LMFDB - Embedded newform 380.2.s.a.259.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(179,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("380.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$56$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			259.2
Character	$\chi$	$=$	380.259
Dual form			380.2.s.a.179.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40034 - 0.197594i) q^{2} +(0.952596 - 0.549982i) q^{3} +(1.92191 + 0.553399i) q^{4} +(-2.22480 - 0.224228i) q^{5} +(-1.44263 + 0.581934i) q^{6} -1.22694 q^{7} +(-2.58199 - 1.15471i) q^{8} +(-0.895041 + 1.55026i) q^{9} +O(q^{10})$	\(q+(-1.40034 - 0.197594i) q^{2} +(0.952596 - 0.549982i) q^{3} +(1.92191 + 0.553399i) q^{4} +(-2.22480 - 0.224228i) q^{5} +(-1.44263 + 0.581934i) q^{6} -1.22694 q^{7} +(-2.58199 - 1.15471i) q^{8} +(-0.895041 + 1.55026i) q^{9} +(3.07117 + 0.753603i) q^{10} +0.0812753i q^{11} +(2.13517 - 0.529851i) q^{12} +(-1.99480 + 3.45509i) q^{13} +(1.71814 + 0.242437i) q^{14} +(-2.24265 + 1.01000i) q^{15} +(3.38750 + 2.12717i) q^{16} +(-4.46708 + 2.57907i) q^{17} +(1.55968 - 1.99403i) q^{18} +(-2.32718 + 3.68568i) q^{19} +(-4.15178 - 1.66215i) q^{20} +(-1.16878 + 0.674796i) q^{21} +(0.0160596 - 0.113813i) q^{22} +(3.94419 - 6.83155i) q^{23} +(-3.09466 + 0.320075i) q^{24} +(4.89944 + 0.997722i) q^{25} +(3.47611 - 4.44415i) q^{26} +5.26891i q^{27} +(-2.35808 - 0.678990i) q^{28} +(-0.920899 - 0.531682i) q^{29} +(3.34005 - 0.971208i) q^{30} -0.146201 q^{31} +(-4.32334 - 3.64812i) q^{32} +(0.0446999 + 0.0774226i) q^{33} +(6.76505 - 2.72891i) q^{34} +(2.72970 + 0.275115i) q^{35} +(-2.57810 + 2.48414i) q^{36} -2.88865 q^{37} +(3.98711 - 4.70137i) q^{38} +4.38841i q^{39} +(5.48548 + 3.14794i) q^{40} +(-10.5269 + 6.07769i) q^{41} +(1.77003 - 0.714001i) q^{42} +(3.50785 + 6.07577i) q^{43} +(-0.0449777 + 0.156204i) q^{44} +(2.33889 - 3.24831i) q^{45} +(-6.87310 + 8.78715i) q^{46} +(-2.81704 + 4.87926i) q^{47} +(4.39682 + 0.163273i) q^{48} -5.49461 q^{49} +(-6.66375 - 2.36525i) q^{50} +(-2.83688 + 4.91363i) q^{51} +(-5.74587 + 5.53647i) q^{52} +(3.68541 - 6.38332i) q^{53} +(1.04111 - 7.37828i) q^{54} +(0.0182242 - 0.180821i) q^{55} +(3.16795 + 1.41676i) q^{56} +(-0.189805 + 4.79087i) q^{57} +(1.18452 + 0.926500i) q^{58} +(-1.76709 - 3.06069i) q^{59} +(-4.86912 + 0.700047i) q^{60} +(1.88854 - 3.27105i) q^{61} +(0.204732 + 0.0288886i) q^{62} +(1.09816 - 1.90208i) q^{63} +(5.33330 + 5.96288i) q^{64} +(5.21275 - 7.23959i) q^{65} +(-0.0472969 - 0.117250i) q^{66} +(8.93896 + 5.16091i) q^{67} +(-10.0126 + 2.48467i) q^{68} -8.67694i q^{69} +(-3.76815 - 0.924628i) q^{70} +(0.376619 + 0.652324i) q^{71} +(4.10107 - 2.96923i) q^{72} +(1.44429 - 0.833861i) q^{73} +(4.04510 + 0.570781i) q^{74} +(5.21592 - 1.74418i) q^{75} +(-6.51229 + 5.79570i) q^{76} -0.0997203i q^{77} +(0.867125 - 6.14527i) q^{78} +(-7.08430 - 12.2704i) q^{79} +(-7.05953 - 5.49209i) q^{80} +(0.212682 + 0.368377i) q^{81} +(15.9421 - 6.43079i) q^{82} -2.81532 q^{83} +(-2.61973 + 0.650097i) q^{84} +(10.5167 - 4.73627i) q^{85} +(-3.71165 - 9.20129i) q^{86} -1.16966 q^{87} +(0.0938492 - 0.209852i) q^{88} +(-0.325562 - 0.187964i) q^{89} +(-3.91710 + 4.08659i) q^{90} +(2.44751 - 4.23920i) q^{91} +(11.3610 - 10.9469i) q^{92} +(-0.139271 + 0.0804080i) q^{93} +(4.90893 - 6.27600i) q^{94} +(6.00393 - 7.67807i) q^{95} +(-6.12479 - 1.09743i) q^{96} +(-2.65080 - 4.59131i) q^{97} +(7.69433 + 1.08570i) q^{98} +(-0.125998 - 0.0727447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 2 q^{5} - 8 q^{6} + 44 q^{9}+O(q^{10}) $ 112 * q - 2 * q^5 - 8 * q^6 + 44 * q^9	$ 112 q - 2 q^{5} - 8 q^{6} + 44 q^{9} + 6 q^{10} - 36 q^{14} - 4 q^{16} + 44 q^{20} - 48 q^{21} + 2 q^{24} - 2 q^{25} - 36 q^{26} - 12 q^{29} - 32 q^{30} - 30 q^{34} + 20 q^{36} - 24 q^{40} - 24 q^{41} - 14 q^{44} + 56 q^{49} + 32 q^{54} - 6 q^{60} - 36 q^{61} - 36 q^{64} + 22 q^{66} + 12 q^{70} + 16 q^{74} - 26 q^{76} + 12 q^{80} - 48 q^{81} - 26 q^{85} - 120 q^{86} - 24 q^{89} + 24 q^{90} - 84 q^{96}+O(q^{100}) $ 112 * q - 2 * q^5 - 8 * q^6 + 44 * q^9 + 6 * q^10 - 36 * q^14 - 4 * q^16 + 44 * q^20 - 48 * q^21 + 2 * q^24 - 2 * q^25 - 36 * q^26 - 12 * q^29 - 32 * q^30 - 30 * q^34 + 20 * q^36 - 24 * q^40 - 24 * q^41 - 14 * q^44 + 56 * q^49 + 32 * q^54 - 6 * q^60 - 36 * q^61 - 36 * q^64 + 22 * q^66 + 12 * q^70 + 16 * q^74 - 26 * q^76 + 12 * q^80 - 48 * q^81 - 26 * q^85 - 120 * q^86 - 24 * q^89 + 24 * q^90 - 84 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−1.40034	−	0.197594i	−0.990191	−	0.139720i
$2$	−1.40034	−	0.197594i	−0.990191	−	0.139720i
$3$	0.952596	−	0.549982i	0.549982	−	0.317532i	−0.199133	−	0.979972i	$-0.563813\pi$
$3$	0.952596	−	0.549982i	0.549982	−	0.317532i	0.749115	+	0.662440i	$0.230479\pi$
$4$	1.92191	+	0.553399i	0.960956	+	0.276700i
$5$	−2.22480	−	0.224228i	−0.994959	−	0.100278i
$5$	−2.22480	−	0.224228i	−0.994959	−	0.100278i
$6$	−1.44263	+	0.581934i	−0.588952	+	0.237574i
$7$	−1.22694			−0.463741			−0.231871	−	0.972747i	$-0.574485\pi$
$7$	−1.22694			−0.463741			−0.231871	+	0.972747i	$0.574485\pi$
$8$	−2.58199	−	1.15471i	−0.912870	−	0.408251i
$9$	−0.895041	+	1.55026i	−0.298347	+	0.516752i
$10$	3.07117	+	0.753603i	0.971189	+	0.238310i
$11$			0.0812753i			0.0245054i	0.999925	+	0.0122527i	$0.00390026\pi$
$11$			0.0812753i			0.0245054i	−0.999925	+	0.0122527i	$0.996100\pi$
$12$	2.13517	−	0.529851i	0.616369	−	0.152955i
$13$	−1.99480	+	3.45509i	−0.553258	+	0.958270i	0.444779	+	0.895640i	$0.353282\pi$
$13$	−1.99480	+	3.45509i	−0.553258	+	0.958270i	−0.998037	+	0.0626299i	$0.980051\pi$
$14$	1.71814	+	0.242437i	0.459192	+	0.0647941i
$15$	−2.24265	+	1.01000i	−0.579051	+	0.260781i
$16$	3.38750	+	2.12717i	0.846875	+	0.531793i
$17$	−4.46708	+	2.57907i	−1.08343	+	0.625517i	−0.931819	−	0.362924i	$-0.881778\pi$
$17$	−4.46708	+	2.57907i	−1.08343	+	0.625517i	−0.151608	+	0.988441i	$0.548445\pi$
$18$	1.55968	−	1.99403i	0.367621	−	0.469998i
$19$	−2.32718	+	3.68568i	−0.533891	+	0.845553i
$19$	−2.32718	+	3.68568i	−0.533891	+	0.845553i
$20$	−4.15178	−	1.66215i	−0.928366	−	0.371667i
$21$	−1.16878	+	0.674796i	−0.255049	+	0.147253i
$22$	0.0160596	−	0.113813i	0.00342391	−	0.0242651i
$23$	3.94419	−	6.83155i	0.822421	−	1.42448i	−0.0814526	−	0.996677i	$-0.525956\pi$
$23$	3.94419	−	6.83155i	0.822421	−	1.42448i	0.903874	−	0.427799i	$-0.140711\pi$
$24$	−3.09466	+	0.320075i	−0.631694	+	0.0653350i
$25$	4.89944	+	0.997722i	0.979889	+	0.199544i
$26$	3.47611	−	4.44415i	0.681720	−	0.871569i
$27$			5.26891i			1.01400i
$28$	−2.35808	−	0.678990i	−0.445635	−	0.128317i
$29$	−0.920899	−	0.531682i	−0.171007	−	0.0987308i	0.412054	−	0.911160i	$-0.364812\pi$
$29$	−0.920899	−	0.531682i	−0.171007	−	0.0987308i	−0.583060	+	0.812429i	$0.698145\pi$
$30$	3.34005	−	0.971208i	0.609807	−	0.177317i
$31$	−0.146201			−0.0262585			−0.0131293	−	0.999914i	$-0.504179\pi$
$31$	−0.146201			−0.0262585			−0.0131293	+	0.999914i	$0.504179\pi$
$32$	−4.32334	−	3.64812i	−0.764265	−	0.644902i
$33$	0.0446999	+	0.0774226i	0.00778126	+	0.0134775i
$34$	6.76505	−	2.72891i	1.16020	−	0.468004i
$35$	2.72970	+	0.275115i	0.461404	+	0.0465029i
$36$	−2.57810	+	2.48414i	−0.429683	+	0.414024i
$37$	−2.88865			−0.474891			−0.237446	−	0.971401i	$-0.576310\pi$
$37$	−2.88865			−0.474891			−0.237446	+	0.971401i	$0.576310\pi$
$38$	3.98711	−	4.70137i	0.646795	−	0.762664i
$39$			4.38841i			0.702708i
$40$	5.48548	+	3.14794i	0.867330	+	0.497733i
$41$	−10.5269	+	6.07769i	−1.64402	+	0.949175i	−0.664636	+	0.747167i	$0.731413\pi$
$41$	−10.5269	+	6.07769i	−1.64402	+	0.949175i	−0.979384	+	0.202008i	$0.935253\pi$
$42$	1.77003	−	0.714001i	0.273122	−	0.110173i
$43$	3.50785	+	6.07577i	0.534942	+	0.926547i	0.999166	+	0.0408291i	$0.0129999\pi$
$43$	3.50785	+	6.07577i	0.534942	+	0.926547i	−0.464224	+	0.885718i	$0.653667\pi$
$44$	−0.0449777	+	0.156204i	−0.00678065	+	0.0235487i
$45$	2.33889	−	3.24831i	0.348662	−	0.484230i
$46$	−6.87310	+	8.78715i	−1.01338	+	1.29559i
$47$	−2.81704	+	4.87926i	−0.410908	+	0.711713i	−0.994989	−	0.0999819i	$-0.968122\pi$
$47$	−2.81704	+	4.87926i	−0.410908	+	0.711713i	0.584082	+	0.811695i	$0.301455\pi$
$48$	4.39682	+	0.163273i	0.634627	+	0.0235664i
$49$	−5.49461			−0.784944
$50$	−6.66375	−	2.36525i	−0.942397	−	0.334498i
$51$	−2.83688	+	4.91363i	−0.397243	+	0.688045i
$52$	−5.74587	+	5.53647i	−0.796809	+	0.767770i
$53$	3.68541	−	6.38332i	0.506230	−	0.876816i	−0.493744	−	0.869607i	$-0.664372\pi$
$53$	3.68541	−	6.38332i	0.506230	−	0.876816i	0.999974	−	0.00720886i	$-0.00229467\pi$
$54$	1.04111	−	7.37828i	0.141677	−	1.00406i
$55$	0.0182242	−	0.180821i	0.00245735	−	0.0243819i
$56$	3.16795	+	1.41676i	0.423335	+	0.189323i
$57$	−0.189805	+	4.79087i	−0.0251402	+	0.634566i
$58$	1.18452	+	0.926500i	0.155535	+	0.121655i
$59$	−1.76709	−	3.06069i	−0.230055	−	0.398468i	0.727769	−	0.685823i	$-0.240557\pi$
$59$	−1.76709	−	3.06069i	−0.230055	−	0.398468i	−0.957824	+	0.287355i	$0.907224\pi$
$60$	−4.86912	+	0.700047i	−0.628600	+	0.0903756i
$61$	1.88854	−	3.27105i	0.241803	−	0.418815i	−0.719425	−	0.694570i	$-0.755595\pi$
$61$	1.88854	−	3.27105i	0.241803	−	0.418815i	0.961228	+	0.275755i	$0.0889280\pi$
$62$	0.204732	+	0.0288886i	0.0260010	+	0.00366885i
$63$	1.09816	−	1.90208i	0.138356	−	0.239639i
$64$	5.33330	+	5.96288i	0.666663	+	0.745360i
$65$	5.21275	−	7.23959i	0.646562	−	0.897961i
$66$	−0.0472969	−	0.117250i	−0.00582185	−	0.0144325i
