LMFDB - Embedded newform 261.2.x.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81062 - 1.33630i) q^{2} +(-1.71999 - 0.204042i) q^{3} +(0.903135 + 2.92789i) q^{4} +(1.51600 - 3.86270i) q^{5} +(2.84158 + 2.66786i) q^{6} +(2.72479 + 0.840488i) q^{7} +(0.790819 - 2.26003i) q^{8} +(2.91673 + 0.701902i) q^{9} +O(q^{10})$	\(q+(-1.81062 - 1.33630i) q^{2} +(-1.71999 - 0.204042i) q^{3} +(0.903135 + 2.92789i) q^{4} +(1.51600 - 3.86270i) q^{5} +(2.84158 + 2.66786i) q^{6} +(2.72479 + 0.840488i) q^{7} +(0.790819 - 2.26003i) q^{8} +(2.91673 + 0.701902i) q^{9} +(-7.90661 + 4.96805i) q^{10} +(4.62838 + 0.875736i) q^{11} +(-0.955969 - 5.22022i) q^{12} +(1.98394 - 0.148676i) q^{13} +(-3.81042 - 5.16293i) q^{14} +(-3.39566 + 6.33449i) q^{15} +(0.611281 - 0.416764i) q^{16} +(-2.69764 - 2.69764i) q^{17} +(-4.34314 - 5.16849i) q^{18} +(-1.65364 - 2.63175i) q^{19} +(12.6787 + 0.950139i) q^{20} +(-4.51512 - 2.00160i) q^{21} +(-7.20997 - 7.77050i) q^{22} +(-0.131870 + 0.874899i) q^{23} +(-1.82134 + 3.72587i) q^{24} +(-8.95697 - 8.31085i) q^{25} +(-3.79084 - 2.38194i) q^{26} +(-4.87354 - 1.80240i) q^{27} +8.73697i q^{28} +(4.32234 + 3.21207i) q^{29} +(14.6130 - 6.93172i) q^{30} +(3.21568 + 7.37041i) q^{31} +(-6.44916 - 0.241310i) q^{32} +(-7.78207 - 2.45064i) q^{33} +(1.27955 + 8.48924i) q^{34} +(7.37734 - 9.25090i) q^{35} +(0.579111 + 9.17379i) q^{36} +(0.565028 + 0.197712i) q^{37} +(-0.522691 + 6.97483i) q^{38} +(-3.44270 - 0.149087i) q^{39} +(-7.53095 - 6.48090i) q^{40} +(-6.38941 - 1.71204i) q^{41} +(5.50042 + 9.65768i) q^{42} +(2.05470 + 0.896455i) q^{43} +(1.61599 + 14.3423i) q^{44} +(7.13301 - 10.2024i) q^{45} +(1.40789 - 1.40789i) q^{46} +(1.01500 - 5.36440i) q^{47} +(-1.13644 + 0.592103i) q^{48} +(0.934414 + 0.637072i) q^{49} +(5.11188 + 27.0169i) q^{50} +(4.08948 + 5.19035i) q^{51} +(2.22708 + 5.67450i) q^{52} +(-3.98576 + 3.17854i) q^{53} +(6.41556 + 9.77594i) q^{54} +(10.3993 - 16.5504i) q^{55} +(4.05435 - 5.49344i) q^{56} +(2.30725 + 4.86399i) q^{57} +(-3.53383 - 11.5917i) q^{58} +(1.00184 - 0.578415i) q^{59} +(-21.6134 - 4.22123i) q^{60} +(7.08377 - 3.74388i) q^{61} +(4.02669 - 17.6421i) q^{62} +(7.35756 + 4.36402i) q^{63} +(10.1976 + 8.13234i) q^{64} +(2.43337 - 7.88878i) q^{65} +(10.8156 + 14.8363i) q^{66} +(0.200151 - 0.293567i) q^{67} +(5.46207 - 10.3347i) q^{68} +(0.405331 - 1.47791i) q^{69} +(-25.7195 + 6.89151i) q^{70} +(-6.90720 - 3.32633i) q^{71} +(3.89293 - 6.03683i) q^{72} +(-10.9768 + 1.23679i) q^{73} +(-0.758847 - 1.11302i) q^{74} +(13.7101 + 16.1222i) q^{75} +(6.21201 - 7.21848i) q^{76} +(11.8753 + 6.27629i) q^{77} +(6.03419 + 4.87041i) q^{78} +(8.37568 + 9.73272i) q^{79} +(-0.683136 - 2.99301i) q^{80} +(8.01467 + 4.09452i) q^{81} +(9.28098 + 11.6380i) q^{82} +(-6.56600 + 7.07647i) q^{83} +(1.78271 - 15.0275i) q^{84} +(-14.5098 + 6.33057i) q^{85} +(-2.52234 - 4.36882i) q^{86} +(-6.77899 - 6.40666i) q^{87} +(5.63940 - 9.76772i) q^{88} +(0.376893 - 3.34502i) q^{89} +(-26.5485 + 8.94082i) q^{90} +(5.53080 + 1.26237i) q^{91} +(-2.68070 + 0.404051i) q^{92} +(-4.02706 - 13.3332i) q^{93} +(-9.00619 + 8.35652i) q^{94} +(-12.6726 + 2.39778i) q^{95} +(11.0433 + 1.73095i) q^{96} +(-0.489854 - 13.0916i) q^{97} +(-0.840547 - 2.40215i) q^{98} +(12.8851 + 5.80295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.81062	−	1.33630i	−1.28030	−	0.944904i	−0.280411	−	0.959880i	$-0.590471\pi$
$2$	−1.81062	−	1.33630i	−1.28030	−	0.944904i	−0.999888	+	0.0149764i	$0.995233\pi$
$3$	−1.71999	−	0.204042i	−0.993037	−	0.117804i
$3$	−1.71999	−	0.204042i	−0.993037	−	0.117804i
$4$	0.903135	+	2.92789i	0.451567	+	1.46395i
$5$	1.51600	−	3.86270i	0.677976	−	1.72745i	−0.00814597	−	0.999967i	$-0.502593\pi$
$5$	1.51600	−	3.86270i	0.677976	−	1.72745i	0.686122	−	0.727487i	$-0.259312\pi$
$6$	2.84158	+	2.66786i	1.16007	+	1.08915i
$7$	2.72479	+	0.840488i	1.02988	+	0.317675i	0.763235	−	0.646121i	$-0.223610\pi$
$7$	2.72479	+	0.840488i	1.02988	+	0.317675i	0.266641	+	0.963796i	$0.414086\pi$
$8$	0.790819	−	2.26003i	0.279597	−	0.799041i
$9$	2.91673	+	0.701902i	0.972244	+	0.233967i
$10$	−7.90661	+	4.96805i	−2.50029	+	1.57104i
$11$	4.62838	+	0.875736i	1.39551	+	0.264044i	0.828648	−	0.559770i	$-0.189110\pi$
$11$	4.62838	+	0.875736i	1.39551	+	0.264044i	0.566860	+	0.823814i	$0.308158\pi$
$12$	−0.955969	−	5.22022i	−0.275965	−	1.50695i
$13$	1.98394	−	0.148676i	0.550247	−	0.0412353i	0.203294	−	0.979118i	$-0.434835\pi$
$13$	1.98394	−	0.148676i	0.550247	−	0.0412353i	0.346953	+	0.937882i	$0.387216\pi$
$14$	−3.81042	−	5.16293i	−1.01838	−	1.37985i
$15$	−3.39566	+	6.33449i	−0.876756	+	1.63556i
$16$	0.611281	−	0.416764i	0.152820	−	0.104191i
$17$	−2.69764	−	2.69764i	−0.654274	−	0.654274i	0.299745	−	0.954019i	$-0.403098\pi$
$17$	−2.69764	−	2.69764i	−0.654274	−	0.654274i	−0.954019	+	0.299745i	$0.903098\pi$
$18$	−4.34314	−	5.16849i	−1.02369	−	1.21823i
$19$	−1.65364	−	2.63175i	−0.379370	−	0.603764i	0.601396	−	0.798951i	$-0.294611\pi$
$19$	−1.65364	−	2.63175i	−0.379370	−	0.603764i	−0.980766	+	0.195187i	$0.937469\pi$
$20$	12.6787	+	0.950139i	2.83505	+	0.212458i
$21$	−4.51512	−	2.00160i	−0.985281	−	0.436786i
$22$	−7.20997	−	7.77050i	−1.53717	−	1.65668i
$23$	−0.131870	+	0.874899i	−0.0274967	+	0.182429i	−0.998363	−	0.0571923i	$-0.981785\pi$
$23$	−0.131870	+	0.874899i	−0.0274967	+	0.182429i	0.970866	+	0.239621i	$0.0770233\pi$
$24$	−1.82134	+	3.72587i	−0.371780	+	0.760540i
$25$	−8.95697	−	8.31085i	−1.79139	−	1.66217i
$26$	−3.79084	−	2.38194i	−0.743444	−	0.467137i
$27$	−4.87354	−	1.80240i	−0.937912	−	0.346872i
$28$			8.73697i			1.65113i
$29$	4.32234	+	3.21207i	0.802639	+	0.596466i
$29$	4.32234	+	3.21207i	0.802639	+	0.596466i
$30$	14.6130	−	6.93172i	2.66795	−	1.26555i
$31$	3.21568	+	7.37041i	0.577553	+	1.32377i	0.922809	+	0.385257i	$0.125887\pi$
$31$	3.21568	+	7.37041i	0.577553	+	1.32377i	−0.345256	+	0.938508i	$0.612208\pi$
$32$	−6.44916	−	0.241310i	−1.14006	−	0.0426581i
$33$	−7.78207	−	2.45064i	−1.35469	−	0.426602i
$34$	1.27955	+	8.48924i	0.219441	+	1.45589i
$35$	7.37734	−	9.25090i	1.24700	−	1.56369i
$36$	0.579111	+	9.17379i	0.0965186	+	1.52896i
$37$	0.565028	+	0.197712i	0.0928900	+	0.0325036i	0.376324	−	0.926488i	$-0.377188\pi$
$37$	0.565028	+	0.197712i	0.0928900	+	0.0325036i	−0.283434	+	0.958992i	$0.591474\pi$
$38$	−0.522691	+	6.97483i	−0.0847917	+	1.13147i
$39$	−3.44270	−	0.149087i	−0.551273	−	0.0238731i
$40$	−7.53095	−	6.48090i	−1.19075	−	1.02472i
$41$	−6.38941	−	1.71204i	−0.997858	−	0.267375i	−0.277310	−	0.960780i	$-0.589443\pi$
$41$	−6.38941	−	1.71204i	−0.997858	−	0.267375i	−0.720548	+	0.693405i	$0.756110\pi$
$42$	5.50042	+	9.65768i	0.848734	+	1.49021i
$43$	2.05470	+	0.896455i	0.313338	+	0.136708i	0.550676	−	0.834719i	$-0.314370\pi$
$43$	2.05470	+	0.896455i	0.313338	+	0.136708i	−0.237338	+	0.971427i	$0.576275\pi$
$44$	1.61599	+	14.3423i	0.243619	+	2.16218i
$45$	7.13301	−	10.2024i	1.06333	−	1.52088i
$46$	1.40789	−	1.40789i	0.207582	−	0.207582i
$47$	1.01500	−	5.36440i	0.148053	−	0.782478i	−0.827289	−	0.561777i	$-0.810118\pi$
$47$	1.01500	−	5.36440i	0.148053	−	0.782478i	0.975342	−	0.220701i	$-0.0708344\pi$
$48$	−1.13644	+	0.592103i	−0.164030	+	0.0854628i
$49$	0.934414	+	0.637072i	0.133488	+	0.0910103i
$50$	5.11188	+	27.0169i	0.722929	+	3.82077i
$51$	4.08948	+	5.19035i	0.572642	+	0.726795i
$52$	2.22708	+	5.67450i	0.308840	+	0.786911i
$53$	−3.98576	+	3.17854i	−0.547486	+	0.436606i	−0.857767	−	0.514039i	$-0.828149\pi$
$53$	−3.98576	+	3.17854i	−0.547486	+	0.436606i	0.310280	+	0.950645i	$0.399577\pi$
$54$	6.41556	+	9.77594i	0.873047	+	1.33034i
$55$	10.3993	−	16.5504i	1.40224	−	2.23166i
$56$	4.05435	−	5.49344i	0.541785	−	0.734092i
$57$	2.30725	+	4.86399i	0.305603	+	0.644251i
$58$	−3.53383	−	11.5917i	−0.464015	−	1.52207i
$59$	1.00184	−	0.578415i	0.130429	−	0.0753032i	−0.433366	−	0.901218i	$-0.642674\pi$
$59$	1.00184	−	0.578415i	0.130429	−	0.0753032i	0.563795	+	0.825915i	$0.309341\pi$
$60$	−21.6134	−	4.22123i	−2.79028	−	0.544958i
$61$	7.08377	−	3.74388i	0.906984	−	0.479355i	0.0523750	−	0.998627i	$-0.483321\pi$
$61$	7.08377	−	3.74388i	0.906984	−	0.479355i	0.854609	+	0.519273i	$0.173797\pi$
$62$	4.02669	−	17.6421i	0.511390	−	2.24055i
$63$	7.35756	+	4.36402i	0.926965	+	0.549814i
$64$	10.1976	+	8.13234i	1.27470	+	1.01654i
$65$	2.43337	−	7.88878i	0.301822	−	0.978483i
$66$	10.8156	+	14.8363i	1.33130	+	1.82623i
$67$	0.200151	−	0.293567i	0.0244523	−	0.0358649i	−0.813818	−	0.581120i	$-0.802615\pi$
$67$	0.200151	−	0.293567i	0.0244523	−	0.0358649i	0.838270	+	0.545255i	$0.183567\pi$
$68$	5.46207	−	10.3347i	0.662373	−	1.25327i
$69$	0.405331	−	1.47791i	0.0487961	−	0.177919i
$70$	−25.7195	+	6.89151i	−3.07406	+	0.823693i
$71$	−6.90720	−	3.32633i	−0.819734	−	0.394763i	−0.0234790	−	0.999724i	$-0.507474\pi$
$71$	−6.90720	−	3.32633i	−0.819734	−	0.394763i	−0.796255	+	0.604961i	$0.793189\pi$
$72$	3.89293	−	6.03683i	0.458786	−	0.711447i
$73$	−10.9768	+	1.23679i	−1.28473	+	0.144755i	−0.727793	−	0.685797i	$-0.759454\pi$
$73$	−10.9768	+	1.23679i	−1.28473	+	0.144755i	−0.556941	+	0.830552i	$0.688025\pi$
$74$	−0.758847	−	1.11302i	−0.0882141	−	0.129386i
$75$	13.7101	+	16.1222i	1.58311	+	1.86163i
$76$	6.21201	−	7.21848i	0.712566	−	0.828017i
$77$	11.8753	+	6.27629i	1.35332	+	0.715250i
$78$	6.03419	+	4.87041i	0.683237	+	0.551465i
$79$	8.37568	+	9.73272i	0.942338	+	1.09502i	0.995341	+	0.0964217i	$0.0307397\pi$
