LMFDB - Embedded newform 67.2.e.c.62.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,2,Mod(9,67)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("67.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.e (of order $11$, degree $10$, 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:	$0.534997693543$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 39 x^{18} - 148 x^{17} + 492 x^{16} - 1282 x^{15} + 2921 x^{14} - 4316 x^{13} + \cdots + 4489 $ x^20 - 7x^19 + 39x^18 - 148x^17 + 492x^16 - 1282x^15 + 2921x^14 - 4316x^13 + 2696x^12 + 9361x^11 - 20998x^10 + 10813x^9 + 44155x^8 - 46933x^7 - 36976x^6 - 49131x^5 + 105828x^4 + 108234x^3 + 143215x^2 + 41004*x + 4489
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			62.1
Root			$-0.127556 - 0.887172i$ of defining polynomial
Character	$\chi$	$=$	67.62
Dual form			67.2.e.c.40.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10181 + 1.27155i) q^{2} +(-1.28775 - 2.81978i) q^{3} +(-0.118239 - 0.822373i) q^{4} +(2.46094 - 0.722597i) q^{5} +(5.00435 + 1.46941i) q^{6} +(2.41674 - 2.78906i) q^{7} +(-1.65486 - 1.06351i) q^{8} +(-4.32827 + 4.99509i) q^{9} +O(q^{10})$	\(q+(-1.10181 + 1.27155i) q^{2} +(-1.28775 - 2.81978i) q^{3} +(-0.118239 - 0.822373i) q^{4} +(2.46094 - 0.722597i) q^{5} +(5.00435 + 1.46941i) q^{6} +(2.41674 - 2.78906i) q^{7} +(-1.65486 - 1.06351i) q^{8} +(-4.32827 + 4.99509i) q^{9} +(-1.79266 + 3.92538i) q^{10} +(-1.90194 + 0.558461i) q^{11} +(-2.16665 + 1.39242i) q^{12} +(1.22191 - 0.785274i) q^{13} +(0.883665 + 6.14602i) q^{14} +(-5.20664 - 6.00878i) q^{15} +(4.77001 - 1.40060i) q^{16} +(-0.713531 + 4.96272i) q^{17} +(-1.58260 - 11.0072i) q^{18} +(1.45689 + 1.68134i) q^{19} +(-0.885225 - 1.93837i) q^{20} +(-10.9767 - 3.22305i) q^{21} +(1.38546 - 3.03374i) q^{22} +(1.18244 + 2.58919i) q^{23} +(-0.867828 + 6.03588i) q^{24} +(1.32781 - 0.853332i) q^{25} +(-0.347792 + 2.41894i) q^{26} +(10.7357 + 3.15229i) q^{27} +(-2.57941 - 1.65768i) q^{28} +1.58568 q^{29} +13.3772 q^{30} +(-1.45066 - 0.932280i) q^{31} +(-1.84033 + 4.02977i) q^{32} +(4.02396 + 4.64390i) q^{33} +(-5.52419 - 6.37525i) q^{34} +(3.93208 - 8.61005i) q^{35} +(4.61960 + 2.96884i) q^{36} +2.65913 q^{37} -3.74313 q^{38} +(-3.78781 - 2.43428i) q^{39} +(-4.84101 - 1.42145i) q^{40} +(-1.18653 + 8.25247i) q^{41} +(16.1925 - 10.4063i) q^{42} +(-0.415275 + 2.88830i) q^{43} +(0.684148 + 1.49807i) q^{44} +(-7.04217 + 15.4202i) q^{45} +(-4.59512 - 1.34925i) q^{46} +(-1.42512 - 3.12058i) q^{47} +(-10.0920 - 11.6467i) q^{48} +(-0.942052 - 6.55212i) q^{49} +(-0.377934 + 2.62859i) q^{50} +(14.9126 - 4.37874i) q^{51} +(-0.790266 - 0.912016i) q^{52} +(-1.94780 - 13.5472i) q^{53} +(-15.8370 + 10.1778i) q^{54} +(-4.27702 + 2.74868i) q^{55} +(-6.96557 + 2.04528i) q^{56} +(2.86490 - 6.27325i) q^{57} +(-1.74712 + 2.01628i) q^{58} +(-1.80007 - 1.15684i) q^{59} +(-4.32583 + 4.99227i) q^{60} +(9.60903 + 2.82146i) q^{61} +(2.78379 - 0.817394i) q^{62} +(3.47133 + 24.1436i) q^{63} +(1.03400 + 2.26414i) q^{64} +(2.43961 - 2.81546i) q^{65} -10.3386 q^{66} +(-4.70762 + 6.69614i) q^{67} +4.16557 q^{68} +(5.77825 - 6.66845i) q^{69} +(6.61575 + 14.4865i) q^{70} +(-0.520416 - 3.61957i) q^{71} +(12.4750 - 3.66300i) q^{72} +(-5.81523 - 1.70750i) q^{73} +(-2.92985 + 3.38122i) q^{74} +(-4.11609 - 2.64525i) q^{75} +(1.21043 - 1.39691i) q^{76} +(-3.03891 + 6.65429i) q^{77} +(7.26876 - 2.13430i) q^{78} +(-11.7180 + 7.53068i) q^{79} +(10.7266 - 6.89358i) q^{80} +(-2.11429 - 14.7052i) q^{81} +(-9.18614 - 10.6014i) q^{82} +(11.6292 - 3.41465i) q^{83} +(-1.35267 + 9.40803i) q^{84} +(1.83009 + 12.7285i) q^{85} +(-3.21508 - 3.71040i) q^{86} +(-2.04196 - 4.47127i) q^{87} +(3.74138 + 1.09857i) q^{88} +(2.99339 - 6.55461i) q^{89} +(-11.8485 - 25.9446i) q^{90} +(0.762857 - 5.30578i) q^{91} +(1.98947 - 1.27855i) q^{92} +(-0.760741 + 5.29107i) q^{93} +(5.53820 + 1.62616i) q^{94} +(4.80025 + 3.08493i) q^{95} +13.7329 q^{96} -15.5529 q^{97} +(9.36933 + 6.02130i) q^{98} +(5.44256 - 11.9175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−1.10181	+	1.27155i	−0.779096	+	0.899124i	−0.997044	−	0.0768359i	$-0.975518\pi$
$2$	−1.10181	+	1.27155i	−0.779096	+	0.899124i	0.217948	+	0.975960i	$0.430064\pi$
$3$	−1.28775	−	2.81978i	−0.743482	−	1.62800i	−0.777740	−	0.628586i	$-0.783634\pi$
$3$	−1.28775	−	2.81978i	−0.743482	−	1.62800i	0.0342572	−	0.999413i	$-0.489093\pi$
$4$	−0.118239	−	0.822373i	−0.0591197	−	0.411187i
$5$	2.46094	−	0.722597i	1.10057	−	0.323155i	0.319489	−	0.947590i	$-0.396489\pi$
$5$	2.46094	−	0.722597i	1.10057	−	0.323155i	0.781077	+	0.624435i	$0.214671\pi$
$6$	5.00435	+	1.46941i	2.04302	+	0.599884i
$7$	2.41674	−	2.78906i	0.913441	−	1.05417i	−0.0848887	−	0.996390i	$-0.527053\pi$
$7$	2.41674	−	2.78906i	0.913441	−	1.05417i	0.998330	−	0.0577765i	$-0.0184011\pi$
$8$	−1.65486	−	1.06351i	−0.585082	−	0.376009i
$9$	−4.32827	+	4.99509i	−1.44276	+	1.66503i
$10$	−1.79266	+	3.92538i	−0.566889	+	1.24131i
$11$	−1.90194	+	0.558461i	−0.573457	+	0.168382i	−0.555588	−	0.831458i	$-0.687507\pi$
$11$	−1.90194	+	0.558461i	−0.573457	+	0.168382i	−0.0178698	+	0.999840i	$0.505688\pi$
$12$	−2.16665	+	1.39242i	−0.625457	+	0.401957i
$13$	1.22191	−	0.785274i	0.338897	−	0.217796i	−0.360112	−	0.932909i	$-0.617261\pi$
$13$	1.22191	−	0.785274i	0.338897	−	0.217796i	0.699008	+	0.715114i	$0.253625\pi$
$14$	0.883665	+	6.14602i	0.236169	+	1.64259i
$15$	−5.20664	−	6.00878i	−1.34435	−	1.55146i
$16$	4.77001	−	1.40060i	1.19250	−	0.350150i
$17$	−0.713531	+	4.96272i	−0.173057	+	1.20364i	0.699323	+	0.714806i	$0.253485\pi$
$17$	−0.713531	+	4.96272i	−0.173057	+	1.20364i	−0.872379	+	0.488829i	$0.837424\pi$
$18$	−1.58260	−	11.0072i	−0.373023	−	2.59443i
$19$	1.45689	+	1.68134i	0.334233	+	0.385726i	0.897843	−	0.440315i	$-0.145133\pi$
$19$	1.45689	+	1.68134i	0.334233	+	0.385726i	−0.563610	+	0.826041i	$0.690588\pi$
$20$	−0.885225	−	1.93837i	−0.197942	−	0.433433i
$21$	−10.9767	−	3.22305i	−2.39531	−	0.703327i
$22$	1.38546	−	3.03374i	0.295382	−	0.646795i
$23$	1.18244	+	2.58919i	0.246556	+	0.539883i	0.991933	−	0.126760i	$-0.0404578\pi$
$23$	1.18244	+	2.58919i	0.246556	+	0.539883i	−0.745377	+	0.666643i	$0.767731\pi$
$24$	−0.867828	+	6.03588i	−0.177145	+	1.23207i
$25$	1.32781	−	0.853332i	0.265562	−	0.170666i
$26$	−0.347792	+	2.41894i	−0.0682076	+	0.474394i
$27$	10.7357	+	3.15229i	2.06609	+	0.606659i
$28$	−2.57941	−	1.65768i	−0.487462	−	0.313273i
$29$	1.58568			0.294454			0.147227	−	0.989103i	$-0.452965\pi$
$29$	1.58568			0.294454			0.147227	+	0.989103i	$0.452965\pi$
$30$	13.3772			2.44233
$31$	−1.45066	−	0.932280i	−0.260546	−	0.167442i	0.403846	−	0.914827i	$-0.367673\pi$
$31$	−1.45066	−	0.932280i	−0.260546	−	0.167442i	−0.664392	+	0.747384i	$0.731309\pi$
$32$	−1.84033	+	4.02977i	−0.325328	+	0.712370i
$33$	4.02396	+	4.64390i	0.700482	+	0.808399i
$34$	−5.52419	−	6.37525i	−0.947390	−	1.09335i
$35$	3.93208	−	8.61005i	0.664642	−	1.45536i
$36$	4.61960	+	2.96884i	0.769933	+	0.494806i
$37$	2.65913			0.437158			0.218579	−	0.975819i	$-0.429858\pi$
$37$	2.65913			0.437158			0.218579	+	0.975819i	$0.429858\pi$
$38$	−3.74313			−0.607215
$39$	−3.78781	−	2.43428i	−0.606535	−	0.389796i
$40$	−4.84101	−	1.42145i	−0.765430	−	0.224751i
$41$	−1.18653	+	8.25247i	−0.185304	+	1.28882i	0.658668	+	0.752434i	$0.271120\pi$
$41$	−1.18653	+	8.25247i	−0.185304	+	1.28882i	−0.843973	+	0.536386i	$0.819789\pi$
$42$	16.1925	−	10.4063i	2.49855	−	1.60572i
$43$	−0.415275	+	2.88830i	−0.0633289	+	0.440462i	0.933346	+	0.358979i	$0.116875\pi$
$43$	−0.415275	+	2.88830i	−0.0633289	+	0.440462i	−0.996675	+	0.0814835i	$0.974034\pi$
$44$	0.684148	+	1.49807i	0.103139	+	0.225843i
$45$	−7.04217	+	15.4202i	−1.04978	+	2.29871i
$46$	−4.59512	−	1.34925i	−0.677513	−	0.198936i
$47$	−1.42512	−	3.12058i	−0.207875	−	0.455184i	0.776762	−	0.629794i	$-0.216861\pi$
$47$	−1.42512	−	3.12058i	−0.207875	−	0.455184i	−0.984638	+	0.174610i	$0.944133\pi$
$48$	−10.0920	−	11.6467i	−1.45665	−	1.68106i
$49$	−0.942052	−	6.55212i	−0.134579	−	0.936017i
$50$	−0.377934	+	2.62859i	−0.0534480	+	0.371739i
$51$	14.9126	−	4.37874i	2.08818	−	0.613146i
$52$	−0.790266	−	0.912016i	−0.109590	−	0.126474i
$53$	−1.94780	−	13.5472i	−0.267550	−	1.86085i	−0.471492	−	0.881871i	$-0.656284\pi$
$53$	−1.94780	−	13.5472i	−0.267550	−	1.86085i	0.203941	−	0.978983i	$-0.434625\pi$
$54$	−15.8370	+	10.1778i	−2.15515	+	1.38503i
$55$	−4.27702	+	2.74868i	−0.576714	+	0.370631i
$56$	−6.96557	+	2.04528i	−0.930814	+	0.273312i
$57$	2.86490	−	6.27325i	0.379465	−	0.830912i
$58$	−1.74712	+	2.01628i	−0.229407	+	0.264750i
$59$	−1.80007	−	1.15684i	−0.234349	−	0.150607i	0.418196	−	0.908357i	$-0.362662\pi$
$59$	−1.80007	−	1.15684i	−0.234349	−	0.150607i	−0.652545	+	0.757750i	$0.726299\pi$
$60$	−4.32583	+	4.99227i	−0.558462	+	0.644500i
$61$	9.60903	+	2.82146i	1.23031	+	0.361252i	0.831367	−	0.555724i	$-0.187559\pi$
$61$	9.60903	+	2.82146i	1.23031	+	0.361252i	0.398943	+	0.916976i	$0.369377\pi$
$62$	2.78379	−	0.817394i	0.353542	−	0.103809i
$63$	3.47133	+	24.1436i	0.437346	+	3.04181i
$64$	1.03400	+	2.26414i	0.129250	+	0.283017i
$65$	2.43961	−	2.81546i	0.302596	−	0.349215i
$66$	−10.3386			−1.27259
$67$	−4.70762	+	6.69614i	−0.575127	+	0.818064i
$67$	−4.70762	+	6.69614i	−0.575127	+	0.818064i
