LMFDB - Embedded newform 484.3.b.h.243.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [484,3,Mod(243,484)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("484.243"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(484, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	484.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,4,-4,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1880447950$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 7x^{8} + 4x^{7} - 7x^{6} + 82x^{5} - 28x^{4} + 64x^{3} + 448x^{2} - 512x + 1024 $ x^10 - 2x^9 + 7x^8 + 4x^7 - 7x^6 + 82x^5 - 28x^4 + 64x^3 + 448x^2 - 512*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			243.9
Root			$1.24026 + 1.56900i$ of defining polynomial
Character	$\chi$	$=$	484.243
Dual form			484.3.b.h.243.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.80007 - 0.871632i) q^{2} +3.93920i q^{3} +(2.48051 - 3.13800i) q^{4} -7.32441 q^{5} +(3.43354 + 7.09085i) q^{6} -5.80518i q^{7} +(1.72992 - 7.81072i) q^{8} -6.51732 q^{9} +(-13.1845 + 6.38420i) q^{10} +(12.3612 + 9.77125i) q^{12} -13.3869 q^{13} +(-5.05998 - 10.4497i) q^{14} -28.8524i q^{15} +(-3.69410 - 15.5677i) q^{16} -18.5822 q^{17} +(-11.7316 + 5.68071i) q^{18} -24.6869i q^{19} +(-18.1683 + 22.9840i) q^{20} +22.8678 q^{21} -3.90291i q^{23} +(30.7680 + 6.81451i) q^{24} +28.6470 q^{25} +(-24.0974 + 11.6685i) q^{26} +9.77977i q^{27} +(-18.2167 - 14.3998i) q^{28} +17.7391 q^{29} +(-25.1486 - 51.9363i) q^{30} -53.7292i q^{31} +(-20.2190 - 24.8031i) q^{32} +(-33.4493 + 16.1968i) q^{34} +42.5195i q^{35} +(-16.1663 + 20.4514i) q^{36} -41.7067 q^{37} +(-21.5179 - 44.4382i) q^{38} -52.7337i q^{39} +(-12.6707 + 57.2090i) q^{40} -28.2740 q^{41} +(41.1637 - 19.9323i) q^{42} +10.8938i q^{43} +47.7356 q^{45} +(-3.40190 - 7.02552i) q^{46} +21.6372i q^{47} +(61.3244 - 14.5518i) q^{48} +15.2999 q^{49} +(51.5667 - 24.9697i) q^{50} -73.1990i q^{51} +(-33.2064 + 42.0081i) q^{52} +58.4573 q^{53} +(8.52436 + 17.6043i) q^{54} +(-45.3427 - 10.0425i) q^{56} +97.2468 q^{57} +(31.9317 - 15.4620i) q^{58} -16.9088i q^{59} +(-90.5387 - 71.5687i) q^{60} -17.7938 q^{61} +(-46.8321 - 96.7164i) q^{62} +37.8342i q^{63} +(-58.0148 - 27.0238i) q^{64} +98.0512 q^{65} +82.7612i q^{67} +(-46.0934 + 58.3109i) q^{68} +15.3744 q^{69} +(37.0614 + 76.5382i) q^{70} -24.9700i q^{71} +(-11.2744 + 50.9050i) q^{72} -67.7523 q^{73} +(-75.0750 + 36.3529i) q^{74} +112.847i q^{75} +(-77.4676 - 61.2363i) q^{76} +(-45.9644 - 94.9244i) q^{78} -12.4825i q^{79} +(27.0571 + 114.024i) q^{80} -97.1804 q^{81} +(-50.8952 + 24.6445i) q^{82} +37.2108i q^{83} +(56.7239 - 71.7591i) q^{84} +136.104 q^{85} +(9.49537 + 19.6096i) q^{86} +69.8781i q^{87} +76.5448 q^{89} +(85.9274 - 41.6079i) q^{90} +77.7134i q^{91} +(-12.2473 - 9.68123i) q^{92} +211.650 q^{93} +(18.8597 + 38.9485i) q^{94} +180.817i q^{95} +(97.7044 - 79.6466i) q^{96} -130.492 q^{97} +(27.5409 - 13.3359i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 4 q^{5} - 6 q^{6} + 12 q^{8} - 30 q^{9} + 2 q^{10} + 40 q^{12} + 4 q^{13} - 4 q^{14} - 40 q^{16} - 20 q^{17} + 22 q^{18} - 64 q^{20} - 32 q^{21} - 36 q^{24} - 10 q^{25} - 36 q^{26} - 40 q^{28}+ \cdots + 568 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 - 4 * q^5 - 6 * q^6 + 12 * q^8 - 30 * q^9 + 2 * q^10 + 40 * q^12 + 4 * q^13 - 4 * q^14 - 40 * q^16 - 20 * q^17 + 22 * q^18 - 64 * q^20 - 32 * q^21 - 36 * q^24 - 10 * q^25 - 36 * q^26 - 40 * q^28 - 28 * q^29 - 126 * q^30 - 80 * q^32 - 88 * q^34 - 4 * q^36 - 100 * q^37 + 40 * q^38 + 12 * q^40 - 100 * q^41 + 260 * q^42 - 44 * q^45 + 130 * q^46 + 24 * q^48 - 22 * q^49 + 198 * q^50 + 176 * q^52 + 100 * q^53 + 350 * q^54 + 136 * q^56 + 112 * q^57 + 116 * q^58 - 136 * q^60 + 52 * q^61 - 134 * q^62 - 368 * q^64 + 184 * q^65 - 176 * q^68 + 184 * q^69 - 36 * q^70 - 360 * q^72 - 84 * q^73 - 362 * q^74 - 504 * q^76 - 232 * q^78 - 120 * q^80 + 330 * q^81 + 220 * q^82 + 40 * q^84 + 216 * q^85 + 556 * q^86 + 28 * q^89 + 520 * q^90 + 152 * q^92 - 72 * q^93 + 272 * q^94 + 704 * q^96 - 180 * q^97 + 568 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.80007	−	0.871632i	0.900036	−	0.435816i
$2$	1.80007	−	0.871632i	0.900036	−	0.435816i
$3$			3.93920i			1.31307i	0.754297	+	0.656534i	$0.227978\pi$
$3$			3.93920i			1.31307i	−0.754297	+	0.656534i	$0.772022\pi$
$4$	2.48051	−	3.13800i	0.620129	−	0.784500i
$5$	−7.32441			−1.46488			−0.732441	−	0.680830i	$-0.761619\pi$
$5$	−7.32441			−1.46488			−0.732441	+	0.680830i	$0.761619\pi$
$6$	3.43354	+	7.09085i	0.572256	+	1.18181i
$7$		−	5.80518i		−	0.829312i	−0.909978	−	0.414656i	$-0.863902\pi$
$7$		−	5.80518i		−	0.829312i	0.909978	−	0.414656i	$-0.136098\pi$
$8$	1.72992	−	7.81072i	0.216240	−	0.976340i
$9$	−6.51732			−0.724147
$10$	−13.1845	+	6.38420i	−1.31845	+	0.638420i
$11$		0			0
$11$		0			0
$12$	12.3612	+	9.77125i	1.03010	+	0.814271i
$13$	−13.3869			−1.02976			−0.514881	−	0.857262i	$-0.672164\pi$
$13$	−13.3869			−1.02976			−0.514881	+	0.857262i	$0.672164\pi$
$14$	−5.05998	−	10.4497i	−0.361427	−	0.746410i
$15$		−	28.8524i		−	1.92349i
$16$	−3.69410	−	15.5677i	−0.230881	−	0.972982i
$17$	−18.5822			−1.09307			−0.546535	−	0.837436i	$-0.684053\pi$
$17$	−18.5822			−1.09307			−0.546535	+	0.837436i	$0.684053\pi$
$18$	−11.7316	+	5.68071i	−0.651758	+	0.315595i
$19$		−	24.6869i		−	1.29931i	−0.760229	−	0.649656i	$-0.774913\pi$
$19$		−	24.6869i		−	1.29931i	0.760229	−	0.649656i	$-0.225087\pi$
$20$	−18.1683	+	22.9840i	−0.908416	+	1.14920i
$21$	22.8678			1.08894
$22$		0			0
$23$		−	3.90291i		−	0.169692i	−0.996394	−	0.0848459i	$-0.972960\pi$
$23$		−	3.90291i		−	0.169692i	0.996394	−	0.0848459i	$-0.0270398\pi$
$24$	30.7680	+	6.81451i	1.28200	+	0.283938i
$25$	28.6470			1.14588
$26$	−24.0974	+	11.6685i	−0.926822	+	0.448787i
$27$			9.77977i			0.362214i
$28$	−18.2167	−	14.3998i	−0.650595	−	0.514280i
$29$	17.7391			0.611695			0.305847	−	0.952081i	$-0.401060\pi$
$29$	17.7391			0.611695			0.305847	+	0.952081i	$0.401060\pi$
$30$	−25.1486	−	51.9363i	−0.838288	−	1.73121i
$31$		−	53.7292i		−	1.73320i	−0.499003	−	0.866600i	$-0.666300\pi$
$31$		−	53.7292i		−	1.73320i	0.499003	−	0.866600i	$-0.333700\pi$
$32$	−20.2190	−	24.8031i	−0.631842	−	0.775097i
$33$		0			0
$34$	−33.4493	+	16.1968i	−0.983802	+	0.476377i
$35$			42.5195i			1.21484i
$36$	−16.1663	+	20.4514i	−0.449064	+	0.568093i
$37$	−41.7067			−1.12721			−0.563604	−	0.826045i	$-0.690585\pi$
$37$	−41.7067			−1.12721			−0.563604	+	0.826045i	$0.690585\pi$
$38$	−21.5179	−	44.4382i	−0.566261	−	1.16943i
$39$		−	52.7337i		−	1.35215i
$40$	−12.6707	+	57.2090i	−0.316766	+	1.43022i
$41$	−28.2740			−0.689609			−0.344805	−	0.938674i	$-0.612055\pi$
$41$	−28.2740			−0.689609			−0.344805	+	0.938674i	$0.612055\pi$
$42$	41.1637	−	19.9323i	0.980087	−	0.474579i
$43$			10.8938i			0.253344i	0.991945	+	0.126672i	$0.0404295\pi$
$43$			10.8938i			0.253344i	−0.991945	+	0.126672i	$0.959570\pi$
$44$		0			0
$45$	47.7356			1.06079
$46$	−3.40190	−	7.02552i	−0.0739544	−	0.152729i
$47$			21.6372i			0.460365i	0.973147	+	0.230183i	$0.0739324\pi$
$47$			21.6372i			0.460365i	−0.973147	+	0.230183i	$0.926068\pi$
$48$	61.3244	−	14.5518i	1.27759	−	0.303163i
$49$	15.2999			0.312242
$50$	51.5667	−	24.9697i	1.03133	−	0.499394i
$51$		−	73.1990i		−	1.43527i
$52$	−33.2064	+	42.0081i	−0.638584	+	0.807848i
$53$	58.4573			1.10297			0.551484	−	0.834186i	$-0.314062\pi$
$53$	58.4573			1.10297			0.551484	+	0.834186i	$0.314062\pi$
$54$	8.52436	+	17.6043i	0.157859	+	0.326005i
$55$		0			0
$56$	−45.3427	−	10.0425i	−0.809690	−	0.179330i
$57$	97.2468			1.70608
$58$	31.9317	−	15.4620i	0.550547	−	0.266586i
