LMFDB - Embedded newform 430.2.q.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	430.101
Dual form			430.2.q.b.281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 - 0.781831i) q^{2} +(-1.07289 + 2.73367i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(1.46834 + 2.54323i) q^{6} +(-1.49192 + 2.58408i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-4.12272 - 3.82532i) q^{9} +O(q^{10})$	\(q+(0.623490 - 0.781831i) q^{2} +(-1.07289 + 2.73367i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(1.46834 + 2.54323i) q^{6} +(-1.49192 + 2.58408i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-4.12272 - 3.82532i) q^{9} +(-0.826239 - 0.563320i) q^{10} +(-0.396251 + 1.73609i) q^{11} +(2.90387 + 0.437688i) q^{12} +(-1.88598 + 1.28584i) q^{13} +(1.09012 + 2.77757i) q^{14} +(2.80620 + 0.865599i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.0358015 + 0.477737i) q^{17} +(-5.56123 + 0.838221i) q^{18} +(-1.79755 + 1.66789i) q^{19} +(-0.955573 + 0.294755i) q^{20} +(-5.46336 - 6.85083i) q^{21} +(1.11027 + 1.39224i) q^{22} +(-7.96879 + 2.45805i) q^{23} +(2.15273 - 1.99744i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(-0.170580 + 2.27623i) q^{26} +(6.94283 - 3.34349i) q^{27} +(2.85127 + 0.879501i) q^{28} +(-2.89065 - 7.36526i) q^{29} +(2.42639 - 1.65429i) q^{30} +(4.28034 + 0.645157i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(-4.32077 - 2.94585i) q^{33} +(0.351188 + 0.325855i) q^{34} +(2.68834 + 1.29464i) q^{35} +(-2.81202 + 4.87057i) q^{36} +(2.89969 + 5.02241i) q^{37} +(0.183249 + 2.44529i) q^{38} +(-1.49162 - 6.53521i) q^{39} +(-0.365341 + 0.930874i) q^{40} +(-1.43174 + 1.79535i) q^{41} -8.76255 q^{42} +(3.29084 + 5.67189i) q^{43} +1.78074 q^{44} +(-3.50654 + 4.39706i) q^{45} +(-3.04668 + 7.76282i) q^{46} +(0.301300 + 1.32008i) q^{47} +(-0.219458 - 2.92846i) q^{48} +(-0.951635 - 1.64828i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.26757 - 0.610428i) q^{51} +(1.67327 + 1.55257i) q^{52} +(9.63308 + 6.56772i) q^{53} +(1.71474 - 7.51276i) q^{54} +(1.76085 + 0.265405i) q^{55} +(2.46536 - 1.68085i) q^{56} +(-2.63088 - 6.70337i) q^{57} +(-7.56068 - 2.33216i) q^{58} +(11.3767 - 5.47871i) q^{59} +(0.219458 - 2.92846i) q^{60} +(-7.26026 + 1.09431i) q^{61} +(3.17315 - 2.94426i) q^{62} +(16.0357 - 4.94635i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.42318 + 1.78462i) q^{65} +(-4.99711 + 1.54141i) q^{66} +(-1.99293 + 1.84917i) q^{67} +(0.473726 - 0.0714027i) q^{68} +(1.83012 - 24.4213i) q^{69} +(2.68834 - 1.29464i) q^{70} +(5.37582 + 1.65822i) q^{71} +(2.05469 + 5.23528i) q^{72} +(11.6204 - 7.92269i) q^{73} +(5.73460 + 0.864352i) q^{74} +(0.653471 - 2.86304i) q^{75} +(2.02606 + 1.38135i) q^{76} +(-3.89502 - 3.61405i) q^{77} +(-6.03944 - 2.90844i) q^{78} +(-7.10122 + 12.2997i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.430278 + 5.74166i) q^{81} +(0.510984 + 2.23877i) q^{82} +(3.49654 - 8.90903i) q^{83} +(-5.46336 + 6.85083i) q^{84} +0.479077 q^{85} +(6.48627 + 0.963482i) q^{86} +23.2355 q^{87} +(1.11027 - 1.39224i) q^{88} +(-3.38637 + 8.62833i) q^{89} +(1.25147 + 5.48304i) q^{90} +(-0.508981 - 6.79188i) q^{91} +(4.16964 + 7.22203i) q^{92} +(-6.35597 + 11.0089i) q^{93} +(1.21994 + 0.587491i) q^{94} +(1.79755 + 1.66789i) q^{95} +(-2.42639 - 1.65429i) q^{96} +(-0.0855609 + 0.374867i) q^{97} +(-1.88201 - 0.283668i) q^{98} +(8.27474 - 5.64162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{13}{21}\right)$

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 $

$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$3$	−1.07289	+	2.73367i	−0.619432	+	1.57829i	0.184024	+	0.982922i	$0.441087\pi$
$3$	−1.07289	+	2.73367i	−0.619432	+	1.57829i	−0.803456	+	0.595364i	$0.797008\pi$
$4$	−0.222521	−	0.974928i	−0.111260	−	0.487464i
$5$	−0.0747301	−	0.997204i	−0.0334203	−	0.445963i
$5$	−0.0747301	−	0.997204i	−0.0334203	−	0.445963i
$6$	1.46834	+	2.54323i	0.599446	+	1.03827i
$7$	−1.49192	+	2.58408i	−0.563892	+	0.976689i	0.433260	+	0.901269i	$0.357363\pi$
$7$	−1.49192	+	2.58408i	−0.563892	+	0.976689i	−0.997152	+	0.0754202i	$0.975970\pi$
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	−4.12272	−	3.82532i	−1.37424	−	1.27511i
$10$	−0.826239	−	0.563320i	−0.261280	−	0.178137i
$11$	−0.396251	+	1.73609i	−0.119474	+	0.523451i	0.879403	+	0.476078i	$0.157942\pi$
$11$	−0.396251	+	1.73609i	−0.119474	+	0.523451i	−0.998877	+	0.0473729i	$0.984915\pi$
$12$	2.90387	+	0.437688i	0.838276	+	0.126350i
$13$	−1.88598	+	1.28584i	−0.523077	+	0.356628i	−0.795892	−	0.605439i	$-0.792998\pi$
$13$	−1.88598	+	1.28584i	−0.523077	+	0.356628i	0.272815	+	0.962066i	$0.412045\pi$
$14$	1.09012	+	2.77757i	0.291346	+	0.742338i
$15$	2.80620	+	0.865599i	0.724559	+	0.223497i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−0.0358015	+	0.477737i	−0.00868313	+	0.115868i	−0.999861	−	0.0166697i	$-0.994694\pi$
$17$	−0.0358015	+	0.477737i	−0.00868313	+	0.115868i	0.991178	+	0.132538i	$0.0423127\pi$
$18$	−5.56123	+	0.838221i	−1.31079	+	0.197570i
$19$	−1.79755	+	1.66789i	−0.412387	+	0.382639i	−0.858905	−	0.512136i	$-0.828855\pi$
$19$	−1.79755	+	1.66789i	−0.412387	+	0.382639i	0.446518	+	0.894775i	$0.352664\pi$
$20$	−0.955573	+	0.294755i	−0.213673	+	0.0659093i
$21$	−5.46336	−	6.85083i	−1.19220	−	1.49497i
$22$	1.11027	+	1.39224i	0.236711	+	0.296826i
$23$	−7.96879	+	2.45805i	−1.66161	+	0.512538i	−0.976429	−	0.215837i	$-0.930752\pi$
$23$	−7.96879	+	2.45805i	−1.66161	+	0.512538i	−0.685178	+	0.728375i	$0.740276\pi$
$24$	2.15273	−	1.99744i	0.439425	−	0.407727i
$25$	−0.988831	+	0.149042i	−0.197766	+	0.0298085i
$26$	−0.170580	+	2.27623i	−0.0334534	+	0.446405i
$27$	6.94283	−	3.34349i	1.33615	−	0.643455i
$28$	2.85127	+	0.879501i	0.538840	+	0.166210i
$29$	−2.89065	−	7.36526i	−0.536781	−	1.36769i	−0.899959	−	0.435975i	$-0.856404\pi$
$29$	−2.89065	−	7.36526i	−0.536781	−	1.36769i	0.363178	−	0.931720i	$-0.381692\pi$
$30$	2.42639	−	1.65429i	0.442997	−	0.302030i
$31$	4.28034	+	0.645157i	0.768772	+	0.115874i	0.521706	−	0.853125i	$-0.325296\pi$
$31$	4.28034	+	0.645157i	0.768772	+	0.115874i	0.247065	+	0.968999i	$0.420534\pi$
$32$	−0.222521	+	0.974928i	−0.0393365	+	0.172345i
$33$	−4.32077	−	2.94585i	−0.752149	−	0.512807i
$34$	0.351188	+	0.325855i	0.0602283	+	0.0558837i
$35$	2.68834	+	1.29464i	0.454413	+	0.218834i
$36$	−2.81202	+	4.87057i	−0.468671	+	0.811761i
$37$	2.89969	+	5.02241i	0.476706	+	0.825679i	0.999644	−	0.0266921i	$-0.00849738\pi$
$37$	2.89969	+	5.02241i	0.476706	+	0.825679i	−0.522938	+	0.852371i	$0.675164\pi$
$38$	0.183249	+	2.44529i	0.0297270	+	0.396679i
$39$	−1.49162	−	6.53521i	−0.238850	−	1.04647i
$40$	−0.365341	+	0.930874i	−0.0577655	+	0.147184i
$41$	−1.43174	+	1.79535i	−0.223601	+	0.280387i	−0.880960	−	0.473191i	$-0.843102\pi$
$41$	−1.43174	+	1.79535i	−0.223601	+	0.280387i	0.657359	+	0.753578i	$0.271674\pi$
$42$	−8.76255			−1.35209
$43$	3.29084	+	5.67189i	0.501849	+	0.864955i
$43$	3.29084	+	5.67189i	0.501849	+	0.864955i
$44$	1.78074			0.268456
$45$	−3.50654	+	4.39706i	−0.522723	+	0.655474i
$46$	−3.04668	+	7.76282i	−0.449209	+	1.14457i
$47$	0.301300	+	1.32008i	0.0439491	+	0.192554i	0.992137	−	0.125156i	$-0.0399433\pi$
$47$	0.301300	+	1.32008i	0.0439491	+	0.192554i	−0.948188	+	0.317710i	$0.897086\pi$
$48$	−0.219458	−	2.92846i	−0.0316760	−	0.422687i
$49$	−0.951635	−	1.64828i	−0.135948	−	0.235469i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−1.26757	−	0.610428i	−0.177495	−	0.0854770i
$52$	1.67327	+	1.55257i	0.232041	+	0.215303i
$53$	9.63308	+	6.56772i	1.32321	+	0.902146i	0.999038	−	0.0438540i	$-0.0139636\pi$
$53$	9.63308	+	6.56772i	1.32321	+	0.902146i	0.324167	+	0.946000i	$0.394916\pi$
$54$	1.71474	−	7.51276i	0.233346	−	1.02236i
$55$	1.76085	+	0.265405i	0.237433	+	0.0357872i
$56$	2.46536	−	1.68085i	0.329448	−	0.224614i
$57$	−2.63088	−	6.70337i	−0.348469	−	0.887884i
$58$	−7.56068	−	2.33216i	−0.992766	−	0.306228i
$59$	11.3767	−	5.47871i	1.48112	−	0.713268i	0.493439	−	0.869780i	$-0.335740\pi$
$59$	11.3767	−	5.47871i	1.48112	−	0.713268i	0.987676	+	0.156513i	$0.0500252\pi$
$60$	0.219458	−	2.92846i	0.0283319	−	0.378063i
$61$	−7.26026	+	1.09431i	−0.929581	+	0.140112i	−0.596342	−	0.802731i	$-0.703380\pi$
$61$	−7.26026	+	1.09431i	−0.929581	+	0.140112i	−0.333239	+	0.942842i	$0.608142\pi$
$62$	3.17315	−	2.94426i	0.402991	−	0.373921i
$63$	16.0357	−	4.94635i	2.02031	−	0.623182i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	1.42318	+	1.78462i	0.176524	+	0.221354i
$66$	−4.99711	+	1.54141i	−0.615102	+	0.189734i
$67$	−1.99293	+	1.84917i	−0.243475	+	0.225912i	−0.792466	−	0.609917i	$-0.791203\pi$
$67$	−1.99293	+	1.84917i	−0.243475	+	0.225912i	0.548990	+	0.835829i	$0.315012\pi$
$68$	0.473726	−	0.0714027i	0.0574477	−	0.00865885i
$69$	1.83012	−	24.4213i	0.220321	−	2.93997i
$70$	2.68834	−	1.29464i	0.321318	−	0.154739i
$71$	5.37582	+	1.65822i	0.637993	+	0.196795i	0.596843	−	0.802358i	$-0.296422\pi$
$71$	5.37582	+	1.65822i	0.637993	+	0.196795i	0.0411502	+	0.999153i	$0.486898\pi$
$72$	2.05469	+	5.23528i	0.242148	+	0.616983i
$73$	11.6204	−	7.92269i	1.36007	−	0.927280i	0.360086	−	0.932919i	$-0.382747\pi$
$73$	11.6204	−	7.92269i	1.36007	−	0.927280i	0.999984	+	0.00563886i	$0.00179492\pi$
$74$	5.73460	+	0.864352i	0.666634	+	0.100479i
$75$	0.653471	−	2.86304i	0.0754563	−	0.330596i
$76$	2.02606	+	1.38135i	0.232405	+	0.158451i
