LMFDB - Embedded newform 637.2.bz.a.478.19

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			478.19
Character	$\chi$	$=$	637.478
Dual form			637.2.bz.a.4.19

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$

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	0.608659	+	0.793432i	$0.291708\pi$
$2$	−0.553189	+	1.14871i	−0.391164	+	0.812260i	−0.999823	+	0.0188280i	$0.994006\pi$
$3$	−1.61228	−	0.497321i	−0.930848	−	0.287129i	−0.207995	−	0.978130i	$-0.566694\pi$
$3$	−1.61228	−	0.497321i	−0.930848	−	0.287129i	−0.722853	+	0.691001i	$0.757170\pi$
$4$	0.233465	+	0.292756i	0.116733	+	0.146378i
$5$	−0.149862	+	0.485842i	−0.0670205	+	0.217275i	−0.982888	−	0.184207i	$-0.941028\pi$
$5$	−0.149862	+	0.485842i	−0.0670205	+	0.217275i	0.915867	+	0.401482i	$0.131505\pi$
$6$	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	0.988021	−	0.154317i	$-0.0493177\pi$
$11$	1.60328	+	2.35158i	0.483407	+	0.709028i	−0.504614	+	0.863345i	$0.668365\pi$
$12$	−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	−0.623028	−	0.782199i	$-0.714098\pi$
$17$	1.14703	−	1.43833i	0.278196	−	0.348847i	0.901225	+	0.433352i	$0.142669\pi$
$18$	0.169198	−	0.0976865i	0.0398803	−	0.0230249i
$19$	1.10058	−	0.635421i	0.252491	−	0.145776i	−0.368413	−	0.929662i	$-0.620099\pi$
$19$	1.10058	−	0.635421i	0.252491	−	0.145776i	0.620904	+	0.783886i	$0.286766\pi$
$20$	−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	−0.992205	−	0.124620i	$-0.960229\pi$
$23$	−4.28226	−	5.36979i	−0.892914	−	1.11968i	0.0992906	−	0.995058i	$-0.468343\pi$
$24$	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	0.418262	−	0.908326i	$-0.362639\pi$
$29$	2.96297	+	0.446595i	0.550209	+	0.0829306i	0.131946	+	0.991257i	$0.457877\pi$
$30$	0.546861	+	0.947191i	0.0998427	+	0.172933i
$31$	6.39647	−	3.69300i	1.14884	−	0.663283i	0.200236	−	0.979748i	$-0.435829\pi$
$31$	6.39647	−	3.69300i	1.14884	−	0.663283i	0.948604	+	0.316465i	$0.102496\pi$
$32$	−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	0.346923	−	0.937894i	$-0.387227\pi$
$37$	−2.98213	−	2.37817i	−0.490259	−	0.390968i	−0.837181	+	0.546926i	$0.815798\pi$
$38$	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	0.975007	−	0.222172i	$-0.0713147\pi$
$41$	4.35793	+	4.69673i	0.680594	+	0.733506i	−0.294413	+	0.955678i	$0.595124\pi$
$42$	−1.08336	−	5.58742i	−0.167167	−	0.862157i
$43$	3.28993	+	3.05261i	0.501710	+	0.465519i	0.889962	−	0.456034i	$-0.150731\pi$
$43$	3.28993	+	3.05261i	0.501710	+	0.465519i	−0.388252	+	0.921553i	$0.626921\pi$
$44$	−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	0.995672	+	0.0929334i	$0.0296244\pi$
$47$	4.92525	+	7.22402i	0.718422	+	1.05373i	−0.277251	+	0.960798i	$0.589423\pi$
$48$	−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	−0.949534	−	0.313665i	$-0.898443\pi$
$53$	−0.292150	+	0.744387i	−0.0401299	+	0.102249i	0.909404	+	0.415914i	$0.136538\pi$
$54$	−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	0.620218	−	0.784430i	$-0.287044\pi$
$59$	6.44190	+	1.47032i	0.838664	+	0.191420i	0.218446	+	0.975849i	$0.429901\pi$
$60$	0.320320	−	0.0240046i	0.0413531	−	0.00309899i
$61$	6.94781	+	1.04721i	0.889576	+	0.134082i	0.577901	−	0.816107i	$-0.303872\pi$
$61$	6.94781	+	1.04721i	0.889576	+	0.134082i	0.311675	+	0.950189i	$0.399110\pi$
$62$	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	0.700868	−	0.713291i	$-0.252796\pi$
$67$	3.54895	+	2.04899i	0.433573	+	0.250324i	−0.267295	+	0.963615i	$0.586130\pi$
$68$	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	0.999508	+	0.0313651i	$0.00998545\pi$
$71$	0.452066	+	2.99926i	0.0536504	+	0.355947i	−0.945858	+	0.324582i	$0.894776\pi$
$72$	0.431835	+	0.169483i	0.0508923	+	0.0199737i
$73$	6.24340	−	9.15739i	0.730735	−	1.07179i	−0.263510	−	0.964657i	$-0.584880\pi$
$73$	6.24340	−	9.15739i	0.730735	−	1.07179i	0.994245	−	0.107134i	$-0.0341675\pi$
$74$	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	0.399779	+	0.916612i	$0.369087\pi$