$59$		−	16.9088i		−	0.286590i	−0.989680	−	0.143295i	$-0.954230\pi$
$59$		−	16.9088i		−	0.286590i	0.989680	−	0.143295i	$-0.0457697\pi$
$60$	−90.5387	−	71.5687i	−1.50898	−	1.19281i
$61$	−17.7938			−0.291702			−0.145851	−	0.989307i	$-0.546592\pi$
$61$	−17.7938			−0.291702			−0.145851	+	0.989307i	$0.546592\pi$
$62$	−46.8321	−	96.7164i	−0.755357	−	1.55994i
$63$			37.8342i			0.600544i
$64$	−58.0148	−	27.0238i	−0.906481	−	0.422248i
$65$	98.0512			1.50848
$66$		0			0
$67$			82.7612i			1.23524i	0.786476	+	0.617621i	$0.211904\pi$
$67$			82.7612i			1.23524i	−0.786476	+	0.617621i	$0.788096\pi$
$68$	−46.0934	+	58.3109i	−0.677844	+	0.857513i
$69$	15.3744			0.222817
$70$	37.0614	+	76.5382i	0.529449	+	1.09340i
$71$		−	24.9700i		−	0.351690i	−0.984418	−	0.175845i	$-0.943734\pi$
$71$		−	24.9700i		−	0.351690i	0.984418	−	0.175845i	$-0.0562658\pi$
$72$	−11.2744	+	50.9050i	−0.156590	+	0.707014i
$73$	−67.7523			−0.928113			−0.464057	−	0.885806i	$-0.653607\pi$
$73$	−67.7523			−0.928113			−0.464057	+	0.885806i	$0.653607\pi$
$74$	−75.0750	+	36.3529i	−1.01453	+	0.491255i
$75$			112.847i			1.50462i
$76$	−77.4676	−	61.2363i	−1.01931	−	0.805740i
$77$		0			0
$78$	−45.9644	−	94.9244i	−0.589287	−	1.21698i
$79$		−	12.4825i		−	0.158007i	−0.996874	−	0.0790033i	$-0.974826\pi$
$79$		−	12.4825i		−	0.158007i	0.996874	−	0.0790033i	$-0.0251737\pi$
$80$	27.0571	+	114.024i	0.338214	+	1.42530i
$81$	−97.1804			−1.19976
$82$	−50.8952	+	24.6445i	−0.620673	+	0.300543i
$83$			37.2108i			0.448323i	0.974552	+	0.224162i	$0.0719644\pi$
$83$			37.2108i			0.448323i	−0.974552	+	0.224162i	$0.928036\pi$
$84$	56.7239	−	71.7591i	0.675284	−	0.854275i
$85$	136.104			1.60122
$86$	9.49537	+	19.6096i	0.110411	+	0.228018i
$87$			69.8781i			0.803197i
$88$		0			0
$89$	76.5448			0.860054			0.430027	−	0.902816i	$-0.358504\pi$
$89$	76.5448			0.860054			0.430027	+	0.902816i	$0.358504\pi$
$90$	85.9274	−	41.6079i	0.954749	−	0.462310i
$91$			77.7134i			0.853993i
$92$	−12.2473	−	9.68123i	−0.133123	−	0.105231i
$93$	211.650			2.27581
$94$	18.8597	+	38.9485i	0.200635	+	0.414345i
$95$			180.817i			1.90334i
$96$	97.7044	−	79.6466i	1.01775	−	0.829652i
$97$	−130.492			−1.34528			−0.672641	−	0.739969i	$-0.734840\pi$
$97$	−130.492			−1.34528			−0.672641	+	0.739969i	$0.734840\pi$
$98$	27.5409	−	13.3359i	0.281029	−	0.136080i
$99$		0			0
$100$	71.0594	−	89.8944i	0.710594	−	0.898944i
$101$	−129.160			−1.27881			−0.639407	−	0.768869i	$-0.720820\pi$
$101$	−129.160			−1.27881			−0.639407	+	0.768869i	$0.720820\pi$
$102$	−63.8026	−	131.763i	−0.625516	−	1.29180i
$103$			26.4552i			0.256847i	0.991719	+	0.128423i	$0.0409916\pi$
$103$			26.4552i			0.256847i	−0.991719	+	0.128423i	$0.959008\pi$
$104$	−23.1583	+	104.561i	−0.222676	+	1.00540i
$105$	−167.493			−1.59517
$106$	105.227	−	50.9532i	0.992710	−	0.480691i
$107$			92.4255i			0.863789i	0.901924	+	0.431895i	$0.142155\pi$
$107$			92.4255i			0.863789i	−0.901924	+	0.431895i	$0.857845\pi$
$108$	30.6889	+	24.2589i	0.284157	+	0.224619i
$109$	22.2234			0.203885			0.101942	−	0.994790i	$-0.467494\pi$
$109$	22.2234			0.203885			0.101942	+	0.994790i	$0.467494\pi$
$110$		0			0
$111$		−	164.291i		−	1.48010i
$112$	−90.3734	+	21.4449i	−0.806905	+	0.191472i
$113$	70.9385			0.627775			0.313887	−	0.949460i	$-0.398369\pi$
$113$	70.9385			0.627775			0.313887	+	0.949460i	$0.398369\pi$
$114$	175.051	−	84.7634i	1.53554	−	0.743539i
$115$			28.5865i			0.248579i
$116$	44.0022	−	55.6655i	0.379329	−	0.479875i
$117$	87.2467			0.745699
$118$	−14.7383	−	30.4370i	−0.124900	−	0.257941i
$119$			107.873i			0.906495i
$120$	−225.358	−	49.9123i	−1.87798	−	0.415936i
$121$		0			0
$122$	−32.0302	+	15.5097i	−0.262543	+	0.127129i
$123$		−	111.377i		−	0.905504i
$124$	−168.602	−	133.276i	−1.35970	−	1.07481i
$125$	−26.7125			−0.213700
$126$	32.9775	+	68.1043i	0.261727	+	0.540511i
$127$		−	64.2837i		−	0.506171i	−0.967444	−	0.253086i	$-0.918555\pi$
$127$		−	64.2837i		−	0.506171i	0.967444	−	0.253086i	$-0.0814454\pi$
$128$	−127.986	+	1.92267i	−0.999887	+	0.0150209i
$129$	−42.9128			−0.332657
$130$	176.499	−	85.4646i	1.35769	−	0.657420i
$131$			169.921i			1.29711i	0.761169	+	0.648554i	$0.224626\pi$
$131$			169.921i			1.29711i	−0.761169	+	0.648554i	$0.775374\pi$
$132$		0			0
$133$	−143.312			−1.07753
$134$	72.1374	+	148.976i	0.538339	+	1.11176i
$135$		−	71.6311i		−	0.530601i
$136$	−32.1457	+	145.140i	−0.236365	+	1.06721i
$137$	−74.3855			−0.542960			−0.271480	−	0.962444i	$-0.587513\pi$
$137$	−74.3855			−0.542960			−0.271480	+	0.962444i	$0.587513\pi$
$138$	27.6749	−	13.4008i	0.200543	−	0.0971072i
$139$			79.5922i			0.572606i	0.958139	+	0.286303i	$0.0924263\pi$
$139$			79.5922i			0.572606i	−0.958139	+	0.286303i	$0.907574\pi$
$140$	133.426	+	105.470i	0.953046	+	0.753360i
$141$	−85.2332			−0.604491
$142$	−21.7647	−	44.9478i	−0.153272	−	0.316534i
$143$		0			0
$144$	24.0756	+	101.460i	0.167192	+	0.704582i
$145$	−129.929			−0.896061
$146$	−121.959	+	59.0551i	−0.835335	+	0.404487i
$147$			60.2693i			0.409995i
$148$	−103.454	+	130.876i	−0.699013	+	0.884294i
$149$	171.827			1.15320			0.576600	−	0.817026i	$-0.304379\pi$
$149$	171.827			1.15320			0.576600	+	0.817026i	$0.304379\pi$
$150$	98.3607	+	203.132i	0.655738	+	1.35421i
$151$		−	203.334i		−	1.34658i	−0.739377	−	0.673292i	$-0.764880\pi$
$151$		−	203.334i		−	1.34658i	0.739377	−	0.673292i	$-0.235120\pi$
$152$	−192.823	−	42.7064i	−1.26857	−	0.280963i
$153$	121.106			0.791543
$154$		0			0
$155$			393.535i			2.53894i
$156$	−165.478	−	130.807i	−1.06076	−	0.838505i
$157$	73.9277			0.470877			0.235439	−	0.971889i	$-0.424347\pi$
$157$	73.9277			0.470877			0.235439	+	0.971889i	$0.424347\pi$
$158$	−10.8802	−	22.4694i	−0.0688618	−	0.142211i
$159$			230.275i			1.44827i
$160$	148.092	+	181.668i	0.925575	+	1.13543i
$161$	−22.6571			−0.140727
$162$	−174.932	+	84.7056i	−1.07983	+	0.522874i
$163$		−	308.757i		−	1.89421i	−0.320921	−	0.947106i	$-0.603992\pi$
$163$		−	308.757i		−	1.89421i	0.320921	−	0.947106i	$-0.396008\pi$
$164$	−70.1340	+	88.7238i	−0.427646	+	0.540999i
$165$		0			0
$166$	32.4342	+	66.9822i	0.195387	+	0.403507i
$167$		−	209.003i		−	1.25151i	−0.780018	−	0.625757i	$-0.784790\pi$
$167$		−	209.003i		−	1.25151i	0.780018	−	0.625757i	$-0.215210\pi$
$168$	39.5594	−	178.614i	0.235473	−	1.06318i
$169$	10.2090			0.0604084
$170$	244.996	−	118.632i	1.44115	−	0.697837i
$171$			160.893i			0.940893i
$172$	34.1847	+	27.0222i	0.198748	+	0.157106i
$173$	221.731			1.28168			0.640841	−	0.767674i	$-0.278586\pi$
$173$	221.731			1.28168			0.640841	+	0.767674i	$0.278586\pi$
$174$	60.9080	+	125.786i	0.350046	+	0.722906i
$175$		−	166.301i		−	0.950293i
$176$		0			0
$177$	66.6072			0.376312
$178$	137.786	−	66.7189i	0.774080	−	0.374826i
$179$		−	185.819i		−	1.03810i	−0.854745	−	0.519048i	$-0.826286\pi$
$179$		−	185.819i		−	1.03810i	0.854745	−	0.519048i	$-0.173714\pi$
$180$	118.409	−	149.794i	0.657827	−	0.832190i
$181$	222.314			1.22825			0.614127	−	0.789207i	$-0.289508\pi$
$181$	222.314			1.22825			0.614127	+	0.789207i	$0.289508\pi$
$182$	67.7375	+	139.890i	0.372184	+	0.768624i
$183$		−	70.0936i		−	0.383025i
$184$	−30.4845	−	6.75172i	−0.165677	−	0.0366941i
$185$	305.477			1.65123
$186$	380.986	−	184.481i	2.04831	−	0.991835i
$187$		0			0
$188$	67.8975	+	53.6713i	0.361157	+	0.285486i
$189$	56.7733			0.300388
$190$	157.606	+	325.484i	0.829506	+	1.71307i
$191$		−	147.914i		−	0.774419i	−0.921992	−	0.387210i	$-0.873439\pi$
$191$		−	147.914i		−	0.774419i	0.921992	−	0.387210i	$-0.126561\pi$
$192$	106.452	−	228.532i	0.554440	−	1.19027i
$193$	44.4373			0.230245			0.115122	−	0.993351i	$-0.463274\pi$
$193$	44.4373			0.230245			0.115122	+	0.993351i	$0.463274\pi$