$77$	−3.89502	−	3.61405i	−0.443878	−	0.411859i
$78$	−6.03944	−	2.90844i	−0.683832	−	0.329316i
$79$	−7.10122	+	12.2997i	−0.798949	+	1.38382i	0.121352	+	0.992610i	$0.461277\pi$
$79$	−7.10122	+	12.2997i	−0.798949	+	1.38382i	−0.920301	+	0.391211i	$0.872056\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	0.430278	+	5.74166i	0.0478086	+	0.637962i
$82$	0.510984	+	2.23877i	0.0564287	+	0.247230i
$83$	3.49654	−	8.90903i	0.383795	−	0.977893i	−0.600225	−	0.799831i	$-0.704922\pi$
$83$	3.49654	−	8.90903i	0.383795	−	0.977893i	0.984019	−	0.178062i	$-0.0569826\pi$
$84$	−5.46336	+	6.85083i	−0.596101	+	0.747487i
$85$	0.479077			0.0519632
$86$	6.48627	+	0.963482i	0.699433	+	0.103895i
$87$	23.2355			2.49111
$88$	1.11027	−	1.39224i	0.118355	−	0.148413i
$89$	−3.38637	+	8.62833i	−0.358954	+	0.914601i	0.631326	+	0.775517i	$0.282511\pi$
$89$	−3.38637	+	8.62833i	−0.358954	+	0.914601i	−0.990281	+	0.139083i	$0.955584\pi$
$90$	1.25147	+	5.48304i	0.131916	+	0.577963i
$91$	−0.508981	−	6.79188i	−0.0533557	−	0.711983i
$92$	4.16964	+	7.22203i	0.434715	+	0.752949i
$93$	−6.35597	+	11.0089i	−0.659083	+	1.14157i
$94$	1.21994	+	0.587491i	0.125827	+	0.0605951i
$95$	1.79755	+	1.66789i	0.184425	+	0.171121i
$96$	−2.42639	−	1.65429i	−0.247643	−	0.168840i
$97$	−0.0855609	+	0.374867i	−0.00868740	+	0.0380620i	−0.979086	−	0.203448i	$-0.934785\pi$
$97$	−0.0855609	+	0.374867i	−0.00868740	+	0.0380620i	0.970398	+	0.241510i	$0.0776425\pi$
$98$	−1.88201	−	0.283668i	−0.190112	−	0.0286548i
$99$	8.27474	−	5.64162i	0.831643	−	0.567004i
$100$	0.365341	+	0.930874i	0.0365341	+	0.0930874i
$101$	12.3994	+	3.82472i	1.23379	+	0.380573i	0.841998	−	0.539481i	$-0.181379\pi$
$101$	12.3994	+	3.82472i	1.23379	+	0.380573i	0.391791	+	0.920054i	$0.371856\pi$
$102$	−1.26757	+	0.610428i	−0.125508	+	0.0604414i
$103$	0.128819	−	1.71897i	0.0126929	−	0.169375i	−0.987255	−	0.159148i	$-0.949125\pi$
$103$	0.128819	−	1.71897i	0.0126929	−	0.169375i	0.999948	−	0.0102273i	$-0.00325552\pi$
$104$	2.25711	−	0.340205i	0.221328	−	0.0333599i
$105$	−6.42340	+	5.96004i	−0.626860	+	0.581641i
$106$	11.1410	−	3.43654i	1.08211	−	0.333786i
$107$	−6.36309	−	7.97906i	−0.615143	−	0.771365i	0.372509	−	0.928029i	$-0.378498\pi$
$107$	−6.36309	−	7.97906i	−0.615143	−	0.771365i	−0.987652	+	0.156663i	$0.949926\pi$
$108$	−4.80459	−	6.02477i	−0.462322	−	0.579733i
$109$	−14.9239	+	4.60342i	−1.42945	+	0.440927i	−0.910369	−	0.413797i	$-0.864202\pi$
$109$	−14.9239	+	4.60342i	−1.42945	+	0.440927i	−0.519082	+	0.854724i	$0.673726\pi$
$110$	1.30537	−	1.21121i	0.124462	−	0.115484i
$111$	−16.8406	+	2.53832i	−1.59844	+	0.240927i
$112$	0.222982	−	2.97549i	0.0210698	−	0.281157i
$113$	−9.18330	+	4.42244i	−0.863892	+	0.416028i	−0.812715	−	0.582661i	$-0.802011\pi$
$113$	−9.18330	+	4.42244i	−0.863892	+	0.416028i	−0.0511767	+	0.998690i	$0.516297\pi$
$114$	−6.88124	−	2.12258i	−0.644487	−	0.198798i
$115$	3.04668	+	7.76282i	0.284105	+	0.723887i
$116$	−6.53737	+	4.45710i	−0.606979	+	0.413832i
$117$	12.6941	+	1.91333i	1.17357	+	0.176887i
$118$	2.80980	−	12.3106i	0.258663	−	1.13328i
$119$	−1.18110	−	0.805259i	−0.108271	−	0.0738179i
$120$	−2.15273	−	1.99744i	−0.196517	−	0.182341i
$121$	7.05366	+	3.39686i	0.641242	+	0.308806i
$122$	−3.67113	+	6.35859i	−0.332369	+	0.575680i
$123$	−3.37180	−	5.84013i	−0.304025	−	0.526587i
$124$	−0.323483	−	4.31658i	−0.0290497	−	0.387641i
$125$	0.222521	+	0.974928i	0.0199029	+	0.0872002i
$126$	6.13087	−	15.6212i	0.546181	−	1.39165i
$127$	−1.55269	+	1.94701i	−0.137779	+	0.172770i	−0.845934	−	0.533288i	$-0.820956\pi$
$127$	−1.55269	+	1.94701i	−0.137779	+	0.172770i	0.708155	+	0.706057i	$0.249528\pi$
$128$	1.00000			0.0883883
$129$	−19.0358	+	2.91079i	−1.67601	+	0.256280i
$130$	2.28261			0.200198
$131$	5.88300	−	7.37704i	0.514000	−	0.644535i	−0.455323	−	0.890326i	$-0.650476\pi$
$131$	5.88300	−	7.37704i	0.514000	−	0.644535i	0.969323	+	0.245791i	$0.0790477\pi$
$132$	−1.91053	+	4.86795i	−0.166290	+	0.423701i
$133$	−1.62814	−	7.13336i	−0.141178	−	0.618541i
$134$	0.203167	+	2.71108i	0.0175510	+	0.234201i
$135$	−3.85298	−	6.67356i	−0.331612	−	0.574369i
$136$	0.239539	−	0.414893i	0.0205403	−	0.0355768i
$137$	−8.96032	−	4.31506i	−0.765532	−	0.368661i	0.0100157	−	0.999950i	$-0.496812\pi$
$137$	−8.96032	−	4.31506i	−0.765532	−	0.368661i	−0.775548	+	0.631289i	$0.782526\pi$
$138$	−17.9522	−	16.6573i	−1.52820	−	1.41796i
$139$	−4.96118	−	3.38248i	−0.420802	−	0.286898i	0.334348	−	0.942450i	$-0.391484\pi$
$139$	−4.96118	−	3.38248i	−0.420802	−	0.286898i	−0.755150	+	0.655552i	$0.772436\pi$
$140$	0.663966	−	2.90902i	0.0561153	−	0.245857i
$141$	−3.93193	−	0.592643i	−0.331128	−	0.0499095i
$142$	4.64822	−	3.16910i	0.390070	−	0.265945i
$143$	−1.48501	−	3.78375i	−0.124183	−	0.316413i
$144$	5.37419	+	1.65772i	0.447849	+	0.138143i
$145$	−7.12865	+	3.43298i	−0.592002	+	0.285093i
$146$	1.05102	−	14.0249i	0.0869834	−	1.16071i
$147$	5.52685	−	0.833039i	0.455847	−	0.0687079i
$148$	4.25124	−	3.94458i	0.349450	−	0.324242i
$149$	11.3315	−	3.49529i	0.928309	−	0.286345i	0.206507	−	0.978445i	$-0.433790\pi$
$149$	11.3315	−	3.49529i	0.928309	−	0.286345i	0.721802	+	0.692100i	$0.243314\pi$
$150$	−1.83099	−	2.29598i	−0.149499	−	0.187466i
$151$	−11.6302	−	14.5839i	−0.946456	−	1.18682i	−0.982272	−	0.187460i	$-0.939975\pi$
$151$	−11.6302	−	14.5839i	−0.946456	−	1.18682i	0.0358162	−	0.999358i	$-0.488597\pi$
$152$	2.34321	−	0.722784i	0.190059	−	0.0586255i
$153$	1.97510	−	1.83262i	0.159677	−	0.148159i
$154$	−5.25408	+	0.791925i	−0.423386	+	0.0638151i
$155$	0.323483	−	4.31658i	0.0259828	−	0.346716i
$156$	−6.03944	+	2.90844i	−0.483542	+	0.232862i
$157$	−8.72333	−	2.69079i	−0.696197	−	0.214748i	−0.0735966	−	0.997288i	$-0.523448\pi$
$157$	−8.72333	−	2.69079i	−0.696197	−	0.214748i	−0.622601	+	0.782540i	$0.713924\pi$
$158$	5.18873	+	13.2207i	0.412793	+	1.05178i
$159$	−28.2892	+	19.2872i	−2.24348	+	1.52958i
$160$	0.988831	+	0.149042i	0.0781739	+	0.0117828i
$161$	5.53700	−	24.2592i	0.436376	−	1.91189i
$162$	4.75728	+	3.24346i	0.373767	+	0.254830i
$163$	−0.795550	−	0.738163i	−0.0623123	−	0.0578174i	0.648402	−	0.761298i	$-0.275438\pi$
$163$	−0.795550	−	0.738163i	−0.0623123	−	0.0578174i	−0.710714	+	0.703481i	$0.751628\pi$
$164$	2.06893	+	0.996345i	0.161556	+	0.0778015i
$165$	−2.61472	+	4.52883i	−0.203556	+	0.352569i
$166$	−4.78530	−	8.28839i	−0.371412	−	0.643304i
$167$	1.60188	+	21.3756i	0.123957	+	1.65410i	0.619120	+	0.785296i	$0.287489\pi$
$167$	1.60188	+	21.3756i	0.123957	+	1.65410i	−0.495163	+	0.868800i	$0.664892\pi$
$168$	1.94985	+	8.54285i	0.150434	+	0.659095i
$169$	−2.84589	+	7.25122i	−0.218915	+	0.557786i
$170$	0.298700	−	0.374558i	0.0229092	−	0.0287273i
$171$	13.7910			1.05462
$172$	4.79740	−	4.47045i	0.365799	−	0.340869i
$173$	10.5324			0.800764			0.400382	−	0.916348i	$-0.368877\pi$
$173$	10.5324			0.800764			0.400382	+	0.916348i	$0.368877\pi$
$174$	14.4871	−	18.1663i	1.09827	−	1.37718i
$175$	1.09012	−	2.77757i	0.0824051	−	0.209965i
$176$	−0.396251	−	1.73609i	−0.0298686	−	0.130863i
$177$	2.77113	+	36.9781i	0.208291	+	2.77944i
$178$	4.63453	+	8.02724i	0.347373	+	0.601667i
$179$	−7.67557	+	13.2945i	−0.573699	+	0.993675i	0.422483	+	0.906371i	$0.361159\pi$
$179$	−7.67557	+	13.2945i	−0.573699	+	0.993675i	−0.996182	+	0.0873044i	$0.972175\pi$
$180$	5.06709	+	2.44018i	0.377679	+	0.181880i
$181$	15.9632	+	14.8117i	1.18654	+	1.10095i	0.992786	+	0.119896i	$0.0382561\pi$
$181$	15.9632	+	14.8117i	1.18654	+	1.10095i	0.193752	+	0.981051i	$0.437934\pi$
$182$	−5.62745	−	3.83673i	−0.417135	−	0.284398i
$183$	4.79796	−	21.0212i	0.354675	−	1.55393i
$184$	8.24614	+	1.24291i	0.607913	+	0.0916282i
$185$	4.79167	−	3.26690i	0.352291	−	0.240188i
$186$	4.64419	+	11.8332i	0.340529	+	0.867653i
$187$	−0.815209	−	0.251459i	−0.0596140	−	0.0183885i
$188$	1.21994	−	0.587491i	0.0889732	−	0.0428472i
$189$	−1.71829	+	22.9290i	−0.124987	+	1.66784i
$190$	2.42476	−	0.365474i	0.175911	−	0.0265143i
$191$	−18.4864	+	17.1529i	−1.33763	+	1.24114i	−0.390376	+	0.920656i	$0.627655\pi$
$191$	−18.4864	+	17.1529i	−1.33763	+	1.24114i	−0.947254	+	0.320484i	$0.896155\pi$
$192$	−2.80620	+	0.865599i	−0.202520	+	0.0624693i
$193$	4.93166	+	6.18410i	0.354988	+	0.445141i	0.926976	−	0.375121i	$-0.122399\pi$
$193$	4.93166	+	6.18410i	0.354988	+	0.445141i	−0.571987	+	0.820262i	$0.693827\pi$
$194$	0.239736	+	0.300620i	0.0172121	+	0.0215833i
$195$	−6.40547	+	1.97583i	−0.458705	+	0.141492i
$196$	−1.39520	+	1.29455i	−0.0996568	+	0.0924680i
$197$	−6.97185	+	1.05084i	−0.496723	+	0.0748690i	−0.392626	−	0.919698i	$-0.628433\pi$
$197$	−6.97185	+	1.05084i	−0.496723	+	0.0748690i	−0.104097	+	0.994567i	$0.533195\pi$
$198$	0.748418	−	9.98695i	0.0531878	−	0.709741i
$199$	−23.0790	+	11.1143i	−1.63603	+	0.787869i	−0.636159	+	0.771558i	$0.719478\pi$
$199$	−23.0790	+	11.1143i	−1.63603	+	0.787869i	−0.999867	+	0.0163106i	$0.994808\pi$
$200$	0.955573	+	0.294755i	0.0675692	+	0.0208423i
$201$	−2.91683	−	7.43197i	−0.205738	−	0.524211i
$202$	10.7212	−	7.30959i	0.754341	−	0.514301i
$203$	23.3450	+	3.51869i	1.63850	+	0.246964i
$204$	−0.313063	+	1.37162i	−0.0219188	+	0.0960325i
$205$	1.89733	+	1.29357i	0.132515	+	0.0903472i
$206$	−1.26363	−	1.17247i	−0.0880410	−	0.0816901i
$207$	42.2559	+	20.3494i	2.93699	+	1.41438i
$208$	1.14130	−	1.97680i	0.0791352	−	0.137066i
$209$	−2.18332	−	3.78162i	−0.151023	−	0.261580i
