LMFDB - Embedded newform 504.2.cs.b.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40280 + 0.179343i) q^{2} +(-0.897491 + 1.48139i) q^{3} +(1.93567 - 0.503164i) q^{4} +(0.991981 + 0.572721i) q^{5} +(0.993320 - 2.23904i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-2.62511 + 1.05299i) q^{8} +(-1.38902 - 2.65906i) q^{9} +O(q^{10})$	\(q+(-1.40280 + 0.179343i) q^{2} +(-0.897491 + 1.48139i) q^{3} +(1.93567 - 0.503164i) q^{4} +(0.991981 + 0.572721i) q^{5} +(0.993320 - 2.23904i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-2.62511 + 1.05299i) q^{8} +(-1.38902 - 2.65906i) q^{9} +(-1.49426 - 0.625505i) q^{10} +(-0.474092 + 0.273717i) q^{11} +(-0.991867 + 3.31907i) q^{12} +(-5.32075 - 3.07193i) q^{13} +(0.856714 + 1.12519i) q^{14} +(-1.73872 + 0.955498i) q^{15} +(3.49365 - 1.94792i) q^{16} -1.96209 q^{17} +(2.42540 + 3.48101i) q^{18} +1.47740i q^{19} +(2.20832 + 0.609470i) q^{20} +(1.73166 + 0.0365561i) q^{21} +(0.615965 - 0.468994i) q^{22} +(-3.27889 + 5.67921i) q^{23} +(0.796135 - 4.83386i) q^{24} +(-1.84398 - 3.19387i) q^{25} +(8.01485 + 3.35506i) q^{26} +(5.18574 + 0.328809i) q^{27} +(-1.40359 - 1.42476i) q^{28} +(-7.59962 + 4.38764i) q^{29} +(2.26770 - 1.65219i) q^{30} +(2.91073 - 5.04154i) q^{31} +(-4.55153 + 3.35910i) q^{32} +(0.0200121 - 0.947973i) q^{33} +(2.75242 - 0.351888i) q^{34} -1.14544i q^{35} +(-4.02663 - 4.44817i) q^{36} -7.77794i q^{37} +(-0.264961 - 2.07249i) q^{38} +(9.32605 - 5.12506i) q^{39} +(-3.20713 - 0.458914i) q^{40} +(3.71515 - 6.43483i) q^{41} +(-2.43573 + 0.259282i) q^{42} +(-8.28148 + 4.78131i) q^{43} +(-0.779962 + 0.768372i) q^{44} +(0.145020 - 3.43326i) q^{45} +(3.58109 - 8.55481i) q^{46} +(-2.23352 - 3.86857i) q^{47} +(-0.249895 + 6.92369i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(3.15953 + 4.14964i) q^{50} +(1.76096 - 2.90662i) q^{51} +(-11.8449 - 3.26905i) q^{52} -11.1630i q^{53} +(-7.33350 + 0.468775i) q^{54} -0.627054 q^{55} +(2.22447 + 1.74692i) q^{56} +(-2.18860 - 1.32595i) q^{57} +(9.87382 - 7.51791i) q^{58} +(7.23203 + 4.17541i) q^{59} +(-2.88481 + 2.72439i) q^{60} +(-4.76156 + 2.74909i) q^{61} +(-3.17900 + 7.59427i) q^{62} +(-1.60831 + 2.53246i) q^{63} +(5.78244 - 5.52842i) q^{64} +(-3.51872 - 6.09460i) q^{65} +(0.141940 + 1.33340i) q^{66} +(-3.02552 - 1.74679i) q^{67} +(-3.79797 + 0.987255i) q^{68} +(-5.47033 - 9.95435i) q^{69} +(0.205427 + 1.60682i) q^{70} -5.49334 q^{71} +(6.44629 + 5.51773i) q^{72} +10.0249 q^{73} +(1.39492 + 10.9109i) q^{74} +(6.38632 + 0.134818i) q^{75} +(0.743374 + 2.85976i) q^{76} +(0.474092 + 0.273717i) q^{77} +(-12.1634 + 8.86197i) q^{78} +(0.890337 + 1.54211i) q^{79} +(4.58125 + 0.0685859i) q^{80} +(-5.14125 + 7.38699i) q^{81} +(-4.05755 + 9.69304i) q^{82} +(-9.70504 + 5.60321i) q^{83} +(3.37033 - 0.800551i) q^{84} +(-1.94636 - 1.12373i) q^{85} +(10.7597 - 8.19243i) q^{86} +(0.320790 - 15.1959i) q^{87} +(0.956325 - 1.21775i) q^{88} -1.94805 q^{89} +(0.412300 + 4.84218i) q^{90} +6.14387i q^{91} +(-3.48929 + 12.6429i) q^{92} +(4.85612 + 8.83666i) q^{93} +(3.82698 + 5.02625i) q^{94} +(-0.846137 + 1.46555i) q^{95} +(-0.891166 - 9.75735i) q^{96} +(7.50375 + 12.9969i) q^{97} +(0.546082 - 1.30453i) q^{98} +(1.38635 + 0.880442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.40280	+	0.179343i	−0.991926	+	0.126815i
$2$	−1.40280	+	0.179343i	−0.991926	+	0.126815i
$3$	−0.897491	+	1.48139i	−0.518167	+	0.855280i
$3$	−0.897491	+	1.48139i	−0.518167	+	0.855280i
$4$	1.93567	−	0.503164i	0.967836	−	0.251582i
$5$	0.991981	+	0.572721i	0.443628	+	0.256129i	0.705135	−	0.709073i	$-0.250886\pi$
$5$	0.991981	+	0.572721i	0.443628	+	0.256129i	−0.261508	+	0.965201i	$0.584220\pi$
$6$	0.993320	−	2.23904i	0.405521	−	0.914086i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−2.62511	+	1.05299i	−0.928118	+	0.372287i
$9$	−1.38902	−	2.65906i	−0.463007	−	0.886355i
$10$	−1.49426	−	0.625505i	−0.472527	−	0.197802i
$11$	−0.474092	+	0.273717i	−0.142944	+	0.0825288i	−0.569766	−	0.821807i	$-0.692966\pi$
$11$	−0.474092	+	0.273717i	−0.142944	+	0.0825288i	0.426822	+	0.904336i	$0.359633\pi$
$12$	−0.991867	+	3.31907i	−0.286327	+	0.958132i
$13$	−5.32075	−	3.07193i	−1.47571	−	0.852001i	−0.476085	−	0.879399i	$-0.657945\pi$
$13$	−5.32075	−	3.07193i	−1.47571	−	0.852001i	−0.999625	+	0.0273978i	$0.991278\pi$
$14$	0.856714	+	1.12519i	0.228966	+	0.300718i
$15$	−1.73872	+	0.955498i	−0.448935	+	0.246708i
$16$	3.49365	−	1.94792i	0.873413	−	0.486980i
$17$	−1.96209			−0.475878			−0.237939	−	0.971280i	$-0.576472\pi$
$17$	−1.96209			−0.475878			−0.237939	+	0.971280i	$0.576472\pi$
$18$	2.42540	+	3.48101i	0.571671	+	0.820483i
$19$			1.47740i			0.338938i	0.985535	+	0.169469i	$0.0542053\pi$
$19$			1.47740i			0.338938i	−0.985535	+	0.169469i	$0.945795\pi$
$20$	2.20832	+	0.609470i	0.493796	+	0.136282i
$21$	1.73166	+	0.0365561i	0.377880	+	0.00797719i
$22$	0.615965	−	0.468994i	0.131324	−	0.0999899i
$23$	−3.27889	+	5.67921i	−0.683696	+	1.18420i	0.290149	+	0.956982i	$0.406295\pi$
$23$	−3.27889	+	5.67921i	−0.683696	+	1.18420i	−0.973845	+	0.227215i	$0.927038\pi$
$24$	0.796135	−	4.83386i	0.162510	−	0.986707i
$25$	−1.84398	−	3.19387i	−0.368796	−	0.638774i
$26$	8.01485	+	3.35506i	1.57184	+	0.657981i
$27$	5.18574	+	0.328809i	0.997996	+	0.0632794i
$28$	−1.40359	−	1.42476i	−0.265253	−	0.269254i
$29$	−7.59962	+	4.38764i	−1.41121	+	0.814765i	−0.995503	−	0.0947315i	$-0.969801\pi$
$29$	−7.59962	+	4.38764i	−1.41121	+	0.814765i	−0.415712	+	0.909497i	$0.636467\pi$
$30$	2.26770	−	1.65219i	0.414024	−	0.301648i
$31$	2.91073	−	5.04154i	0.522783	−	0.905487i	−0.476865	−	0.878976i	$-0.658227\pi$
$31$	2.91073	−	5.04154i	0.522783	−	0.905487i	0.999649	−	0.0265106i	$-0.00843958\pi$
$32$	−4.55153	+	3.35910i	−0.804605	+	0.593810i
$33$	0.0200121	−	0.947973i	0.00348365	−	0.165021i
$34$	2.75242	−	0.351888i	0.472036	−	0.0603483i
$35$		−	1.14544i		−	0.193615i
$36$	−4.02663	−	4.44817i	−0.671105	−	0.741362i
$37$		−	7.77794i		−	1.27868i	−0.768922	−	0.639342i	$-0.779207\pi$
$37$		−	7.77794i		−	1.27868i	0.768922	−	0.639342i	$-0.220793\pi$
$38$	−0.264961	−	2.07249i	−0.0429824	−	0.336202i
$39$	9.32605	−	5.12506i	1.49336	−	0.820666i
$40$	−3.20713	−	0.458914i	−0.507092	−	0.0725607i
$41$	3.71515	−	6.43483i	0.580209	−	1.00495i	−0.415245	−	0.909710i	$-0.636304\pi$
$41$	3.71515	−	6.43483i	0.580209	−	1.00495i	0.995454	−	0.0952420i	$-0.0303625\pi$
$42$	−2.43573	+	0.259282i	−0.375841	+	0.0400080i
$43$	−8.28148	+	4.78131i	−1.26291	+	0.729143i	−0.973637	−	0.228102i	$-0.926748\pi$
$43$	−8.28148	+	4.78131i	−1.26291	+	0.729143i	−0.289276	+	0.957246i	$0.593415\pi$
$44$	−0.779962	+	0.768372i	−0.117584	+	0.115837i
$45$	0.145020	−	3.43326i	0.0216182	−	0.511801i
$46$	3.58109	−	8.55481i	0.528003	−	1.26134i
$47$	−2.23352	−	3.86857i	−0.325793	−	0.564289i	0.655880	−	0.754865i	$-0.272298\pi$
$47$	−2.23352	−	3.86857i	−0.325793	−	0.564289i	−0.981672	+	0.190576i	$0.938964\pi$
$48$	−0.249895	+	6.92369i	−0.0360693	+	0.999349i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	3.15953	+	4.14964i	0.446825	+	0.586848i
$51$	1.76096	−	2.90662i	0.246584	−	0.407008i
$52$	−11.8449	−	3.26905i	−1.64259	−	0.453336i
$53$		−	11.1630i		−	1.53335i	−0.642034	−	0.766676i	$-0.721909\pi$
$53$		−	11.1630i		−	1.53335i	0.642034	−	0.766676i	$-0.278091\pi$
$54$	−7.33350	+	0.468775i	−0.997963	+	0.0637922i
$55$	−0.627054			−0.0845519
$56$	2.22447	+	1.74692i	0.297257	+	0.233442i
$57$	−2.18860	−	1.32595i	−0.289887	−	0.175627i
$58$	9.87382	−	7.51791i	1.29650	−	0.987150i
$59$	7.23203	+	4.17541i	0.941530	+	0.543592i	0.890439	−	0.455102i	$-0.150397\pi$
$59$	7.23203	+	4.17541i	0.941530	+	0.543592i	0.0510901	+	0.998694i	$0.483730\pi$
$60$	−2.88481	+	2.72439i	−0.372428	+	0.351717i
$61$	−4.76156	+	2.74909i	−0.609656	+	0.351985i	−0.772831	−	0.634612i	$-0.781160\pi$
$61$	−4.76156	+	2.74909i	−0.609656	+	0.351985i	0.163175	+	0.986597i	$0.447826\pi$
$62$	−3.17900	+	7.59427i	−0.403733	+	0.964473i
$63$	−1.60831	+	2.53246i	−0.202628	+	0.319060i
$64$	5.78244	−	5.52842i	0.722805	−	0.691052i
$65$	−3.51872	−	6.09460i	−0.436444	−	0.755943i
$66$	0.141940	+	1.33340i	0.0174716	+	0.164130i
$67$	−3.02552	−	1.74679i	−0.369626	−	0.213404i	0.303669	−	0.952778i	$-0.401788\pi$
$67$	−3.02552	−	1.74679i	−0.369626	−	0.213404i	−0.673295	+	0.739374i	$0.735122\pi$
$68$	−3.79797	+	0.987255i	−0.460571	+	0.119722i
$69$	−5.47033	−	9.95435i	−0.658551	−	1.19836i
$70$	0.205427	+	1.60682i	0.0245532	+	0.192052i
$71$	−5.49334			−0.651939			−0.325970	−	0.945380i	$-0.605691\pi$
$71$	−5.49334			−0.651939			−0.325970	+	0.945380i	$0.605691\pi$
$72$	6.44629	+	5.51773i	0.759703	+	0.650270i
$73$	10.0249			1.17332			0.586661	−	0.809833i	$-0.300442\pi$
$73$	10.0249			1.17332			0.586661	+	0.809833i	$0.300442\pi$
$74$	1.39492	+	10.9109i	0.162156	+	1.26836i
$75$	6.38632	+	0.134818i	0.737428	+	0.0155674i
$76$	0.743374	+	2.85976i	0.0852708	+	0.328037i
$77$	0.474092	+	0.273717i	0.0540278	+	0.0311930i
$78$	−12.1634	+	8.86197i	−1.37723	+	1.00342i
$79$	0.890337	+	1.54211i	0.100171	+	0.173501i	0.911755	−	0.410735i	$-0.134728\pi$
