LMFDB - Embedded newform 900.2.o.a.599.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(299,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("900.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.7465802011608416256.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 $ x^16 - x^14 + x^12 + 8x^10 - 20x^8 + 32x^6 + 16x^4 - 64*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			599.8
Root			$-0.977642 + 1.02187i$ of defining polynomial
Character	$\chi$	$=$	900.599
Dual form			900.2.o.a.299.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37379 - 0.335728i) q^{2} +(1.07561 - 1.35760i) q^{3} +(1.77457 - 0.922437i) q^{4} +(1.02187 - 2.22616i) q^{6} +(-0.637910 - 1.10489i) q^{7} +(2.12819 - 1.86301i) q^{8} +(-0.686141 - 2.92048i) q^{9} +(-0.252704 - 0.437696i) q^{11} +(0.656444 - 3.40134i) q^{12} +(-2.05446 - 1.18614i) q^{13} +(-1.24730 - 1.30372i) q^{14} +(2.29822 - 3.27386i) q^{16} -0.792287 q^{17} +(-1.92310 - 3.78176i) q^{18} +4.70285i q^{19} +(-2.18614 - 0.322405i) q^{21} +(-0.494108 - 0.516461i) q^{22} +(2.78912 + 1.61030i) q^{23} +(-0.240111 - 4.89309i) q^{24} +(-3.22060 - 0.939764i) q^{26} +(-4.70285 - 2.20979i) q^{27} +(-2.15121 - 1.37228i) q^{28} +(-2.18614 + 1.26217i) q^{29} +(7.04069 + 4.06494i) q^{31} +(2.05813 - 5.26916i) q^{32} +(-0.866025 - 0.127719i) q^{33} +(-1.08843 + 0.265993i) q^{34} +(-3.91157 - 4.54969i) q^{36} -6.74456i q^{37} +(1.57888 + 6.46071i) q^{38} +(-3.82009 + 1.51330i) q^{39} +(5.87228 + 3.39036i) q^{41} +(-3.11153 + 0.291034i) q^{42} +(3.86473 + 6.69391i) q^{43} +(-0.852189 - 0.543620i) q^{44} +(4.37228 + 1.27582i) q^{46} +(1.03834 - 0.599485i) q^{47} +(-1.97261 - 6.64145i) q^{48} +(2.68614 - 4.65253i) q^{49} +(-0.852189 + 1.07561i) q^{51} +(-4.73992 - 0.209786i) q^{52} +1.87953 q^{53} +(-7.20260 - 1.45689i) q^{54} +(-3.41602 - 1.16300i) q^{56} +(6.38458 + 5.05842i) q^{57} +(-2.57954 + 2.46790i) q^{58} +(-6.18850 + 10.7188i) q^{59} +(1.18614 + 2.05446i) q^{61} +(11.0371 + 3.22060i) q^{62} +(-2.78912 + 2.62112i) q^{63} +(1.05842 - 7.92967i) q^{64} +(-1.23261 + 0.115291i) q^{66} +(3.86473 - 6.69391i) q^{67} +(-1.40597 + 0.730835i) q^{68} +(5.18614 - 2.05446i) q^{69} -11.8716 q^{71} +(-6.90111 - 4.93707i) q^{72} -3.37228i q^{73} +(-2.26434 - 9.26558i) q^{74} +(4.33809 + 8.34556i) q^{76} +(-0.322405 + 0.558422i) q^{77} +(-4.73992 + 3.36147i) q^{78} +(-8.55691 + 4.94034i) q^{79} +(-8.05842 + 4.00772i) q^{81} +(9.20550 + 2.68614i) q^{82} +(6.61659 - 3.82009i) q^{83} +(-4.17686 + 1.44445i) q^{84} +(7.55665 + 7.89850i) q^{86} +(-0.637910 + 4.32550i) q^{87} +(-1.35323 - 0.460714i) q^{88} +11.9769i q^{89} +3.02661i q^{91} +(6.43491 + 0.284805i) q^{92} +(13.0916 - 5.18614i) q^{93} +(1.22519 - 1.17216i) q^{94} +(-4.93967 - 8.46166i) q^{96} +(9.08385 - 5.24456i) q^{97} +(2.12819 - 7.29339i) q^{98} +(-1.10489 + 1.03834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} - 6 q^{6} + 12 q^{9} - 24 q^{14} - 2 q^{16} - 12 q^{21} - 6 q^{24} - 12 q^{29} - 14 q^{34} - 66 q^{36} + 48 q^{41} + 24 q^{46} + 20 q^{49} - 78 q^{54} + 36 q^{56} - 4 q^{61} - 52 q^{64} - 48 q^{66}+ \cdots + 24 q^{96}+O(q^{100}) $ 16 * q + 2 * q^4 - 6 * q^6 + 12 * q^9 - 24 * q^14 - 2 * q^16 - 12 * q^21 - 6 * q^24 - 12 * q^29 - 14 * q^34 - 66 * q^36 + 48 * q^41 + 24 * q^46 + 20 * q^49 - 78 * q^54 + 36 * q^56 - 4 * q^61 - 52 * q^64 - 48 * q^66 + 60 * q^69 + 60 * q^74 - 6 * q^76 - 60 * q^81 - 60 * q^84 + 42 * q^86 + 36 * q^94 + 24 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.37379	−	0.335728i	0.971413	−	0.237396i
$2$	1.37379	−	0.335728i	0.971413	−	0.237396i
$3$	1.07561	−	1.35760i	0.621002	−	0.783809i
$3$	1.07561	−	1.35760i	0.621002	−	0.783809i
$4$	1.77457	−	0.922437i	0.887287	−	0.461219i
$5$		0			0
$5$		0			0
$6$	1.02187	−	2.22616i	0.417176	−	0.908826i
$7$	−0.637910	−	1.10489i	−0.241107	−	0.417610i	0.719923	−	0.694054i	$-0.244177\pi$
$7$	−0.637910	−	1.10489i	−0.241107	−	0.417610i	−0.961030	+	0.276444i	$0.910844\pi$
$8$	2.12819	−	1.86301i	0.752430	−	0.658672i
$9$	−0.686141	−	2.92048i	−0.228714	−	0.973494i
$10$		0			0
$11$	−0.252704	−	0.437696i	−0.0761931	−	0.131970i	0.825411	−	0.564532i	$-0.190943\pi$
$11$	−0.252704	−	0.437696i	−0.0761931	−	0.131970i	−0.901605	+	0.432561i	$0.857610\pi$
$12$	0.656444	−	3.40134i	0.189499	−	0.981881i
$13$	−2.05446	−	1.18614i	−0.569804	−	0.328976i	0.187267	−	0.982309i	$-0.440037\pi$
$13$	−2.05446	−	1.18614i	−0.569804	−	0.328976i	−0.757071	+	0.653333i	$0.773370\pi$
$14$	−1.24730	−	1.30372i	−0.333354	−	0.348434i
$15$		0			0
$16$	2.29822	−	3.27386i	0.574555	−	0.818466i
$17$	−0.792287			−0.192158			−0.0960789	−	0.995374i	$-0.530630\pi$
$17$	−0.792287			−0.192158			−0.0960789	+	0.995374i	$0.530630\pi$
$18$	−1.92310	−	3.78176i	−0.453279	−	0.891369i
$19$			4.70285i			1.07891i	0.842015	+	0.539454i	$0.181369\pi$
$19$			4.70285i			1.07891i	−0.842015	+	0.539454i	$0.818631\pi$
$20$		0			0
$21$	−2.18614	−	0.322405i	−0.477055	−	0.0703546i
$22$	−0.494108	−	0.516461i	−0.105344	−	0.110110i
$23$	2.78912	+	1.61030i	0.581572	+	0.335771i	0.761758	−	0.647862i	$-0.224336\pi$
$23$	2.78912	+	1.61030i	0.581572	+	0.335771i	−0.180186	+	0.983633i	$0.557670\pi$
$24$	−0.240111	−	4.89309i	−0.0490125	−	0.998798i
$25$		0			0
$26$	−3.22060	−	0.939764i	−0.631612	−	0.184303i
$27$	−4.70285	−	2.20979i	−0.905065	−	0.425274i
$28$	−2.15121	−	1.37228i	−0.406541	−	0.259337i
$29$	−2.18614	+	1.26217i	−0.405956	+	0.234379i	−0.689051	−	0.724713i	$-0.741972\pi$
$29$	−2.18614	+	1.26217i	−0.405956	+	0.234379i	0.283095	+	0.959092i	$0.408639\pi$
$30$		0			0
$31$	7.04069	+	4.06494i	1.26455	+	0.730086i	0.973951	−	0.226761i	$-0.0728135\pi$
$31$	7.04069	+	4.06494i	1.26455	+	0.730086i	0.290595	+	0.956846i	$0.406147\pi$
$32$	2.05813	−	5.26916i	0.363830	−	0.931466i
$33$	−0.866025	−	0.127719i	−0.150756	−	0.0222330i
$34$	−1.08843	+	0.265993i	−0.186665	+	0.0456175i
$35$		0			0
$36$	−3.91157	−	4.54969i	−0.651928	−	0.758281i
$37$		−	6.74456i		−	1.10880i	−0.832251	−	0.554400i	$-0.812948\pi$
$37$		−	6.74456i		−	1.10880i	0.832251	−	0.554400i	$-0.187052\pi$
$38$	1.57888	+	6.46071i	0.256128	+	1.04807i
$39$	−3.82009	+	1.51330i	−0.611704	+	0.242322i
$40$		0			0
$41$	5.87228	+	3.39036i	0.917096	+	0.529486i	0.882708	−	0.469923i	$-0.155718\pi$
$41$	5.87228	+	3.39036i	0.917096	+	0.529486i	0.0343887	+	0.999409i	$0.489052\pi$
$42$	−3.11153	+	0.291034i	−0.480119	+	0.0449075i
$43$	3.86473	+	6.69391i	0.589366	+	1.02081i	0.994316	+	0.106473i	$0.0339557\pi$
$43$	3.86473	+	6.69391i	0.589366	+	1.02081i	−0.404950	+	0.914339i	$0.632711\pi$
$44$	−0.852189	−	0.543620i	−0.128472	−	0.0819538i
$45$		0			0
$46$	4.37228	+	1.27582i	0.644658	+	0.188110i
$47$	1.03834	−	0.599485i	0.151457	−	0.0874439i	−0.422356	−	0.906430i	$-0.638797\pi$
$47$	1.03834	−	0.599485i	0.151457	−	0.0874439i	0.573813	+	0.818986i	$0.305463\pi$
$48$	−1.97261	−	6.64145i	−0.284722	−	0.958610i
$49$	2.68614	−	4.65253i	0.383734	−	0.664647i
$50$		0			0
$51$	−0.852189	+	1.07561i	−0.119330	+	0.150615i
$52$	−4.73992	−	0.209786i	−0.657309	−	0.0290921i
$53$	1.87953			0.258173			0.129086	−	0.991633i	$-0.458796\pi$
$53$	1.87953			0.258173			0.129086	+	0.991633i	$0.458796\pi$
$54$	−7.20260	−	1.45689i	−0.980150	−	0.198258i
$55$		0			0
$56$	−3.41602	−	1.16300i	−0.456485	−	0.155412i
$57$	6.38458	+	5.05842i	0.845659	+	0.670004i
$58$	−2.57954	+	2.46790i	−0.338711	+	0.324051i
$59$	−6.18850	+	10.7188i	−0.805674	+	1.39547i	0.110161	+	0.993914i	$0.464863\pi$
$59$	−6.18850	+	10.7188i	−0.805674	+	1.39547i	−0.915835	+	0.401555i	$0.868470\pi$
$60$		0			0
$61$	1.18614	+	2.05446i	0.151870	+	0.263046i	0.931915	−	0.362677i	$-0.118137\pi$
$61$	1.18614	+	2.05446i	0.151870	+	0.263046i	−0.780045	+	0.625723i	$0.784804\pi$
$62$	11.0371	+	3.22060i	1.40172	+	0.409017i
$63$	−2.78912	+	2.62112i	−0.351397	+	0.330230i
$64$	1.05842	−	7.92967i	0.132303	−	0.991209i
$65$		0			0
$66$	−1.23261	+	0.115291i	−0.151724	+	0.0141914i
$67$	3.86473	−	6.69391i	0.472152	−	0.817791i	−0.527340	−	0.849654i	$-0.676811\pi$
$67$	3.86473	−	6.69391i	0.472152	−	0.817791i	0.999492	+	0.0318630i	$0.0101440\pi$
$68$	−1.40597	+	0.730835i	−0.170499	+	0.0886268i
$69$	5.18614	−	2.05446i	0.624338	−	0.247327i
$70$		0			0
$71$	−11.8716			−1.40890			−0.704450	−	0.709754i	$-0.748806\pi$
$71$	−11.8716			−1.40890			−0.704450	+	0.709754i	$0.748806\pi$
$72$	−6.90111	−	4.93707i	−0.813304	−	0.581839i
$73$		−	3.37228i		−	0.394696i	−0.980334	−	0.197348i	$-0.936767\pi$
