LMFDB - Embedded newform 145.2.b.c.59.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(59,145)] 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("145.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.84345856.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 13x^{4} + 41x^{2} + 1 $ x^6 + 13x^4 + 41x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.1
Root			$-2.77035i$ of defining polynomial
Character	$\chi$	$=$	145.59
Dual form			145.2.b.c.59.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.77035i q^{2} +0.269894i q^{3} -5.67486 q^{4} +(-1.96358 - 1.06975i) q^{5} +0.747703 q^{6} -1.86960i q^{7} +10.1807i q^{8} +2.92716 q^{9} +(-2.96358 + 5.43981i) q^{10} -3.25230 q^{11} -1.53161i q^{12} -3.40121i q^{13} -5.17945 q^{14} +(0.288719 - 0.529959i) q^{15} +16.8543 q^{16} -2.40939i q^{17} -8.10926i q^{18} +0.674860 q^{19} +(11.1430 + 6.07067i) q^{20} +0.504595 q^{21} +9.01001i q^{22} -7.41031i q^{23} -2.74770 q^{24} +(2.71128 + 4.20107i) q^{25} -9.42256 q^{26} +1.59971i q^{27} +10.6097i q^{28} +1.00000 q^{29} +(-1.46817 - 0.799853i) q^{30} +5.25230 q^{31} -26.3311i q^{32} -0.877777i q^{33} -6.67486 q^{34} +(-2.00000 + 3.67111i) q^{35} -16.6112 q^{36} +1.86960i q^{37} -1.86960i q^{38} +0.917968 q^{39} +(10.8907 - 19.9905i) q^{40} -1.39791i q^{42} +3.46931i q^{43} +18.4563 q^{44} +(-5.74770 - 3.13132i) q^{45} -20.5292 q^{46} +4.00910i q^{47} +4.54888i q^{48} +3.50459 q^{49} +(11.6384 - 7.51121i) q^{50} +0.650280 q^{51} +19.3014i q^{52} -0.877777i q^{53} +4.43175 q^{54} +(6.38614 + 3.47914i) q^{55} +19.0338 q^{56} +0.182141i q^{57} -2.77035i q^{58} -10.0000 q^{59} +(-1.63844 + 3.00744i) q^{60} +11.8543 q^{61} -14.5507i q^{62} -5.47261i q^{63} -39.2378 q^{64} +(-3.63844 + 6.67855i) q^{65} -2.43175 q^{66} +7.95010i q^{67} +13.6729i q^{68} +2.00000 q^{69} +(10.1703 + 5.54071i) q^{70} +2.00000 q^{71} +29.8004i q^{72} +0.607882i q^{73} +5.17945 q^{74} +(-1.13384 + 0.731759i) q^{75} -3.82973 q^{76} +6.08050i q^{77} -2.54310i q^{78} -8.60202 q^{79} +(-33.0948 - 18.0299i) q^{80} +8.34972 q^{81} +2.40939i q^{83} -2.86350 q^{84} +(-2.57744 + 4.73102i) q^{85} +9.61121 q^{86} +0.269894i q^{87} -33.1105i q^{88} +8.50459 q^{89} +(-8.67486 + 15.9232i) q^{90} -6.35891 q^{91} +42.0525i q^{92} +1.41757i q^{93} +11.1066 q^{94} +(-1.32514 - 0.721929i) q^{95} +7.10661 q^{96} -13.1332i q^{97} -9.70897i q^{98} -9.51998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 14 q^{4} + 3 q^{5} + 14 q^{6} - 12 q^{9} - 3 q^{10} - 10 q^{11} + 8 q^{14} + 7 q^{15} + 42 q^{16} - 16 q^{19} + 13 q^{20} - 16 q^{21} - 26 q^{24} + 11 q^{25} - 46 q^{26} + 6 q^{29} + 25 q^{30} + 22 q^{31}+ \cdots - 16 q^{99}+O(q^{100}) $ 6 * q - 14 * q^4 + 3 * q^5 + 14 * q^6 - 12 * q^9 - 3 * q^10 - 10 * q^11 + 8 * q^14 + 7 * q^15 + 42 * q^16 - 16 * q^19 + 13 * q^20 - 16 * q^21 - 26 * q^24 + 11 * q^25 - 46 * q^26 + 6 * q^29 + 25 * q^30 + 22 * q^31 - 20 * q^34 - 12 * q^35 - 12 * q^36 + 14 * q^39 + 21 * q^40 + 2 * q^44 - 44 * q^45 - 44 * q^46 + 2 * q^49 + 35 * q^50 + 44 * q^51 - 22 * q^54 + 13 * q^55 + 16 * q^56 - 60 * q^59 + 25 * q^60 + 12 * q^61 - 38 * q^64 + 13 * q^65 + 34 * q^66 + 12 * q^69 + 60 * q^70 + 12 * q^71 - 8 * q^74 + 9 * q^75 - 24 * q^76 - 2 * q^79 - 55 * q^80 + 10 * q^81 + 80 * q^84 - 26 * q^85 - 30 * q^86 + 32 * q^89 - 32 * q^90 + 40 * q^91 - 2 * q^94 - 28 * q^95 - 26 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2.77035i		−	1.95894i	−0.201600	−	0.979468i	$-0.564614\pi$
$2$		−	2.77035i		−	1.95894i	0.201600	−	0.979468i	$-0.435386\pi$
$3$			0.269894i			0.155824i	0.996960	+	0.0779118i	$0.0248252\pi$
$3$			0.269894i			0.155824i	−0.996960	+	0.0779118i	$0.975175\pi$
$4$	−5.67486			−2.83743
$5$	−1.96358	−	1.06975i	−0.878139	−	0.478406i
$5$	−1.96358	−	1.06975i	−0.878139	−	0.478406i
$6$	0.747703			0.305248
$7$		−	1.86960i		−	0.706643i	−0.935502	−	0.353321i	$-0.885052\pi$
$7$		−	1.86960i		−	0.706643i	0.935502	−	0.353321i	$-0.114948\pi$
$8$			10.1807i			3.59941i
$9$	2.92716			0.975719
$10$	−2.96358	+	5.43981i	−0.937166	+	1.72022i
$11$	−3.25230			−0.980605			−0.490302	−	0.871552i	$-0.663114\pi$
$11$	−3.25230			−0.980605			−0.490302	+	0.871552i	$0.663114\pi$
$12$		−	1.53161i		−	0.442138i
$13$		−	3.40121i		−	0.943327i	−0.881779	−	0.471663i	$-0.843654\pi$
$13$		−	3.40121i		−	0.943327i	0.881779	−	0.471663i	$-0.156346\pi$
$14$	−5.17945			−1.38427
$15$	0.288719	−	0.529959i	0.0745469	−	0.136835i
$16$	16.8543			4.21358
$17$		−	2.40939i		−	0.584363i	−0.956363	−	0.292181i	$-0.905619\pi$
$17$		−	2.40939i		−	0.584363i	0.956363	−	0.292181i	$-0.0943811\pi$
$18$		−	8.10926i		−	1.91137i
$19$	0.674860			0.154823			0.0774117	−	0.996999i	$-0.475334\pi$
$19$	0.674860			0.154823			0.0774117	+	0.996999i	$0.475334\pi$
$20$	11.1430	+	6.07067i	2.49166	+	1.35744i
$21$	0.504595			0.110112
$22$			9.01001i			1.92094i
$23$		−	7.41031i		−	1.54516i	−0.634920	−	0.772578i	$-0.718967\pi$
$23$		−	7.41031i		−	1.54516i	0.634920	−	0.772578i	$-0.281033\pi$
$24$	−2.74770			−0.560872
$25$	2.71128	+	4.20107i	0.542256	+	0.840213i
$26$	−9.42256			−1.84792
$27$			1.59971i			0.307864i
$28$			10.6097i			2.00505i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$	−1.46817	−	0.799853i	−0.268050	−	0.146033i
$31$	5.25230			0.943340			0.471670	−	0.881775i	$-0.343651\pi$
$31$	5.25230			0.943340			0.471670	+	0.881775i	$0.343651\pi$
$32$		−	26.3311i		−	4.65472i
$33$		−	0.877777i		−	0.152801i
$34$	−6.67486			−1.14473
$35$	−2.00000	+	3.67111i	−0.338062	+	0.620530i
$36$	−16.6112			−2.76853
$37$			1.86960i			0.307360i	0.988121	+	0.153680i	$0.0491126\pi$
$37$			1.86960i			0.307360i	−0.988121	+	0.153680i	$0.950887\pi$
$38$		−	1.86960i		−	0.303289i
$39$	0.917968			0.146993
$40$	10.8907	−	19.9905i	1.72198	−	3.16078i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		−	1.39791i		−	0.215701i
$43$			3.46931i			0.529064i	0.964377	+	0.264532i	$0.0852175\pi$
$43$			3.46931i			0.529064i	−0.964377	+	0.264532i	$0.914782\pi$
$44$	18.4563			2.78240
$45$	−5.74770	−	3.13132i	−0.856817	−	0.466789i
$46$	−20.5292			−3.02686
$47$			4.00910i			0.584787i	0.956298	+	0.292393i	$0.0944516\pi$
$47$			4.00910i			0.584787i	−0.956298	+	0.292393i	$0.905548\pi$
$48$			4.54888i			0.656575i
$49$	3.50459			0.500656
$50$	11.6384	−	7.51121i	1.64592	−	1.06225i
$51$	0.650280			0.0910575
$52$			19.3014i			2.67662i
$53$		−	0.877777i		−	0.120572i	−0.998181	−	0.0602859i	$-0.980799\pi$
$53$		−	0.877777i		−	0.120572i	0.998181	−	0.0602859i	$-0.0192013\pi$
$54$	4.43175			0.603085
$55$	6.38614	+	3.47914i	0.861107	+	0.469127i
$56$	19.0338			2.54349
$57$			0.182141i			0.0241251i
$58$		−	2.77035i		−	0.363765i
$59$	−10.0000			−1.30189			−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000			−1.30189			−0.650945	+	0.759125i	$0.725627\pi$
$60$	−1.63844	+	3.00744i	−0.211521	+	0.388259i
$61$	11.8543			1.51779			0.758895	−	0.651213i	$-0.225740\pi$
$61$	11.8543			1.51779			0.758895	+	0.651213i	$0.225740\pi$
$62$		−	14.5507i		−	1.84794i
