LMFDB - Embedded newform 112.2.w.c.53.7

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			53.7
Character	$\chi$	$=$	112.53
Dual form			112.2.w.c.93.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0582062 - 1.41302i) q^{2} +(-0.523249 - 1.95279i) q^{3} +(-1.99322 - 0.164492i) q^{4} +(-0.256983 + 0.959072i) q^{5} +(-2.78978 + 0.625694i) q^{6} +(-0.292831 - 2.62950i) q^{7} +(-0.348448 + 2.80688i) q^{8} +(-0.941530 + 0.543593i) q^{9} +O(q^{10})$	\(q+(0.0582062 - 1.41302i) q^{2} +(-0.523249 - 1.95279i) q^{3} +(-1.99322 - 0.164492i) q^{4} +(-0.256983 + 0.959072i) q^{5} +(-2.78978 + 0.625694i) q^{6} +(-0.292831 - 2.62950i) q^{7} +(-0.348448 + 2.80688i) q^{8} +(-0.941530 + 0.543593i) q^{9} +(1.34023 + 0.418944i) q^{10} +(1.88773 - 0.505816i) q^{11} +(0.721733 + 3.97842i) q^{12} +(-2.10314 + 2.10314i) q^{13} +(-3.73256 + 0.260721i) q^{14} +2.00733 q^{15} +(3.94588 + 0.655741i) q^{16} +(2.83885 - 4.91704i) q^{17} +(0.713302 + 1.36204i) q^{18} +(0.616573 + 0.165210i) q^{19} +(0.669984 - 1.86937i) q^{20} +(-4.98163 + 1.94772i) q^{21} +(-0.604848 - 2.69683i) q^{22} +(5.92691 - 3.42190i) q^{23} +(5.66358 - 0.788251i) q^{24} +(3.47635 + 2.00707i) q^{25} +(2.84936 + 3.09419i) q^{26} +(-2.73445 - 2.73445i) q^{27} +(0.151145 + 5.28934i) q^{28} +(-0.207295 + 0.207295i) q^{29} +(0.116839 - 2.83639i) q^{30} +(-3.94693 + 6.83628i) q^{31} +(1.15625 - 5.53743i) q^{32} +(-1.97551 - 3.42168i) q^{33} +(-6.78261 - 4.29755i) q^{34} +(2.59713 + 0.394889i) q^{35} +(1.96610 - 0.928627i) q^{36} +(-2.57374 + 9.60533i) q^{37} +(0.269333 - 0.861610i) q^{38} +(5.20747 + 3.00653i) q^{39} +(-2.60246 - 1.05551i) q^{40} +2.40202i q^{41} +(2.46219 + 7.15250i) q^{42} +(3.65586 + 3.65586i) q^{43} +(-3.84587 + 0.697687i) q^{44} +(-0.279388 - 1.04269i) q^{45} +(-4.49022 - 8.57399i) q^{46} +(-0.144593 - 0.250442i) q^{47} +(-0.784155 - 8.04861i) q^{48} +(-6.82850 + 1.53999i) q^{49} +(3.03837 - 4.79531i) q^{50} +(-11.0874 - 2.97086i) q^{51} +(4.53798 - 3.84608i) q^{52} +(7.62740 - 2.04376i) q^{53} +(-4.02298 + 3.70466i) q^{54} +1.94045i q^{55} +(7.48272 + 0.0943023i) q^{56} -1.29048i q^{57} +(0.280845 + 0.304976i) q^{58} +(-13.4543 + 3.60507i) q^{59} +(-4.00107 - 0.330191i) q^{60} +(3.61701 + 0.969174i) q^{61} +(9.43003 + 5.97498i) q^{62} +(1.70508 + 2.31657i) q^{63} +(-7.75717 - 1.95611i) q^{64} +(-1.47659 - 2.55754i) q^{65} +(-4.94987 + 2.59226i) q^{66} +(-2.69202 - 10.0468i) q^{67} +(-6.46729 + 9.33379i) q^{68} +(-9.78352 - 9.78352i) q^{69} +(0.709153 - 3.64680i) q^{70} +11.5947i q^{71} +(-1.19773 - 2.83218i) q^{72} +(0.310772 + 0.179424i) q^{73} +(13.4227 + 4.19582i) q^{74} +(2.10040 - 7.83878i) q^{75} +(-1.20179 - 0.430722i) q^{76} +(-1.88283 - 4.81566i) q^{77} +(4.55138 - 7.18323i) q^{78} +(-3.84953 - 6.66758i) q^{79} +(-1.64293 + 3.61587i) q^{80} +(-5.53979 + 9.59520i) q^{81} +(3.39409 + 0.139812i) q^{82} +(-0.424001 + 0.424001i) q^{83} +(10.2499 - 3.06280i) q^{84} +(3.98626 + 3.98626i) q^{85} +(5.37858 - 4.95300i) q^{86} +(0.513270 + 0.296337i) q^{87} +(0.761988 + 5.47488i) q^{88} +(15.2323 - 8.79437i) q^{89} +(-1.48960 + 0.334088i) q^{90} +(6.14607 + 4.91434i) q^{91} +(-12.3765 + 5.84569i) q^{92} +(15.4150 + 4.13045i) q^{93} +(-0.362294 + 0.189734i) q^{94} +(-0.316897 + 0.548881i) q^{95} +(-11.4184 + 0.639544i) q^{96} +12.2678 q^{97} +(1.77858 + 9.73841i) q^{98} +(-1.50240 + 1.50240i) 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 $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0582062	−	1.41302i	0.0411580	−	0.999153i
$2$	0.0582062	−	1.41302i	0.0411580	−	0.999153i
$3$	−0.523249	−	1.95279i	−0.302098	−	1.12744i	−0.935415	−	0.353552i	$-0.884974\pi$
$3$	−0.523249	−	1.95279i	−0.302098	−	1.12744i	0.633317	−	0.773893i	$-0.281693\pi$
$4$	−1.99322	−	0.164492i	−0.996612	−	0.0822462i
$5$	−0.256983	+	0.959072i	−0.114926	+	0.428910i	−0.999281	−	0.0379045i	$-0.987932\pi$
$5$	−0.256983	+	0.959072i	−0.114926	+	0.428910i	0.884355	+	0.466814i	$0.154598\pi$
$6$	−2.78978	+	0.625694i	−1.13892	+	0.255439i
$7$	−0.292831	−	2.62950i	−0.110680	−	0.993856i
$7$	−0.292831	−	2.62950i	−0.110680	−	0.993856i
$8$	−0.348448	+	2.80688i	−0.123195	+	0.992382i
$9$	−0.941530	+	0.543593i	−0.313843	+	0.181198i
$10$	1.34023	+	0.418944i	0.423816	+	0.132482i
$11$	1.88773	−	0.505816i	0.569172	−	0.152509i	0.0372551	−	0.999306i	$-0.488139\pi$
$11$	1.88773	−	0.505816i	0.569172	−	0.152509i	0.531917	+	0.846797i	$0.321472\pi$
$12$	0.721733	+	3.97842i	0.208346	+	1.14847i
$13$	−2.10314	+	2.10314i	−0.583307	+	0.583307i	−0.935810	−	0.352504i	$-0.885330\pi$
$13$	−2.10314	+	2.10314i	−0.583307	+	0.583307i	0.352504	+	0.935810i	$0.385330\pi$
$14$	−3.73256	+	0.260721i	−0.997569	+	0.0696807i
$15$	2.00733			0.518291
$16$	3.94588	+	0.655741i	0.986471	+	0.163935i
$17$	2.83885	−	4.91704i	0.688523	−	1.19256i	−0.283792	−	0.958886i	$-0.591593\pi$
$17$	2.83885	−	4.91704i	0.688523	−	1.19256i	0.972316	−	0.233672i	$-0.0750741\pi$
$18$	0.713302	+	1.36204i	0.168127	+	0.321035i
$19$	0.616573	+	0.165210i	0.141451	+	0.0379018i	0.328850	−	0.944382i	$-0.393339\pi$
$19$	0.616573	+	0.165210i	0.141451	+	0.0379018i	−0.187399	+	0.982284i	$0.560006\pi$
$20$	0.669984	−	1.86937i	0.149813	−	0.418005i
$21$	−4.98163	+	1.94772i	−1.08708	+	0.425027i
$22$	−0.604848	−	2.69683i	−0.128954	−	0.574967i
$23$	5.92691	−	3.42190i	1.23585	−	0.713516i	0.267604	−	0.963529i	$-0.413768\pi$
$23$	5.92691	−	3.42190i	1.23585	−	0.713516i	0.968243	+	0.250013i	$0.0804348\pi$
$24$	5.66358	−	0.788251i	1.15607	−	0.160901i
$25$	3.47635	+	2.00707i	0.695270	+	0.401414i
$26$	2.84936	+	3.09419i	0.558805	+	0.606820i
$27$	−2.73445	−	2.73445i	−0.526245	−	0.526245i
$28$	0.151145	+	5.28934i	0.0285637	+	0.999592i
$29$	−0.207295	+	0.207295i	−0.0384937	+	0.0384937i	−0.726092	−	0.687598i	$-0.758665\pi$
$29$	−0.207295	+	0.207295i	−0.0384937	+	0.0384937i	0.687598	+	0.726092i	$0.258665\pi$
$30$	0.116839	−	2.83639i	0.0213318	−	0.517852i
$31$	−3.94693	+	6.83628i	−0.708889	+	1.22783i	0.256381	+	0.966576i	$0.417470\pi$
$31$	−3.94693	+	6.83628i	−0.708889	+	1.22783i	−0.965270	+	0.261255i	$0.915864\pi$
$32$	1.15625	−	5.53743i	0.204397	−	0.978888i
$33$	−1.97551	−	3.42168i	−0.343891	−	0.595637i
$34$	−6.78261	−	4.29755i	−1.16321	−	0.737023i
$35$	2.59713	+	0.394889i	0.438995	+	0.0667484i
$36$	1.96610	−	0.928627i	0.327683	−	0.154771i
$37$	−2.57374	+	9.60533i	−0.423120	+	1.57911i	0.344873	+	0.938649i	$0.387922\pi$
$37$	−2.57374	+	9.60533i	−0.423120	+	1.57911i	−0.767994	+	0.640457i	$0.778745\pi$
$38$	0.269333	−	0.861610i	0.0436916	−	0.139772i
$39$	5.20747	+	3.00653i	0.833862	+	0.481430i
$40$	−2.60246	−	1.05551i	−0.411484	−	0.166890i
$41$			2.40202i			0.375132i	0.982252	+	0.187566i	$0.0600599\pi$
$41$			2.40202i			0.375132i	−0.982252	+	0.187566i	$0.939940\pi$
$42$	2.46219	+	7.15250i	0.379925	+	1.10365i
$43$	3.65586	+	3.65586i	0.557514	+	0.557514i	0.928599	−	0.371085i	$-0.121014\pi$
$43$	3.65586	+	3.65586i	0.557514	+	0.557514i	−0.371085	+	0.928599i	$0.621014\pi$
$44$	−3.84587	+	0.697687i	−0.579787	+	0.105180i
$45$	−0.279388	−	1.04269i	−0.0416486	−	0.155435i
$46$	−4.49022	−	8.57399i	−0.662047	−	1.26417i
$47$	−0.144593	−	0.250442i	−0.0210910	−	0.0365307i	0.855287	−	0.518154i	$-0.173381\pi$
$47$	−0.144593	−	0.250442i	−0.0210910	−	0.0365307i	−0.876378	+	0.481623i	$0.840047\pi$
$48$	−0.784155	−	8.04861i	−0.113183	−	1.16172i
$49$	−6.82850	+	1.53999i	−0.975500	+	0.219999i
$50$	3.03837	−	4.79531i	0.429690	−	0.678159i
$51$	−11.0874	−	2.97086i	−1.55254	−	0.416003i
$52$	4.53798	−	3.84608i	0.629305	−	0.533356i
$53$	7.62740	−	2.04376i	1.04770	−	0.280732i	0.306402	−	0.951902i	$-0.400875\pi$
$53$	7.62740	−	2.04376i	1.04770	−	0.280732i	0.741303	+	0.671171i	$0.234208\pi$
$54$	−4.02298	+	3.70466i	−0.547459	+	0.504140i
$55$			1.94045i			0.261651i
$56$	7.48272	+	0.0943023i	0.999921	+	0.0126017i
$57$		−	1.29048i		−	0.170929i
$58$	0.280845	+	0.304976i	0.0368767	+	0.0400454i
$59$	−13.4543	+	3.60507i	−1.75160	+	0.469340i	−0.984967	−	0.172744i	$-0.944737\pi$
$59$	−13.4543	+	3.60507i	−1.75160	+	0.469340i	−0.766634	+	0.642084i	$0.778070\pi$
$60$	−4.00107	−	0.330191i	−0.516535	−	0.0426275i
$61$	3.61701	+	0.969174i	0.463110	+	0.124090i	0.482827	−	0.875716i	$-0.339610\pi$
$61$	3.61701	+	0.969174i	0.463110	+	0.124090i	−0.0197171	+	0.999806i	$0.506277\pi$
$62$	9.43003	+	5.97498i	1.19761	+	0.758823i
$63$	1.70508	+	2.31657i	0.214820	+	0.291860i
$64$	−7.75717	−	1.95611i	−0.969646	−	0.244513i
$65$	−1.47659	−	2.55754i	−0.183149	−	0.317223i
$66$	−4.94987	+	2.59226i	−0.609286	+	0.319085i
$67$	−2.69202	−	10.0468i	−0.328883	−	1.22741i	−0.910350	−	0.413838i	$-0.864188\pi$
$67$	−2.69202	−	10.0468i	−0.328883	−	1.22741i	0.581467	−	0.813570i	$-0.302479\pi$
$68$	−6.46729	+	9.33379i	−0.784274	+	1.13189i
$69$	−9.78352	−	9.78352i	−1.17780	−	1.17780i
$70$	0.709153	−	3.64680i	0.0847600	−	0.435876i
$71$			11.5947i			1.37603i	0.725695	+	0.688017i	$0.241518\pi$
$71$			11.5947i			1.37603i	−0.725695	+	0.688017i	$0.758482\pi$
$72$	−1.19773	−	2.83218i	−0.141153	−	0.333775i
$73$	0.310772	+	0.179424i	0.0363731	+	0.0210000i	0.518076	−	0.855334i	$-0.326648\pi$
$73$	0.310772	+	0.179424i	0.0363731	+	0.0210000i	−0.481703	+	0.876334i	$0.659982\pi$
$74$	13.4227	+	4.19582i	1.56035	+	0.487755i
$75$	2.10040	−	7.83878i	0.242533	−	0.905145i
$76$	−1.20179	−	0.430722i	−0.137855	−	0.0494073i
$77$	−1.88283	−	4.81566i	−0.214568	−	0.548795i
$78$	4.55138	−	7.18323i	0.515342	−	0.813341i
