LMFDB - Embedded newform 889.2.bm.a.445.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [889,2,Mod(2,889)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(889, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([14, 24]))

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

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

chi := DirichletCharacter("889.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 889 = 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	889.bm (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.09870073969$
Analytic rank:	$0$
Dimension:	$1008$
Relative dimension:	$84$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			445.14
Character	$\chi$	$=$	889.445
Dual form			889.2.bm.a.2.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73594 - 1.18354i) q^{2} +(-1.77532 - 0.547615i) q^{3} +(0.882028 + 2.24737i) q^{4} +(0.0270140 - 0.0688306i) q^{5} +(2.43373 + 3.05180i) q^{6} +(0.776326 - 2.52929i) q^{7} +(0.193674 - 0.848541i) q^{8} +(0.373178 + 0.254429i) q^{9} +O(q^{10})$	\(q+(-1.73594 - 1.18354i) q^{2} +(-1.77532 - 0.547615i) q^{3} +(0.882028 + 2.24737i) q^{4} +(0.0270140 - 0.0688306i) q^{5} +(2.43373 + 3.05180i) q^{6} +(0.776326 - 2.52929i) q^{7} +(0.193674 - 0.848541i) q^{8} +(0.373178 + 0.254429i) q^{9} +(-0.128359 + 0.0875135i) q^{10} +(-0.769292 + 0.524494i) q^{11} +(-0.335192 - 4.47282i) q^{12} +(0.581928 + 0.729714i) q^{13} +(-4.34118 + 3.47188i) q^{14} +(-0.0856514 + 0.107403i) q^{15} +(2.19906 - 2.04043i) q^{16} +(4.93251 - 0.743457i) q^{17} +(-0.346688 - 0.883346i) q^{18} +(-2.74163 - 4.74864i) q^{19} +0.178515 q^{20} +(-2.76331 + 4.06519i) q^{21} +1.95621 q^{22} +(-4.32229 - 2.94688i) q^{23} +(-0.808508 + 1.40038i) q^{24} +(3.66125 + 3.39714i) q^{25} +(-0.146543 - 1.95548i) q^{26} +(2.95189 + 3.70156i) q^{27} +(6.36900 - 0.486213i) q^{28} +(-1.34140 - 5.87706i) q^{29} +(0.275802 - 0.0850737i) q^{30} +(-3.66138 - 9.32905i) q^{31} +(-7.95366 + 1.19882i) q^{32} +(1.65296 - 0.509872i) q^{33} +(-9.44245 - 4.54725i) q^{34} +(-0.153121 - 0.121761i) q^{35} +(-0.242642 + 1.06308i) q^{36} +(-2.53754 - 4.39514i) q^{37} +(-0.860920 + 11.4882i) q^{38} +(-0.633508 - 1.61415i) q^{39} +(-0.0531737 - 0.0362532i) q^{40} +(3.35628 + 4.20865i) q^{41} +(9.60826 - 3.78642i) q^{42} +(0.299343 + 1.31151i) q^{43} +(-1.85727 - 1.26627i) q^{44} +(0.0275935 - 0.0188130i) q^{45} +(4.01546 + 10.2312i) q^{46} +(-1.70107 - 0.256395i) q^{47} +(-5.02142 + 2.41819i) q^{48} +(-5.79464 - 3.92711i) q^{49} +(-2.33504 - 10.2305i) q^{50} +(-9.16394 - 1.38124i) q^{51} +(-1.12666 + 1.95143i) q^{52} +(0.0172795 - 0.230579i) q^{53} +(-0.743354 - 9.91937i) q^{54} +(0.0153196 + 0.0671196i) q^{55} +(-1.99585 - 1.14860i) q^{56} +(2.26685 + 9.93173i) q^{57} +(-4.62717 + 11.7898i) q^{58} +(-6.42544 + 11.1292i) q^{59} +(-0.316922 - 0.0977575i) q^{60} +(3.09114 - 2.86816i) q^{61} +(-4.68540 + 20.5281i) q^{62} +(0.933233 - 0.746357i) q^{63} +(9.82034 + 4.72923i) q^{64} +(0.0659469 - 0.0203419i) q^{65} +(-3.47290 - 1.07125i) q^{66} +(5.65462 + 1.74422i) q^{67} +(6.02144 + 10.4294i) q^{68} +(6.05970 + 7.59863i) q^{69} +(0.121699 + 0.392596i) q^{70} +(-0.861327 + 0.414793i) q^{71} +(0.288168 - 0.267381i) q^{72} +(-8.70897 + 5.93767i) q^{73} +(-0.796832 + 10.6330i) q^{74} +(-4.63958 - 8.03599i) q^{75} +(8.25375 - 10.3499i) q^{76} +(0.729378 + 2.35294i) q^{77} +(-0.810687 + 3.55185i) q^{78} +(0.507736 + 0.346169i) q^{79} +(-0.0810387 - 0.206483i) q^{80} +(-3.70857 - 9.44928i) q^{81} +(-0.845189 - 11.2783i) q^{82} +(-12.0297 + 5.79320i) q^{83} +(-11.5733 - 2.62457i) q^{84} +(0.0820745 - 0.359592i) q^{85} +(1.03258 - 2.63098i) q^{86} +(-0.836945 + 11.1683i) q^{87} +(0.296063 + 0.754357i) q^{88} +(8.68731 + 5.92291i) q^{89} -0.0701667 q^{90} +(2.29743 - 0.905368i) q^{91} +(2.81036 - 12.3130i) q^{92} +(1.39141 + 18.5671i) q^{93} +(2.64950 + 2.45838i) q^{94} +(-0.400914 + 0.0604281i) q^{95} +(14.7768 + 2.22725i) q^{96} +(-1.89631 + 8.30827i) q^{97} +(5.41123 + 13.6754i) q^{98} -0.420530 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1008 q - 7 q^{3} + 84 q^{4} - 9 q^{5} - 28 q^{6} - 19 q^{7} - 30 q^{8} + 67 q^{9}+O(q^{10}) $ 1008 * q - 7 * q^3 + 84 * q^4 - 9 * q^5 - 28 * q^6 - 19 * q^7 - 30 * q^8 + 67 * q^9	\( 1008 q - 7 q^{3} + 84 q^{4} - 9 q^{5} - 28 q^{6} - 19 q^{7} - 30 q^{8} + 67 q^{9} - 13 q^{10} - 19 q^{11} - 17 q^{12} - 36 q^{13} + 6 q^{14} + 6 q^{15} + 112 q^{16} + q^{17} - 25 q^{18} - 34 q^{19} - 232 q^{20} + 8 q^{21} - 40 q^{22} - 15 q^{23} + 78 q^{24} + 97 q^{25} + 43 q^{26} - 4 q^{27} + 68 q^{28} + 64 q^{29} - 25 q^{30} + q^{31} - 32 q^{32} - 25 q^{33} + 132 q^{34} - 46 q^{35} - 188 q^{36} - 6 q^{37} + 15 q^{38} + 19 q^{39} - 53 q^{40} - 34 q^{41} + 4 q^{42} - 8 q^{43} - 132 q^{44} - 55 q^{45} - 35 q^{46} + 25 q^{47} - 40 q^{48} + 83 q^{49} - 104 q^{50} - 32 q^{51} + 8 q^{52} - 17 q^{53} - 57 q^{54} + 6 q^{55} + 4 q^{56} + 34 q^{57} + 13 q^{58} + 140 q^{59} - 78 q^{60} + 7 q^{61} - 100 q^{62} + 60 q^{63} - 146 q^{64} - 6 q^{65} - 32 q^{66} - 71 q^{67} - 28 q^{68} - 8 q^{69} - 200 q^{70} - 38 q^{71} - 4 q^{72} - 18 q^{73} + 24 q^{74} - 42 q^{75} + 50 q^{76} + 4 q^{77} + 36 q^{78} - 37 q^{79} - 11 q^{80} - 61 q^{81} + 55 q^{82} + 40 q^{83} + 274 q^{84} - 48 q^{85} - 83 q^{86} + q^{87} - 34 q^{88} - 29 q^{89} - 244 q^{90} + 34 q^{91} - 254 q^{92} - 81 q^{93} + 67 q^{94} + 15 q^{95} + 55 q^{96} - 32 q^{97} + 249 q^{98} - 176 q^{99}+O(q^{100}) \) 1008 * q - 7 * q^3 + 84 * q^4 - 9 * q^5 - 28 * q^6 - 19 * q^7 - 30 * q^8 + 67 * q^9 - 13 * q^10 - 19 * q^11 - 17 * q^12 - 36 * q^13 + 6 * q^14 + 6 * q^15 + 112 * q^16 + q^17 - 25 * q^18 - 34 * q^19 - 232 * q^20 + 8 * q^21 - 40 * q^22 - 15 * q^23 + 78 * q^24 + 97 * q^25 + 43 * q^26 - 4 * q^27 + 68 * q^28 + 64 * q^29 - 25 * q^30 + q^31 - 32 * q^32 - 25 * q^33 + 132 * q^34 - 46 * q^35 - 188 * q^36 - 6 * q^37 + 15 * q^38 + 19 * q^39 - 53 * q^40 - 34 * q^41 + 4 * q^42 - 8 * q^43 - 132 * q^44 - 55 * q^45 - 35 * q^46 + 25 * q^47 - 40 * q^48 + 83 * q^49 - 104 * q^50 - 32 * q^51 + 8 * q^52 - 17 * q^53 - 57 * q^54 + 6 * q^55 + 4 * q^56 + 34 * q^57 + 13 * q^58 + 140 * q^59 - 78 * q^60 + 7 * q^61 - 100 * q^62 + 60 * q^63 - 146 * q^64 - 6 * q^65 - 32 * q^66 - 71 * q^67 - 28 * q^68 - 8 * q^69 - 200 * q^70 - 38 * q^71 - 4 * q^72 - 18 * q^73 + 24 * q^74 - 42 * q^75 + 50 * q^76 + 4 * q^77 + 36 * q^78 - 37 * q^79 - 11 * q^80 - 61 * q^81 + 55 * q^82 + 40 * q^83 + 274 * q^84 - 48 * q^85 - 83 * q^86 + q^87 - 34 * q^88 - 29 * q^89 - 244 * q^90 + 34 * q^91 - 254 * q^92 - 81 * q^93 + 67 * q^94 + 15 * q^95 + 55 * q^96 - 32 * q^97 + 249 * q^98 - 176 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/889\mathbb{Z}\right)^\times$.

$n$	$255$	$638$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{7}\right)$

Coefficient data

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

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

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

$2$	−1.73594	−	1.18354i	−1.22749	−	0.836891i	−0.236610	−	0.971605i	$-0.576036\pi$
$2$	−1.73594	−	1.18354i	−1.22749	−	0.836891i	−0.990885	+	0.134713i	$0.956989\pi$
$3$	−1.77532	−	0.547615i	−1.02498	−	0.316166i	−0.263714	−	0.964601i	$-0.584948\pi$
$3$	−1.77532	−	0.547615i	−1.02498	−	0.316166i	−0.761270	+	0.648435i	$0.775424\pi$
$4$	0.882028	+	2.24737i	0.441014	+	1.12368i
$5$	0.0270140	−	0.0688306i	0.0120810	−	0.0307820i	−0.924706	−	0.380682i	$-0.875689\pi$
$5$	0.0270140	−	0.0688306i	0.0120810	−	0.0307820i	0.936787	+	0.349900i	$0.113784\pi$
$6$	2.43373	+	3.05180i	0.993566	+	1.24589i
$7$	0.776326	−	2.52929i	0.293424	−	0.955982i
$7$	0.776326	−	2.52929i	0.293424	−	0.955982i
$8$	0.193674	−	0.848541i	0.0684741	−	0.300005i
$9$	0.373178	+	0.254429i	0.124393	+	0.0848096i
$10$	−0.128359	+	0.0875135i	−0.0405906	+	0.0276742i
$11$	−0.769292	+	0.524494i	−0.231950	+	0.158141i	−0.673718	−	0.738988i	$-0.735304\pi$
$11$	−0.769292	+	0.524494i	−0.231950	+	0.158141i	0.441768	+	0.897129i	$0.354351\pi$
$12$	−0.335192	−	4.47282i	−0.0967615	−	1.29119i
$13$	0.581928	+	0.729714i	0.161398	+	0.202386i	0.855954	−	0.517052i	$-0.172971\pi$
$13$	0.581928	+	0.729714i	0.161398	+	0.202386i	−0.694556	+	0.719438i	$0.744399\pi$
$14$	−4.34118	+	3.47188i	−1.16023	+	0.927899i
$15$	−0.0856514	+	0.107403i	−0.0221151	+	0.0277314i
$16$	2.19906	−	2.04043i	0.549766	−	0.510108i
$17$	4.93251	−	0.743457i	1.19631	−	0.180315i	0.479474	−	0.877556i	$-0.340828\pi$
$17$	4.93251	−	0.743457i	1.19631	−	0.180315i	0.716836	+	0.697241i	$0.245589\pi$
$18$	−0.346688	−	0.883346i	−0.0817150	−	0.208207i
$19$	−2.74163	−	4.74864i	−0.628972	−	1.08941i	−0.987758	−	0.155992i	$-0.950143\pi$
$19$	−2.74163	−	4.74864i	−0.628972	−	1.08941i	0.358786	−	0.933420i	$-0.383191\pi$
$20$	0.178515			0.0399172
$21$	−2.76331	+	4.06519i	−0.603004	+	0.887096i
$22$	1.95621			0.417064
$23$	−4.32229	−	2.94688i	−0.901259	−	0.614468i	0.0215323	−	0.999768i	$-0.493146\pi$
$23$	−4.32229	−	2.94688i	−0.901259	−	0.614468i	−0.922791	+	0.385300i	$0.874098\pi$
$24$	−0.808508	+	1.40038i	−0.165036	+	0.285851i
$25$	3.66125	+	3.39714i	0.732250	+	0.679429i
$26$	−0.146543	−	1.95548i	−0.0287394	−	0.383500i
$27$	2.95189	+	3.70156i	0.568092	+	0.712365i
$28$	6.36900	−	0.486213i	1.20363	−	0.0918857i
$29$	−1.34140	−	5.87706i	−0.249092	−	1.09134i	−0.932461	−	0.361270i	$-0.882343\pi$
$29$	−1.34140	−	5.87706i	−0.249092	−	1.09134i	0.683369	−	0.730073i	$-0.260514\pi$
$30$	0.275802	−	0.0850737i	0.0503543	−	0.0155323i
$31$	−3.66138	−	9.32905i	−0.657604	−	1.67555i	−0.734587	−	0.678514i	$-0.762624\pi$
$31$	−3.66138	−	9.32905i	−0.657604	−	1.67555i	0.0769835	−	0.997032i	$-0.475471\pi$
$32$	−7.95366	+	1.19882i	−1.40602	+	0.211924i
$33$	1.65296	−	0.509872i	0.287744	−	0.0887573i
$34$	−9.44245	−	4.54725i	−1.61937	−	0.779846i
$35$	−0.153121	−	0.121761i	−0.0258822	−	0.0205814i
$36$	−0.242642	+	1.06308i	−0.0404403	+	0.177181i
$37$	−2.53754	−	4.39514i	−0.417168	−	0.722557i	0.578485	−	0.815693i	$-0.303644\pi$
$37$	−2.53754	−	4.39514i	−0.417168	−	0.722557i	−0.995653	+	0.0931361i	$0.970311\pi$
$38$	−0.860920	+	11.4882i	−0.139660	+	1.86363i
$39$	−0.633508	−	1.61415i	−0.101442	−	0.258471i
$40$	−0.0531737	−	0.0362532i	−0.00840750	−	0.00573214i
