LMFDB - Embedded newform 966.2.q.f.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (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:	$7.71354883526$
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			169.2
Character	$\chi$	$=$	966.169
Dual form			966.2.q.f.463.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.150642 - 0.173850i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.150642 - 0.173850i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.193519 + 0.124367i) q^{10} +(-0.117920 - 0.820150i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(2.13919 - 1.37478i) q^{13} +(-0.654861 + 0.755750i) q^{14} +(0.0955606 - 0.209248i) q^{15} +(0.841254 + 0.540641i) q^{16} +(3.16250 - 0.928594i) q^{17} +(0.654861 + 0.755750i) q^{18} +(1.67782 + 0.492651i) q^{19} +(0.0955606 + 0.209248i) q^{20} +(0.142315 - 0.989821i) q^{21} -0.828583 q^{22} +(4.22042 - 2.27774i) q^{23} -1.00000 q^{24} +(0.704043 - 4.89673i) q^{25} +(-1.05634 - 2.31307i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(0.654861 + 0.755750i) q^{28} +(-2.74321 + 0.805480i) q^{29} +(-0.193519 - 0.124367i) q^{30} +(2.53383 - 5.54831i) q^{31} +(0.654861 - 0.755750i) q^{32} +(0.697049 - 0.447966i) q^{33} +(-0.469072 - 3.26246i) q^{34} +(0.0327376 + 0.227695i) q^{35} +(0.841254 - 0.540641i) q^{36} +(2.36101 - 2.72475i) q^{37} +(0.726415 - 1.59063i) q^{38} +(2.13919 + 1.37478i) q^{39} +(0.220718 - 0.0648087i) q^{40} +(-1.88739 - 2.17817i) q^{41} +(-0.959493 - 0.281733i) q^{42} +(2.86651 + 6.27677i) q^{43} +(-0.117920 + 0.820150i) q^{44} +0.230036 q^{45} +(-1.65392 - 4.50161i) q^{46} +8.09362 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-4.74669 - 1.39375i) q^{50} +(2.15843 + 2.49096i) q^{51} +(-2.43986 + 0.716407i) q^{52} +(1.19392 + 0.767284i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(-0.124819 + 0.144049i) q^{55} +(0.841254 - 0.540641i) q^{56} +(0.248859 + 1.73085i) q^{57} +(0.406881 + 2.82992i) q^{58} +(-3.59294 + 2.30904i) q^{59} +(-0.150642 + 0.173850i) q^{60} +(3.88160 - 8.49953i) q^{61} +(-5.13124 - 3.29765i) q^{62} +(0.959493 - 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.561256 - 0.164800i) q^{65} +(-0.344206 - 0.753706i) q^{66} +(1.30757 - 9.09435i) q^{67} -3.29601 q^{68} +(3.82513 + 2.89282i) q^{69} +0.230036 q^{70} +(-0.768477 + 5.34487i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(0.777561 + 0.228313i) q^{73} +(-2.36101 - 2.72475i) q^{74} +(4.74669 - 1.39375i) q^{75} +(-1.47106 - 0.945390i) q^{76} +(-0.344206 + 0.753706i) q^{77} +(1.66522 - 1.92177i) q^{78} +(-0.112053 + 0.0720118i) q^{79} +(-0.0327376 - 0.227695i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-2.42460 + 1.55820i) q^{82} +(-2.71713 + 3.13574i) q^{83} +(-0.415415 + 0.909632i) q^{84} +(-0.637841 - 0.409915i) q^{85} +(6.62083 - 1.94405i) q^{86} +(-1.87226 - 2.16071i) q^{87} +(0.795020 + 0.233439i) q^{88} +(-2.22041 - 4.86202i) q^{89} +(0.0327376 - 0.227695i) q^{90} -2.54286 q^{91} +(-4.69117 + 0.996443i) q^{92} +6.09951 q^{93} +(1.15184 - 8.01124i) q^{94} +(-0.167102 - 0.365902i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-2.78786 - 3.21737i) q^{97} +(0.959493 - 0.281733i) q^{98} +(0.697049 + 0.447966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 10 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 10 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 10 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9} - 12 q^{10} - 9 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} + 9 q^{17} + 3 q^{18} - 18 q^{19} + q^{20} + 3 q^{21} + 20 q^{22} + q^{23} - 30 q^{24} + 5 q^{25} + 32 q^{26} - 3 q^{27} + 3 q^{28} - 23 q^{29} - 12 q^{30} - q^{31} + 3 q^{32} + 2 q^{33} - 9 q^{34} - q^{35} - 3 q^{36} - q^{37} + 7 q^{38} + 12 q^{39} - q^{40} + 7 q^{41} - 3 q^{42} - 10 q^{43} - 9 q^{44} - 10 q^{45} - q^{46} + 68 q^{47} - 3 q^{48} - 3 q^{49} + 50 q^{50} + 9 q^{51} + q^{52} + 42 q^{53} + 3 q^{54} - 66 q^{55} - 3 q^{56} + 4 q^{57} + q^{58} + 25 q^{59} - 10 q^{60} + 10 q^{61} - 10 q^{62} + 3 q^{63} - 3 q^{64} - 54 q^{65} - 2 q^{66} - 6 q^{67} - 2 q^{68} - 21 q^{69} - 10 q^{70} - 13 q^{71} + 3 q^{72} + 33 q^{73} + q^{74} - 50 q^{75} + 26 q^{76} - 2 q^{77} - 12 q^{78} - 8 q^{79} + q^{80} - 3 q^{81} + 4 q^{82} - 2 q^{83} + 3 q^{84} - 77 q^{85} - 45 q^{86} - q^{87} - 13 q^{88} + 64 q^{89} - q^{90} - 12 q^{91} + 12 q^{92} - 56 q^{93} - 24 q^{94} + 59 q^{95} + 3 q^{96} + 2 q^{97} + 3 q^{98} + 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 10 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9 - 12 * q^10 - 9 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 + 9 * q^17 + 3 * q^18 - 18 * q^19 + q^20 + 3 * q^21 + 20 * q^22 + q^23 - 30 * q^24 + 5 * q^25 + 32 * q^26 - 3 * q^27 + 3 * q^28 - 23 * q^29 - 12 * q^30 - q^31 + 3 * q^32 + 2 * q^33 - 9 * q^34 - q^35 - 3 * q^36 - q^37 + 7 * q^38 + 12 * q^39 - q^40 + 7 * q^41 - 3 * q^42 - 10 * q^43 - 9 * q^44 - 10 * q^45 - q^46 + 68 * q^47 - 3 * q^48 - 3 * q^49 + 50 * q^50 + 9 * q^51 + q^52 + 42 * q^53 + 3 * q^54 - 66 * q^55 - 3 * q^56 + 4 * q^57 + q^58 + 25 * q^59 - 10 * q^60 + 10 * q^61 - 10 * q^62 + 3 * q^63 - 3 * q^64 - 54 * q^65 - 2 * q^66 - 6 * q^67 - 2 * q^68 - 21 * q^69 - 10 * q^70 - 13 * q^71 + 3 * q^72 + 33 * q^73 + q^74 - 50 * q^75 + 26 * q^76 - 2 * q^77 - 12 * q^78 - 8 * q^79 + q^80 - 3 * q^81 + 4 * q^82 - 2 * q^83 + 3 * q^84 - 77 * q^85 - 45 * q^86 - q^87 - 13 * q^88 + 64 * q^89 - q^90 - 12 * q^91 + 12 * q^92 - 56 * q^93 - 24 * q^94 + 59 * q^95 + 3 * q^96 + 2 * q^97 + 3 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−0.150642	−	0.173850i	−0.0673691	−	0.0777480i	0.721065	−	0.692868i	$-0.243653\pi$
$5$	−0.150642	−	0.173850i	−0.0673691	−	0.0777480i	−0.788434	+	0.615120i	$0.789108\pi$
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	−0.841254	−	0.540641i	−0.317964	−	0.204343i
$7$	−0.841254	−	0.540641i	−0.317964	−	0.204343i
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−0.193519	+	0.124367i	−0.0611961	+	0.0393283i
$11$	−0.117920	−	0.820150i	−0.0355541	−	0.247284i	0.964292	−	0.264842i	$-0.0853199\pi$
$11$	−0.117920	−	0.820150i	−0.0355541	−	0.247284i	−0.999846	+	0.0175580i	$0.994411\pi$
$12$	−0.142315	−	0.989821i	−0.0410828	−	0.285737i
$13$	2.13919	−	1.37478i	0.593305	−	0.381294i	−0.209259	−	0.977860i	$-0.567105\pi$
$13$	2.13919	−	1.37478i	0.593305	−	0.381294i	0.802564	+	0.596566i	$0.203469\pi$
$14$	−0.654861	+	0.755750i	−0.175019	+	0.201983i
$15$	0.0955606	−	0.209248i	0.0246736	−	0.0540277i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	3.16250	−	0.928594i	0.767019	−	0.225217i	0.125261	−	0.992124i	$-0.460023\pi$
$17$	3.16250	−	0.928594i	0.767019	−	0.225217i	0.641759	+	0.766907i	$0.278205\pi$
$18$	0.654861	+	0.755750i	0.154352	+	0.178132i
$19$	1.67782	+	0.492651i	0.384917	+	0.113022i	0.468465	−	0.883482i	$-0.344807\pi$
$19$	1.67782	+	0.492651i	0.384917	+	0.113022i	−0.0835482	+	0.996504i	$0.526625\pi$
$20$	0.0955606	+	0.209248i	0.0213680	+	0.0467894i
$21$	0.142315	−	0.989821i	0.0310556	−	0.215997i
$22$	−0.828583			−0.176655
$23$	4.22042	−	2.27774i	0.880018	−	0.474941i
$23$	4.22042	−	2.27774i	0.880018	−	0.474941i
$24$	−1.00000			−0.204124
$25$	0.704043	−	4.89673i	0.140809	−	0.979346i
$26$	−1.05634	−	2.31307i	−0.207166	−	0.453630i
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$	0.654861	+	0.755750i	0.123757	+	0.142823i
$29$	−2.74321	+	0.805480i	−0.509402	+	0.149574i	−0.526326	−	0.850283i	$-0.676431\pi$
$29$	−2.74321	+	0.805480i	−0.509402	+	0.149574i	0.0169241	+	0.999857i	$0.494613\pi$
$30$	−0.193519	−	0.124367i	−0.0353316	−	0.0227062i
$31$	2.53383	−	5.54831i	0.455089	−	0.996506i	−0.533490	−	0.845806i	$-0.679120\pi$
$31$	2.53383	−	5.54831i	0.455089	−	0.996506i	0.988580	−	0.150700i	$-0.0481528\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$	0.697049	−	0.447966i	0.121341	−	0.0779809i
$34$	−0.469072	−	3.26246i	−0.0804451	−	0.559508i
$35$	0.0327376	+	0.227695i	0.00553366	+	0.0384875i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	2.36101	−	2.72475i	0.388147	−	0.447945i	−0.527725	−	0.849415i	$-0.676955\pi$
$37$	2.36101	−	2.72475i	0.388147	−	0.447945i	0.915872	+	0.401470i	$0.131500\pi$
$38$	0.726415	−	1.59063i	0.117840	−	0.258034i
$39$	2.13919	+	1.37478i	0.342545	+	0.220140i
$40$	0.220718	−	0.0648087i	0.0348986	−	0.0102472i
$41$	−1.88739	−	2.17817i	−0.294761	−	0.340173i	0.588981	−	0.808147i	$-0.299529\pi$
$41$	−1.88739	−	2.17817i	−0.294761	−	0.340173i	−0.883742	+	0.467974i	$0.844984\pi$
$42$	−0.959493	−	0.281733i	−0.148053	−	0.0434723i
$43$	2.86651	+	6.27677i	0.437138	+	0.957199i	0.992115	+	0.125333i	$0.0400000\pi$
$43$	2.86651	+	6.27677i	0.437138	+	0.957199i	−0.554976	+	0.831866i	$0.687273\pi$
$44$	−0.117920	+	0.820150i	−0.0177771	+	0.123642i
$45$	0.230036			0.0342918
$46$	−1.65392	−	4.50161i	−0.243858	−	0.663727i
$47$	8.09362			1.18058			0.590288	−	0.807193i	$-0.299014\pi$
$47$	8.09362			1.18058			0.590288	+	0.807193i	$0.299014\pi$
$48$	−0.142315	+	0.989821i	−0.0205414	+	0.142868i
$49$	0.415415	+	0.909632i	0.0593450	+	0.129947i
$50$	−4.74669	−	1.39375i	−0.671284	−	0.197107i
$51$	2.15843	+	2.49096i	0.302241	+	0.348804i
$52$	−2.43986	+	0.716407i	−0.338348	+	0.0993478i
$53$	1.19392	+	0.767284i	0.163997	+	0.105395i	0.620065	−	0.784550i	$-0.287106\pi$
$53$	1.19392	+	0.767284i	0.163997	+	0.105395i	−0.456068	+	0.889945i	$0.650743\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	−0.124819	+	0.144049i	−0.0168306	+	0.0194236i
$56$	0.841254	−	0.540641i	0.112417	−	0.0722462i
$57$	0.248859	+	1.73085i	0.0329621	+	0.229257i
$58$	0.406881	+	2.82992i	0.0534261	+	0.371587i
$59$	−3.59294	+	2.30904i	−0.467761	+	0.300612i	−0.753208	−	0.657783i	$-0.771494\pi$
$59$	−3.59294	+	2.30904i	−0.467761	+	0.300612i	0.285446	+	0.958395i	$0.407858\pi$
