LMFDB - Embedded newform 465.2.c.a.94.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(94,465)] 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("465.94"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.1016580161536.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 12x^{8} + 48x^{6} + 72x^{4} + 36x^{2} + 4 $ x^10 + 12x^8 + 48x^6 + 72x^4 + 36x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			94.7
Root			$-0.815403i$ of defining polynomial
Character	$\chi$	$=$	465.94
Dual form			465.2.c.a.94.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.697747i q^{2} -1.00000i q^{3} +1.51315 q^{4} +(0.815403 - 2.08209i) q^{5} +0.697747 q^{6} -0.302253i q^{7} +2.45129i q^{8} -1.00000 q^{9} +(1.45277 + 0.568945i) q^{10} +2.71947 q^{11} -1.51315i q^{12} +3.96444i q^{13} +0.210896 q^{14} +(-2.08209 - 0.815403i) q^{15} +1.31592 q^{16} -6.05458i q^{17} -0.697747i q^{18} -0.452774 q^{19} +(1.23383 - 3.15052i) q^{20} -0.302253 q^{21} +1.89750i q^{22} -4.37050i q^{23} +2.45129 q^{24} +(-3.67024 - 3.39549i) q^{25} -2.76617 q^{26} +1.00000i q^{27} -0.457355i q^{28} +3.48564 q^{29} +(0.568945 - 1.45277i) q^{30} -1.00000 q^{31} +5.82076i q^{32} -2.71947i q^{33} +4.22456 q^{34} +(-0.629320 - 0.246458i) q^{35} -1.51315 q^{36} +1.56089i q^{37} -0.315922i q^{38} +3.96444 q^{39} +(5.10381 + 1.99879i) q^{40} -9.00441 q^{41} -0.210896i q^{42} +8.93693i q^{43} +4.11496 q^{44} +(-0.815403 + 2.08209i) q^{45} +3.04950 q^{46} -6.64299i q^{47} -1.31592i q^{48} +6.90864 q^{49} +(2.36919 - 2.56089i) q^{50} -6.05458 q^{51} +5.99879i q^{52} +8.49423i q^{53} -0.697747 q^{54} +(2.21746 - 5.66218i) q^{55} +0.740910 q^{56} +0.452774i q^{57} +2.43209i q^{58} +3.25033 q^{59} +(-3.15052 - 1.23383i) q^{60} -5.35535 q^{61} -0.697747i q^{62} +0.302253i q^{63} -1.42957 q^{64} +(8.25433 + 3.23262i) q^{65} +1.89750 q^{66} +4.26548i q^{67} -9.16149i q^{68} -4.37050 q^{69} +(0.171966 - 0.439106i) q^{70} +8.83190 q^{71} -2.45129i q^{72} +10.4968i q^{73} -1.08911 q^{74} +(-3.39549 + 3.67024i) q^{75} -0.685115 q^{76} -0.821968i q^{77} +2.76617i q^{78} -14.6348 q^{79} +(1.07301 - 2.73987i) q^{80} +1.00000 q^{81} -6.28279i q^{82} +10.2063i q^{83} -0.457355 q^{84} +(-12.6062 - 4.93693i) q^{85} -6.23571 q^{86} -3.48564i q^{87} +6.66619i q^{88} -15.6279 q^{89} +(-1.45277 - 0.568945i) q^{90} +1.19827 q^{91} -6.61323i q^{92} +1.00000i q^{93} +4.63512 q^{94} +(-0.369194 + 0.942719i) q^{95} +5.82076 q^{96} +8.85267i q^{97} +4.82048i q^{98} -2.71947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 6 q^{4} - 6 q^{6} - 10 q^{9} + 2 q^{10} - 32 q^{14} + 2 q^{15} + 6 q^{16} + 8 q^{19} + 28 q^{20} - 16 q^{21} + 18 q^{24} - 2 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} - 10 q^{31} - 12 q^{34} + 4 q^{35}+ \cdots - 2 q^{96}+O(q^{100}) $ 10 * q - 6 * q^4 - 6 * q^6 - 10 * q^9 + 2 * q^10 - 32 * q^14 + 2 * q^15 + 6 * q^16 + 8 * q^19 + 28 * q^20 - 16 * q^21 + 18 * q^24 - 2 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 - 10 * q^31 - 12 * q^34 + 4 * q^35 + 6 * q^36 + 12 * q^39 + 14 * q^40 - 12 * q^44 - 32 * q^46 + 22 * q^49 + 40 * q^50 - 16 * q^51 + 6 * q^54 + 36 * q^56 - 20 * q^59 - 6 * q^60 - 28 * q^61 - 22 * q^64 + 20 * q^65 - 12 * q^66 + 8 * q^69 + 32 * q^70 + 12 * q^71 + 8 * q^74 - 8 * q^75 - 16 * q^76 + 48 * q^79 - 20 * q^80 + 10 * q^81 + 36 * q^84 - 4 * q^85 + 8 * q^86 - 20 * q^89 - 2 * q^90 - 24 * q^94 - 20 * q^95 - 2 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			0.697747i			0.493381i	0.969094	+	0.246691i	$0.0793432\pi$
$2$			0.697747i			0.493381i	−0.969094	+	0.246691i	$0.920657\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.51315			0.756575
$5$	0.815403	−	2.08209i	0.364659	−	0.931141i
$5$	0.815403	−	2.08209i	0.364659	−	0.931141i
$6$	0.697747			0.284854
$7$		−	0.302253i		−	0.114241i	−0.998367	−	0.0571205i	$-0.981808\pi$
$7$		−	0.302253i		−	0.114241i	0.998367	−	0.0571205i	$-0.0181919\pi$
$8$			2.45129i			0.866661i
$9$	−1.00000			−0.333333
$10$	1.45277	+	0.568945i	0.459408	+	0.179916i
$11$	2.71947			0.819950			0.409975	−	0.912097i	$-0.365537\pi$
$11$	2.71947			0.819950			0.409975	+	0.912097i	$0.365537\pi$
$12$		−	1.51315i		−	0.436809i
$13$			3.96444i			1.09954i	0.835317	+	0.549769i	$0.185284\pi$
$13$			3.96444i			1.09954i	−0.835317	+	0.549769i	$0.814716\pi$
$14$	0.210896			0.0563644
$15$	−2.08209	−	0.815403i	−0.537594	−	0.210536i
$16$	1.31592			0.328980
$17$		−	6.05458i		−	1.46845i	−0.678905	−	0.734226i	$-0.737545\pi$
$17$		−	6.05458i		−	1.46845i	0.678905	−	0.734226i	$-0.262455\pi$
$18$		−	0.697747i		−	0.164460i
$19$	−0.452774			−0.103874			−0.0519368	−	0.998650i	$-0.516539\pi$
$19$	−0.452774			−0.103874			−0.0519368	+	0.998650i	$0.516539\pi$
$20$	1.23383	−	3.15052i	0.275892	−	0.704478i
$21$	−0.302253			−0.0659571
$22$			1.89750i			0.404548i
$23$		−	4.37050i		−	0.911313i	−0.890156	−	0.455657i	$-0.849404\pi$
$23$		−	4.37050i		−	0.911313i	0.890156	−	0.455657i	$-0.150596\pi$
$24$	2.45129			0.500367
$25$	−3.67024	−	3.39549i	−0.734047	−	0.679099i
$26$	−2.76617			−0.542491
$27$			1.00000i			0.192450i
$28$		−	0.457355i		−	0.0864319i
$29$	3.48564			0.647267			0.323633	−	0.946183i	$-0.395096\pi$
$29$	3.48564			0.647267			0.323633	+	0.946183i	$0.395096\pi$
$30$	0.568945	−	1.45277i	0.103875	−	0.265239i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$			5.82076i			1.02897i
$33$		−	2.71947i		−	0.473398i
$34$	4.22456			0.724507
$35$	−0.629320	−	0.246458i	−0.106375	−	0.0416591i
$36$	−1.51315			−0.252192
$37$			1.56089i			0.256609i	0.991735	+	0.128305i	$0.0409535\pi$
$37$			1.56089i			0.256609i	−0.991735	+	0.128305i	$0.959046\pi$
$38$		−	0.315922i		−	0.0512493i
$39$	3.96444			0.634818
$40$	5.10381	+	1.99879i	0.806984	+	0.316036i
$41$	−9.00441			−1.40625			−0.703126	−	0.711065i	$-0.748213\pi$
$41$	−9.00441			−1.40625			−0.703126	+	0.711065i	$0.748213\pi$
$42$		−	0.210896i		−	0.0325420i
$43$			8.93693i			1.36287i	0.731879	+	0.681434i	$0.238643\pi$
$43$			8.93693i			1.36287i	−0.731879	+	0.681434i	$0.761357\pi$
$44$	4.11496			0.620353
$45$	−0.815403	+	2.08209i	−0.121553	+	0.310380i
$46$	3.04950			0.449625
$47$		−	6.64299i		−	0.968979i	−0.874797	−	0.484490i	$-0.839005\pi$
$47$		−	6.64299i		−	0.968979i	0.874797	−	0.484490i	$-0.160995\pi$
$48$		−	1.31592i		−	0.189937i
$49$	6.90864			0.986949
$50$	2.36919	−	2.56089i	0.335055	−	0.362165i
$51$	−6.05458			−0.847811
$52$			5.99879i			0.831882i
$53$			8.49423i			1.16677i	0.812195	+	0.583386i	$0.198272\pi$
$53$			8.49423i			1.16677i	−0.812195	+	0.583386i	$0.801728\pi$
$54$	−0.697747			−0.0949513
$55$	2.21746	−	5.66218i	0.299002	−	0.763489i
$56$	0.740910			0.0990083
$57$			0.452774i			0.0599714i
$58$			2.43209i			0.319349i
$59$	3.25033			0.423156			0.211578	−	0.977361i	$-0.432140\pi$
$59$	3.25033			0.423156			0.211578	+	0.977361i	$0.432140\pi$
$60$	−3.15052	−	1.23383i	−0.406730	−	0.159286i
$61$	−5.35535			−0.685682			−0.342841	−	0.939393i	$-0.611389\pi$
$61$	−5.35535			−0.685682			−0.342841	+	0.939393i	$0.611389\pi$
$62$		−	0.697747i		−	0.0886139i
$63$			0.302253i			0.0380804i
$64$	−1.42957			−0.178696
$65$	8.25433	+	3.23262i	1.02382	+	0.400957i
