LMFDB - Embedded newform 605.2.g.f.511.2

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			511.2
Root			$-1.14412 + 0.831254i$ of defining polynomial
Character	$\chi$	$=$	605.511
Dual form			605.2.g.f.251.2

$q$-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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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	0.759268	+	0.650778i	$0.225557\pi$
$2$	0.746033	+	2.29605i	0.527525	+	1.62356i	−0.231743	+	0.972777i	$0.574443\pi$
$3$	2.28825	+	1.66251i	1.32112	+	0.959849i	0.999918	+	0.0128385i	$0.00408672\pi$
$3$	2.28825	+	1.66251i	1.32112	+	0.959849i	0.321202	+	0.947011i	$0.395913\pi$
$4$	−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	$-0.576624\pi$
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	0.849963	+	0.526842i	$0.176624\pi$
$8$	−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	$-0.151945\pi$
$13$	−0.362036	−	1.11423i	−0.100411	−	0.309032i	−0.988626	+	0.150395i	$0.951945\pi$
$14$	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	−0.277301	−	0.960783i	$-0.589440\pi$
$17$	2.11010	−	6.49422i	0.511774	−	1.57508i	0.789075	−	0.614297i	$-0.210560\pi$
$18$	−9.76570	+	7.09520i	−2.30180	+	1.67235i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	−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	$-0.589732\pi$
$29$	2.95846	−	2.14944i	0.549372	−	0.399142i	0.827554	+	0.561386i	$0.189732\pi$
$30$	−5.52431	−	4.01365i	−1.00860	−	0.732789i
$31$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$31$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$32$	−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	0.0524248	−	0.998625i	$-0.483305\pi$
$37$	6.19453	−	4.50059i	1.01837	−	0.739892i	0.965949	+	0.258733i	$0.0833050\pi$
$38$		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	$-0.455213\pi$
$41$	−4.85410	−	3.52671i	−0.758083	−	0.550780i	−0.898322	+	0.439338i	$0.855213\pi$
$42$	4.22020	+	12.9884i	0.651191	+	2.00416i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$		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	0.408256	−	0.912868i	$-0.366137\pi$
$47$	−2.28825	−	1.66251i	−0.333775	−	0.242502i	−0.742031	+	0.670366i	$0.766137\pi$
$48$	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	0.817275	+	0.576248i	$0.195484\pi$
$53$	3.60217	+	11.0863i	0.494796	+	1.52282i	−0.322480	+	0.946576i	$0.604516\pi$
$54$	−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	−0.671611	−	0.740904i	$-0.734397\pi$
$59$	−1.34042	+	0.973874i	−0.174508	+	0.126788i	0.497103	+	0.867692i	$0.334397\pi$
$60$	3.34617	−	10.2984i	0.431988	−	1.32952i
$61$	−2.87809	+	8.85786i	−0.368502	+	1.13413i	0.579257	+	0.815145i	$0.303343\pi$
$61$	−2.87809	+	8.85786i	−0.368502	+	1.13413i	−0.947759	+	0.318988i	$0.896657\pi$
$62$		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	−0.497414	−	0.867513i	$-0.665717\pi$
$71$	3.49613	−	10.7600i	0.414914	−	1.27697i	0.912328	−	0.409461i	$-0.134283\pi$
$72$	6.82034	−	20.9908i	0.803784	−	2.47379i
$73$	0.947822	−	0.688633i	0.110934	−	0.0805984i	−0.530935	−	0.847413i	$-0.678159\pi$
$73$	0.947822	−	0.688633i	0.110934	−	0.0805984i	0.641869	+	0.766814i	$0.278159\pi$
$74$	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	$-0.0277560\pi$
$79$	1.23607	+	3.80423i	0.139069	+	0.428009i	−0.857132	+	0.515097i	$0.827756\pi$
$80$	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	0.796257	+	0.604959i	$0.206810\pi$
$83$	−1.85410	+	5.70634i	−0.203514	+	0.626352i	−0.999771	+	0.0213936i	$0.993190\pi$
$84$	−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	0.991892	−	0.127083i	$-0.0405614\pi$