$67$	8.93896	+	5.16091i	1.09207	+	0.630506i	0.934126	−	0.356943i	$-0.116181\pi$
$67$	8.93896	+	5.16091i	1.09207	+	0.630506i	0.157942	+	0.987448i	$0.449514\pi$
$68$	−10.0126	+	2.48467i	−1.21421	+	0.301311i
$69$		−	8.67694i		−	1.04458i
$70$	−3.76815	−	0.924628i	−0.450380	−	0.110514i
$71$	0.376619	+	0.652324i	0.0446965	+	0.0774166i	0.887508	−	0.460792i	$-0.152435\pi$
$71$	0.376619	+	0.652324i	0.0446965	+	0.0774166i	−0.842812	+	0.538209i	$0.819101\pi$
$72$	4.10107	−	2.96923i	0.483316	−	0.349927i
$73$	1.44429	−	0.833861i	0.169041	−	0.0975960i	−0.413092	−	0.910689i	$-0.635551\pi$
$73$	1.44429	−	0.833861i	0.169041	−	0.0975960i	0.582134	+	0.813093i	$0.302218\pi$
$74$	4.04510	+	0.570781i	0.470233	+	0.0663520i
$75$	5.21592	−	1.74418i	0.602282	−	0.201400i
$76$	−6.51229	+	5.79570i	−0.747011	+	0.664812i
$77$		−	0.0997203i		−	0.0113642i
$78$	0.867125	−	6.14527i	0.0981826	−	0.695815i
$79$	−7.08430	−	12.2704i	−0.797046	−	1.38052i	−0.921532	−	0.388303i	$-0.873061\pi$
$79$	−7.08430	−	12.2704i	−0.797046	−	1.38052i	0.124486	−	0.992221i	$-0.460272\pi$
$80$	−7.05953	−	5.49209i	−0.789279	−	0.614035i
$81$	0.212682	+	0.368377i	0.0236314	+	0.0409307i
$82$	15.9421	−	6.43079i	1.76051	−	0.710162i
$83$	−2.81532			−0.309021			−0.154511	−	0.987991i	$-0.549380\pi$
$83$	−2.81532			−0.309021			−0.154511	+	0.987991i	$0.549380\pi$
$84$	−2.61973	+	0.650097i	−0.285836	+	0.0709314i
$85$	10.5167	−	4.73627i	1.14069	−	0.513720i
$86$	−3.71165	−	9.20129i	−0.400237	−	0.992201i
$87$	−1.16966			−0.125401
$88$	0.0938492	−	0.209852i	0.0100044	−	0.0223703i
$89$	−0.325562	−	0.187964i	−0.0345095	−	0.0199241i	0.482646	−	0.875816i	$-0.339676\pi$
$89$	−0.325562	−	0.187964i	−0.0345095	−	0.0199241i	−0.517156	+	0.855891i	$0.673009\pi$
$90$	−3.91710	+	4.08659i	−0.412898	+	0.430765i
$91$	2.44751	−	4.23920i	0.256568	−	0.444389i
$92$	11.3610	−	10.9469i	1.18446	−	1.14130i
$93$	−0.139271	+	0.0804080i	−0.0144417	+	0.00833792i
$94$	4.90893	−	6.27600i	0.506318	−	0.647320i
$95$	6.00393	−	7.67807i	0.615990	−	0.787754i
$96$	−6.12479	−	1.09743i	−0.625109	−	0.112005i
$97$	−2.65080	−	4.59131i	−0.269148	−	0.466177i	0.699494	−	0.714638i	$-0.253409\pi$
$97$	−2.65080	−	4.59131i	−0.269148	−	0.466177i	−0.968642	+	0.248461i	$0.920075\pi$
$98$	7.69433	+	1.08570i	0.777245	+	0.109673i
$99$	−0.125998	−	0.0727447i	−0.0126632	−	0.00731112i
$100$	8.86417	+	4.62888i	0.886417	+	0.462888i
$101$	−7.39207	+	12.8034i	−0.735538	+	1.27399i	0.218949	+	0.975736i	$0.429737\pi$
$101$	−7.39207	+	12.8034i	−0.735538	+	1.27399i	−0.954487	+	0.298253i	$0.903596\pi$
$102$	4.94351	−	6.32020i	0.489481	−	0.625793i
$103$		−	13.9312i		−	1.37269i	−0.727278	−	0.686343i	$-0.759215\pi$
$103$		−	13.9312i		−	1.37269i	0.727278	−	0.686343i	$-0.240785\pi$
$104$	9.14016	−	6.61759i	0.896267	−	0.648908i
$105$	2.75161	−	1.23921i	0.268530	−	0.120935i
$106$	−6.42214	+	8.21061i	−0.623774	+	0.797485i
$107$		−	3.15177i		−	0.304693i	−0.988327	−	0.152347i	$-0.951317\pi$
$107$		−	3.15177i		−	0.304693i	0.988327	−	0.152347i	$-0.0486830\pi$
$108$	−2.91581	+	10.1264i	−0.280574	+	0.974412i
$109$	8.43069	−	4.86746i	0.807514	−	0.466218i	−0.0385778	−	0.999256i	$-0.512283\pi$
$109$	8.43069	−	4.86746i	0.807514	−	0.466218i	0.846092	+	0.533037i	$0.178949\pi$
$110$	−0.0612493	+	0.249610i	−0.00583989	+	0.0237994i
$111$	−2.75172	+	1.58870i	−0.261181	+	0.150793i
$112$	−4.15627	−	2.60992i	−0.392731	−	0.246614i
$113$	4.15050			0.390446			0.195223	−	0.980759i	$-0.437457\pi$
$113$	4.15050			0.390446			0.195223	+	0.980759i	$0.437457\pi$
$114$	1.21244	−	6.67135i	0.113555	−	0.624829i
$115$	−10.3069	+	14.3144i	−0.961119	+	1.33483i
$116$	−1.47566	−	1.53147i	−0.137011	−	0.142193i
$117$	−3.57085	−	6.18490i	−0.330125	−	0.571794i
$118$	1.86975	+	4.63517i	0.172125	+	0.426702i
$119$	5.48086	−	3.16438i	0.502430	−	0.290078i
$120$	6.95675	−	0.0181940i	0.635062	−	0.00166088i
$121$	10.9934			0.999399
$122$	−3.29094	+	4.20742i	−0.297948	+	0.380922i
$123$	−6.68523	+	11.5792i	−0.602787	+	1.04406i
$124$	−0.280986	−	0.0809077i	−0.0252333	−	0.00726573i
$125$	−10.6766	−	3.31832i	−0.954940	−	0.296800i
$126$	−1.91365	+	2.44657i	−0.170481	+	0.217957i
$127$	−2.96611	−	1.71249i	−0.263200	−	0.151959i	0.362593	−	0.931947i	$-0.381891\pi$
$127$	−2.96611	−	1.71249i	−0.263200	−	0.151959i	−0.625793	+	0.779989i	$0.715225\pi$
$128$	−6.29021	−	9.40389i	−0.555982	−	0.831195i
$129$	6.68313	+	3.85851i	0.588417	+	0.339722i
$130$	−8.73013	+	9.10789i	−0.765683	+	0.798815i
$131$	15.0829	−	8.70810i	1.31780	−	0.760830i	0.334423	−	0.942423i	$-0.391459\pi$
$131$	15.0829	−	8.70810i	1.31780	−	0.760830i	0.983374	+	0.181593i	$0.0581253\pi$
$132$	0.0430638	+	0.173536i	0.00374822	+	0.0151044i
$133$	2.85532	−	4.52212i	0.247587	−	0.392118i
$134$	−11.4978	−	8.99333i	−0.993261	−	0.776905i
$135$	1.18144	−	11.7223i	0.101682	−	1.00889i
$136$	14.5120	−	1.50095i	1.24440	−	0.128706i
$137$	−4.38598	−	2.53224i	−0.374719	−	0.216344i	0.300799	−	0.953688i	$-0.402747\pi$
$137$	−4.38598	−	2.53224i	−0.374719	−	0.216344i	−0.675518	+	0.737343i	$0.736080\pi$
$138$	−1.71451	+	12.1507i	−0.145949	+	1.03433i
$139$	17.1855	+	9.92203i	1.45765	+	0.841576i	0.998896	−	0.0469863i	$-0.0149617\pi$
$139$	17.1855	+	9.92203i	1.45765	+	0.841576i	0.458756	+	0.888562i	$0.348295\pi$
$140$	5.09400	+	2.03936i	0.430522	+	0.172358i
$141$			6.19728i			0.521905i
$142$	−0.398500	−	0.987894i	−0.0334414	−	0.0829022i
$143$	−0.280814	−	0.162128i	−0.0234828	−	0.0135578i
$144$	−6.32961	+	3.34758i	−0.527467	+	0.278965i
$145$	1.92960	+	1.38937i	0.160244	+	0.115381i
$146$	−2.18726	+	0.882306i	−0.181019	+	0.0730202i
$147$	−5.23414	+	3.02193i	−0.431705	+	0.249245i
$148$	−5.55174	−	1.59858i	−0.456350	−	0.131402i
$149$	9.68521	+	16.7753i	0.793443	+	1.37428i	0.923823	+	0.382820i	$0.125047\pi$
$149$	9.68521	+	16.7753i	0.793443	+	1.37428i	−0.130380	+	0.991464i	$0.541620\pi$
$150$	−7.64871	+	1.41181i	−0.624514	+	0.115274i
$151$	−21.0787			−1.71536			−0.857681	−	0.514182i	$-0.828096\pi$
$151$	−21.0787			−1.71536			−0.857681	+	0.514182i	$0.828096\pi$
$152$	10.2646	−	6.82916i	0.832571	−	0.553918i
$153$		−	9.23350i		−	0.746484i
$154$	−0.0197042	+	0.139642i	−0.00158781	+	0.0112527i
$155$	0.325268	+	0.0327824i	0.0261262	+	0.00263314i
$156$	−2.42854	+	8.43414i	−0.194439	+	0.675272i
$157$	−19.4015	+	11.2015i	−1.54841	+	0.893973i	−0.550143	+	0.835070i	$0.685427\pi$
$157$	−19.4015	+	11.2015i	−1.54841	+	0.893973i	−0.998264	+	0.0589032i	$0.981240\pi$
$158$	7.49588	+	18.5825i	0.596340	+	1.47835i
$159$		−	8.10763i		−	0.642977i
$160$	8.80054	+	9.08573i	0.695744	+	0.718290i
$161$	−4.83931	+	8.38192i	−0.381391	+	0.660588i
$162$	−0.225039	−	0.557878i	−0.0176807	−	0.0438310i
$163$	−16.7661			−1.31322			−0.656610	−	0.754231i	$-0.728010\pi$
$163$	−16.7661			−1.31322			−0.656610	+	0.754231i	$0.728010\pi$
$164$	−23.5951	+	5.85523i	−1.84247	+	0.457216i
$165$	−0.0820880	−	0.182272i	−0.00639054	−	0.0141899i
$166$	3.94241	+	0.556291i	0.305990	+	0.0431766i
$167$	10.2224	+	5.90193i	0.791036	+	0.456705i	0.840327	−	0.542080i	$-0.182363\pi$
$167$	10.2224	+	5.90193i	0.791036	+	0.456705i	−0.0492911	+	0.998784i	$0.515696\pi$
$168$	3.79697	−	0.392714i	0.292943	−	0.0302985i
$169$	−1.45844	−	2.52609i	−0.112188	−	0.194315i
$170$	−15.6628	+	4.55436i	−1.20128	+	0.349303i
$171$	−3.63083	−	6.90656i	−0.277656	−	0.528158i
$172$	3.37945	+	13.6184i	0.257681	+	1.03839i
$173$	6.30969	+	10.9287i	0.479717	+	0.830893i	0.999729	−	0.0232650i	$-0.00740616\pi$
$173$	6.30969	+	10.9287i	0.479717	+	0.830893i	−0.520013	+	0.854158i	$0.674073\pi$
$174$	1.63792	+	0.231118i	0.124171	+	0.0175210i
$175$	−6.01134	−	1.22415i	−0.454415	−	0.0925370i
$176$	−0.172887	+	0.275320i	−0.0130318	+	0.0207530i
$177$	−3.36664	−	1.94373i	−0.253052	−	0.146100i
$178$	0.418758	+	0.327542i	0.0313872	+	0.0245503i
$179$	−10.7351			−0.802380			−0.401190	−	0.915995i	$-0.631403\pi$
$179$	−10.7351			−0.802380			−0.401190	+	0.915995i	$0.631403\pi$
$180$	6.29276	−	4.94863i	0.469035	−	0.368849i
$181$	11.8226	+	6.82580i	0.878769	+	0.507357i	0.870252	−	0.492606i	$-0.163956\pi$
$181$	11.8226	+	6.82580i	0.878769	+	0.507357i	0.00851659	+	0.999964i	$0.497289\pi$
$182$	−4.26499	+	5.45272i	−0.316142	+	0.404183i
$183$		−	4.15465i		−	0.307120i
$184$	−18.0723	+	13.0846i	−1.33231	+	0.964607i
$185$	6.42666	+	0.647716i	0.472498	+	0.0476210i
$186$	0.210915	−	0.0850796i	0.0154650	−	0.00623834i
$187$	−0.209615	−	0.363064i	−0.0153286	−	0.0265498i
$188$	−8.11429	+	7.81856i	−0.591795	+	0.570227i
$189$		−	6.46466i		−	0.470235i
$190$	−9.92470	+	9.56558i	−0.720013	+	0.693960i
$191$			15.3439i			1.11024i	0.831769	+	0.555122i	$0.187328\pi$
$191$			15.3439i			1.11024i	−0.831769	+	0.555122i	$0.812672\pi$
$192$	8.35995	+	2.74699i	0.603328	+	0.198247i
$193$	5.53452	+	9.58606i	0.398383	+	0.690020i	0.993527	−	0.113600i	$-0.0362381\pi$
$193$	5.53452	+	9.58606i	0.398383	+	0.690020i	−0.595143	+	0.803620i	$0.702905\pi$
$194$	2.80480	+	6.95319i	0.201373	+	0.499210i
$195$	0.984003	−	9.76332i	0.0704659	−	0.699166i
$196$	−10.5602	−	3.04071i	−0.754297	−	0.217194i
$197$			0.0913269i			0.00650678i	0.999995	+	0.00325339i	$0.00103559\pi$
$197$			0.0913269i			0.00650678i	−0.999995	+	0.00325339i	$0.998964\pi$
$198$	0.162066	+	0.126764i	0.0115175	+	0.00900872i
$199$	1.09600	+	0.632776i	0.0776934	+	0.0448563i	0.538343	−	0.842726i	$-0.319050\pi$