$79$	0.890337	+	1.54211i	0.100171	+	0.173501i	−0.811584	+	0.584236i	$0.801394\pi$
$80$	4.58125	+	0.0685859i	0.512200	+	0.00766813i
$81$	−5.14125	+	7.38699i	−0.571250	+	0.820776i
$82$	−4.05755	+	9.69304i	−0.448082	+	1.07042i
$83$	−9.70504	+	5.60321i	−1.06527	+	0.615032i	−0.926884	−	0.375347i	$-0.877524\pi$
$83$	−9.70504	+	5.60321i	−1.06527	+	0.615032i	−0.138382	+	0.990379i	$0.544190\pi$
$84$	3.37033	−	0.800551i	0.367733	−	0.0873473i
$85$	−1.94636	−	1.12373i	−0.211112	−	0.121886i
$86$	10.7597	−	8.19243i	1.16025	−	0.883413i
$87$	0.320790	−	15.1959i	0.0343923	−	1.62917i
$88$	0.956325	−	1.21775i	0.101945	−	0.129813i
$89$	−1.94805			−0.206493			−0.103247	−	0.994656i	$-0.532923\pi$
$89$	−1.94805			−0.206493			−0.103247	+	0.994656i	$0.532923\pi$
$90$	0.412300	+	4.84218i	0.0434602	+	0.510410i
$91$			6.14387i			0.644053i
$92$	−3.48929	+	12.6429i	−0.363783	+	1.31811i
$93$	4.85612	+	8.83666i	0.503556	+	0.916319i
$94$	3.82698	+	5.02625i	0.394722	+	0.518418i
$95$	−0.846137	+	1.46555i	−0.0868118	+	0.150362i
$96$	−0.891166	−	9.75735i	−0.0909542	−	0.995855i
$97$	7.50375	+	12.9969i	0.761891	+	1.31963i	0.941875	+	0.335964i	$0.109062\pi$
$97$	7.50375	+	12.9969i	0.761891	+	1.31963i	−0.179984	+	0.983670i	$0.557605\pi$
$98$	0.546082	−	1.30453i	0.0551626	−	0.131777i
$99$	1.38635	+	0.880442i	0.139334	+	0.0884878i
$100$	−5.17638	−	5.25446i	−0.517638	−	0.525446i
$101$	9.35952	−	5.40372i	0.931307	−	0.537690i	0.0440823	−	0.999028i	$-0.485964\pi$
$101$	9.35952	−	5.40372i	0.931307	−	0.537690i	0.887225	+	0.461338i	$0.152630\pi$
$102$	−1.94899	+	4.39321i	−0.192978	+	0.434993i
$103$	3.93931	−	6.82309i	0.388152	−	0.672299i	−0.604049	−	0.796947i	$-0.706447\pi$
$103$	3.93931	−	6.82309i	0.388152	−	0.672299i	0.992201	+	0.124648i	$0.0397803\pi$
$104$	17.2023	+	2.46151i	1.68682	+	0.241370i
$105$	1.69684	+	1.02802i	0.165595	+	0.100325i
$106$	2.00200	+	15.6594i	0.194452	+	1.52097i
$107$			5.73856i			0.554768i	0.960759	+	0.277384i	$0.0894674\pi$
$107$			5.73856i			0.554768i	−0.960759	+	0.277384i	$0.910533\pi$
$108$	10.2033	−	1.97281i	0.981816	−	0.189834i
$109$		−	1.95495i		−	0.187250i	−0.995608	−	0.0936252i	$-0.970154\pi$
$109$		−	1.95495i		−	0.187250i	0.995608	−	0.0936252i	$-0.0298455\pi$
$110$	0.879628	−	0.112458i	0.0838693	−	0.0107224i
$111$	11.5221	+	6.98063i	1.09363	+	0.662572i
$112$	−3.43377	−	2.05163i	−0.324461	−	0.193861i
$113$	−7.39939	+	12.8161i	−0.696076	+	1.20564i	0.273741	+	0.961804i	$0.411739\pi$
$113$	−7.39939	+	12.8161i	−0.696076	+	1.20564i	−0.969817	+	0.243836i	$0.921594\pi$
$114$	3.30796	+	1.46753i	0.309819	+	0.137447i
$115$	−6.50520	+	3.75578i	−0.606613	+	0.350228i
$116$	−12.5027	+	12.3169i	−1.16084	+	1.14359i
$117$	−0.777850	+	18.4152i	−0.0719122	+	1.70248i
$118$	−10.8939	−	4.56024i	−1.00286	−	0.419804i
$119$	0.981047	+	1.69922i	0.0899324	+	0.155768i
$120$	3.55820	−	4.33913i	0.324818	−	0.396107i
$121$	−5.35016	+	9.26675i	−0.486378	+	0.842431i
$122$	6.18647	−	4.71037i	0.560097	−	0.426456i
$123$	6.19816	+	11.2788i	0.558870	+	1.01697i
$124$	3.09750	−	11.2233i	0.278164	−	1.00789i
$125$		−	9.95155i		−	0.890094i
$126$	1.80195	−	3.84096i	0.160530	−	0.342180i
$127$	−0.630502			−0.0559480			−0.0279740	−	0.999609i	$-0.508906\pi$
$127$	−0.630502			−0.0559480			−0.0279740	+	0.999609i	$0.508906\pi$
$128$	−7.12010	+	8.79228i	−0.629334	+	0.777135i
$129$	0.349572	−	16.5593i	0.0307781	−	1.45796i
$130$	6.02907	+	7.91843i	0.528785	+	0.694492i
$131$	6.41115	+	3.70148i	0.560144	+	0.323400i	0.753203	−	0.657788i	$-0.228508\pi$
$131$	6.41115	+	3.70148i	0.560144	+	0.323400i	−0.193059	+	0.981187i	$0.561841\pi$
$132$	−0.438249	−	1.84503i	−0.0381447	−	0.160590i
$133$	1.27946	−	0.738699i	0.110944	−	0.0640534i
$134$	4.55746	+	1.90778i	0.393705	+	0.164807i
$135$	4.95584	+	3.29615i	0.426531	+	0.283688i
$136$	5.15072	−	2.06606i	0.441670	−	0.177163i
$137$	−5.21818	−	9.03816i	−0.445820	−	0.772182i	0.552289	−	0.833652i	$-0.313754\pi$
$137$	−5.21818	−	9.03816i	−0.445820	−	0.772182i	−0.998109	+	0.0614704i	$0.980421\pi$
$138$	9.45900	+	12.9828i	0.805204	+	1.10517i
$139$	−8.45543	−	4.88174i	−0.717180	−	0.414064i	0.0965340	−	0.995330i	$-0.469224\pi$
$139$	−8.45543	−	4.88174i	−0.717180	−	0.414064i	−0.813714	+	0.581266i	$0.802558\pi$
$140$	−0.576345	−	2.21720i	−0.0487100	−	0.187388i
$141$	7.73542	+	0.163298i	0.651440	+	0.0137521i
$142$	7.70603	−	0.985193i	0.646676	−	0.0826755i
$143$	3.36336			0.281259
$144$	−10.0324	−	6.58415i	−0.836033	−	0.548679i
$145$	−10.0516			−0.834738
$146$	−14.0628	+	1.79789i	−1.16385	+	0.148795i
$147$	−0.834174	−	1.51794i	−0.0688015	−	0.125198i
$148$	−3.91358	−	15.0555i	−0.321694	−	1.23756i
$149$	−13.2094	−	7.62646i	−1.08216	−	0.624784i	−0.150680	−	0.988583i	$-0.548146\pi$
$149$	−13.2094	−	7.62646i	−1.08216	−	0.624784i	−0.931478	+	0.363798i	$0.881480\pi$
$150$	−8.98288	+	0.956222i	−0.733449	+	0.0780752i
$151$	6.48770	+	11.2370i	0.527962	+	0.914456i	0.999469	+	0.0325941i	$0.0103769\pi$
$151$	6.48770	+	11.2370i	0.527962	+	0.914456i	−0.471507	+	0.881862i	$0.656290\pi$
$152$	−1.55568	−	3.87834i	−0.126182	−	0.314575i
$153$	2.72539	+	5.21733i	0.220334	+	0.421796i
$154$	−0.714143	−	0.298944i	−0.0575473	−	0.0240896i
$155$	5.77479	−	3.33407i	0.463842	−	0.267799i
$156$	15.4734	−	14.6130i	1.23887	−	1.16997i
$157$	0.498395	+	0.287749i	0.0397763	+	0.0229648i	0.519756	−	0.854315i	$-0.326023\pi$
$157$	0.498395	+	0.287749i	0.0397763	+	0.0229648i	−0.479980	+	0.877279i	$0.659356\pi$
$158$	−1.52553	−	2.00359i	−0.121365	−	0.159397i
$159$	16.5367	+	10.0187i	1.31145	+	0.794532i
$160$	−6.43886	+	0.725405i	−0.509037	+	0.0573483i
$161$	6.55778			0.516826
$162$	5.88731	−	11.2845i	0.462551	−	0.886593i
$163$			0.509984i			0.0399450i	0.999801	+	0.0199725i	$0.00635787\pi$
$163$			0.509984i			0.0399450i	−0.999801	+	0.0199725i	$0.993642\pi$
$164$	3.95354	−	14.3250i	0.308719	−	1.11860i
$165$	0.562775	−	0.928910i	0.0438120	−	0.0723155i
$166$	12.6093	−	9.60069i	0.978671	−	0.745158i
$167$	−3.16594	+	5.48357i	−0.244988	+	0.424331i	−0.962128	−	0.272597i	$-0.912117\pi$
$167$	−3.16594	+	5.48357i	−0.244988	+	0.424331i	0.717140	+	0.696929i	$0.245451\pi$
$168$	−4.58431	+	1.72746i	−0.353687	+	0.133276i
$169$	12.3736	+	21.4316i	0.951813	+	1.64859i
$170$	2.93188	+	1.22730i	0.224865	+	0.0941296i
$171$	3.92850	−	2.05214i	0.300420	−	0.156931i
$172$	−13.6244	+	13.4220i	−1.03885	+	1.02342i
$173$	−7.32658	+	4.23000i	−0.557030	+	0.321601i	−0.751952	−	0.659217i	$-0.770888\pi$
$173$	−7.32658	+	4.23000i	−0.557030	+	0.321601i	0.194923	+	0.980819i	$0.437554\pi$
$174$	2.27527	+	21.3742i	0.172488	+	1.62038i
$175$	−1.84398	+	3.19387i	−0.139392	+	0.241434i
$176$	−1.12313	+	1.87977i	−0.0846593	+	0.141693i
$177$	−12.6761	+	6.96604i	−0.952793	+	0.523600i
$178$	2.73272	−	0.349370i	0.204826	−	0.0261864i
$179$		−	16.7632i		−	1.25294i	−0.779444	−	0.626472i	$-0.784498\pi$
$179$		−	16.7632i		−	1.25294i	0.779444	−	0.626472i	$-0.215502\pi$
$180$	−1.44678	−	6.71864i	−0.107837	−	0.500778i
$181$			9.14129i			0.679467i	0.940522	+	0.339733i	$0.110337\pi$
$181$			9.14129i			0.679467i	−0.940522	+	0.339733i	$0.889663\pi$
$182$	−1.10186	−	8.61859i	−0.0816754	−	0.638853i
$183$	0.200992	−	9.52100i	0.0148578	−	0.703813i
$184$	2.62734	−	18.3612i	0.193690	−	1.35360i
$185$	4.45459	−	7.71557i	0.327508	−	0.567260i
$186$	−8.39693	−	11.5251i	−0.615693	−	0.845063i
$187$	0.930213	−	0.537059i	0.0680239	−	0.0392736i
$188$	−6.26989	−	6.36446i	−0.457279	−	0.464176i
$189$	−2.30811	−	4.65539i	−0.167890	−	0.338630i
$190$	0.924120	−	2.20762i	0.0670427	−	0.160158i
$191$	−9.11753	−	15.7920i	−0.659722	−	1.14267i	−0.980688	−	0.195581i	$-0.937341\pi$
$191$	−9.11753	−	15.7920i	−0.659722	−	1.14267i	0.320966	−	0.947091i	$-0.395992\pi$
$192$	3.00004	+	13.5277i	0.216509	+	0.976281i
$193$	−12.7933	+	22.1587i	−0.920883	+	1.59502i	−0.122832	+	0.992428i	$0.539198\pi$
$193$	−12.7933	+	22.1587i	−0.920883	+	1.59502i	−0.798052	+	0.602589i	$0.794136\pi$
$194$	−12.8571	−	16.8862i	−0.923089	−	1.21236i
$195$	12.1865	+	0.257261i	0.872693	+	0.0184229i
$196$	−0.532083	+	1.92792i	−0.0380059	+	0.137709i
$197$			4.24236i			0.302255i	0.988514	+	0.151128i	$0.0482905\pi$
$197$			4.24236i			0.302255i	−0.988514	+	0.151128i	$0.951710\pi$
$198$	−2.10267	−	0.986448i	−0.149430	−	0.0701038i
$199$	−4.91294			−0.348269			−0.174134	−	0.984722i	$-0.555713\pi$
$199$	−4.91294			−0.348269			−0.174134	+	0.984722i	$0.555713\pi$
$200$	8.20376	+	6.44258i	0.580094	+	0.455560i
$201$	5.30305	−	2.91425i	0.374048	−	0.205555i
$202$	−12.1604	+	9.25888i	−0.855601	+	0.651453i
$203$	7.59962	+	4.38764i	0.533389	+	0.307952i
$204$	1.94614	−	6.51232i	0.136257	−	0.455954i
$205$	7.37072	−	4.25549i	0.514793	−	0.297216i
$206$	−4.30237	+	10.2779i	−0.299761	+	0.716094i
$207$	19.6558	+	0.830253i	1.36617	+	0.0577066i
$208$	−24.5727	−	0.367878i	−1.70381	−	0.0255077i
$209$	−0.404389	−	0.700423i	−0.0279722	−	0.0484493i
$210$	−2.56469	−	1.13779i	−0.176981	−	0.0785149i
$211$	12.8264	+	7.40533i	0.883006	+	0.509804i	0.871648	−	0.490132i	$-0.163051\pi$
