LMFDB - Embedded newform 99.2.p.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(2,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.p (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	99.2
Dual form			99.2.p.a.50.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.780898 + 0.867275i) q^{2} +(0.189274 - 1.72168i) q^{3} +(0.0666926 - 0.634537i) q^{4} +(-1.15400 - 1.03907i) q^{5} +(1.64097 - 1.18030i) q^{6} +(1.76474 + 3.96367i) q^{7} +(2.49070 - 1.80960i) q^{8} +(-2.92835 - 0.651738i) q^{9} -1.81224i q^{10} +(-3.19970 + 0.872887i) q^{11} +(-1.07985 - 0.234925i) q^{12} +(1.05340 + 4.95585i) q^{13} +(-2.05951 + 4.62574i) q^{14} +(-2.00736 + 1.79015i) q^{15} +(2.26622 + 0.481700i) q^{16} +(0.248154 + 0.763741i) q^{17} +(-1.72151 - 3.04863i) q^{18} +(-2.19592 - 3.02243i) q^{19} +(-0.736289 + 0.662958i) q^{20} +(7.15819 - 2.28809i) q^{21} +(-3.25567 - 2.09338i) q^{22} +(2.42777 - 1.40167i) q^{23} +(-2.64412 - 4.63069i) q^{24} +(-0.270585 - 2.57445i) q^{25} +(-3.47549 + 4.78360i) q^{26} +(-1.67634 + 4.91832i) q^{27} +(2.63279 - 0.855447i) q^{28} +(-6.68223 + 2.97512i) q^{29} +(-3.12009 - 0.343010i) q^{30} +(6.42298 - 1.36525i) q^{31} +(-1.72675 - 2.99082i) q^{32} +(0.897210 + 5.67407i) q^{33} +(-0.468590 + 0.811622i) q^{34} +(2.08201 - 6.40776i) q^{35} +(-0.608852 + 1.81468i) q^{36} +(-3.70044 - 2.68853i) q^{37} +(0.906484 - 4.26467i) q^{38} +(8.73176 - 0.875599i) q^{39} +(-4.75456 - 0.499724i) q^{40} +(-0.302935 - 0.134876i) q^{41} +(7.57422 + 4.42135i) q^{42} +(-0.967761 - 0.558737i) q^{43} +(0.340483 + 2.08854i) q^{44} +(2.70212 + 3.79485i) q^{45} +(3.11148 + 1.01098i) q^{46} +(5.62759 - 0.591483i) q^{47} +(1.25827 - 3.81053i) q^{48} +(-7.91248 + 8.78770i) q^{49} +(2.02145 - 2.24505i) q^{50} +(1.36188 - 0.282686i) q^{51} +(3.21493 - 0.337902i) q^{52} +(-5.13255 - 1.66767i) q^{53} +(-5.57459 + 2.38685i) q^{54} +(4.59944 + 2.31739i) q^{55} +(11.5681 + 6.67884i) q^{56} +(-5.61928 + 3.20860i) q^{57} +(-7.79839 - 3.47207i) q^{58} +(6.97083 + 0.732664i) q^{59} +(1.00204 + 1.39313i) q^{60} +(-0.842120 + 3.96186i) q^{61} +(6.19973 + 4.50437i) q^{62} +(-2.58450 - 12.7572i) q^{63} +(2.67734 - 8.24001i) q^{64} +(3.93383 - 6.81360i) q^{65} +(-4.22035 + 5.20899i) q^{66} +(-5.22518 - 9.05028i) q^{67} +(0.501172 - 0.106527i) q^{68} +(-1.95372 - 4.44514i) q^{69} +(7.18312 - 3.19813i) q^{70} +(4.20477 - 1.36621i) q^{71} +(-8.47302 + 3.67585i) q^{72} +(-1.44520 + 1.98915i) q^{73} +(-0.557974 - 5.30877i) q^{74} +(-4.48358 - 0.0214156i) q^{75} +(-2.06429 + 1.19182i) q^{76} +(-9.10648 - 11.1421i) q^{77} +(7.57800 + 6.88908i) q^{78} +(0.476003 - 0.428595i) q^{79} +(-2.11470 - 2.91063i) q^{80} +(8.15047 + 3.81704i) q^{81} +(-0.119587 - 0.368052i) q^{82} +(1.82050 + 0.386959i) q^{83} +(-0.974484 - 4.69474i) q^{84} +(0.507207 - 1.13920i) q^{85} +(-0.271144 - 1.27563i) q^{86} +(3.85743 + 12.0678i) q^{87} +(-6.38991 + 7.96427i) q^{88} +5.49170i q^{89} +(-1.18111 + 5.30687i) q^{90} +(-17.7844 + 12.9211i) q^{91} +(-0.727500 - 1.63399i) q^{92} +(-1.13481 - 11.3167i) q^{93} +(4.90755 + 4.41878i) q^{94} +(-0.606408 + 5.76958i) q^{95} +(-5.47606 + 2.40683i) q^{96} +(1.29476 + 1.43798i) q^{97} -13.8002 q^{98} +(9.93873 - 0.470752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27}+ \cdots + 35 q^{99}+O(q^{100}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.780898	+	0.867275i	0.552178	+	0.613256i	0.953026	−	0.302889i	$-0.0979510\pi$
$2$	0.780898	+	0.867275i	0.552178	+	0.613256i	−0.400848	+	0.916145i	$0.631284\pi$
$3$	0.189274	−	1.72168i	0.109278	−	0.994011i
$3$	0.189274	−	1.72168i	0.109278	−	0.994011i
$4$	0.0666926	−	0.634537i	0.0333463	−	0.317269i
$5$	−1.15400	−	1.03907i	−0.516084	−	0.464684i	0.369455	−	0.929249i	$-0.379544\pi$
$5$	−1.15400	−	1.03907i	−0.516084	−	0.464684i	−0.885539	+	0.464564i	$0.846211\pi$
$6$	1.64097	−	1.18030i	0.669924	−	0.481856i
$7$	1.76474	+	3.96367i	0.667009	+	1.49813i	0.856447	+	0.516235i	$0.172667\pi$
$7$	1.76474	+	3.96367i	0.667009	+	1.49813i	−0.189438	+	0.981893i	$0.560666\pi$
$8$	2.49070	−	1.80960i	0.880595	−	0.639790i
$9$	−2.92835	−	0.651738i	−0.976117	−	0.217246i
$10$		−	1.81224i		−	0.573080i
$11$	−3.19970	+	0.872887i	−0.964745	+	0.263185i
$11$	−3.19970	+	0.872887i	−0.964745	+	0.263185i
$12$	−1.07985	−	0.234925i	−0.311725	−	0.0678169i
$13$	1.05340	+	4.95585i	0.292160	+	1.37451i	0.842109	+	0.539307i	$0.181314\pi$
$13$	1.05340	+	4.95585i	0.292160	+	1.37451i	−0.549949	+	0.835198i	$0.685353\pi$
$14$	−2.05951	+	4.62574i	−0.550428	+	1.23628i
$15$	−2.00736	+	1.79015i	−0.518298	+	0.462214i
$16$	2.26622	+	0.481700i	0.566555	+	0.120425i
$17$	0.248154	+	0.763741i	0.0601863	+	0.185234i	0.976629	−	0.214931i	$-0.0689527\pi$
$17$	0.248154	+	0.763741i	0.0601863	+	0.185234i	−0.916443	+	0.400165i	$0.868953\pi$
$18$	−1.72151	−	3.04863i	−0.405763	−	0.718568i
$19$	−2.19592	−	3.02243i	−0.503779	−	0.693392i	0.479076	−	0.877773i	$-0.340972\pi$
$19$	−2.19592	−	3.02243i	−0.503779	−	0.693392i	−0.982855	+	0.184381i	$0.940972\pi$
$20$	−0.736289	+	0.662958i	−0.164639	+	0.148242i
$21$	7.15819	−	2.28809i	1.56204	−	0.499303i
$22$	−3.25567	−	2.09338i	−0.694111	−	0.446311i
