LMFDB - Embedded newform 1122.2.h.g.1121.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(1121,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("1122.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.h (of order $2$, degree $1$, 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:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.17
Character	$\chi$	$=$	1122.1121
Dual form			1122.2.h.g.1121.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.524078 - 1.65086i) q^{3} +1.00000 q^{4} -3.81008 q^{5} +(-0.524078 + 1.65086i) q^{6} -0.269313 q^{7} -1.00000 q^{8} +(-2.45068 - 1.73036i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.524078 - 1.65086i) q^{3} +1.00000 q^{4} -3.81008 q^{5} +(-0.524078 + 1.65086i) q^{6} -0.269313 q^{7} -1.00000 q^{8} +(-2.45068 - 1.73036i) q^{9} +3.81008 q^{10} +(-3.18733 - 0.917024i) q^{11} +(0.524078 - 1.65086i) q^{12} -5.86421i q^{13} +0.269313 q^{14} +(-1.99678 + 6.28991i) q^{15} +1.00000 q^{16} +(3.56790 - 2.06642i) q^{17} +(2.45068 + 1.73036i) q^{18} +0.208190i q^{19} -3.81008 q^{20} +(-0.141141 + 0.444598i) q^{21} +(3.18733 + 0.917024i) q^{22} -1.63790 q^{23} +(-0.524078 + 1.65086i) q^{24} +9.51672 q^{25} +5.86421i q^{26} +(-4.14094 + 3.13889i) q^{27} -0.269313 q^{28} +3.84487i q^{29} +(1.99678 - 6.28991i) q^{30} +5.05736i q^{31} -1.00000 q^{32} +(-3.18429 + 4.78124i) q^{33} +(-3.56790 + 2.06642i) q^{34} +1.02610 q^{35} +(-2.45068 - 1.73036i) q^{36} +3.41040i q^{37} -0.208190i q^{38} +(-9.68100 - 3.07331i) q^{39} +3.81008 q^{40} +5.05441i q^{41} +(0.141141 - 0.444598i) q^{42} +6.12589i q^{43} +(-3.18733 - 0.917024i) q^{44} +(9.33730 + 6.59282i) q^{45} +1.63790 q^{46} -2.90273i q^{47} +(0.524078 - 1.65086i) q^{48} -6.92747 q^{49} -9.51672 q^{50} +(-1.54151 - 6.97307i) q^{51} -5.86421i q^{52} +3.84226i q^{53} +(4.14094 - 3.13889i) q^{54} +(12.1440 + 3.49393i) q^{55} +0.269313 q^{56} +(0.343692 + 0.109108i) q^{57} -3.84487i q^{58} +9.06325i q^{59} +(-1.99678 + 6.28991i) q^{60} -1.75411 q^{61} -5.05736i q^{62} +(0.660000 + 0.466008i) q^{63} +1.00000 q^{64} +22.3431i q^{65} +(3.18429 - 4.78124i) q^{66} -11.2937 q^{67} +(3.56790 - 2.06642i) q^{68} +(-0.858388 + 2.70395i) q^{69} -1.02610 q^{70} -5.55374 q^{71} +(2.45068 + 1.73036i) q^{72} -0.116536 q^{73} -3.41040i q^{74} +(4.98751 - 15.7108i) q^{75} +0.208190i q^{76} +(0.858388 + 0.246966i) q^{77} +(9.68100 + 3.07331i) q^{78} +12.9766 q^{79} -3.81008 q^{80} +(3.01170 + 8.48114i) q^{81} -5.05441i q^{82} +17.3693 q^{83} +(-0.141141 + 0.444598i) q^{84} +(-13.5940 + 7.87322i) q^{85} -6.12589i q^{86} +(6.34735 + 2.01501i) q^{87} +(3.18733 + 0.917024i) q^{88} -11.6319i q^{89} +(-9.33730 - 6.59282i) q^{90} +1.57931i q^{91} -1.63790 q^{92} +(8.34900 + 2.65045i) q^{93} +2.90273i q^{94} -0.793220i q^{95} +(-0.524078 + 1.65086i) q^{96} -12.7636i q^{97} +6.92747 q^{98} +(6.22435 + 7.76257i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{2} + 28 q^{4} - 28 q^{8} + 2 q^{9}+O(q^{10}) $ 28 * q - 28 * q^2 + 28 * q^4 - 28 * q^8 + 2 * q^9	$ 28 q - 28 q^{2} + 28 q^{4} - 28 q^{8} + 2 q^{9} - 8 q^{15} + 28 q^{16} - 24 q^{17} - 2 q^{18} + 36 q^{21} + 80 q^{25} + 8 q^{30} - 28 q^{32} - 10 q^{33} + 24 q^{34} + 2 q^{36} - 36 q^{42} - 24 q^{49} - 80 q^{50} + 26 q^{51} - 4 q^{55} - 8 q^{60} + 28 q^{64} + 10 q^{66} - 40 q^{67} - 24 q^{68} - 4 q^{69} - 2 q^{72} + 4 q^{77} + 14 q^{81} + 12 q^{83} + 36 q^{84} + 48 q^{87} + 56 q^{93} + 24 q^{98}+O(q^{100}) $ 28 * q - 28 * q^2 + 28 * q^4 - 28 * q^8 + 2 * q^9 - 8 * q^15 + 28 * q^16 - 24 * q^17 - 2 * q^18 + 36 * q^21 + 80 * q^25 + 8 * q^30 - 28 * q^32 - 10 * q^33 + 24 * q^34 + 2 * q^36 - 36 * q^42 - 24 * q^49 - 80 * q^50 + 26 * q^51 - 4 * q^55 - 8 * q^60 + 28 * q^64 + 10 * q^66 - 40 * q^67 - 24 * q^68 - 4 * q^69 - 2 * q^72 + 4 * q^77 + 14 * q^81 + 12 * q^83 + 36 * q^84 + 48 * q^87 + 56 * q^93 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.524078	−	1.65086i	0.302577	−	0.953125i
$3$	0.524078	−	1.65086i	0.302577	−	0.953125i
$4$	1.00000			0.500000
$5$	−3.81008			−1.70392			−0.851960	−	0.523607i	$-0.824586\pi$
$5$	−3.81008			−1.70392			−0.851960	+	0.523607i	$0.824586\pi$
$6$	−0.524078	+	1.65086i	−0.213954	+	0.673961i
$7$	−0.269313			−0.101791			−0.0508953	−	0.998704i	$-0.516207\pi$
$7$	−0.269313			−0.101791			−0.0508953	+	0.998704i	$0.516207\pi$
$8$	−1.00000			−0.353553
$9$	−2.45068	−	1.73036i	−0.816895	−	0.576787i
$10$	3.81008			1.20485
$11$	−3.18733	−	0.917024i	−0.961016	−	0.276493i
$11$	−3.18733	−	0.917024i	−0.961016	−	0.276493i
$12$	0.524078	−	1.65086i	0.151288	−	0.476563i
$13$		−	5.86421i		−	1.62644i	−0.581957	−	0.813220i	$-0.697713\pi$
$13$		−	5.86421i		−	1.62644i	0.581957	−	0.813220i	$-0.302287\pi$
$14$	0.269313			0.0719769
$15$	−1.99678	+	6.28991i	−0.515567	+	1.62405i
$16$	1.00000			0.250000
$17$	3.56790	−	2.06642i	0.865343	−	0.501180i
$17$	3.56790	−	2.06642i	0.865343	−	0.501180i
$18$	2.45068	+	1.73036i	0.577632	+	0.407850i
$19$			0.208190i			0.0477620i	0.999715	+	0.0238810i	$0.00760228\pi$
$19$			0.208190i			0.0477620i	−0.999715	+	0.0238810i	$0.992398\pi$
$20$	−3.81008			−0.851960
$21$	−0.141141	+	0.444598i	−0.0307995	+	0.0970192i
$22$	3.18733	+	0.917024i	0.679541	+	0.195510i
$23$	−1.63790			−0.341526			−0.170763	−	0.985312i	$-0.554623\pi$
$23$	−1.63790			−0.341526			−0.170763	+	0.985312i	$0.554623\pi$
$24$	−0.524078	+	1.65086i	−0.106977	+	0.336981i
$25$	9.51672			1.90334
$26$			5.86421i			1.15007i
$27$	−4.14094	+	3.13889i	−0.796923	+	0.604080i
$28$	−0.269313			−0.0508953
$29$			3.84487i			0.713975i	0.934109	+	0.356987i	$0.116196\pi$
$29$			3.84487i			0.713975i	−0.934109	+	0.356987i	$0.883804\pi$
$30$	1.99678	−	6.28991i	0.364561	−	1.14838i
$31$			5.05736i			0.908329i	0.890918	+	0.454165i	$0.150062\pi$
$31$			5.05736i			0.908329i	−0.890918	+	0.454165i	$0.849938\pi$
$32$	−1.00000			−0.176777
$33$	−3.18429	+	4.78124i	−0.554314	+	0.832308i
$34$	−3.56790	+	2.06642i	−0.611890	+	0.354388i
$35$	1.02610			0.173443
$36$	−2.45068	−	1.73036i	−0.408447	−	0.288394i
$37$			3.41040i			0.560667i	0.959903	+	0.280333i	$0.0904450\pi$
$37$			3.41040i			0.560667i	−0.959903	+	0.280333i	$0.909555\pi$
$38$		−	0.208190i		−	0.0337728i
$39$	−9.68100	−	3.07331i	−1.55020	−	0.492123i
$40$	3.81008			0.602427
$41$			5.05441i			0.789366i	0.918817	+	0.394683i	$0.129146\pi$
$41$			5.05441i			0.789366i	−0.918817	+	0.394683i	$0.870854\pi$
$42$	0.141141	−	0.444598i	0.0217785	−	0.0686029i
$43$			6.12589i			0.934190i	0.884207	+	0.467095i	$0.154699\pi$
$43$			6.12589i			0.934190i	−0.884207	+	0.467095i	$0.845301\pi$
$44$	−3.18733	−	0.917024i	−0.480508	−	0.138247i
$45$	9.33730	+	6.59282i	1.39192	+	0.982799i
$46$	1.63790			0.241495
$47$		−	2.90273i		−	0.423406i	−0.977334	−	0.211703i	$-0.932099\pi$
$47$		−	2.90273i		−	0.423406i	0.977334	−	0.211703i	$-0.0679010\pi$
$48$	0.524078	−	1.65086i	0.0756442	−	0.238281i
$49$	−6.92747			−0.989639
$50$	−9.51672			−1.34587
$51$	−1.54151	−	6.97307i	−0.215854	−	0.976426i
$52$		−	5.86421i		−	0.813220i
$53$			3.84226i			0.527775i	0.964554	+	0.263887i	$0.0850047\pi$
$53$			3.84226i			0.527775i	−0.964554	+	0.263887i	$0.914995\pi$
$54$	4.14094	−	3.13889i	0.563510	−	0.427149i
$55$	12.1440	+	3.49393i	1.63749	+	0.471122i
$56$	0.269313			0.0359884
$57$	0.343692	+	0.109108i	0.0455232	+	0.0144517i
$58$		−	3.84487i		−	0.504856i
$59$			9.06325i			1.17993i	0.807427	+	0.589967i	$0.200859\pi$
$59$			9.06325i			1.17993i	−0.807427	+	0.589967i	$0.799141\pi$
$60$	−1.99678	+	6.28991i	−0.257783	+	0.812024i
$61$	−1.75411			−0.224591			−0.112295	−	0.993675i	$-0.535820\pi$
$61$	−1.75411			−0.224591			−0.112295	+	0.993675i	$0.535820\pi$
$62$		−	5.05736i		−	0.642286i
$63$	0.660000	+	0.466008i	0.0831522	+	0.0587115i
$64$	1.00000			0.125000
$65$			22.3431i			2.77132i
$66$	3.18429	−	4.78124i	0.391959	−	0.588531i