$199$	1.09600	+	0.632776i	0.0776934	+	0.0448563i	−0.460650	+	0.887582i	$0.652384\pi$
$200$	−11.4982	−	8.23353i	−0.813047	−	0.582198i
$201$	11.3536			0.800823
$202$	12.8813	−	16.4685i	0.906325	−	1.15872i
$203$	1.12989	+	0.652343i	0.0793029	+	0.0457855i
$204$	−8.17144	+	7.87363i	−0.572115	+	0.551265i
$205$	24.7829	−	11.1612i	1.73091	−	0.779532i
$206$	−2.75273	+	19.5085i	−0.191792	+	1.35922i
$207$	7.06043	+	12.2290i	0.490734	+	0.849976i
$208$	−14.1069	+	7.46084i	−0.978141	+	0.517316i
$209$	−0.299555	−	0.189142i	−0.0207206	−	0.0130832i
$210$	−4.09806	+	1.19162i	−0.282793	+	0.0822294i
$211$	−7.81616	−	13.5380i	−0.538087	−	0.931993i	−0.999007	−	0.0445520i	$-0.985814\pi$
$211$	−7.81616	−	13.5380i	−0.538087	−	0.931993i	0.460920	−	0.887441i	$-0.347519\pi$
$212$	10.6156	−	10.2287i	0.729080	−	0.702508i
$213$	0.717532	+	0.414267i	0.0491645	+	0.0283851i
$214$	−0.622773	+	4.41356i	−0.0425719	+	0.301705i
$215$	−6.44190	−	14.3039i	−0.439334	−	0.975519i
$216$	6.08405	−	13.6043i	0.413967	−	0.925652i
$217$	0.179381			0.0121772
$218$	−12.7676	+	5.15025i	−0.864733	+	0.348819i
$219$	0.917216	−	1.58866i	0.0619797	−	0.107352i
$220$	0.135092	−	0.337437i	0.00910787	−	0.0227500i
$221$		−	20.5789i		−	1.38429i
$222$	4.16726	−	1.68101i	0.279688	−	0.112822i
$223$	0.459865	−	0.265503i	0.0307948	−	0.0177794i	−0.484524	−	0.874778i	$-0.661007\pi$
$223$	0.459865	−	0.265503i	0.0307948	−	0.0177794i	0.515318	+	0.856999i	$0.327674\pi$
$224$	5.30449	+	4.47603i	0.354421	+	0.299068i
$225$	−5.93193	+	6.70239i	−0.395462	+	0.446826i
$226$	−5.81212	−	0.820116i	−0.386616	−	0.0545533i
$227$			14.6912i			0.975087i	0.873099	+	0.487544i	$0.162107\pi$
$227$			14.6912i			0.975087i	−0.873099	+	0.487544i	$0.837893\pi$
$228$	−3.01605	+	9.10260i	−0.199743	+	0.602834i
$229$	2.03907			0.134745			0.0673726	−	0.997728i	$-0.478538\pi$
$229$	2.03907			0.134745			0.0673726	+	0.997728i	$0.478538\pi$
$230$	17.2616	−	18.0085i	1.13819	−	1.18744i
$231$	−0.0548443	−	0.0949931i	−0.00360849	−	0.00625009i
$232$	1.76381	+	2.43616i	0.115800	+	0.159942i
$233$	−5.93828	+	3.42847i	−0.389030	+	0.224606i	−0.681740	−	0.731595i	$-0.738776\pi$
$233$	−5.93828	+	3.42847i	−0.389030	+	0.224606i	0.292710	+	0.956201i	$0.405443\pi$
$234$	3.77831	+	9.36655i	0.246996	+	0.612310i
$235$	7.36141	−	10.2237i	0.480205	−	0.666921i
$236$	−1.70241	−	6.86028i	−0.110817	−	0.446566i
$237$	−13.4969	−	7.79247i	−0.876721	−	0.506175i
$238$	−8.30034	+	3.34822i	−0.538031	+	0.217033i
$239$			4.35333i			0.281594i	0.990039	+	0.140797i	$0.0449664\pi$
$239$			4.35333i			0.281594i	−0.990039	+	0.140797i	$0.955034\pi$
$240$	−9.74543	−	1.34914i	−0.629065	−	0.0870865i
$241$	−0.453652	−	0.261916i	−0.0292223	−	0.0168715i	0.485318	−	0.874338i	$-0.338704\pi$
$241$	−0.453652	−	0.261916i	−0.0292223	−	0.0168715i	−0.514540	+	0.857466i	$0.672037\pi$
$242$	−15.3945	−	2.17223i	−0.989596	−	0.139636i
$243$	−13.2838	−	7.66943i	−0.852158	−	0.491994i
$244$	5.43981	−	5.24155i	0.348248	−	0.335556i
$245$	12.2244	+	1.23204i	0.780988	+	0.0787124i
$246$	11.6496	−	14.8938i	0.742750	−	0.949595i
$247$	−8.09211	−	15.3928i	−0.514889	−	0.979421i
$248$	0.377490	+	0.168820i	0.0239706	+	0.0107201i
$249$	−2.68186	+	1.54837i	−0.169956	+	0.0981241i
$250$	14.2951	+	6.75641i	0.904104	+	0.427313i
$251$	18.6380	+	10.7606i	1.17642	+	0.679205i	0.955183	−	0.296015i	$-0.0956580\pi$
$251$	18.6380	+	10.7606i	1.17642	+	0.679205i	0.221235	+	0.975221i	$0.428991\pi$
$252$	3.16319	−	3.04790i	0.199262	−	0.192000i
$253$	0.555236	+	0.320566i	0.0349074	+	0.0201538i
$254$	3.81520	+	2.98415i	0.239387	+	0.187242i
$255$	7.41326	−	10.2957i	0.464236	−	0.644743i
$256$	6.95029	+	14.4116i	0.434393	+	0.900723i
$257$	2.40880	−	4.17216i	0.150257	−	0.260252i	−0.781065	−	0.624450i	$-0.785323\pi$
$257$	2.40880	−	4.17216i	0.150257	−	0.260252i	0.931322	+	0.364197i	$0.118657\pi$
$258$	−8.59624	−	6.72377i	−0.535179	−	0.418604i
$259$	3.54421			0.220227
$260$	14.0248	−	11.0291i	0.869783	−	0.683998i
$261$	1.64848	−	0.951753i	0.102039	−	0.0589120i
$262$	−22.8418	+	9.21402i	−1.41117	+	0.569244i
$263$	−2.42351	−	4.19764i	−0.149440	−	0.258838i	0.781581	−	0.623804i	$-0.214414\pi$
$263$	−2.42351	−	4.19764i	−0.149440	−	0.258838i	−0.931021	+	0.364967i	$0.881080\pi$
$264$	−0.0260142	−	0.251519i	−0.00160106	−	0.0154799i
$265$	−9.63061	+	13.3752i	−0.591603	+	0.821633i
$266$	−4.89197	+	5.76832i	−0.299946	+	0.353679i
$267$	−0.413506			−0.0253062
$268$	14.3239	+	14.8656i	0.874969	+	0.908063i
$269$	−12.1862	+	7.03573i	−0.743008	+	0.428976i	−0.823162	−	0.567806i	$-0.807792\pi$
$269$	−12.1862	+	7.03573i	−0.743008	+	0.428976i	0.0801537	+	0.996783i	$0.474459\pi$
$270$	−3.97067	+	16.1817i	−0.241647	+	0.984788i
$271$	24.0459	−	13.8829i	1.46068	−	0.843326i	0.461641	−	0.887067i	$-0.347261\pi$
$271$	24.0459	−	13.8829i	1.46068	−	0.843326i	0.999043	+	0.0437408i	$0.0139276\pi$
$272$	−20.6184	−	0.765648i	−1.25017	−	0.0464242i
$273$		−	5.38433i		−	0.325875i
$274$	5.64151	+	4.41265i	0.340816	+	0.266578i
$275$	−0.0810902	+	0.398204i	−0.00488992	+	0.0240126i
$276$	4.80181	−	16.6763i	0.289035	−	1.00380i
$277$			20.8888i			1.25508i	0.778583	+	0.627542i	$0.215939\pi$
$277$			20.8888i			1.25508i	−0.778583	+	0.627542i	$0.784061\pi$
$278$	−22.1050	−	17.2900i	−1.32577	−	1.03698i
$279$	0.130856	−	0.226649i	0.00783415	−	0.0135691i
$280$	−6.73037	−	3.86235i	−0.402217	−	0.230819i
$281$	−13.2260	−	7.63602i	−0.788995	−	0.455527i	0.0506134	−	0.998718i	$-0.483882\pi$
$281$	−13.2260	−	7.63602i	−0.788995	−	0.455527i	−0.839609	+	0.543192i	$0.817216\pi$
$282$	1.22455	−	8.67831i	0.0729208	−	0.516786i
$283$	13.5783	+	23.5183i	0.807147	+	1.39802i	0.914832	+	0.403835i	$0.132323\pi$
$283$	13.5783	+	23.5183i	0.807147	+	1.39802i	−0.107685	+	0.994185i	$0.534344\pi$
$284$	0.362834	+	1.46213i	0.0215302	+	0.0867614i
$285$	1.49652	−	10.6162i	0.0886463	−	0.628847i
$286$	0.361200	+	0.282522i	0.0213582	+	0.0167059i
$287$	12.9159	−	7.45698i	0.762400	−	0.440172i
$288$	9.52508	−	3.43707i	0.561271	−	0.202531i
$289$	4.80322	−	8.31943i	0.282543	−	0.489378i
$290$	−2.42756	−	2.32688i	−0.142551	−	0.136639i
$291$	−5.05028	−	2.91578i	−0.296052	−	0.170926i
$292$	3.23726	−	0.803339i	0.189446	−	0.0470119i
$293$	12.1703			0.710996			0.355498	−	0.934677i	$-0.384311\pi$
$293$	12.1703			0.710996			0.355498	+	0.934677i	$0.384311\pi$
$294$	7.92670	−	3.19750i	0.462295	−	0.186482i
$295$	3.24512	+	7.20564i	0.188938	+	0.419528i
$296$	7.45846	+	3.33555i	0.433514	+	0.193875i
$297$	−0.428233			−0.0248486
$298$	−10.2479	−	25.4049i	−0.593645	−	1.47166i
$299$	15.7357	+	27.2551i	0.910022	+	1.57620i
$300$	10.9898	−	0.465671i	0.634495	−	0.0268855i
$301$	−4.30393	−	7.45463i	−0.248075	−	0.429678i
$302$	29.5174	+	4.16504i	1.69854	+	0.239671i
$303$			16.2620i			0.934227i
$304$	−15.7234	+	7.53493i	−0.901798	+	0.432158i
$305$	−4.93508	+	6.85395i	−0.282582	+	0.392456i
$306$	−1.82449	+	12.9300i	−0.104299	+	0.739162i
$307$	−21.4920	+	12.4084i	−1.22661	+	0.708186i	−0.966320	−	0.257343i	$-0.917153\pi$
$307$	−21.4920	+	12.4084i	−1.22661	+	0.708186i	−0.260295	+	0.965529i	$0.583820\pi$
$308$	0.0551851	−	0.191654i	0.00314447	−	0.0109205i
$309$	−7.66192	−	13.2708i	−0.435871	−	0.754951i
$310$	−0.449009	−	0.110178i	−0.0255020	−	0.00625767i
$311$			4.53863i			0.257362i	0.991686	+	0.128681i	$0.0410743\pi$
$311$			4.53863i			0.257362i	−0.991686	+	0.128681i	$0.958926\pi$
$312$	5.06733	−	11.3308i	0.286881	−	0.641481i
$313$	7.98450	+	4.60985i	0.451310	+	0.260564i	0.708383	−	0.705828i	$-0.249425\pi$
$313$	7.98450	+	4.60985i	0.451310	+	0.260564i	−0.257073	+	0.966392i	$0.582758\pi$
$314$	29.3821	−	11.8522i	1.65813	−	0.668860i
$315$	−2.86969	+	3.98550i	−0.161689	+	0.224557i
$316$	−6.82499	−	27.5030i	−0.383936	−	1.54717i
$317$	−5.75948	+	9.97572i	−0.323485	+	0.560292i	−0.981205	−	0.192971i	$-0.938188\pi$
$317$	−5.75948	+	9.97572i	−0.323485	+	0.560292i	0.657720	+	0.753263i	$0.271521\pi$
$318$	−1.60202	+	11.3535i	−0.0898370	+	0.636670i
$319$	0.0432126	−	0.0748464i	0.00241944	−	0.00419059i
$320$	−10.5285	−	14.4621i	−0.588559	−	0.808454i
$321$	−1.73342	−	3.00237i	−0.0967499	−	0.167576i
$322$	8.43290	−	10.7813i	0.469947	−	0.600820i
$323$	0.890066	−	22.4662i	0.0495246	−	1.25005i
$324$	0.204898	+	0.825686i	0.0113832	+	0.0458714i
$325$	−13.2206	+	14.9378i	−0.733348	+	0.828599i
$326$	23.4782	+	3.31288i	1.30034	+	0.183483i
$327$	5.35403	−	9.27345i	0.296078	−	0.512823i
$328$	34.1982	−	3.53706i	1.88828	−	0.195301i
$329$	3.45635	−	5.98658i	0.190555	−	0.330051i
$330$	0.0789352	+	0.271464i	0.00434524	+	0.0149436i
$331$	0.491970			0.0270411			0.0135206	−	0.999909i	$-0.495696\pi$
$331$	0.491970			0.0270411			0.0135206	+	0.999909i	$0.495696\pi$
$332$	−5.41080	−	1.55800i	−0.296956	−	0.0855061i
$333$	2.58546	−	4.47815i	0.141682	−	0.245401i
$334$	−13.1487	−	10.2846i	−0.719466	−	0.562749i
$335$	−18.7302	−	13.4863i	−1.02334	−	0.736838i
$336$	−5.39465	−	0.200327i	−0.294302	−	0.0109287i
$337$	−14.2705	−	24.7173i	−0.777366	−	1.34644i	−0.933455	−	0.358694i	$-0.883222\pi$
$337$	−14.2705	−	24.7173i	−0.777366	−	1.34644i	0.156089	−	0.987743i	$-0.450111\pi$
$338$	1.54317	+	3.82558i	0.0839376	+	0.208084i
$339$	3.95375	−	2.28270i	0.214738	−	0.123979i
$340$	22.8331	−	3.28278i	1.23830	−	0.178034i
$341$		−	0.0118826i		−	0.000643477i
$342$	3.71970	+	10.3890i	0.201139	+	0.561771i
$343$	15.3302			0.827752
$344$	−2.04148	−	19.7381i	−0.110069	−	1.06421i
$345$	−1.94561	+	19.3044i	−0.104748	+	1.03932i
