LMFDB - Embedded newform 966.2.q.j.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	966.85
Dual form			966.2.q.j.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.479771 + 1.05055i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.479771 + 1.05055i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-1.10814 - 0.325379i) q^{10} +(1.74634 + 2.01538i) q^{11} +(0.654861 + 0.755750i) q^{12} +(2.97114 + 0.872404i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-0.971581 - 0.624397i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.910290 - 6.33121i) q^{17} +(0.415415 + 0.909632i) q^{18} +(-0.717196 - 4.98821i) q^{19} +(0.971581 - 0.624397i) q^{20} +(-0.654861 + 0.755750i) q^{21} -2.66673 q^{22} +(-1.66122 + 4.49893i) q^{23} -1.00000 q^{24} +(2.40082 - 2.77070i) q^{25} +(-2.60500 + 1.67413i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.136215 + 0.947393i) q^{29} +(1.10814 - 0.325379i) q^{30} +(3.04773 + 1.95866i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-2.55871 - 0.751305i) q^{33} +(4.18869 + 4.83401i) q^{34} +(0.756312 + 0.872830i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.81849 - 6.17164i) q^{37} +(4.23950 + 2.72456i) q^{38} +(-2.97114 + 0.872404i) q^{39} +(-0.164362 + 1.14316i) q^{40} +(4.74077 + 10.3808i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(-1.82362 + 1.17197i) q^{43} +(1.74634 - 2.01538i) q^{44} +1.15492 q^{45} +(-2.31219 - 4.20164i) q^{46} +9.44514 q^{47} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.521749 + 3.62884i) q^{50} +(2.65712 + 5.81829i) q^{51} +(0.440688 - 3.06505i) q^{52} +(-2.51764 + 0.739246i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-1.27942 + 2.80154i) q^{55} +(0.959493 + 0.281733i) q^{56} +(3.30017 + 3.80860i) q^{57} +(-0.626790 - 0.723355i) q^{58} +(9.31693 + 2.73570i) q^{59} +(-0.479771 + 1.05055i) q^{60} +(-6.86556 - 4.41222i) q^{61} +(-3.47610 + 1.02067i) q^{62} +(0.142315 - 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.508959 + 3.53989i) q^{65} +(2.24340 - 1.44174i) q^{66} +(-2.87870 + 3.32220i) q^{67} -6.39631 q^{68} +(-1.03480 - 4.68286i) q^{69} -1.15492 q^{70} +(0.375833 - 0.433734i) q^{71} +(0.841254 - 0.540641i) q^{72} +(2.04187 + 14.2015i) q^{73} +(2.81849 + 6.17164i) q^{74} +(-0.521749 + 3.62884i) q^{75} +(-4.83537 + 1.41979i) q^{76} +(2.24340 + 1.44174i) q^{77} +(1.28636 - 2.81674i) q^{78} +(-2.63983 - 0.775123i) q^{79} +(-0.756312 - 0.872830i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-10.9499 - 3.21517i) q^{82} +(-5.09144 + 11.1487i) q^{83} +(0.841254 + 0.540641i) q^{84} +(7.08799 - 2.08122i) q^{85} +(0.308503 - 2.14568i) q^{86} +(-0.397608 - 0.870641i) q^{87} +(0.379515 + 2.63959i) q^{88} +(-8.82095 + 5.66888i) q^{89} +(-0.756312 + 0.872830i) q^{90} +3.09657 q^{91} +(4.68955 + 1.00405i) q^{92} -3.62285 q^{93} +(-6.18525 + 7.13816i) q^{94} +(4.89628 - 3.14665i) q^{95} +(0.142315 + 0.989821i) q^{96} +(4.53488 + 9.92999i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(2.55871 - 0.751305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{14} - 7 q^{15} - 4 q^{16} + 5 q^{17} - 4 q^{18} + 44 q^{19} + 7 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 40 q^{24} + 2 q^{25} + 24 q^{26} + 4 q^{27} + 4 q^{28} + 35 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 11 q^{33} + 5 q^{34} - 7 q^{35} - 4 q^{36} + 20 q^{37} - 11 q^{38} + 20 q^{39} - 4 q^{40} + 11 q^{41} - 4 q^{42} - 42 q^{43} - 11 q^{44} - 4 q^{45} - 6 q^{46} + 40 q^{47} + 4 q^{48} - 4 q^{49} - 53 q^{50} + 17 q^{51} - 9 q^{52} - 32 q^{53} + 4 q^{54} + 29 q^{55} + 4 q^{56} - 11 q^{57} - 31 q^{58} - 25 q^{59} + 4 q^{60} - 30 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 80 q^{65} - 88 q^{67} - 28 q^{68} + 6 q^{69} + 4 q^{70} - 45 q^{71} - 4 q^{72} - 39 q^{73} + 20 q^{74} + 53 q^{75} - 22 q^{76} - 2 q^{78} + 26 q^{79} + 7 q^{80} - 4 q^{81} + 22 q^{83} - 4 q^{84} + 77 q^{85} - 31 q^{86} + 9 q^{87} - 11 q^{88} + 20 q^{89} + 7 q^{90} - 24 q^{91} - 17 q^{92} - 42 q^{93} - 26 q^{94} + 84 q^{95} + 4 q^{96} + 74 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 11 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^14 - 7 * q^15 - 4 * q^16 + 5 * q^17 - 4 * q^18 + 44 * q^19 + 7 * q^20 - 4 * q^21 + 22 * q^22 - 6 * q^23 - 40 * q^24 + 2 * q^25 + 24 * q^26 + 4 * q^27 + 4 * q^28 + 35 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 11 * q^33 + 5 * q^34 - 7 * q^35 - 4 * q^36 + 20 * q^37 - 11 * q^38 + 20 * q^39 - 4 * q^40 + 11 * q^41 - 4 * q^42 - 42 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 40 * q^47 + 4 * q^48 - 4 * q^49 - 53 * q^50 + 17 * q^51 - 9 * q^52 - 32 * q^53 + 4 * q^54 + 29 * q^55 + 4 * q^56 - 11 * q^57 - 31 * q^58 - 25 * q^59 + 4 * q^60 - 30 * q^61 - 24 * q^62 + 4 * q^63 - 4 * q^64 + 80 * q^65 - 88 * q^67 - 28 * q^68 + 6 * q^69 + 4 * q^70 - 45 * q^71 - 4 * q^72 - 39 * q^73 + 20 * q^74 + 53 * q^75 - 22 * q^76 - 2 * q^78 + 26 * q^79 + 7 * q^80 - 4 * q^81 + 22 * q^83 - 4 * q^84 + 77 * q^85 - 31 * q^86 + 9 * q^87 - 11 * q^88 + 20 * q^89 + 7 * q^90 - 24 * q^91 - 17 * q^92 - 42 * q^93 - 26 * q^94 + 84 * q^95 + 4 * q^96 + 74 * q^97 - 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.479771	+	1.05055i	0.214560	+	0.469821i	0.986056	−	0.166413i	$-0.0532185\pi$
$5$	0.479771	+	1.05055i	0.214560	+	0.469821i	−0.771496	+	0.636234i	$0.780491\pi$
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−1.10814	−	0.325379i	−0.350424	−	0.102894i
$11$	1.74634	+	2.01538i	0.526540	+	0.607660i	0.955256	−	0.295779i	$-0.0955793\pi$
$11$	1.74634	+	2.01538i	0.526540	+	0.607660i	−0.428716	+	0.903439i	$0.641034\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	2.97114	+	0.872404i	0.824045	+	0.241961i	0.666457	−	0.745543i	$-0.267810\pi$
$13$	2.97114	+	0.872404i	0.824045	+	0.241961i	0.157588	+	0.987505i	$0.449628\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	−0.971581	−	0.624397i	−0.250861	−	0.161219i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.910290	−	6.33121i	0.220778	−	1.53554i	−0.514330	−	0.857592i	$-0.671959\pi$
$17$	0.910290	−	6.33121i	0.220778	−	1.53554i	0.735108	−	0.677950i	$-0.237132\pi$
$18$	0.415415	+	0.909632i	0.0979143	+	0.214402i
$19$	−0.717196	−	4.98821i	−0.164536	−	1.14437i	−0.889949	−	0.456059i	$-0.849260\pi$
$19$	−0.717196	−	4.98821i	−0.164536	−	1.14437i	0.725413	−	0.688313i	$-0.241649\pi$
$20$	0.971581	−	0.624397i	0.217252	−	0.139619i
$21$	−0.654861	+	0.755750i	−0.142902	+	0.164918i
$22$	−2.66673			−0.568549
$23$	−1.66122	+	4.49893i	−0.346388	+	0.938091i
$23$	−1.66122	+	4.49893i	−0.346388	+	0.938091i
$24$	−1.00000			−0.204124
$25$	2.40082	−	2.77070i	0.480165	−	0.554140i
$26$	−2.60500	+	1.67413i	−0.510883	+	0.328324i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	−0.415415	−	0.909632i	−0.0785061	−	0.171904i
$29$	−0.136215	+	0.947393i	−0.0252944	+	0.175926i	−0.998552	−	0.0537885i	$-0.982870\pi$
$29$	−0.136215	+	0.947393i	−0.0252944	+	0.175926i	0.973258	+	0.229715i	$0.0737794\pi$
$30$	1.10814	−	0.325379i	0.202317	−	0.0594057i
$31$	3.04773	+	1.95866i	0.547389	+	0.351786i	0.784923	−	0.619594i	$-0.212703\pi$
$31$	3.04773	+	1.95866i	0.547389	+	0.351786i	−0.237534	+	0.971379i	$0.576339\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	−2.55871	−	0.751305i	−0.445414	−	0.130785i
$34$	4.18869	+	4.83401i	0.718355	+	0.829026i
$35$	0.756312	+	0.872830i	0.127840	+	0.147535i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	2.81849	−	6.17164i	0.463357	−	1.01461i	−0.523352	−	0.852116i	$-0.675319\pi$
$37$	2.81849	−	6.17164i	0.463357	−	1.01461i	0.986709	−	0.162494i	$-0.0519539\pi$
$38$	4.23950	+	2.72456i	0.687737	+	0.441982i
$39$	−2.97114	+	0.872404i	−0.475763	+	0.139697i
$40$	−0.164362	+	1.14316i	−0.0259880	+	0.180750i
$41$	4.74077	+	10.3808i	0.740384	+	1.62122i	0.782921	+	0.622121i	$0.213729\pi$
$41$	4.74077	+	10.3808i	0.740384	+	1.62122i	−0.0425367	+	0.999095i	$0.513544\pi$
$42$	−0.142315	−	0.989821i	−0.0219597	−	0.152733i
$43$	−1.82362	+	1.17197i	−0.278100	+	0.178724i	−0.672254	−	0.740320i	$-0.734674\pi$
$43$	−1.82362	+	1.17197i	−0.278100	+	0.178724i	0.394154	+	0.919044i	$0.371038\pi$
$44$	1.74634	−	2.01538i	0.263270	−	0.303830i
$45$	1.15492			0.172165
$46$	−2.31219	−	4.20164i	−0.340915	−	0.619498i
$47$	9.44514			1.37771			0.688857	−	0.724897i	$-0.258113\pi$
$47$	9.44514			1.37771			0.688857	+	0.724897i	$0.258113\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	0.521749	+	3.62884i	0.0737864	+	0.513196i
$51$	2.65712	+	5.81829i	0.372072	+	0.814723i
$52$	0.440688	−	3.06505i	0.0611124	−	0.425046i
$53$	−2.51764	+	0.739246i	−0.345824	+	0.101543i	−0.450032	−	0.893012i	$-0.648587\pi$
$53$	−2.51764	+	0.739246i	−0.345824	+	0.101543i	0.104208	+	0.994556i	$0.466769\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	−1.27942	+	2.80154i	−0.172517	+	0.377759i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	3.30017	+	3.80860i	0.437118	+	0.504461i
$58$	−0.626790	−	0.723355i	−0.0823016	−	0.0949811i
$59$	9.31693	+	2.73570i	1.21296	+	0.356157i	0.824795	−	0.565432i	$-0.191291\pi$
$59$	9.31693	+	2.73570i	1.21296	+	0.356157i	0.388166	+	0.921589i	$0.373109\pi$
$60$	−0.479771	+	1.05055i	−0.0619382	+	0.135626i
$61$	−6.86556	−	4.41222i	−0.879044	−	0.564927i	0.0214624	−	0.999770i	$-0.493168\pi$
$61$	−6.86556	−	4.41222i	−0.879044	−	0.564927i	−0.900507	+	0.434842i	$0.856804\pi$
$62$	−3.47610	+	1.02067i	−0.441465	+	0.129626i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.508959	+	3.53989i	0.0631286	+	0.439069i
$66$	2.24340	−	1.44174i	0.276143	−	0.177466i
$67$	−2.87870	+	3.32220i	−0.351689	+	0.405871i	−0.903838	−	0.427874i	$-0.859263\pi$