$66$	1.89750			0.233566
$67$			4.26548i			0.521111i	0.965459	+	0.260556i	$0.0839057\pi$
$67$			4.26548i			0.521111i	−0.965459	+	0.260556i	$0.916094\pi$
$68$		−	9.16149i		−	1.11099i
$69$	−4.37050			−0.526147
$70$	0.171966	−	0.439106i	0.0205538	−	0.0524832i
$71$	8.83190			1.04815			0.524077	−	0.851671i	$-0.324410\pi$
$71$	8.83190			1.04815			0.524077	+	0.851671i	$0.324410\pi$
$72$		−	2.45129i		−	0.288887i
$73$			10.4968i			1.22855i	0.789091	+	0.614276i	$0.210552\pi$
$73$			10.4968i			1.22855i	−0.789091	+	0.614276i	$0.789448\pi$
$74$	−1.08911			−0.126606
$75$	−3.39549	+	3.67024i	−0.392078	+	0.423802i
$76$	−0.685115			−0.0785881
$77$		−	0.821968i		−	0.0936719i
$78$			2.76617i			0.313207i
$79$	−14.6348			−1.64654			−0.823270	−	0.567650i	$-0.807853\pi$
$79$	−14.6348			−1.64654			−0.823270	+	0.567650i	$0.807853\pi$
$80$	1.07301	−	2.73987i	0.119966	−	0.306327i
$81$	1.00000			0.111111
$82$		−	6.28279i		−	0.693818i
$83$			10.2063i			1.12029i	0.828395	+	0.560144i	$0.189254\pi$
$83$			10.2063i			1.12029i	−0.828395	+	0.560144i	$0.810746\pi$
$84$	−0.457355			−0.0499015
$85$	−12.6062	−	4.93693i	−1.36734	−	0.535485i
$86$	−6.23571			−0.672414
$87$		−	3.48564i		−	0.373700i
$88$			6.66619i			0.710619i
$89$	−15.6279			−1.65656			−0.828279	−	0.560316i	$-0.810680\pi$
$89$	−15.6279			−1.65656			−0.828279	+	0.560316i	$0.810680\pi$
$90$	−1.45277	−	0.568945i	−0.153136	−	0.0599720i
$91$	1.19827			0.125612
$92$		−	6.61323i		−	0.689477i
$93$			1.00000i			0.103695i
$94$	4.63512			0.478076
$95$	−0.369194	+	0.942719i	−0.0378785	+	0.0967209i
$96$	5.82076			0.594078
$97$			8.85267i			0.898853i	0.893317	+	0.449426i	$0.148372\pi$
$97$			8.85267i			0.898853i	−0.893317	+	0.449426i	$0.851628\pi$
$98$			4.82048i			0.486942i
$99$	−2.71947			−0.273317
$100$	−5.55362	−	5.13789i	−0.555362	−	0.513789i
$101$	−18.9217			−1.88278			−0.941390	−	0.337321i	$-0.890479\pi$
$101$	−18.9217			−1.88278			−0.941390	+	0.337321i	$0.890479\pi$
$102$		−	4.22456i		−	0.418294i
$103$		−	1.14577i		−	0.112896i	−0.998406	−	0.0564478i	$-0.982023\pi$
$103$		−	1.14577i		−	0.112896i	0.998406	−	0.0564478i	$-0.0179775\pi$
$104$	−9.71798			−0.952926
$105$	−0.246458	+	0.629320i	−0.0240519	+	0.0614154i
$106$	−5.92682			−0.575663
$107$		−	8.34317i		−	0.806565i	−0.915076	−	0.403282i	$-0.867869\pi$
$107$		−	8.34317i		−	0.806565i	0.915076	−	0.403282i	$-0.132131\pi$
$108$			1.51315i			0.145603i
$109$	15.8135			1.51466			0.757328	−	0.653034i	$-0.226504\pi$
$109$	15.8135			1.51466			0.757328	+	0.653034i	$0.226504\pi$
$110$	3.95077	+	1.54723i	0.376691	+	0.147522i
$111$	1.56089			0.148153
$112$		−	0.397742i		−	0.0375831i
$113$		−	3.55793i		−	0.334702i	−0.985897	−	0.167351i	$-0.946479\pi$
$113$		−	3.55793i		−	0.334702i	0.985897	−	0.167351i	$-0.0535213\pi$
$114$	−0.315922			−0.0295888
$115$	−9.09980	−	3.56372i	−0.848561	−	0.332319i
$116$	5.27429			0.489706
$117$		−	3.96444i		−	0.366512i
$118$			2.26790i			0.208777i
$119$	−1.83002			−0.167758
$120$	1.99879	−	5.10381i	0.182464	−	0.465912i
$121$	−3.60451			−0.327682
$122$		−	3.73668i		−	0.338303i
$123$			9.00441i			0.811900i
$124$	−1.51315			−0.135885
$125$	−10.0625	+	4.87308i	−0.900014	+	0.435862i
$126$	−0.210896			−0.0187881
$127$			5.58891i			0.495936i	0.968768	+	0.247968i	$0.0797628\pi$
$127$			5.58891i			0.495936i	−0.968768	+	0.247968i	$0.920237\pi$
$128$			10.6440i			0.940809i
$129$	8.93693			0.786853
$130$	−2.25555	+	5.75943i	−0.197824	+	0.505136i
$131$	14.5221			1.26880			0.634401	−	0.773004i	$-0.281247\pi$
$131$	14.5221			1.26880			0.634401	+	0.773004i	$0.281247\pi$
$132$		−	4.11496i		−	0.358161i
$133$			0.136853i			0.0118666i
$134$	−2.97622			−0.257107
$135$	2.08209	+	0.815403i	0.179198	+	0.0701787i
$136$	14.8415			1.27265
$137$			2.20929i			0.188752i	0.995537	+	0.0943761i	$0.0300856\pi$
$137$			2.20929i			0.188752i	−0.995537	+	0.0943761i	$0.969914\pi$
$138$		−	3.04950i		−	0.259591i
$139$	1.96283			0.166485			0.0832425	−	0.996529i	$-0.473472\pi$
$139$	1.96283			0.166485			0.0832425	+	0.996529i	$0.473472\pi$
$140$	−0.952256	−	0.372929i	−0.0804803	−	0.0315182i
$141$	−6.64299			−0.559441
$142$			6.16243i			0.517140i
$143$			10.7812i			0.901565i
$144$	−1.31592			−0.109660
$145$	2.84220	−	7.25743i	0.236032	−	0.602697i
$146$	−7.32407			−0.606145
$147$		−	6.90864i		−	0.569815i
$148$			2.36187i			0.194144i
$149$	−15.5134			−1.27091			−0.635455	−	0.772138i	$-0.719187\pi$
$149$	−15.5134			−1.27091			−0.635455	+	0.772138i	$0.719187\pi$
$150$	−2.56089	−	2.36919i	−0.209096	−	0.193444i
$151$	3.50914			0.285570			0.142785	−	0.989754i	$-0.454394\pi$
$151$	3.50914			0.285570			0.142785	+	0.989754i	$0.454394\pi$
$152$		−	1.10988i		−	0.0900232i
$153$			6.05458i			0.489484i
$154$	0.573525			0.0462160
$155$	−0.815403	+	2.08209i	−0.0654948	+	0.167238i
$156$	5.99879			0.480287
$157$		−	23.0764i		−	1.84170i	−0.389920	−	0.920849i	$-0.627497\pi$
$157$		−	23.0764i		−	1.84170i	0.389920	−	0.920849i	$-0.372503\pi$
$158$		−	10.2114i		−	0.812372i
$159$	8.49423			0.673636
$160$	12.1194	+	4.74626i	0.958120	+	0.375225i
$161$	−1.32100			−0.104109
$162$			0.697747i			0.0548201i
$163$		−	16.6343i		−	1.30290i	−0.758691	−	0.651450i	$-0.774161\pi$
$163$		−	16.6343i		−	1.30290i	0.758691	−	0.651450i	$-0.225839\pi$
$164$	−13.6250			−1.06393
$165$	−5.66218	−	2.21746i	−0.440800	−	0.172629i
$166$	−7.12142			−0.552730
$167$		−	5.65485i		−	0.437585i	−0.975771	−	0.218793i	$-0.929788\pi$
$167$		−	5.65485i		−	0.437585i	0.975771	−	0.218793i	$-0.0702118\pi$
$168$		−	0.740910i		−	0.0571625i
$169$	−2.71677			−0.208982
$170$	3.44472	−	8.79594i	0.264198	−	0.674618i
$171$	0.452774			0.0346245
$172$			13.5229i			1.03111i
$173$			14.1686i			1.07722i	0.842555	+	0.538610i	$0.181051\pi$
$173$			14.1686i			1.07722i	−0.842555	+	0.538610i	$0.818949\pi$
$174$	2.43209			0.184376
$175$	−1.02630	+	1.10934i	−0.0775810	+	0.0838583i
$176$	3.57860			0.269747
$177$		−	3.25033i		−	0.244309i
$178$		−	10.9043i		−	0.817315i
$179$	5.04745			0.377264			0.188632	−	0.982048i	$-0.439595\pi$
$179$	5.04745			0.377264			0.188632	+	0.982048i	$0.439595\pi$
$180$	−1.23383	+	3.15052i	−0.0919640	+	0.234826i
$181$	−2.43964			−0.181337			−0.0906687	−	0.995881i	$-0.528900\pi$
$181$	−2.43964			−0.181337			−0.0906687	+	0.995881i	$0.528900\pi$
$182$			0.836085i			0.0619748i
$183$			5.35535i			0.395879i
$184$	10.7134			0.789800
$185$	3.24993	+	1.27276i	0.238940	+	0.0935750i
$186$	−0.697747			−0.0511613
$187$		−	16.4652i		−	1.20406i
$188$		−	10.0518i		−	0.733106i
$189$	0.302253			0.0219857
$190$	−0.657779	−	0.257604i	−0.0477203	−	0.0186885i
$191$	4.10435			0.296981			0.148490	−	0.988914i	$-0.452559\pi$
$191$	4.10435			0.296981			0.148490	+	0.988914i	$0.452559\pi$
$192$			1.42957i			0.103170i
$193$			16.5430i			1.19079i	0.803432	+	0.595396i	$0.203005\pi$
$193$			16.5430i			1.19079i	−0.803432	+	0.595396i	$0.796995\pi$
$194$	−6.17692			−0.443477
$195$	3.23262	−	8.25433i	0.231492	−	0.591105i
$196$	10.4538			0.746701
$197$			15.5640i			1.10889i	0.832221	+	0.554443i	$0.187069\pi$
$197$			15.5640i			1.10889i	−0.832221	+	0.554443i	$0.812931\pi$
