LMFDB - Embedded newform 637.2.bl.b.625.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.13
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.b.53.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.296505 + 0.202154i) q^{2} +(1.23401 - 1.14499i) q^{3} +(-0.683633 + 1.74187i) q^{4} +(1.06645 + 0.328957i) q^{5} +(-0.134425 + 0.588954i) q^{6} +(2.51862 + 0.810284i) q^{7} +(-0.309133 - 1.35440i) q^{8} +(-0.0124224 + 0.165766i) q^{9} +O(q^{10})$	\(q+(-0.296505 + 0.202154i) q^{2} +(1.23401 - 1.14499i) q^{3} +(-0.683633 + 1.74187i) q^{4} +(1.06645 + 0.328957i) q^{5} +(-0.134425 + 0.588954i) q^{6} +(2.51862 + 0.810284i) q^{7} +(-0.309133 - 1.35440i) q^{8} +(-0.0124224 + 0.165766i) q^{9} +(-0.382709 + 0.118050i) q^{10} +(0.480500 + 6.41182i) q^{11} +(1.15081 + 2.93223i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(-0.910585 + 0.268895i) q^{14} +(1.69266 - 0.815143i) q^{15} +(-2.37794 - 2.20641i) q^{16} +(-6.27369 - 0.945606i) q^{17} +(-0.0298268 - 0.0516616i) q^{18} +(-0.779506 + 1.35014i) q^{19} +(-1.30206 + 1.63274i) q^{20} +(4.03575 - 1.88390i) q^{21} +(-1.43864 - 1.80400i) q^{22} +(5.97501 - 0.900588i) q^{23} +(-1.93224 - 1.31738i) q^{24} +(-3.10208 - 2.11497i) q^{25} +(0.354853 - 0.0534855i) q^{26} +(3.32318 + 4.16714i) q^{27} +(-3.13322 + 3.83317i) q^{28} +(2.37316 - 2.97585i) q^{29} +(-0.337098 + 0.583872i) q^{30} +(2.08186 + 3.60589i) q^{31} +(3.89853 + 0.587609i) q^{32} +(7.93441 + 7.36206i) q^{33} +(2.05134 - 0.987872i) q^{34} +(2.41944 + 1.69265i) q^{35} +(-0.280250 - 0.134961i) q^{36} +(-3.54457 - 9.03142i) q^{37} +(-0.0418092 - 0.557904i) q^{38} +(-1.60859 + 0.496185i) q^{39} +(0.115864 - 1.54609i) q^{40} +(1.28397 + 5.62545i) q^{41} +(-0.815784 + 1.37443i) q^{42} +(-1.79284 + 7.85494i) q^{43} +(-11.4970 - 3.54637i) q^{44} +(-0.0677778 + 0.172695i) q^{45} +(-1.58956 + 1.47490i) q^{46} +(7.59796 - 5.18020i) q^{47} -5.46071 q^{48} +(5.68688 + 4.08159i) q^{49} +1.34733 q^{50} +(-8.82447 + 6.01642i) q^{51} +(1.37170 - 1.27275i) q^{52} +(3.49245 - 8.89862i) q^{53} +(-1.82774 - 0.563784i) q^{54} +(-1.59679 + 6.99597i) q^{55} +(0.318860 - 3.66170i) q^{56} +(0.583986 + 2.55861i) q^{57} +(-0.102075 + 1.36210i) q^{58} +(3.91641 - 1.20805i) q^{59} +(0.262712 + 3.50565i) q^{60} +(1.70007 + 4.33172i) q^{61} +(-1.34622 - 0.648308i) q^{62} +(-0.165605 + 0.407435i) q^{63} +(4.57058 - 2.20107i) q^{64} +(-0.818112 - 0.759097i) q^{65} +(-3.84086 - 0.578916i) q^{66} +(-0.455470 - 0.788898i) q^{67} +(5.93602 - 10.2815i) q^{68} +(6.34203 - 7.95265i) q^{69} +(-1.05955 - 0.0127796i) q^{70} +(-6.92638 - 8.68541i) q^{71} +(0.228353 - 0.0344187i) q^{72} +(6.64006 + 4.52712i) q^{73} +(2.87672 + 1.96131i) q^{74} +(-6.24960 + 0.941976i) q^{75} +(-1.81888 - 2.28080i) q^{76} +(-3.98520 + 16.5383i) q^{77} +(0.376650 - 0.472304i) q^{78} +(3.13622 - 5.43209i) q^{79} +(-1.81015 - 3.13528i) q^{80} +(8.37903 + 1.26294i) q^{81} +(-1.51791 - 1.40841i) q^{82} +(11.0683 - 5.33020i) q^{83} +(0.522527 + 8.31765i) q^{84} +(-6.37953 - 3.07222i) q^{85} +(-1.05632 - 2.69146i) q^{86} +(-0.478824 - 6.38946i) q^{87} +(8.53563 - 2.63289i) q^{88} +(0.125789 - 1.67853i) q^{89} +(-0.0148145 - 0.0649064i) q^{90} +(-1.91763 - 1.82283i) q^{91} +(-2.51601 + 11.0234i) q^{92} +(6.69773 + 2.06598i) q^{93} +(-1.20564 + 3.07191i) q^{94} +(-1.27545 + 1.18344i) q^{95} +(5.48362 - 3.73867i) q^{96} -12.3898 q^{97} +(-2.51130 - 0.0605882i) q^{98} -1.06883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.296505	+	0.202154i	−0.209661	+	0.142944i	−0.663598	−	0.748089i	$-0.730971\pi$
$2$	−0.296505	+	0.202154i	−0.209661	+	0.142944i	0.453937	+	0.891034i	$0.350019\pi$
$3$	1.23401	−	1.14499i	0.712453	−	0.661060i	−0.238235	−	0.971207i	$-0.576569\pi$
$3$	1.23401	−	1.14499i	0.712453	−	0.661060i	0.950688	+	0.310148i	$0.100378\pi$
$4$	−0.683633	+	1.74187i	−0.341816	+	0.870934i
$5$	1.06645	+	0.328957i	0.476932	+	0.147114i	0.523896	−	0.851782i	$-0.324478\pi$
$5$	1.06645	+	0.328957i	0.476932	+	0.147114i	−0.0469632	+	0.998897i	$0.514954\pi$
$6$	−0.134425	+	0.588954i	−0.0548787	+	0.240439i
$7$	2.51862	+	0.810284i	0.951948	+	0.306258i
$7$	2.51862	+	0.810284i	0.951948	+	0.306258i
$8$	−0.309133	−	1.35440i	−0.109295	−	0.478852i
$9$	−0.0124224	+	0.165766i	−0.00414081	+	0.0552552i
$10$	−0.382709	+	0.118050i	−0.121023	+	0.0373307i
$11$	0.480500	+	6.41182i	0.144876	+	1.93324i	0.317517	+	0.948253i	$0.397151\pi$
$11$	0.480500	+	6.41182i	0.144876	+	1.93324i	−0.172641	+	0.984985i	$0.555230\pi$
$12$	1.15081	+	2.93223i	0.332211	+	0.846461i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$14$	−0.910585	+	0.268895i	−0.243364	+	0.0718652i
$15$	1.69266	−	0.815143i	0.437043	−	0.210469i
$16$	−2.37794	−	2.20641i	−0.594486	−	0.551603i
$17$	−6.27369	−	0.945606i	−1.52159	−	0.229343i	−0.665591	−	0.746316i	$-0.731821\pi$
$17$	−6.27369	−	0.945606i	−1.52159	−	0.229343i	−0.856002	+	0.516973i	$0.827059\pi$
$18$	−0.0298268	−	0.0516616i	−0.00703025	−	0.0121768i
$19$	−0.779506	+	1.35014i	−0.178831	+	0.309744i	−0.941480	−	0.337068i	$-0.890565\pi$
$19$	−0.779506	+	1.35014i	−0.178831	+	0.309744i	0.762649	+	0.646812i	$0.223898\pi$
$20$	−1.30206	+	1.63274i	−0.291150	+	0.365091i
$21$	4.03575	−	1.88390i	0.880674	−	0.411100i
$22$	−1.43864	−	1.80400i	−0.306720	−	0.384615i
$23$	5.97501	−	0.900588i	1.24588	−	0.187786i	0.507189	−	0.861835i	$-0.330685\pi$
$23$	5.97501	−	0.900588i	1.24588	−	0.187786i	0.738686	+	0.674049i	$0.235446\pi$
$24$	−1.93224	−	1.31738i	−0.394418	−	0.268909i
$25$	−3.10208	−	2.11497i	−0.620417	−	0.422993i
$26$	0.354853	−	0.0534855i	0.0695924	−	0.0104894i
$27$	3.32318	+	4.16714i	0.639547	+	0.801966i
$28$	−3.13322	+	3.83317i	−0.592123	+	0.724400i
$29$	2.37316	−	2.97585i	0.440685	−	0.552602i	−0.511038	−	0.859558i	$-0.670739\pi$
$29$	2.37316	−	2.97585i	0.440685	−	0.552602i	0.951724	+	0.306956i	$0.0993105\pi$
$30$	−0.337098	+	0.583872i	−0.0615455	+	0.106600i
$31$	2.08186	+	3.60589i	0.373913	+	0.647636i	0.990164	−	0.139914i	$-0.0446825\pi$
$31$	2.08186	+	3.60589i	0.373913	+	0.647636i	−0.616251	+	0.787550i	$0.711349\pi$
$32$	3.89853	+	0.587609i	0.689170	+	0.103876i
$33$	7.93441	+	7.36206i	1.38120	+	1.28157i
$34$	2.05134	−	0.987872i	0.351801	−	0.169419i
$35$	2.41944	+	1.69265i	0.408960	+	0.286110i
$36$	−0.280250	−	0.134961i	−0.0467083	−	0.0224935i
$37$	−3.54457	−	9.03142i	−0.582724	−	1.48476i	−0.852967	−	0.521965i	$-0.825199\pi$
$37$	−3.54457	−	9.03142i	−0.582724	−	1.48476i	0.270243	−	0.962792i	$-0.412896\pi$
$38$	−0.0418092	−	0.557904i	−0.00678234	−	0.0905040i
$39$	−1.60859	+	0.496185i	−0.257581	+	0.0794532i
$40$	0.115864	−	1.54609i	0.0183197	−	0.244459i
$41$	1.28397	+	5.62545i	0.200523	+	0.878548i	0.970619	+	0.240620i	$0.0773509\pi$
$41$	1.28397	+	5.62545i	0.200523	+	0.878548i	−0.770096	+	0.637927i	$0.779792\pi$
$42$	−0.815784	+	1.37443i	−0.125878	+	0.212079i
$43$	−1.79284	+	7.85494i	−0.273405	+	1.19787i	0.632559	+	0.774512i	$0.282005\pi$
$43$	−1.79284	+	7.85494i	−0.273405	+	1.19787i	−0.905964	+	0.423354i	$0.860853\pi$
$44$	−11.4970	−	3.54637i	−1.73324	−	0.534635i
$45$	−0.0677778	+	0.172695i	−0.0101037	+	0.0257438i
$46$	−1.58956	+	1.47490i	−0.234368	+	0.217462i
$47$	7.59796	−	5.18020i	1.10828	−	0.755610i	0.136295	−	0.990668i	$-0.456480\pi$
$47$	7.59796	−	5.18020i	1.10828	−	0.755610i	0.971981	+	0.235058i	$0.0755280\pi$
$48$	−5.46071			−0.788186
$49$	5.68688	+	4.08159i	0.812412	+	0.583084i
$50$	1.34733			0.190541
$51$	−8.82447	+	6.01642i	−1.23567	+	0.842468i
$52$	1.37170	−	1.27275i	0.190221	−	0.176499i
$53$	3.49245	−	8.89862i	0.479725	−	1.22232i	−0.462284	−	0.886732i	$-0.652970\pi$
$53$	3.49245	−	8.89862i	0.479725	−	1.22232i	0.942009	−	0.335588i	$-0.108935\pi$
$54$	−1.82774	−	0.563784i	−0.248724	−	0.0767213i
$55$	−1.59679	+	6.99597i	−0.215311	+	0.943337i
$56$	0.318860	−	3.66170i	0.0426094	−	0.489315i
$57$	0.583986	+	2.55861i	0.0773509	+	0.338896i
$58$	−0.102075	+	1.36210i	−0.0134031	+	0.178852i
$59$	3.91641	−	1.20805i	0.509874	−	0.157275i	−0.0291348	−	0.999575i	$-0.509275\pi$
$59$	3.91641	−	1.20805i	0.509874	−	0.157275i	0.539009	+	0.842300i	$0.318799\pi$
$60$	0.262712	+	3.50565i	0.0339160	+	0.452578i
$61$	1.70007	+	4.33172i	0.217672	+	0.554620i	0.997445	−	0.0714433i	$-0.0227605\pi$
$61$	1.70007	+	4.33172i	0.217672	+	0.554620i	−0.779772	+	0.626063i	$0.784665\pi$
$62$	−1.34622	−	0.648308i	−0.170971	−	0.0823352i
$63$	−0.165605	+	0.407435i	−0.0208642	+	0.0513320i
$64$	4.57058	−	2.20107i	0.571322	−	0.275134i
$65$	−0.818112	−	0.759097i	−0.101474	−	0.0941544i
$66$	−3.84086	−	0.578916i	−0.472777	−	0.0712597i
$67$	−0.455470	−	0.788898i	−0.0556446	−	0.0963792i	0.836861	−	0.547415i	$-0.184388\pi$
$67$	−0.455470	−	0.788898i	−0.0556446	−	0.0963792i	−0.892506	+	0.451036i	$0.851055\pi$
$68$	5.93602	−	10.2815i	0.719848	−	1.24681i
$69$	6.34203	−	7.95265i	0.763490	−	0.957387i
$70$	−1.05955	−	0.0127796i	−0.126641	−	0.00152746i
$71$	−6.92638	−	8.68541i	−0.822011	−	1.03077i	−0.998916	−	0.0465409i	$-0.985180\pi$
$71$	−6.92638	−	8.68541i	−0.822011	−	1.03077i	0.176906	−	0.984228i	$-0.443391\pi$
$72$	0.228353	−	0.0344187i	0.0269117	−	0.00405628i
$73$	6.64006	+	4.52712i	0.777160	+	0.529859i	0.885714	−	0.464232i	$-0.153669\pi$
$73$	6.64006	+	4.52712i	0.777160	+	0.529859i	−0.108553	+	0.994091i	$0.534622\pi$
$74$	2.87672	+	1.96131i	0.334412	+	0.227998i
$75$	−6.24960	+	0.941976i	−0.721642	+	0.108770i
$76$	−1.81888	−	2.28080i	−0.208640	−	0.261626i
