LMFDB - Embedded newform 245.2.x.a.103.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(3,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([63, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.x (of order $84$, degree $24$, 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:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$624$
Relative dimension:	$26$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			103.7
Character	$\chi$	$=$	245.103
Dual form			245.2.x.a.157.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16101 + 1.57311i) q^{2} +(-0.170810 + 0.0323191i) q^{3} +(-0.537222 - 1.74163i) q^{4} +(0.333429 + 2.21107i) q^{5} +(0.147471 - 0.306226i) q^{6} +(-0.899782 - 2.48805i) q^{7} +(-0.327375 - 0.114553i) q^{8} +(-2.76449 + 1.08498i) q^{9} +(-3.86536 - 2.04254i) q^{10} +(-1.91028 + 4.86731i) q^{11} +(0.148051 + 0.280126i) q^{12} +(2.70690 + 0.304995i) q^{13} +(4.95862 + 1.47319i) q^{14} +(-0.128413 - 0.366898i) q^{15} +(3.57210 - 2.43542i) q^{16} +(-7.61120 - 0.284791i) q^{17} +(1.50280 - 5.60851i) q^{18} +(-0.370025 + 0.640901i) q^{19} +(3.67174 - 1.76854i) q^{20} +(0.234104 + 0.395905i) q^{21} +(-5.43896 - 8.65605i) q^{22} +(-0.164714 - 4.40206i) q^{23} +(0.0596213 + 0.00898646i) q^{24} +(-4.77765 + 1.47447i) q^{25} +(-3.62252 + 3.90415i) q^{26} +(0.878725 - 0.552139i) q^{27} +(-3.84988 + 2.90372i) q^{28} +(1.76959 - 0.403898i) q^{29} +(0.726257 + 0.223963i) q^{30} +(1.23878 - 0.715207i) q^{31} +(-0.290121 + 7.75364i) q^{32} +(0.168988 - 0.893126i) q^{33} +(9.28465 - 11.6426i) q^{34} +(5.20124 - 2.81907i) q^{35} +(3.37478 + 4.23184i) q^{36} +(-2.12687 + 1.12408i) q^{37} +(-0.578606 - 1.32618i) q^{38} +(-0.472225 + 0.0353883i) q^{39} +(0.144129 - 0.762044i) q^{40} +(4.49252 + 9.32882i) q^{41} +(-0.894597 - 0.0913777i) q^{42} +(2.16091 + 6.17553i) q^{43} +(9.50329 + 0.712173i) q^{44} +(-3.32073 - 5.75071i) q^{45} +(7.11615 + 4.85171i) q^{46} +(1.57187 + 1.16009i) q^{47} +(-0.531441 + 0.531441i) q^{48} +(-5.38078 + 4.47741i) q^{49} +(3.22738 - 9.22763i) q^{50} +(1.30928 - 0.197342i) q^{51} +(-0.923019 - 4.87827i) q^{52} +(0.0704225 + 0.0372194i) q^{53} +(-0.151630 + 2.02337i) q^{54} +(-11.3989 - 2.60085i) q^{55} +(0.00955142 + 0.917598i) q^{56} +(0.0424907 - 0.121431i) q^{57} +(-1.41913 + 3.25269i) q^{58} +(0.259332 + 3.46055i) q^{59} +(-0.570013 + 0.420753i) q^{60} +(-3.48636 + 11.3025i) q^{61} +(-0.313128 + 2.77909i) q^{62} +(5.18693 + 5.90194i) q^{63} +(-5.10025 - 4.06731i) q^{64} +(0.228197 + 6.08685i) q^{65} +(1.20879 + 1.30276i) q^{66} +(13.1907 + 3.53444i) q^{67} +(3.59290 + 13.4089i) q^{68} +(0.170405 + 0.746595i) q^{69} +(-1.60397 + 11.4551i) q^{70} +(2.59551 - 11.3717i) q^{71} +(1.02931 - 0.0385142i) q^{72} +(-10.9771 + 8.10149i) q^{73} +(0.701004 - 4.65086i) q^{74} +(0.768419 - 0.406264i) q^{75} +(1.31500 + 0.300140i) q^{76} +(13.8289 + 0.373349i) q^{77} +(0.492586 - 0.783946i) q^{78} +(-2.66312 - 1.53756i) q^{79} +(6.57591 + 7.08612i) q^{80} +(6.39876 - 5.93718i) q^{81} +(-19.8911 - 3.76360i) q^{82} +(1.09712 + 9.73722i) q^{83} +(0.563754 - 0.620410i) q^{84} +(-1.90810 - 16.9238i) q^{85} +(-12.2236 - 3.77048i) q^{86} +(-0.289211 + 0.126182i) q^{87} +(1.18294 - 1.37461i) q^{88} +(-0.853906 - 2.17572i) q^{89} +(12.9019 + 1.45274i) q^{90} +(-1.67678 - 7.00934i) q^{91} +(-7.57827 + 2.65175i) q^{92} +(-0.188481 + 0.162201i) q^{93} +(-3.64989 + 1.12584i) q^{94} +(-1.54045 - 0.604454i) q^{95} +(-0.201035 - 1.33378i) q^{96} +(-4.67598 - 4.67598i) q^{97} +(-0.796316 - 13.6628i) q^{98} -15.5282i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) $ 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.16101	+	1.57311i	−0.820955	+	1.11235i	0.170938	+	0.985282i	$0.445320\pi$
$2$	−1.16101	+	1.57311i	−0.820955	+	1.11235i	−0.991893	+	0.127073i	$0.959442\pi$
$3$	−0.170810	+	0.0323191i	−0.0986175	+	0.0186594i	−0.234986	−	0.971999i	$-0.575504\pi$
$3$	−0.170810	+	0.0323191i	−0.0986175	+	0.0186594i	0.136369	+	0.990658i	$0.456457\pi$
$4$	−0.537222	−	1.74163i	−0.268611	−	0.870815i
$5$	0.333429	+	2.21107i	0.149114	+	0.988820i
$5$	0.333429	+	2.21107i	0.149114	+	0.988820i
$6$	0.147471	−	0.306226i	0.0602046	−	0.125016i
$7$	−0.899782	−	2.48805i	−0.340086	−	0.940394i
$7$	−0.899782	−	2.48805i	−0.340086	−	0.940394i
$8$	−0.327375	−	0.114553i	−0.115744	−	0.0405007i
$9$	−2.76449	+	1.08498i	−0.921497	+	0.361661i
$10$	−3.86536	−	2.04254i	−1.22233	−	0.645909i
$11$	−1.91028	+	4.86731i	−0.575970	+	1.46755i	0.284816	+	0.958582i	$0.408068\pi$
$11$	−1.91028	+	4.86731i	−0.575970	+	1.46755i	−0.860786	+	0.508967i	$0.830028\pi$
$12$	0.148051	+	0.280126i	0.0427386	+	0.0808654i
$13$	2.70690	+	0.304995i	0.750760	+	0.0845903i	0.479049	−	0.877788i	$-0.340982\pi$
$13$	2.70690	+	0.304995i	0.750760	+	0.0845903i	0.271712	+	0.962379i	$0.412410\pi$
$14$	4.95862	+	1.47319i	1.32525	+	0.393726i
$15$	−0.128413	−	0.366898i	−0.0331561	−	0.0947325i
$16$	3.57210	−	2.43542i	0.893025	−	0.608854i
$17$	−7.61120	−	0.284791i	−1.84599	−	0.0690719i	−0.908662	−	0.417532i	$-0.862895\pi$
$17$	−7.61120	−	0.284791i	−1.84599	−	0.0690719i	−0.937324	+	0.348460i	$0.886705\pi$
$18$	1.50280	−	5.60851i	0.354212	−	1.32194i
$19$	−0.370025	+	0.640901i	−0.0848895	+	0.147033i	−0.905344	−	0.424679i	$-0.860387\pi$
$19$	−0.370025	+	0.640901i	−0.0848895	+	0.147033i	0.820455	+	0.571712i	$0.193720\pi$
$20$	3.67174	−	1.76854i	0.821025	−	0.395459i
$21$	0.234104	+	0.395905i	0.0510856	+	0.0863935i
$22$	−5.43896	−	8.65605i	−1.15959	−	1.84548i
$23$	−0.164714	−	4.40206i	−0.0343451	−	0.917893i	−0.904849	−	0.425732i	$-0.860017\pi$
$23$	−0.164714	−	4.40206i	−0.0343451	−	0.917893i	0.870504	−	0.492161i	$-0.163793\pi$
$24$	0.0596213	+	0.00898646i	0.0121701	+	0.00183435i
$25$	−4.77765	+	1.47447i	−0.955530	+	0.294894i
$26$	−3.62252	+	3.90415i	−0.710435	+	0.765667i
$27$	0.878725	−	0.552139i	0.169111	−	0.106259i
$28$	−3.84988	+	2.90372i	−0.727559	+	0.548752i
$29$	1.76959	−	0.403898i	0.328605	−	0.0750020i	−0.0550357	−	0.998484i	$-0.517527\pi$
$29$	1.76959	−	0.403898i	0.328605	−	0.0750020i	0.383641	+	0.923482i	$0.374670\pi$
$30$	0.726257	+	0.223963i	0.132596	+	0.0408898i
$31$	1.23878	−	0.715207i	0.222491	−	0.128455i	−0.384612	−	0.923078i	$-0.625665\pi$
$31$	1.23878	−	0.715207i	0.222491	−	0.128455i	0.607103	+	0.794623i	$0.292332\pi$
$32$	−0.290121	+	7.75364i	−0.0512866	+	1.37066i
$33$	0.168988	−	0.893126i	0.0294171	−	0.155473i
$34$	9.28465	−	11.6426i	1.59230	−	1.99669i
$35$	5.20124	−	2.81907i	0.879169	−	0.476510i
$36$	3.37478	+	4.23184i	0.562463	+	0.705307i
$37$	−2.12687	+	1.12408i	−0.349655	+	0.184798i	−0.632869	−	0.774259i	$-0.718123\pi$
$37$	−2.12687	+	1.12408i	−0.349655	+	0.184798i	0.283215	+	0.959057i	$0.408599\pi$
$38$	−0.578606	−	1.32618i	−0.0938623	−	0.215135i
$39$	−0.472225	+	0.0353883i	−0.0756165	+	0.00566667i
$40$	0.144129	−	0.762044i	0.0227888	−	0.120490i
$41$	4.49252	+	9.32882i	0.701614	+	1.45692i	0.880989	+	0.473136i	$0.156878\pi$
$41$	4.49252	+	9.32882i	0.701614	+	1.45692i	−0.179375	+	0.983781i	$0.557408\pi$
$42$	−0.894597	−	0.0913777i	−0.138039	−	0.0140999i
$43$	2.16091	+	6.17553i	0.329536	+	0.941760i	0.982807	+	0.184636i	$0.0591106\pi$
$43$	2.16091	+	6.17553i	0.329536	+	0.941760i	−0.653271	+	0.757124i	$0.726604\pi$
$44$	9.50329	+	0.712173i	1.43267	+	0.107364i
$45$	−3.32073	−	5.75071i	−0.495026	−	0.857265i
$46$	7.11615	+	4.85171i	1.04922	+	0.715345i
$47$	1.57187	+	1.16009i	0.229280	+	0.169217i	0.702402	−	0.711781i	$-0.252111\pi$
$47$	1.57187	+	1.16009i	0.229280	+	0.169217i	−0.473122	+	0.880997i	$0.656873\pi$
$48$	−0.531441	+	0.531441i	−0.0767070	+	0.0767070i
$49$	−5.38078	+	4.47741i	−0.768683	+	0.639629i
$50$	3.22738	−	9.22763i	0.456420	−	1.30498i
$51$	1.30928	−	0.197342i	0.183335	−	0.0276334i
$52$	−0.923019	−	4.87827i	−0.128000	−	0.676495i
$53$	0.0704225	+	0.0372194i	0.00967327	+	0.00511247i	0.472098	−	0.881546i	$-0.343497\pi$
$53$	0.0704225	+	0.0372194i	0.00967327	+	0.00511247i	−0.462425	+	0.886658i	$0.653021\pi$
$54$	−0.151630	+	2.02337i	−0.0206343	+	0.275345i
$55$	−11.3989	−	2.60085i	−1.53703	−	0.350699i
$56$	0.00955142	+	0.917598i	0.00127636	+	0.122619i
$57$	0.0424907	−	0.121431i	0.00562803	−	0.0160840i
$58$	−1.41913	+	3.25269i	−0.186341	+	0.427099i
$59$	0.259332	+	3.46055i	0.0337622	+	0.450525i	0.988309	+	0.152464i	$0.0487208\pi$
$59$	0.259332	+	3.46055i	0.0337622	+	0.450525i	−0.954547	+	0.298061i	$0.903660\pi$
$60$	−0.570013	+	0.420753i	−0.0735884	+	0.0543190i
$61$	−3.48636	+	11.3025i	−0.446383	+	1.44714i	0.400961	+	0.916095i	$0.368676\pi$
$61$	−3.48636	+	11.3025i	−0.446383	+	1.44714i	−0.847344	+	0.531044i	$0.821800\pi$
$62$	−0.313128	+	2.77909i	−0.0397673	+	0.352944i
$63$	5.18693	+	5.90194i	0.653492	+	0.743575i
$64$	−5.10025	−	4.06731i	−0.637531	−	0.508414i
$65$	0.228197	+	6.08685i	0.0283044	+	0.754980i
$66$	1.20879	+	1.30276i	0.148791	+	0.160359i
$67$	13.1907	+	3.53444i	1.61150	+	0.431801i	0.948490	−	0.316808i	$-0.102611\pi$
$67$	13.1907	+	3.53444i	1.61150	+	0.431801i	0.663012	+	0.748609i	$0.269278\pi$
$68$	3.59290	+	13.4089i	0.435703	+	1.62607i
$69$	0.170405	+	0.746595i	0.0205144	+	0.0898794i
$70$	−1.60397	+	11.4551i	−0.191711	+	1.36914i
$71$	2.59551	−	11.3717i	0.308030	−	1.34957i	−0.549654	−	0.835393i	$-0.685240\pi$
$71$	2.59551	−	11.3717i	0.308030	−	1.34957i	0.857684	−	0.514177i	$-0.171903\pi$
$72$	1.02931	−	0.0385142i	0.121306	−	0.00453894i
$73$	−10.9771	+	8.10149i	−1.28478	+	0.948208i	−0.999946	−	0.0103706i	$-0.996699\pi$
$73$	−10.9771	+	8.10149i	−1.28478	+	0.948208i	−0.284829	+	0.958578i	$0.591937\pi$