$79$	8.37568	+	9.73272i	0.942338	+	1.09502i	−0.0530030	+	0.998594i	$0.516879\pi$
$80$	−0.683136	−	2.99301i	−0.0763769	−	0.334629i
$81$	8.01467	+	4.09452i	0.890519	+	0.454947i
$82$	9.28098	+	11.6380i	1.02491	+	1.28520i
$83$	−6.56600	+	7.07647i	−0.720713	+	0.776744i	−0.982074	−	0.188498i	$-0.939638\pi$
$83$	−6.56600	+	7.07647i	−0.720713	+	0.776744i	0.261361	+	0.965241i	$0.415829\pi$
$84$	1.78271	−	15.0275i	0.194510	−	1.63964i
$85$	−14.5098	+	6.33057i	−1.57381	+	0.686647i
$86$	−2.52234	−	4.36882i	−0.271991	−	0.471102i
$87$	−6.77899	−	6.40666i	−0.726784	−	0.686866i
$88$	5.63940	−	9.76772i	0.601162	−	1.04124i
$89$	0.376893	−	3.34502i	0.0399506	−	0.354572i	−0.957794	−	0.287454i	$-0.907191\pi$
$89$	0.376893	−	3.34502i	0.0399506	−	0.354572i	0.997745	−	0.0671176i	$-0.0213803\pi$
$90$	−26.5485	+	8.94082i	−2.79846	+	0.942445i
$91$	5.53080	+	1.26237i	0.579786	+	0.132332i
$92$	−2.68070	+	0.404051i	−0.279483	+	0.0421252i
$93$	−4.02706	−	13.3332i	−0.417587	−	1.38259i
$94$	−9.00619	+	8.35652i	−0.928918	+	0.861910i
$95$	−12.6726	+	2.39778i	−1.30018	+	0.246007i
$96$	11.0433	+	1.73095i	1.12710	+	0.176665i
$97$	−0.489854	−	13.0916i	−0.0497371	−	1.32925i	−0.771108	−	0.636704i	$-0.780297\pi$
$97$	−0.489854	−	13.0916i	−0.0497371	−	1.32925i	0.721371	−	0.692549i	$-0.243512\pi$
$98$	−0.840547	−	2.40215i	−0.0849081	−	0.242653i
$99$	12.8851	+	5.80295i	1.29500	+	0.583219i
$100$	16.2439	−	33.7308i	1.62439	−	3.37308i
$101$	−4.83111	+	11.0730i	−0.480714	+	1.10181i	0.492167	+	0.870501i	$0.336205\pi$
$101$	−4.83111	+	11.0730i	−0.480714	+	1.10181i	−0.972881	+	0.231307i	$0.925700\pi$
$102$	−0.468644	−	14.8625i	−0.0464027	−	1.47161i
$103$	−0.298439	−	3.98239i	−0.0294060	−	0.392396i	−0.992416	−	0.122929i	$-0.960771\pi$
$103$	−0.298439	−	3.98239i	−0.0294060	−	0.392396i	0.963009	−	0.269468i	$-0.0868477\pi$
$104$	1.23293	−	4.60135i	0.120899	−	0.451200i
$105$	−14.5765	+	14.4062i	−1.42252	+	1.40590i
$106$	11.4642	−	0.428958i	1.11350	−	0.0416641i
$107$	0.235333	+	0.488675i	0.0227505	+	0.0472420i	0.912034	−	0.410114i	$-0.134511\pi$
$107$	0.235333	+	0.488675i	0.0227505	+	0.0472420i	−0.889284	+	0.457356i	$0.848797\pi$
$108$	0.875775	−	15.8970i	0.0842715	−	1.52969i
$109$	−9.98192	+	2.27831i	−0.956095	+	0.218222i	−0.671981	−	0.740568i	$-0.734556\pi$
$109$	−9.98192	+	2.27831i	−0.956095	+	0.218222i	−0.284114	+	0.958791i	$0.591699\pi$
$110$	−40.9455	+	16.0699i	−3.90400	+	1.53221i
$111$	−0.931500	−	0.455352i	−0.0884141	−	0.0432201i
$112$	2.01590	−	0.621823i	0.190485	−	0.0587567i
$113$	−0.296982	+	7.93702i	−0.0279378	+	0.746652i	0.912977	+	0.408010i	$0.133777\pi$
$113$	−0.296982	+	7.93702i	−0.0279378	+	0.746652i	−0.940915	+	0.338642i	$0.890032\pi$
$114$	2.32218	−	11.8900i	0.217492	−	1.11360i
$115$	3.17956	+	1.83572i	0.296495	+	0.171182i
$116$	−5.50092	+	15.5563i	−0.510748	+	1.44436i
$117$	5.89099	+	0.958886i	0.544623	+	0.0886490i
$118$	−2.58689	−	0.291472i	−0.238142	−	0.0268322i
$119$	−5.08318	−	9.61786i	−0.465975	−	0.881667i
$120$	11.6308	+	12.6837i	1.06174	+	1.15786i
$121$	10.4153	+	4.08772i	0.946849	+	0.371611i
$122$	−17.8289	−	2.68728i	−1.61415	−	0.243295i
$123$	10.6404	+	4.24840i	0.959412	+	0.383065i
$124$	−18.6756	+	16.0716i	−1.67712	+	1.44328i
$125$	−26.9881	+	12.9968i	−2.41389	+	1.16247i
$126$	−7.49010	−	17.7334i	−0.667271	−	1.57982i
$127$	2.53119	−	0.885703i	0.224607	−	0.0785934i	−0.215629	−	0.976475i	$-0.569180\pi$
$127$	2.53119	−	0.885703i	0.224607	−	0.0785934i	0.440236	+	0.897882i	$0.354895\pi$
$128$	−4.25612	−	15.8841i	−0.376192	−	1.40397i
$129$	−3.35114	−	1.96114i	−0.295052	−	0.172669i
$130$	−14.9476	+	11.0319i	−1.31099	+	0.967558i
$131$	−1.57585	+	1.16303i	−0.137682	+	0.101614i	−0.660484	−	0.750840i	$-0.729649\pi$
$131$	−1.57585	+	1.16303i	−0.137682	+	0.101614i	0.522802	+	0.852454i	$0.324887\pi$
$132$	0.146951	−	24.9983i	0.0127904	−	2.17582i
$133$	−2.29387	−	8.56082i	−0.198903	−	0.742318i
$134$	−0.754689	+	0.264077i	−0.0651952	+	0.0228128i
$135$	−14.3504	+	16.0926i	−1.23509	+	1.38503i
$136$	−8.23010	+	3.96341i	−0.705725	+	0.339859i
$137$	12.5087	−	10.7646i	1.06869	−	0.919680i	0.0717143	−	0.997425i	$-0.477153\pi$
$137$	12.5087	−	10.7646i	1.06869	−	0.919680i	0.996973	+	0.0777452i	$0.0247721\pi$
$138$	−2.70882	+	2.13429i	−0.230590	+	0.181682i
$139$	−0.908986	−	0.137008i	−0.0770992	−	0.0116208i	0.110379	−	0.993890i	$-0.464793\pi$
$139$	−0.908986	−	0.137008i	−0.0770992	−	0.0116208i	−0.187479	+	0.982269i	$0.560032\pi$
$140$	33.7483	+	13.2452i	2.85226	+	1.11943i
$141$	−2.84035	+	9.01961i	−0.239201	+	0.759588i
$142$	8.06133	+	15.2528i	0.676491	+	1.27998i
$143$	9.31264	+	1.04928i	0.778762	+	0.0877454i
$144$	2.07547	−	0.786531i	0.172956	−	0.0655443i
$145$	18.9599	−	11.8264i	1.57454	−	0.982132i
$146$	21.5274	+	12.4289i	1.78162	+	1.02862i
$147$	−1.47719	−	1.28642i	−0.121837	−	0.106102i
$148$	−0.0685823	+	1.83290i	−0.00563743	+	0.150663i
$149$	5.20039	−	1.60411i	0.426033	−	0.131414i	−0.0743218	−	0.997234i	$-0.523679\pi$
$149$	5.20039	−	1.60411i	0.426033	−	0.131414i	0.500354	+	0.865821i	$0.333203\pi$
$150$	−3.27978	−	47.5119i	−0.267793	−	3.87933i
$151$	11.9450	−	4.68807i	0.972071	−	0.381510i	0.174448	−	0.984666i	$-0.444186\pi$
$151$	11.9450	−	4.68807i	0.972071	−	0.381510i	0.797623	+	0.603157i	$0.206091\pi$
$152$	−7.25555	+	1.65603i	−0.588503	+	0.134322i
$153$	−5.97482	−	9.76178i	−0.483036	−	0.789193i
$154$	−13.1147	−	27.2329i	−1.05681	−	2.19449i
$155$	33.3447	−	1.24767i	2.67831	−	0.100215i
$156$	−2.67271	−	10.2145i	−0.213988	−	0.817815i
$157$	4.53407	−	16.9214i	0.361858	−	1.35047i	−0.509772	−	0.860309i	$-0.670270\pi$
$157$	4.53407	−	16.9214i	0.361858	−	1.35047i	0.871630	−	0.490164i	$-0.163063\pi$
$158$	−2.15936	−	28.8146i	−0.171789	−	2.29237i
$159$	7.50403	−	4.65379i	0.595108	−	0.369070i
$160$	−10.7090	+	24.5454i	−0.846623	+	1.94048i
$161$	−1.09466	+	2.27308i	−0.0862713	+	0.179144i
$162$	−9.04000	−	18.1236i	−0.710249	−	1.42392i
$163$	6.19352	+	17.7001i	0.485114	+	1.38638i	0.883186	+	0.469022i	$0.155394\pi$
$163$	6.19352	+	17.7001i	0.485114	+	1.38638i	−0.398072	+	0.917354i	$0.630321\pi$
$164$	−0.757840	−	20.2537i	−0.0591773	−	1.58155i
$165$	−21.2637	+	26.3447i	−1.65538	+	2.05093i
$166$	21.3448	−	4.03865i	1.65668	−	0.313460i
$167$	−2.39748	+	2.22454i	−0.185523	+	0.172140i	−0.767466	−	0.641089i	$-0.778483\pi$
$167$	−2.39748	+	2.22454i	−0.185523	+	0.172140i	0.581944	+	0.813229i	$0.302292\pi$
$168$	−8.09433	+	8.62141i	−0.624491	+	0.665156i
$169$	−8.94087	+	1.34762i	−0.687759	+	0.103663i
$170$	34.7312	+	7.92717i	2.66376	+	0.607986i
$171$	−2.97599	−	8.83679i	−0.227579	−	0.675766i
$172$	−0.769054	+	6.82554i	−0.0586398	+	0.520443i
$173$	−4.45522	+	7.71667i	−0.338724	+	0.586687i	−0.984193	−	0.177099i	$-0.943329\pi$
$173$	−4.45522	+	7.71667i	−0.338724	+	0.586687i	0.645469	+	0.763787i	$0.276662\pi$
$174$	3.71295	+	20.6587i	0.281478	+	1.56613i
$175$	−17.4207	−	30.1736i	−1.31688	−	2.28091i
$176$	3.19421	−	1.39362i	0.240773	−	0.105048i
$177$	−1.84118	+	0.790450i	−0.138392	+	0.0594138i
$178$	−5.15235	+	5.55291i	−0.386185	+	0.416208i
$179$	2.28672	+	2.86746i	0.170918	+	0.214324i	0.859911	−	0.510443i	$-0.170519\pi$
$179$	2.28672	+	2.86746i	0.170918	+	0.214324i	−0.688994	+	0.724767i	$0.741947\pi$
$180$	36.3136	+	11.6705i	2.70665	+	0.869869i
$181$	1.03476	+	4.53358i	0.0769132	+	0.336979i	0.998715	−	0.0506833i	$-0.0161399\pi$
$181$	1.03476	+	4.53358i	0.0769132	+	0.336979i	−0.921802	+	0.387662i	$0.873283\pi$
$182$	−8.32726	−	9.67645i	−0.617258	−	0.717266i
$183$	−12.9479	+	4.99405i	−0.957138	+	0.369171i
$184$	1.87301	+	0.989916i	0.138080	+	0.0729776i
$185$	1.62028	−	1.88280i	0.119126	−	0.138426i
$186$	−10.5256	+	29.5226i	−0.771775	+	2.16470i
$187$	−10.1233	−	14.8481i	−0.740288	−	1.08580i
$188$	16.6230	−	1.87297i	1.21236	−	0.136600i
$189$	−11.7645	−	9.00732i	−0.855740	−	0.655186i
$190$	26.1493	+	12.5928i	1.89707	+	0.913580i
$191$	−23.7079	+	6.35251i	−1.71544	+	0.459651i	−0.976748	−	0.214389i	$-0.931224\pi$
$191$	−23.7079	+	6.35251i	−1.71544	+	0.459651i	−0.738694	+	0.674041i	$0.764557\pi$
$192$	−15.8805	−	16.0683i	−1.14608	−	1.15963i
$193$	−7.15926	+	13.5460i	−0.515335	+	0.975061i	0.479878	+	0.877335i	$0.340681\pi$
$193$	−7.15926	+	13.5460i	−0.515335	+	0.975061i	−0.995213	+	0.0977262i	$0.968843\pi$
$194$	−16.6073	+	24.3585i	−1.19234	+	1.74884i
$195$	−5.79501	+	13.0721i	−0.414990	+	0.936114i
$196$	−1.02138	+	3.31122i	−0.0729555	+	0.236516i
$197$	21.3437	+	17.0210i	1.52067	+	1.21270i	0.905531	+	0.424281i	$0.139473\pi$
$197$	21.3437	+	17.0210i	1.52067	+	1.21270i	0.615143	+	0.788416i	$0.289098\pi$
$198$	−15.5754	−	27.7252i	−1.10690	−	1.97034i
$199$	−0.369564	+	1.61916i	−0.0261977	+	0.114780i	−0.986336	−	0.164745i	$-0.947320\pi$
$199$	−0.369564	+	1.61916i	−0.0261977	+	0.114780i	0.960138	+	0.279525i	$0.0901769\pi$
$200$	−25.8661	+	13.6706i	−1.82901	+	0.966660i
$201$	−0.404158	+	0.464094i	−0.0285071	+	0.0327346i
$202$	23.5441	−	13.5932i	1.65656	−	0.956415i
$203$	9.07779	+	12.3851i	0.637136	+	0.869263i
$204$	−11.5034	+	16.6612i	−0.805401	+	1.16651i
$205$	−16.2994	+	22.0849i	−1.13840	+	1.54248i
$206$	−4.78129	+	7.60938i	−0.333128	+	0.530170i
$207$	−0.998722	+	2.45929i	−0.0694160	+	0.170932i
$208$	1.15078	−	0.917720i	0.0797926	−	0.0636325i
$209$	−5.34893	−	13.6289i	−0.369993	−	0.942728i
$210$	45.6434	−	6.60547i	3.14969	−	0.455821i
$211$	−2.03156	−	10.7370i	−0.139858	−	0.739169i	−0.980338	−	0.197326i	$-0.936774\pi$