$60$	−0.150642	+	0.173850i	−0.0194478	+	0.0224439i
$61$	3.88160	−	8.49953i	0.496988	−	1.08825i	−0.480448	−	0.877023i	$-0.659526\pi$
$61$	3.88160	−	8.49953i	0.496988	−	1.08825i	0.977436	−	0.211230i	$-0.0677468\pi$
$62$	−5.13124	−	3.29765i	−0.651668	−	0.418801i
$63$	0.959493	−	0.281733i	0.120885	−	0.0354950i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−0.561256	−	0.164800i	−0.0696153	−	0.0204409i
$66$	−0.344206	−	0.753706i	−0.0423688	−	0.0927748i
$67$	1.30757	−	9.09435i	0.159745	−	1.11105i	−0.739357	−	0.673313i	$-0.764871\pi$
$67$	1.30757	−	9.09435i	0.159745	−	1.11105i	0.899102	−	0.437738i	$-0.144220\pi$
$68$	−3.29601			−0.399700
$69$	3.82513	+	2.89282i	0.460491	+	0.348255i
$70$	0.230036			0.0274946
$71$	−0.768477	+	5.34487i	−0.0912014	+	0.634320i	0.892033	+	0.451971i	$0.149279\pi$
$71$	−0.768477	+	5.34487i	−0.0912014	+	0.634320i	−0.983234	+	0.182348i	$0.941630\pi$
$72$	−0.415415	−	0.909632i	−0.0489571	−	0.107201i
$73$	0.777561	+	0.228313i	0.0910066	+	0.0267220i	0.326919	−	0.945052i	$-0.393990\pi$
$73$	0.777561	+	0.228313i	0.0910066	+	0.0267220i	−0.235912	+	0.971774i	$0.575808\pi$
$74$	−2.36101	−	2.72475i	−0.274461	−	0.316745i
$75$	4.74669	−	1.39375i	0.548101	−	0.160937i
$76$	−1.47106	−	0.945390i	−0.168742	−	0.108444i
$77$	−0.344206	+	0.753706i	−0.0392259	+	0.0858928i
$78$	1.66522	−	1.92177i	0.188549	−	0.217597i
$79$	−0.112053	+	0.0720118i	−0.0126069	+	0.00810196i	−0.546929	−	0.837179i	$-0.684203\pi$
$79$	−0.112053	+	0.0720118i	−0.0126069	+	0.00810196i	0.534322	+	0.845281i	$0.320567\pi$
$80$	−0.0327376	−	0.227695i	−0.00366017	−	0.0254571i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−2.42460	+	1.55820i	−0.267753	+	0.172074i
$83$	−2.71713	+	3.13574i	−0.298244	+	0.344192i	−0.885016	−	0.465560i	$-0.845853\pi$
$83$	−2.71713	+	3.13574i	−0.298244	+	0.344192i	0.586772	+	0.809752i	$0.300398\pi$
$84$	−0.415415	+	0.909632i	−0.0453255	+	0.0992490i
$85$	−0.637841	−	0.409915i	−0.0691836	−	0.0444616i
$86$	6.62083	−	1.94405i	0.713943	−	0.209633i
$87$	−1.87226	−	2.16071i	−0.200728	−	0.231652i
$88$	0.795020	+	0.233439i	0.0847494	+	0.0248847i
$89$	−2.22041	−	4.86202i	−0.235363	−	0.515373i	0.754688	−	0.656084i	$-0.227788\pi$
$89$	−2.22041	−	4.86202i	−0.235363	−	0.515373i	−0.990051	+	0.140711i	$0.955061\pi$
$90$	0.0327376	−	0.227695i	0.00345085	−	0.0240012i
$91$	−2.54286			−0.266564
$92$	−4.69117	+	0.996443i	−0.489089	+	0.103886i
$93$	6.09951			0.632490
$94$	1.15184	−	8.01124i	0.118803	−	0.826296i
$95$	−0.167102	−	0.365902i	−0.0171443	−	0.0375407i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	−2.78786	−	3.21737i	−0.283065	−	0.326674i	0.596355	−	0.802720i	$-0.296615\pi$
$97$	−2.78786	−	3.21737i	−0.283065	−	0.326674i	−0.879420	+	0.476046i	$0.842069\pi$
$98$	0.959493	−	0.281733i	0.0969234	−	0.0284593i
$99$	0.697049	+	0.447966i	0.0700560	+	0.0450223i
$100$	−2.05509	+	4.50003i	−0.205509	+	0.450003i
$101$	−11.7415	+	13.5504i	−1.16832	+	1.34832i	−0.242594	+	0.970128i	$0.577998\pi$
$101$	−11.7415	+	13.5504i	−1.16832	+	1.34832i	−0.925729	+	0.378188i	$0.876547\pi$
$102$	2.77278	−	1.78196i	0.274546	−	0.176440i
$103$	−0.191178	−	1.32968i	−0.0188374	−	0.131017i	0.978233	−	0.207511i	$-0.0665363\pi$
$103$	−0.191178	−	1.32968i	−0.0188374	−	0.131017i	−0.997070	+	0.0764944i	$0.975627\pi$
$104$	0.361887	+	2.51698i	0.0354860	+	0.246810i
$105$	−0.193519	+	0.124367i	−0.0188855	+	0.0121370i
$106$	0.929387	−	1.07257i	0.0902700	−	0.104177i
$107$	−5.48926	+	12.0198i	−0.530667	+	1.16200i	0.434574	+	0.900636i	$0.356899\pi$
$107$	−5.48926	+	12.0198i	−0.530667	+	1.16200i	−0.965241	+	0.261362i	$0.915828\pi$
$108$	0.841254	+	0.540641i	0.0809497	+	0.0520232i
$109$	10.4707	−	3.07447i	1.00291	−	0.294481i	0.261261	−	0.965268i	$-0.415862\pi$
$109$	10.4707	−	3.07447i	1.00291	−	0.294481i	0.741650	+	0.670787i	$0.234044\pi$
$110$	0.124819	+	0.144049i	0.0119011	+	0.0137345i
$111$	3.45931	+	1.01575i	0.328343	+	0.0964103i
$112$	−0.415415	−	0.909632i	−0.0392530	−	0.0859521i
$113$	0.481302	−	3.34753i	0.0452771	−	0.314909i	−0.954579	−	0.297957i	$-0.903695\pi$
$113$	0.481302	−	3.34753i	0.0452771	−	0.314909i	0.999856	−	0.0169518i	$-0.00539620\pi$
$114$	1.74865			0.163776
$115$	−1.03176	−	0.390597i	−0.0962117	−	0.0364233i
$116$	2.85902			0.265454
$117$	−0.361887	+	2.51698i	−0.0334565	+	0.232695i
$118$	1.77421	+	3.88498i	0.163329	+	0.357642i
$119$	−3.16250	−	0.928594i	−0.289906	−	0.0851241i
$120$	0.150642	+	0.173850i	0.0137517	+	0.0158703i
$121$	9.89568	−	2.90563i	0.899607	−	0.264149i
$122$	−7.86060	−	5.05170i	−0.711666	−	0.457360i
$123$	1.19728	−	2.62168i	0.107955	−	0.236389i
$124$	−3.99433	+	4.60970i	−0.358702	+	0.413964i
$125$	−1.92495	+	1.23709i	−0.172173	+	0.110649i
$126$	−0.142315	−	0.989821i	−0.0126784	−	0.0881803i
$127$	2.53094	+	17.6031i	0.224585	+	1.56202i	0.720378	+	0.693581i	$0.243968\pi$
$127$	2.53094	+	17.6031i	0.224585	+	1.56202i	−0.495794	+	0.868440i	$0.665123\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$	−4.51877	+	5.21493i	−0.397855	+	0.459149i
$130$	−0.242997	+	0.532090i	−0.0213123	+	0.0466674i
$131$	−14.0011	−	8.99797i	−1.22328	−	0.786156i	−0.240452	−	0.970661i	$-0.577296\pi$
$131$	−14.0011	−	8.99797i	−1.22328	−	0.786156i	−0.982832	+	0.184505i	$0.940932\pi$
$132$	−0.795020	+	0.233439i	−0.0691976	+	0.0203183i
$133$	−1.14512	−	1.32154i	−0.0992946	−	0.114592i
$134$	−8.81570	−	2.58852i	−0.761560	−	0.223614i
$135$	0.0955606	+	0.209248i	0.00822454	+	0.0180092i
$136$	−0.469072	+	3.26246i	−0.0402226	+	0.279754i
$137$	−6.91996			−0.591212			−0.295606	−	0.955310i	$-0.595522\pi$
$137$	−6.91996			−0.591212			−0.295606	+	0.955310i	$0.595522\pi$
$138$	3.40775	−	3.37450i	0.290087	−	0.287257i
$139$	7.33408			0.622068			0.311034	−	0.950399i	$-0.399325\pi$
$139$	7.33408			0.622068			0.311034	+	0.950399i	$0.399325\pi$
$140$	0.0327376	−	0.227695i	0.00276683	−	0.0192437i
$141$	3.36221	+	7.36221i	0.283149	+	0.620010i
$142$	5.18110	+	1.52131i	0.434789	+	0.127665i
$143$	−1.37977	−	1.59234i	−0.115383	−	0.133159i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	0.553275	+	0.355568i	0.0459470	+	0.0295283i
$146$	0.336647	−	0.737154i	0.0278611	−	0.0610073i
$147$	−0.654861	+	0.755750i	−0.0540120	+	0.0623332i
$148$	−3.03302	+	1.94920i	−0.249312	+	0.160223i
$149$	0.439876	+	3.05941i	0.0360361	+	0.250636i	0.999874	−	0.0158514i	$-0.00504588\pi$
$149$	0.439876	+	3.05941i	0.0360361	+	0.250636i	−0.963838	+	0.266488i	$0.914137\pi$
$150$	−0.704043	−	4.89673i	−0.0574849	−	0.399816i
$151$	4.05733	−	2.60749i	0.330181	−	0.212194i	−0.365038	−	0.930993i	$-0.618944\pi$
$151$	4.05733	−	2.60749i	0.330181	−	0.212194i	0.695219	+	0.718798i	$0.255308\pi$
$152$	−1.14512	+	1.32154i	−0.0928816	+	0.107191i
$153$	−1.36921	+	2.99816i	−0.110694	+	0.242387i
$154$	0.697049	+	0.447966i	0.0561698	+	0.0360981i
$155$	−1.34627	+	0.395302i	−0.108135	+	0.0317514i
$156$	−1.66522	−	1.92177i	−0.133324	−	0.153865i
$157$	−17.9608	−	5.27377i	−1.43343	−	0.420893i	−0.529404	−	0.848370i	$-0.677584\pi$
$157$	−17.9608	−	5.27377i	−1.43343	−	0.420893i	−0.904026	+	0.427477i	$0.859402\pi$
$158$	0.0553321	+	0.121160i	0.00440199	+	0.00963900i
$159$	−0.201975	+	1.40477i	−0.0160177	+	0.111405i
$160$	−0.230036			−0.0181860
$161$	−4.78188	−	0.365576i	−0.376865	−	0.0288114i
$162$	−1.00000			−0.0785674
$163$	−0.788131	+	5.48157i	−0.0617312	+	0.429350i	0.935396	+	0.353602i	$0.115043\pi$
$163$	−0.788131	+	5.48157i	−0.0617312	+	0.429350i	−0.997127	+	0.0757476i	$0.975866\pi$
$164$	1.19728	+	2.62168i	0.0934919	+	0.204719i
$165$	−0.182884	−	0.0536994i	−0.0142375	−	0.00418050i
$166$	2.71713	+	3.13574i	0.210891	+	0.243381i
$167$	−18.5996	+	5.46134i	−1.43928	+	0.422611i	−0.905982	−	0.423316i	$-0.860866\pi$
$167$	−18.5996	+	5.46134i	−1.43928	+	0.422611i	−0.533299	+	0.845927i	$0.679048\pi$
$168$	0.841254	+	0.540641i	0.0649041	+	0.0417113i
$169$	−2.71426	+	5.94340i	−0.208789	+	0.457184i
$170$	−0.496517	+	0.573012i	−0.0380811	+	0.0439480i
$171$	−1.47106	+	0.945390i	−0.112494	+	0.0722958i
$172$	−0.982022	−	6.83011i	−0.0748784	−	0.520791i
$173$	0.448550	+	3.11973i	0.0341026	+	0.237189i	0.999742	−	0.0226952i	$-0.00722473\pi$
$173$	0.448550	+	3.11973i	0.0341026	+	0.237189i	−0.965640	+	0.259884i	$0.916316\pi$
$174$	−2.40516	+	1.54570i	−0.182335	+	0.117180i
$175$	−3.23965	+	3.73876i	−0.244895	+	0.282623i
$176$	0.344206	−	0.753706i	0.0259455	−	0.0568127i
$177$	−3.59294	−	2.30904i	−0.270062	−	0.173558i
$178$	−5.12853	+	1.50587i	−0.384400	+	0.112870i
$179$	6.33844	+	7.31495i	0.473757	+	0.546745i	0.941453	−	0.337145i	$-0.109461\pi$
$179$	6.33844	+	7.31495i	0.473757	+	0.546745i	−0.467696	+	0.883890i	$0.654916\pi$
$180$	−0.220718	−	0.0648087i	−0.0164514	−	0.00483056i
$181$	−5.99927	−	13.1366i	−0.445922	−	0.976433i	−0.990473	−	0.137706i	$-0.956027\pi$
$181$	−5.99927	−	13.1366i	−0.445922	−	0.976433i	0.544551	−	0.838728i	$-0.316700\pi$
$182$	−0.361887	+	2.51698i	−0.0268249	+	0.186571i
$183$	9.34392			0.690722
$184$	0.318677	+	4.78523i	0.0234932	+	0.352772i
$185$	−0.829363			−0.0609760
$186$	0.868051	−	6.03743i	0.0636486	−	0.442686i
$187$	−1.13451	−	2.48423i	−0.0829634	−	0.181665i
$188$	−7.76577	−	2.28024i	−0.566377	−	0.166303i
$189$	0.654861	+	0.755750i	0.0476341	+	0.0549727i
$190$	−0.385959	+	0.113328i	−0.0280004	+	0.00822165i
$191$	11.7411	+	7.54555i	0.849557	+	0.545977i	0.891437	−	0.453146i	$-0.149698\pi$
$191$	11.7411	+	7.54555i	0.849557	+	0.545977i	−0.0418796	+	0.999123i	$0.513335\pi$
$192$	0.415415	−	0.909632i	0.0299800	−	0.0656470i
$193$	2.05241	−	2.36861i	0.147736	−	0.170496i	−0.677058	−	0.735930i	$-0.736745\pi$
$193$	2.05241	−	2.36861i	0.147736	−	0.170496i	0.824794	+	0.565433i	$0.191291\pi$
$194$	−3.58137	+	2.30161i	−0.257128	+	0.165246i
$195$	−0.0832472	−	0.578997i	−0.00596146	−	0.0414628i
$196$	−0.142315	−	0.989821i	−0.0101653	−	0.0707015i
