
$690$	−6.37113	−	3.55864i	−0.242545	−	0.135475i
$691$	−29.7608			−1.13215			−0.566077	−	0.824352i	$-0.691540\pi$
$691$	−29.7608			−1.13215			−0.566077	+	0.824352i	$0.691540\pi$
$692$	−4.08599	−	4.71548i	−0.155326	−	0.179256i
$693$	−0.322656	−	0.207358i	−0.0122567	−	0.00787690i
$694$	2.74386	−	19.0839i	0.104155	−	0.724416i
$695$	8.80490	−	19.2800i	0.333989	−	0.731333i
$696$	−1.00057	−	6.95915i	−0.0379267	−	0.263786i
$697$	9.83185	+	2.88689i	0.372408	+	0.109349i
$698$	−5.20805	+	3.34701i	−0.197128	+	0.126686i
$699$	−4.74291	−	10.3855i	−0.179393	−	0.392817i
$700$	0.737058	−	0.216420i	0.0278582	−	0.00817990i
$701$	20.8821	−	24.0992i	0.788704	−	0.910213i	−0.209001	−	0.977915i	$-0.567021\pi$
$701$	20.8821	−	24.0992i	0.788704	−	0.910213i	0.997706	+	0.0677020i	$0.0215667\pi$
$702$	3.62624	−	4.18491i	0.136864	−	0.157949i
$703$	11.0663	−	3.24936i	0.417374	−	0.122552i
$704$	0.416871	+	0.912821i	0.0157114	+	0.0344032i
$705$	−10.7055	+	6.88002i	−0.403193	+	0.259117i
$706$	14.6287	+	4.29536i	0.550557	+	0.161658i
$707$	1.62899	+	11.3299i	0.0612644	+	0.426104i
$708$	−0.000912449		0.00199799i	−3.42919e−5		7.50889e-5i
$709$	−3.56174	+	24.7724i	−0.133764	+	0.930348i	0.806823	+	0.590794i	$0.201185\pi$
$709$	−3.56174	+	24.7724i	−0.133764	+	0.930348i	−0.940586	+	0.339554i	$0.889724\pi$
$710$	0.225044	+	0.144627i	0.00844574	+	0.00542775i
$711$	−5.63098	−	6.49850i	−0.211178	−	0.243713i
$712$	42.9180			1.60842
$713$	−38.0786	+	13.7881i	−1.42606	+	0.516367i
$714$	9.97846			0.373434
$715$	−0.375327	−	0.433151i	−0.0140365	−	0.0161989i
$716$	6.82448	+	4.38583i	0.255043	+	0.163906i
$717$	−0.921796	+	6.41123i	−0.0344251	+	0.239432i
$718$	−22.9594	+	50.2741i	−0.856837	+	1.87621i
$719$	2.82546	+	19.6515i	0.105372	+	0.732876i	0.972180	+	0.234235i	$0.0752585\pi$
$719$	2.82546	+	19.6515i	0.105372	+	0.732876i	−0.866808	+	0.498641i	$0.833832\pi$
$720$	−4.34783	−	1.27664i	−0.162034	−	0.0475774i
$721$	9.97068	−	6.40776i	0.371327	−	0.238638i
$722$	4.04630	+	8.86016i	0.150588	+	0.329741i
$723$	−8.46355	+	2.48512i	−0.314763	+	0.0924227i
$724$	−4.64761	+	5.36363i	−0.172727	+	0.199338i
$725$	1.79616	−	2.07288i	0.0667077	−	0.0769848i
$726$	16.0240	−	4.70507i	0.594706	−	0.174622i
$727$	−5.22227	−	11.4352i	−0.193683	−	0.424107i	0.787728	−	0.616023i	$-0.211257\pi$
$727$	−5.22227	−	11.4352i	−0.193683	−	0.424107i	−0.981411	+	0.191916i	$0.938530\pi$
$728$	19.1101	−	12.2813i	0.708269	−	0.455177i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−0.806410	−	5.60871i	−0.0298466	−	0.207588i
$731$	5.25868	−	11.5149i	0.194499	−	0.425894i
$732$	−0.226716	+	1.57684i	−0.00837966	+	0.0582818i
$733$	−31.0791	−	19.9733i	−1.14793	−	0.737732i	−0.178707	−	0.983902i	$-0.557191\pi$
$733$	−31.0791	−	19.9733i	−1.14793	−	0.737732i	−0.969227	+	0.246170i	$0.920828\pi$
$734$	3.47294	+	4.00798i	0.128188	+	0.147937i
$735$	−1.06958			−0.0394521
$736$	−1.72335	−	8.30479i	−0.0635236	−	0.306119i
$737$	1.26932			0.0467560