$210$	0.654826	+	8.73804i	0.0451873	+	0.602982i
$211$	−2.77965	−	12.1784i	−0.191359	−	0.838397i	−0.975882	−	0.218298i	$-0.929949\pi$
$211$	−2.77965	−	12.1784i	−0.191359	−	0.838397i	0.784523	−	0.620099i	$-0.212908\pi$
$212$	4.25949	−	10.8530i	0.292543	−	0.745388i
$213$	−10.3007	+	12.9167i	−0.705791	+	0.885034i
$214$	−10.2056			−0.697641
$215$	5.41011	−	3.70550i	0.368966	−	0.252713i
$216$	−7.70596			−0.524324
$217$	−8.05305	+	10.0982i	−0.546677	+	0.685511i
$218$	−5.70581	+	14.5382i	−0.386446	+	0.984649i
$219$	9.19059	+	40.2666i	0.621043	+	2.72097i
$220$	−0.133075	−	1.77576i	−0.00897189	−	0.119722i
$221$	−0.546773	−	0.947039i	−0.0367799	−	0.0637047i
$222$	−8.51543	+	14.7492i	−0.571519	+	0.989899i
$223$	−12.2969	−	5.92188i	−0.823462	−	0.396558i	−0.0258029	−	0.999667i	$-0.508214\pi$
$223$	−12.2969	−	5.92188i	−0.823462	−	0.396558i	−0.797659	+	0.603109i	$0.793929\pi$
$224$	−2.18731	−	2.02952i	−0.146146	−	0.135603i
$225$	4.64681	+	3.16814i	0.309787	+	0.211209i
$226$	−2.26809	+	9.93714i	−0.150871	+	0.661009i
$227$	11.0930	+	1.67200i	0.736270	+	0.110975i	0.506463	−	0.862261i	$-0.330953\pi$
$227$	11.0930	+	1.67200i	0.736270	+	0.110975i	0.229807	+	0.973236i	$0.426191\pi$
$228$	−5.94988	+	4.05656i	−0.394040	+	0.268652i
$229$	−9.02518	−	22.9958i	−0.596401	−	1.51960i	−0.835998	−	0.548732i	$-0.815111\pi$
$229$	−9.02518	−	22.9958i	−0.596401	−	1.51960i	0.239597	−	0.970872i	$-0.422985\pi$
$230$	7.96879	+	2.45805i	0.525446	+	0.162079i
$231$	14.0585	−	6.77023i	0.924983	−	0.445449i
$232$	−0.591280	+	7.89008i	−0.0388194	+	0.518009i
$233$	4.32182	−	0.651409i	0.283132	−	0.0426752i	−0.00594108	−	0.999982i	$-0.501891\pi$
$233$	4.32182	−	0.651409i	0.283132	−	0.0426752i	0.289073	+	0.957307i	$0.406653\pi$
$234$	9.41055	−	8.73172i	0.615187	−	0.570810i
$235$	1.29387	−	0.399107i	0.0844030	−	0.0260349i
$236$	−7.87289	−	9.87230i	−0.512482	−	0.642632i
$237$	−26.0045	−	32.6085i	−1.68917	−	2.11815i
$238$	−1.36598	+	0.421349i	−0.0885432	+	0.0273120i
$239$	13.6757	−	12.6892i	0.884608	−	0.820797i	−0.100106	−	0.994977i	$-0.531918\pi$
$239$	13.6757	−	12.6892i	0.884608	−	0.820797i	0.984714	+	0.174180i	$0.0557276\pi$
$240$	−2.90387	+	0.437688i	−0.187444	+	0.0282527i
$241$	−0.767256	+	10.2383i	−0.0494233	+	0.659508i	0.916393	+	0.400280i	$0.131087\pi$
$241$	−0.767256	+	10.2383i	−0.0494233	+	0.659508i	−0.965816	+	0.259228i	$0.916532\pi$
$242$	7.05366	−	3.39686i	0.453427	−	0.218359i
$243$	5.93339	+	1.83021i	0.380627	+	0.117408i
$244$	2.68243	+	6.83472i	0.171725	+	0.437548i
$245$	−1.57256	+	1.07215i	−0.100467	+	0.0684971i
$246$	−6.66828	−	1.00508i	−0.425154	−	0.0640817i
$247$	1.24552	−	5.45697i	0.0792503	−	0.347218i
$248$	−3.57653	−	2.43844i	−0.227110	−	0.154841i
$249$	20.6030	+	19.1168i	1.30566	+	1.21148i
$250$	0.900969	+	0.433884i	0.0569823	+	0.0274412i
$251$	9.64912	−	16.7128i	0.609047	−	1.05490i	−0.382351	−	0.924017i	$-0.624885\pi$
$251$	9.64912	−	16.7128i	0.609047	−	1.05490i	0.991398	−	0.130883i	$-0.0417812\pi$
$252$	−8.39061	−	14.5330i	−0.528559	−	0.915491i
$253$	−1.10975	−	14.8085i	−0.0697692	−	0.931005i
$254$	0.554149	+	2.42789i	0.0347704	+	0.152339i
$255$	−0.513996	+	1.30964i	−0.0321877	+	0.0820128i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	1.68772			0.105277			0.0526385	−	0.998614i	$-0.483237\pi$
$257$	1.68772			0.105277			0.0526385	+	0.998614i	$0.483237\pi$
$258$	−9.59288	+	16.6976i	−0.597226	+	1.03955i
$259$	−17.3044			−1.07524
$260$	1.42318	−	1.78462i	0.0882621	−	0.110677i
$261$	−16.2572	+	41.4226i	−1.00629	+	2.56399i
$262$	−2.09962	−	9.19902i	−0.129715	−	0.568318i
$263$	1.27227	+	16.9772i	0.0784512	+	1.04686i	0.888011	+	0.459822i	$0.152087\pi$
$263$	1.27227	+	16.9772i	0.0784512	+	1.04686i	−0.809560	+	0.587037i	$0.800294\pi$
$264$	2.61472	+	4.52883i	0.160925	+	0.278730i
$265$	5.82948	−	10.0969i	0.358102	−	0.620251i
$266$	−6.59222	−	3.17465i	−0.404195	−	0.194650i
$267$	−19.9538	−	18.5144i	−1.22115	−	1.13307i
$268$	2.24628	+	1.53149i	0.137213	+	0.0935504i
$269$	5.60971	−	24.5777i	0.342030	−	1.49853i	−0.452752	−	0.891636i	$-0.649558\pi$
$269$	5.60971	−	24.5777i	0.342030	−	1.49853i	0.794782	−	0.606895i	$-0.207585\pi$
$270$	−7.61990	−	1.14851i	−0.463732	−	0.0698964i
$271$	0.685643	−	0.467464i	0.0416499	−	0.0283964i	−0.542316	−	0.840174i	$-0.682452\pi$
$271$	0.685643	−	0.467464i	0.0416499	−	0.0283964i	0.583966	+	0.811778i	$0.301500\pi$
$272$	−0.175027	−	0.445960i	−0.0106125	−	0.0270403i
$273$	19.1129	+	5.89554i	1.15676	+	0.356814i
$274$	−8.96032	+	4.31506i	−0.541313	+	0.260682i
$275$	0.133075	−	1.77576i	0.00802470	−	0.107082i
$276$	−24.2162	+	3.65001i	−1.45764	+	0.219705i
$277$	−16.7030	+	15.4981i	−1.00359	+	0.931191i	−0.997631	−	0.0687908i	$-0.978086\pi$
$277$	−16.7030	+	15.4981i	−1.00359	+	0.931191i	−0.00595460	+	0.999982i	$0.501895\pi$
$278$	−5.73778	+	1.76987i	−0.344129	+	0.106150i
$279$	−15.1787	−	19.0335i	−0.908725	−	1.13950i
$280$	−1.86039	−	2.33286i	−0.111180	−	0.139415i
$281$	27.7747	−	8.56737i	1.65690	−	0.511086i	0.681555	−	0.731767i	$-0.261304\pi$
$281$	27.7747	−	8.56737i	1.65690	−	0.511086i	0.975346	+	0.220681i	$0.0708280\pi$
$282$	−2.91486	+	2.70460i	−0.173578	+	0.161057i
$283$	−2.16999	+	0.327074i	−0.128993	+	0.0194425i	−0.213221	−	0.977004i	$-0.568396\pi$
$283$	−2.16999	+	0.327074i	−0.128993	+	0.0194425i	0.0842285	+	0.996446i	$0.473157\pi$
$284$	0.420414	−	5.61003i	0.0249470	−	0.332894i
$285$	−6.48802	+	3.12447i	−0.384317	+	0.185077i
$286$	−3.88414	−	1.19810i	−0.229674	−	0.0708451i
$287$	−2.50328	−	6.37825i	−0.147764	−	0.376496i
$288$	4.64681	−	3.16814i	0.273816	−	0.186684i
$289$	16.5832	+	2.49951i	0.975481	+	0.147030i
$290$	−1.76063	+	7.71383i	−0.103388	+	0.452971i
$291$	−0.932966	−	0.636085i	−0.0546914	−	0.0372880i
$292$	−10.3098	−	9.56613i	−0.603338	−	0.559816i
$293$	−22.0901	−	10.6380i	−1.29052	−	0.621480i	−0.342445	−	0.939538i	$-0.611255\pi$
$293$	−22.0901	−	10.6380i	−1.29052	−	0.621480i	−0.948071	+	0.318058i	$0.896969\pi$
$294$	2.79464	−	4.84046i	0.162987	−	0.282301i
$295$	−6.31357	−	10.9354i	−0.367590	−	0.636685i
$296$	−0.433388	−	5.78316i	−0.0251902	−	0.336139i
$297$	3.05350	+	13.3783i	0.177182	+	0.776285i
$298$	4.33232	−	11.0386i	0.250964	−	0.639447i
$299$	11.8683	−	14.8824i	0.686363	−	0.860672i
$300$	−2.93667			−0.169549
$301$	−19.5663	+	0.0417973i	−1.12778	+	0.00240916i
$302$	−18.6535			−1.07339
$303$	−23.7587	+	29.7925i	−1.36490	+	1.71153i
$304$	0.895871	−	2.28264i	0.0513817	−	0.130919i
$305$	1.63381	+	7.15818i	0.0935516	+	0.409876i
$306$	−0.201349	−	2.68682i	−0.0115104	−	0.153595i
$307$	14.8569	+	25.7328i	0.847926	+	1.46865i	0.883056	+	0.469268i	$0.155482\pi$
$307$	14.8569	+	25.7328i	0.847926	+	1.46865i	−0.0351303	+	0.999383i	$0.511185\pi$
$308$	−2.65671	+	4.60156i	−0.151380	+	0.262198i
$309$	4.56088	+	2.19641i	0.259460	+	0.124949i
$310$	−3.17315	−	2.94426i	−0.180223	−	0.167222i
$311$	13.5021	+	9.20555i	0.765631	+	0.521999i	0.882024	−	0.471205i	$-0.156181\pi$
$311$	13.5021	+	9.20555i	0.765631	+	0.521999i	−0.116392	+	0.993203i	$0.537133\pi$
$312$	−1.49162	+	6.53521i	−0.0844463	+	0.369984i
$313$	1.09873	+	0.165607i	0.0621040	+	0.00936068i	0.180021	−	0.983663i	$-0.442383\pi$
$313$	1.09873	+	0.165607i	0.0621040	+	0.00936068i	−0.117917	+	0.993023i	$0.537622\pi$
$314$	−7.54265	+	5.14249i	−0.425656	+	0.290208i
$315$	−6.13087	−	15.6212i	−0.345435	−	0.880155i
$316$	13.5715	+	4.18624i	0.763454	+	0.235494i
$317$	−14.5701	+	7.01661i	−0.818340	+	0.394092i	−0.795729	−	0.605652i	$-0.792912\pi$
$317$	−14.5701	+	7.01661i	−0.818340	+	0.394092i	−0.0226109	+	0.999744i	$0.507198\pi$
$318$	−2.55865	+	34.1428i	−0.143482	+	1.91463i
$319$	13.9322	−	2.09994i	0.780053	−	0.117574i
$320$	0.733052	−	0.680173i	0.0409788	−	0.0380228i
$321$	28.6390	−	8.83397i	1.59847	−	0.493064i
$322$	−15.5143	−	19.4543i	−0.864579	−	1.08415i
$323$	−0.732457	−	0.918471i	−0.0407550	−	0.0511051i
$324$	5.50196	−	1.69713i	0.305664	−	0.0942849i
$325$	1.67327	−	1.55257i	0.0928164	−	0.0861210i
$326$	−1.07314	+	0.161749i	−0.0594355	+	0.00895846i
$327$	3.42744	−	45.7360i	0.189538	−	2.52921i
$328$	2.06893	−	0.996345i	0.114238	−	0.0550139i
$329$	−3.86071	−	1.19087i	−0.212848	−	0.0656548i
$330$	1.91053	+	4.86795i	0.105171	+	0.267972i
$331$	12.0837	−	8.23852i	0.664180	−	0.452830i	−0.183726	−	0.982978i	$-0.558816\pi$
$331$	12.0837	−	8.23852i	0.664180	−	0.452830i	0.847905	+	0.530148i	$0.177863\pi$
$332$	−9.46371	−	1.42643i	−0.519389	−	0.0782853i
$333$	7.25773	−	31.7982i	0.397721	−	1.74253i
$334$	17.7109	+	12.0751i	0.969098	+	0.660720i
$335$	1.99293	+	1.84917i	0.108886	+	0.101031i
$336$	7.89478	+	3.80193i	0.430696	+	0.207412i
$337$	−9.81428	+	16.9988i	−0.534618	+	0.925985i	0.464564	+	0.885540i	$0.346211\pi$
$337$	−9.81428	+	16.9988i	−0.534618	+	0.925985i	−0.999182	+	0.0404456i	$0.987122\pi$
$338$	3.89485	+	6.74607i	0.211852	+	0.366938i
$339$	−2.23687	−	29.8489i	−0.121490	−	1.62117i
$340$	−0.106605	−	0.467066i	−0.00578145	−	0.0253302i
$341$	−2.81614	+	7.17541i	−0.152503	+	0.388570i
$342$	8.59855	−	10.7822i	0.464956	−	0.583037i
$343$	−15.2078			−0.821144
$344$	−0.504006	−	6.53804i	−0.0271742	−	0.352508i
$345$	−24.4897			−1.31848
$346$	6.56685	−	8.23457i	0.353036	−	0.442693i
$347$	3.13789	−	7.99522i	0.168451	−	0.429206i	−0.821573	−	0.570103i	$-0.806903\pi$
$347$	3.13789	−	7.99522i	0.168451	−	0.429206i	0.990024	+	0.140897i	$0.0449986\pi$