$41$	3.35628	+	4.20865i	0.524164	+	0.657280i	0.971487	−	0.237092i	$-0.0761942\pi$
$41$	3.35628	+	4.20865i	0.524164	+	0.657280i	−0.447324	+	0.894372i	$0.647623\pi$
$42$	9.60826	−	3.78642i	1.48259	−	0.584257i
$43$	0.299343	+	1.31151i	0.0456494	+	0.200003i	0.992610	−	0.121346i	$-0.0387210\pi$
$43$	0.299343	+	1.31151i	0.0456494	+	0.200003i	−0.946961	+	0.321349i	$0.895864\pi$
$44$	−1.85727	−	1.26627i	−0.279994	−	0.190897i
$45$	0.0275935	−	0.0188130i	0.00411340	−	0.00280447i
$46$	4.01546	+	10.2312i	0.592047	+	1.50851i
$47$	−1.70107	−	0.256395i	−0.248126	−	0.0373991i	0.0238013	−	0.999717i	$-0.492423\pi$
$47$	−1.70107	−	0.256395i	−0.248126	−	0.0373991i	−0.271928	+	0.962318i	$0.587661\pi$
$48$	−5.02142	+	2.41819i	−0.724780	+	0.349035i
$49$	−5.79464	−	3.92711i	−0.827805	−	0.561016i
$50$	−2.33504	−	10.2305i	−0.330225	−	1.44681i
$51$	−9.16394	−	1.38124i	−1.28321	−	0.193412i
$52$	−1.12666	+	1.95143i	−0.156240	+	0.270615i
$53$	0.0172795	−	0.230579i	0.00237352	−	0.0316724i	−0.995891	−	0.0905569i	$-0.971135\pi$
$53$	0.0172795	−	0.230579i	0.00237352	−	0.0316724i	0.998265	+	0.0588845i	$0.0187544\pi$
$54$	−0.743354	−	9.91937i	−0.101158	−	1.34986i
$55$	0.0153196	+	0.0671196i	0.00206569	+	0.00905040i
$56$	−1.99585	−	1.14860i	−0.266707	−	0.153489i
$57$	2.26685	+	9.93173i	0.300252	+	1.31549i
$58$	−4.62717	+	11.7898i	−0.607577	+	1.54808i
$59$	−6.42544	+	11.1292i	−0.836521	+	1.44890i	0.0562647	+	0.998416i	$0.482081\pi$
$59$	−6.42544	+	11.1292i	−0.836521	+	1.44890i	−0.892786	+	0.450481i	$0.851252\pi$
$60$	−0.316922	−	0.0977575i	−0.0409145	−	0.0126204i
$61$	3.09114	−	2.86816i	0.395780	−	0.367231i	−0.457030	−	0.889451i	$-0.651087\pi$
$61$	3.09114	−	2.86816i	0.395780	−	0.367231i	0.852810	+	0.522221i	$0.174896\pi$
$62$	−4.68540	+	20.5281i	−0.595046	+	2.60707i
$63$	0.933233	−	0.746357i	0.117576	−	0.0940322i
$64$	9.82034	+	4.72923i	1.22754	+	0.591153i
$65$	0.0659469	−	0.0203419i	0.00817970	−	0.00252310i
$66$	−3.47290	−	1.07125i	−0.427484	−	0.131861i
$67$	5.65462	+	1.74422i	0.690821	+	0.213090i	0.620236	−	0.784416i	$-0.287037\pi$
$67$	5.65462	+	1.74422i	0.690821	+	0.213090i	0.0705858	+	0.997506i	$0.477513\pi$
$68$	6.02144	+	10.4294i	0.730206	+	1.26475i
$69$	6.05970	+	7.59863i	0.729502	+	0.914767i
$70$	0.121699	+	0.392596i	0.0145458	+	0.0469242i
$71$	−0.861327	+	0.414793i	−0.102221	+	0.0492269i	−0.484295	−	0.874905i	$-0.660924\pi$
$71$	−0.861327	+	0.414793i	−0.102221	+	0.0492269i	0.382075	+	0.924131i	$0.375210\pi$
$72$	0.288168	−	0.267381i	0.0339610	−	0.0315112i
$73$	−8.70897	+	5.93767i	−1.01931	+	0.694952i	−0.953038	−	0.302850i	$-0.902062\pi$
$73$	−8.70897	+	5.93767i	−1.01931	+	0.694952i	−0.0662691	+	0.997802i	$0.521110\pi$
$74$	−0.796832	+	10.6330i	−0.0926298	+	1.23606i
$75$	−4.63958	−	8.03599i	−0.535733	−	0.927916i
$76$	8.25375	−	10.3499i	0.946771	−	1.18721i
$77$	0.729378	+	2.35294i	0.0831203	+	0.268143i
$78$	−0.810687	+	3.55185i	−0.0917922	+	0.402168i
$79$	0.507736	+	0.346169i	0.0571248	+	0.0389470i	0.591546	−	0.806271i	$-0.298518\pi$
$79$	0.507736	+	0.346169i	0.0571248	+	0.0389470i	−0.534421	+	0.845218i	$0.679470\pi$
$80$	−0.0810387	−	0.206483i	−0.00906040	−	0.0230855i
$81$	−3.70857	−	9.44928i	−0.412063	−	1.04992i
$82$	−0.845189	−	11.2783i	−0.0933355	−	1.24548i
$83$	−12.0297	+	5.79320i	−1.32043	+	0.635886i	−0.955457	−	0.295132i	$-0.904636\pi$
$83$	−12.0297	+	5.79320i	−1.32043	+	0.635886i	−0.364974	+	0.931018i	$0.618922\pi$
$84$	−11.5733	−	2.62457i	−1.26275	−	0.286364i
$85$	0.0820745	−	0.359592i	0.00890223	−	0.0390032i
$86$	1.03258	−	2.63098i	0.111346	−	0.283706i
$87$	−0.836945	+	11.1683i	−0.0897300	+	1.19736i
$88$	0.296063	+	0.754357i	0.0315604	+	0.0804147i
$89$	8.68731	+	5.92291i	0.920853	+	0.627827i	0.928174	−	0.372146i	$-0.121378\pi$
$89$	8.68731	+	5.92291i	0.920853	+	0.627827i	−0.00732136	+	0.999973i	$0.502330\pi$
$90$	−0.0701667			−0.00739622
$91$	2.29743	−	0.905368i	0.240836	−	0.0949084i
$92$	2.81036	−	12.3130i	0.293001	−	1.28372i
$93$	1.39141	+	18.5671i	0.144283	+	1.92532i
$94$	2.64950	+	2.45838i	0.273275	+	0.253562i
$95$	−0.400914	+	0.0604281i	−0.0411329	+	0.00619979i
$96$	14.7768	+	2.22725i	1.50815	+	0.227317i
$97$	−1.89631	+	8.30827i	−0.192541	+	0.843577i	0.782694	+	0.622406i	$0.213845\pi$
$97$	−1.89631	+	8.30827i	−0.192541	+	0.843577i	−0.975235	+	0.221170i	$0.929012\pi$
$98$	5.41123	+	13.6754i	0.546616	+	1.38143i
$99$	−0.420530			−0.0422648
$100$	−4.40532	+	11.2246i	−0.440532	+	1.12246i
$101$	−6.25843	+	4.26693i	−0.622737	+	0.424575i	−0.833157	−	0.553036i	$-0.813469\pi$
$101$	−6.25843	+	4.26693i	−0.622737	+	0.424575i	0.210420	+	0.977611i	$0.432517\pi$
$102$	14.2733	+	13.2437i	1.41327	+	1.31132i
$103$	−0.0900938	−	0.156047i	−0.00887720	−	0.0153758i	0.861553	−	0.507668i	$-0.169492\pi$
$103$	−0.0900938	−	0.156047i	−0.00887720	−	0.0153758i	−0.870430	+	0.492292i	$0.836159\pi$
$104$	0.731897	−	0.352463i	0.0717684	−	0.0345618i
$105$	0.205161	+	0.300017i	0.0200217	+	0.0292787i
$106$	−0.302896	+	0.379820i	−0.0294199	+	0.0368913i
$107$	6.58451	+	11.4047i	0.636549	+	1.10254i	0.986185	+	0.165649i	$0.0529720\pi$
$107$	6.58451	+	11.4047i	0.636549	+	1.10254i	−0.349636	+	0.936886i	$0.613695\pi$
$108$	−5.71512	+	9.89888i	−0.549938	+	0.952520i
$109$	−5.57901	−	14.2151i	−0.534372	−	1.36156i	−0.902061	−	0.431609i	$-0.857946\pi$
$109$	−5.57901	−	14.2151i	−0.534372	−	1.36156i	0.367688	−	0.929949i	$-0.380149\pi$
$110$	0.0528450	−	0.134647i	0.00503857	−	0.0128381i
$111$	2.09810	+	9.19240i	0.199143	+	0.872504i
$112$	−3.45366	−	7.14611i	−0.326340	−	0.675244i
$113$	13.9430	+	6.71461i	1.31165	+	0.631658i	0.953327	−	0.301940i	$-0.0976342\pi$
$113$	13.9430	+	6.71461i	1.31165	+	0.631658i	0.358323	+	0.933598i	$0.383349\pi$
$114$	7.81951	−	19.9238i	0.732364	−	1.86603i
$115$	−0.319598	+	0.217898i	−0.0298027	+	0.0203191i
$116$	12.0248	−	8.19835i	1.11647	−	0.761198i
$117$	0.0315026	+	0.420373i	0.00291241	+	0.0388635i
$118$	24.3261	−	11.7148i	2.23939	−	1.07844i
$119$	1.94882	−	13.0529i	0.178648	−	1.19656i
$120$	0.0745478	+	0.0934800i	0.00680525	+	0.00853351i
$121$	−3.70204	+	9.43263i	−0.336549	+	0.857512i
$122$	−8.76063	+	1.32045i	−0.793150	+	0.119548i
$123$	−3.65377	−	9.30967i	−0.329450	−	0.839424i
$124$	17.7364	−	16.4570i	1.59277	−	1.47788i
$125$	0.665830	−	0.320647i	0.0595536	−	0.0286795i
$126$	−2.50338	+	0.191110i	−0.223019	+	0.0170254i
$127$	6.41370	−	9.26631i	0.569124	−	0.822252i
$127$	6.41370	−	9.26631i	0.569124	−	0.822252i
$128$	−3.40677	−	5.90070i	−0.301119	−	0.521553i
$129$	0.186770	−	2.49228i	0.0164442	−	0.219433i
$130$	−0.138555	−	0.0427387i	−0.0121521	−	0.00374843i
$131$	−7.24359	−	1.09180i	−0.632876	−	0.0953906i	−0.175233	−	0.984527i	$-0.556068\pi$
$131$	−7.24359	−	1.09180i	−0.632876	−	0.0953906i	−0.457642	+	0.889136i	$0.651306\pi$
$132$	2.60383	+	3.26510i	0.226634	+	0.284191i
$133$	−14.1391	+	3.24788i	−1.22601	+	0.281627i
$134$	−7.75171	−	9.72034i	−0.669646	−	0.839710i
$135$	0.334523	−	0.103187i	0.0287912	−	0.00888090i
$136$	0.324446	−	4.32943i	0.0278210	−	0.371245i
$137$	−15.4254	+	10.5168i	−1.31788	+	0.898515i	−0.998788	−	0.0492097i	$-0.984330\pi$
$137$	−15.4254	+	10.5168i	−1.31788	+	0.898515i	−0.319090	+	0.947724i	$0.603377\pi$
$138$	−1.52597	−	20.3627i	−0.129899	−	1.73339i
$139$	−15.2556	−	7.34671i	−1.29396	−	0.623140i	−0.345023	−	0.938594i	$-0.612129\pi$
$139$	−15.2556	−	7.34671i	−1.29396	−	0.623140i	−0.948941	+	0.315454i	$0.897843\pi$
$140$	0.138586	−	0.451517i	0.0117126	−	0.0381601i
$141$	2.87954	+	1.38672i	0.242501	+	0.116783i
$142$	1.98614	+	0.299362i	0.166673	+	0.0251219i
$143$	−0.830403	−	0.256145i	−0.0694418	−	0.0214200i
$144$	1.33979	−	0.201940i	0.111649	−	0.0168284i
$145$	−0.440758	−	0.0664336i	−0.0366030	−	0.00551701i
$146$	22.1457			1.83279
$147$	8.13681	+	10.1451i	0.671113	+	0.836756i
$148$	7.63933	−	9.57942i	0.627949	−	0.787424i
$149$	−11.4549	−	19.8404i	−0.938418	−	1.62539i	−0.768422	−	0.639943i	$-0.778958\pi$
$149$	−11.4549	−	19.8404i	−0.938418	−	1.62539i	−0.169996	−	0.985445i	$-0.554375\pi$
$150$	−1.45691	+	19.4411i	−0.118956	+	1.58736i
$151$	8.39489	−	14.5404i	0.683166	−	1.18328i	−0.290843	−	0.956771i	$-0.593936\pi$
$151$	8.39489	−	14.5404i	0.683166	−	1.18328i	0.974009	−	0.226508i	$-0.0727308\pi$
$152$	−4.56040	+	1.40670i	−0.369897	+	0.114098i
$153$	2.02986	+	0.977531i	0.164105	+	0.0790287i
$154$	1.51865	−	4.94782i	0.122377	−	0.398706i
$155$	−0.741033			−0.0595212
$156$	3.06882	−	2.84745i	0.245703	−	0.227979i
$157$	−7.22923	−	6.70775i	−0.576956	−	0.535337i	0.336813	−	0.941572i	$-0.390651\pi$
$157$	−7.22923	−	6.70775i	−0.576956	−	0.535337i	−0.913769	+	0.406235i	$0.866841\pi$
$158$	−0.471694	−	1.20186i	−0.0375259	−	0.0956145i
$159$	−0.156945	+	0.399890i	−0.0124466	+	0.0317133i
$160$	−0.132345	+	0.579840i	−0.0104628	+	0.0458404i
$161$	−10.8090	+	8.64458i	−0.851871	+	0.681288i
$162$	−4.74578	+	20.7926i	−0.372864	+	1.63362i
$163$	−21.2529	+	6.55567i	−1.66466	+	0.513479i	−0.977124	−	0.212671i	$-0.931784\pi$
$163$	−21.2529	+	6.55567i	−1.66466	+	0.513479i	−0.687536	+	0.726151i	$0.741307\pi$
$164$	−6.49805	+	11.2550i	−0.507413	+	0.878864i
$165$	0.00955842	−	0.127548i	0.000744122	−	0.00992962i
$166$	27.7393	+	4.18103i	2.15299	+	0.324511i
$167$	−21.9040	+	10.5484i	−1.69498	+	0.816260i	−0.700232	+	0.713915i	$0.746920\pi$
$167$	−21.9040	+	10.5484i	−1.69498	+	0.816260i	−0.994749	+	0.102345i	$0.967365\pi$
$168$	2.91430	+	3.13210i	0.224843	+	0.241647i
$169$	2.69893	−	11.8248i	0.207610	−	0.909599i
$170$	−0.568069	+	0.527091i	−0.0435689	+	0.0404260i
$171$	0.185074	−	2.46964i	0.0141529	−	0.188858i
$172$	−2.68341	+	1.82952i	−0.204608	+	0.139500i
$173$	−11.7650	−	1.77329i	−0.894479	−	0.134821i	−0.314313	−	0.949319i	$-0.601774\pi$
$173$	−11.7650	−	1.77329i	−0.894479	−	0.134821i	−0.580166	+	0.814498i	$0.697012\pi$
$174$	14.6710	−	18.3969i	1.11221	−	1.39466i
$175$	11.4347	−	6.62308i	0.864382	−	0.500658i
$176$	−0.621526	+	2.72308i	−0.0468493	+	0.205260i
$177$	17.5018	−	16.2393i	1.31551	−	1.22062i
$178$	−8.07062	−	20.5636i	−0.604919	−	1.54131i
$179$	3.03065	−	5.24924i	0.226522	−	0.392347i	−0.730253	−	0.683177i	$-0.760598\pi$
$179$	3.03065	−	5.24924i	0.226522	−	0.392347i	0.956775	+	0.290830i	$0.0939313\pi$
$180$	0.0666180	+	0.0454194i	0.00496541	+	0.00338536i
