LMFDB - Embedded newform 525.2.n.b.421.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
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} - 8 x^{19} + 31 x^{18} - 74 x^{17} + 109 x^{16} - 72 x^{15} - 51 x^{14} + 9 x^{13} + 866 x^{12} + \cdots + 3125 $ x^20 - 8x^19 + 31x^18 - 74x^17 + 109x^16 - 72x^15 - 51x^14 + 9x^13 + 866x^12 - 3240x^11 + 6385x^10 - 6775x^9 + 330x^8 + 11325x^7 - 18525x^6 + 12000x^5 + 5875x^4 - 21250x^3 + 22500x^2 - 12500*x + 3125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$-1.14371 + 0.271822i$ of defining polynomial
Character	$\chi$	$=$	525.421
Dual form			525.2.n.b.106.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.401368 + 1.23528i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.253205 + 0.183964i) q^{4} +(-0.860419 + 2.06390i) q^{5} +(-1.05079 + 0.763447i) q^{6} -1.00000 q^{7} +(-2.43047 + 1.76584i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.401368 + 1.23528i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.253205 + 0.183964i) q^{4} +(-0.860419 + 2.06390i) q^{5} +(-1.05079 + 0.763447i) q^{6} -1.00000 q^{7} +(-2.43047 + 1.76584i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-2.20416 - 1.89124i) q^{10} +(-0.475459 + 1.46331i) q^{11} +(0.0967158 + 0.297661i) q^{12} +(-0.626612 - 1.92851i) q^{13} +(0.401368 - 1.23528i) q^{14} +(-1.90922 + 1.16399i) q^{15} +(-1.01237 - 3.11574i) q^{16} +(0.317108 - 0.230392i) q^{17} -1.29885 q^{18} +(-0.666763 + 0.484432i) q^{19} +(-0.597547 + 0.364304i) q^{20} +(-0.809017 - 0.587785i) q^{21} +(-1.61677 - 1.17465i) q^{22} +(-0.225235 + 0.693202i) q^{23} -3.00422 q^{24} +(-3.51936 - 3.55164i) q^{25} +2.63376 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.253205 - 0.183964i) q^{28} +(3.95733 + 2.87517i) q^{29} +(-0.671554 - 2.82562i) q^{30} +(5.01337 - 3.64243i) q^{31} -1.75329 q^{32} +(-1.24477 + 0.904376i) q^{33} +(0.157323 + 0.484190i) q^{34} +(0.860419 - 2.06390i) q^{35} +(-0.0967158 + 0.297661i) q^{36} +(3.09993 + 9.54061i) q^{37} +(-0.330793 - 1.01808i) q^{38} +(0.626612 - 1.92851i) q^{39} +(-1.55329 - 6.53560i) q^{40} +(2.46561 + 7.58836i) q^{41} +(1.05079 - 0.763447i) q^{42} -3.72006 q^{43} +(-0.389586 + 0.283051i) q^{44} +(-2.22877 - 0.180527i) q^{45} +(-0.765899 - 0.556458i) q^{46} +(2.52837 + 1.83697i) q^{47} +(1.01237 - 3.11574i) q^{48} +1.00000 q^{49} +(5.79983 - 2.92189i) q^{50} +0.391967 q^{51} +(0.196116 - 0.603584i) q^{52} +(-11.1744 - 8.11869i) q^{53} +(-1.05079 - 0.763447i) q^{54} +(-2.61103 - 2.24036i) q^{55} +(2.43047 - 1.76584i) q^{56} -0.824165 q^{57} +(-5.14000 + 3.73443i) q^{58} +(0.688868 + 2.12012i) q^{59} +(-0.697558 - 0.0565013i) q^{60} +(0.0109802 - 0.0337937i) q^{61} +(2.48722 + 7.65489i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(2.72845 - 8.39729i) q^{64} +(4.51941 + 0.366066i) q^{65} +(-0.617551 - 1.90063i) q^{66} +(-1.49884 + 1.08897i) q^{67} +0.122677 q^{68} +(-0.589673 + 0.428423i) q^{69} +(2.20416 + 1.89124i) q^{70} +(8.42883 + 6.12390i) q^{71} +(-2.43047 - 1.76584i) q^{72} +(1.96847 - 6.05831i) q^{73} -13.0296 q^{74} +(-0.759621 - 4.94196i) q^{75} -0.257946 q^{76} +(0.475459 - 1.46331i) q^{77} +(2.13076 + 1.54809i) q^{78} +(4.10397 + 2.98171i) q^{79} +(7.30164 + 0.591423i) q^{80} +(-0.809017 + 0.587785i) q^{81} -10.3634 q^{82} +(-2.14925 + 1.56152i) q^{83} +(-0.0967158 - 0.297661i) q^{84} +(0.202661 + 0.852712i) q^{85} +(1.49311 - 4.59533i) q^{86} +(1.51157 + 4.65213i) q^{87} +(-1.42838 - 4.39611i) q^{88} +(-0.601521 + 1.85129i) q^{89} +(1.11756 - 2.68070i) q^{90} +(0.626612 + 1.92851i) q^{91} +(-0.184555 + 0.134087i) q^{92} +6.19687 q^{93} +(-3.28398 + 2.38595i) q^{94} +(-0.426123 - 1.79295i) q^{95} +(-1.41844 - 1.03056i) q^{96} +(15.5501 + 11.2978i) q^{97} +(-0.401368 + 1.23528i) q^{98} -1.53862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9 - 15 * q^10 + 12 * q^11 + 5 * q^12 - 17 * q^13 + 2 * q^14 + 15 * q^15 - 28 * q^16 - 9 * q^17 - 2 * q^18 - 9 * q^19 - 20 * q^20 - 5 * q^21 - 21 * q^22 + 7 * q^23 + 6 * q^24 - 15 * q^25 - 20 * q^26 + 5 * q^27 + 28 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^35 - 5 * q^36 - 5 * q^37 - 6 * q^38 + 17 * q^39 - 10 * q^40 + 11 * q^41 + 3 * q^42 + 28 * q^43 - 17 * q^44 + 5 * q^45 - 43 * q^46 - 24 * q^47 + 28 * q^48 + 20 * q^49 + 10 * q^50 - 36 * q^51 - 9 * q^52 - 26 * q^53 - 3 * q^54 - 25 * q^55 - 4 * q^56 + 24 * q^57 - 16 * q^58 + 64 * q^59 + 5 * q^60 + 8 * q^61 + 27 * q^62 + 5 * q^63 + 26 * q^64 + 25 * q^65 - 4 * q^66 - 3 * q^67 + 80 * q^68 - 2 * q^69 + 15 * q^70 + 19 * q^71 + 4 * q^72 + 31 * q^73 + 8 * q^74 - 5 * q^75 - 72 * q^76 - 12 * q^77 - 30 * q^78 + 43 * q^79 - 25 * q^80 - 5 * q^81 - 6 * q^82 + 32 * q^83 - 5 * q^84 + 35 * q^85 + 53 * q^86 + 17 * q^87 - 61 * q^88 - 47 * q^89 + 10 * q^90 + 17 * q^91 + 41 * q^92 + 4 * q^93 + 12 * q^94 - 40 * q^95 - 6 * q^96 - 45 * q^97 - 2 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	−0.401368	+	1.23528i	−0.283810	+	0.873477i	0.702943	+	0.711246i	$0.251869\pi$
$2$	−0.401368	+	1.23528i	−0.283810	+	0.873477i	−0.986753	+	0.162231i	$0.948131\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.253205	+	0.183964i	0.126603	+	0.0919822i
$5$	−0.860419	+	2.06390i	−0.384791	+	0.923004i
$5$	−0.860419	+	2.06390i	−0.384791	+	0.923004i
$6$	−1.05079	+	0.763447i	−0.428985	+	0.311676i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.43047	+	1.76584i	−0.859300	+	0.624318i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−2.20416	−	1.89124i	−0.697015	−	0.598064i
$11$	−0.475459	+	1.46331i	−0.143356	+	0.441205i	−0.996796	−	0.0799866i	$-0.974512\pi$
$11$	−0.475459	+	1.46331i	−0.143356	+	0.441205i	0.853440	+	0.521191i	$0.174512\pi$
$12$	0.0967158	+	0.297661i	0.0279194	+	0.0859272i
$13$	−0.626612	−	1.92851i	−0.173791	−	0.534873i	0.825785	−	0.563985i	$-0.190732\pi$
$13$	−0.626612	−	1.92851i	−0.173791	−	0.534873i	−0.999576	+	0.0291112i	$0.990732\pi$
$14$	0.401368	−	1.23528i	0.107270	−	0.330143i
$15$	−1.90922	+	1.16399i	−0.492959	+	0.300540i
$16$	−1.01237	−	3.11574i	−0.253092	−	0.778936i
$17$	0.317108	−	0.230392i	0.0769099	−	0.0558783i	−0.548666	−	0.836042i	$-0.684864\pi$
$17$	0.317108	−	0.230392i	0.0769099	−	0.0558783i	0.625576	+	0.780163i	$0.284864\pi$
$18$	−1.29885			−0.306143
$19$	−0.666763	+	0.484432i	−0.152966	+	0.111136i	−0.661636	−	0.749825i	$-0.730137\pi$
$19$	−0.666763	+	0.484432i	−0.152966	+	0.111136i	0.508670	+	0.860962i	$0.330137\pi$
$20$	−0.597547	+	0.364304i	−0.133615	+	0.0814608i
$21$	−0.809017	−	0.587785i	−0.176542	−	0.128265i
$22$	−1.61677	−	1.17465i	−0.344696	−	0.250437i
$23$	−0.225235	+	0.693202i	−0.0469648	+	0.144543i	−0.971789	−	0.235852i	$-0.924212\pi$
$23$	−0.225235	+	0.693202i	−0.0469648	+	0.144543i	0.924824	+	0.380395i	$0.124212\pi$
$24$	−3.00422			−0.613234
$25$	−3.51936	−	3.55164i	−0.703872	−	0.710327i
$26$	2.63376			0.516523
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.253205	−	0.183964i	−0.0478513	−	0.0347660i
$29$	3.95733	+	2.87517i	0.734858	+	0.533906i	0.891097	−	0.453813i	$-0.149937\pi$
$29$	3.95733	+	2.87517i	0.734858	+	0.533906i	−0.156238	+	0.987719i	$0.549937\pi$
$30$	−0.671554	−	2.82562i	−0.122608	−	0.515885i
$31$	5.01337	−	3.64243i	0.900428	−	0.654199i	−0.0381479	−	0.999272i	$-0.512146\pi$
$31$	5.01337	−	3.64243i	0.900428	−	0.654199i	0.938576	+	0.345073i	$0.112146\pi$
$32$	−1.75329			−0.309940
$33$	−1.24477	+	0.904376i	−0.216686	+	0.157432i
$34$	0.157323	+	0.484190i	0.0269806	+	0.0830379i
$35$	0.860419	−	2.06390i	0.145437	−	0.348863i
$36$	−0.0967158	+	0.297661i	−0.0161193	+	0.0496101i
$37$	3.09993	+	9.54061i	0.509626	+	1.56847i	0.792853	+	0.609414i	$0.208595\pi$
$37$	3.09993	+	9.54061i	0.509626	+	1.56847i	−0.283227	+	0.959053i	$0.591405\pi$
$38$	−0.330793	−	1.01808i	−0.0536617	−	0.165154i
$39$	0.626612	−	1.92851i	0.100338	−	0.308809i
$40$	−1.55329	−	6.53560i	−0.245597	−	1.03337i
$41$	2.46561	+	7.58836i	0.385063	+	1.18510i	0.936435	+	0.350842i	$0.114105\pi$
$41$	2.46561	+	7.58836i	0.385063	+	1.18510i	−0.551371	+	0.834260i	$0.685895\pi$
$42$	1.05079	−	0.763447i	0.162141	−	0.117802i
$43$	−3.72006			−0.567304			−0.283652	−	0.958927i	$-0.591546\pi$
$43$	−3.72006			−0.567304			−0.283652	+	0.958927i	$0.591546\pi$
$44$	−0.389586	+	0.283051i	−0.0587322	+	0.0426715i
$45$	−2.22877	−	0.180527i	−0.332245	−	0.0269114i
$46$	−0.765899	−	0.556458i	−0.112926	−	0.0820453i
$47$	2.52837	+	1.83697i	0.368801	+	0.267949i	0.756713	−	0.653747i	$-0.226804\pi$
$47$	2.52837	+	1.83697i	0.368801	+	0.267949i	−0.387913	+	0.921696i	$0.626804\pi$
$48$	1.01237	−	3.11574i	0.146123	−	0.449719i
$49$	1.00000			0.142857
$50$	5.79983	−	2.92189i	0.820220	−	0.413218i
$51$	0.391967			0.0548863
$52$	0.196116	−	0.603584i	0.0271964	−	0.0837020i
$53$	−11.1744	−	8.11869i	−1.53492	−	1.11519i	−0.953421	−	0.301643i	$-0.902465\pi$
$53$	−11.1744	−	8.11869i	−1.53492	−	1.11519i	−0.581503	−	0.813544i	$-0.697535\pi$
$54$	−1.05079	−	0.763447i	−0.142995	−	0.103892i
$55$	−2.61103	−	2.24036i	−0.352072	−	0.302090i
$56$	2.43047	−	1.76584i	0.324785	−	0.235970i
$57$	−0.824165			−0.109163
$58$	−5.14000	+	3.73443i	−0.674915	+	0.490354i
$59$	0.688868	+	2.12012i	0.0896829	+	0.276016i	0.985832	−	0.167738i	$-0.0536464\pi$
$59$	0.688868	+	2.12012i	0.0896829	+	0.276016i	−0.896149	+	0.443754i	$0.853646\pi$
$60$	−0.697558	−	0.0565013i	−0.0900543	−	0.00729428i
