LMFDB - Embedded newform 418.2.u.b.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	418.5
Dual form			418.2.u.b.251.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615661 - 0.788011i) q^{2} +(1.44037 - 1.39095i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(1.24695 - 0.779183i) q^{5} +(-1.98287 - 0.278674i) q^{6} +(0.930267 + 0.414181i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.0352282 - 1.00880i) q^{9} +O(q^{10})$	\(q+(-0.615661 - 0.788011i) q^{2} +(1.44037 - 1.39095i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(1.24695 - 0.779183i) q^{5} +(-1.98287 - 0.278674i) q^{6} +(0.930267 + 0.414181i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.0352282 - 1.00880i) q^{9} +(-1.38171 - 0.502900i) q^{10} +(2.19752 + 2.48413i) q^{11} +(1.00118 + 1.73409i) q^{12} +(4.07270 - 2.16549i) q^{13} +(-0.246350 - 0.988056i) q^{14} +(0.712272 - 2.85677i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(-0.137311 - 3.93207i) q^{17} +(-0.816638 + 0.593322i) q^{18} +(-3.36791 - 2.76716i) q^{19} +(0.454373 + 1.39842i) q^{20} +(1.91604 - 0.697380i) q^{21} +(0.604593 - 3.26105i) q^{22} +(-4.68447 + 3.93074i) q^{23} +(0.750095 - 1.85655i) q^{24} +(-1.24409 + 2.55076i) q^{25} +(-4.21384 - 1.87612i) q^{26} +(2.66705 + 2.96206i) q^{27} +(-0.626930 + 0.802434i) q^{28} +(-4.36949 + 1.25293i) q^{29} +(-2.68968 + 1.19752i) q^{30} +(4.79833 - 5.32908i) q^{31} +(0.173648 + 0.984808i) q^{32} +(6.62055 + 0.521429i) q^{33} +(-3.01398 + 2.52903i) q^{34} +(1.48272 - 0.208383i) q^{35} +(0.970316 + 0.278234i) q^{36} +(-3.55405 + 2.58217i) q^{37} +(-0.107064 + 4.35758i) q^{38} +(2.85411 - 8.78405i) q^{39} +(0.822227 - 1.21900i) q^{40} +(-0.264623 + 0.255543i) q^{41} +(-1.72917 - 1.08051i) q^{42} +(-7.84612 - 6.58368i) q^{43} +(-2.94197 + 1.53128i) q^{44} +(-0.742116 - 1.28538i) q^{45} +(5.98151 + 1.27141i) q^{46} +(6.29540 + 9.33331i) q^{47} +(-1.92479 + 0.551923i) q^{48} +(-3.99006 - 4.43142i) q^{49} +(2.77596 - 0.590049i) q^{50} +(-5.66710 - 5.47266i) q^{51} +(1.11589 + 4.47561i) q^{52} +(-8.91446 - 5.57037i) q^{53} +(0.692135 - 3.92529i) q^{54} +(4.67580 + 1.38533i) q^{55} +1.01830 q^{56} +(-8.70003 + 0.698850i) q^{57} +(3.67745 + 2.67182i) q^{58} +(-0.405331 + 0.600928i) q^{59} +(2.59959 + 1.38223i) q^{60} +(-0.707129 - 1.75021i) q^{61} +(-7.15352 - 0.500223i) q^{62} +(0.450600 - 0.923867i) q^{63} +(0.669131 - 0.743145i) q^{64} +(3.39116 - 5.87365i) q^{65} +(-3.66513 - 5.53809i) q^{66} +(13.2649 + 4.82802i) q^{67} +(3.84849 + 0.818022i) q^{68} +(-1.27992 + 12.1776i) q^{69} +(-1.07706 - 1.04011i) q^{70} +(-8.46107 + 5.28707i) q^{71} +(-0.378135 - 0.935917i) q^{72} +(2.68400 + 5.50301i) q^{73} +(4.22287 + 1.21089i) q^{74} +(1.75603 + 5.40451i) q^{75} +(3.49974 - 2.59843i) q^{76} +(1.01540 + 3.22108i) q^{77} +(-8.67909 + 3.15893i) q^{78} +(13.7683 - 1.93501i) q^{79} +(-1.46680 + 0.102569i) q^{80} +(10.9825 + 0.767972i) q^{81} +(0.364289 + 0.0511975i) q^{82} +(-3.68403 + 0.783065i) q^{83} +(0.213134 + 2.02783i) q^{84} +(-3.23503 - 4.79612i) q^{85} +(-0.357454 + 10.2361i) q^{86} +(-4.55093 + 7.88243i) q^{87} +(3.01792 + 1.37555i) q^{88} +(-0.234148 - 1.32792i) q^{89} +(-0.556003 + 1.37616i) q^{90} +(4.68561 - 0.327650i) q^{91} +(-2.68070 - 5.49625i) q^{92} +(-0.501117 - 14.3501i) q^{93} +(3.47892 - 10.7070i) q^{94} +(-6.35575 - 0.826309i) q^{95} +(1.61994 + 1.17695i) q^{96} +(8.28131 + 10.5996i) q^{97} +(-1.03547 + 5.87247i) q^{98} +(2.58342 - 2.12936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$3$	1.44037	−	1.39095i	0.831599	−	0.803066i	−0.151052	−	0.988526i	$-0.548266\pi$
$3$	1.44037	−	1.39095i	0.831599	−	0.803066i	0.982652	+	0.185459i	$0.0593773\pi$
$4$	−0.241922	+	0.970296i	−0.120961	+	0.485148i
$5$	1.24695	−	0.779183i	0.557655	−	0.348461i	−0.221630	−	0.975131i	$-0.571138\pi$
$5$	1.24695	−	0.779183i	0.557655	−	0.348461i	0.779285	+	0.626669i	$0.215582\pi$
$6$	−1.98287	−	0.278674i	−0.809502	−	0.113768i
$7$	0.930267	+	0.414181i	0.351608	+	0.156546i	0.574938	−	0.818197i	$-0.305026\pi$
$7$	0.930267	+	0.414181i	0.351608	+	0.156546i	−0.223330	+	0.974743i	$0.571693\pi$
$8$	0.913545	−	0.406737i	0.322987	−	0.143803i
$9$	0.0352282	−	1.00880i	0.0117427	−	0.336268i
$10$	−1.38171	−	0.502900i	−0.436934	−	0.159031i
$11$	2.19752	+	2.48413i	0.662577	+	0.748994i
$11$	2.19752	+	2.48413i	0.662577	+	0.748994i
$12$	1.00118	+	1.73409i	0.289015	+	0.500588i
$13$	4.07270	−	2.16549i	1.12956	−	0.600600i	0.203917	−	0.978988i	$-0.434633\pi$
$13$	4.07270	−	2.16549i	1.12956	−	0.600600i	0.925647	+	0.378388i	$0.123521\pi$
$14$	−0.246350	−	0.988056i	−0.0658398	−	0.264069i
$15$	0.712272	−	2.85677i	0.183908	−	0.737614i
$16$	−0.882948	−	0.469472i	−0.220737	−	0.117368i
$17$	−0.137311	−	3.93207i	−0.0333028	−	0.953668i	−0.894952	−	0.446163i	$-0.852790\pi$
$17$	−0.137311	−	3.93207i	−0.0333028	−	0.953668i	0.861649	−	0.507505i	$-0.169432\pi$
$18$	−0.816638	+	0.593322i	−0.192483	+	0.139847i
$19$	−3.36791	−	2.76716i	−0.772651	−	0.634831i
$19$	−3.36791	−	2.76716i	−0.772651	−	0.634831i
$20$	0.454373	+	1.39842i	0.101601	+	0.312695i
$21$	1.91604	−	0.697380i	0.418114	−	0.152181i
$22$	0.604593	−	3.26105i	0.128900	−	0.695259i
$23$	−4.68447	+	3.93074i	−0.976780	+	0.819616i	−0.983600	−	0.180361i	$-0.942273\pi$
$23$	−4.68447	+	3.93074i	−0.976780	+	0.819616i	0.00682063	+	0.999977i	$0.497829\pi$
$24$	0.750095	−	1.85655i	0.153112	−	0.378967i
$25$	−1.24409	+	2.55076i	−0.248818	+	0.510152i
$26$	−4.21384	−	1.87612i	−0.826402	−	0.367938i
$27$	2.66705	+	2.96206i	0.513274	+	0.570049i
$28$	−0.626930	+	0.802434i	−0.118479	+	0.151646i
$29$	−4.36949	+	1.25293i	−0.811394	+	0.232663i	−0.655583	−	0.755123i	$-0.727577\pi$
$29$	−4.36949	+	1.25293i	−0.811394	+	0.232663i	−0.155811	+	0.987787i	$0.549799\pi$
$30$	−2.68968	+	1.19752i	−0.491066	+	0.218637i
$31$	4.79833	−	5.32908i	0.861805	−	0.957131i	−0.137639	−	0.990483i	$-0.543951\pi$
$31$	4.79833	−	5.32908i	0.861805	−	0.957131i	0.999444	+	0.0333511i	$0.0106179\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	6.62055	+	0.521429i	1.15249	+	0.0907691i
$34$	−3.01398	+	2.52903i	−0.516893	+	0.433725i
$35$	1.48272	−	0.208383i	0.250626	−	0.0352232i
$36$	0.970316	+	0.278234i	0.161719	+	0.0463723i
$37$	−3.55405	+	2.58217i	−0.584282	+	0.424506i	−0.840265	−	0.542175i	$-0.817601\pi$
$37$	−3.55405	+	2.58217i	−0.584282	+	0.424506i	0.255983	+	0.966681i	$0.417601\pi$
$38$	−0.107064	+	4.35758i	−0.0173681	+	0.706893i
$39$	2.85411	−	8.78405i	0.457024	−	1.40657i
$40$	0.822227	−	1.21900i	0.130005	−	0.192741i
$41$	−0.264623	+	0.255543i	−0.0413271	+	0.0399092i	−0.715035	−	0.699088i	$-0.753589\pi$
$41$	−0.264623	+	0.255543i	−0.0413271	+	0.0399092i	0.673708	+	0.738998i	$0.264701\pi$
$42$	−1.72917	−	1.08051i	−0.266817	−	0.166726i
$43$	−7.84612	−	6.58368i	−1.19652	−	1.00400i	−0.999722	−	0.0235574i	$-0.992501\pi$
$43$	−7.84612	−	6.58368i	−1.19652	−	1.00400i	−0.196799	−	0.980444i	$-0.563055\pi$
$44$	−2.94197	+	1.53128i	−0.443519	+	0.230849i
$45$	−0.742116	−	1.28538i	−0.110628	−	0.191613i
$46$	5.98151	+	1.27141i	0.881926	+	0.187459i
$47$	6.29540	+	9.33331i	0.918278	+	1.36140i	0.932371	+	0.361503i	$0.117736\pi$
$47$	6.29540	+	9.33331i	0.918278	+	1.36140i	−0.0140929	+	0.999901i	$0.504486\pi$
$48$	−1.92479	+	0.551923i	−0.277819	+	0.0796633i
$49$	−3.99006	−	4.43142i	−0.570009	−	0.633059i
$50$	2.77596	−	0.590049i	0.392580	−	0.0834455i
$51$	−5.66710	−	5.47266i	−0.793553	−	0.766325i
$52$	1.11589	+	4.47561i	0.154747	+	0.620655i
$53$	−8.91446	−	5.57037i	−1.22450	−	0.765149i	−0.245572	−	0.969378i	$-0.578976\pi$
$53$	−8.91446	−	5.57037i	−1.22450	−	0.765149i	−0.978923	+	0.204229i	$0.934531\pi$
$54$	0.692135	−	3.92529i	0.0941876	−	0.534165i
$55$	4.67580	+	1.38533i	0.630485	+	0.186797i
$56$	1.01830			0.136077
$57$	−8.70003	+	0.698850i	−1.15235	+	0.0925649i
$58$	3.67745	+	2.67182i	0.482873	+	0.350828i
$59$	−0.405331	+	0.600928i	−0.0527696	+	0.0782341i	−0.854499	−	0.519453i	$-0.826136\pi$
$59$	−0.405331	+	0.600928i	−0.0527696	+	0.0782341i	0.801729	+	0.597687i	$0.203914\pi$
$60$	2.59959	+	1.38223i	0.335606	+	0.178445i
$61$	−0.707129	−	1.75021i	−0.0905386	−	0.224091i	0.875120	−	0.483907i	$-0.160783\pi$
$61$	−0.707129	−	1.75021i	−0.0905386	−	0.224091i	−0.965658	+	0.259816i	$0.916338\pi$
$62$	−7.15352	−	0.500223i	−0.908498	−	0.0635284i
$63$	0.450600	−	0.923867i	0.0567702	−	0.116396i
$64$	0.669131	−	0.743145i	0.0836413	−	0.0928931i
$65$	3.39116	−	5.87365i	0.420621	−	0.728537i
$66$	−3.66513	−	5.53809i	−0.451146	−	0.681692i
$67$	13.2649	+	4.82802i	1.62056	+	0.589836i	0.983489	−	0.180968i	$-0.0579230\pi$
$67$	13.2649	+	4.82802i	1.62056	+	0.589836i	0.637072	+	0.770804i	$0.280145\pi$
$68$	3.84849	+	0.818022i	0.466698	+	0.0991998i
$69$	−1.27992	+	12.1776i	−0.154084	+	1.46601i
$70$	−1.07706	−	1.04011i	−0.128734	−	0.124317i
$71$	−8.46107	+	5.28707i	−1.00414	+	0.627459i	−0.929142	−	0.369724i	$-0.879452\pi$
$71$	−8.46107	+	5.28707i	−1.00414	+	0.627459i	−0.0750032	+	0.997183i	$0.523897\pi$
$72$	−0.378135	−	0.935917i	−0.0445637	−	0.110299i
$73$	2.68400	+	5.50301i	0.314138	+	0.644079i	0.996189	−	0.0872265i	$-0.0278004\pi$
$73$	2.68400	+	5.50301i	0.314138	+	0.644079i	−0.682050	+	0.731305i	$0.738912\pi$
$74$	4.22287	+	1.21089i	0.490898	+	0.140763i
$75$	1.75603	+	5.40451i	0.202769	+	0.624059i
$76$	3.49974	−	2.59843i	0.401447	−	0.298060i
$77$	1.01540	+	3.22108i	0.115716	+	0.367076i
$78$	−8.67909	+	3.15893i	−0.982714	+	0.357679i
$79$	13.7683	−	1.93501i	1.54906	−	0.217706i	0.687809	−	0.725892i	$-0.258573\pi$
