LMFDB - Embedded newform 112.2.w.c.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(37,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("112.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.w (of order $12$, degree $4$, 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:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	112.37
Dual form			112.2.w.c.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.805226 - 1.16259i) q^{2} +(1.16533 + 0.312249i) q^{3} +(-0.703221 + 1.87229i) q^{4} +(0.980942 - 0.262843i) q^{5} +(-0.575337 - 1.60623i) q^{6} +(2.60251 + 0.476386i) q^{7} +(2.74296 - 0.690063i) q^{8} +(-1.33758 - 0.772254i) q^{9} +O(q^{10})$	\(q+(-0.805226 - 1.16259i) q^{2} +(1.16533 + 0.312249i) q^{3} +(-0.703221 + 1.87229i) q^{4} +(0.980942 - 0.262843i) q^{5} +(-0.575337 - 1.60623i) q^{6} +(2.60251 + 0.476386i) q^{7} +(2.74296 - 0.690063i) q^{8} +(-1.33758 - 0.772254i) q^{9} +(-1.09546 - 0.928784i) q^{10} +(0.635020 - 2.36993i) q^{11} +(-1.40411 + 1.96226i) q^{12} +(-2.65786 + 2.65786i) q^{13} +(-1.54177 - 3.40924i) q^{14} +1.22519 q^{15} +(-3.01096 - 2.63327i) q^{16} +(-0.509128 - 0.881836i) q^{17} +(0.179244 + 2.17690i) q^{18} +(-0.0250951 - 0.0936561i) q^{19} +(-0.197701 + 2.02145i) q^{20} +(2.88403 + 1.36778i) q^{21} +(-3.26658 + 1.17006i) q^{22} +(1.67238 + 0.965551i) q^{23} +(3.41192 + 0.0523353i) q^{24} +(-3.43697 + 1.98433i) q^{25} +(5.23017 + 0.949817i) q^{26} +(-3.87683 - 3.87683i) q^{27} +(-2.72207 + 4.53765i) q^{28} +(-5.05325 + 5.05325i) q^{29} +(-0.986557 - 1.42439i) q^{30} +(4.28249 + 7.41749i) q^{31} +(-0.636906 + 5.62089i) q^{32} +(1.48001 - 2.56346i) q^{33} +(-0.615248 + 1.30198i) q^{34} +(2.67813 - 0.216743i) q^{35} +(2.38650 - 1.96128i) q^{36} +(-7.71428 + 2.06704i) q^{37} +(-0.0886762 + 0.104590i) q^{38} +(-3.92719 + 2.26737i) q^{39} +(2.50930 - 1.39788i) q^{40} -8.51782i q^{41} +(-0.732134 - 4.45431i) q^{42} +(-4.47950 - 4.47950i) q^{43} +(3.99064 + 2.85553i) q^{44} +(-1.51507 - 0.405963i) q^{45} +(-0.224109 - 2.72178i) q^{46} +(6.02995 - 10.4442i) q^{47} +(-2.68652 - 4.00880i) q^{48} +(6.54611 + 2.47960i) q^{49} +(5.07450 + 2.39794i) q^{50} +(-0.317949 - 1.18660i) q^{51} +(-3.10723 - 6.84535i) q^{52} +(0.381000 - 1.42191i) q^{53} +(-1.38543 + 7.62888i) q^{54} -2.49167i q^{55} +(7.46731 - 0.489188i) q^{56} -0.116976i q^{57} +(9.94385 + 1.80584i) q^{58} +(-1.86535 + 6.96158i) q^{59} +(-0.861581 + 2.29392i) q^{60} +(-1.18609 - 4.42654i) q^{61} +(5.17511 - 10.9515i) q^{62} +(-3.11318 - 2.64701i) q^{63} +(7.04763 - 3.78563i) q^{64} +(-1.90861 + 3.30580i) q^{65} +(-4.17199 + 0.343519i) q^{66} +(-3.38700 - 0.907543i) q^{67} +(2.00908 - 0.333111i) q^{68} +(1.64738 + 1.64738i) q^{69} +(-2.40848 - 2.93903i) q^{70} +5.43131i q^{71} +(-4.20184 - 1.19524i) q^{72} +(7.34303 - 4.23950i) q^{73} +(8.61485 + 7.30410i) q^{74} +(-4.62480 + 1.23921i) q^{75} +(0.192999 + 0.0188756i) q^{76} +(2.78165 - 5.86524i) q^{77} +(5.79829 + 2.73996i) q^{78} +(-0.433595 + 0.751008i) q^{79} +(-3.64571 - 1.79168i) q^{80} +(-0.990483 - 1.71557i) q^{81} +(-9.90271 + 6.85877i) q^{82} +(-5.44318 + 5.44318i) q^{83} +(-4.58899 + 4.43790i) q^{84} +(-0.731209 - 0.731209i) q^{85} +(-1.60080 + 8.81482i) q^{86} +(-7.46657 + 4.31083i) q^{87} +(0.106434 - 6.93881i) q^{88} +(3.93155 + 2.26988i) q^{89} +(0.748010 + 2.08830i) q^{90} +(-8.18327 + 5.65093i) q^{91} +(-2.98385 + 2.45219i) q^{92} +(2.67441 + 9.98102i) q^{93} +(-16.9977 + 1.39958i) q^{94} +(-0.0492336 - 0.0852752i) q^{95} +(-2.49732 + 6.35131i) q^{96} +16.4025 q^{97} +(-2.38835 - 9.60707i) q^{98} +(-2.67958 + 2.67958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24} - 10 q^{26} - 24 q^{27} - 10 q^{28} + 24 q^{29} - 4 q^{30} + 28 q^{31} + 16 q^{32} + 16 q^{33} - 44 q^{34} + 28 q^{35} - 72 q^{36} - 24 q^{37} + 20 q^{38} + 26 q^{40} + 6 q^{42} - 40 q^{43} + 6 q^{44} - 28 q^{45} - 14 q^{46} - 20 q^{47} + 56 q^{48} + 56 q^{50} + 24 q^{51} - 16 q^{52} - 16 q^{53} + 64 q^{54} + 40 q^{56} - 6 q^{58} - 20 q^{59} + 46 q^{60} + 8 q^{61} + 24 q^{62} - 16 q^{63} + 80 q^{64} + 8 q^{65} - 20 q^{66} + 48 q^{67} - 40 q^{69} + 82 q^{70} - 32 q^{72} - 8 q^{74} - 4 q^{75} - 36 q^{76} - 20 q^{77} + 116 q^{78} - 36 q^{79} - 28 q^{80} + 2 q^{82} - 8 q^{83} + 28 q^{84} - 20 q^{86} - 42 q^{88} - 20 q^{90} + 64 q^{91} + 76 q^{92} + 8 q^{93} - 72 q^{94} - 4 q^{95} - 120 q^{96} - 48 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.805226	−	1.16259i	−0.569381	−	0.822074i
$2$	−0.805226	−	1.16259i	−0.569381	−	0.822074i
$3$	1.16533	+	0.312249i	0.672803	+	0.180277i	0.579017	−	0.815315i	$-0.303436\pi$
$3$	1.16533	+	0.312249i	0.672803	+	0.180277i	0.0937859	+	0.995592i	$0.470103\pi$
$4$	−0.703221	+	1.87229i	−0.351611	+	0.936146i
$5$	0.980942	−	0.262843i	0.438691	−	0.117547i	−0.0327122	−	0.999465i	$-0.510414\pi$
$5$	0.980942	−	0.262843i	0.438691	−	0.117547i	0.471403	+	0.881918i	$0.343748\pi$
$6$	−0.575337	−	1.60623i	−0.234880	−	0.655740i
$7$	2.60251	+	0.476386i	0.983656	+	0.180057i
$7$	2.60251	+	0.476386i	0.983656	+	0.180057i
$8$	2.74296	−	0.690063i	0.969782	−	0.243974i
$9$	−1.33758	−	0.772254i	−0.445861	−	0.257418i
$10$	−1.09546	−	0.928784i	−0.346414	−	0.293707i
$11$	0.635020	−	2.36993i	0.191466	−	0.714560i	−0.801688	−	0.597743i	$-0.796064\pi$
$11$	0.635020	−	2.36993i	0.191466	−	0.714560i	0.993153	−	0.116817i	$-0.0372690\pi$
$12$	−1.40411	+	1.96226i	−0.405330	+	0.566455i
$13$	−2.65786	+	2.65786i	−0.737157	+	0.737157i	−0.972027	−	0.234870i	$-0.924534\pi$
$13$	−2.65786	+	2.65786i	−0.737157	+	0.737157i	0.234870	+	0.972027i	$0.424534\pi$
$14$	−1.54177	−	3.40924i	−0.412055	−	0.911159i
$15$	1.22519			0.316343
$16$	−3.01096	−	2.63327i	−0.752740	−	0.658318i
$17$	−0.509128	−	0.881836i	−0.123482	−	0.213877i	0.797657	−	0.603112i	$-0.206073\pi$
$17$	−0.509128	−	0.881836i	−0.123482	−	0.213877i	−0.921138	+	0.389235i	$0.872739\pi$
$18$	0.179244	+	2.17690i	0.0422482	+	0.513100i
$19$	−0.0250951	−	0.0936561i	−0.00575721	−	0.0214862i	0.962987	−	0.269546i	$-0.0868737\pi$
$19$	−0.0250951	−	0.0936561i	−0.00575721	−	0.0214862i	−0.968745	+	0.248060i	$0.920207\pi$
$20$	−0.197701	+	2.02145i	−0.0442073	+	0.452009i
$21$	2.88403	+	1.36778i	0.629347	+	0.298474i
$22$	−3.26658	+	1.17006i	−0.696438	+	0.249458i
$23$	1.67238	+	0.965551i	0.348716	+	0.201331i	0.664120	−	0.747626i	$-0.268807\pi$
$23$	1.67238	+	0.965551i	0.348716	+	0.201331i	−0.315404	+	0.948958i	$0.602140\pi$
$24$	3.41192	+	0.0523353i	0.696455	+	0.0106829i
$25$	−3.43697	+	1.98433i	−0.687393	+	0.396867i
$26$	5.23017	+	0.949817i	1.02572	+	0.186274i
$27$	−3.87683	−	3.87683i	−0.746096	−	0.746096i
$28$	−2.72207	+	4.53765i	−0.514424	+	0.857536i
$29$	−5.05325	+	5.05325i	−0.938365	+	0.938365i	−0.998208	−	0.0598432i	$-0.980940\pi$
$29$	−5.05325	+	5.05325i	−0.938365	+	0.938365i	0.0598432	+	0.998208i	$0.480940\pi$
$30$	−0.986557	−	1.42439i	−0.180120	−	0.260058i
$31$	4.28249	+	7.41749i	0.769158	+	1.33222i	0.938020	+	0.346581i	$0.112657\pi$
$31$	4.28249	+	7.41749i	0.769158	+	1.33222i	−0.168862	+	0.985640i	$0.554009\pi$
$32$	−0.636906	+	5.62089i	−0.112590	+	0.993642i
$33$	1.48001	−	2.56346i	0.257637	−	0.446241i
$34$	−0.615248	+	1.30198i	−0.105514	+	0.223288i
$35$	2.67813	−	0.216743i	0.452686	−	0.0366363i
$36$	2.38650	−	1.96128i	0.397751	−	0.326880i
$37$	−7.71428	+	2.06704i	−1.26822	+	0.339818i	−0.829349	−	0.558732i	$-0.811288\pi$
$37$	−7.71428	+	2.06704i	−1.26822	+	0.339818i	−0.438871	+	0.898550i	$0.644622\pi$
$38$	−0.0886762	+	0.104590i	−0.0143852	+	0.0169667i
$39$	−3.92719	+	2.26737i	−0.628854	+	0.363069i
$40$	2.50930	−	1.39788i	0.396756	−	0.221024i
$41$		−	8.51782i		−	1.33026i	−0.746728	−	0.665130i	$-0.768376\pi$
$41$		−	8.51782i		−	1.33026i	0.746728	−	0.665130i	$-0.231624\pi$
$42$	−0.732134	−	4.45431i	−0.112971	−	0.687315i
$43$	−4.47950	−	4.47950i	−0.683117	−	0.683117i	0.277584	−	0.960701i	$-0.410466\pi$
$43$	−4.47950	−	4.47950i	−0.683117	−	0.683117i	−0.960701	+	0.277584i	$0.910466\pi$
$44$	3.99064	+	2.85553i	0.601611	+	0.430487i
$45$	−1.51507	−	0.405963i	−0.225854	−	0.0605174i
$46$	−0.224109	−	2.72178i	−0.0330431	−	0.401304i
$47$	6.02995	−	10.4442i	0.879559	−	1.52344i	0.0277324	−	0.999615i	$-0.491171\pi$
$47$	6.02995	−	10.4442i	0.879559	−	1.52344i	0.851826	−	0.523825i	$-0.175495\pi$
$48$	−2.68652	−	4.00880i	−0.387766	−	0.578620i
$49$	6.54611	+	2.47960i	0.935159	+	0.354229i
$50$	5.07450	+	2.39794i	0.717642	+	0.339120i
$51$	−0.317949	−	1.18660i	−0.0445218	−	0.166158i
$52$	−3.10723	−	6.84535i	−0.430895	−	0.949279i
$53$	0.381000	−	1.42191i	0.0523344	−	0.195315i	−0.934809	−	0.355150i	$-0.884430\pi$
$53$	0.381000	−	1.42191i	0.0523344	−	0.195315i	0.987144	+	0.159836i	$0.0510964\pi$
$54$	−1.38543	+	7.62888i	−0.188533	+	1.03816i
$55$		−	2.49167i		−	0.335977i
$56$	7.46731	−	0.489188i	0.997861	−	0.0653704i
$57$		−	0.116976i		−	0.0154939i
$58$	9.94385	+	1.80584i	1.30569	+	0.237118i
$59$	−1.86535	+	6.96158i	−0.242848	+	0.906320i	0.731605	+	0.681729i	$0.238771\pi$
$59$	−1.86535	+	6.96158i	−0.242848	+	0.906320i	−0.974453	+	0.224592i	$0.927895\pi$
$60$	−0.861581	+	2.29392i	−0.111230	+	0.296144i
$61$	−1.18609	−	4.42654i	−0.151863	−	0.566760i	−0.999354	−	0.0359500i	$-0.988554\pi$
$61$	−1.18609	−	4.42654i	−0.151863	−	0.566760i	0.847491	−	0.530810i	$-0.178112\pi$
$62$	5.17511	−	10.9515i	0.657240	−	1.39085i
$63$	−3.11318	−	2.64701i	−0.392224	−	0.333491i
$64$	7.04763	−	3.78563i	0.880953	−	0.473203i
$65$	−1.90861	+	3.30580i	−0.236734	+	0.410034i
$66$	−4.17199	+	0.343519i	−0.513537	+	0.0422842i
$67$	−3.38700	−	0.907543i	−0.413787	−	0.110874i	0.0459185	−	0.998945i	$-0.485379\pi$
$67$	−3.38700	−	0.907543i	−0.413787	−	0.110874i	−0.459706	+	0.888071i	$0.652045\pi$