$67$	−2.87870	+	3.32220i	−0.351689	+	0.405871i	0.552149	+	0.833746i	$0.313808\pi$
$68$	−6.39631			−0.775667
$69$	−1.03480	−	4.68286i	−0.124575	−	0.563750i
$70$	−1.15492			−0.138039
$71$	0.375833	−	0.433734i	0.0446032	−	0.0514748i	−0.733010	−	0.680218i	$-0.761885\pi$
$71$	0.375833	−	0.433734i	0.0446032	−	0.0514748i	0.777613	+	0.628743i	$0.216430\pi$
$72$	0.841254	−	0.540641i	0.0991427	−	0.0637151i
$73$	2.04187	+	14.2015i	0.238983	+	1.66216i	0.657126	+	0.753781i	$0.271772\pi$
$73$	2.04187	+	14.2015i	0.238983	+	1.66216i	−0.418143	+	0.908381i	$0.637319\pi$
$74$	2.81849	+	6.17164i	0.327643	+	0.717438i
$75$	−0.521749	+	3.62884i	−0.0602464	+	0.419023i
$76$	−4.83537	+	1.41979i	−0.554654	+	0.162861i
$77$	2.24340	+	1.44174i	0.255659	+	0.164302i
$78$	1.28636	−	2.81674i	0.145652	−	0.318933i
$79$	−2.63983	−	0.775123i	−0.297004	−	0.0872081i	0.129836	−	0.991535i	$-0.458555\pi$
$79$	−2.63983	−	0.775123i	−0.297004	−	0.0872081i	−0.426840	+	0.904327i	$0.640373\pi$
$80$	−0.756312	−	0.872830i	−0.0845582	−	0.0975854i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−10.9499	−	3.21517i	−1.20921	−	0.355056i
$83$	−5.09144	+	11.1487i	−0.558858	+	1.22373i	0.393662	+	0.919255i	$0.371208\pi$
$83$	−5.09144	+	11.1487i	−0.558858	+	1.22373i	−0.952521	+	0.304474i	$0.901519\pi$
$84$	0.841254	+	0.540641i	0.0917883	+	0.0589887i
$85$	7.08799	−	2.08122i	0.768801	−	0.225740i
$86$	0.308503	−	2.14568i	0.0332667	−	0.231375i
$87$	−0.397608	−	0.870641i	−0.0426281	−	0.0933425i
$88$	0.379515	+	2.63959i	0.0404565	+	0.281381i
$89$	−8.82095	+	5.66888i	−0.935019	+	0.600900i	−0.916978	−	0.398937i	$-0.869379\pi$
$89$	−8.82095	+	5.66888i	−0.935019	+	0.600900i	−0.0180407	+	0.999837i	$0.505743\pi$
$90$	−0.756312	+	0.872830i	−0.0797223	+	0.0920044i
$91$	3.09657			0.324609
$92$	4.68955	+	1.00405i	0.488920	+	0.104679i
$93$	−3.62285			−0.375672
$94$	−6.18525	+	7.13816i	−0.637960	+	0.736245i
$95$	4.89628	−	3.14665i	0.502348	−	0.322839i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	4.53488	+	9.92999i	0.460447	+	1.00824i	0.987385	+	0.158335i	$0.0506125\pi$
$97$	4.53488	+	9.92999i	0.460447	+	1.00824i	−0.526939	+	0.849903i	$0.676660\pi$
$98$	−0.142315	+	0.989821i	−0.0143760	+	0.0999871i
$99$	2.55871	−	0.751305i	0.257160	−	0.0755090i
$100$	−3.08417	−	1.98208i	−0.308417	−	0.198208i
$101$	2.51370	−	5.50424i	0.250123	−	0.547692i	−0.742371	−	0.669989i	$-0.766299\pi$
$101$	2.51370	−	5.50424i	0.250123	−	0.547692i	0.992494	+	0.122297i	$0.0390260\pi$
$102$	−6.13722	−	1.80205i	−0.607675	−	0.178429i
$103$	3.34592	+	3.86139i	0.329683	+	0.380475i	0.896256	−	0.443537i	$-0.146277\pi$
$103$	3.34592	+	3.86139i	0.329683	+	0.380475i	−0.566573	+	0.824012i	$0.691731\pi$
$104$	2.02782	+	2.34023i	0.198844	+	0.229479i
$105$	−1.10814	−	0.325379i	−0.108143	−	0.0317537i
$106$	1.09002	−	2.38681i	0.105872	−	0.231827i
$107$	8.47329	+	5.44545i	0.819144	+	0.526432i	0.881811	−	0.471603i	$-0.156324\pi$
$107$	8.47329	+	5.44545i	0.819144	+	0.526432i	−0.0626673	+	0.998034i	$0.519961\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	2.41768	−	16.8153i	0.231572	−	1.61062i	−0.459735	−	0.888056i	$-0.652056\pi$
$109$	2.41768	−	16.8153i	0.231572	−	1.61062i	0.691307	−	0.722561i	$-0.257035\pi$
$110$	−1.27942	−	2.80154i	−0.121988	−	0.267116i
$111$	0.965572	+	6.71570i	0.0916481	+	0.637426i
$112$	−0.841254	+	0.540641i	−0.0794910	+	0.0510858i
$113$	4.41550	−	5.09576i	0.415375	−	0.479369i	−0.509047	−	0.860739i	$-0.670002\pi$
$113$	4.41550	−	5.09576i	0.415375	−	0.479369i	0.924422	+	0.381370i	$0.124548\pi$
$114$	−5.03950			−0.471992
$115$	−5.52336	+	0.413257i	−0.515056	+	0.0385364i
$116$	0.957135			0.0888678
$117$	2.02782	−	2.34023i	0.187472	−	0.216354i
$118$	−8.16879	+	5.24977i	−0.751998	+	0.483280i
$119$	−0.910290	−	6.33121i	−0.0834461	−	0.580381i
$120$	−0.479771	−	1.05055i	−0.0437969	−	0.0959019i
$121$	0.553399	−	3.84897i	0.0503090	−	0.349907i
$122$	7.83052	−	2.29925i	0.708942	−	0.208164i
$123$	−9.60050	−	6.16987i	−0.865648	−	0.556318i
$124$	1.50499	−	3.29546i	0.135152	−	0.295941i
$125$	9.60330	+	2.81978i	0.858945	+	0.252209i
$126$	0.654861	+	0.755750i	0.0583396	+	0.0673275i
$127$	4.76278	+	5.49655i	0.422629	+	0.487740i	0.926636	−	0.375960i	$-0.122687\pi$
$127$	4.76278	+	5.49655i	0.422629	+	0.487740i	−0.504007	+	0.863699i	$0.668141\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	0.900515	−	1.97185i	0.0792859	−	0.173612i
$130$	−3.00857	−	1.93349i	−0.263869	−	0.169578i
$131$	12.1609	−	3.57077i	1.06251	−	0.311980i	0.296646	−	0.954988i	$-0.404132\pi$
$131$	12.1609	−	3.57077i	1.06251	−	0.311980i	0.765860	+	0.643008i	$0.222314\pi$
$132$	−0.379515	+	2.63959i	−0.0330326	+	0.229747i
$133$	−2.09348	−	4.58409i	−0.181528	−	0.397491i
$134$	−0.625602	−	4.35115i	−0.0540437	−	0.375883i
$135$	−0.971581	+	0.624397i	−0.0836204	+	0.0537395i
$136$	4.18869	−	4.83401i	0.359177	−	0.414513i
$137$	−3.62600			−0.309790			−0.154895	−	0.987931i	$-0.549504\pi$
$137$	−3.62600			−0.309790			−0.154895	+	0.987931i	$0.549504\pi$
$138$	4.21672	+	2.28458i	0.358951	+	0.194476i
$139$	−0.260574			−0.0221016			−0.0110508	−	0.999939i	$-0.503518\pi$
$139$	−0.260574			−0.0221016			−0.0110508	+	0.999939i	$0.503518\pi$
$140$	0.756312	−	0.872830i	0.0639200	−	0.0737676i
$141$	−7.94576	+	5.10643i	−0.669153	+	0.430039i
$142$	0.0816763	+	0.568071i	0.00685412	+	0.0476715i
$143$	3.43038	+	7.51148i	0.286863	+	0.628142i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−1.06064	+	0.311431i	−0.0880812	+	0.0258630i
$146$	−12.0699	−	7.75687i	−0.998915	−	0.641964i
$147$	−0.415415	+	0.909632i	−0.0342629	+	0.0750252i
$148$	−6.50993	−	1.91149i	−0.535113	−	0.157123i
$149$	0.151262	+	0.174566i	0.0123919	+	0.0143010i	0.761912	−	0.647681i	$-0.224261\pi$
$149$	0.151262	+	0.174566i	0.0123919	+	0.0143010i	−0.749520	+	0.661982i	$0.769716\pi$
$150$	−2.40082	−	2.77070i	−0.196026	−	0.226227i
$151$	−20.4962	−	6.01823i	−1.66796	−	0.489757i	−0.694667	−	0.719332i	$-0.744448\pi$
$151$	−20.4962	−	6.01823i	−1.66796	−	0.489757i	−0.973291	+	0.229575i	$0.926266\pi$
$152$	2.09348	−	4.58409i	0.169804	−	0.371819i
$153$	−5.38092	−	3.45811i	−0.435022	−	0.279571i
$154$	−2.55871	+	0.751305i	−0.206187	+	0.0605419i
$155$	−0.595460	+	4.14151i	−0.0478285	+	0.332654i
$156$	1.28636	+	2.81674i	0.102991	+	0.225520i
$157$	−1.45253	−	10.1026i	−0.115925	−	0.806274i	−0.961968	−	0.273161i	$-0.911931\pi$
$157$	−1.45253	−	10.1026i	−0.115925	−	0.806274i	0.846044	−	0.533114i	$-0.178978\pi$
$158$	2.31452	−	1.48745i	0.184133	−	0.118335i
$159$	1.71831	−	1.98303i	0.136271	−	0.157265i
$160$	1.15492			0.0913045
$161$	−0.326435	+	4.78471i	−0.0257266	+	0.377088i
$162$	1.00000			0.0785674
$163$	−11.6413	+	13.4348i	−0.911816	+	1.05229i	0.0866116	+	0.996242i	$0.472396\pi$
$163$	−11.6413	+	13.4348i	−0.911816	+	1.05229i	−0.998428	+	0.0560500i	$0.982149\pi$
$164$	9.60050	−	6.16987i	0.749673	−	0.481786i
$165$	−0.438310	−	3.04851i	−0.0341224	−	0.237326i
$166$	−5.09144	−	11.1487i	−0.395173	−	0.865307i
$167$	−3.17519	+	22.0839i	−0.245703	+	1.70890i	0.376806	+	0.926292i	$0.377022\pi$
$167$	−3.17519	+	22.0839i	−0.245703	+	1.70890i	−0.622509	+	0.782612i	$0.713887\pi$
$168$	−0.959493	+	0.281733i	−0.0740265	+	0.0217361i
$169$	−2.86973	−	1.84426i	−0.220749	−	0.141866i
$170$	−3.06877	+	6.71966i	−0.235364	+	0.515374i
$171$	−4.83537	−	1.41979i	−0.369770	−	0.108574i
$172$	1.41957	+	1.63827i	0.108241	+	0.124917i
$173$	−12.0016	−	13.8506i	−0.912466	−	1.05304i	−0.998389	−	0.0567403i	$-0.981929\pi$
$173$	−12.0016	−	13.8506i	−0.912466	−	1.05304i	0.0859228	−	0.996302i	$-0.472616\pi$
$174$	0.918365	+	0.269656i	0.0696210	+	0.0204426i
$175$	1.52298	−	3.33486i	0.115126	−	0.252091i
$176$	−2.24340	−	1.44174i	−0.169102	−	0.108675i
$177$	−9.31693	+	2.73570i	−0.700303	+	0.205628i
$178$	1.49224	−	10.3788i	0.111848	−	0.777921i
$179$	−6.95745	−	15.2347i	−0.520024	−	1.13869i	−0.969430	−	0.245366i	$-0.921092\pi$
$179$	−6.95745	−	15.2347i	−0.520024	−	1.13869i	0.449406	−	0.893327i	$-0.351636\pi$
$180$	−0.164362	−	1.14316i	−0.0122508	−	0.0852065i
$181$	19.1669	−	12.3178i	1.42466	−	0.915575i	0.424715	−	0.905327i	$-0.360374\pi$
$181$	19.1669	−	12.3178i	1.42466	−	0.915575i	0.999947	−	0.0102476i	$-0.00326197\pi$
$182$	−2.02782	+	2.34023i	−0.150312	+	0.173469i
$183$	8.16110			0.603286
$184$	−3.82981	+	2.88662i	−0.282337	+	0.212804i
$185$	7.83586			0.576104
$186$	2.37246	−	2.73797i	0.173957	−	0.200757i
$187$	14.3495	−	9.22184i	1.04934	−	0.674368i
$188$	−1.34418	−	9.34900i	−0.0980346	−	0.681846i
$189$	0.415415	+	0.909632i	0.0302170	+	0.0661660i
$190$	−0.828304	+	5.76098i	−0.0600915	+	0.417945i
$191$	−4.51450	+	1.32558i	−0.326658	+	0.0959154i	−0.440950	−	0.897532i	$-0.645358\pi$
$191$	−4.51450	+	1.32558i	−0.326658	+	0.0959154i	0.114292	+	0.993447i	$0.463540\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	3.20348	−	7.01465i	0.230592	−	0.504925i	−0.758599	−	0.651557i	$-0.774116\pi$
$193$	3.20348	−	7.01465i	0.230592	−	0.504925i	0.989191	+	0.146632i	$0.0468433\pi$
$194$	−10.4743	−	3.07553i	−0.752011	−	0.220810i
$195$	−2.34197	−	2.70278i	−0.167712	−	0.193550i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	−4.91359	−	1.44276i	−0.350079	−	0.102792i	0.101966	−	0.994788i	$-0.467487\pi$
$197$	−4.91359	−	1.44276i	−0.350079	−	0.102792i	−0.452044	+	0.891996i	$0.649305\pi$
$198$	−1.10780	+	2.42574i	−0.0787279	+	0.172390i
$199$	0.960278	+	0.617133i	0.0680723	+	0.0437474i	0.574234	−	0.818691i	$-0.305300\pi$
$199$	0.960278	+	0.617133i	0.0680723	+	0.0437474i	−0.506162	+	0.862438i	$0.668936\pi$
$200$	3.51765	−	1.03288i	0.248736	−	0.0730354i