$73$		−	3.37228i		−	0.394696i	0.980334	−	0.197348i	$-0.0632328\pi$
$74$	−2.26434	−	9.26558i	−0.263224	−	1.07710i
$75$		0			0
$76$	4.33809	+	8.34556i	0.497613	+	0.957301i
$77$	−0.322405	+	0.558422i	−0.0367415	+	0.0636381i
$78$	−4.73992	+	3.36147i	−0.536691	+	0.380611i
$79$	−8.55691	+	4.94034i	−0.962728	+	0.555831i	−0.897012	−	0.442007i	$-0.854267\pi$
$79$	−8.55691	+	4.94034i	−0.962728	+	0.555831i	−0.0657165	+	0.997838i	$0.520933\pi$
$80$		0			0
$81$	−8.05842	+	4.00772i	−0.895380	+	0.445302i
$82$	9.20550	+	2.68614i	1.01658	+	0.296635i
$83$	6.61659	−	3.82009i	0.726265	−	0.419309i	−0.0907894	−	0.995870i	$-0.528939\pi$
$83$	6.61659	−	3.82009i	0.726265	−	0.419309i	0.817054	+	0.576561i	$0.195606\pi$
$84$	−4.17686	+	1.44445i	−0.455733	+	0.157602i
$85$		0			0
$86$	7.55665	+	7.89850i	0.814854	+	0.851717i
$87$	−0.637910	+	4.32550i	−0.0683912	+	0.463742i
$88$	−1.35323	−	0.460714i	−0.144255	−	0.0491122i
$89$			11.9769i			1.26955i	0.772698	+	0.634773i	$0.218907\pi$
$89$			11.9769i			1.26955i	−0.772698	+	0.634773i	$0.781093\pi$
$90$		0			0
$91$			3.02661i			0.317274i
$92$	6.43491	+	0.284805i	0.670885	+	0.0296930i
$93$	13.0916	−	5.18614i	1.35753	−	0.537778i
$94$	1.22519	−	1.17216i	0.126369	−	0.120899i
$95$		0			0
$96$	−4.93967	−	8.46166i	−0.504152	−	0.863615i
$97$	9.08385	−	5.24456i	0.922325	−	0.532505i	0.0379490	−	0.999280i	$-0.487918\pi$
$97$	9.08385	−	5.24456i	0.922325	−	0.532505i	0.884376	+	0.466775i	$0.154584\pi$
$98$	2.12819	−	7.29339i	0.214980	−	0.736744i
$99$	−1.10489	+	1.03834i	−0.111046	+	0.104357i
$100$		0			0
$101$	1.06930	−	0.617359i	0.106399	−	0.0614295i	−0.445856	−	0.895105i	$-0.647101\pi$
$101$	1.06930	−	0.617359i	0.106399	−	0.0614295i	0.552255	+	0.833675i	$0.313767\pi$
$102$	−0.809613	+	1.76376i	−0.0801637	+	0.174638i
$103$	0.237482	−	0.411331i	0.0233998	−	0.0405297i	−0.854088	−	0.520128i	$-0.825884\pi$
$103$	0.237482	−	0.411331i	0.0233998	−	0.0405297i	0.877488	+	0.479598i	$0.159218\pi$
$104$	−6.58207	+	1.30312i	−0.645425	+	0.127782i
$105$		0			0
$106$	2.58207	−	0.631011i	0.250793	−	0.0612892i
$107$			12.5652i			1.21472i	0.794427	+	0.607360i	$0.207771\pi$
$107$			12.5652i			1.21472i	−0.794427	+	0.607360i	$0.792229\pi$
$108$	−10.3839	+	0.416661i	−0.999196	+	0.0400933i
$109$	−13.4891			−1.29202			−0.646012	−	0.763327i	$-0.723564\pi$
$109$	−13.4891			−1.29202			−0.646012	+	0.763327i	$0.723564\pi$
$110$		0			0
$111$	−9.15640	−	7.25450i	−0.869087	−	0.688566i
$112$	−5.08333	−	0.450854i	−0.480329	−	0.0426017i
$113$	−3.63903	+	6.30298i	−0.342331	+	0.592935i	−0.984865	−	0.173322i	$-0.944550\pi$
$113$	−3.63903	+	6.30298i	−0.342331	+	0.592935i	0.642534	+	0.766257i	$0.277883\pi$
$114$	10.4693	+	4.80570i	0.980540	+	0.450095i
$115$		0			0
$116$	−2.71519	+	4.25639i	−0.252099	+	0.395196i
$117$	−2.05446	+	6.81386i	−0.189935	+	0.629942i
$118$	−4.90307	+	16.8030i	−0.451364	+	1.54684i
$119$	0.505408	+	0.875393i	0.0463307	+	0.0802471i
$120$		0			0
$121$	5.37228	−	9.30506i	0.488389	−	0.845915i
$122$	2.31924	+	2.42416i	0.209974	+	0.219473i
$123$	10.9190	−	4.32550i	0.984534	−	0.390017i
$124$	16.2439	+	0.718945i	1.45874	+	0.0645632i
$125$		0			0
$126$	−2.95167	+	4.53724i	−0.262956	+	0.404210i
$127$	−7.65492			−0.679265			−0.339632	−	0.940558i	$-0.610303\pi$
$127$	−7.65492			−0.679265			−0.339632	+	0.940558i	$0.610303\pi$
$128$	−1.20817	−	11.2490i	−0.106788	−	0.994282i
$129$	13.2446	+	1.95327i	1.16612	+	0.171975i
$130$		0			0
$131$	−3.82009	+	6.61659i	−0.333763	+	0.578094i	−0.983246	−	0.182282i	$-0.941652\pi$
$131$	−3.82009	+	6.61659i	−0.333763	+	0.578094i	0.649484	+	0.760375i	$0.274985\pi$
$132$	−1.65464	+	0.572208i	−0.144018	+	0.0498043i
$133$	5.19615	−	3.00000i	0.450564	−	0.260133i
$134$	3.06198	−	10.4935i	0.264514	−	0.906500i
$135$		0			0
$136$	−1.68614	+	1.47603i	−0.144585	+	0.126569i
$137$	−2.74555	−	4.75544i	−0.234568	−	0.406284i	0.724579	−	0.689192i	$-0.242034\pi$
$137$	−2.74555	−	4.75544i	−0.234568	−	0.406284i	−0.959147	+	0.282908i	$0.908701\pi$
$138$	6.43491	−	4.56352i	0.547776	−	0.388472i
$139$	13.3233	+	7.69219i	1.13006	+	0.652443i	0.943951	−	0.330085i	$-0.107077\pi$
$139$	13.3233	+	7.69219i	1.13006	+	0.652443i	0.186114	+	0.982528i	$0.440411\pi$
$140$		0			0
$141$	0.302985	−	2.05446i	0.0255159	−	0.173016i
$142$	−16.3090	+	3.98563i	−1.36862	+	0.334467i
$143$			1.19897i			0.100263i
$144$	−11.1382	−	4.46557i	−0.928180	−	0.372131i
$145$		0			0
$146$	−1.13217	−	4.63279i	−0.0936991	−	0.383413i
$147$	−3.42703	−	8.65099i	−0.282657	−	0.713522i
$148$	−6.22144	−	11.9687i	−0.511399	−	0.983823i
$149$	11.1861	+	6.45832i	0.916404	+	0.529086i	0.882486	−	0.470338i	$-0.155868\pi$
$149$	11.1861	+	6.45832i	0.916404	+	0.529086i	0.0339182	+	0.999425i	$0.489201\pi$
$150$		0			0
$151$	−2.62112	+	1.51330i	−0.213304	+	0.123151i	−0.602846	−	0.797858i	$-0.705967\pi$
$151$	−2.62112	+	1.51330i	−0.213304	+	0.123151i	0.389542	+	0.921009i	$0.372633\pi$
$152$	8.76144	+	10.0086i	0.710647	+	0.811804i
$153$	0.543620	+	2.31386i	0.0439491	+	0.187064i
$154$	−0.255437	+	0.875393i	−0.0205837	+	0.0705411i
$155$		0			0
$156$	−5.38310	+	6.20926i	−0.430993	+	0.497139i
$157$	−10.2723	−	5.93070i	−0.819817	−	0.473322i	0.0305363	−	0.999534i	$-0.490278\pi$
$157$	−10.2723	−	5.93070i	−0.819817	−	0.473322i	−0.850353	+	0.526212i	$0.823612\pi$
$158$	−10.0968	+	9.65976i	−0.803255	+	0.768489i
$159$	2.02163	−	2.55164i	0.160326	−	0.202358i
$160$		0			0
$161$		−	4.10891i		−	0.323828i
$162$	−9.72504	+	8.21119i	−0.764071	+	0.645132i
$163$	−1.75079			−0.137132			−0.0685660	−	0.997647i	$-0.521842\pi$
$163$	−1.75079			−0.137132			−0.0685660	+	0.997647i	$0.521842\pi$
$164$	13.5482	+	0.599636i	1.05794	+	0.0468237i
$165$		0			0
$166$	7.80726	−	7.46936i	0.605961	−	0.579734i
$167$	15.1469	+	8.74507i	1.17210	+	0.676714i	0.954174	−	0.299251i	$-0.0967368\pi$
$167$	15.1469	+	8.74507i	1.17210	+	0.676714i	0.217928	+	0.975965i	$0.430070\pi$
$168$	−5.25317	+	3.38665i	−0.405291	+	0.261286i
$169$	−3.68614	−	6.38458i	−0.283549	−	0.491122i
$170$		0			0
$171$	13.7346	−	3.22682i	1.05031	−	0.246761i
$172$	13.0330	+	8.31386i	0.993754	+	0.633926i
$173$	−8.83518	−	15.3030i	−0.671726	−	1.16346i	−0.977414	−	0.211333i	$-0.932220\pi$
$173$	−8.83518	−	15.3030i	−0.671726	−	1.16346i	0.305688	−	0.952132i	$-0.401114\pi$
$174$	0.575839	+	6.15647i	0.0436543	+	0.466721i
$175$		0			0
$176$	−2.01373	−	0.178603i	−0.151790	−	0.0134627i
$177$	7.89542	+	19.9307i	0.593456	+	1.49808i
$178$	4.02098	+	16.4537i	0.301385	+	1.23325i
$179$	8.83915			0.660669			0.330334	−	0.943864i	$-0.392838\pi$
$179$	8.83915			0.660669			0.330334	+	0.943864i	$0.392838\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	1.01612	+	4.15791i	0.0753196	+	0.308205i
$183$	4.06494	+	0.599485i	0.300489	+	0.0443152i
$184$	8.93580	−	1.76912i	0.658756	−	0.130421i
$185$		0			0
$186$	16.2439	−	11.5199i	1.19106	−	0.844677i
$187$	0.200214	+	0.346781i	0.0146411	+	0.0253591i
$188$	1.28962	−	2.02163i	0.0940552	−	0.147443i
$189$	0.558422	+	6.60580i	0.0406192	+	0.480501i
$190$		0			0
$191$	7.54610	+	13.0702i	0.546017	+	0.945728i	0.998542	+	0.0539770i	$0.0171898\pi$
$191$	7.54610	+	13.0702i	0.546017	+	0.945728i	−0.452526	+	0.891751i	$0.649477\pi$
$192$	−9.62686	−	9.96612i	−0.694759	−	0.719243i
$193$	6.70699	+	3.87228i	0.482780	+	0.278733i	0.721574	−	0.692337i	$-0.243419\pi$
$193$	6.70699	+	3.87228i	0.482780	+	0.278733i	−0.238795	+	0.971070i	$0.576752\pi$
$194$	10.7185	−	10.2546i	0.769544	−	0.736238i
$195$		0			0
$196$	0.475083	−	10.7341i	0.0339345	−	0.766718i
$197$	−23.9538			−1.70663			−0.853317	−	0.521392i	$-0.825413\pi$
$197$	−23.9538			−1.70663			−0.853317	+	0.521392i	$0.825413\pi$
$198$	−1.16929	+	1.79740i	−0.0830976	+	0.127736i
$199$		−	12.9073i		−	0.914973i	−0.889217	−	0.457486i	$-0.848750\pi$
$199$		−	12.9073i		−	0.914973i	0.889217	−	0.457486i	$-0.151250\pi$
$200$		0			0
$201$	−4.93070	−	12.4468i	−0.347785	−	0.877927i
$202$	1.26172	−	1.20711i	0.0887743	−	0.0849321i
$203$	2.78912	+	1.61030i	0.195758	+	0.113021i
$204$	−0.520092	+	2.69483i	−0.0364137	+	0.188676i
$205$		0			0
$206$	0.188154	−	0.644810i	0.0131093	−	0.0449261i
$207$	2.78912	−	9.25048i	0.193857	−	0.642953i
$208$	−8.60485	+	4.00000i	−0.596639	+	0.277350i
$209$	2.05842	−	1.18843i	0.142384	−	0.0822055i
$210$		0			0
$211$	15.1863	+	8.76780i	1.04547	+	0.603600i	0.921377	−	0.388671i	$-0.127066\pi$
$211$	15.1863	+	8.76780i	1.04547	+	0.603600i	0.124090	+	0.992271i	$0.460399\pi$
$212$	3.33536	−	1.73375i	0.229073	−	0.119074i
$213$	−12.7692	+	16.1168i	−0.874929	+	1.10431i
