LMFDB - Embedded newform 605.2.g.l.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.1
Root			$1.14412 - 0.831254i$ of defining polynomial
Character	$\chi$	$=$	605.251
Dual form			605.2.g.l.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.746033 + 2.29605i) q^{2} +(2.28825 - 1.66251i) q^{3} +(-3.09726 - 2.25029i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(2.11010 + 6.49422i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(3.57117 - 2.59461i) q^{8} +(1.54508 - 4.75528i) q^{9} +O(q^{10})$	\(q+(-0.746033 + 2.29605i) q^{2} +(2.28825 - 1.66251i) q^{3} +(-3.09726 - 2.25029i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(2.11010 + 6.49422i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(3.57117 - 2.59461i) q^{8} +(1.54508 - 4.75528i) q^{9} +2.41421 q^{10} -10.8284 q^{12} +(0.362036 - 1.11423i) q^{13} +(3.90628 - 2.83808i) q^{14} +(-2.28825 - 1.66251i) q^{15} +(0.927051 + 2.85317i) q^{16} +(-2.11010 - 6.49422i) q^{17} +(9.76570 + 7.09520i) q^{18} +(-1.18305 + 3.64105i) q^{20} -5.65685 q^{21} -2.82843 q^{23} +(3.85816 - 11.8742i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(2.28825 + 1.66251i) q^{26} +(-1.74806 - 5.37999i) q^{27} +(2.36610 + 7.28210i) q^{28} +(-2.95846 - 2.14944i) q^{29} +(5.52431 - 4.01365i) q^{30} +1.58579 q^{32} +16.4853 q^{34} +(-0.618034 + 1.90211i) q^{35} +(-15.4863 + 11.2515i) q^{36} +(6.19453 + 4.50059i) q^{37} +(-1.02399 - 3.15152i) q^{39} +(-3.57117 - 2.59461i) q^{40} +(4.85410 - 3.52671i) q^{41} +(4.22020 - 12.9884i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(2.11010 - 6.49422i) q^{46} +(-2.28825 + 1.66251i) q^{47} +(6.86474 + 4.98752i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(-0.746033 - 2.29605i) q^{50} +(-15.6251 - 11.3523i) q^{51} +(-3.62867 + 2.63638i) q^{52} +(3.60217 - 11.0863i) q^{53} +13.6569 q^{54} -8.82843 q^{56} +(7.14235 - 5.18922i) q^{58} +(-1.34042 - 0.973874i) q^{59} +(3.34617 + 10.2984i) q^{60} +(2.87809 + 8.85786i) q^{61} +(-8.09017 + 5.87785i) q^{63} +(-3.03715 + 9.34739i) q^{64} -1.17157 q^{65} +12.4853 q^{67} +(-8.07836 + 24.8626i) q^{68} +(-6.47214 + 4.70228i) q^{69} +(-3.90628 - 2.83808i) q^{70} +(3.49613 + 10.7600i) q^{71} +(-6.82034 - 20.9908i) q^{72} +(-0.947822 - 0.688633i) q^{73} +(-14.9549 + 10.8654i) q^{74} +(-0.874032 + 2.68999i) q^{75} +8.00000 q^{78} +(-1.23607 + 3.80423i) q^{79} +(2.42705 - 1.76336i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(4.47620 + 13.7763i) q^{82} +(1.85410 + 5.70634i) q^{83} +(17.5208 + 12.7296i) q^{84} +(-5.52431 + 4.01365i) q^{85} +(-4.47620 + 13.7763i) q^{86} -10.3431 q^{87} -13.3137 q^{89} +(3.73017 - 11.4803i) q^{90} +(-1.89564 + 1.37727i) q^{91} +(8.76038 + 6.36479i) q^{92} +(-2.11010 - 6.49422i) q^{94} +(3.62867 - 2.63638i) q^{96} +(1.13003 - 3.47788i) q^{97} +7.24264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9 + 8 * q^10 - 64 * q^12 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 8 * q^17 + 10 * q^18 + 2 * q^20 - 8 * q^24 - 2 * q^25 - 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^32 + 64 * q^34 + 4 * q^35 - 10 * q^36 + 4 * q^37 - 16 * q^39 - 6 * q^40 + 12 * q^41 - 16 * q^42 + 48 * q^43 - 40 * q^45 - 8 * q^46 + 6 * q^49 + 2 * q^50 - 16 * q^51 + 8 * q^52 - 12 * q^53 + 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 20 * q^63 + 14 * q^64 - 32 * q^65 + 32 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 + 30 * q^72 - 8 * q^73 - 20 * q^74 + 64 * q^78 + 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 - 12 * q^83 + 32 * q^84 - 8 * q^85 + 12 * q^86 - 128 * q^87 - 16 * q^89 - 10 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^94 - 8 * q^96 + 4 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.746033	+	2.29605i	−0.527525	+	1.62356i	0.231743	+	0.972777i	$0.425557\pi$
$2$	−0.746033	+	2.29605i	−0.527525	+	1.62356i	−0.759268	+	0.650778i	$0.774443\pi$
$3$	2.28825	−	1.66251i	1.32112	−	0.959849i	0.321202	−	0.947011i	$-0.395913\pi$
$3$	2.28825	−	1.66251i	1.32112	−	0.959849i	0.999918	−	0.0128385i	$-0.00408672\pi$
$4$	−3.09726	−	2.25029i	−1.54863	−	1.12515i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	2.11010	+	6.49422i	0.861445	+	2.65125i
$7$	−1.61803	−	1.17557i	−0.611559	−	0.444324i	0.238404	−	0.971166i	$-0.423376\pi$
$7$	−1.61803	−	1.17557i	−0.611559	−	0.444324i	−0.849963	+	0.526842i	$0.823376\pi$
$8$	3.57117	−	2.59461i	1.26260	−	0.917333i
$9$	1.54508	−	4.75528i	0.515028	−	1.58509i
$10$	2.41421			0.763441
$11$		0			0
$11$		0			0
$12$	−10.8284			−3.12590
$13$	0.362036	−	1.11423i	0.100411	−	0.309032i	−0.888215	−	0.459428i	$-0.848055\pi$
$13$	0.362036	−	1.11423i	0.100411	−	0.309032i	0.988626	+	0.150395i	$0.0480546\pi$
$14$	3.90628	−	2.83808i	1.04400	−	0.758508i
$15$	−2.28825	−	1.66251i	−0.590822	−	0.429258i
$16$	0.927051	+	2.85317i	0.231763	+	0.713292i
$17$	−2.11010	−	6.49422i	−0.511774	−	1.57508i	−0.789075	−	0.614297i	$-0.789440\pi$
$17$	−2.11010	−	6.49422i	−0.511774	−	1.57508i	0.277301	−	0.960783i	$-0.410560\pi$
$18$	9.76570	+	7.09520i	2.30180	+	1.67235i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	−1.18305	+	3.64105i	−0.264538	+	0.814164i
$21$	−5.65685			−1.23443
$22$		0			0
$23$	−2.82843			−0.589768			−0.294884	−	0.955533i	$-0.595281\pi$
$23$	−2.82843			−0.589768			−0.294884	+	0.955533i	$0.595281\pi$
$24$	3.85816	−	11.8742i	0.787544	−	2.42381i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	2.28825	+	1.66251i	0.448762	+	0.326045i
$27$	−1.74806	−	5.37999i	−0.336415	−	1.03538i
$28$	2.36610	+	7.28210i	0.447151	+	1.37619i
$29$	−2.95846	−	2.14944i	−0.549372	−	0.399142i	0.278182	−	0.960528i	$-0.410268\pi$
$29$	−2.95846	−	2.14944i	−0.549372	−	0.399142i	−0.827554	+	0.561386i	$0.810268\pi$
$30$	5.52431	−	4.01365i	1.00860	−	0.732789i
$31$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$31$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$32$	1.58579			0.280330
$33$		0			0
$34$	16.4853			2.82720
$35$	−0.618034	+	1.90211i	−0.104467	+	0.321516i
$36$	−15.4863	+	11.2515i	−2.58105	+	1.87524i
$37$	6.19453	+	4.50059i	1.01837	+	0.739892i	0.965949	−	0.258733i	$-0.0833050\pi$
$37$	6.19453	+	4.50059i	1.01837	+	0.739892i	0.0524248	+	0.998625i	$0.483305\pi$
$38$		0			0
$39$	−1.02399	−	3.15152i	−0.163970	−	0.504648i
$40$	−3.57117	−	2.59461i	−0.564652	−	0.410244i
$41$	4.85410	−	3.52671i	0.758083	−	0.550780i	−0.140238	−	0.990118i	$-0.544787\pi$
$41$	4.85410	−	3.52671i	0.758083	−	0.550780i	0.898322	+	0.439338i	$0.144787\pi$
$42$	4.22020	−	12.9884i	0.651191	−	2.00416i
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$	−5.00000			−0.745356
$46$	2.11010	−	6.49422i	0.311117	−	0.957521i
$47$	−2.28825	+	1.66251i	−0.333775	+	0.242502i	−0.742031	−	0.670366i	$-0.766137\pi$
$47$	−2.28825	+	1.66251i	−0.333775	+	0.242502i	0.408256	+	0.912868i	$0.366137\pi$
$48$	6.86474	+	4.98752i	0.990839	+	0.719887i
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$	−0.746033	−	2.29605i	−0.105505	−	0.324711i
$51$	−15.6251	−	11.3523i	−2.18795	−	1.58964i
$52$	−3.62867	+	2.63638i	−0.503206	+	0.365600i
$53$	3.60217	−	11.0863i	0.494796	−	1.52282i	−0.322480	−	0.946576i	$-0.604516\pi$
$53$	3.60217	−	11.0863i	0.494796	−	1.52282i	0.817275	−	0.576248i	$-0.195484\pi$
$54$	13.6569			1.85846
$55$		0			0
$56$	−8.82843			−1.17975
$57$		0			0
$58$	7.14235	−	5.18922i	0.937836	−	0.681378i
$59$	−1.34042	−	0.973874i	−0.174508	−	0.126788i	0.497103	−	0.867692i	$-0.334397\pi$
$59$	−1.34042	−	0.973874i	−0.174508	−	0.126788i	−0.671611	+	0.740904i	$0.734397\pi$
$60$	3.34617	+	10.2984i	0.431988	+	1.32952i
$61$	2.87809	+	8.85786i	0.368502	+	1.13413i	0.947759	+	0.318988i	$0.103343\pi$
$61$	2.87809	+	8.85786i	0.368502	+	1.13413i	−0.579257	+	0.815145i	$0.696657\pi$
$62$		0			0
$63$	−8.09017	+	5.87785i	−1.01927	+	0.740540i
$64$	−3.03715	+	9.34739i	−0.379644	+	1.16842i
$65$	−1.17157			−0.145316
$66$		0			0
$67$	12.4853			1.52532			0.762660	−	0.646800i	$-0.223893\pi$
$67$	12.4853			1.52532			0.762660	+	0.646800i	$0.223893\pi$
$68$	−8.07836	+	24.8626i	−0.979646	+	3.01504i
$69$	−6.47214	+	4.70228i	−0.779154	+	0.566088i
$70$	−3.90628	−	2.83808i	−0.466890	−	0.339215i
$71$	3.49613	+	10.7600i	0.414914	+	1.27697i	0.912328	+	0.409461i	$0.134283\pi$
$71$	3.49613	+	10.7600i	0.414914	+	1.27697i	−0.497414	+	0.867513i	$0.665717\pi$
$72$	−6.82034	−	20.9908i	−0.803784	−	2.47379i
$73$	−0.947822	−	0.688633i	−0.110934	−	0.0805984i	0.530935	−	0.847413i	$-0.321841\pi$