$194$	−234.895	+	113.741i	−1.21080	+	0.586295i
$195$			386.244i			1.98074i
$196$	37.9516	−	48.0110i	0.193630	−	0.244954i
$197$	−61.2376			−0.310851			−0.155425	−	0.987848i	$-0.549675\pi$
$197$	−61.2376			−0.310851			−0.155425	+	0.987848i	$0.549675\pi$
$198$		0			0
$199$		−	292.227i		−	1.46848i	−0.678892	−	0.734238i	$-0.737540\pi$
$199$		−	292.227i		−	1.46848i	0.678892	−	0.734238i	$-0.262460\pi$
$200$	49.5571	−	223.754i	0.247785	−	1.11877i
$201$	−326.013			−1.62196
$202$	−232.498	+	112.580i	−1.15098	+	0.557328i
$203$		−	102.979i		−	0.507286i
$204$	−229.699	−	181.571i	−1.12597	−	0.890055i
$205$	207.090			1.01020
$206$	23.0592	+	47.6212i	0.111938	+	0.231171i
$207$			25.4365i			0.122882i
$208$	49.4525	+	208.403i	0.237752	+	1.00194i
$209$		0			0
$210$	−301.500	+	145.992i	−1.43571	+	0.695202i
$211$			131.168i			0.621647i	0.950468	+	0.310824i	$0.100605\pi$
$211$			131.168i			0.621647i	−0.950468	+	0.310824i	$0.899395\pi$
$212$	145.004	−	183.439i	0.683982	−	0.865278i
$213$	98.3620			0.461793
$214$	80.5610	+	166.372i	0.376453	+	0.777441i
$215$		−	79.7906i		−	0.371119i
$216$	76.3870	+	16.9182i	0.353644	+	0.0783251i
$217$	−311.908			−1.43736
$218$	40.0038	−	19.3707i	0.183504	−	0.0888563i
$219$		−	266.890i		−	1.21868i
$220$		0			0
$221$	248.758			1.12560
$222$	−143.201	−	295.736i	−0.645051	−	1.33214i
$223$		−	42.6819i		−	0.191399i	−0.995410	−	0.0956994i	$-0.969491\pi$
$223$		−	42.6819i		−	0.191399i	0.995410	−	0.0956994i	$-0.0305088\pi$
$224$	−143.986	+	117.375i	−0.642797	+	0.523994i
$225$	−186.702			−0.829787
$226$	127.694	−	61.8323i	0.565020	−	0.273594i
$227$		−	383.274i		−	1.68843i	−0.536005	−	0.844215i	$-0.680067\pi$
$227$		−	383.274i		−	1.68843i	0.536005	−	0.844215i	$-0.319933\pi$
$228$	241.222	−	305.161i	1.05799	−	1.33842i
$229$	172.329			0.752527			0.376263	−	0.926513i	$-0.377209\pi$
$229$	172.329			0.752527			0.376263	+	0.926513i	$0.377209\pi$
$230$	24.9169	+	51.4578i	0.108335	+	0.223730i
$231$		0			0
$232$	30.6873	−	138.556i	0.132273	−	0.597222i
$233$	174.344			0.748259			0.374129	−	0.927377i	$-0.377942\pi$
$233$	174.344			0.748259			0.374129	+	0.927377i	$0.377942\pi$
$234$	157.050	−	76.0471i	0.671155	−	0.324987i
$235$		−	158.480i		−	0.674381i
$236$	−53.0598	−	41.9425i	−0.224830	−	0.177723i
$237$	49.1712			0.207473
$238$	94.0255	+	194.179i	0.395065	+	0.815878i
$239$		−	124.374i		−	0.520394i	−0.965556	−	0.260197i	$-0.916212\pi$
$239$		−	124.374i		−	0.520394i	0.965556	−	0.260197i	$-0.0837875\pi$
$240$	−449.165	+	106.583i	−1.87152	+	0.444098i
$241$	−171.826			−0.712970			−0.356485	−	0.934301i	$-0.616025\pi$
$241$	−171.826			−0.712970			−0.356485	+	0.934301i	$0.616025\pi$
$242$		0			0
$243$		−	294.795i		−	1.21315i
$244$	−44.1379	+	55.8371i	−0.180893	+	0.228841i
$245$	−112.063			−0.457398
$246$	−97.0798	−	200.487i	−0.394633	−	0.814986i
$247$			330.481i			1.33798i
$248$	−419.664	−	92.9473i	−1.69219	−	0.374787i
$249$	−146.581			−0.588679
$250$	−48.0843	+	23.2834i	−0.192337	+	0.0931337i
$251$		−	4.25687i		−	0.0169596i	−0.999964	−	0.00847982i	$-0.997301\pi$
$251$		−	4.25687i		−	0.0169596i	0.999964	−	0.00847982i	$-0.00269924\pi$
$252$	118.724	+	93.8484i	0.471126	+	0.372414i
$253$		0			0
$254$	−56.0318	−	115.715i	−0.220598	−	0.455572i
$255$			536.140i			2.10251i
$256$	−228.707	+	115.017i	−0.893388	+	0.449286i
$257$	414.591			1.61320			0.806598	−	0.591100i	$-0.201306\pi$
$257$	414.591			1.61320			0.806598	+	0.591100i	$0.201306\pi$
$258$	−77.2461	+	37.4042i	−0.299404	+	0.144977i
$259$			242.115i			0.934806i
$260$	243.217	−	307.685i	0.935451	−	1.18340i
$261$	−115.612			−0.442957
$262$	148.109	+	305.870i	0.565300	+	1.16744i
$263$		−	238.004i		−	0.904959i	−0.891775	−	0.452479i	$-0.850540\pi$
$263$		−	238.004i		−	0.904959i	0.891775	−	0.452479i	$-0.149460\pi$
$264$		0			0
$265$	−428.165			−1.61572
$266$	−257.972	+	124.915i	−0.969819	+	0.469607i
$267$			301.526i			1.12931i
$268$	259.705	+	205.290i	0.969048	+	0.766009i
$269$	−492.368			−1.83036			−0.915182	−	0.403042i	$-0.867953\pi$
$269$	−492.368			−1.83036			−0.915182	+	0.403042i	$0.867953\pi$
$270$	−62.4360	−	128.941i	−0.231244	−	0.477559i
$271$			219.809i			0.811103i	0.914072	+	0.405551i	$0.132920\pi$
$271$			219.809i			0.811103i	−0.914072	+	0.405551i	$0.867080\pi$
$272$	68.6444	+	289.282i	0.252369	+	1.06354i
$273$	−306.129			−1.12135
$274$	−133.899	+	64.8368i	−0.488683	+	0.236631i
$275$		0			0
$276$	38.1363	−	48.2447i	0.138175	−	0.174800i
$277$	124.193			0.448352			0.224176	−	0.974549i	$-0.428031\pi$
$277$	124.193			0.448352			0.224176	+	0.974549i	$0.428031\pi$
$278$	69.3751	+	143.272i	0.249551	+	0.515365i
$279$			350.171i			1.25509i
$280$	332.108	+	73.5554i	1.18610	+	0.262698i
$281$	309.426			1.10116			0.550581	−	0.834782i	$-0.314406\pi$
$281$	309.426			1.10116			0.550581	+	0.834782i	$0.314406\pi$
$282$	−153.426	+	74.2920i	−0.544063	+	0.263447i
$283$		−	315.046i		−	1.11324i	−0.830768	−	0.556619i	$-0.812098\pi$
$283$		−	315.046i		−	1.11324i	0.830768	−	0.556619i	$-0.187902\pi$
$284$	−78.3559	−	61.9385i	−0.275901	−	0.218093i
$285$	−712.276			−2.49921
$286$		0			0
$287$			164.136i			0.571901i
$288$	131.774	+	161.650i	0.457547	+	0.561284i
$289$	56.2975			0.194801
$290$	−233.881	+	113.250i	−0.806487	+	0.390518i
$291$		−	514.036i		−	1.76645i
$292$	−168.060	+	212.607i	−0.575550	+	0.728105i
$293$	−52.9652			−0.180768			−0.0903842	−	0.995907i	$-0.528810\pi$
$293$	−52.9652			−0.180768			−0.0903842	+	0.995907i	$0.528810\pi$
$294$	52.5327	+	108.489i	0.178683	+	0.369010i
$295$			123.847i			0.419821i
$296$	−72.1492	+	325.759i	−0.243747	+	1.10054i
$297$		0			0
$298$	309.301	−	149.770i	1.03792	−	0.502583i
$299$			52.2479i			0.174742i
$300$	354.112	+	279.917i	1.18037	+	0.933058i
$301$	63.2404			0.210101
$302$	−177.233	−	366.016i	−0.586863	−	1.21197i
$303$		−	508.788i		−	1.67917i
$304$	−384.319	+	91.1959i	−1.26421	+	0.299986i
$305$	130.329			0.427310
$306$	218.000	−	105.560i	0.712417	−	0.344967i
$307$			491.403i			1.60066i	0.599558	+	0.800331i	$0.295343\pi$
$307$			491.403i			1.60066i	−0.599558	+	0.800331i	$0.704657\pi$
$308$		0			0
$309$	−104.212			−0.337257
$310$	343.018	+	708.391i	1.10651	+	2.28513i
$311$		−	5.43852i		−	0.0174872i	−0.999962	−	0.00874360i	$-0.997217\pi$
$311$		−	5.43852i		−	0.0174872i	0.999962	−	0.00874360i	$-0.00278321\pi$
$312$	−411.888	−	91.2251i	−1.32015	−	0.292388i
$313$	−330.116			−1.05468			−0.527341	−	0.849653i	$-0.676811\pi$
$313$	−330.116			−1.05468			−0.527341	+	0.849653i	$0.676811\pi$
$314$	133.075	−	64.4378i	0.423806	−	0.205216i
$315$		−	277.114i		−	0.879726i
$316$	−39.1701	−	30.9631i	−0.123956	−	0.0979843i
$317$	−172.447			−0.543996			−0.271998	−	0.962298i	$-0.587684\pi$
$317$	−172.447			−0.543996			−0.271998	+	0.962298i	$0.587684\pi$
$318$	200.715	+	414.512i	0.631180	+	1.30350i
$319$		0			0
$320$	424.924	+	197.934i	1.32789	+	0.618543i
$321$	−364.083			−1.13421
$322$	−40.7844	+	19.7487i	−0.126660	+	0.0613312i
$323$			458.737i			1.42024i
$324$	−241.057	+	304.952i	−0.744004	+	0.941210i
$325$	−383.495			−1.17998
$326$	−269.122	−	555.784i	−0.825528	−	1.70486i
$327$			87.5426i			0.267715i
$328$	−48.9117	+	220.840i	−0.149121	+	0.673293i
$329$	125.608			0.381786
$330$		0			0
$331$		−	163.853i		−	0.495024i	−0.968885	−	0.247512i	$-0.920387\pi$
$331$		−	163.853i		−	0.495024i	0.968885	−	0.247512i	$-0.0796129\pi$
$332$	116.768	+	92.3020i	0.351710	+	0.278018i
$333$	271.816			0.816264
$334$	−182.174	−	376.220i	−0.545430	−	1.12641i
$335$		−	606.178i		−	1.80949i
$336$	−84.4758	−	355.999i	−0.251416	−	1.05952i
$337$	−412.255			−1.22331			−0.611654	−	0.791125i	$-0.709496\pi$