$738$	3.79189	+	4.37607i	0.139581	+	0.161085i
$739$	9.85609	+	6.33412i	0.362562	+	0.233004i	0.709220	−	0.704987i	$-0.249047\pi$
$739$	9.85609	+	6.33412i	0.362562	+	0.233004i	−0.346658	+	0.937992i	$0.612684\pi$
$740$	−0.145869	+	1.01454i	−0.00536226	+	0.0372953i
$741$	5.36585	−	11.7496i	0.197119	−	0.431631i
$742$	−3.89780	−	27.1098i	−0.143093	−	0.995231i
$743$	−30.1264	−	8.84591i	−1.10523	−	0.324525i	−0.322302	−	0.946637i	$-0.604457\pi$
$743$	−30.1264	−	8.84591i	−1.10523	−	0.324525i	−0.782928	+	0.622112i	$0.786275\pi$
$744$	−18.2096	+	11.7026i	−0.667596	+	0.429038i
$745$	3.38769	+	7.41800i	0.124115	+	0.271774i
$746$	−9.86367	+	2.89623i	−0.361135	+	0.106039i
$747$	−4.67583	+	5.39620i	−0.171080	+	0.197437i
$748$	0.0876073	−	0.101104i	0.00320324	−	0.00369674i
$749$	−34.6061	+	10.1613i	−1.26448	+	0.371285i
$750$	−0.632119	−	1.38415i	−0.0230817	−	0.0505419i
$751$	21.0465	−	13.5257i	0.767996	−	0.493561i	−0.0970338	−	0.995281i	$-0.530935\pi$
$751$	21.0465	−	13.5257i	0.767996	−	0.493561i	0.865030	+	0.501720i	$0.167299\pi$
$752$	−55.3290	−	16.2461i	−2.01764	−	0.592433i
$753$	0.987042	+	6.86503i	0.0359698	+	0.250176i
$754$	−6.30937	+	13.8156i	−0.229774	+	0.503134i
$755$	−0.0419660	+	0.291880i	−0.00152730	+	0.0106226i
$756$	0.646230	+	0.415307i	0.0235031	+	0.0151046i
$757$	−16.5596	−	19.1108i	−0.601869	−	0.694594i	0.370290	−	0.928916i	$-0.379258\pi$
$757$	−16.5596	−	19.1108i	−0.601869	−	0.694594i	−0.972159	+	0.234322i	$0.924713\pi$
$758$	−36.9619			−1.34252
$759$	−0.753883	+	0.0466566i	−0.0273642	+	0.00169353i
$760$	−9.09847			−0.330036
$761$	13.4782	+	15.5546i	0.488584	+	0.563856i	0.945487	−	0.325661i	$-0.105587\pi$
$761$	13.4782	+	15.5546i	0.488584	+	0.563856i	−0.456903	+	0.889517i	$0.651041\pi$
$762$	−17.7695	−	11.4198i	−0.643723	−	0.413695i
$763$	−1.72741	+	12.0144i	−0.0625365	+	0.434951i
$764$	1.83777	−	4.02415i	0.0664880	−	0.145588i
$765$	−0.383225	−	2.66539i	−0.0138555	−	0.0963674i
$766$	51.5891	+	15.1479i	1.86399	+	0.547317i
$767$	−0.0213171	+	0.0136996i	−0.000769715	+	0.000494665i
$768$	−3.07081	−	6.72413i	−0.110808	−	0.242636i
$769$	−13.9539	+	4.09723i	−0.503190	+	0.147750i	−0.523469	−	0.852045i	$-0.675362\pi$
$769$	−13.9539	+	4.09723i	−0.503190	+	0.147750i	0.0202797	+	0.999794i	$0.493544\pi$
$770$	0.382189	−	0.441070i	0.0137732	−	0.0158951i
$771$	−14.8421	+	17.1286i	−0.534523	+	0.616873i
$772$	−1.59816	+	0.469262i	−0.0575190	+	0.0168891i
$773$	−9.18634	−	20.1153i	−0.330410	−	0.723496i	0.669402	−	0.742900i	$-0.266550\pi$
$773$	−9.18634	−	20.1153i	−0.330410	−	0.723496i	−0.999812	+	0.0194043i	$0.993823\pi$
$774$	6.01776	−	3.86738i	0.216304	−	0.139010i
$775$	−8.10237	−	2.37907i	−0.291046	−	0.0854587i
$776$	−5.13221	−	35.6953i	−0.184235	−	1.28139i
$777$	−3.28716	+	7.19788i	−0.117926	+	0.258223i
$778$	−0.0289153	+	0.201110i	−0.00103666	+	0.00721015i
$779$	11.3627	+	7.30237i	0.407111	+	0.261634i
$780$	0.751722	+	0.867534i	0.0269160	+	0.0310627i
$781$	0.0276881			0.000990759