$63$		−	5.47261i		−	0.689485i
$64$	−39.2378			−4.90473
$65$	−3.63844	+	6.67855i	−0.451293	+	0.828372i
$66$	−2.43175			−0.299328
$67$			7.95010i			0.971259i	0.874165	+	0.485629i	$0.161410\pi$
$67$			7.95010i			0.971259i	−0.874165	+	0.485629i	$0.838590\pi$
$68$			13.6729i			1.65809i
$69$	2.00000			0.240772
$70$	10.1703	+	5.54071i	1.21558	+	0.662241i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$			29.8004i			3.51201i
$73$			0.607882i			0.0711472i	0.999367	+	0.0355736i	$0.0113258\pi$
$73$			0.607882i			0.0711472i	−0.999367	+	0.0355736i	$0.988674\pi$
$74$	5.17945			0.602099
$75$	−1.13384	+	0.731759i	−0.130925	+	0.0844963i
$76$	−3.82973			−0.439301
$77$			6.08050i			0.692937i
$78$		−	2.54310i		−	0.287949i
$79$	−8.60202			−0.967803			−0.483901	−	0.875123i	$-0.660781\pi$
$79$	−8.60202			−0.967803			−0.483901	+	0.875123i	$0.660781\pi$
$80$	−33.0948	−	18.0299i	−3.70011	−	2.01580i
$81$	8.34972			0.927747
$82$		0			0
$83$			2.40939i			0.264465i	0.991219	+	0.132232i	$0.0422145\pi$
$83$			2.40939i			0.264465i	−0.991219	+	0.132232i	$0.957785\pi$
$84$	−2.86350			−0.312434
$85$	−2.57744	+	4.73102i	−0.279562	+	0.513152i
$86$	9.61121			1.03640
$87$			0.269894i			0.0289357i
$88$		−	33.1105i		−	3.52960i
$89$	8.50459			0.901485			0.450743	−	0.892654i	$-0.351159\pi$
$89$	8.50459			0.901485			0.450743	+	0.892654i	$0.351159\pi$
$90$	−8.67486	+	15.9232i	−0.914411	+	1.67845i
$91$	−6.35891			−0.666595
$92$			42.0525i			4.38427i
$93$			1.41757i			0.146995i
$94$	11.1066			1.14556
$95$	−1.32514	−	0.721929i	−0.135957	−	0.0740684i
$96$	7.10661			0.725315
$97$		−	13.1332i		−	1.33347i	−0.745295	−	0.666735i	$-0.767691\pi$
$97$		−	13.1332i		−	1.33347i	0.745295	−	0.666735i	$-0.232309\pi$
$98$		−	9.70897i		−	0.980754i
$99$	−9.51998			−0.956794
$100$	−15.3861	−	23.8405i	−1.53861	−	2.38405i
$101$	4.84513			0.482108			0.241054	−	0.970512i	$-0.422507\pi$
$101$	4.84513			0.482108			0.241054	+	0.970512i	$0.422507\pi$
$102$		−	1.80151i		−	0.178376i
$103$		−	14.8887i		−	1.46703i	−0.679674	−	0.733514i	$-0.737879\pi$
$103$		−	14.8887i		−	1.46703i	0.679674	−	0.733514i	$-0.262121\pi$
$104$	34.6266			3.39542
$105$	−0.990811	−	0.539789i	−0.0966932	−	0.0526780i
$106$	−2.43175			−0.236193
$107$			1.86960i			0.180741i	0.995908	+	0.0903705i	$0.0288051\pi$
$107$			1.86960i			0.180741i	−0.995908	+	0.0903705i	$0.971195\pi$
$108$		−	9.07811i		−	0.873541i
$109$	8.77228			0.840232			0.420116	−	0.907470i	$-0.361989\pi$
$109$	8.77228			0.840232			0.420116	+	0.907470i	$0.361989\pi$
$110$	9.63844	−	17.6919i	0.918989	−	1.68685i
$111$	−0.504595			−0.0478940
$112$		−	31.5108i		−	2.97749i
$113$		−	10.0699i		−	0.947299i	−0.880713	−	0.473650i	$-0.842936\pi$
$113$		−	10.0699i		−	0.947299i	0.880713	−	0.473650i	$-0.157064\pi$
$114$	0.504595			0.0472596
$115$	−7.92716	+	14.5507i	−0.739211	+	1.35686i
$116$	−5.67486			−0.526898
$117$		−	9.95588i		−	0.920422i
$118$			27.7035i			2.55032i
$119$	−4.50459			−0.412936
$120$	5.39533	+	2.93935i	0.492524	+	0.268325i
$121$	−0.422563			−0.0384148
$122$		−	32.8406i		−	2.97325i
$123$		0			0
$124$	−29.8061			−2.67666
$125$	−0.829735	−	11.1495i	−0.0742137	−	0.997242i
$126$	−15.1611			−1.35066
$127$			18.6739i			1.65704i	0.559961	+	0.828519i	$0.310816\pi$
$127$			18.6739i			1.65704i	−0.559961	+	0.828519i	$0.689184\pi$
$128$			56.0404i			4.95332i
$129$	−0.936346			−0.0824407
$130$	18.5019	+	10.0798i	1.62273	+	0.884054i
$131$	−11.0338			−0.964025			−0.482012	−	0.876164i	$-0.660094\pi$
$131$	−11.0338			−0.964025			−0.482012	+	0.876164i	$0.660094\pi$
$132$			4.98126i			0.433563i
$133$		−	1.26172i		−	0.109405i
$134$	22.0246			1.90263
$135$	1.71128	−	3.14115i	0.147284	−	0.270347i
$136$	24.5292			2.10336
$137$			11.8714i			1.01425i	0.861874	+	0.507123i	$0.169291\pi$
$137$			11.8714i			1.01425i	−0.861874	+	0.507123i	$0.830709\pi$
$138$		−	5.54071i		−	0.471656i
$139$	−14.8451			−1.25915			−0.629574	−	0.776941i	$-0.716770\pi$
$139$	−14.8451			−1.25915			−0.629574	+	0.776941i	$0.716770\pi$
$140$	11.3497	−	20.8330i	0.959226	−	1.76071i
$141$	−1.08203			−0.0911235
$142$		−	5.54071i		−	0.464966i
$143$			11.0618i			0.925030i
$144$	49.3352			4.11127
$145$	−1.96358	−	1.06975i	−0.163066	−	0.0888377i
$146$	1.68405			0.139373
$147$			0.945870i			0.0780141i
$148$		−	10.6097i		−	0.872114i
$149$	−17.2769			−1.41538			−0.707688	−	0.706525i	$-0.750262\pi$
$149$	−17.2769			−1.41538			−0.707688	+	0.706525i	$0.750262\pi$
$150$	2.02723	+	3.14115i	0.165523	+	0.256474i
$151$	0.504595			0.0410633			0.0205317	−	0.999789i	$-0.493464\pi$
$151$	0.504595			0.0410633			0.0205317	+	0.999789i	$0.493464\pi$
$152$			6.87052i			0.557273i
$153$		−	7.05266i		−	0.570174i
$154$	16.8451			1.35742
$155$	−10.3133	−	5.61863i	−0.828384	−	0.451299i
$156$	−5.20934			−0.417081
$157$		−	17.9519i		−	1.43272i	−0.697731	−	0.716360i	$-0.745807\pi$
$157$		−	17.9519i		−	1.43272i	0.697731	−	0.716360i	$-0.254193\pi$
$158$			23.8306i			1.89586i
$159$	0.236907			0.0187879
$160$	−28.1676	+	51.7032i	−2.22685	+	4.08749i
$161$	−13.8543			−1.09187
$162$		−	23.1317i		−	1.81740i
$163$			5.45295i			0.427108i	0.976931	+	0.213554i	$0.0685040\pi$
$163$			5.45295i			0.427108i	−0.976931	+	0.213554i	$0.931496\pi$
$164$		0			0
$165$	−0.938999	+	1.72358i	−0.0731010	+	0.134181i
$166$	6.67486			0.518070
$167$		−	1.51195i		−	0.116998i	−0.998287	−	0.0584992i	$-0.981368\pi$
$167$		−	1.51195i		−	0.116998i	0.998287	−	0.0584992i	$-0.0186315\pi$
$168$			5.13711i			0.396336i
$169$	1.43175			0.110135
$170$	13.1066	+	7.14041i	1.00523	+	0.547645i
$171$	1.97542			0.151064
$172$		−	19.6878i		−	1.50118i
$173$		−	8.74012i		−	0.664499i	−0.943192	−	0.332249i	$-0.892192\pi$
$173$		−	8.74012i		−	0.664499i	0.943192	−	0.332249i	$-0.107808\pi$
$174$	0.747703			0.0566832
$175$	7.85431	−	5.06901i	0.593730	−	0.383181i
$176$	−54.8152			−4.13185
$177$		−	2.69894i		−	0.202865i
$178$		−	23.5607i		−	1.76595i
$179$	9.49541			0.709720			0.354860	−	0.934919i	$-0.384529\pi$
$179$	9.49541			0.709720			0.354860	+	0.934919i	$0.384529\pi$
$180$	32.6174	+	17.7698i	2.43116	+	1.32448i
$181$	14.9363			1.11021			0.555105	−	0.831780i	$-0.312678\pi$
$181$	14.9363			1.11021			0.555105	+	0.831780i	$0.312678\pi$
$182$			17.6164i			1.30582i
$183$			3.19941i			0.236507i
$184$	75.4418			5.56165
$185$	2.00000	−	3.67111i	0.147043	−	0.269905i
$186$	3.92716			0.287953
$187$			7.83605i			0.573029i
$188$		−	22.7511i		−	1.65929i
$189$	2.99081			0.217549
$190$	−2.00000	+	3.67111i	−0.145095	+	0.266330i
$191$	10.5292			0.761864			0.380932	−	0.924603i	$-0.375603\pi$
$191$	10.5292			0.761864			0.380932	+	0.924603i	$0.375603\pi$
$192$		−	10.5901i		−	0.764272i
$193$			18.1341i			1.30532i	0.757651	+	0.652660i	$0.226347\pi$
$193$			18.1341i			1.30532i	−0.757651	+	0.652660i	$0.773653\pi$
$194$	−36.3835			−2.61218
$195$	−1.80250	−	0.981994i	−0.129080	−	0.0703220i
$196$	−19.8881			−1.42058
$197$			16.9798i			1.20976i	0.796317	+	0.604879i	$0.206779\pi$
$197$			16.9798i			1.20976i	−0.796317	+	0.604879i	$0.793221\pi$