$181$	7.43341	+	3.57974i	0.552521	+	0.266080i	0.689244	−	0.724529i	$-0.257943\pi$
$181$	7.43341	+	3.57974i	0.552521	+	0.266080i	−0.136723	+	0.990609i	$0.543657\pi$
$182$	−5.05973	−	1.14744i	−0.375052	−	0.0850537i
$183$	−7.05843	+	3.39916i	−0.521774	+	0.251273i
$184$	−3.33767	+	3.09690i	−0.246056	+	0.228307i
$185$	−0.371070	+	0.0559297i	−0.0272816	+	0.00411204i
$186$	19.5596	−	33.8782i	1.43418	−	2.48407i
$187$	−3.40460	+	3.15901i	−0.248969	+	0.231010i
$188$	−0.924176	−	4.04908i	−0.0674025	−	0.295310i
$189$	11.6540	−	4.59259i	0.847700	−	0.334061i
$190$	0.767482	+	0.369600i	0.0556790	+	0.0268136i
$191$	−1.12374	−	14.9953i	−0.0813111	−	1.08502i	−0.877374	−	0.479807i	$-0.840707\pi$
$191$	−1.12374	−	14.9953i	−0.0813111	−	1.08502i	0.796063	−	0.605214i	$-0.206912\pi$
$192$	−14.8445	−	13.7737i	−1.07131	−	0.994030i
$193$	−2.53708	−	0.782587i	−0.182623	−	0.0563318i	0.202095	−	0.979366i	$-0.435225\pi$
$193$	−2.53708	−	0.782587i	−0.182623	−	0.0563318i	−0.384718	+	0.923034i	$0.625701\pi$
$194$	13.1251	−	12.1783i	0.942325	−	0.874350i
$195$	−0.128217			−0.00918179
$196$	3.71464	−	16.4865i	0.265332	−	1.17761i
$197$	4.72656	+	20.7084i	0.336754	+	1.47541i	0.805772	+	0.592226i	$0.201751\pi$
$197$	4.72656	+	20.7084i	0.336754	+	1.47541i	−0.469018	+	0.883189i	$0.655392\pi$
$198$	0.730014	+	0.497715i	0.0518798	+	0.0353711i
$199$	7.91868	+	2.44259i	0.561340	+	0.173150i	0.562424	−	0.826849i	$-0.309869\pi$
$199$	7.91868	+	2.44259i	0.561340	+	0.173150i	−0.00108399	+	0.999999i	$0.500345\pi$
$200$	3.59171	−	2.44878i	0.253972	−	0.173155i
$201$	−9.08362	−	6.19311i	−0.640709	−	0.436828i
$202$	15.9144			1.11973
$203$	−15.9062	−	1.16972i	−1.11639	−	0.0820984i
$204$	−4.97869	−	21.8131i	−0.348578	−	1.52722i
$205$	0.380351	−	0.117323i	0.0265648	−	0.00819417i
$206$	−0.0282911	+	0.377518i	−0.00197113	+	0.0263029i
$207$	−0.863212	−	2.19943i	−0.0599974	−	0.152871i
$208$	2.76863	+	0.417303i	0.191970	+	0.0289348i
$209$	4.59975	+	2.21512i	0.318171	+	0.153223i
$210$	−0.00106377	−	0.763629i	−7.34068e−5	−	0.0526954i
$211$	0.378373	+	1.65776i	0.0260483	+	0.114125i	0.986281	−	0.165077i	$-0.0527873\pi$
$211$	0.378373	+	1.65776i	0.0260483	+	0.114125i	−0.960232	+	0.279202i	$0.909930\pi$
$212$	0.533437	−	0.164543i	0.0366366	−	0.0113009i
$213$	1.75628	−	0.264717i	0.120338	−	0.0181381i
$214$	2.06766	−	27.5909i	0.141342	−	1.88608i
$215$	0.0983584	+	0.0148251i	0.00670799	+	0.00101107i
$216$	3.71263	−	1.78791i	0.252612	−	0.121652i
$217$	−26.4383	+	2.01832i	−1.79475	+	0.137012i
$218$	−7.13935	+	31.2795i	−0.483538	+	2.11852i
$219$	18.7128	−	5.77213i	1.26449	−	0.390045i
$220$	−0.137330	+	0.0936301i	−0.00925880	+	0.00631254i
$221$	3.41288	+	3.16669i	0.229575	+	0.213014i
$222$	7.23742	−	18.4406i	0.485744	−	1.23765i
$223$	14.7655	−	18.5153i	0.988769	−	1.23988i	0.0180058	−	0.999838i	$-0.494268\pi$
$223$	14.7655	−	18.5153i	0.988769	−	1.23988i	0.970763	−	0.240039i	$-0.0771603\pi$
$224$	−3.14247	+	21.0478i	−0.209965	+	1.40632i
$225$	0.501969	+	2.19927i	0.0334646	+	0.146618i
$226$	−16.2572	−	28.1583i	−1.08141	−	1.87306i
$227$	0.113607	−	0.0171235i	0.00754037	−	0.00113653i	−0.145271	−	0.989392i	$-0.546405\pi$
$227$	0.113607	−	0.0171235i	0.00754037	−	0.00113653i	0.152811	+	0.988255i	$0.451167\pi$
$228$	−20.3208	+	13.8545i	−1.34578	+	0.917538i
$229$	−20.8953	+	6.44534i	−1.38080	+	0.425920i	−0.894185	−	0.447697i	$-0.852244\pi$
$229$	−20.8953	+	6.44534i	−1.38080	+	0.425920i	−0.486614	+	0.873617i	$0.661768\pi$
$230$	0.812695			0.0535876
$231$	−0.00637546	−	4.57666i	−0.000419475	−	0.301122i
$232$	−5.24672			−0.344464
$233$	8.78419	+	1.32400i	0.575471	+	0.0867383i	0.430328	−	0.902672i	$-0.358398\pi$
$233$	8.78419	+	1.32400i	0.575471	+	0.0867383i	0.145143	+	0.989411i	$0.453636\pi$
$234$	0.442843	−	0.767026i	0.0289495	−	0.0501421i
$235$	−0.0636006	+	0.110159i	−0.00414884	+	0.00718601i
$236$	−30.6788	−	4.62409i	−1.99702	−	0.301003i
$237$	−0.711830	−	0.892606i	−0.0462383	−	0.0579810i
$238$	−18.8317	+	20.3526i	−1.22068	+	1.31926i
$239$	−0.459730	+	0.576483i	−0.0297374	+	0.0372896i	−0.796478	−	0.604668i	$-0.793306\pi$
$239$	−0.459730	+	0.576483i	−0.0297374	+	0.0372896i	0.766740	+	0.641957i	$0.221877\pi$
$240$	0.0307966	+	0.410953i	0.00198791	+	0.0265269i
$241$	14.4909	−	2.18415i	0.933441	−	0.140694i	0.335324	−	0.942103i	$-0.391154\pi$
$241$	14.4909	−	2.18415i	0.933441	−	0.140694i	0.598117	+	0.801409i	$0.295916\pi$
$242$	17.5904	−	11.9930i	1.13076	−	0.770936i
$243$	0.347923	+	4.64271i	0.0223193	+	0.297830i
$244$	9.17230	+	4.41715i	0.587196	+	0.282779i
$245$	−0.426842	+	0.292761i	−0.0272699	+	0.0187038i
$246$	−4.67566	+	20.4854i	−0.298109	+	1.30610i
$247$	1.86972	−	4.76397i	0.118967	−	0.303124i
$248$	−8.62520	+	1.30004i	−0.547701	+	0.0825526i
$249$	24.5291	−	3.69716i	1.55447	−	0.234298i
$250$	−1.53534	−	0.231415i	−0.0971034	−	0.0146360i
$251$	−1.84857	−	8.09913i	−0.116681	−	0.511212i	−0.999165	−	0.0408692i	$-0.986987\pi$
$251$	−1.84857	−	8.09913i	−0.116681	−	0.511212i	0.882484	−	0.470343i	$-0.155870\pi$
$252$	2.50048	+	1.43901i	0.157515	+	0.0906492i
$253$	4.87072			0.306220
$254$	−22.1009	+	8.49486i	−1.38673	+	0.533015i
$255$	−0.342627	+	0.593447i	−0.0214561	+	0.0371631i
$256$	0.559293	−	7.46325i	0.0349558	−	0.466453i
$257$	3.61935	−	3.35826i	0.225769	−	0.209483i	−0.559175	−	0.829049i	$-0.688882\pi$
$257$	3.61935	−	3.35826i	0.225769	−	0.209483i	0.784944	+	0.619567i	$0.212692\pi$
$258$	−3.27394	+	4.10539i	−0.203827	+	0.255590i
$259$	−13.0866	+	3.00611i	−0.813159	+	0.186790i
$260$	0.103883	+	0.130265i	0.00644254	+	0.00807869i
$261$	0.994711	−	2.53448i	0.0615711	−	0.156881i
$262$	11.2822	+	10.4684i	0.697019	+	0.646740i
$263$	1.52672	−	20.3727i	0.0941419	−	1.25624i	−0.727450	−	0.686160i	$-0.759295\pi$
$263$	1.52672	−	20.3727i	0.0941419	−	1.25624i	0.821592	−	0.570075i	$-0.193086\pi$
$264$	−0.112511	−	1.50136i	−0.00692458	−	0.0924021i
$265$	−0.0154041	−	0.00741822i	−0.000946266	−	0.000455698i
$266$	28.3886	+	11.0961i	1.74062	+	0.680345i
$267$	−12.1793	−	15.2724i	−0.745362	−	0.934654i
$268$	1.06763	+	14.2465i	0.0652156	+	0.870241i
$269$	5.45617	+	13.9021i	0.332669	+	0.847626i	0.995134	+	0.0985331i	$0.0314150\pi$
$269$	5.45617	+	13.9021i	0.332669	+	0.847626i	−0.662465	+	0.749093i	$0.730490\pi$
$270$	−0.702838	−	0.216797i	−0.0427733	−	0.0131938i
$271$	−2.88130	+	7.34143i	−0.175026	+	0.445960i	−0.991286	−	0.131725i	$-0.957949\pi$
$271$	−2.88130	+	7.34143i	−0.175026	+	0.445960i	0.816260	+	0.577685i	$0.196044\pi$
$272$	9.32993	−	11.6994i	0.565710	−	0.709378i
$273$	−4.57447	+	0.349218i	−0.276859	+	0.0211356i
$274$	39.2247			2.36965
$275$	−4.59836	−	0.693091i	−0.277291	−	0.0417949i
$276$	−11.7321	+	20.3206i	−0.706189	+	1.22316i
$277$	−0.380438	+	5.07659i	−0.0228583	+	0.305023i	0.974043	+	0.226362i	$0.0726834\pi$
$277$	−0.380438	+	5.07659i	−0.0228583	+	0.305023i	−0.996901	+	0.0786606i	$0.974936\pi$
$278$	17.7876	+	30.8091i	1.06683	+	1.84781i
$279$	1.00723	−	4.41296i	0.0603013	−	0.264197i
$280$	−0.132975	+	0.106348i	−0.00794678	+	0.00635548i
$281$	−7.61585	−	9.54997i	−0.454323	−	0.569703i	0.500932	−	0.865487i	$-0.332991\pi$
$281$	−7.61585	−	9.54997i	−0.454323	−	0.569703i	−0.955255	+	0.295783i	$0.904419\pi$
$282$	−3.35748	−	5.81532i	−0.199935	−	0.346297i
$283$	10.2720	+	3.16848i	0.610605	+	0.188347i	0.584609	−	0.811315i	$-0.301248\pi$
$283$	10.2720	+	3.16848i	0.610605	+	0.188347i	0.0259962	+	0.999662i	$0.491724\pi$
$284$	−1.69191	−	1.56986i	−0.100396	−	0.0931542i
$285$	0.744844	+	0.112267i	0.0441208	+	0.00665013i
$286$	1.13837	+	1.42747i	0.0673132	+	0.0844081i
$287$	13.2505	−	5.22174i	0.782150	−	0.308230i
$288$	−3.27315	−	1.57627i	−0.192872	−	0.0928823i
$289$	7.53222	−	2.32338i	0.443072	−	0.136669i
$290$	0.686503	+	0.636981i	0.0403128	+	0.0374048i
$291$	7.91630	−	13.7114i	0.464061	−	0.803778i
$292$	−21.0257	−	14.3351i	−1.23044	−	0.838897i
$293$	3.10056	−	3.88798i	0.181137	−	0.227138i	−0.682971	−	0.730446i	$-0.739312\pi$
$293$	3.10056	−	3.88798i	0.181137	−	0.227138i	0.864107	+	0.503308i	$0.167884\pi$
$294$	−2.11781	−	27.2416i	−0.123513	−	1.58876i
$295$	0.592452	+	0.742912i	0.0344939	+	0.0432540i
$296$	−4.22091	+	1.30198i	−0.245336	+	0.0756760i
$297$	−4.21232	−	1.29933i	−0.244423	−	0.0753946i
$298$	−3.59703	+	47.9990i	−0.208370	+	2.78051i
$299$	−0.364874	−	4.86891i	−0.0211012	−	0.281576i
$300$	13.9676	−	17.5148i	0.806420	−	1.01122i
$301$	3.54957	+	0.261032i	0.204594	+	0.0150456i
$302$	−31.7822	+	15.3055i	−1.82886	+	0.880732i
$303$	13.4474	−	4.14797i	0.772532	−	0.238295i
$304$	−15.7183	−	4.84845i	−0.901505	−	0.278078i
$305$	−0.113913	−	0.290246i	−0.00652265	−	0.0166194i
$306$	−2.36677	−	4.09937i	−0.135299	−	0.234345i
$307$	−11.9413	+	5.75063i	−0.681526	+	0.328206i	−0.742416	−	0.669939i	$-0.766320\pi$
$307$	−11.9413	+	5.75063i	−0.681526	+	0.328206i	0.0608904	+	0.998144i	$0.480606\pi$
$308$	−4.64460	+	3.71454i	−0.264651	+	0.211656i
$309$	0.0744920	+	0.326371i	0.00423770	+	0.0185666i
$310$	1.28639	+	0.877045i	0.0730619	+	0.0498128i
$311$	−19.1733	−	5.91419i	−1.08722	−	0.335363i	−0.301198	−	0.953562i	$-0.597386\pi$
$311$	−19.1733	−	5.91419i	−1.08722	−	0.335363i	−0.786022	+	0.618199i	$0.787863\pi$
$312$	−1.49237	+	0.224938i	−0.0844887	+	0.0127346i
$313$	9.88268	+	17.1173i	0.558602	+	0.967527i	0.997613	+	0.0690457i	$0.0219954\pi$
$313$	9.88268	+	17.1173i	0.558602	+	0.967527i	−0.439011	+	0.898481i	$0.644671\pi$
$314$	4.61060	+	20.2003i	0.260191	+	1.13997i
$315$	−0.0261619	−	0.0843971i	−0.00147405	−	0.00475524i
$316$	−0.330132	+	1.44640i	−0.0185714	+	0.0813665i
$317$	−0.110828	−	1.47889i	−0.00622470	−	0.0830629i	0.993226	−	0.116197i	$-0.0370703\pi$
$317$	−0.110828	−	1.47889i	−0.00622470	−	0.0830629i	−0.999451	+	0.0331338i	$0.989451\pi$
$318$	0.745734	−	0.508433i	0.0418187	−	0.0285115i
$319$	4.11441	+	3.81762i	0.230363	+	0.213746i
$320$	0.590803	−	0.548185i	0.0330269	−	0.0306445i
$321$	−5.44426	−	23.8528i	−0.303869	−	1.33134i
$322$	28.9951	−	2.21350i	1.61583	−	0.123354i
$323$	−17.0535	−	21.3844i	−0.948883	−	1.18986i
$324$	17.9650	−	16.6691i	0.998054	−	0.926059i
$325$	−0.348361	+	4.64856i	−0.0193236	+	0.257856i
$326$	44.6527	+	13.7735i	2.47309	+	0.762846i
$327$	2.12016	+	28.2915i	0.117245	+	1.56453i
$328$	4.22124	−	2.03284i	0.233079	−	0.112245i