$97$	1.13003	+	3.47788i	0.114737	+	0.353125i	−0.877155	+	0.480207i	$0.840561\pi$
$98$	−7.24264			−0.731617
$99$		0			0
$100$	3.82843			0.382843
$101$	2.87809	+	8.85786i	0.286381	+	0.881390i	0.985981	+	0.166856i	$0.0533615\pi$
$101$	2.87809	+	8.85786i	0.286381	+	0.881390i	−0.699600	+	0.714534i	$0.746639\pi$
$102$	37.7224	+	27.4069i	3.73507	+	2.71369i
$103$	−5.52431	+	4.01365i	−0.544327	+	0.395477i	−0.825689	−	0.564125i	$-0.809214\pi$
$103$	−5.52431	+	4.01365i	−0.544327	+	0.395477i	0.281363	+	0.959602i	$0.409214\pi$
$104$	−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	$-0.420679\pi$
$107$	−6.19453	−	4.50059i	−0.598847	−	0.435088i	−0.845470	+	0.534024i	$0.820679\pi$
$108$	−6.69234	−	20.5969i	−0.643970	−	1.98194i
$109$	−7.65685			−0.733394			−0.366697	−	0.930341i	$-0.619511\pi$
$109$	−7.65685			−0.733394			−0.366697	+	0.930341i	$0.619511\pi$
$110$		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	−0.971940	−	0.235230i	$-0.924416\pi$
$113$	−15.9027	−	11.5540i	−1.49600	−	1.08691i	−0.524063	−	0.851679i	$-0.675584\pi$
$114$		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	$-0.838277\pi$
$127$	1.34211	−	4.13058i	0.119093	−	0.366529i	0.992779	+	0.119961i	$0.0382769\pi$
$128$	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	$-0.664554\pi$
$131$	−11.3137			−0.988483			−0.494242	+	0.869325i	$0.664554\pi$
$132$		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	0.695336	+	0.718685i	$0.255256\pi$
$137$	−3.39009	+	10.4336i	−0.289635	+	0.891405i	−0.984971	+	0.172720i	$0.944744\pi$
$138$	5.96826	−	18.3684i	0.508052	−	1.56362i
$139$	3.23607	−	2.35114i	0.274480	−	0.199421i	−0.442026	−	0.897002i	$-0.645740\pi$
$139$	3.23607	−	2.35114i	0.274480	−	0.199421i	0.716506	+	0.697581i	$0.245740\pi$
$140$	−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	$-0.895526\pi$
$149$	0.106038	−	0.326351i	0.00868696	−	0.0267357i	0.955306	+	0.295619i	$0.0955258\pi$
$150$	5.52431	−	4.01365i	0.451058	−	0.327713i
$151$	9.70820	+	7.05342i	0.790042	+	0.573999i	0.907976	−	0.419022i	$-0.137627\pi$
$151$	9.70820	+	7.05342i	0.790042	+	0.573999i	−0.117934	+	0.993021i	$0.537627\pi$
$152$		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	0.939473	−	0.342623i	$-0.111315\pi$
$157$	11.3262	+	8.22899i	0.903932	+	0.656745i	−0.0355408	+	0.999368i	$0.511315\pi$
$158$	−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	0.925794	+	0.378030i	$0.123398\pi$
$163$	5.09423	+	15.6784i	0.399011	+	1.22803i	−0.526782	+	0.850000i	$0.676602\pi$
$164$	22.9706			1.79370
$165$		0			0
$166$	−14.4853			−1.12428
$167$	−7.09829	−	21.8463i	−0.549283	−	1.69052i	−0.710584	−	0.703613i	$-0.751569\pi$
$167$	−7.09829	−	21.8463i	−0.549283	−	1.69052i	0.161301	−	0.986905i	$-0.448431\pi$
$168$	−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	0.998320	+	0.0579465i	$0.0184553\pi$
$173$	17.9134	+	13.0148i	1.36193	+	0.989499i	0.363608	+	0.931552i	$0.381545\pi$
$174$	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	0.256204	−	0.966623i	$-0.417528\pi$
$179$	−7.81256	−	5.67616i	−0.583938	−	0.424256i	−0.840142	+	0.542367i	$0.817528\pi$
$180$	15.4863	−	11.2515i	1.15428	−	0.838635i
$181$	6.58630	−	20.2705i	0.489556	−	1.50670i	−0.335717	−	0.941963i	$-0.608979\pi$
$181$	6.58630	−	20.2705i	0.489556	−	1.50670i	0.825273	−	0.564735i	$-0.191021\pi$
$182$	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	−0.680536	−	0.732715i	$-0.738253\pi$
$191$	−2.68085	+	1.94775i	−0.193979	+	0.140934i	0.486556	+	0.873649i	$0.338253\pi$
$192$	8.59036	−	26.4384i	0.619956	−	1.90803i
$193$	−0.362036	+	1.11423i	−0.0260599	+	0.0802042i	−0.963241	−	0.268640i	$-0.913426\pi$