$77$	−3.98520	+	16.5383i	−0.454156	+	1.88471i
$78$	0.376650	−	0.472304i	0.0426472	−	0.0534779i
$79$	3.13622	−	5.43209i	0.352852	−	0.611157i	−0.633896	−	0.773418i	$-0.718545\pi$
$79$	3.13622	−	5.43209i	0.352852	−	0.611157i	0.986748	+	0.162261i	$0.0518786\pi$
$80$	−1.81015	−	3.13528i	−0.202381	−	0.350534i
$81$	8.37903	+	1.26294i	0.931004	+	0.140326i
$82$	−1.51791	−	1.40841i	−0.167625	−	0.155533i
$83$	11.0683	−	5.33020i	1.21490	−	0.585065i	0.287013	−	0.957927i	$-0.407338\pi$
$83$	11.0683	−	5.33020i	1.21490	−	0.585065i	0.927887	+	0.372862i	$0.121623\pi$
$84$	0.522527	+	8.31765i	0.0570124	+	0.907530i
$85$	−6.37953	−	3.07222i	−0.691957	−	0.333229i
$86$	−1.05632	−	2.69146i	−0.113906	−	0.290227i
$87$	−0.478824	−	6.38946i	−0.0513353	−	0.685022i
$88$	8.53563	−	2.63289i	0.909901	−	0.280667i
$89$	0.125789	−	1.67853i	0.0133336	−	0.177924i	−0.986561	−	0.163394i	$-0.947756\pi$
$89$	0.125789	−	1.67853i	0.0133336	−	0.177924i	0.999894	−	0.0145300i	$-0.00462520\pi$
$90$	−0.0148145	−	0.0649064i	−0.00156158	−	0.00684174i
$91$	−1.91763	−	1.82283i	−0.201022	−	0.191084i
$92$	−2.51601	+	11.0234i	−0.262312	+	1.14926i
$93$	6.69773	+	2.06598i	0.694522	+	0.214232i
$94$	−1.20564	+	3.07191i	−0.124352	+	0.316843i
$95$	−1.27545	+	1.18344i	−0.130858	+	0.121419i
$96$	5.48362	−	3.73867i	0.559669	−	0.381576i
$97$	−12.3898			−1.25800			−0.628999	−	0.777406i	$-0.716535\pi$
$97$	−12.3898			−1.25800			−0.628999	+	0.777406i	$0.716535\pi$
$98$	−2.51130	−	0.0605882i	−0.253679	−	0.00612033i
$99$	−1.06883			−0.107421
$100$	5.80468	−	3.95756i	0.580468	−	0.395756i
$101$	−10.5100	+	9.75188i	−1.04579	+	0.970348i	−0.999591	−	0.0285843i	$-0.990900\pi$
$101$	−10.5100	+	9.75188i	−1.04579	+	0.970348i	−0.0461952	+	0.998932i	$0.514710\pi$
$102$	1.40026	−	3.56780i	0.138646	−	0.353265i
$103$	3.82090	+	1.17859i	0.376485	+	0.116130i	0.477222	−	0.878783i	$-0.341644\pi$
$103$	3.82090	+	1.17859i	0.376485	+	0.116130i	−0.100737	+	0.994913i	$0.532120\pi$
$104$	−0.309133	+	1.35440i	−0.0303130	+	0.132810i
$105$	4.92367	−	0.681498i	0.480501	−	0.0665074i
$106$	0.763360	+	3.34450i	0.0741441	+	0.324846i
$107$	1.26086	−	16.8251i	0.121892	−	1.62654i	−0.516122	−	0.856515i	$-0.672625\pi$
$107$	1.26086	−	16.8251i	0.121892	−	1.62654i	0.638014	−	0.770024i	$-0.279756\pi$
$108$	−9.53044	+	2.93975i	−0.917067	+	0.282878i
$109$	−0.638433	−	8.51929i	−0.0611507	−	0.816000i	−0.940494	−	0.339811i	$-0.889637\pi$
$109$	−0.638433	−	8.51929i	−0.0611507	−	0.816000i	0.879343	−	0.476189i	$-0.157982\pi$
$110$	−0.940807	−	2.39714i	−0.0897024	−	0.228558i
$111$	−14.7149	−	7.08633i	−1.39668	−	0.672604i
$112$	−4.20132	−	7.48392i	−0.396987	−	0.707164i
$113$	5.68092	−	2.73579i	0.534416	−	0.257361i	−0.147155	−	0.989113i	$-0.547012\pi$
$113$	5.68092	−	2.73579i	0.534416	−	0.257361i	0.681571	+	0.731752i	$0.261297\pi$
$114$	−0.690387	−	0.640586i	−0.0646607	−	0.0599964i
$115$	6.66832	+	1.00509i	0.621824	+	0.0937249i
$116$	3.56117	+	6.16813i	0.330646	+	0.572696i
$117$	0.0831153	−	0.143960i	0.00768401	−	0.0133091i
$118$	−0.917024	+	1.14991i	−0.0844189	+	0.105858i
$119$	−15.0348	−	7.46509i	−1.37824	−	0.684323i
$120$	−1.62729	−	2.04055i	−0.148550	−	0.186276i
$121$	−30.0035	+	4.52229i	−2.72759	+	0.411118i
$122$	−1.37975	−	0.940700i	−0.124917	−	0.0851670i
$123$	8.02551	+	5.47170i	0.723636	+	0.493367i
$124$	−7.70421	+	1.16122i	−0.691858	+	0.104281i
$125$	−6.09168	−	7.63872i	−0.544856	−	0.683228i
$126$	−0.0332619	−	0.154284i	−0.00296320	−	0.0137447i
$127$	−1.56798	+	1.96619i	−0.139136	+	0.174471i	−0.846517	−	0.532361i	$-0.821305\pi$
$127$	−1.56798	+	1.96619i	−0.139136	+	0.174471i	0.707382	+	0.706832i	$0.249876\pi$
$128$	−4.85281	+	8.40532i	−0.428932	+	0.742932i
$129$	6.78145	+	11.7458i	0.597073	+	1.03416i
$130$	0.396029	+	0.0596917i	0.0347340	+	0.00523531i
$131$	−9.51529	−	8.82890i	−0.831355	−	0.771384i	0.144570	−	0.989495i	$-0.453820\pi$
$131$	−9.51529	−	8.82890i	−0.831355	−	0.771384i	−0.975924	+	0.218110i	$0.930011\pi$
$132$	−18.2480	+	8.78775i	−1.58828	+	0.764876i
$133$	−3.05728	+	2.76888i	−0.265100	+	0.240092i
$134$	0.294528	+	0.141837i	0.0254433	+	0.0122529i
$135$	2.17321	+	5.53724i	0.187040	+	0.476570i
$136$	0.658674	+	8.78939i	0.0564808	+	0.753684i
$137$	3.64010	−	1.12282i	0.310995	−	0.0959292i	−0.135329	−	0.990801i	$-0.543209\pi$
$137$	3.64010	−	1.12282i	0.310995	−	0.0959292i	0.446324	+	0.894872i	$0.352733\pi$
$138$	−0.272785	+	3.64007i	−0.0232210	+	0.309863i
$139$	5.02663	+	22.0231i	0.426353	+	1.86798i	0.492732	+	0.870181i	$0.335998\pi$
$139$	5.02663	+	22.0231i	0.426353	+	1.86798i	−0.0663788	+	0.997794i	$0.521145\pi$
$140$	−4.60238	+	3.05720i	−0.388972	+	0.258380i
$141$	3.44465	−	15.0920i	0.290092	−	1.27097i
$142$	3.80950	+	1.17507i	0.319686	+	0.0986100i
$143$	2.34907	−	5.98533i	0.196439	−	0.500519i
$144$	0.395287	−	0.366773i	0.0329406	−	0.0305644i
$145$	3.50979	−	2.39294i	0.291473	−	0.198723i
$146$	−2.88398			−0.238680
$147$	11.6910	−	1.47471i	0.964259	−	0.121632i
$148$	18.1547			1.49231
$149$	13.7576	−	9.37975i	1.12706	−	0.768419i	0.151570	−	0.988446i	$-0.451567\pi$
$149$	13.7576	−	9.37975i	1.12706	−	0.768419i	0.975494	+	0.220027i	$0.0706146\pi$
$150$	1.66261	−	1.54268i	0.135752	−	0.125959i
$151$	1.24658	−	3.17622i	0.101445	−	0.258477i	−0.871136	−	0.491042i	$-0.836616\pi$
$151$	1.24658	−	3.17622i	0.101445	−	0.258477i	0.972581	+	0.232564i	$0.0747116\pi$
$152$	2.06960	+	0.638388i	0.167867	+	0.0517801i
$153$	0.234684	−	1.02822i	0.0189730	−	0.0831263i
$154$	−2.16164	−	5.70930i	−0.174190	−	0.460069i
$155$	1.03402	+	4.53035i	0.0830548	+	0.363887i
$156$	0.235398	−	3.14116i	0.0188469	−	0.251494i
$157$	6.11045	−	1.88483i	0.487667	−	0.150425i	−0.0411640	−	0.999152i	$-0.513107\pi$
$157$	6.11045	−	1.88483i	0.487667	−	0.150425i	0.528831	+	0.848727i	$0.322630\pi$
$158$	0.168212	+	2.24464i	0.0133823	+	0.178574i
$159$	−5.87913	−	14.9798i	−0.466245	−	1.18797i
$160$	3.96431	+	1.90911i	0.313406	+	0.150928i
$161$	15.7785	+	2.57321i	1.24352	+	0.202798i
$162$	−2.73973	+	1.31939i	−0.215254	+	0.103661i
$163$	−16.0839	−	14.9237i	−1.25979	−	1.16891i	−0.977811	−	0.209491i	$-0.932819\pi$
$163$	−16.0839	−	14.9237i	−1.25979	−	1.16891i	−0.281977	−	0.959421i	$-0.590990\pi$
$164$	−10.6766	−	1.60923i	−0.833699	−	0.125660i
$165$	6.03988	+	10.4614i	0.470204	+	0.814417i
$166$	−2.20428	+	3.81792i	−0.171085	+	0.296328i
$167$	5.62527	−	7.05387i	0.435297	−	0.545845i	−0.515000	−	0.857190i	$-0.672208\pi$
$167$	5.62527	−	7.05387i	0.435297	−	0.545845i	0.950297	+	0.311345i	$0.100780\pi$
$168$	−3.79913	−	4.88365i	−0.293109	−	0.376782i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	2.51262	−	0.378717i	0.192709	−	0.0290463i
$171$	−0.214124	−	0.145987i	−0.0163745	−	0.0111639i
$172$	−12.4566	−	8.49278i	−0.949809	−	0.647569i
$173$	11.2930	−	1.70215i	0.858595	−	0.129412i	0.295034	−	0.955487i	$-0.404669\pi$
$173$	11.2930	−	1.70215i	0.858595	−	0.129412i	0.563561	+	0.826075i	$0.309431\pi$
$174$	1.43363	+	1.79771i	0.108683	+	0.136284i
$175$	−6.09925	−	7.84036i	−0.461060	−	0.592675i
$176$	13.0045	−	16.3071i	0.980252	−	1.22920i
$177$	3.44967	−	5.97500i	0.259293	−	0.449108i
$178$	0.302025	+	0.523122i	0.0226377	+	0.0392097i
$179$	−11.9370	−	1.79921i	−0.892213	−	0.134479i	−0.313093	−	0.949722i	$-0.601365\pi$
$179$	−11.9370	−	1.79921i	−0.892213	−	0.134479i	−0.579119	+	0.815243i	$0.696603\pi$
$180$	−0.254477	−	0.236120i	−0.0189676	−	0.0175993i
$181$	−6.62687	+	3.19133i	−0.492571	+	0.237210i	−0.663644	−	0.748049i	$-0.730991\pi$
$181$	−6.62687	+	3.19133i	−0.492571	+	0.237210i	0.171073	+	0.985258i	$0.445277\pi$
$182$	0.937078	+	0.152822i	0.0694608	+	0.0113279i
$183$	7.05767	+	3.39880i	0.521718	+	0.251246i
$184$	−3.06683	−	7.81414i	−0.226089	−	0.576066i
$185$	−0.809169	−	10.7976i	−0.0594913	−	0.793856i
$186$	−2.40355	+	0.741398i	−0.176237	+	0.0543620i
$187$	3.04856	−	40.6801i	0.222932	−	2.97483i
$188$	3.82901	+	16.7760i	0.279260	+	1.22352i
$189$	4.99326	+	13.1882i	0.363207	+	0.959297i
$190$	0.138939	−	0.608732i	0.0100797	−	0.0441621i
$191$	−4.98219	−	1.53680i	−0.360499	−	0.111199i	0.109214	−	0.994018i	$-0.465166\pi$
$191$	−4.98219	−	1.53680i	−0.360499	−	0.111199i	−0.469713	+	0.882819i	$0.655643\pi$
$192$	3.11991	−	7.94940i	0.225160	−	0.573699i
$193$	−6.10132	+	5.66120i	−0.439183	+	0.407502i	−0.868529	−	0.495638i	$-0.834934\pi$
$193$	−6.10132	+	5.66120i	−0.439183	+	0.407502i	0.429347	+	0.903140i	$0.358744\pi$
$194$	3.67365	−	2.50465i	0.263753	−	0.179824i
$195$	−1.87871			−0.134537
$196$	−10.9973	+	7.11549i	−0.785524	+	0.508249i
$197$	8.73812			0.622565			0.311283	−	0.950317i	$-0.399241\pi$
$197$	8.73812			0.622565			0.311283	+	0.950317i	$0.399241\pi$
$198$	0.316913	−	0.216068i	0.0225220	−	0.0153553i
$199$	−17.3061	+	16.0577i	−1.22679	+	1.13830i	−0.240968	+	0.970533i	$0.577465\pi$
$199$	−17.3061	+	16.0577i	−1.22679	+	1.13830i	−0.985827	+	0.167766i	$0.946345\pi$
$200$	−1.90555	+	4.85526i	−0.134743	+	0.343319i
$201$	−1.46533	−	0.451995i	−0.103357	−	0.0318813i
$202$	1.14490	−	5.01612i	0.0805547	−	0.352933i
$203$	8.38838	−	5.57210i	0.588749	−	0.391085i
$204$	−4.44712	−	19.4841i	−0.311360	−	1.36416i
$205$	−0.481236	+	6.42165i	−0.0336110	+	0.448508i
$206$	−1.37117	+	0.422951i	−0.0955342	+	0.0294684i
$207$	0.0750625	+	1.00164i	0.00521720	+	0.0696187i
$208$	1.18513	+	3.01966i	0.0821739	+	0.209376i
$209$	−9.03144	−	4.34931i	−0.624718	−	0.300848i