$68$	2.00908	−	0.333111i	0.243637	−	0.0403957i
$69$	1.64738	+	1.64738i	0.198322	+	0.198322i
$70$	−2.40848	−	2.93903i	−0.287868	−	0.351281i
$71$			5.43131i			0.644578i	0.946641	+	0.322289i	$0.104452\pi$
$71$			5.43131i			0.644578i	−0.946641	+	0.322289i	$0.895548\pi$
$72$	−4.20184	−	1.19524i	−0.495191	−	0.140861i
$73$	7.34303	−	4.23950i	0.859436	−	0.496196i	−0.00438712	−	0.999990i	$-0.501396\pi$
$73$	7.34303	−	4.23950i	0.859436	−	0.496196i	0.863824	+	0.503795i	$0.168063\pi$
$74$	8.61485	+	7.30410i	1.00146	+	0.849084i
$75$	−4.62480	+	1.23921i	−0.534026	+	0.143092i
$76$	0.192999	+	0.0188756i	0.0221385	+	0.00216518i
$77$	2.78165	−	5.86524i	0.316998	−	0.668406i
$78$	5.79829	+	2.73996i	0.656527	+	0.310240i
$79$	−0.433595	+	0.751008i	−0.0487832	+	0.0844950i	−0.889386	−	0.457157i	$-0.848868\pi$
$79$	−0.433595	+	0.751008i	−0.0487832	+	0.0844950i	0.840603	+	0.541652i	$0.182201\pi$
$80$	−3.64571	−	1.79168i	−0.407603	−	0.200316i
$81$	−0.990483	−	1.71557i	−0.110054	−	0.190619i
$82$	−9.90271	+	6.85877i	−1.09357	+	0.757425i
$83$	−5.44318	+	5.44318i	−0.597466	+	0.597466i	−0.939638	−	0.342171i	$-0.888838\pi$
$83$	−5.44318	+	5.44318i	−0.597466	+	0.597466i	0.342171	+	0.939638i	$0.388838\pi$
$84$	−4.58899	+	4.43790i	−0.500700	+	0.484214i
$85$	−0.731209	−	0.731209i	−0.0793108	−	0.0793108i
$86$	−1.60080	+	8.81482i	−0.172619	+	0.950526i
$87$	−7.46657	+	4.31083i	−0.800500	+	0.462169i
$88$	0.106434	−	6.93881i	0.0113459	−	0.739680i
$89$	3.93155	+	2.26988i	0.416744	+	0.240607i	0.693683	−	0.720280i	$-0.255987\pi$
$89$	3.93155	+	2.26988i	0.416744	+	0.240607i	−0.276939	+	0.960887i	$0.589320\pi$
$90$	0.748010	+	2.08830i	0.0788471	+	0.220126i
$91$	−8.18327	+	5.65093i	−0.857840	+	0.592379i
$92$	−2.98385	+	2.45219i	−0.311088	+	0.255659i
$93$	2.67441	+	9.98102i	0.277323	+	1.03498i
$94$	−16.9977	+	1.39958i	−1.75318	+	0.144356i
$95$	−0.0492336	−	0.0852752i	−0.00505126	−	0.00874905i
$96$	−2.49732	+	6.35131i	−0.254882	+	0.648228i
$97$	16.4025			1.66542			0.832712	−	0.553706i	$-0.186787\pi$
$97$	16.4025			1.66542			0.832712	+	0.553706i	$0.186787\pi$
$98$	−2.38835	−	9.60707i	−0.241260	−	0.970461i
$99$	−2.67958	+	2.67958i	−0.269308	+	0.269308i
$100$	−1.29831	−	7.83043i	−0.129831	−	0.783043i
$101$	2.38049	−	8.88412i	0.236868	−	0.884003i	−0.740430	−	0.672134i	$-0.765378\pi$
$101$	2.38049	−	8.88412i	0.236868	−	0.884003i	0.977298	−	0.211870i	$-0.0679552\pi$
$102$	−1.12351	+	1.32513i	−0.111244	+	0.131207i
$103$	6.69469	+	3.86518i	0.659647	+	0.380848i	0.792143	−	0.610336i	$-0.208966\pi$
$103$	6.69469	+	3.86518i	0.659647	+	0.380848i	−0.132495	+	0.991184i	$0.542299\pi$
$104$	−5.45630	+	9.12448i	−0.535034	+	0.894729i
$105$	3.18858	+	0.583665i	0.311173	+	0.0569599i
$106$	−1.95989	+	0.702015i	−0.190361	+	0.0681857i
$107$	18.2555	−	4.89154i	1.76482	−	0.472883i	0.777137	−	0.629332i	$-0.216671\pi$
$107$	18.2555	−	4.89154i	1.76482	−	0.472883i	0.987686	+	0.156449i	$0.0500046\pi$
$108$	9.98483	−	4.53229i	0.960791	−	0.436120i
$109$	15.8026	+	4.23429i	1.51361	+	0.405571i	0.917633	−	0.397428i	$-0.130097\pi$
$109$	15.8026	+	4.23429i	1.51361	+	0.405571i	0.595980	+	0.802999i	$0.296764\pi$
$110$	−2.89679	+	2.00636i	−0.276198	+	0.191299i
$111$	−9.63510			−0.914524
$112$	−6.58160	−	8.28750i	−0.621902	−	0.783095i
$113$	−20.1152			−1.89228			−0.946138	−	0.323765i	$-0.895051\pi$
$113$	−20.1152			−1.89228			−0.946138	+	0.323765i	$0.895051\pi$
$114$	−0.135995	+	0.0941922i	−0.0127371	+	0.00882191i
$115$	1.89430	+	0.507576i	0.176644	+	0.0473317i
$116$	−5.90761	−	13.0147i	−0.548508	−	1.20839i
$117$	5.60765	−	1.50257i	0.518428	−	0.138912i
$118$	9.59547	−	3.43701i	0.883335	−	0.316403i
$119$	−0.904916	−	2.53753i	−0.0829535	−	0.232615i
$120$	3.36065	−	0.845460i	0.306784	−	0.0771796i
$121$	4.31298	+	2.49010i	0.392089	+	0.226373i
$122$	−4.19117	+	4.94330i	−0.379451	+	0.447545i
$123$	2.65968	−	9.92606i	0.239815	−	0.895003i
$124$	−16.8992	+	2.80194i	−1.51760	+	0.251621i
$125$	−6.44039	+	6.44039i	−0.576046	+	0.576046i
$126$	−0.570560	+	5.75079i	−0.0508296	+	0.512321i
$127$	−0.988901			−0.0877508			−0.0438754	−	0.999037i	$-0.513970\pi$
$127$	−0.988901			−0.0877508			−0.0438754	+	0.999037i	$0.513970\pi$
$128$	−10.0761	−	5.14520i	−0.890606	−	0.454776i
$129$	−3.82137	−	6.61880i	−0.336453	−	0.582753i
$130$	5.38015	−	0.442997i	0.471870	−	0.0388534i
$131$	−2.03878	−	7.60883i	−0.178129	−	0.664786i	−0.995998	−	0.0893811i	$-0.971511\pi$
$131$	−2.03878	−	7.60883i	−0.178129	−	0.664786i	0.817869	−	0.575405i	$-0.195156\pi$
$132$	3.75877	+	4.57370i	0.327159	+	0.398089i
$133$	−0.0206937	−	0.255696i	−0.00179437	−	0.0221716i
$134$	1.67220	+	4.66846i	0.144456	+	0.403293i
$135$	−4.82194	−	2.78395i	−0.415007	−	0.239604i
$136$	−2.00504	−	2.06751i	−0.171931	−	0.177287i
$137$	−9.57893	+	5.53040i	−0.818383	+	0.472494i	−0.849859	−	0.527011i	$-0.823313\pi$
$137$	−9.57893	+	5.53040i	−0.818383	+	0.472494i	0.0314753	+	0.999505i	$0.489979\pi$
$138$	0.588712	−	3.24175i	0.0501145	−	0.275956i
$139$	12.4154	+	12.4154i	1.05306	+	1.05306i	0.998511	+	0.0545473i	$0.0173716\pi$
$139$	12.4154	+	12.4154i	1.05306	+	1.05306i	0.0545473	+	0.998511i	$0.482628\pi$
$140$	−1.47751	+	5.16665i	−0.124872	+	0.436662i
$141$	10.2881	−	10.2881i	0.866411	−	0.866411i
$142$	6.31438	−	4.37344i	0.529891	−	0.367011i
$143$	4.61114	+	7.98672i	0.385603	+	0.667883i
$144$	1.99386	+	5.84745i	0.166155	+	0.487287i
$145$	−3.62873	+	6.28515i	−0.301350	+	0.521954i
$146$	−10.8416	−	5.12316i	−0.897256	−	0.423996i
$147$	6.85412	+	4.93357i	0.565318	+	0.406914i
$148$	1.55475	−	15.8970i	0.127800	−	1.30672i
$149$	−5.06147	+	1.35622i	−0.414652	+	0.111106i	−0.460113	−	0.887861i	$-0.652191\pi$
$149$	−5.06147	+	1.35622i	−0.414652	+	0.111106i	0.0454610	+	0.998966i	$0.485524\pi$
$150$	5.16471	+	4.37889i	0.421696	+	0.357535i
$151$	1.18073	−	0.681693i	0.0960862	−	0.0554754i	−0.451187	−	0.892429i	$-0.648999\pi$
$151$	1.18073	−	0.681693i	0.0960862	−	0.0554754i	0.547273	+	0.836954i	$0.315666\pi$
$152$	−0.133463	−	0.239578i	−0.0108253	−	0.0194323i
$153$			1.57271i			0.127146i
$154$	−9.05871	+	1.48894i	−0.729972	+	0.119982i
$155$	6.15051	+	6.15051i	0.494021	+	0.494021i
$156$	−1.48349	−	8.94732i	−0.118774	−	0.716359i
$157$	0.306970	+	0.0822524i	0.0244989	+	0.00656446i	0.271048	−	0.962566i	$-0.412630\pi$
$157$	0.306970	+	0.0822524i	0.0244989	+	0.00656446i	−0.246549	+	0.969130i	$0.579297\pi$
$158$	1.22226	−	0.100640i	0.0972374	−	0.00800645i
$159$	0.887981	−	1.53803i	0.0704215	−	0.121974i
$160$	0.852640	+	5.68117i	0.0674071	+	0.449136i
$161$	3.89242	+	3.30955i	0.306765	+	0.260829i
$162$	−1.19693	+	2.53294i	−0.0940400	+	0.199007i
$163$	−3.84175	−	14.3376i	−0.300909	−	1.12301i	−0.936410	−	0.350907i	$-0.885873\pi$
$163$	−3.84175	−	14.3376i	−0.300909	−	1.12301i	0.635501	−	0.772100i	$-0.280794\pi$
$164$	15.9478	+	5.98991i	1.24532	+	0.467733i
$165$	0.778022	−	2.90362i	0.0605689	−	0.226046i
$166$	10.7112	+	1.94518i	0.831347	+	0.150975i
$167$		−	14.5986i		−	1.12967i	−0.825204	−	0.564836i	$-0.808940\pi$
$167$		−	14.5986i		−	1.12967i	0.825204	−	0.564836i	$-0.191060\pi$
$168$	8.85462	+	1.76159i	0.683149	+	0.135910i
$169$		−	1.12842i		−	0.0868018i
$170$	−0.261306	+	1.43888i	−0.0200413	+	0.110357i
$171$	−0.0387596	+	0.144653i	−0.00296402	+	0.0110619i
$172$	11.5370	−	5.23685i	0.879688	−	0.399306i
$173$	−3.19660	−	11.9299i	−0.243033	−	0.907011i	−0.974362	−	0.224986i	$-0.927766\pi$
$173$	−3.19660	−	11.9299i	−0.243033	−	0.907011i	0.731329	−	0.682025i	$-0.238900\pi$
$174$	11.0240	+	5.20935i	0.835727	+	0.394920i
$175$	−9.89005	+	3.52692i	−0.747617	+	0.266610i
$176$	−8.15268	+	5.46357i	−0.614531	+	0.411832i
$177$	−4.34749	+	7.53008i	−0.326777	+	0.565995i
$178$	−0.526851	−	6.39855i	−0.0394892	−	0.479591i
$179$	0.455619	+	0.122083i	0.0340545	+	0.00912489i	0.275806	−	0.961213i	$-0.411055\pi$
$179$	0.455619	+	0.122083i	0.0340545	+	0.00912489i	−0.241752	+	0.970338i	$0.577722\pi$
$180$	1.82551	−	2.55118i	0.136066	−	0.190154i
$181$	15.4654	+	15.4654i	1.14953	+	1.14953i	0.986645	+	0.162887i	$0.0520807\pi$
$181$	15.4654	+	15.4654i	1.14953	+	1.14953i	0.162887	+	0.986645i	$0.447919\pi$
$182$	13.1591	+	4.96349i	0.975417	+	0.367918i
$183$		−	5.52873i		−	0.408696i
$184$	5.25356	+	1.49441i	0.387298	+	0.110170i
$185$	−7.02396	+	4.05528i	−0.516412	+	0.298150i
$186$	9.45031	−	11.1462i	0.692930	−	0.817280i
$187$	−2.41319	+	0.646613i	−0.176470	+	0.0472850i
$188$	15.3142	+	18.6344i	1.11690	+	1.35905i
$189$	−8.24262	−	11.9364i	−0.599562	−	0.868242i
$190$	−0.0594956	+	0.125904i	−0.00431627	+	0.00913405i
$191$	−3.04108	+	5.26731i	−0.220045	+	0.381129i	−0.954821	−	0.297180i	$-0.903954\pi$
$191$	−3.04108	+	5.26731i	−0.220045	+	0.381129i	0.734776	+	0.678309i	$0.237287\pi$
$192$	9.39486	−	2.21088i	0.678016	−	0.159557i
$193$	−5.03089	−	8.71375i	−0.362131	−	0.627229i	0.626180	−	0.779678i	$-0.284617\pi$
$193$	−5.03089	−	8.71375i	−0.362131	−	0.627229i	−0.988311	+	0.152449i	$0.951284\pi$
$194$	−13.2077	−	19.0694i	−0.948261	−	1.36910i
$195$	−3.25639	+	3.25639i	−0.233195	+	0.233195i
$196$	−9.24590	+	10.5125i	−0.660422	+	0.750895i
$197$	−10.0837	−	10.0837i	−0.718432	−	0.718432i	0.249852	−	0.968284i	$-0.419618\pi$
$197$	−10.0837	−	10.0837i	−0.718432	−	0.718432i	−0.968284	+	0.249852i	$0.919618\pi$
$198$	5.27291	+	0.957578i	0.374730	+	0.0680521i
$199$	10.0980	−	5.83005i	0.715825	−	0.413282i	−0.0973893	−	0.995246i	$-0.531049\pi$
$199$	10.0980	−	5.83005i	0.715825	−	0.413282i	0.813214	+	0.581965i	$0.197716\pi$
$200$	−8.05814	+	7.81466i	−0.569796	+	0.552580i
$201$	−3.66359	−	2.11517i	−0.258409	−	0.149193i
$202$	−12.2454	+	4.38620i	−0.861584	+	0.308612i
$203$	−15.5584	+	10.7438i	−1.09199	+	0.754069i
$204$	2.44526	+	0.239150i	0.171202	+	0.0167439i