$68$	4.16557			0.505150
$69$	5.77825	−	6.66845i	0.695619	−	0.802787i
$70$	6.61575	+	14.4865i	0.790733	+	1.73146i
$71$	−0.520416	−	3.61957i	−0.0617620	−	0.429564i	−0.997119	−	0.0758581i	$-0.975830\pi$
$71$	−0.520416	−	3.61957i	−0.0617620	−	0.429564i	0.935357	−	0.353706i	$-0.115079\pi$
$72$	12.4750	−	3.66300i	1.47020	−	0.431688i
$73$	−5.81523	−	1.70750i	−0.680621	−	0.199848i	−0.0768935	−	0.997039i	$-0.524500\pi$
$73$	−5.81523	−	1.70750i	−0.680621	−	0.199848i	−0.603727	+	0.797191i	$0.706318\pi$
$74$	−2.92985	+	3.38122i	−0.340588	+	0.393059i
$75$	−4.11609	−	2.64525i	−0.475286	−	0.305448i
$76$	1.21043	−	1.39691i	0.138846	−	0.160236i
$77$	−3.03891	+	6.65429i	−0.346316	+	0.758327i
$78$	7.26876	−	2.13430i	0.823024	−	0.241662i
$79$	−11.7180	+	7.53068i	−1.31837	+	0.847267i	−0.995084	−	0.0990325i	$-0.968425\pi$
$79$	−11.7180	+	7.53068i	−1.31837	+	0.847267i	−0.323290	+	0.946300i	$0.604789\pi$
$80$	10.7266	−	6.89358i	1.19927	−	0.770726i
$81$	−2.11429	−	14.7052i	−0.234921	−	1.63391i
$82$	−9.18614	−	10.6014i	−1.01444	−	1.17073i
$83$	11.6292	−	3.41465i	1.27647	−	0.374806i	0.427872	−	0.903839i	$-0.359263\pi$
$83$	11.6292	−	3.41465i	1.27647	−	0.374806i	0.848601	+	0.529033i	$0.177445\pi$
$84$	−1.35267	+	9.40803i	−0.147588	+	1.02650i
$85$	1.83009	+	12.7285i	0.198501	+	1.38060i
$86$	−3.21508	−	3.71040i	−0.346691	−	0.400103i
$87$	−2.04196	−	4.47127i	−0.218921	−	0.479370i
$88$	3.74138	+	1.09857i	0.398833	+	0.117108i
$89$	2.99339	−	6.55461i	0.317299	−	0.694788i	−0.682033	−	0.731321i	$-0.738904\pi$
$89$	2.99339	−	6.55461i	0.317299	−	0.694788i	0.999332	+	0.0365332i	$0.0116315\pi$
$90$	−11.8485	−	25.9446i	−1.24894	−	2.73480i
$91$	0.762857	−	5.30578i	0.0799691	−	0.556197i
$92$	1.98947	−	1.27855i	0.207416	−	0.133298i
$93$	−0.760741	+	5.29107i	−0.0788852	+	0.548659i
$94$	5.53820	+	1.62616i	0.571222	+	0.167726i
$95$	4.80025	+	3.08493i	0.492495	+	0.316507i
$96$	13.7329			1.40161
$97$	−15.5529			−1.57915			−0.789577	−	0.613652i	$-0.789700\pi$
$97$	−15.5529			−1.57915			−0.789577	+	0.613652i	$0.789700\pi$
$98$	9.36933	+	6.02130i	0.946446	+	0.608244i
$99$	5.44256	−	11.9175i	0.546997	−	1.19776i
$100$	−0.858757	−	0.991059i	−0.0858757	−	0.0991059i
$101$	4.30161	+	4.96433i	0.428027	+	0.493969i	0.928265	−	0.371919i	$-0.121300\pi$
$101$	4.30161	+	4.96433i	0.428027	+	0.493969i	−0.500239	+	0.865887i	$0.666754\pi$
$102$	−10.8630	+	23.7867i	−1.07560	+	2.35524i
$103$	0.0418731	+	0.0269102i	0.00412588	+	0.00265154i	0.542702	−	0.839925i	$-0.317401\pi$
$103$	0.0418731	+	0.0269102i	0.00412588	+	0.00265154i	−0.538576	+	0.842577i	$0.681038\pi$
$104$	−2.85724			−0.280175
$105$	−29.3419			−2.86348
$106$	19.3721	+	12.4497i	1.88159	+	1.20922i
$107$	−13.2450	−	3.88909i	−1.28045	−	0.375973i	−0.430380	−	0.902648i	$-0.641620\pi$
$107$	−13.2450	−	3.88909i	−1.28045	−	0.375973i	−0.850067	+	0.526675i	$0.823438\pi$
$108$	1.32298	−	9.20150i	0.127303	−	0.885415i
$109$	12.2843	−	7.89466i	1.17663	−	0.756171i	0.201862	−	0.979414i	$-0.435301\pi$
$109$	12.2843	−	7.89466i	1.17663	−	0.756171i	0.974763	+	0.223243i	$0.0716643\pi$
$110$	1.21737	−	8.46698i	0.116071	−	0.807295i
$111$	−3.42429	−	7.49815i	−0.325019	−	0.711693i
$112$	7.62149	−	16.6887i	0.720163	−	1.57694i
$113$	4.57740	+	1.34405i	0.430605	+	0.126437i	0.489851	−	0.871806i	$-0.337051\pi$
$113$	4.57740	+	1.34405i	0.430605	+	0.126437i	−0.0592453	+	0.998243i	$0.518869\pi$
$114$	4.82021	+	10.5548i	0.451454	+	0.988546i
$115$	4.78086	+	5.51741i	0.445817	+	0.514501i
$116$	−0.187490	−	1.30402i	−0.0174080	−	0.121075i
$117$	−1.36624	+	9.50242i	−0.126309	+	0.878499i
$118$	3.45431	−	1.01428i	0.317995	−	0.0933718i
$119$	12.1169	+	13.9837i	1.11076	+	1.28188i
$120$	2.22584	+	15.4810i	0.203190	+	1.41322i
$121$	−5.94828	+	3.82273i	−0.540753	+	0.347521i
$122$	−14.1749	+	9.10968i	−1.28334	+	0.824752i
$123$	24.7981	−	7.28138i	2.23597	−	0.656540i
$124$	−0.595158	+	1.30321i	−0.0534467	+	0.117032i
$125$	−5.74700	+	6.63239i	−0.514027	+	0.593219i
$126$	−34.5247	−	22.1876i	−3.07570	−	1.97663i
$127$	0.620821	−	0.716466i	0.0550890	−	0.0635761i	−0.727536	−	0.686069i	$-0.759335\pi$
$127$	0.620821	−	0.716466i	0.0550890	−	0.0635761i	0.782625	+	0.622493i	$0.213880\pi$
$128$	−12.5196	−	3.67607i	−1.10658	−	0.324922i
$129$	8.67914	−	2.54843i	0.764156	−	0.224376i
$130$	0.892028	+	6.20419i	0.0782360	+	0.544143i
$131$	0.130553	+	0.285872i	0.0114065	+	0.0249767i	0.915250	−	0.402888i	$-0.131993\pi$
$131$	0.130553	+	0.285872i	0.0114065	+	0.0249767i	−0.903843	+	0.427864i	$0.859266\pi$
$132$	3.34323	−	3.85829i	0.290991	−	0.335821i
$133$	8.21028			0.711922
$134$	−3.32762	−	13.3639i	−0.287462	−	1.15446i
$135$	28.6978			2.46992
$136$	6.45872	−	7.45375i	0.553830	−	0.639154i
$137$	−7.01365	−	15.3578i	−0.599217	−	1.31210i	−0.929710	−	0.368293i	$-0.879942\pi$
$137$	−7.01365	−	15.3578i	−0.599217	−	1.31210i	0.330493	−	0.943808i	$-0.392785\pi$
$138$	2.11278	+	14.6947i	0.179852	+	1.25090i
$139$	−9.60781	+	2.82111i	−0.814924	+	0.239283i	−0.662529	−	0.749036i	$-0.730517\pi$
$139$	−9.60781	+	2.82111i	−0.814924	+	0.239283i	−0.152395	+	0.988320i	$0.548699\pi$
$140$	−7.54560	−	2.21559i	−0.637719	−	0.187251i
$141$	−6.96415	+	8.03706i	−0.586487	+	0.676842i
$142$	5.17588	+	3.32634i	0.434350	+	0.279140i
$143$	−1.88546	+	2.17593i	−0.157670	+	0.181961i
$144$	−13.6497	+	29.8888i	−1.13748	+	2.49073i
$145$	3.90226	−	1.14581i	0.324065	−	0.0951542i
$146$	8.57844	−	5.51303i	0.709957	−	0.456262i
$147$	−17.2624	+	11.0939i	−1.42378	+	0.915007i
$148$	−0.314414	−	2.18680i	−0.0258446	−	0.179753i
$149$	9.06978	+	10.4671i	0.743025	+	0.857497i	0.993873	−	0.110530i	$-0.0352547\pi$
$149$	9.06978	+	10.4671i	0.743025	+	0.857497i	−0.250847	+	0.968027i	$0.580709\pi$
$150$	7.89873	−	2.31928i	0.644928	−	0.189368i
$151$	2.66733	−	18.5517i	0.217064	−	1.50972i	−0.531730	−	0.846914i	$-0.678458\pi$
$151$	2.66733	−	18.5517i	0.217064	−	1.50972i	0.748795	−	0.662802i	$-0.230633\pi$
$152$	−0.622820	−	4.33181i	−0.0505173	−	0.351356i
$153$	−21.7008	−	25.0441i	−1.75441	−	2.02470i
$154$	−5.11299	−	11.1959i	−0.412017	−	0.902191i
$155$	−4.24364	−	1.24605i	−0.340857	−	0.100085i
$156$	−1.55402	+	3.40282i	−0.124421	+	0.272444i
$157$	−4.15905	−	9.10706i	−0.331929	−	0.726822i	0.667920	−	0.744233i	$-0.267185\pi$
$157$	−4.15905	−	9.10706i	−0.331929	−	0.726822i	−0.999848	+	0.0174109i	$0.994458\pi$
$158$	3.33528	−	23.1974i	0.265341	−	1.84548i
$159$	−35.6919	+	22.9378i	−2.83055	+	1.81908i
$160$	−1.61705	+	11.2468i	−0.127839	+	0.889141i
$161$	10.0791	+	2.95948i	0.794341	+	0.233240i
$162$	21.0280	+	13.5139i	1.65212	+	1.06175i
$163$	−11.8428			−0.927601			−0.463801	−	0.885940i	$-0.653515\pi$
$163$	−11.8428			−0.927601			−0.463801	+	0.885940i	$0.653515\pi$
$164$	6.92691			0.540901
$165$	13.2584	+	8.52065i	1.03216	+	0.663332i
$166$	−8.47126	+	18.5495i	−0.657497	+	1.43972i
$167$	−1.45173	−	1.67538i	−0.112338	−	0.129645i	0.696795	−	0.717270i	$-0.254609\pi$
$167$	−1.45173	−	1.67538i	−0.112338	−	0.129645i	−0.809133	+	0.587625i	$0.800063\pi$
$168$	14.7371	+	17.0076i	1.13699	+	1.31216i
$169$	−4.52399	+	9.90615i	−0.347999	+	0.762011i
$170$	−18.2014	−	11.6974i	−1.39599	−	0.897146i
$171$	−14.7042			−1.12446
$172$	2.42437			0.184856
$173$	4.17645	+	2.68404i	0.317530	+	0.204064i	0.689690	−	0.724104i	$-0.257747\pi$
$173$	4.17645	+	2.68404i	0.317530	+	0.204064i	−0.372161	+	0.928168i	$0.621383\pi$
$174$	7.93530	+	2.33002i	0.601574	+	0.176638i
$175$	0.828972	−	5.76563i	0.0626644	−	0.435840i
$176$	−8.29010	+	5.32772i	−0.624890	+	0.401592i
$177$	−0.943979	+	6.56552i	−0.0709538	+	0.493494i
$178$	5.03640	+	11.0282i	0.377494	+	0.826597i
$179$	0.746885	−	1.63545i	0.0558248	−	0.122239i	−0.879664	−	0.475596i	$-0.842232\pi$
$179$	0.746885	−	1.63545i	0.0558248	−	0.122239i	0.935489	+	0.353357i	$0.114960\pi$
$180$	13.5138	+	3.96802i	1.00726	+	0.295758i
$181$	−5.79454	−	12.6883i	−0.430704	−	0.943111i	−0.993212	−	0.116319i	$-0.962891\pi$
$181$	−5.79454	−	12.6883i	−0.430704	−	0.943111i	0.562507	−	0.826792i	$-0.309837\pi$
$182$	5.90607	+	6.81597i	0.437787	+	0.505233i
$183$	−4.41811	−	30.7287i	−0.326596	−	2.27153i
$184$	0.796861	−	5.54229i	0.0587454	−	0.408583i
$185$	6.54395	−	1.92148i	0.481121	−	0.141270i
$186$	−5.88969	−	6.79707i	−0.431853	−	0.498385i
$187$	−1.41439	−	9.83728i	−0.103430	−	0.719373i
$188$	−2.39778	+	1.54096i	−0.174876	+	0.112386i
$189$	34.7374	−	22.3244i	2.52677	−	1.62386i
$190$	−9.21161	+	2.70477i	−0.668280	+	0.196225i
$191$	−3.54961	+	7.77255i	−0.256840	+	0.562402i	−0.993496	−	0.113866i	$-0.963677\pi$
$191$	−3.54961	+	7.77255i	−0.256840	+	0.562402i	0.736656	+	0.676268i	$0.236404\pi$
$192$	5.05284	−	5.83128i	0.364657	−	0.420837i
$193$	22.0129	+	14.1468i	1.58452	+	1.01831i	0.974066	+	0.226262i	$0.0726506\pi$
$193$	22.0129	+	14.1468i	1.58452	+	1.01831i	0.610457	+	0.792049i	$0.290986\pi$
$194$	17.1363	−	19.7763i	1.23031	−	1.41986i
$195$	−11.0806	−	3.25355i	−0.793497	−	0.232992i
$196$	−5.27690	+	1.54944i	−0.376921	+	0.110674i
$197$	−3.03122	−	21.0826i	−0.215966	−	1.50207i	−0.752723	−	0.658337i	$-0.771260\pi$
$197$	−3.03122	−	21.0826i	−0.215966	−	1.50207i	0.536757	−	0.843737i	$-0.319649\pi$
$198$	9.15714	+	20.0513i	0.650769	+	1.42499i
$199$	4.08414	−	4.71335i	0.289517	−	0.334121i	−0.592295	−	0.805721i	$-0.701778\pi$