$782$	15.8436	−	11.6250i	0.566568	−	0.415709i
$783$	2.74281			0.0980201
$784$	−3.17390	−	3.66287i	−0.113354	−	0.130817i
$785$	−15.3925	−	9.89218i	−0.549383	−	0.353067i
$786$	1.28035	−	8.90502i	0.0456685	−	0.317632i
$787$	−13.3105	+	29.1460i	−0.474469	+	1.03894i	0.509478	+	0.860484i	$0.329839\pi$
$787$	−13.3105	+	29.1460i	−0.474469	+	1.03894i	−0.983947	+	0.178459i	$0.942889\pi$
$788$	−0.581431	−	4.04394i	−0.0207126	−	0.144060i
$789$	−9.47605	−	2.78242i	−0.337356	−	0.0990567i
$790$	11.0073	−	7.07393i	0.391621	−	0.251679i
$791$	−0.0296725	−	0.0649737i	−0.00105503	−	0.00231020i
$792$	−0.387360	+	0.113739i	−0.0137643	+	0.00404155i
$793$	−12.0352	+	13.8894i	−0.427384	+	0.493227i
$794$	−0.397514	+	0.458756i	−0.0141072	+	0.0162806i
$795$	−7.09172	+	2.08232i	−0.251517	+	0.0738521i
$796$	0.122136	+	0.267441i	0.00432900	+	0.00947918i
$797$	13.7969	−	8.86671i	0.488710	−	0.314075i	−0.272976	−	0.962021i	$-0.588008\pi$
$797$	13.7969	−	8.86671i	0.488710	−	0.314075i	0.761686	+	0.647946i	$0.224372\pi$
$798$	12.6202	+	3.70563i	0.446750	+	0.131178i
$799$	−4.87680	−	33.9189i	−0.172529	−	1.19996i
$800$	0.734686	−	1.60874i	0.0259751	−	0.0568775i
$801$	−2.38279	+	16.5727i	−0.0841919	+	0.585568i
$802$	−3.80567	−	2.44576i	−0.134383	−	0.0863626i
$803$	−0.384068	−	0.443238i	−0.0135535	−	0.0156415i
$804$	−2.54225			−0.0896582
$805$	9.41623	−	6.90899i	0.331879	−	0.243510i
$806$	46.7604			1.64706
$807$	4.64578	+	5.36152i	0.163539	+	0.188734i
$808$	10.1357	+	6.51384i	0.356574	+	0.229156i
$809$	3.44796	−	23.9811i	0.121224	−	0.843129i	−0.834949	−	0.550327i	$-0.814503\pi$
$809$	3.44796	−	23.9811i	0.121224	−	0.843129i	0.956173	−	0.292802i	$-0.0945878\pi$
$810$	0.632119	−	1.38415i	0.0222104	−	0.0486340i
$811$	0.992419	+	6.90243i	0.0348485	+	0.242377i	0.999799	−	0.0200557i	$-0.00638435\pi$
$811$	0.992419	+	6.90243i	0.0348485	+	0.242377i	−0.964950	+	0.262433i	$0.915475\pi$
$812$	−2.02161	−	0.593599i	−0.0709447	−	0.0208312i
$813$	−11.9608	+	7.68672i	−0.419483	+	0.269585i
$814$	0.323493	+	0.708352i	0.0113384	+	0.0248277i
$815$	17.6713	−	5.18877i	0.619000	−	0.181755i
$816$	7.99067	−	9.22172i	0.279729	−	0.322825i
$817$	10.9271	−	12.6105i	0.382291	−	0.441187i
$818$	−52.9100	+	15.5358i	−1.84995	+	0.543195i
$819$	3.68143	+	8.06120i	0.128639	+	0.281681i
$820$	−1.00980	+	0.648957i	−0.0352636	+	0.0226625i
$821$	23.0225	+	6.76002i	0.803491	+	0.235926i	0.657593	−	0.753373i	$-0.271575\pi$
$821$	23.0225	+	6.76002i	0.803491	+	0.235926i	0.145898	+	0.989300i	$0.453393\pi$
$822$	4.48315e−5	0	0.000311810i	1.56368e−6	0	1.08756e-5i
$823$	−2.96728	+	6.49743i	−0.103433	+	0.226486i	−0.954272	−	0.298940i	$-0.903367\pi$
$823$	−2.96728	+	6.49743i	−0.103433	+	0.226486i	0.850839	+	0.525426i	$0.176094\pi$
$824$	1.77545	−	12.3485i	0.0618507	−	0.430181i
$825$	−0.132494	−	0.0851489i	−0.00461286	−	0.00296450i
$826$	−0.0168973	−	0.0195005i	−0.000587933	−	0.000678511i
$827$	−25.7772			−0.896360			−0.448180	−	0.893943i	$-0.647928\pi$
