LMFDB - Embedded newform 507.2.p.a.25.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.10
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.759337 + 0.287979i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.00336 - 0.888900i) q^{4} +(0.883771 + 0.107309i) q^{5} +(0.194351 + 0.788513i) q^{6} +(2.17066 + 4.13585i) q^{7} +(-1.26072 - 2.40210i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(0.759337 + 0.287979i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.00336 - 0.888900i) q^{4} +(0.883771 + 0.107309i) q^{5} +(0.194351 + 0.788513i) q^{6} +(2.17066 + 4.13585i) q^{7} +(-1.26072 - 2.40210i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.640177 + 0.335991i) q^{10} +(-2.95232 + 1.11967i) q^{11} +(0.161576 - 1.33070i) q^{12} +(1.59439 + 3.23387i) q^{13} +(0.457227 + 3.76561i) q^{14} +(0.413725 + 0.788288i) q^{15} +(0.0575956 + 0.474342i) q^{16} +(4.74587 - 2.49083i) q^{17} +(-0.538529 + 0.607874i) q^{18} +0.468406i q^{19} +(-0.791354 - 0.893253i) q^{20} +(-2.17066 + 4.13585i) q^{21} -2.56424 q^{22} +7.19259 q^{23} +(1.26072 - 2.40210i) q^{24} +(-4.08517 - 1.00690i) q^{25} +(0.279394 + 2.91475i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(1.49840 - 6.07925i) q^{28} +(-0.957578 + 2.52492i) q^{29} +(0.0871470 + 0.717720i) q^{30} +(0.422658 + 1.71479i) q^{31} +(-1.39131 + 5.64479i) q^{32} +(-2.59857 - 1.79367i) q^{33} +(4.32102 - 0.524667i) q^{34} +(1.47455 + 3.88807i) q^{35} +(1.18693 - 0.622950i) q^{36} +(-1.98749 - 8.06358i) q^{37} +(-0.134891 + 0.355678i) q^{38} +(-1.75571 + 3.14921i) q^{39} +(-0.856419 - 2.25819i) q^{40} +(-1.98282 + 1.36864i) q^{41} +(-2.83930 + 2.51540i) q^{42} +(7.15574 + 1.76373i) q^{43} +(3.95751 + 1.50088i) q^{44} +(-0.413725 + 0.788288i) q^{45} +(5.46160 + 2.07131i) q^{46} +(-5.61174 - 6.33435i) q^{47} +(-0.357658 + 0.316857i) q^{48} +(-8.41702 + 12.1942i) q^{49} +(-2.81206 - 1.94102i) q^{50} +(4.74587 + 2.49083i) q^{51} +(1.27484 - 4.66199i) q^{52} +(8.64517 - 4.53734i) q^{53} +(-0.806190 - 0.0978892i) q^{54} +(-2.72932 + 0.672717i) q^{55} +(7.19812 - 10.4283i) q^{56} +(-0.385490 + 0.266085i) q^{57} +(-1.45425 + 1.64151i) q^{58} +(-1.32181 - 0.160496i) q^{59} +(0.285593 - 1.15870i) q^{60} +(-10.8759 - 5.70811i) q^{61} +(-0.172883 + 1.42382i) q^{62} +(-4.63681 + 0.563011i) q^{63} +(-2.13918 + 3.09914i) q^{64} +(1.06205 + 3.02909i) q^{65} +(-1.45666 - 2.11033i) q^{66} +(-7.76378 - 8.76350i) q^{67} +(-6.97592 - 1.71941i) q^{68} +(4.08586 + 5.91939i) q^{69} +3.37700i q^{70} +(12.2968 - 8.48786i) q^{71} +(2.69306 - 0.326996i) q^{72} +(-11.8407 + 4.49058i) q^{73} +(0.812961 - 6.69533i) q^{74} +(-1.49198 - 3.93402i) q^{75} +(0.416366 - 0.469980i) q^{76} +(-11.0392 - 9.77991i) q^{77} +(-2.24008 + 1.88570i) q^{78} +(1.24134 - 1.09973i) q^{79} +0.425390i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-1.89977 + 0.468250i) q^{82} +(-2.06255 - 1.42367i) q^{83} +(5.85431 - 2.22025i) q^{84} +(4.46155 - 1.69204i) q^{85} +(4.92570 + 3.39997i) q^{86} +(-2.62194 + 0.646250i) q^{87} +(6.41158 + 5.68017i) q^{88} -13.8231i q^{89} +(-0.541167 + 0.479432i) q^{90} +(-9.91392 + 13.6138i) q^{91} +(-7.21676 - 6.39349i) q^{92} +(-1.17115 + 1.32195i) q^{93} +(-2.43705 - 6.42597i) q^{94} +(-0.0502642 + 0.413963i) q^{95} +(-5.43592 + 2.06157i) q^{96} +(13.4915 - 1.63817i) q^{97} +(-9.90301 + 6.83555i) q^{98} -3.15750i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	0.759337	+	0.287979i	0.536932	+	0.203632i	0.608140	−	0.793830i	$-0.291916\pi$
$2$	0.759337	+	0.287979i	0.536932	+	0.203632i	−0.0712074	+	0.997462i	$0.522685\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	−1.00336	−	0.888900i	−0.501680	−	0.444450i
$5$	0.883771	+	0.107309i	0.395234	+	0.0479901i	0.315741	−	0.948845i	$-0.397747\pi$
$5$	0.883771	+	0.107309i	0.395234	+	0.0479901i	0.0794930	+	0.996835i	$0.474670\pi$
$6$	0.194351	+	0.788513i	0.0793434	+	0.321909i
$7$	2.17066	+	4.13585i	0.820432	+	1.56320i	0.826306	+	0.563221i	$0.190438\pi$
$7$	2.17066	+	4.13585i	0.820432	+	1.56320i	−0.00587397	+	0.999983i	$0.501870\pi$
$8$	−1.26072	−	2.40210i	−0.445731	−	0.849270i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	0.640177	+	0.335991i	0.202442	+	0.106250i
$11$	−2.95232	+	1.11967i	−0.890157	+	0.337592i	−0.756932	−	0.653494i	$-0.773302\pi$
$11$	−2.95232	+	1.11967i	−0.890157	+	0.337592i	−0.133225	+	0.991086i	$0.542533\pi$
$12$	0.161576	−	1.33070i	0.0466431	−	0.384141i
$13$	1.59439	+	3.23387i	0.442204	+	0.896914i
$13$	1.59439	+	3.23387i	0.442204	+	0.896914i
$14$	0.457227	+	3.76561i	0.122199	+	1.00640i
$15$	0.413725	+	0.788288i	0.106823	+	0.203535i
$16$	0.0575956	+	0.474342i	0.0143989	+	0.118586i
$17$	4.74587	−	2.49083i	1.15104	−	0.604114i	0.222352	−	0.974967i	$-0.428627\pi$
$17$	4.74587	−	2.49083i	1.15104	−	0.604114i	0.928692	+	0.370852i	$0.120934\pi$
$18$	−0.538529	+	0.607874i	−0.126933	+	0.143277i
$19$			0.468406i			0.107460i	0.998556	+	0.0537298i	$0.0171110\pi$
$19$			0.468406i			0.107460i	−0.998556	+	0.0537298i	$0.982889\pi$
$20$	−0.791354	−	0.893253i	−0.176952	−	0.199738i
$21$	−2.17066	+	4.13585i	−0.473677	+	0.902516i
$22$	−2.56424			−0.546698
$23$	7.19259			1.49976			0.749880	−	0.661574i	$-0.230111\pi$
$23$	7.19259			1.49976			0.749880	+	0.661574i	$0.230111\pi$
$24$	1.26072	−	2.40210i	0.257343	−	0.490326i
$25$	−4.08517	−	1.00690i	−0.817035	−	0.201381i
$26$	0.279394	+	2.91475i	0.0547937	+	0.571629i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	1.49840	−	6.07925i	0.283171	−	1.14887i
$29$	−0.957578	+	2.52492i	−0.177818	+	0.468867i	−0.994059	−	0.108845i	$-0.965285\pi$
$29$	−0.957578	+	2.52492i	−0.177818	+	0.468867i	0.816241	+	0.577711i	$0.196054\pi$
$30$	0.0871470	+	0.717720i	0.0159108	+	0.131037i
$31$	0.422658	+	1.71479i	0.0759115	+	0.307985i	0.996608	−	0.0822940i	$-0.0262246\pi$
$31$	0.422658	+	1.71479i	0.0759115	+	0.307985i	−0.920697	+	0.390279i	$0.872378\pi$
$32$	−1.39131	+	5.64479i	−0.245952	+	0.997867i
$33$	−2.59857	−	1.79367i	−0.452353	−	0.312237i
$34$	4.32102	−	0.524667i	0.741049	−	0.0899797i
$35$	1.47455	+	3.88807i	0.249245	+	0.657204i
$36$	1.18693	−	0.622950i	0.197822	−	0.103825i
$37$	−1.98749	−	8.06358i	−0.326742	−	1.32565i	−0.872874	−	0.487946i	$-0.837746\pi$
$37$	−1.98749	−	8.06358i	−0.326742	−	1.32565i	0.546132	−	0.837699i	$-0.316100\pi$
$38$	−0.134891	+	0.355678i	−0.0218822	+	0.0576985i
$39$	−1.75571	+	3.14921i	−0.281138	+	0.504276i
$40$	−0.856419	−	2.25819i	−0.135412	−	0.357051i
$41$	−1.98282	+	1.36864i	−0.309664	+	0.213746i	−0.712753	−	0.701415i	$-0.752552\pi$
$41$	−1.98282	+	1.36864i	−0.309664	+	0.213746i	0.403089	+	0.915161i	$0.367937\pi$
$42$	−2.83930	+	2.51540i	−0.438113	+	0.388134i
$43$	7.15574	+	1.76373i	1.09124	+	0.268966i	0.743575	−	0.668652i	$-0.233129\pi$
$43$	7.15574	+	1.76373i	1.09124	+	0.268966i	0.347665	+	0.937619i	$0.386975\pi$
$44$	3.95751	+	1.50088i	0.596617	+	0.226267i
$45$	−0.413725	+	0.788288i	−0.0616745	+	0.117511i
$46$	5.46160	+	2.07131i	0.805269	+	0.305398i
$47$	−5.61174	−	6.33435i	−0.818557	−	0.923960i	0.179655	−	0.983730i	$-0.442502\pi$
$47$	−5.61174	−	6.33435i	−0.818557	−	0.923960i	−0.998212	+	0.0597698i	$0.980963\pi$
$48$	−0.357658	+	0.316857i	−0.0516235	+	0.0457344i
$49$	−8.41702	+	12.1942i	−1.20243	+	1.74202i
$50$	−2.81206	−	1.94102i	−0.397685	−	0.274502i
$51$	4.74587	+	2.49083i	0.664555	+	0.348785i
$52$	1.27484	−	4.66199i	0.176788	−	0.646502i
$53$	8.64517	−	4.53734i	1.18751	−	0.623251i	0.248996	−	0.968505i	$-0.419899\pi$
$53$	8.64517	−	4.53734i	1.18751	−	0.623251i	0.938509	+	0.345254i	$0.112207\pi$
$54$	−0.806190	−	0.0978892i	−0.109709	−	0.0133210i
$55$	−2.72932	+	0.672717i	−0.368022	+	0.0907092i
$56$	7.19812	−	10.4283i	0.961889	−	1.39354i
$57$	−0.385490	+	0.266085i	−0.0510594	+	0.0352438i
$58$	−1.45425	+	1.64151i	−0.190952	+	0.215540i
$59$	−1.32181	−	0.160496i	−0.172085	−	0.0208948i	0.0340408	−	0.999420i	$-0.489162\pi$
$59$	−1.32181	−	0.160496i	−0.172085	−	0.0208948i	−0.206125	+	0.978526i	$0.566085\pi$
$60$	0.285593	−	1.15870i	0.0368699	−	0.149587i
$61$	−10.8759	−	5.70811i	−1.39252	−	0.730849i	−0.409147	−	0.912468i	$-0.634174\pi$
$61$	−10.8759	−	5.70811i	−1.39252	−	0.730849i	−0.983369	+	0.181619i	$0.941866\pi$
$62$	−0.172883	+	1.42382i	−0.0219562	+	0.180825i
$63$	−4.63681	+	0.563011i	−0.584183	+	0.0709327i
$64$	−2.13918	+	3.09914i	−0.267398	+	0.387393i
$65$	1.06205	+	3.02909i	0.131731	+	0.375713i
$66$	−1.45666	−	2.11033i	−0.179302	−	0.259764i
$67$	−7.76378	−	8.76350i	−0.948497	−	1.07063i	−0.997417	−	0.0718294i	$-0.977116\pi$
$67$	−7.76378	−	8.76350i	−0.948497	−	1.07063i	0.0489197	−	0.998803i	$-0.484422\pi$
$68$	−6.97592	−	1.71941i	−0.845954	−	0.208509i
$69$	4.08586	+	5.91939i	0.491879	+	0.712610i
$70$			3.37700i			0.403628i
$71$	12.2968	−	8.48786i	1.45936	−	1.00732i	0.466959	−	0.884279i	$-0.345350\pi$
$71$	12.2968	−	8.48786i	1.45936	−	1.00732i	0.992401	−	0.123044i	$-0.0392658\pi$
$72$	2.69306	−	0.326996i	0.317380	−	0.0385369i
$73$	−11.8407	+	4.49058i	−1.38585	+	0.525582i	−0.931010	−	0.364993i	$-0.881071\pi$
$73$	−11.8407	+	4.49058i	−1.38585	+	0.525582i	−0.454836	+	0.890575i	$0.650302\pi$
$74$	0.812961	−	6.69533i	0.0945048	−	0.778317i
$75$	−1.49198	−	3.93402i	−0.172279	−	0.454261i
$76$	0.416366	−	0.469980i	0.0477604	−	0.0539103i
$77$	−11.0392	−	9.77991i	−1.25804	−	1.11452i