$346$	−6.67627	−	16.5507i	−0.358918	−	0.889769i
$347$	12.0204	+	20.8200i	0.645289	+	1.11767i	0.984235	+	0.176868i	$0.0565964\pi$
$347$	12.0204	+	20.8200i	0.645289	+	1.11767i	−0.338946	+	0.940806i	$0.610070\pi$
$348$	−2.24798	−	0.647289i	−0.120505	−	0.0346983i
$349$	−19.2314			−1.02943			−0.514717	−	0.857360i	$-0.672103\pi$
$349$	−19.2314			−1.02943			−0.514717	+	0.857360i	$0.672103\pi$
$350$	8.17605	+	2.90203i	0.437028	+	0.155120i
$351$	−18.2046	−	10.5104i	−0.971688	−	0.561005i
$352$	0.296502	−	0.351381i	0.0158036	−	0.0187287i
$353$		−	7.26969i		−	0.386926i	−0.981108	−	0.193463i	$-0.938028\pi$
$353$		−	7.26969i		−	0.386926i	0.981108	−	0.193463i	$-0.0619720\pi$
$354$	4.33038	+	3.38712i	0.230157	+	0.180023i
$355$	−0.691632	−	1.53574i	−0.0367080	−	0.0815084i
$356$	−0.521684	−	0.541416i	−0.0276492	−	0.0286950i
$357$	3.48070	−	6.02874i	0.184218	−	0.319075i
$358$	15.0328	+	2.12120i	0.794510	+	0.112109i
$359$	−18.2195	+	10.5191i	−0.961591	+	0.555175i	−0.896662	−	0.442715i	$-0.854015\pi$
$359$	−18.2195	+	10.5191i	−0.961591	+	0.555175i	−0.0649284	+	0.997890i	$0.520682\pi$
$360$	−9.78984	+	5.68636i	−0.515970	+	0.299697i
$361$	−8.16848	−	17.1545i	−0.429920	−	0.902867i
$362$	−15.2070	−	11.8945i	−0.799261	−	0.625163i
$363$	10.4723	−	6.04616i	0.549651	−	0.317341i
$364$	7.04987	−	6.79293i	0.369513	−	0.356046i
$365$	−3.40022	+	1.53132i	−0.177976	+	0.0801530i
$366$	−0.820935	+	5.81793i	−0.0429110	+	0.304108i
$367$	−4.70169	+	8.14356i	−0.245426	+	0.425091i	−0.962251	−	0.272162i	$-0.912261\pi$
$367$	−4.70169	+	8.14356i	−0.245426	+	0.425091i	0.716825	+	0.697253i	$0.245595\pi$
$368$	27.8928	−	14.7519i	1.45401	−	0.768995i
$369$		−	21.7591i		−	1.13273i
$370$	−8.87154	−	2.17690i	−0.461209	−	0.113171i
$371$	−4.52179	+	7.83197i	−0.234760	+	0.406616i
$372$	−0.312164	+	0.0774648i	−0.0161850	+	0.00401636i
$373$	−17.3681			−0.899287			−0.449644	−	0.893208i	$-0.648449\pi$
$373$	−17.3681			−0.899287			−0.449644	+	0.893208i	$0.648449\pi$
$374$	0.221793	+	0.549832i	0.0114687	+	0.0284311i
$375$	−11.9955	+	2.71089i	−0.619443	+	0.139990i
$376$	12.9077	−	9.34532i	0.665663	−	0.481948i
$377$	3.67402	−	2.12119i	0.189222	−	0.109247i
$378$	−1.27738	+	9.05273i	−0.0657014	+	0.465622i
$379$	0.237583			0.0122038			0.00610190	−	0.999981i	$-0.498058\pi$
$379$	0.237583			0.0122038			0.00610190	+	0.999981i	$0.498058\pi$
$380$	15.7881	−	11.4340i	0.809911	−	0.586553i
$381$	−3.76734			−0.193007
$382$	3.03186	−	21.4867i	0.155124	−	1.09935i
$383$	−2.81490	+	1.62518i	−0.143835	+	0.0830429i	−0.570190	−	0.821513i	$-0.693131\pi$
$383$	−2.81490	+	1.62518i	−0.143835	+	0.0830429i	0.426356	+	0.904556i	$0.359797\pi$
$384$	−11.1640	−	5.49861i	−0.569710	−	0.280600i
$385$	−0.0223600	+	0.221857i	−0.00113957	+	0.0113069i
$386$	−5.85606	−	14.5174i	−0.298066	−	0.738914i
$387$	−12.5587			−0.638393
$388$	−2.55377	−	10.2911i	−0.129648	−	0.522449i
$389$	−13.0959	+	22.6828i	−0.663990	+	1.15006i	0.315569	+	0.948903i	$0.397805\pi$
$389$	−13.0959	+	22.6828i	−0.663990	+	1.15006i	−0.979558	+	0.201161i	$0.935529\pi$
$390$	−3.30712	+	13.4775i	−0.167462	+	0.682462i
$391$			40.6894i			2.05775i
$392$	14.1870	+	6.34467i	0.716552	+	0.320454i
$393$	9.57859	−	16.5906i	0.483176	−	0.836885i
$394$	0.0180457	−	0.127889i	0.000909129	−	0.00644295i
$395$	13.0098	+	28.8876i	0.654593	+	1.45349i
$396$	−0.201899	−	0.209536i	−0.0101458	−	0.0105296i
$397$	1.30084	−	0.751039i	0.0652871	−	0.0376935i	−0.467001	−	0.884257i	$-0.654666\pi$
$397$	1.30084	−	0.751039i	0.0652871	−	0.0376935i	0.532288	+	0.846563i	$0.321332\pi$
$398$	−1.40974	−	1.10267i	−0.0706639	−	0.0552716i
$399$	0.232880	−	5.87813i	0.0116586	−	0.294274i
$400$	14.4745	+	13.8017i	0.723727	+	0.690087i
$401$	10.3006	−	5.94706i	0.514388	−	0.296982i	−0.220248	−	0.975444i	$-0.570687\pi$
$401$	10.3006	−	5.94706i	0.514388	−	0.296982i	0.734635	+	0.678462i	$0.237353\pi$
$402$	−15.8990	−	2.24341i	−0.792968	−	0.111891i
$403$	0.291642	−	0.505139i	0.0145277	−	0.0251628i
$404$	−21.2923	+	20.5163i	−1.05933	+	1.02073i
$405$	−0.390575	−	0.867252i	−0.0194078	−	0.0430941i
$406$	−1.45334	−	1.13676i	−0.0721278	−	0.0564166i
$407$		−	0.234776i		−	0.0116374i
$408$	12.9986	−	9.41114i	0.643526	−	0.465921i
$409$	25.4178	+	14.6750i	1.25683	+	0.725630i	0.972456	−	0.233085i	$-0.0748820\pi$
$409$	25.4178	+	14.6750i	1.25683	+	0.725630i	0.284371	+	0.958714i	$0.408215\pi$
$410$	−36.9099	+	10.7325i	−1.82285	+	0.530042i
$411$	−5.57075			−0.274785
$412$	7.70953	−	26.7746i	0.379822	−	1.31909i
$413$	2.16812	+	3.75529i	0.106686	+	0.184786i
$414$	−7.47063	−	18.5199i	−0.367161	−	0.910204i
$415$	6.26351	+	0.631272i	0.307464	+	0.0309879i
$416$	21.2288	−	7.66027i	1.04083	−	0.375576i
$417$	21.8277			1.06891
$418$	0.382106	+	0.324054i	0.0186894	+	0.0158500i
$419$			11.8194i			0.577417i	0.957417	+	0.288708i	$0.0932258\pi$
$419$			11.8194i			0.577417i	−0.957417	+	0.288708i	$0.906774\pi$
$420$	5.97413	−	0.858918i	0.291508	−	0.0419109i
$421$	8.95752	−	5.17163i	0.436563	−	0.252050i	−0.265576	−	0.964090i	$-0.585562\pi$
$421$	8.95752	−	5.17163i	0.436563	−	0.252050i	0.702139	+	0.712040i	$0.252229\pi$
$422$	8.27026	+	20.5022i	0.402590	+	0.998033i
$423$	−5.04273	−	8.73427i	−0.245186	−	0.424675i
$424$	−16.8865	+	12.2261i	−0.820083	+	0.593750i
$425$	−24.4594	+	8.17911i	−1.18646	+	0.396745i
$426$	−0.922933	−	0.721896i	−0.0447162	−	0.0349760i
$427$	−2.31713	+	4.01339i	−0.112134	+	0.194222i
$428$	1.74419	−	6.05743i	0.0843086	−	0.292797i
$429$	−0.356669			−0.0172202
$430$	6.19448	+	21.3033i	0.298724	+	1.02733i
$431$	4.04812	−	7.01155i	0.194991	−	0.337735i	−0.751906	−	0.659270i	$-0.770866\pi$
$431$	4.04812	−	7.01155i	0.194991	−	0.337735i	0.946898	+	0.321535i	$0.104199\pi$
$432$	−11.2079	+	17.8484i	−0.539239	+	0.858733i
$433$	−18.2911	+	31.6812i	−0.879015	+	1.52250i	−0.0265926	+	0.999646i	$0.508466\pi$
$433$	−18.2911	+	31.6812i	−0.879015	+	1.52250i	−0.852423	+	0.522853i	$0.824868\pi$
$434$	−0.251194	−	0.0354446i	−0.0120577	−	0.00170140i
$435$	2.60226	+	0.262270i	0.124769	+	0.0125749i
$436$	18.8967	−	4.68930i	0.904988	−	0.224577i
$437$	16.0000	+	30.4353i	0.765386	+	1.45592i
$438$	−1.59833	+	2.04344i	−0.0763710	+	0.0976392i
$439$	−15.6240	−	27.0616i	−0.745695	−	1.29158i	−0.949869	−	0.312647i	$-0.898784\pi$
$439$	−15.6240	−	27.0616i	−0.745695	−	1.29158i	0.204174	−	0.978935i	$-0.434549\pi$
$440$	−0.255850	+	0.445834i	−0.0121972	+	0.0212543i
$441$	4.91790	−	8.51805i	0.234186	−	0.405621i
$442$	−4.06628	+	28.8175i	−0.193413	+	1.37071i
$443$	9.81767	−	17.0047i	0.466452	−	0.807918i	−0.532814	−	0.846232i	$-0.678866\pi$
$443$	9.81767	−	17.0047i	0.466452	−	0.807918i	0.999266	+	0.0383145i	$0.0121989\pi$
$444$	−6.16775	+	1.53055i	−0.292708	+	0.0726369i
$445$	0.682164	+	0.491181i	0.0323377	+	0.0232842i
$446$	−0.696429	+	0.280928i	−0.0329769	+	0.0133023i
$447$	18.4522	+	10.6534i	0.872758	+	0.503887i
$448$	−6.54366	−	7.31611i	−0.309159	−	0.345654i
$449$			19.5787i			0.923978i	0.886886	+	0.461989i	$0.152864\pi$
$449$			19.5787i			0.923978i	−0.886886	+	0.461989i	$0.847136\pi$
$450$	9.63108	−	8.21352i	0.454013	−	0.387189i
$451$	−0.493966	−	0.855574i	−0.0232600	−	0.0402874i
$452$	7.97690	+	2.29688i	0.375202	+	0.108036i
$453$	−20.0795	+	11.5929i	−0.943418	+	0.544683i
$454$	2.90289	−	20.5727i	0.136240	−	0.965523i
$455$	−6.39575	+	8.88257i	−0.299837	+	0.416421i
$456$	6.02212	−	12.1508i	0.282012	−	0.569013i
$457$		−	0.570456i		−	0.0266848i	−0.999911	−	0.0133424i	$-0.995753\pi$
$457$		−	0.570456i		−	0.0266848i	0.999911	−	0.0133424i	$-0.00424714\pi$
$458$	−2.85539	−	0.402908i	−0.133424	−	0.0188267i
$459$	−13.5889	−	23.5367i	−0.634276	−	1.09860i
$460$	−27.7305	+	21.8072i	−1.29294	+	1.01677i
$461$	−18.6604	−	32.3207i	−0.869101	−	1.50533i	−0.862917	−	0.505346i	$-0.831365\pi$
$461$	−18.6604	−	32.3207i	−0.869101	−	1.50533i	−0.00618416	−	0.999981i	$-0.501968\pi$
$462$	0.0580307	+	0.143860i	0.00269983	+	0.00669296i
$463$	−1.82377			−0.0847576			−0.0423788	−	0.999102i	$-0.513494\pi$
$463$	−1.82377			−0.0847576			−0.0423788	+	0.999102i	$0.513494\pi$
$464$	−1.98857	−	3.75998i	−0.0923169	−	0.174553i
$465$	0.327879	−	0.147663i	0.0152050	−	0.00684771i
$466$	8.99307	−	3.62766i	0.416596	−	0.168048i
$467$	0.936777			0.0433489			0.0216744	−	0.999765i	$-0.493100\pi$
$467$	0.936777			0.0433489			0.0216744	+	0.999765i	$0.493100\pi$
$468$	−3.44015	−	13.8629i	−0.159021	−	0.640815i
$469$	−10.9676	−	6.33215i	−0.506437	−	0.292391i
$470$	−12.3286	+	12.8621i	−0.568678	+	0.593285i
$471$	−12.3212	+	21.3409i	−0.567730	+	0.983338i
$472$	1.02840	+	9.94312i	0.0473359	+	0.457669i
$473$	−0.493811	+	0.285102i	−0.0227054	+	0.0131090i
$474$	17.3606	+	13.5790i	0.797398	+	0.623706i
$475$	−15.0792	+	15.7359i	−0.691880	+	0.722013i
$476$	12.2849	−	3.04855i	0.563078	−	0.139730i
$477$	6.59718	+	11.4267i	0.302064	+	0.523191i
$478$	0.860194	−	6.09615i	0.0393444	−	0.278832i
$479$	4.06906	+	2.34927i	0.185920	+	0.107341i	0.590071	−	0.807351i	$-0.299100\pi$
$479$	4.06906	+	2.34927i	0.185920	+	0.107341i	−0.404151	+	0.914692i	$0.632433\pi$
$480$	13.3803	+	3.81490i	0.610726	+	0.174125i
$481$	5.76228	−	9.98056i	0.262737	−	0.455074i
$482$	0.583515	+	0.456412i	0.0265784	+	0.0207890i
$483$			10.6461i			0.484415i
$484$	21.1283	+	6.08374i	0.960379	+	0.276534i
$485$	4.86798	+	10.8091i	0.221044	+	0.490817i
$486$	17.0865	+	13.3646i	0.775058	+	0.606232i
$487$		−	37.3267i		−	1.69143i	−0.533633	−	0.845716i	$-0.679174\pi$