$337$	−412.255			−1.22331			−0.611654	+	0.791125i	$0.709496\pi$
$338$	18.3770	−	8.89851i	0.0543697	−	0.0263269i
$339$			279.441i			0.824311i
$340$	337.607	−	427.093i	0.992962	−	1.25616i
$341$		0			0
$342$	140.239	+	289.618i	0.410056	+	0.846837i
$343$		−	373.272i		−	1.08826i
$344$	85.0883	+	18.8454i	0.247350	+	0.0547830i
$345$	−112.608			−0.326400
$346$	399.131	−	193.268i	1.15356	−	0.558578i
$347$			378.806i			1.09166i	0.837896	+	0.545831i	$0.183786\pi$
$347$			378.806i			1.09166i	−0.837896	+	0.545831i	$0.816214\pi$
$348$	219.278	+	173.334i	0.630108	+	0.498085i
$349$	−199.304			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$349$	−199.304			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$350$	−144.954	−	299.354i	−0.414153	−	0.855298i
$351$		−	130.921i		−	0.372994i
$352$		0			0
$353$	−9.83774			−0.0278690			−0.0139345	−	0.999903i	$-0.504436\pi$
$353$	−9.83774			−0.0278690			−0.0139345	+	0.999903i	$0.504436\pi$
$354$	119.898	−	58.0570i	0.338694	−	0.164003i
$355$			182.891i			0.515185i
$356$	189.871	−	240.198i	0.533344	−	0.674713i
$357$	−424.933			−1.19029
$358$	−161.966	−	334.488i	−0.452419	−	0.934324i
$359$		−	104.379i		−	0.290749i	−0.989377	−	0.145375i	$-0.953561\pi$
$359$		−	104.379i		−	0.290749i	0.989377	−	0.145375i	$-0.0464387\pi$
$360$	82.5787	−	372.849i	0.229385	−	1.03569i
$361$	−248.444			−0.688210
$362$	400.181	−	193.776i	1.10547	−	0.535293i
$363$		0			0
$364$	243.865	+	192.769i	0.669958	+	0.529585i
$365$	496.246			1.35958
$366$	−61.0958	−	126.173i	−0.166928	−	0.344736i
$367$		−	92.4715i		−	0.251966i	−0.992032	−	0.125983i	$-0.959792\pi$
$367$		−	92.4715i		−	0.251966i	0.992032	−	0.125983i	$-0.0402085\pi$
$368$	−60.7594	+	14.4177i	−0.165107	+	0.0391786i
$369$	184.271			0.499379
$370$	549.880	−	266.263i	1.48616	−	0.719631i
$371$		−	339.355i		−	0.914704i
$372$	525.002	−	664.159i	1.41129	−	1.78537i
$373$	210.811			0.565176			0.282588	−	0.959241i	$-0.408807\pi$
$373$	210.811			0.565176			0.282588	+	0.959241i	$0.408807\pi$
$374$		0			0
$375$		−	105.226i		−	0.280602i
$376$	169.002	+	37.4306i	0.449473	+	0.0995494i
$377$	−237.472			−0.629900
$378$	102.196	−	49.4855i	0.270360	−	0.130914i
$379$		−	474.260i		−	1.25135i	−0.780085	−	0.625673i	$-0.784824\pi$
$379$		−	474.260i		−	1.25135i	0.780085	−	0.625673i	$-0.215176\pi$
$380$	567.405	+	448.520i	1.49317	+	1.18031i
$381$	253.227			0.664637
$382$	−128.927	−	266.256i	−0.337505	−	0.697005i
$383$		−	352.236i		−	0.919677i	−0.888003	−	0.459838i	$-0.847907\pi$
$383$		−	352.236i		−	0.919677i	0.888003	−	0.459838i	$-0.152093\pi$
$384$	−7.57380	−	504.161i	−0.0197234	−	1.31292i
$385$		0			0
$386$	79.9903	−	38.7330i	0.207229	−	0.100344i
$387$		−	70.9983i		−	0.183458i
$388$	−323.688	+	409.485i	−0.834247	+	1.05537i
$389$	−183.305			−0.471220			−0.235610	−	0.971848i	$-0.575709\pi$
$389$	−183.305			−0.471220			−0.235610	+	0.971848i	$0.575709\pi$
$390$	336.662	+	695.266i	0.863237	+	1.78273i
$391$			72.5246i			0.185485i
$392$	26.4676	−	119.503i	0.0675193	−	0.304855i
$393$	−669.354			−1.70319
$394$	−110.232	+	53.3766i	−0.279777	+	0.135474i
$395$			91.4271i			0.231461i
$396$		0			0
$397$	−641.230			−1.61519			−0.807594	−	0.589739i	$-0.799231\pi$
$397$	−641.230			−1.61519			−0.807594	+	0.589739i	$0.799231\pi$
$398$	−254.714	−	526.029i	−0.639985	−	1.32168i
$399$		−	564.535i		−	1.41488i
$400$	−105.825	−	445.969i	−0.264562	−	1.11492i
$401$	493.400			1.23043			0.615213	−	0.788361i	$-0.289070\pi$
$401$	493.400			1.23043			0.615213	+	0.788361i	$0.289070\pi$
$402$	−586.847	+	284.164i	−1.45982	+	0.706875i
$403$			719.268i			1.78478i
$404$	−320.384	+	405.305i	−0.793029	+	1.00323i
$405$	711.790			1.75751
$406$	−89.7598	−	185.369i	−0.221083	−	0.456575i
$407$		0			0
$408$	−571.737	−	126.628i	−1.40132	−	0.310364i
$409$	−256.241			−0.626507			−0.313253	−	0.949670i	$-0.601419\pi$
$409$	−256.241			−0.626507			−0.313253	+	0.949670i	$0.601419\pi$
$410$	372.777	−	180.507i	0.909213	−	0.440260i
$411$		−	293.020i		−	0.712943i
$412$	83.0164	+	65.6225i	0.201496	+	0.159278i
$413$	−98.1586			−0.237672
$414$	22.1713	+	45.7876i	0.0535539	+	0.110598i
$415$		−	272.548i		−	0.656741i
$416$	270.669	+	332.037i	0.650647	+	0.798165i
$417$	−313.530			−0.751870
$418$		0			0
$419$			638.082i			1.52287i	0.648243	+	0.761434i	$0.275504\pi$
$419$			638.082i			1.52287i	−0.648243	+	0.761434i	$0.724496\pi$
$420$	−415.469	+	525.594i	−0.989212	+	1.25141i
$421$	638.939			1.51767			0.758835	−	0.651283i	$-0.225769\pi$
$421$	638.939			1.51767			0.758835	+	0.651283i	$0.225769\pi$
$422$	114.330	+	236.111i	0.270924	+	0.559505i
$423$		−	141.016i		−	0.333372i
$424$	101.126	−	456.593i	0.238506	−	1.07687i
$425$	−532.325			−1.25253
$426$	177.059	−	85.7355i	0.415630	−	0.201257i
$427$			103.296i			0.241912i
$428$	290.031	+	229.263i	0.677643	+	0.535661i
$429$		0			0
$430$	−69.5480	−	143.629i	−0.161740	−	0.334020i
$431$			21.7364i			0.0504326i	0.999682	+	0.0252163i	$0.00802744\pi$
$431$			21.7364i			0.0504326i	−0.999682	+	0.0252163i	$0.991973\pi$
$432$	152.249	−	36.1274i	0.352427	−	0.0836283i
$433$	553.476			1.27823			0.639117	−	0.769109i	$-0.279300\pi$
$433$	553.476			1.27823			0.639117	+	0.769109i	$0.279300\pi$
$434$	−561.456	+	271.869i	−1.29368	+	0.626426i
$435$		−	511.816i		−	1.17659i
$436$	55.1256	−	69.7372i	0.126435	−	0.159948i
$437$	−96.3508			−0.220482
$438$	−232.630	−	480.421i	−0.531119	−	1.09685i
$439$		−	763.723i		−	1.73969i	−0.493328	−	0.869844i	$-0.664220\pi$
$439$		−	763.723i		−	1.73969i	0.493328	−	0.869844i	$-0.335780\pi$
$440$		0			0
$441$	−99.7142			−0.226109
$442$	447.782	−	216.825i	1.01308	−	0.490555i
$443$			23.5641i			0.0531921i	0.999646	+	0.0265961i	$0.00846679\pi$
$443$			23.5641i			0.0531921i	−0.999646	+	0.0265961i	$0.991533\pi$
$444$	−515.545	−	407.526i	−1.16114	−	0.917852i
$445$	−560.646			−1.25988
$446$	−37.2030	−	76.8305i	−0.0834147	−	0.172266i
$447$			676.861i			1.51423i
$448$	−156.878	+	336.786i	−0.350175	+	0.751755i
$449$	−387.403			−0.862814			−0.431407	−	0.902157i	$-0.641983\pi$
$449$	−387.403			−0.862814			−0.431407	+	0.902157i	$0.641983\pi$
$450$	−336.077	+	162.736i	−0.746838	+	0.361635i
$451$		0			0
$452$	175.964	−	222.605i	0.389301	−	0.492489i
$453$	800.974			1.76816
$454$	−334.074	−	689.920i	−0.735845	−	1.51965i
$455$		−	569.205i		−	1.25100i
$456$	168.229	−	759.568i	0.368924	−	1.66572i
$457$	84.9126			0.185804			0.0929021	−	0.995675i	$-0.470386\pi$
$457$	84.9126			0.185804			0.0929021	+	0.995675i	$0.470386\pi$
$458$	310.204	−	150.207i	0.677301	−	0.327963i
$459$		−	181.729i		−	0.395925i
$460$	89.7046	+	70.9093i	0.195010	+	0.154151i
$461$	−661.135			−1.43413			−0.717066	−	0.697005i	$-0.754515\pi$
$461$	−661.135			−1.43413			−0.717066	+	0.697005i	$0.754515\pi$
$462$		0			0
$463$			170.691i			0.368663i	0.982864	+	0.184331i	$0.0590120\pi$
$463$			170.691i			0.368663i	−0.982864	+	0.184331i	$0.940988\pi$
$464$	−65.5301	−	276.158i	−0.141229	−	0.595168i
$465$	−1550.21			−3.33379
$466$	313.832	−	151.964i	0.673460	−	0.326103i
$467$			714.245i			1.52943i	0.644367	+	0.764717i	$0.277121\pi$
$467$			714.245i			1.52943i	−0.644367	+	0.764717i	$0.722879\pi$
$468$	216.417	−	273.780i	0.462429	−	0.585001i
$469$	480.444			1.02440
$470$	−138.136	−	285.275i	−0.293906	−	0.606967i
$471$			291.216i			0.618294i
$472$	−132.070	−	29.2509i	−0.279809	−	0.0619722i
$473$		0			0
$474$	88.5116	−	42.8592i	0.186733	−	0.0904202i
$475$		−	707.207i		−	1.48886i
$476$	338.505	+	267.580i	0.711146	+	0.562144i
$477$	−380.985			−0.798711
$478$	−108.409	−	223.882i	−0.226796	−	0.468373i
$479$			801.041i			1.67232i	0.548485	+	0.836160i	$0.315205\pi$
$479$			801.041i			1.67232i	−0.548485	+	0.836160i	$0.684795\pi$
