LMFDB - Embedded newform 475.2.n.b.39.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.8
Character	$\chi$	$=$	475.39
Dual form			475.2.n.b.134.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.695076 - 0.956690i) q^{2} +(-0.0684675 - 0.0222464i) q^{3} +(0.185909 - 0.572168i) q^{4} +(2.00266 - 0.994659i) q^{5} +(0.0263072 + 0.0809651i) q^{6} -2.31826i q^{7} +(-2.92592 + 0.950690i) q^{8} +(-2.42286 - 1.76031i) q^{9} +O(q^{10})$	\(q+(-0.695076 - 0.956690i) q^{2} +(-0.0684675 - 0.0222464i) q^{3} +(0.185909 - 0.572168i) q^{4} +(2.00266 - 0.994659i) q^{5} +(0.0263072 + 0.0809651i) q^{6} -2.31826i q^{7} +(-2.92592 + 0.950690i) q^{8} +(-2.42286 - 1.76031i) q^{9} +(-2.34358 - 1.22456i) q^{10} +(1.67319 - 1.21565i) q^{11} +(-0.0254574 + 0.0350391i) q^{12} +(-1.34918 + 1.85698i) q^{13} +(-2.21786 + 1.61137i) q^{14} +(-0.159245 + 0.0235497i) q^{15} +(1.96982 + 1.43116i) q^{16} +(-0.0223713 + 0.00726887i) q^{17} +3.54147i q^{18} +(0.309017 + 0.951057i) q^{19} +(-0.196800 - 1.33077i) q^{20} +(-0.0515731 + 0.158726i) q^{21} +(-2.32599 - 0.755762i) q^{22} +(-0.579298 - 0.797335i) q^{23} +0.221480 q^{24} +(3.02131 - 3.98393i) q^{25} +2.71434 q^{26} +(0.253672 + 0.349150i) q^{27} +(-1.32644 - 0.430985i) q^{28} +(1.75630 - 5.40532i) q^{29} +(0.133217 + 0.135979i) q^{30} +(0.335977 + 1.03403i) q^{31} +3.27372i q^{32} +(-0.141603 + 0.0460097i) q^{33} +(0.0225038 + 0.0163500i) q^{34} +(-2.30588 - 4.64270i) q^{35} +(-1.45762 + 1.05903i) q^{36} +(-3.51315 + 4.83544i) q^{37} +(0.695076 - 0.956690i) q^{38} +(0.133686 - 0.0971285i) q^{39} +(-4.91402 + 4.81420i) q^{40} +(-0.436100 - 0.316845i) q^{41} +(0.187698 - 0.0609869i) q^{42} -0.299565i q^{43} +(-0.384493 - 1.18335i) q^{44} +(-6.60307 - 1.11539i) q^{45} +(-0.360146 + 1.10842i) q^{46} +(-7.99721 - 2.59845i) q^{47} +(-0.103031 - 0.141809i) q^{48} +1.62565 q^{49} +(-5.91143 - 0.121319i) q^{50} +0.00169341 q^{51} +(0.811683 + 1.11719i) q^{52} +(-2.09603 - 0.681041i) q^{53} +(0.157707 - 0.485371i) q^{54} +(2.14169 - 4.09879i) q^{55} +(2.20395 + 6.78306i) q^{56} -0.0719909i q^{57} +(-6.39198 + 2.07688i) q^{58} +(-6.17128 - 4.48370i) q^{59} +(-0.0161306 + 0.0954929i) q^{60} +(10.0087 - 7.27174i) q^{61} +(0.755717 - 1.04015i) q^{62} +(-4.08086 + 5.61682i) q^{63} +(7.07158 - 5.13780i) q^{64} +(-0.854880 + 5.06088i) q^{65} +(0.142442 + 0.103490i) q^{66} +(3.64005 - 1.18272i) q^{67} +0.0141515i q^{68} +(0.0219252 + 0.0674788i) q^{69} +(-2.83886 + 5.43304i) q^{70} +(-1.85412 + 5.70640i) q^{71} +(8.76260 + 2.84714i) q^{72} +(3.09543 + 4.26049i) q^{73} +7.06793 q^{74} +(-0.295489 + 0.205556i) q^{75} +0.601613 q^{76} +(-2.81819 - 3.87891i) q^{77} +(-0.185844 - 0.0603843i) q^{78} +(3.65399 - 11.2458i) q^{79} +(5.36841 + 0.906827i) q^{80} +(2.76675 + 8.51517i) q^{81} +0.637444i q^{82} +(7.13190 - 2.31730i) q^{83} +(0.0812299 + 0.0590169i) q^{84} +(-0.0375721 + 0.0368089i) q^{85} +(-0.286591 + 0.208221i) q^{86} +(-0.240498 + 0.331017i) q^{87} +(-3.73993 + 5.14758i) q^{88} +(4.80056 - 3.48781i) q^{89} +(3.52256 + 7.09237i) q^{90} +(4.30498 + 3.12775i) q^{91} +(-0.563906 + 0.183224i) q^{92} -0.0782717i q^{93} +(3.07276 + 9.45698i) q^{94} +(1.56483 + 1.59728i) q^{95} +(0.0728285 - 0.224143i) q^{96} +(8.09445 + 2.63005i) q^{97} +(-1.12995 - 1.55525i) q^{98} -6.19383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.695076	−	0.956690i	−0.491493	−	0.676482i	0.489169	−	0.872189i	$-0.337300\pi$
$2$	−0.695076	−	0.956690i	−0.491493	−	0.676482i	−0.980662	+	0.195707i	$0.937300\pi$
$3$	−0.0684675	−	0.0222464i	−0.0395297	−	0.0128440i	0.289185	−	0.957273i	$-0.406616\pi$
$3$	−0.0684675	−	0.0222464i	−0.0395297	−	0.0128440i	−0.328715	+	0.944429i	$0.606616\pi$
$4$	0.185909	−	0.572168i	0.0929543	−	0.286084i
$5$	2.00266	−	0.994659i	0.895617	−	0.444825i
$5$	2.00266	−	0.994659i	0.895617	−	0.444825i
$6$	0.0263072	+	0.0809651i	0.0107399	+	0.0330539i
$7$		−	2.31826i		−	0.876221i	−0.898921	−	0.438111i	$-0.855648\pi$
$7$		−	2.31826i		−	0.876221i	0.898921	−	0.438111i	$-0.144352\pi$
$8$	−2.92592	+	0.950690i	−1.03447	+	0.336120i
$9$	−2.42286	−	1.76031i	−0.807619	−	0.586770i
$10$	−2.34358	−	1.22456i	−0.741106	−	0.387241i
$11$	1.67319	−	1.21565i	0.504487	−	0.366531i	−0.306241	−	0.951954i	$-0.599071\pi$
$11$	1.67319	−	1.21565i	0.504487	−	0.366531i	0.810728	+	0.585423i	$0.199071\pi$
$12$	−0.0254574	+	0.0350391i	−0.00734892	+	0.0101149i
$13$	−1.34918	+	1.85698i	−0.374194	+	0.515034i	−0.954035	−	0.299696i	$-0.903115\pi$
$13$	−1.34918	+	1.85698i	−0.374194	+	0.515034i	0.579840	+	0.814730i	$0.303115\pi$
$14$	−2.21786	+	1.61137i	−0.592748	+	0.430657i
$15$	−0.159245	+	0.0235497i	−0.0411168	+	0.00608051i
$16$	1.96982	+	1.43116i	0.492456	+	0.357790i
$17$	−0.0223713	+	0.00726887i	−0.00542583	+	0.00176296i	−0.311729	−	0.950171i	$-0.600908\pi$
$17$	−0.0223713	+	0.00726887i	−0.00542583	+	0.00176296i	0.306303	+	0.951934i	$0.400908\pi$
$18$			3.54147i			0.834733i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	−0.196800	−	1.33077i	−0.0440058	−	0.297570i
$21$	−0.0515731	+	0.158726i	−0.0112542	+	0.0346368i
$22$	−2.32599	−	0.755762i	−0.495904	−	0.161129i
$23$	−0.579298	−	0.797335i	−0.120792	−	0.166256i	0.744339	−	0.667802i	$-0.232765\pi$
$23$	−0.579298	−	0.797335i	−0.120792	−	0.166256i	−0.865131	+	0.501546i	$0.832765\pi$
$24$	0.221480			0.0452094
$25$	3.02131	−	3.98393i	0.604261	−	0.796786i
$26$	2.71434			0.532325
$27$	0.253672	+	0.349150i	0.0488192	+	0.0671939i
$28$	−1.32644	−	0.430985i	−0.250673	−	0.0814486i
$29$	1.75630	−	5.40532i	0.326136	−	1.00374i	−0.644789	−	0.764360i	$-0.723055\pi$
$29$	1.75630	−	5.40532i	0.326136	−	1.00374i	0.970925	−	0.239383i	$-0.0769451\pi$
$30$	0.133217	+	0.135979i	0.0243220	+	0.0248263i
$31$	0.335977	+	1.03403i	0.0603432	+	0.185717i	0.976684	−	0.214682i	$-0.0688715\pi$
$31$	0.335977	+	1.03403i	0.0603432	+	0.185717i	−0.916341	+	0.400399i	$0.868871\pi$
$32$			3.27372i			0.578717i
$33$	−0.141603	+	0.0460097i	−0.0246499	+	0.00800925i
$34$	0.0225038	+	0.0163500i	0.00385937	+	0.00280400i
$35$	−2.30588	−	4.64270i	−0.389765	−	0.784759i
$36$	−1.45762	+	1.05903i	−0.242937	+	0.176504i
$37$	−3.51315	+	4.83544i	−0.577559	+	0.794942i	−0.993425	−	0.114484i	$-0.963478\pi$
$37$	−3.51315	+	4.83544i	−0.577559	+	0.794942i	0.415866	+	0.909426i	$0.363478\pi$
$38$	0.695076	−	0.956690i	0.112756	−	0.155196i
$39$	0.133686	−	0.0971285i	0.0214069	−	0.0155530i
$40$	−4.91402	+	4.81420i	−0.776975	+	0.761193i
$41$	−0.436100	−	0.316845i	−0.0681074	−	0.0494829i	0.553211	−	0.833041i	$-0.313402\pi$
$41$	−0.436100	−	0.316845i	−0.0681074	−	0.0494829i	−0.621318	+	0.783559i	$0.713402\pi$
$42$	0.187698	−	0.0609869i	0.0289625	−	0.00941049i
$43$		−	0.299565i		−	0.0456833i	−0.999739	−	0.0228416i	$-0.992729\pi$
$43$		−	0.299565i		−	0.0456833i	0.999739	−	0.0228416i	$-0.00727135\pi$
$44$	−0.384493	−	1.18335i	−0.0579645	−	0.178396i
$45$	−6.60307	−	1.11539i	−0.984328	−	0.166272i
$46$	−0.360146	+	1.10842i	−0.0531007	+	0.163427i
$47$	−7.99721	−	2.59845i	−1.16651	−	0.379023i	−0.339173	−	0.940724i	$-0.610147\pi$
$47$	−7.99721	−	2.59845i	−1.16651	−	0.379023i	−0.827340	+	0.561701i	$0.810147\pi$
$48$	−0.103031	−	0.141809i	−0.0148712	−	0.0204684i
$49$	1.62565			0.232236
$50$	−5.91143	−	0.121319i	−0.836002	−	0.0171571i
$51$	0.00169341			0.000237125
$52$	0.811683	+	1.11719i	0.112560	+	0.154926i
$53$	−2.09603	−	0.681041i	−0.287912	−	0.0935482i	0.161501	−	0.986873i	$-0.448367\pi$
$53$	−2.09603	−	0.681041i	−0.287912	−	0.0935482i	−0.449412	+	0.893324i	$0.648367\pi$
$54$	0.157707	−	0.485371i	0.0214611	−	0.0660506i
$55$	2.14169	−	4.09879i	0.288785	−	0.552680i
$56$	2.20395	+	6.78306i	0.294515	+	0.906424i
$57$		−	0.0719909i		−	0.00953543i
$58$	−6.39198	+	2.07688i	−0.839308	+	0.272708i
$59$	−6.17128	−	4.48370i	−0.803433	−	0.583728i	0.108486	−	0.994098i	$-0.465400\pi$
$59$	−6.17128	−	4.48370i	−0.803433	−	0.583728i	−0.911919	+	0.410370i	$0.865400\pi$
$60$	−0.0161306	+	0.0954929i	−0.00208245	+	0.0123281i
$61$	10.0087	−	7.27174i	1.28148	−	0.931051i	0.281885	−	0.959448i	$-0.409040\pi$
$61$	10.0087	−	7.27174i	1.28148	−	0.931051i	0.999597	+	0.0283973i	$0.00904036\pi$
$62$	0.755717	−	1.04015i	0.0959761	−	0.132100i
$63$	−4.08086	+	5.61682i	−0.514140	+	0.707653i
$64$	7.07158	−	5.13780i	0.883947	−	0.642225i
$65$	−0.854880	+	5.06088i	−0.106035	+	0.627725i
$66$	0.142442	+	0.103490i	0.0175334	+	0.0127388i
$67$	3.64005	−	1.18272i	0.444703	−	0.144493i	−0.0781016	−	0.996945i	$-0.524886\pi$
$67$	3.64005	−	1.18272i	0.444703	−	0.144493i	0.522804	+	0.852453i	$0.324886\pi$
$68$			0.0141515i			0.00171612i
$69$	0.0219252	+	0.0674788i	0.00263948	+	0.00812349i
$70$	−2.83886	+	5.43304i	−0.339309	+	0.649373i
$71$	−1.85412	+	5.70640i	−0.220044	+	0.677225i	0.778713	+	0.627380i	$0.215873\pi$
$71$	−1.85412	+	5.70640i	−0.220044	+	0.677225i	−0.998757	+	0.0498451i	$0.984127\pi$
$72$	8.76260	+	2.84714i	1.03268	+	0.335539i
$73$	3.09543	+	4.26049i	0.362293	+	0.498653i	0.950786	−	0.309849i	$-0.100279\pi$
$73$	3.09543	+	4.26049i	0.362293	+	0.498653i	−0.588493	+	0.808502i	$0.700279\pi$
$74$	7.06793			0.821630
$75$	−0.295489	+	0.205556i	−0.0341202	+	0.0237356i
$76$	0.601613			0.0690098