$193$	−0.362036	+	1.11423i	−0.0260599	+	0.0802042i	0.937181	+	0.348844i	$0.113426\pi$
$194$	−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	$-0.626056\pi$
$197$	−10.8284			−0.771493			−0.385747	+	0.922605i	$0.626056\pi$
$198$		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	−0.964012	−	0.265859i	$-0.914345\pi$
$211$	−4.94427	−	15.2169i	−0.340378	−	1.04757i	0.623634	−	0.781716i	$-0.285655\pi$
$212$	−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	0.841111	−	0.540862i	$-0.181902\pi$
$223$	8.76038	+	6.36479i	0.586639	+	0.426218i	−0.254473	+	0.967080i	$0.581902\pi$
$224$	−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	−0.360762	+	0.932658i	$0.617483\pi$
$227$	−20.4792	+	14.8790i	−1.35925	+	0.987556i	−0.998492	+	0.0548975i	$0.982517\pi$
$228$		0			0
$229$	0.405958	+	1.24941i	0.0268265	+	0.0825634i	0.963573	−	0.267444i	$-0.0861791\pi$
$229$	0.405958	+	1.24941i	0.0268265	+	0.0825634i	−0.936747	+	0.350007i	$0.886179\pi$
$230$	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	$-0.164482\pi$
$233$	−1.89802	−	5.84152i	−0.124344	−	0.382691i	−0.993781	+	0.111353i	$0.964482\pi$
$234$	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	$-0.0281125\pi$
$239$	18.8612	+	13.7035i	1.22003	+	0.886403i	0.223926	+	0.974606i	$0.428113\pi$
$240$	2.62210	+	8.06998i	0.169256	+	0.520915i
$241$	6.00000			0.386494			0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000			0.386494			0.193247	+	0.981150i	$0.438098\pi$
$242$		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	0.997245	+	0.0741818i	$0.0236345\pi$
$251$	3.70820	+	11.4127i	0.234060	+	0.720362i	−0.763185	+	0.646180i	$0.776365\pi$
$252$	−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	−0.327431	−	0.944875i	$-0.606183\pi$
$257$	7.53495	−	5.47446i	0.470017	−	0.341487i	0.797448	+	0.603388i	$0.206183\pi$
$258$	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	$-0.609831\pi$
$263$	−10.9706			−0.676474			−0.338237	+	0.941061i	$0.609831\pi$
$264$		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	−0.644683	−	0.764450i	$-0.723010\pi$
$269$	5.35023	−	16.4663i	0.326209	−	1.00397i	0.970892	−	0.239519i	$-0.0769896\pi$
$270$	4.22020	−	12.9884i	0.256833	−	0.790451i
$271$	−5.91691	+	4.29889i	−0.359427	+	0.261139i	−0.752813	−	0.658234i	$-0.771304\pi$
$271$	−5.91691	+	4.29889i	−0.359427	+	0.261139i	0.393386	+	0.919373i	$0.371304\pi$
$272$	−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	$-0.0342350\pi$
$277$	2.11010	+	6.49422i	0.126784	+	0.390200i	−0.867438	+	0.497545i	$0.834235\pi$
$278$	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	−0.654837	−	0.755770i	$-0.727263\pi$
$281$	5.35023	−	16.4663i	0.319168	−	0.982298i	0.974005	−	0.226528i	$-0.0727374\pi$
$282$	15.6251	−	11.3523i	0.930462	−	0.676020i
$283$	−26.3961	−	19.1779i	−1.56909	−	1.14001i	−0.928024	−	0.372521i	$-0.878493\pi$
$283$	−26.3961	−	19.1779i	−1.56909	−	1.14001i	−0.641064	−	0.767488i	$-0.721507\pi$
$284$	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	$-0.613669\pi$
$293$	7.41996	−	5.39092i	0.433479	−	0.314941i	0.783038	+	0.621973i	$0.213669\pi$
$294$	−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	$-0.654441\pi$
$307$	−16.3431			−0.932753			−0.466376	+	0.884586i	$0.654441\pi$
$308$		0			0
$309$	−19.3137			−1.09872
$310$		0			0
$311$	−3.79129	−	2.75453i	−0.214984	−	0.156195i	0.475082	−	0.879942i	$-0.342419\pi$
$311$	−3.79129	−	2.75453i	−0.214984	−	0.156195i	−0.690066	+	0.723746i	$0.742419\pi$
$312$	−11.8338	+	8.59778i	−0.669959	+	0.486753i
$313$	−0.405958	+	1.24941i	−0.0229461	+	0.0706209i	−0.961874	−	0.273493i	$-0.911821\pi$
$313$	−0.405958	+	1.24941i	−0.0229461	+	0.0706209i	0.938928	+	0.344114i	$0.111821\pi$