$201$	0.625602	−	4.35115i	0.0441265	−	0.306907i
$202$	2.51370	+	5.50424i	0.176863	+	0.387277i
$203$	0.136215	+	0.947393i	0.00956039	+	0.0664940i
$204$	5.38092	−	3.45811i	0.376740	−	0.242116i
$205$	−8.63114	+	9.96086i	−0.602825	+	0.695697i
$206$	−5.10936			−0.355986
$207$	3.40227	+	3.38002i	0.236474	+	0.234928i
$208$	−3.09657			−0.214708
$209$	8.80066	−	10.1565i	0.608755	−	0.702540i
$210$	0.971581	−	0.624397i	0.0670454	−	0.0430875i
$211$	−3.02198	−	21.0183i	−0.208042	−	1.44696i	−0.779537	−	0.626356i	$-0.784546\pi$
$211$	−3.02198	−	21.0183i	−0.208042	−	1.44696i	0.571495	−	0.820605i	$-0.306363\pi$
$212$	1.09002	+	2.38681i	0.0748628	+	0.163927i
$213$	−0.0816763	+	0.568071i	−0.00559637	+	0.0389236i
$214$	−9.66422	+	2.83767i	−0.660633	+	0.193979i
$215$	−2.10614	−	1.35353i	−0.143638	−	0.0923103i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	3.47610	+	1.02067i	0.235973	+	0.0692879i
$218$	11.1249	+	12.8389i	0.753476	+	0.869558i
$219$	−9.39565	−	10.8432i	−0.634899	−	0.732713i
$220$	2.95510	+	0.867697i	0.199233	+	0.0585001i
$221$	8.22797	−	18.0167i	0.553473	−	1.21194i
$222$	−5.70770	−	3.66812i	−0.383076	−	0.246188i
$223$	20.8690	−	6.12768i	1.39749	−	0.410340i	0.505668	−	0.862728i	$-0.331246\pi$
$223$	20.8690	−	6.12768i	1.39749	−	0.410340i	0.891821	+	0.452389i	$0.149428\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	−1.52298	−	3.33486i	−0.101532	−	0.222324i
$226$	0.959580	+	6.67402i	0.0638303	+	0.443949i
$227$	−8.04904	+	5.17280i	−0.534233	+	0.343331i	−0.779780	−	0.626054i	$-0.784669\pi$
$227$	−8.04904	+	5.17280i	−0.534233	+	0.343331i	0.245546	+	0.969385i	$0.421033\pi$
$228$	3.30017	−	3.80860i	0.218559	−	0.252231i
$229$	1.82735			0.120755			0.0603775	−	0.998176i	$-0.480770\pi$
$229$	1.82735			0.120755			0.0603775	+	0.998176i	$0.480770\pi$
$230$	3.30472	−	4.44491i	0.217906	−	0.293088i
$231$	−2.66673			−0.175458
$232$	−0.626790	+	0.723355i	−0.0411508	+	0.0474906i
$233$	24.5002	−	15.7453i	1.60506	−	1.03151i	0.640387	−	0.768053i	$-0.278774\pi$
$233$	24.5002	−	15.7453i	1.60506	−	1.03151i	0.964671	−	0.263456i	$-0.0848623\pi$
$234$	0.440688	+	3.06505i	0.0288087	+	0.200369i
$235$	4.53151	+	9.92261i	0.295603	+	0.647280i
$236$	1.38191	−	9.61143i	0.0899550	−	0.625651i
$237$	2.63983	−	0.775123i	0.171475	−	0.0503496i
$238$	5.38092	+	3.45811i	0.348793	+	0.224156i
$239$	−10.2443	+	22.4319i	−0.662649	+	1.45100i	0.217384	+	0.976086i	$0.430248\pi$
$239$	−10.2443	+	22.4319i	−0.662649	+	1.45100i	−0.880033	+	0.474913i	$0.842479\pi$
$240$	1.10814	+	0.325379i	0.0715300	+	0.0210031i
$241$	−3.21698	−	3.71260i	−0.207224	−	0.239149i	0.642618	−	0.766187i	$-0.277848\pi$
$241$	−3.21698	−	3.71260i	−0.207224	−	0.239149i	−0.849842	+	0.527037i	$0.823303\pi$
$242$	2.54646	+	2.93877i	0.163693	+	0.188911i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	−3.39024	+	7.42360i	−0.217038	+	0.475247i
$245$	0.971581	+	0.624397i	0.0620720	+	0.0398913i
$246$	10.9499	−	3.21517i	0.698138	−	0.204992i
$247$	2.22085	−	15.4463i	0.141309	−	0.982826i
$248$	1.50499	+	3.29546i	0.0955667	+	0.209262i
$249$	−1.74425	−	12.1315i	−0.110537	−	0.768804i
$250$	−8.41987	+	5.41112i	−0.532520	+	0.342230i
$251$	2.60966	−	3.01170i	0.164720	−	0.190097i	−0.667389	−	0.744710i	$-0.732588\pi$
$251$	2.60966	−	3.01170i	0.164720	−	0.190097i	0.832109	+	0.554612i	$0.187133\pi$
$252$	−1.00000			−0.0629941
$253$	−11.9681	+	4.50865i	−0.752428	+	0.283457i
$254$	−7.27297			−0.456347
$255$	−4.83761	+	5.58290i	−0.302943	+	0.349614i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−4.09372	−	28.4725i	−0.255359	−	1.77606i	−0.564883	−	0.825171i	$-0.691079\pi$
$257$	−4.09372	−	28.4725i	−0.255359	−	1.77606i	0.309524	−	0.950892i	$-0.399830\pi$
$258$	0.900515	+	1.97185i	0.0560636	+	0.122762i
$259$	0.965572	−	6.71570i	0.0599977	−	0.417293i
$260$	3.43143	−	1.00756i	0.212808	−	0.0624861i
$261$	0.805193	+	0.517466i	0.0498402	+	0.0320304i
$262$	−5.26511	+	11.5290i	−0.325279	+	0.712262i
$263$	−12.1293	−	3.56148i	−0.747925	−	0.219610i	−0.114509	−	0.993422i	$-0.536529\pi$
$263$	−12.1293	−	3.56148i	−0.747925	−	0.219610i	−0.633416	+	0.773812i	$0.718348\pi$
$264$	−1.74634	−	2.01538i	−0.107480	−	0.124038i
$265$	−1.98451	−	2.29024i	−0.121907	−	0.140689i
$266$	4.83537	+	1.41979i	0.296475	+	0.0870530i
$267$	4.35583	−	9.53793i	0.266572	−	0.583712i
$268$	3.69807	+	2.37660i	0.225895	+	0.145174i
$269$	−11.2236	+	3.29556i	−0.684318	+	0.200934i	−0.605369	−	0.795945i	$-0.706974\pi$
$269$	−11.2236	+	3.29556i	−0.684318	+	0.200934i	−0.0789485	+	0.996879i	$0.525156\pi$
$270$	0.164362	−	1.14316i	0.0100028	−	0.0695708i
$271$	7.96987	+	17.4516i	0.484135	+	1.06011i	0.981306	+	0.192456i	$0.0616452\pi$
$271$	7.96987	+	17.4516i	0.484135	+	1.06011i	−0.497170	+	0.867653i	$0.665628\pi$
$272$	0.910290	+	6.33121i	0.0551944	+	0.383886i
$273$	−2.60500	+	1.67413i	−0.157662	+	0.101323i
$274$	2.37452	−	2.74035i	0.143450	−	0.165550i
$275$	9.77666			0.589555
$276$	−4.48793	+	1.69070i	−0.270142	+	0.101768i
$277$	−15.9472			−0.958172			−0.479086	−	0.877768i	$-0.659032\pi$
$277$	−15.9472			−0.958172			−0.479086	+	0.877768i	$0.659032\pi$
$278$	0.170640	−	0.196929i	0.0102343	−	0.0118110i
$279$	3.04773	−	1.95866i	0.182463	−	0.117262i
$280$	0.164362	+	1.14316i	0.00982253	+	0.0683172i
$281$	5.31224	+	11.6322i	0.316902	+	0.693918i	0.999313	−	0.0370499i	$-0.0117960\pi$
$281$	5.31224	+	11.6322i	0.316902	+	0.693918i	−0.682412	+	0.730968i	$0.739069\pi$
$282$	1.34418	−	9.34900i	0.0800449	−	0.556725i
$283$	−15.6576	+	4.59747i	−0.930745	+	0.273291i	−0.711749	−	0.702434i	$-0.752097\pi$
$283$	−15.6576	+	4.59747i	−0.930745	+	0.273291i	−0.218997	+	0.975726i	$0.570278\pi$
$284$	−0.482806	−	0.310281i	−0.0286493	−	0.0184118i
$285$	−2.41781	+	5.29426i	−0.143219	+	0.313605i
$286$	−7.92322	−	2.32647i	−0.468510	−	0.137567i
$287$	7.47336	+	8.62472i	0.441139	+	0.509101i
$288$	−0.654861	−	0.755750i	−0.0385880	−	0.0445330i
$289$	−22.9442	−	6.73701i	−1.34966	−	0.396295i
$290$	0.459206	−	1.00552i	0.0269655	−	0.0590462i
$291$	−9.18354	−	5.90190i	−0.538349	−	0.345976i
$292$	13.7664	−	4.04217i	0.805616	−	0.236550i
$293$	2.46681	−	17.1570i	0.144112	−	1.00232i	−0.781515	−	0.623887i	$-0.785553\pi$
$293$	2.46681	−	17.1570i	0.144112	−	1.00232i	0.925627	−	0.378437i	$-0.123538\pi$
$294$	−0.415415	−	0.909632i	−0.0242275	−	0.0530508i
$295$	1.59600	+	11.1004i	0.0929228	+	0.646292i
$296$	5.70770	−	3.66812i	0.331754	−	0.213205i
$297$	−1.74634	+	2.01538i	−0.101333	+	0.116944i
$298$	−0.230984			−0.0133805
$299$	−8.86060	+	11.9177i	−0.512422	+	0.689217i
$300$	3.66616			0.211666
$301$	−1.41957	+	1.63827i	−0.0818228	+	0.0944285i
$302$	17.9704	−	11.5489i	1.03408	−	0.664564i
$303$	0.861156	+	5.98947i	0.0494721	+	0.344086i
$304$	2.09348	+	4.58409i	0.120070	+	0.262916i
$305$	1.34138	−	9.32948i	0.0768070	−	0.534205i
$306$	6.13722	−	1.80205i	0.350841	−	0.103016i
$307$	14.1924	+	9.12091i	0.810004	+	0.520558i	0.878866	−	0.477068i	$-0.158301\pi$
$307$	14.1924	+	9.12091i	0.810004	+	0.520558i	−0.0688623	+	0.997626i	$0.521937\pi$
$308$	1.10780	−	2.42574i	0.0631227	−	0.138220i
$309$	−4.90239	−	1.43947i	−0.278887	−	0.0818887i
$310$	−2.74000	−	3.16213i	−0.155622	−	0.179597i
$311$	−11.7068	−	13.5104i	−0.663832	−	0.766103i	0.319566	−	0.947564i	$-0.396463\pi$
$311$	−11.7068	−	13.5104i	−0.663832	−	0.766103i	−0.983398	+	0.181461i	$0.941917\pi$
$312$	−2.97114	−	0.872404i	−0.168208	−	0.0493902i
$313$	8.01366	−	17.5475i	0.452959	−	0.991842i	−0.536077	−	0.844169i	$-0.680094\pi$
$313$	8.01366	−	17.5475i	0.452959	−	0.991842i	0.989036	−	0.147673i	$-0.0471783\pi$
$314$	8.58624	+	5.51804i	0.484549	+	0.311401i
$315$	1.10814	−	0.325379i	0.0624365	−	0.0183330i
$316$	−0.391547	+	2.72327i	−0.0220262	+	0.153196i
$317$	−1.43232	−	3.13635i	−0.0804474	−	0.176155i	0.865134	−	0.501541i	$-0.167233\pi$
$317$	−1.43232	−	3.13635i	−0.0804474	−	0.176155i	−0.945581	+	0.325385i	$0.894506\pi$
$318$	0.373424	+	2.59722i	0.0209406	+	0.145645i
$319$	−2.14723	+	1.37994i	−0.120222	+	0.0772620i
$320$	−0.756312	+	0.872830i	−0.0422791	+	0.0487927i
$321$	−10.0722			−0.562176
$322$	−3.40227	−	3.38002i	−0.189601	−	0.188361i
$323$	−32.2342			−1.79356
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	9.55035	−	6.13763i	0.529758	−	0.340455i
$326$	−2.52989	−	17.5958i	−0.140118	−	0.974541i
$327$	7.05718	+	15.4531i	0.390263	+	0.854556i
$328$	−1.62412	+	11.2960i	−0.0896768	+	0.623716i
$329$	9.06254	−	2.66100i	0.499634	−	0.146706i
$330$	2.59094	+	1.66510i	0.142627	+	0.0916606i
$331$	9.33292	−	20.4363i	0.512984	−	1.12328i	−0.459044	−	0.888413i	$-0.651808\pi$
$331$	9.33292	−	20.4363i	0.512984	−	1.12328i	0.972028	−	0.234865i	$-0.0754647\pi$
$332$	11.7598	+	3.45299i	0.645404	+	0.189508i
$333$	−4.44307	−	5.12758i	−0.243479	−	0.280990i
$334$	−14.6106	−	16.8615i	−0.799457	−	0.922622i
$335$	−4.87126	−	1.43033i	−0.266145	−	0.0781474i
$336$	0.415415	−	0.909632i	0.0226627	−	0.0496245i
$337$	18.0385	+	11.5926i	0.982620	+	0.631491i	0.930169	−	0.367132i	$-0.119660\pi$
$337$	18.0385	+	11.5926i	0.982620	+	0.631491i	0.0524511	+	0.998623i	$0.483297\pi$
$338$	3.27308	−	0.961062i	0.178032	−	0.0522749i
$339$	−0.959580	+	6.67402i	−0.0521172	+	0.362483i
$340$	−3.06877	−	6.71966i	−0.166427	−	0.364425i
$341$	1.37493	+	9.56282i	0.0744564	+	0.517856i
$342$	4.23950	−	2.72456i	0.229246	−	0.147327i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	−2.16775			−0.116877
$345$	4.42313	−	3.33381i	0.238133	−	0.179486i
$346$	18.3270			0.985264
$347$	−18.3143	+	21.1359i	−0.983165	+	1.13463i	0.00772609	+	0.999970i	$0.497541\pi$
$347$	−18.3143	+	21.1359i	−0.983165	+	1.13463i	−0.990891	+	0.134663i	$0.957005\pi$
