LMFDB - Embedded newform 637.2.bz.a.4.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(4,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 7]))

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

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

chi := DirichletCharacter("637.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bz (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$756$
Relative dimension:	$63$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			4.19
Character	$\chi$	$=$	637.4
Dual form			637.2.bz.a.478.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.553189 - 1.14871i) q^{2} +(-1.61228 + 0.497321i) q^{3} +(0.233465 - 0.292756i) q^{4} +(-0.149862 - 0.485842i) q^{5} +(1.46317 + 1.57692i) q^{6} +(1.56147 + 2.13584i) q^{7} +(-2.95145 - 0.673650i) q^{8} +(-0.126610 + 0.0863216i) q^{9} +(-0.475189 + 0.440911i) q^{10} +(1.60328 - 2.35158i) q^{11} +(-0.230816 + 0.588111i) q^{12} +(1.40206 + 3.32178i) q^{13} +(1.58967 - 2.97520i) q^{14} +(0.483239 + 0.708782i) q^{15} +(0.692238 + 3.03289i) q^{16} +(1.14703 + 1.43833i) q^{17} +(0.169198 + 0.0976865i) q^{18} +(1.10058 + 0.635421i) q^{19} +(-0.177221 - 0.0695540i) q^{20} +(-3.57972 - 2.66702i) q^{21} +(-3.58820 - 0.540834i) q^{22} +(-4.28226 + 5.36979i) q^{23} +(5.09358 - 0.381711i) q^{24} +(3.91761 - 2.67098i) q^{25} +(3.04016 - 3.44813i) q^{26} +(3.31712 - 4.15954i) q^{27} +(0.989829 + 0.0415155i) q^{28} +(2.96297 - 0.446595i) q^{29} +(0.546861 - 0.947191i) q^{30} +(6.39647 + 3.69300i) q^{31} +(-1.63279 + 1.30210i) q^{32} +(-1.41544 + 4.58874i) q^{33} +(1.01770 - 2.11328i) q^{34} +(0.803676 - 1.07871i) q^{35} +(-0.00428798 + 0.0572191i) q^{36} +(-2.98213 + 2.37817i) q^{37} +(0.121084 - 1.61576i) q^{38} +(-3.91250 - 4.65835i) q^{39} +(0.115024 + 1.53489i) q^{40} +(4.35793 - 4.69673i) q^{41} +(-1.08336 + 5.58742i) q^{42} +(3.28993 - 3.05261i) q^{43} +(-0.314129 - 1.01838i) q^{44} +(0.0609128 + 0.0485763i) q^{45} +(8.53723 + 1.94857i) q^{46} +(4.92525 - 7.22402i) q^{47} +(-2.62440 - 4.54560i) q^{48} +(-2.12364 + 6.67009i) q^{49} +(-5.23536 - 3.02264i) q^{50} +(-2.56465 - 1.74855i) q^{51} +(1.29980 + 0.365059i) q^{52} +(-0.292150 - 0.744387i) q^{53} +(-6.61310 - 1.50940i) q^{54} +(-1.38277 - 0.426527i) q^{55} +(-3.16979 - 7.35571i) q^{56} +(-2.09045 - 0.477131i) q^{57} +(-2.15209 - 3.15653i) q^{58} +(6.44190 - 1.47032i) q^{59} +(0.320320 + 0.0240046i) q^{60} +(6.94781 - 1.04721i) q^{61} +(0.703729 - 9.39061i) q^{62} +(-0.382067 - 0.135632i) q^{63} +(8.00461 + 3.85482i) q^{64} +(1.40374 - 1.17899i) q^{65} +(6.05414 - 0.912514i) q^{66} +(3.54895 - 2.04899i) q^{67} +0.688873 q^{68} +(4.23368 - 10.7872i) q^{69} +(-1.68371 - 0.326460i) q^{70} +(0.452066 - 2.99926i) q^{71} +(0.431835 - 0.169483i) q^{72} +(6.24340 + 9.15739i) q^{73} +(4.38150 + 2.11002i) q^{74} +(-4.98793 + 6.25467i) q^{75} +(0.442971 - 0.173853i) q^{76} +(7.52607 - 0.247563i) q^{77} +(-3.18674 + 7.07128i) q^{78} +(-5.27887 - 9.14328i) q^{79} +(1.36977 - 0.790835i) q^{80} +(-3.11154 + 7.92807i) q^{81} +(-7.80594 - 2.40781i) q^{82} +(-2.69459 + 5.59538i) q^{83} +(-1.61652 + 0.425328i) q^{84} +(0.526906 - 0.772829i) q^{85} +(-5.32652 - 2.09050i) q^{86} +(-4.55502 + 2.19358i) q^{87} +(-6.31614 + 5.86053i) q^{88} +(-5.50106 + 11.4231i) q^{89} +(0.0221038 - 0.0968430i) q^{90} +(-4.90553 + 8.18143i) q^{91} +(0.572279 + 2.50732i) q^{92} +(-12.1495 - 2.77304i) q^{93} +(-11.0229 - 1.66143i) q^{94} +(0.143778 - 0.629934i) q^{95} +(1.98494 - 2.91137i) q^{96} +(-1.90742 + 1.10125i) q^{97} +(8.83677 - 1.25038i) q^{98} +0.436132i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 756 q - 21 q^{2} - 5 q^{3} + 115 q^{4} - 15 q^{6} - 14 q^{7} + 50 q^{9} - 16 q^{10} - 24 q^{11} - 26 q^{12} - 10 q^{13} - 38 q^{14} - 6 q^{15} - 125 q^{16} + 15 q^{17} - 9 q^{18} - 27 q^{19} - 15 q^{20}+ \cdots + 105 q^{98}+O(q^{100}) $ 756 * q - 21 * q^2 - 5 * q^3 + 115 * q^4 - 15 * q^6 - 14 * q^7 + 50 * q^9 - 16 * q^10 - 24 * q^11 - 26 * q^12 - 10 * q^13 - 38 * q^14 - 6 * q^15 - 125 * q^16 + 15 * q^17 - 9 * q^18 - 27 * q^19 - 15 * q^20 - 16 * q^21 - q^22 - 5 * q^23 - 39 * q^24 - 79 * q^25 - 34 * q^26 - 50 * q^27 - 142 * q^28 - 3 * q^29 - 11 * q^30 - 15 * q^31 - 21 * q^32 - 6 * q^33 - 12 * q^35 - 84 * q^36 + 7 * q^37 - 2 * q^38 - 6 * q^39 - 24 * q^40 - 6 * q^41 + 88 * q^42 - 5 * q^43 + 108 * q^44 - 21 * q^45 - 21 * q^46 + 63 * q^47 - 154 * q^48 - 34 * q^49 + 135 * q^50 + 26 * q^51 + 89 * q^52 + 16 * q^53 - 21 * q^54 - 4 * q^55 + 58 * q^56 - 63 * q^57 - 18 * q^58 - 21 * q^59 + 15 * q^60 - 75 * q^61 - 87 * q^62 + 147 * q^63 + 4 * q^64 - 20 * q^65 + 85 * q^66 - 27 * q^67 + 312 * q^68 - 182 * q^69 - 228 * q^70 - 30 * q^71 - 120 * q^72 + 6 * q^73 - 43 * q^74 + 83 * q^75 + 21 * q^76 + 3 * q^77 + 79 * q^78 + 12 * q^79 + 57 * q^80 + 72 * q^81 - 248 * q^82 + 147 * q^83 - 14 * q^84 - 24 * q^85 - 60 * q^86 - 37 * q^87 + 70 * q^88 - 126 * q^89 + 117 * q^90 - 55 * q^91 + 88 * q^92 - 21 * q^93 + 210 * q^94 + 9 * q^95 - 12 * q^96 - 156 * q^97 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−0.553189	−	1.14871i	−0.391164	−	0.812260i	−0.999823	−	0.0188280i	$-0.994006\pi$
$2$	−0.553189	−	1.14871i	−0.391164	−	0.812260i	0.608659	−	0.793432i	$-0.291708\pi$
$3$	−1.61228	+	0.497321i	−0.930848	+	0.287129i	−0.722853	−	0.691001i	$-0.757170\pi$
$3$	−1.61228	+	0.497321i	−0.930848	+	0.287129i	−0.207995	+	0.978130i	$0.566694\pi$
$4$	0.233465	−	0.292756i	0.116733	−	0.146378i
$5$	−0.149862	−	0.485842i	−0.0670205	−	0.217275i	0.915867	−	0.401482i	$-0.131505\pi$
$5$	−0.149862	−	0.485842i	−0.0670205	−	0.217275i	−0.982888	+	0.184207i	$0.941028\pi$
$6$	1.46317	+	1.57692i	0.597337	+	0.643776i
$7$	1.56147	+	2.13584i	0.590179	+	0.807272i
$7$	1.56147	+	2.13584i	0.590179	+	0.807272i
$8$	−2.95145	−	0.673650i	−1.04350	−	0.238171i
$9$	−0.126610	+	0.0863216i	−0.0422035	+	0.0287739i
$10$	−0.475189	+	0.440911i	−0.150268	+	0.139428i
$11$	1.60328	−	2.35158i	0.483407	−	0.709028i	−0.504614	−	0.863345i	$-0.668365\pi$
$11$	1.60328	−	2.35158i	0.483407	−	0.709028i	0.988021	+	0.154317i	$0.0493177\pi$
$12$	−0.230816	+	0.588111i	−0.0666310	+	0.169773i
$13$	1.40206	+	3.32178i	0.388861	+	0.921296i
$13$	1.40206	+	3.32178i	0.388861	+	0.921296i
$14$	1.58967	−	2.97520i	0.424858	−	0.795155i
$15$	0.483239	+	0.708782i	0.124772	+	0.183007i
$16$	0.692238	+	3.03289i	0.173060	+	0.758223i
$17$	1.14703	+	1.43833i	0.278196	+	0.348847i	0.901225	−	0.433352i	$-0.142669\pi$
$17$	1.14703	+	1.43833i	0.278196	+	0.348847i	−0.623028	+	0.782199i	$0.714098\pi$
$18$	0.169198	+	0.0976865i	0.0398803	+	0.0230249i
$19$	1.10058	+	0.635421i	0.252491	+	0.145776i	0.620904	−	0.783886i	$-0.286766\pi$
$19$	1.10058	+	0.635421i	0.252491	+	0.145776i	−0.368413	+	0.929662i	$0.620099\pi$
$20$	−0.177221	−	0.0695540i	−0.0396278	−	0.0155528i
$21$	−3.57972	−	2.66702i	−0.781158	−	0.581990i
$22$	−3.58820	−	0.540834i	−0.765007	−	0.115306i
$23$	−4.28226	+	5.36979i	−0.892914	+	1.11968i	0.0992906	+	0.995058i	$0.468343\pi$
$23$	−4.28226	+	5.36979i	−0.892914	+	1.11968i	−0.992205	+	0.124620i	$0.960229\pi$
$24$	5.09358	−	0.381711i	1.03972	−	0.0779164i
$25$	3.91761	−	2.67098i	0.783522	−	0.534196i
$26$	3.04016	−	3.44813i	0.596224	−	0.676234i
$27$	3.31712	−	4.15954i	0.638381	−	0.800504i
$28$	0.989829	+	0.0415155i	0.187060	+	0.00784570i
$29$	2.96297	−	0.446595i	0.550209	−	0.0829306i	0.131946	−	0.991257i	$-0.457877\pi$
$29$	2.96297	−	0.446595i	0.550209	−	0.0829306i	0.418262	+	0.908326i	$0.362639\pi$
$30$	0.546861	−	0.947191i	0.0998427	−	0.172933i
$31$	6.39647	+	3.69300i	1.14884	+	0.663283i	0.948604	−	0.316465i	$-0.102496\pi$
$31$	6.39647	+	3.69300i	1.14884	+	0.663283i	0.200236	+	0.979748i	$0.435829\pi$
$32$	−1.63279	+	1.30210i	−0.288639	+	0.230182i
$33$	−1.41544	+	4.58874i	−0.246396	+	0.798797i
$34$	1.01770	−	2.11328i	0.174534	−	0.362424i
$35$	0.803676	−	1.07871i	0.135846	−	0.182335i
$36$	−0.00428798	+	0.0572191i	−0.000714663	+	0.00953651i
$37$	−2.98213	+	2.37817i	−0.490259	+	0.390968i	−0.837181	−	0.546926i	$-0.815798\pi$
$37$	−2.98213	+	2.37817i	−0.490259	+	0.390968i	0.346923	+	0.937894i	$0.387227\pi$
$38$	0.121084	−	1.61576i	0.0196424	−	0.262110i
$39$	−3.91250	−	4.65835i	−0.626501	−	0.745934i
$40$	0.115024	+	1.53489i	0.0181870	+	0.242688i
$41$	4.35793	−	4.69673i	0.680594	−	0.733506i	−0.294413	−	0.955678i	$-0.595124\pi$
$41$	4.35793	−	4.69673i	0.680594	−	0.733506i	0.975007	+	0.222172i	$0.0713147\pi$
$42$	−1.08336	+	5.58742i	−0.167167	+	0.862157i
$43$	3.28993	−	3.05261i	0.501710	−	0.465519i	−0.388252	−	0.921553i	$-0.626921\pi$
$43$	3.28993	−	3.05261i	0.501710	−	0.465519i	0.889962	+	0.456034i	$0.150731\pi$
$44$	−0.314129	−	1.01838i	−0.0473568	−	0.153527i
$45$	0.0609128	+	0.0485763i	0.00908034	+	0.00724133i
$46$	8.53723	+	1.94857i	1.25875	+	0.287301i
$47$	4.92525	−	7.22402i	0.718422	−	1.05373i	−0.277251	−	0.960798i	$-0.589423\pi$
$47$	4.92525	−	7.22402i	0.718422	−	1.05373i	0.995672	−	0.0929334i	$-0.0296244\pi$
$48$	−2.62440	−	4.54560i	−0.378800	−	0.656100i
$49$	−2.12364	+	6.67009i	−0.303377	+	0.952871i
$50$	−5.23536	−	3.02264i	−0.740392	−	0.427465i
$51$	−2.56465	−	1.74855i	−0.359123	−	0.244846i
$52$	1.29980	+	0.365059i	0.180250	+	0.0506245i
$53$	−0.292150	−	0.744387i	−0.0401299	−	0.102249i	0.909404	−	0.415914i	$-0.136538\pi$
$53$	−0.292150	−	0.744387i	−0.0401299	−	0.102249i	−0.949534	+	0.313665i	$0.898443\pi$
$54$	−6.61310	−	1.50940i	−0.899929	−	0.205403i
$55$	−1.38277	−	0.426527i	−0.186452	−	0.0575129i
$56$	−3.16979	−	7.35571i	−0.423581	−	0.982949i
$57$	−2.09045	−	0.477131i	−0.276887	−	0.0631976i
$58$	−2.15209	−	3.15653i	−0.282583	−	0.414473i
$59$	6.44190	−	1.47032i	0.838664	−	0.191420i	0.218446	−	0.975849i	$-0.429901\pi$
$59$	6.44190	−	1.47032i	0.838664	−	0.191420i	0.620218	+	0.784430i	$0.287044\pi$
$60$	0.320320	+	0.0240046i	0.0413531	+	0.00309899i