$74$	0.701004	−	4.65086i	0.0814901	−	0.540651i
$75$	0.768419	−	0.406264i	0.0887294	−	0.0469114i
$76$	1.31500	+	0.300140i	0.150841	+	0.0344284i
$77$	13.8289	+	0.373349i	1.57595	+	0.0425471i
$78$	0.492586	−	0.783946i	0.0557744	−	0.0887644i
$79$	−2.66312	−	1.53756i	−0.299625	−	0.172988i	0.342650	−	0.939463i	$-0.388676\pi$
$79$	−2.66312	−	1.53756i	−0.299625	−	0.172988i	−0.642274	+	0.766475i	$0.722009\pi$
$80$	6.57591	+	7.08612i	0.735210	+	0.792252i
$81$	6.39876	−	5.93718i	0.710973	−	0.659686i
$82$	−19.8911	−	3.76360i	−2.19660	−	0.415620i
$83$	1.09712	+	9.73722i	0.120425	+	1.06880i	0.897996	+	0.440004i	$0.145023\pi$
$83$	1.09712	+	9.73722i	0.120425	+	1.06880i	−0.777571	+	0.628795i	$0.783548\pi$
$84$	0.563754	−	0.620410i	0.0615106	−	0.0676923i
$85$	−1.90810	−	16.9238i	−0.206963	−	1.83565i
$86$	−12.2236	−	3.77048i	−1.31811	−	0.406582i
$87$	−0.289211	+	0.126182i	−0.0310067	+	0.0135281i
$88$	1.18294	−	1.37461i	0.126102	−	0.146533i
$89$	−0.853906	−	2.17572i	−0.0905139	−	0.230626i	0.878447	−	0.477840i	$-0.158580\pi$
$89$	−0.853906	−	2.17572i	−0.0905139	−	0.230626i	−0.968961	+	0.247214i	$0.920485\pi$
$90$	12.9019	+	1.45274i	1.35998	+	0.153132i
$91$	−1.67678	−	7.00934i	−0.175774	−	0.734779i
$92$	−7.57827	+	2.65175i	−0.790090	+	0.276464i
$93$	−0.188481	+	0.162201i	−0.0195446	+	0.0168195i
$94$	−3.64989	+	1.12584i	−0.376458	+	0.116122i
$95$	−1.54045	−	0.604454i	−0.158047	−	0.0620157i
$96$	−0.201035	−	1.33378i	−0.0205180	−	0.136128i
$97$	−4.67598	−	4.67598i	−0.474774	−	0.474774i	0.428682	−	0.903456i	$-0.358978\pi$
$97$	−4.67598	−	4.67598i	−0.474774	−	0.474774i	−0.903456	+	0.428682i	$0.858978\pi$
$98$	−0.796316	−	13.6628i	−0.0804401	−	1.38016i
$99$		−	15.5282i		−	1.56065i
$100$	5.13464	+	7.52878i	0.513464	+	0.752878i
$101$	1.05890	−	1.55312i	0.105364	−	0.154541i	−0.769936	−	0.638122i	$-0.779712\pi$
$101$	1.05890	−	1.55312i	0.105364	−	0.154541i	0.875300	+	0.483581i	$0.160664\pi$
$102$	−1.20964	+	2.28875i	−0.119772	+	0.226620i
$103$	−7.87381	−	9.14954i	−0.775830	−	0.901531i	0.221455	−	0.975171i	$-0.428919\pi$
$103$	−7.87381	−	9.14954i	−0.775830	−	0.901531i	−0.997285	+	0.0736398i	$0.976538\pi$
$104$	−0.851234	−	0.409933i	−0.0834703	−	0.0401972i
$105$	−0.797316	+	0.649626i	−0.0778100	+	0.0633970i
$106$	−0.140311	+	0.0675702i	−0.0136282	+	0.00656300i
$107$	8.29338	+	3.61837i	0.801752	+	0.349801i	0.760492	−	0.649348i	$-0.224958\pi$
$107$	8.29338	+	3.61837i	0.801752	+	0.349801i	0.0412601	+	0.999148i	$0.486863\pi$
$108$	−1.43369	−	1.23379i	−0.137957	−	0.118722i
$109$	13.8647	+	5.44151i	1.32800	+	0.521202i	0.920050	−	0.391802i	$-0.128148\pi$
$109$	13.8647	+	5.44151i	1.32800	+	0.521202i	0.407951	+	0.913004i	$0.366243\pi$
$110$	17.3256	−	14.9121i	1.65193	−	1.42181i
$111$	0.326962	−	0.260743i	0.0310338	−	0.0247487i
$112$	−9.27355	−	6.69622i	−0.876268	−	0.632733i
$113$	0.458492	−	0.0516596i	0.0431313	−	0.00485973i	−0.0903725	−	0.995908i	$-0.528806\pi$
$113$	0.458492	−	0.0516596i	0.0431313	−	0.00485973i	0.133504	+	0.991048i	$0.457377\pi$
$114$	0.141693	+	0.207825i	0.0132707	+	0.0194646i
$115$	9.67834	−	1.83197i	0.902510	−	0.170832i
$116$	−1.65410	−	2.86499i	−0.153580	−	0.266008i
$117$	−7.81412	+	2.09379i	−0.722416	+	0.193571i
$118$	−5.74490	−	3.60976i	−0.528861	−	0.332305i
$119$	6.13984	+	19.1933i	0.562839	+	1.75945i
$120$	9.80617e−6		0.134823i	8.95177e−7		0.0123076i
$121$	−11.9780	−	11.1139i	−1.08891	−	1.01036i
$122$	−13.7324	−	18.6067i	−1.24327	−	1.68457i
$123$	−1.06887	−	1.44827i	−0.0963767	−	0.130586i
$124$	−1.91112	−	1.77326i	−0.171624	−	0.159244i
$125$	−4.85317	−	10.0721i	−0.434080	−	0.900874i
$126$	−15.3064	+	1.30741i	−1.36361	+	0.116473i
$127$	14.3929	+	9.04366i	1.27716	+	0.802495i	0.987951	−	0.154769i	$-0.0494634\pi$
$127$	14.3929	+	9.04366i	1.27716	+	0.802495i	0.289214	+	0.957265i	$0.406606\pi$
$128$	−2.66962	+	0.715322i	−0.235963	+	0.0632261i
$129$	−0.568694	−	0.985007i	−0.0500707	−	0.0867250i
$130$	−9.84020	−	6.70789i	−0.863043	−	0.588321i
$131$	2.06567	+	3.02979i	0.180479	+	0.264714i	0.905808	−	0.423688i	$-0.139265\pi$
$131$	2.06567	+	3.02979i	0.180479	+	0.264714i	−0.725329	+	0.688402i	$0.758312\pi$
$132$	−1.64628	+	0.185491i	−0.143290	+	0.0161449i
$133$	1.92754	+	0.343968i	0.167139	+	0.0298258i
$134$	−20.8745	+	16.6469i	−1.80329	+	1.43807i
$135$	1.51381	+	1.75882i	0.130288	+	0.151375i
$136$	2.45909	+	0.965122i	0.210865	+	0.0827585i
$137$	−5.92157	−	5.09592i	−0.505914	−	0.435374i	0.361934	−	0.932204i	$-0.382116\pi$
$137$	−5.92157	−	5.09592i	−0.505914	−	0.435374i	−0.867848	+	0.496830i	$0.834497\pi$
$138$	−1.37232	−	0.598735i	−0.116819	−	0.0509677i
$139$	−6.91254	+	3.32890i	−0.586314	+	0.282354i	−0.703430	−	0.710764i	$-0.748349\pi$
$139$	−6.91254	+	3.32890i	−0.586314	+	0.282354i	0.117116	+	0.993118i	$0.462635\pi$
$140$	−7.70399	−	7.54416i	−0.651106	−	0.637598i
$141$	−0.305984	−	0.147354i	−0.0257685	−	0.0124095i
$142$	14.8755	+	17.2856i	1.24832	+	1.45058i
$143$	−6.65544	+	12.5927i	−0.556556	+	1.05306i
$144$	−7.23265	+	10.6083i	−0.602721	+	0.884029i
$145$	1.48308	+	3.77802i	0.123163	+	0.313747i
$146$		−	26.6741i		−	2.20756i
$147$	0.774389	−	0.938690i	0.0638705	−	0.0774218i
$148$	3.10033	+	3.10033i	0.254846	+	0.254846i
$149$	−2.66989	−	17.7135i	−0.218726	−	1.45115i	−0.781172	−	0.624316i	$-0.785378\pi$
$149$	−2.66989	−	17.7135i	−0.218726	−	1.45115i	0.562446	−	0.826834i	$-0.309860\pi$
$150$	−0.253042	+	1.68048i	−0.0206608	+	0.137211i
$151$	15.5336	−	4.79149i	1.26411	−	0.389926i	0.410989	−	0.911640i	$-0.365183\pi$
$151$	15.5336	−	4.79149i	1.26411	−	0.389926i	0.853121	+	0.521714i	$0.174707\pi$
$152$	0.194554	−	0.167427i	0.0157804	−	0.0135802i
$153$	21.3501	−	7.47071i	1.72605	−	0.603971i
$154$	−16.6428	+	21.3209i	−1.34112	+	1.71809i
$155$	1.99442	+	2.50055i	0.160195	+	0.200849i
$156$	0.315323	+	0.803429i	0.0252460	+	0.0643258i
$157$	−1.91963	+	2.23065i	−0.153203	+	0.178025i	−0.829329	−	0.558761i	$-0.811277\pi$
$157$	−1.91963	+	2.23065i	−0.153203	+	0.178025i	0.676125	+	0.736787i	$0.263658\pi$
$158$	5.51064	−	2.40427i	0.438403	−	0.191273i
$159$	−0.0132318	−	0.00408147i	−0.00104935	−	0.000323681i
$160$	−17.2406	+	1.94381i	−1.36299	+	0.153672i
$161$	−10.8043	+	4.37071i	−0.851501	+	0.344460i
$162$	1.91082	+	16.9590i	0.150129	+	1.33243i
$163$	−3.97310	−	0.751750i	−0.311197	−	0.0588816i	0.0279673	−	0.999609i	$-0.491097\pi$
$163$	−3.97310	−	0.751750i	−0.311197	−	0.0588816i	−0.339164	+	0.940727i	$0.610144\pi$
$164$	13.8339	−	12.8360i	1.08024	−	1.00232i
$165$	2.03111	+	0.0758508i	0.158122	+	0.00590497i
$166$	−16.5915	−	9.57908i	−1.28775	−	0.743481i
$167$	−4.42397	+	7.04070i	−0.342337	+	0.544826i	−0.972875	−	0.231333i	$-0.925691\pi$
$167$	−4.42397	+	7.04070i	−0.342337	+	0.544826i	0.630538	+	0.776158i	$0.282834\pi$
$168$	−0.0312874	−	0.156427i	−0.00241388	−	0.0120686i
$169$	−5.43976	−	1.24159i	−0.418443	−	0.0955068i
$170$	28.8383	+	16.6470i	2.21180	+	1.27677i
$171$	0.327562	−	2.17324i	0.0250493	−	0.166191i
$172$	9.59460	−	7.08114i	0.731582	−	0.539932i
$173$	−1.34411	+	0.0502931i	−0.102191	+	0.00382372i	−0.0884378	−	0.996082i	$-0.528187\pi$
$173$	−1.34411	+	0.0502931i	−0.102191	+	0.00382372i	−0.0137532	+	0.999905i	$0.504378\pi$
$174$	0.137279	−	0.601458i	0.0104071	−	0.0455964i
$175$	7.96740	+	10.5603i	0.602279	+	0.798286i
$176$	5.03022	+	22.0388i	0.379167	+	1.66124i
$177$	−0.156138	−	0.582716i	−0.0117361	−	0.0437997i
$178$	4.41403	+	1.18274i	0.330845	+	0.0886498i
$179$	−11.5233	−	12.4192i	−0.861291	−	0.928251i	0.136763	−	0.990604i	$-0.456330\pi$
$179$	−11.5233	−	12.4192i	−0.861291	−	0.928251i	−0.998054	+	0.0623524i	$0.980140\pi$
$180$	−8.23164	+	8.87289i	−0.613550	+	0.661346i
$181$	−0.483950	−	0.385937i	−0.0359717	−	0.0286865i	0.605339	−	0.795968i	$-0.293038\pi$
$181$	−0.483950	−	0.385937i	−0.0359717	−	0.0286865i	−0.641311	+	0.767281i	$0.721609\pi$
$182$	12.9732	+	5.50013i	0.961638	+	0.407697i
$183$	0.230221	−	2.04326i	0.0170184	−	0.151042i
$184$	−0.450348	+	1.45999i	−0.0332001	+	0.107632i
$185$	−3.19458	−	4.32785i	−0.234870	−	0.318190i
$186$	−0.0363320	−	0.484817i	−0.00266399	−	0.0355485i
$187$	15.9257	−	36.5020i	1.16460	−	2.66929i
$188$	1.17601	−	3.36083i	0.0857691	−	0.245114i
$189$	−2.16441	−	1.68951i	−0.157438	−	0.122893i
$190$	2.73935	−	1.72152i	0.198733	−	0.124893i
$191$	−0.309248	+	4.12662i	−0.0223764	+	0.298592i	0.974776	+	0.223184i	$0.0716450\pi$
$191$	−0.309248	+	4.12662i	−0.0223764	+	0.298592i	−0.997153	+	0.0754082i	$0.975974\pi$
$192$	1.00263	+	0.529904i	0.0723584	+	0.0382425i
$193$	−2.11432	−	11.1744i	−0.152192	−	0.804354i	−0.972584	−	0.232552i	$-0.925292\pi$
$193$	−2.11432	−	11.1744i	−0.152192	−	0.804354i	0.820392	−	0.571801i	$-0.193755\pi$
$194$	12.7847	−	1.92698i	0.917885	−	0.138349i
$195$	−0.235700	−	1.03232i	−0.0168788	−	0.0739261i
$196$	10.6887	+	6.96597i	0.763475	+	0.497570i
$197$	−1.07609	+	1.07609i	−0.0766680	+	0.0766680i	−0.744401	−	0.667733i	$-0.767265\pi$
$197$	−1.07609	+	1.07609i	−0.0766680	+	0.0766680i	0.667733	+	0.744401i	$0.267265\pi$
$198$	24.4276	+	18.0284i	1.73599	+	1.28122i
$199$	11.6136	+	7.91799i	0.823264	+	0.561292i	0.900066	−	0.435755i	$-0.143518\pi$
$199$	11.6136	+	7.91799i	0.823264	+	0.561292i	−0.0768017	+	0.997046i	$0.524471\pi$
$200$	1.73299	+	0.0645914i	0.122541	+	0.00456730i
$201$	−2.36734	−	0.177408i	−0.166979	−	0.0125134i
$202$	1.21383	+	3.46893i	0.0854049	+	0.244073i
$203$	−2.59717	−	4.03941i	−0.182285	−	0.283511i
$204$	−1.04707	−	2.17426i	−0.0733094	−	0.152228i
$205$	−19.1287	+	13.0438i	−1.33601	+	0.911017i