$314$	−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	0.939009	−	0.343894i	$-0.111746\pi$
$317$	−0.405958	−	1.24941i	−0.0228009	−	0.0701739i	−0.961810	+	0.273720i	$0.911746\pi$
$318$	−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	$-0.511587\pi$
$337$	16.5729	−	12.0409i	0.902786	−	0.655912i	0.939180	+	0.343425i	$0.111587\pi$
$338$	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	$-0.804858\pi$
$347$	3.39009	−	10.4336i	0.181990	−	0.560106i	0.999884	+	0.0152627i	$0.00485845\pi$
$348$	−32.0354	+	23.2751i	−1.71728	+	1.24768i
$349$	−21.8196	−	15.8529i	−1.16798	−	0.848586i	−0.177213	−	0.984172i	$-0.556708\pi$
$349$	−21.8196	−	15.8529i	−1.16798	−	0.848586i	−0.990766	+	0.135586i	$0.956708\pi$
$350$	−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	$-0.705765\pi$
$359$	−0.555221	+	0.403392i	−0.0293035	+	0.0212902i	0.573037	+	0.819529i	$0.305765\pi$
$360$	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	−0.394022	−	0.919101i	$-0.628916\pi$
$367$	6.86474	−	4.98752i	0.358336	−	0.260347i	0.752358	+	0.658755i	$0.228916\pi$
$368$	−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	$-0.122547\pi$
$373$	35.7990			1.85360			0.926801	+	0.375554i	$0.122547\pi$
$374$		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	−0.211046	−	0.977476i	$-0.567687\pi$
$379$	10.4005	−	32.0096i	0.534240	−	1.64422i	0.745286	−	0.666745i	$-0.232313\pi$
$380$		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	0.894097	−	0.447873i	$-0.147818\pi$
$383$	−1.81018	−	5.57116i	−0.0924959	−	0.284673i	−0.986593	+	0.163200i	$0.947818\pi$
$384$	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	−0.924071	−	0.382220i	$-0.875160\pi$
$389$	−16.6879	+	12.1245i	−0.846112	+	0.614736i	0.0779595	+	0.996957i	$0.475160\pi$
$390$	−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	−0.983648	−	0.180102i	$-0.942357\pi$
$401$	−1.64203	+	5.05364i	−0.0819989	+	0.252367i	0.901649	+	0.432468i	$0.142357\pi$
$402$	−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	$-0.0918978\pi$
$409$	0.318114	+	0.979053i	0.0157297	+	0.0484111i	−0.942884	+	0.333122i	$0.891898\pi$
$410$	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	0.699756	−	0.714382i	$-0.253292\pi$
$421$	4.85410	+	3.52671i	0.236574	+	0.171881i	−0.463181	+	0.886264i	$0.653292\pi$
$422$	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	$-0.187844\pi$
$431$	−3.49613	−	10.7600i	−0.168403	−	0.518290i	−0.999271	+	0.0381792i	$0.987844\pi$
$432$	13.7295	+	9.97505i	0.660560	+	0.479925i
$433$	6.19453	−	4.50059i	0.297690	−	0.216284i	−0.428907	−	0.903349i	$-0.641101\pi$
$433$	6.19453	−	4.50059i	0.297690	−	0.216284i	0.726596	+	0.687065i	$0.241101\pi$
$434$		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	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$		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	0.968552	−	0.248810i	$-0.0800394\pi$
$443$	21.7047	+	15.7694i	1.03122	+	0.749225i	0.0626669	+	0.998035i	$0.480039\pi$
$444$	−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	0.910009	+	0.414589i	$0.136075\pi$
$449$	8.84636	+	27.2263i	0.417485	+	1.28489i	−0.492523	+	0.870299i	$0.663925\pi$
$450$	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	$-0.896387\pi$
$457$	0.149960	−	0.461530i	0.00701484	−	0.0215895i	0.954503	+	0.298202i	$0.0963870\pi$
$458$	−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	$-0.404994\pi$
$461$	12.6274			0.588117			0.294059	+	0.955787i	$0.404994\pi$
$462$		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	0.787310	+	0.616557i	$0.211473\pi$
$467$	−4.58224	+	14.1027i	−0.212041	+	0.652594i	−0.999350	+	0.0360364i	$0.988527\pi$