$61$	0.0109802	−	0.0337937i	0.00140588	−	0.00432684i	−0.950351	−	0.311180i	$-0.899276\pi$
$61$	0.0109802	−	0.0337937i	0.00140588	−	0.00432684i	0.951757	+	0.306853i	$0.0992759\pi$
$62$	2.48722	+	7.65489i	0.315878	+	0.972172i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	2.72845	−	8.39729i	0.341056	−	1.04966i
$65$	4.51941	+	0.366066i	0.560563	+	0.0454049i
$66$	−0.617551	−	1.90063i	−0.0760153	−	0.233951i
$67$	−1.49884	+	1.08897i	−0.183112	+	0.133039i	−0.675565	−	0.737300i	$-0.736100\pi$
$67$	−1.49884	+	1.08897i	−0.183112	+	0.133039i	0.492453	+	0.870339i	$0.336100\pi$
$68$	0.122677			0.0148768
$69$	−0.589673	+	0.428423i	−0.0709883	+	0.0515760i
$70$	2.20416	+	1.89124i	0.263447	+	0.226047i
$71$	8.42883	+	6.12390i	1.00032	+	0.726773i	0.962156	−	0.272498i	$-0.0878499\pi$
$71$	8.42883	+	6.12390i	1.00032	+	0.726773i	0.0381615	+	0.999272i	$0.487850\pi$
$72$	−2.43047	−	1.76584i	−0.286433	−	0.208106i
$73$	1.96847	−	6.05831i	0.230391	−	0.709072i	−0.767308	−	0.641279i	$-0.778404\pi$
$73$	1.96847	−	6.05831i	0.230391	−	0.709072i	0.997699	−	0.0677931i	$-0.0215958\pi$
$74$	−13.0296			−1.51466
$75$	−0.759621	−	4.94196i	−0.0877135	−	0.570648i
$76$	−0.257946			−0.0295884
$77$	0.475459	−	1.46331i	0.0541835	−	0.166760i
$78$	2.13076	+	1.54809i	0.241261	+	0.175286i
$79$	4.10397	+	2.98171i	0.461733	+	0.335469i	0.794211	−	0.607643i	$-0.207885\pi$
$79$	4.10397	+	2.98171i	0.461733	+	0.335469i	−0.332478	+	0.943111i	$0.607885\pi$
$80$	7.30164	+	0.591423i	0.816348	+	0.0661231i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−10.3634			−1.14444
$83$	−2.14925	+	1.56152i	−0.235911	+	0.171399i	−0.699460	−	0.714672i	$-0.746576\pi$
$83$	−2.14925	+	1.56152i	−0.235911	+	0.171399i	0.463549	+	0.886071i	$0.346576\pi$
$84$	−0.0967158	−	0.297661i	−0.0105526	−	0.0324774i
$85$	0.202661	+	0.852712i	0.0219816	+	0.0924896i
$86$	1.49311	−	4.59533i	0.161006	−	0.495527i
$87$	1.51157	+	4.65213i	0.162057	+	0.498760i
$88$	−1.42838	−	4.39611i	−0.152266	−	0.468627i
$89$	−0.601521	+	1.85129i	−0.0637611	+	0.196236i	−0.977862	−	0.209250i	$-0.932898\pi$
$89$	−0.601521	+	1.85129i	−0.0637611	+	0.196236i	0.914101	+	0.405486i	$0.132898\pi$
$90$	1.11756	−	2.68070i	0.117801	−	0.282571i
$91$	0.626612	+	1.92851i	0.0656868	+	0.202163i
$92$	−0.184555	+	0.134087i	−0.0192412	+	0.0139796i
$93$	6.19687			0.642585
$94$	−3.28398	+	2.38595i	−0.338717	+	0.246092i
$95$	−0.426123	−	1.79295i	−0.0437192	−	0.183952i
$96$	−1.41844	−	1.03056i	−0.144769	−	0.105181i
$97$	15.5501	+	11.2978i	1.57887	+	1.14712i	0.917977	+	0.396634i	$0.129822\pi$
$97$	15.5501	+	11.2978i	1.57887	+	1.14712i	0.660892	+	0.750481i	$0.270178\pi$
$98$	−0.401368	+	1.23528i	−0.0405443	+	0.124782i
$99$	−1.53862			−0.154637
$100$	−0.237745	−	1.54673i	−0.0237745	−	0.154673i
$101$	8.76865			0.872514			0.436257	−	0.899822i	$-0.356304\pi$
$101$	8.76865			0.872514			0.436257	+	0.899822i	$0.356304\pi$
$102$	−0.157323	+	0.484190i	−0.0155773	+	0.0479419i
$103$	−7.80614	−	5.67149i	−0.769162	−	0.558829i	0.132545	−	0.991177i	$-0.457685\pi$
$103$	−7.80614	−	5.67149i	−0.769162	−	0.558829i	−0.901707	+	0.432348i	$0.857685\pi$
$104$	4.92840	+	3.58069i	0.483269	+	0.351116i
$105$	1.90922	−	1.16399i	0.186321	−	0.113594i
$106$	14.5139	−	10.5450i	1.40972	−	1.02422i
$107$	−5.84258			−0.564823			−0.282412	−	0.959293i	$-0.591134\pi$
$107$	−5.84258			−0.564823			−0.282412	+	0.959293i	$0.591134\pi$
$108$	−0.253205	+	0.183964i	−0.0243647	+	0.0177020i
$109$	−0.904450	−	2.78361i	−0.0866306	−	0.266622i	0.898352	−	0.439277i	$-0.144765\pi$
$109$	−0.904450	−	2.78361i	−0.0866306	−	0.266622i	−0.984982	+	0.172655i	$0.944765\pi$
$110$	3.81546	−	2.32616i	0.363790	−	0.221790i
$111$	−3.09993	+	9.54061i	−0.294232	+	0.905555i
$112$	1.01237	+	3.11574i	0.0956596	+	0.294410i
$113$	3.02222	+	9.30142i	0.284306	+	0.875004i	0.986606	+	0.163123i	$0.0521567\pi$
$113$	3.02222	+	9.30142i	0.284306	+	0.875004i	−0.702300	+	0.711882i	$0.747843\pi$
$114$	0.330793	−	1.01808i	0.0309816	−	0.0953516i
$115$	−1.23690	−	1.06131i	−0.115342	−	0.0989674i
$116$	0.473089	+	1.45602i	0.0439252	+	0.135188i
$117$	1.64049	−	1.19189i	0.151663	−	0.110190i
$118$	−2.89543			−0.266546
$119$	−0.317108	+	0.230392i	−0.0290692	+	0.0211200i
$120$	2.58489	−	6.20041i	0.235967	−	0.566017i
$121$	6.98397	+	5.07415i	0.634906	+	0.461286i
$122$	0.0373377	+	0.0271274i	0.00338039	+	0.00245600i
$123$	−2.46561	+	7.58836i	−0.222316	+	0.684219i
$124$	1.93949			0.174171
$125$	10.3583	−	4.20770i	0.926478	−	0.376348i
$126$	1.29885			0.115711
$127$	−4.05475	+	12.4792i	−0.359801	+	1.10735i	0.593372	+	0.804928i	$0.297796\pi$
$127$	−4.05475	+	12.4792i	−0.359801	+	1.10735i	−0.953173	+	0.302426i	$0.902204\pi$
$128$	6.44105	+	4.67970i	0.569314	+	0.413631i
$129$	−3.00959	−	2.18660i	−0.264980	−	0.192519i
$130$	−2.26614	+	5.43582i	−0.198754	+	0.476753i
$131$	10.1853	−	7.40006i	0.889895	−	0.646547i	−0.0459556	−	0.998943i	$-0.514633\pi$
$131$	10.1853	−	7.40006i	0.889895	−	0.646547i	0.935851	+	0.352397i	$0.114633\pi$
$132$	−0.481554			−0.0419139
$133$	0.666763	−	0.484432i	0.0578157	−	0.0420056i
$134$	−0.743601	−	2.28857i	−0.0642374	−	0.197702i
$135$	−1.69700	−	1.45609i	−0.146055	−	0.125320i
$136$	−0.363884	+	1.11992i	−0.0312028	+	0.0960324i
$137$	2.54319	+	7.82714i	0.217280	+	0.668718i	0.998984	+	0.0450687i	$0.0143507\pi$
$137$	2.54319	+	7.82714i	0.217280	+	0.668718i	−0.781704	+	0.623649i	$0.785649\pi$
$138$	−0.292547	−	0.900368i	−0.0249033	−	0.0766444i
$139$	3.12291	−	9.61133i	0.264882	−	0.815222i	−0.726839	−	0.686808i	$-0.759011\pi$
$139$	3.12291	−	9.61133i	0.264882	−	0.815222i	0.991721	−	0.128414i	$-0.0409887\pi$
$140$	0.597547	−	0.364304i	0.0505019	−	0.0307893i
$141$	0.965751	+	2.97228i	0.0813309	+	0.250311i
$142$	−10.9478	+	7.95405i	−0.918720	+	0.667489i
$143$	3.11994			0.260903
$144$	2.65041	−	1.92564i	0.220867	−	0.160470i
$145$	−9.33903	+	5.69368i	−0.775564	+	0.472835i
$146$	6.69365	+	4.86322i	0.553971	+	0.402483i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	−0.970213	+	2.98601i	−0.0797510	+	0.245448i
$149$	−3.34972			−0.274420			−0.137210	−	0.990542i	$-0.543813\pi$
$149$	−3.34972			−0.274420			−0.137210	+	0.990542i	$0.543813\pi$
$150$	6.40961	+	1.04520i	0.523342	+	0.0853400i
$151$	−3.79986			−0.309228			−0.154614	−	0.987975i	$-0.549413\pi$
$151$	−3.79986			−0.309228			−0.154614	+	0.987975i	$0.549413\pi$
$152$	0.765118	−	2.35479i	0.0620592	−	0.190999i
$153$	0.317108	+	0.230392i	0.0256366	+	0.0186261i
$154$	1.61677	+	1.17465i	0.130283	+	0.0946562i
$155$	3.20400	+	13.4811i	0.257352	+	1.08283i
$156$	0.513439	−	0.373035i	0.0411080	−	0.0298667i
$157$	19.8512			1.58429			0.792147	−	0.610330i	$-0.208963\pi$
$157$	19.8512			1.58429			0.792147	+	0.610330i	$0.208963\pi$
$158$	−5.33046	+	3.87281i	−0.424069	+	0.308104i
$159$	−4.26825	−	13.1363i	−0.338494	−	1.04178i
$160$	1.50856	−	3.61860i	0.119262	−	0.286076i
$161$	0.225235	−	0.693202i	0.0177510	−	0.0546320i
$162$	−0.401368	−	1.23528i	−0.0315344	−	0.0970530i
$163$	6.68171	+	20.5642i	0.523352	+	1.61071i	0.767552	+	0.640987i	$0.221475\pi$
$163$	6.68171	+	20.5642i	0.523352	+	1.61071i	−0.244200	+	0.969725i	$0.578525\pi$
$164$	−0.771683	+	2.37500i	−0.0602583	+	0.185456i
$165$	−0.795519	−	3.34721i	−0.0619311	−	0.260580i
$166$	−1.06628	−	3.28168i	−0.0827595	−	0.254707i
$167$	15.6346	−	11.3592i	1.20984	−	0.879000i	0.214624	−	0.976697i	$-0.431148\pi$
$167$	15.6346	−	11.3592i	1.20984	−	0.879000i	0.995216	+	0.0976968i	$0.0311475\pi$
$168$	3.00422			0.231781
$169$	7.19070	−	5.22435i	0.553131	−	0.401873i
$170$	−1.13468	−	0.0919078i	−0.0870262	−	0.00704901i
$171$	−0.666763	−	0.484432i	−0.0509887	−	0.0370454i
$172$	−0.941938	−	0.684358i	−0.0718221	−	0.0521818i
$173$	−0.199932	+	0.615327i	−0.0152005	+	0.0467824i	−0.958369	−	0.285532i	$-0.907830\pi$
$173$	−0.199932	+	0.615327i	−0.0152005	+	0.0467824i	0.943169	+	0.332315i	$0.107830\pi$
$174$	−6.35339			−0.481649
$175$	3.51936	+	3.55164i	0.266038	+	0.268478i
$176$	5.04064			0.379952
$177$	−0.688868	+	2.12012i	−0.0517785	+	0.159358i
$178$	−2.04544	−	1.48610i	−0.153312	−	0.111388i
$179$	−10.0836	−	7.32619i	−0.753686	−	0.547585i	0.143281	−	0.989682i	$-0.454235\pi$
$179$	−10.0836	−	7.32619i	−0.753686	−	0.547585i	−0.896967	+	0.442097i	$0.854235\pi$
$180$	−0.531125	−	0.455725i	−0.0395877	−	0.0339677i
$181$	4.73674	−	3.44145i	0.352079	−	0.255801i	−0.397661	−	0.917532i	$-0.630178\pi$
$181$	4.73674	−	3.44145i	0.352079	−	0.255801i	0.749741	+	0.661732i	$0.230178\pi$
$182$	−2.63376			−0.195227
$183$	0.0287466	−	0.0208856i	0.00212501	−	0.00154391i
$184$	−0.676656	−	2.08253i	−0.0498837	−	0.153526i
$185$	−22.3581	−	1.81098i	−1.64380	−	0.133146i
$186$	−2.48722	+	7.65489i	−0.182372	+	0.561284i
$187$	0.186364	+	0.573569i	0.0136283	+	0.0419435i
$188$	0.302260	+	0.930260i	0.0220446	+	0.0678462i
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	2.38583	+	0.193249i	0.173086	+	0.0140198i
$191$	−2.15514	−	6.63285i	−0.155941	−	0.479936i	0.842314	−	0.538987i	$-0.181193\pi$
$191$	−2.15514	−	6.63285i	−0.155941	−	0.479936i	−0.998255	+	0.0590506i	$0.981193\pi$
$192$	7.14316	−	5.18981i	0.515513	−	0.374542i
$193$	−6.36168			−0.457924			−0.228962	−	0.973435i	$-0.573533\pi$
$193$	−6.36168			−0.457924			−0.228962	+	0.973435i	$0.573533\pi$
$194$	−20.1972	+	14.6742i	−1.45008	+	1.05354i
$195$	3.44111	+	2.95259i	0.246423	+	0.211440i