$206$	23.5348	−	1.76369i	1.63974	−	0.122882i
$207$	5.23151	+	11.9907i	0.363615	+	0.833414i
$208$	10.4121	−	5.50296i	0.721950	−	0.381562i
$209$	−2.41261	−	3.02532i	−0.166884	−	0.209266i
$210$	−0.0962426	−	2.00848i	−0.00664137	−	0.138598i
$211$	−7.84835	+	9.84152i	−0.540303	+	0.677518i	−0.974781	−	0.223164i	$-0.928361\pi$
$211$	−7.84835	+	9.84152i	−0.540303	+	0.677518i	0.434478	+	0.900682i	$0.356933\pi$
$212$	0.0269899	−	0.142645i	0.00185367	−	0.00979689i
$213$	−0.0758183	+	2.02629i	−0.00519498	+	0.138839i
$214$	−15.3207	+	8.84544i	−1.04730	+	0.604662i
$215$	−12.9340	+	6.83703i	−0.882093	+	0.466282i
$216$	−0.350922	+	0.0800956i	−0.0238772	+	0.00544981i
$217$	−2.89410	−	2.43860i	−0.196464	−	0.165543i
$218$	−24.6571	+	15.4931i	−1.66999	+	1.04933i
$219$	1.61318	−	1.73859i	0.109008	−	0.117483i
$220$	1.59401	+	21.2499i	0.107468	+	1.43267i
$221$	−20.5159	−	3.09228i	−1.38005	−	0.208009i
$222$	0.0305726	+	0.817071i	0.00205190	+	0.0548382i
$223$	4.47084	+	7.11530i	0.299389	+	0.476475i	0.962212	−	0.272301i	$-0.0877846\pi$
$223$	4.47084	+	7.11530i	0.299389	+	0.476475i	−0.662823	+	0.748776i	$0.730642\pi$
$224$	19.5525	−	6.25475i	1.30641	−	0.417913i
$225$	11.6080	−	9.25982i	0.773866	−	0.617322i
$226$	−0.451046	+	0.781234i	−0.0300031	+	0.0519669i
$227$	1.57468	−	5.87679i	0.104515	−	0.390056i	−0.893774	−	0.448517i	$-0.851952\pi$
$227$	1.57468	−	5.87679i	0.104515	−	0.390056i	0.998290	+	0.0584604i	$0.0186191\pi$
$228$	−0.234316	−	0.00876747i	−0.0155179	−	0.000580640i
$229$	−8.07013	+	5.50212i	−0.533289	+	0.363590i	−0.799824	−	0.600235i	$-0.795074\pi$
$229$	−8.07013	+	5.50212i	−0.533289	+	0.363590i	0.266535	+	0.963825i	$0.414121\pi$
$230$	−8.35473	+	17.3520i	−0.550894	+	1.14416i
$231$	−2.37419	+	0.383167i	−0.156210	+	0.0252105i
$232$	−0.625588	−	0.0704868i	−0.0410718	−	0.00462769i
$233$	−4.57829	−	8.66255i	−0.299934	−	0.567502i	0.687377	−	0.726300i	$-0.258762\pi$
$233$	−4.57829	−	8.66255i	−0.299934	−	0.567502i	−0.987311	+	0.158798i	$0.949238\pi$
$234$	5.77849	−	14.7234i	0.377752	−	0.962496i
$235$	−2.04093	+	3.86231i	−0.133136	+	0.251950i
$236$	5.88767	−	2.31074i	0.383255	−	0.150416i
$237$	0.504582	+	0.176561i	0.0327761	+	0.0114689i
$238$	−37.3215	−	12.6249i	−2.41919	−	0.818350i
$239$	0.0397348	−	0.0825102i	0.00257023	−	0.00533714i	−0.899680	−	0.436550i	$-0.856200\pi$
$239$	0.0397348	−	0.0825102i	0.00257023	−	0.00533714i	0.902250	+	0.431213i	$0.141914\pi$
$240$	−1.35225	−	0.997855i	−0.0872875	−	0.0644113i
$241$	3.73873	+	12.1207i	0.240833	+	0.780761i	0.992610	+	0.121344i	$0.0387205\pi$
$241$	3.73873	+	12.1207i	0.240833	+	0.780761i	−0.751778	+	0.659417i	$0.770803\pi$
$242$	31.3899	−	5.93929i	2.01782	−	0.381792i
$243$	−2.74988	+	3.72595i	−0.176405	+	0.239020i
$244$	21.5577			1.38009
$245$	−11.6940	−	10.4044i	−0.747100	−	0.664712i
$246$	3.51924			0.224379
$247$	−1.19709	+	1.62200i	−0.0761692	+	0.103206i
$248$	−0.487473	+	0.0922349i	−0.0309546	+	0.00585692i
$249$	−0.502098	−	1.62776i	−0.0318192	−	0.103155i
$250$	21.4790	+	4.05920i	1.35845	+	0.256726i
$251$	3.77556	−	7.84002i	0.238311	−	0.494858i	−0.747172	−	0.664630i	$-0.768589\pi$
$251$	3.77556	−	7.84002i	0.238311	−	0.494858i	0.985483	+	0.169773i	$0.0543033\pi$
$252$	7.49246	−	12.2044i	0.471981	−	0.768802i
$253$	21.7408	+	7.60745i	1.36683	+	0.478276i
$254$	−30.9369	+	12.1418i	−1.94115	+	0.761847i
$255$	0.872887	+	2.82910i	0.0546623	+	0.177165i
$256$	6.74074	−	17.1751i	0.421296	−	1.07345i
$257$	6.20696	+	11.7441i	0.387180	+	0.732579i	0.998259	−	0.0589902i	$-0.0187881\pi$
$257$	6.20696	+	11.7441i	0.387180	+	0.732579i	−0.611079	+	0.791570i	$0.709264\pi$
$258$	2.20978	+	0.248982i	0.137575	+	0.0155010i
$259$	4.71049	+	4.28032i	0.292696	+	0.265966i
$260$	10.4784	−	3.66742i	0.649845	−	0.227444i
$261$	−4.45380	+	3.03655i	−0.275683	+	0.187958i
$262$	−7.16444	−	0.268075i	−0.442621	−	0.0165617i
$263$	0.481364	−	1.79647i	0.0296822	−	0.110775i	−0.949495	−	0.313781i	$-0.898404\pi$
$263$	0.481364	−	1.79647i	0.0296822	−	0.110775i	0.979178	+	0.203006i	$0.0650709\pi$
$264$	−0.157633	+	0.273029i	−0.00970165	+	0.0168037i
$265$	−0.0588136	+	0.168119i	−0.00361289	+	0.0103275i
$266$	−2.77898	+	2.63287i	−0.170390	+	0.161432i
$267$	0.216173	+	0.344038i	0.0132296	+	0.0210548i
$268$	−0.930648	−	24.8721i	−0.0568484	−	1.51931i
$269$	7.92431	+	1.19440i	0.483153	+	0.0728237i	0.386103	−	0.922456i	$-0.373821\pi$
$269$	7.92431	+	1.19440i	0.483153	+	0.0728237i	0.0970507	+	0.995279i	$0.469059\pi$
$270$	−4.52436	+	0.339385i	−0.275344	+	0.0206543i
$271$	7.60270	−	8.19376i	0.461831	−	0.497736i	−0.458599	−	0.888644i	$-0.651648\pi$
$271$	7.60270	−	8.19376i	0.461831	−	0.497736i	0.920430	+	0.390908i	$0.127839\pi$
$272$	−27.8815	+	17.5191i	−1.69057	+	1.06225i
$273$	0.512947	+	1.14308i	0.0310450	+	0.0691821i
$274$	14.8914	−	3.39887i	0.899623	−	0.205333i
$275$	1.94993	−	26.0709i	0.117585	−	1.57214i
$276$	1.20875	−	0.697870i	0.0727580	−	0.0420068i
$277$	−0.261455	+	6.98754i	−0.0157093	+	0.419840i	0.969149	+	0.246477i	$0.0792730\pi$
$277$	−0.261455	+	6.98754i	−0.0157093	+	0.419840i	−0.984858	+	0.173363i	$0.944537\pi$
$278$	2.78878	−	14.7390i	0.167260	−	0.883989i
$279$	−2.64859	+	3.32123i	−0.158567	+	0.198837i
$280$	−2.02569	+	0.327073i	−0.121058	+	0.0195463i
$281$	0.794053	+	0.995711i	0.0473692	+	0.0593991i	0.804952	−	0.593340i	$-0.202191\pi$
$281$	0.794053	+	0.995711i	0.0473692	+	0.0593991i	−0.757583	+	0.652739i	$0.773620\pi$
$282$	0.587054	−	0.310267i	0.0349585	−	0.0184761i
$283$	−10.7136	−	24.5559i	−0.636860	−	1.45970i	−0.872872	−	0.487948i	$-0.837745\pi$
$283$	−10.7136	−	24.5559i	−0.636860	−	1.45970i	0.236013	−	0.971750i	$-0.424159\pi$
$284$	−21.1996	+	1.58869i	−1.25797	+	0.0942715i
$285$	0.282661	+	0.0534611i	0.0167434	+	0.00316676i
$286$	−12.0827	−	25.0899i	−0.714464	−	1.48360i
$287$	19.1683	−	19.5715i	1.13147	−	1.15527i
$288$	−7.61052	−	21.7496i	−0.448454	−	1.28161i
$289$	40.8967	+	3.06479i	2.40569	+	0.180282i
$290$	−7.66509	−	2.05326i	−0.450110	−	0.120571i
$291$	0.949830	+	0.647583i	0.0556800	+	0.0379620i
$292$	20.0069	+	14.7658i	1.17082	+	0.864103i
$293$	−18.7429	+	18.7429i	−1.09497	+	1.09497i	−0.0999832	+	0.994989i	$0.531879\pi$
$293$	−18.7429	+	18.7429i	−1.09497	+	1.09497i	−0.994989	+	0.0999832i	$0.968121\pi$
$294$	0.577590	+	2.30802i	0.0336857	+	0.134607i
$295$	−7.56504	+	1.72725i	−0.440454	+	0.100564i
$296$	0.825050	−	0.124356i	0.0479551	−	0.00722806i
$297$	1.00882	+	5.33176i	0.0585379	+	0.309380i
$298$	30.9651	+	16.3655i	1.79376	+	0.948029i
$299$	0.896742	−	11.9662i	0.0518599	−	0.692023i
$300$	−1.12037	−	1.12005i	−0.0646848	−	0.0646660i
$301$	13.4207	−	10.9331i	0.773555	−	0.630173i
$302$	−10.4971	+	29.9990i	−0.604041	+	1.72625i
$303$	−0.130675	+	0.299511i	−0.00750710	+	0.0172064i
$304$	0.239097	+	3.19053i	0.0137131	+	0.182989i
$305$	−26.1531	−	3.94000i	−1.49752	−	0.225604i
$306$	−13.0353	+	42.2595i	−0.745180	+	2.41581i
$307$	1.05299	−	9.34552i	0.0600971	−	0.533377i	−0.927209	−	0.374545i	$-0.877799\pi$
$307$	1.05299	−	9.34552i	0.0600971	−	0.533377i	0.987306	−	0.158831i	$-0.0507726\pi$
$308$	−6.77897	−	24.2855i	−0.386268	−	1.38379i
$309$	1.64063	+	1.30836i	0.0933324	+	0.0744301i
$310$	−6.24916	+	0.234282i	−0.354928	+	0.0133063i
$311$	−10.2897	−	11.0897i	−0.583475	−	0.628836i	0.370461	−	0.928848i	$-0.379200\pi$
$311$	−10.2897	−	11.0897i	−0.583475	−	0.628836i	−0.953936	+	0.300012i	$0.903009\pi$
$312$	0.158648	+	0.0425097i	0.00898169	+	0.00240664i
$313$	1.82060	+	6.79456i	0.102906	+	0.384051i	0.998099	−	0.0616273i	$-0.0196290\pi$
$313$	1.82060	+	6.79456i	0.102906	+	0.384051i	−0.895193	+	0.445679i	$0.852962\pi$
$314$	−1.28035	−	5.60959i	−0.0722544	−	0.316567i
$315$	−11.3201	+	13.4365i	−0.637817	+	0.757063i
$316$	−1.24716	+	5.46418i	−0.0701584	+	0.307384i
$317$	22.6945	−	0.849169i	1.27465	−	0.0476941i	0.608526	−	0.793534i	$-0.291761\pi$
$317$	22.6945	−	0.849169i	1.27465	−	0.0476941i	0.666125	+	0.745840i	$0.267952\pi$
$318$	0.0217828	−	0.0160764i	0.00122152	−	0.000901521i
$319$	−1.41452	+	9.38471i	−0.0791978	+	0.525443i
$320$	7.29254	−	12.6332i	0.407665	−	0.706215i
$321$	−1.53354	−	0.350020i	−0.0855938	−	0.0195362i
$322$	5.66831	−	22.0708i	0.315882	−	1.22996i
$323$	2.99885	−	4.77265i	0.166861	−	0.265557i
$324$	−13.7779	−	7.95468i	−0.765440	−	0.441927i
$325$	−13.3823	+	2.53409i	−0.742319	+	0.140566i
$326$	5.79537	−	5.37732i	0.320976	−	0.297822i
$327$	−2.54411	−	0.481371i	−0.140689	−	0.0266199i
$328$	−0.402091	−	3.56865i	−0.0222017	−	0.197046i
$329$	1.47203	−	4.95471i	0.0811554	−	0.273162i
$330$	−2.47745	+	3.10709i	−0.136379	+	0.171040i
$331$	−5.87598	−	1.81250i	−0.322973	−	0.0996241i	0.129029	−	0.991641i	$-0.458814\pi$
$331$	−5.87598	−	1.81250i	−0.322973	−	0.0996241i	−0.452002	+	0.892017i	$0.649290\pi$
$332$	16.3692	−	7.14182i	0.898378	−	0.391959i
$333$	4.66009	−	5.41513i	0.255372	−	0.296747i
$334$	−5.93953	−	15.1337i	−0.324997	−	0.828078i
$335$	−3.41672	+	30.3440i	−0.186675	+	1.65787i
$336$	1.80043	+	0.844071i	0.0982217	+	0.0460479i
$337$	−27.2334	+	9.52937i	−1.48350	+	0.519098i	−0.945999	−	0.324168i	$-0.894916\pi$
$337$	−27.2334	+	9.52937i	−1.48350	+	0.519098i	−0.537497	+	0.843266i	$0.680630\pi$
$338$	8.26874	−	7.11583i	0.449760	−	0.387050i
$339$	−0.0766456	+	0.0236420i	−0.00416282	+	0.00128406i
$340$	−28.4500	+	12.4151i	−1.54292	+	0.673301i
$341$	1.11473	+	7.39575i	0.0603660	+	0.400502i
$342$	3.03843	+	3.03843i	0.164299	+	0.164299i
$343$	15.9815	+	9.35897i	0.862922	+	0.505337i
$344$		−	2.26925i		−	0.122350i
$345$	−1.59395	+	0.625715i	−0.0858156	+	0.0336873i