$61$	6.94781	−	1.04721i	0.889576	−	0.134082i	0.311675	−	0.950189i	$-0.399110\pi$
$61$	6.94781	−	1.04721i	0.889576	−	0.134082i	0.577901	+	0.816107i	$0.303872\pi$
$62$	0.703729	−	9.39061i	0.0893737	−	1.19261i
$63$	−0.382067	−	0.135632i	−0.0481360	−	0.0170880i
$64$	8.00461	+	3.85482i	1.00058	+	0.481852i
$65$	1.40374	−	1.17899i	0.174113	−	0.146236i
$66$	6.05414	−	0.912514i	0.745213	−	0.112323i
$67$	3.54895	−	2.04899i	0.433573	−	0.250324i	−0.267295	−	0.963615i	$-0.586130\pi$
$67$	3.54895	−	2.04899i	0.433573	−	0.250324i	0.700868	+	0.713291i	$0.252796\pi$
$68$	0.688873			0.0835382
$69$	4.23368	−	10.7872i	0.509675	−	1.29863i
$70$	−1.68371	−	0.326460i	−0.201242	−	0.0390195i
$71$	0.452066	−	2.99926i	0.0536504	−	0.355947i	−0.945858	−	0.324582i	$-0.894776\pi$
$71$	0.452066	−	2.99926i	0.0536504	−	0.355947i	0.999508	−	0.0313651i	$-0.00998545\pi$
$72$	0.431835	−	0.169483i	0.0508923	−	0.0199737i
$73$	6.24340	+	9.15739i	0.730735	+	1.07179i	0.994245	+	0.107134i	$0.0341675\pi$
$73$	6.24340	+	9.15739i	0.730735	+	1.07179i	−0.263510	+	0.964657i	$0.584880\pi$
$74$	4.38150	+	2.11002i	0.509339	+	0.245285i
$75$	−4.98793	+	6.25467i	−0.575957	+	0.722227i
$76$	0.442971	−	0.173853i	0.0508122	−	0.0199423i
$77$	7.52607	−	0.247563i	0.857676	−	0.0282125i
$78$	−3.18674	+	7.07128i	−0.360827	+	0.800664i
$79$	−5.27887	−	9.14328i	−0.593920	−	1.02870i	−0.993698	−	0.112087i	$-0.964246\pi$
$79$	−5.27887	−	9.14328i	−0.593920	−	1.02870i	0.399779	−	0.916612i	$-0.369087\pi$
$80$	1.36977	−	0.790835i	0.153145	−	0.0884180i
$81$	−3.11154	+	7.92807i	−0.345727	+	0.880897i
$82$	−7.80594	−	2.40781i	−0.862021	−	0.265898i
$83$	−2.69459	+	5.59538i	−0.295770	+	0.614173i	−0.994905	−	0.100817i	$-0.967854\pi$
$83$	−2.69459	+	5.59538i	−0.295770	+	0.614173i	0.699135	+	0.714990i	$0.253569\pi$
$84$	−1.61652	+	0.425328i	−0.176377	+	0.0464071i
$85$	0.526906	−	0.772829i	0.0571510	−	0.0838251i
$86$	−5.32652	−	2.09050i	−0.574373	−	0.225425i
$87$	−4.55502	+	2.19358i	−0.488349	+	0.235177i
$88$	−6.31614	+	5.86053i	−0.673303	+	0.624734i
$89$	−5.50106	+	11.4231i	−0.583111	+	1.21084i	0.375685	+	0.926748i	$0.377408\pi$
$89$	−5.50106	+	11.4231i	−0.583111	+	1.21084i	−0.958796	+	0.284096i	$0.908307\pi$
$90$	0.0221038	−	0.0968430i	0.00232994	−	0.0102081i
$91$	−4.90553	+	8.18143i	−0.514239	+	0.857647i
$92$	0.572279	+	2.50732i	0.0596642	+	0.261406i
$93$	−12.1495	−	2.77304i	−1.25984	−	0.287551i
$94$	−11.0229	−	1.66143i	−1.13692	−	0.171364i
$95$	0.143778	−	0.629934i	0.0147514	−	0.0646299i
$96$	1.98494	−	2.91137i	0.202587	−	0.297141i
$97$	−1.90742	+	1.10125i	−0.193669	+	0.111815i	−0.593699	−	0.804687i	$-0.702333\pi$
$97$	−1.90742	+	1.10125i	−0.193669	+	0.111815i	0.400030	+	0.916502i	$0.369000\pi$
$98$	8.83677	−	1.25038i	0.892649	−	0.126308i
$99$			0.436132i			0.0438329i
$100$	0.132680	−	1.77049i	0.0132680	−	0.177049i
$101$	−0.114432	+	0.0352976i	−0.0113864	+	0.00351224i	−0.300443	−	0.953800i	$-0.597135\pi$
$101$	−0.114432	+	0.0352976i	−0.0113864	+	0.00351224i	0.289057	+	0.957312i	$0.406658\pi$
$102$	−0.589837	+	3.91331i	−0.0584026	+	0.387476i
$103$	−6.46941	+	1.99555i	−0.637450	+	0.196627i	−0.596601	−	0.802538i	$-0.703482\pi$
$103$	−6.46941	+	1.99555i	−0.637450	+	0.196627i	−0.0408491	+	0.999165i	$0.513006\pi$
$104$	−1.90039	−	10.7486i	−0.186349	−	1.05398i
$105$	−0.759283	+	2.13886i	−0.0740984	+	0.208732i
$106$	−0.693470	+	0.747383i	−0.0673557	+	0.0725922i
$107$	4.21676	+	2.03069i	0.407650	+	0.196314i	0.626460	−	0.779454i	$-0.284503\pi$
$107$	4.21676	+	2.03069i	0.407650	+	0.196314i	−0.218810	+	0.975767i	$0.570218\pi$
$108$	−0.443298	−	1.94222i	−0.0426564	−	0.186890i
$109$	−1.81814	−	0.136251i	−0.174146	−	0.0130504i	−0.0126283	−	0.999920i	$-0.504020\pi$
$109$	−1.81814	−	0.136251i	−0.174146	−	0.0130504i	−0.161518	+	0.986870i	$0.551639\pi$
$110$	0.274976	+	1.82435i	0.0262180	+	0.173945i
$111$	3.62530	−	5.31734i	0.344098	−	0.504699i
$112$	−5.39687	+	6.21428i	−0.509956	+	0.587194i
$113$	1.19145	+	15.8988i	0.112082	+	1.49563i	0.715730	+	0.698378i	$0.246094\pi$
$113$	1.19145	+	15.8988i	0.112082	+	1.49563i	−0.603648	+	0.797251i	$0.706287\pi$
$114$	0.608329	+	2.66526i	0.0569752	+	0.249625i
$115$	3.25062	+	1.27577i	0.303122	+	0.118967i
$116$	0.561006	−	0.971691i	0.0520881	−	0.0902192i
$117$	−0.464257	−	0.299544i	−0.0429206	−	0.0276929i
$118$	−5.25256	−	6.58650i	−0.483537	−	0.606337i
$119$	−1.28100	+	4.69579i	−0.117429	+	0.430463i
$120$	−0.948786	−	2.41747i	−0.0866120	−	0.220684i
$121$	1.05933	+	2.69913i	0.0963027	+	0.245375i
$122$	−5.04640	−	7.40171i	−0.456879	−	0.670119i
$123$	−4.69040	+	9.73972i	−0.422919	+	0.878201i
$124$	2.57450	−	1.01042i	0.231197	−	0.0907382i
$125$	−3.87231	−	3.08806i	−0.346350	−	0.276205i
$126$	0.0555542	+	0.513914i	0.00494916	+	0.0457831i
$127$	−16.3776	+	2.46853i	−1.45328	+	0.219047i	−0.827725	−	0.561134i	$-0.810365\pi$
$127$	−16.3776	+	2.46853i	−1.45328	+	0.219047i	−0.625555	+	0.780180i	$0.715127\pi$
$128$		−	7.15058i		−	0.632028i
$129$	−3.78615	+	6.55780i	−0.333352	+	0.577382i
$130$	−2.13085	−	0.960290i	−0.186888	−	0.0842230i
$131$	−6.88285	+	6.38635i	−0.601357	+	0.557978i	−0.921001	−	0.389560i	$-0.872627\pi$
$131$	−6.88285	+	6.38635i	−0.601357	+	0.557978i	0.319644	+	0.947538i	$0.396437\pi$
$132$	1.01293	+	1.48569i	0.0881639	+	0.129313i
$133$	0.361364	+	3.34286i	0.0313342	+	0.289862i
$134$	−4.31693	−	2.94323i	−0.372926	−	0.254257i
$135$	−2.51799	−	0.988239i	−0.216714	−	0.0850541i
$136$	−2.41648	−	5.01787i	−0.207211	−	0.430279i
$137$	16.5011	−	3.76628i	1.40979	−	0.321775i	0.551170	−	0.834393i	$-0.314182\pi$
$137$	16.5011	−	3.76628i	1.40979	−	0.321775i	0.858617	+	0.512618i	$0.171324\pi$
$138$	−14.7334	+	1.10412i	−1.25419	+	0.0939888i
$139$	3.54341	−	1.09300i	0.300548	−	0.0927069i	−0.140813	−	0.990036i	$-0.544972\pi$
$139$	3.54341	−	1.09300i	0.300548	−	0.0927069i	0.441362	+	0.897329i	$0.354496\pi$
$140$	−0.128168	−	0.487122i	−0.0108322	−	0.0411693i
$141$	−4.34821	+	14.0965i	−0.366185	+	1.18714i
$142$	−3.69536	+	1.13987i	−0.310107	+	0.0956555i
$143$	10.0593	+	2.02869i	0.841203	+	0.169648i
$144$	−0.349449	−	0.324241i	−0.0291207	−	0.0270201i
$145$	−0.661012	−	1.37260i	−0.0548940	−	0.113989i
$146$	7.06539	−	12.2376i	0.584736	−	1.01279i
$147$	0.106712	−	11.8102i	0.00880142	−	0.974086i
$148$			1.42825i			0.117402i
$149$	−8.91176	−	0.667844i	−0.730079	−	0.0547119i	−0.295497	−	0.955344i	$-0.595485\pi$
$149$	−8.91176	−	0.667844i	−0.730079	−	0.0547119i	−0.434583	+	0.900632i	$0.643104\pi$
$150$	9.94407	+	2.26967i	0.811930	+	0.185318i
$151$	−13.2759	+	5.21041i	−1.08038	+	0.424017i	−0.837723	−	0.546095i	$-0.816114\pi$
$151$	−13.2759	+	5.21041i	−1.08038	+	0.424017i	−0.242655	+	0.970113i	$0.578018\pi$
$152$	−2.82026	−	2.61682i	−0.228753	−	0.212252i
$153$	−0.269386	−	0.0830945i	−0.0217785	−	0.00671779i
$154$	−4.44772	−	8.50832i	−0.358407	−	0.685620i
$155$	0.835626	−	3.66112i	0.0671191	−	0.294068i
$156$	−2.27719	+	0.0578445i	−0.182321	+	0.00463127i
$157$	18.0980	+	5.58249i	1.44438	+	0.445531i	0.915207	−	0.402985i	$-0.132027\pi$
$157$	18.0980	+	5.58249i	1.44438	+	0.445531i	0.529170	+	0.848516i	$0.322504\pi$
$158$	−7.58275	+	11.1219i	−0.603251	+	0.884807i
$159$	0.841227	+	1.05486i	0.0667136	+	0.0836562i
$160$	0.877310	+	0.598140i	0.0693575	+	0.0472871i
$161$	−18.1556	−	0.761486i	−1.43086	−	0.0600135i
$162$	10.8283	−	0.811470i	0.850753	−	0.0637551i
$163$	−1.85864	+	6.02558i	−0.145580	+	0.471960i	−0.998767	−	0.0496462i	$-0.984191\pi$
$163$	−1.85864	+	6.02558i	−0.145580	+	0.471960i	0.853187	+	0.521606i	$0.174667\pi$
$164$	−0.357572	−	2.37233i	−0.0279217	−	0.185248i
$165$	2.44152			0.190072
$166$	7.91809			0.614563
$167$	0.330262	+	2.19115i	0.0255565	+	0.169556i	0.997968	−	0.0637155i	$-0.0202950\pi$
$167$	0.330262	+	2.19115i	0.0255565	+	0.169556i	−0.972412	+	0.233271i	$0.925057\pi$
$168$	8.76873	+	10.2830i	0.676522	+	0.793354i
$169$	−9.06846	+	9.31467i	−0.697574	+	0.716513i
$170$	−1.17923	−	0.177741i	−0.0904432	−	0.0136321i
$171$	−0.194196	+	0.0145530i	−0.0148505	+	0.00111289i
$172$	−0.125586	−	1.67583i	−0.00957582	−	0.127781i
$173$	2.46373	+	6.27749i	0.187314	+	0.477269i	0.993423	−	0.114498i	$-0.0365259\pi$
$173$	2.46373	+	6.27749i	0.187314	+	0.477269i	−0.806109	+	0.591767i	$0.798431\pi$
$174$	5.03957	+	4.01892i	0.382049	+	0.304674i
$175$	11.8220	+	4.19674i	0.893660	+	0.317244i
$176$	8.24194	+	3.23472i	0.621260	+	0.243827i
$177$	−9.65490	+	5.57426i	−0.725707	+	0.418987i
$178$	16.1649			1.21161
$179$	5.50028	−	14.0145i	0.411110	−	1.04749i	−0.564000	−	0.825774i	$-0.690738\pi$
$179$	5.50028	−	14.0145i	0.411110	−	1.04749i	0.975111	−	0.221718i	$-0.0711664\pi$
$180$	0.0284420	−	0.00649171i	0.00211994	−	0.000483863i
$181$	−13.1749	−	6.34472i	−0.979286	−	0.471599i	−0.125427	−	0.992103i	$-0.540030\pi$
$181$	−13.1749	−	6.34472i	−0.979286	−	0.471599i	−0.853859	+	0.520504i	$0.825744\pi$
$182$	12.1118	+	1.10915i	0.897784	+	0.0822154i
$183$	−10.6810	+	5.14369i	−0.789561	+	0.380233i
$184$	16.2563	−	12.9639i	1.19843	−	0.955714i
$185$	1.60232	+	1.09244i	0.117805	+	0.0803181i
$186$	3.53555	+	15.4902i	0.259239	+	1.13580i
$187$	5.22137	−	0.391288i	0.381825	−	0.0286138i
$188$	−0.965000	−	3.12845i	−0.0703799	−	0.228166i
$189$	14.0637	+	0.589862i	1.02298	+	0.0429061i
$190$	−0.803148	+	0.183313i	−0.0582665	+	0.0132989i
$191$	−17.6425	−	16.3698i	−1.27656	−	1.18448i	−0.972778	−	0.231738i	$-0.925559\pi$
$191$	−17.6425	−	16.3698i	−1.27656	−	1.18448i	−0.303786	−	0.952740i	$-0.598251\pi$
$192$	−14.8227	−	2.23417i	−1.06974	−	0.161237i
$193$	6.13931	+	19.9031i	0.441917	+	1.43266i	0.853407	+	0.521245i	$0.174532\pi$
$193$	6.13931	+	19.9031i	0.441917	+	1.43266i	−0.411490	+	0.911414i	$0.634991\pi$
$194$	2.32018	+	1.58187i	0.166579	+	0.113572i
$195$	−1.67689	+	2.59897i	−0.120084	+	0.186116i
$196$	1.45692	+	2.17894i	0.104065	+	0.155639i