$348$	−5.17040	−	22.6530i	−0.277162	−	1.21433i
$349$	−0.439445	−	5.86398i	−0.0235229	−	0.313892i	−0.996537	−	0.0831472i	$-0.973503\pi$
$349$	−0.439445	−	5.86398i	−0.0235229	−	0.313892i	0.973014	−	0.230745i	$-0.0741162\pi$
$350$	−1.49192	−	2.58408i	−0.0797463	−	0.138125i
$351$	−8.79485	+	15.2331i	−0.469435	+	0.813085i
$352$	−1.60439	−	0.772633i	−0.0855142	−	0.0411815i
$353$	−19.2715	−	17.8814i	−1.02572	−	0.951728i	−0.0268677	−	0.999639i	$-0.508553\pi$
$353$	−19.2715	−	17.8814i	−1.02572	−	0.951728i	−0.998852	+	0.0479106i	$0.984744\pi$
$354$	30.6384	+	20.8889i	1.62841	+	1.11023i
$355$	1.25185	−	5.48471i	0.0664413	−	0.291098i
$356$	9.16553	+	1.38148i	0.485772	+	0.0732184i
$357$	3.46850	−	2.36478i	0.183572	−	0.125157i
$358$	5.60840	+	14.2900i	0.296413	+	0.755248i
$359$	−7.14989	−	2.20545i	−0.377357	−	0.116399i	0.100274	−	0.994960i	$-0.468028\pi$
$359$	−7.14989	−	2.20545i	−0.377357	−	0.116399i	−0.477631	+	0.878561i	$0.658504\pi$
$360$	5.06709	−	2.44018i	0.267059	−	0.128609i
$361$	−0.970517	+	12.9506i	−0.0510798	+	0.681613i
$362$	21.5332	−	3.24561i	1.13176	−	0.170585i
$363$	−16.8537	+	15.6379i	−0.884590	+	0.820779i
$364$	−6.50834	+	2.00756i	−0.341130	+	0.105225i
$365$	−8.76893	−	10.9959i	−0.458987	−	0.575551i
$366$	−13.4436	−	16.8577i	−0.702707	−	0.881167i
$367$	−16.9424	+	5.22602i	−0.884384	+	0.272796i	−0.703489	−	0.710706i	$-0.748376\pi$
$367$	−16.9424	+	5.22602i	−0.884384	+	0.272796i	−0.180895	+	0.983502i	$0.557899\pi$
$368$	6.11313	−	5.67215i	0.318669	−	0.295681i
$369$	12.7705	−	1.92484i	0.664805	−	0.100203i
$370$	0.433388	−	5.78316i	0.0225308	−	0.300652i
$371$	−31.3433	+	15.0941i	−1.62726	+	0.783647i
$372$	12.1472	+	3.74691i	0.629802	+	0.194268i
$373$	−8.80918	−	22.4454i	−0.456122	−	1.16218i	−0.955289	−	0.295674i	$-0.904456\pi$
$373$	−8.80918	−	22.4454i	−0.456122	−	1.16218i	0.499167	−	0.866506i	$-0.333639\pi$
$374$	−0.704873	+	0.480574i	−0.0364481	+	0.0248499i
$375$	−2.90387	−	0.437688i	−0.149955	−	0.0226021i
$376$	0.301300	−	1.32008i	0.0155384	−	0.0680780i
$377$	14.9223	+	10.1738i	0.768535	+	0.523979i
$378$	16.8553	+	15.6394i	0.866943	+	0.804406i
$379$	4.45732	+	2.14653i	0.228957	+	0.110260i	0.544846	−	0.838536i	$-0.316588\pi$
$379$	4.45732	+	2.14653i	0.228957	+	0.110260i	−0.315888	+	0.948796i	$0.602303\pi$
$380$	1.22608	−	2.12362i	0.0628963	−	0.108940i
$381$	−3.65663	−	6.33348i	−0.187335	−	0.324474i
$382$	1.88458	+	25.1479i	0.0964233	+	1.28668i
$383$	0.119561	+	0.523829i	0.00610926	+	0.0267664i	0.977891	−	0.209117i	$-0.0670589\pi$
$383$	0.119561	+	0.523829i	0.00610926	+	0.0267664i	−0.971781	+	0.235883i	$0.924202\pi$
$384$	−1.07289	+	2.73367i	−0.0547505	+	0.139502i
$385$	−3.31287	+	4.15420i	−0.168839	+	0.211718i
$386$	7.90976			0.402596
$387$	8.12960	−	35.9721i	0.413251	−	1.82857i
$388$	0.384507			0.0195204
$389$	14.3912	−	18.0460i	0.729664	−	0.914969i	−0.269178	−	0.963090i	$-0.586752\pi$
$389$	14.3912	−	18.0460i	0.729664	−	0.914969i	0.998842	+	0.0481213i	$0.0153234\pi$
$390$	−2.44898	+	6.23990i	−0.124009	+	0.315970i
$391$	−0.889006	−	3.89499i	−0.0449590	−	0.196978i
$392$	0.142232	+	1.89795i	0.00718378	+	0.0958608i
$393$	13.8546	+	23.9969i	0.698873	+	1.21048i
$394$	−3.52530	+	6.10599i	−0.177602	+	0.307616i
$395$	12.7960	+	6.16221i	0.643834	+	0.310054i
$396$	−7.34148	−	6.81190i	−0.368923	−	0.342311i
$397$	1.85809	+	1.26682i	0.0932549	+	0.0635801i	0.609050	−	0.793132i	$-0.291551\pi$
$397$	1.85809	+	1.26682i	0.0932549	+	0.0635801i	−0.515795	+	0.856712i	$0.672503\pi$
$398$	−5.70004	+	24.9735i	−0.285717	+	1.25181i
$399$	21.2471	+	3.20248i	1.06368	+	0.160325i
$400$	0.826239	−	0.563320i	0.0413119	−	0.0281660i
$401$	5.64075	+	14.3724i	0.281686	+	0.717723i	0.999763	+	0.0217602i	$0.00692703\pi$
$401$	5.64075	+	14.3724i	0.281686	+	0.717723i	−0.718078	+	0.695963i	$0.754978\pi$
$402$	−7.62917	−	2.35329i	−0.380508	−	0.117371i
$403$	−8.90221	+	4.28708i	−0.443451	+	0.213555i
$404$	0.969691	−	12.9396i	0.0482439	−	0.643770i
$405$	5.69345	−	0.858149i	0.282910	−	0.0426418i
$406$	17.3064	−	16.0580i	0.858902	−	0.796945i
$407$	−9.86836	+	3.04399i	−0.489156	+	0.150885i
$408$	0.877183	+	1.09995i	0.0434270	+	0.0544558i
$409$	3.86456	+	4.84600i	0.191090	+	0.239619i	0.868142	−	0.496316i	$-0.165314\pi$
$409$	3.86456	+	4.84600i	0.191090	+	0.239619i	−0.677052	+	0.735935i	$0.736743\pi$
$410$	2.19432	−	0.676858i	0.108370	−	0.0334276i
$411$	21.4094	−	19.8650i	1.05605	−	0.979868i
$412$	−1.70453	+	0.256917i	−0.0839764	+	0.0126574i
$413$	−2.81563	+	37.5720i	−0.138548	+	1.84879i
$414$	42.2559	−	20.3494i	2.07676	−	1.00012i
$415$	−9.14541	−	2.82099i	−0.448931	−	0.138477i
$416$	−0.833931	−	2.12482i	−0.0408868	−	0.104178i
$417$	14.5694	−	9.93323i	0.713465	−	0.486432i
$418$	−4.31786	−	0.650813i	−0.211194	−	0.0318323i
$419$	−5.13438	+	22.4952i	−0.250831	+	1.09896i	0.679913	+	0.733292i	$0.262017\pi$
$419$	−5.13438	+	22.4952i	−0.250831	+	1.09896i	−0.930744	+	0.365670i	$0.880840\pi$
$420$	7.23996	+	4.93612i	0.353274	+	0.240858i
$421$	15.3838	+	14.2741i	0.749759	+	0.695675i	0.959383	−	0.282107i	$-0.0910334\pi$
$421$	15.3838	+	14.2741i	0.749759	+	0.695675i	−0.209624	+	0.977782i	$0.567224\pi$
$422$	−11.2546	−	5.41991i	−0.547863	−	0.263837i
$423$	3.80756	−	6.59489i	0.185130	−	0.320655i
$424$	−5.82948	−	10.0969i	−0.283104	−	0.490351i
$425$	−0.0358015	−	0.477737i	−0.00173663	−	0.0231737i
$426$	3.67627	+	16.1068i	0.178116	+	0.780377i
$427$	8.00393	−	20.3937i	0.387337	−	0.986920i
$428$	−6.36309	+	7.97906i	−0.307572	+	0.385683i
$429$	11.9368			0.576313
$430$	0.476068	−	6.54013i	0.0229580	−	0.315393i
$431$	26.9264			1.29700			0.648499	−	0.761216i	$-0.275397\pi$
$431$	26.9264			1.29700			0.648499	+	0.761216i	$0.275397\pi$
$432$	−4.80459	+	6.02477i	−0.231161	+	0.289867i
$433$	5.51135	−	14.0427i	0.264859	−	0.674849i	−0.735137	−	0.677919i	$-0.762882\pi$
$433$	5.51135	−	14.0427i	0.264859	−	0.674849i	0.999995	+	0.00307010i	$0.000977245\pi$
$434$	2.87410	+	12.5923i	0.137961	+	0.604448i
$435$	−1.73639	−	23.1706i	−0.0832537	−	1.11094i
$436$	7.80888	+	13.5254i	0.373978	+	0.647748i
$437$	10.2246	−	17.7095i	0.489108	−	0.847160i
$438$	37.2120	+	17.9203i	1.77806	+	0.856267i
$439$	−9.11008	−	8.45292i	−0.434801	−	0.403436i	0.432173	−	0.901791i	$-0.357747\pi$
$439$	−9.11008	−	8.45292i	−0.434801	−	0.403436i	−0.866973	+	0.498355i	$0.833938\pi$
$440$	−1.47131	−	1.00313i	−0.0701422	−	0.0478221i
$441$	−2.38188	+	10.4357i	−0.113423	+	0.496938i
$442$	−1.08133	−	0.162985i	−0.0514337	−	0.00775238i
$443$	25.7116	−	17.5298i	1.22159	−	0.832868i	0.231439	−	0.972850i	$-0.425657\pi$
$443$	25.7116	−	17.5298i	1.22159	−	0.832868i	0.990154	+	0.139982i	$0.0447044\pi$
$444$	6.22208	+	15.8536i	0.295287	+	0.752378i
$445$	8.85726	+	2.73210i	0.419875	+	0.129514i
$446$	−12.2969	+	5.92188i	−0.582276	+	0.280409i
$447$	−2.60239	+	34.7265i	−0.123089	+	1.64251i
$448$	−2.95051	+	0.444717i	−0.139398	+	0.0210109i
$449$	4.45904	−	4.13739i	0.210435	−	0.195255i	−0.567912	−	0.823089i	$-0.692249\pi$
$449$	4.45904	−	4.13739i	0.210435	−	0.195255i	0.778347	+	0.627834i	$0.216058\pi$
$450$	5.37419	−	1.65772i	0.253342	−	0.0781455i
$451$	−2.54956	−	3.19705i	−0.120054	−	0.150543i
$452$	6.35504	+	7.96897i	0.298916	+	0.374829i
$453$	52.3454	−	16.1464i	2.45940	−	0.758625i
$454$	8.22361	−	7.63040i	0.385953	−	0.358112i
$455$	−6.73486	+	1.01512i	−0.315735	+	0.0475894i
$456$	−0.538144	+	7.18103i	−0.0252009	+	0.336282i
$457$	−19.1901	+	9.24145i	−0.897673	+	0.432297i	−0.825048	−	0.565063i	$-0.808852\pi$
$457$	−19.1901	+	9.24145i	−0.897673	+	0.432297i	−0.0726251	+	0.997359i	$0.523138\pi$
$458$	−23.6059	−	7.28147i	−1.10303	−	0.340241i
$459$	1.34875	+	3.43655i	0.0629542	+	0.160405i
$460$	6.89024	−	4.69768i	0.321259	−	0.219031i
$461$	−23.3432	−	3.51842i	−1.08720	−	0.163869i	−0.419100	−	0.907940i	$-0.637655\pi$
$461$	−23.3432	−	3.51842i	−1.08720	−	0.163869i	−0.668101	+	0.744071i	$0.732893\pi$
$462$	3.47217	−	15.2126i	0.161540	−	0.707753i
$463$	6.20672	+	4.23167i	0.288451	+	0.196663i	0.698897	−	0.715222i	$-0.253675\pi$
$463$	6.20672	+	4.23167i	0.288451	+	0.196663i	−0.410446	+	0.911885i	$0.634627\pi$
$464$	5.80005	+	5.38166i	0.269261	+	0.249837i
$465$	11.4531	+	5.51550i	0.531123	+	0.255775i
$466$	2.18532	−	3.78508i	0.101233	−	0.175340i
$467$	−2.89465	−	5.01368i	−0.133948	−	0.232005i	0.791247	−	0.611497i	$-0.209432\pi$
$467$	−2.89465	−	5.01368i	−0.133948	−	0.232005i	−0.925195	+	0.379492i	$0.876099\pi$
$468$	−0.959348	−	12.8016i	−0.0443459	−	0.591754i
$469$	−1.80511	−	7.90870i	−0.0833522	−	0.365190i
$470$	0.494683	−	1.26043i	0.0228180	−	0.0581393i
$471$	16.7149	−	20.9598i	0.770181	−	0.965777i
$472$	−12.6271			−0.581211
$473$	−11.1509	+	3.46571i	−0.512720	+	0.159353i
$474$	−41.7079			−1.91571
$475$	1.52889	−	1.91717i	0.0701503	−	0.0879657i
$476$	−0.522250	+	1.33067i	−0.0239373	+	0.0609912i
$477$	−14.5908	−	63.9265i	−0.668067	−	2.92699i
$478$	−1.39415	−	18.6037i	−0.0637671	−	0.850913i
$479$	11.3664	+	19.6871i	0.519342	+	0.899528i	0.999747	+	0.0224807i	$0.00715643\pi$
$479$	11.3664	+	19.6871i	0.519342	+	0.899528i	−0.480405	+	0.877047i	$0.659510\pi$
$480$	−1.46834	+	2.54323i	−0.0670201	+	0.116082i
$481$	−11.9268	−	5.74363i	−0.543814	−	0.261887i
$482$	7.52626	+	6.98335i	0.342812	+	0.318083i
$483$	60.3760	+	41.1637i	2.74720	+	1.87301i
$484$	1.74211	−	7.63269i	0.0791868	−	0.346940i