$346$	1.48141	−	2.17282i	0.0796409	−	0.116812i
$347$	−11.7995	+	22.3257i	−0.633430	+	1.19851i	0.333327	+	0.942811i	$0.391829\pi$
$347$	−11.7995	+	22.3257i	−0.633430	+	1.19851i	−0.966757	+	0.255697i	$0.917695\pi$
$348$	0.375132	+	0.435911i	0.0201092	+	0.0233673i
$349$	6.35485	+	3.06034i	0.340167	+	0.163816i	0.596166	−	0.802861i	$-0.296690\pi$
$349$	6.35485	+	3.06034i	0.340167	+	0.163816i	−0.255999	+	0.966677i	$0.582404\pi$
$350$	−25.8627	+	0.272972i	−1.38242	+	0.0145910i
$351$	2.54702	−	1.22658i	0.135950	−	0.0654701i
$352$	−37.1851	−	16.2237i	−1.98197	−	0.864727i
$353$	19.5755	+	16.8461i	1.04190	+	0.896628i	0.994758	−	0.102260i	$-0.0326074\pi$
$353$	19.5755	+	16.8461i	1.04190	+	0.896628i	0.0471429	+	0.998888i	$0.484988\pi$
$354$	1.09795	+	0.430915i	0.0583556	+	0.0229029i
$355$	26.0090	+	1.94720i	1.38041	+	0.103347i
$356$	−3.33056	+	2.65603i	−0.176519	+	0.140769i
$357$	−1.66906	−	3.07998i	−0.0883360	−	0.163010i
$358$	32.9153	−	3.70866i	1.73963	−	0.196009i
$359$	−13.5626	−	19.8927i	−0.715806	−	1.04989i	−0.995948	−	0.0899360i	$-0.971334\pi$
$359$	−13.5626	−	19.8927i	−0.715806	−	1.04989i	0.280141	−	0.959959i	$-0.409619\pi$
$360$	0.428361	+	2.26304i	0.0225766	+	0.119273i
$361$	9.22616	+	15.9802i	0.485588	+	0.841062i
$362$	1.16899	−	0.313230i	0.0614407	−	0.0164630i
$363$	2.40515	+	1.51126i	0.126238	+	0.0793205i
$364$	−11.3069	+	6.68590i	−0.592641	+	0.350436i
$365$	−21.5730	−	21.5699i	−1.12918	−	1.12902i
$366$	2.94699	+	2.73440i	0.154041	+	0.142930i
$367$	−5.62480	−	7.62134i	−0.293612	−	0.397831i	0.632816	−	0.774302i	$-0.281899\pi$
$367$	−5.62480	−	7.62134i	−0.293612	−	0.397831i	−0.926428	+	0.376472i	$0.877137\pi$
$368$	−11.3092	−	15.3235i	−0.589534	−	0.798790i
$369$	−22.5411	−	20.9151i	−1.17344	−	1.08880i
$370$	10.5171		0.000764947i	0.546758		3.97677e-5i
$371$	0.0292388	−	0.208704i	0.00151800	−	0.0108354i
$372$	0.383750	+	0.241126i	0.0198965	+	0.0125018i
$373$	−22.6886	+	6.07940i	−1.17477	+	0.314779i	−0.792851	−	0.609415i	$-0.791404\pi$
$373$	−22.6886	+	6.07940i	−1.17477	+	0.314779i	−0.381921	+	0.924195i	$0.624738\pi$
$374$	38.9318	+	67.4318i	2.01312	+	3.48682i
$375$	1.15449	+	1.56357i	0.0596177	+	0.0807422i
$376$	−0.381697	−	0.559847i	−0.0196845	−	0.0288719i
$377$	4.91330	−	0.553596i	0.253048	−	0.0285117i
$378$	5.17067	−	1.44332i	0.265950	−	0.0742366i
$379$	11.9563	−	9.53485i	0.614155	−	0.489772i	−0.266307	−	0.963888i	$-0.585804\pi$
$379$	11.9563	−	9.53485i	0.614155	−	0.489772i	0.880462	+	0.474116i	$0.157232\pi$
$380$	−0.225170	+	3.00763i	−0.0115510	+	0.154288i
$381$	−2.75074	−	1.07959i	−0.140925	−	0.0553089i
$382$	−6.13258	−	5.27752i	−0.313770	−	0.270021i
$383$	−17.0459	−	7.43704i	−0.871003	−	0.380015i	−0.0836340	−	0.996497i	$-0.526653\pi$
$383$	−17.0459	−	7.43704i	−0.871003	−	0.380015i	−0.787369	+	0.616482i	$0.788557\pi$
$384$	0.432880	−	0.208464i	0.0220903	−	0.0106381i
$385$	3.78548	+	30.7012i	0.192926	+	1.56468i
$386$	20.0333	+	9.64754i	1.01967	+	0.491047i
$387$	−12.6742	−	14.7276i	−0.644264	−	0.748648i
$388$	−5.63179	+	10.6559i	−0.285911	+	0.540970i
$389$	−21.9159	+	32.1447i	−1.11118	+	1.62980i	−0.419172	+	0.907907i	$0.637679\pi$
$389$	−21.9159	+	32.1447i	−1.11118	+	1.62980i	−0.692006	+	0.721892i	$0.743273\pi$
$390$	1.89760	+	0.827751i	0.0960888	+	0.0419148i
$391$			33.5519i			1.69679i
$392$	2.27443	−	0.849402i	0.114876	−	0.0429013i
$393$	−0.450759	−	0.450759i	−0.0227378	−	0.0227378i
$394$	−0.443457	−	2.94214i	−0.0223410	−	0.148223i
$395$	2.51168	−	6.40102i	0.126376	−	0.322070i
$396$	−27.0444	+	8.34211i	−1.35903	+	0.419207i
$397$	−17.5436	+	15.0975i	−0.880490	+	0.757723i	−0.971228	−	0.238152i	$-0.923458\pi$
$397$	−17.5436	+	15.0975i	−0.880490	+	0.757723i	0.0907382	+	0.995875i	$0.471077\pi$
$398$	−25.9393	+	9.07655i	−1.30022	+	0.454966i
$399$	−0.340360	+	0.00354286i	−0.0170393	+	0.000177365i
$400$	−13.4753	+	16.9025i	−0.673764	+	0.845126i
$401$	−9.95305	−	25.3600i	−0.497031	−	1.26642i	−0.930845	−	0.365413i	$-0.880928\pi$
$401$	−9.95305	−	25.3600i	−0.497031	−	1.26642i	0.433814	−	0.901002i	$-0.357167\pi$
$402$	3.02758	−	3.51811i	0.151002	−	0.175467i
$403$	3.57138	−	1.55818i	0.177903	−	0.0776183i
$404$	−3.27381	−	1.00984i	−0.162878	−	0.0502413i
$405$	15.2610	+	12.1685i	0.758327	+	0.604656i
$406$	9.36976	+	0.604164i	0.465013	+	0.0299841i
$407$	−1.40835	−	12.4994i	−0.0698092	−	0.619574i
$408$	−0.451230	−	0.0853773i	−0.0223392	−	0.00422681i
$409$	14.3472	−	13.3123i	0.709423	−	0.658248i	−0.240530	−	0.970642i	$-0.577321\pi$
$409$	14.3472	−	13.3123i	0.709423	−	0.658248i	0.949953	+	0.312393i	$0.101131\pi$
$410$	1.68930	−	45.2354i	0.0834284	−	2.23402i
$411$	1.17616	+	0.679057i	0.0580158	+	0.0334954i
$412$	−11.7051	+	18.6286i	−0.576670	+	0.917765i
$413$	8.37668	−	3.75897i	0.412189	−	0.184967i
$414$	−24.9365	−	5.69160i	−1.22556	−	0.279727i
$415$	−21.1639	+	5.67249i	−1.03889	+	0.278451i
$416$	−3.15015	+	20.8999i	−0.154449	+	1.02470i
$417$	1.07315	−	0.792018i	0.0525522	−	0.0387853i
$418$	7.56022	−	0.282883i	0.369782	−	0.0138363i
$419$	5.49947	−	24.0947i	0.268667	−	1.17711i	−0.642899	−	0.765951i	$-0.722269\pi$
$419$	5.49947	−	24.0947i	0.268667	−	1.17711i	0.911566	−	0.411154i	$-0.134874\pi$
$420$	1.55974	+	1.03964i	0.0761076	+	0.0507290i
$421$	−1.58396	−	6.93978i	−0.0771974	−	0.338224i	0.921550	−	0.388260i	$-0.126924\pi$
$421$	−1.58396	−	6.93978i	−0.0771974	−	0.338224i	−0.998747	+	0.0500357i	$0.984066\pi$
$422$	−6.36978	−	23.7724i	−0.310076	−	1.15722i
$423$	−5.60409	−	1.50161i	−0.272480	−	0.0730108i
$424$	−0.0187909	−	0.0202518i	−0.000912569	−	0.000983515i
$425$	36.7835	−	9.86186i	1.78426	−	0.478370i
$426$	−3.09954	−	2.47180i	−0.150173	−	0.119759i
$427$	31.2582	−	1.49555i	1.51269	−	0.0723749i
$428$	1.84647	−	16.3879i	0.0892525	−	0.792137i
$429$	0.729834	−	2.36606i	0.0352367	−	0.114235i
$430$	4.26109	−	28.2844i	0.205488	−	1.36400i
$431$	0.289341	+	3.86098i	0.0139370	+	0.185977i	0.999827	+	0.0185840i	$0.00591581\pi$
$431$	0.289341	+	3.86098i	0.0139370	+	0.185977i	−0.985890	+	0.167393i	$0.946465\pi$
$432$	1.79420	−	4.11236i	0.0863236	−	0.197856i
$433$	4.11505	−	11.7601i	0.197757	−	0.565156i	−0.801714	−	0.597708i	$-0.796078\pi$
$433$	4.11505	−	11.7601i	0.197757	−	0.565156i	0.999470	+	0.0325529i	$0.0103637\pi$
$434$	7.19625	−	1.72149i	0.345431	−	0.0826344i
$435$	−0.375428	−	0.597393i	−0.0180004	−	0.0286428i
$436$	2.02866	−	27.0705i	0.0971550	−	1.29644i
$437$	2.88223	+	1.52331i	0.137876	+	0.0728696i
$438$	0.862082	+	4.55621i	0.0411919	+	0.217704i
$439$	21.3018	−	3.21072i	1.01668	−	0.153239i	0.380499	−	0.924781i	$-0.375752\pi$
$439$	21.3018	−	3.21072i	1.01668	−	0.153239i	0.636178	+	0.771542i	$0.280514\pi$
$440$	3.43377	+	2.15724i	0.163699	+	0.102842i
$441$	10.0172	−	18.2158i	0.477010	−	0.867419i
$442$	28.6836	−	28.6836i	1.36434	−	1.36434i
$443$	10.9312	+	8.06757i	0.519355	+	0.383302i	0.821721	−	0.569890i	$-0.193014\pi$
$443$	10.9312	+	8.06757i	0.519355	+	0.383302i	−0.302365	+	0.953192i	$0.597776\pi$
$444$	−0.629769	−	0.429369i	−0.0298875	−	0.0203770i
$445$	4.52594	−	2.61349i	0.214550	−	0.123892i
$446$	−16.3838	−	1.22780i	−0.775795	−	0.0581378i
$447$	1.02853	+	2.93937i	0.0486478	+	0.139027i
$448$	−5.53056	+	16.3494i	−0.261295	+	0.772435i
$449$	8.29519	+	17.2251i	0.391474	+	0.812904i	0.999815	+	0.0192287i	$0.00612105\pi$
$449$	8.29519	+	17.2251i	0.391474	+	0.812904i	−0.608341	+	0.793676i	$0.708165\pi$
$450$	1.08975	+	29.0113i	0.0513715	+	1.36761i
$451$	−53.9882	+	4.04586i	−2.54221	+	0.190512i
$452$	−0.336284	−	0.770770i	−0.0158175	−	0.0362540i
$453$	−2.49845	+	1.32047i	−0.117388	+	0.0620411i
$454$	7.41661	+	9.30013i	0.348079	+	0.436477i
$455$	14.9390	−	6.04460i	0.700353	−	0.283375i
$456$	−0.0278208	+	0.0348861i	−0.00130283	+	0.00163369i
$457$	−2.15775	+	11.4040i	−0.100935	+	0.533456i	0.895203	+	0.445658i	$0.147030\pi$
$457$	−2.15775	+	11.4040i	−0.100935	+	0.533456i	−0.996138	+	0.0877973i	$0.972017\pi$
$458$	0.714042	−	19.0832i	0.0333650	−	0.891698i
$459$	−6.84539	+	3.95219i	−0.319515	+	0.184472i
$460$	−8.39003	−	15.8719i	−0.391187	−	0.740032i
$461$	19.0847	−	4.35595i	0.888861	−	0.202877i	0.246375	−	0.969174i	$-0.420760\pi$
$461$	19.0847	−	4.35595i	0.888861	−	0.202877i	0.642486	+	0.766298i	$0.277903\pi$
$462$	2.15369	−	4.17972i	0.100199	−	0.194458i
$463$	26.6475	−	16.7437i	1.23841	−	0.778146i	0.256329	−	0.966590i	$-0.417487\pi$
$463$	26.6475	−	16.7437i	1.23841	−	0.778146i	0.982084	+	0.188444i	$0.0603442\pi$
$464$	5.33750	−	5.75246i	0.247787	−	0.267051i
$465$	−0.421482	−	0.362662i	−0.0195458	−	0.0168180i
$466$	18.9425	+	2.85513i	0.877496	+	0.132261i
$467$	1.01004	+	26.9938i	0.0467390	+	1.24913i	0.803448	+	0.595375i	$0.202996\pi$
$467$	1.01004	+	26.9938i	0.0467390	+	1.24913i	−0.756709	+	0.653752i	$0.773194\pi$
$468$	7.84452	+	12.4845i	0.362613	+	0.577095i
$469$	−3.07490	−	35.9994i	−0.141986	−	1.66230i
$470$	−3.70630	−	7.69478i	−0.170959	−	0.354934i
$471$	0.255800	−	0.443059i	0.0117867	−	0.0204151i
$472$	0.311519	−	1.16260i	0.0143388	−	0.0535132i
$473$	−34.1862	−	1.27916i	−1.57188	−	0.0588157i
$474$	−0.863572	+	0.588773i	−0.0396652	+	0.0270432i
$475$	0.822857	−	3.60759i	0.0377553	−	0.165528i
$476$	30.1291	−	21.0044i	1.38097	−	0.962734i
$477$	−0.235065	−	0.0264854i	−0.0107629	−	0.00121268i
$478$	0.0836651	+	0.158302i	0.00382675	+	0.00724057i
$479$	−9.69814	+	24.7105i	−0.443119	+	1.12905i	0.518601	+	0.855016i	$0.326453\pi$
$479$	−9.69814	+	24.7105i	−0.443119	+	1.12905i	−0.961720	+	0.274033i	$0.911642\pi$
$480$	2.88205	−	0.889223i	0.131547	−	0.0405873i