$79$	13.7683	−	1.93501i	1.54906	−	0.217706i	0.861247	+	0.508186i	$0.169684\pi$
$80$	−1.46680	+	0.102569i	−0.163993	+	0.0114675i
$81$	10.9825	+	0.767972i	1.22028	+	0.0853302i
$82$	0.364289	+	0.0511975i	0.0402290	+	0.00565382i
$83$	−3.68403	+	0.783065i	−0.404375	+	0.0859525i	−0.405609	−	0.914047i	$-0.632941\pi$
$83$	−3.68403	+	0.783065i	−0.404375	+	0.0859525i	0.00123405	+	0.999999i	$0.499607\pi$
$84$	0.213134	+	2.02783i	0.0232548	+	0.221255i
$85$	−3.23503	−	4.79612i	−0.350888	−	0.520213i
$86$	−0.357454	+	10.2361i	−0.0385453	+	1.10379i
$87$	−4.55093	+	7.88243i	−0.487910	+	0.845086i
$88$	3.01792	+	1.37555i	0.321712	+	0.146635i
$89$	−0.234148	−	1.32792i	−0.0248196	−	0.140759i	0.969880	−	0.243584i	$-0.0783230\pi$
$89$	−0.234148	−	1.32792i	−0.0248196	−	0.140759i	−0.994699	+	0.102825i	$0.967212\pi$
$90$	−0.556003	+	1.37616i	−0.0586079	+	0.145060i
$91$	4.68561	−	0.327650i	0.491185	−	0.0343470i
$92$	−2.68070	−	5.49625i	−0.279483	−	0.573024i
$93$	−0.501117	−	14.3501i	−0.0519634	−	1.48804i
$94$	3.47892	−	10.7070i	0.358823	−	1.10434i
$95$	−6.35575	−	0.826309i	−0.652087	−	0.0847775i
$96$	1.61994	+	1.17695i	0.165334	+	0.120122i
$97$	8.28131	+	10.5996i	0.840839	+	1.07623i	0.996089	+	0.0883501i	$0.0281594\pi$
$97$	8.28131	+	10.5996i	0.840839	+	1.07623i	−0.155250	+	0.987875i	$0.549618\pi$
$98$	−1.03547	+	5.87247i	−0.104599	+	0.593209i
$99$	2.58342	−	2.12936i	0.259643	−	0.214008i
$100$	−2.17402	−	1.82422i	−0.217402	−	0.182422i
$101$	−3.69174	+	1.96293i	−0.367342	+	0.195319i	−0.642872	−	0.765973i	$-0.722257\pi$
$101$	−3.69174	+	1.96293i	−0.367342	+	0.195319i	0.275531	+	0.961292i	$0.411146\pi$
$102$	−0.823496	+	7.83504i	−0.0815383	+	0.775785i
$103$	0.797702	+	7.58963i	0.0785999	+	0.747828i	0.960854	+	0.277055i	$0.0893584\pi$
$103$	0.797702	+	7.58963i	0.0785999	+	0.747828i	−0.882254	+	0.470773i	$0.843975\pi$
$104$	2.83981	−	3.63480i	0.278467	−	0.356421i
$105$	1.84582	−	2.36255i	0.180134	−	0.230561i
$106$	1.09878	+	10.4542i	0.106723	+	1.01540i
$107$	−1.55822	+	14.8254i	−0.150638	+	1.43323i	0.614273	+	0.789094i	$0.289449\pi$
$107$	−1.55822	+	14.8254i	−0.150638	+	1.43323i	−0.764911	+	0.644136i	$0.777217\pi$
$108$	−3.51929	+	1.87124i	−0.338644	+	0.180060i
$109$	−9.48535	−	7.95916i	−0.908532	−	0.762349i	0.0633070	−	0.997994i	$-0.479835\pi$
$109$	−9.48535	−	7.95916i	−0.908532	−	0.762349i	−0.971839	+	0.235645i	$0.924280\pi$
$110$	−1.78706	−	4.53747i	−0.170389	−	0.432631i
$111$	−1.52748	+	8.66280i	−0.144982	+	0.822236i
$112$	−0.626930	−	0.802434i	−0.0592394	−	0.0758229i
$113$	0.177337	+	0.128843i	0.0166824	+	0.0121205i	0.596095	−	0.802914i	$-0.296718\pi$
$113$	0.177337	+	0.128843i	0.0166824	+	0.0121205i	−0.579413	+	0.815034i	$0.696718\pi$
$114$	5.90698	+	6.42547i	0.553239	+	0.601800i
$115$	−2.77855	+	8.55151i	−0.259102	+	0.797433i
$116$	−0.158638	−	4.54281i	−0.0147292	−	0.421789i
$117$	−2.04109	−	4.18485i	−0.188699	−	0.386889i
$118$	0.723084	−	0.0505630i	0.0665653	−	0.00465470i
$119$	1.50086	−	3.71475i	0.137583	−	0.340531i
$120$	−0.511259	−	2.89949i	−0.0466713	−	0.264686i
$121$	−1.34181	+	10.9179i	−0.121983	+	0.992532i
$122$	−0.943829	+	1.63476i	−0.0854503	+	0.148004i
$123$	−0.0257071	+	0.736155i	−0.00231793	+	0.0663769i
$124$	4.00997	+	5.94502i	0.360106	+	0.533878i
$125$	1.20467	+	11.4617i	0.107749	+	1.02516i
$126$	−1.00543	+	0.213712i	−0.0895712	+	0.0190389i
$127$	6.38571	+	0.897453i	0.566640	+	0.0796361i	0.416675	−	0.909055i	$-0.363195\pi$
$127$	6.38571	+	0.897453i	0.566640	+	0.0796361i	0.149965	+	0.988691i	$0.452084\pi$
$128$	−0.997564	−	0.0697565i	−0.0881730	−	0.00616566i
$129$	−20.4589	+	1.43063i	−1.80131	+	0.125960i
$130$	−6.71631	+	0.943915i	−0.589059	+	0.0827869i
$131$	−2.09363	+	0.762020i	−0.182922	+	0.0665780i	−0.431857	−	0.901942i	$-0.642142\pi$
$131$	−2.09363	+	0.762020i	−0.182922	+	0.0665780i	0.248935	+	0.968520i	$0.419919\pi$
$132$	−2.10760	+	6.29775i	−0.183443	+	0.548149i
$133$	−1.98694	−	3.96913i	−0.172290	−	0.344167i
$134$	−4.36214	−	13.4253i	−0.376831	−	1.15977i
$135$	5.63368	+	1.61543i	0.484870	+	0.139034i
$136$	−1.72476	−	3.53628i	−0.147897	−	0.303233i
$137$	−2.14403	−	5.30665i	−0.183177	−	0.453378i	0.807457	−	0.589927i	$-0.200843\pi$
$137$	−2.14403	−	5.30665i	−0.183177	−	0.453378i	−0.990633	+	0.136549i	$0.956399\pi$
$138$	10.3841	−	6.48869i	0.883951	−	0.552354i
$139$	9.30676	+	8.98744i	0.789389	+	0.762305i	0.975447	−	0.220234i	$-0.0706822\pi$
$139$	9.30676	+	8.98744i	0.789389	+	0.762305i	−0.186058	+	0.982539i	$0.559571\pi$
$140$	−0.156510	+	1.48909i	−0.0132275	+	0.125851i
$141$	22.0499	+	4.68685i	1.85694	+	0.394704i
$142$	9.37542	+	3.41237i	0.786768	+	0.286360i
$143$	14.3292	+	5.35841i	1.19827	+	0.448092i
$144$	−0.504710	+	0.874183i	−0.0420591	+	0.0728486i
$145$	−4.47229	+	4.96698i	−0.371403	+	0.412485i
$146$	2.68400	−	5.50301i	0.222129	−	0.455432i
$147$	−11.9111	−	0.832903i	−0.982408	−	0.0686967i
$148$	−1.64566	−	4.07316i	−0.135273	−	0.334812i
$149$	−2.56306	−	1.36280i	−0.209974	−	0.111645i	0.361154	−	0.932506i	$-0.382383\pi$
$149$	−2.56306	−	1.36280i	−0.209974	−	0.111645i	−0.571128	+	0.820861i	$0.693494\pi$
$150$	3.17769	−	4.71112i	0.259457	−	0.384661i
$151$	−9.87995	−	7.17820i	−0.804019	−	0.584154i	0.108072	−	0.994143i	$-0.465532\pi$
$151$	−9.87995	−	7.17820i	−0.804019	−	0.584154i	−0.912090	+	0.409989i	$0.865532\pi$
$152$	−4.20224	−	1.15808i	−0.340847	−	0.0939326i
$153$	−3.97153			−0.321079
$154$	1.91310	−	2.78324i	0.154162	−	0.224280i
$155$	1.83096	−	10.3839i	0.147066	−	0.834055i
$156$	7.83266	+	4.89439i	0.627114	+	0.391865i
$157$	−2.06625	−	8.28727i	−0.164905	−	0.661396i	−0.994654	−	0.103261i	$-0.967072\pi$
$157$	−2.06625	−	8.28727i	−0.164905	−	0.661396i	0.829750	−	0.558136i	$-0.188483\pi$
$158$	−10.0014	−	9.65827i	−0.795671	−	0.768371i
$159$	−20.5883	+	4.37617i	−1.63276	+	0.347053i
$160$	0.983877	+	1.09271i	0.0777823	+	0.0863860i
$161$	−5.98585	+	1.71641i	−0.471751	+	0.135272i
$162$	−6.15634	−	9.12715i	−0.483688	−	0.717097i
$163$	−8.86429	−	1.88416i	−0.694305	−	0.147579i	−0.152775	−	0.988261i	$-0.548821\pi$
$163$	−8.86429	−	1.88416i	−0.694305	−	0.147579i	−0.541529	+	0.840682i	$0.682154\pi$
$164$	−0.183935	−	0.318584i	−0.0143629	−	0.0248772i
$165$	8.66181	−	4.50843i	0.674321	−	0.350981i
$166$	2.88518	+	2.42095i	0.223933	+	0.187902i
$167$	−9.71887	−	6.07303i	−0.752069	−	0.469945i	0.0989416	−	0.995093i	$-0.468454\pi$
$167$	−9.71887	−	6.07303i	−0.752069	−	0.469945i	−0.851011	+	0.525148i	$0.824010\pi$
$168$	1.46674	−	1.41641i	0.113161	−	0.109279i
$169$	4.62803	−	6.86134i	0.356003	−	0.527796i
$170$	−1.78772	+	5.50203i	−0.137112	+	0.421986i
$171$	−2.91017	+	3.30008i	−0.222547	+	0.252363i
$172$	8.28626	−	6.02032i	0.631821	−	0.459045i
$173$	−12.8952	−	3.69765i	−0.980407	−	0.281127i	−0.253101	−	0.967440i	$-0.581450\pi$
$173$	−12.8952	−	3.69765i	−0.980407	−	0.281127i	−0.727307	+	0.686313i	$0.759228\pi$
$174$	9.01327	−	1.26673i	0.683294	−	0.0960308i
$175$	−2.21381	+	1.85761i	−0.167348	+	0.140422i
$176$	−0.774067	−	3.22503i	−0.0583475	−	0.243096i
$177$	0.252034	+	1.42936i	0.0189440	+	0.107437i
$178$	−0.902258	+	1.00206i	−0.0676271	+	0.0751075i
$179$	20.3498	−	9.06030i	1.52101	−	0.677199i	0.535151	−	0.844757i	$-0.320255\pi$
$179$	20.3498	−	9.06030i	1.52101	−	0.677199i	0.985862	+	0.167558i	$0.0535882\pi$
$180$	1.42674	−	0.409110i	0.106343	−	0.0304932i
$181$	11.9310	−	15.2709i	0.886821	−	1.13508i	−0.103270	−	0.994653i	$-0.532931\pi$
$181$	11.9310	−	15.2709i	0.886821	−	1.13508i	0.990091	−	0.140426i	$-0.0448471\pi$
$182$	−3.14294	−	3.49059i	−0.232970	−	0.258740i
$183$	−3.45298	−	1.53737i	−0.255252	−	0.113645i
$184$	−2.68070	+	5.49625i	−0.197624	+	0.405189i
$185$	−2.41975	+	5.98910i	−0.177904	+	0.440328i
$186$	−10.9995	+	9.22969i	−0.806524	+	0.676754i
$187$	9.46604	−	8.98191i	0.692225	−	0.656822i
$188$	−10.5791	+	3.85047i	−0.771558	+	0.280824i
$189$	1.25424	+	3.86015i	0.0912324	+	0.280785i
$190$	3.26185	+	5.51713i	0.236640	+	0.400255i
$191$	−16.5270	+	12.0076i	−1.19585	+	0.868838i	−0.993870	−	0.110551i	$-0.964738\pi$
$191$	−16.5270	+	12.0076i	−1.19585	+	0.868838i	−0.201983	+	0.979389i	$0.564738\pi$
$192$	−0.0698811	−	2.00113i	−0.00504324	−	0.144419i
$193$	4.04281	+	2.14960i	0.291008	+	0.154732i	0.608557	−	0.793510i	$-0.291749\pi$
$193$	4.04281	+	2.14960i	0.291008	+	0.154732i	−0.317549	+	0.948242i	$0.602860\pi$
$194$	3.25411	−	13.0515i	0.233631	−	0.937044i
$195$	−3.28544	−	13.1772i	−0.235275	−	0.943638i
$196$	5.26507	−	2.79949i	0.376076	−	0.199963i
$197$	−4.85682	−	8.41225i	−0.346034	−	0.599348i	0.639507	−	0.768785i	$-0.279138\pi$
$197$	−4.85682	−	8.41225i	−0.346034	−	0.599348i	−0.985541	+	0.169437i	$0.945805\pi$
$198$	−3.26847	−	0.724797i	−0.232280	−	0.0515091i
$199$	−22.9308	−	8.34614i	−1.62552	−	0.591642i	−0.641100	−	0.767458i	$-0.721521\pi$
$199$	−22.9308	−	8.34614i	−1.62552	−	0.591642i	−0.984423	+	0.175816i	$0.943744\pi$
$200$	−0.0990440	+	2.83625i	−0.00700347	+	0.200553i
$201$	25.8219	−	11.4966i	1.82134	−	0.810911i
$202$	3.81967	+	1.70063i	0.268751	+	0.119656i
$203$	−4.58373	−	0.644201i	−0.321715	−	0.0452141i
$204$	6.68109	−	4.17481i	0.467770	−	0.292295i
$205$	−0.130857	+	0.524840i	−0.00913948	+	0.0366564i
$206$	5.48959	−	5.30124i	0.382478	−	0.369355i
$207$	3.80032	+	4.86419i	0.264141	+	0.338085i
$208$	−4.61262			−0.319828
$209$	−0.527049	−	14.4472i	−0.0364568	−	0.999335i
$210$	−2.99811			−0.206889
$211$	13.6690	+	17.4955i	0.941012	+	1.20444i	0.978730	+	0.205153i	$0.0657690\pi$