$23$	2.42777	−	1.40167i	0.506225	−	0.292269i	−0.225055	−	0.974346i	$-0.572256\pi$
$23$	2.42777	−	1.40167i	0.506225	−	0.292269i	0.731281	+	0.682077i	$0.238923\pi$
$24$	−2.64412	−	4.63069i	−0.539729	−	0.945236i
$25$	−0.270585	−	2.57445i	−0.0541171	−	0.514889i
$26$	−3.47549	+	4.78360i	−0.681599	+	0.938141i
$27$	−1.67634	+	4.91832i	−0.322613	+	0.946531i
$28$	2.63279	−	0.855447i	0.497551	−	0.161664i
$29$	−6.68223	+	2.97512i	−1.24086	+	0.552466i	−0.918976	−	0.394313i	$-0.870983\pi$
$29$	−6.68223	+	2.97512i	−1.24086	+	0.552466i	−0.321883	+	0.946779i	$0.604316\pi$
$30$	−3.12009	−	0.343010i	−0.569648	−	0.0626248i
$31$	6.42298	−	1.36525i	1.15360	−	0.245205i	0.408884	−	0.912586i	$-0.365918\pi$
$31$	6.42298	−	1.36525i	1.15360	−	0.245205i	0.744717	+	0.667381i	$0.232585\pi$
$32$	−1.72675	−	2.99082i	−0.305250	−	0.528708i
$33$	0.897210	+	5.67407i	0.156184	+	0.987728i
$34$	−0.468590	+	0.811622i	−0.0803625	+	0.139192i
$35$	2.08201	−	6.40776i	0.351923	−	1.08311i
$36$	−0.608852	+	1.81468i	−0.101475	+	0.302447i
$37$	−3.70044	−	2.68853i	−0.608349	−	0.441991i	0.240483	−	0.970653i	$-0.422694\pi$
$37$	−3.70044	−	2.68853i	−0.608349	−	0.441991i	−0.848833	+	0.528662i	$0.822694\pi$
$38$	0.906484	−	4.26467i	0.147051	−	0.691821i
$39$	8.73176	−	0.875599i	1.39820	−	0.140208i
$40$	−4.75456	−	0.499724i	−0.751761	−	0.0790133i
$41$	−0.302935	−	0.134876i	−0.0473106	−	0.0210640i	0.382945	−	0.923771i	$-0.374910\pi$
$41$	−0.302935	−	0.134876i	−0.0473106	−	0.0210640i	−0.430256	+	0.902707i	$0.641577\pi$
$42$	7.57422	+	4.42135i	1.16873	+	0.682229i
$43$	−0.967761	−	0.558737i	−0.147582	−	0.0852066i	0.424391	−	0.905479i	$-0.360488\pi$
$43$	−0.967761	−	0.558737i	−0.147582	−	0.0852066i	−0.571973	+	0.820273i	$0.693822\pi$
$44$	0.340483	+	2.08854i	0.0513298	+	0.314860i
$45$	2.70212	+	3.79485i	0.402808	+	0.565704i
$46$	3.11148	+	1.01098i	0.458762	+	0.149061i
$47$	5.62759	−	0.591483i	0.820868	−	0.0862767i	0.315222	−	0.949018i	$-0.397921\pi$
$47$	5.62759	−	0.591483i	0.820868	−	0.0862767i	0.505646	+	0.862741i	$0.331254\pi$
$48$	1.25827	−	3.81053i	0.181616	−	0.550002i
$49$	−7.91248	+	8.78770i	−1.13035	+	1.25539i
$50$	2.02145	−	2.24505i	0.285877	−	0.317498i
$51$	1.36188	−	0.282686i	0.190702	−	0.0395839i
$52$	3.21493	−	0.337902i	0.445830	−	0.0468586i
$53$	−5.13255	−	1.66767i	−0.705010	−	0.229072i	−0.0654981	−	0.997853i	$-0.520864\pi$
$53$	−5.13255	−	1.66767i	−0.705010	−	0.229072i	−0.639512	+	0.768781i	$0.720864\pi$
$54$	−5.57459	+	2.38685i	−0.758606	+	0.324810i
$55$	4.59944	+	2.31739i	0.620188	+	0.312476i
$56$	11.5681	+	6.67884i	1.54585	+	0.892498i
$57$	−5.61928	+	3.20860i	−0.744291	+	0.424990i