$205$	−2.23885	−	8.35549i	−0.156368	−	0.583572i
$206$	−0.897128	−	10.8955i	−0.0625058	−	0.759126i
$207$	−1.49130	−	2.58301i	−0.103653	−	0.179532i
$208$	15.0016	−	1.00384i	1.04017	−	0.0696038i
$209$	−0.237894			−0.0164555
$210$	−1.88896	−	4.17698i	−0.130351	−	0.288239i
$211$	6.53423	−	6.53423i	0.449835	−	0.449835i	−0.445465	−	0.895300i	$-0.646962\pi$
$211$	6.53423	−	6.53423i	0.449835	−	0.449835i	0.895300	+	0.445465i	$0.146962\pi$
$212$	2.39431	+	1.71326i	0.164442	+	0.117667i
$213$	−1.69592	+	6.32927i	−0.116203	+	0.433674i
$214$	−20.3866	−	17.2848i	−1.39360	−	1.18156i
$215$	−5.57153	−	3.21672i	−0.379975	−	0.219379i
$216$	−13.3092	−	7.95872i	−0.905579	−	0.541522i
$217$	7.61163	+	21.3442i	0.516711	+	1.44894i
$218$	−7.80192	−	21.7815i	−0.528413	−	1.47523i
$219$	9.88082	−	2.64756i	0.667684	−	0.178905i
$220$	4.66514	+	1.75220i	0.314523	+	0.118133i
$221$	3.69698	+	0.990604i	0.248686	+	0.0666352i
$222$	7.75844	+	11.2017i	0.520712	+	0.751806i
$223$	−23.3350			−1.56263			−0.781315	−	0.624137i	$-0.785451\pi$
$223$	−23.3350			−1.56263			−0.781315	+	0.624137i	$0.785451\pi$
$224$	−4.33527	+	14.3250i	−0.289662	+	0.957129i
$225$	6.12964			0.408643
$226$	16.1973	+	23.3856i	1.07743	+	1.55559i
$227$	15.1161	+	4.05036i	1.00329	+	0.268832i	0.722824	−	0.691032i	$-0.242844\pi$
$227$	15.1161	+	4.05036i	1.00329	+	0.268832i	0.280468	+	0.959863i	$0.409510\pi$
$228$	0.219013	+	0.0822601i	0.0145045	+	0.00544781i
$229$	−25.8292	+	6.92092i	−1.70684	+	0.457347i	−0.974647	−	0.223747i	$-0.928171\pi$
$229$	−25.8292	+	6.92092i	−1.70684	+	0.457347i	−0.732196	+	0.681094i	$0.761504\pi$
$230$	−0.935237	−	2.61100i	−0.0616677	−	0.172164i
$231$	5.07295	−	5.96637i	0.333775	−	0.392558i
$232$	−10.3738	+	17.3479i	−0.681072	+	1.13895i
$233$	−11.0402	−	6.37405i	−0.723267	−	0.417578i	0.0926872	−	0.995695i	$-0.470454\pi$
$233$	−11.0402	−	6.37405i	−0.723267	−	0.417578i	−0.815954	+	0.578117i	$0.803788\pi$
$234$	−6.26229	−	5.30948i	−0.409379	−	0.347092i
$235$	3.16986	−	11.8301i	0.206779	−	0.771708i
$236$	−11.7224	−	8.38801i	−0.763061	−	0.546013i
$237$	−0.739782	+	0.739782i	−0.0480540	+	0.0480540i
$238$	−2.22144	+	3.09533i	−0.143994	+	0.200640i
$239$	14.9688			0.968253			0.484127	−	0.874998i	$-0.339137\pi$
$239$	14.9688			0.968253			0.484127	+	0.874998i	$0.339137\pi$
$240$	−3.68901	−	3.22627i	−0.238124	−	0.208255i
$241$	−9.90526	−	17.1564i	−0.638054	−	1.10514i	−0.985859	−	0.167575i	$-0.946406\pi$
$241$	−9.90526	−	17.1564i	−0.638054	−	1.10514i	0.347805	−	0.937567i	$-0.386927\pi$
$242$	−0.577964	−	7.01931i	−0.0371530	−	0.451218i
$243$	3.63850	+	13.5791i	0.233410	+	0.871098i
$244$	9.12186	+	0.892134i	0.583967	+	0.0571130i
$245$	7.07310	+	0.711747i	0.451884	+	0.0454718i
$246$	−13.6816	+	4.90061i	−0.872305	+	0.312452i
$247$	0.315624	+	0.182226i	0.0200827	+	0.0115947i
$248$	16.8652	+	17.3907i	1.07094	+	1.10431i
$249$	−8.04272	+	4.64346i	−0.509686	+	0.294268i
$250$	12.6735	+	2.30155i	0.801542	+	0.145563i
$251$	9.23966	+	9.23966i	0.583202	+	0.583202i	0.935782	−	0.352580i	$-0.114695\pi$
$251$	9.23966	+	9.23966i	0.583202	+	0.583202i	−0.352580	+	0.935782i	$0.614695\pi$
$252$	7.14523	−	3.96736i	0.450107	−	0.249920i
$253$	3.35028	−	3.35028i	0.210630	−	0.210630i
$254$	0.796289	+	1.14968i	0.0499636	+	0.0721376i
$255$	−0.623780	−	1.08042i	−0.0390626	−	0.0676584i
$256$	2.13176	+	15.8574i	0.133235	+	0.991084i
$257$	−11.6109	+	20.1107i	−0.724271	+	1.25447i	0.235003	+	0.971995i	$0.424490\pi$
$257$	−11.6109	+	20.1107i	−0.724271	+	1.25447i	−0.959273	+	0.282479i	$0.908843\pi$
$258$	−4.61788	+	9.77231i	−0.287496	+	0.608398i
$259$	−21.0612	+	1.70450i	−1.30868	+	0.105913i
$260$	−4.84726	−	5.89818i	−0.300614	−	0.365790i
$261$	10.6615	−	2.85675i	0.659933	−	0.176828i
$262$	−7.20425	+	8.49709i	−0.445080	+	0.524952i
$263$	−3.91454	+	2.26006i	−0.241381	+	0.139361i	−0.615811	−	0.787894i	$-0.711172\pi$
$263$	−3.91454	+	2.26006i	−0.241381	+	0.139361i	0.374430	+	0.927255i	$0.377838\pi$
$264$	2.29067	−	8.05276i	0.140981	−	0.495613i
$265$		−	1.49496i		−	0.0918345i
$266$	−0.280606	+	0.229951i	−0.0172050	+	0.0140992i
$267$	3.87278	+	3.87278i	0.237011	+	0.237011i
$268$	4.08099	−	5.70325i	0.249286	−	0.348381i
$269$	−0.385363	−	0.103258i	−0.0234960	−	0.00629574i	0.247052	−	0.969002i	$-0.420538\pi$
$269$	−0.385363	−	0.103258i	−0.0234960	−	0.00629574i	−0.270548	+	0.962707i	$0.587205\pi$
$270$	0.646168	+	7.84764i	0.0393246	+	0.477592i
$271$	−5.31084	+	9.19864i	−0.322611	+	0.558778i	−0.981026	−	0.193877i	$-0.937894\pi$
$271$	−5.31084	+	9.19864i	−0.322611	+	0.558778i	0.658415	+	0.752655i	$0.271227\pi$
$272$	−0.789149	+	3.99584i	−0.0478492	+	0.242284i
$273$	−11.3007	+	4.02998i	−0.683949	+	0.243906i
$274$	14.1428	+	6.68313i	0.854397	+	0.403742i
$275$	2.52018	+	9.40545i	0.151973	+	0.567170i
$276$	−4.24286	+	1.92591i	−0.255390	+	0.115926i
$277$	−2.98011	+	11.1219i	−0.179058	+	0.668252i	0.816767	+	0.576967i	$0.195764\pi$
$277$	−2.98011	+	11.1219i	−0.179058	+	0.668252i	−0.995825	+	0.0912848i	$0.970903\pi$
$278$	4.43678	−	24.4312i	0.266100	−	1.46528i
$279$		−	13.2287i		−	0.791981i
$280$	7.19642	−	2.44259i	0.430068	−	0.145973i
$281$			18.6360i			1.11173i	0.831272	+	0.555866i	$0.187613\pi$
$281$			18.6360i			1.11173i	−0.831272	+	0.555866i	$0.812387\pi$
$282$	−20.2450	−	3.67656i	−1.20557	−	0.218936i
$283$	2.35222	−	8.77861i	0.139825	−	0.521834i	−0.860106	−	0.510115i	$-0.829603\pi$
$283$	2.35222	−	8.77861i	0.139825	−	0.521834i	0.999931	−	0.0117192i	$-0.00373043\pi$
$284$	−10.1690	−	3.81942i	−0.603420	−	0.226641i
$285$	−0.0307463	−	0.114747i	−0.00182125	−	0.00679701i
$286$	5.57226	−	11.7920i	0.329495	−	0.697274i
$287$	4.05777	−	22.1677i	0.239523	−	1.30852i
$288$	5.19267	−	7.02655i	0.305981	−	0.414044i
$289$	7.98158	−	13.8245i	0.469505	−	0.813206i
$290$	10.2290	−	0.842247i	0.600667	−	0.0494585i
$291$	19.1143	+	5.12167i	1.12050	+	0.300238i
$292$	2.77381	+	16.7296i	0.162325	+	0.979026i
$293$	−12.0193	−	12.0193i	−0.702174	−	0.702174i	0.262703	−	0.964877i	$-0.415386\pi$
$293$	−12.0193	−	12.0193i	−0.702174	−	0.702174i	−0.964877	+	0.262703i	$0.915386\pi$
$294$	0.216586	−	11.9412i	0.0126316	−	0.696422i
$295$			7.31920i			0.426140i
$296$	−19.7336	+	10.9931i	−1.14699	+	0.638962i
$297$	−11.6497	+	6.72594i	−0.675982	+	0.390278i
$298$	5.65235	+	4.79234i	0.327432	+	0.277613i
$299$	−7.01125	+	1.87866i	−0.405471	+	0.108646i
$300$	0.932092	−	9.53042i	0.0538143	−	0.550239i
$301$	−9.52396	−	13.7919i	−0.548952	−	0.794952i
$302$	−1.74328	−	0.823782i	−0.100315	−	0.0474033i
$303$	5.54812	−	9.60962i	0.318731	−	0.552058i
$304$	−0.171062	+	0.348077i	−0.00981106	+	0.0199636i
$305$	−2.32697	−	4.03043i	−0.133242	−	0.230781i
$306$	1.82841	−	1.26638i	0.104523	−	0.0723944i
$307$	17.8339	−	17.8339i	1.01784	−	1.01784i	0.0179975	−	0.999838i	$-0.494271\pi$
$307$	17.8339	−	17.8339i	1.01784	−	1.01784i	0.999838	−	0.0179975i	$-0.00572909\pi$
$308$	9.02534	+	9.33262i	0.514266	+	0.531775i
$309$	6.59462	+	6.59462i	0.375155	+	0.375155i
$310$	2.19795	−	12.1031i	0.124835	−	0.687407i
$311$	−5.66778	+	3.27229i	−0.321390	+	0.185555i	−0.652012	−	0.758209i	$-0.726075\pi$
$311$	−5.66778	+	3.27229i	−0.321390	+	0.185555i	0.330622	+	0.943763i	$0.392742\pi$
$312$	−9.20750	+	8.92930i	−0.521272	+	0.505522i
$313$	16.6047	+	9.58671i	0.938551	+	0.541873i	0.889506	−	0.456924i	$-0.151049\pi$
$313$	16.6047	+	9.58671i	0.938551	+	0.541873i	0.0490453	+	0.998797i	$0.484382\pi$
$314$	−0.151555	−	0.423112i	−0.00855274	−	0.0238776i
$315$	−3.74960	−	1.77828i	−0.211266	−	0.100195i
$316$	−1.10119	−	1.33994i	−0.0619470	−	0.0753776i
$317$	4.87115	+	18.1794i	0.273591	+	1.02106i	0.956780	+	0.290814i	$0.0939260\pi$
$317$	4.87115	+	18.1794i	0.273591	+	1.02106i	−0.683189	+	0.730242i	$0.739407\pi$
$318$	−2.50312	+	0.206105i	−0.140368	+	0.0115578i
$319$	8.76691	+	15.1847i	0.490853	+	0.850182i
$320$	5.91829	−	5.56590i	0.330842	−	0.311143i
$321$	22.8010			1.27263
$322$	0.713372	−	7.19022i	0.0397547	−	0.400695i
$323$	−0.0698127	+	0.0698127i	−0.00388448	+	0.00388448i
$324$	3.90857	−	0.648051i	0.217143	−	0.0360028i
$325$	3.86089	−	14.4090i	0.214164	−	0.799270i
$326$	−13.5752	+	16.0114i	−0.751863	+	0.886788i
$327$	17.0931	+	9.86868i	0.945248	+	0.545739i
$328$	−5.87783	−	23.3640i	−0.324549	−	1.29006i
$329$	20.6685	−	24.3085i	1.13949	−	1.34017i
$330$	−4.00219	+	1.43355i	−0.220313	+	0.0789143i
$331$	−9.45985	+	2.53476i	−0.519960	+	0.139323i	−0.509248	−	0.860620i	$-0.670076\pi$
$331$	−9.45985	+	2.53476i	−0.519960	+	0.139323i	−0.0107120	+	0.999943i	$0.503410\pi$
$332$	−6.36346	−	14.0190i	−0.349240	−	0.769391i
$333$	11.9148	+	3.19255i	0.652926	+	0.174951i
$334$	−16.9721	+	11.7552i	−0.928673	+	0.643213i
$335$	−3.56099			−0.194558
$336$	−5.08196	−	11.7128i	−0.277244	−	0.638983i
$337$	4.91600			0.267792			0.133896	−	0.990995i	$-0.457251\pi$
$337$	4.91600			0.267792			0.133896	+	0.990995i	$0.457251\pi$
$338$	−1.31189	+	0.908636i	−0.0713575	+	0.0494233i
$339$	−23.4408	−	6.28094i	−1.27313	−	0.341134i
$340$	1.88324	−	0.854836i	0.102133	−	0.0463600i
$341$	20.2984	−	5.43893i	1.09922	−	0.294535i
$342$	0.199382	−	0.0714167i	0.0107813	−	0.00386178i
$343$	15.8551	+	9.57166i	0.856093	+	0.516821i
$344$	−15.3782	−	9.19593i	−0.829137	−	0.495811i
$345$	2.04899	+	1.18299i	0.110314	+	0.0636898i
$346$	−11.2955	+	13.3226i	−0.607252	+	0.716226i
$347$	2.42076	−	9.03438i	0.129953	−	0.484991i	−0.870015	−	0.493026i	$-0.835891\pi$
$347$	2.42076	−	9.03438i	0.129953	−	0.484991i	0.999968	+	0.00803463i	$0.00255753\pi$
$348$	−2.82048	−	17.0111i	−0.151193	−	0.911889i
$349$	−17.2061	+	17.2061i	−0.921021	+	0.921021i	−0.997102	−	0.0760810i	$-0.975759\pi$
$349$	−17.2061	+	17.2061i	−0.921021	+	0.921021i	0.0760810	+	0.997102i	$0.475759\pi$
