LMFDB - Embedded newform 261.2.q.a.103.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(7,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 18]))

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

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

chi := DirichletCharacter("261.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.q (of order $21$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			103.27
Character	$\chi$	$=$	261.103
Dual form			261.2.q.a.223.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.187058 + 2.49612i) q^{2} +(-1.72664 - 0.136835i) q^{3} +(-4.21795 + 0.635753i) q^{4} +(-0.730934 + 0.498342i) q^{5} +(0.0185754 - 4.33548i) q^{6} +(-3.13454 - 0.472455i) q^{7} +(-1.26192 - 5.52885i) q^{8} +(2.96255 + 0.472530i) q^{9} +(-1.38065 - 1.73128i) q^{10} +(3.88874 - 1.19952i) q^{11} +(7.36986 - 0.520551i) q^{12} +(-0.789571 - 0.732615i) q^{13} +(0.592963 - 7.91255i) q^{14} +(1.33025 - 0.760439i) q^{15} +(5.41243 - 1.66951i) q^{16} -5.99968 q^{17} +(-0.625320 + 7.48327i) q^{18} +(-2.35611 - 2.95447i) q^{19} +(2.76622 - 2.56667i) q^{20} +(5.34756 + 1.24467i) q^{21} +(3.72155 + 9.48236i) q^{22} +(0.229754 - 3.06585i) q^{23} +(1.42234 + 9.71899i) q^{24} +(-1.54079 + 3.92586i) q^{25} +(1.68100 - 2.10790i) q^{26} +(-5.05059 - 1.22127i) q^{27} +13.5217 q^{28} +(-4.05681 - 3.54152i) q^{29} +(2.14698 + 3.17821i) q^{30} +(-4.60383 + 3.13884i) q^{31} +(1.03602 + 2.63973i) q^{32} +(-6.87857 + 1.53901i) q^{33} +(-1.12229 - 14.9759i) q^{34} +(2.52658 - 1.21674i) q^{35} +(-12.7963 - 0.109654i) q^{36} +(2.53992 + 11.1281i) q^{37} +(6.93398 - 6.43379i) q^{38} +(1.26306 + 1.37300i) q^{39} +(3.67764 + 3.41235i) q^{40} +(-2.13847 + 3.70394i) q^{41} +(-2.10655 + 13.5810i) q^{42} +(-4.83932 - 3.29939i) q^{43} +(-15.6399 + 7.53177i) q^{44} +(-2.40091 + 1.13098i) q^{45} +7.69570 q^{46} +(4.69688 - 1.44880i) q^{47} +(-9.57375 + 2.14203i) q^{48} +(2.91310 + 0.898572i) q^{49} +(-10.0876 - 3.11162i) q^{50} +(10.3593 + 0.820968i) q^{51} +(3.79613 + 2.58816i) q^{52} +(2.95463 + 1.42288i) q^{53} +(2.10368 - 12.8353i) q^{54} +(-2.24464 + 2.81469i) q^{55} +(1.34341 + 17.9266i) q^{56} +(3.66388 + 5.42370i) q^{57} +(8.08118 - 10.7887i) q^{58} +(-1.23521 + 2.13945i) q^{59} +(-5.12746 + 4.05320i) q^{60} +(-4.04854 - 0.610220i) q^{61} +(-8.69610 - 10.9046i) q^{62} +(-9.06298 - 2.88084i) q^{63} +(3.81101 - 1.83529i) q^{64} +(0.942217 + 0.142016i) q^{65} +(-5.12825 - 16.8818i) q^{66} +(-6.60889 - 2.03857i) q^{67} +(25.3063 - 3.81432i) q^{68} +(-0.816218 + 5.26217i) q^{69} +(3.50974 + 6.07905i) q^{70} +(2.34734 - 10.2844i) q^{71} +(-1.12597 - 16.9758i) q^{72} +(-8.54599 + 4.11553i) q^{73} +(-27.3020 + 8.42155i) q^{74} +(3.19757 - 6.56770i) q^{75} +(11.8163 + 10.9639i) q^{76} +(-12.7561 + 1.92267i) q^{77} +(-3.19091 + 3.40957i) q^{78} +(7.61429 - 7.06503i) q^{79} +(-3.12414 + 3.91755i) q^{80} +(8.55343 + 2.79979i) q^{81} +(-9.64548 - 4.64502i) q^{82} +(-3.73059 + 9.50538i) q^{83} +(-23.3470 - 1.85024i) q^{84} +(4.38537 - 2.98990i) q^{85} +(7.33043 - 12.6967i) q^{86} +(6.52003 + 6.67003i) q^{87} +(-11.5392 - 19.9865i) q^{88} +(11.8062 + 5.68557i) q^{89} +(-3.27216 - 5.78139i) q^{90} +(2.12881 + 2.66945i) q^{91} +(0.980035 + 13.0777i) q^{92} +(8.37866 - 4.78967i) q^{93} +(4.49495 + 11.4530i) q^{94} +(3.19450 + 0.985373i) q^{95} +(-1.42762 - 4.69963i) q^{96} +(-2.49026 + 6.34507i) q^{97} +(-1.69802 + 7.43952i) q^{98} +(12.0874 - 1.71609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19}+ \cdots + 196 q^{99}+O(q^{100}) $ 336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.187058	+	2.49612i	0.132270	+	1.76502i	0.530452	+	0.847715i	$0.322022\pi$
$2$	0.187058	+	2.49612i	0.132270	+	1.76502i	−0.398182	+	0.917306i	$0.630359\pi$
$3$	−1.72664	−	0.136835i	−0.996874	−	0.0790019i
$3$	−1.72664	−	0.136835i	−0.996874	−	0.0790019i
$4$	−4.21795	+	0.635753i	−2.10897	+	0.317877i
$5$	−0.730934	+	0.498342i	−0.326883	+	0.222865i	−0.715630	−	0.698479i	$-0.753860\pi$
$5$	−0.730934	+	0.498342i	−0.326883	+	0.222865i	0.388747	+	0.921345i	$0.372908\pi$
$6$	0.0185754	−	4.33548i	0.00758337	−	1.76995i
$7$	−3.13454	−	0.472455i	−1.18474	−	0.178571i	−0.473033	−	0.881044i	$-0.656841\pi$
$7$	−3.13454	−	0.472455i	−1.18474	−	0.178571i	−0.711710	+	0.702473i	$0.752079\pi$
$8$	−1.26192	−	5.52885i	−0.446157	−	1.95474i
$9$	2.96255	+	0.472530i	0.987517	+	0.157510i
$10$	−1.38065	−	1.73128i	−0.436599	−	0.547478i
$11$	3.88874	−	1.19952i	1.17250	−	0.361668i	0.353484	−	0.935441i	$-0.384997\pi$
$11$	3.88874	−	1.19952i	1.17250	−	0.361668i	0.819014	+	0.573773i	$0.194521\pi$
$12$	7.36986	−	0.520551i	2.12749	−	0.150270i
$13$	−0.789571	−	0.732615i	−0.218988	−	0.203191i	0.563049	−	0.826424i	$-0.309628\pi$
$13$	−0.789571	−	0.732615i	−0.218988	−	0.203191i	−0.782036	+	0.623233i	$0.785819\pi$
$14$	0.592963	−	7.91255i	0.158476	−	2.11472i
$15$	1.33025	−	0.760439i	0.343469	−	0.196344i
$16$	5.41243	−	1.66951i	1.35311	−	0.417378i
$17$	−5.99968			−1.45514			−0.727569	−	0.686035i	$-0.759350\pi$
$17$	−5.99968			−1.45514			−0.727569	+	0.686035i	$0.759350\pi$
$18$	−0.625320	+	7.48327i	−0.147389	+	1.76382i
$19$	−2.35611	−	2.95447i	−0.540530	−	0.677803i	0.434296	−	0.900770i	$-0.356997\pi$
$19$	−2.35611	−	2.95447i	−0.540530	−	0.677803i	−0.974826	+	0.222967i	$0.928426\pi$
$20$	2.76622	−	2.56667i	0.618545	−	0.573926i
$21$	5.34756	+	1.24467i	1.16693	+	0.271610i
$22$	3.72155	+	9.48236i	0.793437	+	2.02165i
$23$	0.229754	−	3.06585i	0.0479070	−	0.639274i	−0.920635	−	0.390424i	$-0.872328\pi$
$23$	0.229754	−	3.06585i	0.0479070	−	0.639274i	0.968542	−	0.248850i	$-0.0800526\pi$
$24$	1.42234	+	9.71899i	0.290334	+	1.98388i
$25$	−1.54079	+	3.92586i	−0.308157	+	0.785172i
$26$	1.68100	−	2.10790i	0.329671	−	0.413394i
$27$	−5.05059	−	1.22127i	−0.971987	−	0.235033i
$28$	13.5217			2.55536
$29$	−4.05681	−	3.54152i	−0.753330	−	0.657643i
$29$	−4.05681	−	3.54152i	−0.753330	−	0.657643i
$30$	2.14698	+	3.17821i	0.391983	+	0.580259i
$31$	−4.60383	+	3.13884i	−0.826873	+	0.563753i	−0.901161	−	0.433484i	$-0.857284\pi$
$31$	−4.60383	+	3.13884i	−0.826873	+	0.563753i	0.0742880	+	0.997237i	$0.476332\pi$
$32$	1.03602	+	2.63973i	0.183144	+	0.466644i
$33$	−6.87857	+	1.53901i	−1.19741	+	0.267908i
$34$	−1.12229	−	14.9759i	−0.192471	−	2.56835i
$35$	2.52658	−	1.21674i	0.427071	−	0.205666i
$36$	−12.7963	−	0.109654i	−2.13272	−	0.0182756i
$37$	2.53992	+	11.1281i	0.417561	+	1.82945i	0.546062	+	0.837744i	$0.316126\pi$
$37$	2.53992	+	11.1281i	0.417561	+	1.82945i	−0.128502	+	0.991709i	$0.541017\pi$
$38$	6.93398	−	6.43379i	1.12484	−	1.04370i
$39$	1.26306	+	1.37300i	0.202251	+	0.219856i
$40$	3.67764	+	3.41235i	0.581486	+	0.539540i
$41$	−2.13847	+	3.70394i	−0.333973	+	0.578458i	−0.983287	−	0.182062i	$-0.941723\pi$
$41$	−2.13847	+	3.70394i	−0.333973	+	0.578458i	0.649314	+	0.760520i	$0.275056\pi$
$42$	−2.10655	+	13.5810i	−0.325047	+	2.09559i
$43$	−4.83932	−	3.29939i	−0.737989	−	0.503152i	0.135028	−	0.990842i	$-0.456888\pi$
$43$	−4.83932	−	3.29939i	−0.737989	−	0.503152i	−0.873017	+	0.487689i	$0.837840\pi$
$44$	−15.6399	+	7.53177i	−2.35780	+	1.13546i
$45$	−2.40091	+	1.13098i	−0.357907	+	0.168596i
$46$	7.69570			1.13467
$47$	4.69688	−	1.44880i	0.685110	−	0.211329i	0.0673904	−	0.997727i	$-0.478533\pi$
$47$	4.69688	−	1.44880i	0.685110	−	0.211329i	0.617720	+	0.786398i	$0.288057\pi$
$48$	−9.57375	+	2.14203i	−1.38185	+	0.309176i
$49$	2.91310	+	0.898572i	0.416157	+	0.128367i
$50$	−10.0876	−	3.11162i	−1.42660	−	0.440049i
$51$	10.3593	+	0.820968i	1.45059	+	0.114959i
$52$	3.79613	+	2.58816i	0.526429	+	0.358913i
$53$	2.95463	+	1.42288i	0.405850	+	0.195447i	0.625661	−	0.780095i	$-0.284830\pi$
$53$	2.95463	+	1.42288i	0.405850	+	0.195447i	−0.219810	+	0.975543i	$0.570544\pi$
$54$	2.10368	−	12.8353i	0.286274	−	1.74667i
$55$	−2.24464	+	2.81469i	−0.302667	+	0.379532i
$56$	1.34341	+	17.9266i	0.179521	+	2.39554i
$57$	3.66388	+	5.42370i	0.485293	+	0.718387i
$58$	8.08118	−	10.7887i	1.06111	−	1.41663i
$59$	−1.23521	+	2.13945i	−0.160811	+	0.278532i	−0.935160	−	0.354226i	$-0.884744\pi$
$59$	−1.23521	+	2.13945i	−0.160811	+	0.278532i	0.774349	+	0.632759i	$0.218078\pi$
$60$	−5.12746	+	4.05320i	−0.661953	+	0.523266i
$61$	−4.04854	−	0.610220i	−0.518363	−	0.0781306i	−0.115350	−	0.993325i	$-0.536799\pi$
$61$	−4.04854	−	0.610220i	−0.518363	−	0.0781306i	−0.403013	+	0.915194i	$0.632037\pi$
$62$	−8.69610	−	10.9046i	−1.10441	−	1.38488i
$63$	−9.06298	−	2.88084i	−1.14183	−	0.362951i
$64$	3.81101	−	1.83529i	0.476376	−	0.229411i
$65$	0.942217	+	0.142016i	0.116868	+	0.0176150i
$66$	−5.12825	−	16.8818i	−0.631244	−	2.07801i
$67$	−6.60889	−	2.03857i	−0.807404	−	0.249051i	−0.136543	−	0.990634i	$-0.543599\pi$
$67$	−6.60889	−	2.03857i	−0.807404	−	0.249051i	−0.670861	+	0.741583i	$0.734075\pi$
$68$	25.3063	−	3.81432i	3.06884	−	0.462554i
$69$	−0.816218	+	5.26217i	−0.0982611	+	0.633491i
$70$	3.50974	+	6.07905i	0.419494	+	0.726585i
$71$	2.34734	−	10.2844i	0.278578	−	1.22053i	−0.621014	−	0.783800i	$-0.713279\pi$
$71$	2.34734	−	10.2844i	0.278578	−	1.22053i	0.899592	−	0.436731i	$-0.143864\pi$
$72$	−1.12597	−	16.9758i	−0.132697	−	2.00062i
$73$	−8.54599	+	4.11553i	−1.00023	+	0.481686i	−0.861017	−	0.508576i	$-0.830172\pi$
$73$	−8.54599	+	4.11553i	−1.00023	+	0.481686i	−0.139215	+	0.990262i	$0.544458\pi$
$74$	−27.3020	+	8.42155i	−3.17379	+	0.978986i
$75$	3.19757	−	6.56770i	0.369224	−	0.758373i