$210$	−1.32212	+	1.19740i	−0.0912352	+	0.0826288i
$211$	−1.59023	+	0.765812i	−0.109476	+	0.0527207i	−0.487820	−	0.872944i	$-0.662208\pi$
$211$	−1.59023	+	0.765812i	−0.109476	+	0.0527207i	0.378344	+	0.925665i	$0.376494\pi$
$212$	13.1127	+	12.1668i	0.900582	+	0.835618i
$213$	−18.4919	−	2.78721i	−1.26704	−	0.190976i
$214$	3.02739	+	5.24360i	0.206948	+	0.358445i
$215$	−4.49592	+	7.78716i	−0.306619	+	0.531080i
$216$	4.61666	−	5.78911i	0.314124	−	0.393899i
$217$	2.32162	+	10.7687i	0.157602	+	0.731030i
$218$	1.91150	+	2.39695i	0.129463	+	0.162342i
$219$	13.3774	−	2.01631i	0.903959	−	0.136250i
$220$	−11.0945	−	7.56407i	−0.747988	−	0.509969i
$221$	5.24211	+	3.57401i	0.352623	+	0.240414i
$222$	5.79557	−	0.873542i	0.388973	−	0.0586283i
$223$	−17.2606	−	21.6441i	−1.15585	−	1.44939i	−0.871312	−	0.490729i	$-0.836731\pi$
$223$	−17.2606	−	21.6441i	−1.15585	−	1.44939i	−0.284540	−	0.958664i	$-0.591841\pi$
$224$	9.34279	+	4.63888i	0.624241	+	0.309948i
$225$	0.389124	−	0.487946i	0.0259416	−	0.0325298i
$226$	−1.13137	+	1.95959i	−0.0752577	+	0.130350i
$227$	9.93348	+	17.2053i	0.659308	+	1.14196i	0.980795	+	0.195041i	$0.0624842\pi$
$227$	9.93348	+	17.2053i	0.659308	+	1.14196i	−0.321487	+	0.946914i	$0.604183\pi$
$228$	−4.85600	−	0.731924i	−0.321596	−	0.0484728i
$229$	−10.6460	−	9.87803i	−0.703507	−	0.652759i	0.244998	−	0.969524i	$-0.421213\pi$
$229$	−10.6460	−	9.87803i	−0.703507	−	0.652759i	−0.948504	+	0.316765i	$0.897403\pi$
$230$	−2.18037	+	1.05001i	−0.143770	+	0.0692358i
$231$	14.0184	+	24.9713i	0.922343	+	1.64299i
$232$	−4.76411	−	2.29428i	−0.312779	−	0.150627i
$233$	−5.17693	−	13.1906i	−0.339152	−	0.864146i	−0.994100	−	0.108471i	$-0.965404\pi$
$233$	−5.17693	−	13.1906i	−0.339152	−	0.864146i	0.654947	−	0.755675i	$-0.272691\pi$
$234$	0.00445793	+	0.0594869i	0.000291424	+	0.00388878i
$235$	9.80694	−	3.02504i	0.639734	−	0.197332i
$236$	−0.573119	+	7.64774i	−0.0373069	+	0.497826i
$237$	−2.34957	−	10.2942i	−0.152621	−	0.668677i
$238$	5.96699	−	0.825908i	0.386783	−	0.0535357i
$239$	−2.17450	+	9.52709i	−0.140656	+	0.616256i	0.854627	+	0.519243i	$0.173786\pi$
$239$	−2.17450	+	9.52709i	−0.140656	+	0.616256i	−0.995283	+	0.0970131i	$0.969071\pi$
$240$	−5.82359	−	1.79634i	−0.375911	−	0.115953i
$241$	0.201292	−	0.512882i	0.0129663	−	0.0330377i	−0.924244	−	0.381802i	$-0.875304\pi$
$241$	0.201292	−	0.512882i	0.0129663	−	0.0330377i	0.937210	+	0.348765i	$0.113399\pi$
$242$	7.98198	−	7.40619i	0.513101	−	0.476088i
$243$	−1.42567	+	0.972004i	−0.0914567	+	0.0623541i
$244$	−8.70751			−0.557441
$245$	4.72212	+	6.22357i	0.301685	+	0.397609i
$246$	−3.48573			−0.222242
$247$	1.28812	−	0.878223i	0.0819609	−	0.0558800i
$248$	4.24024	−	3.93437i	0.269255	−	0.249832i
$249$	7.55528	−	19.2505i	0.478796	−	1.21995i
$250$	3.35041	+	1.03346i	0.211898	+	0.0653620i
$251$	−1.28884	+	5.64678i	−0.0813509	+	0.356421i	−0.999177	−	0.0405610i	$-0.987085\pi$
$251$	−1.28884	+	5.64678i	−0.0813509	+	0.356421i	0.917826	+	0.396982i	$0.129943\pi$
$252$	−0.596485	−	0.566997i	−0.0375750	−	0.0357175i
$253$	8.64540	+	37.8780i	0.543532	+	2.38137i
$254$	0.0674424	−	0.899957i	0.00423171	−	0.0564683i
$255$	−11.3900	+	3.51336i	−0.713272	+	0.220015i
$256$	0.497923	+	6.64432i	0.0311202	+	0.415270i
$257$	5.62336	+	14.3281i	0.350776	+	0.893761i	0.991980	+	0.126392i	$0.0403396\pi$
$257$	5.62336	+	14.3281i	0.350776	+	0.893761i	−0.641205	+	0.767370i	$0.721565\pi$
$258$	−4.38519	−	2.11180i	−0.273010	−	0.131475i
$259$	−1.60941	−	25.6188i	−0.100004	−	1.59188i
$260$	1.88154	−	0.906100i	0.116688	−	0.0561939i
$261$	0.463814	+	0.430356i	0.0287094	+	0.0266384i
$262$	4.60612	+	0.694262i	0.284567	+	0.0428916i
$263$	−0.608089	−	1.05324i	−0.0374964	−	0.0649457i	0.846668	−	0.532121i	$-0.178605\pi$
$263$	−0.608089	−	1.05324i	−0.0374964	−	0.0649457i	−0.884165	+	0.467176i	$0.845272\pi$
$264$	7.51838	−	13.0222i	0.462724	−	0.801462i
$265$	6.65180	−	8.34110i	0.408617	−	0.512390i
$266$	0.346759	−	1.43903i	0.0212612	−	0.0882323i
$267$	−1.76668	−	2.21535i	−0.108119	−	0.135577i
$268$	1.68553	−	0.254053i	0.102960	−	0.0155188i
$269$	12.4269	+	8.47250i	0.757680	+	0.516577i	0.879456	−	0.475980i	$-0.157907\pi$
$269$	12.4269	+	8.47250i	0.757680	+	0.516577i	−0.121776	+	0.992558i	$0.538859\pi$
$270$	−1.76374	−	1.20250i	−0.107338	−	0.0731817i
$271$	3.00176	−	0.452442i	0.182344	−	0.0274839i	−0.0572355	−	0.998361i	$-0.518229\pi$
$271$	3.00176	−	0.452442i	0.182344	−	0.0274839i	0.239579	+	0.970877i	$0.422990\pi$
$272$	12.8321	+	16.0909i	0.778060	+	0.975656i
$273$	−4.45348	−	0.0537151i	−0.269537	−	0.00325098i
$274$	−0.852326	+	1.06878i	−0.0514909	+	0.0645675i
$275$	12.0702	−	20.9063i	0.727862	−	1.26069i
$276$	9.51685	+	16.4837i	0.572847	+	0.992201i
$277$	−1.01396	−	0.152830i	−0.0609229	−	0.00918264i	0.118510	−	0.992953i	$-0.462188\pi$
$277$	−1.01396	−	0.152830i	−0.0609229	−	0.00918264i	−0.179433	+	0.983770i	$0.557426\pi$
$278$	−5.94247	−	5.51381i	−0.356406	−	0.330696i
$279$	−0.623594	+	0.300307i	−0.0373336	+	0.0179789i
$280$	1.54459	−	3.80014i	0.0923070	−	0.227102i
$281$	8.51263	+	4.09946i	0.507821	+	0.244554i	0.670208	−	0.742174i	$-0.266205\pi$
$281$	8.51263	+	4.09946i	0.507821	+	0.244554i	−0.162387	+	0.986727i	$0.551919\pi$
$282$	2.02954	+	5.17120i	0.120858	+	0.307940i
$283$	−0.491360	−	6.55675i	−0.0292083	−	0.389758i	−0.992580	−	0.121590i	$-0.961201\pi$
$283$	−0.491360	−	6.55675i	−0.0292083	−	0.389758i	0.963372	−	0.268168i	$-0.0864183\pi$
$284$	19.8639	−	6.12722i	1.17871	−	0.363583i
$285$	−0.218880	+	2.92075i	−0.0129653	+	0.173010i
$286$	0.513446	+	2.24955i	0.0303607	+	0.133019i
$287$	−1.32437	+	15.2088i	−0.0781753	+	0.897744i
$288$	−0.145835	+	0.638944i	−0.00859339	+	0.0376501i
$289$	22.2202	+	6.85404i	1.30707	+	0.403179i
$290$	−0.556931	+	1.41904i	−0.0327041	+	0.0833287i
$291$	−15.2891	+	14.1862i	−0.896265	+	0.831612i
$292$	−12.4250	+	8.47123i	−0.727119	+	0.495741i
$293$	8.63818			0.504648			0.252324	−	0.967643i	$-0.418805\pi$
$293$	8.63818			0.504648			0.252324	+	0.967643i	$0.418805\pi$
$294$	−3.16833	+	2.80064i	−0.184781	+	0.163337i
$295$	4.57407			0.266313
$296$	−11.1364	+	7.59267i	−0.647291	+	0.441315i
$297$	−25.1222	+	23.3100i	−1.45774	+	1.35258i
$298$	−2.18304	+	5.56229i	−0.126460	+	0.322215i
$299$	−5.77405	−	1.78106i	−0.333922	−	0.103001i
$300$	2.63164	−	11.5299i	0.151938	−	0.665682i
$301$	−10.8802	+	18.3309i	−0.627124	+	1.05657i
$302$	0.272469	+	1.19377i	0.0156788	+	0.0686935i
$303$	−1.80363	+	24.0677i	−0.103616	+	1.38266i
$304$	4.83259	−	1.49066i	0.277168	−	0.0854951i
$305$	0.388099	+	5.17883i	0.0222225	+	0.296539i
$306$	0.138273	+	0.352313i	0.00790453	+	0.0201404i
$307$	−0.688414	−	0.331523i	−0.0392899	−	0.0189210i	0.414136	−	0.910215i	$-0.364084\pi$
$307$	−0.688414	−	0.331523i	−0.0392899	−	0.0189210i	−0.453426	+	0.891294i	$0.649798\pi$
$308$	−26.0831	−	18.2478i	−1.48622	−	1.03977i
$309$	6.06449	−	2.92050i	0.344997	−	0.166142i
$310$	−1.22242	−	1.13424i	−0.0694288	−	0.0644205i
$311$	12.1363	+	1.82925i	0.688186	+	0.103727i	0.483821	−	0.875167i	$-0.339249\pi$
$311$	12.1363	+	1.82925i	0.688186	+	0.103727i	0.204366	+	0.978895i	$0.434487\pi$
$312$	1.16930	+	2.02529i	0.0661986	+	0.114659i
$313$	−9.34427	+	16.1848i	−0.528170	+	0.914816i	0.471291	+	0.881978i	$0.343788\pi$
$313$	−9.34427	+	16.1848i	−0.528170	+	0.914816i	−0.999461	+	0.0328388i	$0.989545\pi$
$314$	−1.43076	+	1.79411i	−0.0807422	+	0.101248i
$315$	−0.310638	+	0.380034i	−0.0175025	+	0.0214125i
$316$	7.31796	+	9.17643i	0.411667	+	0.516214i
$317$	−12.8080	+	1.93049i	−0.719367	+	0.108427i	−0.498516	−	0.866880i	$-0.666122\pi$
$317$	−12.8080	+	1.93049i	−0.719367	+	0.108427i	−0.220851	+	0.975308i	$0.570883\pi$
$318$	4.77140	+	3.25309i	0.267567	+	0.182424i
$319$	20.2209	+	13.7864i	1.13216	+	0.771890i
$320$	5.59837	−	0.843818i	0.312958	−	0.0471709i
$321$	−17.7086	−	22.2059i	−0.988398	−	1.23941i
$322$	−5.19859	+	2.42671i	−0.289706	+	0.135235i
$323$	6.16708	−	7.73328i	0.343146	−	0.430291i
$324$	−7.92805	+	13.7318i	−0.440447	+	0.762877i
$325$	1.87723	+	3.25146i	0.104130	+	0.180359i
$326$	7.78583	+	1.17352i	0.431217	+	0.0649955i
$327$	−10.5423	−	9.78185i	−0.582992	−	0.540937i
$328$	7.22219	−	3.47802i	0.398779	−	0.192042i
$329$	23.3338	−	6.89045i	1.28643	−	0.379883i
$330$	−3.90566	−	1.88087i	−0.214999	−	0.103538i
$331$	4.41414	+	11.2470i	0.242623	+	0.618193i	0.999369	−	0.0355156i	$-0.0113073\pi$
$331$	4.41414	+	11.2470i	0.242623	+	0.618193i	−0.756746	+	0.653709i	$0.773212\pi$
$332$	1.71787	+	22.9234i	0.0942803	+	1.25808i
$333$	1.54113	−	0.475377i	0.0844536	−	0.0260505i
$334$	−0.241956	+	3.22868i	−0.0132392	+	0.176665i
$335$	−0.226224	−	0.991153i	−0.0123600	−	0.0541525i
$336$	−13.7535	−	4.42473i	−0.750312	−	0.241389i
$337$	−2.63045	+	11.5247i	−0.143290	+	0.627793i	0.851368	+	0.524568i	$0.175773\pi$
$337$	−2.63045	+	11.5247i	−0.143290	+	0.627793i	−0.994658	+	0.103225i	$0.967084\pi$
$338$	−0.342918	−	0.105776i	−0.0186523	−	0.00575347i
$339$	3.87784	−	9.88057i	0.210615	−	0.536639i
$340$	9.71266	−	9.01203i	0.526743	−	0.488746i
$341$	−22.1200	+	15.0811i	−1.19786	+	0.816690i
$342$	0.0930008			0.00502891
$343$	11.0158	+	14.8880i	0.594799	+	0.803874i
$344$	11.1929			0.603483
$345$	9.37956	−	6.39488i	0.504979	−	0.344289i
$346$	−3.00435	+	2.78763i	−0.161515	+	0.149864i
$347$	−7.19600	+	18.3351i	−0.386302	+	0.984281i	0.596991	+	0.802248i	$0.296363\pi$
$347$	−7.19600	+	18.3351i	−0.386302	+	0.984281i	−0.983292	+	0.182033i	$0.941732\pi$