$77$	−2.81819	−	3.87891i	−0.321163	−	0.442042i
$78$	−0.185844	−	0.0603843i	−0.0210427	−	0.00683718i
$79$	3.65399	−	11.2458i	0.411106	−	1.26525i	−0.504583	−	0.863363i	$-0.668354\pi$
$79$	3.65399	−	11.2458i	0.411106	−	1.26525i	0.915688	−	0.401889i	$-0.131646\pi$
$80$	5.36841	+	0.906827i	0.600206	+	0.101386i
$81$	2.76675	+	8.51517i	0.307416	+	0.946130i
$82$			0.637444i			0.0703939i
$83$	7.13190	−	2.31730i	0.782828	−	0.254356i	0.109781	−	0.993956i	$-0.464985\pi$
$83$	7.13190	−	2.31730i	0.782828	−	0.254356i	0.673047	+	0.739600i	$0.264985\pi$
$84$	0.0812299	+	0.0590169i	0.00886290	+	0.00643928i
$85$	−0.0375721	+	0.0368089i	−0.00407526	+	0.00399248i
$86$	−0.286591	+	0.208221i	−0.0309039	+	0.0224530i
$87$	−0.240498	+	0.331017i	−0.0257841	+	0.0354888i
$88$	−3.73993	+	5.14758i	−0.398678	+	0.548733i
$89$	4.80056	−	3.48781i	0.508859	−	0.369707i	−0.303532	−	0.952821i	$-0.598166\pi$
$89$	4.80056	−	3.48781i	0.508859	−	0.369707i	0.812390	+	0.583114i	$0.198166\pi$
$90$	3.52256	+	7.09237i	0.371310	+	0.747602i
$91$	4.30498	+	3.12775i	0.451284	+	0.327877i
$92$	−0.563906	+	0.183224i	−0.0587913	+	0.0191024i
$93$		−	0.0782717i		−	0.00811639i
$94$	3.07276	+	9.45698i	0.316931	+	0.975413i
$95$	1.56483	+	1.59728i	0.160549	+	0.163877i
$96$	0.0728285	−	0.224143i	0.00743303	−	0.0228765i
$97$	8.09445	+	2.63005i	0.821867	+	0.267041i	0.689616	−	0.724176i	$-0.257780\pi$
$97$	8.09445	+	2.63005i	0.821867	+	0.267041i	0.132251	+	0.991216i	$0.457780\pi$
$98$	−1.12995	−	1.55525i	−0.114142	−	0.157104i
$99$	−6.19383			−0.622503
$100$	−1.71779	−	2.46934i	−0.171779	−	0.246934i
$101$	9.54442			0.949705			0.474853	−	0.880065i	$-0.342501\pi$
$101$	9.54442			0.949705			0.474853	+	0.880065i	$0.342501\pi$
$102$	−0.00117705	−	0.00162007i	−0.000116545	−	0.000160411i
$103$	12.2293	+	3.97355i	1.20499	+	0.391525i	0.841595	−	0.540110i	$-0.181617\pi$
$103$	12.2293	+	3.97355i	1.20499	+	0.391525i	0.363396	+	0.931635i	$0.381617\pi$
$104$	2.18217	−	6.71604i	0.213980	−	0.658561i
$105$	0.0545944	+	0.369171i	0.00532787	+	0.0360274i
$106$	0.805354	+	2.47863i	0.0782229	+	0.240745i
$107$		−	16.9911i		−	1.64259i	−0.570501	−	0.821297i	$-0.693251\pi$
$107$		−	16.9911i		−	1.64259i	0.570501	−	0.821297i	$-0.306749\pi$
$108$	0.246932	−	0.0802331i	0.0237610	−	0.00772043i
$109$	14.0549	+	10.2115i	1.34621	+	0.978081i	0.999191	+	0.0402247i	$0.0128074\pi$
$109$	14.0549	+	10.2115i	1.34621	+	0.978081i	0.347023	+	0.937857i	$0.387193\pi$
$110$	−5.40991	+	0.800037i	−0.515814	+	0.0762806i
$111$	0.348108	−	0.252915i	0.0330409	−	0.0240056i
$112$	3.31781	−	4.56657i	0.313503	−	0.431500i
$113$	−7.12014	+	9.80003i	−0.669806	+	0.921909i	−0.999756	−	0.0220891i	$-0.992968\pi$
$113$	−7.12014	+	9.80003i	−0.669806	+	0.921909i	0.329950	+	0.943999i	$0.392968\pi$
$114$	−0.0688730	+	0.0500392i	−0.00645055	+	0.00468660i
$115$	−1.95321	−	1.02059i	−0.182138	−	0.0951703i
$116$	−2.76624	−	2.00979i	−0.256839	−	0.186605i
$117$	6.53773	−	2.12424i	0.604413	−	0.196386i
$118$			9.02052i			0.830406i
$119$	0.0168512	+	0.0518625i	0.00154474	+	0.00475423i
$120$	0.443549	−	0.220297i	0.0404903	−	0.0201103i
$121$	−2.07740	+	6.39359i	−0.188855	+	0.581236i
$122$	−13.9136	−	4.52080i	−1.25968	−	0.409294i
$123$	0.0228100	+	0.0313953i	0.00205671	+	0.00283082i
$124$	0.654100			0.0587399
$125$	2.08800	−	10.9836i	0.186757	−	0.982406i
$126$	8.21007			0.731411
$127$	−9.09777	−	12.5220i	−0.807296	−	1.11115i	−0.991735	−	0.128304i	$-0.959047\pi$
$127$	−9.09777	−	12.5220i	−0.807296	−	1.11115i	0.184439	−	0.982844i	$-0.440953\pi$
$128$	−3.60359	−	1.17088i	−0.318515	−	0.103492i
$129$	−0.00666426	+	0.0205105i	−0.000586755	+	0.00180585i
$130$	5.43590	−	2.69984i	0.476760	−	0.236792i
$131$	−0.144680	−	0.445278i	−0.0126407	−	0.0389041i	0.944537	−	0.328404i	$-0.106511\pi$
$131$	−0.144680	−	0.445278i	−0.0126407	−	0.0389041i	−0.957178	+	0.289500i	$0.906511\pi$
$132$			0.0895744i			0.00779645i
$133$	2.20480	−	0.716383i	0.191180	−	0.0621183i
$134$	−3.66161	−	2.66032i	−0.316315	−	0.229816i
$135$	0.855304	+	0.446911i	0.0736128	+	0.0384640i
$136$	0.0585462	−	0.0425363i	0.00502029	−	0.00364746i
$137$	−5.70018	+	7.84562i	−0.486999	+	0.670296i	−0.979831	−	0.199828i	$-0.935962\pi$
$137$	−5.70018	+	7.84562i	−0.486999	+	0.670296i	0.492832	+	0.870124i	$0.335962\pi$
$138$	0.0493166	−	0.0678785i	0.00419811	−	0.00577820i
$139$	5.75920	−	4.18431i	0.488489	−	0.354908i	−0.316114	−	0.948721i	$-0.602378\pi$
$139$	5.75920	−	4.18431i	0.488489	−	0.354908i	0.804603	+	0.593813i	$0.202378\pi$
$140$	−3.08509	+	0.456234i	−0.260737	+	0.0385588i
$141$	0.489743	+	0.355819i	0.0412438	+	0.0299653i
$142$	6.74801	−	2.19256i	0.566281	−	0.183996i
$143$			4.74722i			0.396982i
$144$	−2.25332	−	6.93500i	−0.187776	−	0.577916i
$145$	−1.85919	−	12.5719i	−0.154397	−	1.04404i
$146$	1.92441	−	5.92273i	0.159266	−	0.490169i
$147$	−0.111304	−	0.0361650i	−0.00918023	−	0.00298284i
$148$	2.11356	+	2.90906i	0.173734	+	0.239124i
$149$	−0.420414			−0.0344417			−0.0172208	−	0.999852i	$-0.505482\pi$
$149$	−0.420414			−0.0344417			−0.0172208	+	0.999852i	$0.505482\pi$
$150$	0.402041	+	0.139814i	0.0328265	+	0.0114158i
$151$	12.9053			1.05022			0.525109	−	0.851035i	$-0.324025\pi$
$151$	12.9053			1.05022			0.525109	+	0.851035i	$0.324025\pi$
$152$	−1.80832	−	2.48894i	−0.146674	−	0.201880i
$153$	0.0669979	+	0.0217689i	0.00541646	+	0.00175991i
$154$	−1.75205	+	5.39227i	−0.141185	+	0.434521i
$155$	1.70135	+	1.73663i	0.136656	+	0.139489i
$156$	−0.0307205	−	0.0945479i	−0.00245961	−	0.00756989i
$157$			20.6744i			1.65000i	0.565134	+	0.824999i	$0.308825\pi$
$157$			20.6744i			1.65000i	−0.565134	+	0.824999i	$0.691175\pi$
$158$	−13.2986	+	4.32096i	−1.05798	+	0.343757i
$159$	0.128359	+	0.0932583i	0.0101795	+	0.00739587i
$160$	3.25623	+	6.55615i	0.257428	+	0.518309i
$161$	−1.84843	+	1.34296i	−0.145677	+	0.105840i
$162$	6.22328	−	8.56561i	0.488947	−	0.672978i
$163$	8.05207	−	11.0827i	0.630687	−	0.868066i	−0.367389	−	0.930067i	$-0.619748\pi$
$163$	8.05207	−	11.0827i	0.630687	−	0.868066i	0.998076	+	0.0620012i	$0.0197483\pi$
$164$	−0.262364	+	0.190618i	−0.0204872	+	0.0148848i
$165$	−0.237819	+	0.232989i	−0.0185142	+	0.0181381i
$166$	−7.17415	−	5.21232i	−0.556822	−	0.404555i
$167$	8.34322	−	2.71088i	0.645618	−	0.209774i	0.0321367	−	0.999483i	$-0.489769\pi$
$167$	8.34322	−	2.71088i	0.645618	−	0.209774i	0.613481	+	0.789710i	$0.289769\pi$
$168$		−	0.513449i		−	0.0396134i
$169$	2.38911	+	7.35294i	0.183778	+	0.565611i
$170$	0.0613301	+	0.0103598i	0.00470381	+	0.000794564i
$171$	0.925449	−	2.84824i	0.0707709	−	0.217810i
$172$	−0.171402	−	0.0556918i	−0.0130693	−	0.00424646i
$173$	8.81815	+	12.1371i	0.670431	+	0.922769i	0.999770	−	0.0214424i	$-0.00682586\pi$
$173$	8.81815	+	12.1371i	0.670431	+	0.922769i	−0.329339	+	0.944212i	$0.606826\pi$
$174$	0.483846			0.0366802
$175$	−9.23580	−	7.00419i	−0.698161	−	0.529467i
$176$	5.03568			0.379579
$177$	0.322786	+	0.444277i	0.0242621	+	0.0333939i
$178$	−6.67351	−	2.16836i	−0.500201	−	0.162525i
$179$	−0.0459994	+	0.141571i	−0.00343815	+	0.0105816i	−0.952761	−	0.303721i	$-0.901771\pi$
$179$	−0.0459994	+	0.141571i	−0.00343815	+	0.0105816i	0.949323	+	0.314303i	$0.101771\pi$
$180$	−1.86576	+	3.57071i	−0.139065	+	0.266145i
$181$	6.08100	+	18.7154i	0.451997	+	1.39111i	0.874624	+	0.484801i	$0.161108\pi$
$181$	6.08100	+	18.7154i	0.451997	+	1.39111i	−0.422627	+	0.906304i	$0.638892\pi$
$182$		−	6.29255i		−	0.466435i
$183$	−0.847040	+	0.275220i	−0.0626150	+	0.0203448i
$184$	2.45300	+	1.78221i	0.180837	+	0.131386i
$185$	−2.22604	+	13.1781i	−0.163662	+	0.968876i
$186$	−0.0748817	+	0.0544048i	−0.00549059	+	0.00398915i
$187$	−0.0285951	+	0.0393578i	−0.00209108	+	0.00287813i
$188$	−2.97350	+	4.09268i	−0.216865	+	0.298489i
$189$	0.809421	−	0.588078i	0.0588767	−	0.0427764i
$190$	0.440422	−	2.60729i	0.0319515	−	0.189153i
$191$	−17.9636	−	13.0513i	−1.29980	−	0.944362i	−0.299849	−	0.953987i	$-0.596936\pi$
$191$	−17.9636	−	13.0513i	−1.29980	−	0.944362i	−0.999954	+	0.00962456i	$0.996936\pi$
$192$	−0.598471	+	0.194455i	−0.0431909	+	0.0140336i
$193$		−	5.11297i		−	0.368040i	−0.982923	−	0.184020i	$-0.941089\pi$
$193$		−	5.11297i		−	0.368040i	0.982923	−	0.184020i	$-0.0589110\pi$
$194$	−3.11012	−	9.57196i	−0.223293	−	0.687227i
$195$	0.171118	−	0.327487i	0.0122540	−	0.0234519i
$196$	0.302223	−	0.930147i	0.0215874	−	0.0664391i
$197$	−13.6887	−	4.44773i	−0.975280	−	0.316888i	−0.222335	−	0.974970i	$-0.571368\pi$
$197$	−13.6887	−	4.44773i	−0.975280	−	0.316888i	−0.752946	+	0.658083i	$0.771368\pi$
$198$	4.30518	+	5.92557i	0.305956	+	0.421112i
$199$	−5.10808			−0.362102			−0.181051	−	0.983474i	$-0.557950\pi$
$199$	−5.10808			−0.362102			−0.181051	+	0.983474i	$0.557950\pi$
$200$	−5.05263	+	14.5290i	−0.357275	+	1.02736i
$201$	−0.275536			−0.0194348
$202$	−6.63410	−	9.13105i	−0.466774	−	0.642459i
$203$	−12.5310	−	4.07156i	−0.879501	−	0.285767i
$204$	0.000314820	0	0.000968916i	2.20418e−5	0	6.78377e-5i
$205$	−1.18851	−	0.200763i	−0.0830094	−	0.0140219i
$206$	−4.69885	−	14.4616i	−0.327385	−	1.00759i
$207$			2.95157i			0.205148i
$208$	−5.31528	+	1.72704i	−0.368548	+	0.119749i
$209$	1.67319	+	1.21565i	0.115737	+	0.0840881i