$487$		−	37.3267i		−	1.69143i	0.533633	−	0.845716i	$-0.320826\pi$
$488$	−8.65329	+	6.26509i	−0.391716	+	0.283607i
$489$	−15.9713	+	9.22102i	−0.722246	+	0.416989i
$490$	−16.8749	−	4.14075i	−0.762329	−	0.187060i
$491$	18.6443	−	10.7643i	0.841405	−	0.485786i	−0.0163364	−	0.999867i	$-0.505200\pi$
$491$	18.6443	−	10.7643i	0.841405	−	0.485786i	0.857742	+	0.514081i	$0.171867\pi$
$492$	−19.2563	+	18.5545i	−0.868142	+	0.836503i
$493$	5.48498			0.247031
$494$	8.29019	+	23.1541i	0.372993	+	1.04175i
$495$	0.264008	+	0.190094i	0.0118663	+	0.00854411i
$496$	−0.495257	−	0.310995i	−0.0222377	−	0.0139641i
$497$	−0.462091	−	0.800364i	−0.0207276	−	0.0359013i
$498$	4.06147	−	1.63833i	0.181999	−	0.0734153i
$499$	20.0425	−	11.5716i	0.897227	−	0.518014i	0.0209273	−	0.999781i	$-0.493338\pi$
$499$	20.0425	−	11.5716i	0.897227	−	0.518014i	0.876299	+	0.481767i	$0.160005\pi$
$500$	−18.6830	−	12.2859i	−0.835531	−	0.549443i
$501$	12.9838			0.580074
$502$	−23.9733	−	18.7513i	−1.06998	−	0.836912i
$503$	−3.91303	+	6.77756i	−0.174473	+	0.302196i	−0.939979	−	0.341233i	$-0.889156\pi$
$503$	−3.91303	+	6.77756i	−0.174473	+	0.302196i	0.765506	+	0.643429i	$0.222489\pi$
$504$	−5.03179	+	3.64308i	−0.224134	+	0.162276i
$505$	19.3167	−	26.8275i	0.859583	−	1.19381i
$506$	−0.714178	−	0.558613i	−0.0317491	−	0.0248334i
$507$	−2.77861	−	1.60423i	−0.123402	−	0.0712464i
$508$	−4.75292	−	4.93270i	−0.210877	−	0.218853i
$509$	27.5486	+	15.9052i	1.22107	+	0.704986i	0.965146	−	0.261711i	$-0.0842866\pi$
$509$	27.5486	+	15.9052i	1.22107	+	0.704986i	0.255925	+	0.966697i	$0.417620\pi$
$510$	−12.4155	+	12.9527i	−0.549766	+	0.573555i
$511$	−1.77206	+	1.02310i	−0.0783914	+	0.0452593i
$512$	−6.88513	−	21.5545i	−0.304283	−	0.952582i
$513$	−19.4195	−	12.2617i	−0.857393	−	0.541367i
$514$	−4.19754	+	5.36649i	−0.185145	+	0.236706i
$515$	−3.12377	+	30.9942i	−0.137650	+	1.36577i
$516$	10.7091	+	11.1141i	0.471442	+	0.489273i
$517$	−0.396563	−	0.228956i	−0.0174408	−	0.0100695i
$518$	−4.96311	−	0.700317i	−0.218066	−	0.0307702i
$519$	12.0212	+	6.94042i	0.527670	+	0.304651i
$520$	−21.8189	+	12.6733i	−0.956820	+	0.555762i
$521$			8.24631i			0.361277i	0.983550	+	0.180639i	$0.0578164\pi$
$521$			8.24631i			0.361277i	−0.983550	+	0.180639i	$0.942184\pi$
$522$	−2.49650	+	1.00705i	−0.109269	+	0.0440773i
$523$	22.7049	+	13.1087i	0.992816	+	0.573202i	0.906115	−	0.423032i	$-0.139034\pi$
$523$	22.7049	+	13.1087i	0.992816	+	0.573202i	0.0867008	+	0.996234i	$0.472368\pi$
$524$	33.8070	−	8.38936i	1.47687	−	0.366491i
$525$	−6.39964	+	2.14001i	−0.279303	+	0.0933976i
$526$	2.56431	+	6.35700i	0.111809	+	0.277178i
$527$	0.653093	−	0.377064i	0.0284492	−	0.0164252i
$528$	−0.0132700	+	0.357353i	−0.000577505	+	0.0155518i
$529$	−19.6133	−	33.9713i	−0.852754	−	1.47701i
$530$	16.1290	−	16.8269i	0.700599	−	0.730915i
$531$	6.32646			0.274545
$532$	7.99021	−	7.11100i	0.346420	−	0.308301i
$533$		−	48.4950i		−	2.10055i
$534$	0.579050	+	0.0817065i	0.0250579	+	0.00353578i
$535$	−0.706715	+	7.01206i	−0.0305539	+	0.303158i
$536$	−17.1209	−	23.6473i	−0.739511	−	1.02141i
$537$	−10.2262	+	5.90412i	−0.441294	+	0.254781i
$538$	18.4551	−	7.44449i	0.795657	−	0.320955i
$539$		−	0.446576i		−	0.0192354i
$540$	8.75771	−	21.8754i	0.376872	−	0.941366i
$541$	−11.4082	+	19.7596i	−0.490478	+	0.849533i	−0.999940	−	0.0109601i	$-0.996511\pi$
$541$	−11.4082	+	19.7596i	−0.490478	+	0.849533i	0.509462	+	0.860493i	$0.329845\pi$
$542$	−36.4156	+	14.6895i	−1.56419	+	0.630967i
$543$	15.0162			0.644409
$544$	28.7215	+	5.14624i	1.23142	+	0.220643i
$545$	−19.8480	+	8.93872i	−0.850195	+	0.382893i
$546$	−1.06391	+	7.53990i	−0.0455313	+	0.322678i
$547$	1.85110	+	1.06873i	0.0791472	+	0.0456957i	0.539051	−	0.842273i	$-0.318783\pi$
$547$	1.85110	+	1.06873i	0.0791472	+	0.0456957i	−0.459904	+	0.887969i	$0.652116\pi$
$548$	−7.02812	−	7.29395i	−0.300226	−	0.311582i
$549$	3.38064	+	5.85544i	0.144282	+	0.249904i
$550$	0.192237	−	0.541599i	0.00819701	−	0.0230938i
$551$	4.10271	−	2.15682i	0.174781	−	0.0918838i
$552$	−10.0193	+	22.4037i	−0.426451	+	0.953566i
$553$	8.69204	+	15.0551i	0.369623	+	0.640206i
$554$	4.12750	−	29.2514i	0.175361	−	1.24277i
$555$	6.47824	−	2.91753i	0.274986	−	0.123842i
$556$	27.5381	+	28.5797i	1.16788	+	1.21205i
$557$	−23.4056	−	13.5132i	−0.991725	−	0.572573i	−0.0859357	−	0.996301i	$-0.527388\pi$
$557$	−23.4056	−	13.5132i	−0.991725	−	0.572573i	−0.905790	+	0.423728i	$0.860721\pi$
$558$	−0.228028	+	0.291530i	−0.00965319	+	0.0123415i
$559$	−27.9898			−1.18384
$560$	8.66164	+	6.73849i	0.366021	+	0.284753i
$561$	−0.399357	−	0.230569i	−0.0168609	−	0.00973462i
$562$	17.0120	+	13.3064i	0.717610	+	0.561297i
$563$		−	24.2620i		−	1.02252i	−0.859426	−	0.511261i	$-0.829179\pi$
$563$		−	24.2620i		−	1.02252i	0.859426	−	0.511261i	$-0.170821\pi$
$564$	−3.42957	+	11.9106i	−0.144411	+	0.501528i
$565$	−9.23402	−	0.930657i	−0.388478	−	0.0391530i
$566$	−14.3672	−	35.6167i	−0.603898	−	1.49708i
$567$	−0.260949	−	0.451977i	−0.0109588	−	0.0189813i
$568$	−0.219183	−	2.11918i	−0.00919670	−	0.0889186i
$569$			21.3403i			0.894633i	0.894376	+	0.447316i	$0.147620\pi$
$569$			21.3403i			0.894633i	−0.894376	+	0.447316i	$0.852380\pi$
$570$	−4.19333	+	14.5705i	−0.175639	+	0.610293i
$571$		−	7.88759i		−	0.330086i	−0.986286	−	0.165043i	$-0.947224\pi$
$571$		−	7.88759i		−	0.330086i	0.986286	−	0.165043i	$-0.0527762\pi$
$572$	−0.449978	−	0.466998i	−0.0188145	−	0.0195262i
$573$	8.43885	+	14.6165i	0.352538	+	0.610614i
$574$	−19.5601	+	7.89022i	−0.816422	+	0.329331i
$575$	26.1403	−	29.5356i	1.09013	−	1.23172i
$576$	−14.0175	+	2.93097i	−0.584063	+	0.122124i
$577$			2.83456i			0.118004i	0.998258	+	0.0590022i	$0.0187919\pi$
$577$			2.83456i			0.118004i	−0.998258	+	0.0590022i	$0.981208\pi$
$578$	−8.37002	+	10.7009i	−0.348147	+	0.445101i
$579$	10.5443	+	6.08776i	0.438207	+	0.252999i
$580$	2.93964	+	3.73809i	0.122062	+	0.155216i
$581$	3.45424			0.143306
$582$	6.49597	+	5.08099i	0.269267	+	0.210614i
$583$	0.518806	+	0.299533i	0.0214868	+	0.0124054i
$584$	−4.69200	+	0.485285i	−0.194156	+	0.0200812i
$585$	6.55759	+	14.5608i	0.271123	+	0.602016i
$586$	−17.0426	−	2.40478i	−0.704021	−	0.0993406i
$587$	−6.78111	−	11.7452i	−0.279886	−	0.484778i	0.691470	−	0.722405i	$-0.256963\pi$
$587$	−6.78111	−	11.7452i	−0.279886	−	0.484778i	−0.971356	+	0.237628i	$0.923630\pi$
$588$	−11.7319	+	2.91132i	−0.483815	+	0.120061i
$589$	0.340237	−	0.538851i	0.0140192	−	0.0222030i
$590$	−3.12049	−	10.7316i	−0.128468	−	0.441812i
$591$	0.0502281	+	0.0869977i	0.00206611	+	0.00357861i
$592$	−9.78530	−	6.14465i	−0.402173	−	0.252544i
$593$	−4.84058	−	2.79471i	−0.198779	−	0.114765i	0.397307	−	0.917686i	$-0.369945\pi$
$593$	−4.84058	−	2.79471i	−0.198779	−	0.114765i	−0.596086	+	0.802921i	$0.703278\pi$
$594$	0.599672	+	0.0846164i	0.0246048	+	0.00347185i
$595$	−12.9033	+	5.81113i	−0.528986	+	0.238233i
$596$	9.33070	+	37.6004i	0.382200	+	1.54017i
$597$	1.39206			0.0569732
$598$	−16.6500	−	41.2758i	−0.680868	−	1.68789i
$599$	−0.970121	+	1.68030i	−0.0396381	+	0.0686551i	−0.885164	−	0.465279i	$-0.845954\pi$
$599$	−0.970121	+	1.68030i	−0.0396381	+	0.0686551i	0.845526	+	0.533935i	$0.179287\pi$
$600$	−15.4814	−	1.51942i	−0.632027	−	0.0620300i
$601$			7.40590i			0.302093i	0.988527	+	0.151046i	$0.0482643\pi$
$601$			7.40590i			0.302093i	−0.988527	+	0.151046i	$0.951736\pi$
$602$	4.55398	+	11.2895i	0.185607	+	0.460124i
$603$	−16.0015	+	9.23845i	−0.651630	+	0.376219i
$604$	−40.5115	−	11.6650i	−1.64839	−	0.474640i
$605$	−24.4581	−	2.46502i	−0.994362	−	0.100217i
$606$	3.21328	−	22.7724i	0.130531	−	0.925064i
$607$		−	37.4075i		−	1.51832i	−0.650902	−	0.759161i	$-0.725609\pi$
$607$		−	37.4075i		−	1.51832i	0.650902	−	0.759161i	$-0.274391\pi$
$608$	23.5070	−	7.44462i	0.953333	−	0.301919i
$609$	1.43511			0.0581535
$610$	8.26510	−	8.62273i	0.334644	−	0.349124i
$611$	−11.2389	−	19.4663i	−0.454676	−	0.787521i
$612$	5.10981	−	17.7460i	0.206552	−	0.717339i
$613$	20.5641	−	11.8727i	0.830576	−	0.479533i	−0.0234737	−	0.999724i	$-0.507473\pi$
$613$	20.5641	−	11.8727i	0.830576	−	0.479533i	0.854050	+	0.520191i	$0.174139\pi$
$614$	32.5480	−	13.1293i	1.31353	−	0.529857i
$615$	17.4697	−	24.2623i	0.704444	−	0.978349i
$616$	−0.115148	+	0.257476i	−0.00463944	+	0.0103740i
$617$	33.5771	+	19.3857i	1.35176	+	0.780441i	0.988496	−	0.151245i	$-0.0483281\pi$
$617$	33.5771	+	19.3857i	1.35176	+	0.780441i	0.363266	+	0.931685i	$0.381661\pi$
$618$	8.10706	+	20.0977i	0.326114	+	0.808446i
$619$		−	11.9472i		−	0.480197i	−0.970748	−	0.240099i	$-0.922820\pi$
$619$		−	11.9472i		−	0.480197i	0.970748	−	0.240099i	$-0.0771798\pi$
$620$	0.606995	+	0.243008i	0.0243775	+	0.00975944i
$621$	35.9948	+	20.7816i	1.44442	+	0.833938i
$622$	0.896807	−	6.35563i	0.0359587	−	0.254837i
$623$	0.399447	+	0.230621i	0.0160035	+	0.00923962i
$624$	−9.33490	+	14.8657i	−0.373695	+	0.595105i
$625$	23.0091	+	9.77657i	0.920364	+	0.391063i
$626$	−10.2701	−	8.03306i	−0.410477	−	0.321066i
$627$	−0.389380	−	0.0154264i	−0.0155503	−	0.000616072i
$628$	−43.4868	+	10.7914i	−1.73531	+	0.430626i
$629$	12.9038	−	7.45004i	0.514510	−	0.297053i
$630$	4.80606	−	5.01402i	0.191478	−	0.199763i
$631$	27.0293	+	15.6054i	1.07602	+	0.621240i	0.929820	−	0.368015i	$-0.119962\pi$
$631$	27.0293	+	15.6054i	1.07602	+	0.621240i	0.146200	+	0.989255i	$0.453296\pi$
$632$	4.12288	+	39.8622i	0.163999	+	1.58563i