$198$		−	1.89750i		−	0.134849i
$199$	2.17021			0.153842			0.0769212	−	0.997037i	$-0.475491\pi$
$199$	2.17021			0.153842			0.0769212	+	0.997037i	$0.475491\pi$
$200$	8.32333	−	8.99680i	0.588548	−	0.636170i
$201$	4.26548			0.300864
$202$		−	13.2025i		−	0.928928i
$203$		−	1.05355i		−	0.0739445i
$204$	−9.16149			−0.641433
$205$	−7.34222	+	18.7480i	−0.512803	+	1.30942i
$206$	0.799454			0.0557006
$207$			4.37050i			0.303771i
$208$			5.21689i			0.361726i
$209$	−1.23130			−0.0851711
$210$	−0.439106	−	0.171966i	−0.0303012	−	0.0118667i
$211$	19.8604			1.36724			0.683622	−	0.729836i	$-0.260404\pi$
$211$	19.8604			1.36724			0.683622	+	0.729836i	$0.260404\pi$
$212$			12.8530i			0.882750i
$213$		−	8.83190i		−	0.605152i
$214$	5.82142			0.397944
$215$	18.6075	+	7.28720i	1.26902	+	0.496983i
$216$	−2.45129			−0.166789
$217$			0.302253i			0.0205183i
$218$			11.0338i			0.747303i
$219$	10.4968			0.709305
$220$	3.35535	−	8.56773i	0.226218	−	0.577636i
$221$	24.0030			1.61462
$222$			1.08911i			0.0730962i
$223$		−	2.56154i		−	0.171534i	−0.996315	−	0.0857668i	$-0.972666\pi$
$223$		−	2.56154i		−	0.171534i	0.996315	−	0.0857668i	$-0.0273340\pi$
$224$	1.75934			0.117551
$225$	3.67024	+	3.39549i	0.244682	+	0.226366i
$226$	2.48253			0.165136
$227$		−	4.46459i		−	0.296325i	−0.988963	−	0.148163i	$-0.952664\pi$
$227$		−	4.46459i		−	0.296325i	0.988963	−	0.148163i	$-0.0473359\pi$
$228$			0.685115i			0.0453729i
$229$	5.62097			0.371444			0.185722	−	0.982602i	$-0.440538\pi$
$229$	5.62097			0.371444			0.185722	+	0.982602i	$0.440538\pi$
$230$	2.48658	−	6.34936i	0.163960	−	0.418664i
$231$	−0.821968			−0.0540815
$232$			8.54430i			0.560961i
$233$			4.15427i			0.272155i	0.990698	+	0.136077i	$0.0434496\pi$
$233$			4.15427i			0.272155i	−0.990698	+	0.136077i	$0.956550\pi$
$234$	2.76617			0.180830
$235$	−13.8313	−	5.41671i	−0.902256	−	0.353347i
$236$	4.91823			0.320149
$237$			14.6348i			0.950631i
$238$		−	1.27689i		−	0.0827684i
$239$	−19.9161			−1.28827			−0.644134	−	0.764913i	$-0.722782\pi$
$239$	−19.9161			−1.28827			−0.644134	+	0.764913i	$0.722782\pi$
$240$	−2.73987	−	1.07301i	−0.176858	−	0.0692623i
$241$	−23.9190			−1.54076			−0.770380	−	0.637584i	$-0.779934\pi$
$241$	−23.9190			−1.54076			−0.770380	+	0.637584i	$0.779934\pi$
$242$		−	2.51503i		−	0.161672i
$243$		−	1.00000i		−	0.0641500i
$244$	−8.10345			−0.518770
$245$	5.63333	−	14.3844i	0.359900	−	0.918989i
$246$	−6.28279			−0.400576
$247$		−	1.79500i		−	0.114213i
$248$		−	2.45129i		−	0.155657i
$249$	10.2063			0.646799
$250$	−3.40018	−	7.02105i	−0.215046	−	0.444050i
$251$	25.3168			1.59798			0.798992	−	0.601341i	$-0.205367\pi$
$251$	25.3168			1.59798			0.798992	+	0.601341i	$0.205367\pi$
$252$			0.457355i			0.0288106i
$253$		−	11.8854i		−	0.747231i
$254$	−3.89964			−0.244685
$255$	−4.93693	+	12.6062i	−0.309162	+	0.789432i
$256$	−10.2860			−0.642874
$257$		−	3.55326i		−	0.221646i	−0.993840	−	0.110823i	$-0.964651\pi$
$257$		−	3.55326i		−	0.221646i	0.993840	−	0.110823i	$-0.0353487\pi$
$258$			6.23571i			0.388218i
$259$	0.471786			0.0293153
$260$	12.4900	+	4.89143i	0.774600	+	0.303354i
$261$	−3.48564			−0.215756
$262$			10.1327i			0.626003i
$263$			10.2740i			0.633524i	0.948505	+	0.316762i	$0.102596\pi$
$263$			10.2740i			0.633524i	−0.948505	+	0.316762i	$0.897404\pi$
$264$	6.66619			0.410276
$265$	17.6858	+	6.92622i	1.08643	+	0.425474i
$266$	−0.0954884			−0.00585477
$267$			15.6279i			0.956414i
$268$			6.45431i			0.394260i
$269$	−8.38317			−0.511131			−0.255565	−	0.966792i	$-0.582262\pi$
$269$	−8.38317			−0.511131			−0.255565	+	0.966792i	$0.582262\pi$
$270$	−0.568945	+	1.45277i	−0.0346249	+	0.0884130i
$271$	8.34595			0.506980			0.253490	−	0.967338i	$-0.418421\pi$
$271$	8.34595			0.506980			0.253490	+	0.967338i	$0.418421\pi$
$272$		−	7.96736i		−	0.483092i
$273$		−	1.19827i		−	0.0725223i
$274$	−1.54152			−0.0931268
$275$	−9.98108	−	9.23393i	−0.601882	−	0.556827i
$276$	−6.61323			−0.398070
$277$			6.19221i			0.372054i	0.982545	+	0.186027i	$0.0595611\pi$
$277$			6.19221i			0.372054i	−0.982545	+	0.186027i	$0.940439\pi$
$278$			1.36956i			0.0821406i
$279$	1.00000			0.0598684
$280$	0.604141	−	1.54265i	0.0361043	−	0.0921907i
$281$	19.6063			1.16962			0.584808	−	0.811172i	$-0.301170\pi$
$281$	19.6063			1.16962			0.584808	+	0.811172i	$0.301170\pi$
$282$		−	4.63512i		−	0.276018i
$283$		−	32.4535i		−	1.92916i	−0.263789	−	0.964581i	$-0.584972\pi$
$283$		−	32.4535i		−	1.92916i	0.263789	−	0.964581i	$-0.415028\pi$
$284$	13.3640			0.793007
$285$	0.942719	+	0.369194i	0.0558418	+	0.0218691i
$286$	−7.52251			−0.444815
$287$			2.72161i			0.160652i
$288$		−	5.82076i		−	0.342991i
$289$	−19.6580			−1.15635
$290$	5.06385	+	1.98314i	0.297359	+	0.116454i
$291$	8.85267			0.518953
$292$			15.8832i			0.929491i
$293$		−	14.7700i		−	0.862873i	−0.902143	−	0.431437i	$-0.858007\pi$
$293$		−	14.7700i		−	0.862873i	0.902143	−	0.431437i	$-0.141993\pi$
$294$	4.82048			0.281136
$295$	2.65033	−	6.76748i	0.154308	−	0.394018i
$296$	−3.82620			−0.222393
$297$			2.71947i			0.157799i
$298$		−	10.8244i		−	0.627043i
$299$	17.3266			1.00202
$300$	−5.13789	+	5.55362i	−0.296636	+	0.320638i
$301$	2.70122			0.155696
$302$			2.44849i			0.140895i
$303$			18.9217i			1.08702i
$304$	−0.595815			−0.0341724
$305$	−4.36677	+	11.1503i	−0.250041	+	0.638467i
$306$	−4.22456			−0.241502
$307$		−	23.5695i		−	1.34518i	−0.740015	−	0.672590i	$-0.765182\pi$
$307$		−	23.5695i		−	1.34518i	0.740015	−	0.672590i	$-0.234818\pi$
$308$		−	1.24376i		−	0.0708698i
$309$	−1.14577			−0.0651803
$310$	−1.45277	−	0.568945i	−0.0825120	−	0.0323139i
$311$	−9.96325			−0.564964			−0.282482	−	0.959273i	$-0.591158\pi$
$311$	−9.96325			−0.564964			−0.282482	+	0.959273i	$0.591158\pi$
$312$			9.71798i			0.550172i
$313$		−	10.1209i		−	0.572067i	−0.958220	−	0.286033i	$-0.907663\pi$
$313$		−	10.1209i		−	0.572067i	0.958220	−	0.286033i	$-0.0923368\pi$
$314$	16.1015			0.908659
$315$	0.629320	+	0.246458i	0.0354582	+	0.0138864i
$316$	−22.1446			−1.24573
$317$		−	2.12717i		−	0.119474i	−0.998214	−	0.0597370i	$-0.980974\pi$
$317$		−	2.12717i		−	0.119474i	0.998214	−	0.0597370i	$-0.0190262\pi$
$318$			5.92682i			0.332359i
$319$	9.47907			0.530726
$320$	−1.16568	+	2.97650i	−0.0651632	+	0.166391i
$321$	−8.34317			−0.465670
$322$		−	0.921723i		−	0.0513656i
$323$			2.74136i			0.152533i
$324$	1.51315			0.0840639
$325$	13.4612	−	14.5504i	0.746694	−	0.807112i
$326$	11.6065			0.642827
$327$		−	15.8135i		−	0.874487i
$328$		−	22.0724i		−	1.21874i
$329$	−2.00787			−0.110697
$330$	1.54723	−	3.95077i	0.0851720	−	0.217483i
$331$	5.67365			0.311852			0.155926	−	0.987769i	$-0.450164\pi$
$331$	5.67365			0.311852			0.155926	+	0.987769i	$0.450164\pi$
$332$			15.4437i			0.847582i
$333$		−	1.56089i		−	0.0855365i
$334$	3.94565			0.215896
$335$	8.88113	+	3.47809i	0.485228	+	0.190028i
$336$	−0.397742			−0.0216986
$337$		−	8.30083i		−	0.452175i	−0.974107	−	0.226087i	$-0.927407\pi$
$337$		−	8.30083i		−	0.452175i	0.974107	−	0.226087i	$-0.0725935\pi$
$338$		−	1.89562i		−	0.103108i
$339$	−3.55793			−0.193240
$340$	−19.0751	−	7.47031i	−1.03449	−	0.405134i
$341$	−2.71947			−0.147267