$348$	−0.805193	+	0.517466i	−0.0431629	+	0.0277391i
$349$	0.764822	+	5.31945i	0.0409400	+	0.284744i	0.999999	+	0.00153687i	$0.000489203\pi$
$349$	0.764822	+	5.31945i	0.0409400	+	0.284744i	−0.959059	+	0.283207i	$0.908602\pi$
$350$	1.52298	+	3.33486i	0.0814066	+	0.178256i
$351$	−0.440688	+	3.06505i	−0.0235222	+	0.163600i
$352$	2.55871	−	0.751305i	0.136380	−	0.0400447i
$353$	8.69674	+	5.58906i	0.462881	+	0.297475i	0.751219	−	0.660053i	$-0.229466\pi$
$353$	8.69674	+	5.58906i	0.462881	+	0.297475i	−0.288338	+	0.957529i	$0.593103\pi$
$354$	4.03379	−	8.83277i	0.214393	−	0.469456i
$355$	0.635974	+	0.186739i	0.0337540	+	0.00991107i
$356$	6.86653	+	7.92440i	0.363926	+	0.419992i
$357$	4.18869	+	4.83401i	0.221689	+	0.255843i
$358$	16.0698	+	4.71851i	0.849314	+	0.249381i
$359$	−7.42050	+	16.2486i	−0.391639	+	0.857570i	0.606411	+	0.795151i	$0.292609\pi$
$359$	−7.42050	+	16.2486i	−0.391639	+	0.857570i	−0.998050	+	0.0624187i	$0.980119\pi$
$360$	0.971581	+	0.624397i	0.0512068	+	0.0329086i
$361$	−6.13746	+	1.80212i	−0.323024	+	0.0948484i
$362$	−3.24246	+	22.5518i	−0.170420	+	1.18530i
$363$	1.61536	+	3.53715i	0.0847846	+	0.185652i
$364$	−0.440688	−	3.06505i	−0.0230983	−	0.160652i
$365$	−13.9398	+	8.95857i	−0.729643	+	0.468913i
$366$	−5.34438	+	6.16775i	−0.279355	+	0.322393i
$367$	−2.36079			−0.123232			−0.0616161	−	0.998100i	$-0.519625\pi$
$367$	−2.36079			−0.123232			−0.0616161	+	0.998100i	$0.519625\pi$
$368$	0.326435	−	4.78471i	0.0170166	−	0.249420i
$369$	11.4121			0.594092
$370$	−5.13140	+	5.92195i	−0.266769	+	0.307867i
$371$	−2.20739	+	1.41860i	−0.114602	+	0.0736501i
$372$	0.515585	+	3.58597i	0.0267318	+	0.185924i
$373$	6.29993	+	13.7949i	0.326198	+	0.714274i	0.999689	−	0.0249212i	$-0.00793349\pi$
$373$	6.29993	+	13.7949i	0.326198	+	0.714274i	−0.673492	+	0.739195i	$0.735206\pi$
$374$	−2.42750	+	16.8836i	−0.125523	+	0.873031i
$375$	−9.60330	+	2.81978i	−0.495912	+	0.145613i
$376$	7.94576	+	5.10643i	0.409771	+	0.263344i
$377$	−1.23122	+	2.69600i	−0.0634112	+	0.138851i
$378$	−0.959493	−	0.281733i	−0.0493510	−	0.0144908i
$379$	−17.5266	−	20.2267i	−0.900278	−	1.03898i	−0.999037	−	0.0438653i	$-0.986033\pi$
$379$	−17.5266	−	20.2267i	−0.900278	−	1.03898i	0.0987590	−	0.995111i	$-0.468513\pi$
$380$	−3.81143	−	4.39863i	−0.195522	−	0.225645i
$381$	−6.97837	−	2.04903i	−0.357513	−	0.104975i
$382$	1.95457	−	4.27990i	0.100004	−	0.218979i
$383$	−22.6035	−	14.5264i	−1.15499	−	0.742264i	−0.184359	−	0.982859i	$-0.559021\pi$
$383$	−22.6035	−	14.5264i	−1.15499	−	0.742264i	−0.970626	+	0.240595i	$0.922657\pi$
$384$	0.959493	−	0.281733i	0.0489639	−	0.0143771i
$385$	−0.438310	+	3.04851i	−0.0223383	+	0.155367i
$386$	3.20348	+	7.01465i	0.163053	+	0.357036i
$387$	0.308503	+	2.14568i	0.0156821	+	0.109071i
$388$	9.18354	−	5.90190i	0.466224	−	0.299624i
$389$	−22.5990	+	26.0807i	−1.14582	+	1.32234i	−0.206835	+	0.978376i	$0.566316\pi$
$389$	−22.5990	+	26.0807i	−1.14582	+	1.32234i	−0.938982	+	0.343967i	$0.888229\pi$
$390$	3.57629			0.181093
$391$	26.9714	+	14.6129i	1.36400	+	0.739004i
$392$	1.00000			0.0505076
$393$	−8.29992	+	9.57862i	−0.418676	+	0.483177i
$394$	4.30808	−	2.76864i	0.217038	−	0.139482i
$395$	−0.452205	−	3.14516i	−0.0227529	−	0.158250i
$396$	−1.10780	−	2.42574i	−0.0556690	−	0.121898i
$397$	−1.40733	+	9.78820i	−0.0706319	+	0.491256i	0.923545	+	0.383491i	$0.125278\pi$
$397$	−1.40733	+	9.78820i	−0.0706319	+	0.491256i	−0.994176	+	0.107765i	$0.965631\pi$
$398$	−1.09525	+	0.321593i	−0.0548997	+	0.0161200i
$399$	4.23950	+	2.72456i	0.212240	+	0.136399i
$400$	−1.52298	+	3.33486i	−0.0761489	+	0.166743i
$401$	−3.41669	−	1.00323i	−0.170621	−	0.0500989i	0.195306	−	0.980742i	$-0.437430\pi$
$401$	−3.41669	−	1.00323i	−0.170621	−	0.0500989i	−0.365927	+	0.930643i	$0.619248\pi$
$402$	2.87870	+	3.32220i	0.143577	+	0.165696i
$403$	7.34649	+	8.47830i	0.365955	+	0.422334i
$404$	−5.80595	−	1.70478i	−0.288857	−	0.0848160i
$405$	0.479771	−	1.05055i	0.0238400	−	0.0522024i
$406$	−0.805193	−	0.517466i	−0.0399611	−	0.0256814i
$407$	17.3602	−	5.09742i	0.860515	−	0.252670i
$408$	−0.910290	+	6.33121i	−0.0450661	+	0.313441i
$409$	11.2157	+	24.5589i	0.554579	+	1.21436i	0.954610	+	0.297858i	$0.0962721\pi$
$409$	11.2157	+	24.5589i	0.554579	+	1.21436i	−0.400031	+	0.916502i	$0.631001\pi$
$410$	−1.87573	−	13.0460i	−0.0926355	−	0.644294i
$411$	3.05038	−	1.96036i	0.150464	−	0.0966976i
$412$	3.34592	−	3.86139i	0.164842	−	0.190237i
$413$	9.71026			0.477811
$414$	−4.78246	+	0.357823i	−0.235045	+	0.0175861i
$415$	−14.1550			−0.694843
$416$	2.02782	−	2.34023i	0.0994221	−	0.114739i
$417$	0.219209	−	0.140877i	0.0107347	−	0.00689878i
$418$	1.91257	+	13.3022i	0.0935467	+	0.650632i
$419$	−1.95512	−	4.28111i	−0.0955137	−	0.209146i	0.855844	−	0.517234i	$-0.173038\pi$
$419$	−1.95512	−	4.28111i	−0.0955137	−	0.209146i	−0.951358	+	0.308088i	$0.900311\pi$
$420$	−0.164362	+	1.14316i	−0.00802006	+	0.0557807i
$421$	−3.74189	+	1.09872i	−0.182369	+	0.0535483i	−0.371642	−	0.928376i	$-0.621205\pi$
$421$	−3.74189	+	1.09872i	−0.182369	+	0.0535483i	0.189273	+	0.981924i	$0.439387\pi$
$422$	17.8636	+	11.4802i	0.869585	+	0.558848i
$423$	3.92365	−	8.59160i	0.190774	−	0.417738i
$424$	−2.51764	−	0.739246i	−0.122267	−	0.0359009i
$425$	−15.3564	−	17.7222i	−0.744896	−	0.859655i
$426$	−0.375833	−	0.433734i	−0.0182092	−	0.0210145i
$427$	−7.83052	−	2.29925i	−0.378945	−	0.111268i
$428$	4.18415	−	9.16201i	0.202249	−	0.442863i
$429$	−6.94683	−	4.46446i	−0.335396	−	0.215546i
$430$	2.40216	−	0.705339i	0.115843	−	0.0340144i
$431$	2.67126	−	18.5790i	0.128670	−	0.894921i	−0.818572	−	0.574403i	$-0.805234\pi$
$431$	2.67126	−	18.5790i	0.128670	−	0.894921i	0.947243	−	0.320517i	$-0.103857\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	4.81095	+	33.4609i	0.231200	+	1.60803i	0.692927	+	0.721008i	$0.256321\pi$
$433$	4.81095	+	33.4609i	0.231200	+	1.60803i	−0.461727	+	0.887022i	$0.652770\pi$
$434$	−3.04773	+	1.95866i	−0.146296	+	0.0940187i
$435$	0.723893	−	0.835417i	0.0347080	−	0.0400552i
$436$	−16.9883			−0.813590
$437$	23.6330	+	5.05989i	1.13052	+	0.242048i
$438$	14.3476			0.685553
$439$	14.7011	−	16.9660i	0.701645	−	0.809741i	−0.287329	−	0.957832i	$-0.592767\pi$
$439$	14.7011	−	16.9660i	0.701645	−	0.809741i	0.988974	+	0.148091i	$0.0473128\pi$
$440$	−2.59094	+	1.66510i	−0.123518	+	0.0793804i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	8.22797	+	18.0167i	0.391365	+	0.856969i
$443$	−1.76687	+	12.2888i	−0.0839465	+	0.583861i	0.903819	+	0.427915i	$0.140752\pi$
$443$	−1.76687	+	12.2888i	−0.0839465	+	0.583861i	−0.987766	+	0.155946i	$0.950157\pi$
$444$	6.50993	−	1.91149i	0.308948	−	0.0907152i
$445$	−10.1875	−	6.54711i	−0.482934	−	0.310363i
$446$	−9.03527	+	19.7845i	−0.427832	+	0.936822i
$447$	−0.221627	−	0.0650757i	−0.0104826	−	0.00307797i
$448$	0.654861	+	0.755750i	0.0309393	+	0.0357058i
$449$	−10.9850	−	12.6774i	−0.518416	−	0.598284i	0.434818	−	0.900519i	$-0.356813\pi$
$449$	−10.9850	−	12.6774i	−0.518416	−	0.598284i	−0.953234	+	0.302235i	$0.902267\pi$
$450$	3.51765	+	1.03288i	0.165824	+	0.0486903i
$451$	−12.6424	+	27.6829i	−0.595306	+	1.30354i
$452$	−5.67228	−	3.64535i	−0.266802	−	0.171463i
$453$	20.4962	−	6.01823i	0.962996	−	0.282761i
$454$	1.36166	−	9.47052i	0.0639057	−	0.444474i
$455$	1.48564	+	3.25311i	0.0696481	+	0.152508i
$456$	0.717196	+	4.98821i	0.0335858	+	0.233594i
$457$	23.4916	−	15.0972i	1.09889	−	0.706215i	0.140047	−	0.990145i	$-0.455275\pi$
$457$	23.4916	−	15.0972i	1.09889	−	0.706215i	0.958845	+	0.283930i	$0.0916382\pi$
$458$	−1.19666	+	1.38102i	−0.0559164	+	0.0645309i
$459$	6.39631			0.298554
$460$	1.19511	+	5.40833i	0.0557222	+	0.252165i
$461$	−22.6752			−1.05609			−0.528045	−	0.849217i	$-0.677075\pi$
$461$	−22.6752			−1.05609			−0.528045	+	0.849217i	$0.677075\pi$
$462$	1.74634	−	2.01538i	0.0812469	−	0.0937640i
$463$	−6.06427	+	3.89727i	−0.281830	+	0.181121i	−0.673917	−	0.738807i	$-0.735390\pi$
$463$	−6.06427	+	3.89727i	−0.281830	+	0.181121i	0.392087	+	0.919928i	$0.371753\pi$
$464$	−0.136215	−	0.947393i	−0.00632360	−	0.0439816i
$465$	−1.73814	−	3.80599i	−0.0806042	−	0.176499i
$466$	−4.14469	+	28.8270i	−0.191999	+	1.33538i
$467$	−20.5404	+	6.03122i	−0.950499	+	0.279092i	−0.719994	−	0.693980i	$-0.755856\pi$
$467$	−20.5404	+	6.03122i	−0.950499	+	0.279092i	−0.230504	+	0.973071i	$0.574038\pi$
$468$	−2.60500	−	1.67413i	−0.120416	−	0.0773868i
$469$	−1.82612	+	3.99865i	−0.0843225	+	0.184641i
$470$	−10.4665	−	3.07325i	−0.482784	−	0.141758i
$471$	6.68382	+	7.71354i	0.307974	+	0.355421i
$472$	6.35887	+	7.33853i	0.292691	+	0.337783i
$473$	−5.54663	−	1.62864i	−0.255034	−	0.0748849i
$474$	−1.14292	+	2.50264i	−0.0524960	+	0.114950i
$475$	−15.5427	−	9.98867i	−0.713147	−	0.458312i
$476$	−6.13722	+	1.80205i	−0.281299	+	0.0825968i
$477$	−0.373424	+	2.59722i	−0.0170979	+	0.118918i
$478$	−10.2443	−	22.4319i	−0.468564	−	1.02601i
$479$	−1.76980	−	12.3093i	−0.0808644	−	0.562424i	−0.989467	−	0.144762i	$-0.953758\pi$
$479$	−1.76980	−	12.3093i	−0.0808644	−	0.562424i	0.908602	−	0.417663i	$-0.137151\pi$
$480$	−0.971581	+	0.624397i	−0.0443464	+	0.0284997i
$481$	13.7583	−	15.8779i	0.627324	−	0.723970i
$482$	4.91247			0.223757
$483$	−2.31219	−	4.20164i	−0.105209	−	0.191181i
$484$	−3.88855			−0.176752
$485$	−8.25628	+	9.52825i	−0.374898	+	0.432656i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	3.49747	+	24.3254i	0.158485	+	1.10229i	0.901426	+	0.432933i	$0.142521\pi$
$487$	3.49747	+	24.3254i	0.158485	+	1.10229i	−0.742941	+	0.669357i	$0.766570\pi$
$488$	−3.39024	−	7.42360i	−0.153469	−	0.336051i