$350$	12.0641	+	8.65808i	0.644852	+	0.462794i
$351$	20.6081			1.09998
$352$	12.9166	+	5.07879i	0.688459	+	0.270701i
$353$	4.08472	+	7.07494i	0.217408	+	0.376561i	0.954015	−	0.299760i	$-0.0969066\pi$
$353$	4.08472	+	7.07494i	0.217408	+	0.376561i	−0.736607	+	0.676321i	$0.763573\pi$
$354$	12.2551	−	1.00907i	0.651351	−	0.0536317i
$355$	1.42758	+	5.32780i	0.0757681	+	0.282771i
$356$	−7.01464	+	5.76479i	−0.371775	+	0.305533i
$357$	−0.262185	−	3.23961i	−0.0138763	−	0.171459i
$358$	−0.224944	−	0.628001i	−0.0118887	−	0.0331909i
$359$	−10.0193	−	5.78465i	−0.528799	−	0.305302i	0.211728	−	0.977329i	$-0.432091\pi$
$359$	−10.0193	−	5.78465i	−0.528799	−	0.305302i	−0.740527	+	0.672027i	$0.765424\pi$
$360$	−4.43592	−	0.0680425i	−0.233794	−	0.00358615i
$361$	16.4463	−	9.49530i	0.865597	−	0.499753i
$362$	5.52673	−	30.4330i	0.290478	−	1.59952i
$363$	4.24851	+	4.24851i	0.222989	+	0.222989i
$364$	−4.82555	−	19.2953i	−0.252928	−	1.01135i
$365$	6.08876	−	6.08876i	0.318700	−	0.318700i
$366$	−6.42764	+	4.45188i	−0.335978	+	0.232703i
$367$	−4.25356	−	7.36738i	−0.222034	−	0.384574i	0.733392	−	0.679807i	$-0.237936\pi$
$367$	−4.25356	−	7.36738i	−0.222034	−	0.384574i	−0.955425	+	0.295232i	$0.904603\pi$
$368$	−2.49292	−	7.31107i	−0.129952	−	0.381116i
$369$	−6.57792	+	11.3933i	−0.342433	+	0.593111i
$370$	10.3705	+	4.90055i	0.539136	+	0.254767i
$371$	1.66894	−	3.51904i	0.0866469	−	0.182699i
$372$	−20.5681	−	2.01159i	−1.06641	−	0.104296i
$373$	−5.06649	+	1.35756i	−0.262333	+	0.0702919i	−0.387588	−	0.921833i	$-0.626692\pi$
$373$	−5.06649	+	1.35756i	−0.262333	+	0.0702919i	0.125255	+	0.992125i	$0.460025\pi$
$374$	2.69491	+	2.28488i	0.139350	+	0.118148i
$375$	−9.51618	+	5.49417i	−0.491414	+	0.283718i
$376$	9.33275	−	32.8090i	0.481300	−	1.69199i
$377$		−	26.8616i		−	1.38344i
$378$	−7.23989	+	19.1942i	−0.372380	+	0.987245i
$379$	−3.62966	−	3.62966i	−0.186443	−	0.186443i	0.607713	−	0.794156i	$-0.292087\pi$
$379$	−3.62966	−	3.62966i	−0.186443	−	0.186443i	−0.794156	+	0.607713i	$0.792087\pi$
$380$	0.194282	−	0.0322125i	0.00996647	−	0.00165246i
$381$	−1.15239	−	0.308783i	−0.0590390	−	0.0158194i
$382$	8.57247	−	0.705850i	0.438605	−	0.0361144i
$383$	3.48127	−	6.02973i	0.177884	−	0.308105i	−0.763271	−	0.646078i	$-0.776408\pi$
$383$	3.48127	−	6.02973i	0.177884	−	0.308105i	0.941156	+	0.337973i	$0.109741\pi$
$384$	−10.1353	−	9.14209i	−0.517217	−	0.466530i
$385$	1.18700	−	6.48460i	0.0604950	−	0.330486i
$386$	−6.07950	+	12.8654i	−0.309438	+	0.654831i
$387$	2.53239	+	9.45101i	0.128729	+	0.480422i
$388$	−11.5346	+	30.7103i	−0.585581	+	1.55908i
$389$	−3.41145	+	12.7317i	−0.172967	+	0.645523i	0.823922	+	0.566704i	$0.191782\pi$
$389$	−3.41145	+	12.7317i	−0.172967	+	0.645523i	−0.996889	+	0.0788190i	$0.974885\pi$
$390$	6.40797	+	1.16371i	0.324480	+	0.0589267i
$391$		−	1.96636i		−	0.0994429i
$392$	19.6668	+	2.28421i	0.993323	+	0.115370i
$393$		−	9.50339i		−	0.479383i
$394$	−3.60352	+	19.8428i	−0.181543	+	0.999665i
$395$	−0.227934	+	0.850663i	−0.0114686	+	0.0428015i
$396$	−3.13262	−	6.90129i	−0.157420	−	0.346803i
$397$	1.61554	+	6.02928i	0.0810817	+	0.302601i	0.994543	−	0.104324i	$-0.0332678\pi$
$397$	1.61554	+	6.02928i	0.0810817	+	0.302601i	−0.913462	+	0.406925i	$0.866601\pi$
$398$	−14.9091	−	7.04524i	−0.747325	−	0.353146i
$399$	0.0557258	−	0.304431i	0.00278978	−	0.0152406i
$400$	15.5739	+	3.07572i	0.778693	+	0.153786i
$401$	7.95077	−	13.7711i	0.397042	−	0.687697i	−0.596317	−	0.802749i	$-0.703370\pi$
$401$	7.95077	−	13.7711i	0.397042	−	0.687697i	0.993360	+	0.115051i	$0.0367033\pi$
$402$	0.490942	+	5.96243i	0.0244860	+	0.297379i
$403$	−31.0969	−	8.33239i	−1.54905	−	0.415066i
$404$	14.9597	+	10.7045i	0.744271	+	0.532568i
$405$	−1.42253	−	1.42253i	−0.0706861	−	0.0706861i
$406$	25.0187	+	9.43682i	1.24166	+	0.468342i
$407$			19.5949i			0.971282i
$408$	−1.69095	−	3.03540i	−0.0837146	−	0.150275i
$409$	4.93864	−	2.85133i	0.244200	−	0.140989i	−0.372906	−	0.927869i	$-0.621638\pi$
$409$	4.93864	−	2.85133i	0.244200	−	0.140989i	0.617106	+	0.786880i	$0.288305\pi$
$410$	−7.91121	+	9.33091i	−0.390707	+	0.460821i
$411$	−12.8895	+	3.45372i	−0.635791	+	0.170360i
$412$	−11.9446	+	9.81634i	−0.588468	+	0.483616i
$413$	−8.17099	+	17.2289i	−0.402068	+	0.847781i
$414$	−1.80214	+	3.81368i	−0.0885704	+	0.187432i
$415$	−3.90874	+	6.77014i	−0.191873	+	0.332333i
$416$	−13.2467	−	16.6323i	−0.649473	−	0.815467i
$417$	10.5913	+	18.3447i	0.518659	+	0.898343i
$418$	0.191558	+	0.276573i	0.00936943	+	0.0135276i
$419$	−4.57142	+	4.57142i	−0.223328	+	0.223328i	−0.809898	−	0.586570i	$-0.800478\pi$
$419$	−4.57142	+	4.57142i	−0.223328	+	0.223328i	0.586570	+	0.809898i	$0.300478\pi$
$420$	−3.33507	+	5.55950i	−0.162735	+	0.271276i
$421$	0.421252	+	0.421252i	0.0205306	+	0.0205306i	0.717298	−	0.696767i	$-0.245379\pi$
$421$	0.421252	+	0.421252i	0.0205306	+	0.0205306i	−0.696767	+	0.717298i	$0.745379\pi$
$422$	−12.8581	−	2.33508i	−0.625925	−	0.113670i
$423$	−16.1311	+	9.31331i	−0.784322	+	0.452829i
$424$	0.0638586	−	4.16316i	0.00310125	−	0.202181i
$425$	3.49971	+	2.02056i	0.169761	+	0.0980115i
$426$	8.72393	−	3.12483i	0.422676	−	0.151399i
$427$	−0.978062	−	12.0852i	−0.0473317	−	0.584841i
$428$	−3.67924	+	37.6194i	−0.177843	+	1.81840i
$429$	2.87964	+	10.7470i	0.139031	+	0.518869i
$430$	0.746617	+	9.06758i	0.0360051	+	0.437278i
$431$	10.5518	+	18.2762i	0.508262	+	0.880336i	0.999954	+	0.00956658i	$0.00304518\pi$
$431$	10.5518	+	18.2762i	0.508262	+	0.880336i	−0.491692	+	0.870769i	$0.663621\pi$
$432$	1.46423	+	21.8817i	0.0704479	+	1.05279i
$433$	−13.9717			−0.671436			−0.335718	−	0.941962i	$-0.608979\pi$
$433$	−13.9717			−0.671436			−0.335718	+	0.941962i	$0.608979\pi$
$434$	18.6854	−	26.0361i	0.896930	−	1.24977i
$435$	−6.19120	+	6.19120i	−0.296845	+	0.296845i
$436$	−19.0405	+	26.6094i	−0.911877	+	1.27436i
$437$	0.0484611	−	0.180859i	0.00231821	−	0.00865168i
$438$	−11.0343	−	9.35544i	−0.527240	−	0.447020i
$439$	4.69322	+	2.70963i	0.223995	+	0.129324i	0.607799	−	0.794091i	$-0.292053\pi$
$439$	4.69322	+	2.70963i	0.223995	+	0.129324i	−0.383804	+	0.923415i	$0.625386\pi$
$440$	−1.71941	−	6.83455i	−0.0819696	−	0.325824i
$441$	−6.84109	−	8.37194i	−0.325766	−	0.398664i
$442$	−1.82525	−	5.09573i	−0.0868181	−	0.242379i
$443$	−5.83698	+	1.56401i	−0.277323	+	0.0743085i	−0.394800	−	0.918767i	$-0.629186\pi$
$443$	−5.83698	+	1.56401i	−0.277323	+	0.0743085i	0.117477	+	0.993076i	$0.462519\pi$
$444$	6.77561	−	18.0397i	0.321556	−	0.856128i
$445$	4.45325	+	1.19324i	0.211104	+	0.0565652i
$446$	18.7900	+	27.1290i	0.889732	+	1.28460i
$447$	−6.32175			−0.299009
$448$	20.1449	−	6.49473i	0.951759	−	0.306847i
$449$	18.4262			0.869587			0.434794	−	0.900530i	$-0.356821\pi$
$449$	18.4262			0.869587			0.434794	+	0.900530i	$0.356821\pi$
$450$	−4.93575	−	7.12625i	−0.232673	−	0.335934i
$451$	−20.1866	−	5.40898i	−0.950550	−	0.254699i
$452$	14.1454	−	37.6615i	0.665344	−	1.77145i
$453$	1.58879	−	0.425716i	0.0746480	−	0.0200019i
$454$	−7.46301	−	20.8353i	−0.350257	−	0.977848i
$455$	−6.54201	+	7.69415i	−0.306694	+	0.360707i
$456$	−0.0807208	−	0.320860i	−0.00378010	−	0.0150257i
$457$	−31.1530	−	17.9862i	−1.45728	−	0.841358i	−0.458399	−	0.888747i	$-0.651577\pi$
$457$	−31.1530	−	17.9862i	−1.45728	−	0.841358i	−0.998877	+	0.0473884i	$0.984910\pi$
$458$	28.8445	+	24.4558i	1.34782	+	1.14275i
$459$	−1.44492	+	5.39253i	−0.0674433	+	0.251702i
$460$	−2.28244	+	3.18974i	−0.106419	+	0.148723i
$461$	−0.903879	+	0.903879i	−0.0420978	+	0.0420978i	−0.727842	−	0.685745i	$-0.759477\pi$
$461$	−0.903879	+	0.903879i	−0.0420978	+	0.0420978i	0.685745	+	0.727842i	$0.259477\pi$
$462$	−11.0213	−	1.09347i	−0.512757	−	0.0508728i
$463$	−12.5999			−0.585565			−0.292782	−	0.956179i	$-0.594581\pi$
$463$	−12.5999			−0.585565			−0.292782	+	0.956179i	$0.594581\pi$
$464$	28.5217	−	1.90855i	1.32409	−	0.0886022i
$465$	5.24687	+	9.08785i	0.243318	+	0.421439i
$466$	1.47945	+	17.9677i	0.0685342	+	0.832340i
$467$	−2.14538	−	8.00668i	−0.0992765	−	0.370505i	0.898357	−	0.439267i	$-0.144762\pi$
$467$	−2.14538	−	8.00668i	−0.0992765	−	0.370505i	−0.997633	+	0.0687620i	$0.978095\pi$
$468$	−1.13018	+	11.5558i	−0.0522424	+	0.534167i
$469$	−8.38235	−	3.97541i	−0.387061	−	0.183567i
$470$	−16.3059	+	5.84064i	−0.752137	+	0.269409i
$471$	0.332038	+	0.191702i	0.0152995	+	0.00883318i
$472$	−0.312647	+	20.3825i	−0.0143907	+	0.938181i
$473$	−13.4606	+	7.77151i	−0.618921	+	0.357334i
$474$	1.45575	+	0.264370i	0.0668650	+	0.0121429i
$475$	0.272096	+	0.272096i	0.0124846	+	0.0124846i
$476$	5.38735	+	0.0901754i	0.246929	+	0.00413318i
$477$	−1.60770	+	1.60770i	−0.0736114	+	0.0736114i
$478$	−12.0533	−	17.4026i	−0.551305	−	0.795975i
$479$	−4.63918	−	8.03529i	−0.211969	−	0.367142i	0.740361	−	0.672209i	$-0.234654\pi$
$479$	−4.63918	−	8.03529i	−0.211969	−	0.367142i	−0.952331	+	0.305067i	$0.901321\pi$
$480$	−0.780333	+	6.88667i	−0.0356172	+	0.314332i
$481$	15.0096	−	25.9974i	0.684378	−	1.18538i
$482$	−11.9699	+	25.3305i	−0.545212	+	1.15377i
$483$	3.50254	+	5.07212i	0.159371	+	0.230790i
$484$	−7.69517	+	6.32407i	−0.349781	+	0.287458i
$485$	16.0899	−	4.31128i	0.730606	−	0.195765i
$486$	12.8570	−	15.1643i	0.583207	−	0.687867i
$487$	−33.5037	+	19.3434i	−1.51820	+	0.876533i	−0.518429	+	0.855121i	$0.673483\pi$
$487$	−33.5037	+	19.3434i	−1.51820	+	0.876533i	−0.999771	+	0.0214118i	$0.993184\pi$
$488$	−6.30798	−	11.3233i	−0.285549	−	0.512583i
$489$		−	17.9076i		−	0.809810i
$490$	−4.86798	−	8.79622i	−0.219913	−	0.397373i
$491$	−29.8086	−	29.8086i	−1.34524	−	1.34524i	−0.890750	−	0.454494i	$-0.849820\pi$
$491$	−29.8086	−	29.8086i	−1.34524	−	1.34524i	−0.454494	−	0.890750i	$-0.650180\pi$
