LMFDB - Embedded newform 507.2.m.b.40.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.5
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68275 - 0.414759i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.888694 + 0.466423i) q^{4} +(0.797976 - 1.15607i) q^{5} +(-0.614568 + 1.62048i) q^{6} +(-1.62398 - 1.43872i) q^{7} +(1.29250 + 1.14506i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(-1.68275 - 0.414759i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.888694 + 0.466423i) q^{4} +(0.797976 - 1.15607i) q^{5} +(-0.614568 + 1.62048i) q^{6} +(-1.62398 - 1.43872i) q^{7} +(1.29250 + 1.14506i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-1.82228 + 1.61440i) q^{10} +(-5.00516 + 1.23366i) q^{11} +(0.570142 - 0.825993i) q^{12} +(-1.03780 + 3.45296i) q^{13} +(2.13602 + 3.09456i) q^{14} +(-1.05145 - 0.931507i) q^{15} +(-2.84032 - 4.11491i) q^{16} +(-3.12382 - 2.76746i) q^{17} +(1.53459 + 0.805415i) q^{18} +6.62362 q^{19} +(1.24837 - 0.655197i) q^{20} +(-1.62398 + 1.43872i) q^{21} +8.93407 q^{22} -2.75739 q^{23} +(1.29250 - 1.14506i) q^{24} +(1.07330 + 2.83005i) q^{25} +(3.17851 - 5.38002i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(-0.772169 - 2.03604i) q^{28} +(-8.87966 - 2.18864i) q^{29} +(1.38298 + 2.00359i) q^{30} +(0.0507137 - 0.133721i) q^{31} +(1.84819 + 4.87328i) q^{32} +(0.621361 + 5.11736i) q^{33} +(4.10876 + 5.95257i) q^{34} +(-2.95916 + 0.729366i) q^{35} +(-0.751248 - 0.665547i) q^{36} +(-0.189711 + 0.500227i) q^{37} +(-11.1459 - 2.74721i) q^{38} +(3.30270 + 1.44645i) q^{39} +(2.35516 - 0.580494i) q^{40} +(-1.41745 + 11.6738i) q^{41} +(3.32947 - 1.74744i) q^{42} +(1.29503 + 3.41471i) q^{43} +(-5.02346 - 1.23817i) q^{44} +(-1.05145 + 0.931507i) q^{45} +(4.63999 + 1.14366i) q^{46} +(3.60078 - 1.88984i) q^{47} +(-4.42727 + 2.32361i) q^{48} +(-0.276364 - 2.27606i) q^{49} +(-0.632295 - 5.20741i) q^{50} +(-3.12382 + 2.76746i) q^{51} +(-2.53283 + 2.58457i) q^{52} +(-0.331951 - 0.294083i) q^{53} +(0.984516 - 1.42632i) q^{54} +(-2.56780 + 6.77073i) q^{55} +(-0.451581 - 3.71911i) q^{56} +(0.798389 - 6.57532i) q^{57} +(14.0344 + 7.36584i) q^{58} +(-1.09363 + 1.58439i) q^{59} +(-0.499945 - 1.31825i) q^{60} +(-11.1722 + 9.89771i) q^{61} +(-0.140800 + 0.203984i) q^{62} +(1.23248 + 1.78556i) q^{63} +(0.116568 + 0.960026i) q^{64} +(3.16372 + 3.95516i) q^{65} +(1.07688 - 8.86893i) q^{66} +(9.45492 - 4.96233i) q^{67} +(-1.48531 - 3.91645i) q^{68} +(-0.332367 + 2.73729i) q^{69} +5.28202 q^{70} +(-1.50113 + 12.3629i) q^{71} +(-0.980916 - 1.42110i) q^{72} +(-14.2807 + 3.51988i) q^{73} +(0.526709 - 0.763070i) q^{74} +(2.93879 - 0.724346i) q^{75} +(5.88637 + 3.08940i) q^{76} +(9.90316 + 5.19758i) q^{77} +(-4.95767 - 3.80382i) q^{78} +(0.0932751 - 0.0489545i) q^{79} -7.02362 q^{80} +(0.885456 + 0.464723i) q^{81} +(7.22702 - 19.0561i) q^{82} +(-1.35827 - 11.1864i) q^{83} +(-2.11427 + 0.521121i) q^{84} +(-5.69211 + 1.40298i) q^{85} +(-0.762920 - 6.28321i) q^{86} +(-3.24300 + 8.55110i) q^{87} +(-7.88180 - 4.13669i) q^{88} -3.07953 q^{89} +(2.15568 - 1.13139i) q^{90} +(6.65322 - 4.11443i) q^{91} +(-2.45048 - 1.28611i) q^{92} +(-0.126633 - 0.0664622i) q^{93} +(-6.84303 + 1.68665i) q^{94} +(5.28549 - 7.65735i) q^{95} +(5.06052 - 1.24731i) q^{96} +(-5.61387 - 8.13310i) q^{97} +(-0.478968 + 3.94465i) q^{98} +5.15495 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	−1.68275	−	0.414759i	−1.18988	−	0.293279i	−0.405814	−	0.913956i	$-0.633012\pi$
$2$	−1.68275	−	0.414759i	−1.18988	−	0.293279i	−0.784067	+	0.620677i	$0.786858\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	0.888694	+	0.466423i	0.444347	+	0.233211i
$5$	0.797976	−	1.15607i	0.356866	−	0.517009i	−0.602898	−	0.797818i	$-0.705987\pi$
$5$	0.797976	−	1.15607i	0.356866	−	0.517009i	0.959764	+	0.280809i	$0.0906027\pi$
$6$	−0.614568	+	1.62048i	−0.250896	+	0.661559i
$7$	−1.62398	−	1.43872i	−0.613806	−	0.543785i	0.297916	−	0.954592i	$-0.403709\pi$
$7$	−1.62398	−	1.43872i	−0.613806	−	0.543785i	−0.911722	+	0.410807i	$0.865247\pi$
$8$	1.29250	+	1.14506i	0.456970	+	0.404840i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−1.82228	+	1.61440i	−0.576256	+	0.510518i
$11$	−5.00516	+	1.23366i	−1.50911	+	0.371963i	−0.905164	−	0.425062i	$-0.860252\pi$
$11$	−5.00516	+	1.23366i	−1.50911	+	0.371963i	−0.603947	+	0.797024i	$0.706406\pi$
$12$	0.570142	−	0.825993i	0.164586	−	0.238444i
$13$	−1.03780	+	3.45296i	−0.287835	+	0.957680i
$13$	−1.03780	+	3.45296i	−0.287835	+	0.957680i
$14$	2.13602	+	3.09456i	0.570875	+	0.827056i
$15$	−1.05145	−	0.931507i	−0.271484	−	0.240514i
$16$	−2.84032	−	4.11491i	−0.710079	−	1.02873i
$17$	−3.12382	−	2.76746i	−0.757638	−	0.671208i	0.193109	−	0.981177i	$-0.438143\pi$
$17$	−3.12382	−	2.76746i	−0.757638	−	0.671208i	−0.950747	+	0.309969i	$0.899681\pi$
$18$	1.53459	+	0.805415i	0.361706	+	0.189838i
$19$	6.62362			1.51956			0.759781	−	0.650179i	$-0.225306\pi$
$19$	6.62362			1.51956			0.759781	+	0.650179i	$0.225306\pi$
$20$	1.24837	−	0.655197i	0.279145	−	0.146506i
$21$	−1.62398	+	1.43872i	−0.354381	+	0.313954i
$22$	8.93407			1.90475
$23$	−2.75739			−0.574956			−0.287478	−	0.957787i	$-0.592817\pi$
$23$	−2.75739			−0.574956			−0.287478	+	0.957787i	$0.592817\pi$
$24$	1.29250	−	1.14506i	0.263831	−	0.233734i
$25$	1.07330	+	2.83005i	0.214659	+	0.566010i
$26$	3.17851	−	5.38002i	0.623357	−	1.05511i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	−0.772169	−	2.03604i	−0.145926	−	0.384776i
$29$	−8.87966	−	2.18864i	−1.64891	−	0.406420i	−0.698052	−	0.716047i	$-0.745950\pi$
$29$	−8.87966	−	2.18864i	−1.64891	−	0.406420i	−0.950858	+	0.309627i	$0.899796\pi$
$30$	1.38298	+	2.00359i	0.252496	+	0.365804i
$31$	0.0507137	−	0.133721i	0.00910844	−	0.0240170i	−0.930385	−	0.366584i	$-0.880527\pi$
$31$	0.0507137	−	0.133721i	0.00910844	−	0.0240170i	0.939493	+	0.342567i	$0.111296\pi$
$32$	1.84819	+	4.87328i	0.326717	+	0.861482i
$33$	0.621361	+	5.11736i	0.108165	+	0.890819i
$34$	4.10876	+	5.95257i	0.704647	+	1.02086i
$35$	−2.95916	+	0.729366i	−0.500189	+	0.123285i
$36$	−0.751248	−	0.665547i	−0.125208	−	0.110925i
$37$	−0.189711	+	0.500227i	−0.0311883	+	0.0822368i	−0.949706	−	0.313143i	$-0.898618\pi$
$37$	−0.189711	+	0.500227i	−0.0311883	+	0.0822368i	0.918518	+	0.395380i	$0.129387\pi$
$38$	−11.1459	−	2.74721i	−1.80810	−	0.445656i
$39$	3.30270	+	1.44645i	0.528854	+	0.231617i
$40$	2.35516	−	0.580494i	0.372383	−	0.0917841i
$41$	−1.41745	+	11.6738i	−0.221369	+	1.82314i	0.282399	+	0.959297i	$0.408870\pi$
$41$	−1.41745	+	11.6738i	−0.221369	+	1.82314i	−0.503767	+	0.863839i	$0.668053\pi$
$42$	3.32947	−	1.74744i	0.513748	−	0.269636i
$43$	1.29503	+	3.41471i	0.197490	+	0.520738i	0.996778	−	0.0802099i	$-0.0255591\pi$
$43$	1.29503	+	3.41471i	0.197490	+	0.520738i	−0.799288	+	0.600948i	$0.794790\pi$
$44$	−5.02346	−	1.23817i	−0.757315	−	0.186661i
$45$	−1.05145	+	0.931507i	−0.156741	+	0.138861i
$46$	4.63999	+	1.14366i	0.684129	+	0.168623i
$47$	3.60078	−	1.88984i	0.525228	−	0.275661i	−0.181199	−	0.983446i	$-0.557998\pi$
$47$	3.60078	−	1.88984i	0.525228	−	0.275661i	0.706428	+	0.707785i	$0.250306\pi$
$48$	−4.42727	+	2.32361i	−0.639021	+	0.335384i
$49$	−0.276364	−	2.27606i	−0.0394805	−	0.325151i
$50$	−0.632295	−	5.20741i	−0.0894200	−	0.736440i
$51$	−3.12382	+	2.76746i	−0.437422	+	0.387522i
$52$	−2.53283	+	2.58457i	−0.351240	+	0.358416i
$53$	−0.331951	−	0.294083i	−0.0455970	−	0.0403954i	0.640016	−	0.768361i	$-0.278928\pi$
$53$	−0.331951	−	0.294083i	−0.0455970	−	0.0403954i	−0.685613	+	0.727966i	$0.740466\pi$
$54$	0.984516	−	1.42632i	0.133976	−	0.194097i
$55$	−2.56780	+	6.77073i	−0.346242	+	0.912966i
$56$	−0.451581	−	3.71911i	−0.0603451	−	0.496986i
$57$	0.798389	−	6.57532i	0.105749	−	0.870923i
$58$	14.0344	+	7.36584i	1.84281	+	0.967182i
$59$	−1.09363	+	1.58439i	−0.142378	+	0.206270i	−0.887685	−	0.460451i	$-0.847688\pi$
$59$	−1.09363	+	1.58439i	−0.142378	+	0.206270i	0.745307	+	0.666722i	$0.232303\pi$
$60$	−0.499945	−	1.31825i	−0.0645426	−	0.170185i
$61$	−11.1722	+	9.89771i	−1.43045	+	1.26727i	−0.519683	+	0.854359i	$0.673950\pi$
$61$	−11.1722	+	9.89771i	−1.43045	+	1.26727i	−0.910771	+	0.412913i	$0.864511\pi$
$62$	−0.140800	+	0.203984i	−0.0178816	+	0.0259060i
$63$	1.23248	+	1.78556i	0.155278	+	0.224959i
$64$	0.116568	+	0.960026i	0.0145710	+	0.120003i
$65$	3.16372	+	3.95516i	0.392411	+	0.490577i
$66$	1.07688	−	8.86893i	0.132555	−	1.09169i
$67$	9.45492	−	4.96233i	1.15510	−	0.606245i	0.225295	−	0.974291i	$-0.427665\pi$
$67$	9.45492	−	4.96233i	1.15510	−	0.606245i	0.929808	+	0.368046i	$0.119973\pi$
$68$	−1.48531	−	3.91645i	−0.180121	−	0.474939i
$69$	−0.332367	+	2.73729i	−0.0400123	+	0.329531i
$70$	5.28202			0.631322
$71$	−1.50113	+	12.3629i	−0.178151	+	1.46721i	0.579728	+	0.814810i	$0.303159\pi$
$71$	−1.50113	+	12.3629i	−0.178151	+	1.46721i	−0.757879	+	0.652395i	$0.773764\pi$
$72$	−0.980916	−	1.42110i	−0.115602	−	0.167479i
$73$	−14.2807	+	3.51988i	−1.67143	+	0.411971i	−0.957544	−	0.288288i	$-0.906914\pi$
$73$	−14.2807	+	3.51988i	−1.67143	+	0.411971i	−0.713888	+	0.700259i	$0.753068\pi$
$74$	0.526709	−	0.763070i	0.0612287	−	0.0887051i
$75$	2.93879	−	0.724346i	0.339342	−	0.0836403i
$76$	5.88637	+	3.08940i	0.675213	+	0.354379i
$77$	9.90316	+	5.19758i	1.12857	+	0.592319i