$79$	−5.27887	+	9.14328i	−0.593920	+	1.02870i	−0.993698	+	0.112087i	$0.964246\pi$
$80$	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	0.699135	−	0.714990i	$-0.253569\pi$
$83$	−2.69459	−	5.59538i	−0.295770	−	0.614173i	−0.994905	+	0.100817i	$0.967854\pi$
$84$	−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	−0.958796	−	0.284096i	$-0.908307\pi$
$89$	−5.50106	−	11.4231i	−0.583111	−	1.21084i	0.375685	−	0.926748i	$-0.377408\pi$
$90$	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	0.400030	−	0.916502i	$-0.369000\pi$
$97$	−1.90742	−	1.10125i	−0.193669	−	0.111815i	−0.593699	+	0.804687i	$0.702333\pi$
$98$	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	0.289057	−	0.957312i	$-0.406658\pi$
$101$	−0.114432	−	0.0352976i	−0.0113864	−	0.00351224i	−0.300443	+	0.953800i	$0.597135\pi$
$102$	−0.589837	−	3.91331i	−0.0584026	−	0.387476i
$103$	−6.46941	−	1.99555i	−0.637450	−	0.196627i	−0.0408491	−	0.999165i	$-0.513006\pi$
$103$	−6.46941	−	1.99555i	−0.637450	−	0.196627i	−0.596601	+	0.802538i	$0.703482\pi$
$104$	−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	−0.218810	−	0.975767i	$-0.570218\pi$
$107$	4.21676	−	2.03069i	0.407650	−	0.196314i	0.626460	+	0.779454i	$0.284503\pi$
$108$	−0.443298	+	1.94222i	−0.0426564	+	0.186890i
$109$	−1.81814	+	0.136251i	−0.174146	+	0.0130504i	−0.161518	−	0.986870i	$-0.551639\pi$
$109$	−1.81814	+	0.136251i	−0.174146	+	0.0130504i	−0.0126283	+	0.999920i	$0.504020\pi$
$110$	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	−0.603648	−	0.797251i	$-0.706287\pi$
$113$	1.19145	−	15.8988i	0.112082	−	1.49563i	0.715730	−	0.698378i	$-0.246094\pi$
$114$	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	−0.625555	−	0.780180i	$-0.715127\pi$
$127$	−16.3776	−	2.46853i	−1.45328	−	0.219047i	−0.827725	+	0.561134i	$0.810365\pi$
$128$			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	0.319644	−	0.947538i	$-0.396437\pi$
$131$	−6.88285	−	6.38635i	−0.601357	−	0.557978i	−0.921001	+	0.389560i	$0.872627\pi$
$132$	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	0.858617	−	0.512618i	$-0.171324\pi$
$137$	16.5011	+	3.76628i	1.40979	+	0.321775i	0.551170	+	0.834393i	$0.314182\pi$
$138$	−14.7334	−	1.10412i	−1.25419	−	0.0939888i
$139$	3.54341	+	1.09300i	0.300548	+	0.0927069i	0.441362	−	0.897329i	$-0.354496\pi$
$139$	3.54341	+	1.09300i	0.300548	+	0.0927069i	−0.140813	+	0.990036i	$0.544972\pi$
$140$	−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	−0.434583	−	0.900632i	$-0.643104\pi$
$149$	−8.91176	+	0.667844i	−0.730079	+	0.0547119i	−0.295497	+	0.955344i	$0.595485\pi$
$150$	9.94407	−	2.26967i	0.811930	−	0.185318i
$151$	−13.2759	−	5.21041i	−1.08038	−	0.424017i	−0.242655	−	0.970113i	$-0.578018\pi$
$151$	−13.2759	−	5.21041i	−1.08038	−	0.424017i	−0.837723	+	0.546095i	$0.816114\pi$
$152$	−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	0.529170	−	0.848516i	$-0.322504\pi$
$157$	18.0980	−	5.58249i	1.44438	−	0.445531i	0.915207	+	0.402985i	$0.132027\pi$
$158$	−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	0.853187	−	0.521606i	$-0.174667\pi$
$163$	−1.85864	−	6.02558i	−0.145580	−	0.471960i	−0.998767	+	0.0496462i	$0.984191\pi$
$164$	−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	−0.972412	−	0.233271i	$-0.925057\pi$
$167$	0.330262	−	2.19115i	0.0255565	−	0.169556i	0.997968	+	0.0637155i	$0.0202950\pi$
$168$	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	−0.806109	−	0.591767i	$-0.798431\pi$
$173$	2.46373	−	6.27749i	0.187314	−	0.477269i	0.993423	+	0.114498i	$0.0365259\pi$
$174$	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	0.975111	+	0.221718i	$0.0711664\pi$
$179$	5.50028	+	14.0145i	0.411110	+	1.04749i	−0.564000	+	0.825774i	$0.690738\pi$
$180$	0.0284420	+	0.00649171i	0.00211994	+	0.000483863i
$181$	−13.1749	+	6.34472i	−0.979286	+	0.471599i	−0.853859	−	0.520504i	$-0.825744\pi$
$181$	−13.1749	+	6.34472i	−0.979286	+	0.471599i	−0.125427	+	0.992103i	$0.540030\pi$
$182$	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	−0.303786	+	0.952740i	$0.598251\pi$