$211$	−2.03156	−	10.7370i	−0.139858	−	0.739169i	0.840480	−	0.541843i	$-0.182273\pi$
$212$	−12.9061	−	8.79923i	−0.886394	−	0.604333i
$213$	11.2016	+	7.13062i	0.767521	+	0.488582i
$214$	0.226916	−	1.19928i	0.0155116	−	0.0819809i
$215$	6.57766	−	6.57766i	0.448592	−	0.448592i
$216$	−7.92756	+	9.58896i	−0.539402	+	0.652446i
$217$	2.56732	+	22.7856i	0.174281	+	1.54679i
$218$	21.1179	+	9.21366i	1.43029	+	0.624028i
$219$	19.1323	+	0.112468i	1.29284	+	0.00759988i
$220$	57.8498	+	15.5008i	3.90024	+	1.04507i
$221$	−5.75305	−	4.95090i	−0.386992	−	0.333033i
$222$	1.07811	+	2.06923i	0.0723577	+	0.138877i
$223$	−0.151362	+	2.01979i	−0.0101360	+	0.135255i	−0.999976	−	0.00693050i	$-0.997794\pi$
$223$	−0.151362	+	2.01979i	−0.0101360	+	0.135255i	0.989840	+	0.142186i	$0.0454130\pi$
$224$	−17.3698	−	6.07796i	−1.16057	−	0.406101i
$225$	−20.2917	−	30.5274i	−1.35278	−	2.03516i
$226$	11.1439	−	13.9740i	0.741283	−	0.929540i
$227$	1.36204	+	9.03652i	0.0904016	+	0.599775i	0.987461	+	0.157865i	$0.0504610\pi$
$227$	1.36204	+	9.03652i	0.0904016	+	0.599775i	−0.897059	+	0.441910i	$0.854301\pi$
$228$	−12.1575	+	11.1482i	−0.805148	+	0.738308i
$229$	−0.385539	−	0.0144258i	−0.0254771	−	0.000953286i	0.0246496	−	0.999696i	$-0.492153\pi$
$229$	−0.385539	−	0.0144258i	−0.0254771	−	0.000953286i	−0.0501267	+	0.998743i	$0.515963\pi$
$230$	−3.30390	−	7.57262i	−0.217853	−	0.499323i
$231$	−19.1448	−	13.2182i	−1.25964	−	0.869696i
$232$	10.6776	−	7.22846i	0.701016	−	0.474572i
$233$			2.81133i			0.184177i	0.995751	+	0.0920883i	$0.0293542\pi$
$233$			2.81133i			0.184177i	−0.995751	+	0.0920883i	$0.970646\pi$
$234$	−9.38497	−	9.60828i	−0.613515	−	0.628113i
$235$	−19.1823	−	12.0531i	−1.25132	−	0.786255i
$236$	2.59834	+	2.41090i	0.169137	+	0.156936i
$237$	−12.4202	−	18.4492i	−0.806779	−	1.19840i
$238$	−3.64860	+	24.2069i	−0.236504	+	1.56910i
$239$	2.90398	+	3.12974i	0.187843	+	0.202446i	0.819951	−	0.572434i	$-0.194001\pi$
$239$	2.90398	+	3.12974i	0.187843	+	0.202446i	−0.632108	+	0.774880i	$0.717810\pi$
$240$	0.564285	+	5.28734i	0.0364245	+	0.341296i
$241$	2.73574	+	0.205016i	0.176225	+	0.0132062i	0.162550	−	0.986700i	$-0.448028\pi$
$241$	2.73574	+	0.205016i	0.176225	+	0.0132062i	0.0136746	+	0.999906i	$0.495647\pi$
$242$	−13.3958	−	21.3193i	−0.861113	−	1.37045i
$243$	−12.9497	−	8.67787i	−0.830723	−	0.556685i
$244$	17.3593	+	17.3593i	1.11131	+	1.11131i
$245$	3.87739	−	2.64356i	0.247718	−	0.168891i
$246$	−13.5886	−	21.9109i	−0.866375	−	1.39699i
$247$	−3.67200	−	4.97538i	−0.233644	−	0.316576i
$248$	19.2004	−	1.43887i	1.21923	−	0.0913683i
$249$	12.7374	−	10.8317i	0.807198	−	0.686432i
$250$	66.2325	+	12.5319i	4.18891	+	0.792585i
$251$	17.7429	−	11.1486i	1.11992	−	0.703694i	0.160885	−	0.986973i	$-0.448565\pi$
$251$	17.7429	−	11.1486i	1.11992	−	0.703694i	0.959038	+	0.283279i	$0.0914222\pi$
$252$	−6.13250	+	25.4834i	−0.386311	+	1.60530i
$253$	−1.37652	+	3.93388i	−0.0865413	+	0.247321i
$254$	−5.76658	−	1.77875i	−0.361827	−	0.111609i
$255$	26.2484	−	7.92790i	1.64374	−	0.496464i
$256$	−3.98912	+	10.1641i	−0.249320	+	0.635258i
$257$	5.19547	+	16.8433i	0.324085	+	1.05066i	0.960259	+	0.279111i	$0.0900398\pi$
$257$	5.19547	+	16.8433i	0.324085	+	1.05066i	−0.636174	+	0.771545i	$0.719484\pi$
$258$	3.44697	+	8.02898i	0.214599	+	0.499863i
$259$	1.37341	+	1.01362i	0.0853395	+	0.0629834i
$260$	25.2952			1.56874
$261$	10.3526	+	12.4026i	0.640808	+	0.767702i
$262$	4.40740			0.272290
$263$	23.6998	+	17.4912i	1.46139	+	1.07856i	0.979295	+	0.202438i	$0.0648864\pi$
$263$	23.6998	+	17.4912i	1.46139	+	1.07856i	0.482096	+	0.876118i	$0.339875\pi$
$264$	−11.6927	+	15.6497i	−0.719638	+	0.963173i
$265$	6.23534	+	20.2145i	0.383034	+	1.24177i
$266$	−7.28648	+	18.5657i	−0.446763	+	1.13833i
$267$	−1.33078	+	5.67650i	−0.0814423	+	0.347396i
$268$	1.04030	+	0.320889i	0.0635462	+	0.0196014i
$269$	−0.647264	+	1.84977i	−0.0394644	+	0.112783i	−0.961929	−	0.273298i	$-0.911886\pi$
$269$	−0.647264	+	1.84977i	−0.0394644	+	0.112783i	0.922465	+	0.386080i	$0.126171\pi$
$270$	47.4876	−	9.96109i	2.89000	−	0.606213i
$271$	−21.9933	+	13.8193i	−1.33600	+	0.839464i	−0.994930	−	0.100574i	$-0.967932\pi$
$271$	−21.9933	+	13.8193i	−1.33600	+	0.839464i	−0.341070	+	0.940038i	$0.610789\pi$
$272$	−2.77330	−	0.524736i	−0.168156	−	0.0318168i
$273$	−9.25535	−	3.29978i	−0.560159	−	0.199712i
$274$	−37.0331	+	2.77524i	−2.23725	+	0.167659i
$275$	−34.1781	−	46.3097i	−2.06102	−	2.79258i
$276$	4.69323	−	0.147987i	0.282499	−	0.00890776i
$277$	−0.0365003	+	0.0248855i	−0.00219309	+	0.00149522i	−0.564416	−	0.825490i	$-0.690899\pi$
$277$	−0.0365003	+	0.0248855i	−0.00219309	+	0.00149522i	0.562223	+	0.826986i	$0.309946\pi$
$278$	1.46274	+	1.46274i	0.0877294	+	0.0877294i
$279$	4.20597	+	23.7546i	0.251805	+	1.42215i
$280$	−15.0732	−	23.9888i	−0.900794	−	1.43360i
$281$	14.5168	+	1.08788i	0.865997	+	0.0648975i	0.500316	−	0.865843i	$-0.333217\pi$
$281$	14.5168	+	1.08788i	0.865997	+	0.0648975i	0.365681	+	0.930740i	$0.380836\pi$
$282$	17.1956	−	12.5355i	1.02399	−	0.746478i
$283$	18.2525	+	19.6715i	1.08500	+	1.16935i	0.984675	+	0.174397i	$0.0557976\pi$
$283$	18.2525	+	19.6715i	1.08500	+	1.16935i	0.100325	+	0.994955i	$0.468012\pi$
$284$	3.50101	−	23.2277i	0.207746	−	1.37831i
$285$	22.2859	−	1.53842i	1.32010	−	0.0911279i
$286$	−15.4595	−	14.3443i	−0.914138	−	0.848196i
$287$	−15.9709	−	10.0352i	−0.942731	−	0.592357i
$288$	−18.6411	−	5.23051i	−1.09844	−	0.308211i
$289$		−	2.44545i		−	0.143850i
$290$	−50.1328	−	3.92293i	−2.94390	−	0.230362i
$291$	−1.82870	+	22.6174i	−0.107200	+	1.32586i
$292$	−13.5347	−	31.0218i	−0.792057	−	1.81541i
$293$	21.3371	+	0.798379i	1.24653	+	0.0466418i	0.652492	−	0.757796i	$-0.273724\pi$
$293$	21.3371	+	0.798379i	1.24653	+	0.0466418i	0.594037	+	0.804438i	$0.297533\pi$
$294$	0.955594	+	4.30318i	0.0557314	+	0.250966i
$295$	−0.715451	−	4.74670i	−0.0416551	−	0.276364i
$296$	0.893669	−	1.12063i	0.0519434	−	0.0651350i
$297$	−20.9781	−	12.6101i	−1.21727	−	0.731713i
$298$	−11.5595	−	4.04484i	−0.669622	−	0.234311i
$299$	−0.131546	+	1.75536i	−0.00760749	+	0.101515i
$300$	−34.8219	+	54.7023i	−2.01044	+	3.15824i
$301$	4.84516	+	4.16960i	0.279271	+	0.240332i
$302$	−27.8925	−	7.47376i	−1.60503	−	0.430067i
$303$	10.5688	−	18.0598i	0.607164	−	1.03751i
$304$	−2.10765	−	0.919560i	−0.120882	−	0.0527404i
$305$	−3.72251	−	33.0382i	−0.213151	−	1.89176i
$306$	−2.22652	+	25.6590i	−0.127281	+	1.46683i
$307$	−10.6150	+	10.6150i	−0.605831	+	0.605831i	−0.941854	−	0.336023i	$-0.890918\pi$
$307$	−10.6150	+	10.6150i	−0.605831	+	0.605831i	0.336023	+	0.941854i	$0.390918\pi$
$308$	−7.65128	+	40.4380i	−0.435972	+	2.30417i
$309$	−0.299264	+	6.91056i	−0.0170245	+	0.393128i
$310$	−62.0417	−	42.2993i	−3.52373	−	2.40244i
$311$	0.501016	+	2.64794i	0.0284100	+	0.150151i	0.993899	−	0.110293i	$-0.0351789\pi$
$311$	0.501016	+	2.64794i	0.0284100	+	0.150151i	−0.965489	+	0.260443i	$0.916131\pi$
$312$	−3.05949	+	7.66271i	−0.173210	+	0.433815i
$313$	−0.942025	−	2.40024i	−0.0532464	−	0.135670i	0.901776	−	0.432204i	$-0.142264\pi$
$313$	−0.942025	−	2.40024i	−0.0532464	−	0.135670i	−0.955022	+	0.296535i	$0.904169\pi$
$314$	−30.8214	+	24.5793i	−1.73935	+	1.38709i
$315$	28.0110	−	21.8042i	1.57824	−	1.22853i
$316$	−20.9320	+	33.3130i	−1.17751	+	1.87400i
$317$	3.63354	−	4.92327i	0.204080	−	0.276519i	−0.690590	−	0.723247i	$-0.742649\pi$
$317$	3.63354	−	4.92327i	0.204080	−	0.276519i	0.894670	+	0.446728i	$0.147411\pi$
$318$	−19.8058	−	1.60137i	−1.11065	−	0.0898003i
$319$	17.1925	+	18.6519i	0.962595	+	1.04430i
$320$	46.8724	−	27.0618i	2.62025	−	1.51280i
$321$	−0.305061	−	0.888534i	−0.0170268	−	0.0495931i
$322$	5.01952	−	2.65289i	0.279727	−	0.147840i
$323$	−2.63859	+	11.5604i	−0.146815	+	0.643239i
$324$	−4.74998	+	27.1640i	−0.263888	+	1.50911i
$325$	−19.0058	−	15.1566i	−1.05425	−	0.840736i
$326$	12.4384	−	40.3244i	0.688901	−	2.23336i
$327$	17.6337	−	1.88193i	0.975145	−	0.104071i
$328$	−8.92212	+	13.0863i	−0.492642	+	0.722573i
$329$	7.27437	−	13.7638i	0.401049	−	0.758822i
$330$	73.7047	−	19.2855i	4.05731	−	1.06163i
$331$	−30.9958	+	8.30530i	−1.70368	+	0.456501i	−0.973863	−	0.227138i	$-0.927063\pi$
$331$	−30.9958	+	8.30530i	−1.70368	+	0.456501i	−0.729821	+	0.683639i	$0.760396\pi$
$332$	−26.6491	−	12.8335i	−1.46256	−	0.704332i
$333$	1.50926	+	0.973266i	0.0827070	+	0.0533347i
$334$	7.31356	−	0.824040i	0.400180	−	0.0450895i
$335$	−0.830535	−	1.21817i	−0.0453770	−	0.0665558i
$336$	−3.59421	+	0.658200i	−0.196080	+	0.0359078i
$337$	6.19773	−	7.20189i	0.337612	−	0.392312i	−0.563344	−	0.826222i	$-0.690486\pi$
$337$	6.19773	−	7.20189i	0.337612	−	0.392312i	0.900956	+	0.433910i	$0.142866\pi$
$338$	17.9893	+	9.50762i	0.978489	+	0.517146i
$339$	2.13030	−	13.5910i	0.115702	−	0.738162i
$340$	−31.6395	−	36.7658i	−1.71589	−	1.99391i
$341$	8.42883	+	36.9291i	0.456447	+	1.99982i
$342$	−6.42019	+	19.9768i	−0.347164	+	1.08022i
$343$	−10.4344	−	13.0844i	−0.563407	−	0.706490i
$344$	3.65091	−	3.93474i	0.196844	−	0.212147i
$345$	−5.09425	−	3.80619i	−0.274265	−	0.204918i
$346$	18.3784	−	8.01843i	0.988031	−	0.431074i
$347$	−7.18301	−	12.4413i	−0.385604	−	0.667886i	0.606249	−	0.795275i	$-0.292674\pi$
$347$	−7.18301	−	12.4413i	−0.385604	−	0.667886i	−0.991853	+	0.127389i	$0.959340\pi$
$348$	12.6357	−	25.6342i	0.677343	−	1.37414i
$349$	16.3304	−	28.2850i	0.874145	−	1.51406i	0.0164734	−	0.999864i	$-0.494756\pi$
$349$	16.3304	−	28.2850i	0.874145	−	1.51406i	0.857671	−	0.514198i	$-0.171911\pi$