$827$	−25.7772			−0.896360			−0.448180	+	0.893943i	$0.647928\pi$
$828$	1.50991	−	0.0934458i	0.0524730	−	0.00324747i
$829$	31.3952			1.09040			0.545200	−	0.838306i	$-0.316454\pi$
$829$	31.3952			1.09040			0.545200	+	0.838306i	$0.316454\pi$
$830$	−7.11502	−	8.21117i	−0.246966	−	0.285014i
$831$	14.1202	+	9.07447i	0.489823	+	0.314790i
$832$	3.29982	−	22.9508i	0.114401	−	0.795675i
$833$	1.19646	−	2.61989i	0.0414550	−	0.0907739i
$834$	4.58996	+	31.9239i	0.158937	+	1.10543i
$835$	18.8843	+	5.54493i	0.653517	+	0.191890i
$836$	0.148347	−	0.0953370i	0.00513070	−	0.00329730i
$837$	−3.50794	−	7.68132i	−0.121252	−	0.265505i
$838$	−26.1440	+	7.67657i	−0.903130	+	0.265183i
$839$	26.2849	−	30.3343i	0.907454	−	1.04726i	−0.0912227	−	0.995831i	$-0.529078\pi$
$839$	26.2849	−	30.3343i	0.907454	−	1.04726i	0.998677	−	0.0514273i	$-0.0163770\pi$
$840$	4.08785	−	4.71763i	0.141044	−	0.162774i
$841$	20.6070	−	6.05076i	0.710587	−	0.208647i
$842$	6.81590	+	14.9247i	0.234892	+	0.514341i
$843$	0.511065	−	0.328441i	0.0176020	−	0.0113121i
$844$	−2.31881	−	0.680863i	−0.0798166	−	0.0234363i
$845$	0.0345648	+	0.240403i	0.00118906	+	0.00827013i
$846$	8.04415	−	17.6142i	0.276563	−	0.605589i
$847$	−3.80369	+	26.4552i	−0.130696	+	0.909013i
$848$	−28.1752	−	18.1071i	−0.967540	−	0.621800i
$849$	−13.9192	−	16.0636i	−0.477706	−	0.551303i
$850$	4.09752			0.140544
$851$	3.16629	+	15.2583i	0.108539	+	0.523047i
$852$	−0.0554550			−0.00189986
$853$	17.1265	+	19.7650i	0.586400	+	0.676742i	0.968968	−	0.247185i	$-0.0795057\pi$
$853$	17.1265	+	19.7650i	0.586400	+	0.676742i	−0.382568	+	0.923927i	$0.624960\pi$
$854$	−15.7435	−	10.1177i	−0.538731	−	0.346221i
$855$	0.505144	−	3.51336i	0.0172756	−	0.120154i
$856$	−15.7708	+	34.5332i	−0.539035	+	1.18032i
$857$	2.90454	+	20.2015i	0.0992173	+	0.690072i	0.977346	+	0.211647i	$0.0678828\pi$
$857$	2.90454	+	20.2015i	0.0992173	+	0.690072i	−0.878129	+	0.478424i	$0.841208\pi$
$858$	0.836797	+	0.245706i	0.0285678	+	0.00838825i
$859$	29.5383	−	18.9831i	1.00783	−	0.647696i	0.0710028	−	0.997476i	$-0.477380\pi$
$859$	29.5383	−	18.9831i	1.00783	−	0.647696i	0.936832	+	0.349780i	$0.113744\pi$
$860$	0.616014	+	1.34888i	0.0210059	+	0.0459965i
$861$	−8.89148	+	2.61077i	−0.303021	+	0.0889749i
$862$	−25.3931	+	29.3051i	−0.864891	+	0.998137i
$863$	−21.2155	+	24.4840i	−0.722184	+	0.833445i	−0.991568	−	0.129588i	$-0.958634\pi$
$863$	−21.2155	+	24.4840i	−0.722184	+	0.833445i	0.269384	+	0.963033i	$0.413180\pi$
$864$	1.69692	−	0.498261i	0.0577304	−	0.0169512i
$865$	−8.21699	−	17.9927i	−0.279386	−	0.611770i
$866$	37.9978	−	24.4197i	1.29122	−	0.829815i
$867$	−9.35394	−	2.74656i	−0.317676	−	0.0932782i
$868$	0.923167	+	6.42077i	0.0313343	+	0.217935i
$869$	0.562584	−	1.23189i	0.0190844	−	0.0417889i
$870$	−0.593968	+	4.13114i	−0.0201374	+	0.140059i
$871$	−24.6728	−	15.8563i	−0.836007	−	0.537269i
$872$	8.36671	+	9.65570i	0.283333	+	0.326983i
$873$	14.0686			0.476150
$874$	24.3553	−	8.81892i	0.823829	−	0.298304i