$191$	−17.6425	+	16.3698i	−1.27656	+	1.18448i	−0.972778	+	0.231738i	$0.925559\pi$
$192$	−14.8227	+	2.23417i	−1.06974	+	0.161237i
$193$	6.13931	−	19.9031i	0.441917	−	1.43266i	−0.411490	−	0.911414i	$-0.634991\pi$
$193$	6.13931	−	19.9031i	0.441917	−	1.43266i	0.853407	−	0.521245i	$-0.174532\pi$
$194$	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	−0.354880	−	0.934912i	$-0.615478\pi$
$197$	3.89261	−	2.24740i	0.277337	−	0.160121i	0.632217	+	0.774791i	$0.282145\pi$
$198$	0.500989	+	0.241264i	0.0356037	+	0.0171459i
$199$	5.65825	+	24.7904i	0.401103	+	1.75735i	0.622948	+	0.782264i	$0.285935\pi$
$199$	5.65825	+	24.7904i	0.401103	+	1.75735i	−0.221845	+	0.975082i	$0.571208\pi$
$200$	−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	0.624369	−	0.781130i	$-0.285356\pi$
$211$	1.82072	+	1.24135i	0.125344	+	0.0854579i	−0.499025	+	0.866587i	$0.666309\pi$
$212$	−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	0.426695	−	0.904396i	$-0.359678\pi$
$223$	1.85679	+	0.728735i	0.124340	+	0.0487997i	−0.302355	+	0.953195i	$0.597773\pi$
$224$	−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	$0.0139626\pi$
$227$			1.32136i			0.0877015i	−0.999038	+	0.0438507i	$0.986037\pi$
$228$	−0.627730	−	0.500598i	−0.0415725	−	0.0331529i
$229$	6.83858	−	7.37024i	0.451906	−	0.487039i	−0.465468	−	0.885065i	$-0.654114\pi$
$229$	6.83858	−	7.37024i	0.451906	−	0.487039i	0.917374	+	0.398025i	$0.130304\pi$
$230$	−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	0.850774	−	0.525531i	$-0.176133\pi$
$233$	−1.98954	−	5.06928i	−0.130339	−	0.332099i	−0.981114	+	0.193432i	$0.938038\pi$
$234$	−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	0.603071	−	0.797688i	$-0.293944\pi$
$239$	12.3726	+	2.82396i	0.800315	+	0.182667i	0.197244	+	0.980354i	$0.436801\pi$
$240$	−1.81514	−	1.95626i	−0.117167	−	0.126276i
$241$	8.81472	−	7.02950i	0.567806	−	0.452810i	−0.297028	−	0.954869i	$-0.595995\pi$
$241$	8.81472	−	7.02950i	0.567806	−	0.452810i	0.864833	+	0.502059i	$0.167424\pi$
$242$	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	0.999883	+	0.0152643i	$0.00485896\pi$
$251$	17.2661	+	16.0206i	1.08983	+	1.01121i	0.0899430	+	0.995947i	$0.471332\pi$
$252$	−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	−0.0120009	+	0.999928i	$0.503820\pi$
$257$	−15.7777	+	19.7847i	−0.984188	+	1.23413i	−0.972187	+	0.234205i	$0.924751\pi$
$258$	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	0.360296	+	0.932838i	$0.382676\pi$
$263$	−10.1798	+	17.6319i	−0.627714	+	1.08723i	−0.988009	+	0.154394i	$0.950658\pi$
$264$	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	−0.438925	−	0.898523i	$-0.644641\pi$
$269$	−0.165604	+	0.0797509i	−0.0100971	+	0.00486250i	0.428828	+	0.903386i	$0.358927\pi$
$270$	0.257727	−	3.43912i	0.0156847	−	0.209298i
$271$	12.6391	−	10.0794i	0.767771	−	0.612277i	−0.159271	−	0.987235i	$-0.550914\pi$
$271$	12.6391	−	10.0794i	0.767771	−	0.612277i	0.927042	+	0.374958i	$0.122343\pi$
$272$	−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	−0.987660	−	0.156611i	$-0.949943\pi$
$277$	−10.2390	+	12.8393i	−0.615201	+	0.771437i	0.372460	+	0.928048i	$0.378514\pi$
$278$	−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	−0.955477	−	0.295065i	$-0.904659\pi$
$281$	−2.16337	+	4.49227i	−0.129056	+	0.267987i	0.826422	+	0.563052i	$0.190373\pi$
$282$	18.5982	+	2.80323i	1.10751	+	0.166930i
$283$	−22.2815	+	15.1913i	−1.32450	+	0.903028i	−0.999094	−	0.0425466i	$-0.986453\pi$
$283$	−22.2815	+	15.1913i	−1.32450	+	0.903028i	−0.325405	+	0.945575i	$0.605501\pi$
$284$	−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	0.457531	−	0.889194i	$-0.348734\pi$
$293$	−1.43386	−	0.827841i	−0.0837672	−	0.0483630i	−0.541299	+	0.840830i	$0.682067\pi$
$294$	−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	0.142374	−	0.989813i	$-0.454526\pi$
$307$	14.4985	−	30.1064i	0.827472	−	1.71826i	0.685098	−	0.728451i	$-0.259759\pi$