$485$	0.380213	+	0.0573078i	0.0172646	+	0.00260221i
$486$	5.13032	−	3.49779i	0.232716	−	0.158663i
$487$	7.16764	+	18.2628i	0.324797	+	0.827568i	0.996250	+	0.0865215i	$0.0275751\pi$
$487$	7.16764	+	18.2628i	0.324797	+	0.827568i	−0.671453	+	0.741047i	$0.734330\pi$
$488$	7.01607	+	2.16417i	0.317603	+	0.0979674i
$489$	2.87143	−	1.38281i	0.129851	−	0.0625327i
$490$	−0.142232	+	1.89795i	−0.00642536	+	0.0857405i
$491$	−3.52287	+	0.530987i	−0.158985	+	0.0239631i	−0.228052	−	0.973649i	$-0.573236\pi$
$491$	−3.52287	+	0.530987i	−0.158985	+	0.0239631i	0.0690675	+	0.997612i	$0.477998\pi$
$492$	−4.94341	+	4.58681i	−0.222866	+	0.206790i
$493$	3.62215	−	1.11729i	0.163133	−	0.0503200i
$494$	−3.48986	−	4.37615i	−0.157016	−	0.196892i
$495$	−6.24422	−	7.83000i	−0.280657	−	0.351932i
$496$	−4.13638	+	1.27590i	−0.185729	+	0.0572897i
$497$	−12.3053	+	11.4176i	−0.551966	+	0.512150i
$498$	27.7918	−	4.18894i	1.24538	−	0.187711i
$499$	−0.683997	+	9.12731i	−0.0306199	+	0.408595i	0.960742	+	0.277442i	$0.0894867\pi$
$499$	−0.683997	+	9.12731i	−0.0306199	+	0.408595i	−0.991362	+	0.131152i	$0.958132\pi$
$500$	0.900969	−	0.433884i	0.0402926	−	0.0194039i
$501$	−60.1526	−	18.5546i	−2.68742	−	0.828959i
$502$	−7.05044	−	17.9642i	−0.314676	−	0.801782i
$503$	16.8358	−	11.4785i	0.750673	−	0.511800i	−0.126505	−	0.991966i	$-0.540376\pi$
$503$	16.8358	−	11.4785i	0.750673	−	0.511800i	0.877178	+	0.480166i	$0.159424\pi$
$504$	−16.5938	−	2.50111i	−0.739146	−	0.111408i
$505$	2.88741	−	12.6506i	0.128488	−	0.562943i
$506$	−12.2697	−	8.36534i	−0.545455	−	0.371885i
$507$	−16.7691	−	15.5595i	−0.744743	−	0.691021i
$508$	2.24370	+	1.08051i	0.0995483	+	0.0479399i
$509$	3.16170	−	5.47622i	0.140140	−	0.242729i	−0.787409	−	0.616431i	$-0.788578\pi$
$509$	3.16170	−	5.47622i	0.140140	−	0.242729i	0.927549	+	0.373701i	$0.121911\pi$
$510$	0.703446	+	1.21840i	0.0311491	+	0.0539519i
$511$	3.13608	+	41.8481i	0.138732	+	1.85125i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	−6.90355	+	17.5900i	−0.304799	+	0.776616i
$514$	1.05227	−	1.31951i	0.0464139	−	0.0582011i
$515$	−1.72379			−0.0759592
$516$	7.07367	+	17.9108i	0.311401	+	0.788480i
$517$	−2.41117			−0.106043
$518$	−10.7891	+	13.5291i	−0.474046	+	0.594435i
$519$	−11.3001	+	28.7921i	−0.496019	+	1.26383i
$520$	−0.507928	−	2.22538i	−0.0222741	−	0.0975894i
$521$	1.73649	+	23.1718i	0.0760768	+	1.01517i	0.896392	+	0.443263i	$0.146179\pi$
$521$	1.73649	+	23.1718i	0.0760768	+	1.01517i	−0.820315	+	0.571912i	$0.806202\pi$
$522$	22.2493	+	38.5369i	0.973825	+	1.68671i
$523$	10.8275	−	18.7537i	0.473452	−	0.820043i	−0.526086	−	0.850431i	$-0.676341\pi$
$523$	10.8275	−	18.7537i	0.473452	−	0.820043i	0.999538	+	0.0303886i	$0.00967449\pi$
$524$	−8.50118	−	4.09395i	−0.371376	−	0.178845i
$525$	6.42340	+	5.96004i	0.280340	+	0.260118i
$526$	14.0666	+	9.59042i	0.613331	+	0.418162i
$527$	−0.461458	+	2.02178i	−0.0201014	+	0.0880702i
$528$	5.17103	+	0.779408i	0.225040	+	0.0339194i
$529$	38.4561	−	26.2190i	1.67201	−	1.13995i
$530$	−4.25949	−	10.8530i	−0.185021	−	0.471425i
$531$	−67.8606	−	20.9322i	−2.94490	−	0.908381i
$532$	−6.59222	+	3.17465i	−0.285809	+	0.137638i
$533$	0.391709	−	5.22699i	0.0169668	−	0.226406i
$534$	−26.9162	+	4.05696i	−1.16478	+	0.175562i
$535$	−7.48124	+	6.94157i	−0.323442	+	0.300110i
$536$	2.59790	−	0.801345i	0.112212	−	0.0346128i
$537$	−28.1077	−	35.2459i	−1.21294	−	1.52097i
$538$	−15.7181	−	19.7098i	−0.677653	−	0.849751i
$539$	3.23865	−	0.998991i	0.139499	−	0.0430296i
$540$	−5.64887	+	5.24139i	−0.243089	+	0.225553i
$541$	30.7898	−	4.64082i	1.32376	−	0.199524i	0.551149	−	0.834407i	$-0.314190\pi$
$541$	30.7898	−	4.64082i	1.32376	−	0.199524i	0.772609	+	0.634882i	$0.218951\pi$
$542$	0.0620138	−	0.827516i	0.00266372	−	0.0355449i
$543$	−57.6171	+	27.7469i	−2.47259	+	1.19074i
$544$	−0.457793	−	0.141210i	−0.0196277	−	0.00605435i
$545$	5.70581	+	14.5382i	0.244410	+	0.622747i
$546$	16.5260	−	11.2672i	0.707247	−	0.482193i
$547$	3.97669	+	0.599389i	0.170031	+	0.0256280i	0.233506	−	0.972355i	$-0.424980\pi$
$547$	3.97669	+	0.599389i	0.170031	+	0.0256280i	−0.0634749	+	0.997983i	$0.520218\pi$
$548$	−2.21302	+	9.69586i	−0.0945354	+	0.414187i
$549$	34.1181	+	23.2613i	1.45612	+	0.992769i
$550$	−1.30537	−	1.21121i	−0.0556613	−	0.0516461i
$551$	17.4805	+	8.41817i	0.744695	+	0.358626i
$552$	−12.2449	+	21.2087i	−0.521176	+	0.902704i
$553$	−21.1889	−	36.7002i	−0.901042	−	1.56065i
$554$	1.70277	+	22.7218i	0.0723436	+	0.965359i
$555$	3.78972	+	16.6039i	0.160865	+	0.704795i
$556$	−2.19371	+	5.58947i	−0.0930338	+	0.237046i
$557$	9.83746	−	12.3358i	0.416827	−	0.522684i	−0.528445	−	0.848967i	$-0.677225\pi$
$557$	9.83746	−	12.3358i	0.416827	−	0.522684i	0.945272	+	0.326283i	$0.105796\pi$
$558$	−24.3447			−1.03060
$559$	−13.4996	−	6.46558i	−0.570973	−	0.273465i
$560$	−2.98383			−0.126090
$561$	1.56203	−	1.95873i	0.0659491	−	0.0826975i
$562$	10.6190	−	27.0568i	0.447936	−	1.14132i
$563$	7.98054	+	34.9650i	0.336340	+	1.47360i	0.806613	+	0.591080i	$0.201298\pi$
$563$	7.98054	+	34.9650i	0.336340	+	1.47360i	−0.470273	+	0.882521i	$0.655845\pi$
$564$	0.297152	+	3.96522i	0.0125124	+	0.166966i
$565$	5.09634	+	8.82713i	0.214405	+	0.371360i
$566$	−1.09725	+	1.90050i	−0.0461209	+	0.0798838i
$567$	−15.4788	−	7.45421i	−0.650049	−	0.313047i
$568$	−4.12397	−	3.82649i	−0.173038	−	0.160556i
$569$	−22.0285	−	15.0188i	−0.923485	−	0.629621i	0.00540199	−	0.999985i	$-0.498280\pi$
$569$	−22.0285	−	15.0188i	−0.923485	−	0.629621i	−0.928887	+	0.370364i	$0.879233\pi$
$570$	−1.60241	+	7.02062i	−0.0671176	+	0.294061i
$571$	−38.0760	−	5.73903i	−1.59343	−	0.240171i	−0.708436	−	0.705775i	$-0.750599\pi$
$571$	−38.0760	−	5.73903i	−1.59343	−	0.240171i	−0.884993	+	0.465604i	$0.845837\pi$
$572$	−3.35844	+	2.28974i	−0.140423	+	0.0957390i
$573$	−27.0565	−	68.9389i	−1.13030	−	2.87996i
$574$	−6.54749	−	2.01963i	−0.273287	−	0.0842979i
$575$	7.51343	−	3.61828i	0.313332	−	0.150893i
$576$	0.420285	−	5.60832i	0.0175119	−	0.233680i
$577$	34.7278	−	5.23437i	1.44574	−	0.217910i	0.621170	−	0.783676i	$-0.286658\pi$
$577$	34.7278	−	5.23437i	1.44574	−	0.217910i	0.824566	+	0.565766i	$0.191420\pi$
$578$	12.2936	−	11.4068i	0.511348	−	0.474461i
$579$	−22.1964	+	6.84669i	−0.922452	+	0.284539i
$580$	4.93318	+	6.18601i	0.204839	+	0.256860i
$581$	17.8051	+	22.3269i	0.738679	+	0.926274i
$582$	−1.07901	+	0.332829i	−0.0447262	+	0.0137962i
$583$	−15.2193	+	14.1214i	−0.630318	+	0.584850i
$584$	−13.9072	+	2.09617i	−0.575483	+	0.0867402i
$585$	0.959348	−	12.8016i	0.0396641	−	0.529281i
$586$	−22.0901	+	10.6380i	−0.912533	+	0.439453i
$587$	−26.5822	−	8.19953i	−1.09717	−	0.338431i	−0.307240	−	0.951632i	$-0.599405\pi$
$587$	−26.5822	−	8.19953i	−1.09717	−	0.338431i	−0.789927	+	0.613201i	$0.789881\pi$
$588$	−2.04199	−	5.20291i	−0.0842104	−	0.214565i
$589$	−8.77019	+	5.97941i	−0.361369	+	0.246377i
$590$	−12.4861	−	1.88198i	−0.514045	−	0.0774798i
$591$	4.60736	−	20.1862i	0.189521	−	0.830348i
$592$	−4.79167	−	3.26690i	−0.196936	−	0.134269i
$593$	8.48719	+	7.87497i	0.348527	+	0.323386i	0.834938	−	0.550344i	$-0.185504\pi$
$593$	8.48719	+	7.87497i	0.348527	+	0.323386i	−0.486410	+	0.873730i	$0.661694\pi$
$594$	12.3634	+	5.95388i	0.507275	+	0.244291i
$595$	−0.714743	+	1.23797i	−0.0293016	+	0.0507519i
$596$	−5.92914	−	10.2696i	−0.242867	−	0.420658i
$597$	−5.62157	−	75.0147i	−0.230076	−	3.07015i
$598$	−4.23576	−	18.5581i	−0.173213	−	0.758896i
$599$	−9.42070	+	24.0036i	−0.384919	+	0.980759i	0.598776	+	0.800917i	$0.295654\pi$
$599$	−9.42070	+	24.0036i	−0.384919	+	0.980759i	−0.983695	+	0.179842i	$0.942441\pi$
$600$	−1.83099	+	2.29598i	−0.0747497	+	0.0937331i
$601$	18.2308			0.743649			0.371825	−	0.928303i	$-0.378732\pi$
$601$	18.2308			0.743649			0.371825	+	0.928303i	$0.378732\pi$
$602$	−12.1667	+	15.3236i	−0.495877	+	0.624543i
$603$	15.2900			0.622656
$604$	−11.6302	+	14.5839i	−0.473228	+	0.593409i
$605$	2.86025	−	7.28779i	0.116286	−	0.296291i
$606$	8.47938	+	37.1506i	0.344451	+	1.50914i
$607$	−1.64946	−	22.0105i	−0.0669496	−	0.893380i	−0.925037	−	0.379876i	$-0.875966\pi$
$607$	−1.64946	−	22.0105i	−0.0669496	−	0.893380i	0.858088	−	0.513503i	$-0.171653\pi$
$608$	−1.22608	−	2.12362i	−0.0497239	−	0.0861244i
$609$	−34.6655	+	60.0424i	−1.40472	+	2.43304i
$610$	6.61515	+	3.18569i	0.267840	+	0.128985i
$611$	−2.26566	−	2.10222i	−0.0916587	−	0.0850469i
$612$	−2.22618	−	1.51778i	−0.0899879	−	0.0613527i
$613$	−6.60262	+	28.9280i	−0.266677	+	1.16839i	0.647174	+	0.762342i	$0.275951\pi$
$613$	−6.60262	+	28.9280i	−0.266677	+	1.16839i	−0.913852	+	0.406048i	$0.866907\pi$
$614$	29.3818	+	4.42860i	1.18575	+	0.178724i
$615$	−5.57182	+	3.79881i	−0.224678	+	0.153183i
$616$	1.94121	+	4.94613i	0.0782137	+	0.199285i
$617$	9.80363	+	3.02402i	0.394679	+	0.121742i	0.485741	−	0.874103i	$-0.338550\pi$
$617$	9.80363	+	3.02402i	0.394679	+	0.121742i	−0.0910616	+	0.995845i	$0.529026\pi$
$618$	4.56088	−	2.19641i	0.183466	−	0.0883524i
$619$	0.466123	−	6.21998i	0.0187351	−	0.250002i	−0.979971	−	0.199142i	$-0.936185\pi$
$619$	0.466123	−	6.21998i	0.0187351	−	0.250002i	0.998706	−	0.0508604i	$-0.0161964\pi$
$620$	−4.28034	+	0.645157i	−0.171903	+	0.0259101i
$621$	−47.1075	+	43.7094i	−1.89036	+	1.75400i
$622$	15.6156	−	4.81677i	0.626128	−	0.193135i
$623$	−17.2441	−	21.6234i	−0.690869	−	0.866323i
$624$	4.17942	+	5.24083i	0.167311	+	0.209801i