$197$	3.89261	+	2.24740i	0.277337	+	0.160121i	0.632217	−	0.774791i	$-0.282145\pi$
$197$	3.89261	+	2.24740i	0.277337	+	0.160121i	−0.354880	+	0.934912i	$0.615478\pi$
$198$	0.500989	−	0.241264i	0.0356037	−	0.0171459i
$199$	5.65825	−	24.7904i	0.401103	−	1.75735i	−0.221845	−	0.975082i	$-0.571208\pi$
$199$	5.65825	−	24.7904i	0.401103	−	1.75735i	0.622948	−	0.782264i	$-0.285935\pi$
$200$	−13.3619	+	5.24418i	−0.944832	+	0.370819i
$201$	−4.70288	+	5.06850i	−0.331716	+	0.357504i
$202$	0.103849	+	0.111923i	0.00730680	+	0.00787486i
$203$	5.58043	+	5.63108i	0.391669	+	0.395224i
$204$	−1.11065	+	0.342591i	−0.0777614	+	0.0239862i
$205$	−2.93496	−	1.41340i	−0.204986	−	0.0987162i
$206$	5.87111	+	6.32756i	0.409060	+	0.440862i
$207$	0.0786509	−	1.04952i	0.00546662	−	0.0729469i
$208$	−9.10405	+	6.55176i	−0.631252	+	0.454283i
$209$	3.25878	−	1.56935i	0.225415	−	0.108554i
$210$	2.87696	−	0.311000i	0.198529	−	0.0214610i
$211$	1.82072	−	1.24135i	0.125344	−	0.0854579i	−0.499025	−	0.866587i	$-0.666309\pi$
$211$	1.82072	−	1.24135i	0.125344	−	0.0854579i	0.624369	+	0.781130i	$0.285356\pi$
$212$	−0.286131	−	0.0882596i	−0.0196515	−	0.00606170i
$213$	0.762742	+	5.06046i	0.0522622	+	0.346737i
$214$		−	5.96719i		−	0.407908i
$215$	−1.97612	−	1.14092i	−0.134770	−	0.0778098i
$216$	−12.5924	+	10.0421i	−0.856804	+	0.683279i
$217$	2.10021	+	19.4284i	0.142572	+	1.31888i
$218$	0.849261	+	2.16388i	0.0575192	+	0.146557i
$219$	−14.6202	−	11.6593i	−0.987945	−	0.787860i
$220$	−0.447697	+	0.305234i	−0.0301837	+	0.0205789i
$221$	−3.16962	+	5.82682i	−0.213212	+	0.391955i
$222$	−8.11355	−	1.22292i	−0.544546	−	0.0820771i
$223$	1.85679	−	0.728735i	0.124340	−	0.0487997i	−0.302355	−	0.953195i	$-0.597773\pi$
$223$	1.85679	−	0.728735i	0.124340	−	0.0487997i	0.426695	+	0.904396i	$0.359678\pi$
$224$	−5.33063	−	1.45418i	−0.356168	−	0.0971616i
$225$	−0.265447	+	0.676348i	−0.0176965	+	0.0450899i
$226$	17.6039	−	10.1636i	1.17100	−	0.676075i
$227$		−	1.32136i		−	0.0877015i	−0.999038	−	0.0438507i	$-0.986037\pi$
$227$		−	1.32136i		−	0.0877015i	0.999038	−	0.0438507i	$-0.0139626\pi$
$228$	−0.627730	+	0.500598i	−0.0415725	+	0.0331529i
$229$	6.83858	+	7.37024i	0.451906	+	0.487039i	0.917374	−	0.398025i	$-0.130304\pi$
$229$	6.83858	+	7.37024i	0.451906	+	0.487039i	−0.465468	+	0.885065i	$0.654114\pi$
$230$	−0.332714	−	4.43976i	−0.0219385	−	0.292749i
$231$	−12.0110	+	4.14202i	−0.790265	+	0.272525i
$232$	−9.04590	−	0.677896i	−0.593892	−	0.0445061i
$233$	−1.98954	+	5.06928i	−0.130339	+	0.332099i	−0.981114	−	0.193432i	$-0.938038\pi$
$233$	−1.98954	+	5.06928i	−0.130339	+	0.332099i	0.850774	+	0.525531i	$0.176133\pi$
$234$	−0.0872675	+	0.699001i	−0.00570485	+	0.0456951i
$235$	−4.24784	−	1.31028i	−0.277098	−	0.0854736i
$236$	1.07351	−	2.22917i	0.0698798	−	0.145107i
$237$	13.0581	+	12.1162i	0.848218	+	0.787031i
$238$	6.10274	−	1.12617i	0.395582	−	0.0729986i
$239$	12.3726	−	2.82396i	0.800315	−	0.182667i	0.197244	−	0.980354i	$-0.436801\pi$
$239$	12.3726	−	2.82396i	0.800315	−	0.182667i	0.603071	+	0.797688i	$0.293944\pi$
$240$	−1.81514	+	1.95626i	−0.117167	+	0.126276i
$241$	8.81472	+	7.02950i	0.567806	+	0.452810i	0.864833	−	0.502059i	$-0.167424\pi$
$241$	8.81472	+	7.02950i	0.567806	+	0.452810i	−0.297028	+	0.954869i	$0.595995\pi$
$242$	2.51450	−	2.70999i	0.161638	−	0.174205i
$243$	−0.118888	+	1.58645i	−0.00762668	+	0.101771i
$244$	1.31549	−	2.27850i	0.0842159	−	0.145866i
$245$	3.55887	+	0.0321564i	0.227368	+	0.00205439i
$246$	13.7828			0.878758
$247$	−0.567649	+	4.54679i	−0.0361186	+	0.289305i
$248$	−16.3911	−	15.2087i	−1.04083	−	0.965754i
$249$	1.56173	−	10.3614i	0.0989704	−	0.656626i
$250$	−1.40517	+	6.15644i	−0.0888706	+	0.389368i
$251$	17.2661	−	16.0206i	1.08983	−	1.01121i	0.0899430	−	0.995947i	$-0.471332\pi$
$251$	17.2661	−	16.0206i	1.08983	−	1.01121i	0.999883	−	0.0152643i	$-0.00485896\pi$
$252$	−0.128906	+	0.0801873i	−0.00812034	+	0.00505132i
$253$	5.76182	+	18.6794i	0.362243	+	1.17436i
$254$	11.8956	+	17.4476i	0.746393	+	1.09476i
$255$	−0.465174	+	1.50806i	−0.0291303	+	0.0944381i
$256$	7.79528	−	3.75401i	0.487205	−	0.234625i
$257$	−15.7777	−	19.7847i	−0.984188	−	1.23413i	−0.972187	−	0.234205i	$-0.924751\pi$
$257$	−15.7777	−	19.7847i	−0.984188	−	1.23413i	−0.0120009	−	0.999928i	$-0.503820\pi$
$258$	9.62747	+	0.721479i	0.599380	+	0.0449173i
$259$	−9.73588	−	2.65592i	−0.604958	−	0.165031i
$260$	−0.0174308	−	0.686208i	−0.00108101	−	0.0425568i
$261$	−0.336592	+	0.312311i	−0.0208345	+	0.0193316i
$262$	11.1436	+	4.37353i	0.688453	+	0.270198i
$263$	−10.1798	−	17.6319i	−0.627714	−	1.08723i	−0.988009	−	0.154394i	$-0.950658\pi$
$263$	−10.1798	−	17.6319i	−0.627714	−	1.08723i	0.360296	−	0.932838i	$-0.382676\pi$
$264$	7.26880	−	12.5899i	0.447364	−	0.774857i
$265$	−0.317872	+	0.253494i	−0.0195267	+	0.0155720i
$266$	3.64007	−	2.26433i	0.223187	−	0.138835i
$267$	3.18829	−	21.1529i	0.195120	−	1.29454i
$268$	0.228703	−	1.51734i	0.0139702	−	0.0926865i
$269$	−0.165604	−	0.0797509i	−0.0100971	−	0.00486250i	0.428828	−	0.903386i	$-0.358927\pi$
$269$	−0.165604	−	0.0797509i	−0.0100971	−	0.00486250i	−0.438925	+	0.898523i	$0.644641\pi$
$270$	0.257727	+	3.43912i	0.0156847	+	0.209298i
$271$	12.6391	+	10.0794i	0.767771	+	0.612277i	0.927042	−	0.374958i	$-0.122343\pi$
$271$	12.6391	+	10.0794i	0.767771	+	0.612277i	−0.159271	+	0.987235i	$0.550914\pi$
$272$	−3.56829	+	4.47450i	−0.216360	+	0.271306i
$273$	3.84027	−	15.6303i	0.232423	−	0.945992i
$274$	−13.4546	−	16.8715i	−0.812822	−	1.01925i
$275$		−	13.4949i		−	0.813773i
$276$	−2.16961	−	3.75788i	−0.130595	−	0.226198i
$277$	−10.2390	−	12.8393i	−0.615201	−	0.771437i	0.372460	−	0.928048i	$-0.378514\pi$
$277$	−10.2390	−	12.8393i	−0.615201	−	0.771437i	−0.987660	+	0.156611i	$0.949943\pi$
$278$	−3.21571	−	3.46571i	−0.192866	−	0.207860i
$279$	−1.12865	+	0.0845803i	−0.0675703	+	0.00506369i
$280$	−3.09868	+	2.64236i	−0.185182	+	0.157911i
$281$	−2.16337	−	4.49227i	−0.129056	−	0.267987i	0.826422	−	0.563052i	$-0.190373\pi$
$281$	−2.16337	−	4.49227i	−0.129056	−	0.267987i	−0.955477	+	0.295065i	$0.904659\pi$
$282$	18.5982	−	2.80323i	1.10751	−	0.166930i
$283$	−22.2815	−	15.1913i	−1.32450	−	0.903028i	−0.325405	−	0.945575i	$-0.605501\pi$
$283$	−22.2815	−	15.1913i	−1.32450	−	0.903028i	−0.999094	+	0.0425466i	$0.986453\pi$
$284$	−0.772510	−	0.832568i	−0.0458401	−	0.0494038i
$285$	0.0814693	+	1.08713i	0.00482582	+	0.0643961i
$286$	−3.23434	−	12.6775i	−0.191250	−	0.749636i
$287$	16.8362	+	1.97405i	0.993812	+	0.116525i
$288$	0.0943283	−	0.305805i	0.00555835	−	0.0180197i
$289$	3.02974	−	13.2741i	0.178220	−	0.780832i
$290$	−1.21106	+	1.51862i	−0.0711159	+	0.0891765i
$291$	2.52761	−	2.72412i	0.148171	−	0.159691i
$292$	4.13850	+	0.310137i	0.242187	+	0.0181494i
$293$	−1.43386	+	0.827841i	−0.0837672	+	0.0483630i	−0.541299	−	0.840830i	$-0.682067\pi$
$293$	−1.43386	+	0.827841i	−0.0837672	+	0.0483630i	0.457531	+	0.889194i	$0.348734\pi$
$294$	−13.6255	+	6.41067i	−0.794654	+	0.373878i
$295$	−1.67974	−	2.90940i	−0.0977984	−	0.169392i
$296$	10.4037	−	5.01014i	0.604700	−	0.291208i
$297$	−4.46322	−	14.4694i	−0.258982	−	0.839599i
$298$	4.16273	+	10.6065i	0.241140	+	0.614416i
$299$	−23.8413	−	6.69598i	−1.37878	−	0.387239i
$300$	0.666584	+	2.92050i	0.0384852	+	0.168615i
$301$	11.6570	+	2.26022i	0.671899	+	0.130277i
$302$	13.3293	+	12.3678i	0.767017	+	0.711688i
$303$	0.166942	−	0.113819i	0.00959054	−	0.00653872i
$304$	−1.16530	+	3.77781i	−0.0668345	+	0.216672i
$305$	−1.55000	−	3.21860i	−0.0887525	−	0.184297i
$306$	0.0535699	+	0.355413i	0.00306238	+	0.0203176i
$307$	14.4985	+	30.1064i	0.827472	+	1.71826i	0.685098	+	0.728451i	$0.259759\pi$
$307$	14.4985	+	30.1064i	0.827472	+	1.71826i	0.142374	+	0.989813i	$0.454526\pi$
$308$	1.68460	−	2.26110i	0.0959890	−	0.128838i
$309$	9.43805	−	6.43475i	0.536912	−	0.366060i
$310$	−4.66782	+	1.06540i	−0.265114	+	0.0605106i
$311$	−22.0387	+	3.32179i	−1.24970	+	0.188362i	−0.740363	−	0.672207i	$-0.765346\pi$
$311$	−22.0387	+	3.32179i	−1.24970	+	0.188362i	−0.509335	+	0.860569i	$0.670108\pi$
$312$	8.40945	+	16.3846i	0.476092	+	0.927593i
$313$	−10.5053	−	18.1957i	−0.593796	−	1.02848i	−0.993716	−	0.111934i	$-0.964295\pi$
$313$	−10.5053	−	18.1957i	−0.593796	−	1.02848i	0.399920	−	0.916550i	$-0.369038\pi$
$314$	−3.59895	−	23.8775i	−0.203101	−	1.34748i
$315$	−0.00863800	+	0.205950i	−0.000486696	+	0.0116040i
$316$	−3.90918	−	0.589215i	−0.219909	−	0.0331459i
$317$	1.30201	−	8.63830i	0.0731284	−	0.485175i	−0.922048	−	0.387075i	$-0.873485\pi$
$317$	1.30201	−	8.63830i	0.0731284	−	0.485175i	0.995177	−	0.0981000i	$-0.0312765\pi$
$318$	0.746375	−	1.54986i	0.0418546	−	0.0869121i
$319$	3.70026	−	7.68367i	0.207175	−	0.430203i
$320$	0.673242	−	4.46667i	0.0376354	−	0.249694i
$321$	−7.80849	−	1.17694i	−0.435827	−	0.0656904i
$322$	9.16878	+	21.2768i	0.510956	+	1.18571i
$323$	0.348456	+	2.31185i	0.0193886	+	0.128635i
$324$	1.59456	+	2.76185i	0.0885864	+	0.153436i
$325$	14.3651	+	9.26857i	0.796834	+	0.514128i
$326$	7.94982	−	1.19824i	0.440300	−	0.0663645i
$327$	2.99910	−	0.684525i	0.165851	−	0.0378543i
$328$	−16.0262	+	10.9265i	−0.884897	+	0.603313i
$329$	23.1200	−	0.760511i	1.27465	−	0.0419283i
$330$	−1.35062	−	2.80460i	−0.0743494	−	0.154388i
$331$	−2.83549	−	18.8122i	−0.155852	−	1.03401i	−0.920832	−	0.389959i	$-0.872489\pi$
$331$	−2.83549	−	18.8122i	−0.155852	−	1.03401i	0.764980	−	0.644054i	$-0.222749\pi$
$332$	1.00899	+	2.09519i	0.0553754	+	0.114988i
$333$	0.172281	−	0.558523i	0.00944096	−	0.0306069i
$334$	2.33429	−	1.59149i	0.127727	−	0.0870827i
$335$	−1.52734	−	1.41716i	−0.0834474	−	0.0774278i
$336$	5.61076	−	12.7031i	0.306092	−	0.693011i
$337$	−0.00607939	−	0.0266356i	−0.000331166	−	0.00145093i	0.974762	−	0.223246i	$-0.0716654\pi$
$337$	−0.00607939	−	0.0266356i	−0.000331166	−	0.00145093i	−0.975093	+	0.221795i	$0.928808\pi$