$329$	−1.96908	+	4.10346i	−0.108559	+	0.226231i
$330$	−0.167552	+	0.210103i	−0.00922342	+	0.0115658i
$331$	−11.1363	+	10.3330i	−0.612106	+	0.567951i	−0.924109	−	0.382130i	$-0.875191\pi$
$331$	−11.1363	+	10.3330i	−0.612106	+	0.567951i	0.312003	+	0.950081i	$0.399000\pi$
$332$	−23.6300	−	21.9254i	−1.29686	−	1.20331i
$333$	0.171297	−	2.28579i	0.00938700	−	0.125261i
$334$	50.5085	+	7.61293i	2.76370	+	0.416561i
$335$	0.272810	−	0.342093i	0.0149052	−	0.0186905i
$336$	2.21804	+	14.5779i	0.121004	+	0.795292i
$337$	21.4372	−	10.3236i	1.16776	−	0.562362i	0.253436	−	0.967352i	$-0.418439\pi$
$337$	21.4372	−	10.3236i	1.16776	−	0.562362i	0.914321	+	0.404990i	$0.132725\pi$
$338$	−18.6803	+	17.3328i	−1.01608	+	0.942780i
$339$	−21.0764	−	19.5560i	−1.14471	−	1.06214i
$340$	0.880528	−	0.132718i	0.0477533	−	0.00719765i
$341$	7.70971	+	5.25639i	0.417504	+	0.284649i
$342$	−3.24420	+	4.06810i	−0.175426	+	0.219978i
$343$	−14.4313	+	11.6076i	−0.779219	+	0.626752i
$344$	1.17084			0.0631276
$345$	0.686715	−	0.211824i	0.0369715	−	0.0114042i
$346$	18.3246	+	17.0028i	0.985138	+	0.914074i
$347$	25.1850	−	17.1708i	1.35200	−	0.921778i	0.352101	−	0.935962i	$-0.385467\pi$
$347$	25.1850	−	17.1708i	1.35200	−	0.921778i	0.999899	+	0.0141842i	$0.00451512\pi$
$348$	−25.8374	+	7.96979i	−1.38503	+	0.427226i
$349$	16.2786	+	20.4127i	0.871375	+	1.09267i	0.994954	+	0.100335i	$0.0319913\pi$
$349$	16.2786	+	20.4127i	0.871375	+	1.09267i	−0.123579	+	0.992335i	$0.539437\pi$
$350$	−27.6886	−	2.03619i	−1.48002	−	0.108839i
$351$	−0.983291	+	4.30808i	−0.0524842	+	0.229948i
$352$	5.48991	−	5.09389i	0.292613	−	0.271505i
$353$	11.3074	−	19.5850i	0.601834	−	1.04241i	−0.390710	−	0.920514i	$-0.627770\pi$
$353$	11.3074	−	19.5850i	0.601834	−	1.04241i	0.992543	−	0.121892i	$-0.0388963\pi$
$354$	−49.6018	+	7.47627i	−2.63631	+	0.397360i
$355$	0.00528257	+	0.0704909i	0.000280369	+	0.00374127i
$356$	−5.64851	+	24.7478i	−0.299371	+	1.31163i
$357$	−10.6078	+	22.1060i	−0.561423	+	1.16997i
$358$	−11.4737	+	5.52546i	−0.606406	+	0.292030i
$359$	−0.672849	−	1.16541i	−0.0355116	−	0.0615079i	0.847723	−	0.530439i	$-0.177973\pi$
$359$	−0.672849	−	1.16541i	−0.0355116	−	0.0615079i	−0.883235	+	0.468931i	$0.844639\pi$
$360$	−0.0106194	−	0.0270578i	−0.000559693	−	0.00142607i
$361$	−5.53304	+	9.58350i	−0.291213	+	0.504395i
$362$	−8.66716	−	15.0120i	−0.455536	−	0.789012i
$363$	11.7378	−	14.7187i	0.616073	−	0.772531i
$364$	4.06109	+	4.36460i	0.212859	+	0.228767i
$365$	0.173429	+	0.759844i	0.00907771	+	0.0397721i
$366$	16.2761	+	2.45322i	0.850764	+	0.128232i
$367$	0.588325	−	0.401113i	0.0307103	−	0.0209379i	−0.547868	−	0.836565i	$-0.684560\pi$
$367$	0.588325	−	0.401113i	0.0307103	−	0.0209379i	0.578578	+	0.815627i	$0.303608\pi$
$368$	−15.5179	+	2.33895i	−0.808926	+	0.121926i
$369$	0.181692	+	2.42451i	0.00945851	+	0.126215i
$370$	0.710349	+	0.342086i	0.0369293	+	0.0177842i
$371$	−0.569786	−	0.222709i	−0.0295818	−	0.0115625i
$372$	−40.4999	+	19.5037i	−2.09982	+	1.01122i
$373$	−8.08043	+	2.49248i	−0.418389	+	0.129056i	−0.496800	−	0.867865i	$-0.665492\pi$
$373$	−8.08043	+	2.49248i	−0.418389	+	0.129056i	0.0784109	+	0.996921i	$0.475015\pi$
$374$	9.64901	−	1.45435i	0.498938	−	0.0752029i
$375$	−1.35766	+	0.204634i	−0.0701090	+	0.0105672i
$376$	−0.547015	+	1.39377i	−0.0282101	+	0.0718782i
$377$	3.50798	−	4.39886i	0.180670	−	0.226553i
$378$	−25.6661	−	5.82051i	−1.32012	−	0.299375i
$379$	12.7407	−	6.13560i	0.654446	−	0.315165i	−0.0770327	−	0.997029i	$-0.524545\pi$
$379$	12.7407	−	6.13560i	0.654446	−	0.315165i	0.731479	+	0.681864i	$0.238830\pi$
$380$	−0.489422	−	0.847703i	−0.0251068	−	0.0434863i
$381$	−16.4608	+	12.9385i	−0.843311	+	0.662858i
$382$	−15.7968	+	27.3609i	−0.808236	+	1.39991i
$383$	−22.5437	−	15.3700i	−1.15193	−	0.785372i	−0.172074	−	0.985084i	$-0.555047\pi$
$383$	−22.5437	−	15.3700i	−1.15193	−	0.785372i	−0.979855	+	0.199712i	$0.935999\pi$
$384$	2.81681	+	12.3413i	0.143745	+	0.629787i
$385$	0.181658	+	0.0133589i	0.00925815	+	0.000680834i
$386$	3.47800	+	4.36127i	0.177025	+	0.221983i
$387$	−0.221977	+	0.565588i	−0.0112837	+	0.0287505i
$388$	−20.3443	+	3.06642i	−1.03283	+	0.155674i
$389$	−7.36022	−	6.82929i	−0.373178	−	0.346259i	0.471181	−	0.882037i	$-0.343828\pi$
$389$	−7.36022	−	6.82929i	−0.373178	−	0.346259i	−0.844359	+	0.535778i	$0.820018\pi$
$390$	0.222576	+	0.151750i	0.0112706	+	0.00768416i
$391$	−23.5106	−	11.3221i	−1.18898	−	0.572584i
$392$	−4.45459	+	4.15641i	−0.224991	+	0.209930i
$393$	12.2618	+	5.90499i	0.618528	+	0.297867i
$394$	16.3043	−	41.5427i	0.821399	−	2.09289i
$395$	0.0375430	−	0.0255964i	0.00188899	−	0.00128789i
$396$	−0.370919	−	0.945086i	−0.0186394	−	0.0474923i
$397$	−9.93610	+	9.21936i	−0.498679	+	0.462706i	−0.888957	−	0.457991i	$-0.848569\pi$
$397$	−9.93610	+	9.21936i	−0.498679	+	0.462706i	0.390278	+	0.920697i	$0.372379\pi$
$398$	−10.8554	−	13.6123i	−0.544134	−	0.682322i
$399$	26.8801	+	1.97673i	1.34569	+	0.0989603i
$400$	14.9830			0.749148
$401$	5.18500	+	8.98069i	0.258927	+	0.448474i	0.965955	−	0.258711i	$-0.0832978\pi$
$401$	5.18500	+	8.98069i	0.258927	+	0.448474i	−0.707028	+	0.707186i	$0.749964\pi$
$402$	8.43880	+	21.5017i	0.420889	+	1.07241i
$403$	4.67688	−	8.10059i	0.232972	−	0.403519i
$404$	−15.1095	−	10.3015i	−0.751725	−	0.512517i
$405$	−0.750584			−0.0372968
$406$	26.2277	+	20.8562i	1.30166	+	1.03508i
$407$	4.25733	+	2.05022i	0.211028	+	0.101626i
$408$	−2.94686	+	7.50847i	−0.145891	+	0.371725i
$409$	−8.59918	+	14.8942i	−0.425202	+	0.736472i	−0.996439	−	0.0843134i	$-0.973130\pi$
$409$	−8.59918	+	14.8942i	−0.425202	+	0.736472i	0.571237	+	0.820785i	$0.306464\pi$
$410$	−0.799122	−	0.246496i	−0.0394658	−	0.0121736i
$411$	33.1442	−	10.2236i	1.63488	−	0.504295i
$412$	0.271230	−	0.340112i	0.0133625	−	0.0167561i
$413$	23.1607	+	24.8917i	1.13967	+	1.22484i
$414$	−1.10463	+	4.83972i	−0.0542898	+	0.237859i
$415$	0.0737788	+	0.984509i	0.00362166	+	0.0483277i
$416$	−5.50325	−	5.10627i	−0.269819	−	0.250355i
$417$	23.0605	+	21.3970i	1.12928	+	1.04782i
$418$	−5.36319	−	9.28931i	−0.262322	−	0.454355i
$419$	−34.5371	+	16.6322i	−1.68725	+	0.812536i	−0.691303	+	0.722565i	$0.742963\pi$
$419$	−34.5371	+	16.6322i	−1.68725	+	0.812536i	−0.995944	+	0.0899711i	$0.971323\pi$
$420$	−0.493292	+	0.725697i	−0.0240702	+	0.0354104i
$421$	−1.23612	+	0.595282i	−0.0602446	+	0.0290123i	−0.463763	−	0.885959i	$-0.653501\pi$
$421$	−1.23612	+	0.595282i	−0.0602446	+	0.0290123i	0.403519	+	0.914971i	$0.367787\pi$
$422$	1.30520	−	3.32559i	0.0635361	−	0.161887i
$423$	−0.569568	−	0.528482i	−0.0276934	−	0.0256957i
$424$	−0.192309	−	0.0593195i	−0.00933935	−	0.00288081i
$425$	20.5848	+	14.0345i	0.998509	+	0.680772i
$426$	−3.36210	−	1.61910i	−0.162894	−	0.0784458i
$427$	−4.85468	−	10.0450i	−0.234935	−	0.486113i
$428$	−19.8229	+	24.8571i	−0.958175	+	1.20151i
$429$	1.33397	+	0.909483i	0.0644045	+	0.0439102i
$430$	−0.153198	−	0.142147i	−0.00738786	−	0.00685493i
$431$	14.8188	+	4.57099i	0.713796	+	0.220177i	0.630323	−	0.776333i	$-0.282922\pi$
$431$	14.8188	+	4.57099i	0.713796	+	0.220177i	0.0834732	+	0.996510i	$0.473399\pi$
$432$	14.0442	+	2.11682i	0.675701	+	0.101845i
$433$	−31.6508			−1.52104			−0.760519	−	0.649316i	$-0.775055\pi$
$433$	−31.6508			−1.52104			−0.760519	+	0.649316i	$0.775055\pi$
$434$	48.2841	+	27.7872i	2.31771	+	1.33383i
$435$	0.746109	+	0.359307i	0.0357732	+	0.0172275i
$436$	27.0257	−	25.0762i	1.29430	−	1.20093i
$437$	−2.14359	+	28.6042i	−0.102542	+	1.36833i
$438$	−39.3158	−	12.1273i	−1.87858	−	0.579466i
$439$	6.38037	−	16.2569i	0.304518	−	0.775900i	−0.693921	−	0.720051i	$-0.744118\pi$
$439$	6.38037	−	16.2569i	0.304518	−	0.775900i	0.998439	−	0.0558486i	$-0.0177864\pi$
$440$	0.0599207			0.00285661
$441$	−1.16326	−	2.93984i	−0.0553935	−	0.139992i
$442$	−2.17663	−	9.53646i	−0.103532	−	0.453603i
$443$	12.8483	−	3.96316i	0.610439	−	0.188295i	0.0259045	−	0.999664i	$-0.491753\pi$
$443$	12.8483	−	3.96316i	0.610439	−	0.188295i	0.584534	+	0.811369i	$0.301277\pi$
$444$	−18.8081	+	12.8232i	−0.892594	+	0.608561i
$445$	0.642357	−	0.437951i	0.0304506	−	0.0207609i
$446$	−47.5456	+	14.6659i	−2.25135	+	0.694450i
$447$	9.47119	+	41.4960i	0.447972	+	1.96269i
$448$	19.5854	−	21.1671i	0.925323	−	1.00005i
$449$	−11.5839			−0.546680			−0.273340	−	0.961917i	$-0.588128\pi$
$449$	−11.5839			−0.546680			−0.273340	+	0.961917i	$0.588128\pi$
$450$	1.73154	−	4.41190i	0.0816257	−	0.207979i
$451$	−4.78937	−	1.47733i	−0.225523	−	0.0695646i
$452$	−2.79207	+	37.2576i	−0.131328	+	1.75245i
$453$	−22.8662	+	21.2167i	−1.07435	+	0.996848i
$454$	−0.217481	−	0.104734i	−0.0102069	−	0.00491539i
$455$	−0.000254356	−	0.182591i	−1.19244e−5	−	0.00855999i
$456$	8.86651			0.415212
$457$	15.7692	+	2.37682i	0.737651	+	0.111183i	0.507112	−	0.861880i	$-0.330713\pi$
$457$	15.7692	+	2.37682i	0.737651	+	0.111183i	0.230539	+	0.973063i	$0.425951\pi$
$458$	43.9013	+	13.5418i	2.05137	+	0.632765i
$459$	17.3122	+	16.0634i	0.808065	+	0.749774i
$460$	−0.771593	−	0.526063i	−0.0359757	−	0.0245278i
$461$	−0.954557	+	1.19698i	−0.0444582	+	0.0557488i	−0.803564	−	0.595219i	$-0.797065\pi$
$461$	−0.954557	+	1.19698i	−0.0444582	+	0.0557488i	0.759105	+	0.650968i	$0.225637\pi$
$462$	−5.40560	+	7.95234i	−0.251491	+	0.369976i
$463$	0.539343	+	0.259734i	0.0250654	+	0.0120709i	0.446374	−	0.894846i	$-0.352715\pi$
$463$	0.539343	+	0.259734i	0.0250654	+	0.0120709i	−0.421309	+	0.906917i	$0.638429\pi$
$464$	−14.9416	−	10.1870i	−0.693645	−	0.472919i
$465$	1.31557	+	0.405801i	0.0610083	+	0.0188186i
$466$	−13.6818	−	12.6949i	−0.633797	−	0.588078i
$467$	4.96039	−	12.6389i	0.229539	−	0.584857i	−0.768979	−	0.639274i	$-0.779235\pi$
$467$	4.96039	−	12.6389i	0.229539	−	0.584857i	0.998518	+	0.0544175i	$0.0173302\pi$
$468$	−0.916947	+	0.441578i	−0.0423859	+	0.0204120i
$469$	8.80147	−	12.9481i	0.406414	−	0.597888i
$470$	0.240785	−	0.115956i	0.0111066	−	0.00534865i
$471$	9.16097	+	15.8673i	0.422115	+	0.731125i
$472$	8.19914	+	7.60769i	0.377396	+	0.350172i
$473$	−0.918161	−	0.851929i	−0.0422171	−	0.0391717i
$474$	0.179255	+	2.39199i	0.00823345	+	0.109868i
$475$	6.09402	−	26.6997i	0.279613	−	1.22506i
$476$	31.0537	−	7.13333i	1.42334	−	0.326955i
$477$	0.0651142	−	0.0816506i	0.00298137	−	0.00373852i
$478$	1.48035	−	0.456629i	0.0677098	−	0.0208857i