$67$	−11.2937			−1.37974			−0.689872	−	0.723932i	$-0.742333\pi$
$67$	−11.2937			−1.37974			−0.689872	+	0.723932i	$0.742333\pi$
$68$	3.56790	−	2.06642i	0.432672	−	0.250590i
$69$	−0.858388	+	2.70395i	−0.103338	+	0.325517i
$70$	−1.02610			−0.122643
$71$	−5.55374			−0.659108			−0.329554	−	0.944137i	$-0.606898\pi$
$71$	−5.55374			−0.659108			−0.329554	+	0.944137i	$0.606898\pi$
$72$	2.45068	+	1.73036i	0.288816	+	0.203925i
$73$	−0.116536			−0.0136395			−0.00681973	−	0.999977i	$-0.502171\pi$
$73$	−0.116536			−0.0136395			−0.00681973	+	0.999977i	$0.502171\pi$
$74$		−	3.41040i		−	0.396451i
$75$	4.98751	−	15.7108i	0.575908	−	1.81412i
$76$			0.208190i			0.0238810i
$77$	0.858388	+	0.246966i	0.0978224	+	0.0281444i
$78$	9.68100	+	3.07331i	1.09616	+	0.347983i
$79$	12.9766			1.45998			0.729988	−	0.683460i	$-0.239526\pi$
$79$	12.9766			1.45998			0.729988	+	0.683460i	$0.239526\pi$
$80$	−3.81008			−0.425980
$81$	3.01170	+	8.48114i	0.334633	+	0.942348i
$82$		−	5.05441i		−	0.558166i
$83$	17.3693			1.90653			0.953264	−	0.302139i	$-0.0977007\pi$
$83$	17.3693			1.90653			0.953264	+	0.302139i	$0.0977007\pi$
$84$	−0.141141	+	0.444598i	−0.0153997	+	0.0485096i
$85$	−13.5940	+	7.87322i	−1.47448	+	0.853971i
$86$		−	6.12589i		−	0.660572i
$87$	6.34735	+	2.01501i	0.680507	+	0.216032i
$88$	3.18733	+	0.917024i	0.339770	+	0.0977551i
$89$		−	11.6319i		−	1.23298i	−0.787362	−	0.616491i	$-0.788554\pi$
$89$		−	11.6319i		−	1.23298i	0.787362	−	0.616491i	$-0.211446\pi$
$90$	−9.33730	−	6.59282i	−0.984238	−	0.694944i
$91$			1.57931i			0.165556i
$92$	−1.63790			−0.170763
$93$	8.34900	+	2.65045i	0.865751	+	0.274839i
$94$			2.90273i			0.299393i
$95$		−	0.793220i		−	0.0813826i
$96$	−0.524078	+	1.65086i	−0.0534885	+	0.168490i
$97$		−	12.7636i		−	1.29595i	−0.761663	−	0.647974i	$-0.775617\pi$
$97$		−	12.7636i		−	1.29595i	0.761663	−	0.647974i	$-0.224383\pi$
$98$	6.92747			0.699780
$99$	6.22435	+	7.76257i	0.625571	+	0.780167i
$100$	9.51672			0.951672
$101$	−3.49705			−0.347970			−0.173985	−	0.984748i	$-0.555664\pi$
$101$	−3.49705			−0.347970			−0.173985	+	0.984748i	$0.555664\pi$
$102$	1.54151	+	6.97307i	0.152632	+	0.690437i
$103$	0.0298399			0.00294022			0.00147011	−	0.999999i	$-0.499532\pi$
$103$	0.0298399			0.00294022			0.00147011	+	0.999999i	$0.499532\pi$
$104$			5.86421i			0.575033i
$105$	0.537759	−	1.69395i	0.0524799	−	0.165313i
$106$		−	3.84226i		−	0.373193i
$107$		−	14.6035i		−	1.41177i	−0.708325	−	0.705886i	$-0.750549\pi$
$107$		−	14.6035i		−	1.41177i	0.708325	−	0.705886i	$-0.249451\pi$
$108$	−4.14094	+	3.13889i	−0.398462	+	0.302040i
$109$	−7.02399			−0.672776			−0.336388	−	0.941724i	$-0.609205\pi$
$109$	−7.02399			−0.672776			−0.336388	+	0.941724i	$0.609205\pi$
$110$	−12.1440	−	3.49393i	−1.15788	−	0.333134i
$111$	5.63010	+	1.78732i	0.534385	+	0.169645i
$112$	−0.269313			−0.0254477
$113$	3.62351			0.340871			0.170436	−	0.985369i	$-0.445482\pi$
$113$	3.62351			0.340871			0.170436	+	0.985369i	$0.445482\pi$
$114$	−0.343692	−	0.109108i	−0.0321897	−	0.0102189i
$115$	6.24053			0.581933
$116$			3.84487i			0.356987i
$117$	−10.1472	+	14.3713i	−0.938109	+	1.32863i
$118$		−	9.06325i		−	0.834340i
$119$	−0.960881	+	0.556513i	−0.0880838	+	0.0510154i
$120$	1.99678	−	6.28991i	0.182280	−	0.574188i
$121$	9.31813	+	5.84571i	0.847103	+	0.531428i
$122$	1.75411			0.158809
$123$	8.34413	+	2.64891i	0.752365	+	0.238844i
$124$			5.05736i			0.454165i
$125$	−17.2091			−1.53922
$126$	−0.660000	−	0.466008i	−0.0587975	−	0.0415153i
$127$			12.9055i			1.14518i	0.819842	+	0.572589i	$0.194061\pi$
$127$			12.9055i			1.14518i	−0.819842	+	0.572589i	$0.805939\pi$
$128$	−1.00000			−0.0883883
$129$	10.1130	+	3.21045i	0.890400	+	0.282664i
$130$		−	22.3431i		−	1.95962i
$131$		−	18.3231i		−	1.60090i	−0.599401	−	0.800449i	$-0.704594\pi$
$131$		−	18.3231i		−	1.60090i	0.599401	−	0.800449i	$-0.295406\pi$
$132$	−3.18429	+	4.78124i	−0.277157	+	0.416154i
$133$		−	0.0560682i		−	0.00486173i
$134$	11.2937			0.975626
$135$	15.7773	−	11.9594i	1.35789	−	1.02930i
$136$	−3.56790	+	2.06642i	−0.305945	+	0.177194i
$137$			18.3288i			1.56593i	0.622065	+	0.782965i	$0.286294\pi$
$137$			18.3288i			1.56593i	−0.622065	+	0.782965i	$0.713706\pi$
$138$	0.858388	−	2.70395i	0.0730709	−	0.230175i
$139$	−14.6357			−1.24138			−0.620691	−	0.784055i	$-0.713148\pi$
$139$	−14.6357			−1.24138			−0.620691	+	0.784055i	$0.713148\pi$
$140$	1.02610			0.0867216
$141$	−4.79200	−	1.52126i	−0.403559	−	0.128113i
$142$	5.55374			0.466059
$143$	−5.37762	+	18.6912i	−0.449699	+	1.56303i
$144$	−2.45068	−	1.73036i	−0.204224	−	0.144197i
$145$		−	14.6493i		−	1.21656i
$146$	0.116536			0.00964455
$147$	−3.63054	+	11.4363i	−0.299442	+	0.943249i
$148$			3.41040i			0.280333i
$149$	−18.4154			−1.50865			−0.754323	−	0.656503i	$-0.772035\pi$
$149$	−18.4154			−1.50865			−0.754323	+	0.656503i	$0.772035\pi$
$150$	−4.98751	+	15.7108i	−0.407228	+	1.28278i
$151$			18.1694i			1.47861i	0.673373	+	0.739303i	$0.264845\pi$
$151$			18.1694i			1.47861i	−0.673373	+	0.739303i	$0.735155\pi$
$152$		−	0.208190i		−	0.0168864i
$153$	−12.3194	−	1.10962i	−0.995968	−	0.0897074i
$154$	−0.858388	−	0.246966i	−0.0691709	−	0.0199011i
$155$		−	19.2690i		−	1.54772i
$156$	−9.68100	−	3.07331i	−0.775100	−	0.246061i
$157$	−10.0860			−0.804947			−0.402474	−	0.915432i	$-0.631849\pi$
$157$	−10.0860			−0.804947			−0.402474	+	0.915432i	$0.631849\pi$
$158$	−12.9766			−1.03236
$159$	6.34303	+	2.01364i	0.503035	+	0.159692i
$160$	3.81008			0.301213
$161$	0.441108			0.0347641
$162$	−3.01170	−	8.48114i	−0.236622	−	0.666341i
$163$		−	11.3349i		−	0.887815i	−0.896073	−	0.443907i	$-0.853592\pi$
$163$		−	11.3349i		−	0.887815i	0.896073	−	0.443907i	$-0.146408\pi$
$164$			5.05441i			0.394683i
$165$	12.1324	−	18.2169i	0.944506	−	1.41819i
$166$	−17.3693			−1.34812
$167$			16.5010i			1.27689i	0.769668	+	0.638444i	$0.220422\pi$
$167$			16.5010i			1.27689i	−0.769668	+	0.638444i	$0.779578\pi$
$168$	0.141141	−	0.444598i	0.0108893	−	0.0343015i
$169$	−21.3890			−1.64530
$170$	13.5940	−	7.87322i	1.04261	−	0.603848i
$171$	0.360243	−	0.510207i	0.0275485	−	0.0390165i
$172$			6.12589i			0.467095i
$173$		−	17.6882i		−	1.34481i	−0.740183	−	0.672406i	$-0.765261\pi$
$173$		−	17.6882i		−	1.34481i	0.740183	−	0.672406i	$-0.234739\pi$
$174$	−6.34735	−	2.01501i	−0.481191	−	0.152758i
$175$	−2.56297			−0.193743
$176$	−3.18733	−	0.917024i	−0.240254	−	0.0691233i
$177$	14.9622	+	4.74985i	1.12463	+	0.357021i
$178$			11.6319i			0.871850i
$179$		−	13.1756i		−	0.984787i	−0.870373	−	0.492394i	$-0.836122\pi$
$179$		−	13.1756i		−	0.984787i	0.870373	−	0.492394i	$-0.163878\pi$
$180$	9.33730	+	6.59282i	0.695961	+	0.491399i
$181$			12.9449i			0.962188i	0.876669	+	0.481094i	$0.159761\pi$
$181$			12.9449i			0.962188i	−0.876669	+	0.481094i	$0.840239\pi$
$182$		−	1.57931i		−	0.117066i
$183$	−0.919290	+	2.89579i	−0.0679559	+	0.214063i
$184$	1.63790			0.120748
$185$		−	12.9939i		−	0.955331i
$186$	−8.34900	−	2.65045i	−0.612178	−	0.194341i
$187$	−13.2670	+	3.31451i	−0.970181	+	0.242381i
$188$		−	2.90273i		−	0.211703i
$189$	1.11521	−	0.845344i	0.0811194	−	0.0614897i
$190$			0.793220i			0.0575462i
$191$		−	3.19904i		−	0.231474i	−0.993280	−	0.115737i	$-0.963077\pi$
$191$		−	3.19904i		−	0.231474i	0.993280	−	0.115737i	$-0.0369230\pi$
$192$	0.524078	−	1.65086i	0.0378221	−	0.119141i
$193$	19.3152			1.39034			0.695170	−	0.718845i	$-0.255329\pi$
$193$	19.3152			1.39034			0.695170	+	0.718845i	$0.255329\pi$
$194$			12.7636i			0.916374i
$195$	36.8854	+	11.7095i	2.64142	+	0.838538i
$196$	−6.92747			−0.494819
$197$			19.6491i			1.39994i	0.714172	+	0.699971i	$0.246804\pi$
$197$			19.6491i			1.39994i	−0.714172	+	0.699971i	$0.753196\pi$
$198$	−6.22435	−	7.76257i	−0.442346	−	0.551662i
$199$			24.6476i			1.74722i	0.486624	+	0.873611i	$0.338228\pi$
$199$			24.6476i			1.74722i	−0.486624	+	0.873611i	$0.661772\pi$