$211$	13.6690	+	17.4955i	0.941012	+	1.20444i	−0.0377176	+	0.999288i	$0.512009\pi$
$212$	7.56151	−	7.30207i	0.519327	−	0.501508i
$213$	−4.83305	+	19.3843i	−0.331155	+	1.32819i
$214$	12.6419	−	7.89956i	0.864185	−	0.540003i
$215$	−14.9136	−	2.09598i	−1.01710	−	0.142944i
$216$	3.64125	+	1.62119i	0.247756	+	0.110308i
$217$	6.67093	−	2.97009i	0.452852	−	0.201623i
$218$	−0.432134	+	12.3747i	−0.0292678	+	0.838121i
$219$	11.5204	+	4.19307i	0.778475	+	0.283342i
$220$	−2.47535	+	4.20177i	−0.166888	+	0.283283i
$221$	−9.07411	−	15.7168i	−0.610391	−	1.05723i
$222$	7.76679	−	4.12968i	0.521273	−	0.277166i
$223$	3.55670	+	14.2651i	0.238174	+	0.955264i	0.963682	+	0.267051i	$0.0860492\pi$
$223$	3.55670	+	14.2651i	0.238174	+	0.955264i	−0.725508	+	0.688213i	$0.758395\pi$
$224$	−0.246350	+	0.988056i	−0.0164600	+	0.0660173i
$225$	2.52939	+	1.34490i	0.168626	+	0.0896600i
$226$	−0.00764998	−	0.219067i	−0.000508869	−	0.0145721i
$227$	5.03071	−	3.65502i	0.333900	−	0.242592i	−0.408184	−	0.912900i	$-0.633838\pi$
$227$	5.03071	−	3.65502i	0.333900	−	0.242592i	0.742084	+	0.670307i	$0.233838\pi$
$228$	1.42664	−	8.61067i	0.0944814	−	0.570256i
$229$	−6.70990	−	20.6510i	−0.443403	−	1.36465i	−0.884226	−	0.467060i	$-0.845313\pi$
$229$	−6.70990	−	20.6510i	−0.443403	−	1.36465i	0.440823	−	0.897594i	$-0.354687\pi$
$230$	8.44933	−	3.07531i	0.557133	−	0.202780i
$231$	5.94291	+	3.22718i	0.391015	+	0.212333i
$232$	−3.48211	+	2.92184i	−0.228612	+	0.191828i
$233$	4.00400	−	9.91024i	0.262311	−	0.649242i	−0.737344	−	0.675517i	$-0.763920\pi$
$233$	4.00400	−	9.91024i	0.262311	−	0.649242i	0.999655	+	0.0262757i	$0.00836479\pi$
$234$	−2.04109	+	4.18485i	−0.133430	+	0.273572i
$235$	15.1224	+	6.73294i	0.986479	+	0.439209i
$236$	−0.485019	−	0.538669i	−0.0315721	−	0.0350643i
$237$	17.1400	−	21.9382i	1.11336	−	1.42504i
$238$	−3.85128	+	1.10434i	−0.249642	+	0.0715836i
$239$	4.09994	−	1.82541i	0.265203	−	0.118076i	−0.269828	−	0.962909i	$-0.586967\pi$
$239$	4.09994	−	1.82541i	0.265203	−	0.118076i	0.535031	+	0.844833i	$0.320300\pi$
$240$	−1.97007	+	2.18798i	−0.127167	+	0.141234i
$241$	−0.796551	−	4.51746i	−0.0513103	−	0.290995i	0.948345	−	0.317240i	$-0.102756\pi$
$241$	−0.796551	−	4.51746i	−0.0513103	−	0.290995i	−0.999656	+	0.0262449i	$0.991645\pi$
$242$	9.42949	−	5.66434i	0.606150	−	0.364118i
$243$	7.72712	−	6.48382i	0.495695	−	0.415937i
$244$	1.86929	−	0.262711i	0.119669	−	0.0168184i
$245$	−8.42831	−	2.41678i	−0.538465	−	0.154402i
$246$	0.595925	−	0.432965i	0.0379948	−	0.0276048i
$247$	−19.7088	−	3.97665i	−1.25404	−	0.253028i
$248$	2.21596	−	6.82001i	0.140713	−	0.433071i
$249$	−4.21717	+	6.25221i	−0.267252	+	0.396218i
$250$	8.29026	−	8.00581i	0.524322	−	0.506332i
$251$	−1.93950	−	1.21194i	−0.122420	−	0.0764968i	0.467327	−	0.884085i	$-0.345217\pi$
$251$	−1.93950	−	1.21194i	−0.122420	−	0.0764968i	−0.589747	+	0.807588i	$0.700773\pi$
$252$	0.787414	+	0.660719i	0.0496024	+	0.0416214i
$253$	−20.0587	−	2.99896i	−1.26108	−	0.188543i
$254$	−3.22423	−	5.58453i	−0.202306	−	0.350405i
$255$	−11.3308	−	2.40844i	−0.709564	−	0.150822i
$256$	0.559193	+	0.829038i	0.0349496	+	0.0518148i
$257$	10.5116	−	3.01415i	0.655695	−	0.188018i	0.0687370	−	0.997635i	$-0.478103\pi$
$257$	10.5116	−	3.01415i	0.655695	−	0.188018i	0.586958	+	0.809617i	$0.300325\pi$
$258$	13.7231	+	15.2411i	0.854364	+	0.948867i
$259$	−4.37570	+	0.930084i	−0.271893	+	0.0577926i
$260$	4.87879	+	4.71139i	0.302570	+	0.292188i
$261$	1.11003	+	4.45210i	0.0687093	+	0.275578i
$262$	1.88945	+	1.18066i	0.116731	+	0.0729414i
$263$	−0.715818	+	4.05960i	−0.0441392	+	0.250326i	−0.998891	−	0.0470771i	$-0.985009\pi$
$263$	−0.715818	+	4.05960i	−0.0441392	+	0.250326i	0.954752	+	0.297403i	$0.0961205\pi$
$264$	6.26026	−	2.21647i	0.385292	−	0.136414i
$265$	−15.4563			−0.949471
$266$	−1.90443	+	4.00937i	−0.116768	+	0.245830i
$267$	−2.18433	−	1.58701i	−0.133679	−	0.0971233i
$268$	−7.89367	+	11.7028i	−0.482182	+	0.714865i
$269$	3.13411	+	1.66643i	0.191090	+	0.101604i	0.562260	−	0.826961i	$-0.309932\pi$
$269$	3.13411	+	1.66643i	0.191090	+	0.101604i	−0.371170	+	0.928565i	$0.621043\pi$
$270$	−2.19546	−	5.43396i	−0.133612	−	0.330700i
$271$	30.0772	+	2.10320i	1.82706	+	0.127760i	0.941552	−	0.336868i	$-0.109367\pi$
$271$	30.0772	+	2.10320i	1.82706	+	0.127760i	0.885506	+	0.464628i	$0.153812\pi$
$272$	−1.72476	+	3.53628i	−0.104579	+	0.214418i
$273$	6.29328	−	6.98939i	0.380886	−	0.423017i
$274$	−2.86170	+	4.95662i	−0.172882	+	0.299440i
$275$	−9.07033	+	2.51487i	−0.546961	+	0.151652i
$276$	−11.5062	−	4.18793i	−0.692594	−	0.252084i
$277$	−14.5934	−	3.10192i	−0.876831	−	0.186376i	−0.252557	−	0.967582i	$-0.581272\pi$
$277$	−14.5934	−	3.10192i	−0.876831	−	0.186376i	−0.624274	+	0.781206i	$0.714605\pi$
$278$	1.35238	−	12.8670i	0.0811104	−	0.771714i
$279$	−5.20697	−	5.02831i	−0.311733	−	0.301037i
$280$	1.26978	−	0.793445i	0.0758838	−	0.0474174i
$281$	−0.248560	−	0.615208i	−0.0148279	−	0.0367003i	0.919588	−	0.392883i	$-0.128522\pi$
$281$	−0.248560	−	0.615208i	−0.0148279	−	0.0367003i	−0.934416	+	0.356183i	$0.884078\pi$
$282$	−9.88199	−	20.2611i	−0.588464	−	1.20653i
$283$	−13.1317	−	3.76545i	−0.780599	−	0.223833i	−0.138405	−	0.990376i	$-0.544198\pi$
$283$	−13.1317	−	3.76545i	−0.780599	−	0.223833i	−0.642193	+	0.766543i	$0.721975\pi$
$284$	−3.08310	−	9.48880i	−0.182948	−	0.563057i
$285$	−10.3040	+	7.65036i	−0.610357	+	0.453168i
$286$	−4.59947	−	14.5905i	−0.271972	−	0.862757i
$287$	−0.352011	+	0.128122i	−0.0207786	+	0.00756278i
$288$	0.999596	−	0.140484i	0.0589018	−	0.00827810i
$289$	1.51624	−	0.106026i	0.0891906	−	0.00623681i
$290$	6.66745	+	0.466233i	0.391526	+	0.0273782i
$291$	26.6717	+	3.74846i	1.56352	+	0.219739i
$292$	−5.98887	+	1.27297i	−0.350472	+	0.0744951i
$293$	−0.0306143	−	0.291276i	−0.00178851	−	0.0170165i	0.993591	−	0.113033i	$-0.0360565\pi$
$293$	−0.0306143	−	0.291276i	−0.00178851	−	0.0170165i	−0.995380	+	0.0960164i	$0.969390\pi$
$294$	6.67685	+	9.89883i	0.389402	+	0.577312i
$295$	−0.0371961	+	1.06516i	−0.00216564	+	0.0620158i
$296$	−2.19652	+	3.80449i	−0.127670	+	0.221132i
$297$	−1.49725	+	13.1345i	−0.0868790	+	0.762141i
$298$	0.504074	+	2.85875i	0.0292002	+	0.165603i
$299$	−10.5665	+	26.1529i	−0.611075	+	1.51246i
$300$	−5.66879	+	0.396401i	−0.327288	+	0.0228862i
$301$	−4.57215	−	9.37429i	−0.263534	−	0.540325i
$302$	0.426203	+	12.2048i	0.0245252	+	0.702310i
$303$	−2.58713	+	7.96238i	−0.148627	+	0.457427i
$304$	1.67458	+	4.02440i	0.0960438	+	0.230815i
$305$	−2.24549	−	1.63144i	−0.128576	−	0.0934162i
$306$	2.44512	+	3.12961i	0.139778	+	0.178908i
$307$	−4.27868	+	24.2656i	−0.244197	+	1.38491i	0.578153	+	0.815929i	$0.303774\pi$
$307$	−4.27868	+	24.2656i	−0.244197	+	1.38491i	−0.822350	+	0.568982i	$0.807337\pi$
$308$	−3.37104	+	0.205989i	−0.192083	+	0.0117373i
$309$	11.7058	+	9.82233i	0.665919	+	0.558773i
$310$	−9.30988	+	4.95015i	−0.528765	+	0.281150i
$311$	−0.649531	+	6.17987i	−0.0368315	+	0.350428i	0.960550	+	0.278108i	$0.0897072\pi$
$311$	−0.649531	+	6.17987i	−0.0368315	+	0.350428i	−0.997381	+	0.0723208i	$0.976959\pi$
$312$	−0.965435	−	9.18550i	−0.0546570	−	0.520027i
$313$	9.20044	−	11.7760i	0.520039	−	0.665620i	−0.454262	−	0.890868i	$-0.650097\pi$
$313$	9.20044	−	11.7760i	0.520039	−	0.665620i	0.974301	+	0.225248i	$0.0723192\pi$
$314$	−5.25835	+	6.73038i	−0.296746	+	0.379817i
$315$	−0.157984	−	1.50312i	−0.00890140	−	0.0846912i
$316$	−1.45332	+	13.8275i	−0.0817559	+	0.777855i
$317$	−25.6656	+	13.6466i	−1.44152	+	0.766472i	−0.991933	−	0.126762i	$-0.959542\pi$
$317$	−25.6656	+	13.6466i	−1.44152	+	0.766472i	−0.449591	+	0.893234i	$0.648430\pi$
$318$	16.1239	+	13.5295i	0.904182	+	0.758698i
$319$	−12.7145	−	8.10104i	−0.711874	−	0.453571i
$320$	0.255329	−	1.44804i	0.0142733	−	0.0809481i
$321$	18.3771	+	23.5216i	1.02571	+	1.31285i
$322$	5.03781	+	3.66018i	0.280746	+	0.203974i
$323$	−10.4182	+	13.6228i	−0.579686	+	0.757994i
$324$	−3.40207	+	10.4705i	−0.189004	+	0.581694i
$325$	0.456853	+	13.0825i	0.0253416	+	0.725689i
$326$	3.97266	+	8.14516i	0.220025	+	0.451119i
$327$	−24.7332	+	1.72952i	−1.36775	+	0.0956425i
$328$	−0.137806	+	0.341082i	−0.00760907	+	0.0188331i
$329$	1.99072	+	11.2899i	0.109752	+	0.622433i
$330$	−8.88543	−	4.04994i	−0.489127	−	0.222942i
$331$	10.8057	−	18.7161i	0.593936	−	1.02873i	−0.399760	−	0.916620i	$-0.630907\pi$
$331$	10.8057	−	18.7161i	0.593936	−	1.02873i	0.993696	−	0.112108i	$-0.0357602\pi$
$332$	0.131443	−	3.76404i	0.00721388	−	0.206579i
$333$	2.47970	+	3.67631i	0.135887	+	0.201460i
$334$	1.19793	+	11.3975i	0.0655476	+	0.623644i
$335$	20.3026	−	4.31545i	1.10925	−	0.235778i
$336$	−2.01916	−	0.283775i	−0.110154	−	0.0154812i
$337$	−16.0383	−	1.12151i	−0.873661	−	0.0610923i	−0.374118	−	0.927381i	$-0.622054\pi$
$337$	−16.0383	−	1.12151i	−0.873661	−	0.0610923i	−0.499543	+	0.866289i	$0.666499\pi$
$338$	−8.25611	+	0.577324i	−0.449073	+	0.0314023i
$339$	0.434645	−	0.0610853i	0.0236067	−	0.00331770i
$340$	5.43628	−	1.97865i	0.294824	−	0.107307i
$341$	23.7826	+	0.208904i	1.28790	+	0.0113128i
$342$	4.39218	+	0.261517i	0.237502	+	0.0141412i
$343$	−4.07913	−	12.5543i	−0.220252	−	0.677866i
$344$	−9.84561	−	2.82318i	−0.530840	−	0.152216i
$345$	7.89259	+	16.1822i	0.424923	+	0.871220i
$346$	5.02532	+	12.4381i	0.270163	+	0.668676i
$347$	13.6467	−	8.52741i	0.732594	−	0.457775i	−0.111641	−	0.993749i	$-0.535611\pi$
$347$	13.6467	−	8.52741i	0.732594	−	0.457775i	0.844235	+	0.535973i	$0.180055\pi$
$348$	−6.54732	−	6.32268i	−0.350973	−	0.338931i