$481$	−6.10006	+	2.39410i	−0.278139	+	0.109162i
$482$	−23.4078	−	8.19075i	−1.06620	−	0.373078i
$483$	1.70424	−	1.09575i	0.0775455	−	0.0498583i
$484$	−12.9215	+	26.8318i	−0.587342	+	1.21963i
$485$	8.77981	−	11.8980i	0.398670	−	0.540262i
$486$	−2.66870	−	8.65171i	−0.121055	−	0.392449i
$487$	−1.95800	+	0.370473i	−0.0887252	+	0.0167877i	−0.230085	−	0.973171i	$-0.573900\pi$
$487$	−1.95800	+	0.370473i	−0.0887252	+	0.0167877i	0.141359	+	0.989958i	$0.454853\pi$
$488$	2.43609	−	3.30078i	0.110277	−	0.149419i
$489$	0.702942			0.0317881
$490$	29.9440	−	6.31631i	1.35273	−	0.285342i
$491$	−3.98825			−0.179987			−0.0899936	−	0.995942i	$-0.528685\pi$
$491$	−3.98825			−0.179987			−0.0899936	+	0.995942i	$0.528685\pi$
$492$	−1.94812	+	2.63961i	−0.0878282	+	0.119003i
$493$	−13.5837	+	2.57018i	−0.611781	+	0.115755i
$494$	−1.16175	−	3.76631i	−0.0522697	−	0.169454i
$495$	34.3340	−	5.17757i	1.54320	−	0.232715i
$496$	2.68320	−	5.57172i	0.120479	−	0.250178i
$497$	−30.6287	+	3.77427i	−1.37388	+	0.169299i
$498$	3.14358	+	1.09999i	0.140867	+	0.0492916i
$499$	2.23668	−	0.877833i	0.100128	−	0.0392972i	−0.314748	−	0.949175i	$-0.601920\pi$
$499$	2.23668	−	0.877833i	0.100128	−	0.0392972i	0.414876	+	0.909878i	$0.363825\pi$
$500$	−14.9346	+	13.8634i	−0.667896	+	0.619988i
$501$	0.528111	−	1.34560i	0.0235942	−	0.0601171i
$502$	7.94975	+	15.0417i	0.354815	+	0.671342i
$503$	25.5268	+	2.87618i	1.13818	+	0.128242i	0.660876	−	0.750495i	$-0.270185\pi$
$503$	25.5268	+	2.87618i	1.13818	+	0.128242i	0.477306	+	0.878737i	$0.341613\pi$
$504$	−1.02198	−	2.52633i	−0.0455227	−	0.112532i
$505$	3.78711	+	1.82344i	0.168524	+	0.0811419i
$506$	−37.2086	+	25.3684i	−1.65412	+	1.12776i
$507$	0.969294	+	0.0362684i	0.0430479	+	0.00161074i
$508$	8.01853	−	29.9256i	0.355765	−	1.32773i
$509$	−17.4869	+	30.2883i	−0.775095	+	1.34250i	0.159646	+	0.987174i	$0.448965\pi$
$509$	−17.4869	+	30.2883i	−0.775095	+	1.34250i	−0.934741	+	0.355330i	$0.884369\pi$
$510$	−5.46391	−	1.91146i	−0.241946	−	0.0846407i
$511$	30.0339	+	20.0221i	1.32862	+	0.885724i
$512$	16.2514	+	25.8640i	0.718219	+	1.14304i
$513$	0.0287171	+	0.767481i	0.00126789	+	0.0338851i
$514$	−25.6811	−	3.87081i	−1.13275	−	0.170734i
$515$	17.6049	−	20.4603i	0.775764	−	0.901587i
$516$	−1.41000	+	1.51962i	−0.0620719	+	0.0668976i
$517$	−8.64922	+	5.43466i	−0.380392	+	0.239016i
$518$	−12.2023	+	2.44063i	−0.536139	+	0.107235i
$519$	0.227963	−	0.0520311i	0.0100065	−	0.00228391i
$520$	0.622563	−	2.01882i	0.0273012	−	0.0885311i
$521$	26.2881	−	15.1774i	1.15170	−	0.664936i	0.202401	−	0.979303i	$-0.435126\pi$
$521$	26.2881	−	15.1774i	1.15170	−	0.664936i	0.949301	+	0.314367i	$0.101792\pi$
$522$	0.394070	−	10.5318i	0.0172480	−	0.460962i
$523$	−7.55412	+	39.9245i	−0.330319	+	1.74578i	0.285953	+	0.958244i	$0.407690\pi$
$523$	−7.55412	+	39.9245i	−0.330319	+	1.74578i	−0.616272	+	0.787533i	$0.711358\pi$
$524$	4.16704	−	5.22531i	0.182038	−	0.228269i
$525$	−1.70222	−	1.54632i	−0.0742908	−	0.0674867i
$526$	2.26718	+	2.84295i	0.0988537	+	0.123959i
$527$	−9.63224	+	5.09079i	−0.419587	+	0.221758i
$528$	−1.57149	−	3.60189i	−0.0683903	−	0.156752i
$529$	3.58467	−	0.268634i	0.155855	−	0.0116797i
$530$	−0.196186	−	0.287707i	−0.00852178	−	0.0124972i
$531$	−4.47156	−	9.28528i	−0.194049	−	0.402947i
$532$	−0.436449	−	3.54184i	−0.0189225	−	0.153558i
$533$	9.31559	+	26.6224i	0.403503	+	1.15314i
$534$	−0.792187	−	0.0593662i	−0.0342813	−	0.00256903i
$535$	−5.23520	+	19.5437i	−0.226337	+	0.844948i
$536$	−3.91342	−	2.66813i	−0.169034	−	0.115246i
$537$	2.36967	+	1.74890i	0.102259	+	0.0754706i
$538$	−11.0791	+	11.0791i	−0.477653	+	0.477653i
$539$	−11.5141	−	34.7430i	−0.495948	−	1.49649i
$540$	2.24996	−	3.58137i	0.0968230	−	0.154118i
$541$	12.9639	−	1.95400i	0.557362	−	0.0840089i	0.135680	−	0.990753i	$-0.456678\pi$
$541$	12.9639	−	1.95400i	0.557362	−	0.0840089i	0.421682	+	0.906744i	$0.361440\pi$
$542$	4.06289	+	21.4729i	0.174516	+	0.922339i
$543$	0.0951368	+	0.0502813i	0.00408271	+	0.00215777i
$544$	4.41633	−	58.9318i	0.189349	−	2.52668i
$545$	−7.40864	+	32.4703i	−0.317351	+	1.39087i
$546$	−2.39372	−	0.520198i	−0.102442	−	0.0222624i
$547$	9.73350	−	27.8168i	0.416175	−	1.18936i	−0.524901	−	0.851163i	$-0.675898\pi$
$547$	9.73350	−	27.8168i	0.416175	−	1.18936i	0.941076	−	0.338195i	$-0.109816\pi$
$548$	−5.69401	+	13.0508i	−0.243236	+	0.557503i
$549$	−2.62501	−	35.0283i	−0.112033	−	1.49497i
$550$	38.7485	+	33.3360i	1.65224	+	1.42145i
$551$	−0.395934	+	1.28359i	−0.0168674	+	0.0546826i
$552$	0.0297385	−	0.263937i	0.00126576	−	0.0112339i
$553$	−1.42928	+	8.00945i	−0.0607793	+	0.340596i
$554$	−10.6886	−	8.52387i	−0.454115	−	0.362145i
$555$	0.685540	+	0.635996i	0.0290996	+	0.0269965i
$556$	9.51128	+	10.2507i	0.403368	+	0.434727i
$557$	−0.0623614	−	0.0167097i	−0.00264234	−	0.000708012i	0.257498	−	0.966279i	$-0.417102\pi$
$557$	−0.0623614	−	0.0167097i	−0.00264234	−	0.000708012i	−0.260140	+	0.965571i	$0.583769\pi$
$558$	−2.14962	−	8.02249i	−0.0910007	−	0.339619i
$559$	3.96588	+	17.3756i	0.167739	+	0.734911i
$560$	11.7137	−	22.7372i	0.494995	−	0.960821i
$561$	−1.54056	+	6.74963i	−0.0650424	+	0.284970i
$562$	−2.48826	+	0.0931042i	−0.104961	+	0.00392736i
$563$	−15.5333	+	11.4641i	−0.654652	+	0.483155i	−0.869786	−	0.493429i	$-0.835743\pi$
$563$	−15.5333	+	11.4641i	−0.654652	+	0.483155i	0.215134	+	0.976585i	$0.430981\pi$
$564$	−0.0922552	+	0.612073i	−0.00388464	+	0.0257729i
$565$	0.267098	+	0.996532i	0.0112369	+	0.0419244i
$566$	51.0677	+	11.6559i	2.14654	+	0.489933i
$567$	−20.5295	−	10.5783i	−0.862157	−	0.444245i
$568$	−2.15237	+	3.42548i	−0.0903114	+	0.143730i
$569$	15.0945	+	8.71479i	0.632793	+	0.365343i	0.781833	−	0.623488i	$-0.214285\pi$
$569$	15.0945	+	8.71479i	0.632793	+	0.365343i	−0.149040	+	0.988831i	$0.547618\pi$
$570$	−0.412271	+	0.382588i	−0.0172681	+	0.0160248i
$571$	−22.9472	+	21.2919i	−0.960311	+	0.891038i	−0.994108	−	0.108391i	$-0.965430\pi$
$571$	−22.9472	+	21.2919i	−0.960311	+	0.891038i	0.0337976	+	0.999429i	$0.489240\pi$
$572$	25.5073	+	4.82624i	1.06651	+	0.201795i
$573$	−0.0805459	−	0.714865i	−0.00336485	−	0.0298639i
$574$	8.53363	+	52.8764i	0.356187	+	2.20702i
$575$	7.27765	+	20.7886i	0.303499	+	0.866946i
$576$	18.5125	+	5.71036i	0.771356	+	0.237932i
$577$	15.7885	−	6.88846i	0.657284	−	0.286770i	−0.0446598	−	0.999002i	$-0.514220\pi$
$577$	15.7885	−	6.88846i	0.657284	−	0.286770i	0.701944	+	0.712232i	$0.252316\pi$
$578$	−52.3026	+	60.7767i	−2.17550	+	2.52798i
$579$	0.722295	+	1.84038i	0.0300176	+	0.0764835i
$580$	5.78317	−	4.61261i	0.240133	−	0.191528i
$581$	23.2395	−	11.4911i	0.964138	−	0.476730i
$582$	−2.12148	+	0.742337i	−0.0879380	+	0.0307708i
$583$	−0.315685	+	0.271669i	−0.0130743	+	0.0112514i
$584$	4.52169	−	1.39476i	0.187109	−	0.0577154i
$585$	−7.23497	−	16.5794i	−0.299129	−	0.685475i
$586$	−7.72398	−	51.2452i	−0.319075	−	2.11692i
$587$	−10.5987	−	10.5987i	−0.437454	−	0.437454i	0.453700	−	0.891154i	$-0.350104\pi$
$587$	−10.5987	−	10.5987i	−0.437454	−	0.437454i	−0.891154	+	0.453700i	$0.850104\pi$
$588$	−2.05087	−	0.844414i	−0.0845764	−	0.0348230i
$589$			1.05858i			0.0436179i
$590$	6.06591	−	13.9060i	0.249730	−	0.572500i
$591$	0.149029	−	0.218585i	0.00613022	−	0.00899139i
$592$	−4.85977	+	9.19514i	−0.199735	+	0.377918i
$593$	25.7811	+	29.9582i	1.05870	+	1.23023i	0.972242	+	0.233979i	$0.0751747\pi$
$593$	25.7811	+	29.9582i	1.05870	+	1.23023i	0.0864605	+	0.996255i	$0.472444\pi$
$594$	−9.55869	−	4.60322i	−0.392198	−	0.188872i
$595$	−40.3905	+	19.9752i	−1.65585	+	0.818904i
$596$	−29.4161	+	14.1661i	−1.20493	+	0.580264i
$597$	−2.23962	−	0.977137i	−0.0916616	−	0.0399915i
$598$	17.7830	+	15.3035i	0.727200	+	0.625807i
$599$	19.0795	+	7.48815i	0.779567	+	0.305958i	0.721554	−	0.692358i	$-0.243428\pi$
$599$	19.0795	+	7.48815i	0.779567	+	0.305958i	0.0580133	+	0.998316i	$0.481523\pi$
$600$	−0.298100	+	0.0449757i	−0.0121699	+	0.00183612i
$601$	7.62230	−	6.07859i	0.310920	−	0.247951i	−0.455580	−	0.890195i	$-0.650568\pi$
$601$	7.62230	−	6.07859i	0.310920	−	0.247951i	0.766500	+	0.642244i	$0.221997\pi$
$602$	1.61743	+	33.8056i	0.0659216	+	1.37781i
$603$	−40.3004	+	4.54076i	−1.64116	+	0.184914i
$604$	−16.6900	−	24.4798i	−0.679107	−	0.996067i
$605$	20.5798	−	30.1898i	0.836690	−	1.22739i
$606$	−0.319448	−	0.553300i	−0.0129767	−	0.0224763i
$607$	6.75234	−	1.80929i	0.274069	−	0.0734366i	−0.119167	−	0.992874i	$-0.538022\pi$
$607$	6.75234	−	1.80929i	0.274069	−	0.0734366i	0.393236	+	0.919438i	$0.371356\pi$
$608$	−4.86196	−	3.05497i	−0.197179	−	0.123896i
$609$	0.574173	+	0.606036i	0.0232667	+	0.0245578i
$610$	36.5620	−	36.5673i	1.48035	−	1.48057i
$611$	3.90107	+	3.61966i	0.157820	+	0.146436i
$612$	−24.4809	−	33.1705i	−0.989583	−	1.34084i
$613$	3.83701	+	5.19897i	0.154976	+	0.209984i	0.875206	−	0.483751i	$-0.160726\pi$
$613$	3.83701	+	5.19897i	0.154976	+	0.209984i	−0.720230	+	0.693735i	$0.755964\pi$
$614$	13.4790	+	12.5067i	0.543967	+	0.504728i
$615$	2.84582	−	2.84624i	0.114755	−	0.114771i
$616$	−4.48448	−	1.70638i	−0.180685	−	0.0687519i
$617$	12.3355	+	7.75089i	0.496607	+	0.312039i	0.756945	−	0.653479i	$-0.226691\pi$
$617$	12.3355	+	7.75089i	0.496607	+	0.312039i	−0.260338	+	0.965518i	$0.583834\pi$
$618$	−3.96298	+	1.06188i	−0.159414	+	0.0427150i
$619$	14.7913	+	25.6193i	0.594512	+	1.02973i	0.993616	+	0.112819i	$0.0359881\pi$
$619$	14.7913	+	25.6193i	0.594512	+	1.02973i	−0.399103	+	0.916906i	$0.630679\pi$
$620$	3.28358	−	4.81688i	0.131872	−	0.193451i
$621$	−2.57529	−	3.77725i	−0.103343	−	0.151576i
$622$	29.3916	−	3.31164i	1.17850	−	0.132785i