$479$	−4.10730	−	1.26694i	−0.187667	−	0.0578878i	0.199497	−	0.979898i	$-0.436069\pi$
$479$	−4.10730	−	1.26694i	−0.187667	−	0.0578878i	−0.387164	+	0.922011i	$0.626545\pi$
$480$	0.552484	−	0.956931i	0.0252173	−	0.0436777i
$481$	1.73053	−	4.40933i	0.0789056	−	0.201048i
$482$	−27.7404	−	13.3591i	−1.26354	−	0.608488i
$483$	23.9234	−	9.42774i	1.08855	−	0.428977i
$484$	−24.4639			−1.11200
$485$	0.520636	+	0.354964i	0.0236409	+	0.0161181i
$486$	4.89088	−	8.47125i	0.221855	−	0.384264i
$487$	8.27379	+	21.0813i	0.374921	+	0.955284i	0.986450	+	0.164062i	$0.0524597\pi$
$487$	8.27379	+	21.0813i	0.374921	+	0.955284i	−0.611529	+	0.791222i	$0.709445\pi$
$488$	−1.83508	−	3.17845i	−0.0830702	−	0.143882i
$489$	41.3209			1.86859
$490$	1.08747	−	0.00302978i	0.0491268	−	0.000136871i
$491$	−20.9350	−	26.2517i	−0.944786	−	1.18472i	−0.982655	−	0.185441i	$-0.940629\pi$
$491$	−20.9350	−	26.2517i	−0.944786	−	1.18472i	0.0378699	−	0.999283i	$-0.487943\pi$
$492$	17.6995	−	16.4228i	0.797957	−	0.740396i
$493$	−10.9858	−	27.9914i	−0.494776	−	1.26067i
$494$	−8.88408	+	6.05706i	−0.399714	+	0.272520i
$495$	−0.0113602	+	0.0289453i	−0.000510603	+	0.00130100i
$496$	−27.0869	−	13.0444i	−1.21624	−	0.585709i
$497$	0.380463	+	2.50056i	0.0170661	+	0.112166i
$498$	−46.9567	−	22.6132i	−2.10418	−	1.01332i
$499$	23.6921	+	16.1530i	1.06060	+	0.723106i	0.962284	−	0.272049i	$-0.0877011\pi$
$499$	23.6921	+	16.1530i	1.06060	+	0.723106i	0.0983188	+	0.995155i	$0.468654\pi$
$500$	1.30789	+	1.21355i	0.0584907	+	0.0542715i
$501$	44.6631	−	6.73189i	1.99540	−	0.300758i
$502$	−6.37666	+	16.2475i	−0.284604	+	0.725160i
$503$	−12.5712	−	15.7638i	−0.560524	−	0.702875i	0.418131	−	0.908387i	$-0.362685\pi$
$503$	−12.5712	−	15.7638i	−0.560524	−	0.702875i	−0.978655	+	0.205512i	$0.934114\pi$
$504$	−0.452572	−	0.936436i	−0.0201592	−	0.0417122i
$505$	0.124630	+	0.546039i	0.00554595	+	0.0242984i
$506$	−8.45528	−	5.76471i	−0.375883	−	0.256273i
$507$	−11.2669	+	19.5148i	−0.500381	+	0.866685i
$508$	26.4819	+	6.24081i	1.17494	+	0.276891i
$509$	13.2577	+	22.9630i	0.587636	+	1.01782i	0.994541	+	0.104345i	$0.0332745\pi$
$509$	13.2577	+	22.9630i	0.587636	+	1.01782i	−0.406905	+	0.913470i	$0.633392\pi$
$510$	1.29715	−	0.624674i	0.0574387	−	0.0276610i
$511$	8.25711	+	26.6371i	0.365273	+	1.17836i
$512$	−18.3003	+	22.9479i	−0.808767	+	1.01416i
$513$	9.48437	−	24.1658i	0.418745	−	1.06694i
$514$	−10.2576	+	1.54609i	−0.452444	+	0.0681950i
$515$	−0.0131746	+	0.00198575i	−0.000580543	+	8.75027e-5i
$516$	5.76580	−	1.77852i	0.253825	−	0.0782948i
$517$	1.44310	−	0.694959i	0.0634673	−	0.0305643i
$518$	26.2753	+	10.2701i	1.15447	+	0.451242i
$519$	19.9157	+	9.59088i	0.874201	+	0.420993i
$520$	−0.00448876	−	0.0598983i	−0.000196845	−	0.00262672i
$521$	−25.6703	+	3.86917i	−1.12464	+	0.169512i	−0.684915	−	0.728623i	$-0.740161\pi$
$521$	−25.6703	+	3.86917i	−1.12464	+	0.169512i	−0.439721	+	0.898135i	$0.644923\pi$
$522$	−4.72643	+	3.22242i	−0.206870	+	0.141042i
$523$	−32.2873	−	4.86653i	−1.41183	−	0.212799i	−0.601545	−	0.798839i	$-0.705448\pi$
$523$	−32.2873	−	4.86653i	−1.41183	−	0.212799i	−0.810282	+	0.586040i	$0.800686\pi$
$524$	−3.93538	−	17.2420i	−0.171918	−	0.753221i
$525$	−23.9272	+	5.49631i	−1.04427	+	0.239878i
$526$	−26.7623	+	33.5589i	−1.16689	+	1.46324i
$527$	−24.9956	−	43.2936i	−1.08882	−	1.88590i
$528$	2.59461	−	4.49400i	0.112916	−	0.195576i
$529$	1.59518	+	4.06446i	0.0693559	+	0.176716i
$530$	0.0179608	+	0.0311090i	0.000780166	+	0.00135129i
$531$	−5.22942	+	2.51836i	−0.226938	+	0.109287i
$532$	−19.7703	−	28.9110i	−0.857150	−	1.25345i
$533$	−1.11799	+	4.89826i	−0.0484257	+	0.212167i
$534$	3.06703	+	40.9267i	0.132723	+	1.77107i
$535$	0.962868	−	0.145129i	0.0416284	−	0.00627447i
$536$	2.57519	−	4.46037i	0.111231	−	0.192658i
$537$	−8.25496	+	7.65948i	−0.356228	+	0.330531i
$538$	6.98215	−	30.5908i	0.301022	−	1.31886i
$539$	6.51751	−	0.0181583i	0.280729	−	0.000782135i
$540$	0.526957	+	0.660784i	0.0226766	+	0.0284356i
$541$	−19.3933	+	5.98203i	−0.833781	+	0.257187i	−0.682116	−	0.731244i	$-0.738940\pi$
$541$	−19.3933	+	5.98203i	−0.833781	+	0.257187i	−0.151666	+	0.988432i	$0.548464\pi$
$542$	13.6907	−	9.33414i	0.588064	−	0.400935i
$543$	−11.2364	−	10.4258i	−0.482200	−	0.447416i
$544$	−38.3403	+	11.8264i	−1.64383	+	0.507053i
$545$	−1.12914			−0.0483673
$546$	8.35431	+	4.80786i	0.357532	+	0.205757i
$547$	10.0361	−	12.5849i	0.429113	−	0.538090i	−0.519525	−	0.854455i	$-0.673891\pi$
$547$	10.0361	−	12.5849i	0.429113	−	0.538090i	0.948638	+	0.316365i	$0.102462\pi$
$548$	−37.2408	−	25.3904i	−1.59085	−	1.08462i
$549$	1.88329	−	0.283861i	0.0803769	−	0.0121149i
$550$	7.16216	+	6.64551i	0.305396	+	0.283366i
$551$	−24.2304	+	22.4825i	−1.03225	+	0.957788i
$552$	7.62135	−	3.67025i	0.324386	−	0.156216i
$553$	1.26973	−	1.01547i	0.0539945	−	0.0431823i
$554$	6.66879	−	8.36239i	0.283330	−	0.355284i
$555$	0.689397	+	0.103910i	0.0292633	+	0.00441073i
$556$	3.05491	−	40.7650i	0.129557	−	1.72882i
$557$	−21.9680	−	20.3834i	−0.930816	−	0.863671i	0.0600946	−	0.998193i	$-0.480860\pi$
$557$	−21.9680	−	20.3834i	−0.930816	−	0.863671i	−0.990911	+	0.134522i	$0.957050\pi$
$558$	−6.97142	+	6.46853i	−0.295124	+	0.273835i
$559$	−0.782830	+	0.981637i	−0.0331102	+	0.0415188i
$560$	−0.585169	+	0.0446721i	−0.0247279	+	0.00188774i
$561$	7.77420	−	3.74386i	0.328227	−	0.158066i
$562$	1.91784	+	25.5918i	0.0808994	+	1.07953i
$563$	44.0016	+	13.5727i	1.85445	+	0.572021i	0.998488	+	0.0549744i	$0.0175077\pi$
$563$	44.0016	+	13.5727i	1.85445	+	0.572021i	0.855957	+	0.517046i	$0.172968\pi$
$564$	−0.576625	+	7.69452i	−0.0242803	+	0.323998i
$565$	0.838829	−	0.778319i	0.0352898	−	0.0327441i
$566$	−14.0815	−	17.6576i	−0.591888	−	0.742204i
$567$	−26.7791	+	2.04433i	−1.12461	+	0.0858538i
$568$	0.185153	+	0.811206i	0.00776883	+	0.0340375i
$569$	27.9912	−	25.9720i	1.17345	−	1.08880i	0.178975	−	0.983854i	$-0.442722\pi$
$569$	27.9912	−	25.9720i	1.17345	−	1.08880i	0.994477	−	0.104951i	$-0.0334685\pi$
$570$	−1.16013	−	1.07644i	−0.0485925	−	0.0450873i
$571$	−12.0952	+	8.24638i	−0.506169	+	0.345100i	−0.789327	−	0.613973i	$-0.789570\pi$
$571$	−12.0952	+	8.24638i	−0.506169	+	0.345100i	0.283158	+	0.959073i	$0.408618\pi$
$572$	−0.156785	−	2.09215i	−0.00655551	−	0.0874772i
$573$	−6.21664	+	27.2369i	−0.259704	+	1.13784i
$574$	−29.1822	−	6.61788i	−1.21804	−	0.276225i
$575$	−5.81398	−	25.4727i	−0.242460	−	1.06229i
$576$	2.46149	+	4.26342i	0.102562	+	0.177643i
$577$	13.6670	−	2.05997i	0.568964	−	0.0857576i	0.141741	−	0.989904i	$-0.454730\pi$
$577$	13.6670	−	2.05997i	0.568964	−	0.0857576i	0.427223	+	0.904146i	$0.359492\pi$
$578$	−15.8253	−	4.88146i	−0.658245	−	0.203042i
$579$	4.07559	+	2.77869i	0.169376	+	0.115478i
$580$	−0.239460	−	1.04914i	−0.00994304	−	0.0435633i
$581$	5.31372	+	34.9240i	0.220450	+	1.44889i
$582$	−29.9703	+	14.4329i	−1.24231	+	0.598264i
$583$	0.107644	+	0.186445i	0.00445817	+	0.00772178i
$584$	3.35166	+	8.53989i	0.138693	+	0.353383i
$585$	0.0297855	+	0.00918762i	0.00123148	+	0.000379861i
$586$	−9.98398	+	3.07965i	−0.412434	+	0.127219i
$587$	30.2115	−	14.5491i	1.24696	−	0.600505i	0.310266	−	0.950650i	$-0.399582\pi$
$587$	30.2115	−	14.5491i	1.24696	−	0.600505i	0.936696	+	0.350144i	$0.113868\pi$
$588$	−15.6230	+	27.2347i	−0.644280	+	1.12314i
$589$	−34.2621	+	42.9634i	−1.41175	+	1.77027i
$590$	−0.149193	−	1.99084i	−0.00614218	−	0.0819617i
$591$	2.94906	−	39.3525i	0.121308	−	1.61875i
$592$	−14.5482	−	4.48752i	−0.597927	−	0.184436i
$593$	−16.3238	+	5.03523i	−0.670339	+	0.206772i	−0.611198	−	0.791477i	$-0.709312\pi$
$593$	−16.3238	+	5.03523i	−0.670339	+	0.206772i	−0.0591406	+	0.998250i	$0.518836\pi$
$594$	5.77451	+	7.24101i	0.236931	+	0.297102i
$595$	−0.845796	−	0.486751i	−0.0346743	−	0.0199548i
$596$	34.4852	−	43.2431i	1.41257	−	1.77130i
$597$	−12.7206	−	8.67277i	−0.520620	−	0.354953i
$598$	−5.12916	+	8.88397i	−0.209747	+	0.363292i
$599$	−10.7063	−	9.93399i	−0.437447	−	0.405892i	0.430467	−	0.902607i	$-0.358349\pi$
$599$	−10.7063	−	9.93399i	−0.437447	−	0.405892i	−0.867914	+	0.496715i	$0.834540\pi$
$600$	−7.71744	+	2.38051i	−0.315063	+	0.0971841i
$601$	5.99797	+	2.88847i	0.244662	+	0.117823i	0.552197	−	0.833714i	$-0.313790\pi$
$601$	5.99797	+	2.88847i	0.244662	+	0.117823i	−0.307535	+	0.951537i	$0.599504\pi$
$602$	−5.85290	−	4.65421i	−0.238546	−	0.189691i
$603$	1.66640	+	2.08960i	0.0678611	+	0.0850952i
$604$	40.0821	+	6.04141i	1.63092	+	0.245821i
$605$	0.549247	+	0.509627i	0.0223301	+	0.0207193i
$606$	−28.2531	−	8.71494i	−1.14771	−	0.354020i
$607$	−5.31194	−	9.20055i	−0.215605	−	0.373439i	0.737855	−	0.674960i	$-0.235839\pi$
$607$	−5.31194	−	9.20055i	−0.215605	−	0.373439i	−0.953460	+	0.301521i	$0.902506\pi$
$608$	27.4987	+	34.4823i	1.11522	+	1.39844i
$609$	27.5980	+	10.7871i	1.11833	+	0.437115i
$610$	−0.145772	+	0.638671i	−0.00590215	+	0.0258590i
$611$	−0.802804	−	1.39050i	−0.0324780	−	0.0562535i
$612$	−0.406477	+	5.42407i	−0.0164309	+	0.219255i
$613$	3.91491	−	6.78083i	0.158122	−	0.273875i	−0.776070	−	0.630647i	$-0.782789\pi$
$613$	3.91491	−	6.78083i	0.158122	−	0.273875i	0.934191	+	0.356772i	$0.116123\pi$
$614$	27.5355	+	4.15030i	1.11124	+	0.167493i
$615$	−0.739493			−0.0298193
$616$	2.13783	−	0.163203i	0.0861356	−	0.00657565i
$617$	25.6207	−	32.1274i	1.03145	−	1.29340i	0.0763639	−	0.997080i	$-0.475669\pi$
$617$	25.6207	−	32.1274i	1.03145	−	1.29340i	0.955089	−	0.296321i	$-0.0957597\pi$
$618$	0.256960	−	0.654724i	0.0103365	−	0.0263369i
$619$	29.9090	+	9.22569i	1.20214	+	0.370812i	0.830211	−	0.557449i	$-0.188220\pi$
$619$	29.9090	+	9.22569i	1.20214	+	0.370812i	0.371931	+	0.928260i	$0.378696\pi$
$620$	−0.653612	−	1.66538i	−0.0262497	−	0.0668831i
$621$	−1.85087	−	24.6981i	−0.0742727	−	0.991100i
$622$	26.2840	+	32.9591i	1.05389	+	1.32154i
$623$	21.7249	−	17.3746i	0.870391	−	0.696100i
$624$	−4.68669	−	2.25699i	−0.187618	−	0.0903519i
$625$	1.86213	+	24.8483i	0.0744850	+	0.993934i
$626$	3.10334	−	41.4112i	0.124034	−	1.65512i
$627$	−6.95301	−	6.45145i	−0.277676	−	0.257646i
$628$	8.69841	−	22.1632i	0.347104	−	0.884407i
$629$	−15.7840	−	19.7925i	−0.629351	−	0.789181i
$630$	−0.0544722	+	0.177472i	−0.00217023	+	0.00707065i
$631$	24.6200	−	30.8725i	0.980106	−	1.22901i	0.00668854	−	0.999978i	$-0.497871\pi$