$210$	0.315235	−	0.308832i	0.0217533	−	0.0213114i
$211$	−7.71482	+	5.60515i	−0.531110	+	0.385874i	−0.820773	−	0.571255i	$-0.806457\pi$
$211$	−7.71482	+	5.60515i	−0.531110	+	0.385874i	0.289663	+	0.957129i	$0.406457\pi$
$212$	−0.779340	+	1.07267i	−0.0535253	+	0.0736713i
$213$	0.253894	−	0.349455i	0.0173965	−	0.0239443i
$214$	−16.2552	+	11.8101i	−1.11119	+	0.807323i
$215$	−0.297965	−	0.599928i	−0.0203211	−	0.0409148i
$216$	−1.07416	−	0.780421i	−0.0730871	−	0.0531009i
$217$	2.39715	−	0.778882i	0.162729	−	0.0528740i
$218$		−	20.5439i		−	1.39141i
$219$	−0.117155	−	0.360567i	−0.00791663	−	0.0243649i
$220$	−1.94704	−	1.98741i	−0.131269	−	0.133991i
$221$	0.0166846	−	0.0513501i	0.00112233	−	0.00345418i
$222$	−0.483923	−	0.157236i	−0.0324788	−	0.0105530i
$223$	6.71208	+	9.23838i	0.449474	+	0.618648i	0.972284	−	0.233801i	$-0.0751164\pi$
$223$	6.71208	+	9.23838i	0.449474	+	0.618648i	−0.522810	+	0.852449i	$0.675116\pi$
$224$	7.58934			0.507084
$225$	−14.3331	+	4.33406i	−0.955543	+	0.288938i
$226$	14.3246			0.952860
$227$	−9.91928	−	13.6527i	−0.658366	−	0.906163i	0.341060	−	0.940041i	$-0.389214\pi$
$227$	−9.91928	−	13.6527i	−0.658366	−	0.906163i	−0.999426	+	0.0338787i	$0.989214\pi$
$228$	−0.0411909	−	0.0133837i	−0.00272794	−	0.000886360i
$229$	1.50507	−	4.63212i	0.0994576	−	0.306099i	−0.888932	−	0.458039i	$-0.848552\pi$
$229$	1.50507	−	4.63212i	0.0994576	−	0.306099i	0.988390	+	0.151940i	$0.0485520\pi$
$230$	0.381245	+	2.57801i	0.0251386	+	0.169989i
$231$	0.106663	+	0.328273i	0.00701788	+	0.0215988i
$232$			17.4852i			1.14796i
$233$	19.7167	−	6.40636i	1.29169	−	0.419694i	0.419005	−	0.907984i	$-0.362379\pi$
$233$	19.7167	−	6.40636i	1.29169	−	0.419694i	0.872682	+	0.488289i	$0.162379\pi$
$234$	−6.57646	−	4.77807i	−0.429916	−	0.312353i
$235$	−18.6003	+	2.75068i	−1.21335	+	0.179435i
$236$	−3.71273	+	2.69745i	−0.241678	+	0.175589i
$237$	−0.500358	+	0.688684i	−0.0325018	+	0.0447348i
$238$	0.0379035	−	0.0521697i	0.00245692	−	0.00338166i
$239$	4.57717	−	3.32551i	0.296073	−	0.215109i	−0.429825	−	0.902912i	$-0.641425\pi$
$239$	4.57717	−	3.32551i	0.296073	−	0.215109i	0.725897	+	0.687803i	$0.241425\pi$
$240$	−0.347387	−	0.181516i	−0.0224238	−	0.0117168i
$241$	−16.6171	−	12.0730i	−1.07040	−	0.777691i	−0.0944162	−	0.995533i	$-0.530098\pi$
$241$	−16.6171	−	12.0730i	−1.07040	−	0.777691i	−0.975984	+	0.217841i	$0.930098\pi$
$242$	7.56064	−	2.45660i	0.486017	−	0.157916i
$243$		−	1.93928i		−	0.124405i
$244$	−2.29996	−	7.07853i	−0.147240	−	0.453157i
$245$	3.25563	−	1.61697i	0.207995	−	0.103304i
$246$	0.0141809	−	0.0436442i	0.000904138	−	0.00278265i
$247$	−2.18301	−	0.709304i	−0.138902	−	0.0451320i
$248$	−1.96608	−	2.70608i	−0.124846	−	0.171836i
$249$	−0.539855			−0.0342119
$250$	−11.9593	+	5.63689i	−0.756370	+	0.356508i
$251$	1.06756			0.0673840			0.0336920	−	0.999432i	$-0.489273\pi$
$251$	1.06756			0.0673840			0.0336920	+	0.999432i	$0.489273\pi$
$252$	2.45510	+	3.37916i	0.154657	+	0.212867i
$253$	−1.93855	−	0.629875i	−0.121876	−	0.0395999i
$254$	−5.65604	+	17.4075i	−0.354891	+	1.09224i
$255$	0.00339133	−	0.00168437i	0.000212373	−	0.000105479i
$256$	−4.01760	−	12.3649i	−0.251100	−	0.772807i
$257$			0.680843i			0.0424698i	0.999775	+	0.0212349i	$0.00675979\pi$
$257$			0.680843i			0.0424698i	−0.999775	+	0.0212349i	$0.993240\pi$
$258$	0.0242543	−	0.00788071i	0.00151001	−	0.000490632i
$259$	11.2098	+	8.14442i	0.696545	+	0.506069i
$260$	2.73674	+	1.43000i	0.169726	+	0.0886846i
$261$	−13.7703	+	10.0047i	−0.852360	+	0.619276i
$262$	−0.325430	+	0.447915i	−0.0201051	+	0.0276723i
$263$	−7.98515	+	10.9906i	−0.492386	+	0.677711i	−0.980826	−	0.194887i	$-0.937566\pi$
$263$	−7.98515	+	10.9906i	−0.492386	+	0.677711i	0.488440	+	0.872597i	$0.337566\pi$
$264$	0.370579	−	0.269241i	0.0228076	−	0.0165707i
$265$	−4.87504	+	0.720940i	−0.299471	+	0.0442870i
$266$	−2.21786	−	1.61137i	−0.135986	−	0.0987994i
$267$	−0.406274	+	0.132006i	−0.0248635	+	0.00807865i
$268$		−	2.30260i		−	0.140654i
$269$	−0.540142	−	1.66239i	−0.0329331	−	0.101358i	0.933239	−	0.359257i	$-0.116970\pi$
$269$	−0.540142	−	1.66239i	−0.0329331	−	0.101358i	−0.966172	+	0.257899i	$0.916970\pi$
$270$	−0.166946	−	1.12890i	−0.0101600	−	0.0687025i
$271$	−9.22624	+	28.3955i	−0.560454	+	1.72490i	0.120631	+	0.992697i	$0.461508\pi$
$271$	−9.22624	+	28.3955i	−0.560454	+	1.72490i	−0.681085	+	0.732204i	$0.738492\pi$
$272$	−0.0544704	−	0.0176985i	−0.00330275	−	0.00107313i
$273$	−0.225170	−	0.309919i	−0.0136279	−	0.0187572i
$274$	11.4679			0.692800
$275$	0.212180	−	10.3387i	0.0127949	−	0.623449i
$276$	0.0426853			0.00256935
$277$	−7.18335	−	9.88703i	−0.431605	−	0.594054i	0.536715	−	0.843763i	$-0.319665\pi$
$277$	−7.18335	−	9.88703i	−0.431605	−	0.594054i	−0.968321	+	0.249709i	$0.919665\pi$
$278$	−8.00617	−	2.60136i	−0.480178	−	0.156019i
$279$	1.00619	−	3.09673i	0.0602389	−	0.185396i
$280$	11.1606	+	11.3920i	0.666973	+	0.680802i
$281$	−1.09234	−	3.36187i	−0.0651634	−	0.200552i	0.913174	−	0.407571i	$-0.133624\pi$
$281$	−1.09234	−	3.36187i	−0.0651634	−	0.200552i	−0.978337	+	0.207018i	$0.933624\pi$
$282$		−	0.715853i		−	0.0426284i
$283$	7.24025	−	2.35250i	0.430388	−	0.139842i	−0.0858085	−	0.996312i	$-0.527347\pi$
$283$	7.24025	−	2.35250i	0.430388	−	0.139842i	0.516197	+	0.856470i	$0.327347\pi$
$284$	2.92032	+	2.12174i	0.173289	+	0.125902i
$285$	−0.0716064	−	0.144173i	−0.00424160	−	0.00854010i
$286$	4.54162	−	3.29968i	0.268551	−	0.195114i
$287$	−0.734531	+	1.01100i	−0.0433580	+	0.0596772i
$288$	5.76275	−	7.93175i	0.339574	−	0.467383i
$289$	−13.7528	+	9.99202i	−0.808991	+	0.587766i
$290$	−10.7352	+	10.5171i	−0.630392	+	0.617587i
$291$	−0.495697	−	0.360145i	−0.0290583	−	0.0211121i
$292$	3.01319	−	0.979043i	0.176333	−	0.0572942i
$293$		−	3.72244i		−	0.217467i	−0.994071	−	0.108734i	$-0.965320\pi$
$293$		−	3.72244i		−	0.217467i	0.994071	−	0.108734i	$-0.0346795\pi$
$294$	0.0427663	+	0.131621i	0.00249418	+	0.00767630i
$295$	−16.8187	−	2.84101i	−0.979225	−	0.165410i
$296$	5.68221	−	17.4880i	0.330272	−	1.01647i
$297$	0.848885	+	0.275819i	0.0492573	+	0.0160047i
$298$	0.292220	+	0.402206i	0.0169278	+	0.0232992i
$299$	2.26221			0.130827
$300$	0.0626787	+	0.207284i	0.00361876	+	0.0119676i
$301$	−0.694472			−0.0400287
$302$	−8.97015	−	12.3464i	−0.516174	−	0.710453i
$303$	−0.653482	−	0.212329i	−0.0375416	−	0.0121980i
$304$	−0.752405	+	2.31567i	−0.0431534	+	0.132813i
$305$	12.8111	−	24.5181i	0.733563	−	1.40390i
$306$	−0.0257425	−	0.0792273i	−0.00147160	−	0.00452912i
$307$			5.42173i			0.309434i	0.987959	+	0.154717i	$0.0494466\pi$
$307$			5.42173i			0.309434i	−0.987959	+	0.154717i	$0.950553\pi$
$308$	−2.74331	+	0.891356i	−0.156315	+	0.0507897i
$309$	−0.748913	−	0.544117i	−0.0426042	−	0.0309537i
$310$	0.478845	−	2.83476i	0.0271966	−	0.161003i
$311$	−26.1866	+	19.0256i	−1.48490	+	1.07885i	−0.508968	+	0.860786i	$0.669973\pi$
$311$	−26.1866	+	19.0256i	−1.48490	+	1.07885i	−0.975935	+	0.218059i	$0.930027\pi$
$312$	−0.298816	+	0.411284i	−0.0169171	+	0.0232844i
$313$	14.1066	−	19.4161i	0.797352	−	1.09746i	−0.195801	−	0.980644i	$-0.562731\pi$
$313$	14.1066	−	19.4161i	0.797352	−	1.09746i	0.993153	−	0.116817i	$-0.0372692\pi$
$314$	19.7790	−	14.3703i	1.11619	−	0.810963i
$315$	−2.58576	+	15.3077i	−0.145691	+	0.862489i
$316$	−5.75519	−	4.18139i	−0.323755	−	0.235221i
$317$	11.9904	−	3.89590i	0.673445	−	0.218816i	0.0477220	−	0.998861i	$-0.484804\pi$
$317$	11.9904	−	3.89590i	0.673445	−	0.218816i	0.625723	+	0.780045i	$0.284804\pi$
$318$		−	0.187621i		−	0.0105213i
$319$	−3.63234	−	11.1792i	−0.203372	−	0.625915i
$320$	9.05162	−	17.3231i	0.506001	−	0.968390i
$321$	−0.377992	+	1.16334i	−0.0210974	+	0.0649312i
$322$	2.56960	+	0.834914i	0.143198	+	0.0465280i
$323$	−0.0138262	−	0.0190301i	−0.000769311	−	0.00105887i
$324$	5.38647			0.299249
$325$	3.32181	+	10.9855i	0.184261	+	0.609368i
$326$	−16.1995			−0.897209
$327$	−0.735133	−	1.01182i	−0.0406530	−	0.0559540i
$328$	1.57722	+	0.512469i	0.0870872	+	0.0282963i
$329$	−6.02390	+	18.5397i	−0.332108	+	1.02212i
$330$	0.388200	+	0.0655745i	0.0213697	+	0.00360976i
$331$	−0.846283	−	2.60459i	−0.0465159	−	0.143161i	0.925101	−	0.379721i	$-0.123980\pi$
$331$	−0.846283	−	2.60459i	−0.0465159	−	0.143161i	−0.971617	+	0.236560i	$0.923980\pi$
$332$		−	4.51145i		−	0.247598i
$333$	17.0237	−	5.53135i	0.932895	−	0.303116i
$334$	−8.39264	−	6.09761i	−0.459225	−	0.333646i
$335$	6.11338	−	5.98920i	0.334010	−	0.327225i
$336$	−0.328752	+	0.238852i	−0.0179349	+	0.0130304i
$337$	−11.3030	+	15.5573i	−0.615715	+	0.847459i	−0.997032	−	0.0769852i	$-0.975471\pi$
$337$	−11.3030	+	15.5573i	−0.615715	+	0.847459i	0.381317	+	0.924444i	$0.375471\pi$
$338$	5.37387	−	7.39649i	0.292300	−	0.402316i
$339$	0.705513	−	0.512586i	0.0383182	−	0.0278398i
$340$	0.0140759	+	0.0283406i	0.000763373	+	0.00153699i
$341$	1.81917	+	1.32170i	0.0985135	+	0.0715743i
$342$	−3.36814	+	1.09438i	−0.182128	+	0.0591770i
$343$		−	19.9965i		−	1.07971i
$344$	0.284794	+	0.876505i	0.0153550	+	0.0472580i
$345$	0.111027	+	0.113329i	0.00597750	+	0.00610143i
$346$	5.48220	−	16.8725i	0.294725	−	0.907069i
$347$	−1.12687	−	0.366142i	−0.0604936	−	0.0196555i	0.278614	−	0.960403i	$-0.410125\pi$