$211$	12.8264	+	7.40533i	0.883006	+	0.509804i	0.0113578	+	0.999935i	$0.496385\pi$
$212$	−5.61681	−	21.6079i	−0.385764	−	1.48403i
$213$	4.93022	−	8.13776i	0.337813	−	0.557590i
$214$	−1.02917	−	8.05003i	−0.0703528	−	0.550289i
$215$	−10.9534			−0.747018
$216$	−13.9594	+	4.59735i	−0.949816	+	0.312810i
$217$	−5.82147			−0.395187
$218$	0.350607	+	2.74240i	0.0237461	+	0.185739i
$219$	−8.99722	+	14.8507i	−0.607976	+	1.00352i
$220$	−1.21377	+	0.315511i	−0.0818324	+	0.0212717i
$221$	10.4398	+	6.02742i	0.702257	+	0.405448i
$222$	−17.4151	−	7.72598i	−1.16883	−	0.518534i
$223$	−8.23914	−	14.2706i	−0.551734	−	0.955631i	−0.998150	−	0.0608053i	$-0.980633\pi$
$223$	−8.23914	−	14.2706i	−0.551734	−	0.955631i	0.446416	−	0.894826i	$-0.352700\pi$
$224$	5.18483	+	2.26220i	0.346426	+	0.151149i
$225$	−5.93138	+	9.33962i	−0.395425	+	0.622641i
$226$	8.08135	−	19.3054i	0.537563	−	1.28418i
$227$	−7.53645	+	4.35117i	−0.500212	+	0.288797i	−0.728801	−	0.684726i	$-0.759922\pi$
$227$	−7.53645	+	4.35117i	−0.500212	+	0.288797i	0.228589	+	0.973523i	$0.426589\pi$
$228$	−4.90358	−	1.46538i	−0.324748	−	0.0970474i
$229$	−0.700847	−	0.404634i	−0.0463133	−	0.0267390i	0.476665	−	0.879085i	$-0.341846\pi$
$229$	−0.700847	−	0.404634i	−0.0463133	−	0.0267390i	−0.522978	+	0.852346i	$0.675179\pi$
$230$	8.45189	−	6.43525i	0.557301	−	0.424328i
$231$	−0.830974	+	0.456655i	−0.0546741	+	0.0300457i
$232$	15.3297	−	19.5204i	1.00645	−	1.28157i
$233$	2.64009			0.172958			0.0864789	−	0.996254i	$-0.472438\pi$
$233$	2.64009			0.172958			0.0864789	+	0.996254i	$0.472438\pi$
$234$	−2.21148	−	25.9723i	−0.144569	−	1.69786i
$235$		−	5.11674i		−	0.333779i
$236$	16.0997	+	4.44333i	1.04800	+	0.289236i
$237$	−3.08353	−	0.0650945i	−0.200297	−	0.00422834i
$238$	−1.68095	−	2.20772i	−0.108960	−	0.143105i
$239$	−13.2905	+	23.0198i	−0.859689	+	1.48902i	0.0125372	+	0.999921i	$0.496009\pi$
$239$	−13.2905	+	23.0198i	−0.859689	+	1.48902i	−0.872226	+	0.489103i	$0.837324\pi$
$240$	−4.21324	+	6.72506i	−0.271963	+	0.434101i
$241$	2.38158	+	4.12501i	0.153411	+	0.265716i	0.932479	−	0.361223i	$-0.117641\pi$
$241$	2.38158	+	4.12501i	0.153411	+	0.265716i	−0.779068	+	0.626939i	$0.784308\pi$
$242$	5.84325	−	13.9589i	0.375618	−	0.897310i
$243$	−6.32877	−	14.2459i	−0.405991	−	0.913877i
$244$	−7.83358	+	7.71718i	−0.501494	+	0.494042i
$245$	−0.991981	+	0.572721i	−0.0633754	+	0.0365898i
$246$	−10.7175	−	14.7102i	−0.683325	−	0.937890i
$247$	4.53847	−	7.86086i	0.288776	−	0.500175i
$248$	−2.33234	+	16.2996i	−0.148103	+	1.03502i
$249$	0.409663	−	19.4058i	0.0259613	−	1.22979i
$250$	1.78474	+	13.9600i	0.112877	+	0.882908i
$251$		−	9.95248i		−	0.628195i	−0.949391	−	0.314097i	$-0.898298\pi$
$251$		−	9.95248i		−	0.628195i	0.949391	−	0.314097i	$-0.101702\pi$
$252$	−1.83891	+	5.71125i	−0.115841	+	0.359775i
$253$		−	3.58995i		−	0.225698i
$254$	0.884465	−	0.113076i	0.0554963	−	0.00709503i
$255$	3.41152	−	1.87478i	0.213638	−	0.117403i
$256$	8.41121	−	13.6107i	0.525701	−	0.850670i
$257$	8.92012	−	15.4501i	0.556422	−	0.963751i	−0.441370	−	0.897325i	$-0.645507\pi$
$257$	8.92012	−	15.4501i	0.556422	−	0.963751i	0.997791	−	0.0664255i	$-0.0211595\pi$
$258$	2.47941	+	23.2920i	0.154362	+	1.45009i
$259$	−6.73589	+	3.88897i	−0.418548	+	0.241649i
$260$	−9.87768	−	10.0267i	−0.612587	−	0.621827i
$261$	22.2231	+	14.1134i	1.37557	+	0.873595i
$262$	−9.65736	−	4.04262i	−0.596634	−	0.249754i
$263$	6.36165	+	11.0187i	0.392276	+	0.679443i	0.992749	−	0.120202i	$-0.0383544\pi$
$263$	6.36165	+	11.0187i	0.392276	+	0.679443i	−0.600473	+	0.799645i	$0.705021\pi$
$264$	0.945668	+	2.50961i	0.0582018	+	0.154456i
$265$	6.39327	−	11.0735i	0.392735	−	0.680237i
$266$	−1.66235	+	1.26571i	−0.101925	+	0.0776055i
$267$	1.74836	−	2.88582i	0.106998	−	0.176610i
$268$	−6.73534	−	1.85887i	−0.411426	−	0.113549i
$269$		−	17.7810i		−	1.08413i	−0.840337	−	0.542065i	$-0.817643\pi$
$269$		−	17.7810i		−	1.08413i	0.840337	−	0.542065i	$-0.182357\pi$
$270$	−7.54317	−	3.73503i	−0.459063	−	0.227307i
$271$	−26.2023			−1.59167			−0.795837	−	0.605511i	$-0.792969\pi$
$271$	−26.2023			−1.59167			−0.795837	+	0.605511i	$0.792969\pi$
$272$	−6.85487	+	3.82200i	−0.415638	+	0.231743i
$273$	−9.10145	−	5.51407i	−0.550845	−	0.333727i
$274$	8.94098	+	11.7428i	0.540144	+	0.709411i
$275$	1.74843	+	1.00946i	0.105435	+	0.0608726i
$276$	−15.5974	−	16.5159i	−0.938855	−	0.994139i
$277$	1.16334	−	0.671653i	0.0698982	−	0.0403557i	−0.464644	−	0.885498i	$-0.653818\pi$
$277$	1.16334	−	0.671653i	0.0698982	−	0.0403557i	0.534542	+	0.845142i	$0.320484\pi$
$278$	12.7367	+	5.33166i	0.763899	+	0.319772i
$279$	−17.4488	−	0.737032i	−1.04463	−	0.0441249i
$280$	1.20613	+	3.00691i	0.0720803	+	0.179697i
$281$	−0.780520	−	1.35190i	−0.0465619	−	0.0806476i	0.841805	−	0.539781i	$-0.181493\pi$
$281$	−0.780520	−	1.35190i	−0.0465619	−	0.0806476i	−0.888367	+	0.459134i	$0.848160\pi$
$282$	−10.8805	+	1.15822i	−0.647924	+	0.0689711i
$283$	23.5485	+	13.5957i	1.39981	+	0.808183i	0.994373	−	0.105939i	$-0.0337847\pi$
$283$	23.5485	+	13.5957i	1.39981	+	0.808183i	0.405441	+	0.914121i	$0.367118\pi$
$284$	−10.6333	+	2.76405i	−0.630970	+	0.164016i
$285$	−1.41165	−	2.56878i	−0.0836190	−	0.152161i
$286$	−4.71811	+	0.603197i	−0.278988	+	0.0356678i
$287$	−7.43030			−0.438597
$288$	15.2542	+	7.43697i	0.898864	+	0.438228i
$289$	−13.1502			−0.773540
$290$	14.1003	−	1.80268i	0.827999	−	0.105857i
$291$	−25.9880	−	0.548616i	−1.52344	−	0.0321604i
$292$	19.4048	−	5.04415i	1.13558	−	0.295186i
$293$	−8.08380	−	4.66718i	−0.472260	−	0.272660i	0.244925	−	0.969542i	$-0.421237\pi$
$293$	−8.08380	−	4.66718i	−0.472260	−	0.272660i	−0.717185	+	0.696882i	$0.754570\pi$
$294$	1.44241	+	1.97976i	0.0841230	+	0.115462i
$295$	4.78269	+	8.28386i	0.278459	+	0.482305i
$296$	8.19006	+	20.4180i	0.476037	+	1.18677i
$297$	−2.54852	+	1.26354i	−0.147880	+	0.0733180i
$298$	19.8979	+	8.32935i	1.15265	+	0.482506i
$299$	34.8923	−	20.1451i	2.01787	−	1.16502i
$300$	12.4297	−	2.95240i	0.717626	−	0.170457i
$301$	8.28148	+	4.78131i	0.477336	+	0.275590i
$302$	−11.1162	−	14.5997i	−0.639666	−	0.840120i
$303$	−0.395078	+	18.7149i	−0.0226966	+	1.07514i
$304$	2.87786	+	5.16152i	0.165056	+	0.296033i
$305$	−6.29784			−0.360613
$306$	−4.75886	−	6.83007i	−0.272046	−	0.390449i
$307$		−	26.1141i		−	1.49041i	−0.666836	−	0.745205i	$-0.732352\pi$
$307$		−	26.1141i		−	1.49041i	0.666836	−	0.745205i	$-0.267648\pi$
$308$	1.05541	+	0.291281i	0.0601376	+	0.0165972i
$309$	6.57214	+	11.9593i	0.373876	+	0.680341i
$310$	−7.50290	+	5.71269i	−0.426136	+	0.324459i
$311$	−8.65829	+	14.9966i	−0.490967	+	0.850379i	−0.999946	−	0.0103997i	$-0.996690\pi$
$311$	−8.65829	+	14.9966i	−0.490967	+	0.850379i	0.508979	+	0.860779i	$0.330023\pi$
$312$	−19.0853	+	23.2741i	−1.08049	+	1.31763i
$313$	7.95261	+	13.7743i	0.449508	+	0.778571i	0.998354	−	0.0573525i	$-0.0182659\pi$
$313$	7.95261	+	13.7743i	0.449508	+	0.778571i	−0.548846	+	0.835924i	$0.684933\pi$
$314$	−0.750753	−	0.314269i	−0.0423674	−	0.0177352i
$315$	−3.04580	+	1.59104i	−0.171612	+	0.0896450i
$316$	2.49933	+	2.53703i	0.140599	+	0.142719i
$317$	7.12538	−	4.11384i	0.400201	−	0.231056i	−0.286370	−	0.958119i	$-0.592448\pi$
$317$	7.12538	−	4.11384i	0.400201	−	0.231056i	0.686571	+	0.727063i	$0.259115\pi$
$318$	−24.9944	−	11.0884i	−1.40162	−	0.621807i
$319$	2.40195	−	4.16029i	0.134483	−	0.232932i
$320$	8.90231	−	2.17236i	0.497654	−	0.121439i
$321$	−8.50104	−	5.15031i	−0.474482	−	0.287462i
$322$	−9.19923	+	1.17609i	−0.512653	+	0.0655412i
$323$		−	2.89879i		−	0.161293i
$324$	−6.23490	+	16.8857i	−0.346384	+	0.938093i
$325$			22.6584i			1.25686i
$326$	−0.0914621	−	0.715403i	−0.00506562	−	0.0396225i
$327$	2.89604	+	1.75455i	0.160151	+	0.0970269i
$328$	−2.97691	+	20.8042i	−0.164372	+	1.14872i
$329$	−2.23352	+	3.86857i	−0.123138	+	0.213281i
$330$	−0.622865	+	1.40400i	−0.0342876	+	0.0772877i
$331$	−9.14708	+	5.28107i	−0.502769	+	0.290274i	−0.729856	−	0.683601i	$-0.760413\pi$
$331$	−9.14708	+	5.28107i	−0.502769	+	0.290274i	0.227087	+	0.973874i	$0.427080\pi$
$332$	−15.9664	+	15.7292i	−0.876272	+	0.863252i
$333$	−20.6820	+	10.8037i	−1.13337	+	0.592039i
$334$	3.45773	−	8.26012i	0.189198	−	0.451974i
$335$	−2.00084	−	3.46556i	−0.109318	−	0.189344i
$336$	6.12104	−	3.24543i	0.333930	−	0.177053i
$337$	16.9160	−	29.2993i	0.921472	−	1.59604i	0.124334	−	0.992240i	$-0.460321\pi$
$337$	16.9160	−	29.2993i	0.921472	−	1.59604i	0.797138	−	0.603797i	$-0.206346\pi$
$338$	−21.2012	−	27.8451i	−1.15319	−	1.51457i
$339$	−12.3448	−	22.4637i	−0.670475	−	1.22006i
$340$	−4.33294	−	1.19584i	−0.234986	−	0.0648534i
$341$			3.18687i			0.172579i
$342$	−5.14284	+	3.58328i	−0.278093	+	0.193761i
$343$	1.00000			0.0539949
$344$	16.7052	−	21.2718i	0.900682	−	1.14690i
$345$	0.274593	−	13.0075i	0.0147836	−	0.700300i
$346$	9.51907	−	7.24780i	0.511749	−	0.389644i
$347$	12.0087	+	6.93321i	0.644660	+	0.372194i	0.786407	−	0.617708i	$-0.211939\pi$
$347$	12.0087	+	6.93321i	0.644660	+	0.372194i	−0.141748	+	0.989903i	$0.545272\pi$
$348$	−7.02506	−	29.5756i	−0.376583	−	1.58542i
$349$	22.8045	−	13.1662i	1.22070	−	0.704769i	0.255629	−	0.966775i	$-0.417717\pi$