$76$	11.8163	+	10.9639i	1.35542	+	1.25765i
$77$	−12.7561	+	1.92267i	−1.45369	+	0.219109i
$78$	−3.19091	+	3.40957i	−0.361299	+	0.386057i
$79$	7.61429	−	7.06503i	0.856674	−	0.794878i	−0.123639	−	0.992327i	$-0.539456\pi$
$79$	7.61429	−	7.06503i	0.856674	−	0.794878i	0.980313	+	0.197450i	$0.0632659\pi$
$80$	−3.12414	+	3.91755i	−0.349289	+	0.437995i
$81$	8.55343	+	2.79979i	0.950381	+	0.311088i
$82$	−9.64548	−	4.64502i	−1.06517	−	0.512956i
$83$	−3.73059	+	9.50538i	−0.409485	+	1.04335i	0.566218	+	0.824255i	$0.308406\pi$
$83$	−3.73059	+	9.50538i	−0.409485	+	1.04335i	−0.975703	+	0.219096i	$0.929689\pi$
$84$	−23.3470	−	1.85024i	−2.54737	−	0.201878i
$85$	4.38537	−	2.98990i	0.475660	−	0.324300i
$86$	7.33043	−	12.6967i	0.790461	−	1.36912i
$87$	6.52003	+	6.67003i	0.699020	+	0.715102i
$88$	−11.5392	−	19.9865i	−1.23009	−	2.13057i
$89$	11.8062	+	5.68557i	1.25146	+	0.602669i	0.937902	−	0.346901i	$-0.112766\pi$
$89$	11.8062	+	5.68557i	1.25146	+	0.602669i	0.313554	+	0.949570i	$0.398480\pi$
$90$	−3.27216	−	5.78139i	−0.344916	−	0.609412i
$91$	2.12881	+	2.66945i	0.223160	+	0.279834i
$92$	0.980035	+	13.0777i	0.102176	+	1.36344i
$93$	8.37866	−	4.78967i	0.868826	−	0.496666i
$94$	4.49495	+	11.4530i	0.463619	+	1.18128i
$95$	3.19450	+	0.985373i	0.327749	+	0.101097i
$96$	−1.42762	−	4.69963i	−0.145706	−	0.479654i
$97$	−2.49026	+	6.34507i	−0.252847	+	0.644244i	−0.999787	−	0.0206477i	$-0.993427\pi$
$97$	−2.49026	+	6.34507i	−0.252847	+	0.644244i	0.746940	+	0.664892i	$0.231522\pi$
$98$	−1.69802	+	7.43952i	−0.171526	+	0.751505i
$99$	12.0874	−	1.71609i	1.21483	−	0.172473i
$100$	4.00308	−	17.5386i	0.400308	−	1.75386i
$101$	9.98856	+	6.81009i	0.993899	+	0.677629i	0.946988	−	0.321270i	$-0.104110\pi$
$101$	9.98856	+	6.81009i	0.993899	+	0.677629i	0.0469115	+	0.998899i	$0.485062\pi$
$102$	−0.111446	+	26.0115i	−0.0110348	+	2.57553i
$103$	−13.6037	−	12.6224i	−1.34041	−	1.24372i	−0.945752	−	0.324890i	$-0.894673\pi$
$103$	−13.6037	−	12.6224i	−1.34041	−	1.24372i	−0.394658	−	0.918828i	$-0.629137\pi$
$104$	−3.05414	+	5.28992i	−0.299483	+	0.518720i
$105$	−4.52899	+	1.75514i	−0.441984	+	0.171284i
$106$	−2.99898	+	7.64127i	−0.291287	+	0.742186i
$107$	2.91384	+	12.7663i	0.281691	+	1.23417i	0.895624	+	0.444811i	$0.146729\pi$
$107$	2.91384	+	12.7663i	0.281691	+	1.23417i	−0.613933	+	0.789358i	$0.710414\pi$
$108$	22.0796	+	1.94032i	2.12461	+	0.186707i
$109$	−3.52478	+	4.41994i	−0.337613	+	0.423353i	−0.921438	−	0.388527i	$-0.872984\pi$
$109$	−3.52478	+	4.41994i	−0.337613	+	0.423353i	0.583824	+	0.811880i	$0.301556\pi$
$110$	−7.44567	−	5.07637i	−0.709916	−	0.484013i
$111$	−2.86281	−	19.5618i	−0.271725	−	1.85672i
$112$	−17.7542	+	2.67602i	−1.67762	+	0.252860i
$113$	−0.877706	−	2.23636i	−0.0825677	−	0.210379i	0.883628	−	0.468190i	$-0.155094\pi$
$113$	−0.877706	−	2.23636i	−0.0825677	−	0.210379i	−0.966195	+	0.257811i	$0.916999\pi$
$114$	−12.8528	+	10.1600i	−1.20378	+	0.951573i
$115$	1.35991	+	2.35543i	0.126812	+	0.219645i
$116$	19.3629	+	12.3588i	1.79780	+	1.14749i
$117$	−1.99296	−	2.54351i	−0.184250	−	0.235147i
$118$	−5.57137	−	2.68303i	−0.512886	−	0.246993i
$119$	18.8062	+	2.83458i	1.72396	+	0.259846i
$120$	−5.88302	−	6.39512i	−0.537044	−	0.583792i
$121$	4.59480	−	3.13268i	0.417709	−	0.284789i
$122$	0.765867	−	10.2198i	0.0693383	−	0.925255i
$123$	4.19919	−	6.10274i	0.378628	−	0.550265i
$124$	17.4232	−	16.1664i	1.56465	−	1.45178i
$125$	−1.81448	−	7.94974i	−0.162292	−	0.711046i
$126$	5.49560	−	23.1611i	0.489587	−	2.06336i
$127$	−0.808610	+	3.54275i	−0.0717525	+	0.314368i	−0.998050	−	0.0624257i	$-0.980116\pi$
$127$	−0.808610	+	3.54275i	−0.0717525	+	0.314368i	0.926297	+	0.376794i	$0.122974\pi$
$128$	8.12973	+	14.0811i	0.718573	+	1.24461i
$129$	7.90427	+	6.35904i	0.695933	+	0.559882i
$130$	−0.178240	+	2.37845i	−0.0156327	+	0.208604i
$131$	−0.651429	+	8.69272i	−0.0569156	+	0.759486i	0.893611	+	0.448843i	$0.148164\pi$
$131$	−0.651429	+	8.69272i	−0.0569156	+	0.759486i	−0.950526	+	0.310644i	$0.899455\pi$
$132$	28.0350	−	10.8645i	2.44013	−	0.945637i
$133$	5.98947	+	10.3741i	0.519353	+	0.899546i
$134$	3.85227	−	16.8779i	0.332785	−	1.45803i
$135$	4.30026	−	1.62426i	0.370107	−	0.139794i
$136$	7.57114	+	33.1713i	0.649220	+	2.84442i
$137$	9.12378	−	8.46563i	0.779498	−	0.723268i	−0.186321	−	0.982489i	$-0.559656\pi$
$137$	9.12378	−	8.46563i	0.779498	−	0.723268i	0.965818	+	0.259221i	$0.0834658\pi$
$138$	−13.2877	−	1.05304i	−1.13112	−	0.0896410i
$139$	−1.45591	+	19.4278i	−0.123489	+	1.64784i	0.500010	+	0.866020i	$0.333330\pi$
$139$	−1.45591	+	19.4278i	−0.123489	+	1.64784i	−0.623499	+	0.781824i	$0.714289\pi$
$140$	−9.88345	+	6.73842i	−0.835304	+	0.569500i
$141$	−8.30806	+	1.85885i	−0.699664	+	0.156543i
$142$	26.1101	+	3.93546i	2.19111	+	0.330257i
$143$	−3.94922	−	1.90184i	−0.330250	−	0.159040i
$144$	16.8235	−	2.38849i	1.40196	−	0.199041i
$145$	4.73014	+	0.566936i	0.392817	+	0.0470814i
$146$	−11.8714	−	20.5619i	−0.982488	−	1.70172i
$147$	−4.90691	−	1.95012i	−0.404715	−	0.160843i
$148$	−17.7880	−	45.3231i	−1.46216	−	3.72554i
$149$	−6.34835	+	0.956859i	−0.520077	+	0.0783890i	−0.403835	−	0.914832i	$-0.632323\pi$
$149$	−6.34835	+	0.956859i	−0.520077	+	0.0783890i	−0.116242	+	0.993221i	$0.537085\pi$
$150$	16.9919	+	6.75298i	1.38738	+	0.551378i
$151$	1.35513	+	0.923912i	0.110279	+	0.0751869i	0.617204	−	0.786803i	$-0.288265\pi$
$151$	1.35513	+	0.923912i	0.110279	+	0.0751869i	−0.506925	+	0.861990i	$0.669218\pi$
$152$	−13.3616	+	16.7549i	−1.08377	+	1.35900i
$153$	−17.7744	−	2.83503i	−1.43697	−	0.229199i
$154$	−7.18535	−	31.4811i	−0.579012	−	2.53682i
$155$	1.80088	−	4.58857i	0.144650	−	0.368563i
$156$	−6.20039	−	4.98826i	−0.496429	−	0.399380i
$157$	6.60828	−	11.4459i	0.527398	−	0.913481i	−0.472092	−	0.881549i	$-0.656501\pi$
$157$	6.60828	−	11.4459i	0.527398	−	0.913481i	0.999490	−	0.0319312i	$-0.0101657\pi$
$158$	19.0594	+	17.6846i	1.51629	+	1.40691i
$159$	−4.90688	−	2.86109i	−0.389141	−	0.226899i
$160$	−2.07275	−	1.41318i	−0.163865	−	0.111722i
$161$	−2.16865	+	9.50148i	−0.170914	+	0.748821i
$162$	−5.38861	+	21.8741i	−0.423369	+	1.71859i
$163$	−4.13036	+	18.0963i	−0.323515	+	1.41741i	0.507735	+	0.861513i	$0.330483\pi$
$163$	−4.13036	+	18.0963i	−0.323515	+	1.41741i	−0.831250	+	0.555899i	$0.812374\pi$
$164$	6.66516	−	16.9825i	0.520461	−	1.32611i
$165$	4.26082	−	4.55280i	0.331705	−	0.354435i
$166$	−24.4244	−	7.53392i	−1.89570	−	0.584746i
$167$	−1.34700	−	3.43211i	−0.104234	−	0.265585i	0.869236	−	0.494397i	$-0.164611\pi$
$167$	−1.34700	−	3.43211i	−0.104234	−	0.265585i	−0.973471	+	0.228812i	$0.926516\pi$
$168$	0.133404	−	31.1365i	0.0102924	−	2.40223i
$169$	−0.884793	−	11.8067i	−0.0680610	−	0.908211i
$170$	8.28345	+	10.3871i	0.635311	+	0.796655i
$171$	−5.58403	−	9.86612i	−0.427022	−	0.754481i
$172$	22.5096	+	10.8400i	1.71634	+	0.826545i
$173$	−9.19208	−	15.9212i	−0.698861	−	1.21046i	−0.968862	−	0.247603i	$-0.920357\pi$
$173$	−9.19208	−	15.9212i	−0.698861	−	1.21046i	0.270000	−	0.962860i	$-0.412976\pi$
$174$	−15.4295	+	17.5224i	−1.16971	+	1.32837i
$175$	6.68444	−	11.5778i	0.505297	−	0.875199i
$176$	19.0449	−	12.9846i	1.43556	−	0.978751i
$177$	2.42551	−	3.52503i	0.182313	−	0.264958i
$178$	−11.9834	+	30.5332i	−0.898194	+	2.28856i
$179$	−5.72547	−	2.75724i	−0.427942	−	0.206086i	0.207499	−	0.978235i	$-0.433468\pi$
$179$	−5.72547	−	2.75724i	−0.427942	−	0.206086i	−0.635441	+	0.772149i	$0.719182\pi$
$180$	9.40789	−	6.29678i	0.701223	−	0.469335i
$181$	0.610028	−	0.764951i	0.0453430	−	0.0568583i	−0.758643	−	0.651507i	$-0.774137\pi$
$181$	0.610028	−	0.764951i	0.0453430	−	0.0568583i	0.803986	+	0.594648i	$0.202709\pi$
$182$	−6.26504	+	5.81311i	−0.464396	+	0.430896i
$183$	6.90686	+	1.60761i	0.510570	+	0.118838i
$184$	−17.2406	+	2.59860i	−1.27099	+	0.191571i
$185$	−7.40213	−	6.86818i	−0.544216	−	0.504958i
$186$	13.5229	+	20.0182i	0.991546	+	1.46780i
$187$	−23.3312	+	7.19672i	−1.70615	+	0.526276i
$188$	−18.8901	+	9.09700i	−1.37770	+	0.663467i
$189$	15.2543	+	6.21429i	1.10959	+	0.452023i
$190$	−1.86205	+	8.15817i	−0.135087	+	0.591856i
$191$	−7.67720	−	13.2973i	−0.555503	−	0.962159i	−0.997864	−	0.0653223i	$-0.979192\pi$
$191$	−7.67720	−	13.2973i	−0.555503	−	0.962159i	0.442361	−	0.896837i	$-0.354141\pi$
$192$	−6.83136	+	2.64739i	−0.493011	+	0.191059i
$193$	−21.1364	+	3.18580i	−1.52143	+	0.229319i	−0.855936	−	0.517082i	$-0.827018\pi$
$193$	−21.1364	+	3.18580i	−1.52143	+	0.229319i	−0.665496	+	0.746401i	$0.731780\pi$
$194$	−16.3039	−	5.02907i	−1.17055	−	0.361066i
$195$	−1.60743	−	0.374139i	−0.115111	−	0.0267927i
$196$	−12.8586	−	1.93812i	−0.918469	−	0.138437i
$197$	−2.63806	+	1.27042i	−0.187954	+	0.0905140i	−0.525494	−	0.850797i	$-0.676120\pi$
$197$	−2.63806	+	1.27042i	−0.187954	+	0.0905140i	0.337540	+	0.941311i	$0.390405\pi$
$198$	6.54459	+	29.8505i	0.465104	+	2.12138i
$199$	−10.4646	−	13.1221i	−0.741813	−	0.930204i	0.257536	−	0.966269i	$-0.417089\pi$
$199$	−10.4646	−	13.1221i	−0.741813	−	0.930204i	−0.999349	+	0.0360642i	$0.988518\pi$
$200$	23.6498	+	3.56464i	1.67230	+	0.252058i
$201$	11.1322	+	4.42420i	0.785205	+	0.312059i
$202$	−15.1303	+	26.2065i	−1.06457	+	1.84388i
$203$	11.0430	+	13.0177i	0.775067	+	0.913661i
$204$	−44.2168	+	3.12314i	−3.09580	+	0.218664i
$205$	−0.282749	−	3.77302i	−0.0197480	−	0.263519i
$206$	28.9622	−	36.3175i	2.01789	−	2.53036i
$207$	2.12936	−	8.97418i	0.148001	−	0.623749i