$214$	4.21848	+	17.2618i	0.288369	+	1.17999i
$215$		0			0
$216$	−14.1254	+	4.05859i	−0.961114	+	0.276152i
$217$		−	10.3723i		−	0.704116i
$218$	−18.5312	+	4.52868i	−1.25509	+	0.306721i
$219$	−4.57820	−	3.62725i	−0.309366	−	0.245107i
$220$		0			0
$221$	1.62772	+	0.939764i	0.109492	+	0.0632154i
$222$	−15.0145	−	6.89206i	−1.00771	−	0.462565i
$223$	−4.06494	−	7.04069i	−0.272209	−	0.471479i	0.697218	−	0.716859i	$-0.254421\pi$
$223$	−4.06494	−	7.04069i	−0.272209	−	0.471479i	−0.969427	+	0.245379i	$0.921087\pi$
$224$	−7.13477	+	1.08724i	−0.476712	+	0.0726443i
$225$		0			0
$226$	−2.88316	+	9.88067i	−0.191785	+	0.657253i
$227$	−12.4696	+	7.19932i	−0.827635	+	0.477835i	−0.853042	−	0.521842i	$-0.825245\pi$
$227$	−12.4696	+	7.19932i	−0.827635	+	0.477835i	0.0254070	+	0.999677i	$0.491912\pi$
$228$	15.9960	+	3.08716i	1.05936	+	0.204452i
$229$	1.81386	−	3.14170i	0.119863	−	0.207609i	−0.799850	−	0.600200i	$-0.795088\pi$
$229$	1.81386	−	3.14170i	0.119863	−	0.207609i	0.919713	+	0.392591i	$0.128421\pi$
$230$		0			0
$231$	0.411331	+	1.03834i	0.0270636	+	0.0683177i
$232$	−2.30110	+	6.75893i	−0.151075	+	0.443746i
$233$	−4.84630			−0.317491			−0.158746	−	0.987320i	$-0.550745\pi$
$233$	−4.84630			−0.317491			−0.158746	+	0.987320i	$0.550745\pi$
$234$	−0.534776	+	10.0505i	−0.0349594	+	0.657023i
$235$		0			0
$236$	−1.09453	+	24.7298i	−0.0712477	+	1.60977i
$237$	−2.49689	+	16.9307i	−0.162190	+	1.09977i
$238$	0.988216	+	1.03292i	0.0640566	+	0.0669544i
$239$	6.02987	−	10.4440i	0.390040	−	0.675569i	−0.602414	−	0.798184i	$-0.705794\pi$
$239$	6.02987	−	10.4440i	0.390040	−	0.675569i	0.992454	+	0.122614i	$0.0391278\pi$
$240$		0			0
$241$	3.24456	+	5.61975i	0.209001	+	0.362000i	0.951400	−	0.307958i	$-0.0996456\pi$
$241$	3.24456	+	5.61975i	0.209001	+	0.362000i	−0.742399	+	0.669958i	$0.766312\pi$
$242$	4.25639	−	14.5868i	0.273611	−	0.937674i
$243$	−3.22682	+	15.2508i	−0.207001	+	0.978341i
$244$	4.00000	+	2.55164i	0.256074	+	0.163352i
$245$		0			0
$246$	13.5482	−	9.60812i	0.863801	−	0.612592i
$247$	5.57825	−	9.66181i	0.354935	−	0.614766i
$248$	22.5570	−	4.46585i	1.43237	−	0.283582i
$249$	1.93070	−	13.0916i	0.122353	−	0.829645i
$250$		0			0
$251$	−11.1780			−0.705551			−0.352776	−	0.935708i	$-0.614762\pi$
$251$	−11.1780			−0.705551			−0.352776	+	0.935708i	$0.614762\pi$
$252$	−2.53169	+	7.22416i	−0.159481	+	0.455079i
$253$		−	1.62772i		−	0.102334i
$254$	−10.5162	+	2.56997i	−0.659847	+	0.161255i
$255$		0			0
$256$	−5.43638	−	15.0481i	−0.339774	−	0.940507i
$257$	−7.49927	+	12.9891i	−0.467792	+	0.810239i	−0.999323	−	0.0367996i	$-0.988284\pi$
$257$	−7.49927	+	12.9891i	−0.467792	+	0.810239i	0.531531	+	0.847039i	$0.321617\pi$
$258$	18.8510	−	1.76321i	1.17361	−	0.109772i
$259$	−7.45202	+	4.30243i	−0.463046	+	0.267340i
$260$		0			0
$261$	5.18614	+	5.51856i	0.321014	+	0.341590i
$262$	−3.02661	+	10.3723i	−0.186984	+	0.640802i
$263$	−24.2267	+	13.9873i	−1.49388	+	0.862494i	−0.999975	−	0.00701993i	$-0.997765\pi$
$263$	−24.2267	+	13.9873i	−1.49388	+	0.862494i	−0.493908	+	0.869514i	$0.664432\pi$
$264$	−2.08101	+	1.34160i	−0.128077	+	0.0825698i
$265$		0			0
$266$	6.13121	−	5.86585i	0.375929	−	0.359658i
$267$	16.2598	+	12.8824i	0.995082	+	0.788391i
$268$	0.683534	−	15.4438i	0.0417535	−	0.943380i
$269$			21.4843i			1.30992i	0.755663	+	0.654961i	$0.227315\pi$
$269$			21.4843i			1.30992i	−0.755663	+	0.654961i	$0.772685\pi$
$270$		0			0
$271$		−	29.9679i		−	1.82042i	−0.414146	−	0.910211i	$-0.635920\pi$
$271$		−	29.9679i		−	1.82042i	0.414146	−	0.910211i	$-0.364080\pi$
$272$	−1.82085	+	2.59384i	−0.110405	+	0.157275i
$273$	4.10891	+	3.25544i	0.248683	+	0.197028i
$274$	−5.36834	−	5.61119i	−0.324313	−	0.338984i
$275$		0			0
$276$	7.30808	−	8.42967i	0.439895	−	0.507407i
$277$	5.51856	−	3.18614i	0.331578	−	0.191437i	−0.324963	−	0.945727i	$-0.605352\pi$
$277$	5.51856	−	3.18614i	0.331578	−	0.191437i	0.656541	+	0.754290i	$0.272019\pi$
$278$	20.8858	+	6.09442i	1.25265	+	0.365519i
$279$	7.04069	−	23.3513i	0.421515	−	1.39801i
$280$		0			0
$281$	−19.9307	+	11.5070i	−1.18897	+	0.686450i	−0.958072	−	0.286529i	$-0.907499\pi$
$281$	−19.9307	+	11.5070i	−1.18897	+	0.686450i	−0.230894	+	0.972979i	$0.574165\pi$
$282$	−0.273503	−	2.92410i	−0.0162869	−	0.174128i
$283$	4.94034	−	8.55691i	0.293673	−	0.508656i	−0.681003	−	0.732281i	$-0.738456\pi$
$283$	4.94034	−	8.55691i	0.293673	−	0.508656i	0.974675	+	0.223625i	$0.0717891\pi$
$284$	−21.0670	+	10.9508i	−1.25010	+	0.649811i
$285$		0			0
$286$	0.402528	+	1.64713i	0.0238020	+	0.0973967i
$287$		−	8.65099i		−	0.510652i
$288$	−16.8007	−	2.39534i	−0.989989	−	0.141147i
$289$	−16.3723			−0.963075
$290$		0			0
$291$	2.65064	−	17.9733i	0.155384	−	1.05361i
$292$	−3.11072	−	5.98436i	−0.182041	−	0.350208i
$293$	−11.6545	+	20.1861i	−0.680862	+	1.17929i	0.293857	+	0.955850i	$0.405061\pi$
$293$	−11.6545	+	20.1861i	−0.680862	+	1.17929i	−0.974718	+	0.223437i	$0.928272\pi$
$294$	−7.61239	−	10.7341i	−0.443964	−	0.626023i
$295$		0			0
$296$	−12.5652	−	14.3537i	−0.730335	−	0.834294i
$297$	0.221215	+	2.61684i	0.0128362	+	0.151845i
$298$	17.5356	+	5.11684i	1.01581	+	0.296411i
$299$	−3.82009	−	6.61659i	−0.220921	−	0.382647i
$300$		0			0
$301$	4.93070	−	8.54023i	0.284201	−	0.492251i
$302$	−3.09279	+	2.95894i	−0.177970	+	0.170268i
$303$	0.312018	−	2.11571i	0.0179250	−	0.121544i
$304$	15.3965	+	10.8082i	0.883050	+	0.619892i
$305$		0			0
$306$	1.52365	+	2.99624i	0.0871010	+	0.171284i
$307$	−1.20128			−0.0685609			−0.0342805	−	0.999412i	$-0.510914\pi$
$307$	−1.20128			−0.0685609			−0.0342805	+	0.999412i	$0.510914\pi$
$308$	−0.0570221	+	1.28836i	−0.00324913	+	0.0734111i
$309$	−0.302985	−	0.764836i	−0.0172362	−	0.0435100i
$310$		0			0
$311$	9.56773	−	16.5718i	0.542536	−	0.939700i	−0.456221	−	0.889866i	$-0.650797\pi$
$311$	9.56773	−	16.5718i	0.542536	−	0.939700i	0.998758	−	0.0498340i	$-0.0158692\pi$
$312$	−5.31060	+	10.3374i	−0.300653	+	0.585243i
$313$	16.0121	−	9.24456i	0.905055	−	0.522534i	0.0262180	−	0.999656i	$-0.491654\pi$
$313$	16.0121	−	9.24456i	0.905055	−	0.522534i	0.878837	+	0.477123i	$0.158320\pi$
$314$	−16.1030	−	4.69882i	−0.908746	−	0.265170i
$315$		0			0
$316$	−10.6277	+	16.6602i	−0.597856	+	0.937210i
$317$	−16.2607	−	28.1644i	−0.913293	−	1.58187i	−0.809381	−	0.587283i	$-0.800197\pi$
$317$	−16.2607	−	28.1644i	−0.913293	−	1.58187i	−0.103911	−	0.994587i	$-0.533136\pi$
$318$	1.92063	−	4.18413i	0.107704	−	0.234634i
$319$	1.10489	+	0.637910i	0.0618621	+	0.0357161i
$320$		0			0
$321$	17.0584	+	13.5152i	0.952108	+	0.754343i
$322$	−1.37948	−	5.64476i	−0.0768753	−	0.314570i
$323$		−	3.72601i		−	0.207321i
$324$	−10.6034	+	14.5454i	−0.589077	+	0.808077i
$325$		0			0
$326$	−2.40520	+	0.587788i	−0.133212	+	0.0325546i
$327$	−14.5090	+	18.3128i	−0.802349	+	1.01270i
$328$	18.8136	−	3.72474i	1.03881	−	0.205664i
$329$	−1.32473	−	0.764836i	−0.0730350	−	0.0421667i
$330$		0			0
$331$	−24.0254	+	13.8711i	−1.32056	+	0.762424i	−0.983817	−	0.179174i	$-0.942657\pi$
$331$	−24.0254	+	13.8711i	−1.32056	+	0.762424i	−0.336739	+	0.941598i	$0.609324\pi$
$332$	8.21782	−	12.8824i	0.451012	−	0.707014i
$333$	−19.6974	+	4.62772i	−1.07941	+	0.253597i
$334$	23.7446	+	6.92860i	1.29924	+	0.379116i
$335$		0			0
$336$	−6.07974	+	6.41617i	−0.331677	+	0.350031i
$337$	13.6352	+	7.87228i	0.742756	+	0.428830i	0.823071	−	0.567939i	$-0.192259\pi$
$337$	13.6352	+	7.87228i	0.742756	+	0.428830i	−0.0803144	+	0.996770i	$0.525592\pi$
$338$	−7.20745	−	7.53351i	−0.392034	−	0.409769i
$339$	4.64275	+	11.7199i	0.252160	+	0.636536i
$340$		0			0
$341$		−	4.10891i		−	0.222510i
$342$	17.7851	−	9.04405i	0.961706	−	0.489046i
$343$	−15.7848			−0.852300
$344$	20.6957	+	7.04593i	1.11584	+	0.379891i
$345$		0			0
$346$	−17.2753	−	18.0568i	−0.928725	−	0.970739i
$347$	−6.01594	−	3.47331i	−0.322953	−	0.186457i	0.329755	−	0.944066i	$-0.393034\pi$
$347$	−6.01594	−	3.47331i	−0.322953	−	0.186457i	−0.652708	+	0.757610i	$0.726367\pi$
$348$	2.85798	+	8.26434i	0.153204	+	0.443015i
$349$	−2.81386	−	4.87375i	−0.150622	−	0.260886i	0.780834	−	0.624739i	$-0.214794\pi$
$349$	−2.81386	−	4.87375i	−0.150622	−	0.260886i	−0.931456	+	0.363853i	$0.881461\pi$
$350$		0			0
$351$	7.04069	+	10.1182i	0.375804	+	0.540067i
$352$	−2.82639	+	0.430703i	−0.150647	+	0.0229566i
$353$	−4.18265	−	7.24456i	−0.222620	−	0.385589i	0.732983	−	0.680247i	$-0.238128\pi$
$353$	−4.18265	−	7.24456i	−0.222620	−	0.385589i	−0.955603	+	0.294658i	$0.904794\pi$
$354$	17.5379	+	24.7298i	0.932130	+	1.31437i