$347$	−1.12687	−	0.366142i	−0.0604936	−	0.0196555i	−0.339107	+	0.940748i	$0.610125\pi$
$348$	0.144687	+	0.199144i	0.00775603	+	0.0106753i
$349$	2.58538			0.138392			0.0691962	−	0.997603i	$-0.477957\pi$
$349$	2.58538			0.138392			0.0691962	+	0.997603i	$0.477957\pi$
$350$	−0.281250	+	13.7042i	−0.0150334	+	0.732523i
$351$	−0.990613			−0.0528750
$352$	3.97968	+	5.47756i	0.212118	+	0.291955i
$353$	5.36374	+	1.74278i	0.285483	+	0.0927590i	0.448258	−	0.893904i	$-0.352045\pi$
$353$	5.36374	+	1.74278i	0.285483	+	0.0927590i	−0.162775	+	0.986663i	$0.552045\pi$
$354$	0.200674	−	0.617612i	0.0106657	−	0.0328257i
$355$	1.96274	+	13.2722i	0.104172	+	0.704416i
$356$	−1.10315	−	3.39514i	−0.0584668	−	0.179942i
$357$		−	0.00392577i		−	0.000207774i
$358$	0.167413	−	0.0543958i	0.00884806	−	0.00287491i
$359$	18.8037	+	13.6617i	0.992424	+	0.721038i	0.960450	−	0.278451i	$-0.0898209\pi$
$359$	18.8037	+	13.6617i	0.992424	+	0.721038i	0.0319731	+	0.999489i	$0.489821\pi$
$360$	20.3805	−	3.01394i	1.07414	−	0.158849i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	13.6781	−	18.8263i	0.718904	−	0.989487i
$363$	0.284469	−	0.391538i	0.0149308	−	0.0205504i
$364$	2.58993	−	1.88169i	0.135749	−	0.0986276i
$365$	10.4368	+	5.45343i	0.546289	+	0.285445i
$366$	0.852057	+	0.619056i	0.0445377	+	0.0323586i
$367$	23.9140	−	7.77012i	1.24830	−	0.405597i	0.390988	−	0.920396i	$-0.372134\pi$
$367$	23.9140	−	7.77012i	1.24830	−	0.405597i	0.857311	+	0.514799i	$0.172134\pi$
$368$		−	2.39968i		−	0.125092i
$369$	0.498863	+	1.53534i	0.0259698	+	0.0799267i
$370$	14.1547	−	7.03018i	0.735866	−	0.365482i
$371$	−1.57883	+	4.85915i	−0.0819689	+	0.252274i
$372$	−0.0447845	−	0.0145514i	−0.00232197	−	0.000754454i
$373$	−2.36959	−	3.26147i	−0.122693	−	0.168872i	0.743252	−	0.669011i	$-0.233282\pi$
$373$	−2.36959	−	3.26147i	−0.122693	−	0.168872i	−0.865945	+	0.500139i	$0.833282\pi$
$374$	0.0575290			0.00297475
$375$	−0.387307	+	0.705571i	−0.0200004	+	0.0364355i
$376$	25.8695			1.33412
$377$	7.66804	+	10.5541i	0.394924	+	0.543566i
$378$	−1.12522	−	0.365605i	−0.0578750	−	0.0188047i
$379$	−8.58386	+	26.4184i	−0.440923	+	1.35702i	0.445970	+	0.895048i	$0.352859\pi$
$379$	−8.58386	+	26.4184i	−0.440923	+	1.35702i	−0.886893	+	0.461974i	$0.847141\pi$
$380$	1.20483	−	0.598400i	0.0618064	−	0.0306973i
$381$	0.344331	+	1.05974i	0.0176406	+	0.0542922i
$382$			26.2573i			1.34344i
$383$	22.9601	−	7.46017i	1.17320	−	0.381197i	0.343366	−	0.939202i	$-0.388433\pi$
$383$	22.9601	−	7.46017i	1.17320	−	0.381197i	0.829838	+	0.558005i	$0.188433\pi$
$384$	0.220681	+	0.160334i	0.0112616	+	0.00818201i
$385$	−9.50207	−	4.96500i	−0.484270	−	0.253040i
$386$	−4.89153	+	3.55390i	−0.248972	+	0.180889i
$387$	−0.527328	+	0.725804i	−0.0268056	+	0.0368947i
$388$	3.00966	−	4.14244i	0.152792	−	0.210300i
$389$	−23.7228	+	17.2356i	−1.20279	+	0.873879i	−0.994556	−	0.104200i	$-0.966772\pi$
$389$	−23.7228	+	17.2356i	−1.20279	+	0.873879i	−0.208235	+	0.978079i	$0.566772\pi$
$390$	−0.432244	+	0.0639219i	−0.0218875	+	0.00323681i
$391$	0.0187553	+	0.0136266i	0.000948499	+	0.000689125i
$392$	−4.75654	+	1.54549i	−0.240241	+	0.0780591i
$393$			0.0337056i			0.00170022i
$394$	5.25960	+	16.1874i	0.264975	+	0.815508i
$395$	−3.86805	−	26.1560i	−0.194623	−	1.31605i
$396$	−1.15149	+	3.54391i	−0.0578644	+	0.178088i
$397$	−21.7568	−	7.06923i	−1.09194	−	0.354794i	−0.292947	−	0.956129i	$-0.594636\pi$
$397$	−21.7568	−	7.06923i	−1.09194	−	0.354794i	−0.798997	+	0.601334i	$0.794636\pi$
$398$	3.55050	+	4.88685i	0.177971	+	0.244955i
$399$	−0.166894			−0.00835515
$400$	11.6531	−	3.52367i	0.582654	−	0.176183i
$401$	27.3010			1.36335			0.681674	−	0.731656i	$-0.261252\pi$
$401$	27.3010			1.36335			0.681674	+	0.731656i	$0.261252\pi$
$402$	0.191519	+	0.263603i	0.00955208	+	0.0131473i
$403$	−2.37347	−	0.771186i	−0.118231	−	0.0384155i
$404$	1.77439	−	5.46101i	0.0882792	−	0.271696i
$405$	14.0106	+	14.3010i	0.696190	+	0.710624i
$406$	4.81475	+	14.8183i	0.238952	+	0.735419i
$407$			12.3614i			0.612731i
$408$	−0.00495479	+	0.00160991i	−0.000245299	+	7.97023e-5i
$409$	−12.5354	−	9.10748i	−0.619834	−	0.450336i	0.233029	−	0.972470i	$-0.425136\pi$
$409$	−12.5354	−	9.10748i	−0.619834	−	0.450336i	−0.852864	+	0.522134i	$0.825136\pi$
$410$	0.634040	+	1.27659i	0.0313130	+	0.0630460i
$411$	0.564813	−	0.410361i	0.0278602	−	0.0202416i
$412$	4.54707	−	6.25851i	0.224018	−	0.308335i
$413$	−10.3944	+	14.3067i	−0.511475	+	0.703985i
$414$	2.82374	−	2.05157i	0.138779	−	0.100829i
$415$	11.9779	−	11.7346i	0.587970	−	0.576027i
$416$	−6.07924	−	4.41682i	−0.298059	−	0.216553i
$417$	−0.487404	+	0.158367i	−0.0238683	+	0.00775527i
$418$		−	2.44570i		−	0.119623i
$419$	−2.95419	−	9.09207i	−0.144322	−	0.444177i	0.852601	−	0.522562i	$-0.175024\pi$
$419$	−2.95419	−	9.09207i	−0.144322	−	0.444177i	−0.996923	+	0.0783852i	$0.975024\pi$
$420$	0.221378	+	0.0373950i	0.0108021	+	0.00182469i
$421$	−7.04109	+	21.6702i	−0.343162	+	1.05614i	0.619399	+	0.785076i	$0.287376\pi$
$421$	−7.04109	+	21.6702i	−0.343162	+	1.05614i	−0.962561	+	0.271066i	$0.912624\pi$
$422$	10.7248	+	3.48469i	0.522074	+	0.169632i
$423$	14.8020	+	20.3733i	0.719700	+	0.990581i
$424$	6.78028			0.329279
$425$	−0.0386318	+	0.111087i	−0.00187392	+	0.00538852i
$426$	−0.510796			−0.0247481
$427$	−16.8578	−	23.2028i	−0.815807	−	1.12286i
$428$	−9.72178	−	3.15880i	−0.469920	−	0.152686i
$429$	0.105609	−	0.325030i	0.00509883	−	0.0156926i
$430$	−0.366837	+	0.702056i	−0.0176904	+	0.0338562i
$431$	−9.00030	−	27.7001i	−0.433529	−	1.33427i	−0.894586	−	0.446896i	$-0.852530\pi$
$431$	−9.00030	−	27.7001i	−0.433529	−	1.33427i	0.461057	−	0.887371i	$-0.347470\pi$
$432$			1.05081i			0.0505570i
$433$	14.9784	−	4.86676i	0.719814	−	0.233882i	0.0738714	−	0.997268i	$-0.476465\pi$
$433$	14.9784	−	4.86676i	0.719814	−	0.233882i	0.645943	+	0.763386i	$0.276465\pi$
$434$	−2.41135	−	1.75195i	−0.115749	−	0.0840963i
$435$	−0.152387	+	0.902129i	−0.00730640	+	0.0432538i
$436$	8.45560	−	6.14335i	0.404950	−	0.294213i
$437$	0.579298	−	0.797335i	0.0277116	−	0.0381417i
$438$	−0.263519	+	0.362703i	−0.0125914	+	0.0173306i
$439$	−26.8193	+	19.4854i	−1.28002	+	0.929986i	−0.999554	−	0.0298792i	$-0.990488\pi$
$439$	−26.8193	+	19.4854i	−1.28002	+	0.929986i	−0.280462	+	0.959865i	$0.590488\pi$
$440$	−2.36974	+	14.0288i	−0.112973	+	0.668797i
$441$	−3.93873	−	2.86165i	−0.187558	−	0.136269i
$442$	−0.0607232	+	0.0197302i	−0.00288831	+	0.000938468i
$443$			30.9068i			1.46842i	0.678920	+	0.734212i	$0.262448\pi$
$443$			30.9068i			1.46842i	−0.678920	+	0.734212i	$0.737552\pi$
$444$	−0.0799937	−	0.246195i	−0.00379633	−	0.0116839i
$445$	6.14472	−	11.7598i	0.291288	−	0.557469i
$446$	4.17287	−	12.8428i	0.197591	−	0.608122i
$447$	0.0287847	+	0.00935272i	0.00136147	+	0.000442368i
$448$	−11.9108	−	16.3938i	−0.562732	−	0.774534i
$449$	−10.8098			−0.510146			−0.255073	−	0.966922i	$-0.582099\pi$
$449$	−10.8098			−0.510146			−0.255073	+	0.966922i	$0.582099\pi$
$450$	14.1090	+	10.6999i	0.665104	+	0.504397i
$451$	−1.11485			−0.0524963
$452$	4.28357	+	5.89583i	0.201482	+	0.277316i
$453$	−0.883592	−	0.287096i	−0.0415148	−	0.0134890i
$454$	−6.16677	+	18.9794i	−0.289421	+	0.890745i
$455$	11.7325	+	1.98184i	0.550026	+	0.0929100i
$456$	0.0684410	+	0.210640i	0.00320505	+	0.00986411i
$457$			24.9010i			1.16482i	0.812895	+	0.582411i	$0.197891\pi$
$457$			24.9010i			1.16482i	−0.812895	+	0.582411i	$0.802109\pi$
$458$	−5.47764	+	1.77979i	−0.255953	+	0.0831642i
$459$	−0.00821289	−	0.00596701i	−0.000383345	−	0.000278516i
$460$	−0.947067	+	0.927830i	−0.0441572	+	0.0432603i
$461$	5.00907	−	3.63930i	0.233295	−	0.169499i	−0.464996	−	0.885313i	$-0.653944\pi$
$461$	5.00907	−	3.63930i	0.233295	−	0.169499i	0.698291	+	0.715814i	$0.253944\pi$
$462$	0.239917	−	0.330218i	0.0111620	−	0.0153631i
$463$	15.0817	−	20.7582i	0.700906	−	0.964714i	−0.299039	−	0.954241i	$-0.596666\pi$
$463$	15.0817	−	20.7582i	0.700906	−	0.964714i	0.999945	−	0.0104732i	$-0.00333379\pi$
$464$	11.1955	−	8.13399i	0.519737	−	0.377611i
$465$	−0.0778536	−	0.156752i	−0.00361037	−	0.00726918i
$466$	−19.8335	−	14.4099i	−0.918771	−	0.667526i
$467$	12.2240	−	3.97182i	0.565659	−	0.183794i	−0.0122068	−	0.999925i	$-0.503886\pi$
$467$	12.2240	−	3.97182i	0.565659	−	0.183794i	0.577866	+	0.816132i	$0.303886\pi$
$468$		−	4.13559i		−	0.191168i
$469$	−2.74186	−	8.43859i	−0.126608	−	0.389658i
$470$	15.5602	+	15.8828i	0.717737	+	0.732618i
$471$	0.459932	−	1.41553i	0.0211925	−	0.0652239i
$472$	22.3193	+	7.25198i	1.02733	+	0.333799i
$473$	−0.364166	−	0.501231i	−0.0167444	−	0.0230466i
$474$	1.00664			0.0462367
$475$	4.72258	+	1.64233i	0.216687	+	0.0753553i
$476$	0.0328069			0.00150370
$477$	3.87954	+	5.33973i	0.177632	+	0.244489i
$478$	−6.36297	−	2.06745i	−0.291035	−	0.0945631i
$479$	−4.45130	+	13.6997i	−0.203385	+	0.625956i	0.796391	+	0.604783i	$0.206740\pi$
$479$	−4.45130	+	13.6997i	−0.203385	+	0.625956i	−0.999776	+	0.0211729i	$0.993260\pi$
$480$	−0.0770951	−	0.521322i	−0.00351889	−	0.0237950i
$481$	−4.23946	−	13.0477i	−0.193303	−	0.594925i
$482$			24.2891i			1.10634i
$483$	0.156434	−	0.0508284i	0.00711797	−	0.00231277i