$197$	1.97161	−	1.26708i	0.140471	−	0.0902754i	−0.468518	−	0.883454i	$-0.655212\pi$
$197$	1.97161	−	1.26708i	0.140471	−	0.0902754i	0.608989	+	0.793179i	$0.291575\pi$
$198$	0.542607	−	0.626202i	0.0385614	−	0.0445022i
$199$	−6.33256	+	13.8664i	−0.448904	+	0.982962i	0.540974	+	0.841039i	$0.318056\pi$
$199$	−6.33256	+	13.8664i	−0.448904	+	0.982962i	−0.989878	+	0.141923i	$0.954672\pi$
$200$	4.16175	+	2.67460i	0.294280	+	0.189122i
$201$	8.81570	−	2.58852i	0.621811	−	0.182580i
$202$	11.7415	+	13.5504i	0.826129	+	0.953404i
$203$	2.74321	+	0.805480i	0.192536	+	0.0565336i
$204$	−1.36921	−	2.99816i	−0.0958641	−	0.209913i
$205$	−0.0943540	+	0.656246i	−0.00658997	+	0.0458342i
$206$	−1.34335			−0.0935955
$207$	−1.04239	+	4.68118i	−0.0724509	+	0.325364i
$208$	2.54286			0.176316
$209$	0.206200	−	1.43415i	0.0142632	−	0.0992024i
$210$	0.0955606	+	0.209248i	0.00659431	+	0.0144395i
$211$	−2.18417	−	0.641331i	−0.150365	−	0.0441510i	0.205684	−	0.978618i	$-0.434058\pi$
$211$	−2.18417	−	0.641331i	−0.150365	−	0.0441510i	−0.356049	+	0.934467i	$0.615876\pi$
$212$	−0.929387	−	1.07257i	−0.0638305	−	0.0736644i
$213$	−5.18110	+	1.52131i	−0.355003	+	0.104238i
$214$	11.1163	+	7.14399i	0.759892	+	0.488353i
$215$	0.659401	−	1.44389i	0.0449708	−	0.0984722i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	−5.13124	+	3.29765i	−0.348331	+	0.223859i
$218$	−1.55304	−	10.8017i	−0.105185	−	0.731581i
$219$	0.115330	+	0.802139i	0.00779329	+	0.0542035i
$220$	0.160347	−	0.103048i	0.0108106	−	0.00694753i
$221$	5.48859	−	6.33417i	0.369203	−	0.426082i
$222$	1.49772	−	3.27955i	0.100520	−	0.220109i
$223$	9.38750	+	6.03298i	0.628633	+	0.403998i	0.815803	−	0.578329i	$-0.196295\pi$
$223$	9.38750	+	6.03298i	0.628633	+	0.403998i	−0.187170	+	0.982328i	$0.559932\pi$
$224$	−0.959493	+	0.281733i	−0.0641088	+	0.0188240i
$225$	3.23965	+	3.73876i	0.215977	+	0.249250i
$226$	−3.24496	−	0.952806i	−0.215852	−	0.0633797i
$227$	0.373980	+	0.818903i	0.0248220	+	0.0543525i	0.921637	−	0.388053i	$-0.126852\pi$
$227$	0.373980	+	0.818903i	0.0248220	+	0.0543525i	−0.896815	+	0.442406i	$0.854125\pi$
$228$	0.248859	−	1.73085i	0.0164811	−	0.114628i
$229$	18.6451			1.23210			0.616050	−	0.787707i	$-0.288732\pi$
$229$	18.6451			1.23210			0.616050	+	0.787707i	$0.288732\pi$
$230$	−0.533455	+	0.965666i	−0.0351750	+	0.0636741i
$231$	−0.828583			−0.0545168
$232$	0.406881	−	2.82992i	0.0267131	−	0.185794i
$233$	6.11676	+	13.3938i	0.400722	+	0.877460i	0.997197	+	0.0748272i	$0.0238405\pi$
$233$	6.11676	+	13.3938i	0.400722	+	0.877460i	−0.596474	+	0.802632i	$0.703432\pi$
$234$	2.43986	+	0.716407i	0.159499	+	0.0468330i
$235$	−1.21924	−	1.40707i	−0.0795343	−	0.0917874i
$236$	4.09794	−	1.20326i	0.266753	−	0.0783257i
$237$	−0.112053	−	0.0720118i	−0.00727860	−	0.00467767i
$238$	−1.36921	+	2.99816i	−0.0887529	+	0.194342i
$239$	−16.6741	+	19.2430i	−1.07856	+	1.24472i	−0.110535	+	0.993872i	$0.535256\pi$
$239$	−16.6741	+	19.2430i	−1.07856	+	1.24472i	−0.968025	+	0.250852i	$0.919289\pi$
$240$	0.193519	−	0.124367i	0.0124916	−	0.00802786i
$241$	−2.00622	−	13.9536i	−0.129232	−	0.898830i	−0.946530	−	0.322615i	$-0.895438\pi$
$241$	−2.00622	−	13.9536i	−0.129232	−	0.898830i	0.817298	−	0.576215i	$-0.195471\pi$
$242$	−1.46776	−	10.2085i	−0.0943510	−	0.656226i
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$	−6.11896	+	7.06166i	−0.391727	+	0.452077i
$245$	0.0955606	−	0.209248i	0.00610514	−	0.0133684i
$246$	−2.42460	−	1.55820i	−0.154587	−	0.0993470i
$247$	4.26645	−	1.25274i	0.271468	−	0.0797102i
$248$	3.99433	+	4.60970i	0.253640	+	0.292717i
$249$	−3.98111	−	1.16896i	−0.252292	−	0.0740798i
$250$	0.950549	+	2.08141i	0.0601180	+	0.131640i
$251$	−1.06291	+	7.39271i	−0.0670904	+	0.466624i	0.928386	+	0.371617i	$0.121196\pi$
$251$	−1.06291	+	7.39271i	−0.0670904	+	0.466624i	−0.995477	+	0.0950071i	$0.969713\pi$
$252$	−1.00000			−0.0629941
$253$	−2.36575	−	3.19278i	−0.148734	−	0.200729i
$254$	17.7841			1.11587
$255$	0.107904	−	0.750486i	0.00675718	−	0.0469972i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−27.4169	−	8.05033i	−1.71022	−	0.502166i	−0.727319	−	0.686300i	$-0.759234\pi$
$257$	−27.4169	−	8.05033i	−1.71022	−	0.502166i	−0.982901	+	0.184134i	$0.941052\pi$
$258$	4.51877	+	5.21493i	0.281326	+	0.324668i
$259$	−3.45931	+	1.01575i	−0.214951	+	0.0631154i
$260$	0.492092	+	0.316248i	0.0305183	+	0.0196129i
$261$	1.18768	−	2.60066i	0.0735156	−	0.160977i
$262$	−10.8990	+	12.5781i	−0.673339	+	0.777075i
$263$	22.0688	−	14.1828i	1.36082	−	0.874546i	0.362472	−	0.931995i	$-0.381933\pi$
$263$	22.0688	−	14.1828i	1.36082	−	0.874546i	0.998348	+	0.0574488i	$0.0182966\pi$
$264$	0.117920	+	0.820150i	0.00725746	+	0.0504767i
$265$	−0.0464616	−	0.323148i	−0.00285411	−	0.0198508i
$266$	−1.47106	+	0.945390i	−0.0901962	+	0.0579656i
$267$	3.50026	−	4.03951i	0.214212	−	0.247214i
$268$	−3.81678	+	8.35758i	−0.233147	+	0.510520i
$269$	10.9929	+	7.06474i	0.670252	+	0.430745i	0.831016	−	0.556248i	$-0.187760\pi$
$269$	10.9929	+	7.06474i	0.670252	+	0.430745i	−0.160765	+	0.986993i	$0.551396\pi$
$270$	0.220718	−	0.0648087i	0.0134325	−	0.00394413i
$271$	12.9297	+	14.9217i	0.785425	+	0.906428i	0.997489	−	0.0708275i	$-0.0225640\pi$
$271$	12.9297	+	14.9217i	0.785425	+	0.906428i	−0.212064	+	0.977256i	$0.568019\pi$
$272$	3.16250	+	0.928594i	0.191755	+	0.0563043i
$273$	−1.05634	−	2.31307i	−0.0639328	−	0.139993i
$274$	−0.984813	+	6.84953i	−0.0594947	+	0.413795i
$275$	−4.09907			−0.247183
$276$	−2.85518	−	3.85330i	−0.171862	−	0.231942i
$277$	23.7245			1.42547			0.712735	−	0.701434i	$-0.247456\pi$
$277$	23.7245			1.42547			0.712735	+	0.701434i	$0.247456\pi$
$278$	1.04375	−	7.25943i	0.0625998	−	0.435391i
$279$	2.53383	+	5.54831i	0.151696	+	0.332169i
$280$	−0.220718	−	0.0648087i	−0.0131904	−	0.00387306i
$281$	0.818955	+	0.945124i	0.0488547	+	0.0563814i	0.779651	−	0.626214i	$-0.215396\pi$
$281$	0.818955	+	0.945124i	0.0488547	+	0.0563814i	−0.730796	+	0.682596i	$0.760851\pi$
$282$	7.76577	−	2.28024i	0.462445	−	0.135786i
$283$	9.00167	+	5.78502i	0.535093	+	0.343884i	0.780117	−	0.625633i	$-0.215159\pi$
$283$	9.00167	+	5.78502i	0.535093	+	0.343884i	−0.245024	+	0.969517i	$0.578796\pi$
$284$	2.24317	−	4.91186i	0.133108	−	0.291465i
$285$	0.263419	−	0.304002i	0.0156036	−	0.0180075i
$286$	−1.77250	+	1.13912i	−0.104810	+	0.0673573i
$287$	0.410170	+	2.85279i	0.0242116	+	0.168395i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	−5.16218	+	3.31753i	−0.303658	+	0.195149i
$290$	0.430688	−	0.497041i	0.0252909	−	0.0291872i
$291$	1.76850	−	3.87247i	0.103671	−	0.227008i
$292$	−0.681741	−	0.438129i	−0.0398959	−	0.0256395i
$293$	−6.62456	+	1.94515i	−0.387011	+	0.113637i	−0.469449	−	0.882960i	$-0.655547\pi$
$293$	−6.62456	+	1.94515i	−0.387011	+	0.113637i	0.0824383	+	0.996596i	$0.473729\pi$
$294$	0.654861	+	0.755750i	0.0381923	+	0.0440762i
$295$	0.942674	+	0.276794i	0.0548846	+	0.0161156i
$296$	1.49772	+	3.27955i	0.0870531	+	0.190620i
$297$	−0.117920	+	0.820150i	−0.00684240	+	0.0475899i
$298$	3.09087			0.179049
$299$	5.89691	−	10.6746i	0.341027	−	0.617330i
$300$	−4.94708			−0.285620
$301$	0.982022	−	6.83011i	0.0566028	−	0.393681i
$302$	−2.00353	−	4.38711i	−0.115290	−	0.252450i
$303$	−17.2035	−	5.05140i	−0.988314	−	0.290195i
$304$	1.14512	+	1.32154i	0.0656772	+	0.0757955i
$305$	−2.06237	+	0.605567i	−0.118091	+	0.0346747i
$306$	2.77278	+	1.78196i	0.158509	+	0.101868i
$307$	−3.18517	+	6.97454i	−0.181787	+	0.398058i	−0.978485	−	0.206320i	$-0.933851\pi$
$307$	−3.18517	+	6.97454i	−0.181787	+	0.398058i	0.796697	+	0.604378i	$0.206578\pi$
$308$	0.542607	−	0.626202i	0.0309179	−	0.0356811i
$309$	1.13010	−	0.726269i	0.0642889	−	0.0413160i
$310$	0.199683	+	1.38883i	0.0113413	+	0.0788802i
$311$	1.36916	+	9.52268i	0.0776377	+	0.539982i	0.991106	+	0.133073i	$0.0424844\pi$
$311$	1.36916	+	9.52268i	0.0776377	+	0.539982i	−0.913469	+	0.406909i	$0.866607\pi$
$312$	−2.13919	+	1.37478i	−0.121108	+	0.0778313i
$313$	3.23532	−	3.73376i	0.182871	−	0.211045i	−0.656911	−	0.753968i	$-0.728137\pi$
$313$	3.23532	−	3.73376i	0.182871	−	0.211045i	0.839782	+	0.542924i	$0.182683\pi$
$314$	−7.77619	+	17.0275i	−0.438836	+	0.960916i
$315$	−0.193519	−	0.124367i	−0.0109036	−	0.00700729i
$316$	0.127802	−	0.0375260i	0.00718941	−	0.00211100i
$317$	−9.43807	−	10.8921i	−0.530095	−	0.611762i	0.426035	−	0.904707i	$-0.359910\pi$
$317$	−9.43807	−	10.8921i	−0.530095	−	0.611762i	−0.956129	+	0.292945i	$0.905365\pi$
$318$	1.36172	+	0.399838i	0.0763617	+	0.0224218i
$319$	0.984093	+	2.15486i	0.0550986	+	0.120649i
$320$	−0.0327376	+	0.227695i	−0.00183009	+	0.0127285i
$321$	−13.2139			−0.737529
$322$	−1.04239	+	4.68118i	−0.0580900	+	0.260872i
$323$	5.76357			0.320693
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−5.22582	−	11.4429i	−0.289876	−	0.634740i
$326$	5.31362	+	1.56022i	0.294294	+	0.0864125i
$327$	7.14632	+	8.24730i	0.395193	+	0.456077i
$328$	2.76538	−	0.811990i	0.152693	−	0.0448346i
$329$	−6.80878	−	4.37574i	−0.375380	−	0.241242i
$330$	−0.0791799	+	0.173380i	−0.00435871	+	0.00954424i
$331$	−7.55163	+	8.71505i	−0.415075	+	0.479022i	−0.924330	−	0.381593i	$-0.875376\pi$
$331$	−7.55163	+	8.71505i	−0.415075	+	0.479022i	0.509255	+	0.860616i	$0.329921\pi$
$332$	3.49051	−	2.24322i	0.191567	−	0.123112i
$333$	0.513095	+	3.56866i	0.0281175	+	0.195561i
$334$	2.75875	+	19.1875i	0.150952	+	1.04989i
$335$	−1.77803	+	1.14267i	−0.0971440	+	0.0624306i
$336$	0.654861	−	0.755750i	0.0357256	−	0.0412295i
$337$	1.43017	−	3.13163i	0.0779062	−	0.170591i	−0.866671	−	0.498880i	$-0.833745\pi$
$337$	1.43017	−	3.13163i	0.0779062	−	0.170591i	0.944577	+	0.328289i	$0.106472\pi$
$338$	5.49662	+	3.53247i	0.298977	+	0.192141i
$339$	3.24496	−	0.952806i	0.176242	−	0.0517493i
$340$	0.496517	+	0.573012i	0.0269274	+	0.0310759i
$341$	−4.84924	−	1.42386i	−0.262601	−	0.0771066i
$342$	0.726415	+	1.59063i	0.0392800	+	0.0860112i
