LMFDB - Embedded newform 127.2.i.a.100.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [127,2,Mod(25,127)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("127.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(127, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	127.i (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.01410010567$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.1
Character	$\chi$	$=$	127.100
Dual form			127.2.i.a.47.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28584 + 1.61239i) q^{2} +(-0.108909 + 1.45329i) q^{3} +(-0.501385 - 2.19671i) q^{4} +(-0.531843 + 2.33016i) q^{5} +(-2.20323 - 2.04430i) q^{6} +(-0.486645 - 0.451541i) q^{7} +(0.470479 + 0.226571i) q^{8} +(0.866309 + 0.130575i) q^{9} +(-3.07327 - 3.85376i) q^{10} +(-0.332971 + 0.848397i) q^{11} +(3.24706 - 0.489415i) q^{12} +(-1.80737 - 1.67699i) q^{13} +(1.35381 - 0.204054i) q^{14} +(-3.32847 - 1.02670i) q^{15} +(3.08985 - 1.48799i) q^{16} +(-0.225779 + 0.0696437i) q^{17} +(-1.32448 + 1.22893i) q^{18} -2.38642 q^{19} +5.38535 q^{20} +(0.709219 - 0.658059i) q^{21} +(-0.939802 - 1.62778i) q^{22} +(2.37940 + 6.06262i) q^{23} +(-0.380511 + 0.659065i) q^{24} +(-0.641937 - 0.309140i) q^{25} +(5.02797 - 0.757844i) q^{26} +(-1.25699 + 5.50725i) q^{27} +(-0.747908 + 1.29542i) q^{28} +(2.81243 + 1.91748i) q^{29} +(5.93532 - 4.04663i) q^{30} +(3.40394 + 1.04998i) q^{31} +(-1.80622 + 7.91359i) q^{32} +(-1.19670 - 0.576301i) q^{33} +(0.178023 - 0.453596i) q^{34} +(1.31098 - 0.893812i) q^{35} +(-0.147519 - 1.96850i) q^{36} +(5.59312 + 9.68757i) q^{37} +(3.06856 - 3.84785i) q^{38} +(2.63399 - 2.44399i) q^{39} +(-0.778166 + 0.975789i) q^{40} +(1.81475 - 0.559775i) q^{41} +(0.149107 + 1.98970i) q^{42} +(-8.06130 - 5.49610i) q^{43} +(2.03063 + 0.306068i) q^{44} +(-0.765002 + 1.94919i) q^{45} +(-12.8349 - 3.95903i) q^{46} +(-1.42049 - 6.22356i) q^{47} +(1.82597 + 4.65250i) q^{48} +(-0.490176 - 6.54095i) q^{49} +(1.32388 - 0.637549i) q^{50} +(-0.0766229 - 0.335707i) q^{51} +(-2.77769 + 4.81109i) q^{52} +(3.22337 + 0.485845i) q^{53} +(-7.26356 - 9.10821i) q^{54} +(-1.79981 - 1.22709i) q^{55} +(-0.126650 - 0.322700i) q^{56} +(0.259902 - 3.46815i) q^{57} +(-6.70808 + 2.06917i) q^{58} +(-5.34599 - 9.25953i) q^{59} +(-0.586512 + 7.82646i) q^{60} +(12.6002 - 6.06794i) q^{61} +(-6.06990 + 4.13839i) q^{62} +(-0.362625 - 0.454718i) q^{63} +(-6.16081 - 7.72542i) q^{64} +(4.86890 - 3.31956i) q^{65} +(2.46799 - 1.18852i) q^{66} +(-0.695840 + 9.28533i) q^{67} +(0.266189 + 0.461054i) q^{68} +(-9.06987 + 2.79768i) q^{69} +(-0.244537 + 3.26312i) q^{70} +(2.24118 + 5.71045i) q^{71} +(0.377995 + 0.257713i) q^{72} +(3.36115 + 4.21475i) q^{73} +(-22.8120 - 3.43836i) q^{74} +(0.519182 - 0.899250i) q^{75} +(1.19652 + 5.24228i) q^{76} +(0.545125 - 0.262518i) q^{77} +(0.553776 + 7.38962i) q^{78} +(-1.11284 - 2.83548i) q^{79} +(1.82395 + 7.99123i) q^{80} +(-5.35520 - 1.65186i) q^{81} +(-1.43090 + 3.64587i) q^{82} +(-5.47851 - 0.825752i) q^{83} +(-1.80116 - 1.22801i) q^{84} +(-0.0422016 - 0.563141i) q^{85} +(19.2274 - 5.93088i) q^{86} +(-3.09295 + 3.87844i) q^{87} +(-0.348877 + 0.323711i) q^{88} +(6.79091 - 8.51553i) q^{89} +(-2.15920 - 3.73984i) q^{90} +(0.122317 + 1.63220i) q^{91} +(12.1248 - 8.26657i) q^{92} +(-1.89664 + 4.83255i) q^{93} +(11.8614 + 5.71213i) q^{94} +(1.26920 - 5.56074i) q^{95} +(-11.3040 - 3.48682i) q^{96} +(10.8174 - 7.37520i) q^{97} +(11.1769 + 7.62026i) q^{98} +(-0.399235 + 0.691496i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 5 q^{2} - 15 q^{3} - 17 q^{4} - 6 q^{5} + 7 q^{6} + 2 q^{7} - 22 q^{8} + 2 q^{9} - 10 q^{10} + 9 q^{12} - 14 q^{13} - 20 q^{14} + 4 q^{15} + 27 q^{16} - 8 q^{17} + 7 q^{18} - 16 q^{19} - 80 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 108 * q - 5 * q^2 - 15 * q^3 - 17 * q^4 - 6 * q^5 + 7 * q^6 + 2 * q^7 - 22 * q^8 + 2 * q^9 - 10 * q^10 + 9 * q^12 - 14 * q^13 - 20 * q^14 + 4 * q^15 + 27 * q^16 - 8 * q^17 + 7 * q^18 - 16 * q^19 - 80 * q^20 - 59 * q^21 - 13 * q^22 - 20 * q^23 + 41 * q^24 - 6 * q^25 - 56 * q^26 - 24 * q^27 - 19 * q^28 + 33 * q^29 + 23 * q^30 - 3 * q^31 + 39 * q^32 - 61 * q^33 + 16 * q^34 - 5 * q^35 + 48 * q^36 - 3 * q^37 + 3 * q^38 + 7 * q^39 - 6 * q^40 - 38 * q^41 + 14 * q^42 - 9 * q^43 + 134 * q^44 - 70 * q^45 - q^46 + 17 * q^47 - 76 * q^48 + 93 * q^49 + 24 * q^50 + 31 * q^51 - 54 * q^52 - 12 * q^53 - 44 * q^54 + 15 * q^55 + 30 * q^56 - 42 * q^57 - 52 * q^58 + 77 * q^59 + 36 * q^60 - 70 * q^61 + 41 * q^62 + 82 * q^63 - 6 * q^64 - 43 * q^65 + 160 * q^66 + 54 * q^67 + 6 * q^68 - 19 * q^69 + 49 * q^70 - 31 * q^71 + 11 * q^72 + 46 * q^73 - 111 * q^74 + 18 * q^75 - 19 * q^76 - 65 * q^77 + 27 * q^78 + 119 * q^79 + 114 * q^80 - 55 * q^81 - 44 * q^82 - 34 * q^83 + 34 * q^84 + 6 * q^85 + 89 * q^86 + 22 * q^87 - 118 * q^88 - 22 * q^89 + 121 * q^90 + 58 * q^91 + 115 * q^92 + 104 * q^93 + 62 * q^94 - 18 * q^95 + 31 * q^96 + 14 * q^97 + 87 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/127\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{21}\right)$

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 $

$2$	−1.28584	+	1.61239i	−0.909227	+	1.14014i	0.0804410	+	0.996759i	$0.474367\pi$
$2$	−1.28584	+	1.61239i	−0.909227	+	1.14014i	−0.989668	+	0.143376i	$0.954204\pi$
$3$	−0.108909	+	1.45329i	−0.0628785	+	0.839056i	0.873222	+	0.487323i	$0.162027\pi$
$3$	−0.108909	+	1.45329i	−0.0628785	+	0.839056i	−0.936100	+	0.351733i	$0.885593\pi$
$4$	−0.501385	−	2.19671i	−0.250693	−	1.09836i
$5$	−0.531843	+	2.33016i	−0.237848	+	1.04208i	0.705092	+	0.709116i	$0.250906\pi$
$5$	−0.531843	+	2.33016i	−0.237848	+	1.04208i	−0.942940	+	0.332963i	$0.891952\pi$
$6$	−2.20323	−	2.04430i	−0.899466	−	0.834583i
$7$	−0.486645	−	0.451541i	−0.183935	−	0.170666i	0.582831	−	0.812593i	$-0.301945\pi$
$7$	−0.486645	−	0.451541i	−0.183935	−	0.170666i	−0.766766	+	0.641927i	$0.778135\pi$
$8$	0.470479	+	0.226571i	0.166339	+	0.0801048i
$9$	0.866309	+	0.130575i	0.288770	+	0.0435250i
$10$	−3.07327	−	3.85376i	−0.971853	−	1.21866i
$11$	−0.332971	+	0.848397i	−0.100395	+	0.255801i	−0.972243	−	0.233975i	$-0.924826\pi$
$11$	−0.332971	+	0.848397i	−0.100395	+	0.255801i	0.871848	+	0.489777i	$0.162922\pi$
$12$	3.24706	−	0.489415i	0.937345	−	0.141282i
$13$	−1.80737	−	1.67699i	−0.501274	−	0.465115i	0.388544	−	0.921430i	$-0.372978\pi$
$13$	−1.80737	−	1.67699i	−0.501274	−	0.465115i	−0.889818	+	0.456316i	$0.849169\pi$
$14$	1.35381	−	0.204054i	0.361821	−	0.0545358i
$15$	−3.32847	−	1.02670i	−0.859407	−	0.265092i
$16$	3.08985	−	1.48799i	0.772463	−	0.371999i
$17$	−0.225779	+	0.0696437i	−0.0547595	+	0.0168911i	−0.322014	−	0.946735i	$-0.604360\pi$
$17$	−0.225779	+	0.0696437i	−0.0547595	+	0.0168911i	0.267254	+	0.963626i	$0.413884\pi$
$18$	−1.32448	+	1.22893i	−0.312182	+	0.289662i
$19$	−2.38642			−0.547482			−0.273741	−	0.961803i	$-0.588261\pi$
$19$	−2.38642			−0.547482			−0.273741	+	0.961803i	$0.588261\pi$
$20$	5.38535			1.20420
$21$	0.709219	−	0.658059i	0.154764	−	0.143600i
$22$	−0.939802	−	1.62778i	−0.200366	−	0.347045i
$23$	2.37940	+	6.06262i	0.496140	+	1.26414i	0.931452	+	0.363864i	$0.118543\pi$
$23$	2.37940	+	6.06262i	0.496140	+	1.26414i	−0.435312	+	0.900280i	$0.643362\pi$
$24$	−0.380511	+	0.659065i	−0.0776716	+	0.134531i
$25$	−0.641937	−	0.309140i	−0.128387	−	0.0618281i
$26$	5.02797	−	0.757844i	0.986066	−	0.148626i
$27$	−1.25699	+	5.50725i	−0.241908	+	1.05987i
$28$	−0.747908	+	1.29542i	−0.141341	+	0.244811i
$29$	2.81243	+	1.91748i	0.522256	+	0.356068i	0.795575	−	0.605856i	$-0.207169\pi$
$29$	2.81243	+	1.91748i	0.522256	+	0.356068i	−0.273319	+	0.961923i	$0.588121\pi$
$30$	5.93532	−	4.04663i	1.08364	−	0.738811i
$31$	3.40394	+	1.04998i	0.611365	+	0.188581i	0.584949	−	0.811070i	$-0.301114\pi$
$31$	3.40394	+	1.04998i	0.611365	+	0.188581i	0.0264159	+	0.999651i	$0.491591\pi$
$32$	−1.80622	+	7.91359i	−0.319298	+	1.39894i
$33$	−1.19670	−	0.576301i	−0.208319	−	0.100321i
$34$	0.178023	−	0.453596i	0.0305307	−	0.0777910i
$35$	1.31098	−	0.893812i	0.221596	−	0.151082i
$36$	−0.147519	−	1.96850i	−0.0245865	−	0.328083i
$37$	5.59312	+	9.68757i	0.919503	+	1.59263i	0.800171	+	0.599772i	$0.204742\pi$
$37$	5.59312	+	9.68757i	0.919503	+	1.59263i	0.119332	+	0.992854i	$0.461925\pi$
$38$	3.06856	−	3.84785i	0.497786	−	0.624204i
$39$	2.63399	−	2.44399i	0.421777	−	0.391352i
$40$	−0.778166	+	0.975789i	−0.123039	+	0.154286i
$41$	1.81475	−	0.559775i	0.283416	−	0.0874221i	−0.149788	−	0.988718i	$-0.547859\pi$
$41$	1.81475	−	0.559775i	0.283416	−	0.0874221i	0.433204	+	0.901296i	$0.357383\pi$
$42$	0.149107	+	1.98970i	0.0230078	+	0.307017i
$43$	−8.06130	−	5.49610i	−1.22934	−	0.838147i	−0.238228	−	0.971209i	$-0.576567\pi$
$43$	−8.06130	−	5.49610i	−1.22934	−	0.838147i	−0.991108	+	0.133062i	$0.957519\pi$
$44$	2.03063	+	0.306068i	0.306129	+	0.0461415i
$45$	−0.765002	+	1.94919i	−0.114040	+	0.290568i
$46$	−12.8349	−	3.95903i	−1.89240	−	0.583728i
$47$	−1.42049	−	6.22356i	−0.207199	−	0.907800i	−0.966420	−	0.256967i	$-0.917277\pi$
$47$	−1.42049	−	6.22356i	−0.207199	−	0.907800i	0.759221	−	0.650833i	$-0.225580\pi$
$48$	1.82597	+	4.65250i	0.263556	+	0.671531i
$49$	−0.490176	−	6.54095i	−0.0700252	−	0.934421i
$50$	1.32388	−	0.637549i	0.187226	−	0.0901631i
$51$	−0.0766229	−	0.335707i	−0.0107294	−	0.0470084i
$52$	−2.77769	+	4.81109i	−0.385196	+	0.667179i
$53$	3.22337	+	0.485845i	0.442764	+	0.0667360i	0.366641	−	0.930362i	$-0.380508\pi$
$53$	3.22337	+	0.485845i	0.442764	+	0.0667360i	0.0761231	+	0.997098i	$0.475746\pi$
$54$	−7.26356	−	9.10821i	−0.988445	−	1.23947i
$55$	−1.79981	−	1.22709i	−0.242686	−	0.165461i
$56$	−0.126650	−	0.322700i	−0.0169244	−	0.0431226i
$57$	0.259902	−	3.46815i	0.0344249	−	0.459368i