$199$	4.08414	−	4.71335i	0.289517	−	0.334121i	0.881812	+	0.471600i	$0.156323\pi$
$200$	−3.10487			−0.219548
$201$	24.9439	+	4.65149i	1.75940	+	0.328091i
$202$	−11.0520			−0.777613
$203$	3.83217	−	4.42256i	0.268966	−	0.310403i
$204$	−5.36421	−	11.7460i	−0.375570	−	0.822384i
$205$	3.04324	+	21.1662i	0.212549	+	1.47831i
$206$	−0.0803538	+	0.0235940i	−0.00559852	+	0.00164387i
$207$	−18.0511	−	5.30029i	−1.25464	−	0.368396i
$208$	4.72866	−	5.45717i	0.327874	−	0.378386i
$209$	−3.70988	−	2.38420i	−0.256618	−	0.164918i
$210$	32.3292	−	37.3099i	2.23093	−	2.57463i
$211$	3.78396	−	8.28572i	0.260499	−	0.570413i	−0.733514	−	0.679674i	$-0.762121\pi$
$211$	3.78396	−	8.28572i	0.260499	−	0.570413i	0.994013	+	0.109261i	$0.0348485\pi$
$212$	−10.9106	+	3.20363i	−0.749341	+	0.220026i
$213$	−9.53623	+	6.12856i	−0.653411	+	0.419922i
$214$	19.5387	−	12.5567i	1.33564	−	0.858362i
$215$	1.06511	+	7.40802i	0.0726400	+	0.505222i
$216$	−14.4136	−	16.6342i	−0.980723	−	1.13181i
$217$	−6.10604	+	1.79290i	−0.414505	+	0.121710i
$218$	−3.49648	+	24.3186i	−0.236812	+	1.64706i
$219$	2.67377	+	18.5965i	0.180677	+	1.25663i
$220$	2.76615	+	3.19231i	0.186494	+	0.215225i
$221$	3.02522	+	6.62431i	0.203498	+	0.445599i
$222$	13.3072	+	3.90735i	0.893121	+	0.262244i
$223$	−10.2315	+	22.4038i	−0.685151	+	1.50027i	0.171941	+	0.985107i	$0.444996\pi$
$223$	−10.2315	+	22.4038i	−0.685151	+	1.50027i	−0.857092	+	0.515164i	$0.827731\pi$
$224$	6.79168	+	14.8717i	0.453788	+	0.993658i
$225$	−1.48465	+	10.3260i	−0.0989768	+	0.688398i
$226$	−6.75244	+	4.33953i	−0.449166	+	0.288661i
$227$	−3.39520	+	23.6141i	−0.225347	+	1.56732i	0.491993	+	0.870599i	$0.336269\pi$
$227$	−3.39520	+	23.6141i	−0.225347	+	1.56732i	−0.717340	+	0.696724i	$0.754640\pi$
$228$	−5.49770	−	1.61427i	−0.364094	−	0.106908i
$229$	3.80914	+	2.44798i	0.251715	+	0.161767i	0.660414	−	0.750902i	$-0.270381\pi$
$229$	3.80914	+	2.44798i	0.251715	+	0.161767i	−0.408699	+	0.912669i	$0.634017\pi$
$230$	−12.2833			−0.809935
$231$	22.6770			1.49204
$232$	−2.62408	−	1.68639i	−0.172279	−	0.110717i
$233$	1.88592	−	4.12958i	0.123551	−	0.270538i	−0.837743	−	0.546065i	$-0.816125\pi$
$233$	1.88592	−	4.12958i	0.123551	−	0.270538i	0.961293	+	0.275527i	$0.0888524\pi$
$234$	−10.5775	−	12.2071i	−0.691473	−	0.798002i
$235$	−5.76206	−	6.64978i	−0.375876	−	0.433784i
$236$	−0.738511	+	1.61711i	−0.0480730	+	0.105265i
$237$	36.3246	+	23.3444i	2.35954	+	1.51638i
$238$	−31.1315			−2.01796
$239$	−6.17280			−0.399285			−0.199643	−	0.979869i	$-0.563978\pi$
$239$	−6.17280			−0.399285			−0.199643	+	0.979869i	$0.563978\pi$
$240$	−33.2516	−	21.3695i	−2.14638	−	1.37940i
$241$	11.0477	+	3.24389i	0.711644	+	0.208957i	0.617465	−	0.786598i	$-0.288160\pi$
$241$	11.0477	+	3.24389i	0.711644	+	0.208957i	0.0941780	+	0.995555i	$0.469978\pi$
$242$	1.69306	−	11.7755i	0.108834	−	0.756956i
$243$	−10.5045	+	6.75085i	−0.673865	+	0.433067i
$244$	1.18413	−	8.23582i	0.0758062	−	0.527244i
$245$	−7.05288	−	15.4436i	−0.450592	−	0.986658i
$246$	−18.0641	+	39.5548i	−1.15172	+	2.52192i
$247$	3.10050	+	0.910389i	0.197280	+	0.0579266i
$248$	1.40914	+	3.08559i	0.0894805	+	0.195935i
$249$	−24.6041	−	28.3946i	−1.55922	−	1.79944i
$250$	−2.10135	−	14.6152i	−0.132901	−	0.924349i
$251$	−1.76471	+	12.2738i	−0.111388	+	0.774717i	0.855185	+	0.518323i	$0.173444\pi$
$251$	−1.76471	+	12.2738i	−0.111388	+	0.774717i	−0.966572	+	0.256394i	$0.917466\pi$
$252$	19.4446	−	5.70946i	1.22490	−	0.359662i
$253$	−3.69490	−	4.26414i	−0.232296	−	0.268084i
$254$	0.226999	+	1.57882i	0.0142432	+	0.0990637i
$255$	33.5350	−	21.5516i	2.10004	−	1.34961i
$256$	14.2806	−	9.17758i	0.892537	−	0.573599i
$257$	−1.02159	+	0.299965i	−0.0637248	+	0.0187113i	−0.313440	−	0.949608i	$-0.601481\pi$
$257$	−1.02159	+	0.299965i	−0.0637248	+	0.0187113i	0.249715	+	0.968319i	$0.419663\pi$
$258$	−6.32229	+	13.8439i	−0.393608	+	0.861882i
$259$	6.42641	−	7.41647i	0.399318	−	0.460837i
$260$	−2.60382	−	1.67337i	−0.161482	−	0.103778i
$261$	−6.86325	+	7.92061i	−0.424824	+	0.490274i
$262$	−0.507346	−	0.148970i	−0.0313439	−	0.00920340i
$263$	−13.4316	+	3.94389i	−0.828231	+	0.243190i	−0.668257	−	0.743931i	$-0.732959\pi$
$263$	−13.4316	+	3.94389i	−0.828231	+	0.243190i	−0.159974	+	0.987121i	$0.551141\pi$
$264$	−1.72024	−	11.9645i	−0.105874	−	0.736367i
$265$	−14.5826	−	31.9314i	−0.895801	−	1.96153i
$266$	−9.04615	+	10.4398i	−0.554655	+	0.640106i
$267$	−22.3373			−1.36702
$268$	6.06336	+	3.07967i	0.370378	+	0.188121i
$269$	−8.82949			−0.538343			−0.269172	−	0.963092i	$-0.586750\pi$
$269$	−8.82949			−0.538343			−0.269172	+	0.963092i	$0.586750\pi$
$270$	−31.6195	+	36.4908i	−1.92430	+	2.22076i
$271$	2.97706	+	6.51884i	0.180843	+	0.395991i	0.978244	−	0.207459i	$-0.0665194\pi$
$271$	2.97706	+	6.51884i	0.180843	+	0.395991i	−0.797400	+	0.603450i	$0.793792\pi$
$272$	3.54723	+	24.6716i	0.215083	+	1.49593i
$273$	−15.9435	+	4.68143i	−0.964944	+	0.283333i
$274$	27.2559	+	8.00306i	1.64659	+	0.483482i
$275$	−2.04887	+	2.36452i	−0.123551	+	0.142586i
$276$	−6.16717	−	3.96340i	−0.371220	−	0.238569i
$277$	0.0427530	−	0.0493395i	0.00256878	−	0.00296453i	−0.754464	−	0.656342i	$-0.772103\pi$
$277$	0.0427530	−	0.0493395i	0.00256878	−	0.00296453i	0.757033	+	0.653377i	$0.226648\pi$
$278$	6.99877	−	15.3252i	0.419758	−	0.919143i
$279$	10.9356	−	3.21100i	0.654700	−	0.192237i
$280$	−15.6639	+	10.0666i	−0.936100	+	0.601595i
$281$	17.6140	−	11.3198i	1.05076	−	0.675285i	0.103138	−	0.994667i	$-0.467112\pi$
$281$	17.6140	−	11.3198i	1.05076	−	0.675285i	0.947626	+	0.319382i	$0.103475\pi$
$282$	−2.54640	−	17.7106i	−0.151636	−	1.05465i
$283$	5.02616	+	5.80049i	0.298774	+	0.344804i	0.885210	−	0.465192i	$-0.154015\pi$
$283$	5.02616	+	5.80049i	0.298774	+	0.344804i	−0.586436	+	0.809996i	$0.699469\pi$
$284$	−2.91511	+	0.855953i	−0.172980	+	0.0507914i
$285$	2.51731	−	17.5083i	0.149112	−	1.03710i
$286$	−0.689406	−	4.79492i	−0.0407654	−	0.283530i
$287$	20.1492	+	23.2534i	1.18937	+	1.37260i
$288$	−12.1636	−	26.6346i	−0.716747	−	1.56946i
$289$	−7.80805	−	2.29265i	−0.459297	−	0.134862i
$290$	−2.84259	+	6.22440i	−0.166923	+	0.365509i
$291$	20.0282	+	43.8556i	1.17407	+	2.57086i
$292$	−0.716617	+	4.98418i	−0.0419368	+	0.291677i
$293$	9.31951	−	5.98929i	0.544452	−	0.349898i	−0.239326	−	0.970939i	$-0.576927\pi$
$293$	9.31951	−	5.98929i	0.544452	−	0.349898i	0.783778	+	0.621041i	$0.213290\pi$
$294$	4.91339	−	34.1734i	0.286555	−	1.99303i
$295$	−5.26579	−	1.54618i	−0.306586	−	0.0900219i
$296$	−4.40049	−	2.82802i	−0.255773	−	0.164375i
$297$	−22.1792			−1.28697
$298$	−23.3026			−1.34988
$299$	3.47806	+	2.23521i	0.201141	+	0.129266i
$300$	−1.68870	+	3.69774i	−0.0974972	+	0.213489i
$301$	7.05205	+	8.13850i	0.406473	+	0.469095i
$302$	20.6506	+	23.8321i	1.18831	+	1.37138i
$303$	8.45890	−	18.5224i	0.485951	−	1.06408i
$304$	9.30426	+	5.97948i	0.533636	+	0.342947i
$305$	25.6860			1.47078
$306$	55.7551			3.18731
$307$	5.74300	+	3.69080i	0.327770	+	0.210645i	0.694168	−	0.719813i	$-0.255773\pi$
$307$	5.74300	+	3.69080i	0.327770	+	0.210645i	−0.366397	+	0.930458i	$0.619409\pi$
$308$	5.83163	+	1.71232i	0.332288	+	0.0975686i
$309$	0.0219587	−	0.152726i	0.00124919	−	0.00868830i
$310$	6.26009	−	4.02312i	0.355549	−	0.228498i
$311$	3.84808	−	26.7640i	0.218205	−	1.51765i	−0.526455	−	0.850203i	$-0.676479\pi$
$311$	3.84808	−	26.7640i	0.218205	−	1.51765i	0.744660	−	0.667444i	$-0.232612\pi$
$312$	3.67941	+	8.05678i	0.208306	+	0.456125i
$313$	−8.09922	+	17.7348i	−0.457795	+	1.00243i	0.530190	+	0.847879i	$0.322121\pi$
$313$	−8.09922	+	17.7348i	−0.457795	+	1.00243i	−0.987985	+	0.154552i	$0.950607\pi$
$314$	16.1626	+	4.74577i	0.912108	+	0.267819i
$315$	25.9888	+	56.9076i	1.46431	+	3.20638i
$316$	7.57855	+	8.74612i	0.426327	+	0.492008i
$317$	−0.319183	−	2.21997i	−0.0179271	−	0.124686i	0.978893	−	0.204375i	$-0.0655163\pi$
$317$	−0.319183	−	2.21997i	−0.0179271	−	0.124686i	−0.996820	+	0.0796893i	$0.974607\pi$
$318$	10.1590	−	70.6572i	0.569687	−	3.96226i
$319$	−3.01587	+	0.885540i	−0.168857	+	0.0495807i
$320$	4.18066	+	4.82474i	0.233706	+	0.269711i
$321$	6.08991	+	42.3562i	0.339906	+	2.36410i
$322$	−14.8683	+	9.55529i	−0.828580	+	0.532496i
$323$	−9.38355	+	6.03044i	−0.522115	+	0.335543i
$324$	−11.8432	+	3.47747i	−0.657955	+	0.193193i
$325$	0.952365	−	2.08539i	0.0528277	−	0.115677i
$326$	13.0485	−	15.0588i	0.722690	−	0.834029i
$327$	−38.0803	−	24.4727i	−2.10585	−	1.35335i
$328$	10.7402	−	12.3948i	0.593026	−	0.684389i
$329$	−12.1476	−	3.56687i	−0.669722	−	0.196648i
$330$	−25.4427	+	7.47064i	−1.40057	+	0.411245i
$331$	−4.95231	−	34.4441i	−0.272203	−	1.89322i	−0.425376	−	0.905017i	$-0.639858\pi$
$331$	−4.95231	−	34.4441i	−0.272203	−	1.89322i	0.153172	−	0.988200i	$-0.451051\pi$
$332$	−4.18315	−	9.15982i	−0.229580	−	0.502710i
$333$	−11.5094	+	13.2826i	−0.630712	+	0.727880i
$334$	3.72986			0.204089
$335$	−6.74655	+	19.8805i	−0.368604	+	1.08619i
$336$	−56.8731			−3.10268
$337$	−21.2757	+	24.5535i	−1.15896	+	1.33752i	−0.227458	+	0.973788i	$0.573041\pi$
$337$	−21.2757	+	24.5535i	−1.15896	+	1.33752i	−0.931505	+	0.363727i	$0.881504\pi$
$338$	−7.61164	−	16.6672i	−0.414019	−	0.906574i
$339$	−2.10463	−	14.6380i	−0.114308	−	0.795029i
$340$	10.2512	−	3.01003i	0.555951	−	0.163242i
$341$	3.27971	+	0.963009i	0.177606	+	0.0521499i