$342$			0.315922i			0.0170831i
$343$		−	4.20394i		−	0.226991i
$344$	−21.9070			−1.18115
$345$	−3.56372	+	9.09980i	−0.191864	+	0.489917i
$346$	−9.88611			−0.531481
$347$		−	16.8933i		−	0.906879i	−0.891287	−	0.453440i	$-0.850197\pi$
$347$		−	16.8933i		−	0.906879i	0.891287	−	0.453440i	$-0.149803\pi$
$348$		−	5.27429i		−	0.282732i
$349$	11.1328			0.595925			0.297963	−	0.954578i	$-0.403693\pi$
$349$	11.1328			0.595925			0.297963	+	0.954578i	$0.403693\pi$
$350$	−0.774039	−	0.716097i	−0.0413741	−	0.0382770i
$351$	−3.96444			−0.211606
$352$			15.8293i			0.843707i
$353$			2.73101i			0.145357i	0.997355	+	0.0726784i	$0.0231547\pi$
$353$			2.73101i			0.145357i	−0.997355	+	0.0726784i	$0.976845\pi$
$354$	2.26790			0.120538
$355$	7.20156	−	18.3889i	0.382219	−	0.975979i
$356$	−23.6474			−1.25331
$357$			1.83002i			0.0968549i
$358$			3.52184i			0.186135i
$359$	−7.53229			−0.397539			−0.198770	−	0.980046i	$-0.563695\pi$
$359$	−7.53229			−0.397539			−0.198770	+	0.980046i	$0.563695\pi$
$360$	−5.10381	−	1.99879i	−0.268995	−	0.105345i
$361$	−18.7950			−0.989210
$362$		−	1.70225i		−	0.0894685i
$363$			3.60451i			0.189188i
$364$	1.81315			0.0950351
$365$	21.8552	+	8.55908i	1.14395	+	0.448003i
$366$	−3.73668			−0.195319
$367$		−	25.4201i		−	1.32692i	−0.748213	−	0.663458i	$-0.769088\pi$
$367$		−	25.4201i		−	1.32692i	0.748213	−	0.663458i	$-0.230912\pi$
$368$		−	5.75124i		−	0.299804i
$369$	9.00441			0.468751
$370$	−0.888062	+	2.26763i	−0.0461682	+	0.117888i
$371$	2.56741			0.133293
$372$			1.51315i			0.0784532i
$373$		−	12.8612i		−	0.665929i	−0.942939	−	0.332965i	$-0.891951\pi$
$373$		−	12.8612i		−	0.665929i	0.942939	−	0.332965i	$-0.108049\pi$
$374$	11.4886			0.594059
$375$	4.87308	+	10.0625i	0.251645	+	0.519623i
$376$	16.2839			0.839777
$377$			13.8186i			0.711694i
$378$			0.210896i			0.0108473i
$379$	−27.2868			−1.40163			−0.700816	−	0.713342i	$-0.747180\pi$
$379$	−27.2868			−1.40163			−0.700816	+	0.713342i	$0.747180\pi$
$380$	−0.558645	+	1.42647i	−0.0286579	+	0.0731766i
$381$	5.58891			0.286329
$382$			2.86380i			0.146525i
$383$		−	19.4253i		−	0.992586i	−0.868155	−	0.496293i	$-0.834694\pi$
$383$		−	19.4253i		−	0.992586i	0.868155	−	0.496293i	$-0.165306\pi$
$384$	10.6440			0.543176
$385$	−1.71141	−	0.670235i	−0.0872218	−	0.0341584i
$386$	−11.5428			−0.587515
$387$		−	8.93693i		−	0.454290i
$388$			13.3954i			0.680049i
$389$	−33.8195			−1.71471			−0.857357	−	0.514722i	$-0.827895\pi$
$389$	−33.8195			−1.71471			−0.857357	+	0.514722i	$0.827895\pi$
$390$	5.75943	+	2.25555i	0.291640	+	0.114214i
$391$	−26.4616			−1.33822
$392$			16.9351i			0.855350i
$393$		−	14.5221i		−	0.732543i
$394$	−10.8597			−0.547104
$395$	−11.9332	+	30.4710i	−0.600426	+	1.53316i
$396$	−4.11496			−0.206784
$397$			5.75310i			0.288740i	0.989524	+	0.144370i	$0.0461155\pi$
$397$			5.75310i			0.288740i	−0.989524	+	0.144370i	$0.953884\pi$
$398$			1.51426i			0.0759030i
$399$	0.136853			0.00685120
$400$	−4.82974	−	4.46820i	−0.241487	−	0.223410i
$401$	30.9973			1.54793			0.773965	−	0.633228i	$-0.218270\pi$
$401$	30.9973			1.54793			0.773965	+	0.633228i	$0.218270\pi$
$402$			2.97622i			0.148441i
$403$		−	3.96444i		−	0.197483i
$404$	−28.6314			−1.42446
$405$	0.815403	−	2.08209i	0.0405177	−	0.103460i
$406$	0.735108			0.0364828
$407$			4.24480i			0.210407i
$408$		−	14.8415i		−	0.734765i
$409$	−0.233213			−0.0115316			−0.00576582	−	0.999983i	$-0.501835\pi$
$409$	−0.233213			−0.0115316			−0.00576582	+	0.999983i	$0.501835\pi$
$410$	−13.0814	−	5.12301i	−0.646043	−	0.253007i
$411$	2.20929			0.108976
$412$		−	1.73371i		−	0.0854140i
$413$		−	0.982422i		−	0.0483418i
$414$	−3.04950			−0.149875
$415$	21.2505	+	8.32226i	1.04315	+	0.408524i
$416$	−23.0760			−1.13140
$417$		−	1.96283i		−	0.0961202i
$418$		−	0.859138i		−	0.0420218i
$419$	−3.34632			−0.163478			−0.0817391	−	0.996654i	$-0.526047\pi$
$419$	−3.34632			−0.163478			−0.0817391	+	0.996654i	$0.526047\pi$
$420$	−0.372929	+	0.952256i	−0.0181970	+	0.0464653i
$421$	−9.12325			−0.444640			−0.222320	−	0.974974i	$-0.571363\pi$
$421$	−9.12325			−0.444640			−0.222320	+	0.974974i	$0.571363\pi$
$422$			13.8575i			0.674573i
$423$			6.64299i			0.322993i
$424$	−20.8218			−1.01120
$425$	−20.5583	+	22.2217i	−0.997224	+	1.07791i
$426$	6.16243			0.298571
$427$			1.61867i			0.0783331i
$428$		−	12.6245i		−	0.610226i
$429$	10.7812			0.520519
$430$	−5.08462	+	12.9833i	−0.245202	+	0.626112i
$431$	21.4495			1.03318			0.516592	−	0.856231i	$-0.327200\pi$
$431$	21.4495			1.03318			0.516592	+	0.856231i	$0.327200\pi$
$432$			1.31592i			0.0633123i
$433$			12.9480i			0.622242i	0.950370	+	0.311121i	$0.100704\pi$
$433$			12.9480i			0.622242i	−0.950370	+	0.311121i	$0.899296\pi$
$434$	−0.210896			−0.0101233
$435$	−7.25743	−	2.84220i	−0.347967	−	0.136273i
$436$	23.9282			1.14595
$437$			1.97885i			0.0946613i
$438$			7.32407i			0.349958i
$439$	36.5832			1.74602			0.873011	−	0.487701i	$-0.162164\pi$
$439$	36.5832			1.74602			0.873011	+	0.487701i	$0.162164\pi$
$440$	13.8796	+	5.43564i	0.661686	+	0.259134i
$441$	−6.90864			−0.328983
$442$			16.7480i			0.796622i
$443$		−	18.4925i		−	0.878604i	−0.898339	−	0.439302i	$-0.855226\pi$
$443$		−	18.4925i		−	0.878604i	0.898339	−	0.439302i	$-0.144774\pi$
$444$	2.36187			0.112089
$445$	−12.7431	+	32.5388i	−0.604079	+	1.54249i
$446$	1.78731			0.0846315
$447$			15.5134i			0.733760i
$448$			0.432092i			0.0204144i
$449$	−14.1531			−0.667924			−0.333962	−	0.942587i	$-0.608386\pi$
$449$	−14.1531			−0.667924			−0.333962	+	0.942587i	$0.608386\pi$
$450$	−2.36919	+	2.56089i	−0.111685	+	0.120722i
$451$	−24.4872			−1.15306
$452$		−	5.38368i		−	0.253227i
$453$		−	3.50914i		−	0.164874i
$454$	3.11515			0.146201
$455$	0.977069	−	2.49490i	0.0458057	−	0.116963i
$456$	−1.10988			−0.0519749
$457$		−	14.2373i		−	0.665994i	−0.942928	−	0.332997i	$-0.891940\pi$
$457$		−	14.2373i		−	0.665994i	0.942928	−	0.332997i	$-0.108060\pi$
$458$			3.92201i			0.183264i
$459$	6.05458			0.282604
$460$	−13.7694	−	5.39245i	−0.642000	−	0.251424i
$461$	5.69980			0.265466			0.132733	−	0.991152i	$-0.457625\pi$
$461$	5.69980			0.265466			0.132733	+	0.991152i	$0.457625\pi$
$462$		−	0.573525i		−	0.0266828i
$463$			10.1278i			0.470677i	0.971913	+	0.235339i	$0.0756199\pi$
$463$			10.1278i			0.470677i	−0.971913	+	0.235339i	$0.924380\pi$
$464$	4.58683			0.212938
$465$	2.08209	+	0.815403i	0.0965548	+	0.0378134i
$466$	−2.89862			−0.134276
$467$			14.9241i			0.690604i	0.938492	+	0.345302i	$0.112224\pi$
$467$			14.9241i			0.690604i	−0.938492	+	0.345302i	$0.887776\pi$
$468$		−	5.99879i		−	0.277294i
$469$	1.28926			0.0595323
$470$	3.77949	−	9.65076i	0.174335	−	0.445156i
$471$	−23.0764			−1.06330
$472$			7.96748i			0.366733i
$473$			24.3037i			1.11748i
$474$	−10.2114			−0.469023
$475$	1.66179	+	1.53739i	0.0762481	+	0.0705404i
$476$	−2.76909			−0.126921
$477$		−	8.49423i		−	0.388924i
$478$		−	13.8964i		−	0.635607i
$479$	5.73952			0.262246			0.131123	−	0.991366i	$-0.458142\pi$
$479$	5.73952			0.262246			0.131123	+	0.991366i	$0.458142\pi$
$480$	4.74626	−	12.1194i	0.216636	−	0.553171i
$481$	−6.18807			−0.282152