$78$	−4.95767	−	3.80382i	−0.561345	−	0.430698i
$79$	0.0932751	−	0.0489545i	0.0104943	−	0.00550781i	−0.459468	−	0.888194i	$-0.651960\pi$
$79$	0.0932751	−	0.0489545i	0.0104943	−	0.00550781i	0.469962	+	0.882687i	$0.344268\pi$
$80$	−7.02362			−0.785265
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	7.22702	−	19.0561i	0.798090	−	2.10439i
$83$	−1.35827	−	11.1864i	−0.149089	−	1.22786i	−0.854647	−	0.519209i	$-0.826226\pi$
$83$	−1.35827	−	11.1864i	−0.149089	−	1.22786i	0.705558	−	0.708653i	$-0.250697\pi$
$84$	−2.11427	+	0.521121i	−0.230686	+	0.0568590i
$85$	−5.69211	+	1.40298i	−0.617396	+	0.152174i
$86$	−0.762920	−	6.28321i	−0.0822678	−	0.677536i
$87$	−3.24300	+	8.55110i	−0.347687	+	0.916774i
$88$	−7.88180	−	4.13669i	−0.840203	−	0.440973i
$89$	−3.07953			−0.326429			−0.163215	−	0.986591i	$-0.552186\pi$
$89$	−3.07953			−0.326429			−0.163215	+	0.986591i	$0.552186\pi$
$90$	2.15568	−	1.13139i	0.227229	−	0.119259i
$91$	6.65322	−	4.11443i	0.697447	−	0.431310i
$92$	−2.45048	−	1.28611i	−0.255480	−	0.134086i
$93$	−0.126633	−	0.0664622i	−0.0131312	−	0.00689181i
$94$	−6.84303	+	1.68665i	−0.705804	+	0.173965i
$95$	5.28549	−	7.65735i	0.542280	−	0.785628i
$96$	5.06052	−	1.24731i	0.516487	−	0.127303i
$97$	−5.61387	−	8.13310i	−0.570002	−	0.825791i	0.426912	−	0.904293i	$-0.359602\pi$
$97$	−5.61387	−	8.13310i	−0.570002	−	0.825791i	−0.996914	+	0.0785024i	$0.974986\pi$
$98$	−0.478968	+	3.94465i	−0.0483830	+	0.398470i
$99$	5.15495			0.518092
$100$	−0.366167	+	3.01566i	−0.0366167	+	0.301566i
$101$	−7.00573	−	18.4726i	−0.697096	−	1.83809i	−0.520623	−	0.853787i	$-0.674300\pi$
$101$	−7.00573	−	18.4726i	−0.697096	−	1.83809i	−0.176473	−	0.984305i	$-0.556469\pi$
$102$	6.40442	−	3.36130i	0.634132	−	0.332818i
$103$	1.86955	−	15.3971i	0.184212	−	1.51712i	−0.548250	−	0.836315i	$-0.684706\pi$
$103$	1.86955	−	15.3971i	0.184212	−	1.51712i	0.732462	−	0.680808i	$-0.238371\pi$
$104$	−5.29522	+	3.27463i	−0.519239	+	0.321104i
$105$	0.367362	+	3.02550i	0.0358508	+	0.295258i
$106$	0.436616	+	0.632547i	0.0424079	+	0.0614384i
$107$	3.41137	−	4.94222i	0.329789	−	0.477782i	−0.622654	−	0.782497i	$-0.713946\pi$
$107$	3.41137	−	4.94222i	0.329789	−	0.477782i	0.952444	+	0.304715i	$0.0985611\pi$
$108$	−0.751248	+	0.665547i	−0.0722889	+	0.0640423i
$109$	2.48691	+	6.55745i	0.238203	+	0.628090i	0.999801	−	0.0199603i	$-0.00635400\pi$
$109$	2.48691	+	6.55745i	0.238203	+	0.628090i	−0.761598	+	0.648050i	$0.775585\pi$
$110$	7.12918	−	10.3284i	0.679741	−	0.984774i
$111$	0.473713	+	0.248623i	0.0449628	+	0.0235983i
$112$	−1.30759	+	10.7689i	−0.123555	+	1.01757i
$113$	0.517104	+	4.25874i	0.0486451	+	0.400628i	0.996611	+	0.0822568i	$0.0262128\pi$
$113$	0.517104	+	4.25874i	0.0486451	+	0.400628i	−0.947966	+	0.318371i	$0.896864\pi$
$114$	−4.07066	+	10.7335i	−0.381252	+	1.00528i
$115$	−2.20034	+	3.18774i	−0.205182	+	0.297258i
$116$	−6.87046	−	6.08670i	−0.637907	−	0.565136i
$117$	1.83400	−	3.10427i	0.169553	−	0.286989i
$118$	2.49744	−	2.21254i	0.229908	−	0.203681i
$119$	1.09141	+	8.98860i	0.100050	+	0.823984i
$120$	−0.292379	−	2.40795i	−0.0266904	−	0.219815i
$121$	13.7897	−	7.23737i	1.25360	−	0.657943i
$122$	22.9051	−	12.0215i	2.07373	−	1.08838i
$123$	11.4178	+	2.81423i	1.02951	+	0.253751i
$124$	0.107439	−	0.0951830i	0.00964834	−	0.00854768i
$125$	10.9477	+	2.69838i	0.979196	+	0.241350i
$126$	−1.33337	−	3.51582i	−0.118786	−	0.313214i
$127$	−1.78988	+	0.939400i	−0.158826	+	0.0833583i	−0.542263	−	0.840209i	$-0.682432\pi$
$127$	−1.78988	+	0.939400i	−0.158826	+	0.0833583i	0.383437	+	0.923567i	$0.374740\pi$
$128$	1.45849	−	12.0118i	0.128914	−	1.06170i
$129$	3.54591	−	0.873988i	0.312200	−	0.0769504i
$130$	−3.68330	−	7.96770i	−0.323047	−	0.698814i
$131$	−6.33163	−	1.56061i	−0.553197	−	0.136351i	−0.0471993	−	0.998885i	$-0.515030\pi$
$131$	−6.33163	−	1.56061i	−0.553197	−	0.136351i	−0.505998	+	0.862535i	$0.668876\pi$
$132$	−1.83465	+	4.83759i	−0.159686	+	0.421058i
$133$	−10.7566	−	9.52953i	−0.932717	−	0.826315i
$134$	−17.9684	+	4.42881i	−1.55223	+	0.382591i
$135$	0.797976	+	1.15607i	0.0686789	+	0.0994985i
$136$	−0.868643	−	7.15392i	−0.0744855	−	0.613443i
$137$	0.129704	+	0.342001i	0.0110814	+	0.0292191i	0.940443	−	0.339952i	$-0.110411\pi$
$137$	0.129704	+	0.342001i	0.0110814	+	0.0292191i	−0.929361	+	0.369171i	$0.879642\pi$
$138$	1.69461	−	4.46831i	0.144254	−	0.380368i
$139$	−11.9982	−	17.3823i	−1.01767	−	1.47435i	−0.874725	−	0.484619i	$-0.838958\pi$
$139$	−11.9982	−	17.3823i	−1.01767	−	1.47435i	−0.142945	−	0.989731i	$-0.545657\pi$
$140$	−2.96998	−	0.732033i	−0.251009	−	0.0618681i
$141$	−1.44203	−	3.80232i	−0.121441	−	0.320213i
$142$	7.65364	−	20.1810i	0.642279	−	1.69355i
$143$	0.934583	−	18.5629i	0.0781537	−	1.55231i
$144$	1.77302	+	4.67507i	0.147752	+	0.389589i
$145$	−9.61597	+	8.51901i	−0.798563	+	0.707465i
$146$	25.4907			2.10963
$147$	−2.29278			−0.189105
$148$	−0.401912	+	0.356063i	−0.0330370	+	0.0292682i
$149$	5.87353	−	3.08267i	0.481179	−	0.252542i	−0.206650	−	0.978415i	$-0.566256\pi$
$149$	5.87353	−	3.08267i	0.481179	−	0.252542i	0.687829	+	0.725873i	$0.258564\pi$
$150$	−5.24566			−0.428306
$151$	5.35196	+	2.80892i	0.435536	+	0.228587i	0.668217	−	0.743966i	$-0.267058\pi$
$151$	5.35196	+	2.80892i	0.435536	+	0.228587i	−0.232681	+	0.972553i	$0.574750\pi$
$152$	8.56106	+	7.58443i	0.694393	+	0.615179i
$153$	2.37075	+	3.43462i	0.191664	+	0.277673i
$154$	−14.5088	−	12.8536i	−1.16915	−	1.03578i
$155$	−0.114122	−	0.165335i	−0.00916652	−	0.0132800i
$156$	2.26043	+	2.82590i	0.180979	+	0.226253i
$157$	−5.31733	+	7.70348i	−0.424369	+	0.614805i	−0.975602	−	0.219547i	$-0.929542\pi$
$157$	−5.31733	+	7.70348i	−0.424369	+	0.614805i	0.551233	+	0.834351i	$0.314158\pi$
$158$	−0.177262	+	0.0436913i	−0.0141022	+	0.00347589i
$159$	−0.331951	+	0.294083i	−0.0263254	+	0.0233223i
$160$	7.10865	+	1.75213i	0.561988	+	0.138518i
$161$	4.47795	+	3.96712i	0.352912	+	0.312653i
$162$	−1.29725	−	1.14926i	−0.101921	−	0.0902945i
$163$	0.895337	−	2.36081i	0.0701282	−	0.184913i	−0.895370	−	0.445323i	$-0.853089\pi$
$163$	0.895337	−	2.36081i	0.0701282	−	0.184913i	0.965498	+	0.260411i	$0.0838579\pi$
$164$	−6.70459	+	9.71328i	−0.523541	+	0.758479i
$165$	6.41185	+	3.36520i	0.499162	+	0.261981i
$166$	−2.35403	+	19.3871i	−0.182708	+	1.50473i
$167$	−4.64188	−	1.14412i	−0.359200	−	0.0885348i	0.0555860	−	0.998454i	$-0.482297\pi$
$167$	−4.64188	−	1.14412i	−0.359200	−	0.0885348i	−0.414786	+	0.909919i	$0.636143\pi$
$168$	−3.74642			−0.289043
$169$	−10.8459	−	7.16700i	−0.834302	−	0.551307i
$170$	10.1603			0.779257
$171$	−6.43115	−	1.58513i	−0.491802	−	0.121218i
$172$	−0.441813	+	3.63866i	−0.0336880	+	0.277445i
$173$	−0.940088	−	0.493396i	−0.0714736	−	0.0375122i	0.428608	−	0.903491i	$-0.359004\pi$
$173$	−0.940088	−	0.493396i	−0.0714736	−	0.0375122i	−0.500081	+	0.865978i	$0.666697\pi$
$174$	9.00380	−	13.0443i	0.682576	−	0.988883i
$175$	2.32864	−	6.14012i	0.176029	−	0.464149i
$176$	19.2926	+	17.0918i	1.45424	+	1.28834i
$177$	1.44102	+	1.27663i	0.108314	+	0.0959575i
$178$	5.18206	+	1.27726i	0.388412	+	0.0957349i
$179$	−15.4222	+	13.6629i	−1.15271	+	1.02121i	−0.153257	+	0.988186i	$0.548976\pi$
$179$	−15.4222	+	13.6629i	−1.15271	+	1.02121i	−0.999454	+	0.0330274i	$0.989485\pi$
$180$	−1.36890	+	0.337403i	−0.102032	+	0.0251485i
$181$	−2.62914	+	3.80897i	−0.195422	+	0.283118i	−0.908429	−	0.418039i	$-0.862718\pi$
$181$	−2.62914	+	3.80897i	−0.195422	+	0.283118i	0.713007	+	0.701157i	$0.247333\pi$
$182$	−12.9022	+	4.16406i	−0.956373	+	0.308661i
$183$	8.47888	+	12.2838i	0.626777	+	0.908043i
$184$	−3.56395	−	3.15738i	−0.262738	−	0.232765i
$185$	0.426912	+	0.618488i	0.0313872	+	0.0454722i
$186$	0.185525	+	0.164361i	0.0136034	+	0.0120515i
$187$	19.0493	+	9.99785i	1.39302	+	0.731115i
$188$	4.08146			0.297671
$189$	1.92110	−	1.00827i	0.139739	−	0.0733408i
$190$	−12.0701	+	10.6932i	−0.875656	+	0.775764i
$191$	−24.2264			−1.75296			−0.876480	−	0.481438i	$-0.840115\pi$
$191$	−24.2264			−1.75296			−0.876480	+	0.481438i	$0.840115\pi$
$192$	0.967077			0.0697928
$193$	3.10609	−	2.75175i	0.223581	−	0.198076i	−0.543895	−	0.839153i	$-0.683051\pi$
$193$	3.10609	−	2.75175i	0.223581	−	0.198076i	0.767476	+	0.641078i	$0.221512\pi$
$194$	6.07344	+	16.0143i	0.436047	+	1.14976i
$195$	4.30766	−	2.66391i	0.308478	−	0.190767i
$196$	0.816003	−	2.15162i	0.0582859	−	0.153687i
$197$	−5.86000	−	15.4515i	−0.417507	−	1.10088i	−0.964580	−	0.263791i	$-0.915027\pi$
$197$	−5.86000	−	15.4515i	−0.417507	−	1.10088i	0.547072	−	0.837085i	$-0.315742\pi$
$198$	−8.67447	−	2.13806i	−0.616467	−	0.151946i
$199$	−11.0806	−	16.0530i	−0.785481	−	1.13797i	−0.987350	−	0.158554i	$-0.949317\pi$
$199$	−11.0806	−	16.0530i	−0.785481	−	1.13797i	0.201869	−	0.979413i	$-0.435298\pi$
$200$	−1.85334	+	4.88684i	−0.131051	+	0.345552i
$201$	−3.78648	−	9.98413i	−0.267078	−	0.704226i
$202$	4.12718	+	33.9904i	0.290387	+	2.39155i
$203$	11.2715	+	16.3296i	0.791107	+	1.14612i
$204$	−4.06693	+	1.00241i	−0.284742	+	0.0701825i
$205$	12.3646	+	10.9541i	0.863580	+	0.765065i
$206$	−9.53207	+	25.1340i	−0.664131	+	1.75117i
$207$	2.67727	+	0.659888i	0.186083	+	0.0458654i
$208$	17.1563	−	5.53705i	1.18958	−	0.383925i
$209$	−33.1522	+	8.17129i	−2.29319	+	0.565220i
$210$	0.636677	−	5.24350i	0.0439349	−	0.361836i