$484$	3.27200	+	2.37725i	0.148727	+	0.108057i
$485$	18.8264	−	2.78412i	0.854864	−	0.126421i
$486$	−1.85529	+	1.34795i	−0.0841577	+	0.0611441i
$487$	−15.6239	+	21.5044i	−0.707984	+	0.974457i	0.291854	+	0.956463i	$0.405728\pi$
$487$	−15.6239	+	21.5044i	−0.707984	+	0.974457i	−0.999838	+	0.0179939i	$0.994272\pi$
$488$	−22.3715	+	30.7917i	−1.01271	+	1.39387i
$489$	−0.797856	+	0.579676i	−0.0360803	+	0.0262139i
$490$	−3.80985	−	1.99071i	−0.172112	−	0.0899313i
$491$	−8.48705	−	6.16620i	−0.383015	−	0.278277i	0.379572	−	0.925162i	$-0.376071\pi$
$491$	−8.48705	−	6.16620i	−0.383015	−	0.278277i	−0.762587	+	0.646885i	$0.776071\pi$
$492$	0.0222039	−	0.00721450i	0.00100103	−	0.000325255i
$493$			0.133690i			0.00602111i
$494$	0.838777	+	2.58149i	0.0377383	+	0.116147i
$495$	−12.4041	+	6.16075i	−0.557525	+	0.276905i
$496$	−0.818048	+	2.51769i	−0.0367314	+	0.113048i
$497$	13.2289	+	4.29834i	0.593399	+	0.192807i
$498$	0.375240	+	0.516474i	0.0168149	+	0.0231437i
$499$	−9.46038			−0.423505			−0.211752	−	0.977323i	$-0.567917\pi$
$499$	−9.46038			−0.423505			−0.211752	+	0.977323i	$0.567917\pi$
$500$	−5.89631	−	3.23664i	−0.263691	−	0.144747i
$501$	−0.631546			−0.0282154
$502$	−0.742038	−	1.02133i	−0.0331188	−	0.0455841i
$503$	−12.2677	−	3.98602i	−0.546990	−	0.177728i	0.0224693	−	0.999748i	$-0.492847\pi$
$503$	−12.2677	−	3.98602i	−0.546990	−	0.177728i	−0.569459	+	0.822020i	$0.692847\pi$
$504$	6.60043	−	20.3140i	0.294006	−	0.904858i
$505$	19.1142	−	9.49344i	0.850573	−	0.422453i
$506$	0.744848	+	2.29241i	0.0331125	+	0.101910i
$507$		−	0.556586i		−	0.0247189i
$508$	−8.85605	+	2.87750i	−0.392923	+	0.127669i
$509$	−27.2263	−	19.7811i	−1.20679	−	0.876782i	−0.211852	−	0.977302i	$-0.567949\pi$
$509$	−27.2263	−	19.7811i	−1.20679	−	0.876782i	−0.994935	+	0.100520i	$0.967949\pi$
$510$	−0.00396865	−	0.00207369i	−0.000175735	−	9.18244e-5i
$511$	9.87694	−	7.17602i	0.436930	−	0.317448i
$512$	−13.4911	+	18.5689i	−0.596229	+	0.820639i
$513$	−0.253672	+	0.349150i	−0.0111999	+	0.0154153i
$514$	0.651356	−	0.473238i	0.0287301	−	0.0208736i
$515$	28.4435	−	4.20633i	1.25337	−	0.185353i
$516$	0.0104965	+	0.00762615i	0.000462083	+	0.000335723i
$517$	−16.5397	+	5.37407i	−0.727415	+	0.236351i
$518$		−	16.3853i		−	0.719930i
$519$	−0.333748	−	1.02717i	−0.0146499	−	0.0450878i
$520$	−2.31001	−	15.6205i	−0.101301	−	0.685003i
$521$	1.44175	−	4.43724i	0.0631641	−	0.194399i	−0.914494	−	0.404598i	$-0.867411\pi$
$521$	1.44175	−	4.43724i	0.0631641	−	0.194399i	0.977659	+	0.210199i	$0.0674113\pi$
$522$	19.1428	+	6.21987i	0.837858	+	0.272237i
$523$	−10.2673	−	14.1317i	−0.448956	−	0.617934i	0.523217	−	0.852199i	$-0.324732\pi$
$523$	−10.2673	−	14.1317i	−0.448956	−	0.617934i	−0.972173	+	0.234265i	$0.924732\pi$
$524$	−0.281671			−0.0123049
$525$	0.476534	+	0.685022i	0.0207976	+	0.0298968i
$526$	16.0649			0.700463
$527$	−0.0150325	−	0.0206904i	−0.000654824	−	0.000901288i
$528$	−0.344780	−	0.112026i	−0.0150046	−	0.00487530i
$529$	6.80723	−	20.9505i	0.295967	−	0.910892i
$530$	4.07824	+	4.16280i	0.177147	+	0.180820i
$531$	7.05945	+	21.7267i	0.306354	+	0.942860i
$532$		−	1.39470i		−	0.0604678i
$533$	1.17675	−	0.382350i	0.0509708	−	0.0165614i
$534$	0.408680	+	0.296924i	0.0176853	+	0.0128491i
$535$	−16.9004	−	34.0275i	−0.730667	−	1.47114i
$536$	−9.52609	+	6.92111i	−0.411465	+	0.298946i
$537$	0.00629892	−	0.00866972i	0.000271818	−	0.000374126i
$538$	−1.21495	+	1.67223i	−0.0523802	+	0.0720952i
$539$	2.72003	−	1.97622i	0.117160	−	0.0851219i
$540$	0.414717	−	0.406293i	0.0178466	−	0.0174841i
$541$	−7.55029	−	5.48561i	−0.324612	−	0.235845i	0.413529	−	0.910491i	$-0.364296\pi$
$541$	−7.55029	−	5.48561i	−0.324612	−	0.235845i	−0.738141	+	0.674646i	$0.764296\pi$
$542$	33.5786	−	10.9103i	1.44232	−	0.468640i
$543$		−	1.41668i		−	0.0607954i
$544$	−0.0237962	−	0.0732372i	−0.00102025	−	0.00314002i
$545$	38.3041	+	6.47030i	1.64077	+	0.277157i
$546$	−0.139987	+	0.430835i	−0.00599088	+	0.0184380i
$547$	−10.8671	−	3.53095i	−0.464646	−	0.150973i	0.0673325	−	0.997731i	$-0.478551\pi$
$547$	−10.8671	−	3.53095i	−0.464646	−	0.150973i	−0.531978	+	0.846758i	$0.678551\pi$
$548$	3.42930	+	4.72003i	0.146492	+	0.201630i
$549$	−37.0502			−1.58126
$550$	−10.0384	+	6.98322i	−0.428041	+	0.297765i
$551$	5.68349			0.242125
$552$	−0.128303	−	0.176594i	−0.00546093	−	0.00751632i
$553$	−26.0708	−	8.47090i	−1.10864	−	0.360219i
$554$	−4.46585	+	13.7445i	−0.189736	+	0.583947i
$555$	0.445578	−	0.852752i	0.0189137	−	0.0361973i
$556$	−1.32344	−	4.07313i	−0.0561264	−	0.172739i
$557$			35.6819i			1.51189i	0.654634	+	0.755946i	$0.272823\pi$
$557$			35.6819i			1.51189i	−0.654634	+	0.755946i	$0.727177\pi$
$558$	−3.66199	+	1.18985i	−0.155024	+	0.0503705i
$559$	0.556288	+	0.404167i	0.0235285	+	0.0170944i
$560$	2.10226	−	12.4454i	0.0888369	−	0.525913i
$561$	0.00283341	−	0.00205859i	0.000119626	−	8.69137e-5i
$562$	−2.45701	+	3.38178i	−0.103643	+	0.142652i
$563$	−11.0702	+	15.2368i	−0.466552	+	0.642154i	−0.975851	−	0.218435i	$-0.929905\pi$
$563$	−11.0702	+	15.2368i	−0.466552	+	0.642154i	0.509299	+	0.860590i	$0.329905\pi$
$564$	0.294636	−	0.214065i	0.0124064	−	0.00901377i
$565$	−4.51154	+	26.7083i	−0.189802	+	1.12362i
$566$	−7.28314	−	5.29151i	−0.306133	−	0.222419i
$567$	19.7404	−	6.41405i	0.829020	−	0.269365i
$568$		−	18.4592i		−	0.774530i
$569$	14.3496	+	44.1635i	0.601566	+	1.85143i	0.518865	+	0.854856i	$0.326355\pi$
$569$	14.3496	+	44.1635i	0.601566	+	1.85143i	0.0827011	+	0.996574i	$0.473645\pi$
$570$	−0.0881574	+	0.168717i	−0.00369251	+	0.00706677i
$571$	5.57696	−	17.1641i	0.233388	−	0.718296i	−0.763943	−	0.645284i	$-0.776739\pi$
$571$	5.57696	−	17.1641i	0.233388	−	0.718296i	0.997331	−	0.0730117i	$-0.0232610\pi$
$572$	2.71621	+	0.882549i	0.113570	+	0.0369012i
$573$	0.939578	+	1.29322i	0.0392515	+	0.0540250i
$574$	1.47776			0.0616807
$575$	−4.92676	−	0.101111i	−0.205460	−	0.00421663i
$576$	−26.1776			−1.09073
$577$	14.7119	+	20.2492i	0.612465	+	0.842986i	0.996777	−	0.0802173i	$-0.0255614\pi$
$577$	14.7119	+	20.2492i	0.612465	+	0.842986i	−0.384312	+	0.923203i	$0.625561\pi$
$578$	19.1185	+	6.21199i	0.795227	+	0.258385i
$579$	−0.113745	+	0.350072i	−0.00472709	+	0.0145485i
$580$	−7.53891	−	1.27347i	−0.313036	−	0.0528778i
$581$	−5.37210	−	16.5336i	−0.222872	−	0.685931i
$582$			0.724557i			0.0300338i
$583$	−4.33497	+	1.40852i	−0.179536	+	0.0583348i
$584$	−13.1074	−	9.52308i	−0.542388	−	0.394068i
$585$	10.9800	−	10.7569i	0.453966	−	0.444745i
$586$	−3.56122	+	2.58738i	−0.147113	+	0.106884i
$587$	−19.6716	+	27.0757i	−0.811935	+	1.11753i	0.179087	+	0.983833i	$0.442686\pi$
$587$	−19.6716	+	27.0757i	−0.811935	+	1.11753i	−0.991022	+	0.133699i	$0.957314\pi$
$588$	−0.0413849	+	0.0569614i	−0.00170668	+	0.00234905i
$589$	−0.879598	+	0.639065i	−0.0362432	+	0.0263322i
$590$	8.97234	+	18.0650i	0.369385	+	0.743726i
$591$	0.838285	+	0.609050i	0.0344824	+	0.0250530i
$592$	−13.8406	+	4.49708i	−0.568844	+	0.184829i
$593$		−	0.620136i		−	0.0254659i	−0.999919	−	0.0127330i	$-0.995947\pi$
$593$		−	0.620136i		−	0.0254659i	0.999919	−	0.0127330i	$-0.00405314\pi$
$594$	−0.326166	−	1.00384i	−0.0133828	−	0.0411879i
$595$	0.0853327	+	0.0871019i	0.00349830	+	0.00357083i
$596$	−0.0781587	+	0.240548i	−0.00320150	+	0.00985322i
$597$	0.349737	+	0.113636i	0.0143138	+	0.00465083i
$598$	−1.57241	−	2.16424i	−0.0643006	−	0.0885022i
$599$	−14.2470			−0.582116			−0.291058	−	0.956705i	$-0.594007\pi$
$599$	−14.2470			−0.582116			−0.291058	+	0.956705i	$0.594007\pi$
$600$	0.669159	−	0.882360i	0.0273183	−	0.0360222i
$601$	21.4067			0.873198			0.436599	−	0.899656i	$-0.356183\pi$
$601$	21.4067			0.873198			0.436599	+	0.899656i	$0.356183\pi$
$602$	0.482711	+	0.664394i	0.0196738	+	0.0270787i
$603$	−10.9013	−	3.54204i	−0.443934	−	0.144243i
$604$	2.39920	−	7.38399i	0.0976222	−	0.300450i
$605$	2.19911	+	14.8705i	0.0894065	+	0.604572i
$606$	0.251087	+	0.772765i	0.0101997	+	0.0313914i
$607$		−	9.74218i		−	0.395423i	−0.980260	−	0.197712i	$-0.936649\pi$
$607$		−	9.74218i		−	0.395423i	0.980260	−	0.197712i	$-0.0633509\pi$
$608$	−3.11349	+	1.01163i	−0.126269	+	0.0410272i
$609$	0.767386	+	0.557538i	0.0310960	+	0.0225926i
$610$	−32.3609	+	4.78565i	−1.31025	+	0.193765i
$611$	15.6149	−	11.3449i	0.631713	−	0.458966i
$612$	0.0249110	−	0.0342870i	0.00100697	−	0.00138597i
$613$	8.09152	−	11.1370i	0.326814	−	0.449820i	−0.613719	−	0.789525i	$-0.710327\pi$
$613$	8.09152	−	11.1370i	0.326814	−	0.449820i	0.940532	+	0.339705i	$0.110327\pi$
$614$	5.18691	−	3.76851i	0.209327	−	0.152085i
$615$	0.0769083	+	0.0401859i	0.00310124	+	0.00162045i
$616$	11.9334	+	8.67015i	0.480812	+	0.349330i
$617$	10.8987	−	3.54120i	0.438764	−	0.142563i	−0.0813011	−	0.996690i	$-0.525908\pi$
$617$	10.8987	−	3.54120i	0.438764	−	0.142563i	0.520065	+	0.854126i	$0.325908\pi$
$618$			1.09468i			0.0440345i
$619$	−2.96659	−	9.13024i	−0.119238	−	0.366975i	0.873570	−	0.486699i	$-0.161799\pi$
$619$	−2.96659	−	9.13024i	−0.119238	−	0.366975i	−0.992807	+	0.119724i	$0.961799\pi$
$620$	1.30994	−	0.650606i	0.0526085	−	0.0261290i
$621$	0.131437	−	0.404523i	0.00527440	−	0.0162329i
$622$	36.4033	+	11.8281i	1.45964	+	0.474265i
$623$	−8.08567	−	11.1290i	−0.323946	−	0.445873i