$208$	−5.49661	−	2.64703i	−0.381121	−	0.183538i
$209$	−12.7062	−	8.66297i	−0.878909	−	0.599230i
$210$	−5.22822	−	10.9766i	−0.360781	−	0.757455i
$211$	20.7853	+	6.41142i	1.43092	+	0.441380i	0.910848	−	0.412742i	$-0.135429\pi$
$211$	20.7853	+	6.41142i	1.43092	+	0.441380i	0.520072	+	0.854122i	$0.325905\pi$
$212$	−13.3671	−	4.12320i	−0.918055	−	0.283183i
$213$	−5.46027	+	17.4362i	−0.374132	+	1.19471i
$214$	−31.3212	+	9.66132i	−2.14108	+	0.660434i
$215$	5.18145			0.353372
$216$	−0.378748	+	29.4651i	−0.0257706	+	2.00485i
$217$	15.9139	−	7.66371i	1.08030	−	0.520246i
$218$	−11.6920	−	7.97149i	−0.791884	−	0.539897i
$219$	15.3190	−	5.93664i	1.03516	−	0.401161i
$220$	7.67832	−	13.2992i	0.517672	−	0.896634i
$221$	4.73718	+	4.39546i	0.318657	+	0.295671i
$222$	48.2930	−	10.8051i	3.24122	−	0.725190i
$223$	15.1181	−	14.0275i	1.01238	−	0.939352i	0.0142155	−	0.999899i	$-0.495475\pi$
$223$	15.1181	−	14.0275i	1.01238	−	0.939352i	0.998165	+	0.0605468i	$0.0192844\pi$
$224$	−2.00028	−	8.76382i	−0.133650	−	0.585557i
$225$	−6.41974	+	10.9025i	−0.427983	+	0.726833i
$226$	5.41803	−	2.60919i	0.360402	−	0.173561i
$227$	−2.04778	−	27.3257i	−0.135916	−	1.81367i	−0.482766	−	0.875750i	$-0.660368\pi$
$227$	−2.04778	−	27.3257i	−0.135916	−	1.81367i	0.346850	−	0.937921i	$-0.387251\pi$
$228$	−18.9022	−	20.5476i	−1.25183	−	1.36080i
$229$	−2.89065	−	7.36526i	−0.191020	−	0.486710i	0.802991	−	0.595991i	$-0.203240\pi$
$229$	−2.89065	−	7.36526i	−0.191020	−	0.486710i	−0.994011	+	0.109281i	$0.965145\pi$
$230$	−5.62505	+	3.83509i	−0.370905	+	0.252878i
$231$	22.2883	−	1.57427i	1.46646	−	0.103580i
$232$	−14.4611	+	26.8986i	−0.949419	+	1.76598i
$233$	−0.137282			−0.00899364			−0.00449682	−	0.999990i	$-0.501431\pi$
$233$	−0.137282			−0.00899364			−0.00449682	+	0.999990i	$0.501431\pi$
$234$	5.97609	−	5.45045i	0.390669	−	0.356307i
$235$	−2.71111	+	3.39963i	−0.176853	+	0.221767i
$236$	3.84989	−	9.80936i	0.250607	−	0.638535i
$237$	−14.1139	+	11.1568i	−0.916794	+	0.724714i
$238$	−3.55759	+	47.4728i	−0.230605	+	3.07720i
$239$	−6.83054	−	17.4039i	−0.441831	−	1.12577i	−0.962325	−	0.271901i	$-0.912348\pi$
$239$	−6.83054	−	17.4039i	−0.441831	−	1.12577i	0.520495	−	0.853865i	$-0.325748\pi$
$240$	5.93031	−	6.33669i	0.382800	−	0.409031i
$241$	−14.3976	+	13.3590i	−0.927429	+	0.860529i	−0.990505	−	0.137480i	$-0.956100\pi$
$241$	−14.3976	+	13.3590i	−0.927429	+	0.860529i	0.0630751	+	0.998009i	$0.479909\pi$
$242$	8.67903	+	10.8832i	0.557909	+	0.699596i
$243$	−14.3856	−	6.00463i	−0.922834	−	0.385197i
$244$	17.4645			1.11805
$245$	−2.57708	+	0.794924i	−0.164644	+	0.0507858i
$246$	16.0186	+	9.34010i	1.02131	+	0.595503i
$247$	−0.304172	+	4.05889i	−0.0193540	+	0.258261i
$248$	23.1639	+	21.4929i	1.47091	+	1.36480i
$249$	7.74204	−	15.9019i	0.490632	−	1.00774i
$250$	19.5041	−	6.01621i	1.23355	−	0.380498i
$251$	6.72717	+	8.43561i	0.424615	+	0.532451i	0.947416	−	0.320004i	$-0.103684\pi$
$251$	6.72717	+	8.43561i	0.424615	+	0.532451i	−0.522801	+	0.852455i	$0.675113\pi$
$252$	40.0587	+	6.38939i	2.52346	+	0.402494i
$253$	−2.78409	−	12.1979i	−0.175034	−	0.766874i
$254$	−8.99437	−	1.35568i	−0.564357	−	0.0850632i
$255$	−7.98107	+	4.56239i	−0.499794	+	0.285708i
$256$	−26.6375	+	18.1612i	−1.66485	+	1.13507i
$257$	27.3546	−	4.12305i	1.70633	−	0.257189i	0.777820	−	0.628487i	$-0.216325\pi$
$257$	27.3546	−	4.12305i	1.70633	−	0.257189i	0.928514	+	0.371298i	$0.121087\pi$
$258$	−14.3944	+	20.9195i	−0.896153	+	1.30239i
$259$	−2.70394	−	36.0815i	−0.168015	−	2.24200i
$260$	−4.06451			−0.252070
$261$	−10.3450	−	12.4089i	−0.640341	−	0.768091i
$262$	−21.8199			−1.34804
$263$	1.81231	+	24.1836i	0.111752	+	1.49122i	0.718052	+	0.695989i	$0.245034\pi$
$263$	1.81231	+	24.1836i	0.111752	+	1.49122i	−0.606301	+	0.795236i	$0.707347\pi$
$264$	17.1892	+	36.0885i	1.05792	+	2.22109i
$265$	−2.86872	+	0.432390i	−0.176224	+	0.0265615i
$266$	−24.7745	+	16.8910i	−1.51902	+	1.03565i
$267$	−19.6070	−	11.4324i	−1.19993	−	0.699653i
$268$	29.1720	+	4.39697i	1.78196	+	0.268587i
$269$	3.73894	+	16.3814i	0.227967	+	0.998791i	0.951294	+	0.308285i	$0.0997549\pi$
$269$	3.73894	+	16.3814i	0.227967	+	0.998791i	−0.723327	+	0.690506i	$0.757388\pi$
$270$	4.85873	+	10.4301i	0.295693	+	0.634757i
$271$	−0.616154	−	0.772632i	−0.0374287	−	0.0469341i	0.762765	−	0.646676i	$-0.223841\pi$
$271$	−0.616154	−	0.772632i	−0.0374287	−	0.0469341i	−0.800194	+	0.599742i	$0.795270\pi$
$272$	−32.4729	+	10.0166i	−1.96896	+	0.607343i
$273$	−3.31041	−	4.90046i	−0.200355	−	0.296590i
$274$	22.8379	+	21.1905i	1.37969	+	1.28016i
$275$	−1.28258	+	17.1148i	−0.0773424	+	1.03206i
$276$	0.0973202	−	22.7145i	0.00585799	−	1.36725i
$277$	5.76285	−	1.77760i	0.346256	−	0.106806i	−0.116749	−	0.993161i	$-0.537247\pi$
$277$	5.76285	−	1.77760i	0.346256	−	0.106806i	0.463005	+	0.886356i	$0.346771\pi$
$278$	−48.7664			−2.92481
$279$	−15.1223	+	7.12353i	−0.905348	+	0.426475i
$280$	−9.91551	−	12.4337i	−0.592565	−	0.743053i
$281$	−2.69477	+	2.50038i	−0.160757	+	0.149160i	−0.756450	−	0.654052i	$-0.773068\pi$
$281$	−2.69477	+	2.50038i	−0.160757	+	0.149160i	0.595693	+	0.803212i	$0.296877\pi$
$282$	−6.19398	−	20.3902i	−0.368846	−	1.21422i
$283$	−2.00570	−	5.11045i	−0.119227	−	0.303785i	0.858785	−	0.512337i	$-0.171220\pi$
$283$	−2.00570	−	5.11045i	−0.119227	−	0.303785i	−0.978011	+	0.208552i	$0.933125\pi$
$284$	−3.36264	+	44.8713i	−0.199536	+	2.66262i
$285$	−5.38091	−	2.13850i	−0.318738	−	0.126674i
$286$	4.00849	−	10.2135i	0.237027	−	0.603935i
$287$	8.45306	−	10.5998i	0.498968	−	0.625686i
$288$	1.82191	+	8.30990i	0.107357	+	0.489666i
$289$	18.9962			1.11742
$290$	−0.530326	+	11.9130i	−0.0311418	+	0.699558i
$291$	5.16800	−	10.6149i	0.302953	−	0.622255i
$292$	33.4301	−	22.7922i	1.95635	−	1.33381i
$293$	10.0571	+	25.6250i	0.587541	+	1.49703i	0.847170	+	0.531322i	$0.178304\pi$
$293$	10.0571	+	25.6250i	0.587541	+	1.49703i	−0.259629	+	0.965708i	$0.583600\pi$
$294$	3.94986	−	12.6130i	0.230360	−	0.735605i
$295$	−0.163320	−	2.17935i	−0.00950885	−	0.126887i
$296$	58.3205	−	28.0857i	3.38981	−	1.63245i
$297$	−21.1054	+	1.30908i	−1.22466	+	0.0759603i
$298$	−3.57594	−	15.6672i	−0.207149	−	0.907578i
$299$	−2.42750	+	2.25239i	−0.140386	+	0.130259i
$300$	−9.31176	+	29.7351i	−0.537615	+	1.71675i
$301$	13.6102	+	12.6284i	0.784479	+	0.727890i
$302$	−2.05270	+	3.55539i	−0.118120	+	0.204590i
$303$	−16.3148	−	13.1253i	−0.937259	−	0.754031i
$304$	−17.6848	−	12.0573i	−1.01430	−	0.691535i
$305$	3.26331	−	1.57153i	0.186857	−	0.0899855i
$306$	3.75172	−	44.8972i	0.214472	−	2.56660i
$307$	−8.42970			−0.481108			−0.240554	−	0.970636i	$-0.577329\pi$
$307$	−8.42970			−0.481108			−0.240554	+	0.970636i	$0.577329\pi$
$308$	52.5822	−	16.2195i	2.99615	−	0.924190i
$309$	21.7614	+	23.6557i	1.23796	+	1.34573i
$310$	11.7905	+	3.63688i	0.669654	+	0.206561i
$311$	−24.9091	−	7.68345i	−1.41247	−	0.435689i	−0.507678	−	0.861547i	$-0.669496\pi$
$311$	−24.9091	−	7.68345i	−1.41247	−	0.435689i	−0.904790	+	0.425859i	$0.859972\pi$
$312$	5.99724	−	8.71586i	0.339527	−	0.493439i
$313$	2.73544	+	1.86499i	0.154616	+	0.105416i	0.638157	−	0.769906i	$-0.279697\pi$
$313$	2.73544	+	1.86499i	0.154616	+	0.105416i	−0.483541	+	0.875322i	$0.660649\pi$
$314$	29.8064	+	14.3540i	1.68207	+	0.810043i
$315$	8.06008	−	2.41076i	0.454134	−	0.135831i
$316$	−27.6250	+	34.6407i	−1.55403	+	1.94869i
$317$	1.77512	+	23.6873i	0.0997005	+	1.33041i	0.792761	+	0.609532i	$0.208643\pi$
$317$	1.77512	+	23.6873i	0.0997005	+	1.33041i	−0.693061	+	0.720879i	$0.743738\pi$
$318$	6.22374	−	12.7833i	0.349010	−	0.716854i
$319$	−20.0239	−	8.90581i	−1.12113	−	0.498630i
$320$	−1.87100	+	3.24066i	−0.104592	+	0.181158i
$321$	−3.28425	−	22.4416i	−0.183309	−	1.25257i
$322$	−24.1225	−	3.63588i	−1.34429	−	0.202619i
$323$	14.1359	+	17.7259i	0.786545	+	0.986296i
$324$	−37.8579	−	6.37149i	−2.10322	−	0.353971i
$325$	4.09270	−	1.97094i	0.227022	−	0.109328i
$326$	−45.9431	−	6.92481i	−2.54455	−	0.383530i
$327$	6.69083	−	7.14932i	0.370004	−	0.395358i
$328$	23.1771	+	7.14919i	1.27974	+	0.394748i
$329$	−15.4070	+	2.32224i	−0.849418	+	0.128029i
$330$	12.1613	+	9.78388i	0.669460	+	0.538585i
$331$	10.4506	+	18.1009i	0.574415	+	0.994916i	0.996105	+	0.0881761i	$0.0281038\pi$
$331$	10.4506	+	18.1009i	0.574415	+	0.994916i	−0.421690	+	0.906740i	$0.638563\pi$
$332$	9.69234	−	42.4649i	0.531936	−	2.33057i
$333$	2.26628	+	34.1679i	0.124191	+	1.87239i
$334$	8.31498	−	4.00428i	0.454975	−	0.219105i
$335$	5.84657	−	1.80343i	0.319432	−	0.0985317i
$336$	31.0213	−	2.19111i	1.69235	−	0.119535i
$337$	−6.18563	−	5.73942i	−0.336953	−	0.312646i	0.493489	−	0.869752i	$-0.335721\pi$
$337$	−6.18563	−	5.73942i	−0.336953	−	0.312646i	−0.830442	+	0.557106i	$0.811912\pi$
$338$	29.3055	−	4.41709i	1.59401	−	0.240258i
$339$	1.20947	+	3.98148i	0.0656893	+	0.216244i
$340$	−16.5964	+	15.3992i	−0.900067	+	0.835140i
$341$	−14.1380	+	17.7285i	−0.765616	+	0.960052i
$342$	23.5824	−	15.7839i	1.27519	−	0.853498i
$343$	11.2855	+	5.43479i	0.609357	+	0.293451i
$344$	−12.1350	+	30.9194i	−0.654274	+	1.66706i
$345$	−2.02576	−	4.25306i	−0.109063	−	0.228977i
$346$	38.0216	−	25.9227i	2.04405	−	1.39361i
$347$	1.60263	−	2.77583i	0.0860334	−	0.149014i	−0.819798	−	0.572653i	$-0.805914\pi$
$347$	1.60263	−	2.77583i	0.0860334	−	0.149014i	0.905831	+	0.423639i	$0.139247\pi$
$348$	−31.7416	−	23.9887i	−1.70153	−	1.28593i