$349$	3.70431	−	35.2442i	0.198287	−	1.88658i	−0.215946	−	0.976405i	$-0.569283\pi$
$349$	3.70431	−	35.2442i	0.198287	−	1.88658i	0.414233	−	0.910171i	$-0.364050\pi$
$350$	2.82677	+	0.600849i	0.151097	+	0.0321167i
$351$	17.2764	+	6.28811i	0.922148	+	0.335634i
$352$	−2.06480	+	2.59550i	−0.110054	+	0.138341i
$353$	5.38662	−	9.32990i	0.286701	−	0.496580i	−0.686319	−	0.727300i	$-0.740775\pi$
$353$	5.38662	−	9.32990i	0.286701	−	0.496580i	0.973020	+	0.230720i	$0.0741081\pi$
$354$	0.971180	−	1.07860i	0.0516176	−	0.0573272i
$355$	−6.43098	+	13.1855i	−0.341321	+	0.699811i
$356$	1.34512	+	0.0940598i	0.0712911	+	0.00498516i
$357$	−3.00524	−	7.43824i	−0.159054	−	0.393673i
$358$	−19.6682	−	10.4578i	−1.03950	−	0.552710i
$359$	−13.0273	+	19.3138i	−0.687557	+	1.01935i	0.310085	+	0.950709i	$0.399643\pi$
$359$	−13.0273	+	19.3138i	−0.687557	+	1.01935i	−0.997642	+	0.0686363i	$0.978135\pi$
$360$	−1.20077	−	0.872409i	−0.0632861	−	0.0459800i
$361$	3.68561	+	18.6391i	0.193979	+	0.981006i
$362$	−19.3791			−1.01854
$363$	13.2535	+	17.5922i	0.695629	+	0.923349i
$364$	−0.815634	+	4.62569i	−0.0427508	+	0.242452i
$365$	7.63468	+	4.77068i	0.399617	+	0.249709i
$366$	0.914406	+	3.66748i	0.0477968	+	0.191702i
$367$	−8.99672	−	8.68804i	−0.469625	−	0.453512i	0.421794	−	0.906692i	$-0.361401\pi$
$367$	−8.99672	−	8.68804i	−0.469625	−	0.453512i	−0.891419	+	0.453180i	$0.850289\pi$
$368$	5.98151	−	1.27141i	0.311808	−	0.0662768i
$369$	0.248471	+	0.275955i	0.0129349	+	0.0143656i
$370$	6.20923	−	1.78047i	0.322802	−	0.0925621i
$371$	−5.98568	−	8.87414i	−0.310761	−	0.460722i
$372$	14.0451	+	2.98537i	0.728203	+	0.154784i
$373$	−8.43082	−	14.6026i	−0.436532	−	0.756095i	0.560888	−	0.827892i	$-0.310460\pi$
$373$	−8.43082	−	14.6026i	−0.436532	−	0.756095i	−0.997419	+	0.0717970i	$0.977127\pi$
$374$	−12.9057	−	1.92953i	−0.667339	−	0.0997734i
$375$	17.6778	+	14.8335i	0.912879	+	0.765996i
$376$	9.54733	+	5.96584i	0.492366	+	0.307664i
$377$	−15.0824	+	14.5649i	−0.776784	+	0.750131i
$378$	2.26965	−	3.36490i	0.116738	−	0.173072i
$379$	3.26675	−	10.0540i	0.167802	−	0.516440i	−0.831430	−	0.555629i	$-0.812477\pi$
$379$	3.26675	−	10.0540i	0.167802	−	0.516440i	0.999232	+	0.0391889i	$0.0124774\pi$
$380$	2.33936	−	5.96706i	0.120007	−	0.306104i
$381$	10.4461	−	7.58954i	0.535171	−	0.388824i
$382$	19.6372	+	5.63086i	1.00472	+	0.288100i
$383$	0.283869	−	0.0398951i	0.0145050	−	0.00203855i	−0.131917	−	0.991261i	$-0.542113\pi$
$383$	0.283869	−	0.0398951i	0.0145050	−	0.00203855i	0.146422	+	0.989222i	$0.453224\pi$
$384$	−1.53389	+	1.28709i	−0.0782761	+	0.0656814i
$385$	3.77597	+	3.22535i	0.192441	+	0.164379i
$386$	−0.795095	−	4.50921i	−0.0404693	−	0.229513i
$387$	−6.91805	+	7.68327i	−0.351664	+	0.390563i
$388$	−12.2882	+	5.47104i	−0.623837	+	0.277750i
$389$	−11.5668	+	3.31673i	−0.586461	+	0.168165i	−0.555730	−	0.831363i	$-0.687561\pi$
$389$	−11.5668	+	3.31673i	−0.586461	+	0.168165i	−0.0307308	+	0.999528i	$0.509783\pi$
$390$	−8.36104	+	10.7016i	−0.423378	+	0.541899i
$391$	16.0992	+	17.8800i	0.814171	+	0.904228i
$392$	−5.44752	−	2.42539i	−0.275142	−	0.122501i
$393$	−1.95568	+	4.00974i	−0.0986509	+	0.202264i
$394$	−3.63879	+	9.00632i	−0.183320	+	0.453732i
$395$	15.6607	−	13.1409i	0.787977	−	0.661191i
$396$	1.44112	+	3.02182i	0.0724191	+	0.151852i
$397$	0.0531407	−	0.0193416i	0.00266705	−	0.000970728i	−0.340686	−	0.940177i	$-0.610659\pi$
$397$	0.0531407	−	0.0193416i	0.00266705	−	0.000970728i	0.343353	+	0.939206i	$0.388437\pi$
$398$	7.54078	+	23.2081i	0.377985	+	1.16332i
$399$	−8.38280	−	2.95328i	−0.419665	−	0.147849i
$400$	2.29597	−	1.66812i	0.114799	−	0.0834061i
$401$	−0.485562	−	13.9047i	−0.0242478	−	0.694367i	−0.949272	−	0.314457i	$-0.898177\pi$
$401$	−0.485562	−	13.9047i	−0.0242478	−	0.694367i	0.925024	−	0.379909i	$-0.124045\pi$
$402$	−24.9570	−	13.2699i	−1.24474	−	0.661842i
$403$	8.00206	−	32.0945i	0.398611	−	1.59874i
$404$	−1.01151	−	4.05695i	−0.0503246	−	0.201841i
$405$	14.2931	−	7.59977i	0.710229	−	0.377635i
$406$	2.31439	+	4.00864i	0.114861	+	0.198945i
$407$	−14.2245	−	3.15436i	−0.705084	−	0.156356i
$408$	−7.40309	−	2.69450i	−0.366507	−	0.133398i
$409$	0.547680	−	15.6835i	0.0270810	−	0.775499i	−0.907563	−	0.419915i	$-0.862060\pi$
$409$	0.547680	−	15.6835i	0.0270810	−	0.775499i	0.934644	−	0.355584i	$-0.115718\pi$
$410$	0.494144	−	0.220007i	0.0244040	−	0.0108654i
$411$	−10.4695	−	4.66132i	−0.516422	−	0.229926i
$412$	−7.55717	−	1.06209i	−0.372315	−	0.0523254i
$413$	−0.625959	+	0.391143i	−0.0308014	+	0.0192469i
$414$	1.49332	−	5.98939i	0.0733928	−	0.294362i
$415$	−3.98367	+	3.84698i	−0.195550	+	0.188841i
$416$	2.83981	+	3.63480i	0.139233	+	0.178210i
$417$	25.9063			1.26864
$418$	−11.0601	+	9.30992i	−0.540966	+	0.455363i
$419$	7.16181			0.349877			0.174939	−	0.984579i	$-0.444027\pi$
$419$	7.16181			0.349877			0.174939	+	0.984579i	$0.444027\pi$
$420$	1.84582	+	2.36255i	0.0900669	+	0.115280i
$421$	5.59569	−	5.40370i	0.272717	−	0.263360i	−0.545705	−	0.837977i	$-0.683738\pi$
$421$	5.59569	−	5.40370i	0.272717	−	0.263360i	0.818422	+	0.574617i	$0.194849\pi$
$422$	5.37118	−	21.5426i	0.261465	−	1.04868i
$423$	9.63726	−	6.02203i	0.468580	−	0.292801i
$424$	−10.4094	−	1.46295i	−0.505527	−	0.0710472i
$425$	10.2006	+	4.54160i	0.494802	+	0.220300i
$426$	18.2506	−	8.12567i	0.884242	−	0.393690i
$427$	0.0670841	−	1.92104i	0.00324643	−	0.0929656i
$428$	−14.0081	−	5.09853i	−0.677107	−	0.246447i
$429$	28.0927	−	12.2131i	1.35633	−	0.589656i
$430$	7.53010	+	13.0425i	0.363134	+	0.628966i
$431$	0.0587401	−	0.0312327i	0.00282941	−	0.00150442i	−0.468056	−	0.883699i	$-0.655046\pi$
$431$	0.0587401	−	0.0312327i	0.00282941	−	0.00150442i	0.470886	+	0.882194i	$0.343934\pi$
$432$	−0.964263	−	3.86745i	−0.0463931	−	0.186073i
$433$	−4.48277	+	17.9794i	−0.215428	+	0.864035i	0.761098	+	0.648637i	$0.224661\pi$
$433$	−4.48277	+	17.9794i	−0.215428	+	0.864035i	−0.976526	+	0.215398i	$0.930895\pi$
$434$	−6.44750	−	3.42820i	−0.309490	−	0.164559i
$435$	0.467067	+	13.3750i	0.0223941	+	0.641284i
$436$	10.0175	−	7.27810i	0.479749	−	0.348558i
$437$	26.6539	−	0.275663i	1.27503	−	0.0131868i
$438$	−3.78846	−	11.6597i	−0.181020	−	0.557122i
$439$	18.8196	−	6.84976i	0.898208	−	0.326921i	0.148674	−	0.988886i	$-0.452500\pi$
$439$	18.8196	−	6.84976i	0.898208	−	0.326921i	0.749535	+	0.661965i	$0.230277\pi$
$440$	4.83502	−	0.636262i	0.230500	−	0.0303326i
$441$	−4.61100	+	3.86908i	−0.219571	+	0.184242i
$442$	−6.79844	+	16.8267i	−0.323369	+	0.800366i
$443$	5.27208	−	10.8094i	0.250484	−	0.513569i	−0.736090	−	0.676884i	$-0.763330\pi$
$443$	5.27208	−	10.8094i	0.250484	−	0.513569i	0.986574	+	0.163315i	$0.0522187\pi$
$444$	−8.03594	−	3.57783i	−0.381369	−	0.169796i
$445$	−1.32666	−	1.47341i	−0.0628898	−	0.0698463i
$446$	9.05136	−	11.5852i	0.428594	−	0.548576i
$447$	−5.58736	+	1.60215i	−0.264273	+	0.0757791i
$448$	0.930267	−	0.414181i	0.0439510	−	0.0195682i
$449$	−18.2983	+	20.3223i	−0.863551	+	0.959071i	−0.999499	−	0.0316451i	$-0.989925\pi$
$449$	−18.2983	+	20.3223i	−0.863551	+	0.959071i	0.135948	+	0.990716i	$0.456592\pi$
$450$	−0.497452	−	2.82119i	−0.0234501	−	0.132992i
$451$	−1.21632	−	0.0957960i	−0.0572741	−	0.00451086i
$452$	−0.167917	+	0.140899i	−0.00789816	+	0.00662734i
$453$	−24.2153	+	3.40324i	−1.13774	+	0.159898i
$454$	−5.97741	−	1.71399i	−0.280534	−	0.0804417i
$455$	5.58744	−	4.05951i	0.261943	−	0.190313i
$456$	−7.66363	+	4.17705i	−0.358882	+	0.195608i
$457$	−0.322823	+	0.993547i	−0.0151010	+	0.0464762i	−0.958323	−	0.285687i	$-0.907778\pi$
$457$	−0.322823	+	0.993547i	−0.0151010	+	0.0464762i	0.943222	+	0.332163i	$0.107778\pi$
$458$	−12.1421	+	18.0015i	−0.567365	+	0.841154i
$459$	11.2808	−	10.8938i	0.526544	−	0.508477i
$460$	−7.62530	−	4.76482i	−0.355532	−	0.222161i
$461$	6.87899	+	5.77216i	0.320386	+	0.268836i	0.788769	−	0.614690i	$-0.210719\pi$
$461$	6.87899	+	5.77216i	0.320386	+	0.268836i	−0.468383	+	0.883526i	$0.655163\pi$
$462$	−1.11577	−	6.66993i	−0.0519104	−	0.310313i
$463$	2.66274	+	4.61200i	0.123748	+	0.214338i	0.921243	−	0.388988i	$-0.127175\pi$
$463$	2.66274	+	4.61200i	0.123748	+	0.214338i	−0.797495	+	0.603326i	$0.793842\pi$
$464$	4.44624	+	0.945078i	0.206412	+	0.0438742i
$465$	−11.8062	−	17.5035i	−0.547501	−	0.811704i
$466$	−10.2745	+	2.94616i	−0.475956	+	0.136478i
$467$	25.3825	+	28.1902i	1.17456	+	1.30449i	0.943433	+	0.331563i	$0.107576\pi$
$467$	25.3825	+	28.1902i	1.17456	+	1.30449i	0.231131	+	0.972923i	$0.425757\pi$
$468$	4.55432	−	0.968051i	0.210524	−	0.0447482i
$469$	10.3402	+	9.98541i	0.477466	+	0.461083i
$470$	−4.00467	−	16.0619i	−0.184722	−	0.740878i
$471$	−14.5034	−	9.06271i	−0.668280	−	0.417587i
$472$	−0.125869	+	0.713838i	−0.00579358	+	0.0328571i
$473$	−0.887297	−	33.9585i	−0.0407980	−	1.56142i
$474$	−27.8400			−1.27873
$475$	11.2483	−	5.14812i	0.516109	−	0.236212i
$476$	3.24132	+	2.35495i	0.148565	+	0.107939i
$477$	−5.93346	+	8.79671i	−0.271674	+	0.402774i
$478$	−3.96262	−	2.10696i	−0.181246	−	0.0963702i
$479$	−8.76806	−	21.7017i	−0.400623	−	0.991577i	−0.983806	−	0.179236i	$-0.942637\pi$
$479$	−8.76806	−	21.7017i	−0.400623	−	0.991577i	0.583183	−	0.812341i	$-0.301807\pi$
$480$	2.93705	+	0.205379i	0.134057	+	0.00937421i
$481$	−8.88292	+	18.2127i	−0.405026	+	0.830427i
$482$	−3.06940	+	3.40892i	−0.139808	+	0.155272i
$483$	−6.23440	+	10.7983i	−0.283675	+	0.491340i
$484$	−10.2689	−	3.94322i	−0.466770	−	0.179237i
$485$	18.5854	+	6.76454i	0.843921	+	0.307162i
$486$	−9.86661	−	2.09721i	−0.447558	−	0.0951315i