$624$	0.402344			0.0161067
$625$	−6.74341	−	24.0734i	−0.269736	−	0.962934i
$626$	−28.3803			−1.13431
$627$	−0.0875156	−	0.120455i	−0.00349503	−	0.00481050i
$628$	11.8292	+	3.84355i	0.472038	+	0.153375i
$629$	0.0434455	−	0.133712i	0.00173229	−	0.00533143i
$630$	16.4420	−	8.16622i	0.655065	−	0.325350i
$631$	15.0578	+	46.3430i	0.599440	+	1.84489i	0.531254	+	0.847213i	$0.321721\pi$
$631$	15.0578	+	46.3430i	0.599440	+	1.84489i	0.0681856	+	0.997673i	$0.478279\pi$
$632$			36.3782i			1.44705i
$633$	0.652909	−	0.212143i	0.0259508	−	0.00843192i
$634$	−12.0614	−	8.76311i	−0.479019	−	0.348027i
$635$	−30.6749	−	16.0282i	−1.21730	−	0.636058i
$636$	0.0772225	−	0.0561054i	0.00306207	−	0.00222473i
$637$	−2.19329	+	3.01881i	−0.0869015	+	0.119610i
$638$	−8.17027	+	11.2454i	−0.323464	+	0.445210i
$639$	14.5373	−	10.5620i	0.575087	−	0.417825i
$640$	−8.38140	+	1.23947i	−0.331304	+	0.0489945i
$641$	−10.9750	−	7.97381i	−0.433487	−	0.314946i	0.349555	−	0.936916i	$-0.386333\pi$
$641$	−10.9750	−	7.97381i	−0.433487	−	0.314946i	−0.783042	+	0.621969i	$0.786333\pi$
$642$	1.37569	−	0.446988i	0.0542941	−	0.0176412i
$643$		−	34.0329i		−	1.34213i	−0.741400	−	0.671064i	$-0.765838\pi$
$643$		−	34.0329i		−	1.34213i	0.741400	−	0.671064i	$-0.234162\pi$
$644$	0.424762	+	1.30728i	0.0167380	+	0.0515142i
$645$	0.00705468	+	0.0477042i	0.000277778	+	0.00187835i
$646$	−0.00859568	+	0.0264548i	−0.000338193	+	0.00104085i
$647$	−16.8597	−	5.47805i	−0.662824	−	0.215365i	−0.0417638	−	0.999128i	$-0.513298\pi$
$647$	−16.8597	−	5.47805i	−0.662824	−	0.215365i	−0.621060	+	0.783763i	$0.713298\pi$
$648$	−16.1906	−	22.2844i	−0.636026	−	0.875414i
$649$	−15.7764			−0.619276
$650$	8.20085	−	10.8137i	0.321664	−	0.424150i
$651$	−0.181454			−0.00711176
$652$	−4.84423	−	6.66751i	−0.189715	−	0.261120i
$653$	42.2960	+	13.7428i	1.65517	+	0.537798i	0.979851	−	0.199728i	$-0.0640059\pi$
$653$	42.2960	+	13.7428i	1.65517	+	0.537798i	0.675319	+	0.737526i	$0.264006\pi$
$654$	−0.457029	+	1.40659i	−0.0178712	+	0.0550020i
$655$	−0.732644	−	0.747834i	−0.0286268	−	0.0292203i
$656$	−0.405584	−	1.24826i	−0.0158354	−	0.0487363i
$657$		−	15.7715i		−	0.615304i
$658$	21.9238	−	7.12346i	0.854677	−	0.277702i
$659$	7.43298	+	5.40038i	0.289548	+	0.210369i	0.723071	−	0.690774i	$-0.242730\pi$
$659$	7.43298	+	5.40038i	0.289548	+	0.210369i	−0.433523	+	0.901142i	$0.642730\pi$
$660$	0.0890960	+	0.179387i	0.00346806	+	0.00698264i
$661$	−22.4547	+	16.3143i	−0.873385	+	0.634551i	−0.931493	−	0.363759i	$-0.881493\pi$
$661$	−22.4547	+	16.3143i	−0.873385	+	0.634551i	0.0581083	+	0.998310i	$0.481493\pi$
$662$	−1.90356	+	2.62002i	−0.0739838	+	0.101830i
$663$	−0.00228471	+	0.00314463i	−8.87308e−5	+	0.000122127i
$664$	−18.6644	+	13.5605i	−0.724318	+	0.526248i
$665$	3.70291	−	3.62770i	0.143593	−	0.140676i
$666$	−17.1246	−	12.4417i	−0.663564	−	0.482108i
$667$	−5.32727	+	1.73093i	−0.206273	+	0.0670221i
$668$		−	5.27770i		−	0.204200i
$669$	−0.254038	−	0.781848i	−0.00982167	−	0.0302280i
$670$	−9.97907	−	1.68566i	−0.385525	−	0.0651226i
$671$	7.90662	−	24.3341i	0.305232	−	0.939406i
$672$	−0.519623	−	0.168836i	−0.0200449	−	0.00651298i
$673$	−18.6449	−	25.6625i	−0.718709	−	0.989219i	−0.999566	−	0.0294687i	$-0.990618\pi$
$673$	−18.6449	−	25.6625i	−0.718709	−	0.989219i	0.280856	−	0.959750i	$-0.409382\pi$
$674$	22.7400			0.875911
$675$	2.15741	+	0.0442761i	0.0830387	+	0.00170419i
$676$	4.65127			0.178895
$677$	−10.0219	−	13.7939i	−0.385171	−	0.530143i	0.571774	−	0.820411i	$-0.306255\pi$
$677$	−10.0219	−	13.7939i	−0.385171	−	0.530143i	−0.956945	+	0.290269i	$0.906255\pi$
$678$	−0.980771	−	0.318672i	−0.0376663	−	0.0122385i
$679$	6.09714	−	18.7651i	0.233987	−	0.720137i
$680$	0.0749391	−	0.143419i	0.00287378	−	0.00549988i
$681$	0.375424	+	1.15544i	0.0143863	+	0.0442764i
$682$		−	2.65907i		−	0.101821i
$683$	−37.5085	+	12.1872i	−1.43522	+	0.466332i	−0.920404	−	0.390968i	$-0.872140\pi$
$683$	−37.5085	+	12.1872i	−1.43522	+	0.466332i	−0.514817	+	0.857300i	$0.672140\pi$
$684$	−1.45762	−	1.05903i	−0.0557336	−	0.0404928i
$685$	−3.61181	+	21.3819i	−0.138000	+	0.816959i
$686$	−19.1305	+	13.8991i	−0.730406	+	0.530671i
$687$	−0.206096	+	0.283667i	−0.00786306	+	0.0108226i
$688$	0.428726	−	0.590091i	0.0163450	−	0.0224970i
$689$	4.09260	−	2.97345i	0.155916	−	0.113279i
$690$	0.0312485	−	0.184991i	0.00118961	−	0.00704248i
$691$	20.9645	+	15.2316i	0.797526	+	0.579437i	0.910187	−	0.414197i	$-0.135937\pi$
$691$	20.9645	+	15.2316i	0.797526	+	0.579437i	−0.112661	+	0.993633i	$0.535937\pi$
$692$	8.58385	−	2.78906i	0.326309	−	0.106024i
$693$			14.3589i			0.545450i
$694$	0.432976	+	1.33256i	0.0164355	+	0.0505834i
$695$	7.37178	−	14.1082i	0.279627	−	0.535154i
$696$	0.388984	−	1.19717i	0.0147444	−	0.0453786i
$697$	0.0120592	+	0.00391828i	0.000456776	+	0.000148415i
$698$	−1.79704	−	2.47341i	−0.0680189	−	0.0936200i
$699$	−1.49247			−0.0564505
$700$	−5.72459	+	3.98229i	−0.216369	+	0.150517i
$701$	38.8909			1.46889			0.734445	−	0.678668i	$-0.237443\pi$
$701$	38.8909			1.46889			0.734445	+	0.678668i	$0.237443\pi$
$702$	0.688551	+	0.947710i	0.0259877	+	0.0357690i
$703$	−5.68440	−	1.84697i	−0.214391	−	0.0696599i
$704$	5.58637	−	17.1931i	0.210544	−	0.647989i
$705$	1.33471	+	0.225458i	0.0502680	+	0.00849123i
$706$	−2.06090	−	6.34280i	−0.0775630	−	0.238715i
$707$		−	22.1265i		−	0.832152i
$708$	0.314210	−	0.102093i	0.0118087	−	0.00383689i
$709$	6.07967	+	4.41714i	0.228327	+	0.165889i	0.696067	−	0.717977i	$-0.254932\pi$
$709$	6.07967	+	4.41714i	0.228327	+	0.165889i	−0.467740	+	0.883866i	$0.654932\pi$
$710$	11.3331	−	11.1029i	0.425325	−	0.416686i
$711$	−28.6492	+	20.8149i	−1.07443	+	0.780618i
$712$	−10.7302	+	14.7689i	−0.402133	+	0.553488i
$713$	0.629837	−	0.866897i	0.0235876	−	0.0324655i
$714$	−0.00375575	+	0.00272871i	−0.000140555	+	0.000102119i
$715$	4.72186	+	9.50707i	0.176588	+	0.355544i
$716$	0.0724510	+	0.0526387i	0.00270762	+	0.00196720i
$717$	−0.387368	+	0.125863i	−0.0144665	+	0.00470046i
$718$		−	27.4853i		−	1.02574i
$719$	−10.7607	−	33.1179i	−0.401305	−	1.23509i	−0.923942	−	0.382534i	$-0.875052\pi$
$719$	−10.7607	−	33.1179i	−0.401305	−	1.23509i	0.522637	−	0.852556i	$-0.324948\pi$
$720$	−11.4106	−	11.6472i	−0.425248	−	0.434064i
$721$	9.21173	−	28.3508i	0.343063	−	1.05584i
$722$	1.12466	+	0.365423i	0.0418554	+	0.0135996i
$723$	0.869148	+	1.19628i	0.0323240	+	0.0444901i
$724$	11.8389			0.439988
$725$	−16.2281	−	23.3281i	−0.602697	−	0.866384i
$726$	−0.572309			−0.0212404
$727$	−6.82775	−	9.39759i	−0.253227	−	0.348537i	0.663411	−	0.748255i	$-0.269108\pi$
$727$	−6.82775	−	9.39759i	−0.253227	−	0.348537i	−0.916638	+	0.399718i	$0.869108\pi$
$728$	−15.5695	−	5.05885i	−0.577046	−	0.187493i
$729$	8.25710	−	25.4127i	0.305819	−	0.941213i
$730$	−2.03715	−	13.7754i	−0.0753984	−	0.509849i
$731$	0.00217750	+	0.00670166i	8.05378e−5	+	0.000247870i
$732$			0.535815i			0.0198043i
$733$	7.97280	−	2.59052i	0.294482	−	0.0956830i	−0.158050	−	0.987431i	$-0.550521\pi$
$733$	7.97280	−	2.59052i	0.294482	−	0.0956830i	0.452532	+	0.891748i	$0.350521\pi$
$734$	−24.0556	−	17.4774i	−0.887909	−	0.645104i
$735$	−0.258877	+	0.0382837i	−0.00954881	+	0.00141211i
$736$	2.61025	−	1.89646i	0.0962150	−	0.0699043i
$737$	4.65273	−	6.40394i	0.171386	−	0.235892i
$738$	1.12210	−	1.54444i	0.0413050	−	0.0568515i
$739$	−12.1623	+	8.83641i	−0.447397	+	0.325053i	−0.788567	−	0.614949i	$-0.789177\pi$
$739$	−12.1623	+	8.83641i	−0.447397	+	0.325053i	0.341170	+	0.940001i	$0.389177\pi$
$740$	7.12627	+	3.72360i	0.261967	+	0.136882i
$741$	0.133686	+	0.0971285i	0.00491108	+	0.00356811i
$742$	5.74611	−	1.86702i	0.210946	−	0.0685406i
$743$			38.8198i			1.42416i	0.702099	+	0.712079i	$0.252246\pi$
$743$			38.8198i			1.42416i	−0.702099	+	0.712079i	$0.747754\pi$
$744$	0.0744120	+	0.229017i	0.00272808	+	0.00839616i
$745$	−0.841948	+	0.418169i	−0.0308466	+	0.0153205i
$746$	−1.47316	+	4.53394i	−0.0539364	+	0.165999i
$747$	−21.3587	−	6.93988i	−0.781476	−	0.253917i
$748$	0.0172032	+	0.0236782i	0.000629011	+	0.000865760i
$749$	−39.3899			−1.43928
$750$	0.944220	−	0.119893i	0.0344781	−	0.00437787i
$751$	−34.9948			−1.27698			−0.638490	−	0.769630i	$-0.720441\pi$
$751$	−34.9948			−1.27698			−0.638490	+	0.769630i	$0.720441\pi$
$752$	−12.0343	−	16.5638i	−0.438846	−	0.604019i
$753$	−0.0730934	−	0.0237495i	−0.00266367	−	0.000865479i
$754$	4.76718	−	14.6719i	0.173610	−	0.534318i
$755$	25.8449	−	12.8364i	0.940593	−	0.467163i
$756$	−0.186001	−	0.572454i	−0.00676481	−	0.0208199i
$757$			24.1152i			0.876484i	0.898857	+	0.438242i	$0.144399\pi$
$757$			24.1152i			0.876484i	−0.898857	+	0.438242i	$0.855601\pi$
$758$	31.2407	−	10.1507i	1.13471	−	0.368690i
$759$	0.118715	+	0.0862518i	0.00430910	+	0.00313074i
$760$	−6.09710	−	3.18584i	−0.221165	−	0.115563i
$761$	5.87645	−	4.26949i	0.213021	−	0.154769i	−0.476158	−	0.879360i	$-0.657971\pi$
$761$	5.87645	−	4.26949i	0.213021	−	0.154769i	0.689180	+	0.724591i	$0.257971\pi$
$762$	0.774509	−	1.06602i	0.0280575	−	0.0386178i
$763$	23.6729	−	32.5829i	0.857016	−	1.17958i
$764$	−10.8072	+	7.85186i	−0.390989	+	0.284070i
$765$	0.155827	−	0.0230443i	0.00563393	−	0.000833167i