$349$	−2.78553	−	4.82468i	−0.149106	−	0.258259i	0.781791	−	0.623540i	$-0.214306\pi$
$349$	−2.78553	−	4.82468i	−0.149106	−	0.258259i	−0.930897	+	0.365281i	$0.880973\pi$
$350$	30.1499	+	14.5194i	1.61158	+	0.776096i
$351$	3.09308	+	4.66442i	0.165097	+	0.248968i
$352$	7.19521	+	9.02251i	0.383506	+	0.480901i
$353$	−0.789451	−	10.5345i	−0.0420183	−	0.560695i	−0.977994	−	0.208631i	$-0.933099\pi$
$353$	−0.789451	−	10.5345i	−0.0420183	−	0.560695i	0.935976	−	0.352063i	$-0.114520\pi$
$354$	9.25260	+	5.39498i	0.491770	+	0.286740i
$355$	3.40939	+	8.68698i	0.180951	+	0.461057i
$356$	−53.4126	−	16.4756i	−2.83086	−	0.873205i
$357$	−32.0837	−	7.46765i	−1.69805	−	0.395230i
$358$	5.81140	−	14.8072i	0.307142	−	0.782586i
$359$	−3.72680	+	16.3282i	−0.196693	+	0.861769i	0.776195	+	0.630493i	$0.217147\pi$
$359$	−3.72680	+	16.3282i	−0.196693	+	0.861769i	−0.972888	+	0.231276i	$0.925710\pi$
$360$	9.28276	+	11.8471i	0.489244	+	0.624395i
$361$	1.05026	−	4.60147i	0.0552767	−	0.242183i
$362$	2.02352	+	1.37961i	0.106354	+	0.0725107i
$363$	−8.36221	+	4.78027i	−0.438902	+	0.250899i
$364$	−10.6763	−	9.90618i	−0.559592	−	0.519225i
$365$	4.19561	−	7.26701i	0.219608	−	0.380372i
$366$	−2.72080	+	17.5411i	−0.142219	+	0.916886i
$367$	12.7261	−	32.4256i	0.664297	−	1.69260i	−0.0555376	−	0.998457i	$-0.517687\pi$
$367$	12.7261	−	32.4256i	0.664297	−	1.69260i	0.719835	−	0.694145i	$-0.244218\pi$
$368$	−3.87495	−	16.9773i	−0.201996	−	0.885002i
$369$	−8.08555	+	9.96262i	−0.420917	+	0.518633i
$370$	15.7591	−	19.7613i	0.819279	−	1.02734i
$371$	−8.58917	−	5.85599i	−0.445927	−	0.304028i
$372$	−32.2957	+	25.5293i	−1.67445	+	1.32363i
$373$	0.450470	−	0.0678974i	0.0233244	−	0.00351559i	−0.137370	−	0.990520i	$-0.543865\pi$
$373$	0.450470	−	0.0678974i	0.0233244	−	0.00351559i	0.160694	+	0.987004i	$0.448627\pi$
$374$	−22.3281	−	56.8912i	−1.15456	−	2.94177i
$375$	2.04514	+	13.9746i	0.105610	+	0.721645i
$376$	−13.9373	−	24.1401i	−0.718760	−	1.24493i
$377$	0.608570	+	5.76836i	0.0313429	+	0.297085i
$378$	−12.6582	+	39.2389i	−0.651066	+	2.01823i
$379$	2.09017	+	1.00658i	0.107365	+	0.0517043i	0.486795	−	0.873516i	$-0.338166\pi$
$379$	2.09017	+	1.00658i	0.107365	+	0.0517043i	−0.379430	+	0.925220i	$0.623880\pi$
$380$	−14.1007	−	2.12534i	−0.723350	−	0.109027i
$381$	1.88095	−	6.00640i	0.0963639	−	0.307717i
$382$	31.7555	−	21.6506i	1.62475	−	1.10774i
$383$	−1.00028	+	13.3479i	−0.0511121	+	0.682044i	0.911524	+	0.411246i	$0.134906\pi$
$383$	−1.00028	+	13.3479i	−0.0511121	+	0.682044i	−0.962636	+	0.270797i	$0.912713\pi$
$384$	−12.1103	−	25.4254i	−0.618001	−	1.29748i
$385$	8.36572	−	7.76225i	0.426356	−	0.395601i
$386$	−11.9059	−	52.1630i	−0.605993	−	2.65503i
$387$	−12.7777	−	12.0613i	−0.649526	−	0.613112i
$388$	6.46987	−	28.3463i	0.328458	−	1.43907i
$389$	−16.0062	−	27.7235i	−0.811544	−	1.40564i	−0.911783	−	0.410672i	$-0.865294\pi$
$389$	−16.0062	−	27.7235i	−0.811544	−	1.40564i	0.100239	−	0.994963i	$-0.468039\pi$
$390$	0.633212	−	4.08233i	0.0320639	−	0.206717i
$391$	−1.37845	+	18.3941i	−0.0697112	+	0.930232i
$392$	1.29196	−	17.2400i	0.0652538	−	0.870752i
$393$	2.31425	−	14.9200i	0.116739	−	0.752616i
$394$	−3.66460	−	6.34727i	−0.184620	−	0.319771i
$395$	−2.04474	+	8.95859i	−0.102882	+	0.450755i
$396$	−49.8929	+	14.9229i	−2.50721	+	0.749906i
$397$	−3.06938	−	13.4479i	−0.154048	−	0.674928i	−0.991684	−	0.128699i	$-0.958920\pi$
$397$	−3.06938	−	13.4479i	−0.154048	−	0.674928i	0.837636	−	0.546229i	$-0.183937\pi$
$398$	30.7969	−	28.5754i	1.54371	−	1.43235i
$399$	−8.92210	−	18.7318i	−0.446664	−	0.937764i
$400$	−1.78512	+	23.8208i	−0.0892561	+	1.19104i
$401$	10.6382	−	7.25301i	0.531247	−	0.362198i	−0.267792	−	0.963477i	$-0.586294\pi$
$401$	10.6382	−	7.25301i	0.531247	−	0.362198i	0.799040	+	0.601278i	$0.205342\pi$
$402$	−8.96096	+	28.6149i	−0.446932	+	1.42718i
$403$	5.93462	+	0.894500i	0.295624	+	0.0445582i
$404$	−46.4607	−	22.3743i	−2.31151	−	1.11316i
$405$	−7.64724	+	2.21608i	−0.379995	+	0.110118i
$406$	−30.4279	+	29.9997i	−1.51011	+	1.48886i
$407$	23.2255	+	40.2277i	1.15124	+	1.99401i
$408$	−8.53360	−	58.3109i	−0.422476	−	2.88682i
$409$	−2.48140	−	6.32251i	−0.122697	−	0.312628i	0.856307	−	0.516467i	$-0.172753\pi$
$409$	−2.48140	−	6.32251i	−0.122697	−	0.312628i	−0.979004	+	0.203839i	$0.934658\pi$
$410$	9.36501	−	1.41155i	0.462505	−	0.0697114i
$411$	−16.9119	+	13.3686i	−0.834201	+	0.659426i
$412$	65.4043	+	44.5919i	3.22224	+	2.19688i
$413$	4.88261	−	6.12260i	0.240257	−	0.301273i
$414$	22.7989	+	3.63645i	1.12051	+	0.178722i
$415$	−2.01012	−	8.80691i	−0.0986729	−	0.432314i
$416$	1.11590	−	2.84326i	0.0547114	−	0.139402i
$417$	5.17224	−	33.3455i	0.253286	−	1.63294i
$418$	19.2470	−	33.3367i	0.941401	−	1.63055i
$419$	−0.221291	−	0.205328i	−0.0108108	−	0.0100309i	0.674749	−	0.738047i	$-0.264252\pi$
$419$	−0.221291	−	0.205328i	−0.0108108	−	0.0100309i	−0.685560	+	0.728016i	$0.740442\pi$
$420$	17.9872	−	10.2824i	0.877684	−	0.501730i
$421$	8.62075	+	5.87753i	0.420150	+	0.286453i	0.754883	−	0.655860i	$-0.227694\pi$
$421$	8.62075	+	5.87753i	0.420150	+	0.286453i	−0.334733	+	0.942313i	$0.608646\pi$
$422$	−12.1156	+	53.0819i	−0.589778	+	2.58398i
$423$	14.5994	−	2.07272i	0.709845	−	0.100779i
$424$	4.13835	−	18.1313i	0.200976	−	0.880533i
$425$	9.24423	−	23.5539i	0.448411	−	1.14253i
$426$	−44.5441	−	10.3679i	−2.15817	−	0.502326i
$427$	12.4020	+	3.82551i	0.600175	+	0.185129i
$428$	−20.4066	−	51.9953i	−0.986392	−	2.51329i
$429$	6.55863	+	3.82419i	0.316654	+	0.184633i
$430$	0.969231	+	12.9335i	0.0467405	+	0.623708i
$431$	−10.1298	−	12.7023i	−0.487934	−	0.611850i	0.475526	−	0.879702i	$-0.342258\pi$
$431$	−10.1298	−	12.7023i	−0.487934	−	0.611850i	−0.963460	+	0.267852i	$0.913686\pi$
$432$	−29.3749	+	1.82200i	−1.41330	+	0.0876611i
$433$	18.6301	+	8.97180i	0.895307	+	0.431157i	0.824192	−	0.566311i	$-0.191630\pi$
$433$	18.6301	+	8.97180i	0.895307	+	0.431157i	0.0711152	+	0.997468i	$0.477344\pi$
$434$	22.1063	+	38.2893i	1.06114	+	1.83794i
$435$	−8.08966	−	1.62614i	−0.387870	−	0.0779676i
$436$	12.0574	−	20.8840i	0.577443	−	1.00016i
$437$	−9.59930	+	6.54469i	−0.459197	+	0.313075i
$438$	17.6841	+	37.1274i	0.844978	+	1.77402i
$439$	−3.95578	+	10.0792i	−0.188799	+	0.481052i	−0.993662	−	0.112408i	$-0.964144\pi$
$439$	−3.95578	+	10.0792i	−0.188799	+	0.481052i	0.804863	+	0.593461i	$0.202239\pi$
$440$	18.3945	+	8.85834i	0.876925	+	0.422305i
$441$	8.20561	+	4.03859i	0.390743	+	0.192314i
$442$	−10.0855	+	12.6468i	−0.479716	+	0.601545i
$443$	9.89605	−	9.18219i	0.470175	−	0.436259i	−0.409159	−	0.912463i	$-0.634178\pi$
$443$	9.89605	−	9.18219i	0.470175	−	0.436259i	0.879335	+	0.476204i	$0.157988\pi$
$444$	24.5116	+	80.6906i	1.16327	+	3.82940i
$445$	−11.4629	+	1.72776i	−0.543394	+	0.0819035i
$446$	37.8423	+	35.1125i	1.79188	+	1.66263i
$447$	11.0922	−	0.783471i	0.524644	−	0.0370569i
$448$	−12.8128	+	3.95224i	−0.605350	+	0.186726i
$449$	−17.8781	+	8.60963i	−0.843718	+	0.406313i	−0.805242	−	0.592946i	$-0.797965\pi$
$449$	−17.8781	+	8.60963i	−0.843718	+	0.406313i	−0.0384763	+	0.999260i	$0.512250\pi$
$450$	−28.4148	−	13.9850i	−1.33948	−	0.659261i
$451$	−3.87301	+	16.9688i	−0.182373	+	0.799028i
$452$	5.12389	+	8.87484i	0.241008	+	0.417437i
$453$	−2.21339	−	1.78069i	−0.103994	−	0.0836641i
$454$	67.8251	−	10.2230i	3.18319	−	0.479788i
$455$	−2.88632	−	0.890311i	−0.135313	−	0.0417384i
$456$	25.3633	−	27.1013i	1.18775	−	1.26914i
$457$	−3.45918	−	0.521388i	−0.161814	−	0.0243895i	0.0676357	−	0.997710i	$-0.478454\pi$
$457$	−3.45918	−	0.521388i	−0.161814	−	0.0243895i	−0.229449	+	0.973321i	$0.573693\pi$
$458$	17.8438	−	8.59313i	0.833787	−	0.401531i
$459$	30.3020	+	7.32723i	1.41437	+	0.342006i
$460$	−7.23349	−	9.07051i	−0.337263	−	0.422915i
$461$	−2.98783	−	0.450343i	−0.139157	−	0.0209746i	0.0790943	−	0.996867i	$-0.474797\pi$
$461$	−2.98783	−	0.450343i	−0.139157	−	0.0209746i	−0.218251	+	0.975893i	$0.570035\pi$
$462$	8.09877	+	55.3396i	0.376789	+	2.57463i
$463$	−17.5448	+	30.3885i	−0.815377	+	1.41227i	0.0936794	+	0.995602i	$0.470137\pi$
$463$	−17.5448	+	30.3885i	−0.815377	+	1.41227i	−0.909057	+	0.416672i	$0.863196\pi$
$464$	−27.8698	−	12.3953i	−1.29382	−	0.575438i
$465$	−3.73735	+	7.67637i	−0.173315	+	0.355983i
$466$	−0.0256797	−	0.342672i	−0.00118959	−	0.0158740i
$467$	0.619173	−	0.776418i	0.0286519	−	0.0359284i	−0.767299	−	0.641289i	$-0.778400\pi$
$467$	0.619173	−	0.776418i	0.0286519	−	0.0359284i	0.795951	+	0.605361i	$0.206971\pi$
$468$	10.0233	+	9.46134i	0.463325	+	0.437351i
$469$	19.7527	+	9.51239i	0.912094	+	0.439241i
$470$	−8.99300	−	6.13132i	−0.414816	−	0.282817i
$471$	−12.9763	+	18.8586i	−0.597917	+	0.868960i
$472$	13.3874	+	4.12947i	0.616206	+	0.190074i
$473$	−22.7765	−	7.02562i	−1.04726	−	0.323038i
$474$	−30.4889	−	33.1429i	−1.40040	−	1.52230i
$475$	15.2291	−	4.69756i	0.698760	−	0.215539i
$476$	−81.1258			−3.71839
$477$	8.08091	+	5.61150i	0.369999	+	0.256933i
$478$	42.1645	−	20.3054i	1.92856	−	0.928745i
$479$	0.343405	+	0.234130i	0.0156906	+	0.0106977i	0.571140	−	0.820853i	$-0.306501\pi$
$479$	0.343405	+	0.234130i	0.0156906	+	0.0106977i	−0.555449	+	0.831550i	$0.687454\pi$
$480$	3.38552	+	2.72367i	0.154527	+	0.124318i
$481$	6.14719	−	10.6472i	0.280288	−	0.485472i
$482$	−36.0388	−	33.4391i	−1.64152	−	1.52311i
$483$	5.04461	−	16.1089i	0.229538	−	0.732978i
$484$	−17.3890	+	16.1346i	−0.790409	+	0.733393i
$485$	−1.34180	−	5.87882i	−0.0609282	−	0.266944i