$200$	−9.51672			−0.672933
$201$	−5.91878	+	18.6443i	−0.417478	+	1.31507i
$202$	3.49705			0.246052
$203$		−	1.03547i		−	0.0726759i
$204$	−1.54151	−	6.97307i	−0.107927	−	0.488213i
$205$		−	19.2577i		−	1.34502i
$206$	−0.0298399			−0.00207905
$207$	4.01398	+	2.83416i	0.278991	+	0.196988i
$208$		−	5.86421i		−	0.406610i
$209$	0.190915	−	0.663569i	0.0132059	−	0.0459001i
$210$	−0.537759	+	1.69395i	−0.0371089	+	0.116894i
$211$	9.47591			0.652348			0.326174	−	0.945310i	$-0.394240\pi$
$211$	9.47591			0.652348			0.326174	+	0.945310i	$0.394240\pi$
$212$			3.84226i			0.263887i
$213$	−2.91059	+	9.16845i	−0.199431	+	0.628212i
$214$			14.6035i			0.998274i
$215$		−	23.3401i		−	1.59178i
$216$	4.14094	−	3.13889i	0.281755	−	0.213575i
$217$		−	1.36201i		−	0.0924594i
$218$	7.02399			0.475724
$219$	−0.0610738	+	0.192384i	−0.00412698	+	0.0130001i
$220$	12.1440	+	3.49393i	0.818747	+	0.235561i
$221$	−12.1179	−	20.9229i	−0.815139	−	1.40743i
$222$	−5.63010	−	1.78732i	−0.377868	−	0.119957i
$223$	−4.37502			−0.292973			−0.146486	−	0.989213i	$-0.546796\pi$
$223$	−4.37502			−0.292973			−0.146486	+	0.989213i	$0.546796\pi$
$224$	0.269313			0.0179942
$225$	−23.3225	−	16.4674i	−1.55483	−	1.09782i
$226$	−3.62351			−0.241032
$227$		−	2.57358i		−	0.170815i	−0.996346	−	0.0854073i	$-0.972781\pi$
$227$		−	2.57358i		−	0.170815i	0.996346	−	0.0854073i	$-0.0272192\pi$
$228$	0.343692	+	0.109108i	0.0227616	+	0.00722584i
$229$	−15.5344			−1.02655			−0.513273	−	0.858226i	$-0.671567\pi$
$229$	−15.5344			−1.02655			−0.513273	+	0.858226i	$0.671567\pi$
$230$	−6.24053			−0.411489
$231$	0.857570	−	1.28765i	0.0564239	−	0.0847212i
$232$		−	3.84487i		−	0.252428i
$233$		−	17.0363i		−	1.11608i	−0.829813	−	0.558042i	$-0.811553\pi$
$233$		−	17.0363i		−	1.11608i	0.829813	−	0.558042i	$-0.188447\pi$
$234$	10.1472	−	14.3713i	0.663343	−	0.939483i
$235$			11.0596i			0.721450i
$236$			9.06325i			0.589967i
$237$	6.80073	−	21.4225i	0.441755	−	1.39154i
$238$	0.960881	−	0.556513i	0.0622847	−	0.0360734i
$239$	−20.4682			−1.32398			−0.661989	−	0.749514i	$-0.730287\pi$
$239$	−20.4682			−1.32398			−0.661989	+	0.749514i	$0.730287\pi$
$240$	−1.99678	+	6.28991i	−0.128892	+	0.406012i
$241$	5.03541			0.324360			0.162180	−	0.986761i	$-0.448148\pi$
$241$	5.03541			0.324360			0.162180	+	0.986761i	$0.448148\pi$
$242$	−9.31813	−	5.84571i	−0.598992	−	0.375777i
$243$	15.5795	−	0.527120i	0.999428	−	0.0338148i
$244$	−1.75411			−0.112295
$245$	26.3942			1.68627
$246$	−8.34413	−	2.64891i	−0.532002	−	0.168888i
$247$	1.22087			0.0776820
$248$		−	5.05736i		−	0.321143i
$249$	9.10287	−	28.6743i	0.576871	−	1.81716i
$250$	17.2091			1.08840
$251$			0.148694i			0.00938550i	0.999989	+	0.00469275i	$0.00149375\pi$
$251$			0.148694i			0.00938550i	−0.999989	+	0.00469275i	$0.998506\pi$
$252$	0.660000	+	0.466008i	0.0415761	+	0.0293558i
$253$	5.22053	+	1.50199i	0.328212	+	0.0944295i
$254$		−	12.9055i		−	0.809764i
$255$	5.87328	+	26.5680i	0.367799	+	1.66375i
$256$	1.00000			0.0625000
$257$		−	10.4139i		−	0.649601i	−0.945783	−	0.324801i	$-0.894703\pi$
$257$		−	10.4139i		−	0.649601i	0.945783	−	0.324801i	$-0.105297\pi$
$258$	−10.1130	−	3.21045i	−0.629608	−	0.199874i
$259$		−	0.918465i		−	0.0570706i
$260$			22.3431i			1.38566i
$261$	6.65301	−	9.42256i	0.411811	−	0.583242i
$262$			18.3231i			1.13201i
$263$	−7.90242			−0.487284			−0.243642	−	0.969865i	$-0.578342\pi$
$263$	−7.90242			−0.487284			−0.243642	+	0.969865i	$0.578342\pi$
$264$	3.18429	−	4.78124i	0.195979	−	0.294265i
$265$		−	14.6393i		−	0.899286i
$266$			0.0560682i			0.00343776i
$267$	−19.2027	−	6.09604i	−1.17519	−	0.373072i
$268$	−11.2937			−0.689872
$269$	17.6109			1.07375			0.536876	−	0.843661i	$-0.319604\pi$
$269$	17.6109			1.07375			0.536876	+	0.843661i	$0.319604\pi$
$270$	−15.7773	+	11.9594i	−0.960176	+	0.727828i
$271$		−	13.4427i		−	0.816589i	−0.912850	−	0.408294i	$-0.866124\pi$
$271$		−	13.4427i		−	0.816589i	0.912850	−	0.408294i	$-0.133876\pi$
$272$	3.56790	−	2.06642i	0.216336	−	0.125295i
$273$	2.60722	+	0.827680i	0.157796	+	0.0500935i
$274$		−	18.3288i		−	1.10728i
$275$	−30.3329	−	8.72705i	−1.82914	−	0.526261i
$276$	−0.858388	+	2.70395i	−0.0516689	+	0.162758i
$277$	−25.8070			−1.55059			−0.775296	−	0.631597i	$-0.782400\pi$
$277$	−25.8070			−1.55059			−0.775296	+	0.631597i	$0.782400\pi$
$278$	14.6357			0.877790
$279$	8.75106	−	12.3940i	0.523912	−	0.742009i
$280$	−1.02610			−0.0613214
$281$	21.1784			1.26340			0.631700	−	0.775213i	$-0.282357\pi$
$281$	21.1784			1.26340			0.631700	+	0.775213i	$0.282357\pi$
$282$	4.79200	+	1.52126i	0.285359	+	0.0905895i
$283$	−22.6034			−1.34363			−0.671817	−	0.740717i	$-0.734486\pi$
$283$	−22.6034			−1.34363			−0.671817	+	0.740717i	$0.734486\pi$
$284$	−5.55374			−0.329554
$285$	−1.30950	−	0.415709i	−0.0775678	−	0.0246245i
$286$	5.37762	−	18.6912i	0.317985	−	1.10523i
$287$		−	1.36122i		−	0.0803501i
$288$	2.45068	+	1.73036i	0.144408	+	0.101963i
$289$	8.45983	−	14.7456i	0.497637	−	0.867385i
$290$			14.6493i			0.860235i
$291$	−21.0709	−	6.68913i	−1.23520	−	0.392124i
$292$	−0.116536			−0.00681973
$293$	−10.2935			−0.601352			−0.300676	−	0.953726i	$-0.597212\pi$
$293$	−10.2935			−0.601352			−0.300676	+	0.953726i	$0.597212\pi$
$294$	3.63054	−	11.4363i	0.211737	−	0.666978i
$295$		−	34.5317i		−	2.01051i
$296$		−	3.41040i		−	0.198226i
$297$	16.0770	−	6.20735i	0.932880	−	0.360187i
$298$	18.4154			1.06677
$299$			9.60499i			0.555471i
$300$	4.98751	−	15.7108i	0.287954	−	0.907062i
$301$		−	1.64978i		−	0.0950918i
$302$		−	18.1694i		−	1.04553i
$303$	−1.83273	+	5.77314i	−0.105288	+	0.331658i
$304$			0.208190i			0.0119405i
$305$	6.68329			0.382684
$306$	12.3194	+	1.10962i	0.704256	+	0.0634327i
$307$			17.4371i			0.995190i	0.867409	+	0.497595i	$0.165783\pi$
$307$			17.4371i			0.995190i	−0.867409	+	0.497595i	$0.834217\pi$
$308$	0.858388	+	0.246966i	0.0489112	+	0.0140722i
$309$	0.0156385	−	0.0492616i	0.000889641	−	0.00280239i
$310$			19.2690i			1.09440i
$311$	3.25884			0.184792			0.0923959	−	0.995722i	$-0.470547\pi$
$311$	3.25884			0.184792			0.0923959	+	0.995722i	$0.470547\pi$
$312$	9.68100	+	3.07331i	0.548078	+	0.173992i
$313$			12.0002i			0.678292i	0.940734	+	0.339146i	$0.110138\pi$
$313$			12.0002i			0.678292i	−0.940734	+	0.339146i	$0.889862\pi$
$314$	10.0860			0.569184
$315$	−2.51465	−	1.77553i	−0.141685	−	0.100040i
$316$	12.9766			0.729988
$317$	−19.1540			−1.07580			−0.537898	−	0.843010i	$-0.680781\pi$
$317$	−19.1540			−1.07580			−0.537898	+	0.843010i	$0.680781\pi$
$318$	−6.34303	−	2.01364i	−0.355700	−	0.112920i
$319$	3.52584	−	12.2549i	0.197409	−	0.686141i
$320$	−3.81008			−0.212990
$321$	−24.1083	−	7.65337i	−1.34560	−	0.427170i
$322$	−0.441108			−0.0245820
$323$	0.430207	+	0.742800i	0.0239374	+	0.0413305i
$324$	3.01170	+	8.48114i	0.167317	+	0.471174i
$325$		−	55.8080i		−	3.09567i
$326$			11.3349i			0.627780i
$327$	−3.68112	+	11.5956i	−0.203566	+	0.641240i
$328$		−	5.05441i		−	0.279083i
$329$			0.781741i			0.0430988i
$330$	−12.1324	+	18.2169i	−0.667867	+	1.00281i
$331$	−3.54602			−0.194907			−0.0974534	−	0.995240i	$-0.531070\pi$
$331$	−3.54602			−0.194907			−0.0974534	+	0.995240i	$0.531070\pi$
$332$	17.3693			0.953264
$333$	5.90123	−	8.35782i	0.323385	−	0.458006i
$334$		−	16.5010i		−	0.902896i
$335$	43.0299			2.35097
$336$	−0.141141	+	0.444598i	−0.00769987	+	0.0242548i
$337$	−12.9518			−0.705530			−0.352765	−	0.935712i	$-0.614758\pi$
$337$	−12.9518			−0.705530			−0.352765	+	0.935712i	$0.614758\pi$
$338$	21.3890			1.16341
$339$	1.89900	−	5.98191i	0.103140	−	0.324893i
$340$	−13.5940	+	7.87322i	−0.737238	+	0.426985i
$341$	4.63772	−	16.1195i	0.251147	−	0.872919i
$342$	−0.360243	+	0.510207i	−0.0194797	+	0.0275888i
$343$	3.75085			0.202527
$344$		−	6.12589i		−	0.330286i
$345$	3.27053	−	10.3023i	0.176079	−	0.554655i
$346$			17.6882i			0.950925i