$875$	2.43525			0.0823263
$876$	0.769228	+	0.887737i	0.0259898	+	0.0299938i
$877$	6.11945	+	3.93273i	0.206639	+	0.132799i	0.639867	−	0.768485i	$-0.278989\pi$
$877$	6.11945	+	3.93273i	0.206639	+	0.132799i	−0.433228	+	0.901284i	$0.642626\pi$
$878$	−2.37012	+	16.4846i	−0.0799878	+	0.556327i
$879$	−0.258202	+	0.565384i	−0.00870895	+	0.0190699i
$880$	−0.101567	−	0.706411i	−0.00342381	−	0.0238131i
$881$	14.7749	+	4.33831i	0.497780	+	0.146161i	0.520979	−	0.853569i	$-0.325567\pi$
$881$	14.7749	+	4.33831i	0.497780	+	0.146161i	−0.0231989	+	0.999731i	$0.507385\pi$
$882$	1.36917	−	0.879913i	0.0461024	−	0.0296282i
$883$	3.47562	+	7.61055i	0.116964	+	0.256115i	0.959055	−	0.283220i	$-0.0914027\pi$
$883$	3.47562	+	7.61055i	0.116964	+	0.256115i	−0.842091	+	0.539336i	$0.818675\pi$
$884$	−2.96588	+	0.870862i	−0.0997534	+	0.0292903i
$885$	−0.00455993	+	0.00526244i	−0.000153280	+	0.000176895i
$886$	−14.8829	+	17.1758i	−0.500002	+	0.577033i
$887$	−6.42055	+	1.88524i	−0.215581	+	0.0633003i	−0.387740	−	0.921769i	$-0.626744\pi$
$887$	−6.42055	+	1.88524i	−0.215581	+	0.0633003i	0.172159	+	0.985069i	$0.444926\pi$
$888$	3.46004	+	7.57644i	0.116111	+	0.254249i
$889$	28.4382	−	18.2761i	0.953787	−	0.612961i
$890$	−24.4453	−	7.17778i	−0.819408	−	0.240600i
$891$	−0.0224141	−	0.155893i	−0.000750899	−	0.00522262i
$892$	−3.28334	+	7.18951i	−0.109934	+	0.240723i
$893$	6.42830	−	44.7098i	0.215115	−	1.49616i
$894$	−10.4391	−	6.70883i	−0.349137	−	0.224377i
$895$	16.8412	+	19.4358i	0.562941	+	0.649668i
$896$	32.2245			1.07654
$897$	15.2367	+	8.51056i	0.508738	+	0.284159i
$898$	43.0746			1.43742
$899$	15.1675	+	17.5043i	0.505866	+	0.583800i
$900$	0.265365	+	0.170540i	0.00884551	+	0.00568466i
$901$	2.83246	−	19.7002i	0.0943629	−	0.656308i
$902$	−0.378843	+	0.829550i	−0.0126141	+	0.0276210i
$903$	1.62923	+	11.3316i	0.0542175	+	0.377091i
$904$	−0.0721396	−	0.0211821i	−0.00239933	−	0.000704506i
$905$	−18.9274	+	12.1639i	−0.629168	+	0.404342i
$906$	−0.186400	−	0.408159i	−0.00619273	−	0.0135602i
$907$	22.2279	−	6.52669i	0.738064	−	0.216715i	0.108971	−	0.994045i	$-0.465245\pi$
$907$	22.2279	−	6.52669i	0.738064	−	0.216715i	0.629093	+	0.777330i	$0.283426\pi$
$908$	3.08616	−	3.56161i	0.102418	−	0.118196i
$909$	−3.07804	+	3.55225i	−0.102092	+	0.117821i
$910$	−12.9388	+	3.79916i	−0.428915	+	0.125941i
$911$	−18.4474	−	40.3941i	−0.611189	−	1.33832i	−0.921758	−	0.387767i	$-0.873247\pi$
$911$	−18.4474	−	40.3941i	−0.611189	−	1.33832i	0.310568	−	0.950551i	$-0.399481\pi$
$912$	13.5308	−	8.69570i	0.448048	−	0.287943i
$913$	−1.07900	−	0.316824i	−0.0357097	−	0.0104853i
$914$	−5.01344	−	34.8693i	−0.165830	−	1.15337i
$915$	−2.09796	+	4.59389i	−0.0693563	+	0.151869i
$916$	−0.693463	+	4.82314i	−0.0229127	+	0.159361i
$917$	12.1124	+	7.78418i	0.399987	+	0.257056i
$918$	2.68330	+	3.09670i	0.0885622	+	0.102206i
$919$	−28.0150			−0.924130			−0.462065	−	0.886846i	$-0.652891\pi$
$919$	−28.0150			−0.924130			−0.462065	+	0.886846i	$0.652891\pi$