$73$	−0.947822	−	0.688633i	−0.110934	−	0.0805984i	−0.641869	+	0.766814i	$0.721841\pi$
$74$	−14.9549	+	10.8654i	−1.73847	+	1.26307i
$75$	−0.874032	+	2.68999i	−0.100925	+	0.310614i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	−1.23607	+	3.80423i	−0.139069	+	0.428009i	−0.996201	−	0.0870877i	$-0.972244\pi$
$79$	−1.23607	+	3.80423i	−0.139069	+	0.428009i	0.857132	+	0.515097i	$0.172244\pi$
$80$	2.42705	−	1.76336i	0.271353	−	0.197149i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	4.47620	+	13.7763i	0.494313	+	1.52134i
$83$	1.85410	+	5.70634i	0.203514	+	0.626352i	0.999771	+	0.0213936i	$0.00681031\pi$
$83$	1.85410	+	5.70634i	0.203514	+	0.626352i	−0.796257	+	0.604959i	$0.793190\pi$
$84$	17.5208	+	12.7296i	1.91167	+	1.38891i
$85$	−5.52431	+	4.01365i	−0.599196	+	0.435341i
$86$	−4.47620	+	13.7763i	−0.482681	+	1.48554i
$87$	−10.3431			−1.10890
$88$		0			0
$89$	−13.3137			−1.41125			−0.705625	−	0.708585i	$-0.749334\pi$
$89$	−13.3137			−1.41125			−0.705625	+	0.708585i	$0.749334\pi$
$90$	3.73017	−	11.4803i	0.393194	−	1.21013i
$91$	−1.89564	+	1.37727i	−0.198718	+	0.144377i
$92$	8.76038	+	6.36479i	0.913333	+	0.663575i
$93$		0			0
$94$	−2.11010	−	6.49422i	−0.217640	−	0.669828i
$95$		0			0
$96$	3.62867	−	2.63638i	0.370349	−	0.269075i
$97$	1.13003	−	3.47788i	0.114737	−	0.353125i	−0.877155	−	0.480207i	$-0.840561\pi$
$97$	1.13003	−	3.47788i	0.114737	−	0.353125i	0.991892	+	0.127083i	$0.0405614\pi$
$98$	7.24264			0.731617
$99$		0			0
$100$	3.82843			0.382843
$101$	−2.87809	+	8.85786i	−0.286381	+	0.881390i	0.699600	+	0.714534i	$0.253361\pi$
$101$	−2.87809	+	8.85786i	−0.286381	+	0.881390i	−0.985981	+	0.166856i	$0.946639\pi$
$102$	37.7224	−	27.4069i	3.73507	−	2.71369i
$103$	−5.52431	−	4.01365i	−0.544327	−	0.395477i	0.281363	−	0.959602i	$-0.409214\pi$
$103$	−5.52431	−	4.01365i	−0.544327	−	0.395477i	−0.825689	+	0.564125i	$0.809214\pi$
$104$	−1.59810	−	4.91846i	−0.156707	−	0.482294i
$105$	1.74806	+	5.37999i	0.170594	+	0.525033i
$106$	22.7675	+	16.5415i	2.21137	+	1.60666i
$107$	6.19453	−	4.50059i	0.598847	−	0.435088i	−0.246622	−	0.969112i	$-0.579321\pi$
$107$	6.19453	−	4.50059i	0.598847	−	0.435088i	0.845470	+	0.534024i	$0.179321\pi$
$108$	−6.69234	+	20.5969i	−0.643970	+	1.98194i
$109$	7.65685			0.733394			0.366697	−	0.930341i	$-0.380489\pi$
$109$	7.65685			0.733394			0.366697	+	0.930341i	$0.380489\pi$
$110$		0			0
$111$	21.6569			2.05558
$112$	1.85410	−	5.70634i	0.175196	−	0.539198i
$113$	−15.9027	+	11.5540i	−1.49600	+	1.08691i	−0.524063	+	0.851679i	$0.675584\pi$
$113$	−15.9027	+	11.5540i	−1.49600	+	1.08691i	−0.971940	+	0.235230i	$0.924416\pi$
$114$		0			0
$115$	0.874032	+	2.68999i	0.0815039	+	0.250843i
$116$	4.32624	+	13.3148i	0.401681	+	1.23625i
$117$	−4.73911	−	3.44317i	−0.438131	−	0.318321i
$118$	3.23607	−	2.35114i	0.297904	−	0.216440i
$119$	−4.22020	+	12.9884i	−0.386865	+	1.19065i
$120$	−12.4853			−1.13975
$121$		0			0
$122$	−22.4853			−2.03572
$123$	5.24419	−	16.1400i	0.472853	−	1.45529i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	−7.46033	−	22.9605i	−0.664619	−	2.04549i
$127$	−1.34211	−	4.13058i	−0.119093	−	0.366529i	0.873686	−	0.486490i	$-0.161723\pi$
$127$	−1.34211	−	4.13058i	−0.119093	−	0.366529i	−0.992779	+	0.119961i	$0.961723\pi$
$128$	−16.6304	−	12.0827i	−1.46994	−	1.06797i
$129$	13.7295	−	9.97505i	1.20881	−	0.878254i
$130$	0.874032	−	2.68999i	0.0766577	−	0.235928i
$131$	11.3137			0.988483			0.494242	−	0.869325i	$-0.335446\pi$
$131$	11.3137			0.988483			0.494242	+	0.869325i	$0.335446\pi$
$132$		0			0
$133$		0			0
$134$	−9.31443	+	28.6669i	−0.804644	+	2.47644i
$135$	−4.57649	+	3.32502i	−0.393882	+	0.286172i
$136$	−24.3855	−	17.7171i	−2.09104	−	1.51923i
$137$	−3.39009	−	10.4336i	−0.289635	−	0.891405i	−0.984971	−	0.172720i	$-0.944744\pi$
$137$	−3.39009	−	10.4336i	−0.289635	−	0.891405i	0.695336	−	0.718685i	$-0.255256\pi$
$138$	−5.96826	−	18.3684i	−0.508052	−	1.56362i
$139$	−3.23607	−	2.35114i	−0.274480	−	0.199421i	0.442026	−	0.897002i	$-0.354260\pi$
$139$	−3.23607	−	2.35114i	−0.274480	−	0.199421i	−0.716506	+	0.697581i	$0.754260\pi$
$140$	6.19453	−	4.50059i	0.523533	−	0.380369i
$141$	−2.47214	+	7.60845i	−0.208191	+	0.640747i
$142$	−27.3137			−2.29212
$143$		0			0
$144$	15.0000			1.25000
$145$	−1.13003	+	3.47788i	−0.0938439	+	0.288822i
$146$	2.28825	−	1.66251i	0.189377	−	0.137590i
$147$	−6.86474	−	4.98752i	−0.566194	−	0.411364i
$148$	−9.05843	−	27.8790i	−0.744599	−	2.29164i
$149$	−0.106038	−	0.326351i	−0.00868696	−	0.0267357i	0.946619	−	0.322354i	$-0.104474\pi$
$149$	−0.106038	−	0.326351i	−0.00868696	−	0.0267357i	−0.955306	+	0.295619i	$0.904474\pi$
$150$	−5.52431	−	4.01365i	−0.451058	−	0.327713i
$151$	−9.70820	+	7.05342i	−0.790042	+	0.573999i	−0.907976	−	0.419022i	$-0.862373\pi$
$151$	−9.70820	+	7.05342i	−0.790042	+	0.573999i	0.117934	+	0.993021i	$0.462373\pi$
$152$		0			0
$153$	−34.1421			−2.76023
$154$		0			0
$155$		0			0
$156$	−3.92028	+	12.0654i	−0.313874	+	0.966004i
$157$	11.3262	−	8.22899i	0.903932	−	0.656745i	−0.0355408	−	0.999368i	$-0.511315\pi$
$157$	11.3262	−	8.22899i	0.903932	−	0.656745i	0.939473	+	0.342623i	$0.111315\pi$
$158$	−7.81256	−	5.67616i	−0.621534	−	0.451571i
$159$	−10.1885	−	31.3569i	−0.807998	−	2.48676i
$160$	−0.490035	−	1.50817i	−0.0387407	−	0.119232i
$161$	4.57649	+	3.32502i	0.360678	+	0.262048i
$162$	1.95314	−	1.41904i	0.153453	−	0.111490i
$163$	5.09423	−	15.6784i	0.399011	−	1.22803i	−0.526782	−	0.850000i	$-0.676602\pi$
$163$	5.09423	−	15.6784i	0.399011	−	1.22803i	0.925794	−	0.378030i	$-0.123398\pi$
$164$	−22.9706			−1.79370
$165$		0			0
$166$	−14.4853			−1.12428
$167$	7.09829	−	21.8463i	0.549283	−	1.69052i	−0.161301	−	0.986905i	$-0.551569\pi$
$167$	7.09829	−	21.8463i	0.549283	−	1.69052i	0.710584	−	0.703613i	$-0.248431\pi$
$168$	−20.2016	+	14.6773i	−1.55859	+	1.13238i
$169$	9.40678	+	6.83442i	0.723598	+	0.525725i
$170$	−5.09423	−	15.6784i	−0.390710	−	1.20248i
$171$		0			0
$172$	−18.5836	−	13.5018i	−1.41698	−	1.02950i
$173$	−17.9134	+	13.0148i	−1.36193	+	0.989499i	−0.363608	+	0.931552i	$0.618455\pi$
$173$	−17.9134	+	13.0148i	−1.36193	+	0.989499i	−0.998320	+	0.0579465i	$0.981545\pi$
$174$	7.71633	−	23.7484i	0.584973	−	1.80036i
$175$	2.00000			0.151186
$176$		0			0
$177$	−4.68629			−0.352243
$178$	9.93247	−	30.5690i	0.744470	−	2.29124i
$179$	−7.81256	+	5.67616i	−0.583938	+	0.424256i	−0.840142	−	0.542367i	$-0.817528\pi$
$179$	−7.81256	+	5.67616i	−0.583938	+	0.424256i	0.256204	+	0.966623i	$0.417528\pi$
$180$	15.4863	+	11.2515i	1.15428	+	0.838635i
$181$	6.58630	+	20.2705i	0.489556	+	1.50670i	0.825273	+	0.564735i	$0.191021\pi$
$181$	6.58630	+	20.2705i	0.489556	+	1.50670i	−0.335717	+	0.941963i	$0.608979\pi$
$182$	−1.74806	−	5.37999i	−0.129575	−	0.398791i
$183$	21.3121	+	15.4841i	1.57543	+	1.14462i
$184$	−10.1008	+	7.33866i	−0.744641	+	0.541014i
$185$	2.36610	−	7.28210i	0.173959	−	0.535391i
$186$		0			0
$187$		0			0
$188$	10.8284			0.789744
$189$	−3.49613	+	10.7600i	−0.254306	+	0.782673i
$190$		0			0
$191$	−2.68085	−	1.94775i	−0.193979	−	0.140934i	0.486556	−	0.873649i	$-0.338253\pi$
$191$	−2.68085	−	1.94775i	−0.193979	−	0.140934i	−0.680536	+	0.732715i	$0.738253\pi$
$192$	8.59036	+	26.4384i	0.619956	+	1.90803i
$193$	0.362036	+	1.11423i	0.0260599	+	0.0802042i	0.963241	−	0.268640i	$-0.0865742\pi$
$193$	0.362036	+	1.11423i	0.0260599	+	0.0802042i	−0.937181	+	0.348844i	$0.886574\pi$
$194$	7.14235	+	5.18922i	0.512791	+	0.372564i
$195$	−2.68085	+	1.94775i	−0.191979	+	0.139481i
$196$	−3.54915	+	10.9232i	−0.253511	+	0.780225i
$197$	10.8284			0.771493			0.385747	−	0.922605i	$-0.373944\pi$
$197$	10.8284			0.771493			0.385747	+	0.922605i	$0.373944\pi$
$198$		0			0
$199$	10.3431			0.733206			0.366603	−	0.930377i	$-0.380521\pi$
$199$	10.3431			0.733206			0.366603	+	0.930377i	$0.380521\pi$
$200$	−1.36407	+	4.19817i	−0.0964541	+	0.296855i
$201$	28.5694	−	20.7569i	2.01513	−	1.46408i
$202$	−18.1910	−	13.2165i	−1.27991	−	0.929911i
$203$	2.26006	+	6.95575i	0.158625	+	0.488198i
$204$	22.8491	+	70.3222i	1.59975	+	4.92354i
$205$	−4.85410	−	3.52671i	−0.339025	−	0.246316i
$206$	13.3369	−	9.68981i	0.929224	−	0.675121i
$207$	−4.37016	+	13.4500i	−0.303747	+	0.934838i
$208$	3.51472			0.243702
$209$		0			0
$210$	−13.6569			−0.942412
$211$	4.94427	−	15.2169i	0.340378	−	1.04757i	−0.623634	−	0.781716i	$-0.714345\pi$