$625$	0.955573	−	0.294755i	0.0382229	−	0.0117902i
$626$	0.814526	−	0.755769i	0.0325550	−	0.0302066i
$627$	12.6802	−	1.91123i	0.506397	−	0.0763270i
$628$	−0.682204	+	9.10337i	−0.0272229	+	0.363264i
$629$	−2.50321	+	1.20548i	−0.0998093	+	0.0480656i
$630$	−16.0357	−	4.94635i	−0.638877	−	0.197067i
$631$	15.0224	+	38.2765i	0.598033	+	1.52376i	0.833865	+	0.551968i	$0.186123\pi$
$631$	15.0224	+	38.2765i	0.598033	+	1.52376i	−0.235833	+	0.971794i	$0.575782\pi$
$632$	11.7346	−	8.00052i	0.466777	−	0.318243i
$633$	36.2741	+	5.46743i	1.44176	+	0.217311i
$634$	−3.59853	+	15.7662i	−0.142916	+	0.626155i
$635$	2.05760	+	1.40285i	0.0816535	+	0.0556704i
$636$	25.0986	+	23.2881i	0.995225	+	0.923434i
$637$	3.91419	+	1.88497i	0.155086	+	0.0746854i
$638$	7.04478	−	12.2019i	0.278905	−	0.483078i
$639$	−15.8198	−	27.4006i	−0.625820	−	1.08395i
$640$	−0.0747301	−	0.997204i	−0.00295397	−	0.0394179i
$641$	−8.81398	−	38.6166i	−0.348131	−	1.52526i	−0.781419	−	0.624007i	$-0.785504\pi$
$641$	−8.81398	−	38.6166i	−0.348131	−	1.52526i	0.433287	−	0.901256i	$-0.357354\pi$
$642$	10.9495	−	27.8988i	0.432141	−	1.10108i
$643$	1.26406	−	1.58508i	0.0498496	−	0.0625094i	−0.756282	−	0.654246i	$-0.772986\pi$
$643$	1.26406	−	1.58508i	0.0498496	−	0.0625094i	0.806131	+	0.591737i	$0.201557\pi$
$644$	−24.8830			−0.980529
$645$	4.32519	+	18.7650i	0.170304	+	0.738873i
$646$	−1.17477			−0.0462207
$647$	−17.5220	+	21.9718i	−0.688859	+	0.863802i	−0.996137	−	0.0878177i	$-0.972011\pi$
$647$	−17.5220	+	21.9718i	−0.688859	+	0.863802i	0.307277	+	0.951620i	$0.400582\pi$
$648$	2.10354	−	5.35974i	0.0826350	−	0.210551i
$649$	5.00352	+	21.9219i	0.196405	+	0.860508i
$650$	−0.170580	−	2.27623i	−0.00669068	−	0.0892810i
$651$	−18.9652	−	32.8486i	−0.743303	−	1.28744i
$652$	−0.542629	+	0.939861i	−0.0212510	+	0.0368078i
$653$	−22.4392	−	10.8061i	−0.878113	−	0.422877i	−0.0601782	−	0.998188i	$-0.519167\pi$
$653$	−22.4392	−	10.8061i	−0.878113	−	0.422877i	−0.817935	+	0.575311i	$0.804881\pi$
$654$	−33.6209	−	31.1956i	−1.31468	−	1.21985i
$655$	−7.79605	−	5.31526i	−0.304617	−	0.207684i
$656$	0.510984	−	2.23877i	0.0199506	−	0.0874091i
$657$	−78.2146	−	11.7890i	−3.05144	−	0.459931i
$658$	−3.33817	+	2.27593i	−0.130135	+	0.0887248i
$659$	5.29092	+	13.4810i	0.206105	+	0.525146i	0.996126	−	0.0879325i	$-0.0280260\pi$
$659$	5.29092	+	13.4810i	0.206105	+	0.525146i	−0.790022	+	0.613079i	$0.789931\pi$
$660$	4.99711	+	1.54141i	0.194512	+	0.0599991i
$661$	27.7298	−	13.3539i	1.07856	−	0.519408i	0.191706	−	0.981452i	$-0.438598\pi$
$661$	27.7298	−	13.3539i	1.07856	−	0.519408i	0.886857	+	0.462044i	$0.152884\pi$
$662$	1.09292	−	14.5840i	0.0424777	−	0.566825i
$663$	3.17552	−	0.478632i	0.123327	−	0.0185885i
$664$	−7.01575	+	6.50967i	−0.272264	+	0.252624i
$665$	−6.99175	+	2.15667i	−0.271128	+	0.0836320i
$666$	−20.3357	−	25.5002i	−0.787993	−	0.988112i
$667$	41.1392	+	51.5869i	1.59291	+	1.99745i
$668$	20.4833	−	6.31825i	0.792521	−	0.244460i
$669$	29.3817	−	27.2622i	1.13596	−	1.05402i
$670$	2.68831	−	0.405198i	0.103859	−	0.0156542i
$671$	0.977070	−	13.0381i	0.0377194	−	0.503330i
$672$	7.89478	−	3.80193i	0.304548	−	0.146662i
$673$	38.4738	+	11.8676i	1.48306	+	0.457462i	0.927439	−	0.373976i	$-0.122006\pi$
$673$	38.4738	+	11.8676i	1.48306	+	0.457462i	0.555618	+	0.831438i	$0.312482\pi$
$674$	7.17112	+	18.2717i	0.276221	+	0.703800i
$675$	−6.36697	+	4.34092i	−0.245065	+	0.167082i
$676$	7.70269	+	1.16099i	0.296257	+	0.0446536i
$677$	3.88063	−	17.0022i	0.149145	−	0.653446i	−0.843979	−	0.536377i	$-0.819793\pi$
$677$	3.88063	−	17.0022i	0.149145	−	0.653446i	0.993124	−	0.117070i	$-0.0373501\pi$
$678$	−24.7315	−	16.8616i	−0.949806	−	0.647567i
$679$	−0.841035	−	0.780366i	−0.0322760	−	0.0299477i
$680$	−0.431634	−	0.207864i	−0.0165524	−	0.00797121i
$681$	−16.4723	+	28.5308i	−0.631219	+	1.09330i
$682$	3.85413	+	6.67555i	0.147582	+	0.255620i
$683$	2.31915	+	30.9469i	0.0887399	+	1.18415i	0.846780	+	0.531943i	$0.178538\pi$
$683$	2.31915	+	30.9469i	0.0887399	+	1.18415i	−0.758040	+	0.652208i	$0.773843\pi$
$684$	−3.06879	−	13.4452i	−0.117338	−	0.514092i
$685$	−3.63339	+	9.25773i	−0.138825	+	0.353720i
$686$	−9.48191	+	11.8899i	−0.362021	+	0.453960i
$687$	72.5460			2.76780
$688$	−5.42589	−	3.68235i	−0.206860	−	0.140388i
$689$	−26.6128			−1.01387
$690$	−15.2691	+	19.1468i	−0.581285	+	0.728908i
$691$	−3.82075	+	9.73512i	−0.145348	+	0.370341i	−0.984945	−	0.172869i	$-0.944696\pi$
$691$	−3.82075	+	9.73512i	−0.145348	+	0.370341i	0.839597	+	0.543210i	$0.182791\pi$
$692$	−2.34368	−	10.2683i	−0.0890934	−	0.390344i
$693$	2.23316	+	29.7994i	0.0848306	+	1.13199i
$694$	−4.29447	−	7.43824i	−0.163016	−	0.282352i
$695$	−3.00227	+	5.20009i	−0.113883	+	0.197250i
$696$	−20.9345	−	10.0815i	−0.793520	−	0.382139i
$697$	−0.806448	−	0.748274i	−0.0305464	−	0.0283429i
$698$	−4.85864	−	3.31256i	−0.183902	−	0.125382i
$699$	−2.85608	+	12.5133i	−0.108027	+	0.473297i
$700$	−2.95051	−	0.444717i	−0.111519	−	0.0168087i
$701$	40.3885	−	27.5364i	1.52545	−	1.04004i	0.546140	−	0.837694i	$-0.316097\pi$
$701$	40.3885	−	27.5364i	1.52545	−	1.04004i	0.979315	−	0.202343i	$-0.0648556\pi$
$702$	6.42624	+	16.3738i	0.242543	+	0.617989i
$703$	−13.5891	−	4.19170i	−0.512524	−	0.158093i
$704$	−1.60439	+	0.772633i	−0.0604677	+	0.0291197i
$705$	−0.297152	+	3.96522i	−0.0111914	+	0.149339i
$706$	−25.9958	+	3.91824i	−0.978365	+	0.147465i
$707$	−28.3823	+	26.3349i	−1.06743	+	0.990426i
$708$	35.4343	−	10.9300i	1.33170	−	0.410776i
$709$	31.6190	+	39.6490i	1.18748	+	1.48905i	0.832368	+	0.554224i	$0.186985\pi$
$709$	31.6190	+	39.6490i	1.18748	+	1.48905i	0.355109	+	0.934825i	$0.384444\pi$
$710$	−3.50760	−	4.39840i	−0.131638	−	0.165069i
$711$	76.3265	−	23.5436i	2.86247	−	0.882954i
$712$	6.79470	−	6.30456i	0.254642	−	0.236273i
$713$	−35.6950	+	5.38015i	−1.33679	+	0.201488i
$714$	0.313712	−	4.18620i	0.0117404	−	0.156664i
$715$	−3.66219	+	1.76362i	−0.136958	+	0.0659556i
$716$	14.6691	+	4.52483i	0.548211	+	0.169101i
$717$	20.0156	+	50.9990i	0.747497	+	1.90459i
$718$	−6.18218	+	4.21494i	−0.230717	+	0.157300i
$719$	38.7920	+	5.84695i	1.44670	+	0.218054i	0.824969	−	0.565179i	$-0.191193\pi$
$719$	38.7920	+	5.84695i	1.44670	+	0.218054i	0.621728	+	0.783233i	$0.286431\pi$
$720$	1.25147	−	5.48304i	0.0466395	−	0.204341i
$721$	4.24976	+	2.89744i	0.158269	+	0.107906i
$722$	9.52011	+	8.83337i	0.354302	+	0.328744i
$723$	−27.1650	−	13.0820i	−1.01028	−	0.486524i
$724$	10.8882	−	18.8589i	0.404657	−	0.700886i
$725$	3.95610	+	6.85217i	0.146926	+	0.254483i
$726$	1.71813	+	22.9268i	0.0637658	+	0.850895i
$727$	0.0873574	+	0.382738i	0.00323991	+	0.0141950i	0.976522	−	0.215418i	$-0.0691113\pi$
$727$	0.0873574	+	0.382738i	0.00323991	+	0.0141950i	−0.973282	+	0.229613i	$0.926254\pi$
$728$	−2.48831	+	6.34012i	−0.0922230	+	0.234980i
$729$	−22.1387	+	27.7611i	−0.819954	+	1.02819i
$730$	−14.0643			−0.520542
$731$	−2.82749	+	1.36910i	−0.104579	+	0.0506379i
$732$	−21.5618			−0.796948
$733$	6.88286	−	8.63083i	0.254224	−	0.318787i	−0.638299	−	0.769788i	$-0.720362\pi$
$733$	6.88286	−	8.63083i	0.254224	−	0.318787i	0.892523	+	0.451001i	$0.148933\pi$
$734$	−6.47752	+	16.5044i	−0.239089	+	0.609190i
$735$	−1.24373	−	5.44914i	−0.0458757	−	0.200995i
$736$	−0.623195	−	8.31596i	−0.0229713	−	0.306530i
$737$	−2.42063	−	4.19265i	−0.0891649	−	0.154438i
$738$	6.45736	−	11.1845i	0.237699	−	0.411706i
$739$	42.7638	+	20.5940i	1.57309	+	0.757562i	0.998160	−	0.0606387i	$-0.0193137\pi$
$739$	42.7638	+	20.5940i	1.57309	+	0.757562i	0.574933	+	0.818200i	$0.305028\pi$
$740$	−4.25124	−	3.94458i	−0.156279	−	0.145006i
$741$	13.5813	+	9.25954i	0.498920	+	0.340158i
$742$	−7.74114	+	33.9162i	−0.284186	+	1.24510i
$743$	−22.5786	−	3.40318i	−0.828330	−	0.124851i	−0.278826	−	0.960342i	$-0.589945\pi$
$743$	−22.5786	−	3.40318i	−0.828330	−	0.124851i	−0.549504	+	0.835491i	$0.685183\pi$
$744$	10.5031	−	7.16089i	0.385062	−	0.262531i
$745$	−4.33232	−	11.0386i	−0.158724	−	0.404422i
$746$	−23.0410	−	7.10720i	−0.843590	−	0.260213i
$747$	−48.4951	+	23.3540i	−1.77434	+	0.854479i
$748$	−0.0637530	+	0.850725i	−0.00233104	+	0.0311056i
$749$	30.1117	−	4.53861i	1.10026	−	0.165837i
$750$	−2.15273	+	1.99744i	−0.0786067	+	0.0729364i
$751$	−21.0914	+	6.50583i	−0.769635	+	0.237401i	−0.654615	−	0.755962i	$-0.727169\pi$
$751$	−21.0914	+	6.50583i	−0.769635	+	0.237401i	−0.115020	+	0.993363i	$0.536693\pi$
$752$	−0.844224	−	1.05862i	−0.0307857	−	0.0386040i
$753$	35.3348	+	44.3084i	1.28767	+	1.61469i
$754$	17.2581	−	5.32342i	0.628503	−	0.193867i
$755$	−13.6740	+	12.6876i	−0.497646	+	0.461748i
$756$	22.7365	−	3.42698i	0.826919	−	0.124638i
$757$	1.77791	−	23.7246i	0.0646193	−	0.862285i	−0.866874	−	0.498527i	$-0.833874\pi$
$757$	1.77791	−	23.7246i	0.0646193	−	0.862285i	0.931493	−	0.363758i	$-0.118507\pi$
$758$	4.45732	−	2.14653i	0.161897	−	0.0779656i
$759$	41.6723	+	12.8542i	1.51261	+	0.466578i
$760$	−0.895871	−	2.28264i	−0.0324967	−	0.0828001i
$761$	−7.12801	+	4.85979i	−0.258390	+	0.176167i	−0.685586	−	0.727992i	$-0.740454\pi$
$761$	−7.12801	+	4.85979i	−0.258390	+	0.176167i	0.427196	+	0.904159i	$0.359502\pi$
$762$	−7.23158	−	1.08999i	−0.261973	−	0.0394860i
$763$	10.3697	−	45.4324i	0.375407	−	1.64476i
$764$	20.8364	+	14.2060i	0.753836	+	0.513957i
$765$	−1.97510	−	1.83262i	−0.0714099	−	0.0662587i
$766$	0.484091	+	0.233126i	0.0174909	+	0.00842318i