$308$	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	−0.509335	−	0.860569i	$-0.670108\pi$
$311$	−22.0387	−	3.32179i	−1.24970	−	0.188362i	−0.740363	+	0.672207i	$0.765346\pi$
$312$	8.40945	−	16.3846i	0.476092	−	0.927593i
$313$	−10.5053	+	18.1957i	−0.593796	+	1.02848i	0.399920	+	0.916550i	$0.369038\pi$
$313$	−10.5053	+	18.1957i	−0.593796	+	1.02848i	−0.993716	+	0.111934i	$0.964295\pi$
$314$	−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	0.995177	+	0.0981000i	$0.0312765\pi$
$317$	1.30201	+	8.63830i	0.0731284	+	0.485175i	−0.922048	+	0.387075i	$0.873485\pi$
$318$	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	0.764980	+	0.644054i	$0.222749\pi$
$331$	−2.83549	+	18.8122i	−0.155852	+	1.03401i	−0.920832	+	0.389959i	$0.872489\pi$
$332$	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	−0.975093	−	0.221795i	$-0.928808\pi$
$337$	−0.00607939	+	0.0266356i	−0.000331166	+	0.00145093i	0.974762	+	0.223246i	$0.0716654\pi$
$338$	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	0.778908	−	0.627138i	$-0.215774\pi$
$347$	−0.108588	−	0.136165i	−0.00582932	−	0.00730974i	−0.784738	+	0.619828i	$0.787202\pi$
$348$	−0.421254	−	1.84563i	−0.0225816	−	0.0989363i
$349$	−4.74311	−	15.3768i	−0.253893	−	0.823101i	−0.989353	−	0.145533i	$-0.953510\pi$
$349$	−4.74311	−	15.3768i	−0.253893	−	0.823101i	0.735460	−	0.677568i	$-0.236966\pi$
$350$	−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	0.184462	−	0.982840i	$-0.440946\pi$
$353$	21.6210	−	23.3019i	1.15077	−	1.24023i	0.966307	−	0.257394i	$-0.0828638\pi$
$354$	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	−0.712672	−	0.701497i	$-0.752515\pi$
$359$	0.760196	−	0.819296i	0.0401216	−	0.0432408i	0.752794	+	0.658256i	$0.228706\pi$
$360$	−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	−0.995905	−	0.0904111i	$-0.971182\pi$
$367$	0.0450512	−	0.601166i	0.00235165	−	0.0313806i	0.998256	+	0.0590305i	$0.0188009\pi$
$368$	−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	0.766339	+	0.642436i	$0.222076\pi$
$373$	18.1454	+	31.4288i	0.939536	+	1.62732i	0.173197	+	0.984887i	$0.444590\pi$
$374$	−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	−0.950886	−	0.309540i	$-0.899825\pi$
$379$	−35.9187	+	2.69173i	−1.84502	+	0.138265i	−0.894131	+	0.447805i	$0.852206\pi$
$380$	−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	0.0399701	+	0.999201i	$0.487274\pi$
$383$	−17.7066	+	25.9707i	−0.904762	+	1.32704i	−0.944733	+	0.327842i	$0.893679\pi$
$384$	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	−0.413229	−	0.910627i	$-0.635599\pi$
$389$	9.15093	−	8.49082i	0.463971	−	0.430502i	0.877200	+	0.480125i	$0.159409\pi$
$390$	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	0.344271	−	0.938870i	$-0.388126\pi$
$397$	−12.3076	−	13.2644i	−0.617701	−	0.665724i	−0.961972	+	0.273147i	$0.911936\pi$
$398$	−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	−0.831065	−	0.556176i	$-0.812268\pi$
$401$	−14.9735	−	31.0928i	−0.747740	−	1.55270i	0.0833246	−	0.996522i	$-0.473446\pi$
$402$	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	0.852165	−	0.523273i	$-0.175289\pi$
$409$	10.7517	+	8.57419i	0.531637	+	0.423966i	−0.320528	+	0.947239i	$0.603860\pi$
$410$		−	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	−0.756783	−	0.653667i	$-0.773230\pi$
$419$	4.96558	−	12.6521i	0.242585	−	0.618095i	0.999367	+	0.0355713i	$0.0113251\pi$
$420$	0.448899	−	0.721634i	0.0219040	−	0.0352122i
$421$	6.70851	+	5.34986i	0.326953	+	0.260736i	0.773184	−	0.634181i	$-0.218663\pi$
$421$	6.70851	+	5.34986i	0.326953	+	0.260736i	−0.446231	+	0.894918i	$0.647234\pi$
$422$	−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	−0.991389	−	0.130950i	$-0.958197\pi$
$431$	−16.3327	+	17.6025i	−0.786718	+	0.847881i	0.204670	+	0.978831i	$0.434388\pi$
$432$	14.9117	−	7.18109i	0.717439	−	0.345500i
$433$	7.28381	+	2.24676i	0.350038	+	0.107972i	0.464788	−	0.885422i	$-0.346131\pi$
$433$	7.28381	+	2.24676i	0.350038	+	0.107972i	−0.114750	+	0.993394i	$0.536607\pi$