$920$	0.994545	−	12.2530i	0.0327892	−	0.403968i
$921$	11.1010			0.365791
$922$	−7.60597	−	8.77776i	−0.250489	−	0.289080i
$923$	−0.538197	−	0.345878i	−0.0177150	−	0.0113847i
$924$	−0.0172179	+	0.119753i	−0.000566428	+	0.00393959i
$925$	−1.34983	+	2.95571i	−0.0443821	+	0.0971832i
$926$	5.28671	+	36.7699i	0.173732	+	1.20833i
$927$	4.66978	+	1.37117i	0.153376	+	0.0450352i
$928$	−4.08077	+	2.62255i	−0.133958	+	0.0860896i
$929$	−23.4616	−	51.3737i	−0.769749	−	1.68552i	−0.727205	−	0.686421i	$-0.759181\pi$
$929$	−23.4616	−	51.3737i	−0.769749	−	1.68552i	−0.0425444	−	0.999095i	$-0.513546\pi$
$930$	12.3290	−	3.62013i	0.404285	−	0.118709i
$931$	2.48615	−	2.86917i	0.0814804	−	0.0940334i
$932$	−2.35846	+	2.72181i	−0.0772540	+	0.0891559i
$933$	−1.77363	+	0.520785i	−0.0580660	+	0.0170497i
$934$	24.1414	+	52.8623i	0.789931	+	1.72971i
$935$	0.356780	−	0.229289i	0.0116680	−	0.00749855i
$936$	8.95027	+	2.62804i	0.292549	+	0.0859001i
$937$	−1.16305	−	8.08917i	−0.0379951	−	0.264262i	0.961965	−	0.273172i	$-0.0880728\pi$
$937$	−1.16305	−	8.08917i	−0.0379951	−	0.264262i	−0.999960	+	0.00891040i	$0.997164\pi$
$938$	12.4063	−	27.1660i	0.405080	−	0.887002i
$939$	1.83864	−	12.7880i	0.0600016	−	0.417320i
$940$	3.37695	+	2.17024i	0.110144	+	0.0707853i
$941$	7.39588	+	8.53530i	0.241099	+	0.278243i	0.863384	−	0.504548i	$-0.168341\pi$
$941$	7.39588	+	8.53530i	0.241099	+	0.278243i	−0.622285	+	0.782791i	$0.713795\pi$
$942$	27.8420			0.907141
$943$	−11.0762	+	14.5040i	−0.360690	+	0.472315i
$944$	−0.0315529			−0.00102696
$945$	1.59475	+	1.84044i	0.0518771	+	0.0598694i
$946$	0.947774	+	0.609097i	0.0308148	+	0.0198035i
$947$	−2.23548	+	15.5481i	−0.0726435	+	0.505247i	0.920719	+	0.390225i	$0.127603\pi$
$947$	−2.23548	+	15.5481i	−0.0726435	+	0.505247i	−0.993363	+	0.115022i	$0.963306\pi$
$948$	−1.12677	+	2.46728i	−0.0365957	+	0.0801335i
$949$	1.92855	+	13.4133i	0.0626033	+	0.435416i
$950$	5.18231	+	1.52166i	0.168137	+	0.0493693i
$951$	−20.3379	+	13.0704i	−0.659502	+	0.423836i
$952$	6.98284	+	15.2903i	0.226315	+	0.495561i
$953$	−10.4237	+	3.06067i	−0.337657	+	0.0991450i	−0.446165	−	0.894951i	$-0.647211\pi$
$953$	−10.4237	+	3.06067i	−0.337657	+	0.0991450i	0.108509	+	0.994096i	$0.465392\pi$
$954$	7.36504	−	8.49971i	0.238452	−	0.275188i
$955$	9.18416	−	10.5991i	0.297193	−	0.342979i
$956$	1.96040	−	0.575624i	0.0634037	−	0.0186170i
$957$	0.179452	+	0.392945i	0.00580086	+	0.0127021i
$958$	−44.1065	+	28.3455i	−1.42502	+	0.915802i
$959$	−0.000483728	0	0.000142035i	−1.56204e−5	0	4.58656e-6i
$960$	−0.906775	−	6.30676i	−0.0292660	−	0.203550i
$961$	16.7447	−	36.6658i	0.540152	−	1.18277i
$962$	2.56067	−	17.8099i	0.0825595	−	0.574214i
$963$	−12.4593	−	8.00713i	−0.401497	−	0.258026i
$964$	1.82212	+	2.10284i	0.0586865	+	0.0677278i
$965$	−5.28033			−0.169980
$966$	−6.36989	+	16.5906i	−0.204948	+	0.533795i
$967$	42.2130			1.35748			0.678740	−	0.734379i	$-0.262526\pi$
$967$	42.2130			1.35748			0.678740	+	0.734379i	$0.262526\pi$