$342$	16.2012	−	18.6972i	0.876063	−	1.01103i
$343$	1.18132	+	0.759188i	0.0637853	+	0.0409923i
$344$	3.75897	−	4.33809i	0.202670	−	0.233894i
$345$	9.40131	−	20.5860i	0.506150	−	1.10831i
$346$	−8.01455	+	2.35329i	−0.430865	+	0.126513i
$347$	−5.82403	+	3.74288i	−0.312650	+	0.200928i	−0.687550	−	0.726137i	$-0.741314\pi$
$347$	−5.82403	+	3.74288i	−0.312650	+	0.200928i	0.374899	+	0.927066i	$0.377677\pi$
$348$	−3.43561	+	2.20793i	−0.184168	+	0.118358i
$349$	2.15034	+	14.9559i	0.115105	+	0.800572i	0.962825	+	0.270127i	$0.0870659\pi$
$349$	2.15034	+	14.9559i	0.115105	+	0.800572i	−0.847720	+	0.530444i	$0.822025\pi$
$350$	6.41794	+	7.40670i	0.343053	+	0.395905i
$351$	15.5935	−	4.57867i	0.832320	−	0.244391i
$352$	1.24974	−	8.69215i	0.0666115	−	0.463293i
$353$	−2.21032	−	15.3731i	−0.117643	−	0.818227i	−0.960139	−	0.279524i	$-0.909823\pi$
$353$	−2.21032	−	15.3731i	−0.117643	−	0.818227i	0.842495	−	0.538704i	$-0.181086\pi$
$354$	−7.30832	−	8.43426i	−0.388433	−	0.448276i
$355$	−3.89621	−	8.53150i	−0.206789	−	0.452805i
$356$	−5.74428	−	1.68667i	−0.304446	−	0.0893934i
$357$	23.8273	−	52.1745i	1.26107	−	2.76137i
$358$	1.25664	+	2.75166i	0.0664155	+	0.145430i
$359$	−2.61133	+	18.1622i	−0.137821	+	0.958565i	0.797135	+	0.603801i	$0.206348\pi$
$359$	−2.61133	+	18.1622i	−0.137821	+	0.958565i	−0.934956	+	0.354764i	$0.884561\pi$
$360$	28.0534	−	18.0288i	1.47854	−	0.950203i
$361$	1.99960	−	13.9076i	0.105242	−	0.731977i
$362$	22.5183	+	6.61196i	1.18353	+	0.347517i
$363$	18.4391	+	11.8501i	0.967804	+	0.621970i
$364$	−4.45353			−0.233429
$365$	−15.5448			−0.813650
$366$	43.9411	+	28.2392i	2.29684	+	1.47609i
$367$	10.9654	−	24.0108i	0.572388	−	1.25335i	−0.373129	−	0.927780i	$-0.621715\pi$
$367$	10.9654	−	24.0108i	0.572388	−	1.25335i	0.945516	−	0.325575i	$-0.105558\pi$
$368$	9.26667	+	10.6943i	0.483059	+	0.557480i
$369$	−36.0862	−	41.6457i	−1.87857	−	2.16799i
$370$	−4.76691	+	10.4381i	−0.247820	+	0.542650i
$371$	−42.4914	−	27.3075i	−2.20604	−	1.41774i
$372$	4.44119			0.230265
$373$	−8.96114			−0.463990			−0.231995	−	0.972717i	$-0.574525\pi$
$373$	−8.96114			−0.463990			−0.231995	+	0.972717i	$0.574525\pi$
$374$	14.0670	+	9.04032i	0.727388	+	0.467464i
$375$	26.1026	+	7.66440i	1.34793	+	0.395788i
$376$	−0.960406	+	6.67977i	−0.0495291	+	0.344483i
$377$	1.93756	−	1.24519i	0.0997893	−	0.0641307i
$378$	−9.88729	+	68.7676i	−0.508547	+	3.53702i
$379$	−3.53006	−	7.72975i	−0.181327	−	0.397051i	0.797040	−	0.603926i	$-0.206398\pi$
$379$	−3.53006	−	7.72975i	−0.181327	−	0.397051i	−0.978367	+	0.206875i	$0.933671\pi$
$380$	1.96939	−	4.31236i	0.101027	−	0.221219i
$381$	−2.81974	−	0.827949i	−0.144459	−	0.0424171i
$382$	−5.97224	−	13.0774i	−0.305566	−	0.669097i
$383$	22.7365	+	26.2393i	1.16178	+	1.34077i	0.929808	+	0.368045i	$0.119973\pi$
$383$	22.7365	+	26.2393i	1.16178	+	1.34077i	0.231974	+	0.972722i	$0.425482\pi$
$384$	5.75634	+	40.0362i	0.293752	+	2.04309i
$385$	−2.67021	+	18.5717i	−0.136087	+	0.946503i
$386$	−42.2425	+	12.4035i	−2.15008	+	0.631322i
$387$	−12.6299	−	14.5757i	−0.642014	−	0.740923i
$388$	1.83896	+	12.7903i	0.0933591	+	0.649327i
$389$	3.11703	−	2.00319i	0.158039	−	0.101566i	−0.459231	−	0.888317i	$-0.651875\pi$
$389$	3.11703	−	2.00319i	0.158039	−	0.101566i	0.617270	+	0.786751i	$0.288239\pi$
$390$	16.3457	−	10.5048i	0.827698	−	0.531929i
$391$	−13.6931	+	4.02066i	−0.692491	+	0.203334i
$392$	−5.40931	+	11.8447i	−0.273211	+	0.598249i
$393$	0.637974	−	0.736262i	0.0321816	−	0.0371395i
$394$	30.1475	+	19.3746i	1.51881	+	0.976080i
$395$	−23.3956	+	26.9999i	−1.17716	+	1.35851i
$396$	−10.4442	−	3.06669i	−0.524840	−	0.154107i
$397$	−5.81381	+	1.70709i	−0.291787	+	0.0856763i	−0.424350	−	0.905498i	$-0.639497\pi$
$397$	−5.81381	+	1.70709i	−0.291787	+	0.0856763i	0.132563	+	0.991175i	$0.457679\pi$
$398$	1.49334	+	10.3864i	0.0748545	+	0.520624i
$399$	−10.5728	−	23.1512i	−0.529301	−	1.15901i
$400$	5.13849	−	5.93013i	0.256924	−	0.296507i
$401$	18.2872			0.913220			0.456610	−	0.889667i	$-0.349063\pi$
$401$	18.2872			0.913220			0.456610	+	0.889667i	$0.349063\pi$
$402$	−33.3980	+	26.5924i	−1.66574	+	1.32631i
$403$	−2.50467			−0.124766
$404$	3.57391	−	4.12451i	0.177809	−	0.205202i
$405$	−15.8291	−	34.6609i	−0.786554	−	1.72231i
$406$	1.40121	+	9.74563i	0.0695409	+	0.483668i
$407$	−5.05751	+	1.48502i	−0.250691	+	0.0736096i
$408$	−29.3351	−	8.61357i	−1.45231	−	0.426435i
$409$	15.7236	−	18.1460i	0.777481	−	0.897261i	−0.219444	−	0.975625i	$-0.570424\pi$
$409$	15.7236	−	18.1460i	0.777481	−	0.897261i	0.996925	+	0.0783644i	$0.0249698\pi$
$410$	−30.2671	−	19.4515i	−1.49478	−	0.960639i
$411$	−34.2736	+	39.5539i	−1.69059	+	1.95105i
$412$	0.0171792	−	0.0376171i	0.000846357	−	0.00185326i
$413$	−7.57679	+	2.22475i	−0.372829	+	0.109473i
$414$	26.6285	−	17.1131i	1.30872	−	0.841063i
$415$	26.1514	−	16.8065i	1.28372	−	0.824998i
$416$	0.915750	+	6.36918i	0.0448983	+	0.312275i
$417$	20.3274	+	23.4590i	0.995435	+	1.14879i
$418$	7.11921	−	2.09039i	0.348212	−	0.102244i
$419$	−0.510704	+	3.55202i	−0.0249495	+	0.173528i	−0.998486	−	0.0550032i	$-0.982483\pi$
$419$	−0.510704	+	3.55202i	−0.0249495	+	0.173528i	0.973537	+	0.228531i	$0.0733922\pi$
$420$	3.46938	+	24.1300i	0.169288	+	1.17743i
$421$	11.9539	+	13.7955i	0.582596	+	0.672351i	0.968161	−	0.250329i	$-0.0805389\pi$
$421$	11.9539	+	13.7955i	0.582596	+	0.672351i	−0.385565	+	0.922681i	$0.625993\pi$
$422$	6.36654	+	13.9408i	0.309919	+	0.678627i
$423$	21.7559	+	6.38810i	1.05781	+	0.310600i
$424$	−11.1843	+	24.4903i	−0.543159	+	1.18935i
$425$	3.28741	+	7.19843i	0.159463	+	0.349175i
$426$	2.71429	−	18.8783i	0.131508	−	0.914658i
$427$	31.0917	−	19.9814i	1.50463	−	0.966970i
$428$	−1.63220	+	11.3522i	−0.0788954	+	0.548730i
$429$	8.56365	+	2.51451i	0.413457	+	0.121402i
$430$	−10.5932	−	6.80786i	−0.510851	−	0.328304i
$431$	−1.70162			−0.0819640			−0.0409820	−	0.999160i	$-0.513049\pi$
$431$	−1.70162			−0.0819640			−0.0409820	+	0.999160i	$0.513049\pi$
$432$	55.6246			2.67624
$433$	−26.7291	−	17.1777i	−1.28452	−	0.825510i	−0.293080	−	0.956088i	$-0.594680\pi$
$433$	−26.7291	−	17.1777i	−1.28452	−	0.825510i	−0.991438	+	0.130578i	$0.958317\pi$
$434$	4.44792	−	9.73959i	0.213507	−	0.467515i
$435$	−8.25606	−	9.52801i	−0.395848	−	0.456833i
$436$	−7.94485	−	9.16884i	−0.380489	−	0.439108i
$437$	−2.63062	+	5.76025i	−0.125839	+	0.275550i
$438$	−26.5924	−	17.0899i	−1.27063	−	0.816587i
$439$	−6.48857			−0.309683			−0.154841	−	0.987939i	$-0.549487\pi$
$439$	−6.48857			−0.309683			−0.154841	+	0.987939i	$0.549487\pi$
$440$	10.0011			0.476785
$441$	36.8058	+	23.6537i	1.75266	+	1.12637i
$442$	−11.7564	−	3.45198i	−0.559194	−	0.164194i
$443$	1.69679	−	11.8014i	0.0806168	−	0.560702i	−0.908981	−	0.416838i	$-0.863138\pi$
$443$	1.69679	−	11.8014i	0.0806168	−	0.560702i	0.989597	−	0.143864i	$-0.0459528\pi$
$444$	−5.76139	+	3.70262i	−0.273424	+	0.175719i
$445$	2.63021	−	18.2935i	0.124684	−	0.867196i
$446$	−17.2145	−	37.6946i	−0.815132	−	1.78489i
$447$	17.8352	−	39.0537i	0.843578	−	1.84718i
$448$	8.81372	+	2.58794i	0.416409	+	0.122269i
$449$	−8.45237	−	18.5081i	−0.398892	−	0.873452i	−0.997381	−	0.0723209i	$-0.976959\pi$
$449$	−8.45237	−	18.5081i	−0.398892	−	0.873452i	0.598489	−	0.801131i	$-0.295768\pi$
$450$	−11.4942	−	13.2651i	−0.541844	−	0.625321i
$451$	−2.35198	−	16.3584i	−0.110750	−	0.770285i
$452$	0.564078	−	3.92325i	0.0265320	−	0.184534i
$453$	−55.7465	+	16.3687i	−2.61920	+	0.769067i
$454$	−26.2858	−	30.3354i	−1.23365	−	1.42371i
$455$	−1.95660	−	13.6085i	−0.0917268	−	0.637974i
$456$	−11.4127	+	7.33449i	−0.534448	+	0.343469i
$457$	14.7429	−	9.47469i	0.689644	−	0.443207i	−0.148315	−	0.988940i	$-0.547385\pi$
$457$	14.7429	−	9.47469i	0.689644	−	0.443207i	0.837959	+	0.545733i	$0.183749\pi$
$458$	−7.30968	+	2.14632i	−0.341559	+	0.100291i
$459$	−23.3042	+	51.0291i	−1.08775	+	2.38184i
$460$	3.97208	−	4.58403i	0.185199	−	0.213731i
$461$	−31.1937	−	20.0469i	−1.45283	−	0.933679i	−0.999095	−	0.0425446i	$-0.986454\pi$
$461$	−31.1937	−	20.0469i	−1.45283	−	0.933679i	−0.453739	−	0.891135i	$-0.649910\pi$
$462$	−24.9857	+	28.8350i	−1.16244	+	1.34153i
$463$	29.0112	+	8.51846i	1.34827	+	0.395886i	0.874611	−	0.484825i	$-0.161117\pi$
$463$	29.0112	+	8.51846i	1.34827	+	0.395886i	0.473654	+	0.880711i	$0.342935\pi$
$464$	7.56371	−	2.22090i	0.351136	−	0.103103i
$465$	1.95117	+	13.5707i	0.0904836	+	0.629327i
$466$	3.17307	+	6.94805i	0.146990	+	0.321862i
$467$	13.8976	−	16.0387i	0.643103	−	0.742180i	−0.336817	−	0.941570i	$-0.609350\pi$
$467$	13.8976	−	16.0387i	0.643103	−	0.742180i	0.979920	+	0.199390i	$0.0638959\pi$
$468$	7.97608			0.368694
$469$	7.29889	+	29.3127i	0.337031	+	1.35353i
$470$	14.8042			0.682869
$471$	−20.3241	+	23.4552i	−0.936483	+	1.08076i
$472$	1.74856	+	3.82880i	0.0804838	+	0.176235i
$473$	−0.823174	−	5.72530i	−0.0378496	−	0.263250i
$474$	−69.7065	+	20.4677i	−3.20172	+	0.940111i
$475$	3.36921	+	0.989291i	0.154590	+	0.0453918i
$476$	10.0671	−	11.6180i	0.461425	−	0.532512i
$477$	76.1001	+	48.9066i	3.48438	+	2.23928i
$478$	6.80124	−	7.84905i	0.311081	−	0.359007i
$479$	−3.59847	+	7.87954i	−0.164418	+	0.360025i	−0.973851	−	0.227187i	$-0.927047\pi$
$479$	−3.59847	+	7.87954i	−0.164418	+	0.360025i	0.809433	+	0.587212i	$0.199775\pi$