$78$	−2.24008	+	1.88570i	−0.253639	+	0.213514i
$79$	1.24134	−	1.09973i	0.139661	−	0.123729i	−0.590400	−	0.807111i	$-0.701030\pi$
$79$	1.24134	−	1.09973i	0.139661	−	0.123729i	0.730061	+	0.683382i	$0.239492\pi$
$80$			0.425390i			0.0475601i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−1.89977	+	0.468250i	−0.209794	+	0.0517096i
$83$	−2.06255	−	1.42367i	−0.226394	−	0.156269i	0.449469	−	0.893296i	$-0.351613\pi$
$83$	−2.06255	−	1.42367i	−0.226394	−	0.156269i	−0.675863	+	0.737028i	$0.736229\pi$
$84$	5.85431	−	2.22025i	0.638757	−	0.242249i
$85$	4.46155	−	1.69204i	0.483923	−	0.183528i
$86$	4.92570	+	3.39997i	0.531152	+	0.366628i
$87$	−2.62194	+	0.646250i	−0.281101	+	0.0692852i
$88$	6.41158	+	5.68017i	0.683477	+	0.605508i
$89$		−	13.8231i		−	1.46524i	−0.680636	−	0.732622i	$-0.738296\pi$
$89$		−	13.8231i		−	1.46524i	0.680636	−	0.732622i	$-0.261704\pi$
$90$	−0.541167	+	0.479432i	−0.0570440	+	0.0505366i
$91$	−9.91392	+	13.6138i	−1.03926	+	1.42711i
$92$	−7.21676	−	6.39349i	−0.752399	−	0.666568i
$93$	−1.17115	+	1.32195i	−0.121442	+	0.137080i
$94$	−2.43705	−	6.42597i	−0.251362	−	0.662788i
$95$	−0.0502642	+	0.413963i	−0.00515700	+	0.0424717i
$96$	−5.43592	+	2.06157i	−0.554802	+	0.210409i
$97$	13.4915	−	1.63817i	1.36986	−	0.166331i	0.597679	−	0.801735i	$-0.296090\pi$
$97$	13.4915	−	1.63817i	1.36986	−	0.166331i	0.772180	+	0.635404i	$0.219167\pi$
$98$	−9.90301	+	6.83555i	−1.00035	+	0.690495i
$99$		−	3.15750i		−	0.317341i
$100$	3.20386	+	4.64160i	0.320386	+	0.464160i
$101$	2.47148	+	0.609165i	0.245921	+	0.0606142i	0.360350	−	0.932817i	$-0.382657\pi$
$101$	2.47148	+	0.609165i	0.245921	+	0.0606142i	−0.114428	+	0.993432i	$0.536504\pi$
$102$	2.88641	+	3.25809i	0.285797	+	0.322599i
$103$	9.92643	+	14.3809i	0.978080	+	1.41699i	0.907770	+	0.419468i	$0.137784\pi$
$103$	9.92643	+	14.3809i	0.978080	+	1.41699i	0.0703102	+	0.997525i	$0.477601\pi$
$104$	5.75800	−	7.90688i	0.564618	−	0.775334i
$105$	−2.36218	+	3.42221i	−0.230525	+	0.333973i
$106$	7.87125	−	0.955743i	0.764524	−	0.0928300i
$107$	0.819403	−	6.74839i	0.0792146	−	0.652391i	−0.897979	−	0.440039i	$-0.854965\pi$
$107$	0.819403	−	6.74839i	0.0792146	−	0.652391i	0.977193	−	0.212352i	$-0.0681124\pi$
$108$	1.18693	+	0.622950i	0.114213	+	0.0599434i
$109$	2.56924	−	10.4238i	0.246088	−	0.998420i	−0.709733	−	0.704471i	$-0.751184\pi$
$109$	2.56924	−	10.4238i	0.246088	−	0.998420i	0.955821	−	0.293949i	$-0.0949696\pi$
$110$	−2.26620	−	0.275167i	−0.216074	−	0.0262361i
$111$	5.50717	−	6.21631i	0.522718	−	0.590026i
$112$	−1.83679	+	1.26784i	−0.173560	+	0.119800i
$113$	8.21215	−	11.8973i	0.772534	−	1.11921i	−0.217178	−	0.976132i	$-0.569685\pi$
$113$	8.21215	−	11.8973i	0.772534	−	1.11921i	0.989712	−	0.143076i	$-0.0456994\pi$
$114$	−0.369344	+	0.0910350i	−0.0345922	+	0.00852621i
$115$	6.35660	+	0.771831i	0.592756	+	0.0719736i
$116$	3.20520	−	1.68222i	0.297595	−	0.156190i
$117$	−3.58910	+	0.344034i	−0.331812	+	0.0318060i
$118$	−0.957477	−	0.502523i	−0.0881429	−	0.0462610i
$119$	20.6034	+	14.2215i	1.88871	+	1.30368i
$120$	1.37195	−	1.98762i	0.125242	−	0.181444i
$121$	−0.771103	+	0.683138i	−0.0701003	+	0.0621034i
$122$	−6.61466	−	7.46641i	−0.598863	−	0.675977i
$123$	−2.25274	−	0.854351i	−0.203123	−	0.0770342i
$124$	1.10020	−	2.09625i	0.0988007	−	0.188249i
$125$	−7.66435	−	2.90671i	−0.685521	−	0.259984i
$126$	−3.68304	−	0.907787i	−0.328111	−	0.0808721i
$127$	7.86223	−	6.96533i	0.697660	−	0.618073i	−0.237880	−	0.971295i	$-0.576452\pi$
$127$	7.86223	−	6.96533i	0.697660	−	0.618073i	0.935540	+	0.353222i	$0.114914\pi$
$128$	7.05235	−	4.86789i	0.623346	−	0.430265i
$129$	2.61340	+	6.89097i	0.230097	+	0.606716i
$130$	−0.0658588	+	2.60595i	−0.00577620	+	0.228557i
$131$	−7.45783	+	19.6647i	−0.651594	+	1.71811i	0.0433628	+	0.999059i	$0.486193\pi$
$131$	−7.45783	+	19.6647i	−0.651594	+	1.71811i	−0.694956	+	0.719052i	$0.744576\pi$
$132$	1.01292	+	4.10956i	0.0881631	+	0.357692i
$133$	−1.93725	+	1.01675i	−0.167981	+	0.0881633i
$134$	−3.37163	−	8.89026i	−0.291264	−	0.768001i
$135$	−0.883771	+	0.107309i	−0.0760629	+	0.00923571i
$136$	−11.9664	−	8.25982i	−1.02611	−	0.708274i
$137$	−1.13237	+	4.59421i	−0.0967450	+	0.392510i	−0.999273	−	0.0381211i	$-0.987863\pi$
$137$	−1.13237	+	4.59421i	−0.0967450	+	0.392510i	0.902528	+	0.430631i	$0.141709\pi$
$138$	1.39789	+	5.67145i	0.118996	+	0.482786i
$139$	−0.0294085	−	0.242201i	−0.00249440	−	0.0205432i	0.991409	−	0.130802i	$-0.0417552\pi$
$139$	−0.0294085	−	0.242201i	−0.00249440	−	0.0205432i	−0.993903	+	0.110259i	$0.964832\pi$
$140$	1.97660	−	5.21187i	0.167053	−	0.440483i
$141$	2.02523	−	8.21670i	0.170555	−	0.691971i
$142$	11.7817	−	2.90393i	0.988701	−	0.243693i
$143$	−8.32800	−	7.76222i	−0.696422	−	0.649110i
$144$	−0.463941	−	0.114351i	−0.0386618	−	0.00952927i
$145$	−1.11723	+	2.12870i	−0.0927806	+	0.176779i
$146$	−10.2843			−0.851131
$147$	−14.8170			−1.22209
$148$	−5.17354	+	9.85736i	−0.425263	+	0.810270i
$149$	−8.32366	−	9.39547i	−0.681901	−	0.769707i	0.301043	−	0.953610i	$-0.402665\pi$
$149$	−8.32366	−	9.39547i	−0.681901	−	0.769707i	−0.982944	+	0.183903i	$0.941127\pi$
$150$		−	3.41690i		−	0.278989i
$151$	−10.9917	+	12.4071i	−0.894491	+	1.00967i	0.105393	+	0.994431i	$0.466390\pi$
$151$	−10.9917	+	12.4071i	−0.894491	+	1.00967i	−0.999884	+	0.0152409i	$0.995148\pi$
$152$	1.12516	−	0.590527i	0.0912622	−	0.0478981i
$153$	0.646053	+	5.32073i	0.0522303	+	0.430155i
$154$	−5.56610	−	10.6053i	−0.448529	−	0.854601i
$155$	0.189520	+	1.56084i	0.0152226	+	0.125369i
$156$	4.56093	−	1.59914i	0.365167	−	0.128034i
$157$	−0.458755	+	3.77819i	−0.0366126	+	0.301532i	0.962887	+	0.269904i	$0.0869921\pi$
$157$	−0.458755	+	3.77819i	−0.0366126	+	0.301532i	−0.999500	+	0.0316276i	$0.989931\pi$
$158$	1.25929	−	0.477586i	0.100184	−	0.0379947i
$159$	8.64517	+	4.53734i	0.685607	+	0.359834i
$160$	−1.83534	+	4.83940i	−0.145096	+	0.382588i
$161$	15.6127	+	29.7475i	1.23045	+	2.34443i
$162$	−0.377407	−	0.719089i	−0.0296519	−	0.0564969i
$163$	−0.110355	−	0.447726i	−0.00864364	−	0.0350686i	0.966462	−	0.256811i	$-0.0826718\pi$
$163$	−0.110355	−	0.447726i	−0.00864364	−	0.0350686i	−0.975105	+	0.221742i	$0.928826\pi$
$164$	3.20607	+	0.389287i	0.250352	+	0.0303982i
$165$	−2.10407	−	1.86404i	−0.163801	−	0.145115i
$166$	−1.15618	−	1.67502i	−0.0897371	−	0.130007i
$167$	−7.83713	−	2.97223i	−0.606455	−	0.229998i	0.0322120	−	0.999481i	$-0.489745\pi$
$167$	−7.83713	−	2.97223i	−0.606455	−	0.229998i	−0.638667	+	0.769483i	$0.720514\pi$
$168$	12.6713			0.977612
$169$	−7.91584	+	10.3121i	−0.608911	+	0.793239i
$170$	3.87509			0.297206
$171$	−0.437967	−	0.166099i	−0.0334922	−	0.0127019i
$172$	−5.61200	−	8.13039i	−0.427911	−	0.619937i
$173$	−1.45412	−	1.28824i	−0.110555	−	0.0979430i	0.606035	−	0.795438i	$-0.292759\pi$
$173$	−1.45412	−	1.28824i	−0.110555	−	0.0979430i	−0.716589	+	0.697495i	$0.754298\pi$
$174$	−2.17704	−	0.264341i	−0.165041	−	0.0200396i
$175$	−4.70312	−	19.0813i	−0.355522	−	1.44241i
$176$	−0.701145	−	1.33592i	−0.0528508	−	0.100699i
$177$	−0.618786	−	1.17900i	−0.0465108	−	0.0886189i
$178$	3.98075	−	10.4964i	0.298370	−	0.786737i
$179$	−0.368249	−	0.193272i	−0.0275242	−	0.0144458i	0.450905	−	0.892572i	$-0.351101\pi$
$179$	−0.368249	−	0.193272i	−0.0275242	−	0.0144458i	−0.478429	+	0.878126i	$0.658794\pi$
$180$	1.11582	−	0.423176i	0.0831686	−	0.0315417i
$181$	1.26680	−	10.4330i	0.0941605	−	0.775481i	−0.866773	−	0.498702i	$-0.833810\pi$
$181$	1.26680	−	10.4330i	0.0941605	−	0.775481i	0.960934	−	0.276779i	$-0.0892669\pi$
$182$	−11.4485	+	7.48246i	−0.848618	+	0.554637i
$183$	−1.48053	−	12.1933i	−0.109444	−	0.901352i
$184$	−9.06783	−	17.2773i	−0.668489	−	1.27370i
$185$	−0.891193	−	7.33964i	−0.0655218	−	0.539621i
$186$	−1.26999	+	0.666542i	−0.0931201	+	0.0488732i
$187$	−11.2224	+	12.6675i	−0.820665	+	0.926339i
$188$			11.3439i			0.827340i
$189$	−3.09736	−	3.49619i	−0.225300	−	0.254311i
$190$	−0.157380	+	0.299863i	−0.0114175	+	0.0217543i
$191$	18.7452			1.35636			0.678178	−	0.734898i	$-0.262770\pi$
$191$	18.7452			1.35636			0.678178	+	0.734898i	$0.262770\pi$
$192$	−3.76574			−0.271769
$193$	−8.80598	+	16.7784i	−0.633868	+	1.20773i	0.330659	+	0.943750i	$0.392729\pi$
$193$	−8.80598	+	16.7784i	−0.633868	+	1.20773i	−0.964527	+	0.263984i	$0.914963\pi$
$194$	10.7164	+	2.64135i	0.769392	+	0.189638i
$195$	−1.88958	+	2.59477i	−0.135316	+	0.185816i
$196$	19.2847	−	4.75325i	1.37748	−	0.339518i
$197$	−4.13279	+	16.7674i	−0.294449	+	1.19463i	0.618246	+	0.785985i	$0.287844\pi$
$197$	−4.13279	+	16.7674i	−0.294449	+	1.19463i	−0.912695	+	0.408642i	$0.866002\pi$
$198$	0.909293	−	2.39761i	0.0646206	−	0.170391i
$199$	−1.11548	−	9.18679i	−0.0790741	−	0.651234i	−0.977324	−	0.211749i	$-0.932084\pi$
$199$	−1.11548	−	9.18679i	−0.0790741	−	0.651234i	0.898250	−	0.439485i	$-0.144839\pi$
$200$	2.73157	+	11.0824i	0.193151	+	0.783645i
$201$	2.80189	−	11.3677i	0.197630	−	0.801816i
$202$	1.70126	+	1.17429i	0.119700	+	0.0826231i
$203$	−12.5213	+	1.52036i	−0.878821	+	0.106708i
$204$	−2.54773	−	6.71780i	−0.178377	−	0.470340i
$205$	−1.89922	+	0.996790i	−0.132648	+	0.0696188i
$206$	3.39611	+	13.7786i	0.236618	+	0.959998i
$207$	−2.55053	+	6.72519i	−0.177274	+	0.467433i
$208$	−1.44213	+	0.942543i	−0.0999938	+	0.0653536i
$209$	−0.524457	−	1.38288i	−0.0362775	−	0.0956559i
$210$	−2.77921	+	1.91835i	−0.191784	+	0.132379i