$211$	4.94427	−	15.2169i	0.340378	−	1.04757i	0.964012	−	0.265859i	$-0.0856555\pi$
$212$	−36.1043	+	26.2313i	−2.47966	+	1.80158i
$213$	25.8885	+	18.8091i	1.77385	+	1.28878i
$214$	5.71227	+	17.5805i	0.390482	+	1.20178i
$215$	−1.85410	−	5.70634i	−0.126449	−	0.389169i
$216$	−20.2016	−	14.6773i	−1.37455	−	0.998666i
$217$		0			0
$218$	−5.71227	+	17.5805i	−0.386883	+	1.19070i
$219$	−3.31371			−0.223920
$220$		0			0
$221$	−8.00000			−0.538138
$222$	−16.1567	+	49.7253i	−1.08437	+	3.33734i
$223$	8.76038	−	6.36479i	0.586639	−	0.426218i	−0.254473	−	0.967080i	$-0.581902\pi$
$223$	8.76038	−	6.36479i	0.586639	−	0.426218i	0.841111	+	0.540862i	$0.181902\pi$
$224$	−2.56586	−	1.86420i	−0.171438	−	0.124557i
$225$	1.54508	+	4.75528i	0.103006	+	0.317019i
$226$	−14.6647	−	45.1332i	−0.975479	−	3.00222i
$227$	20.4792	+	14.8790i	1.35925	+	0.987556i	0.998492	+	0.0548975i	$0.0174832\pi$
$227$	20.4792	+	14.8790i	1.35925	+	0.987556i	0.360762	+	0.932658i	$0.382517\pi$
$228$		0			0
$229$	0.405958	−	1.24941i	0.0268265	−	0.0825634i	−0.936747	−	0.350007i	$-0.886179\pi$
$229$	0.405958	−	1.24941i	0.0268265	−	0.0825634i	0.963573	+	0.267444i	$0.0861791\pi$
$230$	−6.82843			−0.450253
$231$		0			0
$232$	−16.1421			−1.05978
$233$	1.89802	−	5.84152i	0.124344	−	0.382691i	−0.869437	−	0.494043i	$-0.835518\pi$
$233$	1.89802	−	5.84152i	0.124344	−	0.382691i	0.993781	+	0.111353i	$0.0355184\pi$
$234$	11.4412	−	8.31254i	0.747936	−	0.543408i
$235$	2.28825	+	1.66251i	0.149269	+	0.108450i
$236$	1.96014	+	6.03269i	0.127594	+	0.392695i
$237$	3.49613	+	10.7600i	0.227098	+	0.698936i
$238$	−26.6737	−	19.3796i	−1.72900	−	1.25619i
$239$	−18.8612	+	13.7035i	−1.22003	+	0.886403i	−0.996102	−	0.0882033i	$-0.971887\pi$
$239$	−18.8612	+	13.7035i	−1.22003	+	0.886403i	−0.223926	+	0.974606i	$0.571887\pi$
$240$	2.62210	−	8.06998i	0.169256	−	0.520915i
$241$	−6.00000			−0.386494			−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000			−0.386494			−0.193247	+	0.981150i	$0.561902\pi$
$242$		0			0
$243$	14.1421			0.907218
$244$	11.0186	−	33.9117i	0.705392	−	2.17097i
$245$	−2.42705	+	1.76336i	−0.155059	+	0.112657i
$246$	33.1459	+	24.0819i	2.11330	+	1.53541i
$247$		0			0
$248$		0			0
$249$	13.7295	+	9.97505i	0.870070	+	0.632143i
$250$	−1.95314	+	1.41904i	−0.123527	+	0.0897479i
$251$	3.70820	−	11.4127i	0.234060	−	0.720362i	−0.763185	−	0.646180i	$-0.776365\pi$
$251$	3.70820	−	11.4127i	0.234060	−	0.720362i	0.997245	−	0.0741818i	$-0.0236345\pi$
$252$	38.2843			2.41168
$253$		0			0
$254$	10.4853			0.657905
$255$	−5.96826	+	18.3684i	−0.373747	+	1.15028i
$256$	24.2467	−	17.6163i	1.51542	−	1.10102i
$257$	7.53495	+	5.47446i	0.470017	+	0.341487i	0.797448	−	0.603388i	$-0.206183\pi$
$257$	7.53495	+	5.47446i	0.470017	+	0.341487i	−0.327431	+	0.944875i	$0.606183\pi$
$258$	12.6606	+	38.9653i	0.788215	+	2.42587i
$259$	−4.73220	−	14.5642i	−0.294044	−	0.904975i
$260$	3.62867	+	2.63638i	0.225040	+	0.163501i
$261$	−14.7923	+	10.7472i	−0.915620	+	0.665237i
$262$	−8.44040	+	25.9769i	−0.521450	+	1.60486i
$263$	10.9706			0.676474			0.338237	−	0.941061i	$-0.390169\pi$
$263$	10.9706			0.676474			0.338237	+	0.941061i	$0.390169\pi$
$264$		0			0
$265$	−11.6569			−0.716075
$266$		0			0
$267$	−30.4650	+	22.1341i	−1.86443	+	1.35459i
$268$	−38.6702	−	28.0955i	−2.36216	−	1.71621i
$269$	5.35023	+	16.4663i	0.326209	+	1.00397i	0.970892	+	0.239519i	$0.0769896\pi$
$269$	5.35023	+	16.4663i	0.326209	+	1.00397i	−0.644683	+	0.764450i	$0.723010\pi$
$270$	−4.22020	−	12.9884i	−0.256833	−	0.790451i
$271$	5.91691	+	4.29889i	0.359427	+	0.261139i	0.752813	−	0.658234i	$-0.228696\pi$
$271$	5.91691	+	4.29889i	0.359427	+	0.261139i	−0.393386	+	0.919373i	$0.628696\pi$
$272$	16.5729	−	12.0409i	1.00488	−	0.730090i
$273$	−2.04798	+	6.30305i	−0.123950	+	0.381478i
$274$	26.4853			1.60003
$275$		0			0
$276$	30.6274			1.84355
$277$	−2.11010	+	6.49422i	−0.126784	+	0.390200i	−0.994222	−	0.107345i	$-0.965765\pi$
$277$	−2.11010	+	6.49422i	−0.126784	+	0.390200i	0.867438	+	0.497545i	$0.165765\pi$
$278$	7.81256	−	5.67616i	0.468566	−	0.340433i
$279$		0			0
$280$	2.72813	+	8.39633i	0.163037	+	0.501777i
$281$	−5.35023	−	16.4663i	−0.319168	−	0.982298i	−0.974005	−	0.226528i	$-0.927263\pi$
$281$	−5.35023	−	16.4663i	−0.319168	−	0.982298i	0.654837	−	0.755770i	$-0.272737\pi$
$282$	−15.6251	−	11.3523i	−0.930462	−	0.676020i
$283$	26.3961	−	19.1779i	1.56909	−	1.14001i	0.641064	−	0.767488i	$-0.278493\pi$
$283$	26.3961	−	19.1779i	1.56909	−	1.14001i	0.928024	−	0.372521i	$-0.121507\pi$
$284$	13.3847	−	41.1938i	0.794234	−	2.44440i
$285$		0			0
$286$		0			0
$287$	−12.0000			−0.708338
$288$	2.45017	−	7.54086i	0.144378	−	0.444350i
$289$	−23.9691	+	17.4146i	−1.40995	+	1.02439i
$290$	−7.14235	−	5.18922i	−0.419413	−	0.304721i
$291$	−3.19621	−	9.83692i	−0.187365	−	0.576650i
$292$	1.38603	+	4.26576i	0.0811112	+	0.249634i
$293$	−7.41996	−	5.39092i	−0.433479	−	0.314941i	0.349560	−	0.936914i	$-0.386331\pi$
$293$	−7.41996	−	5.39092i	−0.433479	−	0.314941i	−0.783038	+	0.621973i	$0.786331\pi$
$294$	16.5729	−	12.0409i	0.966554	−	0.702242i
$295$	−0.511996	+	1.57576i	−0.0298096	+	0.0917444i
$296$	33.7990			1.96453
$297$		0			0
$298$	0.828427			0.0479895
$299$	−1.02399	+	3.15152i	−0.0592190	+	0.182257i
$300$	8.76038	−	6.36479i	0.505781	−	0.367471i
$301$	−9.70820	−	7.05342i	−0.559572	−	0.406553i
$302$	−8.95240	−	27.5526i	−0.515153	−	1.58548i
$303$	8.14048	+	25.0538i	0.467658	+	1.43930i
$304$		0			0
$305$	7.53495	−	5.47446i	0.431450	−	0.313467i
$306$	25.4712	−	78.3922i	1.45609	−	4.48138i
$307$	16.3431			0.932753			0.466376	−	0.884586i	$-0.345559\pi$
$307$	16.3431			0.932753			0.466376	+	0.884586i	$0.345559\pi$
$308$		0			0
$309$	−19.3137			−1.09872
$310$		0			0
$311$	−3.79129	+	2.75453i	−0.214984	+	0.156195i	−0.690066	−	0.723746i	$-0.742419\pi$
$311$	−3.79129	+	2.75453i	−0.214984	+	0.156195i	0.475082	+	0.879942i	$0.342419\pi$
$312$	−11.8338	−	8.59778i	−0.669959	−	0.486753i
$313$	−0.405958	−	1.24941i	−0.0229461	−	0.0706209i	0.938928	−	0.344114i	$-0.111821\pi$
$313$	−0.405958	−	1.24941i	−0.0229461	−	0.0706209i	−0.961874	+	0.273493i	$0.911821\pi$
$314$	10.4445	+	32.1447i	0.589415	+	1.81403i
$315$	8.09017	+	5.87785i	0.455829	+	0.331179i
$316$	12.3891	−	9.00117i	0.696939	−	0.506355i
$317$	−0.405958	+	1.24941i	−0.0228009	+	0.0701739i	−0.961810	−	0.273720i	$-0.911746\pi$
$317$	−0.405958	+	1.24941i	−0.0228009	+	0.0701739i	0.939009	+	0.343894i	$0.111746\pi$
$318$	79.5980			4.46363
$319$		0			0
$320$	9.82843			0.549426
$321$	6.69234	−	20.5969i	0.373530	−	1.14961i
$322$	−11.0486	+	8.02730i	−0.615716	+	0.447344i
$323$		0			0
$324$	1.18305	+	3.64105i	0.0657249	+	0.202281i
$325$	0.362036	+	1.11423i	0.0200821	+	0.0618065i
$326$	32.1981	+	23.3933i	1.78329	+	1.29563i
$327$	17.5208	−	12.7296i	0.968900	−	0.703947i
$328$	8.18440	−	25.1890i	0.451908	−	1.39083i
$329$	5.65685			0.311872
$330$		0			0
$331$	−7.31371			−0.401998			−0.200999	−	0.979591i	$-0.564419\pi$
$331$	−7.31371			−0.401998			−0.200999	+	0.979591i	$0.564419\pi$
$332$	7.09829	−	21.8463i	0.389570	−	1.19897i
$333$	30.9726	−	22.5029i	1.69729	−	1.23315i
$334$	44.8647	+	32.5961i	2.45489	+	1.78358i
$335$	−3.85816	−	11.8742i	−0.210794	−	0.648757i
$336$	−5.24419	−	16.1400i	−0.286094	−	0.880507i
$337$	−16.5729	−	12.0409i	−0.902786	−	0.655912i	0.0363944	−	0.999338i	$-0.488413\pi$
$337$	−16.5729	−	12.0409i	−0.902786	−	0.655912i	−0.939180	+	0.343425i	$0.888413\pi$
$338$	−22.7100	+	16.4998i	−1.23526	+	0.897469i
$339$	−17.1807	+	52.8768i	−0.933129	+	2.87187i
$340$	26.1421			1.41776
$341$		0			0
$342$		0			0
$343$	−6.18034	+	19.0211i	−0.333707	+	1.02704i
$344$	21.4270	−	15.5677i	1.15527	−	0.839352i
$345$	6.47214	+	4.70228i	0.348448	+	0.253162i
$346$	−16.5188	−	50.8395i	−0.888054	−	2.73315i
$347$	−3.39009	−	10.4336i	−0.181990	−	0.560106i	0.817894	−	0.575369i	$-0.195142\pi$
$347$	−3.39009	−	10.4336i	−0.181990	−	0.560106i	−0.999884	+	0.0152627i	$0.995142\pi$
$348$	32.0354	+	23.2751i	1.71728	+	1.24768i
$349$	21.8196	−	15.8529i	1.16798	−	0.848586i	0.177213	−	0.984172i	$-0.443292\pi$
$349$	21.8196	−	15.8529i	1.16798	−	0.848586i	0.990766	+	0.135586i	$0.0432918\pi$
$350$	−1.49207	+	4.59211i	−0.0797543	+	0.245458i
$351$	−6.62742			−0.353745
$352$		0			0
$353$	21.3137			1.13441			0.567207	−	0.823575i	$-0.308024\pi$
$353$	21.3137			1.13441			0.567207	+	0.823575i	$0.308024\pi$
$354$	3.49613	−	10.7600i	0.185817	−	0.571886i