$196$	0.253205	+	0.183964i	0.0180861	+	0.0131403i
$197$	−15.8642	−	11.5260i	−1.13028	−	0.821196i	−0.144544	−	0.989498i	$-0.546172\pi$
$197$	−15.8642	−	11.5260i	−1.13028	−	0.821196i	−0.985735	+	0.168302i	$0.946172\pi$
$198$	0.617551	−	1.90063i	0.0438874	−	0.135072i
$199$	11.1676			0.791648			0.395824	−	0.918326i	$-0.370459\pi$
$199$	11.1676			0.791648			0.395824	+	0.918326i	$0.370459\pi$
$200$	14.8253	+	2.41752i	1.04831	+	0.170944i
$201$	−1.85267			−0.130677
$202$	−3.51946	+	10.8318i	−0.247628	+	0.762121i
$203$	−3.95733	−	2.87517i	−0.277750	−	0.201797i
$204$	0.0992480	+	0.0721079i	0.00694875	+	0.00504856i
$205$	−17.7831	−	1.44040i	−1.24202	−	0.100602i
$206$	10.1390	−	7.36644i	0.706420	−	0.513244i
$207$	−0.728876			−0.0506604
$208$	−5.37439	+	3.90472i	−0.372647	+	0.270744i
$209$	−0.391856	−	1.20601i	−0.0271053	−	0.0834214i
$210$	0.671554	+	2.82562i	0.0463416	+	0.194986i
$211$	−4.45147	+	13.7002i	−0.306452	+	0.943162i	0.672680	+	0.739934i	$0.265143\pi$
$211$	−4.45147	+	13.7002i	−0.306452	+	0.943162i	−0.979131	+	0.203228i	$0.934857\pi$
$212$	−1.33587	−	4.11139i	−0.0917480	−	0.282371i
$213$	3.21953	+	9.90868i	0.220598	+	0.678932i
$214$	2.34502	−	7.21724i	0.160302	−	0.493360i
$215$	3.20081	−	7.67782i	0.218293	−	0.523623i
$216$	−0.928355	−	2.85718i	−0.0631666	−	0.194407i
$217$	−5.01337	+	3.64243i	−0.340330	+	0.247264i
$218$	3.80157			0.257474
$219$	5.15351	−	3.74424i	0.348242	−	0.253013i
$220$	−0.248981	−	1.04761i	−0.0167863	−	0.0706297i
$221$	−0.643018	−	0.467180i	−0.0432541	−	0.0314259i
$222$	−10.5411	−	7.65859i	−0.707475	−	0.514011i
$223$	7.69910	−	23.6954i	0.515570	−	1.58676i	−0.266673	−	0.963787i	$-0.585924\pi$
$223$	7.69910	−	23.6954i	0.515570	−	1.58676i	0.782243	−	0.622974i	$-0.214076\pi$
$224$	1.75329			0.117146
$225$	2.29027	−	4.44462i	0.152684	−	0.296308i
$226$	−12.7029			−0.844985
$227$	8.47459	−	26.0821i	0.562478	−	1.73113i	−0.112849	−	0.993612i	$-0.535998\pi$
$227$	8.47459	−	26.0821i	0.562478	−	1.73113i	0.675327	−	0.737518i	$-0.264002\pi$
$228$	−0.208683	−	0.151617i	−0.0138204	−	0.0100411i
$229$	−9.33093	−	6.77932i	−0.616606	−	0.447990i	0.235129	−	0.971964i	$-0.424449\pi$
$229$	−9.33093	−	6.77932i	−0.616606	−	0.447990i	−0.851734	+	0.523974i	$0.824449\pi$
$230$	1.80747	−	1.10195i	0.119181	−	0.0726605i
$231$	1.24477	−	0.904376i	0.0818996	−	0.0595036i
$232$	−14.6953			−0.964790
$233$	−10.8906	+	7.91249i	−0.713467	+	0.518364i	−0.884290	−	0.466937i	$-0.845357\pi$
$233$	−10.8906	+	7.91249i	−0.713467	+	0.518364i	0.170823	+	0.985302i	$0.445357\pi$
$234$	0.813877	+	2.50486i	0.0532048	+	0.163748i
$235$	−5.96677	+	3.63774i	−0.389229	+	0.237300i
$236$	−0.215601	+	0.663552i	−0.0140344	+	0.0431935i
$237$	1.56758	+	4.82451i	0.101825	+	0.313385i
$238$	−0.157323	−	0.484190i	−0.0101977	−	0.0313854i
$239$	7.58447	−	23.3426i	0.490598	−	1.50991i	−0.333107	−	0.942889i	$-0.608097\pi$
$239$	7.58447	−	23.3426i	0.490598	−	1.50991i	0.823706	−	0.567017i	$-0.191903\pi$
$240$	5.55952	+	4.77027i	0.358865	+	0.307919i
$241$	−2.58961	−	7.97000i	−0.166811	−	0.513393i	0.832354	−	0.554245i	$-0.186993\pi$
$241$	−2.58961	−	7.97000i	−0.166811	−	0.513393i	−0.999165	+	0.0408520i	$0.986993\pi$
$242$	−9.07115	+	6.59058i	−0.583116	+	0.423658i
$243$	−1.00000			−0.0641500
$244$	0.00899709	−	0.00653677i	0.000575980	−	0.000418474i
$245$	−0.860419	+	2.06390i	−0.0549702	+	0.131858i
$246$	−8.38416	−	6.09145i	−0.534554	−	0.388376i
$247$	1.35204	+	0.982311i	0.0860279	+	0.0625030i
$248$	−5.75290	+	17.7056i	−0.365309	+	1.12431i
$249$	−2.65662			−0.168356
$250$	1.04020	+	14.4843i	0.0657880	+	0.916069i
$251$	−26.5436			−1.67542			−0.837710	−	0.546115i	$-0.816106\pi$
$251$	−26.5436			−1.67542			−0.837710	+	0.546115i	$0.816106\pi$
$252$	0.0967158	−	0.297661i	0.00609252	−	0.0187509i
$253$	−0.907280	−	0.659178i	−0.0570402	−	0.0414422i
$254$	−13.7880	−	10.0175i	−0.865133	−	0.628556i
$255$	−0.337256	+	0.808980i	−0.0211198	+	0.0506603i
$256$	5.92035	−	4.30138i	0.370022	−	0.268836i
$257$	0.0307040			0.00191526			0.000957631	−	1.00000i	$-0.499695\pi$
$257$	0.0307040			0.00191526			0.000957631		1.00000i	$0.499695\pi$
$258$	3.90902	−	2.84007i	0.243365	−	0.176815i
$259$	−3.09993	−	9.54061i	−0.192620	−	0.592825i
$260$	1.07699	+	0.924100i	0.0667923	+	0.0573102i
$261$	−1.51157	+	4.65213i	−0.0935637	+	0.287959i
$262$	5.05312	+	15.5519i	0.312183	+	0.960799i
$263$	−8.25511	−	25.4066i	−0.509032	−	1.56664i	−0.793885	−	0.608068i	$-0.791945\pi$
$263$	−8.25511	−	25.4066i	−0.509032	−	1.56664i	0.284853	−	0.958571i	$-0.408055\pi$
$264$	1.42838	−	4.39611i	0.0879109	−	0.270562i
$265$	26.3708	−	16.0774i	1.61995	−	0.987626i
$266$	0.330793	+	1.01808i	0.0202822	+	0.0624223i
$267$	−1.57480	+	1.14416i	−0.0963763	+	0.0700215i
$268$	−0.579846			−0.0354197
$269$	−20.5000	+	14.8942i	−1.24991	+	0.908113i	−0.998217	−	0.0596944i	$-0.980987\pi$
$269$	−20.5000	+	14.8942i	−1.24991	+	0.908113i	−0.251693	+	0.967807i	$0.580987\pi$
$270$	2.47980	−	1.51185i	0.150916	−	0.0920082i
$271$	−6.99139	−	5.07954i	−0.424696	−	0.308560i	0.354828	−	0.934932i	$-0.384539\pi$
$271$	−6.99139	−	5.07954i	−0.424696	−	0.308560i	−0.779525	+	0.626371i	$0.784539\pi$
$272$	−1.03887	−	0.754785i	−0.0629909	−	0.0457656i
$273$	−0.626612	+	1.92851i	−0.0379243	+	0.116719i
$274$	−10.6895			−0.645776
$275$	6.87046	−	3.46126i	0.414304	−	0.208722i
$276$	−0.228123			−0.0137314
$277$	3.76289	−	11.5810i	0.226090	−	0.695833i	−0.772089	−	0.635514i	$-0.780788\pi$
$277$	3.76289	−	11.5810i	0.226090	−	0.695833i	0.998179	−	0.0603191i	$-0.0192118\pi$
$278$	10.6193	+	7.71536i	0.636902	+	0.462736i
$279$	5.01337	+	3.64243i	0.300143	+	0.218066i
$280$	1.55329	+	6.53560i	0.0928268	+	0.390577i
$281$	−8.09108	+	5.87851i	−0.482673	+	0.350683i	−0.802360	−	0.596841i	$-0.796422\pi$
$281$	−8.09108	+	5.87851i	−0.482673	+	0.350683i	0.319687	+	0.947523i	$0.396422\pi$
$282$	−4.05923			−0.241723
$283$	−8.21619	+	5.96941i	−0.488402	+	0.354845i	−0.804569	−	0.593859i	$-0.797604\pi$
$283$	−8.21619	+	5.96941i	−0.488402	+	0.354845i	0.316167	+	0.948703i	$0.397604\pi$
$284$	1.00764	+	3.10121i	0.0597926	+	0.184023i
$285$	0.709127	−	1.70099i	0.0420051	−	0.100758i
$286$	−1.25224	+	3.85401i	−0.0740468	+	0.227893i
$287$	−2.46561	−	7.58836i	−0.145540	−	0.447927i
$288$	−0.541795	−	1.66747i	−0.0319256	−	0.0982568i
$289$	−5.20581	+	16.0218i	−0.306224	+	0.942461i
$290$	−3.28493	−	13.8216i	−0.192898	−	0.811633i
$291$	5.93959	+	18.2802i	0.348185	+	1.07160i
$292$	1.61294	−	1.17187i	0.0943901	−	0.0685785i
$293$	−10.4190			−0.608686			−0.304343	−	0.952563i	$-0.598437\pi$
$293$	−10.4190			−0.608686			−0.304343	+	0.952563i	$0.598437\pi$
$294$	−1.05079	+	0.763447i	−0.0612836	+	0.0445251i
$295$	−4.96842	−	0.402436i	−0.289273	−	0.0234307i
$296$	−24.3814	−	17.7142i	−1.41714	−	1.02961i
$297$	−1.24477	−	0.904376i	−0.0722287	−	0.0524772i
$298$	1.34447	−	4.13785i	0.0778830	−	0.239699i
$299$	1.47798			0.0854741
$300$	0.716805	−	1.39107i	0.0413847	−	0.0803137i
$301$	3.72006			0.214421
$302$	1.52514	−	4.69391i	0.0877621	−	0.270104i
$303$	7.09399	+	5.15408i	0.407539	+	0.296094i
$304$	2.18437	+	1.58704i	0.125282	+	0.0910230i
$305$	0.0602992	+	0.0517388i	0.00345272	+	0.00296256i
$306$	−0.411877	+	0.299246i	−0.0235454	+	0.0171067i
$307$	−4.76893			−0.272177			−0.136088	−	0.990697i	$-0.543453\pi$
$307$	−4.76893			−0.272177			−0.136088	+	0.990697i	$0.543453\pi$
$308$	0.389586	−	0.283051i	0.0221987	−	0.0161283i
$309$	−2.98168	−	9.17667i	−0.169622	−	0.522042i
$310$	−17.9390	−	1.45303i	−1.01886	−	0.0825267i
$311$	−0.762185	+	2.34577i	−0.0432196	+	0.133016i	−0.970338	−	0.241752i	$-0.922278\pi$
$311$	−0.762185	+	2.34577i	−0.0432196	+	0.133016i	0.927118	+	0.374769i	$0.122278\pi$
$312$	1.88248	+	5.79368i	0.106575	+	0.328003i
$313$	5.27222	+	16.2262i	0.298004	+	0.917161i	0.982196	+	0.187859i	$0.0601549\pi$
$313$	5.27222	+	16.2262i	0.298004	+	0.917161i	−0.684192	+	0.729302i	$0.739845\pi$
$314$	−7.96762	+	24.5218i	−0.449639	+	1.38385i
$315$	2.22877	+	0.180527i	0.125577	+	0.0101716i
$316$	0.490619	+	1.50997i	0.0275995	+	0.0849424i
$317$	22.8735	−	16.6186i	1.28470	−	0.933391i	0.285019	−	0.958522i	$-0.408000\pi$
$317$	22.8735	−	16.6186i	1.28470	−	0.933391i	0.999684	+	0.0251308i	$0.00800022\pi$
$318$	17.9402			1.00604
$319$	−6.08882	+	4.42379i	−0.340908	+	0.247684i
$320$	14.9836	+	12.8564i	0.837606	+	0.718696i
$321$	−4.72674	−	3.43418i	−0.263821	−	0.191677i
$322$	0.765899	+	0.556458i	0.0426819	+	0.0310102i
$323$	−0.0998264	+	0.307234i	−0.00555449	+	0.0170950i
$324$	−0.312979			−0.0173877
$325$	−4.64411	+	9.01263i	−0.257609	+	0.499931i
$326$	−28.0844			−1.55545
$327$	0.904450	−	2.78361i	0.0500162	−	0.153934i
$328$	−19.3924	−	14.0894i	−1.07076	−	0.777956i
$329$	−2.52837	−	1.83697i	−0.139394	−	0.101275i
$330$	4.45405	+	0.360773i	0.245188	+	0.0198599i
$331$	25.0486	−	18.1989i	1.37680	−	1.00030i	0.379624	−	0.925141i	$-0.376053\pi$
$331$	25.0486	−	18.1989i	1.37680	−	1.00030i	0.997172	−	0.0751595i	$-0.0239466\pi$
$332$	−0.831465			−0.0456326
$333$	−8.11573	+	5.89642i	−0.444739	+	0.323122i
$334$	7.75659	+	23.8723i	0.424422	+	1.30624i
$335$	−0.957895	−	4.03042i	−0.0523354	−	0.220206i
$336$	−1.01237	+	3.11574i	−0.0552291	+	0.169978i
$337$	9.31641	+	28.6730i	0.507497	+	1.56192i	0.796531	+	0.604598i	$0.206666\pi$
$337$	9.31641	+	28.6730i	0.507497	+	1.56192i	−0.289034	+	0.957319i	$0.593334\pi$