$968$	18.4232	+	21.2615i	0.592143	+	0.683370i
$969$	8.04074	+	5.16747i	0.258306	+	0.166003i
$970$	−3.04662	+	21.1897i	−0.0978209	+	0.680360i
$971$	−2.67402	+	5.85529i	−0.0858135	+	0.187905i	−0.947674	−	0.319241i	$-0.896572\pi$
$971$	−2.67402	+	5.85529i	−0.0858135	+	0.187905i	0.861860	+	0.507146i	$0.169299\pi$
$972$	0.0448918	+	0.312230i	0.00143991	+	0.0100148i
$973$	−49.5252	−	14.5419i	−1.58771	−	0.466193i
$974$	40.7452	−	26.1853i	1.30556	−	0.839033i
$975$	1.51173	+	3.31022i	0.0484140	+	0.106012i
$976$	−21.9577	+	6.44736i	−0.702848	+	0.206375i
$977$	17.9552	−	20.7214i	0.574439	−	0.662938i	−0.391961	−	0.919982i	$-0.628203\pi$
$977$	17.9552	−	20.7214i	0.574439	−	0.662938i	0.966400	+	0.257044i	$0.0827486\pi$
$978$	−18.3524	+	21.1798i	−0.586845	+	0.677256i
$979$	−2.53016	+	0.742923i	−0.0808644	+	0.0237439i
$980$	0.140157	+	0.306900i	0.00447714	+	0.00980356i
$981$	−4.19305	+	2.69471i	−0.133874	+	0.0860354i
$982$	5.37233	+	1.57746i	0.171438	+	0.0503387i
$983$	1.36963	+	9.52601i	0.0436845	+	0.303832i	0.999936	+	0.0112875i	$0.00359301\pi$
$983$	1.36963	+	9.52601i	0.0436845	+	0.303832i	−0.956252	+	0.292545i	$0.905498\pi$
$984$	−4.05205	+	8.87276i	−0.129175	+	0.282853i
$985$	1.84324	−	12.8200i	0.0587304	−	0.408479i
$986$	−9.45461	−	6.07611i	−0.301096	−	0.193503i
$987$	20.2942	+	23.4208i	0.645972	+	0.745492i
$988$	−4.07449			−0.129627
$989$	15.7883	+	16.0940i	0.502038	+	0.511761i
$990$	0.239655			0.00761675
$991$	16.2302	+	18.7307i	0.515570	+	0.594999i	0.952516	−	0.304489i	$-0.0984855\pi$
$991$	16.2302	+	18.7307i	0.515570	+	0.594999i	−0.436946	+	0.899488i	$0.643940\pi$
$992$	12.5637	+	8.07419i	0.398897	+	0.256356i
$993$	−1.34043	+	9.32293i	−0.0425374	+	0.295854i
$994$	0.270623	−	0.592582i	0.00858364	−	0.0187956i
$995$	0.132646	+	0.922574i	0.00420516	+	0.0292476i
$996$	2.16107	+	0.634548i	0.0684762	+	0.0201064i
$997$	−50.7147	+	32.5924i	−1.60615	+	1.03221i	−0.642056	+	0.766658i	$0.721918\pi$
$997$	−50.7147	+	32.5924i	−1.60615	+	1.03221i	−0.964096	+	0.265553i	$0.914445\pi$
$998$	−2.14856	−	4.70469i	−0.0680114	−	0.148924i
$999$	−3.11773	+	0.915447i	−0.0986405	+	0.0289635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.a.151.3	yes	30
23.4	even	11		7935.2.a.bp.1.4		15
23.16	even	11	inner	345.2.m.a.16.3	✓	30
23.19	odd	22		7935.2.a.bq.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.16.3	✓	30	23.16	even	11	inner
345.2.m.a.151.3	yes	30	1.1	even	1	trivial
7935.2.a.bp.1.4		15	23.4	even	11
7935.2.a.bq.1.4		15	23.19	odd	22

