LMFDB - Embedded newform 175.2.x.a.108.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			108.16
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.112907 + 2.15440i) q^{2} +(1.03639 + 0.839249i) q^{3} +(-2.63964 + 0.277438i) q^{4} +(-1.72250 + 1.42583i) q^{5} +(-1.69106 + 2.32755i) q^{6} +(-2.35863 - 1.19869i) q^{7} +(-0.220776 - 1.39393i) q^{8} +(-0.253977 - 1.19487i) q^{9} +(-3.26629 - 3.54997i) q^{10} +(4.15290 + 0.882727i) q^{11} +(-2.96853 - 1.92779i) q^{12} +(2.42110 + 4.75167i) q^{13} +(2.31615 - 5.21677i) q^{14} +(-2.98180 + 0.0321037i) q^{15} +(-2.21422 + 0.470646i) q^{16} +(4.69838 + 1.80354i) q^{17} +(2.54555 - 0.682078i) q^{18} +(0.174994 - 1.66496i) q^{19} +(4.15121 - 4.24157i) q^{20} +(-1.43845 - 3.22179i) q^{21} +(-1.43285 + 9.04668i) q^{22} +(1.59498 - 0.0835893i) q^{23} +(0.941042 - 1.62993i) q^{24} +(0.934017 - 4.91199i) q^{25} +(-9.96363 + 5.75250i) q^{26} +(2.55587 - 5.01618i) q^{27} +(6.55850 + 2.50974i) q^{28} +(-4.43795 - 6.10831i) q^{29} +(-0.405831 - 6.42037i) q^{30} +(0.987291 + 2.21749i) q^{31} +(-1.99450 - 7.44359i) q^{32} +(3.56319 + 4.40017i) q^{33} +(-3.35506 + 10.3258i) q^{34} +(5.77187 - 1.29826i) q^{35} +(1.00191 + 3.08356i) q^{36} +(-1.89683 + 2.92087i) q^{37} +(3.60674 + 0.189021i) q^{38} +(-1.47864 + 6.95647i) q^{39} +(2.36779 + 2.08625i) q^{40} +(3.63618 + 1.18147i) q^{41} +(6.77860 - 3.46276i) q^{42} +(-4.20125 - 4.20125i) q^{43} +(-11.2071 - 1.17791i) q^{44} +(2.14116 + 1.69603i) q^{45} +(0.360169 + 3.42678i) q^{46} +(3.17750 + 8.27767i) q^{47} +(-2.68977 - 1.37051i) q^{48} +(4.12628 + 5.65454i) q^{49} +(10.6878 + 1.45765i) q^{50} +(3.35572 + 5.81227i) q^{51} +(-7.70912 - 11.8710i) q^{52} +(2.88373 - 3.56111i) q^{53} +(11.0954 + 4.94001i) q^{54} +(-8.41200 + 4.40084i) q^{55} +(-1.15016 + 3.55240i) q^{56} +(1.57868 - 1.57868i) q^{57} +(12.6587 - 10.2508i) q^{58} +(-4.69130 - 5.21022i) q^{59} +(7.86199 - 0.912006i) q^{60} +(-8.51131 - 7.66362i) q^{61} +(-4.66589 + 2.37739i) q^{62} +(-0.833240 + 3.12270i) q^{63} +(11.5055 - 3.73836i) q^{64} +(-10.9454 - 4.73268i) q^{65} +(-9.07741 + 8.17334i) q^{66} +(3.28790 - 8.56528i) q^{67} +(-12.9024 - 3.45719i) q^{68} +(1.72317 + 1.25195i) q^{69} +(3.44866 + 12.2883i) q^{70} +(11.8782 - 8.63004i) q^{71} +(-1.60949 + 0.617824i) q^{72} +(-2.58291 + 1.67736i) q^{73} +(-6.50688 - 3.75675i) q^{74} +(5.09038 - 4.30684i) q^{75} +4.44344i q^{76} +(-8.73705 - 7.06008i) q^{77} +(-15.1540 - 2.40015i) q^{78} +(-3.71304 + 8.33963i) q^{79} +(3.14293 - 3.96778i) q^{80} +(3.51084 - 1.56313i) q^{81} +(-2.13480 + 7.96717i) q^{82} +(-0.313217 + 0.0496087i) q^{83} +(4.69084 + 8.10528i) q^{84} +(-10.6645 + 3.59249i) q^{85} +(8.57682 - 9.52553i) q^{86} +(0.526966 - 10.0551i) q^{87} +(0.313594 - 5.98373i) q^{88} +(-3.99368 + 4.43543i) q^{89} +(-3.41218 + 4.80440i) q^{90} +(-0.0146888 - 14.1096i) q^{91} +(-4.18698 + 0.663153i) q^{92} +(-0.837814 + 3.12676i) q^{93} +(-17.4746 + 7.78021i) q^{94} +(2.07252 + 3.11740i) q^{95} +(4.17995 - 9.38833i) q^{96} +(-4.27210 - 0.676635i) q^{97} +(-11.7162 + 9.52809i) q^{98} -5.18637i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

Coefficient data

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

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

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

$2$	0.112907	+	2.15440i	0.0798375	+	1.52339i	0.685737	+	0.727849i	$0.259480\pi$
$2$	0.112907	+	2.15440i	0.0798375	+	1.52339i	−0.605900	+	0.795541i	$0.707187\pi$
$3$	1.03639	+	0.839249i	0.598358	+	0.484541i	0.879997	−	0.474980i	$-0.157545\pi$
$3$	1.03639	+	0.839249i	0.598358	+	0.484541i	−0.281639	+	0.959521i	$0.590878\pi$
$4$	−2.63964	+	0.277438i	−1.31982	+	0.138719i
$5$	−1.72250	+	1.42583i	−0.770326	+	0.637651i
$5$	−1.72250	+	1.42583i	−0.770326	+	0.637651i
$6$	−1.69106	+	2.32755i	−0.690373	+	0.950217i
$7$	−2.35863	−	1.19869i	−0.891479	−	0.453063i
$7$	−2.35863	−	1.19869i	−0.891479	−	0.453063i
$8$	−0.220776	−	1.39393i	−0.0780562	−	0.492827i
$9$	−0.253977	−	1.19487i	−0.0846591	−	0.398290i
$10$	−3.26629	−	3.54997i	−1.03289	−	1.12260i
$11$	4.15290	+	0.882727i	1.25215	+	0.266152i	0.785818	−	0.618458i	$-0.212242\pi$
$11$	4.15290	+	0.882727i	1.25215	+	0.266152i	0.466330	+	0.884611i	$0.345576\pi$
$12$	−2.96853	−	1.92779i	−0.856940	−	0.556504i
$13$	2.42110	+	4.75167i	0.671491	+	1.31788i	0.935490	+	0.353353i	$0.114958\pi$
$13$	2.42110	+	4.75167i	0.671491	+	1.31788i	−0.263999	+	0.964523i	$0.585042\pi$
$14$	2.31615	−	5.21677i	0.619018	−	1.39424i
$15$	−2.98180	+	0.0321037i	−0.769898	+	0.00828914i
$16$	−2.21422	+	0.470646i	−0.553554	+	0.117662i
$17$	4.69838	+	1.80354i	1.13952	+	0.437422i	0.853651	−	0.520845i	$-0.174383\pi$
$17$	4.69838	+	1.80354i	1.13952	+	0.437422i	0.285873	+	0.958268i	$0.407716\pi$
$18$	2.54555	−	0.682078i	0.599992	−	0.160767i
$19$	0.174994	−	1.66496i	0.0401464	−	0.381967i	−0.955939	−	0.293567i	$-0.905158\pi$
$19$	0.174994	−	1.66496i	0.0401464	−	0.381967i	0.996085	−	0.0884007i	$-0.0281756\pi$
$20$	4.15121	−	4.24157i	0.928238	−	0.948443i
$21$	−1.43845	−	3.22179i	−0.313896	−	0.703052i
$22$	−1.43285	+	9.04668i	−0.305485	+	1.92876i
$23$	1.59498	−	0.0835893i	0.332576	−	0.0174296i	0.114683	−	0.993402i	$-0.463415\pi$
$23$	1.59498	−	0.0835893i	0.332576	−	0.0174296i	0.217893	+	0.975973i	$0.430082\pi$
$24$	0.941042	−	1.62993i	0.192089	−	0.332709i
$25$	0.934017	−	4.91199i	0.186803	−	0.982397i
$26$	−9.96363	+	5.75250i	−1.95403	+	1.12816i
$27$	2.55587	−	5.01618i	0.491878	−	0.965365i
$28$	6.55850	+	2.50974i	1.23944	+	0.474297i
$29$	−4.43795	−	6.10831i	−0.824106	−	1.13428i	−0.988992	−	0.147972i	$-0.952725\pi$
$29$	−4.43795	−	6.10831i	−0.824106	−	1.13428i	0.164885	−	0.986313i	$-0.447275\pi$
$30$	−0.405831	−	6.42037i	−0.0740943	−	1.17219i
$31$	0.987291	+	2.21749i	0.177323	+	0.398273i	0.980239	−	0.197819i	$-0.0633858\pi$
$31$	0.987291	+	2.21749i	0.177323	+	0.398273i	−0.802916	+	0.596092i	$0.796719\pi$
$32$	−1.99450	−	7.44359i	−0.352582	−	1.31585i
$33$	3.56319	+	4.40017i	0.620271	+	0.765971i
$34$	−3.35506	+	10.3258i	−0.575388	+	1.77086i
$35$	5.77187	−	1.29826i	0.975625	−	0.219446i
$36$	1.00191	+	3.08356i	0.166985	+	0.513927i
$37$	−1.89683	+	2.92087i	−0.311838	+	0.480188i	−0.959488	−	0.281750i	$-0.909085\pi$
$37$	−1.89683	+	2.92087i	−0.311838	+	0.480188i	0.647650	+	0.761938i	$0.275752\pi$
$38$	3.60674	+	0.189021i	0.585090	+	0.0306633i
$39$	−1.47864	+	6.95647i	−0.236772	+	1.11393i
$40$	2.36779	+	2.08625i	0.374380	+	0.329865i
$41$	3.63618	+	1.18147i	0.567875	+	0.184514i	0.578862	−	0.815426i	$-0.303497\pi$
$41$	3.63618	+	1.18147i	0.567875	+	0.184514i	−0.0109864	+	0.999940i	$0.503497\pi$
$42$	6.77860	−	3.46276i	1.04596	−	0.534316i
$43$	−4.20125	−	4.20125i	−0.640685	−	0.640685i	0.310039	−	0.950724i	$-0.399658\pi$
$43$	−4.20125	−	4.20125i	−0.640685	−	0.640685i	−0.950724	+	0.310039i	$0.899658\pi$
$44$	−11.2071	−	1.17791i	−1.68953	−	0.177577i
$45$	2.14116	+	1.69603i	0.319185	+	0.252830i
$46$	0.360169	+	3.42678i	0.0531041	+	0.505251i
$47$	3.17750	+	8.27767i	0.463486	+	1.20742i	0.943856	+	0.330356i	$0.107169\pi$
$47$	3.17750	+	8.27767i	0.463486	+	1.20742i	−0.480371	+	0.877066i	$0.659498\pi$
$48$	−2.68977	−	1.37051i	−0.388235	−	0.197816i
$49$	4.12628	+	5.65454i	0.589468	+	0.807791i
$50$	10.6878	+	1.45765i	1.51149	+	0.206142i
$51$	3.35572	+	5.81227i	0.469894	+	0.813881i
$52$	−7.70912	−	11.8710i	−1.06906	−	1.64621i
$53$	2.88373	−	3.56111i	0.396110	−	0.489156i	−0.539602	−	0.841920i	$-0.681425\pi$
$53$	2.88373	−	3.56111i	0.396110	−	0.489156i	0.935712	+	0.352765i	$0.114758\pi$
$54$	11.0954	+	4.94001i	1.50990	+	0.672250i
$55$	−8.41200	+	4.40084i	−1.13427	+	0.593409i
$56$	−1.15016	+	3.55240i	−0.153696	+	0.474710i
$57$	1.57868	−	1.57868i	0.209101	−	0.209101i
$58$	12.6587	−	10.2508i	1.66216	−	1.34599i
$59$	−4.69130	−	5.21022i	−0.610755	−	0.678312i	0.355862	−	0.934539i	$-0.384187\pi$
$59$	−4.69130	−	5.21022i	−0.610755	−	0.678312i	−0.966617	+	0.256226i	$0.917521\pi$
$60$	7.86199	−	0.912006i	1.01498	−	0.117740i
$61$	−8.51131	−	7.66362i	−1.08976	−	0.981226i	−0.0898706	−	0.995953i	$-0.528645\pi$
$61$	−8.51131	−	7.66362i	−1.08976	−	0.981226i	−0.999892	+	0.0147272i	$0.995312\pi$
$62$	−4.66589	+	2.37739i	−0.592569	+	0.301929i
$63$	−0.833240	+	3.12270i	−0.104978	+	0.393423i
$64$	11.5055	−	3.73836i	1.43819	−	0.467295i
$65$	−10.9454	−	4.73268i	−1.35761	−	0.587017i
$66$	−9.07741	+	8.17334i	−1.11735	+	1.00607i
$67$	3.28790	−	8.56528i	0.401681	−	1.04642i	−0.572351	−	0.820009i	$-0.693969\pi$
$67$	3.28790	−	8.56528i	0.401681	−	1.04642i	0.974033	−	0.226407i	$-0.0726981\pi$
$68$	−12.9024	−	3.45719i	−1.56465	−	0.419246i
$69$	1.72317	+	1.25195i	0.207445	+	0.150718i
$70$	3.44866	+	12.2883i	0.412193	+	1.46874i
$71$	11.8782	−	8.63004i	1.40969	−	1.02420i	0.416319	−	0.909218i	$-0.363320\pi$
$71$	11.8782	−	8.63004i	1.40969	−	1.02420i	0.993368	−	0.114979i	$-0.0366802\pi$
$72$	−1.60949	+	0.617824i	−0.189680	+	0.0728113i
$73$	−2.58291	+	1.67736i	−0.302307	+	0.196320i	−0.686874	−	0.726777i	$-0.741017\pi$
$73$	−2.58291	+	1.67736i	−0.302307	+	0.196320i	0.384567	+	0.923097i	$0.374351\pi$
$74$	−6.50688	−	3.75675i	−0.756410	−	0.436713i
$75$	5.09038	−	4.30684i	0.587787	−	0.497312i
$76$			4.44344i			0.509698i
$77$	−8.73705	−	7.06008i	−0.995679	−	0.804570i
$78$	−15.1540	−	2.40015i	−1.71585	−	0.271764i
$79$	−3.71304	+	8.33963i	−0.417750	+	0.938281i	0.575008	+	0.818148i	$0.304999\pi$