$79$	−3.84953	−	6.66758i	−0.433106	−	0.750161i	0.564033	−	0.825752i	$-0.309249\pi$
$79$	−3.84953	−	6.66758i	−0.433106	−	0.750161i	−0.997139	+	0.0755910i	$0.975916\pi$
$80$	−1.64293	+	3.61587i	−0.183685	+	0.404267i
$81$	−5.53979	+	9.59520i	−0.615532	+	1.06613i
$82$	3.39409	+	0.139812i	0.374814	+	0.0154397i
$83$	−0.424001	+	0.424001i	−0.0465402	+	0.0465402i	−0.729994	−	0.683454i	$-0.760477\pi$
$83$	−0.424001	+	0.424001i	−0.0465402	+	0.0465402i	0.683454	+	0.729994i	$0.260477\pi$
$84$	10.2499	−	3.06280i	1.11836	−	0.334179i
$85$	3.98626	+	3.98626i	0.432371	+	0.432371i
$86$	5.37858	−	4.95300i	0.579988	−	0.534095i
$87$	0.513270	+	0.296337i	0.0550283	+	0.0317706i
$88$	0.761988	+	5.47488i	0.0812282	+	0.583625i
$89$	15.2323	−	8.79437i	1.61462	−	0.932201i	0.626340	−	0.779550i	$-0.284552\pi$
$89$	15.2323	−	8.79437i	1.61462	−	0.932201i	0.988280	−	0.152652i	$-0.0487813\pi$
$90$	−1.48960	+	0.334088i	−0.157017	+	0.0352160i
$91$	6.14607	+	4.91434i	0.644283	+	0.515163i
$92$	−12.3765	+	5.84569i	−1.29034	+	0.609455i
$93$	15.4150	+	4.13045i	1.59847	+	0.428308i
$94$	−0.362294	+	0.189734i	−0.0373678	+	0.0195696i
$95$	−0.316897	+	0.548881i	−0.0325129	+	0.0563140i
$96$	−11.4184	+	0.639544i	−1.16539	+	0.0652732i
$97$	12.2678			1.24560			0.622802	−	0.782379i	$-0.285994\pi$
$97$	12.2678			1.24560			0.622802	+	0.782379i	$0.285994\pi$
$98$	1.77858	+	9.73841i	0.179663	+	0.983728i
$99$	−1.50240	+	1.50240i	−0.150997	+	0.150997i
$100$	−6.59899	−	4.57237i	−0.659899	−	0.457237i
$101$	1.16857	−	0.313118i	0.116277	−	0.0311564i	−0.200211	−	0.979753i	$-0.564163\pi$
$101$	1.16857	−	0.313118i	0.116277	−	0.0311564i	0.316488	+	0.948596i	$0.397496\pi$
$102$	−4.84322	+	15.4937i	−0.479550	+	1.53411i
$103$	−5.06181	+	2.92244i	−0.498755	+	0.287956i	−0.728199	−	0.685365i	$-0.759643\pi$
$103$	−5.06181	+	2.92244i	−0.498755	+	0.287956i	0.229444	+	0.973322i	$0.426309\pi$
$104$	−5.17043	−	6.63611i	−0.507003	−	0.650724i
$105$	−0.587809	−	5.27828i	−0.0573643	−	0.515107i
$106$	−2.44390	−	10.8966i	−0.237372	−	1.05837i
$107$	−0.971295	+	3.62492i	−0.0938987	+	0.350435i	−0.996850	−	0.0793079i	$-0.974729\pi$
$107$	−0.971295	+	3.62492i	−0.0938987	+	0.350435i	0.902952	+	0.429742i	$0.141396\pi$
$108$	5.00058	+	5.90017i	0.481181	+	0.567744i
$109$	−2.59283	−	9.67656i	−0.248348	−	0.926846i	−0.971671	−	0.236337i	$-0.924053\pi$
$109$	−2.59283	−	9.67656i	−0.248348	−	0.926846i	0.723323	−	0.690509i	$-0.242614\pi$
$110$	2.74189	+	0.112946i	0.261429	+	0.0107690i
$111$	20.1039			1.90818
$112$	0.568791	−	10.5677i	0.0537457	−	0.998555i
$113$	5.07461			0.477379			0.238689	−	0.971096i	$-0.423282\pi$
$113$	5.07461			0.477379			0.238689	+	0.971096i	$0.423282\pi$
$114$	−1.82347	−	0.0751142i	−0.170784	−	0.00703509i
$115$	1.75874	+	6.56370i	0.164003	+	0.612069i
$116$	0.447283	−	0.379086i	0.0415292	−	0.0351973i
$117$	0.836919	−	3.12342i	0.0773732	−	0.288761i
$118$	4.31089	+	19.2210i	0.396850	+	1.76943i
$119$	−13.7606	−	6.02490i	−1.26144	−	0.552301i
$120$	−0.699452	+	5.63435i	−0.0638509	+	0.514343i
$121$	−6.21861	+	3.59031i	−0.565328	+	0.326392i
$122$	1.57999	−	5.05447i	0.143046	−	0.457611i
$123$	4.69064	−	1.25685i	0.422941	−	0.113327i
$124$	8.99162	−	12.9770i	0.807472	−	1.16537i
$125$	−6.32873	+	6.32873i	−0.566059	+	0.566059i
$126$	3.37259	−	2.27447i	0.300454	−	0.202626i
$127$	−11.1710			−0.991270			−0.495635	−	0.868531i	$-0.665065\pi$
$127$	−11.1710			−0.991270			−0.495635	+	0.868531i	$0.665065\pi$
$128$	−3.21552	+	10.8471i	−0.284215	+	0.958761i
$129$	5.22621	−	9.05207i	0.460142	−	0.796990i
$130$	−3.69978	+	1.93758i	−0.324492	+	0.169937i
$131$	12.1789	+	3.26332i	1.06407	+	0.285118i	0.748056	−	0.663636i	$-0.230988\pi$
$131$	12.1789	+	3.26332i	1.06407	+	0.285118i	0.316017	+	0.948753i	$0.397654\pi$
$132$	3.37478	+	7.14512i	0.293737	+	0.621903i
$133$	0.253868	−	1.66965i	0.0220131	−	0.144777i
$134$	−14.3529	+	3.21909i	−1.23990	+	0.278087i
$135$	3.32524	−	1.91983i	0.286191	−	0.165233i
$136$	12.8124	+	9.68166i	1.09865	+	0.830196i
$137$	−14.0325	−	8.10166i	−1.19888	−	0.692172i	−0.238572	−	0.971125i	$-0.576679\pi$
$137$	−14.0325	−	8.10166i	−1.19888	−	0.692172i	−0.960305	+	0.278953i	$0.910013\pi$
$138$	−14.3937	+	13.2548i	−1.22527	+	1.12832i
$139$	10.5018	+	10.5018i	0.890748	+	0.890748i	0.994593	−	0.103846i	$-0.0331148\pi$
$139$	10.5018	+	10.5018i	0.890748	+	0.890748i	−0.103846	+	0.994593i	$0.533115\pi$
$140$	−5.11170	−	1.21431i	−0.432018	−	0.102628i
$141$	−0.413403	+	0.413403i	−0.0348148	+	0.0348148i
$142$	16.3834	+	0.674881i	1.37487	+	0.0566348i
$143$	−2.90636	+	5.03397i	−0.243042	+	0.420961i
$144$	−4.07162	+	1.52755i	−0.339302	+	0.127296i
$145$	−0.145539	−	0.252082i	−0.0120864	−	0.0209342i
$146$	0.271618	−	0.428682i	0.0224793	−	0.0354780i
$147$	6.58030	+	12.5288i	0.542734	+	1.03336i
$148$	6.71005	−	18.7222i	0.551562	−	1.53896i
$149$	2.57749	−	9.61931i	0.211156	−	0.788045i	−0.776328	−	0.630329i	$-0.782920\pi$
$149$	2.57749	−	9.61931i	0.211156	−	0.788045i	0.987484	−	0.157716i	$-0.0504132\pi$
$150$	−10.9541	−	3.42416i	−0.894395	−	0.279581i
$151$	−8.97638	−	5.18252i	−0.730487	−	0.421747i	0.0881130	−	0.996110i	$-0.471916\pi$
$151$	−8.97638	−	5.18252i	−0.730487	−	0.421747i	−0.818600	+	0.574363i	$0.805250\pi$
$152$	−0.678569	+	1.67308i	−0.0550392	+	0.135705i
$153$			6.17272i			0.499035i
$154$	−6.91419	+	2.38016i	−0.557162	+	0.191799i
$155$	−5.54219	−	5.54219i	−0.445159	−	0.445159i
$156$	−9.88509	−	6.84928i	−0.791441	−	0.548381i
$157$	−1.06781	−	3.98512i	−0.0852205	−	0.318047i	0.910135	−	0.414311i	$-0.135977\pi$
$157$	−1.06781	−	3.98512i	−0.0852205	−	0.318047i	−0.995356	+	0.0962637i	$0.969311\pi$
$158$	−9.64546	+	5.05135i	−0.767351	+	0.401864i
$159$	−7.98206	−	13.8253i	−0.633019	−	1.09642i
$160$	5.01366	+	2.53195i	0.396364	+	0.200168i
$161$	−10.7335	−	14.5828i	−0.845916	−	1.14928i
$162$	13.2357	+	8.38631i	1.03990	+	0.658891i
$163$	−7.98280	−	2.13899i	−0.625261	−	0.167538i	−0.0677429	−	0.997703i	$-0.521580\pi$
$163$	−7.98280	−	2.13899i	−0.625261	−	0.167538i	−0.557518	+	0.830165i	$0.688246\pi$
$164$	0.395114	−	4.78776i	0.0308532	−	0.373861i
$165$	3.78930	−	1.01534i	0.294997	−	0.0790442i
$166$	0.574440	+	0.623799i	0.0445852	+	0.0484162i
$167$		−	8.92669i		−	0.690768i	−0.938462	−	0.345384i	$-0.887749\pi$
$167$		−	8.92669i		−	0.690768i	0.938462	−	0.345384i	$-0.112251\pi$
$168$	−3.73117	−	14.6615i	−0.287866	−	1.13116i
$169$			4.15359i			0.319507i
$170$	5.86467	−	5.40062i	0.449800	−	0.414209i
$171$	−0.670329	+	0.179614i	−0.0512613	+	0.0137354i
$172$	−6.68559	−	7.88832i	−0.509772	−	0.601478i
$173$	−5.26383	−	1.41044i	−0.400202	−	0.107234i	0.0531037	−	0.998589i	$-0.483089\pi$
$173$	−5.26383	−	1.41044i	−0.400202	−	0.107234i	−0.453305	+	0.891355i	$0.649755\pi$
$174$	0.448604	−	0.708010i	0.0340086	−	0.0536741i
$175$	4.25960	−	9.72878i	0.321996	−	0.735426i
$176$	7.78045	−	0.758029i	0.586473	−	0.0571386i
$177$	14.0799	+	24.3871i	1.05831	+	1.83305i
$178$	−11.5400	−	22.0354i	−0.864957	−	1.65162i
$179$	2.52526	+	9.42440i	0.188747	+	0.704413i	0.993797	+	0.111207i	$0.0354715\pi$
$179$	2.52526	+	9.42440i	0.188747	+	0.704413i	−0.805050	+	0.593206i	$0.797862\pi$
$180$	0.385368	+	2.12427i	0.0287236	+	0.158334i
$181$	−8.42976	−	8.42976i	−0.626579	−	0.626579i	0.320627	−	0.947206i	$-0.396106\pi$
$181$	−8.42976	−	8.42976i	−0.626579	−	0.626579i	−0.947206	+	0.320627i	$0.896106\pi$
$182$	7.30178	−	8.39844i	0.541244	−	0.622534i
$183$		−	7.57038i		−	0.559619i
$184$	7.53966	+	17.8285i	0.555831	+	1.31433i
$185$	−8.55080	−	4.93680i	−0.628667	−	0.362961i
$186$	6.73364	−	21.5413i	0.493734	−	1.57948i
$187$	2.87187	−	10.7180i	0.210012	−	0.783776i
$188$	0.247010	+	0.522971i	0.0180150	+	0.0381416i
$189$	−6.38950	+	7.99096i	−0.464767	+	0.581257i
$190$	0.757132	+	0.479728i	0.0549282	+	0.0348032i
$191$	2.46522	+	4.26989i	0.178377	+	0.308958i	0.941325	−	0.337502i	$-0.109582\pi$
$191$	2.46522	+	4.26989i	0.178377	+	0.308958i	−0.762948	+	0.646460i	$0.776249\pi$
$192$	0.239061	+	16.1717i	0.0172527	+	1.16709i
$193$	−10.9543	+	18.9735i	−0.788510	+	1.36574i	0.138370	+	0.990381i	$0.455814\pi$
$193$	−10.9543	+	18.9735i	−0.788510	+	1.36574i	−0.926880	+	0.375358i	$0.877520\pi$
$194$	0.714061	−	17.3346i	0.0512666	−	1.24455i
$195$	−4.22171	+	4.22171i	−0.302323	+	0.302323i
$196$	13.8640	−	1.94632i	0.990289	−	0.139023i
$197$	7.61984	+	7.61984i	0.542891	+	0.542891i	0.924375	−	0.381484i	$-0.124587\pi$
$197$	7.61984	+	7.61984i	0.542891	+	0.542891i	−0.381484	+	0.924375i	$0.624587\pi$
$198$	2.03546	+	2.21036i	0.144654	+	0.157083i
$199$	3.09710	+	1.78811i	0.219547	+	0.126756i	0.605741	−	0.795662i	$-0.292877\pi$
$199$	3.09710	+	1.78811i	0.219547	+	0.126756i	−0.386193	+	0.922418i	$0.626210\pi$
$200$	−6.84494	+	9.05834i	−0.484010	+	0.640521i
$201$	−18.2106	+	10.5139i	−1.28448	+	0.741595i
$202$	−0.374422	−	1.66944i	−0.0263443	−	0.117461i
$203$	0.605783	+	0.484378i	0.0425176	+	0.0339967i
$204$	21.6110	+	7.74537i	1.51307	+	0.542285i
$205$	−2.30371	−	0.617276i	−0.160898	−	0.0431125i
$206$	3.83482	+	7.32252i	0.267185	+	0.510184i
$207$	−3.72024	+	6.44365i	−0.258575	+	0.447865i
$208$	−9.67787	+	6.91964i	−0.671040	+	0.479791i
$209$	1.24749			0.0862906
$210$	−7.49250	+	0.523355i	−0.517031	+	0.0361149i
$211$	7.33737	−	7.33737i	0.505126	−	0.505126i	−0.407901	−	0.913026i	$-0.633739\pi$
$211$	7.33737	−	7.33737i	0.505126	−	0.505126i	0.913026	+	0.407901i	$0.133739\pi$
$212$	−15.5393	+	2.81901i	−1.06724	+	0.193611i