$58$	−6.70808	+	2.06917i	−0.880815	+	0.271695i
$59$	−5.34599	−	9.25953i	−0.695989	−	1.20549i	−0.969846	−	0.243718i	$-0.921633\pi$
$59$	−5.34599	−	9.25953i	−0.695989	−	1.20549i	0.273857	−	0.961770i	$-0.411700\pi$
$60$	−0.586512	+	7.82646i	−0.0757183	+	1.01039i
$61$	12.6002	−	6.06794i	1.61329	−	0.776920i	0.613374	−	0.789792i	$-0.289812\pi$
$61$	12.6002	−	6.06794i	1.61329	−	0.776920i	0.999917	+	0.0128721i	$0.00409742\pi$
$62$	−6.06990	+	4.13839i	−0.770878	+	0.525576i
$63$	−0.362625	−	0.454718i	−0.0456865	−	0.0572891i
$64$	−6.16081	−	7.72542i	−0.770102	−	0.965677i
$65$	4.86890	−	3.31956i	0.603913	−	0.411741i
$66$	2.46799	−	1.18852i	0.303789	−	0.146297i
$67$	−0.695840	+	9.28533i	−0.0850103	+	1.13438i	0.777683	+	0.628657i	$0.216395\pi$
$67$	−0.695840	+	9.28533i	−0.0850103	+	1.13438i	−0.862693	+	0.505727i	$0.831224\pi$
$68$	0.266189	+	0.461054i	0.0322802	+	0.0559110i
$69$	−9.06987	+	2.79768i	−1.09188	+	0.336802i
$70$	−0.244537	+	3.26312i	−0.0292278	+	0.390017i
$71$	2.24118	+	5.71045i	0.265980	+	0.677705i	0.999999	−	0.00142343i	$-0.000453092\pi$
$71$	2.24118	+	5.71045i	0.265980	+	0.677705i	−0.734019	+	0.679129i	$0.762358\pi$
$72$	0.377995	+	0.257713i	0.0445472	+	0.0303718i
$73$	3.36115	+	4.21475i	0.393393	+	0.493299i	0.938603	−	0.345000i	$-0.112121\pi$
$73$	3.36115	+	4.21475i	0.393393	+	0.493299i	−0.545209	+	0.838300i	$0.683550\pi$
$74$	−22.8120	−	3.43836i	−2.65185	−	0.399702i
$75$	0.519182	−	0.899250i	0.0599500	−	0.103836i
$76$	1.19652	+	5.24228i	0.137250	+	0.601330i
$77$	0.545125	−	0.262518i	0.0621227	−	0.0299167i
$78$	0.553776	+	7.38962i	0.0627027	+	0.836710i
$79$	−1.11284	−	2.83548i	−0.125205	−	0.319017i	0.854503	−	0.519446i	$-0.173862\pi$
$79$	−1.11284	−	2.83548i	−0.125205	−	0.319017i	−0.979708	+	0.200429i	$0.935766\pi$
$80$	1.82395	+	7.99123i	0.203923	+	0.893446i
$81$	−5.35520	−	1.65186i	−0.595022	−	0.183540i
$82$	−1.43090	+	3.64587i	−0.158016	+	0.402619i
$83$	−5.47851	−	0.825752i	−0.601344	−	0.0906381i	−0.158687	−	0.987329i	$-0.550726\pi$
$83$	−5.47851	−	0.825752i	−0.601344	−	0.0906381i	−0.442657	+	0.896691i	$0.645964\pi$
$84$	−1.80116	−	1.22801i	−0.196522	−	0.133987i
$85$	−0.0422016	−	0.563141i	−0.00457740	−	0.0610812i
$86$	19.2274	−	5.93088i	2.07335	−	0.639543i
$87$	−3.09295	+	3.87844i	−0.331600	+	0.415813i
$88$	−0.348877	+	0.323711i	−0.0371905	+	0.0345077i
$89$	6.79091	−	8.51553i	0.719835	−	0.902644i	−0.278494	−	0.960438i	$-0.589835\pi$
$89$	6.79091	−	8.51553i	0.719835	−	0.902644i	0.998329	+	0.0577940i	$0.0184066\pi$
$90$	−2.15920	−	3.73984i	−0.227599	−	0.394213i
$91$	0.122317	+	1.63220i	0.0128223	+	0.171101i
$92$	12.1248	−	8.26657i	1.26410	−	0.861850i
$93$	−1.89664	+	4.83255i	−0.196672	+	0.501112i
$94$	11.8614	+	5.71213i	1.22341	+	0.589161i
$95$	1.26920	−	5.56074i	0.130217	−	0.570519i
$96$	−11.3040	−	3.48682i	−1.15371	−	0.355872i
$97$	10.8174	−	7.37520i	1.09834	−	0.748838i	0.128292	−	0.991736i	$-0.459051\pi$
$97$	10.8174	−	7.37520i	1.09834	−	0.748838i	0.970052	+	0.242899i	$0.0780982\pi$
$98$	11.1769	+	7.62026i	1.12903	+	0.769763i
$99$	−0.399235	+	0.691496i	−0.0401247	+	0.0694980i
$100$	−0.357235	+	1.56515i	−0.0357235	+	0.156515i
$101$	7.04470	−	1.06182i	0.700974	−	0.105655i	0.211121	−	0.977460i	$-0.432289\pi$
$101$	7.04470	−	1.06182i	0.700974	−	0.105655i	0.489853	+	0.871805i	$0.337050\pi$
$102$	0.639817	+	0.308120i	0.0633513	+	0.0305084i
$103$	9.21105	−	15.9540i	0.907592	−	1.57200i	0.0901924	−	0.995924i	$-0.471252\pi$
$103$	9.21105	−	15.9540i	0.907592	−	1.57200i	0.817400	−	0.576071i	$-0.195415\pi$
$104$	−0.470371	−	1.19849i	−0.0461237	−	0.117521i
$105$	1.15619	+	2.00258i	0.112832	+	0.195431i
$106$	−4.92812	+	4.57263i	−0.478661	+	0.444133i
$107$	−1.12978			−0.109220			−0.0546102	−	0.998508i	$-0.517392\pi$
$107$	−1.12978			−0.109220			−0.0546102	+	0.998508i	$0.517392\pi$
$108$	12.7281			1.22476
$109$	−11.5343	+	10.7023i	−1.10478	+	1.02509i	−0.105254	+	0.994445i	$0.533565\pi$
$109$	−11.5343	+	10.7023i	−1.10478	+	1.02509i	−0.999530	+	0.0306444i	$0.990244\pi$
$110$	4.29282	−	1.32416i	0.409305	−	0.126254i
$111$	−14.6880	+	7.07335i	−1.39412	+	0.671373i
$112$	−2.17555	−	0.671069i	−0.205570	−	0.0634101i
$113$	−3.76025	+	0.566767i	−0.353735	+	0.0533170i	−0.323506	−	0.946226i	$-0.604862\pi$
$113$	−3.76025	+	0.566767i	−0.353735	+	0.0533170i	−0.0302288	+	0.999543i	$0.509624\pi$
$114$	5.25784	+	4.87856i	0.492442	+	0.456919i
$115$	−15.3923	+	2.32002i	−1.43534	+	0.216343i
$116$	2.80205	−	7.13950i	0.260164	−	0.662886i
$117$	−1.34677	−	1.68879i	−0.124509	−	0.156129i
$118$	21.8041	+	3.28644i	2.00723	+	0.302542i
$119$	0.141321	+	0.0680568i	0.0129549	+	0.00623875i
$120$	−1.33335	−	1.23717i	−0.121718	−	0.112938i
$121$	7.45466	+	6.91692i	0.677697	+	0.628811i
$122$	−6.41796	+	28.1189i	−0.581055	+	2.54577i
$123$	0.615872	+	2.69831i	0.0555313	+	0.243298i
$124$	0.599810	−	8.00391i	0.0538646	−	0.718773i
$125$	−6.38921	+	8.01181i	−0.571468	+	0.716598i
$126$	1.19946			0.106857
$127$	11.1027	−	1.93116i	0.985208	−	0.171363i
$127$	11.1027	−	1.93116i	0.985208	−	0.171363i
$128$	4.14406			0.366286
$129$	8.86536	−	11.1168i	0.780551	−	0.978780i
$130$	−0.908195	+	12.1190i	−0.0796540	+	1.06291i
$131$	2.52466	+	11.0613i	0.220580	+	0.966426i	0.957043	+	0.289947i	$0.0936378\pi$
$131$	2.52466	+	11.0613i	0.220580	+	0.966426i	−0.736462	+	0.676479i	$0.763505\pi$
$132$	−0.665959	+	2.91776i	−0.0579643	+	0.253958i
$133$	1.16134	+	1.07757i	0.100701	+	0.0934368i
$134$	−14.0769	−	13.0614i	−1.21606	−	1.12834i
$135$	−12.1642	−	5.85799i	−1.04693	−	0.504175i
$136$	−0.122003	−	0.0183891i	−0.0104617	−	0.00157685i
$137$	−10.9947	−	13.7869i	−0.939340	−	1.17790i	−0.983870	−	0.178887i	$-0.942750\pi$
$137$	−10.9947	−	13.7869i	−0.939340	−	1.17790i	0.0445296	−	0.999008i	$-0.485821\pi$
$138$	7.15144	−	18.2216i	0.608771	−	1.55112i
$139$	2.31869	−	0.349486i	0.196669	−	0.0296431i	−0.0499691	−	0.998751i	$-0.515912\pi$
$139$	2.31869	−	0.349486i	0.196669	−	0.0296431i	0.246638	+	0.969108i	$0.420674\pi$
$140$	−2.62075	−	2.43170i	−0.221494	−	0.205516i
$141$	9.19933	−	1.38658i	0.774723	−	0.116771i
$142$	−12.0893	−	3.72905i	−1.01451	−	0.312935i
$143$	2.02456	−	0.974976i	0.169302	−	0.0815316i
$144$	2.87106	−	0.885606i	0.239255	−	0.0738005i
$145$	−5.96382	+	5.53361i	−0.495268	+	0.459541i
$146$	−11.1178			−0.920112
$147$	9.55926			0.788434
$148$	18.4765	−	17.1437i	1.51876	−	1.40920i
$149$	−6.04066	−	10.4627i	−0.494870	−	0.857140i	0.505113	−	0.863053i	$-0.331451\pi$
$149$	−6.04066	−	10.4627i	−0.494870	−	0.857140i	−0.999983	+	0.00591379i	$0.998118\pi$
$150$	0.782360	+	1.99342i	0.0638794	+	0.162762i
$151$	−6.46907	+	11.2048i	−0.526446	+	0.911831i	0.473079	+	0.881020i	$0.343142\pi$
$151$	−6.46907	+	11.2048i	−0.526446	+	0.911831i	−0.999525	+	0.0308111i	$0.990191\pi$
$152$	−1.12276	−	0.540692i	−0.0910678	−	0.0438559i
$153$	−0.204688	+	0.0308518i	−0.0165481	+	0.00249422i
$154$	−0.277661	+	1.21651i	−0.0223746	+	0.0980294i
$155$	−4.25697	+	7.37329i	−0.341928	+	0.592237i
$156$	−6.68939	−	4.56075i	−0.535580	−	0.365152i
$157$	13.5435	−	9.23382i	1.08089	−	0.736939i	0.114347	−	0.993441i	$-0.463522\pi$
$157$	13.5435	−	9.23382i	1.08089	−	0.736939i	0.966544	+	0.256502i	$0.0825700\pi$
$158$	6.00286	+	1.85164i	0.477562	+	0.147308i
$159$	−1.05713	+	4.63157i	−0.0838356	+	0.367308i
$160$	−17.4793	−	8.41758i	−1.38186	−	0.665468i
$161$	1.57960	−	4.02474i	0.124490	−	0.317194i
$162$	9.54938	−	6.51066i	0.750271	−	0.511526i
$163$	−0.622947	−	8.31265i	−0.0487930	−	0.651097i	−0.966964	−	0.254913i	$-0.917953\pi$
$163$	−0.622947	−	8.31265i	−0.0487930	−	0.651097i	0.918171	−	0.396184i	$-0.129666\pi$
$164$	−2.13955	−	3.70581i	−0.167071	−	0.289375i
$165$	1.97933	−	2.48200i	0.154091	−	0.193223i
$166$	8.37593	−	7.77173i	0.650098	−	0.603203i
$167$	−0.586593	+	0.735564i	−0.0453919	+	0.0569197i	−0.804009	−	0.594617i	$-0.797304\pi$
$167$	−0.586593	+	0.735564i	−0.0453919	+	0.0569197i	0.758617	+	0.651536i	$0.225875\pi$
$168$	0.482769	−	0.148914i	0.0372464	−	0.0114890i
$169$	−0.517214	−	6.90175i	−0.0397857	−	0.530904i
$170$	0.962270	+	0.656064i	0.0738027	+	0.0503178i
$171$	−2.06738	−	0.311607i	−0.158096	−	0.0238292i
$172$	−8.03153	+	20.4640i	−0.612399	+	1.56037i
$173$	−14.1051	−	4.35084i	−1.07239	−	0.330789i	−0.292217	−	0.956352i	$-0.594393\pi$
$173$	−14.1051	−	4.35084i	−1.07239	−	0.330789i	−0.780173	+	0.625564i	$0.784869\pi$
$174$	−2.27653	−	9.97412i	−0.172583	−	0.756136i
$175$	0.172806	+	0.440302i	0.0130629	+	0.0332837i
$176$	0.233578	+	3.11688i	0.0176066	+	0.234944i
$177$	14.0390	−	6.76082i	1.05523	−	0.508174i
$178$	4.99836	+	21.8992i	0.374643	+	1.64142i
$179$	−7.80341	+	13.5159i	−0.583254	+	1.01023i	0.411836	+	0.911258i	$0.364888\pi$
$179$	−7.80341	+	13.5159i	−0.583254	+	1.01023i	−0.995091	+	0.0989683i	$0.968446\pi$
$180$	4.66538	+	0.703192i	0.347737	+	0.0524128i
$181$	6.41541	+	8.04466i	0.476853	+	0.597955i	0.960834	−	0.277123i	$-0.0893810\pi$
$181$	6.41541	+	8.04466i	0.476853	+	0.597955i	−0.483981	+	0.875079i	$0.660810\pi$
$182$	−2.78904	−	1.90153i	−0.206737	−	0.140951i
$183$	7.44619	+	18.9726i	0.550438	+	1.40249i
$184$	−0.254153	+	3.39144i	−0.0187364	+	0.250020i
$185$	−25.5482	+	7.88059i	−1.87834	+	0.579392i
$186$	−5.35320	−	9.27202i	−0.392516	−	0.679857i
$187$	0.0160925	−	0.214740i	0.00117680	−	0.0157033i
$188$	−12.9592	+	6.24080i	−0.945144	+	0.455157i
$189$	3.09846	−	2.11249i	0.225379	−	0.153661i
$190$	7.33411	+	9.19668i	0.532072	+	0.667197i
$191$	−2.80709	−	3.51998i	−0.203114	−	0.254697i	0.669833	−	0.742512i	$-0.266366\pi$
$191$	−2.80709	−	3.51998i	−0.203114	−	0.254697i	−0.872947	+	0.487815i	$0.837794\pi$
$192$	11.8982	−	8.11207i	0.858680	−	0.585438i
$193$	−5.53901	+	2.66745i	−0.398707	+	0.192007i	−0.622483	−	0.782634i	$-0.713876\pi$