$468$	−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	0.286861	+	0.957972i	$0.407388\pi$
$479$	−11.1246	+	34.2380i	−0.508296	+	1.56438i	−0.795157	+	0.606403i	$0.792612\pi$
$480$	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	0.937857	−	0.347023i	$-0.112807\pi$
$487$	19.8090	+	14.3921i	0.897632	+	0.652168i	−0.0402248	+	0.999191i	$0.512807\pi$
$488$	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	$-0.695070\pi$
$491$	0.555221	−	0.403392i	0.0250568	−	0.0182048i	0.600243	+	0.799818i	$0.295070\pi$
$492$	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	−0.748759	−	0.662842i	$-0.769350\pi$
$499$	−7.81256	+	5.67616i	−0.349738	+	0.254100i	0.399021	+	0.916942i	$0.369350\pi$
$500$	−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	$-0.420879\pi$
$503$	−13.4519	−	9.77335i	−0.599789	−	0.435772i	−0.845804	+	0.533494i	$0.820879\pi$
$504$	−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	0.800325	−	0.599567i	$-0.204660\pi$
$509$	10.7710	+	7.82560i	0.477417	+	0.346864i	−0.322908	+	0.946430i	$0.604660\pi$
$510$	−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	−0.937748	−	0.347316i	$-0.887093\pi$
$521$	−20.4792	+	14.8790i	−0.897211	+	0.651862i	0.0405372	+	0.999178i	$0.487093\pi$
$522$	−13.6407	+	41.9817i	−0.597036	+	1.83749i
$523$	−12.8545	+	39.5620i	−0.562087	+	1.72993i	0.114364	+	0.993439i	$0.463517\pi$
$523$	−12.8545	+	39.5620i	−0.562087	+	1.72993i	−0.676451	+	0.736488i	$0.736483\pi$
$524$	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	$-0.0588297\pi$
$541$	1.85410	+	5.70634i	0.0797141	+	0.245335i	−0.903255	+	0.429103i	$0.858830\pi$
$542$	−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	$-0.0409754\pi$
$547$	27.5066	+	19.9847i	1.17610	+	0.854484i	0.184370	+	0.982857i	$0.440975\pi$
$548$	−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	$-0.766971\pi$
$557$	−7.97518	+	5.79431i	−0.337919	+	0.245513i	0.405864	+	0.913933i	$0.366971\pi$
$558$		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	$-0.0976983\pi$
$563$	0.106038	+	0.326351i	0.00446896	+	0.0137541i	−0.948797	+	0.315886i	$0.897698\pi$
$564$	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	$-0.530956\pi$
$569$	−25.6109	−	18.6074i	−1.07367	−	0.780064i	−0.976568	+	0.215211i	$0.930956\pi$
$570$		0			0
$571$	−21.9411			−0.918208			−0.459104	−	0.888383i	$-0.651829\pi$
$571$	−21.9411			−0.918208			−0.459104	+	0.888383i	$0.651829\pi$
$572$		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	0.613560	+	0.789648i	$0.289737\pi$
$577$	−8.33436	+	25.6505i	−0.346964	+	1.06785i	−0.960524	+	0.278197i	$0.910263\pi$
$578$	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	−0.551446	−	0.834211i	$-0.685924\pi$
$587$	1.73302	−	1.25912i	0.0715296	−	0.0519693i	0.622975	+	0.782241i	$0.285924\pi$
$588$	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	$-0.477009\pi$
$593$	3.51472			0.144332			0.0721661	+	0.997393i	$0.477009\pi$
$594$		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	−0.980396	−	0.197036i	$-0.936868\pi$
$599$	−1.74806	+	5.37999i	−0.0714240	+	0.219820i	0.908972	+	0.416857i	$0.136868\pi$
$600$	−3.85816	+	11.8742i	−0.157509	+	0.484763i
$601$	−19.3688	+	14.0722i	−0.790069	+	0.574019i	−0.907984	−	0.419005i	$-0.862379\pi$
$601$	−19.3688	+	14.0722i	−0.790069	+	0.574019i	0.117915	+	0.993024i	$0.462379\pi$
$602$	−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	0.838835	+	0.544385i	$0.183237\pi$
$607$	11.8305	+	36.4105i	0.480185	+	1.47786i	−0.358651	+	0.933472i	$0.616763\pi$
$608$		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	$-0.128135\pi$