$79$	−3.71304	+	8.33963i	−0.417750	+	0.938281i	−0.992758	+	0.120133i	$0.961668\pi$
$80$	3.14293	−	3.96778i	0.351390	−	0.443612i
$81$	3.51084	−	1.56313i	0.390093	−	0.173681i
$82$	−2.13480	+	7.96717i	−0.235749	+	0.879826i
$83$	−0.313217	+	0.0496087i	−0.0343800	+	0.00544526i	−0.173601	−	0.984816i	$-0.555540\pi$
$83$	−0.313217	+	0.0496087i	−0.0343800	+	0.00544526i	0.139221	+	0.990261i	$0.455540\pi$
$84$	4.69084	+	8.10528i	0.511813	+	0.884359i
$85$	−10.6645	+	3.59249i	−1.15673	+	0.389661i
$86$	8.57682	−	9.52553i	0.924863	−	1.02716i
$87$	0.526966	−	10.0551i	0.0564967	−	1.07802i
$88$	0.313594	−	5.98373i	0.0334292	−	0.637868i
$89$	−3.99368	+	4.43543i	−0.423329	+	0.470155i	−0.916649	−	0.399693i	$-0.869117\pi$
$89$	−3.99368	+	4.43543i	−0.423329	+	0.470155i	0.493320	+	0.869848i	$0.335783\pi$
$90$	−3.41218	+	4.80440i	−0.359676	+	0.506428i
$91$	−0.0146888	−	14.1096i	−0.00153981	−	1.47909i
$92$	−4.18698	+	0.663153i	−0.436523	+	0.0691384i
$93$	−0.837814	+	3.12676i	−0.0868772	+	0.324230i
$94$	−17.4746	+	7.78021i	−1.80237	+	0.802467i
$95$	2.07252	+	3.11740i	0.212636	+	0.319839i
$96$	4.17995	−	9.38833i	0.426615	−	0.958192i
$97$	−4.27210	−	0.676635i	−0.433767	−	0.0687019i	−0.0642669	−	0.997933i	$-0.520471\pi$
$97$	−4.27210	−	0.676635i	−0.433767	−	0.0687019i	−0.369500	+	0.929231i	$0.620471\pi$
$98$	−11.7162	+	9.52809i	−1.18352	+	0.962482i
$99$		−	5.18637i		−	0.521250i
$100$	−1.10270	+	13.2250i	−0.110270	+	1.32250i
$101$	−6.64971	−	3.83921i	−0.661671	−	0.382016i	0.131243	−	0.991350i	$-0.458103\pi$
$101$	−6.64971	−	3.83921i	−0.661671	−	0.382016i	−0.792913	+	0.609335i	$0.791437\pi$
$102$	−12.1431	+	7.88580i	−1.20234	+	0.780811i
$103$	8.62251	−	3.30987i	0.849601	−	0.326131i	0.105681	−	0.994400i	$-0.466298\pi$
$103$	8.62251	−	3.30987i	0.849601	−	0.326131i	0.743920	+	0.668269i	$0.232964\pi$
$104$	6.08896	−	4.42389i	0.597071	−	0.433798i
$105$	7.07146	+	3.49854i	0.690103	+	0.341423i
$106$	7.99764	+	5.81062i	0.776799	+	0.564378i
$107$	6.30346	+	1.68901i	0.609379	+	0.163282i	0.550295	−	0.834971i	$-0.314515\pi$
$107$	6.30346	+	1.68901i	0.609379	+	0.163282i	0.0590839	+	0.998253i	$0.481182\pi$
$108$	−5.35491	+	13.9500i	−0.515277	+	1.34234i
$109$	−3.56919	+	3.21371i	−0.341866	+	0.307818i	−0.822123	−	0.569310i	$-0.807210\pi$
$109$	−3.56919	+	3.21371i	−0.341866	+	0.307818i	0.480256	+	0.877128i	$0.340544\pi$
$110$	−10.4309	−	17.6259i	−0.994551	−	1.68056i
$111$	−4.41719	+	1.43523i	−0.419261	+	0.136226i
$112$	5.78668	+	1.54408i	0.546790	+	0.145902i
$113$	−7.35684	+	3.74850i	−0.692074	+	0.352629i	−0.764391	−	0.644752i	$-0.776960\pi$
$113$	−7.35684	+	3.74850i	−0.692074	+	0.352629i	0.0723177	+	0.997382i	$0.476960\pi$
$114$	3.57934	+	3.22285i	0.335236	+	0.301848i
$115$	−2.62817	+	2.41815i	−0.245078	+	0.225494i
$116$	13.4093	+	14.8925i	1.24502	+	1.38273i
$117$	5.06272	−	4.09971i	0.468048	−	0.379018i
$118$	10.6952	−	10.6952i	0.984573	−	0.984573i
$119$	−8.91985	−	9.88579i	−0.817682	−	0.906228i
$120$	0.703062	+	4.14933i	0.0641805	+	0.378780i
$121$	6.41841	+	2.85766i	0.583492	+	0.259787i
$122$	15.5495	−	19.2020i	1.40779	−	1.73847i
$123$	2.77694	+	4.27611i	0.250388	+	0.385564i
$124$	−3.22131	−	5.57947i	−0.289282	−	0.501052i
$125$	5.39481	+	9.79265i	0.482527	+	0.875881i
$126$	−6.82161	−	1.44256i	−0.607717	−	0.128513i
$127$	−3.78945	−	1.93082i	−0.336260	−	0.171333i	0.277705	−	0.960666i	$-0.410426\pi$
$127$	−3.78945	−	1.93082i	−0.336260	−	0.171333i	−0.613965	+	0.789334i	$0.710426\pi$
$128$	3.82968	+	9.97666i	0.338499	+	0.881820i
$129$	−0.828224	−	7.88002i	−0.0729210	−	0.693797i
$130$	8.96026	−	24.1151i	0.785867	−	2.11504i
$131$	6.01402	+	0.632099i	0.525447	+	0.0552267i	0.363539	−	0.931579i	$-0.381568\pi$
$131$	6.01402	+	0.632099i	0.525447	+	0.0552267i	0.161908	+	0.986806i	$0.448235\pi$
$132$	−10.6263	−	10.6263i	−0.924901	−	0.924901i
$133$	−2.40852	+	3.71726i	−0.208845	+	0.322327i
$134$	18.8243	+	6.11637i	1.62617	+	0.528374i
$135$	2.74973	+	12.2846i	0.236659	+	1.05729i
$136$	1.47671	−	6.94737i	0.126627	−	0.595732i
$137$	−11.4808	−	0.601681i	−0.980867	−	0.0514051i	−0.444844	−	0.895608i	$-0.646741\pi$
$137$	−11.4808	−	0.601681i	−0.980867	−	0.0514051i	−0.536023	+	0.844203i	$0.680074\pi$
$138$	−2.50265	+	3.85374i	−0.213040	+	0.328052i
$139$	0.823086	+	2.53320i	0.0698133	+	0.214863i	0.979876	−	0.199608i	$-0.0639667\pi$
$139$	0.823086	+	2.53320i	0.0698133	+	0.214863i	−0.910063	+	0.414471i	$0.863967\pi$
$140$	−14.8755	+	5.02828i	−1.25721	+	0.424967i
$141$	−3.65391	+	11.2456i	−0.307715	+	0.947048i
$142$	19.9337	+	24.6161i	1.67280	+	2.06573i
$143$	5.86015	+	21.8704i	0.490051	+	1.82889i
$144$	1.12472	+	2.52617i	0.0937268	+	0.210514i
$145$	16.3538	+	4.19381i	1.35811	+	0.348277i
$146$	−3.90533	−	5.37523i	−0.323208	−	0.444857i
$147$	−0.469148	+	9.32327i	−0.0386947	+	0.768970i
$148$	4.19660	−	8.23630i	0.344959	−	0.677020i
$149$	3.45077	−	1.99230i	0.282698	−	0.163216i	−0.351946	−	0.936020i	$-0.614480\pi$
$149$	3.45077	−	1.99230i	0.282698	−	0.163216i	0.634644	+	0.772804i	$0.281147\pi$
$150$	9.85340	+	10.4804i	0.804527	+	0.855725i
$151$	6.75608	−	11.7019i	0.549802	−	0.952285i	−0.448486	−	0.893790i	$-0.648036\pi$
$151$	6.75608	−	11.7019i	0.549802	−	0.952285i	0.998288	−	0.0584952i	$-0.0186302\pi$
$152$	−2.35946	+	0.123654i	−0.191378	+	0.0100297i
$153$	0.961711	−	6.07200i	0.0777497	−	0.490892i
$154$	14.2237	−	19.6202i	1.14618	−	1.58104i
$155$	−4.86238	−	2.41192i	−0.390556	−	0.193730i
$156$	1.97310	−	18.7728i	0.157975	−	1.50303i
$157$	−16.7460	+	4.48709i	−1.33648	+	0.358108i	−0.855127	−	0.518419i	$-0.826521\pi$
$157$	−16.7460	+	4.48709i	−1.33648	+	0.358108i	−0.481352	+	0.876527i	$0.659854\pi$
$158$	−18.3861	−	7.05777i	−1.46272	−	0.561486i
$159$	5.97731	−	1.27052i	0.474032	−	0.100759i
$160$	14.0488	+	9.97777i	1.11066	+	0.788812i
$161$	−3.86216	−	1.71473i	−0.304381	−	0.135140i
$162$	3.76400	+	7.38726i	0.295728	+	0.580398i
$163$	−7.01130	−	4.55319i	−0.549168	−	0.356634i	0.240037	−	0.970764i	$-0.422840\pi$
$163$	−7.01130	−	4.55319i	−0.549168	−	0.356634i	−0.789205	+	0.614130i	$0.789507\pi$
$164$	−9.92598	−	2.10983i	−0.775089	−	0.164750i
$165$	−12.4115	−	2.49880i	−0.966233	−	0.194531i
$166$	−0.142241	−	0.669193i	−0.0110401	−	0.0519394i
$167$	1.42776	+	9.01453i	0.110484	+	0.697565i	0.979297	+	0.202427i	$0.0648828\pi$
$167$	1.42776	+	9.01453i	0.110484	+	0.697565i	−0.868814	+	0.495139i	$0.835117\pi$
$168$	−4.17336	+	2.71639i	−0.321982	+	0.209574i
$169$	−9.07544	+	12.4913i	−0.698110	+	0.960867i
$170$	−8.94376	−	22.5700i	−0.685955	−	1.73104i
$171$	−2.03385	+	0.213766i	−0.155532	+	0.0163471i
$172$	12.2554	+	9.92422i	0.934465	+	0.756715i
$173$	−0.179729	−	3.42944i	−0.0136646	−	0.260735i	−0.996916	−	0.0784797i	$-0.974993\pi$
$173$	−0.179729	−	3.42944i	−0.0136646	−	0.260735i	0.983251	−	0.182256i	$-0.0583399\pi$
$174$	21.7222			1.64676
$175$	−8.09096	+	10.4660i	−0.611619	+	0.791153i
$176$	−9.61088			−0.724447
$177$	−0.489330	−	9.33697i	−0.0367803	−	0.701810i
$178$	−10.0066	−	8.10318i	−0.750026	−	0.607359i
$179$	7.63431	−	0.802398i	0.570615	−	0.0599741i	0.185173	−	0.982706i	$-0.440716\pi$
$179$	7.63431	−	0.802398i	0.570615	−	0.0599741i	0.385442	+	0.922732i	$0.374049\pi$
$180$	−6.12243	−	3.88289i	−0.456339	−	0.289413i
$181$	−3.50984	+	4.83088i	−0.260884	+	0.359076i	−0.919286	−	0.393591i	$-0.871233\pi$
$181$	−3.50984	+	4.83088i	−0.260884	+	0.359076i	0.658402	+	0.752667i	$0.271233\pi$
$182$	30.3960	−	1.62472i	2.25310	−	0.120432i
$183$	−2.38932	−	15.0856i	−0.176624	−	1.11516i
$184$	−0.468651	−	2.20483i	−0.0345494	−	0.162542i
$185$	−0.897364	−	7.73576i	−0.0659755	−	0.568745i
$186$	−6.83089	−	1.45195i	−0.500865	−	0.106462i
$187$	17.9199	+	11.6373i	1.31043	+	0.851004i
$188$	−10.6840	−	20.9685i	−0.779210	−	1.52929i
$189$	−12.0412	+	8.76762i	−0.875870	+	0.637751i
$190$	−6.48212	+	4.81701i	−0.470263	+	0.349463i
$191$	2.69046	−	0.571876i	0.194675	−	0.0413795i	−0.109542	−	0.993982i	$-0.534938\pi$
$191$	2.69046	−	0.571876i	0.194675	−	0.0413795i	0.304217	+	0.952603i	$0.401605\pi$
$192$	15.0616	+	5.78159i	1.08697	+	0.417250i
$193$	21.7655	−	5.83205i	1.56671	−	0.419800i	0.631933	−	0.775023i	$-0.282262\pi$
$193$	21.7655	−	5.83205i	1.56671	−	0.419800i	0.934782	+	0.355223i	$0.115595\pi$
$194$	0.975390	−	9.28021i	0.0700289	−	0.666281i
$195$	−7.37178	−	14.0908i	−0.527904	−	1.00906i
$196$	−12.4607	−	13.7812i	−0.890049	−	0.984370i
$197$	−3.11365	+	19.6588i	−0.221838	+	1.40063i	0.585563	+	0.810627i	$0.300874\pi$
$197$	−3.11365	+	19.6588i	−0.221838	+	1.40063i	−0.807401	+	0.590003i	$0.799126\pi$
$198$	11.1735	−	0.585579i	0.794067	−	0.0416153i
$199$	9.82305	−	17.0140i	0.696338	−	1.20609i	−0.273390	−	0.961903i	$-0.588145\pi$
$199$	9.82305	−	17.0140i	0.696338	−	1.20609i	0.969728	−	0.244189i	$-0.0785217\pi$
$200$	−7.05316	−	0.217501i	−0.498734	−	0.0153796i
$201$	10.5959	−	6.11757i	0.747381	−	0.431500i
$202$	7.52039	−	14.7596i	0.529133	−	1.03848i
$203$	3.14550	+	19.7270i	0.220771	+	1.38456i
$204$	−10.4704	−	14.4113i	−0.733077	−	1.00899i
$205$	−7.94788	+	3.14949i	−0.555104	+	0.219970i
$206$	8.10433	+	18.2026i	0.564655	+	1.26824i
$207$	−0.504966	−	1.88456i	−0.0350976	−	0.130986i
$208$	−7.59718	−	9.38174i	−0.526770	−	0.650507i
$209$	2.19644	−	6.75994i	0.151931	−	0.467595i
$210$	−6.73883	+	15.6297i	−0.465024	+	1.07856i
$211$	−2.50458	−	7.70829i	−0.172422	−	0.530661i	0.827084	−	0.562078i	$-0.189998\pi$
$211$	−2.50458	−	7.70829i	−0.172422	−	0.530661i	−0.999506	+	0.0314174i	$0.989998\pi$
$212$	−6.62402	+	10.2001i	−0.454940	+	0.700546i