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.996473 + 1.14999i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.0448918 + 0.312230i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.216554 - 1.50617i) q^{6} +(2.33660 + 0.686088i) q^{7} +(2.15640 - 1.38584i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.996473 + 1.14999i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.0448918 + 0.312230i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.216554 - 1.50617i) q^{6} +(2.33660 + 0.686088i) q^{7} +(2.15640 - 1.38584i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.46002 + 0.428700i) q^{10} +(-0.103138 + 0.119028i) q^{11} +(0.206570 - 0.238394i) q^{12} +(3.49167 - 1.02525i) q^{13} +(1.53937 + 3.37074i) q^{14} +(0.841254 - 0.540641i) q^{15} +(4.34783 + 1.27664i) q^{16} +(0.383225 + 2.66539i) q^{17} +(-0.632119 + 1.38415i) q^{18} +(-0.505144 + 3.51336i) q^{19} +(-0.265365 - 0.170540i) q^{20} +(-1.59475 - 1.84044i) q^{21} -0.239655 q^{22} +(-4.67624 - 1.06432i) q^{23} -2.56332 q^{24} +(-0.654861 - 0.755750i) q^{25} +(4.65838 + 2.99376i) q^{26} +(0.142315 - 0.989821i) q^{27} +(-0.319111 + 0.698756i) q^{28} +(0.390343 + 2.71489i) q^{29} +(1.46002 + 0.428700i) q^{30} +(7.10391 - 4.56540i) q^{31} +(0.734686 + 1.60874i) q^{32} +(0.151117 - 0.0443718i) q^{33} +(-2.68330 + 3.09670i) q^{34} +(-1.59475 + 1.84044i) q^{35} +(-0.302663 + 0.0888698i) q^{36} +(-1.34983 - 2.95571i) q^{37} +(-4.54369 + 2.92005i) q^{38} +(-3.49167 - 1.02525i) q^{39} +(0.364799 + 2.53723i) q^{40} +(1.58078 - 3.46143i) q^{41} +(0.527363 - 3.66789i) q^{42} +(-3.95474 - 2.54156i) q^{43} +(-0.0325339 - 0.0375462i) q^{44} -1.00000 q^{45} +(-3.43579 - 6.43821i) q^{46} -12.7257 q^{47} +(-2.96742 - 3.42459i) q^{48} +(-0.899789 - 0.578259i) q^{49} +(0.216554 - 1.50617i) q^{50} +(1.11863 - 2.44946i) q^{51} +(0.163365 + 1.13623i) q^{52} +(-7.09172 - 2.08232i) q^{53} +(1.28010 - 0.822670i) q^{54} +(-0.0654263 - 0.143264i) q^{55} +(5.98946 - 1.75866i) q^{56} +(2.32442 - 2.68252i) q^{57} +(-2.73314 + 3.15421i) q^{58} +(-0.00668115 + 0.00196176i) q^{59} +(0.131039 + 0.286935i) q^{60} +(-4.24856 + 2.73038i) q^{61} +(12.3290 + 3.62013i) q^{62} +(0.346572 + 2.41046i) q^{63} +(2.64686 - 5.79583i) q^{64} +(-0.517895 + 3.60204i) q^{65} +(0.201611 + 0.129567i) q^{66} +(-5.27776 - 6.09086i) q^{67} -0.849417 q^{68} +(3.35849 + 3.42353i) q^{69} -3.70561 q^{70} +(-0.115126 - 0.132862i) q^{71} +(2.15640 + 1.38584i) q^{72} +(-0.529955 + 3.68592i) q^{73} +(2.05398 - 4.49758i) q^{74} +(0.142315 + 0.989821i) q^{75} +(-1.07430 - 0.315442i) q^{76} +(-0.322656 + 0.207358i) q^{77} +(-2.30033 - 5.03702i) q^{78} +(-8.25044 + 2.42255i) q^{79} +(-2.96742 + 3.42459i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(5.55582 - 1.63134i) q^{82} +(2.96614 + 6.49495i) q^{83} +(0.646230 - 0.415307i) q^{84} +(-2.58372 - 0.758649i) q^{85} +(-1.01802 - 7.08051i) q^{86} +(1.13941 - 2.49495i) q^{87} +(-0.0574544 + 0.399604i) q^{88} +(14.0852 + 9.05201i) q^{89} +(-0.996473 - 1.14999i) q^{90} +8.86204 q^{91} +(0.542238 - 1.41228i) q^{92} -8.44443 q^{93} +(-12.6808 - 14.6344i) q^{94} +(-2.98602 - 1.91900i) q^{95} +(0.251692 - 1.75056i) q^{96} +(5.84431 - 12.7972i) q^{97} +(-0.231623 - 1.61097i) q^{98} +(-0.151117 - 0.0443718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Introduction

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