$211$	−6.84006	+	6.05976i	−0.470889	+	0.417171i	−0.864908	−	0.501931i	$-0.832623\pi$
$211$	−6.84006	+	6.05976i	−0.470889	+	0.417171i	0.394018	+	0.919103i	$0.371085\pi$
$212$	−12.7075	−	3.13211i	−0.872752	−	0.215114i
$213$	13.9707	+	5.29840i	0.957259	+	0.363041i
$214$	2.56559	−	4.88833i	0.175380	−	0.334159i
$215$	6.13477	+	2.32661i	0.418388	+	0.158674i
$216$	1.79894	+	2.03059i	0.122403	+	0.138164i
$217$	−6.17466	+	5.47027i	−0.419163	+	0.371346i
$218$	4.95275	−	7.17530i	0.335443	−	0.485973i
$219$	−10.4219	−	7.19375i	−0.704250	−	0.486109i
$220$	3.33647	+	1.75111i	0.224945	+	0.118060i
$221$	15.6218	+	11.3762i	1.05083	+	0.765245i
$222$	5.97197	−	3.13433i	0.400812	−	0.210362i
$223$	24.9017	+	3.02361i	1.66754	+	0.202476i	0.899191	−	0.437556i	$-0.144156\pi$
$223$	24.9017	+	3.02361i	1.66754	+	0.202476i	0.768349	+	0.640032i	$0.221079\pi$
$224$	−26.3660	+	6.49865i	−1.76166	+	0.434209i
$225$	2.39009	−	3.46265i	0.159340	−	0.230843i
$226$	9.66197	−	6.66917i	0.642705	−	0.443627i
$227$	6.40733	−	7.23238i	0.425269	−	0.480030i	−0.496351	−	0.868122i	$-0.665327\pi$
$227$	6.40733	−	7.23238i	0.425269	−	0.480030i	0.921621	+	0.388092i	$0.126866\pi$
$228$	0.623308	+	0.0756833i	0.0412796	+	0.00501225i
$229$	−2.19736	+	8.91502i	−0.145205	+	0.589121i	0.852579	+	0.522598i	$0.175037\pi$
$229$	−2.19736	+	8.91502i	−0.145205	+	0.589121i	−0.997785	+	0.0665237i	$0.978809\pi$
$230$	4.60453	+	2.41665i	0.303614	+	0.159349i
$231$	1.77771	−	14.6407i	0.116965	−	0.963290i
$232$	7.27235	−	0.883023i	0.477453	−	0.0579733i
$233$	−0.0137552	+	0.0199278i	−0.000901130	+	0.00130551i	−0.823434	−	0.567412i	$-0.807945\pi$
$233$	−0.0137552	+	0.0199278i	−0.000901130	+	0.00130551i	0.822533	+	0.568717i	$0.192560\pi$
$234$	−2.82441	−	0.772346i	−0.184638	−	0.0504898i
$235$	−4.27976	−	6.20031i	−0.279181	−	0.404463i
$236$	1.18358	+	1.33599i	0.0770447	+	0.0869655i
$237$	1.61022	+	0.396883i	0.104595	+	0.0257803i
$238$	11.5494	+	16.7322i	0.748637	+	1.08459i
$239$		−	0.434746i		−	0.0281214i	−0.999901	−	0.0140607i	$-0.995524\pi$
$239$		−	0.434746i		−	0.0281214i	0.999901	−	0.0140607i	$-0.00447580\pi$
$240$	−0.350089	+	0.241649i	−0.0225982	+	0.0155984i
$241$	−15.2197	+	1.84801i	−0.980388	+	0.119041i	−0.595010	−	0.803718i	$-0.702852\pi$
$241$	−15.2197	+	1.84801i	−0.980388	+	0.119041i	−0.385378	+	0.922759i	$0.625929\pi$
$242$	−0.782256	+	0.296671i	−0.0502853	+	0.0190707i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	5.83851	+	15.3949i	0.373772	+	0.985556i
$245$	−8.74726	+	9.87361i	−0.558842	+	0.630802i
$246$	−1.46455	−	1.29748i	−0.0933765	−	0.0827243i
$247$	−1.51476	+	0.746821i	−0.0963821	+	0.0475191i
$248$	3.58624	−	3.17713i	0.227726	−	0.201748i
$249$		−	2.50618i		−	0.158823i
$250$	−4.98276	−	4.41434i	−0.315137	−	0.279187i
$251$	11.9363	−	2.94203i	0.753412	−	0.185699i	0.156136	−	0.987735i	$-0.450096\pi$
$251$	11.9363	−	2.94203i	0.753412	−	0.185699i	0.597276	+	0.802036i	$0.296250\pi$
$252$	5.15285	+	3.55676i	0.324599	+	0.224055i
$253$	−21.2348	+	8.05330i	−1.33502	+	0.506306i
$254$	7.97595	−	3.02488i	0.500455	−	0.189798i
$255$	3.92698	+	2.71060i	0.245917	+	0.169744i
$256$	14.0696	−	3.46784i	0.879349	−	0.216740i
$257$	6.39849	+	5.66856i	0.399127	+	0.353595i	0.838683	−	0.544620i	$-0.183326\pi$
$257$	6.39849	+	5.66856i	0.399127	+	0.353595i	−0.439557	+	0.898215i	$0.644864\pi$
$258$			5.98517i			0.372621i
$259$	29.0356	−	25.7233i	1.80418	−	1.59837i
$260$	1.62694	−	3.98333i	0.100899	−	0.247036i
$261$	−2.02128	−	1.79070i	−0.125114	−	0.110842i
$262$	−11.3260	+	12.7844i	−0.699723	+	0.789825i
$263$	−1.14326	−	3.01453i	−0.0704964	−	0.185884i	0.895137	−	0.445791i	$-0.147077\pi$
$263$	−1.14326	−	3.01453i	−0.0704964	−	0.185884i	−0.965634	+	0.259907i	$0.916308\pi$
$264$	−1.03249	+	8.50333i	−0.0635455	+	0.523344i
$265$	8.12725	−	3.08226i	0.499253	−	0.189342i
$266$	−1.76383	+	0.214168i	−0.108147	+	0.0131315i
$267$	11.3762	−	7.85241i	0.696211	−	0.480560i
$268$			15.6942i			0.958674i
$269$	9.36218	+	13.5635i	0.570822	+	0.826978i	0.996979	−	0.0776708i	$-0.0247483\pi$
$269$	9.36218	+	13.5635i	0.570822	+	0.826978i	−0.426157	+	0.904649i	$0.640133\pi$
$270$	−0.701983	−	0.173023i	−0.0427213	−	0.0105299i
$271$	11.1409	+	12.5755i	0.676764	+	0.763908i	0.982105	−	0.188335i	$-0.0603090\pi$
$271$	11.1409	+	12.5755i	0.676764	+	0.763908i	−0.305341	+	0.952243i	$0.598770\pi$
$272$	1.45484	+	2.10771i	0.0882129	+	0.127798i
$273$	−16.8357	−	0.425479i	−1.01894	−	0.0257512i
$274$	−2.18288	+	3.16245i	−0.131873	+	0.191051i
$275$	13.1881	−	1.60133i	0.795273	−	0.0965637i
$276$	1.16215	−	9.57120i	0.0699534	−	0.576118i
$277$	−8.53115	−	4.47750i	−0.512587	−	0.269027i	0.188536	−	0.982066i	$-0.439626\pi$
$277$	−8.53115	−	4.47750i	−0.512587	−	0.269027i	−0.701124	+	0.713040i	$0.747318\pi$
$278$	0.0474177	−	0.192381i	0.00284393	−	0.0115383i
$279$	−1.75323	−	0.212881i	−0.104963	−	0.0127448i
$280$	7.48054	−	8.44378i	0.447048	−	0.504613i
$281$	−5.52802	+	3.81572i	−0.329774	+	0.227627i	−0.721434	−	0.692484i	$-0.756516\pi$
$281$	−5.52802	+	3.81572i	−0.329774	+	0.227627i	0.391660	+	0.920110i	$0.371901\pi$
$282$	3.90407	−	5.65602i	0.232484	−	0.336811i
$283$	13.6041	−	3.35311i	0.808680	−	0.199322i	0.186763	−	0.982405i	$-0.440200\pi$
$283$	13.6041	−	3.35311i	0.808680	−	0.199322i	0.621917	+	0.783083i	$0.286354\pi$
$284$	−19.8830	−	2.41423i	−1.17984	−	0.143258i
$285$	−0.369238	+	0.193791i	−0.0218718	+	0.0114792i
$286$	−4.08840	−	8.29243i	−0.241752	−	0.490342i
$287$	−9.96451	−	5.22978i	−0.588187	−	0.308704i
$288$	−4.78460	−	3.30257i	−0.281935	−	0.194606i
$289$	6.66200	−	9.65157i	0.391882	−	0.567739i
$290$	−1.46137	+	1.29466i	−0.0858147	+	0.0760252i
$291$	9.01226	+	10.1727i	0.528308	+	0.596337i
$292$	15.8721	+	6.01951i	0.928847	+	0.352265i
$293$	−3.07408	+	5.85716i	−0.179589	+	0.342179i	−0.958564	−	0.284876i	$-0.908048\pi$
$293$	−3.07408	+	5.85716i	−0.179589	+	0.342179i	0.778975	+	0.627055i	$0.215740\pi$
$294$	−11.2511	−	4.26698i	−0.656177	−	0.248855i
$295$	−1.15095	−	0.283684i	−0.0670110	−	0.0165167i
$296$	−16.8638	+	14.9401i	−0.980191	+	0.868374i
$297$	2.59857	−	1.79367i	0.150784	−	0.104079i
$298$	−3.61477	−	9.53137i	−0.209398	−	0.552137i
$299$	11.4678	+	23.2599i	0.663200	+	1.34516i
$300$	−1.99996	+	5.27346i	−0.115468	+	0.304463i
$301$	8.23815	+	33.4235i	0.474839	+	1.92650i
$302$	−11.9194	+	6.25576i	−0.685882	+	0.359979i
$303$	0.902627	+	2.38003i	0.0518546	+	0.136729i
$304$	−0.222184	+	0.0269781i	−0.0127432	+	0.00154730i
$305$	−8.99927	−	6.21175i	−0.515297	−	0.355684i
$306$	−1.04168	+	4.22628i	−0.0595491	+	0.241600i
$307$	−1.34639	−	5.46251i	−0.0768424	−	0.311762i	0.919926	−	0.392092i	$-0.128249\pi$
$307$	−1.34639	−	5.46251i	−0.0768424	−	0.311762i	−0.996768	+	0.0803304i	$0.974402\pi$
$308$	2.38297	+	19.6256i	0.135783	+	1.11827i
$309$	−6.19641	+	16.3386i	−0.352501	+	0.929469i
$310$	−0.305578	+	1.23978i	−0.0173557	+	0.0704147i
$311$	−30.2023	+	7.44419i	−1.71261	+	0.422121i	−0.969114	−	0.246615i	$-0.920682\pi$
$311$	−30.2023	+	7.44419i	−1.71261	+	0.422121i	−0.743500	+	0.668736i	$0.766836\pi$
$312$	9.77815	+	0.247118i	0.553579	+	0.0139903i
$313$	−14.2160	−	3.50392i	−0.803534	−	0.198053i	−0.183901	−	0.982945i	$-0.558873\pi$
$313$	−14.2160	−	3.50392i	−0.803534	−	0.198053i	−0.619633	+	0.784891i	$0.712719\pi$
$314$	−1.43639	+	2.73681i	−0.0810600	+	0.154447i
$315$	−4.15830			−0.234293
$316$	−2.22306			−0.125057
$317$	−5.33847	+	10.1716i	−0.299839	+	0.571295i	−0.988035	−	0.154230i	$-0.950710\pi$
$317$	−5.33847	+	10.1716i	−0.299839	+	0.571295i	0.688196	+	0.725524i	$0.258403\pi$
$318$	5.25794	+	5.93499i	0.294851	+	0.332818i
$319$		−	8.52654i		−	0.477395i
$320$	−2.22311	+	2.50938i	−0.124276	+	0.140278i
$321$	6.01929	−	3.15917i	0.335964	−	0.176327i
$322$	3.28865	+	27.0845i	0.183269	+	1.50936i
$323$	1.16672	+	2.22299i	0.0649179	+	0.123691i
$324$	0.161576	+	1.33070i	0.00897647	+	0.0739279i
$325$	−3.25716	−	14.8163i	−0.180675	−	0.821862i
$326$	0.0451392	−	0.371755i	0.00250003	−	0.0205896i
$327$	10.0381	−	3.80696i	0.555109	−	0.210525i
$328$	5.78738	+	3.03745i	0.319555	+	0.167715i
$329$	14.0167	−	36.9590i	0.772767	−	2.03762i
$330$	−1.06089	−	2.02136i	−0.0584002	−	0.111272i
$331$	0.480429	+	0.915381i	0.0264068	+	0.0503139i	0.898302	−	0.439379i	$-0.144801\pi$
$331$	0.480429	+	0.915381i	0.0264068	+	0.0503139i	−0.871895	+	0.489693i	$0.837109\pi$
$332$	0.803976	+	3.26186i	0.0441239	+	0.179018i
$333$	8.24436	+	1.00105i	0.451788	+	0.0548570i
$334$	−5.09509	−	4.51385i	−0.278791	−	0.246987i
$335$	−5.92100	−	8.57805i	−0.323499	−	0.468669i
$336$	−2.08683	−	0.791429i	−0.113846	−	0.0431760i
$337$	19.1079			1.04087			0.520436	−	0.853901i	$-0.325770\pi$
$337$	19.1079			1.04087			0.520436	+	0.853901i	$0.325770\pi$
$338$	−8.98045	+	5.55077i	−0.488472	+	0.301922i
$339$	14.4564			0.785161
$340$	−5.98060	−	2.26814i	−0.324344	−	0.123007i
$341$	−3.16781	−	4.58936i	−0.171546	−	0.248528i
$342$	−0.284731	−	0.252250i	−0.0153965	−	0.0136401i
$343$	−36.2460	−	4.40106i	−1.95710	−	0.237635i
$344$	−4.78472	−	19.4124i	−0.257975	−	1.04664i
$345$	2.97576	+	5.66983i	0.160209	+	0.305253i
$346$	−0.733183	−	1.39696i	−0.0394162	−	0.0751012i
$347$	10.5410	−	27.7944i	0.565872	−	1.49208i	−0.280694	−	0.959797i	$-0.590564\pi$
$347$	10.5410	−	27.7944i	0.565872	−	1.49208i	0.846566	−	0.532284i	$-0.178666\pi$