$486$	12.2973	−	37.0313i	0.557818	−	1.67977i
$487$	−6.26437	+	3.01676i	−0.283866	+	0.136702i	−0.570399	−	0.821368i	$-0.693211\pi$
$487$	−6.26437	+	3.01676i	−0.283866	+	0.136702i	0.286533	+	0.958070i	$0.407497\pi$
$488$	1.73514	+	23.1538i	0.0785460	+	1.04812i
$489$	9.60785	−	30.6806i	0.434482	−	1.38742i
$490$	−2.46629	−	6.28399i	−0.111415	−	0.283882i
$491$	−0.610617	+	0.416312i	−0.0275568	+	0.0187879i	−0.577020	−	0.816730i	$-0.695785\pi$
$491$	−0.610617	+	0.416312i	−0.0275568	+	0.0187879i	0.549463	+	0.835518i	$0.314832\pi$
$492$	−13.8321	+	28.4107i	−0.623600	+	1.28085i
$493$	24.3395	+	21.2480i	1.09620	+	0.956961i
$494$	−10.1884			−0.458396
$495$	−7.97988	+	7.27800i	−0.358669	+	0.327122i
$496$	−19.6776	+	24.6749i	−0.883550	+	1.10794i
$497$	−12.2167	+	31.1277i	−0.547996	+	1.39627i
$498$	41.1411	+	16.3505i	1.84358	+	0.732682i
$499$	0.421807	−	5.62863i	0.0188827	−	0.251972i	−0.979772	−	0.200117i	$-0.935868\pi$
$499$	0.421807	−	5.62863i	0.0188827	−	0.251972i	0.998655	−	0.0518546i	$-0.0165133\pi$
$500$	12.7074	+	32.3780i	0.568294	+	1.44799i
$501$	1.85615	+	6.11033i	0.0829268	+	0.272989i
$502$	−19.7979	+	18.3698i	−0.883623	+	0.819882i
$503$	−8.14676	−	10.2157i	−0.363246	−	0.455496i	0.566302	−	0.824198i	$-0.308374\pi$
$503$	−8.14676	−	10.2157i	−0.363246	−	0.455496i	−0.929548	+	0.368702i	$0.879802\pi$
$504$	−4.49092	+	53.7432i	−0.200041	+	2.39391i
$505$	−10.6947			−0.475909
$506$	29.9265	−	9.23112i	1.33040	−	0.410373i
$507$	−0.0878624	+	20.5070i	−0.00390211	+	0.910749i
$508$	1.15836	−	15.4572i	0.0513938	−	0.685802i
$509$	1.78841	+	1.65940i	0.0792699	+	0.0735517i	0.718813	−	0.695204i	$-0.244686\pi$
$509$	1.78841	+	1.65940i	0.0792699	+	0.0735517i	−0.639543	+	0.768755i	$0.720876\pi$
$510$	−12.8812	−	19.0682i	−0.570388	−	0.844356i
$511$	28.7321	−	8.86269i	1.27103	−	0.392062i
$512$	−30.0399	−	37.6689i	−1.32759	−	1.66474i
$513$	8.29157	+	17.7993i	0.366082	+	0.785858i
$514$	15.4085	+	67.5091i	0.679640	+	2.97770i
$515$	16.2336	+	2.44683i	0.715340	+	0.107820i
$516$	−37.3826	−	21.7969i	−1.64568	−	0.959556i
$517$	16.5271	−	11.2680i	0.726860	−	0.495565i
$518$	89.5580	−	13.4987i	3.93495	−	0.593098i
$519$	13.6928	+	28.7479i	0.601048	+	1.26189i
$520$	−0.403819	−	5.38859i	−0.0177086	−	0.236305i
$521$	26.6176			1.16614			0.583070	−	0.812422i	$-0.301851\pi$
$521$	26.6176			1.16614			0.583070	+	0.812422i	$0.301851\pi$
$522$	29.0389	−	28.1436i	1.27100	−	1.23181i
$523$	−26.3711			−1.15313			−0.576564	−	0.817052i	$-0.695607\pi$
$523$	−26.3711			−1.15313			−0.576564	+	0.817052i	$0.695607\pi$
$524$	−2.77873	−	37.0796i	−0.121389	−	1.61983i
$525$	−13.1259	+	19.0760i	−0.572860	+	0.832544i
$526$	−60.0261	+	9.04747i	−2.61726	+	0.394489i
$527$	27.6216	−	18.8321i	1.20321	−	0.820337i
$528$	−34.6604	+	19.8137i	−1.50840	+	0.862279i
$529$	13.3965	+	2.01919i	0.582454	+	0.0877909i
$530$	−1.61591	−	7.07978i	−0.0701908	−	0.307526i
$531$	−4.67033	+	5.75455i	−0.202675	+	0.249726i
$532$	−31.8586	−	39.9494i	−1.38125	−	1.73203i
$533$	4.40204	−	1.35785i	0.190673	−	0.0588149i
$534$	24.8690	−	51.0800i	1.07619	−	2.21045i
$535$	−8.49183	−	7.87927i	−0.367134	−	0.340650i
$536$	−2.93104	+	39.1121i	−0.126602	+	1.68938i
$537$	9.50853	+	5.54421i	0.410323	+	0.239250i
$538$	−40.1904	+	12.3971i	−1.73273	+	0.534477i
$539$	12.4061			0.534370
$540$	−17.1056	+	9.58493i	−0.736109	+	0.412470i
$541$	1.36338	+	1.70962i	0.0586163	+	0.0735025i	0.810275	−	0.586049i	$-0.199318\pi$
$541$	1.36338	+	1.70962i	0.0586163	+	0.0735025i	−0.751659	+	0.659552i	$0.770746\pi$
$542$	1.81332	−	1.68252i	0.0778889	−	0.0722704i
$543$	−1.15797	+	1.23732i	−0.0496932	+	0.0530984i
$544$	−6.21579	−	15.8376i	−0.266500	−	0.679030i
$545$	0.373741	−	4.98723i	0.0160093	−	0.213629i
$546$	11.6129	−	9.17985i	0.496986	−	0.392861i
$547$	−3.46885	+	8.83848i	−0.148317	+	0.377906i	−0.985653	−	0.168782i	$-0.946017\pi$
$547$	−3.46885	+	8.83848i	−0.148317	+	0.377906i	0.837336	+	0.546688i	$0.184112\pi$
$548$	−33.1016	+	41.5081i	−1.41403	+	1.77314i
$549$	−11.7057	−	3.72086i	−0.499586	−	0.158803i
$550$	−42.9605			−1.83184
$551$	−0.905017	+	20.3299i	−0.0385550	+	0.866085i
$552$	30.1238	−	2.12772i	1.28215	−	0.0905616i
$553$	−27.2052	+	18.5482i	−1.15688	+	0.788749i
$554$	5.51509	+	14.0522i	0.234314	+	0.597022i
$555$	11.8410	+	12.8717i	0.502622	+	0.546374i
$556$	−6.21032	−	82.8710i	−0.263376	−	3.51451i
$557$	11.3897	−	5.48500i	0.482598	−	0.232407i	−0.176734	−	0.984259i	$-0.556553\pi$
$557$	11.3897	−	5.48500i	0.482598	−	0.232407i	0.659332	+	0.751852i	$0.270839\pi$
$558$	−20.6099	−	36.4145i	−0.872487	−	1.54155i
$559$	1.40380	+	6.15046i	0.0593745	+	0.260137i
$560$	11.6436	−	10.8037i	0.492032	−	0.456539i
$561$	41.2693	−	9.23359i	1.74239	−	0.389843i
$562$	−6.74532	−	6.25875i	−0.284534	−	0.264009i
$563$	−10.7605	+	18.6377i	−0.453499	+	0.785484i	−0.998601	−	0.0528862i	$-0.983158\pi$
$563$	−10.7605	+	18.6377i	−0.453499	+	0.785484i	0.545101	+	0.838370i	$0.316491\pi$
$564$	33.8612	−	13.1224i	1.42581	−	0.552552i
$565$	1.75602	+	1.19723i	0.0738762	+	0.0503679i
$566$	12.3811	−	5.96242i	0.520416	−	0.250619i
$567$	−25.4883	−	12.8172i	−1.07041	−	0.538270i
$568$	−59.8229			−2.51011
$569$	1.91961	−	0.592121i	0.0804743	−	0.0248230i	−0.254257	−	0.967137i	$-0.581831\pi$
$569$	1.91961	−	0.592121i	0.0804743	−	0.0248230i	0.334731	+	0.942314i	$0.391355\pi$
$570$	4.33141	−	13.8314i	0.181423	−	0.579334i
$571$	−42.6242	−	13.1478i	−1.78377	−	0.550220i	−0.786077	−	0.618129i	$-0.787891\pi$
$571$	−42.6242	−	13.1478i	−1.78377	−	0.550220i	−0.997691	+	0.0679096i	$0.978367\pi$
$572$	17.8667	+	5.51114i	0.747044	+	0.230432i
$573$	11.4362	+	24.0101i	0.477754	+	1.00304i
$574$	28.0396	+	19.1170i	1.17035	+	0.797930i
$575$	11.6821	+	5.62580i	0.487177	+	0.234612i
$576$	12.1575	−	3.63631i	0.506564	−	0.151513i
$577$	15.5915	−	19.5511i	0.649081	−	0.813922i	−0.343025	−	0.939326i	$-0.611451\pi$
$577$	15.5915	−	19.5511i	0.649081	−	0.813922i	0.992106	+	0.125405i	$0.0400229\pi$
$578$	3.55339	+	47.4167i	0.147802	+	1.97228i
$579$	36.9308	−	2.60852i	1.53479	−	0.108406i
$580$	−20.3119	+	0.615898i	−0.843406	+	0.0255738i
$581$	16.1845	−	28.0324i	0.671448	−	1.16298i
$582$	27.4627	+	10.9143i	1.13837	+	0.452413i
$583$	13.1966	+	1.98906i	0.546546	+	0.0823785i
$584$	33.5385	+	42.0560i	1.38783	+	1.74029i
$585$	2.72426	+	0.865957i	0.112634	+	0.0358029i
$586$	−62.0818	+	29.8970i	−2.56458	+	1.23503i
$587$	8.01721	+	1.20840i	0.330906	+	0.0498760i	0.312394	−	0.949953i	$-0.398869\pi$
$587$	8.01721	+	1.20840i	0.330906	+	0.0498760i	0.0185117	+	0.999829i	$0.494107\pi$
$588$	21.9369	+	5.10593i	0.904662	+	0.210565i
$589$	20.1208	+	6.20644i	0.829063	+	0.255732i
$590$	5.40937	−	0.815331i	0.222700	−	0.0335666i
$591$	4.72882	−	1.83258i	0.194518	−	0.0753824i
$592$	32.3257	+	55.9898i	1.32858	+	2.30117i
$593$	3.54355	−	15.5253i	0.145516	−	0.637547i	−0.848582	−	0.529064i	$-0.822543\pi$
$593$	3.54355	−	15.5253i	0.145516	−	0.637547i	0.994098	−	0.108484i	$-0.0345996\pi$
$594$	−7.21553	−	52.4366i	−0.296057	−	2.15150i
$595$	−15.1587	+	7.30005i	−0.621446	+	0.299273i
$596$	26.1687	−	8.07196i	1.07191	−	0.330640i
$597$	16.2729	+	24.0891i	0.666007	+	0.985902i
$598$	−6.07630	−	5.63799i	−0.248479	−	0.230554i
$599$	−1.56835	+	0.236390i	−0.0640808	+	0.00965863i	−0.181004	−	0.983482i	$-0.557935\pi$
$599$	−1.56835	+	0.236390i	−0.0640808	+	0.00965863i	0.116924	+	0.993141i	$0.462697\pi$
$600$	−40.3469	−	9.39097i	−1.64716	−	0.383385i
$601$	−5.61986	+	5.21447i	−0.229239	+	0.212703i	−0.786426	−	0.617684i	$-0.788071\pi$
$601$	−5.61986	+	5.21447i	−0.229239	+	0.212703i	0.557187	+	0.830387i	$0.311881\pi$
$602$	−28.9761	+	36.3349i	−1.18098	+	1.48090i
$603$	−18.6159	−	9.16227i	−0.758098	−	0.373117i
$604$	−6.30324	−	3.03548i	−0.256475	−	0.123512i
$605$	−1.79735	+	4.57956i	−0.0730725	+	0.186186i
$606$	29.7106	−	43.1787i	1.20691	−	1.75402i
$607$	4.27104	−	2.91194i	0.173356	−	0.118192i	−0.473534	−	0.880776i	$-0.657022\pi$
$607$	4.27104	−	2.91194i	0.173356	−	0.118192i	0.646890	+	0.762584i	$0.276069\pi$
$608$	5.35805	−	9.28041i	0.217298	−	0.376370i
$609$	−17.2860	−	23.9879i	−0.700463	−	0.972037i
$610$	4.53315	+	7.85164i	0.183542	+	0.317904i
$611$	−4.76993	−	2.29708i	−0.192971	−	0.0929298i
$612$	76.7737	+	0.657887i	3.10339	+	0.0265935i
$613$	−6.69400	−	8.39402i	−0.270368	−	0.339031i	0.628049	−	0.778174i	$-0.283854\pi$
$613$	−6.69400	−	8.39402i	−0.270368	−	0.339031i	−0.898417	+	0.439143i	$0.855282\pi$
$614$	−1.57684	−	21.0415i	−0.0636362	−	0.849167i
$615$	−0.0280778	+	6.55333i	−0.00113220	+	0.264256i
$616$	26.7274	+	68.1003i	1.07688	+	2.74384i
$617$	25.2213	+	7.77973i	1.01537	+	0.313200i	0.757399	−	0.652952i	$-0.226470\pi$
$617$	25.2213	+	7.77973i	1.01537	+	0.313200i	0.257971	+	0.966153i	$0.416946\pi$
$618$	−54.9768	+	58.7440i	−2.21149	+	2.36303i
$619$	−2.60230	+	6.63056i	−0.104595	+	0.266505i	−0.973585	−	0.228326i	$-0.926675\pi$
$619$	−2.60230	+	6.63056i	−0.104595	+	0.266505i	0.868989	+	0.494831i	$0.164770\pi$
$620$	−4.67882	+	20.4993i	−0.187906	+	0.823270i
$621$	−4.90462	+	15.2038i	−0.196816	+	0.610107i
$622$	14.5193	−	63.6134i	0.582172	−	2.55066i
$623$	−34.3208	−	23.3995i	−1.37503	−	0.937483i
$624$	9.12845	+	5.32259i	0.365430	+	0.213074i
$625$	−10.1699	−	9.43627i	−0.406795	−	0.377451i
$626$	−4.14356	+	7.17685i	−0.165610	+	0.286845i
$627$	20.7537	+	16.6965i	0.828822	+	0.666793i
$628$	−20.5966	+	52.4793i	−0.821895	+	2.09415i