$347$			14.1605i			0.760177i	0.924950	+	0.380088i	$0.124106\pi$
$347$			14.1605i			0.760177i	−0.924950	+	0.380088i	$0.875894\pi$
$348$	6.34735	+	2.01501i	0.340254	+	0.108016i
$349$		−	20.9198i		−	1.11981i	−0.828556	−	0.559907i	$-0.810837\pi$
$349$		−	20.9198i		−	1.11981i	0.828556	−	0.559907i	$-0.189163\pi$
$350$	2.56297			0.136997
$351$	18.4071	+	24.2833i	0.982500	+	1.29615i
$352$	3.18733	+	0.917024i	0.169885	+	0.0488775i
$353$			32.5359i			1.73171i	0.500296	+	0.865854i	$0.333225\pi$
$353$			32.5359i			1.73171i	−0.500296	+	0.865854i	$0.666775\pi$
$354$	−14.9622	−	4.74985i	−0.795230	−	0.252452i
$355$	21.1602			1.12307
$356$		−	11.6319i		−	0.616491i
$357$	0.415148	+	1.87794i	0.0219720	+	0.0993910i
$358$			13.1756i			0.696350i
$359$	−21.9753			−1.15981			−0.579907	−	0.814683i	$-0.696911\pi$
$359$	−21.9753			−1.15981			−0.579907	+	0.814683i	$0.696911\pi$
$360$	−9.33730	−	6.59282i	−0.492119	−	0.347472i
$361$	18.9567			0.997719
$362$		−	12.9449i		−	0.680370i
$363$	14.5339	−	12.3193i	0.762832	−	0.646597i
$364$			1.57931i			0.0827781i
$365$	0.444010			0.0232405
$366$	0.919290	−	2.89579i	0.0480521	−	0.151365i
$367$		−	15.0883i		−	0.787604i	−0.919195	−	0.393802i	$-0.871160\pi$
$367$		−	15.0883i		−	0.787604i	0.919195	−	0.393802i	$-0.128840\pi$
$368$	−1.63790			−0.0853815
$369$	8.74595	−	12.3868i	0.455296	−	0.644829i
$370$			12.9939i			0.675521i
$371$		−	1.03477i		−	0.0537225i
$372$	8.34900	+	2.65045i	0.432876	+	0.137420i
$373$		−	5.93570i		−	0.307339i	−0.988122	−	0.153670i	$-0.950891\pi$
$373$		−	5.93570i		−	0.307339i	0.988122	−	0.153670i	$-0.0491091\pi$
$374$	13.2670	−	3.31451i	0.686022	−	0.171389i
$375$	−9.01889	+	28.4098i	−0.465734	+	1.46707i
$376$			2.90273i			0.149697i
$377$	22.5471			1.16124
$378$	−1.11521	+	0.845344i	−0.0573600	+	0.0434798i
$379$			22.7715i			1.16969i	0.811143	+	0.584847i	$0.198846\pi$
$379$			22.7715i			1.16969i	−0.811143	+	0.584847i	$0.801154\pi$
$380$		−	0.793220i		−	0.0406913i
$381$	21.3052	+	6.76350i	1.09150	+	0.346504i
$382$			3.19904i			0.163677i
$383$			17.8676i			0.912991i	0.889726	+	0.456496i	$0.150896\pi$
$383$			17.8676i			0.912991i	−0.889726	+	0.456496i	$0.849104\pi$
$384$	−0.524078	+	1.65086i	−0.0267443	+	0.0842451i
$385$	−3.27053	−	0.940961i	−0.166682	−	0.0479558i
$386$	−19.3152			−0.983119
$387$	10.6000	−	15.0126i	0.538829	−	0.763135i
$388$		−	12.7636i		−	0.647974i
$389$		−	19.2714i		−	0.977101i	−0.872536	−	0.488550i	$-0.837526\pi$
$389$		−	19.2714i		−	0.977101i	0.872536	−	0.488550i	$-0.162474\pi$
$390$	−36.8854	−	11.7095i	−1.86776	−	0.592936i
$391$	−5.84387	+	3.38459i	−0.295537	+	0.171166i
$392$	6.92747			0.349890
$393$	−30.2489	−	9.60275i	−1.52586	−	0.484395i
$394$		−	19.6491i		−	0.989908i
$395$	−49.4417			−2.48768
$396$	6.22435	+	7.76257i	0.312786	+	0.390084i
$397$			25.6830i			1.28899i	0.764606	+	0.644497i	$0.222933\pi$
$397$			25.6830i			1.28899i	−0.764606	+	0.644497i	$0.777067\pi$
$398$		−	24.6476i		−	1.23547i
$399$	−0.0925607	−	0.0293841i	−0.00463383	−	0.00147105i
$400$	9.51672			0.475836
$401$	−18.8429			−0.940971			−0.470486	−	0.882408i	$-0.655921\pi$
$401$	−18.8429			−0.940971			−0.470486	+	0.882408i	$0.655921\pi$
$402$	5.91878	−	18.6443i	0.295202	−	0.929893i
$403$	29.6574			1.47734
$404$	−3.49705			−0.173985
$405$	−11.4748	−	32.3138i	−0.570189	−	1.60569i
$406$			1.03547i			0.0513896i
$407$	3.12742	−	10.8701i	0.155020	−	0.538810i
$408$	1.54151	+	6.97307i	0.0763161	+	0.345219i
$409$		−	26.5587i		−	1.31324i	−0.754221	−	0.656621i	$-0.771985\pi$
$409$		−	26.5587i		−	1.31324i	0.754221	−	0.656621i	$-0.228015\pi$
$410$			19.2577i			0.951071i
$411$	30.2582	+	9.60570i	1.49253	+	0.473814i
$412$	0.0298399			0.00147011
$413$		−	2.44085i		−	0.120106i
$414$	−4.01398	−	2.83416i	−0.197276	−	0.139291i
$415$	−66.1784			−3.24857
$416$			5.86421i			0.287517i
$417$	−7.67024	+	24.1615i	−0.375614	+	1.18319i
$418$	−0.190915	+	0.663569i	−0.00933796	+	0.0324562i
$419$	−12.8821			−0.629333			−0.314666	−	0.949202i	$-0.601893\pi$
$419$	−12.8821			−0.629333			−0.314666	+	0.949202i	$0.601893\pi$
$420$	0.537759	−	1.69395i	0.0262399	−	0.0826565i
$421$	−27.6448			−1.34733			−0.673663	−	0.739039i	$-0.735280\pi$
$421$	−27.6448			−1.34733			−0.673663	+	0.739039i	$0.735280\pi$
$422$	−9.47591			−0.461280
$423$	−5.02277	+	7.11367i	−0.244215	+	0.345878i
$424$		−	3.84226i		−	0.186597i
$425$	33.9547	−	19.6655i	1.64704	−	0.953918i
$426$	2.91059	−	9.16845i	0.141019	−	0.444213i
$427$	0.472404			0.0228612
$428$		−	14.6035i		−	0.705886i
$429$	28.0382	+	18.6733i	1.35370	+	0.901557i
$430$			23.3401i			1.12556i
$431$			19.3110i			0.930179i	0.885264	+	0.465089i	$0.153978\pi$
$431$			19.3110i			0.930179i	−0.885264	+	0.465089i	$0.846022\pi$
$432$	−4.14094	+	3.13889i	−0.199231	+	0.151020i
$433$	8.00193			0.384548			0.192274	−	0.981341i	$-0.438414\pi$
$433$	8.00193			0.384548			0.192274	+	0.981341i	$0.438414\pi$
$434$			1.36201i			0.0653787i
$435$	−24.1839	−	7.67737i	−1.15953	−	0.368101i
$436$	−7.02399			−0.336388
$437$		−	0.340994i		−	0.0163120i
$438$	0.0610738	−	0.192384i	0.00291822	−	0.00919247i
$439$	22.5863			1.07799			0.538994	−	0.842310i	$-0.318805\pi$
$439$	22.5863			1.07799			0.538994	+	0.842310i	$0.318805\pi$
$440$	−12.1440	−	3.49393i	−0.578942	−	0.166567i
$441$	16.9770	+	11.9870i	0.808430	+	0.570811i
$442$	12.1179	+	20.9229i	0.576390	+	0.995202i
$443$			23.8935i			1.13521i	0.823300	+	0.567607i	$0.192131\pi$
$443$			23.8935i			1.13521i	−0.823300	+	0.567607i	$0.807869\pi$
$444$	5.63010	+	1.78732i	0.267193	+	0.0848224i
$445$			44.3186i			2.10090i
$446$	4.37502			0.207163
$447$	−9.65110	+	30.4012i	−0.456482	+	1.43793i
$448$	−0.269313			−0.0127238
$449$	−26.3217			−1.24220			−0.621099	−	0.783732i	$-0.713314\pi$
$449$	−26.3217			−1.24220			−0.621099	+	0.783732i	$0.713314\pi$
$450$	23.3225	+	16.4674i	1.09943	+	0.776279i
$451$	4.63501	−	16.1101i	0.218254	−	0.758594i
$452$	3.62351			0.170436
$453$	29.9952	+	9.52220i	1.40930	+	0.447392i
$454$			2.57358i			0.120784i
$455$		−	6.01729i		−	0.282095i
$456$	−0.343692	−	0.109108i	−0.0160949	−	0.00510944i
$457$			4.89134i			0.228807i	0.993434	+	0.114404i	$0.0364957\pi$
$457$			4.89134i			0.228807i	−0.993434	+	0.114404i	$0.963504\pi$
$458$	15.5344			0.725877
$459$	−8.28818	+	19.7562i	−0.386859	+	0.922139i
$460$	6.24053			0.290966
$461$	−12.4471			−0.579718			−0.289859	−	0.957069i	$-0.593608\pi$
$461$	−12.4471			−0.579718			−0.289859	+	0.957069i	$0.593608\pi$
$462$	−0.857570	+	1.28765i	−0.0398977	+	0.0599069i
$463$	−13.4617			−0.625618			−0.312809	−	0.949816i	$-0.601270\pi$
$463$	−13.4617			−0.625618			−0.312809	+	0.949816i	$0.601270\pi$
$464$			3.84487i			0.178494i
$465$	−31.8104	−	10.0984i	−1.47517	−	0.468304i
$466$			17.0363i			0.789190i
$467$			38.7575i			1.79348i	0.442555	+	0.896741i	$0.354072\pi$
$467$			38.7575i			1.79348i	−0.442555	+	0.896741i	$0.645928\pi$
$468$	−10.1472	+	14.3713i	−0.469055	+	0.664315i
$469$	3.04153			0.140445
$470$		−	11.0596i		−	0.510143i
$471$	−5.28583	+	16.6505i	−0.243558	+	0.767215i
$472$		−	9.06325i		−	0.417170i
$473$	5.61759	−	19.5252i	0.258297	−	0.897771i
$474$	−6.80073	+	21.4225i	−0.312368	+	0.983967i
$475$			1.98128i			0.0909075i
$476$	−0.960881	+	0.556513i	−0.0440419	+	0.0255077i
$477$	6.64849	−	9.41616i	0.304414	−	0.431136i
$478$	20.4682			0.936193
$479$			24.4680i			1.11797i	0.829177	+	0.558987i	$0.188810\pi$
$479$			24.4680i			1.11797i	−0.829177	+	0.558987i	$0.811190\pi$
$480$	1.99678	−	6.28991i	0.0911402	−	0.287094i
$481$	19.9993			0.911890
$482$	−5.03541			−0.229357
$483$	0.231175	−	0.728207i	0.0105188	−	0.0331346i
$484$	9.31813	+	5.84571i	0.423552	+	0.265714i
$485$			48.6304i			2.20819i
$486$	−15.5795	+	0.527120i	−0.706702	+	0.0239106i
$487$			21.1813i			0.959817i	0.877319	+	0.479909i	$0.159330\pi$
$487$			21.1813i			0.959817i	−0.877319	+	0.479909i	$0.840670\pi$