$211$	−7.24703	+	3.80353i	−0.498906	+	0.261846i	−0.695353	−	0.718668i	$-0.744752\pi$
$211$	−7.24703	+	3.80353i	−0.498906	+	0.261846i	0.196447	+	0.980514i	$0.437060\pi$
$212$	−0.157836	−	0.416179i	−0.0108402	−	0.0285833i
$213$	12.0918	+	2.98036i	0.828518	+	0.204211i
$214$	−7.79029	+	6.90160i	−0.532533	+	0.471783i
$215$	4.98104	+	1.22772i	0.339704	+	0.0837295i
$216$	−1.52898	+	0.802469i	−0.104034	+	0.0546011i
$217$	−0.274745	+	0.144197i	−0.0186509	+	0.00978875i
$218$	−1.46508	−	12.0660i	−0.0992275	−	0.817212i
$219$	1.77287	+	14.6009i	0.119799	+	0.986636i
$220$	−5.44001	+	4.81943i	−0.366766	+	0.324926i
$221$	12.7979	−	7.91436i	0.860877	−	0.532377i
$222$	−0.694018	−	0.614847i	−0.0465795	−	0.0412658i
$223$	1.81063	−	2.62315i	0.121249	−	0.175659i	−0.757659	−	0.652650i	$-0.773657\pi$
$223$	1.81063	−	2.62315i	0.121249	−	0.175659i	0.878908	+	0.476991i	$0.158273\pi$
$224$	4.00986	−	10.5731i	0.267920	−	0.706447i
$225$	−0.364833	−	3.00467i	−0.0243222	−	0.200311i
$226$	0.896196	−	7.38084i	0.0596141	−	0.490966i
$227$	12.4828	+	6.55148i	0.828513	+	0.434837i	0.824984	−	0.565157i	$-0.191184\pi$
$227$	12.4828	+	6.55148i	0.828513	+	0.434837i	0.00352941	+	0.999994i	$0.498877\pi$
$228$	3.77640	−	5.47106i	0.250098	−	0.362330i
$229$	−5.26227	−	13.8755i	−0.347741	−	0.916917i	−0.988776	−	0.149406i	$-0.952264\pi$
$229$	−5.26227	−	13.8755i	−0.347741	−	0.916917i	0.641035	−	0.767511i	$-0.278505\pi$
$230$	5.02475	−	4.45154i	0.331322	−	0.293526i
$231$	6.35338	−	9.20446i	0.418022	−	0.605609i
$232$	−8.97088	−	12.9966i	−0.588967	−	0.853266i
$233$	−0.259903	−	2.14050i	−0.0170268	−	0.140229i	0.981716	−	0.190350i	$-0.0609623\pi$
$233$	−0.259903	−	2.14050i	−0.0170268	−	0.140229i	−0.998743	+	0.0501213i	$0.984039\pi$
$234$	−4.37367	+	4.46302i	−0.285916	+	0.291757i
$235$	0.688559	−	5.67080i	0.0449167	−	0.369922i
$236$	−1.71090	+	0.897948i	−0.111370	+	0.0584514i
$237$	−0.0373545	−	0.0984958i	−0.00242644	−	0.00639799i
$238$	1.89154	−	15.5782i	0.122610	−	1.00978i
$239$	−11.4935			−0.743451			−0.371726	−	0.928343i	$-0.621234\pi$
$239$	−11.4935			−0.743451			−0.371726	+	0.928343i	$0.621234\pi$
$240$	−0.846604	+	6.97241i	−0.0546480	+	0.450067i
$241$	17.3968	+	25.2037i	1.12063	+	1.62351i	0.695795	+	0.718240i	$0.255052\pi$
$241$	17.3968	+	25.2037i	1.12063	+	1.62351i	0.424834	+	0.905271i	$0.360332\pi$
$242$	−26.2062	+	6.45926i	−1.68460	+	0.415217i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	−14.5452	+	3.58507i	−0.931160	+	0.229510i
$245$	−2.85181	−	1.49675i	−0.182196	−	0.0956236i
$246$	−18.0460	−	9.47128i	−1.15057	−	0.603867i
$247$	−6.87401	+	22.8711i	−0.437383	+	1.45525i
$248$	0.218666	−	0.114765i	0.0138853	−	0.00728757i
$249$	−11.2685			−0.714113
$250$	−17.3031	−	9.08136i	−1.09434	−	0.574356i
$251$	8.67197	−	22.8661i	0.547370	−	1.44330i	−0.320856	−	0.947128i	$-0.603971\pi$
$251$	8.67197	−	22.8661i	0.547370	−	1.44330i	0.868226	−	0.496168i	$-0.165260\pi$
$252$	0.262474	+	2.16167i	0.0165343	+	0.136172i
$253$	13.8012	−	3.40169i	0.867673	−	0.213862i
$254$	3.40153	−	0.838402i	0.213431	−	0.0526060i
$255$	0.706642	+	5.81972i	0.0442516	+	0.364445i
$256$	−6.75040	+	17.7993i	−0.421900	+	1.11246i
$257$	16.1896	+	8.49695i	1.00988	+	0.530025i	0.886693	−	0.462358i	$-0.152997\pi$
$257$	16.1896	+	8.49695i	1.00988	+	0.530025i	0.123186	+	0.992384i	$0.460689\pi$
$258$	−6.32936			−0.394049
$259$	1.02777	−	0.539417i	0.0638627	−	0.0335177i
$260$	0.966805	+	4.99055i	0.0599587	+	0.309501i
$261$	8.09785	+	4.25008i	0.501245	+	0.263073i
$262$	10.0073	+	5.25221i	0.618250	+	0.324483i
$263$	27.1000	−	6.67955i	1.67106	−	0.411879i	0.713624	−	0.700529i	$-0.247053\pi$
$263$	27.1000	−	6.67955i	1.67106	−	0.411879i	0.957435	+	0.288650i	$0.0932065\pi$
$264$	−5.05657	+	7.32571i	−0.311211	+	0.450866i
$265$	−0.604869	+	0.149087i	−0.0371568	+	0.00915834i
$266$	14.1482	+	20.4972i	0.867480	+	1.25676i
$267$	−0.371196	+	3.05707i	−0.0227168	+	0.187090i
$268$	10.7171			0.654649
$269$	−1.65812	+	13.6559i	−0.101097	+	0.832612i	0.850650	+	0.525732i	$0.176208\pi$
$269$	−1.65812	+	13.6559i	−0.101097	+	0.832612i	−0.951748	+	0.306881i	$0.900715\pi$
$270$	−0.863301	−	2.27634i	−0.0525388	−	0.138533i
$271$	−10.4933	+	5.50730i	−0.637421	+	0.334544i	−0.752286	−	0.658837i	$-0.771049\pi$
$271$	−10.4933	+	5.50730i	−0.637421	+	0.334544i	0.114865	+	0.993381i	$0.463357\pi$
$272$	−2.51522	+	20.7147i	−0.152508	+	1.25601i
$273$	−3.28248	−	7.10065i	−0.198665	−	0.429751i
$274$	−0.0764105	−	0.629297i	−0.00461613	−	0.0380172i
$275$	−8.86334	−	12.8408i	−0.534479	−	0.774327i
$276$	−1.57211	+	2.27759i	−0.0946297	+	0.137095i
$277$	−2.72738	+	2.41624i	−0.163872	+	0.145178i	−0.741074	−	0.671424i	$-0.765683\pi$
$277$	−2.72738	+	2.41624i	−0.163872	+	0.145178i	0.577202	+	0.816602i	$0.304145\pi$
$278$	12.9803	+	34.2264i	0.778510	+	2.05276i
$279$	−0.0812415	+	0.117699i	−0.00486380	+	0.00704644i
$280$	−4.65989	−	2.44570i	−0.278482	−	0.146159i
$281$	−1.99635	+	16.4414i	−0.119092	+	0.980814i	0.803571	+	0.595209i	$0.202931\pi$
$281$	−1.99635	+	16.4414i	−0.119092	+	0.980814i	−0.922664	+	0.385606i	$0.873992\pi$
$282$	0.849521	+	6.99644i	0.0505883	+	0.416632i
$283$	−10.7958	+	28.4661i	−0.641741	+	1.69213i	0.0771582	+	0.997019i	$0.475415\pi$
$283$	−10.7958	+	28.4661i	−0.641741	+	1.69213i	−0.718900	+	0.695114i	$0.755354\pi$
$284$	−7.10038	+	10.2867i	−0.421330	+	0.610402i
$285$	−6.96443	−	6.16994i	−0.412537	−	0.365476i
$286$	−9.27181	+	30.8490i	−0.548254	+	1.82414i
$287$	19.0972	−	16.9186i	1.12727	−	0.998676i
$288$	−0.628234	−	5.17397i	−0.0370190	−	0.304879i
$289$	0.0502758	+	0.414058i	0.00295740	+	0.0243564i
$290$	19.7146	−	10.3470i	1.15768	−	0.607597i
$291$	−8.75048	+	4.59260i	−0.512962	+	0.269223i
$292$	−14.3329	−	3.53275i	−0.838772	−	0.206739i
$293$	−12.8245	+	11.3615i	−0.749216	+	0.663748i	−0.948709	−	0.316152i	$-0.897609\pi$
$293$	−12.8245	+	11.3615i	−0.749216	+	0.663748i	0.199492	+	0.979899i	$0.436071\pi$
$294$	3.85816	+	0.950951i	0.225012	+	0.0554606i
$295$	0.958978	+	2.52862i	0.0558339	+	0.147222i
$296$	−0.817992	+	0.429315i	−0.0475448	+	0.0249534i
$297$	0.621361	−	5.11736i	0.0360550	−	0.296940i
$298$	−11.1622	+	2.75124i	−0.646610	+	0.159375i
$299$	2.86163	−	9.52118i	0.165492	−	0.550624i
$300$	2.94953	+	0.726995i	0.170291	+	0.0419731i
$301$	2.80971	−	7.40860i	0.161949	−	0.427025i
$302$	−7.84095	−	6.94648i	−0.451196	−	0.399725i
$303$	−19.1824	+	4.72803i	−1.10200	+	0.271618i
$304$	−18.8132	−	27.2556i	−1.07901	−	1.56321i
$305$	2.52727	+	20.8140i	0.144711	+	1.19180i
$306$	−2.56483	−	6.76289i	−0.146621	−	0.386609i
$307$	0.653018	−	1.72187i	0.0372697	−	0.0982722i	−0.915089	−	0.403251i	$-0.867880\pi$
$307$	0.653018	−	1.72187i	0.0372697	−	0.0982722i	0.952359	+	0.304979i	$0.0986494\pi$
$308$	6.37661	+	9.23811i	0.363341	+	0.526390i
$309$	−15.0595	−	3.71183i	−0.856705	−	0.211159i
$310$	0.123465	+	0.325549i	0.00701232	+	0.0184900i
$311$	7.91532	−	20.8710i	0.448837	−	1.18349i	−0.499526	−	0.866299i	$-0.666493\pi$
$311$	7.91532	−	20.8710i	0.448837	−	1.18349i	0.948363	−	0.317187i	$-0.102738\pi$
$312$	2.61248	+	5.65132i	0.147903	+	0.319943i
$313$	−9.44445	−	24.9030i	−0.533832	−	1.40760i	−0.882482	−	0.470346i	$-0.844129\pi$
$313$	−9.44445	−	24.9030i	−0.533832	−	1.40760i	0.348650	−	0.937253i	$-0.386640\pi$
$314$	12.1428	−	10.7576i	0.685258	−	0.607086i
$315$	3.04772			0.171719
$316$	0.105726			0.00594758
$317$	3.01915	−	2.67473i	0.169572	−	0.150228i	−0.574069	−	0.818807i	$-0.694636\pi$
$317$	3.01915	−	2.67473i	0.169572	−	0.150228i	0.743641	+	0.668579i	$0.233097\pi$
$318$	0.680563	−	0.357187i	0.0381641	−	0.0200301i
$319$	47.1441			2.63956
$320$	1.20287	+	0.631317i	0.0672427	+	0.0352917i
$321$	−4.49499	−	3.98221i	−0.250886	−	0.222265i
$322$	−5.88985	−	8.53292i	−0.328228	−	0.475521i
$323$	−20.6910	−	18.3306i	−1.15128	−	1.01994i
$324$	0.570142	+	0.825993i	0.0316746	+	0.0458885i
$325$	−10.8859	+	0.769019i	−0.603843	+	0.0426575i
$326$	−2.48579	+	3.60129i	−0.137675	+	0.199457i
$327$	6.80940	−	1.67837i	0.376561	−	0.0928139i
$328$	−15.1992	+	13.4653i	−0.839237	+	0.743499i
$329$	−8.56654	−	2.11146i	−0.472289	−	0.116409i
$330$	−9.39377	−	8.32215i	−0.517110	−	0.458119i
$331$	−16.6030	−	14.7090i	−0.912584	−	0.808479i	0.0693714	−	0.997591i	$-0.477901\pi$
$331$	−16.6030	−	14.7090i	−0.912584	−	0.808479i	−0.981956	+	0.189112i	$0.939439\pi$
$332$	4.01048	−	10.5748i	0.220104	−	0.580366i
$333$	0.303910	−	0.440290i	0.0166542	−	0.0241278i
$334$	7.33657	+	3.85053i	0.401439	+	0.210692i
$335$	1.80802	−	14.8904i	0.0987825	−	0.813547i
$336$	10.5328	+	2.59611i	0.574612	+	0.141629i
$337$	3.64103			0.198339			0.0991697	−	0.995071i	$-0.468381\pi$
$337$	3.64103			0.198339			0.0991697	+	0.995071i	$0.468381\pi$
$338$	15.2784	+	16.5587i	0.831033	+	0.900673i
$339$	4.29001			0.233002
$340$	−5.71292	−	1.40811i	−0.309827	−	0.0763655i
$341$	−0.0888636	+	0.731858i	−0.00481223	+	0.0396323i
$342$	10.1645	+	5.33476i	0.549635	+	0.288471i
$343$	−11.4532	+	16.5928i	−0.618413	+	0.895926i
$344$	−2.23621	+	5.89641i	−0.120569	+	0.317913i
$345$	2.89927	+	2.56853i	0.156092	+	0.138285i
$346$	1.37729	+	1.22017i	0.0740434	+	0.0655968i
$347$	10.2983	+	2.53831i	0.552843	+	0.136263i	0.505834	−	0.862631i	$-0.331185\pi$
$347$	10.2983	+	2.53831i	0.552843	+	0.136263i	0.0470089	+	0.998894i	$0.485031\pi$