$766$	−23.0961	−	16.7803i	−0.834494	−	0.606296i
$767$	16.6523	−	5.41066i	0.601280	−	0.195368i
$768$			0.935971i			0.0337739i
$769$	7.48391	+	23.0331i	0.269877	+	0.830595i	0.990530	+	0.137299i	$0.0438422\pi$
$769$	7.48391	+	23.0331i	0.269877	+	0.830595i	−0.720653	+	0.693296i	$0.756158\pi$
$770$	1.85470	+	12.5416i	0.0668387	+	0.451967i
$771$	0.0151463	−	0.0466156i	0.000545482	−	0.00167882i
$772$	−2.92548	−	0.950545i	−0.105290	−	0.0342109i
$773$	11.9197	+	16.4061i	0.428723	+	0.590087i	0.967660	−	0.252259i	$-0.0811736\pi$
$773$	11.9197	+	16.4061i	0.428723	+	0.590087i	−0.538936	+	0.842347i	$0.681174\pi$
$774$	1.06090			0.0381334
$775$	5.13459	+	1.78561i	0.184440	+	0.0641411i
$776$	−26.1841			−0.939954
$777$	−0.586324	−	0.807006i	−0.0210343	−	0.0289512i
$778$	32.9782	+	10.7153i	1.18233	+	0.384161i
$779$	0.166575	−	0.512666i	0.00596818	−	0.0183682i
$780$	−0.155566	−	0.158791i	−0.00557014	−	0.00568563i
$781$	3.83466	+	11.8019i	0.137215	+	0.422304i
$782$		−	0.0274146i		−	0.000980342i
$783$	2.33279	−	0.757969i	0.0833671	−	0.0270876i
$784$	3.20225	+	2.32657i	0.114366	+	0.0830918i
$785$	20.5640	+	41.4039i	0.733961	+	1.47777i
$786$	0.0322459	−	0.0234280i	0.00115017	−	0.000835649i
$787$	−11.5440	+	15.8890i	−0.411499	+	0.566380i	−0.963583	−	0.267408i	$-0.913833\pi$
$787$	−11.5440	+	15.8890i	−0.411499	+	0.566380i	0.552084	+	0.833788i	$0.313833\pi$
$788$	−5.08970	+	7.00537i	−0.181313	+	0.249556i
$789$	0.791225	−	0.574859i	0.0281684	−	0.0204655i
$790$	−22.3346	+	21.8810i	−0.794630	+	0.778489i
$791$	22.7191	+	16.5064i	0.807797	+	0.586899i
$792$	18.1227	−	5.88841i	0.643961	−	0.209235i
$793$			28.3968i			1.00840i
$794$	8.35960	+	25.7282i	0.296671	+	0.913060i
$795$	0.349820	+	0.0590913i	0.0124068	+	0.00209575i
$796$	−0.949636	+	2.92268i	−0.0336590	+	0.103592i
$797$	−49.3689	−	16.0409i	−1.74874	−	0.568198i	−0.752798	−	0.658251i	$-0.771296\pi$
$797$	−49.3689	−	16.0409i	−1.74874	−	0.568198i	−0.995937	+	0.0900530i	$0.971296\pi$
$798$	0.116004	+	0.159666i	0.00410650	+	0.00565211i
$799$	0.197796			0.00699751
$800$	13.0423	+	9.89090i	0.461114	+	0.349696i
$801$	−17.7707			−0.627897
$802$	−18.9763	−	26.1186i	−0.670076	−	0.922280i
$803$	10.3585	+	3.36568i	0.365544	+	0.118772i
$804$	−0.0512246	+	0.157653i	−0.00180655	+	0.00555999i
$805$	−2.36599	+	4.52806i	−0.0833903	+	0.159593i
$806$	0.911954	+	2.80671i	0.0321222	+	0.0988620i
$807$			0.125836i			0.00442962i
$808$	−27.9262	+	9.07378i	−0.982441	+	0.319215i
$809$	19.4983	+	14.1664i	0.685525	+	0.498063i	0.875186	−	0.483787i	$-0.160739\pi$
$809$	19.4983	+	14.1664i	0.685525	+	0.498063i	−0.189661	+	0.981850i	$0.560739\pi$
$810$	3.94326	−	23.3441i	0.138552	−	0.820227i
$811$	−7.98004	+	5.79784i	−0.280217	+	0.203590i	−0.719012	−	0.694998i	$-0.755405\pi$
$811$	−7.98004	+	5.79784i	−0.280217	+	0.203590i	0.438795	+	0.898587i	$0.355405\pi$
$812$	−4.65923	+	6.41288i	−0.163507	+	0.225048i
$813$	1.26339	−	1.73891i	0.0443092	−	0.0609864i
$814$	11.8260	−	8.59210i	0.414502	−	0.301153i
$815$	5.10204	−	30.2040i	0.178717	−	1.05800i
$816$	0.00333572	+	0.00242354i	0.000116774	+	8.48409e-5i
$817$	0.284904	−	0.0925708i	0.00996752	−	0.00323864i
$818$			18.3229i			0.640644i
$819$	−4.92454	−	15.1562i	−0.172077	−	0.529600i
$820$	−0.335825	+	0.642706i	−0.0117275	+	0.0224443i
$821$	2.77755	−	8.54841i	0.0969370	−	0.298341i	−0.890817	−	0.454363i	$-0.849867\pi$
$821$	2.77755	−	8.54841i	0.0969370	−	0.298341i	0.987754	+	0.156022i	$0.0498669\pi$
$822$	−0.785177	−	0.255119i	−0.0273862	−	0.00889831i
$823$	−21.6783	−	29.8376i	−0.755657	−	1.04007i	−0.997563	−	0.0697726i	$-0.977773\pi$
$823$	−21.6783	−	29.8376i	−0.755657	−	1.04007i	0.241906	−	0.970300i	$-0.422227\pi$
$824$	−39.5596			−1.37813
$825$	−0.244527	+	0.703146i	−0.00851335	+	0.0244804i
$826$	20.9119			0.727620
$827$	16.6351	+	22.8963i	0.578460	+	0.796182i	0.993525	−	0.113610i	$-0.0362413\pi$
$827$	16.6351	+	22.8963i	0.578460	+	0.796182i	−0.415065	+	0.909792i	$0.636241\pi$
$828$	1.68880	+	0.548723i	0.0586897	+	0.0190694i
$829$	−15.3820	+	47.3409i	−0.534239	+	1.64422i	0.211049	+	0.977475i	$0.432312\pi$
$829$	−15.3820	+	47.3409i	−0.534239	+	1.64422i	−0.745288	+	0.666743i	$0.767688\pi$
$830$	−19.5519	−	3.30269i	−0.678656	−	0.114638i
$831$	0.271874	+	0.836743i	0.00943122	+	0.0290263i
$832$			20.0636i			0.695580i
$833$	−0.0363679	+	0.0118167i	−0.00126007	+	0.000409423i
$834$	0.490291	+	0.356217i	0.0169774	+	0.0123348i
$835$	14.0122	−	13.7276i	0.484914	−	0.475064i
$836$	1.00662	−	0.731349i	0.0348145	−	0.0252942i
$837$	−0.275803	+	0.379610i	−0.00953315	+	0.0131213i
$838$	−6.64490	+	9.14593i	−0.229544	+	0.315941i
$839$	23.0580	−	16.7526i	0.796049	−	0.578364i	−0.113703	−	0.993515i	$-0.536271\pi$
$839$	23.0580	−	16.7526i	0.796049	−	0.578364i	0.909752	+	0.415151i	$0.136271\pi$
$840$	−0.510706	−	1.02826i	−0.0176210	−	0.0354785i
$841$	−2.67144	−	1.94092i	−0.0921188	−	0.0669282i
$842$	25.6258	−	8.32632i	0.883123	−	0.286944i
$843$			0.254479i			0.00876473i
$844$	1.77283	+	5.45622i	0.0610235	+	0.187811i
$845$	12.0983	+	12.3491i	0.416193	+	0.424822i
$846$	9.20235	−	28.3219i	0.316383	−	0.973728i
$847$	14.8220	+	4.81597i	0.509291	+	0.165479i
$848$	−3.15413	−	4.34128i	−0.108313	−	0.149080i
$849$	−0.548056			−0.0188092
$850$	0.133128	−	0.0402553i	0.00456625	−	0.00138075i
$851$	5.89063			0.201928
$852$	−0.152746	−	0.210237i	−0.00523299	−	0.00720260i
$853$	−7.51959	−	2.44326i	−0.257466	−	0.0836558i	0.177440	−	0.984132i	$-0.443218\pi$
$853$	−7.51959	−	2.44326i	−0.257466	−	0.0836558i	−0.434906	+	0.900476i	$0.643218\pi$
$854$	−10.4804	+	32.2554i	−0.358632	+	1.10376i
$855$	−0.979666	−	6.62457i	−0.0335039	−	0.226555i
$856$	16.1533	+	49.7147i	0.552108	+	1.69921i
$857$		−	24.8935i		−	0.850345i	−0.905112	−	0.425172i	$-0.860213\pi$
$857$		−	24.8935i		−	0.850345i	0.905112	−	0.425172i	$-0.139787\pi$
$858$	−0.384359	+	0.124886i	−0.0131218	+	0.00426353i
$859$	45.1759	+	32.8222i	1.54138	+	1.11988i	0.949463	+	0.313880i	$0.101629\pi$
$859$	45.1759	+	32.8222i	1.54138	+	1.11988i	0.591917	+	0.805999i	$0.298371\pi$
$860$	−0.398654	+	0.0589545i	−0.0135940	+	0.00201033i
$861$	0.0727825	−	0.0528796i	0.00248042	−	0.00180213i
$862$	−20.2445	+	27.8642i	−0.689531	+	0.949057i
$863$	−12.0132	+	16.5348i	−0.408935	+	0.562851i	−0.962958	−	0.269650i	$-0.913092\pi$
$863$	−12.0132	+	16.5348i	−0.408935	+	0.562851i	0.554023	+	0.832501i	$0.313092\pi$
$864$	−1.14302	+	0.830450i	−0.0388862	+	0.0282525i
$865$	29.7321	+	15.5355i	1.01092	+	0.528224i
$866$	−15.0671	−	10.9469i	−0.512000	−	0.371990i
$867$	1.16391	−	0.378177i	0.0395284	−	0.0128436i
$868$		−	1.51638i		−	0.0514691i
$869$	−7.55711	−	23.2584i	−0.256357	−	0.788987i
$870$	0.968979	−	0.481261i	0.0328515	−	0.0163163i
$871$	−2.71477	+	8.35521i	−0.0919865	+	0.283105i
$872$	−50.8314	−	16.5161i	−1.72137	−	0.559307i
$873$	−14.9820	−	20.6210i	−0.507064	−	0.697914i
$874$	−1.16546			−0.0394222
$875$	−25.4630	−	4.84054i	−0.860805	−	0.163640i
$876$	−0.228085			−0.00770629
$877$	4.90361	+	6.74924i	0.165583	+	0.227906i	0.883743	−	0.467972i	$-0.155015\pi$
$877$	4.90361	+	6.74924i	0.165583	+	0.227906i	−0.718160	+	0.695878i	$0.755015\pi$
$878$	37.2829	+	12.1140i	1.25824	+	0.408826i
$879$	−0.0828109	+	0.254866i	−0.00279314	+	0.00859641i
$880$	10.0848	−	5.00879i	0.339957	−	0.168846i
$881$	7.50756	+	23.1059i	0.252936	+	0.778457i	0.994229	+	0.107276i	$0.0342128\pi$
$881$	7.50756	+	23.1059i	0.252936	+	0.778457i	−0.741293	+	0.671181i	$0.765787\pi$
$882$			5.75721i			0.193855i
$883$	−31.6181	+	10.2733i	−1.06403	+	0.345726i	−0.788161	−	0.615469i	$-0.788967\pi$
$883$	−31.6181	+	10.2733i	−1.06403	+	0.345726i	−0.275873	+	0.961194i	$0.588967\pi$
$884$	−0.0262791	−	0.0190928i	−0.000883860	−	0.000642162i
$885$	1.08833	+	0.568674i	0.0365840	+	0.0191158i
$886$	29.5682	−	21.4825i	0.993363	−	0.721720i
$887$	10.0394	−	13.8180i	0.337089	−	0.463964i	−0.606499	−	0.795084i	$-0.707427\pi$
$887$	10.0394	−	13.8180i	0.337089	−	0.463964i	0.943589	+	0.331120i	$0.107427\pi$
$888$	−0.778093	+	1.07095i	−0.0261111	+	0.0359388i
$889$	−29.0293	+	21.0910i	−0.973612	+	0.707370i
$890$	−15.5216	+	2.29539i	−0.520284	+	0.0769415i
$891$	14.9808	+	10.8842i	0.501874	+	0.364633i
$892$	6.53374	−	2.12294i	0.218766	−	0.0710813i
$893$		−	8.40877i		−	0.281389i
$894$	−0.0110599	−	0.0340389i	−0.000369899	−	0.00113843i
$895$	0.0486942	+	0.329273i	0.00162767	+	0.0110064i
$896$	−2.71440	+	8.35407i	−0.0906819	+	0.279090i
$897$	−0.154888	−	0.0503261i	−0.00517156	−	0.00168034i
$898$	7.51363	+	10.3416i	0.250733	+	0.345105i
$899$	6.17934			0.206092
$900$	−0.184843	+	9.00671i	−0.00616144	+	0.300224i
$901$	0.0518413			0.00172708
$902$	0.774907	+	1.06657i	0.0258016	+	0.0355128i
$903$	0.0475487	+	0.0154495i	0.00158232	+	0.000514127i
$904$	11.5162	−	35.4432i	0.383023	−	1.17882i
$905$	30.7936	+	31.4321i	1.02362	+	1.04484i
$906$	0.339501	+	1.04488i	0.0112792	+	0.0347137i
$907$		−	36.0971i		−	1.19858i	−0.800531	−	0.599292i	$-0.795449\pi$
$907$		−	36.0971i		−	1.19858i	0.800531	−	0.599292i	$-0.204551\pi$
$908$	−9.65573	+	3.13734i	−0.320437	+	0.104116i
$909$	−23.1248	−	16.8011i	−0.767000	−	0.557258i
$910$	−6.25894	−	12.6018i	−0.207482	−	0.417747i