$58$	−7.79839	−	3.47207i	−1.02398	−	0.455905i
$59$	6.97083	+	0.732664i	0.907525	+	0.0953847i	0.546777	−	0.837279i	$-0.315855\pi$
$59$	6.97083	+	0.732664i	0.907525	+	0.0953847i	0.360748	+	0.932663i	$0.382521\pi$
$60$	1.00204	+	1.39313i	0.129363	+	0.179853i
$61$	−0.842120	+	3.96186i	−0.107822	+	0.507265i	0.890781	+	0.454433i	$0.150158\pi$
$61$	−0.842120	+	3.96186i	−0.107822	+	0.507265i	−0.998603	+	0.0528318i	$0.983175\pi$
$62$	6.19973	+	4.50437i	0.787367	+	0.572056i
$63$	−2.58450	−	12.7572i	−0.325617	−	1.60725i
$64$	2.67734	−	8.24001i	0.334667	−	1.03000i
$65$	3.93383	−	6.81360i	0.487932	−	0.845123i
$66$	−4.22035	+	5.20899i	−0.519489	+	0.641183i
$67$	−5.22518	−	9.05028i	−0.638357	−	1.10567i	−0.985793	−	0.167964i	$-0.946281\pi$
$67$	−5.22518	−	9.05028i	−0.638357	−	1.10567i	0.347436	−	0.937704i	$-0.387052\pi$
$68$	0.501172	−	0.106527i	0.0607760	−	0.0129183i
$69$	−1.95372	−	4.44514i	−0.235200	−	0.535132i
$70$	7.18312	−	3.19813i	0.858548	−	0.382250i
$71$	4.20477	−	1.36621i	0.499014	−	0.162139i	−0.0486863	−	0.998814i	$-0.515503\pi$
$71$	4.20477	−	1.36621i	0.499014	−	0.162139i	0.547700	+	0.836675i	$0.315503\pi$
$72$	−8.47302	+	3.67585i	−0.998555	+	0.433204i
$73$	−1.44520	+	1.98915i	−0.169148	+	0.232812i	−0.885173	−	0.465263i	$-0.845960\pi$
$73$	−1.44520	+	1.98915i	−0.169148	+	0.232812i	0.716025	+	0.698075i	$0.245960\pi$
$74$	−0.557974	−	5.30877i	−0.0648632	−	0.617132i
$75$	−4.48358	−	0.0214156i	−0.517720	−	0.00247286i
$76$	−2.06429	+	1.19182i	−0.236791	+	0.136711i
$77$	−9.10648	−	11.1421i	−1.03778	−	1.26976i
$78$	7.57800	+	6.88908i	0.858039	+	0.780035i
$79$	0.476003	−	0.428595i	0.0535545	−	0.0482207i	−0.641919	−	0.766773i	$-0.721861\pi$
$79$	0.476003	−	0.428595i	0.0535545	−	0.0482207i	0.695473	+	0.718552i	$0.255195\pi$
$80$	−2.11470	−	2.91063i	−0.236431	−	0.325419i
$81$	8.15047	+	3.81704i	0.905608	+	0.424115i
$82$	−0.119587	−	0.368052i	−0.0132062	−	0.0406446i
$83$	1.82050	+	0.386959i	0.199826	+	0.0424742i	0.306737	−	0.951794i	$-0.400763\pi$
$83$	1.82050	+	0.386959i	0.199826	+	0.0424742i	−0.106911	+	0.994269i	$0.534096\pi$
$84$	−0.974484	−	4.69474i	−0.106325	−	0.512238i
$85$	0.507207	−	1.13920i	0.0550143	−	0.123564i
$86$	−0.271144	−	1.27563i	−0.0292382	−	0.137555i
$87$	3.85743	+	12.0678i	0.413560	+	1.29380i
$88$	−6.38991	+	7.96427i	−0.681167	+	0.848994i
$89$			5.49170i			0.582119i	0.956705	+	0.291060i	$0.0940078\pi$
$89$			5.49170i			0.582119i	−0.956705	+	0.291060i	$0.905992\pi$
$90$	−1.18111	+	5.30687i	−0.124499	+	0.559393i
$91$	−17.7844	+	12.9211i	−1.86431	+	1.35450i