$198$			26.3737i			1.87430i
$199$	−7.49541			−0.531335			−0.265668	−	0.964065i	$-0.585592\pi$
$199$	−7.49541			−0.531335			−0.265668	+	0.964065i	$0.585592\pi$
$200$	−42.7696	+	27.6026i	−3.02427	+	1.95180i
$201$	−2.14569			−0.151345
$202$		−	13.4227i		−	0.944419i
$203$		−	1.86960i		−	0.131220i
$204$	−3.69025			−0.258369
$205$		0			0
$206$	−41.2470			−2.87381
$207$		−	21.6911i		−	1.50764i
$208$		−	57.3251i		−	3.97478i
$209$	−2.19484			−0.151821
$210$	−1.49541	+	2.74490i	−0.103193	+	0.189416i
$211$	18.0974			1.24588			0.622939	−	0.782270i	$-0.285938\pi$
$211$	18.0974			1.24588			0.622939	+	0.782270i	$0.285938\pi$
$212$			4.98126i			0.342114i
$213$			0.539789i			0.0369857i
$214$	5.17945			0.354060
$215$	3.71128	−	6.81226i	0.253107	−	0.464592i
$216$	−16.2861			−1.10813
$217$		−	9.81970i		−	0.666604i
$218$		−	24.3023i		−	1.64596i
$219$	−0.164064			−0.0110864
$220$	−36.2405	−	19.7436i	−2.44333	−	1.33111i
$221$	−8.19484			−0.551245
$222$			1.39791i			0.0938213i
$223$			6.33073i			0.423937i	0.977276	+	0.211969i	$0.0679874\pi$
$223$			6.33073i			0.423937i	−0.977276	+	0.211969i	$0.932013\pi$
$224$	−49.2286			−3.28923
$225$	7.93635	+	12.2972i	0.529090	+	0.819812i
$226$	−27.8973			−1.85570
$227$		−	24.8905i		−	1.65204i	−0.563638	−	0.826022i	$-0.690599\pi$
$227$		−	24.8905i		−	1.65204i	0.563638	−	0.826022i	$-0.309401\pi$
$228$		−	1.03362i		−	0.0684534i
$229$	−2.14569			−0.141791			−0.0708955	−	0.997484i	$-0.522586\pi$
$229$	−2.14569			−0.141791			−0.0708955	+	0.997484i	$0.522586\pi$
$230$	40.3106	+	21.9610i	2.65801	+	1.44807i
$231$	−1.64109			−0.107976
$232$			10.1807i			0.668393i
$233$			5.33891i			0.349763i	0.984589	+	0.174882i	$0.0559543\pi$
$233$			5.33891i			0.349763i	−0.984589	+	0.174882i	$0.944046\pi$
$234$	−27.5813			−1.80305
$235$	4.28872	−	7.87217i	0.279765	−	0.513524i
$236$	56.7486			3.69402
$237$		−	2.32164i		−	0.150806i
$238$			12.4793i			0.808914i
$239$	2.00000			0.129369			0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000			0.129369			0.0646846	+	0.997906i	$0.479396\pi$
$240$	4.86616	−	8.93209i	0.314109	−	0.576564i
$241$	−6.77228			−0.436241			−0.218121	−	0.975922i	$-0.569993\pi$
$241$	−6.77228			−0.436241			−0.218121	+	0.975922i	$0.569993\pi$
$242$			1.17065i			0.0752521i
$243$			7.05266i			0.452428i
$244$	−67.2716			−4.30662
$245$	−6.88155	−	3.74903i	−0.439646	−	0.239517i
$246$		0			0
$247$		−	2.29534i		−	0.146049i
$248$			53.4719i			3.39547i
$249$	−0.650280			−0.0412098
$250$	−30.8881	+	2.29866i	−1.95353	+	0.145380i
$251$	20.2615			1.27889			0.639447	−	0.768835i	$-0.279163\pi$
$251$	20.2615			1.27889			0.639447	+	0.768835i	$0.279163\pi$
$252$			31.0563i			1.95636i
$253$			24.1005i			1.51519i
$254$	51.7332			3.24603
$255$	−1.27688	−	0.695636i	−0.0799611	−	0.0435624i
$256$	76.7762			4.79851
$257$			19.4376i			1.21248i	0.795280	+	0.606242i	$0.207324\pi$
$257$			19.4376i			1.21248i	−0.795280	+	0.606242i	$0.792676\pi$
$258$			2.59401i			0.161496i
$259$	3.49541			0.217194
$260$	20.6476	−	37.8998i	1.28051	−	2.35045i
$261$	2.92716			0.181186
$262$			30.5674i			1.88846i
$263$			8.28808i			0.511065i	0.966800	+	0.255533i	$0.0822508\pi$
$263$			8.28808i			0.511065i	−0.966800	+	0.255533i	$0.917749\pi$
$264$	8.93635			0.549994
$265$	−0.938999	+	1.72358i	−0.0576823	+	0.105879i
$266$	−3.49541			−0.214317
$267$			2.29534i			0.140473i
$268$		−	45.1157i		−	2.75588i
$269$	23.8543			1.45442			0.727212	−	0.686413i	$-0.240816\pi$
$269$	23.8543			1.45442			0.727212	+	0.686413i	$0.240816\pi$
$270$	−8.70209	−	4.74085i	−0.529592	−	0.288519i
$271$	−0.893389			−0.0542695			−0.0271347	−	0.999632i	$-0.508638\pi$
$271$	−0.893389			−0.0542695			−0.0271347	+	0.999632i	$0.508638\pi$
$272$		−	40.6086i		−	2.46226i
$273$		−	1.71623i		−	0.103871i
$274$	32.8881			1.98684
$275$	−8.81789	−	13.6631i	−0.531739	−	0.823917i
$276$	−11.3497			−0.683173
$277$		−	3.55706i		−	0.213723i	−0.994274	−	0.106862i	$-0.965920\pi$
$277$		−	3.55706i		−	0.213723i	0.994274	−	0.106862i	$-0.0340801\pi$
$278$			41.1262i			2.46659i
$279$	15.3743			0.920435
$280$	−37.3743	−	20.3613i	−2.23354	−	1.21682i
$281$	7.76309			0.463107			0.231554	−	0.972822i	$-0.425619\pi$
$281$	7.76309			0.463107			0.231554	+	0.972822i	$0.425619\pi$
$282$			2.99761i			0.178505i
$283$			30.7889i			1.83021i	0.403215	+	0.915105i	$0.367893\pi$
$283$			30.7889i			1.83021i	−0.403215	+	0.915105i	$0.632107\pi$
$284$	−11.3497			−0.673482
$285$	0.194845	−	0.357648i	0.0115416	−	0.0211852i
$286$	30.6450			1.81208
$287$		0			0
$288$		−	77.0752i		−	4.54170i
$289$	11.1948			0.658520
$290$	−2.96358	+	5.43981i	−0.174027	+	0.319436i
$291$	3.54456			0.207786
$292$		−	3.44965i		−	0.201875i
$293$			6.33073i			0.369845i	0.982753	+	0.184923i	$0.0592034\pi$
$293$			6.33073i			0.369845i	−0.982753	+	0.184923i	$0.940797\pi$
$294$	2.62039			0.152825
$295$	19.6358	+	10.6975i	1.14324	+	0.622831i
$296$	−19.0338			−1.10632
$297$		−	5.20272i		−	0.301892i
$298$			47.8631i			2.77263i
$299$	−25.2040			−1.45759
$300$	6.43440	−	4.15263i	0.371491	−	0.239752i
$301$	6.48622			0.373859
$302$		−	1.39791i		−	0.0804404i
$303$			1.30767i			0.0751238i
$304$	11.3743			0.652361
$305$	−23.2769	−	12.6811i	−1.33283	−	0.726119i
$306$	−19.5384			−1.11693
$307$		−	12.5671i		−	0.717241i	−0.933483	−	0.358620i	$-0.883247\pi$
$307$		−	12.5671i		−	0.717241i	0.933483	−	0.358620i	$-0.116753\pi$
$308$		−	34.5060i		−	1.96616i
$309$	4.01838			0.228598
$310$	−15.5656	+	28.5715i	−0.884066	+	1.62275i
$311$	24.3835			1.38266			0.691330	−	0.722539i	$-0.257025\pi$
$311$	24.3835			1.38266			0.691330	+	0.722539i	$0.257025\pi$
$312$			9.34552i			0.529086i
$313$		−	34.6618i		−	1.95920i	−0.200954	−	0.979601i	$-0.564404\pi$
$313$		−	34.6618i		−	1.95920i	0.200954	−	0.979601i	$-0.435596\pi$
$314$	−49.7332			−2.80661
$315$	−5.85431	+	10.7459i	−0.329853	+	0.605463i
$316$	48.8152			2.74607
$317$			25.7880i			1.44840i	0.689591	+	0.724199i	$0.257790\pi$
$317$			25.7880i			1.44840i	−0.689591	+	0.724199i	$0.742210\pi$
$318$		−	0.656316i		−	0.0368044i
$319$	−3.25230			−0.182094
$320$	77.0465	+	41.9745i	4.30703	+	2.34645i
$321$	−0.504595			−0.0281637
$322$			38.3814i			2.13891i
$323$		−	1.62600i		−	0.0904730i
$324$	−47.3835			−2.63242
$325$	14.2887	−	9.22164i	0.792596	−	0.511525i
$326$	15.1066			0.836678
$327$			2.36759i			0.130928i
$328$		0			0
$329$	7.49541			0.413235
$330$	4.77494	+	2.60136i	0.262852	+	0.143200i
$331$	−16.9609			−0.932257			−0.466128	−	0.884717i	$-0.654352\pi$
$331$	−16.9609			−0.932257			−0.466128	+	0.884717i	$0.654352\pi$
$332$		−	13.6729i		−	0.750400i
$333$			5.47261i			0.299897i
$334$	−4.18864			−0.229192
$335$	8.50459	−	15.6106i	0.464656	−	0.852900i
$336$	8.50459			0.463964
$337$			22.5952i			1.23084i	0.788200	+	0.615420i	$0.211013\pi$
$337$			22.5952i			1.23084i	−0.788200	+	0.615420i	$0.788987\pi$
$338$		−	3.96646i		−	0.215747i
$339$	2.71782			0.147612
$340$	14.6266	−	26.8479i	0.793239	−	1.45603i
$341$	−17.0820			−0.925044
$342$		−	5.47261i		−	0.295925i