$487$	1.23841	−	11.7826i	0.0561175	−	0.533923i	−0.929963	−	0.367653i	$-0.880161\pi$
$487$	1.23841	−	11.7826i	0.0561175	−	0.533923i	0.986080	−	0.166269i	$-0.0531721\pi$
$488$	−1.35787	−	1.31128i	−0.0614678	−	0.0593587i
$489$	−15.3887	+	9.61590i	−0.695899	+	0.434846i
$490$	3.28454	+	8.12952i	0.148380	+	0.367254i
$491$	10.7130	+	21.9648i	0.483469	+	0.991259i	0.991523	+	0.129934i	$0.0414764\pi$
$491$	10.7130	+	21.9648i	0.483469	+	0.991259i	−0.508053	+	0.861326i	$0.669635\pi$
$492$	−0.708069	−	0.203036i	−0.0319222	−	0.00915355i
$493$	5.52659	+	17.0091i	0.248905	+	0.766052i
$494$	9.00028	+	17.9790i	0.404942	+	0.808913i
$495$	1.56224	−	4.66817i	0.0702176	−	0.209818i
$496$	−6.73852	+	2.45262i	−0.302569	+	0.110126i
$497$	−10.0609	+	1.41396i	−0.451291	+	0.0634249i
$498$	7.52316	−	0.526071i	0.337121	−	0.0235738i
$499$	−35.1968	−	2.46120i	−1.57563	−	0.110179i	−0.745021	−	0.667041i	$-0.767561\pi$
$499$	−35.1968	−	2.46120i	−1.57563	−	0.110179i	−0.830605	+	0.556862i	$0.812005\pi$
$500$	−11.4127	−	1.60394i	−0.510390	−	0.0717306i
$501$	−22.4461	+	4.77106i	−1.00282	+	0.213155i
$502$	0.239059	+	2.27449i	0.0106697	+	0.101516i
$503$	−8.50149	−	12.6040i	−0.379063	−	0.561984i	0.590435	−	0.807085i	$-0.298956\pi$
$503$	−8.50149	−	12.6040i	−0.379063	−	0.561984i	−0.969497	+	0.245102i	$0.921179\pi$
$504$	0.0358730	−	1.02727i	0.00159791	−	0.0457582i
$505$	−3.07394	+	5.32423i	−0.136789	+	0.236925i
$506$	9.98615	+	17.6528i	0.443938	+	0.784763i
$507$	−2.87770	−	16.3203i	−0.127803	−	0.724808i
$508$	−2.41564	+	5.97891i	−0.107177	+	0.265271i
$509$	9.94244	−	0.695243i	0.440691	−	0.0308161i	0.152312	−	0.988332i	$-0.451328\pi$
$509$	9.94244	−	0.695243i	0.440691	−	0.0308161i	0.288379	+	0.957516i	$0.406884\pi$
$510$	5.07807	+	10.4116i	0.224861	+	0.461033i
$511$	0.217589	+	6.23093i	0.00962557	+	0.275640i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−0.785876	−	17.3561i	−0.0346973	−	0.766291i
$514$	−8.84677	−	6.42755i	−0.390214	−	0.283507i
$515$	6.90841	+	8.84236i	0.304421	+	0.389641i
$516$	3.56133	−	20.1973i	0.156779	−	0.889136i
$517$	−9.35090	+	36.1487i	−0.411252	+	1.58982i
$518$	3.42687	+	2.87548i	0.150568	+	0.126341i
$519$	−23.7172	+	12.6107i	−1.04107	+	0.553547i
$520$	0.708945	−	6.74516i	0.0310893	−	0.295795i
$521$	3.88502	+	36.9635i	0.170206	+	1.61940i	0.662561	+	0.749008i	$0.269469\pi$
$521$	3.88502	+	36.9635i	0.170206	+	1.61940i	−0.492355	+	0.870394i	$0.663864\pi$
$522$	2.82490	−	3.61570i	0.123642	−	0.158255i
$523$	3.66702	−	4.69357i	0.160348	−	0.205236i	−0.701127	−	0.713037i	$-0.747319\pi$
$523$	3.66702	−	4.69357i	0.160348	−	0.205236i	0.861474	+	0.507801i	$0.169542\pi$
$524$	−0.232889	−	2.21579i	−0.0101738	−	0.0967974i
$525$	−0.604870	+	5.75495i	−0.0263987	+	0.251167i
$526$	3.63971	−	1.93527i	0.158699	−	0.0843818i
$527$	−21.6132	−	18.1356i	−0.941486	−	0.790001i
$528$	−5.60081	−	3.56856i	−0.243744	−	0.155301i
$529$	2.49966	−	14.1763i	0.108681	−	0.616360i
$530$	9.51583	+	12.1797i	0.413341	+	0.529052i
$531$	0.591940	+	0.430069i	0.0256880	+	0.0186634i
$532$	4.33191	−	0.967706i	0.187812	−	0.0419554i
$533$	−0.524353	+	1.61379i	−0.0227122	+	0.0699011i
$534$	0.0942279	+	2.69833i	0.00407764	+	0.116768i
$535$	9.60871	+	19.7008i	0.415421	+	0.851739i
$536$	14.0818	−	0.984695i	0.608241	−	0.0425323i
$537$	16.7088	−	41.3557i	0.721038	−	1.78463i
$538$	−0.616381	−	3.49567i	−0.0265741	−	0.150709i
$539$	2.23997	−	19.6500i	0.0964822	−	0.846384i
$540$	−2.93036	+	5.07553i	−0.126102	+	0.218416i
$541$	−0.0492654	+	1.41078i	−0.00211808	+	0.0606540i	−0.999990	−	0.00455643i	$-0.998550\pi$
$541$	−0.0492654	+	1.41078i	−0.00211808	+	0.0606540i	0.997872	+	0.0652104i	$0.0207719\pi$
$542$	−16.8600	−	24.9960i	−0.724199	−	1.07367i
$543$	−4.05610	−	38.5912i	−0.174064	−	1.65611i
$544$	3.84849	−	0.818022i	0.165003	−	0.0350724i
$545$	−18.0294	−	2.53387i	−0.772297	−	0.108539i
$546$	−9.38224	−	0.656070i	−0.401523	−	0.0280772i
$547$	−39.9608	+	2.79433i	−1.70860	+	0.119477i	−0.890318	−	0.455339i	$-0.849518\pi$
$547$	−39.9608	+	2.79433i	−1.70860	+	0.119477i	−0.818283	+	0.574816i	$0.805074\pi$
$548$	5.66771	−	0.796545i	0.242113	−	0.0340267i
$549$	−1.79053	+	0.651699i	−0.0764178	+	0.0278138i
$550$	7.56599	+	5.59921i	0.322615	+	0.238751i
$551$	18.1831	+	7.87134i	0.774626	+	0.335330i
$552$	3.78381	+	11.6454i	0.161050	+	0.495660i
$553$	13.6097	+	3.90250i	0.578741	+	0.165951i
$554$	6.54023	+	13.4095i	0.277868	+	0.569714i
$555$	4.84520	+	11.9923i	0.205667	+	0.509045i
$556$	−10.9720	+	6.85606i	−0.465316	+	0.290762i
$557$	14.9798	+	14.4658i	0.634714	+	0.612936i	0.940757	−	0.339082i	$-0.110116\pi$
$557$	14.9798	+	14.4658i	0.634714	+	0.612936i	−0.306043	+	0.952018i	$0.599005\pi$
$558$	−0.756633	+	7.19888i	−0.0320308	+	0.304753i
$559$	−46.2118	−	9.82263i	−1.95455	−	0.415453i
$560$	−1.40700	−	0.512105i	−0.0594565	−	0.0216404i
$561$	1.14122	−	26.1041i	0.0481824	−	1.10212i
$562$	−0.331762	+	0.574628i	−0.0139945	+	0.0242392i
$563$	25.8958	−	28.7602i	1.09138	−	1.21210i	0.115609	−	0.993295i	$-0.463118\pi$
$563$	25.8958	−	28.7602i	1.09138	−	1.21210i	0.975769	−	0.218803i	$-0.0702153\pi$
$564$	−9.88199	+	20.2611i	−0.416107	+	0.853145i
$565$	0.321523	+	0.0224831i	0.0135266	+	0.000945870i
$566$	5.11746	+	12.6662i	0.215103	+	0.532399i
$567$	9.89859	+	5.26317i	0.415702	+	0.221032i
$568$	−5.57913	+	8.27140i	−0.234095	+	0.347060i
$569$	24.0015	+	17.4381i	1.00620	+	0.731044i	0.963408	−	0.268040i	$-0.0863758\pi$
$569$	24.0015	+	17.4381i	1.00620	+	0.731044i	0.0427885	+	0.999084i	$0.486376\pi$
$570$	12.3723	+	3.40964i	0.518220	+	0.142814i
$571$	23.0545			0.964801			0.482401	−	0.875951i	$-0.339765\pi$
$571$	23.0545			0.964801			0.482401	+	0.875951i	$0.339765\pi$
$572$	−8.66579	+	12.6073i	−0.362335	+	0.527136i
$573$	−7.10310	+	40.2837i	−0.296736	+	1.68287i
$574$	0.317681	+	0.198509i	0.0132597	+	0.00828561i
$575$	−4.19847	−	16.8391i	−0.175088	−	0.702241i
$576$	−0.726116	−	0.701202i	−0.0302548	−	0.0292167i
$577$	7.96132	−	1.69223i	0.331434	−	0.0704485i	−0.0391892	−	0.999232i	$-0.512477\pi$
$577$	7.96132	−	1.69223i	0.331434	−	0.0704485i	0.370623	+	0.928783i	$0.379144\pi$
$578$	−1.01704	−	1.12954i	−0.0423033	−	0.0469826i
$579$	8.81315	−	2.52713i	0.366262	−	0.105024i
$580$	−3.73749	−	5.54106i	−0.155191	−	0.230080i
$581$	−3.75146	−	0.797398i	−0.155637	−	0.0330816i
$582$	−13.4669	−	23.3254i	−0.558221	−	0.966867i
$583$	−5.75217	−	34.3857i	−0.238231	−	1.42411i
$584$	4.69023	+	3.93557i	0.194083	+	0.162855i
$585$	−5.80591	−	3.62793i	−0.240045	−	0.149997i
$586$	−0.210680	+	0.203452i	−0.00870312	+	0.00840451i
$587$	24.8592	−	36.8553i	1.02605	−	1.52118i	0.183170	−	0.983081i	$-0.441364\pi$
$587$	24.8592	−	36.8553i	1.02605	−	1.52118i	0.842880	−	0.538101i	$-0.180858\pi$
$588$	3.68971	−	11.3558i	0.152161	−	0.468304i
$589$	−30.9068	+	4.67010i	−1.27349	+	0.192428i
$590$	0.862255	−	0.626465i	0.0354985	−	0.0257912i
$591$	−18.6967	−	5.36118i	−0.769078	−	0.220530i
$592$	4.35029	−	0.611394i	0.178796	−	0.0251281i
$593$	7.39597	−	6.20596i	0.303716	−	0.254848i	−0.478173	−	0.878266i	$-0.658701\pi$
$593$	7.39597	−	6.20596i	0.303716	−	0.254848i	0.781889	+	0.623418i	$0.214256\pi$
$594$	11.2719	−	6.90656i	0.462492	−	0.283379i
$595$	−1.02297	−	5.80156i	−0.0419378	−	0.237841i
$596$	1.94238	−	2.15724i	0.0795632	−	0.0883639i
$597$	−44.6380	+	19.8741i	−1.82691	+	0.813393i
$598$	27.1142	−	7.77486i	1.10878	−	0.317938i
$599$	20.7825	−	26.6004i	0.849150	−	1.08686i	−0.146077	−	0.989273i	$-0.546665\pi$
$599$	20.7825	−	26.6004i	0.849150	−	1.08686i	0.995227	−	0.0975895i	$-0.0311132\pi$
$600$	3.80243	+	4.22302i	0.155233	+	0.172404i
$601$	−25.1574	−	11.2008i	−1.02619	−	0.456891i	−0.176574	−	0.984287i	$-0.556502\pi$
$601$	−25.1574	−	11.2008i	−1.02619	−	0.456891i	−0.849619	+	0.527396i	$0.823168\pi$
$602$	−4.57215	+	9.37429i	−0.186347	+	0.382068i
$603$	5.33782	−	13.2116i	0.217373	−	0.538017i
$604$	9.35515	−	7.84991i	0.380656	−	0.319408i
$605$	6.83384	+	14.6596i	0.277835	+	0.595997i
$606$	7.86724	−	2.86344i	0.319585	−	0.116319i
$607$	−5.15839	−	15.8759i	−0.209373	−	0.644383i	−0.999505	−	0.0314469i	$-0.989988\pi$
$607$	−5.15839	−	15.8759i	−0.209373	−	0.644383i	0.790133	−	0.612936i	$-0.210012\pi$
$608$	2.14029	−	3.79725i	0.0868004	−	0.153999i
$609$	−7.49833	+	5.44786i	−0.303848	+	0.220758i
$610$	0.0968663	+	2.77389i	0.00392200	+	0.112311i
$611$	45.8505	+	24.3792i	1.85491	+	0.986275i
$612$	0.960800	−	3.85356i	0.0388381	−	0.155771i
$613$	11.9191	+	47.8049i	0.481408	+	1.93082i	0.337950	+	0.941164i	$0.390267\pi$
$613$	11.9191	+	47.8049i	0.481408	+	1.93082i	0.143458	+	0.989656i	$0.454178\pi$
$614$	21.7558	−	11.5677i	0.877992	−	0.466836i
$615$	0.541544	+	0.937982i	0.0218372	+	0.0378231i
$616$	2.23774	+	2.52960i	0.0901612	+	0.101920i
$617$	−2.17305	−	0.790926i	−0.0874838	−	0.0318415i	0.297907	−	0.954595i	$-0.403711\pi$
$617$	−2.17305	−	0.790926i	−0.0874838	−	0.0318415i	−0.385391	+	0.922753i	$0.625934\pi$
$618$	0.533293	−	15.2715i	0.0214522	−	0.614311i
$619$	32.5830	−	14.5069i	1.30962	−	0.583081i	0.371194	−	0.928555i	$-0.378949\pi$
$619$	32.5830	−	14.5069i	1.30962	−	0.583081i	0.938428	+	0.345474i	$0.112282\pi$
$620$	9.63250	+	4.28867i	0.386851	+	0.172237i
$621$	−24.1368	−	3.39221i	−0.968577	−	0.136125i
$622$	5.26970	−	3.29287i	0.211296	−	0.132032i
$623$	0.332179	−	1.33230i	0.0133085	−	0.0533774i
$624$	−6.64389	+	6.41593i	−0.265969	+	0.256843i
$625$	1.69675	+	2.17174i	0.0678701	+	0.0868698i
$626$	−14.9440			−0.597282
$627$	−20.8545	−	20.0763i	−0.832850	−	0.801769i