$492$	16.7141	+	11.9599i	0.753532	+	0.539195i
$493$	7.02889	+	1.88338i	0.316565	+	0.0848234i
$494$	−0.0422954	−	0.513673i	−0.00190296	−	0.0231113i
$495$	−1.92420	+	3.33282i	−0.0864865	+	0.149799i
$496$	6.63786	−	33.6107i	0.298049	−	1.50917i
$497$	−2.58740	+	14.1350i	−0.116061	+	0.634044i
$498$	11.8746	+	5.61132i	0.532115	+	0.251449i
$499$	−2.89367	−	10.7993i	−0.129538	−	0.483444i	0.870422	−	0.492306i	$-0.163846\pi$
$499$	−2.89367	−	10.7993i	−0.129538	−	0.483444i	−0.999961	+	0.00886191i	$0.997179\pi$
$500$	−7.52928	−	16.5873i	−0.336720	−	0.741808i
$501$	4.55839	−	17.0121i	0.203654	−	0.760046i
$502$	3.30190	−	18.1819i	0.147371	−	0.811499i
$503$			18.1532i			0.809409i	0.914448	+	0.404704i	$0.132626\pi$
$503$			18.1532i			0.809409i	−0.914448	+	0.404704i	$0.867374\pi$
$504$	−10.3659	−	5.11233i	−0.461735	−	0.227721i
$505$		−	9.34050i		−	0.415647i
$506$	−6.59273	−	1.19726i	−0.293082	−	0.0532248i
$507$	0.352349	−	1.31498i	0.0156484	−	0.0584005i
$508$	0.695416	−	1.85151i	0.0308541	−	0.0821475i
$509$	0.530258	+	1.97895i	0.0235033	+	0.0877154i	0.976681	−	0.214694i	$-0.0688756\pi$
$509$	0.530258	+	1.97895i	0.0235033	+	0.0877154i	−0.953178	+	0.302410i	$0.902209\pi$
$510$	−0.753798	+	1.59518i	−0.0333787	+	0.0706358i
$511$	21.1299	−	7.53522i	0.934733	−	0.333338i
$512$	16.7190	−	15.2471i	0.738883	−	0.673834i
$513$	−0.265799	+	0.460378i	−0.0117353	+	0.0203262i
$514$	32.7299	−	2.69496i	1.44366	−	0.118869i
$515$	7.58304	+	2.03187i	0.334149	+	0.0895348i
$516$	15.0796	−	2.50024i	0.663843	−	0.110067i
$517$	−20.9228	−	20.9228i	−0.920183	−	0.920183i
$518$	18.9407	+	23.1130i	0.832205	+	1.01553i
$519$		−	14.9004i		−	0.654053i
$520$	−2.95401	+	10.3847i	−0.129542	+	0.455401i
$521$	−2.51905	+	1.45437i	−0.110361	+	0.0637172i	−0.554165	−	0.832407i	$-0.686962\pi$
$521$	−2.51905	+	1.45437i	−0.110361	+	0.0637172i	0.443803	+	0.896124i	$0.353629\pi$
$522$	−11.9062	−	10.0946i	−0.521119	−	0.441831i
$523$	−16.0023	+	4.28781i	−0.699732	+	0.187493i	−0.591111	−	0.806590i	$-0.701310\pi$
$523$	−16.0023	+	4.28781i	−0.699732	+	0.187493i	−0.108622	+	0.994083i	$0.534644\pi$
$524$	15.6797	+	1.53350i	0.684969	+	0.0669911i
$525$	−12.6264	+	1.02187i	−0.551063	+	0.0445980i
$526$	5.77962	+	2.73114i	0.252003	+	0.119083i
$527$	4.36067	−	7.55290i	0.189954	−	0.329010i
$528$	−11.2065	+	3.82119i	−0.487702	+	0.166296i
$529$	−9.63542	−	16.6890i	−0.418931	−	0.725611i
$530$	−1.73802	+	1.20378i	−0.0754947	+	0.0522888i
$531$	7.87117	−	7.87117i	0.341580	−	0.341580i
$532$	0.493290	+	0.141066i	0.0213868	+	0.00611599i
$533$	22.6392	+	22.6392i	0.980611	+	0.980611i
$534$	1.38398	−	7.62092i	0.0598909	−	0.329789i
$535$	16.6219	−	9.59663i	0.718625	−	0.414899i
$536$	−9.91665	−	0.152111i	−0.428334	−	0.00657020i
$537$	0.492826	+	0.284533i	0.0212670	+	0.0122785i
$538$	0.190258	+	0.531165i	0.00820262	+	0.0229001i
$539$	10.0334	−	13.9392i	0.432168	−	0.600404i
$540$	8.60326	−	7.07035i	0.370225	−	0.304260i
$541$	1.87978	+	7.01543i	0.0808180	+	0.301617i	0.994489	−	0.104837i	$-0.0334320\pi$
$541$	1.87978	+	7.01543i	0.0808180	+	0.301617i	−0.913671	+	0.406453i	$0.866765\pi$
$542$	14.9707	−	1.23267i	0.643045	−	0.0529478i
$543$	13.1932	+	22.8513i	0.566174	+	0.980643i
$544$	5.28096	−	2.30010i	0.226419	−	0.0986161i
$545$	16.6144			0.711682
$546$	13.7848	+	9.89301i	0.589936	+	0.423382i
$547$	18.2712	−	18.2712i	0.781218	−	0.781218i	−0.198818	−	0.980036i	$-0.563710\pi$
$547$	18.2712	−	18.2712i	0.781218	−	0.781218i	0.980036	+	0.198818i	$0.0637103\pi$
$548$	−3.61842	−	21.8237i	−0.154571	−	0.932260i
$549$	−1.83192	+	6.83683i	−0.0781846	+	0.291789i
$550$	8.90534	−	10.5034i	0.379725	−	0.447868i
$551$	0.600079	+	0.346456i	0.0255642	+	0.0147595i
$552$	5.65550	+	3.38190i	0.240714	+	0.143943i
$553$	−1.48621	+	1.74795i	−0.0631999	+	0.0743303i
$554$	15.3299	−	5.49103i	0.651305	−	0.233291i
$555$	−9.45148	+	2.53252i	−0.401193	+	0.107499i
$556$	−31.9760	+	14.5145i	−1.35608	+	0.615550i
$557$	−4.78640	−	1.28251i	−0.202806	−	0.0543418i	0.155986	−	0.987759i	$-0.450145\pi$
$557$	−4.78640	−	1.28251i	−0.202806	−	0.0543418i	−0.358792	+	0.933417i	$0.616811\pi$
$558$	−15.3795	+	10.6521i	−0.651067	+	0.450939i
$559$	23.8117			1.00713
$560$	−8.63447	−	6.39963i	−0.364873	−	0.270434i
$561$	−3.01407			−0.127254
$562$	21.6660	−	15.0062i	0.913925	−	0.632999i
$563$	23.4858	+	6.29301i	0.989809	+	0.265219i	0.717170	−	0.696898i	$-0.245437\pi$
$563$	23.4858	+	6.29301i	0.989809	+	0.265219i	0.272639	+	0.962116i	$0.412104\pi$
$564$	12.0275	+	26.4970i	0.506448	+	1.11573i
$565$	−19.7318	+	5.28712i	−0.830123	+	0.222431i
$566$	−12.1000	+	4.33410i	−0.508600	+	0.182176i
$567$	−1.76047	−	4.93663i	−0.0739327	−	0.207319i
$568$	3.74795	+	14.8979i	0.157260	+	0.625100i
$569$	2.33865	+	1.35022i	0.0980412	+	0.0566041i	0.548219	−	0.836335i	$-0.315306\pi$
$569$	2.33865	+	1.35022i	0.0980412	+	0.0566041i	−0.450178	+	0.892939i	$0.648639\pi$
$570$	−0.108645	+	0.128142i	−0.00455066	+	0.00536729i
$571$	−3.43500	+	12.8196i	−0.143750	+	0.536484i	0.856058	+	0.516881i	$0.172907\pi$
$571$	−3.43500	+	12.8196i	−0.143750	+	0.536484i	−0.999808	+	0.0196030i	$0.993760\pi$
$572$	−18.1961	+	3.01696i	−0.760818	+	0.126146i
$573$	−5.18857	+	5.18857i	−0.216756	+	0.216756i
$574$	−29.0393	+	13.1325i	−1.21208	+	0.548140i
$575$	−7.66390			−0.319607
$576$	−12.3503	−	0.378970i	−0.514594	−	0.0157904i
$577$	12.4461	+	21.5572i	0.518137	+	0.897439i	0.999778	+	0.0210709i	$0.00670757\pi$
$577$	12.4461	+	21.5572i	0.518137	+	0.897439i	−0.481641	+	0.876369i	$0.659959\pi$
$578$	−22.4992	+	1.85256i	−0.935842	+	0.0770565i
$579$	−3.14178	−	11.7253i	−0.130568	−	0.487286i
$580$	−9.21584	−	11.2139i	−0.382667	−	0.465632i
$581$	−16.7590	+	11.5729i	−0.695279	+	0.480123i
$582$	−9.43697	−	26.3462i	−0.391175	−	1.09209i
$583$	−3.12788	−	1.80589i	−0.129544	−	0.0747921i
$584$	17.2161	−	16.6959i	0.712407	−	0.690882i
$585$	5.10584	−	2.94786i	0.211101	−	0.121879i
$586$	−4.29523	+	23.6517i	−0.177434	+	0.977044i
$587$	23.9315	+	23.9315i	0.987758	+	0.987758i	0.999926	−	0.0121684i	$-0.00387340\pi$
$587$	23.9315	+	23.9315i	0.987758	+	0.987758i	−0.0121684	+	0.999926i	$0.503873\pi$
$588$	−14.0570	+	9.36353i	−0.579703	+	0.386146i
$589$	0.587224	−	0.587224i	0.0241961	−	0.0241961i
$590$	8.50921	−	5.89361i	0.350319	−	0.242636i
$591$	−8.60218	−	14.8994i	−0.353846	−	0.612880i
$592$	28.6705	+	14.0900i	1.17835	+	0.579097i
$593$	−0.895084	+	1.55033i	−0.0367567	+	0.0636645i	−0.883819	−	0.467830i	$-0.845036\pi$
$593$	−0.895084	+	1.55033i	−0.0367567	+	0.0636645i	0.847062	+	0.531494i	$0.178369\pi$
$594$	17.2001	+	8.12786i	0.705729	+	0.333490i
$595$	−1.55464	−	2.25132i	−0.0637341	−	0.0922950i
$596$	1.02010	−	10.4303i	0.0417849	−	0.427241i
$597$	13.5879	−	3.64086i	0.556114	−	0.149010i
$598$	7.82975	+	6.63845i	0.320182	+	0.271466i
$599$	37.3788	−	21.5806i	1.52726	−	0.881761i	0.527779	−	0.849381i	$-0.323025\pi$
$599$	37.3788	−	21.5806i	1.52726	−	0.881761i	0.999476	−	0.0323796i	$-0.0103085\pi$
$600$	−11.8305	+	6.59051i	−0.482978	+	0.269056i
$601$			27.6564i			1.12813i	0.825730	+	0.564065i	$0.190763\pi$
$601$			27.6564i			1.12813i	−0.825730	+	0.564065i	$0.809237\pi$
$602$	−8.36536	+	22.1780i	−0.340946	+	0.903910i
$603$	3.82954	+	3.82954i	0.155951	+	0.155951i
$604$	0.446017	+	2.69005i	0.0181482	+	0.109457i
$605$	4.88529	+	1.30901i	0.198615	+	0.0532188i
$606$	−15.6395	+	1.28775i	−0.635312	+	0.0523111i
$607$	10.7968	−	18.7006i	0.438228	−	0.759032i	−0.559325	−	0.828948i	$-0.688940\pi$
$607$	10.7968	−	18.7006i	0.438228	−	0.759032i	0.997553	+	0.0699158i	$0.0222731\pi$
$608$	0.542413	−	0.0814064i	0.0219978	−	0.00330147i
$609$	−21.4854	+	7.66199i	−0.870634	+	0.310480i
$610$	−2.81199	+	5.95071i	−0.113854	+	0.240937i
$611$	11.7324	+	43.7859i	0.474642	+	1.77139i
$612$	−2.94457	−	1.10596i	−0.119027	−	0.0447058i
$613$	−2.56885	+	9.58708i	−0.103755	+	0.387219i	−0.998201	−	0.0599573i	$-0.980904\pi$
$613$	−2.56885	+	9.58708i	−0.103755	+	0.387219i	0.894446	+	0.447176i	$0.147570\pi$
$614$	−35.0938	−	6.37316i	−1.41627	−	0.257200i
$615$		−	10.4360i		−	0.420819i
$616$	3.58255	−	18.0076i	0.144345	−	0.725547i
$617$			14.2458i			0.573515i	0.958003	+	0.286758i	$0.0925774\pi$
$617$			14.2458i			0.573515i	−0.958003	+	0.286758i	$0.907423\pi$
$618$	2.35666	−	12.9770i	0.0947989	−	0.522011i
$619$	9.45579	−	35.2895i	0.380060	−	1.41840i	−0.465748	−	0.884917i	$-0.654215\pi$
$619$	9.45579	−	35.2895i	0.380060	−	1.41840i	0.845808	−	0.533487i	$-0.179119\pi$
$620$	−15.8407	+	7.19038i	−0.636178	+	0.288773i
$621$	−2.74027	−	10.2268i	−0.109963	−	0.410388i
$622$	8.36817	+	3.95435i	0.335533	+	0.158555i
$623$	9.15056	+	7.78033i	0.366610	+	0.311712i
$624$	17.7952	+	3.51442i	0.712379	+	0.140689i
$625$	5.29682	−	9.17437i	0.211873	−	0.366975i
$626$	−2.22512	−	27.0239i	−0.0889338	−	1.08009i
$627$	−0.277225	−	0.0742821i	−0.0110713	−	0.00296654i
$628$	−0.369869	+	0.516897i	−0.0147594	+	0.0206264i
$629$	5.75034	+	5.75034i	0.229281	+	0.229281i
$630$	0.951866	+	5.79116i	0.0379232	+	0.230725i
$631$		−	4.87006i		−	0.193874i	−0.995291	−	0.0969370i	$-0.969095\pi$
$631$		−	4.87006i		−	0.193874i	0.995291	−	0.0969370i	$-0.0309045\pi$
$632$	−0.671089	+	2.35919i	−0.0266945	+	0.0938436i
$633$	9.65483	−	5.57422i	0.383745	−	0.221555i
$634$	17.2127	−	20.3016i	0.683605	−	0.806282i
$635$	−0.970054	+	0.259925i	−0.0384954	+	0.0103148i
$636$	2.25519	+	2.74414i	0.0894242	+	0.108812i
$637$	−23.9891	+	10.8082i	−0.950481	+	0.428237i
$638$	10.5942	−	22.4195i	0.419430	−	0.887595i
$639$	4.19436	−	7.26484i	0.165926	−	0.287393i
$640$	−11.2364	−	2.39873i	−0.444158	−	0.0948180i
$641$	−17.1939	−	29.7808i	−0.679120	−	1.17627i	−0.975246	−	0.221121i	$-0.929028\pi$
$641$	−17.1939	−	29.7808i	−0.679120	−	1.17627i	0.296126	−	0.955149i	$-0.404305\pi$