$488$	1.75411			0.0794047
$489$	−18.7123	−	5.94036i	−0.846199	−	0.268632i
$490$	−26.3942			−1.19237
$491$	12.1109			0.546558			0.273279	−	0.961935i	$-0.411892\pi$
$491$	12.1109			0.546558			0.273279	+	0.961935i	$0.411892\pi$
$492$	8.34413	+	2.64891i	0.376182	+	0.119422i
$493$	7.94511	+	13.7181i	0.357830	+	0.617833i
$494$	−1.22087			−0.0549295
$495$	−23.7153	−	29.5760i	−1.06592	−	1.32934i
$496$			5.05736i			0.227082i
$497$	1.49569			0.0670910
$498$	−9.10287	+	28.6743i	−0.407909	+	1.28493i
$499$		−	28.5486i		−	1.27801i	−0.769202	−	0.639006i	$-0.779346\pi$
$499$		−	28.5486i		−	1.27801i	0.769202	−	0.639006i	$-0.220654\pi$
$500$	−17.2091			−0.769612
$501$	27.2409	+	8.64784i	1.21703	+	0.386357i
$502$		−	0.148694i		−	0.00663655i
$503$			11.2713i			0.502564i	0.967914	+	0.251282i	$0.0808521\pi$
$503$			11.2713i			0.502564i	−0.967914	+	0.251282i	$0.919148\pi$
$504$	−0.660000	−	0.466008i	−0.0293988	−	0.0207577i
$505$	13.3240			0.592912
$506$	−5.22053	−	1.50199i	−0.232081	−	0.0667718i
$507$	−11.2095	+	35.3102i	−0.497831	+	1.56818i
$508$			12.9055i			0.572589i
$509$			7.04140i			0.312104i	0.987749	+	0.156052i	$0.0498768\pi$
$509$			7.04140i			0.312104i	−0.987749	+	0.156052i	$0.950123\pi$
$510$	−5.87328	−	26.5680i	−0.260073	−	1.17645i
$511$	0.0313845			0.00138837
$512$	−1.00000			−0.0441942
$513$	−0.653485	−	0.862100i	−0.0288521	−	0.0380627i
$514$			10.4139i			0.459337i
$515$	−0.113693			−0.00500989
$516$	10.1130	+	3.21045i	0.445200	+	0.141332i
$517$	−2.66187	+	9.25195i	−0.117069	+	0.406900i
$518$			0.918465i			0.0403550i
$519$	−29.2008	−	9.27002i	−1.28177	−	0.406909i
$520$		−	22.3431i		−	0.979810i
$521$	1.40526			0.0615655			0.0307828	−	0.999526i	$-0.490200\pi$
$521$	1.40526			0.0615655			0.0307828	+	0.999526i	$0.490200\pi$
$522$	−6.65301	+	9.42256i	−0.291195	+	0.412414i
$523$		−	11.2578i		−	0.492270i	−0.969236	−	0.246135i	$-0.920839\pi$
$523$		−	11.2578i		−	0.492270i	0.969236	−	0.246135i	$-0.0791607\pi$
$524$		−	18.3231i		−	0.800449i
$525$	−1.34320	+	4.23111i	−0.0586220	+	0.184661i
$526$	7.90242			0.344562
$527$	10.4506	+	18.0442i	0.455236	+	0.786016i
$528$	−3.18429	+	4.78124i	−0.138578	+	0.208077i
$529$	−20.3173			−0.883360
$530$			14.6393i			0.635891i
$531$	15.6827	−	22.2112i	0.680571	−	0.963882i
$532$		−	0.0560682i		−	0.00243086i
$533$	29.6401			1.28386
$534$	19.2027	+	6.09604i	0.830982	+	0.263802i
$535$			55.6405i			2.40555i
$536$	11.2937			0.487813
$537$	−21.7510	−	6.90502i	−0.938625	−	0.297974i
$538$	−17.6109			−0.759258
$539$	22.0801	+	6.35266i	0.951059	+	0.273628i
$540$	15.7773	−	11.9594i	0.678947	−	0.514652i
$541$	−39.0116			−1.67724			−0.838620	−	0.544716i	$-0.816637\pi$
$541$	−39.0116			−1.67724			−0.838620	+	0.544716i	$0.816637\pi$
$542$			13.4427i			0.577416i
$543$	21.3703	+	6.78415i	0.917086	+	0.291136i
$544$	−3.56790	+	2.06642i	−0.152972	+	0.0885970i
$545$	26.7620			1.14636
$546$	−2.60722	−	0.827680i	−0.111579	−	0.0354215i
$547$	27.5470			1.17783			0.588913	−	0.808197i	$-0.299556\pi$
$547$	27.5470			1.17783			0.588913	+	0.808197i	$0.299556\pi$
$548$			18.3288i			0.782965i
$549$	4.29876	+	3.03524i	0.183467	+	0.129541i
$550$	30.3329	+	8.72705i	1.29340	+	0.372123i
$551$	−0.800463			−0.0341009
$552$	0.858388	−	2.70395i	0.0365354	−	0.115088i
$553$	−3.49475			−0.148612
$554$	25.8070			1.09643
$555$	−21.4511	−	6.80983i	−0.910550	−	0.289061i
$556$	−14.6357			−0.620691
$557$	3.16908			0.134278			0.0671392	−	0.997744i	$-0.478613\pi$
$557$	3.16908			0.134278			0.0671392	+	0.997744i	$0.478613\pi$
$558$	−8.75106	+	12.3940i	−0.370462	+	0.524680i
$559$	35.9235			1.51940
$560$	1.02610			0.0433608
$561$	−1.48118	+	23.6391i	−0.0625353	+	0.998043i
$562$	−21.1784			−0.893359
$563$	−9.09841			−0.383452			−0.191726	−	0.981448i	$-0.561409\pi$
$563$	−9.09841			−0.383452			−0.191726	+	0.981448i	$0.561409\pi$
$564$	−4.79200	−	1.52126i	−0.201780	−	0.0640565i
$565$	−13.8059			−0.580817
$566$	22.6034			0.950093
$567$	−0.811089	−	2.28408i	−0.0340626	−	0.0959222i
$568$	5.55374			0.233030
$569$	−41.2110			−1.72765			−0.863827	−	0.503788i	$-0.831939\pi$
$569$	−41.2110			−1.72765			−0.863827	+	0.503788i	$0.831939\pi$
$570$	1.30950	+	0.415709i	0.0548487	+	0.0174122i
$571$	22.5012			0.941645			0.470823	−	0.882228i	$-0.343957\pi$
$571$	22.5012			0.941645			0.470823	+	0.882228i	$0.343957\pi$
$572$	−5.37762	+	18.6912i	−0.224850	+	0.781517i
$573$	−5.28117	−	1.67655i	−0.220624	−	0.0700388i
$574$			1.36122i			0.0568161i
$575$	−15.5874			−0.650041
$576$	−2.45068	−	1.73036i	−0.102112	−	0.0720984i
$577$	−26.3913			−1.09869			−0.549343	−	0.835597i	$-0.685122\pi$
$577$	−26.3913			−1.09869			−0.549343	+	0.835597i	$0.685122\pi$
$578$	−8.45983	+	14.7456i	−0.351883	+	0.613334i
$579$	10.1227	−	31.8867i	0.420685	−	1.32517i
$580$		−	14.6493i		−	0.608278i
$581$	−4.67777			−0.194067
$582$	21.0709	+	6.68913i	0.873419	+	0.277273i
$583$	3.52344	−	12.2465i	0.145926	−	0.507200i
$584$	0.116536			0.00482228
$585$	38.6617	−	54.7559i	1.59846	−	2.26388i
$586$	10.2935			0.425220
$587$		−	9.28281i		−	0.383142i	−0.981479	−	0.191571i	$-0.938642\pi$
$587$		−	9.28281i		−	0.383142i	0.981479	−	0.191571i	$-0.0613583\pi$
$588$	−3.63054	+	11.4363i	−0.149721	+	0.471625i
$589$	−1.05289			−0.0433836
$590$			34.5317i			1.42165i
$591$	32.4380	+	10.2977i	1.33432	+	0.423590i
$592$			3.41040i			0.140167i
$593$	16.9168			0.694689			0.347344	−	0.937738i	$-0.387084\pi$
$593$	16.9168			0.694689			0.347344	+	0.937738i	$0.387084\pi$
$594$	−16.0770	+	6.20735i	−0.659646	+	0.254691i
$595$	3.66103	−	2.12036i	0.150088	−	0.0869262i
$596$	−18.4154			−0.754323
$597$	40.6898	+	12.9173i	1.66532	+	0.528669i
$598$		−	9.60499i		−	0.392777i
$599$		−	27.9929i		−	1.14376i	−0.820338	−	0.571879i	$-0.806215\pi$
$599$		−	27.9929i		−	1.14376i	0.820338	−	0.571879i	$-0.193785\pi$
$600$	−4.98751	+	15.7108i	−0.203614	+	0.641390i
$601$	−21.8984			−0.893253			−0.446626	−	0.894721i	$-0.647375\pi$
$601$	−21.8984			−0.893253			−0.446626	+	0.894721i	$0.647375\pi$
$602$			1.64978i			0.0672400i
$603$	27.6773	+	19.5422i	1.12710	+	0.795818i
$604$			18.1694i			0.739303i
$605$	−35.5028	−	22.2726i	−1.44340	−	0.905512i
$606$	1.83273	−	5.77314i	0.0744495	−	0.234518i
$607$	−6.99844			−0.284058			−0.142029	−	0.989863i	$-0.545363\pi$
$607$	−6.99844			−0.284058			−0.142029	+	0.989863i	$0.545363\pi$
$608$		−	0.208190i		−	0.00844321i
$609$	−1.70942	−	0.542669i	−0.0692692	−	0.0219901i
$610$	−6.68329			−0.270599
$611$	−17.0222			−0.688645
$612$	−12.3194	−	1.10962i	−0.497984	−	0.0448537i
$613$		−	47.2562i		−	1.90866i	−0.298754	−	0.954330i	$-0.596571\pi$
$613$		−	47.2562i		−	1.90866i	0.298754	−	0.954330i	$-0.403429\pi$
$614$		−	17.4371i		−	0.703706i
$615$	−31.7918	−	10.0926i	−1.28197	−	0.406971i
$616$	−0.858388	−	0.246966i	−0.0345855	−	0.00995055i
$617$	−9.53425			−0.383835			−0.191917	−	0.981411i	$-0.561471\pi$
$617$	−9.53425			−0.383835			−0.191917	+	0.981411i	$0.561471\pi$
$618$	−0.0156385	+	0.0492616i	−0.000629071	+	0.00198159i
$619$		−	9.14235i		−	0.367462i	−0.982977	−	0.183731i	$-0.941182\pi$
$619$		−	9.14235i		−	0.367462i	0.982977	−	0.183731i	$-0.0588175\pi$
$620$		−	19.2690i		−	0.773860i
$621$	6.78244	−	5.14120i	0.272170	−	0.206309i
$622$	−3.25884			−0.130668
$623$			3.13263i			0.125506i
$624$	−9.68100	−	3.07331i	−0.387550	−	0.123031i
$625$	17.9843			0.719372
$626$		−	12.0002i		−	0.479625i
$627$	−0.995406	−	0.662936i	−0.0397527	−	0.0264751i
$628$	−10.0860			−0.402474
$629$	7.04732	+	12.1680i	0.280995	+	0.485169i
$630$	2.51465	+	1.77553i	0.100186	+	0.0707388i
$631$	−47.3286			−1.88412			−0.942061	−	0.335441i	$-0.891115\pi$
$631$	−47.3286			−1.88412			−0.942061	+	0.335441i	$0.891115\pi$
$632$	−12.9766			−0.516180
$633$	4.96612	−	15.6434i	0.197386	−	0.621770i
$634$	19.1540			0.760702
$635$		−	49.1710i		−	1.95129i