$355$		0			0
$356$	11.0479	+	21.2538i	0.585539	+	1.12645i
$357$	1.73205	+	0.255437i	0.0916698	+	0.0135192i
$358$	12.1431	−	2.96755i	0.641782	−	0.156840i
$359$	−1.38712			−0.0732096			−0.0366048	−	0.999330i	$-0.511654\pi$
$359$	−1.38712			−0.0732096			−0.0366048	+	0.999330i	$0.511654\pi$
$360$		0			0
$361$	−3.11684			−0.164044
$362$	−5.49514	+	1.34291i	−0.288818	+	0.0705820i
$363$	−6.85407	−	17.3020i	−0.359745	−	0.908119i
$364$	2.79185	+	5.37093i	0.146333	+	0.281513i
$365$		0			0
$366$	5.78563	−	0.541153i	0.302420	−	0.0282865i
$367$	3.18955	+	5.52447i	0.166493	+	0.288375i	0.937185	−	0.348834i	$-0.113422\pi$
$367$	3.18955	+	5.52447i	0.166493	+	0.288375i	−0.770691	+	0.637209i	$0.780089\pi$
$368$	11.6819	−	5.43039i	0.608962	−	0.283079i
$369$	5.87228	−	19.4762i	0.305699	−	1.01389i
$370$		0			0
$371$	−1.19897	−	2.07668i	−0.0622474	−	0.107816i
$372$	18.4481	−	21.2793i	0.956487	−	1.10328i
$373$	−17.2005	−	9.93070i	−0.890607	−	0.514192i	−0.0164662	−	0.999864i	$-0.505242\pi$
$373$	−17.2005	−	9.93070i	−0.890607	−	0.514192i	−0.874141	+	0.485672i	$0.838575\pi$
$374$	0.391475	+	0.409185i	0.0202427	+	0.0211585i
$375$		0			0
$376$	1.09294	−	3.21025i	0.0563642	−	0.165556i
$377$	5.98844			0.308420
$378$	2.98491	+	8.88747i	0.153527	+	0.457122i
$379$		−	6.45364i		−	0.331501i	−0.986168	−	0.165751i	$-0.946995\pi$
$379$		−	6.45364i		−	0.331501i	0.986168	−	0.165751i	$-0.0530047\pi$
$380$		0			0
$381$	−8.23369	+	10.3923i	−0.421825	+	0.532414i
$382$	14.7548	+	15.4222i	0.754919	+	0.789071i
$383$	−7.49198	−	4.32550i	−0.382822	−	0.221023i	0.296223	−	0.955119i	$-0.404273\pi$
$383$	−7.49198	−	4.32550i	−0.382822	−	0.221023i	−0.679045	+	0.734096i	$0.737606\pi$
$384$	−16.5711	−	10.4593i	−0.845643	−	0.533749i
$385$		0			0
$386$	10.5140	+	3.06796i	0.535148	+	0.156155i
$387$	16.8977	−	15.8798i	0.858958	−	0.807217i
$388$	11.2822	−	17.6861i	0.572766	−	0.897878i
$389$	−27.3030	+	15.7634i	−1.38432	+	0.799235i	−0.992667	−	0.120879i	$-0.961429\pi$
$389$	−27.3030	+	15.7634i	−1.38432	+	0.799235i	−0.391649	+	0.920115i	$0.628095\pi$
$390$		0			0
$391$	−2.20979	−	1.27582i	−0.111754	−	0.0645210i
$392$	−2.95106	−	14.9058i	−0.149051	−	0.752856i
$393$	4.87375	+	12.3030i	0.245848	+	0.620603i
$394$	−32.9073	+	8.04195i	−1.65785	+	0.405148i
$395$		0			0
$396$	−1.00291	+	2.86180i	−0.0503982	+	0.143811i
$397$		−	18.7446i		−	0.940763i	−0.882463	−	0.470381i	$-0.844116\pi$
$397$		−	18.7446i		−	0.940763i	0.882463	−	0.470381i	$-0.155884\pi$
$398$	−4.33334	−	17.7318i	−0.217211	−	0.888816i
$399$	1.51622	−	10.2811i	0.0759062	−	0.514699i
$400$		0			0
$401$	3.98913	+	2.30312i	0.199207	+	0.115012i	0.596286	−	0.802772i	$-0.296643\pi$
$401$	3.98913	+	2.30312i	0.199207	+	0.115012i	−0.397078	+	0.917785i	$0.629976\pi$
$402$	−10.9525	−	15.4438i	−0.546259	−	0.770267i
$403$	−9.64319	−	16.7025i	−0.480362	−	0.832011i
$404$	1.32807	−	2.08191i	0.0660740	−	0.103579i
$405$		0			0
$406$	4.37228	+	1.27582i	0.216993	+	0.0633179i
$407$	−2.95207	+	1.70438i	−0.146329	+	0.0844829i
$408$	0.190237	+	3.87673i	0.00941813	+	0.191927i
$409$	6.87228	−	11.9031i	0.339812	−	0.588572i	−0.644585	−	0.764533i	$-0.722970\pi$
$409$	6.87228	−	11.9031i	0.339812	−	0.588572i	0.984397	+	0.175960i	$0.0563031\pi$
$410$		0			0
$411$	−9.40910	−	1.38762i	−0.464117	−	0.0684465i
$412$	0.0420022	−	0.948999i	0.00206930	−	0.0467538i
$413$	15.7908			0.777016
$414$	0.726011	−	13.6446i	0.0356815	−	0.670593i
$415$		0			0
$416$	−10.4783	+	8.38403i	−0.513741	+	0.411061i
$417$	24.7735	−	9.81386i	1.21316	−	0.480587i
$418$	2.42884	−	2.32372i	0.118798	−	0.113657i
$419$	13.4819	−	23.3513i	0.658634	−	1.14079i	−0.322336	−	0.946625i	$-0.604468\pi$
$419$	13.4819	−	23.3513i	0.658634	−	1.14079i	0.980970	−	0.194162i	$-0.0621986\pi$
$420$		0			0
$421$	5.30298	+	9.18504i	0.258452	+	0.447651i	0.965827	−	0.259186i	$-0.0834544\pi$
$421$	5.30298	+	9.18504i	0.258452	+	0.447651i	−0.707376	+	0.706838i	$0.750121\pi$
$422$	23.8063	+	6.94661i	1.15887	+	0.338156i
$423$	−2.46323	−	2.62112i	−0.119766	−	0.127443i
$424$	4.00000	−	3.50157i	0.194257	−	0.170051i
$425$		0			0
$426$	−12.1312	+	26.4281i	−0.587759	+	1.28044i
$427$	1.51330	−	2.62112i	0.0732339	−	0.126845i
$428$	11.5906	+	22.2978i	0.560251	+	1.07780i
$429$	1.62772	+	1.28962i	0.0785870	+	0.0622635i
$430$		0			0
$431$	31.1952			1.50262			0.751310	−	0.659949i	$-0.229422\pi$
$431$	31.1952			1.50262			0.751310	+	0.659949i	$0.229422\pi$
$432$	−18.0427	+	10.3179i	−0.868081	+	0.496422i
$433$			8.62772i			0.414622i	0.978275	+	0.207311i	$0.0664712\pi$
$433$			8.62772i			0.414622i	−0.978275	+	0.207311i	$0.933529\pi$
$434$	−3.48227	−	14.2493i	−0.167154	−	0.683988i
$435$		0			0
$436$	−23.9374	+	12.4429i	−1.14640	+	0.595906i
$437$	−7.57301	+	13.1168i	−0.362266	+	0.627464i
$438$	−7.50723	−	3.44603i	−0.358710	−	0.164658i
$439$	5.65357	−	3.26409i	0.269830	−	0.155786i	−0.358980	−	0.933345i	$-0.616876\pi$
$439$	5.65357	−	3.26409i	0.269830	−	0.155786i	0.628810	+	0.777559i	$0.283542\pi$
$440$		0			0
$441$	−15.4307	−	4.65253i	−0.734795	−	0.221549i
$442$	2.55164	+	0.744563i	0.121369	+	0.0354152i
$443$	−10.7188	+	6.18850i	−0.509265	+	0.294025i	−0.732532	−	0.680733i	$-0.761661\pi$
$443$	−10.7188	+	6.18850i	−0.509265	+	0.294025i	0.223266	+	0.974758i	$0.428328\pi$
$444$	−22.9405	−	4.42743i	−1.08871	−	0.210116i
$445$		0			0
$446$	−7.94812	−	8.30768i	−0.376354	−	0.393380i
$447$	20.7997	−	8.23966i	0.983791	−	0.389723i
$448$	−9.43662	+	3.88898i	−0.445838	+	0.183737i
$449$		−	19.4024i		−	0.915657i	−0.889041	−	0.457828i	$-0.848627\pi$
$449$		−	19.4024i		−	0.915657i	0.889041	−	0.457828i	$-0.151373\pi$
$450$		0			0
$451$		−	3.42703i		−	0.161373i
$452$	−0.643616	+	14.5419i	−0.0302731	+	0.683993i
$453$	−0.764836	+	5.18614i	−0.0359351	+	0.243666i
$454$	−14.7135	+	14.0767i	−0.690540	+	0.660653i
$455$		0			0
$456$	23.0115	−	1.12921i	1.07761	−	0.0528800i
$457$	34.6222	−	19.9891i	1.61956	−	0.935052i	0.632523	−	0.774541i	$-0.282019\pi$
$457$	34.6222	−	19.9891i	1.61956	−	0.935052i	0.987034	−	0.160510i	$-0.0513140\pi$
$458$	1.43710	−	4.92498i	0.0671511	−	0.230129i
$459$	3.72601	+	1.75079i	0.173915	+	0.0817196i
$460$		0			0
$461$	0.302985	−	0.174928i	0.0141114	−	0.00814722i	−0.492928	−	0.870070i	$-0.664073\pi$
$461$	0.302985	−	0.174928i	0.0141114	−	0.00814722i	0.507039	+	0.861923i	$0.330740\pi$
$462$	0.913680	+	1.28836i	0.0425083	+	0.0599399i
$463$	−2.38870	+	4.13734i	−0.111012	+	0.192279i	−0.916179	−	0.400770i	$-0.868743\pi$
$463$	−2.38870	+	4.13734i	−0.111012	+	0.192279i	0.805167	+	0.593049i	$0.202076\pi$
$464$	−0.892059	+	10.0579i	−0.0414128	+	0.466925i
$465$		0			0
$466$	−6.65777	+	1.62704i	−0.308415	+	0.0753711i
$467$		−	5.11313i		−	0.236608i	−0.992977	−	0.118304i	$-0.962254\pi$
$467$		−	5.11313i		−	0.236608i	0.992977	−	0.118304i	$-0.0377457\pi$
$468$	2.63958	+	13.9868i	0.122014	+	0.646540i
$469$	−9.86141			−0.455357
$470$		0			0
$471$	−19.1004	+	7.56651i	−0.880102	+	0.348647i
$472$	6.79885	+	34.3409i	0.312942	+	1.58067i
$473$	1.95327	−	3.38316i	0.0898113	−	0.155558i
$474$	2.25393	+	24.0974i	0.103526	+	1.10683i
$475$		0			0
$476$	1.70438	+	1.08724i	0.0781201	+	0.0498336i
$477$	−1.28962	−	5.48913i	−0.0590477	−	0.251330i
$478$	4.77739	−	16.3723i	0.218513	−	0.748851i
$479$	6.53528	+	11.3194i	0.298605	+	0.517198i	0.975817	−	0.218589i	$-0.0701455\pi$
$479$	6.53528	+	11.3194i	0.298605	+	0.517198i	−0.677212	+	0.735788i	$0.736812\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	6.34404	+	6.63104i	0.288963	+	0.302035i
$483$	−5.57825	−	4.41957i	−0.253819	−	0.201098i
$484$	0.950167	−	21.4681i	0.0431894	−	0.975823i
$485$		0			0
$486$	0.687175	+	22.0347i	0.0311709	+	0.999514i
$487$	−42.8752			−1.94286			−0.971430	−	0.237325i	$-0.923729\pi$
$487$	−42.8752			−1.94286			−0.971430	+	0.237325i	$0.923729\pi$
$488$	6.35180	+	2.16249i	0.287532	+	0.0978915i
$489$	−1.88316	+	2.37686i	−0.0851593	+	0.107485i
$490$		0			0
$491$	6.88206	−	11.9201i	0.310583	−	0.537946i	−0.667906	−	0.744246i	$-0.732809\pi$
$491$	6.88206	−	11.9201i	0.310583	−	0.537946i	0.978489	+	0.206300i	$0.0661423\pi$
$492$	15.3866	−	17.7480i	0.693681	−	0.800142i
$493$	1.73205	−	1.00000i	0.0780076	−	0.0450377i
$494$	4.41957	−	15.1460i	0.198846	−	0.681452i
$495$		0			0
$496$	29.4891	−	13.7081i	1.32410	−	0.615513i
$497$	7.57301	+	13.1168i	0.339696	+	0.588371i
$498$	−1.74284	−	18.6332i	−0.0780985	−	0.834974i
$499$	−2.96790	−	1.71352i	−0.132861	−	0.0767076i	0.432096	−	0.901828i	$-0.357774\pi$