$628$	8.54097			0.340822
$629$	10.6413	+	13.6202i	0.424296	+	0.543074i
$630$	−1.08721	+	1.04991i	−0.0433155	+	0.0418292i
$631$	−3.90174	+	15.6490i	−0.155326	+	0.622978i	0.841276	+	0.540606i	$0.181805\pi$
$631$	−3.90174	+	15.6490i	−0.155326	+	0.622978i	−0.996602	+	0.0823716i	$0.973751\pi$
$632$	11.7909	−	7.36780i	0.469018	−	0.293075i
$633$	44.0239	+	6.18715i	1.74979	+	0.245917i
$634$	26.5550	+	11.8231i	1.05464	+	0.469554i
$635$	8.66196	−	3.85656i	0.343740	−	0.153043i
$636$	0.734572	−	21.0354i	0.0291277	−	0.834108i
$637$	−25.8466	−	9.40738i	−1.02408	−	0.372734i
$638$	1.44411	+	15.0066i	0.0571729	+	0.594119i
$639$	5.03555	+	8.72183i	0.199203	+	0.345030i
$640$	−1.29827	+	0.690302i	−0.0513186	+	0.0272866i
$641$	−9.34814	−	37.4933i	−0.369229	−	1.48090i	−0.811678	−	0.584105i	$-0.801446\pi$
$641$	−9.34814	−	37.4933i	−0.369229	−	1.48090i	0.442449	−	0.896794i	$-0.354110\pi$
$642$	7.22120	−	28.9626i	0.284998	−	1.14306i
$643$	−35.5971	−	18.9273i	−1.40381	−	0.746421i	−0.417096	−	0.908862i	$-0.636952\pi$
$643$	−35.5971	−	18.9273i	−1.40381	−	0.746421i	−0.986718	+	0.162441i	$0.948063\pi$
$644$	−0.217322	−	6.22328i	−0.00856368	−	0.245232i
$645$	−24.3966	+	17.7252i	−0.960615	+	0.697928i
$646$	17.1490	−	0.177361i	0.674720	−	0.00697818i
$647$	−10.3067	−	31.7207i	−0.405198	−	1.24707i	−0.920730	−	0.390200i	$-0.872406\pi$
$647$	−10.3067	−	31.7207i	−0.405198	−	1.24707i	0.515533	−	0.856870i	$-0.327594\pi$
$648$	10.3454	−	3.76541i	0.406405	−	0.147919i
$649$	−2.38351	+	0.313656i	−0.0935608	+	0.0123121i
$650$	10.0279	−	8.41442i	0.393327	−	0.330041i
$651$	5.47738	−	13.5570i	0.214675	−	0.531340i
$652$	3.97266	−	8.14516i	0.155581	−	0.318989i
$653$	16.3100	+	7.26168i	0.638259	+	0.284171i	0.700242	−	0.713906i	$-0.253076\pi$
$653$	16.3100	+	7.26168i	0.638259	+	0.284171i	−0.0619823	+	0.998077i	$0.519742\pi$
$654$	16.5902	+	18.4253i	0.648728	+	0.720485i
$655$	−2.01691	+	2.58153i	−0.0788072	+	0.100869i
$656$	0.353618	−	0.101398i	0.0138065	−	0.00395894i
$657$	5.64602	−	2.51377i	0.220272	−	0.0980714i
$658$	7.67096	−	8.51947i	0.299045	−	0.332123i
$659$	6.17157	+	35.0007i	0.240410	+	1.36343i	0.830915	+	0.556400i	$0.187818\pi$
$659$	6.17157	+	35.0007i	0.240410	+	1.36343i	−0.590504	+	0.807034i	$0.701071\pi$
$660$	2.27903	+	9.49521i	0.0887109	+	0.369601i
$661$	23.8357	−	20.0005i	0.927102	−	0.777931i	−0.0481930	−	0.998838i	$-0.515346\pi$
$661$	23.8357	−	20.0005i	0.927102	−	0.777931i	0.975295	+	0.220907i	$0.0709018\pi$
$662$	−21.4011	+	3.00773i	−0.831778	+	0.116899i
$663$	−34.9314	−	10.0164i	−1.35662	−	0.389006i
$664$	−3.04703	+	2.21380i	−0.118248	+	0.0859119i
$665$	−5.57031	−	3.40112i	−0.216007	−	0.131890i
$666$	1.37031	−	4.21739i	0.0530986	−	0.163421i
$667$	15.5438	−	23.0446i	0.601858	−	0.892292i
$668$	8.24384	−	7.96098i	0.318964	−	0.308020i
$669$	24.9651	+	15.5999i	0.965206	+	0.603128i
$670$	−15.9001	−	13.3418i	−0.614276	−	0.515439i
$671$	2.79381	−	5.60271i	0.107854	−	0.216290i
$672$	1.01950	+	1.76583i	0.0393281	+	0.0681183i
$673$	29.9076	+	6.35706i	1.15285	+	0.245047i	0.744401	−	0.667733i	$-0.232735\pi$
$673$	29.9076	+	6.35706i	1.15285	+	0.245047i	0.408453	+	0.912779i	$0.366068\pi$
$674$	8.99039	+	13.3288i	0.346297	+	0.513406i
$675$	−10.8735	+	3.11794i	−0.418523	+	0.120010i
$676$	5.53791	+	6.15047i	0.212996	+	0.236557i
$677$	−3.10800	+	0.660625i	−0.119450	+	0.0253899i	−0.267249	−	0.963628i	$-0.586115\pi$
$677$	−3.10800	+	0.660625i	−0.119450	+	0.0253899i	0.147799	+	0.989017i	$0.452781\pi$
$678$	−0.315730	−	0.304897i	−0.0121255	−	0.0117095i
$679$	3.31367	+	13.2904i	0.127167	+	0.510039i
$680$	−4.90610	−	3.06567i	−0.188141	−	0.117563i
$681$	2.16213	−	12.2621i	0.0828531	−	0.469883i
$682$	−14.4774	−	18.8695i	−0.554368	−	0.722551i
$683$	14.5375			0.556261			0.278131	−	0.960543i	$-0.410285\pi$
$683$	14.5375			0.556261			0.278131	+	0.960543i	$0.410285\pi$
$684$	−2.49802	−	3.62209i	−0.0955141	−	0.138494i
$685$	−6.80836	−	4.94656i	−0.260134	−	0.188998i
$686$	−7.38153	+	10.9436i	−0.281828	+	0.417827i
$687$	−38.3892	−	20.4119i	−1.46464	−	0.778763i
$688$	3.83686	+	9.49657i	0.146279	+	0.362053i
$689$	−48.3685	−	3.38226i	−1.84269	−	0.128854i
$690$	7.89259	−	16.1822i	0.300466	−	0.616046i
$691$	12.9998	−	14.4377i	0.494534	−	0.549236i	−0.443276	−	0.896385i	$-0.646184\pi$
$691$	12.9998	−	14.4377i	0.494534	−	0.549236i	0.937810	+	0.347149i	$0.112850\pi$
$692$	6.70746	−	11.6177i	0.254979	−	0.441637i
$693$	3.28521	−	0.910867i	0.124795	−	0.0346010i
$694$	−15.1214	−	5.50375i	−0.574002	−	0.208920i
$695$	18.6080	+	3.95525i	0.705841	+	0.150031i
$696$	−0.951402	+	9.05199i	−0.0360628	+	0.343115i
$697$	1.04115	+	1.00543i	0.0394364	+	0.0380833i
$698$	−30.0534	+	18.7794i	−1.13754	+	0.710812i
$699$	−8.01742	−	19.8438i	−0.303247	−	0.750562i
$700$	−1.26686	−	2.59745i	−0.0478828	−	0.0981743i
$701$	21.9546	+	6.29538i	0.829214	+	0.237773i	0.663287	−	0.748365i	$-0.269161\pi$
$701$	21.9546	+	6.29538i	0.829214	+	0.237773i	0.165926	+	0.986138i	$0.446939\pi$
$702$	−5.68134	−	17.4854i	−0.214428	−	0.659942i
$703$	19.1150	+	1.13813i	0.720936	+	0.0429255i
$704$	3.31650	+	0.0291319i	0.124995	+	0.00109795i
$705$	31.1471	−	11.3366i	1.17307	−	0.426962i
$706$	−10.6684	+	1.49934i	−0.401510	+	0.0564286i
$707$	−4.24731	+	0.297001i	−0.159737	+	0.0111699i
$708$	−1.44787	−	0.101245i	−0.0544143	−	0.00380502i
$709$	10.6692	+	1.49946i	0.400690	+	0.0563134i	0.336640	−	0.941633i	$-0.390709\pi$
$709$	10.6692	+	1.49946i	0.400690	+	0.0563134i	0.0640501	+	0.997947i	$0.479598\pi$
$710$	14.3496	−	3.05010i	0.538530	−	0.114468i
$711$	−1.46701	−	13.9577i	−0.0550173	−	0.523455i
$712$	−0.754017	−	1.11788i	−0.0282580	−	0.0418942i
$713$	−1.53040	+	43.8249i	−0.0573139	+	1.64126i
$714$	−4.01120	+	6.94760i	−0.150115	+	0.260008i
$715$	22.0431	−	4.48340i	0.824364	−	0.167670i
$716$	3.86812	+	21.9372i	0.144558	+	0.819831i
$717$	3.36638	−	8.33209i	0.125720	−	0.311168i
$718$	23.2399	−	1.62510i	0.867307	−	0.0606480i
$719$	13.0620	+	26.7810i	0.487130	+	0.998764i	0.990859	+	0.134902i	$0.0430721\pi$
$719$	13.0620	+	26.7810i	0.487130	+	0.998764i	−0.503729	+	0.863862i	$0.668039\pi$
$720$	0.0517989	+	1.48333i	0.00193043	+	0.0552804i
$721$	−2.40141	+	7.39077i	−0.0894331	+	0.275247i
$722$	12.4187	−	14.3797i	0.462177	−	0.535156i
$723$	−7.43090	−	5.39887i	−0.276358	−	0.200786i
$724$	11.9310	+	15.2709i	0.443410	+	0.567539i
$725$	2.24010	−	12.7043i	0.0831954	−	0.471825i
$726$	5.70315	−	21.2747i	0.211664	−	0.789579i
$727$	−0.180447	−	0.151413i	−0.00669242	−	0.00561560i	0.639435	−	0.768845i	$-0.279168\pi$
$727$	−0.180447	−	0.151413i	−0.00669242	−	0.00561560i	−0.646128	+	0.763229i	$0.723613\pi$
$728$	4.14725	−	2.20513i	0.153707	−	0.0817276i
$729$	−1.34112	+	12.7599i	−0.0496711	+	0.472589i
$730$	−0.941033	−	8.95333i	−0.0348292	−	0.331378i
$731$	−24.8101	+	31.7555i	−0.917636	+	1.17452i
$732$	2.32705	−	2.97849i	0.0860103	−	0.110088i
$733$	−2.42582	−	23.0802i	−0.0895998	−	0.852485i	−0.943349	−	0.331801i	$-0.892344\pi$
$733$	−2.42582	−	23.0802i	−0.0895998	−	0.852485i	0.853749	−	0.520684i	$-0.174323\pi$
$734$	−1.30733	+	12.4384i	−0.0482544	+	0.459110i
$735$	−15.5015	+	8.24231i	−0.571783	+	0.304022i
$736$	−4.68447	−	3.93074i	−0.172672	−	0.144889i
$737$	17.1564	+	43.5613i	0.631964	+	1.60460i
$738$	0.0644815	−	0.365693i	0.00237360	−	0.0134613i
$739$	11.8562	+	15.1752i	0.436137	+	0.558229i	0.954992	−	0.296633i	$-0.0958637\pi$
$739$	11.8562	+	15.1752i	0.436137	+	0.558229i	−0.518855	+	0.854862i	$0.673642\pi$
$740$	−5.22581	−	3.79677i	−0.192105	−	0.139572i
$741$	−33.9193	+	21.6861i	−1.24606	+	0.796658i
$742$	−3.30776	+	10.1802i	−0.121432	+	0.373728i
$743$	1.11959	+	32.0609i	0.0410738	+	1.17620i	0.828571	+	0.559883i	$0.189154\pi$
$743$	1.11959	+	32.0609i	0.0410738	+	1.17620i	−0.787498	+	0.616318i	$0.788624\pi$
$744$	−6.29451	−	12.9057i	−0.230768	−	0.473144i
$745$	−4.25790	+	0.297741i	−0.155997	+	0.0109084i
$746$	−6.31649	+	15.6338i	−0.231263	+	0.572396i
$747$	0.660178	+	3.74405i	0.0241546	+	0.136988i
$748$	6.42507	+	11.3578i	0.234924	+	0.415282i
$749$	−7.58998	+	13.1462i	−0.277332	+	0.480353i
$750$	0.805367	−	23.0627i	0.0294079	−	0.842131i
$751$	2.76563	+	4.10021i	0.100919	+	0.149619i	0.876115	−	0.482102i	$-0.160127\pi$
$751$	2.76563	+	4.10021i	0.100919	+	0.149619i	−0.775196	+	0.631721i	$0.782349\pi$
$752$	−1.17678	−	11.1963i	−0.0429128	−	0.408288i
$753$	−4.47935	+	0.952116i	−0.163237	+	0.0346970i
$754$	20.7630	+	2.91805i	0.756143	+	0.106269i
$755$	−17.9130	−	1.25260i	−0.651920	−	0.0455867i
$756$	−4.04891	+	0.283128i	−0.147258	+	0.0102973i
$757$	9.72321	−	1.36651i	0.353396	−	0.0496666i	0.0397585	−	0.999209i	$-0.487341\pi$
$757$	9.72321	−	1.36651i	0.353396	−	0.0496666i	0.313638	+	0.949543i	$0.398452\pi$
$758$	−9.93389	+	3.61564i	−0.360815	+	0.131326i
$759$	−33.0634	+	23.5810i	−1.20013	+	0.855938i
$760$	−6.14236	+	1.83025i	−0.222807	+	0.0663901i
$761$	−12.0776	−	37.1710i	−0.437812	−	1.34745i	−0.890177	−	0.455614i	$-0.849420\pi$
$761$	−12.0776	−	37.1710i	−0.437812	−	1.34745i	0.452365	−	0.891833i	$-0.350580\pi$
$762$	−12.4119	−	3.55906i	−0.449636	−	0.128931i
$763$	−5.52737	−	11.3328i	−0.200104	−	0.410275i
$764$	−7.65266	−	18.9410i	−0.276863	−	0.685261i
$765$	−4.95232	+	3.09455i	−0.179051	+	0.111884i
$766$	−0.206205	−	0.199130i	−0.00745048	−	0.00719484i
$767$	−0.349487	+	3.32514i	−0.0126192	+	0.120064i
$768$	1.95860	+	0.416313i	0.0706748	+	0.0150224i
$769$	−49.7207	−	18.0969i	−1.79297	−	0.652589i	−0.999003	−	0.0446334i	$-0.985788\pi$