$633$	−14.8913	−	8.59749i	−0.591875	−	0.341719i
$634$	10.0364	−	12.8314i	0.398596	−	0.509599i
$635$	6.21502	+	4.47502i	0.246635	+	0.177586i
$636$	4.48676	−	15.5822i	0.177912	−	0.617873i
$637$	10.9606	−	18.9844i	0.434276	−	0.752189i
$638$	−0.0753016	+	0.0962720i	−0.00298122	+	0.00381144i
$639$	−1.34836			−0.0533402
$640$	11.8858	+	22.3322i	0.469829	+	0.882758i
$641$	19.8637	−	11.4683i	0.784567	−	0.452970i	−0.0534792	−	0.998569i	$-0.517031\pi$
$641$	19.8637	−	11.4683i	0.784567	−	0.452970i	0.838046	+	0.545599i	$0.183698\pi$
$642$	1.83413	+	4.54685i	0.0723871	+	0.179450i
$643$	3.18820	+	5.52212i	0.125730	+	0.217771i	0.922018	−	0.387147i	$-0.126539\pi$
$643$	3.18820	+	5.52212i	0.125730	+	0.217771i	−0.796288	+	0.604918i	$0.793206\pi$
$644$	−13.9393	+	13.4313i	−0.549284	+	0.529266i
$645$	−14.0034	−	10.0829i	−0.551384	−	0.397015i
$646$	−5.68559	+	31.2845i	−0.223697	+	1.23087i
$647$	−16.6045			−0.652792			−0.326396	−	0.945233i	$-0.605834\pi$
$647$	−16.6045			−0.652792			−0.326396	+	0.945233i	$0.605834\pi$
$648$	−0.123776	−	1.19673i	−0.00486236	−	0.0470120i
$649$	0.248758	−	0.143621i	0.00976462	−	0.00563761i
$650$	21.4650	−	18.3057i	0.841927	−	0.718007i
$651$	0.170877	−	0.0986561i	0.00669721	−	0.00386664i
$652$	−32.2229	−	9.27833i	−1.26195	−	0.363367i
$653$			35.6107i			1.39356i	0.717287	+	0.696778i	$0.245384\pi$
$653$			35.6107i			1.39356i	−0.717287	+	0.696778i	$0.754616\pi$
$654$	−9.32985	+	11.9281i	−0.364826	+	0.466425i
$655$	−35.5089	+	15.9918i	−1.38745	+	0.624850i
$656$	−48.5880	−	1.80428i	−1.89704	−	0.0704453i
$657$			2.98536i			0.116470i
$658$	−6.02299	+	7.70030i	−0.234801	+	0.300189i
$659$	−24.1984	+	41.9128i	−0.942634	+	1.63269i	−0.182215	+	0.983259i	$0.558327\pi$
$659$	−24.1984	+	41.9128i	−0.942634	+	1.63269i	−0.760420	+	0.649432i	$0.775007\pi$
$660$	−0.0568965	−	0.395739i	−0.00221469	−	0.0154041i
$661$	−27.5331	−	15.8962i	−1.07091	−	0.618292i	−0.142482	−	0.989797i	$-0.545508\pi$
$661$	−27.5331	−	15.8962i	−1.07091	−	0.618292i	−0.928431	+	0.371505i	$0.878842\pi$
$662$	−0.688926	−	0.0972106i	−0.0267759	−	0.00377820i
$663$	−11.3180	−	19.6034i	−0.439556	−	0.761333i
$664$	7.26911	+	3.25087i	0.282096	+	0.126158i
$665$	−7.36649	+	9.42057i	−0.285660	+	0.365314i
$666$	−4.50539	+	5.76007i	−0.174580	+	0.223198i
$667$	−7.26441	+	4.19411i	−0.281279	+	0.162397i
$668$	16.3805	+	17.0001i	0.633781	+	0.657753i
$669$	0.292043	−	0.505834i	0.0112910	−	0.0195567i
$670$	23.5638	+	22.5865i	0.910349	+	0.872591i
$671$	0.265856	+	0.153492i	0.0102632	+	0.00592548i
$672$	7.51477	+	1.34648i	0.289889	+	0.0519416i
$673$	−39.0748			−1.50622			−0.753111	−	0.657893i	$-0.771448\pi$
$673$	−39.0748			−1.50622			−0.753111	+	0.657893i	$0.771448\pi$
$674$	15.0996	+	37.4324i	0.581616	+	1.44184i
$675$	−5.25691	+	25.8147i	−0.202339	+	0.993610i
$676$	−1.40506	−	5.66203i	−0.0540407	−	0.217771i
$677$	17.5697			0.675258			0.337629	−	0.941279i	$-0.390375\pi$
$677$	17.5697			0.675258			0.337629	+	0.941279i	$0.390375\pi$
$678$	−5.98765	+	2.41532i	−0.229954	+	0.0927597i
$679$	3.25238	+	5.63329i	0.124815	+	0.216186i
$680$	−32.6229	+	0.0853187i	−1.25103	+	0.00327182i
$681$	8.07987	+	13.9947i	0.309621	+	0.536280i
$682$	−0.00234793	+	0.0166396i	−8.99068e−5	+	0.000637165i
$683$			38.3326i			1.46676i	0.679821	+	0.733378i	$0.262057\pi$
$683$			38.3326i			1.46676i	−0.679821	+	0.733378i	$0.737943\pi$
$684$	−3.15605	−	15.2831i	−0.120675	−	0.584364i
$685$	9.19011	+	6.61719i	0.351136	+	0.252830i
$686$	−21.4675	−	3.02916i	−0.819633	−	0.115654i
$687$	1.94241	−	1.12145i	0.0741074	−	0.0427859i
$688$	−1.04137	+	28.0435i	−0.0397020	+	1.06915i
$689$	14.7033	+	25.4669i	0.560151	+	0.970210i
$690$	6.53896	−	26.6483i	0.248934	−	1.01449i
$691$		−	31.8958i		−	1.21337i	−0.794941	−	0.606687i	$-0.792498\pi$
$691$		−	31.8958i		−	1.21337i	0.794941	−	0.606687i	$-0.207502\pi$
$692$	6.07873	+	24.4958i	0.231079	+	0.931190i
$693$	0.154592	+	0.0892537i	0.00587246	+	0.00339047i
$694$	−12.7188	−	31.5302i	−0.482798	−	1.19687i
$695$	−36.0094	−	25.9280i	−1.36591	−	0.983504i
$696$	3.02005	+	1.35062i	0.114475	+	0.0511949i
$697$	31.3496	−	54.2991i	1.18745	−	2.05672i
$698$	26.9306	+	3.80002i	1.01934	+	0.143833i
$699$	−3.77119	+	6.53189i	−0.142639	+	0.247059i
$700$	−10.8758	−	5.67938i	−0.411068	−	0.214660i
$701$	11.2539	+	19.4924i	0.425055	+	0.736218i	0.996426	−	0.0844749i	$-0.0269213\pi$
$701$	11.2539	+	19.4924i	0.425055	+	0.736218i	−0.571370	+	0.820692i	$0.693588\pi$
$702$	23.4158	+	18.3153i	0.883773	+	0.691266i
$703$	6.72241	−	10.6466i	0.253540	−	0.401546i
$704$	−0.484635	+	0.433466i	−0.0182654	+	0.0163369i
$705$	1.38960	−	13.7877i	0.0523355	−	0.519275i
$706$	−1.43645	+	10.1800i	−0.0540615	+	0.383131i
$707$	9.06965	−	15.7091i	0.341099	−	0.590801i
$708$	−5.39473	−	5.59878i	−0.202747	−	0.210415i
$709$	5.40437	−	9.36065i	0.202966	−	0.351547i	−0.746517	−	0.665366i	$-0.768275\pi$
$709$	5.40437	−	9.36065i	0.202966	−	0.351547i	0.949483	+	0.313820i	$0.101609\pi$
$710$	0.665069	+	2.28722i	0.0249596	+	0.0858377i
$711$	25.3629			0.951185
$712$	0.623555	+	0.861249i	0.0233687	+	0.0322767i
$713$	−0.576646	+	0.998781i	−0.0215956	+	0.0374046i
$714$	−6.06541	+	7.75453i	−0.226992	+	0.290206i
$715$	0.588400	+	0.423668i	0.0220049	+	0.0158443i
$716$	−20.6320	−	5.94081i	−0.771052	−	0.222018i
$717$	2.39425	+	4.14697i	0.0894150	+	0.154871i
$718$	27.5921	−	11.1302i	1.02973	−	0.415375i
$719$	27.8786	−	16.0957i	1.03970	−	0.600269i	0.119949	−	0.992780i	$-0.461727\pi$
$719$	27.8786	−	16.0957i	1.03970	−	0.600269i	0.919747	+	0.392511i	$0.128394\pi$
$720$	14.8327	−	6.02842i	0.552783	−	0.224666i
$721$			17.0928i			0.636571i
$722$	8.04903	+	25.6362i	0.299554	+	0.954079i
$723$	−0.576197			−0.0214290
$724$	18.9447	+	19.6612i	0.704073	+	0.730703i
$725$	−3.98142	−	3.52375i	−0.147866	−	0.130869i
$726$	−15.8594	+	6.39743i	−0.588599	+	0.237431i
$727$	−9.95683	−	17.2457i	−0.369278	−	0.639609i	0.620174	−	0.784464i	$-0.287062\pi$
$727$	−9.95683	−	17.2457i	−0.369278	−	0.639609i	−0.989453	+	0.144855i	$0.953728\pi$
$728$	−11.2145	+	8.11941i	−0.415636	+	0.300925i
$729$	−18.1483			−0.672158
$730$	5.06406	−	1.47251i	0.187429	−	0.0544999i
$731$	−31.3397	−	18.0940i	−1.15914	−	0.669231i
$732$	2.29918	−	7.98487i	0.0849801	−	0.295129i
$733$		−	20.9350i		−	0.773252i	−0.922237	−	0.386626i	$-0.873640\pi$
$733$		−	20.9350i		−	0.773252i	0.922237	−	0.386626i	$-0.126360\pi$
$734$	8.19309	−	10.4747i	0.302413	−	0.386630i
$735$	12.3225	−	5.54955i	0.454522	−	0.204698i
$736$	−41.9744	+	15.1462i	−1.54720	+	0.558296i
$737$	−0.419455	+	0.726517i	−0.0154508	+	0.0267616i
$738$	−4.29948	+	30.4702i	−0.158266	+	1.12162i
$739$	−39.4227	+	22.7607i	−1.45019	+	0.837265i	−0.998491	−	0.0549075i	$-0.982514\pi$
$739$	−39.4227	+	22.7607i	−1.45019	+	0.837265i	−0.451694	+	0.892173i	$0.649180\pi$
$740$	11.9930	+	4.80136i	0.440873	+	0.176502i
$741$	−16.1743	−	10.2126i	−0.594177	−	0.375170i
$742$	7.87961	−	10.0740i	0.289269	−	0.369827i
$743$	−45.5803	+	26.3158i	−1.67218	+	0.965432i	−0.705762	+	0.708449i	$0.749395\pi$
$743$	−45.5803	+	26.3158i	−1.67218	+	0.965432i	−0.966416	+	0.256983i	$0.917272\pi$
$744$	0.452443	−	0.0467954i	0.0165874	−	0.00171560i
$745$	−17.7861	−	39.4933i	−0.651634	−	1.44692i
$746$	24.3213	+	3.43184i	0.890466	+	0.125649i
$747$	2.51982	−	4.36446i	0.0921955	−	0.159687i
$748$	−0.201942	−	0.813778i	−0.00738375	−	0.0297547i
$749$			3.86705i			0.141299i
$750$	17.3334	−	1.42593i	0.632926	−	0.0520677i
$751$	−8.84221	+	15.3152i	−0.322657	+	0.558858i	−0.981035	−	0.193829i	$-0.937909\pi$
$751$	−8.84221	+	15.3152i	−0.322657	+	0.558858i	0.658378	+	0.752687i	$0.271243\pi$
$752$	−19.9217	+	10.5362i	−0.726471	+	0.384214i
$753$	23.6726			0.862678
$754$	−5.56402	+	2.24443i	−0.202629	+	0.0817374i
$755$	46.8959	+	4.72643i	1.70672	+	0.172013i
$756$	3.57754	−	12.4245i	0.130114	−	0.451875i
$757$	32.2795	−	18.6366i	1.17322	−	0.677358i	0.218782	−	0.975774i	$-0.429792\pi$
$757$	32.2795	−	18.6366i	1.17322	−	0.677358i	0.954436	+	0.298416i	$0.0964583\pi$
$758$	−0.332697	−	0.0469450i	−0.0120841	−	0.00170512i
$759$	0.705221			0.0255979
$760$	−24.3680	+	12.8919i	−0.883920	+	0.467638i
$761$	27.3424			0.991162			0.495581	−	0.868562i	$-0.334955\pi$
$761$	27.3424			0.991162			0.495581	+	0.868562i	$0.334955\pi$
$762$	5.27557	+	0.744406i	0.191114	+	0.0269670i
$763$	−10.3440	+	5.97210i	−0.374477	+	0.216205i
$764$	−8.49129	+	29.4896i	−0.307204	+	1.06690i
$765$	−2.07041	+	20.5427i	−0.0748557	+	0.742721i
$766$	4.26295	−	1.71960i	0.154027	−	0.0621318i
$767$	14.0999			0.509119
$768$	14.5469	+	9.90588i	0.524917	+	0.357448i
$769$	1.84072	−	3.18822i	0.0663781	−	0.114970i	−0.830926	−	0.556382i	$-0.812189\pi$
$769$	1.84072	−	3.18822i	0.0663781	−	0.114970i	0.897304	+	0.441412i	$0.145522\pi$
$770$	0.0751495	−	0.306258i	0.00270820	−	0.0110368i
$771$		−	5.29918i		−	0.190845i
$772$	5.33194	+	21.4864i	0.191901	+	0.773312i
$773$	−12.1916	+	21.1164i	−0.438500	+	0.759504i	−0.997574	−	0.0696137i	$-0.977823\pi$
$773$	−12.1916	+	21.1164i	−0.438500	+	0.759504i	0.559074	+	0.829118i	$0.311157\pi$
$774$	17.5864	+	2.48152i	0.632131	+	0.0891965i
$775$	−0.716305	−	0.145868i	−0.0257304	−	0.00523974i
$776$	1.54269	+	14.9156i	0.0553795	+	0.535439i
$777$	3.37620	−	1.94925i	0.121121	−	0.0699290i
$778$	22.8208	−	29.1760i	0.818164	−	1.04601i
$779$	2.09748	−	52.9425i	0.0751499	−	1.89686i
$780$	7.29418	−	18.2197i	0.261174	−	0.652370i