$480$	33.7960	−	9.92339i	1.54257	−	0.452939i
$481$	3.24921	−	2.08814i	0.148151	−	0.0952111i
$482$	−16.2972	+	10.4736i	−0.742317	+	0.477058i
$483$	−4.63423	−	32.2318i	−0.210865	−	1.46660i
$484$	3.84703	+	4.43971i	0.174865	+	0.201805i
$485$	−38.2747	+	11.2385i	−1.73796	+	0.510312i
$486$	2.98990	−	20.7952i	0.135625	−	0.943290i
$487$	−1.06065	−	7.37701i	−0.0480628	−	0.334284i	−0.999639	−	0.0268709i	$-0.991446\pi$
$487$	−1.06065	−	7.37701i	−0.0480628	−	0.334284i	0.951576	−	0.307413i	$-0.0994634\pi$
$488$	−12.9009	−	14.8885i	−0.583998	−	0.673969i
$489$	15.2506	+	33.3941i	0.689655	+	1.51013i
$490$	27.4083	+	8.04782i	1.23818	+	0.363563i
$491$	16.0438	−	35.1311i	0.724048	−	1.58544i	−0.0840947	−	0.996458i	$-0.526800\pi$
$491$	16.0438	−	35.1311i	0.724048	−	1.58544i	0.808143	−	0.588987i	$-0.200473\pi$
$492$	−8.92012	−	19.5323i	−0.402150	−	0.880586i
$493$	−1.13143	+	7.86928i	−0.0509571	+	0.354415i
$494$	−4.57376	+	2.93938i	−0.205783	+	0.132249i
$495$	4.78223	−	33.2611i	0.214945	−	1.49498i
$496$	−8.22539	−	2.41519i	−0.369331	−	0.108445i
$497$	−11.3529	−	7.29608i	−0.509248	−	0.327274i
$498$	63.2142			2.83270
$499$	−8.38778			−0.375488			−0.187744	−	0.982218i	$-0.560118\pi$
$499$	−8.38778			−0.375488			−0.187744	+	0.982218i	$0.560118\pi$
$500$	6.13382	+	3.94197i	0.274313	+	0.176290i
$501$	−2.85474	+	6.25102i	−0.127541	+	0.279275i
$502$	−13.6625	−	15.7673i	−0.609786	−	0.703730i
$503$	14.3796	+	16.5950i	0.641156	+	0.739934i	0.979579	−	0.201061i	$-0.0644388\pi$
$503$	14.3796	+	16.5950i	0.641156	+	0.739934i	−0.338423	+	0.940994i	$0.609893\pi$
$504$	19.9325	−	43.6461i	0.887865	−	1.94415i
$505$	14.1732	+	9.10857i	0.630700	+	0.405326i
$506$	9.49315			0.422022
$507$	33.7589			1.49929
$508$	−0.662608	−	0.425832i	−0.0293985	−	0.0188933i
$509$	−6.82648	−	2.00443i	−0.302578	−	0.0888450i	0.126919	−	0.991913i	$-0.459491\pi$
$509$	−6.82648	−	2.00443i	−0.302578	−	0.0888450i	−0.429497	+	0.903068i	$0.641309\pi$
$510$	−9.54505	+	66.3873i	−0.422662	+	2.93968i
$511$	−18.8162	+	12.0924i	−0.832380	+	0.534938i
$512$	−0.350806	+	2.43991i	−0.0155036	+	0.107830i
$513$	10.3407	+	22.6430i	0.456553	+	0.999711i
$514$	0.744171	−	1.62951i	0.0328240	−	0.0718744i
$515$	0.122492	+	0.0359670i	0.00539766	+	0.00158490i
$516$	−3.12197	−	6.83617i	−0.137437	−	0.300946i
$517$	4.45322	+	5.13929i	0.195853	+	0.226026i
$518$	2.34978	+	16.3431i	0.103243	+	0.718073i
$519$	2.19018	−	15.2330i	0.0961383	−	0.668656i
$520$	−7.03150	+	2.06463i	−0.308351	+	0.0905402i
$521$	−6.69757	−	7.72941i	−0.293426	−	0.338632i	0.589826	−	0.807530i	$-0.299196\pi$
$521$	−6.69757	−	7.72941i	−0.293426	−	0.338632i	−0.883252	+	0.468899i	$0.844651\pi$
$522$	−2.50950	−	17.4540i	−0.109838	−	0.763940i
$523$	−8.72569	+	5.60766i	−0.381548	+	0.245206i	−0.717330	−	0.696734i	$-0.754636\pi$
$523$	−8.72569	+	5.60766i	−0.381548	+	0.245206i	0.335782	+	0.941940i	$0.391000\pi$
$524$	0.219657	−	0.141165i	0.00959574	−	0.00616681i
$525$	−17.3253	+	5.08717i	−0.756138	+	0.222022i
$526$	9.78423	−	21.4245i	0.426613	−	0.934151i
$527$	5.66173	−	6.53399i	0.246629	−	0.284625i
$528$	25.6986	+	16.5155i	1.11839	+	0.718743i
$529$	9.75607	−	11.2591i	0.424177	−	0.489526i
$530$	56.6697	+	16.6397i	2.46158	+	0.722784i
$531$	13.5697	−	3.98442i	0.588874	−	0.172909i
$532$	−0.970779	−	6.75192i	−0.0420886	−	0.292733i
$533$	5.03062	+	11.0155i	0.217900	+	0.477135i
$534$	24.6114	−	28.4031i	1.06504	−	1.22912i
$535$	−35.4055			−1.53071
$536$	14.9119	−	6.07456i	0.644096	−	0.262381i
$537$	−5.57341			−0.240510
$538$	9.72840	−	11.2272i	0.419421	−	0.484038i
$539$	5.45083	+	11.9357i	0.234784	+	0.514105i
$540$	−3.39321	−	23.6003i	−0.146021	−	1.01560i
$541$	31.3652	−	9.20966i	1.34850	−	0.395954i	0.473803	−	0.880631i	$-0.342881\pi$
$541$	31.3652	−	9.20966i	1.34850	−	0.395954i	0.874693	+	0.484677i	$0.161063\pi$
$542$	−11.5692	−	3.39702i	−0.496940	−	0.145915i
$543$	−28.3162	+	32.6786i	−1.21516	+	1.40237i
$544$	−18.6855	−	12.0084i	−0.801133	−	0.514857i
$545$	24.5263	−	28.3049i	1.05059	−	1.21245i
$546$	11.6140	−	25.4311i	0.497032	−	1.08835i
$547$	−16.0529	+	4.71355i	−0.686371	+	0.201537i	−0.606280	−	0.795251i	$-0.707339\pi$
$547$	−16.0529	+	4.71355i	−0.686371	+	0.201537i	−0.0800904	+	0.996788i	$0.525521\pi$
$548$	−11.8005	+	7.58373i	−0.504093	+	0.323961i
$549$	−55.6839	+	35.7859i	−2.37653	+	1.52730i
$550$	−0.749155	−	5.21049i	−0.0319441	−	0.222176i
$551$	2.31016	+	2.66607i	0.0984162	+	0.113578i
$552$	−16.6542	+	4.89011i	−0.708849	+	0.208137i
$553$	−7.31570	+	50.8818i	−0.311095	+	2.16371i
$554$	0.0156324	+	0.108725i	0.000664155	+	0.00461930i
$555$	−13.8451	−	15.9781i	−0.587692	−	0.678233i
$556$	3.45603	+	7.56764i	0.146568	+	0.320940i
$557$	−20.2890	−	5.95740i	−0.859674	−	0.252423i	−0.177956	−	0.984038i	$-0.556948\pi$
$557$	−20.2890	−	5.95740i	−0.859674	−	0.252423i	−0.681718	+	0.731615i	$0.738767\pi$
$558$	−7.96603	+	17.4432i	−0.337229	+	0.738428i
$559$	1.76068	+	3.85535i	0.0744688	+	0.163064i
$560$	6.69679	−	46.5772i	0.282991	−	1.96825i
$561$	−25.9176	+	16.6562i	−1.09424	+	0.703226i
$562$	−5.01347	+	34.8695i	−0.211481	+	1.47088i
$563$	17.3328	+	5.08936i	0.730490	+	0.214491i	0.625767	−	0.780010i	$-0.284786\pi$
$563$	17.3328	+	5.08936i	0.730490	+	0.214491i	0.104723	+	0.994501i	$0.466604\pi$
$564$	7.43290	+	4.77683i	0.312981	+	0.201141i
$565$	12.2359			0.514768
$566$	−12.9135			−0.542795
$567$	−46.1235	−	29.6418i	−1.93700	−	1.24484i
$568$	−2.98825	+	6.54336i	−0.125384	+	0.274553i
$569$	−2.66951	−	3.08078i	−0.111912	−	0.129153i	0.697030	−	0.717042i	$-0.254505\pi$
$569$	−2.66951	−	3.08078i	−0.111912	−	0.129153i	−0.808941	+	0.587889i	$0.799959\pi$
$570$	19.4891	+	22.4916i	0.816309	+	0.942070i
$571$	0.757738	−	1.65921i	0.0317104	−	0.0694360i	−0.893114	−	0.449830i	$-0.851484\pi$
$571$	0.757738	−	1.65921i	0.0317104	−	0.0694360i	0.924824	+	0.380394i	$0.124212\pi$
$572$	2.01237	+	1.29327i	0.0841412	+	0.0540743i
$573$	26.4879			1.10655
$574$	−51.7684			−2.16077
$575$	3.77950	+	2.42894i	0.157616	+	0.101294i
$576$	−15.7850	−	4.63489i	−0.657707	−	0.193120i
$577$	1.66948	−	11.6115i	0.0695013	−	0.483392i	−0.925109	−	0.379703i	$-0.876026\pi$
$577$	1.66948	−	11.6115i	0.0695013	−	0.483392i	0.994610	−	0.103689i	$-0.0330647\pi$
$578$	11.5182	−	7.40230i	0.479094	−	0.307895i
$579$	11.5438	−	80.2891i	0.479745	−	3.33670i
$580$	−1.40368	−	3.07364i	−0.0582848	−	0.127626i
$581$	18.5811	−	40.6869i	0.770874	−	1.68798i
$582$	−77.8320	−	22.8535i	−3.22624	−	0.947310i
$583$	11.2702	+	24.6783i	0.466763	+	1.02207i
$584$	7.80743	+	9.01026i	0.323074	+	0.372847i
$585$	3.50418	+	24.3721i	0.144880	+	1.00766i
$586$	−2.65261	+	18.4493i	−0.109578	+	0.762134i
$587$	39.1106	−	11.4839i	1.61427	−	0.473991i	0.654796	−	0.755805i	$-0.272754\pi$
$587$	39.1106	−	11.4839i	1.61427	−	0.473991i	0.959469	+	0.281814i	$0.0909362\pi$
$588$	11.1644	+	12.8844i	0.460412	+	0.531344i
$589$	−0.545966	−	3.79728i	−0.0224961	−	0.156464i
$590$	7.76794	−	4.99215i	0.319801	−	0.205524i
$591$	−55.5448	+	35.6965i	−2.28481	+	1.46836i
$592$	12.6841	−	3.72437i	0.521311	−	0.153071i
$593$	−4.84795	+	10.6155i	−0.199081	+	0.435927i	−0.982673	−	0.185349i	$-0.940658\pi$
$593$	−4.84795	+	10.6155i	−0.199081	+	0.435927i	0.783591	+	0.621276i	$0.213386\pi$
$594$	24.4372	−	28.2020i	1.00267	−	1.15714i
$595$	39.9236	+	25.6573i	1.63671	+	1.05185i
$596$	7.53545	−	8.69637i	0.308664	−	0.356217i
$597$	−18.5500	−	5.44676i	−0.759200	−	0.222921i
$598$	−6.67435	+	1.95976i	−0.272934	+	0.0801407i
$599$	4.59319	+	31.9464i	0.187673	+	1.30529i	0.838013	+	0.545650i	$0.183717\pi$
$599$	4.59319	+	31.9464i	0.187673	+	1.30529i	−0.650340	+	0.759643i	$0.725374\pi$
$600$	3.99830	+	8.75505i	0.163230	+	0.357423i
$601$	−20.6435	+	23.8238i	−0.842065	+	0.971795i	−0.999877	−	0.0156744i	$-0.995010\pi$
$601$	−20.6435	+	23.8238i	−0.842065	+	0.971795i	0.157812	+	0.987469i	$0.449556\pi$
$602$	−18.1185			−0.738457
$603$	−13.0720	−	52.4977i	−0.532332	−	2.13787i
$604$	−15.5718			−0.633608
$605$	−11.8761	+	13.7057i	−0.482831	+	0.557217i
$606$	14.2322	+	31.1641i	0.578142	+	1.26595i
$607$	2.52933	+	17.5919i	0.102662	+	0.714032i	0.974525	+	0.224281i	$0.0720032\pi$
$607$	2.52933	+	17.5919i	0.102662	+	0.714032i	−0.871862	+	0.489751i	$0.837088\pi$
$608$	−9.45658	+	2.77670i	−0.383515	+	0.112610i
$609$	−17.4055	−	5.11072i	−0.705308	−	0.207097i
$610$	−28.3011	+	32.6612i	−1.14588	+	1.32241i
$611$	−4.19188	−	2.69396i	−0.169585	−	0.108986i
$612$	−18.0297	+	20.8074i	−0.728808	+	0.841089i
$613$	5.26407	−	11.5267i	0.212614	−	0.465559i	−0.773036	−	0.634362i	$-0.781263\pi$
$613$	5.26407	−	11.5267i	0.212614	−	0.465559i	0.985650	+	0.168803i	$0.0539902\pi$
$614$	−11.0207	+	3.23598i	−0.444761	+	0.130594i
$615$	55.7651	−	35.8381i	2.24867	−	1.44513i
$616$	12.1059	−	7.78000i	0.487761	−	0.313465i
$617$	4.67695	+	32.5289i	0.188287	+	1.30956i	0.836442	+	0.548056i	$0.184632\pi$
$617$	4.67695	+	32.5289i	0.188287	+	1.30956i	−0.648155	+	0.761508i	$0.724459\pi$
$618$	0.170005	+	0.196197i	0.00683862	+	0.00789219i
$619$	38.7891	−	11.3895i	1.55907	−	0.457783i	0.615272	−	0.788315i	$-0.289046\pi$
$619$	38.7891	−	11.3895i	1.55907	−	0.457783i	0.943795	+	0.330531i	$0.107228\pi$
$620$	−0.522949	+	3.63719i	−0.0210021	+	0.146073i
$621$	4.53250	+	31.5242i	0.181883	+	1.26502i