$642$	−18.3600	−	26.5082i	−0.724610	−	1.04619i
$643$	−11.9018	+	11.9018i	−0.469361	+	0.469361i	−0.901708	−	0.432346i	$-0.857686\pi$
$643$	−11.9018	+	11.9018i	−0.469361	+	0.469361i	0.432346	+	0.901708i	$0.357686\pi$
$644$	−8.93369	+	4.96039i	−0.352037	+	0.195467i
$645$	−5.48825	−	5.48825i	−0.216099	−	0.216099i
$646$	0.137378	+	0.0249484i	0.00540508	+	0.000981581i
$647$	−4.56190	+	2.63381i	−0.179347	+	0.103546i	−0.586986	−	0.809597i	$-0.699686\pi$
$647$	−4.56190	+	2.63381i	−0.179347	+	0.103546i	0.407639	+	0.913143i	$0.366352\pi$
$648$	−3.90070	−	4.02223i	−0.153234	−	0.158008i
$649$	15.3139	+	8.84148i	0.601123	+	0.347058i
$650$	−19.8607	+	7.11392i	−0.779000	+	0.279031i
$651$	2.20535	+	27.2497i	0.0864343	+	1.06800i
$652$	29.5458	+	2.88963i	1.15710	+	0.113167i
$653$	−8.87812	−	33.1336i	−0.347427	−	1.29662i	−0.889751	−	0.456447i	$-0.849122\pi$
$653$	−8.87812	−	33.1336i	−0.347427	−	1.29662i	0.542323	−	0.840170i	$-0.317545\pi$
$654$	−2.29057	−	27.8187i	−0.0895684	−	1.08780i
$655$	−3.99985	−	6.92794i	−0.156287	−	0.270697i
$656$	−22.4297	+	25.6468i	−0.875734	+	1.00134i
$657$	−13.0959			−0.510919
$658$	−44.9035	−	4.45507i	−1.75052	−	0.173677i
$659$	−14.4817	+	14.4817i	−0.564126	+	0.564126i	−0.930477	−	0.366351i	$-0.880607\pi$
$659$	−14.4817	+	14.4817i	−0.564126	+	0.564126i	0.366351	+	0.930477i	$0.380607\pi$
$660$	4.88930	+	3.49857i	0.190316	+	0.136182i
$661$	−4.10893	+	15.3347i	−0.159819	+	0.596452i	0.838826	+	0.544400i	$0.183243\pi$
$661$	−4.10893	+	15.3347i	−0.159819	+	0.596452i	−0.998644	+	0.0520518i	$0.983424\pi$
$662$	10.5642	+	8.95685i	0.410589	+	0.348118i
$663$	3.99889	+	2.30876i	0.155304	+	0.0896648i
$664$	−11.1743	+	18.6865i	−0.433646	+	0.725178i
$665$	−0.0875071	−	0.245384i	−0.00339338	−	0.00951557i
$666$	−5.88246	−	16.4227i	−0.227941	−	0.636367i
$667$	−13.3301	+	3.57180i	−0.516145	+	0.138301i
$668$	27.3328	+	10.2660i	1.05754	+	0.397204i
$669$	−27.1930	−	7.28634i	−1.05134	−	0.281706i
$670$	2.86740	+	4.13996i	0.110777	+	0.159941i
$671$	−11.2438			−0.434061
$672$	−9.52498	+	15.3396i	−0.367434	+	0.591740i
$673$	−8.09831			−0.312167			−0.156083	−	0.987744i	$-0.549887\pi$
$673$	−8.09831			−0.312167			−0.156083	+	0.987744i	$0.549887\pi$
$674$	−3.95849	−	5.71528i	−0.152476	−	0.220145i
$675$	21.0175	+	5.63161i	0.808962	+	0.216761i
$676$	2.11274	+	0.793531i	0.0812592	+	0.0305204i
$677$	21.8750	−	5.86138i	0.840724	−	0.225271i	0.187337	−	0.982296i	$-0.440014\pi$
$677$	21.8750	−	5.86138i	0.840724	−	0.225271i	0.653386	+	0.757025i	$0.273348\pi$
$678$	11.5730	+	32.3095i	0.444458	+	1.24084i
$679$	42.6877	+	7.81394i	1.63820	+	0.299871i
$680$	−2.51026	−	1.50110i	−0.0962639	−	0.0575644i
$681$	16.3505	+	9.43999i	0.626554	+	0.361741i
$682$	−22.6680	−	19.2191i	−0.868003	−	0.735936i
$683$	9.86156	−	36.8038i	0.377342	−	1.40826i	−0.472550	−	0.881304i	$-0.656666\pi$
$683$	9.86156	−	36.8038i	0.377342	−	1.40826i	0.849892	−	0.526956i	$-0.176667\pi$
$684$	−0.243576	−	0.174292i	−0.00931335	−	0.00666423i
$685$	−7.94275	+	7.94275i	−0.303477	+	0.303477i
$686$	−1.63902	−	26.1403i	−0.0625781	−	0.998040i
$687$	−32.2606			−1.23082
$688$	1.69185	+	25.2833i	0.0645012	+	0.963917i
$689$	2.76660	+	4.79189i	0.105399	+	0.182556i
$690$	−0.274577	−	3.33470i	−0.0104530	−	0.126950i
$691$	6.40271	+	23.8952i	0.243571	+	0.909018i	0.974096	+	0.226133i	$0.0726084\pi$
$691$	6.40271	+	23.8952i	0.243571	+	0.909018i	−0.730526	+	0.682885i	$0.760725\pi$
$692$	24.5841	+	2.40437i	0.934548	+	0.0914004i
$693$	−8.25014	+	5.69711i	−0.313397	+	0.216415i
$694$	−12.4525	+	4.46038i	−0.472691	+	0.169314i
$695$	15.4421	+	8.91547i	0.585750	+	0.338183i
$696$	−17.5057	+	16.9768i	−0.663553	+	0.643504i
$697$	−7.51132	+	4.33666i	−0.284511	+	0.164263i
$698$	33.8584	+	6.14879i	1.28156	+	0.232735i
$699$	−10.8752	−	10.8752i	−0.411336	−	0.411336i
$700$	0.351460	−	20.9973i	0.0132839	−	0.793622i
$701$	−10.6300	+	10.6300i	−0.401489	+	0.401489i	−0.878757	−	0.477269i	$-0.841627\pi$
$701$	−10.6300	+	10.6300i	−0.401489	+	0.401489i	0.477269	+	0.878757i	$0.341627\pi$
$702$	−16.5942	−	23.9588i	−0.626308	−	0.904265i
$703$	0.387181	+	0.670617i	0.0146028	+	0.0252928i
$704$	−4.49627	−	19.1063i	−0.169460	−	0.720096i
$705$	7.38785	−	12.7961i	0.278242	−	0.481930i
$706$	4.93612	−	10.4458i	0.185773	−	0.393132i
$707$	10.4275	−	21.9870i	0.392168	−	0.826905i
$708$	−11.0413	−	13.4351i	−0.414956	−	0.504921i
$709$	3.42184	−	0.916878i	0.128510	−	0.0344341i	−0.193991	−	0.981003i	$-0.562143\pi$
$709$	3.42184	−	0.916878i	0.128510	−	0.0344341i	0.322501	+	0.946569i	$0.395477\pi$
$710$	5.04452	−	5.94978i	0.189317	−	0.223291i
$711$	1.15994	−	0.669691i	0.0435011	−	0.0251154i
$712$	12.3504	+	3.51317i	0.462852	+	0.131662i
$713$			16.5398i			0.619422i
$714$	−3.55522	+	2.91343i	−0.133051	+	0.109033i
$715$	6.62251	+	6.62251i	0.247668	+	0.247668i
$716$	−0.548975	+	0.767200i	−0.0205162	+	0.0286716i
$717$	17.4436	+	4.67400i	0.651444	+	0.174554i
$718$	1.34265	+	16.3063i	0.0501071	+	0.608545i
$719$	−8.10598	+	14.0400i	−0.302302	+	0.523603i	−0.976657	−	0.214805i	$-0.931089\pi$
$719$	−8.10598	+	14.0400i	−0.302302	+	0.523603i	0.674355	+	0.738407i	$0.264422\pi$
$720$	3.49282	+	5.21194i	0.130170	+	0.194237i
$721$	15.5817	+	13.2484i	0.580292	+	0.493397i
$722$	−24.2821	−	11.4745i	−0.903688	−	0.427035i
$723$	−6.18582	−	23.0858i	−0.230053	−	0.858569i
$724$	−39.8313	+	18.0801i	−1.48032	+	0.671942i
$725$	7.34051	−	27.3952i	0.272620	−	1.01743i
$726$	1.51825	−	8.36028i	0.0563477	−	0.310279i
$727$			14.2822i			0.529699i	0.964290	+	0.264849i	$0.0853223\pi$
$727$			14.2822i			0.529699i	−0.964290	+	0.264849i	$0.914678\pi$
$728$	−18.5469	+	21.1472i	−0.687392	+	0.783769i
$729$			22.9031i			0.848263i
$730$	−11.9816	−	2.17589i	−0.443457	−	0.0805333i
$731$	−1.66954	+	6.23082i	−0.0617503	+	0.230455i
$732$	10.3514	+	3.88792i	0.382599	+	0.143702i
$733$	−8.91206	−	33.2603i	−0.329175	−	1.22850i	−0.910048	−	0.414502i	$-0.863956\pi$
$733$	−8.91206	−	33.2603i	−0.329175	−	1.22850i	0.580874	−	0.813994i	$-0.302711\pi$
$734$	−5.14015	+	10.8775i	−0.189726	+	0.401497i
$735$	8.02025	+	3.03799i	0.295831	+	0.112058i
$736$	−6.49240	+	8.78531i	−0.239313	+	0.323831i
$737$	−4.30162	+	7.45062i	−0.158452	+	0.274447i
$738$	18.5424	−	1.52677i	0.682556	−	0.0562011i
$739$	20.1534	+	5.40009i	0.741356	+	0.198646i	0.609681	−	0.792647i	$-0.291298\pi$
$739$	20.1534	+	5.40009i	0.741356	+	0.198646i	0.131675	+	0.991293i	$0.457964\pi$
$740$	−2.65328	−	16.0027i	−0.0975366	−	0.588270i
$741$	0.310906	+	0.310906i	0.0114214	+	0.0114214i
$742$	−5.43506	+	0.893336i	−0.199527	+	0.0327954i
$743$		−	30.1201i		−	1.10500i	−0.833513	−	0.552500i	$-0.813674\pi$
$743$		−	30.1201i		−	1.10500i	0.833513	−	0.552500i	$-0.186326\pi$
$744$	14.2233	+	25.5320i	0.521452	+	0.936048i
$745$	−4.60854	+	2.66074i	−0.168844	+	0.0974820i
$746$	5.65796	+	4.79710i	0.207153	+	0.175634i
$747$	11.4842	−	3.07719i	0.420186	−	0.112588i
$748$	0.486359	−	4.97291i	0.0177831	−	0.181828i
$749$	49.8403	−	4.03362i	1.82112	−	0.147385i
$750$	14.0501	+	6.63935i	0.513039	+	0.242435i
$751$	−22.6093	+	39.1605i	−0.825026	+	1.42899i	0.0768741	+	0.997041i	$0.475506\pi$
$751$	−22.6093	+	39.1605i	−0.825026	+	1.42899i	−0.901900	+	0.431946i	$0.857827\pi$
$752$	−45.6583	+	15.5685i	−1.66499	+	0.567725i
$753$	7.88217	+	13.6523i	0.287242	+	0.497518i
$754$	−31.2290	+	21.6297i	−1.13729	+	0.787707i
$755$	0.979047	−	0.979047i	0.0356312	−	0.0356312i
$756$	28.1447	−	7.03869i	1.02361	−	0.255995i
$757$	−10.1353	−	10.1353i	−0.368375	−	0.368375i	0.498509	−	0.866884i	$-0.333881\pi$
$757$	−10.1353	−	10.1353i	−0.368375	−	0.368375i	−0.866884	+	0.498509i	$0.833881\pi$
$758$	−1.29710	+	7.14250i	−0.0471128	+	0.259427i
$759$	4.95030	−	2.85806i	0.179684	−	0.103741i
$760$	−0.193891	−	0.199932i	−0.00703316	−	0.00725229i
$761$	−17.0843	−	9.86363i	−0.619306	−	0.357556i	0.157293	−	0.987552i	$-0.449723\pi$
$761$	−17.0843	−	9.86363i	−0.619306	−	0.357556i	−0.776599	+	0.629996i	$0.783057\pi$
$762$	0.568951	+	1.58840i	0.0206109	+	0.0575417i
$763$	39.1092	+	18.5479i	1.41585	+	0.671480i
$764$	−7.72339	−	9.39788i	−0.279422	−	0.340003i
$765$	0.413374	+	1.54273i	0.0149456	+	0.0557776i
$766$	−9.81330	+	0.808019i	−0.354569	+	0.0291949i
$767$	−13.5451	−	23.4607i	−0.489084	−	0.847118i
$768$	−2.46724	+	19.1447i	−0.0890290	+	0.690824i
$769$	−41.2736			−1.48837			−0.744183	−	0.667976i	$-0.767161\pi$
$769$	−41.2736			−1.48837			−0.744183	+	0.667976i	$0.767161\pi$
$770$	−8.49471	+	3.84158i	−0.306128	+	0.138441i
$771$	−19.8101	+	19.8101i	−0.713444	+	0.713444i
$772$	19.8525	−	3.29160i	0.714508	−	0.118467i
$773$	−13.8201	+	51.5773i	−0.497074	+	1.85511i	0.0210159	+	0.999779i	$0.493310\pi$
$773$	−13.8201	+	51.5773i	−0.497074	+	1.85511i	−0.518090	+	0.855326i	$0.673357\pi$
$774$	8.94848	−	10.5543i	0.321647	−	0.379368i
$775$	−29.4375	−	16.9958i	−1.05743	−	0.610506i
$776$	44.9914	−	11.3188i	1.61510	−	0.406320i
$777$	−25.0754	−	4.59003i	−0.899577	−	0.164666i
$778$	17.5487	−	6.28579i	0.629152	−	0.225356i
$779$	−0.797746	+	0.213755i	−0.0285822	+	0.00765858i
$780$	−3.80695	−	8.38687i	−0.136311	−	0.300298i
$781$	12.8718	+	3.44899i	0.460590	+	0.123415i
$782$	−2.28606	+	1.58336i	−0.0817494	+	0.0566209i
$783$	39.1812			1.40022
$784$	−13.1806	−	24.7037i	−0.470736	−	0.882274i
$785$	0.322740			0.0115191
$786$	−11.0485	+	7.65238i	−0.394088	+	0.272951i
$787$	0.494375	+	0.132467i	0.0176226	+	0.00472196i	0.267620	−	0.963525i	$-0.413763\pi$
$787$	0.494375	+	0.132467i	0.0176226	+	0.00472196i	−0.249997	+	0.968247i	$0.580430\pi$
$788$	25.9706	−	11.7885i	0.925165	−	0.419949i
$789$	−5.26743	+	1.41140i	−0.187526	+	0.0502473i
$790$	1.17251	−	0.419982i	0.0417160	−	0.0149423i