$349$	22.8045	−	13.1662i	1.22070	−	0.704769i	0.965066	+	0.262006i	$0.0843841\pi$
$350$	2.01393	−	4.81105i	0.107649	−	0.257162i
$351$	−26.5819	−	17.6798i	−1.41884	−	0.943676i
$352$	1.23840	−	2.83835i	0.0660071	−	0.151285i
$353$	1.23661	+	2.14187i	0.0658182	+	0.114000i	0.897057	−	0.441916i	$-0.145701\pi$
$353$	1.23661	+	2.14187i	0.0658182	+	0.114000i	−0.831238	+	0.555916i	$0.812368\pi$
$354$	16.5326	−	12.0453i	0.878700	−	0.640201i
$355$	−5.44929	−	3.14615i	−0.289218	−	0.166980i
$356$	−3.77079	+	0.980191i	−0.199852	+	0.0519500i
$357$	−3.39769	−	0.0717265i	−0.179825	−	0.00379617i
$358$	3.00638	+	23.5154i	0.158892	+	1.24283i
$359$	14.0737			0.742779			0.371390	−	0.928477i	$-0.378881\pi$
$359$	14.0737			0.742779			0.371390	+	0.928477i	$0.378881\pi$
$360$	3.23449	+	9.16541i	0.170472	+	0.483059i
$361$	16.8173			0.885121
$362$	−1.63943	−	12.8234i	−0.0861665	−	0.673981i
$363$	−8.92593	−	16.2425i	−0.468490	−	0.852509i
$364$	3.09137	+	11.8925i	0.162032	+	0.623337i
$365$	9.94448	+	5.74145i	0.520518	+	0.300521i
$366$	1.42558	+	13.3921i	0.0745161	+	0.700015i
$367$	−7.56697	−	13.1064i	−0.394992	−	0.684147i	0.598108	−	0.801416i	$-0.295919\pi$
$367$	−7.56697	−	13.1064i	−0.394992	−	0.684147i	−0.993100	+	0.117269i	$0.962586\pi$
$368$	−0.392662	+	26.2282i	−0.0204689	+	1.36724i
$369$	−22.2710	−	0.940719i	−1.15938	−	0.0489719i
$370$	−4.86514	+	11.6223i	−0.252926	+	0.604213i
$371$	−9.66742	+	5.58149i	−0.501907	+	0.289776i
$372$	13.8461	+	14.6615i	0.717889	+	0.760161i
$373$	0.419793	+	0.242368i	0.0217361	+	0.0125493i	0.510829	−	0.859683i	$-0.329339\pi$
$373$	0.419793	+	0.242368i	0.0217361	+	0.0125493i	−0.489093	+	0.872232i	$0.662672\pi$
$374$	−1.20858	+	0.920211i	−0.0624942	+	0.0475830i
$375$	14.7421	+	8.93143i	0.761279	+	0.461217i
$376$	9.93680	+	7.80357i	0.512451	+	0.402439i
$377$	53.9142			2.77672
$378$	4.07272	+	6.11661i	0.209478	+	0.314605i
$379$		−	5.49156i		−	0.282083i	−0.990004	−	0.141041i	$-0.954955\pi$
$379$		−	5.49156i		−	0.282083i	0.990004	−	0.141041i	$-0.0450450\pi$
$380$	−0.900430	+	3.26257i	−0.0461911	+	0.167366i
$381$	0.565869	−	0.934017i	0.0289904	−	0.0478512i
$382$	15.6222	+	20.5178i	0.799303	+	1.04978i
$383$	−1.81491	+	3.14351i	−0.0927375	+	0.160626i	−0.908662	−	0.417532i	$-0.862895\pi$
$383$	−1.81491	+	3.14351i	−0.0927375	+	0.160626i	0.815925	+	0.578158i	$0.196228\pi$
$384$	−6.63455	−	18.4386i	−0.338568	−	0.940942i
$385$	0.313527	+	0.543045i	0.0159788	+	0.0276761i
$386$	13.9724	−	33.3785i	0.711177	−	1.69892i
$387$	24.2170	+	15.3796i	1.23102	+	0.781791i
$388$	21.0644	+	21.3821i	1.06938	+	1.08551i
$389$	16.6739	−	9.62670i	0.845402	−	0.488093i	−0.0136945	−	0.999906i	$-0.504359\pi$
$389$	16.6739	−	9.62670i	0.845402	−	0.488093i	0.859097	+	0.511813i	$0.171026\pi$
$390$	−17.1413	+	1.82468i	−0.867983	+	0.0923963i
$391$	6.43349	−	11.1431i	0.325356	−	0.563533i
$392$	0.400644	−	2.79991i	0.0202356	−	0.141417i
$393$	−11.2373	+	6.17535i	−0.566845	+	0.311505i
$394$	−0.760838	−	5.95116i	−0.0383305	−	0.299815i
$395$			2.03966i			0.102626i
$396$	3.12653	+	1.00668i	0.157114	+	0.0505878i
$397$			38.1748i			1.91594i	0.286872	+	0.957969i	$0.407385\pi$
$397$			38.1748i			1.91594i	−0.286872	+	0.957969i	$0.592615\pi$
$398$	6.89185	−	0.881102i	0.345457	−	0.0441657i
$399$	−0.0540079	+	2.55836i	−0.00270378	+	0.128078i
$400$	−12.6636	−	7.56634i	−0.633182	−	0.378317i
$401$	7.03485	−	12.1847i	0.351304	−	0.608476i	−0.635174	−	0.772369i	$-0.719072\pi$
$401$	7.03485	−	12.1847i	0.351304	−	0.608476i	0.986478	+	0.163893i	$0.0524051\pi$
$402$	−6.91644	+	5.03916i	−0.344961	+	0.251330i
$403$	−30.9746	+	17.8832i	−1.54295	+	0.890824i
$404$	15.3980	−	15.1692i	0.766079	−	0.754696i
$405$	−9.33070	+	4.38325i	−0.463646	+	0.217806i
$406$	−11.4476	−	4.79203i	−0.568135	−	0.237824i
$407$	2.12895	+	3.68746i	0.105528	+	0.182780i
$408$	−1.56209	+	9.48448i	−0.0773351	+	0.469552i
$409$	8.83365	−	15.3003i	0.436796	−	0.756552i	−0.560645	−	0.828057i	$-0.689447\pi$
$409$	8.83365	−	15.3003i	0.436796	−	0.756552i	0.997440	+	0.0715042i	$0.0227799\pi$
$410$	−9.57642	+	7.29147i	−0.472946	+	0.360100i
$411$	18.0723	+	0.381513i	0.891440	+	0.0188186i
$412$	4.19208	−	15.1894i	0.206529	−	0.748327i
$413$		−	8.35082i		−	0.410917i
$414$	−27.7220	+	2.36046i	−1.36246	+	0.116010i
$415$	−12.8363			−0.630109
$416$	34.5365	−	3.89090i	1.69329	−	0.190767i
$417$	14.8204	−	8.14444i	0.725759	−	0.398835i
$418$	0.692892	+	0.910026i	0.0338904	+	0.0445108i
$419$	−14.0105	−	8.08898i	−0.684459	−	0.395173i	0.117074	−	0.993123i	$-0.462649\pi$
$419$	−14.0105	−	8.08898i	−0.684459	−	0.395173i	−0.801533	+	0.597951i	$0.795982\pi$
$420$	3.80180	+	1.13613i	0.185509	+	0.0554373i
$421$	7.03405	−	4.06111i	0.342819	−	0.197926i	−0.318699	−	0.947856i	$-0.603246\pi$
$421$	7.03405	−	4.06111i	0.342819	−	0.197926i	0.661518	+	0.749929i	$0.269913\pi$
$422$	−19.3209	−	8.08784i	−0.940528	−	0.393710i
$423$	−7.18438	+	11.3126i	−0.349316	+	0.550037i
$424$	11.7545	+	29.3041i	0.570847	+	1.42313i
$425$	3.61807	+	6.26667i	0.175502	+	0.303978i
$426$	−5.45664	+	12.2998i	−0.264375	+	0.595928i
$427$	4.76156	+	2.74909i	0.230428	+	0.133038i
$428$	2.88744	+	11.1080i	0.139570	+	0.536924i
$429$	−3.01859	+	4.98245i	−0.145739	+	0.240555i
$430$	15.3654	−	1.96442i	0.740987	−	0.0947329i
$431$	8.96113			0.431643			0.215821	−	0.976433i	$-0.430757\pi$
$431$	8.96113			0.431643			0.215821	+	0.976433i	$0.430757\pi$
$432$	18.7577	−	8.95266i	0.902478	−	0.430735i
$433$	25.7964			1.23970			0.619849	−	0.784721i	$-0.287194\pi$
$433$	25.7964			1.23970			0.619849	+	0.784721i	$0.287194\pi$
$434$	8.16633	−	1.04404i	0.391996	−	0.0501156i
$435$	9.02120	−	14.8903i	0.432533	−	0.713935i
$436$	−0.983661	−	3.78414i	−0.0471088	−	0.181228i
$437$	−8.39045	−	4.84423i	−0.401370	−	0.231731i
$438$	9.95789	−	22.4461i	0.475806	−	1.07252i
$439$	−5.35925	−	9.28250i	−0.255783	−	0.443030i	0.709325	−	0.704882i	$-0.249000\pi$
$439$	−5.35925	−	9.28250i	−0.255783	−	0.443030i	−0.965108	+	0.261852i	$0.915667\pi$
$440$	1.64609	−	0.660279i	0.0784741	−	0.0314776i
$441$	2.99733	+	0.126606i	0.142730	+	0.00602885i
$442$	−15.7259	−	6.58294i	−0.748004	−	0.313118i
$443$	−33.1952	+	19.1653i	−1.57715	+	0.910569i	−0.581898	+	0.813262i	$0.697690\pi$
$443$	−33.1952	+	19.1653i	−1.57715	+	0.910569i	−0.995254	+	0.0973073i	$0.968977\pi$
$444$	25.8155	+	7.71468i	1.22515	+	0.366123i
$445$	−1.93243	−	1.11569i	−0.0916062	−	0.0528888i
$446$	14.1172	+	18.5411i	0.668468	+	0.877948i
$447$	23.1531	−	12.7236i	1.09510	−	0.601805i
$448$	−7.67897	−	2.24353i	−0.362797	−	0.105997i
$449$	−19.0365			−0.898388			−0.449194	−	0.893434i	$-0.648289\pi$
$449$	−19.0365			−0.898388			−0.449194	+	0.893434i	$0.648289\pi$
$450$	6.64552	−	14.1653i	0.313273	−	0.667760i
$451$			4.06760i			0.191536i
$452$	−7.87418	+	28.5309i	−0.370370	+	1.34198i
$453$	−22.4691	−	0.474330i	−1.05569	−	0.0222860i
$454$	9.79175	−	7.45542i	0.459550	−	0.349900i
$455$	−3.51872	+	6.09460i	−0.164960	+	0.285719i
$456$	7.14153	+	1.17621i	0.334433	+	0.0550810i
$457$	4.99425	+	8.65030i	0.233621	+	0.404644i	0.958871	−	0.283842i	$-0.0916091\pi$
$457$	4.99425	+	8.65030i	0.233621	+	0.404644i	−0.725250	+	0.688486i	$0.758276\pi$
$458$	1.05571	+	0.441927i	0.0493302	+	0.0206499i
$459$	−10.1749	−	0.645155i	−0.474924	−	0.0301133i
$460$	−10.7022	+	10.5431i	−0.498991	+	0.491576i
$461$	−30.4418	+	17.5756i	−1.41781	+	0.818576i	−0.996107	−	0.0881562i	$-0.971903\pi$
$461$	−30.4418	+	17.5756i	−1.41781	+	0.818576i	−0.421708	+	0.906732i	$0.638569\pi$
$462$	1.08379	−	0.789624i	0.0504224	−	0.0367366i
$463$	−0.284343	+	0.492496i	−0.0132145	+	0.0228882i	−0.872557	−	0.488512i	$-0.837540\pi$
$463$	−0.284343	+	0.492496i	−0.0132145	+	0.0228882i	0.859343	+	0.511400i	$0.170873\pi$
$464$	−18.0037	+	30.1324i	−0.835799	+	1.39886i
$465$	−0.243761	+	11.5470i	−0.0113042	+	0.535479i
$466$	−3.70350	+	0.473482i	−0.171561	+	0.0219336i
$467$		−	5.58011i		−	0.258217i	−0.991630	−	0.129108i	$-0.958788\pi$
$467$		−	5.58011i		−	0.258217i	0.991630	−	0.129108i	$-0.0412115\pi$
$468$	7.76020	+	36.0371i	0.358715	+	1.66582i
$469$			3.49357i			0.161318i
$470$	0.917652	+	7.17774i	0.0423281	+	0.331084i
$471$	−0.873573	+	0.480065i	−0.0402521	+	0.0221202i
$472$	−23.3815	−	3.34571i	−1.07622	−	0.153999i
$473$	2.61745	−	4.53356i	0.120351	−	0.208453i
$474$	4.33724	−	0.461696i	0.199216	−	0.0212064i
$475$	4.71862	−	2.72430i	0.216505	−	0.124999i
$476$	2.75397	+	2.79551i	0.126228	+	0.128132i
$477$	−29.6831	+	15.5056i	−1.35909	+	0.709952i
$478$	14.5154	−	34.6756i	0.663918	−	1.58602i
$479$	12.0799	+	20.9230i	0.551944	+	0.955995i	0.998134	+	0.0610572i	$0.0194472\pi$
$479$	12.0799	+	20.9230i	0.551944	+	0.955995i	−0.446190	+	0.894938i	$0.647219\pi$
$480$	4.70422	−	10.1895i	0.214717	−	0.465085i
$481$	−23.8933	+	41.3844i	−1.08944	+	1.88697i
$482$	−4.08066	−	5.35943i	−0.185869	−	0.244115i
$483$	−5.88555	+	9.71462i	−0.267802	+	0.442030i
$484$	−5.69346	+	20.6294i	−0.258794	+	0.937699i
$485$			17.1902i			0.780568i
$486$	11.4329	+	18.8491i	0.518606	+	0.855013i