$348$	11.4569	+	3.53400i	0.614157	+	0.189442i
$349$	7.06147	−	30.9383i	0.377992	−	1.65609i	−0.325617	−	0.945502i	$-0.605572\pi$
$349$	7.06147	−	30.9383i	0.377992	−	1.65609i	0.703609	−	0.710588i	$-0.251571\pi$
$350$	3.39341	+	1.09172i	0.181386	+	0.0583549i
$351$	−1.18603	−	5.19634i	−0.0633056	−	0.277360i
$352$	−1.89440	+	25.2791i	−0.100972	+	1.34738i
$353$	−6.21187	+	1.91611i	−0.330624	+	0.101984i	−0.455623	−	0.890173i	$-0.650584\pi$
$353$	−6.21187	+	1.91611i	−0.330624	+	0.101984i	0.124999	+	0.992157i	$0.460107\pi$
$354$	0.185024	+	2.46898i	0.00983394	+	0.131225i
$355$	−4.52954	−	11.5411i	−0.240403	−	0.612536i
$356$	2.83779	+	1.36661i	0.150403	+	0.0724301i
$357$	−27.1005	+	8.00275i	−1.43431	+	0.423551i
$358$	3.90309	−	1.87963i	0.206285	−	0.0993416i
$359$	8.70503	+	8.07708i	0.459434	+	0.426292i	0.875630	−	0.482983i	$-0.160447\pi$
$359$	8.70503	+	8.07708i	0.459434	+	0.426292i	−0.416196	+	0.909275i	$0.636637\pi$
$360$	0.254850	+	0.0384125i	0.0134318	+	0.00202452i
$361$	8.28474	+	14.3496i	0.436039	+	0.755242i
$362$	1.31976	−	2.28589i	0.0693651	−	0.120144i
$363$	−31.8464	+	39.9342i	−1.67150	+	2.09600i
$364$	4.48608	−	2.09411i	0.235134	−	0.109761i
$365$	5.59209	+	7.01226i	0.292703	+	0.367038i
$366$	−2.77971	+	0.418974i	−0.145298	+	0.0219001i
$367$	−5.09033	−	3.47053i	−0.265713	−	0.181160i	0.423133	−	0.906067i	$-0.360930\pi$
$367$	−5.09033	−	3.47053i	−0.265713	−	0.181160i	−0.688846	+	0.724907i	$0.741883\pi$
$368$	−16.1953	−	11.0418i	−0.844239	−	0.575592i
$369$	−0.948457	+	0.142957i	−0.0493747	+	0.00744204i
$370$	2.42270	+	3.03797i	0.125950	+	0.157936i
$371$	16.0066	−	19.5824i	0.831019	−	1.01667i
$372$	−8.17744	+	10.2542i	−0.423981	+	0.531655i
$373$	6.73015	−	11.6570i	0.348474	−	0.603574i	−0.637505	−	0.770446i	$-0.720033\pi$
$373$	6.73015	−	11.6570i	0.348474	−	0.603574i	0.985979	+	0.166872i	$0.0533667\pi$
$374$	7.31973	+	12.6781i	0.378494	+	0.655571i
$375$	−16.2634	−	2.45132i	−0.839839	−	0.126585i
$376$	−9.36484	−	8.68930i	−0.482955	−	0.448117i
$377$	−3.42932	+	1.65147i	−0.176619	+	0.0850552i
$378$	−4.14656	−	2.90095i	−0.213276	−	0.149209i
$379$	−11.1232	−	5.35663i	−0.571358	−	0.275152i	0.125816	−	0.992054i	$-0.459845\pi$
$379$	−11.1232	−	5.35663i	−0.571358	−	0.275152i	−0.697174	+	0.716902i	$0.745559\pi$
$380$	−1.18946	−	3.03070i	−0.0610181	−	0.155472i
$381$	0.316365	+	4.22160i	0.0162079	+	0.216279i
$382$	1.78792	−	0.551499i	0.0914777	−	0.0282171i
$383$	1.05085	−	14.0227i	0.0536961	−	0.716524i	−0.903777	−	0.428003i	$-0.859217\pi$
$383$	1.05085	−	14.0227i	0.0536961	−	0.716524i	0.957473	−	0.288521i	$-0.0931637\pi$
$384$	3.63560	+	15.9286i	0.185529	+	0.812854i
$385$	−9.69042	+	16.3263i	−0.493869	+	0.832068i
$386$	0.664640	−	2.91198i	0.0338293	−	0.148216i
$387$	−1.27981	−	0.394769i	−0.0650563	−	0.0200672i
$388$	8.47011	−	21.5815i	0.430005	−	1.09563i
$389$	−12.5391	+	11.6346i	−0.635757	+	0.589897i	−0.930774	−	0.365596i	$-0.880865\pi$
$389$	−12.5391	+	11.6346i	−0.635757	+	0.589897i	0.295017	+	0.955492i	$0.404675\pi$
$390$	0.557048	−	0.379789i	0.0282072	−	0.0192313i
$391$	−38.3369			−1.93878
$392$	3.77010	−	8.96406i	0.190419	−	0.452753i
$393$	−21.8509			−1.10223
$394$	−2.59090	+	1.76644i	−0.130527	+	0.0889921i
$395$	5.13155	−	4.76139i	0.258196	−	0.239571i
$396$	0.730687	−	1.86176i	0.0367184	−	0.0935570i
$397$	4.69385	+	1.44786i	0.235578	+	0.0726661i	0.410296	−	0.911952i	$-0.365425\pi$
$397$	4.69385	+	1.44786i	0.235578	+	0.0726661i	−0.174718	+	0.984618i	$0.555902\pi$
$398$	1.88522	−	8.25967i	0.0944973	−	0.414020i
$399$	−0.602362	+	6.91736i	−0.0301558	+	0.346301i
$400$	2.71010	+	11.8737i	0.135505	+	0.593687i
$401$	0.712526	−	9.50799i	0.0355818	−	0.474807i	−0.950742	−	0.309985i	$-0.899676\pi$
$401$	0.712526	−	9.50799i	0.0355818	−	0.474807i	0.986323	−	0.164822i	$-0.0527049\pi$
$402$	0.525851	−	0.162204i	0.0262271	−	0.00808998i
$403$	−0.311155	−	4.15208i	−0.0154997	−	0.206830i
$404$	−9.80149	−	24.9738i	−0.487642	−	1.24249i
$405$	8.52039	+	4.10321i	0.423382	+	0.203890i
$406$	−1.36077	+	3.34790i	−0.0675341	+	0.166153i
$407$	56.2047	−	27.0668i	2.78597	−	1.34165i
$408$	10.8766	+	10.0920i	0.538470	+	0.499628i
$409$	19.2226	+	2.89734i	0.950496	+	0.143264i	0.605948	−	0.795504i	$-0.292794\pi$
$409$	19.2226	+	2.89734i	0.950496	+	0.143264i	0.344548	+	0.938769i	$0.388032\pi$
$410$	−1.15547	−	2.00134i	−0.0570647	−	0.0988389i
$411$	3.20628	−	5.55345i	0.158154	−	0.273931i
$412$	−4.66505	+	5.84978i	−0.229830	+	0.288198i
$413$	10.8428	+	0.130779i	0.533540	+	0.00643523i
$414$	−0.224741	−	0.281817i	−0.0110454	−	0.0138505i
$415$	13.5572	−	2.04342i	0.665497	−	0.100307i
$416$	−3.25750	−	2.22093i	−0.159712	−	0.108890i
$417$	31.4191	+	21.4212i	1.53860	+	1.04900i
$418$	3.55710	−	0.536146i	0.173983	−	0.0262238i
$419$	0.699456	+	0.877090i	0.0341707	+	0.0428487i	0.798623	−	0.601831i	$-0.205562\pi$
$419$	0.699456	+	0.877090i	0.0341707	+	0.0428487i	−0.764453	+	0.644680i	$0.776991\pi$
$420$	−2.17890	+	9.04227i	−0.106319	+	0.441218i
$421$	−15.2792	+	19.1595i	−0.744663	+	0.933778i	−0.999448	−	0.0332197i	$-0.989424\pi$
$421$	−15.2792	+	19.1595i	−0.744663	+	0.933778i	0.254785	+	0.966998i	$0.417995\pi$
$422$	0.316698	−	0.548537i	0.0154166	−	0.0267024i
$423$	0.764315	+	1.32383i	0.0371623	+	0.0643669i
$424$	−13.1319	−	1.97932i	−0.637742	−	0.0961242i
$425$	17.4616	+	16.2020i	0.847011	+	0.785912i
$426$	6.04638	−	2.91178i	0.292948	−	0.141076i
$427$	0.771918	+	12.2875i	0.0373558	+	0.594633i
$428$	28.4451	+	13.6984i	1.37494	+	0.662138i
$429$	−3.95438	−	10.0756i	−0.190919	−	0.486454i
$430$	−0.241141	−	3.21780i	−0.0116288	−	0.155176i
$431$	29.8672	−	9.21281i	1.43865	−	0.443766i	0.525294	−	0.850921i	$-0.323955\pi$
$431$	29.8672	−	9.21281i	1.43865	−	0.443766i	0.913359	+	0.407155i	$0.133479\pi$
$432$	1.29207	−	17.2415i	0.0621649	−	0.829533i
$433$	−7.84035	−	34.3508i	−0.376783	−	1.65079i	−0.707240	−	0.706974i	$-0.750060\pi$
$433$	−7.84035	−	34.3508i	−0.376783	−	1.65079i	0.330457	−	0.943821i	$-0.392797\pi$
$434$	−2.86531	−	2.72366i	−0.137539	−	0.130740i
$435$	1.59122	−	6.97158i	0.0762930	−	0.334261i
$436$	15.2759	+	4.71200i	0.731585	+	0.225664i
$437$	−3.44163	+	8.76914i	−0.164636	+	0.419485i
$438$	−3.55885	+	3.30213i	−0.170049	+	0.157782i
$439$	12.0736	−	8.23161i	0.576239	−	0.392873i	−0.239841	−	0.970812i	$-0.577095\pi$
$439$	12.0736	−	8.23161i	0.576239	−	0.392873i	0.816080	+	0.577939i	$0.196143\pi$
$440$	9.96896			0.475251
$441$	−0.747233	+	0.891987i	−0.0355825	+	0.0424756i
$442$	−2.27681			−0.108297
$443$	−24.5045	+	16.7069i	−1.16424	+	0.793767i	−0.981887	−	0.189465i	$-0.939325\pi$
$443$	−24.5045	+	16.7069i	−1.16424	+	0.793767i	−0.182355	+	0.983233i	$0.558372\pi$
$444$	22.4030	−	20.7870i	1.06320	−	0.986507i
$445$	0.686314	−	1.74870i	0.0325344	−	0.0828963i
$446$	9.49327	+	2.92828i	0.449519	+	0.138658i
$447$	6.23719	−	27.3269i	0.295009	−	1.29252i
$448$	13.2950	−	1.84020i	0.628132	−	0.0869414i
$449$	−4.61924	−	20.2382i	−0.217995	−	0.955100i	−0.958957	−	0.283553i	$-0.908487\pi$
$449$	−4.61924	−	20.2382i	−0.217995	−	0.955100i	0.740961	−	0.671548i	$-0.234370\pi$
$450$	−0.0167371	+	0.223341i	−0.000788995	+	0.0105284i
$451$	−35.4525	+	10.9356i	−1.66939	+	0.514939i
$452$	0.881716	+	11.7657i	0.0414725	+	0.553411i
$453$	−2.09846	−	5.34679i	−0.0985943	−	0.251214i
$454$	−6.42344	−	3.09337i	−0.301467	−	0.145179i
$455$	−1.44543	−	2.57478i	−0.0677627	−	0.120707i
$456$	3.28485	−	1.58190i	0.153827	−	0.0740793i
$457$	6.95731	+	6.45544i	0.325449	+	0.301973i	0.825928	−	0.563776i	$-0.190652\pi$
$457$	6.95731	+	6.45544i	0.325449	+	0.301973i	−0.500478	+	0.865749i	$0.666842\pi$
$458$	5.15347	+	0.776760i	0.240806	+	0.0362956i
$459$	−16.9081	−	29.2857i	−0.789204	−	1.36694i
$460$	−6.30942	+	10.9282i	−0.294178	+	0.509531i
$461$	−0.958499	+	1.20192i	−0.0446417	+	0.0559790i	−0.803651	−	0.595101i	$-0.797112\pi$
$461$	−0.958499	+	1.20192i	−0.0446417	+	0.0559790i	0.759009	+	0.651080i	$0.225684\pi$
$462$	−9.20457	−	4.57025i	−0.428235	−	0.212627i
$463$	7.21254	+	9.04423i	0.335195	+	0.420321i	0.920653	−	0.390381i	$-0.127657\pi$
$463$	7.21254	+	9.04423i	0.335195	+	0.420321i	−0.585458	+	0.810703i	$0.699085\pi$
$464$	−12.2092	+	1.84024i	−0.566798	+	0.0854310i
$465$	6.46320	+	4.40653i	0.299724	+	0.204348i
$466$	4.20152	+	2.86455i	0.194632	+	0.132698i
$467$	5.63829	−	0.849835i	0.260909	−	0.0393257i	−0.0172851	−	0.999851i	$-0.505502\pi$
$467$	5.63829	−	0.849835i	0.260909	−	0.0393257i	0.278194	+	0.960525i	$0.410264\pi$
$468$	0.193939	+	0.243192i	0.00896483	+	0.0112415i
$469$	−0.507925	−	2.35599i	−0.0234538	−	0.108790i
$470$	−2.29628	+	2.87945i	−0.105920	+	0.132819i
$471$	5.38223	−	9.32229i	0.248000	−	0.429548i
$472$	−2.84688	−	4.93094i	−0.131038	−	0.226965i
$473$	−51.2259	−	7.72107i	−2.35537	−	0.355015i
$474$	2.77766	+	2.57729i	0.127582	+	0.118379i
$475$	5.27360	−	2.53963i	0.241969	−	0.116526i
$476$	23.2815	−	21.0853i	1.06711	−	0.966443i
$477$	1.43170	+	0.689471i	0.0655531	+	0.0315687i
$478$	−1.28119	−	3.26441i	−0.0586001	−	0.149311i
$479$	0.548202	+	7.31525i	0.0250480	+	0.334242i	0.995624	+	0.0934481i	$0.0297889\pi$
$479$	0.548202	+	7.31525i	0.0250480	+	0.334242i	−0.970576	+	0.240794i	$0.922592\pi$
$480$	7.07788	−	2.18324i	0.323060	−	0.0996507i
$481$	−0.725038	+	9.67496i	−0.0330589	+	0.441140i
$482$	0.0439971	+	0.192764i	0.00200401	+	0.00878016i
$483$	22.4171	−	14.8909i	1.02001	−	0.677557i