$213$	19.5532	+	1.02474i	1.33976	+	0.0702140i
$214$	−2.92709	+	13.7709i	−0.200092	+	0.941357i
$215$	13.2269	+	1.24639i	0.902070	+	0.0850030i
$216$	−7.55647	−	2.45525i	−0.514152	−	0.167058i
$217$	0.329433	−	6.41370i	0.0223634	−	0.435391i
$218$	−7.32660	−	7.32660i	−0.496220	−	0.496220i
$219$	−4.08462	−	0.429310i	−0.276013	−	0.0290101i
$220$	20.9837	−	13.9504i	1.41472	−	0.940539i
$221$	2.80541	+	26.6917i	0.188712	+	1.79548i
$222$	−3.59080	−	9.35434i	−0.240998	−	0.627822i
$223$	−12.4458	−	6.34144i	−0.833431	−	0.424654i	−0.0154367	−	0.999881i	$-0.504914\pi$
$223$	−12.4458	−	6.34144i	−0.833431	−	0.424654i	−0.817994	+	0.575227i	$0.804914\pi$
$224$	−4.21827	+	19.9475i	−0.281845	+	1.33280i
$225$	−6.10640	+	0.131505i	−0.407093	+	0.00876699i
$226$	−8.90640	−	15.4263i	−0.592445	−	1.02615i
$227$	10.3321	+	15.9100i	0.685764	+	1.05598i	0.994490	+	0.104832i	$0.0334306\pi$
$227$	10.3321	+	15.9100i	0.685764	+	1.05598i	−0.308726	+	0.951151i	$0.599903\pi$
$228$	−3.72915	+	4.60512i	−0.246969	+	0.304982i
$229$	−11.4091	−	5.07966i	−0.753935	−	0.335673i	−0.00647374	−	0.999979i	$-0.502061\pi$
$229$	−11.4091	−	5.07966i	−0.753935	−	0.335673i	−0.747461	+	0.664306i	$0.768727\pi$
$230$	−5.50640	−	5.38909i	−0.363081	−	0.355346i
$231$	−3.12980	−	14.6495i	−0.205926	−	0.963869i
$232$	−7.53474	+	7.53474i	−0.494680	+	0.494680i
$233$	−18.1395	+	14.6891i	−1.18836	+	0.962316i	−0.999805	−	0.0197470i	$-0.993714\pi$
$233$	−18.1395	+	14.6891i	−1.18836	+	0.962316i	−0.188556	+	0.982062i	$0.560381\pi$
$234$	9.40402	+	10.4442i	0.614760	+	0.682760i
$235$	−17.2758	−	9.72771i	−1.12695	−	0.634566i
$236$	13.8289	+	12.4516i	0.900182	+	0.810528i
$237$	−10.8472	+	5.52691i	−0.704599	+	0.359011i
$238$	20.2908	−	20.3331i	1.31526	−	1.31800i
$239$	25.8543	−	8.40057i	1.67238	−	0.543388i	0.688967	−	0.724792i	$-0.258064\pi$
$239$	25.8543	−	8.40057i	1.67238	−	0.543388i	0.983409	+	0.181404i	$0.0580643\pi$
$240$	6.58725	−	1.47446i	0.425205	−	0.0951759i
$241$	−12.5012	+	11.2562i	−0.805275	+	0.725073i	−0.965046	−	0.262081i	$-0.915591\pi$
$241$	−12.5012	+	11.2562i	−0.805275	+	0.725073i	0.159771	+	0.987154i	$0.448925\pi$
$242$	−5.43185	+	14.1505i	−0.349173	+	0.909626i
$243$	−11.3634	−	3.04483i	−0.728966	−	0.195326i
$244$	24.5930	+	17.8679i	1.57441	+	1.14387i
$245$	−15.1699	−	3.85658i	−0.969171	−	0.246388i
$246$	−8.89891	+	6.46544i	−0.567374	+	0.412221i
$247$	8.33500	−	3.19951i	0.530343	−	0.203580i
$248$	2.87305	−	1.86578i	0.182439	−	0.118477i
$249$	−0.366248	−	0.211453i	−0.0232100	−	0.0134003i
$250$	−20.4882	+	12.7282i	−1.29578	+	0.805005i
$251$		−	10.7847i		−	0.680726i	−0.940294	−	0.340363i	$-0.889450\pi$
$251$		−	10.7847i		−	0.680726i	0.940294	−	0.340363i	$-0.110550\pi$
$252$	1.33310	−	8.47397i	0.0839776	−	0.533810i
$253$	6.69758	+	1.06079i	0.421073	+	0.0666914i
$254$	3.73191	−	8.38200i	0.234161	−	0.525933i
$255$	−14.0675	−	5.22696i	−0.880944	−	0.327325i
$256$	1.04210	−	0.463971i	0.0651310	−	0.0289982i
$257$	−2.80502	+	10.4685i	−0.174973	+	0.653006i	0.821584	+	0.570088i	$0.193091\pi$
$257$	−2.80502	+	10.4685i	−0.174973	+	0.653006i	−0.996556	+	0.0829186i	$0.973576\pi$
$258$	16.8832	−	2.67404i	1.05110	−	0.166478i
$259$	7.97515	−	4.61553i	0.495552	−	0.286795i
$260$	30.2050	+	9.45591i	1.87323	+	0.586431i
$261$	−6.17149	+	6.85414i	−0.382006	+	0.424260i
$262$	−0.682767	+	13.0280i	−0.0421815	+	0.804870i
$263$	−1.37973	+	26.3268i	−0.0850777	+	1.62338i	0.539200	+	0.842178i	$0.318727\pi$
$263$	−1.37973	+	26.3268i	−0.0850777	+	1.62338i	−0.624278	+	0.781202i	$0.714607\pi$
$264$	5.34685	−	5.93827i	0.329076	−	0.365475i
$265$	0.110311	+	10.2457i	0.00677634	+	0.629389i
$266$	−8.28039	−	4.76920i	−0.507703	−	0.292418i
$267$	−7.86143	+	1.24513i	−0.481112	+	0.0762006i
$268$	−6.30256	+	23.5215i	−0.384990	+	1.43680i
$269$	17.0342	−	7.58410i	1.03859	−	0.462411i	0.184663	−	0.982802i	$-0.440881\pi$
$269$	17.0342	−	7.58410i	1.03859	−	0.462411i	0.853928	+	0.520391i	$0.174214\pi$
$270$	−26.1555	+	7.31104i	−1.59177	+	0.444936i
$271$	−7.26990	+	16.3285i	−0.441615	+	0.991884i	0.546400	+	0.837525i	$0.315998\pi$
$271$	−7.26990	+	16.3285i	−0.441615	+	0.991884i	−0.988015	+	0.154359i	$0.950669\pi$
$272$	−11.2521	−	1.78215i	−0.682256	−	0.108059i
$273$	11.8262	−	14.6353i	0.715756	−	0.885769i
$274$		−	24.8021i		−	1.49835i
$275$	8.21483	−	19.5745i	0.495373	−	1.18039i
$276$	−4.89588	−	2.82664i	−0.294697	−	0.170144i
$277$	−26.3362	+	17.1029i	−1.58239	+	1.02762i	−0.610548	+	0.791979i	$0.709051\pi$
$277$	−26.3362	+	17.1029i	−1.58239	+	1.02762i	−0.971841	+	0.235637i	$0.924282\pi$
$278$	−5.36459	+	2.05927i	−0.321747	+	0.123507i
$279$	2.39886	−	1.74288i	0.143616	−	0.104343i
$280$	−3.08397	−	7.75894i	−0.184303	−	0.463685i
$281$	−6.68322	−	4.85564i	−0.398687	−	0.289663i	0.370319	−	0.928905i	$-0.379248\pi$
$281$	−6.68322	−	4.85564i	−0.398687	−	0.289663i	−0.769006	+	0.639241i	$0.779248\pi$
$282$	−24.6400	−	6.60227i	−1.46729	−	0.393159i
$283$	−3.22429	+	8.39955i	−0.191664	+	0.499301i	−0.995413	−	0.0956663i	$-0.969502\pi$
$283$	−3.22429	+	8.39955i	−0.191664	+	0.499301i	0.803750	+	0.594968i	$0.202835\pi$
$284$	−28.9600	+	26.0757i	−1.71846	+	1.54731i
$285$	−0.468347	+	4.97019i	−0.0277425	+	0.294409i
$286$	−46.4559	+	15.0944i	−2.74699	+	0.892553i
$287$	−7.16018	−	7.14529i	−0.422652	−	0.421773i
$288$	−8.38756	+	4.27367i	−0.494242	+	0.251829i
$289$	6.18854	+	5.57219i	0.364032	+	0.327776i
$290$	−7.18868	+	35.7061i	−0.422134	+	2.09673i
$291$	−3.85969	−	4.28662i	−0.226259	−	0.251286i
$292$	6.35259	−	5.14423i	0.371757	−	0.301043i
$293$	13.9569	−	13.9569i	0.815373	−	0.815373i	−0.170060	−	0.985434i	$-0.554396\pi$
$293$	13.9569	−	13.9569i	0.815373	−	0.815373i	0.985434	+	0.170060i	$0.0543962\pi$
$294$	−20.1390	+	0.0419316i	−1.17453	+	0.00244550i
$295$	15.5097	+	2.28560i	0.903007	+	0.133073i
$296$	4.49025	+	1.99919i	0.260991	+	0.116201i
$297$	15.0422	−	18.5756i	0.872838	−	1.07787i
$298$	4.68183	+	7.20939i	0.271211	+	0.417629i
$299$	4.25878	+	7.37643i	0.246292	+	0.426590i
$300$	−12.2419	+	12.7808i	−0.706787	+	0.737899i
$301$	4.87320	+	14.9452i	0.280887	+	0.861428i
$302$	25.9733	+	13.2341i	1.49460	+	0.761535i
$303$	−3.66961	−	9.55967i	−0.210814	−	0.549189i
$304$	0.396131	+	3.76894i	0.0227197	+	0.216163i
$305$	25.5878	+	1.06491i	1.46515	+	0.0609763i
$306$	13.1901	+	1.38634i	0.754028	+	0.0792515i
$307$	0.0420455	+	0.0420455i	0.00239966	+	0.00239966i	0.708306	−	0.705906i	$-0.249460\pi$
$307$	0.0420455	+	0.0420455i	0.00239966	+	0.00239966i	−0.705906	+	0.708306i	$0.749460\pi$
$308$	25.0214	+	16.2121i	1.42573	+	0.923769i
$309$	11.7141	+	3.80613i	0.666390	+	0.216523i
$310$	4.64725	−	10.7478i	0.263946	−	0.610435i
$311$	3.48044	−	16.3742i	0.197357	−	0.928494i	−0.762279	−	0.647249i	$-0.775919\pi$
$311$	3.48044	−	16.3742i	0.197357	−	0.928494i	0.959636	−	0.281245i	$-0.0907473\pi$
$312$	10.0233	+	0.525297i	0.567455	+	0.0297391i
$313$	2.11009	−	3.24925i	0.119269	−	0.183658i	−0.773994	−	0.633194i	$-0.781744\pi$
$313$	2.11009	−	3.24925i	0.119269	−	0.183658i	0.893263	+	0.449535i	$0.148410\pi$
$314$	−11.5577	−	35.5710i	−0.652240	−	2.00739i
$315$	−3.01718	−	6.56690i	−0.169999	−	0.370003i
$316$	7.48737	−	23.0438i	0.421198	−	1.29631i
$317$	−6.76570	−	8.35494i	−0.380000	−	0.469260i	0.550881	−	0.834584i	$-0.314292\pi$
$317$	−6.76570	−	8.35494i	−0.380000	−	0.469260i	−0.930881	+	0.365323i	$0.880958\pi$
$318$	3.41208	+	12.7341i	0.191340	+	0.714091i
$319$	−13.0384	−	29.2847i	−0.730010	−	1.63963i
$320$	−14.4879	+	22.8442i	−0.809901	+	1.27703i
$321$	5.11532	+	7.04064i	0.285510	+	0.392970i
$322$	3.25815	−	8.51424i	0.181569	−	0.474480i
$323$	3.82500	−	7.50699i	0.212829	−	0.417700i
$324$	−8.83369	+	5.10013i	−0.490761	+	0.283341i
$325$	25.6015	−	7.45425i	1.42011	−	0.413487i
$326$	9.01777	−	15.6192i	0.499448	−	0.865069i
$327$	−6.39616	+	0.335209i	−0.353709	+	0.0185371i
$328$	0.844094	−	5.32940i	0.0466073	−	0.294267i
$329$	2.42782	−	23.3328i	0.133850	−	1.28638i
$330$	3.98205	−	27.0214i	0.219205	−	1.48748i
$331$	0.986032	−	9.38147i	0.0541972	−	0.515652i	−0.933422	−	0.358781i	$-0.883193\pi$
$331$	0.986032	−	9.38147i	0.0541972	−	0.515652i	0.987619	−	0.156871i	$-0.0501408\pi$
$332$	0.813017	−	0.217847i	0.0446201	−	0.0119559i
$333$	3.97181	+	1.52463i	0.217654	+	0.0835495i
$334$	−19.2597	+	4.09377i	−1.05384	+	0.224001i
$335$	6.54922	+	19.4417i	0.357822	+	1.06221i
$336$	4.70137	+	6.45673i	0.256481	+	0.352244i
$337$	−13.0162	−	25.5457i	−0.709037	−	1.39156i	−0.911097	−	0.412191i	$-0.864764\pi$
$337$	−13.0162	−	25.5457i	−0.709037	−	1.39156i	0.202060	−	0.979373i	$-0.435236\pi$
$338$	−27.9358	−	18.1418i	−1.51951	−	0.986781i
$339$	−10.7705	−	2.28933i	−0.584971	−	0.124339i
$340$	27.1538	−	12.4416i	1.47262	−	0.674742i
$341$	2.14269	+	10.0805i	0.116033	+	0.545892i
$342$	−0.690174	−	4.35759i	−0.0373203	−	0.235631i
$343$	−2.95432	−	18.2831i	−0.159518	−	0.987195i
$344$	−4.92870	+	6.78378i	−0.265738	+	0.365757i
$345$	−4.75323	+	0.300452i	−0.255905	+	0.0161758i
$346$	7.36809	−	0.774417i	0.396111	−	0.0416329i
$347$	8.97370	+	7.26676i	0.481734	+	0.390100i	0.839198	−	0.543827i	$-0.183025\pi$
$347$	8.97370	+	7.26676i	0.481734	+	0.390100i	−0.357464	+	0.933927i	$0.616358\pi$
$348$	1.39866	+	26.6881i	0.0749763	+	1.43063i
$349$	12.4271			0.665206			0.332603	−	0.943067i	$-0.392073\pi$
$349$	12.4271			0.665206			0.332603	+	0.943067i	$0.392073\pi$
$350$	−23.4614	−	16.2495i	−1.25406	−	0.868570i
$351$	30.0233			1.60252