$343$		−	19.6394i		−	1.06043i
$344$	−35.3198			−1.90432
$345$	−3.92716	−	2.13949i	−0.211431	−	0.115187i
$346$	−24.2132			−1.30171
$347$		−	12.0469i		−	0.646714i	−0.946277	−	0.323357i	$-0.895189\pi$
$347$		−	12.0469i		−	0.646714i	0.946277	−	0.323357i	$-0.104811\pi$
$348$		−	1.53161i		−	0.0821030i
$349$	1.56825			0.0839464			0.0419732	−	0.999119i	$-0.486636\pi$
$349$	1.56825			0.0839464			0.0419732	+	0.999119i	$0.486636\pi$
$350$	−14.0430	−	21.7592i	−0.750628	−	1.16308i
$351$	5.44094			0.290416
$352$			85.6365i			4.56444i
$353$			7.66054i			0.407730i	0.978999	+	0.203865i	$0.0653503\pi$
$353$			7.66054i			0.407730i	−0.978999	+	0.203865i	$0.934650\pi$
$354$	−7.47703			−0.397400
$355$	−3.92716	−	2.13949i	−0.208432	−	0.113553i
$356$	−48.2624			−2.55790
$357$		−	1.21576i		−	0.0643451i
$358$		−	26.3056i		−	1.39030i
$359$	−17.5928			−0.928514			−0.464257	−	0.885701i	$-0.653679\pi$
$359$	−17.5928			−0.928514			−0.464257	+	0.885701i	$0.653679\pi$
$360$	31.8789	−	58.5154i	1.68017	−	3.08403i
$361$	−18.5446			−0.976030
$362$		−	41.3790i		−	2.17483i
$363$		−	0.114047i		−	0.00598593i
$364$	36.0859			1.89142
$365$	0.650280	−	1.19362i	0.0340372	−	0.0624772i
$366$	8.86350			0.463303
$367$			9.88779i			0.516138i	0.966126	+	0.258069i	$0.0830863\pi$
$367$			9.88779i			0.516138i	−0.966126	+	0.258069i	$0.916914\pi$
$368$		−	124.896i		−	6.51064i
$369$		0			0
$370$	−10.1703	−	5.54071i	−0.528727	−	0.288048i
$371$	−1.64109			−0.0852012
$372$		−	8.04448i		−	0.417087i
$373$			16.2841i			0.843161i	0.906791	+	0.421580i	$0.138524\pi$
$373$			16.2841i			0.843161i	−0.906791	+	0.421580i	$0.861476\pi$
$374$	21.7086			1.12253
$375$	3.00919	−	0.223941i	0.155394	−	0.0115642i
$376$	−40.8152			−2.10489
$377$		−	3.40121i		−	0.175171i
$378$		−	8.28560i		−	0.426166i
$379$	2.52917			0.129915			0.0649575	−	0.997888i	$-0.479309\pi$
$379$	2.52917			0.129915			0.0649575	+	0.997888i	$0.479309\pi$
$380$	7.51998	+	4.09685i	0.385767	+	0.210164i
$381$	−5.03997			−0.258205
$382$		−	29.1695i		−	1.49244i
$383$		−	5.60880i		−	0.286596i	−0.989680	−	0.143298i	$-0.954229\pi$
$383$		−	5.60880i		−	0.286596i	0.989680	−	0.143298i	$-0.0457708\pi$
$384$	−15.1250			−0.771844
$385$	6.50459	−	11.9395i	0.331505	−	0.608495i
$386$	50.2378			2.55704
$387$			10.1552i			0.516218i
$388$			74.5288i			3.78363i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$	−2.72047	+	4.99357i	−0.137756	+	0.252859i
$391$	−17.8543			−0.902931
$392$			35.6791i			1.80207i
$393$		−	2.97795i		−	0.150218i
$394$	47.0400			2.36984
$395$	16.8907	+	9.20198i	0.849865	+	0.463002i
$396$	54.0246			2.71484
$397$		−	27.8660i		−	1.39856i	−0.714850	−	0.699278i	$-0.753505\pi$
$397$		−	27.8660i		−	1.39856i	0.714850	−	0.699278i	$-0.246495\pi$
$398$			20.7649i			1.04085i
$399$	0.340531			0.0170479
$400$	45.6968	+	70.8061i	2.28484	+	3.54030i
$401$	−15.6174			−0.779896			−0.389948	−	0.920837i	$-0.627507\pi$
$401$	−15.6174			−0.779896			−0.389948	+	0.920837i	$0.627507\pi$
$402$			5.94431i			0.296475i
$403$		−	17.8642i		−	0.889878i
$404$	−27.4954			−1.36795
$405$	−16.3953	−	8.93209i	−0.814691	−	0.443839i
$406$	−5.17945			−0.257052
$407$		−	6.08050i		−	0.301399i
$408$			6.62028i			0.327753i
$409$	30.5538			1.51079			0.755393	−	0.655272i	$-0.227446\pi$
$409$	30.5538			1.51079			0.755393	+	0.655272i	$0.227446\pi$
$410$		0			0
$411$	−3.20403			−0.158043
$412$			84.4913i			4.16259i
$413$			18.6960i			0.919970i
$414$	−60.0921			−2.95337
$415$	2.57744	−	4.73102i	0.126521	−	0.232237i
$416$	−89.5576			−4.39092
$417$		−	4.00661i		−	0.196205i
$418$			6.08050i			0.297407i
$419$	10.0492			0.490934			0.245467	−	0.969405i	$-0.421059\pi$
$419$	10.0492			0.490934			0.245467	+	0.969405i	$0.421059\pi$
$420$	5.62271	+	3.06322i	0.274360	+	0.149470i
$421$	−16.1948			−0.789288			−0.394644	−	0.918834i	$-0.629132\pi$
$421$	−16.1948			−0.789288			−0.394644	+	0.918834i	$0.629132\pi$
$422$		−	50.1363i		−	2.44060i
$423$			11.7353i			0.570587i
$424$	8.93635			0.433987
$425$	10.1220	−	6.53253i	0.490989	−	0.316874i
$426$	1.49541			0.0724526
$427$		−	22.1628i		−	1.07253i
$428$		−	10.6097i		−	0.512840i
$429$	−2.98550			−0.144142
$430$	−18.8724	−	10.2816i	−0.910106	−	0.495821i
$431$	11.1857			0.538794			0.269397	−	0.963029i	$-0.413176\pi$
$431$	11.1857			0.538794			0.269397	+	0.963029i	$0.413176\pi$
$432$			26.9619i			1.29721i
$433$			14.0306i			0.674267i	0.941457	+	0.337134i	$0.109457\pi$
$433$			14.0306i			0.674267i	−0.941457	+	0.337134i	$0.890543\pi$
$434$	−27.2040			−1.30584
$435$	0.288719	−	0.529959i	0.0138430	−	0.0254096i
$436$	−49.7815			−2.38410
$437$		−	5.00092i		−	0.239226i
$438$			0.454515i			0.0217176i
$439$	−9.65947			−0.461021			−0.230511	−	0.973070i	$-0.574040\pi$
$439$	−9.65947			−0.461021			−0.230511	+	0.973070i	$0.574040\pi$
$440$	−35.4199	+	65.0151i	−1.68858	+	3.09948i
$441$	10.2585			0.488500
$442$			22.7026i			1.07985i
$443$		−	9.75160i		−	0.463313i	−0.972798	−	0.231656i	$-0.925586\pi$
$443$		−	9.75160i		−	0.463313i	0.972798	−	0.231656i	$-0.0744145\pi$
$444$	2.86350			0.135896
$445$	−16.6994	−	9.09777i	−0.791629	−	0.431276i
$446$	17.5384			0.830466
$447$		−	4.66293i		−	0.220549i
$448$			73.3590i			3.46589i
$449$	−8.86350			−0.418295			−0.209147	−	0.977884i	$-0.567069\pi$
$449$	−8.86350			−0.418295			−0.209147	+	0.977884i	$0.567069\pi$
$450$	34.0675	−	21.9865i	1.60596	−	1.03645i
$451$		0			0
$452$			57.1454i			2.68790i
$453$			0.136187i			0.00639863i
$454$	−68.9556			−3.23625
$455$	12.4862	+	6.80243i	0.585363	+	0.318903i
$456$	−1.85431			−0.0868362
$457$		−	24.5041i		−	1.14625i	−0.819466	−	0.573127i	$-0.805730\pi$
$457$		−	24.5041i		−	1.14625i	0.819466	−	0.573127i	$-0.194270\pi$
$458$			5.94431i			0.277759i
$459$	3.85431			0.179904
$460$	44.9855	−	82.5733i	2.09746	−	3.85000i
$461$	−37.4173			−1.74270			−0.871348	−	0.490666i	$-0.836753\pi$
$461$	−37.4173			−1.74270			−0.871348	+	0.490666i	$0.836753\pi$
$462$			4.54640i			0.211518i
$463$			2.45534i			0.114109i	0.998371	+	0.0570547i	$0.0181710\pi$
$463$			2.45534i			0.114109i	−0.998371	+	0.0570547i	$0.981829\pi$
$464$	16.8543			0.782442
$465$	1.51644	−	2.78350i	0.0703231	−	0.129082i
$466$	14.7907			0.685164
$467$			34.4182i			1.59268i	0.604846	+	0.796342i	$0.293235\pi$
$467$			34.4182i			1.59268i	−0.604846	+	0.796342i	$0.706765\pi$
$468$			56.4982i			2.61163i
$469$	14.8635			0.686333
$470$	−21.8087	−	11.8813i	−1.00596	−	0.548042i
$471$	4.84513			0.223252
$472$		−	101.807i		−	4.68603i
$473$		−	11.2832i		−	0.518803i
$474$	−6.43175			−0.295420
$475$	1.82973	+	2.83513i	0.0839540	+	0.130085i
$476$	25.5629			1.17168
$477$		−	2.56939i		−	0.117644i
$478$		−	5.54071i		−	0.253426i
$479$	9.41636			0.430245			0.215122	−	0.976587i	$-0.430985\pi$
$479$	9.41636			0.430245			0.215122	+	0.976587i	$0.430985\pi$
$480$	−13.9544	−	7.60228i	−0.636928	−	0.346995i
$481$	6.35891			0.289941
$482$			18.7616i			0.854568i
$483$		−	3.73920i		−	0.170140i
$484$	2.39798			0.108999
$485$	−14.0492	+	25.7880i	−0.637939	+	1.17097i