$92$	−0.727500	−	1.63399i	−0.0758472	−	0.170356i
$93$	−1.13481	−	11.3167i	−0.117674	−	1.17349i
$94$	4.90755	+	4.41878i	0.506175	+	0.455762i
$95$	−0.606408	+	5.76958i	−0.0622161	+	0.591947i
$96$	−5.47606	+	2.40683i	−0.558898	+	0.245646i
$97$	1.29476	+	1.43798i	0.131463	+	0.146005i	0.805282	−	0.592892i	$-0.202014\pi$
$97$	1.29476	+	1.43798i	0.131463	+	0.146005i	−0.673819	+	0.738897i	$0.735347\pi$
$98$	−13.8002			−1.39403
$99$	9.93873	−	0.470752i	0.998880	−	0.0473124i
$100$	−1.65163			−0.165163
$101$	−8.89682	−	9.88092i	−0.885267	−	0.983188i	0.114681	−	0.993402i	$-0.463415\pi$
$101$	−8.89682	−	9.88092i	−0.885267	−	0.983188i	−0.999948	+	0.0102141i	$0.996749\pi$
$102$	1.30866	+	0.960380i	0.129577	+	0.0950918i
$103$	0.227332	−	2.16292i	0.0223997	−	0.213119i	−0.977597	−	0.210486i	$-0.932495\pi$
$103$	0.227332	−	2.16292i	0.0223997	−	0.213119i	0.999997	−	0.00263271i	$-0.000838018\pi$
$104$	11.5918	+	10.4373i	1.13667	+	1.02346i
$105$	−10.6380	−	4.79737i	−1.03817	−	0.468175i
$106$	−2.56167	−	5.75361i	−0.248812	−	0.558840i
$107$	4.92945	−	3.58146i	0.476548	−	0.346232i	−0.323440	−	0.946249i	$-0.604839\pi$
$107$	4.92945	−	3.58146i	0.476548	−	0.346232i	0.799988	+	0.600016i	$0.204839\pi$
$108$	3.00906	+	1.39172i	0.289547	+	0.133918i
$109$		−	8.21860i		−	0.787199i	−0.919282	−	0.393600i	$-0.871230\pi$
$109$		−	8.21860i		−	0.787199i	0.919282	−	0.393600i	$-0.128770\pi$
$110$	1.58188	+	5.79862i	0.150826	+	0.552877i
$111$	−5.32918	+	5.86210i	−0.505823	+	0.556406i
$112$	2.08999	+	9.83263i	0.197486	+	0.929097i
$113$	−2.23354	+	5.01661i	−0.210114	+	0.471923i	−0.987603	−	0.156973i	$-0.949826\pi$
$113$	−2.23354	+	5.01661i	−0.210114	+	0.471923i	0.777489	+	0.628896i	$0.216493\pi$
$114$	−7.17082	−	2.36787i	−0.671609	−	0.221771i
$115$	−4.25808	−	0.905082i	−0.397068	−	0.0843994i
$116$	1.44217	+	4.43855i	0.133902	+	0.412109i
$117$	0.145198	−	15.1990i	0.0134236	−	1.40515i
$118$	4.80809	+	6.61776i	0.442620	+	0.609214i
$119$	−2.58929	+	2.33141i	−0.237360	+	0.213720i
$120$	−1.76028	+	8.09123i	−0.160691	+	0.738625i
$121$	9.47614	−	5.58595i	0.861467	−	0.507813i
$122$	−4.09364	+	2.36346i	−0.370620	+	0.213978i
$123$	−0.289550	+	0.496029i	−0.0261079	+	0.0447254i
$124$	−0.437935	−	4.16667i	−0.0393277	−	0.374178i
$125$	−6.92650	+	9.53351i	−0.619525	+	0.852703i
$126$	9.04575	−	12.2035i	0.805859	−	1.08718i
$127$	4.26924	−	1.38716i	0.378834	−	0.123091i	−0.113409	−	0.993548i	$-0.536177\pi$
$127$	4.26924	−	1.38716i	0.378834	−	0.123091i	0.492243	+	0.870458i	$0.336177\pi$
$128$	2.92721	−	1.30328i	0.258731	−	0.115195i
$129$	−1.14514	+	1.56042i	−0.100824	+	0.137387i