$343$	0.142315	−	0.989821i	0.00768428	−	0.0534453i
$344$	−6.90035			−0.372042
$345$	−0.0733073	−	1.10078i	−0.00394673	−	0.0592639i
$346$	3.15181			0.169443
$347$	0.317498	−	2.20825i	0.0170442	−	0.118545i	−0.979523	−	0.201332i	$-0.935473\pi$
$347$	0.317498	−	2.20825i	0.0170442	−	0.118545i	0.996567	+	0.0827870i	$0.0263821\pi$
$348$	1.18768	+	2.60066i	0.0636664	+	0.139410i
$349$	−24.6628	−	7.24166i	−1.32017	−	0.387637i	−0.455616	−	0.890176i	$-0.650581\pi$
$349$	−24.6628	−	7.24166i	−1.32017	−	0.387637i	−0.864555	+	0.502539i	$0.832399\pi$
$350$	3.23965	+	3.73876i	0.173167	+	0.199845i
$351$	−2.43986	+	0.716407i	−0.130230	+	0.0382390i
$352$	−0.697049	−	0.447966i	−0.0371528	−	0.0238767i
$353$	−4.82579	+	10.5670i	−0.256851	+	0.562425i	−0.993498	−	0.113852i	$-0.963681\pi$
$353$	−4.82579	+	10.5670i	−0.256851	+	0.562425i	0.736647	+	0.676278i	$0.236408\pi$
$354$	−2.79687	+	3.22776i	−0.148652	+	0.171554i
$355$	1.04497	−	0.671562i	0.0554613	−	0.0356428i
$356$	0.760679	+	5.29064i	0.0403159	+	0.280403i
$357$	−0.469072	−	3.26246i	−0.0248259	−	0.172668i
$358$	8.14255	−	5.23290i	0.430347	−	0.276567i
$359$	18.3415	−	21.1673i	0.968030	−	1.11717i	−0.0250453	−	0.999686i	$-0.507973\pi$
$359$	18.3415	−	21.1673i	0.968030	−	1.11717i	0.993075	−	0.117480i	$-0.0374815\pi$
$360$	−0.0955606	+	0.209248i	−0.00503648	+	0.0110284i
$361$	−13.4115	−	8.61902i	−0.705866	−	0.453633i
$362$	−13.8566	+	4.06868i	−0.728289	+	0.213845i
$363$	6.75387	+	7.79439i	0.354486	+	0.409099i
$364$	2.43986	+	0.716407i	0.127883	+	0.0375499i
$365$	−0.0774411	−	0.169572i	−0.00405345	−	0.00887582i
$366$	1.32978	−	9.24881i	0.0695086	−	0.483443i
$367$	−0.762326			−0.0397931			−0.0198965	−	0.999802i	$-0.506334\pi$
$367$	−0.762326			−0.0397931			−0.0198965	+	0.999802i	$0.506334\pi$
$368$	4.78188	+	0.365576i	0.249273	+	0.0190570i
$369$	2.88213			0.150038
$370$	−0.118031	+	0.820921i	−0.00613612	+	0.0426777i
$371$	−0.589562	−	1.29096i	−0.0306085	−	0.0670234i
$372$	−5.85244	−	1.71843i	−0.303435	−	0.0890965i
$373$	−6.61274	−	7.63151i	−0.342395	−	0.395144i	0.558270	−	0.829659i	$-0.311465\pi$
$373$	−6.61274	−	7.63151i	−0.342395	−	0.395144i	−0.900665	+	0.434515i	$0.856920\pi$
$374$	−2.62040	+	0.769418i	−0.135497	+	0.0397856i
$375$	−1.92495	−	1.23709i	−0.0994039	−	0.0638830i
$376$	−3.36221	+	7.36221i	−0.173393	+	0.379677i
$377$	−4.76091	+	5.49438i	−0.245199	+	0.282975i
$378$	0.841254	−	0.540641i	0.0432694	−	0.0278076i
$379$	3.20866	+	22.3167i	0.164818	+	1.14633i	0.889395	+	0.457139i	$0.151126\pi$
$379$	3.20866	+	22.3167i	0.164818	+	1.14633i	−0.724578	+	0.689193i	$0.757965\pi$
$380$	0.0572465	+	0.398158i	0.00293668	+	0.0204251i
$381$	−14.9609	+	9.61481i	−0.766472	+	0.492582i
$382$	9.13969	−	10.5478i	0.467627	−	0.539670i
$383$	9.36237	−	20.5007i	0.478395	−	1.04754i	−0.504507	−	0.863408i	$-0.668326\pi$
$383$	9.36237	−	20.5007i	0.478395	−	1.04754i	0.982902	−	0.184131i	$-0.0589470\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	0.182884	−	0.0536994i	0.00932061	−	0.00273678i
$386$	−2.05241	−	2.36861i	−0.104465	−	0.120559i
$387$	−6.62083	−	1.94405i	−0.336556	−	0.0988217i
$388$	1.76850	+	3.87247i	0.0897819	+	0.196595i
$389$	−2.12092	+	14.7513i	−0.107535	+	0.747922i	0.862693	+	0.505728i	$0.168776\pi$
$389$	−2.12092	+	14.7513i	−0.107535	+	0.747922i	−0.970228	+	0.242194i	$0.922133\pi$
$390$	−0.584951			−0.0296201
$391$	11.2320	−	11.1224i	0.568026	−	0.562484i
$392$	−1.00000			−0.0505076
$393$	2.36857	−	16.4738i	0.119478	−	0.830991i
$394$	−0.973590	−	2.13186i	−0.0490487	−	0.107402i
$395$	0.0293990	+	0.00863234i	0.00147923	+	0.000434340i
$396$	−0.542607	−	0.626202i	−0.0272670	−	0.0314678i
$397$	−16.5454	+	4.85818i	−0.830392	+	0.243825i	−0.669185	−	0.743095i	$-0.733357\pi$
$397$	−16.5454	+	4.85818i	−0.830392	+	0.243825i	−0.161207	+	0.986921i	$0.551539\pi$
$398$	12.8240	+	8.24150i	0.642810	+	0.413109i
$399$	0.726415	−	1.59063i	0.0363662	−	0.0796309i
$400$	3.23965	−	3.73876i	0.161983	−	0.186938i
$401$	13.7768	−	8.85379i	0.687979	−	0.442137i	−0.149388	−	0.988779i	$-0.547730\pi$
$401$	13.7768	−	8.85379i	0.687979	−	0.442137i	0.837367	+	0.546642i	$0.184094\pi$
$402$	−1.30757	−	9.09435i	−0.0652157	−	0.453585i
$403$	−2.20734	−	15.3524i	−0.109955	−	0.764755i
$404$	15.0835	−	9.69356i	0.750431	−	0.482273i
$405$	−0.150642	+	0.173850i	−0.00748545	+	0.00863867i
$406$	1.18768	−	2.60066i	0.0589436	−	0.129069i
$407$	−2.51311	−	1.61508i	−0.124570	−	0.0800564i
$408$	−3.16250	+	0.928594i	−0.156567	+	0.0459723i
$409$	−0.359045	−	0.414360i	−0.0177537	−	0.0204888i	0.746803	−	0.665045i	$-0.231588\pi$
$409$	−0.359045	−	0.414360i	−0.0177537	−	0.0204888i	−0.764557	+	0.644556i	$0.777042\pi$
$410$	0.636139	+	0.186787i	0.0314167	+	0.00922476i
$411$	−2.87466	−	6.29462i	−0.141796	−	0.310491i
$412$	−0.191178	+	1.32968i	−0.00941868	+	0.0655084i
$413$	4.27094			0.210159
$414$	4.48518	+	1.69798i	0.220435	+	0.0834511i
$415$	0.954462			0.0468527
$416$	0.361887	−	2.51698i	0.0177430	−	0.123405i
$417$	3.04669	+	6.67131i	0.149197	+	0.326696i
$418$	−1.39021	−	0.408202i	−0.0679974	−	0.0199658i
$419$	2.32809	+	2.68676i	0.113735	+	0.131257i	0.809762	−	0.586759i	$-0.199596\pi$
$419$	2.32809	+	2.68676i	0.113735	+	0.131257i	−0.696027	+	0.718015i	$0.745051\pi$
$420$	0.220718	−	0.0648087i	0.0107700	−	0.00316234i
$421$	21.5102	+	13.8238i	1.04834	+	0.673730i	0.947037	−	0.321125i	$-0.104061\pi$
$421$	21.5102	+	13.8238i	1.04834	+	0.673730i	0.101308	+	0.994855i	$0.467697\pi$
$422$	−0.945643	+	2.07067i	−0.0460332	+	0.100799i
$423$	−5.30019	+	6.11675i	−0.257704	+	0.297406i
$424$	−1.19392	+	0.767284i	−0.0579818	+	0.0372626i
$425$	−2.32054	−	16.1397i	−0.112563	−	0.782890i
$426$	0.768477	+	5.34487i	0.0372328	+	0.258960i
$427$	−7.86060	+	5.05170i	−0.380401	+	0.244469i
$428$	8.65328	−	9.98642i	0.418272	−	0.482712i
$429$	0.875269	−	1.91657i	0.0422584	−	0.0925329i
$430$	−1.33535	−	0.858176i	−0.0643962	−	0.0413849i
$431$	20.9701	−	6.15737i	1.01009	−	0.296590i	0.265502	−	0.964110i	$-0.414462\pi$
$431$	20.9701	−	6.15737i	1.01009	−	0.296590i	0.744592	+	0.667520i	$0.232644\pi$
$432$	−0.654861	−	0.755750i	−0.0315070	−	0.0363610i
$433$	−33.3157	−	9.78236i	−1.60105	−	0.470110i	−0.645211	−	0.764004i	$-0.723231\pi$
$433$	−33.3157	−	9.78236i	−1.60105	−	0.470110i	−0.955838	+	0.293894i	$0.905049\pi$
$434$	2.53383	+	5.54831i	0.121628	+	0.266328i
$435$	−0.0935975	+	0.650985i	−0.00448766	+	0.0312123i
$436$	−10.9127			−0.522625
$437$	8.20321	−	1.74243i	0.392413	−	0.0833516i
$438$	0.810387			0.0387218
$439$	3.25909	−	22.6674i	0.155548	−	1.08186i	−0.751167	−	0.660112i	$-0.770509\pi$
$439$	3.25909	−	22.6674i	0.155548	−	1.08186i	0.906714	−	0.421745i	$-0.138582\pi$
$440$	−0.0791799	−	0.173380i	−0.00377475	−	0.00826556i
$441$	−0.959493	−	0.281733i	−0.0456901	−	0.0134158i
$442$	−5.48859	−	6.33417i	−0.261066	−	0.301286i
$443$	0.588745	−	0.172871i	0.0279721	−	0.00821335i	−0.267717	−	0.963498i	$-0.586269\pi$
$443$	0.588745	−	0.172871i	0.0279721	−	0.00821335i	0.295689	+	0.955284i	$0.404451\pi$
$444$	−3.03302	−	1.94920i	−0.143941	−	0.0925050i
$445$	−0.510775	+	1.11844i	−0.0242131	+	0.0530192i
$446$	7.30755	−	8.43336i	0.346023	−	0.399331i
$447$	−2.60020	+	1.67105i	−0.122985	+	0.0790379i
$448$	0.142315	+	0.989821i	0.00672374	+	0.0467647i
$449$	−2.60587	−	18.1243i	−0.122979	−	0.855336i	−0.954152	−	0.299323i	$-0.903239\pi$
$449$	−2.60587	−	18.1243i	−0.122979	−	0.855336i	0.831173	−	0.556014i	$-0.187670\pi$
$450$	4.16175	−	2.67460i	0.196187	−	0.126082i
$451$	−1.56386	+	1.80479i	−0.0736394	+	0.0849844i
$452$	−1.40491	+	3.07633i	−0.0660816	+	0.144699i
$453$	4.05733	+	2.60749i	0.190630	+	0.122510i
$454$	0.863791	−	0.253632i	0.0405397	−	0.0119035i
$455$	0.383061	+	0.442076i	0.0179582	+	0.0207249i
$456$	−1.67782	−	0.492651i	−0.0785709	−	0.0230705i
$457$	−11.9200	−	26.1012i	−0.557595	−	1.22096i	−0.953144	−	0.302518i	$-0.902173\pi$
$457$	−11.9200	−	26.1012i	−0.557595	−	1.22096i	0.395548	−	0.918445i	$-0.370555\pi$
$458$	2.65347	−	18.4553i	0.123988	−	0.862359i
$459$	−3.29601			−0.153845
$460$	0.879918	+	0.665454i	0.0410264	+	0.0310270i
$461$	−13.5230			−0.629830			−0.314915	−	0.949120i	$-0.601976\pi$
$461$	−13.5230			−0.629830			−0.314915	+	0.949120i	$0.601976\pi$
$462$	−0.117920	+	0.820150i	−0.00548612	+	0.0381568i
$463$	0.902787	+	1.97683i	0.0419561	+	0.0918710i	0.929449	−	0.368949i	$-0.120282\pi$
$463$	0.902787	+	1.97683i	0.0419561	+	0.0918710i	−0.887493	+	0.460820i	$0.847555\pi$
$464$	−2.74321	−	0.805480i	−0.127350	−	0.0373935i
$465$	−0.918842	−	1.06040i	−0.0426103	−	0.0491749i
$466$	14.1280	−	4.14836i	0.654468	−	0.192169i
$467$	−15.2959	−	9.83011i	−0.707812	−	0.454883i	0.136566	−	0.990631i	$-0.456393\pi$
$467$	−15.2959	−	9.83011i	−0.707812	−	0.454883i	−0.844378	+	0.535748i	$0.820030\pi$
$468$	1.05634	−	2.31307i	0.0488295	−	0.106922i
$469$	−6.01678	+	6.94373i	−0.277829	+	0.320632i
$470$	−1.56627	+	1.00658i	−0.0722466	+	0.0464300i
$471$	−2.66400	−	18.5285i	−0.122751	−	0.853750i
$472$	−0.607818	−	4.22747i	−0.0279771	−	0.194585i
$473$	4.80988	−	3.09112i	0.221158	−	0.142130i
$474$	−0.0872256	+	0.100664i	−0.00400640	+	0.00462364i
$475$	3.59363	−	7.86896i	0.164887	−	0.361053i
$476$	2.77278	+	1.78196i	0.127090	+	0.0816760i
$477$	−1.36172	+	0.399838i	−0.0623491	+	0.0183073i
$478$	16.6741	+	19.2430i	0.762657	+	0.880153i
$479$	7.12343	+	2.09163i	0.325478	+	0.0955689i	0.440390	−	0.897807i	$-0.354840\pi$
$479$	7.12343	+	2.09163i	0.325478	+	0.0955689i	−0.114912	+	0.993376i	$0.536659\pi$
$480$	−0.0955606	−	0.209248i	−0.00436172	−	0.00955084i
$481$	1.30473	−	9.07461i	0.0594906	−	0.413766i
$482$	−14.0971			−0.642105
$483$	−1.65392	−	4.50161i	−0.0752561	−	0.204831i
$484$	−10.3134			−0.468793
$485$	−0.139370	+	0.969340i	−0.00632847	+	0.0440155i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	−13.8574	−	4.06891i	−0.627940	−	0.184380i	−0.0477477	−	0.998859i	$-0.515204\pi$