$636$	6.34303	+	2.01364i	0.251518	+	0.0798462i
$637$			40.6241i			1.60959i
$638$	−3.52584	+	12.2549i	−0.139589	+	0.485175i
$639$	13.6105	+	9.60997i	0.538421	+	0.380165i
$640$	3.81008			0.150607
$641$	−31.0101			−1.22482			−0.612412	−	0.790539i	$-0.709801\pi$
$641$	−31.0101			−1.22482			−0.612412	+	0.790539i	$0.709801\pi$
$642$	24.1083	+	7.65337i	0.951480	+	0.302055i
$643$			24.4740i			0.965161i	0.875852	+	0.482580i	$0.160300\pi$
$643$			24.4740i			0.965161i	−0.875852	+	0.482580i	$0.839700\pi$
$644$	0.441108			0.0173821
$645$	−38.5313	−	12.2321i	−1.51717	−	0.481637i
$646$	−0.430207	−	0.742800i	−0.0169263	−	0.0292251i
$647$			28.5158i			1.12107i	0.828130	+	0.560536i	$0.189405\pi$
$647$			28.5158i			1.12107i	−0.828130	+	0.560536i	$0.810595\pi$
$648$	−3.01170	−	8.48114i	−0.118311	−	0.333170i
$649$	8.31122	−	28.8876i	0.326244	−	1.13394i
$650$			55.8080i			2.18897i
$651$	−2.24849	−	0.713801i	−0.0881254	−	0.0279761i
$652$		−	11.3349i		−	0.443907i
$653$	9.02355			0.353119			0.176559	−	0.984290i	$-0.443503\pi$
$653$	9.02355			0.353119			0.176559	+	0.984290i	$0.443503\pi$
$654$	3.68112	−	11.5956i	0.143943	−	0.453425i
$655$			69.8125i			2.72780i
$656$			5.05441i			0.197342i
$657$	0.285592	+	0.201649i	0.0111420	+	0.00786706i
$658$		−	0.781741i		−	0.0304755i
$659$	27.0968			1.05554			0.527770	−	0.849387i	$-0.323028\pi$
$659$	27.0968			1.05554			0.527770	+	0.849387i	$0.323028\pi$
$660$	12.1324	−	18.2169i	0.472253	−	0.709093i
$661$	−39.2996			−1.52858			−0.764289	−	0.644874i	$-0.776910\pi$
$661$	−39.2996			−1.52858			−0.764289	+	0.644874i	$0.776910\pi$
$662$	3.54602			0.137820
$663$	−40.8916	+	9.03974i	−1.58810	+	0.351074i
$664$	−17.3693			−0.674059
$665$			0.213624i			0.00828399i
$666$	−5.90123	+	8.35782i	−0.228668	+	0.323859i
$667$		−	6.29752i		−	0.243841i
$668$			16.5010i			0.638444i
$669$	−2.29285	+	7.22254i	−0.0886468	+	0.279240i
$670$	−43.0299			−1.66239
$671$	5.59092	+	1.60856i	0.215835	+	0.0620977i
$672$	0.141141	−	0.444598i	0.00544463	−	0.0171507i
$673$	−6.02707			−0.232326			−0.116163	−	0.993230i	$-0.537060\pi$
$673$	−6.02707			−0.232326			−0.116163	+	0.993230i	$0.537060\pi$
$674$	12.9518			0.498885
$675$	−39.4081	+	29.8720i	−1.51682	+	1.14977i
$676$	−21.3890			−0.822652
$677$		−	26.4702i		−	1.01733i	−0.860964	−	0.508666i	$-0.830139\pi$
$677$		−	26.4702i		−	1.01733i	0.860964	−	0.508666i	$-0.169861\pi$
$678$	−1.89900	+	5.98191i	−0.0729308	+	0.229734i
$679$			3.43740i			0.131915i
$680$	13.5940	−	7.87322i	0.521306	−	0.301924i
$681$	−4.24863	−	1.34876i	−0.162808	−	0.0516845i
$682$	−4.63772	+	16.1195i	−0.177588	+	0.617247i
$683$	9.64828			0.369181			0.184591	−	0.982816i	$-0.440904\pi$
$683$	9.64828			0.369181			0.184591	+	0.982816i	$0.440904\pi$
$684$	0.360243	−	0.510207i	0.0137743	−	0.0195083i
$685$		−	69.8340i		−	2.66822i
$686$	−3.75085			−0.143208
$687$	−8.14127	+	25.6452i	−0.310609	+	0.978426i
$688$			6.12589i			0.233547i
$689$	22.5318			0.858393
$690$	−3.27053	+	10.3023i	−0.124507	+	0.392200i
$691$		−	1.08690i		−	0.0413474i	−0.999786	−	0.0206737i	$-0.993419\pi$
$691$		−	1.08690i		−	0.0413474i	0.999786	−	0.0206737i	$-0.00658112\pi$
$692$		−	17.6882i		−	0.672406i
$693$	−1.67630	−	2.09056i	−0.0636773	−	0.0794137i
$694$		−	14.1605i		−	0.537526i
$695$	55.7631			2.11522
$696$	−6.34735	−	2.01501i	−0.240596	−	0.0763789i
$697$	10.4445	+	18.0336i	0.395615	+	0.683073i
$698$			20.9198i			0.791827i
$699$	−28.1245	−	8.92834i	−1.06377	−	0.337701i
$700$	−2.56297			−0.0968713
$701$	−6.24159			−0.235742			−0.117871	−	0.993029i	$-0.537607\pi$
$701$	−6.24159			−0.235742			−0.117871	+	0.993029i	$0.537607\pi$
$702$	−18.4071	−	24.2833i	−0.694732	−	0.916515i
$703$	−0.710011			−0.0267786
$704$	−3.18733	−	0.917024i	−0.120127	−	0.0345616i
$705$	18.2579	+	5.79611i	0.687632	+	0.218294i
$706$		−	32.5359i		−	1.22450i
$707$	0.941800			0.0354200
$708$	14.9622	+	4.74985i	0.562313	+	0.178510i
$709$		−	31.1513i		−	1.16991i	−0.811065	−	0.584956i	$-0.801112\pi$
$709$		−	31.1513i		−	1.16991i	0.811065	−	0.584956i	$-0.198888\pi$
$710$	−21.1602			−0.794128
$711$	−31.8014	−	22.4541i	−1.19265	−	0.842095i
$712$			11.6319i			0.435925i
$713$		−	8.28346i		−	0.310218i
$714$	−0.415148	−	1.87794i	−0.0155365	−	0.0702800i
$715$	20.4892	−	71.2149i	0.766251	−	2.66328i
$716$		−	13.1756i		−	0.492394i
$717$	−10.7269	+	33.7901i	−0.400605	+	1.26192i
$718$	21.9753			0.820112
$719$	23.2545			0.867245			0.433622	−	0.901095i	$-0.357235\pi$
$719$	23.2545			0.867245			0.433622	+	0.901095i	$0.357235\pi$
$720$	9.33730	+	6.59282i	0.347981	+	0.245700i
$721$	−0.00803628			−0.000299287
$722$	−18.9567			−0.705494
$723$	2.63895	−	8.31277i	0.0981437	−	0.309155i
$724$			12.9449i			0.481094i
$725$			36.5905i			1.35894i
$726$	−14.5339	+	12.3193i	−0.539403	+	0.457213i
$727$	37.6407			1.39602			0.698008	−	0.716090i	$-0.254070\pi$
$727$	37.6407			1.39602			0.698008	+	0.716090i	$0.254070\pi$
$728$		−	1.57931i		−	0.0585330i
$729$	7.29470	−	25.9959i	0.270174	−	0.962811i
$730$	−0.444010			−0.0164335
$731$	12.6587	+	21.8566i	0.468197	+	0.808395i
$732$	−0.919290	+	2.89579i	−0.0339779	+	0.107031i
$733$		−	17.8701i		−	0.660048i	−0.943973	−	0.330024i	$-0.892943\pi$
$733$		−	17.8701i		−	0.660048i	0.943973	−	0.330024i	$-0.107057\pi$
$734$			15.0883i			0.556920i
$735$	13.8326	−	43.5732i	0.510225	−	1.60722i
$736$	1.63790			0.0603738
$737$	35.9967	+	10.3566i	1.32596	+	0.381489i
$738$	−8.74595	+	12.3868i	−0.321943	+	0.455963i
$739$		−	14.1890i		−	0.521951i	−0.965345	−	0.260975i	$-0.915956\pi$
$739$		−	14.1890i		−	0.521951i	0.965345	−	0.260975i	$-0.0840441\pi$
$740$		−	12.9939i		−	0.477666i
$741$	0.639831	−	2.01548i	0.0235048	−	0.0740407i
$742$			1.03477i			0.0379876i
$743$			8.05189i			0.295395i	0.989033	+	0.147698i	$0.0471862\pi$
$743$			8.05189i			0.295395i	−0.989033	+	0.147698i	$0.952814\pi$
$744$	−8.34900	−	2.65045i	−0.306089	−	0.0971704i
$745$	70.1641			2.57061
$746$			5.93570i			0.217322i
$747$	−42.5666	−	30.0552i	−1.55743	−	1.09966i
$748$	−13.2670	+	3.31451i	−0.485091	+	0.121190i
$749$			3.93291i			0.143705i
$750$	9.01889	−	28.4098i	0.329323	−	1.03738i
$751$		−	51.0587i		−	1.86316i	−0.363536	−	0.931580i	$-0.618431\pi$
$751$		−	51.0587i		−	1.86316i	0.363536	−	0.931580i	$-0.381569\pi$
$752$		−	2.90273i		−	0.105852i
$753$	0.245474	+	0.0779275i	0.00894556	+	0.00283984i
$754$	−22.5471			−0.821118
$755$		−	69.2270i		−	2.51943i
$756$	1.11521	−	0.845344i	0.0405597	−	0.0307449i
$757$	6.55550			0.238264			0.119132	−	0.992878i	$-0.461989\pi$
$757$	6.55550			0.238264			0.119132	+	0.992878i	$0.461989\pi$
$758$		−	22.7715i		−	0.827099i
$759$	5.21555	−	7.83120i	0.189312	−	0.284255i
$760$			0.793220i			0.0287731i
$761$	10.6078			0.384534			0.192267	−	0.981343i	$-0.438416\pi$
$761$	10.6078			0.384534			0.192267	+	0.981343i	$0.438416\pi$
$762$	−21.3052	−	6.76350i	−0.771806	−	0.245016i
$763$	1.89165			0.0684823
$764$		−	3.19904i		−	0.115737i
$765$	46.9381	+	4.22774i	1.69705	+	0.152854i
$766$		−	17.8676i		−	0.645582i
$767$	53.1488			1.91909
$768$	0.524078	−	1.65086i	0.0189110	−	0.0595703i
$769$			0.919165i			0.0331459i	0.999863	+	0.0165730i	$0.00527558\pi$
$769$			0.919165i			0.0331459i	−0.999863	+	0.0165730i	$0.994724\pi$
$770$	3.27053	+	0.940961i	0.117862	+	0.0339099i
$771$	−17.1919	−	5.45770i	−0.619151	−	0.196554i
$772$	19.3152			0.695170
$773$			43.8952i			1.57880i	0.613879	+	0.789400i	$0.289608\pi$
$773$			43.8952i			1.57880i	−0.613879	+	0.789400i	$0.710392\pi$
$774$	−10.6000	+	15.0126i	−0.381009	+	0.539618i
$775$			48.1295i			1.72886i
$776$			12.7636i			0.458187i
$777$	−1.51626	−	0.481348i	−0.0543954	−	0.0172682i
$778$			19.2714i			0.690915i
$779$	−1.05228			−0.0377017
$780$	36.8854	+	11.7095i	1.32071	+	0.419269i
$781$	17.7016	+	5.09291i	0.633413	+	0.182239i
$782$	5.84387	−	3.38459i	0.208976	−	0.121033i