$622$	29.7920	+	34.3818i	1.19455	+	1.37859i
$623$	−11.0470	−	24.1895i	−0.442588	−	0.969134i
$624$	−21.4773	−	6.30631i	−0.859781	−	0.252455i
$625$	−12.6289	+	27.6534i	−0.505155	+	1.10613i
$626$	−13.6270	−	29.8390i	−0.544644	−	1.19260i
$627$	−1.94551	+	13.5313i	−0.0776960	+	0.540388i
$628$	−6.99764	+	4.49711i	−0.279236	+	0.179454i
$629$	−1.89737	+	13.1965i	−0.0756531	+	0.526179i
$630$	−100.996	−	29.6551i	−4.02377	−	1.18149i
$631$	−9.19777	−	5.91105i	−0.366157	−	0.235315i	0.344604	−	0.938748i	$-0.388013\pi$
$631$	−9.19777	−	5.91105i	−0.366157	−	0.235315i	−0.710762	+	0.703433i	$0.751649\pi$
$632$	27.4006			1.08994
$633$	−28.2367			−1.12231
$634$	3.17449	+	2.04012i	0.126075	+	0.0810235i
$635$	1.01009	−	2.21178i	0.0400841	−	0.0877719i
$636$	23.0836	+	26.6399i	0.915324	+	1.05634i
$637$	−6.29631	−	7.26633i	−0.249469	−	0.287902i
$638$	2.19690	−	4.81054i	0.0869761	−	0.190451i
$639$	20.3326	+	13.0670i	0.804344	+	0.516921i
$640$	−33.4662			−1.32287
$641$	−14.9802			−0.591684			−0.295842	−	0.955237i	$-0.595600\pi$
$641$	−14.9802			−0.591684			−0.295842	+	0.955237i	$0.595600\pi$
$642$	−60.5682	−	38.9248i	−2.39043	−	1.53624i
$643$	20.3877	+	5.98636i	0.804011	+	0.236079i	0.657818	−	0.753177i	$-0.271480\pi$
$643$	20.3877	+	5.98636i	0.804011	+	0.236079i	0.146193	+	0.989256i	$0.453298\pi$
$644$	1.24205	−	8.63868i	0.0489438	−	0.340412i
$645$	19.5174	−	12.5430i	0.768495	−	0.493882i
$646$	2.67084	−	18.5761i	0.105083	−	0.730866i
$647$	4.59789	+	10.0680i	0.180762	+	0.395813i	0.978223	−	0.207557i	$-0.0665513\pi$
$647$	4.59789	+	10.0680i	0.180762	+	0.395813i	−0.797461	+	0.603370i	$0.793824\pi$
$648$	−12.1404	+	26.5837i	−0.476918	+	1.04431i
$649$	4.06968	+	1.19497i	0.159749	+	0.0469065i
$650$	1.60236	+	3.50868i	0.0628498	+	0.137622i
$651$	12.9186	+	14.9089i	0.506321	+	0.584325i
$652$	1.40029	+	9.73922i	0.0548395	+	0.381417i
$653$	3.05243	−	21.2301i	0.119451	−	0.830798i	−0.838712	−	0.544575i	$-0.816691\pi$
$653$	3.05243	−	21.2301i	0.119451	−	0.830798i	0.958163	−	0.286223i	$-0.0923999\pi$
$654$	73.0756	−	21.4569i	2.85748	−	0.839032i
$655$	0.527853	+	0.609175i	0.0206249	+	0.0238024i
$656$	5.89868	+	41.0262i	0.230305	+	1.60180i
$657$	33.6990	−	21.6570i	1.31472	−	0.844921i
$658$	17.9198	−	11.5164i	0.698588	−	0.448955i
$659$	28.8088	−	8.45902i	1.12223	−	0.329517i	0.332581	−	0.943075i	$-0.392081\pi$
$659$	28.8088	−	8.45902i	1.12223	−	0.329517i	0.789649	+	0.613558i	$0.210262\pi$
$660$	5.43949	−	11.9108i	0.211732	−	0.463628i
$661$	−9.81822	+	11.3308i	−0.381885	+	0.440718i	−0.913853	−	0.406046i	$-0.866907\pi$
$661$	−9.81822	+	11.3308i	−0.381885	+	0.440718i	0.531968	+	0.846764i	$0.321453\pi$
$662$	49.2540	+	31.6536i	1.91431	+	1.23025i
$663$	14.7834	−	17.0609i	0.574138	−	0.662590i
$664$	−22.8763	−	6.71708i	−0.887772	−	0.260673i
$665$	20.2050	−	5.93273i	0.783517	−	0.230061i
$666$	−4.20834	−	29.2697i	−0.163070	−	1.13418i
$667$	1.87498	+	4.10563i	0.0725994	+	0.158970i
$668$	−1.20614	+	1.39196i	−0.0466669	+	0.0538564i
$669$	76.3494			2.95184
$670$	−17.8457	−	30.4831i	−0.689441	−	1.17767i
$671$	−19.8515			−0.766358
$672$	33.1889	−	38.3021i	1.28029	−	1.47753i
$673$	−6.54498	−	14.3315i	−0.252290	−	0.552439i	0.740534	−	0.672019i	$-0.234573\pi$
$673$	−6.54498	−	14.3315i	−0.252290	−	0.552439i	−0.992825	+	0.119580i	$0.961845\pi$
$674$	−7.77934	−	54.1065i	−0.299649	−	2.08410i
$675$	16.9450	−	4.97549i	0.652212	−	0.191507i
$676$	8.68147	+	2.54911i	0.333903	+	0.0980426i
$677$	−17.9123	+	20.6719i	−0.688426	+	0.794487i	−0.987140	−	0.159856i	$-0.948897\pi$
$677$	−17.9123	+	20.6719i	−0.688426	+	0.794487i	0.298714	+	0.954343i	$0.403442\pi$
$678$	20.9320	+	13.4522i	0.803887	+	0.516627i
$679$	−37.5872	+	43.3779i	−1.44246	+	1.66469i
$680$	10.5084	−	23.0103i	0.402981	−	0.882404i
$681$	70.9587	−	20.8354i	2.71914	−	0.798412i
$682$	−4.83812	+	3.10927i	−0.185261	+	0.119060i
$683$	−10.3663	+	6.66201i	−0.396655	+	0.254915i	−0.723729	−	0.690084i	$-0.757574\pi$
$683$	−10.3663	+	6.66201i	−0.396655	+	0.254915i	0.327074	+	0.944999i	$0.393937\pi$
$684$	1.73862	+	12.0924i	0.0664779	+	0.462364i
$685$	−28.3576	−	32.7265i	−1.08349	−	1.25041i
$686$	−2.26694	+	0.665633i	−0.0865520	+	0.0254140i
$687$	1.99756	−	13.8933i	0.0762116	−	0.530063i
$688$	2.06449	+	14.3589i	0.0787080	+	0.547426i
$689$	−13.0183	−	15.0239i	−0.495958	−	0.572366i
$690$	15.8178	+	34.6361i	0.602172	+	1.31857i
$691$	29.7154	+	8.72524i	1.13043	+	0.331924i	0.792876	−	0.609383i	$-0.208583\pi$
$691$	29.7154	+	8.72524i	1.13043	+	0.331924i	0.337553	+	0.941307i	$0.390401\pi$
$692$	1.71346	−	3.75196i	0.0651361	−	0.142628i
$693$	−20.0855	−	43.9812i	−0.762986	−	1.67071i
$694$	1.65769	−	11.5295i	0.0629251	−	0.437654i
$695$	−21.6057	+	13.8852i	−0.819552	+	0.526694i
$696$	−1.37610	+	9.57098i	−0.0521609	+	0.362787i
$697$	−40.1081	−	11.7768i	−1.51920	−	0.446078i
$698$	−21.3865	−	13.7443i	−0.809492	−	0.520229i
$699$	−14.0731			−0.532293
$700$	−4.83952			−0.182917
$701$	−37.2290	−	23.9256i	−1.40612	−	0.903658i	−0.406171	−	0.913797i	$-0.633136\pi$
$701$	−37.2290	−	23.9256i	−1.40612	−	0.903658i	−0.999949	+	0.0101389i	$0.996773\pi$
$702$	−11.3590	+	24.8728i	−0.428719	+	0.938763i
$703$	3.87405	+	4.47090i	0.146113	+	0.168623i
$704$	−3.23104	−	3.72881i	−0.121774	−	0.140535i
$705$	−11.3308	+	24.8110i	−0.426743	+	0.934436i
$706$	21.9831	+	14.1277i	0.827344	+	0.531702i
$707$	24.2417			0.911703
$708$	5.51092			0.207113
$709$	6.70072	+	4.30629i	0.251651	+	0.161726i	0.660385	−	0.750927i	$-0.270393\pi$
$709$	6.70072	+	4.30629i	0.251651	+	0.161726i	−0.408734	+	0.912654i	$0.634030\pi$
$710$	15.1411	+	4.44584i	0.568237	+	0.166849i
$711$	13.1021	−	91.1270i	0.491367	−	3.41753i
$712$	−11.9246	+	7.66346i	−0.446892	+	0.287200i
$713$	0.698531	−	4.85839i	0.0261602	−	0.181948i
$714$	40.0896	+	87.7839i	1.50031	+	3.28523i
$715$	−3.06767	+	6.71727i	−0.114724	+	0.251212i
$716$	−1.43326	−	0.420844i	−0.0535635	−	0.0157277i
$717$	7.94902	+	17.4059i	0.296862	+	0.650036i
$718$	−20.2171	−	23.3317i	−0.754494	−	0.870732i
$719$	3.12679	+	21.7473i	0.116610	+	0.811039i	0.961245	+	0.275696i	$0.0889084\pi$
$719$	3.12679	+	21.7473i	0.116610	+	0.811039i	−0.844635	+	0.535342i	$0.820183\pi$
$720$	−11.9937	+	83.4177i	−0.446977	+	3.10879i
$721$	0.176250	−	0.0517518i	0.00656391	−	0.00192734i
$722$	15.4810	+	17.8661i	0.576144	+	0.664906i
$723$	−5.07959	−	35.3293i	−0.188912	−	1.31391i
$724$	−9.74935	+	6.26552i	−0.362332	+	0.232856i
$725$	2.10548	−	1.35311i	0.0781957	−	0.0502533i
$726$	−35.3845	+	10.3898i	−1.31324	+	0.385602i
$727$	14.2910	−	31.2928i	0.530022	−	1.16059i	−0.435482	−	0.900198i	$-0.643422\pi$
$727$	14.2910	−	31.2928i	0.530022	−	1.16059i	0.965504	−	0.260389i	$-0.0838508\pi$
$728$	−6.90520	+	7.96902i	−0.255924	+	0.295352i
$729$	−4.93101	−	3.16897i	−0.182630	−	0.117369i
$730$	17.1273	−	19.7660i	0.633911	−	0.731572i
$731$	−14.0375	−	4.12179i	−0.519196	−	0.152450i
$732$	−24.7480	+	7.26668i	−0.914714	+	0.268584i
$733$	−4.75011	−	33.0378i	−0.175449	−	1.22028i	−0.867133	−	0.498077i	$-0.834040\pi$
$733$	−4.75011	−	33.0378i	−0.175449	−	1.22028i	0.691684	−	0.722201i	$-0.256869\pi$
$734$	18.4493	+	40.3984i	0.680977	+	1.49113i
$735$	−34.4653	+	39.7751i	−1.27127	+	1.46713i
$736$	−12.6099			−0.464808
$737$	5.21409	−	15.3647i	0.192063	−	0.565966i
$738$	92.7148			3.41288
$739$	17.3719	−	20.0483i	0.639037	−	0.737488i	−0.340167	−	0.940365i	$-0.610484\pi$
$739$	17.3719	−	20.0483i	0.639037	−	0.737488i	0.979204	+	0.202877i	$0.0650291\pi$
$740$	−2.35393	−	5.15438i	−0.0865320	−	0.189479i
$741$	−1.42557	−	9.91507i	−0.0523697	−	0.364239i
$742$	81.5403	−	23.9424i	2.99344	−	0.878953i
$743$	4.45812	+	1.30902i	0.163553	+	0.0480234i	0.362484	−	0.931990i	$-0.381929\pi$
$743$	4.45812	+	1.30902i	0.163553	+	0.0480234i	−0.198931	+	0.980013i	$0.563747\pi$
$744$	6.88605	−	7.94693i	0.252455	−	0.291349i
$745$	29.8837	+	19.2051i	1.09485	+	0.703619i
$746$	9.87346	−	11.3946i	0.361493	−	0.417185i
$747$	−33.2779	+	72.8685i	−1.21758	+	2.66612i
$748$	−7.92268	+	2.32631i	−0.289682	+	0.0850583i
$749$	−42.8567	+	27.5423i	−1.56595	+	1.00638i
$750$	−38.5057	+	24.7461i	−1.40603	+	0.903600i
$751$	7.74333	+	53.8560i	0.282558	+	1.96523i	0.260483	+	0.965478i	$0.416118\pi$
$751$	7.74333	+	53.8560i	0.282558	+	1.96523i	0.0220748	+	0.999756i	$0.492973\pi$
$752$	−11.1685	−	12.8892i	−0.407274	−	0.470020i
$753$	36.8820	−	10.8295i	1.34405	−	0.394650i
$754$	−0.551487	+	3.83567i	−0.0200840	+	0.139687i
$755$	−6.84126	−	47.5820i	−0.248979	−	1.73169i
$756$	−22.4663	−	25.9275i	−0.817091	−	0.942973i
$757$	−10.4066	−	22.7874i	−0.378236	−	0.828221i	−0.999021	−	0.0442403i	$-0.985913\pi$
$757$	−10.4066	−	22.7874i	−0.378236	−	0.828221i	0.620785	−	0.783981i	$-0.286814\pi$
$758$	13.7182	+	4.02804i	0.498269	+	0.146305i
$759$	−7.26582	+	15.9099i	−0.263733	+	0.577494i
$760$	−4.66287	−	10.2103i	−0.169140	−	0.370365i
$761$	−3.08953	+	21.4881i	−0.111995	+	0.778944i	0.853979	+	0.520307i	$0.174182\pi$
$761$	−3.08953	+	21.4881i	−0.111995	+	0.778944i	−0.965975	+	0.258637i	$0.916727\pi$
$762$	4.15959	−	2.67321i	0.150686	−	0.0968400i
$763$	7.66929	−	53.3411i	0.277647	−	1.93108i
$764$	6.81164	+	2.00008i	0.246437	+	0.0723603i
$765$	−71.5013	−	45.9511i	−2.58513	−	1.66136i
$766$	−58.4160			−2.11066
$767$	−3.10796			−0.112222
$768$	−44.2686	−	28.4497i	−1.59740	−	1.02659i