$338$	3.56744	+	10.9794i	0.194043	+	0.597203i
$339$	−3.02222	+	9.30142i	−0.164144	+	0.505184i
$340$	−0.105554	+	0.253194i	−0.00572446	+	0.0137313i
$341$	2.94635	+	9.06794i	0.159554	+	0.491057i
$342$	0.866028	−	0.629206i	0.0468294	−	0.0340236i
$343$	−1.00000			−0.0539949
$344$	9.04147	−	6.56902i	0.487484	−	0.354178i
$345$	−0.376855	−	1.58565i	−0.0202892	−	0.0853684i
$346$	−0.679857	−	0.493945i	−0.0365493	−	0.0265546i
$347$	−20.4005	−	14.8219i	−1.09516	−	0.795679i	−0.114896	−	0.993378i	$-0.536653\pi$
$347$	−20.4005	−	14.8219i	−1.09516	−	0.795679i	−0.980263	+	0.197698i	$0.936653\pi$
$348$	−0.473089	+	1.45602i	−0.0253602	+	0.0780507i
$349$	11.5807			0.619901			0.309951	−	0.950753i	$-0.399687\pi$
$349$	11.5807			0.619901			0.309951	+	0.950753i	$0.399687\pi$
$350$	−5.79983	+	2.92189i	−0.310014	+	0.156182i
$351$	2.02776			0.108234
$352$	0.833615	−	2.56560i	0.0444318	−	0.136747i
$353$	7.68486	+	5.58338i	0.409024	+	0.297173i	0.773207	−	0.634154i	$-0.218652\pi$
$353$	7.68486	+	5.58338i	0.409024	+	0.297173i	−0.364183	+	0.931328i	$0.618652\pi$
$354$	−2.34246	−	1.70189i	−0.124500	−	0.0904546i
$355$	−19.8914	+	12.1271i	−1.05573	+	0.643641i
$356$	−0.492880	+	0.358098i	−0.0261226	+	0.0189792i
$357$	−0.391967			−0.0207451
$358$	13.0972	−	9.51565i	0.692207	−	0.502918i
$359$	−8.94934	−	27.5432i	−0.472328	−	1.45368i	−0.849528	−	0.527544i	$-0.823113\pi$
$359$	−8.94934	−	27.5432i	−0.472328	−	1.45368i	0.377200	−	0.926132i	$-0.376887\pi$
$360$	5.73573	−	3.49688i	0.302299	−	0.184302i
$361$	−5.66142	+	17.4241i	−0.297970	+	0.917056i
$362$	2.34998	+	7.23251i	0.123512	+	0.380132i
$363$	2.66764	+	8.21015i	0.140015	+	0.430921i
$364$	−0.196116	+	0.603584i	−0.0102793	+	0.0316364i
$365$	10.8100	+	9.27540i	0.565823	+	0.485497i
$366$	0.0142617	+	0.0438931i	0.000745472	+	0.00229433i
$367$	25.4898	−	18.5194i	1.33055	−	0.966704i	0.330819	−	0.943694i	$-0.392675\pi$
$367$	25.4898	−	18.5194i	1.33055	−	0.966704i	0.999735	−	0.0230101i	$-0.00732498\pi$
$368$	2.38786			0.124476
$369$	−6.45504	+	4.68986i	−0.336036	+	0.244144i
$370$	11.2109	−	26.8917i	0.582826	−	1.39803i
$371$	11.1744	+	8.11869i	0.580147	+	0.421501i
$372$	1.56908	+	1.14000i	0.0813530	+	0.0591064i
$373$	8.97686	−	27.6279i	0.464804	−	1.43052i	−0.394424	−	0.918929i	$-0.629056\pi$
$373$	8.97686	−	27.6279i	0.464804	−	1.43052i	0.859228	−	0.511592i	$-0.170944\pi$
$374$	−0.783321			−0.0405046
$375$	10.8533	+	2.68438i	0.560462	+	0.138621i
$376$	−9.38890			−0.484196
$377$	3.06509	−	9.43339i	0.157860	−	0.485844i
$378$	1.05079	+	0.763447i	0.0540471	+	0.0392675i
$379$	−6.92215	−	5.02924i	−0.355567	−	0.258335i	0.395634	−	0.918408i	$-0.370525\pi$
$379$	−6.92215	−	5.02924i	−0.355567	−	0.258335i	−0.751201	+	0.660074i	$0.770525\pi$
$380$	0.221942	−	0.532375i	0.0113854	−	0.0273102i
$381$	−10.6155	+	7.71260i	−0.543848	+	0.395128i
$382$	9.05845			0.463471
$383$	6.98417	−	5.07430i	0.356875	−	0.259285i	−0.394873	−	0.918736i	$-0.629211\pi$
$383$	6.98417	−	5.07430i	0.356875	−	0.259285i	0.751747	+	0.659451i	$0.229211\pi$
$384$	2.46026	+	7.57191i	0.125550	+	0.386402i
$385$	2.61103	+	2.24036i	0.133071	+	0.114179i
$386$	2.55337	−	7.85848i	0.129963	−	0.399986i
$387$	−1.14956	−	3.53799i	−0.0584355	−	0.179846i
$388$	1.85897	+	5.72131i	0.0943747	+	0.290456i
$389$	−6.70388	+	20.6324i	−0.339900	+	1.04611i	0.624357	+	0.781139i	$0.285361\pi$
$389$	−6.70388	+	20.6324i	−0.339900	+	1.04611i	−0.964258	+	0.264967i	$0.914639\pi$
$390$	−5.02844	+	3.06567i	−0.254625	+	0.155236i
$391$	0.0882846	+	0.271712i	0.00446475	+	0.0137411i
$392$	−2.43047	+	1.76584i	−0.122757	+	0.0891882i
$393$	12.5897			0.635068
$394$	20.6053	−	14.9706i	1.03808	−	0.754210i
$395$	−9.68508	+	5.90466i	−0.487309	+	0.297096i
$396$	−0.389586	−	0.283051i	−0.0195774	−	0.0142238i
$397$	9.20695	+	6.68924i	0.462083	+	0.335723i	0.794348	−	0.607463i	$-0.207813\pi$
$397$	9.20695	+	6.68924i	0.462083	+	0.335723i	−0.332265	+	0.943186i	$0.607813\pi$
$398$	−4.48230	+	13.7951i	−0.224678	+	0.691487i
$399$	0.824165			0.0412598
$400$	−7.50311	+	14.5610i	−0.375155	+	0.728049i
$401$	−11.3354			−0.566063			−0.283032	−	0.959111i	$-0.591340\pi$
$401$	−11.3354			−0.566063			−0.283032	+	0.959111i	$0.591340\pi$
$402$	0.743601	−	2.28857i	0.0370875	−	0.114143i
$403$	−10.1659	−	7.38596i	−0.506400	−	0.367921i
$404$	2.22027	+	1.61312i	0.110462	+	0.0802557i
$405$	−0.517036	−	2.17547i	−0.0256917	−	0.108100i
$406$	5.14000	−	3.73443i	0.255094	−	0.185337i
$407$	−15.4348			−0.765073
$408$	−0.952662	+	0.692149i	−0.0471638	+	0.0342665i
$409$	4.09170	+	12.5930i	0.202322	+	0.622682i	0.999813	+	0.0193513i	$0.00616011\pi$
$409$	4.09170	+	12.5930i	0.202322	+	0.622682i	−0.797491	+	0.603331i	$0.793840\pi$
$410$	8.91686	−	21.3890i	0.440372	−	1.05633i
$411$	−2.54319	+	7.82714i	−0.125446	+	0.386085i
$412$	−0.933203	−	2.87210i	−0.0459756	−	0.141498i
$413$	−0.688868	−	2.12012i	−0.0338970	−	0.104324i
$414$	0.292547	−	0.900368i	0.0143779	−	0.0442507i
$415$	−1.37357	−	5.77940i	−0.0674257	−	0.283699i
$416$	1.09863	+	3.38123i	0.0538648	+	0.165779i
$417$	8.17588	−	5.94013i	0.400375	−	0.290889i
$418$	1.64704			0.0805594
$419$	16.3677	−	11.8919i	0.799617	−	0.580955i	−0.111185	−	0.993800i	$-0.535465\pi$
$419$	16.3677	−	11.8919i	0.799617	−	0.580955i	0.910802	+	0.412844i	$0.135465\pi$
$420$	0.697558	+	0.0565013i	0.0340373	+	0.00275698i
$421$	−7.88031	−	5.72538i	−0.384063	−	0.279038i	0.378955	−	0.925415i	$-0.376283\pi$
$421$	−7.88031	−	5.72538i	−0.384063	−	0.279038i	−0.763018	+	0.646377i	$0.776283\pi$
$422$	−15.1370	−	10.9977i	−0.736856	−	0.535357i
$423$	−0.965751	+	2.97228i	−0.0469564	+	0.144517i
$424$	41.4953			2.01519
$425$	−1.93428	−	0.315419i	−0.0938266	−	0.0153000i
$426$	−13.5322			−0.655639
$427$	−0.0109802	+	0.0337937i	−0.000531371	+	0.00163539i
$428$	−1.47937	−	1.07483i	−0.0715081	−	0.0519537i
$429$	2.52409	+	1.83386i	0.121864	+	0.0885394i
$430$	8.19959	+	7.03554i	0.395419	+	0.339284i
$431$	−5.89040	+	4.27963i	−0.283731	+	0.206142i	−0.720543	−	0.693410i	$-0.756107\pi$
$431$	−5.89040	+	4.27963i	−0.283731	+	0.206142i	0.436812	+	0.899553i	$0.356107\pi$
$432$	3.27609			0.157621
$433$	−2.70803	+	1.96750i	−0.130140	+	0.0945520i	−0.650951	−	0.759120i	$-0.725630\pi$
$433$	−2.70803	+	1.96750i	−0.130140	+	0.0945520i	0.520811	+	0.853672i	$0.325630\pi$
$434$	−2.48722	−	7.65489i	−0.119391	−	0.367446i
$435$	−10.9021	−	0.883056i	−0.522716	−	0.0423393i
$436$	0.283074	−	0.871211i	0.0135568	−	0.0417235i
$437$	−0.185631	−	0.571313i	−0.00887992	−	0.0273296i
$438$	2.55675	+	7.86886i	0.122166	+	0.375989i
$439$	7.06321	−	21.7383i	0.337109	−	1.03751i	−0.628565	−	0.777757i	$-0.716358\pi$
$439$	7.06321	−	21.7383i	0.337109	−	1.03751i	0.965674	−	0.259757i	$-0.0836425\pi$
$440$	10.3021	+	0.834459i	0.491135	+	0.0397813i
$441$	0.309017	+	0.951057i	0.0147151	+	0.0452884i
$442$	0.835186	−	0.606798i	0.0397258	−	0.0288625i
$443$	−2.72868			−0.129644			−0.0648218	−	0.997897i	$-0.520648\pi$
$443$	−2.72868			−0.129644			−0.0648218	+	0.997897i	$0.520648\pi$
$444$	−2.54005	+	1.84546i	−0.120545	+	0.0875814i
$445$	−3.30332	−	2.83436i	−0.156592	−	0.134362i
$446$	26.1804	+	19.0211i	1.23968	+	0.900677i
$447$	−2.70998	−	1.96891i	−0.128178	−	0.0931265i
$448$	−2.72845	+	8.39729i	−0.128907	+	0.396735i
$449$	−5.12903			−0.242054			−0.121027	−	0.992649i	$-0.538619\pi$
$449$	−5.12903			−0.242054			−0.121027	+	0.992649i	$0.538619\pi$
$450$	4.57113	+	4.61306i	0.215485	+	0.217462i
$451$	−12.2764			−0.578074
$452$	−0.945890	+	2.91115i	−0.0444909	+	0.136929i
$453$	−3.07415	−	2.23350i	−0.144436	−	0.104939i
$454$	28.8174	+	20.9370i	1.35247	+	0.982624i
$455$	−4.51941	−	0.366066i	−0.211873	−	0.0171614i
$456$	2.00310	−	1.45534i	0.0938039	−	0.0681526i
$457$	−4.85077			−0.226909			−0.113455	−	0.993543i	$-0.536192\pi$
$457$	−4.85077			−0.226909			−0.113455	+	0.993543i	$0.536192\pi$
$458$	12.1195	−	8.80535i	0.566308	−	0.411447i
$459$	0.121124	+	0.372782i	0.00565360	+	0.0174000i
$460$	−0.117948	−	0.496274i	−0.00549934	−	0.0231389i
$461$	−9.20998	+	28.3454i	−0.428952	+	1.32018i	0.470208	+	0.882556i	$0.344179\pi$
$461$	−9.20998	+	28.3454i	−0.428952	+	1.32018i	−0.899159	+	0.437622i	$0.855821\pi$
$462$	0.617551	+	1.90063i	0.0287311	+	0.0884252i
$463$	2.64189	+	8.13089i	0.122779	+	0.377874i	0.993490	−	0.113921i	$-0.0363409\pi$
$463$	2.64189	+	8.13089i	0.122779	+	0.377874i	−0.870711	+	0.491795i	$0.836341\pi$
$464$	4.95202	−	15.2408i	0.229892	−	0.707535i
$465$	−5.33190	+	12.7897i	−0.247261	+	0.593108i
$466$	−5.40303	−	16.6288i	−0.250290	−	0.770314i
$467$	−5.97139	+	4.33847i	−0.276323	+	0.200760i	−0.717312	−	0.696752i	$-0.754628\pi$
$467$	−5.97139	+	4.33847i	−0.276323	+	0.200760i	0.440989	+	0.897512i	$0.354628\pi$
$468$	0.634646			0.0293365
$469$	1.49884	−	1.08897i	0.0692100	−	0.0502840i
$470$	−2.09876	−	8.83073i	−0.0968088	−	0.407331i
$471$	16.0599	+	11.6682i	0.740002	+	0.537643i
$472$	−5.41805	−	3.93644i	−0.249386	−	0.181190i
$473$	1.76873	−	5.44360i	0.0813264	−	0.250297i
$474$	−6.58881			−0.302634
$475$	4.06710	+	0.663211i	0.186612	+	0.0304302i
$476$	−0.122677			−0.00562290
$477$	4.26825	−	13.1363i	0.195430	−	0.601470i
$478$	25.7905	+	18.7379i	1.17963	+	0.857053i
$479$	11.8819	+	8.63269i	0.542897	+	0.394438i	0.825160	−	0.564899i	$-0.191085\pi$
$479$	11.8819	+	8.63269i	0.542897	+	0.394438i	−0.282263	+	0.959337i	$0.591085\pi$