$911$	32.9154	−	23.9145i	1.09054	−	0.792321i	0.111047	−	0.993815i	$-0.464580\pi$
$911$	32.9154	−	23.9145i	1.09054	−	0.792321i	0.979490	+	0.201494i	$0.0645796\pi$
$912$	0.103031	−	0.141809i	0.00341168	−	0.00469578i
$913$	9.11605	−	12.5472i	0.301697	−	0.415250i
$914$	23.8226	−	17.3081i	0.787981	−	0.572502i
$915$	−1.42258	+	1.39369i	−0.0470292	+	0.0460739i
$916$	−2.37055	−	1.72230i	−0.0783250	−	0.0569065i
$917$	−1.03227	+	0.335405i	−0.0340886	+	0.0110761i
$918$			0.0120047i			0.000396215i
$919$	14.7661	+	45.4454i	0.487089	+	1.49911i	0.828932	+	0.559349i	$0.188949\pi$
$919$	14.7661	+	45.4454i	0.487089	+	1.49911i	−0.341843	+	0.939757i	$0.611051\pi$
$920$	6.68521	+	1.12926i	0.220405	+	0.0372306i
$921$	0.120614	−	0.371212i	0.00397437	−	0.0122318i
$922$	−6.96336	−	2.26253i	−0.229326	−	0.0745126i
$923$	−8.09515	−	11.1420i	−0.266455	−	0.366744i
$924$	0.207657			0.00683142
$925$	8.64975	+	28.6055i	0.284402	+	0.940543i
$926$	−30.3421			−0.997102
$927$	−22.6352	−	31.1547i	−0.743439	−	1.02326i
$928$	17.6955	+	5.74962i	0.580883	+	0.188740i
$929$	−5.90690	+	18.1796i	−0.193799	+	0.596452i	0.806190	+	0.591657i	$0.201526\pi$
$929$	−5.90690	+	18.1796i	−0.193799	+	0.596452i	−0.999989	+	0.00479458i	$0.998474\pi$
$930$	−0.0958486	+	0.183436i	−0.00314300	+	0.00601511i
$931$	0.502355	+	1.54609i	0.0164640	+	0.0506710i
$932$		−	12.4723i		−	0.408543i
$933$	2.21618	−	0.720080i	0.0725544	−	0.0235744i
$934$	−12.2964	−	8.93386i	−0.402351	−	0.292325i
$935$	−0.0181187	+	0.107263i	−0.000592546	+	0.00350787i
$936$	−17.1094	+	12.4307i	−0.559238	+	0.406310i
$937$	31.1905	−	42.9301i	1.01895	−	1.40246i	0.106012	−	0.994365i	$-0.466192\pi$
$937$	31.1905	−	42.9301i	1.01895	−	1.40246i	0.912938	−	0.408099i	$-0.133808\pi$
$938$	−6.16731	+	8.48858i	−0.201370	+	0.277162i
$939$	−1.39778	+	1.01555i	−0.0456149	+	0.0331411i
$940$	−1.88410	+	11.1539i	−0.0614527	+	0.363799i
$941$	−34.3448	−	24.9529i	−1.11961	−	0.813443i	−0.135458	−	0.990783i	$-0.543251\pi$
$941$	−34.3448	−	24.9529i	−1.11961	−	0.813443i	−0.984150	+	0.177340i	$0.943251\pi$
$942$	−1.67391	+	0.543885i	−0.0545388	+	0.0177207i
$943$			0.531265i			0.0173004i
$944$	−5.73944	−	17.6642i	−0.186803	−	0.574921i
$945$	1.03606	−	1.98282i	0.0337030	−	0.0645011i
$946$	−0.226400	+	0.696788i	−0.00736090	+	0.0226545i
$947$	36.8241	+	11.9649i	1.19662	+	0.388806i	0.838517	−	0.544875i	$-0.183423\pi$
$947$	36.8241	+	11.9649i	1.19662	+	0.388806i	0.358105	+	0.933681i	$0.383423\pi$
$948$	0.301022	+	0.414321i	0.00977674	+	0.0134565i
$949$	−12.0879			−0.392391
$950$	−1.71135	−	5.65959i	−0.0555235	−	0.183621i
$951$	−0.907619			−0.0294316
$952$	−0.0986103	−	0.135725i	−0.00319598	−	0.00439889i
$953$	17.5001	+	5.68612i	0.566883	+	0.184191i	0.578416	−	0.815742i	$-0.303671\pi$
$953$	17.5001	+	5.68612i	0.566883	+	0.184191i	−0.0115330	+	0.999933i	$0.503671\pi$
$954$	2.41189	−	7.42303i	0.0780878	−	0.240330i
$955$	−48.9567	−	8.26973i	−1.58420	−	0.267602i
$956$	−1.05181	−	3.23715i	−0.0340181	−	0.104697i
$957$			0.846217i			0.0273543i
$958$	16.2004	−	5.26382i	0.523410	−	0.170066i
$959$	18.1882	+	13.2145i	0.587328	+	0.426719i
$960$	−1.00512	+	0.984702i	−0.0324400	+	0.0317811i
$961$	24.1232	−	17.5265i	0.778167	−	0.565372i
$962$	−9.53589	+	13.1250i	−0.307449	+	0.423168i
$963$	−29.9096	+	41.1671i	−0.963824	+	1.32659i
$964$	−9.99706	+	7.26329i	−0.321983	+	0.233935i
$965$	−5.08566	−	10.2395i	−0.163713	−	0.329623i
$966$	−0.157360	−	0.114329i	−0.00506298	−	0.00367847i
$967$	−2.71283	+	0.881451i	−0.0872386	+	0.0283455i	−0.352311	−	0.935883i	$-0.614604\pi$
$967$	−2.71283	+	0.881451i	−0.0872386	+	0.0283455i	0.265073	+	0.964228i	$0.414604\pi$
$968$		−	20.6821i		−	0.664749i
$969$	0.000523293		0.00161053i	1.68106e−5		5.17377e-5i
$970$	−15.7494	−	16.0759i	−0.505681	−	0.516166i
$971$	9.61276	−	29.5850i	0.308488	−	0.949429i	−0.669864	−	0.742484i	$-0.733648\pi$
$971$	9.61276	−	29.5850i	0.308488	−	0.949429i	0.978352	−	0.206945i	$-0.0663523\pi$
$972$	−1.10959	−	0.360529i	−0.0355903	−	0.0115640i
$973$	−9.70032	−	13.3513i	−0.310978	−	0.428025i
$974$	31.4328			1.00717
$975$	0.0169529	−	0.826051i	0.000542927	−	0.0264548i
$976$	30.1224			0.964194
$977$	14.7238	+	20.2656i	0.471057	+	0.648354i	0.976756	−	0.214356i	$-0.0687653\pi$
$977$	14.7238	+	20.2656i	0.471057	+	0.648354i	−0.505699	+	0.862710i	$0.668765\pi$
$978$	1.10914	+	0.360382i	0.0354664	+	0.0115237i
$979$	3.79233	−	11.6716i	0.121203	−	0.373025i
$980$	−0.319929	−	2.16338i	−0.0102197	−	0.0691066i
$981$	−16.0776	−	49.4819i	−0.513319	−	1.57983i
$982$			12.4055i			0.395874i
$983$	−48.2572	+	15.6797i	−1.53916	+	0.500105i	−0.951146	−	0.308742i	$-0.900092\pi$
$983$	−48.2572	+	15.6797i	−1.53916	+	0.500105i	−0.588019	+	0.808847i	$0.700092\pi$
$984$	−0.0965874	−	0.0701748i	−0.00307909	−	0.00223709i
$985$	−31.8378	+	4.70830i	−1.01444	+	0.150019i
$986$	0.127900	−	0.0929249i	0.00407317	−	0.00295933i
$987$	0.824882	−	1.13535i	0.0262563	−	0.0361387i
$988$	−0.811683	+	1.11719i	−0.0258231	+	0.0355424i
$989$	−0.238854	+	0.173538i	−0.00759511	+	0.00551817i
$990$	14.5157	+	7.58473i	0.461341	+	0.241059i
$991$	34.6860	+	25.2009i	1.10184	+	0.800532i	0.981359	−	0.192184i	$-0.0615572\pi$
$991$	34.6860	+	25.2009i	1.10184	+	0.800532i	0.120478	+	0.992716i	$0.461557\pi$
$992$	−3.38512	+	1.09989i	−0.107478	+	0.0349216i
$993$			0.197157i			0.00625657i
$994$	−5.08294	−	15.6437i	−0.161221	−	0.496187i
$995$	−10.2297	+	5.08079i	−0.324305	+	0.161072i
$996$	−0.100364	+	0.308888i	−0.00318015	+	0.00978748i
$997$	−35.5690	−	11.5571i	−1.12648	−	0.366016i	−0.314244	−	0.949342i	$-0.601751\pi$
$997$	−35.5690	−	11.5571i	−1.12648	−	0.366016i	−0.812238	+	0.583326i	$0.801751\pi$
$998$	6.57568	+	9.05065i	0.208150	+	0.286493i
$999$	−2.57948			−0.0816111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.b.39.8	✓	96
25.9	even	10	inner	475.2.n.b.134.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.b.39.8	✓	96	1.1	even	1	trivial
475.2.n.b.134.8	yes	96	25.9	even	10	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.695076 - 0.956690i) q^{2} +(-0.0684675 - 0.0222464i) q^{3} +(0.185909 - 0.572168i) q^{4} +(2.00266 - 0.994659i) q^{5} +(0.0263072 + 0.0809651i) q^{6} -2.31826i q^{7} +(-2.92592 + 0.950690i) q^{8} +(-2.42286 - 1.76031i) q^{9} +O(q^{10})\)	\(q+(-0.695076 - 0.956690i) q^{2} +(-0.0684675 - 0.0222464i) q^{3} +(0.185909 - 0.572168i) q^{4} +(2.00266 - 0.994659i) q^{5} +(0.0263072 + 0.0809651i) q^{6} -2.31826i q^{7} +(-2.92592 + 0.950690i) q^{8} +(-2.42286 - 1.76031i) q^{9} +(-2.34358 - 1.22456i) q^{10} +(1.67319 - 1.21565i) q^{11} +(-0.0254574 + 0.0350391i) q^{12} +(-1.34918 + 1.85698i) q^{13} +(-2.21786 + 1.61137i) q^{14} +(-0.159245 + 0.0235497i) q^{15} +(1.96982 + 1.43116i) q^{16} +(-0.0223713 + 0.00726887i) q^{17} +3.54147i q^{18} +(0.309017 + 0.951057i) q^{19} +(-0.196800 - 1.33077i) q^{20} +(-0.0515731 + 0.158726i) q^{21} +(-2.32599 - 0.755762i) q^{22} +(-0.579298 - 0.797335i) q^{23} +0.221480 q^{24} +(3.02131 - 3.98393i) q^{25} +2.71434 q^{26} +(0.253672 + 0.349150i) q^{27} +(-1.32644 - 0.430985i) q^{28} +(1.75630 - 5.40532i) q^{29} +(0.133217 + 0.135979i) q^{30} +(0.335977 + 1.03403i) q^{31} +3.27372i q^{32} +(-0.141603 + 0.0460097i) q^{33} +(0.0225038 + 0.0163500i) q^{34} +(-2.30588 - 4.64270i) q^{35} +(-1.45762 + 1.05903i) q^{36} +(-3.51315 + 4.83544i) q^{37} +(0.695076 - 0.956690i) q^{38} +(0.133686 - 0.0971285i) q^{39} +(-4.91402 + 4.81420i) q^{40} +(-0.436100 - 0.316845i) q^{41} +(0.187698 - 0.0609869i) q^{42} -0.299565i q^{43} +(-0.384493 - 1.18335i) q^{44} +(-6.60307 - 1.11539i) q^{45} +(-0.360146 + 1.10842i) q^{46} +(-7.99721 - 2.59845i) q^{47} +(-0.103031 - 0.141809i) q^{48} +1.62565 q^{49} +(-5.91143 - 0.121319i) q^{50} +0.00169341 q^{51} +(0.811683 + 1.11719i) q^{52} +(-2.09603 - 0.681041i) q^{53} +(0.157707 - 0.485371i) q^{54} +(2.14169 - 4.09879i) q^{55} +(2.20395 + 6.78306i) q^{56} -0.0719909i q^{57} +(-6.39198 + 2.07688i) q^{58} +(-6.17128 - 4.48370i) q^{59} +(-0.0161306 + 0.0954929i) q^{60} +(10.0087 - 7.27174i) q^{61} +(0.755717 - 1.04015i) q^{62} +(-4.08086 + 5.61682i) q^{63} +(7.07158 - 5.13780i) q^{64} +(-0.854880 + 5.06088i) q^{65} +(0.142442 + 0.103490i) q^{66} +(3.64005 - 1.18272i) q^{67} +0.0141515i q^{68} +(0.0219252 + 0.0674788i) q^{69} +(-2.83886 + 5.43304i) q^{70} +(-1.85412 + 5.70640i) q^{71} +(8.76260 + 2.84714i) q^{72} +(3.09543 + 4.26049i) q^{73} +7.06793 q^{74} +(-0.295489 + 0.205556i) q^{75} +0.601613 q^{76} +(-2.81819 - 3.87891i) q^{77} +(-0.185844 - 0.0603843i) q^{78} +(3.65399 - 11.2458i) q^{79} +(5.36841 + 0.906827i) q^{80} +(2.76675 + 8.51517i) q^{81} +0.637444i q^{82} +(7.13190 - 2.31730i) q^{83} +(0.0812299 + 0.0590169i) q^{84} +(-0.0375721 + 0.0368089i) q^{85} +(-0.286591 + 0.208221i) q^{86} +(-0.240498 + 0.331017i) q^{87} +(-3.73993 + 5.14758i) q^{88} +(4.80056 - 3.48781i) q^{89} +(3.52256 + 7.09237i) q^{90} +(4.30498 + 3.12775i) q^{91} +(-0.563906 + 0.183224i) q^{92} -0.0782717i q^{93} +(3.07276 + 9.45698i) q^{94} +(1.56483 + 1.59728i) q^{95} +(0.0728285 - 0.224143i) q^{96} +(8.09445 + 2.63005i) q^{97} +(-1.12995 - 1.55525i) q^{98} -6.19383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more