$767$	−14.4114	+	24.9613i	−0.520366	+	0.901301i
$768$	1.46834	+	2.54323i	0.0529840	+	0.0917710i
$769$	−0.794903	−	10.6072i	−0.0286649	−	0.382507i	−0.993024	−	0.117911i	$-0.962380\pi$
$769$	−0.794903	−	10.6072i	−0.0286649	−	0.382507i	0.964359	−	0.264596i	$-0.0852387\pi$
$770$	1.18235	+	5.18021i	0.0426089	+	0.186682i
$771$	−1.81073	+	4.61367i	−0.0652119	+	0.166157i
$772$	4.93166	−	6.18410i	0.177494	−	0.222571i
$773$	−0.179820			−0.00646768			−0.00323384	−	0.999995i	$-0.501029\pi$
$773$	−0.179820			−0.00646768			−0.00323384	+	0.999995i	$0.501029\pi$
$774$	−23.0554	−	28.7842i	−0.828710	−	1.03463i
$775$	−4.32869			−0.155491
$776$	0.239736	−	0.300620i	0.00860603	−	0.0107916i
$777$	18.5656	−	47.3045i	0.666039	−	1.69704i
$778$	−5.13617	−	22.5030i	−0.184140	−	0.806772i
$779$	−0.420803	−	5.61523i	−0.0150768	−	0.201186i
$780$	3.35164	+	5.80521i	0.120008	+	0.207860i
$781$	−5.00900	+	8.67585i	−0.179236	+	0.310446i
$782$	−3.59951	−	1.73343i	−0.128718	−	0.0619875i
$783$	−44.6950	−	41.4709i	−1.59727	−	1.48205i
$784$	1.57256	+	1.07215i	0.0561627	+	0.0382911i
$785$	−2.03137	+	8.90002i	−0.0725028	+	0.317655i
$786$	27.3998	+	4.12985i	0.977317	+	0.147307i
$787$	−34.8725	+	23.7757i	−1.24307	+	0.847511i	−0.992697	−	0.120638i	$-0.961506\pi$
$787$	−34.8725	+	23.7757i	−1.24307	+	0.847511i	−0.250374	+	0.968149i	$0.580554\pi$
$788$	2.57587	+	6.56321i	0.0917616	+	0.233805i
$789$	−47.7751	−	14.7367i	−1.70084	−	0.524639i
$790$	12.7960	−	6.16221i	0.455260	−	0.219241i
$791$	2.27279	−	30.3283i	0.0808111	−	1.07835i
$792$	−9.90309	+	1.49265i	−0.351891	+	0.0530390i
$793$	12.2856	−	11.3994i	0.436275	−	0.404804i
$794$	2.14894	−	0.662862i	0.0762632	−	0.0235241i
$795$	21.3474	+	26.7688i	0.757113	+	0.949390i
$796$	15.9712	+	20.0272i	0.566083	+	0.709845i
$797$	−34.9485	+	10.7802i	−1.23794	+	0.381854i	−0.843531	−	0.537081i	$-0.819527\pi$
$797$	−34.9485	+	10.7802i	−1.23794	+	0.381854i	−0.394409	+	0.918935i	$0.629051\pi$
$798$	15.7511	−	14.6149i	0.557584	−	0.517363i
$799$	−0.641439	+	0.0966814i	−0.0226925	+	0.00342034i
$800$	0.0747301	−	0.997204i	0.00264211	−	0.0352565i
$801$	46.9672	−	22.6182i	1.65950	−	0.799175i
$802$	14.7537	+	4.55093i	0.520973	+	0.160699i
$803$	9.14988	+	23.3135i	0.322892	+	0.822716i
$804$	−6.59658	+	4.49747i	−0.232644	+	0.158614i
$805$	−24.6051	−	3.70862i	−0.867216	−	0.130712i
$806$	−2.19866	+	9.63297i	−0.0774446	+	0.339307i
$807$	61.1689	+	41.7042i	2.15325	+	1.46806i
$808$	−9.51201	−	8.82586i	−0.334631	−	0.310493i
$809$	−17.2968	−	8.32971i	−0.608124	−	0.292857i	0.104366	−	0.994539i	$-0.466719\pi$
$809$	−17.2968	−	8.32971i	−0.608124	−	0.292857i	−0.712490	+	0.701682i	$0.752433\pi$
$810$	2.87888	−	4.98636i	0.101153	−	0.175203i
$811$	6.49116	+	11.2430i	0.227936	+	0.394796i	0.957196	−	0.289440i	$-0.0934691\pi$
$811$	6.49116	+	11.2430i	0.227936	+	0.394796i	−0.729261	+	0.684236i	$0.760136\pi$
$812$	−1.76428	−	23.5427i	−0.0619141	−	0.826186i
$813$	0.542274	+	2.37586i	0.0190184	+	0.0833250i
$814$	−3.77294	+	9.61329i	−0.132241	+	0.336946i
$815$	−0.676647	+	0.848489i	−0.0237019	+	0.0297213i
$816$	1.40689			0.0492511
$817$	−15.3755	−	4.70678i	−0.537922	−	0.164669i
$818$	6.19827			0.216717
$819$	−23.8828	+	29.9480i	−0.834531	+	1.04647i
$820$	0.838947	−	2.13760i	0.0292973	−	0.0746483i
$821$	−4.66842	−	20.4537i	−0.162929	−	0.713838i	−0.988709	−	0.149846i	$-0.952122\pi$
$821$	−4.66842	−	20.4537i	−0.162929	−	0.713838i	0.825781	−	0.563992i	$-0.190735\pi$
$822$	−2.18255	−	29.1241i	−0.0761253	−	1.01582i
$823$	−1.64429	−	2.84799i	−0.0573164	−	0.0992748i	0.835944	−	0.548815i	$-0.184921\pi$
$823$	−1.64429	−	2.84799i	−0.0573164	−	0.0992748i	−0.893260	+	0.449541i	$0.851588\pi$
$824$	−0.861894	+	1.49284i	−0.0300255	+	0.0520057i
$825$	4.71157	+	2.26897i	0.164036	+	0.0789954i
$826$	27.6194	+	25.6271i	0.961002	+	0.891680i
$827$	−38.9865	−	26.5805i	−1.35569	−	0.924296i	−0.355746	−	0.934583i	$-0.615773\pi$
$827$	−38.9865	−	26.5805i	−1.35569	−	0.924296i	−0.999947	+	0.0102867i	$0.996726\pi$
$828$	10.4363	−	45.7246i	0.362688	−	1.58904i
$829$	8.65069	+	1.30388i	0.300451	+	0.0452857i	0.297538	−	0.954710i	$-0.403835\pi$
$829$	8.65069	+	1.30388i	0.300451	+	0.0452857i	0.00291317	+	0.999996i	$0.499073\pi$
$830$	−7.90761	+	5.39132i	−0.274477	+	0.187135i
$831$	−24.4463	−	62.2882i	−0.848034	−	2.16075i
$832$	−2.18120	−	0.672811i	−0.0756195	−	0.0233255i
$833$	0.821515	−	0.395621i	0.0284638	−	0.0137074i
$834$	1.31774	−	17.5841i	0.0456297	−	0.608886i
$835$	21.1962	−	3.19481i	0.733523	−	0.110561i
$836$	−3.20097	+	2.97007i	−0.110708	+	0.102722i
$837$	31.8748	−	9.83206i	1.10175	−	0.339846i
$838$	14.3862	+	18.0398i	0.496964	+	0.623173i
$839$	−25.7838	−	32.3319i	−0.890157	−	1.11622i	−0.992594	−	0.121482i	$-0.961235\pi$
$839$	−25.7838	−	32.3319i	−0.890157	−	1.11622i	0.102436	−	0.994740i	$-0.467336\pi$
$840$	8.37325	−	2.58281i	0.288905	−	0.0891153i
$841$	−24.6327	+	22.8558i	−0.849403	+	0.788131i
$842$	20.7515	−	3.12779i	0.715145	−	0.107791i
$843$	−6.37877	+	85.1188i	−0.219696	+	2.93165i
$844$	−11.2546	+	5.41991i	−0.387398	+	0.186561i
$845$	7.44362	+	2.29605i	0.256068	+	0.0789866i
$846$	−2.78212	−	7.08872i	−0.0956512	−	0.243715i
$847$	−19.3012	+	13.1594i	−0.663198	+	0.452161i
$848$	−11.5287	−	1.73768i	−0.395898	−	0.0596721i
$849$	1.43404	−	6.28296i	0.0492163	−	0.215631i
$850$	−0.395832	−	0.269874i	−0.0135769	−	0.00925659i
$851$	−35.4523	−	32.8949i	−1.21529	−	1.12762i
$852$	14.8849	+	7.16820i	0.509949	+	0.245579i
$853$	−6.17191	+	10.6901i	−0.211322	+	0.366021i	−0.952129	−	0.305698i	$-0.901110\pi$
$853$	−6.17191	+	10.6901i	−0.211322	+	0.366021i	0.740806	+	0.671719i	$0.234444\pi$
$854$	−10.9541	−	18.9730i	−0.374840	−	0.649242i
$855$	−1.03060	−	13.7524i	−0.0352459	−	0.470324i
$856$	2.27096	+	9.94973i	0.0776198	+	0.340075i
$857$	11.4336	−	29.1323i	0.390564	−	0.995140i	−0.591452	−	0.806340i	$-0.701445\pi$
$857$	11.4336	−	29.1323i	0.390564	−	0.995140i	0.982016	−	0.188800i	$-0.0604597\pi$
$858$	7.44246	−	9.33255i	0.254081	−	0.318608i
$859$	26.6704			0.909981			0.454990	−	0.890496i	$-0.349643\pi$
$859$	26.6704			0.909981			0.454990	+	0.890496i	$0.349643\pi$
$860$	−4.81646	−	4.44991i	−0.164240	−	0.151741i
$861$	20.1218			0.685749
$862$	16.7883	−	21.0519i	0.571812	−	0.717030i
$863$	5.83999	−	14.8800i	0.198796	−	0.506523i	−0.796361	−	0.604821i	$-0.793245\pi$
$863$	5.83999	−	14.8800i	0.198796	−	0.506523i	0.995157	+	0.0982982i	$0.0313399\pi$
$864$	1.71474	+	7.51276i	0.0583366	+	0.255589i
$865$	−0.787088	−	10.5030i	−0.0267618	−	0.357111i
$866$	−7.54275	−	13.0644i	−0.256313	−	0.443947i
$867$	−24.6247	+	42.6513i	−0.836299	+	1.44851i
$868$	11.6370	+	5.60408i	0.394985	+	0.190215i
$869$	−18.5395	−	17.2021i	−0.628909	−	0.583542i
$870$	−19.1981	−	13.0890i	−0.650877	−	0.443760i
$871$	1.38089	−	6.05009i	0.0467898	−	0.205000i
$872$	15.4433	+	2.32771i	0.522977	+	0.0788261i
$873$	1.78673	−	1.21817i	0.0604717	−	0.0412289i
$874$	−7.47092	−	19.0356i	−0.252708	−	0.643889i
$875$	−2.85127	−	0.879501i	−0.0963906	−	0.0297326i
$876$	37.2120	−	17.9203i	1.25728	−	0.605472i
$877$	1.52571	−	20.3591i	0.0515194	−	0.687479i	−0.910327	−	0.413890i	$-0.864170\pi$
$877$	1.52571	−	20.3591i	0.0515194	−	0.687479i	0.961847	−	0.273590i	$-0.0882110\pi$
$878$	−12.2888	+	1.85224i	−0.414727	+	0.0625100i
$879$	52.7810	−	48.9736i	1.78026	−	1.65184i
$880$	−1.70162	+	0.524882i	−0.0573617	+	0.0176938i
$881$	28.1800	+	35.3367i	0.949410	+	1.19052i	0.981582	+	0.191040i	$0.0611859\pi$
$881$	28.1800	+	35.3367i	0.949410	+	1.19052i	−0.0321726	+	0.999482i	$0.510243\pi$
$882$	6.67388	+	8.36878i	0.224721	+	0.281792i
$883$	26.9138	−	8.30182i	0.905723	−	0.279378i	0.193309	−	0.981138i	$-0.438078\pi$
$883$	26.9138	−	8.30182i	0.905723	−	0.279378i	0.712414	+	0.701760i	$0.247602\pi$
$884$	−0.801626	+	0.743800i	−0.0269616	+	0.0250167i
$885$	36.6676	−	5.52675i	1.23257	−	0.185780i
$886$	2.32551	−	31.0318i	0.0781270	−	1.04253i
$887$	19.8923	−	9.57964i	0.667919	−	0.321653i	−0.0690167	−	0.997616i	$-0.521986\pi$
$887$	19.8923	−	9.57964i	0.667919	−	0.321653i	0.736936	+	0.675963i	$0.236272\pi$
$888$	16.2742	+	5.01994i	0.546128	+	0.168458i
$889$	−2.71475	−	6.91706i	−0.0910496	−	0.231991i
$890$	7.65846	−	5.22145i	0.256712	−	0.175023i
$891$	−10.1385	−	1.52814i	−0.339654	−	0.0511946i
$892$	−3.03709	+	13.3063i	−0.101689	+	0.445529i
$893$	−2.74335	−	1.87038i	−0.0918026	−	0.0625900i
$894$	25.5277	+	23.6863i	0.853775	+	0.792187i
$895$	13.8309	+	6.66061i	0.462316	+	0.222640i
$896$	−1.49192	+	2.58408i	−0.0498415	+	0.0863279i
$897$	27.9503	+	48.4113i	0.933232	+	1.61641i
$898$	−0.454572	−	6.06584i	−0.0151693	−	0.202420i
$899$	−7.62122	−	33.3907i	−0.254182	−	1.11364i
$900$	2.05469	−	5.23528i	0.0684898	−	0.174509i
$901$	−3.48252	+	4.36695i	−0.116020	+	0.145484i
$902$	−4.08918			−0.136155
$903$	20.8781	−	53.5326i	0.694781	−	1.78145i
$904$	10.1927			0.339004
$905$	13.5774	−	17.0255i	0.451327	−	0.565946i
$906$	20.0131	−	50.9924i	0.664889	−	1.69411i
$907$	2.10358	+	9.21637i	0.0698481	+	0.306024i	0.997770	−	0.0667510i	$-0.0212633\pi$
$907$	2.10358	+	9.21637i	0.0698481	+	0.306024i	−0.927922	+	0.372775i	$0.878406\pi$
$908$	−0.838347	−	11.1870i	−0.0278215	−	0.371252i
$909$	−36.4885	−	63.2000i	−1.21025	−	2.09621i
$910$	−3.40546	+	5.89844i	−0.112890	+	0.195531i
$911$	−43.0985	−	20.7551i	−1.42792	−	0.687648i	−0.449307	−	0.893378i	$-0.648329\pi$