$484$	12.6341	−	55.3537i	0.574278	−	2.51608i
$485$	−13.2132	−	4.07573i	−0.599980	−	0.185069i
$486$	0.226223	−	0.576408i	0.0102617	−	0.0261464i
$487$	−5.32927	+	4.94484i	−0.241492	+	0.224072i	−0.791628	−	0.611003i	$-0.790766\pi$
$487$	−5.32927	+	4.94484i	−0.241492	+	0.224072i	0.550136	+	0.835075i	$0.314576\pi$
$488$	5.34133	−	3.64166i	0.241791	−	0.164850i
$489$	−36.9351			−1.67026
$490$	−2.65825	−	0.890724i	−0.120088	−	0.0402388i
$491$	−21.1014			−0.952294			−0.476147	−	0.879366i	$-0.657967\pi$
$491$	−21.1014			−0.952294			−0.476147	+	0.879366i	$0.657967\pi$
$492$	−15.0175	+	10.2387i	−0.677041	+	0.461598i
$493$	−17.7025	+	16.4255i	−0.797279	+	0.739767i
$494$	−0.204397	+	0.520795i	−0.00919625	+	0.0234317i
$495$	−1.13986	−	0.351599i	−0.0512328	−	0.0158032i
$496$	3.00552	−	13.1680i	0.134952	−	0.591262i
$497$	−10.4073	−	27.4876i	−0.466830	−	1.23299i
$498$	1.65139	+	7.23521i	0.0740005	+	0.324217i
$499$	2.81459	−	37.5581i	0.125998	−	1.68133i	−0.473375	−	0.880861i	$-0.656964\pi$
$499$	2.81459	−	37.5581i	0.125998	−	1.68133i	0.599373	−	0.800470i	$-0.295417\pi$
$500$	17.4701	−	5.38882i	0.781288	−	0.240995i
$501$	−1.13499	−	15.1454i	−0.0507076	−	0.676646i
$502$	−0.759369	−	1.93484i	−0.0338923	−	0.0863562i
$503$	34.2115	+	16.4754i	1.52542	+	0.734602i	0.993674	−	0.112304i	$-0.0358231\pi$
$503$	34.2115	+	16.4754i	1.52542	+	0.734602i	0.531743	+	0.846906i	$0.321537\pi$
$504$	0.603023	+	0.0983432i	0.0268608	+	0.00438056i
$505$	−14.4164	+	6.94257i	−0.641521	+	0.308940i
$506$	−10.2206	−	9.48331i	−0.454360	−	0.421584i
$507$	1.66458	+	0.250895i	0.0739265	+	0.0111426i
$508$	−2.35291	−	4.07536i	−0.104394	−	0.180815i
$509$	5.77640	−	10.0050i	0.256035	−	0.443465i	−0.709141	−	0.705066i	$-0.750917\pi$
$509$	5.77640	−	10.0050i	0.256035	−	0.443465i	0.965176	+	0.261601i	$0.0842506\pi$
$510$	2.66696	−	3.34427i	0.118095	−	0.148087i
$511$	13.0555	+	16.7824i	0.577543	+	0.742410i
$512$	−13.5935	−	17.0457i	−0.600755	−	0.753322i
$513$	−8.21668	+	1.23846i	−0.362775	+	0.0546796i
$514$	−4.56383	−	3.11157i	−0.201302	−	0.137245i
$515$	3.68711	+	2.51383i	0.162473	+	0.110772i
$516$	−25.0957	+	3.78257i	−1.10478	+	0.166518i
$517$	36.8654	+	46.2277i	1.62134	+	2.03309i
$518$	5.65614	+	7.27076i	0.248516	+	0.319459i
$519$	11.9867	−	15.0309i	0.526159	−	0.659783i
$520$	−0.775215	+	1.34271i	−0.0339954	+	0.0588818i
$521$	5.08738	+	8.81161i	0.222882	+	0.386044i	0.955682	−	0.294401i	$-0.0951201\pi$
$521$	5.08738	+	8.81161i	0.222882	+	0.386044i	−0.732800	+	0.680444i	$0.761787\pi$
$522$	−0.224521	−	0.0338411i	−0.00982703	−	0.00148119i
$523$	28.1083	+	26.0807i	1.22909	+	1.14043i	0.985342	+	0.170590i	$0.0545673\pi$
$523$	28.1083	+	26.0807i	1.22909	+	1.14043i	0.243747	+	0.969839i	$0.421623\pi$
$524$	21.8837	−	10.5387i	0.955996	−	0.460383i
$525$	−16.5036	−	2.69147i	−0.720277	−	0.117465i
$526$	0.393218	+	0.189364i	0.0171451	+	0.00825666i
$527$	−9.65119	−	24.5908i	−0.420412	−	1.07119i
$528$	−2.62387	−	35.0131i	−0.114189	−	1.52375i
$529$	12.9115	−	3.98267i	0.561370	−	0.173160i
$530$	−0.286109	+	3.81786i	−0.0124278	+	0.165837i
$531$	0.151603	+	0.664214i	0.00657899	+	0.0288244i
$532$	−2.73296	−	7.21827i	−0.118489	−	0.312952i
$533$	1.28397	−	5.62545i	0.0556150	−	0.243665i
$534$	0.971669	+	0.299720i	0.0420482	+	0.0129702i
$535$	6.87938	−	17.5284i	0.297421	−	0.757817i
$536$	−0.927682	+	0.860763i	−0.0400698	+	0.0371793i
$537$	−16.7904	+	11.4475i	−0.724559	+	0.493996i
$538$	−5.39738			−0.232697
$539$	−23.4379	+	38.4245i	−1.00954	+	1.65506i
$540$	−11.1308			−0.478995
$541$	−33.3663	+	22.7488i	−1.43453	+	0.978046i	−0.437647	+	0.899147i	$0.644188\pi$
$541$	−33.3663	+	22.7488i	−1.43453	+	0.978046i	−0.996883	+	0.0788986i	$0.974860\pi$
$542$	−0.798573	+	0.740968i	−0.0343017	+	0.0318273i
$543$	−4.52355	+	11.5258i	−0.194124	+	0.494620i
$544$	−23.9025	−	7.37295i	−1.02481	−	0.316113i
$545$	2.12162	−	9.29544i	0.0908804	−	0.398173i
$546$	1.33134	−	0.884361i	0.0569760	−	0.0378472i
$547$	−2.96483	−	12.9898i	−0.126767	−	0.555403i	−0.997924	−	0.0643987i	$-0.979487\pi$
$547$	−2.96483	−	12.9898i	−0.126767	−	0.555403i	0.871157	−	0.491004i	$-0.163370\pi$
$548$	−0.532684	+	7.10818i	−0.0227551	+	0.303646i
$549$	−0.739170	+	0.228004i	−0.0315470	+	0.00973096i
$550$	0.647392	+	8.63885i	0.0276049	+	0.368362i
$551$	2.16793	+	5.52381i	0.0923571	+	0.235322i
$552$	−12.7316	−	6.13121i	−0.541893	−	0.260962i
$553$	12.3005	−	11.1401i	0.523069	−	0.473726i
$554$	0.331539	−	0.159661i	0.0140857	−	0.00678333i
$555$	−13.3617	−	12.3978i	−0.567171	−	0.526258i
$556$	−41.7977	−	6.29999i	−1.77262	−	0.267179i
$557$	−3.72569	−	6.45309i	−0.157863	−	0.273426i	0.776235	−	0.630444i	$-0.217127\pi$
$557$	−3.72569	−	6.45309i	−0.157863	−	0.273426i	−0.934098	+	0.357017i	$0.883794\pi$
$558$	0.124191	−	0.215104i	0.00525741	−	0.00910610i
$559$	5.02342	−	6.29917i	0.212468	−	0.266427i
$560$	−2.01862	−	9.36330i	−0.0853023	−	0.395672i
$561$	−42.8164	−	53.6901i	−1.80771	−	2.26680i
$562$	−3.35276	+	0.505347i	−0.141428	+	0.0213168i
$563$	−31.5850	−	21.5343i	−1.33115	−	0.907561i	−0.331789	−	0.943354i	$-0.607652\pi$
$563$	−31.5850	−	21.5343i	−1.33115	−	0.907561i	−0.999359	+	0.0357924i	$0.988604\pi$
$564$	23.9334	+	16.3175i	1.00778	+	0.687091i
$565$	6.95839	−	1.04881i	0.292742	−	0.0441237i
$566$	1.47116	+	1.84478i	0.0618375	+	0.0775418i
$567$	20.0803	+	9.97025i	0.843291	+	0.418711i
$568$	−9.62234	+	12.0660i	−0.403744	+	0.506279i
$569$	17.3277	−	30.0125i	0.726417	−	1.25819i	−0.231972	−	0.972723i	$-0.574518\pi$
$569$	17.3277	−	30.0125i	0.726417	−	1.25819i	0.958388	−	0.285468i	$-0.0921490\pi$
$570$	−0.525541	−	0.910263i	−0.0220125	−	0.0381267i
$571$	27.2163	+	4.10220i	1.13897	+	0.171672i	0.691327	−	0.722542i	$-0.257026\pi$
$571$	27.2163	+	4.10220i	1.13897	+	0.171672i	0.447641	+	0.894213i	$0.352264\pi$
$572$	8.81976	+	8.18354i	0.368773	+	0.342171i
$573$	−7.90767	+	3.80814i	−0.330348	+	0.159087i
$574$	−2.68182	−	4.77720i	−0.111937	−	0.199396i
$575$	−20.4397	−	9.84324i	−0.852394	−	0.410491i
$576$	0.308085	+	0.784988i	0.0128369	+	0.0327078i
$577$	0.0168873	+	0.225345i	0.000703027	+	0.00938125i	0.997544	−	0.0700386i	$-0.0223123\pi$
$577$	0.0168873	+	0.225345i	0.000703027	+	0.00938125i	−0.996841	+	0.0794199i	$0.974693\pi$
$578$	−7.97398	+	2.45965i	−0.331674	+	0.102308i
$579$	−1.04705	+	13.9719i	−0.0435139	+	0.580652i
$580$	1.76877	+	7.74949i	0.0734442	+	0.321780i
$581$	32.1957	−	4.45630i	1.33570	−	0.184878i
$582$	1.66550	−	7.29705i	0.0690373	−	0.302472i
$583$	58.7345	+	18.1172i	2.43254	+	0.750338i
$584$	4.07886	−	10.3928i	0.168785	−	0.430056i
$585$	0.135995	−	0.126185i	0.00562271	−	0.00521711i
$586$	−2.56126	+	1.74624i	−0.105805	+	0.0721365i
$587$	15.8494			0.654174			0.327087	−	0.944994i	$-0.393933\pi$
$587$	15.8494			0.654174			0.327087	+	0.944994i	$0.393933\pi$
$588$	−5.42361	+	21.3724i	−0.223666	+	0.881382i
$589$	−6.49129			−0.267469
$590$	−1.35623	+	0.924665i	−0.0558353	+	0.0380679i
$591$	10.7829	−	10.0051i	0.443549	−	0.411553i
$592$	−11.4982	+	29.2970i	−0.472574	+	1.20410i
$593$	−32.8943	−	10.1466i	−1.35081	−	0.416669i	−0.466892	−	0.884314i	$-0.654626\pi$
$593$	−32.8943	−	10.1466i	−1.35081	−	0.416669i	−0.883916	+	0.467645i	$0.845103\pi$
$594$	2.73665	−	11.9901i	0.112286	−	0.491958i
$595$	−13.5782	−	12.9070i	−0.556653	−	0.529135i
$596$	6.93317	+	30.3762i	0.283994	+	1.24426i
$597$	−2.96990	+	39.6305i	−0.121550	+	1.62197i
$598$	2.07208	−	0.639152i	0.0847337	−	0.0261369i
$599$	−1.49370	−	19.9321i	−0.0610311	−	0.814404i	−0.940791	−	0.338986i	$-0.889916\pi$
$599$	−1.49370	−	19.9321i	−0.0610311	−	0.814404i	0.879760	−	0.475418i	$-0.157703\pi$
$600$	3.20777	+	8.17326i	0.130957	+	0.333672i
$601$	25.0940	+	12.0846i	1.02361	+	0.492942i	0.868884	−	0.495016i	$-0.164838\pi$
$601$	25.0940	+	12.0846i	1.02361	+	0.492942i	0.154721	+	0.987958i	$0.450552\pi$
$602$	−0.479621	−	7.63467i	−0.0195479	−	0.311166i
$603$	0.136430	−	0.0657014i	0.00555587	−	0.00267557i
$604$	4.68036	+	4.34274i	0.190441	+	0.176704i
$605$	−33.4849	−	5.04704i	−1.36136	−	0.205191i
$606$	−4.33060	−	7.50081i	−0.175918	−	0.304700i
$607$	−8.56172	+	14.8293i	−0.347510	+	0.601904i	−0.985806	−	0.167886i	$-0.946306\pi$
$607$	−8.56172	+	14.8293i	−0.347510	+	0.601904i	0.638297	+	0.769790i	$0.279639\pi$
$608$	−3.83229	+	4.80554i	−0.155420	+	0.194890i
$609$	3.97130	−	16.4806i	0.160925	−	0.667828i
$610$	−1.16199	−	1.45709i	−0.0470477	−	0.0589959i
$611$	−9.09313	+	1.37057i	−0.367869	+	0.0554473i
$612$	1.63058	+	1.11171i	0.0659123	+	0.0449382i
$613$	−18.6924	−	12.7443i	−0.754979	−	0.514736i	0.123600	−	0.992332i	$-0.460556\pi$
$613$	−18.6924	−	12.7443i	−0.754979	−	0.514736i	−0.878580	+	0.477596i	$0.841508\pi$
$614$	0.271137	−	0.0408673i	0.0109422	−	0.00164927i
$615$	6.75888	+	8.47536i	0.272544	+	0.341760i
$616$	23.6314	+	0.285027i	0.952136	+	0.0114841i
$617$	−2.72160	+	3.41278i	−0.109567	+	0.137393i	−0.833591	−	0.552382i	$-0.813719\pi$
$617$	−2.72160	+	3.41278i	−0.109567	+	0.137393i	0.724024	+	0.689775i	$0.242291\pi$
$618$	−1.20776	+	2.09190i	−0.0485832	+	0.0841486i
$619$	−9.66748	−	16.7446i	−0.388569	−	0.673021i	0.603689	−	0.797220i	$-0.293697\pi$
$619$	−9.66748	−	16.7446i	−0.388569	−	0.673021i	−0.992257	+	0.124200i	$0.960364\pi$
$620$	−8.59817	−	1.29597i	−0.345311	−	0.0520472i
$621$	23.6089	+	21.9059i	0.947393	+	0.879052i
$622$	−3.96826	+	1.91101i	−0.159113	+	0.0766247i
$623$	1.67690	−	4.12566i	0.0671837	−	0.165291i