$213$	22.6420	−	6.06690i	1.55140	−	0.415697i
$214$	5.06554	+	1.58345i	0.346273	+	0.108242i
$215$	−4.44573	+	2.56674i	−0.303196	+	0.175050i
$216$	8.62809	−	6.72246i	0.587067	−	0.457406i
$217$	19.1317	+	8.37655i	1.29875	+	0.568637i
$218$	−13.8240	+	3.10047i	−0.936283	+	0.209990i
$219$	0.187767	−	0.700757i	0.0126881	−	0.0473528i
$220$	0.319190	−	3.86776i	0.0215198	−	0.260764i
$221$	4.37072	+	16.3117i	0.294006	+	1.09725i
$222$	1.17017	−	28.4071i	0.0785368	−	1.90656i
$223$	4.26037			0.285295			0.142648	−	0.989774i	$-0.454438\pi$
$223$	4.26037			0.285295			0.142648	+	0.989774i	$0.454438\pi$
$224$	−14.8992	−	1.41882i	−0.995496	−	0.0947987i
$225$	−4.36411			−0.290941
$226$	0.295373	−	7.17049i	0.0196479	−	0.476974i
$227$	1.25223	+	4.67340i	0.0831136	+	0.310184i	0.994950	−	0.100369i	$-0.0320023\pi$
$227$	1.25223	+	4.67340i	0.0831136	+	0.310184i	−0.911837	+	0.410553i	$0.865336\pi$
$228$	−0.212275	+	2.57222i	−0.0140583	+	0.170350i
$229$	−5.07737	+	18.9490i	−0.335522	+	1.25218i	0.567781	+	0.823180i	$0.307802\pi$
$229$	−5.07737	+	18.9490i	−0.335522	+	1.25218i	−0.903302	+	0.429005i	$0.858864\pi$
$230$	9.37698	−	2.10308i	0.618300	−	0.138673i
$231$	−8.41879	+	6.19656i	−0.553916	+	0.407703i
$232$	−0.509620	−	0.654083i	−0.0334582	−	0.0429427i
$233$	−4.38681	+	2.53273i	−0.287390	+	0.165925i	−0.636764	−	0.771059i	$-0.719727\pi$
$233$	−4.38681	+	2.53273i	−0.287390	+	0.165925i	0.349374	+	0.936983i	$0.386394\pi$
$234$	−4.36473	−	1.36438i	−0.285331	−	0.0891924i
$235$	0.277349	−	0.0743155i	0.0180923	−	0.00484781i
$236$	27.4104	−	4.97258i	1.78427	−	0.323687i
$237$	−11.0061	+	11.0061i	−0.714925	+	0.714925i
$238$	−9.31423	+	19.0933i	−0.603752	+	1.23764i
$239$	−9.32494			−0.603181			−0.301590	−	0.953438i	$-0.597517\pi$
$239$	−9.32494			−0.603181			−0.301590	+	0.953438i	$0.597517\pi$
$240$	7.92071	+	1.31629i	0.511279	+	0.0849662i
$241$	−12.8663	+	22.2850i	−0.828789	+	1.43550i	0.0702006	+	0.997533i	$0.477636\pi$
$241$	−12.8663	+	22.2850i	−0.828789	+	1.43550i	−0.898989	+	0.437971i	$0.855697\pi$
$242$	4.71121	+	8.99596i	0.302848	+	0.578282i
$243$	10.4301	+	2.79475i	0.669093	+	0.179283i
$244$	−7.05008	−	2.52675i	−0.451335	−	0.161759i
$245$	0.277839	−	6.94477i	0.0177505	−	0.443685i
$246$	−1.50293	−	6.70110i	−0.0958232	−	0.427247i
$247$	−1.64420	+	0.949280i	−0.104618	+	0.0604012i
$248$	−17.8133	−	13.4606i	−1.13115	−	0.854752i
$249$	1.04984	+	0.606128i	0.0665312	+	0.0384118i
$250$	8.57422	+	9.31097i	0.542282	+	0.588877i
$251$	−3.64372	−	3.64372i	−0.229990	−	0.229990i	0.582699	−	0.812688i	$-0.301997\pi$
$251$	−3.64372	−	3.64372i	−0.229990	−	0.229990i	−0.812688	+	0.582699i	$0.801997\pi$
$252$	−3.01756	−	4.89791i	−0.190088	−	0.308540i
$253$	9.45755	−	9.45755i	0.594591	−	0.594591i
$254$	−0.650224	+	15.7849i	−0.0407987	+	0.990430i
$255$	5.69853	−	9.87014i	0.356856	−	0.618092i
$256$	15.1400	+	5.17495i	0.946251	+	0.323435i
$257$	1.87774	+	3.25234i	0.117130	+	0.202875i	0.918629	−	0.395121i	$-0.129297\pi$
$257$	1.87774	+	3.25234i	0.117130	+	0.202875i	−0.801499	+	0.597996i	$0.795964\pi$
$258$	−12.4865	−	7.91160i	−0.777376	−	0.492555i
$259$	26.0108	+	3.95490i	1.61624	+	0.245746i
$260$	2.52249	+	5.34063i	0.156438	+	0.331212i
$261$	0.0824903	−	0.307858i	0.00510602	−	0.0190559i
$262$	5.32001	−	17.0190i	0.328671	−	1.05144i
$263$	16.3252	+	9.42534i	1.00665	+	0.581191i	0.910210	−	0.414147i	$-0.135920\pi$
$263$	16.3252	+	9.42534i	1.00665	+	0.581191i	0.0964430	+	0.995339i	$0.469253\pi$
$264$	10.2926	−	4.35273i	0.633466	−	0.267892i
$265$			7.84044i			0.481634i
$266$	−2.34447	−	0.455904i	−0.143749	−	0.0279532i
$267$	−25.1439	−	25.1439i	−1.53878	−	1.53878i
$268$	3.71319	+	20.4683i	0.226819	+	1.25030i
$269$	−4.43839	−	16.5643i	−0.270614	−	1.00994i	−0.958724	−	0.284338i	$-0.908226\pi$
$269$	−4.43839	−	16.5643i	−0.270614	−	1.00994i	0.688111	−	0.725606i	$-0.258440\pi$
$270$	−2.51920	−	4.81036i	−0.153313	−	0.292749i
$271$	−2.65608	−	4.60046i	−0.161345	−	0.279458i	0.774006	−	0.633178i	$-0.218250\pi$
$271$	−2.65608	−	4.60046i	−0.161345	−	0.279458i	−0.935351	+	0.353720i	$0.884917\pi$
$272$	14.4261	−	17.5405i	0.874711	−	1.06355i
$273$	6.38076	−	14.5734i	0.386181	−	0.882023i
$274$	−12.2646	+	19.3566i	−0.740929	+	1.16937i
$275$	7.57761	+	2.03042i	0.456947	+	0.122439i
$276$	17.8914	+	21.1101i	1.07694	+	1.27068i
$277$	14.6832	−	3.93434i	0.882226	−	0.236392i	0.210859	−	0.977517i	$-0.432374\pi$
$277$	14.6832	−	3.93434i	0.882226	−	0.236392i	0.671367	+	0.741125i	$0.265707\pi$
$278$	15.4504	−	14.2279i	0.926654	−	0.853331i
$279$		−	8.58208i		−	0.513795i
$280$	−2.01337	+	7.15223i	−0.120322	+	0.427428i
$281$		−	3.15786i		−	0.188382i	−0.995554	−	0.0941910i	$-0.969974\pi$
$281$		−	3.15786i		−	0.188382i	0.995554	−	0.0941910i	$-0.0300264\pi$
$282$	0.560082	+	0.608207i	0.0333524	+	0.0362182i
$283$	13.6357	−	3.65368i	0.810559	−	0.217189i	0.170344	−	0.985385i	$-0.445512\pi$
$283$	13.6357	−	3.65368i	0.810559	−	0.217189i	0.640215	+	0.768196i	$0.278845\pi$
$284$	1.90723	−	23.1108i	0.113174	−	1.37137i
$285$	1.23767	+	0.331632i	0.0733131	+	0.0196442i
$286$	6.94390	+	4.39974i	0.410602	+	0.260162i
$287$	6.31609	−	0.703385i	0.372827	−	0.0415195i
$288$	1.92146	+	5.84218i	0.113223	+	0.344254i
$289$	−7.61819	−	13.1951i	−0.448129	−	0.776182i
$290$	−0.364666	+	0.190977i	−0.0214140	+	0.0112145i
$291$	−6.41911	−	23.9564i	−0.376295	−	1.40435i
$292$	−0.589925	−	0.408753i	−0.0345227	−	0.0239204i
$293$	−10.9335	−	10.9335i	−0.638743	−	0.638743i	0.311502	−	0.950245i	$-0.399168\pi$
$293$	−10.9335	−	10.9335i	−0.638743	−	0.638743i	−0.950245	+	0.311502i	$0.899168\pi$
$294$	18.0865	−	8.56880i	1.05482	−	0.499743i
$295$		−	13.8301i		−	0.805219i
$296$	−26.0642	−	10.5711i	−1.51495	−	0.614435i
$297$	−6.54503	−	3.77878i	−0.379781	−	0.219267i
$298$	−13.4422	−	4.20193i	−0.778686	−	0.243411i
$299$	−5.26839	+	19.6619i	−0.304679	+	1.13708i
$300$	−5.47598	+	15.2789i	−0.316156	+	0.882131i
$301$	8.54253	−	10.6836i	0.492383	−	0.615794i
$302$	−7.84545	+	12.3821i	−0.451455	+	0.712510i
$303$	−1.22291	−	2.11814i	−0.0702543	−	0.121684i
$304$	2.32459	+	1.05621i	0.133324	+	0.0605779i
$305$	−1.85902	+	3.21991i	−0.106447	+	0.184371i
$306$	8.72215	+	0.359291i	0.498612	+	0.0205393i
$307$	−14.7735	+	14.7735i	−0.843170	+	0.843170i	−0.989270	−	0.146100i	$-0.953328\pi$
$307$	−14.7735	+	14.7735i	−0.843170	+	0.843170i	0.146100	+	0.989270i	$0.453328\pi$
$308$	2.96075	+	9.90840i	0.168705	+	0.564583i
$309$	8.35550	+	8.35550i	0.475328	+	0.475328i
$310$	−8.15379	+	7.50861i	−0.463104	+	0.426460i
$311$	7.56549	+	4.36794i	0.429000	+	0.247683i	0.698920	−	0.715199i	$-0.253664\pi$
$311$	7.56549	+	4.36794i	0.429000	+	0.247683i	−0.269921	+	0.962883i	$0.586998\pi$
$312$	−10.2535	+	13.5691i	−0.580491	+	0.768200i
$313$	−3.56615	+	2.05892i	−0.201571	+	0.116377i	−0.597388	−	0.801952i	$-0.703795\pi$
$313$	−3.56615	+	2.05892i	−0.201571	+	0.116377i	0.395817	+	0.918329i	$0.370461\pi$
$314$	−5.69319	+	1.27687i	−0.321285	+	0.0720581i
$315$	−2.65993	+	1.03998i	−0.149870	+	0.0585962i
$316$	6.57621	+	13.9232i	0.369940	+	0.783241i
$317$	−23.5962	−	6.32257i	−1.32529	−	0.355111i	−0.474335	−	0.880345i	$-0.657311\pi$
$317$	−23.5962	−	6.32257i	−1.32529	−	0.355111i	−0.850958	+	0.525234i	$0.823978\pi$
$318$	−20.0000	+	10.4741i	−1.12155	+	0.587356i
$319$	−0.286463	+	0.496169i	−0.0160389	+	0.0277801i
$320$	3.86950	−	6.93700i	0.216312	−	0.387790i
$321$	7.58695			0.423462
$322$	−21.2304	+	14.3177i	−1.18312	+	0.797897i
$323$	2.56271	−	2.56271i	0.142593	−	0.142593i
$324$	12.6204	−	18.2141i	0.701133	−	1.01190i
$325$	−11.5324	+	3.09010i	−0.639703	+	0.171408i
$326$	−3.48707	+	11.1553i	−0.193131	+	0.617836i
$327$	−17.5396	+	10.1265i	−0.969943	+	0.559997i
$328$	−6.74218	−	0.836979i	−0.372274	−	0.0462144i
$329$	−0.616194	+	0.453543i	−0.0339719	+	0.0250046i
$330$	−1.21413	−	5.41344i	−0.0668357	−	0.298000i
$331$	1.89039	−	7.05503i	0.103905	−	0.387780i	−0.894313	−	0.447441i	$-0.852335\pi$
$331$	1.89039	−	7.05503i	0.103905	−	0.387780i	0.998219	+	0.0596615i	$0.0190021\pi$
$332$	0.914874	−	0.775384i	0.0502102	−	0.0425547i
$333$	−2.79813	−	10.4428i	−0.153337	−	0.572260i
$334$	−12.6135	−	0.519588i	−0.690182	−	0.0284306i
$335$	10.3274			0.564245
$336$	−20.9342	+	4.41881i	−1.14205	+	0.241066i
$337$	−9.53985			−0.519669			−0.259834	−	0.965653i	$-0.583668\pi$
$337$	−9.53985			−0.519669			−0.259834	+	0.965653i	$0.583668\pi$
$338$	5.86908	+	0.241765i	0.319236	+	0.0131503i
$339$	−2.65528	−	9.90965i	−0.144215	−	0.538218i
$340$	−7.28980	−	8.60122i	−0.395345	−	0.466467i
$341$	−3.99283	+	14.9015i	−0.216224	+	0.806959i
$342$	0.214780	+	0.957639i	0.0116140	+	0.0517832i
$343$	6.04901	+	17.5046i	0.326616	+	0.945157i
$344$	−11.5355	+	8.98769i	−0.621950	+	0.484584i
$345$	11.8973	−	6.86890i	0.640528	−	0.369809i
$346$	−2.29936	+	7.35578i	−0.123614	+	0.395449i
$347$	−8.82567	+	2.36483i	−0.473787	+	0.126951i	−0.487808	−	0.872951i	$-0.662203\pi$
$347$	−8.82567	+	2.36483i	−0.473787	+	0.126951i	0.0140212	+	0.999902i	$0.495537\pi$
$348$	−0.974317	−	0.675094i	−0.0522289	−	0.0361889i
$349$	24.4862	−	24.4862i	1.31072	−	1.31072i	0.389831	−	0.920887i	$-0.372533\pi$
$349$	24.4862	−	24.4862i	1.31072	−	1.31072i	0.920887	−	0.389831i	$-0.127467\pi$
$350$	−13.4990	−	6.58516i	−0.721550	−	0.351992i
$351$	11.5019			0.613925
$352$	−0.618236	−	11.0380i	−0.0329521	−	0.588328i
$353$	13.0352	−	22.5776i	0.693793	−	1.20168i	−0.276793	−	0.960930i	$-0.589272\pi$
$353$	13.0352	−	22.5776i	0.693793	−	1.20168i	0.970586	−	0.240755i	$-0.0773950\pi$