$623$	−4.64497	+	4.08223i	−0.186097	+	0.163551i
$624$	−1.60065	+	1.27647i	−0.0640772	+	0.0510999i
$625$	20.6519	−	14.0890i	0.826075	−	0.563560i
$626$	−12.8023	−	5.02453i	−0.511683	−	0.200821i
$627$	0.509875	+	0.438783i	0.0203625	+	0.0175233i
$628$	4.91623	+	2.14493i	0.196179	+	0.0855921i
$629$	16.5081	−	7.94990i	0.658222	−	0.316983i
$630$	−7.99438	−	33.4077i	−0.318504	−	1.33099i
$631$	−12.4101	−	5.97641i	−0.494040	−	0.237917i	0.170238	−	0.985403i	$-0.445546\pi$
$631$	−12.4101	−	5.97641i	−0.494040	−	0.237917i	−0.664278	+	0.747486i	$0.731261\pi$
$632$	0.695707	+	0.808426i	0.0276737	+	0.0321575i
$633$	1.02251	−	1.93469i	0.0406412	−	0.0768968i
$634$	−25.0126	+	36.6868i	−0.993379	+	1.45702i
$635$	−15.1971	+	34.8391i	−0.603080	+	1.38255i
$636$			0.0252375i			0.00100073i
$637$	−15.9309	+	10.4788i	−0.631203	+	0.415185i
$638$	−13.1209	−	13.1209i	−0.519461	−	0.519461i
$639$	5.16280	+	34.2530i	0.204237	+	1.35503i
$640$	−2.47175	−	5.66420i	−0.0977046	−	0.223897i
$641$	−2.80948	+	0.866611i	−0.110968	+	0.0342291i	−0.349742	−	0.936846i	$-0.613731\pi$
$641$	−2.80948	+	0.866611i	−0.110968	+	0.0342291i	0.238774	+	0.971075i	$0.423255\pi$
$642$	2.33107	−	2.00605i	0.0919999	−	0.0791723i
$643$	10.3554	−	3.62350i	0.408375	−	0.142897i	−0.118271	−	0.992981i	$-0.537735\pi$
$643$	10.3554	−	3.62350i	0.408375	−	0.142897i	0.526646	+	0.850085i	$0.323449\pi$
$644$	13.4165	+	16.4691i	0.528684	+	0.648974i
$645$	1.98830	−	1.58585i	0.0782892	−	0.0624429i
$646$	4.02620	+	10.2586i	0.158409	+	0.403619i
$647$	−11.1900	+	13.0030i	−0.439923	+	0.511200i	−0.933537	−	0.358481i	$-0.883295\pi$
$647$	−11.1900	+	13.0030i	−0.439923	+	0.511200i	0.493614	+	0.869681i	$0.335676\pi$
$648$	−2.77491	+	1.21068i	−0.109009	+	0.0475601i
$649$	−17.3390	−	5.34836i	−0.680614	−	0.209941i
$650$	11.5506	−	23.9940i	0.453051	−	0.941121i
$651$	0.573156	+	0.323004i	0.0224637	+	0.0126595i
$652$	0.825162	+	7.32352i	0.0323158	+	0.286811i
$653$	25.7592	+	4.87390i	1.00803	+	0.190730i	0.663606	−	0.748082i	$-0.269025\pi$
$653$	25.7592	+	4.87390i	1.00803	+	0.190730i	0.344428	+	0.938813i	$0.388073\pi$
$654$	3.71097	−	3.44328i	0.145111	−	0.134643i
$655$	−6.01031	+	5.57757i	−0.234842	+	0.217934i
$656$	38.7673	+	22.3823i	1.51361	+	0.873882i
$657$	21.5562	−	34.3065i	0.840987	−	1.33842i
$658$	6.08526	+	8.06810i	0.237228	+	0.314527i
$659$	13.1324	+	2.99738i	0.511565	+	0.116761i	0.470509	−	0.882395i	$-0.344070\pi$
$659$	13.1324	+	2.99738i	0.511565	+	0.116761i	0.0410567	+	0.999157i	$0.486928\pi$
$660$	−0.959051	−	3.57819i	−0.0373310	−	0.139281i
$661$	1.28273	−	8.51037i	0.0498925	−	0.331015i	−0.949935	−	0.312447i	$-0.898851\pi$
$661$	1.28273	−	8.51037i	0.0498925	−	0.331015i	0.999828	−	0.0185679i	$-0.00591067\pi$
$662$	9.67331	−	7.13923i	0.375964	−	0.277474i
$663$	3.60427	−	0.134862i	0.139978	−	0.00523762i
$664$	0.756262	−	3.31340i	0.0293486	−	0.128585i
$665$	−0.117840	+	4.37660i	−0.00456962	+	0.169717i
$666$	3.10818	+	13.6178i	0.120440	+	0.527680i
$667$	−2.06946	−	7.72333i	−0.0801298	−	0.299048i
$668$	14.6389	+	3.92249i	0.566398	+	0.151766i
$669$	−0.993625	−	1.07087i	−0.0384158	−	0.0414024i
$670$	−43.7676	−	40.6045i	−1.69089	−	1.56869i
$671$	−48.3529	−	38.5602i	−1.86664	−	1.48860i
$672$	−3.13762	+	1.70029i	−0.121036	+	0.0655903i
$673$	−2.53859	+	22.5306i	−0.0978554	+	0.868490i	0.844882	+	0.534953i	$0.179671\pi$
$673$	−2.53859	+	22.5306i	−0.0978554	+	0.868490i	−0.942737	+	0.333537i	$0.891758\pi$
$674$	16.6274	−	53.9047i	0.640463	−	2.07633i
$675$	−3.38412	+	3.93358i	−0.130255	+	0.151404i
$676$	0.759966	+	10.1410i	0.0292295	+	0.390040i
$677$	−12.0032	+	27.5115i	−0.461319	+	1.05735i	0.518064	+	0.855342i	$0.326653\pi$
$677$	−12.0032	+	27.5115i	−0.461319	+	1.05735i	−0.979383	+	0.202013i	$0.935252\pi$
$678$	0.0517946	−	0.148020i	0.00198916	−	0.00568469i
$679$	−7.42671	+	15.8414i	−0.285011	+	0.607939i
$680$	−1.31402	+	5.75902i	−0.0503903	+	0.220848i
$681$	−0.0790396	+	1.05471i	−0.00302880	+	0.0404166i
$682$	−12.9285	−	6.83292i	−0.495058	−	0.261646i
$683$	−3.60007	−	19.0268i	−0.137753	−	0.728042i	−0.981524	−	0.191339i	$-0.938717\pi$
$683$	−3.60007	−	19.0268i	−0.137753	−	0.728042i	0.843771	−	0.536703i	$-0.180330\pi$
$684$	−3.96094	+	0.597016i	−0.151450	+	0.0228275i
$685$	9.29301	−	14.7921i	0.355068	−	0.565178i
$686$	−33.2773	+	14.2749i	−1.27053	+	0.545017i
$687$	1.20064	−	1.20064i	0.0458072	−	0.0458072i
$688$	22.7590	+	16.7969i	0.867678	+	0.640376i
$689$	0.179275	+	0.122228i	0.00682984	+	0.00465651i
$690$	0.866274	−	3.23392i	0.0329785	−	0.123113i
$691$	−26.3229	−	1.97263i	−1.00137	−	0.0750422i	−0.436057	−	0.899919i	$-0.643625\pi$
$691$	−26.3229	−	1.97263i	−1.00137	−	0.0750422i	−0.565312	+	0.824877i	$0.691244\pi$
$692$	0.809678	+	2.31393i	0.0307793	+	0.0879623i
$693$	−38.6350	+	13.9720i	−1.46762	+	0.530754i
$694$	−21.4215	−	44.4822i	−0.813149	−	1.68852i
$695$	−9.66528	−	14.1741i	−0.366625	−	0.537656i
$696$	0.109135	−	0.00817854i	0.00413675	−	0.000310007i
$697$	−31.5367	−	72.2829i	−1.19454	−	2.73791i
$698$	−12.1923	+	6.44380i	−0.461484	+	0.243901i
$699$	1.06199	+	1.33169i	0.0401680	+	0.0503690i
$700$	14.1119	−	19.5495i	0.533380	−	0.738901i
$701$	−7.91984	+	9.93116i	−0.299128	+	0.375095i	−0.908568	−	0.417738i	$-0.862823\pi$
$701$	−7.91984	+	9.93116i	−0.299128	+	0.375095i	0.609440	+	0.792833i	$0.291395\pi$
$702$	−1.02756	+	5.43081i	−0.0387829	+	0.204973i
$703$	0.0665674	−	1.77905i	0.00251064	−	0.0670981i
$704$	29.5398	−	17.0548i	1.11332	−	0.642777i
$705$	0.223786	−	0.725685i	0.00842828	−	0.0273309i
$706$	−49.2281	+	11.2360i	−1.85272	+	0.422872i
$707$	−4.81700	−	1.23712i	−0.181162	−	0.0465267i
$708$	−0.930995	+	0.584983i	−0.0349889	+	0.0219850i
$709$	19.4023	−	20.9107i	0.728669	−	0.785318i	−0.254684	−	0.967024i	$-0.581972\pi$
$709$	19.4023	−	20.9107i	0.728669	−	0.785318i	0.983353	+	0.181706i	$0.0581620\pi$
$710$	−33.2597	+	38.6542i	−1.24822	+	1.45067i
$711$	9.03040	+	1.36111i	0.338666	+	0.0510457i
$712$	0.0303115	+	0.810093i	0.00113597	+	0.0303595i
$713$	−3.35243	−	5.33536i	−0.125549	−	0.199811i
$714$	6.78293	+	0.950266i	0.253845	+	0.0355628i
$715$	−30.0625	−	10.5169i	−1.12427	−	0.393308i
$716$	−15.4390	+	26.7411i	−0.576983	+	0.999364i
$717$	−0.00412047	+	0.0153778i	−0.000153882	+	0.000574294i
$718$	47.0396	+	1.76010i	1.75550	+	0.0656862i
$719$	−30.6152	+	20.8731i	−1.14175	+	0.778435i	−0.978111	−	0.208085i	$-0.933277\pi$
$719$	−30.6152	+	20.8731i	−1.14175	+	0.778435i	−0.163643	+	0.986520i	$0.552325\pi$
$720$	−25.8674	−	12.4547i	−0.964019	−	0.464161i
$721$	−15.6798	+	27.8230i	−0.583946	+	1.03618i
$722$	−35.8502	−	4.03935i	−1.33421	−	0.150329i
$723$	−1.03034	−	1.94951i	−0.0383189	−	0.0725029i
$724$	−0.412171	+	1.05019i	−0.0153182	+	0.0390302i
$725$	−7.85896	+	4.53889i	−0.291874	+	0.168570i
$726$	−5.16977	+	2.02898i	−0.191868	+	0.0753027i
$727$	−21.1386	−	7.39670i	−0.783986	−	0.274329i	−0.0915430	−	0.995801i	$-0.529180\pi$
$727$	−21.1386	−	7.39670i	−0.783986	−	0.274329i	−0.692443	+	0.721473i	$0.743466\pi$
$728$	−0.254008	+	2.48676i	−0.00941416	+	0.0921655i
$729$	−11.0127	+	22.8682i	−0.407879	+	0.846969i
$730$	58.9782	−	8.89392i	2.18288	−	0.329179i
$731$	−14.6884	−	47.6186i	−0.543270	−	1.76124i
$732$	−3.68229	+	0.696727i	−0.136101	+	0.0257518i
$733$	7.77683	−	10.5372i	0.287244	−	0.389201i	−0.637088	−	0.770791i	$-0.719861\pi$
$733$	7.77683	−	10.5372i	0.287244	−	0.389201i	0.924332	+	0.381589i	$0.124623\pi$
$734$	18.5196			0.683572
$735$	2.33371	+	1.39924i	0.0860802	+	0.0516117i
$736$	34.1798			1.25988
$737$	−42.4011	+	57.4515i	−1.56187	+	2.11625i
$738$	59.0721	−	11.1770i	2.17448	−	0.411433i
$739$	−5.74514	−	18.6253i	−0.211338	−	0.685142i	−0.997725	−	0.0674082i	$-0.978527\pi$
$739$	−5.74514	−	18.6253i	−0.211338	−	0.685142i	0.786387	−	0.617734i	$-0.211949\pi$
$740$	−5.82131	+	7.88879i	−0.213996	+	0.289998i
$741$	0.152054	−	0.315744i	0.00558585	−	0.0115991i
$742$	0.294367	+	0.288302i	0.0108066	+	0.0105839i
$743$	2.94354	+	1.02999i	0.107988	+	0.0377867i	0.383732	−	0.923444i	$-0.374639\pi$
$743$	2.94354	+	1.02999i	0.107988	+	0.0377867i	−0.275744	+	0.961231i	$0.588924\pi$
$744$	0.0802846	−	0.0315094i	0.00294337	−	0.00115519i
$745$	38.2756	−	11.8095i	1.40231	−	0.432667i
$746$	16.7781	−	42.7499i	0.614289	−	1.56518i
$747$	−13.5977	−	25.7281i	−0.497514	−	0.941342i
$748$	−72.1286	−	8.12694i	−2.63728	−	0.297150i
$749$	1.54044	−	23.8901i	0.0562864	−	0.872925i
$750$	−3.80003		0.000829170i	−0.138757		3.02770e-5i
$751$	9.05136	−	6.17111i	0.330289	−	0.225187i	−0.386809	−	0.922160i	$-0.626423\pi$
$751$	9.05136	−	6.17111i	0.330289	−	0.225187i	0.717097	+	0.696973i	$0.245470\pi$
$752$	8.44016	+	0.315809i	0.307781	+	0.0115164i
$753$	−0.391522	+	1.46118i	−0.0142679	+	0.0532484i
$754$	−4.83351	+	8.37188i	−0.176026	+	0.304886i
$755$	15.7737	+	32.7483i	0.574064	+	1.19183i
$756$	−1.77972	+	4.67724i	−0.0647280	+	0.170110i
$757$	10.7935	+	17.1778i	0.392297	+	0.624338i	0.983227	−	0.182385i	$-0.0583818\pi$
$757$	10.7935	+	17.1778i	0.392297	+	0.624338i	−0.590930	+	0.806723i	$0.701239\pi$
$758$	1.11798	+	29.8786i	0.0406068	+	1.08524i
$759$	−3.95943	−	0.596788i	−0.143718	−	0.0216620i
$760$	0.435063	+	0.374347i	0.0157814	+	0.0135790i
$761$	33.4824	−	36.0854i	1.21373	−	1.30810i	0.275828	−	0.961207i	$-0.411048\pi$
$761$	33.4824	−	36.0854i	1.21373	−	1.30810i	0.937906	−	0.346888i	$-0.112762\pi$
$762$	4.89193	−	3.07381i	0.177216	−	0.111352i
$763$	1.06350	−	39.3923i	0.0385014	−	1.42610i
$764$	7.35318	−	1.67832i	0.266029	−	0.0607193i
$765$	23.6370	+	44.7155i	0.854597	+	1.61669i