$350$	−8.77858	+	77.9120i	−0.469235	+	4.16457i
$351$	−9.93680	−	2.85129i	−0.530387	−	0.152190i
$352$	−29.6378	−	6.76464i	−1.57970	−	0.360556i
$353$	−14.5971	+	2.20017i	−0.776928	+	0.117103i	−0.525523	−	0.850779i	$-0.676131\pi$
$353$	−14.5971	+	2.20017i	−0.776928	+	0.117103i	−0.251404	+	0.967882i	$0.580892\pi$
$354$	4.38995	+	1.02916i	0.233323	+	0.0546995i
$355$	−23.3200	+	21.6378i	−1.23769	+	1.14841i
$356$	10.1342	−	1.91750i	0.537114	−	0.101627i
$357$	6.78058	+	17.5798i	0.358866	+	0.930422i
$358$	−0.308603	−	8.24760i	−0.0163102	−	0.435899i
$359$	−6.82117	−	19.4938i	−0.360008	−	1.02884i	−0.971386	−	0.237505i	$-0.923670\pi$
$359$	−6.82117	−	19.4938i	−0.360008	−	1.02884i	0.611379	−	0.791338i	$-0.290615\pi$
$360$	−17.4168	−	24.1891i	−0.917946	−	1.27488i
$361$	4.05222	−	8.41452i	0.213275	−	0.442869i
$362$	4.18465	−	9.59133i	0.219940	−	0.504109i
$363$	−17.0802	−	9.15601i	−0.896479	−	0.480566i
$364$	1.29898	+	17.3337i	0.0680850	+	0.908531i
$365$	−11.8634	+	44.2750i	−0.620961	+	2.31746i
$366$	30.1172	+	8.25995i	1.57425	+	0.431754i
$367$	8.77384	−	0.328294i	0.457991	−	0.0171368i	0.192599	−	0.981278i	$-0.438308\pi$
$367$	8.77384	−	0.328294i	0.457991	−	0.0171368i	0.265391	+	0.964141i	$0.414499\pi$
$368$	0.284017	+	0.589768i	0.0148054	+	0.0307438i
$369$	−17.4345	−	9.47829i	−0.907605	−	0.493420i
$370$	−5.44969	+	1.24386i	−0.283316	+	0.0646650i
$371$	−13.5319	+	5.31088i	−0.702541	+	0.275727i
$372$	35.4011	−	23.8324i	1.83546	−	1.23565i
$373$	−0.877488	+	0.270669i	−0.0454346	+	0.0140147i	−0.317389	−	0.948295i	$-0.602806\pi$
$373$	−0.877488	+	0.270669i	−0.0454346	+	0.0140147i	0.271955	+	0.962310i	$0.412330\pi$
$374$	−1.51211	+	40.4119i	−0.0781893	+	2.08965i
$375$	49.0711	−	16.8476i	2.53402	−	0.870006i
$376$	−11.3210	−	6.53619i	−0.583837	−	0.337078i
$377$	9.05284	+	5.72993i	0.466245	+	0.295106i
$378$	9.26453	+	32.0296i	0.476516	+	1.64743i
$379$	−2.74748	−	0.309567i	−0.141129	−	0.0159014i	0.0411175	−	0.999154i	$-0.486908\pi$
$379$	−2.74748	−	0.309567i	−0.141129	−	0.0159014i	−0.182246	+	0.983253i	$0.558337\pi$
$380$	−18.4655	−	34.9384i	−0.947258	−	1.79230i
$381$	−4.53435	+	1.00693i	−0.232302	+	0.0515866i
$382$	51.4147	+	20.1788i	2.63061	+	1.03244i
$383$	−19.2902	−	2.90753i	−0.985683	−	0.148568i	−0.363631	−	0.931543i	$-0.618463\pi$
$383$	−19.2902	−	2.90753i	−0.985683	−	0.148568i	−0.622053	+	0.782975i	$0.713701\pi$
$384$	4.07947	+	28.1889i	0.208179	+	1.43851i
$385$	42.2465	−	36.3560i	2.15308	−	1.85287i
$386$	31.0641	−	14.9597i	1.58112	−	0.761428i
$387$	5.36378	+	4.05691i	0.272656	+	0.206224i
$388$	37.8884	−	13.2577i	1.92349	−	0.673059i
$389$	−5.29771	−	19.7713i	−0.268605	−	1.00245i	−0.960007	−	0.279976i	$-0.909673\pi$
$389$	−5.29771	−	19.7713i	−0.268605	−	1.00245i	0.691402	−	0.722470i	$-0.256993\pi$
$390$	27.9608	−	15.9247i	1.41585	−	0.806381i
$391$	2.71590	−	2.00443i	0.137349	−	0.101368i
$392$	2.17875	−	1.60799i	0.110044	−	0.0812160i
$393$	2.94775	−	1.67886i	0.148694	−	0.0846871i
$394$	−15.9001	−	59.3400i	−0.801035	−	2.98950i
$395$	50.2921	−	17.5980i	2.53047	−	0.885450i
$396$	−5.35347	+	42.9669i	−0.269022	+	2.15917i
$397$	−12.2093	+	5.87971i	−0.612769	+	0.295094i	−0.714410	−	0.699727i	$-0.753305\pi$
$397$	−12.2093	+	5.87971i	−0.612769	+	0.295094i	0.101641	+	0.994821i	$0.467591\pi$
$398$	2.83282	−	2.43784i	0.141996	−	0.122198i
$399$	2.19866	+	15.1926i	0.110071	+	0.760580i
$400$	−8.93889	−	1.34732i	−0.446945	−	0.0673661i
$401$	−27.8918	−	10.9467i	−1.39285	−	0.546654i	−0.454008	−	0.890998i	$-0.650006\pi$
$401$	−27.8918	−	10.9467i	−1.39285	−	0.546654i	−0.938844	+	0.344343i	$0.888102\pi$
$402$	1.35194	−	0.300221i	0.0674287	−	0.0149737i
$403$	7.47553	+	14.1444i	0.372383	+	0.704583i
$404$	−36.7838	−	4.14454i	−1.83006	−	0.206198i
$405$	27.9662	−	24.7510i	1.38965	−	1.22989i
$406$	0.113753	−	34.5553i	0.00564547	−	1.71495i
$407$	2.44202	+	1.40990i	0.121046	+	0.0698861i
$408$	14.9644	−	5.13773i	0.740848	−	0.254356i
$409$	0.239333	−	6.39631i	0.0118343	−	0.316277i	−0.980792	−	0.195059i	$-0.937510\pi$
$409$	0.239333	−	6.39631i	0.0118343	−	0.316277i	0.992626	−	0.121219i	$-0.0386802\pi$
$410$	59.0240	−	18.2065i	2.91499	−	0.899155i
$411$	−23.7112	+	15.9627i	−1.16959	+	0.787381i
$412$	11.3905	−	4.47043i	0.561168	−	0.220242i
$413$	3.21597	−	0.734024i	0.158248	−	0.0361190i
$414$	5.09464	−	3.11824i	0.250388	−	0.153253i
$415$	17.3802	+	36.0905i	0.853163	+	1.77161i
$416$	−12.8306	+	0.480089i	−0.629074	+	0.0235383i
$417$	1.53549	+	0.421123i	0.0751934	+	0.0206225i
$418$	−8.52732	+	31.8244i	−0.417085	+	1.55658i
$419$	1.08010	+	14.4129i	0.0527664	+	0.704118i	0.959373	+	0.282141i	$0.0910446\pi$
$419$	1.08010	+	14.4129i	0.0527664	+	0.704118i	−0.906607	+	0.421977i	$0.861336\pi$
$420$	−55.3442	−	29.6678i	−2.70052	−	1.44764i
$421$	3.61568	−	8.28723i	0.176218	−	0.403895i	−0.805929	−	0.592012i	$-0.798334\pi$
$421$	3.61568	−	8.28723i	0.176218	−	0.403895i	0.982147	+	0.188117i	$0.0602385\pi$
$422$	−10.6695	+	22.1554i	−0.519383	+	1.07851i
$423$	6.72576	−	14.9341i	0.327018	−	0.726120i
$424$	4.03158	+	11.5216i	0.195791	+	0.559538i
$425$	1.74299	+	46.5824i	0.0845474	+	2.25958i
$426$	−10.7532	−	27.8795i	−0.520994	−	1.35076i
$427$	22.4485	−	4.24749i	1.08636	−	0.205550i
$428$	−1.21825	+	1.13037i	−0.0588863	+	0.0546385i
$429$	−15.8036	−	3.70493i	−0.763003	−	0.178876i
$430$	−20.6993	+	3.11992i	−0.998209	+	0.150456i
$431$	−17.7472	−	4.05067i	−0.854850	−	0.195114i	−0.227430	−	0.973795i	$-0.573032\pi$
$431$	−17.7472	−	4.05067i	−0.854850	−	0.195114i	−0.627421	+	0.778681i	$0.715889\pi$
$432$	−3.73028	+	0.929342i	−0.179473	+	0.0447130i
$433$	2.36138	−	20.9578i	0.113481	−	1.00717i	−0.799920	−	0.600106i	$-0.795125\pi$
$433$	2.36138	−	20.9578i	0.113481	−	1.00717i	0.913401	−	0.407062i	$-0.133447\pi$
$434$	25.7999	−	44.6867i	1.23843	−	2.14503i
$435$	−35.0240	+	16.4727i	−1.67927	+	0.789807i
$436$	−15.6857	−	27.1684i	−0.751207	−	1.30113i
$437$	2.52057	−	1.09972i	0.120575	−	0.0526065i
$438$	−34.4910	−	25.7700i	−1.64804	−	1.23134i
$439$	−9.39663	+	10.1272i	−0.448476	+	0.483343i	−0.916308	−	0.400475i	$-0.868845\pi$
$439$	−9.39663	+	10.1272i	−0.448476	+	0.483343i	0.467831	+	0.883818i	$0.345036\pi$
$440$	−29.1805	−	36.5912i	−1.39113	−	1.74442i
$441$	2.27827	+	2.51404i	0.108489	+	0.119716i
$442$	3.80070	+	16.6519i	0.180781	+	0.792052i
$443$	24.7759	+	28.7901i	1.17714	+	1.36786i	0.915312	+	0.402745i	$0.131944\pi$
$443$	24.7759	+	28.7901i	1.17714	+	1.36786i	0.261827	+	0.965115i	$0.415675\pi$
$444$	0.491950	−	3.13858i	0.0233469	−	0.148950i
$445$	−12.3495	−	6.52688i	−0.585420	−	0.309404i
$446$	2.97309	−	3.45480i	0.140780	−	0.163589i
$447$	−9.27193	+	1.69795i	−0.438547	+	0.0803103i
$448$	20.9513	+	30.7299i	0.989857	+	1.45185i
$449$	40.8652	−	4.60440i	1.92855	−	0.217295i	0.937222	−	0.348734i	$-0.113388\pi$
$449$	40.8652	−	4.60440i	1.92855	−	0.217295i	0.991324	+	0.131439i	$0.0419598\pi$
$450$	−4.05324	+	82.3892i	−0.191072	+	3.88386i
$451$	−28.0733	−	13.5194i	−1.32192	−	0.636603i
$452$	−23.5070	+	6.29867i	−1.10567	+	0.296264i
$453$	−21.5019	+	5.62615i	−1.01025	+	0.264339i
$454$	9.60934	−	18.1818i	0.450989	−	0.853312i
$455$	13.2609	−	19.4501i	0.621678	−	0.911835i
$456$	12.8174	−	1.36792i	0.600229	−	0.0640587i
$457$	7.27204	−	23.5754i	0.340172	−	1.10281i	−0.610345	−	0.792136i	$-0.708969\pi$
$457$	7.27204	−	23.5754i	0.340172	−	1.10281i	0.950517	−	0.310674i	$-0.100555\pi$
$458$	0.678785	+	0.541313i	0.0317175	+	0.0252939i
$459$	8.28482	+	18.0093i	0.386702	+	0.840602i
$460$	−2.50322	+	10.9673i	−0.116713	+	0.511353i
$461$	20.3074	−	10.7328i	0.945811	−	0.499876i	0.0781004	−	0.996945i	$-0.475115\pi$
$461$	20.3074	−	10.7328i	0.945811	−	0.499876i	0.867711	+	0.497070i	$0.165591\pi$
$462$	17.0005	+	49.5163i	0.790933	+	2.30371i
$463$	−35.7417	+	20.6355i	−1.66106	+	0.959013i	−0.688849	+	0.724905i	$0.741884\pi$
$463$	−35.7417	+	20.6355i	−1.66106	+	0.959013i	−0.972211	+	0.234108i	$0.924783\pi$
$464$	3.98084	+	0.162077i	0.184806	+	0.00752424i
$465$	−57.6071	−	4.65775i	−2.67147	−	0.215998i
$466$	3.75677	−	5.09024i	0.174029	−	0.235801i
$467$	−9.33731	+	14.8602i	−0.432079	+	0.687650i	−0.989814	−	0.142369i	$-0.954528\pi$
$467$	−9.33731	+	14.8602i	−0.432079	+	0.687650i	0.557734	+	0.830019i	$0.311671\pi$
$468$	2.51285	+	18.1142i	0.116156	+	0.837329i
$469$	0.792109	−	0.631686i	0.0365762	−	0.0291686i
$470$	18.6254	+	47.4567i	0.859125	+	2.18902i
$471$	−11.2512	+	28.1795i	−0.518429	+	1.29844i
$472$	−0.514958	−	2.72162i	−0.0237029	−	0.125273i
$473$	8.72485	+	5.94850i	0.401169	+	0.273512i
$474$	−2.16533	+	50.0014i	−0.0994568	+	2.29664i
$475$	−7.06049	+	37.3156i	−0.323957	+	1.71216i
$476$	23.5692	−	23.5692i	1.08029	−	1.08029i
$477$	−13.8564	+	6.47334i	−0.634442	+	0.296394i
$478$	−1.07573	−	9.54733i	−0.0492026	−	0.436685i
$479$	20.7629	+	9.05875i	0.948680	+	0.413905i	0.816516	−	0.577323i	$-0.195903\pi$
$479$	20.7629	+	9.05875i	0.948680	+	0.413905i	0.132164	+	0.991228i	$0.457807\pi$
$480$	23.4277	−	40.0327i	1.06932	−	1.82723i
$481$	1.15038	+	0.308243i	0.0524527	+	0.0140547i
$482$	−4.67942	−	4.02697i	−0.213142	−	0.183423i
$483$	2.34661	−	3.68633i	0.106774	−	0.167734i
$484$	−2.56194	+	34.1867i	−0.116452	+	1.55394i
$485$	−51.3117	−	17.9547i	−2.32994	−	0.815282i
$486$	11.8507	+	33.0169i	0.537560	+	1.49768i
$487$	−11.7700	+	14.7591i	−0.533348	+	0.668797i	−0.973383	−	0.229183i	$-0.926394\pi$