$348$	−6.87046	+	6.08670i	−0.368296	+	0.326281i
$349$	−23.4835	+	5.78816i	−1.25704	+	0.309833i	−0.810930	−	0.585143i	$-0.801038\pi$
$349$	−23.4835	+	5.78816i	−1.25704	+	0.309833i	−0.446113	+	0.894976i	$0.647192\pi$
$350$	−6.46518	+	9.36643i	−0.345578	+	0.500657i
$351$	−2.86057	−	2.19480i	−0.152686	−	0.117150i
$352$	−15.2624	−	22.1115i	−0.813491	−	1.17855i
$353$	−4.73645	−	4.19613i	−0.252096	−	0.223337i	0.527605	−	0.849490i	$-0.323090\pi$
$353$	−4.73645	−	4.19613i	−0.252096	−	0.223337i	−0.779701	+	0.626153i	$0.784629\pi$
$354$	−1.89537	−	2.74592i	−0.100738	−	0.145944i
$355$	13.0945	+	11.6007i	0.694983	+	0.615701i
$356$	−2.73676	−	1.43636i	−0.145048	−	0.0761269i
$357$	9.05462			0.479221
$358$	31.6185	−	16.5947i	1.67109	−	0.877056i
$359$	6.03810	−	5.34929i	0.318679	−	0.282325i	−0.488584	−	0.872517i	$-0.662486\pi$
$359$	6.03810	−	5.34929i	0.318679	−	0.282325i	0.807263	+	0.590192i	$0.200948\pi$
$360$	−2.42564			−0.127842
$361$	24.8723			1.30907
$362$	6.00398	−	5.31906i	0.315562	−	0.279563i
$363$	−5.52244	−	14.5615i	−0.289853	−	0.764279i
$364$	7.83174	−	0.553261i	0.410495	−	0.0289987i
$365$	−7.32645	+	19.3183i	−0.383484	+	1.01116i
$366$	−9.17298	−	24.1872i	−0.479480	−	1.26428i
$367$	19.5066	+	4.80796i	1.01824	+	0.250973i	0.712896	−	0.701269i	$-0.247383\pi$
$367$	19.5066	+	4.80796i	1.01824	+	0.250973i	0.305342	+	0.952243i	$0.401229\pi$
$368$	7.83187	+	11.3464i	0.408264	+	0.591473i
$369$	4.16998	−	10.9953i	0.217080	−	0.572394i
$370$	−0.461860	−	1.21782i	−0.0240109	−	0.0633116i
$371$	0.115979	+	0.955170i	0.00602131	+	0.0495899i
$372$	−0.0815386	−	0.118129i	−0.00422758	−	0.00612471i
$373$	−12.5999	+	3.10560i	−0.652399	+	0.160802i	−0.551605	−	0.834105i	$-0.685984\pi$
$373$	−12.5999	+	3.10560i	−0.652399	+	0.160802i	−0.100794	+	0.994907i	$0.532138\pi$
$374$	−27.9084	−	24.7247i	−1.44311	−	1.27848i
$375$	3.99831	−	10.5427i	0.206472	−	0.544421i
$376$	6.81801	+	1.68049i	0.351612	+	0.0866645i
$377$	16.7726	−	28.3898i	0.863834	−	1.46215i
$378$	−3.65091	+	0.899868i	−0.187782	+	0.0462842i
$379$	0.364037	−	2.99811i	0.0186993	−	0.154003i	−0.980368	−	0.197175i	$-0.936823\pi$
$379$	0.364037	−	2.99811i	0.0186993	−	0.154003i	0.999068	+	0.0431722i	$0.0137464\pi$
$380$	8.26874	−	4.33977i	0.424178	−	0.222626i
$381$	0.716805	+	1.89006i	0.0367230	+	0.0968307i
$382$	40.7669	+	10.0481i	2.08581	+	0.514107i
$383$	23.0265	−	20.3997i	1.17660	−	1.04237i	0.178305	−	0.983975i	$-0.442939\pi$
$383$	23.0265	−	20.3997i	1.17660	−	1.04237i	0.998293	−	0.0583994i	$-0.0185997\pi$
$384$	−11.7484	−	2.89572i	−0.599532	−	0.147771i
$385$	13.9112	−	7.30118i	0.708983	−	0.372103i
$386$	−6.36807	+	3.34222i	−0.324126	+	0.170115i
$387$	−0.440204	−	3.62540i	−0.0223768	−	0.184290i
$388$	−1.19555	−	9.84627i	−0.0606950	−	0.499869i
$389$	−7.72771	+	6.84616i	−0.391811	+	0.347114i	−0.835913	−	0.548862i	$-0.815061\pi$
$389$	−7.72771	+	6.84616i	−0.391811	+	0.347114i	0.444102	+	0.895976i	$0.353523\pi$
$390$	−8.35358	+	2.69604i	−0.423000	+	0.136519i
$391$	8.61360	+	7.63098i	0.435609	+	0.385915i
$392$	2.24902	−	3.25827i	0.113593	−	0.164568i
$393$	−2.31242	+	6.09736i	−0.116646	+	0.307571i
$394$	3.45221	+	28.4315i	0.173920	+	1.43236i
$395$	0.0178365	−	0.146897i	0.000897452	−	0.00739118i
$396$	4.58117	+	2.40438i	0.230213	+	0.120825i
$397$	0.809618	−	1.17293i	0.0406336	−	0.0588679i	−0.802141	−	0.597135i	$-0.796306\pi$
$397$	0.809618	−	1.17293i	0.0406336	−	0.0588679i	0.842774	+	0.538267i	$0.180921\pi$
$398$	11.9877	+	31.6089i	0.600887	+	1.58441i
$399$	−10.7566	+	9.52953i	−0.538504	+	0.477073i
$400$	8.59690	−	12.4548i	0.429845	−	0.622738i
$401$	11.5228	+	16.6936i	0.575419	+	0.833638i	0.997332	−	0.0729980i	$-0.0232567\pi$
$401$	11.5228	+	16.6936i	0.575419	+	0.833638i	−0.421913	+	0.906636i	$0.638641\pi$
$402$	2.23067	+	18.3712i	0.111256	+	0.916273i
$403$	0.409103	+	0.313889i	0.0203789	+	0.0156359i
$404$	2.39008	−	19.6841i	0.118911	−	0.979321i
$405$	1.24382	−	0.652810i	0.0618061	−	0.0324384i
$406$	−12.1943	−	32.1536i	−0.605191	−	1.59576i
$407$	0.332423	−	2.73775i	0.0164776	−	0.135705i
$408$	−7.20646			−0.356773
$409$	2.37101	−	19.5270i	0.117239	−	0.965549i	−0.808790	−	0.588097i	$-0.799877\pi$
$409$	2.37101	−	19.5270i	0.117239	−	0.965549i	0.926029	−	0.377452i	$-0.123200\pi$
$410$	−16.2631	−	23.5612i	−0.803179	−	1.16361i
$411$	0.355142	−	0.0875346i	0.0175179	−	0.00431776i
$412$	8.84302	−	12.8113i	0.435664	−	0.631168i
$413$	4.05553	−	0.999598i	0.199559	−	0.0491870i
$414$	−4.23147	−	2.22085i	−0.207965	−	0.109149i
$415$	−14.0161	−	7.35620i	−0.688021	−	0.361101i
$416$	−18.7453	+	1.32423i	−0.919064	+	0.0649258i
$417$	−18.7018	+	9.81546i	−0.915831	+	0.480665i
$418$	59.1759			2.89439
$419$	4.10220	+	2.15300i	0.200405	+	0.105181i	0.561941	−	0.827178i	$-0.310055\pi$
$419$	4.10220	+	2.15300i	0.200405	+	0.105181i	−0.361535	+	0.932358i	$0.617747\pi$
$420$	−1.08469	+	2.86008i	−0.0529273	+	0.139558i
$421$	2.03193	+	16.7344i	0.0990300	+	0.815585i	0.954598	+	0.297896i	$0.0962847\pi$
$421$	2.03193	+	16.7344i	0.0990300	+	0.815585i	−0.855568	+	0.517690i	$0.826792\pi$
$422$	13.7725	−	3.39461i	0.670433	−	0.165247i
$423$	−3.94842	+	0.973198i	−0.191979	+	0.0473185i
$424$	−0.0923059	−	0.760208i	−0.00448277	−	0.0369190i
$425$	4.47927	−	11.8109i	0.217277	−	0.572912i
$426$	−19.1113	−	10.0304i	−0.925946	−	0.485974i
$427$	32.3835			1.56715
$428$	5.33682	−	2.80098i	0.257965	−	0.135391i
$429$	−18.3149	−	3.16528i	−0.884253	−	0.152821i
$430$	−7.87261	−	4.13187i	−0.379651	−	0.199256i
$431$	15.1091	+	7.92986i	0.727779	+	0.381968i	0.787555	−	0.616244i	$-0.211346\pi$
$431$	15.1091	+	7.92986i	0.727779	+	0.381968i	−0.0597765	+	0.998212i	$0.519039\pi$
$432$	4.85470	−	1.19658i	0.233572	−	0.0575702i
$433$	12.7984	−	18.5416i	0.615050	−	0.891054i	−0.384434	−	0.923152i	$-0.625604\pi$
$433$	12.7984	−	18.5416i	0.615050	−	0.891054i	0.999485	+	0.0320981i	$0.0102189\pi$
$434$	0.522133	−	0.128694i	0.0250632	−	0.00617752i
$435$	7.29782	+	10.5727i	0.349904	+	0.506923i
$436$	−0.848438	+	6.98752i	−0.0406328	+	0.334641i
$437$	−18.2639			−0.873682
$438$	3.07257	−	25.3049i	0.146813	−	1.20911i
$439$	6.92238	+	18.2528i	0.330387	+	0.871160i	0.992554	+	0.121804i	$0.0388678\pi$
$439$	6.92238	+	18.2528i	0.330387	+	0.871160i	−0.662167	+	0.749356i	$0.730363\pi$
$440$	−11.0718	+	5.81092i	−0.527827	+	0.277025i
$441$	−0.276364	+	2.27606i	−0.0131602	+	0.108384i
$442$	−24.8181	+	8.00981i	−1.18048	+	0.380988i
$443$	−0.502316	−	4.13694i	−0.0238657	−	0.196552i	0.975899	−	0.218221i	$-0.0700252\pi$
$443$	−0.502316	−	4.13694i	−0.0238657	−	0.196552i	−0.999765	+	0.0216685i	$0.993102\pi$
$444$	0.305022	+	0.441900i	0.0144757	+	0.0209717i
$445$	−2.45739	+	3.56014i	−0.116491	+	0.168767i
$446$	−4.13481	+	3.66312i	−0.195789	+	0.173454i
$447$	−2.35222	−	6.20228i	−0.111256	−	0.293358i
$448$	1.19190	−	1.72677i	0.0563122	−	0.0815823i
$449$	−10.6867	−	5.60880i	−0.504335	−	0.264695i	0.193312	−	0.981137i	$-0.438077\pi$
$449$	−10.6867	−	5.60880i	−0.504335	−	0.264695i	−0.697647	+	0.716442i	$0.745769\pi$
$450$	−0.632295	+	5.20741i	−0.0298067	+	0.245480i
$451$	−7.30689	−	60.1777i	−0.344068	−	2.83366i
$452$	−1.52682	+	4.02590i	−0.0718157	+	0.189362i
$453$	3.43355	−	4.97436i	0.161322	−	0.233716i
$454$	−18.2881	−	16.2018i	−0.858303	−	0.760390i
$455$	0.552545	−	10.9748i	0.0259037	−	0.514506i
$456$	8.56106	−	7.58443i	0.400908	−	0.355174i
$457$	−4.05070	−	33.3605i	−0.189484	−	1.56054i	−0.708460	−	0.705751i	$-0.750610\pi$
$457$	−4.05070	−	33.3605i	−0.189484	−	1.56054i	0.518976	−	0.854789i	$-0.326313\pi$
$458$	3.10008	+	25.5315i	0.144857	+	1.19301i
$459$	3.69534	−	1.93947i	0.172484	−	0.0905265i
$460$	−3.44226	+	1.80664i	−0.160496	+	0.0842348i
$461$	−18.0781	−	4.45586i	−0.841983	−	0.207530i	−0.205342	−	0.978690i	$-0.565831\pi$
$461$	−18.0781	−	4.45586i	−0.841983	−	0.207530i	−0.636641	+	0.771160i	$0.719677\pi$
$462$	−14.5088	+	12.8536i	−0.675008	+	0.598005i
$463$	−9.32689	−	2.29887i	−0.433458	−	0.106838i	0.0165488	−	0.999863i	$-0.494732\pi$
$463$	−9.32689	−	2.29887i	−0.433458	−	0.106838i	−0.450006	+	0.893025i	$0.648578\pi$
$464$	16.2150	+	42.7554i	0.752762	+	1.98487i
$465$	−0.177885	+	0.0933613i	−0.00824922	+	0.00432953i
$466$	−0.450440	+	3.70971i	−0.0208662	+	0.171849i
$467$	17.1356	−	4.22355i	0.792941	−	0.195442i	0.178016	−	0.984028i	$-0.443032\pi$
$467$	17.1356	−	4.22355i	0.792941	−	0.195442i	0.614926	+	0.788585i	$0.289186\pi$
$468$	3.07776	−	1.90332i	0.142269	−	0.0879812i
$469$	−22.4940	−	5.54427i	−1.03868	−	0.256011i
$470$	−3.51069	+	9.25692i	−0.161936	+	0.426990i
$471$	7.00638	+	6.20711i	0.322837	+	0.286009i
$472$	−3.22774	+	0.795567i	−0.148569	+	0.0366190i
$473$	−10.6944	−	15.4935i	−0.491729	−	0.712393i
$474$	0.0220061	+	0.181236i	0.00101077	+	0.00832447i
$475$	7.10910	+	18.7452i	0.326188	+	0.860087i
$476$	−3.22255	+	8.49718i	−0.147706	+	0.389467i
$477$	0.251927	+	0.364979i	0.0115349	+	0.0167112i
$478$	19.3406	+	4.76703i	0.884618	+	0.218039i
$479$	6.83144	+	18.0130i	0.312137	+	0.823036i	0.995656	+	0.0931045i	$0.0296791\pi$
$479$	6.83144	+	18.0130i	0.312137	+	0.823036i	−0.683520	+	0.729932i	$0.739552\pi$
$480$	2.59620	−	6.84563i	0.118500	−	0.312459i
$481$	−1.53038	−	1.17420i	−0.0697795	−	0.0535390i
$482$	−18.8210	−	49.6269i	−0.857273	−	2.26044i