$434$	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	0.540874	−	0.841104i	$-0.318094\pi$
$439$	4.62001	+	2.22488i	0.220501	+	0.106188i	−0.320372	+	0.947292i	$0.603808\pi$
$440$	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	0.686794	−	0.726852i	$-0.259017\pi$
$443$	33.9774	−	23.1654i	1.61432	−	1.10062i	0.927522	−	0.373769i	$-0.121935\pi$
$444$	−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	−0.991910	−	0.126944i	$-0.959483\pi$
$449$	−2.13688	+	6.92758i	−0.100845	+	0.326933i	0.891065	+	0.453877i	$0.149959\pi$
$450$	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	0.0174697	−	0.999847i	$-0.494439\pi$
$457$	−8.56403	−	1.95468i	−0.400608	−	0.0914362i	−0.418078	+	0.908411i	$0.637296\pi$
$458$	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	0.221879	−	0.975074i	$-0.428781\pi$
$461$	22.4961	−	8.82905i	1.04775	−	0.411210i	0.825867	+	0.563864i	$0.190686\pi$
$462$	11.4023	−	11.5058i	0.530484	−	0.535299i
$463$	−27.2098	+	21.6991i	−1.26455	+	1.00844i	−0.265531	+	0.964102i	$0.585547\pi$
$463$	−27.2098	+	21.6991i	−1.26455	+	1.00844i	−0.999016	+	0.0443404i	$0.985881\pi$
$464$	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	−0.0767496	−	0.997050i	$-0.524454\pi$
$467$	3.10747	−	0.468375i	0.143796	−	0.0216738i	0.220546	+	0.975377i	$0.429216\pi$
$468$	−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	0.870518	−	0.492137i	$-0.163784\pi$
$479$	2.06527	+	3.02920i	0.0943648	+	0.138408i	−0.776153	+	0.630545i	$0.782832\pi$
$480$	−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	0.653694	−	0.756759i	$-0.273219\pi$
$487$	34.6689	−	7.91295i	1.57100	−	0.358570i	0.917303	+	0.398190i	$0.130361\pi$
$488$	−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	−0.847915	−	0.530132i	$-0.822142\pi$
$491$	−19.5674	−	33.8918i	−0.883065	−	1.52951i	−0.0351504	−	0.999382i	$-0.511191\pi$
$492$	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	0.597470	−	0.801892i	$-0.296173\pi$
$499$	23.8741	+	1.78911i	1.06875	+	0.0800918i	0.471281	+	0.881983i	$0.343792\pi$
$500$	−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	−0.992708	−	0.120545i	$-0.961536\pi$
$503$	−27.8815	+	19.0093i	−1.24317	+	0.847581i	−0.250465	+	0.968126i	$0.580583\pi$
$504$	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	$0.0226876\pi$
$509$			3.21336i			0.142430i	−0.997461	+	0.0712149i	$0.977312\pi$
$510$	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	0.716936	−	0.697139i	$-0.245544\pi$
$521$	−5.59843	−	9.69677i	−0.245272	−	0.424823i	−0.962208	+	0.272316i	$0.912211\pi$
$522$	0.544954	−	0.213879i	0.0238520	−	0.00936121i
$523$	0.137114	−	0.600735i	0.00599557	−	0.0262683i	−0.971842	−	0.235635i	$-0.924283\pi$
$523$	0.137114	−	0.600735i	0.00599557	−	0.0262683i	0.977837	+	0.209367i	$0.0671402\pi$
$524$	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	0.915451	−	0.402430i	$-0.131834\pi$
$541$	4.80045	+	7.04097i	0.206388	+	0.302715i	−0.709063	+	0.705145i	$0.750882\pi$
$542$	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	0.952212	+	0.305439i	$0.0988032\pi$
$547$	5.30496	+	23.2425i	0.226824	+	0.993779i	−0.725388	+	0.688340i	$0.758340\pi$
$548$	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	0.864760	−	0.502185i	$-0.167470\pi$
$557$	20.3495	+	11.7488i	0.862235	+	0.497812i	−0.00252512	+	0.999997i	$0.500804\pi$
$558$	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	−0.785590	−	0.618748i	$-0.787640\pi$
$563$	−18.7838	+	9.04578i	−0.791641	+	0.381234i	−0.00605093	+	0.999982i	$0.501926\pi$
$564$	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	0.894919	−	0.446229i	$-0.147233\pi$
$571$	38.6762	+	5.82950i	1.61855	+	0.243957i	0.723631	+	0.690187i	$0.242472\pi$
$572$	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	−0.0821247	−	0.996622i	$-0.526171\pi$
$577$	−0.355349	+	0.0266297i	−0.0147934	+	0.00110861i	0.0673314	+	0.997731i	$0.478552\pi$
$578$	−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	−0.915503	−	0.402312i	$-0.868207\pi$