$480$	−715.628	+	583.365i	−1.49089	+	1.21534i
$481$	558.323			1.16075
$482$	−309.299	+	149.769i	−0.641698	+	0.310724i
$483$		−	89.2509i		−	0.184785i
$484$		0			0
$485$	955.780			1.97068
$486$	−256.953	−	530.653i	−0.528710	−	1.09188i
$487$			116.427i			0.239070i	0.992830	+	0.119535i	$0.0381404\pi$
$487$			116.427i			0.239070i	−0.992830	+	0.119535i	$0.961860\pi$
$488$	−30.7819	+	138.983i	−0.0630777	+	0.284801i
$489$	1216.25			2.48723
$490$	−201.721	+	97.6774i	−0.411675	+	0.199342i
$491$		−	658.338i		−	1.34081i	−0.741995	−	0.670406i	$-0.766120\pi$
$491$		−	658.338i		−	1.34081i	0.741995	−	0.670406i	$-0.233880\pi$
$492$	−349.501	−	276.272i	−0.710368	−	0.561529i
$493$	−329.632			−0.668625
$494$	288.058	+	594.890i	0.583114	+	1.20423i
$495$		0			0
$496$	−836.441	+	198.481i	−1.68637	+	0.400163i
$497$	−144.955			−0.291661
$498$	−263.856	+	127.765i	−0.529832	+	0.256556i
$499$			433.519i			0.868776i	0.900726	+	0.434388i	$0.143035\pi$
$499$			433.519i			0.868776i	−0.900726	+	0.434388i	$0.856965\pi$
$500$	−66.2606	+	83.8237i	−0.132521	+	0.167647i
$501$	823.305			1.64332
$502$	−3.71042	−	7.66267i	−0.00739128	−	0.0152643i
$503$			566.370i			1.12598i	0.826462	+	0.562992i	$0.190350\pi$
$503$			566.370i			1.12598i	−0.826462	+	0.562992i	$0.809650\pi$
$504$	295.513	+	65.4502i	0.586335	+	0.129862i
$505$	946.023			1.87331
$506$		0			0
$507$			40.2154i			0.0793203i
$508$	−201.722	−	159.457i	−0.397091	−	0.313891i
$509$	491.065			0.964764			0.482382	−	0.875961i	$-0.339772\pi$
$509$	491.065			0.964764			0.482382	+	0.875961i	$0.339772\pi$
$510$	467.317	+	965.090i	0.916307	+	1.89233i
$511$			393.314i			0.769695i
$512$	−311.437	+	406.388i	−0.608275	+	0.793727i
$513$	241.432			0.470628
$514$	746.294	−	361.371i	1.45193	−	0.703057i
$515$		−	193.769i		−	0.376250i
$516$	−106.446	+	134.660i	−0.206290	+	0.260970i
$517$		0			0
$518$	211.035	+	435.824i	0.407403	+	0.841359i
$519$			873.443i			1.68293i
$520$	169.621	−	765.850i	0.326194	−	1.47279i
$521$	103.457			0.198573			0.0992867	−	0.995059i	$-0.468344\pi$
$521$	103.457			0.198573			0.0992867	+	0.995059i	$0.468344\pi$
$522$	−208.109	+	100.771i	−0.398677	+	0.193048i
$523$		−	402.098i		−	0.768829i	−0.923161	−	0.384415i	$-0.874403\pi$
$523$		−	402.098i		−	0.768829i	0.923161	−	0.384415i	$-0.125597\pi$
$524$	533.212	+	421.492i	1.01758	+	0.804373i
$525$	655.095			1.24780
$526$	−207.452	−	428.424i	−0.394396	−	0.814495i
$527$			998.406i			1.89451i
$528$		0			0
$529$	513.767			0.971205
$530$	−770.728	+	373.203i	−1.45420	+	0.704156i
$531$			110.200i			0.207533i
$532$	−355.488	+	449.713i	−0.668210	+	0.845326i
$533$	378.501			0.710133
$534$	262.819	+	542.768i	0.492171	+	1.01642i
$535$		−	676.962i		−	1.26535i
$536$	646.425	+	143.170i	1.20602	+	0.267109i
$537$	731.980			1.36309
$538$	−886.297	+	429.164i	−1.64739	+	0.797702i
$539$		0			0
$540$	−224.778	−	177.682i	−0.416256	−	0.329041i
$541$	−1044.09			−1.92992			−0.964961	−	0.262394i	$-0.915488\pi$
$541$	−1044.09			−1.92992			−0.964961	+	0.262394i	$0.915488\pi$
$542$	191.592	+	395.672i	0.353492	+	0.730021i
$543$			875.740i			1.61278i
$544$	375.712	+	460.896i	0.690648	+	0.847235i
$545$	−162.774			−0.298667
$546$	−551.054	+	266.832i	−1.00926	+	0.488703i
$547$			942.124i			1.72235i	0.508312	+	0.861173i	$0.330270\pi$
$547$			942.124i			1.72235i	−0.508312	+	0.861173i	$0.669730\pi$
$548$	−184.514	+	233.422i	−0.336705	+	0.425952i
$549$	115.968			0.211235
$550$		0			0
$551$		−	437.925i		−	0.794782i
$552$	26.5964	−	120.085i	0.0481819	−	0.217545i
$553$	−72.4632			−0.131037
$554$	223.557	−	108.251i	0.403532	−	0.195399i
$555$			1203.34i			2.16817i
$556$	249.760	+	197.430i	0.449209	+	0.355089i
$557$	−172.165			−0.309094			−0.154547	−	0.987985i	$-0.549392\pi$
$557$	−172.165			−0.309094			−0.154547	+	0.987985i	$0.549392\pi$
$558$	305.220	+	630.332i	0.546989	+	1.12963i
$559$		−	145.834i		−	0.260884i
$560$	661.932	−	157.071i	1.18202	−	0.280485i
$561$		0			0
$562$	556.990	−	269.706i	0.991085	−	0.479904i
$563$			837.976i			1.48841i	0.667950	+	0.744206i	$0.267172\pi$
$563$			837.976i			1.48841i	−0.667950	+	0.744206i	$0.732828\pi$
$564$	−211.422	+	267.462i	−0.374862	+	0.474223i
$565$	−519.583			−0.919616
$566$	−274.605	−	567.106i	−0.485167	−	1.00195i
$567$			564.150i			0.994973i
$568$	−195.034	−	43.1961i	−0.343369	−	0.0760495i
$569$	538.014			0.945542			0.472771	−	0.881185i	$-0.343254\pi$
$569$	538.014			0.945542			0.472771	+	0.881185i	$0.343254\pi$
$570$	−1282.15	+	620.843i	−2.24938	+	1.08920i
$571$		−	179.926i		−	0.315108i	−0.987510	−	0.157554i	$-0.949639\pi$
$571$		−	179.926i		−	0.315108i	0.987510	−	0.157554i	$-0.0503608\pi$
$572$		0			0
$573$	582.664			1.01687
$574$	143.066	+	295.456i	0.249244	+	0.514731i
$575$		−	111.807i		−	0.194447i
$576$	378.101	+	176.123i	0.656425	+	0.305769i
$577$	−450.823			−0.781322			−0.390661	−	0.920535i	$-0.627754\pi$
$577$	−450.823			−0.781322			−0.390661	+	0.920535i	$0.627754\pi$
$578$	101.340	−	49.0707i	0.175328	−	0.0848975i
$579$			175.047i			0.302327i
$580$	−322.290	+	407.717i	−0.555673	+	0.702960i
$581$	216.016			0.371800
$582$	−448.050	−	925.301i	−0.769846	−	1.58986i
$583$		0			0
$584$	−117.206	+	529.194i	−0.200695	+	0.906154i
$585$	−639.031			−1.09236
$586$	−95.3411	+	46.1661i	−0.162698	+	0.0787818i
$587$		−	811.334i		−	1.38217i	−0.722773	−	0.691085i	$-0.757133\pi$
$587$		−	811.334i		−	1.38217i	0.722773	−	0.691085i	$-0.242867\pi$
$588$	189.125	+	149.499i	0.321641	+	0.254250i
$589$	−1326.41			−2.25197
$590$	107.949	+	222.934i	0.182965	+	0.377853i
$591$		−	241.227i		−	0.408168i
$592$	154.068	+	649.277i	0.260251	+	1.09675i
$593$	624.543			1.05319			0.526596	−	0.850115i	$-0.323468\pi$
$593$	624.543			1.05319			0.526596	+	0.850115i	$0.323468\pi$
$594$		0			0
$595$		−	790.106i		−	1.32791i
$596$	426.219	−	539.193i	0.715133	−	0.904686i
$597$	1151.14			1.92821
$598$	45.5409	+	94.0499i	0.0761554	+	0.157274i
$599$			302.388i			0.504822i	0.967620	+	0.252411i	$0.0812234\pi$
$599$			302.388i			0.504822i	−0.967620	+	0.252411i	$0.918777\pi$
$600$	881.413	+	195.215i	1.46902	+	0.325359i
$601$	852.409			1.41832			0.709159	−	0.705049i	$-0.249075\pi$
$601$	852.409			1.41832			0.709159	+	0.705049i	$0.249075\pi$
$602$	113.837	−	55.1223i	0.189098	−	0.0915653i
$603$		−	539.382i		−	0.894497i
$604$	−638.063	−	504.373i	−1.05640	−	0.835055i
$605$		0			0
$606$	−443.476	−	915.855i	−0.731809	−	1.51131i
$607$		−	633.424i		−	1.04353i	−0.853088	−	0.521766i	$-0.825273\pi$
$607$		−	633.424i		−	1.04353i	0.853088	−	0.521766i	$-0.174727\pi$
$608$	−612.312	+	499.144i	−1.00709	+	0.820960i
$609$	405.655			0.666100
$610$	234.602	−	113.599i	0.384594	−	0.186229i
$611$		−	289.655i		−	0.474066i
$612$	300.405	−	380.031i	0.490859	−	0.620966i
$613$	−81.3226			−0.132663			−0.0663316	−	0.997798i	$-0.521130\pi$
$613$	−81.3226			−0.132663			−0.0663316	+	0.997798i	$0.521130\pi$
$614$	428.323	+	884.561i	0.697594	+	1.44065i
$615$			815.771i			1.32646i
$616$		0			0
$617$	−798.403			−1.29401			−0.647004	−	0.762487i	$-0.723978\pi$
$617$	−798.403			−1.29401			−0.647004	+	0.762487i	$0.723978\pi$
$618$	−187.590	+	90.8349i	−0.303543	+	0.146982i
$619$		−	775.210i		−	1.25236i	−0.779679	−	0.626179i	$-0.784618\pi$
$619$		−	775.210i		−	1.25236i	0.779679	−	0.626179i	$-0.215382\pi$
$620$	1234.91	+	976.169i	1.99180	+	1.57447i
$621$	38.1696			0.0614647
$622$	−4.74039	−	9.78972i	−0.00762120	−	0.0157391i
$623$		−	444.357i		−	0.713253i
$624$	−820.943	+	194.803i	−1.31561	+	0.312185i
$625$	−520.523			−0.832837
$626$	−594.232	+	287.740i	−0.949252	+	0.459648i
$627$		0			0
$628$	183.379	−	231.985i	0.292004	−	0.369403i
$629$	775.001			1.23212