$487$	−20.7451			−0.940049			−0.470024	−	0.882653i	$-0.655755\pi$
$487$	−20.7451			−0.940049			−0.470024	+	0.882653i	$0.655755\pi$
$488$	9.60489	−	12.2305i	0.434793	−	0.553650i
$489$	−0.755484	−	0.457706i	−0.0341641	−	0.0206982i
$490$	1.28883	−	0.981315i	0.0582236	−	0.0443313i
$491$	−0.527791	−	0.304721i	−0.0238189	−	0.0137518i	0.488043	−	0.872819i	$-0.337711\pi$
$491$	−0.527791	−	0.304721i	−0.0238189	−	0.0137518i	−0.511862	+	0.859068i	$0.671044\pi$
$492$	17.6727	+	18.7133i	0.796746	+	0.843662i
$493$	14.9112	−	8.60897i	0.671565	−	0.387728i
$494$	−4.95676	+	11.8411i	−0.223015	+	0.532758i
$495$	0.870990	+	1.66738i	0.0391481	+	0.0749430i
$496$	0.348573	−	23.2833i	0.0156514	−	1.04545i
$497$	2.74667	+	4.75737i	0.123205	+	0.213397i
$498$	2.90562	+	27.2958i	0.130204	+	1.22315i
$499$	6.71669	+	3.87788i	0.300680	+	0.173598i	0.642748	−	0.766077i	$-0.277794\pi$
$499$	6.71669	+	3.87788i	0.300680	+	0.173598i	−0.342068	+	0.939675i	$0.611127\pi$
$500$	−5.00726	−	19.2629i	−0.223932	−	0.861465i
$501$	−5.28189	−	9.61144i	−0.235978	−	0.429408i
$502$	1.78491	+	13.9613i	0.0796644	+	0.623123i
$503$	−9.33084			−0.416041			−0.208021	−	0.978124i	$-0.566702\pi$
$503$	−9.33084			−0.416041			−0.208021	+	0.978124i	$0.566702\pi$
$504$	1.55535	−	8.34152i	0.0692806	−	0.371561i
$505$	12.3793			0.550871
$506$	0.643834	+	5.03597i	0.0286219	+	0.223876i
$507$	−42.8537	−	0.904659i	−1.90320	−	0.0401773i
$508$	−1.22044	+	0.317246i	−0.0541485	+	0.0140755i
$509$	8.81997	+	5.09221i	0.390938	+	0.225708i	0.682567	−	0.730823i	$-0.260864\pi$
$509$	8.81997	+	5.09221i	0.390938	+	0.225708i	−0.291628	+	0.956532i	$0.594197\pi$
$510$	−4.44944	+	3.24176i	−0.197025	+	0.143548i
$511$	−5.01243	−	8.68178i	−0.221737	−	0.384059i
$512$	−9.35822	+	20.6015i	−0.413579	+	0.910468i
$513$	−0.485783	+	7.66140i	−0.0214478	+	0.338259i
$514$	−9.74224	+	23.2731i	−0.429712	+	1.02653i
$515$	7.81544	−	4.51225i	0.344390	−	0.198833i
$516$	−7.65537	−	32.2292i	−0.337009	−	1.41881i
$517$	2.11779	+	1.22271i	0.0931402	+	0.0537745i
$518$	8.75162	−	6.66346i	0.384524	−	0.292776i
$519$	0.309265	−	14.6499i	0.0135752	−	0.643059i
$520$	15.6546	+	12.2939i	0.686499	+	0.539122i
$521$	16.3621			0.716837			0.358418	−	0.933561i	$-0.383316\pi$
$521$	16.3621			0.716837			0.358418	+	0.933561i	$0.383316\pi$
$522$	−33.7055	−	15.8126i	−1.47525	−	0.692099i
$523$		−	30.0183i		−	1.31261i	−0.754497	−	0.656304i	$-0.772119\pi$
$523$		−	30.0183i		−	1.31261i	0.754497	−	0.656304i	$-0.227881\pi$
$524$	14.2723	+	3.93899i	0.623489	+	0.172075i
$525$	−3.07640	−	5.59812i	−0.134265	−	0.244322i
$526$	−10.9002	−	14.3161i	−0.475273	−	0.624211i
$527$	−5.71113	+	9.89197i	−0.248781	+	0.430901i
$528$	−1.77666	−	3.35087i	−0.0773192	−	0.145828i
$529$	−10.0023	−	17.3244i	−0.434881	−	0.753235i
$530$	−6.98250	+	16.6804i	−0.303300	+	0.724550i
$531$	1.05726	−	25.0302i	0.0458813	−	1.08622i
$532$	2.10494	−	2.07366i	0.0912606	−	0.0899046i
$533$	−39.5348	+	22.8254i	−1.71244	+	0.988678i
$534$	−1.93504	+	4.36178i	−0.0837374	+	0.188753i
$535$	−3.28659	+	5.69255i	−0.142092	+	0.246110i
$536$	9.78168	+	1.39968i	0.422504	+	0.0604569i
$537$	24.8329	+	15.0449i	1.07162	+	0.649234i
$538$	3.18891	+	24.9432i	0.137484	+	1.07538i
$539$		−	0.547434i		−	0.0235797i
$540$	11.2514	+	3.88667i	0.484183	+	0.167256i
$541$		−	3.82509i		−	0.164454i	−0.996614	−	0.0822268i	$-0.973797\pi$
$541$		−	3.82509i		−	0.164454i	0.996614	−	0.0822268i	$-0.0262032\pi$
$542$	36.7564	−	4.69920i	1.57882	−	0.201848i
$543$	−13.5418	−	8.20423i	−0.581134	−	0.352077i
$544$	8.93054	−	6.59086i	0.382894	−	0.282581i
$545$	1.11964	−	1.93927i	0.0479601	−	0.0830694i
$546$	13.7564	+	6.10283i	0.588719	+	0.261177i
$547$	26.4258	−	15.2570i	1.12989	−	0.652341i	0.185980	−	0.982553i	$-0.440454\pi$
$547$	26.4258	−	15.2570i	1.12989	−	0.652341i	0.943906	+	0.330213i	$0.107121\pi$
$548$	−14.6484	−	14.8693i	−0.625747	−	0.635185i
$549$	13.9239	+	8.84276i	0.594258	+	0.377400i
$550$	−2.63374	−	1.10249i	−0.112303	−	0.0470105i
$551$	−6.48230	−	11.2277i	−0.276155	−	0.478315i
$552$	24.8420	+	20.3711i	1.05735	+	0.867052i
$553$	0.890337	−	1.54211i	0.0378610	−	0.0655772i
$554$	−1.51147	+	1.15083i	−0.0642161	+	0.0488940i
$555$	7.43180	+	13.5236i	0.315462	+	0.574046i
$556$	−18.8232	−	5.19499i	−0.798283	−	0.220316i
$557$		−	5.61658i		−	0.237982i	−0.992895	−	0.118991i	$-0.962034\pi$
$557$		−	5.61658i		−	0.237982i	0.992895	−	0.118991i	$-0.0379660\pi$
$558$	24.6093	−	2.09543i	1.04180	−	0.0887065i
$559$	58.7515			2.48492
$560$	−2.23123	−	4.00177i	−0.0942866	−	0.169106i
$561$	−0.0392655	+	1.86001i	−0.00165779	+	0.0785297i
$562$	1.33736	+	1.75646i	0.0564133	+	0.0740917i
$563$	−23.0313	−	13.2971i	−0.970653	−	0.560407i	−0.0712177	−	0.997461i	$-0.522689\pi$
$563$	−23.0313	−	13.2971i	−0.970653	−	0.560407i	−0.899435	+	0.437054i	$0.856022\pi$
$564$	15.0554	−	3.57609i	0.633947	−	0.150581i
$565$	−14.6801	+	8.47557i	−0.617597	+	0.356570i
$566$	−35.4721	−	14.8488i	−1.49100	−	0.624141i
$567$	8.96794	+	0.758958i	0.376618	+	0.0318732i
$568$	14.4206	−	5.78441i	0.605076	−	0.242708i
$569$	−14.0906	−	24.4057i	−0.590710	−	1.02314i	−0.994137	−	0.108128i	$-0.965514\pi$
$569$	−14.0906	−	24.4057i	−0.590710	−	1.02314i	0.403426	−	0.915012i	$-0.367819\pi$
$570$	2.44095	+	3.35030i	0.102240	+	0.140329i
$571$	−32.8351	−	18.9574i	−1.37411	−	0.793341i	−0.382665	−	0.923887i	$-0.624994\pi$
$571$	−32.8351	−	18.9574i	−1.37411	−	0.793341i	−0.991442	+	0.130546i	$0.958327\pi$
$572$	6.51037	−	1.69232i	0.272212	−	0.0707596i
$573$	31.5770	+	0.666603i	1.31915	+	0.0278477i
$574$	10.4232	−	1.33257i	0.435056	−	0.0556206i
$575$	24.1849			1.00858
$576$	−22.7323	−	7.69681i	−0.947181	−	0.320700i
$577$	−5.72223			−0.238219			−0.119110	−	0.992881i	$-0.538004\pi$
$577$	−5.72223			−0.238219			−0.119110	+	0.992881i	$0.538004\pi$
$578$	18.4470	−	2.35840i	0.767295	−	0.0980964i
$579$	−21.3437	−	38.8391i	−0.887014	−	1.61410i
$580$	−19.4566	+	5.05759i	−0.807890	+	0.210005i
$581$	9.70504	+	5.60321i	0.402633	+	0.232460i
$582$	36.5542	−	3.89117i	1.51522	−	0.161294i
$583$	3.05550	+	5.29227i	0.126546	+	0.219184i
$584$	−26.3164	+	10.5560i	−1.08898	+	0.436812i
$585$	−11.3184	+	17.8220i	−0.467957	+	0.736850i
$586$	12.1769	+	5.09733i	0.503025	+	0.210569i
$587$	−1.06210	+	0.613203i	−0.0438375	+	0.0253096i	−0.521759	−	0.853093i	$-0.674724\pi$
$587$	−1.06210	+	0.613203i	−0.0438375	+	0.0253096i	0.477921	+	0.878403i	$0.341390\pi$
$588$	−2.37846	−	2.51852i	−0.0980861	−	0.103862i
$589$	7.44836	+	4.30031i	0.306904	+	0.177191i
$590$	−8.19479	−	10.7628i	−0.337374	−	0.443098i
$591$	−6.28458	−	3.80748i	−0.258513	−	0.156619i
$592$	−15.1508	−	27.1734i	−0.622694	−	1.11682i
$593$	28.7093			1.17895			0.589475	−	0.807787i	$-0.299335\pi$
$593$	28.7093			1.17895			0.589475	+	0.807787i	$0.299335\pi$
$594$	3.34844	−	2.22955i	0.137388	−	0.0914794i
$595$			2.24746i			0.0921370i
$596$	−29.4065	−	8.11583i	−1.20454	−	0.332437i
$597$	4.40932	−	7.27797i	0.180461	−	0.297867i
$598$	−45.3339	+	34.5171i	−1.85384	+	1.41151i
$599$	11.6245	−	20.1343i	0.474966	−	0.822665i	−0.524623	−	0.851335i	$-0.675794\pi$
$599$	11.6245	−	20.1343i	0.474966	−	0.822665i	0.999589	+	0.0286694i	$0.00912700\pi$
$600$	−16.9068	+	6.37079i	−0.690216	+	0.260086i
$601$	−22.2462	−	38.5315i	−0.907440	−	1.57173i	−0.817608	−	0.575776i	$-0.804700\pi$
$601$	−22.2462	−	38.5315i	−0.907440	−	1.57173i	−0.0898323	−	0.995957i	$-0.528633\pi$
$602$	−12.4747	−	5.22198i	−0.508432	−	0.212832i
$603$	−0.442307	+	10.4714i	−0.0180121	+	0.426428i
$604$	18.2121	+	18.4868i	0.741041	+	0.752218i
$605$	−10.6145	+	6.12829i	−0.431541	+	0.249151i
$606$	−2.80217	−	26.3240i	−0.113830	−	1.06934i
$607$	15.0590	−	26.0830i	0.611227	−	1.05868i	−0.379807	−	0.925066i	$-0.624010\pi$
$607$	15.0590	−	26.0830i	0.611227	−	1.05868i	0.991034	−	0.133611i	$-0.0426572\pi$
$608$	−4.96273	−	6.72443i	−0.201265	−	0.272712i
$609$	−13.3204	+	7.32012i	−0.539770	+	0.296626i
$610$	8.83459	−	1.12948i	0.357702	−	0.0457311i
$611$			27.4449i			1.11030i
$612$	7.90063	+	8.72773i	0.319364	+	0.352798i
$613$		−	43.1894i		−	1.74440i	−0.489146	−	0.872202i	$-0.662692\pi$
$613$		−	43.1894i		−	1.74440i	0.489146	−	0.872202i	$-0.337308\pi$
$614$	4.68338	+	36.6327i	0.189006	+	1.47838i
$615$	−0.311128	+	14.7382i	−0.0125459	+	0.594300i
$616$	−1.53277	−	0.219326i	−0.0617569	−	0.00883691i
$617$	12.8159	−	22.1977i	0.515948	−	0.893647i	−0.483881	−	0.875134i	$-0.660773\pi$
$617$	12.8159	−	22.1977i	0.515948	−	0.893647i	0.999829	−	0.0185136i	$-0.00589340\pi$
$618$	−11.3642	−	15.5978i	−0.457135	−	0.627435i
$619$	−27.7495	+	16.0212i	−1.11535	+	0.643947i	−0.940209	−	0.340597i	$-0.889371\pi$
$619$	−27.7495	+	16.0212i	−1.11535	+	0.643947i	−0.175139	+	0.984544i	$0.556037\pi$
$620$	9.50051	−	9.35934i	0.381550	−	0.375880i
$621$	−18.8708	+	28.3727i	−0.757261	+	1.13856i
$622$	9.45627	−	22.5900i	0.379162	−	0.905775i
$623$	0.974027	+	1.68706i	0.0390236	+	0.0675908i
$624$	22.5988	−	36.0716i	0.904675	−	1.44402i
$625$	−3.52045	+	6.09759i	−0.140818	+	0.243904i
$626$	−13.6262	−	17.8963i	−0.544614	−	0.715281i
$627$	1.40053	+	0.0295658i	0.0559319	+	0.00118074i