$487$	−11.7700	+	14.7591i	−0.533348	+	0.668797i	0.440035	+	0.897980i	$0.354966\pi$
$488$	−2.85931	−	18.9703i	−0.129435	−	0.858743i
$489$	−7.04123	−	31.7077i	−0.318416	−	1.43387i
$490$	−10.5530	−	0.394867i	−0.476738	−	0.0178383i
$491$	6.39602	+	14.6598i	0.288648	+	0.661589i	0.999111	−	0.0421455i	$-0.0134193\pi$
$491$	6.39602	+	14.6598i	0.288648	+	0.661589i	−0.710463	+	0.703734i	$0.751515\pi$
$492$	−2.82913	+	34.9908i	−0.127547	+	1.57751i
$493$	−2.99513	−	20.3251i	−0.134894	−	0.915398i
$494$			13.9154i			0.626082i
$495$	41.9488	−	40.9739i	1.88546	−	1.84164i
$496$	5.03741	+	3.16521i	0.226186	+	0.142122i
$497$	−16.0250	−	14.8690i	−0.718818	−	0.666965i
$498$	−37.5369	+	2.59120i	−1.68207	+	0.116114i
$499$	−0.845115	+	5.60697i	−0.0378326	+	0.251003i	−0.999751	−	0.0223357i	$-0.992890\pi$
$499$	−0.845115	+	5.60697i	−0.0378326	+	0.251003i	0.961918	+	0.273338i	$0.0881278\pi$
$500$	−62.4270	−	67.2803i	−2.79182	−	3.00886i
$501$	4.57754	−	3.33699i	0.204510	−	0.149086i
$502$	−47.0234	−	3.52392i	−2.09876	−	0.157280i
$503$	−8.11946	−	12.9221i	−0.362029	−	0.576166i	0.615195	−	0.788375i	$-0.289077\pi$
$503$	−8.11946	−	12.9221i	−0.362029	−	0.576166i	−0.977224	+	0.212209i	$0.931934\pi$
$504$	15.6813	−	13.1772i	0.698501	−	0.586957i
$505$	35.4479	+	35.4479i	1.57741	+	1.57741i
$506$	7.74918	−	5.28330i	0.344493	−	0.234871i
$507$	15.6532	−	0.493576i	0.695182	−	0.0219205i
$508$	4.87925	+	6.61115i	0.216482	+	0.293322i
$509$	−1.27955	+	0.0958892i	−0.0567152	+	0.00425021i	−0.103057	−	0.994675i	$-0.532863\pi$
$509$	−1.27955	+	0.0958892i	−0.0567152	+	0.00425021i	0.0463423	+	0.998926i	$0.485244\pi$
$510$	−58.1199	−	20.7213i	−2.57359	−	0.917555i
$511$	−30.9490	−	5.85586i	−1.36910	−	0.259048i
$512$	−7.04269	+	4.42522i	−0.311246	+	0.195569i
$513$	3.31559	+	15.8064i	0.146387	+	0.697870i
$514$	13.1006	−	37.4394i	0.577844	−	1.65138i
$515$	−15.8352	−	4.88452i	−0.697783	−	0.215237i
$516$	2.71547	−	11.5829i	0.119542	−	0.509911i
$517$	9.39559	−	23.9396i	0.413218	−	1.05286i
$518$	−1.13222	−	3.67056i	−0.0497468	−	0.161275i
$519$	9.23746	−	12.3635i	0.405480	−	0.542699i
$520$	−15.9045	−	11.7381i	−0.697460	−	0.514749i
$521$	−16.1665			−0.708265			−0.354133	−	0.935195i	$-0.615224\pi$
$521$	−16.1665			−0.708265			−0.354133	+	0.935195i	$0.615224\pi$
$522$	−2.17098	−	36.2904i	−0.0950212	−	1.58839i
$523$	8.22037			0.359452			0.179726	−	0.983717i	$-0.442479\pi$
$523$	8.22037			0.359452			0.179726	+	0.983717i	$0.442479\pi$
$524$	−4.82842	−	3.56353i	−0.210930	−	0.155674i
$525$	23.8068	+	55.4528i	1.03901	+	2.42016i
$526$	−19.5378	−	63.3398i	−0.851887	−	2.76175i
$527$	11.2080	−	28.5575i	0.488228	−	1.24398i
$528$	−5.77838	+	1.74526i	−0.251471	+	0.0759527i
$529$	21.2301	+	6.54862i	0.923049	+	0.284723i
$530$	15.7227	−	44.9329i	0.682951	−	1.95176i
$531$	3.32810	−	0.983886i	0.144427	−	0.0426970i
$532$	22.9935	−	14.4478i	0.996894	−	0.626390i
$533$	−12.9308	−	2.44663i	−0.560094	−	0.105975i
$534$	9.99501	−	8.49965i	0.432527	−	0.367816i
$535$	2.24437	−	0.168192i	0.0970327	−	0.00727159i
$536$	−0.505188	−	0.684505i	−0.0218208	−	0.0295661i
$537$	−3.34805	−	5.39859i	−0.144479	−	0.232966i
$538$	3.64379	−	2.48429i	0.157095	−	0.107106i
$539$	3.76691	+	3.76691i	0.162252	+	0.162252i
$540$	−60.0777	−	27.4827i	−2.58533	−	1.18267i
$541$	−20.4692	−	32.5765i	−0.880038	−	1.40057i	−0.915982	−	0.401219i	$-0.868587\pi$
$541$	−20.4692	−	32.5765i	−0.880038	−	1.40057i	0.0359440	−	0.999354i	$-0.488556\pi$
$542$	58.2882	+	4.36810i	2.50369	+	0.187626i
$543$	−0.854736	−	8.00886i	−0.0366802	−	0.343693i
$544$	16.7466	+	18.0485i	0.718002	+	0.773823i
$545$	−6.33216	+	42.0111i	−0.271240	+	1.79956i
$546$	12.3484	+	18.3425i	0.528463	+	0.784987i
$547$	16.5334	+	15.3407i	0.706916	+	0.655922i	0.949341	−	0.314248i	$-0.101752\pi$
$547$	16.5334	+	15.3407i	0.706916	+	0.655922i	−0.242425	+	0.970170i	$0.577943\pi$
$548$	42.8145	+	26.9021i	1.82895	+	1.14920i
$549$	23.2893	−	5.94779i	0.993963	−	0.253846i
$550$			129.521i			5.52280i
$551$	1.30576	−	16.6869i	0.0556274	−	0.710885i
$552$	−3.01958	−	2.08482i	−0.128522	−	0.0887358i
$553$	14.6418	+	33.5593i	0.622632	+	1.42709i
$554$	0.0993425	+	0.00371713i	0.00422066	+	0.000157926i
$555$	−3.17104	+	2.90780i	−0.134603	+	0.123429i
$556$	−0.419794	−	2.78515i	−0.0178032	−	0.118117i
$557$	−18.3856	+	23.0548i	−0.779024	+	0.976865i	0.220975	+	0.975280i	$0.429076\pi$
$557$	−18.3856	+	23.0548i	−0.779024	+	0.976865i	−0.999999	+	0.00158560i	$0.999495\pi$
$558$	24.1278	−	48.6309i	1.02141	−	2.05871i
$559$	4.20968	+	1.47303i	0.178051	+	0.0623026i
$560$	0.654186	−	8.72951i	0.0276444	−	0.368889i
$561$	14.3823	+	27.6042i	0.607221	+	1.16545i
$562$	−24.8306	−	21.3684i	−1.04741	−	0.901372i
$563$	−16.9495	−	4.54160i	−0.714336	−	0.191406i	−0.116693	−	0.993168i	$-0.537229\pi$
$563$	−16.9495	−	4.54160i	−0.714336	−	0.191406i	−0.597643	+	0.801762i	$0.703896\pi$
$564$	−28.9736	−	0.170320i	−1.22001	−	0.00717175i
$565$	30.2081	+	13.1797i	1.27087	+	0.554473i
$566$	−6.76132	−	60.0084i	−0.284200	−	2.52234i
$567$	18.3969	+	17.8930i	0.772598	+	0.751434i
$568$	−12.9800	+	12.9800i	−0.544627	+	0.544627i
$569$	−4.40967	+	23.3057i	−0.184863	+	0.977025i	0.760090	+	0.649818i	$0.225155\pi$
$569$	−4.40967	+	23.3057i	−0.184863	+	0.977025i	−0.944953	+	0.327207i	$0.893893\pi$
$570$	−42.4070	−	26.9951i	−1.77624	−	1.13070i
$571$	−18.5456	−	12.6442i	−0.776110	−	0.529143i	0.109270	−	0.994012i	$-0.465149\pi$
$571$	−18.5456	−	12.6442i	−0.776110	−	0.529143i	−0.885379	+	0.464870i	$0.846101\pi$
$572$	5.33838	+	28.2140i	0.223209	+	1.17969i
$573$	42.0735	−	6.08884i	1.75765	−	0.254365i
$574$	15.5072	+	39.5117i	0.647257	+	1.64918i
$575$	8.45231	−	6.74049i	0.352486	−	0.281098i
$576$	24.0357	+	30.8776i	1.00149	+	1.28657i
$577$	−3.75312	+	5.97305i	−0.156244	+	0.248661i	−0.915668	−	0.401934i	$-0.868338\pi$
$577$	−3.75312	+	5.97305i	−0.156244	+	0.248661i	0.759424	+	0.650596i	$0.225481\pi$
$578$	−3.26785	+	4.42778i	−0.135925	+	0.184171i
$579$	15.0778	−	21.8382i	0.626613	−	0.907563i
$580$	51.7499	+	44.8317i	2.14880	+	1.86154i
$581$	−23.8387	+	13.7633i	−0.988996	+	0.570997i
$582$	33.5346	−	38.5078i	1.39005	−	1.59620i
$583$	−21.2312	+	11.2210i	−0.879305	+	0.464726i
$584$	−5.88547	+	25.7859i	−0.243542	+	1.06703i
$585$	12.6346	−	21.3015i	0.522378	−	0.880708i
$586$	−37.5665	−	29.9583i	−1.55186	−	1.23757i
$587$	−1.60048	+	5.18864i	−0.0660590	+	0.214158i	−0.982584	−	0.185820i	$-0.940506\pi$
$587$	−1.60048	+	5.18864i	−0.0660590	+	0.214158i	0.916525	+	0.399978i	$0.130982\pi$
$588$	2.43239	−	5.48687i	0.100310	−	0.226275i
$589$	14.0795	−	20.6508i	0.580135	−	0.850902i
$590$	−5.04759	+	9.55051i	−0.207806	+	0.393188i
$591$	−33.2379	−	33.6310i	−1.36722	−	1.38339i
$592$	0.427790	−	0.114626i	0.0175821	−	0.00471110i
$593$	31.0947	+	14.9744i	1.27691	+	0.614926i	0.944593	−	0.328243i	$-0.106457\pi$
$593$	31.0947	+	14.9744i	1.27691	+	0.614926i	0.332313	+	0.943169i	$0.392171\pi$
$594$	21.1325	+	50.8651i	0.867076	+	2.08702i
$595$	−44.8570	+	5.05417i	−1.83896	+	0.207201i
$596$	9.39331	+	13.7775i	0.384765	+	0.564346i
$597$	0.966024	−	2.70954i	0.0395367	−	0.110894i
$598$	2.58385	−	3.00249i	0.105662	−	0.122781i
$599$	24.6654	+	13.0360i	1.00780	+	0.532638i	0.887846	−	0.460141i	$-0.152201\pi$
$599$	24.6654	+	13.0360i	1.00780	+	0.532638i	0.119955	+	0.992779i	$0.461725\pi$
$600$	47.2789	−	18.2356i	1.93015	−	0.744465i
$601$	25.6215	+	29.7728i	1.04512	+	1.21446i	0.976209	+	0.216834i	$0.0695730\pi$
$601$	25.6215	+	29.7728i	1.04512	+	1.21446i	0.0689157	+	0.997622i	$0.478046\pi$
$602$	−3.20091	−	14.0241i	−0.130459	−	0.571580i
$603$	0.789842	−	0.715771i	0.0321648	−	0.0291485i
$604$	24.5141	+	30.7397i	0.997465	+	1.25078i
$605$	31.5793	−	34.0344i	1.28388	−	1.38369i
$606$	−43.2693	+	18.5762i	−1.75769	+	0.754606i
$607$	20.0946	−	8.76718i	0.815615	−	0.355849i	0.0496782	−	0.998765i	$-0.484180\pi$
$607$	20.0946	−	8.76718i	0.815615	−	0.355849i	0.765937	+	0.642916i	$0.222276\pi$
$608$	10.0295	+	17.3716i	0.406749	+	0.704511i
$609$	−13.0866	−	23.1545i	−0.530297	−	0.938267i
$610$	−37.4088	+	64.7939i	−1.51464	+	2.62343i
$611$	1.21614	−	10.7936i	0.0491999	−	0.436661i
$612$	23.1854	−	26.3098i	0.937213	−	1.06351i
$613$	7.18809	+	1.64063i	0.290324	+	0.0662646i	0.365203	−	0.930928i	$-0.381000\pi$
$613$	7.18809	+	1.64063i	0.290324	+	0.0662646i	−0.0748784	+	0.997193i	$0.523857\pi$
$614$	33.4045	−	5.03492i	1.34810	−	0.203193i
$615$	32.5411	−	34.6601i	1.31219	−	1.39763i
$616$	23.5758	−	21.8752i	0.949898	−	0.881376i
$617$	−44.5525	+	8.42979i	−1.79362	+	0.339371i	−0.972769	−	0.231777i	$-0.925546\pi$
$617$	−44.5525	+	8.42979i	−1.79362	+	0.339371i	−0.820848	+	0.571147i	$0.806499\pi$
$618$	9.77640	−	12.1125i	0.393265	−	0.487235i
$619$	0.335192	+	8.95819i	0.0134725	+	0.360060i	0.989686	+	0.143251i	$0.0457555\pi$
$619$	0.335192	+	8.95819i	0.0134725	+	0.360060i	−0.976214	+	0.216809i	$0.930435\pi$
$620$	33.7678	+	96.5028i	1.35615	+	3.87565i
$621$	2.21959	−	4.02617i	0.0890691	−	0.161565i
$622$	2.63128	−	5.46390i	0.105505	−	0.219082i
$623$	3.83841	−	8.79772i	0.153782	−	0.352473i
$624$	−2.16659	+	1.34366i	−0.0867331	+	0.0537895i
$625$	4.72323	+	63.0271i	0.188929	+	2.52108i
$626$	−1.50178	+	5.60474i	−0.0600234	+	0.224010i
$627$	6.41925	+	24.5329i	0.256360	+	0.979750i
$628$	53.6388	−	2.00702i	2.14042	−	0.0800889i
$629$	−0.990887	−	2.05760i	−0.0395092	−	0.0820418i
$630$	−79.8540	+	2.04816i	−3.18146	+	0.0816006i
$631$	14.6256	−	3.33820i	0.582236	−	0.132892i	0.0787494	−	0.996894i	$-0.474907\pi$