$482$		−	16.6894i		−	0.760183i
$483$			1.32100i			0.0601076i
$484$	−5.45416			−0.247916
$485$	18.4321	+	7.21850i	0.836959	+	0.327775i
$486$	0.697747			0.0316504
$487$			29.2234i			1.32424i	0.749398	+	0.662120i	$0.230343\pi$
$487$			29.2234i			1.32424i	−0.749398	+	0.662120i	$0.769657\pi$
$488$		−	13.1275i		−	0.594254i
$489$	−16.6343			−0.752230
$490$	10.0367	+	3.93064i	0.453412	+	0.177568i
$491$	−24.4759			−1.10458			−0.552292	−	0.833651i	$-0.686247\pi$
$491$	−24.4759			−1.10458			−0.552292	+	0.833651i	$0.686247\pi$
$492$			13.6250i			0.614263i
$493$		−	21.1041i		−	0.950480i
$494$	1.25245			0.0563505
$495$	−2.21746	+	5.66218i	−0.0996675	+	0.254496i
$496$	−1.31592			−0.0590866
$497$		−	2.66947i		−	0.119742i
$498$			7.12142i			0.319119i
$499$	43.1187			1.93026			0.965128	−	0.261777i	$-0.0843086\pi$
$499$	43.1187			1.93026			0.965128	+	0.261777i	$0.0843086\pi$
$500$	−15.2260	+	7.37370i	−0.680928	+	0.329762i
$501$	−5.65485			−0.252640
$502$			17.6647i			0.788416i
$503$			3.57111i			0.159228i	0.996826	+	0.0796140i	$0.0253688\pi$
$503$			3.57111i			0.159228i	−0.996826	+	0.0796140i	$0.974631\pi$
$504$	−0.740910			−0.0330028
$505$	−15.4288	+	39.3968i	−0.686573	+	1.75313i
$506$	8.29302			0.368670
$507$			2.71677i			0.120656i
$508$			8.45686i			0.375213i
$509$	−36.1976			−1.60443			−0.802215	−	0.597036i	$-0.796345\pi$
$509$	−36.1976			−1.60443			−0.802215	+	0.597036i	$0.796345\pi$
$510$	−8.79594	−	3.44472i	−0.389491	−	0.152535i
$511$	3.17268			0.140351
$512$			14.1111i			0.623627i
$513$		−	0.452774i		−	0.0199905i
$514$	2.47927			0.109356
$515$	−2.38559	−	0.934261i	−0.105122	−	0.0411685i
$516$	13.5229			0.595313
$517$		−	18.0654i		−	0.794514i
$518$			0.329187i			0.0144636i
$519$	14.1686			0.621934
$520$	−7.92407	+	20.2338i	−0.347494	+	0.887309i
$521$	20.1464			0.882630			0.441315	−	0.897352i	$-0.354512\pi$
$521$	20.1464			0.882630			0.441315	+	0.897352i	$0.354512\pi$
$522$		−	2.43209i		−	0.106450i
$523$			26.2012i			1.14570i	0.819661	+	0.572848i	$0.194162\pi$
$523$			26.2012i			1.14570i	−0.819661	+	0.572848i	$0.805838\pi$
$524$	21.9741			0.959943
$525$	1.10934	+	1.02630i	0.0484156	+	0.0447914i
$526$	−7.16867			−0.312569
$527$			6.05458i			0.263742i
$528$		−	3.57860i		−	0.155739i
$529$	3.89869			0.169508
$530$	−4.83275	+	12.3402i	−0.209921	+	0.536024i
$531$	−3.25033			−0.141052
$532$			0.207078i			0.00897799i
$533$		−	35.6974i		−	1.54623i
$534$	−10.9043			−0.471877
$535$	−17.3713	−	6.80305i	−0.751025	−	0.294121i
$536$	−10.4559			−0.451627
$537$		−	5.04745i		−	0.217813i
$538$		−	5.84933i		−	0.252182i
$539$	18.7878			0.809249
$540$	3.15052	+	1.23383i	0.135577	+	0.0530955i
$541$	13.9835			0.601196			0.300598	−	0.953751i	$-0.402814\pi$
$541$	13.9835			0.601196			0.300598	+	0.953751i	$0.402814\pi$
$542$			5.82335i			0.250134i
$543$			2.43964i			0.104695i
$544$	35.2423			1.51100
$545$	12.8944	−	32.9252i	0.552334	−	1.41036i
$546$	0.836085			0.0357811
$547$		−	41.0507i		−	1.75520i	−0.479392	−	0.877601i	$-0.659143\pi$
$547$		−	41.0507i		−	1.75520i	0.479392	−	0.877601i	$-0.340857\pi$
$548$			3.34298i			0.142805i
$549$	5.35535			0.228561
$550$	6.44294	−	6.96426i	0.274728	−	0.296957i
$551$	−1.57821			−0.0672339
$552$		−	10.7134i		−	0.455991i
$553$			4.42341i			0.188103i
$554$	−4.32059			−0.183564
$555$	1.27276	−	3.24993i	0.0540256	−	0.137952i
$556$	2.97006			0.125958
$557$			6.60110i			0.279697i	0.990173	+	0.139849i	$0.0446616\pi$
$557$			6.60110i			0.279697i	−0.990173	+	0.139849i	$0.955338\pi$
$558$			0.697747i			0.0295380i
$559$	−35.4299			−1.49852
$560$	−0.828136	−	0.324320i	−0.0349951	−	0.0137050i
$561$	−16.4652			−0.695163
$562$			13.6803i			0.577067i
$563$		−	21.0671i		−	0.887872i	−0.896059	−	0.443936i	$-0.853582\pi$
$563$		−	21.0671i		−	0.887872i	0.896059	−	0.443936i	$-0.146418\pi$
$564$	−10.0518			−0.423259
$565$	−7.40795	−	2.90115i	−0.311655	−	0.122052i
$566$	22.6443			0.951812
$567$		−	0.302253i		−	0.0126935i
$568$			21.6495i			0.908394i
$569$	10.5055			0.440412			0.220206	−	0.975453i	$-0.429327\pi$
$569$	10.5055			0.440412			0.220206	+	0.975453i	$0.429327\pi$
$570$	−0.257604	+	0.657779i	−0.0107898	+	0.0275513i
$571$	−16.4974			−0.690393			−0.345196	−	0.938530i	$-0.612188\pi$
$571$	−16.4974			−0.690393			−0.345196	+	0.938530i	$0.612188\pi$
$572$			16.3135i			0.682102i
$573$		−	4.10435i		−	0.171462i
$574$	−1.89900			−0.0792626
$575$	−14.8400	+	16.0408i	−0.618872	+	0.668947i
$576$	1.42957			0.0595654
$577$		−	21.4180i		−	0.891642i	−0.895122	−	0.445821i	$-0.852912\pi$
$577$		−	21.4180i		−	0.891642i	0.895122	−	0.445821i	$-0.147088\pi$
$578$		−	13.7163i		−	0.570522i
$579$	16.5430			0.687504
$580$	4.30068	−	10.9816i	0.178576	−	0.455985i
$581$	3.08489			0.127983
$582$			6.17692i			0.256042i
$583$			23.0998i			0.956694i
$584$	−25.7306			−1.06474
$585$	−8.25433	−	3.23262i	−0.341275	−	0.133652i
$586$	10.3057			0.425725
$587$		−	46.8914i		−	1.93542i	−0.252076	−	0.967708i	$-0.581113\pi$
$587$		−	46.8914i		−	1.93542i	0.252076	−	0.967708i	$-0.418887\pi$
$588$		−	10.4538i		−	0.431108i
$589$	0.452774			0.0186562
$590$	4.72199	+	1.84926i	0.194401	+	0.0761326i
$591$	15.5640			0.640216
$592$			2.05401i			0.0844195i
$593$		−	41.4585i		−	1.70250i	−0.524764	−	0.851248i	$-0.675846\pi$
$593$		−	41.4585i		−	1.70250i	0.524764	−	0.851248i	$-0.324154\pi$
$594$	−1.89750			−0.0778553
$595$	−1.49220	+	3.81027i	−0.0611744	+	0.156206i
$596$	−23.4741			−0.961538
$597$		−	2.17021i		−	0.0888210i
$598$			12.0896i			0.494379i
$599$	7.10882			0.290459			0.145229	−	0.989398i	$-0.453608\pi$
$599$	7.10882			0.290459			0.145229	+	0.989398i	$0.453608\pi$
$600$	−8.99680	−	8.32333i	−0.367293	−	0.339799i
$601$	29.2479			1.19305			0.596523	−	0.802596i	$-0.296548\pi$
$601$	29.2479			1.19305			0.596523	+	0.802596i	$0.296548\pi$
$602$			1.88476i			0.0768173i
$603$		−	4.26548i		−	0.173704i
$604$	5.30986			0.216055
$605$	−2.93913	+	7.50492i	−0.119492	+	0.305119i
$606$	−13.2025			−0.536317
$607$			0.717581i			0.0291257i	0.999894	+	0.0145629i	$0.00463566\pi$
$607$			0.717581i			0.0291257i	−0.999894	+	0.0145629i	$0.995364\pi$
$608$		−	2.63549i		−	0.106883i
$609$	−1.05355			−0.0426918
$610$	−7.78012	−	3.04690i	−0.315008	−	0.123365i
$611$	26.3357			1.06543
$612$			9.16149i			0.370331i
$613$		−	38.5954i		−	1.55885i	−0.626493	−	0.779427i	$-0.715510\pi$
$613$		−	38.5954i		−	1.55885i	0.626493	−	0.779427i	$-0.284490\pi$
$614$	16.4455			0.663687
$615$	18.7480	+	7.34222i	0.755993	+	0.296067i
$616$	2.01488			0.0811818
$617$		−	40.7474i		−	1.64043i	−0.572056	−	0.820214i	$-0.693854\pi$
$617$		−	40.7474i		−	1.64043i	0.572056	−	0.820214i	$-0.306146\pi$
$618$		−	0.799454i		−	0.0321588i
$619$	34.8629			1.40126			0.700628	−	0.713526i	$-0.252903\pi$
$619$	34.8629			1.40126			0.700628	+	0.713526i	$0.252903\pi$
$620$	−1.23383	+	3.15052i	−0.0495517	+	0.126528i
$621$	4.37050			0.175382
$622$		−	6.95182i		−	0.278743i
$623$			4.72360i			0.189247i
$624$	5.21689			0.208843
$625$	1.94125	+	24.9245i	0.0776501	+	0.996981i
$626$	7.06182			0.282247
$627$			1.23130i			0.0491735i
$628$		−	34.9181i		−	1.39338i
$629$	9.45056			0.376819