$480$	3.34741	−	2.04080i	0.152788	−	0.0931495i
$481$	16.4567	−	11.9565i	0.750363	−	0.545170i
$482$	10.8846			0.495780
$483$	0.589673	−	0.428423i	0.0268310	−	0.0194939i
$484$	0.834915	+	2.56960i	0.0379507	+	0.116800i
$485$	−36.6970	+	22.3729i	−1.66633	+	1.01590i
$486$	0.401368	−	1.23528i	0.0182064	−	0.0560336i
$487$	5.63728	+	17.3498i	0.255450	+	0.786193i	0.993741	+	0.111711i	$0.0356330\pi$
$487$	5.63728	+	17.3498i	0.255450	+	0.786193i	−0.738291	+	0.674482i	$0.764367\pi$
$488$	0.0329871	+	0.101524i	0.00149325	+	0.00459576i
$489$	−6.68171	+	20.5642i	−0.302157	+	0.929945i
$490$	−2.20416	−	1.89124i	−0.0995736	−	0.0854377i
$491$	9.04832	+	27.8479i	0.408345	+	1.25676i	0.918070	+	0.396419i	$0.129747\pi$
$491$	9.04832	+	27.8479i	0.408345	+	1.25676i	−0.509725	+	0.860337i	$0.670253\pi$
$492$	−2.02029	+	1.46783i	−0.0910818	+	0.0661748i
$493$	1.91732			0.0863517
$494$	−1.75610	+	1.27588i	−0.0790105	+	0.0574045i
$495$	1.32385	−	3.17555i	0.0595028	−	0.142730i
$496$	−16.4242	−	11.9329i	−0.737470	−	0.535803i
$497$	−8.42883	−	6.12390i	−0.378085	−	0.274695i
$498$	1.06628	−	3.28168i	0.0477812	−	0.147055i
$499$	2.55506			0.114380			0.0571900	−	0.998363i	$-0.481786\pi$
$499$	2.55506			0.114380			0.0571900	+	0.998363i	$0.481786\pi$
$500$	3.39685	+	0.840153i	0.151912	+	0.0375728i
$501$	19.3254			0.863395
$502$	10.6538	−	32.7889i	0.475501	−	1.46344i
$503$	−9.10225	−	6.61317i	−0.405849	−	0.294867i	0.366070	−	0.930587i	$-0.380703\pi$
$503$	−9.10225	−	6.61317i	−0.405849	−	0.294867i	−0.771919	+	0.635721i	$0.780703\pi$
$504$	2.43047	+	1.76584i	0.108262	+	0.0786566i
$505$	−7.54472	+	18.0976i	−0.335735	+	0.805333i
$506$	1.17842	−	0.856176i	0.0523874	−	0.0380616i
$507$	8.88819			0.394739
$508$	−3.32242	+	2.41388i	−0.147409	+	0.107099i
$509$	4.03692	+	12.4244i	0.178933	+	0.550700i	0.999791	−	0.0204321i	$-0.00650420\pi$
$509$	4.03692	+	12.4244i	0.178933	+	0.550700i	−0.820858	+	0.571133i	$0.806504\pi$
$510$	−0.863955	−	0.741305i	−0.0382566	−	0.0328255i
$511$	−1.96847	+	6.05831i	−0.0870798	+	0.268004i
$512$	7.85771	+	24.1836i	0.347265	+	1.06877i
$513$	−0.254681	−	0.783827i	−0.0112444	−	0.0346068i
$514$	−0.0123236	+	0.0379281i	−0.000543570	+	0.00167294i
$515$	18.4219	−	11.2312i	0.811767	−	0.494907i
$516$	−0.359788	−	1.10731i	−0.0158388	−	0.0487468i
$517$	−3.89019	+	2.82639i	−0.171090	+	0.124304i
$518$	13.0296			0.572486
$519$	−0.523428	+	0.380293i	−0.0229760	+	0.0166930i
$520$	−11.6307	+	7.09082i	−0.510039	+	0.310953i
$521$	−28.2006	−	20.4889i	−1.23549	−	0.897636i	−0.238201	−	0.971216i	$-0.576558\pi$
$521$	−28.2006	−	20.4889i	−1.23549	−	0.897636i	−0.997289	+	0.0735800i	$0.976558\pi$
$522$	−5.14000	−	3.73443i	−0.224972	−	0.163451i
$523$	7.40599	−	22.7933i	0.323841	−	0.996681i	−0.648120	−	0.761539i	$-0.724444\pi$
$523$	7.40599	−	22.7933i	0.323841	−	0.996681i	0.971961	−	0.235143i	$-0.0755557\pi$
$524$	3.94032			0.172134
$525$	0.759621	+	4.94196i	0.0331526	+	0.215685i
$526$	34.6977			1.51289
$527$	0.750592	−	2.31008i	0.0326963	−	0.100629i
$528$	4.07796	+	2.96281i	0.177471	+	0.128940i
$529$	18.1776	+	13.2068i	0.790330	+	0.574208i
$530$	9.27573	+	39.0284i	0.402912	+	1.69529i
$531$	−1.80348	+	1.31030i	−0.0782643	+	0.0568624i
$532$	0.257946			0.0111834
$533$	13.0893	−	9.50991i	0.566959	−	0.411920i
$534$	−0.781287	−	2.40456i	−0.0338096	−	0.104055i
$535$	5.02707	−	12.0585i	0.217339	−	0.521334i
$536$	1.71993	−	5.29341i	0.0742898	−	0.228641i
$537$	−3.85161	−	11.8540i	−0.166209	−	0.511539i
$538$	−10.1704	−	31.3014i	−0.438479	−	1.34950i
$539$	−0.475459	+	1.46331i	−0.0204794	+	0.0630293i
$540$	−0.161821	−	0.680876i	−0.00696368	−	0.0293003i
$541$	−5.00056	−	15.3901i	−0.214991	−	0.661674i	−0.999154	−	0.0411193i	$-0.986908\pi$
$541$	−5.00056	−	15.3901i	−0.214991	−	0.661674i	0.784163	−	0.620554i	$-0.213092\pi$
$542$	9.08079	−	6.59758i	0.390053	−	0.283390i
$543$	5.85494			0.251259
$544$	−0.555980	+	0.403943i	−0.0238375	+	0.0173189i
$545$	6.52330	+	0.528379i	0.279427	+	0.0226333i
$546$	−2.13076	−	1.54809i	−0.0911881	−	0.0662520i
$547$	−26.0970	−	18.9606i	−1.11583	−	0.810695i	−0.132255	−	0.991216i	$-0.542222\pi$
$547$	−26.0970	−	18.9606i	−1.11583	−	0.810695i	−0.983571	+	0.180521i	$0.942222\pi$
$548$	−0.795966	+	2.44973i	−0.0340020	+	0.104647i
$549$	0.0355328			0.00151650
$550$	1.51805	+	9.87620i	0.0647301	+	0.421123i
$551$	−4.03143			−0.171745
$552$	0.676656	−	2.08253i	0.0288004	−	0.0886385i
$553$	−4.10397	−	2.98171i	−0.174519	−	0.126795i
$554$	12.7955	+	9.29646i	0.543628	+	0.394969i
$555$	−17.0236	−	14.6069i	−0.722612	−	0.620027i
$556$	2.55888	−	1.85913i	0.108521	−	0.0788448i
$557$	−6.49888			−0.275367			−0.137683	−	0.990476i	$-0.543966\pi$
$557$	−6.49888			−0.275367			−0.137683	+	0.990476i	$0.543966\pi$
$558$	−6.51164	+	4.73098i	−0.275660	+	0.200278i
$559$	2.33103	+	7.17418i	0.0985922	+	0.303436i
$560$	−7.30164	−	0.591423i	−0.308551	−	0.0249922i
$561$	−0.186364	+	0.573569i	−0.00786829	+	0.0242161i
$562$	−4.01413	−	12.3542i	−0.169326	−	0.521131i
$563$	−8.95699	−	27.5668i	−0.377492	−	1.16180i	−0.941782	−	0.336225i	$-0.890850\pi$
$563$	−8.95699	−	27.5668i	−0.377492	−	1.16180i	0.564290	−	0.825577i	$-0.309150\pi$
$564$	−0.302260	+	0.930260i	−0.0127274	+	0.0391710i
$565$	−21.7976	−	1.76558i	−0.917031	−	0.0742783i
$566$	−4.07620	−	12.5453i	−0.171336	−	0.527317i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	−31.2998			−1.31331
$569$	24.2582	−	17.6246i	1.01696	−	0.738863i	0.0513007	−	0.998683i	$-0.483663\pi$
$569$	24.2582	−	17.6246i	1.01696	−	0.738863i	0.965657	+	0.259820i	$0.0836633\pi$
$570$	1.81659	+	1.55870i	0.0760885	+	0.0652866i
$571$	−4.65762	−	3.38396i	−0.194915	−	0.141614i	0.486047	−	0.873933i	$-0.338438\pi$
$571$	−4.65762	−	3.38396i	−0.194915	−	0.141614i	−0.680962	+	0.732318i	$0.738438\pi$
$572$	0.789986	+	0.573958i	0.0330310	+	0.0239984i
$573$	2.15514	−	6.63285i	0.0900324	−	0.277091i
$574$	10.3634			0.432559
$575$	3.25468	−	1.63967i	0.135730	−	0.0683791i
$576$	8.82943			0.367893
$577$	−6.54648	+	20.1480i	−0.272534	+	0.838772i	0.717328	+	0.696736i	$0.245365\pi$
$577$	−6.54648	+	20.1480i	−0.272534	+	0.838772i	−0.989861	+	0.142036i	$0.954635\pi$
$578$	−17.7021	−	12.8613i	−0.736309	−	0.534960i
$579$	−5.14671	−	3.73930i	−0.213890	−	0.155400i
$580$	−3.41213	−	0.276378i	−0.141681	−	0.0114760i
$581$	2.14925	−	1.56152i	0.0891659	−	0.0647828i
$582$	−24.9652			−1.03484
$583$	17.1931	−	12.4915i	0.712067	−	0.517347i
$584$	5.91371	+	18.2005i	0.244711	+	0.753143i
$585$	1.04842	+	4.41133i	0.0433470	+	0.182386i
$586$	4.18186	−	12.8705i	0.172751	−	0.531673i
$587$	−2.92963	−	9.01649i	−0.120919	−	0.372150i	0.872217	−	0.489120i	$-0.162682\pi$
$587$	−2.92963	−	9.01649i	−0.120919	−	0.372150i	−0.993135	+	0.116970i	$0.962682\pi$
$588$	0.0967158	+	0.297661i	0.00398849	+	0.0122753i
$589$	−1.57822	+	4.85727i	−0.0650296	+	0.200140i
$590$	2.49129	−	5.97588i	0.102565	−	0.246023i
$591$	−6.05960	−	18.6495i	−0.249259	−	0.767139i
$592$	26.5878	−	19.3172i	1.09275	−	0.793931i
$593$	46.3831			1.90473			0.952364	−	0.304965i	$-0.0986446\pi$
$593$	46.3831			1.90473			0.952364	+	0.304965i	$0.0986446\pi$
$594$	1.61677	−	1.17465i	0.0663369	−	0.0481966i
$595$	−0.202661	−	0.852712i	−0.00830828	−	0.0349578i
$596$	−0.848166	−	0.616229i	−0.0347422	−	0.0252417i
$597$	9.03476	+	6.56413i	0.369768	+	0.268652i
$598$	−0.593216	+	1.82573i	−0.0242584	+	0.0746596i
$599$	19.6591			0.803250			0.401625	−	0.915804i	$-0.368446\pi$
$599$	19.6591			0.803250			0.401625	+	0.915804i	$0.368446\pi$
$600$	10.5729	+	10.6699i	0.431638	+	0.435597i
$601$	−14.4812			−0.590700			−0.295350	−	0.955389i	$-0.595436\pi$
$601$	−14.4812			−0.590700			−0.295350	+	0.955389i	$0.595436\pi$
$602$	−1.49311	+	4.59533i	−0.0608547	+	0.187291i
$603$	−1.49884	−	1.08897i	−0.0610375	−	0.0443463i
$604$	−0.962145	−	0.699039i	−0.0391491	−	0.0284435i
$605$	−16.4817	+	10.0483i	−0.670075	+	0.408522i
$606$	−9.21405	+	6.69440i	−0.374295	+	0.271942i
$607$	−3.33312			−0.135287			−0.0676435	−	0.997710i	$-0.521548\pi$
$607$	−3.33312			−0.135287			−0.0676435	+	0.997710i	$0.521548\pi$
$608$	1.16903	−	0.849347i	0.0474103	−	0.0344456i
$609$	−1.51157	−	4.65213i	−0.0612518	−	0.188514i
$610$	−0.0881143	+	0.0537202i	−0.00356764	+	0.00217507i
$611$	1.95831	−	6.02706i	0.0792248	−	0.243829i
$612$	0.0379094	+	0.116673i	0.00153240	+	0.00471623i
$613$	0.206889	+	0.636740i	0.00835618	+	0.0257177i	0.955148	−	0.296130i	$-0.0956961\pi$
$613$	0.206889	+	0.636740i	0.00835618	+	0.0257177i	−0.946791	+	0.321848i	$0.895696\pi$
$614$	1.91409	−	5.89098i	0.0772465	−	0.237740i
$615$	−13.5401	−	11.6179i	−0.545991	−	0.468480i
$616$	1.42838	+	4.39611i	0.0575512	+	0.177124i
$617$	37.7959	−	27.4603i	1.52160	−	1.10551i	0.560920	−	0.827870i	$-0.310448\pi$
$617$	37.7959	−	27.4603i	1.52160	−	1.10551i	0.960685	−	0.277641i	$-0.0895525\pi$
$618$	12.5325			0.504132
$619$	−34.5760	+	25.1209i	−1.38973	+	1.00969i	−0.393830	+	0.919183i	$0.628850\pi$
$619$	−34.5760	+	25.1209i	−1.38973	+	1.00969i	−0.995895	+	0.0905111i	$0.971150\pi$
$620$	−1.66877	+	4.00291i	−0.0670195	+	0.160761i
$621$	−0.589673	−	0.428423i	−0.0236628	−	0.0171920i
$622$	−2.59177	−	1.88303i	−0.103920	−	0.0755026i
$623$	0.601521	−	1.85129i	0.0240994	−	0.0741704i
$624$	−6.64311			−0.265937
$625$	−0.228241	+	24.9990i	−0.00912963	+	0.999958i
$626$	−22.1601			−0.885696
$627$	0.391856	−	1.20601i	0.0156492	−	0.0481634i