$486$	19.5384			0.886278
$487$		−	33.0909i		−	1.49949i	−0.661726	−	0.749745i	$-0.730176\pi$
$487$		−	33.0909i		−	1.49949i	0.661726	−	0.749745i	$-0.269824\pi$
$488$			120.685i			5.46314i
$489$	−1.47172			−0.0665535
$490$	−10.3861	+	19.0643i	−0.469198	+	0.861238i
$491$	28.9609			1.30699			0.653494	−	0.756932i	$-0.273302\pi$
$491$	28.9609			1.30699			0.653494	+	0.756932i	$0.273302\pi$
$492$		0			0
$493$		−	2.40939i		−	0.108513i
$494$	−6.35891			−0.286101
$495$	18.6932	+	10.1840i	0.840199	+	0.457736i
$496$	88.5239			3.97484
$497$		−	3.73920i		−	0.167726i
$498$			1.80151i			0.0807274i
$499$	−33.8727			−1.51635			−0.758175	−	0.652051i	$-0.773909\pi$
$499$	−33.8727			−1.51635			−0.758175	+	0.652051i	$0.773909\pi$
$500$	4.70863	+	63.2719i	0.210576	+	2.82961i
$501$	0.408067			0.0182311
$502$		−	56.1315i		−	2.50527i
$503$		−	0.945870i		−	0.0421743i	−0.999778	−	0.0210871i	$-0.993287\pi$
$503$		−	0.945870i		−	0.0421743i	0.999778	−	0.0210871i	$-0.00671274\pi$
$504$	55.7148			2.48174
$505$	−9.51378	−	5.18306i	−0.423358	−	0.230643i
$506$	66.7670			2.96815
$507$			0.386422i			0.0171616i
$508$		−	105.972i		−	4.70173i
$509$	−32.1404			−1.42460			−0.712299	−	0.701877i	$-0.752346\pi$
$509$	−32.1404			−1.42460			−0.712299	+	0.701877i	$0.752346\pi$
$510$	−1.92716	+	3.53740i	−0.0853359	+	0.156639i
$511$	1.13650			0.0502757
$512$		−	100.616i		−	4.44665i
$513$			1.07958i			0.0476645i
$514$	53.8490			2.37518
$515$	−15.9272	+	29.2351i	−0.701834	+	1.28825i
$516$	5.31363			0.233920
$517$		−	13.0388i		−	0.573444i
$518$		−	9.68351i		−	0.425469i
$519$	2.35891			0.103545
$520$	−67.9920	−	37.0417i	−2.98165	−	1.62439i
$521$	−8.43175			−0.369402			−0.184701	−	0.982795i	$-0.559132\pi$
$521$	−8.43175			−0.369402			−0.184701	+	0.982795i	$0.559132\pi$
$522$		−	8.10926i		−	0.354933i
$523$		−	21.8273i		−	0.954442i	−0.878783	−	0.477221i	$-0.841644\pi$
$523$		−	21.8273i		−	0.954442i	0.878783	−	0.477221i	$-0.158356\pi$
$524$	62.6151			2.73535
$525$	1.36810	+	2.11983i	0.0597087	+	0.0925172i
$526$	22.9609			1.00114
$527$		−	12.6548i		−	0.551253i
$528$		−	14.7943i		−	0.643840i
$529$	−31.9127			−1.38751
$530$	4.77494	+	2.60136i	0.207410	+	0.112996i
$531$	−29.2716			−1.27028
$532$			7.16007i			0.310429i
$533$		0			0
$534$	6.35891			0.275177
$535$	2.00000	−	3.67111i	0.0864675	−	0.158716i
$536$	−80.9372			−3.49596
$537$			2.56276i			0.110591i
$538$		−	66.0849i		−	2.84912i
$539$	−11.3980			−0.490946
$540$	−9.71128	+	17.8256i	−0.417907	+	0.767091i
$541$	−25.5138			−1.09692			−0.548462	−	0.836176i	$-0.684786\pi$
$541$	−25.5138			−1.09692			−0.548462	+	0.836176i	$0.684786\pi$
$542$			2.47500i			0.106310i
$543$			4.03123i			0.172997i
$544$	−63.4418			−2.72005
$545$	−17.2251	−	9.38413i	−0.737841	−	0.401972i
$546$	−4.75457			−0.203477
$547$			17.7698i			0.759781i	0.925031	+	0.379891i	$0.124038\pi$
$547$			17.7698i			0.759781i	−0.925031	+	0.379891i	$0.875962\pi$
$548$		−	67.3687i		−	2.87785i
$549$	34.6994			1.48094
$550$	−37.8517	+	24.4287i	−1.61400	+	1.04164i
$551$	0.674860			0.0287500
$552$			20.3613i			0.866635i
$553$			16.0823i			0.683890i
$554$	−9.85431			−0.418670
$555$	0.990811	+	0.539789i	0.0420576	+	0.0229128i
$556$	84.2440			3.57274
$557$			42.1665i			1.78665i	0.449409	+	0.893326i	$0.351635\pi$
$557$			42.1665i			1.78665i	−0.449409	+	0.893326i	$0.648365\pi$
$558$		−	42.5922i		−	1.80307i
$559$	11.7998			0.499080
$560$	−33.7086	+	61.8740i	−1.42445	+	2.61465i
$561$	−2.11491			−0.0892914
$562$		−	21.5065i		−	0.907198i
$563$		−	5.76465i		−	0.242951i	−0.992594	−	0.121475i	$-0.961237\pi$
$563$		−	5.76465i		−	0.242951i	0.992594	−	0.121475i	$-0.0387626\pi$
$564$	6.14038			0.258557
$565$	−10.7723	+	19.7731i	−0.453193	+	0.831861i
$566$	85.2961			3.58526
$567$		−	15.6106i		−	0.655585i
$568$			20.3613i			0.854342i
$569$	−1.49541			−0.0626907			−0.0313453	−	0.999509i	$-0.509979\pi$
$569$	−1.49541			−0.0626907			−0.0313453	+	0.999509i	$0.509979\pi$
$570$	−0.990811	−	0.539789i	−0.0415005	−	0.0226093i
$571$	−7.03997			−0.294614			−0.147307	−	0.989091i	$-0.547060\pi$
$571$	−7.03997			−0.294614			−0.147307	+	0.989091i	$0.547060\pi$
$572$		−	62.7739i		−	2.62471i
$573$			2.84176i			0.118716i
$574$		0			0
$575$	31.1312	−	20.0914i	1.29826	−	0.837870i
$576$	−114.855			−4.78563
$577$			34.7102i			1.44501i	0.691368	+	0.722503i	$0.257009\pi$
$577$			34.7102i			1.44501i	−0.691368	+	0.722503i	$0.742991\pi$
$578$		−	31.0137i		−	1.29000i
$579$	−4.89428			−0.203399
$580$	11.1430	+	6.07067i	0.462689	+	0.252071i
$581$	4.50459			0.186882
$582$		−	9.81970i		−	0.407040i
$583$			2.85479i			0.118233i
$584$	−6.18864			−0.256088
$585$	−10.6503	+	19.5492i	−0.440335	+	0.808258i
$586$	17.5384			0.724503
$587$			37.4158i			1.54432i	0.635430	+	0.772158i	$0.280823\pi$
$587$			37.4158i			1.54432i	−0.635430	+	0.772158i	$0.719177\pi$
$588$		−	5.36768i		−	0.221359i
$589$	3.54456			0.146051
$590$	29.6358	−	54.3981i	1.22009	−	2.23953i
$591$	−4.58274			−0.188509
$592$			31.5108i			1.29509i
$593$			32.6388i			1.34032i	0.742218	+	0.670158i	$0.233774\pi$
$593$			32.6388i			1.34032i	−0.742218	+	0.670158i	$0.766226\pi$
$594$	−14.4134			−0.591388
$595$	8.84513	+	4.81878i	0.362615	+	0.197551i
$596$	98.0439			4.01603
$597$		−	2.02297i		−	0.0827945i
$598$			69.8241i			2.85532i
$599$	38.1466			1.55863			0.779314	−	0.626634i	$-0.215568\pi$
$599$	38.1466			1.55863			0.779314	+	0.626634i	$0.215568\pi$
$600$	−7.44979	−	11.5433i	−0.304137	−	0.471252i
$601$	−16.7178			−0.681934			−0.340967	−	0.940075i	$-0.610754\pi$
$601$	−16.7178			−0.681934			−0.340967	+	0.940075i	$0.610754\pi$
$602$		−	17.9691i		−	0.732366i
$603$			23.2712i			0.947676i
$604$	−2.86350			−0.116514
$605$	0.829735	+	0.452035i	0.0337335	+	0.0183778i
$606$	3.62271			0.147163
$607$		−	0.673496i		−	0.0273364i	−0.999907	−	0.0136682i	$-0.995649\pi$
$607$		−	0.673496i		−	0.0273364i	0.999907	−	0.0136682i	$-0.00435085\pi$
$608$		−	17.7698i		−	0.720660i
$609$	0.504595			0.0204472
$610$	−35.1312	+	64.4852i	−1.42242	+	2.61093i
$611$	13.6358			0.551645
$612$			40.0229i			1.61783i
$613$		−	26.4615i		−	1.06877i	−0.845241	−	0.534385i	$-0.820543\pi$
$613$		−	26.4615i		−	1.06877i	0.845241	−	0.534385i	$-0.179457\pi$
$614$	−34.8152			−1.40503
$615$		0			0
$616$	−61.9035			−2.49416
$617$			27.9538i			1.12538i	0.826669	+	0.562688i	$0.190233\pi$
$617$			27.9538i			1.12538i	−0.826669	+	0.562688i	$0.809767\pi$
$618$		−	11.1323i		−	0.447808i
$619$	−24.6512			−0.990814			−0.495407	−	0.868661i	$-0.664981\pi$
$619$	−24.6512			−0.990814			−0.495407	+	0.868661i	$0.664981\pi$
$620$	58.5265	+	31.8849i	2.35048	+	1.28053i
$621$	11.8543			0.475697
$622$		−	67.5509i		−	2.70854i
$623$		−	15.9002i		−	0.637028i
$624$	15.4717			0.619365
$625$	−10.2979	+	22.7805i	−0.411916	+	0.911222i
$626$	−96.0255			−3.83795
$627$		−	0.592376i		−	0.0236572i
$628$			101.875i			4.06524i
$629$	4.50459			0.179610
$630$	29.7700	+	16.2185i	1.18606	+	0.646161i
$631$	11.8052			0.469956			0.234978	−	0.972001i	$-0.424498\pi$