$499$	−2.96790	−	1.71352i	−0.132861	−	0.0767076i	−0.564958	+	0.825120i	$0.691107\pi$
$500$		0			0
$501$	28.1644	−	11.1571i	1.25829	−	0.498464i
$502$	−15.3562	+	3.75278i	−0.685382	+	0.167495i
$503$		−	19.3236i		−	0.861597i	−0.902448	−	0.430799i	$-0.858232\pi$
$503$		−	19.3236i		−	0.861597i	0.902448	−	0.430799i	$-0.141768\pi$
$504$	−1.05264	+	10.7744i	−0.0468884	+	0.479930i
$505$		0			0
$506$	−0.546471	−	2.23614i	−0.0242936	−	0.0994084i
$507$	−12.6325	−	1.86301i	−0.561030	−	0.0827390i
$508$	−13.5842	+	7.06119i	−0.602702	+	0.313290i
$509$	−12.8139	−	7.39809i	−0.567964	−	0.327914i	0.188372	−	0.982098i	$-0.439679\pi$
$509$	−12.8139	−	7.39809i	−0.567964	−	0.327914i	−0.756336	+	0.654183i	$0.773012\pi$
$510$		0			0
$511$	−3.72601	+	2.15121i	−0.164829	+	0.0951641i
$512$	−12.5205	−	18.8477i	−0.553333	−	0.832960i
$513$	10.3923	−	22.1168i	0.458831	−	0.976483i
$514$	−5.94158	+	20.3620i	−0.262072	+	0.898129i
$515$		0			0
$516$	25.3052	−	8.75107i	1.11400	−	0.385244i
$517$	−0.524785	−	0.302985i	−0.0230800	−	0.0133252i
$518$	−8.79303	+	8.41247i	−0.386344	+	0.369623i
$519$	−30.2785	−	4.46537i	−1.32908	−	0.196008i
$520$		0			0
$521$		−	26.0357i		−	1.14064i	−0.821421	−	0.570322i	$-0.806819\pi$
$521$		−	26.0357i		−	1.14064i	0.821421	−	0.570322i	$-0.193181\pi$
$522$	8.97738	+	5.84018i	0.392929	+	0.255618i
$523$	9.40571			0.411283			0.205641	−	0.978627i	$-0.434072\pi$
$523$	9.40571			0.411283			0.205641	+	0.978627i	$0.434072\pi$
$524$	−0.675639	+	15.2654i	−0.0295154	+	0.666872i
$525$		0			0
$526$	−28.5864	+	27.3492i	−1.24643	+	1.19248i
$527$	−5.57825	−	3.22060i	−0.242992	−	0.140292i
$528$	−2.40845	+	2.54172i	−0.104814	+	0.110614i
$529$	−6.31386	−	10.9359i	−0.274516	−	0.475475i
$530$		0			0
$531$	35.5502	+	10.7188i	1.54275	+	0.465156i
$532$	6.45364	−	10.1168i	0.279801	−	0.438621i
$533$	−8.04290	−	13.9307i	−0.348376	−	0.603406i
$534$	26.6624	+	12.2388i	1.15380	+	0.529625i
$535$		0			0
$536$	−4.24589	−	21.4460i	−0.183395	−	0.926324i
$537$	9.50744	−	12.0000i	0.410276	−	0.517838i
$538$	7.21290	+	29.5149i	0.310970	+	1.27248i
$539$	−2.71519			−0.116952
$540$		0			0
$541$	−8.97825			−0.386005			−0.193003	−	0.981198i	$-0.561823\pi$
$541$	−8.97825			−0.386005			−0.193003	+	0.981198i	$0.561823\pi$
$542$	−10.0611	−	41.1695i	−0.432160	−	1.76838i
$543$	−4.30243	+	5.43039i	−0.184635	+	0.233040i
$544$	−1.63063	+	4.17469i	−0.0699127	+	0.178988i
$545$		0			0
$546$	6.73771	+	3.09279i	0.288347	+	0.132359i
$547$	11.1192	+	19.2591i	0.475424	+	0.823458i	0.999604	−	0.0281494i	$-0.00896140\pi$
$547$	11.1192	+	19.2591i	0.475424	+	0.823458i	−0.524180	+	0.851608i	$0.675628\pi$
$548$	−9.25878	−	5.90627i	−0.395515	−	0.252303i
$549$	5.18614	−	4.87375i	0.221339	−	0.208006i
$550$		0			0
$551$	−5.93580	−	10.2811i	−0.252873	−	0.437990i
$552$	7.20965	−	14.0341i	0.306863	−	0.597331i
$553$	10.9171	+	6.30298i	0.464242	+	0.268030i
$554$	6.51164	−	6.22981i	0.276653	−	0.264679i
$555$		0			0
$556$	30.7387	+	1.36048i	1.30361	+	0.0576971i
$557$	7.22316			0.306055			0.153027	−	0.988222i	$-0.451098\pi$
$557$	7.22316			0.306055			0.153027	+	0.988222i	$0.451098\pi$
$558$	1.83270	−	34.4435i	0.0775842	−	1.45811i
$559$		−	18.3365i		−	0.775549i
$560$		0			0
$561$	0.686141	+	0.101190i	0.0289689	+	0.00427224i
$562$	−23.5173	+	22.4994i	−0.992017	+	0.949082i
$563$	13.6709	+	7.89288i	0.576158	+	0.332645i	0.759605	−	0.650384i	$-0.225392\pi$
$563$	13.6709	+	7.89288i	0.576158	+	0.332645i	−0.183447	+	0.983030i	$0.558726\pi$
$564$	−1.35744	−	3.92527i	−0.0571585	−	0.165284i
$565$		0			0
$566$	3.91416	−	13.4140i	0.164525	−	0.563831i
$567$	9.56866	+	6.34713i	0.401846	+	0.266554i
$568$	−25.2651	+	22.1168i	−1.06010	+	0.928002i
$569$	21.9891	−	12.6954i	0.921832	−	0.532220i	0.0376130	−	0.999292i	$-0.488025\pi$
$569$	21.9891	−	12.6954i	0.921832	−	0.532220i	0.884219	+	0.467072i	$0.154691\pi$
$570$		0			0
$571$	−3.66146	−	2.11395i	−0.153227	−	0.0884659i	0.421426	−	0.906863i	$-0.361530\pi$
$571$	−3.66146	−	2.11395i	−0.153227	−	0.0884659i	−0.574653	+	0.818397i	$0.694863\pi$
$572$	1.10597	+	2.12766i	0.0462431	+	0.0889619i
$573$	25.8607	+	3.81386i	1.08035	+	0.159326i
$574$	−2.90438	−	11.8846i	−0.121227	−	0.496054i
$575$		0			0
$576$	−23.8847	+	2.34977i	−0.995196	+	0.0979071i
$577$			31.8397i			1.32550i	0.748840	+	0.662751i	$0.230611\pi$
$577$			31.8397i			1.32550i	−0.748840	+	0.662751i	$0.769389\pi$
$578$	−22.4920	+	5.49664i	−0.935544	+	0.228630i
$579$	12.4711	−	4.94034i	0.518280	−	0.205313i
$580$		0			0
$581$	−8.44158	−	4.87375i	−0.350216	−	0.202197i
$582$	−2.39273	−	25.5813i	−0.0991817	−	1.06038i
$583$	−0.474964	−	0.822662i	−0.0196710	−	0.0340712i
$584$	−6.28258	−	7.17687i	−0.259975	−	0.296981i
$585$		0			0
$586$	−9.23369	+	31.6442i	−0.381440	+	1.30721i
$587$	−3.38977	+	1.95708i	−0.139911	+	0.0807774i	−0.568321	−	0.822807i	$-0.692407\pi$
$587$	−3.38977	+	1.95708i	−0.139911	+	0.0807774i	0.428411	+	0.903584i	$0.359074\pi$
$588$	−14.0615	−	12.1906i	−0.579887	−	0.502732i
$589$	−19.1168	+	33.1113i	−0.787696	+	1.36433i
$590$		0			0
$591$	−25.7648	+	32.5196i	−1.05982	+	1.33768i
$592$	−22.0808	−	15.5005i	−0.907515	−	0.637066i
$593$	8.80773			0.361690			0.180845	−	0.983512i	$-0.442117\pi$
$593$	8.80773			0.361690			0.180845	+	0.983512i	$0.442117\pi$
$594$	1.18245	+	3.52071i	0.0485165	+	0.144457i
$595$		0			0
$596$	25.8080	+	1.14225i	1.05714	+	0.0467883i
$597$	−17.5229	−	13.8832i	−0.717164	−	0.568200i
$598$	−7.46936	−	7.80726i	−0.305445	−	0.319263i
$599$	0.0940770	−	0.162946i	0.00384388	−	0.00665780i	−0.864097	−	0.503325i	$-0.832110\pi$
$599$	0.0940770	−	0.162946i	0.00384388	−	0.00665780i	0.867941	+	0.496667i	$0.165443\pi$
$600$		0			0
$601$	−7.98913	−	13.8376i	−0.325883	−	0.564446i	0.655807	−	0.754928i	$-0.272328\pi$
$601$	−7.98913	−	13.8376i	−0.325883	−	0.564446i	−0.981691	+	0.190482i	$0.938995\pi$
$602$	3.90653	−	13.3878i	0.159218	−	0.545647i
$603$	−22.2012	−	6.69391i	−0.904102	−	0.272597i
$604$	−3.25544	+	5.10328i	−0.132462	+	0.207650i
$605$		0			0
$606$	−0.281658	−	3.01128i	−0.0114416	−	0.122325i
$607$	−1.98827	+	3.44378i	−0.0807013	+	0.139779i	−0.903551	−	0.428480i	$-0.859049\pi$
$607$	−1.98827	+	3.44378i	−0.0807013	+	0.139779i	0.822850	+	0.568259i	$0.192383\pi$
$608$	24.7801	+	9.67909i	1.00497	+	0.392539i
$609$	5.18614	−	2.05446i	0.210153	−	0.0832508i
$610$		0			0
$611$	−2.84429			−0.115068
$612$	3.09908	+	3.60466i	0.125273	+	0.145710i
$613$		−	4.23369i		−	0.170997i	−0.996338	−	0.0854985i	$-0.972752\pi$
$613$		−	4.23369i		−	0.170997i	0.996338	−	0.0854985i	$-0.0272483\pi$
$614$	−1.65031	+	0.403305i	−0.0666010	+	0.0162761i
$615$		0			0
$616$	0.354202	+	1.78907i	0.0142712	+	0.0720838i
$617$	2.45060	−	4.24456i	0.0986574	−	0.170880i	−0.812472	−	0.583001i	$-0.801879\pi$
$617$	2.45060	−	4.24456i	0.0986574	−	0.170880i	0.911129	+	0.412121i	$0.135212\pi$
$618$	−0.673013	−	0.948999i	−0.0270725	−	0.0381744i
$619$	−8.08103	+	4.66559i	−0.324804	+	0.187526i	−0.653532	−	0.756899i	$-0.726713\pi$
$619$	−8.08103	+	4.66559i	−0.324804	+	0.187526i	0.328728	+	0.944425i	$0.393380\pi$
$620$		0			0
$621$	−9.55842	−	13.7364i	−0.383566	−	0.551222i
$622$	7.58039	−	25.9783i	0.303946	−	1.04163i
$623$	13.2332	−	7.64018i	0.530176	−	0.306097i
$624$	−3.82505	+	15.9844i	−0.153124	+	0.639886i
$625$		0			0
$626$	18.8935	−	18.0757i	0.755135	−	0.722452i
$627$	0.600642	−	4.07279i	0.0239873	−	0.162652i
$628$	−23.6996	−	1.04893i	−0.945717	−	0.0418569i
$629$			5.34363i			0.213064i
$630$		0			0
$631$		−	42.8752i		−	1.70683i	−0.521228	−	0.853417i	$-0.674526\pi$
$631$		−	42.8752i		−	1.70683i	0.521228	−	0.853417i	$-0.325474\pi$
$632$	−9.00690	+	26.4556i	−0.358275	+	1.05235i
$633$	28.2376	−	11.1861i	1.12234	−	0.444609i
$634$	−31.7943	−	33.2326i	−1.26271	−	1.31984i
$635$		0			0
$636$	1.23380	−	6.39290i	0.0489235	−	0.253495i
$637$	−11.0371	+	6.37228i	−0.437306	+	0.252479i
$638$	1.73205	+	0.505408i	0.0685725	+	0.0200093i
$639$	8.14558	+	34.6708i	0.322234	+	1.37155i
$640$		0			0
$641$	18.1277	−	10.4660i	0.716002	−	0.413384i	−0.0972775	−	0.995257i	$-0.531013\pi$
$641$	18.1277	−	10.4660i	0.716002	−	0.413384i	0.813279	+	0.581873i	$0.197680\pi$
$642$	27.9720	+	12.8399i	1.10397	+	0.506752i
$643$	−17.9733	+	31.1307i	−0.708798	+	1.22767i	0.256506	+	0.966543i	$0.417429\pi$
$643$	−17.9733	+	31.1307i	−0.708798	+	1.22767i	−0.965303	+	0.261131i	$0.915905\pi$
$644$	−3.79021	−	7.29156i	−0.149355	−	0.287328i
$645$		0			0
$646$	−1.25093	−	5.11874i	−0.0492171	−	0.201394i
$647$		−	46.0993i		−	1.81235i	−0.422904	−	0.906174i	$-0.638989\pi$