$630$	−241.541	−	498.824i	−0.383399	−	0.791785i
$631$		−	916.853i		−	1.45302i	−0.687158	−	0.726508i	$-0.741142\pi$
$631$		−	916.853i		−	1.45302i	0.687158	−	0.726508i	$-0.258858\pi$
$632$	−97.4974	−	21.5938i	−0.154268	−	0.0341673i
$633$	−516.696			−0.816265
$634$	−310.416	+	150.310i	−0.489616	+	0.237082i
$635$			470.841i			0.741481i
$636$	722.603	+	571.201i	1.13617	+	0.898114i
$637$	−204.818			−0.321535
$638$		0			0
$639$			162.738i			0.254676i
$640$	937.419	−	14.0824i	1.46472	−	0.0220038i
$641$	−401.005			−0.625592			−0.312796	−	0.949820i	$-0.601266\pi$
$641$	−401.005			−0.625592			−0.312796	+	0.949820i	$0.601266\pi$
$642$	−655.375	+	317.346i	−1.02083	+	0.494309i
$643$		−	227.345i		−	0.353569i	−0.984250	−	0.176785i	$-0.943430\pi$
$643$		−	227.345i		−	0.353569i	0.984250	−	0.176785i	$-0.0565696\pi$
$644$	−56.2013	+	71.0980i	−0.0872690	+	0.110401i
$645$	314.311			0.487304
$646$	399.850	+	825.759i	0.618963	+	1.27826i
$647$			273.880i			0.423307i	0.977345	+	0.211654i	$0.0678849\pi$
$647$			273.880i			0.423307i	−0.977345	+	0.211654i	$0.932115\pi$
$648$	−168.114	+	759.049i	−0.259436	+	1.17137i
$649$		0			0
$650$	−690.318	+	334.267i	−1.06203	+	0.514256i
$651$		−	1228.67i		−	1.88736i
$652$	−968.878	−	765.875i	−1.48601	−	1.17465i
$653$	−751.947			−1.15153			−0.575764	−	0.817616i	$-0.695295\pi$
$653$	−751.947			−1.15153			−0.575764	+	0.817616i	$0.695295\pi$
$654$	76.3050	+	157.583i	0.116674	+	0.240953i
$655$		−	1244.57i		−	1.90011i
$656$	104.447	+	440.161i	0.159218	+	0.670977i
$657$	441.564			0.672091
$658$	226.103	−	109.484i	0.343621	−	0.166389i
$659$		−	1125.72i		−	1.70822i	−0.520090	−	0.854112i	$-0.674101\pi$
$659$		−	1125.72i		−	1.70822i	0.520090	−	0.854112i	$-0.325899\pi$
$660$		0			0
$661$	−886.587			−1.34128			−0.670641	−	0.741782i	$-0.733981\pi$
$661$	−886.587			−1.34128			−0.670641	+	0.741782i	$0.733981\pi$
$662$	−142.819	−	294.947i	−0.215739	−	0.445539i
$663$			979.907i			1.47799i
$664$	290.644	+	64.3718i	0.437716	+	0.0969454i
$665$	1049.68			1.57846
$666$	489.288	−	236.923i	0.734666	−	0.355741i
$667$		−	69.2343i		−	0.103800i
$668$	−655.851	−	518.435i	−0.981813	−	0.776100i
$669$	168.133			0.251320
$670$	−528.364	−	1091.16i	−0.788603	−	1.62860i
$671$		0			0
$672$	−462.363	−	567.192i	−0.688040	−	0.844036i
$673$	−1253.65			−1.86278			−0.931392	−	0.364018i	$-0.881405\pi$
$673$	−1253.65			−1.86278			−0.931392	+	0.364018i	$0.881405\pi$
$674$	−742.088	+	359.335i	−1.10102	+	0.533138i
$675$			280.161i			0.415054i
$676$	25.3236	−	32.0359i	0.0374610	−	0.0473904i
$677$	829.568			1.22536			0.612679	−	0.790332i	$-0.290092\pi$
$677$	829.568			1.22536			0.612679	+	0.790332i	$0.290092\pi$
$678$	243.570	+	503.014i	0.359248	+	0.741909i
$679$			757.531i			1.11566i
$680$	235.448	−	1063.07i	0.346248	−	1.56333i
$681$	1509.79			2.21702
$682$		0			0
$683$		−	596.596i		−	0.873493i	−0.899585	−	0.436746i	$-0.856131\pi$
$683$		−	596.596i		−	0.873493i	0.899585	−	0.436746i	$-0.143869\pi$
$684$	504.881	+	399.096i	0.738130	+	0.583474i
$685$	544.830			0.795372
$686$	−325.356	−	671.917i	−0.474280	−	0.979471i
$687$			678.838i			0.988119i
$688$	169.591	−	40.2427i	0.246499	−	0.0584923i
$689$	−782.561			−1.13579
$690$	−202.703	+	98.1529i	−0.293772	+	0.142251i
$691$			138.107i			0.199865i	0.994994	+	0.0999323i	$0.0318626\pi$
$691$			138.107i			0.199865i	−0.994994	+	0.0999323i	$0.968137\pi$
$692$	550.007	−	695.792i	0.794807	−	1.00548i
$693$		0			0
$694$	330.180	+	681.879i	0.475764	+	0.982534i
$695$		−	582.966i		−	0.838800i
$696$	545.798	+	120.884i	0.784193	+	0.173683i
$697$	525.392			0.753791
$698$	−358.762	+	173.720i	−0.513986	+	0.248883i
$699$			686.778i			0.982514i
$700$	−521.853	−	412.513i	−0.745505	−	0.589304i
$701$	−192.374			−0.274427			−0.137214	−	0.990541i	$-0.543815\pi$
$701$	−192.374			−0.274427			−0.137214	+	0.990541i	$0.543815\pi$
$702$	−114.115	−	235.667i	−0.162557	−	0.335708i
$703$			1029.61i			1.46459i
$704$		0			0
$705$	624.283			0.885508
$706$	−17.7086	+	8.57489i	−0.0250831	+	0.0121457i
$707$			749.798i			1.06054i
$708$	165.220	−	209.013i	0.233362	−	0.295217i
$709$	622.551			0.878069			0.439035	−	0.898470i	$-0.355321\pi$
$709$	622.551			0.878069			0.439035	+	0.898470i	$0.355321\pi$
$710$	159.413	+	329.216i	0.224526	+	0.463685i
$711$			81.3526i			0.114420i
$712$	132.416	−	597.870i	0.185978	−	0.839706i
$713$	−209.700			−0.294110
$714$	−764.911	+	370.386i	−1.07130	+	0.518747i
$715$		0			0
$716$	−583.101	−	460.927i	−0.814387	−	0.643753i
$717$	489.935			0.683313
$718$	−90.9801	−	187.890i	−0.126713	−	0.261685i
$719$			1004.18i			1.39664i	0.715788	+	0.698318i	$0.246068\pi$
$719$			1004.18i			1.39664i	−0.715788	+	0.698318i	$0.753932\pi$
$720$	−176.340	−	743.134i	−0.244917	−	1.03213i
$721$	153.577			0.213006
$722$	−447.217	+	216.552i	−0.619414	+	0.299933i
$723$		−	676.856i		−	0.936178i
$724$	551.453	−	697.621i	0.761675	−	0.963565i
$725$	508.174			0.700930
$726$		0			0
$727$			454.468i			0.625128i	0.949897	+	0.312564i	$0.101188\pi$
$727$			454.468i			0.625128i	−0.949897	+	0.312564i	$0.898812\pi$
$728$	606.997	+	134.438i	0.833788	+	0.184667i
$729$	286.636			0.393190
$730$	893.278	−	432.544i	1.22367	−	0.592526i
$731$		−	202.430i		−	0.276922i
$732$	−219.954	−	173.868i	−0.300483	−	0.237525i
$733$	929.155			1.26761			0.633803	−	0.773495i	$-0.281493\pi$
$733$	929.155			1.26761			0.633803	+	0.773495i	$0.281493\pi$
$734$	−80.6011	−	166.455i	−0.109811	−	0.226778i
$735$		−	441.437i		−	0.600595i
$736$	−96.8043	+	78.9128i	−0.131528	+	0.107218i
$737$		0			0
$738$	331.700	−	160.616i	0.449459	−	0.217637i
$739$			953.768i			1.29062i	0.763921	+	0.645310i	$0.223272\pi$
$739$			953.768i			1.29062i	−0.763921	+	0.645310i	$0.776728\pi$
$740$	757.740	−	958.587i	1.02397	−	1.29539i
$741$	−1301.83			−1.75686
$742$	−295.793	−	610.863i	−0.398643	−	0.823266i
$743$			610.718i			0.821962i	0.911644	+	0.410981i	$0.134814\pi$
$743$			610.718i			0.821962i	−0.911644	+	0.410981i	$0.865186\pi$
$744$	366.138	−	1653.14i	0.492121	−	2.22196i
$745$	−1258.53			−1.68930
$746$	379.474	−	183.749i	0.508679	−	0.246313i
$747$		−	242.515i		−	0.324652i
$748$		0			0
$749$	536.547			0.716351
$750$	−91.7182	−	189.414i	−0.122291	−	0.252552i
$751$			737.978i			0.982660i	0.870974	+	0.491330i	$0.163489\pi$
$751$			737.978i			0.982660i	−0.870974	+	0.491330i	$0.836511\pi$
$752$	336.841	−	79.9298i	0.447927	−	0.106290i
$753$	16.7687			0.0222692
$754$	−427.467	+	206.988i	−0.566932	+	0.274520i
$755$			1489.30i			1.97259i
$756$	140.827	−	178.155i	0.186279	−	0.235654i
$757$	314.110			0.414940			0.207470	−	0.978241i	$-0.433477\pi$
$757$	314.110			0.414940			0.207470	+	0.978241i	$0.433477\pi$
$758$	−413.381	−	853.702i	−0.545357	−	1.12626i
$759$		0			0
$760$	1412.31	+	312.799i	1.85831	+	0.411578i
$761$	582.044			0.764841			0.382421	−	0.923988i	$-0.375090\pi$
$761$	582.044			0.764841			0.382421	+	0.923988i	$0.375090\pi$
$762$	455.826	−	220.721i	0.598197	−	0.289660i
$763$		−	129.011i		−	0.169084i
$764$	−464.155	−	366.903i	−0.607532	−	0.480240i
$765$	−887.031			−1.15952
$766$	−307.021	−	634.050i	−0.400810	−	0.827742i
$767$			226.356i			0.295119i
$768$	−453.077	−	900.925i	−0.589943	−	1.17308i
$769$	940.119			1.22252			0.611260	−	0.791429i	$-0.290663\pi$
$769$	940.119			1.22252			0.611260	+	0.791429i	$0.290663\pi$
$770$		0			0
$771$			1633.16i			2.11824i
$772$	110.227	−	139.444i	0.142781	−	0.180627i
$773$	189.525			0.245181			0.122591	−	0.992457i	$-0.460880\pi$
$773$	189.525			0.245181			0.122591	+	0.992457i	$0.460880\pi$
$774$	−61.8844	−	127.802i	−0.0799540	−	0.165119i
$775$		−	1539.18i		−	1.98604i
$776$	−225.741	+	1019.24i	−0.290904	+	1.31345i