$631$	24.6200	−	30.8725i	0.980106	−	1.22901i	0.973418	−	0.229037i	$-0.0735576\pi$
$632$	0.392074	−	0.363791i	0.0155959	−	0.0144708i
$633$	0.236080	−	3.15027i	0.00938333	−	0.125212i
$634$	−1.55794	+	2.69844i	−0.0618738	+	0.107169i
$635$	−0.464546	−	0.691779i	−0.0184349	−	0.0274524i
$636$	−1.03713			−0.0411249
$637$	−0.506389	−	6.51372i	−0.0200639	−	0.258083i
$638$	−2.62406	−	11.4967i	−0.103887	−	0.455160i
$639$	−0.426964	−	0.0643545i	−0.0168904	−	0.00254582i
$640$	−0.498179	+	0.0750885i	−0.0196923	+	0.00296813i
$641$	−25.8627	+	3.89818i	−1.02152	+	0.153969i	−0.638378	−	0.769723i	$-0.720394\pi$
$641$	−25.8627	+	3.89818i	−1.02152	+	0.153969i	−0.383137	+	0.923691i	$0.625156\pi$
$642$	−18.7800	+	47.8506i	−0.741186	+	1.88851i
$643$	−6.85677	+	30.0415i	−0.270405	+	1.18472i	0.639133	+	0.769097i	$0.279294\pi$
$643$	−6.85677	+	30.0415i	−0.270405	+	1.18472i	−0.909537	+	0.415623i	$0.863564\pi$
$644$	−28.9614	−	16.6671i	−1.14124	−	0.656778i
$645$	−0.166500	−	0.0801820i	−0.00655591	−	0.00315716i
$646$	4.29446	+	57.3056i	0.168963	+	2.25466i
$647$	20.5695	−	14.0240i	0.808669	−	0.551341i	−0.0869244	−	0.996215i	$-0.527704\pi$
$647$	20.5695	−	14.0240i	0.808669	−	0.551341i	0.895593	+	0.444874i	$0.146751\pi$
$648$	−8.73636	+	1.31679i	−0.343197	+	0.0517286i
$649$	−0.894158	−	11.9317i	−0.0350988	−	0.468360i
$650$	6.10650	−	7.65731i	0.239517	−	0.300345i
$651$	48.0419	+	10.8949i	1.88291	+	0.427003i
$652$	−33.4787	−	41.9810i	−1.31113	−	1.64410i
$653$	−2.87372	−	0.433143i	−0.112457	−	0.0169502i	0.0925725	−	0.995706i	$-0.470491\pi$
$653$	−2.87372	−	0.433143i	−0.112457	−	0.0169502i	−0.205030	+	0.978756i	$0.565729\pi$
$654$	29.8038	−	51.6217i	1.16542	−	2.01857i
$655$	−0.270828	+	0.469087i	−0.0105821	+	0.0183288i
$656$	15.9681	+	2.40681i	0.623451	+	0.0939701i
$657$	−4.76071			−0.185733
$658$	8.27482	−	4.79285i	0.322586	−	0.186845i
$659$	−18.4662			−0.719342			−0.359671	−	0.933079i	$-0.617111\pi$
$659$	−18.4662			−0.719342			−0.359671	+	0.933079i	$0.617111\pi$
$660$	0.295079	−	0.0910198i	0.0114859	−	0.00354294i
$661$	26.1707	−	17.8429i	1.01792	−	0.694007i	0.0652057	−	0.997872i	$-0.479230\pi$
$661$	26.1707	−	17.8429i	1.01792	−	0.694007i	0.952715	+	0.303865i	$0.0982773\pi$
$662$	31.5614	−	4.75712i	1.22667	−	0.184891i
$663$	−4.32484	−	7.49084i	−0.167963	−	0.290920i
$664$	2.58593	+	11.3297i	0.100353	+	0.439677i
$665$	−0.158400	+	1.06094i	−0.00614248	+	0.0411415i
$666$	−3.00270	+	3.76526i	−0.116352	+	0.145901i
$667$	−11.5211	+	29.3553i	−0.446099	+	1.13664i
$668$	−43.0261	−	39.9224i	−1.66473	−	1.54464i
$669$	−36.3528	+	24.7849i	−1.40548	+	0.958239i
$670$	−0.878462	+	0.270970i	−0.0339380	+	0.0104685i
$671$	−0.873657	+	3.82774i	−0.0337272	+	0.147768i
$672$	17.1050	−	35.6458i	0.659839	−	1.37507i
$673$	15.4297	−	7.43057i	0.594773	−	0.286427i	−0.112180	−	0.993688i	$-0.535783\pi$
$673$	15.4297	−	7.43057i	0.594773	−	0.286427i	0.706953	+	0.707260i	$0.250069\pi$
$674$	−49.4321	−	7.45068i	−1.90405	−	0.286990i
$675$	−1.76710	+	23.5803i	−0.0680158	+	0.907608i
$676$	28.9552	−	4.36429i	1.11366	−	0.167857i
$677$	4.99128	−	1.53961i	0.191831	−	0.0591719i	−0.197351	−	0.980333i	$-0.563234\pi$
$677$	4.99128	−	1.53961i	0.191831	−	0.0591719i	0.389182	+	0.921161i	$0.372758\pi$
$678$	13.4419	+	58.8929i	0.516234	+	2.26177i
$679$	19.5419	+	11.2462i	0.749949	+	0.431591i
$680$	−0.289233	−	0.139287i	−0.0110916	−	0.00534142i
$681$	−0.211067	−	0.0318132i	−0.00808809	−	0.00121908i
$682$	−7.16242	−	18.2495i	−0.274263	−	0.698811i
$683$	−1.77838	+	23.7309i	−0.0680479	+	0.908036i	0.853829	+	0.520554i	$0.174274\pi$
$683$	−1.77838	+	23.7309i	−0.0680479	+	0.908036i	−0.921877	+	0.387483i	$0.873345\pi$
$684$	5.71343	−	1.76236i	0.218458	−	0.0673855i
$685$	0.307179	+	1.34584i	0.0117367	+	0.0514219i
$686$	38.7900	−	3.06998i	1.48101	−	0.117212i
$687$	40.6255			1.54996
$688$	3.33432	+	2.27330i	0.127120	+	0.0866687i
$689$	0.178312	−	0.121571i	0.00679314	−	0.00463149i
$690$	−1.44280	−	0.445044i	−0.0549264	−	0.0169425i
$691$	25.0682	+	17.0912i	0.953638	+	0.650179i	0.936869	−	0.349680i	$-0.113710\pi$
$691$	25.0682	+	17.0912i	0.953638	+	0.650179i	0.0167685	+	0.999859i	$0.494662\pi$
$692$	−6.39184	−	28.0045i	−0.242981	−	1.06457i
$693$	−0.326468	+	1.06364i	−0.0124015	+	0.0404044i
$694$	−64.0420			−2.43100
$695$	−0.917794	+	0.851589i	−0.0348139	+	0.0323026i
$696$	9.31463	+	2.87318i	0.353070	+	0.108908i
$697$	19.6839	+	18.2640i	0.745579	+	0.691797i
$698$	−4.09933	−	54.7017i	−0.155162	−	2.07049i
$699$	−14.8697	−	7.16089i	−0.562425	−	0.270850i
$700$	24.9702	+	19.8563i	0.943786	+	0.750496i
$701$	−7.85309	−	34.4066i	−0.296607	−	1.29952i	−0.875143	−	0.483864i	$-0.839233\pi$
$701$	−7.85309	−	34.4066i	−0.296607	−	1.29952i	0.578536	−	0.815657i	$-0.303624\pi$
$702$	6.80573	−	6.31479i	0.256866	−	0.238336i
$703$	−13.9140	+	24.0997i	−0.524775	+	0.908937i
$704$	−10.0352	+	1.51256i	−0.378214	+	0.0570067i
$705$	0.173237	−	0.160740i	0.00652447	−	0.00605382i
$706$	−42.8087	+	20.6156i	−1.61113	+	0.775878i
$707$	5.93372	+	19.1419i	0.223161	+	0.719907i
$708$	51.9326	+	25.0094i	1.95175	+	0.939913i
$709$	−39.1481	−	26.6907i	−1.47024	−	1.00239i	−0.992281	−	0.124008i	$-0.960425\pi$
$709$	−39.1481	−	26.6907i	−1.47024	−	1.00239i	−0.477957	−	0.878383i	$-0.658623\pi$
$710$	0.0742589	−	0.128620i	0.00278689	−	0.00482703i
$711$	0.101401	+	0.258366i	0.00380283	+	0.00968946i
$712$	6.70833	−	6.22442i	0.251405	−	0.233270i
$713$	−11.6661	+	51.1125i	−0.436899	+	1.91418i
$714$	44.5778	−	25.8199i	1.66828	−	0.966285i
$715$	−0.0400632	+	0.0502377i	−0.00149828	+	0.00187878i
$716$	14.4701	+	2.18102i	0.540773	+	0.0815085i
$717$	1.13186	−	0.771689i	0.0422701	−	0.0288193i
$718$	−0.211287	+	2.81942i	−0.00788515	+	0.105220i
$719$	−20.6189	+	19.1315i	−0.768955	+	0.713486i	−0.963588	−	0.267390i	$-0.913839\pi$
$719$	−20.6189	+	19.1315i	−0.768955	+	0.713486i	0.194633	+	0.980876i	$0.437648\pi$
$720$	0.0222934	−	0.0976736i	0.000830825	−	0.00364008i
$721$	−0.464630	+	0.106730i	−0.0173037	+	0.00397483i
$722$	20.9475	−	10.0878i	0.779586	−	0.375429i
$723$	−26.9221	−	4.05786i	−1.00124	−	0.150913i
$724$	−1.48853	+	19.8630i	−0.0553208	+	0.738204i
$725$	15.0540	−	26.0743i	0.559092	−	0.968376i
$726$	−37.7963	+	11.6586i	−1.40275	+	0.432691i
$727$	0.987952	−	4.32850i	0.0366411	−	0.160535i	−0.953297	−	0.302033i	$-0.902335\pi$
$727$	0.987952	−	4.32850i	0.0366411	−	0.160535i	0.989939	+	0.141498i	$0.0451918\pi$
$728$	−0.323291	−	2.12481i	−0.0119820	−	0.0787506i
$729$	−4.85167	+	21.2566i	−0.179692	+	0.787281i
$730$	0.598245	−	1.52430i	0.0221421	−	0.0564170i
$731$	2.45156	+	6.24648i	0.0906743	+	0.231034i
$732$	−13.8649	−	12.8648i	−0.512462	−	0.475495i
$733$	−17.0506	+	15.8206i	−0.629777	+	0.584348i	−0.929111	−	0.369801i	$-0.879426\pi$
$733$	−17.0506	+	15.8206i	−0.629777	+	0.584348i	0.299334	+	0.954148i	$0.403236\pi$
$734$	−1.49603			−0.0552195
$735$	0.918104	−	0.286001i	0.0338648	−	0.0105493i
$736$	37.9108	+	18.2569i	1.39741	+	0.672957i
$737$	−5.26488	+	1.62400i	−0.193935	+	0.0598209i
$738$	2.55411	−	4.42384i	0.0940180	−	0.162844i
$739$	3.28992	−	43.9009i	0.121022	−	1.61492i	−0.524659	−	0.851312i	$-0.675807\pi$
$739$	3.28992	−	43.9009i	0.121022	−	1.61492i	0.645681	−	0.763608i	$-0.276574\pi$
$740$	−0.452988	−	0.784599i	−0.0166522	−	0.0288424i
$741$	−5.92818	+	7.43370i	−0.217777	+	0.273084i
$742$	0.725528	+	1.06098i	0.0266350	+	0.0389497i
$743$	15.4189			0.565665			0.282832	−	0.959169i	$-0.408726\pi$
$743$	15.4189			0.565665			0.282832	+	0.959169i	$0.408726\pi$
$744$	16.0244	+	2.41530i	0.587485	+	0.0885491i
$745$	−1.67507	+	0.252476i	−0.0613698	+	0.00925000i
$746$	16.9771	+	5.23674i	0.621575	+	0.191731i
$747$	−5.96318	−	0.898805i	−0.218181	−	0.0328855i
$748$	−10.1024	−	4.86507i	−0.369381	−	0.177885i
$749$	33.9576	−	7.80038i	1.24078	−	0.285020i
$750$	2.59900	+	1.25161i	0.0949020	+	0.0457024i
$751$	−0.826099	−	11.0235i	−0.0301448	−	0.402254i	−0.991783	−	0.127933i	$-0.959166\pi$
$751$	−0.826099	−	11.0235i	−0.0301448	−	0.402254i	0.961638	−	0.274321i	$-0.0884532\pi$
$752$	−4.26391	+	2.90709i	−0.155489	+	0.106011i
$753$	−1.15339	+	15.3909i	−0.0420318	+	0.560875i
$754$	−11.2959	+	3.48432i	−0.411371	+	0.126891i
$755$	−0.774043	−	0.970619i	−0.0281703	−	0.0353245i
$756$	20.6003	+	22.1400i	0.749227	+	0.805223i
$757$	4.97701	+	6.24097i	0.180892	+	0.226832i	0.864008	−	0.503479i	$-0.167947\pi$
$757$	4.97701	+	6.24097i	0.180892	+	0.226832i	−0.683115	+	0.730311i	$0.739375\pi$
$758$	−29.3789	−	4.42815i	−1.06709	−	0.160838i
$759$	−8.64712	−	2.66728i	−0.313870	−	0.0968162i
$760$	−0.0263709	+	0.351895i	−0.000956574	+	0.0127646i
$761$	−0.280024	−	0.485015i	−0.0101508	−	0.0175818i	0.860905	−	0.508765i	$-0.169898\pi$
$761$	−0.280024	−	0.485015i	−0.0101508	−	0.0175818i	−0.871056	+	0.491183i	$0.836565\pi$
$762$	43.8881	−	2.97836i	1.58990	−	0.107895i
$763$	−40.2852	+	3.07540i	−1.45842	+	0.111337i
$764$	32.7088	−	15.7517i	1.18336	−	0.569877i
$765$	0.122119	−	0.113310i	0.00441522	−	0.00409672i
$766$	20.9434	+	53.3629i	0.756715	+	1.92808i
$767$	−11.8603	+	1.78765i	−0.428249	+	0.0645482i
$768$	−5.07991	+	12.9434i	−0.183306	+	0.467055i
$769$	−20.4477	−	25.6406i	−0.737363	−	0.924624i	0.261817	−	0.965118i	$-0.415678\pi$
$769$	−20.4477	−	25.6406i	−0.737363	−	0.924624i	−0.999180	+	0.0404936i	$0.987107\pi$
$770$	−0.299536	−	0.238190i	−0.0107945	−	0.00858378i
$771$	−8.26455	+	3.98000i	−0.297641	+	0.143336i
$772$	−0.479017	−	6.39203i	−0.0172402	−	0.230054i
$773$	29.6192	−	20.1940i	1.06533	−	0.726328i	0.102034	−	0.994781i	$-0.467465\pi$
$773$	29.6192	−	20.1940i	1.06533	−	0.726328i	0.963293	+	0.268453i	$0.0865125\pi$
$774$	1.05474	−	0.719107i	0.0379117	−	0.0258478i
$775$	18.2869	−	46.5942i	0.656885	−	1.67371i
$776$	6.68264	+	3.21819i	0.239893	+	0.115526i
$777$	24.8791	+	1.82958i	0.892532	+	0.0656358i
$778$	4.69414	+	20.5664i	0.168293	+	0.737340i
$779$	10.7837	−	27.4763i	0.386365	−	0.984441i
$780$	−0.113091	−	0.288150i	−0.00404929	−	0.0103174i
$781$	0.445055	−	0.770859i	0.0159253	−	0.0275835i
$782$	27.4128	+	47.4803i	0.980279	+	1.69789i
$783$	17.7946	−	22.3137i	0.635927	−	0.797428i
$784$	−20.7558	+	3.18759i	−0.741277	+	0.113843i
$785$	−0.656989	+	0.316389i	−0.0234490	+	0.0112924i
$786$	−14.2970	−	24.7631i	−0.509957	−	0.883271i