$647$		−	46.0993i		−	1.81235i	0.422904	−	0.906174i	$-0.361011\pi$
$648$	−9.68348	+	23.5421i	−0.380403	+	0.924821i
$649$	6.25544			0.245547
$650$		0			0
$651$	−14.0814	−	11.1565i	−0.551893	−	0.437258i
$652$	−3.10690	+	1.61499i	−0.121675	+	0.0632479i
$653$	2.20193	−	3.81386i	0.0861683	−	0.149248i	−0.819720	−	0.572764i	$-0.805871\pi$
$653$	2.20193	−	3.81386i	0.0861683	−	0.149248i	0.905888	+	0.423516i	$0.139204\pi$
$654$	−13.7841	+	30.0289i	−0.539002	+	1.17422i
$655$		0			0
$656$	24.5954	−	11.4333i	0.960288	−	0.446394i
$657$	−9.84868	+	2.31386i	−0.384234	+	0.0902723i
$658$	−2.07668	−	0.605969i	−0.0809573	−	0.0236231i
$659$	−6.02987	−	10.4440i	−0.234891	−	0.406842i	0.724350	−	0.689432i	$-0.242140\pi$
$659$	−6.02987	−	10.4440i	−0.234891	−	0.406842i	−0.959241	+	0.282590i	$0.908807\pi$
$660$		0			0
$661$	−7.81386	+	13.5340i	−0.303924	+	0.526412i	−0.977021	−	0.213142i	$-0.931630\pi$
$661$	−7.81386	+	13.5340i	−0.303924	+	0.526412i	0.673097	+	0.739554i	$0.264964\pi$
$662$	−28.3489	+	27.1219i	−1.10181	+	1.05412i
$663$	3.02661	−	1.19897i	0.117544	−	0.0465641i
$664$	6.96454	−	20.4566i	0.270276	−	0.793871i
$665$		0			0
$666$	−25.5063	+	12.9705i	−0.988349	+	0.502595i
$667$	−8.12989			−0.314791
$668$	34.9461	+	1.54669i	1.35210	+	0.0598434i
$669$	−13.9307	−	2.05446i	−0.538592	−	0.0794299i
$670$		0			0
$671$	0.599485	−	1.03834i	0.0231429	−	0.0400846i
$672$	−6.19817	+	10.8556i	−0.239100	+	0.418763i
$673$	−25.8607	+	14.9307i	−0.996858	+	0.575536i	−0.907317	−	0.420447i	$-0.861873\pi$
$673$	−25.8607	+	14.9307i	−0.996858	+	0.575536i	−0.0895410	+	0.995983i	$0.528540\pi$
$674$	21.3748	+	6.23711i	0.823326	+	0.240244i
$675$		0			0
$676$	−12.4307	−	7.92967i	−0.478104	−	0.304987i
$677$	−1.75950	−	3.04755i	−0.0676232	−	0.117127i	0.830231	−	0.557419i	$-0.188208\pi$
$677$	−1.75950	−	3.04755i	−0.0676232	−	0.117127i	−0.897855	+	0.440292i	$0.854875\pi$
$678$	10.3128	+	14.5419i	0.396062	+	0.558478i
$679$	−11.5894	−	6.69112i	−0.444759	−	0.256782i
$680$		0			0
$681$	−3.63859	+	24.6723i	−0.139431	+	0.945445i
$682$	−1.37948	−	5.64476i	−0.0528229	−	0.216149i
$683$		−	20.0172i		−	0.765936i	−0.923762	−	0.382968i	$-0.874902\pi$
$683$		−	20.0172i		−	0.765936i	0.923762	−	0.382968i	$-0.125098\pi$
$684$	21.3965	−	18.3955i	0.818116	−	0.703371i
$685$		0			0
$686$	−21.6849	+	5.29941i	−0.827935	+	0.202332i
$687$	−2.31416	−	5.84172i	−0.0882907	−	0.222876i
$688$	30.7969	+	2.73146i	1.17412	+	0.104136i
$689$	−3.86141	−	2.22938i	−0.147108	−	0.0849328i
$690$		0			0
$691$	−17.3961	+	10.0436i	−0.661777	+	0.382077i	−0.792954	−	0.609282i	$-0.791458\pi$
$691$	−17.3961	+	10.0436i	−0.661777	+	0.382077i	0.131177	+	0.991359i	$0.458125\pi$
$692$	−29.7947	−	19.0064i	−1.13263	−	0.722513i
$693$	1.85208	+	0.558422i	0.0703546	+	0.0212127i
$694$	−9.43070	−	2.75186i	−0.357985	−	0.104459i
$695$		0			0
$696$	6.70082	+	10.3939i	0.253994	+	0.393981i
$697$	−4.65253	−	2.68614i	−0.176227	−	0.101745i
$698$	−5.50189	−	5.75079i	−0.208250	−	0.217671i
$699$	−5.21271	+	6.57932i	−0.197163	+	0.248853i
$700$		0			0
$701$		−	32.7615i		−	1.23738i	−0.785634	−	0.618692i	$-0.787663\pi$
$701$		−	32.7615i		−	1.23738i	0.785634	−	0.618692i	$-0.212337\pi$
$702$	13.0693	+	11.5364i	0.493271	+	0.435414i
$703$	31.7187			1.19629
$704$	−3.73826	+	1.54059i	−0.140891	+	0.0580633i
$705$		0			0
$706$	−8.17827	−	8.54824i	−0.307793	−	0.321717i
$707$	−1.36423	−	0.787639i	−0.0513072	−	0.0296222i
$708$	32.3958	+	28.0855i	1.21751	+	1.05552i
$709$	11.9307	+	20.6646i	0.448067	+	0.776075i	0.998260	−	0.0589626i	$-0.0187793\pi$
$709$	11.9307	+	20.6646i	0.448067	+	0.776075i	−0.550193	+	0.835037i	$0.685446\pi$
$710$		0			0
$711$	20.2994	+	21.6005i	0.761287	+	0.810084i
$712$	22.3130	+	25.4891i	0.836215	+	0.955245i
$713$	13.0916	+	22.6753i	0.490283	+	0.849195i
$714$	2.46522	−	0.230582i	0.0922587	−	0.00862933i
$715$		0			0
$716$	15.6857	−	8.15356i	0.586202	−	0.304713i
$717$	−7.69304	−	19.4198i	−0.287302	−	0.725247i
$718$	−1.90561	+	0.465697i	−0.0711168	+	0.0173797i
$719$	16.2912			0.607558			0.303779	−	0.952743i	$-0.401752\pi$
$719$	16.2912			0.607558			0.303779	+	0.952743i	$0.401752\pi$
$720$		0			0
$721$	−0.605969			−0.0225675
$722$	−4.28187	+	1.04641i	−0.159355	+	0.0389434i
$723$	11.1192	+	1.63983i	0.413528	+	0.0609859i
$724$	−7.09829	+	3.68975i	−0.263806	+	0.137128i
$725$		0			0
$726$	−15.2248	−	21.4681i	−0.565045	−	0.796756i
$727$	19.0489	+	32.9937i	0.706485	+	1.22367i	0.966153	+	0.257969i	$0.0830534\pi$
$727$	19.0489	+	32.9937i	0.706485	+	1.22367i	−0.259668	+	0.965698i	$0.583613\pi$
$728$	5.63858	+	6.44121i	0.208980	+	0.238727i
$729$	17.2337	+	20.7846i	0.638285	+	0.769800i
$730$		0			0
$731$	−3.06198	−	5.30350i	−0.113251	−	0.196157i
$732$	7.76653	−	2.68583i	0.287059	−	0.0992710i
$733$	0.322405	+	0.186141i	0.0119083	+	0.00687526i	0.505942	−	0.862567i	$-0.331145\pi$
$733$	0.322405	+	0.186141i	0.0119083	+	0.00687526i	−0.494034	+	0.869443i	$0.664478\pi$
$734$	6.23648	+	6.51861i	0.230193	+	0.240606i
$735$		0			0
$736$	14.2253	−	11.3821i	0.524352	−	0.419551i
$737$	−3.90653			−0.143899
$738$	1.52856	−	28.7275i	0.0562670	−	1.05748i
$739$			6.45364i			0.237401i	0.992930	+	0.118700i	$0.0378728\pi$
$739$			6.45364i			0.237401i	−0.992930	+	0.118700i	$0.962127\pi$
$740$		0			0
$741$	−7.11684	−	17.9653i	−0.261444	−	0.659972i
$742$	−2.34433	−	2.45038i	−0.0860630	−	0.0899563i
$743$	18.3226	+	10.5785i	0.672190	+	0.388089i	0.796906	−	0.604103i	$-0.206469\pi$
$743$	18.3226	+	10.5785i	0.672190	+	0.388089i	−0.124716	+	0.992193i	$0.539802\pi$
$744$	18.1996	−	35.4268i	0.667230	−	1.29881i
$745$		0			0
$746$	−26.9638	−	7.86797i	−0.987215	−	0.288067i
$747$	−15.6964	−	16.7025i	−0.574301	−	0.611112i
$748$	0.675178	+	0.430703i	0.0246870	+	0.0157481i
$749$	13.8832	−	8.01544i	0.507279	−	0.292878i
$750$		0			0
$751$	18.7832	+	10.8445i	0.685408	+	0.395721i	0.801890	−	0.597472i	$-0.203828\pi$
$751$	18.7832	+	10.8445i	0.685408	+	0.395721i	−0.116481	+	0.993193i	$0.537162\pi$
$752$	0.423696	−	4.77713i	0.0154506	−	0.174204i
$753$	−12.0232	+	15.1753i	−0.438149	+	0.553017i
$754$	8.22683	−	2.01049i	0.299604	−	0.0732177i
$755$		0			0
$756$	7.08440	+	11.2074i	0.257657	+	0.407608i
$757$			14.0000i			0.508839i	0.967094	+	0.254419i	$0.0818843\pi$
$757$			14.0000i			0.508839i	−0.967094	+	0.254419i	$0.918116\pi$
$758$	−2.16667	−	8.86592i	−0.0786970	−	0.322025i
$759$	−2.20979	−	1.75079i	−0.0802102	−	0.0635495i
$760$		0			0
$761$	15.0475	+	8.68771i	0.545473	+	0.314929i	0.747294	−	0.664493i	$-0.231353\pi$
$761$	15.0475	+	8.68771i	0.545473	+	0.314929i	−0.201821	+	0.979422i	$0.564686\pi$
$762$	−7.82233	+	17.0411i	−0.283373	+	0.617333i
$763$	8.60485	+	14.9040i	0.311517	+	0.539563i
$764$	25.4476	+	16.2333i	0.920661	+	0.587299i
$765$		0			0
$766$	−11.7446	−	3.42703i	−0.424348	−	0.123824i
$767$	25.4280	−	14.6809i	0.918152	−	0.530095i
$768$	−26.2767	−	8.80544i	−0.948178	−	0.317739i
$769$	4.04755	−	7.01056i	0.145958	−	0.252807i	−0.783772	−	0.621049i	$-0.786707\pi$
$769$	4.04755	−	7.01056i	0.145958	−	0.252807i	0.929730	+	0.368242i	$0.120040\pi$
$770$		0			0
$771$	9.56773	+	24.1522i	0.344573	+	0.869820i
$772$	15.4740	+	0.684870i	0.556921	+	0.0246490i
$773$	−0.699713			−0.0251669			−0.0125835	−	0.999921i	$-0.504006\pi$
$773$	−0.699713			−0.0251669			−0.0125835	+	0.999921i	$0.504006\pi$
$774$	17.8825	−	27.4885i	0.642773	−	0.988054i
$775$		0			0
$776$	9.56155	−	28.0847i	0.343240	−	1.00818i
$777$	−2.17448	+	14.7446i	−0.0780091	+	0.528958i
$778$	−32.2162	+	30.8219i	−1.15501	+	1.10502i
$779$	−15.9444	+	27.6165i	−0.571267	+	0.989463i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−3.46410	−	1.01082i	−0.123876	−	0.0361467i
$783$	13.0702	−	1.10489i	0.467092	−	0.0394857i
$784$	−9.05842	−	19.4866i	−0.323515	−	0.695950i
$785$		0			0
$786$	10.8259	+	15.2654i	0.386149	+	0.544499i
$787$	17.3727	−	30.0903i	0.619268	−	1.07260i	−0.370351	−	0.928892i	$-0.620763\pi$
$787$	17.3727	−	30.0903i	0.619268	−	1.07260i	0.989620	−	0.143712i	$-0.0459040\pi$
$788$	−42.5077	+	22.0958i	−1.51427	+	0.787132i
$789$	−7.06930	+	47.9350i	−0.251674	+	1.70653i
$790$		0			0
$791$	9.28550			0.330154
$792$	−0.416997	+	4.26821i	−0.0148173	+	0.151664i
$793$		−	5.62772i		−	0.199846i
$794$	−6.29308	−	25.7510i	−0.223333	−	0.913869i
$795$		0			0
$796$	−11.9062	−	22.9049i	−0.422003	−	0.811843i
$797$	−11.9494	+	20.6970i	−0.423270	+	0.733126i	−0.996257	−	0.0864387i	$-0.972451\pi$
$797$	−11.9494	+	20.6970i	−0.423270	+	0.733126i	0.572987	+	0.819565i	$0.305785\pi$