$628$	5.02642	+	3.65190i	0.200576	+	0.145727i
$629$	3.18109	+	2.31120i	0.126839	+	0.0921536i
$630$	−1.11756	+	2.68070i	−0.0445246	+	0.106802i
$631$	−19.0008	+	13.8049i	−0.756412	+	0.549565i	−0.897808	−	0.440388i	$-0.854841\pi$
$631$	−19.0008	+	13.8049i	−0.756412	+	0.549565i	0.141396	+	0.989953i	$0.454841\pi$
$632$	−15.2398			−0.606206
$633$	−11.6541	+	8.46720i	−0.463209	+	0.336541i
$634$	11.3479	+	34.9254i	0.450685	+	1.38706i
$635$	−22.2671	−	19.1060i	−0.883644	−	0.758198i
$636$	1.33587	−	4.11139i	0.0529707	−	0.163027i
$637$	−0.626612	−	1.92851i	−0.0248273	−	0.0764105i
$638$	−3.02077	−	9.29698i	−0.119594	−	0.368071i
$639$	−3.21953	+	9.90868i	−0.127362	+	0.391981i
$640$	−15.2004	+	9.26717i	−0.600849	+	0.366317i
$641$	2.81611	+	8.66710i	0.111230	+	0.342330i	0.991142	−	0.132806i	$-0.0423988\pi$
$641$	2.81611	+	8.66710i	0.111230	+	0.342330i	−0.879912	+	0.475136i	$0.842399\pi$
$642$	6.13935	−	4.46050i	0.242301	−	0.176042i
$643$	−42.1474			−1.66213			−0.831066	−	0.556173i	$-0.812269\pi$
$643$	−42.1474			−1.66213			−0.831066	+	0.556173i	$0.812269\pi$
$644$	0.184555	−	0.134087i	0.00727249	−	0.00528378i
$645$	7.10242	−	4.33010i	0.279658	−	0.170498i
$646$	−0.339454	−	0.246628i	−0.0133556	−	0.00970344i
$647$	−3.44178	−	2.50060i	−0.135311	−	0.0983088i	0.518071	−	0.855338i	$-0.326650\pi$
$647$	−3.44178	−	2.50060i	−0.135311	−	0.0983088i	−0.653382	+	0.757029i	$0.726650\pi$
$648$	0.928355	−	2.85718i	0.0364692	−	0.112241i
$649$	−3.42992			−0.134636
$650$	−9.26915	−	9.35417i	−0.363566	−	0.366901i
$651$	−6.19687			−0.242874
$652$	−2.09123	+	6.43616i	−0.0818991	+	0.252059i
$653$	37.1960	+	27.0244i	1.45559	+	1.05755i	0.984485	+	0.175471i	$0.0561449\pi$
$653$	37.1960	+	27.0244i	1.45559	+	1.05755i	0.471106	+	0.882077i	$0.343855\pi$
$654$	3.07553	+	2.23450i	0.120263	+	0.0873760i
$655$	6.50934	+	27.3886i	0.254341	+	1.07016i
$656$	21.1473	−	15.3644i	0.825662	−	0.599879i
$657$	6.37009			0.248521
$658$	3.28398	−	2.38595i	0.128023	−	0.0930141i
$659$	−4.76312	−	14.6594i	−0.185545	−	0.571048i	0.814413	−	0.580286i	$-0.197059\pi$
$659$	−4.76312	−	14.6594i	−0.185545	−	0.571048i	−0.999957	+	0.00923827i	$0.997059\pi$
$660$	0.414339	−	0.993880i	0.0161281	−	0.0386867i
$661$	9.36277	−	28.8156i	0.364169	−	1.12080i	−0.586330	−	0.810072i	$-0.699428\pi$
$661$	9.36277	−	28.8156i	0.364169	−	1.12080i	0.950500	−	0.310726i	$-0.100572\pi$
$662$	12.4271	+	38.2466i	0.482991	+	1.48649i
$663$	−0.245611	−	0.755913i	−0.00953874	−	0.0293572i
$664$	2.46629	−	7.59045i	0.0957105	−	0.294566i
$665$	0.426123	+	1.79295i	0.0165243	+	0.0695275i
$666$	−4.02636	−	12.3919i	−0.156018	−	0.480175i
$667$	−2.88441	+	2.09564i	−0.111685	+	0.0811436i
$668$	6.04844			0.234021
$669$	20.1565	−	14.6446i	0.779295	−	0.566191i
$670$	5.36319	+	0.434411i	0.207198	+	0.0167828i
$671$	0.0442300	+	0.0321350i	0.00170748	+	0.00124056i
$672$	1.41844	+	1.03056i	0.0547174	+	0.0397545i
$673$	10.9753	−	33.7784i	0.423066	−	1.30206i	−0.481769	−	0.876298i	$-0.660005\pi$
$673$	10.9753	−	33.7784i	0.423066	−	1.30206i	0.904834	−	0.425764i	$-0.139995\pi$
$674$	−39.1586			−1.50833
$675$	4.46535	−	2.24959i	0.171871	−	0.0865868i
$676$	2.78182			0.106993
$677$	−10.8462	+	33.3811i	−0.416852	+	1.28294i	0.493731	+	0.869615i	$0.335633\pi$
$677$	−10.8462	+	33.3811i	−0.416852	+	1.28294i	−0.910584	+	0.413325i	$0.864367\pi$
$678$	−10.2769	−	7.46659i	−0.394681	−	0.286753i
$679$	−15.5501	−	11.2978i	−0.596756	−	0.433569i
$680$	−1.99831	−	1.71462i	−0.0766317	−	0.0657528i
$681$	22.1868	−	16.1196i	0.850199	−	0.617705i
$682$	−12.3840			−0.474210
$683$	20.4453	−	14.8544i	0.782317	−	0.568387i	−0.123356	−	0.992362i	$-0.539366\pi$
$683$	20.4453	−	14.8544i	0.782317	−	0.568387i	0.905674	+	0.423976i	$0.139366\pi$
$684$	−0.0797097	−	0.245321i	−0.00304778	−	0.00938010i
$685$	−18.3426	−	1.48573i	−0.700837	−	0.0567668i
$686$	0.401368	−	1.23528i	0.0153243	−	0.0471633i
$687$	−3.56410	−	10.9692i	−0.135979	−	0.418500i
$688$	3.76606	+	11.5907i	0.143580	+	0.441893i
$689$	−8.65498	+	26.6373i	−0.329728	+	1.01480i
$690$	2.10998	+	0.170906i	0.0803257	+	0.00650627i
$691$	−11.2099	−	34.5006i	−0.426446	−	1.31247i	−0.901603	−	0.432564i	$-0.857609\pi$
$691$	−11.2099	−	34.5006i	−0.426446	−	1.31247i	0.475157	−	0.879901i	$-0.342391\pi$
$692$	−0.163822	+	0.119024i	−0.00622758	+	0.00452460i
$693$	1.53862			0.0584472
$694$	26.4973	−	19.2514i	1.00582	−	0.730774i
$695$	17.1498	+	14.7151i	0.650529	+	0.558177i
$696$	−11.8887	−	8.63765i	−0.450640	−	0.327409i
$697$	2.53016	+	1.83827i	0.0958367	+	0.0696294i
$698$	−4.64813	+	14.3055i	−0.175934	+	0.541470i
$699$	−13.4615			−0.509162
$700$	0.237745	+	1.54673i	0.00898593	+	0.0584609i
$701$	−15.2493			−0.575957			−0.287978	−	0.957637i	$-0.592983\pi$
$701$	−15.2493			−0.575957			−0.287978	+	0.957637i	$0.592983\pi$
$702$	−0.813877	+	2.50486i	−0.0307178	+	0.0945397i
$703$	−6.68869	−	4.85962i	−0.252269	−	0.183284i
$704$	10.9906	+	7.98513i	0.414223	+	0.300951i
$705$	−6.96543	−	0.564191i	−0.262333	−	0.0212487i
$706$	−9.98152	+	7.25200i	−0.375659	+	0.272932i
$707$	−8.76865			−0.329779
$708$	−0.564451	+	0.410098i	−0.0212134	+	0.0154124i
$709$	14.6878	+	45.2044i	0.551612	+	1.69769i	0.704726	+	0.709480i	$0.251070\pi$
$709$	14.6878	+	45.2044i	0.551612	+	1.69769i	−0.153114	+	0.988209i	$0.548930\pi$
$710$	−6.99665	−	29.4390i	−0.262580	−	1.10483i
$711$	−1.56758	+	4.82451i	−0.0587888	+	0.180933i
$712$	−1.80710	−	5.56169i	−0.0677240	−	0.208433i
$713$	1.39575	+	4.29568i	0.0522713	+	0.160875i
$714$	0.157323	−	0.484190i	0.00588766	−	0.0181204i
$715$	−2.68446	+	6.43925i	−0.100393	+	0.240814i
$716$	−1.20547	−	3.71006i	−0.0450506	−	0.138651i
$717$	19.8564	−	14.4265i	0.741550	−	0.538768i
$718$	37.6157			1.40380
$719$	20.8882	−	15.1762i	0.778998	−	0.565975i	−0.125680	−	0.992071i	$-0.540111\pi$
$719$	20.8882	−	15.1762i	0.778998	−	0.565975i	0.904678	+	0.426096i	$0.140111\pi$
$720$	1.69385	+	7.12703i	0.0631262	+	0.265609i
$721$	7.80614	+	5.67149i	0.290716	+	0.211217i
$722$	−19.2514	−	13.9869i	−0.716461	−	0.520539i
$723$	2.58961	−	7.97000i	0.0963086	−	0.296407i
$724$	1.83247			0.0681033
$725$	−3.71571	−	24.1738i	−0.137998	−	0.897791i
$726$	−11.2126			−0.416137
$727$	−7.19628	+	22.1479i	−0.266895	+	0.821420i	0.724355	+	0.689427i	$0.242138\pi$
$727$	−7.19628	+	22.1479i	−0.266895	+	0.821420i	−0.991251	+	0.131993i	$0.957862\pi$
$728$	−4.92840	−	3.58069i	−0.182659	−	0.132709i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−15.7966	+	9.63062i	−0.584657	+	0.356445i
$731$	−1.17966	+	0.857072i	−0.0436313	+	0.0317000i
$732$	0.0111210			0.000411044
$733$	12.8965	−	9.36987i	0.476344	−	0.346084i	−0.323565	−	0.946206i	$-0.604881\pi$
$733$	12.8965	−	9.36987i	0.476344	−	0.346084i	0.799908	+	0.600122i	$0.204881\pi$
$734$	12.6459	+	38.9202i	0.466770	+	1.43657i
$735$	−1.90922	+	1.16399i	−0.0704228	+	0.0429343i
$736$	0.394901	−	1.21538i	0.0145563	−	0.0447995i
$737$	−0.880867	−	2.71103i	−0.0324471	−	0.0998620i
$738$	−3.20246	−	9.85617i	−0.117884	−	0.362810i
$739$	−15.6871	+	48.2799i	−0.577059	+	1.77601i	0.0519982	+	0.998647i	$0.483441\pi$
$739$	−15.6871	+	48.2799i	−0.577059	+	1.77601i	−0.629058	+	0.777359i	$0.716559\pi$
$740$	−5.32803	−	4.57164i	−0.195862	−	0.168057i
$741$	0.516431	+	1.58941i	0.0189716	+	0.0583885i
$742$	−14.5139	+	10.5450i	−0.532823	+	0.387119i
$743$	20.3765			0.747540			0.373770	−	0.927521i	$-0.378065\pi$
$743$	20.3765			0.747540			0.373770	+	0.927521i	$0.378065\pi$
$744$	−15.0613	+	10.9427i	−0.552173	+	0.401177i
$745$	2.88216	−	6.91348i	0.105594	−	0.253290i
$746$	30.5253	+	22.1779i	1.11761	+	0.811992i
$747$	−2.14925	−	1.56152i	−0.0786369	−	0.0571331i
$748$	−0.0583280	+	0.179515i	−0.00213268	+	0.00656372i
$749$	5.84258			0.213483
$750$	−7.67213	+	12.3295i	−0.280147	+	0.450209i
$751$	24.3899			0.890002			0.445001	−	0.895530i	$-0.353203\pi$
$751$	24.3899			0.890002			0.445001	+	0.895530i	$0.353203\pi$
$752$	3.16388	−	9.73744i	0.115375	−	0.355088i
$753$	−21.4743	−	15.6020i	−0.782566	−	0.568567i
$754$	10.4227	+	7.57252i	0.379572	+	0.275775i
$755$	3.26947	−	7.84253i	0.118988	−	0.285419i
$756$	0.253205	−	0.183964i	0.00920899	−	0.00669072i
$757$	−35.3790			−1.28587			−0.642937	−	0.765919i	$-0.722284\pi$
$757$	−35.3790			−1.28587			−0.642937	+	0.765919i	$0.722284\pi$
$758$	8.99087	−	6.53225i	0.326563	−	0.237262i
$759$	−0.346550	−	1.06657i	−0.0125790	−	0.0387141i
$760$	4.20173	+	3.60523i	0.152413	+	0.130776i
$761$	−3.46758	+	10.6721i	−0.125700	+	0.386864i	−0.994028	−	0.109126i	$-0.965195\pi$
$761$	−3.46758	+	10.6721i	−0.125700	+	0.386864i	0.868328	+	0.495990i	$0.165195\pi$
$762$	−5.26653	−	16.2087i	−0.190786	−	0.587180i
$763$	0.904450	+	2.78361i	0.0327433	+	0.100773i
$764$	0.674514	−	2.07594i	0.0244031	−	0.0751049i
$765$	−0.748352	+	0.456244i	−0.0270567	+	0.0164956i
$766$	3.46497	+	10.6641i	0.125195	+	0.385309i
$767$	3.65702	−	2.65698i	0.132047	−	0.0959380i
$768$	7.31795			0.264064
$769$	−37.0767	+	26.9378i	−1.33702	+	0.971402i	−0.337472	+	0.941336i	$0.609572\pi$
$769$	−37.0767	+	26.9378i	−1.33702	+	0.971402i	−0.999548	+	0.0300664i	$0.990428\pi$
$770$	−3.81546	+	2.32616i	−0.137500	+	0.0838289i
$771$	0.0248400	+	0.0180473i	0.000894592	+	0.000649959i
$772$	−1.61081	−	1.17032i	−0.0579743	−	0.0421208i
$773$	6.98128	−	21.4862i	0.251099	−	0.772804i	−0.743474	−	0.668765i	$-0.766823\pi$