$352$	−1.71233	−	32.6731i	−0.0912673	−	1.74148i
$353$	−4.64507	−	3.76151i	−0.247232	−	0.200205i	0.497692	−	0.867354i	$-0.334181\pi$
$353$	−4.64507	−	3.76151i	−0.247232	−	0.200205i	−0.744924	+	0.667149i	$0.767514\pi$
$354$	20.0603	−	2.10842i	1.06619	−	0.112061i
$355$	−8.15529	+	31.8016i	−0.432838	+	1.68785i
$356$	9.31133	−	12.8159i	0.493499	−	0.679244i
$357$	−0.947778	−	17.7315i	−0.0501618	−	0.938449i
$358$	2.59065	+	16.3567i	0.136920	+	0.864481i
$359$	3.91045	+	18.3972i	0.206385	+	0.970967i	0.952356	+	0.304988i	$0.0986526\pi$
$359$	3.91045	+	18.3972i	0.206385	+	0.970967i	−0.745971	+	0.665979i	$0.768014\pi$
$360$	1.89143	−	3.35906i	0.0996872	−	0.177038i
$361$	15.8433	+	3.36761i	0.833860	+	0.177242i
$362$	−10.8039	−	7.01615i	−0.567841	−	0.368760i
$363$	4.25366	+	8.34829i	0.223259	+	0.438171i
$364$	3.95330	+	37.2402i	0.207209	+	1.95191i
$365$	2.05743	−	6.57204i	0.107691	−	0.343996i
$366$	32.2306	−	6.85083i	1.68472	−	0.358098i
$367$	−16.9549	−	6.50839i	−0.885041	−	0.339735i	−0.126969	−	0.991907i	$-0.540525\pi$
$367$	−16.9549	−	6.50839i	−0.885041	−	0.339735i	−0.758072	+	0.652171i	$0.773858\pi$
$368$	−3.49229	+	0.935755i	−0.182048	+	0.0487796i
$369$	0.488190	−	4.64482i	0.0254142	−	0.241800i
$370$	16.5646	−	2.80670i	0.861152	−	0.145914i
$371$	−11.0703	+	4.94264i	−0.574742	+	0.256609i
$372$	1.34405	−	8.48598i	0.0696856	−	0.439977i
$373$	−12.6202	+	0.661395i	−0.653448	+	0.0342457i	−0.376179	−	0.926547i	$-0.622762\pi$
$373$	−12.6202	+	0.661395i	−0.653448	+	0.0342457i	−0.277268	+	0.960793i	$0.589429\pi$
$374$	−23.0481	+	39.9205i	−1.19179	+	2.06424i
$375$	−2.62736	+	14.6766i	−0.135676	+	0.757895i
$376$	10.8369	−	6.25671i	0.558873	−	0.322665i
$377$	18.2800	−	35.8765i	0.941466	−	1.84773i
$378$	−20.2485	−	24.9517i	−1.04147	−	1.28337i
$379$	−5.60769	−	7.71832i	−0.288047	−	0.396463i	0.640331	−	0.768099i	$-0.278797\pi$
$379$	−5.60769	−	7.71832i	−0.288047	−	0.396463i	−0.928379	+	0.371636i	$0.878797\pi$
$380$	−6.33559	−	7.65383i	−0.325009	−	0.392633i
$381$	−2.30690	−	5.18138i	−0.118186	−	0.265450i
$382$	1.53582	+	5.73176i	0.0785794	+	0.293262i
$383$	−14.8022	−	18.2793i	−0.756360	−	0.934026i	0.242992	−	0.970028i	$-0.421871\pi$
$383$	−14.8022	−	18.2793i	−0.756360	−	0.934026i	−0.999352	+	0.0360020i	$0.988538\pi$
$384$	−4.40387	+	13.5537i	−0.224734	+	0.691661i
$385$	25.1160	−	0.296563i	1.28003	−	0.0151143i
$386$	15.0220	+	46.2331i	0.764601	+	2.35320i
$387$	−3.95293	+	6.08697i	−0.200939	+	0.309418i
$388$	11.4646	+	0.600832i	0.582024	+	0.0305026i
$389$	7.04144	−	33.1274i	0.357015	−	1.67963i	−0.322978	−	0.946407i	$-0.604684\pi$
$389$	7.04144	−	33.1274i	0.357015	−	1.67963i	0.679993	−	0.733219i	$-0.261983\pi$
$390$	29.5249	−	17.4727i	1.49505	−	0.884765i
$391$	7.64457	+	2.48387i	0.386602	+	0.125615i
$392$	6.97103	−	7.00012i	0.352090	−	0.353559i
$393$	5.70236	+	5.70236i	0.287646	+	0.287646i
$394$	−42.7044	−	4.48841i	−2.15142	−	0.226123i
$395$	−5.49517	−	19.6592i	−0.276492	−	0.989160i
$396$	1.43889	+	13.6902i	0.0723071	+	0.687956i
$397$	−12.0321	−	31.3446i	−0.603873	−	1.57314i	−0.804806	−	0.593538i	$-0.797731\pi$
$397$	−12.0321	−	31.3446i	−0.603873	−	1.57314i	0.200933	−	0.979605i	$-0.435603\pi$
$398$	37.7641	+	19.2418i	1.89294	+	0.964502i
$399$	−5.61586	+	1.83117i	−0.281145	+	0.0916731i
$400$	0.243692	+	11.3158i	0.0121846	+	0.565790i
$401$	7.80159	+	13.5127i	0.389593	+	0.674794i	0.992395	−	0.123097i	$-0.0392825\pi$
$401$	7.80159	+	13.5127i	0.389593	+	0.674794i	−0.602802	+	0.797891i	$0.705949\pi$
$402$	14.3761	+	22.1372i	0.717012	+	1.10410i
$403$	−8.14646	+	10.0600i	−0.405804	+	0.501126i
$404$	18.6180	+	8.28926i	0.926279	+	0.412406i
$405$	−3.81867	+	7.69835i	−0.189751	+	0.382534i
$406$	−42.1446	+	9.00398i	−2.09160	+	0.446860i
$407$	−10.4557	+	10.4557i	−0.518270	+	0.518270i
$408$	7.36102	−	5.96084i	0.364425	−	0.295105i
$409$	5.33710	+	5.92744i	0.263902	+	0.293093i	0.860503	−	0.509445i	$-0.170149\pi$
$409$	5.33710	+	5.92744i	0.263902	+	0.293093i	−0.596601	+	0.802538i	$0.703482\pi$
$410$	−7.68264	−	16.7673i	−0.379419	−	0.828078i
$411$	−11.3935	−	10.2588i	−0.562002	−	0.506029i
$412$	−21.8421	+	11.1291i	−1.07608	+	0.548291i
$413$	4.81960	+	17.9124i	0.237157	+	0.881411i
$414$	4.00308	−	1.30068i	0.196741	−	0.0639249i
$415$	0.468783	−	0.532045i	0.0230116	−	0.0261171i
$416$	30.5406	−	27.4989i	1.49738	−	1.34824i
$417$	−1.27295	+	3.31615i	−0.0623366	+	0.162392i
$418$	14.8116	+	3.96875i	0.724459	+	0.194118i
$419$	−1.71609	−	1.24682i	−0.0838367	−	0.0609109i	0.545077	−	0.838386i	$-0.316500\pi$
$419$	−1.71609	−	1.24682i	−0.0838367	−	0.0609109i	−0.628914	+	0.777475i	$0.716500\pi$
$420$	−19.6367	−	7.27301i	−0.958175	−	0.354886i
$421$	4.94015	−	3.58923i	0.240768	−	0.174928i	−0.460857	−	0.887474i	$-0.652458\pi$
$421$	4.94015	−	3.58923i	0.240768	−	0.174928i	0.701625	+	0.712546i	$0.252458\pi$
$422$	16.3239	−	6.26618i	0.794637	−	0.305033i
$423$	9.08372	−	5.89903i	0.441665	−	0.286821i
$424$	−5.60058	−	3.23350i	−0.271988	−	0.157032i
$425$	13.2473	−	21.3938i	0.642589	−	1.03775i
$426$			42.2411i			2.04659i
$427$	10.8887	+	28.2781i	0.526943	+	1.36847i
$428$	−17.1075	−	2.70956i	−0.826921	−	0.130971i
$429$	−12.2813	+	27.5843i	−0.592948	+	1.33178i
$430$	−1.19180	+	28.6368i	−0.0574737	+	1.38099i
$431$	−33.7201	+	15.0132i	−1.62424	+	0.723158i	−0.998387	−	0.0567827i	$-0.981916\pi$
$431$	−33.7201	+	15.0132i	−1.62424	+	0.723158i	−0.625853	+	0.779941i	$0.715249\pi$
$432$	−3.29841	+	12.3098i	−0.158695	+	0.592257i
$433$	−13.8318	+	2.19074i	−0.664712	+	0.105280i	−0.479668	−	0.877450i	$-0.659243\pi$
$433$	−13.8318	+	2.19074i	−0.664712	+	0.105280i	−0.185044	+	0.982730i	$0.559243\pi$
$434$	13.8549	−	0.0144236i	0.665055	−	0.000692357i
$435$	13.4292	+	18.0713i	0.643880	+	0.866453i
$436$	8.52977	−	9.47327i	0.408502	−	0.453688i
$437$	0.139939	−	2.67020i	0.00669420	−	0.127733i
$438$	0.463723	−	8.84836i	0.0221575	−	0.422791i
$439$	−21.0590	+	23.3884i	−1.00509	+	1.11627i	−0.0118841	+	0.999929i	$0.503783\pi$
$439$	−21.0590	+	23.3884i	−1.00509	+	1.11627i	−0.993209	+	0.116340i	$0.962884\pi$
$440$	7.99162	+	10.7541i	0.380985	+	0.512682i
$441$	5.70845	−	6.36649i	0.271831	−	0.303166i
$442$	−57.1877	+	9.05765i	−2.72014	+	0.430828i
$443$	−2.86872	+	10.7062i	−0.136297	+	0.508667i	0.863692	+	0.504019i	$0.168146\pi$
$443$	−2.86872	+	10.7062i	−0.136297	+	0.508667i	−0.999989	+	0.00464730i	$0.998521\pi$
$444$	11.2616	−	5.01399i	0.534453	−	0.237954i
$445$	0.554945	−	13.3343i	0.0263069	−	0.632108i
$446$	12.2568	−	27.5292i	0.580375	−	1.30354i
$447$	5.24837	+	0.831261i	0.248240	+	0.0393173i
$448$	−31.6183	−	4.97412i	−1.49383	−	0.235005i
$449$			41.7666i			1.97109i	0.169422	+	0.985544i	$0.445810\pi$
$449$			41.7666i			1.97109i	−0.169422	+	0.985544i	$0.554190\pi$
$450$	−0.972771	−	13.1408i	−0.0458569	−	0.619462i
$451$	14.0578	+	8.11626i	0.661955	+	0.382180i
$452$	18.3795	−	11.9358i	0.864497	−	0.561411i
$453$	16.8227	−	6.45763i	0.790400	−	0.303406i
$454$	−33.1099	+	24.0558i	−1.55392	+	1.12899i
$455$	20.1432	+	24.2828i	0.944326	+	1.13840i
$456$	−2.54909	−	1.85202i	−0.119372	−	0.0867290i
$457$	31.6050	+	8.46854i	1.47842	+	0.396142i	0.905810	−	0.423685i	$-0.139264\pi$
$457$	31.6050	+	8.46854i	1.47842	+	0.396142i	0.572612	+	0.819827i	$0.305930\pi$
$458$	9.65544	−	25.1533i	0.451169	−	1.17534i
$459$	21.0553	−	18.9583i	0.982779	−	0.884898i
$460$	6.26653	−	7.11220i	0.292179	−	0.331608i
$461$	37.0645	−	12.0430i	1.72627	−	0.560898i	0.733365	−	0.679835i	$-0.237949\pi$
$461$	37.0645	−	12.0430i	1.72627	−	0.560898i	0.992902	+	0.118937i	$0.0379487\pi$
$462$	31.2076	−	8.39687i	1.45191	−	0.390658i
$463$	−17.2312	+	8.77973i	−0.800801	+	0.408028i	−0.805969	−	0.591958i	$-0.798355\pi$
$463$	−17.2312	+	8.77973i	−0.800801	+	0.408028i	0.00516769	+	0.999987i	$0.498355\pi$
$464$	12.7014	+	11.4364i	0.589649	+	0.530922i
$465$	−3.01510	−	6.58043i	−0.139822	−	0.305160i
$466$	−33.6943	−	37.4213i	−1.56086	−	1.73351i
$467$	0.490088	−	0.396866i	0.0226786	−	0.0183647i	−0.617914	−	0.786246i	$-0.712022\pi$
$467$	0.490088	−	0.396866i	0.0226786	−	0.0183647i	0.640593	+	0.767881i	$0.278689\pi$
$468$	−12.2263	+	12.2263i	−0.565163	+	0.565163i
$469$	−18.0221	+	16.2612i	−0.832183	+	0.750871i
$470$	19.0068	−	38.3173i	0.876719	−	1.76744i
$471$	−21.1212	−	9.40374i	−0.973211	−	0.433302i
$472$	−6.22693	+	7.68962i	−0.286618	+	0.353943i
$473$	−13.7388	−	21.1560i	−0.631713	−	0.972752i
$474$	−13.1319	−	22.7451i	−0.603168	−	1.04472i
$475$	−8.01480	−	2.41467i	−0.367744	−	0.110792i
$476$	26.2879	+	23.6202i	1.20490	+	1.08263i
$477$	−4.98746	−	2.54124i	−0.228360	−	0.116355i
$478$	21.0173	+	54.7520i	0.961310	+	2.50430i
$479$	2.38297	+	22.6725i	0.108881	+	1.03593i	0.903431	+	0.428734i	$0.141040\pi$
$479$	2.38297	+	22.6725i	0.108881	+	1.03593i	−0.794550	+	0.607199i	$0.792293\pi$
$480$	6.18619	+	22.1313i	0.282360	+	1.01015i
$481$	−18.4714	−	1.94142i	−0.842224	−	0.0885213i
$482$	−25.6617	−	25.6617i	−1.16886	−	1.16886i
$483$	−2.56361	−	5.01844i	−0.116648	−	0.228347i
$484$	−17.7351	−	5.76249i	−0.806142	−	0.261931i
$485$	8.32347	−	4.92579i	0.377949	−	0.223669i
$486$	5.27676	−	24.8252i	0.239358	−	1.12609i
$487$	29.6253	+	1.55260i	1.34245	+	0.0703549i	0.709976	−	0.704226i	$-0.248706\pi$
$487$	29.6253	+	1.55260i	1.34245	+	0.0703549i	0.632475	+	0.774581i	$0.282039\pi$
$488$	−8.80343	+	13.5561i	−0.398513	+	0.613655i
$489$	−3.44516	−	10.6031i	−0.155795	−	0.479489i
$490$	6.59581	−	33.1175i	0.297968	−	1.49610i