$787$	−6.62252	−	6.14480i	−0.236067	−	0.219039i	0.553264	−	0.833006i	$-0.313382\pi$
$787$	−6.62252	−	6.14480i	−0.236067	−	0.219039i	−0.789331	+	0.613967i	$0.789573\pi$
$788$	−42.3705	+	28.8878i	−1.50939	+	1.02908i
$789$	−13.8668	+	35.3321i	−0.493673	+	1.25786i
$790$	−0.0954669			−0.00339656
$791$	27.8076	−	30.0533i	0.988723	−	1.06857i
$792$	−0.0814457	+	0.356837i	−0.00289405	+	0.0126796i
$793$	3.89176	+	0.586588i	0.138200	+	0.0208304i
$794$	28.1600	−	4.24443i	0.999360	−	0.150629i
$795$	0.0232849	+	0.0216053i	0.000825831	+	0.000766260i
$796$	1.49509	+	19.9506i	0.0529922	+	0.707131i
$797$	3.21440	−	14.0832i	0.113860	−	0.498853i	−0.885551	−	0.464542i	$-0.846219\pi$
$797$	3.21440	−	14.0832i	0.113860	−	0.498853i	0.999411	−	0.0343113i	$-0.0109238\pi$
$798$	−44.3226	−	35.2452i	−1.56900	−	1.24767i
$799$	−8.58117			−0.303580
$800$	−33.1929	−	22.6305i	−1.17355	−	0.800111i
$801$	1.73496	+	4.42060i	0.0613017	+	0.156194i
$802$	1.62818	−	21.7266i	0.0574932	−	0.767193i
$803$	3.58546	−	9.13561i	0.126528	−	0.322389i
$804$	5.90620	−	25.8767i	0.208296	−	0.912603i
$805$	0.303016	+	0.977518i	0.0106799	+	0.0344530i
$806$	−17.7062	+	8.52685i	−0.623673	+	0.300345i
$807$	−2.07348	−	27.6686i	−0.0729898	−	0.973981i
$808$	2.40857	+	6.13693i	0.0847331	+	0.215897i
$809$	−8.26161	−	21.0503i	−0.290463	−	0.740087i	−0.999394	−	0.0348096i	$-0.988918\pi$
$809$	−8.26161	−	21.0503i	−0.290463	−	0.740087i	0.708931	−	0.705278i	$-0.249178\pi$
$810$	1.30297	+	0.888348i	0.0457816	+	0.0312134i
$811$	3.50295	−	15.3474i	0.123005	−	0.538922i	−0.875447	−	0.483314i	$-0.839433\pi$
$811$	3.50295	−	15.3474i	0.123005	−	0.538922i	0.998453	−	0.0556081i	$-0.0177097\pi$
$812$	−11.4009	−	36.7788i	−0.400092	−	1.29068i
$813$	9.13552	−	11.4556i	0.320397	−	0.401765i
$814$	−4.96394	−	8.59780i	−0.173986	−	0.301353i
$815$	−0.122897	+	1.63995i	−0.00430490	+	0.0574449i
$816$	−22.9704	+	15.6610i	−0.804125	+	0.548243i
$817$	5.40719	−	5.01714i	0.189174	−	0.175527i
$818$	32.5556	−	15.6780i	1.13828	−	0.548167i
$819$	1.08770	+	0.246667i	0.0380074	+	0.00861925i
$820$	0.599147	+	0.751307i	0.0209231	+	0.0262368i
$821$	3.35709	+	5.81464i	0.117163	+	0.202932i	0.918642	−	0.395090i	$-0.129287\pi$
$821$	3.35709	+	5.81464i	0.117163	+	0.202932i	−0.801479	+	0.598023i	$0.795953\pi$
$822$	−69.6365	−	21.4800i	−2.42885	−	0.749201i
$823$	−46.4941	−	14.3415i	−1.62068	−	0.499914i	−0.654129	−	0.756383i	$-0.726965\pi$
$823$	−46.4941	−	14.3415i	−1.62068	−	0.499914i	−0.966553	+	0.256469i	$0.917441\pi$
$824$	−0.149861	+	0.0462260i	−0.00522066	+	0.00161036i
$825$	7.78403	+	3.74859i	0.271005	+	0.130509i
$826$	−10.7452	−	70.6222i	−0.373874	−	2.45726i
$827$	−4.29970	+	18.8382i	−0.149515	+	0.655069i	0.843505	+	0.537122i	$0.180488\pi$
$827$	−4.29970	+	18.8382i	−0.149515	+	0.655069i	−0.993020	+	0.117947i	$0.962369\pi$
$828$	4.18155	−	3.87991i	0.145319	−	0.134836i
$829$	41.4214	+	12.7768i	1.43863	+	0.443757i	0.913350	−	0.407175i	$-0.133486\pi$
$829$	41.4214	+	12.7768i	1.43863	+	0.443757i	0.525275	+	0.850932i	$0.323962\pi$
$830$	1.03713	−	1.79637i	0.0359994	−	0.0623529i
$831$	3.45542	−	8.80427i	0.119867	−	0.305417i
$832$	2.26374	+	9.91811i	0.0784812	+	0.343849i
$833$	−31.5017	−	15.0625i	−1.09147	−	0.521884i
$834$	−14.7073	−	64.4370i	−0.509273	−	2.23127i
$835$	0.134338	+	1.79262i	0.00464897	+	0.0620362i
$836$	−0.921093	+	12.2911i	−0.0318567	+	0.425098i
$837$	23.7240	−	41.0912i	0.820022	−	1.42032i
$838$	79.6392	+	12.0037i	2.75109	+	0.414660i
$839$	−1.02239	−	4.47940i	−0.0352970	−	0.154646i	0.954208	−	0.299143i	$-0.0967008\pi$
$839$	−1.02239	−	4.47940i	−0.0352970	−	0.154646i	−0.989505	+	0.144497i	$0.953844\pi$
$840$	0.294312	−	0.115982i	0.0101547	−	0.00400176i
$841$	−6.61239	+	3.18436i	−0.228013	+	0.109805i
$842$	2.85036	+	0.429623i	0.0982300	+	0.0148058i
$843$	8.29089	+	21.1248i	0.285553	+	0.727578i
$844$	−3.39187	+	2.31253i	−0.116753	+	0.0796007i
$845$	−0.740998	−	0.505204i	−0.0254911	−	0.0173795i
$846$	0.363254	+	1.59152i	0.0124889	+	0.0547176i
$847$	20.9839	+	16.6863i	0.721015	+	0.573349i
$848$	−0.432481	−	0.542315i	−0.0148515	−	0.0186232i
$849$	−16.5010	−	11.2502i	−0.566312	−	0.386105i
$850$	−19.1235	−	48.7260i	−0.655932	−	1.67129i
$851$	−1.98402	+	26.4749i	−0.0680113	+	0.907548i
$852$	2.14401	+	3.71353i	0.0734525	+	0.127223i
$853$	−7.12081	+	31.1983i	−0.243812	+	1.06821i	0.693702	+	0.720262i	$0.255978\pi$
$853$	−7.12081	+	31.1983i	−0.243812	+	1.06821i	−0.937514	+	0.347948i	$0.886879\pi$
$854$	−3.46130	+	23.1833i	−0.118443	+	0.793316i
$855$	−0.164987	−	0.0794536i	−0.00564244	−	0.00271726i
$856$	10.9526	−	3.37843i	0.374353	−	0.115473i
$857$	28.8441	−	4.34754i	0.985294	−	0.148509i	0.363419	−	0.931626i	$-0.381609\pi$
$857$	28.8441	−	4.34754i	0.985294	−	0.148509i	0.621875	+	0.783116i	$0.286371\pi$
$858$	−1.23927	−	3.15761i	−0.0423080	−	0.107799i
$859$	45.7748	−	14.1196i	1.56182	−	0.481756i	0.611030	−	0.791607i	$-0.290755\pi$
$859$	45.7748	−	14.1196i	1.56182	−	0.481756i	0.950785	+	0.309851i	$0.100279\pi$
$860$	0.0534372	+	0.234124i	0.00182219	+	0.00798356i
$861$	−26.3834	+	2.01412i	−0.899143	+	0.0686412i
$862$	−20.3146	−	25.4736i	−0.691916	−	0.867636i
$863$	2.85132	+	38.0482i	0.0970600	+	1.29518i	0.806847	+	0.590760i	$0.201172\pi$
$863$	2.85132	+	38.0482i	0.0970600	+	1.29518i	−0.709787	+	0.704416i	$0.751209\pi$
$864$	−27.9159	−	25.9021i	−0.949717	−	0.881209i
$865$	−0.439878	+	0.761891i	−0.0149563	+	0.0259051i
$866$	54.9438	+	37.4600i	1.86707	+	1.27294i
$867$	−14.6444			−0.497351
$868$	−27.8552	−	57.6365i	−0.945468	−	1.95631i
$869$	−0.572161			−0.0194092
$870$	−0.869944	−	1.50679i	−0.0294939	−	0.0510849i
$871$	2.01780	+	5.14126i	0.0683704	+	0.174205i
$872$	−13.1426	+	1.98093i	−0.445064	+	0.0670827i
$873$	−2.82152	+	2.61799i	−0.0954941	+	0.0886056i
$874$	37.5755	−	47.1182i	1.27101	−	1.59380i
$875$	−0.294108	−	1.93300i	−0.00994267	−	0.0653475i
$876$	29.4773	+	36.9634i	0.995947	+	1.24888i
$877$	0.0119411	+	0.159343i	0.000403222	+	0.00538063i	0.997402	−	0.0720395i	$-0.0229508\pi$
$877$	0.0119411	+	0.159343i	0.000403222	+	0.00538063i	−0.996999	+	0.0774201i	$0.975332\pi$
$878$	−30.3167	+	20.6696i	−1.02314	+	0.697564i
$879$	−7.63362	+	5.20451i	−0.257476	+	0.175544i
$880$	0.170642	+	0.116342i	0.00575233	+	0.00392187i
$881$	8.34154	−	36.5467i	0.281034	−	1.23129i	−0.615437	−	0.788186i	$-0.711020\pi$
$881$	8.34154	−	36.5467i	0.281034	−	1.23129i	0.896471	−	0.443103i	$-0.146122\pi$
$882$	−1.46007	+	6.48015i	−0.0491631	+	0.218198i
$883$	−6.88266	−	8.63058i	−0.231620	−	0.290442i	0.652416	−	0.757861i	$-0.273755\pi$
$883$	−6.88266	−	8.63058i	−0.231620	−	0.290442i	−0.884036	+	0.467419i	$0.845184\pi$
$884$	−4.10646	+	10.4631i	−0.138115	+	0.351912i
$885$	−0.644965	−	1.64334i	−0.0216803	−	0.0552404i
$886$	−26.9944	−	8.32666i	−0.906893	−	0.279739i
$887$	35.3176	+	24.0792i	1.18585	+	0.808499i	0.985241	−	0.171172i	$-0.0547554\pi$
$887$	35.3176	+	24.0792i	1.18585	+	0.808499i	0.200609	+	0.979671i	$0.435708\pi$
$888$	8.20648			0.275391
$889$	−18.4581	−	23.4158i	−0.619064	−	0.785341i
$890$	−1.63343			−0.0547526
$891$	7.80907	+	5.32413i	0.261614	+	0.178365i
$892$	54.6343	+	16.8525i	1.82929	+	0.564262i
$893$	3.44617	+	8.78070i	0.115322	+	0.293835i
$894$	32.6709	−	83.2440i	1.09268	−	2.78410i
$895$	−0.279439	−	0.350405i	−0.00934060	−	0.0117127i
$896$	−17.5694	+	4.03585i	−0.586951	+	0.134828i
$897$	−2.01852	+	8.84370i	−0.0673963	+	0.295283i
$898$	20.1090	+	13.7101i	0.671047	+	0.457512i
$899$	−49.9160	+	34.0322i	−1.66479	+	1.13504i
$900$	−4.49982	+	3.06793i	−0.149994	+	0.102264i
$901$	−0.0861940	−	1.15018i	−0.00287154	−	0.0383180i
$902$	6.56558	+	8.23298i	0.218610	+	0.274128i
$903$	−6.15870	−	2.40722i	−0.204949	−	0.0801072i
$904$	8.39803	−	10.5308i	0.279314	−	0.350249i
$905$	0.447202	−	0.414943i	0.0148655	−	0.0137932i
$906$	64.8052	−	9.76781i	2.15301	−	0.324514i
$907$	−13.5156	−	34.4373i	−0.448780	−	1.14347i	−0.958994	−	0.283425i	$-0.908529\pi$
$907$	−13.5156	−	34.4373i	−0.448780	−	1.14347i	0.510215	−	0.860047i	$-0.329566\pi$
$908$	0.138687	+	0.240214i	0.00460251	+	0.00797177i
$909$	−3.42114			−0.113472
$910$	−0.215663	+	0.317268i	−0.00714915	+	0.0105173i
$911$	−12.0640			−0.399697			−0.199849	−	0.979827i	$-0.564045\pi$
$911$	−12.0640			−0.399697			−0.199849	+	0.979827i	$0.564045\pi$
$912$	25.2500	+	17.2151i	0.836110	+	0.570050i
$913$	6.21585	−	10.7662i	0.205715	−	0.356308i
$914$	−24.5613	−	22.7895i	−0.812414	−	0.753810i
$915$	0.0432897	+	0.577661i	0.00143111	+	0.0190969i
$916$	−32.9153	−	41.2745i	−1.08755	−	1.36375i
$917$	−8.38486	+	17.4736i	−0.276892	+	0.577028i
$918$	−11.0412	−	48.3748i	−0.364415	−	1.59661i
$919$	6.51178	−	2.00862i	0.214804	−	0.0662582i	−0.185486	−	0.982647i	$-0.559386\pi$
$919$	6.51178	−	2.00862i	0.214804	−	0.0662582i	0.400289	+	0.916389i	$0.368910\pi$
$920$	0.122998	+	0.313394i	0.00405512	+	0.0103323i
$921$	24.3488	−	3.66999i	0.802320	−	0.120930i
$922$	3.07373	−	0.948119i	0.101228	−	0.0312246i
$923$	−0.803911	−	0.387143i	−0.0264610	−	0.0127430i
$924$	10.2798	−	4.05106i	0.338181	−	0.133270i
$925$	5.64038	−	24.7121i	0.185454	−	0.812529i
$926$	−0.628861	−	1.08922i	−0.0206656	−	0.0357939i
$927$	0.00608179	−	0.0811558i	0.000199752	−	0.00266551i
$928$	17.7146	+	45.1360i	0.581510	+	1.48166i
$929$	28.6457	+	19.5303i	0.939834	+	0.640768i	0.933257	−	0.359210i	$-0.116954\pi$
$929$	28.6457	+	19.5303i	0.939834	+	0.640768i	0.00657751	+	0.999978i	$0.497906\pi$
$930$	−1.80347	−	2.26148i	−0.0591382	−	0.0741570i
$931$	−2.76170	+	38.2833i	−0.0905110	+	1.25468i
$932$	4.77237	+	20.9091i	0.156324	+	0.684901i
$933$	30.8002	+	20.9992i	1.00835	+	0.687483i
$934$	−23.5696	+	16.0695i	−0.771220	+	0.525809i
$935$	0.125465	+	0.319679i	0.00410313	+	0.0104546i
$936$	0.362805	+	0.0546840i	0.0118586	+	0.00178740i
$937$	−7.54559	+	3.63376i	−0.246504	+	0.118710i	−0.553057	−	0.833144i	$-0.686539\pi$
$937$	−7.54559	+	3.63376i	−0.246504	+	0.118710i	0.306553	+	0.951854i	$0.400824\pi$
$938$	−30.6034	+	12.0602i	−0.999238	+	0.393779i
$939$	−8.17127	−	35.8007i	−0.266659	−	1.16831i
$940$	−0.303666	−	0.0457704i	−0.00990451	−	0.00149286i
$941$	16.0409	−	27.7836i	0.522918	−	0.905721i	−0.476726	−	0.879052i	$-0.658177\pi$
$941$	16.0409	−	27.7836i	0.522918	−	0.905721i	0.999644	−	0.0266689i	$-0.00848997\pi$