$193$	−5.53901	+	2.66745i	−0.398707	+	0.192007i	0.223776	+	0.974641i	$0.428162\pi$
$194$	−2.01777	+	26.9253i	−0.144868	+	1.93312i
$195$	4.29401	+	7.43744i	0.307500	+	0.532606i
$196$	−14.1228	+	4.35631i	−1.00877	+	0.311165i
$197$	0.333376	−	4.44860i	0.0237521	−	0.316949i	−0.972655	−	0.232255i	$-0.925390\pi$
$197$	0.333376	−	4.44860i	0.0237521	−	0.316949i	0.996407	−	0.0846943i	$-0.0269914\pi$
$198$	−0.601611	−	1.53288i	−0.0427546	−	0.108937i
$199$	−6.12715	−	4.17742i	−0.434342	−	0.296129i	0.326342	−	0.945252i	$-0.394184\pi$
$199$	−6.12715	−	4.17742i	−0.434342	−	0.296129i	−0.760684	+	0.649122i	$0.775136\pi$
$200$	−0.231975	−	0.290888i	−0.0164031	−	0.0205689i
$201$	−13.4185	−	2.02251i	−0.946466	−	0.142657i
$202$	−7.34630	+	12.7242i	−0.516884	+	0.895270i
$203$	−0.502835	−	2.20306i	−0.0352921	−	0.154625i
$204$	−0.699034	+	0.336637i	−0.0489422	+	0.0235693i
$205$	0.339203	+	4.52636i	0.0236910	+	0.316134i
$206$	13.8802	+	35.3662i	0.967080	+	2.46408i
$207$	1.26967	+	5.56280i	0.0882483	+	0.386641i
$208$	−8.07987	−	2.49231i	−0.560238	−	0.172811i
$209$	0.794609	−	2.02463i	0.0549642	−	0.140047i
$210$	−4.71562	−	0.710765i	−0.325408	−	0.0490474i
$211$	10.7584	+	7.33499i	0.740642	+	0.504961i	0.873891	−	0.486121i	$-0.161589\pi$
$211$	10.7584	+	7.33499i	0.740642	+	0.504961i	−0.133249	+	0.991083i	$0.542541\pi$
$212$	−0.548889	−	7.32441i	−0.0376979	−	0.503043i
$213$	−8.54300	+	2.63517i	−0.585357	+	0.180559i
$214$	1.45272	−	1.82166i	0.0993062	−	0.124526i
$215$	17.0941	−	15.8610i	1.16581	−	1.08171i
$216$	−1.83917	+	2.30624i	−0.125140	+	0.156920i
$217$	−1.18240	−	2.04798i	−0.0802668	−	0.139026i
$218$	−2.42499	−	32.3592i	−0.164241	−	2.19164i
$219$	−6.49131	+	4.42570i	−0.438642	+	0.299061i
$220$	−1.79316	+	4.56891i	−0.120895	+	0.308036i
$221$	0.524859	+	0.252759i	0.0353058	+	0.0170024i
$222$	7.48136	−	32.7780i	0.502116	−	2.19991i
$223$	−7.54992	−	2.32884i	−0.505580	−	0.155951i	0.0314642	−	0.999505i	$-0.489983\pi$
$223$	−7.54992	−	2.32884i	−0.505580	−	0.155951i	−0.537044	+	0.843554i	$0.680459\pi$
$224$	4.45230	−	3.03552i	0.297482	−	0.202820i
$225$	−0.515750	−	0.351632i	−0.0343833	−	0.0234421i
$226$	3.92124	−	6.79179i	0.260837	−	0.451783i
$227$	5.19999	−	22.7826i	0.345136	−	1.51214i	−0.442936	−	0.896553i	$-0.646063\pi$
$227$	5.19999	−	22.7826i	0.345136	−	1.51214i	0.788071	−	0.615584i	$-0.211080\pi$
$228$	−7.74885	+	1.16795i	−0.513180	+	0.0773494i
$229$	24.4152	+	11.7578i	1.61340	+	0.776974i	0.999919	−	0.0127328i	$-0.00405309\pi$
$229$	24.4152	+	11.7578i	1.61340	+	0.776974i	0.613484	+	0.789707i	$0.289767\pi$
$230$	16.0513	−	27.8017i	1.05839	−	1.83319i
$231$	0.322145	+	0.820813i	0.0211956	+	0.0540055i
$232$	0.888744	+	1.53935i	0.0583489	+	0.101063i
$233$	5.07975	−	4.71332i	0.332785	−	0.308780i	−0.496026	−	0.868308i	$-0.665208\pi$
$233$	5.07975	−	4.71332i	0.332785	−	0.308780i	0.828812	+	0.559528i	$0.189018\pi$
$234$	4.45473			0.291215
$235$	15.2574			0.995280
$236$	−17.6601	+	16.3862i	−1.14958	+	1.06665i
$237$	4.24197	−	1.30847i	0.275546	−	0.0849945i
$238$	−0.291451	+	0.140355i	−0.0188920	+	0.00909790i
$239$	−7.60390	−	2.34549i	−0.491855	−	0.151717i	0.0388987	−	0.999243i	$-0.487615\pi$
$239$	−7.60390	−	2.34549i	−0.491855	−	0.151717i	−0.530754	+	0.847526i	$0.678091\pi$
$240$	−11.8122	+	1.78040i	−0.762474	+	0.114924i
$241$	−3.32824	−	3.08815i	−0.214391	−	0.198925i	0.565666	−	0.824635i	$-0.308619\pi$
$241$	−3.32824	−	3.08815i	−0.214391	−	0.198925i	−0.780056	+	0.625709i	$0.784810\pi$
$242$	−20.7383	+	3.12580i	−1.33311	+	0.200934i
$243$	−3.20744	+	8.17243i	−0.205758	+	0.524262i
$244$	−19.6471	−	24.6367i	−1.25778	−	1.57720i
$245$	15.5021	+	2.33657i	0.990395	+	0.149278i
$246$	−5.14265	−	2.47657i	−0.327884	−	0.157900i
$247$	4.31314	+	4.00201i	0.274439	+	0.254642i
$248$	1.36359	+	1.26522i	0.0865878	+	0.0803417i
$249$	1.79671	−	7.87191i	0.113862	−	0.498862i
$250$	−4.70269	−	20.6038i	−0.297424	−	1.30310i
$251$	0.759047	−	10.1288i	0.0479106	−	0.639323i	−0.920625	−	0.390448i	$-0.872320\pi$
$251$	0.759047	−	10.1288i	0.0479106	−	0.639323i	0.968536	−	0.248875i	$-0.0800608\pi$
$252$	−0.817069	+	1.02457i	−0.0514705	+	0.0645420i
$253$	−5.93578			−0.373179
$254$	−11.1626	+	20.3851i	−0.700401	+	1.27908i
$255$	0.823002			0.0515384
$256$	6.99303	−	8.76898i	0.437064	−	0.548061i
$257$	−1.02664	+	13.6995i	−0.0640397	+	0.854551i	0.869008	+	0.494798i	$0.164758\pi$
$257$	−1.02664	+	13.6995i	−0.0640397	+	0.854551i	−0.933048	+	0.359753i	$0.882861\pi$
$258$	6.52523	+	28.5889i	0.406243	+	1.77987i
$259$	1.65247	−	7.23993i	0.102679	−	0.449867i
$260$	−9.73332	−	9.03120i	−0.603635	−	0.560091i
$261$	2.18606	+	2.02837i	0.135314	+	0.125553i
$262$	−21.0814	−	10.1523i	−1.30241	−	0.627210i
$263$	31.6099	+	4.76442i	1.94915	+	0.293787i	0.999792	−	0.0204135i	$-0.00649826\pi$
$263$	31.6099	+	4.76442i	1.94915	+	0.293787i	0.949357	+	0.314200i	$0.101736\pi$
$264$	−0.432449	−	0.542274i	−0.0266154	−	0.0333747i
$265$	−2.84642	+	7.25257i	−0.174854	+	0.445522i
$266$	−3.23076	+	0.486959i	−0.198091	+	0.0298574i
$267$	11.6359	+	10.7966i	0.712107	+	0.660738i
$268$	20.7461	−	3.12697i	1.26727	−	0.191010i
$269$	−11.2401	−	3.46711i	−0.685322	−	0.211394i	−0.0675085	−	0.997719i	$-0.521505\pi$
$269$	−11.2401	−	3.46711i	−0.685322	−	0.211394i	−0.617813	+	0.786325i	$0.711981\pi$
$270$	25.0867	−	12.0811i	1.52673	−	0.735232i
$271$	−8.54909	+	2.63704i	−0.519320	+	0.160189i	−0.543324	−	0.839523i	$-0.682835\pi$
$271$	−8.54909	+	2.63704i	−0.519320	+	0.160189i	0.0240043	+	0.999712i	$0.492358\pi$
$272$	−0.593995	+	0.551147i	−0.0360162	+	0.0334182i
$273$	−2.38538			−0.144370
$274$	36.3674			2.19703
$275$	0.476020	−	0.441682i	0.0287051	−	0.0266344i
$276$	10.6932	+	18.5212i	0.643655	+	1.11484i
$277$	4.29814	+	10.9515i	0.258250	+	0.658012i	0.999919	−	0.0127555i	$-0.00406030\pi$
$277$	4.29814	+	10.9515i	0.258250	+	0.658012i	−0.741668	+	0.670767i	$0.765965\pi$
$278$	−2.41796	+	4.18803i	−0.145020	+	0.251181i
$279$	2.81176	+	1.35407i	0.168336	+	0.0810662i
$280$	0.819300	−	0.123490i	0.0489625	−	0.00737991i
$281$	4.27386	−	18.7250i	0.254957	−	1.11704i	−0.671608	−	0.740907i	$-0.734396\pi$
$281$	4.27386	−	18.7250i	0.254957	−	1.11704i	0.926565	−	0.376134i	$-0.122747\pi$
$282$	−9.59317	+	16.6159i	−0.571265	+	0.989460i
$283$	−26.7154	−	18.2142i	−1.58806	−	1.08272i	−0.949777	−	0.312926i	$-0.898691\pi$
$283$	−26.7154	−	18.2142i	−1.58806	−	1.08272i	−0.638287	−	0.769798i	$-0.720357\pi$
$284$	11.4205	−	7.78637i	0.677682	−	0.462036i
$285$	7.94312	+	2.45013i	0.470510	+	0.145133i
$286$	−1.03122	+	4.51805i	−0.0609771	+	0.267158i
$287$	−1.13590	−	0.547020i	−0.0670499	−	0.0322896i
$288$	−2.59807	+	6.61976i	−0.153093	+	0.390073i
$289$	−13.9999	+	9.54499i	−0.823525	+	0.561470i
$290$	−1.25384	−	16.7314i	−0.0736282	−	0.982500i
$291$	9.54017	+	16.5241i	0.559255	+	0.968657i
$292$	7.57337	−	9.49670i	0.443198	−	0.555752i
$293$	−15.1493	+	14.0565i	−0.885034	+	0.821192i	−0.984777	−	0.173822i	$-0.944388\pi$
$293$	−15.1493	+	14.0565i	−0.885034	+	0.821192i	0.0997430	+	0.995013i	$0.468198\pi$
$294$	−12.2917	+	15.4133i	−0.716866	+	0.898922i
$295$	24.4194	−	7.53239i	1.42175	−	0.438553i
$296$	0.436526	+	5.82503i	0.0253725	+	0.338573i
$297$	−4.25379	−	2.90018i	−0.246830	−	0.168286i
$298$	24.6374	+	3.71348i	1.42720	+	0.215116i
$299$	5.86652	−	14.9476i	0.339270	−	0.864445i
$300$	−2.23570	−	0.689623i	−0.129078	−	0.0398154i
$301$	1.44128	+	6.31465i	0.0830739	+	0.363971i
$302$	−9.74830	−	24.8383i	−0.560951	−	1.42928i
$303$	0.775897	+	10.3536i	0.0445741	+	0.594800i
$304$	−7.37369	+	3.55098i	−0.422910	+	0.203663i
$305$	7.43793	+	32.5877i	0.425894	+	1.86597i
$306$	0.213452	−	0.369709i	0.0122022	−	0.0211348i
$307$	17.3876	+	2.62076i	0.992365	+	0.149575i	0.625103	−	0.780543i	$-0.285057\pi$
$307$	17.3876	+	2.62076i	0.992365	+	0.149575i	0.367262	+	0.930118i	$0.380295\pi$
$308$	−0.849994	−	1.06586i	−0.0484329	−	0.0607330i
$309$	22.1826	+	15.1238i	1.26192	+	0.860365i
$310$	−6.41486	−	16.3448i	−0.364340	−	0.928322i
$311$	0.431970	−	5.76423i	0.0244947	−	0.326860i	−0.971473	−	0.237149i	$-0.923787\pi$
$311$	0.431970	−	5.76423i	0.0244947	−	0.326860i	0.995968	−	0.0897102i	$-0.0285941\pi$
$312$	1.79297	−	0.553059i	0.101507	−	0.0313108i
$313$	−9.93056	−	17.2002i	−0.561309	−	0.972215i	−0.997383	−	0.0723043i	$-0.976965\pi$
$313$	−9.93056	−	17.2002i	−0.561309	−	0.972215i	0.436074	−	0.899911i	$-0.356369\pi$
$314$	−2.52627	+	33.7107i	−0.142566	+	1.90241i
$315$	1.25242	−	0.603136i	0.0705661	−	0.0339829i
$316$	−5.67077	+	3.86627i	−0.319006	+	0.217495i
$317$	3.24946	+	4.07469i	0.182508	+	0.228857i	0.864666	−	0.502347i	$-0.167530\pi$
$317$	3.24946	+	4.07469i	0.182508	+	0.228857i	−0.682158	+	0.731204i	$0.738959\pi$
$318$	−6.10862	−	7.65997i	−0.342555	−	0.429550i
$319$	−2.56325	+	1.74759i	−0.143514	+	0.0978463i
$320$	21.2780	−	10.2470i	1.18948	−	0.572823i
$321$	0.123044	−	1.64190i	0.00686762	−	0.0916420i
$322$	4.45836	+	7.72211i	0.248455	+	0.430337i
$323$	0.538804	−	0.166199i	0.0299798	−	0.00924756i
$324$	−0.943643	+	12.5920i	−0.0524246	+	0.699558i
$325$	0.641790	+	1.63526i	0.0356001	+	0.0907076i
$326$	14.2043	+	9.68431i	0.786702	+	0.536364i
$327$	−14.2973	−	17.9282i	−0.790640	−	0.991432i
$328$	0.980627	+	0.147806i	0.0541461	+	0.00816121i
$329$	−2.11892	+	3.67007i	−0.116820	+	0.202338i
$330$	1.45686	+	6.38292i	0.0801975	+	0.351368i
$331$	−24.2290	+	11.6681i	−1.33174	+	0.641334i	−0.958152	−	0.286259i	$-0.907588\pi$
$331$	−24.2290	+	11.6681i	−1.33174	+	0.641334i	−0.373592	+	0.927593i	$0.621874\pi$
$332$	0.932903	+	12.4487i	0.0511997	+	0.683212i
$333$	3.58042	+	9.12275i	0.196206	+	0.499924i
$334$	−0.431754	−	1.89164i	−0.0236245	−	0.103506i
$335$	−21.2662	−	6.55976i	−1.16190	−	0.358398i
$336$	1.21219	−	3.08862i	0.0661306	−	0.168498i