$338$	15.7164	+	5.26425i	0.854860	+	0.286337i
$339$	−9.82773	−	25.0406i	−0.533769	−	1.36002i
$340$	−0.103236	−	0.334684i	−0.00559877	−	0.0181508i
$341$	18.9397	−	9.12089i	1.02564	−	0.493924i
$342$	0.124144	+	0.215024i	0.00671294	+	0.0116272i
$343$	−17.5623	+	5.87938i	−0.948273	+	0.317457i
$344$	−11.7665	+	6.79337i	−0.634405	+	0.366274i
$345$	−5.87537	−	0.440298i	−0.316319	−	0.0237048i
$346$	5.84810	−	6.30275i	0.314396	−	0.338838i
$347$	−0.108588	+	0.136165i	−0.00582932	+	0.00730974i	−0.784738	−	0.619828i	$-0.787202\pi$
$347$	−0.108588	+	0.136165i	−0.00582932	+	0.00730974i	0.778908	+	0.627138i	$0.215774\pi$
$348$	−0.421254	+	1.84563i	−0.0225816	+	0.0989363i
$349$	−4.74311	+	15.3768i	−0.253893	+	0.823101i	0.735460	+	0.677568i	$0.236966\pi$
$349$	−4.74311	+	15.3768i	−0.253893	+	0.823101i	−0.989353	+	0.145533i	$0.953510\pi$
$350$	−1.71897	−	15.9016i	−0.0918829	−	0.849979i
$351$	18.4679	+	5.18683i	0.985743	+	0.276853i
$352$	0.444187	+	5.92727i	0.0236753	+	0.315924i
$353$	21.6210	+	23.3019i	1.15077	+	1.24023i	0.966307	+	0.257394i	$0.0828638\pi$
$353$	21.6210	+	23.3019i	1.15077	+	1.24023i	0.184462	+	0.982840i	$0.440946\pi$
$354$	11.7442	+	8.00705i	0.624196	+	0.425570i
$355$	−1.52491	+	0.229844i	−0.0809341	+	0.0121988i
$356$	2.05987	+	4.27736i	0.109173	+	0.226700i
$357$	−0.269994	−	8.20798i	−0.0142896	−	0.434413i
$358$	−19.1413	+	1.43444i	−1.01165	+	0.0758125i
$359$	0.760196	+	0.819296i	0.0401216	+	0.0432408i	0.752794	−	0.658256i	$-0.228706\pi$
$359$	0.760196	+	0.819296i	0.0401216	+	0.0432408i	−0.712672	+	0.701497i	$0.752515\pi$
$360$	−0.147058	−	0.184405i	−0.00775062	−	0.00971897i
$361$	−8.69248	−	15.0558i	−0.457499	−	0.792411i
$362$			18.6440i			0.979907i
$363$	−3.05027	−	3.82491i	−0.160097	−	0.200756i
$364$	1.24989	+	3.34620i	0.0655122	+	0.175389i
$365$	3.51339	−	4.40565i	0.183899	−	0.230602i
$366$	11.8172	+	9.42392i	0.617696	+	0.492596i
$367$	0.0450512	+	0.601166i	0.00235165	+	0.0313806i	0.998256	−	0.0590305i	$-0.0188009\pi$
$367$	0.0450512	+	0.601166i	0.00235165	+	0.0313806i	−0.995905	+	0.0904111i	$0.971182\pi$
$368$	−19.2503	−	9.27048i	−1.00349	−	0.483257i
$369$	−0.146330	+	0.970838i	−0.00761765	+	0.0505398i
$370$	0.368514	−	2.44493i	0.0191581	−	0.127106i
$371$	1.13371	−	1.78632i	0.0588593	−	0.0927413i
$372$	−3.64831	+	2.90943i	−0.189156	+	0.150847i
$373$	18.1454	−	31.4288i	0.939536	−	1.62732i	0.173197	−	0.984887i	$-0.444590\pi$
$373$	18.1454	−	31.4288i	0.939536	−	1.62732i	0.766339	−	0.642436i	$-0.222076\pi$
$374$	−3.33788	−	5.78138i	−0.172598	−	0.298948i
$375$	7.77899	+	3.05303i	0.401706	+	0.157658i
$376$	−19.4031	+	18.0034i	−1.00064	+	0.928456i
$377$	5.63775	+	9.21617i	0.290359	+	0.474657i
$378$	−7.10231	−	16.4814i	−0.365303	−	0.847712i
$379$	−35.9187	−	2.69173i	−1.84502	−	0.138265i	−0.894131	−	0.447805i	$-0.852206\pi$
$379$	−35.9187	−	2.69173i	−1.84502	−	0.138265i	−0.950886	+	0.309540i	$0.899825\pi$
$380$	−0.150850	−	0.189160i	−0.00773843	−	0.00970369i
$381$	25.1776	−	12.1249i	1.28989	−	0.621177i
$382$	−9.04454	+	29.3217i	−0.462759	+	1.50023i
$383$	−17.7066	−	25.9707i	−0.904762	−	1.32704i	−0.944733	−	0.327842i	$-0.893679\pi$
$383$	−17.7066	−	25.9707i	−0.904762	−	1.32704i	0.0399701	−	0.999201i	$-0.487274\pi$
$384$	3.55614	+	11.5287i	0.181473	+	0.588322i
$385$	−1.24815	−	3.61938i	−0.0636117	−	0.184461i
$386$	19.4667	−	18.0625i	0.990830	−	0.919356i
$387$	−0.153034	+	0.670484i	−0.00777914	+	0.0340826i
$388$	−0.122919	+	0.815512i	−0.00624025	+	0.0414014i
$389$	9.15093	+	8.49082i	0.463971	+	0.430502i	0.877200	−	0.480125i	$-0.159409\pi$
$389$	9.15093	+	8.49082i	0.463971	+	0.430502i	−0.413229	+	0.910627i	$0.635599\pi$
$390$	3.91309	+	0.488535i	0.198147	+	0.0247379i
$391$	−12.6355			−0.639002
$392$	10.7611	−	18.2559i	0.543519	−	0.922061i
$393$	7.92099	−	13.7196i	0.399561	−	0.692060i
$394$	0.428259	−	5.71472i	0.0215754	−	0.287903i
$395$	−3.65108	+	3.93493i	−0.183706	+	0.197988i
$396$	0.127680	+	0.101822i	0.00641618	+	0.00511673i
$397$	−12.3076	+	13.2644i	−0.617701	+	0.665724i	−0.961972	−	0.273147i	$-0.911936\pi$
$397$	−12.3076	+	13.2644i	−0.617701	+	0.665724i	0.344271	+	0.938870i	$0.388126\pi$
$398$	−31.6071	+	7.21410i	−1.58432	+	0.361610i
$399$	−2.24509	−	5.20989i	−0.112395	−	0.260821i
$400$	10.8127	+	10.0327i	0.540636	+	0.501637i
$401$	−14.9735	+	31.0928i	−0.747740	+	1.55270i	0.0833246	+	0.996522i	$0.473446\pi$
$401$	−14.9735	+	31.0928i	−0.747740	+	1.55270i	−0.831065	+	0.556176i	$0.812268\pi$
$402$	8.42381	+	2.59840i	0.420142	+	0.129597i
$403$	−3.29912	+	26.4255i	−0.164341	+	1.31635i
$404$	−0.0163823	+	0.0417414i	−0.000815049	+	0.00207671i
$405$	4.31809	+	0.323596i	0.214568	+	0.0160796i
$406$	3.38144	−	9.52534i	0.167818	−	0.472735i
$407$	0.811265	+	10.8256i	0.0402129	+	0.536604i
$408$	6.39153	+	6.88843i	0.316428	+	0.341028i
$409$	10.7517	−	8.57419i	0.531637	−	0.423966i	−0.320528	−	0.947239i	$-0.603860\pi$
$409$	10.7517	−	8.57419i	0.531637	−	0.423966i	0.852165	+	0.523273i	$0.175289\pi$
$410$			4.15329i			0.205116i
$411$	−24.7313	+	14.2786i	−1.21991	+	0.704313i
$412$	−0.926173	+	2.35985i	−0.0456293	+	0.116262i
$413$	13.1992	+	11.4630i	0.649490	+	0.564058i
$414$	−1.24911	+	0.490238i	−0.0613902	+	0.0240939i
$415$	3.12229	+	0.470609i	0.153267	+	0.0231013i
$416$	−6.61457	−	3.59813i	−0.324306	−	0.176413i
$417$	−5.16939	+	3.52443i	−0.253146	+	0.172592i
$418$	−3.60545	−	2.87525i	−0.176348	−	0.140633i
$419$	4.96558	+	12.6521i	0.242585	+	0.618095i	0.999367	−	0.0355713i	$-0.0113251\pi$
$419$	4.96558	+	12.6521i	0.242585	+	0.618095i	−0.756783	+	0.653667i	$0.773230\pi$
$420$	0.448899	+	0.721634i	0.0219040	+	0.0352122i
$421$	6.70851	−	5.34986i	0.326953	−	0.260736i	−0.446231	−	0.894918i	$-0.647234\pi$
$421$	6.70851	−	5.34986i	0.326953	−	0.260736i	0.773184	+	0.634181i	$0.218663\pi$
$422$	−2.43315	−	1.40478i	−0.118444	−	0.0683837i
$423$			1.33979i			0.0651429i
$424$	0.360812	+	2.39383i	0.0175226	+	0.116255i
$425$	8.33539	+	2.57113i	0.404326	+	0.124718i
$426$	5.39106	−	3.67556i	0.261198	−	0.178081i
$427$	13.0855	+	13.2042i	0.633250	+	0.638998i
$428$	1.57896	−	0.760388i	0.0763220	−	0.0367547i
$429$	−17.2273	+	1.73191i	−0.831743	+	0.0836174i
$430$	−0.217410	+	2.90113i	−0.0104844	+	0.139905i
$431$	−16.3327	−	17.6025i	−0.786718	−	0.847881i	0.204670	−	0.978831i	$-0.434388\pi$
$431$	−16.3327	−	17.6025i	−0.786718	−	0.847881i	−0.991389	+	0.130950i	$0.958197\pi$
$432$	14.9117	+	7.18109i	0.717439	+	0.345500i
$433$	7.28381	−	2.24676i	0.350038	−	0.107972i	−0.114750	−	0.993394i	$-0.536607\pi$
$433$	7.28381	−	2.24676i	0.350038	−	0.107972i	0.464788	+	0.885422i	$0.346131\pi$
$434$	21.1557	−	13.1601i	1.01551	−	0.631704i
$435$	1.74836	+	1.88428i	0.0838274	+	0.0903445i
$436$	−0.464360	+	0.500461i	−0.0222388	+	0.0239677i
$437$	−8.12506	+	3.18885i	−0.388674	+	0.152543i
$438$	−5.30533	+	23.2442i	−0.253499	+	1.11065i
$439$	4.62001	−	2.22488i	0.220501	−	0.106188i	−0.320372	−	0.947292i	$-0.603808\pi$
$439$	4.62001	−	2.22488i	0.220501	−	0.106188i	0.540874	+	0.841104i	$0.318094\pi$
$440$	3.79384	+	2.19038i	0.180864	+	0.104422i
$441$	−0.306898	−	1.02782i	−0.0146142	−	0.0489438i
$442$	8.44673	+	0.417639i	0.401770	+	0.0198650i
$443$	33.9774	+	23.1654i	1.61432	+	1.10062i	0.927522	+	0.373769i	$0.121935\pi$
$443$	33.9774	+	23.1654i	1.61432	+	1.10062i	0.686794	+	0.726852i	$0.259017\pi$
$444$	−0.710302	−	2.30274i	−0.0337094	−	0.109283i
$445$	6.37421	+	0.960757i	0.302166	+	0.0455443i
$446$	−1.86426	−	1.72978i	−0.0882752	−	0.0819074i
$447$	14.7003	−	3.35526i	0.695302	−	0.158698i
$448$	4.26566	+	23.1157i	0.201533	+	1.09212i
$449$	−2.13688	−	6.92758i	−0.100845	−	0.326933i	0.891065	−	0.453877i	$-0.149959\pi$
$449$	−2.13688	−	6.92758i	−0.100845	−	0.326933i	−0.991910	+	0.126944i	$0.959483\pi$
$450$	0.923770	−	0.0692270i	0.0435469	−	0.00326339i
$451$	−4.05776	−	17.7782i	−0.191072	−	0.837142i
$452$	4.93262	+	3.36300i	0.232011	+	0.158182i
$453$	18.8132	−	15.0030i	0.883920	−	0.704903i
$454$	−1.51785	+	0.730960i	−0.0712364	+	0.0343056i
$455$	4.71004	+	1.15722i	0.220810	+	0.0542514i
$456$	5.84844	+	2.81646i	0.273878	+	0.131893i
$457$	−8.56403	+	1.95468i	−0.400608	+	0.0914362i	−0.418078	−	0.908411i	$-0.637296\pi$
$457$	−8.56403	+	1.95468i	−0.400608	+	0.0914362i	0.0174697	+	0.999847i	$0.494439\pi$
$458$	4.68323	−	11.9327i	0.218833	−	0.557578i
$459$	9.78766			0.456849
$460$	1.13240	−	0.653790i	0.0527983	−	0.0304831i
$461$	22.4961	+	8.82905i	1.04775	+	0.411210i	0.825867	−	0.563864i	$-0.190686\pi$
$461$	22.4961	+	8.82905i	1.04775	+	0.411210i	0.221879	+	0.975074i	$0.428781\pi$
$462$	11.4023	+	11.5058i	0.530484	+	0.535299i
$463$	−27.2098	−	21.6991i	−1.26455	−	1.00844i	−0.999016	−	0.0443404i	$-0.985881\pi$
$463$	−27.2098	−	21.6991i	−1.26455	−	1.00844i	−0.265531	−	0.964102i	$-0.585547\pi$
$464$	3.40555	+	8.67721i	0.158099	+	0.402829i
$465$	0.473492	+	6.31830i	0.0219576	+	0.293004i
$466$	6.92372	−	0.518861i	0.320735	−	0.0240358i
$467$	3.10747	+	0.468375i	0.143796	+	0.0216738i	0.220546	−	0.975377i	$-0.429216\pi$
$467$	3.10747	+	0.468375i	0.143796	+	0.0216738i	−0.0767496	+	0.997050i	$0.524454\pi$
$468$	−0.196081	+	0.0659808i	−0.00906386	+	0.00304996i
$469$	9.91788	+	4.38057i	0.457965	+	0.202276i
$470$	0.844722	+	5.60437i	0.0389641	+	0.258510i
$471$	−31.9552			−1.47242
$472$	−20.0034			−0.920733
$473$	−1.90378	−	12.6307i	−0.0875357	−	0.580761i
$474$	6.69435	−	21.7026i	0.307482	−	0.996832i
$475$	6.00885	−	0.450301i	0.275705	−	0.0206612i
$476$	1.07565	+	1.47132i	0.0493025	+	0.0674381i
$477$	0.101246	+	0.0690283i	0.00463573	+	0.00316059i
$478$	−10.0883	−	12.6503i	−0.461427	−	0.578611i
$479$	2.06527	−	3.02920i	0.0943648	−	0.138408i	−0.776153	−	0.630545i	$-0.782832\pi$
$479$	2.06527	−	3.02920i	0.0943648	−	0.138408i	0.870518	+	0.492137i	$0.163784\pi$
$480$	−1.71193	−	0.528062i	−0.0781387	−	0.0241026i
$481$	−12.0809	−	6.57164i	−0.550840	−	0.299641i