$348$	3.20520	+	1.68222i	0.171817	+	0.0901764i
$349$	−14.8370	+	5.62692i	−0.794205	+	0.301202i	−0.718138	−	0.695900i	$-0.755005\pi$
$349$	−14.8370	+	5.62692i	−0.794205	+	0.301202i	−0.0760669	+	0.997103i	$0.524236\pi$
$350$	1.92375	−	15.8435i	0.102829	−	0.846873i
$351$	−2.32198	−	2.75834i	−0.123938	−	0.147229i
$352$	−2.21267	−	18.2230i	−0.117936	−	0.971289i
$353$	−7.58459	−	14.4512i	−0.403687	−	0.769161i	0.595734	−	0.803182i	$-0.296861\pi$
$353$	−7.58459	−	14.4512i	−0.403687	−	0.769161i	−0.999421	+	0.0340206i	$0.989169\pi$
$354$	−0.130341	−	1.07345i	−0.00692754	−	0.0570534i
$355$	11.7784	−	6.18176i	0.625131	−	0.328094i
$356$	−12.2873	+	13.8695i	−0.651228	+	0.735084i
$357$			25.0349i			1.32499i
$358$	−0.223967	−	0.252807i	−0.0118370	−	0.0133612i
$359$	−1.10601	+	2.10733i	−0.0583732	+	0.111221i	−0.912895	−	0.408195i	$-0.866158\pi$
$359$	−1.10601	+	2.10733i	−0.0583732	+	0.111221i	0.854521	+	0.519416i	$0.173851\pi$
$360$	2.41514			0.127289
$361$	18.7806			0.988452
$362$	3.96642	−	7.55738i	0.208470	−	0.397207i
$363$	−1.00025	−	0.246539i	−0.0524994	−	0.0129399i
$364$	22.0485	−	4.84706i	1.15566	−	0.254055i
$365$	−10.9463	+	2.69803i	−0.572957	+	0.141221i
$366$	2.38718	−	9.68516i	0.124780	−	0.506251i
$367$	6.11612	−	16.1269i	0.319259	−	0.841816i	−0.675291	−	0.737552i	$-0.735982\pi$
$367$	6.11612	−	16.1269i	0.319259	−	0.841816i	0.994550	−	0.104265i	$-0.0332489\pi$
$368$	0.414261	+	3.41175i	0.0215949	+	0.177850i
$369$	−0.576584	−	2.33929i	−0.0300158	−	0.121779i
$370$	1.43694	−	5.82990i	0.0747031	−	0.303082i
$371$	37.5315	+	25.9061i	1.94854	+	1.34498i
$372$	2.35016	−	0.285362i	0.121850	−	0.0147953i
$373$	8.95855	+	23.6217i	0.463856	+	1.22309i	0.939225	+	0.343301i	$0.111545\pi$
$373$	8.95855	+	23.6217i	0.463856	+	1.22309i	−0.475369	+	0.879786i	$0.657686\pi$
$374$	−12.1696	+	6.38708i	−0.629273	+	0.330268i
$375$	−1.96168	−	7.95884i	−0.101301	−	0.410993i
$376$	−8.14090	+	21.4658i	−0.419835	+	1.10701i
$377$	−9.69203	+	0.929033i	−0.499165	+	0.0478476i
$378$	−1.34511	−	3.54676i	−0.0691850	−	0.182426i
$379$	−6.22372	+	4.29592i	−0.319691	+	0.220667i	−0.717092	−	0.696978i	$-0.754527\pi$
$379$	−6.22372	+	4.29592i	−0.319691	+	0.220667i	0.397401	+	0.917645i	$0.369912\pi$
$380$	0.418405	−	0.370674i	0.0214637	−	0.0190152i
$381$	10.1986	+	2.51373i	0.522490	+	0.128782i
$382$	14.2339	+	5.39822i	0.728271	+	0.276197i
$383$	1.38148	−	2.63219i	0.0705903	−	0.134499i	−0.847603	−	0.530630i	$-0.821955\pi$
$383$	1.38148	−	2.63219i	0.0705903	−	0.134499i	0.918194	+	0.396132i	$0.129648\pi$
$384$	8.01239	+	3.03870i	0.408880	+	0.155068i
$385$	−8.70668	−	9.82781i	−0.443734	−	0.500872i
$386$	−11.5185	+	10.2045i	−0.586277	+	0.519396i
$387$	−4.18658	+	6.06530i	−0.212816	+	0.308317i
$388$	−14.9931	−	10.3490i	−0.761157	−	0.525389i
$389$	−21.0645	−	11.0555i	−1.06801	−	0.560536i	−0.163307	−	0.986575i	$-0.552216\pi$
$389$	−21.0645	−	11.0555i	−1.06801	−	0.560536i	−0.904705	+	0.426039i	$0.859909\pi$
$390$	−2.18207	+	1.42615i	−0.110493	+	0.0722158i
$391$	34.1351	−	17.9155i	1.72629	−	0.906026i
$392$	39.9030	+	4.84511i	2.01541	+	0.244715i
$393$	−20.4202	+	5.03314i	−1.03007	+	0.253888i
$394$	−7.96683	+	11.5419i	−0.401363	+	0.581475i
$395$	1.21507	−	0.838701i	0.0611367	−	0.0421996i
$396$	−2.80670	+	3.16811i	−0.141042	+	0.159204i
$397$	6.97655	+	0.847106i	0.350143	+	0.0425150i	0.293719	−	0.955892i	$-0.405107\pi$
$397$	6.97655	+	0.847106i	0.350143	+	0.0425150i	0.0564240	+	0.998407i	$0.482030\pi$
$398$	1.79857	−	7.29710i	0.0901544	−	0.365771i
$399$	−1.93725	−	1.01675i	−0.0969840	−	0.0509011i
$400$	0.242329	−	1.99576i	0.0121165	−	0.0997881i
$401$	19.0000	−	2.30701i	0.948814	−	0.115207i	0.368525	−	0.929618i	$-0.379863\pi$
$401$	19.0000	−	2.30701i	0.948814	−	0.115207i	0.580289	+	0.814411i	$0.302940\pi$
$402$	5.40123	−	7.82504i	0.269389	−	0.390277i
$403$	−4.87152	+	4.10086i	−0.242668	+	0.204279i
$404$	−1.93830	−	2.80811i	−0.0964339	−	0.139709i
$405$	−0.590353	−	0.666371i	−0.0293349	−	0.0331122i
$406$	−9.94570	−	2.45140i	−0.493597	−	0.121661i
$407$	14.8962	+	21.5809i	0.738379	+	1.06973i
$408$		−	14.5403i		−	0.719851i
$409$	−24.8103	+	17.1253i	−1.22679	+	0.846792i	−0.992121	−	0.125283i	$-0.960016\pi$
$409$	−24.8103	+	17.1253i	−1.22679	+	0.846792i	−0.234669	+	0.972075i	$0.575401\pi$
$410$	−1.72921	+	0.209964i	−0.0853994	+	0.0103694i
$411$	−4.42422	+	1.67789i	−0.218231	+	0.0827640i
$412$	2.82341	−	23.2528i	0.139099	−	1.14559i
$413$	−2.20540	−	5.81517i	−0.108521	−	0.286146i
$414$	−3.87342	+	4.37219i	−0.190368	+	0.214881i
$415$	−1.67005	−	1.47953i	−0.0819794	−	0.0726274i
$416$	−20.4728	+	4.50066i	−1.00376	+	0.220663i
$417$	0.182622	−	0.161789i	0.00894302	−	0.00792282i
$418$		−	1.20111i		−	0.0587480i
$419$	21.1973	+	18.7792i	1.03556	+	0.917423i	0.996647	−	0.0818195i	$-0.0260731\pi$
$419$	21.1973	+	18.7792i	1.03556	+	0.917423i	0.0389096	+	0.999243i	$0.487612\pi$
$420$	5.41212	−	1.33397i	0.264084	−	0.0650910i
$421$	4.72029	+	3.25818i	0.230053	+	0.158794i	0.677515	−	0.735509i	$-0.263057\pi$
$421$	4.72029	+	3.25818i	0.230053	+	0.158794i	−0.447462	+	0.894303i	$0.647672\pi$
$422$	−6.93899	+	2.63161i	−0.337785	+	0.128105i
$423$	7.91267	−	3.00088i	0.384727	−	0.145908i
$424$	−21.7982	−	15.0462i	−1.05862	−	0.730710i
$425$	−21.8957	+	5.39682i	−1.06210	+	0.261784i
$426$	9.08268	+	8.04655i	0.440057	+	0.389857i
$427$		−	57.3714i		−	2.77640i
$428$	−6.82080	+	6.04270i	−0.329696	+	0.292085i
$429$	1.65734	−	11.2633i	0.0800172	−	0.543795i
$430$	3.98834	+	3.53336i	0.192335	+	0.170394i
$431$	0.649772	−	0.733441i	0.0312984	−	0.0353286i	−0.732653	−	0.680602i	$-0.761718\pi$
$431$	0.649772	−	0.733441i	0.0312984	−	0.0353286i	0.763951	+	0.645274i	$0.223257\pi$
$432$	−0.169439	−	0.446775i	−0.00815216	−	0.0214955i
$433$	0.609548	−	5.02008i	0.0292930	−	0.241250i	−0.970707	−	0.240268i	$-0.922765\pi$
$433$	0.609548	−	5.02008i	0.0292930	−	0.241250i	1.00000		0.000981232i	$-0.000312336\pi$
$434$	−6.26397	+	2.37561i	−0.300680	+	0.114033i
$435$	−2.38654	+	0.289779i	−0.114426	+	0.0138938i
$436$	−11.8436	+	8.17504i	−0.567205	+	0.391514i
$437$			3.36905i			0.161163i
$438$	−5.84212	−	8.46378i	−0.279147	−	0.404415i
$439$	−31.9176	−	7.86697i	−1.52334	−	0.375470i	−0.613254	−	0.789886i	$-0.710140\pi$
$439$	−31.9176	−	7.86697i	−1.52334	−	0.375470i	−0.910088	+	0.414416i	$0.863986\pi$
$440$	5.05684	+	5.70799i	0.241075	+	0.272118i
$441$	−8.41702	−	12.1942i	−0.400810	−	0.580674i
$442$	8.58610	+	13.1371i	0.408399	+	0.624868i
$443$	8.47062	−	12.2718i	0.402451	−	0.583052i	−0.568394	−	0.822756i	$-0.692435\pi$
$443$	8.47062	−	12.2718i	0.402451	−	0.583052i	0.970846	+	0.239705i	$0.0770506\pi$
$444$	−11.0514	+	1.34188i	−0.524474	+	0.0636827i
$445$	1.48334	−	12.2164i	0.0703173	−	0.579115i
$446$	18.0380	+	9.46709i	0.854126	+	0.448280i
$447$	3.00394	−	12.1875i	0.142082	−	0.576448i
$448$	−17.4610	−	2.12015i	−0.824955	−	0.100168i
$449$	3.60235	−	4.06621i	0.170005	−	0.191896i	−0.657333	−	0.753600i	$-0.728315\pi$
$449$	3.60235	−	4.06621i	0.170005	−	0.191896i	0.827338	+	0.561704i	$0.189854\pi$
$450$	2.81206	−	1.94102i	0.132562	−	0.0915007i
$451$	4.32149	−	6.26075i	0.203491	−	0.294807i
$452$	−18.8153	+	4.63755i	−0.884997	+	0.218132i
$453$	−16.4548	−	1.99797i	−0.773114	−	0.0938730i
$454$	6.94809	−	3.64664i	0.326090	−	0.171145i
$455$	−10.2225	+	10.9676i	−0.479239	+	0.514170i
$456$	1.12516	+	0.590527i	0.0526903	+	0.0276540i
$457$	12.5596	+	8.66929i	0.587515	+	0.405532i	0.824402	−	0.566005i	$-0.191512\pi$
$457$	12.5596	+	8.66929i	0.587515	+	0.405532i	−0.236887	+	0.971537i	$0.576127\pi$
$458$	−4.23587	+	6.13672i	−0.197929	+	0.286750i
$459$	−4.01187	+	3.55421i	−0.187258	+	0.165896i
$460$	−5.69188	−	6.42481i	−0.265385	−	0.299558i
$461$	−24.4922	−	9.28868i	−1.14072	−	0.432617i	−0.289368	−	0.957218i	$-0.593445\pi$
$461$	−24.4922	−	9.28868i	−1.14072	−	0.432617i	−0.851348	+	0.524601i	$0.824215\pi$
$462$	5.56610	−	10.6053i	0.258958	−	0.493404i
$463$	11.3406	+	4.30094i	0.527044	+	0.199881i	0.603752	−	0.797172i	$-0.293672\pi$
$463$	11.3406	+	4.30094i	0.527044	+	0.199881i	−0.0767080	+	0.997054i	$0.524441\pi$
$464$	−1.25283	−	0.308795i	−0.0581612	−	0.0143354i
$465$	−1.17688	+	1.04263i	−0.0545766	+	0.0483507i
$466$	−0.0161836	+	0.0111707i	−0.000749690	+	0.000517473i
$467$	−2.78167	−	7.33465i	−0.128720	−	0.339407i	0.855127	−	0.518419i	$-0.173479\pi$
$467$	−2.78167	−	7.33465i	−0.128720	−	0.339407i	−0.983847	+	0.179012i	$0.942710\pi$
$468$	3.90697	+	2.84516i	0.180600	+	0.131518i
$469$	19.3920	−	51.1324i	0.895438	−	2.36108i
$470$	−1.46423	−	5.94060i	−0.0675397	−	0.274019i
$471$	−3.36999	+	1.76871i	−0.155281	+	0.0814977i
$472$	1.28090	+	3.37745i	0.0589581	+	0.155460i
$473$	−23.1008	+	2.80494i	−1.06218	+	0.128971i
$474$	1.10840	+	0.765077i	0.0509107	+	0.0351411i
$475$	0.471640	−	1.91352i	0.0216403	−	0.0877982i
$476$	−8.03113	−	32.5836i	−0.368106	−	1.49347i
$477$	1.17686	+	9.69234i	0.0538848	+	0.443782i
$478$	0.125197	−	0.330118i	0.00572640	−	0.0150993i
$479$	−1.76979	+	7.18030i	−0.0808636	+	0.328076i	−0.997416	−	0.0718373i	$-0.977114\pi$
$479$	−1.76979	+	7.18030i	−0.0808636	+	0.328076i	0.916553	+	0.399914i	$0.130960\pi$
$480$	−5.02534	+	1.23863i	−0.229374	+	0.0565357i
$481$	22.9077	−	19.2838i	1.04450	−	0.879266i
$482$	−12.0891	−	2.97969i	−0.550643	−	0.135721i
$483$	−15.6127	+	29.7475i	−0.710401	+	1.35356i