$337$	−17.6800	−	2.66484i	−0.963094	−	0.145163i	−0.351372	−	0.936236i	$-0.614285\pi$
$337$	−17.6800	−	2.66484i	−0.963094	−	0.145163i	−0.611722	+	0.791073i	$0.709523\pi$
$338$	11.7934	+	8.04060i	0.641476	+	0.437351i
$339$	−0.414151	−	5.52646i	−0.0224936	−	0.300156i
$340$	−1.21590	+	0.375055i	−0.0659414	+	0.0203402i
$341$	−2.02421	+	2.53828i	−0.109617	+	0.137455i
$342$	3.16075	−	2.93275i	0.170914	−	0.158585i
$343$	−5.61234	+	7.03765i	−0.303038	+	0.379998i
$344$	−2.54741	−	4.41225i	−0.137347	−	0.237892i
$345$	−1.69530	−	22.6222i	−0.0912717	−	1.21794i
$346$	25.1522	−	17.1485i	1.35219	−	0.921908i
$347$	4.63817	−	11.8179i	0.248990	−	0.634416i	−0.750665	−	0.660683i	$-0.770267\pi$
$347$	4.63817	−	11.8179i	0.248990	−	0.634416i	0.999655	+	0.0262673i	$0.00836209\pi$
$348$	10.0706	+	4.84974i	0.539840	+	0.259973i
$349$	4.85413	−	21.2673i	0.259836	−	1.13841i	−0.661592	−	0.749864i	$-0.730119\pi$
$349$	4.85413	−	21.2673i	0.259836	−	1.13841i	0.921427	−	0.388551i	$-0.127024\pi$
$350$	−0.932142	−	0.287528i	−0.0498251	−	0.0153690i
$351$	11.5075	−	7.84566i	0.614224	−	0.418771i
$352$	−6.11244	−	4.16739i	−0.325794	−	0.222123i
$353$	−8.92822	+	15.4641i	−0.475201	+	0.823072i	−0.999597	−	0.0284025i	$-0.990958\pi$
$353$	−8.92822	+	15.4641i	−0.475201	+	0.823072i	0.524396	+	0.851475i	$0.324291\pi$
$354$	−7.15081	+	31.3297i	−0.380061	+	1.66516i
$355$	−14.4982	+	2.18525i	−0.769485	+	0.115981i
$356$	−22.1110	−	10.6481i	−1.17188	−	0.564349i
$357$	−0.114297	+	0.197969i	−0.00604925	+	0.0104776i
$358$	−11.7590	−	29.9615i	−0.621483	−	1.58351i
$359$	14.6763	+	25.4202i	0.774588	+	1.34163i	0.935026	+	0.354580i	$0.115376\pi$
$359$	14.6763	+	25.4202i	0.774588	+	1.34163i	−0.160438	+	0.987046i	$0.551291\pi$
$360$	−0.801546	+	0.743726i	−0.0422452	+	0.0391978i
$361$	−13.3050			−0.700263
$362$	−21.2204			−1.11532
$363$	−10.8641	+	10.0805i	−0.570220	+	0.529087i
$364$	3.52415	−	1.08706i	0.184716	−	0.0569773i
$365$	−11.6086	+	5.59043i	−0.607624	+	0.292616i
$366$	−40.1659	−	12.3895i	−2.09951	−	0.647612i
$367$	−16.2603	+	2.45084i	−0.848780	+	0.127933i	−0.559007	−	0.829163i	$-0.688818\pi$
$367$	−16.2603	+	2.45084i	−0.848780	+	0.127933i	−0.289772	+	0.957096i	$0.593580\pi$
$368$	16.3732	+	15.1921i	0.853510	+	0.791941i
$369$	1.64522	−	0.247977i	0.0856469	−	0.0129092i
$370$	20.1444	−	51.3270i	1.04726	−	2.66836i
$371$	−1.34926	−	1.69192i	−0.0700501	−	0.0878400i
$372$	11.5667	+	1.74339i	0.599704	+	0.0903908i
$373$	23.3571	+	11.2482i	1.20938	+	0.582409i	0.926336	−	0.376697i	$-0.122940\pi$
$373$	23.3571	+	11.2482i	1.20938	+	0.582409i	0.283048	+	0.959106i	$0.408655\pi$
$374$	0.325553	+	0.302069i	0.0168339	+	0.0156196i
$375$	−10.9476	−	10.1579i	−0.565333	−	0.524552i
$376$	0.741767	−	3.24989i	0.0382537	−	0.167600i
$377$	−1.86750	−	8.18204i	−0.0961810	−	0.421396i
$378$	−0.577954	+	7.71226i	−0.0297268	+	0.396676i
$379$	7.85390	−	9.84848i	0.403428	−	0.505883i	−0.538071	−	0.842900i	$-0.680847\pi$
$379$	7.85390	−	9.84848i	0.403428	−	0.505883i	0.941498	+	0.337017i	$0.109418\pi$
$380$	−12.8517			−0.659278
$381$	1.59734	+	16.3458i	0.0818344	+	0.837420i
$382$	9.28507			0.475065
$383$	−0.0613730	+	0.0769593i	−0.00313601	+	0.00393244i	−0.783397	−	0.621522i	$-0.786515\pi$
$383$	−0.0613730	+	0.0769593i	−0.00313601	+	0.00393244i	0.780261	+	0.625454i	$0.215086\pi$
$384$	−0.451324	+	6.02250i	−0.0230315	+	0.307335i
$385$	0.321788	+	1.40985i	0.0163998	+	0.0718524i
$386$	2.82132	−	12.3610i	0.143601	−	0.629158i
$387$	−6.26592	−	5.81393i	−0.318515	−	0.295538i
$388$	−21.6249	−	20.0650i	−1.09784	−	1.01864i
$389$	−21.8542	−	10.5244i	−1.10805	−	0.533610i	−0.211872	−	0.977297i	$-0.567956\pi$
$389$	−21.8542	−	10.5244i	−1.10805	−	0.533610i	−0.896182	+	0.443687i	$0.853670\pi$
$390$	−17.5135	−	2.63974i	−0.886831	−	0.133668i
$391$	−0.959443	−	1.20310i	−0.0485211	−	0.0608435i
$392$	1.25137	−	3.18843i	0.0632036	−	0.161040i
$393$	−16.3501	+	2.46439i	−0.824755	+	0.124312i
$394$	6.74423	+	6.25773i	0.339769	+	0.315260i
$395$	7.19898	−	1.08507i	0.362220	−	0.0545959i
$396$	1.71919	+	0.530300i	0.0863925	+	0.0266486i
$397$	−1.64272	+	0.791093i	−0.0824459	+	0.0397038i	−0.474652	−	0.880173i	$-0.657426\pi$
$397$	−1.64272	+	0.791093i	−0.0824459	+	0.0397038i	0.392206	+	0.919877i	$0.371712\pi$
$398$	14.6142	−	4.50788i	0.732543	−	0.225960i
$399$	−1.69249	+	1.57040i	−0.0847306	+	0.0786185i
$400$	−2.44349			−0.122174
$401$	−3.58668			−0.179110			−0.0895552	−	0.995982i	$-0.528545\pi$
$401$	−3.58668			−0.179110			−0.0895552	+	0.995982i	$0.528545\pi$
$402$	20.5151	−	19.0353i	1.02320	−	0.949392i
$403$	−4.39137	−	7.60608i	−0.218750	−	0.378886i
$404$	−5.86462	−	14.9428i	−0.291776	−	0.743432i
$405$	6.69722	−	11.5999i	0.332788	−	0.576405i
$406$	4.19877	+	2.02202i	0.208382	+	0.100351i
$407$	−10.0812	+	1.51950i	−0.499709	+	0.0753190i
$408$	0.0400118	−	0.175303i	0.00198088	−	0.00867881i
$409$	−15.1458	+	26.2334i	−0.748914	+	1.29716i	0.199430	+	0.979912i	$0.436091\pi$
$409$	−15.1458	+	26.2334i	−0.748914	+	1.29716i	−0.948344	+	0.317244i	$0.897242\pi$
$410$	−7.73443	−	5.27325i	−0.381976	−	0.260427i
$411$	21.2338	−	14.4769i	1.04738	−	0.714094i
$412$	−39.6647	−	12.2349i	−1.95414	−	0.602772i
$413$	−1.57945	+	6.92004i	−0.0777199	+	0.340513i
$414$	−10.6020	−	5.10566i	−0.521061	−	0.250930i
$415$	4.83784	−	12.3266i	0.237480	−	0.605090i
$416$	16.5356	−	11.2738i	0.810722	−	0.552741i
$417$	0.255378	+	3.40779i	0.0125059	+	0.166880i
$418$	2.24276	+	3.88458i	0.109697	+	0.190001i
$419$	−17.5102	+	21.9571i	−0.855430	+	1.07267i	0.141146	+	0.989989i	$0.454921\pi$
$419$	−17.5102	+	21.9571i	−0.855430	+	1.07267i	−0.996576	+	0.0826860i	$0.973650\pi$
$420$	3.81939	−	3.54387i	0.186367	−	0.172923i
$421$	−12.1488	+	15.2342i	−0.592098	+	0.742467i	−0.984123	−	0.177487i	$-0.943203\pi$
$421$	−12.1488	+	15.2342i	−0.592098	+	0.742467i	0.392025	+	0.919955i	$0.371775\pi$
$422$	−25.6606	+	7.91523i	−1.24914	+	0.385307i
$423$	−0.417939	−	5.57701i	−0.0203209	−	0.271163i
$424$	1.40645	+	0.958901i	0.0683032	+	0.0465683i
$425$	0.166466	+	0.0250906i	0.00807477	+	0.00121708i
$426$	6.73602	−	17.1631i	0.326361	−	0.831555i
$427$	−8.87176	−	2.73657i	−0.429334	−	0.132432i
$428$	0.566457	+	2.48181i	0.0273808	+	0.119963i
$429$	1.19643	+	3.04845i	0.0577641	+	0.147181i
$430$	3.59390	+	47.9573i	0.173313	+	2.31270i
$431$	21.4389	−	10.3244i	1.03267	−	0.497309i	0.160773	−	0.986991i	$-0.448601\pi$
$431$	21.4389	−	10.3244i	1.03267	−	0.497309i	0.871901	+	0.489682i	$0.162887\pi$
$432$	4.31083	+	18.8870i	0.207405	+	0.908700i
$433$	−6.16140	+	10.6718i	−0.296098	+	0.512856i	−0.975240	−	0.221151i	$-0.929019\pi$
$433$	−6.16140	+	10.6718i	−0.296098	+	0.512856i	0.679142	+	0.734007i	$0.262352\pi$
$434$	4.82254	+	0.726881i	0.231489	+	0.0348914i
$435$	−7.39242	−	9.26980i	−0.354439	−	0.444453i
$436$	29.2929	+	19.9716i	1.40287	+	0.956464i
$437$	−5.67825	−	14.4680i	−0.271628	−	0.692096i
$438$	1.21082	−	16.1573i	0.0578553	−	0.772025i
$439$	10.3896	−	3.20478i	0.495871	−	0.152956i	−0.0367255	−	0.999325i	$-0.511693\pi$
$439$	10.3896	−	3.20478i	0.495871	−	0.152956i	0.532596	+	0.846370i	$0.321217\pi$
$440$	−0.568750	−	0.985103i	−0.0271141	−	0.0469630i
$441$	0.429441	−	5.73049i	0.0204496	−	0.272880i
$442$	−1.08243	+	0.521272i	−0.0514860	+	0.0247944i
$443$	24.4513	−	16.6706i	1.16172	−	0.792045i	0.180239	−	0.983623i	$-0.442313\pi$
$443$	24.4513	−	16.6706i	1.16172	−	0.792045i	0.981477	+	0.191578i	$0.0613606\pi$
$444$	22.9024	+	28.7187i	1.08690	+	1.36293i
$445$	16.2308	+	20.3528i	0.769415	+	0.964816i
$446$	13.4630	−	9.17893i	0.637492	−	0.434635i
$447$	15.8632	−	7.63933i	0.750305	−	0.361328i
$448$	−0.490210	+	6.54140i	−0.0231602	+	0.309052i
$449$	13.8919	+	24.0615i	0.655601	+	1.13553i	0.981743	+	0.190213i	$0.0609179\pi$
$449$	13.8919	+	24.0615i	0.655601	+	1.13553i	−0.326142	+	0.945321i	$0.605749\pi$
$450$	1.23014	−	0.379449i	0.0579894	−	0.0178874i
$451$	−0.129347	+	1.72601i	−0.00609070	+	0.0812748i
$452$	3.13036	+	7.97603i	0.147240	+	0.375161i
$453$	−15.5792	−	10.6217i	−0.731975	−	0.499052i
$454$	30.0483	+	37.6793i	1.41023	+	1.76838i
$455$	−3.86835	−	0.583059i	−0.181351	−	0.0273342i
$456$	0.908060	−	1.57281i	0.0425238	−	0.0736534i
$457$	−6.25387	−	27.4000i	−0.292543	−	1.28172i	−0.880972	−	0.473168i	$-0.843110\pi$
$457$	−6.25387	−	27.4000i	−0.292543	−	1.28172i	0.588429	−	0.808549i	$-0.299747\pi$
$458$	−50.3522	+	24.2484i	−2.35281	+	1.13305i
$459$	−0.0997419	−	1.33096i	−0.00465555	−	0.0621240i
$460$	12.8139	+	32.6493i	0.597452	+	1.52228i
$461$	−2.44027	−	10.6915i	−0.113655	−	0.497955i	−0.999427	−	0.0338350i	$-0.989228\pi$
$461$	−2.44027	−	10.6915i	−0.113655	−	0.497955i	0.885773	−	0.464120i	$-0.153629\pi$
$462$	−1.73770	−	0.536010i	−0.0808452	−	0.0249375i
$463$	−6.77344	+	17.2584i	−0.314789	+	0.802068i	0.682664	+	0.730733i	$0.260821\pi$
$463$	−6.77344	+	17.2584i	−0.314789	+	0.802068i	−0.997452	+	0.0713355i	$0.977274\pi$
$464$	11.5432	+	1.73986i	0.535880	+	0.0807709i
$465$	−10.2519	−	6.98962i	−0.475420	−	0.324136i
$466$	1.06797	+	14.2511i	0.0494730	+	0.660171i
$467$	25.1682	−	7.76335i	1.16464	−	0.359245i	0.348620	−	0.937264i	$-0.386650\pi$
$467$	25.1682	−	7.76335i	1.16464	−	0.359245i	0.816023	+	0.578019i	$0.196174\pi$
$468$	−3.03454	+	3.80520i	−0.140272	+	0.175895i
$469$	4.53133	−	4.20446i	0.209238	−	0.194144i
$470$	−19.6186	+	24.6009i	−0.904936	+	1.13475i
$471$	11.9444	+	20.6883i	0.550368	+	0.953266i
$472$	−0.417238	−	5.56766i	−0.0192049	−	0.256272i
$473$	7.34705	−	5.00913i	0.337818	−	0.230320i
$474$	−3.34472	+	8.52222i	−0.153628	+	0.391438i
$475$	1.53193	+	0.737739i	0.0702898	+	0.0338498i
$476$	0.0786447	−	0.344565i	0.00360467	−	0.0157931i
$477$	2.72900	+	0.841784i	0.124952	+	0.0385427i
$478$	13.5593	−	9.24456i	0.620187	−	0.422836i
$479$	−17.4488	−	11.8964i	−0.797254	−	0.543558i	0.0947954	−	0.995497i	$-0.469780\pi$