$487$	−13.8574	−	4.06891i	−0.627940	−	0.184380i	−0.580192	+	0.814480i	$0.697023\pi$
$488$	6.11896	+	7.06166i	0.276993	+	0.319666i
$489$	−5.31362	+	1.56022i	−0.240290	+	0.0705555i
$490$	−0.193519	−	0.124367i	−0.00874229	−	0.00561833i
$491$	0.317927	−	0.696162i	0.0143478	−	0.0314174i	−0.902322	−	0.431062i	$-0.858139\pi$
$491$	0.317927	−	0.696162i	0.0143478	−	0.0314174i	0.916670	+	0.399644i	$0.130866\pi$
$492$	−1.88739	+	2.17817i	−0.0850903	+	0.0981994i
$493$	−7.92745	+	5.09466i	−0.357034	+	0.229452i
$494$	−0.632813	−	4.40131i	−0.0284716	−	0.198024i
$495$	−0.0271258	−	0.188664i	−0.00121922	−	0.00847983i
$496$	5.13124	−	3.29765i	0.230399	−	0.148069i
$497$	3.53614	−	4.08092i	0.158618	−	0.183054i
$498$	−1.72363	+	3.77423i	−0.0772378	+	0.169127i
$499$	−21.5591	−	13.8552i	−0.965119	−	0.620245i	−0.0397091	−	0.999211i	$-0.512643\pi$
$499$	−21.5591	−	13.8552i	−0.965119	−	0.620245i	−0.925410	+	0.378967i	$0.876279\pi$
$500$	2.19550	−	0.644658i	0.0981859	−	0.0288300i
$501$	−12.6944	−	14.6501i	−0.567142	−	0.654517i
$502$	7.16620	+	2.10419i	0.319843	+	0.0939144i
$503$	1.87462	+	4.10485i	0.0835852	+	0.183026i	0.946810	−	0.321794i	$-0.104286\pi$
$503$	1.87462	+	4.10485i	0.0835852	+	0.183026i	−0.863224	+	0.504820i	$0.831559\pi$
$504$	−0.142315	+	0.989821i	−0.00633921	+	0.0440902i
$505$	4.12450			0.183538
$506$	−3.49697	+	1.88729i	−0.155459	+	0.0839005i
$507$	−6.53385			−0.290178
$508$	2.53094	−	17.6031i	0.112292	−	0.781011i
$509$	−0.896289	−	1.96260i	−0.0397273	−	0.0869907i	0.888728	−	0.458435i	$-0.151590\pi$
$509$	−0.896289	−	1.96260i	−0.0397273	−	0.0869907i	−0.928455	+	0.371444i	$0.878863\pi$
$510$	−0.727490	−	0.213610i	−0.0322138	−	0.00945883i
$511$	−0.530691	−	0.612450i	−0.0234764	−	0.0270932i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	−1.47106	−	0.945390i	−0.0649487	−	0.0417400i
$514$	−11.8702	+	25.9922i	−0.523573	+	1.14647i
$515$	−0.202364	+	0.233541i	−0.00891724	+	0.0102910i
$516$	5.80494	−	3.73061i	0.255548	−	0.164231i
$517$	−0.954397	−	6.63798i	−0.0419743	−	0.291938i
$518$	0.513095	+	3.56866i	0.0225441	+	0.156798i
$519$	−2.65147	+	1.70400i	−0.116387	+	0.0747973i
$520$	0.383061	−	0.442076i	0.0167984	−	0.0193863i
$521$	0.958970	−	2.09985i	0.0420133	−	0.0919962i	−0.887462	−	0.460882i	$-0.847533\pi$
$521$	0.958970	−	2.09985i	0.0420133	−	0.0919962i	0.929475	+	0.368885i	$0.120261\pi$
$522$	−2.40516	−	1.54570i	−0.105271	−	0.0676537i
$523$	1.02471	−	0.300883i	0.0448076	−	0.0131567i	−0.259252	−	0.965810i	$-0.583476\pi$
$523$	1.02471	−	0.300883i	0.0448076	−	0.0131567i	0.304060	+	0.952653i	$0.401658\pi$
$524$	10.8990	+	12.5781i	0.476123	+	0.549475i
$525$	−4.74669	−	1.39375i	−0.207163	−	0.0608284i
$526$	−10.8977	−	23.8626i	−0.475161	−	1.04046i
$527$	2.86111	−	19.8994i	0.124632	−	0.866834i
$528$	0.828583			0.0360595
$529$	12.6238	−	19.2260i	0.548862	−	0.835913i
$530$	−0.326471			−0.0141810
$531$	0.607818	−	4.22747i	0.0263771	−	0.183456i
$532$	0.726415	+	1.59063i	0.0314941	+	0.0689624i
$533$	−7.03199	−	2.06478i	−0.304589	−	0.0894355i
$534$	−3.50026	−	4.03951i	−0.151471	−	0.174807i
$535$	2.91655	−	0.856378i	0.126094	−	0.0370244i
$536$	7.72933	+	4.96734i	0.333856	+	0.214556i
$537$	−4.02083	+	8.80439i	−0.173512	+	0.379937i
$538$	8.55729	−	9.87563i	0.368931	−	0.425769i
$539$	0.697049	−	0.447966i	0.0300240	−	0.0192953i
$540$	−0.0327376	−	0.227695i	−0.00140880	−	0.00979843i
$541$	0.802108	+	5.57879i	0.0344853	+	0.239851i	0.999772	−	0.0213411i	$-0.00679358\pi$
$541$	0.802108	+	5.57879i	0.0344853	+	0.239851i	−0.965287	+	0.261192i	$0.915884\pi$
$542$	16.6099	−	10.6745i	0.713456	−	0.458511i
$543$	9.45725	−	10.9143i	0.405850	−	0.468375i
$544$	1.36921	−	2.99816i	0.0587045	−	0.128545i
$545$	−2.11182	−	1.35719i	−0.0904605	−	0.0581354i
$546$	−2.43986	+	0.716407i	−0.104416	+	0.0306594i
$547$	−7.93194	−	9.15395i	−0.339145	−	0.391395i	0.560400	−	0.828222i	$-0.310647\pi$
$547$	−7.93194	−	9.15395i	−0.339145	−	0.391395i	−0.899545	+	0.436828i	$0.856102\pi$
$548$	6.63965	+	1.94958i	0.283632	+	0.0832819i
$549$	3.88160	+	8.49953i	0.165663	+	0.362751i
$550$	−0.583359	+	4.05735i	−0.0248745	+	0.173006i
$551$	−4.99942			−0.212983
$552$	−4.22042	+	2.27774i	−0.179633	+	0.0969469i
$553$	0.133197			0.00566412
$554$	3.37635	−	23.4831i	0.143448	−	0.997700i
$555$	−0.344530	−	0.754415i	−0.0146245	−	0.0320231i
$556$	−7.03700	−	2.06625i	−0.298435	−	0.0876284i
$557$	9.15313	+	10.5633i	0.387831	+	0.447580i	0.915771	−	0.401701i	$-0.131581\pi$
$557$	9.15313	+	10.5633i	0.387831	+	0.447580i	−0.527940	+	0.849282i	$0.677035\pi$
$558$	5.85244	−	1.71843i	0.247754	−	0.0727470i
$559$	14.7612	+	9.48643i	0.624331	+	0.401233i
$560$	−0.0955606	+	0.209248i	−0.00403817	+	0.00884236i
$561$	1.78844	−	2.06397i	0.0755080	−	0.0871408i
$562$	1.05205	−	0.676114i	0.0443782	−	0.0285201i
$563$	0.298377	+	2.07525i	0.0125751	+	0.0874615i	0.995142	−	0.0984451i	$-0.0313869\pi$
$563$	0.298377	+	2.07525i	0.0125751	+	0.0874615i	−0.982567	+	0.185907i	$0.940478\pi$
$564$	−1.15184	−	8.01124i	−0.0485013	−	0.337334i
$565$	−0.654472	+	0.420604i	−0.0275338	+	0.0176949i
$566$	7.00721	−	8.08675i	0.294535	−	0.339911i
$567$	−0.415415	+	0.909632i	−0.0174458	+	0.0382010i
$568$	−4.54263	−	2.91937i	−0.190605	−	0.122494i
$569$	20.9817	−	6.16078i	0.879598	−	0.258273i	0.189405	−	0.981899i	$-0.439344\pi$
$569$	20.9817	−	6.16078i	0.879598	−	0.258273i	0.690193	+	0.723626i	$0.257526\pi$
$570$	−0.263419	−	0.304002i	−0.0110334	−	0.0127333i
$571$	−8.80371	−	2.58500i	−0.368424	−	0.108179i	0.0922796	−	0.995733i	$-0.470585\pi$
$571$	−8.80371	−	2.58500i	−0.368424	−	0.108179i	−0.460703	+	0.887554i	$0.652403\pi$
$572$	0.875269	+	1.91657i	0.0365968	+	0.0801359i
$573$	−1.98624	+	13.8146i	−0.0829765	+	0.577114i
$574$	2.88213			0.120298
$575$	−8.18210	−	22.2699i	−0.341217	−	0.928717i
$576$	1.00000			0.0416667
$577$	5.38668	−	37.4652i	0.224250	−	1.55970i	−0.497451	−	0.867492i	$-0.665731\pi$
$577$	5.38668	−	37.4652i	0.224250	−	1.55970i	0.721702	−	0.692204i	$-0.243360\pi$
$578$	2.54911	+	5.58177i	0.106029	+	0.232171i
$579$	3.00717	+	0.882985i	0.124974	+	0.0366956i
$580$	−0.430688	−	0.497041i	−0.0178834	−	0.0206385i
$581$	3.98111	−	1.16896i	0.165164	−	0.0484966i
$582$	−3.58137	−	2.30161i	−0.148453	−	0.0954048i
$583$	0.488501	−	1.06967i	0.0202317	−	0.0443012i
$584$	−0.530691	+	0.612450i	−0.0219601	+	0.0253434i
$585$	0.492092	−	0.316248i	0.0203455	−	0.0130753i
$586$	0.982574	+	6.83395i	0.0405897	+	0.282308i
$587$	2.12367	+	14.7704i	0.0876530	+	0.609640i	0.985544	+	0.169422i	$0.0541900\pi$
$587$	2.12367	+	14.7704i	0.0876530	+	0.609640i	−0.897891	+	0.440219i	$0.854901\pi$
$588$	0.841254	−	0.540641i	0.0346927	−	0.0222957i
$589$	6.98468	−	8.06075i	0.287799	−	0.332137i
$590$	0.408133	−	0.893687i	0.0168026	−	0.0367925i
$591$	1.97161	+	1.26708i	0.0811011	+	0.0521205i
$592$	3.45931	−	1.01575i	0.142177	−	0.0417469i
$593$	−6.23362	−	7.19398i	−0.255984	−	0.295421i	0.613182	−	0.789942i	$-0.289889\pi$
$593$	−6.23362	−	7.19398i	−0.255984	−	0.295421i	−0.869166	+	0.494520i	$0.835344\pi$
$594$	0.795020	+	0.233439i	0.0326201	+	0.00957812i
$595$	0.314969	+	0.689686i	0.0129125	+	0.0282744i
$596$	0.439876	−	3.05941i	0.0180180	−	0.125318i
$597$	−15.2439			−0.623893
$598$	−9.72677	−	7.35605i	−0.397757	−	0.300811i
$599$	43.7149			1.78614			0.893072	−	0.449914i	$-0.148546\pi$
$599$	43.7149			1.78614			0.893072	+	0.449914i	$0.148546\pi$
$600$	−0.704043	+	4.89673i	−0.0287424	+	0.199908i
$601$	−1.00684	−	2.20466i	−0.0410697	−	0.0899301i	0.887985	−	0.459872i	$-0.152105\pi$
$601$	−1.00684	−	2.20466i	−0.0410697	−	0.0899301i	−0.929055	+	0.369942i	$0.879378\pi$
$602$	−6.62083	−	1.94405i	−0.269845	−	0.0792336i
$603$	6.01678	+	6.94373i	0.245022	+	0.282771i
$604$	−4.62759	+	1.35878i	−0.188294	+	0.0552881i
$605$	−1.99585	−	1.28265i	−0.0811427	−	0.0521473i
$606$	−7.44829	+	16.3095i	−0.302566	+	0.662528i
$607$	0.287111	−	0.331344i	0.0116535	−	0.0134488i	−0.749893	−	0.661559i	$-0.769895\pi$
$607$	0.287111	−	0.331344i	0.0116535	−	0.0134488i	0.761546	+	0.648110i	$0.224440\pi$
$608$	1.47106	−	0.945390i	0.0596592	−	0.0383406i
$609$	0.406881	+	2.82992i	0.0164877	+	0.114674i
$610$	0.305897	+	2.12756i	0.0123854	+	0.0861425i
$611$	17.3138	−	11.1269i	0.700442	−	0.450146i
$612$	2.15843	−	2.49096i	0.0872494	−	0.100691i
$613$	−11.6599	+	25.5316i	−0.470938	+	1.03121i	0.513919	+	0.857839i	$0.328193\pi$
$613$	−11.6599	+	25.5316i	−0.470938	+	1.03121i	−0.984857	+	0.173371i	$0.944534\pi$
$614$	6.45025	+	4.14533i	0.260311	+	0.167292i
$615$	−0.636139	+	0.186787i	−0.0256516	+	0.00753199i
$616$	−0.542607	−	0.626202i	−0.0218622	−	0.0252304i
$617$	−29.4116	−	8.63603i	−1.18407	−	0.347673i	−0.370326	−	0.928902i	$-0.620754\pi$
$617$	−29.4116	−	8.63603i	−1.18407	−	0.347673i	−0.813741	+	0.581228i	$0.802572\pi$
$618$	−0.558047	−	1.22195i	−0.0224479	−	0.0491541i
$619$	−4.27414	+	29.7273i	−0.171792	+	1.19484i	0.703303	+	0.710890i	$0.251708\pi$
$619$	−4.27414	+	29.7273i	−0.171792	+	1.19484i	−0.875095	+	0.483950i	$0.839202\pi$
$620$	1.40311			0.0563503
$621$	−4.69117	+	0.996443i	−0.188250	+	0.0399859i
$622$	9.62061			0.385751
$623$	−0.760679	+	5.29064i	−0.0304760	+	0.211965i
$624$	1.05634	+	2.31307i	0.0422876	+	0.0925969i
$625$	−23.2284	−	6.82048i	−0.929137	−	0.272819i
$626$	−3.23532	−	3.73376i	−0.129309	−	0.149231i
$627$	1.39021	−	0.408202i	0.0555196	−	0.0163020i
$628$	15.7475	+	10.1203i	0.628393	+	0.403844i
$629$	4.93650	−	10.8094i	0.196831	−	0.431000i
$630$	−0.150642	+	0.173850i	−0.00600171	+	0.00692635i
$631$	−33.3010	+	21.4013i	−1.32569	+	0.851972i	−0.995756	−	0.0920312i	$-0.970664\pi$
$631$	−33.3010	+	21.4013i	−1.32569	+	0.851972i	−0.329937	+	0.944003i	$0.607028\pi$
$632$	−0.0189559	−	0.131841i	−0.000754026	−	0.00524437i
$633$	−0.323963	−	2.25321i	−0.0128764	−	0.0895571i