$484$	1.38094			0.0627698
$485$	12.0992			0.549398
$486$	0.377407	−	0.719089i	0.0171195	−	0.0326185i
$487$	−2.17797	−	2.45842i	−0.0986933	−	0.111402i	0.697089	−	0.716985i	$-0.254478\pi$
$487$	−2.17797	−	2.45842i	−0.0986933	−	0.111402i	−0.795782	+	0.605583i	$0.792940\pi$
$488$			33.3213i			1.50838i
$489$	0.305783	−	0.345158i	0.0138280	−	0.0156086i
$490$	−9.48551	+	4.97838i	−0.428512	+	0.224900i
$491$	−2.86472	−	23.5931i	−0.129283	−	1.06474i	−0.902527	−	0.430632i	$-0.858291\pi$
$491$	−2.86472	−	23.5931i	−0.129283	−	1.06474i	0.773244	−	0.634108i	$-0.218633\pi$
$492$	1.50088	+	2.85968i	0.0676647	+	0.128924i
$493$	1.74461	+	14.3681i	0.0785731	+	0.647108i
$494$	−1.36528	+	0.130870i	−0.0614270	+	0.00588811i
$495$	0.338829	−	2.79051i	0.0152292	−	0.125424i
$496$	−0.789053	+	0.299248i	−0.0354295	+	0.0134367i
$497$	61.7966	+	32.4334i	2.77196	+	1.45484i
$498$	0.721727	−	1.90304i	0.0323414	−	0.0852772i
$499$	−12.6684	−	24.1377i	−0.567117	−	1.08055i	−0.985081	−	0.172088i	$-0.944948\pi$
$499$	−12.6684	−	24.1377i	−0.567117	−	1.08055i	0.417964	−	0.908464i	$-0.362744\pi$
$500$	5.10634	+	9.72932i	0.228362	+	0.435108i
$501$	−2.00590	−	8.13825i	−0.0896170	−	0.363590i
$502$	9.91091	+	1.20340i	0.442346	+	0.0537105i
$503$	15.6124	+	13.8314i	0.696123	+	0.616711i	0.935129	−	0.354307i	$-0.115283\pi$
$503$	15.6124	+	13.8314i	0.696123	+	0.616711i	−0.239006	+	0.971018i	$0.576822\pi$
$504$	7.19812	+	10.4283i	0.320630	+	0.464512i
$505$	2.11885	+	0.803575i	0.0942877	+	0.0357586i
$506$	−18.4435			−0.819916
$507$	−12.9834	−	0.656665i	−0.576613	−	0.0291635i
$508$	−14.0801			−0.624705
$509$	−3.64842	−	1.38366i	−0.161713	−	0.0613298i	0.272420	−	0.962178i	$-0.412176\pi$
$509$	−3.64842	−	1.38366i	−0.161713	−	0.0613298i	−0.434133	+	0.900849i	$0.642945\pi$
$510$	2.20130	+	3.18914i	0.0974754	+	0.141218i
$511$	−44.2744	−	39.2237i	−1.95859	−	1.73516i
$512$	−5.33132	−	0.647339i	−0.235613	−	0.0286086i
$513$	−0.112097	−	0.454794i	−0.00494919	−	0.0200797i
$514$	3.22618	+	6.14698i	0.142301	+	0.271132i
$515$	7.22948	+	13.7746i	0.318569	+	0.606983i
$516$	3.50320	−	9.23718i	0.154220	−	0.406644i
$517$	23.6600	+	12.4177i	1.04057	+	0.546131i
$518$	29.4555	−	11.1710i	1.29420	−	0.490826i
$519$	0.234165	−	1.92852i	0.0102787	−	0.0846527i
$520$	5.93723	−	6.36999i	0.260365	−	0.279342i
$521$	−1.08986	−	8.97580i	−0.0477476	−	0.393237i	−0.996917	−	0.0784696i	$-0.974997\pi$
$521$	−1.08986	−	8.97580i	−0.0477476	−	0.393237i	0.949169	−	0.314767i	$-0.101926\pi$
$522$	−1.01915	−	1.94183i	−0.0446071	−	0.0849917i
$523$	0.603472	+	4.97004i	0.0263880	+	0.217325i	0.999938	−	0.0111501i	$-0.00354926\pi$
$523$	0.603472	+	4.97004i	0.0263880	+	0.217325i	−0.973550	+	0.228475i	$0.926626\pi$
$524$	24.9628	−	13.1015i	1.09051	−	0.572342i
$525$	13.0319	−	14.7100i	0.568760	−	0.641997i
$526$		−	2.61828i		−	0.114162i
$527$	6.27712	+	7.08541i	0.273436	+	0.308645i
$528$	0.701145	−	1.33592i	0.0305134	−	0.0581384i
$529$	28.7334			1.24928
$530$	7.05894			0.306621
$531$	0.618786	−	1.17900i	0.0268530	−	0.0511641i
$532$	2.84755	+	0.701859i	0.123457	+	0.0304294i
$533$	−7.58739	−	4.23003i	−0.328646	−	0.183223i
$534$	10.8997	−	2.68653i	0.471675	−	0.116257i
$535$	1.44833	−	5.87610i	0.0626167	−	0.254046i
$536$	−11.2628	+	29.6977i	−0.486481	+	1.28274i
$537$	−0.0501296	−	0.412854i	−0.00216325	−	0.0178160i
$538$	3.20306	+	12.9953i	0.138094	+	0.560269i
$539$	11.1963	−	45.4252i	0.482259	−	1.95660i
$540$	0.982128	+	0.677914i	0.0422640	+	0.0291728i
$541$	−0.849435	+	0.103140i	−0.0365201	+	0.00443434i	−0.138776	−	0.990324i	$-0.544317\pi$
$541$	−0.849435	+	0.103140i	−0.0365201	+	0.00443434i	0.102256	+	0.994758i	$0.467394\pi$
$542$	4.83825	+	12.7574i	0.207821	+	0.547978i
$543$	9.30584	−	4.88408i	0.399352	−	0.209596i
$544$	7.45718	+	30.2550i	0.319724	+	1.29717i
$545$	3.38919	−	8.93656i	0.145177	−	0.382800i
$546$	−12.6614	−	5.17140i	−0.541859	−	0.221315i
$547$	2.19813	+	5.79598i	0.0939851	+	0.247818i	0.973762	−	0.227568i	$-0.0730775\pi$
$547$	2.19813	+	5.79598i	0.0939851	+	0.247818i	−0.879777	+	0.475386i	$0.842308\pi$
$548$	5.21997	−	3.60308i	0.222986	−	0.153916i
$549$	9.19382	−	8.14502i	0.392383	−	0.347621i
$550$	10.4754	+	2.58195i	0.446671	+	0.110095i
$551$	−1.18269	−	0.448535i	−0.0503842	−	0.0191082i
$552$	9.06783	−	17.2773i	0.385953	−	0.735371i
$553$	7.24283	+	2.74684i	0.307997	+	0.116808i
$554$	−5.18860	−	5.85672i	−0.220442	−	0.248828i
$555$	5.53415	−	4.90283i	0.234911	−	0.208113i
$556$	−0.185785	+	0.269156i	−0.00787904	+	0.0114148i
$557$	−30.6182	−	21.1342i	−1.29733	−	0.895484i	−0.299060	−	0.954234i	$-0.596673\pi$
$557$	−30.6182	−	21.1342i	−1.29733	−	0.895484i	−0.998273	+	0.0587499i	$0.981289\pi$
$558$	−1.26999	−	0.666542i	−0.0537629	−	0.0282170i
$559$	5.70536	+	25.9528i	0.241311	+	1.09769i
$560$	−1.75935	+	0.923378i	−0.0743461	+	0.0390198i
$561$	−16.8002	−	2.03991i	−0.709305	−	0.0861253i
$562$	−5.29647	+	1.30546i	−0.223418	+	0.0550677i
$563$	−4.75546	+	6.88947i	−0.200419	+	0.290357i	−0.910287	−	0.413978i	$-0.864139\pi$
$563$	−4.75546	+	6.88947i	−0.200419	+	0.290357i	0.709868	+	0.704335i	$0.248754\pi$
$564$	−9.33586	+	6.44408i	−0.393111	+	0.271345i
$565$	8.53435	−	9.63329i	0.359043	−	0.405276i
$566$	11.2957	+	1.37155i	0.474795	+	0.0576505i
$567$	1.11781	−	4.53514i	0.0469437	−	0.190458i
$568$	−35.8915	−	18.8373i	−1.50597	−	0.790395i
$569$	0.722196	−	5.94782i	0.0302760	−	0.249346i	−0.969711	−	0.244255i	$-0.921457\pi$
$569$	0.722196	−	5.94782i	0.0302760	−	0.249346i	0.999987	−	0.00509043i	$-0.00162034\pi$
$570$	−0.336184	+	0.0408201i	−0.0140812	+	0.00170977i
$571$	−14.9634	+	21.6782i	−0.626198	+	0.907204i	−0.999792	−	0.0203881i	$-0.993510\pi$
$571$	−14.9634	+	21.6782i	−0.626198	+	0.907204i	0.373594	+	0.927592i	$0.378125\pi$
$572$	1.45614	+	15.1911i	0.0608845	+	0.635170i
$573$	10.6485	+	15.4270i	0.444847	+	0.644472i
$574$	−6.06036	−	6.84073i	−0.252955	−	0.285527i
$575$	−29.3830	−	7.24226i	−1.22536	−	0.302023i
$576$	−2.13918	−	3.09914i	−0.0891326	−	0.129131i
$577$		−	7.43539i		−	0.309539i	−0.987951	−	0.154770i	$-0.950536\pi$
$577$		−	7.43539i		−	0.309539i	0.987951	−	0.154770i	$-0.0494636\pi$
$578$	7.83815	−	5.41028i	0.326024	−	0.225038i
$579$	−18.8107	+	2.28403i	−0.781746	+	0.0949212i
$580$	3.01318	−	1.14275i	0.125115	−	0.0474500i
$581$	1.41101	−	11.6207i	0.0585385	−	0.482108i
$582$	3.91381	+	10.3199i	0.162233	+	0.427773i
$583$	−20.4430	+	23.0753i	−0.846661	+	0.955683i
$584$	25.7146	+	22.7811i	1.06408	+	0.942689i
$585$	−3.20886	−	0.0810959i	−0.132670	−	0.00335290i
$586$	−4.02100	+	3.56229i	−0.166106	+	0.147157i
$587$		−	39.4448i		−	1.62806i	−0.580823	−	0.814030i	$-0.697269\pi$
$587$		−	39.4448i		−	1.62806i	0.580823	−	0.814030i	$-0.302731\pi$
$588$	14.8668	+	13.1708i	0.613096	+	0.543156i
$589$	−0.803217	+	0.197975i	−0.0330960	+	0.00815742i
$590$	−0.792265	−	0.546861i	−0.0326170	−	0.0225139i
$591$	−16.1470	+	6.12374i	−0.664198	+	0.251897i
$592$	3.71043	−	1.40718i	0.152498	−	0.0578347i
$593$	−17.2358	−	11.8970i	−0.707790	−	0.488552i	0.158966	−	0.987284i	$-0.449184\pi$
$593$	−17.2358	−	11.8970i	−0.707790	−	0.488552i	−0.866756	+	0.498732i	$0.833799\pi$
$594$	2.48973	−	0.613663i	0.102155	−	0.0251789i
$595$	16.6826	+	14.7795i	0.683918	+	0.605898i
$596$			16.8259i			0.689218i
$597$	6.92691	−	6.13671i	0.283500	−	0.251159i
$598$	2.00957	+	20.9646i	0.0821774	+	0.857306i
$599$	−33.4424	−	29.6274i	−1.36642	−	1.21054i	−0.954094	−	0.299506i	$-0.903178\pi$
$599$	−33.4424	−	29.6274i	−1.36642	−	1.21054i	−0.412326	−	0.911036i	$-0.635283\pi$
$600$	−7.56894	+	8.54356i	−0.309001	+	0.348790i
$601$	−5.01348	−	13.2195i	−0.204504	−	0.539233i	0.793048	−	0.609159i	$-0.208493\pi$
$601$	−5.01348	−	13.2195i	−0.204504	−	0.539233i	−0.997552	+	0.0699259i	$0.977724\pi$
$602$	−3.36972	+	27.7521i	−0.137339	+	1.13109i
$603$	10.9471	−	4.15168i	0.445800	−	0.169070i
$604$	22.0573	−	2.67824i	0.897497	−	0.108976i
$605$	−0.754785	+	0.520991i	−0.0306864	+	0.0211813i
$606$			2.06718i			0.0839736i
$607$	−11.2389	−	16.2824i	−0.456173	−	0.660881i	0.525645	−	0.850704i	$-0.323824\pi$
$607$	−11.2389	−	16.2824i	−0.456173	−	0.660881i	−0.981818	+	0.189823i	$0.939209\pi$
$608$	−2.64405	−	0.651700i	−0.107230	−	0.0264299i
$609$	−8.36413	−	9.44115i	−0.338932	−	0.382575i
$610$	−5.04463	−	7.30841i	−0.204251	−	0.295909i
$611$	11.5372	−	28.2471i	0.466743	−	1.14275i
$612$	4.08137	−	5.91288i	0.164980	−	0.239014i
$613$	−18.9127	+	2.29641i	−0.763875	+	0.0927512i	−0.493196	−	0.869918i	$-0.664171\pi$
$613$	−18.9127	+	2.29641i	−0.763875	+	0.0927512i	−0.270679	+	0.962670i	$0.587248\pi$
$614$	0.550724	−	4.53562i	0.0222254	−	0.183043i
$615$	−1.89922	−	0.996790i	−0.0765841	−	0.0401945i
$616$	−9.57494	+	38.8471i	−0.385785	+	1.56519i
$617$	−15.0285	−	1.82479i	−0.605025	−	0.0734634i	−0.187709	−	0.982225i	$-0.560106\pi$
$617$	−15.0285	−	1.82479i	−0.605025	−	0.0734634i	−0.417316	+	0.908761i	$0.637029\pi$
$618$	−9.41032	+	10.6221i	−0.378539	+	0.427282i
$619$	−16.1176	+	11.1252i	−0.647822	+	0.447159i	−0.846127	−	0.532981i	$-0.821072\pi$
$619$	−16.1176	+	11.1252i	−0.647822	+	0.447159i	0.198305	+	0.980140i	$0.436456\pi$
$620$	1.19727	−	1.73454i	0.0480835	−	0.0696610i
$621$	−6.98359	+	1.72130i	−0.280242	+	0.0690734i
$622$	−25.0775	−	3.04496i	−1.00551	−	0.122092i
$623$	57.1702	−	30.0052i	2.29047	−	1.20213i
$624$	−1.59492	−	0.651425i	−0.0638480	−	0.0260779i