$766$	31.4896	−	18.1805i	1.13777	−	0.656890i
$767$	−0.353462	+	9.44647i	−0.0127628	+	0.341092i
$768$	−0.596305	+	3.15155i	−0.0215173	+	0.113722i
$769$	−3.02075	+	3.78791i	−0.108931	+	0.136595i	−0.833308	−	0.552809i	$-0.813556\pi$
$769$	−3.02075	+	3.78791i	−0.108931	+	0.136595i	0.724377	+	0.689404i	$0.242127\pi$
$770$	−52.6913	−	29.6894i	−1.89886	−	1.06993i
$771$	−1.43977	−	1.80542i	−0.0518522	−	0.0650206i
$772$	−18.3259	+	9.68551i	−0.659563	+	0.348589i
$773$	−11.4355	−	26.2105i	−0.411307	−	0.942725i	−0.991722	−	0.128404i	$-0.959014\pi$
$773$	−11.4355	−	26.2105i	−0.411307	−	0.942725i	0.580415	−	0.814321i	$-0.302890\pi$
$774$	37.8830	−	2.83894i	1.36167	−	0.102043i
$775$	−4.86388	+	5.24355i	−0.174716	+	0.188354i
$776$	0.995149	+	2.06645i	0.0357238	+	0.0741811i
$777$	−0.942937	−	0.578885i	−0.0338277	−	0.0207674i
$778$	−25.1226	−	71.7961i	−0.900687	−	2.57402i
$779$	−7.64120	−	0.572629i	−0.273774	−	0.0205165i
$780$	−1.67130	+	0.965087i	−0.0598421	+	0.0345557i
$781$	50.3913	+	34.3562i	1.80314	+	1.22936i
$782$	−52.7807	−	38.9539i	−1.88743	−	1.39299i
$783$	1.33198	−	1.33198i	0.0476009	−	0.0476009i
$784$	−8.31635	+	29.0982i	−0.297012	+	1.03922i
$785$	−5.57218	−	3.50067i	−0.198880	−	0.124944i
$786$	1.23243	−	0.185758i	0.0439592	−	0.00662578i
$787$	0.644769	+	3.40768i	0.0229835	+	0.121471i	0.992179	−	0.124821i	$-0.0398356\pi$
$787$	0.644769	+	3.40768i	0.0229835	+	0.121471i	−0.969196	+	0.246291i	$0.920788\pi$
$788$	2.45224	+	1.29605i	0.0873575	+	0.0461698i
$789$	−0.0241616	+	0.322414i	−0.000860175	+	0.0114782i
$790$	7.15341	+	11.3828i	0.254507	+	0.404980i
$791$	−0.541075	−	1.09427i	−0.0192384	−	0.0389077i
$792$	−1.77881	+	5.08355i	−0.0632074	+	0.180636i
$793$	−12.8845	+	29.5315i	−0.457541	+	1.04869i
$794$	−3.38175	−	45.1263i	−0.120014	−	1.60147i
$795$	0.00461254	−	0.0306173i	0.000163590	−	0.00108588i
$796$	7.55116	−	24.4802i	0.267644	−	0.867679i
$797$	1.60592	−	14.2530i	0.0568847	−	0.504866i	−0.932672	−	0.360724i	$-0.882529\pi$
$797$	1.60592	−	14.2530i	0.0568847	−	0.504866i	0.989557	−	0.144141i	$-0.0460419\pi$
$798$	0.389587	−	0.539536i	0.0137912	−	0.0190994i
$799$	−11.6334	−	9.27733i	−0.411560	−	0.328208i
$800$	−10.0464	−	37.4719i	−0.355194	−	1.32483i
$801$	4.72123	+	5.08828i	0.166816	+	0.179785i
$802$	51.4495	+	13.7858i	1.81674	+	0.486795i
$803$	−18.4631	−	68.9052i	−0.651548	−	2.43161i
$804$	0.962808	+	4.21834i	0.0339556	+	0.148769i
$805$	−13.2664	−	22.4318i	−0.467580	−	0.790618i
$806$	−1.69521	+	7.42722i	−0.0597114	+	0.261613i
$807$	−1.39216	+	0.0520908i	−0.0490062	+	0.00183368i
$808$	−0.524570	+	0.387151i	−0.0184543	+	0.0136199i
$809$	4.61287	−	30.6044i	0.162180	−	1.07599i	−0.748577	−	0.663048i	$-0.769262\pi$
$809$	4.61287	−	30.6044i	0.162180	−	1.07599i	0.910756	−	0.412944i	$-0.135500\pi$
$810$	−36.8605	+	9.87960i	−1.29514	+	0.347134i
$811$	−38.6812	−	8.82873i	−1.35828	−	0.310019i	−0.519491	−	0.854476i	$-0.673879\pi$
$811$	−38.6812	−	8.82873i	−1.35828	−	0.310019i	−0.838789	+	0.544457i	$0.816736\pi$
$812$	−5.63991	+	6.69336i	−0.197922	+	0.234891i
$813$	−1.03381	+	1.64529i	−0.0362572	+	0.0577029i
$814$	21.2980	+	12.2964i	0.746496	+	0.430990i
$815$	0.337424	−	9.03544i	0.0118195	−	0.316498i
$816$	4.19625	−	3.89355i	0.146898	−	0.136302i
$817$	−4.75750	−	0.900167i	−0.166444	−	0.0314929i
$818$	4.28442	+	38.0253i	0.149801	+	1.32952i
$819$	12.2405	+	17.5580i	0.427716	+	0.613525i
$820$	32.9938	+	26.3077i	1.15219	+	0.918706i
$821$	21.4591	+	6.61926i	0.748928	+	0.231014i	0.645644	−	0.763638i	$-0.276589\pi$
$821$	21.4591	+	6.61926i	0.748928	+	0.231014i	0.103284	+	0.994652i	$0.467065\pi$
$822$	−2.43376	+	1.06184i	−0.0848871	+	0.0370359i
$823$	17.7791	−	20.6597i	0.619741	−	0.720152i	−0.357112	−	0.934061i	$-0.616239\pi$
$823$	17.7791	−	20.6597i	0.619741	−	0.720152i	0.976854	+	0.213909i	$0.0686196\pi$
$824$	1.52958	+	3.89730i	0.0532854	+	0.135769i
$825$	0.509520	+	4.51621i	0.0177392	+	0.157234i
$826$	−3.81211	+	17.5416i	−0.132640	+	0.610350i
$827$	35.7139	−	12.4968i	1.24189	−	0.434557i	0.372202	−	0.928152i	$-0.378603\pi$
$827$	35.7139	−	12.4968i	1.24189	−	0.434557i	0.869692	+	0.493594i	$0.164317\pi$
$828$	18.0730	−	15.5530i	0.628078	−	0.540505i
$829$	−28.6796	+	8.84648i	−0.996083	+	0.307251i	−0.749596	−	0.661895i	$-0.769752\pi$
$829$	−28.6796	+	8.84648i	−0.996083	+	0.307251i	−0.246487	+	0.969146i	$0.579276\pi$
$830$	15.6479	−	39.8788i	0.543148	−	1.38421i
$831$	−0.181172	−	1.20199i	−0.00628477	−	0.0416967i
$832$	−12.5654	−	12.5654i	−0.435626	−	0.435626i
$833$	42.2293	−	32.5460i	1.46316	−	1.12765i
$834$			2.60771i			0.0902977i
$835$	−17.0426	−	7.43411i	−0.589782	−	0.257268i
$836$	−3.97288	+	5.82715i	−0.137405	+	0.201536i
$837$	0.693648	−	1.31245i	0.0239760	−	0.0453648i
$838$	31.5187	+	36.6254i	1.08880	+	1.26520i
$839$	−10.1308	−	4.87875i	−0.349755	−	0.168433i	0.250755	−	0.968051i	$-0.419321\pi$
$839$	−10.1308	−	4.87875i	−0.349755	−	0.168433i	−0.600510	+	0.799618i	$0.705036\pi$
$840$	0.335438	−	0.121336i	0.0115737	−	0.00418648i
$841$	−23.1598	+	11.1532i	−0.798613	+	0.384592i
$842$	12.7560	+	5.56539i	0.439601	+	0.191796i
$843$	−0.167813	−	0.144415i	−0.00577979	−	0.00497391i
$844$	21.3566	+	8.38184i	0.735124	+	0.288515i
$845$	0.931463	−	12.4417i	0.0320433	−	0.428006i
$846$	8.86857	−	7.07245i	0.304908	−	0.243156i
$847$	−16.8744	+	39.8019i	−0.579813	+	1.36761i
$848$	0.342201	−	0.0385568i	0.0117512	−	0.00132404i
$849$	2.62363	+	3.84815i	0.0900426	+	0.132068i
$850$	−27.1922	+	69.3141i	−0.932683	+	2.37746i
$851$	5.29860	+	9.17745i	0.181634	+	0.314599i
$852$	3.56977	−	0.956517i	0.122298	−	0.0327697i
$853$	−19.6741	−	12.3621i	−0.673630	−	0.423270i	0.151313	−	0.988486i	$-0.451650\pi$
$853$	−19.6741	−	12.3621i	−0.673630	−	0.423270i	−0.824943	+	0.565216i	$0.808793\pi$
$854$	−33.9383	+	50.9088i	−1.16134	+	1.74206i
$855$	4.91439		0.000357441i	0.168069		1.22242e-5i
$856$	−2.30055	−	2.13460i	−0.0786311	−	0.0729590i
$857$	10.8619	+	14.7174i	0.371037	+	0.502737i	0.949843	−	0.312729i	$-0.101243\pi$
$857$	10.8619	+	14.7174i	0.371037	+	0.502737i	−0.578806	+	0.815465i	$0.696481\pi$
$858$	2.87473	+	3.89512i	0.0981417	+	0.132977i
$859$	11.8580	+	11.0026i	0.404590	+	0.375405i	0.856056	−	0.516884i	$-0.172908\pi$
$859$	11.8580	+	11.0026i	0.404590	+	0.375405i	−0.451465	+	0.892289i	$0.649099\pi$
$860$	18.8560	+	18.8533i	0.642985	+	0.642891i
$861$	−2.64161	+	3.96252i	−0.0900258	+	0.135042i
$862$	−6.40966	−	4.02746i	−0.218314	−	0.137176i
$863$	−1.04007	+	0.278686i	−0.0354044	+	0.00948657i	−0.276478	−	0.961020i	$-0.589167\pi$
$863$	−1.04007	+	0.278686i	−0.0354044	+	0.00948657i	0.241073	+	0.970507i	$0.422501\pi$
$864$	4.02615	+	6.97350i	0.136972	+	0.237243i
$865$	−0.559368	−	2.95516i	−0.0190191	−	0.100478i
$866$	13.7223	+	20.1270i	0.466304	+	0.683943i
$867$	−7.08464	+	0.798247i	−0.240607	+	0.0271099i
$868$	−2.69237	+	6.35052i	−0.0913851	+	0.215551i
$869$	12.5711	−	10.0251i	0.426444	−	0.340078i
$870$	1.37564	+	0.102989i	0.0466385	+	0.00349166i
$871$	34.6280	+	13.5905i	1.17332	+	0.460496i
$872$	−3.91562	−	3.36967i	−0.132600	−	0.114111i
$873$	18.0001	+	7.85335i	0.609210	+	0.265795i
$874$	−5.74262	+	2.76550i	−0.194247	+	0.0935444i
$875$	−20.6930	+	21.1376i	−0.699553	+	0.714581i
$876$	−3.89461	−	1.87555i	−0.131587	−	0.0633688i
$877$	3.01861	+	3.50769i	0.101931	+	0.118446i	0.806620	−	0.591070i	$-0.201294\pi$
$877$	3.01861	+	3.50769i	0.101931	+	0.118446i	−0.704689	+	0.709516i	$0.748913\pi$
$878$	−19.6807	+	37.2376i	−0.664190	+	1.25671i
$879$	2.59573	−	3.80724i	0.0875518	−	0.128415i
$880$	−47.0521	+	18.4706i	−1.58613	+	0.622642i
$881$			52.6547i			1.77398i	0.461785	+	0.886992i	$0.347209\pi$
$881$			52.6547i			1.77398i	−0.461785	+	0.886992i	$0.652791\pi$
$882$	17.0254	+	36.9068i	0.573274	+	1.24272i
$883$	20.9566	+	20.9566i	0.705247	+	0.705247i	0.965532	−	0.260285i	$-0.0838165\pi$
$883$	20.9566	+	20.9566i	0.705247	+	0.705247i	−0.260285	+	0.965532i	$0.583816\pi$
$884$	5.63599	+	37.3924i	0.189559	+	1.25764i
$885$	1.23637	−	0.539528i	0.0415600	−	0.0181360i
$886$	−25.3823	+	7.82940i	−0.852735	+	0.263034i
$887$	−34.0201	+	29.2766i	−1.14228	+	0.983013i	−0.999977	−	0.00680959i	$-0.997832\pi$
$887$	−34.0201	+	29.2766i	−1.14228	+	0.983013i	−0.142305	+	0.989823i	$0.545451\pi$
$888$	−0.136908	+	0.0479062i	−0.00459433	+	0.00160763i
$889$	9.55061	−	43.9476i	0.320317	−	1.47396i
$890$	−1.14334	+	10.1541i	−0.0383249	+	0.340366i
$891$	16.6747	+	42.4864i	0.558623	+	1.42335i
$892$	9.99038	−	11.6090i	0.334503	−	0.388699i
$893$	−1.32513	+	0.578149i	−0.0443439	+	0.0193470i
$894$	−5.81807	−	1.79464i	−0.194586	−	0.0600217i
$895$	23.6174	−	29.6197i	0.789443	−	0.990078i
$896$	4.18183	+	5.99851i	0.139705	+	0.200396i
$897$	0.233563	+	2.07293i	0.00779846	+	0.0692132i
$898$	−36.7278	−	6.94927i	−1.22562	−	0.231900i
$899$	1.90326	−	1.76596i	0.0634772	−	0.0588982i
$900$	−22.3632	−	15.2422i	−0.745441	−	0.508075i
$901$	−0.525400	−	0.303340i	−0.0175036	−	0.0101057i
$902$	56.3161	−	89.6265i	1.87512	−	2.98424i
$903$	−1.93905	+	2.30123i	−0.0645274	+	0.0765802i
$904$	−0.156016	−	0.0356097i	−0.00518903	−	0.00118436i
$905$	0.691970	−	1.19873i	0.0230019	−	0.0398471i
$906$	0.823476	−	5.46341i	0.0273582	−	0.181510i
$907$	−2.82886	+	2.08780i	−0.0939309	+	0.0693241i	−0.639773	−	0.768564i	$-0.720972\pi$
$907$	−2.82886	+	2.08780i	−0.0939309	+	0.0693241i	0.545842	+	0.837888i	$0.316210\pi$
$908$	−11.0811	+	0.414627i	−0.367741	+	0.0137599i
$909$	−1.24220	+	5.44245i	−0.0412013	+	0.180515i
$910$	−7.83552	+	30.5185i	−0.259745	+	1.01168i