$630$	−0.171966	+	0.439106i	−0.00685127	+	0.0174944i
$631$	22.2668			0.886426			0.443213	−	0.896416i	$-0.353839\pi$
$631$	22.2668			0.886426			0.443213	+	0.896416i	$0.353839\pi$
$632$		−	35.8740i		−	1.42699i
$633$		−	19.8604i		−	0.789379i
$634$	1.48423			0.0589462
$635$	11.6366	+	4.55722i	0.461786	+	0.180848i
$636$	12.8530			0.509656
$637$			27.3889i			1.08519i
$638$			6.61399i			0.261850i
$639$	−8.83190			−0.349385
$640$	22.1619	+	8.67918i	0.876026	+	0.343075i
$641$	−27.6637			−1.09265			−0.546326	−	0.837572i	$-0.683974\pi$
$641$	−27.6637			−1.09265			−0.546326	+	0.837572i	$0.683974\pi$
$642$		−	5.82142i		−	0.229753i
$643$			33.2383i			1.31079i	0.755285	+	0.655396i	$0.227498\pi$
$643$			33.2383i			1.31079i	−0.755285	+	0.655396i	$0.772502\pi$
$644$	−1.99887			−0.0787666
$645$	7.28720	−	18.6075i	0.286933	−	0.732671i
$646$	−1.91277			−0.0752571
$647$			40.6171i			1.59682i	0.602113	+	0.798411i	$0.294326\pi$
$647$			40.6171i			1.59682i	−0.602113	+	0.798411i	$0.705674\pi$
$648$			2.45129i			0.0962957i
$649$	8.83915			0.346967
$650$	10.1525	+	9.39252i	0.398214	+	0.368405i
$651$	0.302253			0.0118462
$652$		−	25.1702i		−	0.985742i
$653$		−	17.9837i		−	0.703755i	−0.936046	−	0.351878i	$-0.885543\pi$
$653$		−	17.9837i		−	0.703755i	0.936046	−	0.351878i	$-0.114457\pi$
$654$	11.0338			0.431456
$655$	11.8414	−	30.2364i	0.462680	−	1.18143i
$656$	−11.8491			−0.462629
$657$		−	10.4968i		−	0.409517i
$658$		−	1.40098i		−	0.0546160i
$659$	−11.2464			−0.438096			−0.219048	−	0.975714i	$-0.570295\pi$
$659$	−11.2464			−0.438096			−0.219048	+	0.975714i	$0.570295\pi$
$660$	−8.56773	−	3.35535i	−0.333499	−	0.130607i
$661$	−38.5168			−1.49813			−0.749065	−	0.662496i	$-0.769497\pi$
$661$	−38.5168			−1.49813			−0.749065	+	0.662496i	$0.769497\pi$
$662$			3.95877i			0.153862i
$663$		−	24.0030i		−	0.932200i
$664$	−25.0186			−0.970911
$665$	0.284940	+	0.111590i	0.0110495	+	0.00432728i
$666$	1.08911			0.0422021
$667$		−	15.2340i		−	0.589863i
$668$		−	8.55663i		−	0.331066i
$669$	−2.56154			−0.0990350
$670$	−2.42682	+	6.19678i	−0.0937563	+	0.239402i
$671$	−14.5637			−0.562225
$672$		−	1.75934i		−	0.0678682i
$673$			40.8275i			1.57378i	0.617091	+	0.786892i	$0.288311\pi$
$673$			40.8275i			1.57378i	−0.617091	+	0.786892i	$0.711689\pi$
$674$	5.79187			0.223095
$675$	3.39549	−	3.67024i	0.130693	−	0.141267i
$676$	−4.11088			−0.158111
$677$			15.4388i			0.593362i	0.954977	+	0.296681i	$0.0958798\pi$
$677$			15.4388i			0.593362i	−0.954977	+	0.296681i	$0.904120\pi$
$678$		−	2.48253i		−	0.0953412i
$679$	2.67575			0.102686
$680$	12.1018	−	30.9015i	0.464084	−	1.18502i
$681$	−4.46459			−0.171084
$682$		−	1.89750i		−	0.0726589i
$683$			35.3435i			1.35238i	0.736726	+	0.676191i	$0.236371\pi$
$683$			35.3435i			1.35238i	−0.736726	+	0.676191i	$0.763629\pi$
$684$	0.685115			0.0261960
$685$	4.59995	+	1.80146i	0.175755	+	0.0688303i
$686$	2.93328			0.111993
$687$		−	5.62097i		−	0.214453i
$688$			11.7603i			0.448357i
$689$	−33.6748			−1.28291
$690$	−6.34936	−	2.48658i	−0.241716	−	0.0946623i
$691$	43.0687			1.63841			0.819206	−	0.573500i	$-0.194415\pi$
$691$	43.0687			1.63841			0.819206	+	0.573500i	$0.194415\pi$
$692$			21.4393i			0.814998i
$693$			0.821968i			0.0312240i
$694$	11.7872			0.447437
$695$	1.60050	−	4.08680i	0.0607103	−	0.155021i
$696$	8.54430			0.323871
$697$			54.5179i			2.06501i
$698$			7.76787i			0.294018i
$699$	4.15427			0.157129
$700$	−1.55294	+	1.67860i	−0.0586958	+	0.0634451i
$701$	−32.6431			−1.23291			−0.616457	−	0.787388i	$-0.711433\pi$
$701$	−32.6431			−1.23291			−0.616457	+	0.787388i	$0.711433\pi$
$702$		−	2.76617i		−	0.104402i
$703$		−	0.706733i		−	0.0266549i
$704$	−3.88766			−0.146522
$705$	−5.41671	+	13.8313i	−0.204005	+	0.520918i
$706$	−1.90555			−0.0717163
$707$			5.71915i			0.215091i
$708$		−	4.91823i		−	0.184838i
$709$	−7.48673			−0.281170			−0.140585	−	0.990069i	$-0.544898\pi$
$709$	−7.48673			−0.281170			−0.140585	+	0.990069i	$0.544898\pi$
$710$	12.8308	+	5.02486i	0.481530	+	0.188580i
$711$	14.6348			0.548847
$712$		−	38.3086i		−	1.43567i
$713$			4.37050i			0.163677i
$714$	−1.27689			−0.0477864
$715$	22.4474	+	8.79099i	0.839484	+	0.328764i
$716$	7.63754			0.285428
$717$			19.9161i			0.743782i
$718$		−	5.25563i		−	0.196138i
$719$	22.0914			0.823870			0.411935	−	0.911213i	$-0.364853\pi$
$719$	22.0914			0.823870			0.411935	+	0.911213i	$0.364853\pi$
$720$	−1.07301	+	2.73987i	−0.0399886	+	0.102109i
$721$	−0.346312			−0.0128973
$722$		−	13.1141i		−	0.488058i
$723$			23.9190i			0.889559i
$724$	−3.69155			−0.137195
$725$	−12.7931	−	11.8355i	−0.475124	−	0.439558i
$726$	−2.51503			−0.0933416
$727$			10.9437i			0.405881i	0.979191	+	0.202940i	$0.0650497\pi$
$727$			10.9437i			0.405881i	−0.979191	+	0.202940i	$0.934950\pi$
$728$			2.93729i			0.108863i
$729$	−1.00000			−0.0370370
$730$	−5.97207	+	15.2494i	−0.221036	+	0.564406i
$731$	54.1094			2.00131
$732$			8.10345i			0.299512i
$733$			16.8981i			0.624145i	0.950058	+	0.312072i	$0.101023\pi$
$733$			16.8981i			0.624145i	−0.950058	+	0.312072i	$0.898977\pi$
$734$	17.7368			0.654676
$735$	−14.3844	−	5.63333i	−0.530578	−	0.207788i
$736$	25.4396			0.937718
$737$			11.5998i			0.427285i
$738$			6.28279i			0.231273i
$739$	43.3677			1.59531			0.797654	−	0.603115i	$-0.206074\pi$
$739$	43.3677			1.59531			0.797654	+	0.603115i	$0.206074\pi$
$740$	4.91763	+	1.92587i	0.180776	+	0.0707965i
$741$	−1.79500			−0.0659408
$742$			1.79140i			0.0657644i
$743$		−	21.6647i		−	0.794799i	−0.917646	−	0.397400i	$-0.869913\pi$
$743$		−	21.6647i		−	0.794799i	0.917646	−	0.397400i	$-0.130087\pi$
$744$	−2.45129			−0.0898686
$745$	−12.6497	+	32.3004i	−0.463449	+	1.18340i
$746$	8.97388			0.328557
$747$		−	10.2063i		−	0.373430i
$748$		−	24.9144i		−	0.910959i
$749$	−2.52175			−0.0921428
$750$	−7.02105	+	3.40018i	−0.256372	+	0.124157i
$751$	−44.2265			−1.61385			−0.806923	−	0.590656i	$-0.798869\pi$
$751$	−44.2265			−1.61385			−0.806923	+	0.590656i	$0.798869\pi$
$752$		−	8.74165i		−	0.318775i
$753$		−	25.3168i		−	0.922597i
$754$	−9.64188			−0.351136
$755$	2.86136	−	7.30636i	0.104136	−	0.265906i
$756$	0.457355			0.0166338
$757$		−	13.3596i		−	0.485565i	−0.970081	−	0.242782i	$-0.921940\pi$
$757$		−	13.3596i		−	0.485565i	0.970081	−	0.242782i	$-0.0780601\pi$
$758$		−	19.0393i		−	0.691539i
$759$	−11.8854			−0.431414
$760$	−2.31088	−	0.905000i	−0.0838243	−	0.0328278i
$761$	−33.7383			−1.22301			−0.611507	−	0.791239i	$-0.709436\pi$
$761$	−33.7383			−1.22301			−0.611507	+	0.791239i	$0.709436\pi$
$762$			3.89964i			0.141269i
$763$		−	4.77968i		−	0.173036i
$764$	6.21050			0.224688
$765$	12.6062	+	4.93693i	0.455779	+	0.178495i
$766$	13.5539			0.489723
$767$			12.8857i			0.465276i
$768$			10.2860i			0.371163i
$769$	46.9399			1.69269			0.846347	−	0.532631i	$-0.178797\pi$
$769$	46.9399			1.69269			0.846347	+	0.532631i	$0.178797\pi$
$770$	0.467654	−	1.19413i	0.0168531	−	0.0430336i
$771$	−3.55326			−0.127968
$772$			25.0321i			0.900924i
$773$			22.0050i			0.791463i	0.918366	+	0.395732i	$0.129509\pi$
$773$			22.0050i			0.791463i	−0.918366	+	0.395732i	$0.870491\pi$
$774$	6.23571			0.224138