$769$	−49.7207	−	18.0969i	−1.79297	−	0.652589i	−0.793971	−	0.607956i	$-0.791990\pi$
$770$	0.216895	−	4.96123i	0.00781637	−	0.178790i
$771$	10.9481	−	18.9626i	0.394285	−	0.682922i
$772$	−3.06379	+	3.40269i	−0.110268	+	0.122465i
$773$	3.11253	−	6.38164i	0.111950	−	0.229532i	−0.835462	−	0.549549i	$-0.814800\pi$
$773$	3.11253	−	6.38164i	0.111950	−	0.229532i	0.947412	+	0.320017i	$0.103689\pi$
$774$	10.3137	+	0.721202i	0.370717	+	0.0259231i
$775$	7.62366	+	18.8692i	0.273850	+	0.677802i
$776$	11.8766	+	6.31490i	0.426345	+	0.226692i
$777$	−5.00894	+	7.42606i	−0.179695	+	0.266408i
$778$	9.73486	+	7.07279i	0.349012	+	0.253572i
$779$	1.59836	−	0.128391i	0.0572670	−	0.00460010i
$780$	13.5806			0.486263
$781$	−31.7271	−	9.39998i	−1.13529	−	0.336358i
$782$	4.17795	−	23.6943i	0.149403	−	0.847307i
$783$	−15.3649	−	9.60106i	−0.549097	−	0.343114i
$784$	1.44259	+	5.78593i	0.0515212	+	0.206640i
$785$	−9.03382	−	8.72386i	−0.322431	−	0.311368i
$786$	4.36375	−	0.927544i	0.155650	−	0.0330844i
$787$	4.72689	+	5.24974i	0.168495	+	0.187133i	0.821479	−	0.570239i	$-0.193150\pi$
$787$	4.72689	+	5.24974i	0.168495	+	0.187133i	−0.652983	+	0.757372i	$0.726483\pi$
$788$	9.33734	−	2.67744i	0.332629	−	0.0953799i
$789$	4.61567	+	6.84301i	0.164322	+	0.243618i
$790$	−19.9969	−	4.25047i	−0.711457	−	0.151225i
$791$	0.111606	+	0.193308i	0.00396826	+	0.00687323i
$792$	1.49398	−	2.99603i	0.0530863	−	0.106459i
$793$	−6.66999	−	5.59679i	−0.236858	−	0.198748i
$794$	−0.0479581	−	0.0299675i	−0.00170197	−	0.00106351i
$795$	−22.2628	+	21.4989i	−0.789579	+	0.762488i
$796$	13.6457	−	20.2306i	0.483659	−	0.717053i
$797$	9.38213	−	28.8752i	0.332332	−	1.02281i	−0.635689	−	0.771945i	$-0.719284\pi$
$797$	9.38213	−	28.8752i	0.332332	−	1.02281i	0.968021	−	0.250868i	$-0.0807159\pi$
$798$	2.83376	+	8.42396i	0.100314	+	0.298205i
$799$	35.8348	−	26.0355i	1.26775	−	0.921071i
$800$	−2.72804	−	0.782253i	−0.0964508	−	0.0276568i
$801$	−1.34786	+	0.189429i	−0.0476242	+	0.00669315i
$802$	−10.6581	+	8.94321i	−0.376351	+	0.315796i
$803$	−7.77206	+	18.7604i	−0.274270	+	0.662039i
$804$	4.90827	+	27.8362i	0.173101	+	0.981706i
$805$	−6.12668	+	6.80436i	−0.215937	+	0.239822i
$806$	−30.2174	+	13.4536i	−1.06436	+	0.473885i
$807$	6.83221	−	1.95910i	0.240505	−	0.0689637i
$808$	−2.57417	+	3.29479i	−0.0905591	+	0.115910i
$809$	0.0279419	+	0.0310326i	0.000982384	+	0.00109105i	0.743636	−	0.668585i	$-0.233100\pi$
$809$	0.0279419	+	0.0310326i	0.000982384	+	0.00109105i	−0.742653	+	0.669676i	$0.766433\pi$
$810$	−14.7884	−	6.58422i	−0.519611	−	0.231346i
$811$	6.66432	−	13.6639i	0.234016	−	0.479804i	−0.749178	−	0.662369i	$-0.769551\pi$
$811$	6.66432	−	13.6639i	0.234016	−	0.479804i	0.983194	+	0.182565i	$0.0584400\pi$
$812$	1.73397	−	4.29173i	0.0608504	−	0.150610i
$813$	46.2478	−	38.8065i	1.62198	−	1.36100i
$814$	6.27184	+	13.1511i	0.219828	+	0.460946i
$815$	−12.5215	+	4.55744i	−0.438608	+	0.159640i
$816$	2.43450	+	7.49261i	0.0852245	+	0.262294i
$817$	8.20690	+	43.8847i	0.287123	+	1.53533i
$818$	−12.6960	+	9.22415i	−0.443904	+	0.322515i
$819$	−0.165469	−	4.73841i	−0.00578195	−	0.165573i
$820$	−0.477593	−	0.253941i	−0.0166783	−	0.00886800i
$821$	−4.58392	+	18.3851i	−0.159980	+	0.641645i	0.835732	+	0.549138i	$0.185044\pi$
$821$	−4.58392	+	18.3851i	−0.159980	+	0.641645i	−0.995712	+	0.0925073i	$0.970512\pi$
$822$	2.77249	+	11.1199i	0.0967019	+	0.387850i
$823$	−36.0945	+	19.1918i	−1.25818	+	0.668984i	−0.958509	−	0.285061i	$-0.907986\pi$
$823$	−36.0945	+	19.1918i	−1.25818	+	0.668984i	−0.299666	+	0.954044i	$0.596875\pi$
$824$	3.81572	+	6.60902i	0.132927	+	0.230236i
$825$	−9.56659	+	16.2387i	−0.333066	+	0.565360i
$826$	0.693604	+	0.252451i	0.0241336	+	0.00878390i
$827$	1.18687	−	33.9875i	0.0412715	−	1.18186i	−0.785331	−	0.619076i	$-0.787507\pi$
$827$	1.18687	−	33.9875i	0.0412715	−	1.18186i	0.826603	−	0.562786i	$-0.190271\pi$
$828$	−5.63908	+	2.51068i	−0.195972	+	0.0872522i
$829$	−9.58482	−	4.26744i	−0.332895	−	0.148214i	0.233481	−	0.972361i	$-0.424988\pi$
$829$	−9.58482	−	4.26744i	−0.332895	−	0.148214i	−0.566376	+	0.824147i	$0.691655\pi$
$830$	5.48405	+	0.770733i	0.190354	+	0.0267525i
$831$	−25.3345	+	15.8308i	−0.878845	+	0.549163i
$832$	1.11589	−	4.47561i	0.0386867	−	0.155164i
$833$	−16.8768	+	16.2977i	−0.584745	+	0.564682i
$834$	−15.9495	−	20.4144i	−0.552286	−	0.706894i
$835$	−16.8510			−0.583153
$836$	14.1456	+	2.98371i	0.489235	+	0.103194i
$837$	28.5825			0.987954
$838$	−4.40925	−	5.64358i	−0.152315	−	0.194954i
$839$	−12.8271	+	12.3870i	−0.442842	+	0.427648i	−0.882352	−	0.470590i	$-0.844041\pi$
$839$	−12.8271	+	12.3870i	−0.442842	+	0.427648i	0.439510	+	0.898238i	$0.355152\pi$
$840$	0.725309	−	2.90906i	0.0250255	−	0.100372i
$841$	−7.07080	+	4.41833i	−0.243821	+	0.152356i
$842$	−7.70322	−	1.08262i	−0.265471	−	0.0373094i
$843$	−1.21374	−	0.540394i	−0.0418036	−	0.0186122i
$844$	−20.2827	+	9.03042i	−0.698158	+	0.310840i
$845$	0.424702	−	12.1619i	0.0146102	−	0.418381i
$846$	−10.6787	−	3.88673i	−0.367142	−	0.133629i
$847$	−5.77021	+	9.60077i	−0.198267	+	0.329886i
$848$	5.25587	+	9.10343i	0.180487	+	0.312613i
$849$	−24.1521	+	12.8419i	−0.828898	+	0.440733i
$850$	−2.70129	−	10.8343i	−0.0926534	−	0.371612i
$851$	6.49902	−	26.0661i	0.222783	−	0.893536i
$852$	−17.6393	−	9.37897i	−0.604312	−	0.321318i
$853$	1.63963	+	46.9529i	0.0561399	+	1.60764i	0.621921	+	0.783080i	$0.286353\pi$
$853$	1.63963	+	46.9529i	0.0561399	+	1.60764i	−0.565781	+	0.824556i	$0.691425\pi$
$854$	−1.55510	+	1.12985i	−0.0532144	+	0.0386625i
$855$	−1.05749	+	6.38261i	−0.0361653	+	0.218280i
$856$	4.60655	+	14.1775i	0.157449	+	0.484577i
$857$	17.5014	−	6.36998i	0.597835	−	0.217594i	−0.0253369	−	0.999679i	$-0.508066\pi$
$857$	17.5014	−	6.36998i	0.597835	−	0.217594i	0.623172	+	0.782085i	$0.285844\pi$
$858$	−26.9197	−	14.6182i	−0.919023	−	0.499057i
$859$	5.50313	−	4.61768i	0.187765	−	0.157553i	−0.544060	−	0.839046i	$-0.683114\pi$
$859$	5.50313	−	4.61768i	0.187765	−	0.157553i	0.731824	+	0.681493i	$0.238669\pi$
$860$	5.64165	−	13.9636i	0.192379	−	0.476154i
$861$	−0.328816	+	0.674173i	−0.0112060	+	0.0229758i
$862$	−0.0607757	−	0.0270591i	−0.00207003	−	0.000921636i
$863$	−29.5524	−	32.8213i	−1.00598	−	1.11725i	−0.993093	−	0.117332i	$-0.962566\pi$
$863$	−29.5524	−	32.8213i	−1.00598	−	1.11725i	−0.0128827	−	0.999917i	$-0.504101\pi$
$864$	−2.45393	+	3.14089i	−0.0834845	+	0.106855i
$865$	−18.9609	+	5.43696i	−0.644691	+	0.184862i
$866$	16.9278	−	7.53676i	0.575231	−	0.256109i
$867$	2.03647	−	2.26173i	0.0691623	−	0.0768125i
$868$	1.26802	+	7.19131i	0.0430394	+	0.244089i
$869$	35.0630	+	29.9501i	1.18943	+	1.01599i
$870$	10.2521	−	8.60255i	0.347579	−	0.291654i
$871$	64.4789	−	9.06192i	2.18478	−	0.307051i
$872$	−11.9026	−	3.41301i	−0.403072	−	0.115579i
$873$	10.9847	−	7.98082i	0.371774	−	0.270110i
$874$	−16.6270	−	20.8338i	−0.562416	−	0.704714i
$875$	−3.62655	+	11.1614i	−0.122600	+	0.377323i
$876$	−6.85555	+	10.1638i	−0.231628	+	0.343402i
$877$	9.14251	−	8.82882i	0.308721	−	0.298128i	−0.524116	−	0.851647i	$-0.675604\pi$
$877$	9.14251	−	8.82882i	0.308721	−	0.298128i	0.832837	+	0.553519i	$0.186715\pi$
$878$	−16.9842	−	10.6129i	−0.573188	−	0.358167i
$879$	−0.449246	−	0.376962i	−0.0151527	−	0.0127146i
$880$	−3.47812	−	3.41832i	−0.117247	−	0.115232i
$881$	−12.5404	−	21.7206i	−0.422497	−	0.731787i	0.573686	−	0.819075i	$-0.305513\pi$
$881$	−12.5404	−	21.7206i	−0.422497	−	0.731787i	−0.996183	+	0.0872888i	$0.972180\pi$
$882$	5.88769	+	1.25147i	0.198249	+	0.0421391i
$883$	27.0425	+	40.0921i	0.910051	+	1.34921i	0.936911	+	0.349567i	$0.113671\pi$
$883$	27.0425	+	40.0921i	0.910051	+	1.34921i	−0.0268600	+	0.999639i	$0.508551\pi$
$884$	17.4452	−	5.00233i	0.586745	−	0.168246i
$885$	1.42801	+	1.58596i	0.0480019	+	0.0533115i
$886$	−11.7637	+	2.50046i	−0.395210	+	0.0840045i
$887$	−12.4284	−	12.0020i	−0.417305	−	0.402987i	0.456141	−	0.889907i	$-0.349231\pi$
$887$	−12.4284	−	12.0020i	−0.417305	−	0.402987i	−0.873446	+	0.486921i	$0.838120\pi$
$888$	2.12805	+	8.53514i	0.0714127	+	0.286421i
$889$	5.56870	+	3.47971i	0.186768	+	0.116706i
$890$	−0.344286	+	1.95255i	−0.0115405	+	0.0654495i
$891$	22.2266	+	28.9696i	0.744618	+	0.970519i
$892$	−14.7018			−0.492254
$893$	4.62448	−	48.8541i	0.154752	−	1.63484i
$894$	4.70243	+	3.41652i	0.157273	+	0.114265i
$895$	18.3156	−	27.1540i	0.612223	−	0.907657i
$896$	−0.899109	−	0.478065i	−0.0300371	−	0.0159710i
$897$	21.1578	+	52.3674i	0.706439	+	1.74850i
$898$	27.2798	+	1.90759i	0.910339	+	0.0636571i
$899$	−14.2893	+	29.2973i	−0.476574	+	0.977121i
$900$	−1.91687	+	2.12890i	−0.0638955	+	0.0709632i
$901$	−20.6791	+	35.8172i	−0.688919	+	1.19324i
$902$	0.673351	+	1.01745i	0.0224201	+	0.0338773i
$903$	−19.6248	−	7.14284i	−0.653072	−	0.237699i
$904$	0.214410	+	0.0455743i	0.00713118	+	0.00151578i
$905$	2.97850	−	28.3385i	0.0990087	−	0.942005i
$906$	17.5902	+	16.9867i	0.584397	+	0.564345i
$907$	39.7755	−	24.8545i	1.32073	−	0.825281i	0.327884	−	0.944718i	$-0.393665\pi$
$907$	39.7755	−	24.8545i	1.32073	−	0.825281i	0.992842	+	0.119437i	$0.0381091\pi$
$908$	2.32941	+	5.76550i	0.0773043	+	0.191335i
$909$	1.85016	+	3.79339i	0.0613660	+	0.125819i
$910$	−6.63891	−	1.90368i	−0.220078	−	0.0631063i
$911$	−9.57420	−	29.4663i	−0.317207	−	0.976264i	−0.974836	−	0.222922i	$-0.928441\pi$
$911$	−9.57420	−	29.4663i	−0.317207	−	0.976264i	0.657629	−	0.753342i	$-0.271559\pi$
$912$	8.00976	+	3.46737i	0.265230	+	0.114816i
$913$	−10.0410	−	7.43081i	−0.332308	−	0.245924i
$914$	0.981676	−	0.357301i	0.0324709	−	0.0118185i