$791$	−52.3499	−	9.58259i	−1.86135	−	0.340718i
$792$	−5.50089	+	9.19905i	−0.195466	+	0.326874i
$793$	14.9176	+	8.61266i	0.529739	+	0.305845i
$794$	5.70869	−	6.73314i	0.202594	−	0.238950i
$795$	0.466799	−	1.74212i	0.0165556	−	0.0617865i
$796$	3.81447	+	23.0061i	0.135200	+	0.815431i
$797$	35.5605	−	35.5605i	1.25962	−	1.25962i	0.308341	−	0.951276i	$-0.400226\pi$
$797$	35.5605	−	35.5605i	1.25962	−	1.25962i	0.951276	−	0.308341i	$-0.0997736\pi$
$798$	−0.398800	+	0.180350i	−0.0141174	+	0.00638432i
$799$	−12.2801			−0.434438
$800$	−8.96468	−	20.5826i	−0.316949	−	0.727706i
$801$	−3.50586	−	6.07232i	−0.123873	−	0.214555i
$802$	−22.4123	+	1.84541i	−0.791406	+	0.0651638i
$803$	−5.38433	−	20.0946i	−0.190009	−	0.709123i
$804$	6.53653	−	5.37187i	0.230526	−	0.189451i
$805$	4.68813	+	2.22339i	0.165235	+	0.0783641i
$806$	15.3529	+	42.8623i	0.540783	+	1.50976i
$807$	−0.416833	−	0.240659i	−0.0146732	−	0.00847158i
$808$	0.398989	−	26.0115i	0.0140364	−	0.915080i
$809$	−1.17802	+	0.680131i	−0.0414170	+	0.0239121i	−0.520566	−	0.853822i	$-0.674279\pi$
$809$	−1.17802	+	0.680131i	−0.0414170	+	0.0239121i	0.479149	+	0.877734i	$0.340946\pi$
$810$	−0.508358	+	2.79928i	−0.0178619	+	0.0983565i
$811$	12.4370	+	12.4370i	0.436722	+	0.436722i	0.890907	−	0.454186i	$-0.150070\pi$
$811$	12.4370	+	12.4370i	0.436722	+	0.436722i	−0.454186	+	0.890907i	$0.650070\pi$
$812$	−9.17458	−	36.6852i	−0.321964	−	1.28740i
$813$	−9.06114	+	9.06114i	−0.317788	+	0.317788i
$814$	22.7808	−	15.7783i	0.798466	−	0.553030i
$815$	−7.53706	−	13.0546i	−0.264012	−	0.457282i
$816$	−2.16732	+	4.41006i	−0.0758713	+	0.154383i
$817$	−0.307119	+	0.531945i	−0.0107447	+	0.0186104i
$818$	−7.29164	−	3.44564i	−0.254946	−	0.120474i
$819$	15.3098	−	1.23903i	0.534967	−	0.0432953i
$820$	17.2183	+	1.68398i	0.601290	+	0.0588072i
$821$	5.33567	−	1.42969i	0.186216	−	0.0498965i	−0.164506	−	0.986376i	$-0.552603\pi$
$821$	5.33567	−	1.42969i	0.186216	−	0.0498965i	0.350722	+	0.936480i	$0.385936\pi$
$822$	14.3942	+	12.2041i	0.502055	+	0.425667i
$823$	16.5082	−	9.53100i	0.575439	−	0.332230i	−0.183880	−	0.982949i	$-0.558866\pi$
$823$	16.5082	−	9.53100i	0.575439	−	0.332230i	0.759319	+	0.650719i	$0.225532\pi$
$824$	21.0305	+	5.98227i	0.732631	+	0.208402i
$825$			11.7474i			0.408991i
$826$	26.6097	−	4.37371i	0.925868	−	0.152181i
$827$	3.94521	+	3.94521i	0.137188	+	0.137188i	0.772366	−	0.635178i	$-0.219073\pi$
$827$	3.94521	+	3.94521i	0.137188	+	0.137188i	−0.635178	+	0.772366i	$0.719073\pi$
$828$	5.88486	−	0.975725i	0.204513	−	0.0339088i
$829$	25.9036	+	6.94085i	0.899669	+	0.241066i	0.678874	−	0.734255i	$-0.262468\pi$
$829$	25.9036	+	6.94085i	0.899669	+	0.241066i	0.220795	+	0.975320i	$0.429135\pi$
$830$	11.0183	−	0.907238i	0.382451	−	0.0314907i
$831$	−6.94562	+	12.0302i	−0.240941	+	0.417322i
$832$	−8.66994	+	28.7932i	−0.300576	+	0.998226i
$833$	−1.14621	−	7.03503i	−0.0397138	−	0.243749i
$834$	12.7989	−	27.0850i	0.443190	−	0.937875i
$835$	−3.83713	−	14.3203i	−0.132789	−	0.495576i
$836$	0.167292	−	0.445407i	0.00578592	−	0.0154047i
$837$	12.1539	−	45.3588i	0.420099	−	1.56783i
$838$	8.99570	+	1.63365i	0.310751	+	0.0564335i
$839$		−	5.34140i		−	0.184406i	−0.995740	−	0.0922028i	$-0.970609\pi$
$839$		−	5.34140i		−	0.184406i	0.995740	−	0.0922028i	$-0.0293908\pi$
$840$	9.14889	−	0.599349i	0.315667	−	0.0206795i
$841$		−	22.0706i		−	0.761056i
$842$	0.150539	−	0.828947i	0.00518793	−	0.0285674i
$843$	−5.81908	+	21.7171i	−0.200420	+	0.747976i
$844$	7.63898	+	16.8290i	0.262945	+	0.579278i
$845$	−0.296598	−	1.10692i	−0.0102033	−	0.0380791i
$846$	23.8167	+	11.2545i	0.818837	+	0.386939i
$847$	10.0383	+	8.53515i	0.344921	+	0.293271i
$848$	−4.89146	+	3.27804i	−0.167973	+	0.112568i
$849$	5.48222	−	9.49549i	0.188149	−	0.325884i
$850$	−0.468982	−	5.69573i	−0.0160859	−	0.195362i
$851$	−14.8971	−	3.99165i	−0.510664	−	0.136832i
$852$	−10.6576	−	7.62614i	−0.365125	−	0.261267i
$853$	1.42841	+	1.42841i	0.0489078	+	0.0489078i	0.731138	−	0.682230i	$-0.238990\pi$
$853$	1.42841	+	1.42841i	0.0489078	+	0.0489078i	−0.682230	+	0.731138i	$0.738990\pi$
$854$	−13.2625	+	10.8684i	−0.453833	+	0.371908i
$855$			0.152084i			0.00520115i
$856$	46.6985	−	26.0147i	1.59612	−	0.889164i
$857$	−22.1543	+	12.7908i	−0.756778	+	0.436926i	−0.828138	−	0.560525i	$-0.810599\pi$
$857$	−22.1543	+	12.7908i	−0.756778	+	0.436926i	0.0713599	+	0.997451i	$0.477266\pi$
$858$	10.1755	−	12.0016i	0.347387	−	0.409728i
$859$	44.0264	−	11.7968i	1.50216	−	0.402503i	0.588337	−	0.808616i	$-0.299783\pi$
$859$	44.0264	−	11.7968i	1.50216	−	0.402503i	0.913823	+	0.406113i	$0.133116\pi$
$860$	9.94066	−	8.16946i	0.338974	−	0.278576i
$861$	11.6505	−	24.5656i	0.397047	−	0.837194i
$862$	12.7512	−	26.9839i	0.434306	−	0.919075i
$863$	−19.7223	+	34.1601i	−0.671356	+	1.16282i	0.306164	+	0.951979i	$0.400954\pi$
$863$	−19.7223	+	34.1601i	−0.671356	+	1.16282i	−0.977520	+	0.210843i	$0.932379\pi$
$864$	24.2604	−	19.3220i	0.825355	−	0.657349i
$865$	−6.27135	−	10.8623i	−0.213232	−	0.369329i
$866$	11.2504	+	16.2433i	0.382303	+	0.551970i
$867$	13.6178	−	13.6178i	0.462486	−	0.462486i
$868$	−45.3153	−	0.758503i	−1.53810	−	0.0257453i
$869$	1.50449	+	1.50449i	0.0510364	+	0.0510364i
$870$	12.1831	+	2.21250i	0.413047	+	0.0750107i
$871$	11.4143	−	6.59004i	0.386758	−	0.223295i
$872$	46.2677	+	0.709700i	1.56682	+	0.0240335i
$873$	−21.9398	−	12.6669i	−0.742548	−	0.428710i
$874$	−0.249287	+	0.0892924i	−0.00843226	+	0.00302036i
$875$	−19.8293	+	13.6931i	−0.670353	+	0.462910i
$876$	−1.99140	+	20.3616i	−0.0672832	+	0.687955i
$877$	−2.72833	−	10.1823i	−0.0921292	−	0.343831i	0.904439	−	0.426602i	$-0.140290\pi$
$877$	−2.72833	−	10.1823i	−0.0921292	−	0.343831i	−0.996569	+	0.0827714i	$0.973623\pi$
$878$	−0.628918	−	7.63814i	−0.0212250	−	0.257775i
$879$	−10.2534	−	17.7594i	−0.345839	−	0.599011i
$880$	−6.56125	+	7.50232i	−0.221180	+	0.252903i
$881$	−15.4426			−0.520274			−0.260137	−	0.965572i	$-0.583768\pi$
$881$	−15.4426			−0.520274			−0.260137	+	0.965572i	$0.583768\pi$
$882$	−4.22449	+	14.6947i	−0.142246	+	0.494795i
$883$	10.0224	−	10.0224i	0.337280	−	0.337280i	−0.518063	−	0.855343i	$-0.673347\pi$
$883$	10.0224	−	10.0224i	0.337280	−	0.337280i	0.855343	+	0.518063i	$0.173347\pi$
$884$	−4.45450	+	6.22522i	−0.149821	+	0.209377i
$885$	−2.28541	+	8.52927i	−0.0768233	+	0.286708i
$886$	6.51839	+	5.52662i	0.218990	+	0.185670i
$887$	−37.9027	−	21.8831i	−1.27265	−	0.734763i	−0.297162	−	0.954827i	$-0.596040\pi$
$887$	−37.9027	−	21.8831i	−1.27265	−	0.734763i	−0.975485	+	0.220064i	$0.929373\pi$
$888$	−26.4287	+	6.64883i	−0.886888	+	0.223120i
$889$	−2.57362	−	0.471099i	−0.0863166	−	0.0158001i
$890$	−2.19862	−	6.13812i	−0.0736979	−	0.205750i
$891$	−4.69474	+	1.25795i	−0.157280	+	0.0421430i
$892$	16.4097	−	43.6900i	0.549437	−	1.46285i
$893$	−1.12948	−	0.302644i	−0.0377967	−	0.0101276i
$894$	5.09044	+	7.34959i	0.170250	+	0.245807i
$895$	0.479024			0.0160120
$896$	−23.7719	−	18.1905i	−0.794164	−	0.607703i
$897$	−8.75703			−0.292389
$898$	−14.8373	−	21.4221i	−0.495127	−	0.714865i
$899$	−59.1229	−	15.8419i	−1.97186	−	0.528358i
$900$	−4.31049	+	11.4765i	−0.143683	+	0.382549i
$901$	−1.44787	+	0.387956i	−0.0482356	+	0.0129247i
$902$	9.96636	+	27.8242i	0.331844	+	0.926443i
$903$	−6.79204	−	19.0460i	−0.226025	−	0.633810i
$904$	−55.1750	+	13.8807i	−1.83509	+	0.461666i
$905$	19.2356	+	11.1057i	0.639413	+	0.369165i
$906$	−1.77427	−	1.50431i	−0.0589462	−	0.0499775i
$907$	−12.5599	+	46.8743i	−0.417045	+	1.55643i	0.363658	+	0.931533i	$0.381528\pi$
$907$	−12.5599	+	46.8743i	−0.417045	+	1.55643i	−0.780703	+	0.624902i	$0.785139\pi$
$908$	−18.2134	+	25.4535i	−0.604434	+	0.844705i
$909$	−10.0449	+	10.0449i	−0.333169	+	0.333169i
$910$	14.2129	+	1.41012i	0.471154	+	0.0467452i
$911$	−35.2525			−1.16797			−0.583983	−	0.811766i	$-0.698507\pi$
$911$	−35.2525			−1.16797			−0.583983	+	0.811766i	$0.698507\pi$
$912$	−0.308030	+	0.352210i	−0.0101999	+	0.0116628i
$913$	9.44340	+	16.3564i	0.312531	+	0.541319i
$914$	4.17468	+	50.7010i	0.138086	+	1.67704i
$915$	−1.45319	−	5.42336i	−0.0480409	−	0.179291i
$916$	5.20567	−	53.2268i	0.172000	−	1.75866i
$917$	−1.68120	−	20.7733i	−0.0555181	−	0.685994i
$918$	7.43278	−	2.66236i	0.245318	−	0.0878708i
$919$	−22.1228	−	12.7726i	−0.729763	−	0.421329i	0.0885726	−	0.996070i	$-0.471769\pi$
$919$	−22.1228	−	12.7726i	−0.729763	−	0.421329i	−0.818335	+	0.574741i	$0.805103\pi$
$920$	5.54624	+	0.0850736i	0.182854	+	0.00280479i
$921$	26.3510	−	15.2138i	0.868295	−	0.501310i
$922$	1.77867	+	0.323012i	0.0585772	+	0.0106378i
$923$	−14.4357	−	14.4357i	−0.475156	−	0.475156i
$924$	7.60338	+	13.6937i	0.250133	+	0.450490i
$925$	22.4120	−	22.4120i	0.736903	−	0.736903i
$926$	10.1457	+	14.6484i	0.333409	+	0.481377i
$927$	−5.96981	−	10.3400i	−0.196074	−	0.339610i
$928$	−25.1853	−	31.6222i	−0.826747	−	1.03805i
$929$	−1.98515	+	3.43838i	−0.0651306	+	0.112810i	−0.896752	−	0.442534i	$-0.854080\pi$
$929$	−1.98515	+	3.43838i	−0.0651306	+	0.112810i	0.831621	+	0.555343i	$0.187413\pi$
$930$	6.34051	−	13.4177i	0.207913	−	0.439985i
$931$	0.0679545	−	0.675309i	0.00222712	−	0.0221324i
$932$	19.6978	−	16.1881i	0.645222	−	0.530258i
$933$	−7.62660	+	2.04354i	−0.249684	+	0.0669025i
$934$	−7.58095	+	8.94139i	−0.248056	+	0.292571i
$935$	−2.19724	+	1.26858i	−0.0718576	+	0.0414870i
$936$	14.3447	−	7.99110i	0.468871	−	0.261197i
$937$			18.3326i			0.598899i	0.954112	+	0.299450i	$0.0968031\pi$
$937$			18.3326i			0.598899i	−0.954112	+	0.299450i	$0.903197\pi$
$938$	2.12793	+	12.9463i	0.0694793	+	0.422712i
$939$	16.3565	+	16.3565i	0.533773	+	0.533773i
$940$	19.9202	+	14.2540i	0.649726	+	0.464916i
$941$	−28.7932	−	7.71512i	−0.938632	−	0.251506i	−0.243100	−	0.970001i	$-0.578164\pi$