$775$	3.67024	+	3.39549i	0.131839	+	0.121970i
$776$	−21.7005			−0.779001
$777$		−	0.471786i		−	0.0169252i
$778$		−	23.5974i		−	0.846008i
$779$	4.07696			0.146072
$780$	4.89143	−	12.4900i	0.175141	−	0.447215i
$781$	24.0181			0.859433
$782$		−	18.4635i		−	0.660253i
$783$			3.48564i			0.124567i
$784$	9.09123			0.324687
$785$	−48.0472	−	18.8166i	−1.71488	−	0.671592i
$786$	10.1327			0.361423
$787$		−	9.52883i		−	0.339666i	−0.985473	−	0.169833i	$-0.945677\pi$
$787$		−	9.52883i		−	0.339666i	0.985473	−	0.169833i	$-0.0543229\pi$
$788$			23.5506i			0.838956i
$789$	10.2740			0.365765
$790$	−21.2610	−	8.32638i	−0.756433	−	0.296239i
$791$	−1.07540			−0.0382367
$792$		−	6.66619i		−	0.236873i
$793$		−	21.2310i		−	0.753933i
$794$	−4.01421			−0.142459
$795$	6.92622	−	17.6858i	0.245648	−	0.627250i
$796$	3.28386			0.116393
$797$		−	46.7651i		−	1.65650i	−0.560356	−	0.828252i	$-0.689336\pi$
$797$		−	46.7651i		−	1.65650i	0.560356	−	0.828252i	$-0.310664\pi$
$798$			0.0954884i			0.00338025i
$799$	−40.2205			−1.42290
$800$	19.7643	−	21.3635i	0.698775	−	0.755315i
$801$	15.6279			0.552186
$802$			21.6282i			0.763720i
$803$			28.5456i			1.00735i
$804$	6.45431			0.227626
$805$	−1.07715	+	2.75045i	−0.0379645	+	0.0969405i
$806$	2.76617			0.0974343
$807$			8.38317i			0.295102i
$808$		−	46.3825i		−	1.63173i
$809$	41.5538			1.46095			0.730477	−	0.682938i	$-0.239298\pi$
$809$	41.5538			1.46095			0.730477	+	0.682938i	$0.239298\pi$
$810$	1.45277	+	0.568945i	0.0510453	+	0.0199907i
$811$	30.9980			1.08849			0.544244	−	0.838927i	$-0.316817\pi$
$811$	30.9980			1.08849			0.544244	+	0.838927i	$0.316817\pi$
$812$		−	1.59417i		−	0.0559445i
$813$		−	8.34595i		−	0.292705i
$814$	−2.96179			−0.103811
$815$	−34.6342	−	13.5637i	−1.21318	−	0.475115i
$816$	−7.96736			−0.278913
$817$		−	4.04641i		−	0.141566i
$818$		−	0.162723i		−	0.00568949i
$819$	−1.19827			−0.0418708
$820$	−11.1099	+	28.3686i	−0.387974	+	0.990673i
$821$	0.962809			0.0336023			0.0168011	−	0.999859i	$-0.494652\pi$
$821$	0.962809			0.0336023			0.0168011	+	0.999859i	$0.494652\pi$
$822$			1.54152i			0.0537668i
$823$		−	42.5061i		−	1.48167i	−0.671687	−	0.740835i	$-0.734430\pi$
$823$		−	42.5061i		−	1.48167i	0.671687	−	0.740835i	$-0.265570\pi$
$824$	2.80860			0.0978423
$825$	−9.23393	+	9.98108i	−0.321484	+	0.347497i
$826$	0.685482			0.0238510
$827$			12.1193i			0.421429i	0.977548	+	0.210714i	$0.0675790\pi$
$827$			12.1193i			0.421429i	−0.977548	+	0.210714i	$0.932421\pi$
$828$			6.61323i			0.229826i
$829$	15.8215			0.549503			0.274752	−	0.961515i	$-0.411404\pi$
$829$	15.8215			0.549503			0.274752	+	0.961515i	$0.411404\pi$
$830$	−5.80683	+	14.8275i	−0.201558	+	0.514669i
$831$	6.19221			0.214805
$832$		−	5.66744i		−	0.196483i
$833$		−	41.8290i		−	1.44929i
$834$	1.36956			0.0474239
$835$	−11.7739	−	4.61098i	−0.407454	−	0.159570i
$836$	−1.86315			−0.0644383
$837$		−	1.00000i		−	0.0345651i
$838$		−	2.33488i		−	0.0806571i
$839$	−36.7412			−1.26845			−0.634224	−	0.773149i	$-0.718680\pi$
$839$	−36.7412			−1.26845			−0.634224	+	0.773149i	$0.718680\pi$
$840$	−1.54265	−	0.604141i	−0.0532263	−	0.0208448i
$841$	−16.8503			−0.581046
$842$		−	6.36572i		−	0.219377i
$843$		−	19.6063i		−	0.675278i
$844$	30.0517			1.03442
$845$	−2.21526	+	5.65657i	−0.0762073	+	0.194592i
$846$	−4.63512			−0.159359
$847$			1.08947i			0.0374348i
$848$			11.1777i			0.383845i
$849$	−32.4535			−1.11380
$850$	−15.5051	−	14.3445i	−0.531822	−	0.492012i
$851$	6.82189			0.233852
$852$		−	13.3640i		−	0.457843i
$853$		−	1.32430i		−	0.0453430i	−0.999743	−	0.0226715i	$-0.992783\pi$
$853$		−	1.32430i		−	0.0453430i	0.999743	−	0.0226715i	$-0.00721718\pi$
$854$	−1.12942			−0.0386481
$855$	0.369194	−	0.942719i	0.0126262	−	0.0322403i
$856$	20.4515			0.699018
$857$			25.8324i			0.882417i	0.897405	+	0.441208i	$0.145450\pi$
$857$			25.8324i			0.882417i	−0.897405	+	0.441208i	$0.854550\pi$
$858$			7.52251i			0.256814i
$859$	−55.6807			−1.89980			−0.949901	−	0.312550i	$-0.898817\pi$
$859$	−55.6807			−1.89980			−0.949901	+	0.312550i	$0.898817\pi$
$860$	28.1560	+	11.0266i	0.960111	+	0.376005i
$861$	2.72161			0.0927523
$862$			14.9663i			0.509754i
$863$			28.8255i			0.981230i	0.871376	+	0.490615i	$0.163228\pi$
$863$			28.8255i			0.981230i	−0.871376	+	0.490615i	$0.836772\pi$
$864$	−5.82076			−0.198026
$865$	29.5004	+	11.5531i	1.00304	+	0.392819i
$866$	−9.03444			−0.307003
$867$			19.6580i			0.667620i
$868$			0.457355i			0.0155236i
$869$	−39.7988			−1.35008
$870$	1.98314	−	5.06385i	0.0672346	−	0.171680i
$871$	−16.9102			−0.572981
$872$			38.7634i			1.31269i
$873$		−	8.85267i		−	0.299618i
$874$	−1.38074			−0.0467041
$875$	1.47291	+	3.04141i	0.0497933	+	0.102819i
$876$	15.8832			0.536642
$877$			30.4326i			1.02764i	0.857899	+	0.513818i	$0.171769\pi$
$877$			30.4326i			1.02764i	−0.857899	+	0.513818i	$0.828231\pi$
$878$			25.5258i			0.861454i
$879$	−14.7700			−0.498180
$880$	2.91800	−	7.45099i	0.0983659	−	0.251173i
$881$	22.0975			0.744483			0.372242	−	0.928136i	$-0.378589\pi$
$881$	22.0975			0.744483			0.372242	+	0.928136i	$0.378589\pi$
$882$		−	4.82048i		−	0.162314i
$883$			57.3452i			1.92982i	0.262579	+	0.964910i	$0.415427\pi$
$883$			57.3452i			1.92982i	−0.262579	+	0.964910i	$0.584573\pi$
$884$	36.3202			1.22158
$885$	−6.76748	−	2.65033i	−0.227486	−	0.0890897i
$886$	12.9031			0.433487
$887$			5.33250i			0.179048i	0.995985	+	0.0895240i	$0.0285346\pi$
$887$			5.33250i			0.179048i	−0.995985	+	0.0895240i	$0.971465\pi$
$888$			3.82620i			0.128399i
$889$	1.68927			0.0566562
$890$	−22.7039	−	8.89143i	−0.761035	−	0.298041i
$891$	2.71947			0.0911055
$892$		−	3.87600i		−	0.129778i
$893$			3.00777i			0.100651i
$894$	−10.8244			−0.362023
$895$	4.11570	−	10.5093i	0.137573	−	0.351286i
$896$	3.21720			0.107479
$897$		−	17.3266i		−	0.578518i
$898$		−	9.87524i		−	0.329541i
$899$	−3.48564			−0.116253
$900$	5.55362	+	5.13789i	0.185121	+	0.171263i
$901$	51.4290			1.71335
$902$		−	17.0858i		−	0.568896i
$903$		−	2.70122i		−	0.0898909i
$904$	8.72151			0.290073
$905$	−1.98929	+	5.07957i	−0.0661264	+	0.168851i
$906$	2.44849			0.0813457
$907$		−	1.99170i		−	0.0661334i	−0.999453	−	0.0330667i	$-0.989473\pi$
$907$		−	1.99170i		−	0.0661334i	0.999453	−	0.0330667i	$-0.0105274\pi$
$908$		−	6.75560i		−	0.224192i
$909$	18.9217			0.627593
$910$	1.74081	+	0.681747i	0.0577072	+	0.0225997i
$911$	21.8337			0.723383			0.361691	−	0.932298i	$-0.382199\pi$
$911$	21.8337			0.723383			0.361691	+	0.932298i	$0.382199\pi$
$912$			0.595815i			0.0197294i
$913$			27.7557i			0.918580i
$914$	9.93404			0.328589
$915$	11.1503	+	4.36677i	0.368619	+	0.144361i
$916$	8.50537			0.281025
$917$		−	4.38935i		−	0.144949i
$918$			4.22456i			0.139431i
$919$	−32.1622			−1.06093			−0.530466	−	0.847706i	$-0.677983\pi$
$919$	−32.1622			−1.06093			−0.530466	+	0.847706i	$0.677983\pi$
$920$	8.73571	−	22.3062i	0.288008	−	0.735415i
$921$	−23.5695			−0.776640
$922$			3.97702i			0.130976i
$923$			35.0135i			1.15248i
$924$	−1.24376			−0.0409167
$925$	5.30000	−	5.72885i	0.174263	−	0.188363i
$926$	−7.06661			−0.232223
$927$			1.14577i			0.0376319i
$928$			20.2891i			0.666021i