$482$	3.19865	−	14.0142i	0.145694	−	0.638329i
$483$	29.6506	−	7.80146i	1.34915	−	0.354979i
$484$	1.03750	+	0.320027i	0.0471592	+	0.0145467i
$485$	0.820884	+	0.761669i	0.0372744	+	0.0345856i
$486$	1.88814	−	0.741041i	0.0856478	−	0.0336143i
$487$	34.6689	+	7.91295i	1.57100	+	0.358570i	0.917303	−	0.398190i	$-0.130361\pi$
$487$	34.6689	+	7.91295i	1.57100	+	0.358570i	0.653694	+	0.756759i	$0.273219\pi$
$488$	−21.2116	−	1.58959i	−0.960203	−	0.0719573i
$489$		−	10.6392i		−	0.481123i
$490$	−1.93179	−	4.10589i	−0.0872693	−	0.185485i
$491$	−19.5674	+	33.8918i	−0.883065	+	1.52951i	−0.0351504	+	0.999382i	$0.511191\pi$
$491$	−19.5674	+	33.8918i	−0.883065	+	1.52951i	−0.847915	+	0.530132i	$0.822142\pi$
$492$	1.75632	+	3.64703i	0.0791808	+	0.164421i
$493$	4.04097	+	3.74948i	0.181996	+	0.168868i
$494$	5.53695	−	1.86317i	0.249119	−	0.0838280i
$495$	0.211891	−	0.0653598i	0.00952381	−	0.00293771i
$496$	−6.77261	+	21.9563i	−0.304099	+	0.985865i
$497$	7.11183	−	3.71771i	0.319009	−	0.166762i
$498$	−12.7661	+	3.93783i	−0.572064	+	0.176459i
$499$	23.8741	−	1.78911i	1.06875	−	0.0800918i	0.471281	−	0.881983i	$-0.343792\pi$
$499$	23.8741	−	1.78911i	1.06875	−	0.0800918i	0.597470	+	0.801892i	$0.296173\pi$
$500$	−1.80810	+	0.412687i	−0.0808607	+	0.0184559i
$501$	−1.62218	−	3.36849i	−0.0724736	−	0.150493i
$502$	−27.9544	−	10.9713i	−1.24767	−	0.489673i
$503$	−27.8815	−	19.0093i	−1.24317	−	0.847581i	−0.250465	−	0.968126i	$-0.580583\pi$
$503$	−27.8815	−	19.0093i	−1.24317	−	0.847581i	−0.992708	+	0.120545i	$0.961536\pi$
$504$	1.03628	+	0.657690i	0.0461598	+	0.0292958i
$505$	0.0342981	+	0.0503060i	0.00152624	+	0.00223859i
$506$	18.2698	−	16.9519i	0.812191	−	0.753603i
$507$	9.98848	−	19.5278i	0.443604	−	0.867258i
$508$	−3.10093	+	5.37097i	−0.137581	+	0.238298i
$509$		−	3.21336i		−	0.142430i	−0.997461	−	0.0712149i	$-0.977312\pi$
$509$		−	3.21336i		−	0.142430i	0.997461	−	0.0712149i	$-0.0226876\pi$
$510$	1.98965	−	0.299891i	0.0881030	−	0.0132794i
$511$	−9.80986	+	27.6339i	−0.433963	+	1.22245i
$512$	−19.8056	−	15.7945i	−0.875293	−	0.698023i
$513$	6.29382	−	2.47014i	0.277879	−	0.109060i
$514$	−13.9987	+	29.0687i	−0.617458	+	1.28216i
$515$	1.93904	+	2.84405i	0.0854444	+	0.125324i
$516$	1.03590	+	2.63944i	0.0456031	+	0.116195i
$517$	−9.09129	−	23.1642i	−0.399835	−	1.01876i
$518$	2.33490	+	12.6529i	0.102590	+	0.555937i
$519$	−7.09415	−	8.89578i	−0.311398	−	0.390481i
$520$	−4.93731	+	2.53410i	−0.216515	+	0.111128i
$521$	−5.59843	+	9.69677i	−0.245272	+	0.424823i	−0.962208	−	0.272316i	$-0.912211\pi$
$521$	−5.59843	+	9.69677i	−0.245272	+	0.424823i	0.716936	+	0.697139i	$0.245544\pi$
$522$	0.544954	+	0.213879i	0.0238520	+	0.00936121i
$523$	0.137114	+	0.600735i	0.00599557	+	0.0262683i	0.977837	−	0.209367i	$-0.0671402\pi$
$523$	0.137114	+	0.600735i	0.00599557	+	0.0262683i	−0.971842	+	0.235635i	$0.924283\pi$
$524$	0.262737	+	3.50599i	0.0114777	+	0.153160i
$525$	−21.1475	−	0.886971i	−0.922952	−	0.0387106i
$526$	−14.6226	+	21.4474i	−0.637576	+	0.935153i
$527$	2.02519	+	13.4363i	0.0882187	+	0.585293i
$528$	−14.8970	−	1.11637i	−0.648308	−	0.0485840i
$529$	−5.37887	−	23.5664i	−0.233864	−	1.02463i
$530$	0.467035	+	0.224912i	0.0202867	+	0.00976956i
$531$	−0.688691	+	0.742233i	−0.0298867	+	0.0322102i
$532$	1.06301	+	0.674649i	0.0460872	+	0.0292498i
$533$	21.7116	+	7.89099i	0.940433	+	0.341797i
$534$	−26.0623	+	8.03916i	−1.12783	+	0.347888i
$535$	0.354658	−	2.35300i	0.0153332	−	0.101729i
$536$	−11.8548	+	3.65674i	−0.512051	+	0.157947i
$537$	−1.89827	+	25.3306i	−0.0819163	+	1.09310i
$538$			0.234349i			0.0101035i
$539$	12.2805	+	15.6879i	0.528957	+	0.675727i
$540$	−0.877176	+	0.506438i	−0.0377477	+	0.0217936i
$541$	4.80045	−	7.04097i	0.206388	−	0.302715i	−0.709063	−	0.705145i	$-0.750882\pi$
$541$	4.80045	−	7.04097i	0.206388	−	0.302715i	0.915451	+	0.402430i	$0.131834\pi$
$542$	4.58643	−	20.0944i	0.197004	−	0.863131i
$543$	24.3970	+	3.67726i	1.04698	+	0.157806i
$544$	−3.74572	−	0.854937i	−0.160597	−	0.0366551i
$545$	0.206274	+	0.903746i	0.00883581	+	0.0387122i
$546$	−20.0791	+	4.23519i	−0.859307	+	0.181249i
$547$	5.30496	−	23.2425i	0.226824	−	0.993779i	−0.725388	−	0.688340i	$-0.758340\pi$
$547$	5.30496	−	23.2425i	0.226824	−	0.993779i	0.952212	−	0.305439i	$-0.0988032\pi$
$548$	2.74984	−	5.71010i	0.117467	−	0.243923i
$549$	−0.789269	+	0.732334i	−0.0336852	+	0.0312553i
$550$	−15.5017	+	7.46524i	−0.660996	+	0.318319i
$551$	3.54476	+	1.39122i	0.151012	+	0.0592678i
$552$	−19.7623	+	28.9860i	−0.841141	+	1.23373i
$553$	11.2858	−	25.5518i	0.479921	−	1.08657i
$554$	−9.08450	+	18.8642i	−0.385963	+	0.801461i
$555$	−3.12668	−	0.964453i	−0.132720	−	0.0409388i
$556$	0.507281	−	1.29253i	0.0215135	−	0.0548156i
$557$	20.3495	−	11.7488i	0.862235	−	0.497812i	−0.00252512	−	0.999997i	$-0.500804\pi$
$557$	20.3495	−	11.7488i	0.862235	−	0.497812i	0.864760	+	0.502185i	$0.167470\pi$
$558$	0.721513	+	1.24970i	0.0305441	+	0.0529039i
$559$	14.7528	+	6.64849i	0.623976	+	0.281201i
$560$	3.82794	+	1.69074i	0.161760	+	0.0714468i
$561$	−8.22370	+	3.22756i	−0.347205	+	0.136268i
$562$	−3.96357	+	4.97016i	−0.167193	+	0.209653i
$563$	−18.7838	−	9.04578i	−0.791641	−	0.381234i	−0.00605093	−	0.999982i	$-0.501926\pi$
$563$	−18.7838	−	9.04578i	−0.791641	−	0.381234i	−0.785590	+	0.618748i	$0.787640\pi$
$564$	3.11169	+	4.56402i	0.131026	+	0.192180i
$565$	7.54573	−	2.96148i	0.317451	−	0.124590i
$566$	−5.12447	+	33.9986i	−0.215398	+	1.42907i
$567$	−21.7917	+	5.73367i	−0.915164	+	0.240792i
$568$	−3.35470	+	8.54764i	−0.140760	+	0.358651i
$569$	−35.1921			−1.47533			−0.737664	−	0.675168i	$-0.764071\pi$
$569$	−35.1921			−1.47533			−0.737664	+	0.675168i	$0.764071\pi$
$570$	1.20373	−	0.694974i	0.0504187	−	0.0291093i
$571$	38.6762	−	5.82950i	1.61855	−	0.243957i	0.723631	−	0.690187i	$-0.242472\pi$
$571$	38.6762	−	5.82950i	1.61855	−	0.243957i	0.894919	+	0.446229i	$0.147233\pi$
$572$	2.94241	−	2.47130i	0.123029	−	0.103330i
$573$	36.5856	+	17.6187i	1.52839	+	0.736031i
$574$	−7.04601	−	20.4320i	−0.294095	−	0.852814i
$575$	−2.43363	+	32.4746i	−0.101490	+	1.35428i
$576$	−1.34622	+	0.202910i	−0.0560925	+	0.00845459i
$577$	−0.355349	−	0.0266297i	−0.0147934	−	0.00110861i	0.0673314	−	0.997731i	$-0.478552\pi$
$577$	−0.355349	−	0.0266297i	−0.0147934	−	0.00110861i	−0.0821247	+	0.996622i	$0.526171\pi$
$578$	−16.9241	+	3.86283i	−0.703952	+	0.160672i
$579$	−19.7965	−	29.0362i	−0.822715	−	1.20670i
$580$	−0.556162	−	0.126940i	−0.0230934	−	0.00527091i
$581$	−16.1584	+	2.98178i	−0.670362	+	0.123705i
$582$	−4.52747	−	1.39654i	−0.187670	−	0.0578884i
$583$	−2.21888	−	0.506446i	−0.0918968	−	0.0209748i
$584$	−12.2582	−	31.2334i	−0.507249	−	1.29245i
$585$	−0.0759566	+	0.270446i	−0.00314042	+	0.0111816i
$586$	1.74415	+	1.18914i	0.0720500	+	0.0491229i
$587$	−24.8299	−	14.3356i	−1.02484	−	0.591693i	−0.109339	−	0.994005i	$-0.534873\pi$
$587$	−24.8299	−	14.3356i	−1.02484	−	0.591693i	−0.915503	+	0.402312i	$0.868207\pi$
$588$	−3.43258	−	2.78850i	−0.141557	−	0.114996i
$589$	4.69322	+	8.12890i	0.193381	+	0.334946i
$590$	−2.41284	+	3.53898i	−0.0993350	+	0.145698i
$591$	−7.39365	−	1.68755i	−0.304134	−	0.0694166i
$592$	−9.27707	−	7.39821i	−0.381285	−	0.304065i
$593$	4.72976	+	15.3335i	0.194228	+	0.629671i	0.999332	+	0.0365382i	$0.0116331\pi$
$593$	4.72976	+	15.3335i	0.194228	+	0.629671i	−0.805104	+	0.593133i	$0.797891\pi$
$594$	−14.1521	+	13.1312i	−0.580668	+	0.538782i
$595$	2.47339	−	0.0813599i	0.101399	−	0.00333543i
$596$	−2.27610	+	2.45305i	−0.0932327	+	0.100481i
$597$	3.20614	+	42.7830i	0.131219	+	1.75099i
$598$	5.49699	+	31.0908i	0.224789	+	1.27140i
$599$	0.946115	−	12.6250i	0.0386572	−	0.515845i	−0.943943	−	0.330110i	$-0.892914\pi$
$599$	0.946115	−	12.6250i	0.0386572	−	0.515845i	0.982600	−	0.185735i	$-0.0594667\pi$
$600$	18.9351	−	15.1002i	0.773022	−	0.616465i
$601$	−1.00398	+	13.3972i	−0.0409531	+	0.546482i	0.938562	+	0.345111i	$0.112159\pi$
$601$	−1.00398	+	13.3972i	−0.0409531	+	0.546482i	−0.979515	+	0.201371i	$0.935460\pi$
$602$	−3.85220	−	14.6408i	−0.157004	−	0.596716i
$603$	−0.272462	+	0.565774i	−0.0110955	+	0.0230401i
$604$	−1.57408	+	5.10305i	−0.0640485	+	0.207640i
$605$	1.15260	−	0.919165i	0.0468597	−	0.0373694i
$606$	−0.223095	−	0.128804i	−0.00906262	−	0.00523230i
$607$	−5.97807	+	10.3543i	−0.242643	+	0.420269i	−0.961466	−	0.274923i	$-0.911348\pi$
$607$	−5.97807	+	10.3543i	−0.242643	+	0.420269i	0.718824	+	0.695192i	$0.244681\pi$
$608$	−2.62440	+	0.395565i	−0.106433	+	0.0160423i
$609$	−11.7977	−	6.30359i	−0.478065	−	0.255434i
$610$	−2.83979	+	3.56099i	−0.114980	+	0.144180i
$611$	30.9021	+	6.23210i	1.25016	+	0.252124i
$612$	−0.0872186	+	0.0594646i	−0.00352560	+	0.00240372i
$613$	−42.0056	+	3.14789i	−1.69659	+	0.127142i	−0.887581	−	0.460653i	$-0.847615\pi$
$613$	−42.0056	+	3.14789i	−1.69659	+	0.127142i	−0.809010	+	0.587794i	$0.799996\pi$
$614$	26.5631	−	33.3091i	1.07200	−	1.34425i
$615$	5.43488	+	0.819176i	0.219155	+	0.0330324i
$616$	−22.3796	−	4.33926i	−0.901700	−	0.174834i
$617$	−13.0507	−	5.12203i	−0.525402	−	0.206205i	0.0877900	−	0.996139i	$-0.472020\pi$
$617$	−13.0507	−	5.12203i	−0.525402	−	0.206205i	−0.613192	+	0.789934i	$0.710115\pi$
$618$	−12.6127	−	7.28194i	−0.507357	−	0.292923i
$619$	30.7640	+	17.7616i	1.23651	+	0.713900i	0.968379	−	0.249483i	$-0.0802606\pi$
$619$	30.7640	+	17.7616i	1.23651	+	0.713900i	0.268131	+	0.963382i	$0.413594\pi$
$620$	−0.876724	−	1.09938i	−0.0352101	−	0.0441521i
$621$	8.13106	+	35.6245i	0.326288	+	1.42956i
$622$	16.0073	+	23.4784i	0.641835	+	0.941399i
$623$	−32.9876	+	6.08736i	−1.32162	+	0.243885i
$624$	11.4199	−	15.0909i	0.457162	−	0.604119i
$625$	7.74132	−	19.7246i	0.309653	−	0.788983i
$626$	−15.0902	+	22.1332i	−0.603125	+	0.884622i
$627$	−4.47359	+	4.15088i	−0.178658	+	0.165770i
$628$	5.85956	−	3.99498i	0.233822	−	0.159417i