$941$	−28.7932	−	7.71512i	−0.938632	−	0.251506i	−0.695531	+	0.718496i	$0.744831\pi$
$942$	−0.0444951	−	0.540387i	−0.00144973	−	0.0176068i
$943$	8.22438	−	14.2451i	0.267823	−	0.463883i
$944$	23.9482	−	16.0491i	0.779448	−	0.522352i
$945$	−11.2229	−	9.54236i	−0.365081	−	0.310413i
$946$	19.8739	+	9.39136i	0.646157	+	0.305339i
$947$	7.28394	+	27.1840i	0.236696	+	0.883362i	0.977377	+	0.211505i	$0.0678365\pi$
$947$	7.28394	+	27.1840i	0.236696	+	0.883362i	−0.740681	+	0.671857i	$0.765497\pi$
$948$	−0.864858	−	1.90532i	−0.0280893	−	0.0618819i
$949$	−8.24874	+	30.7847i	−0.267765	+	0.999314i
$950$	0.0972366	−	0.535434i	0.00315477	−	0.0173718i
$951$			22.7060i			0.736291i
$952$	−4.23320	−	6.33588i	−0.137199	−	0.205347i
$953$		−	9.54510i		−	0.309196i	−0.987977	−	0.154598i	$-0.950592\pi$
$953$		−	9.54510i		−	0.309196i	0.987977	−	0.154598i	$-0.0494083\pi$
$954$	3.16365	+	0.574530i	0.102427	+	0.0186011i
$955$	−1.59865	+	5.96625i	−0.0517311	+	0.193063i
$956$	−10.5264	+	28.0260i	−0.340448	+	0.906427i
$957$	5.47492	+	20.4327i	0.176979	+	0.660495i
$958$	−5.60615	+	11.8637i	−0.181126	+	0.383298i
$959$	−27.5639	+	9.82964i	−0.890084	+	0.317416i
$960$	8.63470	−	4.63812i	0.278684	−	0.149695i
$961$	−21.1794	+	36.6839i	−0.683208	+	1.18335i
$962$	−42.3103	+	3.48380i	−1.36414	+	0.112322i
$963$	−28.1957	−	7.55502i	−0.908595	−	0.243457i
$964$	39.0874	−	6.48079i	1.25892	−	0.208732i
$965$	−7.22535	−	7.22535i	−0.232592	−	0.232592i
$966$	3.07645	−	8.15622i	0.0989832	−	0.262422i
$967$			54.0255i			1.73734i	0.495388	+	0.868672i	$0.335026\pi$
$967$			54.0255i			1.73734i	−0.495388	+	0.868672i	$0.664974\pi$
$968$	13.5486	+	3.85401i	0.435470	+	0.123873i
$969$	−0.103154	+	0.0595558i	−0.00331377	+	0.00191321i
$970$	−17.9683	−	15.2344i	−0.576927	−	0.489147i
$971$	−5.75433	+	1.54187i	−0.184665	+	0.0494809i	−0.349966	−	0.936762i	$-0.613807\pi$
$971$	−5.75433	+	1.54187i	−0.184665	+	0.0494809i	0.165301	+	0.986243i	$0.447140\pi$
$972$	−27.9827	−	2.73675i	−0.897544	−	0.0877813i
$973$	26.3966	+	38.2257i	0.846237	+	1.22546i
$974$	49.4665	+	23.3752i	1.58501	+	0.748991i
$975$	8.99842	−	15.5857i	0.288180	−	0.499143i
$976$	−8.08502	+	16.4514i	−0.258795	+	0.526597i
$977$	14.6499	+	25.3743i	0.468690	+	0.811795i	0.999360	−	0.0357835i	$-0.0113927\pi$
$977$	14.6499	+	25.3743i	0.468690	+	0.811795i	−0.530669	+	0.847579i	$0.678059\pi$
$978$	−20.8192	+	14.4197i	−0.665723	+	0.461090i
$979$	7.87607	−	7.87607i	0.251720	−	0.251720i
$980$	−6.30655	+	12.7424i	−0.201455	+	0.407041i
$981$	−17.8673	−	17.8673i	−0.570460	−	0.570460i
$982$	−10.6525	+	58.6578i	−0.339934	+	1.87185i
$983$	13.8442	−	7.99296i	0.441562	−	0.254936i	−0.262698	−	0.964878i	$-0.584612\pi$
$983$	13.8442	−	7.99296i	0.441562	−	0.254936i	0.704260	+	0.709942i	$0.251279\pi$
$984$	0.445783	−	29.0621i	0.0142110	−	0.926466i
$985$	−12.5419	−	7.24108i	−0.399619	−	0.230720i
$986$	−3.47024	−	9.68825i	−0.110515	−	0.308537i
$987$	31.6759	−	21.8737i	1.00825	−	0.696247i
$988$	−0.563133	+	0.462795i	−0.0179156	+	0.0147235i
$989$	−3.16625	−	11.8166i	−0.100681	−	0.375746i
$990$	5.42411	−	0.446617i	0.172390	−	0.0141944i
$991$	−10.3826	−	17.9832i	−0.329814	−	0.571255i	0.652661	−	0.757650i	$-0.273653\pi$
$991$	−10.3826	−	17.9832i	−0.329814	−	0.571255i	−0.982475	+	0.186396i	$0.940319\pi$
$992$	−44.4204	+	19.3471i	−1.41035	+	0.614272i
$993$	−11.8153			−0.374948
$994$	18.5167	−	8.37383i	0.587313	−	0.265602i
$995$	8.37312	−	8.37312i	0.265446	−	0.265446i
$996$	−3.03812	−	18.3237i	−0.0962664	−	0.580609i
$997$	12.8681	−	48.0242i	0.407535	−	1.52094i	−0.391796	−	0.920052i	$-0.628146\pi$
$997$	12.8681	−	48.0242i	0.407535	−	1.52094i	0.799331	−	0.600890i	$-0.205187\pi$
$998$	−10.2251	+	12.0600i	−0.323670	+	0.381754i
$999$	37.9205	+	21.8934i	1.19975	+	0.692677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.c.37.5	✓	48
4.3	odd	2		448.2.ba.c.177.4		48
7.2	even	3		784.2.m.j.197.5		24
7.3	odd	6		784.2.x.o.165.12		48
7.4	even	3	inner	112.2.w.c.53.12	yes	48
7.5	odd	6		784.2.m.k.197.5		24
7.6	odd	2		784.2.x.o.373.5		48
8.3	odd	2		896.2.ba.e.737.9		48
8.5	even	2		896.2.ba.f.737.4		48
16.3	odd	4		448.2.ba.c.401.9		48
16.5	even	4		896.2.ba.f.289.9		48
16.11	odd	4		896.2.ba.e.289.4		48
16.13	even	4	inner	112.2.w.c.93.12	yes	48
28.11	odd	6		448.2.ba.c.305.9		48
56.11	odd	6		896.2.ba.e.865.4		48
56.53	even	6		896.2.ba.f.865.9		48
112.11	odd	12		896.2.ba.e.417.9		48
112.13	odd	4		784.2.x.o.765.12		48
112.45	odd	12		784.2.x.o.557.5		48
112.53	even	12		896.2.ba.f.417.4		48
112.61	odd	12		784.2.m.k.589.5		24
112.67	odd	12		448.2.ba.c.81.4		48
112.93	even	12		784.2.m.j.589.5		24
112.109	even	12	inner	112.2.w.c.109.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.5	✓	48	1.1	even	1	trivial
112.2.w.c.53.12	yes	48	7.4	even	3	inner
112.2.w.c.93.12	yes	48	16.13	even	4	inner
112.2.w.c.109.5	yes	48	112.109	even	12	inner
448.2.ba.c.81.4		48	112.67	odd	12
448.2.ba.c.177.4		48	4.3	odd	2
448.2.ba.c.305.9		48	28.11	odd	6
448.2.ba.c.401.9		48	16.3	odd	4
784.2.m.j.197.5		24	7.2	even	3
784.2.m.j.589.5		24	112.93	even	12
784.2.m.k.197.5		24	7.5	odd	6
784.2.m.k.589.5		24	112.61	odd	12
784.2.x.o.165.12		48	7.3	odd	6
784.2.x.o.373.5		48	7.6	odd	2
784.2.x.o.557.5		48	112.45	odd	12
784.2.x.o.765.12		48	112.13	odd	4
896.2.ba.e.289.4		48	16.11	odd	4
896.2.ba.e.417.9		48	112.11	odd	12
896.2.ba.e.737.9		48	8.3	odd	2
896.2.ba.e.865.4		48	56.11	odd	6
896.2.ba.f.289.9		48	16.5	even	4
896.2.ba.f.417.4		48	112.53	even	12
896.2.ba.f.737.4		48	8.5	even	2
896.2.ba.f.865.9		48	56.53	even	6

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.805226 - 1.16259i) q^{2} +(1.16533 + 0.312249i) q^{3} +(-0.703221 + 1.87229i) q^{4} +(0.980942 - 0.262843i) q^{5} +(-0.575337 - 1.60623i) q^{6} +(2.60251 + 0.476386i) q^{7} +(2.74296 - 0.690063i) q^{8} +(-1.33758 - 0.772254i) q^{9} +O(q^{10})\)	\(q+(-0.805226 - 1.16259i) q^{2} +(1.16533 + 0.312249i) q^{3} +(-0.703221 + 1.87229i) q^{4} +(0.980942 - 0.262843i) q^{5} +(-0.575337 - 1.60623i) q^{6} +(2.60251 + 0.476386i) q^{7} +(2.74296 - 0.690063i) q^{8} +(-1.33758 - 0.772254i) q^{9} +(-1.09546 - 0.928784i) q^{10} +(0.635020 - 2.36993i) q^{11} +(-1.40411 + 1.96226i) q^{12} +(-2.65786 + 2.65786i) q^{13} +(-1.54177 - 3.40924i) q^{14} +1.22519 q^{15} +(-3.01096 - 2.63327i) q^{16} +(-0.509128 - 0.881836i) q^{17} +(0.179244 + 2.17690i) q^{18} +(-0.0250951 - 0.0936561i) q^{19} +(-0.197701 + 2.02145i) q^{20} +(2.88403 + 1.36778i) q^{21} +(-3.26658 + 1.17006i) q^{22} +(1.67238 + 0.965551i) q^{23} +(3.41192 + 0.0523353i) q^{24} +(-3.43697 + 1.98433i) q^{25} +(5.23017 + 0.949817i) q^{26} +(-3.87683 - 3.87683i) q^{27} +(-2.72207 + 4.53765i) q^{28} +(-5.05325 + 5.05325i) q^{29} +(-0.986557 - 1.42439i) q^{30} +(4.28249 + 7.41749i) q^{31} +(-0.636906 + 5.62089i) q^{32} +(1.48001 - 2.56346i) q^{33} +(-0.615248 + 1.30198i) q^{34} +(2.67813 - 0.216743i) q^{35} +(2.38650 - 1.96128i) q^{36} +(-7.71428 + 2.06704i) q^{37} +(-0.0886762 + 0.104590i) q^{38} +(-3.92719 + 2.26737i) q^{39} +(2.50930 - 1.39788i) q^{40} -8.51782i q^{41} +(-0.732134 - 4.45431i) q^{42} +(-4.47950 - 4.47950i) q^{43} +(3.99064 + 2.85553i) q^{44} +(-1.51507 - 0.405963i) q^{45} +(-0.224109 - 2.72178i) q^{46} +(6.02995 - 10.4442i) q^{47} +(-2.68652 - 4.00880i) q^{48} +(6.54611 + 2.47960i) q^{49} +(5.07450 + 2.39794i) q^{50} +(-0.317949 - 1.18660i) q^{51} +(-3.10723 - 6.84535i) q^{52} +(0.381000 - 1.42191i) q^{53} +(-1.38543 + 7.62888i) q^{54} -2.49167i q^{55} +(7.46731 - 0.489188i) q^{56} -0.116976i q^{57} +(9.94385 + 1.80584i) q^{58} +(-1.86535 + 6.96158i) q^{59} +(-0.861581 + 2.29392i) q^{60} +(-1.18609 - 4.42654i) q^{61} +(5.17511 - 10.9515i) q^{62} +(-3.11318 - 2.64701i) q^{63} +(7.04763 - 3.78563i) q^{64} +(-1.90861 + 3.30580i) q^{65} +(-4.17199 + 0.343519i) q^{66} +(-3.38700 - 0.907543i) q^{67} +(2.00908 - 0.333111i) q^{68} +(1.64738 + 1.64738i) q^{69} +(-2.40848 - 2.93903i) q^{70} +5.43131i q^{71} +(-4.20184 - 1.19524i) q^{72} +(7.34303 - 4.23950i) q^{73} +(8.61485 + 7.30410i) q^{74} +(-4.62480 + 1.23921i) q^{75} +(0.192999 + 0.0188756i) q^{76} +(2.78165 - 5.86524i) q^{77} +(5.79829 + 2.73996i) q^{78} +(-0.433595 + 0.751008i) q^{79} +(-3.64571 - 1.79168i) q^{80} +(-0.990483 - 1.71557i) q^{81} +(-9.90271 + 6.85877i) q^{82} +(-5.44318 + 5.44318i) q^{83} +(-4.58899 + 4.43790i) q^{84} +(-0.731209 - 0.731209i) q^{85} +(-1.60080 + 8.81482i) q^{86} +(-7.46657 + 4.31083i) q^{87} +(0.106434 - 6.93881i) q^{88} +(3.93155 + 2.26988i) q^{89} +(0.748010 + 2.08830i) q^{90} +(-8.18327 + 5.65093i) q^{91} +(-2.98385 + 2.45219i) q^{92} +(2.67441 + 9.98102i) q^{93} +(-16.9977 + 1.39958i) q^{94} +(-0.0492336 - 0.0852752i) q^{95} +(-2.49732 + 6.35131i) q^{96} +16.4025 q^{97} +(-2.38835 - 9.60707i) q^{98} +(-2.67958 + 2.67958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24} - 10 q^{26} - 24 q^{27} - 10 q^{28} + 24 q^{29} - 4 q^{30} + 28 q^{31} + 16 q^{32} + 16 q^{33} - 44 q^{34} + 28 q^{35} - 72 q^{36} - 24 q^{37} + 20 q^{38} + 26 q^{40} + 6 q^{42} - 40 q^{43} + 6 q^{44} - 28 q^{45} - 14 q^{46} - 20 q^{47} + 56 q^{48} + 56 q^{50} + 24 q^{51} - 16 q^{52} - 16 q^{53} + 64 q^{54} + 40 q^{56} - 6 q^{58} - 20 q^{59} + 46 q^{60} + 8 q^{61} + 24 q^{62} - 16 q^{63} + 80 q^{64} + 8 q^{65} - 20 q^{66} + 48 q^{67} - 40 q^{69} + 82 q^{70} - 32 q^{72} - 8 q^{74} - 4 q^{75} - 36 q^{76} - 20 q^{77} + 116 q^{78} - 36 q^{79} - 28 q^{80} + 2 q^{82} - 8 q^{83} + 28 q^{84} - 20 q^{86} - 42 q^{88} - 20 q^{90} + 64 q^{91} + 76 q^{92} + 8 q^{93} - 72 q^{94} - 4 q^{95} - 120 q^{96} - 48 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

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