$354$	35.2789	−	18.4756i	1.87505	−	0.981969i
$355$	−11.1201	−	2.97963i	−0.590194	−	0.158142i
$356$	−31.8080	+	15.0236i	−1.68582	+	0.796247i
$357$	−4.56513	+	30.0242i	−0.241612	+	1.58905i
$358$	13.4638	−	3.01967i	0.711584	−	0.159595i
$359$	3.01740	−	1.74210i	0.159252	−	0.0919443i	−0.418256	−	0.908329i	$-0.637358\pi$
$359$	3.01740	−	1.74210i	0.159252	−	0.0919443i	0.577508	+	0.816385i	$0.304025\pi$
$360$	3.02406	−	0.420885i	0.159382	−	0.0221826i
$361$	−16.1016	−	9.29627i	−0.847453	−	0.489277i
$362$	−12.4020	+	11.4207i	−0.651837	+	0.600259i
$363$	10.2650	+	10.2650i	0.538773	+	0.538773i
$364$	−11.4421	−	10.8064i	−0.599730	−	0.566407i
$365$	−0.251944	+	0.251944i	−0.0131873	+	0.0131873i
$366$	−10.6971	−	0.440643i	−0.559144	−	0.0230328i
$367$	−12.2280	+	21.1796i	−0.638298	+	1.10556i	0.347508	+	0.937677i	$0.387028\pi$
$367$	−12.2280	+	21.1796i	−0.638298	+	1.10556i	−0.985806	+	0.167888i	$0.946305\pi$
$368$	25.6308	−	9.61592i	1.33610	−	0.501264i
$369$	−1.30572	−	2.26157i	−0.0679730	−	0.117733i
$370$	−7.47349	+	11.7951i	−0.388528	+	0.613196i
$371$	−7.60759	−	19.4578i	−0.394966	−	1.01020i
$372$	−30.0462	−	10.7686i	−1.55782	−	0.558324i
$373$	9.51200	−	35.4993i	0.492513	−	1.83808i	−0.0510246	−	0.998697i	$-0.516249\pi$
$373$	9.51200	−	35.4993i	0.492513	−	1.83808i	0.543537	−	0.839385i	$-0.317085\pi$
$374$	−14.9775	−	4.68185i	−0.774469	−	0.242093i
$375$	15.6702	+	9.04719i	0.809206	+	0.467195i
$376$	0.753343	−	0.318588i	0.0388507	−	0.0164299i
$377$		−	0.871940i		−	0.0449072i
$378$	10.9194	+	9.49358i	0.561635	+	0.488297i
$379$	18.5183	+	18.5183i	0.951222	+	0.951222i	0.998864	−	0.0476420i	$-0.0151707\pi$
$379$	18.5183	+	18.5183i	0.951222	+	0.951222i	−0.0476420	+	0.998864i	$0.515171\pi$
$380$	0.721933	−	1.04192i	0.0370344	−	0.0534492i
$381$	5.84524	+	21.8147i	0.299461	+	1.11760i
$382$	6.17690	−	3.23486i	0.316038	−	0.165510i
$383$	7.89785	+	13.6795i	0.403562	+	0.698989i	0.994153	−	0.107982i	$-0.0344388\pi$
$383$	7.89785	+	13.6795i	0.403562	+	0.698989i	−0.590591	+	0.806971i	$0.701105\pi$
$384$	22.8647	+	0.603494i	1.16681	+	0.0307969i
$385$	5.10242	−	0.568225i	0.260043	−	0.0289594i
$386$	26.1722	+	16.5830i	1.33213	+	0.844053i
$387$	−5.42940	−	1.45480i	−0.275992	−	0.0739519i
$388$	−24.4524	−	2.01796i	−1.24138	−	0.102446i
$389$	−5.50707	+	1.47562i	−0.279220	+	0.0748167i	−0.395711	−	0.918375i	$-0.629502\pi$
$389$	−5.50707	+	1.47562i	−0.279220	+	0.0748167i	0.116492	+	0.993192i	$0.462835\pi$
$390$	5.71961	+	6.21107i	0.289624	+	0.314510i
$391$		−	38.8572i		−	1.96509i
$392$	−1.94320	−	19.7034i	−0.0981466	−	0.995172i
$393$		−	25.4903i		−	1.28582i
$394$	11.2105	−	10.3234i	0.564776	−	0.520087i
$395$	7.38395	−	1.97852i	0.371527	−	0.0995503i
$396$	3.24175	−	2.74748i	0.162904	−	0.138066i
$397$	−0.971927	−	0.260427i	−0.0487796	−	0.0130705i	0.234347	−	0.972153i	$-0.424705\pi$
$397$	−0.971927	−	0.260427i	−0.0487796	−	0.0130705i	−0.283126	+	0.959083i	$0.591372\pi$
$398$	2.70690	−	4.27216i	0.135684	−	0.214144i
$399$	−3.39332	+	0.377894i	−0.169879	+	0.0189183i
$400$	12.4012	+	10.1993i	0.620058	+	0.509963i
$401$	8.70318	+	15.0744i	0.434616	+	0.752777i	0.997264	−	0.0739192i	$-0.0235507\pi$
$401$	8.70318	+	15.0744i	0.434616	+	0.752777i	−0.562648	+	0.826697i	$0.690217\pi$
$402$	13.7964	+	26.3439i	0.688100	+	1.31391i
$403$	−6.07671	−	22.6786i	−0.302703	−	1.12970i
$404$	−2.38073	+	0.431893i	−0.118446	+	0.0214875i
$405$	−7.77886	−	7.77886i	−0.386535	−	0.386535i
$406$	0.719694	−	0.827787i	0.0357178	−	0.0410824i
$407$			19.4341i			0.963313i
$408$	12.2022	−	30.0858i	0.604100	−	1.48947i
$409$	33.0605	+	19.0875i	1.63474	+	0.943815i	0.982605	+	0.185709i	$0.0594582\pi$
$409$	33.0605	+	19.0875i	1.63474	+	0.943815i	0.652131	+	0.758106i	$0.273875\pi$
$410$	−1.00631	+	3.21924i	−0.0496982	+	0.158987i
$411$	−8.47837	+	31.6417i	−0.418207	+	1.56077i
$412$	10.5700	−	4.99245i	0.520749	−	0.245960i
$413$	13.4194	+	34.3224i	0.660323	+	1.68889i
$414$	8.88843	+	5.63182i	0.436843	+	0.276789i
$415$	−0.297687	−	0.515608i	−0.0146129	−	0.0253102i
$416$	9.21424	+	14.0777i	0.451765	+	0.690218i
$417$	15.0127	−	26.0028i	0.735176	−	1.27336i
$418$	0.0726116	−	1.76272i	0.00355155	−	0.0862175i
$419$	−27.0004	+	27.0004i	−1.31905	+	1.31905i	−0.404529	+	0.914525i	$0.632565\pi$
$419$	−27.0004	+	27.0004i	−1.31905	+	1.31905i	−0.914525	+	0.404529i	$0.867435\pi$
$420$	0.303399	+	10.6175i	0.0148043	+	0.518080i
$421$	−19.1472	−	19.1472i	−0.933175	−	0.933175i	0.0647277	−	0.997903i	$-0.479382\pi$
$421$	−19.1472	−	19.1472i	−0.933175	−	0.933175i	−0.997903	+	0.0647277i	$0.979382\pi$
$422$	−9.94074	−	10.7949i	−0.483908	−	0.525488i
$423$	0.272276	+	0.157199i	0.0132385	+	0.00764327i
$424$	3.07883	+	22.1214i	0.149521	+	1.07431i
$425$	19.7377	−	11.3956i	0.957419	−	0.552766i
$426$	−7.25471	−	32.3466i	−0.351492	−	1.56720i
$427$	1.48927	−	9.79471i	0.0720708	−	0.473999i
$428$	2.53228	−	7.06551i	0.122402	−	0.341524i
$429$	11.3510	+	3.04150i	0.548033	+	0.146845i
$430$	3.36808	+	6.43128i	0.162423	+	0.310144i
$431$	−0.628555	+	1.08869i	−0.0302764	+	0.0524403i	−0.880767	−	0.473551i	$-0.842972\pi$
$431$	−0.628555	+	1.08869i	−0.0302764	+	0.0524403i	0.850490	+	0.525991i	$0.176305\pi$
$432$	−8.99674	−	12.5829i	−0.432856	−	0.605396i
$433$	−9.16885			−0.440627			−0.220313	−	0.975429i	$-0.570708\pi$
$433$	−9.16885			−0.440627			−0.220313	+	0.975429i	$0.570708\pi$
$434$	12.9498	−	26.5459i	0.621609	−	1.27424i
$435$	−0.416110	+	0.416110i	−0.0199509	+	0.0199509i
$436$	3.57636	+	19.7141i	0.171277	+	0.944132i
$437$	4.21971	−	1.13067i	0.201856	−	0.0540871i
$438$	−0.979251	−	0.306106i	−0.0467904	−	0.0146263i
$439$	6.89864	−	3.98293i	0.329254	−	0.190095i	−0.326256	−	0.945282i	$-0.605787\pi$
$439$	6.89864	−	3.98293i	0.329254	−	0.190095i	0.655510	+	0.755187i	$0.272454\pi$
$440$	−5.44663	−	0.676148i	−0.259658	−	0.0322341i
$441$	5.59211	−	5.16187i	0.266291	−	0.245803i
$442$	23.3032	−	5.22645i	1.10842	−	0.248597i
$443$	6.47610	−	24.1691i	0.307689	−	1.14831i	−0.622918	−	0.782288i	$-0.714053\pi$
$443$	6.47610	−	24.1691i	0.307689	−	1.14831i	0.930606	−	0.366022i	$-0.119281\pi$
$444$	−40.0716	−	3.30694i	−1.90171	−	0.156941i
$445$	4.52000	+	16.8689i	0.214269	+	0.799661i
$446$	0.247980	−	6.01996i	0.0117422	−	0.285053i
$447$	−20.1332			−0.952267
$448$	−2.87204	+	20.9703i	−0.135691	+	0.990751i
$449$	−8.33038			−0.393135			−0.196567	−	0.980490i	$-0.562979\pi$
$449$	−8.33038			−0.393135			−0.196567	+	0.980490i	$0.562979\pi$
$450$	−0.254018	+	6.16656i	−0.0119745	+	0.290694i
$451$	1.21498	+	4.53436i	0.0572111	+	0.213515i
$452$	−10.1148	−	0.834734i	−0.475761	−	0.0392626i
$453$	−5.42349	+	20.2407i	−0.254818	+	0.950993i
$454$	6.67647	−	1.49740i	0.313342	−	0.0702766i
$455$	−6.29264	+	4.63162i	−0.295003	+	0.217134i
$456$	3.62224	+	0.449667i	0.169627	+	0.0210576i
$457$	12.5338	−	7.23641i	0.586308	−	0.338505i	−0.177328	−	0.984152i	$-0.556745\pi$
$457$	12.5338	−	7.23641i	0.586308	−	0.338505i	0.763636	+	0.645647i	$0.223412\pi$
$458$	26.4797	+	8.27734i	1.23731	+	0.386775i
$459$	−21.2081	+	5.68270i	−0.989910	+	0.265246i
$460$	−2.42588	−	13.3722i	−0.113107	−	0.623483i
$461$	−4.23021	+	4.23021i	−0.197020	+	0.197020i	−0.798721	−	0.601701i	$-0.794490\pi$
$461$	−4.23021	+	4.23021i	−0.197020	+	0.197020i	0.601701	+	0.798721i	$0.294490\pi$
$462$	8.26580	+	12.2566i	0.384560	+	0.570227i
$463$	−25.1987			−1.17108			−0.585542	−	0.810642i	$-0.699118\pi$
$463$	−25.1987			−1.17108			−0.585542	+	0.810642i	$0.699118\pi$
$464$	−0.953892	+	0.682029i	−0.0442833	+	0.0316624i
$465$	−7.92280	+	13.7227i	−0.367411	+	0.636374i
$466$	3.32344	+	6.34605i	0.153956	+	0.293975i
$467$	−14.8411	−	3.97667i	−0.686766	−	0.184018i	−0.101470	−	0.994839i	$-0.532355\pi$
$467$	−14.8411	−	3.97667i	−0.686766	−	0.184018i	−0.585295	+	0.810820i	$0.699021\pi$
$468$	−2.18195	+	6.08802i	−0.100860	+	0.281419i
$469$	−25.6296	+	10.0207i	−1.18347	+	0.462711i
$470$	−0.0888655	−	0.396224i	−0.00409906	−	0.0182765i
$471$	−7.22338	+	4.17042i	−0.332836	+	0.192163i
$472$	−5.43087	−	39.0208i	−0.249976	−	1.79608i
$473$	8.75047	+	5.05209i	0.402347	+	0.232295i
$474$	14.9112	+	16.1925i	0.684894	+	0.743744i
$475$	1.81183	+	1.81183i	0.0831326	+	0.0831326i
$476$	26.4370	+	14.2725i	1.21174	+	0.654179i
$477$	−6.07046	+	6.07046i	−0.277947	+	0.277947i
$478$	−0.542770	+	13.1763i	−0.0248257	+	0.602669i
$479$	10.4147	−	18.0387i	0.475859	−	0.824211i	−0.523759	−	0.851867i	$-0.675471\pi$
$479$	10.4147	−	18.0387i	0.475859	−	0.824211i	0.999618	+	0.0276553i	$0.00880408\pi$
$480$	2.32097	−	11.1155i	0.105937	−	0.507349i
$481$	−14.7884	−	25.6143i	−0.674294	−	1.16791i
$482$	30.7402	+	19.4773i	1.40018	+	0.887169i
$483$	−22.8608	+	28.5906i	−1.04020	+	1.30092i
$484$	12.9857	−	6.13339i	0.590257	−	0.278790i
$485$	−3.15261	+	11.7657i	−0.143152	+	0.534252i
$486$	4.55612	−	14.5753i	0.206670	−	0.661147i
$487$	0.192631	+	0.111216i	0.00872895	+	0.00503966i	0.504358	−	0.863495i	$-0.331729\pi$
$487$	0.192631	+	0.111216i	0.00872895	+	0.00503966i	−0.495629	+	0.868534i	$0.665062\pi$
$488$	−3.98070	+	9.81480i	−0.180198	+	0.444295i
$489$			16.7080i			0.755561i
$490$	−9.79690	−	0.796820i	−0.442579	−	0.0359967i
$491$	18.1586	+	18.1586i	0.819486	+	0.819486i	0.986033	−	0.166547i	$-0.0532618\pi$
$491$	18.1586	+	18.1586i	0.819486	+	0.819486i	−0.166547	+	0.986033i	$0.553262\pi$
$492$	−9.55624	+	1.73361i	−0.430828	+	0.0781574i
$493$	0.430797	+	1.60776i	0.0194021	+	0.0724097i