$628$	1.10951	+	0.306213i	0.0442745	+	0.0122192i
$629$			15.2610i			0.608497i
$630$	3.98730	−	2.77815i	0.158858	−	0.110684i
$631$	−44.9625			−1.78993			−0.894964	−	0.446139i	$-0.852799\pi$
$631$	−44.9625			−1.78993			−0.894964	+	0.446139i	$0.852799\pi$
$632$	−3.96106	−	3.11070i	−0.157562	−	0.123737i
$633$	−22.4818	+	12.3547i	−0.893569	+	0.491054i
$634$	−9.25767	+	7.04877i	−0.367669	+	0.279942i
$635$	−0.625446	−	0.361101i	−0.0248201	−	0.0143299i
$636$	37.0506	+	11.0722i	1.46915	+	0.439041i
$637$	5.32075	−	3.07193i	0.210816	−	0.121714i
$638$	−2.62332	+	6.26681i	−0.103858	+	0.248106i
$639$	7.63035	+	14.6071i	0.301852	+	0.577849i
$640$	−12.0985	+	4.64395i	−0.478236	+	0.183568i
$641$	−23.6763	−	41.0085i	−0.935157	−	1.61974i	−0.774354	−	0.632752i	$-0.781925\pi$
$641$	−23.6763	−	41.0085i	−0.935157	−	1.61974i	−0.160802	−	0.986987i	$-0.551408\pi$
$642$	12.8489	+	5.70023i	0.507105	+	0.224970i
$643$	31.3043	+	18.0735i	1.23452	+	0.712751i	0.967969	−	0.251070i	$-0.0807825\pi$
$643$	31.3043	+	18.0735i	1.23452	+	0.712751i	0.266551	+	0.963821i	$0.414116\pi$
$644$	12.6937	−	3.29964i	0.500202	−	0.130024i
$645$	9.83060	−	16.2263i	0.387080	−	0.638909i
$646$	0.519879	+	4.06642i	0.0204544	+	0.159991i
$647$	28.7535			1.13042			0.565208	−	0.824948i	$-0.308796\pi$
$647$	28.7535			1.13042			0.565208	+	0.824948i	$0.308796\pi$
$648$	5.71797	−	24.8053i	0.224623	−	0.974446i
$649$	−4.57153			−0.179448
$650$	−4.06363	−	31.7851i	−0.159389	−	1.24671i
$651$	5.22471	−	8.62385i	0.204773	−	0.337995i
$652$	0.256605	+	0.987161i	0.0100494	+	0.0386602i
$653$	12.8859	+	7.43967i	0.504264	+	0.291137i	0.730473	−	0.682942i	$-0.239300\pi$
$653$	12.8859	+	7.43967i	0.504264	+	0.291137i	−0.226209	+	0.974079i	$0.572633\pi$
$654$	−4.37722	−	1.94189i	−0.171163	−	0.0759339i
$655$	4.23983	+	7.34359i	0.165664	+	0.286938i
$656$	0.444906	−	29.7179i	0.0173707	−	1.16029i
$657$	−13.9247	−	26.6567i	−0.543255	−	1.03998i
$658$	2.43937	−	5.82738i	0.0950966	−	0.227175i
$659$	−14.4618	+	8.34953i	−0.563352	+	0.325252i	−0.754490	−	0.656312i	$-0.772116\pi$
$659$	−14.4618	+	8.34953i	−0.563352	+	0.325252i	0.191138	+	0.981563i	$0.438782\pi$
$660$	0.621954	−	2.08123i	0.0242095	−	0.0810119i
$661$	−26.6589	−	15.3915i	−1.03691	−	0.598660i	−0.117954	−	0.993019i	$-0.537633\pi$
$661$	−26.6589	−	15.3915i	−1.03691	−	0.598660i	−0.918957	+	0.394359i	$0.870967\pi$
$662$	11.8844	−	9.04873i	0.461899	−	0.351689i
$663$	−18.2986	+	10.0558i	−0.710658	+	0.390536i
$664$	19.5767	−	24.9283i	0.759725	−	0.967407i
$665$	1.69227			0.0656236
$666$	27.0751	−	18.8646i	1.04914	−	0.730988i
$667$		−	57.5464i		−	2.22821i
$668$	−3.36909	+	12.2074i	−0.130354	+	0.472318i
$669$	28.5349	+	0.602382i	1.10322	+	0.0232894i
$670$	3.42830	+	4.50263i	0.132447	+	0.173952i
$671$	1.50495	−	2.60664i	0.0580978	−	0.100628i
$672$	−8.00453	+	5.65045i	−0.308781	+	0.217971i
$673$	−17.9367	−	31.0674i	−0.691411	−	1.19756i	−0.971376	−	0.237548i	$-0.923656\pi$
$673$	−17.9367	−	31.0674i	−0.691411	−	1.19756i	0.279965	−	0.960010i	$-0.409677\pi$
$674$	−18.4750	+	44.1348i	−0.711632	+	1.70001i
$675$	−8.51223	−	17.1689i	−0.327636	−	0.660831i
$676$	34.7348	+	35.2587i	1.33595	+	1.35610i
$677$	29.8809	−	17.2517i	1.14842	−	0.663038i	0.199915	−	0.979813i	$-0.435934\pi$
$677$	29.8809	−	17.2517i	1.14842	−	0.663038i	0.948501	+	0.316776i	$0.102600\pi$
$678$	21.3459	+	29.2981i	0.819784	+	1.12519i
$679$	7.50375	−	12.9969i	0.287968	−	0.498775i
$680$	6.29269	+	0.900433i	0.241314	+	0.0345300i
$681$	0.318124	−	15.0695i	0.0121905	−	0.577466i
$682$	−0.571544	−	4.47053i	−0.0218855	−	0.171185i
$683$			2.92369i			0.111872i	0.998434	+	0.0559359i	$0.0178142\pi$
$683$			2.92369i			0.111872i	−0.998434	+	0.0559359i	$0.982186\pi$
$684$	6.57172	−	5.94894i	0.251276	−	0.227463i
$685$		−	11.9542i		−	0.456748i
$686$	−1.40280	+	0.179343i	−0.0535590	+	0.00684736i
$687$	1.22842	−	0.675070i	0.0468673	−	0.0257555i
$688$	−19.6190	+	32.8359i	−0.747967	+	1.25186i
$689$	−34.2919	+	59.3954i	−1.30642	+	2.26278i
$690$	1.94761	+	18.2961i	0.0741442	+	0.696521i
$691$	13.5658	−	7.83220i	0.516066	−	0.297951i	−0.219257	−	0.975667i	$-0.570363\pi$
$691$	13.5658	−	7.83220i	0.516066	−	0.297951i	0.735324	+	0.677716i	$0.237030\pi$
$692$	−12.0535	+	11.8744i	−0.458204	+	0.451396i
$693$	0.0693083	−	1.64084i	0.00263281	−	0.0623303i
$694$	−18.0891	−	7.57221i	−0.686655	−	0.287437i
$695$	−5.59175	−	9.68519i	−0.212107	−	0.367380i
$696$	15.1589	+	40.2286i	0.574597	+	1.52486i
$697$	−7.28947	+	12.6257i	−0.276108	+	0.478234i
$698$	−29.6287	+	22.5593i	−1.12146	+	0.853881i
$699$	−2.36945	+	3.91099i	−0.0896210	+	0.147927i
$700$	−1.96230	+	7.11011i	−0.0741681	+	0.268737i
$701$			28.1320i			1.06253i	0.847205	+	0.531265i	$0.178283\pi$
$701$			28.1320i			1.06253i	−0.847205	+	0.531265i	$0.821717\pi$
$702$	40.4598	+	20.0338i	1.52706	+	0.756127i
$703$	11.4911			0.433395
$704$	−1.22819	+	4.20373i	−0.0462890	+	0.158434i
$705$	7.57987	+	4.59222i	0.285474	+	0.172953i
$706$	−2.11884	−	2.78283i	−0.0797437	−	0.104733i
$707$	−9.35952	−	5.40372i	−0.352001	−	0.203228i
$708$	−21.0317	+	19.8621i	−0.790419	+	0.746464i
$709$	33.1356	−	19.1308i	1.24443	−	0.718473i	0.274439	−	0.961605i	$-0.411508\pi$
$709$	33.1356	−	19.1308i	1.24443	−	0.718473i	0.969993	+	0.243131i	$0.0781746\pi$
$710$	8.20848	+	3.43611i	0.308059	+	0.128955i
$711$	2.86387	−	4.50948i	0.107404	−	0.169119i
$712$	5.11386	−	2.05127i	0.191650	−	0.0768748i
$713$	19.0880	+	33.0613i	0.714850	+	1.23816i
$714$	4.77913	−	0.508735i	0.178854	−	0.0190389i
$715$	3.33639	+	1.92627i	0.124774	+	0.0720384i
$716$	−8.43466	−	32.4482i	−0.315218	−	1.21264i
$717$	−22.1731	−	40.3484i	−0.828070	−	1.50684i
$718$	−19.7425	+	2.52402i	−0.736782	+	0.0941954i
$719$	−39.0220			−1.45528			−0.727638	−	0.685961i	$-0.759382\pi$
$719$	−39.0220			−1.45528			−0.727638	+	0.685961i	$0.759382\pi$
$720$	−6.18108	−	12.2771i	−0.230355	−	0.457541i
$721$	−7.87862			−0.293415
$722$	−23.5912	+	3.01607i	−0.877975	+	0.112246i
$723$	−8.24819	−	0.174122i	−0.306754	−	0.00647568i
$724$	4.59957	+	17.6945i	0.170942	+	0.657612i
$725$	28.0271	+	16.1815i	1.04090	+	0.600965i
$726$	15.4342	+	21.1841i	0.572818	+	0.786215i
$727$	−20.0070	−	34.6532i	−0.742020	−	1.28522i	−0.951574	−	0.307419i	$-0.900535\pi$
$727$	−20.0070	−	34.6532i	−0.742020	−	1.28522i	0.209555	−	0.977797i	$-0.432799\pi$
$728$	−6.46941	−	16.1284i	−0.239772	−	0.597757i
$729$	26.7838	+	3.41024i	0.991991	+	0.126305i
$730$	−14.9798	−	6.27060i	−0.554426	−	0.232085i
$731$	16.2490	−	9.38138i	0.600992	−	0.346983i
$732$	−4.40157	−	18.5307i	−0.162687	−	0.684913i
$733$	−17.0690	−	9.85480i	−0.630458	−	0.363995i	0.150471	−	0.988614i	$-0.451921\pi$
$733$	−17.0690	−	9.85480i	−0.630458	−	0.363995i	−0.780930	+	0.624619i	$0.785254\pi$
$734$	12.9654	+	17.0285i	0.478563	+	0.628533i
$735$	0.0418729	−	1.98352i	0.00154450	−	0.0731633i
$736$	−4.15302	−	36.8632i	−0.153083	−	1.35880i
$737$	1.91250			0.0704479
$738$	31.4104	−	2.67452i	1.15623	−	0.0984506i
$739$			33.6348i			1.23727i	0.785677	+	0.618637i	$0.212315\pi$
$739$			33.6348i			1.23727i	−0.785677	+	0.618637i	$0.787685\pi$
$740$	4.74042	−	17.1762i	0.174261	−	0.631410i
$741$	7.57175	+	13.7783i	0.278155	+	0.506158i
$742$	12.5604	−	9.56347i	0.461107	−	0.351086i
$743$	17.2195	−	29.8251i	0.631723	−	1.09418i	−0.355477	−	0.934685i	$-0.615681\pi$
$743$	17.2195	−	29.8251i	0.631723	−	1.09418i	0.987199	−	0.159491i	$-0.0509853\pi$
$744$	−22.0527	−	18.0838i	−0.808492	−	0.662985i
$745$	−8.73567	−	15.1306i	−0.320050	−	0.554343i
$746$	−0.632351	−	0.264705i	−0.0231520	−	0.00969156i
$747$	28.3798	+	18.0234i	1.03836	+	0.659440i
$748$	1.53036	−	1.50762i	0.0559554	−	0.0551240i
$749$	4.96974	−	2.86928i	0.181590	−	0.104841i
$750$	−22.2820	−	9.88507i	−0.813622	−	0.360952i
$751$	6.32715	−	10.9589i	0.230881	−	0.399897i	−0.727187	−	0.686440i	$-0.759173\pi$
$751$	6.32715	−	10.9589i	0.230881	−	0.399897i	0.958068	+	0.286542i	$0.0925059\pi$
$752$	−15.3388	−	9.16472i	−0.559349	−	0.334203i
$753$	14.7435	+	8.93226i	0.537282	+	0.325510i
$754$	−75.6306	+	9.66915i	−2.75431	+	0.352130i
$755$			14.8626i			0.540904i
$756$	−6.81017	−	7.84994i	−0.247683	−	0.285500i
$757$			38.0846i			1.38421i	0.721798	+	0.692104i	$0.243316\pi$
$757$			38.0846i			1.38421i	−0.721798	+	0.692104i	$0.756684\pi$
$758$	0.984875	+	7.70354i	0.0357723	+	0.279805i
$759$	5.31811	+	3.22195i	0.193035	+	0.116949i
$760$	0.677999	−	4.73821i	0.0245936	−	0.171873i
$761$	−6.57627	+	11.3904i	−0.238390	+	0.412903i	−0.960252	−	0.279133i	$-0.909953\pi$
$761$	−6.57627	+	11.3904i	−0.238390	+	0.412903i	0.721863	+	0.692036i	$0.243286\pi$
$762$	−0.626290	+	1.41172i	−0.0226881	+	0.0511412i
$763$	−1.69304	+	0.977475i	−0.0612921	+	0.0353870i
$764$	−25.5945	−	25.9806i	−0.925978	−	0.939944i
$765$	−0.284542	+	6.73638i	−0.0102876	+	0.243554i
$766$	1.98218	−	4.73520i	0.0716190	−	0.171090i
$767$	−25.6532	−	44.4326i	−0.926283	−	1.60437i
$768$	12.6138	+	24.6758i	0.455160	+	0.890410i
$769$	−26.1768	+	45.3395i	−0.943959	+	1.63498i	−0.186136	+	0.982524i	$0.559596\pi$