$911$	−8.30776	−	36.3987i	−0.275248	−	1.20594i	−0.903725	−	0.428113i	$-0.859178\pi$
$911$	−8.30776	−	36.3987i	−0.275248	−	1.20594i	0.628477	−	0.777828i	$-0.283679\pi$
$912$	−0.143955	−	0.537248i	−0.00476683	−	0.0177901i
$913$	−49.4899	−	13.2608i	−1.63788	−	0.438867i
$914$	−15.4345	−	16.6345i	−0.510529	−	0.550219i
$915$	4.59456	−	0.172251i	0.151891	−	0.00569444i
$916$	13.9181	+	11.0993i	0.459867	+	0.366732i
$917$	5.67961	−	7.86565i	0.187557	−	0.259747i
$918$	1.73032	−	15.3570i	0.0571092	−	0.506858i
$919$	7.96372	−	25.8177i	0.262699	−	0.851649i	−0.724100	−	0.689695i	$-0.757744\pi$
$919$	7.96372	−	25.8177i	0.262699	−	0.851649i	0.986798	−	0.161953i	$-0.0517794\pi$
$920$	−3.37830	−	0.508946i	−0.111379	−	0.0167794i
$921$	0.122177	+	1.63034i	0.00402588	+	0.0537216i
$922$	−15.3050	+	35.0795i	−0.504044	+	1.15528i
$923$	10.4941	−	29.9904i	0.345418	−	0.987147i
$924$	1.94280	+	3.92912i	0.0639135	+	0.129259i
$925$	8.50400	−	8.50647i	0.279610	−	0.279691i
$926$	−4.59821	+	61.3589i	−0.151107	+	2.01638i
$927$	31.6942	+	16.7509i	1.04097	+	0.550170i
$928$	2.61828	+	13.8380i	0.0859493	+	0.454253i
$929$	9.98896	−	1.50559i	0.327727	−	0.0493969i	0.0168819	−	0.999857i	$-0.494626\pi$
$929$	9.98896	−	1.50559i	0.327727	−	0.0493969i	0.310845	+	0.950461i	$0.399388\pi$
$930$	1.05985	−	0.241985i	0.0347538	−	0.00793500i
$931$	−0.878553	−	5.10530i	−0.0287934	−	0.167320i
$932$	−12.6274	+	12.6274i	−0.413624	+	0.413624i
$933$	2.11599	+	1.56168i	0.0692746	+	0.0511269i
$934$	−43.6369	−	29.7511i	−1.42784	−	0.973487i
$935$	86.0185	+	23.0419i	2.81311	+	0.753550i
$936$	2.79800	+	0.209681i	0.0914554	+	0.00685363i
$937$	2.62149	+	7.49179i	0.0856404	+	0.244746i	0.978737	−	0.205118i	$-0.0657580\pi$
$937$	2.62149	+	7.49179i	0.0856404	+	0.244746i	−0.893097	+	0.449865i	$0.851472\pi$
$938$	60.2009	+	36.9583i	1.96563	+	1.20673i
$939$	−0.530571	−	1.10174i	−0.0173145	−	0.0359540i
$940$	7.82315	+	1.47963i	0.255163	+	0.0482602i
$941$	36.9782	−	2.77113i	1.20545	−	0.0903363i	0.543192	−	0.839608i	$-0.317216\pi$
$941$	36.9782	−	2.77113i	1.20545	−	0.0903363i	0.662262	+	0.749272i	$0.269596\pi$
$942$	0.399994	+	0.916796i	0.0130325	+	0.0298708i
$943$	40.3261	−	21.3129i	1.31320	−	0.694045i
$944$	9.35423	+	11.7298i	0.304454	+	0.381774i
$945$	3.01393	−	5.34899i	0.0980433	−	0.174003i
$946$	41.7026	−	52.2934i	1.35587	−	1.70021i
$947$	3.64538	−	19.2663i	0.118459	−	0.626071i	−0.872138	−	0.489260i	$-0.837267\pi$
$947$	3.64538	−	19.2663i	0.118459	−	0.626071i	0.990597	−	0.136811i	$-0.0436854\pi$
$948$	0.0364313	−	0.973647i	0.00118323	−	0.0316226i
$949$	−32.1849	+	18.5820i	−1.04477	+	0.603197i
$950$	4.71979	+	5.48288i	0.153130	+	0.177888i
$951$	−3.84902	+	0.878513i	−0.124813	+	0.0284877i
$952$	0.188626	−	6.98674i	0.00611339	−	0.226441i
$953$	−28.2465	+	17.7485i	−0.914994	+	0.574929i	−0.905183	−	0.425023i	$-0.860266\pi$
$953$	−28.2465	+	17.7485i	−0.914994	+	0.574929i	−0.00981169	+	0.999952i	$0.503123\pi$
$954$	0.314576	−	0.339032i	0.0101848	−	0.0109766i
$955$	−9.22736	+	0.692170i	−0.298590	+	0.0223981i
$956$	−0.165049	−	0.0248771i	−0.00533805	−	0.000804582i
$957$	−0.0616908	−	1.64872i	−0.00199418	−	0.0532956i
$958$	−27.6126	−	43.9452i	−0.892123	−	1.41981i
$959$	−7.35079	+	19.3184i	−0.237369	+	0.623823i
$960$	−0.837349	+	2.39356i	−0.0270253	+	0.0772520i
$961$	−14.4770	+	25.0748i	−0.466999	+	0.808865i
$962$	3.31604	−	12.3756i	0.106913	−	0.399006i
$963$	−26.8528	−	1.00476i	−0.865321	−	0.0323780i
$964$	19.1012	−	13.0230i	0.615208	−	0.419442i
$965$	24.0025	−	8.40079i	0.772667	−	0.270431i
$966$	−0.254898	+	3.95312i	−0.00820121	+	0.127190i
$967$	39.4095	+	4.44038i	1.26732	+	0.142793i	0.719909	−	0.694069i	$-0.244184\pi$
$967$	39.4095	+	4.44038i	1.26732	+	0.142793i	0.547414	+	0.836862i	$0.315612\pi$
$968$	2.64814	+	5.01053i	0.0851146	+	0.161045i
$969$	−0.357988	+	0.912138i	−0.0115002	+	0.0293021i
$970$	8.52347	+	27.6253i	0.273672	+	0.886994i
$971$	25.1232	−	9.86014i	0.806243	−	0.316427i	0.0738151	−	0.997272i	$-0.476483\pi$
$971$	25.1232	−	9.86014i	0.806243	−	0.316427i	0.732427	+	0.680845i	$0.238387\pi$
$972$	7.96652	+	2.78761i	0.255526	+	0.0894125i
$973$	14.5023	+	14.2035i	0.464921	+	0.455342i
$974$	1.69045	−	3.51026i	0.0541656	−	0.112476i
$975$	2.20394	−	0.865355i	0.0705827	−	0.0277135i
$976$	15.0727	+	48.8645i	0.482465	+	1.56411i
$977$	7.07448	−	1.33856i	0.226333	−	0.0428244i	−0.0715081	−	0.997440i	$-0.522781\pi$
$977$	7.07448	−	1.33856i	0.226333	−	0.0428244i	0.297841	+	0.954616i	$0.403734\pi$
$978$	−0.816120	+	1.10580i	−0.0260966	+	0.0353597i
$979$	12.2211			0.390588
$980$	−11.8383	+	25.9560i	−0.378162	+	0.829134i
$981$	−44.2329			−1.41225
$982$	4.63039	−	6.27395i	0.147762	−	0.200210i
$983$	−16.5027	+	3.12248i	−0.526354	+	0.0995915i	−0.442296	−	0.896869i	$-0.645836\pi$
$983$	−16.5027	+	3.12248i	−0.526354	+	0.0995915i	−0.0840582	+	0.996461i	$0.526788\pi$
$984$	0.184017	+	0.596568i	0.00586624	+	0.0190179i
$985$	−2.73810	−	2.02050i	−0.0872432	−	0.0643786i
$986$	11.7276	−	24.3527i	0.373484	−	0.775547i
$987$	−0.0913056	+	0.893891i	−0.00290629	+	0.0284529i
$988$	3.46803	+	1.21352i	0.110333	+	0.0386071i
$989$	26.8291	−	10.5297i	0.853117	−	0.334824i
$990$	−31.7171	+	60.0223i	−1.00804	+	1.90763i
$991$	−15.3233	+	39.0430i	−0.486760	+	1.24024i	0.450864	+	0.892592i	$0.351116\pi$
$991$	−15.3233	+	39.0430i	−0.486760	+	1.24024i	−0.937624	+	0.347651i	$0.886979\pi$
$992$	5.18606	+	9.81251i	0.164658	+	0.311547i
$993$	1.06226	+	0.119688i	0.0337097	+	0.00379817i
$994$	29.6228	−	52.5642i	0.939577	−	1.66723i
$995$	−13.6349	+	28.3185i	−0.432256	+	0.897756i
$996$	−2.56522	+	1.74894i	−0.0812821	+	0.0554172i
$997$	−4.38660	−	0.164135i	−0.138925	−	0.00519821i	−0.0321618	−	0.999483i	$-0.510239\pi$
$997$	−4.38660	−	0.164135i	−0.138925	−	0.00519821i	−0.106763	+	0.994284i	$0.534049\pi$
$998$	−1.21588	+	4.53771i	−0.0384879	+	0.143639i
$999$	−1.24828	+	2.16209i	−0.0394939	+	0.0684054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.x.a.103.7	✓	624
5.2	odd	4	inner	245.2.x.a.152.7	yes	624
49.10	odd	42	inner	245.2.x.a.108.7	yes	624
245.157	even	84	inner	245.2.x.a.157.7	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.7	✓	624	1.1	even	1	trivial
245.2.x.a.108.7	yes	624	49.10	odd	42	inner
245.2.x.a.152.7	yes	624	5.2	odd	4	inner
245.2.x.a.157.7	yes	624	245.157	even	84	inner

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16101 + 1.57311i) q^{2} +(-0.170810 + 0.0323191i) q^{3} +(-0.537222 - 1.74163i) q^{4} +(0.333429 + 2.21107i) q^{5} +(0.147471 - 0.306226i) q^{6} +(-0.899782 - 2.48805i) q^{7} +(-0.327375 - 0.114553i) q^{8} +(-2.76449 + 1.08498i) q^{9} +(-3.86536 - 2.04254i) q^{10} +(-1.91028 + 4.86731i) q^{11} +(0.148051 + 0.280126i) q^{12} +(2.70690 + 0.304995i) q^{13} +(4.95862 + 1.47319i) q^{14} +(-0.128413 - 0.366898i) q^{15} +(3.57210 - 2.43542i) q^{16} +(-7.61120 - 0.284791i) q^{17} +(1.50280 - 5.60851i) q^{18} +(-0.370025 + 0.640901i) q^{19} +(3.67174 - 1.76854i) q^{20} +(0.234104 + 0.395905i) q^{21} +(-5.43896 - 8.65605i) q^{22} +(-0.164714 - 4.40206i) q^{23} +(0.0596213 + 0.00898646i) q^{24} +(-4.77765 + 1.47447i) q^{25} +(-3.62252 + 3.90415i) q^{26} +(0.878725 - 0.552139i) q^{27} +(-3.84988 + 2.90372i) q^{28} +(1.76959 - 0.403898i) q^{29} +(0.726257 + 0.223963i) q^{30} +(1.23878 - 0.715207i) q^{31} +(-0.290121 + 7.75364i) q^{32} +(0.168988 - 0.893126i) q^{33} +(9.28465 - 11.6426i) q^{34} +(5.20124 - 2.81907i) q^{35} +(3.37478 + 4.23184i) q^{36} +(-2.12687 + 1.12408i) q^{37} +(-0.578606 - 1.32618i) q^{38} +(-0.472225 + 0.0353883i) q^{39} +(0.144129 - 0.762044i) q^{40} +(4.49252 + 9.32882i) q^{41} +(-0.894597 - 0.0913777i) q^{42} +(2.16091 + 6.17553i) q^{43} +(9.50329 + 0.712173i) q^{44} +(-3.32073 - 5.75071i) q^{45} +(7.11615 + 4.85171i) q^{46} +(1.57187 + 1.16009i) q^{47} +(-0.531441 + 0.531441i) q^{48} +(-5.38078 + 4.47741i) q^{49} +(3.22738 - 9.22763i) q^{50} +(1.30928 - 0.197342i) q^{51} +(-0.923019 - 4.87827i) q^{52} +(0.0704225 + 0.0372194i) q^{53} +(-0.151630 + 2.02337i) q^{54} +(-11.3989 - 2.60085i) q^{55} +(0.00955142 + 0.917598i) q^{56} +(0.0424907 - 0.121431i) q^{57} +(-1.41913 + 3.25269i) q^{58} +(0.259332 + 3.46055i) q^{59} +(-0.570013 + 0.420753i) q^{60} +(-3.48636 + 11.3025i) q^{61} +(-0.313128 + 2.77909i) q^{62} +(5.18693 + 5.90194i) q^{63} +(-5.10025 - 4.06731i) q^{64} +(0.228197 + 6.08685i) q^{65} +(1.20879 + 1.30276i) q^{66} +(13.1907 + 3.53444i) q^{67} +(3.59290 + 13.4089i) q^{68} +(0.170405 + 0.746595i) q^{69} +(-1.60397 + 11.4551i) q^{70} +(2.59551 - 11.3717i) q^{71} +(1.02931 - 0.0385142i) q^{72} +(-10.9771 + 8.10149i) q^{73} +(0.701004 - 4.65086i) q^{74} +(0.768419 - 0.406264i) q^{75} +(1.31500 + 0.300140i) q^{76} +(13.8289 + 0.373349i) q^{77} +(0.492586 - 0.783946i) q^{78} +(-2.66312 - 1.53756i) q^{79} +(6.57591 + 7.08612i) q^{80} +(6.39876 - 5.93718i) q^{81} +(-19.8911 - 3.76360i) q^{82} +(1.09712 + 9.73722i) q^{83} +(0.563754 - 0.620410i) q^{84} +(-1.90810 - 16.9238i) q^{85} +(-12.2236 - 3.77048i) q^{86} +(-0.289211 + 0.126182i) q^{87} +(1.18294 - 1.37461i) q^{88} +(-0.853906 - 2.17572i) q^{89} +(12.9019 + 1.45274i) q^{90} +(-1.67678 - 7.00934i) q^{91} +(-7.57827 + 2.65175i) q^{92} +(-0.188481 + 0.162201i) q^{93} +(-3.64989 + 1.12584i) q^{94} +(-1.54045 - 0.604454i) q^{95} +(-0.201035 - 1.33378i) q^{96} +(-4.67598 - 4.67598i) q^{97} +(-0.796316 - 13.6628i) q^{98} -15.5282i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) \) 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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