$479$	−17.4488	−	11.8964i	−0.797254	−	0.543558i	−0.892049	+	0.451938i	$0.850733\pi$
$480$	14.1368	−	24.4857i	0.645254	−	1.11761i
$481$	6.13716	−	26.8887i	0.279830	−	1.22602i
$482$	9.25891	−	1.39556i	0.421732	−	0.0635658i
$483$	5.67708	+	2.73394i	0.258316	+	0.124398i
$484$	11.4568	−	19.8438i	0.520764	−	0.901990i
$485$	11.4322	+	29.1288i	0.519109	+	1.32267i
$486$	−9.05292	−	15.6801i	−0.410649	−	0.711264i
$487$	−1.61505	+	1.49855i	−0.0731850	+	0.0679057i	−0.715917	−	0.698185i	$-0.753991\pi$
$487$	−1.61505	+	1.49855i	−0.0731850	+	0.0679057i	0.642732	+	0.766091i	$0.277801\pi$
$488$	7.30294			0.330589
$489$	12.1485			0.549375
$490$	−23.7008	+	21.9911i	−1.07069	+	0.993457i
$491$	39.0544	−	12.0467i	1.76250	−	0.543660i	0.767281	−	0.641311i	$-0.221609\pi$
$491$	39.0544	−	12.0467i	1.76250	−	0.543660i	0.995221	+	0.0976515i	$0.0311330\pi$
$492$	5.61862	−	2.70579i	0.253307	−	0.121986i
$493$	−0.768529	−	0.237060i	−0.0346128	−	0.0106766i
$494$	−11.9988	+	1.80853i	−0.539854	+	0.0813698i
$495$	−1.39896	−	1.29805i	−0.0628788	−	0.0583430i
$496$	12.0800	−	1.82077i	0.542409	−	0.0817550i
$497$	1.48784	−	3.79095i	0.0667386	−	0.170047i
$498$	10.3823	+	13.0190i	0.465244	+	0.583397i
$499$	−16.8403	−	2.53826i	−0.753873	−	0.113628i	−0.239148	−	0.970983i	$-0.576868\pi$
$499$	−16.8403	−	2.53826i	−0.753873	−	0.113628i	−0.514725	+	0.857355i	$0.672106\pi$
$500$	20.8031	+	10.0182i	0.930343	+	0.448029i
$501$	−1.00510	−	0.932597i	−0.0449046	−	0.0416654i
$502$	15.3556	+	14.2479i	0.685352	+	0.635914i
$503$	4.35133	−	19.0644i	0.194016	−	0.850040i	−0.780399	−	0.625282i	$-0.784984\pi$
$503$	4.35133	−	19.0644i	0.194016	−	0.850040i	0.974415	−	0.224757i	$-0.0721590\pi$
$504$	−0.0675818	−	0.296095i	−0.00301033	−	0.0131891i
$505$	−1.27247	+	16.9800i	−0.0566244	+	0.755600i
$506$	7.63247	−	9.57082i	0.339305	−	0.425475i
$507$	10.0866			0.447959
$508$	−9.80895	−	23.4212i	−0.435202	−	1.03915i
$509$	15.2391			0.675461			0.337731	−	0.941243i	$-0.390341\pi$
$509$	15.2391			0.675461			0.337731	+	0.941243i	$0.390341\pi$
$510$	−1.05825	+	1.32700i	−0.0468601	+	0.0587607i
$511$	0.267444	−	3.56879i	0.0118310	−	0.157874i
$512$	6.99141	+	30.6314i	0.308979	+	1.35373i
$513$	2.99971	−	13.1426i	0.132441	−	0.580260i
$514$	−20.7689	−	19.2707i	−0.916077	−	0.849995i
$515$	32.2765	+	29.9482i	1.42227	+	1.31968i
$516$	−28.8654	−	13.9008i	−1.27073	−	0.611950i
$517$	5.75303	+	0.867130i	0.253018	+	0.0381363i
$518$	9.54881	+	11.9738i	0.419551	+	0.526100i
$519$	7.85920	−	20.0249i	0.344980	−	0.878996i
$520$	3.04283	−	0.458633i	0.133437	−	0.0201124i
$521$	−23.8959	−	22.1722i	−1.04690	−	0.971381i	−0.0472782	−	0.998882i	$-0.515055\pi$
$521$	−23.8959	−	22.1722i	−1.04690	−	0.971381i	−0.999622	+	0.0275005i	$0.991245\pi$
$522$	−6.08146	+	0.916632i	−0.266178	+	0.0401199i
$523$	2.66580	+	0.822291i	0.116567	+	0.0359563i	0.352490	−	0.935816i	$-0.385335\pi$
$523$	2.66580	+	0.822291i	0.116567	+	0.0359563i	−0.235923	+	0.971772i	$0.575811\pi$
$524$	23.0326	−	11.0919i	1.00618	−	0.484552i
$525$	−0.658706	+	0.203184i	−0.0287483	+	0.00886767i
$526$	−48.3274	+	44.8413i	−2.10718	+	1.95517i
$527$	−0.841662			−0.0366634
$528$	−4.55516			−0.198238
$529$	−14.2336	+	13.2069i	−0.618853	+	0.574211i
$530$	−8.03396	−	13.9152i	−0.348973	−	0.604439i
$531$	−3.42222	−	8.71967i	−0.148512	−	0.378402i
$532$	1.78482	−	3.09140i	0.0773819	−	0.134029i
$533$	−4.21866	−	2.03160i	−0.182730	−	0.0879983i
$534$	−32.3703	+	4.87903i	−1.40080	+	0.211136i
$535$	0.600869	−	2.63258i	0.0259778	−	0.113816i
$536$	−2.43116	+	4.21089i	−0.105010	+	0.181883i
$537$	−18.7926	−	12.8126i	−0.810962	−	0.552905i
$538$	20.0434	−	13.6653i	0.864130	−	0.589154i
$539$	5.71253	+	1.76208i	0.246056	+	0.0758983i
$540$	−6.76934	+	29.6584i	−0.291306	+	1.27630i
$541$	−2.84771	−	1.37138i	−0.122433	−	0.0589604i	0.371665	−	0.928367i	$-0.378787\pi$
$541$	−2.84771	−	1.37138i	−0.122433	−	0.0589604i	−0.494097	+	0.869407i	$0.664501\pi$
$542$	6.74082	−	17.1753i	0.289543	−	0.737743i
$543$	−12.3899	+	8.44729i	−0.531702	+	0.362508i
$544$	−0.143323	−	1.91251i	−0.00614493	−	0.0819984i
$545$	−18.8035	−	32.5686i	−0.805454	−	1.39509i
$546$	3.06722	−	3.84618i	0.131265	−	0.164601i
$547$	8.39933	−	7.79344i	0.359130	−	0.333223i	−0.479886	−	0.877331i	$-0.659322\pi$
$547$	8.39933	−	7.79344i	0.359130	−	0.333223i	0.839016	+	0.544107i	$0.183132\pi$
$548$	−24.7733	+	31.0647i	−1.05826	+	1.32702i
$549$	11.7080	−	3.61144i	0.499685	−	0.154132i
$550$	0.100079	+	1.33547i	0.00426739	+	0.0569444i
$551$	−6.71164	−	4.57592i	−0.285926	−	0.194941i
$552$	−4.90105	−	0.738715i	−0.208603	−	0.0314418i
$553$	−0.738775	+	1.88237i	−0.0314159	+	0.0800465i
$554$	−23.1849	−	7.15158i	−0.985030	−	0.303842i
$555$	−8.67033	−	37.9872i	−0.368035	−	1.61247i
$556$	−1.93028	−	4.91827i	−0.0818620	−	0.208581i
$557$	−1.83581	−	24.4971i	−0.0777856	−	1.03798i	−0.890401	−	0.455177i	$-0.849576\pi$
$557$	−1.83581	−	24.4971i	−0.0777856	−	1.03798i	0.812615	−	0.582800i	$-0.198043\pi$
$558$	−5.79878	+	2.79255i	−0.245482	+	0.118218i
$559$	5.35282	+	23.4522i	0.226400	+	0.991924i
$560$	2.72075	−	4.71248i	0.114973	−	0.199139i
$561$	0.310326	+	0.0467741i	0.0131020	+	0.00197480i
$562$	24.6966	+	30.9685i	1.04176	+	1.30633i
$563$	10.5171	+	7.17044i	0.443243	+	0.302198i	0.764299	−	0.644862i	$-0.223085\pi$
$563$	10.5171	+	7.17044i	0.443243	+	0.302198i	−0.321056	+	0.947060i	$0.604038\pi$
$564$	−7.65831	−	19.5131i	−0.322473	−	0.821648i
$565$	0.679209	−	9.06342i	0.0285746	−	0.381301i
$566$	63.7203	−	19.6551i	2.67836	−	0.826166i
$567$	1.86020	+	3.22196i	0.0781210	+	0.135310i
$568$	−0.239389	+	3.19443i	−0.0100446	+	0.134035i
$569$	24.8670	−	11.9753i	1.04248	−	0.502032i	0.167339	−	0.985899i	$-0.446483\pi$
$569$	24.8670	−	11.9753i	1.04248	−	0.502032i	0.875141	+	0.483868i	$0.160768\pi$
$570$	−14.1642	+	9.65697i	−0.593272	+	0.404486i
$571$	6.01800	+	7.54634i	0.251846	+	0.315804i	0.891643	−	0.452739i	$-0.149553\pi$
$571$	6.01800	+	7.54634i	0.251846	+	0.315804i	−0.639797	+	0.768544i	$0.720982\pi$
$572$	−3.15683	−	3.95853i	−0.131994	−	0.165515i
$573$	5.42126	−	3.69615i	0.226476	−	0.154409i
$574$	2.34260	−	1.12814i	0.0977781	−	0.0470875i
$575$	0.346775	−	4.62739i	0.0144615	−	0.192975i
$576$	−4.32842	−	7.49705i	−0.180351	−	0.312377i
$577$	0.428808	−	0.132270i	0.0178515	−	0.00550646i	−0.285817	−	0.958284i	$-0.592265\pi$
$577$	0.428808	−	0.132270i	0.0178515	−	0.00550646i	0.303668	+	0.952778i	$0.401789\pi$
$578$	2.61140	−	34.8468i	0.108620	−	1.44943i
$579$	−3.27332	−	8.34029i	−0.136035	−	0.346611i
$580$	15.1459	+	10.3263i	0.628900	+	0.428777i
$581$	2.29323	+	2.87562i	0.0951391	+	0.119301i
$582$	−38.9104	−	5.86481i	−1.61289	−	0.243104i
$583$	−1.48548	+	2.57293i	−0.0615223	+	0.106560i
$584$	0.626412	+	2.74449i	0.0259211	+	0.113568i
$585$	4.65143	−	2.24001i	0.192313	−	0.0926130i
$586$	−3.18502	−	42.5012i	−0.131572	−	1.75571i
$587$	3.60547	+	9.18658i	0.148814	+	0.379171i	0.985770	−	0.168098i	$-0.0537626\pi$
$587$	3.60547	+	9.18658i	0.148814	+	0.379171i	−0.836957	+	0.547269i	$0.815667\pi$
$588$	−4.79287	−	20.9989i	−0.197655	−	0.865982i
$589$	−8.12322	−	2.50568i	−0.334712	−	0.103245i
$590$	−19.2543	+	49.0592i	−0.792687	+	2.01973i
$591$	6.42878	+	0.968983i	0.264445	+	0.0398586i
$592$	31.6970	+	21.6106i	1.30274	+	0.888191i
$593$	−0.306102	−	4.08464i	−0.0125701	−	0.167736i	−0.999956	−	0.00940278i	$-0.997007\pi$
$593$	−0.306102	−	4.08464i	−0.0125701	−	0.167736i	0.987386	−	0.158333i	$-0.0506121\pi$
$594$	10.1459	−	3.12961i	0.416293	−	0.128409i
$595$	−0.233744	+	0.293106i	−0.00958256	+	0.0120162i
$596$	−19.9549	+	18.5154i	−0.817384	+	0.758422i
$597$	6.73829	−	8.44955i	0.275780	−	0.345817i
$598$	16.5581	+	28.6795i	0.677111	+	1.17279i
$599$	−1.56480	−	20.8808i	−0.0639360	−	0.853167i	−0.933324	−	0.359036i	$-0.883105\pi$
$599$	−1.56480	−	20.8808i	−0.0639360	−	0.853167i	0.869388	−	0.494131i	$-0.164514\pi$
$600$	0.448008	−	0.305446i	0.0182898	−	0.0124698i
$601$	−5.85662	+	14.9224i	−0.238897	+	0.608699i	−0.999163	−	0.0409131i	$-0.986973\pi$
$601$	−5.85662	+	14.9224i	−0.238897	+	0.608699i	0.760266	+	0.649612i	$0.225069\pi$
$602$	−12.0350	−	5.79574i	−0.490509	−	0.236217i
$603$	−1.81525	+	7.95311i	−0.0739225	+	0.323876i
$604$	27.8571	+	8.59279i	1.13349	+	0.349636i
$605$	−20.0822	+	13.6918i	−0.816459	+	0.556652i
$606$	−17.6918	−	12.0621i	−0.718680	−	0.489988i
$607$	−19.9275	+	34.5154i	−0.808832	+	1.40094i	0.104841	+	0.994489i	$0.466566\pi$
$607$	−19.9275	+	34.5154i	−0.808832	+	1.40094i	−0.913673	+	0.406449i	$0.866767\pi$
$608$	4.31041	−	18.8851i	0.174810	−	0.765893i
$609$	3.25645	−	0.490830i	0.131958	−	0.0198894i
$610$	−62.1082	−	29.9097i	−2.51469	−	1.21101i
$611$	−7.86953	+	13.6304i	−0.318367	+	0.551428i
$612$	0.170400	+	0.434173i	0.00688802	+	0.0175504i
$613$	−8.08559	−	14.0047i	−0.326574	−	0.565643i	0.655256	−	0.755407i	$-0.272561\pi$
$613$	−8.08559	−	14.0047i	−0.326574	−	0.565643i	−0.981830	+	0.189764i	$0.939228\pi$
$614$	−26.5834	+	24.6658i	−1.07282	+	0.995432i
$615$	−6.61504			−0.266744
$616$	0.315948			0.0127299
$617$	13.8384	−	12.8402i	0.557114	−	0.516926i	−0.350594	−	0.936527i	$-0.614020\pi$
$617$	13.8384	−	12.8402i	0.557114	−	0.516926i	0.907709	+	0.419601i	$0.137830\pi$
$618$	−52.9089	+	16.3202i	−2.12831	+	0.656496i
$619$	2.29579	−	1.10559i	0.0922754	−	0.0444375i	−0.387177	−	0.922006i	$-0.626550\pi$
$619$	2.29579	−	1.10559i	0.0922754	−	0.0444375i	0.479452	+	0.877568i	$0.340835\pi$
$620$	18.3314	+	5.65448i	0.736206	+	0.227089i
$621$	−36.3792	+	5.48329i	−1.45985	+	0.220037i
$622$	8.73877	+	8.10840i	0.350393	+	0.325117i
$623$	−7.14987	+	1.07767i	−0.286453	+	0.0431759i
$624$	4.50201	−	11.4709i	0.180225	−	0.459205i
$625$	−17.4919	−	21.9341i	−0.699676	−	0.877366i
$626$	40.5027	+	6.10480i	1.61881	+	0.243997i