$491$	−3.57151	+	10.9920i	−0.161180	+	0.496061i	−0.998735	−	0.0502925i	$-0.983985\pi$
$491$	−3.57151	+	10.9920i	−0.161180	+	0.496061i	0.837554	+	0.546354i	$0.183985\pi$
$492$	−8.51648	−	10.5170i	−0.383953	−	0.474142i
$493$	−9.83458	−	36.7032i	−0.442927	−	1.65303i
$494$	7.83410	+	17.5957i	0.352473	+	0.791666i
$495$	7.39488	+	8.93353i	0.332375	+	0.401532i
$496$	−3.22973	−	4.44534i	−0.145019	−	0.199602i
$497$	−38.3611	+	6.11675i	−1.72073	+	0.274374i
$498$	0.414202	−	0.812918i	0.0185609	−	0.0364277i
$499$	20.0934	−	11.6010i	0.899506	−	0.519330i	0.0224659	−	0.999748i	$-0.492848\pi$
$499$	20.0934	−	11.6010i	0.899506	−	0.519330i	0.877040	+	0.480418i	$0.159515\pi$
$500$	−16.9572	−	24.3524i	−0.758350	−	1.08907i
$501$	−6.08573	+	10.5408i	−0.271890	+	0.470928i
$502$	23.2346	−	1.21767i	1.03701	−	0.0543474i
$503$	4.04822	−	25.5595i	0.180501	−	1.13964i	−0.716491	−	0.697596i	$-0.754253\pi$
$503$	4.04822	−	25.5595i	0.180501	−	1.13964i	0.896993	−	0.442045i	$-0.145747\pi$
$504$	4.53677	+	0.472059i	0.202084	+	0.0210272i
$505$	16.9282	−	2.86831i	0.753294	−	0.127638i
$506$	−1.52916	+	14.5490i	−0.0679796	+	0.646783i
$507$	−19.8889	+	5.32923i	−0.883299	+	0.236679i
$508$	10.5385	+	4.04534i	0.467570	+	0.179483i
$509$	−21.2314	+	4.51288i	−0.941066	+	0.200030i	−0.652808	−	0.757523i	$-0.726409\pi$
$509$	−21.2314	+	4.51288i	−0.941066	+	0.200030i	−0.288258	+	0.957553i	$0.593076\pi$
$510$	9.67263	−	30.8973i	0.428311	−	1.36815i
$511$	8.10276	−	0.860164i	0.358445	−	0.0380514i
$512$	10.8203	+	21.2361i	0.478195	+	0.938511i
$513$	−7.90447	−	5.13322i	−0.348991	−	0.226637i
$514$	−22.8700	−	4.86117i	−1.00875	−	0.214417i
$515$	−10.1330	+	17.9955i	−0.446512	+	0.792976i
$516$	4.37243	+	20.5707i	0.192485	+	0.905573i
$517$	5.88893	+	37.1812i	0.258995	+	1.63523i
$518$	10.8441	+	16.6605i	0.476465	+	0.732022i
$519$	2.69189	−	3.70506i	0.118161	−	0.162634i
$520$	−4.18052	+	16.3020i	−0.183328	+	0.714888i
$521$	−24.5177	+	2.57691i	−1.07414	+	0.112896i	−0.625045	−	0.780589i	$-0.714919\pi$
$521$	−24.5177	+	2.57691i	−1.07414	+	0.112896i	−0.449093	+	0.893485i	$0.648253\pi$
$522$	−15.4634	−	12.5220i	−0.676813	−	0.548072i
$523$	−0.548289	−	10.4620i	−0.0239750	−	0.457470i	−0.984068	−	0.177790i	$-0.943105\pi$
$523$	−0.548289	−	10.4620i	−0.0239750	−	0.457470i	0.960093	−	0.279680i	$-0.0902283\pi$
$524$	−16.0502			−0.701157
$525$	−17.1689	+	4.05646i	−0.749313	+	0.177038i
$526$	−56.8742			−2.47983
$527$	0.639335	+	12.1992i	0.0278499	+	0.531407i
$528$	−9.96059	−	8.06593i	−0.433479	−	0.351024i
$529$	−20.3370	+	2.13751i	−0.884219	+	0.0929352i
$530$	−22.0609	+	1.39447i	−0.958264	+	0.0605719i
$531$	−5.03404	+	6.92877i	−0.218459	+	0.300683i
$532$	5.32631	−	10.4804i	0.230925	−	0.454384i
$533$	3.18960	+	20.1383i	0.138157	+	0.872288i
$534$	−3.57011	−	16.7961i	−0.154494	−	0.726837i
$535$	−13.2660	+	6.07835i	−0.573537	+	0.262790i
$536$	−12.6653	−	2.69209i	−0.547056	−	0.116280i
$537$	8.58551	+	5.57549i	0.370492	+	0.240600i
$538$	18.2624	+	35.8421i	0.787350	+	1.54526i
$539$	12.1446	+	27.1251i	0.523106	+	1.16836i
$540$	−10.6665	−	31.6641i	−0.459014	−	1.36261i
$541$	−0.290506	+	0.0617489i	−0.0124898	+	0.00265479i	−0.214152	−	0.976800i	$-0.568699\pi$
$541$	−0.290506	+	0.0617489i	−0.0124898	+	0.00265479i	0.201663	+	0.979455i	$0.435366\pi$
$542$	−35.9989	−	13.8187i	−1.54628	−	0.593563i
$543$	−7.69186	+	2.06103i	−0.330089	+	0.0884471i
$544$	4.05387	−	38.5700i	0.173808	−	1.65367i
$545$	1.56572	−	10.6247i	0.0670682	−	0.455111i
$546$	32.8655	+	23.8260i	1.40652	+	1.01966i
$547$	5.22261	−	32.9743i	0.223303	−	1.40988i	−0.580151	−	0.814509i	$-0.697006\pi$
$547$	5.22261	−	32.9743i	0.223303	−	1.40988i	0.803453	−	0.595368i	$-0.202994\pi$
$548$	30.4720	−	1.59697i	1.30170	−	0.0682192i
$549$	−6.99534	+	12.1163i	−0.298554	+	0.517111i
$550$	43.0989	+	15.4879i	1.83774	+	0.660407i
$551$	−10.9467	+	6.32007i	−0.466345	+	0.269244i
$552$	1.36470	−	2.67837i	0.0580854	−	0.113999i
$553$	18.7543	−	15.2193i	0.797515	−	0.647191i
$554$	−39.8201	−	54.8077i	−1.69179	−	2.32855i
$555$	5.56222	−	8.77035i	0.236103	−	0.372281i
$556$	−2.87546	−	6.45838i	−0.121947	−	0.273896i
$557$	−6.55583	−	24.4667i	−0.277779	−	1.03669i	−0.953956	−	0.299947i	$-0.903031\pi$
$557$	−6.55583	−	24.4667i	−0.277779	−	1.03669i	0.676177	−	0.736740i	$-0.263636\pi$
$558$	4.02570	+	4.97133i	0.170421	+	0.210453i
$559$	9.79133	−	30.1346i	0.414129	−	1.27456i
$560$	−12.1692	+	5.59114i	−0.514241	+	0.236269i
$561$	8.80532	+	27.1000i	0.371761	+	1.14416i
$562$	9.70640	−	14.9465i	0.409440	−	0.630482i
$563$	−9.75958	−	0.511478i	−0.411317	−	0.0215562i	−0.154444	−	0.988001i	$-0.549359\pi$
$563$	−9.75958	−	0.511478i	−0.411317	−	0.0215562i	−0.256873	+	0.966445i	$0.582692\pi$
$564$	6.52507	−	30.6980i	0.274755	−	1.29262i
$565$	7.32745	−	16.9464i	0.308268	−	0.712941i
$566$	−18.4600	−	5.99803i	−0.775933	−	0.252116i
$567$	−10.1545	−	0.521574i	−0.426448	−	0.0219041i
$568$	−14.6521	−	14.6521i	−0.614788	−	0.614788i
$569$	21.2735	+	2.23593i	0.891831	+	0.0937353i	0.539348	−	0.842083i	$-0.318671\pi$
$569$	21.2735	+	2.23593i	0.891831	+	0.0937353i	0.352483	+	0.935818i	$0.385337\pi$
$570$	−10.7607	−	0.447834i	−0.450714	−	0.0187577i
$571$	−0.465891	−	4.43266i	−0.0194969	−	0.185501i	0.980439	−	0.196823i	$-0.0630626\pi$
$571$	−0.465891	−	4.43266i	−0.0194969	−	0.185501i	−0.999936	+	0.0113224i	$0.996396\pi$
$572$	−21.5364	−	56.1042i	−0.900481	−	2.34583i
$573$	3.26831	+	1.66529i	0.136535	+	0.0695683i
$574$	14.5854	−	16.2326i	0.608782	−	0.677538i
$575$	1.07915	−	7.91259i	0.0450036	−	0.329978i
$576$	−7.38898	−	12.7981i	−0.307874	−	0.533254i
$577$	12.4666	+	19.1968i	0.518990	+	0.799175i	0.996854	−	0.0792592i	$-0.0252555\pi$
$577$	12.4666	+	19.1968i	0.518990	+	0.799175i	−0.477864	+	0.878434i	$0.658589\pi$
$578$	−11.3060	+	13.9617i	−0.470267	+	0.580731i
$579$	27.4520	+	12.2224i	1.14087	+	0.507946i
$580$	−44.3316	−	6.53300i	−1.84077	−	0.271268i
$581$	0.798228	+	0.258442i	0.0331161	+	0.0107220i
$582$	8.79929	−	8.79929i	0.364742	−	0.364742i
$583$	15.1193	−	12.2434i	0.626179	−	0.507069i
$584$	2.90836	+	3.23006i	0.120349	+	0.133661i
$585$	−2.87505	+	14.2803i	−0.118869	+	0.590419i
$586$	31.6447	+	28.4930i	1.30723	+	1.17703i
$587$	−17.2600	+	8.79441i	−0.712397	+	0.362984i	−0.772333	−	0.635218i	$-0.780910\pi$
$587$	−17.2600	+	8.79441i	−0.712397	+	0.362984i	0.0599362	+	0.998202i	$0.480910\pi$
$588$	−1.34824	−	24.7402i	−0.0556005	−	1.02027i
$589$	3.86480	−	1.25575i	0.159246	−	0.0517423i
$590$	−3.17295	+	33.6720i	−0.130628	+	1.38626i
$591$	−19.7256	+	17.7610i	−0.811401	+	0.730589i
$592$	2.82531	−	7.36017i	0.116119	−	0.302501i
$593$	28.8400	+	7.72766i	1.18432	+	0.317337i	0.796638	−	0.604457i	$-0.206610\pi$
$593$	28.8400	+	7.72766i	1.18432	+	0.317337i	0.387680	+	0.921794i	$0.373277\pi$
$594$	41.7176	+	30.3096i	1.71169	+	1.24362i
$595$	29.4599	+	4.31008i	1.20774	+	0.176696i
$596$	−8.55606	+	6.21634i	−0.350470	+	0.254631i
$597$	24.4595	−	9.38912i	1.00106	−	0.384271i
$598$	−15.4109	+	10.0080i	−0.630199	+	0.409256i
$599$	3.03174	+	1.75038i	0.123874	+	0.0715185i	0.560656	−	0.828049i	$-0.310549\pi$
$599$	3.03174	+	1.75038i	0.123874	+	0.0715185i	−0.436783	+	0.899567i	$0.643882\pi$
$600$	−7.12726	−	6.14477i	−0.290969	−	0.250859i
$601$		−	19.7324i		−	0.804902i	−0.915442	−	0.402451i	$-0.868158\pi$
$601$		−	19.7324i		−	0.804902i	0.915442	−	0.402451i	$-0.131842\pi$
$602$	−31.6477	+	12.1862i	−1.28987	+	0.496674i
$603$	−11.0694	−	1.75323i	−0.450783	−	0.0713970i
$604$	−14.5871	+	32.7632i	−0.593541	+	1.33311i
$605$	−15.1303	+	4.22924i	−0.615132	+	0.171943i
$606$	20.1810	−	8.98517i	0.819798	−	0.364997i
$607$	−5.32023	+	19.8554i	−0.215942	+	0.805905i	0.769891	+	0.638175i	$0.220310\pi$
$607$	−5.32023	+	19.8554i	−0.215942	+	0.805905i	−0.985833	+	0.167730i	$0.946356\pi$
$608$	−12.7423	+	2.01818i	−0.516768	+	0.0818480i
$609$	−13.2959	+	23.0846i	−0.538777	+	0.935437i
$610$	0.594813	+	55.2465i	0.0240833	+	2.23686i
$611$	−31.6397	+	35.1394i	−1.28001	+	1.42159i
$612$	−0.853971	+	16.2947i	−0.0345197	+	0.658675i
$613$	−0.784863	+	14.9761i	−0.0317003	+	0.604878i	0.935881	+	0.352317i	$0.114606\pi$
$613$	−0.784863	+	14.9761i	−0.0317003	+	0.604878i	−0.967581	+	0.252561i	$0.918727\pi$
$614$	−0.0858355	+	0.0953299i	−0.00346404	+	0.00384720i
$615$	−10.8803	−	3.40616i	−0.438736	−	0.137350i
$616$	−7.91230	+	13.7375i	−0.318795	+	0.553500i
$617$	12.7020	−	2.01180i	0.511362	−	0.0809918i	0.104579	−	0.994517i	$-0.466650\pi$
$617$	12.7020	−	2.01180i	0.511362	−	0.0809918i	0.406783	+	0.913525i	$0.366650\pi$
$618$	−6.87732	+	25.6665i	−0.276646	+	1.03246i
$619$	10.2345	−	4.55670i	0.411360	−	0.183149i	−0.190614	−	0.981665i	$-0.561048\pi$
$619$	10.2345	−	4.55670i	0.411360	−	0.183149i	0.601974	+	0.798516i	$0.294381\pi$
$620$	13.5041	+	5.01761i	0.542337	+	0.201512i
$621$	3.65726	−	8.21435i	0.146761	−	0.329630i
$622$	35.6694	+	5.64948i	1.43021	+	0.226524i
$623$	14.7363	−	5.67435i	0.590398	−	0.227338i
$624$		−	16.0990i		−	0.644478i
$625$	−23.2552	−	9.17576i	−0.930209	−	0.367030i
$626$	7.23842	+	4.17910i	0.289305	+	0.167030i
$627$	7.94963	−	5.16255i	0.317478	−	0.206172i
$628$	42.9586	−	16.4903i	1.71424	−	0.658034i
$629$	−14.1799	+	10.3023i	−0.565391	+	0.410781i
$630$	13.8071	−	7.24165i	0.550087	−	0.288514i
$631$	25.2921	+	18.3758i	1.00686	+	0.731528i	0.963549	−	0.267533i	$-0.0862086\pi$
$631$	25.2921	+	18.3758i	1.00686	+	0.731528i	0.0433135	+	0.999062i	$0.486209\pi$
$632$	12.4446	+	3.33451i	0.495019	+	0.132640i