$634$	−12.1244	+	7.79189i	−0.481522	+	0.309456i
$635$	2.67903	−	3.09177i	0.106314	−	0.122693i
$636$	0.589562	−	1.29096i	0.0233777	−	0.0511899i
$637$	2.13919	+	1.37478i	0.0847579	+	0.0544706i
$638$	2.27298	−	0.667407i	0.0899882	−	0.0264229i
$639$	−3.53614	−	4.08092i	−0.139888	−	0.161439i
$640$	0.220718	+	0.0648087i	0.00872466	+	0.00256179i
$641$	5.93500	+	12.9958i	0.234418	+	0.513305i	0.989883	−	0.141885i	$-0.0453162\pi$
$641$	5.93500	+	12.9958i	0.234418	+	0.513305i	−0.755465	+	0.655189i	$0.772589\pi$
$642$	−1.88054	+	13.0794i	−0.0742189	+	0.516204i
$643$	12.9403			0.510315			0.255158	−	0.966899i	$-0.417873\pi$
$643$	12.9403			0.510315			0.255158	+	0.966899i	$0.417873\pi$
$644$	4.48518	+	1.69798i	0.176741	+	0.0669097i
$645$	1.58733			0.0625011
$646$	0.820241	−	5.70490i	0.0322720	−	0.224456i
$647$	19.3848	+	42.4467i	0.762094	+	1.66875i	0.743326	+	0.668929i	$0.233247\pi$
$647$	19.3848	+	42.4467i	0.762094	+	1.66875i	0.0187673	+	0.999824i	$0.494026\pi$
$648$	0.959493	+	0.281733i	0.0376924	+	0.0110675i
$649$	2.31744	+	2.67447i	0.0909675	+	0.104982i
$650$	−12.0702	+	3.54413i	−0.473432	+	0.139012i
$651$	−5.13124	−	3.29765i	−0.201109	−	0.129245i
$652$	2.30054	−	5.03749i	0.0900963	−	0.197283i
$653$	−15.0686	+	17.3900i	−0.589678	+	0.680525i	−0.969657	−	0.244471i	$-0.921386\pi$
$653$	−15.0686	+	17.3900i	−0.589678	+	0.680525i	0.379979	+	0.924995i	$0.375931\pi$
$654$	9.18038	−	5.89987i	0.358981	−	0.230703i
$655$	0.544857	+	3.78956i	0.0212893	+	0.148070i
$656$	−0.410170	−	2.85279i	−0.0160144	−	0.111383i
$657$	−0.681741	+	0.438129i	−0.0265973	+	0.0170930i
$658$	−5.30019	+	6.11675i	−0.206623	+	0.238456i
$659$	4.84326	−	10.6053i	0.188667	−	0.413123i	−0.791535	−	0.611124i	$-0.790718\pi$
$659$	4.84326	−	10.6053i	0.188667	−	0.413123i	0.980202	+	0.198001i	$0.0634450\pi$
$660$	0.160347	+	0.103048i	0.00624148	+	0.00401116i
$661$	44.2658	−	12.9976i	1.72174	−	0.505549i	0.736458	−	0.676483i	$-0.236497\pi$
$661$	44.2658	−	12.9976i	1.72174	−	0.505549i	0.985282	+	0.170935i	$0.0546788\pi$
$662$	7.55163	+	8.71505i	0.293503	+	0.338720i
$663$	8.04181	+	2.36129i	0.312318	+	0.0917048i
$664$	−1.72363	−	3.77423i	−0.0668899	−	0.146468i
$665$	−0.0572465	+	0.398158i	−0.00221992	+	0.0154399i
$666$	3.60535			0.139705
$667$	−9.74283	+	9.64778i	−0.377244	+	0.373563i
$668$	19.3848			0.750021
$669$	−1.58808	+	11.0454i	−0.0613988	+	0.427038i
$670$	0.877998	+	1.92255i	0.0339200	+	0.0742745i
$671$	−7.42860	−	2.18123i	−0.286778	−	0.0842056i
$672$	−0.654861	−	0.755750i	−0.0252618	−	0.0291537i
$673$	−6.20006	+	1.82050i	−0.238995	+	0.0701752i	−0.399036	−	0.916935i	$-0.630655\pi$
$673$	−6.20006	+	1.82050i	−0.238995	+	0.0701752i	0.160042	+	0.987110i	$0.448837\pi$
$674$	−2.89622	−	1.86129i	−0.111558	−	0.0716942i
$675$	−2.05509	+	4.50003i	−0.0791006	+	0.173206i
$676$	4.27876	−	4.93795i	0.164568	−	0.189921i
$677$	20.5849	−	13.2291i	0.791141	−	0.508435i	−0.0815730	−	0.996667i	$-0.525994\pi$
$677$	20.5849	−	13.2291i	0.791141	−	0.508435i	0.872714	+	0.488232i	$0.162358\pi$
$678$	−0.481302	−	3.34753i	−0.0184843	−	0.128561i
$679$	0.605861	+	4.21385i	0.0232508	+	0.161713i
$680$	0.637841	−	0.409915i	0.0244601	−	0.0157195i
$681$	−0.589543	+	0.680369i	−0.0225913	+	0.0260718i
$682$	−2.09949	+	4.59724i	−0.0803936	+	0.176037i
$683$	22.0281	+	14.1566i	0.842880	+	0.541686i	0.889347	−	0.457234i	$-0.151160\pi$
$683$	22.0281	+	14.1566i	0.842880	+	0.541686i	−0.0464665	+	0.998920i	$0.514796\pi$
$684$	1.67782	−	0.492651i	0.0641529	−	0.0188370i
$685$	1.04244	+	1.20303i	0.0398294	+	0.0459656i
$686$	−0.959493	−	0.281733i	−0.0366336	−	0.0107566i
$687$	7.74544	+	16.9601i	0.295507	+	0.647070i
$688$	−0.982022	+	6.83011i	−0.0374392	+	0.260395i
$689$	3.60886			0.137487
$690$	−1.10001	−	0.0840958i	−0.0418765	−	0.00320147i
$691$	41.2876			1.57065			0.785327	−	0.619081i	$-0.212495\pi$
$691$	41.2876			1.57065			0.785327	+	0.619081i	$0.212495\pi$
$692$	0.448550	−	3.11973i	0.0170513	−	0.118594i
$693$	−0.344206	−	0.753706i	−0.0130753	−	0.0286309i
$694$	−2.14058	−	0.628532i	−0.0812555	−	0.0238588i
$695$	−1.10482	−	1.27503i	−0.0419082	−	0.0483646i
$696$	2.74321	−	0.805480i	0.103981	−	0.0305316i
$697$	−7.99152	−	5.13584i	−0.302700	−	0.194534i
$698$	−10.6778	+	23.3812i	−0.404162	+	0.884992i
$699$	−9.64247	+	11.1280i	−0.364712	+	0.420900i
$700$	4.16175	−	2.67460i	0.157299	−	0.101090i
$701$	7.02798	+	48.8807i	0.265443	+	1.84620i	0.489981	+	0.871733i	$0.337004\pi$
$701$	7.02798	+	48.8807i	0.265443	+	1.84620i	−0.224538	+	0.974465i	$0.572087\pi$
$702$	0.361887	+	2.51698i	0.0136585	+	0.0949973i
$703$	5.30368	−	3.40847i	0.200032	−	0.128553i
$704$	−0.542607	+	0.626202i	−0.0204503	+	0.0236009i
$705$	0.773431	−	1.69358i	0.0291291	−	0.0637838i
$706$	9.77268	+	6.28052i	0.367800	+	0.236370i
$707$	17.2035	−	5.05140i	0.647003	−	0.189977i
$708$	2.79687	+	3.22776i	0.105113	+	0.121307i
$709$	−0.153596	−	0.0451000i	−0.00576843	−	0.00169376i	0.278847	−	0.960336i	$-0.410048\pi$
$709$	−0.153596	−	0.0451000i	−0.00576843	−	0.00169376i	−0.284616	+	0.958642i	$0.591866\pi$
$710$	−0.516011	−	1.12991i	−0.0193656	−	0.0424047i
$711$	0.0189559	−	0.131841i	0.000710903	−	0.00494444i
$712$	5.34504			0.200314
$713$	−1.94377	−	29.1876i	−0.0727949	−	1.09308i
$714$	−3.29601			−0.123350
$715$	−0.0689773	+	0.479747i	−0.00257960	+	0.0179415i
$716$	−4.02083	−	8.80439i	−0.150265	−	0.329035i
$717$	−24.4307	−	7.17350i	−0.912382	−	0.267899i
$718$	−18.3415	−	21.1673i	−0.684501	−	0.789956i
$719$	−37.8000	+	11.0991i	−1.40970	+	0.413926i	−0.896005	−	0.444044i	$-0.853543\pi$
$719$	−37.8000	+	11.0991i	−1.40970	+	0.413926i	−0.513699	+	0.857970i	$0.671725\pi$
$720$	0.193519	+	0.124367i	0.00721202	+	0.00463489i
$721$	−0.558047	+	1.22195i	−0.0207828	+	0.0455079i
$722$	−10.4399	+	12.0483i	−0.388534	+	0.448393i
$723$	11.8592	−	7.62146i	0.441049	−	0.283445i
$724$	2.05526	+	14.2946i	0.0763831	+	0.531256i
$725$	2.01288	+	13.9999i	0.0747563	+	0.519942i
$726$	8.67623	−	5.57587i	0.322005	−	0.206940i
$727$	−5.81723	+	6.71345i	−0.215749	+	0.248988i	−0.853300	−	0.521421i	$-0.825402\pi$
$727$	−5.81723	+	6.71345i	−0.215749	+	0.248988i	0.637551	+	0.770409i	$0.279948\pi$
$728$	1.05634	−	2.31307i	0.0391507	−	0.0857281i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−0.178867	+	0.0525202i	−0.00662018	+	0.00194386i
$731$	14.8939	+	17.1885i	0.550871	+	0.635739i
$732$	−8.96542	−	2.63249i	−0.331372	−	0.0972995i
$733$	−6.91413	−	15.1398i	−0.255379	−	0.559202i	0.737905	−	0.674905i	$-0.235815\pi$
$733$	−6.91413	−	15.1398i	−0.255379	−	0.559202i	−0.993284	+	0.115702i	$0.963088\pi$
$734$	−0.108490	+	0.754567i	−0.00400445	+	0.0278516i
$735$	0.230036			0.00848502
$736$	1.04239	−	4.68118i	0.0384229	−	0.172551i
$737$	−7.61292			−0.280425
$738$	0.410170	−	2.85279i	0.0150986	−	0.105013i
$739$	0.785470	+	1.71994i	0.0288940	+	0.0632690i	0.923529	−	0.383529i	$-0.125291\pi$
$739$	0.785470	+	1.71994i	0.0288940	+	0.0632690i	−0.894635	+	0.446798i	$0.852564\pi$
$740$	0.795768	+	0.233658i	0.0292530	+	0.00858946i
$741$	2.91189	+	3.36049i	0.106971	+	0.123451i
$742$	−1.36172	+	0.399838i	−0.0499905	+	0.0146785i
$743$	22.7641	+	14.6296i	0.835133	+	0.536707i	0.886905	−	0.461952i	$-0.152851\pi$
$743$	22.7641	+	14.6296i	0.835133	+	0.536707i	−0.0517721	+	0.998659i	$0.516487\pi$
$744$	−2.53383	+	5.54831i	−0.0928947	+	0.203411i
$745$	0.465614	−	0.537347i	0.0170588	−	0.0196869i
$746$	−8.49492	+	5.45935i	−0.311021	+	0.199881i
$747$	−0.590490	−	4.10695i	−0.0216049	−	0.150265i
$748$	0.388665	+	2.70322i	0.0142110	+	0.0988397i
$749$	11.1163	−	7.14399i	0.406179	−	0.261036i
$750$	−1.49845	+	1.72930i	−0.0547155	+	0.0631451i
$751$	16.9956	−	37.2151i	0.620177	−	1.35800i	−0.295214	−	0.955431i	$-0.595391\pi$
$751$	16.9956	−	37.2151i	0.620177	−	1.35800i	0.915391	−	0.402567i	$-0.131882\pi$
$752$	6.80878	+	4.37574i	0.248291	+	0.159567i
$753$	−7.16620	+	2.10419i	−0.261151	+	0.0766808i
$754$	4.76091	+	5.49438i	0.173382	+	0.200093i
$755$	−1.06451	−	0.312570i	−0.0387416	−	0.0113756i
$756$	−0.415415	−	0.909632i	−0.0151085	−	0.0330830i
$757$	−6.17435	+	42.9435i	−0.224410	+	1.56081i	0.496659	+	0.867946i	$0.334560\pi$
$757$	−6.17435	+	42.9435i	−0.224410	+	1.56081i	−0.721069	+	0.692863i	$0.756349\pi$
$758$	22.5462			0.818914
$759$	1.92149	−	3.47830i	0.0697456	−	0.126254i
$760$	0.402253			0.0145912
$761$	−4.24534	+	29.5270i	−0.153894	+	1.07035i	0.755719	+	0.654896i	$0.227288\pi$
$761$	−4.24534	+	29.5270i	−0.153894	+	1.07035i	−0.909613	+	0.415457i	$0.863622\pi$
$762$	7.38778	+	16.1770i	0.267631	+	0.586031i
$763$	−10.4707	−	3.07447i	−0.379065	−	0.111303i
$764$	−9.13969	−	10.5478i	−0.330662	−	0.381605i
$765$	0.727490	−	0.213610i	0.0263025	−	0.00772310i
$766$	−18.9597	−	12.1846i	−0.685040	−	0.440249i
$767$	−4.51158	+	9.87898i	−0.162904	+	0.356709i
$768$	−0.654861	+	0.755750i	−0.0236303	+	0.0272708i
$769$	18.3388	−	11.7856i	0.661313	−	0.425000i	−0.166471	−	0.986046i	$-0.553237\pi$
$769$	18.3388	−	11.7856i	0.661313	−	0.425000i	0.827785	+	0.561046i	$0.189601\pi$
$770$	−0.0271258	−	0.188664i	−0.000977547	−	0.00679899i
$771$	−4.06656	−	28.2835i	−0.146454	−	1.01861i
$772$	−2.63659	+	1.69444i	−0.0948931	+	0.0609841i
$773$	−10.5827	+	12.2131i	−0.380632	+	0.439273i	−0.913446	−	0.406959i	$-0.866589\pi$
$773$	−10.5827	+	12.2131i	−0.380632	+	0.439273i	0.532814	+	0.846232i	$0.321135\pi$
$774$	−2.86651	+	6.27677i	−0.103034	+	0.225614i
$775$	−25.3847	−	16.3137i	−0.911844	−	0.586006i
$776$	4.08474	−	1.19939i	0.146634	−	0.0430555i
$777$	−2.36101	−	2.72475i	−0.0847006	−	0.0977497i
$778$	14.2993	+	4.19867i	0.512656	+	0.150529i
$779$	−2.09362	−	4.58439i	−0.0750118	−	0.164253i
$780$	−0.0832472	+	0.578997i	−0.00298073	+	0.0207314i
$781$	4.47421			0.160100
$782$	−9.41071	−	12.7005i	−0.336526	−	0.454170i
$783$	2.85902			0.102173
$784$	−0.142315	+	0.989821i	−0.00508267	+	0.0353508i