$773$	6.98128	−	21.4862i	0.251099	−	0.772804i	0.994573	−	0.104039i	$-0.0331767\pi$
$774$	4.83181			0.173676
$775$	−30.5804	−	4.98667i	−1.09848	−	0.179126i
$776$	−57.7439			−2.07289
$777$	3.09993	−	9.54061i	0.111209	−	0.342267i
$778$	−22.7962	−	16.5624i	−0.817283	−	0.593791i
$779$	−5.32002	−	3.86522i	−0.190609	−	0.138486i
$780$	0.328135	+	1.38065i	0.0117491	+	0.0494353i
$781$	−12.9687	+	9.42233i	−0.464058	+	0.337158i
$782$	−0.371076			−0.0132697
$783$	−3.95733	+	2.87517i	−0.141424	+	0.102750i
$784$	−1.01237	−	3.11574i	−0.0361559	−	0.111277i
$785$	−17.0803	+	40.9708i	−0.609622	+	1.46231i
$786$	−5.05312	+	15.5519i	−0.180239	+	0.554718i
$787$	9.87216	+	30.3834i	0.351905	+	1.08305i	0.957783	+	0.287494i	$0.0928220\pi$
$787$	9.87216	+	30.3834i	0.351905	+	1.08305i	−0.605878	+	0.795558i	$0.707178\pi$
$788$	−1.89653	−	5.83691i	−0.0675609	−	0.207931i
$789$	8.25511	−	25.4066i	0.293890	−	0.904500i
$790$	−3.40665	−	14.3338i	−0.121203	−	0.509972i
$791$	−3.02222	−	9.30142i	−0.107458	−	0.330721i
$792$	3.73955	−	2.71695i	0.132879	−	0.0965424i
$793$	−0.0720519			−0.00255864
$794$	−11.9585	+	8.68834i	−0.424390	+	0.308338i
$795$	30.7845	+	2.49350i	1.09181	+	0.0884355i
$796$	2.82769	+	2.05444i	0.100225	+	0.0728175i
$797$	37.1922	+	27.0217i	1.31741	+	0.957158i	0.999961	+	0.00888446i	$0.00282805\pi$
$797$	37.1922	+	27.0217i	1.31741	+	0.957158i	0.317454	+	0.948274i	$0.397172\pi$
$798$	−0.330793	+	1.01808i	−0.0117100	+	0.0360395i
$799$	1.22499			0.0433370
$800$	6.17044	+	6.22703i	0.218158	+	0.220159i
$801$	−1.94656			−0.0687784
$802$	4.54967	−	14.0024i	0.160654	−	0.494443i
$803$	7.92927	+	5.76095i	0.279818	+	0.203300i
$804$	−0.469105	−	0.340825i	−0.0165441	−	0.0120200i
$805$	1.23690	+	1.06131i	0.0435951	+	0.0374061i
$806$	13.2040	−	9.59329i	0.465092	−	0.337909i
$807$	−25.3394			−0.891991
$808$	−21.3119	+	15.4840i	−0.749750	+	0.544726i
$809$	−12.1672	−	37.4469i	−0.427777	−	1.31656i	−0.900310	−	0.435249i	$-0.856660\pi$
$809$	−12.1672	−	37.4469i	−0.427777	−	1.31656i	0.472533	−	0.881313i	$-0.343340\pi$
$810$	2.89484	+	0.234479i	0.101714	+	0.00823874i
$811$	−15.3166	+	47.1398i	−0.537840	+	1.65530i	0.199592	+	0.979879i	$0.436038\pi$
$811$	−15.3166	+	47.1398i	−0.537840	+	1.65530i	−0.737432	+	0.675421i	$0.763962\pi$
$812$	−0.473089	−	1.45602i	−0.0166022	−	0.0510962i
$813$	−2.67047	−	8.21887i	−0.0936575	−	0.288248i
$814$	6.19502	−	19.0663i	0.217135	−	0.668274i
$815$	−48.1915	−	3.90345i	−1.68807	−	0.136732i
$816$	−0.396814	−	1.22127i	−0.0138913	−	0.0427529i
$817$	2.48040	−	1.80211i	0.0867781	−	0.0630480i
$818$	−17.1982			−0.601320
$819$	−1.64049	+	1.19189i	−0.0573234	+	0.0416479i
$820$	−4.23778	−	3.63617i	−0.147990	−	0.126980i
$821$	20.8956	+	15.1815i	0.729262	+	0.529840i	0.889330	−	0.457266i	$-0.151171\pi$
$821$	20.8956	+	15.1815i	0.729262	+	0.529840i	−0.160068	+	0.987106i	$0.551171\pi$
$822$	−8.64799	−	6.28313i	−0.301633	−	0.219149i
$823$	−2.48555	+	7.64972i	−0.0866407	+	0.266653i	−0.984985	−	0.172639i	$-0.944771\pi$
$823$	−2.48555	+	7.64972i	−0.0866407	+	0.266653i	0.898344	+	0.439292i	$0.144771\pi$
$824$	28.9875			1.00983
$825$	7.59279	+	1.23814i	0.264347	+	0.0431064i
$826$	2.89543			0.100745
$827$	−14.9073	+	45.8798i	−0.518376	+	1.59540i	0.258678	+	0.965964i	$0.416713\pi$
$827$	−14.9073	+	45.8798i	−0.518376	+	1.59540i	−0.777054	+	0.629434i	$0.783287\pi$
$828$	−0.184555	−	0.134087i	−0.00641374	−	0.00465985i
$829$	−21.1803	−	15.3884i	−0.735621	−	0.534460i	0.155716	−	0.987802i	$-0.450232\pi$
$829$	−21.1803	−	15.3884i	−0.735621	−	0.534460i	−0.891337	+	0.453342i	$0.850232\pi$
$830$	7.69050	+	0.622920i	0.266941	+	0.0216219i
$831$	9.85137	−	7.15744i	0.341740	−	0.248289i
$832$	−17.9040			−0.620708
$833$	0.317108	−	0.230392i	0.0109871	−	0.00798262i
$834$	4.05620	+	12.4837i	0.140455	+	0.432275i
$835$	9.99192	+	42.0418i	0.345785	+	1.45492i
$836$	0.122643	−	0.377455i	0.00424169	−	0.0130546i
$837$	1.91494	+	5.89357i	0.0661899	+	0.203712i
$838$	8.12033	+	24.9918i	0.280512	+	0.863328i
$839$	1.26768	−	3.90152i	0.0437652	−	0.134695i	−0.926786	−	0.375589i	$-0.877440\pi$
$839$	1.26768	−	3.90152i	0.0437652	−	0.134695i	0.970552	+	0.240893i	$0.0774404\pi$
$840$	−2.58489	+	6.20041i	−0.0891872	+	0.213934i
$841$	−1.56761	−	4.82461i	−0.0540556	−	0.166366i
$842$	10.2354	−	7.43643i	0.352734	−	0.256276i
$843$	−10.0011			−0.344457
$844$	−3.64749	+	2.65005i	−0.125552	+	0.0912186i
$845$	4.59551	+	19.3360i	0.158090	+	0.665179i
$846$	−3.28398	−	2.38595i	−0.112906	−	0.0820308i
$847$	−6.98397	−	5.07415i	−0.239972	−	0.174350i
$848$	−13.9831	+	43.0357i	−0.480183	+	1.47785i
$849$	−10.1558			−0.348545
$850$	1.16599	−	2.26279i	0.0399932	−	0.0776131i
$851$	−7.31178			−0.250645
$852$	−1.00764	+	3.10121i	−0.0345213	+	0.106246i
$853$	−9.72197	−	7.06343i	−0.332874	−	0.241847i	0.408775	−	0.912635i	$-0.365956\pi$
$853$	−9.72197	−	7.06343i	−0.332874	−	0.241847i	−0.741649	+	0.670788i	$0.765956\pi$
$854$	−0.0373377	−	0.0271274i	−0.00127767	−	0.000928281i
$855$	1.57351	−	0.959317i	0.0538130	−	0.0328080i
$856$	14.2002	−	10.3170i	0.485352	−	0.352629i
$857$	−28.6061			−0.977167			−0.488584	−	0.872517i	$-0.662486\pi$
$857$	−28.6061			−0.977167			−0.488584	+	0.872517i	$0.662486\pi$
$858$	−3.27842	+	2.38191i	−0.111923	+	0.0813171i
$859$	−13.3591	−	41.1151i	−0.455807	−	1.40283i	−0.870185	−	0.492725i	$-0.836001\pi$
$859$	−13.3591	−	41.1151i	−0.455807	−	1.40283i	0.414378	−	0.910105i	$-0.363999\pi$
$860$	2.22291	−	1.35523i	0.0758005	−	0.0462130i
$861$	2.46561	−	7.58836i	0.0840276	−	0.258610i
$862$	−2.92233	−	8.99402i	−0.0995350	−	0.306337i
$863$	2.66455	+	8.20063i	0.0907022	+	0.279153i	0.986110	−	0.166095i	$-0.0531158\pi$
$863$	2.66455	+	8.20063i	0.0907022	+	0.279153i	−0.895408	+	0.445247i	$0.853116\pi$
$864$	0.541795	−	1.66747i	0.0184322	−	0.0567286i
$865$	−1.09795	−	0.942078i	−0.0373313	−	0.0320316i
$866$	−1.34350	−	4.13488i	−0.0456541	−	0.140509i
$867$	−13.6290	+	9.90204i	−0.462865	+	0.336291i
$868$	−1.93949			−0.0658305
$869$	−6.31444	+	4.58771i	−0.214203	+	0.155627i
$870$	5.46658	−	13.1127i	0.185334	−	0.444564i
$871$	3.03929	+	2.20817i	0.102982	+	0.0748210i
$872$	7.11364	+	5.16836i	0.240898	+	0.175023i
$873$	−5.93959	+	18.2802i	−0.201025	+	0.618690i
$874$	0.780239			0.0263920
$875$	−10.3583	+	4.20770i	−0.350176	+	0.142246i
$876$	1.99370			0.0673610
$877$	−2.77661	+	8.54551i	−0.0937593	+	0.288561i	−0.986928	−	0.161160i	$-0.948477\pi$
$877$	−2.77661	+	8.54551i	−0.0937593	+	0.288561i	0.893169	+	0.449721i	$0.148477\pi$
$878$	24.0180	+	17.4501i	0.810570	+	0.588913i
$879$	−8.42917	−	6.12415i	−0.284309	−	0.206562i
$880$	−4.33706	+	10.4034i	−0.146202	+	0.350698i
$881$	−15.1662	+	11.0189i	−0.510964	+	0.371237i	−0.813189	−	0.582000i	$-0.802270\pi$
$881$	−15.1662	+	11.0189i	−0.510964	+	0.371237i	0.302225	+	0.953236i	$0.402270\pi$
$882$	−1.29885			−0.0437347
$883$	−0.798526	+	0.580163i	−0.0268725	+	0.0195240i	−0.601140	−	0.799143i	$-0.705287\pi$
$883$	−0.798526	+	0.580163i	−0.0268725	+	0.0195240i	0.574268	+	0.818667i	$0.305287\pi$
$884$	−0.0768711	−	0.236585i	−0.00258545	−	0.00795721i
$885$	−3.78299	−	3.24594i	−0.127164	−	0.109111i
$886$	1.09521	−	3.37070i	0.0367942	−	0.113241i
$887$	−8.51846	−	26.2171i	−0.286022	−	0.880285i	−0.986091	−	0.166209i	$-0.946847\pi$
$887$	−8.51846	−	26.2171i	−0.286022	−	0.880285i	0.700069	−	0.714075i	$-0.253153\pi$
$888$	−9.31288	−	28.6621i	−0.312520	−	0.961837i
$889$	4.05475	−	12.4792i	0.135992	−	0.418540i
$890$	4.82709	−	2.94291i	0.161804	−	0.0986465i
$891$	−0.475459	−	1.46331i	−0.0159285	−	0.0490228i
$892$	6.30856	−	4.58344i	0.211226	−	0.153465i
$893$	−2.57571			−0.0861928
$894$	3.51987	−	2.55733i	0.117722	−	0.0855300i
$895$	23.7967	−	14.5080i	0.795435	−	0.484949i
$896$	−6.44105	−	4.67970i	−0.215180	−	0.156338i
$897$	1.19571	+	0.868738i	0.0399238	+	0.0290063i
$898$	2.05863	−	6.33581i	0.0686973	−	0.211429i
$899$	30.3122			1.01097
$900$	1.39756	−	0.704075i	0.0465853	−	0.0234692i
$901$	−5.41398			−0.180366
$902$	4.92736	−	15.1649i	0.164063	−	0.504934i
$903$	3.00959	+	2.18660i	0.100153	+	0.0727653i
$904$	−23.7702	−	17.2701i	−0.790585	−	0.574394i
$905$	3.02721	+	12.7372i	0.100628	+	0.423400i
$906$	3.99287	−	2.90099i	0.132654	−	0.0963791i
$907$	9.04358			0.300287			0.150144	−	0.988664i	$-0.452026\pi$
$907$	9.04358			0.300287			0.150144	+	0.988664i	$0.452026\pi$
$908$	6.94399	−	5.04510i	0.230444	−	0.167428i
$909$	2.70966	+	8.33948i	0.0898738	+	0.276603i
$910$	2.26614	−	5.43582i	0.0751218	−	0.180196i
$911$	6.53978	−	20.1274i	0.216673	−	0.666850i	−0.782358	−	0.622829i	$-0.785983\pi$
$911$	6.53978	−	20.1274i	0.216673	−	0.666850i	0.999031	−	0.0440207i	$-0.0140168\pi$
$912$	0.834357	+	2.56789i	0.0276283	+	0.0850312i
$913$	−1.26311	−	3.88746i	−0.0418029	−	0.128656i
$914$	1.94694	−	5.99207i	0.0643991	−	0.198200i
$915$	0.0183717	+	0.0773006i	0.000607350	+	0.00255548i
$916$	−1.11549	−	3.43312i	−0.0368568	−	0.113433i
$917$	−10.1853	+	7.40006i	−0.336349	+	0.244372i
$918$	−0.509107			−0.0168030
$919$	18.1068	−	13.1553i	0.597288	−	0.433955i	−0.247627	−	0.968855i	$-0.579651\pi$
$919$	18.1068	−	13.1553i	0.597288	−	0.433955i	0.844915	+	0.534900i	$0.179651\pi$
$920$	4.88034	+	0.395302i	0.160900	+	0.0130327i
$921$	−3.85814	−	2.80310i	−0.127130	−	0.0923654i
$922$	−31.3180	−	22.7539i	−1.03140	−	0.749359i
$923$	6.52842	−	20.0924i	0.214886	−	0.661350i