$613$	20.5942	+	14.9626i	0.831792	+	0.604333i	−0.0882735	+	0.996096i	$0.528135\pi$
$614$	−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	0.796036	−	0.605249i	$-0.206927\pi$
$619$	11.6038	+	8.43069i	0.466398	+	0.338858i	−0.329638	+	0.944107i	$0.606927\pi$
$620$		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	$-0.700000\pi$
$631$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$632$	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	−0.00579592	−	0.999983i	$-0.501845\pi$
$641$	−24.2705	−	17.6336i	−0.958628	−	0.696484i	−0.952832	+	0.303500i	$0.901845\pi$
$642$	42.2989	−	30.7319i	1.66940	−	1.21289i
$643$	−0.449881	+	1.38459i	−0.0177416	+	0.0546029i	−0.959535	−	0.281588i	$-0.909139\pi$
$643$	−0.449881	+	1.38459i	−0.0177416	+	0.0546029i	0.941794	+	0.336191i	$0.109139\pi$
$644$	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	0.969422	+	0.245398i	$0.0789185\pi$
$647$	8.37828	+	25.7857i	0.329384	+	1.01374i	−0.640038	+	0.768343i	$0.721081\pi$
$648$	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	−0.756816	−	0.653628i	$-0.773246\pi$
$653$	−9.43059	+	6.85173i	−0.369048	+	0.268129i	0.387768	+	0.921757i	$0.373246\pi$
$654$	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	$-0.147314\pi$
$659$	45.9411			1.78961			0.894806	+	0.446455i	$0.147314\pi$
$660$		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	$-0.177356\pi$
$673$	−3.85816	−	11.8742i	−0.148721	−	0.457717i	−0.997471	+	0.0710781i	$0.977356\pi$
$674$	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	−0.719098	−	0.694909i	$-0.755445\pi$
$677$	7.05437	−	21.7111i	0.271122	−	0.834426i	0.990220	−	0.139518i	$-0.0445552\pi$
$678$	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	−0.862526	−	0.506013i	$-0.831119\pi$
$691$	−12.1486	−	37.3896i	−0.462155	−	1.42237i	0.400371	−	0.916353i	$-0.368881\pi$
$692$	−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	$-0.223356\pi$
$701$	10.2158	+	7.42221i	0.385845	+	0.280333i	−0.377906	+	0.925844i	$0.623356\pi$
$702$	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	−0.700344	−	0.713805i	$-0.746970\pi$
$709$	7.61029	−	23.4221i	0.285810	−	0.879634i	0.986155	−	0.165829i	$-0.0530299\pi$
$710$	−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	−0.829051	−	0.559174i	$-0.811118\pi$
$719$	−14.8399	+	10.7818i	−0.553436	+	0.402094i	0.275615	+	0.961268i	$0.411118\pi$
$720$	−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	$-0.595519\pi$
$733$	14.1221	−	10.2603i	0.521611	−	0.378972i	0.817210	+	0.576340i	$0.195519\pi$
$734$	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	0.964025	+	0.265811i	$0.0856396\pi$
$739$	9.25232	+	28.4757i	0.340352	+	1.04750i	−0.623673	+	0.781685i	$0.714360\pi$
$740$	−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	0.113621	+	0.993524i	$0.463755\pi$
$743$	−15.3266	+	47.1705i	−0.562279	+	1.73052i	−0.675900	+	0.736993i	$0.736245\pi$
$744$		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	0.798354	−	0.602189i	$-0.205705\pi$
$751$	12.9443	+	9.40456i	0.472343	+	0.343177i	−0.326011	+	0.945366i	$0.605705\pi$
$752$	−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	0.997566	−	0.0697302i	$-0.0222138\pi$
$757$	4.11416	+	12.6621i	0.149532	+	0.460211i	−0.848034	+	0.529942i	$0.822214\pi$
$758$	81.2548			2.95131
$759$		0			0
$760$		0			0
$761$	−9.27051	−	28.5317i	−0.336056	−	1.03427i	−0.966200	−	0.257795i	$-0.917004\pi$
$761$	−9.27051	−	28.5317i	−0.336056	−	1.03427i	0.630144	−	0.776478i	$-0.282996\pi$
$762$	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	$-0.611121\pi$
$769$	−18.9706			−0.684096			−0.342048	+	0.939682i	$0.611121\pi$