$769$	−26.1768	+	45.3395i	−0.943959	+	1.63498i	−0.757823	+	0.652460i	$0.773737\pi$
$770$	−0.537206	−	0.705552i	−0.0193595	−	0.0254263i
$771$	14.8819	+	27.0805i	0.535957	+	0.975280i
$772$	−13.6142	+	49.3291i	−0.489987	+	1.77539i
$773$			25.5146i			0.917695i	0.888515	+	0.458848i	$0.151738\pi$
$773$			25.5146i			0.917695i	−0.888515	+	0.458848i	$0.848262\pi$
$774$	−36.7297	−	17.2314i	−1.32022	−	0.619368i
$775$	−21.4694			−0.771202
$776$	−33.3837	−	26.2169i	−1.19841	−	0.941133i
$777$	0.284331	−	13.4688i	0.0102003	−	0.483190i
$778$	−21.6636	+	16.4947i	−0.776679	+	0.591362i
$779$	9.50681	+	5.48876i	0.340617	+	0.196655i
$780$	23.7185	−	5.63383i	0.849259	−	0.201723i
$781$	2.60435	−	1.50362i	0.0931908	−	0.0538038i
$782$	−7.02643	+	16.7853i	−0.251265	+	0.600243i
$783$	−40.8524	+	20.2543i	−1.45994	+	0.723831i
$784$	−0.0598772	+	3.99955i	−0.00213847	+	0.142841i
$785$	0.329599	+	0.570883i	0.0117639	+	0.0203757i
$786$	14.6561	−	10.6781i	0.522765	−	0.380875i
$787$	30.7901	+	17.7767i	1.09755	+	0.633671i	0.935576	−	0.353124i	$-0.114881\pi$
$787$	30.7901	+	17.7767i	1.09755	+	0.633671i	0.161974	+	0.986795i	$0.448214\pi$
$788$	2.13460	+	8.21181i	0.0760420	+	0.292534i
$789$	−22.0325	−	0.465114i	−0.784378	−	0.0165585i
$790$	−0.365799	−	2.86122i	−0.0130145	−	0.101798i
$791$	14.7988			0.526184
$792$	−4.56643	−	0.851450i	−0.162261	−	0.0302549i
$793$	33.7801			1.19957
$794$	−6.84639	−	53.5514i	−0.242969	−	1.90047i
$795$	10.6662	+	19.4092i	0.378291	+	0.688375i
$796$	−9.50984	+	2.47201i	−0.337067	+	0.0876182i
$797$	−21.7747	−	12.5716i	−0.771298	−	0.445309i	0.0620396	−	0.998074i	$-0.480240\pi$
$797$	−21.7747	−	12.5716i	−0.771298	−	0.445309i	−0.833337	+	0.552765i	$0.813573\pi$
$798$	−0.383062	−	3.59854i	−0.0135603	−	0.127387i
$799$	4.38238	+	7.59050i	0.155037	+	0.268533i
$800$	19.1215	+	8.34289i	0.676046	+	0.294966i
$801$	2.70589	+	5.18000i	0.0956078	+	0.183026i
$802$	−7.68322	+	18.3543i	−0.271304	+	0.648114i
$803$	−4.75270	+	2.74398i	−0.167719	+	0.0968328i
$804$	8.79862	−	8.30933i	0.310303	−	0.293047i
$805$	6.50520	+	3.75578i	0.229278	+	0.132374i
$806$	40.2437	−	30.6415i	1.41753	−	1.07930i
$807$	26.3406	+	15.9583i	0.927233	+	0.561760i
$808$	−18.8798	+	24.0408i	−0.664188	+	0.845753i
$809$	33.8949			1.19168			0.595840	−	0.803103i	$-0.296819\pi$
$809$	33.8949			1.19168			0.595840	+	0.803103i	$0.296819\pi$
$810$	12.3030	−	7.82221i	0.432282	−	0.274844i
$811$			34.0068i			1.19414i	0.802189	+	0.597070i	$0.203668\pi$
$811$			34.0068i			1.19414i	−0.802189	+	0.597070i	$0.796332\pi$
$812$	16.9181	+	4.66918i	0.593708	+	0.163856i
$813$	23.5163	−	38.8157i	0.824753	−	1.36133i
$814$	−3.64781	−	4.79093i	−0.127856	−	0.167922i
$815$	−0.292078	+	0.505894i	−0.0102311	+	0.0177207i
$816$	0.490318	−	13.5849i	0.0171646	−	0.475568i
$817$	−7.06391	−	12.2350i	−0.247135	−	0.428050i
$818$	−9.64779	+	23.0475i	−0.337327	+	0.805836i
$819$	16.3369	−	8.53396i	0.570859	−	0.298201i
$820$	12.1261	−	11.9459i	0.423461	−	0.417169i
$821$	5.64931	−	3.26163i	0.197162	−	0.113832i	−0.398169	−	0.917312i	$-0.630354\pi$
$821$	5.64931	−	3.26163i	0.197162	−	0.113832i	0.595331	+	0.803480i	$0.297021\pi$
$822$	−25.4202	+	2.70596i	−0.886630	+	0.0943812i
$823$	−23.4624	+	40.6380i	−0.817847	+	1.41655i	0.0894190	+	0.995994i	$0.471499\pi$
$823$	−23.4624	+	40.6380i	−0.817847	+	1.41655i	−0.907266	+	0.420558i	$0.861834\pi$
$824$	−3.15652	+	22.0594i	−0.109963	+	0.768476i
$825$	−3.06460	+	1.68413i	−0.106696	+	0.0586338i
$826$	1.49766	+	11.7145i	0.0521104	+	0.407600i
$827$		−	42.1936i		−	1.46722i	−0.679573	−	0.733608i	$-0.737835\pi$
$827$		−	42.1936i		−	1.46722i	0.679573	−	0.733608i	$-0.262165\pi$
$828$	38.4650	−	8.28300i	1.33675	−	0.287854i
$829$		−	1.07855i		−	0.0374595i	−0.999825	−	0.0187297i	$-0.994038\pi$
$829$		−	1.07855i		−	0.0374595i	0.999825	−	0.0187297i	$-0.00596221\pi$
$830$	18.0067	−	2.30210i	0.625022	−	0.0799072i
$831$	−0.0491060	+	2.32616i	−0.00170347	+	0.0806935i
$832$	−47.7498	+	11.6520i	−1.65543	+	0.403961i
$833$	0.981047	−	1.69922i	0.0339913	−	0.0588746i
$834$	−19.3294	+	14.0829i	−0.669321	+	0.487652i
$835$	−6.28111	+	3.62640i	−0.217367	+	0.125497i
$836$	−1.13519	−	1.15231i	−0.0392614	−	0.0398536i
$837$	16.7520	−	25.1870i	0.579034	−	0.870591i
$838$	21.1046	+	8.83450i	0.729047	+	0.305183i
$839$	−2.00568	−	3.47395i	−0.0692439	−	0.119934i	0.829325	−	0.558767i	$-0.188725\pi$
$839$	−2.00568	−	3.47395i	−0.0692439	−	0.119934i	−0.898569	+	0.438833i	$0.855392\pi$
$840$	−5.53690	−	0.911926i	−0.191041	−	0.0314644i
$841$	24.0028	−	41.5741i	0.827684	−	1.43359i
$842$	−9.13900	+	6.95842i	−0.314951	+	0.239803i
$843$	2.70320	+	0.0570655i	0.0931030	+	0.00196544i
$844$	28.5538	+	7.88050i	0.982863	+	0.271258i
$845$			28.3464i			0.975146i
$846$	8.04938	−	17.1577i	0.276743	−	0.589895i
$847$	10.7003			0.367667
$848$	−21.7446	−	38.9995i	−0.746712	−	1.33925i
$849$	−41.2751	+	22.6824i	−1.41656	+	0.778459i
$850$	−6.19929	−	8.14199i	−0.212634	−	0.279268i
$851$	44.1725	+	25.5030i	1.51421	+	0.874232i
$852$	5.44866	−	18.2327i	0.186668	−	0.624644i
$853$	26.0517	−	15.0409i	0.891992	−	0.514992i	0.0173983	−	0.999849i	$-0.494462\pi$
$853$	26.0517	−	15.0409i	0.891992	−	0.514992i	0.874593	+	0.484857i	$0.161128\pi$
$854$	−7.17253	−	3.00246i	−0.245439	−	0.102742i
$855$	5.07230	+	0.214252i	0.173469	+	0.00732725i
$856$	−6.04263	−	15.0644i	−0.206533	−	0.514890i
$857$	−12.8198	−	22.2045i	−0.437915	−	0.758492i	0.559613	−	0.828754i	$-0.310950\pi$
$857$	−12.8198	−	22.2045i	−0.437915	−	0.758492i	−0.997529	+	0.0702622i	$0.977616\pi$
$858$	3.34090	−	7.53072i	0.114056	−	0.257094i
$859$	0.392816	+	0.226792i	0.0134027	+	0.00773806i	0.506686	−	0.862130i	$-0.330870\pi$
$859$	0.392816	+	0.226792i	0.0134027	+	0.00773806i	−0.493284	+	0.869869i	$0.664204\pi$
$860$	−21.2022	+	5.51137i	−0.722991	+	0.187936i
$861$	6.66863	−	11.0072i	0.227266	−	0.375123i
$862$	−12.5706	+	1.60712i	−0.428158	+	0.0547387i
$863$	−30.4300			−1.03585			−0.517924	−	0.855427i	$-0.673295\pi$
$863$	−30.4300			−1.03585			−0.517924	+	0.855427i	$0.673295\pi$
$864$	−24.7076	+	15.9228i	−0.840569	+	0.541705i
$865$	−9.69044			−0.329485
$866$	−36.1871	+	4.62642i	−1.22969	+	0.157212i
$867$	11.8022	−	19.4805i	0.400823	−	0.661593i
$868$	−11.2684	+	2.92915i	−0.382476	+	0.0994219i
$869$	−0.844203	−	0.487401i	−0.0286376	−	0.0165339i
$870$	−9.98443	+	22.5059i	−0.338504	+	0.763022i
$871$	10.7320	+	18.5884i	0.363641	+	0.629844i
$872$	2.05854	+	5.13197i	0.0697108	+	0.173790i
$873$	24.1367	−	38.0059i	0.816903	−	1.28630i
$874$	12.6389	+	5.29069i	0.427516	+	0.178960i
$875$	−8.61830	+	4.97578i	−0.291352	+	0.168212i
$876$	−9.94333	+	33.2732i	−0.335954	+	1.12420i
$877$	−26.6541	−	15.3888i	−0.900046	−	0.519642i	−0.0228306	−	0.999739i	$-0.507268\pi$
$877$	−26.6541	−	15.3888i	−0.900046	−	0.519642i	−0.877215	+	0.480098i	$0.840601\pi$
$878$	9.18269	+	12.0603i	0.309901	+	0.407016i
$879$	14.1690	−	7.78648i	0.477910	−	0.262632i
$880$	−2.19071	+	1.22145i	−0.0738487	+	0.0411751i
$881$	−52.7733			−1.77798			−0.888988	−	0.457930i	$-0.848591\pi$
$881$	−52.7733			−1.77798			−0.888988	+	0.457930i	$0.848591\pi$
$882$	−4.22734	+	0.359948i	−0.142342	+	0.0121201i
$883$		−	7.72232i		−	0.259877i	−0.991522	−	0.129938i	$-0.958522\pi$
$883$		−	7.72232i		−	0.259877i	0.991522	−	0.129938i	$-0.0414779\pi$
$884$	23.2408	+	6.41418i	0.781673	+	0.215732i
$885$	−16.5640	−	0.349673i	−0.556794	−	0.0117541i
$886$	43.1289	−	32.8383i	1.44895	−	1.10322i
$887$	9.93829	−	17.2136i	0.333695	−	0.577977i	−0.649538	−	0.760329i	$-0.725038\pi$
$887$	9.93829	−	17.2136i	0.333695	−	0.577977i	0.983233	+	0.182352i	$0.0583711\pi$
$888$	−37.5974	−	6.19229i	−1.26169	−	0.207800i
$889$	0.315251	+	0.546030i	0.0105732	+	0.0183133i
$890$	2.91090	+	1.21852i	0.0975737	+	0.0408448i
$891$	0.415480	−	4.90936i	0.0139191	−	0.164470i
$892$	−23.1287	−	23.4776i	−0.774407	−	0.786088i
$893$	5.71542	−	3.29980i	0.191259	−	0.110424i
$894$	−30.1972	+	22.0010i	−1.00994	+	0.735822i
$895$	9.60066	−	16.6288i	0.320915	−	0.555841i
$896$	11.1744	+	1.77005i	0.373310	+	0.0591331i
$897$	−1.47285	+	69.7691i	−0.0491771	+	2.32952i
$898$	26.7043	−	3.41407i	0.891135	−	0.113929i
$899$			51.0850i			1.70378i
$900$	−6.78185	+	21.0629i	−0.226062	+	0.702096i
$901$			21.9028i			0.729688i
$902$	−0.729497	−	5.70601i	−0.0242896	−	0.189989i
$903$	−14.5155	+	7.97689i	−0.483047	+	0.265454i
$904$	5.92904	−	41.4352i	0.197197	−	1.37811i
$905$	−5.23541	+	9.06799i	−0.174031	+	0.301430i
$906$	31.6046	−	3.36428i	1.04999	−	0.111771i
$907$	12.1056	−	6.98920i	0.401961	−	0.232072i	−0.285369	−	0.958418i	$-0.592116\pi$
$907$	12.1056	−	6.98920i	0.401961	−	0.232072i	0.687330	+	0.726345i	$0.258783\pi$
$908$	−12.3987	+	12.2145i	−0.411467	+	0.405353i
$909$	−27.3694	−	17.3817i	−0.907786	−	0.576514i
$910$	3.84302	−	9.18054i	0.127395	−	0.304332i
$911$	19.3384	+	33.4950i	0.640708	+	1.10974i	0.985275	+	0.170978i	$0.0546926\pi$
$911$	19.3384	+	33.4950i	0.640708	+	1.10974i	−0.344566	+	0.938762i	$0.611974\pi$
$912$	−10.2291	−	0.369195i	−0.338718	−	0.0122253i
$913$	3.06739	−	5.31287i	0.101516	−	0.175830i