$494$	1.24564	+	2.37853i	0.0560442	+	0.107015i
$495$	−1.05482	−	1.82700i	−0.0474105	−	0.0821173i
$496$	−20.0569	+	24.3870i	−0.900583	+	1.09501i
$497$	30.4881	−	3.39527i	1.36758	−	0.152299i
$498$	0.917575	−	1.44816i	0.0411175	−	0.0648938i
$499$	−3.39149	−	0.908747i	−0.151824	−	0.0406811i	0.182107	−	0.983279i	$-0.441708\pi$
$499$	−3.39149	−	0.908747i	−0.151824	−	0.0406811i	−0.333930	+	0.942598i	$0.608375\pi$
$500$	13.6556	−	11.5736i	0.610697	−	0.517585i
$501$	−17.4320	+	4.67088i	−0.778802	+	0.208680i
$502$	−5.36072	+	4.93654i	−0.239261	+	0.220329i
$503$		−	7.65278i		−	0.341220i	−0.985339	−	0.170610i	$-0.945426\pi$
$503$		−	7.65278i		−	0.341220i	0.985339	−	0.170610i	$-0.0545739\pi$
$504$	−7.09647	+	3.97876i	−0.316102	+	0.177228i
$505$			1.20121i			0.0534532i
$506$	−12.8132	−	13.9142i	−0.569615	−	0.618560i
$507$	8.11109	−	2.17336i	0.360226	−	0.0965223i
$508$	22.2664	+	1.83755i	0.987912	+	0.0815282i
$509$	30.8730	+	8.27238i	1.36842	+	0.366667i	0.866901	−	0.498480i	$-0.166108\pi$
$509$	30.8730	+	8.27238i	1.36842	+	0.366667i	0.501519	+	0.865147i	$0.332775\pi$
$510$	−13.6150	−	8.62661i	−0.602881	−	0.381993i
$511$	0.380792	−	0.869715i	0.0168452	−	0.0384739i
$512$	8.19353	−	21.0918i	0.362106	−	0.932137i
$513$	−1.23423	−	2.13775i	−0.0544925	−	0.0943838i
$514$	4.70490	−	2.46397i	0.207524	−	0.108681i
$515$	−1.50203	−	5.60566i	−0.0661874	−	0.247015i
$516$	−11.9060	+	17.1831i	−0.524133	+	0.756445i
$517$	−0.399629	−	0.399629i	−0.0175757	−	0.0175757i
$518$	7.10233	−	36.5235i	0.312059	−	1.60475i
$519$			11.0172i			0.483600i
$520$	7.69321	−	3.25345i	0.337370	−	0.142673i
$521$	−2.39816	−	1.38458i	−0.105065	−	0.0606595i	0.446547	−	0.894760i	$-0.352654\pi$
$521$	−2.39816	−	1.38458i	−0.105065	−	0.0606595i	−0.551612	+	0.834101i	$0.685987\pi$
$522$	−0.430207	−	0.134479i	−0.0188296	−	0.00588600i
$523$	5.72293	−	21.3583i	0.250246	−	0.933932i	−0.720427	−	0.693530i	$-0.756054\pi$
$523$	5.72293	−	21.3583i	0.250246	−	0.933932i	0.970674	−	0.240401i	$-0.0772791\pi$
$524$	−23.7384	−	8.50786i	−1.03702	−	0.371668i
$525$	−21.2271	−	3.22754i	−0.926427	−	0.140862i
$526$	14.2684	−	22.5191i	0.622131	−	0.981879i
$527$	22.4095	+	38.8144i	0.976173	+	1.69078i
$528$	−5.55138	−	14.7970i	−0.241593	−	0.643955i
$529$	11.9189	−	20.6441i	0.518211	−	0.897568i
$530$	11.0787	+	0.456362i	0.481226	+	0.0198231i
$531$	10.7079	−	10.7079i	0.464685	−	0.464685i
$532$	−0.780661	+	3.28624i	−0.0338460	+	0.142476i
$533$	−5.05178	−	5.05178i	−0.218817	−	0.218817i
$534$	−36.9922	+	34.0651i	−1.60081	+	1.47414i
$535$	−3.22696	−	1.86308i	−0.139513	−	0.0805481i
$536$	29.1381	−	4.05541i	1.25857	−	0.175167i
$537$	17.0826	−	9.86262i	0.737167	−	0.425603i
$538$	−23.6640	+	5.30737i	−1.02023	+	0.228817i
$539$	−12.1114	+	6.36106i	−0.521675	+	0.273990i
$540$	−6.94375	+	3.27967i	−0.298811	+	0.141135i
$541$	−32.2635	−	8.64497i	−1.38711	−	0.371676i	−0.513414	−	0.858141i	$-0.671619\pi$
$541$	−32.2635	−	8.64497i	−1.38711	−	0.371676i	−0.873700	+	0.486465i	$0.838286\pi$
$542$	−6.65512	+	3.48530i	−0.285862	+	0.149706i
$543$	−12.0507	+	20.8724i	−0.517145	+	0.895721i
$544$	−23.9453	−	21.4053i	−1.02665	−	0.917743i
$545$	9.94683			0.426075
$546$	−20.2211	−	9.86437i	−0.865381	−	0.422156i
$547$	3.45137	−	3.45137i	0.147570	−	0.147570i	−0.629462	−	0.777032i	$-0.716724\pi$
$547$	3.45137	−	3.45137i	0.147570	−	0.147570i	0.777032	+	0.629462i	$0.216724\pi$
$548$	26.6372	+	18.4567i	1.13789	+	0.788430i
$549$	−3.93236	+	1.05367i	−0.167829	+	0.0449696i
$550$	3.31007	−	10.5891i	0.141142	−	0.451521i
$551$	−0.162059	+	0.0935651i	−0.00690396	+	0.00398601i
$552$	30.8702	−	24.0521i	1.31392	−	1.02373i
$553$	−16.4051	+	12.0748i	−0.697616	+	0.513472i
$554$	−4.70464	−	20.9765i	−0.199881	−	0.891208i
$555$	−5.16636	+	19.2811i	−0.219300	+	0.818437i
$556$	−19.2049	−	22.6598i	−0.814469	−	0.960990i
$557$	−5.70879	−	21.3055i	−0.241889	−	0.902742i	−0.974922	−	0.222549i	$-0.928562\pi$
$557$	−5.70879	−	21.3055i	−0.241889	−	0.902742i	0.733032	−	0.680194i	$-0.238104\pi$
$558$	−12.1266	−	0.499530i	−0.513360	−	0.0211468i
$559$	−15.3776			−0.650403
$560$	9.98902	+	3.26123i	0.422113	+	0.137812i
$561$	−22.4327			−0.947109
$562$	−4.46210	−	0.183807i	−0.188222	−	0.00775342i
$563$	−7.14593	−	26.6690i	−0.301165	−	1.12396i	−0.936196	−	0.351477i	$-0.885679\pi$
$563$	−7.14593	−	26.6690i	−0.301165	−	1.12396i	0.635031	−	0.772486i	$-0.280987\pi$
$564$	0.892006	−	0.756002i	0.0375602	−	0.0318334i
$565$	−1.30408	+	4.86691i	−0.0548633	+	0.204752i
$566$	−4.36902	−	19.4801i	−0.183644	−	0.818811i
$567$	26.8528	+	11.7571i	1.12771	+	0.493751i
$568$	−32.5448	−	4.04014i	−1.36555	−	0.169521i
$569$	−30.3657	+	17.5317i	−1.27300	+	0.734965i	−0.975551	−	0.219773i	$-0.929468\pi$
$569$	−30.3657	+	17.5317i	−1.27300	+	0.734965i	−0.297446	+	0.954739i	$0.596135\pi$
$570$	0.540641	−	1.72954i	0.0226450	−	0.0724424i
$571$	1.24755	−	0.334280i	0.0522083	−	0.0139892i	−0.232620	−	0.972568i	$-0.574730\pi$
$571$	1.24755	−	0.334280i	0.0522083	−	0.0139892i	0.284829	+	0.958578i	$0.408063\pi$
$572$	6.62108	−	9.55575i	0.276841	−	0.399546i
$573$	7.04827	−	7.04827i	0.294446	−	0.294446i
$574$	−0.626257	−	8.96568i	−0.0261395	−	0.374220i
$575$	27.4720			1.14566
$576$	8.36693	−	2.37501i	0.348622	−	0.0989586i
$577$	−7.66470	+	13.2757i	−0.319086	+	0.552673i	−0.980298	−	0.197527i	$-0.936709\pi$
$577$	−7.66470	+	13.2757i	−0.319086	+	0.552673i	0.661212	+	0.750199i	$0.270042\pi$
$578$	−19.0883	+	9.99658i	−0.793968	+	0.415803i
$579$	42.7830	+	11.4637i	1.77800	+	0.476414i
$580$	0.248627	+	0.526395i	0.0103237	+	0.0218574i
$581$	1.23907	+	0.990749i	0.0514053	+	0.0411032i
$582$	−34.2244	+	7.67588i	−1.41865	+	0.318176i
$583$	13.3647	−	7.71612i	0.553510	−	0.319569i
$584$	−0.611911	+	0.809780i	−0.0253211	+	0.0335090i
$585$	2.78051	+	1.60533i	0.114960	+	0.0663722i
$586$	−16.0856	+	14.8128i	−0.664491	+	0.611913i
$587$	−27.8270	−	27.8270i	−1.14854	−	1.14854i	−0.986840	−	0.161702i	$-0.948302\pi$
$587$	−27.8270	−	27.8270i	−1.14854	−	1.14854i	−0.161702	−	0.986840i	$-0.551698\pi$
$588$	−11.0551	−	26.0552i	−0.455905	−	1.07450i
$589$	−3.56299	+	3.56299i	−0.146810	+	0.146810i
$590$	−19.5421	−	0.804997i	−0.804536	−	0.0331412i
$591$	10.8929	−	18.8670i	0.448074	−	0.776087i
$592$	−16.4543	+	36.2138i	−0.676267	+	1.48838i
$593$	−8.89810	−	15.4120i	−0.365401	−	0.632894i	0.623439	−	0.781872i	$-0.285735\pi$
$593$	−8.89810	−	15.4120i	−0.365401	−	0.632894i	−0.988840	+	0.148978i	$0.952402\pi$
$594$	−5.72043	+	9.02828i	−0.234712	+	0.370435i
$595$	9.31455	−	11.6492i	0.381859	−	0.477569i
$596$	−6.71981	+	18.7495i	−0.275254	+	0.768008i
$597$	1.87125	−	6.98361i	0.0765853	−	0.285820i
$598$	27.4759	+	8.58875i	1.12357	+	0.351220i
$599$	16.6221	+	9.59676i	0.679159	+	0.392113i	0.799538	−	0.600615i	$-0.205078\pi$
$599$	16.6221	+	9.59676i	0.679159	+	0.392113i	−0.120379	+	0.992728i	$0.538411\pi$
$600$	21.2707	+	8.62697i	0.868371	+	0.352195i
$601$		−	26.9530i		−	1.09944i	−0.835351	−	0.549718i	$-0.814735\pi$
$601$		−	26.9530i		−	1.09944i	0.835351	−	0.549718i	$-0.185265\pi$
$602$	−14.5989	−	12.6926i	−0.595007	−	0.517311i
$603$	7.99597	+	7.99597i	0.325621	+	0.325621i
$604$	17.0395	+	11.8065i	0.693325	+	0.480398i
$605$	−1.84530	−	6.88674i	−0.0750219	−	0.279986i
$606$	−3.06415	+	1.60470i	−0.124472	+	0.0651865i
$607$	14.7276	+	25.5089i	0.597773	+	1.03537i	0.993149	+	0.116854i	$0.0372810\pi$
$607$	14.7276	+	25.5089i	0.597773	+	1.03537i	−0.395376	+	0.918519i	$0.629386\pi$
$608$	1.62775	−	3.22320i	0.0660140	−	0.130718i
$609$	0.628915	−	1.43642i	0.0254849	−	0.0582066i
$610$	4.44157	+	2.81424i	0.179834	+	0.113945i
$611$	0.830813	+	0.222616i	0.0336111	+	0.00900607i
$612$	1.01537	−	12.3036i	0.0410437	−	0.497344i
$613$	24.1091	−	6.46001i	0.973756	−	0.260917i	0.263343	−	0.964702i	$-0.415175\pi$
$613$	24.1091	−	6.46001i	0.973756	−	0.260917i	0.710413	+	0.703785i	$0.248508\pi$
$614$	20.0153	+	21.7351i	0.807752	+	0.877159i
$615$			4.82165i			0.194428i
$616$	14.1731	−	3.60686i	0.571049	−	0.145325i
$617$			10.8407i			0.436431i	0.975901	+	0.218216i	$0.0700236\pi$
$617$			10.8407i			0.436431i	−0.975901	+	0.218216i	$0.929976\pi$
$618$	12.2928	−	11.3201i	0.494489	−	0.455362i
$619$	−19.3962	+	5.19721i	−0.779601	+	0.208893i	−0.626609	−	0.779334i	$-0.715558\pi$
$619$	−19.3962	+	5.19721i	−0.779601	+	0.208893i	−0.152992	+	0.988227i	$0.548891\pi$
$620$	10.1352	+	11.9585i	0.407038	+	0.480264i
$621$	−25.5639	−	6.84982i	−1.02584	−	0.274874i
$622$	6.61232	−	10.4359i	0.265130	−	0.418442i
$623$	−27.5853	−	37.4780i	−1.10518	−	1.50152i
$624$	18.5766	+	15.2782i	0.743657	+	0.611616i
$625$	5.59202	+	9.68566i	0.223681	+	0.387426i
$626$	2.70171	+	5.15887i	0.107982	+	0.206190i
$627$	−0.652747	−	2.43609i	−0.0260682	−	0.0972879i
$628$	1.47286	+	8.11889i	0.0587736	+	0.323979i
$629$	39.9233	+	39.9233i	1.59185	+	1.59185i
$630$	1.31468	+	3.81906i	0.0523782	+	0.152155i
$631$		−	5.71697i		−	0.227589i	−0.993504	−	0.113794i	$-0.963699\pi$
$631$		−	5.71697i		−	0.227589i	0.993504	−	0.113794i	$-0.0363005\pi$
$632$	20.0565	−	8.48186i	0.797803	−	0.337390i
$633$	−18.1676	−	10.4891i	−0.722099	−	0.416904i
$634$	−10.3073	+	32.9737i	−0.409357	+	1.30955i
$635$	2.87076	−	10.7138i	0.113923	−	0.425166i
$636$	13.6359	+	28.8700i	0.540698	+	1.14477i
$637$	11.1225	−	17.6001i	0.440689	−	0.697343i
$638$	0.684421	+	0.433657i	0.0270965	+	0.0171687i
$639$	−6.30277	−	10.9167i	−0.249334	−	0.431859i
$640$	−9.57685	−	5.87144i	−0.378558	−	0.232089i