$769$	−17.0096	+	37.2458i	−0.613381	+	1.34312i	0.306855	+	0.951756i	$0.400723\pi$
$769$	−17.0096	+	37.2458i	−0.613381	+	1.34312i	−0.920237	+	0.391362i	$0.872004\pi$
$770$	−20.6729	−	23.8578i	−0.744999	−	0.859775i
$771$	2.16138	+	2.49437i	0.0778403	+	0.0898325i
$772$	9.03119	−	19.7755i	0.325040	−	0.711737i
$773$	−30.7278	−	19.7476i	−1.10520	−	0.710271i	−0.144960	−	0.989438i	$-0.546305\pi$
$773$	−30.7278	−	19.7476i	−1.10520	−	0.710271i	−0.960243	+	0.279167i	$0.909942\pi$
$774$	32.4495			1.16637
$775$	−2.72174			−0.0977678
$776$	25.7378	+	16.5407i	0.923934	+	0.593776i
$777$	−29.1884	−	8.57049i	−1.04713	−	0.307465i
$778$	−0.887198	+	6.17060i	−0.0318076	+	0.221227i
$779$	−15.6039	+	10.0280i	−0.559066	+	0.359290i
$780$	−1.36547	+	9.49707i	−0.0488918	+	0.340050i
$781$	3.01119	+	6.59359i	0.107749	+	0.235937i
$782$	9.97469	−	21.8415i	0.356694	−	0.781052i
$783$	17.0234	+	4.99853i	0.608368	+	0.178633i
$784$	−13.6705	−	29.9342i	−0.488232	−	1.06908i
$785$	−16.8159	−	19.4066i	−0.600186	−	0.692651i
$786$	0.233271	+	1.62244i	0.00832051	+	0.0578704i
$787$	−3.38066	+	23.5130i	−0.120508	+	0.838148i	0.836476	+	0.548004i	$0.184612\pi$
$787$	−3.38066	+	23.5130i	−0.120508	+	0.838148i	−0.956983	+	0.290144i	$0.906297\pi$
$788$	−16.9794	+	4.98559i	−0.604865	+	0.177604i
$789$	28.4175	+	32.7955i	1.01169	+	1.16755i
$790$	−8.55444	−	59.4974i	−0.304353	−	2.11682i
$791$	14.8110	−	9.51845i	0.526619	−	0.338437i
$792$	−21.6811	+	13.9336i	−0.770406	+	0.495110i
$793$	13.9570	−	4.09814i	0.495627	−	0.145529i
$794$	4.23505	−	9.27346i	0.150296	−	0.329103i
$795$	−71.2608	+	82.2393i	−2.52736	+	2.91673i
$796$	−4.35904	−	2.80139i	−0.154502	−	0.0992925i
$797$	−1.24440	+	1.43612i	−0.0440790	+	0.0508699i	−0.777361	−	0.629055i	$-0.783442\pi$
$797$	−1.24440	+	1.43612i	−0.0440790	+	0.0508699i	0.733282	+	0.679925i	$0.237988\pi$
$798$	41.0871	+	12.0643i	1.45447	+	0.427071i
$799$	16.5034	−	4.84585i	0.583850	−	0.171434i
$800$	0.995117	+	6.92119i	0.0351827	+	0.244701i
$801$	19.7847	+	43.3224i	0.699057	+	1.53072i
$802$	−20.1490	+	23.2532i	−0.711486	+	0.821099i
$803$	12.0138			0.423958
$804$	0.875909	−	21.0632i	0.0308909	−	0.742840i
$805$	26.9425			0.949598
$806$	2.75966	−	3.18482i	0.0972049	−	0.112180i
$807$	11.3702	+	24.8972i	0.400249	+	0.876423i
$808$	−1.83894	−	12.7901i	−0.0646936	−	0.449954i
$809$	−14.2263	+	4.17720i	−0.500168	+	0.146863i	−0.522079	−	0.852897i	$-0.674843\pi$
$809$	−14.2263	+	4.17720i	−0.500168	+	0.146863i	0.0219104	+	0.999760i	$0.493025\pi$
$810$	61.5138	+	18.0621i	2.16137	+	0.634637i
$811$	−8.00237	+	9.23523i	−0.281001	+	0.324293i	−0.878651	−	0.477465i	$-0.841556\pi$
$811$	−8.00237	+	9.23523i	−0.281001	+	0.324293i	0.597650	+	0.801757i	$0.296101\pi$
$812$	−4.09011	−	2.62856i	−0.143535	−	0.0922442i
$813$	14.5480	−	16.7893i	0.510220	−	0.588825i
$814$	3.68412	−	8.06710i	0.129128	−	0.282752i
$815$	−29.1445	+	8.55759i	−1.02089	+	0.299759i
$816$	65.0004	−	41.7732i	2.27547	−	1.46235i
$817$	−5.46123	+	3.50972i	−0.191064	+	0.122790i
$818$	5.74923	+	39.9868i	0.201017	+	1.39810i
$819$	23.2010	+	26.7754i	0.810708	+	0.935607i
$820$	17.0467	−	5.00536i	0.595297	−	0.174795i
$821$	1.33549	−	9.28851i	0.0466088	−	0.324171i	−0.953156	−	0.302479i	$-0.902186\pi$
$821$	1.33549	−	9.28851i	0.0466088	−	0.324171i	0.999765	−	0.0216918i	$-0.00690527\pi$
$822$	−12.5319	−	87.1616i	−0.437102	−	3.04011i
$823$	−22.2076	−	25.6289i	−0.774107	−	0.893367i	0.222562	−	0.974919i	$-0.428558\pi$
$823$	−22.2076	−	25.6289i	−0.774107	−	0.893367i	−0.996669	+	0.0815511i	$0.974013\pi$
$824$	−0.0406747	−	0.0890652i	−0.00141697	−	0.00310273i
$825$	9.30585	+	2.73244i	0.323988	+	0.0951314i
$826$	5.51928	−	12.0855i	0.192040	−	0.420510i
$827$	5.56096	+	12.1768i	0.193374	+	0.423429i	0.981338	−	0.192292i	$-0.0615921\pi$
$827$	5.56096	+	12.1768i	0.193374	+	0.423429i	−0.787964	+	0.615721i	$0.788865\pi$
$828$	−2.22446	+	15.4715i	−0.0773054	+	0.537671i
$829$	17.5198	−	11.2593i	0.608487	−	0.391051i	−0.199803	−	0.979836i	$-0.564030\pi$
$829$	17.5198	−	11.2593i	0.608487	−	0.391051i	0.808289	+	0.588785i	$0.200394\pi$
$830$	−7.44347	+	51.7704i	−0.258366	+	1.79698i
$831$	−0.194182	−	0.0570169i	−0.00673609	−	0.00197789i
$832$	3.04142	+	1.95460i	0.105442	+	0.0677636i
$833$	33.1885			1.14991
$834$	−52.2262			−1.80845
$835$	−4.78324	−	3.07400i	−0.165531	−	0.106380i
$836$	−1.52205	+	3.33281i	−0.0526410	+	0.115268i
$837$	−12.6350	−	14.5816i	−0.436731	−	0.504014i
$838$	−3.95389	−	4.56303i	−0.136585	−	0.157627i
$839$	−2.07877	+	4.55187i	−0.0717671	+	0.157148i	−0.942116	−	0.335288i	$-0.891166\pi$
$839$	−2.07877	+	4.55187i	−0.0717671	+	0.157148i	0.870348	+	0.492436i	$0.163894\pi$
$840$	48.5568	+	31.2056i	1.67537	+	1.07669i
$841$	−26.4856			−0.913297
$842$	−30.7126			−1.05843
$843$	−54.6019	−	35.0905i	−1.88059	−	1.20858i
$844$	−7.26137	−	2.13213i	−0.249947	−	0.0733910i
$845$	−3.97510	+	27.6475i	−0.136748	+	0.951101i
$846$	−32.0936	+	20.6253i	−1.10340	+	0.709113i
$847$	−3.71360	+	25.8287i	−0.127601	+	0.887483i
$848$	−28.2652	−	61.8922i	−0.970632	−	2.12539i
$849$	9.88367	−	21.6422i	0.339207	−	0.742759i
$850$	−12.7753	−	3.75116i	−0.438189	−	0.128664i
$851$	3.14426	+	6.88498i	0.107784	+	0.236014i
$852$	6.16752	+	7.11770i	0.211296	+	0.243848i
$853$	0.714847	+	4.97187i	0.0244759	+	0.170234i	0.998393	−	0.0566709i	$-0.0180486\pi$
$853$	0.714847	+	4.97187i	0.0244759	+	0.170234i	−0.973917	+	0.226904i	$0.927139\pi$
$854$	−8.84963	+	61.5505i	−0.302828	+	2.10622i
$855$	−36.1863	+	10.6252i	−1.23754	+	0.363376i
$856$	17.7826	+	20.5222i	0.607796	+	0.701434i
$857$	5.91329	+	41.1278i	0.201994	+	1.40490i	0.798357	+	0.602185i	$0.205703\pi$
$857$	5.91329	+	41.1278i	0.201994	+	1.40490i	−0.596363	+	0.802715i	$0.703388\pi$
$858$	−12.6328	+	8.11863i	−0.431278	+	0.277165i
$859$	27.7195	−	17.8142i	0.945776	−	0.607813i	0.0257492	−	0.999668i	$-0.491803\pi$
$859$	27.7195	−	17.8142i	0.945776	−	0.607813i	0.920027	+	0.391855i	$0.128166\pi$
$860$	5.96622	−	1.75184i	0.203446	−	0.0597372i
$861$	39.6223	−	86.7606i	1.35032	−	2.95679i
$862$	1.87486	−	2.16370i	0.0638578	−	0.0736959i
$863$	26.2291	+	16.8564i	0.892848	+	0.573799i	0.904661	−	0.426132i	$-0.140124\pi$
$863$	26.2291	+	16.8564i	0.892848	+	0.573799i	−0.0118132	+	0.999930i	$0.503760\pi$
$864$	−32.4604	+	37.4612i	−1.10432	+	1.27446i
$865$	12.2175	+	3.58738i	0.415407	+	0.121974i
$866$	51.2927	−	15.0609i	1.74300	−	0.511791i
$867$	3.59005	+	24.9693i	0.121924	+	0.848003i
$868$	2.19641	+	4.80946i	0.0745509	+	0.163244i
$869$	18.0813	−	20.8669i	0.613366	−	0.707862i
$870$	21.2120			0.719153
$871$	−0.493980	+	11.8788i	−0.0167379	+	0.402499i
$872$	−28.7249			−0.972749
$873$	67.3169	−	77.6879i	2.27833	−	2.62934i
$874$	−4.42603	−	9.69166i	−0.149713	−	0.327825i
$875$	4.60917	+	32.0575i	0.155818	+	1.08374i
$876$	14.9771	−	4.39768i	0.506030	−	0.148584i
$877$	−30.5205	−	8.96163i	−1.03060	−	0.302613i	−0.277648	−	0.960683i	$-0.589555\pi$
$877$	−30.5205	−	8.96163i	−1.03060	−	0.302613i	−0.752957	+	0.658070i	$0.771373\pi$
$878$	7.14916	−	8.25057i	0.241272	−	0.278443i
$879$	−28.8896	−	18.5662i	−0.974424	−	0.626224i
$880$	−16.5516	+	19.1016i	−0.557955	+	0.643915i
$881$	−6.87274	+	15.0492i	−0.231549	+	0.507021i	−0.989366	−	0.145446i	$-0.953538\pi$
$881$	−6.87274	+	15.0492i	−0.231549	+	0.507021i	0.757818	+	0.652466i	$0.226266\pi$
$882$	−70.6299	+	20.7388i	−2.37823	+	0.698312i
$883$	−31.8982	+	20.4997i	−1.07346	+	0.689870i	−0.953037	−	0.302852i	$-0.902061\pi$
$883$	−31.8982	+	20.4997i	−1.07346	+	0.689870i	−0.120422	+	0.992723i	$0.538425\pi$
$884$	5.08995	−	3.27111i	0.171194	−	0.110020i
$885$	2.42115	+	16.8395i	0.0813860	+	0.566052i
$886$	13.1366	+	15.1605i	0.441333	+	0.509325i
$887$	−27.3565	+	8.03260i	−0.918543	+	0.269708i	−0.706633	−	0.707581i	$-0.749787\pi$
$887$	−27.3565	+	8.03260i	−0.918543	+	0.269708i	−0.211910	+	0.977289i	$0.567968\pi$
$888$	−2.30767	+	16.0502i	−0.0774402	+	0.538608i
$889$	−0.497907	−	3.46302i	−0.0166993	−	0.116146i
$890$	20.3632	+	23.5004i	0.682577	+	0.787736i
$891$	12.2336	+	26.7877i	0.409839	+	0.897423i
$892$	19.6341	+	5.76508i	0.657397	+	0.193029i
$893$	3.17051	−	6.94246i	0.106097	−	0.232321i
$894$	30.0079	+	65.7082i	1.00362	+	2.19761i
$895$	0.656268	−	4.56444i	0.0219366	−	0.152572i
$896$	−40.5093	+	26.0337i	−1.35332	+	0.869726i
$897$	1.82394	−	12.6857i	0.0608994	−	0.423565i
$898$	32.8469	+	9.64473i	1.09612	+	0.321849i
$899$	−2.30028	−	1.47830i	−0.0767186	−	0.0493040i
$900$	8.66735			0.288912
$901$	68.6208			2.28609
$902$	23.3920	+	15.0331i	0.778867	+	0.500548i
$903$	13.8675	−	30.3656i	0.461481	−	1.01050i
$904$	−6.14555	−	7.09234i	−0.204398	−	0.235888i
$905$	−23.4285	−	27.0379i	−0.778790	−	0.898771i
$906$	40.6083	−	88.9198i	1.34912	−	2.95416i
$907$	−40.2380	−	25.8594i	−1.33608	−	0.858647i	−0.339446	−	0.940625i	$-0.610240\pi$
$907$	−40.2380	−	25.8594i	−1.33608	−	0.858647i	−0.996634	+	0.0819785i	$0.973876\pi$
$908$	19.8211			0.657785
$909$	−43.4158			−1.44001
$910$	19.4597	+	12.5060i	0.645082	+	0.414569i
$911$	16.8276	+	4.94103i	0.557523	+	0.163704i	0.548342	−	0.836254i	$-0.315259\pi$
$911$	16.8276	+	4.94103i	0.557523	+	0.163704i	0.00918137	+	0.999958i	$0.497077\pi$
$912$	4.87926	−	33.9360i	0.161568	−	1.12373i
$913$	−20.2112	+	12.9889i	−0.668892	+	0.429871i