$483$	4.47795	−	3.96712i	0.203754	−	0.180510i
$484$	15.6305			0.710475
$485$	−13.8822			−0.630356
$486$	−1.29725	+	1.14926i	−0.0588444	+	0.0521316i
$487$	7.89915	−	4.14580i	0.357945	−	0.187864i	−0.276159	−	0.961112i	$-0.589062\pi$
$487$	7.89915	−	4.14580i	0.357945	−	0.187864i	0.634104	+	0.773248i	$0.281369\pi$
$488$	−25.7736			−1.16672
$489$	−2.23567	−	1.17337i	−0.101101	−	0.0530617i
$490$	4.17808	+	3.70146i	0.188747	+	0.167215i
$491$	13.4474	+	19.4819i	0.606872	+	0.879206i	0.999174	−	0.0406301i	$-0.0129365\pi$
$491$	13.4474	+	19.4819i	0.606872	+	0.879206i	−0.392302	+	0.919837i	$0.628321\pi$
$492$	8.83431	+	7.82651i	0.398281	+	0.352846i
$493$	21.6815	+	31.4110i	0.976484	+	1.41468i
$494$	21.0532	−	35.6352i	0.947229	−	1.60330i
$495$	4.11353	−	5.95947i	0.184889	−	0.267858i
$496$	−0.694292	+	0.171128i	−0.0311746	+	0.00768386i
$497$	20.2245	−	17.9174i	0.907195	−	0.803704i
$498$	18.9620	+	4.67372i	0.849709	+	0.209435i
$499$	6.54840	+	5.80137i	0.293147	+	0.259705i	0.796858	−	0.604167i	$-0.206494\pi$
$499$	6.54840	+	5.80137i	0.293147	+	0.259705i	−0.503711	+	0.863872i	$0.668032\pi$
$500$	8.47061	+	7.50430i	0.378817	+	0.335603i
$501$	−1.69530	+	4.47013i	−0.0757403	+	0.199711i
$502$	−24.0767	+	34.8811i	−1.07459	+	1.55682i
$503$	−2.25552	−	1.18379i	−0.100569	−	0.0527825i	0.413689	−	0.910418i	$-0.364240\pi$
$503$	−2.25552	−	1.18379i	−0.100569	−	0.0527825i	−0.514258	+	0.857636i	$0.671932\pi$
$504$	−0.451581	+	3.71911i	−0.0201150	+	0.165662i
$505$	−26.9460	−	6.64159i	−1.19908	−	0.295547i
$506$	−24.6348			−1.09515
$507$	−8.42207	+	9.90296i	−0.374037	+	0.439806i
$508$	−2.02881			−0.0900139
$509$	11.0336	+	2.71954i	0.489056	+	0.120541i	0.476130	−	0.879375i	$-0.342039\pi$
$509$	11.0336	+	2.71954i	0.489056	+	0.120541i	0.0129259	+	0.999916i	$0.495885\pi$
$510$	1.22469	−	10.0862i	0.0542300	−	0.446624i
$511$	28.2557	+	14.8297i	1.24996	+	0.656029i
$512$	4.99450	−	7.23579i	0.220728	−	0.319780i
$513$	−2.34877	+	6.19319i	−0.103701	+	0.273436i
$514$	−23.7188	−	21.0130i	−1.04619	−	0.926843i
$515$	−16.3083	−	14.4479i	−0.718628	−	0.636649i
$516$	3.55888	+	0.877184i	0.156671	+	0.0386159i
$517$	−15.6911	+	13.9011i	−0.690092	+	0.611368i
$518$	−1.95321	+	0.481423i	−0.0858191	+	0.0211525i
$519$	−0.603114	+	0.873761i	−0.0264738	+	0.0383539i
$520$	−0.439764	+	8.73471i	−0.0192849	+	0.383042i
$521$	17.2731	+	25.0244i	0.756748	+	1.09634i	0.992225	+	0.124458i	$0.0397193\pi$
$521$	17.2731	+	25.0244i	0.756748	+	1.09634i	−0.235477	+	0.971880i	$0.575665\pi$
$522$	−11.8639	−	10.5105i	−0.519267	−	0.460031i
$523$	2.07112	+	3.00053i	0.0905637	+	0.131204i	0.865647	−	0.500655i	$-0.166907\pi$
$523$	2.07112	+	3.00053i	0.0905637	+	0.131204i	−0.775083	+	0.631859i	$0.782292\pi$
$524$	−4.89898	−	4.34012i	−0.214013	−	0.189599i
$525$	−5.81466	−	3.05177i	−0.253773	−	0.133190i
$526$	−48.3728			−2.10916
$527$	−0.528488	+	0.277372i	−0.0230213	+	0.0120825i
$528$	19.2926	−	17.0918i	0.839604	−	0.743824i
$529$	−15.3968			−0.669425
$530$	1.07968			0.0468981
$531$	1.44102	−	1.27663i	0.0625349	−	0.0554011i
$532$	−5.11455	−	13.4860i	−0.221744	−	0.584690i
$533$	−38.8381	−	17.0095i	−1.68226	−	0.736763i
$534$	1.89258	−	4.99032i	0.0818999	−	0.215952i
$535$	−2.99135	−	7.88755i	−0.129327	−	0.341008i
$536$	17.9027	+	4.41262i	0.773279	+	0.190596i
$537$	11.7043	+	16.9567i	0.505080	+	0.731734i
$538$	8.45409	−	22.2916i	0.364482	−	0.961060i
$539$	4.19113	+	11.0511i	0.180525	+	0.476004i
$540$	0.169940	+	1.39958i	0.00731307	+	0.0602285i
$541$	−1.70704	−	2.47308i	−0.0733915	−	0.106326i	0.784569	−	0.620041i	$-0.212884\pi$
$541$	−1.70704	−	2.47308i	−0.0733915	−	0.106326i	−0.857961	+	0.513715i	$0.828269\pi$
$542$	19.9417	−	4.91519i	0.856570	−	0.211126i
$543$	3.46429	+	3.06909i	0.148667	+	0.131707i
$544$	7.71320	−	20.3380i	0.330701	−	0.871986i
$545$	9.56536	+	2.35765i	0.409735	+	0.100991i
$546$	2.57851	+	13.3100i	0.110350	+	0.569616i
$547$	6.78960	−	1.67349i	0.290302	−	0.0715531i	−0.0914751	−	0.995807i	$-0.529158\pi$
$547$	6.78960	−	1.67349i	0.290302	−	0.0715531i	0.381778	+	0.924254i	$0.375312\pi$
$548$	−0.0442500	+	0.364431i	−0.00189027	+	0.0155677i
$549$	13.2162	−	6.93642i	0.564055	−	0.296039i
$550$	9.58891	+	25.2839i	0.408873	+	1.07811i
$551$	−58.8154	−	14.4967i	−2.50562	−	0.617580i
$552$	−3.56395	+	3.15738i	−0.151692	+	0.134387i
$553$	−0.221909	−	0.0546956i	−0.00943651	−	0.00232589i
$554$	5.59164	−	2.93472i	0.237566	−	0.124684i
$555$	0.665437	−	0.349248i	0.0282462	−	0.0148248i
$556$	−2.55518	−	21.0438i	−0.108364	−	0.892455i
$557$	3.09349	+	25.4772i	0.131075	+	1.07950i	0.898688	+	0.438588i	$0.144521\pi$
$557$	3.09349	+	25.4772i	0.131075	+	1.07950i	−0.767613	+	0.640914i	$0.778556\pi$
$558$	0.185525	−	0.164361i	0.00785392	−	0.00695796i
$559$	−13.1349	+	0.927890i	−0.555545	+	0.0392456i
$560$	11.4062	+	10.1050i	0.482000	+	0.427015i
$561$	12.2211	−	17.7053i	0.515975	−	0.747519i
$562$	10.1786	−	26.8388i	0.429358	−	1.13212i
$563$	1.26119	+	10.3868i	0.0531527	+	0.437752i	0.994855	+	0.101305i	$0.0323019\pi$
$563$	1.26119	+	10.3868i	0.0531527	+	0.437752i	−0.941703	+	0.336446i	$0.890775\pi$
$564$	0.491965	−	4.05170i	0.0207155	−	0.170607i
$565$	5.33603	+	2.80056i	0.224488	+	0.117821i
$566$	29.9731	−	43.4235i	1.25986	−	1.82523i
$567$	−0.769356	−	2.02862i	−0.0323099	−	0.0851942i
$568$	−16.0965	+	14.2602i	−0.675393	+	0.598346i
$569$	−17.4588	+	25.2935i	−0.731912	+	1.06036i	0.263498	+	0.964660i	$0.415124\pi$
$569$	−17.4588	+	25.2935i	−0.731912	+	1.06036i	−0.995410	+	0.0956981i	$0.969492\pi$
$570$	9.16031	+	13.2710i	0.383683	+	0.555861i
$571$	2.13741	+	17.6031i	0.0894477	+	0.736668i	0.966570	+	0.256401i	$0.0825369\pi$
$571$	2.13741	+	17.6031i	0.0894477	+	0.736668i	−0.877123	+	0.480266i	$0.840540\pi$
$572$	9.48872	−	16.0608i	0.396743	−	0.671538i
$573$	−2.92017	+	24.0498i	−0.121992	+	1.00469i
$574$	−39.1529	+	20.5490i	−1.63421	+	0.857699i
$575$	−2.95950	−	7.80356i	−0.123420	−	0.325431i
$576$	0.116568	−	0.960026i	0.00485701	−	0.0400011i
$577$	5.18422			0.215822			0.107911	−	0.994161i	$-0.465584\pi$
$577$	5.18422			0.215822			0.107911	+	0.994161i	$0.465584\pi$
$578$	0.0871332	−	0.717607i	0.00362427	−	0.0298485i
$579$	−2.35729	−	3.41513i	−0.0979658	−	0.141928i
$580$	−12.5191	+	3.08568i	−0.519828	+	0.128126i
$581$	−13.8882	+	20.1206i	−0.576181	+	0.834742i
$582$	16.6296	−	4.09884i	0.689321	−	0.169902i
$583$	2.02427	+	1.06242i	0.0838366	+	0.0440008i
$584$	−22.4884	−	11.8028i	−0.930576	−	0.488404i
$585$	−2.12526	−	4.59735i	−0.0878686	−	0.190077i
$586$	26.2927	−	13.7995i	1.08614	−	0.570051i
$587$	−42.9071			−1.77096			−0.885482	−	0.464674i	$-0.846172\pi$
$587$	−42.9071			−1.77096			−0.885482	+	0.464674i	$0.846172\pi$
$588$	−2.03758	−	1.06940i	−0.0840282	−	0.0441014i
$589$	0.335908	−	0.885716i	0.0138408	−	0.0364953i
$590$	−0.564948	−	4.65276i	−0.0232585	−	0.191551i
$591$	−16.0452	+	3.95479i	−0.660012	+	0.162678i
$592$	2.59723	−	0.640159i	0.106745	−	0.0263104i
$593$	1.31837	+	10.8577i	0.0541388	+	0.445873i	0.994422	+	0.105479i	$0.0336375\pi$
$593$	1.31837	+	10.8577i	0.0541388	+	0.445873i	−0.940283	+	0.340394i	$0.889439\pi$
$594$	−3.16807	+	8.35350i	−0.129987	+	0.342748i
$595$	11.2624	+	5.91094i	0.461712	+	0.242325i
$596$	6.65760			0.272706
$597$	−17.2716	+	9.06481i	−0.706878	+	0.370998i
$598$	−8.76440	+	14.8348i	−0.358403	+	0.606642i
$599$	8.47172	+	4.44630i	0.346145	+	0.181671i	0.628832	−	0.777541i	$-0.283533\pi$
$599$	8.47172	+	4.44630i	0.346145	+	0.181671i	−0.282687	+	0.959212i	$0.591226\pi$
$600$	4.62782	+	2.42887i	0.188930	+	0.0991580i
$601$	28.3718	−	6.99303i	1.15731	−	0.285251i	0.386484	−	0.922296i	$-0.373690\pi$
$601$	28.3718	−	6.99303i	1.15731	−	0.285251i	0.770827	+	0.637045i	$0.219843\pi$
$602$	−7.80081	+	11.3014i	−0.317937	+	0.460612i
$603$	−10.3677	+	2.55542i	−0.422207	+	0.104065i
$604$	3.44611	+	4.99255i	0.140220	+	0.203144i
$605$	2.63692	−	21.7170i	0.107206	−	0.882923i
$606$	34.2400			1.39091
$607$	3.16864	−	26.0961i	0.128611	−	1.05921i	−0.775331	−	0.631555i	$-0.782417\pi$
$607$	3.16864	−	26.0961i	0.128611	−	1.05921i	0.903942	−	0.427654i	$-0.140660\pi$
$608$	12.2417	+	32.2787i	0.496466	+	1.30907i
$609$	17.5692	−	9.22103i	0.711940	−	0.373655i
$610$	4.38003	−	36.0728i	0.177342	−	1.46055i
$611$	2.78863	+	14.3947i	0.112816	+	0.582345i
$612$	0.504885	+	4.15810i	0.0204088	+	0.168081i
$613$	8.12828	+	11.7758i	0.328298	+	0.475622i	0.952025	−	0.306020i	$-0.0989976\pi$
$613$	8.12828	+	11.7758i	0.328298	+	0.475622i	−0.623727	+	0.781642i	$0.714382\pi$
$614$	−1.81302	+	2.62662i	−0.0731677	+	0.106002i
$615$	12.3646	−	10.9541i	0.498588	−	0.441710i
$616$	6.84835	+	18.0576i	0.275928	+	0.727562i
$617$	1.86131	−	2.69657i	0.0749335	−	0.108560i	−0.783725	−	0.621108i	$-0.786683\pi$
$617$	1.86131	−	2.69657i	0.0749335	−	0.108560i	0.858659	+	0.512548i	$0.171298\pi$
$618$	23.8018	+	12.4921i	0.957448	+	0.502508i
$619$	−1.22983	+	10.1286i	−0.0494312	+	0.407103i	0.946900	+	0.321527i	$0.104196\pi$
$619$	−1.22983	+	10.1286i	−0.0494312	+	0.407103i	−0.996332	+	0.0855759i	$0.972727\pi$
$620$	−0.0243039	−	0.200161i	−0.000976070	−	0.00803866i
$621$	0.977785	−	2.57821i	0.0392372	−	0.103460i
$622$	−21.9759	+	31.8376i	−0.881154	+	1.27657i
$623$	5.00109	+	4.43058i	0.200364	+	0.177507i
$624$	−3.42871	−	17.6987i	−0.137258	−	0.708513i