$627$	2.85583	+	1.37530i	0.114051	+	0.0549240i
$628$	−27.0746	−	25.1215i	−1.08039	−	1.00246i
$629$	−1.93749	−	1.79773i	−0.0772527	−	0.0716800i
$630$	−0.637927	+	2.79494i	−0.0254156	+	0.111353i
$631$	5.65693	+	24.7847i	0.225199	+	0.986661i	0.953497	+	0.301401i	$0.0974544\pi$
$631$	5.65693	+	24.7847i	0.225199	+	0.986661i	−0.728298	+	0.685260i	$0.759689\pi$
$632$	0.118867	−	1.58617i	0.00472828	−	0.0630945i
$633$	−11.8315	+	14.8363i	−0.470261	+	0.589689i
$634$	−10.7483			−0.426869
$635$	−1.40501	+	26.8982i	−0.0557560	+	1.06742i
$636$	10.7043			0.424451
$637$	−10.0832	+	12.6439i	−0.399511	+	0.500971i
$638$	0.478122	−	6.38009i	0.0189290	−	0.252590i
$639$	1.19592	+	5.23965i	0.0473097	+	0.207278i
$640$	−2.20399	+	9.65630i	−0.0871203	+	0.381699i
$641$	−6.29623	−	5.84205i	−0.248686	−	0.230747i	0.545973	−	0.837803i	$-0.316160\pi$
$641$	−6.29623	−	5.84205i	−0.248686	−	0.230747i	−0.794659	+	0.607056i	$0.792351\pi$
$642$	2.48918	+	2.30962i	0.0982401	+	0.0911535i
$643$	29.5565	+	14.2337i	1.16560	+	0.561321i	0.913682	−	0.406429i	$-0.133226\pi$
$643$	29.5565	+	14.2337i	1.16560	+	0.561321i	0.251913	+	0.967750i	$0.418940\pi$
$644$	−9.63319	−	1.45197i	−0.379601	−	0.0572156i
$645$	21.1889	+	26.5701i	0.834314	+	1.04620i
$646$	−0.424838	+	1.08247i	−0.0167150	+	0.0425892i
$647$	36.3610	−	5.48054i	1.42950	−	0.215462i	0.611755	−	0.791047i	$-0.290464\pi$
$647$	36.3610	−	5.48054i	1.42950	−	0.215462i	0.817742	+	0.575585i	$0.195226\pi$
$648$	−2.14524	−	1.99049i	−0.0842731	−	0.0781940i
$649$	9.63582	−	1.45237i	0.378239	−	0.0570103i
$650$	−3.46192	−	1.06786i	−0.135788	−	0.0418849i
$651$	3.10508	−	1.49533i	0.121698	−	0.0586065i
$652$	−17.9482	+	5.53627i	−0.702904	+	0.216817i
$653$	−30.9054	+	28.6760i	−1.20942	+	1.12218i	−0.220244	+	0.975445i	$0.570685\pi$
$653$	−30.9054	+	28.6760i	−1.20942	+	1.12218i	−0.989176	+	0.146733i	$0.953124\pi$
$654$	47.2913			1.84924
$655$	−27.1172			−1.05956
$656$	4.77435	−	4.42995i	0.186407	−	0.172961i
$657$	2.36146	+	4.09016i	0.0921292	+	0.159572i
$658$	−3.19301	−	8.13567i	−0.124477	−	0.317161i
$659$	3.13197	−	5.42473i	0.122004	−	0.211318i	−0.798554	−	0.601924i	$-0.794401\pi$
$659$	3.13197	−	5.42473i	0.122004	−	0.211318i	0.920558	+	0.390606i	$0.127735\pi$
$660$	−6.44465	−	3.10358i	−0.250858	−	0.120807i
$661$	−24.5726	+	3.70372i	−0.955763	+	0.144058i	−0.608363	−	0.793659i	$-0.708173\pi$
$661$	−24.5726	+	3.70372i	−0.955763	+	0.144058i	−0.347400	+	0.937717i	$0.612935\pi$
$662$	12.3411	−	54.0699i	0.479651	−	2.10149i
$663$	−0.424493	+	0.735243i	−0.0164859	+	0.0285545i
$664$	−2.39043	−	1.62977i	−0.0927666	−	0.0632472i
$665$	−3.12855	+	2.13301i	−0.121320	+	0.0827146i
$666$	−19.3133	−	5.95737i	−0.748376	−	0.230843i
$667$	−4.93307	+	21.6132i	−0.191009	+	0.836866i
$668$	1.90993	+	0.919775i	0.0738975	+	0.0355871i
$669$	4.20673	−	10.7186i	0.162642	−	0.414404i
$670$	37.9219	−	25.8547i	1.46505	−	0.998855i
$671$	0.952515	+	12.7104i	0.0367714	+	0.490681i
$672$	3.92660	+	6.80106i	0.151472	+	0.262357i
$673$	18.9773	−	23.7968i	0.731520	−	0.917298i	−0.267408	−	0.963583i	$-0.586167\pi$
$673$	18.9773	−	23.7968i	0.731520	−	0.917298i	0.998928	+	0.0462858i	$0.0147385\pi$
$674$	27.0305	−	25.0807i	1.04118	−	0.966071i
$675$	2.50942	−	3.14671i	0.0965877	−	0.121117i
$676$	−14.9018	+	4.59661i	−0.573147	+	0.176793i
$677$	1.71946	+	22.9447i	0.0660844	+	0.881835i	0.927473	+	0.373889i	$0.121976\pi$
$677$	1.71946	+	22.9447i	0.0660844	+	0.881835i	−0.861389	+	0.507946i	$0.830405\pi$
$678$	9.44336	+	6.43837i	0.362670	+	0.247264i
$679$	−8.59445	−	1.29541i	−0.329825	−	0.0497131i
$680$	0.107736	−	0.274507i	0.00413149	−	0.0105269i
$681$	32.5434	+	10.0383i	1.24707	+	0.384669i
$682$	−1.48989	−	6.52765i	−0.0570509	−	0.249957i
$683$	−14.5214	−	37.0000i	−0.555647	−	1.41577i	−0.882329	−	0.470632i	$-0.844026\pi$
$683$	−14.5214	−	37.0000i	−0.555647	−	1.41577i	0.326682	−	0.945134i	$-0.394069\pi$
$684$	0.352042	+	4.69767i	0.0134606	+	0.179620i
$685$	37.9731	−	18.2869i	1.45088	−	0.698707i
$686$	−4.13089	−	18.0986i	−0.157718	−	0.691008i
$687$	−19.7464	+	34.2018i	−0.753373	+	1.30488i
$688$	−33.0864	−	4.98697i	−1.26141	−	0.190126i
$689$	−5.01107	−	6.28368i	−0.190906	−	0.239389i
$690$	38.6557	+	26.3550i	1.47160	+	1.00332i
$691$	−3.03131	−	7.72364i	−0.115316	−	0.293821i	0.861550	−	0.507673i	$-0.169494\pi$
$691$	−3.03131	−	7.72364i	−0.115316	−	0.293821i	−0.976866	+	0.213852i	$0.931399\pi$
$692$	−2.48547	+	33.1663i	−0.0944833	+	1.26079i
$693$	0.506525	−	0.156242i	0.0192413	−	0.00593515i
$694$	13.0911	+	22.6744i	0.496931	+	0.860710i
$695$	−0.418822	+	5.58879i	−0.0158868	+	0.211995i
$696$	−2.33391	+	1.12395i	−0.0884666	+	0.0426033i
$697$	−0.370747	+	0.252771i	−0.0140430	+	0.00957438i
$698$	28.0497	+	35.1732i	1.06170	+	1.33133i
$699$	6.29657	+	7.89565i	0.238158	+	0.298641i
$700$	0.880575	−	0.600366i	0.0332826	−	0.0226917i
$701$	−16.4317	+	7.91308i	−0.620616	+	0.298873i	−0.717645	−	0.696409i	$-0.754780\pi$
$701$	−16.4317	+	7.91308i	−0.620616	+	0.298873i	0.0970297	+	0.995281i	$0.469066\pi$
$702$	−2.14649	+	28.6429i	−0.0810139	+	1.08106i
$703$	−13.3475	−	23.1186i	−0.503412	−	0.871935i
$704$	8.60559	−	2.65447i	0.324335	−	0.100044i
$705$	−1.66166	+	22.1733i	−0.0625818	+	0.835096i
$706$	−13.4540	−	34.2802i	−0.506348	−	1.29015i
$707$	−3.90773	−	2.66424i	−0.146965	−	0.100199i
$708$	−21.8905	−	27.4498i	−0.822696	−	1.03163i
$709$	6.79556	+	1.02427i	0.255212	+	0.0384671i	0.275402	−	0.961329i	$-0.411189\pi$
$709$	6.79556	+	1.02427i	0.255212	+	0.0384671i	−0.0201898	+	0.999796i	$0.506427\pi$
$710$	15.1189	−	26.1867i	0.567402	−	0.982770i
$711$	−0.593824	−	2.60171i	−0.0222702	−	0.0975719i
$712$	5.12434	−	2.46775i	0.192043	−	0.0924830i
$713$	1.73374	+	23.1351i	0.0649289	+	0.866416i
$714$	−0.172235	−	0.438848i	−0.00644574	−	0.0164235i
$715$	1.19510	+	5.23608i	0.0446942	+	0.195818i
$716$	33.6031	+	10.3652i	1.25581	+	0.387365i
$717$	4.23681	−	10.7952i	0.158226	−	0.403154i
$718$	−59.8588	−	9.02227i	−2.23391	−	0.336708i
$719$	28.0311	+	19.1113i	1.04538	+	0.712730i	0.958964	−	0.283529i	$-0.0915053\pi$
$719$	28.0311	+	19.1113i	1.04538	+	0.712730i	0.0864187	+	0.996259i	$0.472458\pi$
$720$	0.536645	+	7.16104i	0.0199996	+	0.266876i
$721$	−11.6864	+	3.60478i	−0.435224	+	0.134249i
$722$	17.1081	−	21.4529i	0.636699	−	0.798395i
$723$	4.85045	−	4.50056i	0.180390	−	0.167378i
$724$	14.4552	−	18.1263i	0.537224	−	0.673658i
$725$	−1.21263	−	2.10034i	−0.0450360	−	0.0780046i
$726$	−2.28410	−	30.4792i	−0.0847708	−	1.13119i
$727$	12.0406	−	8.20914i	0.446561	−	0.304460i	−0.319081	−	0.947728i	$-0.603374\pi$
$727$	12.0406	−	8.20914i	0.446561	−	0.304460i	0.765642	+	0.643267i	$0.222422\pi$
$728$	−0.312262	+	0.795630i	−0.0115732	+	0.0294880i
$729$	−26.6751	−	12.8461i	−0.987968	−	0.475780i
$730$	5.91290	−	25.9061i	0.218846	−	0.958829i
$731$	2.20284	+	0.679486i	0.0814750	+	0.0251317i
$732$	37.9439	−	25.8697i	1.40245	−	0.956172i
$733$	−19.2003	−	13.0906i	−0.709180	−	0.483511i	0.154216	−	0.988037i	$-0.450715\pi$
$733$	−19.2003	−	13.0906i	−0.709180	−	0.483511i	−0.863396	+	0.504526i	$0.831667\pi$
$734$	16.9564	−	29.3694i	0.625873	−	1.08404i
$735$	−5.08403	+	22.2746i	−0.187527	+	0.821611i
$736$	−52.2748	+	7.87916i	−1.92687	+	0.290430i
$737$	−7.64595	−	3.68210i	−0.281642	−	0.135632i
$738$	−1.71566	+	2.97161i	−0.0631543	+	0.109386i
$739$	6.89955	+	17.5798i	0.253804	+	0.646682i	0.999815	−	0.0192520i	$-0.00612849\pi$
$739$	6.89955	+	17.5798i	0.253804	+	0.646682i	−0.746011	+	0.665934i	$0.768033\pi$
$740$	30.1209	+	52.1709i	1.10727	+	1.91784i
$741$	−6.28582	+	5.83238i	−0.230915	+	0.214258i
$742$	4.46297			0.163841
$743$	−16.8507			−0.618193			−0.309096	−	0.951031i	$-0.600027\pi$
$743$	−16.8507			−0.618193			−0.309096	+	0.951031i	$0.600027\pi$
$744$	−1.98724	+	1.84389i	−0.0728557	+	0.0676002i
$745$	27.5925	−	8.51115i	1.01091	−	0.311825i
$746$	−48.1700	+	23.1975i	−1.76363	+	0.849319i
$747$	−4.63826	−	1.43071i	−0.169705	−	0.0523471i
$748$	−0.479790	+	0.0723167i	−0.0175428	+	0.00264416i
$749$	0.549804	+	0.510144i	0.0200894	+	0.0186403i
$750$	30.4555	−	4.59042i	1.11208	−	0.167619i
$751$	−11.3322	+	28.8741i	−0.413519	+	1.05363i	0.560698	+	0.828020i	$0.310533\pi$
$751$	−11.3322	+	28.8741i	−0.413519	+	1.05363i	−0.974218	+	0.225610i	$0.927563\pi$
$752$	−13.6497	−	17.1162i	−0.497754	−	0.624164i
$753$	14.6374	+	2.20623i	0.533415	+	0.0803993i
$754$	15.5940	+	7.50967i	0.567899	+	0.273486i
$755$	−22.6683	−	21.0331i	−0.824985	−	0.765475i
$756$	−6.19406	−	5.74724i	−0.225276	−	0.209025i
$757$	10.5291	−	46.1312i	0.382688	−	1.67667i	−0.306332	−	0.951925i	$-0.599102\pi$
$757$	10.5291	−	46.1312i	0.382688	−	1.67667i	0.689020	−	0.724742i	$-0.258041\pi$
$758$	5.78076	+	25.3272i	0.209967	+	0.919925i
$759$	0.646459	−	8.62639i	0.0234650	−	0.313118i
$760$	1.85703	−	2.32864i	0.0673616	−	0.0844688i
$761$	−0.407421			−0.0147690			−0.00738449	−	0.999973i	$-0.502351\pi$
$761$	−0.407421			−0.0147690			−0.00738449	+	0.999973i	$0.502351\pi$
$762$	−28.4098	−	18.4425i	−1.02918	−	0.668103i
$763$	10.4456			0.378156
$764$	−6.32495	+	7.93123i	−0.228829	+	0.286942i
$765$	0.0369726	−	0.493365i	0.00133675	−	0.0178376i
$766$	−0.0451728	−	0.197915i	−0.00163216	−	0.00715096i
$767$	−5.86600	+	25.7006i	−0.211809	+	0.927995i
$768$	11.9822	+	11.1179i	0.432372	+	0.401183i
$769$	20.7910	+	19.2912i	0.749742	+	0.695659i	0.959379	−	0.282120i	$-0.0910377\pi$
$769$	20.7910	+	19.2912i	0.749742	+	0.695659i	−0.209637	+	0.977779i	$0.567228\pi$
$770$	−2.68699	−	1.29399i	−0.0968326	−	0.0466321i
$771$	−19.7975	−	2.98399i	−0.712989	−	0.107466i
$772$	8.63680	+	10.8302i	0.310845	+	0.389787i
$773$	14.2200	−	36.2319i	0.511457	−	1.30317i	−0.409075	−	0.912501i	$-0.634148\pi$
$773$	14.2200	−	36.2319i	0.511457	−	1.30317i	0.920531	−	0.390669i	$-0.127756\pi$