$631$	14.6256	−	3.33820i	0.582236	−	0.132892i	0.503487	+	0.864003i	$0.332050\pi$
$632$	28.6199	−	11.2325i	1.13844	−	0.446804i
$633$	1.30345	+	18.8821i	0.0518074	+	0.750498i
$634$	−13.1579	+	4.05867i	−0.522567	+	0.161191i
$635$	0.416080	−	11.1200i	0.0165116	−	0.441283i
$636$	20.4029	+	17.7680i	0.809029	+	0.704546i
$637$	1.94854	+	1.12499i	0.0772041	+	0.0445738i
$638$	−6.20460	−	56.7456i	−0.245642	−	2.24658i
$639$	−17.8117	−	14.5502i	−0.704620	−	0.575597i
$640$	−67.8077	−	7.64010i	−2.68034	−	0.302001i
$641$	−20.7131	−	39.1912i	−0.818119	−	1.54796i	−0.836397	−	0.548125i	$-0.815342\pi$
$641$	−20.7131	−	39.1912i	−0.818119	−	1.54796i	0.0182772	−	0.999833i	$-0.494182\pi$
$642$	−0.634996	+	2.01645i	−0.0250613	+	0.0795828i
$643$	−1.49358	−	0.586186i	−0.0589009	−	0.0231169i	0.335708	−	0.941966i	$-0.391025\pi$
$643$	−1.49358	−	0.586186i	−0.0589009	−	0.0231169i	−0.394609	+	0.918849i	$0.629120\pi$
$644$	−7.64397	−	1.15214i	−0.301214	−	0.0454008i
$645$	−12.6556	+	9.97138i	−0.498315	+	0.392623i
$646$	20.2256	−	17.4055i	0.795766	−	0.684812i
$647$	−20.9353	+	10.0819i	−0.823052	+	0.396361i	−0.797505	−	0.603313i	$-0.793847\pi$
$647$	−20.9353	+	10.0819i	−0.823052	+	0.396361i	−0.0255471	+	0.999674i	$0.508133\pi$
$648$	15.5919	−	14.8754i	0.612507	−	0.584360i
$649$	5.14345	−	1.79977i	0.201898	−	0.0706472i
$650$	14.1584	+	52.8401i	0.555340	+	2.07256i
$651$	0.233461	−	39.7149i	0.00915006	−	1.55655i
$652$	−46.2303	+	34.1195i	−1.81052	+	1.33622i
$653$	8.81178	−	6.50339i	0.344832	−	0.254497i	−0.407610	−	0.913156i	$-0.633638\pi$
$653$	8.81178	−	6.50339i	0.344832	−	0.254497i	0.752442	+	0.658659i	$0.228876\pi$
$654$	−34.4427	−	20.1564i	−1.34681	−	0.788176i
$655$	2.10345	+	7.85018i	0.0821885	+	0.306732i
$656$	−4.61924	+	1.61634i	−0.180351	+	0.0631076i
$657$	−32.8844	−	4.09724i	−1.28294	−	0.159849i
$658$	−31.5636	+	15.2002i	−1.23048	+	0.592566i
$659$	−10.8183	+	9.30990i	−0.421421	+	0.362662i	−0.837287	−	0.546764i	$-0.815860\pi$
$659$	−10.8183	+	9.30990i	−0.421421	+	0.362662i	0.415866	+	0.909426i	$0.363479\pi$
$660$	−96.3384	−	38.4651i	−3.74997	−	1.49725i
$661$	0.667109	+	0.100551i	0.0259475	+	0.00391096i	0.162003	−	0.986790i	$-0.448205\pi$
$661$	0.667109	+	0.100551i	0.0259475	+	0.00391096i	−0.136056	+	0.990701i	$0.543443\pi$
$662$	67.2198	+	26.3818i	2.61257	+	1.02536i
$663$	8.88499	+	9.68936i	0.345065	+	0.376304i
$664$	10.8005	+	20.4356i	0.419141	+	0.793054i
$665$	−36.5454	−	4.11768i	−1.41717	−	0.159677i
$666$	−1.43212	−	3.77903i	−0.0554935	−	0.146434i
$667$	−3.38022	+	3.35804i	−0.130883	+	0.130024i
$668$	−8.67845	−	5.01051i	−0.335779	−	0.193862i
$669$	0.672464	−	3.44313i	0.0259990	−	0.133119i
$670$	−0.124057	+	3.31548i	−0.00479272	+	0.128088i
$671$	36.0650	−	11.1246i	1.39227	−	0.429460i
$672$	28.6357	+	13.9982i	1.10465	+	0.539993i
$673$	−21.3495	+	8.37907i	−0.822964	+	0.322990i	−0.739191	−	0.673495i	$-0.764792\pi$
$673$	−21.3495	+	8.37907i	−0.822964	+	0.322990i	−0.0837726	+	0.996485i	$0.526697\pi$
$674$	−20.8456	+	4.75786i	−0.802941	+	0.183266i
$675$	28.6726	+	56.6473i	1.10361	+	2.18035i
$676$	−12.0205	−	24.9608i	−0.462327	−	0.960031i
$677$	15.7283	−	0.588512i	0.604488	−	0.0226184i	0.266604	−	0.963806i	$-0.414098\pi$
$677$	15.7283	−	0.588512i	0.604488	−	0.0226184i	0.337884	+	0.941188i	$0.390289\pi$
$678$	−22.0187	+	21.7614i	−0.845625	+	0.835741i
$679$	9.66859	−	36.0837i	0.371047	−	1.38476i
$680$	2.83264	+	37.7990i	0.108627	+	1.44952i
$681$	−0.498856	−	15.8206i	−0.0191162	−	0.606248i
$682$	34.0868	−	78.1279i	1.30525	−	2.99167i
$683$	12.6248	−	26.2157i	0.483076	−	1.00312i	−0.506917	−	0.861995i	$-0.669215\pi$
$683$	12.6248	−	26.2157i	0.483076	−	1.00312i	0.989992	−	0.141122i	$-0.0450709\pi$
$684$	23.1854	−	16.6942i	0.886517	−	0.638318i
$685$	−22.6172	−	64.6364i	−0.864161	−	2.46963i
$686$	1.40817	+	37.6343i	0.0537644	+	1.43688i
$687$	0.660179	+	0.103478i	0.0251874	+	0.00394795i
$688$	1.62961	−	0.308338i	0.0621282	−	0.0117553i
$689$	−7.43496	+	6.89863i	−0.283249	+	0.262817i
$690$	4.13754	+	13.6990i	0.157513	+	0.521511i
$691$	24.9655	−	3.76294i	0.949732	−	0.143149i	0.344134	−	0.938920i	$-0.388172\pi$
$691$	24.9655	−	3.76294i	0.949732	−	0.143149i	0.605597	+	0.795771i	$0.292934\pi$
$692$	−26.6172	−	6.07521i	−1.01184	−	0.230945i
$693$	30.2318	+	26.6416i	1.14841	+	1.01203i
$694$	−3.61963	+	32.1251i	−0.137399	+	1.21945i
$695$	−1.90724	+	3.30344i	−0.0723458	+	0.125307i
$696$	−19.8402	+	10.2542i	−0.752041	+	0.388685i
$697$	12.6179	+	21.8548i	0.477936	+	0.827810i
$698$	−67.3652	+	29.3911i	−2.54981	+	1.11247i
$699$	0.573631	−	4.83546i	0.0216967	−	0.182894i
$700$	72.6117	−	78.2568i	2.74446	−	2.95783i
$701$	7.13562	+	8.94778i	0.269509	+	0.337953i	0.898107	−	0.439777i	$-0.144943\pi$
$701$	7.13562	+	8.94778i	0.269509	+	0.337953i	−0.628598	+	0.777730i	$0.716371\pi$
$702$	14.1816	+	18.4411i	0.535249	+	0.696014i
$703$	−0.414023	−	1.81395i	−0.0156152	−	0.0684145i
$704$	40.0767	+	46.5700i	1.51045	+	1.75517i
$705$	30.5341	+	24.6452i	1.14998	+	0.928190i
$706$	29.3699	+	15.5224i	1.10535	+	0.584195i
$707$	−22.4705	+	26.1112i	−0.845092	+	0.982014i
$708$	−3.97719	−	4.67690i	−0.149472	−	0.175769i
$709$	−11.9237	−	17.4889i	−0.447804	−	0.656808i	0.534268	−	0.845315i	$-0.320588\pi$
$709$	−11.9237	−	17.4889i	−0.447804	−	0.656808i	−0.982072	+	0.188507i	$0.939635\pi$
$710$	71.1379	−	8.01532i	2.66976	−	0.300810i
$711$	17.5982	+	34.2666i	0.659985	+	1.28510i
$712$	−7.26179	−	3.49710i	−0.272147	−	0.131059i
$713$	−6.87242	+	1.84146i	−0.257374	+	0.0689632i
$714$	11.2148	−	40.8911i	0.419703	−	1.53031i
$715$	18.1710	−	34.3813i	0.679558	−	1.28579i
$716$	−6.33038	+	9.28497i	−0.236578	+	0.346996i
$717$	−4.35621	−	5.97566i	−0.162686	−	0.223165i
$718$	−13.6989	+	44.4109i	−0.511240	+	1.65740i
$719$	−38.0881	−	30.3742i	−1.42044	−	1.13277i	−0.970893	−	0.239513i	$-0.923012\pi$
$719$	−38.0881	−	30.3742i	−1.42044	−	1.13277i	−0.449552	−	0.893254i	$-0.648416\pi$
$720$	0.108276	−	9.20931i	0.00403522	−	0.343211i
$721$	2.53396	−	11.1020i	0.0943697	−	0.413461i
$722$	−18.5813	+	9.82050i	−0.691524	+	0.365481i
$723$	−4.66362	−	0.910832i	−0.173442	−	0.0338742i
$724$	−12.3393	+	7.12410i	−0.458587	+	0.264765i
$725$	−12.0201	−	64.6927i	−0.446414	−	2.40263i
$726$	18.6906	+	39.4022i	0.693672	+	1.46235i
$727$	4.66945	−	6.32688i	0.173180	−	0.234651i	−0.709408	−	0.704799i	$-0.751037\pi$
$727$	4.66945	−	6.32688i	0.173180	−	0.234651i	0.882588	+	0.470148i	$0.155799\pi$
$728$	7.22685	−	11.5015i	0.267845	−	0.426273i
$729$	20.5027	+	17.5681i	0.759359	+	0.650672i
$730$	80.6446	−	64.3119i	2.98479	−	2.38029i
$731$	−3.12452	−	7.96115i	−0.115565	−	0.294454i
$732$	−26.3158	−	33.3998i	−0.972658	−	1.23449i
$733$	0.680841	+	3.59833i	0.0251474	+	0.132907i	0.992890	−	0.119032i	$-0.0379792\pi$
$733$	0.680841	+	3.59833i	0.0251474	+	0.132907i	−0.967743	+	0.251940i	$0.918932\pi$
$734$	−16.3247	−	11.1300i	−0.602557	−	0.410817i
$735$	−7.20848	+	3.75575i	−0.265889	+	0.138533i
$736$	1.06157	−	5.61054i	0.0391300	−	0.206807i
$737$	1.18346	−	1.18346i	0.0435933	−	0.0435933i
$738$	18.9014	+	40.4592i	0.695771	+	1.48932i
$739$	−0.386282	−	3.42834i	−0.0142096	−	0.126114i	0.984605	−	0.174796i	$-0.0559265\pi$
$739$	−0.386282	−	3.42834i	−0.0142096	−	0.126114i	−0.998814	+	0.0486820i	$0.984498\pi$
$740$	6.97598	+	3.04359i	0.256442	+	0.111885i
$741$	5.30061	+	9.30685i	0.194723	+	0.341896i
$742$	31.5980	+	8.46666i	1.16000	+	0.310821i
$743$	15.0830	+	12.9800i	0.553342	+	0.476189i	0.883952	−	0.467578i	$-0.154873\pi$
$743$	15.0830	+	12.9800i	0.553342	+	0.476189i	−0.330610	+	0.943768i	$0.607254\pi$
$744$	−33.3181	−	1.44285i	−1.22150	−	0.0528974i
$745$	1.68760	−	22.5194i	0.0618287	−	0.825047i
$746$	1.95049	+	0.682505i	0.0714124	+	0.0249883i
$747$	−24.1183	+	16.0315i	−0.882441	+	0.586561i
$748$	34.3310	−	43.0497i	1.25527	−	1.57405i
$749$	0.230510	+	1.52933i	0.00842265	+	0.0558806i
$750$	−111.362	−	35.0689i	−4.06638	−	1.28054i
$751$	9.79549	+	0.366521i	0.357442	+	0.0133746i	0.215510	−	0.976502i	$-0.430859\pi$
$751$	9.79549	+	0.366521i	0.357442	+	0.0133746i	0.141933	+	0.989876i	$0.454668\pi$
$752$	−1.61524	−	3.70217i	−0.0589017	−	0.135004i
$753$	−32.7924	+	15.5552i	−1.19502	+	0.566863i
$754$	−8.73434	−	22.4720i	−0.318086	−	0.818381i
$755$		−	53.2471i		−	1.93786i
$756$	15.7475	−	42.5800i	0.572732	−	1.54862i
$757$	30.9413	+	19.4417i	1.12458	+	0.706622i	0.960072	−	0.279753i	$-0.0902527\pi$
$757$	30.9413	+	19.4417i	1.12458	+	0.706622i	0.164510	+	0.986375i	$0.447396\pi$
$758$	4.56096	+	4.23196i	0.165662	+	0.153712i
$759$	3.17028	−	6.48536i	0.115074	−	0.235404i
$760$	−4.60265	+	30.5366i	−0.166956	+	1.10768i
$761$	−8.68087	−	9.35576i	−0.314681	−	0.339146i	0.555828	−	0.831297i	$-0.312401\pi$
$761$	−8.68087	−	9.35576i	−0.314681	−	0.339146i	−0.870510	+	0.492151i	$0.836211\pi$
$762$	9.55552	+	4.23607i	0.346160	+	0.153456i
$763$	−29.1136	−	2.18176i	−1.05398	−	0.0789851i
$764$	−40.0109	−	63.6769i	−1.44754	−	2.30375i
$765$	−46.7647	+	8.28011i	−1.69078	+	0.299368i
$766$	31.0418	+	31.0418i	1.12159	+	1.12159i
$767$	1.90161	−	1.29649i	0.0686631	−	0.0468137i
$768$	8.93517	−	16.6682i	0.322420	−	0.601463i
$769$	7.43845	+	10.0787i	0.268237	+	0.363449i	0.917926	−	0.396752i	$-0.129863\pi$
$769$	7.43845	+	10.0787i	0.268237	+	0.363449i	−0.649689	+	0.760200i	$0.725101\pi$
$770$	−125.074	+	9.37304i	−4.50737	+	0.337781i
$771$	−5.49941	−	30.0304i	−0.198057	−	1.08152i