$629$	−6.84120	−	1.56146i	−0.272776	−	0.0622594i
$630$	0.241356	−	0.104007i	0.00961584	−	0.00414374i
$631$	−6.80518	−	7.33424i	−0.270910	−	0.291972i	0.582913	−	0.812534i	$-0.301913\pi$
$631$	−6.80518	−	7.33424i	−0.270910	−	0.291972i	−0.853823	+	0.520563i	$0.825722\pi$
$632$	9.42097	+	30.5421i	0.374746	+	1.21490i
$633$	−2.31816	+	2.90688i	−0.0921386	+	0.115538i
$634$	−10.6432	+	3.28298i	−0.422694	+	0.130384i
$635$	3.65371	+	7.58700i	0.144993	+	0.301081i
$636$	0.505215			0.0200331
$637$	−25.1341	+	2.29761i	−0.995848	+	0.0910345i
$638$	−10.8732			−0.430476
$639$	0.201665	+	0.418761i	0.00797773	+	0.0165659i
$640$	−3.47405	+	1.07160i	−0.137324	+	0.0423588i
$641$	−9.27987	+	11.6366i	−0.366533	+	0.459618i	−0.930560	−	0.366138i	$-0.880680\pi$
$641$	−9.27987	+	11.6366i	−0.366533	+	0.459618i	0.564028	+	0.825756i	$0.309251\pi$
$642$	2.96761	+	9.62075i	0.117122	+	0.379701i
$643$	−8.83531	−	9.52220i	−0.348431	−	0.375519i	0.534383	−	0.845243i	$-0.320544\pi$
$643$	−8.83531	−	9.52220i	−0.348431	−	0.375519i	−0.882814	+	0.469724i	$0.844354\pi$
$644$	−4.46164	+	5.13739i	−0.175813	+	0.202442i
$645$	3.75346	+	0.856702i	0.147792	+	0.0337326i
$646$	2.46288	−	1.67917i	0.0969009	−	0.0660659i
$647$	−32.3725	+	30.0373i	−1.27269	+	1.18089i	−0.298691	+	0.954350i	$0.596550\pi$
$647$	−32.3725	+	30.0373i	−1.27269	+	1.18089i	−0.974002	+	0.226538i	$0.927259\pi$
$648$	14.5243	−	21.3032i	0.570568	−	0.836870i
$649$	6.87059	−	17.5060i	0.269694	−	0.687170i
$650$	2.70025	−	21.6286i	0.105913	−	0.848345i
$651$	−13.0483	−	30.2794i	−0.511401	−	1.18674i
$652$	1.33010	+	1.95089i	0.0520906	+	0.0764028i
$653$	−6.36020	−	27.8659i	−0.248894	−	1.09048i	−0.932655	−	0.360770i	$-0.882514\pi$
$653$	−6.36020	−	27.8659i	−0.248894	−	1.09048i	0.683761	−	0.729706i	$-0.260343\pi$
$654$	−2.44539	−	3.06642i	−0.0956223	−	0.119907i
$655$	4.13424	+	2.38690i	0.161538	+	0.0932640i
$656$	17.2614	+	9.96588i	0.673945	+	0.389102i
$657$	−1.58096	−	0.620481i	−0.0616791	−	0.0242073i
$658$	−13.6633	−	26.1374i	−0.532652	−	1.01894i
$659$	−2.77263	−	0.417907i	−0.108007	−	0.0162794i	0.0948166	−	0.995495i	$-0.469774\pi$
$659$	−2.77263	−	0.417907i	−0.108007	−	0.0162794i	−0.202823	+	0.979215i	$0.565012\pi$
$660$	0.570011	−	0.714771i	0.0221876	−	0.0278224i
$661$	−34.1868	+	2.56195i	−1.32971	+	0.0996482i	−0.720554	−	0.693399i	$-0.756112\pi$
$661$	−34.1868	+	2.56195i	−1.32971	+	0.0996482i	−0.609160	+	0.793048i	$0.708493\pi$
$662$	−20.0412	+	13.6639i	−0.778924	+	0.531061i
$663$	2.21250	−	10.9708i	0.0859265	−	0.426069i
$664$	11.7223	−	14.6993i	0.454913	−	0.570443i
$665$	1.56995	−	0.676534i	0.0608799	−	0.0262349i
$666$	−0.736884	+	0.111067i	−0.0285537	+	0.00430378i
$667$	−10.2901	+	17.8229i	−0.398433	+	0.690107i
$668$	0.718576	+	0.414870i	0.0278025	+	0.0160518i
$669$	−2.63124	+	2.09834i	−0.101730	+	0.0811266i
$670$	−0.783000	+	2.53843i	−0.0302499	+	0.0980679i
$671$	8.67668	−	18.0173i	0.334960	−	0.695551i
$672$	9.31765	−	0.306496i	0.359436	−	0.0118233i
$673$	0.553799	−	7.38994i	0.0213474	−	0.284861i	−0.976306	−	0.216395i	$-0.930570\pi$
$673$	0.553799	−	7.38994i	0.0213474	−	0.284861i	0.997653	−	0.0684667i	$-0.0218107\pi$
$674$	−0.0272335	+	0.0217180i	−0.00104899	+	0.000836544i
$675$	1.88514	−	25.1554i	0.0725590	−	0.968233i
$676$	0.609757	+	4.82950i	0.0234522	+	0.185750i
$677$	−1.09034	−	14.5496i	−0.0419052	−	0.559185i	−0.978159	−	0.207860i	$-0.933350\pi$
$677$	−1.09034	−	14.5496i	−0.0419052	−	0.559185i	0.936253	−	0.351325i	$-0.114269\pi$
$678$	−23.3278	+	25.1414i	−0.895900	+	0.965550i
$679$	−5.33047	−	2.35438i	−0.204565	−	0.0903529i
$680$	−2.07575	+	1.92602i	−0.0796015	+	0.0738594i
$681$	0.657138	+	2.13039i	0.0251816	+	0.0816367i
$682$	−20.9545	−	16.7107i	−0.802390	−	0.639884i
$683$	−11.2683	−	2.57190i	−0.431168	−	0.0984112i	0.00142855	−	0.999999i	$-0.499545\pi$
$683$	−11.2683	−	2.57190i	−0.431168	−	0.0984112i	−0.432596	+	0.901588i	$0.642402\pi$
$684$	−0.0410775	+	0.0602496i	−0.00157064	+	0.00230370i
$685$	−4.30271	−	7.45252i	−0.164398	−	0.284746i
$686$	16.4689	+	16.9215i	0.628787	+	0.646066i
$687$	−14.6911	−	8.48189i	−0.560499	−	0.323604i
$688$	11.5357	+	7.86488i	0.439793	+	0.299846i
$689$	2.06308	−	2.01413i	0.0785970	−	0.0767324i
$690$	2.74441	+	6.99265i	0.104478	+	0.266206i
$691$	11.4449	+	2.61223i	0.435385	+	0.0993737i	0.434595	−	0.900626i	$-0.356891\pi$
$691$	11.4449	+	2.61223i	0.435385	+	0.0993737i	0.000789710		1.00000i	$0.499749\pi$
$692$	2.41297	+	0.744302i	0.0917273	+	0.0282941i
$693$	−0.931509	+	0.681006i	−0.0353851	+	0.0258693i
$694$	0.216484	+	0.0494111i	0.00821763	+	0.00187562i
$695$	−1.06205	−	1.55774i	−0.0402858	−	0.0590884i
$696$	14.9216	−	3.40576i	0.565602	−	0.129095i
$697$	11.7542	+	0.880852i	0.445220	+	0.0333647i
$698$	20.2873	−	3.05782i	0.767885	−	0.115740i
$699$	0.686636	−	9.16251i	0.0259709	−	0.346558i
$700$	3.98865	−	2.48117i	0.150757	−	0.0937795i
$701$	39.3739	+	18.9615i	1.48713	+	0.716164i	0.988580	−	0.150697i	$-0.0481516\pi$
$701$	39.3739	+	18.9615i	1.48713	+	0.716164i	0.498550	+	0.866861i	$0.333866\pi$
$702$	−4.25807	−	24.0835i	−0.160711	−	0.908974i
$703$	−4.79321	+	0.722460i	−0.180779	+	0.0272481i
$704$	21.8985	−	12.6431i	0.825332	−	0.476506i
$705$	7.50032			0.282478
$706$	14.8066	−	37.7266i	0.557253	−	1.41986i
$707$	−0.254072	−	0.189292i	−0.00955535	−	0.00711907i
$708$	−0.622185	+	4.12793i	−0.0233831	+	0.155137i
$709$	4.51435	−	1.77175i	0.169540	−	0.0665395i	−0.279053	−	0.960276i	$-0.590021\pi$
$709$	4.51435	−	1.77175i	0.169540	−	0.0665395i	0.448593	+	0.893736i	$0.351925\pi$
$710$	1.10759	+	1.62454i	0.0415671	+	0.0609678i
$711$	1.45762	+	0.701954i	0.0546651	+	0.0263253i
$712$	23.9313	−	30.0089i	0.896862	−	1.12463i
$713$	−47.2220	+	18.5333i	−1.76848	+	0.694077i
$714$	−9.27923	+	4.85071i	−0.347266	+	0.181533i
$715$	−0.521892	−	5.19127i	−0.0195177	−	0.194142i
$716$	−2.81870	−	4.88214i	−0.105340	−	0.182454i
$717$	−18.5436	+	10.7061i	−0.692523	+	0.399828i
$718$	0.520601	−	1.32647i	0.0194287	−	0.0495034i
$719$	21.9909	+	6.78328i	0.820121	+	0.252974i	0.676297	−	0.736629i	$-0.263584\pi$
$719$	21.9909	+	6.78328i	0.820121	+	0.252974i	0.143824	+	0.989603i	$0.454060\pi$
$720$	−0.105161	+	0.218368i	−0.00391911	+	0.00813811i
$721$	−14.3640	−	10.7017i	−0.534942	−	0.398550i
$722$	−12.4862	+	18.3138i	−0.464687	+	0.681571i
$723$	−17.7077	−	6.94975i	−0.658556	−	0.258464i
$724$	−4.93335	+	2.37577i	−0.183346	+	0.0882950i
$725$	10.4149	−	9.66361i	0.386800	−	0.358898i
$726$	−2.70634	+	5.61977i	−0.100442	+	0.208569i
$727$	8.94079	−	39.1722i	0.331596	−	1.45281i	−0.484446	−	0.874821i	$-0.660979\pi$
$727$	8.94079	−	39.1722i	0.331596	−	1.45281i	0.816041	−	0.577994i	$-0.196164\pi$
$728$	19.9898	−	20.8425i	0.740873	−	0.772474i
$729$	−6.28280	−	27.5267i	−0.232696	−	1.01951i
$730$	−7.00438	−	1.59871i	−0.259244	−	0.0591707i
$731$	8.16434	+	1.23058i	0.301969	+	0.0455145i
$732$	−0.987792	+	4.32780i	−0.0365098	+	0.159960i
$733$	14.9039	−	21.8600i	0.550489	−	0.807419i	−0.445650	−	0.895207i	$-0.647027\pi$
$733$	14.9039	−	21.8600i	0.550489	−	0.807419i	0.996139	+	0.0877882i	$0.0279799\pi$
$734$	0.665643	−	0.384309i	0.0245693	−	0.0141851i
$735$	−5.75387	+	1.71805i	−0.212235	+	0.0633714i
$736$		−	14.3437i		−	0.528715i
$737$	0.871603	−	11.6307i	0.0321059	−	0.428424i
$738$	1.19616	−	0.368966i	0.0440312	−	0.0135818i
$739$	4.41798	−	29.3114i	0.162518	−	1.07824i	−0.747679	−	0.664061i	$-0.768832\pi$
$739$	4.41798	−	29.3114i	0.162518	−	1.07824i	0.910197	−	0.414176i	$-0.135930\pi$
$740$	0.693906	−	0.214042i	0.0255085	−	0.00786833i
$741$	−1.34601	−	7.61298i	−0.0494469	−	0.279670i
$742$	−2.67912	−	0.314128i	−0.0983536	−	0.0115320i
$743$	9.52775	−	10.2685i	0.349539	−	0.376714i	−0.533670	−	0.845693i	$-0.679188\pi$
$743$	9.52775	−	10.2685i	0.349539	−	0.376714i	0.883209	+	0.468979i	$0.155378\pi$
$744$	33.9906	+	16.3690i	1.24615	+	0.600116i
$745$	1.01107	+	4.42979i	0.0370428	+	0.162295i
$746$	−46.1405	−	3.45775i	−1.68932	−	0.126597i
$747$	−0.141838	−	0.941035i	−0.00518959	−	0.0344307i
$748$	1.10446	−	1.61994i	0.0403830	−	0.0592309i
$749$	2.24711	+	12.1772i	0.0821077	+	0.444945i
$750$	−0.796212	−	10.6247i	−0.0290735	−	0.387959i
$751$	0.704600	+	3.08705i	0.0257112	+	0.112648i	0.986155	−	0.165825i	$-0.0530287\pi$
$751$	0.704600	+	3.08705i	0.0257112	+	0.112648i	−0.960444	+	0.278473i	$0.910172\pi$
$752$	25.3191	+	9.93702i	0.923293	+	0.362366i
$753$	−19.8703	+	34.4164i	−0.724115	+	1.25420i
$754$	7.46796	−	11.5744i	0.271967	−	0.421515i
$755$	4.52099	+	5.66915i	0.164536	+	0.206321i
$756$	3.45607	−	3.97952i	0.125696	−	0.144734i
$757$	−10.5220	−	26.8097i	−0.382430	−	0.974416i	−0.984408	−	0.175903i	$-0.943716\pi$
$757$	−10.5220	−	26.8097i	−0.382430	−	0.974416i	0.601978	−	0.798513i	$-0.294380\pi$
$758$	16.7778	+	42.7491i	0.609397	+	1.55272i
$759$	−18.5793	−	27.2508i	−0.674386	−	0.989142i
$760$	−0.848710	+	1.76236i	−0.0307859	+	0.0639277i
$761$	−42.3491	+	16.6208i	−1.53515	+	0.602503i	−0.974268	−	0.225391i	$-0.927634\pi$
$761$	−42.3491	+	16.6208i	−1.53515	+	0.602503i	−0.560884	+	0.827894i	$0.689539\pi$
$762$	−27.8560	−	22.2144i	−1.00912	−	0.804742i
$763$	−2.54795	−	4.09600i	−0.0922421	−	0.148285i
$764$	−8.91127	+	1.34316i	−0.322398	+	0.0485937i
$765$			0.143332i			0.00518217i
$766$	−20.0378	+	34.7064i	−0.723993	+	1.25399i
$767$	13.9160	+	19.3371i	0.502478	+	0.698222i
$768$	−10.7012	+	9.92925i	−0.386146	+	0.358291i
$769$	−6.02313	−	8.83431i	−0.217200	−	0.318573i	0.702139	−	0.712039i	$-0.252228\pi$
$769$	−6.02313	−	8.83431i	−0.217200	−	0.318573i	−0.919339	+	0.393466i	$0.871276\pi$
$770$	−3.46715	+	3.43597i	−0.124947	+	0.123824i
$771$	35.2774	+	24.0517i	1.27048	+	0.866202i
$772$	7.26008	+	2.84937i	0.261296	+	0.102551i
$773$	10.5019	+	21.8074i	0.377727	+	0.784358i	0.999999	+	0.00155669i	$0.000495509\pi$
$773$	10.5019	+	21.8074i	0.377727	+	0.784358i	−0.622272	+	0.782801i	$0.713790\pi$