$911$	−43.0985	−	20.7551i	−1.42792	−	0.687648i	−0.978609	+	0.205730i	$0.934043\pi$
$912$	5.27883	+	4.89804i	0.174799	+	0.162190i
$913$	14.0814	+	9.60052i	0.466026	+	0.317731i
$914$	−4.73955	+	20.7653i	−0.156770	+	0.686856i
$915$	−21.3210	−	3.21362i	−0.704851	−	0.106239i
$916$	−20.4109	+	13.9159i	−0.674397	+	0.459796i
$917$	10.2859	+	26.2081i	0.339670	+	0.865466i
$918$	3.52774	+	1.08816i	0.116433	+	0.0359147i
$919$	−30.9636	+	14.9113i	−1.02140	+	0.491878i	−0.868146	−	0.496310i	$-0.834688\pi$
$919$	−30.9636	+	14.9113i	−1.02140	+	0.491878i	−0.153250	+	0.988188i	$0.548974\pi$
$920$	0.623195	−	8.31596i	0.0205461	−	0.274169i
$921$	−86.2848	+	13.0053i	−2.84318	+	0.428541i
$922$	−17.3051	+	16.0568i	−0.569912	+	0.528801i
$923$	−12.2709	+	3.78507i	−0.403902	+	0.124587i
$924$	−9.72881	−	12.1995i	−0.320054	−	0.401335i
$925$	−3.61585	−	4.53413i	−0.118888	−	0.149081i
$926$	7.17828	−	2.21421i	0.235893	−	0.0727634i
$927$	−7.10669	+	6.59404i	−0.233414	+	0.216577i
$928$	7.82383	−	1.17925i	0.256830	−	0.0387109i
$929$	−0.587453	+	7.83902i	−0.0192737	+	0.257190i	0.979241	+	0.202701i	$0.0649720\pi$
$929$	−0.587453	+	7.83902i	−0.0192737	+	0.257190i	−0.998514	+	0.0544888i	$0.982647\pi$
$930$	11.4531	−	5.51550i	0.375561	−	0.180860i
$931$	4.45976	+	1.37565i	0.146163	+	0.0450852i
$932$	−1.59677	−	4.06851i	−0.0523040	−	0.133268i
$933$	−39.6511	+	27.0337i	−1.29812	+	0.885043i
$934$	−5.72463	−	0.862850i	−0.187316	−	0.0282333i
$935$	−0.189835	+	0.831721i	−0.00620827	+	0.0272002i
$936$	−10.6068	−	7.23162i	−0.346695	−	0.236373i
$937$	18.3284	+	17.0062i	0.598761	+	0.555569i	0.920243	−	0.391346i	$-0.127991\pi$
$937$	18.3284	+	17.0062i	0.598761	+	0.555569i	−0.321482	+	0.946916i	$0.604181\pi$
$938$	−7.30874	−	3.51970i	−0.238639	−	0.114922i
$939$	−1.63153	+	2.82590i	−0.0532430	+	0.0922196i
$940$	−0.677015	−	1.17262i	−0.0220818	−	0.0382468i
$941$	−0.170023	−	2.26879i	−0.00554258	−	0.0739605i	0.993747	−	0.111659i	$-0.0356164\pi$
$941$	−0.170023	−	2.26879i	−0.00554258	−	0.0739605i	−0.999289	+	0.0376984i	$0.987997\pi$
$942$	−5.96547	−	26.1364i	−0.194366	−	0.851571i
$943$	6.99622	−	17.8261i	0.227828	−	0.580497i
$944$	−7.87289	+	9.87230i	−0.256241	+	0.321316i
$945$	22.9933			0.747973
$946$	−4.24289	+	10.8790i	−0.137948	+	0.353706i
$947$	21.1087			0.685941			0.342970	−	0.939346i	$-0.388567\pi$
$947$	21.1087			0.685941			0.342970	+	0.939346i	$0.388567\pi$
$948$	−26.0045	+	32.6085i	−0.844585	+	1.05908i
$949$	−11.7286	+	29.8841i	−0.380727	+	0.970078i
$950$	−0.545655	−	2.39067i	−0.0177034	−	0.0775636i
$951$	−3.54899	−	47.3580i	−0.115084	−	1.53569i
$952$	0.714743	+	1.23797i	0.0231650	+	0.0401229i
$953$	−14.3853	+	24.9161i	−0.465987	+	0.807113i	−0.999245	−	0.0388393i	$-0.987634\pi$
$953$	−14.3853	+	24.9161i	−0.465987	+	0.807113i	0.533259	+	0.845952i	$0.320967\pi$
$954$	−59.0770	−	28.4500i	−1.91269	−	0.921102i
$955$	18.4864	+	17.1529i	0.598206	+	0.555054i
$956$	−15.4142	−	10.5092i	−0.498531	−	0.339892i
$957$	−9.20712	+	40.3390i	−0.297624	+	1.30398i
$958$	22.4788	+	3.38814i	0.726258	+	0.109466i
$959$	24.5185	−	16.7164i	0.791744	−	0.539802i
$960$	1.07289	+	2.73367i	0.0346273	+	0.0882289i
$961$	−11.7177	−	3.61442i	−0.377990	−	0.116594i
$962$	−11.9268	+	5.74363i	−0.384534	+	0.185182i
$963$	−4.28927	+	57.2363i	−0.138220	+	1.84441i
$964$	10.1523	−	1.53022i	0.326985	−	0.0492851i
$965$	5.79827	−	5.38001i	0.186653	−	0.173189i
$966$	69.8269	−	21.5387i	2.24664	−	0.692998i
$967$	−6.26751	−	7.85921i	−0.201550	−	0.252735i	0.670777	−	0.741659i	$-0.265961\pi$
$967$	−6.26751	−	7.85921i	−0.201550	−	0.252735i	−0.872326	+	0.488924i	$0.837389\pi$
$968$	−4.88129	−	6.12094i	−0.156890	−	0.196734i
$969$	3.29664	−	1.01688i	0.105903	−	0.0326669i
$970$	0.281864	−	0.261531i	0.00905010	−	0.00839727i
$971$	−12.2855	+	1.85175i	−0.394261	+	0.0594254i	−0.343181	−	0.939269i	$-0.611505\pi$
$971$	−12.2855	+	1.85175i	−0.394261	+	0.0594254i	−0.0510802	+	0.998695i	$0.516266\pi$
$972$	0.464018	−	6.19188i	0.0148834	−	0.198605i
$973$	16.1423	−	7.77370i	0.517497	−	0.249213i
$974$	18.7474	+	5.78281i	0.600706	+	0.185293i
$975$	2.44898	+	6.23990i	0.0784302	+	0.199837i
$976$	6.06647	−	4.13605i	0.194183	−	0.132392i
$977$	45.5653	+	6.86786i	1.45776	+	0.219722i	0.829599	−	0.558359i	$-0.188569\pi$
$977$	45.5653	+	6.86786i	1.45776	+	0.219722i	0.628163	+	0.778082i	$0.283807\pi$
$978$	0.709185	−	3.10714i	0.0226772	−	0.0993554i
$979$	−13.6377	−	9.29803i	−0.435863	−	0.297166i
$980$	1.39520	+	1.29455i	0.0445679	+	0.0413529i
$981$	79.1366	+	38.1102i	2.52664	+	1.21676i
$982$	−1.78133	+	3.08535i	−0.0568445	+	0.0984576i
$983$	−4.00858	−	6.94306i	−0.127854	−	0.221449i	0.794991	−	0.606621i	$-0.207475\pi$
$983$	−4.00858	−	6.94306i	−0.127854	−	0.221449i	−0.922845	+	0.385172i	$0.874142\pi$
$984$	0.503950	+	6.72474i	0.0160653	+	0.214377i
$985$	1.56890	+	6.87382i	0.0499895	+	0.219018i
$986$	1.38484	−	3.52853i	0.0441024	−	0.112371i
$987$	7.39755	−	9.27623i	0.235467	−	0.295266i
$988$	−5.59730			−0.178074
$989$	−40.1658	−	37.1091i	−1.27720	−	1.18000i
$990$	−10.0149			−0.318296
$991$	−22.4913	+	28.2032i	−0.714461	+	0.895905i	−0.998010	−	0.0630521i	$-0.979917\pi$
$991$	−22.4913	+	28.2032i	−0.714461	+	0.895905i	0.283549	+	0.958958i	$0.408488\pi$
$992$	−1.58145	+	4.02946i	−0.0502110	+	0.127936i
$993$	9.55697	+	41.8718i	0.303281	+	1.32876i
$994$	1.25444	+	16.7394i	0.0397886	+	0.530942i
$995$	12.8079	+	22.1839i	0.406037	+	0.703276i
$996$	14.0529	−	24.3403i	0.445282	−	0.771252i
$997$	33.8105	+	16.2823i	1.07079	+	0.515666i	0.884361	−	0.466803i	$-0.154594\pi$
$997$	33.8105	+	16.2823i	1.07079	+	0.515666i	0.186429	+	0.982468i	$0.440308\pi$
$998$	6.70955	+	6.22556i	0.212387	+	0.197067i
$999$	36.9244	+	25.1747i	1.16824	+	0.796491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.b.101.1	✓	48
43.23	even	21	inner	430.2.q.b.281.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.b.101.1	✓	48	1.1	even	1	trivial
430.2.q.b.281.1	yes	48	43.23	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 - 0.781831i) q^{2} +(-1.07289 + 2.73367i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(1.46834 + 2.54323i) q^{6} +(-1.49192 + 2.58408i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-4.12272 - 3.82532i) q^{9} +O(q^{10})\)	\(q+(0.623490 - 0.781831i) q^{2} +(-1.07289 + 2.73367i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(1.46834 + 2.54323i) q^{6} +(-1.49192 + 2.58408i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-4.12272 - 3.82532i) q^{9} +(-0.826239 - 0.563320i) q^{10} +(-0.396251 + 1.73609i) q^{11} +(2.90387 + 0.437688i) q^{12} +(-1.88598 + 1.28584i) q^{13} +(1.09012 + 2.77757i) q^{14} +(2.80620 + 0.865599i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.0358015 + 0.477737i) q^{17} +(-5.56123 + 0.838221i) q^{18} +(-1.79755 + 1.66789i) q^{19} +(-0.955573 + 0.294755i) q^{20} +(-5.46336 - 6.85083i) q^{21} +(1.11027 + 1.39224i) q^{22} +(-7.96879 + 2.45805i) q^{23} +(2.15273 - 1.99744i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(-0.170580 + 2.27623i) q^{26} +(6.94283 - 3.34349i) q^{27} +(2.85127 + 0.879501i) q^{28} +(-2.89065 - 7.36526i) q^{29} +(2.42639 - 1.65429i) q^{30} +(4.28034 + 0.645157i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(-4.32077 - 2.94585i) q^{33} +(0.351188 + 0.325855i) q^{34} +(2.68834 + 1.29464i) q^{35} +(-2.81202 + 4.87057i) q^{36} +(2.89969 + 5.02241i) q^{37} +(0.183249 + 2.44529i) q^{38} +(-1.49162 - 6.53521i) q^{39} +(-0.365341 + 0.930874i) q^{40} +(-1.43174 + 1.79535i) q^{41} -8.76255 q^{42} +(3.29084 + 5.67189i) q^{43} +1.78074 q^{44} +(-3.50654 + 4.39706i) q^{45} +(-3.04668 + 7.76282i) q^{46} +(0.301300 + 1.32008i) q^{47} +(-0.219458 - 2.92846i) q^{48} +(-0.951635 - 1.64828i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.26757 - 0.610428i) q^{51} +(1.67327 + 1.55257i) q^{52} +(9.63308 + 6.56772i) q^{53} +(1.71474 - 7.51276i) q^{54} +(1.76085 + 0.265405i) q^{55} +(2.46536 - 1.68085i) q^{56} +(-2.63088 - 6.70337i) q^{57} +(-7.56068 - 2.33216i) q^{58} +(11.3767 - 5.47871i) q^{59} +(0.219458 - 2.92846i) q^{60} +(-7.26026 + 1.09431i) q^{61} +(3.17315 - 2.94426i) q^{62} +(16.0357 - 4.94635i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.42318 + 1.78462i) q^{65} +(-4.99711 + 1.54141i) q^{66} +(-1.99293 + 1.84917i) q^{67} +(0.473726 - 0.0714027i) q^{68} +(1.83012 - 24.4213i) q^{69} +(2.68834 - 1.29464i) q^{70} +(5.37582 + 1.65822i) q^{71} +(2.05469 + 5.23528i) q^{72} +(11.6204 - 7.92269i) q^{73} +(5.73460 + 0.864352i) q^{74} +(0.653471 - 2.86304i) q^{75} +(2.02606 + 1.38135i) q^{76} +(-3.89502 - 3.61405i) q^{77} +(-6.03944 - 2.90844i) q^{78} +(-7.10122 + 12.2997i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.430278 + 5.74166i) q^{81} +(0.510984 + 2.23877i) q^{82} +(3.49654 - 8.90903i) q^{83} +(-5.46336 + 6.85083i) q^{84} +0.479077 q^{85} +(6.48627 + 0.963482i) q^{86} +23.2355 q^{87} +(1.11027 - 1.39224i) q^{88} +(-3.38637 + 8.62833i) q^{89} +(1.25147 + 5.48304i) q^{90} +(-0.508981 - 6.79188i) q^{91} +(4.16964 + 7.22203i) q^{92} +(-6.35597 + 11.0089i) q^{93} +(1.21994 + 0.587491i) q^{94} +(1.79755 + 1.66789i) q^{95} +(-2.42639 - 1.65429i) q^{96} +(-0.0855609 + 0.374867i) q^{97} +(-1.88201 - 0.283668i) q^{98} +(8.27474 - 5.64162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Introduction

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