$624$	4.91993	+	2.36931i	0.196955	+	0.0948485i
$625$	2.87462	+	7.32442i	0.114985	+	0.292977i
$626$	−0.501184	−	6.68784i	−0.0200314	−	0.267300i
$627$	−16.1248	+	4.97383i	−0.643961	+	0.198636i
$628$	−0.894190	+	11.9321i	−0.0356821	+	0.476144i
$629$	13.6974	+	60.0121i	0.546150	+	2.39284i
$630$	0.0152806	−	0.175479i	0.000608794	−	0.00699123i
$631$	−6.18665	+	27.1055i	−0.246287	+	1.07905i	0.688888	+	0.724867i	$0.258099\pi$
$631$	−6.18665	+	27.1055i	−0.246287	+	1.07905i	−0.935175	+	0.354185i	$0.884758\pi$
$632$	−8.32672	−	2.56845i	−0.331219	−	0.102168i
$633$	−1.08550	+	2.76581i	−0.0431447	+	0.109931i
$634$	3.40737	−	3.16158i	0.135324	−	0.125562i
$635$	−2.31897	+	1.58105i	−0.0920255	+	0.0627419i
$636$	30.1119			1.19402
$637$	−3.35277	−	6.14483i	−0.132841	−	0.243467i
$638$	−8.78258			−0.347706
$639$	1.52579	−	1.04026i	0.0603592	−	0.0411522i
$640$	−7.94029	+	7.36751i	−0.313867	+	0.291226i
$641$	7.43529	−	18.9448i	0.293676	−	0.748275i	−0.705539	−	0.708671i	$-0.749295\pi$
$641$	7.43529	−	18.9448i	0.293676	−	0.748275i	0.999215	−	0.0396040i	$-0.0126096\pi$
$642$	9.73969	+	3.00430i	0.384395	+	0.118570i
$643$	3.24417	−	14.2137i	0.127938	−	0.560532i	−0.869806	−	0.493394i	$-0.835756\pi$
$643$	3.24417	−	14.2137i	0.127938	−	0.560532i	0.997744	−	0.0671378i	$-0.0213867\pi$
$644$	−15.2689	+	25.7249i	−0.601679	+	1.01370i
$645$	3.36823	+	14.7572i	0.132624	+	0.581063i
$646$	−0.265260	+	3.53965i	−0.0104365	+	0.139266i
$647$	−6.41915	+	1.98005i	−0.252363	+	0.0778437i	−0.418356	−	0.908283i	$-0.637393\pi$
$647$	−6.41915	+	1.98005i	−0.252363	+	0.0778437i	0.165993	+	0.986127i	$0.446917\pi$
$648$	−0.879714	−	11.7390i	−0.0345584	−	0.461150i
$649$	9.62767	+	24.5309i	0.377919	+	0.962922i
$650$	−1.21390	−	0.584585i	−0.0476132	−	0.0229293i
$651$	15.1950	+	10.6305i	0.595539	+	0.416641i
$652$	36.9905	−	17.8137i	1.44866	−	0.697639i
$653$	−24.2765	−	22.5253i	−0.950012	−	0.881482i	0.0430502	−	0.999073i	$-0.486292\pi$
$653$	−24.2765	−	22.5253i	−0.950012	−	0.881482i	−0.993062	+	0.117591i	$0.962483\pi$
$654$	5.10329	+	0.769197i	0.199554	+	0.0300780i
$655$	−7.24328	−	12.5457i	−0.283018	−	0.490202i
$656$	9.35884	−	16.2100i	0.365401	−	0.632894i
$657$	−0.832927	+	1.04446i	−0.0324956	+	0.0407481i
$658$	−5.52566	+	6.76007i	−0.215413	+	0.263535i
$659$	−26.5080	−	33.2400i	−1.03261	−	1.29485i	−0.954599	−	0.297894i	$-0.903716\pi$
$659$	−26.5080	−	33.2400i	−1.03261	−	1.29485i	−0.0780066	−	0.996953i	$-0.524856\pi$
$660$	−22.3514	+	3.36893i	−0.870027	+	0.131135i
$661$	−8.94015	−	6.09529i	−0.347731	−	0.237079i	0.376841	−	0.926278i	$-0.377010\pi$
$661$	−8.94015	−	6.09529i	−0.347731	−	0.237079i	−0.724572	+	0.689199i	$0.757963\pi$
$662$	−3.58244	−	2.44247i	−0.139236	−	0.0949293i
$663$	10.5610	−	1.59182i	0.410155	−	0.0618210i
$664$	−10.6408	−	13.3431i	−0.412942	−	0.517813i
$665$	−4.17129	+	1.94716i	−0.161756	+	0.0755078i
$666$	−0.360854	+	0.452497i	−0.0139828	+	0.0175339i
$667$	11.4997	−	19.9180i	0.445268	−	0.771227i
$668$	8.44129	+	14.6207i	0.326603	+	0.565693i
$669$	−46.0818	−	6.94572i	−1.78163	−	0.268537i
$670$	0.267442	+	0.248150i	0.0103322	+	0.00958686i
$671$	−26.9573	+	12.9820i	−1.04068	+	0.501163i
$672$	16.8405	−	4.97299i	0.649637	−	0.191837i
$673$	−26.5658	−	12.7934i	−1.02404	−	0.493151i	−0.155010	−	0.987913i	$-0.549541\pi$
$673$	−26.5658	−	12.7934i	−1.02404	−	0.493151i	−0.869028	+	0.494762i	$0.835255\pi$
$674$	−1.54983	−	3.94890i	−0.0596972	−	0.152106i
$675$	−1.49544	−	19.9552i	−0.0575594	−	0.768077i
$676$	−1.78809	+	0.551551i	−0.0687725	+	0.0212135i
$677$	−3.39107	+	45.2506i	−0.130329	+	1.73912i	0.422973	+	0.906142i	$0.360986\pi$
$677$	−3.39107	+	45.2506i	−0.130329	+	1.73912i	−0.553302	+	0.832980i	$0.686633\pi$
$678$	0.847595	+	3.71356i	0.0325517	+	0.142618i
$679$	−31.2053	−	10.0393i	−1.19755	−	0.385273i
$680$	−2.18889	+	9.59015i	−0.0839401	+	0.367766i
$681$	31.9579	+	9.85769i	1.22463	+	0.377748i
$682$	3.50997	−	8.94327i	0.134404	−	0.342455i
$683$	−25.9522	+	24.0802i	−0.993035	+	0.921402i	−0.996907	−	0.0785905i	$-0.974958\pi$
$683$	−25.9522	+	24.0802i	−0.993035	+	0.921402i	0.00387182	+	0.999993i	$0.498768\pi$
$684$	0.400673	−	0.273174i	0.0153201	−	0.0104451i
$685$	4.25136			0.162436
$686$	−6.27591	−	2.18746i	−0.239615	−	0.0835177i
$687$	−24.4474			−0.932728
$688$	21.5945	−	14.7229i	0.823282	−	0.561304i
$689$	−7.00756	+	6.50206i	−0.266967	+	0.247709i
$690$	−1.48834	+	3.79222i	−0.0566601	+	0.144368i
$691$	29.5497	+	9.11486i	1.12412	+	0.346746i	0.800436	−	0.599419i	$-0.204602\pi$
$691$	29.5497	+	9.11486i	1.12412	+	0.346746i	0.323686	+	0.946164i	$0.395078\pi$
$692$	−4.75537	+	20.8347i	−0.180772	+	0.792015i
$693$	−2.69197	−	0.866055i	−0.102260	−	0.0328987i
$694$	−1.57286	−	6.89115i	−0.0597050	−	0.261585i
$695$	−1.88399	+	25.1402i	−0.0714640	+	0.953621i
$696$	−8.50586	+	2.62371i	−0.322414	+	0.0994515i
$697$	−2.73578	−	36.5065i	−0.103625	−	1.38278i
$698$	4.16053	+	10.6009i	0.157478	+	0.401249i
$699$	−21.4915	−	10.3497i	−0.812882	−	0.391463i
$700$	17.8265	−	5.26416i	0.673779	−	0.198966i
$701$	6.49535	−	3.12800i	0.245326	−	0.118143i	−0.307181	−	0.951651i	$-0.599386\pi$
$701$	6.49535	−	3.12800i	0.245326	−	0.118143i	0.552507	+	0.833508i	$0.313671\pi$
$702$	1.40212	+	1.30098i	0.0529197	+	0.0491023i
$703$	14.9567	+	2.25437i	0.564104	+	0.0850250i
$704$	16.3091	+	28.2481i	0.614671	+	1.06464i
$705$	8.63817	−	14.9618i	0.325332	−	0.563492i
$706$	1.45450	−	1.82389i	0.0547409	−	0.0686429i
$707$	−34.3725	+	16.0452i	−1.29271	+	0.603440i
$708$	8.04935	+	10.0936i	0.302513	+	0.379340i
$709$	−25.4003	+	3.82847i	−0.953927	+	0.143781i	−0.607521	−	0.794303i	$-0.707836\pi$
$709$	−25.4003	+	3.82847i	−0.953927	+	0.143781i	−0.346406	+	0.938085i	$0.612598\pi$
$710$	3.67610	+	2.50632i	0.137962	+	0.0940606i
$711$	0.861494	+	0.587357i	0.0323086	+	0.0220276i
$712$	−2.31229	+	0.348522i	−0.0866567	+	0.0130614i
$713$	15.6865	+	19.6703i	0.587466	+	0.736659i
$714$	6.41764	−	7.85132i	0.240174	−	0.293828i
$715$	4.47409	−	5.61034i	0.167322	−	0.209815i
$716$	11.2945	−	19.5627i	0.422096	−	0.731091i
$717$	8.22508	+	14.2462i	0.307171	+	0.532036i
$718$	−4.21390	−	0.635143i	−0.157261	−	0.0237033i
$719$	−23.3320	−	21.6489i	−0.870135	−	0.807367i	0.112358	−	0.993668i	$-0.464160\pi$
$719$	−23.3320	−	21.6489i	−0.870135	−	0.807367i	−0.982493	+	0.186300i	$0.940350\pi$
$720$	0.542208	−	0.261114i	0.0202069	−	0.00973113i
$721$	8.66840	+	6.06444i	0.322828	+	0.225851i
$722$	−5.35729	−	2.57993i	−0.199378	−	0.0960152i
$723$	−0.338850	−	0.863376i	−0.0126020	−	0.0321093i
$724$	−1.02853	−	13.7248i	−0.0382252	−	0.510080i
$725$	−13.6556	+	4.21219i	−0.507155	+	0.156437i
$726$	1.36979	−	18.2786i	0.0508376	−	0.678381i
$727$	−8.24767	−	36.1354i	−0.305889	−	1.34019i	−0.861082	−	0.508467i	$-0.830213\pi$
$727$	−8.24767	−	36.1354i	−0.305889	−	1.34019i	0.555193	−	0.831722i	$-0.312645\pi$
$728$	−1.87603	+	3.16073i	−0.0695305	+	0.117144i
$729$	−6.30306	+	27.6155i	−0.233447	+	1.02280i
$730$	−3.07563	−	0.948708i	−0.113834	−	0.0351132i
$731$	18.6754	−	47.5841i	0.690734	−	1.75996i
$732$	−10.7451	+	9.97001i	−0.397151	+	0.368502i
$733$	−27.7268	+	18.9038i	−1.02411	+	0.698229i	−0.954153	−	0.299320i	$-0.903240\pi$
$733$	−27.7268	+	18.9038i	−1.02411	+	0.698229i	−0.0699618	+	0.997550i	$0.522288\pi$
$734$	2.21089			0.0816053
$735$	12.9530	+	2.27313i	0.477780	+	0.0838457i
$736$	23.8230			0.878126
$737$	4.83942	−	3.29946i	0.178262	−	0.121537i
$738$	0.252323	−	0.234122i	0.00928814	−	0.00861813i
$739$	5.17710	−	13.1910i	0.190443	−	0.485240i	−0.803478	−	0.595334i	$-0.797020\pi$
$739$	5.17710	−	13.1910i	0.190443	−	0.485240i	0.993921	+	0.110094i	$0.0351150\pi$
$740$	19.3612	+	5.97213i	0.711731	+	0.219540i
$741$	0.583986	−	2.55861i	0.0214533	−	0.0939929i
$742$	−0.787379	+	9.04205i	−0.0289056	+	0.331944i
$743$	7.36489	+	32.2677i	0.270192	+	1.18379i	0.909787	+	0.415075i	$0.136245\pi$
$743$	7.36489	+	32.2677i	0.270192	+	1.18379i	−0.639595	+	0.768712i	$0.720898\pi$
$744$	0.727668	−	9.71006i	0.0266776	−	0.355988i
$745$	17.7573	−	5.47742i	0.650579	−	0.200677i
$746$	0.360975	+	4.81687i	0.0132162	+	0.176358i
$747$	0.746069	+	1.90095i	0.0272972	+	0.0695522i
$748$	68.7754	+	33.1205i	2.51468	+	1.21100i
$749$	16.8087	−	41.3542i	0.614177	−	1.51105i
$750$	5.31773	−	2.56088i	0.194176	−	0.0935102i
$751$	0.462292	+	0.428944i	0.0168693	+	0.0156524i	0.688562	−	0.725177i	$-0.258242\pi$
$751$	0.462292	+	0.428944i	0.0168693	+	0.0156524i	−0.671693	+	0.740830i	$0.734433\pi$
$752$	−29.4972	−	4.44599i	−1.07565	−	0.162128i
$753$	4.87507	+	8.44386i	0.177657	+	0.307711i
$754$	0.682959	−	1.18292i	0.0248719	−	0.0430794i
$755$	2.37426	−	2.97722i	0.0864080	−	0.108352i
$756$	−26.3856	−	0.318246i	−0.959635	−	0.0115745i
$757$	−14.7994	−	18.5578i	−0.537893	−	0.674496i	0.436407	−	0.899749i	$-0.356251\pi$
$757$	−14.7994	−	18.5578i	−0.537893	−	0.674496i	−0.974300	+	0.225253i	$0.927679\pi$
$758$	4.38093	−	0.660320i	0.159123	−	0.0239839i
$759$	54.0383	+	36.8427i	1.96147	+	1.33731i
$760$	1.99713	+	1.36162i	0.0724437	+	0.0493913i
$761$	−25.2672	+	3.80842i	−0.915936	+	0.138055i	−0.590062	−	0.807358i	$-0.700897\pi$
$761$	−25.2672	+	3.80842i	−0.915936	+	0.138055i	−0.325874	+	0.945413i	$0.605659\pi$
$762$	−0.947216	−	1.18777i	−0.0343140	−	0.0430284i
$763$	5.29507	−	21.9742i	0.191695	−	0.795518i
$764$	6.08290	−	7.62771i	0.220072	−	0.275961i
$765$	0.588518	−	1.01934i	0.0212779	−	0.0368544i