$942$	2.87671	−	38.3870i	0.0937282	−	1.25072i
$943$	−2.10442	−	28.0816i	−0.0685294	−	0.914461i
$944$	8.57841	+	37.5845i	0.279203	+	1.22327i
$945$	−0.00129025	−	0.926213i	−4.19719e−5	−	0.0301297i
$946$	0.585577	+	2.56558i	0.0190387	+	0.0834142i
$947$	11.5881	−	29.5260i	0.376563	−	0.959467i	−0.609454	−	0.792821i	$-0.708611\pi$
$947$	11.5881	−	29.5260i	0.376563	−	0.959467i	0.986017	−	0.166645i	$-0.0532935\pi$
$948$	1.37816	−	2.38705i	0.0447606	−	0.0775277i
$949$	−9.40079	−	2.89976i	−0.305163	−	0.0941302i
$950$	−42.1791	+	39.1364i	−1.36847	+	1.26975i
$951$	−0.613109	+	2.68620i	−0.0198814	+	0.0871062i
$952$	−10.6985	−	4.18167i	−0.346741	−	0.135529i
$953$	−10.7134	−	5.15933i	−0.347043	−	0.167127i	0.252239	−	0.967665i	$-0.418833\pi$
$953$	−10.7134	−	5.15933i	−0.347043	−	0.167127i	−0.599282	+	0.800538i	$0.704547\pi$
$954$	−0.209671	+	0.0646750i	−0.00678836	+	0.00209393i
$955$	−1.06249	−	0.327735i	−0.0343814	−	0.0106053i
$956$	−1.70106	−	0.524709i	−0.0550163	−	0.0169703i
$957$	−5.21384	−	9.03063i	−0.168539	−	0.291919i
$958$	5.63056	+	7.06049i	0.181915	+	0.228114i
$959$	14.6250	+	47.1798i	0.472267	+	1.52351i
$960$	−1.34906	+	0.649673i	−0.0435408	+	0.0209681i
$961$	−50.9008	+	47.2291i	−1.64196	+	1.52352i
$962$	−8.22274	+	5.60617i	−0.265112	+	0.180750i
$963$	−0.444488	+	5.93128i	−0.0143234	+	0.191133i
$964$	17.6900	+	30.6399i	0.569756	+	0.986846i
$965$	−0.122403	+	0.153488i	−0.00394029	+	0.00494096i
$966$	−52.6878	−	11.9484i	−1.69520	−	0.384435i
$967$	−7.65175	+	33.5245i	−0.246064	+	1.07808i	0.689324	+	0.724453i	$0.257908\pi$
$967$	−7.65175	+	33.5245i	−0.246064	+	1.07808i	−0.935388	+	0.353623i	$0.884950\pi$
$968$	7.28699	+	4.96818i	0.234213	+	0.159684i
$969$	18.5651	+	47.3031i	0.596397	+	1.51959i
$970$	−0.483678	−	1.23239i	−0.0155300	−	0.0395697i
$971$	0.678271	+	9.05090i	0.0217667	+	0.290457i	0.997455	+	0.0712952i	$0.0227132\pi$
$971$	0.678271	+	9.05090i	0.0217667	+	0.290457i	−0.975689	+	0.219162i	$0.929668\pi$
$972$	−10.1270	+	4.87692i	−0.324824	+	0.156427i
$973$	−30.4253	+	32.8824i	−0.975391	+	1.05416i
$974$	10.5878	−	46.3882i	0.339255	−	1.48637i
$975$	3.16408	−	8.06193i	0.101332	−	0.258188i
$976$	0.945329	−	12.6145i	0.0302592	−	0.403781i
$977$	−14.9775	−	38.1620i	−0.479172	−	1.22091i	−0.942345	−	0.334642i	$-0.891385\pi$
$977$	−14.9775	−	38.1620i	−0.479172	−	1.22091i	0.463174	−	0.886268i	$-0.346711\pi$
$978$	−71.7305	−	48.9050i	−2.29369	−	1.56381i
$979$	−9.78961			−0.312877
$980$	−1.03443	−	0.701048i	−0.0330436	−	0.0223942i
$981$	1.53476	−	6.72422i	0.0490011	−	0.214688i
$982$	5.27192	+	70.3489i	0.168234	+	2.24492i
$983$	0.621502	+	0.576670i	0.0198228	+	0.0183929i	0.690022	−	0.723788i	$-0.257601\pi$
$983$	0.621502	+	0.576670i	0.0198228	+	0.0183929i	−0.670199	+	0.742181i	$0.733791\pi$
$984$	−8.60728	+	1.29734i	−0.274390	+	0.0413576i
$985$	1.55306	+	0.234086i	0.0494845	+	0.00745860i
$986$	−14.0583	+	61.5936i	−0.447708	+	1.96154i
$987$	5.74287	−	6.20667i	0.182798	−	0.197560i
$988$	12.3555			0.393082
$989$	2.57102	−	6.55084i	0.0817536	−	0.208305i
$990$	0.0539787	−	0.0368020i	0.00171555	−	0.00116965i
$991$	20.6380	+	19.1493i	0.655587	+	0.608296i	0.936176	−	0.351532i	$-0.114339\pi$
$991$	20.6380	+	19.1493i	0.655587	+	0.608296i	−0.280588	+	0.959828i	$0.590530\pi$
$992$	40.3053	+	69.8107i	1.27969	+	2.21649i
$993$	25.4290	−	12.2460i	0.806966	−	0.388614i
$994$	2.29906	−	4.79112i	0.0729219	−	0.151965i
$995$	0.382040	−	0.479063i	0.0121115	−	0.0151873i
$996$	29.9442	+	51.8649i	0.948818	+	1.64340i
$997$	14.2600	−	24.6991i	0.451620	−	0.782228i	−0.546867	−	0.837219i	$-0.684180\pi$
$997$	14.2600	−	24.6991i	0.451620	−	0.782228i	0.998487	+	0.0549912i	$0.0175131\pi$
$998$	−22.0102	−	56.0812i	−0.696722	−	1.77522i
$999$	8.77834	−	22.3668i	0.277734	−	0.707655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	889.2.bm.a.445.14	yes	1008
7.2	even	3	inner	889.2.bm.a.191.14	yes	1008
127.2	even	7	inner	889.2.bm.a.256.14	yes	1008
889.2	even	21	inner	889.2.bm.a.2.14	✓	1008

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.bm.a.2.14	✓	1008	889.2	even	21	inner
889.2.bm.a.191.14	yes	1008	7.2	even	3	inner
889.2.bm.a.256.14	yes	1008	127.2	even	7	inner
889.2.bm.a.445.14	yes	1008	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.bm (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73594 - 1.18354i) q^{2} +(-1.77532 - 0.547615i) q^{3} +(0.882028 + 2.24737i) q^{4} +(0.0270140 - 0.0688306i) q^{5} +(2.43373 + 3.05180i) q^{6} +(0.776326 - 2.52929i) q^{7} +(0.193674 - 0.848541i) q^{8} +(0.373178 + 0.254429i) q^{9} +O(q^{10})\)	\(q+(-1.73594 - 1.18354i) q^{2} +(-1.77532 - 0.547615i) q^{3} +(0.882028 + 2.24737i) q^{4} +(0.0270140 - 0.0688306i) q^{5} +(2.43373 + 3.05180i) q^{6} +(0.776326 - 2.52929i) q^{7} +(0.193674 - 0.848541i) q^{8} +(0.373178 + 0.254429i) q^{9} +(-0.128359 + 0.0875135i) q^{10} +(-0.769292 + 0.524494i) q^{11} +(-0.335192 - 4.47282i) q^{12} +(0.581928 + 0.729714i) q^{13} +(-4.34118 + 3.47188i) q^{14} +(-0.0856514 + 0.107403i) q^{15} +(2.19906 - 2.04043i) q^{16} +(4.93251 - 0.743457i) q^{17} +(-0.346688 - 0.883346i) q^{18} +(-2.74163 - 4.74864i) q^{19} +0.178515 q^{20} +(-2.76331 + 4.06519i) q^{21} +1.95621 q^{22} +(-4.32229 - 2.94688i) q^{23} +(-0.808508 + 1.40038i) q^{24} +(3.66125 + 3.39714i) q^{25} +(-0.146543 - 1.95548i) q^{26} +(2.95189 + 3.70156i) q^{27} +(6.36900 - 0.486213i) q^{28} +(-1.34140 - 5.87706i) q^{29} +(0.275802 - 0.0850737i) q^{30} +(-3.66138 - 9.32905i) q^{31} +(-7.95366 + 1.19882i) q^{32} +(1.65296 - 0.509872i) q^{33} +(-9.44245 - 4.54725i) q^{34} +(-0.153121 - 0.121761i) q^{35} +(-0.242642 + 1.06308i) q^{36} +(-2.53754 - 4.39514i) q^{37} +(-0.860920 + 11.4882i) q^{38} +(-0.633508 - 1.61415i) q^{39} +(-0.0531737 - 0.0362532i) q^{40} +(3.35628 + 4.20865i) q^{41} +(9.60826 - 3.78642i) q^{42} +(0.299343 + 1.31151i) q^{43} +(-1.85727 - 1.26627i) q^{44} +(0.0275935 - 0.0188130i) q^{45} +(4.01546 + 10.2312i) q^{46} +(-1.70107 - 0.256395i) q^{47} +(-5.02142 + 2.41819i) q^{48} +(-5.79464 - 3.92711i) q^{49} +(-2.33504 - 10.2305i) q^{50} +(-9.16394 - 1.38124i) q^{51} +(-1.12666 + 1.95143i) q^{52} +(0.0172795 - 0.230579i) q^{53} +(-0.743354 - 9.91937i) q^{54} +(0.0153196 + 0.0671196i) q^{55} +(-1.99585 - 1.14860i) q^{56} +(2.26685 + 9.93173i) q^{57} +(-4.62717 + 11.7898i) q^{58} +(-6.42544 + 11.1292i) q^{59} +(-0.316922 - 0.0977575i) q^{60} +(3.09114 - 2.86816i) q^{61} +(-4.68540 + 20.5281i) q^{62} +(0.933233 - 0.746357i) q^{63} +(9.82034 + 4.72923i) q^{64} +(0.0659469 - 0.0203419i) q^{65} +(-3.47290 - 1.07125i) q^{66} +(5.65462 + 1.74422i) q^{67} +(6.02144 + 10.4294i) q^{68} +(6.05970 + 7.59863i) q^{69} +(0.121699 + 0.392596i) q^{70} +(-0.861327 + 0.414793i) q^{71} +(0.288168 - 0.267381i) q^{72} +(-8.70897 + 5.93767i) q^{73} +(-0.796832 + 10.6330i) q^{74} +(-4.63958 - 8.03599i) q^{75} +(8.25375 - 10.3499i) q^{76} +(0.729378 + 2.35294i) q^{77} +(-0.810687 + 3.55185i) q^{78} +(0.507736 + 0.346169i) q^{79} +(-0.0810387 - 0.206483i) q^{80} +(-3.70857 - 9.44928i) q^{81} +(-0.845189 - 11.2783i) q^{82} +(-12.0297 + 5.79320i) q^{83} +(-11.5733 - 2.62457i) q^{84} +(0.0820745 - 0.359592i) q^{85} +(1.03258 - 2.63098i) q^{86} +(-0.836945 + 11.1683i) q^{87} +(0.296063 + 0.754357i) q^{88} +(8.68731 + 5.92291i) q^{89} -0.0701667 q^{90} +(2.29743 - 0.905368i) q^{91} +(2.81036 - 12.3130i) q^{92} +(1.39141 + 18.5671i) q^{93} +(2.64950 + 2.45838i) q^{94} +(-0.400914 + 0.0604281i) q^{95} +(14.7768 + 2.22725i) q^{96} +(-1.89631 + 8.30827i) q^{97} +(5.41123 + 13.6754i) q^{98} -0.420530 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1008 q - 7 q^{3} + 84 q^{4} - 9 q^{5} - 28 q^{6} - 19 q^{7} - 30 q^{8} + 67 q^{9}+O(q^{10}) \) 1008 * q - 7 * q^3 + 84 * q^4 - 9 * q^5 - 28 * q^6 - 19 * q^7 - 30 * q^8 + 67 * q^9	\( 1008 q - 7 q^{3} + 84 q^{4} - 9 q^{5} - 28 q^{6} - 19 q^{7} - 30 q^{8} + 67 q^{9} - 13 q^{10} - 19 q^{11} - 17 q^{12} - 36 q^{13} + 6 q^{14} + 6 q^{15} + 112 q^{16} + q^{17} - 25 q^{18} - 34 q^{19} - 232 q^{20} + 8 q^{21} - 40 q^{22} - 15 q^{23} + 78 q^{24} + 97 q^{25} + 43 q^{26} - 4 q^{27} + 68 q^{28} + 64 q^{29} - 25 q^{30} + q^{31} - 32 q^{32} - 25 q^{33} + 132 q^{34} - 46 q^{35} - 188 q^{36} - 6 q^{37} + 15 q^{38} + 19 q^{39} - 53 q^{40} - 34 q^{41} + 4 q^{42} - 8 q^{43} - 132 q^{44} - 55 q^{45} - 35 q^{46} + 25 q^{47} - 40 q^{48} + 83 q^{49} - 104 q^{50} - 32 q^{51} + 8 q^{52} - 17 q^{53} - 57 q^{54} + 6 q^{55} + 4 q^{56} + 34 q^{57} + 13 q^{58} + 140 q^{59} - 78 q^{60} + 7 q^{61} - 100 q^{62} + 60 q^{63} - 146 q^{64} - 6 q^{65} - 32 q^{66} - 71 q^{67} - 28 q^{68} - 8 q^{69} - 200 q^{70} - 38 q^{71} - 4 q^{72} - 18 q^{73} + 24 q^{74} - 42 q^{75} + 50 q^{76} + 4 q^{77} + 36 q^{78} - 37 q^{79} - 11 q^{80} - 61 q^{81} + 55 q^{82} + 40 q^{83} + 274 q^{84} - 48 q^{85} - 83 q^{86} + q^{87} - 34 q^{88} - 29 q^{89} - 244 q^{90} + 34 q^{91} - 254 q^{92} - 81 q^{93} + 67 q^{94} + 15 q^{95} + 55 q^{96} - 32 q^{97} + 249 q^{98} - 176 q^{99}+O(q^{100}) \) 1008 * q - 7 * q^3 + 84 * q^4 - 9 * q^5 - 28 * q^6 - 19 * q^7 - 30 * q^8 + 67 * q^9 - 13 * q^10 - 19 * q^11 - 17 * q^12 - 36 * q^13 + 6 * q^14 + 6 * q^15 + 112 * q^16 + q^17 - 25 * q^18 - 34 * q^19 - 232 * q^20 + 8 * q^21 - 40 * q^22 - 15 * q^23 + 78 * q^24 + 97 * q^25 + 43 * q^26 - 4 * q^27 + 68 * q^28 + 64 * q^29 - 25 * q^30 + q^31 - 32 * q^32 - 25 * q^33 + 132 * q^34 - 46 * q^35 - 188 * q^36 - 6 * q^37 + 15 * q^38 + 19 * q^39 - 53 * q^40 - 34 * q^41 + 4 * q^42 - 8 * q^43 - 132 * q^44 - 55 * q^45 - 35 * q^46 + 25 * q^47 - 40 * q^48 + 83 * q^49 - 104 * q^50 - 32 * q^51 + 8 * q^52 - 17 * q^53 - 57 * q^54 + 6 * q^55 + 4 * q^56 + 34 * q^57 + 13 * q^58 + 140 * q^59 - 78 * q^60 + 7 * q^61 - 100 * q^62 + 60 * q^63 - 146 * q^64 - 6 * q^65 - 32 * q^66 - 71 * q^67 - 28 * q^68 - 8 * q^69 - 200 * q^70 - 38 * q^71 - 4 * q^72 - 18 * q^73 + 24 * q^74 - 42 * q^75 + 50 * q^76 + 4 * q^77 + 36 * q^78 - 37 * q^79 - 11 * q^80 - 61 * q^81 + 55 * q^82 + 40 * q^83 + 274 * q^84 - 48 * q^85 - 83 * q^86 + q^87 - 34 * q^88 - 29 * q^89 - 244 * q^90 + 34 * q^91 - 254 * q^92 - 81 * q^93 + 67 * q^94 + 15 * q^95 + 55 * q^96 - 32 * q^97 + 249 * q^98 - 176 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more