$587$	−24.8299	+	14.3356i	−1.02484	+	0.591693i	−0.109339	+	0.994005i	$0.534873\pi$
$588$	−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	−0.805104	−	0.593133i	$-0.797891\pi$
$593$	4.72976	−	15.3335i	0.194228	−	0.629671i	0.999332	−	0.0365382i	$-0.0116331\pi$
$594$	−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	0.982600	+	0.185735i	$0.0594667\pi$
$599$	0.946115	+	12.6250i	0.0386572	+	0.515845i	−0.943943	+	0.330110i	$0.892914\pi$
$600$	18.9351	+	15.1002i	0.773022	+	0.616465i
$601$	−1.00398	−	13.3972i	−0.0409531	−	0.546482i	−0.979515	−	0.201371i	$-0.935460\pi$
$601$	−1.00398	−	13.3972i	−0.0409531	−	0.546482i	0.938562	−	0.345111i	$-0.112159\pi$
$602$	−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	0.718824	−	0.695192i	$-0.244681\pi$
$607$	−5.97807	−	10.3543i	−0.242643	−	0.420269i	−0.961466	+	0.274923i	$0.911348\pi$
$608$	−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	−0.809010	−	0.587794i	$-0.799996\pi$
$613$	−42.0056	−	3.14789i	−1.69659	−	0.127142i	−0.887581	+	0.460653i	$0.847615\pi$
$614$	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	−0.613192	−	0.789934i	$-0.710115\pi$
$617$	−13.0507	+	5.12203i	−0.525402	+	0.206205i	0.0877900	+	0.996139i	$0.472020\pi$
$618$	−12.6127	+	7.28194i	−0.507357	+	0.292923i
$619$	30.7640	−	17.7616i	1.23651	−	0.713900i	0.268131	−	0.963382i	$-0.413594\pi$
$619$	30.7640	−	17.7616i	1.23651	−	0.713900i	0.968379	+	0.249483i	$0.0802606\pi$
$620$	−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	−0.853823	−	0.520563i	$-0.825722\pi$
$631$	−6.80518	+	7.33424i	−0.270910	+	0.291972i	0.582913	+	0.812534i	$0.301913\pi$
$632$	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	0.564028	−	0.825756i	$-0.309251\pi$
$641$	−9.27987	−	11.6366i	−0.366533	−	0.459618i	−0.930560	+	0.366138i	$0.880680\pi$
$642$	2.96761	−	9.62075i	0.117122	−	0.379701i
$643$	−8.83531	+	9.52220i	−0.348431	+	0.375519i	−0.882814	−	0.469724i	$-0.844354\pi$
$643$	−8.83531	+	9.52220i	−0.348431	+	0.375519i	0.534383	+	0.845243i	$0.320544\pi$
$644$	−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	−0.974002	−	0.226538i	$-0.927259\pi$
$647$	−32.3725	−	30.0373i	−1.27269	−	1.18089i	−0.298691	−	0.954350i	$-0.596550\pi$
$648$	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	0.683761	+	0.729706i	$0.260343\pi$
$653$	−6.36020	+	27.8659i	−0.248894	+	1.09048i	−0.932655	+	0.360770i	$0.882514\pi$
$654$	−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	−0.202823	−	0.979215i	$-0.565012\pi$
$659$	−2.77263	+	0.417907i	−0.108007	+	0.0162794i	0.0948166	+	0.995495i	$0.469774\pi$
$660$	0.570011	+	0.714771i	0.0221876	+	0.0278224i
$661$	−34.1868	−	2.56195i	−1.32971	−	0.0996482i	−0.609160	−	0.793048i	$-0.708493\pi$
$661$	−34.1868	−	2.56195i	−1.32971	−	0.0996482i	−0.720554	+	0.693399i	$0.756112\pi$
$662$	−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	0.997653	+	0.0684667i	$0.0218107\pi$
$673$	0.553799	+	7.38994i	0.0213474	+	0.284861i	−0.976306	+	0.216395i	$0.930570\pi$
$674$	−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	0.936253	+	0.351325i	$0.114269\pi$
$677$	−1.09034	+	14.5496i	−0.0419052	+	0.559185i	−0.978159	+	0.207860i	$0.933350\pi$
$678$	−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	−0.432596	−	0.901588i	$-0.642402\pi$
$683$	−11.2683	+	2.57190i	−0.431168	+	0.0984112i	0.00142855	+	0.999999i	$0.499545\pi$
$684$	−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	0.000789710	−	1.00000i	$-0.499749\pi$
$691$	11.4449	−	2.61223i	0.435385	−	0.0993737i	0.434595	+	0.900626i	$0.356891\pi$
$692$	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	0.498550	−	0.866861i	$-0.333866\pi$
$701$	39.3739	−	18.9615i	1.48713	−	0.716164i	0.988580	+	0.150697i	$0.0481516\pi$
$702$	−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	0.448593	−	0.893736i	$-0.351925\pi$
$709$	4.51435	+	1.77175i	0.169540	+	0.0665395i	−0.279053	+	0.960276i	$0.590021\pi$