$489$	2.52989	−	17.5958i	0.114406	−	0.795710i
$490$	−1.10814	+	0.325379i	−0.0500606	+	0.0146991i
$491$	−6.83965	−	4.39558i	−0.308669	−	0.198370i	0.377130	−	0.926160i	$-0.376911\pi$
$491$	−6.83965	−	4.39558i	−0.308669	−	0.198370i	−0.685799	+	0.727791i	$0.740547\pi$
$492$	−4.74077	+	10.3808i	−0.213731	+	0.468005i
$493$	5.87415	+	1.72480i	0.264558	+	0.0776813i
$494$	10.2192	+	11.7936i	0.459784	+	0.530619i
$495$	2.01688	+	2.32760i	0.0906520	+	0.104618i
$496$	−3.47610	−	1.02067i	−0.156081	−	0.0458296i
$497$	0.238412	−	0.522049i	0.0106942	−	0.0234171i
$498$	10.3106	+	6.62625i	0.462031	+	0.296929i
$499$	7.49454	−	2.20059i	0.335502	−	0.0985122i	−0.109643	−	0.993971i	$-0.534971\pi$
$499$	7.49454	−	2.20059i	0.335502	−	0.0985122i	0.445144	+	0.895459i	$0.353152\pi$
$500$	1.42439	−	9.90685i	0.0637006	−	0.443048i
$501$	−9.26833	−	20.2948i	−0.414078	−	0.906705i
$502$	0.567132	+	3.94449i	0.0253124	+	0.176051i
$503$	4.32293	−	2.77818i	0.192750	−	0.123873i	−0.440706	−	0.897651i	$-0.645272\pi$
$503$	4.32293	−	2.77818i	0.192750	−	0.123873i	0.633456	+	0.773779i	$0.281636\pi$
$504$	0.654861	−	0.755750i	0.0291698	−	0.0336638i
$505$	6.98849			0.310984
$506$	4.43002	−	11.9974i	0.196939	−	0.533351i
$507$	3.41126			0.151499
$508$	4.76278	−	5.49655i	0.211314	−	0.243870i
$509$	−7.05832	+	4.53611i	−0.312854	+	0.201059i	−0.687639	−	0.726052i	$-0.741353\pi$
$509$	−7.05832	+	4.53611i	−0.312854	+	0.201059i	0.374785	+	0.927112i	$0.377717\pi$
$510$	−1.05131	−	7.31204i	−0.0465529	−	0.323782i
$511$	5.96019	+	13.0510i	0.263663	+	0.577342i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	4.83537	−	1.41979i	0.213487	−	0.0626853i
$514$	24.1989	+	15.5517i	1.06737	+	0.685954i
$515$	−2.45132	+	5.36765i	−0.108018	+	0.236527i
$516$	−2.07994	−	0.610725i	−0.0915642	−	0.0268857i
$517$	16.4944	+	19.0355i	0.725422	+	0.837182i
$518$	4.44307	+	5.12758i	0.195217	+	0.225293i
$519$	17.5846	+	5.16331i	0.771879	+	0.226644i
$520$	−1.48564	+	3.25311i	−0.0651498	+	0.142658i
$521$	−29.5851	−	19.0132i	−1.29615	−	0.832984i	−0.303361	−	0.952876i	$-0.598109\pi$
$521$	−29.5851	−	19.0132i	−1.29615	−	0.832984i	−0.992787	+	0.119892i	$0.961745\pi$
$522$	−0.918365	+	0.269656i	−0.0401957	+	0.0118025i
$523$	−2.08062	+	14.4710i	−0.0909793	+	0.632775i	0.892405	+	0.451236i	$0.149017\pi$
$523$	−2.08062	+	14.4710i	−0.0909793	+	0.632775i	−0.983384	+	0.181538i	$0.941892\pi$
$524$	−5.26511	−	11.5290i	−0.230007	−	0.503646i
$525$	0.521749	+	3.62884i	0.0227710	+	0.158376i
$526$	10.6346	−	6.83444i	0.463690	−	0.297996i
$527$	15.1750	−	17.5129i	0.661033	−	0.762873i
$528$	2.66673			0.116055
$529$	−17.4807	−	14.9474i	−0.760030	−	0.649888i
$530$	3.03043			0.131633
$531$	6.35887	−	7.33853i	0.275951	−	0.318465i
$532$	−4.23950	+	2.72456i	−0.183806	+	0.118125i
$533$	5.02919	+	34.9788i	0.217838	+	1.51510i
$534$	4.35583	+	9.53793i	0.188495	+	0.412747i
$535$	−1.65549	+	11.5142i	−0.0715732	+	0.497803i
$536$	−4.21783	+	1.23847i	−0.182183	+	0.0534937i
$537$	14.0895	+	9.05475i	0.608006	+	0.390741i
$538$	4.85931	−	10.6404i	0.209500	−	0.458740i
$539$	2.55871	+	0.751305i	0.110211	+	0.0323610i
$540$	0.756312	+	0.872830i	0.0325465	+	0.0375606i
$541$	2.02243	+	2.33401i	0.0869510	+	0.100347i	0.797558	−	0.603243i	$-0.206125\pi$
$541$	2.02243	+	2.33401i	0.0869510	+	0.100347i	−0.710607	+	0.703589i	$0.751579\pi$
$542$	−18.4082	−	5.40513i	−0.790699	−	0.232170i
$543$	−9.46469	+	20.7248i	−0.406169	+	0.889386i
$544$	−5.38092	−	3.45811i	−0.230705	−	0.148265i
$545$	18.8253	−	5.52762i	0.806389	−	0.236777i
$546$	0.440688	−	3.06505i	0.0188597	−	0.131172i
$547$	12.6599	+	27.7212i	0.541297	+	1.18527i	0.960729	+	0.277488i	$0.0895019\pi$
$547$	12.6599	+	27.7212i	0.541297	+	1.18527i	−0.419432	+	0.907787i	$0.637771\pi$
$548$	0.516033	+	3.58909i	0.0220439	+	0.153318i
$549$	−6.86556	+	4.41222i	−0.293015	+	0.188309i
$550$	−6.40235	+	7.38870i	−0.272997	+	0.315055i
$551$	4.82348			0.205487
$552$	1.66122	−	4.49893i	0.0707062	−	0.191487i
$553$	−2.75127			−0.116996
$554$	10.4432	−	12.0521i	0.443688	−	0.512043i
$555$	−6.59194	+	4.23638i	−0.279812	+	0.179825i
$556$	0.0370836	+	0.257922i	0.00157269	+	0.0109383i
$557$	−0.669565	−	1.46614i	−0.0283704	−	0.0621225i	0.894916	−	0.446234i	$-0.147235\pi$
$557$	−0.669565	−	1.46614i	−0.0283704	−	0.0621225i	−0.923287	+	0.384112i	$0.874508\pi$
$558$	−0.515585	+	3.58597i	−0.0218265	+	0.151806i
$559$	−6.44067	+	1.89115i	−0.272411	+	0.0799872i
$560$	−0.971581	−	0.624397i	−0.0410568	−	0.0263856i
$561$	−7.08583	+	15.5158i	−0.299164	+	0.655078i
$562$	−12.2698	−	3.60274i	−0.517570	−	0.151972i
$563$	26.4158	+	30.4855i	1.11329	+	1.28481i	0.954735	+	0.297459i	$0.0961392\pi$
$563$	26.4158	+	30.4855i	1.11329	+	1.28481i	0.158559	+	0.987350i	$0.449315\pi$
$564$	6.18525	+	7.13816i	0.260446	+	0.300571i
$565$	7.47179	+	2.19392i	0.314341	+	0.0922987i
$566$	6.77898	−	14.8439i	0.284942	−	0.623936i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	0.550665	−	0.161690i	0.0231054	−	0.00678436i
$569$	−1.68567	+	11.7241i	−0.0706668	+	0.491498i	0.923496	+	0.383608i	$0.125319\pi$
$569$	−1.68567	+	11.7241i	−0.0706668	+	0.491498i	−0.994163	+	0.107890i	$0.965590\pi$
$570$	−2.41781	−	5.29426i	−0.101271	−	0.221752i
$571$	−6.23228	−	43.3464i	−0.260813	−	1.81399i	−0.526771	−	0.850007i	$-0.676598\pi$
$571$	−6.23228	−	43.3464i	−0.260813	−	1.81399i	0.265959	−	0.963984i	$-0.414312\pi$
$572$	6.94683	−	4.46446i	0.290462	−	0.186668i
$573$	3.08118	−	3.55587i	0.128718	−	0.148549i
$574$	−11.4121			−0.476333
$575$	8.47687	+	15.4039i	0.353510	+	0.642386i
$576$	1.00000			0.0416667
$577$	−21.9828	+	25.3695i	−0.915155	+	1.05615i	0.0830671	+	0.996544i	$0.473528\pi$
$577$	−21.9828	+	25.3695i	−0.915155	+	1.05615i	−0.998222	+	0.0596014i	$0.981017\pi$
$578$	20.1167	−	12.9282i	0.836745	−	0.537744i
$579$	1.09746	+	7.63303i	0.0456090	+	0.317218i
$580$	0.459206	+	1.00552i	0.0190675	+	0.0417520i
$581$	−1.74425	+	12.1315i	−0.0723637	+	0.503301i
$582$	10.4743	−	3.07553i	0.434174	−	0.127485i
$583$	−5.88651	−	3.78303i	−0.243794	−	0.156677i
$584$	−5.96019	+	13.0510i	−0.246634	+	0.540054i
$585$	3.43143	+	1.00756i	0.141872	+	0.0416574i
$586$	11.3510	+	13.0997i	0.468905	+	0.541146i
$587$	6.18299	+	7.13555i	0.255199	+	0.294516i	0.868864	−	0.495051i	$-0.164851\pi$
$587$	6.18299	+	7.13555i	0.255199	+	0.294516i	−0.613665	+	0.789567i	$0.710305\pi$
$588$	0.959493	+	0.281733i	0.0395688	+	0.0116185i
$589$	7.58437	−	16.6075i	0.312509	−	0.684299i
$590$	−9.43431	−	6.06306i	−0.388404	−	0.249612i
$591$	4.91359	−	1.44276i	0.202118	−	0.0593472i
$592$	−0.965572	+	6.71570i	−0.0396848	+	0.276014i
$593$	6.89790	+	15.1043i	0.283263	+	0.620259i	0.996763	−	0.0803959i	$-0.0256185\pi$
$593$	6.89790	+	15.1043i	0.283263	+	0.620259i	−0.713500	+	0.700655i	$0.752891\pi$
$594$	−0.379515	−	2.63959i	−0.0155717	−	0.108304i
$595$	6.21453	−	3.99384i	0.254771	−	0.163731i
$596$	0.151262	−	0.174566i	0.00619594	−	0.00715050i
$597$	−1.14148			−0.0467178
$598$	−3.20432	−	14.5008i	−0.131034	−	0.592982i
$599$	5.28333			0.215871			0.107935	−	0.994158i	$-0.465576\pi$
$599$	5.28333			0.215871			0.107935	+	0.994158i	$0.465576\pi$
$600$	−2.40082	+	2.77070i	−0.0980132	+	0.113113i
$601$	13.6744	−	8.78800i	0.557790	−	0.358470i	−0.231171	−	0.972913i	$-0.574256\pi$
$601$	13.6744	−	8.78800i	0.557790	−	0.358470i	0.788961	+	0.614443i	$0.210619\pi$
$602$	−0.308503	−	2.14568i	−0.0125736	−	0.0874515i
$603$	1.82612	+	3.99865i	0.0743654	+	0.162838i
$604$	−3.04006	+	21.1441i	−0.123698	+	0.860340i
$605$	4.30905	−	1.26525i	0.175188	−	0.0514398i
$606$	−5.09048	−	3.27145i	−0.206786	−	0.132894i
$607$	11.9697	−	26.2099i	0.485834	−	1.06383i	−0.494984	−	0.868902i	$-0.664826\pi$
$607$	11.9697	−	26.2099i	0.485834	−	1.06383i	0.980818	−	0.194926i	$-0.0624466\pi$
$608$	−4.83537	−	1.41979i	−0.196100	−	0.0575801i
$609$	−0.626790	−	0.723355i	−0.0253988	−	0.0293118i
$610$	6.17234	+	7.12326i	0.249911	+	0.288412i
$611$	28.0628	+	8.23998i	1.13530	+	0.333354i
$612$	−2.65712	+	5.81829i	−0.107408	+	0.235190i
$613$	−31.0575	−	19.9594i	−1.25440	−	0.806153i	−0.266891	−	0.963727i	$-0.585996\pi$
$613$	−31.0575	−	19.9594i	−1.25440	−	0.806153i	−0.987507	+	0.157574i	$0.949633\pi$
$614$	−16.1872	+	4.75299i	−0.653261	+	0.191815i
$615$	1.87573	−	13.0460i	0.0756365	−	0.526064i
$616$	1.10780	+	2.42574i	0.0446345	+	0.0977360i
$617$	−1.38135	−	9.60748i	−0.0556109	−	0.386783i	−0.998551	−	0.0538192i	$-0.982861\pi$
$617$	−1.38135	−	9.60748i	−0.0556109	−	0.386783i	0.942940	−	0.332963i	$-0.108049\pi$
$618$	4.29827	−	2.76233i	0.172902	−	0.111117i
$619$	30.5335	−	35.2375i	1.22724	−	1.41632i	0.349672	−	0.936872i	$-0.386293\pi$
$619$	30.5335	−	35.2375i	1.22724	−	1.41632i	0.877573	−	0.479444i	$-0.159162\pi$
$620$	4.18410			0.168038
$621$	−4.68955	−	1.00405i	−0.188185	−	0.0402910i
$622$	17.8768			0.716794
$623$	−6.86653	+	7.92440i	−0.275102	+	0.317484i
$624$	2.60500	−	1.67413i	0.104283	−	0.0670189i
$625$	−0.963688	−	6.70260i	−0.0385475	−	0.268104i
$626$	8.01366	+	17.5475i	0.320290	+	0.701338i
$627$	−1.91257	+	13.3022i	−0.0763806	+	0.531239i
$628$	−9.79304	+	2.87550i	−0.390785	+	0.114745i
$629$	−36.5083	−	23.4624i	−1.45568	−	0.935508i
$630$	−0.479771	+	1.05055i	−0.0191145	+	0.0418550i
$631$	−29.4529	−	8.64816i	−1.17250	−	0.344278i	−0.363223	−	0.931702i	$-0.618324\pi$
$631$	−29.4529	−	8.64816i	−1.17250	−	0.344278i	−0.809279	+	0.587425i	$0.800142\pi$
$632$	−1.80170	−	2.07927i	−0.0716678	−	0.0827090i
$633$	13.9056	+	16.0479i	0.552699	+	0.637848i
$634$	3.30827	+	0.971396i	0.131388	+	0.0385791i
$635$	−3.48936	+	7.64064i	−0.138471	+	0.303210i
$636$	−2.20739	−	1.41860i	−0.0875286	−	0.0562512i