$783$	−12.0686	−	15.9214i	−0.431298	−	0.568983i
$784$	−6.92747			−0.247410
$785$	38.4283			1.37157
$786$	30.2489	+	9.60275i	1.07894	+	0.342519i
$787$	4.88175			0.174016			0.0870078	−	0.996208i	$-0.472269\pi$
$787$	4.88175			0.174016			0.0870078	+	0.996208i	$0.472269\pi$
$788$			19.6491i			0.699971i
$789$	−4.14149	+	13.0458i	−0.147441	+	0.464443i
$790$	49.4417			1.75906
$791$	−0.975858			−0.0346975
$792$	−6.22435	−	7.76257i	−0.221173	−	0.275831i
$793$			10.2865i			0.365283i
$794$		−	25.6830i		−	0.911457i
$795$	−24.1675	−	7.67215i	−0.857132	−	0.272103i
$796$			24.6476i			0.873611i
$797$			17.4545i			0.618269i	0.951018	+	0.309135i	$0.100039\pi$
$797$			17.4545i			0.618269i	−0.951018	+	0.309135i	$0.899961\pi$
$798$	0.0925607	+	0.0293841i	0.00327661	+	0.00104019i
$799$	−5.99825	−	10.3566i	−0.212203	−	0.366392i
$800$	−9.51672			−0.336467
$801$	−20.1274	+	28.5062i	−0.711168	+	1.00722i
$802$	18.8429			0.665367
$803$	0.371437	+	0.106866i	0.0131077	+	0.00377122i
$804$	−5.91878	+	18.6443i	−0.208739	+	0.657534i
$805$	−1.68066			−0.0592353
$806$	−29.6574			−1.04464
$807$	9.22947	−	29.0731i	0.324893	−	1.02342i
$808$	3.49705			0.123026
$809$		−	38.3336i		−	1.34774i	−0.738851	−	0.673869i	$-0.764631\pi$
$809$		−	38.3336i		−	1.34774i	0.738851	−	0.673869i	$-0.235369\pi$
$810$	11.4748	+	32.3138i	0.403184	+	1.13539i
$811$	−3.03947			−0.106730			−0.0533651	−	0.998575i	$-0.516995\pi$
$811$	−3.03947			−0.106730			−0.0533651	+	0.998575i	$0.516995\pi$
$812$		−	1.03547i		−	0.0363380i
$813$	−22.1921	−	7.04505i	−0.778311	−	0.247081i
$814$	−3.12742	+	10.8701i	−0.109616	+	0.380996i
$815$			43.1867i			1.51277i
$816$	−1.54151	−	6.97307i	−0.0539636	−	0.244106i
$817$	−1.27535			−0.0446188
$818$			26.5587i			0.928602i
$819$	2.73277	−	3.87038i	0.0954907	−	0.135242i
$820$		−	19.2577i		−	0.672508i
$821$			27.0637i			0.944531i	0.881456	+	0.472265i	$0.156564\pi$
$821$			27.0637i			0.944531i	−0.881456	+	0.472265i	$0.843436\pi$
$822$	−30.2582	−	9.60570i	−1.05538	−	0.335037i
$823$		−	21.9205i		−	0.764102i	−0.924141	−	0.382051i	$-0.875218\pi$
$823$		−	21.9205i		−	0.764102i	0.924141	−	0.382051i	$-0.124782\pi$
$824$	−0.0298399			−0.00103952
$825$	−30.3040	+	45.5018i	−1.05505	+	1.58417i
$826$			2.44085i			0.0849280i
$827$			8.71197i			0.302945i	0.988461	+	0.151473i	$0.0484015\pi$
$827$			8.71197i			0.302945i	−0.988461	+	0.151473i	$0.951598\pi$
$828$	4.01398	+	2.83416i	0.139495	+	0.0984939i
$829$	15.2626			0.530091			0.265045	−	0.964236i	$-0.414613\pi$
$829$	15.2626			0.530091			0.265045	+	0.964236i	$0.414613\pi$
$830$	66.1784			2.29709
$831$	−13.5249	+	42.6038i	−0.469173	+	1.47791i
$832$		−	5.86421i		−	0.203305i
$833$	−24.7165	+	14.3151i	−0.856377	+	0.495987i
$834$	7.67024	−	24.1615i	0.265599	−	0.836644i
$835$		−	62.8703i		−	2.17572i
$836$	0.190915	−	0.663569i	0.00660293	−	0.0229500i
$837$	−15.8745	−	20.9422i	−0.548704	−	0.723869i
$838$	12.8821			0.445006
$839$	−7.91778			−0.273352			−0.136676	−	0.990616i	$-0.543642\pi$
$839$	−7.91778			−0.273352			−0.136676	+	0.990616i	$0.543642\pi$
$840$	−0.537759	+	1.69395i	−0.0185544	+	0.0584470i
$841$	14.2170			0.490240
$842$	27.6448			0.952703
$843$	11.0992	−	34.9627i	0.382275	−	1.20418i
$844$	9.47591			0.326174
$845$	81.4937			2.80347
$846$	5.02277	−	7.11367i	0.172686	−	0.244573i
$847$	−2.50949	−	1.57433i	−0.0862272	−	0.0540944i
$848$			3.84226i			0.131944i
$849$	−11.8460	+	37.3151i	−0.406553	+	1.28065i
$850$	−33.9547	+	19.6655i	−1.16464	+	0.674522i
$851$		−	5.58590i		−	0.191482i
$852$	−2.91059	+	9.16845i	−0.0997153	+	0.314106i
$853$	49.7498			1.70340			0.851701	−	0.524029i	$-0.175572\pi$
$853$	49.7498			1.70340			0.851701	+	0.524029i	$0.175572\pi$
$854$	−0.472404			−0.0161653
$855$	−1.37256	+	1.94393i	−0.0469405	+	0.0664810i
$856$			14.6035i			0.499137i
$857$			7.50176i			0.256255i	0.991758	+	0.128128i	$0.0408967\pi$
$857$			7.50176i			0.256255i	−0.991758	+	0.128128i	$0.959103\pi$
$858$	−28.0382	−	18.6733i	−0.957209	−	0.637497i
$859$	−28.9765			−0.988665			−0.494333	−	0.869273i	$-0.664587\pi$
$859$	−28.9765			−0.988665			−0.494333	+	0.869273i	$0.664587\pi$
$860$		−	23.3401i		−	0.795892i
$861$	−2.24718	−	0.713384i	−0.0765837	−	0.0243121i
$862$		−	19.3110i		−	0.657736i
$863$		−	2.03665i		−	0.0693283i	−0.999399	−	0.0346641i	$-0.988964\pi$
$863$		−	2.03665i		−	0.0693283i	0.999399	−	0.0346641i	$-0.0110362\pi$
$864$	4.14094	−	3.13889i	0.140877	−	0.106787i
$865$			67.3936i			2.29145i
$866$	−8.00193			−0.271917
$867$	−19.9092	−	21.6938i	−0.676153	−	0.736761i
$868$		−	1.36201i		−	0.0462297i
$869$	−41.3606	−	11.8998i	−1.40306	−	0.403673i
$870$	24.1839	+	7.67737i	0.819911	+	0.260287i
$871$			66.2285i			2.24407i
$872$	7.02399			0.237862
$873$	−22.0856	+	31.2796i	−0.747486	+	1.05865i
$874$			0.340994i			0.0115343i
$875$	4.63462			0.156679
$876$	−0.0610738	+	0.192384i	−0.00206349	+	0.00650005i
$877$	8.67875			0.293061			0.146530	−	0.989206i	$-0.453189\pi$
$877$	8.67875			0.293061			0.146530	+	0.989206i	$0.453189\pi$
$878$	−22.5863			−0.762252
$879$	−5.39459	+	16.9931i	−0.181955	+	0.573163i
$880$	12.1440	+	3.49393i	0.409374	+	0.117781i
$881$	25.2532			0.850801			0.425400	−	0.905005i	$-0.360133\pi$
$881$	25.2532			0.850801			0.425400	+	0.905005i	$0.360133\pi$
$882$	−16.9770	−	11.9870i	−0.571647	−	0.403624i
$883$	−33.0923			−1.11364			−0.556822	−	0.830632i	$-0.687979\pi$
$883$	−33.0923			−1.11364			−0.556822	+	0.830632i	$0.687979\pi$
$884$	−12.1179	−	20.9229i	−0.407569	−	0.703714i
$885$	−57.0071	−	18.0973i	−1.91627	−	0.608335i
$886$		−	23.8935i		−	0.802718i
$887$			8.09508i			0.271806i	0.990722	+	0.135903i	$0.0433936\pi$
$887$			8.09508i			0.271806i	−0.990722	+	0.135903i	$0.956606\pi$
$888$	−5.63010	−	1.78732i	−0.188934	−	0.0599785i
$889$		−	3.47562i		−	0.116568i
$890$		−	44.3186i		−	1.48556i
$891$	−1.82188	−	29.7940i	−0.0610353	−	0.998136i
$892$	−4.37502			−0.146486
$893$	0.604318			0.0202227
$894$	9.65110	−	30.4012i	0.322781	−	1.01677i
$895$			50.1999i			1.67800i
$896$	0.269313			0.00899711
$897$	15.8565	+	5.03377i	0.529433	+	0.168073i
$898$	26.3217			0.878367
$899$	−19.4449			−0.648524
$900$	−23.3225	−	16.4674i	−0.777415	−	0.548912i
$901$	7.93971	+	13.7088i	0.264510	+	0.456706i
$902$	−4.63501	+	16.1101i	−0.154329	+	0.536407i
$903$	−2.72356	−	0.864614i	−0.0906344	−	0.0287726i
$904$	−3.62351			−0.120516
$905$		−	49.3212i		−	1.63949i
$906$	−29.9952	−	9.52220i	−0.996523	−	0.316354i
$907$			5.27434i			0.175132i	0.996159	+	0.0875658i	$0.0279088\pi$
$907$			5.27434i			0.175132i	−0.996159	+	0.0875658i	$0.972091\pi$
$908$		−	2.57358i		−	0.0854073i
$909$	8.57017	+	6.05116i	0.284254	+	0.200704i
$910$			6.01729i			0.199471i
$911$	8.17760			0.270936			0.135468	−	0.990782i	$-0.456746\pi$
$911$	8.17760			0.270936			0.135468	+	0.990782i	$0.456746\pi$
$912$	0.343692	+	0.109108i	0.0113808	+	0.00361292i
$913$	−55.3617	−	15.9281i	−1.83220	−	0.527142i
$914$		−	4.89134i		−	0.161791i
$915$	3.50257	−	11.0332i	0.115791	−	0.364746i
$916$	−15.5344			−0.513273
$917$			4.93465i			0.162956i
$918$	8.28818	−	19.7562i	0.273551	−	0.652051i
$919$			57.1993i			1.88683i	0.331613	+	0.943416i	$0.392407\pi$
$919$			57.1993i			1.88683i	−0.331613	+	0.943416i	$0.607593\pi$
$920$	−6.24053			−0.205744
$921$	28.7863	+	9.13843i	0.948540	+	0.301121i
$922$	12.4471			0.409922
$923$			32.5683i			1.07200i
$924$	0.857570	−	1.28765i	0.0282120	−	0.0423606i
$925$			32.4558i			1.06714i
$926$	13.4617			0.442379
$927$	−0.0731283	−	0.0516339i	−0.00240185	−	0.00169588i
$928$		−	3.84487i		−	0.126214i
$929$	26.5037			0.869558			0.434779	−	0.900537i	$-0.356826\pi$
$929$	26.5037			0.869558			0.434779	+	0.900537i	$0.356826\pi$
$930$	31.8104	+	10.0984i	1.04310	+	0.331141i
$931$		−	1.44223i		−	0.0472671i
$932$		−	17.0363i		−	0.558042i
$933$	1.70789	−	5.37989i	0.0559137	−	0.176130i
$934$		−	38.7575i		−	1.26818i