$710$	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	0.143824	−	0.989603i	$-0.454060\pi$
$719$	21.9909	−	6.78328i	0.820121	−	0.252974i	0.676297	+	0.736629i	$0.263584\pi$
$720$	−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	0.816041	+	0.577994i	$0.196164\pi$
$727$	8.94079	+	39.1722i	0.331596	+	1.45281i	−0.484446	+	0.874821i	$0.660979\pi$
$728$	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	0.996139	−	0.0877882i	$-0.0279799\pi$
$733$	14.9039	+	21.8600i	0.550489	+	0.807419i	−0.445650	+	0.895207i	$0.647027\pi$
$734$	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	0.910197	+	0.414176i	$0.135930\pi$
$739$	4.41798	+	29.3114i	0.162518	+	1.07824i	−0.747679	+	0.664061i	$0.768832\pi$
$740$	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	0.883209	−	0.468979i	$-0.155378\pi$
$743$	9.52775	+	10.2685i	0.349539	+	0.376714i	−0.533670	+	0.845693i	$0.679188\pi$
$744$	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	−0.960444	−	0.278473i	$-0.910172\pi$
$751$	0.704600	−	3.08705i	0.0257112	−	0.112648i	0.986155	+	0.165825i	$0.0530287\pi$
$752$	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	0.601978	+	0.798513i	$0.294380\pi$
$757$	−10.5220	+	26.8097i	−0.382430	+	0.974416i	−0.984408	+	0.175903i	$0.943716\pi$
$758$	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	−0.560884	−	0.827894i	$-0.689539\pi$
$761$	−42.3491	−	16.6208i	−1.53515	−	0.602503i	−0.974268	+	0.225391i	$0.927634\pi$
$762$	−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	−0.919339	−	0.393466i	$-0.871276\pi$
$769$	−6.02313	+	8.83431i	−0.217200	+	0.318573i	0.702139	+	0.712039i	$0.252228\pi$
$770$	−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	−0.622272	−	0.782801i	$-0.713790\pi$
$773$	10.5019	−	21.8074i	0.377727	−	0.784358i	0.999999	−	0.00155669i	$-0.000495509\pi$
$774$	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	−0.539412	−	0.842042i	$-0.681354\pi$
$787$	−18.5169	+	4.22637i	−0.660058	+	0.150654i	−0.120646	+	0.992696i	$0.538496\pi$
$788$	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	−0.717032	−	0.697041i	$-0.754500\pi$
$797$	−9.32013	+	6.35436i	−0.330136	+	0.225083i	0.386896	+	0.922123i	$0.373547\pi$
$798$	−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	−0.955376	−	0.295391i	$-0.904550\pi$
$809$	0.948714	−	12.6597i	0.0333550	−	0.445091i	0.988731	−	0.149700i	$-0.0478309\pi$
$810$	−2.01700	+	5.13924i	−0.0708703	+	0.180575i
$811$	28.1503	−	22.4491i	0.988489	−	0.788294i	0.0111425	−	0.999938i	$-0.496453\pi$
$811$	28.1503	−	22.4491i	0.988489	−	0.788294i	0.977347	+	0.211644i	$0.0678817\pi$
$812$	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	0.926855	−	0.375420i	$-0.122501\pi$
$821$	21.9796	+	17.5281i	0.767093	+	0.611736i	−0.159762	+	0.987155i	$0.551073\pi$
$822$	30.0831	−	20.5103i	1.04927	−	0.715379i
$823$	−0.388397	+	1.70168i	−0.0135387	+	0.0593167i	−0.981246	−	0.192760i	$-0.938256\pi$
$823$	−0.388397	+	1.70168i	−0.0135387	+	0.0593167i	0.967707	+	0.252076i	$0.0811134\pi$
$824$	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	0.801272	−	0.598301i	$-0.204157\pi$
$827$	36.3381	+	8.29394i	1.26360	+	0.288408i	0.462328	+	0.886709i	$0.347014\pi$
$828$	−0.288892	+	0.268053i	−0.0100397	+	0.00931548i
$829$	−33.7325	+	5.08436i	−1.17158	+	0.176587i	−0.705864	−	0.708347i	$-0.749441\pi$
$829$	−33.7325	+	5.08436i	−1.17158	+	0.176587i	−0.465715	+	0.884935i	$0.654203\pi$
$830$	−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	−0.463576	−	0.886057i	$-0.653434\pi$
$839$	13.1691	−	14.1929i	0.454647	−	0.489993i	0.918223	+	0.396064i	$0.129624\pi$
$840$	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	0.450551	−	0.892751i	$-0.351228\pi$
$853$	−9.33310	−	7.44290i	−0.319559	−	0.254840i	−0.770110	+	0.637911i	$0.779799\pi$
$854$	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	−0.0792490	−	0.996855i	$-0.525252\pi$
$857$	−30.3328	−	20.6805i	−1.03615	−	0.706434i	−0.956899	+	0.290421i	$0.906205\pi$
$858$	11.5194	−	18.8311i	0.393267	−	0.642884i