$633$	3.87347	−	10.0907i	0.153957	−	0.401071i
$634$	17.2360	−	15.5193i	0.684528	−	0.616352i
$635$	9.28036	−	2.07727i	0.368280	−	0.0824341i
$636$	−15.4255	+	5.01204i	−0.611660	+	0.198740i
$637$	−16.8784	+	33.2969i	−0.668746	+	1.31927i
$638$	61.6188	−	31.3964i	2.43951	−	1.24299i
$639$	−13.3286	−	12.0011i	−0.527270	−	0.474756i
$640$	−20.8216	−	11.7243i	−0.823048	−	0.463445i
$641$	−1.57640	−	1.75077i	−0.0622642	−	0.0691514i	0.711208	−	0.702982i	$-0.248148\pi$
$641$	−1.57640	−	1.75077i	−0.0622642	−	0.0691514i	−0.773472	+	0.633830i	$0.781482\pi$
$642$	−14.5908	+	11.8154i	−0.575852	+	0.466316i
$643$	1.47359	−	1.47359i	0.0581126	−	0.0581126i	−0.677453	−	0.735566i	$-0.736916\pi$
$643$	1.47359	−	1.47359i	0.0581126	−	0.0581126i	0.735566	+	0.677453i	$0.236916\pi$
$644$	10.6705	+	3.45476i	0.420475	+	0.136137i
$645$	12.6622	+	12.3924i	0.498573	+	0.487952i
$646$	16.6049	+	7.39299i	0.653312	+	0.290873i
$647$	−5.84935	+	7.22334i	−0.229962	+	0.283979i	−0.879045	−	0.476738i	$-0.841819\pi$
$647$	−5.84935	+	7.22334i	−0.229962	+	0.283979i	0.649084	+	0.760717i	$0.275152\pi$
$648$	−2.95399	−	4.54875i	−0.116044	−	0.178692i
$649$	−14.8833	−	25.7787i	−0.584221	−	1.01190i
$650$	18.9500	+	54.3141i	0.743281	+	2.13038i
$651$	5.72412	−	6.37060i	0.224346	−	0.249684i
$652$	19.7706	+	10.0736i	0.774275	+	0.394513i
$653$	9.25686	+	24.1149i	0.362249	+	0.943691i	0.986689	+	0.162618i	$0.0519939\pi$
$653$	9.25686	+	24.1149i	0.362249	+	0.943691i	−0.624440	+	0.781073i	$0.714673\pi$
$654$	−1.44435	−	13.7420i	−0.0564784	−	0.537356i
$655$	−11.2604	+	7.48618i	−0.439981	+	0.292509i
$656$	−8.60733	−	0.904667i	−0.336060	−	0.0353213i
$657$	2.66023	+	2.66023i	0.103785	+	0.103785i
$658$	50.5423	+	2.59605i	1.97034	+	0.101205i
$659$	−9.31890	−	3.02789i	−0.363013	−	0.117950i	0.121831	−	0.992551i	$-0.461123\pi$
$659$	−9.31890	−	3.02789i	−0.363013	−	0.117950i	−0.484844	+	0.874601i	$0.661123\pi$
$660$	33.4551	+	3.15251i	1.30224	+	0.122711i
$661$	4.44160	−	20.8961i	0.172758	−	0.812764i	−0.803355	−	0.595501i	$-0.796954\pi$
$661$	4.44160	−	20.8961i	0.172758	−	0.812764i	0.976113	−	0.217263i	$-0.0697131\pi$
$662$	20.3227	+	1.06507i	0.789866	+	0.0413951i
$663$	−19.4935	+	30.0173i	−0.757064	+	1.16578i
$664$	0.138302	+	0.425649i	0.00536714	+	0.0165184i
$665$	−1.15150	−	9.83711i	−0.0446534	−	0.381467i
$666$	−2.83622	+	8.72900i	−0.109901	+	0.338242i
$667$	−7.58902	−	9.37166i	−0.293848	−	0.362872i
$668$	−6.26975	−	23.3990i	−0.242584	−	0.905335i
$669$	−7.57659	−	17.0173i	−0.292928	−	0.657927i
$670$	−41.1457	+	16.3047i	−1.58960	+	0.629907i
$671$	−28.5818	−	39.3395i	−1.10339	−	1.51868i
$672$	−21.1127	+	17.1331i	−0.814439	+	0.660925i
$673$	2.23671	−	4.38979i	0.0862188	−	0.169214i	−0.843871	−	0.536546i	$-0.819729\pi$
$673$	2.23671	−	4.38979i	0.0862188	−	0.169214i	0.930090	+	0.367332i	$0.119729\pi$
$674$	53.5660	−	30.9264i	2.06329	−	1.19124i
$675$	−22.2522	−	17.2396i	−0.856487	−	0.663553i
$676$	20.4904	−	35.4903i	0.788090	−	1.36501i
$677$	−8.21325	+	0.430438i	−0.315661	+	0.0165431i	−0.209509	−	0.977807i	$-0.567186\pi$
$677$	−8.21325	+	0.430438i	−0.315661	+	0.0165431i	−0.106152	+	0.994350i	$0.533853\pi$
$678$	3.71607	−	23.4623i	0.142715	−	0.901066i
$679$	9.26524	+	6.71687i	0.355567	+	0.257770i
$680$	7.36214	+	14.0724i	0.282325	+	0.539652i
$681$	−2.64443	+	25.1601i	−0.101335	+	0.964137i
$682$	−21.4756	+	5.75437i	−0.822343	+	0.220346i
$683$	1.03000	+	0.395380i	0.0394118	+	0.0151288i	0.377994	−	0.925808i	$-0.376614\pi$
$683$	1.03000	+	0.395380i	0.0394118	+	0.0151288i	−0.338582	+	0.940937i	$0.609947\pi$
$684$	5.30933	−	1.12853i	0.203007	−	0.0431505i
$685$	20.6335	−	15.3332i	0.788366	−	0.585852i
$686$	39.0555	−	8.42908i	1.49115	−	0.321824i
$687$	−7.56114	−	14.8396i	−0.288476	−	0.566165i
$688$	11.2798	+	7.32518i	0.430038	+	0.279270i
$689$	23.9030	+	5.08073i	0.910631	+	0.193561i
$690$	−1.18397	−	10.2064i	−0.0450728	−	0.388552i
$691$	−3.57770	−	16.8317i	−0.136102	−	0.640310i	−0.992320	−	0.123695i	$-0.960525\pi$
$691$	−3.57770	−	16.8317i	−0.136102	−	0.640310i	0.856218	−	0.516614i	$-0.172808\pi$
$692$	1.42588	+	9.00263i	0.0542037	+	0.342229i
$693$	−6.21686	+	12.2327i	−0.236159	+	0.464683i
$694$	−14.6423	+	20.1534i	−0.555814	+	0.765013i
$695$	−5.02968	−	3.18986i	−0.190787	−	0.120998i
$696$	−14.1324	+	1.48538i	−0.535689	+	0.0563031i
$697$	14.9533	+	12.1090i	0.566397	+	0.458659i
$698$	1.40311	+	26.7729i	0.0531084	+	1.01337i
$699$	−31.1274			−1.17735
$700$	18.4536	−	29.8711i	0.697480	−	1.12902i
$701$	4.16683			0.157379			0.0786894	−	0.996899i	$-0.474926\pi$
$701$	4.16683			0.157379			0.0786894	+	0.996899i	$0.474926\pi$
$702$	3.38984	+	64.6821i	0.127941	+	2.44127i
$703$	4.53119	+	3.66928i	0.170897	+	0.138390i
$704$	51.0811	−	5.36884i	1.92519	−	0.202346i
$705$	−9.74042	−	24.5804i	−0.366845	−	0.925750i
$706$	7.57932	−	10.4320i	0.285251	−	0.392615i
$707$	11.0822	+	17.0262i	0.416788	+	0.640337i
$708$	3.88208	+	24.5105i	0.145898	+	0.921161i
$709$	−8.27164	−	38.9150i	−0.310648	−	1.46148i	−0.805546	−	0.592533i	$-0.798128\pi$
$709$	−8.27164	−	38.9150i	−0.310648	−	1.46148i	0.494898	−	0.868951i	$-0.335205\pi$
$710$	−69.4341	−	13.9791i	−2.60582	−	0.524627i
$711$	10.9078	+	2.31852i	0.409074	+	0.0869514i
$712$	7.06437	+	4.58766i	0.264749	+	0.171930i
$713$	1.76007	+	3.45433i	0.0659150	+	0.129366i
$714$	38.0937	−	4.04390i	1.42562	−	0.151339i
$715$	−41.2776	−	29.3162i	−1.54369	−	1.09636i
$716$	−19.9292	+	4.23609i	−0.744790	+	0.158310i
$717$	33.8452	+	12.9920i	1.26397	+	0.485194i
$718$	−39.1934	+	10.5018i	−1.46268	+	0.391925i
$719$	−0.657900	+	6.25950i	−0.0245355	+	0.233440i	0.975381	+	0.220526i	$0.0707774\pi$
$719$	−0.657900	+	6.25950i	−0.0245355	+	0.233440i	−0.999917	+	0.0129139i	$0.995889\pi$
$720$	−5.53922	−	2.74766i	−0.206434	−	0.102399i
$721$	−24.3048	−	2.52896i	−0.905159	−	0.0941835i
$722$	−5.46634	+	34.5131i	−0.203436	+	1.28444i
$723$	−22.4028	+	1.17408i	−0.833171	+	0.0436646i
$724$	7.92444	−	13.7255i	0.294510	−	0.510106i
$725$	−34.1491	+	16.0939i	−1.26826	+	0.597711i
$726$	−17.5053	+	10.1067i	−0.649681	+	0.375094i
$727$	17.1047	−	33.5699i	0.634378	−	1.24504i	−0.320277	−	0.947324i	$-0.603776\pi$
$727$	17.1047	−	33.5699i	0.634378	−	1.24504i	0.954655	−	0.297714i	$-0.0962240\pi$
$728$	−19.6645	+	3.13553i	−0.728814	+	0.116211i
$729$	−15.9983	−	22.0198i	−0.592530	−	0.815547i
$730$	14.3911	+	3.69049i	0.532638	+	0.136591i
$731$	−12.1620	−	27.3162i	−0.449826	−	1.01033i
$732$	10.4923	+	39.1577i	0.387805	+	1.44731i
$733$	−17.4083	−	21.4975i	−0.642991	−	0.794027i	0.346588	−	0.938017i	$-0.387340\pi$
$733$	−17.4083	−	21.4975i	−0.642991	−	0.794027i	−0.989579	+	0.143990i	$0.954007\pi$
$734$	12.1073	−	37.2625i	0.446890	−	1.37539i
$735$	−12.4853	−	16.7283i	−0.460527	−	0.617031i
$736$	−3.80340	−	11.7056i	−0.140195	−	0.431476i
$737$	21.2152	−	32.6685i	0.781471	−	1.20336i
$738$	10.0619	+	0.527322i	0.370384	+	0.0194110i
$739$	−3.56667	+	16.7798i	−0.131202	+	0.617257i	0.862581	+	0.505919i	$0.168847\pi$
$739$	−3.56667	+	16.7798i	−0.131202	+	0.617257i	−0.993783	+	0.111337i	$0.964487\pi$
$740$	4.51491	+	20.1707i	0.165971	+	0.741489i
$741$	11.3235	+	3.67922i	0.415978	+	0.135159i
$742$	−11.8983	−	23.2918i	−0.436801	−	0.855069i
$743$	−25.4400	−	25.4400i	−0.933303	−	0.933303i	0.0646073	−	0.997911i	$-0.479421\pi$
$743$	−25.4400	−	25.4400i	−0.933303	−	0.933303i	−0.997911	+	0.0646073i	$0.979421\pi$
$744$	4.54345	+	0.477536i	0.166571	+	0.0175073i
$745$	−3.10327	+	8.35196i	−0.113695	+	0.305992i
$746$	−2.84982	−	27.1142i	−0.104339	−	0.992721i
$747$	0.138826	+	0.361654i	0.00507937	+	0.0132322i
$748$	−50.5307	−	25.7467i	−1.84759	−	0.941392i
$749$	−12.8429	−	11.5396i	−0.469271	−	0.421650i
$750$	−31.9158	−	4.00330i	−1.16540	−	0.146180i
$751$	3.13814	+	5.43542i	0.114512	+	0.198341i	0.917585	−	0.397540i	$-0.130136\pi$
$751$	3.13814	+	5.43542i	0.114512	+	0.198341i	−0.803072	+	0.595882i	$0.796803\pi$
$752$	−10.9315	−	16.8331i	−0.398632	−	0.613839i
$753$	9.05108	−	11.1771i	0.329840	−	0.407318i
$754$	79.3561	+	35.3316i	2.88998	+	1.28670i
$755$	5.04753	+	29.7895i	0.183699	+	1.08415i
$756$	29.3520	−	26.4841i	1.06752	−	0.963216i
$757$	25.7562	−	25.7562i	0.936126	−	0.936126i	−0.0619526	−	0.998079i	$-0.519733\pi$
$757$	25.7562	−	25.7562i	0.936126	−	0.936126i	0.998079	+	0.0619526i	$0.0197328\pi$
$758$	15.9952	−	12.9526i	0.580971	−	0.470461i
$759$	6.05101	+	6.72033i	0.219638	+	0.243933i
$760$	3.88787	−	3.57719i	0.141028	−	0.129758i
$761$	−9.92182	−	8.93365i	−0.359666	−	0.323844i	0.469411	−	0.882980i	$-0.344466\pi$
$761$	−9.92182	−	8.93365i	−0.359666	−	0.323844i	−0.829076	+	0.559136i	$0.811133\pi$
$762$	10.9023	−	5.55499i	0.394948	−	0.201236i
$763$	12.2706	−	3.30160i	0.444227	−	0.119526i
$764$	−6.94320	+	2.25598i	−0.251196	+	0.0816186i
$765$	7.00110	+	11.8303i	0.253125	+	0.427724i
$766$	37.7095	−	33.9538i	1.36250	−	1.22680i
$767$	13.3991	−	34.9059i	0.483815	−	1.26038i
$768$	1.46940	+	0.393725i	0.0530224	+	0.0142073i
$769$	34.9365	+	25.3828i	1.25984	+	0.915328i	0.998750	−	0.0499857i	$-0.0159176\pi$
$769$	34.9365	+	25.3828i	1.25984	+	0.915328i	0.261091	+	0.965314i	$0.415918\pi$
$770$	3.47470	+	54.0765i	0.125219	+	1.94878i
$771$	−11.6928	+	8.49529i	−0.421104	+	0.305950i
$772$	−55.8351	+	21.4331i	−2.00955	+	0.771393i
$773$	−23.1136	+	15.0101i	−0.831338	+	0.539877i	−0.888707	−	0.458476i	$-0.848396\pi$
$773$	−23.1136	+	15.0101i	−0.831338	+	0.539877i	0.0573688	+	0.998353i	$0.481729\pi$
$774$	−13.5601	−	7.82891i	−0.487407	−	0.281405i