$798$	−1.36869	−	14.6331i	−0.0484511	−	0.518005i
$799$	−0.822662	+	0.474964i	−0.0291037	+	0.0168030i
$800$		0			0
$801$	34.9783	−	8.21782i	1.23590	−	0.290363i
$802$	6.25343	+	1.82473i	0.220816	+	0.0644336i
$803$	−1.47603	+	0.852189i	−0.0520881	+	0.0300731i
$804$	−20.2312	−	17.5394i	−0.713501	−	0.618568i
$805$		0			0
$806$	−18.8552	−	19.7082i	−0.664145	−	0.694190i
$807$	29.1671	+	23.1087i	1.02673	+	0.813464i
$808$	1.12553	−	3.30596i	0.0395960	−	0.116303i
$809$		−	35.8381i		−	1.26000i	−0.776595	−	0.630000i	$-0.783055\pi$
$809$		−	35.8381i		−	1.26000i	0.776595	−	0.630000i	$-0.216945\pi$
$810$		0			0
$811$		−	1.20128i		−	0.0421828i	−0.999778	−	0.0210914i	$-0.993286\pi$
$811$		−	1.20128i		−	0.0421828i	0.999778	−	0.0210914i	$-0.00671410\pi$
$812$	6.43491	+	0.284805i	0.225821	+	0.00999471i
$813$	−40.6844	−	32.2337i	−1.42686	−	1.13048i
$814$	−3.48330	+	3.33254i	−0.122090	+	0.116806i
$815$		0			0
$816$	1.56287	+	5.26193i	0.0547115	+	0.184204i
$817$	−31.4805	+	18.1753i	−1.10136	+	0.635872i
$818$	5.44482	−	18.6596i	0.190374	−	0.652417i
$819$	8.83915	−	2.07668i	0.308865	−	0.0725650i
$820$		0			0
$821$	−15.8139	+	9.13014i	−0.551907	+	0.318644i	−0.749891	−	0.661561i	$-0.769894\pi$
$821$	−15.8139	+	9.13014i	−0.551907	+	0.318644i	0.197983	+	0.980205i	$0.436561\pi$
$822$	−13.3920	+	1.25260i	−0.467098	+	0.0436896i
$823$	7.01701	−	12.1538i	0.244598	−	0.423656i	−0.717421	−	0.696640i	$-0.754677\pi$
$823$	7.01701	−	12.1538i	0.244598	−	0.423656i	0.962018	+	0.272984i	$0.0880108\pi$
$824$	−0.260904	−	1.31782i	−0.00908902	−	0.0459085i
$825$		0			0
$826$	21.6932	−	5.30143i	0.754804	−	0.184460i
$827$			47.4864i			1.65126i	0.564210	+	0.825632i	$0.309181\pi$
$827$			47.4864i			1.65126i	−0.564210	+	0.825632i	$0.690819\pi$
$828$	−3.58348	−	18.9884i	−0.124535	−	0.659894i
$829$	48.2337			1.67523			0.837613	−	0.546265i	$-0.183951\pi$
$829$	48.2337			1.67523			0.837613	+	0.546265i	$0.183951\pi$
$830$		0			0
$831$	1.61030	−	10.9190i	0.0558607	−	0.378776i
$832$	−11.5802	+	15.0357i	−0.401471	+	0.521270i
$833$	−2.12819	+	3.68614i	−0.0737376	+	0.127717i
$834$	30.7387	−	21.7993i	1.06439	−	0.754848i
$835$		0			0
$836$	2.55657	−	4.00772i	0.0884207	−	0.138610i
$837$	−24.1287	−	34.6753i	−0.834009	−	1.19855i
$838$	10.6815	−	36.6060i	0.368987	−	1.26453i
$839$	21.3102	+	36.9104i	0.735711	+	1.27429i	0.954411	+	0.298496i	$0.0964850\pi$
$839$	21.3102	+	36.9104i	0.735711	+	1.27429i	−0.218700	+	0.975792i	$0.570182\pi$
$840$		0			0
$841$	−11.3139	+	19.5962i	−0.390133	+	0.675730i
$842$	10.3688	+	10.8379i	0.357334	+	0.373499i
$843$	−5.81573	+	39.4349i	−0.200304	+	1.35821i
$844$	35.0369	+	1.55071i	1.20602	+	0.0533778i
$845$		0			0
$846$	−4.26393	−	2.77388i	−0.146597	−	0.0953678i
$847$	−13.7081			−0.471017
$848$	4.31957	−	6.15332i	0.148334	−	0.211306i
$849$	−6.30298	−	15.9109i	−0.216318	−	0.546059i
$850$		0			0
$851$	10.8608	−	18.8114i	0.372303	−	0.644847i
$852$	−7.79304	+	40.3793i	−0.266985	+	1.38337i
$853$	−38.6299	+	22.3030i	−1.32266	+	0.763640i	−0.984153	−	0.177323i	$-0.943256\pi$
$853$	−38.6299	+	22.3030i	−1.32266	+	0.763640i	−0.338510	+	0.940963i	$0.609923\pi$
$854$	1.19897	−	4.10891i	0.0410279	−	0.140604i
$855$		0			0
$856$	23.4090	+	26.7411i	0.800102	+	0.913992i
$857$	18.7851	+	32.5367i	0.641685	+	1.11143i	0.985056	+	0.172232i	$0.0550978\pi$
$857$	18.7851	+	32.5367i	0.641685	+	1.11143i	−0.343371	+	0.939200i	$0.611569\pi$
$858$	2.66910	+	1.22519i	0.0911215	+	0.0418273i
$859$	1.58077	+	0.912661i	0.0539353	+	0.0311396i	0.526725	−	0.850036i	$-0.323420\pi$
$859$	1.58077	+	0.912661i	0.0539353	+	0.0311396i	−0.472790	+	0.881175i	$0.656753\pi$
$860$		0			0
$861$	−11.7446	−	9.30506i	−0.400254	−	0.317116i
$862$	42.8555	−	10.4731i	1.45967	−	0.356716i
$863$			40.0344i			1.36279i	0.731918	+	0.681393i	$0.238625\pi$
$863$			40.0344i			1.36279i	−0.731918	+	0.681393i	$0.761375\pi$
$864$	−21.3228	+	20.2321i	−0.725417	+	0.688310i
$865$		0			0
$866$	2.89657	+	11.8526i	0.0984294	+	0.402769i
$867$	−17.6101	+	22.2270i	−0.598072	+	0.754867i
$868$	−9.56778	−	18.4064i	−0.324752	−	0.624753i
$869$	4.32473	+	2.49689i	0.146707	+	0.0847011i
$870$		0			0
$871$	−15.8798	+	9.16823i	−0.538068	+	0.310654i
$872$	−28.7075	+	25.1303i	−0.972158	+	0.851020i
$873$	−21.5494	−	22.9307i	−0.729338	−	0.776087i
$874$	−6.00000	+	20.5622i	−0.202953	+	0.695527i
$875$		0			0
$876$	−11.4703	−	2.21371i	−0.387544	−	0.0747945i
$877$	−18.7302	−	10.8139i	−0.632472	−	0.365158i	0.149237	−	0.988802i	$-0.452318\pi$
$877$	−18.7302	−	10.8139i	−0.632472	−	0.365158i	−0.781709	+	0.623643i	$0.785652\pi$
$878$	6.67094	−	6.38222i	0.225133	−	0.215389i
$879$	14.8690	+	37.5344i	0.501520	+	1.26600i
$880$		0			0
$881$			52.9562i			1.78414i	0.451898	+	0.892070i	$0.350747\pi$
$881$			52.9562i			1.78414i	−0.451898	+	0.892070i	$0.649253\pi$
$882$	−22.7605	−	1.21106i	−0.766385	−	0.0407784i
$883$	−20.0127			−0.673481			−0.336741	−	0.941597i	$-0.609325\pi$
$883$	−20.0127			−0.673481			−0.336741	+	0.941597i	$0.609325\pi$
$884$	3.75538	+	0.166211i	0.126307	+	0.00559028i
$885$		0			0
$886$	−12.6477	+	12.1003i	−0.424907	+	0.406517i
$887$	−16.8977	−	9.75588i	−0.567369	−	0.327571i	0.188729	−	0.982029i	$-0.439563\pi$
$887$	−16.8977	−	9.75588i	−0.567369	−	0.327571i	−0.756098	+	0.654459i	$0.772897\pi$
$888$	−33.0018	+	1.61944i	−1.10747	+	0.0543450i
$889$	4.88316	+	8.45787i	0.163776	+	0.283668i
$890$		0			0
$891$	3.79056	+	2.51437i	0.126989	+	0.0842347i
$892$	−13.7081	−	8.74456i	−0.458982	−	0.292790i
$893$	2.81929	+	4.88316i	0.0943440	+	0.163409i
$894$	25.8080	−	18.3026i	0.863149	−	0.612129i
$895$		0			0
$896$	−11.6583	+	8.51076i	−0.389475	+	0.284325i
$897$	−13.0916	−	1.93070i	−0.437115	−	0.0644643i
$898$	−6.51394	−	26.6548i	−0.217373	−	0.889481i
$899$	−20.5226			−0.684467
$900$		0			0
$901$	−1.48913			−0.0496100
$902$	−1.15055	−	4.70801i	−0.0383092	−	0.156760i
$903$	−6.29069	−	15.8798i	−0.209341	−	0.528448i
$904$	3.99793	+	20.1935i	0.132969	+	0.671626i
$905$		0			0
$906$	0.690414	+	7.38142i	0.0229375	+	0.245231i
$907$	14.9467	+	25.8884i	0.496297	+	0.859611i	0.999991	−	0.00427097i	$-0.00135950\pi$
$907$	14.9467	+	25.8884i	0.496297	+	0.859611i	−0.503694	+	0.863882i	$0.668026\pi$
$908$	−15.4873	+	24.2781i	−0.513963	+	0.805698i
$909$	−2.53667	−	2.69927i	−0.0841361	−	0.0895290i
$910$		0			0
$911$	17.9015	+	31.0063i	0.593102	+	1.02728i	0.993812	+	0.111078i	$0.0354303\pi$
$911$	17.9015	+	31.0063i	0.593102	+	1.02728i	−0.400710	+	0.916205i	$0.631236\pi$
$912$	31.2338	−	9.27690i	1.03425	−	0.307189i
$913$	−3.34408	−	1.93070i	−0.110673	−	0.0638970i
$914$	40.8525	−	39.0844i	1.35128	−	1.29280i
$915$		0			0
$916$	0.320808	−	7.24834i	0.0105998	−	0.239492i
$917$	9.74749			0.321891
$918$	5.70653	+	1.15428i	0.188343	+	0.0380968i
$919$			36.9711i			1.21956i	0.792570	+	0.609781i	$0.208743\pi$
$919$			36.9711i			1.21956i	−0.792570	+	0.609781i	$0.791257\pi$
$920$		0			0
$921$	−1.29211	+	1.63086i	−0.0425765	+	0.0537387i
$922$	0.357508	−	0.342034i	0.0117739	−	0.0112643i
$923$	24.3897	+	14.0814i	0.802796	+	0.463494i
$924$	1.68774	+	1.46318i	0.0555226	+	0.0481351i
$925$		0			0
$926$	−1.89253	+	6.48577i	−0.0621925	+	0.213136i
$927$	−1.36423	−	0.411331i	−0.0448072	−	0.0135099i
$928$	2.15121	+	14.1168i	0.0706170	+	0.463408i
$929$	−16.0693	+	9.27761i	−0.527217	+	0.304389i	−0.739882	−	0.672736i	$-0.765119\pi$
$929$	−16.0693	+	9.27761i	−0.527217	+	0.304389i	0.212666	+	0.977125i	$0.431785\pi$
$930$		0			0
$931$	21.8802	+	12.6325i	0.717094	+	0.414014i
$932$	−8.60011	+	4.47040i	−0.281706	+	0.146433i
$933$	−12.2067	−	30.8139i	−0.399630	−	1.00880i
$934$	−1.71662	−	7.02435i	−0.0561697	−	0.229844i
$935$		0			0
$936$	8.32198	+	18.3287i	0.272012	+	0.599092i
$937$			45.7228i			1.49370i	0.664993	+	0.746850i	$0.268435\pi$
$937$			45.7228i			1.49370i	−0.664993	+	0.746850i	$0.731565\pi$
$938$	−13.5475	+	3.31075i	−0.442340	+	0.108100i
$939$	4.67228	−	31.6814i	0.152474	−	1.03388i
$940$		0			0
$941$	11.6970	+	6.75327i	0.381312	+	0.220150i	0.678389	−	0.734703i	$-0.262678\pi$
$941$	11.6970	+	6.75327i	0.381312	+	0.220150i	−0.297077	+	0.954854i	$0.596012\pi$
$942$	−23.6996	+	16.8073i	−0.772175	+	0.547612i
$943$	10.9190	+	18.9123i	0.355572	+	0.615869i
$944$	20.8694	+	44.8945i	0.679240	+	1.46119i
$945$		0			0
$946$	1.54755	−	5.30350i	0.0503151	−	0.172432i
$947$	5.69005	−	3.28515i	0.184902	−	0.106753i	−0.404692	−	0.914453i	$-0.632621\pi$
$947$	5.69005	−	3.28515i	0.184902	−	0.106753i	0.589594	+	0.807700i	$0.299288\pi$