$772$	−46.1269	−	8.72769i	−1.66014	−	0.314116i
$773$	37.8041	−	23.7539i	1.35972	−	0.854369i	0.362730	−	0.931894i	$-0.381845\pi$
$773$	37.8041	−	23.7539i	1.35972	−	0.854369i	0.996990	+	0.0775253i	$0.0247019\pi$
$774$	−4.29050	−	14.5131i	−0.154219	−	0.521663i
$775$	32.4517	−	92.7416i	1.16570	−	3.33138i
$776$	−29.9748	−	9.24601i	−1.07603	−	0.331913i
$777$	−2.15543	−	2.02365i	−0.0773256	−	0.0725982i
$778$	−16.8282	+	42.8776i	−0.603321	+	1.53724i
$779$	6.06011	+	19.6464i	0.217126	+	0.703905i
$780$	−43.5074	−	5.16128i	−1.55782	−	0.184804i
$781$	−29.0561	−	21.4444i	−1.03971	−	0.767341i
$782$	−7.59596			−0.271631
$783$	−15.2757	−	23.4447i	−0.545907	−	0.837846i
$784$	0.836698			0.0298821
$785$	−58.4886	−	43.1666i	−2.08755	−	1.54068i
$786$	−7.58069	−	0.899296i	−0.270394	−	0.0320768i
$787$	1.85283	+	6.00673i	0.0660462	+	0.214117i	0.982580	−	0.185841i	$-0.0595010\pi$
$787$	1.85283	+	6.00673i	0.0660462	+	0.214117i	−0.916534	+	0.399958i	$0.869025\pi$
$788$	−30.5594	+	77.8642i	−1.08864	+	2.77380i
$789$	−37.1945	−	34.9205i	−1.32416	−	1.24320i
$790$	−114.576	−	35.3420i	−4.07643	−	1.25741i
$791$	−7.48019	+	21.3771i	−0.265965	+	0.760084i
$792$	23.3046	−	24.5315i	0.828093	−	0.871690i
$793$	13.4972	−	8.48084i	0.479299	−	0.301163i
$794$	29.9634	+	5.66939i	1.06336	+	0.201199i
$795$	−6.60012	−	36.0410i	−0.234082	−	1.27824i
$796$	−5.07450	+	0.380281i	−0.179861	+	0.0134787i
$797$	−13.7981	−	18.6958i	−0.488755	−	0.662239i	0.488929	−	0.872324i	$-0.337388\pi$
$797$	−13.7981	−	18.6958i	−0.488755	−	0.662239i	−0.977683	+	0.210085i	$0.932626\pi$
$798$	16.3209	−	30.4460i	0.577752	−	1.07778i
$799$	−17.2093	+	11.7331i	−0.608822	+	0.415088i
$800$	55.7594	+	55.7594i	1.97139	+	1.97139i
$801$	3.44717	−	9.49199i	0.121800	−	0.335383i
$802$	35.8733	+	57.0921i	1.26673	+	2.01599i
$803$	−51.8877	−	3.88845i	−1.83108	−	0.137220i
$804$	−1.72382	−	0.764190i	−0.0607946	−	0.0269509i
$805$	7.12075	+	7.67434i	0.250973	+	0.270485i
$806$	5.36578	−	35.5996i	0.189001	−	1.25394i
$807$	1.49072	−	3.04952i	0.0524758	−	0.107348i
$808$	21.2048	+	19.6752i	0.745984	+	0.692172i
$809$	10.3651	+	6.51282i	0.364417	+	0.228978i	0.701776	−	0.712398i	$-0.252391\pi$
$809$	10.3651	+	6.51282i	0.364417	+	0.228978i	−0.337359	+	0.941376i	$0.609534\pi$
$810$	−83.7106	+	7.44351i	−2.94129	+	0.261538i
$811$		−	23.4600i		−	0.823793i	−0.911231	−	0.411897i	$-0.864866\pi$
$811$		−	23.4600i		−	0.823793i	0.911231	−	0.411897i	$-0.135134\pi$
$812$	−28.0637	+	37.7642i	−0.984844	+	1.32526i
$813$	40.6480	−	19.2815i	1.42559	−	0.676233i
$814$	−2.53751	−	5.81604i	−0.0889398	−	0.203852i
$815$	77.7595	+	2.90956i	2.72380	+	0.101917i
$816$	4.66298	+	1.46841i	0.163237	+	0.0514047i
$817$	−1.03848	−	6.88984i	−0.0363317	−	0.241045i
$818$	−8.98070	+	11.2614i	−0.314003	+	0.393747i
$819$	15.2458	+	7.56407i	0.532732	+	0.264310i
$820$	−79.3829	−	27.7773i	−2.77217	−	0.970025i
$821$	−3.90250	+	52.0752i	−0.136198	+	1.81744i	0.342566	+	0.939494i	$0.388704\pi$
$821$	−3.90250	+	52.0752i	−0.136198	+	1.81744i	−0.478764	+	0.877944i	$0.658915\pi$
$822$	64.2628	+	2.78292i	2.24142	+	0.0970655i
$823$	4.93832	+	4.24977i	0.172139	+	0.148138i	0.734138	−	0.679000i	$-0.237587\pi$
$823$	4.93832	+	4.24977i	0.172139	+	0.148138i	−0.561999	+	0.827138i	$0.689967\pi$
$824$	−9.23632	−	2.47487i	−0.321763	−	0.0862160i
$825$	49.3369	+	86.6260i	1.71769	+	3.01593i
$826$	−6.80376	−	2.96845i	−0.236733	−	0.103286i
$827$	2.73342	+	24.2598i	0.0950503	+	0.843595i	0.947276	+	0.320420i	$0.103824\pi$
$827$	2.73342	+	24.2598i	0.0950503	+	0.843595i	−0.852225	+	0.523175i	$0.824747\pi$
$828$	−8.10250	−	0.703081i	−0.281581	−	0.0244338i
$829$	−20.3590	+	20.3590i	−0.707097	+	0.707097i	−0.965924	−	0.258827i	$-0.916664\pi$
$829$	−20.3590	+	20.3590i	−0.707097	+	0.707097i	0.258827	+	0.965924i	$0.416664\pi$
$830$	16.7586	−	88.5711i	0.581698	−	3.07435i
$831$	0.0678579	−	0.0353552i	0.00235396	−	0.00122646i
$832$	21.4406	+	14.6180i	0.743320	+	0.506787i
$833$	−0.802120	−	4.23931i	−0.0277918	−	0.146883i
$834$	−2.21744	−	2.81436i	−0.0767837	−	0.0974534i
$835$	4.95815	+	12.6332i	0.171584	+	0.437188i
$836$	35.0730	−	27.9698i	1.21302	−	0.967355i
$837$	−2.38728	−	41.7159i	−0.0825165	−	1.44191i
$838$	17.3043	−	27.5396i	0.597767	−	0.951341i
$839$	−16.9493	+	22.9655i	−0.585155	+	0.792857i	−0.992736	−	0.120312i	$-0.961610\pi$
$839$	−16.9493	+	22.9655i	−0.585155	+	0.792857i	0.407581	+	0.913169i	$0.366372\pi$
$840$	21.0310	+	44.3361i	0.725637	+	1.52974i
$841$	8.36527	+	27.7673i	0.288458	+	0.957493i
$842$	−17.6208	+	10.1734i	−0.607253	+	0.350598i
$843$	−24.7467	−	4.83318i	−0.852322	−	0.166464i
$844$	29.6021	−	15.6452i	1.01895	−	0.538529i
$845$	−8.34890	+	36.5789i	−0.287211	+	1.25835i
$846$	−32.1341	+	18.0523i	−1.10479	+	0.620651i
$847$	24.9440	+	19.8922i	0.857085	+	0.683503i
$848$	−1.11172	+	3.60410i	−0.0381766	+	0.123765i
$849$	−27.3803	−	37.5592i	−0.939691	−	1.28903i
$850$	59.0920	−	86.6720i	2.02684	−	2.97282i
$851$	−0.247488	+	0.468270i	−0.00848377	+	0.0160521i
$852$	−10.7611	+	39.2370i	−0.368670	+	1.34424i
$853$	30.9449	−	8.29165i	1.05953	−	0.283901i	0.313346	−	0.949639i	$-0.398550\pi$
$853$	30.9449	−	8.29165i	1.05953	−	0.283901i	0.746185	+	0.665738i	$0.231883\pi$
$854$	−46.3215	−	22.3073i	−1.58509	−	0.763339i
$855$	−38.6455	−	1.90121i	−1.32165	−	0.0650202i
$856$	1.29053	−	0.145407i	0.0441093	−	0.00496992i
$857$	−15.7995	−	23.1736i	−0.539700	−	0.791595i	0.455419	−	0.890277i	$-0.349490\pi$
$857$	−15.7995	−	23.1736i	−0.539700	−	0.791595i	−0.995119	+	0.0986826i	$0.968537\pi$
$858$	23.6633	+	27.8264i	0.807851	+	0.949979i
$859$	−22.7619	+	26.4499i	−0.776628	+	0.902458i	−0.997341	−	0.0728812i	$-0.976781\pi$
$859$	−22.7619	+	26.4499i	−0.776628	+	0.902458i	0.220713	+	0.975339i	$0.429162\pi$
$860$	25.1992	+	13.3181i	0.859285	+	0.454145i
$861$	25.4222	+	20.5191i	0.866385	+	0.699290i
$862$	26.7204	+	31.0497i	0.910100	+	1.05756i
$863$	−6.75686	−	29.6038i	−0.230006	−	1.00772i	−0.949633	−	0.313363i	$-0.898544\pi$
$863$	−6.75686	−	29.6038i	−0.230006	−	1.00772i	0.719627	−	0.694361i	$-0.244313\pi$
$864$	30.9953	+	12.8000i	1.05448	+	0.435465i
$865$	23.0531	+	28.9077i	0.783829	+	0.982890i
$866$	−32.2814	+	34.7910i	−1.09697	+	1.18225i
$867$	−0.498976	+	4.20616i	−0.0169461	+	0.142849i
$868$	−64.3951	+	28.0953i	−2.18571	+	0.953617i
$869$	30.2425	+	52.3816i	1.02591	+	1.77692i
$870$	85.4274	+	16.9766i	2.89626	+	0.575561i
$871$	0.353442	−	0.612179i	0.0119759	−	0.0207429i
$872$	−2.74485	+	24.3612i	−0.0929522	+	0.824974i
$873$	7.76026	−	38.5286i	0.262645	−	1.30400i
$874$	−6.03334	−	1.37707i	−0.204081	−	0.0465801i
$875$	−84.4605	+	12.7304i	−2.85529	+	0.430365i
$876$	16.9498	+	56.1189i	0.572679	+	1.89608i
$877$	−5.22187	+	4.84519i	−0.176330	+	0.163610i	−0.763400	−	0.645925i	$-0.776472\pi$
$877$	−5.22187	+	4.84519i	−0.176330	+	0.163610i	0.587070	+	0.809536i	$0.300281\pi$
$878$	30.5466	−	5.77972i	1.03090	−	0.195056i
$879$	−36.5368	−	5.72689i	−1.23235	−	0.193163i
$880$	−0.540719	−	14.4510i	−0.0182277	−	0.487144i
$881$	−2.70004	−	7.71628i	−0.0909668	−	0.259968i	0.889407	−	0.457116i	$-0.151118\pi$
$881$	−2.70004	−	7.71628i	−0.0909668	−	0.259968i	−0.980374	+	0.197148i	$0.936832\pi$
$882$	−0.765582	−	7.59640i	−0.0257785	−	0.255784i
$883$	7.70135	−	15.9920i	0.259171	−	0.538174i	−0.730262	−	0.683168i	$-0.760602\pi$
$883$	7.70135	−	15.9920i	0.259171	−	0.538174i	0.989433	+	0.144993i	$0.0463161\pi$
$884$	9.29991	−	21.3156i	0.312790	−	0.716922i
$885$	0.262039	+	8.31027i	0.00880836	+	0.279347i
$886$	−6.38754	−	85.2358i	−0.214594	−	2.86355i
$887$	9.95986	−	37.1707i	0.334419	−	1.24807i	−0.570078	−	0.821590i	$-0.693087\pi$
$887$	9.95986	−	37.1707i	0.334419	−	1.24807i	0.904497	−	0.426479i	$-0.140246\pi$
$888$	−1.76576	+	1.74512i	−0.0592549	+	0.0585623i
$889$	7.64140	−	0.285921i	0.256284	−	0.00958949i
$890$	13.6383	+	28.3202i	0.457156	+	0.949295i
$891$	33.5092	+	25.9697i	1.12260	+	0.870018i
$892$	−6.05042	+	1.38097i	−0.202583	+	0.0462383i
$893$	−15.7962	+	6.19954i	−0.528598	+	0.207460i
$894$	19.0569	+	9.31570i	0.637357	+	0.311564i
$895$	14.5428	−	4.48586i	0.486112	−	0.149946i
$896$	1.75330	−	46.8580i	0.0585738	−	1.56542i
$897$	0.584424	−	2.99235i	0.0195134	−	0.0999118i
$898$	−80.1439	−	46.2711i	−2.67444	−	1.54409i
$899$	−9.77499	+	42.1864i	−0.326014	+	1.40700i
$900$	71.0549	−	86.9822i	2.36850	−	2.89941i
$901$	19.3267	+	2.17760i	0.643866	+	0.0725463i
$902$	32.7641	+	61.9926i	1.09092	+	2.06413i
$903$	−7.48286	−	8.16029i	−0.249014	−	0.271558i
$904$	17.7031	+	6.94794i	0.588795	+	0.231085i
$905$	19.0806	+	2.87594i	0.634260	+	0.0955994i
$906$	46.4498	+	18.5460i	1.54319	+	0.616151i
$907$	−13.1709	+	11.3345i	−0.437333	+	0.376356i	−0.843221	−	0.537567i	$-0.819343\pi$
$907$	−13.1709	+	11.3345i	−0.437333	+	0.376356i	0.405888	+	0.913923i	$0.366962\pi$
$908$	−25.2279	+	12.1491i	−0.837216	+	0.403182i
$909$	−21.8632	+	28.9061i	−0.725158	+	0.958755i
$910$	−50.0014	+	17.4962i	−1.65753	+	0.579995i
$911$	−11.0813	−	41.3559i	−0.367139	−	1.37018i	−0.864498	−	0.502637i	$-0.832363\pi$
$911$	−11.0813	−	41.3559i	−0.367139	−	1.37018i	0.497358	−	0.867545i	$-0.334303\pi$
$912$	3.43751	+	2.01168i	0.113827	+	0.0666135i
$913$	−36.5871	+	27.0025i	−1.21085	+	0.893652i
$914$	−44.6706	+	32.9684i	−1.47757	+	1.09050i
$915$	−0.338509	+	57.5850i	−0.0111908	+	1.90370i
$916$	−0.305956	−	1.14184i	−0.0101091	−	0.0377276i
$917$	−5.27137	+	1.84453i	−0.174076	+	0.0609118i
$918$	9.06510	−	43.6789i	0.299193	−	1.44162i