$859$	−29.9185	+	4.50949i	−1.02081	+	0.153862i	−0.638056	−	0.769990i	$-0.720261\pi$
$859$	−29.9185	+	4.50949i	−1.02081	+	0.153862i	−0.382751	+	0.923852i	$0.625023\pi$
$860$	−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	−0.392661	−	0.919683i	$-0.628446\pi$
$863$	−40.7005	−	23.4984i	−1.38546	−	0.799896i	−0.992800	+	0.119787i	$0.961779\pi$
$864$		−	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	0.931796	−	0.362983i	$-0.118242\pi$
$877$	14.8129	+	15.9645i	0.500195	+	0.539082i	−0.431601	+	0.902065i	$0.642051\pi$
$878$	−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	0.999343	−	0.0362514i	$-0.0115417\pi$
$881$	13.8992	+	24.0742i	0.468277	+	0.811079i	−0.531066	+	0.847330i	$0.678208\pi$
$882$	−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	0.998390	+	0.0567180i	$0.0180636\pi$
$887$	3.67757	+	16.1125i	0.123481	+	0.541005i	−0.874909	+	0.484286i	$0.839079\pi$
$888$	−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	0.776473	+	0.630150i	$0.217007\pi$
$907$	−2.56732	+	34.2585i	−0.0852464	+	1.13753i	−0.861720	+	0.507384i	$0.830612\pi$
$908$	−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	−0.992945	−	0.118577i	$-0.962167\pi$
$911$	−19.8117	+	24.8430i	−0.656389	+	0.823086i	0.336555	+	0.941664i	$0.390738\pi$
$912$			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	0.103486	−	0.994631i	$-0.467000\pi$
$919$	−2.75255	−	0.414880i	−0.0907982	−	0.0136856i	−0.194284	+	0.980945i	$0.562238\pi$
$920$	−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	0.878277	−	0.478151i	$-0.158693\pi$
$929$	55.4120	−	4.15256i	1.81801	−	0.136241i	0.939733	+	0.341910i	$0.111074\pi$
$930$	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	−0.997287	−	0.0736074i	$-0.976549\pi$
$937$	−2.04556	+	8.96217i	−0.0668255	+	0.292781i	0.930462	+	0.366389i	$0.119406\pi$
$938$	−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	0.962495	−	0.271298i	$-0.0874528\pi$
$941$	0.442249	+	1.43374i	0.0144169	+	0.0467385i	−0.948079	+	0.318036i	$0.896977\pi$
$942$	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	0.677077	−	0.735912i	$-0.263246\pi$
$947$	29.7825	+	6.79767i	0.967802	+	0.220895i	0.290725	+	0.956807i	$0.406103\pi$
$948$	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	0.722430	−	0.691444i	$-0.243025\pi$
$953$	49.9047	−	7.52192i	1.61657	−	0.243659i	0.894141	+	0.447785i	$0.147787\pi$
$954$	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	−0.979324	−	0.202298i	$-0.935159\pi$
$967$	−6.54779	+	13.5966i	−0.210563	+	0.437238i	0.768761	+	0.639536i	$0.220873\pi$
$968$	−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	−0.152665	−	0.988278i	$-0.548786\pi$
$971$	−35.1620	−	23.9730i	−1.12840	−	0.769332i	−0.975737	+	0.218946i	$0.929738\pi$
$972$	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	0.440038	+	0.897979i	$0.354965\pi$
$977$	−13.4214	+	43.5111i	−0.429388	+	1.39204i	−0.869426	+	0.494063i	$0.835511\pi$
$978$	−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	0.362822	−	0.931859i	$-0.381813\pi$
$983$	−18.6093	−	20.0561i	−0.593545	−	0.639689i	−0.956367	+	0.292169i	$0.905623\pi$
$984$	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	−0.786345	−	0.617788i	$-0.788029\pi$
$991$	−15.6943	+	10.7002i	−0.498546	+	0.339903i	0.287799	+	0.957691i	$0.407077\pi$
$992$	−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	0.101100	−	0.994876i	$-0.467764\pi$
$997$	33.1078	−	41.5159i	1.04854	−	1.31482i	0.947436	−	0.319946i	$-0.103665\pi$
$998$	−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.478.19	yes	756
13.4	even	6		637.2.bp.a.576.19	yes	756
49.4	even	21		637.2.bp.a.543.19	✓	756
637.4	even	42	inner	637.2.bz.a.4.19	yes	756

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bp.a.543.19	✓	756	49.4	even	21
637.2.bp.a.576.19	yes	756	13.4	even	6
637.2.bz.a.4.19	yes	756	637.4	even	42	inner
637.2.bz.a.478.19	yes	756	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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