$770$		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	0.135559	−	0.990769i	$-0.456717\pi$
$773$	−21.2644	−	15.4495i	−0.764828	−	0.555680i	−0.900387	+	0.435089i	$0.856717\pi$
$774$	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	$-0.985973\pi$
$787$	−4.62616	+	14.2379i	−0.164905	+	0.507525i	0.834125	+	0.551576i	$0.185973\pi$
$788$	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	−0.597622	−	0.801778i	$-0.703887\pi$
$797$	10.0824	−	31.0305i	0.357138	−	1.09916i	0.954759	−	0.297379i	$-0.0961125\pi$
$798$		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	$-0.961774\pi$
$809$	−3.39009	+	10.4336i	−0.119189	+	0.366827i	0.873608	+	0.486629i	$0.161774\pi$
$810$	1.95314	−	1.41904i	0.0686263	−	0.0498600i
$811$	−43.6393	−	31.7058i	−1.53238	−	1.11334i	−0.954896	−	0.296941i	$-0.904033\pi$
$811$	−43.6393	−	31.7058i	−1.53238	−	1.11334i	−0.577487	−	0.816400i	$-0.695967\pi$
$812$	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	$-0.443715\pi$
$821$	33.4235	−	24.2836i	1.16649	−	0.847503i	0.990584	+	0.136904i	$0.0437153\pi$
$822$	−60.6048	−	44.0320i	−2.11384	−	1.53579i
$823$	6.03038	+	18.5596i	0.210206	+	0.646947i	0.999459	+	0.0328795i	$0.0104678\pi$
$823$	6.03038	+	18.5596i	0.210206	+	0.646947i	−0.789254	+	0.614068i	$0.789532\pi$
$824$	30.1421			1.05005
$825$		0			0
$826$	−8.00000			−0.278356
$827$	6.88622	+	21.1936i	0.239457	+	0.736974i	0.996499	+	0.0836070i	$0.0266440\pi$
$827$	6.88622	+	21.1936i	0.239457	+	0.736974i	−0.757042	+	0.653367i	$0.773356\pi$
$828$	43.8019	+	31.8239i	1.52222	+	1.10596i
$829$	−14.5623	+	10.5801i	−0.505770	+	0.367463i	−0.811217	−	0.584746i	$-0.801194\pi$
$829$	−14.5623	+	10.5801i	−0.505770	+	0.367463i	0.305447	+	0.952209i	$0.401194\pi$
$830$	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	0.155611	−	0.987818i	$-0.450265\pi$
$839$	−21.3121	−	15.4841i	−0.735774	−	0.534571i	−0.891385	+	0.453247i	$0.850265\pi$
$840$	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	$-0.985572\pi$
$853$	−4.79431	+	14.7554i	−0.164154	+	0.505214i	0.834819	+	0.550525i	$0.185572\pi$
$854$	−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	$-0.360957\pi$
$857$	24.7696			0.846112			0.423056	+	0.906104i	$0.360957\pi$
$858$		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	−0.987636	−	0.156767i	$-0.949893\pi$
$863$	−2.83417	+	8.72268i	−0.0964763	+	0.296924i	0.891159	+	0.453691i	$0.149893\pi$
$864$	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	0.998958	+	0.0456438i	$0.0145339\pi$
$877$	40.0106	+	29.0694i	1.35106	+	0.981604i	0.352105	+	0.935961i	$0.385466\pi$
$878$	−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	−0.0473866	−	0.998877i	$-0.515089\pi$
$883$	−30.0724	−	21.8489i	−1.01202	−	0.735274i	−0.964631	+	0.263603i	$0.915089\pi$
$884$	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	$-0.922198\pi$
$887$	−30.9726	+	22.5029i	−1.03996	+	0.755574i	−0.0696815	+	0.997569i	$0.522198\pi$
$888$	−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	0.704867	+	0.709339i	$0.251007\pi$
$907$	−8.50252	+	26.1681i	−0.282321	+	0.868896i	−0.987189	+	0.159557i	$0.948993\pi$
$908$	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	0.887182	−	0.461420i	$-0.152660\pi$
$911$	−3.07198	−	9.45457i	−0.101779	−	0.313244i	−0.988961	+	0.148176i	$0.952660\pi$
$912$		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	0.644706	+	0.764430i	$0.276980\pi$
$919$	−9.88854	+	30.4338i	−0.326193	+	1.00392i	−0.970899	+	0.239488i	$0.923020\pi$
$920$	−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	−0.920500	−	0.390743i	$-0.872218\pi$
$929$	1.64203	−	5.05364i	0.0538731	−	0.165804i	0.974373	+	0.224939i	$0.0722181\pi$