$637$	2.97114	−	0.872404i	0.117721	−	0.0345659i
$638$	0.363247	−	2.52644i	0.0143811	−	0.100023i
$639$	−0.238412	−	0.522049i	−0.00943143	−	0.0206520i
$640$	−0.164362	−	1.14316i	−0.00649699	−	0.0451876i
$641$	19.9622	−	12.8289i	0.788460	−	0.506713i	−0.0833712	−	0.996519i	$-0.526569\pi$
$641$	19.9622	−	12.8289i	0.788460	−	0.506713i	0.871832	+	0.489806i	$0.162932\pi$
$642$	6.59590	−	7.61208i	0.260319	−	0.300425i
$643$	−8.49660			−0.335073			−0.167537	−	0.985866i	$-0.553581\pi$
$643$	−8.49660			−0.335073			−0.167537	+	0.985866i	$0.553581\pi$
$644$	4.78246	−	0.357823i	0.188455	−	0.0141002i
$645$	2.50357			0.0985782
$646$	21.1089	−	24.3610i	0.830519	−	0.958470i
$647$	40.6328	−	26.1131i	1.59744	−	1.02661i	0.628988	−	0.777415i	$-0.283470\pi$
$647$	40.6328	−	26.1131i	1.59744	−	1.02661i	0.968453	−	0.249197i	$-0.0801668\pi$
$648$	−0.142315	−	0.989821i	−0.00559065	−	0.0388839i
$649$	10.7570	+	23.5546i	0.422250	+	0.924599i
$650$	−1.61563	+	11.2370i	−0.0633703	+	0.440750i
$651$	−3.47610	+	1.02067i	−0.136239	+	0.0400034i
$652$	14.9547	+	9.61083i	0.585673	+	0.376389i
$653$	12.6251	−	27.6452i	0.494059	−	1.08184i	−0.484295	−	0.874905i	$-0.660924\pi$
$653$	12.6251	−	27.6452i	0.494059	−	1.08184i	0.978355	−	0.206935i	$-0.0663487\pi$
$654$	−16.3001	−	4.78615i	−0.637385	−	0.187153i
$655$	9.58574	+	11.0625i	0.374546	+	0.432249i
$656$	−7.47336	−	8.62472i	−0.291786	−	0.336739i
$657$	13.7664	+	4.04217i	0.537078	+	0.157700i
$658$	−3.92365	+	8.59160i	−0.152960	+	0.334935i
$659$	−18.5554	−	11.9248i	−0.722814	−	0.464525i	0.126800	−	0.991928i	$-0.459529\pi$
$659$	−18.5554	−	11.9248i	−0.722814	−	0.464525i	−0.849615	+	0.527404i	$0.823166\pi$
$660$	−2.95510	+	0.867697i	−0.115027	+	0.0337751i
$661$	−0.122025	+	0.848701i	−0.00474622	+	0.0330107i	−0.992057	−	0.125790i	$-0.959854\pi$
$661$	−0.122025	+	0.848701i	−0.00474622	+	0.0330107i	0.987311	+	0.158800i	$0.0507626\pi$
$662$	9.33292	+	20.4363i	0.362734	+	0.794278i
$663$	2.81878	+	19.6050i	0.109472	+	0.761396i
$664$	−10.3106	+	6.62625i	−0.400130	+	0.257148i
$665$	3.81143	−	4.39863i	0.147801	−	0.170572i
$666$	6.78476			0.262904
$667$	−4.03597	−	2.18665i	−0.156273	−	0.0846673i
$668$	22.3110			0.863239
$669$	−14.2432	+	16.4375i	−0.550674	+	0.635512i
$670$	4.27097	−	2.74479i	0.165002	−	0.106040i
$671$	−3.09726	−	21.5419i	−0.119568	−	0.831617i
$672$	0.415415	+	0.909632i	0.0160250	+	0.0350898i
$673$	−3.80753	+	26.4820i	−0.146770	+	1.02080i	0.774693	+	0.632337i	$0.217904\pi$
$673$	−3.80753	+	26.4820i	−0.146770	+	1.02080i	−0.921463	+	0.388467i	$0.873005\pi$
$674$	−20.5738	+	6.04103i	−0.792475	+	0.232692i
$675$	3.08417	+	1.98208i	0.118710	+	0.0762901i
$676$	−1.41709	+	3.10299i	−0.0545033	+	0.119346i
$677$	−44.6603	−	13.1134i	−1.71643	−	0.503990i	−0.732234	−	0.681053i	$-0.761522\pi$
$677$	−44.6603	−	13.1134i	−1.71643	−	0.503990i	−0.984199	+	0.177063i	$0.943340\pi$
$678$	−4.41550	−	5.09576i	−0.169576	−	0.195701i
$679$	7.14878	+	8.25014i	0.274345	+	0.316611i
$680$	7.08799	+	2.08122i	0.271812	+	0.0798113i
$681$	3.97465	−	8.70328i	0.152309	−	0.333510i
$682$	−8.12748	−	5.22322i	−0.311217	−	0.200007i
$683$	3.49655	−	1.02668i	0.133792	−	0.0392848i	−0.214151	−	0.976801i	$-0.568698\pi$
$683$	3.49655	−	1.02668i	0.133792	−	0.0392848i	0.347943	+	0.937516i	$0.386880\pi$
$684$	−0.717196	+	4.98821i	−0.0274227	+	0.190729i
$685$	−1.73965	−	3.80930i	−0.0664686	−	0.145546i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	−1.53727	+	0.987942i	−0.0586505	+	0.0376924i
$688$	1.41957	−	1.63827i	0.0541207	−	0.0624586i
$689$	−8.12517			−0.309544
$690$	−0.377006	+	5.52596i	−0.0143524	+	0.210370i
$691$	−15.8434			−0.602713			−0.301356	−	0.953512i	$-0.597439\pi$
$691$	−15.8434			−0.602713			−0.301356	+	0.953512i	$0.597439\pi$
$692$	−12.0016	+	13.8506i	−0.456233	+	0.526521i
$693$	2.24340	−	1.44174i	0.0852196	−	0.0547673i
$694$	−3.98009	−	27.6821i	−0.151082	−	1.05080i
$695$	−0.125016	−	0.273747i	−0.00474213	−	0.0103838i
$696$	0.136215	−	0.947393i	0.00516320	−	0.0359108i
$697$	70.0388	−	20.5652i	2.65291	−	0.778964i
$698$	−4.52103	−	2.90549i	−0.171123	−	0.109974i
$699$	−12.0983	+	26.4916i	−0.457599	+	1.00200i
$700$	−3.51765	−	1.03288i	−0.132955	−	0.0390391i
$701$	−20.3571	−	23.4933i	−0.768876	−	0.887330i	0.227378	−	0.973807i	$-0.426985\pi$
$701$	−20.3571	−	23.4933i	−0.768876	−	0.887330i	−0.996254	+	0.0864768i	$0.972439\pi$
$702$	−2.02782	−	2.34023i	−0.0765352	−	0.0883263i
$703$	−32.8068	−	9.63295i	−1.23733	−	0.363313i
$704$	−1.10780	+	2.42574i	−0.0417518	+	0.0914236i
$705$	−9.17671	−	5.89752i	−0.345615	−	0.222113i
$706$	−9.91908	+	2.91251i	−0.373310	+	0.109614i
$707$	0.861156	−	5.98947i	0.0323871	−	0.225257i
$708$	4.03379	+	8.83277i	0.151599	+	0.331956i
$709$	5.36449	+	37.3108i	0.201468	+	1.40124i	0.799933	+	0.600089i	$0.204868\pi$
$709$	5.36449	+	37.3108i	0.201468	+	1.40124i	−0.598466	+	0.801148i	$0.704223\pi$
$710$	−0.557603	+	0.358349i	−0.0209264	+	0.0134486i
$711$	−1.80170	+	2.07927i	−0.0675690	+	0.0779788i
$712$	−10.4855			−0.392960
$713$	−13.8748	+	10.4578i	−0.519616	+	0.391647i
$714$	−6.39631			−0.239376
$715$	−6.24541	+	7.20758i	−0.233565	+	0.269548i
$716$	−14.0895	+	9.05475i	−0.526548	+	0.338392i
$717$	−3.50954	−	24.4094i	−0.131066	−	0.911586i
$718$	−7.42050	−	16.2486i	−0.276931	−	0.606394i
$719$	1.10176	−	7.66289i	0.0410886	−	0.285778i	−0.958909	−	0.283713i	$-0.908434\pi$
$719$	1.10176	−	7.66289i	0.0410886	−	0.285778i	0.999998	−	0.00206465i	$-0.000657199\pi$
$720$	−1.10814	+	0.325379i	−0.0412979	+	0.0121261i
$721$	4.29827	+	2.76233i	0.160076	+	0.102874i
$722$	2.65723	−	5.81852i	0.0988918	−	0.216543i
$723$	4.71348	+	1.38400i	0.175296	+	0.0514716i
$724$	−14.9202	−	17.2188i	−0.554503	−	0.639931i
$725$	2.29791	+	2.65193i	0.0853424	+	0.0984903i
$726$	−3.73104	−	1.09553i	−0.138472	−	0.0406590i
$727$	−0.250062	+	0.547559i	−0.00927428	+	0.0203078i	−0.914212	−	0.405235i	$-0.867190\pi$
$727$	−0.250062	+	0.547559i	−0.00927428	+	0.0203078i	0.904938	+	0.425543i	$0.139917\pi$
$728$	2.60500	+	1.67413i	0.0965477	+	0.0620475i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	2.35820	−	16.4016i	0.0872808	−	0.607051i
$731$	5.75997	+	12.6126i	0.213040	+	0.466493i
$732$	−1.16145	−	8.07803i	−0.0429283	−	0.298573i
$733$	−5.04016	+	3.23911i	−0.186163	+	0.119639i	−0.630403	−	0.776268i	$-0.717110\pi$
$733$	−5.04016	+	3.23911i	−0.186163	+	0.119639i	0.444240	+	0.895908i	$0.353474\pi$
$734$	1.54599	−	1.78417i	0.0570635	−	0.0658548i
$735$	−1.15492			−0.0425999
$736$	3.40227	+	3.38002i	0.125409	+	0.124589i
$737$	−11.7227			−0.431810
$738$	−7.47336	+	8.62472i	−0.275098	+	0.317480i
$739$	−15.0505	+	9.67236i	−0.553641	+	0.355803i	−0.787353	−	0.616502i	$-0.788549\pi$
$739$	−15.0505	+	9.67236i	−0.553641	+	0.355803i	0.233712	+	0.972306i	$0.424913\pi$
$740$	−1.11516	−	7.75610i	−0.0409941	−	0.285120i
$741$	6.48262	+	14.1950i	0.238145	+	0.521465i
$742$	0.373424	−	2.59722i	0.0137088	−	0.0953469i
$743$	−32.5539	+	9.55869i	−1.19429	+	0.350674i	−0.817666	−	0.575693i	$-0.804732\pi$
$743$	−32.5539	+	9.55869i	−1.19429	+	0.350674i	−0.376621	+	0.926367i	$0.622914\pi$
$744$	−3.04773	−	1.95866i	−0.111735	−	0.0718079i
$745$	−0.110819	+	0.242661i	−0.00406011	+	0.00889040i
$746$	−14.5511	−	4.27258i	−0.532753	−	0.156430i
$747$	8.02616	+	9.26268i	0.293662	+	0.338904i
$748$	−11.1701	−	12.8910i	−0.408420	−	0.471342i
$749$	9.66422	+	2.83767i	0.353123	+	0.103686i
$750$	4.15777	−	9.10425i	0.151820	−	0.332440i
$751$	−17.4101	−	11.1888i	−0.635304	−	0.408285i	0.182966	−	0.983119i	$-0.441430\pi$
$751$	−17.4101	−	11.1888i	−0.635304	−	0.408285i	−0.818270	+	0.574834i	$0.805067\pi$
$752$	−9.06254	+	2.66100i	−0.330477	+	0.0970368i
$753$	−0.567132	+	3.94449i	−0.0206675	+	0.143745i
$754$	−1.23122	−	2.69600i	−0.0448385	−	0.0981825i
$755$	−3.51102	−	24.4197i	−0.127779	−	0.888724i
$756$	0.841254	−	0.540641i	0.0305961	−	0.0196629i
$757$	−4.78942	+	5.52729i	−0.174074	+	0.200893i	−0.836082	−	0.548605i	$-0.815159\pi$
$757$	−4.78942	+	5.52729i	−0.174074	+	0.200893i	0.662007	+	0.749497i	$0.269705\pi$
$758$	26.7638			0.972104
$759$	7.63064	−	10.2634i	0.276975	−	0.372536i
$760$	5.82022			0.211122
$761$	−22.7453	+	26.2494i	−0.824516	+	0.951542i	−0.999454	−	0.0330376i	$-0.989482\pi$
$761$	−22.7453	+	26.2494i	−0.824516	+	0.951542i	0.174938	+	0.984579i	$0.444027\pi$
$762$	6.11841	−	3.93207i	0.221647	−	0.142444i
$763$	−2.41768	−	16.8153i	−0.0875259	−	0.608756i
$764$	1.95457	+	4.27990i	0.0707137	+	0.154841i
$765$	1.05131	−	7.31204i	0.0380103	−	0.264367i
$766$	25.7805	−	7.56983i	0.931486	−	0.273509i
$767$	25.2952	+	16.2563i	0.913358	+	0.586980i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	27.5374	+	8.08572i	0.993025	+	0.291579i	0.737591	−	0.675248i	$-0.235963\pi$
$769$	27.5374	+	8.08572i	0.993025	+	0.291579i	0.255434	+	0.966826i	$0.417782\pi$
$770$	−2.01688	−	2.32760i	−0.0726833	−	0.0838810i
$771$	18.8372	+	21.7393i	0.678406	+	0.782922i
$772$	−7.39915	−	2.17259i	−0.266301	−	0.0781931i
$773$	0.0741449	−	0.162355i	0.00266681	−	0.00583949i	−0.908294	−	0.418333i	$-0.862615\pi$
$773$	0.0741449	−	0.162355i	0.00266681	−	0.00583949i	0.910961	+	0.412493i	$0.135342\pi$
$774$	−1.82362	−	1.17197i	−0.0655488	−	0.0421257i
$775$	12.7439	−	3.74195i	0.457775	−	0.134415i
$776$	−1.55358	+	10.8054i	−0.0557703	+	0.387891i
$777$	2.81849	+	6.17164i	0.101113	+	0.221406i
$778$	−4.91124	−	34.1584i	−0.176077	−	1.22464i
$779$	48.3817	−	31.0931i	1.73346	−	1.11402i
$780$	−2.34197	+	2.70278i	−0.0838561	+	0.0967751i
$781$	1.53047			0.0547645
$782$	−28.7062	+	10.8143i	−1.02653	+	0.386718i
$783$	−0.957135			−0.0342052