$915$	−5.50360	+	0.773481i	−0.181943	+	0.0255705i
$916$	21.6608	−	1.51467i	0.715693	−	0.0500462i
$917$	−2.26325	−	0.158262i	−0.0747392	−	0.00522627i
$918$	−15.5296	−	2.18254i	−0.512552	−	0.0720345i
$919$	−31.8469	+	6.76927i	−1.05053	+	0.223298i	−0.700657	−	0.713498i	$-0.747110\pi$
$919$	−31.8469	+	6.76927i	−1.05053	+	0.223298i	−0.349876	+	0.936796i	$0.613776\pi$
$920$	0.939877	+	8.94234i	0.0309868	+	0.294820i
$921$	27.5894	+	40.9029i	0.909101	+	1.34780i
$922$	0.313393	−	8.97441i	0.0103211	−	0.295556i
$923$	−23.0103	+	39.8551i	−0.757394	+	1.31185i
$924$	−4.56904	+	4.98566i	−0.150310	+	0.164016i
$925$	−2.16494	−	12.2780i	−0.0711827	−	0.403697i
$926$	1.99496	−	4.93770i	0.0655584	−	0.162263i
$927$	7.68455	−	0.537356i	0.252394	−	0.0176491i
$928$	−1.99265	−	4.08554i	−0.0654119	−	0.134114i
$929$	−0.172501	−	4.93977i	−0.00565956	−	0.162069i	−0.998930	−	0.0462498i	$-0.985273\pi$
$929$	−0.172501	−	4.93977i	−0.00565956	−	0.162069i	0.993270	−	0.115819i	$-0.0369492\pi$
$930$	−6.52427	+	20.0796i	−0.213939	+	0.658437i
$931$	1.17572	+	25.9658i	0.0385325	+	0.850993i
$932$	8.64721	+	6.28257i	0.283249	+	0.205792i
$933$	7.66034	+	9.80479i	0.250788	+	0.320994i
$934$	6.58710	−	37.3573i	0.215537	−	1.22237i
$935$	4.80516	−	18.5758i	0.157146	−	0.607494i
$936$	−3.56676	−	2.99286i	−0.116583	−	0.0978248i
$937$	−27.0431	+	14.3791i	−0.883459	+	0.469743i	−0.848225	−	0.529636i	$-0.822329\pi$
$937$	−27.0431	+	14.3791i	−0.883459	+	0.469743i	−0.0352337	+	0.999379i	$0.511218\pi$
$938$	1.50255	−	14.2958i	0.0490600	−	0.466775i
$939$	−3.12782	−	29.7592i	−0.102073	−	0.971156i
$940$	−10.1914	+	13.0444i	−0.332407	+	0.425461i
$941$	9.98492	−	12.7801i	0.325499	−	0.416620i	−0.597229	−	0.802071i	$-0.703732\pi$
$941$	9.98492	−	12.7801i	0.325499	−	0.416620i	0.922728	+	0.385451i	$0.125954\pi$
$942$	1.78765	+	17.0084i	0.0582448	+	0.554162i
$943$	0.235144	−	2.23725i	0.00765735	−	0.0728548i
$944$	0.640005	−	0.340296i	0.0208304	−	0.0110757i
$945$	4.57174	+	3.83615i	0.148719	+	0.124790i
$946$	−26.2134	+	21.6062i	−0.852272	+	0.702477i
$947$	−3.20412	+	18.1715i	−0.104120	+	0.590494i	0.887448	+	0.460907i	$0.152476\pi$
$947$	−3.20412	+	18.1715i	−0.104120	+	0.590494i	−0.991568	+	0.129586i	$0.958635\pi$
$948$	17.1400	+	21.9382i	0.556681	+	0.712519i
$949$	22.8479	+	16.5999i	0.741673	+	0.538857i
$950$	−10.9819	−	5.69431i	−0.356301	−	0.184748i
$951$	−17.9862	+	55.3559i	−0.583243	+	1.79504i
$952$	−0.139824	−	4.00405i	−0.00453173	−	0.129772i
$953$	21.9248	+	44.9526i	0.710215	+	1.45616i	0.882111	+	0.471042i	$0.156122\pi$
$953$	21.9248	+	44.9526i	0.710215	+	1.45616i	−0.171896	+	0.985115i	$0.554989\pi$
$954$	10.5849	−	0.740169i	0.342699	−	0.0239638i
$955$	−11.2523	+	27.8505i	−0.364117	+	0.901220i
$956$	0.779323	+	4.41976i	0.0252051	+	0.142945i
$957$	−29.5817	+	6.01672i	−0.956242	+	0.194493i
$958$	−11.7030	+	20.2702i	−0.378108	+	0.654902i
$959$	0.203400	−	5.82462i	0.00656813	−	0.188087i
$960$	−1.64639	−	2.44087i	−0.0531370	−	0.0787788i
$961$	−2.13479	−	20.3112i	−0.0688642	−	0.655199i
$962$	19.8207	−	4.21301i	0.639044	−	0.135833i
$963$	14.9011	+	2.09421i	0.480181	+	0.0674850i
$964$	4.57598	+	0.319984i	0.147382	+	0.0103060i
$965$	6.71614	−	0.469638i	0.216200	−	0.0151182i
$966$	12.3475	−	1.73532i	0.397273	−	0.0558331i
$967$	−36.0022	+	13.1037i	−1.15775	+	0.421388i	−0.848295	−	0.529524i	$-0.822370\pi$
$967$	−36.0022	+	13.1037i	−1.15775	+	0.421388i	−0.309460	+	0.950913i	$0.600148\pi$
$968$	3.21489	+	10.5197i	0.103330	+	0.338117i
$969$	3.94254	+	34.1132i	0.126653	+	1.09587i
$970$	−6.11180	−	18.8102i	−0.196238	−	0.603959i
$971$	−41.2203	−	11.8197i	−1.32282	−	0.379313i	−0.461395	−	0.887195i	$-0.652651\pi$
$971$	−41.2203	−	11.8197i	−1.32282	−	0.379313i	−0.861427	+	0.507882i	$0.830429\pi$
$972$	4.42187	+	9.06617i	0.141831	+	0.290797i
$973$	4.93534	+	12.2154i	0.158220	+	0.391608i
$974$	−10.0473	+	6.27824i	−0.321936	+	0.201168i
$975$	18.8552	+	18.2083i	0.603851	+	0.583132i
$976$	−0.197314	+	1.87732i	−0.00631587	+	0.0600915i
$977$	44.5910	+	9.47811i	1.42659	+	0.303232i	0.855563	−	0.517698i	$-0.173211\pi$
$977$	44.5910	+	9.47811i	1.42659	+	0.303232i	0.571029	+	0.820930i	$0.306544\pi$
$978$	17.0516	+	6.20629i	0.545251	+	0.198455i
$979$	2.78418	−	3.49978i	0.0889827	−	0.111853i
$980$	4.38398	−	7.59328i	0.140041	−	0.242559i
$981$	−8.36339	+	9.28848i	−0.267022	+	0.296558i
$982$	10.7130	−	21.9648i	0.341865	−	0.700926i
$983$	−29.4887	−	2.06205i	−0.940544	−	0.0657693i	−0.408753	−	0.912645i	$-0.634036\pi$
$983$	−29.4887	−	2.06205i	−0.940544	−	0.0657693i	−0.531791	+	0.846876i	$0.678481\pi$
$984$	0.275937	+	0.682967i	0.00879654	+	0.0217722i
$985$	−12.6109	−	6.70534i	−0.401817	−	0.213650i
$986$	10.0008	−	14.8269i	0.318492	−	0.472184i
$987$	18.5711	+	13.4927i	0.591124	+	0.429477i
$988$	8.62651	−	18.1613i	0.274446	−	0.577788i
$989$	62.6336			1.99163
$990$	−4.64038	+	1.64295i	−0.147481	+	0.0522163i
$991$	−1.69763	+	9.62772i	−0.0539269	+	0.305835i	−0.999827	−	0.0186246i	$-0.994071\pi$
$991$	−1.69763	+	9.62772i	−0.0539269	+	0.305835i	0.945900	+	0.324459i	$0.105182\pi$
$992$	6.08134	+	3.80004i	0.193083	+	0.120652i
$993$	−10.4689	−	41.9883i	−0.332219	−	1.33246i
$994$	7.30830	+	7.05755i	0.231805	+	0.223852i
$995$	−35.0969	+	7.46007i	−1.11264	+	0.236500i
$996$	−5.04627	−	5.60445i	−0.159897	−	0.177584i
$997$	−29.5257	+	8.46636i	−0.935088	+	0.268132i	−0.708381	−	0.705831i	$-0.750574\pi$
$997$	−29.5257	+	8.46636i	−0.935088	+	0.268132i	−0.226707	+	0.973963i	$0.572796\pi$
$998$	19.7299	+	29.2507i	0.624538	+	0.925916i
$999$	−17.1274	−	3.64054i	−0.541886	−	0.115181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.5.9	✓	264
11.9	even	5	inner	418.2.u.b.119.3	yes	264
19.4	even	9	inner	418.2.u.b.137.3	yes	264
209.42	even	45	inner	418.2.u.b.251.9	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.5.9	✓	264	1.1	even	1	trivial
418.2.u.b.119.3	yes	264	11.9	even	5	inner
418.2.u.b.137.3	yes	264	19.4	even	9	inner
418.2.u.b.251.9	yes	264	209.42	even	45	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615661 - 0.788011i) q^{2} +(1.44037 - 1.39095i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(1.24695 - 0.779183i) q^{5} +(-1.98287 - 0.278674i) q^{6} +(0.930267 + 0.414181i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.0352282 - 1.00880i) q^{9} +O(q^{10})\)	\(q+(-0.615661 - 0.788011i) q^{2} +(1.44037 - 1.39095i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(1.24695 - 0.779183i) q^{5} +(-1.98287 - 0.278674i) q^{6} +(0.930267 + 0.414181i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.0352282 - 1.00880i) q^{9} +(-1.38171 - 0.502900i) q^{10} +(2.19752 + 2.48413i) q^{11} +(1.00118 + 1.73409i) q^{12} +(4.07270 - 2.16549i) q^{13} +(-0.246350 - 0.988056i) q^{14} +(0.712272 - 2.85677i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(-0.137311 - 3.93207i) q^{17} +(-0.816638 + 0.593322i) q^{18} +(-3.36791 - 2.76716i) q^{19} +(0.454373 + 1.39842i) q^{20} +(1.91604 - 0.697380i) q^{21} +(0.604593 - 3.26105i) q^{22} +(-4.68447 + 3.93074i) q^{23} +(0.750095 - 1.85655i) q^{24} +(-1.24409 + 2.55076i) q^{25} +(-4.21384 - 1.87612i) q^{26} +(2.66705 + 2.96206i) q^{27} +(-0.626930 + 0.802434i) q^{28} +(-4.36949 + 1.25293i) q^{29} +(-2.68968 + 1.19752i) q^{30} +(4.79833 - 5.32908i) q^{31} +(0.173648 + 0.984808i) q^{32} +(6.62055 + 0.521429i) q^{33} +(-3.01398 + 2.52903i) q^{34} +(1.48272 - 0.208383i) q^{35} +(0.970316 + 0.278234i) q^{36} +(-3.55405 + 2.58217i) q^{37} +(-0.107064 + 4.35758i) q^{38} +(2.85411 - 8.78405i) q^{39} +(0.822227 - 1.21900i) q^{40} +(-0.264623 + 0.255543i) q^{41} +(-1.72917 - 1.08051i) q^{42} +(-7.84612 - 6.58368i) q^{43} +(-2.94197 + 1.53128i) q^{44} +(-0.742116 - 1.28538i) q^{45} +(5.98151 + 1.27141i) q^{46} +(6.29540 + 9.33331i) q^{47} +(-1.92479 + 0.551923i) q^{48} +(-3.99006 - 4.43142i) q^{49} +(2.77596 - 0.590049i) q^{50} +(-5.66710 - 5.47266i) q^{51} +(1.11589 + 4.47561i) q^{52} +(-8.91446 - 5.57037i) q^{53} +(0.692135 - 3.92529i) q^{54} +(4.67580 + 1.38533i) q^{55} +1.01830 q^{56} +(-8.70003 + 0.698850i) q^{57} +(3.67745 + 2.67182i) q^{58} +(-0.405331 + 0.600928i) q^{59} +(2.59959 + 1.38223i) q^{60} +(-0.707129 - 1.75021i) q^{61} +(-7.15352 - 0.500223i) q^{62} +(0.450600 - 0.923867i) q^{63} +(0.669131 - 0.743145i) q^{64} +(3.39116 - 5.87365i) q^{65} +(-3.66513 - 5.53809i) q^{66} +(13.2649 + 4.82802i) q^{67} +(3.84849 + 0.818022i) q^{68} +(-1.27992 + 12.1776i) q^{69} +(-1.07706 - 1.04011i) q^{70} +(-8.46107 + 5.28707i) q^{71} +(-0.378135 - 0.935917i) q^{72} +(2.68400 + 5.50301i) q^{73} +(4.22287 + 1.21089i) q^{74} +(1.75603 + 5.40451i) q^{75} +(3.49974 - 2.59843i) q^{76} +(1.01540 + 3.22108i) q^{77} +(-8.67909 + 3.15893i) q^{78} +(13.7683 - 1.93501i) q^{79} +(-1.46680 + 0.102569i) q^{80} +(10.9825 + 0.767972i) q^{81} +(0.364289 + 0.0511975i) q^{82} +(-3.68403 + 0.783065i) q^{83} +(0.213134 + 2.02783i) q^{84} +(-3.23503 - 4.79612i) q^{85} +(-0.357454 + 10.2361i) q^{86} +(-4.55093 + 7.88243i) q^{87} +(3.01792 + 1.37555i) q^{88} +(-0.234148 - 1.32792i) q^{89} +(-0.556003 + 1.37616i) q^{90} +(4.68561 - 0.327650i) q^{91} +(-2.68070 - 5.49625i) q^{92} +(-0.501117 - 14.3501i) q^{93} +(3.47892 - 10.7070i) q^{94} +(-6.35575 - 0.826309i) q^{95} +(1.61994 + 1.17695i) q^{96} +(8.28131 + 10.5996i) q^{97} +(-1.03547 + 5.87247i) q^{98} +(2.58342 - 2.12936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

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