$935$	50.5485	−	12.6285i	1.65311	−	0.412997i
$936$	10.1472	−	14.3713i	0.331672	−	0.469741i
$937$		−	1.25415i		−	0.0409713i	−0.999790	−	0.0204856i	$-0.993479\pi$
$937$		−	1.25415i		−	0.0409713i	0.999790	−	0.0204856i	$-0.00652123\pi$
$938$	−3.04153			−0.0993096
$939$	19.8107	+	6.28905i	0.646497	+	0.205236i
$940$			11.0596i			0.360725i
$941$		−	17.3204i		−	0.564629i	−0.959322	−	0.282314i	$-0.908898\pi$
$941$		−	17.3204i		−	0.564629i	0.959322	−	0.282314i	$-0.0911021\pi$
$942$	5.28583	−	16.6505i	0.172222	−	0.542503i
$943$		−	8.27862i		−	0.269589i
$944$			9.06325i			0.294984i
$945$	−4.24903	+	3.22083i	−0.138221	+	0.104774i
$946$	−5.61759	+	19.5252i	−0.182644	+	0.634820i
$947$	24.8033			0.806000			0.403000	−	0.915200i	$-0.367967\pi$
$947$	24.8033			0.806000			0.403000	+	0.915200i	$0.367967\pi$
$948$	6.80073	−	21.4225i	0.220878	−	0.695770i
$949$			0.683389i			0.0221838i
$950$		−	1.98128i		−	0.0642813i
$951$	−10.0382	+	31.6206i	−0.325511	+	1.02537i
$952$	0.960881	−	0.556513i	0.0311423	−	0.0180367i
$953$	5.01668			0.162506			0.0812531	−	0.996693i	$-0.474108\pi$
$953$	5.01668			0.162506			0.0812531	+	0.996693i	$0.474108\pi$
$954$	−6.64849	+	9.41616i	−0.215253	+	0.304859i
$955$			12.1886i			0.394414i
$956$	−20.4682			−0.661989
$957$	−18.3833	−	12.2432i	−0.594247	−	0.395766i
$958$		−	24.4680i		−	0.790526i
$959$		−	4.93617i		−	0.159397i
$960$	−1.99678	+	6.28991i	−0.0644458	+	0.203006i
$961$	5.42309			0.174938
$962$	−19.9993			−0.644804
$963$	−25.2693	+	35.7885i	−0.814292	+	1.15327i
$964$	5.03541			0.162180
$965$	−73.5925			−2.36903
$966$	−0.231175	+	0.728207i	−0.00743793	+	0.0234297i
$967$		−	0.403403i		−	0.0129726i	−0.999979	−	0.00648628i	$-0.997935\pi$
$967$		−	0.403403i		−	0.0129726i	0.999979	−	0.00648628i	$-0.00206466\pi$
$968$	−9.31813	−	5.84571i	−0.299496	−	0.187888i
$969$	1.45172	−	0.320926i	0.0466360	−	0.0103096i
$970$		−	48.6304i		−	1.56143i
$971$			16.5716i			0.531809i	0.963999	+	0.265905i	$0.0856707\pi$
$971$			16.5716i			0.531809i	−0.963999	+	0.265905i	$0.914329\pi$
$972$	15.5795	−	0.527120i	0.499714	−	0.0169074i
$973$	3.94158			0.126361
$974$		−	21.1813i		−	0.678693i
$975$	−92.1313	−	29.2478i	−2.95056	−	0.936679i
$976$	−1.75411			−0.0561476
$977$		−	24.7025i		−	0.790304i	−0.918616	−	0.395152i	$-0.870692\pi$
$977$		−	24.7025i		−	0.790304i	0.918616	−	0.395152i	$-0.129308\pi$
$978$	18.7123	+	5.94036i	0.598353	+	0.189952i
$979$	−10.6668	+	37.0748i	−0.340911	+	1.18492i
$980$	26.3942			0.843133
$981$	17.2136	+	12.1540i	0.549587	+	0.388048i
$982$	−12.1109			−0.386475
$983$	−2.97699			−0.0949512			−0.0474756	−	0.998872i	$-0.515118\pi$
$983$	−2.97699			−0.0949512			−0.0474756	+	0.998872i	$0.515118\pi$
$984$	−8.34413	−	2.64891i	−0.266001	−	0.0844441i
$985$		−	74.8647i		−	2.38539i
$986$	−7.94511	−	13.7181i	−0.253024	−	0.436874i
$987$	1.29055	+	0.409694i	0.0410785	+	0.0130407i
$988$	1.22087			0.0388410
$989$		−	10.0336i		−	0.319050i
$990$	23.7153	+	29.5760i	0.753721	+	0.939987i
$991$		−	3.69608i		−	0.117410i	−0.998275	−	0.0587049i	$-0.981303\pi$
$991$		−	3.69608i		−	0.117410i	0.998275	−	0.0587049i	$-0.0186971\pi$
$992$		−	5.05736i		−	0.160571i
$993$	−1.85839	+	5.85398i	−0.0589742	+	0.185770i
$994$	−1.49569			−0.0474405
$995$		−	93.9094i		−	2.97713i
$996$	9.10287	−	28.6743i	0.288436	−	0.908580i
$997$	21.7776			0.689704			0.344852	−	0.938657i	$-0.387929\pi$
$997$	21.7776			0.689704			0.344852	+	0.938657i	$0.387929\pi$
$998$			28.5486i			0.903691i
$999$	−10.7049	−	14.1223i	−0.338688	−	0.446808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.h.g.1121.17	yes	28
3.2	odd	2		1122.2.h.h.1121.11	yes	28
11.10	odd	2		1122.2.h.h.1121.17	yes	28
17.16	even	2	inner	1122.2.h.g.1121.12	yes	28
33.32	even	2	inner	1122.2.h.g.1121.11	✓	28
51.50	odd	2		1122.2.h.h.1121.18	yes	28
187.186	odd	2		1122.2.h.h.1121.12	yes	28
561.560	even	2	inner	1122.2.h.g.1121.18	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.h.g.1121.11	✓	28	33.32	even	2	inner
1122.2.h.g.1121.12	yes	28	17.16	even	2	inner
1122.2.h.g.1121.17	yes	28	1.1	even	1	trivial
1122.2.h.g.1121.18	yes	28	561.560	even	2	inner
1122.2.h.h.1121.11	yes	28	3.2	odd	2
1122.2.h.h.1121.12	yes	28	187.186	odd	2
1122.2.h.h.1121.17	yes	28	11.10	odd	2
1122.2.h.h.1121.18	yes	28	51.50	odd	2

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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.524078 - 1.65086i) q^{3} +1.00000 q^{4} -3.81008 q^{5} +(-0.524078 + 1.65086i) q^{6} -0.269313 q^{7} -1.00000 q^{8} +(-2.45068 - 1.73036i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.524078 - 1.65086i) q^{3} +1.00000 q^{4} -3.81008 q^{5} +(-0.524078 + 1.65086i) q^{6} -0.269313 q^{7} -1.00000 q^{8} +(-2.45068 - 1.73036i) q^{9} +3.81008 q^{10} +(-3.18733 - 0.917024i) q^{11} +(0.524078 - 1.65086i) q^{12} -5.86421i q^{13} +0.269313 q^{14} +(-1.99678 + 6.28991i) q^{15} +1.00000 q^{16} +(3.56790 - 2.06642i) q^{17} +(2.45068 + 1.73036i) q^{18} +0.208190i q^{19} -3.81008 q^{20} +(-0.141141 + 0.444598i) q^{21} +(3.18733 + 0.917024i) q^{22} -1.63790 q^{23} +(-0.524078 + 1.65086i) q^{24} +9.51672 q^{25} +5.86421i q^{26} +(-4.14094 + 3.13889i) q^{27} -0.269313 q^{28} +3.84487i q^{29} +(1.99678 - 6.28991i) q^{30} +5.05736i q^{31} -1.00000 q^{32} +(-3.18429 + 4.78124i) q^{33} +(-3.56790 + 2.06642i) q^{34} +1.02610 q^{35} +(-2.45068 - 1.73036i) q^{36} +3.41040i q^{37} -0.208190i q^{38} +(-9.68100 - 3.07331i) q^{39} +3.81008 q^{40} +5.05441i q^{41} +(0.141141 - 0.444598i) q^{42} +6.12589i q^{43} +(-3.18733 - 0.917024i) q^{44} +(9.33730 + 6.59282i) q^{45} +1.63790 q^{46} -2.90273i q^{47} +(0.524078 - 1.65086i) q^{48} -6.92747 q^{49} -9.51672 q^{50} +(-1.54151 - 6.97307i) q^{51} -5.86421i q^{52} +3.84226i q^{53} +(4.14094 - 3.13889i) q^{54} +(12.1440 + 3.49393i) q^{55} +0.269313 q^{56} +(0.343692 + 0.109108i) q^{57} -3.84487i q^{58} +9.06325i q^{59} +(-1.99678 + 6.28991i) q^{60} -1.75411 q^{61} -5.05736i q^{62} +(0.660000 + 0.466008i) q^{63} +1.00000 q^{64} +22.3431i q^{65} +(3.18429 - 4.78124i) q^{66} -11.2937 q^{67} +(3.56790 - 2.06642i) q^{68} +(-0.858388 + 2.70395i) q^{69} -1.02610 q^{70} -5.55374 q^{71} +(2.45068 + 1.73036i) q^{72} -0.116536 q^{73} -3.41040i q^{74} +(4.98751 - 15.7108i) q^{75} +0.208190i q^{76} +(0.858388 + 0.246966i) q^{77} +(9.68100 + 3.07331i) q^{78} +12.9766 q^{79} -3.81008 q^{80} +(3.01170 + 8.48114i) q^{81} -5.05441i q^{82} +17.3693 q^{83} +(-0.141141 + 0.444598i) q^{84} +(-13.5940 + 7.87322i) q^{85} -6.12589i q^{86} +(6.34735 + 2.01501i) q^{87} +(3.18733 + 0.917024i) q^{88} -11.6319i q^{89} +(-9.33730 - 6.59282i) q^{90} +1.57931i q^{91} -1.63790 q^{92} +(8.34900 + 2.65045i) q^{93} +2.90273i q^{94} -0.793220i q^{95} +(-0.524078 + 1.65086i) q^{96} -12.7636i q^{97} +6.92747 q^{98} +(6.22435 + 7.76257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{2} + 28 q^{4} - 28 q^{8} + 2 q^{9}+O(q^{10}) \) 28 * q - 28 * q^2 + 28 * q^4 - 28 * q^8 + 2 * q^9	\( 28 q - 28 q^{2} + 28 q^{4} - 28 q^{8} + 2 q^{9} - 8 q^{15} + 28 q^{16} - 24 q^{17} - 2 q^{18} + 36 q^{21} + 80 q^{25} + 8 q^{30} - 28 q^{32} - 10 q^{33} + 24 q^{34} + 2 q^{36} - 36 q^{42} - 24 q^{49} - 80 q^{50} + 26 q^{51} - 4 q^{55} - 8 q^{60} + 28 q^{64} + 10 q^{66} - 40 q^{67} - 24 q^{68} - 4 q^{69} - 2 q^{72} + 4 q^{77} + 14 q^{81} + 12 q^{83} + 36 q^{84} + 48 q^{87} + 56 q^{93} + 24 q^{98}+O(q^{100}) \) 28 * q - 28 * q^2 + 28 * q^4 - 28 * q^8 + 2 * q^9 - 8 * q^15 + 28 * q^16 - 24 * q^17 - 2 * q^18 + 36 * q^21 + 80 * q^25 + 8 * q^30 - 28 * q^32 - 10 * q^33 + 24 * q^34 + 2 * q^36 - 36 * q^42 - 24 * q^49 - 80 * q^50 + 26 * q^51 - 4 * q^55 - 8 * q^60 + 28 * q^64 + 10 * q^66 - 40 * q^67 - 24 * q^68 - 4 * q^69 - 2 * q^72 + 4 * q^77 + 14 * q^81 + 12 * q^83 + 36 * q^84 + 48 * q^87 + 56 * q^93 + 24 * q^98

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