$130$	8.98119	−	1.90901i	0.787702	−	0.167431i
$131$	3.28173	+	5.68413i	0.286726	+	0.496625i	0.973026	−	0.230694i	$-0.0740996\pi$
$131$	3.28173	+	5.68413i	0.286726	+	0.496625i	−0.686300	+	0.727319i	$0.740766\pi$
$132$	3.66024	−	0.190895i	0.318583	−	0.0166153i
$133$	8.10468	−	14.0377i	0.702765	−	1.21722i
$134$	3.76875	−	11.5990i	0.325570	−	1.00200i
$135$	7.04496	−	3.93391i	0.606334	−	0.338577i
$136$	2.00014	+	1.45319i	0.171511	+	0.124610i
$137$	−1.74887	+	8.22778i	−0.149416	+	0.702947i	0.838111	+	0.545499i	$0.183660\pi$
$137$	−1.74887	+	8.22778i	−0.149416	+	0.702947i	−0.987527	+	0.157448i	$0.949673\pi$
$138$	2.32951	−	5.16561i	0.198301	−	0.439726i
$139$	2.03763	+	0.214164i	0.172830	+	0.0181651i	0.190548	−	0.981678i	$-0.438974\pi$
$139$	2.03763	+	0.214164i	0.172830	+	0.0181651i	−0.0177183	+	0.999843i	$0.505640\pi$
$140$	−3.92711	−	1.74846i	−0.331901	−	0.147772i
$141$	0.0468132	−	9.80084i	0.00394239	−	0.825380i
$142$	4.46837	+	2.57982i	0.374978	+	0.216493i
$143$	−7.69645	−	14.9377i	−0.643610	−	1.24916i
$144$	−6.32235	−	2.88757i	−0.526862	−	0.240631i
$145$	10.8026	+	3.50999i	0.897111	+	0.291489i
$146$	−2.85369	+	0.299935i	−0.236173	+	0.0248228i
$147$	13.6320	+	15.2860i	1.12435	+	1.26077i
$148$	−1.95276	+	2.16876i	−0.160516	+	0.178271i
$149$	−1.05580	+	1.17258i	−0.0864944	+	0.0960618i	−0.784838	−	0.619701i	$-0.787254\pi$
$149$	−1.05580	+	1.17258i	−0.0864944	+	0.0960618i	0.698344	+	0.715762i	$0.253921\pi$
$150$	−3.48265	−	3.90522i	−0.284357	−	0.318860i
$151$	−10.0273	+	1.05391i	−0.816011	+	0.0857663i	−0.503333	−	0.864093i	$-0.667893\pi$
$151$	−10.0273	+	1.05391i	−0.816011	+	0.0857663i	−0.312679	+	0.949859i	$0.601226\pi$
$152$	−10.9388	−	3.55422i	−0.887250	−	0.288285i
$153$	−0.228924	−	2.39823i	−0.0185074	−	0.193886i
$154$	2.55207	−	16.5987i	0.205652	−	1.33756i
$155$	−8.83069	−	5.09840i	−0.709298	−	0.409514i
$156$	0.0267435	−	5.59903i	0.00214119	−	0.448281i
$157$	20.3184	+	9.04635i	1.62159	+	0.721977i	0.998202	−	0.0599372i	$-0.0190901\pi$
$157$	20.3184	+	9.04635i	1.62159	+	0.721977i	0.623386	+	0.781915i	$0.285757\pi$
$158$	0.743420	+	0.0781366i	0.0591433	+	0.00621621i
$159$	−3.84265	+	8.52096i	−0.304742	+	0.675756i
$160$	−1.11499	+	5.24562i	−0.0881477	+	0.414702i
$161$	9.84017	+	7.14930i	0.775514	+	0.563444i
$162$	3.05427	+	10.0494i	0.239966	+	0.789557i
$163$	0.588498	−	1.81121i	0.0460947	−	0.141865i	−0.925360	−	0.379089i	$-0.876237\pi$
$163$	0.588498	−	1.81121i	0.0460947	−	0.141865i	0.971455	+	0.237224i	$0.0762375\pi$
$164$	−0.105787	+	0.183229i	−0.00826059	+	0.0143078i
$165$	4.86035	−	7.48013i	0.378378	−	0.582327i