$625$	0.527812	−	0.467600i	0.0211125	−	0.0187040i
$626$	5.56386	+	45.8225i	0.222377	+	1.83144i
$627$	4.11565	+	33.8955i	0.164363	+	1.35365i
$628$	−8.31856	+	4.36592i	−0.331947	+	0.174219i
$629$	1.97698	−	1.03760i	0.0788274	−	0.0413718i
$630$	−5.12853	−	1.26407i	−0.204326	−	0.0503617i
$631$	−9.73293	+	8.62263i	−0.387462	+	0.343261i	−0.834258	−	0.551375i	$-0.814104\pi$
$631$	−9.73293	+	8.62263i	−0.387462	+	0.343261i	0.446796	+	0.894636i	$0.352565\pi$
$632$	0.176614	+	0.0435315i	0.00702534	+	0.00173159i
$633$	2.90227	+	7.65266i	0.115355	+	0.304166i
$634$	−6.18983	+	3.24868i	−0.245830	+	0.129021i
$635$	−0.342269	+	2.81884i	−0.0135825	+	0.111862i
$636$	−0.432170	+	0.106520i	−0.0171367	+	0.00422381i
$637$	8.14596	+	1.40783i	0.322755	+	0.0557802i
$638$	−79.3315	−	19.5535i	−3.14076	−	0.774129i
$639$	4.41614	−	11.6444i	0.174700	−	0.460646i
$640$	−12.7226	−	11.2712i	−0.502904	−	0.445534i
$641$	30.7271	−	7.57355i	1.21365	−	0.299137i	0.420005	−	0.907522i	$-0.362028\pi$
$641$	30.7271	−	7.57355i	1.21365	−	0.299137i	0.793642	+	0.608385i	$0.208182\pi$
$642$	5.91226	+	8.56539i	0.233338	+	0.338049i
$643$	3.19591	+	26.3207i	0.126034	+	1.03799i	0.909254	+	0.416241i	$0.136653\pi$
$643$	3.19591	+	26.3207i	0.126034	+	1.03799i	−0.783220	+	0.621745i	$0.786424\pi$
$644$	2.12917	+	5.61417i	0.0839012	+	0.221229i
$645$	1.81916	−	4.79674i	0.0716294	−	0.188871i
$646$	27.2149	+	39.4275i	1.07075	+	1.55126i
$647$	3.05871	+	0.753905i	0.120250	+	0.0296391i	0.298982	−	0.954259i	$-0.403353\pi$
$647$	3.05871	+	0.753905i	0.120250	+	0.0296391i	−0.178731	+	0.983898i	$0.557199\pi$
$648$	0.612321	+	1.61456i	0.0240542	+	0.0634258i
$649$	3.51917	−	9.27930i	0.138140	−	0.364244i
$650$	18.6372	+	3.22098i	0.731012	+	0.126337i
$651$	0.110029	+	0.290123i	0.00431238	+	0.0113708i
$652$	1.89681	−	1.68043i	0.0742850	−	0.0658108i
$653$	15.3999			0.602645			0.301322	−	0.953522i	$-0.402572\pi$
$653$	15.3999			0.602645			0.301322	+	0.953522i	$0.402572\pi$
$654$	−12.1546			−0.475283
$655$	−6.85666	+	6.07447i	−0.267912	+	0.237349i
$656$	52.0625	−	27.3245i	2.03270	−	1.06684i
$657$	14.7081			0.573818
$658$	13.5396	+	7.10611i	0.527827	+	0.277025i
$659$	26.8823	+	23.8157i	1.04719	+	0.927727i	0.997474	−	0.0710365i	$-0.0226307\pi$
$659$	26.8823	+	23.8157i	1.04719	+	0.927727i	0.0497136	+	0.998764i	$0.484169\pi$
$660$	4.12857	+	5.98127i	0.160704	+	0.232820i
$661$	−16.1250	−	14.2855i	−0.627191	−	0.555643i	0.288523	−	0.957473i	$-0.406836\pi$
$661$	−16.1250	−	14.2855i	−0.627191	−	0.555643i	−0.915714	+	0.401830i	$0.868374\pi$
$662$	21.8379	+	31.6377i	0.848756	+	1.22964i
$663$	−6.31404	−	13.6585i	−0.245217	−	0.530453i
$664$	11.0535	−	16.0137i	0.428958	−	0.621453i
$665$	−19.6003	+	4.83104i	−0.760067	+	0.187340i
$666$	−0.694018	+	0.614847i	−0.0268927	+	0.0238248i
$667$	24.4847	+	6.03494i	0.948052	+	0.233674i
$668$	−3.59157	−	3.18185i	−0.138962	−	0.123110i
$669$	−2.38578	−	2.11361i	−0.0922395	−	0.0817170i
$670$	−9.21835	+	24.3068i	−0.356136	+	0.939053i
$671$	43.7082	−	63.3223i	1.68734	−	2.44453i
$672$	−10.0127	−	5.25507i	−0.386248	−	0.202719i
$673$	−3.80270	+	31.3181i	−0.146583	+	1.20722i	0.714822	+	0.699306i	$0.246508\pi$
$673$	−3.80270	+	31.3181i	−0.146583	+	1.20722i	−0.861406	+	0.507917i	$0.830415\pi$
$674$	−6.12692	−	1.51015i	−0.236000	−	0.0581688i
$675$	−3.02674			−0.116499
$676$	−6.29586	−	11.4281i	−0.242149	−	0.439540i
$677$	−18.7891			−0.722125			−0.361063	−	0.932542i	$-0.617586\pi$
$677$	−18.7891			−0.722125			−0.361063	+	0.932542i	$0.617586\pi$
$678$	−7.21900	−	1.77932i	−0.277244	−	0.0683345i
$679$	−2.58444	+	21.2848i	−0.0991817	+	0.816835i
$680$	−8.96358	−	4.70445i	−0.343737	−	0.180407i
$681$	8.00835	−	11.6021i	0.306881	−	0.444593i
$682$	0.453080	−	1.19467i	0.0173493	−	0.0457464i
$683$	−22.4434	−	19.8831i	−0.858773	−	0.760806i	0.113776	−	0.993506i	$-0.463705\pi$
$683$	−22.4434	−	19.8831i	−0.858773	−	0.760806i	−0.972548	+	0.232700i	$0.925244\pi$
$684$	−4.97598	−	4.40833i	−0.190261	−	0.168557i
$685$	0.498878	+	0.122962i	0.0190611	+	0.00469815i
$686$	26.1548	−	23.1711i	0.998594	−	0.884677i
$687$	−14.4086	+	3.55140i	−0.549722	+	0.135494i
$688$	10.3729	−	15.0278i	0.395464	−	0.572929i
$689$	1.35996	−	0.841015i	0.0518103	−	0.0320401i
$690$	−3.81341	−	5.52468i	−0.145174	−	0.210321i
$691$	30.7462	+	27.2388i	1.16964	+	1.03621i	0.998702	+	0.0509311i	$0.0162189\pi$
$691$	30.7462	+	27.2388i	1.16964	+	1.03621i	0.170940	+	0.985281i	$0.445320\pi$
$692$	−0.605319	−	0.876956i	−0.0230108	−	0.0333369i
$693$	−8.37153	−	7.41653i	−0.318008	−	0.281731i
$694$	−16.2767	−	8.54265i	−0.617853	−	0.324274i
$695$	−29.6694			−1.12542
$696$	−13.9831	+	7.33891i	−0.530029	+	0.278181i
$697$	36.7346	−	32.5440i	1.39142	−	1.23269i
$698$	41.9175			1.58660
$699$	−2.15622			−0.0815557
$700$	4.93334	−	4.37055i	0.186463	−	0.165191i
$701$	−8.37619	−	22.0862i	−0.316364	−	0.834184i	−0.995015	−	0.0997231i	$-0.968204\pi$
$701$	−8.37619	−	22.0862i	−0.316364	−	0.834184i	0.678651	−	0.734461i	$-0.262565\pi$
$702$	3.90329	+	4.87974i	0.147320	+	0.184174i
$703$	−1.25657	+	3.31331i	−0.0473925	+	0.124964i
$704$	−1.76779	−	4.66127i	−0.0666260	−	0.175678i
$705$	−5.54645	−	1.36708i	−0.208892	−	0.0514871i
$706$	6.22986	+	9.02550i	0.234464	+	0.339679i
$707$	−15.1997	+	40.0784i	−0.571645	+	1.50730i
$708$	0.685175	+	1.80666i	0.0257505	+	0.0678984i
$709$	−2.73372	−	22.5142i	−0.102667	−	0.845539i	−0.949519	−	0.313710i	$-0.898428\pi$
$709$	−2.73372	−	22.5142i	−0.102667	−	0.845539i	0.846852	−	0.531829i	$-0.178495\pi$
$710$	−17.2232	−	24.9521i	−0.646375	−	0.936435i
$711$	−0.102280	+	0.0252098i	−0.00383581	+	0.000945442i
$712$	−3.98030	−	3.52624i	−0.149168	−	0.132151i
$713$	−0.139838	+	0.368721i	−0.00523696	+	0.0138087i
$714$	−15.2366	−	3.75549i	−0.570216	−	0.140546i
$715$	−20.7142	−	15.8932i	−0.774668	−	0.594373i
$716$	−20.0783	+	4.94886i	−0.750363	+	0.184948i
$717$	−1.38539	+	11.4097i	−0.0517382	+	0.426102i
$718$	−12.3793	+	6.49714i	−0.461990	+	0.242471i
$719$	−1.15217	−	3.03803i	−0.0429688	−	0.113299i	0.911814	−	0.410603i	$-0.134682\pi$
$719$	−1.15217	−	3.03803i	−0.0429688	−	0.113299i	−0.954783	+	0.297304i	$0.903913\pi$
$720$	6.81953	+	1.68086i	0.254149	+	0.0626420i
$721$	−25.1882	+	22.3148i	−0.938059	+	0.831048i
$722$	−41.8537	−	10.3160i	−1.55763	−	0.383922i
$723$	27.1169	−	14.2320i	1.00849	−	0.529295i
$724$	−4.11309	+	2.15871i	−0.152862	+	0.0802280i
$725$	−3.33655	−	27.4789i	−0.123916	−	1.02054i
$726$	3.25335	+	26.7937i	0.120743	+	0.994409i
$727$	−3.28537	+	2.91059i	−0.121848	+	0.107948i	−0.721846	−	0.692053i	$-0.756706\pi$
$727$	−3.28537	+	2.91059i	−0.121848	+	0.107948i	0.599999	+	0.800001i	$0.295168\pi$
$728$	13.3106	+	2.30041i	0.493323	+	0.0852587i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	20.3410	−	29.4690i	0.752854	−	1.09070i
$731$	5.40464	−	14.2509i	0.199898	−	0.527088i
$732$	1.80570	+	14.8713i	0.0667405	+	0.549658i
$733$	−5.80699	+	47.8249i	−0.214486	+	1.76645i	0.345949	+	0.938253i	$0.387557\pi$
$733$	−5.80699	+	47.8249i	−0.214486	+	1.76645i	−0.560435	+	0.828199i	$0.689366\pi$
$734$	−30.8306	−	16.1811i	−1.13798	−	0.597256i
$735$	−1.82958	+	2.65061i	−0.0674851	+	0.0977691i
$736$	−5.09619	−	13.4375i	−0.187848	−	0.495314i
$737$	−41.2015	+	36.5014i	−1.51768	+	1.34455i
$738$	−11.5774	+	16.7728i	−0.426171	+	0.617415i
$739$	11.3426	+	16.4326i	0.417245	+	0.604484i	0.974098	−	0.226128i	$-0.0726066\pi$
$739$	11.3426	+	16.4326i	0.417245	+	0.604484i	−0.556853	+	0.830611i	$0.687991\pi$
$740$	0.0909169	+	0.748768i	0.00334217	+	0.0275252i
$741$	21.8758	+	9.58070i	0.803627	+	0.351956i
$742$	0.201003	−	1.65541i	0.00737906	−	0.0607720i
$743$	3.15792	−	1.65740i	0.115853	−	0.0608042i	−0.405801	−	0.913961i	$-0.633007\pi$
$743$	3.15792	−	1.65740i	0.115853	−	0.0608042i	0.521654	+	0.853157i	$0.325315\pi$
$744$	−0.0875708	−	0.230905i	−0.00321050	−	0.00846539i
$745$	1.12317	−	9.25010i	0.0411496	−	0.338898i
$746$	22.4905			0.823437
$747$	−1.35827	+	11.1864i	−0.0496965	+	0.409287i
$748$	12.2658	+	17.7701i	0.448482	+	0.649738i
$749$	−12.6505	+	3.11806i	−0.462238	+	0.113931i
$750$	−11.1008	+	16.0823i	−0.405344	+	0.587242i
$751$	−23.7019	+	5.84200i	−0.864896	+	0.213178i	−0.646716	−	0.762731i	$-0.723858\pi$
$751$	−23.7019	+	5.84200i	−0.864896	+	0.213178i	−0.218180	+	0.975909i	$0.570012\pi$
$752$	−18.0039	−	9.44916i	−0.656534	−	0.344575i
$753$	−21.6541	−	11.3650i	−0.789119	−	0.414162i
$754$	−39.9990	+	40.8161i	−1.45668	+	1.48644i
$755$	7.51804	−	3.94577i	0.273610	−	0.143601i
$756$	2.17755			0.0791966
$757$	−29.9223	−	15.7045i	−1.08755	−	0.570788i	−0.177006	−	0.984210i	$-0.556641\pi$
$757$	−29.9223	−	15.7045i	−1.08755	−	0.570788i	−0.910540	+	0.413422i	$0.864334\pi$
$758$	−1.85608	+	4.89407i	−0.0674157	+	0.177761i
$759$	−1.71334	−	14.1106i	−0.0621901	−	0.512182i
$760$	15.5996	−	3.84497i	0.565859	−	0.139472i
$761$	22.2751	−	5.49033i	0.807473	−	0.199024i	0.186092	−	0.982532i	$-0.440418\pi$
$761$	22.2751	−	5.49033i	0.807473	−	0.199024i	0.621382	+	0.783508i	$0.286572\pi$
$762$	−0.422280	−	3.47779i	−0.0152976	−	0.125987i
$763$	5.39564	−	14.2271i	0.195335	−	0.515057i
$764$	−21.5299	−	11.2997i	−0.778923	−	0.408810i
$765$	5.86246			0.211958
$766$	−47.2086	+	24.7770i	−1.70572	+	0.895230i
$767$	−4.33588	−	5.42055i	−0.156560	−	0.195725i