$774$	17.4313	−	2.62735i	0.626556	−	0.0944381i
$775$	−1.86052	−	1.72631i	−0.0668319	−	0.0620110i
$776$	6.76037	−	1.01896i	0.242683	−	0.0365786i
$777$	10.3417	+	3.19000i	0.371008	+	0.114441i
$778$	45.0706	−	21.7049i	1.61586	−	0.778157i
$779$	−4.33074	+	1.33586i	−0.155165	+	0.0478621i
$780$	14.1850	−	13.1617i	0.507903	−	0.471265i
$781$	−5.59097			−0.200061
$782$	3.17357			0.113487
$783$	−14.0953	+	13.0785i	−0.503724	+	0.467387i
$784$	−11.2475	−	19.4812i	−0.401695	−	0.695756i
$785$	14.3132	+	36.4695i	0.510861	+	1.30165i
$786$	17.0501	−	29.5317i	0.608158	−	1.05336i
$787$	−26.1036	−	12.5709i	−0.930494	−	0.448102i	−0.0936881	−	0.995602i	$-0.529866\pi$
$787$	−26.1036	−	12.5709i	−0.930494	−	0.448102i	−0.836806	+	0.547499i	$0.815580\pi$
$788$	−9.93944	+	1.49813i	−0.354078	+	0.0533687i
$789$	−10.3667	+	45.4193i	−0.369063	+	1.61697i
$790$	−7.50719	+	13.0028i	−0.267094	+	0.462620i
$791$	2.08583	+	1.42209i	0.0741635	+	0.0505638i
$792$	−0.344504	+	0.234879i	−0.0122414	+	0.00834607i
$793$	−32.9492	−	10.1635i	−1.17006	−	0.360915i
$794$	0.836726	−	3.66594i	0.0296943	−	0.130099i
$795$	−10.2301	−	4.92654i	−0.362823	−	0.174726i
$796$	−6.10453	+	15.5541i	−0.216369	+	0.551300i
$797$	−27.6292	+	18.8373i	−0.978676	+	0.667250i	−0.943236	−	0.332122i	$-0.892235\pi$
$797$	−27.6292	+	18.8373i	−0.978676	+	0.667250i	−0.0354394	+	0.999372i	$0.511283\pi$
$798$	−0.355833	−	4.74826i	−0.0125963	−	0.168086i
$799$	0.754148	+	1.30622i	0.0266798	+	0.0462108i
$800$	3.60589	−	4.52164i	0.127487	−	0.159864i
$801$	6.99494	−	6.49036i	0.247154	−	0.229325i
$802$	4.61191	−	5.78315i	0.162852	−	0.204210i
$803$	−4.69495	+	1.44820i	−0.165681	+	0.0511059i
$804$	2.28495	+	30.4906i	0.0805841	+	1.07532i
$805$	8.53819	+	5.82124i	0.300932	+	0.205172i
$806$	17.9106	+	2.69959i	0.630874	+	0.0950890i
$807$	6.26286	−	15.9575i	0.220463	−	0.561731i
$808$	3.55496	+	1.09656i	0.125063	+	0.0385768i
$809$	−5.58743	−	24.4801i	−0.196444	−	0.860675i	−0.973033	−	0.230668i	$-0.925909\pi$
$809$	−5.58743	−	24.4801i	−0.196444	−	0.860675i	0.776589	−	0.630007i	$-0.216948\pi$
$810$	10.0921	+	25.7142i	0.354600	+	0.903506i
$811$	−0.429024	−	5.72493i	−0.0150651	−	0.201029i	−0.999658	−	0.0261652i	$-0.991670\pi$
$811$	−0.429024	−	5.72493i	−0.0150651	−	0.201029i	0.984593	−	0.174864i	$-0.0559486\pi$
$812$	−4.58738	+	2.20917i	−0.160986	+	0.0775265i
$813$	−2.90131	−	12.7115i	−0.101753	−	0.445811i
$814$	10.5128	−	18.2088i	0.368475	−	0.638218i
$815$	19.7011	+	2.96946i	0.690099	+	0.104016i
$816$	−0.736283	−	0.923270i	−0.0257751	−	0.0323209i
$817$	19.2376	+	13.1160i	0.673040	+	0.458871i
$818$	−22.8234	−	58.1530i	−0.798001	−	2.03327i
$819$	−0.107161	+	1.42996i	−0.00374451	+	0.0499670i
$820$	9.77303	−	3.01458i	0.341289	−	0.105274i
$821$	24.2295	+	41.9667i	0.845615	+	1.46465i	0.885086	+	0.465427i	$0.154099\pi$
$821$	24.2295	+	41.9667i	0.845615	+	1.46465i	−0.0394712	+	0.999221i	$0.512567\pi$
$822$	−3.96073	+	52.8522i	−0.138146	+	1.84343i
$823$	48.6060	−	23.4074i	1.69430	−	0.815931i	0.699435	−	0.714696i	$-0.253435\pi$
$823$	48.6060	−	23.4074i	1.69430	−	0.815931i	0.994863	−	0.101235i	$-0.0322794\pi$
$824$	7.94831	−	5.41907i	0.276893	−	0.188782i
$825$	0.590048	+	0.739897i	0.0205428	+	0.0257599i
$826$	−9.12691	−	11.4448i	−0.317566	−	0.398215i
$827$	−23.3664	+	15.9309i	−0.812528	+	0.553973i	−0.896782	−	0.442472i	$-0.854102\pi$
$827$	−23.3664	+	15.9309i	−0.812528	+	0.553973i	0.0842540	+	0.996444i	$0.473149\pi$
$828$	11.5833	−	5.57821i	0.402546	−	0.193856i
$829$	−0.155503	+	2.07504i	−0.00540084	+	0.0720692i	−0.999253	−	0.0386467i	$-0.987695\pi$
$829$	−0.155503	+	2.07504i	−0.00540084	+	0.0720692i	0.993852	+	0.110716i	$0.0353144\pi$
$830$	13.6547	+	23.6506i	0.473961	+	0.820924i
$831$	−16.3838	+	5.05373i	−0.568347	+	0.175312i
$832$	−1.82061	+	24.2943i	−0.0631183	+	0.842255i
$833$	0.566207	+	1.44267i	0.0196179	+	0.0499856i
$834$	−5.82307	−	3.97010i	−0.201637	−	0.137473i
$835$	−1.40201	−	1.75806i	−0.0485184	−	0.0608401i
$836$	−4.84594	−	0.730407i	−0.167600	−	0.0252617i
$837$	−10.0612	+	17.4265i	−0.347766	+	0.602348i
$838$	−12.8882	−	56.4667i	−0.445214	−	1.95061i
$839$	18.1998	−	8.76455i	0.628326	−	0.302586i	−0.0924885	−	0.995714i	$-0.529482\pi$
$839$	18.1998	−	8.76455i	0.628326	−	0.302586i	0.720815	+	0.693128i	$0.243768\pi$
$840$	0.0902368	+	1.20413i	0.00311347	+	0.0415463i
$841$	−6.36186	−	16.2097i	−0.219374	−	0.558957i
$842$	−8.94199	−	39.1774i	−0.308161	−	1.35014i
$843$	26.7474	+	8.25047i	0.921228	+	0.284161i
$844$	10.7187	−	27.3109i	0.368954	−	0.940079i
$845$	16.3572	+	2.46546i	0.562706	+	0.0848143i
$846$	9.52974	+	6.49727i	0.327639	+	0.223381i
$847$	−0.504506	−	6.73217i	−0.0173350	−	0.231320i
$848$	10.6827	−	3.29517i	0.366845	−	0.113157i
$849$	29.3801	−	36.8414i	1.00832	−	1.26440i
$850$	−0.254504	+	0.236146i	−0.00872943	+	0.00809973i
$851$	−45.4238	+	56.9596i	−1.55711	+	1.95255i
$852$	10.0720	+	17.4453i	0.345062	+	0.597666i
$853$	3.22660	+	43.0560i	0.110477	+	1.47421i	0.726873	+	0.686772i	$0.240973\pi$
$853$	3.22660	+	43.0560i	0.110477	+	1.47421i	−0.616396	+	0.787436i	$0.711408\pi$
$854$	15.8201	−	10.7860i	0.541353	−	0.369088i
$855$	1.82561	−	4.65159i	0.0624347	−	0.159081i
$856$	−0.531539	−	0.255976i	−0.0181676	−	0.00874908i
$857$	−10.0382	+	43.9803i	−0.342899	+	1.50234i	0.450024	+	0.893017i	$0.351416\pi$
$857$	−10.0382	+	43.9803i	−0.342899	+	1.50234i	−0.792923	+	0.609322i	$0.791442\pi$
$858$	−6.45372	−	1.99071i	−0.220326	−	0.0679617i
$859$	28.8770	−	19.6880i	0.985269	−	0.671745i	0.0403968	−	0.999184i	$-0.487138\pi$
$859$	28.8770	−	19.6880i	0.985269	−	0.671745i	0.944873	+	0.327438i	$0.106185\pi$
$860$	−43.4129	−	29.5984i	−1.48037	−	1.00930i
$861$	0.918686	−	1.59121i	0.0313087	−	0.0542283i
$862$	−10.9200	+	47.8435i	−0.371935	+	1.62955i
$863$	28.3799	−	4.27758i	0.966062	−	0.145610i	0.352981	−	0.935630i	$-0.385168\pi$
$863$	28.3799	−	4.27758i	0.966062	−	0.145610i	0.613081	+	0.790020i	$0.289930\pi$
$864$	−41.3117	−	19.8946i	−1.40545	−	0.676829i
$865$	17.6399	−	30.5531i	0.599773	−	1.03884i
$866$	−9.28465	−	23.6569i	−0.315505	−	0.803894i
$867$	−12.3469	−	21.3855i	−0.419323	−	0.726288i
$868$	−3.90599	+	3.62423i	−0.132578	+	0.123014i
$869$	2.77616			0.0941747
$870$	24.4520			0.829002
$871$	16.8291	−	15.6151i	0.570232	−	0.529098i
$872$	−7.85145	+	2.42185i	−0.265884	+	0.0820142i
$873$	10.3343	−	4.97671i	0.349762	−	0.168436i
$874$	30.6294	+	9.44791i	1.03605	+	0.319580i
$875$	6.72694	−	1.01392i	0.227412	−	0.0342768i
$876$	12.9766	+	12.0406i	0.438440	+	0.406813i
$877$	35.8327	−	5.40092i	1.20999	−	0.182376i	0.487102	−	0.873345i	$-0.338054\pi$
$877$	35.8327	−	5.40092i	1.20999	−	0.182376i	0.722884	+	0.690969i	$0.242816\pi$
$878$	−8.19207	+	20.8730i	−0.276469	+	0.704431i
$879$	−18.7783	−	23.5472i	−0.633376	−	0.794228i
$880$	−7.38705	−	1.11342i	−0.249017	−	0.0375333i
$881$	−6.15177	−	2.96254i	−0.207259	−	0.0998105i	0.327375	−	0.944895i	$-0.393836\pi$
$881$	−6.15177	−	2.96254i	−0.207259	−	0.0998105i	−0.534633	+	0.845084i	$0.679550\pi$
$882$	8.68761	+	8.06093i	0.292527	+	0.271426i
$883$	−16.6798	−	15.4766i	−0.561319	−	0.520828i	0.347687	−	0.937611i	$-0.386967\pi$
$883$	−16.6798	−	15.4766i	−0.561319	−	0.520828i	−0.909006	+	0.416782i	$0.863158\pi$
$884$	0.292082	−	1.27969i	0.00982377	−	0.0430407i
$885$	8.28724	+	36.3088i	0.278572	+	1.22051i
$886$	−4.56089	+	60.8609i	−0.153226	+	2.04466i
$887$	−7.55825	+	9.47774i	−0.253781	+	0.318232i	−0.892359	−	0.451325i	$-0.850951\pi$
$887$	−7.55825	+	9.47774i	−0.253781	+	0.318232i	0.638578	+	0.769557i	$0.279523\pi$
$888$	−8.51298			−0.285677
$889$	−6.27509	−	4.07355i	−0.210460	−	0.136622i
$890$	−53.6870			−1.79959
$891$	3.18456	−	3.99331i	0.106687	−	0.133781i
$892$	−1.33038	+	17.7526i	−0.0445443	+	0.594403i
$893$	3.38988	+	14.8520i	0.113438	+	0.497004i
$894$	−8.07999	+	35.4007i	−0.270235	+	1.18398i
$895$	−27.3440	−	25.3715i	−0.914009	−	0.848077i
$896$	−2.01668	−	1.87121i	−0.0673727	−	0.0625127i
$897$	21.0843	+	10.1537i	0.703985	+	0.339021i
$898$	−56.6595	−	8.54005i	−1.89075	−	0.284985i
$899$	7.56003	+	9.47998i	0.252141	+	0.316175i
$900$	−0.513845	+	1.30926i	−0.0171282	+	0.0436419i
$901$	−0.761606	+	0.114794i	−0.0253728	+	0.00382433i
$902$	−2.61669	−	2.42794i	−0.0871264	−	0.0808415i
$903$	−9.33398	+	1.40687i	−0.310615	+	0.0468177i
$904$	−1.89753	−	0.585311i	−0.0631110	−	0.0194672i
$905$	−22.1573	+	10.6704i	−0.736535	+	0.354696i
$906$	37.1588	−	11.4620i	1.23452	−	0.380798i
$907$	5.37697	−	4.98910i	0.178539	−	0.165660i	−0.585841	−	0.810426i	$-0.699236\pi$
$907$	5.37697	−	4.98910i	0.178539	−	0.165660i	0.764380	+	0.644766i	$0.223045\pi$
$908$	−52.6541			−1.74739
$909$	6.24154			0.207019
$910$	5.91420	−	5.48758i	0.196054	−	0.181911i
$911$	5.35065	+	9.26761i	0.177275	+	0.307049i	0.940946	−	0.338556i	$-0.109938\pi$
$911$	5.35065	+	9.26761i	0.177275	+	0.307049i	−0.763671	+	0.645605i	$0.776605\pi$
$912$	−4.35753	−	11.1028i	−0.144292	−	0.367651i
$913$	2.52475	−	4.37299i	0.0835570	−	0.144725i
$914$	52.2211	+	25.1483i	1.72732	+	0.831833i
$915$	−48.1693	+	7.26036i	−1.59243	+	0.240020i
$916$	13.5870	−	59.5284i	0.448926	−	1.96687i
$917$	3.76599	−	6.52289i	0.124364	−	0.215405i
$918$	2.27429	+	1.55058i	0.0750627	+	0.0511769i
$919$	−36.7651	+	25.0660i	−1.21277	+	0.826852i	−0.989018	−	0.147794i	$-0.952783\pi$
$919$	−36.7651	+	25.0660i	−1.21277	+	0.826852i	−0.223751	+	0.974646i	$0.571830\pi$
$920$	−7.76741	−	2.39593i	−0.256084	−	0.0789914i
$921$	−5.70239	+	24.9838i	−0.187900	+	0.823244i
$922$	20.3768	+	9.81294i	0.671074	+	0.323172i
$923$	5.52574	−	14.0793i	0.181882	−	0.463427i
$924$	1.64157	−	1.11920i	0.0540037	−	0.0368191i
$925$	−0.595610	−	7.94786i	−0.0195835	−	0.261324i
$926$	−19.1179	−	33.1131i	−0.628252	−	1.08816i