$625$	12.1659	+	6.38514i	0.486635	+	0.255406i
$626$	−9.78566	−	6.75455i	−0.391114	−	0.269966i
$627$	0.840163	−	1.21719i	0.0335529	−	0.0486097i
$628$	3.81873	−	3.38310i	0.152384	−	0.135000i
$629$	−29.5174	−	33.3182i	−1.17694	−	1.32849i
$630$	−3.15755	−	1.19750i	−0.125800	−	0.0477095i
$631$	11.5266	−	21.9620i	0.458865	−	0.874294i	−0.540590	−	0.841286i	$-0.681799\pi$
$631$	11.5266	−	21.9620i	0.458865	−	0.874294i	0.999455	−	0.0330079i	$-0.0105087\pi$
$632$	−4.20663	−	1.59537i	−0.167331	−	0.0634602i
$633$	−8.87269	−	2.18692i	−0.352658	−	0.0869223i
$634$	−6.98291	+	6.18632i	−0.277327	+	0.245690i
$635$	7.69585	−	5.31206i	0.305401	−	0.210803i
$636$	−4.64098	−	12.2373i	−0.184027	−	0.485239i
$637$	−52.8543	−	7.77730i	−2.09416	−	0.308148i
$638$	2.45546	−	6.47452i	0.0972126	−	0.256329i
$639$	3.57579	+	14.5075i	0.141456	+	0.573909i
$640$	6.75503	−	3.54531i	0.267016	−	0.140141i
$641$	−1.52504	−	4.02121i	−0.0602356	−	0.158828i	0.901520	−	0.432738i	$-0.142452\pi$
$641$	−1.52504	−	4.02121i	−0.0602356	−	0.158828i	−0.961755	+	0.273909i	$0.911683\pi$
$642$	5.48044	−	0.665446i	0.216296	−	0.0262631i
$643$	10.0636	+	6.94638i	0.396869	+	0.273939i	0.749739	−	0.661734i	$-0.230179\pi$
$643$	10.0636	+	6.94638i	0.396869	+	0.273939i	−0.352871	+	0.935672i	$0.614794\pi$
$644$	10.7774	−	43.7255i	0.424688	−	1.72303i
$645$	1.57018	+	6.37048i	0.0618259	+	0.250837i
$646$	0.245757	+	2.02399i	0.00966918	+	0.0796328i
$647$	−7.97527	+	21.0290i	−0.313540	+	0.826737i	0.681909	+	0.731437i	$0.261150\pi$
$647$	−7.97527	+	21.0290i	−0.313540	+	0.826737i	−0.995449	+	0.0952998i	$0.969619\pi$
$648$	−0.649224	+	2.63401i	−0.0255039	+	0.103474i
$649$	4.08209	−	1.00615i	0.160236	−	0.0394947i
$650$	1.79350	−	12.1886i	0.0703469	−	0.478075i
$651$	−8.00955	−	1.97418i	−0.313919	−	0.0773741i
$652$	−0.287258	+	0.547325i	−0.0112499	+	0.0214349i
$653$	−45.6432			−1.78616			−0.893078	−	0.449903i	$-0.851459\pi$
$653$	−45.6432			−1.78616			−0.893078	+	0.449903i	$0.851459\pi$
$654$	8.71864			0.340926
$655$	−8.70121	+	16.5788i	−0.339985	+	0.647786i
$656$	−0.763405	−	0.861706i	−0.0298060	−	0.0336440i
$657$		−	12.6636i		−	0.494054i
$658$	21.2868	−	24.0279i	0.829847	−	0.936703i
$659$	−37.6655	+	19.7684i	−1.46724	+	0.770067i	−0.993845	−	0.110783i	$-0.964664\pi$
$659$	−37.6655	+	19.7684i	−1.46724	+	0.770067i	−0.473395	+	0.880850i	$0.656972\pi$
$660$	0.454192	+	3.74061i	0.0176794	+	0.145603i
$661$	2.05178	+	3.90934i	0.0798050	+	0.152056i	0.922088	−	0.386979i	$-0.126481\pi$
$661$	2.05178	+	3.90934i	0.0798050	+	0.152056i	−0.842284	+	0.539035i	$0.818789\pi$
$662$	0.101197	+	0.833436i	0.00393315	+	0.0323924i
$663$	−0.488236	+	19.3189i	−0.0189615	+	0.750284i
$664$	−0.819513	+	6.74930i	−0.0318033	+	0.261923i
$665$	−1.82119	+	0.690688i	−0.0706229	+	0.0267837i
$666$	5.97197	+	3.13433i	0.231409	+	0.121453i
$667$	−6.88746	+	18.1607i	−0.266684	+	0.703187i
$668$	5.22145	+	9.94864i	0.202024	+	0.384925i
$669$	11.6574	+	22.2113i	0.450701	+	0.858738i
$670$	−2.02574	−	8.21875i	−0.0782612	−	0.317518i
$671$	38.5003	+	4.67478i	1.48629	+	0.180468i
$672$	−20.3259	−	18.0072i	−0.784089	−	0.694642i
$673$	3.59453	+	5.20757i	0.138559	+	0.200737i	0.886120	−	0.463456i	$-0.153391\pi$
$673$	3.59453	+	5.20757i	0.138559	+	0.200737i	−0.747561	+	0.664193i	$0.768775\pi$
$674$	14.5093	+	5.50265i	0.558878	+	0.211954i
$675$	4.20743			0.161944
$676$	17.1089	−	3.31037i	0.658033	−	0.127322i
$677$	−39.7137			−1.52632			−0.763160	−	0.646209i	$-0.776353\pi$
$677$	−39.7137			−1.52632			−0.763160	+	0.646209i	$0.776353\pi$
$678$	10.9772	+	4.16312i	0.421579	+	0.159884i
$679$	36.0608	+	52.2431i	1.38389	+	2.00491i
$680$	−9.68922	−	8.58390i	−0.371565	−	0.329177i
$681$	9.59191	+	1.16467i	0.367563	+	0.0446302i
$682$	−1.08380	−	4.39713i	−0.0415007	−	0.168375i
$683$	12.9833	+	24.7376i	0.496792	+	0.946559i	0.996754	+	0.0805110i	$0.0256552\pi$
$683$	12.9833	+	24.7376i	0.496792	+	0.946559i	−0.499961	+	0.866048i	$0.666652\pi$
$684$	0.291793	+	0.555966i	0.0111570	+	0.0212579i
$685$	−1.49376	+	3.93871i	−0.0570735	+	0.150491i
$686$	−26.2555	−	13.7799i	−1.00244	−	0.526121i
$687$	−8.58516	+	3.25592i	−0.327544	+	0.124221i
$688$	−0.424473	+	3.49585i	−0.0161829	+	0.133278i
$689$	28.4569	+	20.7231i	1.08412	+	0.789486i
$690$	0.626813	+	5.16227i	0.0238624	+	0.196524i
$691$	8.07393	+	15.3836i	0.307147	+	0.585219i	0.989284	−	0.146005i	$-0.0466416\pi$
$691$	8.07393	+	15.3836i	0.307147	+	0.585219i	−0.682137	+	0.731224i	$0.738949\pi$
$692$	0.313892	+	2.58514i	0.0119324	+	0.0982721i
$693$	13.0589	−	6.85386i	0.496068	−	0.260357i
$694$	16.0084	−	18.0697i	0.607670	−	0.685918i
$695$		−	0.217206i		−	0.00823909i
$696$	4.85788	+	5.48341i	0.184137	+	0.207848i
$697$	−6.00116	+	11.4343i	−0.227310	+	0.433103i
$698$	−12.8867			−0.487769
$699$	−0.0242141			−0.000915860
$700$	−12.2424	+	23.3260i	−0.462721	+	0.881641i
$701$	−26.4274	−	6.51378i	−0.998150	−	0.246022i	−0.293794	−	0.955869i	$-0.594918\pi$
$701$	−26.4274	−	6.51378i	−0.998150	−	0.246022i	−0.704356	+	0.709847i	$0.748764\pi$
$702$	−0.968820	−	2.76319i	−0.0365658	−	0.104290i
$703$	3.77703	−	0.930954i	0.142453	−	0.0351116i
$704$	2.84554	−	11.5448i	0.107245	−	0.435111i
$705$	2.67157	−	7.04435i	0.100617	−	0.265306i
$706$	−1.59762	−	13.1575i	−0.0601271	−	0.495191i
$707$	2.84533	+	11.5439i	0.107010	+	0.434155i
$708$	−0.427146	+	1.73300i	−0.0160531	+	0.0651301i
$709$	−21.1681	−	14.6113i	−0.794983	−	0.548737i	0.0999212	−	0.994995i	$-0.468141\pi$
$709$	−21.1681	−	14.6113i	−0.794983	−	0.548737i	−0.894904	+	0.446258i	$0.852756\pi$
$710$	10.7240	−	1.30213i	0.402463	−	0.0488679i
$711$	0.588080	+	1.55064i	0.0220547	+	0.0581535i
$712$	−33.2044	+	17.4270i	−1.24439	+	0.653105i
$713$	3.04000	+	12.3338i	0.113849	+	0.461904i
$714$	−7.20953	+	19.0100i	−0.269810	+	0.711430i
$715$	−6.52708	−	7.75370i	−0.244099	−	0.289972i
$716$	0.197687	+	0.521258i	0.00738792	+	0.0194803i
$717$	0.357789	−	0.246964i	0.0133619	−	0.00922303i
$718$	−1.44670	+	1.28167i	−0.0539905	+	0.0478314i
$719$	24.9363	+	6.14625i	0.929967	+	0.229216i	0.675071	−	0.737752i	$-0.264113\pi$
$719$	24.9363	+	6.14625i	0.929967	+	0.229216i	0.254895	+	0.966969i	$0.417959\pi$
$720$	−0.397747	−	0.150845i	−0.0148231	−	0.00562168i
$721$	−37.9304	+	72.2703i	−1.41260	+	2.69149i
$722$	14.2608	+	5.40841i	0.530732	+	0.201280i
$723$	−10.1667	−	11.4758i	−0.378102	−	0.426789i
$724$	−10.5450	+	9.34203i	−0.391901	+	0.347194i
$725$	6.45423	−	9.35056i	0.239704	−	0.347271i
$726$	−0.688527	−	0.475256i	−0.0255536	−	0.0176384i
$727$	35.6093	+	18.6892i	1.32068	+	0.693145i	0.969943	−	0.243330i	$-0.0782399\pi$
$727$	35.6093	+	18.6892i	1.32068	+	0.693145i	0.350734	+	0.936475i	$0.385932\pi$
$728$	45.2003	+	6.65105i	1.67524	+	0.246504i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	−9.08893	−	1.10360i	−0.336396	−	0.0408459i
$731$	38.3534	−	9.45326i	1.41855	−	0.349641i
$732$	−9.35309	+	13.5503i	−0.345700	+	0.500833i
$733$	41.0142	−	28.3101i	1.51490	−	1.04566i	0.535303	−	0.844660i	$-0.320197\pi$
$733$	41.0142	−	28.3101i	1.51490	−	1.04566i	0.979592	−	0.200997i	$-0.0644180\pi$
$734$	9.28839	−	10.4844i	0.342841	−	0.386987i
$735$	−13.0948	−	1.59000i	−0.483010	−	0.0586481i
$736$	−10.0072	+	40.6006i	−0.368869	+	1.49656i
$737$	32.7333	+	17.1798i	1.20575	+	0.632825i
$738$	0.235845	−	1.94236i	0.00868157	−	0.0714991i
$739$	16.1981	−	1.96680i	0.595855	−	0.0723499i	0.182947	−	0.983123i	$-0.441436\pi$
$739$	16.1981	−	1.96680i	0.595855	−	0.0723499i	0.412908	+	0.910773i	$0.364513\pi$
$740$	−5.63001	+	8.15648i	−0.206963	+	0.299838i
$741$	−1.47511	−	0.822383i	−0.0541893	−	0.0302110i
$742$	21.0386	+	30.4797i	0.772352	+	1.11895i
$743$	30.5986	+	34.5387i	1.12256	+	1.26710i	0.959876	+	0.280424i	$0.0904751\pi$
$743$	30.5986	+	34.5387i	1.12256	+	1.26710i	0.162679	+	0.986679i	$0.447986\pi$
$744$	4.65194	+	1.14660i	0.170549	+	0.0420364i
$745$	−6.34799	−	9.19665i	−0.232572	−	0.336939i
$746$			20.5167i			0.751171i
$747$	2.06255	−	1.42367i	0.0754647	−	0.0520895i
$748$	22.5203	−	2.73446i	0.823423	−	0.0999816i
$749$	29.6889	−	11.2595i	1.08481	−	0.411414i
$750$	0.802400	−	6.60836i	0.0292995	−	0.241303i
$751$	6.70452	+	17.6784i	0.244651	+	0.645093i	0.999947	−	0.0102914i	$-0.00327591\pi$
$751$	6.70452	+	17.6784i	0.244651	+	0.645093i	−0.755296	+	0.655384i	$0.772507\pi$
$752$	2.68144	−	3.02672i	0.0977819	−	0.110373i
$753$	9.20183	+	8.15211i	0.335333	+	0.297079i
$754$	−7.62706	−	2.08565i	−0.277761	−	0.0759548i
$755$	−11.0455	+	9.78548i	−0.401988	+	0.356130i
$756$			6.26118i			0.227717i
$757$	−5.55605	−	4.92223i	−0.201938	−	0.178901i	0.556093	−	0.831120i	$-0.312300\pi$
$757$	−5.55605	−	4.92223i	−0.201938	−	0.178901i	−0.758031	+	0.652219i	$0.773838\pi$
$758$	−5.96303	+	1.46976i	−0.216587	+	0.0533839i
$759$	−18.6905	−	12.9011i	−0.678421	−	0.468280i
$760$	1.05775	−	0.401151i	0.0383686	−	0.0145513i
$761$	1.09818	−	0.416485i	0.0398090	−	0.0150976i	−0.334620	−	0.942353i	$-0.608608\pi$
$761$	1.09818	−	0.416485i	0.0398090	−	0.0150976i	0.374429	+	0.927256i	$0.377839\pi$
$762$	7.02028	+	4.84575i	0.254318	+	0.175543i
$763$	48.6882	−	12.0006i	1.76263	−	0.434450i
$764$	−18.8082	−	16.6626i	−0.680457	−	0.602832i
$765$			4.77163i			0.172519i
$766$	1.80702	−	1.60088i	0.0652904	−	0.0578422i
$767$	−1.58845	−	4.53045i	−0.0573556	−	0.163585i
$768$	10.8464	+	9.60908i	0.391386	+	0.346738i