$914$	−8.55729	−	11.2389i	−0.283050	−	0.371750i
$915$	5.65226	−	9.32955i	0.186858	−	0.308425i
$916$	−1.56021	−	0.430598i	−0.0515507	−	0.0142274i
$917$		−	7.40295i		−	0.244467i
$918$	14.3890	−	0.919780i	0.474908	−	0.0303573i
$919$	28.8449			0.951507			0.475753	−	0.879579i	$-0.342175\pi$
$919$	28.8449			0.951507			0.475753	+	0.879579i	$0.342175\pi$
$920$	13.1221	−	16.7092i	0.432623	−	0.550887i
$921$	38.6851	+	23.4372i	1.27472	+	0.772280i
$922$	39.5515	−	30.1145i	1.30256	−	0.991767i
$923$	29.2287	+	16.8752i	0.962073	+	0.555453i
$924$	−1.37872	+	1.30205i	−0.0453566	+	0.0428343i
$925$	−24.8417	+	14.3424i	−0.816791	+	0.471574i
$926$	0.310549	−	0.741866i	0.0102053	−	0.0243792i
$927$	−23.6148	−	0.997479i	−0.775612	−	0.0327615i
$928$	19.8514	−	45.4984i	0.651655	−	1.49356i
$929$	16.6545	+	28.8464i	0.546416	+	0.946420i	0.998516	+	0.0544532i	$0.0173416\pi$
$929$	16.6545	+	28.8464i	0.546416	+	0.946420i	−0.452100	+	0.891967i	$0.649325\pi$
$930$	−1.72893	−	16.2418i	−0.0566938	−	0.532590i
$931$	−1.27946	−	0.738699i	−0.0419328	−	0.0242099i
$932$	5.11034	−	1.32840i	0.167395	−	0.0435131i
$933$	−14.4450	−	26.2856i	−0.472909	−	0.860552i
$934$	1.00076	+	7.82775i	0.0327457	+	0.256132i
$935$	1.23034			0.0402364
$936$	−17.3490	−	49.1610i	−0.567070	−	1.60688i
$937$	−7.59372			−0.248076			−0.124038	−	0.992277i	$-0.539584\pi$
$937$	−7.59372			−0.248076			−0.124038	+	0.992277i	$0.539584\pi$
$938$	−0.626549	−	4.90077i	−0.0204575	−	0.160016i
$939$	−27.5425	−	0.581433i	−0.898816	−	0.0189743i
$940$	−2.57456	−	9.90432i	−0.0839728	−	0.323043i
$941$	11.3195	+	6.53531i	0.369005	+	0.213045i	0.673024	−	0.739621i	$-0.264995\pi$
$941$	11.3195	+	6.53531i	0.369005	+	0.213045i	−0.304019	+	0.952666i	$0.598329\pi$
$942$	1.13935	−	0.830103i	0.0371220	−	0.0270462i
$943$	24.3631	+	42.1982i	0.793373	+	1.37416i
$944$	33.3996	+	0.500024i	1.08706	+	0.0162744i
$945$	0.376632	−	5.93996i	0.0122518	−	0.193227i
$946$	−2.85869	+	6.82909i	−0.0929440	+	0.222033i
$947$	−29.7389	+	17.1698i	−0.966385	+	0.557943i	−0.898132	−	0.439725i	$-0.855076\pi$
$947$	−29.7389	+	17.1698i	−0.966385	+	0.557943i	−0.0682529	+	0.997668i	$0.521742\pi$
$948$	−6.00146	+	1.42552i	−0.194918	+	0.0462988i
$949$	−53.3397	−	30.7957i	−1.73148	−	0.999671i
$950$	−6.13068	+	4.66788i	−0.198905	+	0.151446i
$951$	−0.300772	+	14.2476i	−0.00975320	+	0.462010i
$952$	−4.36462	−	3.42762i	−0.141458	−	0.111090i
$953$	−37.6736			−1.22037			−0.610184	−	0.792260i	$-0.708904\pi$
$953$	−37.6736			−1.22037			−0.610184	+	0.792260i	$0.708904\pi$
$954$	38.8585	−	27.0746i	1.25809	−	0.876574i
$955$		−	20.8872i		−	0.675894i
$956$	−14.1433	+	51.2460i	−0.457426	+	1.65741i
$957$	4.00728	+	7.29204i	0.129537	+	0.235718i
$958$	−20.6980	−	27.1842i	−0.668722	−	0.878282i
$959$	−5.21818	+	9.03816i	−0.168504	+	0.291857i
$960$	−4.77164	+	15.1375i	−0.154004	+	0.488559i
$961$	−1.44474	−	2.50236i	−0.0466044	−	0.0807212i
$962$	26.0954	−	62.3390i	0.841350	−	2.00989i
$963$	15.2592	−	7.97098i	0.491721	−	0.256861i
$964$	6.68551	+	6.78635i	0.215326	+	0.218574i
$965$	−25.3815	+	14.6540i	−0.817058	+	0.471729i
$966$	6.51397	−	14.6832i	0.209584	−	0.472423i
$967$	−7.08949	+	12.2794i	−0.227983	+	0.394877i	−0.957210	−	0.289394i	$-0.906546\pi$
$967$	−7.08949	+	12.2794i	−0.227983	+	0.394877i	0.729228	+	0.684271i	$0.239880\pi$
$968$	4.28702	−	29.9599i	0.137790	−	0.962948i
$969$	4.29424	+	2.60164i	0.137951	+	0.0835768i
$970$	−3.08295	−	24.1144i	−0.0989876	−	0.774266i
$971$			19.7926i			0.635174i	0.948229	+	0.317587i	$0.102873\pi$
$971$			19.7926i			0.635174i	−0.948229	+	0.317587i	$0.897127\pi$
$972$	−19.4185	−	24.3911i	−0.622847	−	0.782343i
$973$			9.76348i			0.313003i
$974$	29.1011	−	3.72049i	0.932459	−	0.119212i
$975$	−33.5658	−	20.3357i	−1.07497	−	0.651263i
$976$	−11.2802	+	18.8795i	−0.361072	+	0.604318i
$977$	−0.232369	+	0.402475i	−0.00743415	+	0.0128763i	−0.869719	−	0.493548i	$-0.835700\pi$
$977$	−0.232369	+	0.402475i	−0.00743415	+	0.0128763i	0.862284	+	0.506424i	$0.169033\pi$
$978$	1.14188	+	0.506577i	0.0365132	+	0.0161985i
$979$	0.923557	−	0.533216i	0.0295170	−	0.0170417i
$980$	−1.63198	+	1.60773i	−0.0521316	+	0.0513570i
$981$	−5.19834	+	2.71547i	−0.165970	+	0.0866981i
$982$	0.795033	+	0.332805i	0.0253705	+	0.0106202i
$983$	24.8964	+	43.1218i	0.794072	+	1.37537i	0.923427	+	0.383775i	$0.125376\pi$
$983$	24.8964	+	43.1218i	0.794072	+	1.37537i	−0.129355	+	0.991598i	$0.541291\pi$
$984$	−28.1473	−	23.0815i	−0.897303	−	0.735811i
$985$	−2.42969	+	4.20834i	−0.0774162	+	0.134089i
$986$	−19.3734	+	14.7508i	−0.616974	+	0.469763i
$987$	−3.72629	−	6.78072i	−0.118609	−	0.215833i
$988$	4.82969	−	17.4997i	0.153653	−	0.556738i
$989$		−	62.7096i		−	1.99405i
$990$	−1.52085	−	2.18278i	−0.0483359	−	0.0693734i
$991$	−21.2168			−0.673975			−0.336987	−	0.941509i	$-0.609408\pi$
$991$	−21.2168			−0.673975			−0.336987	+	0.941509i	$0.609408\pi$
$992$	3.68672	+	32.7242i	0.117053	+	1.03899i
$993$	0.386111	−	18.2901i	0.0122529	−	0.580419i
$994$	−4.70622	−	6.18102i	−0.149272	−	0.196050i
$995$	−4.87354	−	2.81374i	−0.154502	−	0.0892016i
$996$	−8.97131	−	37.7693i	−0.284267	−	1.19677i
$997$	26.7513	−	15.4449i	0.847223	−	0.489145i	−0.0124897	−	0.999922i	$-0.503976\pi$
$997$	26.7513	−	15.4449i	0.847223	−	0.489145i	0.859713	+	0.510777i	$0.170642\pi$
$998$	−10.1176	−	4.23528i	−0.320267	−	0.134066i
$999$	2.55746	−	40.3343i	0.0809144	−	1.27612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.1	✓	72
8.5	even	2	inner	504.2.cs.b.85.25	yes	72
9.7	even	3	inner	504.2.cs.b.421.25	yes	72
72.61	even	6	inner	504.2.cs.b.421.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.1	✓	72	1.1	even	1	trivial
504.2.cs.b.85.25	yes	72	8.5	even	2	inner
504.2.cs.b.421.1	yes	72	72.61	even	6	inner
504.2.cs.b.421.25	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40280 + 0.179343i) q^{2} +(-0.897491 + 1.48139i) q^{3} +(1.93567 - 0.503164i) q^{4} +(0.991981 + 0.572721i) q^{5} +(0.993320 - 2.23904i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-2.62511 + 1.05299i) q^{8} +(-1.38902 - 2.65906i) q^{9} +O(q^{10})\)	\(q+(-1.40280 + 0.179343i) q^{2} +(-0.897491 + 1.48139i) q^{3} +(1.93567 - 0.503164i) q^{4} +(0.991981 + 0.572721i) q^{5} +(0.993320 - 2.23904i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-2.62511 + 1.05299i) q^{8} +(-1.38902 - 2.65906i) q^{9} +(-1.49426 - 0.625505i) q^{10} +(-0.474092 + 0.273717i) q^{11} +(-0.991867 + 3.31907i) q^{12} +(-5.32075 - 3.07193i) q^{13} +(0.856714 + 1.12519i) q^{14} +(-1.73872 + 0.955498i) q^{15} +(3.49365 - 1.94792i) q^{16} -1.96209 q^{17} +(2.42540 + 3.48101i) q^{18} +1.47740i q^{19} +(2.20832 + 0.609470i) q^{20} +(1.73166 + 0.0365561i) q^{21} +(0.615965 - 0.468994i) q^{22} +(-3.27889 + 5.67921i) q^{23} +(0.796135 - 4.83386i) q^{24} +(-1.84398 - 3.19387i) q^{25} +(8.01485 + 3.35506i) q^{26} +(5.18574 + 0.328809i) q^{27} +(-1.40359 - 1.42476i) q^{28} +(-7.59962 + 4.38764i) q^{29} +(2.26770 - 1.65219i) q^{30} +(2.91073 - 5.04154i) q^{31} +(-4.55153 + 3.35910i) q^{32} +(0.0200121 - 0.947973i) q^{33} +(2.75242 - 0.351888i) q^{34} -1.14544i q^{35} +(-4.02663 - 4.44817i) q^{36} -7.77794i q^{37} +(-0.264961 - 2.07249i) q^{38} +(9.32605 - 5.12506i) q^{39} +(-3.20713 - 0.458914i) q^{40} +(3.71515 - 6.43483i) q^{41} +(-2.43573 + 0.259282i) q^{42} +(-8.28148 + 4.78131i) q^{43} +(-0.779962 + 0.768372i) q^{44} +(0.145020 - 3.43326i) q^{45} +(3.58109 - 8.55481i) q^{46} +(-2.23352 - 3.86857i) q^{47} +(-0.249895 + 6.92369i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(3.15953 + 4.14964i) q^{50} +(1.76096 - 2.90662i) q^{51} +(-11.8449 - 3.26905i) q^{52} -11.1630i q^{53} +(-7.33350 + 0.468775i) q^{54} -0.627054 q^{55} +(2.22447 + 1.74692i) q^{56} +(-2.18860 - 1.32595i) q^{57} +(9.87382 - 7.51791i) q^{58} +(7.23203 + 4.17541i) q^{59} +(-2.88481 + 2.72439i) q^{60} +(-4.76156 + 2.74909i) q^{61} +(-3.17900 + 7.59427i) q^{62} +(-1.60831 + 2.53246i) q^{63} +(5.78244 - 5.52842i) q^{64} +(-3.51872 - 6.09460i) q^{65} +(0.141940 + 1.33340i) q^{66} +(-3.02552 - 1.74679i) q^{67} +(-3.79797 + 0.987255i) q^{68} +(-5.47033 - 9.95435i) q^{69} +(0.205427 + 1.60682i) q^{70} -5.49334 q^{71} +(6.44629 + 5.51773i) q^{72} +10.0249 q^{73} +(1.39492 + 10.9109i) q^{74} +(6.38632 + 0.134818i) q^{75} +(0.743374 + 2.85976i) q^{76} +(0.474092 + 0.273717i) q^{77} +(-12.1634 + 8.86197i) q^{78} +(0.890337 + 1.54211i) q^{79} +(4.58125 + 0.0685859i) q^{80} +(-5.14125 + 7.38699i) q^{81} +(-4.05755 + 9.69304i) q^{82} +(-9.70504 + 5.60321i) q^{83} +(3.37033 - 0.800551i) q^{84} +(-1.94636 - 1.12373i) q^{85} +(10.7597 - 8.19243i) q^{86} +(0.320790 - 15.1959i) q^{87} +(0.956325 - 1.21775i) q^{88} -1.94805 q^{89} +(0.412300 + 4.84218i) q^{90} +6.14387i q^{91} +(-3.48929 + 12.6429i) q^{92} +(4.85612 + 8.83666i) q^{93} +(3.82698 + 5.02625i) q^{94} +(-0.846137 + 1.46555i) q^{95} +(-0.891166 - 9.75735i) q^{96} +(7.50375 + 12.9969i) q^{97} +(0.546082 - 1.30453i) q^{98} +(1.38635 + 0.880442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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