$768$	16.8559	+	8.84666i	0.608235	+	0.319226i
$769$	15.6546	+	8.21619i	0.564521	+	0.296283i	0.722739	−	0.691121i	$-0.242883\pi$
$769$	15.6546	+	8.21619i	0.564521	+	0.296283i	−0.158219	+	0.987404i	$0.550575\pi$
$770$	−26.4373	+	6.51621i	−0.952735	+	0.234828i
$771$	10.3864	−	15.0474i	0.374058	−	0.541917i
$772$	4.04384	−	0.996718i	0.145541	−	0.0358727i
$773$	−4.68543	−	6.78802i	−0.168523	−	0.244148i	0.729618	−	0.683855i	$-0.239698\pi$
$773$	−4.68543	−	6.78802i	−0.168523	−	0.244148i	−0.898141	+	0.439707i	$0.855082\pi$
$774$	−0.762920	+	6.28321i	−0.0274226	+	0.225845i
$775$	0.432868			0.0155491
$776$	2.05692	−	16.9403i	0.0738392	−	0.608121i
$777$	−0.411600	−	1.08530i	−0.0147661	−	0.0389349i
$778$	15.8433	−	8.31519i	0.568009	−	0.298114i
$779$	−9.38866	+	77.3226i	−0.336384	+	2.77037i
$780$	5.07070	−	0.358211i	0.181560	−	0.0128260i
$781$	−7.73824	−	63.7301i	−0.276896	−	2.28044i
$782$	−11.3295	−	16.4136i	−0.405141	−	0.586948i
$783$	5.19518	−	7.52652i	0.185661	−	0.268976i
$784$	−8.58082	+	7.60194i	−0.306458	+	0.271498i
$785$	4.66265	+	12.2944i	0.166417	+	0.438806i
$786$	6.42016	−	9.30120i	0.228999	−	0.331763i
$787$	−27.5673	−	14.4685i	−0.982670	−	0.515745i	−0.104722	−	0.994502i	$-0.533395\pi$
$787$	−27.5673	−	14.4685i	−0.982670	−	0.515745i	−0.877948	+	0.478757i	$0.841088\pi$
$788$	1.99920	−	16.4649i	0.0712187	−	0.586538i
$789$	−3.36431	−	27.7076i	−0.119772	−	0.986415i
$790$	−0.0909412	+	0.239792i	−0.00323554	+	0.00853142i
$791$	5.28736	−	7.66007i	0.187997	−	0.272361i
$792$	6.66280	+	5.90272i	0.236752	+	0.209744i
$793$	−22.5819	−	48.8491i	−0.801906	−	1.73468i
$794$	−1.84887	+	1.63795i	−0.0656138	+	0.0581288i
$795$	0.0750910	+	0.618430i	0.00266320	+	0.0219334i
$796$	−2.35977	−	19.4344i	−0.0836397	−	0.688835i
$797$	−19.7966	+	10.3900i	−0.701230	+	0.368034i	−0.777353	−	0.629064i	$-0.783438\pi$
$797$	−19.7966	+	10.3900i	−0.701230	+	0.368034i	0.0761228	+	0.997098i	$0.475746\pi$
$798$	22.0531	−	11.5744i	0.780671	−	0.409728i
$799$	−16.4783	−	4.06152i	−0.582959	−	0.143686i
$800$	−11.8080	+	10.4609i	−0.417475	+	0.369850i
$801$	2.99004	+	0.736979i	0.105648	+	0.0260399i
$802$	−12.4660	−	32.8702i	−0.440191	−	1.16069i
$803$	67.1349	−	35.2351i	2.36914	−	1.24342i
$804$	1.29180	−	10.6389i	0.0455583	−	0.375206i
$805$	8.15956	−	2.01115i	0.287587	−	0.0708837i
$806$	−0.558228	−	0.697874i	−0.0196627	−	0.0245816i
$807$	13.3564	+	3.29206i	0.470169	+	0.115886i
$808$	12.0973	−	31.8979i	0.425581	−	1.12216i
$809$	33.4589	+	29.6420i	1.17635	+	1.04216i	0.998309	+	0.0581361i	$0.0185157\pi$
$809$	33.4589	+	29.6420i	1.17635	+	1.04216i	0.178045	+	0.984022i	$0.443023\pi$
$810$	−2.36380	+	0.582624i	−0.0830554	+	0.0204713i
$811$	−12.5932	−	18.2444i	−0.442208	−	0.640649i	0.536982	−	0.843594i	$-0.319564\pi$
$811$	−12.5932	−	18.2444i	−0.442208	−	0.640649i	−0.979190	+	0.202945i	$0.934949\pi$
$812$	2.40043	+	19.7693i	0.0842387	+	0.693768i
$813$	4.20232	+	11.0806i	0.147382	+	0.388614i
$814$	−1.69489	+	4.46906i	−0.0594059	+	0.156641i
$815$	−2.01480	−	2.91894i	−0.0705753	−	0.102246i
$816$	20.2605	+	4.99376i	0.709259	+	0.174817i
$817$	8.57777	+	22.6177i	0.300098	+	0.791294i
$818$	−12.0888	+	31.8756i	−0.422676	+	1.11450i
$819$	−7.44454	+	2.40266i	−0.260133	+	0.0839556i
$820$	5.87911	+	15.5019i	0.205307	+	0.541351i
$821$	26.0927	−	23.1161i	0.910642	−	0.806759i	−0.0710026	−	0.997476i	$-0.522620\pi$
$821$	26.0927	−	23.1161i	0.910642	−	0.806759i	0.981645	+	0.190717i	$0.0610814\pi$
$822$	−0.633919			−0.0221105
$823$	−46.7364			−1.62913			−0.814565	−	0.580073i	$-0.803024\pi$
$823$	−46.7364			−1.62913			−0.814565	+	0.580073i	$0.803024\pi$
$824$	20.0470	−	17.7601i	0.698371	−	0.618702i
$825$	−13.8155	+	7.25093i	−0.480994	+	0.252445i
$826$	−7.23901			−0.251877
$827$	9.35317	+	4.90892i	0.325242	+	0.170700i	0.619439	−	0.785045i	$-0.287360\pi$
$827$	9.35317	+	4.90892i	0.325242	+	0.170700i	−0.294198	+	0.955745i	$0.595052\pi$
$828$	2.07149	+	1.83518i	0.0719891	+	0.0637768i
$829$	−0.152617	−	0.221104i	−0.00530062	−	0.00767927i	0.820325	−	0.571898i	$-0.193793\pi$
$829$	−0.152617	−	0.221104i	−0.00530062	−	0.00767927i	−0.825625	+	0.564219i	$0.809177\pi$
$830$	20.5344	+	18.1919i	0.712760	+	0.631450i
$831$	2.06988	+	2.99874i	0.0718033	+	0.104025i
$832$	−3.43591	−	0.593812i	−0.119119	−	0.0205867i
$833$	−5.43560	+	7.87483i	−0.188332	+	0.272847i
$834$	35.5414	−	8.76018i	1.23070	−	0.303340i
$835$	−5.02679	+	4.45335i	−0.173959	+	0.154115i
$836$	−33.2735	−	8.20117i	−1.15079	−	0.283643i
$837$	0.107048	+	0.0948362i	0.00370012	+	0.00327802i
$838$	−6.00998	−	5.32437i	−0.207611	−	0.183927i
$839$	−10.4828	+	27.6408i	−0.361906	+	0.954267i	0.623161	+	0.782094i	$0.285848\pi$
$839$	−10.4828	+	27.6408i	−0.361906	+	0.954267i	−0.985067	+	0.172174i	$0.944921\pi$
$840$	−2.98956	+	4.33112i	−0.103149	+	0.149438i
$841$	48.3799	+	25.3917i	1.66827	+	0.875577i
$842$	3.52154	−	29.0025i	0.121360	−	0.999492i
$843$	16.0809	+	3.96359i	0.553857	+	0.136513i
$844$	−8.21445			−0.282753
$845$	−16.9403	+	6.81954i	−0.582765	+	0.234599i
$846$	7.04783			0.242309
$847$	−32.8067	−	8.08611i	−1.12725	−	0.277842i
$848$	−0.267279	+	2.20124i	−0.00917839	+	0.0755908i
$849$	26.9572	+	14.1483i	0.925170	+	0.485567i
$850$	−12.4362	+	18.0169i	−0.426556	+	0.617974i
$851$	0.523108	−	1.37932i	0.0179319	−	0.0472826i
$852$	9.35581	+	8.28853i	0.320525	+	0.283960i
$853$	6.39714	+	5.66737i	0.219034	+	0.194047i	0.765503	−	0.643432i	$-0.222490\pi$
$853$	6.39714	+	5.66737i	0.219034	+	0.194047i	−0.546469	+	0.837479i	$0.684029\pi$
$854$	−54.4931	−	13.4313i	−1.86472	−	0.459611i
$855$	−6.96443	+	6.16994i	−0.238178	+	0.211008i
$856$	10.0683	−	2.48162i	0.344129	−	0.0848201i
$857$	0.310066	−	0.449209i	0.0105917	−	0.0153447i	−0.817652	−	0.575712i	$-0.804725\pi$
$857$	0.310066	−	0.449209i	0.0105917	−	0.0153447i	0.828244	+	0.560368i	$0.189340\pi$
$858$	29.5065	+	12.9227i	1.00734	+	0.441172i
$859$	8.56980	+	12.4155i	0.292398	+	0.423611i	0.941460	−	0.337124i	$-0.109454\pi$
$859$	8.56980	+	12.4155i	0.292398	+	0.423611i	−0.649063	+	0.760735i	$0.724839\pi$
$860$	3.85398	+	3.41433i	0.131420	+	0.116428i
$861$	−14.4934	−	20.9973i	−0.493933	−	0.715585i
$862$	−22.1358	−	19.6106i	−0.753947	−	0.667938i
$863$	9.24184	+	4.85049i	0.314596	+	0.165113i	0.614629	−	0.788816i	$-0.289306\pi$
$863$	9.24184	+	4.85049i	0.314596	+	0.165113i	−0.300034	+	0.953929i	$0.596998\pi$
$864$	−5.21197			−0.177315
$865$	−1.32057	+	0.693087i	−0.0449007	+	0.0235657i
$866$	−29.2267	+	25.8926i	−0.993164	+	0.879867i
$867$	0.417099			0.0141654
$868$	−0.311421			−0.0105703
$869$	−0.406463	+	0.360095i	−0.0137883	+	0.0122154i
$870$	−7.89523	−	20.8180i	−0.267673	−	0.705797i
$871$	7.32239	+	37.7974i	0.248110	+	1.28072i
$872$	−4.29432	+	11.3232i	−0.145424	+	0.383452i
$873$	3.50437	+	9.24025i	0.118605	+	0.312735i
$874$	30.7335	+	7.57513i	1.03958	+	0.256233i
$875$	−13.8967	−	20.1328i	−0.469794	−	0.680614i
$876$	−5.23464	+	13.8026i	−0.176862	+	0.466347i
$877$	−11.9620	−	31.5413i	−0.403930	−	1.06507i	−0.970508	−	0.241067i	$-0.922503\pi$
$877$	−11.9620	−	31.5413i	−0.403930	−	1.06507i	0.566579	−	0.824007i	$-0.308267\pi$
$878$	−4.07808	−	33.5860i	−0.137628	−	1.13347i
$879$	9.73287	+	14.1005i	0.328281	+	0.475598i
$880$	35.1543	−	8.66476i	1.18505	−	0.292089i
$881$	−23.9482	−	21.2163i	−0.806836	−	0.714794i	0.155151	−	0.987891i	$-0.450414\pi$
$881$	−23.9482	−	21.2163i	−0.806836	−	0.714794i	−0.961987	+	0.273096i	$0.911952\pi$
$882$	1.40907	−	3.71540i	0.0474457	−	0.125104i
$883$	47.2974	+	11.6578i	1.59168	+	0.392315i	0.932934	−	0.360047i	$-0.117239\pi$
$883$	47.2974	+	11.6578i	1.59168	+	0.392315i	0.658750	+	0.752362i	$0.271085\pi$
$884$	15.0648	−	1.06423i	0.506685	−	0.0357939i
$885$	2.62577	−	0.647195i	0.0882644	−	0.0217552i
$886$	−0.870566	+	7.16976i	−0.0292472	+	0.240873i
$887$	7.09056	−	3.72141i	0.238078	−	0.124953i	−0.341466	−	0.939894i	$-0.610923\pi$
$887$	7.09056	−	3.72141i	0.238078	−	0.124953i	0.579543	+	0.814941i	$0.303231\pi$
$888$	0.327587	+	0.863776i	0.0109931	+	0.0289864i
$889$	4.25826	+	1.04957i	0.142817	+	0.0352013i
$890$	5.61176	−	4.97159i	0.188107	−	0.166648i
$891$	−5.00516	−	1.23366i	−0.167679	−	0.0413292i
$892$	2.83259	−	1.48666i	0.0948422	−	0.0497770i
$893$	23.8502	−	12.5176i	0.798117	−	0.418884i
$894$	1.38572	+	11.4125i	0.0463455	+	0.381690i
$895$	3.48868	+	28.7318i	0.116614	+	0.960399i
$896$	−19.6501	+	17.4085i	−0.656465	+	0.581577i
$897$	−9.10683	−	3.98842i	−0.304068	−	0.133169i
$898$	15.6566	+	13.8706i	0.522469	+	0.462867i
$899$	−0.742987	+	1.07640i	−0.0247800	+	0.0359000i
$900$	1.07722	−	2.84040i	0.0359074	−	0.0946800i
$901$	0.223092	+	1.83733i	0.00743226	+	0.0612102i
$902$	−12.6636	+	104.294i	−0.421653	+	3.47262i
$903$	−7.01591	−	3.68223i	−0.233475	−	0.122537i
$904$	−4.20815	+	6.09655i	−0.139961	+	0.202768i
$905$	2.30543	+	6.07893i	0.0766352	+	0.202070i
$906$	−7.84095	+	6.94648i	−0.260498	+	0.230781i
$907$	3.83874	−	5.56138i	0.127463	−	0.184663i	−0.754056	−	0.656810i	$-0.771906\pi$
$907$	3.83874	−	5.56138i	0.127463	−	0.184663i	0.881520	+	0.472147i	$0.156521\pi$
$908$	8.03764	+	11.6445i	0.266738	+	0.386437i
$909$	2.38138	+	19.6124i	0.0789853	+	0.650502i
$910$	−5.48169	+	18.2386i	−0.181716	+	0.604604i
$911$	3.89378	−	32.0681i	0.129007	−	1.06246i	−0.774105	−	0.633058i	$-0.781800\pi$