$775$	11.8144	−	2.77839i	0.424387	−	0.0998026i
$776$			6.10439i			0.219135i
$777$	12.1389	+	1.90966i	0.435481	+	0.0685088i
$778$	72.1646	+	11.4298i	2.58723	+	0.409777i
$779$	2.60340	−	5.84733i	0.0932764	−	0.209502i
$780$	23.3682	+	35.1495i	0.836715	+	1.25855i
$781$	56.9472	−	25.3545i	2.03773	−	0.907256i
$782$	−4.48812	+	16.7499i	−0.160495	+	0.598975i
$783$	−41.9832	+	6.64949i	−1.50036	+	0.237633i
$784$	−11.7978	−	10.5784i	−0.421349	−	0.377798i
$785$	22.4472	−	31.6060i	0.801176	−	1.12807i
$786$	−11.6413	+	12.9290i	−0.415232	+	0.461162i
$787$	−2.58445	+	49.3143i	−0.0921258	+	1.75787i	0.428002	+	0.903778i	$0.359218\pi$
$787$	−2.58445	+	49.3143i	−0.0921258	+	1.75787i	−0.520128	+	0.854088i	$0.674116\pi$
$788$	2.76482	−	52.7560i	0.0984928	−	1.87935i
$789$	−23.5247	+	26.1268i	−0.837501	+	0.930139i
$790$	41.7333	−	14.0585i	1.48480	−	0.500178i
$791$	21.8454	−	0.0227422i	0.776732	−	0.000808619i
$792$	−7.22942	+	1.14503i	−0.256886	+	0.0406868i
$793$	15.8083	−	58.9973i	0.561368	−	2.09506i
$794$	66.1704	−	29.4609i	2.34830	−	1.04553i
$795$	−8.48438	+	10.7111i	−0.300910	+	0.379884i
$796$	−21.2090	+	47.6362i	−0.751733	+	1.68842i
$797$	−16.7721	−	2.65644i	−0.594098	−	0.0940959i	−0.147857	−	0.989009i	$-0.547238\pi$
$797$	−16.7721	−	2.65644i	−0.594098	−	0.0940959i	−0.446241	+	0.894913i	$0.647238\pi$
$798$	−4.57914	−	11.8920i	−0.162100	−	0.420974i
$799$			44.6223i			1.57863i
$800$	−38.4257	+	2.84454i	−1.35855	+	0.100570i
$801$	6.31406	+	3.64543i	0.223096	+	0.128805i
$802$	−28.2310	+	18.3334i	−0.996871	+	0.647375i
$803$	−12.2072	+	4.68591i	−0.430784	+	0.165362i
$804$	−26.2723	+	19.0879i	−0.926551	+	0.673179i
$805$	9.09749	−	2.55316i	0.320644	−	0.0899872i
$806$	−22.5931	−	16.4149i	−0.795809	−	0.578189i
$807$	24.0189	+	6.43585i	0.845506	+	0.226553i
$808$	−3.88348	+	10.1168i	−0.136620	+	0.355908i
$809$	−7.82039	+	7.04151i	−0.274950	+	0.247566i	−0.795057	−	0.606535i	$-0.792559\pi$
$809$	−7.82039	+	7.04151i	−0.274950	+	0.247566i	0.520106	+	0.854101i	$0.325892\pi$
$810$	−17.0165	−	7.35774i	−0.597898	−	0.258525i
$811$	−24.4183	+	7.93398i	−0.857442	+	0.278600i	−0.704560	−	0.709645i	$-0.748855\pi$
$811$	−24.4183	+	7.93398i	−0.857442	+	0.278600i	−0.152882	+	0.988244i	$0.548855\pi$
$812$	−13.7760	−	51.1995i	−0.483443	−	1.79675i
$813$	−21.2381	+	10.8213i	−0.744852	+	0.379521i
$814$	−23.7063	−	21.3452i	−0.830905	−	0.748150i
$815$	18.5691	−	2.15405i	0.650445	−	0.0754530i
$816$	−10.1658	−	11.2903i	−0.355875	−	0.395239i
$817$	−7.73010	+	6.25971i	−0.270442	+	0.219000i
$818$	−12.1675	+	12.1675i	−0.425426	+	0.425426i
$819$	−16.8554	+	3.60106i	−0.588974	+	0.125831i
$820$	20.1058	−	10.5186i	0.702124	−	0.367325i
$821$	−10.2566	−	4.56654i	−0.357958	−	0.159373i	0.219875	−	0.975528i	$-0.429435\pi$
$821$	−10.2566	−	4.56654i	−0.357958	−	0.159373i	−0.577833	+	0.816155i	$0.696102\pi$
$822$	20.8151	−	25.7045i	0.726010	−	0.896548i
$823$	−3.65309	−	5.62526i	−0.127339	−	0.196084i	0.769251	−	0.638947i	$-0.220630\pi$
$823$	−3.65309	−	5.62526i	−0.127339	−	0.196084i	−0.896589	+	0.442863i	$0.853963\pi$
$824$	−6.51737	−	11.2884i	−0.227043	−	0.393250i
$825$	24.9416	−	13.3925i	0.868357	−	0.466267i
$826$	−38.0463	+	12.4058i	−1.32380	+	0.431653i
$827$	18.6583	+	9.50687i	0.648812	+	0.330586i	0.747237	−	0.664558i	$-0.231380\pi$
$827$	18.6583	+	9.50687i	0.648812	+	0.330586i	−0.0984242	+	0.995145i	$0.531380\pi$
$828$	1.85578	+	4.83447i	0.0644928	+	0.168009i
$829$	1.87853	+	17.8730i	0.0652441	+	0.620756i	0.977471	+	0.211070i	$0.0676949\pi$
$829$	1.87853	+	17.8730i	0.0652441	+	0.620756i	−0.912227	+	0.409686i	$0.865638\pi$
$830$	1.19917	+	0.949873i	0.0416236	+	0.0329706i
$831$	−41.6481	−	4.37739i	−1.44476	−	0.151850i
$832$	45.6193	+	45.6193i	1.58157	+	1.58157i
$833$	9.18864	+	34.0091i	0.318367	+	1.17834i
$834$	−7.28803	−	2.36802i	−0.252364	−	0.0819980i
$835$	−15.3125	−	13.4918i	−0.529911	−	0.466903i
$836$	−3.92234	+	18.4532i	−0.135657	+	0.638217i
$837$	13.6467	+	0.715195i	0.471700	+	0.0247208i
$838$	2.49238	−	3.83792i	0.0860977	−	0.132579i
$839$	−4.99439	−	15.3711i	−0.172425	−	0.530671i	0.827081	−	0.562083i	$-0.190000\pi$
$839$	−4.99439	−	15.3711i	−0.172425	−	0.530671i	−0.999507	+	0.0314117i	$0.990000\pi$
$840$	3.31550	−	10.6295i	0.114396	−	0.366752i
$841$	−8.65458	+	26.6361i	−0.298434	+	0.918485i
$842$	8.29040	+	10.2378i	0.285706	+	0.352818i
$843$	−2.85130	−	10.6412i	−0.0982041	−	0.366503i
$844$	8.74975	+	19.6523i	0.301179	+	0.676459i
$845$	−2.17798	−	34.4562i	−0.0749247	−	1.18533i
$846$	13.7345	+	18.9039i	0.472201	+	0.649930i
$847$	−11.7132	−	14.4339i	−0.402471	−	0.495953i
$848$	−4.70917	+	9.24228i	−0.161714	+	0.317381i
$849$	−10.3909	+	5.99920i	−0.356616	+	0.205892i
$850$	47.5866	+	26.1245i	1.63221	+	0.896063i
$851$	−2.78126	+	4.81728i	−0.0953402	+	0.165134i
$852$	−51.8978	+	2.71985i	−1.77799	+	0.0931804i
$853$	−7.78276	+	49.1384i	−0.266477	+	1.68247i	0.384308	+	0.923205i	$0.374440\pi$
$853$	−7.78276	+	49.1384i	−0.266477	+	1.68247i	−0.650784	+	0.759263i	$0.725560\pi$
$854$	−59.6929	+	26.6515i	−2.04265	+	0.911995i
$855$	3.19851	−	3.26814i	0.109387	−	0.111768i
$856$	0.962697	−	9.15945i	0.0329043	−	0.313064i
$857$	4.24928	−	1.13859i	0.145153	−	0.0388936i	−0.185511	−	0.982642i	$-0.559394\pi$
$857$	4.24928	−	1.13859i	0.145153	−	0.0388936i	0.330664	+	0.943749i	$0.392727\pi$
$858$	−60.8143	−	23.3444i	−2.07616	−	0.796965i
$859$	−9.20956	+	1.95755i	−0.314226	+	0.0667908i	−0.362325	−	0.932052i	$-0.618017\pi$
$859$	−9.20956	+	1.95755i	−0.314226	+	0.0667908i	0.0480991	+	0.998843i	$0.484684\pi$
$860$	−35.2602	+	0.379630i	−1.20236	+	0.0129453i
$861$	−1.42404	−	13.4145i	−0.0485311	−	0.457164i
$862$	−36.1516	−	70.9514i	−1.23133	−	2.41662i
$863$	−27.2298	−	17.6832i	−0.926913	−	0.601944i	−0.00953193	−	0.999955i	$-0.503034\pi$
$863$	−27.2298	−	17.6832i	−0.926913	−	0.601944i	−0.917381	+	0.398010i	$0.869701\pi$
$864$	−42.4361	−	9.02008i	−1.44371	−	0.306869i
$865$	5.19938	+	5.65095i	0.176784	+	0.192138i
$866$	−6.28143	−	29.5518i	−0.213452	−	1.00421i
$867$	1.73727	+	10.9687i	0.0590007	+	0.372516i
$868$	0.909817	+	17.0213i	0.0308812	+	0.577740i
$869$	−22.7815	+	31.3561i	−0.772810	+	1.06368i
$870$	−37.4165	+	30.9722i	−1.26854	+	1.05006i
$871$	48.6597	−	5.11434i	1.64877	−	0.173293i
$872$	5.26767	+	4.26568i	0.178386	+	0.144454i
$873$	0.276527	+	5.27646i	0.00935903	+	0.178581i
$874$	5.76847			0.195121
$875$	−0.986011	−	29.5640i	−0.0333332	−	0.999444i
$876$	10.9010			0.368312
$877$	−0.259825	−	4.95776i	−0.00877367	−	0.167412i	−0.999502	−	0.0315540i	$-0.989954\pi$
$877$	−0.259825	−	4.95776i	−0.00877367	−	0.167412i	0.990728	−	0.135858i	$-0.0433789\pi$
$878$	−52.7657	−	42.7289i	−1.78076	−	1.44203i
$879$	26.1781	−	2.75143i	0.882967	−	0.0928036i
$880$	16.5548	−	13.7035i	0.558061	−	0.461944i
$881$	−8.88435	+	12.2283i	−0.299321	+	0.411980i	−0.932014	−	0.362423i	$-0.881950\pi$
$881$	−8.88435	+	12.2283i	−0.299321	+	0.411980i	0.632693	+	0.774403i	$0.281950\pi$
$882$	14.3605	+	11.5795i	0.483543	+	0.389901i
$883$	3.22415	+	20.3565i	0.108501	+	0.685051i	0.980644	+	0.195799i	$0.0627301\pi$
$883$	3.22415	+	20.3565i	0.108501	+	0.685051i	−0.872143	+	0.489252i	$0.837270\pi$
$884$	−14.8105	−	69.6781i	−0.498132	−	2.34353i
$885$	14.1558	+	15.3852i	0.475842	+	0.517169i
$886$	−23.3893	−	4.97155i	−0.785779	−	0.167023i
$887$	22.2034	+	14.4190i	0.745516	+	0.484144i	0.860644	−	0.509207i	$-0.170061\pi$
$887$	22.2034	+	14.4190i	0.745516	+	0.484144i	−0.115128	+	0.993351i	$0.536728\pi$
$888$	2.97582	+	5.84037i	0.0998620	+	0.195990i
$889$	6.62346	+	9.09648i	0.222144	+	0.305086i
$890$	28.7901	−	0.309970i	0.965048	−	0.0103902i
$891$	15.9600	−	3.39240i	0.534680	−	0.113650i
$892$	34.6117	+	13.2862i	1.15889	+	0.444855i
$893$	14.3380	−	3.84186i	0.479803	−	0.128563i
$894$	−1.19829	+	11.4009i	−0.0400767	+	0.381305i
$895$	−12.0060	+	12.2674i	−0.401317	+	0.410053i
$896$	2.92613	−	28.1219i	0.0977551	−	0.939485i
$897$	−1.77692	+	11.2190i	−0.0593295	+	0.374592i
$898$	−89.9819	+	4.71575i	−3.00273	+	0.157367i
$899$	9.16359	−	15.8718i	0.305623	−	0.529354i
$900$	16.0822	−	2.04127i	0.536074	−	0.0680423i
$901$	19.9714	−	11.5305i	0.665345	−	0.384137i
$902$	−15.8984	+	31.2024i	−0.529360	+	1.03893i
$903$	−7.49224	+	19.5788i	−0.249326	+	0.651543i
$904$	6.84935	+	9.42732i	0.227806	+	0.313548i
$905$	−0.842312	−	13.3256i	−0.0279994	−	0.442958i
$906$	15.8117	+	35.5137i	0.525309	+	1.17986i
$907$	2.65589	+	9.91192i	0.0881874	+	0.329120i	0.995899	−	0.0904755i	$-0.0288387\pi$
$907$	2.65589	+	9.91192i	0.0881874	+	0.329120i	−0.907711	+	0.419595i	$0.862172\pi$
$908$	−31.6870	−	39.1302i	−1.05157	−	1.29858i
$909$	−2.89848	+	8.92060i	−0.0961365	+	0.295878i
$910$	−50.0405	+	46.1381i	−1.65883	+	1.52946i
$911$	−13.6218	−	41.9237i	−0.451312	−	1.38899i	−0.875411	−	0.483379i	$-0.839409\pi$
$911$	−13.6218	−	41.9237i	−0.451312	−	1.38899i	0.424100	−	0.905615i	$-0.360591\pi$
$912$	−2.75253	+	4.23853i	−0.0911454	+	0.140352i
$913$	−1.34455	−	0.0704649i	−0.0444981	−	0.00233205i
$914$	−14.6762	+	69.0460i	−0.485445	+	2.28384i
$915$	25.6251	+	22.5782i	0.847140	+	0.746411i
$916$	31.5252	+	10.2432i	1.04162	+	0.338444i
$917$	−13.4272	−	8.69984i	−0.443404	−	0.287294i
$918$	43.2211	+	43.2211i	1.42651	+	1.42651i
$919$	−1.82753	−	0.192082i	−0.0602848	−	0.00633619i	0.0743381	−	0.997233i	$-0.476316\pi$
$919$	−1.82753	−	0.192082i	−0.0602848	−	0.00633619i	−0.134623	+	0.990897i	$0.542982\pi$
$920$	3.95096	+	3.12960i	0.130259	+	0.103180i