$927$	10.0628	−	12.6184i	0.330506	−	0.414442i
$928$	−20.2541	+	18.7930i	−0.664872	+	0.616911i
$929$	10.2694	−	12.8775i	0.336929	−	0.422496i	−0.584287	−	0.811547i	$-0.698626\pi$
$929$	10.2694	−	12.8775i	0.336929	−	0.422496i	0.921216	+	0.389051i	$0.127197\pi$
$930$	24.4523	−	7.54255i	0.801824	−	0.247330i
$931$	1.16977	+	15.6094i	0.0383375	+	0.511579i
$932$	−12.9007	−	8.79556i	−0.422577	−	0.288108i
$933$	8.33004	+	1.25555i	0.272713	+	0.0411049i
$934$	−19.8447	+	50.5634i	−0.649338	+	1.65449i
$935$	0.491819	+	0.151706i	0.0160842	+	0.00496132i
$936$	−0.250995	−	1.09968i	−0.00820401	−	0.0359441i
$937$	−2.71730	−	6.92356i	−0.0887703	−	0.226183i	0.879593	−	0.475726i	$-0.157815\pi$
$937$	−2.71730	−	6.92356i	−0.0887703	−	0.226183i	−0.968364	+	0.249543i	$0.919719\pi$
$938$	0.952676	+	12.7126i	0.0311060	+	0.415080i
$939$	26.0784	−	12.5587i	0.851037	−	0.409838i
$940$	−7.64982	−	33.5160i	−0.249509	−	1.09317i
$941$	−8.77570	+	15.2000i	−0.286080	+	0.495504i	−0.972870	−	0.231351i	$-0.925686\pi$
$941$	−8.77570	+	15.2000i	−0.286080	+	0.495504i	0.686791	+	0.726855i	$0.259019\pi$
$942$	−48.7163	−	7.34279i	−1.58726	−	0.239241i
$943$	7.71171	+	9.67018i	0.251128	+	0.314904i
$944$	−30.2965	−	20.6558i	−0.986066	−	0.672288i
$945$	3.27455	+	8.34341i	0.106521	+	0.271411i
$946$	−1.37044	+	18.2873i	−0.0445570	+	0.594571i
$947$	−30.3012	+	9.34669i	−0.984657	+	0.303727i	−0.744951	−	0.667119i	$-0.767527\pi$
$947$	−30.3012	+	9.34669i	−0.984657	+	0.303727i	−0.239706	+	0.970846i	$0.577051\pi$
$948$	−5.00120	−	8.66234i	−0.162432	−	0.281340i
$949$	0.993269	−	13.2543i	0.0322429	−	0.430251i
$950$	−3.15934	+	1.52146i	−0.102503	+	0.0493627i
$951$	−6.27559	+	4.27862i	−0.203500	+	0.138744i
$952$	0.0510690	+	0.0640385i	0.00165516	+	0.00207550i
$953$	27.4476	+	34.4182i	0.889115	+	1.11492i	0.992738	+	0.120299i	$0.0383853\pi$
$953$	27.4476	+	34.4182i	0.889115	+	1.11492i	−0.103622	+	0.994617i	$0.533043\pi$
$954$	−4.86635	+	3.31782i	−0.157554	+	0.107418i
$955$	9.69504	−	4.66889i	0.313724	−	0.151082i
$956$	−1.33989	+	17.8796i	−0.0433351	+	0.578267i
$957$	−2.26059	−	3.91546i	−0.0730746	−	0.126569i
$958$	41.6180	−	12.8374i	1.34462	−	0.414759i
$959$	−0.874837	+	11.6739i	−0.0282500	+	0.376969i
$960$	12.5744	+	32.0391i	0.405837	+	1.03406i
$961$	−15.1291	−	10.3148i	−0.488034	−	0.332736i
$962$	35.4637	+	44.4701i	1.14340	+	1.43377i
$963$	−0.978743	−	0.147522i	−0.0315396	−	0.00475382i
$964$	−5.11505	+	8.85953i	−0.164745	+	0.285346i
$965$	−3.26969	−	14.3254i	−0.105255	−	0.461152i
$966$	−11.7080	+	5.63828i	−0.376699	+	0.181409i
$967$	−3.22442	−	43.0269i	−0.103690	−	1.38365i	−0.770032	−	0.638005i	$-0.779760\pi$
$967$	−3.22442	−	43.0269i	−0.103690	−	1.38365i	0.666342	−	0.745647i	$-0.267859\pi$
$968$	1.94009	+	4.94327i	0.0623568	+	0.158883i
$969$	0.182854	+	0.801137i	0.00587413	+	0.0257362i
$970$	−61.6671	−	19.0218i	−1.98001	−	0.610752i
$971$	1.79188	−	4.56562i	0.0575040	−	0.146518i	−0.899235	−	0.437467i	$-0.855876\pi$
$971$	1.79188	−	4.56562i	0.0575040	−	0.146518i	0.956739	+	0.290949i	$0.0939710\pi$
$972$	19.5606	+	2.94829i	0.627408	+	0.0945665i
$973$	−1.28619	−	0.876908i	−0.0412333	−	0.0281124i
$974$	−0.339551	−	4.53100i	−0.0108799	−	0.145183i
$975$	−2.44639	+	0.754612i	−0.0783473	+	0.0241669i
$976$	29.9037	−	37.4981i	0.957195	−	1.20028i
$977$	18.2666	−	16.9489i	0.584400	−	0.542244i	−0.331601	−	0.943420i	$-0.607589\pi$
$977$	18.2666	−	16.9489i	0.584400	−	0.542244i	0.916001	+	0.401176i	$0.131398\pi$
$978$	−15.6211	+	19.5882i	−0.499506	+	0.626361i
$979$	4.96337	+	8.59681i	0.158630	+	0.274755i
$980$	−2.63977	−	35.2253i	−0.0843243	−	1.12523i
$981$	−11.3897	+	7.76537i	−0.363645	+	0.247929i
$982$	−30.7938	+	78.4613i	−0.982669	+	2.50380i
$983$	−28.8623	−	13.8993i	−0.920564	−	0.443320i	−0.0872917	−	0.996183i	$-0.527821\pi$
$983$	−28.8623	−	13.8993i	−0.920564	−	0.443320i	−0.833273	+	0.552862i	$0.813536\pi$
$984$	−0.321603	+	1.40904i	−0.0102523	+	0.0449184i
$985$	10.1886	+	3.14278i	0.324637	+	0.100137i
$986$	1.37044	−	0.934351i	0.0436437	−	0.0297558i
$987$	−5.10290	−	3.47910i	−0.162427	−	0.110741i
$988$	6.62872	−	11.4813i	0.210888	−	0.365268i
$989$	14.1397	−	61.9500i	0.449616	−	1.96990i
$990$	3.89182	−	0.586597i	0.123690	−	0.0186433i
$991$	10.5654	+	5.08803i	0.335621	+	0.161627i	0.594102	−	0.804390i	$-0.297508\pi$
$991$	10.5654	+	5.08803i	0.335621	+	0.161627i	−0.258481	+	0.966016i	$0.583222\pi$
$992$	−14.4573	+	25.0409i	−0.459021	+	0.795048i
$993$	−14.3183	−	36.4824i	−0.454377	−	1.15773i
$994$	4.19938	+	7.27354i	0.133196	+	0.230703i
$995$	12.9927	−	12.0555i	0.411897	−	0.382185i
$996$	−18.1932			−0.576473
$997$	1.36784			0.0433199			0.0216599	−	0.999765i	$-0.493105\pi$
$997$	1.36784			0.0433199			0.0216599	+	0.999765i	$0.493105\pi$
$998$	25.7466	−	23.8893i	0.814994	−	0.756204i
$999$	−60.3823	+	18.6255i	−1.91041	+	0.589284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	127.2.i.a.100.1	yes	108
127.47	even	21	inner	127.2.i.a.47.1	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.2.i.a.47.1	✓	108	127.47	even	21	inner
127.2.i.a.100.1	yes	108	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	127.i (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28584 + 1.61239i) q^{2} +(-0.108909 + 1.45329i) q^{3} +(-0.501385 - 2.19671i) q^{4} +(-0.531843 + 2.33016i) q^{5} +(-2.20323 - 2.04430i) q^{6} +(-0.486645 - 0.451541i) q^{7} +(0.470479 + 0.226571i) q^{8} +(0.866309 + 0.130575i) q^{9} +(-3.07327 - 3.85376i) q^{10} +(-0.332971 + 0.848397i) q^{11} +(3.24706 - 0.489415i) q^{12} +(-1.80737 - 1.67699i) q^{13} +(1.35381 - 0.204054i) q^{14} +(-3.32847 - 1.02670i) q^{15} +(3.08985 - 1.48799i) q^{16} +(-0.225779 + 0.0696437i) q^{17} +(-1.32448 + 1.22893i) q^{18} -2.38642 q^{19} +5.38535 q^{20} +(0.709219 - 0.658059i) q^{21} +(-0.939802 - 1.62778i) q^{22} +(2.37940 + 6.06262i) q^{23} +(-0.380511 + 0.659065i) q^{24} +(-0.641937 - 0.309140i) q^{25} +(5.02797 - 0.757844i) q^{26} +(-1.25699 + 5.50725i) q^{27} +(-0.747908 + 1.29542i) q^{28} +(2.81243 + 1.91748i) q^{29} +(5.93532 - 4.04663i) q^{30} +(3.40394 + 1.04998i) q^{31} +(-1.80622 + 7.91359i) q^{32} +(-1.19670 - 0.576301i) q^{33} +(0.178023 - 0.453596i) q^{34} +(1.31098 - 0.893812i) q^{35} +(-0.147519 - 1.96850i) q^{36} +(5.59312 + 9.68757i) q^{37} +(3.06856 - 3.84785i) q^{38} +(2.63399 - 2.44399i) q^{39} +(-0.778166 + 0.975789i) q^{40} +(1.81475 - 0.559775i) q^{41} +(0.149107 + 1.98970i) q^{42} +(-8.06130 - 5.49610i) q^{43} +(2.03063 + 0.306068i) q^{44} +(-0.765002 + 1.94919i) q^{45} +(-12.8349 - 3.95903i) q^{46} +(-1.42049 - 6.22356i) q^{47} +(1.82597 + 4.65250i) q^{48} +(-0.490176 - 6.54095i) q^{49} +(1.32388 - 0.637549i) q^{50} +(-0.0766229 - 0.335707i) q^{51} +(-2.77769 + 4.81109i) q^{52} +(3.22337 + 0.485845i) q^{53} +(-7.26356 - 9.10821i) q^{54} +(-1.79981 - 1.22709i) q^{55} +(-0.126650 - 0.322700i) q^{56} +(0.259902 - 3.46815i) q^{57} +(-6.70808 + 2.06917i) q^{58} +(-5.34599 - 9.25953i) q^{59} +(-0.586512 + 7.82646i) q^{60} +(12.6002 - 6.06794i) q^{61} +(-6.06990 + 4.13839i) q^{62} +(-0.362625 - 0.454718i) q^{63} +(-6.16081 - 7.72542i) q^{64} +(4.86890 - 3.31956i) q^{65} +(2.46799 - 1.18852i) q^{66} +(-0.695840 + 9.28533i) q^{67} +(0.266189 + 0.461054i) q^{68} +(-9.06987 + 2.79768i) q^{69} +(-0.244537 + 3.26312i) q^{70} +(2.24118 + 5.71045i) q^{71} +(0.377995 + 0.257713i) q^{72} +(3.36115 + 4.21475i) q^{73} +(-22.8120 - 3.43836i) q^{74} +(0.519182 - 0.899250i) q^{75} +(1.19652 + 5.24228i) q^{76} +(0.545125 - 0.262518i) q^{77} +(0.553776 + 7.38962i) q^{78} +(-1.11284 - 2.83548i) q^{79} +(1.82395 + 7.99123i) q^{80} +(-5.35520 - 1.65186i) q^{81} +(-1.43090 + 3.64587i) q^{82} +(-5.47851 - 0.825752i) q^{83} +(-1.80116 - 1.22801i) q^{84} +(-0.0422016 - 0.563141i) q^{85} +(19.2274 - 5.93088i) q^{86} +(-3.09295 + 3.87844i) q^{87} +(-0.348877 + 0.323711i) q^{88} +(6.79091 - 8.51553i) q^{89} +(-2.15920 - 3.73984i) q^{90} +(0.122317 + 1.63220i) q^{91} +(12.1248 - 8.26657i) q^{92} +(-1.89664 + 4.83255i) q^{93} +(11.8614 + 5.71213i) q^{94} +(1.26920 - 5.56074i) q^{95} +(-11.3040 - 3.48682i) q^{96} +(10.8174 - 7.37520i) q^{97} +(11.1769 + 7.62026i) q^{98} +(-0.399235 + 0.691496i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 5 q^{2} - 15 q^{3} - 17 q^{4} - 6 q^{5} + 7 q^{6} + 2 q^{7} - 22 q^{8} + 2 q^{9} - 10 q^{10} + 9 q^{12} - 14 q^{13} - 20 q^{14} + 4 q^{15} + 27 q^{16} - 8 q^{17} + 7 q^{18} - 16 q^{19} - 80 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 108 * q - 5 * q^2 - 15 * q^3 - 17 * q^4 - 6 * q^5 + 7 * q^6 + 2 * q^7 - 22 * q^8 + 2 * q^9 - 10 * q^10 + 9 * q^12 - 14 * q^13 - 20 * q^14 + 4 * q^15 + 27 * q^16 - 8 * q^17 + 7 * q^18 - 16 * q^19 - 80 * q^20 - 59 * q^21 - 13 * q^22 - 20 * q^23 + 41 * q^24 - 6 * q^25 - 56 * q^26 - 24 * q^27 - 19 * q^28 + 33 * q^29 + 23 * q^30 - 3 * q^31 + 39 * q^32 - 61 * q^33 + 16 * q^34 - 5 * q^35 + 48 * q^36 - 3 * q^37 + 3 * q^38 + 7 * q^39 - 6 * q^40 - 38 * q^41 + 14 * q^42 - 9 * q^43 + 134 * q^44 - 70 * q^45 - q^46 + 17 * q^47 - 76 * q^48 + 93 * q^49 + 24 * q^50 + 31 * q^51 - 54 * q^52 - 12 * q^53 - 44 * q^54 + 15 * q^55 + 30 * q^56 - 42 * q^57 - 52 * q^58 + 77 * q^59 + 36 * q^60 - 70 * q^61 + 41 * q^62 + 82 * q^63 - 6 * q^64 - 43 * q^65 + 160 * q^66 + 54 * q^67 + 6 * q^68 - 19 * q^69 + 49 * q^70 - 31 * q^71 + 11 * q^72 + 46 * q^73 - 111 * q^74 + 18 * q^75 - 19 * q^76 - 65 * q^77 + 27 * q^78 + 119 * q^79 + 114 * q^80 - 55 * q^81 - 44 * q^82 - 34 * q^83 + 34 * q^84 + 6 * q^85 + 89 * q^86 + 22 * q^87 - 118 * q^88 - 22 * q^89 + 121 * q^90 + 58 * q^91 + 115 * q^92 + 104 * q^93 + 62 * q^94 - 18 * q^95 + 31 * q^96 + 14 * q^97 + 87 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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