$641$	−14.8475	+	25.7166i	−0.586441	+	1.01575i	0.408253	+	0.912869i	$0.366138\pi$
$641$	−14.8475	+	25.7166i	−0.586441	+	1.01575i	−0.994694	+	0.102877i	$0.967195\pi$
$642$	0.441607	−	10.7205i	0.0174289	−	0.423103i
$643$	3.53512	−	3.53512i	0.139412	−	0.139412i	−0.633957	−	0.773368i	$-0.718570\pi$
$643$	3.53512	−	3.53512i	0.139412	−	0.139412i	0.773368	+	0.633957i	$0.218570\pi$
$644$	18.9954	+	30.8323i	0.748526	+	1.21496i
$645$	7.33854	+	7.33854i	0.288955	+	0.288955i
$646$	−3.47198	−	3.77031i	−0.136603	−	0.148341i
$647$	−12.7788	−	7.37782i	−0.502385	−	0.290052i	0.227313	−	0.973822i	$-0.427006\pi$
$647$	−12.7788	−	7.37782i	−0.502385	−	0.290052i	−0.729698	+	0.683770i	$0.760339\pi$
$648$	−25.0023	−	18.8930i	−0.982182	−	0.742186i
$649$	−23.5746	+	13.6108i	−0.925384	+	0.534270i
$650$	3.69510	+	16.4753i	0.144934	+	0.646216i
$651$	6.34700	−	41.7433i	0.248759	−	1.63605i
$652$	15.5597	+	5.57659i	0.609364	+	0.218396i
$653$	9.56710	+	2.56350i	0.374390	+	0.100317i	0.441107	−	0.897455i	$-0.354586\pi$
$653$	9.56710	+	2.56350i	0.374390	+	0.100317i	−0.0667174	+	0.997772i	$0.521253\pi$
$654$	13.2880	+	25.3732i	0.519601	+	0.992169i
$655$	−6.25952	+	10.8418i	−0.244580	+	0.423624i
$656$	−1.57510	+	9.47808i	−0.0614973	+	0.370057i
$657$	−0.390135			−0.0152206
$658$	0.604996	+	0.897091i	0.0235852	+	0.0349722i
$659$	5.68205	−	5.68205i	0.221341	−	0.221341i	−0.587722	−	0.809063i	$-0.699975\pi$
$659$	5.68205	−	5.68205i	0.221341	−	0.221341i	0.809063	+	0.587722i	$0.199975\pi$
$660$	−7.71995	+	1.40049i	−0.300498	+	0.0545140i
$661$	9.26542	−	2.48266i	0.360383	−	0.0965643i	−0.0740843	−	0.997252i	$-0.523603\pi$
$661$	9.26542	−	2.48266i	0.360383	−	0.0965643i	0.434467	+	0.900688i	$0.356937\pi$
$662$	−9.85883	−	3.08180i	−0.383174	−	0.119777i
$663$	29.5665	−	17.0702i	1.14827	−	0.662952i
$664$	−1.04238	−	1.33786i	−0.0404521	−	0.0519192i
$665$	1.53608	+	0.672550i	0.0595666	+	0.0260804i
$666$	−14.9187	+	3.34597i	−0.578086	+	0.129654i
$667$	−0.519275	+	1.93796i	−0.0201064	+	0.0750381i
$668$	−1.46837	+	17.7929i	−0.0568130	+	0.688427i
$669$	−2.22923	−	8.31961i	−0.0861871	−	0.321655i
$670$	0.601117	−	14.5927i	0.0232232	−	0.563767i
$671$	7.31815			0.282514
$672$	5.02535	+	29.8375i	0.193857	+	1.15101i
$673$	3.24280			0.125001			0.0625004	−	0.998045i	$-0.480093\pi$
$673$	3.24280			0.125001			0.0625004	+	0.998045i	$0.480093\pi$
$674$	−0.555278	+	13.4800i	−0.0213885	+	0.519228i
$675$	−4.01767	−	14.9941i	−0.154640	−	0.577125i
$676$	0.683234	−	8.27903i	0.0262782	−	0.318424i
$677$	8.67832	−	32.3879i	0.333535	−	1.24477i	−0.571914	−	0.820314i	$-0.693799\pi$
$677$	8.67832	−	32.3879i	0.333535	−	1.24477i	0.905449	−	0.424455i	$-0.139534\pi$
$678$	−14.1570	+	3.17515i	−0.543698	+	0.121941i
$679$	−3.59239	−	32.2581i	−0.137863	−	1.23795i
$680$	−12.5780	+	9.79995i	−0.482343	+	0.375811i
$681$	8.47094	−	4.89070i	0.324607	−	0.187412i
$682$	20.8236	+	6.50929i	0.797376	+	0.249254i
$683$	−17.9673	+	4.81432i	−0.687499	+	0.184215i	−0.585624	−	0.810583i	$-0.699151\pi$
$683$	−17.9673	+	4.81432i	−0.687499	+	0.184215i	−0.101874	+	0.994797i	$0.532484\pi$
$684$	1.36566	−	0.247747i	0.0522173	−	0.00947284i
$685$	11.3762	−	11.3762i	0.434662	−	0.434662i
$686$	25.0863	−	7.52846i	0.957799	−	0.287438i
$687$	39.6602			1.51313
$688$	12.0283	+	16.8229i	0.458575	+	0.641367i
$689$	−11.7432	+	20.3398i	−0.447380	+	0.774886i
$690$	−9.01337	−	17.2109i	−0.343133	−	0.655206i
$691$	−20.9303	−	5.60826i	−0.796227	−	0.213348i	−0.162300	−	0.986741i	$-0.551891\pi$
$691$	−20.9303	−	5.60826i	−0.796227	−	0.213348i	−0.633927	+	0.773393i	$0.718558\pi$
$692$	10.2600	+	3.67718i	0.390026	+	0.139786i
$693$	4.39049	+	3.51060i	0.166781	+	0.133357i
$694$	2.82783	+	12.6085i	0.107343	+	0.478611i
$695$	−12.7707	+	7.37317i	−0.484421	+	0.279680i
$696$	−1.01063	+	1.33743i	−0.0383078	+	0.0506952i
$697$	11.8108	+	6.81898i	0.447367	+	0.258287i
$698$	−33.1742	−	36.0247i	−1.25566	−	1.36355i
$699$	7.24128	+	7.24128i	0.273891	+	0.273891i
$700$	−10.0907	+	18.6910i	−0.381391	+	0.706452i
$701$	4.96023	−	4.96023i	0.187345	−	0.187345i	−0.607202	−	0.794547i	$-0.707708\pi$
$701$	4.96023	−	4.96023i	0.187345	−	0.187345i	0.794547	+	0.607202i	$0.207708\pi$
$702$	0.669481	−	16.2523i	0.0252679	−	0.613405i
$703$	−3.17380	+	5.49718i	−0.119702	+	0.207330i
$704$	−15.6329	+	0.231096i	−0.589186	+	0.00870976i
$705$	−0.290246	−	0.502720i	−0.0109313	−	0.0189335i
$706$	−31.1438	−	19.7331i	−1.17211	−	0.742664i
$707$	−1.16554	−	2.98107i	−0.0438345	−	0.112115i
$708$	−24.0529	−	50.9250i	−0.903963	−	1.91388i
$709$	−3.74523	+	13.9774i	−0.140655	+	0.524932i	0.859255	+	0.511547i	$0.170927\pi$
$709$	−3.74523	+	13.9774i	−0.140655	+	0.524932i	−0.999910	+	0.0133851i	$0.995739\pi$
$710$	−4.85752	+	15.5395i	−0.182299	+	0.583185i
$711$	7.24889	+	4.18515i	0.271855	+	0.156955i
$712$	19.3771	+	45.8196i	0.726187	+	1.71716i
$713$			54.0240i			2.02321i
$714$	42.1589	+	8.19819i	1.57776	+	0.306809i
$715$	−4.08105	−	4.08105i	−0.152623	−	0.152623i
$716$	−3.48317	−	19.2003i	−0.130172	−	0.717550i
$717$	4.87927	+	18.2097i	0.182220	+	0.680053i
$718$	−2.28598	−	4.36503i	−0.0853119	−	0.162902i
$719$	−16.5646	−	28.6908i	−0.617756	−	1.06998i	−0.989894	−	0.141808i	$-0.954709\pi$
$719$	−16.5646	−	28.6908i	−0.617756	−	1.06998i	0.372138	−	0.928177i	$-0.378625\pi$
$720$	−0.418698	−	4.29753i	−0.0156039	−	0.160160i
$721$	9.16680	+	12.4542i	0.341389	+	0.463820i
$722$	−14.0730	+	22.2107i	−0.523742	+	0.826598i
$723$	50.2502	+	13.4645i	1.86883	+	0.500751i
$724$	15.4158	+	18.1890i	0.572922	+	0.675990i
$725$	−1.13668	+	0.304573i	−0.0422154	+	0.0113116i
$726$	15.1021	−	13.9071i	0.560492	−	0.516142i
$727$			23.5496i			0.873406i	0.899606	+	0.436703i	$0.143854\pi$
$727$			23.5496i			0.873406i	−0.899606	+	0.436703i	$0.856146\pi$
$728$	−15.9356	+	15.5389i	−0.590611	+	0.575910i
$729$			11.4085i			0.422538i
$730$	0.341336	+	0.370665i	0.0126334	+	0.0137189i
$731$	28.3545	−	7.59756i	1.04873	−	0.281006i
$732$	−1.24527	+	15.0895i	−0.0460265	+	0.557723i
$733$	−1.72774	−	0.462947i	−0.0638156	−	0.0170993i	0.226770	−	0.973948i	$-0.427183\pi$
$733$	−1.72774	−	0.462947i	−0.0638156	−	0.0170993i	−0.290586	+	0.956849i	$0.593850\pi$
$734$	29.2153	+	18.5112i	1.07836	+	0.683260i
$735$	−13.7071	+	3.09128i	−0.505593	+	0.114024i
$736$	−12.0956	−	36.7764i	−0.445849	−	1.35560i
$737$	−10.1636	−	17.6039i	−0.374382	−	0.648448i
$738$	−3.27163	+	1.71336i	−0.120431	+	0.0630698i
$739$	6.06175	+	22.6228i	0.222985	+	0.832192i	0.983202	+	0.182522i	$0.0584261\pi$
$739$	6.06175	+	22.6228i	0.222985	+	0.832192i	−0.760217	+	0.649670i	$0.774907\pi$
$740$	16.2316	+	11.2467i	0.596685	+	0.413437i
$741$	2.71407	+	2.71407i	0.0997039	+	0.0997039i
$742$	−27.9369	+	9.61708i	−1.02560	+	0.353054i
$743$		−	13.9219i		−	0.510747i	−0.966843	−	0.255373i	$-0.917802\pi$
$743$		−	13.9219i		−	0.510747i	0.966843	−	0.255373i	$-0.0821984\pi$
$744$	−16.9650	+	41.8290i	−0.621968	+	1.53352i
$745$	8.56324	+	4.94399i	0.313733	+	0.181134i
$746$	−49.6073	−	15.5069i	−1.81625	−	0.567747i
$747$	0.168726	−	0.629693i	0.00617336	−	0.0230393i
$748$	−7.48732	+	20.8909i	−0.273763	+	0.763848i
$749$	9.81615	+	1.49253i	0.358674	+	0.0545358i
$750$	13.6959	−	21.6156i	0.500104	−	0.789291i
$751$	4.53854	+	7.86098i	0.165614	+	0.286851i	0.936873	−	0.349670i	$-0.113706\pi$
$751$	4.53854	+	7.86098i	0.165614	+	0.286851i	−0.771259	+	0.636521i	$0.780373\pi$
$752$	−0.406321	−	1.08303i	−0.0148170	−	0.0394940i
$753$	−5.20885	+	9.02200i	−0.189821	+	0.328780i
$754$	−1.23207	−	0.0507523i	−0.0448692	−	0.00184829i
$755$	7.27718	−	7.27718i	0.264844	−	0.264844i
$756$	14.0502	−	14.8767i	0.510999	−	0.541062i
$757$	−1.14043	−	1.14043i	−0.0414496	−	0.0414496i	0.686078	−	0.727528i	$-0.259331\pi$
$757$	−1.14043	−	1.14043i	−0.0414496	−	0.0414496i	−0.727528	+	0.686078i	$0.759331\pi$
$758$	27.2446	−	25.0888i	0.989567	−	0.911266i
$759$	−23.4173	−	13.5200i	−0.849994	−	0.490744i
$760$	−1.43022	−	1.08075i	−0.0518796	−	0.0392029i
$761$	7.60476	−	4.39061i	0.275672	−	0.159159i	−0.355790	−	0.934566i	$-0.615788\pi$
$761$	7.60476	−	4.39061i	0.275672	−	0.159159i	0.631463	+	0.775406i	$0.282455\pi$
$762$	31.1648	−	6.98966i	1.12898	−	0.253209i
$763$	−24.6852	+	9.65142i	−0.893665	+	0.349405i
$764$	−4.21137	−	8.91635i	−0.152362	−	0.322582i
$765$	−5.92008	−	1.58628i	−0.214041	−	0.0573521i
$766$	19.7890	−	10.3636i	0.715007	−	0.374451i
$767$	20.7143	−	35.8783i	0.747951	−	1.29549i
$768$	2.18361	−	32.2731i	0.0787944	−	1.16455i
$769$	29.8204			1.07535			0.537676	−	0.843152i	$-0.319303\pi$
$769$	29.8204			1.07535			0.537676	+	0.843152i	$0.319303\pi$
$770$	−0.505918	−	7.24287i	−0.0182320	−	0.261015i
$771$	5.36862	−	5.36862i	0.193346	−	0.193346i
$772$	24.9554	−	36.0164i	0.898165	−	1.29626i
$773$	−44.5476	+	11.9365i	−1.60227	+	0.429326i	−0.945726	−	0.324965i	$-0.894648\pi$
$773$	−44.5476	+	11.9365i	−1.60227	+	0.429326i	−0.656540	+	0.754291i	$0.727981\pi$
$774$	−2.37169	+	7.58715i	−0.0852485	+	0.272715i
$775$	−27.4418	+	15.8435i	−0.985738	+	0.569116i
$776$	−4.27469	+	34.4342i	−0.153452	+	1.23612i
$777$	−5.88705	−	52.8632i	−0.211197	−	1.89646i
$778$	1.76452	+	7.86746i	0.0632611	+	0.282062i
$779$	−0.396838	+	1.48102i	−0.0142182	+	0.0530630i
$780$	9.10925	−	7.72037i	0.326163	−	0.276434i
$781$	5.86476	+	21.8876i	0.209858	+	0.783199i
$782$	−54.9057	−	2.26173i	−1.96343	−	0.0808792i
$783$	1.13367			0.0405142
$784$	−27.9543	+	1.59892i	−0.998368	+	0.0571041i
$785$	4.09643			0.146208