$924$	0.481554			0.0158420
$925$	22.9750	−	44.5866i	0.755413	−	1.46600i
$926$	−11.1043			−0.364911
$927$	2.98168	−	9.17667i	0.0979312	−	0.301401i
$928$	−6.93834	−	5.04100i	−0.227762	−	0.165479i
$929$	18.1074	+	13.1558i	0.594085	+	0.431628i	0.843775	−	0.536698i	$-0.180328\pi$
$929$	18.1074	+	13.1558i	0.594085	+	0.431628i	−0.249689	+	0.968326i	$0.580328\pi$
$930$	−13.6589	−	11.7198i	−0.447892	−	0.384307i
$931$	−0.666763	+	0.484432i	−0.0218523	+	0.0158766i
$932$	−4.21317			−0.138007
$933$	−1.99543	+	1.44976i	−0.0653274	+	0.0474631i
$934$	−2.96251	−	9.11768i	−0.0969364	−	0.298340i
$935$	−1.34414	−	0.108874i	−0.0439581	−	0.00356055i
$936$	−1.88248	+	5.79368i	−0.0615308	+	0.189372i
$937$	5.63356	+	17.3383i	0.184040	+	0.566418i	0.999931	−	0.0117887i	$-0.00375255\pi$
$937$	5.63356	+	17.3383i	0.184040	+	0.566418i	−0.815890	+	0.578207i	$0.803753\pi$
$938$	0.743601	+	2.28857i	0.0242794	+	0.0747244i
$939$	−5.27222	+	16.2262i	−0.172053	+	0.529523i
$940$	−2.18003	−	0.176580i	−0.0711048	−	0.00575940i
$941$	−5.41575	−	16.6680i	−0.176548	−	0.543360i	0.823152	−	0.567821i	$-0.192213\pi$
$941$	−5.41575	−	16.6680i	−0.176548	−	0.543360i	−0.999701	+	0.0244604i	$0.992213\pi$
$942$	−20.8595	+	15.1553i	−0.679639	+	0.493787i
$943$	−5.81561			−0.189382
$944$	5.90835	−	4.29267i	0.192301	−	0.139715i
$945$	1.69700	+	1.45609i	0.0552034	+	0.0473665i
$946$	6.01448	+	4.36977i	0.195548	+	0.142074i
$947$	41.0856	+	29.8504i	1.33510	+	0.970009i	0.999609	+	0.0279668i	$0.00890325\pi$
$947$	41.0856	+	29.8504i	1.33510	+	0.970009i	0.335494	+	0.942042i	$0.391097\pi$
$948$	−0.490619	+	1.50997i	−0.0159346	+	0.0490415i
$949$	−12.9170			−0.419304
$950$	−2.45166	+	4.75783i	−0.0795423	+	0.154365i
$951$	28.2732			0.916821
$952$	0.363884	−	1.11992i	0.0117936	−	0.0362968i
$953$	48.6752	+	35.3646i	1.57674	+	1.14557i	0.920311	+	0.391188i	$0.127936\pi$
$953$	48.6752	+	35.3646i	1.57674	+	1.14557i	0.656434	+	0.754384i	$0.272064\pi$
$954$	14.5139	+	10.5450i	0.469906	+	0.341407i
$955$	15.5439	+	1.25903i	0.502987	+	0.0407413i
$956$	6.21463	−	4.51519i	0.200996	−	0.146032i
$957$	−7.52619			−0.243287
$958$	−15.4328	+	11.2126i	−0.498612	+	0.362263i
$959$	−2.54319	−	7.82714i	−0.0821240	−	0.252752i
$960$	4.56513	+	19.2082i	0.147339	+	0.619941i
$961$	2.28708	−	7.03892i	0.0737769	−	0.227062i
$962$	8.16448	+	25.1277i	0.263234	+	0.810150i
$963$	−1.80546	−	5.55662i	−0.0581800	−	0.179060i
$964$	0.810493	−	2.49444i	0.0261042	−	0.0803405i
$965$	5.47371	−	13.1299i	0.176205	−	0.422665i
$966$	0.292547	+	0.900368i	0.00941256	+	0.0289689i
$967$	18.5199	−	13.4555i	0.595559	−	0.432699i	−0.248741	−	0.968570i	$-0.580017\pi$
$967$	18.5199	−	13.4555i	0.595559	−	0.432699i	0.844300	+	0.535871i	$0.180017\pi$
$968$	−25.9344			−0.833564
$969$	−0.261349	+	0.189881i	−0.00839574	+	0.00609986i
$970$	−12.9079	−	54.3110i	−0.414447	−	1.74382i
$971$	48.2057	+	35.0235i	1.54699	+	1.12396i	0.945752	+	0.324890i	$0.105327\pi$
$971$	48.2057	+	35.0235i	1.54699	+	1.12396i	0.601242	+	0.799067i	$0.294673\pi$
$972$	−0.253205	−	0.183964i	−0.00812156	−	0.00590066i
$973$	−3.12291	+	9.61133i	−0.100116	+	0.308125i
$974$	−23.6945			−0.759221
$975$	−9.05465	+	4.56163i	−0.289981	+	0.146089i
$976$	−0.116408			−0.00372614
$977$	2.27432	−	6.99964i	0.0727620	−	0.223938i	−0.908061	−	0.418837i	$-0.862438\pi$
$977$	2.27432	−	6.99964i	0.0727620	−	0.223938i	0.980823	+	0.194899i	$0.0624378\pi$
$978$	−22.7208	−	16.5076i	−0.726530	−	0.527855i
$979$	−2.42302	−	1.76042i	−0.0774399	−	0.0562634i
$980$	−0.597547	+	0.364304i	−0.0190879	+	0.0116373i
$981$	2.36788	−	1.72037i	0.0756006	−	0.0549271i
$982$	−38.0317			−1.21364
$983$	14.4520	−	10.5000i	0.460949	−	0.334899i	−0.332955	−	0.942943i	$-0.608046\pi$
$983$	14.4520	−	10.5000i	0.460949	−	0.334899i	0.793903	+	0.608044i	$0.208046\pi$
$984$	−7.40723	−	22.7971i	−0.236134	−	0.726745i
$985$	37.4385	−	22.8249i	1.19289	−	0.727263i
$986$	−0.769550	+	2.36843i	−0.0245075	+	0.0754262i
$987$	−0.965751	−	2.97228i	−0.0307402	−	0.0946086i
$988$	0.161632	+	0.497453i	0.00514220	+	0.0158261i
$989$	0.837887	−	2.57875i	0.0266433	−	0.0819996i
$990$	3.39135	+	2.90990i	0.107784	+	0.0924827i
$991$	−11.1182	−	34.2182i	−0.353181	−	1.08698i	−0.957057	−	0.289900i	$-0.906378\pi$
$991$	−11.1182	−	34.2182i	−0.353181	−	1.08698i	0.603876	−	0.797078i	$-0.293622\pi$
$992$	−8.78987	+	6.38621i	−0.279079	+	0.202763i
$993$	30.9618			0.982542
$994$	10.9478	−	7.95405i	0.347244	−	0.252287i
$995$	−9.60879	+	23.0487i	−0.304619	+	0.730694i
$996$	−0.672670	−	0.488723i	−0.0213144	−	0.0154858i
$997$	−16.4110	−	11.9233i	−0.519741	−	0.377614i	0.296766	−	0.954950i	$-0.404092\pi$
$997$	−16.4110	−	11.9233i	−0.519741	−	0.377614i	−0.816506	+	0.577337i	$0.804092\pi$
$998$	−1.02552	+	3.15622i	−0.0324622	+	0.0999083i
$999$	−10.0316			−0.317385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.b.421.2	yes	20
25.6	even	5	inner	525.2.n.b.106.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.b.106.2	✓	20	25.6	even	5	inner
525.2.n.b.421.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.401368 + 1.23528i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.253205 + 0.183964i) q^{4} +(-0.860419 + 2.06390i) q^{5} +(-1.05079 + 0.763447i) q^{6} -1.00000 q^{7} +(-2.43047 + 1.76584i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.401368 + 1.23528i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.253205 + 0.183964i) q^{4} +(-0.860419 + 2.06390i) q^{5} +(-1.05079 + 0.763447i) q^{6} -1.00000 q^{7} +(-2.43047 + 1.76584i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-2.20416 - 1.89124i) q^{10} +(-0.475459 + 1.46331i) q^{11} +(0.0967158 + 0.297661i) q^{12} +(-0.626612 - 1.92851i) q^{13} +(0.401368 - 1.23528i) q^{14} +(-1.90922 + 1.16399i) q^{15} +(-1.01237 - 3.11574i) q^{16} +(0.317108 - 0.230392i) q^{17} -1.29885 q^{18} +(-0.666763 + 0.484432i) q^{19} +(-0.597547 + 0.364304i) q^{20} +(-0.809017 - 0.587785i) q^{21} +(-1.61677 - 1.17465i) q^{22} +(-0.225235 + 0.693202i) q^{23} -3.00422 q^{24} +(-3.51936 - 3.55164i) q^{25} +2.63376 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.253205 - 0.183964i) q^{28} +(3.95733 + 2.87517i) q^{29} +(-0.671554 - 2.82562i) q^{30} +(5.01337 - 3.64243i) q^{31} -1.75329 q^{32} +(-1.24477 + 0.904376i) q^{33} +(0.157323 + 0.484190i) q^{34} +(0.860419 - 2.06390i) q^{35} +(-0.0967158 + 0.297661i) q^{36} +(3.09993 + 9.54061i) q^{37} +(-0.330793 - 1.01808i) q^{38} +(0.626612 - 1.92851i) q^{39} +(-1.55329 - 6.53560i) q^{40} +(2.46561 + 7.58836i) q^{41} +(1.05079 - 0.763447i) q^{42} -3.72006 q^{43} +(-0.389586 + 0.283051i) q^{44} +(-2.22877 - 0.180527i) q^{45} +(-0.765899 - 0.556458i) q^{46} +(2.52837 + 1.83697i) q^{47} +(1.01237 - 3.11574i) q^{48} +1.00000 q^{49} +(5.79983 - 2.92189i) q^{50} +0.391967 q^{51} +(0.196116 - 0.603584i) q^{52} +(-11.1744 - 8.11869i) q^{53} +(-1.05079 - 0.763447i) q^{54} +(-2.61103 - 2.24036i) q^{55} +(2.43047 - 1.76584i) q^{56} -0.824165 q^{57} +(-5.14000 + 3.73443i) q^{58} +(0.688868 + 2.12012i) q^{59} +(-0.697558 - 0.0565013i) q^{60} +(0.0109802 - 0.0337937i) q^{61} +(2.48722 + 7.65489i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(2.72845 - 8.39729i) q^{64} +(4.51941 + 0.366066i) q^{65} +(-0.617551 - 1.90063i) q^{66} +(-1.49884 + 1.08897i) q^{67} +0.122677 q^{68} +(-0.589673 + 0.428423i) q^{69} +(2.20416 + 1.89124i) q^{70} +(8.42883 + 6.12390i) q^{71} +(-2.43047 - 1.76584i) q^{72} +(1.96847 - 6.05831i) q^{73} -13.0296 q^{74} +(-0.759621 - 4.94196i) q^{75} -0.257946 q^{76} +(0.475459 - 1.46331i) q^{77} +(2.13076 + 1.54809i) q^{78} +(4.10397 + 2.98171i) q^{79} +(7.30164 + 0.591423i) q^{80} +(-0.809017 + 0.587785i) q^{81} -10.3634 q^{82} +(-2.14925 + 1.56152i) q^{83} +(-0.0967158 - 0.297661i) q^{84} +(0.202661 + 0.852712i) q^{85} +(1.49311 - 4.59533i) q^{86} +(1.51157 + 4.65213i) q^{87} +(-1.42838 - 4.39611i) q^{88} +(-0.601521 + 1.85129i) q^{89} +(1.11756 - 2.68070i) q^{90} +(0.626612 + 1.92851i) q^{91} +(-0.184555 + 0.134087i) q^{92} +6.19687 q^{93} +(-3.28398 + 2.38595i) q^{94} +(-0.426123 - 1.79295i) q^{95} +(-1.41844 - 1.03056i) q^{96} +(15.5501 + 11.2978i) q^{97} +(-0.401368 + 1.23528i) q^{98} -1.53862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9 - 15 * q^10 + 12 * q^11 + 5 * q^12 - 17 * q^13 + 2 * q^14 + 15 * q^15 - 28 * q^16 - 9 * q^17 - 2 * q^18 - 9 * q^19 - 20 * q^20 - 5 * q^21 - 21 * q^22 + 7 * q^23 + 6 * q^24 - 15 * q^25 - 20 * q^26 + 5 * q^27 + 28 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^35 - 5 * q^36 - 5 * q^37 - 6 * q^38 + 17 * q^39 - 10 * q^40 + 11 * q^41 + 3 * q^42 + 28 * q^43 - 17 * q^44 + 5 * q^45 - 43 * q^46 - 24 * q^47 + 28 * q^48 + 20 * q^49 + 10 * q^50 - 36 * q^51 - 9 * q^52 - 26 * q^53 - 3 * q^54 - 25 * q^55 - 4 * q^56 + 24 * q^57 - 16 * q^58 + 64 * q^59 + 5 * q^60 + 8 * q^61 + 27 * q^62 + 5 * q^63 + 26 * q^64 + 25 * q^65 - 4 * q^66 - 3 * q^67 + 80 * q^68 - 2 * q^69 + 15 * q^70 + 19 * q^71 + 4 * q^72 + 31 * q^73 + 8 * q^74 - 5 * q^75 - 72 * q^76 - 12 * q^77 - 30 * q^78 + 43 * q^79 - 25 * q^80 - 5 * q^81 - 6 * q^82 + 32 * q^83 - 5 * q^84 + 35 * q^85 + 53 * q^86 + 17 * q^87 - 61 * q^88 - 47 * q^89 + 10 * q^90 + 17 * q^91 + 41 * q^92 + 4 * q^93 + 12 * q^94 - 40 * q^95 - 6 * q^96 - 45 * q^97 - 2 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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