$929$	8.94389			0.293439			0.146720	−	0.989178i	$-0.453128\pi$
$929$	8.94389			0.293439			0.146720	+	0.989178i	$0.453128\pi$
$930$	−0.568945	+	1.45277i	−0.0186564	+	0.0476383i
$931$	−3.12806			−0.102518
$932$			6.28603i			0.205906i
$933$			9.96325i			0.326182i
$934$	−10.4132			−0.340731
$935$	−34.2822	−	13.4258i	−1.12115	−	0.439071i
$936$	9.71798			0.317642
$937$			44.9105i			1.46716i	0.679602	+	0.733581i	$0.262153\pi$
$937$			44.9105i			1.46716i	−0.679602	+	0.733581i	$0.737847\pi$
$938$			0.899574i			0.0293721i
$939$	−10.1209			−0.330283
$940$	−20.9289	−	8.19630i	−0.682625	−	0.267334i
$941$	−13.2411			−0.431647			−0.215824	−	0.976432i	$-0.569244\pi$
$941$	−13.2411			−0.431647			−0.215824	+	0.976432i	$0.569244\pi$
$942$		−	16.1015i		−	0.524615i
$943$			39.3538i			1.28154i
$944$	4.27717			0.139210
$945$	0.246458	−	0.629320i	0.00801729	−	0.0204718i
$946$	−16.9578			−0.551346
$947$			15.1047i			0.490836i	0.969417	+	0.245418i	$0.0789252\pi$
$947$			15.1047i			0.490836i	−0.969417	+	0.245418i	$0.921075\pi$
$948$			22.1446i			0.719223i
$949$	−41.6137			−1.35084
$950$	−1.07271	+	1.15951i	−0.0348033	+	0.0376194i
$951$	−2.12717			−0.0689783
$952$		−	4.48590i		−	0.145389i
$953$		−	47.2438i		−	1.53038i	−0.643807	−	0.765188i	$-0.722646\pi$
$953$		−	47.2438i		−	1.53038i	0.643807	−	0.765188i	$-0.277354\pi$
$954$	5.92682			0.191888
$955$	3.34670	−	8.54565i	0.108297	−	0.276531i
$956$	−30.1361			−0.974671
$957$		−	9.47907i		−	0.306415i
$958$			4.00473i			0.129387i
$959$	0.667765			0.0215633
$960$	2.97650	+	1.16568i	0.0960661	+	0.0376220i
$961$	1.00000			0.0322581
$962$		−	4.31770i		−	0.139208i
$963$			8.34317i			0.268855i
$964$	−36.1931			−1.16570
$965$	34.4441	+	13.4892i	1.10880	+	0.434234i
$966$	−0.921723			−0.0296560
$967$			9.85886i			0.317040i	0.987356	+	0.158520i	$0.0506722\pi$
$967$			9.85886i			0.317040i	−0.987356	+	0.158520i	$0.949328\pi$
$968$		−	8.83568i		−	0.283990i
$969$	2.74136			0.0880652
$970$	−5.03668	+	12.8609i	−0.161718	+	0.412940i
$971$	3.20360			0.102808			0.0514042	−	0.998678i	$-0.483630\pi$
$971$	3.20360			0.102808			0.0514042	+	0.998678i	$0.483630\pi$
$972$		−	1.51315i		−	0.0485343i
$973$		−	0.593272i		−	0.0190194i
$974$	−20.3905			−0.653355
$975$	−14.5504	−	13.4612i	−0.465986	−	0.431104i
$976$	−7.04722			−0.225576
$977$		−	31.1531i		−	0.996676i	−0.866983	−	0.498338i	$-0.833944\pi$
$977$		−	31.1531i		−	0.996676i	0.866983	−	0.498338i	$-0.166056\pi$
$978$		−	11.6065i		−	0.371136i
$979$	−42.4996			−1.35829
$980$	8.52407	−	21.7658i	0.272291	−	0.695284i
$981$	−15.8135			−0.504885
$982$		−	17.0780i		−	0.544981i
$983$		−	33.1726i		−	1.05804i	−0.848609	−	0.529021i	$-0.822559\pi$
$983$		−	33.1726i		−	1.05804i	0.848609	−	0.529021i	$-0.177441\pi$
$984$	−22.0724			−0.703642
$985$	32.4056	+	12.6909i	1.03253	+	0.404366i
$986$	14.7253			0.468949
$987$			2.00787i			0.0639111i
$988$		−	2.71610i		−	0.0864106i
$989$	39.0589			1.24200
$990$	−3.95077	−	1.54723i	−0.125564	−	0.0491741i
$991$	−40.0379			−1.27185			−0.635923	−	0.771752i	$-0.719380\pi$
$991$	−40.0379			−1.27185			−0.635923	+	0.771752i	$0.719380\pi$
$992$		−	5.82076i		−	0.184809i
$993$		−	5.67365i		−	0.180048i
$994$	1.86262			0.0590786
$995$	1.76960	−	4.51859i	0.0561001	−	0.143249i
$996$	15.4437			0.489352
$997$			32.1083i			1.01688i	0.861097	+	0.508441i	$0.169778\pi$
$997$			32.1083i			1.01688i	−0.861097	+	0.508441i	$0.830222\pi$
$998$			30.0859i			0.952353i
$999$	−1.56089			−0.0493845

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.c.a.94.7	yes	10
3.2	odd	2		1395.2.c.f.559.4		10
5.2	odd	4		2325.2.a.x.1.2		5
5.3	odd	4		2325.2.a.w.1.4		5
5.4	even	2	inner	465.2.c.a.94.4	✓	10
15.2	even	4		6975.2.a.bs.1.4		5
15.8	even	4		6975.2.a.bv.1.2		5
15.14	odd	2		1395.2.c.f.559.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.c.a.94.4	✓	10	5.4	even	2	inner
465.2.c.a.94.7	yes	10	1.1	even	1	trivial
1395.2.c.f.559.4		10	3.2	odd	2
1395.2.c.f.559.7		10	15.14	odd	2
2325.2.a.w.1.4		5	5.3	odd	4
2325.2.a.x.1.2		5	5.2	odd	4
6975.2.a.bs.1.4		5	15.2	even	4
6975.2.a.bv.1.2		5	15.8	even	4

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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.697747i q^{2} -1.00000i q^{3} +1.51315 q^{4} +(0.815403 - 2.08209i) q^{5} +0.697747 q^{6} -0.302253i q^{7} +2.45129i q^{8} -1.00000 q^{9} +(1.45277 + 0.568945i) q^{10} +2.71947 q^{11} -1.51315i q^{12} +3.96444i q^{13} +0.210896 q^{14} +(-2.08209 - 0.815403i) q^{15} +1.31592 q^{16} -6.05458i q^{17} -0.697747i q^{18} -0.452774 q^{19} +(1.23383 - 3.15052i) q^{20} -0.302253 q^{21} +1.89750i q^{22} -4.37050i q^{23} +2.45129 q^{24} +(-3.67024 - 3.39549i) q^{25} -2.76617 q^{26} +1.00000i q^{27} -0.457355i q^{28} +3.48564 q^{29} +(0.568945 - 1.45277i) q^{30} -1.00000 q^{31} +5.82076i q^{32} -2.71947i q^{33} +4.22456 q^{34} +(-0.629320 - 0.246458i) q^{35} -1.51315 q^{36} +1.56089i q^{37} -0.315922i q^{38} +3.96444 q^{39} +(5.10381 + 1.99879i) q^{40} -9.00441 q^{41} -0.210896i q^{42} +8.93693i q^{43} +4.11496 q^{44} +(-0.815403 + 2.08209i) q^{45} +3.04950 q^{46} -6.64299i q^{47} -1.31592i q^{48} +6.90864 q^{49} +(2.36919 - 2.56089i) q^{50} -6.05458 q^{51} +5.99879i q^{52} +8.49423i q^{53} -0.697747 q^{54} +(2.21746 - 5.66218i) q^{55} +0.740910 q^{56} +0.452774i q^{57} +2.43209i q^{58} +3.25033 q^{59} +(-3.15052 - 1.23383i) q^{60} -5.35535 q^{61} -0.697747i q^{62} +0.302253i q^{63} -1.42957 q^{64} +(8.25433 + 3.23262i) q^{65} +1.89750 q^{66} +4.26548i q^{67} -9.16149i q^{68} -4.37050 q^{69} +(0.171966 - 0.439106i) q^{70} +8.83190 q^{71} -2.45129i q^{72} +10.4968i q^{73} -1.08911 q^{74} +(-3.39549 + 3.67024i) q^{75} -0.685115 q^{76} -0.821968i q^{77} +2.76617i q^{78} -14.6348 q^{79} +(1.07301 - 2.73987i) q^{80} +1.00000 q^{81} -6.28279i q^{82} +10.2063i q^{83} -0.457355 q^{84} +(-12.6062 - 4.93693i) q^{85} -6.23571 q^{86} -3.48564i q^{87} +6.66619i q^{88} -15.6279 q^{89} +(-1.45277 - 0.568945i) q^{90} +1.19827 q^{91} -6.61323i q^{92} +1.00000i q^{93} +4.63512 q^{94} +(-0.369194 + 0.942719i) q^{95} +5.82076 q^{96} +8.85267i q^{97} +4.82048i q^{98} -2.71947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 6 q^{4} - 6 q^{6} - 10 q^{9} + 2 q^{10} - 32 q^{14} + 2 q^{15} + 6 q^{16} + 8 q^{19} + 28 q^{20} - 16 q^{21} + 18 q^{24} - 2 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} - 10 q^{31} - 12 q^{34} + 4 q^{35}+ \cdots - 2 q^{96}+O(q^{100}) \) 10 * q - 6 * q^4 - 6 * q^6 - 10 * q^9 + 2 * q^10 - 32 * q^14 + 2 * q^15 + 6 * q^16 + 8 * q^19 + 28 * q^20 - 16 * q^21 + 18 * q^24 - 2 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 - 10 * q^31 - 12 * q^34 + 4 * q^35 + 6 * q^36 + 12 * q^39 + 14 * q^40 - 12 * q^44 - 32 * q^46 + 22 * q^49 + 40 * q^50 - 16 * q^51 + 6 * q^54 + 36 * q^56 - 20 * q^59 - 6 * q^60 - 28 * q^61 - 22 * q^64 + 20 * q^65 - 12 * q^66 + 8 * q^69 + 32 * q^70 + 12 * q^71 + 8 * q^74 - 8 * q^75 - 16 * q^76 + 48 * q^79 - 20 * q^80 + 10 * q^81 + 36 * q^84 - 4 * q^85 + 8 * q^86 - 20 * q^89 - 2 * q^90 - 24 * q^94 - 20 * q^95 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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