$629$	−15.2387	−	66.7653i	−0.607608	−	2.66211i
$630$	7.52525	+	19.6679i	0.299813	+	0.783590i
$631$	0.371221	−	0.465496i	0.0147781	−	0.0185311i	−0.774388	−	0.632712i	$-0.781942\pi$
$631$	0.371221	−	0.465496i	0.0147781	−	0.0185311i	0.789166	+	0.614180i	$0.210513\pi$
$632$	−48.6701	−	33.1827i	−1.93599	−	1.31994i
$633$	−35.0114	−	13.9144i	−1.39158	−	0.553046i
$634$	−58.7942	+	8.86180i	−2.33502	+	0.351947i
$635$	−1.17446	−	2.99248i	−0.0466071	−	0.118753i
$636$	22.5159	+	8.94836i	0.892814	+	0.354826i
$637$	−1.64179	−	2.84367i	−0.0650502	−	0.112670i
$638$	18.4843	−	51.6480i	0.731801	−	2.04476i
$639$	11.8138	−	29.3588i	0.467347	−	1.16142i
$640$	−12.9595	−	6.24097i	−0.512269	−	0.246696i
$641$	−41.0761	−	6.19123i	−1.62241	−	0.244539i	−0.725977	−	0.687719i	$-0.758612\pi$
$641$	−41.0761	−	6.19123i	−1.62241	−	0.244539i	−0.896432	+	0.443181i	$0.853850\pi$
$642$	55.4024	−	12.3957i	2.18656	−	0.489221i
$643$	−13.8311	+	9.42990i	−0.545446	+	0.371879i	−0.804471	−	0.593992i	$-0.797551\pi$
$643$	−13.8311	+	9.42990i	−0.545446	+	0.371879i	0.259025	+	0.965871i	$0.416599\pi$
$644$	3.10666	−	41.4554i	0.122419	−	1.63357i
$645$	−8.94648	−	0.709005i	−0.352267	−	0.0279170i
$646$	−41.6017	+	38.6007i	−1.63680	+	1.51873i
$647$	−0.331767	−	1.45357i	−0.0130431	−	0.0571456i	0.967988	−	0.250998i	$-0.0807588\pi$
$647$	−0.331767	−	1.45357i	−0.0130431	−	0.0571456i	−0.981031	+	0.193853i	$0.937902\pi$
$648$	4.68583	−	50.8237i	0.184077	−	1.99654i
$649$	−2.23711	+	9.80140i	−0.0878141	+	0.384739i
$650$	5.68528	+	9.84719i	0.222995	+	0.386238i
$651$	−28.5261	+	11.0549i	−1.11803	+	0.433274i
$652$	5.91687	−	78.9551i	0.231722	−	3.09212i
$653$	−2.00722	+	26.7844i	−0.0785484	+	1.04816i	0.809111	+	0.587655i	$0.199949\pi$
$653$	−2.00722	+	26.7844i	−0.0785484	+	1.04816i	−0.887660	+	0.460500i	$0.847670\pi$
$654$	19.0971	+	15.3637i	0.746756	+	0.600770i
$655$	−3.85580	−	6.67843i	−0.150658	−	0.260948i
$656$	−5.39054	+	23.6175i	−0.210465	+	0.922109i
$657$	−27.2626	+	8.15424i	−1.06362	+	0.318127i
$658$	−8.67859	−	38.0234i	−0.338327	−	1.48231i
$659$	−11.9109	+	11.0517i	−0.463982	+	0.430512i	−0.877204	−	0.480118i	$-0.840594\pi$
$659$	−11.9109	+	11.0517i	−0.463982	+	0.430512i	0.413222	+	0.910630i	$0.364403\pi$
$660$	−15.0775	+	21.9123i	−0.586890	+	0.852935i
$661$	−0.0879444	+	1.17354i	−0.00342064	+	0.0456453i	−0.998653	−	0.0518879i	$-0.983476\pi$
$661$	−0.0879444	+	1.17354i	−0.00342064	+	0.0456453i	0.995232	+	0.0975332i	$0.0310952\pi$
$662$	−43.2271	+	29.4718i	−1.68007	+	1.14545i
$663$	−7.57794	−	8.23758i	−0.294303	−	0.319921i
$664$	57.2615	+	8.63078i	2.22218	+	0.334939i
$665$	−9.54774	−	4.59795i	−0.370245	−	0.178301i
$666$	−84.8630	+	12.0483i	−3.28838	+	0.466861i
$667$	−11.7898	+	11.6239i	−0.456504	+	0.450079i
$668$	7.86356	+	13.6201i	0.304250	+	0.526977i
$669$	−28.0229	+	22.1518i	−1.08343	+	0.856436i
$670$	5.59521	+	14.2564i	0.216162	+	0.550771i
$671$	−16.4757	+	2.48331i	−0.636036	+	0.0958671i
$672$	2.25457	+	15.4056i	0.0869718	+	0.594286i
$673$	−39.1126	−	26.6665i	−1.50768	−	1.02792i	−0.984438	−	0.175735i	$-0.943770\pi$
$673$	−39.1126	−	26.6665i	−1.50768	−	1.02792i	−0.523242	−	0.852184i	$-0.675278\pi$
$674$	13.1692	−	16.5136i	0.507258	−	0.636082i
$675$	12.5764	−	17.9462i	0.484066	−	0.690750i
$676$	11.2382	+	49.2377i	0.432238	+	1.89376i
$677$	−8.56297	+	21.8181i	−0.329102	+	0.838538i	0.666556	+	0.745455i	$0.267768\pi$
$677$	−8.56297	+	21.8181i	−0.329102	+	0.838538i	−0.995658	+	0.0930833i	$0.970328\pi$
$678$	−9.71200	+	3.76374i	−0.372987	+	0.144546i
$679$	10.8036	−	18.7123i	0.414603	−	0.718113i
$680$	−22.0647	−	20.4730i	−0.846142	−	0.785105i
$681$	−0.203350	+	47.4618i	−0.00779239	+	1.81874i
$682$	−46.8970	−	31.9739i	−1.79578	−	1.22434i
$683$	−0.00571427	+	0.0250358i	−0.000218650	+	0.000957970i	−0.975037	−	0.222042i	$-0.928728\pi$
$683$	−0.00571427	+	0.0250358i	−0.000218650	+	0.000957970i	0.974818	+	0.223000i	$0.0715850\pi$
$684$	29.8256	+	38.0647i	1.14041	+	1.45544i
$685$	−2.45010	+	10.7346i	−0.0936135	+	0.410147i
$686$	−11.4548	+	29.1864i	−0.437347	+	1.11434i
$687$	3.98328	+	13.1127i	0.151972	+	0.500280i
$688$	−31.7009	−	9.77842i	−1.20858	−	0.372799i
$689$	−1.29047	−	3.28807i	−0.0491631	−	0.125266i
$690$	10.2372	−	5.85211i	0.389723	−	0.222786i
$691$	2.74912	+	36.6844i	0.104581	+	1.39554i	0.764703	+	0.644382i	$0.222885\pi$
$691$	2.74912	+	36.6844i	0.104581	+	1.39554i	−0.660122	+	0.751158i	$0.729495\pi$
$692$	48.8936	+	61.3107i	1.85866	+	2.33068i
$693$	−38.6991	−	0.331619i	−1.47006	−	0.0125972i
$694$	7.22858	+	3.48110i	0.274393	+	0.132141i
$695$	−8.61751	−	14.9260i	−0.326881	−	0.566174i
$696$	28.6498	−	44.4653i	1.08597	−	1.68545i
$697$	12.8301	−	22.2225i	0.485976	−	0.841736i
$698$	11.5219	−	7.85551i	0.436111	−	0.297335i
$699$	0.237036	+	0.0187850i	0.00896553	+	0.000710515i
$700$	−20.8340	+	53.0842i	−0.787451	+	2.00639i
$701$	−31.5385	−	15.1881i	−1.19119	−	0.573648i	−0.270039	−	0.962849i	$-0.587037\pi$
$701$	−31.5385	−	15.1881i	−1.19119	−	0.573648i	−0.921152	+	0.389202i	$0.872751\pi$
$702$	−11.0644	+	8.59322i	−0.417597	+	0.324330i
$703$	26.8934	−	33.7233i	1.01430	−	1.27190i
$704$	12.6186	−	11.7083i	0.475580	−	0.441274i
$705$	5.14630	−	5.49895i	0.193821	−	0.207102i
$706$	26.1477	−	3.94113i	0.984080	−	0.148326i
$707$	−28.0921	−	26.0656i	−1.05651	−	0.980298i
$708$	−7.98963	+	16.4104i	−0.300269	+	0.616741i
$709$	16.2558	−	5.01425i	0.610499	−	0.188314i	0.0259376	−	0.999664i	$-0.491743\pi$
$709$	16.2558	−	5.01425i	0.610499	−	0.188314i	0.584561	+	0.811350i	$0.301267\pi$
$710$	−21.0460	+	10.1352i	−0.789840	+	0.380367i
$711$	25.8962	−	17.3325i	0.971182	−	0.650021i
$712$	16.5361	−	72.4495i	0.619717	−	2.71516i
$713$	8.56547	+	14.8358i	0.320780	+	0.555606i
$714$	12.6386	−	81.4815i	0.472989	−	3.04937i
$715$	3.83438	−	0.577941i	0.143398	−	0.0216138i
$716$	25.9027	+	7.98991i	0.968028	+	0.298597i
$717$	9.41239	+	30.9849i	0.351512	+	1.15715i
$718$	−41.4542	−	6.24821i	−1.54706	−	0.233181i
$719$	−17.7357	+	8.54109i	−0.661432	+	0.318529i	−0.734312	−	0.678812i	$-0.762495\pi$
$719$	−17.7357	+	8.54109i	−0.661432	+	0.318529i	0.0728804	+	0.997341i	$0.476781\pi$
$720$	−11.1066	+	10.1297i	−0.413918	+	0.377511i
$721$	36.6777	+	45.9924i	1.36595	+	1.71285i
$722$	11.6823	+	1.76082i	0.434769	+	0.0655309i
$723$	26.6874	−	21.0960i	0.992514	−	0.784570i
$724$	−2.08674	+	3.61435i	−0.0775532	+	0.134326i
$725$	20.1542	−	10.4697i	0.748507	−	0.388836i
$726$	−13.4963	−	19.9789i	−0.500896	−	0.741485i
$727$	1.95557	+	26.0952i	0.0725279	+	0.967818i	0.908186	+	0.418567i	$0.137468\pi$
$727$	1.95557	+	26.0952i	0.0725279	+	0.967818i	−0.835658	+	0.549250i	$0.814913\pi$
$728$	12.0726	−	15.1385i	0.447439	−	0.561071i
$729$	24.0170	+	12.3363i	0.889519	+	0.456899i
$730$	18.9241	+	9.11337i	0.700413	+	0.337301i
$731$	29.0344	+	19.7953i	1.07388	+	0.732156i
$732$	−30.1548	−	2.38976i	−1.11455	−	0.0883280i
$733$	31.9449	+	9.85370i	1.17991	+	0.363955i	0.821828	−	0.569735i	$-0.192954\pi$
$733$	31.9449	+	9.85370i	1.17991	+	0.363955i	0.358083	+	0.933690i	$0.383430\pi$
$734$	83.3186	+	25.7004i	3.07534	+	0.948618i
$735$	4.55845	−	1.01991i	0.168141	−	0.0376199i
$736$	8.33106	−	2.56979i	0.307087	−	0.0947238i
$737$	−28.1455			−1.03675
$738$	−26.3803	−	18.3189i	−0.971073	−	0.674327i
$739$	4.50561	−	2.16979i	0.165741	−	0.0798168i	−0.349174	−	0.937058i	$-0.613538\pi$
$739$	4.50561	−	2.16979i	0.165741	−	0.0798168i	0.514915	+	0.857241i	$0.327823\pi$
$740$	35.5883	+	24.2637i	1.30825	+	0.891950i
$741$	1.08059	−	6.96661i	0.0396966	−	0.255925i
$742$	13.0106	−	22.5350i	0.477633	−	0.827285i
$743$	−22.8051	−	21.1600i	−0.836638	−	0.776286i	0.140233	−	0.990119i	$-0.455215\pi$
$743$	−22.8051	−	21.1600i	−0.836638	−	0.776286i	−0.976870	+	0.213832i	$0.931405\pi$
$744$	−37.0546	−	40.2801i	−1.35849	−	1.47674i
$745$	4.16338	−	3.86305i	0.152534	−	0.141531i
$746$	0.253744	+	1.11172i	0.00929022	+	0.0407031i
$747$	−15.5436	+	26.3974i	−0.568712	+	0.965830i
$748$	93.8343	−	45.1882i	3.43092	−	1.65225i
$749$	−3.10200	−	41.3932i	−0.113344	−	1.51248i
$750$	−34.4997	+	7.71896i	−1.25975	+	0.281857i
$751$	5.28243	+	13.4594i	0.192759	+	0.491141i	0.994277	−	0.106829i	$-0.0340696\pi$
$751$	5.28243	+	13.4594i	0.192759	+	0.491141i	−0.801519	+	0.597969i	$0.795974\pi$
$752$	23.0028	−	15.6830i	0.838824	−	0.571901i
$753$	−10.4611	−	15.4857i	−0.381224	−	0.564332i
$754$	−14.2847	+	2.59808i	−0.520216	+	0.0946164i
$755$	−1.45093			−0.0528049
$756$	−68.2925	−	16.5136i	−2.48377	−	0.600594i
$757$	−6.49403	+	8.14326i	−0.236030	+	0.295972i	−0.885713	−	0.464233i	$-0.846330\pi$
$757$	−6.49403	+	8.14326i	−0.236030	+	0.295972i	0.649684	+	0.760205i	$0.274901\pi$
$758$	−2.12154	+	5.40561i	−0.0770580	+	0.196341i
$759$	3.13801	+	21.4423i	0.113902	+	0.778305i
$760$	1.41676	−	18.9054i	0.0513914	−	0.685770i
$761$	−4.08835	−	10.4169i	−0.148202	−	0.377614i	0.837424	−	0.546554i	$-0.184061\pi$
$761$	−4.08835	−	10.4169i	−0.148202	−	0.377614i	−0.985626	+	0.168940i	$0.945965\pi$
$762$	15.3445	+	3.57152i	0.555873	+	0.129383i
$763$	13.1368	−	12.1892i	0.475584	−	0.441277i
$764$	40.8358	+	51.2065i	1.47739	+	1.85259i
$765$	14.4047	−	6.78550i	0.520803	−	0.245330i
$766$	−33.5049			−1.21058
$767$	2.54268	−	0.784313i	0.0918108	−	0.0283199i
$768$	48.4784	−	27.7128i	1.74931	−	0.999999i
$769$	0.237992	−	3.17578i	0.00858222	−	0.114522i	−0.991267	−	0.131868i	$-0.957903\pi$