$781$	−0.0530178	+	0.0306099i	−0.00189713	+	0.00109531i
$782$	8.04001	−	56.9791i	0.287510	−	2.03757i
$783$	2.80138	−	4.85214i	0.100113	−	0.173401i
$784$	−18.6130	−	11.6880i	−0.664749	−	0.417428i
$785$	45.6760	−	20.5706i	1.63025	−	0.734197i
$786$	−16.6915	+	21.3398i	−0.595366	+	0.761167i
$787$		−	13.9684i		−	0.497919i	−0.968514	−	0.248960i	$-0.919911\pi$
$787$		−	13.9684i		−	0.497919i	0.968514	−	0.248960i	$-0.0800887\pi$
$788$	−0.0505403	+	0.175522i	−0.00180042	+	0.00625273i
$789$	−4.61725	−	2.66577i	−0.164378	−	0.0949039i
$790$	−12.5101	−	43.0231i	−0.445089	−	1.53069i
$791$	−5.09243			−0.181066
$792$	0.241325	+	0.333316i	0.00857511	+	0.0118439i
$793$	7.53451	+	13.0502i	0.267558	+	0.463425i
$794$	−1.97002	+	0.794672i	−0.0699133	+	0.0282019i
$795$	−1.81796	+	18.0378i	−0.0644762	+	0.639736i
$796$	1.75624	+	1.82267i	0.0622482	+	0.0646027i
$797$	52.7603			1.86887			0.934433	−	0.356138i	$-0.115907\pi$
$797$	52.7603			1.86887			0.934433	+	0.356138i	$0.115907\pi$
$798$	−1.48760	+	8.18537i	−0.0526603	+	0.289759i
$799$		−	29.0614i		−	1.02812i
$800$	−17.5421	−	22.1872i	−0.620208	−	0.784437i
$801$	0.582783	−	0.336470i	0.0205916	−	0.0118886i
$802$	−15.5995	+	6.29257i	−0.550837	+	0.222198i
$803$	0.0677723	+	0.117385i	0.00239163	+	0.00414243i
$804$	21.8207	+	6.28309i	0.769556	+	0.221587i
$805$	12.6459	−	17.5630i	0.445711	−	0.619013i
$806$	−0.508211	+	0.649740i	−0.0179010	+	0.0228861i
$807$	−7.73904	+	13.4044i	−0.272427	+	0.471858i
$808$	33.8704	−	24.5226i	1.19156	−	0.862702i
$809$	−1.33264			−0.0468532			−0.0234266	−	0.999726i	$-0.507458\pi$
$809$	−1.33264			−0.0468532			−0.0234266	+	0.999726i	$0.507458\pi$
$810$	0.375574	+	1.29163i	0.0131963	+	0.0453831i
$811$	19.3075	−	33.4416i	0.677979	−	1.17429i	−0.297609	−	0.954688i	$-0.596189\pi$
$811$	19.3075	−	33.4416i	0.677979	−	1.17429i	0.975589	−	0.219607i	$-0.0704774\pi$
$812$	1.81055	+	1.87903i	0.0635378	+	0.0659410i
$813$	15.2707	−	26.4496i	0.535566	−	0.927628i
$814$	−0.0463905	+	0.328767i	−0.00162598	+	0.0115233i
$815$	37.3011	+	3.75941i	1.30660	+	0.131687i
$816$	−20.0621	+	10.6104i	−0.702313	+	0.371437i
$817$	−30.5568	−	1.21060i	−1.06905	−	0.0423534i
$818$	−32.6939	−	25.5724i	−1.14311	−	0.894116i
$819$	4.38123	+	7.58852i	0.153093	+	0.265164i
$820$	53.8072	−	7.73601i	1.87903	−	0.270153i
$821$	−4.32031	+	7.48300i	−0.150780	+	0.261159i	−0.931514	−	0.363704i	$-0.881512\pi$
$821$	−4.32031	+	7.48300i	−0.150780	+	0.261159i	0.780734	+	0.624863i	$0.214845\pi$
$822$	7.80095	+	1.10075i	0.272089	+	0.0383930i
$823$	24.0786	−	41.7054i	0.839328	−	1.45376i	−0.0511298	−	0.998692i	$-0.516282\pi$
$823$	24.0786	−	41.7054i	0.839328	−	1.45376i	0.890458	−	0.455066i	$-0.150384\pi$
$824$	−16.0865	+	35.9702i	−0.560400	+	1.25308i
$825$	0.141759	+	0.423926i	0.00493540	+	0.0147592i
$826$	−2.29408	−	5.68710i	−0.0798213	−	0.197879i
$827$	−0.396424	−	0.228875i	−0.0137850	−	0.00795878i	0.493092	−	0.869977i	$-0.335867\pi$
$827$	−0.396424	−	0.228875i	−0.0137850	−	0.00795878i	−0.506877	+	0.862019i	$0.669200\pi$
$828$	6.80200	+	27.4104i	0.236386	+	0.952576i
$829$			4.70679i			0.163474i	0.996654	+	0.0817368i	$0.0260467\pi$
$829$			4.70679i			0.163474i	−0.996654	+	0.0817368i	$0.973953\pi$
$830$	−8.64632	−	2.12163i	−0.300118	−	0.0736429i
$831$	11.4884	+	19.8985i	0.398529	+	0.690273i
$832$	−31.2411	+	6.53231i	−1.08309	+	0.226467i
$833$	24.5449	−	14.1710i	0.850430	−	0.490996i
$834$	−30.5663	−	4.31304i	−1.05842	−	0.149348i
$835$	−21.4195	−	15.4227i	−0.741252	−	0.533726i
$836$	−0.471047	−	0.529288i	−0.0162915	−	0.0183058i
$837$		−	0.770322i		−	0.0266262i
$838$	2.33545	−	16.5512i	0.0806769	−	0.571753i
$839$	−19.2235	−	33.2961i	−0.663670	−	1.14951i	−0.979644	−	0.200742i	$-0.935665\pi$
$839$	−19.2235	−	33.2961i	−0.663670	−	1.14951i	0.315974	−	0.948768i	$-0.397669\pi$
$840$	−8.53555	+	0.0223230i	−0.294504	+	0.000770218i
$841$	−13.9346	−	24.1355i	−0.480504	−	0.832258i
$842$	−13.5655	+	5.47209i	−0.467497	+	0.188581i
$843$	−16.7987			−0.578577
$844$	−7.53007	−	30.3443i	−0.259196	−	1.04449i
$845$	2.67832	+	5.94707i	0.0921369	+	0.204585i
$846$	5.33571	+	13.2274i	0.183445	+	0.454767i
$847$	−13.4883			−0.463463
$848$	26.0627	−	13.7840i	0.894998	−	0.473344i
$849$	25.8693	+	14.9356i	0.887832	+	0.512590i
$850$	35.8677	−	6.62050i	1.23025	−	0.227081i
$851$	−11.3934	+	19.7340i	−0.390561	+	0.676471i
$852$	1.14978	+	1.19327i	0.0393908	+	0.0408807i
$853$	−20.9705	+	12.1073i	−0.718016	+	0.414547i	−0.814022	−	0.580834i	$-0.802727\pi$
$853$	−20.9705	+	12.1073i	−0.718016	+	0.414547i	0.0960060	+	0.995381i	$0.469393\pi$
$854$	4.03780	−	5.16227i	0.138171	−	0.176649i
$855$	6.52922	+	16.1798i	0.223294	+	0.553338i
$856$	−3.63938	+	8.13783i	−0.124391	+	0.278145i
$857$	−9.17424	−	15.8903i	−0.313386	−	0.542801i	0.665707	−	0.746213i	$-0.268130\pi$
$857$	−9.17424	−	15.8903i	−0.313386	−	0.542801i	−0.979093	+	0.203412i	$0.934797\pi$
$858$	0.499459	+	0.0704759i	0.0170513	+	0.00240601i
$859$	31.1036	+	17.9577i	1.06124	+	0.612707i	0.925775	−	0.378075i	$-0.123414\pi$
$859$	31.1036	+	17.9577i	1.06124	+	0.612707i	0.135465	+	0.990782i	$0.456747\pi$
$860$	−4.46498	−	31.0558i	−0.152255	−	1.05900i
$861$	8.20240	−	14.2070i	0.279537	−	0.484173i
$862$	−7.05420	+	9.01868i	−0.240267	+	0.307177i
$863$			5.05822i			0.172184i	0.996287	+	0.0860918i	$0.0274378\pi$
$863$			5.05822i			0.172184i	−0.996287	+	0.0860918i	$0.972562\pi$
$864$	19.2216	−	22.7793i	0.653932	−	0.774967i
$865$	−11.5873	−	25.7289i	−0.393978	−	0.874810i
$866$	31.8738	−	40.7502i	1.08312	−	1.38475i
$867$		−	10.5667i		−	0.358865i
$868$	0.344754	+	0.0992692i	0.0117017	+	0.00336942i
$869$	0.997278	−	0.575779i	0.0338303	−	0.0195320i
$870$	−3.59222	−	0.881459i	−0.121788	−	0.0298843i
$871$	−35.6629	+	20.5900i	−1.20839	+	0.697664i
$872$	−27.3884	+	2.83274i	−0.927489	+	0.0959286i
$873$	9.49028			0.321197
$874$	−16.3917	−	45.7813i	−0.554457	−	1.54858i
$875$	13.0995	+	4.07139i	0.442845	+	0.137638i
$876$	2.64197	−	2.54569i	0.0892641	−	0.0860108i
$877$	−7.70981	−	13.3538i	−0.260342	−	0.450925i	0.705991	−	0.708221i	$-0.250502\pi$
$877$	−7.70981	−	13.3538i	−0.260342	−	0.450925i	−0.966333	+	0.257296i	$0.917169\pi$
$878$	16.5318	+	40.9828i	0.557920	+	1.38310i
$879$	11.5934	−	6.69343i	0.391034	−	0.225764i
$880$	0.446372	−	0.573765i	0.0150472	−	0.0193416i
$881$	−54.6549			−1.84137			−0.920685	−	0.390306i	$-0.872369\pi$
$881$	−54.6549			−1.84137			−0.920685	+	0.390306i	$0.872369\pi$
$882$	−8.56986	+	10.9564i	−0.288562	+	0.368922i
$883$	−8.87937	+	15.3795i	−0.298814	+	0.517562i	−0.975865	−	0.218375i	$-0.929925\pi$
$883$	−8.87937	+	15.3795i	−0.298814	+	0.517562i	0.677051	+	0.735937i	$0.263258\pi$
$884$	11.3884	−	39.5509i	0.383032	−	1.33024i
$885$	7.05426	+	5.07930i	0.237126	+	0.170739i
$886$	−17.1081	+	21.8725i	−0.574759	+	0.734820i
$887$	−24.0274	−	13.8722i	−0.806762	−	0.465784i	0.0390684	−	0.999237i	$-0.487561\pi$
$887$	−24.0274	−	13.8722i	−0.806762	−	0.465784i	−0.845830	+	0.533452i	$0.820894\pi$
$888$	8.93938	−	0.924585i	0.299986	−	0.0310270i
$889$	3.63926	+	2.10113i	0.122057	+	0.0704695i
$890$	−0.858208	−	0.822613i	−0.0287672	−	0.0275740i
$891$	−0.0299399	+	0.0172858i	−0.00100303	+	0.000579097i
$892$	1.03075	−	0.255785i	0.0345120	−	0.00856431i
$893$	−11.4276	−	21.7376i	−0.382411	−	0.727422i
$894$	−23.7343	−	18.5644i	−0.793794	−	0.620887i
$895$	23.8835	+	2.40711i	0.798336	+	0.0804608i
$896$	7.71774	+	11.5381i	0.257832	+	0.385459i
$897$	29.9796	+	17.3087i	1.00099	+	0.577922i
$898$	3.86865	−	27.4169i	0.129099	−	0.914915i
$899$	0.134637	+	0.0777325i	0.00449039	+	0.00259253i
$900$	−15.1097	+	9.59869i	−0.503658	+	0.319956i
$901$			38.0198i			1.26662i
$902$	0.522665	+	1.29570i	0.0174028	+	0.0431421i
$903$	−8.19982	−	4.73417i	−0.272873	−	0.157543i
$904$	−10.7165	−	4.79261i	−0.356427	−	0.159400i
$905$	−24.7724	−	17.8370i	−0.823463	−	0.592921i
$906$	30.4089	−	12.2664i	1.01027	−	0.407525i
$907$	19.0046	−	10.9723i	0.631038	−	0.364330i	−0.150116	−	0.988668i	$-0.547965\pi$
$907$	19.0046	−	10.9723i	0.631038	−	0.364330i	0.781154	+	0.624338i	$0.214631\pi$
$908$	−8.13008	+	28.2351i	−0.269806	+	0.937016i
$909$	−13.2324	−	22.9192i	−0.438891	−	0.760181i
$910$	10.7114	−	11.1749i	0.355079	−	0.370443i
$911$	42.7461			1.41624			0.708121	−	0.706091i	$-0.249543\pi$
$911$	42.7461			1.41624			0.708121	+	0.706091i	$0.249543\pi$
$912$	−10.8340	+	15.8253i	−0.358748	+	0.524029i
$913$		−	0.228816i		−	0.00757270i
$914$	−0.112719	+	0.798833i	−0.00372841	+	0.0264231i
$915$	−0.931587	+	9.24325i	−0.0307973	+	0.305572i
$916$	3.91891	+	1.12842i	0.129484	+	0.0372840i
$917$	−18.5058	+	10.6844i	−0.611117	+	0.352828i
$918$	14.3784	+	35.6445i	0.474558	+	1.17644i
$919$			43.6552i			1.44005i	0.693946	+	0.720027i	$0.255870\pi$
$919$			43.6552i			1.44005i	−0.693946	+	0.720027i	$0.744130\pi$
$920$	43.1411	−	25.0582i	1.42232	−	0.826144i
$921$	−13.6488	+	23.6404i	−0.449744	+	0.778979i
$922$	19.7445	+	48.9473i	0.650251	+	1.61199i
$923$	−3.00512			−0.0989146
$924$	−0.0528369	−	0.212919i	−0.00173820	−	0.00700453i
$925$	−14.1528	−	2.88207i	−0.465341	−	0.0947619i
$926$	2.55390	+	0.360366i	0.0839262	+	0.0118424i
$927$	21.5970	+	12.4690i	0.709338	+	0.409536i
$928$	2.04172	+	5.65819i	0.0670228	+	0.185739i
$929$	−12.2961	−	21.2974i	−0.403421	−	0.698745i	0.590716	−	0.806880i	$-0.298846\pi$
$929$	−12.2961	−	21.2974i	−0.403421	−	0.698745i	−0.994136	+	0.108135i	$0.965512\pi$