$631$	11.8052			0.469956			0.234978	+	0.972001i	$0.424498\pi$
$632$		−	87.5742i		−	3.48352i
$633$			4.88439i			0.194137i
$634$	71.4418			2.83732
$635$	19.9763	−	36.6676i	0.792736	−	1.45511i
$636$	−1.34441			−0.0533095
$637$		−	11.9199i		−	0.472283i
$638$			9.01001i			0.356710i
$639$	5.85431			0.231593
$640$	59.9491	−	110.040i	2.36970	−	4.34970i
$641$	13.8727			0.547938			0.273969	−	0.961738i	$-0.411663\pi$
$641$	13.8727			0.547938			0.273969	+	0.961738i	$0.411663\pi$
$642$			1.39791i			0.0551709i
$643$		−	5.29047i		−	0.208636i	−0.994544	−	0.104318i	$-0.966734\pi$
$643$		−	5.29047i		−	0.208636i	0.994544	−	0.104318i	$-0.0332660\pi$
$644$	78.6213			3.09811
$645$	1.83859	+	1.00165i	0.0723944	+	0.0394401i
$646$	−4.50459			−0.177231
$647$			40.7448i			1.60184i	0.598769	+	0.800921i	$0.295657\pi$
$647$			40.7448i			1.60184i	−0.598769	+	0.800921i	$0.704343\pi$
$648$			85.0057i			3.33934i
$649$	32.5230			1.27664
$650$	−25.5472	−	39.5848i	−1.00204	−	1.55264i
$651$	2.65028			0.103873
$652$		−	30.9447i		−	1.21189i
$653$		−	26.8742i		−	1.05167i	−0.850587	−	0.525834i	$-0.823753\pi$
$653$		−	26.8742i		−	1.05167i	0.850587	−	0.525834i	$-0.176247\pi$
$654$	6.55906			0.256480
$655$	21.6657	+	11.8033i	0.846548	+	0.461195i
$656$		0			0
$657$			1.77937i			0.0694197i
$658$		−	20.7649i		−	0.809501i
$659$	−29.1558			−1.13575			−0.567874	−	0.823116i	$-0.692234\pi$
$659$	−29.1558			−1.13575			−0.567874	+	0.823116i	$0.692234\pi$
$660$	5.32869	−	9.78109i	0.207419	−	0.380729i
$661$	19.9035			0.774155			0.387078	−	0.922047i	$-0.373485\pi$
$661$	19.9035			0.774155			0.387078	+	0.922047i	$0.373485\pi$
$662$			46.9878i			1.82623i
$663$		−	2.21174i		−	0.0858969i
$664$	−24.5292			−0.951917
$665$	−1.34972	+	2.47748i	−0.0523399	+	0.0960727i
$666$	15.1611			0.587480
$667$		−	7.41031i		−	0.286928i
$668$			8.58012i			0.331975i
$669$	−1.70863			−0.0660594
$670$	−43.2470	−	23.5607i	−1.67078	−	0.910231i
$671$	−38.5538			−1.48835
$672$		−	13.2865i		−	0.512539i
$673$			8.71383i			0.335893i	0.985796	+	0.167947i	$0.0537136\pi$
$673$			8.71383i			0.335893i	−0.985796	+	0.167947i	$0.946286\pi$
$674$	62.5967			2.41114
$675$	−6.72047	+	4.33725i	−0.258671	+	0.166941i
$676$	−8.12499			−0.312500
$677$			9.70565i			0.373018i	0.982453	+	0.186509i	$0.0597174\pi$
$677$			9.70565i			0.373018i	−0.982453	+	0.186509i	$0.940283\pi$
$678$		−	7.52932i		−	0.289162i
$679$	−24.5538			−0.942287
$680$	−48.1650	−	26.2400i	−1.84704	−	1.00626i
$681$	6.71782			0.257427
$682$			47.3233i			1.81210i
$683$			9.53014i			0.364661i	0.983237	+	0.182330i	$0.0583640\pi$
$683$			9.53014i			0.364661i	−0.983237	+	0.182330i	$0.941636\pi$
$684$	−11.2102			−0.428634
$685$	12.6994	−	23.3105i	0.485221	−	0.890648i
$686$	−54.4081			−2.07731
$687$		−	0.579108i		−	0.0220944i
$688$			58.4728i			2.22925i
$689$	−2.98550			−0.113739
$690$	−5.92716	+	10.8796i	−0.225643	+	0.414180i
$691$	8.50459			0.323530			0.161765	−	0.986829i	$-0.448281\pi$
$691$	8.50459			0.323530			0.161765	+	0.986829i	$0.448281\pi$
$692$			49.5990i			1.88547i
$693$			17.7986i			0.676112i
$694$	−33.3743			−1.26687
$695$	29.1496	+	15.8805i	1.10571	+	0.602383i
$696$	−2.74770			−0.104151
$697$		0			0
$698$		−	4.34460i		−	0.164446i
$699$	−1.44094			−0.0545014
$700$	−44.5721	+	28.7659i	−1.68467	+	1.08725i
$701$	−28.6266			−1.08121			−0.540606	−	0.841276i	$-0.681805\pi$
$701$	−28.6266			−1.08121			−0.540606	+	0.841276i	$0.681805\pi$
$702$		−	15.0733i		−	0.568906i
$703$			1.26172i			0.0475866i
$704$	127.613			4.80960
$705$	2.12465	+	1.15750i	0.0800191	+	0.0435940i
$706$	21.2224			0.798716
$707$		−	9.05845i		−	0.340678i
$708$			15.3161i			0.575615i
$709$	−14.9855			−0.562792			−0.281396	−	0.959592i	$-0.590798\pi$
$709$	−14.9855			−0.562792			−0.281396	+	0.959592i	$0.590798\pi$
$710$	−5.92716	+	10.8796i	−0.222442	+	0.408305i
$711$	−25.1795			−0.944303
$712$			86.5824i			3.24481i
$713$		−	38.9211i		−	1.45761i
$714$	−3.36810			−0.126048
$715$	11.8333	−	21.7206i	0.442540	−	0.812305i
$716$	−53.8851			−2.01378
$717$			0.539789i			0.0201588i
$718$			48.7384i			1.81890i
$719$	36.7486			1.37049			0.685246	−	0.728312i	$-0.259695\pi$
$719$	36.7486			1.37049			0.685246	+	0.728312i	$0.259695\pi$
$720$	−96.8736	−	52.7762i	−3.61027	−	1.96685i
$721$	−27.8359			−1.03666
$722$			51.3750i			1.91198i
$723$		−	1.82780i		−	0.0679766i
$724$	−84.7617			−3.15014
$725$	2.71128	+	4.20107i	0.100694	+	0.156024i
$726$	−0.315951			−0.0117260
$727$		−	39.1647i		−	1.45254i	−0.687410	−	0.726270i	$-0.741252\pi$
$727$		−	39.1647i		−	1.45254i	0.687410	−	0.726270i	$-0.258748\pi$
$728$		−	64.7379i		−	2.39935i
$729$	23.1457			0.857248
$730$	−3.30676	−	1.80151i	−0.122389	−	0.0666768i
$731$	8.35891			0.309165
$732$		−	18.1562i		−	0.671073i
$733$		−	5.38071i		−	0.198741i	−0.995051	−	0.0993705i	$-0.968317\pi$
$733$		−	5.38071i		−	0.198741i	0.995051	−	0.0993705i	$-0.0316829\pi$
$734$	27.3927			1.01108
$735$	1.01184	−	1.85729i	0.0373224	−	0.0685072i
$736$	−195.121			−7.19227
$737$		−	25.8561i		−	0.952421i
$738$		0			0
$739$	9.93336			0.365404			0.182702	−	0.983168i	$-0.441516\pi$
$739$	9.93336			0.365404			0.182702	+	0.983168i	$0.441516\pi$
$740$	−11.3497	+	20.8330i	−0.417224	+	0.765837i
$741$	0.619500			0.0227579
$742$			4.54640i			0.166904i
$743$		−	43.4963i		−	1.59573i	−0.602839	−	0.797863i	$-0.705964\pi$
$743$		−	43.4963i		−	1.59573i	0.602839	−	0.797863i	$-0.294036\pi$
$744$	−14.4318			−0.529094
$745$	33.9245	+	18.4819i	1.24290	+	0.677124i
$746$	45.1128			1.65170
$747$			7.05266i			0.258043i
$748$		−	44.4685i		−	1.62593i
$749$	3.49541			0.127719
$750$	−0.620395	−	8.33652i	−0.0226536	−	0.304407i
$751$	11.3743			0.415054			0.207527	−	0.978229i	$-0.433459\pi$
$751$	11.3743			0.415054			0.207527	+	0.978229i	$0.433459\pi$
$752$			67.5705i			2.46404i
$753$			5.46846i			0.199282i
$754$	−9.42256			−0.343149
$755$	−0.990811	−	0.539789i	−0.0360593	−	0.0196449i
$756$	−16.9724			−0.617281
$757$		−	10.0699i		−	0.365998i	−0.983113	−	0.182999i	$-0.941420\pi$
$757$		−	10.0699i		−	0.365998i	0.983113	−	0.182999i	$-0.0585805\pi$
$758$		−	7.00671i		−	0.254495i
$759$	−6.50459			−0.236102
$760$	7.34972	−	13.4908i	0.266602	−	0.489363i
$761$	−27.0092			−0.979082			−0.489541	−	0.871980i	$-0.662836\pi$
$761$	−27.0092			−0.979082			−0.489541	+	0.871980i	$0.662836\pi$
$762$			13.9625i			0.505808i
$763$		−	16.4007i		−	0.593744i
$764$	−59.7516			−2.16174
$765$	−7.54456	+	13.8485i	−0.272774	+	0.500692i
$766$	−15.5384			−0.561424
$767$			34.0121i			1.22811i
$768$			20.7215i			0.747721i
$769$	−25.7086			−0.927077			−0.463538	−	0.886077i	$-0.653420\pi$
$769$	−25.7086			−0.927077			−0.463538	+	0.886077i	$0.653420\pi$
$770$	−33.0767	−	18.0200i	−1.19200	−	0.649397i
$771$	−5.24610			−0.188934
$772$		−	102.908i		−	3.70375i
$773$		−	32.8185i		−	1.18040i	−0.807257	−	0.590200i	$-0.799049\pi$
$773$		−	32.8185i		−	1.18040i	0.807257	−	0.590200i	$-0.200951\pi$
$774$	28.1335			1.01124
$775$	14.2405	+	22.0652i	0.511532	+	0.792607i