$777$	−953.739			−1.22746
$778$	−329.962	+	159.774i	−0.424115	+	0.205365i
$779$			697.997i			0.896017i
$780$	1212.03	+	958.083i	1.55389	+	1.22831i
$781$		0			0
$782$	63.2148	+	130.549i	0.0808373	+	0.166943i
$783$			173.485i			0.221564i
$784$	−56.5192	−	238.184i	−0.0720909	−	0.303806i
$785$	−541.477			−0.689780
$786$	−1204.88	+	583.430i	−1.53293	+	0.742278i
$787$		−	1475.76i		−	1.87517i	−0.347757	−	0.937585i	$-0.613057\pi$
$787$		−	1475.76i		−	1.87517i	0.347757	−	0.937585i	$-0.386943\pi$
$788$	−151.901	+	192.163i	−0.192767	+	0.243862i
$789$	937.547			1.18827
$790$	79.6908	+	164.575i	0.100874	+	0.208323i
$791$		−	411.811i		−	0.520621i
$792$		0			0
$793$	238.204			0.300384
$794$	−1154.26	+	558.916i	−1.45373	+	0.703925i
$795$		−	1686.63i		−	2.12155i
$796$	−917.007	−	724.872i	−1.15202	−	0.910644i
$797$	275.208			0.345305			0.172653	−	0.984983i	$-0.444766\pi$
$797$	275.208			0.345305			0.172653	+	0.984983i	$0.444766\pi$
$798$	−492.067	−	1016.20i	−0.616625	−	1.27344i
$799$		−	402.066i		−	0.503211i
$800$	−579.213	−	710.535i	−0.724017	−	0.888169i
$801$	−498.867			−0.622806
$802$	888.156	−	430.064i	1.10743	−	0.536239i
$803$		0			0
$804$	−808.681	+	1023.03i	−1.00582	+	1.27243i
$805$	165.950			0.206149
$806$	626.937	+	1294.73i	0.777837	+	1.60637i
$807$		−	1939.54i		−	2.40339i
$808$	−223.437	+	1008.83i	−0.276531	+	1.24856i
$809$	210.974			0.260783			0.130392	−	0.991463i	$-0.458376\pi$
$809$	210.974			0.260783			0.130392	+	0.991463i	$0.458376\pi$
$810$	1281.27	−	620.419i	1.58182	−	0.765949i
$811$		−	1139.50i		−	1.40506i	−0.711655	−	0.702529i	$-0.752054\pi$
$811$		−	1139.50i		−	1.40506i	0.711655	−	0.702529i	$-0.247946\pi$
$812$	−323.148	−	255.441i	−0.397966	−	0.314582i
$813$	−865.872			−1.06503
$814$		0			0
$815$			2261.46i			2.77480i
$816$	−1139.54	+	270.404i	−1.39650	+	0.331378i
$817$	268.934			0.329172
$818$	−461.253	+	223.348i	−0.563879	+	0.273042i
$819$		−	506.483i		−	0.618416i
$820$	513.691	−	649.850i	0.626452	−	0.792500i
$821$	−583.985			−0.711310			−0.355655	−	0.934617i	$-0.615742\pi$
$821$	−583.985			−0.711310			−0.355655	+	0.934617i	$0.615742\pi$
$822$	−255.405	−	527.456i	−0.310712	−	0.641674i
$823$			184.871i			0.224631i	0.993673	+	0.112315i	$0.0358267\pi$
$823$			184.871i			0.224631i	−0.993673	+	0.112315i	$0.964173\pi$
$824$	206.634	+	45.7654i	0.250770	+	0.0555405i
$825$		0			0
$826$	−176.693	+	85.5582i	−0.213914	+	0.103581i
$827$			1127.50i			1.36336i	0.731652	+	0.681678i	$0.238749\pi$
$827$			1127.50i			1.36336i	−0.731652	+	0.681678i	$0.761251\pi$
$828$	79.8198	+	63.0957i	0.0964008	+	0.0762025i
$829$	−708.255			−0.854349			−0.427174	−	0.904169i	$-0.640491\pi$
$829$	−708.255			−0.854349			−0.427174	+	0.904169i	$0.640491\pi$
$830$	−237.561	−	490.605i	−0.286218	−	0.591091i
$831$			489.223i			0.588716i
$832$	776.638	+	361.765i	0.933459	+	0.434814i
$833$	−284.305			−0.341303
$834$	−564.376	+	273.283i	−0.676710	+	0.327677i
$835$			1530.82i			1.83332i
$836$		0			0
$837$	525.459			0.627789
$838$	556.173	+	1148.59i	0.663690	+	1.37064i
$839$			396.430i			0.472503i	0.971692	+	0.236252i	$0.0759189\pi$
$839$			396.430i			0.472503i	−0.971692	+	0.236252i	$0.924081\pi$
$840$	−289.750	+	1308.24i	−0.344940	+	1.55743i
$841$	−526.323			−0.625830
$842$	1150.14	−	556.920i	1.36596	−	0.661425i
$843$			1218.89i			1.44590i
$844$	411.604	+	325.363i	0.487683	+	0.385501i
$845$	−74.7750			−0.0884912
$846$	−122.914	−	253.840i	−0.145289	−	0.300047i
$847$		0			0
$848$	−215.947	−	910.046i	−0.254654	−	1.07317i
$849$	1241.03			1.46176
$850$	−958.222	+	463.991i	−1.12732	+	0.545872i
$851$			162.777i			0.191278i
$852$	243.988	−	308.660i	0.286371	−	0.362277i
$853$	−467.329			−0.547866			−0.273933	−	0.961749i	$-0.588325\pi$
$853$	−467.329			−0.547866			−0.273933	+	0.961749i	$0.588325\pi$
$854$	90.0366	+	185.941i	0.105429	+	0.217730i
$855$		−	1178.44i		−	1.37830i
$856$	721.910	+	159.889i	0.843352	+	0.186786i
$857$	−1539.00			−1.79580			−0.897902	−	0.440195i	$-0.854909\pi$
$857$	−1539.00			−1.79580			−0.897902	+	0.440195i	$0.854909\pi$
$858$		0			0
$859$		−	1510.20i		−	1.75809i	−0.476735	−	0.879047i	$-0.658180\pi$
$859$		−	1510.20i		−	1.75809i	0.476735	−	0.879047i	$-0.341820\pi$
$860$	−250.383	−	197.922i	−0.291143	−	0.230141i
$861$	−646.563			−0.750945
$862$	18.9462	+	39.1271i	0.0219793	+	0.0453911i
$863$		−	547.962i		−	0.634950i	−0.948267	−	0.317475i	$-0.897165\pi$
$863$		−	547.962i		−	0.634950i	0.948267	−	0.317475i	$-0.102835\pi$
$864$	242.569	−	197.737i	0.280751	−	0.228862i
$865$	−1624.05			−1.87751
$866$	996.296	−	482.427i	1.15046	−	0.557075i
$867$			221.767i			0.255787i
$868$	−773.692	+	978.767i	−0.891350	+	1.12761i
$869$		0			0
$870$	−446.116	−	921.306i	−0.512776	−	1.05897i
$871$		−	1107.92i		−	1.27200i
$872$	38.4448	−	173.581i	0.0440880	−	0.199061i
$873$	850.460			0.974181
$874$	−173.438	+	83.9825i	−0.198442	+	0.0960898i
$875$			155.071i			0.177224i
$876$	−837.501	−	662.024i	−0.956051	−	0.755736i
$877$	1265.34			1.44281			0.721404	−	0.692515i	$-0.243497\pi$
$877$	1265.34			1.44281			0.721404	+	0.692515i	$0.243497\pi$
$878$	−665.685	−	1374.76i	−0.758184	−	1.56578i
$879$		−	208.641i		−	0.237361i
$880$		0			0
$881$	1328.16			1.50756			0.753781	−	0.657126i	$-0.228228\pi$
$881$	1328.16			1.50756			0.753781	+	0.657126i	$0.228228\pi$
$882$	−179.493	+	86.9141i	−0.203507	+	0.0985421i
$883$		−	383.184i		−	0.433957i	−0.976176	−	0.216978i	$-0.930380\pi$
$883$		−	383.184i		−	0.433957i	0.976176	−	0.216978i	$-0.0696201\pi$
$884$	617.047	−	780.602i	0.698017	−	0.883034i
$885$	−487.859			−0.551253
$886$	20.5392	+	42.4171i	0.0231820	+	0.0478748i
$887$		−	74.5488i		−	0.0840460i	−0.999117	−	0.0420230i	$-0.986620\pi$
$887$		−	74.5488i		−	0.0840460i	0.999117	−	0.0420230i	$-0.0133803\pi$
$888$	−1283.23	−	284.210i	−1.44508	−	0.320057i
$889$	−373.179			−0.419774
$890$	−1009.20	+	488.677i	−1.13394	+	0.549075i
$891$		0			0
$892$	−133.936	−	105.873i	−0.150152	−	0.118692i
$893$	534.155			0.598158
$894$	589.974	+	1218.40i	0.659926	+	1.36286i
$895$			1361.02i			1.52069i
$896$	11.1615	+	742.979i	0.0124570	+	0.829218i
$897$	−205.815			−0.229448
$898$	−697.354	+	337.673i	−0.776563	+	0.376028i
$899$		−	953.111i		−	1.06019i
$900$	−463.117	+	585.871i	−0.514575	+	0.650968i
$901$	−1086.26			−1.20562
$902$		0			0
$903$			249.117i			0.275877i
$904$	122.718	−	554.081i	0.135750	−	0.612922i
$905$	−1628.32			−1.79925
$906$	1441.81	−	698.155i	1.59140	−	0.770591i
$907$			32.7978i			0.0361607i	0.999837	+	0.0180804i	$0.00575547\pi$
$907$			32.7978i			0.0361607i	−0.999837	+	0.0180804i	$0.994245\pi$
$908$	−1202.71	−	950.716i	−1.32457	−	1.04704i
$909$	841.779			0.926049
$910$	−496.137	−	1024.61i	−0.545206	−	1.12594i
$911$		−	59.0963i		−	0.0648697i	−0.999474	−	0.0324349i	$-0.989674\pi$
$911$		−	59.0963i		−	0.0648697i	0.999474	−	0.0324349i	$-0.0103261\pi$
$912$	−359.239	−	1513.91i	−0.393903	−	1.65999i
$913$		0			0
$914$	152.849	−	74.0125i	0.167231	−	0.0809765i
$915$			513.394i			0.561087i
$916$	427.464	−	540.767i	0.466663	−	0.590358i
$917$	986.423			1.07571
$918$	−158.401	−	327.126i	−0.172550	−	0.356346i
$919$			544.818i			0.592837i	0.955058	+	0.296419i	$0.0957924\pi$
$919$			544.818i			0.592837i	−0.955058	+	0.296419i	$0.904208\pi$
$920$	223.281	+	49.4524i	0.242697	+	0.0537526i
$921$	−1935.74			−2.10178
$922$	−1190.09	+	576.266i	−1.29077	+	0.625018i
$923$			334.271i			0.362157i
$924$		0			0
$925$	−1194.77			−1.29165
$926$	148.780	+	307.256i	0.160669	+	0.331810i
$927$		−	172.417i		−	0.185995i
$928$	−358.667	−	439.986i	−0.386495	−	0.474123i
$929$	−1027.49			−1.10601			−0.553006	−	0.833177i	$-0.686520\pi$