$769$	3.26336	−	3.68357i	0.117680	−	0.132833i	−0.686718	−	0.726924i	$-0.740949\pi$
$769$	3.26336	−	3.68357i	0.117680	−	0.132833i	0.804398	+	0.594091i	$0.202488\pi$
$770$	−3.78111	−	9.96996i	−0.136262	−	0.359292i
$771$	−1.03038	+	8.48596i	−0.0371083	+	0.305615i
$772$	23.7499	−	9.00714i	0.854777	−	0.324174i
$773$	47.3142	−	5.74499i	1.70177	−	0.206633i	0.788800	−	0.614650i	$-0.210703\pi$
$773$	47.3142	−	5.74499i	1.70177	−	0.206633i	0.912974	+	0.408017i	$0.133780\pi$
$774$	−4.92570	+	3.39997i	−0.177051	+	0.122209i
$775$		−	7.43079i		−	0.266922i
$776$	−20.9441	−	30.3427i	−0.751849	−	1.08924i
$777$	37.6639	+	9.28333i	1.35119	+	0.333037i
$778$	−12.8113	−	14.4610i	−0.459307	−	0.518451i
$779$	−0.641079	−	0.928763i	−0.0229690	−	0.0332764i
$780$	4.20242	−	0.923844i	0.150471	−	0.0330789i
$781$	−26.8004	+	38.8271i	−0.958995	+	1.38934i
$782$	31.0793	−	3.77372i	1.11140	−	0.134948i
$783$	0.325498	−	2.68072i	0.0116324	−	0.0958010i
$784$	−6.26898	−	3.29022i	−0.223892	−	0.117508i
$785$	−0.810868	+	3.28982i	−0.0289411	+	0.117419i
$786$	−16.9553	−	2.05874i	−0.604775	−	0.0734330i
$787$	−27.4475	+	30.9818i	−0.978398	+	1.10438i	0.0161259	+	0.999870i	$0.494867\pi$
$787$	−27.4475	+	30.9818i	−0.978398	+	1.10438i	−0.994524	+	0.104513i	$0.966672\pi$
$788$	19.0512	−	13.1501i	0.678671	−	0.468453i
$789$	1.83146	−	2.65333i	0.0652018	−	0.0944611i
$790$	1.16417	−	0.286943i	0.0414195	−	0.0102090i
$791$	67.0314	+	8.13909i	2.38336	+	0.289393i
$792$	−7.58463	+	3.98072i	−0.269508	+	0.141449i
$793$	1.11887	−	44.2722i	0.0397322	−	1.57215i
$794$	5.05360	+	2.65233i	0.179346	+	0.0941278i
$795$	7.15345	+	4.93767i	0.253707	+	0.175121i
$796$	−7.04691	+	10.2092i	−0.249771	+	0.361856i
$797$	−11.6687	+	10.3376i	−0.413326	+	0.366175i	−0.844010	−	0.536328i	$-0.819811\pi$
$797$	−11.6687	+	10.3376i	−0.413326	+	0.366175i	0.430683	+	0.902503i	$0.358273\pi$
$798$	−1.17823	−	1.32994i	−0.0417088	−	0.0470795i
$799$	−42.4104	−	16.0841i	−1.50037	−	0.569016i
$800$	11.3675	−	21.6590i	0.401903	−	0.765762i
$801$	12.9248	+	4.90173i	0.456676	+	0.173194i
$802$	15.0918	+	3.71978i	0.532908	+	0.131350i
$803$	29.9295	−	26.5152i	1.05619	−	0.935701i
$804$	−12.9161	+	8.91531i	−0.455514	+	0.314419i
$805$	10.6058	+	27.9653i	0.373807	+	0.985648i
$806$	−4.88009	+	1.71104i	−0.171894	+	0.0602689i
$807$	−5.84418	+	15.4098i	−0.205725	+	0.542452i
$808$	−1.65256	−	6.70472i	−0.0581370	−	0.235871i
$809$	−24.3581	+	12.7841i	−0.856385	+	0.449465i	−0.834964	−	0.550305i	$-0.814511\pi$
$809$	−24.3581	+	12.7841i	−0.856385	+	0.449465i	−0.0214211	+	0.999771i	$0.506819\pi$
$810$	−0.256376	−	0.676009i	−0.00900815	−	0.0237525i
$811$	−31.5758	+	3.83400i	−1.10878	+	0.134630i	−0.654378	−	0.756168i	$-0.727069\pi$
$811$	−31.5758	+	3.83400i	−1.10878	+	0.134630i	−0.454400	+	0.890798i	$0.650146\pi$
$812$	13.9148	+	9.60469i	0.488314	+	0.337059i
$813$	−4.02068	+	16.3125i	−0.141011	+	0.572105i
$814$	5.09642	+	20.6770i	0.178629	+	0.724728i
$815$	−0.0494831	−	0.407530i	−0.00173332	−	0.0142751i
$816$	−0.908163	+	2.39463i	−0.0317920	+	0.0838287i
$817$	−0.826141	+	3.35179i	−0.0289030	+	0.117264i
$818$	−23.7711	+	5.85905i	−0.831137	+	0.204857i
$819$	−9.21359	−	14.0972i	−0.321949	−	0.492596i
$820$	2.79165	+	0.688081i	0.0974888	+	0.0240288i
$821$	−17.8793	+	34.0661i	−0.623990	+	1.18891i	0.344246	+	0.938879i	$0.388134\pi$
$821$	−17.8793	+	34.0661i	−0.623990	+	1.18891i	−0.968237	+	0.250035i	$0.919558\pi$
$822$	−3.84267			−0.134028
$823$	10.2940			0.358826			0.179413	−	0.983774i	$-0.442580\pi$
$823$	10.2940			0.358826			0.179413	+	0.983774i	$0.442580\pi$
$824$	22.0299	−	41.9745i	0.767449	−	1.46225i
$825$	8.80957	+	9.94395i	0.306710	+	0.346204i
$826$		−	5.05079i		−	0.175739i
$827$	−6.41890	+	7.24544i	−0.223207	+	0.251949i	−0.849437	−	0.527689i	$-0.823059\pi$
$827$	−6.41890	+	7.24544i	−0.223207	+	0.251949i	0.626230	+	0.779638i	$0.284597\pi$
$828$	8.53712	−	4.48063i	0.296685	−	0.155712i
$829$	−4.78351	−	39.3958i	−0.166138	−	1.36827i	−0.802395	−	0.596794i	$-0.796441\pi$
$829$	−4.78351	−	39.3958i	−0.166138	−	1.36827i	0.636257	−	0.771478i	$-0.280482\pi$
$830$	−0.842055	−	1.60440i	−0.0292281	−	0.0556896i
$831$	−1.16134	−	9.56451i	−0.0402865	−	0.331789i
$832$	−13.4329	−	1.97660i	−0.465702	−	0.0685262i
$833$	−9.57257	+	78.8372i	−0.331670	+	2.73155i
$834$	0.185263	−	0.0702610i	0.00641513	−	0.00243294i
$835$	−6.60728	−	3.46777i	−0.228654	−	0.120007i
$836$	−0.703022	+	1.85372i	−0.0243145	+	0.0641122i
$837$	−0.820752	−	1.56381i	−0.0283693	−	0.0540532i
$838$	10.6879	+	20.3641i	0.369208	+	0.703466i
$839$	3.13713	+	12.7279i	0.108306	+	0.439414i	0.999910	−	0.0134010i	$-0.00426581\pi$
$839$	3.13713	+	12.7279i	0.108306	+	0.439414i	−0.891604	+	0.452815i	$0.850420\pi$
$840$	11.1985	+	1.35975i	0.386386	+	0.0469157i
$841$	16.2485	+	14.3949i	0.560294	+	0.496377i
$842$	2.64600	+	3.83340i	0.0911873	+	0.132108i
$843$	−6.28055	−	2.38190i	−0.216313	−	0.0820369i
$844$	12.2496			0.421648
$845$	−8.10237	+	8.26409i	−0.278730	+	0.284293i
$846$	6.87257			0.236284
$847$	−4.49916	−	1.70631i	−0.154593	−	0.0586293i
$848$	2.65017	+	3.83944i	0.0910073	+	0.131847i
$849$	10.4876	+	9.29118i	0.359932	+	0.318872i
$850$	−18.1804	−	2.20750i	−0.623583	−	0.0757167i
$851$	−14.2952	−	57.9981i	−0.490034	−	1.98815i
$852$	−9.30794	−	17.7348i	−0.318885	−	0.607584i
$853$	24.6697	+	47.0042i	0.844675	+	1.60939i	0.791791	+	0.610792i	$0.209149\pi$
$853$	24.6697	+	47.0042i	0.844675	+	1.60939i	0.0528839	+	0.998601i	$0.483159\pi$
$854$	16.5217	−	43.5643i	0.565362	−	1.49074i
$855$	−0.369238	−	0.193791i	−0.0126277	−	0.00662752i
$856$	−17.2433	+	6.53953i	−0.589365	+	0.223517i
$857$	−2.44370	+	20.1257i	−0.0834753	+	0.687481i	0.889559	+	0.456820i	$0.151012\pi$
$857$	−2.44370	+	20.1257i	−0.0834753	+	0.687481i	−0.973034	+	0.230661i	$0.925911\pi$
$858$	4.50206	−	8.07533i	0.153698	−	0.275687i
$859$	1.09483	+	9.01675i	0.0373552	+	0.307647i	0.999396	+	0.0347429i	$0.0110612\pi$
$859$	1.09483	+	9.01675i	0.0373552	+	0.307647i	−0.962041	+	0.272905i	$0.912016\pi$
$860$	−4.08726	−	7.78762i	−0.139374	−	0.265556i
$861$	−1.35646	−	11.1715i	−0.0462282	−	0.380723i
$862$	0.704611	−	0.369809i	0.0239992	−	0.0125957i
$863$	−33.7419	+	38.0867i	−1.14859	+	1.29649i	−0.200061	+	0.979783i	$0.564114\pi$
$863$	−33.7419	+	38.0867i	−1.14859	+	1.29649i	−0.948525	+	0.316703i	$0.897424\pi$
$864$		−	5.81372i		−	0.197787i
$865$	−1.14687	−	1.29455i	−0.0389948	−	0.0440160i
$866$	1.90853	−	3.63639i	0.0648544	−	0.123570i
$867$	11.7275			0.398288
$868$	11.0579			0.375331
$869$	−2.43349	+	4.63663i	−0.0825505	+	0.157287i
$870$	−1.89564	−	0.467233i	−0.0642682	−	0.0158407i
$871$	15.9615	−	39.0795i	0.540836	−	1.32416i
$872$	−28.2781	+	6.96993i	−0.957617	+	0.236031i
$873$	−3.25245	+	13.1957i	−0.110079	+	0.446607i
$874$	−0.970214	+	2.55824i	−0.0328180	+	0.0865339i
$875$	−4.61502	−	38.0081i	−0.156016	−	1.28491i
$876$	4.06245	+	16.4820i	0.137257	+	0.556875i
$877$	−1.97558	+	8.01523i	−0.0667105	+	0.270655i	−0.994820	−	0.101652i	$-0.967587\pi$
$877$	−1.97558	+	8.01523i	−0.0667105	+	0.270655i	0.928110	+	0.372307i	$0.121433\pi$
$878$	−21.9707	−	15.1653i	−0.741474	−	0.511803i
$879$	−6.56663	+	0.797333i	−0.221487	+	0.0268934i
$880$	−0.476295	−	1.25589i	−0.0160559	−	0.0423359i
$881$	10.4175	−	5.46752i	0.350974	−	0.184206i	−0.280018	−	0.959995i	$-0.590340\pi$
$881$	10.4175	−	5.46752i	0.350974	−	0.184206i	0.630992	+	0.775789i	$0.282648\pi$
$882$	−2.87970	−	11.6834i	−0.0969645	−	0.393400i
$883$	−2.40896	+	6.35189i	−0.0810678	+	0.213758i	−0.969422	−	0.245401i	$-0.921080\pi$
$883$	−2.40896	+	6.35189i	−0.0810678	+	0.213758i	0.888354	+	0.459160i	$0.151849\pi$
$884$	−5.56199	−	25.3006i	−0.187070	−	0.850952i
$885$	−0.420348	−	1.10837i	−0.0141298	−	0.0372573i
$886$	9.96608	−	6.87909i	0.334817	−	0.231107i
$887$	−7.55823	+	6.69600i	−0.253780	+	0.224830i	−0.780415	−	0.625262i	$-0.784992\pi$
$887$	−7.55823	+	6.69600i	−0.253780	+	0.224830i	0.526635	+	0.850092i	$0.323454\pi$
$888$	−21.8752	−	5.39175i	−0.734083	−	0.180935i
$889$	45.8738	+	17.3976i	1.53856	+	0.583497i
$890$	4.64443	−	8.84922i	0.155682	−	0.296627i
$891$	2.95232	+	1.11967i	0.0989063	+	0.0375102i
$892$	−22.2977	−	25.1689i	−0.746581	−	0.842716i
$893$	2.96704	−	2.62857i	0.0992883	−	0.0879618i
$894$	5.79074	−	8.38933i	0.193671	−	0.280581i
$895$	−0.304708	−	0.210325i	−0.0101853	−	0.00703038i
$896$	35.4411	+	18.6009i	1.18400	+	0.621413i
$897$	−12.6281	+	22.6509i	−0.421639	+	0.756293i
$898$	3.90638	−	2.05023i	0.130358	−	0.0684170i
$899$	−4.73444	−	0.574865i	−0.157902	−	0.0191728i
$900$	−5.47608	+	1.34973i	−0.182536	+	0.0449910i
$901$	29.7272	−	43.0672i	0.990355	−	1.43478i
$902$	5.08443	−	3.50953i	0.169293	−	0.116854i
$903$	−22.8272	+	25.7666i	−0.759642	+	0.857458i
$904$	−38.9318	−	4.72718i	−1.29485	−	0.157224i
$905$	2.23912	−	9.08447i	0.0744309	−	0.301978i
$906$	−11.9194	−	6.25576i	−0.395994	−	0.207834i
$907$	1.02598	−	8.44974i	0.0340672	−	0.280569i	−0.965713	−	0.259612i	$-0.916405\pi$
$907$	1.02598	−	8.44974i	0.0340672	−	0.280569i	0.999780	−	0.0209575i	$-0.00667145\pi$
$908$	−12.8577	+	1.56121i	−0.426699	+	0.0518106i
$909$	−1.44598	+	2.09486i	−0.0479600	+	0.0694821i
$910$	−10.9208	+	5.38425i	−0.362020	+	0.178486i
$911$	−31.6171	−	45.8052i	−1.04752	−	1.51759i	−0.842396	−	0.538858i	$-0.818856\pi$