$769$	0.237992	−	3.17578i	0.00858222	−	0.114522i	0.999850	+	0.0173459i	$0.00552166\pi$
$770$	20.9404	+	19.4298i	0.754638	+	0.700202i
$771$	−47.7957	+	3.37593i	−1.72132	+	0.121581i
$772$	87.1269	−	26.8751i	3.13576	−	0.967255i
$773$	−21.5343	−	27.0032i	−0.774536	−	0.971237i	0.225460	−	0.974253i	$-0.427612\pi$
$773$	−21.5343	−	27.0032i	−0.774536	−	0.971237i	−0.999995	+	0.00301519i	$0.999040\pi$
$774$	27.7163	−	34.1507i	0.996244	−	1.22752i
$775$	−5.22912	−	22.9103i	−0.187836	−	0.822962i
$776$	38.2234	+	5.76125i	1.37214	+	0.206817i
$777$	−0.268509	+	62.6697i	−0.00963269	+	2.24826i
$778$	66.2069	−	45.1391i	2.37363	−	1.61832i
$779$	15.9817	−	2.40885i	0.572603	−	0.0863060i
$780$	7.01793	+	0.556168i	0.251282	+	0.0199140i
$781$	−3.20808	−	42.8089i	−0.114794	−	1.53182i
$782$	−46.1718			−1.65110
$783$	16.1641	+	22.8412i	0.577659	+	0.816278i
$784$	17.2671			0.616683
$785$	0.873748	+	11.6594i	0.0311854	+	0.416141i
$786$	37.6750	+	2.98573i	1.34382	+	0.106497i
$787$	12.8611	−	1.93849i	0.458447	−	0.0690998i	0.0842411	−	0.996445i	$-0.473153\pi$
$787$	12.8611	−	1.93849i	0.458447	−	0.0690998i	0.374206	+	0.927346i	$0.377915\pi$
$788$	10.3195	−	7.03574i	0.367618	−	0.250638i
$789$	0.179967	−	42.0043i	0.00640701	−	1.49539i
$790$	−22.7442	−	3.42813i	−0.809201	−	0.121967i
$791$	1.69462	+	7.42463i	0.0602539	+	0.263989i
$792$	−24.7413	−	64.6637i	−0.879145	−	2.29773i
$793$	2.74956	+	3.44784i	0.0976396	+	0.122436i
$794$	32.9932	−	10.1771i	1.17089	−	0.361171i
$795$	5.01241	−	0.354039i	0.177772	−	0.0125565i
$796$	52.4814	+	48.6956i	1.86015	+	1.72597i
$797$	1.66546	−	22.2240i	0.0589936	−	0.787215i	−0.886739	−	0.462270i	$-0.847035\pi$
$797$	1.66546	−	22.2240i	0.0589936	−	0.787215i	0.945733	−	0.324945i	$-0.105346\pi$
$798$	45.0879	−	25.7746i	1.59609	−	0.912409i
$799$	−28.1798	+	8.69232i	−0.996930	+	0.307512i
$800$	−11.9595			−0.422833
$801$	32.2899	+	22.4226i	1.14091	+	0.792263i
$802$	20.0943	+	25.1975i	0.709556	+	0.889755i
$803$	−28.2964	+	26.2553i	−0.998560	+	0.926528i
$804$	−49.7677	−	11.5837i	−1.75517	−	0.408526i
$805$	−3.14985	−	8.02568i	−0.111018	−	0.282868i
$806$	−1.12266	+	14.9808i	−0.0395439	+	0.527677i
$807$	−4.21425	−	28.7963i	−0.148349	−	1.01368i
$808$	25.0471	−	63.8190i	0.881155	−	2.24515i
$809$	−19.2405	+	24.1268i	−0.676460	+	0.848254i	−0.995023	−	0.0996477i	$-0.968228\pi$
$809$	−19.2405	+	24.1268i	−0.676460	+	0.848254i	0.318563	+	0.947902i	$0.396800\pi$
$810$	−6.96206	−	18.6739i	−0.244622	−	0.656133i
$811$	−7.84939			−0.275629			−0.137815	−	0.990458i	$-0.544008\pi$
$811$	−7.84939			−0.275629			−0.137815	+	0.990458i	$0.544008\pi$
$812$	−54.8548	−	47.8872i	−1.92503	−	1.68051i
$813$	0.958151	+	1.41837i	0.0336038	+	0.0497443i
$814$	−96.0685	+	65.4984i	−3.36720	+	2.29572i
$815$	−5.99913	−	15.2855i	−0.210140	−	0.535429i
$816$	57.4395	−	12.8515i	2.01078	−	0.449893i
$817$	1.65402	+	22.0714i	0.0578669	+	0.772180i
$818$	15.3176	−	7.37655i	0.535566	−	0.257915i
$819$	5.04533	+	8.91430i	0.176298	+	0.311491i
$820$	3.59133	+	15.7346i	0.125415	+	0.549478i
$821$	−7.88702	+	7.31808i	−0.275259	+	0.255403i	−0.805707	−	0.592315i	$-0.798214\pi$
$821$	−7.88702	+	7.31808i	−0.275259	+	0.255403i	0.530448	+	0.847718i	$0.322024\pi$
$822$	−36.5331	−	39.7133i	−1.27424	−	1.38516i
$823$	−38.0620	−	35.3163i	−1.32676	−	1.23105i	−0.952798	−	0.303605i	$-0.901810\pi$
$823$	−38.0620	−	35.3163i	−1.32676	−	1.23105i	−0.373959	−	0.927445i	$-0.622000\pi$
$824$	−52.6203	+	91.1411i	−1.83312	+	3.17505i
$825$	4.55646	−	29.3756i	0.158636	−	1.02273i
$826$	16.1960	+	11.0423i	0.563533	+	0.384210i
$827$	35.8253	−	17.2526i	1.24577	−	0.599930i	0.309394	−	0.950934i	$-0.399874\pi$
$827$	35.8253	−	17.2526i	1.24577	−	0.599930i	0.936374	+	0.351004i	$0.114160\pi$
$828$	−3.27618	+	39.2064i	−0.113855	+	1.36251i
$829$	−1.49247			−0.0518358			−0.0259179	−	0.999664i	$-0.508251\pi$
$829$	−1.49247			−0.0518358			−0.0259179	+	0.999664i	$0.508251\pi$
$830$	21.6071	−	6.66490i	0.749992	−	0.231342i
$831$	−10.1936	+	2.28071i	−0.353612	+	0.0791171i
$832$	−4.35362	−	1.34291i	−0.150935	−	0.0465572i
$833$	−17.4777	−	5.39115i	−0.605566	−	0.186792i
$834$	84.2018	+	6.67296i	2.91567	+	0.231066i
$835$	2.69494	+	1.83738i	0.0932621	+	0.0635850i
$836$	59.1018	+	28.4619i	2.04408	+	0.984376i
$837$	27.0855	−	10.2305i	0.936211	−	0.353618i
$838$	0.471128	−	0.590775i	0.0162748	−	0.0204080i
$839$	−1.69799	−	22.6581i	−0.0586212	−	0.782245i	−0.946610	−	0.322380i	$-0.895517\pi$
$839$	−1.69799	−	22.6581i	−0.0586212	−	0.782245i	0.887989	−	0.459865i	$-0.152102\pi$
$840$	15.4191	+	22.8252i	0.532011	+	0.787545i
$841$	3.91534	+	28.7345i	0.135012	+	0.990844i
$842$	−13.0584	+	22.6178i	−0.450023	+	0.779463i
$843$	4.99503	−	3.94851i	0.172038	−	0.135994i
$844$	−91.7474	−	13.8287i	−3.15808	−	0.476003i
$845$	6.53052	+	8.18902i	0.224657	+	0.281711i
$846$	7.90467	+	36.0540i	0.271768	+	1.23956i
$847$	−15.8826	+	7.64867i	−0.545733	+	0.262811i
$848$	18.3673	+	2.76842i	0.630735	+	0.0950679i
$849$	2.76383	+	9.09834i	0.0948545	+	0.312254i
$850$	60.5225	+	18.6687i	2.07591	+	0.640332i
$851$	34.7008	−	5.23030i	1.18953	−	0.179292i
$852$	11.9460	−	77.0163i	0.409264	−	2.63853i
$853$	−15.8038	−	27.3729i	−0.541111	−	0.937231i	−0.998841	−	0.0481400i	$-0.984671\pi$
$853$	−15.8038	−	27.3729i	−0.541111	−	0.937231i	0.457730	−	0.889091i	$-0.348663\pi$
$854$	−7.22903	+	31.6724i	−0.247372	+	1.08381i
$855$	8.99826	+	4.42872i	0.307734	+	0.151459i
$856$	66.9061	−	32.2203i	2.28680	−	1.10127i
$857$	16.3464	−	5.04220i	0.558383	−	0.172238i	−0.00270233	−	0.999996i	$-0.500860\pi$
$857$	16.3464	−	5.04220i	0.558383	−	0.172238i	0.561085	+	0.827758i	$0.310384\pi$
$858$	−8.31877	+	17.0864i	−0.283998	+	0.583322i
$859$	−1.35426	−	1.25657i	−0.0462068	−	0.0428736i	0.656731	−	0.754125i	$-0.271939\pi$
$859$	−1.35426	−	1.25657i	−0.0462068	−	0.0428736i	−0.702938	+	0.711251i	$0.748129\pi$
$860$	−21.8551	+	3.29412i	−0.745251	+	0.112329i
$861$	−16.0458	+	17.1453i	−0.546839	+	0.584311i
$862$	29.8117	−	27.6612i	1.01539	−	0.942143i
$863$	19.7728	−	24.7944i	0.673075	−	0.844010i	−0.321621	−	0.946869i	$-0.604228\pi$
$863$	19.7728	−	24.7944i	0.673075	−	0.844010i	0.994696	+	0.102859i	$0.0327990\pi$
$864$	−2.00869	−	14.5975i	−0.0683369	−	0.496617i
$865$	14.6530	+	7.05651i	0.498216	+	0.239928i
$866$	−18.9097	+	48.1812i	−0.642579	+	1.63726i
$867$	−32.7996	−	2.59935i	−1.11393	−	0.0882786i
$868$	−62.2515	+	42.4424i	−2.11296	+	1.44059i
$869$	21.1353	−	36.6075i	0.716967	−	1.24182i
$870$	2.54580	−	20.4969i	0.0863109	−	0.694911i
$871$	3.72470	+	6.45137i	0.126207	+	0.218596i
$872$	28.8852	+	13.9104i	0.978175	+	0.471064i
$873$	−10.3757	+	17.6209i	−0.351166	+	0.596376i
$874$	−18.1319	−	22.7367i	−0.613322	−	0.769082i
$875$	1.93165	+	25.7760i	0.0653015	+	0.871388i
$876$	−60.8404	+	34.7795i	−2.05561	+	1.17509i
$877$	−1.82867	−	4.65937i	−0.0617497	−	0.157336i	0.896669	−	0.442702i	$-0.145980\pi$
$877$	−1.82867	−	4.65937i	−0.0617497	−	0.157336i	−0.958419	+	0.285366i	$0.907885\pi$
$878$	−25.8987	−	7.98870i	−0.874040	−	0.269606i
$879$	−13.8585	−	45.6213i	−0.467436	−	1.53877i
$880$	−7.44979	+	18.9818i	−0.251132	+	0.639875i
$881$	−8.99154	+	39.3945i	−0.302933	+	1.32724i	0.562744	+	0.826631i	$0.309746\pi$
$881$	−8.99154	+	39.3945i	−0.302933	+	1.32724i	−0.865677	+	0.500604i	$0.833111\pi$
$882$	−8.54588	+	21.2376i	−0.287755	+	0.715107i
$883$	−11.7833	+	51.6258i	−0.396538	+	1.73735i	0.244325	+	0.969693i	$0.421434\pi$
$883$	−11.7833	+	51.6258i	−0.396538	+	1.73735i	−0.640864	+	0.767655i	$0.721424\pi$
$884$	−22.7756	−	15.5281i	−0.766026	−	0.522268i
$885$	−0.0162181	+	3.78530i	−0.000545166	+	0.127241i
$886$	24.7710	+	22.9841i	0.832197	+	0.772166i
$887$	15.6494	−	27.1055i	0.525454	−	0.910113i	−0.474107	−	0.880467i	$-0.657229\pi$
$887$	15.6494	−	27.1055i	0.525454	−	0.910113i	0.999560	−	0.0296453i	$-0.00943777\pi$
$888$	−104.542	+	40.5135i	−3.50818	+	1.35954i
$889$	4.20841	−	10.7228i	0.141145	−	0.359633i
$890$	−6.45691	−	28.2896i	−0.216436	−	0.948269i
$891$	36.6204	+	0.627659i	1.22683	+	0.0210274i
$892$	−54.8492	+	68.7787i	−1.83649	+	2.30288i
$893$	−15.3468	−	10.4633i	−0.513562	−	0.350140i
$894$	4.03053	+	27.5409i	0.134801	+	0.921107i
$895$	5.55899	−	0.837883i	0.185817	−	0.0280074i
$896$	−18.8302	−	47.9787i	−0.629074	−	1.60286i
$897$	4.49961	−	3.55689i	0.150238	−	0.118761i
$898$	−24.8349	−	43.0153i	−0.828750	−	1.43544i
$899$	29.7931	+	3.57088i	0.993656	+	0.119096i
$900$	20.1468	−	50.0675i	0.671561	−	1.66892i
$901$	−17.7269	−	8.53681i	−0.590568	−	0.284402i
$902$	−43.0805	−	6.49334i	−1.43442	−	0.216205i
$903$	−21.7719	−	23.6671i	−0.724523	−	0.787591i
$904$	−11.2569	+	7.67482i	−0.374399	+	0.255261i
$905$	−0.0646827	+	0.863131i	−0.00215013	+	0.0286914i
$906$	4.03078	−	5.85798i	0.133914	−	0.194618i
$907$	−24.2045	+	22.4585i	−0.803696	+	0.745721i	−0.970715	−	0.240233i	$-0.922776\pi$
$907$	−24.2045	+	22.4585i	−0.803696	+	0.745721i	0.167020	+	0.985954i	$0.446586\pi$
$908$	26.0098	+	113.956i	0.863166	+	3.78178i
$909$	26.3737	+	24.8951i	0.874759	+	0.825719i
$910$	1.68241	−	7.37113i	0.0557714	−	0.244351i
$911$	19.6029	+	33.9531i	0.649472	+	1.12492i	0.983249	+	0.182266i	$0.0583432\pi$
$911$	19.6029	+	33.9531i	0.649472	+	1.12492i	−0.333778	+	0.942652i	$0.608323\pi$
$912$	28.8854	+	23.2385i	0.956492	+	0.769505i
$913$	−3.10541	+	41.4388i	−0.102774	+	1.37142i
$914$	0.654377	−	8.73205i	0.0216449	−	0.288831i
$915$	−5.84960	+	2.26692i	−0.193382	+	0.0749422i