$785$	1.78881	+	3.91694i	0.0638452	+	0.139802i
$786$	−15.9690	−	4.68892i	−0.569595	−	0.167248i
$787$	26.9662	+	31.1207i	0.961242	+	1.10933i	0.993946	+	0.109868i	$0.0350427\pi$
$787$	26.9662	+	31.1207i	0.961242	+	1.10933i	−0.0327041	+	0.999465i	$0.510412\pi$
$788$	−2.24872	+	0.660284i	−0.0801074	+	0.0235216i
$789$	22.0688	+	14.1828i	0.785670	+	0.504919i
$790$	0.0127284	−	0.0278713i	0.000452856	−	0.000991616i
$791$	−2.21471	+	2.55591i	−0.0787460	+	0.0908777i
$792$	−0.697049	+	0.447966i	−0.0247685	+	0.0159178i
$793$	−3.38144	−	23.5185i	−0.120079	−	0.835165i
$794$	2.45407	+	17.0684i	0.0870917	+	0.605736i
$795$	0.274644	−	0.176503i	0.00974064	−	0.00625993i
$796$	9.98266	−	11.5206i	0.353826	−	0.408337i
$797$	2.70896	−	5.93179i	0.0959562	−	0.210115i	−0.855567	−	0.517693i	$-0.826791\pi$
$797$	2.70896	−	5.93179i	0.0959562	−	0.210115i	0.951523	+	0.307578i	$0.0995184\pi$
$798$	−1.47106	−	0.945390i	−0.0520748	−	0.0334665i
$799$	25.5961	−	7.51569i	0.905524	−	0.265886i
$800$	−3.23965	−	3.73876i	−0.114539	−	0.132185i
$801$	5.12853	+	1.50587i	0.181208	+	0.0532074i
$802$	−6.80303	−	14.8966i	−0.240223	−	0.526016i
$803$	0.0955607	−	0.664639i	0.00337226	−	0.0234546i
$804$	−9.18787			−0.324031
$805$	0.656795	+	0.886400i	0.0231490	+	0.0312415i
$806$	−15.5102			−0.546324
$807$	−1.85968	+	12.9343i	−0.0654637	+	0.455310i
$808$	−7.44829	−	16.3095i	−0.262030	−	0.573766i
$809$	13.7116	+	4.02609i	0.482074	+	0.141550i	0.513735	−	0.857949i	$-0.328261\pi$
$809$	13.7116	+	4.02609i	0.482074	+	0.141550i	−0.0316607	+	0.999499i	$0.510080\pi$
$810$	0.150642	+	0.173850i	0.00529301	+	0.00610846i
$811$	−35.8821	+	10.5359i	−1.25999	+	0.369967i	−0.842491	−	0.538710i	$-0.818912\pi$
$811$	−35.8821	+	10.5359i	−1.25999	+	0.369967i	−0.417500	+	0.908677i	$0.637094\pi$
$812$	−2.40516	−	1.54570i	−0.0844047	−	0.0542436i
$813$	−8.20205	+	17.9600i	−0.287658	+	0.629884i
$814$	−1.95629	+	2.25768i	−0.0685679	+	0.0791316i
$815$	1.07170	−	0.688737i	0.0375399	−	0.0241254i
$816$	0.469072	+	3.26246i	0.0164208	+	0.114209i
$817$	1.71721	+	11.9435i	0.0600776	+	0.417849i
$818$	−0.461240	+	0.296421i	−0.0161269	+	0.0103641i
$819$	1.66522	−	1.92177i	0.0581875	−	0.0671520i
$820$	0.275418	−	0.603081i	0.00961801	−	0.0210605i
$821$	32.0384	+	20.5899i	1.11815	+	0.718591i	0.963054	−	0.269309i	$-0.0867952\pi$
$821$	32.0384	+	20.5899i	1.11815	+	0.718591i	0.155095	+	0.987900i	$0.450432\pi$
$822$	−6.63965	+	1.94958i	−0.231585	+	0.0679994i
$823$	0.783307	+	0.903984i	0.0273044	+	0.0315109i	0.769238	−	0.638963i	$-0.220636\pi$
$823$	0.783307	+	0.903984i	0.0273044	+	0.0315109i	−0.741933	+	0.670474i	$0.766091\pi$
$824$	1.28893	+	0.378465i	0.0449021	+	0.0131845i
$825$	−1.70282	−	3.72865i	−0.0592844	−	0.129815i
$826$	0.607818	−	4.22747i	0.0211487	−	0.147092i
$827$	29.0318			1.00954			0.504768	−	0.863255i	$-0.331578\pi$
$827$	29.0318			1.00954			0.504768	+	0.863255i	$0.331578\pi$
$828$	2.31900	−	4.19788i	0.0805909	−	0.145887i
$829$	6.44862			0.223970			0.111985	−	0.993710i	$-0.464279\pi$
$829$	6.44862			0.223970			0.111985	+	0.993710i	$0.464279\pi$
$830$	0.135834	−	0.944747i	0.00471487	−	0.0327927i
$831$	9.85553	+	21.5806i	0.341885	+	0.748623i
$832$	−2.43986	−	0.716407i	−0.0845869	−	0.0248370i
$833$	2.15843	+	2.49096i	0.0747852	+	0.0863067i
$834$	7.03700	−	2.06625i	0.243671	−	0.0715483i
$835$	3.75133	+	2.41083i	0.129820	+	0.0834303i
$836$	−0.601895	+	1.31797i	−0.0208170	+	0.0455828i
$837$	−3.99433	+	4.60970i	−0.138064	+	0.159335i
$838$	2.99073	−	1.92203i	0.103313	−	0.0663953i
$839$	−2.08351	−	14.4911i	−0.0719308	−	0.500290i	−0.993657	−	0.112450i	$-0.964130\pi$
$839$	−2.08351	−	14.4911i	−0.0719308	−	0.500290i	0.921727	−	0.387840i	$-0.126779\pi$
$840$	−0.0327376	−	0.227695i	−0.00112955	−	0.00785622i
$841$	−17.5199	+	11.2594i	−0.604136	+	0.388254i
$842$	16.7443	−	19.3240i	0.577047	−	0.665948i
$843$	−0.519509	+	1.13757i	−0.0178928	+	0.0391799i
$844$	1.91501	+	1.23070i	0.0659175	+	0.0423626i
$845$	1.44214	−	0.423451i	0.0496111	−	0.0145671i
$846$	5.30019	+	6.11675i	0.182224	+	0.210298i
$847$	−9.89568	−	2.90563i	−0.340020	−	0.0998388i
$848$	0.589562	+	1.29096i	0.0202456	+	0.0443318i
$849$	−1.52281	+	10.5914i	−0.0522628	+	0.363495i
$850$	−16.3057			−0.559279
$851$	3.75818	−	16.8773i	0.128829	−	0.578547i
$852$	5.39983			0.184995
$853$	−0.00193538	+	0.0134609i	−6.62662e−5	+	0.000460892i	−0.989855	−	0.142084i	$-0.954620\pi$
$853$	−0.00193538	+	0.0134609i	−6.62662e−5	+	0.000460892i	0.989788	+	0.142545i	$0.0455287\pi$
$854$	3.88160	+	8.49953i	0.132826	+	0.290848i
$855$	0.385959	+	0.113328i	0.0131995	+	0.00387572i
$856$	−8.65328	−	9.98642i	−0.295763	−	0.341329i
$857$	4.27529	−	1.25534i	0.146041	−	0.0428815i	−0.207895	−	0.978151i	$-0.566661\pi$
$857$	4.27529	−	1.25534i	0.146041	−	0.0428815i	0.353936	+	0.935270i	$0.384843\pi$
$858$	−1.77250	−	1.13912i	−0.0605121	−	0.0388888i
$859$	−11.0733	+	24.2471i	−0.377816	+	0.827302i	0.621230	+	0.783629i	$0.286633\pi$
$859$	−11.0733	+	24.2471i	−0.377816	+	0.827302i	−0.999046	+	0.0436735i	$0.986094\pi$
$860$	−1.03948	+	1.19962i	−0.0354460	+	0.0409069i
$861$	−2.42460	+	1.55820i	−0.0826302	+	0.0531032i
$862$	−3.11034	−	21.6329i	−0.105939	−	0.736820i
$863$	3.14565	+	21.8785i	0.107079	+	0.744753i	0.970645	+	0.240516i	$0.0773168\pi$
$863$	3.14565	+	21.8785i	0.107079	+	0.744753i	−0.863566	+	0.504236i	$0.831774\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	0.474795	−	0.547942i	0.0161435	−	0.0186306i
$866$	−14.4241	+	31.5844i	−0.490151	+	1.07328i
$867$	−5.16218	−	3.31753i	−0.175317	−	0.112669i
$868$	5.85244	−	1.71843i	0.198645	−	0.0583274i
$869$	0.0722737	+	0.0834083i	0.00245172	+	0.00282943i
$870$	0.631039	+	0.185290i	0.0213942	+	0.00628191i
$871$	−9.70555	−	21.2522i	−0.328860	−	0.720103i
$872$	−1.55304	+	10.8017i	−0.0525927	+	0.365790i
$873$	4.25719			0.144084
$874$	−0.557254	−	8.36769i	−0.0188494	−	0.283041i
$875$	2.28819			0.0773550
$876$	0.115330	−	0.802139i	0.00389664	−	0.0271018i
$877$	4.50505	+	9.86469i	0.152125	+	0.333107i	0.970316	−	0.241839i	$-0.0777505\pi$
$877$	4.50505	+	9.86469i	0.152125	+	0.333107i	−0.818192	+	0.574946i	$0.805023\pi$
$878$	−21.9729	−	6.45182i	−0.741549	−	0.217739i
$879$	−4.52131	−	5.21787i	−0.152500	−	0.175994i
$880$	−0.182884	+	0.0536994i	−0.00616500	+	0.00181021i
$881$	−40.6283	−	26.1102i	−1.36880	−	0.879676i	−0.370020	−	0.929024i	$-0.620649\pi$
$881$	−40.6283	−	26.1102i	−1.36880	−	0.879676i	−0.998782	+	0.0493482i	$0.984286\pi$
$882$	−0.415415	+	0.909632i	−0.0139878	+	0.0306289i
$883$	−31.2475	+	36.0615i	−1.05156	+	1.21357i	−0.0752563	+	0.997164i	$0.523978\pi$
$883$	−31.2475	+	36.0615i	−1.05156	+	1.21357i	−0.976304	+	0.216402i	$0.930568\pi$
$884$	−7.05081	+	4.53128i	−0.237144	+	0.152403i
$885$	0.139820	+	0.972471i	0.00470001	+	0.0326893i
$886$	−0.0873243	−	0.607354i	−0.00293372	−	0.0204045i
$887$	−0.817412	+	0.525319i	−0.0274460	+	0.0176385i	−0.554292	−	0.832322i	$-0.687011\pi$
$887$	−0.817412	+	0.525319i	−0.0274460	+	0.0176385i	0.526846	+	0.849961i	$0.323374\pi$
$888$	−2.36101	+	2.72475i	−0.0792301	+	0.0914365i
$889$	7.38778	−	16.1770i	0.247778	−	0.542559i
$890$	1.03437	+	0.664747i	0.0346721	+	0.0222824i
$891$	−0.795020	+	0.233439i	−0.0266342	+	0.00782050i
$892$	−7.30755	−	8.43336i	−0.244675	−	0.282370i
$893$	13.5796	+	3.98733i	0.454424	+	0.133431i
$894$	1.28399	+	2.81155i	0.0429431	+	0.0940324i
$895$	0.316869	−	2.20387i	0.0105918	−	0.0736674i
$896$	1.00000			0.0334077
$897$	12.1597	+	0.929610i	0.405999	+	0.0310388i
$898$	−18.3106			−0.611034
$899$	−2.48178	+	17.2612i	−0.0827720	+	0.575692i
$900$	−2.05509	−	4.50003i	−0.0685031	−	0.150001i
$901$	4.48826	+	1.31787i	0.149526	+	0.0439047i
$902$	1.56386	+	1.80479i	0.0520709	+	0.0600931i
$903$	6.62083	−	1.94405i	0.220328	−	0.0646940i
$904$	2.84508	+	1.82842i	0.0946260	+	0.0608124i
$905$	−1.38005	+	3.02189i	−0.0458744	+	0.100451i
$906$	3.15836	−	3.64495i	0.104930	−	0.121095i
$907$	−49.2503	+	31.6512i	−1.63533	+	1.05096i	−0.690533	+	0.723301i	$0.742624\pi$
$907$	−49.2503	+	31.6512i	−1.63533	+	1.05096i	−0.944795	+	0.327661i	$0.893740\pi$
$908$	−0.128120	−	0.891094i	−0.00425181	−	0.0295720i
$909$	−2.55167	−	17.7473i	−0.0846336	−	0.588640i
$910$	0.492092	−	0.316248i	0.0163127	−	0.0104835i
$911$	−9.08967	+	10.4900i	−0.301154	+	0.347551i	−0.886077	−	0.463539i	$-0.846579\pi$
$911$	−9.08967	+	10.4900i	−0.301154	+	0.347551i	0.584922	+	0.811089i	$0.301125\pi$
$912$	−0.726415	+	1.59063i	−0.0240540	+	0.0526709i
$913$	2.89218	+	1.85869i	0.0957172	+	0.0615137i
$914$	−27.5319	+	8.08411i	−0.910676	+	0.267398i
$915$	−1.40758	−	1.62444i	−0.0465333	−	0.0537023i
$916$	−17.8898	−	5.25292i	−0.591096	−	0.173561i
$917$	6.91382	+	15.1391i	0.228314	+	0.499939i
$918$	−0.469072	+	3.26246i	−0.0154817	+	0.107677i
$919$	18.8702			0.622471			0.311236	−	0.950333i	$-0.399257\pi$
$919$	18.8702			0.622471			0.311236	+	0.950333i	$0.399257\pi$
$920$	0.783906	−	0.776258i	0.0258446	−	0.0255925i
$921$	−7.66743			−0.252651
$922$	−1.92453	+	13.3854i	−0.0633809	+	0.440824i
$923$	5.70408	+	12.4902i	0.187752	+	0.411120i
$924$	0.795020	+	0.233439i	0.0261542	+	0.00767958i
$925$	−11.6801	−	13.4795i	−0.384039	−	0.443205i
$926$	2.08519	−	0.612266i	0.0685235	−	0.0201203i
$927$	1.13010	+	0.726269i	0.0371172	+	0.0238538i
$928$	−1.18768	+	2.60066i	−0.0389875	+	0.0853708i
$929$	16.2677	−	18.7739i	0.533725	−	0.615952i	−0.423288	−	0.905995i	$-0.639124\pi$
$929$	16.2677	−	18.7739i	0.533725	−	0.615952i	0.957014	+	0.290043i	$0.0936696\pi$
$930$	−1.18037	+	0.758579i	−0.0387059	+	0.0248748i
$931$	0.248859	+	1.73085i	0.00815601	+	0.0567263i
$932$	−2.09551	−	14.5746i	−0.0686407	−	0.477406i
$933$	−8.09337	+	5.20129i	−0.264965	+	0.170283i
$934$	−11.9069	+	13.7413i	−0.389605	+	0.449629i
$935$	−0.260978	+	0.571462i	−0.00853489	+	0.0186888i