$911$	−31.6171	−	45.8052i	−1.04752	−	1.51759i	−0.205123	−	0.978736i	$-0.565760\pi$
$912$	−0.148418	−	0.167529i	−0.00491460	−	0.00554744i
$913$	7.68333	+	1.89377i	0.254281	+	0.0626747i
$914$	7.04043	+	10.1998i	0.232877	+	0.337380i
$915$		−	10.9349i		−	0.361498i
$916$	10.1293	−	6.99175i	0.334682	−	0.231014i
$917$	−97.5185	+	11.8409i	−3.22035	+	0.391021i
$918$	−4.06990	+	1.54351i	−0.134327	+	0.0509434i
$919$	−0.768686	+	6.33070i	−0.0253566	+	0.208830i	−0.999881	−	0.0154528i	$-0.995081\pi$
$919$	−0.768686	+	6.33070i	−0.0253566	+	0.208830i	0.974524	+	0.224283i	$0.0720041\pi$
$920$	−6.15987	−	16.2422i	−0.203085	−	0.535491i
$921$	3.73072	−	4.21112i	0.122931	−	0.138761i
$922$	−15.9229	−	14.1065i	−0.524393	−	0.464572i
$923$	47.0545	+	26.2333i	1.54882	+	0.863478i
$924$	−14.7978	+	13.1097i	−0.486813	+	0.431279i
$925$			34.9424i			1.14890i
$926$	7.37279	+	6.53172i	0.242285	+	0.214646i
$927$	−16.9663	+	4.18183i	−0.557248	+	0.137349i
$928$	−12.9204	−	8.91828i	−0.424132	−	0.292757i
$929$	21.3495	−	8.09680i	0.700454	−	0.265647i	0.0214378	−	0.999770i	$-0.493176\pi$
$929$	21.3495	−	8.09680i	0.700454	−	0.265647i	0.679017	+	0.734123i	$0.262406\pi$
$930$	−1.19391	+	0.452789i	−0.0391497	+	0.0148475i
$931$	−5.71181	−	3.94258i	−0.187197	−	0.129213i
$932$	0.0315152	−	0.00776780i	0.00103231	−	0.000254443i
$933$	−23.2833	−	20.6272i	−0.762261	−	0.675304i
$934$		−	6.37053i		−	0.208450i
$935$	−11.2774	+	9.99089i	−0.368810	+	0.326737i
$936$	5.35125	+	8.18764i	0.174911	+	0.267621i
$937$	6.79244	+	6.01758i	0.221899	+	0.196586i	0.766747	−	0.641949i	$-0.221874\pi$
$937$	6.79244	+	6.01758i	0.221899	+	0.196586i	−0.544848	+	0.838535i	$0.683413\pi$
$938$	29.4501	−	33.2423i	0.961579	−	1.08540i
$939$	−5.19192	−	13.6900i	−0.169432	−	0.446755i
$940$	−1.21731	+	10.0254i	−0.0397042	+	0.326993i
$941$	−43.4357	+	16.4730i	−1.41596	+	0.537004i	−0.939609	−	0.342249i	$-0.888811\pi$
$941$	−43.4357	+	16.4730i	−1.41596	+	0.537004i	−0.476355	+	0.879253i	$0.658042\pi$
$942$	−3.06831	+	0.372560i	−0.0999708	+	0.0121387i
$943$	−14.2616	+	9.84407i	−0.464422	+	0.320567i
$944$		−	0.636232i		−	0.0207076i
$945$	−2.36218	−	3.42221i	−0.0768417	−	0.111324i
$946$	−18.3490	−	4.52263i	−0.596579	−	0.147043i
$947$	14.5960	+	16.4755i	0.474307	+	0.535382i	0.936160	−	0.351574i	$-0.114354\pi$
$947$	14.5960	+	16.4755i	0.474307	+	0.535382i	−0.461853	+	0.886957i	$0.652815\pi$
$948$	−1.26284	−	1.82954i	−0.0410151	−	0.0594207i
$949$	−33.4006	−	31.1315i	−1.08423	−	1.01057i
$950$	0.909186	−	1.31718i	0.0294979	−	0.0427351i
$951$	−11.4037	+	1.38466i	−0.369789	+	0.0449006i
$952$	8.18634	−	67.4206i	0.265321	−	2.18511i
$953$	−18.1870	−	9.54527i	−0.589134	−	0.309201i	0.143687	−	0.989623i	$-0.454104\pi$
$953$	−18.1870	−	9.54527i	−0.589134	−	0.309201i	−0.732821	+	0.680422i	$0.761797\pi$
$954$	−1.89755	+	7.69866i	−0.0614354	+	0.249253i
$955$	16.5665	+	2.01153i	0.536078	+	0.0650917i
$956$	−0.386445	+	0.436206i	−0.0124985	+	0.0141079i
$957$	7.01720	−	4.84363i	0.226834	−	0.156572i
$958$	−3.41164	+	4.94261i	−0.110225	+	0.159688i
$959$	−21.4589	+	5.28915i	−0.692945	+	0.170796i
$960$	−3.32805	−	0.404098i	−0.107412	−	0.0130422i
$961$	24.6873	−	12.9569i	0.796364	−	0.417964i
$962$	22.9480	−	8.04597i	0.739874	−	0.259412i
$963$	6.01929	+	3.15917i	0.193969	+	0.101803i
$964$	16.9136	+	11.6746i	0.544749	+	0.376013i
$965$	−9.58294	+	13.8833i	−0.308486	+	0.446919i
$966$	−20.4219	+	18.0922i	−0.657064	+	0.582108i
$967$	−35.0533	−	39.5670i	−1.12724	−	1.27239i	−0.957986	−	0.286816i	$-0.907403\pi$
$967$	−35.0533	−	39.5670i	−1.12724	−	1.27239i	−0.169252	−	0.985573i	$-0.554135\pi$
$968$	2.61311	+	0.991021i	0.0839885	+	0.0318526i
$969$	−1.16672	+	2.22299i	−0.0374803	+	0.0714128i
$970$	9.18739	+	3.48432i	0.294989	+	0.111875i
$971$	17.2887	+	4.26128i	0.554820	+	0.136751i	0.506750	−	0.862093i	$-0.330847\pi$
$971$	17.2887	+	4.26128i	0.554820	+	0.136751i	0.0480701	+	0.998844i	$0.484693\pi$
$972$	−1.00336	+	0.888900i	−0.0321828	+	0.0285115i
$973$	0.937871	−	0.647365i	0.0300668	−	0.0207536i
$974$	−0.945841	−	2.49398i	−0.0303067	−	0.0799122i
$975$	10.3433	−	11.0972i	0.331251	−	0.355396i
$976$	2.08119	−	5.48766i	0.0666174	−	0.175656i
$977$	−1.04025	−	4.22047i	−0.0332806	−	0.135025i	0.951952	−	0.306249i	$-0.0990739\pi$
$977$	−1.04025	−	4.22047i	−0.0332806	−	0.135025i	−0.985232	+	0.171224i	$0.945228\pi$
$978$	0.331590	−	0.174032i	0.0106031	−	0.00556493i
$979$	15.4772	+	40.8101i	0.494655	+	1.30430i
$980$	17.5533	−	2.13136i	0.560720	−	0.0680837i
$981$	8.83537	+	6.09861i	0.282092	+	0.194714i
$982$	4.61901	−	18.7401i	0.147399	−	0.598020i
$983$	3.77374	+	15.3107i	0.120364	+	0.488334i	0.999921	+	0.0125421i	$0.00399239\pi$
$983$	3.77374	+	15.3107i	0.120364	+	0.488334i	−0.879558	+	0.475792i	$0.842161\pi$
$984$	0.787834	+	6.48839i	0.0251152	+	0.206842i
$985$	−5.45173	+	14.3750i	−0.173707	+	0.458027i
$986$	−2.81297	+	11.4127i	−0.0895832	+	0.363453i
$987$	38.3791	−	9.45960i	1.22162	−	0.301102i
$988$	2.18370	+	0.597141i	0.0694728	+	0.0189976i
$989$	51.4683	+	12.6858i	1.63660	+	0.403385i
$990$	1.06089	−	2.02136i	0.0337174	−	0.0642431i
$991$	−31.4259			−0.998276			−0.499138	−	0.866522i	$-0.666350\pi$
$991$	−31.4259			−0.998276			−0.499138	+	0.866522i	$0.666350\pi$
$992$	−10.2677			−0.325999
$993$	−0.480429	+	0.915381i	−0.0152460	+	0.0290487i
$994$	37.5844	+	42.4240i	1.19210	+	1.34561i
$995$		−	8.23871i		−	0.261185i
$996$	−2.22775	+	2.51461i	−0.0705888	+	0.0796783i
$997$	33.8684	−	17.7755i	1.07262	−	0.562957i	0.166532	−	0.986036i	$-0.446743\pi$
$997$	33.8684	−	17.7755i	1.07262	−	0.562957i	0.906093	+	0.423079i	$0.139051\pi$
$998$	−2.66848	−	21.9769i	−0.0844692	−	0.695666i
$999$	3.85948	+	7.35363i	0.122109	+	0.232659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.25.10	✓	168
169.142	even	26	inner	507.2.p.a.142.10	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.25.10	✓	168	1.1	even	1	trivial
507.2.p.a.142.10	yes	168	169.142	even	26	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.759337 + 0.287979i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.00336 - 0.888900i) q^{4} +(0.883771 + 0.107309i) q^{5} +(0.194351 + 0.788513i) q^{6} +(2.17066 + 4.13585i) q^{7} +(-1.26072 - 2.40210i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(0.759337 + 0.287979i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.00336 - 0.888900i) q^{4} +(0.883771 + 0.107309i) q^{5} +(0.194351 + 0.788513i) q^{6} +(2.17066 + 4.13585i) q^{7} +(-1.26072 - 2.40210i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.640177 + 0.335991i) q^{10} +(-2.95232 + 1.11967i) q^{11} +(0.161576 - 1.33070i) q^{12} +(1.59439 + 3.23387i) q^{13} +(0.457227 + 3.76561i) q^{14} +(0.413725 + 0.788288i) q^{15} +(0.0575956 + 0.474342i) q^{16} +(4.74587 - 2.49083i) q^{17} +(-0.538529 + 0.607874i) q^{18} +0.468406i q^{19} +(-0.791354 - 0.893253i) q^{20} +(-2.17066 + 4.13585i) q^{21} -2.56424 q^{22} +7.19259 q^{23} +(1.26072 - 2.40210i) q^{24} +(-4.08517 - 1.00690i) q^{25} +(0.279394 + 2.91475i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(1.49840 - 6.07925i) q^{28} +(-0.957578 + 2.52492i) q^{29} +(0.0871470 + 0.717720i) q^{30} +(0.422658 + 1.71479i) q^{31} +(-1.39131 + 5.64479i) q^{32} +(-2.59857 - 1.79367i) q^{33} +(4.32102 - 0.524667i) q^{34} +(1.47455 + 3.88807i) q^{35} +(1.18693 - 0.622950i) q^{36} +(-1.98749 - 8.06358i) q^{37} +(-0.134891 + 0.355678i) q^{38} +(-1.75571 + 3.14921i) q^{39} +(-0.856419 - 2.25819i) q^{40} +(-1.98282 + 1.36864i) q^{41} +(-2.83930 + 2.51540i) q^{42} +(7.15574 + 1.76373i) q^{43} +(3.95751 + 1.50088i) q^{44} +(-0.413725 + 0.788288i) q^{45} +(5.46160 + 2.07131i) q^{46} +(-5.61174 - 6.33435i) q^{47} +(-0.357658 + 0.316857i) q^{48} +(-8.41702 + 12.1942i) q^{49} +(-2.81206 - 1.94102i) q^{50} +(4.74587 + 2.49083i) q^{51} +(1.27484 - 4.66199i) q^{52} +(8.64517 - 4.53734i) q^{53} +(-0.806190 - 0.0978892i) q^{54} +(-2.72932 + 0.672717i) q^{55} +(7.19812 - 10.4283i) q^{56} +(-0.385490 + 0.266085i) q^{57} +(-1.45425 + 1.64151i) q^{58} +(-1.32181 - 0.160496i) q^{59} +(0.285593 - 1.15870i) q^{60} +(-10.8759 - 5.70811i) q^{61} +(-0.172883 + 1.42382i) q^{62} +(-4.63681 + 0.563011i) q^{63} +(-2.13918 + 3.09914i) q^{64} +(1.06205 + 3.02909i) q^{65} +(-1.45666 - 2.11033i) q^{66} +(-7.76378 - 8.76350i) q^{67} +(-6.97592 - 1.71941i) q^{68} +(4.08586 + 5.91939i) q^{69} +3.37700i q^{70} +(12.2968 - 8.48786i) q^{71} +(2.69306 - 0.326996i) q^{72} +(-11.8407 + 4.49058i) q^{73} +(0.812961 - 6.69533i) q^{74} +(-1.49198 - 3.93402i) q^{75} +(0.416366 - 0.469980i) q^{76} +(-11.0392 - 9.77991i) q^{77} +(-2.24008 + 1.88570i) q^{78} +(1.24134 - 1.09973i) q^{79} +0.425390i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-1.89977 + 0.468250i) q^{82} +(-2.06255 - 1.42367i) q^{83} +(5.85431 - 2.22025i) q^{84} +(4.46155 - 1.69204i) q^{85} +(4.92570 + 3.39997i) q^{86} +(-2.62194 + 0.646250i) q^{87} +(6.41158 + 5.68017i) q^{88} -13.8231i q^{89} +(-0.541167 + 0.479432i) q^{90} +(-9.91392 + 13.6138i) q^{91} +(-7.21676 - 6.39349i) q^{92} +(-1.17115 + 1.32195i) q^{93} +(-2.43705 - 6.42597i) q^{94} +(-0.0502642 + 0.413963i) q^{95} +(-5.43592 + 2.06157i) q^{96} +(13.4915 - 1.63817i) q^{97} +(-9.90301 + 6.83555i) q^{98} -3.15750i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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