$919$	−12.2363	+	5.89270i	−0.403639	+	0.194382i	−0.624678	−	0.780883i	$-0.714770\pi$
$919$	−12.2363	+	5.89270i	−0.403639	+	0.194382i	0.221039	+	0.975265i	$0.429055\pi$
$920$	6.66324	−	5.73418i	0.219680	−	0.189050i
$921$	20.4236	−	16.0918i	0.672981	−	0.530243i
$922$	−51.1111	−	7.70376i	−1.68326	−	0.253710i
$923$	−14.1980	−	5.57232i	−0.467334	−	0.183415i
$924$	21.4112	−	67.9918i	0.704377	−	2.23677i
$925$	−3.41778	−	6.46676i	−0.112376	−	0.212626i
$926$	92.2897	+	10.3986i	3.03283	+	0.341718i
$927$	1.92478	−	11.8250i	0.0632180	−	0.388385i
$928$	−27.1004	−	21.7581i	−0.889613	−	0.714246i
$929$	21.4630	+	12.3917i	0.704178	+	0.406558i	0.808902	−	0.587944i	$-0.200062\pi$
$929$	21.4630	+	12.3917i	0.704178	+	0.406558i	−0.104723	+	0.994501i	$0.533396\pi$
$930$	98.0803	+	85.4135i	3.21618	+	2.80082i
$931$	0.131433	−	3.51262i	0.00430755	−	0.115122i
$932$	−8.23127	+	2.53901i	−0.269624	+	0.0831681i
$933$	−0.321452	−	4.65665i	−0.0105239	−	0.152452i
$934$	36.7640	−	14.4288i	1.20295	−	0.472124i
$935$	−72.7008	+	16.5935i	−2.37757	+	0.542665i
$936$	6.82582	−	12.5555i	0.223109	−	0.410390i
$937$	16.0051	+	33.2350i	0.522864	+	1.08574i	0.980485	+	0.196592i	$0.0629874\pi$
$937$	16.0051	+	33.2350i	0.522864	+	1.08574i	−0.457621	+	0.889147i	$0.651298\pi$
$938$	−2.27833	+	0.0852489i	−0.0743900	+	0.00278348i
$939$	1.13052	+	4.32060i	0.0368932	+	0.140998i
$940$	17.9658	−	67.0493i	0.585980	−	2.18691i
$941$	1.17189	+	15.6377i	0.0382024	+	0.509775i	0.983180	+	0.182640i	$0.0584643\pi$
$941$	1.17189	+	15.6377i	0.0382024	+	0.509775i	−0.944977	+	0.327135i	$0.893917\pi$
$942$	58.0278	−	35.9872i	1.89065	−	1.17253i
$943$	2.34043	−	5.36432i	0.0762148	−	0.174686i
$944$	0.371346	−	0.771107i	0.0120863	−	0.0250974i
$945$	−52.6276	+	31.7876i	−1.71197	+	1.03405i
$946$	−7.84839	−	22.4294i	−0.255173	−	0.729243i
$947$	0.323781	+	8.65322i	0.0105215	+	0.281192i	0.994621	+	0.103577i	$0.0330287\pi$
$947$	0.323781	+	8.65322i	0.0105215	+	0.281192i	−0.984100	+	0.177615i	$0.943162\pi$
$948$	42.8000	−	53.0271i	1.39008	−	1.72224i
$949$	−21.5934	+	4.08570i	−0.700952	+	0.132627i
$950$	62.6485	−	58.1293i	2.03258	−	1.88596i
$951$	−7.25421	+	7.72659i	−0.235234	+	0.250552i
$952$	−25.7565	+	3.88217i	−0.834774	+	0.125822i
$953$	4.28863	+	0.978852i	0.138922	+	0.0317081i	0.291417	−	0.956596i	$-0.405873\pi$
$953$	4.28863	+	0.978852i	0.138922	+	0.0317081i	−0.152494	+	0.988304i	$0.548731\pi$
$954$	33.7390	+	6.79555i	1.09234	+	0.220014i
$955$	−11.4033	+	101.207i	−0.369002	+	3.27498i
$956$	−6.54086	+	11.3291i	−0.211547	+	0.366409i
$957$	−25.7652	−	35.5890i	−0.832869	−	1.15043i
$958$	−25.4884	−	44.1473i	−0.823494	−	1.42633i
$959$	43.1310	−	18.8179i	1.39277	−	0.607661i
$960$	−86.1419	+	36.9821i	−2.78022	+	1.19359i
$961$	−22.8971	+	24.6772i	−0.738615	+	0.796037i
$962$	−1.67099	−	2.09536i	−0.0538749	−	0.0675570i
$963$	0.343403	+	1.59052i	0.0110660	+	0.0512536i
$964$	1.87048	+	8.19512i	0.0602442	+	0.263947i
$965$	41.4707	+	48.1898i	1.33499	+	1.55128i
$966$	−9.17483	+	3.53876i	−0.295195	+	0.113858i
$967$	−20.6900	−	10.9350i	−0.665346	−	0.351645i	0.100255	−	0.994962i	$-0.468034\pi$
$967$	−20.6900	−	10.9350i	−0.665346	−	0.351645i	−0.765600	+	0.643316i	$0.777558\pi$
$968$	17.4750	−	20.3063i	0.561668	−	0.652670i
$969$	6.89717	−	19.3454i	0.221569	−	0.621465i
$970$	68.9129	+	101.077i	2.21266	+	3.24538i
$971$	−29.4343	+	3.31645i	−0.944592	+	0.106430i	−0.570806	−	0.821085i	$-0.693369\pi$
$971$	−29.4343	+	3.31645i	−0.944592	+	0.106430i	−0.373786	+	0.927515i	$0.621941\pi$
$972$	13.7125	−	45.7526i	0.439830	−	1.46751i
$973$	−2.36165	−	1.13731i	−0.0757109	−	0.0364605i
$974$	41.0333	−	10.9949i	1.31479	−	0.352298i
$975$	29.5971	+	29.9472i	0.947867	+	0.959076i
$976$	2.76986	−	5.24083i	0.0886610	−	0.167755i
$977$	24.9398	−	36.5800i	0.797896	−	1.17030i	−0.184380	−	0.982855i	$-0.559028\pi$
$977$	24.9398	−	36.5800i	0.797896	−	1.17030i	0.982276	−	0.187443i	$-0.0600199\pi$
$978$	−29.6219	+	66.8196i	−0.947203	+	2.13666i
$979$	4.67376	−	15.1520i	0.149374	−	0.484259i
$980$	11.2419	+	8.96509i	0.359108	+	0.286379i
$981$	−30.7138	−	0.361110i	−0.980615	−	0.0115294i
$982$	8.00913	−	35.0903i	0.255582	−	1.11978i
$983$	40.5804	−	21.4473i	1.29431	−	0.684064i	0.328795	−	0.944401i	$-0.393358\pi$
$983$	40.5804	−	21.4473i	1.29431	−	0.684064i	0.965518	+	0.260337i	$0.0838337\pi$
$984$	18.0161	−	20.6879i	0.574333	−	0.659506i
$985$	98.1041	−	56.6404i	3.12586	−	1.80471i
$986$	−21.7374	+	40.8034i	−0.692259	+	1.29944i
$987$	−15.3202	+	22.1893i	−0.487649	+	0.706293i
$988$	11.2511	−	15.2446i	0.357944	−	0.484997i
$989$	−1.05526	+	1.67944i	−0.0335553	+	0.0534029i
$990$	−130.706	+	18.1319i	−4.15412	+	0.576271i
$991$	−41.0396	+	32.7280i	−1.30366	+	1.03964i	−0.307554	+	0.951531i	$0.599510\pi$
$991$	−41.0396	+	32.7280i	−1.30366	+	1.03964i	−0.996111	+	0.0881072i	$0.971918\pi$
$992$	−18.9599	−	48.3089i	−0.601976	−	1.53381i
$993$	55.0071	−	7.96058i	1.74560	−	0.252621i
$994$	9.14569	+	48.3361i	0.290084	+	1.53313i
$995$	5.69409	+	3.88217i	0.180515	+	0.123073i
$996$	43.2176	+	27.5111i	1.36940	+	0.871723i
$997$	−5.47253	+	28.9230i	−0.173317	+	0.916002i	0.782636	+	0.622480i	$0.213875\pi$
$997$	−5.47253	+	28.9230i	−0.173317	+	0.916002i	−0.955952	+	0.293522i	$0.905173\pi$
$998$	9.02275	−	9.02275i	0.285610	−	0.285610i
$999$	−2.39733	−	1.98196i	−0.0758480	−	0.0627065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.4	✓	672
3.2	odd	2		783.2.be.a.89.25		672
9.4	even	3		783.2.be.a.611.25		672
9.5	odd	6	inner	261.2.x.a.176.4	yes	672
29.15	odd	28	inner	261.2.x.a.218.4	yes	672
87.44	even	28		783.2.be.a.305.25		672
261.131	even	84	inner	261.2.x.a.131.4	yes	672
261.247	odd	84		783.2.be.a.44.25		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.4	✓	672	1.1	even	1	trivial
261.2.x.a.131.4	yes	672	261.131	even	84	inner
261.2.x.a.176.4	yes	672	9.5	odd	6	inner
261.2.x.a.218.4	yes	672	29.15	odd	28	inner
783.2.be.a.44.25		672	261.247	odd	84
783.2.be.a.89.25		672	3.2	odd	2
783.2.be.a.305.25		672	87.44	even	28
783.2.be.a.611.25		672	9.4	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.81062 - 1.33630i) q^{2} +(-1.71999 - 0.204042i) q^{3} +(0.903135 + 2.92789i) q^{4} +(1.51600 - 3.86270i) q^{5} +(2.84158 + 2.66786i) q^{6} +(2.72479 + 0.840488i) q^{7} +(0.790819 - 2.26003i) q^{8} +(2.91673 + 0.701902i) q^{9} +O(q^{10})\)	\(q+(-1.81062 - 1.33630i) q^{2} +(-1.71999 - 0.204042i) q^{3} +(0.903135 + 2.92789i) q^{4} +(1.51600 - 3.86270i) q^{5} +(2.84158 + 2.66786i) q^{6} +(2.72479 + 0.840488i) q^{7} +(0.790819 - 2.26003i) q^{8} +(2.91673 + 0.701902i) q^{9} +(-7.90661 + 4.96805i) q^{10} +(4.62838 + 0.875736i) q^{11} +(-0.955969 - 5.22022i) q^{12} +(1.98394 - 0.148676i) q^{13} +(-3.81042 - 5.16293i) q^{14} +(-3.39566 + 6.33449i) q^{15} +(0.611281 - 0.416764i) q^{16} +(-2.69764 - 2.69764i) q^{17} +(-4.34314 - 5.16849i) q^{18} +(-1.65364 - 2.63175i) q^{19} +(12.6787 + 0.950139i) q^{20} +(-4.51512 - 2.00160i) q^{21} +(-7.20997 - 7.77050i) q^{22} +(-0.131870 + 0.874899i) q^{23} +(-1.82134 + 3.72587i) q^{24} +(-8.95697 - 8.31085i) q^{25} +(-3.79084 - 2.38194i) q^{26} +(-4.87354 - 1.80240i) q^{27} +8.73697i q^{28} +(4.32234 + 3.21207i) q^{29} +(14.6130 - 6.93172i) q^{30} +(3.21568 + 7.37041i) q^{31} +(-6.44916 - 0.241310i) q^{32} +(-7.78207 - 2.45064i) q^{33} +(1.27955 + 8.48924i) q^{34} +(7.37734 - 9.25090i) q^{35} +(0.579111 + 9.17379i) q^{36} +(0.565028 + 0.197712i) q^{37} +(-0.522691 + 6.97483i) q^{38} +(-3.44270 - 0.149087i) q^{39} +(-7.53095 - 6.48090i) q^{40} +(-6.38941 - 1.71204i) q^{41} +(5.50042 + 9.65768i) q^{42} +(2.05470 + 0.896455i) q^{43} +(1.61599 + 14.3423i) q^{44} +(7.13301 - 10.2024i) q^{45} +(1.40789 - 1.40789i) q^{46} +(1.01500 - 5.36440i) q^{47} +(-1.13644 + 0.592103i) q^{48} +(0.934414 + 0.637072i) q^{49} +(5.11188 + 27.0169i) q^{50} +(4.08948 + 5.19035i) q^{51} +(2.22708 + 5.67450i) q^{52} +(-3.98576 + 3.17854i) q^{53} +(6.41556 + 9.77594i) q^{54} +(10.3993 - 16.5504i) q^{55} +(4.05435 - 5.49344i) q^{56} +(2.30725 + 4.86399i) q^{57} +(-3.53383 - 11.5917i) q^{58} +(1.00184 - 0.578415i) q^{59} +(-21.6134 - 4.22123i) q^{60} +(7.08377 - 3.74388i) q^{61} +(4.02669 - 17.6421i) q^{62} +(7.35756 + 4.36402i) q^{63} +(10.1976 + 8.13234i) q^{64} +(2.43337 - 7.88878i) q^{65} +(10.8156 + 14.8363i) q^{66} +(0.200151 - 0.293567i) q^{67} +(5.46207 - 10.3347i) q^{68} +(0.405331 - 1.47791i) q^{69} +(-25.7195 + 6.89151i) q^{70} +(-6.90720 - 3.32633i) q^{71} +(3.89293 - 6.03683i) q^{72} +(-10.9768 + 1.23679i) q^{73} +(-0.758847 - 1.11302i) q^{74} +(13.7101 + 16.1222i) q^{75} +(6.21201 - 7.21848i) q^{76} +(11.8753 + 6.27629i) q^{77} +(6.03419 + 4.87041i) q^{78} +(8.37568 + 9.73272i) q^{79} +(-0.683136 - 2.99301i) q^{80} +(8.01467 + 4.09452i) q^{81} +(9.28098 + 11.6380i) q^{82} +(-6.56600 + 7.07647i) q^{83} +(1.78271 - 15.0275i) q^{84} +(-14.5098 + 6.33057i) q^{85} +(-2.52234 - 4.36882i) q^{86} +(-6.77899 - 6.40666i) q^{87} +(5.63940 - 9.76772i) q^{88} +(0.376893 - 3.34502i) q^{89} +(-26.5485 + 8.94082i) q^{90} +(5.53080 + 1.26237i) q^{91} +(-2.68070 + 0.404051i) q^{92} +(-4.02706 - 13.3332i) q^{93} +(-9.00619 + 8.35652i) q^{94} +(-12.6726 + 2.39778i) q^{95} +(11.0433 + 1.73095i) q^{96} +(-0.489854 - 13.0916i) q^{97} +(-0.840547 - 2.40215i) q^{98} +(12.8851 + 5.80295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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