$355$	9.15298	−	6.65003i	0.485790	−	0.352947i
$356$	41.2361	+	29.9597i	2.18551	+	1.58786i
$357$	11.9365	+	36.7369i	0.631748	+	1.94432i
$358$	−7.20433	−	22.1727i	−0.380761	−	1.17186i
$359$	0.555221	+	0.403392i	0.0293035	+	0.0212902i	0.602341	−	0.798239i	$-0.294235\pi$
$359$	0.555221	+	0.403392i	0.0293035	+	0.0212902i	−0.573037	+	0.819529i	$0.694235\pi$
$360$	−17.8559	+	12.9730i	−0.941087	+	0.683740i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$	−51.4558			−2.70446
$363$		0			0
$364$	8.97056			0.470185
$365$	−0.362036	+	1.11423i	−0.0189498	+	0.0583216i
$366$	−51.4518	+	37.3820i	−2.68943	+	1.95399i
$367$	6.86474	+	4.98752i	0.358336	+	0.260347i	0.752358	−	0.658755i	$-0.228916\pi$
$367$	6.86474	+	4.98752i	0.358336	+	0.260347i	−0.394022	+	0.919101i	$0.628916\pi$
$368$	−2.62210	−	8.06998i	−0.136686	−	0.420677i
$369$	−9.27051	−	28.5317i	−0.482603	−	1.48530i
$370$	14.9549	+	10.8654i	0.777469	+	0.564864i
$371$	−18.8612	+	13.7035i	−0.979224	+	0.711448i
$372$		0			0
$373$	−35.7990			−1.85360			−0.926801	−	0.375554i	$-0.877453\pi$
$373$	−35.7990			−1.85360			−0.926801	+	0.375554i	$0.877453\pi$
$374$		0			0
$375$	2.82843			0.146059
$376$	−3.85816	+	11.8742i	−0.198970	+	0.612366i
$377$	−3.46605	+	2.51823i	−0.178511	+	0.129696i
$378$	−22.0973	−	16.0546i	−1.13656	−	0.825759i
$379$	10.4005	+	32.0096i	0.534240	+	1.64422i	0.745286	+	0.666745i	$0.232313\pi$
$379$	10.4005	+	32.0096i	0.534240	+	1.64422i	−0.211046	+	0.977476i	$0.567687\pi$
$380$		0			0
$381$	−9.93818	−	7.22051i	−0.509149	−	0.369918i
$382$	6.47214	−	4.70228i	0.331143	−	0.240590i
$383$	−1.81018	+	5.57116i	−0.0924959	+	0.284673i	−0.986593	−	0.163200i	$-0.947818\pi$
$383$	−1.81018	+	5.57116i	−0.0924959	+	0.284673i	0.894097	+	0.447873i	$0.147818\pi$
$384$	−58.1421			−2.96705
$385$		0			0
$386$	−2.82843			−0.143963
$387$	9.27051	−	28.5317i	0.471246	−	1.45035i
$388$	−11.3262	+	8.22899i	−0.575003	+	0.417764i
$389$	−16.6879	−	12.1245i	−0.846112	−	0.614736i	0.0779595	−	0.996957i	$-0.475160\pi$
$389$	−16.6879	−	12.1245i	−0.846112	−	0.614736i	−0.924071	+	0.382220i	$0.875160\pi$
$390$	−2.47214	−	7.60845i	−0.125181	−	0.385269i
$391$	5.96826	+	18.3684i	0.301828	+	0.928931i
$392$	−10.7135	−	7.78383i	−0.541115	−	0.393143i
$393$	25.8885	−	18.8091i	1.30590	−	0.948795i
$394$	−8.07836	+	24.8626i	−0.406982	+	1.25256i
$395$	4.00000			0.201262
$396$		0			0
$397$	−9.31371			−0.467442			−0.233721	−	0.972304i	$-0.575090\pi$
$397$	−9.31371			−0.467442			−0.233721	+	0.972304i	$0.575090\pi$
$398$	−7.71633	+	23.7484i	−0.386785	+	1.19040i
$399$		0			0
$400$	−2.42705	−	1.76336i	−0.121353	−	0.0881678i
$401$	−1.64203	−	5.05364i	−0.0819989	−	0.252367i	0.901649	−	0.432468i	$-0.142357\pi$
$401$	−1.64203	−	5.05364i	−0.0819989	−	0.252367i	−0.983648	+	0.180102i	$0.942357\pi$
$402$	26.3452	+	81.0822i	1.31398	+	4.04401i
$403$		0			0
$404$	28.8470	−	20.9586i	1.43519	−	1.04273i
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	−17.6569			−0.876295
$407$		0			0
$408$	−85.2548			−4.22074
$409$	−0.318114	+	0.979053i	−0.0157297	+	0.0484111i	−0.958613	−	0.284711i	$-0.908102\pi$
$409$	−0.318114	+	0.979053i	−0.0157297	+	0.0484111i	0.942884	+	0.333122i	$0.108102\pi$
$410$	11.7188	−	8.51423i	0.578752	−	0.420488i
$411$	−25.1033	−	18.2386i	−1.23826	−	0.899646i
$412$	8.07836	+	24.8626i	0.397992	+	1.22489i
$413$	1.02399	+	3.15152i	0.0503874	+	0.155076i
$414$	−27.6216	−	20.0682i	−1.35753	−	0.986300i
$415$	4.85410	−	3.52671i	0.238278	−	0.173119i
$416$	0.574112	−	1.76693i	0.0281481	−	0.0866311i
$417$	−11.3137			−0.554035
$418$		0			0
$419$	−25.6569			−1.25342			−0.626710	−	0.779253i	$-0.715599\pi$
$419$	−25.6569			−1.25342			−0.626710	+	0.779253i	$0.715599\pi$
$420$	6.69234	−	20.5969i	0.326553	−	1.00503i
$421$	4.85410	−	3.52671i	0.236574	−	0.171881i	−0.463181	−	0.886264i	$-0.653292\pi$
$421$	4.85410	−	3.52671i	0.236574	−	0.171881i	0.699756	+	0.714382i	$0.253292\pi$
$422$	31.2502	+	22.7046i	1.52124	+	1.10524i
$423$	4.37016	+	13.4500i	0.212484	+	0.653960i
$424$	−15.9007	−	48.9374i	−0.772208	−	2.37661i
$425$	5.52431	+	4.01365i	0.267969	+	0.194691i
$426$	−62.5005	+	45.4093i	−3.02816	+	2.20009i
$427$	5.75619	−	17.7157i	0.278561	−	0.857324i
$428$	−29.3137			−1.41693
$429$		0			0
$430$	14.4853			0.698542
$431$	3.49613	−	10.7600i	0.168403	−	0.518290i	−0.830868	−	0.556469i	$-0.812156\pi$
$431$	3.49613	−	10.7600i	0.168403	−	0.518290i	0.999271	+	0.0381792i	$0.0121558\pi$
$432$	13.7295	−	9.97505i	0.660560	−	0.479925i
$433$	6.19453	+	4.50059i	0.297690	+	0.216284i	0.726596	−	0.687065i	$-0.241101\pi$
$433$	6.19453	+	4.50059i	0.297690	+	0.216284i	−0.428907	+	0.903349i	$0.641101\pi$
$434$		0			0
$435$	3.19621	+	9.83692i	0.153246	+	0.471644i
$436$	−23.7153	−	17.2302i	−1.13576	−	0.825175i
$437$		0			0
$438$	2.47214	−	7.60845i	0.118123	−	0.363546i
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$		0			0
$441$	−15.0000			−0.714286
$442$	5.96826	−	18.3684i	0.283881	−	0.873697i
$443$	21.7047	−	15.7694i	1.03122	−	0.749225i	0.0626669	−	0.998035i	$-0.480039\pi$
$443$	21.7047	−	15.7694i	1.03122	−	0.749225i	0.968552	+	0.248810i	$0.0800394\pi$
$444$	−67.0770	−	48.7343i	−3.18333	−	2.31283i
$445$	4.11416	+	12.6621i	0.195030	+	0.600241i
$446$	8.07836	+	24.8626i	0.382522	+	1.17728i
$447$	−0.785202	−	0.570482i	−0.0371388	−	0.0269829i
$448$	15.9027	−	11.5540i	0.751333	−	0.545876i
$449$	8.84636	−	27.2263i	0.417485	−	1.28489i	−0.492523	−	0.870299i	$-0.663925\pi$
$449$	8.84636	−	27.2263i	0.417485	−	1.28489i	0.910009	−	0.414589i	$-0.136075\pi$
$450$	−12.0711			−0.569036
$451$		0			0
$452$	75.2548			3.53969
$453$	−10.4884	+	32.2799i	−0.492787	+	1.51664i
$454$	−49.4412	+	35.9211i	−2.32039	+	1.68586i
$455$	1.89564	+	1.37727i	0.0888692	+	0.0645673i
$456$		0			0
$457$	−0.149960	−	0.461530i	−0.00701484	−	0.0215895i	0.947488	−	0.319792i	$-0.103613\pi$
$457$	−0.149960	−	0.461530i	−0.00701484	−	0.0215895i	−0.954503	+	0.298202i	$0.903613\pi$
$458$	2.56586	+	1.86420i	0.119895	+	0.0871085i
$459$	−31.2502	+	22.7046i	−1.45864	+	1.05976i
$460$	3.34617	−	10.2984i	0.156016	−	0.480168i
$461$	−12.6274			−0.588117			−0.294059	−	0.955787i	$-0.595006\pi$
$461$	−12.6274			−0.588117			−0.294059	+	0.955787i	$0.595006\pi$
$462$		0			0
$463$	−6.14214			−0.285449			−0.142725	−	0.989762i	$-0.545586\pi$
$463$	−6.14214			−0.285449			−0.142725	+	0.989762i	$0.545586\pi$
$464$	3.39009	−	10.4336i	0.157381	−	0.484369i
$465$		0			0
$466$	11.9964	+	8.71593i	0.555725	+	0.403758i
$467$	−4.58224	−	14.1027i	−0.212041	−	0.652594i	−0.999350	−	0.0360364i	$-0.988527\pi$
$467$	−4.58224	−	14.1027i	−0.212041	−	0.652594i	0.787310	−	0.616557i	$-0.211473\pi$
$468$	6.93014	+	21.3288i	0.320346	+	0.985923i
$469$	−20.2016	−	14.6773i	−0.932824	−	0.677736i
$470$	−5.52431	+	4.01365i	−0.254818	+	0.185136i
$471$	12.2364	−	37.6599i	0.563826	−	1.73528i
$472$	−7.31371			−0.336641
$473$		0			0
$474$	−27.3137			−1.25456
$475$		0			0
$476$	42.2989	−	30.7319i	1.93877	−	1.40860i
$477$	−47.1530	−	34.2586i	−2.15899	−	1.56860i
$478$	−17.3928	−	53.5295i	−0.795528	−	2.44838i
$479$	11.1246	+	34.2380i	0.508296	+	1.56438i	0.795157	+	0.606403i	$0.207388\pi$
$479$	11.1246	+	34.2380i	0.508296	+	1.56438i	−0.286861	+	0.957972i	$0.592612\pi$
$480$	−3.62867	−	2.63638i	−0.165625	−	0.120334i
$481$	7.25734	−	5.27276i	0.330906	−	0.240417i
$482$	4.47620	−	13.7763i	0.203885	−	0.627494i
$483$	16.0000			0.728025
$484$		0			0
$485$	−3.65685			−0.166049
$486$	−10.5505	+	32.4711i	−0.478580	+	1.47292i
$487$	19.8090	−	14.3921i	0.897632	−	0.652168i	−0.0402248	−	0.999191i	$-0.512807\pi$
$487$	19.8090	−	14.3921i	0.897632	−	0.652168i	0.937857	+	0.347023i	$0.112807\pi$
$488$	33.2609	+	24.1654i	1.50565	+	1.09392i
$489$	−14.4087	−	44.3453i	−0.651582	−	2.00536i
$490$	−2.23810	−	6.88816i	−0.101107	−	0.311175i
$491$	−0.555221	−	0.403392i	−0.0250568	−	0.0182048i	0.575186	−	0.818022i	$-0.304930\pi$
$491$	−0.555221	−	0.403392i	−0.0250568	−	0.0182048i	−0.600243	+	0.799818i	$0.704930\pi$
$492$	−52.5623	+	38.1887i	−2.36969	+	1.72168i
$493$	−7.71633	+	23.7484i	−0.347526	+	1.06957i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.99226	−	21.5200i	0.313646	−	0.965302i
$498$	−33.1459	+	24.0819i	−1.48530	+	1.07914i
$499$	−7.81256	−	5.67616i	−0.349738	−	0.254100i	0.399021	−	0.916942i	$-0.369350\pi$
$499$	−7.81256	−	5.67616i	−0.349738	−	0.254100i	−0.748759	+	0.662842i	$0.769350\pi$