$166$	1.08602	+	1.88105i	0.0842917	+	0.145998i
$167$	14.7609	−	3.13752i	1.14223	−	0.242789i	0.402323	−	0.915498i	$-0.368203\pi$
$167$	14.7609	−	3.13752i	1.14223	−	0.242789i	0.739907	+	0.672709i	$0.234869\pi$
$168$	13.6884	−	18.6524i	1.05608	−	1.43906i
$169$	−11.5747	+	5.15340i	−0.890363	+	0.396415i
$170$	1.38408	−	0.449715i	0.106154	−	0.0344916i
$171$	4.46060	+	10.2819i	0.341110	+	0.786276i
$172$	−0.419082	+	0.576817i	−0.0319547	+	0.0439819i
$173$	2.29437	+	21.8295i	0.174438	+	1.65967i	0.635353	+	0.772222i	$0.280855\pi$
$173$	2.29437	+	21.8295i	0.174438	+	1.65967i	−0.460915	+	0.887444i	$0.652479\pi$
$174$	−7.45382	+	12.7691i	−0.565072	+	0.968026i
$175$	9.72675	−	5.61574i	0.735273	−	0.424510i
$176$	−7.67169	+	0.436859i	−0.578275	+	0.0329295i
$177$	2.58081	−	11.8629i	0.193986	−	0.891667i
$178$	−4.76282	+	4.28846i	−0.356988	+	0.321434i
$179$	15.1400	+	20.8384i	1.13162	+	1.55754i	0.784962	+	0.619544i	$0.212682\pi$
$179$	15.1400	+	20.8384i	1.13162	+	1.55754i	0.346654	+	0.937993i	$0.387318\pi$
$180$	2.58819	−	1.46151i	0.192912	−	0.108934i
$181$	3.96028	+	12.1885i	0.294365	+	0.905964i	0.983434	+	0.181267i	$0.0580199\pi$
$181$	3.96028	+	12.1885i	0.294365	+	0.905964i	−0.689068	+	0.724696i	$0.741980\pi$
$182$	−25.0940	−	5.33389i	−1.86009	−	0.395374i
$183$	6.66166	+	2.19974i	0.492444	+	0.162609i
$184$	3.51038	−	7.88444i	0.258789	−	0.581249i
$185$	1.47675	+	6.94757i	0.108573	+	0.510795i
$186$	8.92852	−	9.82138i	0.654671	−	0.720139i
$187$	−1.46068	−	2.22713i	−0.106815	−	0.162864i
$188$		−	3.61036i		−	0.263313i
$189$	−22.4529	+	2.03508i	−1.63321	+	0.148030i
$190$	−5.47736	+	3.97953i	−0.397369	+	0.288706i
$191$	−0.394348	−	0.885721i	−0.0285340	−	0.0640885i	0.898716	−	0.438531i	$-0.144501\pi$
$191$	−0.394348	−	0.885721i	−0.0285340	−	0.0640885i	−0.927250	+	0.374442i	$0.877834\pi$
$192$	−13.6799	−	6.16914i	−0.987261	−	0.445219i
$193$	−16.2667	−	14.6466i	−1.17090	−	1.05428i	−0.997588	−	0.0694165i	$-0.977886\pi$
$193$	−16.2667	−	14.6466i	−1.17090	−	1.05428i	−0.173313	−	0.984867i	$-0.555447\pi$
$194$	−0.236046	+	2.24583i	−0.0169472	+	0.161241i
$195$	−10.9863	−	8.06243i	−0.786742	−	0.577363i
$196$	5.04842	+	5.60684i	0.360602	+	0.400489i
$197$	−0.389682			−0.0277637			−0.0138818	−	0.999904i	$-0.504419\pi$
$197$	−0.389682			−0.0277637			−0.0138818	+	0.999904i	$0.504419\pi$
$198$	8.16941	+	8.25200i	0.580574	+	0.586444i
$199$	−18.7233			−1.32726			−0.663630	−	0.748061i	$-0.730985\pi$
$199$	−18.7233			−1.32726			−0.663630	+	0.748061i	$0.730985\pi$
$200$	−5.33266	−	5.92252i	−0.377076	−	0.418785i