$776$	133.704			4.79970
$777$			0.943390i			0.0338439i
$778$		−	33.2442i		−	1.19186i
$779$		0			0
$780$	10.2289	+	5.57268i	0.366255	+	0.199534i
$781$	−6.50459			−0.232753
$782$			49.4628i			1.76878i
$783$			1.59971i			0.0571688i
$784$	59.0675			2.10955
$785$	−19.2040	+	35.2500i	−0.685421	+	1.25813i
$786$	−8.24998			−0.294267
$787$		−	21.1973i		−	0.755602i	−0.925887	−	0.377801i	$-0.876680\pi$
$787$		−	21.1973i		−	0.755602i	0.925887	−	0.377801i	$-0.123320\pi$
$788$		−	96.3578i		−	3.43261i
$789$	−2.23691			−0.0796360
$790$	25.4928	−	46.7933i	0.906991	−	1.66483i
$791$	−18.8267			−0.669402
$792$		−	96.9197i		−	3.44389i
$793$		−	40.3190i		−	1.43177i
$794$	−77.1987			−2.73968
$795$	−0.465185	−	0.253431i	−0.0164984	−	0.00898825i
$796$	42.5354			1.50763
$797$			21.7305i			0.769732i	0.922972	+	0.384866i	$0.125752\pi$
$797$			21.7305i			0.769732i	−0.922972	+	0.384866i	$0.874248\pi$
$798$		−	0.943390i		−	0.0333956i
$799$	9.65947			0.341727
$800$	110.619	−	71.3910i	3.91096	−	2.52405i
$801$	24.8943			0.879596
$802$			43.2657i			1.52777i
$803$		−	1.97701i		−	0.0697673i
$804$	12.1765			0.429431
$805$	27.2040	+	14.8206i	0.958816	+	0.522358i
$806$	−49.4901			−1.74321
$807$			6.43814i			0.226633i
$808$			49.3266i			1.73530i
$809$	7.20403			0.253280			0.126640	−	0.991949i	$-0.459581\pi$
$809$	7.20403			0.253280			0.126640	+	0.991949i	$0.459581\pi$
$810$	−24.7450	+	45.4209i	−0.869452	+	1.59593i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$			10.6097i			0.372328i
$813$		−	0.241121i		−	0.00845647i
$814$	−16.8451			−0.590421
$815$	5.83328	−	10.7073i	0.204331	−	0.375060i
$816$	10.9600			0.383678
$817$			2.34130i			0.0819116i
$818$		−	84.6447i		−	2.95953i
$819$	−18.6135			−0.650409
$820$		0			0
$821$	24.1220			0.841864			0.420932	−	0.907092i	$-0.361703\pi$
$821$	24.1220			0.841864			0.420932	+	0.907092i	$0.361703\pi$
$822$			8.87631i			0.309597i
$823$			17.2300i			0.600600i	0.953845	+	0.300300i	$0.0970868\pi$
$823$			17.2300i			0.600600i	−0.953845	+	0.300300i	$0.902913\pi$
$824$	151.577			5.28043
$825$	3.68760	−	2.37990i	0.128386	−	0.0828575i
$826$	51.7945			1.80216
$827$			3.46931i			0.120640i	0.998179	+	0.0603198i	$0.0192121\pi$
$827$			3.46931i			0.120640i	−0.998179	+	0.0603198i	$0.980788\pi$
$828$			123.094i			4.27782i
$829$	−7.52619			−0.261395			−0.130698	−	0.991422i	$-0.541722\pi$
$829$	−7.52619			−0.261395			−0.130698	+	0.991422i	$0.541722\pi$
$830$	−13.1066	−	7.14041i	−0.454937	−	0.247847i
$831$	0.960030			0.0333031
$832$			133.456i			4.62676i
$833$		−	8.44393i		−	0.292565i
$834$	−11.0997			−0.384353
$835$	−1.61741	+	2.96884i	−0.0559727	+	0.102741i
$836$	12.4554			0.430780
$837$			8.40213i			0.290420i
$838$		−	27.8397i		−	0.961707i
$839$	9.61121			0.331816			0.165908	−	0.986141i	$-0.446945\pi$
$839$	9.61121			0.331816			0.165908	+	0.986141i	$0.446945\pi$
$840$	5.49541	−	10.0871i	0.189610	−	0.348038i
$841$	1.00000			0.0344828
$842$			44.8654i			1.54617i
$843$			2.09521i			0.0721630i
$844$	−102.700			−3.53509
$845$	−2.81136	−	1.53161i	−0.0967136	−	0.0526891i
$846$	32.5108			1.11774
$847$			0.790023i			0.0271455i
$848$		−	14.7943i		−	0.508039i
$849$	−8.30975			−0.285190
$850$	−18.0974	−	28.0415i	−0.620736	−	0.961816i
$851$	13.8543			0.474920
$852$		−	3.06322i		−	0.104944i
$853$		−	20.8330i		−	0.713309i	−0.934236	−	0.356654i	$-0.883917\pi$
$853$		−	20.8330i		−	0.713309i	0.934236	−	0.356654i	$-0.116083\pi$
$854$	−61.3989			−2.10103
$855$	−3.87889	−	2.11320i	−0.132655	−	0.0722699i
$856$	−19.0338			−0.650561
$857$		−	33.0424i		−	1.12871i	−0.825533	−	0.564354i	$-0.809125\pi$
$857$		−	33.0424i		−	1.12871i	0.825533	−	0.564354i	$-0.190875\pi$
$858$			8.27090i			0.282364i
$859$	−49.8061			−1.69936			−0.849680	−	0.527298i	$-0.823205\pi$
$859$	−49.8061			−1.69936			−0.849680	+	0.527298i	$0.823205\pi$
$860$	−21.0610	+	38.6586i	−0.718174	+	1.31825i
$861$		0			0
$862$		−	30.9882i		−	1.05546i
$863$			9.03631i			0.307599i	0.988102	+	0.153800i	$0.0491511\pi$
$863$			9.03631i			0.307599i	−0.988102	+	0.153800i	$0.950849\pi$
$864$	42.1220			1.43302
$865$	−9.34972	+	17.1619i	−0.317900	+	0.583522i
$866$	38.8697			1.32085
$867$			3.02143i			0.102613i
$868$			55.7254i			1.89144i
$869$	27.9763			0.949032
$870$	−1.46817	−	0.799853i	−0.0497757	−	0.0271176i
$871$	27.0400			0.916214
$872$			89.3076i			3.02434i
$873$		−	38.4428i		−	1.30109i
$874$	−13.8543			−0.468629
$875$	−20.8451	+	1.55127i	−0.704694	+	0.0524426i
$876$	0.931040			0.0314569
$877$		−	24.0809i		−	0.813153i	−0.913617	−	0.406576i	$-0.866722\pi$
$877$		−	24.0809i		−	0.813153i	0.913617	−	0.406576i	$-0.133278\pi$
$878$			26.7601i			0.903111i
$879$	−1.70863			−0.0576306
$880$	107.634	+	58.6385i	3.62834	+	1.97670i
$881$	−0.814344			−0.0274360			−0.0137180	−	0.999906i	$-0.504367\pi$
$881$	−0.814344			−0.0274360			−0.0137180	+	0.999906i	$0.504367\pi$
$882$		−	28.4197i		−	0.956940i
$883$		−	31.8751i		−	1.07268i	−0.844001	−	0.536341i	$-0.819806\pi$
$883$		−	31.8751i		−	1.07268i	0.844001	−	0.536341i	$-0.180194\pi$
$884$	46.5046			1.56412
$885$	−2.88719	+	5.29959i	−0.0970517	+	0.178144i
$886$	−27.0154			−0.907600
$887$		−	45.6358i		−	1.53230i	−0.642661	−	0.766150i	$-0.722170\pi$
$887$		−	45.6358i		−	1.53230i	0.642661	−	0.766150i	$-0.277830\pi$
$888$		−	5.13711i		−	0.172390i
$889$	34.9127			1.17093
$890$	−25.2040	+	46.2634i	−0.844841	+	1.55075i
$891$	−27.1558			−0.909753
$892$		−	35.9260i		−	1.20289i
$893$			2.70558i			0.0905387i
$894$	−12.9180			−0.432041
$895$	−18.6450	−	10.1577i	−0.623233	−	0.339534i
$896$	104.773			3.50023
$897$		−	6.80243i		−	0.227126i
$898$			24.5550i			0.819412i
$899$	5.25230			0.175174
$900$	−45.0377	−	69.7848i	−1.50126	−	2.32616i
$901$	−2.11491			−0.0704577
$902$		0			0
$903$			1.75059i			0.0582561i
$904$	102.519			3.40972
$905$	−29.3287	−	15.9781i	−0.974919	−	0.531131i
$906$	0.377287			0.0125345
$907$			18.5820i			0.617004i	0.951224	+	0.308502i	$0.0998276\pi$
$907$			18.5820i			0.617004i	−0.951224	+	0.308502i	$0.900172\pi$
$908$			141.250i			4.68756i
$909$	14.1824			0.470402
$910$	18.8451	−	34.5912i	0.624710	−	1.14669i
$911$	−45.6296			−1.51178			−0.755888	−	0.654701i	$-0.772794\pi$
$911$	−45.6296			−1.51178			−0.755888	+	0.654701i	$0.772794\pi$
$912$			3.06986i			0.101653i
$913$		−	7.83605i		−	0.259335i
$914$	−67.8851			−2.24544
$915$	3.42256	−	6.28230i	0.113146	−	0.207686i
$916$	12.1765			0.402322
$917$			20.6287i			0.681221i
$918$		−	10.6778i		−	0.352420i
$919$	−24.6994			−0.814759			−0.407380	−	0.913259i	$-0.633557\pi$
$919$	−24.6994			−0.814759			−0.407380	+	0.913259i	$0.633557\pi$
$920$	−148.136	−	80.7037i	−4.88390	−	2.66072i
$921$	3.39178			0.111763
$922$			103.659i			3.41383i
$923$		−	6.80243i		−	0.223905i
$924$	9.31296			0.306374
$925$	−7.85431	+	5.06901i	−0.258248	+	0.166668i
$926$	6.80217			0.223533
$927$		−	43.5816i		−	1.43141i
$928$		−	26.3311i		−	0.864360i
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$	−7.71128	−	4.20107i	−0.252863	−	0.137758i