$500$	−1.18305	−	3.64105i	−0.0529076	−	0.162833i
$501$	−20.0770	−	61.7907i	−0.896975	−	2.76060i
$502$	23.4377	+	17.0285i	1.04607	+	0.760018i
$503$	13.4519	−	9.77335i	0.599789	−	0.435772i	−0.246015	−	0.969266i	$-0.579121\pi$
$503$	13.4519	−	9.77335i	0.599789	−	0.435772i	0.845804	+	0.533494i	$0.179121\pi$
$504$	−13.6407	+	41.9817i	−0.607604	+	1.87001i
$505$	9.31371			0.414455
$506$		0			0
$507$	32.8873			1.46058
$508$	−5.13815	+	15.8136i	−0.227969	+	0.701616i
$509$	10.7710	−	7.82560i	0.477417	−	0.346864i	−0.322908	−	0.946430i	$-0.604660\pi$
$509$	10.7710	−	7.82560i	0.477417	−	0.346864i	0.800325	+	0.599567i	$0.204660\pi$
$510$	−37.7224	−	27.4069i	−1.67037	−	1.21360i
$511$	0.724072	+	2.22846i	0.0320311	+	0.0985814i
$512$	9.65451	+	29.7135i	0.426673	+	1.31316i
$513$		0			0
$514$	−18.1910	+	13.2165i	−0.802369	+	0.582956i
$515$	−2.11010	+	6.49422i	−0.0929821	+	0.286170i
$516$	−64.9706			−2.86017
$517$		0			0
$518$	36.9706			1.62439
$519$	−19.3529	+	59.5622i	−0.849500	+	2.61449i
$520$	−4.18389	+	3.03977i	−0.183476	+	0.133303i
$521$	−20.4792	−	14.8790i	−0.897211	−	0.651862i	0.0405372	−	0.999178i	$-0.487093\pi$
$521$	−20.4792	−	14.8790i	−0.897211	−	0.651862i	−0.937748	+	0.347316i	$0.887093\pi$
$522$	−13.6407	−	41.9817i	−0.597036	−	1.83749i
$523$	12.8545	+	39.5620i	0.562087	+	1.72993i	0.676451	+	0.736488i	$0.263517\pi$
$523$	12.8545	+	39.5620i	0.562087	+	1.72993i	−0.114364	+	0.993439i	$0.536483\pi$
$524$	−35.0415	−	25.4592i	−1.53080	−	1.11219i
$525$	4.57649	−	3.32502i	0.199734	−	0.145116i
$526$	−8.18440	+	25.1890i	−0.356857	+	1.09829i
$527$		0			0
$528$		0			0
$529$	−15.0000			−0.652174
$530$	8.69640	−	26.7648i	0.377747	−	1.16259i
$531$	−6.70212	+	4.86937i	−0.290847	+	0.211313i
$532$		0			0
$533$	−2.17222	−	6.68539i	−0.0940891	−	0.289576i
$534$	−28.0933	−	86.4622i	−1.21571	−	3.74158i
$535$	−6.19453	−	4.50059i	−0.267813	−	0.194577i
$536$	44.5871	−	32.3944i	1.92587	−	1.39923i
$537$	−8.44040	+	25.9769i	−0.364230	+	1.12099i
$538$	−41.7990			−1.80208
$539$		0			0
$540$	21.6569			0.931963
$541$	−1.85410	+	5.70634i	−0.0797141	+	0.245335i	−0.982970	−	0.183768i	$-0.941170\pi$
$541$	−1.85410	+	5.70634i	−0.0797141	+	0.245335i	0.903255	+	0.429103i	$0.141170\pi$
$542$	−14.2847	+	10.3784i	−0.613580	+	0.445792i
$543$	48.7710	+	35.4342i	2.09296	+	1.52063i
$544$	−3.34617	−	10.2984i	−0.143466	−	0.441542i
$545$	−2.36610	−	7.28210i	−0.101353	−	0.311931i
$546$	−12.9443	−	9.40456i	−0.553964	−	0.402478i
$547$	−27.5066	+	19.9847i	−1.17610	+	0.854484i	−0.991726	−	0.128373i	$-0.959025\pi$
$547$	−27.5066	+	19.9847i	−1.17610	+	0.854484i	−0.184370	+	0.982857i	$0.559025\pi$
$548$	−12.9787	+	39.9444i	−0.554423	+	1.70634i
$549$	46.5685			1.98750
$550$		0			0
$551$		0			0
$552$	−10.9125	+	33.5853i	−0.464468	+	1.42949i
$553$	6.47214	−	4.70228i	0.275223	−	0.199961i
$554$	−13.3369	−	9.68981i	−0.566629	−	0.411680i
$555$	−6.69234	−	20.5969i	−0.284074	−	0.874289i
$556$	4.73220	+	14.5642i	0.200690	+	0.617660i
$557$	7.97518	+	5.79431i	0.337919	+	0.245513i	0.743783	−	0.668421i	$-0.233029\pi$
$557$	7.97518	+	5.79431i	0.337919	+	0.245513i	−0.405864	+	0.913933i	$0.633029\pi$
$558$		0			0
$559$	2.17222	−	6.68539i	0.0918749	−	0.282762i
$560$	−6.00000			−0.253546
$561$		0			0
$562$	41.7990			1.76318
$563$	−0.106038	+	0.326351i	−0.00446896	+	0.0137541i	−0.953266	−	0.302132i	$-0.902302\pi$
$563$	−0.106038	+	0.326351i	−0.00446896	+	0.0137541i	0.948797	+	0.315886i	$0.102302\pi$
$564$	24.7781	−	18.0023i	1.04335	−	0.758035i
$565$	15.9027	+	11.5540i	0.669033	+	0.486081i
$566$	24.3411	+	74.9143i	1.02313	+	3.14888i
$567$	0.618034	+	1.90211i	0.0259550	+	0.0798812i
$568$	40.4032	+	29.3547i	1.69528	+	1.23169i
$569$	25.6109	−	18.6074i	1.07367	−	0.780064i	0.0970985	−	0.995275i	$-0.469044\pi$
$569$	25.6109	−	18.6074i	1.07367	−	0.780064i	0.976568	+	0.215211i	$0.0690438\pi$
$570$		0			0
$571$	21.9411			0.918208			0.459104	−	0.888383i	$-0.348171\pi$
$571$	21.9411			0.918208			0.459104	+	0.888383i	$0.348171\pi$
$572$		0			0
$573$	−9.37258			−0.391545
$574$	8.95240	−	27.5526i	0.373666	−	1.15003i
$575$	2.28825	−	1.66251i	0.0954264	−	0.0693314i
$576$	39.7568	+	28.8850i	1.65653	+	1.20354i
$577$	−8.33436	−	25.6505i	−0.346964	−	1.06785i	−0.960524	−	0.278197i	$-0.910263\pi$
$577$	−8.33436	−	25.6505i	−0.346964	−	1.06785i	0.613560	−	0.789648i	$-0.289737\pi$
$578$	−22.1030	−	68.0261i	−0.919365	−	2.82951i
$579$	2.68085	+	1.94775i	0.111412	+	0.0809457i
$580$	11.3262	−	8.22899i	0.470296	−	0.341690i
$581$	3.70820	−	11.4127i	0.153842	−	0.473478i
$582$	24.9706			1.03506
$583$		0			0
$584$	−5.17157			−0.214001
$585$	−1.81018	+	5.57116i	−0.0748417	+	0.230339i
$586$	17.9134	−	13.0148i	0.739994	−	0.537637i
$587$	1.73302	+	1.25912i	0.0715296	+	0.0519693i	0.622975	−	0.782241i	$-0.285924\pi$
$587$	1.73302	+	1.25912i	0.0715296	+	0.0519693i	−0.551446	+	0.834211i	$0.685924\pi$
$588$	10.0385	+	30.8953i	0.413981	+	1.27410i
$589$		0			0
$590$	−3.23607	−	2.35114i	−0.133227	−	0.0967949i
$591$	24.7781	−	18.0023i	1.01923	−	0.740517i
$592$	−7.09829	+	21.8463i	−0.291738	+	0.897878i
$593$	−3.51472			−0.144332			−0.0721661	−	0.997393i	$-0.522991\pi$
$593$	−3.51472			−0.144332			−0.0721661	+	0.997393i	$0.522991\pi$
$594$		0			0
$595$	13.6569			0.559876
$596$	−0.405958	+	1.24941i	−0.0166287	+	0.0511779i
$597$	23.6677	−	17.1956i	0.968653	−	0.703767i
$598$	−6.47214	−	4.70228i	−0.264665	−	0.192291i
$599$	−1.74806	−	5.37999i	−0.0714240	−	0.219820i	0.908972	−	0.416857i	$-0.136868\pi$
$599$	−1.74806	−	5.37999i	−0.0714240	−	0.219820i	−0.980396	+	0.197036i	$0.936868\pi$
$600$	3.85816	+	11.8742i	0.157509	+	0.484763i
$601$	19.3688	+	14.0722i	0.790069	+	0.574019i	0.907984	−	0.419005i	$-0.137621\pi$
$601$	19.3688	+	14.0722i	0.790069	+	0.574019i	−0.117915	+	0.993024i	$0.537621\pi$
$602$	23.4377	−	17.0285i	0.955248	−	0.694029i
$603$	19.2908	−	59.3710i	0.785583	−	2.41778i
$604$	45.9411			1.86932
$605$		0			0
$606$	−63.5980			−2.58349
$607$	−11.8305	+	36.4105i	−0.480185	+	1.47786i	0.358651	+	0.933472i	$0.383237\pi$
$607$	−11.8305	+	36.4105i	−0.480185	+	1.47786i	−0.838835	+	0.544385i	$0.816763\pi$
$608$		0			0
$609$	16.7356	+	12.1591i	0.678159	+	0.492711i
$610$	6.94833	+	21.3848i	0.281330	+	0.865844i
$611$	1.02399	+	3.15152i	0.0414263	+	0.127497i
$612$	105.747	+	76.8298i	4.27458	+	3.10566i
$613$	−20.5942	+	14.9626i	−0.831792	+	0.604333i	−0.920066	−	0.391764i	$-0.871865\pi$
$613$	−20.5942	+	14.9626i	−0.831792	+	0.604333i	0.0882735	+	0.996096i	$0.471865\pi$
$614$	−12.1925	+	37.5247i	−0.492050	+	1.51438i
$615$	−16.9706			−0.684319
$616$		0			0
$617$	0.343146			0.0138145			0.00690726	−	0.999976i	$-0.497801\pi$
$617$	0.343146			0.0138145			0.00690726	+	0.999976i	$0.497801\pi$
$618$	14.4087	−	44.3453i	0.579601	−	1.78383i
$619$	11.6038	−	8.43069i	0.466398	−	0.338858i	−0.329638	−	0.944107i	$-0.606927\pi$
$619$	11.6038	−	8.43069i	0.466398	−	0.338858i	0.796036	+	0.605249i	$0.206927\pi$
$620$		0			0
$621$	4.94427	+	15.2169i	0.198407	+	0.610633i
$622$	−3.49613	−	10.7600i	−0.140182	−	0.431436i
$623$	21.5420	+	15.6512i	0.863063	+	0.627052i
$624$	8.04254	−	5.84325i	0.321959	−	0.233917i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	3.17157			0.126762
$627$		0			0
$628$	−53.5980			−2.13879
$629$	16.1567	−	49.7253i	0.644211	−	1.98268i
$630$	−19.5314	+	14.1904i	−0.778150	+	0.565359i
$631$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$631$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$632$	5.45627	+	16.7927i	0.217039	+	0.667976i
$633$	−13.9845	−	43.0399i	−0.555834	−	1.71068i
$634$	−2.56586	−	1.86420i	−0.101903	−	0.0740370i
$635$	−3.51368	+	2.55284i	−0.139436	+	0.101306i
$636$	−39.0058	+	120.047i	−1.54668	+	4.76019i
$637$	−3.51472			−0.139258
$638$		0			0
$639$	56.5685			2.23782
$640$	−6.35226	+	19.5502i	−0.251095	+	0.772791i
$641$	−24.2705	+	17.6336i	−0.958628	+	0.696484i	−0.952832	−	0.303500i	$-0.901845\pi$
$641$	−24.2705	+	17.6336i	−0.958628	+	0.696484i	−0.00579592	+	0.999983i	$0.501845\pi$
$642$	42.2989	+	30.7319i	1.66940	+	1.21289i
$643$	−0.449881	−	1.38459i	−0.0177416	−	0.0546029i	0.941794	−	0.336191i	$-0.109139\pi$
$643$	−0.449881	−	1.38459i	−0.0177416	−	0.0546029i	−0.959535	+	0.281588i	$0.909139\pi$
$644$	−6.69234	−	20.5969i	−0.263715	−	0.811631i
$645$	−13.7295	−	9.97505i	−0.540597	−	0.392767i
$646$		0			0
$647$	8.37828	−	25.7857i	0.329384	−	1.01374i	−0.640038	−	0.768343i	$-0.721081\pi$