$774$	0.854848	−	0.195114i	0.0307269	−	0.00701321i
$775$	34.9228	−	2.61710i	1.25446	−	0.0940092i
$776$	6.37152	−	1.96535i	0.228724	−	0.0705520i
$777$	17.0178	−	0.559785i	0.610509	−	0.0200822i
$778$	4.69129	−	15.2088i	0.168191	−	0.545262i
$779$	7.78066	−	2.40001i	0.278771	−	0.0859894i
$780$	0.369369	+	1.09769i	0.0132255	+	0.0393035i
$781$	−6.32821	−	5.87173i	−0.226441	−	0.210107i
$782$	6.98980	+	14.5145i	0.249955	+	0.519036i
$783$	7.97089	−	13.8060i	0.284856	−	0.493386i
$784$	−21.6997	−	1.82348i	−0.774991	−	0.0651241i
$785$		−	9.62936i		−	0.343687i
$786$	−20.1416	−	1.50940i	−0.718426	−	0.0538386i
$787$	−18.5169	−	4.22637i	−0.660058	−	0.150654i	−0.120646	−	0.992696i	$-0.538496\pi$
$787$	−18.5169	−	4.22637i	−0.660058	−	0.150654i	−0.539412	+	0.842042i	$0.681354\pi$
$788$	1.56673	−	0.614896i	0.0558125	−	0.0219048i
$789$	25.1814	+	23.3649i	0.896482	+	0.831813i
$790$	6.53983	+	2.01727i	0.232677	+	0.0717713i
$791$	−32.0968	+	27.3701i	−1.14123	+	0.973170i
$792$	0.293800	−	1.28722i	0.0104397	−	0.0457395i
$793$	13.2199	+	21.6109i	0.469451	+	0.767424i
$794$	22.0454	+	6.80011i	0.782363	+	0.241327i
$795$	0.386429	−	0.566788i	0.0137052	−	0.0201019i
$796$	−5.93654	−	7.44418i	−0.210415	−	0.263852i
$797$	−9.32013	−	6.35436i	−0.330136	−	0.225083i	0.386896	−	0.922123i	$-0.373547\pi$
$797$	−9.32013	−	6.35436i	−0.330136	−	0.225083i	−0.717032	+	0.697041i	$0.754500\pi$
$798$	−4.74269	+	5.46101i	−0.167890	+	0.193318i
$799$	16.0400	−	1.20203i	0.567454	−	0.0425248i
$800$	−2.91873	+	9.46228i	−0.103193	+	0.334542i
$801$	−0.289565	−	1.92114i	−0.0102313	−	0.0678802i
$802$	43.9997			1.55368
$803$	31.5442			1.11317
$804$	0.385875	+	2.56011i	0.0136088	+	0.0902883i
$805$	2.35089	+	8.93489i	0.0828578	+	0.314913i
$806$	32.1802	−	10.8286i	1.13350	−	0.381420i
$807$	0.306662	+	0.0462219i	0.0107950	+	0.00162709i
$808$	0.361518	−	0.0270921i	0.0127182	−	0.000953095i
$809$	0.948714	+	12.6597i	0.0333550	+	0.445091i	0.988731	+	0.149700i	$0.0478309\pi$
$809$	0.948714	+	12.6597i	0.0333550	+	0.445091i	−0.955376	+	0.295391i	$0.904550\pi$
$810$	−2.01700	−	5.13924i	−0.0708703	−	0.180575i
$811$	28.1503	+	22.4491i	0.988489	+	0.788294i	0.977347	−	0.211644i	$-0.0678817\pi$
$811$	28.1503	+	22.4491i	0.988489	+	0.788294i	0.0111425	+	0.999938i	$0.496453\pi$
$812$	2.95137	−	0.319044i	0.103573	−	0.0111962i
$813$	−25.3904	−	9.96500i	−0.890481	−	0.349488i
$814$	11.9867	−	6.92050i	0.420132	−	0.242563i
$815$	3.20602			0.112302
$816$	3.52781	−	8.98872i	0.123498	−	0.314668i
$817$	5.56053	−	1.26915i	0.194538	−	0.0444021i
$818$	−15.7970	−	7.60742i	−0.552328	−	0.265987i
$819$	−0.0851426	−	1.45931i	−0.00297512	−	0.0509923i
$820$	−1.09899	+	0.529247i	−0.0383785	+	0.0184821i
$821$	21.9796	−	17.5281i	0.767093	−	0.611736i	−0.159762	−	0.987155i	$-0.551073\pi$
$821$	21.9796	−	17.5281i	0.767093	−	0.611736i	0.926855	+	0.375420i	$0.122501\pi$
$822$	30.0831	+	20.5103i	1.04927	+	0.715379i
$823$	−0.388397	−	1.70168i	−0.0135387	−	0.0593167i	0.967707	−	0.252076i	$-0.0811134\pi$
$823$	−0.388397	−	1.70168i	−0.0135387	−	0.0593167i	−0.981246	+	0.192760i	$0.938256\pi$
$824$	20.4385	−	1.53165i	0.712007	−	0.0533576i
$825$	6.71130	+	21.7575i	0.233658	+	0.757499i
$826$	5.86602	−	21.5032i	0.204105	−	0.748194i
$827$	36.3381	−	8.29394i	1.26360	−	0.288408i	0.462328	−	0.886709i	$-0.347014\pi$
$827$	36.3381	−	8.29394i	1.26360	−	0.288408i	0.801272	+	0.598301i	$0.204157\pi$
$828$	−0.288892	−	0.268053i	−0.0100397	−	0.00931548i
$829$	−33.7325	−	5.08436i	−1.17158	−	0.176587i	−0.465715	−	0.884935i	$-0.654203\pi$
$829$	−33.7325	−	5.08436i	−1.17158	−	0.176587i	−0.705864	+	0.708347i	$0.749441\pi$
$830$	−1.18662	−	3.84694i	−0.0411883	−	0.133529i
$831$	22.8933	+	15.6084i	0.794160	+	0.541449i
$832$	−1.58192	+	31.9942i	−0.0548431	+	1.10920i
$833$	−12.0297	+	4.59632i	−0.416805	+	0.159253i
$834$	6.90819	+	3.98845i	0.239211	+	0.138109i
$835$	1.01506	−	0.488826i	0.0351275	−	0.0169165i
$836$	0.301376	−	1.32042i	0.0104233	−	0.0456676i
$837$	36.5791	−	14.3562i	1.26436	−	0.496224i
$838$	11.7867	−	12.7030i	0.407164	−	0.438818i
$839$	13.1691	+	14.1929i	0.454647	+	0.489993i	0.918223	−	0.396064i	$-0.129624\pi$
$839$	13.1691	+	14.1929i	0.454647	+	0.489993i	−0.463576	+	0.886057i	$0.653434\pi$
$840$	3.68183	−	5.80126i	0.127035	−	0.200162i
$841$	−19.1319	+	5.90141i	−0.659721	+	0.203497i
$842$	−9.85651	−	4.74664i	−0.339678	−	0.163580i
$843$	5.72205	+	6.16690i	0.197078	+	0.212399i
$844$	0.0616633	−	0.822839i	0.00212254	−	0.0283233i
$845$	5.88448	+	3.00992i	0.202432	+	0.103544i
$846$	1.53903	−	0.741158i	0.0529130	−	0.0254815i
$847$	−4.11080	+	6.47716i	−0.141249	+	0.222558i
$848$	2.05541	−	1.40135i	0.0705830	−	0.0481227i
$849$	43.4789	+	13.4115i	1.49219	+	0.460281i
$850$	−1.65757	−	10.9973i	−0.0568542	−	0.377203i
$851$		−	26.1973i		−	0.898033i
$852$	1.65955	+	0.958144i	0.0568554	+	0.0328255i
$853$	−9.33310	+	7.44290i	−0.319559	+	0.254840i	−0.770110	−	0.637911i	$-0.779799\pi$
$853$	−9.33310	+	7.44290i	−0.319559	+	0.254840i	0.450551	+	0.892751i	$0.351228\pi$
$854$	7.92909	−	22.3358i	0.271328	−	0.764317i
$855$	0.0361731	+	0.0921675i	0.00123709	+	0.00315206i
$856$	−11.0776	−	8.83409i	−0.378624	−	0.301943i
$857$	−30.3328	+	20.6805i	−1.03615	+	0.706434i	−0.956899	−	0.290421i	$-0.906205\pi$
$857$	−30.3328	+	20.6805i	−1.03615	+	0.706434i	−0.0792490	+	0.996855i	$0.525252\pi$
$858$	11.5194	+	18.8311i	0.393267	+	0.642884i
$859$	−29.9185	−	4.50949i	−1.02081	−	0.153862i	−0.382751	−	0.923852i	$-0.625023\pi$
$859$	−29.9185	−	4.50949i	−1.02081	−	0.153862i	−0.638056	+	0.769990i	$0.720261\pi$
$860$	−0.795366	+	0.312158i	−0.0271217	+	0.0106445i
$861$	−28.1264	+	5.19030i	−0.958545	+	0.176885i
$862$	−11.1850	+	28.4990i	−0.380964	+	0.970680i
$863$	−40.7005	+	23.4984i	−1.38546	+	0.799896i	−0.992800	−	0.119787i	$-0.961779\pi$
$863$	−40.7005	+	23.4984i	−1.38546	+	0.799896i	−0.392661	+	0.919683i	$0.628446\pi$
$864$			11.1109i			0.378000i
$865$	2.68065	−	2.13774i	0.0911447	−	0.0726855i
$866$	−6.61020	−	7.12410i	−0.224624	−	0.242087i
$867$	1.71674	+	22.9083i	0.0583036	+	0.778008i
$868$	6.17809	+	3.92100i	0.209698	+	0.133087i
$869$	−29.9647	−	2.24554i	−1.01648	−	0.0761748i
$870$	1.19732	−	3.05072i	0.0405929	−	0.103429i
$871$	11.7821	+	8.91603i	0.399222	+	0.302108i
$872$	5.27436	+	1.62692i	0.178612	+	0.0550946i
$873$	0.146438	−	0.304081i	0.00495617	−	0.0102916i
$874$	8.15776	+	7.56929i	0.275940	+	0.256035i
$875$	0.549130	−	13.0926i	0.0185640	−	0.442609i
$876$	−6.82664	+	1.55814i	−0.230651	+	0.0526445i
$877$	14.8129	−	15.9645i	0.500195	−	0.539082i	−0.431601	−	0.902065i	$-0.642051\pi$
$877$	14.8129	−	15.9645i	0.500195	−	0.539082i	0.931796	+	0.362983i	$0.118242\pi$
$878$	−5.11148	−	4.07627i	−0.172504	−	0.137567i
$879$	1.90008	−	2.04780i	0.0640881	−	0.0690706i
$880$	0.336407	−	4.48904i	0.0113403	−	0.151326i
$881$	13.8992	−	24.0742i	0.468277	−	0.811079i	−0.531066	−	0.847330i	$-0.678208\pi$
$881$	13.8992	−	24.0742i	0.468277	−	0.811079i	0.999343	+	0.0362514i	$0.0115417\pi$
$882$	−1.01089	+	0.921115i	−0.0340385	+	0.0310156i
$883$	39.3904			1.32559			0.662797	−	0.748799i	$-0.269369\pi$
$883$	39.3904			1.32559			0.662797	+	0.748799i	$0.269369\pi$
$884$	0.965842	+	2.28829i	0.0324848	+	0.0769634i
$885$	4.15511	+	3.85538i	0.139673	+	0.129597i
$886$	7.81438	−	51.8450i	0.262529	−	1.74177i
$887$	3.67757	−	16.1125i	0.123481	−	0.541005i	−0.874909	−	0.484286i	$-0.839079\pi$
$887$	3.67757	−	16.1125i	0.123481	−	0.541005i	0.998390	−	0.0567180i	$-0.0180636\pi$
$888$	−14.2819	+	13.2517i	−0.479270	+	0.444697i
$889$	−30.8455	−	31.1255i	−1.03453	−	1.04392i
$890$	−2.42251	−	7.85359i	−0.0812028	−	0.263253i
$891$	13.6548	+	20.0280i	0.457454	+	0.670962i
$892$	0.220153	−	0.713720i	0.00737128	−	0.0238971i
$893$	10.0109	−	4.82101i	0.335003	−	0.161329i
$894$	−11.9863	−	15.0303i	−0.400881	−	0.502689i
$895$	−7.63311	−	0.572023i	−0.255147	−	0.0191206i
$896$	15.2725	−	11.1654i	0.510219	−	0.373010i
$897$	41.7687	−	1.06100i	1.39462	−	0.0354256i
$898$	−6.77568	+	6.28691i	−0.226107	+	0.209797i
$899$	20.6018	+	8.08561i	0.687108	+	0.269670i
$900$	0.136032	+	0.235615i	0.00453441	+	0.00785384i
$901$	0.735571	−	1.27405i	0.0245054	−	0.0424446i
$902$	−18.1773	+	14.4959i	−0.605237	+	0.482660i
$903$	−19.9184	+	2.15318i	−0.662842	+	0.0716534i
$904$	7.19369	−	47.7270i	0.239259	−	1.58738i
$905$	−1.10810	+	7.35178i	−0.0368346	+	0.244381i
$906$	−27.6413	−	13.3114i	−0.918322	−	0.442241i
$907$	−2.56732	−	34.2585i	−0.0852464	−	1.13753i	−0.861720	−	0.507384i	$-0.830612\pi$
$907$	−2.56732	−	34.2585i	−0.0852464	−	1.13753i	0.776473	−	0.630150i	$-0.217007\pi$
$908$	−0.386835	−	0.308491i	−0.0128376	−	0.0102376i
$909$	0.0114413	−	0.0143470i	0.000379485	−	0.000475859i
$910$	−1.27623	−	6.05062i	−0.0423066	−	0.200576i
$911$	−19.8117	−	24.8430i	−0.656389	−	0.823086i	0.336555	−	0.941664i	$-0.390738\pi$
$911$	−19.8117	−	24.8430i	−0.656389	−	0.823086i	−0.992945	+	0.118577i	$0.962167\pi$
$912$		−	6.67040i		−	0.220879i
$913$	8.83780	+	15.3075i	0.292488	+	0.506605i
$914$	6.98289	+	8.75627i	0.230973	+	0.289632i
$915$	4.09970	+	4.41843i	0.135532	+	0.146069i
$916$	3.75425	−	0.281342i	0.124044	−	0.00929582i
$917$	−24.3876	−	4.72860i	−0.805349	−	0.156152i
$918$	−5.41443	−	11.2432i	−0.178703	−	0.371080i
$919$	−2.75255	+	0.414880i	−0.0907982	+	0.0136856i	−0.194284	−	0.980945i	$-0.562238\pi$
$919$	−2.75255	+	0.414880i	−0.0907982	+	0.0136856i	0.103486	+	0.994631i	$0.467000\pi$
$920$	−8.73462	−	5.95516i	−0.287972	−	0.196336i
$921$	−38.3481	−	41.3294i	−1.26361	−	1.36185i
$922$	−2.30256	−	30.7256i	−0.0758309	−	1.01189i
$923$	10.5967	−	2.70348i	0.348795	−	0.0889861i
$924$	−1.59155	+	4.48331i	−0.0523580	+	0.147490i
$925$	−5.33077	+	17.2819i	−0.175275	+	0.568227i
$926$	−9.87378	+	43.2599i	−0.324473	+	1.42161i
$927$	0.646836	−	0.811107i	0.0212449	−	0.0266403i