$931$	2.36511			0.0775133
$932$		−	30.2975i		−	0.992429i
$933$			6.58096i			0.215451i
$934$	95.3506			3.11997
$935$	8.38259	−	15.3867i	0.274140	−	0.503199i
$936$	101.357			3.31297
$937$			46.4389i			1.51709i	0.651620	+	0.758546i	$0.274090\pi$
$937$			46.4389i			1.51709i	−0.651620	+	0.758546i	$0.725910\pi$
$938$		−	41.1772i		−	1.34448i
$939$	9.35503			0.305290
$940$	−24.3379	+	44.6735i	−0.793814	+	1.45709i
$941$	−14.2861			−0.465712			−0.232856	−	0.972511i	$-0.574807\pi$
$941$	−14.2861			−0.465712			−0.232856	+	0.972511i	$0.574807\pi$
$942$		−	13.4227i		−	0.437336i
$943$		0			0
$944$	−168.543			−5.48561
$945$	−5.87269	−	3.19941i	−0.191039	−	0.104077i
$946$	−31.2585			−1.01630
$947$			29.3713i			0.954440i	0.878784	+	0.477220i	$0.158356\pi$
$947$			29.3713i			0.954440i	−0.878784	+	0.477220i	$0.841644\pi$
$948$			13.1750i			0.427903i
$949$	2.06754			0.0671151
$950$	7.85431	−	5.06901i	0.254828	−	0.164460i
$951$	−6.96003			−0.225694
$952$		−	45.8598i		−	1.48632i
$953$			22.5911i			0.731796i	0.930655	+	0.365898i	$0.119238\pi$
$953$			22.5911i			0.731796i	−0.930655	+	0.365898i	$0.880762\pi$
$954$	−7.11812			−0.230458
$955$	−20.6749	−	11.2636i	−0.669023	−	0.364480i
$956$	−11.3497			−0.367076
$957$		−	0.877777i		−	0.0283745i
$958$		−	26.0867i		−	0.842821i
$959$	22.1948			0.716709
$960$	−11.3287	+	20.7944i	−0.365632	+	0.671137i
$961$	−3.41337			−0.110109
$962$		−	17.6164i		−	0.567976i
$963$			5.47261i			0.176353i
$964$	38.4318			1.23780
$965$	19.3989	−	35.6077i	0.624472	−	1.14625i
$966$	−10.3589			−0.333292
$967$			48.4316i			1.55746i	0.627362	+	0.778728i	$0.284135\pi$
$967$			48.4316i			1.55746i	−0.627362	+	0.778728i	$0.715865\pi$
$968$		−	4.30197i		−	0.138270i
$969$	0.438848			0.0140978
$970$	71.4418	+	38.9211i	2.29386	+	1.24968i
$971$	47.0829			1.51096			0.755482	−	0.655170i	$-0.227403\pi$
$971$	47.0829			1.51096			0.755482	+	0.655170i	$0.227403\pi$
$972$		−	40.0229i		−	1.28373i
$973$			27.7545i			0.889767i
$974$	−91.6734			−2.93741
$975$	2.48887	+	3.85644i	0.0797076	+	0.123505i
$976$	199.796			6.39532
$977$		−	51.1987i		−	1.63799i	−0.573800	−	0.818995i	$-0.694532\pi$
$977$		−	51.1987i		−	1.63799i	0.573800	−	0.818995i	$-0.305468\pi$
$978$			4.07719i			0.130374i
$979$	−27.6595			−0.884000
$980$	39.0518	+	21.2752i	1.24746	+	0.679612i
$981$	25.6778			0.819831
$982$		−	80.2320i		−	2.56031i
$983$			23.5123i			0.749926i	0.927040	+	0.374963i	$0.122345\pi$
$983$			23.5123i			0.749926i	−0.927040	+	0.374963i	$0.877655\pi$
$984$		0			0
$985$	18.1641	−	33.3411i	0.578755	−	1.06234i
$986$	−6.67486			−0.212571
$987$			2.02297i			0.0643918i
$988$			13.0257i			0.414404i
$989$	25.7086			0.817487
$990$	28.2132	−	51.7869i	0.896675	−	1.64590i
$991$	−7.64109			−0.242727			−0.121364	−	0.992608i	$-0.538727\pi$
$991$	−7.64109			−0.242727			−0.121364	+	0.992608i	$0.538727\pi$
$992$		−	138.299i		−	4.39099i
$993$		−	4.57766i		−	0.145268i
$994$	−10.3589			−0.328565
$995$	14.7178	+	8.01819i	0.466586	+	0.254194i
$996$	3.69025			0.116930
$997$			3.71043i			0.117510i	0.998272	+	0.0587552i	$0.0187131\pi$
$997$			3.71043i			0.117510i	−0.998272	+	0.0587552i	$0.981287\pi$
$998$			93.8393i			2.97043i
$999$	−2.99081			−0.0946251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.b.c.59.1	✓	6
3.2	odd	2		1305.2.c.h.784.6		6
4.3	odd	2		2320.2.d.g.929.3		6
5.2	odd	4		725.2.a.l.1.6		6
5.3	odd	4		725.2.a.l.1.1		6
5.4	even	2	inner	145.2.b.c.59.6	yes	6
15.2	even	4		6525.2.a.bt.1.1		6
15.8	even	4		6525.2.a.bt.1.6		6
15.14	odd	2		1305.2.c.h.784.1		6
20.19	odd	2		2320.2.d.g.929.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.c.59.1	✓	6	1.1	even	1	trivial
145.2.b.c.59.6	yes	6	5.4	even	2	inner
725.2.a.l.1.1		6	5.3	odd	4
725.2.a.l.1.6		6	5.2	odd	4
1305.2.c.h.784.1		6	15.14	odd	2
1305.2.c.h.784.6		6	3.2	odd	2
2320.2.d.g.929.3		6	4.3	odd	2
2320.2.d.g.929.4		6	20.19	odd	2
6525.2.a.bt.1.1		6	15.2	even	4
6525.2.a.bt.1.6		6	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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.77035i q^{2} +0.269894i q^{3} -5.67486 q^{4} +(-1.96358 - 1.06975i) q^{5} +0.747703 q^{6} -1.86960i q^{7} +10.1807i q^{8} +2.92716 q^{9} +(-2.96358 + 5.43981i) q^{10} -3.25230 q^{11} -1.53161i q^{12} -3.40121i q^{13} -5.17945 q^{14} +(0.288719 - 0.529959i) q^{15} +16.8543 q^{16} -2.40939i q^{17} -8.10926i q^{18} +0.674860 q^{19} +(11.1430 + 6.07067i) q^{20} +0.504595 q^{21} +9.01001i q^{22} -7.41031i q^{23} -2.74770 q^{24} +(2.71128 + 4.20107i) q^{25} -9.42256 q^{26} +1.59971i q^{27} +10.6097i q^{28} +1.00000 q^{29} +(-1.46817 - 0.799853i) q^{30} +5.25230 q^{31} -26.3311i q^{32} -0.877777i q^{33} -6.67486 q^{34} +(-2.00000 + 3.67111i) q^{35} -16.6112 q^{36} +1.86960i q^{37} -1.86960i q^{38} +0.917968 q^{39} +(10.8907 - 19.9905i) q^{40} -1.39791i q^{42} +3.46931i q^{43} +18.4563 q^{44} +(-5.74770 - 3.13132i) q^{45} -20.5292 q^{46} +4.00910i q^{47} +4.54888i q^{48} +3.50459 q^{49} +(11.6384 - 7.51121i) q^{50} +0.650280 q^{51} +19.3014i q^{52} -0.877777i q^{53} +4.43175 q^{54} +(6.38614 + 3.47914i) q^{55} +19.0338 q^{56} +0.182141i q^{57} -2.77035i q^{58} -10.0000 q^{59} +(-1.63844 + 3.00744i) q^{60} +11.8543 q^{61} -14.5507i q^{62} -5.47261i q^{63} -39.2378 q^{64} +(-3.63844 + 6.67855i) q^{65} -2.43175 q^{66} +7.95010i q^{67} +13.6729i q^{68} +2.00000 q^{69} +(10.1703 + 5.54071i) q^{70} +2.00000 q^{71} +29.8004i q^{72} +0.607882i q^{73} +5.17945 q^{74} +(-1.13384 + 0.731759i) q^{75} -3.82973 q^{76} +6.08050i q^{77} -2.54310i q^{78} -8.60202 q^{79} +(-33.0948 - 18.0299i) q^{80} +8.34972 q^{81} +2.40939i q^{83} -2.86350 q^{84} +(-2.57744 + 4.73102i) q^{85} +9.61121 q^{86} +0.269894i q^{87} -33.1105i q^{88} +8.50459 q^{89} +(-8.67486 + 15.9232i) q^{90} -6.35891 q^{91} +42.0525i q^{92} +1.41757i q^{93} +11.1066 q^{94} +(-1.32514 - 0.721929i) q^{95} +7.10661 q^{96} -13.1332i q^{97} -9.70897i q^{98} -9.51998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 14 q^{4} + 3 q^{5} + 14 q^{6} - 12 q^{9} - 3 q^{10} - 10 q^{11} + 8 q^{14} + 7 q^{15} + 42 q^{16} - 16 q^{19} + 13 q^{20} - 16 q^{21} - 26 q^{24} + 11 q^{25} - 46 q^{26} + 6 q^{29} + 25 q^{30} + 22 q^{31}+ \cdots - 16 q^{99}+O(q^{100}) \) 6 * q - 14 * q^4 + 3 * q^5 + 14 * q^6 - 12 * q^9 - 3 * q^10 - 10 * q^11 + 8 * q^14 + 7 * q^15 + 42 * q^16 - 16 * q^19 + 13 * q^20 - 16 * q^21 - 26 * q^24 + 11 * q^25 - 46 * q^26 + 6 * q^29 + 25 * q^30 + 22 * q^31 - 20 * q^34 - 12 * q^35 - 12 * q^36 + 14 * q^39 + 21 * q^40 + 2 * q^44 - 44 * q^45 - 44 * q^46 + 2 * q^49 + 35 * q^50 + 44 * q^51 - 22 * q^54 + 13 * q^55 + 16 * q^56 - 60 * q^59 + 25 * q^60 + 12 * q^61 - 38 * q^64 + 13 * q^65 + 34 * q^66 + 12 * q^69 + 60 * q^70 + 12 * q^71 - 8 * q^74 + 9 * q^75 - 24 * q^76 - 2 * q^79 - 55 * q^80 + 10 * q^81 + 80 * q^84 - 26 * q^85 - 30 * q^86 + 32 * q^89 - 32 * q^90 + 40 * q^91 - 2 * q^94 - 28 * q^95 - 26 * q^96 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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