$948$	11.1866	+	32.3480i	0.363324	+	1.05061i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$		0			0
$951$	−55.7260	−	8.21830i	−1.80704	−	0.266497i
$952$	2.70647	+	0.921427i	0.0877171	+	0.0298636i
$953$	10.2997			0.333641			0.166821	−	0.985987i	$-0.446650\pi$
$953$	10.2997			0.333641			0.166821	+	0.985987i	$0.446650\pi$
$954$	−3.61452	−	7.10792i	−0.117024	−	0.230127i
$955$		0			0
$956$	1.06647	−	24.0959i	0.0344922	−	0.779317i
$957$	2.05446	−	0.813859i	0.0664111	−	0.0263083i
$958$	12.7783	+	13.3564i	0.412849	+	0.431526i
$959$	−3.50283	+	6.06709i	−0.113112	+	0.195916i
$960$		0			0
$961$	17.5475	+	30.3932i	0.566050	+	0.980427i
$962$	−6.33830	+	21.7216i	−0.204355	+	0.700331i
$963$	36.6963	−	8.62146i	1.18252	−	0.277823i
$964$	10.9416	+	6.97975i	0.352404	+	0.224802i
$965$		0			0
$966$	−9.14709	−	4.19877i	−0.294303	−	0.135093i
$967$	−23.4259	+	40.5748i	−0.753325	+	1.30480i	0.192878	+	0.981223i	$0.438218\pi$
$967$	−23.4259	+	40.5748i	−0.753325	+	1.30480i	−0.946203	+	0.323574i	$0.895115\pi$
$968$	−5.90213	−	29.8116i	−0.189702	−	0.958180i
$969$	−5.05842	−	4.00772i	−0.162500	−	0.128747i
$970$		0			0
$971$	−37.0019			−1.18745			−0.593724	−	0.804669i	$-0.702343\pi$
$971$	−37.0019			−1.18745			−0.593724	+	0.804669i	$0.702343\pi$
$972$	8.34170	+	30.0402i	0.267560	+	0.963541i
$973$		−	19.6277i		−	0.629236i
$974$	−58.9013	+	14.3944i	−1.88732	+	0.461227i
$975$		0			0
$976$	9.45202	+	0.838325i	0.302552	+	0.0268341i
$977$	27.3441	−	47.3614i	0.874816	−	1.51523i	0.0178572	−	0.999841i	$-0.494316\pi$
$977$	27.3441	−	47.3614i	0.874816	−	1.51523i	0.856959	−	0.515385i	$-0.172351\pi$
$978$	−1.78907	+	3.89753i	−0.0572082	+	0.124629i
$979$	5.24224	−	3.02661i	0.167543	−	0.0967307i
$980$		0			0
$981$	9.25544	+	39.3947i	0.295503	+	1.25778i
$982$	5.45257	−	18.6861i	0.173998	−	0.596299i
$983$	29.8050	−	17.2079i	0.950631	−	0.548847i	0.0573540	−	0.998354i	$-0.481734\pi$
$983$	29.8050	−	17.2079i	0.950631	−	0.548847i	0.893277	+	0.449507i	$0.148400\pi$
$984$	15.1794	−	29.5477i	0.483900	−	0.941945i
$985$		0			0
$986$	2.04374	−	1.95528i	0.0650859	−	0.0622689i
$987$	−2.46323	+	0.975793i	−0.0784055	+	0.0310598i
$988$	0.986595	−	22.2912i	0.0313878	−	0.709177i
$989$			24.8935i			0.791568i
$990$		0			0
$991$		−	7.65492i		−	0.243167i	−0.992581	−	0.121583i	$-0.961203\pi$
$991$		−	7.65492i		−	0.243167i	0.992581	−	0.121583i	$-0.0387972\pi$
$992$	35.9095	−	28.7324i	1.14013	−	0.912254i
$993$	−7.01056	+	47.5367i	−0.222473	+	1.50853i
$994$	14.8074	+	15.4773i	0.469662	+	0.490909i
$995$		0			0
$996$	−8.64998	−	25.0129i	−0.274085	−	0.792564i
$997$	−20.9046	+	12.0693i	−0.662056	+	0.382238i	−0.793060	−	0.609143i	$-0.791513\pi$
$997$	−20.9046	+	12.0693i	−0.662056	+	0.382238i	0.131004	+	0.991382i	$0.458180\pi$
$998$	−4.65253	−	1.35760i	−0.147273	−	0.0429740i
$999$	−14.9040	+	31.7187i	−0.471543	+	1.00354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.o.a.599.8		16
4.3	odd	2	inner	900.2.o.a.599.3		16
5.2	odd	4		900.2.r.c.851.2		8
5.3	odd	4		36.2.h.a.23.3	yes	8
5.4	even	2	inner	900.2.o.a.599.1		16
9.2	odd	6	inner	900.2.o.a.299.6		16
15.8	even	4		108.2.h.a.71.2		8
20.3	even	4		36.2.h.a.23.4	yes	8
20.7	even	4		900.2.r.c.851.1		8
20.19	odd	2	inner	900.2.o.a.599.6		16
36.11	even	6	inner	900.2.o.a.299.1		16
40.3	even	4		576.2.s.f.383.4		8
40.13	odd	4		576.2.s.f.383.1		8
45.2	even	12		900.2.r.c.551.1		8
45.13	odd	12		324.2.b.b.323.8		8
45.23	even	12		324.2.b.b.323.1		8
45.29	odd	6	inner	900.2.o.a.299.3		16
45.38	even	12		36.2.h.a.11.4	yes	8
45.43	odd	12		108.2.h.a.35.1		8
60.23	odd	4		108.2.h.a.71.1		8
120.53	even	4		1728.2.s.f.1151.1		8
120.83	odd	4		1728.2.s.f.1151.2		8
180.23	odd	12		324.2.b.b.323.7		8
180.43	even	12		108.2.h.a.35.2		8
180.47	odd	12		900.2.r.c.551.2		8
180.83	odd	12		36.2.h.a.11.3	✓	8
180.103	even	12		324.2.b.b.323.2		8
180.119	even	6	inner	900.2.o.a.299.8		16
360.13	odd	12		5184.2.c.j.5183.1		8
360.43	even	12		1728.2.s.f.575.1		8
360.83	odd	12		576.2.s.f.191.1		8
360.133	odd	12		1728.2.s.f.575.2		8
360.173	even	12		576.2.s.f.191.4		8
360.203	odd	12		5184.2.c.j.5183.8		8
360.283	even	12		5184.2.c.j.5183.2		8
360.293	even	12		5184.2.c.j.5183.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.3	✓	8	180.83	odd	12
36.2.h.a.11.4	yes	8	45.38	even	12
36.2.h.a.23.3	yes	8	5.3	odd	4
36.2.h.a.23.4	yes	8	20.3	even	4
108.2.h.a.35.1		8	45.43	odd	12
108.2.h.a.35.2		8	180.43	even	12
108.2.h.a.71.1		8	60.23	odd	4
108.2.h.a.71.2		8	15.8	even	4
324.2.b.b.323.1		8	45.23	even	12
324.2.b.b.323.2		8	180.103	even	12
324.2.b.b.323.7		8	180.23	odd	12
324.2.b.b.323.8		8	45.13	odd	12
576.2.s.f.191.1		8	360.83	odd	12
576.2.s.f.191.4		8	360.173	even	12
576.2.s.f.383.1		8	40.13	odd	4
576.2.s.f.383.4		8	40.3	even	4
900.2.o.a.299.1		16	36.11	even	6	inner
900.2.o.a.299.3		16	45.29	odd	6	inner
900.2.o.a.299.6		16	9.2	odd	6	inner
900.2.o.a.299.8		16	180.119	even	6	inner
900.2.o.a.599.1		16	5.4	even	2	inner
900.2.o.a.599.3		16	4.3	odd	2	inner
900.2.o.a.599.6		16	20.19	odd	2	inner
900.2.o.a.599.8		16	1.1	even	1	trivial
900.2.r.c.551.1		8	45.2	even	12
900.2.r.c.551.2		8	180.47	odd	12
900.2.r.c.851.1		8	20.7	even	4
900.2.r.c.851.2		8	5.2	odd	4
1728.2.s.f.575.1		8	360.43	even	12
1728.2.s.f.575.2		8	360.133	odd	12
1728.2.s.f.1151.1		8	120.53	even	4
1728.2.s.f.1151.2		8	120.83	odd	4
5184.2.c.j.5183.1		8	360.13	odd	12
5184.2.c.j.5183.2		8	360.283	even	12
5184.2.c.j.5183.7		8	360.293	even	12
5184.2.c.j.5183.8		8	360.203	odd	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37379 - 0.335728i) q^{2} +(1.07561 - 1.35760i) q^{3} +(1.77457 - 0.922437i) q^{4} +(1.02187 - 2.22616i) q^{6} +(-0.637910 - 1.10489i) q^{7} +(2.12819 - 1.86301i) q^{8} +(-0.686141 - 2.92048i) q^{9} +(-0.252704 - 0.437696i) q^{11} +(0.656444 - 3.40134i) q^{12} +(-2.05446 - 1.18614i) q^{13} +(-1.24730 - 1.30372i) q^{14} +(2.29822 - 3.27386i) q^{16} -0.792287 q^{17} +(-1.92310 - 3.78176i) q^{18} +4.70285i q^{19} +(-2.18614 - 0.322405i) q^{21} +(-0.494108 - 0.516461i) q^{22} +(2.78912 + 1.61030i) q^{23} +(-0.240111 - 4.89309i) q^{24} +(-3.22060 - 0.939764i) q^{26} +(-4.70285 - 2.20979i) q^{27} +(-2.15121 - 1.37228i) q^{28} +(-2.18614 + 1.26217i) q^{29} +(7.04069 + 4.06494i) q^{31} +(2.05813 - 5.26916i) q^{32} +(-0.866025 - 0.127719i) q^{33} +(-1.08843 + 0.265993i) q^{34} +(-3.91157 - 4.54969i) q^{36} -6.74456i q^{37} +(1.57888 + 6.46071i) q^{38} +(-3.82009 + 1.51330i) q^{39} +(5.87228 + 3.39036i) q^{41} +(-3.11153 + 0.291034i) q^{42} +(3.86473 + 6.69391i) q^{43} +(-0.852189 - 0.543620i) q^{44} +(4.37228 + 1.27582i) q^{46} +(1.03834 - 0.599485i) q^{47} +(-1.97261 - 6.64145i) q^{48} +(2.68614 - 4.65253i) q^{49} +(-0.852189 + 1.07561i) q^{51} +(-4.73992 - 0.209786i) q^{52} +1.87953 q^{53} +(-7.20260 - 1.45689i) q^{54} +(-3.41602 - 1.16300i) q^{56} +(6.38458 + 5.05842i) q^{57} +(-2.57954 + 2.46790i) q^{58} +(-6.18850 + 10.7188i) q^{59} +(1.18614 + 2.05446i) q^{61} +(11.0371 + 3.22060i) q^{62} +(-2.78912 + 2.62112i) q^{63} +(1.05842 - 7.92967i) q^{64} +(-1.23261 + 0.115291i) q^{66} +(3.86473 - 6.69391i) q^{67} +(-1.40597 + 0.730835i) q^{68} +(5.18614 - 2.05446i) q^{69} -11.8716 q^{71} +(-6.90111 - 4.93707i) q^{72} -3.37228i q^{73} +(-2.26434 - 9.26558i) q^{74} +(4.33809 + 8.34556i) q^{76} +(-0.322405 + 0.558422i) q^{77} +(-4.73992 + 3.36147i) q^{78} +(-8.55691 + 4.94034i) q^{79} +(-8.05842 + 4.00772i) q^{81} +(9.20550 + 2.68614i) q^{82} +(6.61659 - 3.82009i) q^{83} +(-4.17686 + 1.44445i) q^{84} +(7.55665 + 7.89850i) q^{86} +(-0.637910 + 4.32550i) q^{87} +(-1.35323 - 0.460714i) q^{88} +11.9769i q^{89} +3.02661i q^{91} +(6.43491 + 0.284805i) q^{92} +(13.0916 - 5.18614i) q^{93} +(1.22519 - 1.17216i) q^{94} +(-4.93967 - 8.46166i) q^{96} +(9.08385 - 5.24456i) q^{97} +(2.12819 - 7.29339i) q^{98} +(-1.10489 + 1.03834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} - 6 q^{6} + 12 q^{9} - 24 q^{14} - 2 q^{16} - 12 q^{21} - 6 q^{24} - 12 q^{29} - 14 q^{34} - 66 q^{36} + 48 q^{41} + 24 q^{46} + 20 q^{49} - 78 q^{54} + 36 q^{56} - 4 q^{61} - 52 q^{64} - 48 q^{66}+ \cdots + 24 q^{96}+O(q^{100}) \) 16 * q + 2 * q^4 - 6 * q^6 + 12 * q^9 - 24 * q^14 - 2 * q^16 - 12 * q^21 - 6 * q^24 - 12 * q^29 - 14 * q^34 - 66 * q^36 + 48 * q^41 + 24 * q^46 + 20 * q^49 - 78 * q^54 + 36 * q^56 - 4 * q^61 - 52 * q^64 - 48 * q^66 + 60 * q^69 + 60 * q^74 - 6 * q^76 - 60 * q^81 - 60 * q^84 + 42 * q^86 + 36 * q^94 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more