$929$	−1027.49			−1.10601			−0.553006	+	0.833177i	$0.686520\pi$
$930$	−2790.50	+	1351.22i	−3.00053	+	1.45292i
$931$		−	377.707i		−	0.405700i
$932$	432.463	−	547.092i	0.464017	−	0.587009i
$933$	21.4234			0.0229619
$934$	622.559	+	1285.69i	0.666552	+	1.37654i
$935$		0			0
$936$	150.930	−	681.460i	0.161250	−	0.728056i
$937$	−318.343			−0.339747			−0.169873	−	0.985466i	$-0.554336\pi$
$937$	−318.343			−0.339747			−0.169873	+	0.985466i	$0.554336\pi$
$938$	864.834	−	418.771i	0.921997	−	0.446450i
$939$		−	1300.39i		−	1.38487i
$940$	−497.309	−	393.111i	−0.529052	−	0.418203i
$941$	−112.117			−0.119147			−0.0595735	−	0.998224i	$-0.518974\pi$
$941$	−112.117			−0.119147			−0.0595735	+	0.998224i	$0.518974\pi$
$942$	253.834	+	524.210i	0.269462	+	0.556487i
$943$			110.351i			0.117021i
$944$	−263.231	+	62.4628i	−0.278847	+	0.0661682i
$945$	−415.831			−0.440033
$946$		0			0
$947$		−	1761.09i		−	1.85965i	−0.368005	−	0.929824i	$-0.619959\pi$
$947$		−	1761.09i		−	1.85965i	0.368005	−	0.929824i	$-0.380041\pi$
$948$	121.970	−	154.299i	0.128660	−	0.162763i
$949$	906.993			0.955735
$950$	−616.425	−	1273.02i	−0.648868	−	1.34002i
$951$		−	679.303i		−	0.714304i
$952$	842.565	+	186.612i	0.885048	+	0.196021i
$953$	1392.57			1.46125			0.730625	−	0.682779i	$-0.239229\pi$
$953$	1392.57			1.46125			0.730625	+	0.682779i	$0.239229\pi$
$954$	−685.800	+	332.079i	−0.718868	+	0.348091i
$955$			1083.38i			1.13443i
$956$	−390.286	−	308.512i	−0.408249	−	0.322711i
$957$		0			0
$958$	698.214	+	1441.93i	0.728824	+	1.50515i
$959$			431.821i			0.450283i
$960$	−779.702	+	1673.86i	−0.812189	+	1.74361i
$961$	−1925.83			−2.00398
$962$	1005.02	−	486.652i	1.04472	−	0.505875i
$963$		−	602.367i		−	0.625511i
$964$	−426.216	+	539.189i	−0.442133	+	0.559325i
$965$	−325.477			−0.337282
$966$	−77.7940	−	160.658i	−0.0805321	−	0.166313i
$967$		−	373.578i		−	0.386326i	−0.981167	−	0.193163i	$-0.938125\pi$
$967$		−	373.578i		−	0.386326i	0.981167	−	0.193163i	$-0.0618747\pi$
$968$		0			0
$969$	−1807.06			−1.86487
$970$	1720.47	−	833.088i	1.77368	−	0.858854i
$971$			516.552i			0.531979i	0.963976	+	0.265990i	$0.0856987\pi$
$971$			516.552i			0.531979i	−0.963976	+	0.265990i	$0.914301\pi$
$972$	−925.068	−	731.244i	−0.951716	−	0.752309i
$973$	462.047			0.474868
$974$	101.482	+	209.577i	0.104191	+	0.215172i
$975$		−	1510.66i		−	1.54940i
$976$	65.7322	+	277.009i	0.0673486	+	0.283821i
$977$	295.602			0.302560			0.151280	−	0.988491i	$-0.451660\pi$
$977$	295.602			0.302560			0.151280	+	0.988491i	$0.451660\pi$
$978$	2189.35	−	1060.13i	2.23859	−	1.08397i
$979$		0			0
$980$	−277.973	+	351.653i	−0.283646	+	0.358829i
$981$	−144.837			−0.147643
$982$	−573.829	−	1185.06i	−0.584347	−	1.20678i
$983$			1511.98i			1.53813i	0.639169	+	0.769066i	$0.279278\pi$
$983$			1511.98i			1.53813i	−0.639169	+	0.769066i	$0.720722\pi$
$984$	−869.935	−	192.673i	−0.884080	−	0.195806i
$985$	448.529			0.455360
$986$	−593.361	+	287.318i	−0.601786	+	0.291398i
$987$			494.794i			0.501311i
$988$	1037.05	+	819.763i	1.04965	+	0.829720i
$989$	42.5174			0.0429903
$990$		0			0
$991$		−	462.791i		−	0.466994i	−0.972358	−	0.233497i	$-0.924983\pi$
$991$		−	462.791i		−	0.466994i	0.972358	−	0.233497i	$-0.0750168\pi$
$992$	−1332.65	+	1086.35i	−1.34340	+	1.09511i
$993$	645.450			0.650000
$994$	−260.930	+	126.348i	−0.262505	+	0.127111i
$995$			2140.39i			2.15114i
$996$	−363.596	+	459.971i	−0.365057	+	0.461819i
$997$	361.841			0.362930			0.181465	−	0.983397i	$-0.441916\pi$
$997$	361.841			0.362930			0.181465	+	0.983397i	$0.441916\pi$
$998$	377.870	+	780.366i	0.378627	+	0.781930i
$999$		−	407.881i		−	0.408290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.3.b.h.243.9		10
4.3	odd	2	inner	484.3.b.h.243.10		10
11.10	odd	2		44.3.b.a.23.2	yes	10
33.32	even	2		396.3.g.c.199.9		10
44.43	even	2		44.3.b.a.23.1	✓	10
88.21	odd	2		704.3.d.d.639.2		10
88.43	even	2		704.3.d.d.639.9		10
132.131	odd	2		396.3.g.c.199.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.b.a.23.1	✓	10	44.43	even	2
44.3.b.a.23.2	yes	10	11.10	odd	2
396.3.g.c.199.9		10	33.32	even	2
396.3.g.c.199.10		10	132.131	odd	2
484.3.b.h.243.9		10	1.1	even	1	trivial
484.3.b.h.243.10		10	4.3	odd	2	inner
704.3.d.d.639.2		10	88.21	odd	2
704.3.d.d.639.9		10	88.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	484.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80007 - 0.871632i) q^{2} +3.93920i q^{3} +(2.48051 - 3.13800i) q^{4} -7.32441 q^{5} +(3.43354 + 7.09085i) q^{6} -5.80518i q^{7} +(1.72992 - 7.81072i) q^{8} -6.51732 q^{9} +(-13.1845 + 6.38420i) q^{10} +(12.3612 + 9.77125i) q^{12} -13.3869 q^{13} +(-5.05998 - 10.4497i) q^{14} -28.8524i q^{15} +(-3.69410 - 15.5677i) q^{16} -18.5822 q^{17} +(-11.7316 + 5.68071i) q^{18} -24.6869i q^{19} +(-18.1683 + 22.9840i) q^{20} +22.8678 q^{21} -3.90291i q^{23} +(30.7680 + 6.81451i) q^{24} +28.6470 q^{25} +(-24.0974 + 11.6685i) q^{26} +9.77977i q^{27} +(-18.2167 - 14.3998i) q^{28} +17.7391 q^{29} +(-25.1486 - 51.9363i) q^{30} -53.7292i q^{31} +(-20.2190 - 24.8031i) q^{32} +(-33.4493 + 16.1968i) q^{34} +42.5195i q^{35} +(-16.1663 + 20.4514i) q^{36} -41.7067 q^{37} +(-21.5179 - 44.4382i) q^{38} -52.7337i q^{39} +(-12.6707 + 57.2090i) q^{40} -28.2740 q^{41} +(41.1637 - 19.9323i) q^{42} +10.8938i q^{43} +47.7356 q^{45} +(-3.40190 - 7.02552i) q^{46} +21.6372i q^{47} +(61.3244 - 14.5518i) q^{48} +15.2999 q^{49} +(51.5667 - 24.9697i) q^{50} -73.1990i q^{51} +(-33.2064 + 42.0081i) q^{52} +58.4573 q^{53} +(8.52436 + 17.6043i) q^{54} +(-45.3427 - 10.0425i) q^{56} +97.2468 q^{57} +(31.9317 - 15.4620i) q^{58} -16.9088i q^{59} +(-90.5387 - 71.5687i) q^{60} -17.7938 q^{61} +(-46.8321 - 96.7164i) q^{62} +37.8342i q^{63} +(-58.0148 - 27.0238i) q^{64} +98.0512 q^{65} +82.7612i q^{67} +(-46.0934 + 58.3109i) q^{68} +15.3744 q^{69} +(37.0614 + 76.5382i) q^{70} -24.9700i q^{71} +(-11.2744 + 50.9050i) q^{72} -67.7523 q^{73} +(-75.0750 + 36.3529i) q^{74} +112.847i q^{75} +(-77.4676 - 61.2363i) q^{76} +(-45.9644 - 94.9244i) q^{78} -12.4825i q^{79} +(27.0571 + 114.024i) q^{80} -97.1804 q^{81} +(-50.8952 + 24.6445i) q^{82} +37.2108i q^{83} +(56.7239 - 71.7591i) q^{84} +136.104 q^{85} +(9.49537 + 19.6096i) q^{86} +69.8781i q^{87} +76.5448 q^{89} +(85.9274 - 41.6079i) q^{90} +77.7134i q^{91} +(-12.2473 - 9.68123i) q^{92} +211.650 q^{93} +(18.8597 + 38.9485i) q^{94} +180.817i q^{95} +(97.7044 - 79.6466i) q^{96} -130.492 q^{97} +(27.5409 - 13.3359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 4 q^{5} - 6 q^{6} + 12 q^{8} - 30 q^{9} + 2 q^{10} + 40 q^{12} + 4 q^{13} - 4 q^{14} - 40 q^{16} - 20 q^{17} + 22 q^{18} - 64 q^{20} - 32 q^{21} - 36 q^{24} - 10 q^{25} - 36 q^{26} - 40 q^{28}+ \cdots + 568 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 - 4 * q^5 - 6 * q^6 + 12 * q^8 - 30 * q^9 + 2 * q^10 + 40 * q^12 + 4 * q^13 - 4 * q^14 - 40 * q^16 - 20 * q^17 + 22 * q^18 - 64 * q^20 - 32 * q^21 - 36 * q^24 - 10 * q^25 - 36 * q^26 - 40 * q^28 - 28 * q^29 - 126 * q^30 - 80 * q^32 - 88 * q^34 - 4 * q^36 - 100 * q^37 + 40 * q^38 + 12 * q^40 - 100 * q^41 + 260 * q^42 - 44 * q^45 + 130 * q^46 + 24 * q^48 - 22 * q^49 + 198 * q^50 + 176 * q^52 + 100 * q^53 + 350 * q^54 + 136 * q^56 + 112 * q^57 + 116 * q^58 - 136 * q^60 + 52 * q^61 - 134 * q^62 - 368 * q^64 + 184 * q^65 - 176 * q^68 + 184 * q^69 - 36 * q^70 - 360 * q^72 - 84 * q^73 - 362 * q^74 - 504 * q^76 - 232 * q^78 - 120 * q^80 + 330 * q^81 + 220 * q^82 + 40 * q^84 + 216 * q^85 + 556 * q^86 + 28 * q^89 + 520 * q^90 + 152 * q^92 - 72 * q^93 + 272 * q^94 + 704 * q^96 - 180 * q^97 + 568 * q^98

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