$786$	−36.0182	−	1.48370i	−1.28473	−	0.0529217i
$787$	6.78154	+	25.3091i	0.241736	+	0.902170i	0.974996	+	0.222222i	$0.0713311\pi$
$787$	6.78154	+	25.3091i	0.241736	+	0.902170i	−0.733260	+	0.679948i	$0.762002\pi$
$788$	−13.9347	−	16.4415i	−0.496401	−	0.585703i
$789$	9.86360	−	36.8115i	0.351153	−	1.31052i
$790$	−2.36589	−	10.5488i	−0.0841746	−	0.375309i
$791$	−1.48600	−	13.3437i	−0.0528361	−	0.474446i
$792$	−3.69354	−	4.74056i	−0.131244	−	0.168448i
$793$	−9.64539	+	5.56877i	−0.342518	+	0.197753i
$794$	−0.424560	+	1.35819i	−0.0150671	+	0.0482003i
$795$	15.3107	−	4.10250i	0.543016	−	0.145501i
$796$	−5.87908	−	4.07355i	−0.208378	−	0.144383i
$797$	−16.7419	+	16.7419i	−0.593028	+	0.593028i	−0.938448	−	0.345420i	$-0.887736\pi$
$797$	−16.7419	+	16.7419i	−0.593028	+	0.593028i	0.345420	+	0.938448i	$0.387736\pi$
$798$	0.336457	+	4.81681i	0.0119104	+	0.170513i
$799$	−1.64191			−0.0580866
$800$	15.1335	−	16.9294i	0.535051	−	0.598543i
$801$	−9.56111	+	16.5603i	−0.337825	+	0.585130i
$802$	21.8069	−	11.4203i	0.770027	−	0.403265i
$803$	0.677409	+	0.181511i	0.0239053	+	0.00640540i
$804$	38.0274	−	17.9611i	1.34112	−	0.633439i
$805$	16.7442	−	6.54665i	0.590156	−	0.230739i
$806$	−32.3989	+	7.26645i	−1.14120	+	0.255950i
$807$	−30.0243	+	17.3345i	−1.05690	+	0.610204i
$808$	0.471698	+	3.38915i	0.0165943	+	0.119230i
$809$	−30.7720	−	17.7662i	−1.08189	−	0.624628i	−0.150482	−	0.988613i	$-0.548083\pi$
$809$	−30.7720	−	17.7662i	−1.08189	−	0.624628i	−0.931405	+	0.363985i	$0.881416\pi$
$810$	−11.4444	+	10.5389i	−0.402116	+	0.370298i
$811$	29.5602	+	29.5602i	1.03800	+	1.03800i	0.999249	+	0.0387507i	$0.0123378\pi$
$811$	29.5602	+	29.5602i	1.03800	+	1.03800i	0.0387507	+	0.999249i	$0.487662\pi$
$812$	−1.12778	−	1.06512i	−0.0395775	−	0.0373784i
$813$	−7.59395	+	7.59395i	−0.266331	+	0.266331i
$814$	27.4607	+	1.13119i	0.962497	+	0.0396480i
$815$	4.10288	−	7.10640i	0.143718	−	0.248926i
$816$	−41.8014	−	18.9931i	−1.46334	−	0.664892i
$817$	1.65012	+	2.85809i	0.0577304	+	0.0999920i
$818$	28.8952	−	45.6040i	1.01030	−	1.59451i
$819$	−8.45811	−	1.28604i	−0.295550	−	0.0449379i
$820$	4.49027	+	1.60931i	0.156807	+	0.0561996i
$821$	2.04620	−	7.63653i	0.0714129	−	0.266517i	−0.920983	−	0.389602i	$-0.872612\pi$
$821$	2.04620	−	7.63653i	0.0714129	−	0.266517i	0.992396	+	0.123086i	$0.0392791\pi$
$822$	44.2167	+	13.8218i	1.54224	+	0.482091i
$823$	−43.2107	−	24.9477i	−1.50623	−	0.869623i	−0.999974	−	0.00724096i	$-0.997695\pi$
$823$	−43.2107	−	24.9477i	−1.50623	−	0.869623i	−0.506258	−	0.862382i	$-0.668972\pi$
$824$	−6.43916	−	15.2262i	−0.224319	−	0.530431i
$825$		−	15.8599i		−	0.552171i
$826$	49.2791	−	16.9640i	1.71464	−	0.590252i
$827$	−8.11672	−	8.11672i	−0.282246	−	0.282246i	0.551758	−	0.834004i	$-0.313957\pi$
$827$	−8.11672	−	8.11672i	−0.282246	−	0.282246i	−0.834004	+	0.551758i	$0.813957\pi$
$828$	8.47521	−	12.2317i	0.294534	−	0.425080i
$829$	−1.84091	−	6.87035i	−0.0639373	−	0.238617i	0.926561	−	0.376146i	$-0.122751\pi$
$829$	−1.84091	−	6.87035i	−0.0639373	−	0.238617i	−0.990498	+	0.137528i	$0.956084\pi$
$830$	−0.745890	+	0.390624i	−0.0258902	+	0.0135588i
$831$	−15.3659	−	26.6145i	−0.533037	−	0.923248i
$832$	20.4284	−	12.2005i	0.708227	−	0.422975i
$833$	−11.8129	+	37.9478i	−0.409293	+	1.31481i
$834$	−35.8685	−	22.7267i	−1.24202	−	0.786962i
$835$	8.56133	+	2.29400i	0.296277	+	0.0793872i
$836$	−2.48652	−	0.205202i	−0.0859982	−	0.00709708i
$837$	29.4861	−	7.90079i	1.01919	−	0.273091i
$838$	36.5803	+	39.7235i	1.26365	+	1.37223i
$839$		−	3.57060i		−	0.123271i	−0.998099	−	0.0616354i	$-0.980368\pi$
$839$		−	3.57060i		−	0.123271i	0.998099	−	0.0616354i	$-0.0196316\pi$
$840$	15.0203	+	0.189296i	0.518250	+	0.00653134i
$841$			28.9141i			0.997036i
$842$	−28.1697	+	25.9407i	−0.970792	+	0.893977i
$843$	−6.16664	+	1.65235i	−0.212390	+	0.0569098i
$844$	−15.8320	+	13.4181i	−0.544959	+	0.461870i
$845$	−3.98359	−	1.06740i	−0.137040	−	0.0367197i
$846$	0.237973	−	0.375581i	0.00818167	−	0.0129127i
$847$	11.2617	+	15.3004i	0.386957	+	0.525730i
$848$	31.4370	−	3.06283i	1.07955	−	0.105178i
$849$	−14.2697	−	24.7159i	−0.489736	−	0.848248i
$850$	−14.9532	−	28.5530i	−0.512892	−	0.979358i
$851$	17.6142	+	65.7370i	0.603806	+	2.25344i
$852$	−46.1285	+	8.36825i	−1.58034	+	0.286691i
$853$	13.8958	+	13.8958i	0.475784	+	0.475784i	0.903780	−	0.427996i	$-0.140780\pi$
$853$	13.8958	+	13.8958i	0.475784	+	0.475784i	−0.427996	+	0.903780i	$0.640780\pi$
$854$	−13.7534	−	2.67447i	−0.470631	−	0.0915185i
$855$		−	0.689051i		−	0.0235650i
$856$	−9.83628	−	3.98941i	−0.336197	−	0.136355i
$857$	−34.8241	−	20.1057i	−1.18957	−	0.686798i	−0.231360	−	0.972868i	$-0.574318\pi$
$857$	−34.8241	−	20.1057i	−1.18957	−	0.686798i	−0.958209	+	0.286070i	$0.907651\pi$
$858$	4.95839	−	15.8622i	0.169277	−	0.541525i
$859$	6.71022	−	25.0429i	0.228950	−	0.854452i	−0.751834	−	0.659353i	$-0.770830\pi$
$859$	6.71022	−	25.0429i	0.228950	−	0.854452i	0.980784	−	0.195099i	$-0.0625029\pi$
$860$	9.28354	−	4.38480i	0.316566	−	0.149521i
$861$	−4.67845	−	11.9660i	−0.159441	−	0.407799i
$862$	1.50175	+	0.951526i	0.0511497	+	0.0324091i
$863$	−8.22908	−	14.2532i	−0.280121	−	0.485184i	0.691293	−	0.722574i	$-0.257041\pi$
$863$	−8.22908	−	14.2532i	−0.280121	−	0.485184i	−0.971414	+	0.237390i	$0.923708\pi$
$864$	−18.3035	+	11.9801i	−0.622698	+	0.407572i
$865$	2.70543	−	4.68593i	0.0919872	−	0.159327i
$866$	−0.533684	+	12.9557i	−0.0181353	+	0.440253i
$867$	−21.7811	+	21.7811i	−0.739724	+	0.739724i
$868$	−36.7560	−	19.8434i	−1.24758	−	0.673528i
$869$	−10.6394	−	10.6394i	−0.360918	−	0.360918i
$870$	0.563749	+	0.612189i	0.0191129	+	0.0207552i
$871$	26.7915	+	15.4681i	0.907795	+	0.524116i
$872$	28.0644	−	3.90598i	0.950381	−	0.132273i
$873$	−11.5505	+	6.66868i	−0.390925	+	0.225700i
$874$	−1.35204	−	6.02832i	−0.0457333	−	0.203911i
$875$	18.4946	+	14.7881i	0.625232	+	0.499930i
$876$	−0.489531	+	1.36588i	−0.0165397	+	0.0461488i
$877$	−22.0521	−	5.90884i	−0.744646	−	0.199527i	−0.133504	−	0.991048i	$-0.542623\pi$
$877$	−22.0521	−	5.90884i	−0.744646	−	0.199527i	−0.611142	+	0.791521i	$0.709290\pi$
$878$	−5.22640	−	9.97971i	−0.176382	−	0.336799i
$879$	−15.6299	+	27.0718i	−0.527185	+	0.913111i
$880$	−1.27243	+	7.65681i	−0.0428938	+	0.258111i
$881$	5.29761			0.178481			0.0892405	−	0.996010i	$-0.471556\pi$
$881$	5.29761			0.178481			0.0892405	+	0.996010i	$0.471556\pi$
$882$	−6.96831	−	8.20219i	−0.234635	−	0.276182i
$883$	−30.7426	+	30.7426i	−1.03457	+	1.03457i	−0.0351900	+	0.999381i	$0.511204\pi$
$883$	−30.7426	+	30.7426i	−1.03457	+	1.03457i	−0.999381	+	0.0351900i	$0.988796\pi$
$884$	−6.02866	−	33.2319i	−0.202766	−	1.11771i
$885$	−27.0073	+	7.23658i	−0.907840	+	0.243255i
$886$	−33.7744	−	10.5576i	−1.13467	−	0.354690i
$887$	−5.04199	+	2.91100i	−0.169294	+	0.0977417i	−0.582253	−	0.813008i	$-0.697829\pi$
$887$	−5.04199	+	2.91100i	−0.169294	+	0.0977417i	0.412959	+	0.910750i	$0.364495\pi$
$888$	−7.00518	+	56.4293i	−0.235078	+	1.89364i
$889$	3.27123	+	29.3742i	0.109713	+	0.985180i
$890$	24.0991	−	5.40496i	0.807802	−	0.181175i
$891$	−5.60423	+	20.9153i	−0.187749	+	0.700688i
$892$	−8.49186	−	0.700798i	−0.284329	−	0.0234645i
$893$	−0.0477763	−	0.178304i	−0.00159877	−	0.00596671i
$894$	−1.17188	+	28.4485i	−0.0391934	+	0.951460i
$895$	−9.68763			−0.323822
$896$	29.4641	+	5.27883i	0.984327	+	0.176353i
$897$	41.1522			1.37403
$898$	−0.484880	+	11.7710i	−0.0161806	+	0.392802i
$899$	−0.598947	−	2.23530i	−0.0199760	−	0.0745514i
$900$	8.69866	+	0.717864i	0.289955	+	0.0239288i
$901$	11.6039	−	43.3062i	0.386581	−	1.44274i
$902$	6.47784	−	1.45285i	0.215688	−	0.0483748i
$903$	−25.3328	−	11.0916i	−0.843022	−	0.369105i
$904$	−1.76824	+	14.2438i	−0.0588107	+	0.473742i
$905$	10.2510	−	5.91844i	0.340756	−	0.196736i
$906$	28.2848	+	8.84161i	0.939700	+	0.293743i
$907$	20.3319	−	5.44791i	0.675108	−	0.180895i	0.0950536	−	0.995472i	$-0.469698\pi$
$907$	20.3319	−	5.44791i	0.675108	−	0.180895i	0.580055	+	0.814577i	$0.303031\pi$
$908$	−1.72724	−	9.52111i	−0.0573205	−	0.315969i
$909$	−0.930037	+	0.930037i	−0.0308474	+	0.0308474i
$910$	6.17828	+	9.16118i	0.204808	+	0.303690i
$911$	−46.3231			−1.53475			−0.767376	−	0.641197i	$-0.778438\pi$
$911$	−46.3231			−1.53475			−0.767376	+	0.641197i	$0.778438\pi$
$912$	0.846223	−	5.09210i	0.0280212	−	0.168616i
$913$	−0.585933	+	1.01487i	−0.0193916	+	0.0335872i
$914$	−9.49561	−	18.1317i	−0.314087	−	0.599743i
$915$	7.26054	+	1.94546i	0.240026	+	0.0643148i
$916$	13.2373	−	36.9344i	0.437373	−	1.22035i
$917$	5.01454	−	32.9799i	0.165595	−	1.08909i
$918$	6.79529	+	30.2982i	0.224278	+	0.999988i
$919$	−12.8775	+	7.43484i	−0.424790	+	0.245253i	−0.697125	−	0.716950i	$-0.745538\pi$
$919$	−12.8775	+	7.43484i	−0.424790	+	0.245253i	0.272335	+	0.962203i	$0.412204\pi$
$920$	−19.0364	+	2.64946i	−0.627610	+	0.0873501i
$921$	36.5799	+	21.1194i	1.20535	+	0.695908i
$922$	5.73112	+	6.22357i	0.188744	+	0.204962i
$923$	−24.3852	−	24.3852i	−0.802649	−	0.802649i
$924$	17.7998	−	10.9663i	0.585571	−	0.360765i
$925$	−28.2258	+	28.2258i	−0.928058	+	0.928058i
$926$	−1.46672	+	35.6062i	−0.0481995	+	1.17009i
$927$	3.17723	−	5.50313i	0.104354	−	0.180746i
$928$	0.908195	+	1.38756i	0.0298130	+	0.0455490i
$929$	25.8504	+	44.7742i	0.848124	+	1.46899i	0.882881	+	0.469598i	$0.155601\pi$
$929$	25.8504	+	44.7742i	0.848124	+	1.46899i	−0.0347569	+	0.999396i	$0.511066\pi$
$930$	18.9292	+	11.9938i	0.620713	+	0.393291i
$931$	−4.46469	−	0.178619i	−0.146324	−	0.00585399i