$930$		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	$-0.107570\pi$
$937$	−0.449881	−	1.38459i	−0.0146970	−	0.0452326i	−0.958136	+	0.286313i	$0.907570\pi$
$938$	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	$-0.934760\pi$
$941$	−2.06618	+	6.35904i	−0.0673555	+	0.207299i	0.911714	+	0.410826i	$0.134760\pi$
$942$	−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	−0.397971	+	0.917398i	$0.630285\pi$
$953$	−43.0167	+	31.2535i	−1.39345	+	1.01240i	−0.995477	+	0.0950009i	$0.969715\pi$
$954$	−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	$-0.577380\pi$
$967$	−14.9706			−0.481421			−0.240710	+	0.970597i	$0.577380\pi$
$968$		0			0
$969$		0			0
$970$	−2.72813	−	8.39633i	−0.0875951	−	0.269590i
$971$	7.02736	+	5.10567i	0.225519	+	0.163849i	0.694807	−	0.719196i	$-0.255490\pi$
$971$	7.02736	+	5.10567i	0.225519	+	0.163849i	−0.469289	+	0.883045i	$0.655490\pi$
$972$	−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	0.973753	+	0.227608i	$0.0730906\pi$
$977$	9.99458	+	30.7602i	0.319755	+	0.984105i	−0.653998	+	0.756496i	$0.726909\pi$
$978$	−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	−0.268913	−	0.963165i	$-0.586664\pi$
$983$	17.6834	−	12.8477i	0.564012	−	0.409779i	0.832925	+	0.553386i	$0.186664\pi$
$984$	−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	$-0.472053\pi$
$997$	33.5385	−	24.3671i	1.06217	−	0.771715i	0.974489	+	0.224433i	$0.0720531\pi$
$998$	−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.f.511.2		8
11.2	odd	10		605.2.g.l.251.1		8
11.3	even	5		55.2.a.b.1.2	✓	2
11.4	even	5	inner	605.2.g.f.366.1		8
11.5	even	5	inner	605.2.g.f.81.1		8
11.6	odd	10		605.2.g.l.81.2		8
11.7	odd	10		605.2.g.l.366.2		8
11.8	odd	10		605.2.a.d.1.1		2
11.9	even	5	inner	605.2.g.f.251.2		8
11.10	odd	2		605.2.g.l.511.1		8
33.8	even	10		5445.2.a.y.1.2		2
33.14	odd	10		495.2.a.b.1.1		2
44.3	odd	10		880.2.a.m.1.2		2
44.19	even	10		9680.2.a.bn.1.2		2
55.3	odd	20		275.2.b.d.199.1		4
55.14	even	10		275.2.a.c.1.1		2
55.19	odd	10		3025.2.a.o.1.2		2
55.47	odd	20		275.2.b.d.199.4		4
77.69	odd	10		2695.2.a.f.1.2		2
88.3	odd	10		3520.2.a.bo.1.1		2
88.69	even	10		3520.2.a.bn.1.2		2
132.47	even	10		7920.2.a.ch.1.2		2
143.25	even	10		9295.2.a.g.1.1		2
165.14	odd	10		2475.2.a.x.1.2		2
165.47	even	20		2475.2.c.l.199.1		4
165.113	even	20		2475.2.c.l.199.4		4
220.3	even	20		4400.2.b.q.4049.3		4
220.47	even	20		4400.2.b.q.4049.2		4
220.179	odd	10		4400.2.a.bn.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.b.1.2	✓	2	11.3	even	5
275.2.a.c.1.1		2	55.14	even	10
275.2.b.d.199.1		4	55.3	odd	20
275.2.b.d.199.4		4	55.47	odd	20
495.2.a.b.1.1		2	33.14	odd	10
605.2.a.d.1.1		2	11.8	odd	10
605.2.g.f.81.1		8	11.5	even	5	inner
605.2.g.f.251.2		8	11.9	even	5	inner
605.2.g.f.366.1		8	11.4	even	5	inner
605.2.g.f.511.2		8	1.1	even	1	trivial
605.2.g.l.81.2		8	11.6	odd	10
605.2.g.l.251.1		8	11.2	odd	10
605.2.g.l.366.2		8	11.7	odd	10
605.2.g.l.511.1		8	11.10	odd	2
880.2.a.m.1.2		2	44.3	odd	10
2475.2.a.x.1.2		2	165.14	odd	10
2475.2.c.l.199.1		4	165.47	even	20
2475.2.c.l.199.4		4	165.113	even	20
2695.2.a.f.1.2		2	77.69	odd	10
3025.2.a.o.1.2		2	55.19	odd	10
3520.2.a.bn.1.2		2	88.69	even	10
3520.2.a.bo.1.1		2	88.3	odd	10
4400.2.a.bn.1.1		2	220.179	odd	10
4400.2.b.q.4049.2		4	220.47	even	20
4400.2.b.q.4049.3		4	220.3	even	20
5445.2.a.y.1.2		2	33.8	even	10
7920.2.a.ch.1.2		2	132.47	even	10
9295.2.a.g.1.1		2	143.25	even	10
9680.2.a.bn.1.2		2	44.19	even	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

Varieties

Fields

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Database

Properties

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