$936$	−2.13919	−	1.37478i	−0.0699217	−	0.0449359i
$937$	7.40746	−	2.17503i	0.241991	−	0.0710550i	−0.158488	−	0.987361i	$-0.550662\pi$
$937$	7.40746	−	2.17503i	0.241991	−	0.0710550i	0.400479	+	0.916306i	$0.368844\pi$
$938$	6.01678	+	6.94373i	0.196455	+	0.226721i
$939$	4.74035	+	1.39189i	0.154695	+	0.0454227i
$940$	0.773431	+	1.69358i	0.0252265	+	0.0552384i
$941$	−1.08297	+	7.53219i	−0.0353037	+	0.245543i	−0.999830	−	0.0184446i	$-0.994129\pi$
$941$	−1.08297	+	7.53219i	−0.0353037	+	0.245543i	0.964526	+	0.263987i	$0.0850377\pi$
$942$	−18.7191			−0.609900
$943$	−12.9269	−	4.89379i	−0.420957	−	0.159364i
$944$	−4.27094			−0.139007
$945$	0.0327376	−	0.227695i	0.00106495	−	0.00740692i
$946$	−2.37514	−	5.20083i	−0.0772225	−	0.169094i
$947$	−41.0527	−	12.0542i	−1.33403	−	0.391708i	−0.464497	−	0.885575i	$-0.653765\pi$
$947$	−41.0527	−	12.0542i	−1.33403	−	0.391708i	−0.869537	+	0.493867i	$0.835583\pi$
$948$	0.0872256	+	0.100664i	0.00283296	+	0.00326940i
$949$	1.97723	−	0.580567i	0.0641836	−	0.0188460i
$950$	−7.27744	−	4.67693i	−0.236111	−	0.151739i
$951$	5.98710	−	13.1099i	0.194145	−	0.425118i
$952$	2.15843	−	2.49096i	0.0699551	−	0.0807325i
$953$	25.1663	−	16.1734i	0.815218	−	0.523909i	−0.0653315	−	0.997864i	$-0.520810\pi$
$953$	25.1663	−	16.1734i	0.815218	−	0.523909i	0.880549	+	0.473955i	$0.157174\pi$
$954$	0.201975	+	1.40477i	0.00653918	+	0.0454810i
$955$	−0.456908	−	3.17787i	−0.0147852	−	0.102833i
$956$	21.4201	−	13.7659i	0.692775	−	0.445219i
$957$	−1.55133	+	1.79032i	−0.0501472	+	0.0578730i
$958$	3.08411	−	6.75325i	0.0996430	−	0.218188i
$959$	5.82144	+	3.74121i	0.187984	+	0.120810i
$960$	−0.220718	+	0.0648087i	−0.00712365	+	0.00209169i
$961$	−4.06280	−	4.68872i	−0.131058	−	0.151249i
$962$	−8.79656	−	2.58290i	−0.283612	−	0.0832761i
$963$	−5.48926	−	12.0198i	−0.176889	−	0.387333i
$964$	−2.00622	+	13.9536i	−0.0646161	+	0.449415i
$965$	−0.720963			−0.0232086
$966$	−4.69117	+	0.996443i	−0.150936	+	0.0320600i
$967$	5.19701			0.167125			0.0835623	−	0.996503i	$-0.473370\pi$
$967$	5.19701			0.167125			0.0835623	+	0.996503i	$0.473370\pi$
$968$	−1.46776	+	10.2085i	−0.0471755	+	0.328113i
$969$	2.39427	+	5.24272i	0.0769151	+	0.168421i
$970$	0.939639	+	0.275903i	0.0301700	+	0.00885871i
$971$	−25.2938	−	29.1905i	−0.811715	−	0.936769i	0.187247	−	0.982313i	$-0.440043\pi$
$971$	−25.2938	−	29.1905i	−0.811715	−	0.936769i	−0.998962	+	0.0455436i	$0.985498\pi$
$972$	−0.959493	+	0.281733i	−0.0307758	+	0.00903658i
$973$	−6.16982	−	3.96510i	−0.197795	−	0.127115i
$974$	−5.99961	+	13.1373i	−0.192240	+	0.420947i
$975$	8.23799	−	9.50714i	0.263827	−	0.304472i
$976$	7.86060	−	5.05170i	0.251612	−	0.161701i
$977$	1.45398	+	10.1126i	0.0465169	+	0.323532i	0.999772	+	0.0213647i	$0.00680111\pi$
$977$	1.45398	+	10.1126i	0.0465169	+	0.323532i	−0.953255	+	0.302168i	$0.902290\pi$
$978$	0.788131	+	5.48157i	0.0252017	+	0.175281i
$979$	−3.72576	+	2.39440i	−0.119076	+	0.0765253i
$980$	−0.150642	+	0.173850i	−0.00481208	+	0.00555343i
$981$	−4.53332	+	9.92658i	−0.144738	+	0.316931i
$982$	−0.643831	−	0.413765i	−0.0205455	−	0.0132038i
$983$	−4.15477	+	1.21995i	−0.132517	+	0.0389104i	−0.347318	−	0.937747i	$-0.612908\pi$
$983$	−4.15477	+	1.21995i	−0.132517	+	0.0389104i	0.214802	+	0.976658i	$0.431089\pi$
$984$	1.88739	+	2.17817i	0.0601679	+	0.0694375i
$985$	−0.517288	−	0.151889i	−0.0164822	−	0.00483960i
$986$	3.91461	+	8.57181i	0.124667	+	0.272982i
$987$	1.15184	−	8.01124i	0.0366635	−	0.255000i
$988$	−4.44657			−0.141464
$989$	26.3947	+	19.9615i	0.839302	+	0.634738i
$990$	−0.190604			−0.00605780
$991$	−7.09515	+	49.3479i	−0.225385	+	1.56759i	0.491803	+	0.870707i	$0.336338\pi$
$991$	−7.09515	+	49.3479i	−0.225385	+	1.56759i	−0.717188	+	0.696880i	$0.754571\pi$
$992$	−2.53383	−	5.54831i	−0.0804492	−	0.176159i
$993$	−11.0645	−	3.24884i	−0.351123	−	0.103099i
$994$	−3.53614	−	4.08092i	−0.112160	−	0.129439i
$995$	3.36462	−	0.987941i	0.106666	−	0.0313198i
$996$	3.49051	+	2.24322i	0.110601	+	0.0710790i
$997$	4.06198	−	8.89449i	0.128644	−	0.281691i	−0.834340	−	0.551251i	$-0.814151\pi$
$997$	4.06198	−	8.89449i	0.128644	−	0.281691i	0.962984	+	0.269559i	$0.0868781\pi$
$998$	−16.7824	+	19.3679i	−0.531237	+	0.613080i
$999$	−3.03302	+	1.94920i	−0.0959604	+	0.0616700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.f.169.2	✓	30
23.3	even	11	inner	966.2.q.f.463.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.f.169.2	✓	30	1.1	even	1	trivial
966.2.q.f.463.2	yes	30	23.3	even	11	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.150642 - 0.173850i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.150642 - 0.173850i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.193519 + 0.124367i) q^{10} +(-0.117920 - 0.820150i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(2.13919 - 1.37478i) q^{13} +(-0.654861 + 0.755750i) q^{14} +(0.0955606 - 0.209248i) q^{15} +(0.841254 + 0.540641i) q^{16} +(3.16250 - 0.928594i) q^{17} +(0.654861 + 0.755750i) q^{18} +(1.67782 + 0.492651i) q^{19} +(0.0955606 + 0.209248i) q^{20} +(0.142315 - 0.989821i) q^{21} -0.828583 q^{22} +(4.22042 - 2.27774i) q^{23} -1.00000 q^{24} +(0.704043 - 4.89673i) q^{25} +(-1.05634 - 2.31307i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(0.654861 + 0.755750i) q^{28} +(-2.74321 + 0.805480i) q^{29} +(-0.193519 - 0.124367i) q^{30} +(2.53383 - 5.54831i) q^{31} +(0.654861 - 0.755750i) q^{32} +(0.697049 - 0.447966i) q^{33} +(-0.469072 - 3.26246i) q^{34} +(0.0327376 + 0.227695i) q^{35} +(0.841254 - 0.540641i) q^{36} +(2.36101 - 2.72475i) q^{37} +(0.726415 - 1.59063i) q^{38} +(2.13919 + 1.37478i) q^{39} +(0.220718 - 0.0648087i) q^{40} +(-1.88739 - 2.17817i) q^{41} +(-0.959493 - 0.281733i) q^{42} +(2.86651 + 6.27677i) q^{43} +(-0.117920 + 0.820150i) q^{44} +0.230036 q^{45} +(-1.65392 - 4.50161i) q^{46} +8.09362 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-4.74669 - 1.39375i) q^{50} +(2.15843 + 2.49096i) q^{51} +(-2.43986 + 0.716407i) q^{52} +(1.19392 + 0.767284i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(-0.124819 + 0.144049i) q^{55} +(0.841254 - 0.540641i) q^{56} +(0.248859 + 1.73085i) q^{57} +(0.406881 + 2.82992i) q^{58} +(-3.59294 + 2.30904i) q^{59} +(-0.150642 + 0.173850i) q^{60} +(3.88160 - 8.49953i) q^{61} +(-5.13124 - 3.29765i) q^{62} +(0.959493 - 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.561256 - 0.164800i) q^{65} +(-0.344206 - 0.753706i) q^{66} +(1.30757 - 9.09435i) q^{67} -3.29601 q^{68} +(3.82513 + 2.89282i) q^{69} +0.230036 q^{70} +(-0.768477 + 5.34487i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(0.777561 + 0.228313i) q^{73} +(-2.36101 - 2.72475i) q^{74} +(4.74669 - 1.39375i) q^{75} +(-1.47106 - 0.945390i) q^{76} +(-0.344206 + 0.753706i) q^{77} +(1.66522 - 1.92177i) q^{78} +(-0.112053 + 0.0720118i) q^{79} +(-0.0327376 - 0.227695i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-2.42460 + 1.55820i) q^{82} +(-2.71713 + 3.13574i) q^{83} +(-0.415415 + 0.909632i) q^{84} +(-0.637841 - 0.409915i) q^{85} +(6.62083 - 1.94405i) q^{86} +(-1.87226 - 2.16071i) q^{87} +(0.795020 + 0.233439i) q^{88} +(-2.22041 - 4.86202i) q^{89} +(0.0327376 - 0.227695i) q^{90} -2.54286 q^{91} +(-4.69117 + 0.996443i) q^{92} +6.09951 q^{93} +(1.15184 - 8.01124i) q^{94} +(-0.167102 - 0.365902i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-2.78786 - 3.21737i) q^{97} +(0.959493 - 0.281733i) q^{98} +(0.697049 + 0.447966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 10 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 10 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 10 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9} - 12 q^{10} - 9 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} + 9 q^{17} + 3 q^{18} - 18 q^{19} + q^{20} + 3 q^{21} + 20 q^{22} + q^{23} - 30 q^{24} + 5 q^{25} + 32 q^{26} - 3 q^{27} + 3 q^{28} - 23 q^{29} - 12 q^{30} - q^{31} + 3 q^{32} + 2 q^{33} - 9 q^{34} - q^{35} - 3 q^{36} - q^{37} + 7 q^{38} + 12 q^{39} - q^{40} + 7 q^{41} - 3 q^{42} - 10 q^{43} - 9 q^{44} - 10 q^{45} - q^{46} + 68 q^{47} - 3 q^{48} - 3 q^{49} + 50 q^{50} + 9 q^{51} + q^{52} + 42 q^{53} + 3 q^{54} - 66 q^{55} - 3 q^{56} + 4 q^{57} + q^{58} + 25 q^{59} - 10 q^{60} + 10 q^{61} - 10 q^{62} + 3 q^{63} - 3 q^{64} - 54 q^{65} - 2 q^{66} - 6 q^{67} - 2 q^{68} - 21 q^{69} - 10 q^{70} - 13 q^{71} + 3 q^{72} + 33 q^{73} + q^{74} - 50 q^{75} + 26 q^{76} - 2 q^{77} - 12 q^{78} - 8 q^{79} + q^{80} - 3 q^{81} + 4 q^{82} - 2 q^{83} + 3 q^{84} - 77 q^{85} - 45 q^{86} - q^{87} - 13 q^{88} + 64 q^{89} - q^{90} - 12 q^{91} + 12 q^{92} - 56 q^{93} - 24 q^{94} + 59 q^{95} + 3 q^{96} + 2 q^{97} + 3 q^{98} + 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 10 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9 - 12 * q^10 - 9 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 + 9 * q^17 + 3 * q^18 - 18 * q^19 + q^20 + 3 * q^21 + 20 * q^22 + q^23 - 30 * q^24 + 5 * q^25 + 32 * q^26 - 3 * q^27 + 3 * q^28 - 23 * q^29 - 12 * q^30 - q^31 + 3 * q^32 + 2 * q^33 - 9 * q^34 - q^35 - 3 * q^36 - q^37 + 7 * q^38 + 12 * q^39 - q^40 + 7 * q^41 - 3 * q^42 - 10 * q^43 - 9 * q^44 - 10 * q^45 - q^46 + 68 * q^47 - 3 * q^48 - 3 * q^49 + 50 * q^50 + 9 * q^51 + q^52 + 42 * q^53 + 3 * q^54 - 66 * q^55 - 3 * q^56 + 4 * q^57 + q^58 + 25 * q^59 - 10 * q^60 + 10 * q^61 - 10 * q^62 + 3 * q^63 - 3 * q^64 - 54 * q^65 - 2 * q^66 - 6 * q^67 - 2 * q^68 - 21 * q^69 - 10 * q^70 - 13 * q^71 + 3 * q^72 + 33 * q^73 + q^74 - 50 * q^75 + 26 * q^76 - 2 * q^77 - 12 * q^78 - 8 * q^79 + q^80 - 3 * q^81 + 4 * q^82 - 2 * q^83 + 3 * q^84 - 77 * q^85 - 45 * q^86 - q^87 - 13 * q^88 + 64 * q^89 - q^90 - 12 * q^91 + 12 * q^92 - 56 * q^93 - 24 * q^94 + 59 * q^95 + 3 * q^96 + 2 * q^97 + 3 * q^98 + 2 * q^99

Introduction

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