$930$	−0.488320	+	0.141992i	−0.0160126	+	0.00465609i
$931$	12.7869	−	20.2514i	0.419075	−	0.663712i
$932$	−13.3102	+	3.30298i	−0.435989	+	0.108193i
$933$	2.49616	+	4.32348i	0.0817206	+	0.141544i
$934$	−1.31181	−	0.185102i	−0.0429237	−	0.00605672i
$935$	0.384942	+	0.854745i	0.0125889	+	0.0279531i
$936$	2.07814	+	20.0926i	0.0679262	+	0.656747i
$937$	32.6690	+	18.8614i	1.06725	+	0.616176i	0.927429	−	0.374000i	$-0.122014\pi$
$937$	32.6690	+	18.8614i	1.06725	+	0.616176i	0.139820	+	0.990177i	$0.455347\pi$
$938$	14.1072	+	11.0343i	0.460616	+	0.360283i
$939$	10.1413			0.330950
$940$	19.8058	−	15.5753i	0.645993	−	0.508009i
$941$	5.07253	+	2.92862i	0.165360	+	0.0954704i	0.580396	−	0.814334i	$-0.302898\pi$
$941$	5.07253	+	2.92862i	0.165360	+	0.0954704i	−0.415036	+	0.909805i	$0.636231\pi$
$942$	21.4707	−	27.4500i	0.699554	−	0.894369i
$943$			95.8863i			3.12249i
$944$	0.524595	−	14.1270i	0.0170741	−	0.459794i
$945$	−1.44956	+	14.3826i	−0.0471540	+	0.467865i
$946$	0.747838	−	0.301666i	0.0243143	−	0.00980799i
$947$	−26.6270	−	46.1194i	−0.865262	−	1.49868i	−0.866787	−	0.498679i	$-0.833819\pi$
$947$	−26.6270	−	46.1194i	−0.865262	−	1.49868i	0.00152484	−	0.999999i	$-0.499515\pi$
$948$	−21.6276	−	22.4456i	−0.702432	−	0.729001i
$949$			6.65354i			0.215983i
$950$	24.2253	−	19.0561i	0.785973	−	0.618261i
$951$			12.6704i			0.410867i
$952$	−17.8054	+	1.84158i	−0.577077	+	0.0596861i
$953$	6.32715	+	10.9589i	0.204957	+	0.354995i	0.950119	−	0.311888i	$-0.100961\pi$
$953$	6.32715	+	10.9589i	0.204957	+	0.354995i	−0.745162	+	0.666883i	$0.767628\pi$
$954$	−6.98047	−	17.3048i	−0.226001	−	0.560263i
$955$	3.44052	−	34.1370i	0.111333	−	1.10465i
$956$	−2.40913	+	8.36673i	−0.0779169	+	0.270599i
$957$		−	0.0950645i		−	0.00307300i
$958$	−5.23387	−	4.09381i	−0.169099	−	0.132265i
$959$	5.38135	+	3.10692i	0.173773	+	0.100328i
$960$	−17.9832	−	7.98604i	−0.580407	−	0.257748i
$961$	−30.9786			−0.999310
$962$	−10.0413	+	12.8376i	−0.323743	+	0.413901i
$963$	4.88606	+	2.82097i	0.157451	+	0.0909043i
$964$	−0.726936	−	0.754431i	−0.0234130	−	0.0242986i
$965$	−10.1637	−	22.5680i	−0.327182	−	0.726491i
$966$	2.10361	−	14.9082i	0.0676826	−	0.479663i
$967$	1.82093	+	3.15394i	0.0585571	+	0.101424i	0.893818	−	0.448430i	$-0.148017\pi$
$967$	1.82093	+	3.15394i	0.0585571	+	0.101424i	−0.835261	+	0.549854i	$0.814683\pi$
$968$	−28.3848	−	12.6942i	−0.912322	−	0.408006i
$969$	−11.5081	−	21.8907i	−0.369694	−	0.703232i
$970$	−4.68102	−	16.0984i	−0.150298	−	0.516887i
$971$	−14.3443	−	24.8450i	−0.460330	−	0.797315i	0.538647	−	0.842531i	$-0.318936\pi$
$971$	−14.3443	−	24.8450i	−0.460330	−	0.797315i	−0.998977	+	0.0452163i	$0.985602\pi$
$972$	−21.2861	−	22.0912i	−0.682753	−	0.708577i
$973$	−21.0856	−	12.1738i	−0.675973	−	0.390273i
$974$	−7.37554	+	52.2701i	−0.236328	+	1.67484i
$975$	−4.37841	+	21.5008i	−0.140221	+	0.688576i
$976$	13.3555	−	7.06342i	0.427499	−	0.226095i
$977$	−7.87522			−0.251951			−0.125975	−	0.992033i	$-0.540206\pi$
$977$	−7.87522			−0.251951			−0.125975	+	0.992033i	$0.540206\pi$
$978$	24.1873	−	9.75675i	0.773424	−	0.311986i
$979$	0.0152768	−	0.0264602i	0.000488249	−	0.000845672i
$980$	22.8124	+	9.13285i	0.728715	+	0.291738i
$981$			17.4263i			0.556379i
$982$	−28.2353	+	11.3897i	−0.901026	+	0.363459i
$983$	−15.1246	+	8.73222i	−0.482401	+	0.278514i	−0.721417	−	0.692501i	$-0.756509\pi$
$983$	−15.1246	+	8.73222i	−0.482401	+	0.278514i	0.239015	+	0.971016i	$0.423175\pi$
$984$	30.6317	−	22.1777i	0.976503	−	0.707001i
$985$	0.0204780	−	0.203184i	0.000652484	−	0.00647398i
$986$	−7.68084	−	1.08380i	−0.244608	−	0.0345153i
$987$		−	7.60372i		−	0.242029i
$988$	−7.03397	−	34.0618i	−0.223780	−	1.08365i
$989$	55.3426			1.75979
$990$	−0.332139	−	0.318364i	−0.0105561	−	0.0101183i
$991$	14.4642	+	25.0527i	0.459470	+	0.795825i	0.998933	−	0.0461840i	$-0.0147061\pi$
$991$	14.4642	+	25.0527i	0.459470	+	0.795825i	−0.539463	+	0.842009i	$0.681373\pi$
$992$	0.632078	+	0.533359i	0.0200685	+	0.0169342i
$993$	0.468649	−	0.270575i	0.0148721	−	0.00858642i
$994$	0.488937	+	1.21209i	0.0155081	+	0.0384452i
$995$	−2.29649	−	1.65355i	−0.0728037	−	0.0524211i
$996$	−6.01117	+	1.49170i	−0.190471	+	0.0472663i
$997$	5.82024	+	3.36032i	0.184329	+	0.106422i	0.589325	−	0.807896i	$-0.299394\pi$
$997$	5.82024	+	3.36032i	0.184329	+	0.106422i	−0.404996	+	0.914318i	$0.632727\pi$
$998$	−30.3529	+	12.2438i	−0.960803	+	0.387572i
$999$		−	15.2201i		−	0.481541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.s.a.259.2	yes	112
4.3	odd	2	inner	380.2.s.a.259.36	yes	112
5.4	even	2	inner	380.2.s.a.259.55	yes	112
19.8	odd	6	inner	380.2.s.a.179.21	yes	112
20.19	odd	2	inner	380.2.s.a.259.21	yes	112
76.27	even	6	inner	380.2.s.a.179.55	yes	112
95.84	odd	6	inner	380.2.s.a.179.36	yes	112
380.179	even	6	inner	380.2.s.a.179.2	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.s.a.179.2	✓	112	380.179	even	6	inner
380.2.s.a.179.21	yes	112	19.8	odd	6	inner
380.2.s.a.179.36	yes	112	95.84	odd	6	inner
380.2.s.a.179.55	yes	112	76.27	even	6	inner
380.2.s.a.259.2	yes	112	1.1	even	1	trivial
380.2.s.a.259.21	yes	112	20.19	odd	2	inner
380.2.s.a.259.36	yes	112	4.3	odd	2	inner
380.2.s.a.259.55	yes	112	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40034 - 0.197594i) q^{2} +(0.952596 - 0.549982i) q^{3} +(1.92191 + 0.553399i) q^{4} +(-2.22480 - 0.224228i) q^{5} +(-1.44263 + 0.581934i) q^{6} -1.22694 q^{7} +(-2.58199 - 1.15471i) q^{8} +(-0.895041 + 1.55026i) q^{9} +O(q^{10})\)	\(q+(-1.40034 - 0.197594i) q^{2} +(0.952596 - 0.549982i) q^{3} +(1.92191 + 0.553399i) q^{4} +(-2.22480 - 0.224228i) q^{5} +(-1.44263 + 0.581934i) q^{6} -1.22694 q^{7} +(-2.58199 - 1.15471i) q^{8} +(-0.895041 + 1.55026i) q^{9} +(3.07117 + 0.753603i) q^{10} +0.0812753i q^{11} +(2.13517 - 0.529851i) q^{12} +(-1.99480 + 3.45509i) q^{13} +(1.71814 + 0.242437i) q^{14} +(-2.24265 + 1.01000i) q^{15} +(3.38750 + 2.12717i) q^{16} +(-4.46708 + 2.57907i) q^{17} +(1.55968 - 1.99403i) q^{18} +(-2.32718 + 3.68568i) q^{19} +(-4.15178 - 1.66215i) q^{20} +(-1.16878 + 0.674796i) q^{21} +(0.0160596 - 0.113813i) q^{22} +(3.94419 - 6.83155i) q^{23} +(-3.09466 + 0.320075i) q^{24} +(4.89944 + 0.997722i) q^{25} +(3.47611 - 4.44415i) q^{26} +5.26891i q^{27} +(-2.35808 - 0.678990i) q^{28} +(-0.920899 - 0.531682i) q^{29} +(3.34005 - 0.971208i) q^{30} -0.146201 q^{31} +(-4.32334 - 3.64812i) q^{32} +(0.0446999 + 0.0774226i) q^{33} +(6.76505 - 2.72891i) q^{34} +(2.72970 + 0.275115i) q^{35} +(-2.57810 + 2.48414i) q^{36} -2.88865 q^{37} +(3.98711 - 4.70137i) q^{38} +4.38841i q^{39} +(5.48548 + 3.14794i) q^{40} +(-10.5269 + 6.07769i) q^{41} +(1.77003 - 0.714001i) q^{42} +(3.50785 + 6.07577i) q^{43} +(-0.0449777 + 0.156204i) q^{44} +(2.33889 - 3.24831i) q^{45} +(-6.87310 + 8.78715i) q^{46} +(-2.81704 + 4.87926i) q^{47} +(4.39682 + 0.163273i) q^{48} -5.49461 q^{49} +(-6.66375 - 2.36525i) q^{50} +(-2.83688 + 4.91363i) q^{51} +(-5.74587 + 5.53647i) q^{52} +(3.68541 - 6.38332i) q^{53} +(1.04111 - 7.37828i) q^{54} +(0.0182242 - 0.180821i) q^{55} +(3.16795 + 1.41676i) q^{56} +(-0.189805 + 4.79087i) q^{57} +(1.18452 + 0.926500i) q^{58} +(-1.76709 - 3.06069i) q^{59} +(-4.86912 + 0.700047i) q^{60} +(1.88854 - 3.27105i) q^{61} +(0.204732 + 0.0288886i) q^{62} +(1.09816 - 1.90208i) q^{63} +(5.33330 + 5.96288i) q^{64} +(5.21275 - 7.23959i) q^{65} +(-0.0472969 - 0.117250i) q^{66} +(8.93896 + 5.16091i) q^{67} +(-10.0126 + 2.48467i) q^{68} -8.67694i q^{69} +(-3.76815 - 0.924628i) q^{70} +(0.376619 + 0.652324i) q^{71} +(4.10107 - 2.96923i) q^{72} +(1.44429 - 0.833861i) q^{73} +(4.04510 + 0.570781i) q^{74} +(5.21592 - 1.74418i) q^{75} +(-6.51229 + 5.79570i) q^{76} -0.0997203i q^{77} +(0.867125 - 6.14527i) q^{78} +(-7.08430 - 12.2704i) q^{79} +(-7.05953 - 5.49209i) q^{80} +(0.212682 + 0.368377i) q^{81} +(15.9421 - 6.43079i) q^{82} -2.81532 q^{83} +(-2.61973 + 0.650097i) q^{84} +(10.5167 - 4.73627i) q^{85} +(-3.71165 - 9.20129i) q^{86} -1.16966 q^{87} +(0.0938492 - 0.209852i) q^{88} +(-0.325562 - 0.187964i) q^{89} +(-3.91710 + 4.08659i) q^{90} +(2.44751 - 4.23920i) q^{91} +(11.3610 - 10.9469i) q^{92} +(-0.139271 + 0.0804080i) q^{93} +(4.90893 - 6.27600i) q^{94} +(6.00393 - 7.67807i) q^{95} +(-6.12479 - 1.09743i) q^{96} +(-2.65080 - 4.59131i) q^{97} +(7.69433 + 1.08570i) q^{98} +(-0.125998 - 0.0727447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 2 q^{5} - 8 q^{6} + 44 q^{9}+O(q^{10}) \) 112 * q - 2 * q^5 - 8 * q^6 + 44 * q^9	\( 112 q - 2 q^{5} - 8 q^{6} + 44 q^{9} + 6 q^{10} - 36 q^{14} - 4 q^{16} + 44 q^{20} - 48 q^{21} + 2 q^{24} - 2 q^{25} - 36 q^{26} - 12 q^{29} - 32 q^{30} - 30 q^{34} + 20 q^{36} - 24 q^{40} - 24 q^{41} - 14 q^{44} + 56 q^{49} + 32 q^{54} - 6 q^{60} - 36 q^{61} - 36 q^{64} + 22 q^{66} + 12 q^{70} + 16 q^{74} - 26 q^{76} + 12 q^{80} - 48 q^{81} - 26 q^{85} - 120 q^{86} - 24 q^{89} + 24 q^{90} - 84 q^{96}+O(q^{100}) \) 112 * q - 2 * q^5 - 8 * q^6 + 44 * q^9 + 6 * q^10 - 36 * q^14 - 4 * q^16 + 44 * q^20 - 48 * q^21 + 2 * q^24 - 2 * q^25 - 36 * q^26 - 12 * q^29 - 32 * q^30 - 30 * q^34 + 20 * q^36 - 24 * q^40 - 24 * q^41 - 14 * q^44 + 56 * q^49 + 32 * q^54 - 6 * q^60 - 36 * q^61 - 36 * q^64 + 22 * q^66 + 12 * q^70 + 16 * q^74 - 26 * q^76 + 12 * q^80 - 48 * q^81 - 26 * q^85 - 120 * q^86 - 24 * q^89 + 24 * q^90 - 84 * q^96

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