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	9.91642	−	6.37289i	0.353932	−	0.227458i
$786$	−1.80374	−	12.5453i	−0.0643374	−	0.447477i
$787$	2.27638	+	4.98457i	0.0811441	+	0.177681i	0.945855	−	0.324589i	$-0.105226\pi$
$787$	2.27638	+	4.98457i	0.0811441	+	0.177681i	−0.864711	+	0.502269i	$0.832499\pi$
$788$	−0.728798	+	5.06890i	−0.0259623	+	0.180572i
$789$	12.1293	−	3.56148i	0.431815	−	0.126792i
$790$	2.67308	+	1.71789i	0.0951040	+	0.0611196i
$791$	2.80100	−	6.13333i	0.0995921	−	0.218076i
$792$	2.55871	+	0.751305i	0.0909198	+	0.0266964i
$793$	−16.5493	−	19.0989i	−0.587681	−	0.678221i
$794$	−6.47582	−	7.47350i	−0.229818	−	0.265224i
$795$	2.90767	+	0.853770i	0.103125	+	0.0302801i
$796$	0.474190	−	1.03833i	0.0168072	−	0.0368027i
$797$	−36.7029	−	23.5875i	−1.30008	−	0.835513i	−0.306863	−	0.951754i	$-0.599279\pi$
$797$	−36.7029	−	23.5875i	−1.30008	−	0.835513i	−0.993221	+	0.116240i	$0.962916\pi$
$798$	−4.83537	+	1.41979i	−0.171170	+	0.0502601i
$799$	8.59781	−	59.7991i	0.304169	−	2.11554i
$800$	−1.52298	−	3.33486i	−0.0538454	−	0.117905i
$801$	1.49224	+	10.3788i	0.0527257	+	0.366715i
$802$	2.99564	−	1.92518i	0.105780	−	0.0679806i
$803$	−25.0557	+	28.9158i	−0.884195	+	1.02042i
$804$	−4.39590			−0.155031
$805$	−5.18320	+	1.95263i	−0.182684	+	0.0688211i
$806$	−11.2184			−0.395151
$807$	7.66022	−	8.84036i	0.269652	−	0.311195i
$808$	5.09048	−	3.27145i	0.179082	−	0.115089i
$809$	−1.67230	−	11.6311i	−0.0587949	−	0.408927i	−0.997871	−	0.0652182i	$-0.979226\pi$
$809$	−1.67230	−	11.6311i	−0.0587949	−	0.408927i	0.939076	−	0.343709i	$-0.111683\pi$
$810$	0.479771	+	1.05055i	0.0168574	+	0.0369126i
$811$	−2.40798	+	16.7479i	−0.0845557	+	0.588097i	0.902858	+	0.429939i	$0.141465\pi$
$811$	−2.40798	+	16.7479i	−0.0845557	+	0.588097i	−0.987414	+	0.158159i	$0.949444\pi$
$812$	0.918365	−	0.269656i	0.0322283	−	0.00946308i
$813$	−16.1397	−	10.3724i	−0.566045	−	0.363775i
$814$	−7.51616	+	16.4581i	−0.263441	+	0.576856i
$815$	−19.6991	−	5.78417i	−0.690029	−	0.202611i
$816$	−4.18869	−	4.83401i	−0.146634	−	0.169224i
$817$	7.15394	+	8.25608i	0.250285	+	0.288844i
$818$	−25.9051	−	7.60642i	−0.905750	−	0.265952i
$819$	1.28636	−	2.81674i	0.0449491	−	0.0984248i
$820$	11.0878	+	7.12570i	0.387203	+	0.248840i
$821$	−27.3601	+	8.03365i	−0.954875	+	0.280376i	−0.721815	−	0.692086i	$-0.756692\pi$
$821$	−27.3601	+	8.03365i	−0.954875	+	0.280376i	−0.233059	+	0.972462i	$0.574874\pi$
$822$	−0.516033	+	3.58909i	−0.0179987	+	0.125184i
$823$	−0.624970	−	1.36849i	−0.0217851	−	0.0477027i	0.898427	−	0.439124i	$-0.144711\pi$
$823$	−0.624970	−	1.36849i	−0.0217851	−	0.0477027i	−0.920212	+	0.391421i	$0.871984\pi$
$824$	0.727137	+	5.05735i	0.0253310	+	0.176181i
$825$	−8.22465	+	5.28566i	−0.286345	+	0.184023i
$826$	−6.35887	+	7.33853i	−0.221253	+	0.255340i
$827$	−33.2285			−1.15547			−0.577734	−	0.816225i	$-0.696063\pi$
$827$	−33.2285			−1.15547			−0.577734	+	0.816225i	$0.696063\pi$
$828$	2.86142	−	3.84867i	0.0994413	−	0.133751i
$829$	−44.3976			−1.54199			−0.770997	−	0.636839i	$-0.780242\pi$
$829$	−44.3976			−1.54199			−0.770997	+	0.636839i	$0.780242\pi$
$830$	9.26957	−	10.6977i	0.321751	−	0.371321i
$831$	13.4156	−	8.62168i	0.465382	−	0.299083i
$832$	0.440688	+	3.06505i	0.0152781	+	0.106262i
$833$	−2.65712	−	5.81829i	−0.0920639	−	0.201592i
$834$	−0.0370836	+	0.257922i	−0.00128410	+	0.00893111i
$835$	−24.7237	+	7.25952i	−0.855598	+	0.251226i
$836$	−11.3056	−	7.26566i	−0.391012	−	0.251288i
$837$	−1.50499	+	3.29546i	−0.0520199	+	0.113908i
$838$	4.51578	+	1.32595i	0.155995	+	0.0458042i
$839$	4.77023	+	5.50514i	0.164687	+	0.190058i	0.832094	−	0.554634i	$-0.187142\pi$
$839$	4.77023	+	5.50514i	0.164687	+	0.190058i	−0.667408	+	0.744692i	$0.732596\pi$
$840$	−0.756312	−	0.872830i	−0.0260952	−	0.0301155i
$841$	26.9463	+	7.91215i	0.929183	+	0.272833i
$842$	1.62006	−	3.54744i	0.0558310	−	0.122253i
$843$	−10.7578	−	6.91361i	−0.370518	−	0.238117i
$844$	−20.3743	+	5.98244i	−0.701313	+	0.205924i
$845$	0.560682	−	3.89963i	0.0192880	−	0.134151i
$846$	3.92365	+	8.59160i	0.134898	+	0.295385i
$847$	−0.553399	−	3.84897i	−0.0190150	−	0.132252i
$848$	2.20739	−	1.41860i	0.0758020	−	0.0487150i
$849$	10.6864	−	12.3328i	0.366756	−	0.423259i
$850$	23.4499			0.804325
$851$	23.0836	+	22.9326i	0.791296	+	0.786121i
$852$	0.573913			0.0196619
$853$	−14.5361	+	16.7755i	−0.497706	+	0.574383i	−0.947908	−	0.318543i	$-0.896806\pi$
$853$	−14.5361	+	16.7755i	−0.497706	+	0.574383i	0.450203	+	0.892926i	$0.351352\pi$
$854$	6.86556	−	4.41222i	0.234934	−	0.150983i
$855$	−0.828304	−	5.76098i	−0.0283274	−	0.197021i
$856$	4.18415	+	9.16201i	0.143011	+	0.313151i
$857$	−0.00557206	+	0.0387545i	−0.000190338	+	0.00132383i	−0.989916	−	0.141653i	$-0.954758\pi$
$857$	−0.00557206	+	0.0387545i	−0.000190338	+	0.00132383i	0.989726	+	0.142977i	$0.0456674\pi$
$858$	7.92322	−	2.32647i	0.270494	−	0.0794243i
$859$	13.5942	+	8.73646i	0.463828	+	0.298084i	0.751605	−	0.659613i	$-0.229280\pi$
$859$	13.5942	+	8.73646i	0.463828	+	0.298084i	−0.287777	+	0.957697i	$0.592916\pi$
$860$	−1.04002	+	2.27733i	−0.0354645	+	0.0776564i
$861$	−10.9499	−	3.21517i	−0.373170	−	0.109573i
$862$	12.2918	+	14.1855i	0.418660	+	0.483160i
$863$	−10.2287	−	11.8045i	−0.348188	−	0.401831i	0.554460	−	0.832211i	$-0.312925\pi$
$863$	−10.2287	−	11.8045i	−0.348188	−	0.401831i	−0.902648	+	0.430380i	$0.858380\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	8.79276	−	19.2534i	0.298963	−	0.654637i
$866$	−28.4386	−	18.2764i	−0.966383	−	0.621056i
$867$	22.9442	−	6.73701i	0.779224	−	0.228801i
$868$	0.515585	−	3.58597i	0.0175001	−	0.121716i
$869$	−3.04786	−	6.67388i	−0.103392	−	0.226396i
$870$	0.157317	+	1.09416i	0.00533354	+	0.0370956i
$871$	−11.4513	+	7.35931i	−0.388013	+	0.249361i
$872$	11.1249	−	12.8389i	0.376738	−	0.434779i
$873$	10.9165			0.369467
$874$	−19.3003	+	14.5471i	−0.652844	+	0.492063i
$875$	10.0087			0.338357
$876$	−9.39565	+	10.8432i	−0.317450	+	0.366356i
$877$	43.9390	−	28.2379i	1.48371	−	0.953526i	0.486927	−	0.873443i	$-0.338118\pi$
$877$	43.9390	−	28.2379i	1.48371	−	0.953526i	0.996788	−	0.0800827i	$-0.0255184\pi$
$878$	3.19485	+	22.2207i	0.107821	+	0.749912i
$879$	7.20058	+	15.7671i	0.242869	+	0.531810i
$880$	0.438310	−	3.04851i	0.0147754	−	0.102765i
$881$	23.0941	−	6.78103i	0.778059	−	0.228459i	0.131494	−	0.991317i	$-0.458023\pi$
$881$	23.0941	−	6.78103i	0.778059	−	0.228459i	0.646566	+	0.762858i	$0.276205\pi$
$882$	0.841254	+	0.540641i	0.0283265	+	0.0182043i
$883$	17.9215	−	39.2426i	0.603106	−	1.32062i	−0.324084	−	0.946028i	$-0.605056\pi$
$883$	17.9215	−	39.2426i	0.603106	−	1.32062i	0.927190	−	0.374590i	$-0.122217\pi$
$884$	−19.0043	−	5.58017i	−0.639184	−	0.187681i
$885$	−7.34399	−	8.47541i	−0.246865	−	0.284898i
$886$	−8.13024	−	9.38279i	−0.273141	−	0.315221i
$887$	29.9717	+	8.80049i	1.00635	+	0.295492i	0.743060	−	0.669225i	$-0.233374\pi$
$887$	29.9717	+	8.80049i	1.00635	+	0.295492i	0.263292	+	0.964716i	$0.415192\pi$
$888$	−2.81849	+	6.17164i	−0.0945824	+	0.207107i
$889$	6.11841	+	3.93207i	0.205205	+	0.131877i
$890$	11.6194	−	3.41175i	0.389482	−	0.114362i
$891$	0.379515	−	2.63959i	0.0127142	−	0.0884295i
$892$	−9.03527	−	19.7845i	−0.302523	−	0.662433i
$893$	−6.77401	−	47.1143i	−0.226684	−	1.57662i
$894$	0.194316	−	0.124879i	0.00649890	−	0.00417659i
$895$	12.6669	−	14.6183i	0.423406	−	0.488637i
$896$	−1.00000			−0.0334077
$897$	1.01083	−	14.8162i	0.0337505	−	0.494698i
$898$	16.7746			0.559776
$899$	−2.27077	+	2.62060i	−0.0757343	+	0.0874020i
$900$	−3.08417	+	1.98208i	−0.102806	+	0.0660692i
$901$	2.38853	+	16.6126i	0.0795736	+	0.553447i
$902$	−12.6424	−	27.6829i	−0.420945	−	0.921740i
$903$	0.308503	−	2.14568i	0.0102663	−	0.0714038i
$904$	6.46953	−	1.89963i	0.215173	−	0.0631806i
$905$	22.1362	+	14.2261i	0.735832	+	0.472891i
$906$	−8.87389	+	19.4311i	−0.294815	+	0.645555i
$907$	44.5648	+	13.0854i	1.47975	+	0.434494i	0.919254	−	0.393664i	$-0.128793\pi$
$907$	44.5648	+	13.0854i	1.47975	+	0.434494i	0.560495	+	0.828158i	$0.310611\pi$
$908$	6.26565	+	7.23094i	0.207933	+	0.239967i
$909$	−3.96260	−	4.57309i	−0.131431	−	0.151680i
$910$	−3.43143	−	1.00756i	−0.113751	−	0.0334002i
$911$	4.54592	−	9.95418i	0.150613	−	0.329797i	−0.819254	−	0.573431i	$-0.805612\pi$
$911$	4.54592	−	9.95418i	0.150613	−	0.329797i	0.969867	+	0.243634i	$0.0783395\pi$
$912$	−4.23950	−	2.72456i	−0.140384	−	0.0902192i
$913$	−31.3602	+	9.20820i	−1.03787	+	0.304747i
$914$	−3.97408	+	27.6403i	−0.131451	+	0.914261i
$915$	3.91546	+	8.57366i	0.129441	+	0.283437i
$916$	−0.260060	−	1.80875i	−0.00859261	−	0.0597629i
$917$	10.6623	−	6.85226i	0.352101	−	0.226282i
$918$	−4.18869	+	4.83401i	−0.138247	+	0.159546i
$919$	−42.8164			−1.41238			−0.706191	−	0.708022i	$-0.749588\pi$
$919$	−42.8164			−1.41238			−0.706191	+	0.708022i	$0.749588\pi$
$920$	−4.86997	−	2.63850i	−0.160558	−	0.0869888i
$921$	−16.8706			−0.555904
$922$	14.8491	−	17.1368i	0.489029	−	0.564369i
$923$	1.49504	−	0.960806i	0.0492099	−	0.0316253i
$924$	0.379515	+	2.63959i	0.0124851	+	0.0868360i
$925$	−10.3330	−	22.6262i	−0.339748	−	0.743945i
$926$	1.02589	−	7.13524i	0.0337129	−	0.234478i
$927$	4.90239	−	1.43947i	0.161016	−	0.0472785i
$928$	0.805193	+	0.517466i	0.0264318	+	0.0169867i
$929$	20.6037	−	45.1157i	0.675984	−	1.48020i	−0.190858	−	0.981618i	$-0.561127\pi$
$929$	20.6037	−	45.1157i	0.675984	−	1.48020i	0.866843	−	0.498582i	$-0.166146\pi$
$930$	4.01462	+	1.17880i	0.131644	+	0.0386543i
$931$	−3.30017	−	3.80860i	−0.108159	−	0.124822i
$932$	−19.0718	−	22.0100i	−0.624716	−	0.720961i
$933$	17.1526	+	5.03647i	0.561552	+	0.164887i
$934$	8.89304	−	19.4730i	0.290989	−	0.637177i