$647$	8.37828	−	25.7857i	0.329384	−	1.01374i	0.969422	−	0.245398i	$-0.0789185\pi$
$648$	−4.41421			−0.173407
$649$		0			0
$650$	−2.82843			−0.110940
$651$		0			0
$652$	−51.0592	+	37.0967i	−1.99963	+	1.45282i
$653$	−9.43059	−	6.85173i	−0.369048	−	0.268129i	0.387768	−	0.921757i	$-0.373246\pi$
$653$	−9.43059	−	6.85173i	−0.369048	−	0.268129i	−0.756816	+	0.653628i	$0.773246\pi$
$654$	16.1567	+	49.7253i	0.631778	+	1.94441i
$655$	−3.49613	−	10.7600i	−0.136605	−	0.420427i
$656$	14.5623	+	10.5801i	0.568563	+	0.413085i
$657$	−4.73911	+	3.44317i	−0.184890	+	0.134331i
$658$	−4.22020	+	12.9884i	−0.164521	+	0.506342i
$659$	−45.9411			−1.78961			−0.894806	−	0.446455i	$-0.852686\pi$
$659$	−45.9411			−1.78961			−0.894806	+	0.446455i	$0.852686\pi$
$660$		0			0
$661$	44.6274			1.73581			0.867903	−	0.496734i	$-0.165468\pi$
$661$	44.6274			1.73581			0.867903	+	0.496734i	$0.165468\pi$
$662$	5.45627	−	16.7927i	0.212064	−	0.652666i
$663$	−18.3060	+	13.3001i	−0.710945	+	0.516532i
$664$	21.4270	+	15.5677i	0.831531	+	0.604142i
$665$		0			0
$666$	28.5613	+	87.9027i	1.10673	+	3.40616i
$667$	8.36778	+	6.07955i	0.324002	+	0.235401i
$668$	−71.1459	+	51.6905i	−2.75272	+	1.99997i
$669$	9.46439	−	29.1284i	0.365915	−	1.12617i
$670$	30.1421			1.16449
$671$		0			0
$672$	−8.97056			−0.346047
$673$	3.85816	−	11.8742i	0.148721	−	0.457717i	−0.848749	−	0.528795i	$-0.822644\pi$
$673$	3.85816	−	11.8742i	0.148721	−	0.457717i	0.997471	+	0.0710781i	$0.0226440\pi$
$674$	40.0106	−	29.0694i	1.54115	−	1.11971i
$675$	4.57649	+	3.32502i	0.176149	+	0.127980i
$676$	−13.7558	−	42.3360i	−0.529069	−	1.62831i
$677$	−7.05437	−	21.7111i	−0.271122	−	0.834426i	−0.990220	−	0.139518i	$-0.955445\pi$
$677$	−7.05437	−	21.7111i	−0.271122	−	0.834426i	0.719098	−	0.694909i	$-0.244555\pi$
$678$	−108.591	−	78.8957i	−4.17040	−	3.02997i
$679$	−5.91691	+	4.29889i	−0.227070	+	0.164976i
$680$	−9.31443	+	28.6669i	−0.357192	+	1.09932i
$681$	71.5980			2.74364
$682$		0			0
$683$	−7.79899			−0.298420			−0.149210	−	0.988806i	$-0.547673\pi$
$683$	−7.79899			−0.298420			−0.149210	+	0.988806i	$0.547673\pi$
$684$		0			0
$685$	−8.87537	+	6.44833i	−0.339111	+	0.246378i
$686$	−39.0628	−	28.3808i	−1.49142	−	1.08358i
$687$	−1.14822	−	3.53387i	−0.0438075	−	0.134825i
$688$	5.56231	+	17.1190i	0.212061	+	0.652656i
$689$	−11.0486	−	8.02730i	−0.420919	−	0.305816i
$690$	−15.6251	+	11.3523i	−0.594838	+	0.432175i
$691$	−12.1486	+	37.3896i	−0.462155	+	1.42237i	0.400371	+	0.916353i	$0.368881\pi$
$691$	−12.1486	+	37.3896i	−0.462155	+	1.42237i	−0.862526	+	0.506013i	$0.831119\pi$
$692$	84.7696			3.22245
$693$		0			0
$694$	26.4853			1.00537
$695$	−1.23607	+	3.80423i	−0.0468867	+	0.144303i
$696$	−36.9372	+	26.8364i	−1.40010	+	1.01723i
$697$	−33.1459	−	24.0819i	−1.25549	−	0.912167i
$698$	20.1209	+	61.9259i	0.761588	+	2.34393i
$699$	−5.36842	−	16.5223i	−0.203052	−	0.624931i
$700$	−6.19453	−	4.50059i	−0.234131	−	0.170106i
$701$	−10.2158	+	7.42221i	−0.385845	+	0.280333i	−0.763751	−	0.645511i	$-0.776644\pi$
$701$	−10.2158	+	7.42221i	−0.385845	+	0.280333i	0.377906	+	0.925844i	$0.376644\pi$
$702$	4.94427	−	15.2169i	0.186610	−	0.574325i
$703$		0			0
$704$		0			0
$705$	8.00000			0.301297
$706$	−15.9007	+	48.9374i	−0.598432	+	1.84178i
$707$	15.0699	−	10.9489i	0.566762	−	0.411777i
$708$	14.5147	+	10.5455i	0.545495	+	0.396325i
$709$	7.61029	+	23.4221i	0.285810	+	0.879634i	0.986155	+	0.165829i	$0.0530299\pi$
$709$	7.61029	+	23.4221i	0.285810	+	0.879634i	−0.700344	+	0.713805i	$0.746970\pi$
$710$	8.44040	+	25.9769i	0.316763	+	0.974895i
$711$	16.1803	+	11.7557i	0.606810	+	0.440873i
$712$	−47.5456	+	34.5439i	−1.78185	+	1.29459i
$713$		0			0
$714$	−93.2548			−3.48997
$715$		0			0
$716$	36.9706			1.38165
$717$	−20.3769	+	62.7137i	−0.760990	+	2.34209i
$718$	−1.34042	+	0.973874i	−0.0500242	+	0.0363447i
$719$	−14.8399	−	10.7818i	−0.553436	−	0.402094i	0.275615	−	0.961268i	$-0.411118\pi$
$719$	−14.8399	−	10.7818i	−0.553436	−	0.402094i	−0.829051	+	0.559174i	$0.811118\pi$
$720$	−4.63525	−	14.2658i	−0.172746	−	0.531657i
$721$	4.22020	+	12.9884i	0.157168	+	0.483715i
$722$	−37.1097	−	26.9617i	−1.38108	−	1.00341i
$723$	−13.7295	+	9.97505i	−0.510605	+	0.370976i
$724$	25.2152	−	77.6043i	0.937114	−	2.88414i
$725$	3.65685			0.135812
$726$		0			0
$727$	−19.5147			−0.723761			−0.361880	−	0.932225i	$-0.617865\pi$
$727$	−19.5147			−0.723761			−0.361880	+	0.932225i	$0.617865\pi$
$728$	−3.19621	+	9.83692i	−0.118459	+	0.364580i
$729$	34.7877	−	25.2748i	1.28843	−	0.936102i
$730$	−2.28825	−	1.66251i	−0.0846918	−	0.0615322i
$731$	−12.6606	−	38.9653i	−0.468269	−	1.44118i
$732$	−31.1652	−	95.9167i	−1.15190	−	3.54518i
$733$	−14.1221	−	10.2603i	−0.521611	−	0.378972i	0.295600	−	0.955312i	$-0.404481\pi$
$733$	−14.1221	−	10.2603i	−0.521611	−	0.378972i	−0.817210	+	0.576340i	$0.804481\pi$
$734$	−16.5729	+	12.0409i	−0.611718	+	0.444439i
$735$	−2.62210	+	8.06998i	−0.0967175	+	0.297666i
$736$	−4.48528			−0.165330
$737$		0			0
$738$	72.4264			2.66605
$739$	−9.25232	+	28.4757i	−0.340352	+	1.04750i	0.623673	+	0.781685i	$0.285640\pi$
$739$	−9.25232	+	28.4757i	−0.340352	+	1.04750i	−0.964025	+	0.265811i	$0.914360\pi$
$740$	−23.7153	+	17.2302i	−0.871791	+	0.633393i
$741$		0			0
$742$	−17.3928	−	53.5295i	−0.638510	−	1.96513i
$743$	15.3266	+	47.1705i	0.562279	+	1.73052i	0.675900	+	0.736993i	$0.263755\pi$
$743$	15.3266	+	47.1705i	0.562279	+	1.73052i	−0.113621	+	0.993524i	$0.536245\pi$
$744$		0			0
$745$	−0.277611	+	0.201696i	−0.0101709	+	0.00738957i
$746$	26.7072	−	82.1964i	0.977821	−	3.00942i
$747$	30.0000			1.09764
$748$		0			0
$749$	−15.3137			−0.559551
$750$	−2.11010	+	6.49422i	−0.0770500	+	0.237135i
$751$	12.9443	−	9.40456i	0.472343	−	0.343177i	−0.326011	−	0.945366i	$-0.605705\pi$
$751$	12.9443	−	9.40456i	0.472343	−	0.343177i	0.798354	+	0.602189i	$0.205705\pi$
$752$	−6.86474	−	4.98752i	−0.250331	−	0.181876i
$753$	−10.4884	−	32.2799i	−0.382218	−	1.17635i
$754$	−3.19621	−	9.83692i	−0.116399	−	0.358239i
$755$	9.70820	+	7.05342i	0.353318	+	0.256700i
$756$	35.0415	−	25.4592i	1.27445	−	0.925941i
$757$	4.11416	−	12.6621i	0.149532	−	0.460211i	−0.848034	−	0.529942i	$-0.822214\pi$
$757$	4.11416	−	12.6621i	0.149532	−	0.460211i	0.997566	+	0.0697302i	$0.0222138\pi$
$758$	−81.2548			−2.95131
$759$		0			0
$760$		0			0
$761$	9.27051	−	28.5317i	0.336056	−	1.03427i	−0.630144	−	0.776478i	$-0.717004\pi$
$761$	9.27051	−	28.5317i	0.336056	−	1.03427i	0.966200	−	0.257795i	$-0.0829959\pi$
$762$	23.9929	−	17.4319i	0.869171	−	0.631490i
$763$	−12.3891	−	9.00117i	−0.448514	−	0.325864i
$764$	3.92028	+	12.0654i	0.141831	+	0.436510i
$765$	10.5505	+	32.4711i	0.381454	+	1.17400i
$766$	−11.4412	−	8.31254i	−0.413388	−	0.300344i
$767$	−1.57040	+	1.14096i	−0.0567040	+	0.0411979i
$768$	26.1952	−	80.6206i	0.945239	−	2.90915i
$769$	18.9706			0.684096			0.342048	−	0.939682i	$-0.388879\pi$
$769$	18.9706			0.684096			0.342048	+	0.939682i	$0.388879\pi$
$770$		0			0
$771$	26.3431			0.948725
$772$	1.38603	−	4.26576i	0.0498842	−	0.153528i
$773$	−21.2644	+	15.4495i	−0.764828	+	0.555680i	−0.900387	−	0.435089i	$-0.856717\pi$
$773$	−21.2644	+	15.4495i	−0.764828	+	0.555680i	0.135559	+	0.990769i	$0.456717\pi$
$774$	58.5942	+	42.5712i	2.10612	+	1.53019i
$775$		0			0
$776$	−4.98819	−	15.3521i	−0.179066	−	0.551108i
$777$	−35.0415	−	25.4592i	−1.25711	−	0.913342i
$778$	40.2882	−	29.2711i	1.44440	−	1.04942i
$779$		0			0
$780$	12.6863			0.454242
$781$		0			0
$782$	−46.6274			−1.66739
$783$	−6.39242	+	19.6738i	−0.228446	+	0.703085i
$784$	7.28115	−	5.29007i	0.260041	−	0.188931i
$785$	−11.3262	−	8.22899i	−0.404251	−	0.293705i
$786$	23.8731	+	73.4737i	0.851524	+	2.62072i
$787$	4.62616	+	14.2379i	0.164905	+	0.507525i	0.999029	−	0.0440516i	$-0.0140266\pi$
$787$	4.62616	+	14.2379i	0.164905	+	0.507525i	−0.834125	+	0.551576i	$0.814027\pi$
$788$	−33.5385	−	24.3671i	−1.19476	−	0.868043i
$789$	25.1033	−	18.2386i	0.893703	−	0.649313i
$790$	−2.98413	+	9.18421i	−0.106171	+	0.326760i
$791$	39.3137			1.39783
$792$		0			0
$793$	10.9117			0.387485
$794$	6.94833	−	21.3848i	0.246587	−	0.758917i
$795$	−26.6737	+	19.3796i	−0.946020	+	0.687324i
$796$	−32.0354	−	23.2751i	−1.13547	−	0.824964i
$797$	10.0824	+	31.0305i	0.357138	+	1.09916i	0.954759	+	0.297379i	$0.0961125\pi$
$797$	10.0824	+	31.0305i	0.357138	+	1.09916i	−0.597622	+	0.801778i	$0.703887\pi$
$798$		0			0
$799$	15.6251	+	11.3523i	0.552777	+	0.401616i