$766$	2.52315	+	4.37022i	0.0911651	+	0.157903i
$767$	−4.05272	−	0.610850i	−0.146335	−	0.0220565i
$768$	8.22211	+	7.62900i	0.296690	+	0.275288i
$769$	−1.34618	+	0.648284i	−0.0485443	+	0.0233777i	−0.457998	−	0.888953i	$-0.651433\pi$
$769$	−1.34618	+	0.648284i	−0.0485443	+	0.0233777i	0.409454	+	0.912331i	$0.365719\pi$
$770$	−0.427173	−	6.79980i	−0.0153943	−	0.245048i
$771$	23.3448	+	11.2422i	0.840741	+	0.404880i
$772$	−5.69000	−	14.4979i	−0.204787	−	0.521790i
$773$	1.65729	+	22.1150i	0.0596086	+	0.795422i	0.944267	+	0.329182i	$0.106773\pi$
$773$	1.65729	+	22.1150i	0.0596086	+	0.795422i	−0.884658	+	0.466240i	$0.845608\pi$
$774$	0.459273	−	0.141667i	0.0165082	−	0.00509212i
$775$	1.16822	−	15.5888i	0.0419637	−	0.559967i
$776$	3.83011	+	16.7808i	0.137493	+	0.602395i
$777$	−31.3193	−	29.7710i	−1.12357	−	1.06803i
$778$	1.36593	−	5.98453i	0.0489710	−	0.214556i
$779$	−8.59603	−	2.65153i	−0.307985	−	0.0950008i
$780$	1.28435	−	3.27247i	0.0459871	−	0.117173i
$781$	52.3612	−	48.5841i	1.87363	−	1.73848i
$782$	11.3671	−	7.74995i	0.406486	−	0.277138i
$783$	20.2872			0.725007
$784$	−4.51742	−	22.2534i	−0.161337	−	0.794764i
$785$	7.13654			0.254714
$786$	6.47890	−	4.41724i	0.231095	−	0.157558i
$787$	18.9834	−	17.6140i	0.676684	−	0.627871i	−0.265048	−	0.964235i	$-0.585388\pi$
$787$	18.9834	−	17.6140i	0.676684	−	0.627871i	0.941732	+	0.336364i	$0.109197\pi$
$788$	−5.97367	+	15.2207i	−0.212803	+	0.542213i
$789$	−1.95634	−	0.603450i	−0.0696474	−	0.0214834i
$790$	−0.558999	+	2.44914i	−0.0198883	+	0.0871364i
$791$	16.5248	−	2.28725i	0.587555	−	0.0813252i
$792$	0.330410	+	1.44762i	0.0117406	+	0.0514390i
$793$	0.347748	−	4.64038i	0.0123489	−	0.164785i
$794$	−1.68444	+	0.519581i	−0.0597786	+	0.0184393i
$795$	−1.34211	−	17.9092i	−0.0475997	−	0.635174i
$796$	−16.1394	−	41.1225i	−0.572045	−	1.45755i
$797$	1.35004	+	0.650147i	0.0478210	+	0.0230294i	0.457641	−	0.889137i	$-0.348694\pi$
$797$	1.35004	+	0.650147i	0.0478210	+	0.0230294i	−0.409820	+	0.912166i	$0.634409\pi$
$798$	−1.21977	−	2.17280i	−0.0431793	−	0.0769163i
$799$	−52.5657	+	25.3143i	−1.85964	+	0.895555i
$800$	−10.8508	−	10.0681i	−0.383634	−	0.355960i
$801$	0.276681	+	0.0417029i	0.00977603	+	0.00147350i
$802$	1.71081	+	2.96321i	0.0604107	+	0.104634i
$803$	−25.8365	+	44.7502i	−0.911751	+	1.57920i
$804$	1.78907	−	2.24342i	0.0630955	−	0.0791193i
$805$	15.9806	+	7.93467i	0.563241	+	0.279660i
$806$	0.931616	+	1.16821i	0.0328148	+	0.0411484i
$807$	25.0358	−	3.77353i	0.881300	−	0.132835i
$808$	16.4569	+	11.2201i	0.578953	+	0.394723i
$809$	15.8823	+	10.8284i	0.558392	+	0.380705i	0.809380	−	0.587285i	$-0.199803\pi$
$809$	15.8823	+	10.8284i	0.558392	+	0.380705i	−0.250988	+	0.967990i	$0.580756\pi$
$810$	−3.35582	+	0.505808i	−0.117911	+	0.0177723i
$811$	−6.76836	−	8.48726i	−0.237669	−	0.298028i	0.648665	−	0.761074i	$-0.275328\pi$
$811$	−6.76836	−	8.48726i	−0.237669	−	0.298028i	−0.886334	+	0.463046i	$0.846756\pi$
$812$	3.97130	+	18.4207i	0.139365	+	0.646440i
$813$	3.18614	−	3.99530i	0.111743	−	0.140121i
$814$	−11.1933	+	19.3874i	−0.392326	+	0.679529i
$815$	−12.2435	−	21.2063i	−0.428870	−	0.742825i
$816$	34.2588	+	5.16368i	1.19930	+	0.180765i
$817$	−9.20777	−	8.54356i	−0.322139	−	0.298901i
$818$	−6.28530	+	3.02684i	−0.219760	+	0.105831i
$819$	0.325984	−	0.295233i	0.0113908	−	0.0103163i
$820$	−10.8567	−	5.22830i	−0.379132	−	0.182580i
$821$	2.42028	+	6.16677i	0.0844683	+	0.215222i	0.966867	−	0.255281i	$-0.0821679\pi$
$821$	2.42028	+	6.16677i	0.0844683	+	0.215222i	−0.882399	+	0.470502i	$0.844073\pi$
$822$	0.171970	+	2.29479i	0.00599816	+	0.0800399i
$823$	31.5426	−	9.72962i	1.09951	−	0.339153i	0.308664	−	0.951171i	$-0.400118\pi$
$823$	31.5426	−	9.72962i	1.09951	−	0.339153i	0.790844	+	0.612018i	$0.209642\pi$
$824$	0.415118	−	5.53937i	0.0144613	−	0.192973i
$825$	−9.04271	−	39.6187i	−0.314827	−	1.37935i
$826$	−3.24139	+	2.15314i	−0.112782	+	0.0749173i
$827$	−10.0199	+	43.8999i	−0.348425	+	1.52655i	0.432333	+	0.901714i	$0.357691\pi$
$827$	−10.0199	+	43.8999i	−0.348425	+	1.52655i	−0.780758	+	0.624834i	$0.785167\pi$
$828$	−1.79604	−	0.554005i	−0.0624167	−	0.0192530i
$829$	3.36212	−	8.56654i	0.116771	−	0.297528i	−0.860524	−	0.509410i	$-0.829864\pi$
$829$	3.36212	−	8.56654i	0.116771	−	0.297528i	0.977295	+	0.211881i	$0.0679591\pi$
$830$	−3.60669	+	3.34652i	−0.125190	+	0.116159i
$831$	−1.42622	+	0.972379i	−0.0494750	+	0.0337315i
$832$	−5.07296			−0.175873
$833$	−31.8181	−	30.9842i	−1.10243	−	1.07354i
$834$	−13.6463			−0.472533
$835$	8.31951	−	5.67215i	0.287908	−	0.196293i
$836$	13.7501	−	12.7582i	0.475558	−	0.441253i
$837$	−8.10783	+	20.6584i	−0.280248	+	0.714059i
$838$	−0.384699	−	0.118664i	−0.0132892	−	0.00409918i
$839$	−1.72091	+	7.53981i	−0.0594125	+	0.260303i	−0.995908	−	0.0903776i	$-0.971193\pi$
$839$	−1.72091	+	7.53981i	−0.0594125	+	0.260303i	0.936495	+	0.350681i	$0.114050\pi$
$840$	−2.44509	−	6.45793i	−0.0843635	−	0.222820i
$841$	3.22931	+	14.1486i	0.111356	+	0.487881i
$842$	0.657194	−	8.76964i	0.0226484	−	0.302222i
$843$	15.1985	−	4.68811i	0.523463	−	0.161467i
$844$	−0.246814	−	3.29350i	−0.00849568	−	0.113367i
$845$	0.407734	+	1.03889i	0.0140265	+	0.0357388i
$846$	−0.494241	−	0.238014i	−0.0169923	−	0.00818308i
$847$	−79.2316	−	12.9214i	−2.72243	−	0.443984i
$848$	−27.9389	+	13.4547i	−0.959425	+	0.462035i
$849$	−8.11375	−	7.52846i	−0.278463	−	0.258376i
$850$	−8.45274	−	1.27404i	−0.289926	−	0.0436994i
$851$	−29.3124	−	50.7706i	−1.00482	−	1.74040i
$852$	17.4966	−	30.3050i	0.599424	−	1.03823i
$853$	4.94552	−	6.20148i	0.169331	−	0.212335i	−0.689924	−	0.723882i	$-0.742356\pi$
$853$	4.94552	−	6.20148i	0.169331	−	0.212335i	0.859255	+	0.511547i	$0.170927\pi$
$854$	−2.71284	−	3.48726i	−0.0928314	−	0.119331i
$855$	−0.180330	−	0.226127i	−0.00616715	−	0.00773336i
$856$	−23.1776	+	3.49346i	−0.792194	+	0.119404i
$857$	−18.1173	−	12.3521i	−0.618874	−	0.421941i	0.212886	−	0.977077i	$-0.431714\pi$
$857$	−18.1173	−	12.3521i	−0.618874	−	0.421941i	−0.831759	+	0.555136i	$0.812666\pi$
$858$	3.20931	+	2.18807i	0.109564	+	0.0746995i
$859$	16.9870	−	2.56039i	0.579591	−	0.0873592i	0.147297	−	0.989092i	$-0.452943\pi$
$859$	16.9870	−	2.56039i	0.579591	−	0.0873592i	0.432293	+	0.901733i	$0.357705\pi$
$860$	−10.4906	−	13.1549i	−0.357728	−	0.448577i
$861$	15.7796	+	20.2841i	0.537766	+	0.691279i
$862$	−6.99337	+	8.76941i	−0.238195	+	0.298687i
$863$	22.0512	−	38.1938i	0.750631	−	1.30013i	−0.196886	−	0.980426i	$-0.563083\pi$
$863$	22.0512	−	38.1938i	0.750631	−	1.30013i	0.947517	−	0.319705i	$-0.103584\pi$
$864$	10.5069	+	18.1985i	0.357452	+	0.619124i
$865$	12.6034	+	1.89966i	0.428530	+	0.0645905i
$866$	9.26884	+	8.60023i	0.314968	+	0.292248i
$867$	35.2677	−	16.9840i	1.19775	−	0.576808i
$868$	−20.3449	−	3.31792i	−0.690550	−	0.112617i
$869$	36.3365	+	17.4988i	1.23263	+	0.593604i
$870$	0.937526	+	2.38878i	0.0317851	+	0.0809871i
$871$	0.0680747	+	0.908394i	0.00230662	+	0.0307797i
$872$	−11.3412	+	3.49828i	−0.384060	+	0.118467i
$873$	0.153912	−	2.05381i	0.00520913	−	0.0695110i
$874$	−0.752252	−	3.29583i	−0.0254453	−	0.111483i
$875$	−9.15308	−	24.1750i	−0.309431	−	0.817265i
$876$	−5.63306	+	24.6800i	−0.190323	+	0.833861i
$877$	39.2526	+	12.1078i	1.32547	+	0.408853i	0.875079	−	0.483980i	$-0.160809\pi$
$877$	39.2526	+	12.1078i	1.32547	+	0.408853i	0.450388	+	0.892833i	$0.351286\pi$
$878$	−1.91582	+	4.88143i	−0.0646558	+	0.164740i
$879$	10.6596	−	9.89062i	0.359538	−	0.333602i
$880$	19.2331	−	13.1129i	0.648346	−	0.442035i
$881$	34.9643			1.17798			0.588989	−	0.808141i	$-0.299526\pi$
$881$	34.9643			1.17798			0.588989	+	0.808141i	$0.299526\pi$
$882$	0.0412398	−	0.415534i	0.00138862	−	0.0139918i
$883$	−48.7765			−1.64146			−0.820730	−	0.571316i	$-0.806433\pi$
$883$	−48.7765			−1.64146			−0.820730	+	0.571316i	$0.806433\pi$
$884$	−9.80914	+	6.68776i	−0.329917	+	0.224934i
$885$	5.64443	−	5.23726i	0.189735	−	0.176049i
$886$	3.88834	−	9.90734i	0.130631	−	0.332844i
$887$	−12.9577	−	3.99692i	−0.435076	−	0.134203i	0.0694775	−	0.997584i	$-0.477867\pi$
$887$	−12.9577	−	3.99692i	−0.435076	−	0.134203i	−0.504554	+	0.863380i	$0.668343\pi$
$888$	−5.04885	+	22.1205i	−0.169428	+	0.742314i
$889$	−5.54231	+	3.68156i	−0.185883	+	0.123476i
$890$	0.150010	+	0.657239i	0.00502836	+	0.0220307i
$891$	−4.07160	+	54.3317i	−0.136404	+	1.82018i
$892$	49.5010	−	15.2690i	1.65742	−	0.511245i
$893$	1.07136	+	14.2963i	0.0358518	+	0.478409i
$894$	3.67488	+	9.36344i	0.122906	+	0.313160i
$895$	−12.1384	−	5.84554i	−0.405741	−	0.195395i
$896$	−19.0331	+	17.2376i	−0.635850	+	0.575869i
$897$	−9.16450	+	4.41339i	−0.305994	+	0.147359i
$898$	5.46086	+	5.06693i	0.182231	+	0.169086i
$899$	15.6712	+	2.36205i	0.522663	+	0.0787788i
$900$	0.583920	+	1.01138i	0.0194640	+	0.0337126i
$901$	−30.3251	+	52.5247i	−1.01028	+	1.74985i
$902$	8.30115	−	10.4093i	0.276398	−	0.346592i
$903$	7.56244	+	35.0781i	0.251662	+	1.16733i
$904$	−5.46150	−	6.84851i	−0.181647	−	0.227778i
$905$	−8.11706	+	1.22345i	−0.269820	+	0.0406689i
$906$	1.70308	+	1.16114i	0.0565810	+	0.0385763i
$907$	28.8728	+	19.6851i	0.958704	+	0.653633i	0.938177	−	0.346156i	$-0.112513\pi$
$907$	28.8728	+	19.6851i	0.958704	+	0.653633i	0.0205271	+	0.999789i	$0.493466\pi$
$908$	−36.7602	+	5.54071i	−1.21993	+	0.183875i
$909$	−1.48597	−	1.86334i	−0.0492864	−	0.0618032i
$910$	0.949078	+	0.471236i	0.0314616	+	0.0156213i
$911$	0.557372	−	0.698923i	0.0184666	−	0.0231563i	−0.772512	−	0.635000i	$-0.781000\pi$