$932$	9.16052	−	4.32670i	0.300063	−	0.141726i
$933$	4.57104	−	17.0593i	0.149649	−	0.558498i
$934$	−6.48294	+	20.7393i	−0.212128	+	0.678610i
$935$	9.54129	+	5.50867i	0.312034	+	0.180153i
$936$	8.47546	+	3.43748i	0.277029	+	0.112358i
$937$		−	50.1408i		−	1.63803i	−0.573773	−	0.819014i	$-0.694521\pi$
$937$		−	50.1408i		−	1.63803i	0.573773	−	0.819014i	$-0.305479\pi$
$938$	12.6676	+	36.7983i	0.413610	+	1.20151i
$939$	5.88663	+	5.88663i	0.192103	+	0.192103i
$940$	−0.565044	+	0.102506i	−0.0184297	+	0.00334337i
$941$	11.6055	+	43.3123i	0.378328	+	1.41194i	0.848421	+	0.529322i	$0.177554\pi$
$941$	11.6055	+	43.3123i	0.378328	+	1.41194i	−0.470093	+	0.882617i	$0.655780\pi$
$942$	5.47243	+	10.4495i	0.178301	+	0.340463i
$943$	8.21947	+	14.2365i	0.267663	+	0.463606i
$944$	−55.4531	+	5.40265i	−1.80485	+	0.175841i
$945$	−6.02192	−	8.18152i	−0.195893	−	0.266145i
$946$	7.64801	−	12.0705i	0.248658	−	0.392445i
$947$	−1.59414	−	0.427149i	−0.0518027	−	0.0138805i	0.232825	−	0.972519i	$-0.425203\pi$
$947$	−1.59414	−	0.427149i	−0.0518027	−	0.0138805i	−0.284627	+	0.958638i	$0.591870\pi$
$948$	23.7481	−	20.1273i	0.771303	−	0.653703i
$949$	−1.03095	+	0.276243i	−0.0334661	+	0.00896723i
$950$	2.66561	−	2.45469i	0.0864837	−	0.0796406i
$951$			49.3867i			1.60147i
$952$	21.7060	−	36.5251i	0.703497	−	1.18379i
$953$		−	40.9510i		−	1.32653i	−0.748384	−	0.663266i	$-0.769170\pi$
$953$		−	40.9510i		−	1.32653i	0.748384	−	0.663266i	$-0.230830\pi$
$954$	8.22431	+	8.93099i	0.266272	+	0.289151i
$955$	−4.72865	+	1.26704i	−0.153015	+	0.0410003i
$956$	18.5867	+	1.53388i	0.601137	+	0.0496093i
$957$	1.11881	+	0.299783i	0.0361659	+	0.00969062i
$958$	−24.8828	−	15.7661i	−0.803927	−	0.509378i
$959$	−17.1941	+	39.2708i	−0.555228	+	1.26812i
$960$	−15.5712	−	3.92656i	−0.502559	−	0.126729i
$961$	−15.6564	−	27.1177i	−0.505046	−	0.874766i
$962$	−37.0542	+	19.4054i	−1.19468	+	0.625654i
$963$	−1.05598	−	3.94096i	−0.0340284	−	0.126996i
$964$	29.3111	−	42.3026i	0.944045	−	1.36248i
$965$	−15.3818	−	15.3818i	−0.495159	−	0.495159i
$966$	39.0684	+	33.9668i	1.25700	+	1.09286i
$967$			14.6315i			0.470518i	0.971933	+	0.235259i	$0.0755938\pi$
$967$			14.6315i			0.470518i	−0.971933	+	0.235259i	$0.924406\pi$
$968$	−7.91072	−	18.7059i	−0.254260	−	0.601231i
$969$	−6.34536	−	3.66350i	−0.203842	−	0.117688i
$970$	16.4416	+	5.13952i	0.527908	+	0.165020i
$971$	6.32211	−	23.5944i	0.202886	−	0.757181i	−0.787197	−	0.616701i	$-0.788469\pi$
$971$	6.32211	−	23.5944i	0.202886	−	0.757181i	0.990084	−	0.140480i	$-0.0448646\pi$
$972$	−20.3299	−	7.28623i	−0.652081	−	0.233706i
$973$	24.5391	−	30.6896i	0.786687	−	0.983863i
$974$	0.168362	−	0.265717i	0.00539466	−	0.00851413i
$975$	12.0686	+	20.9035i	0.386506	+	0.669448i
$976$	13.6368	+	6.19607i	0.436502	+	0.198331i
$977$	2.85781	−	4.94988i	0.0914295	−	0.158361i	−0.816683	−	0.577086i	$-0.804190\pi$
$977$	2.85781	−	4.94988i	0.0914295	−	0.158361i	0.908113	+	0.418725i	$0.137523\pi$
$978$	23.6086	+	0.972507i	0.754920	+	0.0310974i
$979$	24.3061	−	24.3061i	0.776827	−	0.776827i
$980$	−1.69616	+	13.7968i	−0.0541818	+	0.440722i
$981$	7.70133	+	7.70133i	0.245885	+	0.245885i
$982$	26.7153	−	24.6014i	0.852520	−	0.785063i
$983$	−18.6714	−	10.7799i	−0.595525	−	0.343827i	0.171754	−	0.985140i	$-0.445057\pi$
$983$	−18.6714	−	10.7799i	−0.595525	−	0.343827i	−0.767279	+	0.641313i	$0.778390\pi$
$984$	1.89339	+	13.6040i	0.0603591	+	0.433680i
$985$	−9.26615	+	5.34981i	−0.295244	+	0.170459i
$986$	2.29686	−	0.515141i	0.0731469	−	0.0164054i
$987$	1.20810	+	0.965983i	0.0384542	+	0.0307476i
$988$	3.43341	−	1.62167i	0.109231	−	0.0515921i
$989$	34.1780	+	9.15796i	1.08680	+	0.291206i
$990$	−2.64297	+	1.38413i	−0.0839991	+	0.0439905i
$991$	17.3811	−	30.1049i	0.552128	−	0.956314i	−0.445993	−	0.895037i	$-0.647149\pi$
$991$	17.3811	−	30.1049i	0.552128	−	0.956314i	0.998121	−	0.0612772i	$-0.0195174\pi$
$992$	33.2918	+	29.7602i	1.05701	+	0.944888i
$993$	−14.7661			−0.468590
$994$	−3.02298	−	43.2778i	−0.0958830	−	1.37269i
$995$	−2.51082	+	2.51082i	−0.0795985	+	0.0795985i
$996$	−1.99287	−	1.38084i	−0.0631465	−	0.0437536i
$997$	−4.95586	+	1.32792i	−0.156954	+	0.0420556i	−0.336440	−	0.941705i	$-0.609223\pi$
$997$	−4.95586	+	1.32792i	−0.156954	+	0.0420556i	0.179487	+	0.983760i	$0.442556\pi$
$998$	−1.48148	+	4.73933i	−0.0468954	+	0.150021i
$999$	33.3031	−	19.2275i	1.05366	−	0.608332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.c.53.7	yes	48
4.3	odd	2		448.2.ba.c.305.10		48
7.2	even	3	inner	112.2.w.c.37.3	✓	48
7.3	odd	6		784.2.m.k.197.10		24
7.4	even	3		784.2.m.j.197.10		24
7.5	odd	6		784.2.x.o.373.3		48
7.6	odd	2		784.2.x.o.165.7		48
8.3	odd	2		896.2.ba.e.865.3		48
8.5	even	2		896.2.ba.f.865.10		48
16.3	odd	4		448.2.ba.c.81.3		48
16.5	even	4		896.2.ba.f.417.3		48
16.11	odd	4		896.2.ba.e.417.10		48
16.13	even	4	inner	112.2.w.c.109.3	yes	48
28.23	odd	6		448.2.ba.c.177.3		48
56.37	even	6		896.2.ba.f.737.3		48
56.51	odd	6		896.2.ba.e.737.10		48
112.13	odd	4		784.2.x.o.557.3		48
112.37	even	12		896.2.ba.f.289.10		48
112.45	odd	12		784.2.m.k.589.10		24
112.51	odd	12		448.2.ba.c.401.10		48
112.61	odd	12		784.2.x.o.765.7		48
112.93	even	12	inner	112.2.w.c.93.7	yes	48
112.107	odd	12		896.2.ba.e.289.3		48
112.109	even	12		784.2.m.j.589.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.3	✓	48	7.2	even	3	inner
112.2.w.c.53.7	yes	48	1.1	even	1	trivial
112.2.w.c.93.7	yes	48	112.93	even	12	inner
112.2.w.c.109.3	yes	48	16.13	even	4	inner
448.2.ba.c.81.3		48	16.3	odd	4
448.2.ba.c.177.3		48	28.23	odd	6
448.2.ba.c.305.10		48	4.3	odd	2
448.2.ba.c.401.10		48	112.51	odd	12
784.2.m.j.197.10		24	7.4	even	3
784.2.m.j.589.10		24	112.109	even	12
784.2.m.k.197.10		24	7.3	odd	6
784.2.m.k.589.10		24	112.45	odd	12
784.2.x.o.165.7		48	7.6	odd	2
784.2.x.o.373.3		48	7.5	odd	6
784.2.x.o.557.3		48	112.13	odd	4
784.2.x.o.765.7		48	112.61	odd	12
896.2.ba.e.289.3		48	112.107	odd	12
896.2.ba.e.417.10		48	16.11	odd	4
896.2.ba.e.737.10		48	56.51	odd	6
896.2.ba.e.865.3		48	8.3	odd	2
896.2.ba.f.289.10		48	112.37	even	12
896.2.ba.f.417.3		48	16.5	even	4
896.2.ba.f.737.3		48	56.37	even	6
896.2.ba.f.865.10		48	8.5	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.0582062 - 1.41302i) q^{2} +(-0.523249 - 1.95279i) q^{3} +(-1.99322 - 0.164492i) q^{4} +(-0.256983 + 0.959072i) q^{5} +(-2.78978 + 0.625694i) q^{6} +(-0.292831 - 2.62950i) q^{7} +(-0.348448 + 2.80688i) q^{8} +(-0.941530 + 0.543593i) q^{9} +O(q^{10})\)	\(q+(0.0582062 - 1.41302i) q^{2} +(-0.523249 - 1.95279i) q^{3} +(-1.99322 - 0.164492i) q^{4} +(-0.256983 + 0.959072i) q^{5} +(-2.78978 + 0.625694i) q^{6} +(-0.292831 - 2.62950i) q^{7} +(-0.348448 + 2.80688i) q^{8} +(-0.941530 + 0.543593i) q^{9} +(1.34023 + 0.418944i) q^{10} +(1.88773 - 0.505816i) q^{11} +(0.721733 + 3.97842i) q^{12} +(-2.10314 + 2.10314i) q^{13} +(-3.73256 + 0.260721i) q^{14} +2.00733 q^{15} +(3.94588 + 0.655741i) q^{16} +(2.83885 - 4.91704i) q^{17} +(0.713302 + 1.36204i) q^{18} +(0.616573 + 0.165210i) q^{19} +(0.669984 - 1.86937i) q^{20} +(-4.98163 + 1.94772i) q^{21} +(-0.604848 - 2.69683i) q^{22} +(5.92691 - 3.42190i) q^{23} +(5.66358 - 0.788251i) q^{24} +(3.47635 + 2.00707i) q^{25} +(2.84936 + 3.09419i) q^{26} +(-2.73445 - 2.73445i) q^{27} +(0.151145 + 5.28934i) q^{28} +(-0.207295 + 0.207295i) q^{29} +(0.116839 - 2.83639i) q^{30} +(-3.94693 + 6.83628i) q^{31} +(1.15625 - 5.53743i) q^{32} +(-1.97551 - 3.42168i) q^{33} +(-6.78261 - 4.29755i) q^{34} +(2.59713 + 0.394889i) q^{35} +(1.96610 - 0.928627i) q^{36} +(-2.57374 + 9.60533i) q^{37} +(0.269333 - 0.861610i) q^{38} +(5.20747 + 3.00653i) q^{39} +(-2.60246 - 1.05551i) q^{40} +2.40202i q^{41} +(2.46219 + 7.15250i) q^{42} +(3.65586 + 3.65586i) q^{43} +(-3.84587 + 0.697687i) q^{44} +(-0.279388 - 1.04269i) q^{45} +(-4.49022 - 8.57399i) q^{46} +(-0.144593 - 0.250442i) q^{47} +(-0.784155 - 8.04861i) q^{48} +(-6.82850 + 1.53999i) q^{49} +(3.03837 - 4.79531i) q^{50} +(-11.0874 - 2.97086i) q^{51} +(4.53798 - 3.84608i) q^{52} +(7.62740 - 2.04376i) q^{53} +(-4.02298 + 3.70466i) q^{54} +1.94045i q^{55} +(7.48272 + 0.0943023i) q^{56} -1.29048i q^{57} +(0.280845 + 0.304976i) q^{58} +(-13.4543 + 3.60507i) q^{59} +(-4.00107 - 0.330191i) q^{60} +(3.61701 + 0.969174i) q^{61} +(9.43003 + 5.97498i) q^{62} +(1.70508 + 2.31657i) q^{63} +(-7.75717 - 1.95611i) q^{64} +(-1.47659 - 2.55754i) q^{65} +(-4.94987 + 2.59226i) q^{66} +(-2.69202 - 10.0468i) q^{67} +(-6.46729 + 9.33379i) q^{68} +(-9.78352 - 9.78352i) q^{69} +(0.709153 - 3.64680i) q^{70} +11.5947i q^{71} +(-1.19773 - 2.83218i) q^{72} +(0.310772 + 0.179424i) q^{73} +(13.4227 + 4.19582i) q^{74} +(2.10040 - 7.83878i) q^{75} +(-1.20179 - 0.430722i) q^{76} +(-1.88283 - 4.81566i) q^{77} +(4.55138 - 7.18323i) q^{78} +(-3.84953 - 6.66758i) q^{79} +(-1.64293 + 3.61587i) q^{80} +(-5.53979 + 9.59520i) q^{81} +(3.39409 + 0.139812i) q^{82} +(-0.424001 + 0.424001i) q^{83} +(10.2499 - 3.06280i) q^{84} +(3.98626 + 3.98626i) q^{85} +(5.37858 - 4.95300i) q^{86} +(0.513270 + 0.296337i) q^{87} +(0.761988 + 5.47488i) q^{88} +(15.2323 - 8.79437i) q^{89} +(-1.48960 + 0.334088i) q^{90} +(6.14607 + 4.91434i) q^{91} +(-12.3765 + 5.84569i) q^{92} +(15.4150 + 4.13045i) q^{93} +(-0.362294 + 0.189734i) q^{94} +(-0.316897 + 0.548881i) q^{95} +(-11.4184 + 0.639544i) q^{96} +12.2678 q^{97} +(1.77858 + 9.73841i) q^{98} +(-1.50240 + 1.50240i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more