$928$	−4.25638	+	4.58728i	−0.139722	+	0.150585i
$929$	55.4120	+	4.15256i	1.81801	+	0.136241i	0.939733	−	0.341910i	$-0.111074\pi$
$929$	55.4120	+	4.15256i	1.81801	+	0.136241i	0.878277	+	0.478151i	$0.158693\pi$
$930$	6.99596	−	4.03912i	0.229407	−	0.132448i
$931$	−6.57555	+	5.99158i	−0.215505	+	0.196366i
$932$	1.01957	+	1.76595i	0.0333972	+	0.0578456i
$933$	33.8804	−	16.3159i	1.10919	−	0.534160i
$934$	−1.18099	−	3.82867i	−0.0386432	−	0.125278i
$935$	−0.972592	−	2.47812i	−0.0318071	−	0.0810433i
$936$	1.16844	+	1.19684i	0.0381918	+	0.0391198i
$937$	−2.04556	−	8.96217i	−0.0668255	−	0.292781i	0.930462	−	0.366389i	$-0.119406\pi$
$937$	−2.04556	−	8.96217i	−0.0668255	−	0.292781i	−0.997287	+	0.0736074i	$0.976549\pi$
$938$	−0.454466	−	13.8160i	−0.0148388	−	0.451110i
$939$	25.9866	+	24.1120i	0.848041	+	0.786867i
$940$	−1.37532	+	0.937675i	−0.0448579	+	0.0305836i
$941$	0.442249	−	1.43374i	0.0144169	−	0.0467385i	−0.948079	−	0.318036i	$-0.896977\pi$
$941$	0.442249	−	1.43374i	0.0144169	−	0.0467385i	0.962495	+	0.271298i	$0.0874528\pi$
$942$	17.6773	+	36.7073i	0.575957	+	1.19599i
$943$	6.55865	+	43.5138i	0.213579	+	1.41700i
$944$	8.91866	+	18.5198i	0.290278	+	0.602767i
$945$	−1.82104	−	6.92113i	−0.0592384	−	0.225145i
$946$	−13.4559	+	9.17407i	−0.437488	+	0.298275i
$947$	29.7825	−	6.79767i	0.967802	−	0.220895i	0.290725	−	0.956807i	$-0.406103\pi$
$947$	29.7825	−	6.79767i	0.967802	−	0.220895i	0.677077	+	0.735912i	$0.263246\pi$
$948$	6.59571	−	0.994144i	0.214219	−	0.0322883i
$949$	−21.6652	+	33.5784i	−0.703283	+	1.09000i
$950$	−3.84129	−	6.65332i	−0.124628	−	0.215862i
$951$	2.19680	+	14.5748i	0.0712363	+	0.472622i
$952$	6.94413	−	12.9965i	0.225060	−	0.421218i
$953$	49.9047	+	7.52192i	1.61657	+	0.243659i	0.894141	−	0.447785i	$-0.147787\pi$
$953$	49.9047	+	7.52192i	1.61657	+	0.243659i	0.722430	+	0.691444i	$0.243025\pi$
$954$	0.0232853	−	0.154488i	0.000753889	−	0.00500173i
$955$	−5.30920	+	11.0247i	−0.171802	+	0.356750i
$956$	2.06183	−	4.28144i	0.0666844	−	0.138472i
$957$	−2.14459	+	14.2284i	−0.0693247	+	0.459939i
$958$	−4.62216	−	0.696678i	−0.149335	−	0.0225087i
$959$	33.8101	+	29.3629i	1.09179	+	0.948177i
$960$	1.13592	+	7.53632i	0.0366616	+	0.243234i
$961$	11.7766	+	20.3976i	0.379889	+	0.657987i
$962$	−0.865898	+	17.5128i	−0.0279177	+	0.564634i
$963$	−0.709178	+	0.106891i	−0.0228529	+	0.00344453i
$964$	4.11586	−	0.939418i	0.132563	−	0.0302566i
$965$	8.74973	−	5.96547i	0.281664	−	0.192035i
$966$	−25.3640	−	29.7442i	−0.816073	−	0.957005i
$967$	−6.54779	−	13.5966i	−0.210563	−	0.437238i	0.768761	−	0.639536i	$-0.220873\pi$
$967$	−6.54779	−	13.5966i	−0.210563	−	0.437238i	−0.979324	+	0.202298i	$0.935159\pi$
$968$	−1.30829	−	8.67996i	−0.0420502	−	0.278985i
$969$	−1.71154	−	3.55405i	−0.0549826	−	0.114173i
$970$	0.420832	−	1.36430i	0.0135121	−	0.0438052i
$971$	−35.1620	+	23.9730i	−1.12840	+	0.769332i	−0.975737	−	0.218946i	$-0.929738\pi$
$971$	−35.1620	+	23.9730i	−1.12840	+	0.769332i	−0.152665	+	0.988278i	$0.548786\pi$
$972$	0.436688	+	0.405187i	0.0140068	+	0.0129964i
$973$	7.86739	+	5.86149i	0.252217	+	0.187911i
$974$	−10.0888	−	44.2018i	−0.323265	−	1.41632i
$975$	−27.7700	−	7.79940i	−0.889353	−	0.249781i
$976$	7.98563	+	20.3471i	0.255614	+	0.651293i
$977$	−13.4214	−	43.5111i	−0.429388	−	1.39204i	−0.869426	−	0.494063i	$-0.835511\pi$
$977$	−13.4214	−	43.5111i	−0.429388	−	1.39204i	0.440038	−	0.897979i	$-0.354965\pi$
$978$	−12.2214	+	5.88551i	−0.390797	+	0.188198i
$979$	18.0425	+	31.2506i	0.576642	+	0.998772i
$980$	0.840285	−	1.03437i	0.0268419	−	0.0330418i
$981$	0.241957	−	0.139694i	0.00772508	−	0.00446008i
$982$	49.7563	+	3.72872i	1.58779	+	0.118988i
$983$	−18.6093	+	20.0561i	−0.593545	+	0.639689i	−0.956367	−	0.292169i	$-0.905623\pi$
$983$	−18.6093	+	20.0561i	−0.593545	+	0.639689i	0.362822	+	0.931859i	$0.381813\pi$
$984$	20.4046	−	25.5866i	0.650476	−	0.815672i
$985$	0.508526	−	2.22800i	0.0162030	−	0.0709899i
$986$	2.07163	−	6.71607i	0.0659743	−	0.213883i
$987$	−36.8976	+	12.7242i	−1.17446	+	0.405016i
$988$	1.19857	+	1.22770i	0.0381317	+	0.0390583i
$989$	2.30352	+	30.7383i	0.0732476	+	0.977422i
$990$	−0.192295	−	0.207245i	−0.00611155	−	0.00658668i
$991$	−15.6943	−	10.7002i	−0.498546	−	0.339903i	0.287799	−	0.957691i	$-0.407077\pi$
$991$	−15.6943	−	10.7002i	−0.498546	−	0.339903i	−0.786345	+	0.617788i	$0.788029\pi$
$992$	−15.2528	+	2.29898i	−0.484275	+	0.0729928i
$993$	13.9273	+	28.9203i	0.441970	+	0.917759i
$994$	−8.20475	−	6.11283i	−0.260239	−	0.193887i
$995$	−12.8922	+	0.966135i	−0.408710	+	0.0306285i
$996$	−2.66875	−	2.87623i	−0.0845625	−	0.0911367i
$997$	33.1078	+	41.5159i	1.04854	+	1.31482i	0.947436	+	0.319946i	$0.103665\pi$
$997$	33.1078	+	41.5159i	1.04854	+	1.31482i	0.101100	+	0.994876i	$0.467764\pi$
$998$	−15.2620	−	26.4346i	−0.483112	−	0.836774i
$999$			20.2930i			0.642041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bz.a.4.19	yes	756
13.10	even	6		637.2.bp.a.543.19	✓	756
49.37	even	21		637.2.bp.a.576.19	yes	756
637.478	even	42	inner	637.2.bz.a.478.19	yes	756

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bp.a.543.19	✓	756	13.10	even	6
637.2.bp.a.576.19	yes	756	49.37	even	21
637.2.bz.a.4.19	yes	756	1.1	even	1	trivial
637.2.bz.a.478.19	yes	756	637.478	even	42	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bz (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.553189 - 1.14871i) q^{2} +(-1.61228 + 0.497321i) q^{3} +(0.233465 - 0.292756i) q^{4} +(-0.149862 - 0.485842i) q^{5} +(1.46317 + 1.57692i) q^{6} +(1.56147 + 2.13584i) q^{7} +(-2.95145 - 0.673650i) q^{8} +(-0.126610 + 0.0863216i) q^{9} +(-0.475189 + 0.440911i) q^{10} +(1.60328 - 2.35158i) q^{11} +(-0.230816 + 0.588111i) q^{12} +(1.40206 + 3.32178i) q^{13} +(1.58967 - 2.97520i) q^{14} +(0.483239 + 0.708782i) q^{15} +(0.692238 + 3.03289i) q^{16} +(1.14703 + 1.43833i) q^{17} +(0.169198 + 0.0976865i) q^{18} +(1.10058 + 0.635421i) q^{19} +(-0.177221 - 0.0695540i) q^{20} +(-3.57972 - 2.66702i) q^{21} +(-3.58820 - 0.540834i) q^{22} +(-4.28226 + 5.36979i) q^{23} +(5.09358 - 0.381711i) q^{24} +(3.91761 - 2.67098i) q^{25} +(3.04016 - 3.44813i) q^{26} +(3.31712 - 4.15954i) q^{27} +(0.989829 + 0.0415155i) q^{28} +(2.96297 - 0.446595i) q^{29} +(0.546861 - 0.947191i) q^{30} +(6.39647 + 3.69300i) q^{31} +(-1.63279 + 1.30210i) q^{32} +(-1.41544 + 4.58874i) q^{33} +(1.01770 - 2.11328i) q^{34} +(0.803676 - 1.07871i) q^{35} +(-0.00428798 + 0.0572191i) q^{36} +(-2.98213 + 2.37817i) q^{37} +(0.121084 - 1.61576i) q^{38} +(-3.91250 - 4.65835i) q^{39} +(0.115024 + 1.53489i) q^{40} +(4.35793 - 4.69673i) q^{41} +(-1.08336 + 5.58742i) q^{42} +(3.28993 - 3.05261i) q^{43} +(-0.314129 - 1.01838i) q^{44} +(0.0609128 + 0.0485763i) q^{45} +(8.53723 + 1.94857i) q^{46} +(4.92525 - 7.22402i) q^{47} +(-2.62440 - 4.54560i) q^{48} +(-2.12364 + 6.67009i) q^{49} +(-5.23536 - 3.02264i) q^{50} +(-2.56465 - 1.74855i) q^{51} +(1.29980 + 0.365059i) q^{52} +(-0.292150 - 0.744387i) q^{53} +(-6.61310 - 1.50940i) q^{54} +(-1.38277 - 0.426527i) q^{55} +(-3.16979 - 7.35571i) q^{56} +(-2.09045 - 0.477131i) q^{57} +(-2.15209 - 3.15653i) q^{58} +(6.44190 - 1.47032i) q^{59} +(0.320320 + 0.0240046i) q^{60} +(6.94781 - 1.04721i) q^{61} +(0.703729 - 9.39061i) q^{62} +(-0.382067 - 0.135632i) q^{63} +(8.00461 + 3.85482i) q^{64} +(1.40374 - 1.17899i) q^{65} +(6.05414 - 0.912514i) q^{66} +(3.54895 - 2.04899i) q^{67} +0.688873 q^{68} +(4.23368 - 10.7872i) q^{69} +(-1.68371 - 0.326460i) q^{70} +(0.452066 - 2.99926i) q^{71} +(0.431835 - 0.169483i) q^{72} +(6.24340 + 9.15739i) q^{73} +(4.38150 + 2.11002i) q^{74} +(-4.98793 + 6.25467i) q^{75} +(0.442971 - 0.173853i) q^{76} +(7.52607 - 0.247563i) q^{77} +(-3.18674 + 7.07128i) q^{78} +(-5.27887 - 9.14328i) q^{79} +(1.36977 - 0.790835i) q^{80} +(-3.11154 + 7.92807i) q^{81} +(-7.80594 - 2.40781i) q^{82} +(-2.69459 + 5.59538i) q^{83} +(-1.61652 + 0.425328i) q^{84} +(0.526906 - 0.772829i) q^{85} +(-5.32652 - 2.09050i) q^{86} +(-4.55502 + 2.19358i) q^{87} +(-6.31614 + 5.86053i) q^{88} +(-5.50106 + 11.4231i) q^{89} +(0.0221038 - 0.0968430i) q^{90} +(-4.90553 + 8.18143i) q^{91} +(0.572279 + 2.50732i) q^{92} +(-12.1495 - 2.77304i) q^{93} +(-11.0229 - 1.66143i) q^{94} +(0.143778 - 0.629934i) q^{95} +(1.98494 - 2.91137i) q^{96} +(-1.90742 + 1.10125i) q^{97} +(8.83677 - 1.25038i) q^{98} +0.436132i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 756 q - 21 q^{2} - 5 q^{3} + 115 q^{4} - 15 q^{6} - 14 q^{7} + 50 q^{9} - 16 q^{10} - 24 q^{11} - 26 q^{12} - 10 q^{13} - 38 q^{14} - 6 q^{15} - 125 q^{16} + 15 q^{17} - 9 q^{18} - 27 q^{19} - 15 q^{20}+ \cdots + 105 q^{98}+O(q^{100}) \) 756 * q - 21 * q^2 - 5 * q^3 + 115 * q^4 - 15 * q^6 - 14 * q^7 + 50 * q^9 - 16 * q^10 - 24 * q^11 - 26 * q^12 - 10 * q^13 - 38 * q^14 - 6 * q^15 - 125 * q^16 + 15 * q^17 - 9 * q^18 - 27 * q^19 - 15 * q^20 - 16 * q^21 - q^22 - 5 * q^23 - 39 * q^24 - 79 * q^25 - 34 * q^26 - 50 * q^27 - 142 * q^28 - 3 * q^29 - 11 * q^30 - 15 * q^31 - 21 * q^32 - 6 * q^33 - 12 * q^35 - 84 * q^36 + 7 * q^37 - 2 * q^38 - 6 * q^39 - 24 * q^40 - 6 * q^41 + 88 * q^42 - 5 * q^43 + 108 * q^44 - 21 * q^45 - 21 * q^46 + 63 * q^47 - 154 * q^48 - 34 * q^49 + 135 * q^50 + 26 * q^51 + 89 * q^52 + 16 * q^53 - 21 * q^54 - 4 * q^55 + 58 * q^56 - 63 * q^57 - 18 * q^58 - 21 * q^59 + 15 * q^60 - 75 * q^61 - 87 * q^62 + 147 * q^63 + 4 * q^64 - 20 * q^65 + 85 * q^66 - 27 * q^67 + 312 * q^68 - 182 * q^69 - 228 * q^70 - 30 * q^71 - 120 * q^72 + 6 * q^73 - 43 * q^74 + 83 * q^75 + 21 * q^76 + 3 * q^77 + 79 * q^78 + 12 * q^79 + 57 * q^80 + 72 * q^81 - 248 * q^82 + 147 * q^83 - 14 * q^84 - 24 * q^85 - 60 * q^86 - 37 * q^87 + 70 * q^88 - 126 * q^89 + 117 * q^90 - 55 * q^91 + 88 * q^92 - 21 * q^93 + 210 * q^94 + 9 * q^95 - 12 * q^96 - 156 * q^97 + 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more