$921$	0.00828873	+	0.0788620i	0.000273123	+	0.00259859i
$922$	30.1303	+	78.4920i	0.992287	+	2.58500i
$923$	69.7655	+	35.5473i	2.29636	+	1.17005i
$924$	12.3259	+	37.8012i	0.405492	+	1.24357i
$925$	12.5756	+	12.0454i	0.413483	+	0.396049i
$926$	−20.8606	−	36.1315i	−0.685520	−	1.18736i
$927$	−6.14479	−	9.46214i	−0.201821	−	0.310778i
$928$	−36.6163	+	45.2173i	−1.20199	+	1.48433i
$929$	8.39495	+	3.73767i	0.275429	+	0.122629i	0.539803	−	0.841791i	$-0.318499\pi$
$929$	8.39495	+	3.73767i	0.275429	+	0.122629i	−0.264374	+	0.964420i	$0.585165\pi$
$930$	13.8364	−	7.23870i	0.453715	−	0.237366i
$931$	10.1366	−	5.88057i	0.332215	−	0.192728i
$932$	43.8066	−	43.8066i	1.43493	−	1.43493i
$933$	17.3491	−	14.0490i	0.567984	−	0.459944i
$934$	0.910341	+	1.01104i	0.0297873	+	0.0330821i
$935$	−47.4598	+	5.50544i	−1.55210	+	0.180047i
$936$	−6.83242	−	6.15194i	−0.223325	−	0.201082i
$937$	−10.5675	+	5.38439i	−0.345224	+	0.175900i	−0.618002	−	0.786177i	$-0.712058\pi$
$937$	−10.5675	+	5.38439i	−0.345224	+	0.175900i	0.272778	+	0.962077i	$0.412058\pi$
$938$	−37.0678	−	36.9908i	−1.21031	−	1.20779i
$939$	4.91379	−	1.59659i	0.160356	−	0.0521027i
$940$	48.3007	+	20.8847i	1.57540	+	0.681185i
$941$	−38.7868	+	34.9238i	−1.26441	+	1.13848i	−0.280498	+	0.959855i	$0.590500\pi$
$941$	−38.7868	+	34.9238i	−1.26441	+	1.13848i	−0.983916	+	0.178629i	$0.942834\pi$
$942$	17.8747	−	46.5651i	0.582389	−	1.51717i
$943$	5.89838	+	1.58047i	0.192078	+	0.0514670i
$944$	12.8397	+	9.32860i	0.417897	+	0.303620i
$945$	8.23986	−	32.2710i	0.268043	−	1.04977i
$946$	44.0272	−	31.9876i	1.43145	−	1.04001i
$947$	5.06926	−	1.94591i	0.164729	−	0.0632335i	−0.274606	−	0.961557i	$-0.588547\pi$
$947$	5.06926	−	1.94591i	0.164729	−	0.0632335i	0.439335	+	0.898323i	$0.355214\pi$
$948$	27.0993	−	17.5985i	0.880143	−	0.571572i
$949$	−14.2237	−	8.21207i	−0.461722	−	0.266575i
$950$	4.29723	−	17.5397i	0.139420	−	0.569063i
$951$		−	14.3371i		−	0.464911i
$952$	−11.8108	+	14.6162i	−0.382789	+	0.473713i
$953$	−9.35630	−	1.48189i	−0.303080	−	0.0480032i	0.00304207	−	0.999995i	$-0.499032\pi$
$953$	−9.35630	−	1.48189i	−0.303080	−	0.0480032i	−0.306122	+	0.951992i	$0.599032\pi$
$954$	4.91172	−	11.0319i	0.159023	−	0.357171i
$955$	−3.81893	+	4.82120i	−0.123578	+	0.156010i
$956$	−65.9155	+	29.3475i	−2.13186	+	0.949165i
$957$	11.0644	−	41.2928i	0.357660	−	1.33481i
$958$	−48.5765	+	7.69377i	−1.56944	+	0.248574i
$959$	26.3576	+	15.1810i	0.851133	+	0.490221i
$960$	−34.1871	+	11.5164i	−1.10338	+	0.371691i
$961$	16.8005	−	18.6589i	0.541952	−	0.601899i
$962$	2.09704	−	40.0140i	0.0676114	−	1.29010i
$963$	0.417207	−	7.96078i	0.0134443	−	0.256533i
$964$	29.8759	−	33.1805i	0.962238	−	1.06867i
$965$	−29.1756	+	41.0796i	−0.939195	+	1.32240i
$966$	10.5223	−	6.08965i	0.338549	−	0.195931i
$967$	34.8857	−	5.52535i	1.12185	−	0.177683i	0.432164	−	0.901795i	$-0.357750\pi$
$967$	34.8857	−	5.52535i	1.12185	−	0.177683i	0.689683	+	0.724112i	$0.257750\pi$
$968$	2.56634	−	9.57769i	0.0824851	−	0.307839i
$969$	10.2644	−	4.57001i	0.329741	−	0.146810i
$970$	11.5519	+	17.3759i	0.370909	+	0.557907i
$971$	9.50176	−	21.3413i	0.304926	−	0.684875i	−0.694474	−	0.719518i	$-0.744363\pi$
$971$	9.50176	−	21.3413i	0.304926	−	0.684875i	0.999400	+	0.0346431i	$0.0110295\pi$
$972$	30.8402	+	4.88461i	0.989199	+	0.156674i
$973$	1.09517	−	6.96151i	0.0351094	−	0.223176i
$974$			64.0000i			2.05069i
$975$	32.7890	+	13.7605i	1.05009	+	0.440690i
$976$	22.4527	+	12.9631i	0.718695	+	0.414939i
$977$	6.37182	−	4.13791i	0.203853	−	0.132383i	−0.438676	−	0.898646i	$-0.644552\pi$
$977$	6.37182	−	4.13791i	0.203853	−	0.132383i	0.642528	+	0.766262i	$0.277886\pi$
$978$	22.4543	−	8.61941i	0.718010	−	0.275618i
$979$	−20.5006	+	14.8946i	−0.655203	+	0.476033i
$980$	41.1131	+	5.97127i	1.31331	+	0.190745i
$981$	4.74646	+	3.44850i	0.151543	+	0.110102i
$982$	−24.0844	−	6.45339i	−0.768563	−	0.205936i
$983$	−14.8915	+	38.7937i	−0.474965	+	1.23733i	0.461680	+	0.887047i	$0.347247\pi$
$983$	−14.8915	+	38.7937i	−0.474965	+	1.23733i	−0.936645	+	0.350280i	$0.886086\pi$
$984$	5.34750	−	4.81491i	0.170472	−	0.153494i
$985$	−22.6668	−	38.3018i	−0.722225	−	1.22040i
$986$	77.9628	−	25.3317i	2.48284	−	0.806724i
$987$	22.0982	−	22.1443i	0.703393	−	0.704859i
$988$	−21.1138	+	10.7580i	−0.671718	+	0.342257i
$989$	−7.05209	−	6.34973i	−0.224243	−	0.201910i
$990$	−18.4114	+	16.9402i	−0.585154	+	0.538394i
$991$	26.4144	+	29.3362i	0.839081	+	0.931894i	0.998469	−	0.0553220i	$-0.0176185\pi$
$991$	26.4144	+	29.3362i	0.839081	+	0.931894i	−0.159387	+	0.987216i	$0.550952\pi$
$992$	14.5370	−	11.7718i	0.461549	−	0.373755i
$993$	8.89530	−	8.89530i	0.282284	−	0.282284i
$994$	−17.5092	−	81.9545i	−0.555357	−	2.59944i
$995$	7.33889	+	43.3127i	0.232659	+	1.37310i
$996$	1.02543	+	0.456550i	0.0324919	+	0.0144663i
$997$	−23.7118	+	29.2816i	−0.750961	+	0.927359i	−0.999145	−	0.0413538i	$-0.986833\pi$
$997$	−23.7118	+	29.2816i	−0.750961	+	0.927359i	0.248184	+	0.968713i	$0.420166\pi$
$998$	27.2618	+	41.9794i	0.862956	+	1.32884i
$999$	9.80355	+	16.9802i	0.310170	+	0.537231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.108.16	yes	288
5.2	odd	4		875.2.bb.b.857.3		288
5.3	odd	4		875.2.bb.a.857.16		288
5.4	even	2		875.2.bb.c.143.3		288
7.5	odd	6	inner	175.2.x.a.33.16	✓	288
25.3	odd	20		875.2.bb.c.507.3		288
25.4	even	10		875.2.bb.a.493.3		288
25.21	even	5		875.2.bb.b.493.16		288
25.22	odd	20	inner	175.2.x.a.122.16	yes	288
35.12	even	12		875.2.bb.b.607.16		288
35.19	odd	6		875.2.bb.c.768.3		288
35.33	even	12		875.2.bb.a.607.3		288
175.47	even	60	inner	175.2.x.a.47.16	yes	288
175.54	odd	30		875.2.bb.a.243.16		288
175.96	odd	30		875.2.bb.b.243.3		288
175.103	even	60		875.2.bb.c.257.3		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.16	✓	288	7.5	odd	6	inner
175.2.x.a.47.16	yes	288	175.47	even	60	inner
175.2.x.a.108.16	yes	288	1.1	even	1	trivial
175.2.x.a.122.16	yes	288	25.22	odd	20	inner
875.2.bb.a.243.16		288	175.54	odd	30
875.2.bb.a.493.3		288	25.4	even	10
875.2.bb.a.607.3		288	35.33	even	12
875.2.bb.a.857.16		288	5.3	odd	4
875.2.bb.b.243.3		288	175.96	odd	30
875.2.bb.b.493.16		288	25.21	even	5
875.2.bb.b.607.16		288	35.12	even	12
875.2.bb.b.857.3		288	5.2	odd	4
875.2.bb.c.143.3		288	5.4	even	2
875.2.bb.c.257.3		288	175.103	even	60
875.2.bb.c.507.3		288	25.3	odd	20
875.2.bb.c.768.3		288	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.112907 + 2.15440i) q^{2} +(1.03639 + 0.839249i) q^{3} +(-2.63964 + 0.277438i) q^{4} +(-1.72250 + 1.42583i) q^{5} +(-1.69106 + 2.32755i) q^{6} +(-2.35863 - 1.19869i) q^{7} +(-0.220776 - 1.39393i) q^{8} +(-0.253977 - 1.19487i) q^{9} +(-3.26629 - 3.54997i) q^{10} +(4.15290 + 0.882727i) q^{11} +(-2.96853 - 1.92779i) q^{12} +(2.42110 + 4.75167i) q^{13} +(2.31615 - 5.21677i) q^{14} +(-2.98180 + 0.0321037i) q^{15} +(-2.21422 + 0.470646i) q^{16} +(4.69838 + 1.80354i) q^{17} +(2.54555 - 0.682078i) q^{18} +(0.174994 - 1.66496i) q^{19} +(4.15121 - 4.24157i) q^{20} +(-1.43845 - 3.22179i) q^{21} +(-1.43285 + 9.04668i) q^{22} +(1.59498 - 0.0835893i) q^{23} +(0.941042 - 1.62993i) q^{24} +(0.934017 - 4.91199i) q^{25} +(-9.96363 + 5.75250i) q^{26} +(2.55587 - 5.01618i) q^{27} +(6.55850 + 2.50974i) q^{28} +(-4.43795 - 6.10831i) q^{29} +(-0.405831 - 6.42037i) q^{30} +(0.987291 + 2.21749i) q^{31} +(-1.99450 - 7.44359i) q^{32} +(3.56319 + 4.40017i) q^{33} +(-3.35506 + 10.3258i) q^{34} +(5.77187 - 1.29826i) q^{35} +(1.00191 + 3.08356i) q^{36} +(-1.89683 + 2.92087i) q^{37} +(3.60674 + 0.189021i) q^{38} +(-1.47864 + 6.95647i) q^{39} +(2.36779 + 2.08625i) q^{40} +(3.63618 + 1.18147i) q^{41} +(6.77860 - 3.46276i) q^{42} +(-4.20125 - 4.20125i) q^{43} +(-11.2071 - 1.17791i) q^{44} +(2.14116 + 1.69603i) q^{45} +(0.360169 + 3.42678i) q^{46} +(3.17750 + 8.27767i) q^{47} +(-2.68977 - 1.37051i) q^{48} +(4.12628 + 5.65454i) q^{49} +(10.6878 + 1.45765i) q^{50} +(3.35572 + 5.81227i) q^{51} +(-7.70912 - 11.8710i) q^{52} +(2.88373 - 3.56111i) q^{53} +(11.0954 + 4.94001i) q^{54} +(-8.41200 + 4.40084i) q^{55} +(-1.15016 + 3.55240i) q^{56} +(1.57868 - 1.57868i) q^{57} +(12.6587 - 10.2508i) q^{58} +(-4.69130 - 5.21022i) q^{59} +(7.86199 - 0.912006i) q^{60} +(-8.51131 - 7.66362i) q^{61} +(-4.66589 + 2.37739i) q^{62} +(-0.833240 + 3.12270i) q^{63} +(11.5055 - 3.73836i) q^{64} +(-10.9454 - 4.73268i) q^{65} +(-9.07741 + 8.17334i) q^{66} +(3.28790 - 8.56528i) q^{67} +(-12.9024 - 3.45719i) q^{68} +(1.72317 + 1.25195i) q^{69} +(3.44866 + 12.2883i) q^{70} +(11.8782 - 8.63004i) q^{71} +(-1.60949 + 0.617824i) q^{72} +(-2.58291 + 1.67736i) q^{73} +(-6.50688 - 3.75675i) q^{74} +(5.09038 - 4.30684i) q^{75} +4.44344i q^{76} +(-8.73705 - 7.06008i) q^{77} +(-15.1540 - 2.40015i) q^{78} +(-3.71304 + 8.33963i) q^{79} +(3.14293 - 3.96778i) q^{80} +(3.51084 - 1.56313i) q^{81} +(-2.13480 + 7.96717i) q^{82} +(-0.313217 + 0.0496087i) q^{83} +(4.69084 + 8.10528i) q^{84} +(-10.6645 + 3.59249i) q^{85} +(8.57682 - 9.52553i) q^{86} +(0.526966 - 10.0551i) q^{87} +(0.313594 - 5.98373i) q^{88} +(-3.99368 + 4.43543i) q^{89} +(-3.41218 + 4.80440i) q^{90} +(-0.0146888 - 14.1096i) q^{91} +(-4.18698 + 0.663153i) q^{92} +(-0.837814 + 3.12676i) q^{93} +(-17.4746 + 7.78021i) q^{94} +(2.07252 + 3.11740i) q^{95} +(4.17995 - 9.38833i) q^{96} +(-4.27210 - 0.676635i) q^{97} +(-11.7162 + 9.52809i) q^{98} -5.18637i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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