$800$	−1.28293	+	0.932102i	−0.0453584	+	0.0329548i
$801$	−20.5708	+	63.3104i	−0.726834	+	2.23696i
$802$	12.8284			0.452988
$803$		0			0
$804$	−135.196			−4.76799
$805$	1.74806	−	5.37999i	0.0616112	−	0.189620i
$806$		0			0
$807$	39.6180	+	28.7842i	1.39462	+	1.01325i
$808$	12.7045	+	39.1005i	0.446944	+	1.37555i
$809$	3.39009	+	10.4336i	0.119189	+	0.366827i	0.992798	−	0.119803i	$-0.0382262\pi$
$809$	3.39009	+	10.4336i	0.119189	+	0.366827i	−0.873608	+	0.486629i	$0.838226\pi$
$810$	−1.95314	−	1.41904i	−0.0686263	−	0.0498600i
$811$	43.6393	−	31.7058i	1.53238	−	1.11334i	0.577487	−	0.816400i	$-0.304033\pi$
$811$	43.6393	−	31.7058i	1.53238	−	1.11334i	0.954896	−	0.296941i	$-0.0959665\pi$
$812$	8.65248	−	26.6296i	0.303642	−	0.934515i
$813$	20.6863			0.725500
$814$		0			0
$815$	−16.4853			−0.577454
$816$	17.9048	−	55.1053i	0.626793	−	1.92907i
$817$		0			0
$818$	−2.01063	−	1.46081i	−0.0703002	−	0.0510761i
$819$	3.62036	+	11.1423i	0.126506	+	0.389344i
$820$	7.09829	+	21.8463i	0.247883	+	0.762906i
$821$	−33.4235	−	24.2836i	−1.16649	−	0.847503i	−0.175904	−	0.984407i	$-0.556285\pi$
$821$	−33.4235	−	24.2836i	−1.16649	−	0.847503i	−0.990584	+	0.136904i	$0.956285\pi$
$822$	60.6048	−	44.0320i	2.11384	−	1.53579i
$823$	6.03038	−	18.5596i	0.210206	−	0.646947i	−0.789254	−	0.614068i	$-0.789532\pi$
$823$	6.03038	−	18.5596i	0.210206	−	0.646947i	0.999459	−	0.0328795i	$-0.0104678\pi$
$824$	−30.1421			−1.05005
$825$		0			0
$826$	−8.00000			−0.278356
$827$	−6.88622	+	21.1936i	−0.239457	+	0.736974i	0.757042	+	0.653367i	$0.226644\pi$
$827$	−6.88622	+	21.1936i	−0.239457	+	0.736974i	−0.996499	+	0.0836070i	$0.973356\pi$
$828$	43.8019	−	31.8239i	1.52222	−	1.10596i
$829$	−14.5623	−	10.5801i	−0.505770	−	0.367463i	0.305447	−	0.952209i	$-0.401194\pi$
$829$	−14.5623	−	10.5801i	−0.505770	−	0.367463i	−0.811217	+	0.584746i	$0.801194\pi$
$830$	4.47620	+	13.7763i	0.155371	+	0.478183i
$831$	5.96826	+	18.3684i	0.207037	+	0.637194i
$832$	9.31560	+	6.76818i	0.322960	+	0.234644i
$833$	−16.5729	+	12.0409i	−0.574218	+	0.417194i
$834$	8.44040	−	25.9769i	0.292267	−	0.899506i
$835$	−22.9706			−0.794929
$836$		0			0
$837$		0			0
$838$	19.1409	−	58.9095i	0.661210	−	2.03500i
$839$	−21.3121	+	15.4841i	−0.735774	+	0.534571i	−0.891385	−	0.453247i	$-0.850265\pi$
$839$	−21.3121	+	15.4841i	−0.735774	+	0.534571i	0.155611	+	0.987818i	$0.450265\pi$
$840$	20.2016	+	14.6773i	0.697022	+	0.506416i
$841$	−4.82914	−	14.8626i	−0.166522	−	0.512502i
$842$	4.47620	+	13.7763i	0.154260	+	0.474763i
$843$	−39.6180	−	28.7842i	−1.36452	−	0.991380i
$844$	−49.5562	+	36.0047i	−1.70579	+	1.23933i
$845$	3.59307	−	11.0583i	0.123605	−	0.380418i
$846$	−34.1421			−1.17383
$847$		0			0
$848$	34.9706			1.20089
$849$	28.5174	−	87.7676i	0.978715	−	3.01217i
$850$	−13.3369	+	9.68981i	−0.457451	+	0.332358i
$851$	−17.5208	−	12.7296i	−0.600604	−	0.436364i
$852$	−37.8576	−	116.514i	−1.29698	−	3.99169i
$853$	4.79431	+	14.7554i	0.164154	+	0.505214i	0.998973	−	0.0453103i	$-0.0144277\pi$
$853$	4.79431	+	14.7554i	0.164154	+	0.505214i	−0.834819	+	0.550525i	$0.814428\pi$
$854$	36.3819	+	26.4330i	1.24496	+	0.904520i
$855$		0			0
$856$	10.4445	−	32.1447i	0.356984	−	1.09868i
$857$	−24.7696			−0.846112			−0.423056	−	0.906104i	$-0.639043\pi$
$857$	−24.7696			−0.846112			−0.423056	+	0.906104i	$0.639043\pi$
$858$		0			0
$859$	24.2843			0.828569			0.414284	−	0.910148i	$-0.364032\pi$
$859$	24.2843			0.828569			0.414284	+	0.910148i	$0.364032\pi$
$860$	−7.09829	+	21.8463i	−0.242050	+	0.744953i
$861$	−27.4589	+	19.9501i	−0.935798	+	0.679897i
$862$	22.0973	+	16.0546i	0.752635	+	0.546822i
$863$	−2.83417	−	8.72268i	−0.0964763	−	0.296924i	0.891159	−	0.453691i	$-0.149893\pi$
$863$	−2.83417	−	8.72268i	−0.0964763	−	0.296924i	−0.987636	+	0.156767i	$0.949893\pi$
$864$	−2.77206	−	8.53151i	−0.0943073	−	0.290248i
$865$	17.9134	+	13.0148i	0.609073	+	0.442517i
$866$	−14.9549	+	10.8654i	−0.508188	+	0.369220i
$867$	−25.8953	+	79.6976i	−0.879451	+	2.70667i
$868$		0			0
$869$		0			0
$870$	−24.9706			−0.846581
$871$	4.52012	−	13.9115i	0.153158	−	0.471373i
$872$	27.3440	−	19.8665i	0.925983	−	0.672766i
$873$	−14.7923	−	10.7472i	−0.500643	−	0.363738i
$874$		0			0
$875$	−0.618034	−	1.90211i	−0.0208934	−	0.0643032i
$876$	10.2634	+	7.45682i	0.346769	+	0.251942i
$877$	−40.0106	+	29.0694i	−1.35106	+	0.981604i	−0.352105	+	0.935961i	$0.614534\pi$
$877$	−40.0106	+	29.0694i	−1.35106	+	0.981604i	−0.998958	+	0.0456438i	$0.985466\pi$
$878$	−11.9365	+	36.7369i	−0.402838	+	1.23981i
$879$	−25.9411			−0.874972
$880$		0			0
$881$	−7.37258			−0.248389			−0.124194	−	0.992258i	$-0.539635\pi$
$881$	−7.37258			−0.248389			−0.124194	+	0.992258i	$0.539635\pi$
$882$	11.1905	−	34.4408i	0.376804	−	1.15968i
$883$	−30.0724	+	21.8489i	−1.01202	+	0.735274i	−0.964631	−	0.263603i	$-0.915089\pi$
$883$	−30.0724	+	21.8489i	−1.01202	+	0.735274i	−0.0473866	+	0.998877i	$0.515089\pi$
$884$	24.7781	+	18.0023i	0.833378	+	0.605484i
$885$	1.44814	+	4.45693i	0.0486788	+	0.149818i
$886$	20.0149	+	61.5995i	0.672413	+	2.06948i
$887$	30.9726	+	22.5029i	1.03996	+	0.755574i	0.970278	−	0.241995i	$-0.0778017\pi$
$887$	30.9726	+	22.5029i	1.03996	+	0.755574i	0.0696815	+	0.997569i	$0.477802\pi$
$888$	77.3404	−	56.1911i	2.59537	−	1.88565i
$889$	−2.68421	+	8.26115i	−0.0900256	+	0.277070i
$890$	−32.1421			−1.07741
$891$		0			0
$892$	−41.4558			−1.38804
$893$		0			0
$894$	1.89564	−	1.37727i	0.0633998	−	0.0460627i
$895$	7.81256	+	5.67616i	0.261145	+	0.189733i
$896$	12.7045	+	39.1005i	0.424428	+	1.30626i
$897$	2.89629	+	8.91386i	0.0967042	+	0.297625i
$898$	55.9133	+	40.6234i	1.86585	+	1.35562i
$899$		0			0
$900$	5.91525	−	18.2053i	0.197175	−	0.606842i
$901$	−79.5980			−2.65179
$902$		0			0
$903$	−33.9411			−1.12949
$904$	−26.8133	+	82.5227i	−0.891796	+	2.74467i
$905$	17.2432	−	12.5279i	0.573182	−	0.416441i
$906$	−66.2918	−	48.1638i	−2.20240	−	1.60013i
$907$	−8.50252	−	26.1681i	−0.282321	−	0.868896i	−0.987189	−	0.159557i	$-0.948993\pi$
$907$	−8.50252	−	26.1681i	−0.282321	−	0.868896i	0.704867	−	0.709339i	$-0.251007\pi$
$908$	−29.9474	−	92.1685i	−0.993838	−	3.05872i
$909$	37.6747	+	27.3723i	1.24959	+	0.907882i
$910$	−4.57649	+	3.32502i	−0.151709	+	0.110223i
$911$	−3.07198	+	9.45457i	−0.101779	+	0.313244i	−0.988961	−	0.148176i	$-0.952660\pi$
$911$	−3.07198	+	9.45457i	−0.101779	+	0.313244i	0.887182	+	0.461420i	$0.152660\pi$
$912$		0			0
$913$		0			0
$914$	1.17157			0.0387522
$915$	8.14048	−	25.0538i	0.269116	−	0.828254i
$916$	−4.06890	+	2.95623i	−0.134440	+	0.0976766i
$917$	−18.3060	−	13.3001i	−0.604516	−	0.439207i
$918$	−28.8173	−	88.6906i	−0.951114	−	2.92723i
$919$	9.88854	+	30.4338i	0.326193	+	1.00392i	0.970899	+	0.239488i	$0.0769797\pi$
$919$	9.88854	+	30.4338i	0.326193	+	1.00392i	−0.644706	+	0.764430i	$0.723020\pi$
$920$	10.1008	+	7.33866i	0.333014	+	0.241949i
$921$	37.3971	−	27.1706i	1.23228	−	0.895302i
$922$	9.42047	−	28.9932i	0.310247	−	0.954841i
$923$	13.2548			0.436288
$924$		0			0
$925$	−7.65685			−0.251756
$926$	4.58224	−	14.1027i	0.150582	−	0.463443i
$927$	−27.6216	+	20.0682i	−0.907211	+	0.659128i
$928$	−4.69148	−	3.40856i	−0.154005	−	0.111891i
$929$	1.64203	+	5.05364i	0.0538731	+	0.165804i	0.974373	−	0.224939i	$-0.0722181\pi$
$929$	1.64203	+	5.05364i	0.0538731	+	0.165804i	−0.920500	+	0.390743i	$0.872218\pi$
$930$		0			0
$931$		0			0
$932$	−19.0238	+	13.8216i	−0.623146	+	0.452742i
$933$	−4.09597	+	12.6061i	−0.134096	+	0.412705i
$934$	35.7990			1.17138
$935$		0			0
$936$	−25.8579			−0.845191
$937$	0.449881	−	1.38459i	0.0146970	−	0.0452326i	−0.943439	−	0.331546i	$-0.892430\pi$
$937$	0.449881	−	1.38459i	0.0146970	−	0.0452326i	0.958136	+	0.286313i	$0.0924298\pi$
$938$	48.7710	−	35.4342i	1.59243	−	1.15697i
$939$	−3.00609	−	2.18405i	−0.0981000	−	0.0712738i
$940$	−3.34617	−	10.2984i	−0.109140	−	0.335898i
$941$	2.06618	+	6.35904i	0.0673555	+	0.207299i	0.979069	−	0.203527i	$-0.0652405\pi$
$941$	2.06618	+	6.35904i	0.0673555	+	0.207299i	−0.911714	+	0.410826i	$0.865240\pi$
$942$	77.3404	+	56.1911i	2.51989	+	1.83080i
$943$	−13.7295	+	9.97505i	−0.447093	+	0.324832i
$944$	1.53599	−	4.72729i	0.0499922	−	0.153860i
$945$	11.3137			0.368035
$946$		0			0
$947$	41.1716			1.33790			0.668948	−	0.743309i	$-0.266745\pi$
$947$	41.1716			1.33790			0.668948	+	0.743309i	$0.266745\pi$
$948$	13.3847	−	41.1938i	0.434714	−	1.33791i
$949$	−1.11044	+	0.806784i	−0.0360465	+	0.0261893i