$911$	0.557372	−	0.698923i	0.0184666	−	0.0231563i	0.790979	+	0.611843i	$0.209572\pi$
$912$	4.25666	−	7.37275i	0.140952	−	0.244136i
$913$	39.4946	+	68.4066i	1.30708	+	2.26393i
$914$	−3.36787	−	0.507624i	−0.111399	−	0.0167907i
$915$	6.40862	+	5.94633i	0.211862	+	0.196580i
$916$	24.4842	−	11.7910i	0.808980	−	0.389584i
$917$	−16.8115	−	29.9467i	−0.555164	−	0.988927i
$918$	10.9336	+	5.26533i	0.360861	+	0.173782i
$919$	18.9408	+	48.2604i	0.624800	+	1.59196i	0.795036	+	0.606562i	$0.207452\pi$
$919$	18.9408	+	48.2604i	0.624800	+	1.59196i	−0.170236	+	0.985403i	$0.554453\pi$
$920$	−0.700107	−	9.34228i	−0.0230818	−	0.308006i
$921$	−1.22910	+	0.379126i	−0.0405001	+	0.0124926i
$922$	0.0412272	−	0.550139i	0.00135775	−	0.0181179i
$923$	2.47200	+	10.8305i	0.0813668	+	0.356491i
$924$	−53.0802	+	7.34698i	−1.74621	+	0.241698i
$925$	−8.10558	+	35.5129i	−0.266510	+	1.16766i
$926$	−3.96688	−	1.22362i	−0.130360	−	0.0402106i
$927$	−0.242835	+	0.618734i	−0.00797575	+	0.0203219i
$928$	11.0005	−	10.2070i	0.361109	−	0.335060i
$929$	19.5560	−	13.3330i	0.641610	−	0.437442i	−0.198320	−	0.980137i	$-0.563548\pi$
$929$	19.5560	−	13.3330i	0.641610	−	0.437442i	0.839930	+	0.542695i	$0.182596\pi$
$930$	−2.80717			−0.0920506
$931$	−9.94369	+	4.49648i	−0.325891	+	0.147366i
$932$	26.5154			0.868542
$933$	17.0707	−	11.6386i	0.558871	−	0.381031i
$934$	−1.49998	+	1.39178i	−0.0490810	+	0.0455405i
$935$	16.6332	−	42.3806i	0.543963	−	1.38599i
$936$	−0.220673	−	0.0680685i	−0.00721292	−	0.00222489i
$937$	−8.51332	+	37.2993i	−0.278118	+	1.21852i	0.622052	+	0.782976i	$0.286299\pi$
$937$	−8.51332	+	37.2993i	−0.278118	+	1.21852i	−0.900170	+	0.435539i	$0.856558\pi$
$938$	0.626875	+	0.595885i	0.0204682	+	0.0194563i
$939$	7.00049	+	30.6712i	0.228452	+	1.00092i
$940$	−1.43512	+	19.1504i	−0.0468086	+	0.624618i
$941$	−11.0416	+	3.40588i	−0.359946	+	0.111029i	−0.469453	−	0.882957i	$-0.655549\pi$
$941$	−11.0416	+	3.40588i	−0.359946	+	0.111029i	0.109507	+	0.993986i	$0.465073\pi$
$942$	0.288678	+	3.85214i	0.00940564	+	0.125510i
$943$	12.7380	+	32.4558i	0.414805	+	1.05691i
$944$	−11.9785	−	5.76853i	−0.389866	−	0.187750i
$945$	0.986745	+	15.7071i	0.0320988	+	0.510953i
$946$	16.7496	−	8.06617i	0.544576	−	0.262254i
$947$	24.4959	+	22.7289i	0.796009	+	0.738589i	0.969193	−	0.246301i	$-0.0792151\pi$
$947$	24.4959	+	22.7289i	0.796009	+	0.738589i	−0.173184	+	0.984889i	$0.555406\pi$
$948$	19.5373	+	2.94478i	0.634542	+	0.0956419i
$949$	−4.01825	−	6.95981i	−0.130438	−	0.225925i
$950$	−1.05025	+	1.81909i	−0.0340747	+	0.0590191i
$951$	−13.5947	+	17.0472i	−0.440839	+	0.552794i
$952$	−5.46295	+	22.6708i	−0.177055	+	0.734766i
$953$	−7.64613	−	9.58794i	−0.247682	−	0.310584i	0.642413	−	0.766359i	$-0.277934\pi$
$953$	−7.64613	−	9.58794i	−0.247682	−	0.310584i	−0.890095	+	0.455775i	$0.849362\pi$
$954$	−0.563886	+	0.0849921i	−0.0182565	+	0.00275172i
$955$	−4.80773	−	3.27786i	−0.155575	−	0.106069i
$956$	−15.1084	−	10.3007i	−0.488640	−	0.333149i
$957$	40.7380	−	6.14027i	1.31687	−	0.198487i
$958$	−1.64135	−	2.05819i	−0.0530296	−	0.0664970i
$959$	10.0778	+	0.121552i	0.325430	+	0.00392513i
$960$	5.94225	−	7.45135i	0.191785	−	0.240491i
$961$	6.83172	−	11.8329i	0.220378	−	0.381706i
$962$	−1.74085	−	3.01524i	−0.0561273	−	0.0972154i
$963$	2.77335	+	0.418016i	0.0893701	+	0.0134704i
$964$	0.755764	+	0.701247i	0.0243415	+	0.0225856i
$965$	−8.36906	+	4.03033i	−0.269410	+	0.129741i
$966$	−3.63653	+	8.94690i	−0.117003	+	0.287862i
$967$	−50.5560	−	24.3465i	−1.62577	−	0.782930i	−0.999996	−	0.00292580i	$-0.999069\pi$
$967$	−50.5560	−	24.3465i	−1.62577	−	0.782930i	−0.625775	−	0.780004i	$-0.715217\pi$
$968$	15.4000	+	39.2387i	0.494976	+	1.26118i
$969$	−1.24431	−	16.6041i	−0.0399730	−	0.533402i
$970$	4.74170	−	1.46262i	0.152247	−	0.0469619i
$971$	−0.434655	+	5.80006i	−0.0139487	+	0.186133i	0.985877	+	0.167470i	$0.0535599\pi$
$971$	−0.434655	+	5.80006i	−0.0139487	+	0.186133i	−0.999826	+	0.0186625i	$0.994059\pi$
$972$	−0.718469	−	3.14782i	−0.0230449	−	0.100966i
$973$	−5.18480	+	59.5408i	−0.166217	+	1.90879i
$974$	0.580538	−	2.54350i	0.0186016	−	0.0814991i
$975$	6.03940	+	1.86291i	0.193416	+	0.0596608i
$976$	5.51487	−	14.0516i	0.176527	−	0.449782i
$977$	−40.4528	+	37.5347i	−1.29420	+	1.20084i	−0.327521	+	0.944844i	$0.606213\pi$
$977$	−40.4528	+	37.5347i	−1.29420	+	1.20084i	−0.966677	+	0.255997i	$0.917596\pi$
$978$	10.9514	−	7.46656i	0.350188	−	0.238754i
$979$	10.8229			0.345901
$980$	−14.0688	+	3.97068i	−0.449412	+	0.126839i
$981$	1.42014			0.0453415
$982$	6.25668	−	4.26573i	0.199659	−	0.136125i
$983$	18.7333	−	17.3820i	0.597500	−	0.554399i	−0.322375	−	0.946612i	$-0.604481\pi$
$983$	18.7333	−	17.3820i	0.597500	−	0.554399i	0.919874	+	0.392214i	$0.128291\pi$
$984$	4.92992	−	12.5612i	0.157160	−	0.400437i
$985$	9.31880	+	2.87447i	0.296922	+	0.0915882i
$986$	1.92840	−	8.44886i	0.0614126	−	0.269066i
$987$	20.9045	−	35.2198i	0.665399	−	1.12106i
$988$	0.649150	+	2.84411i	0.0206522	+	0.0904832i
$989$	−3.63816	+	48.5479i	−0.115687	+	1.54373i
$990$	0.409050	−	0.126175i	0.0130005	−	0.00401011i
$991$	1.78982	+	23.8835i	0.0568554	+	0.758683i	0.950662	+	0.310230i	$0.100406\pi$
$991$	1.78982	+	23.8835i	0.0568554	+	0.758683i	−0.893806	+	0.448453i	$0.851975\pi$
$992$	5.99735	+	15.2810i	0.190416	+	0.485172i
$993$	18.3248	+	8.82476i	0.581520	+	0.280045i
$994$	8.64252	+	6.04633i	0.274124	+	0.191778i
$995$	−23.7384	+	11.4318i	−0.752558	+	0.362413i
$996$	28.3669	+	26.3206i	0.898838	+	0.834000i
$997$	−50.5420	−	7.61799i	−1.60068	−	0.241264i	−0.712811	−	0.701356i	$-0.752578\pi$
$997$	−50.5420	−	7.61799i	−1.60068	−	0.241264i	−0.887871	+	0.460092i	$0.847816\pi$
$998$	6.75797	+	11.7051i	0.213920	+	0.370520i
$999$	25.8559	−	44.7838i	0.818046	−	1.41690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.625.13	yes	348
49.4	even	21	inner	637.2.bl.b.53.13	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.13	✓	348	49.4	even	21	inner
637.2.bl.b.625.13	yes	348	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.296505 + 0.202154i) q^{2} +(1.23401 - 1.14499i) q^{3} +(-0.683633 + 1.74187i) q^{4} +(1.06645 + 0.328957i) q^{5} +(-0.134425 + 0.588954i) q^{6} +(2.51862 + 0.810284i) q^{7} +(-0.309133 - 1.35440i) q^{8} +(-0.0124224 + 0.165766i) q^{9} +O(q^{10})\)	\(q+(-0.296505 + 0.202154i) q^{2} +(1.23401 - 1.14499i) q^{3} +(-0.683633 + 1.74187i) q^{4} +(1.06645 + 0.328957i) q^{5} +(-0.134425 + 0.588954i) q^{6} +(2.51862 + 0.810284i) q^{7} +(-0.309133 - 1.35440i) q^{8} +(-0.0124224 + 0.165766i) q^{9} +(-0.382709 + 0.118050i) q^{10} +(0.480500 + 6.41182i) q^{11} +(1.15081 + 2.93223i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(-0.910585 + 0.268895i) q^{14} +(1.69266 - 0.815143i) q^{15} +(-2.37794 - 2.20641i) q^{16} +(-6.27369 - 0.945606i) q^{17} +(-0.0298268 - 0.0516616i) q^{18} +(-0.779506 + 1.35014i) q^{19} +(-1.30206 + 1.63274i) q^{20} +(4.03575 - 1.88390i) q^{21} +(-1.43864 - 1.80400i) q^{22} +(5.97501 - 0.900588i) q^{23} +(-1.93224 - 1.31738i) q^{24} +(-3.10208 - 2.11497i) q^{25} +(0.354853 - 0.0534855i) q^{26} +(3.32318 + 4.16714i) q^{27} +(-3.13322 + 3.83317i) q^{28} +(2.37316 - 2.97585i) q^{29} +(-0.337098 + 0.583872i) q^{30} +(2.08186 + 3.60589i) q^{31} +(3.89853 + 0.587609i) q^{32} +(7.93441 + 7.36206i) q^{33} +(2.05134 - 0.987872i) q^{34} +(2.41944 + 1.69265i) q^{35} +(-0.280250 - 0.134961i) q^{36} +(-3.54457 - 9.03142i) q^{37} +(-0.0418092 - 0.557904i) q^{38} +(-1.60859 + 0.496185i) q^{39} +(0.115864 - 1.54609i) q^{40} +(1.28397 + 5.62545i) q^{41} +(-0.815784 + 1.37443i) q^{42} +(-1.79284 + 7.85494i) q^{43} +(-11.4970 - 3.54637i) q^{44} +(-0.0677778 + 0.172695i) q^{45} +(-1.58956 + 1.47490i) q^{46} +(7.59796 - 5.18020i) q^{47} -5.46071 q^{48} +(5.68688 + 4.08159i) q^{49} +1.34733 q^{50} +(-8.82447 + 6.01642i) q^{51} +(1.37170 - 1.27275i) q^{52} +(3.49245 - 8.89862i) q^{53} +(-1.82774 - 0.563784i) q^{54} +(-1.59679 + 6.99597i) q^{55} +(0.318860 - 3.66170i) q^{56} +(0.583986 + 2.55861i) q^{57} +(-0.102075 + 1.36210i) q^{58} +(3.91641 - 1.20805i) q^{59} +(0.262712 + 3.50565i) q^{60} +(1.70007 + 4.33172i) q^{61} +(-1.34622 - 0.648308i) q^{62} +(-0.165605 + 0.407435i) q^{63} +(4.57058 - 2.20107i) q^{64} +(-0.818112 - 0.759097i) q^{65} +(-3.84086 - 0.578916i) q^{66} +(-0.455470 - 0.788898i) q^{67} +(5.93602 - 10.2815i) q^{68} +(6.34203 - 7.95265i) q^{69} +(-1.05955 - 0.0127796i) q^{70} +(-6.92638 - 8.68541i) q^{71} +(0.228353 - 0.0344187i) q^{72} +(6.64006 + 4.52712i) q^{73} +(2.87672 + 1.96131i) q^{74} +(-6.24960 + 0.941976i) q^{75} +(-1.81888 - 2.28080i) q^{76} +(-3.98520 + 16.5383i) q^{77} +(0.376650 - 0.472304i) q^{78} +(3.13622 - 5.43209i) q^{79} +(-1.81015 - 3.13528i) q^{80} +(8.37903 + 1.26294i) q^{81} +(-1.51791 - 1.40841i) q^{82} +(11.0683 - 5.33020i) q^{83} +(0.522527 + 8.31765i) q^{84} +(-6.37953 - 3.07222i) q^{85} +(-1.05632 - 2.69146i) q^{86} +(-0.478824 - 6.38946i) q^{87} +(8.53563 - 2.63289i) q^{88} +(0.125789 - 1.67853i) q^{89} +(-0.0148145 - 0.0649064i) q^{90} +(-1.91763 - 1.82283i) q^{91} +(-2.51601 + 11.0234i) q^{92} +(6.69773 + 2.06598i) q^{93} +(-1.20564 + 3.07191i) q^{94} +(-1.27545 + 1.18344i) q^{95} +(5.48362 - 3.73867i) q^{96} -12.3898 q^{97} +(-2.51130 - 0.0605882i) q^{98} -1.06883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

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