$914$	−4.19627	+	29.1857i	−0.138800	+	0.965376i
$915$	−33.0772	−	72.4289i	−1.09350	−	2.39442i
$916$	1.56277	−	3.42198i	0.0516353	−	0.113065i
$917$	1.11283	+	0.326755i	0.0367488	+	0.0107904i
$918$	−39.2095	−	85.8569i	−1.29411	−	2.83370i
$919$	24.0509	+	27.7562i	0.793367	+	0.915594i	0.997998	−	0.0632451i	$-0.0201450\pi$
$919$	24.0509	+	27.7562i	0.793367	+	0.915594i	−0.204631	+	0.978839i	$0.565600\pi$
$920$	−2.04382	−	14.2151i	−0.0673826	−	0.468656i
$921$	3.01170	−	20.9468i	0.0992388	−	0.690221i
$922$	59.8602	−	17.5765i	1.97139	−	0.578852i
$923$	−3.47826	−	4.01412i	−0.114488	−	0.132126i
$924$	−2.68131	−	18.6489i	−0.0882088	−	0.613505i
$925$	3.53082	−	2.26912i	0.116093	−	0.0746082i
$926$	−42.7965	+	27.5036i	−1.40638	+	0.903825i
$927$	−0.315657	+	0.0926851i	−0.0103675	+	0.00304418i
$928$	−2.91818	+	6.38993i	−0.0957941	+	0.209760i
$929$	13.5231	−	15.6065i	0.443680	−	0.512034i	−0.489225	−	0.872158i	$-0.662720\pi$
$929$	13.5231	−	15.6065i	0.443680	−	0.512034i	0.932904	+	0.360124i	$0.117266\pi$
$930$	−19.4057	−	12.4713i	−0.636339	−	0.408950i
$931$	9.64387	−	11.1296i	0.316065	−	0.364759i
$932$	−3.61905	−	1.06265i	−0.118546	−	0.0348082i
$933$	−80.4239	+	23.6146i	−2.63296	+	0.773107i
$934$	5.08156	+	35.3430i	0.166274	+	1.15646i
$935$	−10.5891	−	23.1869i	−0.346301	−	0.758294i
$936$	12.3669	−	14.2722i	0.404225	−	0.466500i
$937$	29.2575			0.955802			0.477901	−	0.878414i	$-0.341398\pi$
$937$	29.2575			0.955802			0.477901	+	0.878414i	$0.341398\pi$
$938$	−45.3146	−	23.0160i	−1.47957	−	0.751499i
$939$	60.4380			1.97232
$940$	−4.78730	+	5.52483i	−0.156144	+	0.180200i
$941$	18.2225	+	39.9018i	0.594037	+	1.30076i	0.932971	+	0.359950i	$0.117206\pi$
$941$	18.2225	+	39.9018i	0.594037	+	1.30076i	−0.338934	+	0.940810i	$0.610066\pi$
$942$	−7.43137	−	51.6863i	−0.242127	−	1.68403i
$943$	−22.7702	+	6.68594i	−0.741500	+	0.217724i
$944$	−10.2066	−	2.99693i	−0.332197	−	0.0975418i
$945$	69.3551	−	80.0400i	2.25612	−	2.60370i
$946$	8.18701	+	5.26147i	0.266183	+	0.171065i
$947$	2.01820	−	2.32912i	0.0655826	−	0.0756864i	−0.722010	−	0.691882i	$-0.756782\pi$
$947$	2.01820	−	2.32912i	0.0655826	−	0.0756864i	0.787593	+	0.616196i	$0.211327\pi$
$948$	14.9028	−	32.6326i	0.484021	−	1.05986i
$949$	−8.44654	+	2.48013i	−0.274186	+	0.0805083i
$950$	−4.97016	+	3.19413i	−0.161253	+	0.103631i
$951$	−5.84879	+	3.75879i	−0.189660	+	0.121887i
$952$	−5.17998	−	36.0275i	−0.167884	−	1.16766i
$953$	5.90205	+	6.81133i	0.191186	+	0.220641i	0.843247	−	0.537526i	$-0.180641\pi$
$953$	5.90205	+	6.81133i	0.191186	+	0.220641i	−0.652061	+	0.758166i	$0.726095\pi$
$954$	−146.035	+	42.8798i	−4.72806	+	1.38828i
$955$	−3.11894	+	21.6927i	−0.100927	+	0.701960i
$956$	0.729868	+	5.07635i	0.0236056	+	0.164181i
$957$	6.38072	+	7.36374i	0.206259	+	0.238036i
$958$	−6.05444	−	13.2574i	−0.195610	−	0.428327i
$959$	−59.7839	−	17.5541i	−1.93052	−	0.566853i
$960$	8.22106	−	18.0016i	0.265333	−	0.580999i
$961$	−11.6426	−	25.4938i	−0.375568	−	0.822379i
$962$	−0.924822	+	6.43228i	−0.0298175	+	0.207385i
$963$	76.7544	−	49.3271i	2.47338	−	1.58954i
$964$	1.36142	−	9.46887i	0.0438483	−	0.304972i
$965$	64.3949	+	18.9080i	2.07295	+	0.608672i
$966$	46.0905	+	29.6206i	1.48294	+	0.953026i
$967$	31.4999			1.01297			0.506485	−	0.862249i	$-0.330945\pi$
$967$	31.4999			1.01297			0.506485	+	0.862249i	$0.330945\pi$
$968$	13.9091			0.447056
$969$	29.0882	+	18.6938i	0.934446	+	0.600532i
$970$	27.8810	−	61.0509i	0.895205	−	1.96023i
$971$	16.8687	+	19.4675i	0.541341	+	0.624741i	0.958844	−	0.283935i	$-0.0916399\pi$
$971$	16.8687	+	19.4675i	0.541341	+	0.624741i	−0.417502	+	0.908676i	$0.637094\pi$
$972$	6.79377	+	7.84042i	0.217910	+	0.251482i
$973$	−15.3513	+	33.6147i	−0.492140	+	1.07764i
$974$	10.5489	+	6.77937i	0.338009	+	0.217225i
$975$	−7.10674			−0.227598
$976$	49.7868			1.59364
$977$	23.6624	+	15.2069i	0.757026	+	0.486511i	0.861337	−	0.508034i	$-0.169627\pi$
$977$	23.6624	+	15.2069i	0.757026	+	0.486511i	−0.104311	+	0.994545i	$0.533264\pi$
$978$	−59.2656	−	17.4020i	−1.89511	−	0.556453i
$979$	−2.03277	+	14.1382i	−0.0649675	+	0.451859i
$980$	−11.8665	+	7.62615i	−0.379062	+	0.243608i
$981$	−13.7353	+	95.5314i	−0.438536	+	3.05008i
$982$	26.9939	+	59.1083i	0.861409	+	1.88622i
$983$	−18.0681	+	39.5637i	−0.576284	+	1.26189i	0.367100	+	0.930182i	$0.380351\pi$
$983$	−18.0681	+	39.5637i	−0.576284	+	1.26189i	−0.943384	+	0.331704i	$0.892376\pi$
$984$	−48.7812	−	14.3235i	−1.55509	−	0.456615i
$985$	−22.6939	−	49.6927i	−0.723088	−	1.58334i
$986$	−8.75960	−	10.1091i	−0.278962	−	0.321940i
$987$	5.58534	+	38.8469i	0.177783	+	1.23651i
$988$	0.382078	−	2.65741i	0.0121555	−	0.0845435i
$989$	−7.96940	+	2.34003i	−0.253412	+	0.0744085i
$990$	37.0242	+	42.7282i	1.17671	+	1.35799i
$991$	−5.28839	−	36.7816i	−0.167991	−	1.16841i	−0.883029	−	0.469319i	$-0.844499\pi$
$991$	−5.28839	−	36.7816i	−0.167991	−	1.16841i	0.715037	−	0.699086i	$-0.246410\pi$
$992$	6.42657	−	4.13010i	0.204044	−	0.131131i
$993$	−90.7472	+	58.3197i	−2.87978	+	1.85072i
$994$	21.7861	−	6.39698i	0.691013	−	0.202900i
$995$	6.64498	−	14.5505i	0.210660	−	0.461281i
$996$	−20.4418	+	23.5911i	−0.647723	+	0.747513i
$997$	1.46901	+	0.944073i	0.0465239	+	0.0298991i	0.563696	−	0.825982i	$-0.309379\pi$
$997$	1.46901	+	0.944073i	0.0465239	+	0.0298991i	−0.517172	+	0.855881i	$0.673015\pi$
$998$	9.24172	−	10.6655i	0.292541	−	0.337611i
$999$	28.5477	+	8.38235i	0.903208	+	0.265206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.c.62.1	yes	20
3.2	odd	2		603.2.u.c.397.1		20
67.24	even	11		4489.2.a.l.1.9		10
67.40	even	11	inner	67.2.e.c.40.1	✓	20
67.43	odd	22		4489.2.a.m.1.2		10
201.107	odd	22		603.2.u.c.442.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.c.40.1	✓	20	67.40	even	11	inner
67.2.e.c.62.1	yes	20	1.1	even	1	trivial
603.2.u.c.397.1		20	3.2	odd	2
603.2.u.c.442.1		20	201.107	odd	22
4489.2.a.l.1.9		10	67.24	even	11
4489.2.a.m.1.2		10	67.43	odd	22

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:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10181 + 1.27155i) q^{2} +(-1.28775 - 2.81978i) q^{3} +(-0.118239 - 0.822373i) q^{4} +(2.46094 - 0.722597i) q^{5} +(5.00435 + 1.46941i) q^{6} +(2.41674 - 2.78906i) q^{7} +(-1.65486 - 1.06351i) q^{8} +(-4.32827 + 4.99509i) q^{9} +O(q^{10})\)	\(q+(-1.10181 + 1.27155i) q^{2} +(-1.28775 - 2.81978i) q^{3} +(-0.118239 - 0.822373i) q^{4} +(2.46094 - 0.722597i) q^{5} +(5.00435 + 1.46941i) q^{6} +(2.41674 - 2.78906i) q^{7} +(-1.65486 - 1.06351i) q^{8} +(-4.32827 + 4.99509i) q^{9} +(-1.79266 + 3.92538i) q^{10} +(-1.90194 + 0.558461i) q^{11} +(-2.16665 + 1.39242i) q^{12} +(1.22191 - 0.785274i) q^{13} +(0.883665 + 6.14602i) q^{14} +(-5.20664 - 6.00878i) q^{15} +(4.77001 - 1.40060i) q^{16} +(-0.713531 + 4.96272i) q^{17} +(-1.58260 - 11.0072i) q^{18} +(1.45689 + 1.68134i) q^{19} +(-0.885225 - 1.93837i) q^{20} +(-10.9767 - 3.22305i) q^{21} +(1.38546 - 3.03374i) q^{22} +(1.18244 + 2.58919i) q^{23} +(-0.867828 + 6.03588i) q^{24} +(1.32781 - 0.853332i) q^{25} +(-0.347792 + 2.41894i) q^{26} +(10.7357 + 3.15229i) q^{27} +(-2.57941 - 1.65768i) q^{28} +1.58568 q^{29} +13.3772 q^{30} +(-1.45066 - 0.932280i) q^{31} +(-1.84033 + 4.02977i) q^{32} +(4.02396 + 4.64390i) q^{33} +(-5.52419 - 6.37525i) q^{34} +(3.93208 - 8.61005i) q^{35} +(4.61960 + 2.96884i) q^{36} +2.65913 q^{37} -3.74313 q^{38} +(-3.78781 - 2.43428i) q^{39} +(-4.84101 - 1.42145i) q^{40} +(-1.18653 + 8.25247i) q^{41} +(16.1925 - 10.4063i) q^{42} +(-0.415275 + 2.88830i) q^{43} +(0.684148 + 1.49807i) q^{44} +(-7.04217 + 15.4202i) q^{45} +(-4.59512 - 1.34925i) q^{46} +(-1.42512 - 3.12058i) q^{47} +(-10.0920 - 11.6467i) q^{48} +(-0.942052 - 6.55212i) q^{49} +(-0.377934 + 2.62859i) q^{50} +(14.9126 - 4.37874i) q^{51} +(-0.790266 - 0.912016i) q^{52} +(-1.94780 - 13.5472i) q^{53} +(-15.8370 + 10.1778i) q^{54} +(-4.27702 + 2.74868i) q^{55} +(-6.96557 + 2.04528i) q^{56} +(2.86490 - 6.27325i) q^{57} +(-1.74712 + 2.01628i) q^{58} +(-1.80007 - 1.15684i) q^{59} +(-4.32583 + 4.99227i) q^{60} +(9.60903 + 2.82146i) q^{61} +(2.78379 - 0.817394i) q^{62} +(3.47133 + 24.1436i) q^{63} +(1.03400 + 2.26414i) q^{64} +(2.43961 - 2.81546i) q^{65} -10.3386 q^{66} +(-4.70762 + 6.69614i) q^{67} +4.16557 q^{68} +(5.77825 - 6.66845i) q^{69} +(6.61575 + 14.4865i) q^{70} +(-0.520416 - 3.61957i) q^{71} +(12.4750 - 3.66300i) q^{72} +(-5.81523 - 1.70750i) q^{73} +(-2.92985 + 3.38122i) q^{74} +(-4.11609 - 2.64525i) q^{75} +(1.21043 - 1.39691i) q^{76} +(-3.03891 + 6.65429i) q^{77} +(7.26876 - 2.13430i) q^{78} +(-11.7180 + 7.53068i) q^{79} +(10.7266 - 6.89358i) q^{80} +(-2.11429 - 14.7052i) q^{81} +(-9.18614 - 10.6014i) q^{82} +(11.6292 - 3.41465i) q^{83} +(-1.35267 + 9.40803i) q^{84} +(1.83009 + 12.7285i) q^{85} +(-3.21508 - 3.71040i) q^{86} +(-2.04196 - 4.47127i) q^{87} +(3.74138 + 1.09857i) q^{88} +(2.99339 - 6.55461i) q^{89} +(-11.8485 - 25.9446i) q^{90} +(0.762857 - 5.30578i) q^{91} +(1.98947 - 1.27855i) q^{92} +(-0.760741 + 5.29107i) q^{93} +(5.53820 + 1.62616i) q^{94} +(4.80025 + 3.08493i) q^{95} +13.7329 q^{96} -15.5529 q^{97} +(9.36933 + 6.02130i) q^{98} +(5.44256 - 11.9175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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