$950$		0			0
$951$	1.14822	+	3.53387i	0.0372337	+	0.114594i
$952$	18.6289	+	57.3337i	0.603765	+	1.85820i
$953$	43.0167	+	31.2535i	1.39345	+	1.01240i	0.995477	+	0.0950009i	$0.0302854\pi$
$953$	43.0167	+	31.2535i	1.39345	+	1.01240i	0.397971	+	0.917398i	$0.369715\pi$
$954$	113.837	−	82.7077i	3.68562	−	2.67776i
$955$	−1.02399	+	3.15152i	−0.0331356	+	0.101981i
$956$	89.2548			2.88671
$957$		0			0
$958$	−86.9117			−2.80799
$959$	−6.78018	+	20.8673i	−0.218943	+	0.673839i
$960$	22.4899	−	16.3398i	0.725857	−	0.527366i
$961$	25.0795	+	18.2213i	0.809017	+	0.587785i
$962$	6.69234	+	20.5969i	0.215770	+	0.664070i
$963$	−11.8305	−	36.4105i	−0.381232	−	1.17331i
$964$	18.5836	+	13.5018i	0.598537	+	0.434862i
$965$	0.947822	−	0.688633i	0.0305115	−	0.0221679i
$966$	−11.9365	+	36.7369i	−0.384052	+	1.18199i
$967$	14.9706			0.481421			0.240710	−	0.970597i	$-0.422620\pi$
$967$	14.9706			0.481421			0.240710	+	0.970597i	$0.422620\pi$
$968$		0			0
$969$		0			0
$970$	2.72813	−	8.39633i	0.0875951	−	0.269590i
$971$	7.02736	−	5.10567i	0.225519	−	0.163849i	−0.469289	−	0.883045i	$-0.655490\pi$
$971$	7.02736	−	5.10567i	0.225519	−	0.163849i	0.694807	+	0.719196i	$0.255490\pi$
$972$	−43.8019	−	31.8239i	−1.40495	−	1.02075i
$973$	2.47214	+	7.60845i	0.0792530	+	0.243916i
$974$	18.2668	+	56.2195i	0.585307	+	1.80139i
$975$	2.68085	+	1.94775i	0.0858558	+	0.0623779i
$976$	−22.6048	+	16.4234i	−0.723563	+	0.525700i
$977$	9.99458	−	30.7602i	0.319755	−	0.984105i	−0.653998	−	0.756496i	$-0.726909\pi$
$977$	9.99458	−	30.7602i	0.319755	−	0.984105i	0.973753	−	0.227608i	$-0.0730906\pi$
$978$	112.569			3.59955
$979$		0			0
$980$	11.4853			0.366884
$981$	11.8305	−	36.4105i	0.377718	−	1.16250i
$982$	1.34042	−	0.973874i	0.0427746	−	0.0310776i
$983$	17.6834	+	12.8477i	0.564012	+	0.409779i	0.832925	−	0.553386i	$-0.186664\pi$
$983$	17.6834	+	12.8477i	0.564012	+	0.409779i	−0.268913	+	0.963165i	$0.586664\pi$
$984$	−23.1490	−	71.2452i	−0.737963	−	2.27122i
$985$	−3.34617	−	10.2984i	−0.106618	−	0.328136i
$986$	−48.7710	−	35.4342i	−1.55319	−	1.12845i
$987$	12.9443	−	9.40456i	0.412021	−	0.299351i
$988$		0			0
$989$	−16.9706			−0.539633
$990$		0			0
$991$	−57.9411			−1.84056			−0.920280	−	0.391260i	$-0.872039\pi$
$991$	−57.9411			−1.84056			−0.920280	+	0.391260i	$0.872039\pi$
$992$		0			0
$993$	−16.7356	+	12.1591i	−0.531087	+	0.385857i
$994$	44.1945	+	32.1092i	1.40176	+	1.01844i
$995$	−3.19621	−	9.83692i	−0.101327	−	0.311851i
$996$	−20.0770	−	61.7907i	−0.636164	−	1.95791i
$997$	−33.5385	−	24.3671i	−1.06217	−	0.771715i	−0.0876850	−	0.996148i	$-0.527947\pi$
$997$	−33.5385	−	24.3671i	−1.06217	−	0.771715i	−0.974489	+	0.224433i	$0.927947\pi$
$998$	18.8612	−	13.7035i	0.597040	−	0.433775i
$999$	13.3847	−	41.1938i	0.423472	−	1.30331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.l.251.1		8
11.2	odd	10		605.2.g.f.366.1		8
11.3	even	5	inner	605.2.g.l.81.2		8
11.4	even	5		605.2.a.d.1.1		2
11.5	even	5	inner	605.2.g.l.511.1		8
11.6	odd	10		605.2.g.f.511.2		8
11.7	odd	10		55.2.a.b.1.2	✓	2
11.8	odd	10		605.2.g.f.81.1		8
11.9	even	5	inner	605.2.g.l.366.2		8
11.10	odd	2		605.2.g.f.251.2		8
33.26	odd	10		5445.2.a.y.1.2		2
33.29	even	10		495.2.a.b.1.1		2
44.7	even	10		880.2.a.m.1.2		2
44.15	odd	10		9680.2.a.bn.1.2		2
55.4	even	10		3025.2.a.o.1.2		2
55.7	even	20		275.2.b.d.199.4		4
55.18	even	20		275.2.b.d.199.1		4
55.29	odd	10		275.2.a.c.1.1		2
77.62	even	10		2695.2.a.f.1.2		2
88.29	odd	10		3520.2.a.bn.1.2		2
88.51	even	10		3520.2.a.bo.1.1		2
132.95	odd	10		7920.2.a.ch.1.2		2
143.51	odd	10		9295.2.a.g.1.1		2
165.29	even	10		2475.2.a.x.1.2		2
165.62	odd	20		2475.2.c.l.199.1		4
165.128	odd	20		2475.2.c.l.199.4		4
220.7	odd	20		4400.2.b.q.4049.2		4
220.139	even	10		4400.2.a.bn.1.1		2
220.183	odd	20		4400.2.b.q.4049.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.b.1.2	✓	2	11.7	odd	10
275.2.a.c.1.1		2	55.29	odd	10
275.2.b.d.199.1		4	55.18	even	20
275.2.b.d.199.4		4	55.7	even	20
495.2.a.b.1.1		2	33.29	even	10
605.2.a.d.1.1		2	11.4	even	5
605.2.g.f.81.1		8	11.8	odd	10
605.2.g.f.251.2		8	11.10	odd	2
605.2.g.f.366.1		8	11.2	odd	10
605.2.g.f.511.2		8	11.6	odd	10
605.2.g.l.81.2		8	11.3	even	5	inner
605.2.g.l.251.1		8	1.1	even	1	trivial
605.2.g.l.366.2		8	11.9	even	5	inner
605.2.g.l.511.1		8	11.5	even	5	inner
880.2.a.m.1.2		2	44.7	even	10
2475.2.a.x.1.2		2	165.29	even	10
2475.2.c.l.199.1		4	165.62	odd	20
2475.2.c.l.199.4		4	165.128	odd	20
2695.2.a.f.1.2		2	77.62	even	10
3025.2.a.o.1.2		2	55.4	even	10
3520.2.a.bn.1.2		2	88.29	odd	10
3520.2.a.bo.1.1		2	88.51	even	10
4400.2.a.bn.1.1		2	220.139	even	10
4400.2.b.q.4049.2		4	220.7	odd	20
4400.2.b.q.4049.3		4	220.183	odd	20
5445.2.a.y.1.2		2	33.26	odd	10
7920.2.a.ch.1.2		2	132.95	odd	10
9295.2.a.g.1.1		2	143.51	odd	10
9680.2.a.bn.1.2		2	44.15	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.746033 + 2.29605i) q^{2} +(2.28825 - 1.66251i) q^{3} +(-3.09726 - 2.25029i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(2.11010 + 6.49422i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(3.57117 - 2.59461i) q^{8} +(1.54508 - 4.75528i) q^{9} +O(q^{10})\)	\(q+(-0.746033 + 2.29605i) q^{2} +(2.28825 - 1.66251i) q^{3} +(-3.09726 - 2.25029i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(2.11010 + 6.49422i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(3.57117 - 2.59461i) q^{8} +(1.54508 - 4.75528i) q^{9} +2.41421 q^{10} -10.8284 q^{12} +(0.362036 - 1.11423i) q^{13} +(3.90628 - 2.83808i) q^{14} +(-2.28825 - 1.66251i) q^{15} +(0.927051 + 2.85317i) q^{16} +(-2.11010 - 6.49422i) q^{17} +(9.76570 + 7.09520i) q^{18} +(-1.18305 + 3.64105i) q^{20} -5.65685 q^{21} -2.82843 q^{23} +(3.85816 - 11.8742i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(2.28825 + 1.66251i) q^{26} +(-1.74806 - 5.37999i) q^{27} +(2.36610 + 7.28210i) q^{28} +(-2.95846 - 2.14944i) q^{29} +(5.52431 - 4.01365i) q^{30} +1.58579 q^{32} +16.4853 q^{34} +(-0.618034 + 1.90211i) q^{35} +(-15.4863 + 11.2515i) q^{36} +(6.19453 + 4.50059i) q^{37} +(-1.02399 - 3.15152i) q^{39} +(-3.57117 - 2.59461i) q^{40} +(4.85410 - 3.52671i) q^{41} +(4.22020 - 12.9884i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(2.11010 - 6.49422i) q^{46} +(-2.28825 + 1.66251i) q^{47} +(6.86474 + 4.98752i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(-0.746033 - 2.29605i) q^{50} +(-15.6251 - 11.3523i) q^{51} +(-3.62867 + 2.63638i) q^{52} +(3.60217 - 11.0863i) q^{53} +13.6569 q^{54} -8.82843 q^{56} +(7.14235 - 5.18922i) q^{58} +(-1.34042 - 0.973874i) q^{59} +(3.34617 + 10.2984i) q^{60} +(2.87809 + 8.85786i) q^{61} +(-8.09017 + 5.87785i) q^{63} +(-3.03715 + 9.34739i) q^{64} -1.17157 q^{65} +12.4853 q^{67} +(-8.07836 + 24.8626i) q^{68} +(-6.47214 + 4.70228i) q^{69} +(-3.90628 - 2.83808i) q^{70} +(3.49613 + 10.7600i) q^{71} +(-6.82034 - 20.9908i) q^{72} +(-0.947822 - 0.688633i) q^{73} +(-14.9549 + 10.8654i) q^{74} +(-0.874032 + 2.68999i) q^{75} +8.00000 q^{78} +(-1.23607 + 3.80423i) q^{79} +(2.42705 - 1.76336i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(4.47620 + 13.7763i) q^{82} +(1.85410 + 5.70634i) q^{83} +(17.5208 + 12.7296i) q^{84} +(-5.52431 + 4.01365i) q^{85} +(-4.47620 + 13.7763i) q^{86} -10.3431 q^{87} -13.3137 q^{89} +(3.73017 - 11.4803i) q^{90} +(-1.89564 + 1.37727i) q^{91} +(8.76038 + 6.36479i) q^{92} +(-2.11010 - 6.49422i) q^{94} +(3.62867 - 2.63638i) q^{96} +(1.13003 - 3.47788i) q^{97} +7.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9 + 8 * q^10 - 64 * q^12 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 8 * q^17 + 10 * q^18 + 2 * q^20 - 8 * q^24 - 2 * q^25 - 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^32 + 64 * q^34 + 4 * q^35 - 10 * q^36 + 4 * q^37 - 16 * q^39 - 6 * q^40 + 12 * q^41 - 16 * q^42 + 48 * q^43 - 40 * q^45 - 8 * q^46 + 6 * q^49 + 2 * q^50 - 16 * q^51 + 8 * q^52 - 12 * q^53 + 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 20 * q^63 + 14 * q^64 - 32 * q^65 + 32 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 + 30 * q^72 - 8 * q^73 - 20 * q^74 + 64 * q^78 + 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 - 12 * q^83 + 32 * q^84 - 8 * q^85 + 12 * q^86 - 128 * q^87 - 16 * q^89 - 10 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^94 - 8 * q^96 + 4 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

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