$935$	16.5725	+	10.6505i	0.541978	+	0.348308i
$936$	2.97114	−	0.872404i	0.0971146	−	0.0285154i
$937$	5.30901	−	36.9250i	0.173438	−	1.20629i	−0.698115	−	0.715985i	$-0.745978\pi$
$937$	5.30901	−	36.9250i	0.173438	−	1.20629i	0.871553	−	0.490301i	$-0.163113\pi$
$938$	−1.82612	−	3.99865i	−0.0596250	−	0.130561i
$939$	2.74536	+	19.0944i	0.0895914	+	0.623122i
$940$	9.17671	−	5.89752i	0.299311	−	0.192356i
$941$	11.3648	−	13.1157i	0.370483	−	0.427561i	−0.539641	−	0.841895i	$-0.681440\pi$
$941$	11.3648	−	13.1157i	0.370483	−	0.427561i	0.910125	+	0.414334i	$0.135986\pi$
$942$	−10.2065			−0.332545
$943$	−54.5781	+	4.08353i	−1.77731	+	0.132978i
$944$	−9.71026			−0.316042
$945$	−0.756312	+	0.872830i	−0.0246028	+	0.0283932i
$946$	4.86312	−	3.12533i	0.158114	−	0.101613i
$947$	−1.54910	−	10.7742i	−0.0503390	−	0.350115i	−0.999388	−	0.0349862i	$-0.988861\pi$
$947$	−1.54910	−	10.7742i	−0.0503390	−	0.350115i	0.949049	−	0.315129i	$-0.102048\pi$
$948$	−1.14292	−	2.50264i	−0.0371203	−	0.0812821i
$949$	−6.32279	+	43.9760i	−0.205247	+	1.42752i
$950$	17.7272	−	5.20518i	0.575147	−	0.168878i
$951$	2.90059	+	1.86410i	0.0940581	+	0.0604474i
$952$	2.65712	−	5.81829i	0.0861179	−	0.188572i
$953$	−40.4844	−	11.8873i	−1.31142	−	0.385067i	−0.450029	−	0.893014i	$-0.648586\pi$
$953$	−40.4844	−	11.8873i	−1.31142	−	0.385067i	−0.861388	+	0.507947i	$0.830404\pi$
$954$	−1.71831	−	1.98303i	−0.0556322	−	0.0642030i
$955$	−3.55852	−	4.10675i	−0.115151	−	0.132891i
$956$	23.6615	+	6.94764i	0.765268	+	0.224703i
$957$	1.06031	−	2.32176i	0.0342751	−	0.0750520i
$958$	10.4617	+	6.72332i	0.338002	+	0.217221i
$959$	−3.47912	+	1.02156i	−0.112347	+	0.0329880i
$960$	0.164362	−	1.14316i	0.00530477	−	0.0368955i
$961$	−7.42553	−	16.2596i	−0.239533	−	0.524505i
$962$	2.98996	+	20.7956i	0.0964002	+	0.670478i
$963$	8.47329	−	5.44545i	0.273048	−	0.175477i
$964$	−3.21698	+	3.71260i	−0.103612	+	0.119575i
$965$	8.90619			0.286700
$966$	4.68955	+	1.00405i	0.150884	+	0.0323047i
$967$	36.2407			1.16542			0.582711	−	0.812679i	$-0.301992\pi$
$967$	36.2407			1.16542			0.582711	+	0.812679i	$0.301992\pi$
$968$	2.54646	−	2.93877i	0.0818463	−	0.0944557i
$969$	27.1171	−	17.4271i	0.871128	−	0.559840i
$970$	−1.79426	−	12.4794i	−0.0576102	−	0.400688i
$971$	−20.9544	−	45.8838i	−0.672460	−	1.47248i	−0.870440	−	0.492275i	$-0.836165\pi$
$971$	−20.9544	−	45.8838i	−0.672460	−	1.47248i	0.197980	−	0.980206i	$-0.436562\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	−0.250019	+	0.0734122i	−0.00801524	+	0.00235349i
$974$	−20.6743	−	13.2866i	−0.662447	−	0.425729i
$975$	−4.71601	+	10.3266i	−0.151033	+	0.330716i
$976$	7.83052	+	2.29925i	0.250649	+	0.0735971i
$977$	27.0201	+	31.1828i	0.864449	+	0.997628i	0.999977	+	0.00685392i	$0.00218169\pi$
$977$	27.0201	+	31.1828i	0.864449	+	0.997628i	−0.135527	+	0.990774i	$0.543273\pi$
$978$	11.6413	+	13.4348i	0.372247	+	0.429596i
$979$	−26.8293	−	7.87779i	−0.857468	−	0.251775i
$980$	0.479771	−	1.05055i	0.0153257	−	0.0335587i
$981$	−14.2914	−	9.18455i	−0.456290	−	0.293240i
$982$	7.80098	−	2.29057i	0.248939	−	0.0730951i
$983$	0.715715	−	4.97791i	0.0228278	−	0.158771i	−0.975219	−	0.221242i	$-0.928989\pi$
$983$	0.715715	−	4.97791i	0.0228278	−	0.158771i	0.998047	+	0.0624711i	$0.0198981\pi$
$984$	−4.74077	−	10.3808i	−0.151130	−	0.330929i
$985$	−0.841703	−	5.85418i	−0.0268189	−	0.186530i
$986$	−5.15027	+	3.30988i	−0.164018	+	0.105408i
$987$	−6.18525	+	7.13816i	−0.196879	+	0.227210i
$988$	−15.6052			−0.496466
$989$	−2.24318	−	10.1513i	−0.0713289	−	0.322791i
$990$	−3.07986			−0.0978844
$991$	−19.7157	+	22.7531i	−0.626289	+	0.722776i	−0.976889	−	0.213749i	$-0.931432\pi$
$991$	−19.7157	+	22.7531i	−0.626289	+	0.722776i	0.350599	+	0.936526i	$0.385978\pi$
$992$	3.04773	−	1.95866i	0.0967656	−	0.0621875i
$993$	3.19732	+	22.2378i	0.101464	+	0.705696i
$994$	0.238412	+	0.522049i	0.00756197	+	0.0165584i
$995$	−0.187617	+	1.30490i	−0.00594786	+	0.0413683i
$996$	−11.7598	+	3.45299i	−0.372624	+	0.109412i
$997$	−0.317329	−	0.203935i	−0.0100499	−	0.00645868i	0.535606	−	0.844468i	$-0.320083\pi$
$997$	−0.317329	−	0.203935i	−0.0100499	−	0.00645868i	−0.545656	+	0.838009i	$0.683720\pi$
$998$	−3.24478	+	7.10508i	−0.102712	+	0.224907i
$999$	6.50993	+	1.91149i	0.205965	+	0.0604768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.j.85.3	✓	40
23.13	even	11	inner	966.2.q.j.841.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.j.85.3	✓	40	1.1	even	1	trivial
966.2.q.j.841.3	yes	40	23.13	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.479771 + 1.05055i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.479771 + 1.05055i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-1.10814 - 0.325379i) q^{10} +(1.74634 + 2.01538i) q^{11} +(0.654861 + 0.755750i) q^{12} +(2.97114 + 0.872404i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-0.971581 - 0.624397i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.910290 - 6.33121i) q^{17} +(0.415415 + 0.909632i) q^{18} +(-0.717196 - 4.98821i) q^{19} +(0.971581 - 0.624397i) q^{20} +(-0.654861 + 0.755750i) q^{21} -2.66673 q^{22} +(-1.66122 + 4.49893i) q^{23} -1.00000 q^{24} +(2.40082 - 2.77070i) q^{25} +(-2.60500 + 1.67413i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.136215 + 0.947393i) q^{29} +(1.10814 - 0.325379i) q^{30} +(3.04773 + 1.95866i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-2.55871 - 0.751305i) q^{33} +(4.18869 + 4.83401i) q^{34} +(0.756312 + 0.872830i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.81849 - 6.17164i) q^{37} +(4.23950 + 2.72456i) q^{38} +(-2.97114 + 0.872404i) q^{39} +(-0.164362 + 1.14316i) q^{40} +(4.74077 + 10.3808i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(-1.82362 + 1.17197i) q^{43} +(1.74634 - 2.01538i) q^{44} +1.15492 q^{45} +(-2.31219 - 4.20164i) q^{46} +9.44514 q^{47} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.521749 + 3.62884i) q^{50} +(2.65712 + 5.81829i) q^{51} +(0.440688 - 3.06505i) q^{52} +(-2.51764 + 0.739246i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-1.27942 + 2.80154i) q^{55} +(0.959493 + 0.281733i) q^{56} +(3.30017 + 3.80860i) q^{57} +(-0.626790 - 0.723355i) q^{58} +(9.31693 + 2.73570i) q^{59} +(-0.479771 + 1.05055i) q^{60} +(-6.86556 - 4.41222i) q^{61} +(-3.47610 + 1.02067i) q^{62} +(0.142315 - 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.508959 + 3.53989i) q^{65} +(2.24340 - 1.44174i) q^{66} +(-2.87870 + 3.32220i) q^{67} -6.39631 q^{68} +(-1.03480 - 4.68286i) q^{69} -1.15492 q^{70} +(0.375833 - 0.433734i) q^{71} +(0.841254 - 0.540641i) q^{72} +(2.04187 + 14.2015i) q^{73} +(2.81849 + 6.17164i) q^{74} +(-0.521749 + 3.62884i) q^{75} +(-4.83537 + 1.41979i) q^{76} +(2.24340 + 1.44174i) q^{77} +(1.28636 - 2.81674i) q^{78} +(-2.63983 - 0.775123i) q^{79} +(-0.756312 - 0.872830i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-10.9499 - 3.21517i) q^{82} +(-5.09144 + 11.1487i) q^{83} +(0.841254 + 0.540641i) q^{84} +(7.08799 - 2.08122i) q^{85} +(0.308503 - 2.14568i) q^{86} +(-0.397608 - 0.870641i) q^{87} +(0.379515 + 2.63959i) q^{88} +(-8.82095 + 5.66888i) q^{89} +(-0.756312 + 0.872830i) q^{90} +3.09657 q^{91} +(4.68955 + 1.00405i) q^{92} -3.62285 q^{93} +(-6.18525 + 7.13816i) q^{94} +(4.89628 - 3.14665i) q^{95} +(0.142315 + 0.989821i) q^{96} +(4.53488 + 9.92999i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(2.55871 - 0.751305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{14} - 7 q^{15} - 4 q^{16} + 5 q^{17} - 4 q^{18} + 44 q^{19} + 7 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 40 q^{24} + 2 q^{25} + 24 q^{26} + 4 q^{27} + 4 q^{28} + 35 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 11 q^{33} + 5 q^{34} - 7 q^{35} - 4 q^{36} + 20 q^{37} - 11 q^{38} + 20 q^{39} - 4 q^{40} + 11 q^{41} - 4 q^{42} - 42 q^{43} - 11 q^{44} - 4 q^{45} - 6 q^{46} + 40 q^{47} + 4 q^{48} - 4 q^{49} - 53 q^{50} + 17 q^{51} - 9 q^{52} - 32 q^{53} + 4 q^{54} + 29 q^{55} + 4 q^{56} - 11 q^{57} - 31 q^{58} - 25 q^{59} + 4 q^{60} - 30 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 80 q^{65} - 88 q^{67} - 28 q^{68} + 6 q^{69} + 4 q^{70} - 45 q^{71} - 4 q^{72} - 39 q^{73} + 20 q^{74} + 53 q^{75} - 22 q^{76} - 2 q^{78} + 26 q^{79} + 7 q^{80} - 4 q^{81} + 22 q^{83} - 4 q^{84} + 77 q^{85} - 31 q^{86} + 9 q^{87} - 11 q^{88} + 20 q^{89} + 7 q^{90} - 24 q^{91} - 17 q^{92} - 42 q^{93} - 26 q^{94} + 84 q^{95} + 4 q^{96} + 74 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 11 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^14 - 7 * q^15 - 4 * q^16 + 5 * q^17 - 4 * q^18 + 44 * q^19 + 7 * q^20 - 4 * q^21 + 22 * q^22 - 6 * q^23 - 40 * q^24 + 2 * q^25 + 24 * q^26 + 4 * q^27 + 4 * q^28 + 35 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 11 * q^33 + 5 * q^34 - 7 * q^35 - 4 * q^36 + 20 * q^37 - 11 * q^38 + 20 * q^39 - 4 * q^40 + 11 * q^41 - 4 * q^42 - 42 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 40 * q^47 + 4 * q^48 - 4 * q^49 - 53 * q^50 + 17 * q^51 - 9 * q^52 - 32 * q^53 + 4 * q^54 + 29 * q^55 + 4 * q^56 - 11 * q^57 - 31 * q^58 - 25 * q^59 + 4 * q^60 - 30 * q^61 - 24 * q^62 + 4 * q^63 - 4 * q^64 + 80 * q^65 - 88 * q^67 - 28 * q^68 + 6 * q^69 + 4 * q^70 - 45 * q^71 - 4 * q^72 - 39 * q^73 + 20 * q^74 + 53 * q^75 - 22 * q^76 - 2 * q^78 + 26 * q^79 + 7 * q^80 - 4 * q^81 + 22 * q^83 - 4 * q^84 + 77 * q^85 - 31 * q^86 + 9 * q^87 - 11 * q^88 + 20 * q^89 + 7 * q^90 - 24 * q^91 - 17 * q^92 - 42 * q^93 - 26 * q^94 + 84 * q^95 + 4 * q^96 + 74 * q^97 - 4 * q^98 + 11 * q^99

Introduction

L-functions

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