$916$	16.8751	+	29.2285i	0.557569	+	0.965737i
$917$	6.14885	−	26.9399i	0.203053	−	0.889633i
$918$	−12.6214	+	77.0079i	−0.416568	+	2.54164i
$919$	13.1695	+	57.6995i	0.434423	+	1.90333i	0.428915	+	0.903345i	$0.358896\pi$
$919$	13.1695	+	57.6995i	0.434423	+	1.90333i	0.00550808	+	0.999985i	$0.498247\pi$
$920$	11.3067	−	10.4911i	0.372771	−	0.345881i
$921$	14.5550	+	1.15348i	0.479605	+	0.0380085i
$922$	0.565211	−	7.54221i	0.0186142	−	0.248390i
$923$	−9.38788	+	6.40055i	−0.309006	+	0.210677i
$924$	−93.0098	+	20.8100i	−3.05980	+	0.684600i
$925$	−47.6010	−	7.17469i	−1.56511	−	0.235902i
$926$	−79.1352	−	38.1095i	−2.60054	−	1.25236i
$927$	−34.3371	−	43.8226i	−1.12778	−	1.43932i
$928$	5.14573	−	14.3780i	0.168917	−	0.471980i
$929$	−11.2940	−	19.5618i	−0.370544	−	0.641801i	0.619105	−	0.785308i	$-0.287495\pi$
$929$	−11.2940	−	19.5618i	−0.370544	−	0.641801i	−0.989649	+	0.143507i	$0.954162\pi$
$930$	−19.8602	−	7.89292i	−0.651242	−	0.258819i
$931$	−4.20879	−	10.7238i	−0.137937	−	0.351459i
$932$	0.579048	−	0.0872774i	0.0189673	−	0.00285887i
$933$	41.9577	+	16.6750i	1.37363	+	0.545914i
$934$	2.05385	+	1.40029i	0.0672041	+	0.0458190i
$935$	13.4671	−	16.8872i	0.440422	−	0.552272i
$936$	−11.5477	+	14.2285i	−0.377448	+	0.465073i
$937$	−4.65368	−	20.3891i	−0.152029	−	0.666083i	−0.992294	−	0.123906i	$-0.960458\pi$
$937$	−4.65368	−	20.3891i	−0.152029	−	0.666083i	0.840265	−	0.542176i	$-0.182399\pi$
$938$	−20.0491	+	51.0843i	−0.654627	+	1.66796i
$939$	−4.46792	−	3.59447i	−0.145805	−	0.117301i
$940$	9.27400	−	16.0630i	0.302485	−	0.523919i
$941$	−9.36425	−	8.68875i	−0.305266	−	0.283245i	0.512632	−	0.858608i	$-0.328670\pi$
$941$	−9.36425	−	8.68875i	−0.305266	−	0.283245i	−0.817898	+	0.575363i	$0.804861\pi$
$942$	−49.5007	−	28.8627i	−1.61282	−	0.940398i
$943$	10.8644	+	7.40722i	0.353794	+	0.241212i
$944$	−3.11366	+	13.6418i	−0.101341	+	0.444003i
$945$	−14.2467	+	3.05961i	−0.463446	+	0.0995292i
$946$	13.2762	−	58.1670i	0.431648	−	1.89117i
$947$	−11.5612	+	29.4575i	−0.375689	+	0.957240i	0.610559	+	0.791971i	$0.290945\pi$
$947$	−11.5612	+	29.4575i	−0.375689	+	0.957240i	−0.986248	+	0.165270i	$0.947151\pi$
$948$	52.4385	−	56.0318i	1.70312	−	1.81983i
$949$	9.76277	+	3.01142i	0.316913	+	0.0977547i
$950$	14.5744	+	37.1349i	0.472856	+	1.20482i
$951$	0.176274	−	41.1423i	0.00571608	−	1.33413i
$952$	−8.06004	−	107.554i	−0.261227	−	3.48584i
$953$	−7.65483	−	9.59885i	−0.247964	−	0.310937i	0.642236	−	0.766507i	$-0.278007\pi$
$953$	−7.65483	−	9.59885i	−0.247964	−	0.310937i	−0.890200	+	0.455570i	$0.849436\pi$
$954$	−12.4954	+	21.2206i	−0.404552	+	0.687041i
$955$	12.2381	+	5.89357i	0.396017	+	0.190712i
$956$	39.8754	+	69.0663i	1.28966	+	2.23376i
$957$	33.3555	+	18.1171i	1.07823	+	0.585642i
$958$	−0.520178	+	0.900975i	−0.0168062	+	0.0291092i
$959$	−32.5985	+	22.2253i	−1.05266	+	0.717691i
$960$	3.67397	−	5.33943i	0.118577	−	0.172329i
$961$	0.0173985	−	0.0443307i	0.000561242	−	0.00143002i
$962$	27.7266	+	13.3524i	0.893943	+	0.430500i
$963$	2.59991	+	39.1978i	0.0837809	+	1.26313i
$964$	52.2352	−	65.5008i	1.68238	−	2.10964i
$965$	13.8617	−	12.8618i	0.446224	−	0.414035i
$966$	41.1532	+	9.57864i	1.32408	+	0.308188i
$967$	−34.4923	+	5.19888i	−1.10920	+	0.167185i	−0.677992	−	0.735069i	$-0.737150\pi$
$967$	−34.4923	+	5.19888i	−1.10920	+	0.167185i	−0.431205	+	0.902254i	$0.641912\pi$
$968$	−23.1184	−	21.4507i	−0.743053	−	0.689453i
$969$	−21.9821	−	32.5405i	−0.706167	−	1.04535i
$970$	14.4232	−	4.44898i	0.463102	−	0.142848i
$971$	−4.81331	+	2.31797i	−0.154466	+	0.0743871i	−0.509520	−	0.860459i	$-0.670177\pi$
$971$	−4.81331	+	2.31797i	−0.154466	+	0.0743871i	0.355053	+	0.934846i	$0.384463\pi$
$972$	64.4950	+	16.1815i	2.06868	+	0.519023i
$973$	13.7424	−	60.2093i	0.440560	−	1.93022i
$974$	−8.70199	−	15.0723i	−0.278830	−	0.482947i
$975$	−7.33631	+	2.84308i	−0.234950	+	0.0910513i
$976$	−22.9312	+	3.45633i	−0.734011	+	0.110634i
$977$	−3.00569	−	0.927134i	−0.0961607	−	0.0296616i	0.246301	−	0.969193i	$-0.420785\pi$
$977$	−3.00569	−	0.927134i	−0.0961607	−	0.0296616i	−0.342462	+	0.939532i	$0.611261\pi$
$978$	78.3795	+	18.2433i	2.50630	+	0.583356i
$979$	52.7311	+	7.94794i	1.68529	+	0.254017i
$980$	10.3646	−	4.99133i	0.331085	−	0.159442i
$981$	−12.5309	+	11.4287i	−0.400081	+	0.364891i
$982$	−1.15338	−	1.44630i	−0.0368059	−	0.0461532i
$983$	29.7635	+	4.48613i	0.949308	+	0.143085i	0.605403	−	0.795919i	$-0.293012\pi$
$983$	29.7635	+	4.48613i	0.949308	+	0.143085i	0.343905	+	0.939004i	$0.388250\pi$
$984$	−39.0402	−	15.5155i	−1.24455	−	0.494616i
$985$	1.29514	−	2.24325i	0.0412667	−	0.0714760i
$986$	−48.4845	+	64.7290i	−1.54406	+	2.06139i
$987$	26.9201	−	1.90144i	0.856877	−	0.0605233i
$988$	−1.29747	−	17.3136i	−0.0412781	−	0.550818i
$989$	−11.2273	+	14.0786i	−0.357007	+	0.447673i
$990$	−19.6594	−	18.5573i	−0.624818	−	0.589790i
$991$	−44.1488	−	21.2609i	−1.40243	−	0.675375i	−0.428778	−	0.903410i	$-0.641056\pi$
$991$	−44.1488	−	21.2609i	−1.40243	−	0.675375i	−0.973653	+	0.228034i	$0.926770\pi$
$992$	−13.0554	−	8.90100i	−0.414508	−	0.282607i
$993$	−15.5675	−	32.6837i	−0.494020	−	1.03719i
$994$	−79.9837	−	24.6717i	−2.53693	−	0.782539i
$995$	14.1882	+	4.37649i	0.449797	+	0.138744i
$996$	−22.5459	+	71.9953i	−0.714393	+	2.28126i
$997$	−47.0161	+	14.5025i	−1.48901	+	0.459300i	−0.929281	−	0.369373i	$-0.879572\pi$
$997$	−47.0161	+	14.5025i	−1.48901	+	0.459300i	−0.559733	+	0.828673i	$0.689096\pi$
$998$	14.1286			0.447233
$999$	0.762322	−	59.3056i	0.0241188	−	1.87635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.q.a.103.27	yes	336
3.2	odd	2		783.2.u.a.712.2		336
9.2	odd	6		783.2.u.a.451.2		336
9.7	even	3	inner	261.2.q.a.16.27	✓	336
29.20	even	7	inner	261.2.q.a.49.27	yes	336
87.20	odd	14		783.2.u.a.658.2		336
261.20	odd	42		783.2.u.a.397.2		336
261.223	even	21	inner	261.2.q.a.223.27	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.q.a.16.27	✓	336	9.7	even	3	inner
261.2.q.a.49.27	yes	336	29.20	even	7	inner
261.2.q.a.103.27	yes	336	1.1	even	1	trivial
261.2.q.a.223.27	yes	336	261.223	even	21	inner
783.2.u.a.397.2		336	261.20	odd	42
783.2.u.a.451.2		336	9.2	odd	6
783.2.u.a.658.2		336	87.20	odd	14
783.2.u.a.712.2		336	3.2	odd	2

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.187058 + 2.49612i) q^{2} +(-1.72664 - 0.136835i) q^{3} +(-4.21795 + 0.635753i) q^{4} +(-0.730934 + 0.498342i) q^{5} +(0.0185754 - 4.33548i) q^{6} +(-3.13454 - 0.472455i) q^{7} +(-1.26192 - 5.52885i) q^{8} +(2.96255 + 0.472530i) q^{9} +(-1.38065 - 1.73128i) q^{10} +(3.88874 - 1.19952i) q^{11} +(7.36986 - 0.520551i) q^{12} +(-0.789571 - 0.732615i) q^{13} +(0.592963 - 7.91255i) q^{14} +(1.33025 - 0.760439i) q^{15} +(5.41243 - 1.66951i) q^{16} -5.99968 q^{17} +(-0.625320 + 7.48327i) q^{18} +(-2.35611 - 2.95447i) q^{19} +(2.76622 - 2.56667i) q^{20} +(5.34756 + 1.24467i) q^{21} +(3.72155 + 9.48236i) q^{22} +(0.229754 - 3.06585i) q^{23} +(1.42234 + 9.71899i) q^{24} +(-1.54079 + 3.92586i) q^{25} +(1.68100 - 2.10790i) q^{26} +(-5.05059 - 1.22127i) q^{27} +13.5217 q^{28} +(-4.05681 - 3.54152i) q^{29} +(2.14698 + 3.17821i) q^{30} +(-4.60383 + 3.13884i) q^{31} +(1.03602 + 2.63973i) q^{32} +(-6.87857 + 1.53901i) q^{33} +(-1.12229 - 14.9759i) q^{34} +(2.52658 - 1.21674i) q^{35} +(-12.7963 - 0.109654i) q^{36} +(2.53992 + 11.1281i) q^{37} +(6.93398 - 6.43379i) q^{38} +(1.26306 + 1.37300i) q^{39} +(3.67764 + 3.41235i) q^{40} +(-2.13847 + 3.70394i) q^{41} +(-2.10655 + 13.5810i) q^{42} +(-4.83932 - 3.29939i) q^{43} +(-15.6399 + 7.53177i) q^{44} +(-2.40091 + 1.13098i) q^{45} +7.69570 q^{46} +(4.69688 - 1.44880i) q^{47} +(-9.57375 + 2.14203i) q^{48} +(2.91310 + 0.898572i) q^{49} +(-10.0876 - 3.11162i) q^{50} +(10.3593 + 0.820968i) q^{51} +(3.79613 + 2.58816i) q^{52} +(2.95463 + 1.42288i) q^{53} +(2.10368 - 12.8353i) q^{54} +(-2.24464 + 2.81469i) q^{55} +(1.34341 + 17.9266i) q^{56} +(3.66388 + 5.42370i) q^{57} +(8.08118 - 10.7887i) q^{58} +(-1.23521 + 2.13945i) q^{59} +(-5.12746 + 4.05320i) q^{60} +(-4.04854 - 0.610220i) q^{61} +(-8.69610 - 10.9046i) q^{62} +(-9.06298 - 2.88084i) q^{63} +(3.81101 - 1.83529i) q^{64} +(0.942217 + 0.142016i) q^{65} +(-5.12825 - 16.8818i) q^{66} +(-6.60889 - 2.03857i) q^{67} +(25.3063 - 3.81432i) q^{68} +(-0.816218 + 5.26217i) q^{69} +(3.50974 + 6.07905i) q^{70} +(2.34734 - 10.2844i) q^{71} +(-1.12597 - 16.9758i) q^{72} +(-8.54599 + 4.11553i) q^{73} +(-27.3020 + 8.42155i) q^{74} +(3.19757 - 6.56770i) q^{75} +(11.8163 + 10.9639i) q^{76} +(-12.7561 + 1.92267i) q^{77} +(-3.19091 + 3.40957i) q^{78} +(7.61429 - 7.06503i) q^{79} +(-3.12414 + 3.91755i) q^{80} +(8.55343 + 2.79979i) q^{81} +(-9.64548 - 4.64502i) q^{82} +(-3.73059 + 9.50538i) q^{83} +(-23.3470 - 1.85024i) q^{84} +(4.38537 - 2.98990i) q^{85} +(7.33043 - 12.6967i) q^{86} +(6.52003 + 6.67003i) q^{87} +(-11.5392 - 19.9865i) q^{88} +(11.8062 + 5.68557i) q^{89} +(-3.27216 - 5.78139i) q^{90} +(2.12881 + 2.66945i) q^{91} +(0.980035 + 13.0777i) q^{92} +(8.37866 - 4.78967i) q^{93} +(4.49495 + 11.4530i) q^{94} +(3.19450 + 0.985373i) q^{95} +(-1.42762 - 4.69963i) q^{96} +(-2.49026 + 6.34507i) q^{97} +(-1.69802 + 7.43952i) q^{98} +(12.0874 - 1.71609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19}+ \cdots + 196 q^{99}+O(q^{100}) \) 336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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