$911$	3.89378	−	32.0681i	0.129007	−	1.06246i	0.903111	−	0.429407i	$-0.141277\pi$
$912$	−29.3245	+	15.3907i	−0.971032	+	0.509637i
$913$	20.5985	+	54.3138i	0.681711	+	1.79752i
$914$	−7.02030	+	57.8174i	−0.232211	+	1.91243i
$915$	20.9668			0.693142
$916$	1.79528	−	14.7855i	0.0593178	−	0.488526i
$917$	8.03716	+	11.6438i	0.265411	+	0.384514i
$918$	−7.02273	+	1.73095i	−0.231785	+	0.0571298i
$919$	8.84009	−	12.8071i	0.291608	−	0.422467i	−0.649610	−	0.760268i	$-0.725068\pi$
$919$	8.84009	−	12.8071i	0.291608	−	0.422467i	0.941218	+	0.337801i	$0.109683\pi$
$920$	−6.49409	+	1.60065i	−0.214104	+	0.0527719i
$921$	−1.63060	−	0.855805i	−0.0537301	−	0.0281997i
$922$	28.5728	+	14.9962i	0.940994	+	0.493872i
$923$	−41.1308	−	18.0136i	−1.35384	−	0.592925i
$924$	9.93937	−	5.21659i	0.326981	−	0.171613i
$925$	−1.61928			−0.0532417
$926$	14.7413	+	7.73684i	0.484429	+	0.254248i
$927$	−5.49999	+	14.5023i	−0.180643	+	0.476318i
$928$	−5.74545	−	47.3180i	−0.188604	−	1.55329i
$929$	24.1027	−	5.94079i	0.790785	−	0.194911i	0.176819	−	0.984243i	$-0.443419\pi$
$929$	24.1027	−	5.94079i	0.790785	−	0.194911i	0.613966	+	0.789332i	$0.289573\pi$
$930$	0.338058	−	0.0833237i	0.0110853	−	0.00273229i
$931$	−1.83053	−	15.0757i	−0.0599931	−	0.494088i
$932$	0.767401	−	2.02347i	0.0251371	−	0.0662810i
$933$	−19.7647	−	10.3733i	−0.647068	−	0.339608i
$934$	−30.5866			−1.00082
$935$	26.7591	−	14.0443i	0.875116	−	0.459296i
$936$	5.92502	−	1.91224i	0.193665	−	0.0625037i
$937$	30.6786	+	16.1013i	1.00222	+	0.526008i	0.884253	−	0.467009i	$-0.154668\pi$
$937$	30.6786	+	16.1013i	1.00222	+	0.526008i	0.117972	+	0.993017i	$0.462361\pi$
$938$	35.5521	+	18.6592i	1.16082	+	0.609244i
$939$	−25.8598	+	6.37387i	−0.843903	+	0.208003i
$940$	3.25691	−	4.71844i	0.106229	−	0.153899i
$941$	−56.1535	+	13.8406i	−1.83055	+	0.451191i	−0.995143	−	0.0984383i	$-0.968615\pi$
$941$	−56.1535	+	13.8406i	−1.83055	+	0.451191i	−0.835409	+	0.549629i	$0.814769\pi$
$942$	−9.21550	−	13.3510i	−0.300257	−	0.434998i
$943$	3.90847	−	32.1892i	0.127277	−	1.04822i
$944$	9.62588			0.313296
$945$	0.367362	−	3.02550i	0.0119503	−	0.0984194i
$946$	11.5699	+	30.5073i	0.376169	+	0.991877i
$947$	26.2172	−	13.7598i	0.851944	−	0.447135i	0.0185593	−	0.999828i	$-0.494092\pi$
$947$	26.2172	−	13.7598i	0.851944	−	0.447135i	0.833385	+	0.552693i	$0.186400\pi$
$948$	0.0127439	−	0.104956i	0.000413903	−	0.00340880i
$949$	2.66655	−	52.9638i	0.0865600	−	1.71928i
$950$	−4.18808	−	34.4919i	−0.135879	−	1.11907i
$951$	−2.29131	−	3.31954i	−0.0743010	−	0.107644i
$952$	−8.88183	+	12.8675i	−0.287862	+	0.417040i
$953$	−14.7491	+	13.0666i	−0.477772	+	0.423269i	−0.867330	−	0.497733i	$-0.834166\pi$
$953$	−14.7491	+	13.0666i	−0.477772	+	0.423269i	0.389559	+	0.921002i	$0.372628\pi$
$954$	−0.272550	−	0.718655i	−0.00882413	−	0.0232673i
$955$	−19.3321	+	28.0074i	−0.625572	+	0.906297i
$956$	−10.2142	−	5.36082i	−0.330350	−	0.173381i
$957$	5.68259	−	46.8004i	0.183692	−	1.51284i
$958$	−4.02450	−	33.1447i	−0.130026	−	1.07086i
$959$	0.281408	−	0.742011i	0.00908712	−	0.0239608i
$960$	0.771704	−	1.11801i	0.0249067	−	0.0360835i
$961$	23.1885	+	20.5432i	0.748017	+	0.662685i
$962$	2.08823	+	2.61062i	0.0673273	+	0.0841699i
$963$	−4.49499	+	3.98221i	−0.144849	+	0.128325i
$964$	3.70490	+	30.5126i	0.119327	+	0.982746i
$965$	−0.702631	−	5.78669i	−0.0226185	−	0.186280i
$966$	−9.18065	+	4.81838i	−0.295383	+	0.155029i
$967$	21.3068	−	11.1827i	0.685182	−	0.359611i	−0.0859388	−	0.996300i	$-0.527389\pi$
$967$	21.3068	−	11.1827i	0.685182	−	0.359611i	0.771120	+	0.636689i	$0.219697\pi$
$968$	26.1104	+	6.43564i	0.839220	+	0.206849i
$969$	−20.6910	+	18.3306i	−0.664690	+	0.588864i
$970$	23.3601	+	5.75775i	0.750049	+	0.184870i
$971$	−11.2486	−	29.6600i	−0.360984	−	0.951836i	−0.985326	−	0.170685i	$-0.945402\pi$
$971$	−11.2486	−	29.6600i	−0.360984	−	0.951836i	0.624342	−	0.781151i	$-0.285367\pi$
$972$	0.888694	−	0.466423i	0.0285049	−	0.0149605i
$973$	−5.52355	+	45.4905i	−0.177077	+	1.45836i
$974$	−15.0118	+	3.70007i	−0.481008	+	0.118558i
$975$	−0.548742	+	10.8993i	−0.0175738	+	0.349056i
$976$	72.4608	+	17.8600i	2.31941	+	0.571684i
$977$	15.7886	−	41.6311i	0.505122	−	1.33190i	−0.403767	−	0.914862i	$-0.632300\pi$
$977$	15.7886	−	41.6311i	0.505122	−	1.33190i	0.908890	−	0.417036i	$-0.136931\pi$
$978$	3.27540	+	2.90175i	0.104736	+	0.0927879i
$979$	15.4135	−	3.79909i	0.492618	−	0.121419i
$980$	−1.83627	−	2.66030i	−0.0586575	−	0.0849801i
$981$	−0.845347	−	6.96206i	−0.0269899	−	0.222281i
$982$	−14.5482	−	38.3605i	−0.464253	−	1.22413i
$983$	−0.574728	+	1.51543i	−0.0183310	+	0.0483348i	−0.943869	−	0.330319i	$-0.892844\pi$
$983$	−0.574728	+	1.51543i	−0.0183310	+	0.0483348i	0.925538	+	0.378654i	$0.123613\pi$
$984$	11.5351	+	16.7115i	0.367725	+	0.532742i
$985$	−22.5392	−	5.55541i	−0.718158	−	0.177010i
$986$	−23.4564	−	61.8493i	−0.747003	−	1.96968i
$987$	−3.12865	+	8.24957i	−0.0995861	+	0.262587i
$988$	−16.7765	+	17.1192i	−0.533731	+	0.544635i
$989$	−3.57090	−	9.41570i	−0.113548	−	0.299402i
$990$	−9.39377	+	8.32215i	−0.298554	+	0.264495i
$991$	−35.5594			−1.12958			−0.564790	−	0.825234i	$-0.691043\pi$
$991$	−35.5594			−1.12958			−0.564790	+	0.825234i	$0.691043\pi$
$992$	0.745388			0.0236661
$993$	−16.6030	+	14.7090i	−0.526881	+	0.466776i
$994$	−41.4642	+	21.7621i	−1.31516	+	0.690251i
$995$	−27.4004			−0.868651
$996$	−10.0143	−	5.25589i	−0.317314	−	0.166539i
$997$	−6.85926	−	6.07677i	−0.217235	−	0.192453i	0.547486	−	0.836815i	$-0.315585\pi$
$997$	−6.85926	−	6.07677i	−0.217235	−	0.192453i	−0.764721	+	0.644361i	$0.777123\pi$
$998$	−8.61311	−	12.4782i	−0.272643	−	0.394992i
$999$	−0.400448	−	0.354766i	−0.0126696	−	0.0112243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.5	✓	204
169.131	even	13	inner	507.2.m.b.469.5	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.5	✓	204	1.1	even	1	trivial
507.2.m.b.469.5	yes	204	169.131	even	13	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68275 - 0.414759i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.888694 + 0.466423i) q^{4} +(0.797976 - 1.15607i) q^{5} +(-0.614568 + 1.62048i) q^{6} +(-1.62398 - 1.43872i) q^{7} +(1.29250 + 1.14506i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(-1.68275 - 0.414759i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.888694 + 0.466423i) q^{4} +(0.797976 - 1.15607i) q^{5} +(-0.614568 + 1.62048i) q^{6} +(-1.62398 - 1.43872i) q^{7} +(1.29250 + 1.14506i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-1.82228 + 1.61440i) q^{10} +(-5.00516 + 1.23366i) q^{11} +(0.570142 - 0.825993i) q^{12} +(-1.03780 + 3.45296i) q^{13} +(2.13602 + 3.09456i) q^{14} +(-1.05145 - 0.931507i) q^{15} +(-2.84032 - 4.11491i) q^{16} +(-3.12382 - 2.76746i) q^{17} +(1.53459 + 0.805415i) q^{18} +6.62362 q^{19} +(1.24837 - 0.655197i) q^{20} +(-1.62398 + 1.43872i) q^{21} +8.93407 q^{22} -2.75739 q^{23} +(1.29250 - 1.14506i) q^{24} +(1.07330 + 2.83005i) q^{25} +(3.17851 - 5.38002i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(-0.772169 - 2.03604i) q^{28} +(-8.87966 - 2.18864i) q^{29} +(1.38298 + 2.00359i) q^{30} +(0.0507137 - 0.133721i) q^{31} +(1.84819 + 4.87328i) q^{32} +(0.621361 + 5.11736i) q^{33} +(4.10876 + 5.95257i) q^{34} +(-2.95916 + 0.729366i) q^{35} +(-0.751248 - 0.665547i) q^{36} +(-0.189711 + 0.500227i) q^{37} +(-11.1459 - 2.74721i) q^{38} +(3.30270 + 1.44645i) q^{39} +(2.35516 - 0.580494i) q^{40} +(-1.41745 + 11.6738i) q^{41} +(3.32947 - 1.74744i) q^{42} +(1.29503 + 3.41471i) q^{43} +(-5.02346 - 1.23817i) q^{44} +(-1.05145 + 0.931507i) q^{45} +(4.63999 + 1.14366i) q^{46} +(3.60078 - 1.88984i) q^{47} +(-4.42727 + 2.32361i) q^{48} +(-0.276364 - 2.27606i) q^{49} +(-0.632295 - 5.20741i) q^{50} +(-3.12382 + 2.76746i) q^{51} +(-2.53283 + 2.58457i) q^{52} +(-0.331951 - 0.294083i) q^{53} +(0.984516 - 1.42632i) q^{54} +(-2.56780 + 6.77073i) q^{55} +(-0.451581 - 3.71911i) q^{56} +(0.798389 - 6.57532i) q^{57} +(14.0344 + 7.36584i) q^{58} +(-1.09363 + 1.58439i) q^{59} +(-0.499945 - 1.31825i) q^{60} +(-11.1722 + 9.89771i) q^{61} +(-0.140800 + 0.203984i) q^{62} +(1.23248 + 1.78556i) q^{63} +(0.116568 + 0.960026i) q^{64} +(3.16372 + 3.95516i) q^{65} +(1.07688 - 8.86893i) q^{66} +(9.45492 - 4.96233i) q^{67} +(-1.48531 - 3.91645i) q^{68} +(-0.332367 + 2.73729i) q^{69} +5.28202 q^{70} +(-1.50113 + 12.3629i) q^{71} +(-0.980916 - 1.42110i) q^{72} +(-14.2807 + 3.51988i) q^{73} +(0.526709 - 0.763070i) q^{74} +(2.93879 - 0.724346i) q^{75} +(5.88637 + 3.08940i) q^{76} +(9.90316 + 5.19758i) q^{77} +(-4.95767 - 3.80382i) q^{78} +(0.0932751 - 0.0489545i) q^{79} -7.02362 q^{80} +(0.885456 + 0.464723i) q^{81} +(7.22702 - 19.0561i) q^{82} +(-1.35827 - 11.1864i) q^{83} +(-2.11427 + 0.521121i) q^{84} +(-5.69211 + 1.40298i) q^{85} +(-0.762920 - 6.28321i) q^{86} +(-3.24300 + 8.55110i) q^{87} +(-7.88180 - 4.13669i) q^{88} -3.07953 q^{89} +(2.15568 - 1.13139i) q^{90} +(6.65322 - 4.11443i) q^{91} +(-2.45048 - 1.28611i) q^{92} +(-0.126633 - 0.0664622i) q^{93} +(-6.84303 + 1.68665i) q^{94} +(5.28549 - 7.65735i) q^{95} +(5.06052 - 1.24731i) q^{96} +(-5.61387 - 8.13310i) q^{97} +(-0.478968 + 3.94465i) q^{98} +5.15495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

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