$201$	−16.5707	+	7.28310i	−1.16880	+	0.513710i
$202$	1.62197	−	15.4320i	0.114121	−	1.08579i
$203$	−23.5848	−	21.2359i	−1.65533	−	1.49047i
$204$	−0.0885470	−	0.883020i	−0.00619953	−	0.0618238i
$205$	0.209443	+	0.470416i	0.0146281	+	0.0328553i
$206$	2.05337	−	1.49186i	0.143065	−	0.103943i
$207$	−8.02289	+	2.52232i	−0.557629	+	0.175313i
$208$			11.7385i			0.813917i
$209$	9.66452	+	7.75406i	0.668509	+	0.536360i
$210$	−4.14658	−	12.9724i	−0.286141	−	0.895177i
$211$	5.03305	+	23.6787i	0.346490	+	1.63011i	0.714042	+	0.700103i	$0.246863\pi$
$211$	5.03305	+	23.6787i	0.346490	+	1.63011i	−0.367552	+	0.930003i	$0.619804\pi$
$212$	−1.40050	+	3.14558i	−0.0961868	+	0.216039i
$213$	−1.55632	−	7.49784i	−0.106637	−	0.513744i
$214$	6.95550	+	1.47844i	0.475468	+	0.101064i
$215$	0.536231	+	1.65035i	0.0365706	+	0.112553i
$216$	4.72491	+	15.2836i	0.321490	+	1.03991i
$217$	16.7463	+	23.0493i	1.13681	+	1.56469i
$218$	7.12779	−	6.41789i	0.482755	−	0.434674i
$219$	3.15113	+	2.86466i	0.212934	+	0.193576i
$220$	1.77722	−	2.76396i	0.119820	−	0.186346i
$221$	−3.52358	+	2.03434i	−0.237022	+	0.136844i
$222$	−9.24560	−	0.0441611i	−0.620524	−	0.00296390i
$223$	−2.64226	−	25.1394i	−0.176939	−	1.68346i	−0.618153	−	0.786058i	$-0.712119\pi$
$223$	−2.64226	−	25.1394i	−0.176939	−	1.68346i	0.441215	−	0.897402i	$-0.354548\pi$
$224$	8.80737	−	12.1223i	0.588467	−	0.809956i
$225$	−0.885497	+	7.71523i	−0.0590332	+	0.514349i
$226$	−6.09495	+	1.98037i	−0.405430	+	0.131732i
$227$	13.9031	−	6.19004i	0.922778	−	0.410847i	0.110339	−	0.993894i	$-0.464806\pi$
$227$	13.9031	−	6.19004i	0.922778	−	0.410847i	0.812439	+	0.583047i	$0.198140\pi$
$228$	1.66121	+	3.77963i	0.110017	+	0.250312i
$229$	−7.66099	+	1.62839i	−0.506252	+	0.107607i	−0.453956	−	0.891024i	$-0.649988\pi$
$229$	−7.66099	+	1.62839i	−0.506252	+	0.107607i	−0.0522967	+	0.998632i	$0.516654\pi$
$230$	−2.54017	−	4.39970i	−0.167494	−	0.290108i
$231$	−20.9068	+	13.5695i	−1.37557	+	0.892808i
$232$	−11.2597	+	19.5023i	−0.739232	+	1.28039i
$233$	−2.52277	+	7.76427i	−0.165272	+	0.508655i	−0.999056	−	0.0434357i	$-0.986170\pi$
$233$	−2.52277	+	7.76427i	−0.165272	+	0.508655i	0.833784	+	0.552090i	$0.186170\pi$
$234$	13.2951	−	11.7429i	0.869128	−	0.767661i
$235$	−7.10882	−	5.16486i	−0.463728	−	0.336918i
$236$	0.929805	−	4.37439i	0.0605252	−	0.284749i
$237$	−0.647808	−	0.900646i	−0.0420796	−	0.0585033i
$238$	−4.04394	−	0.425035i	−0.262130	−	0.0275510i
$239$	17.0647	+	7.59768i	1.10382	+	0.491453i	0.876030	−	0.482257i	$-0.160183\pi$
$239$	17.0647	+	7.59768i	1.10382	+	0.491453i	0.227792	+	0.973710i	$0.426849\pi$
$240$	−5.41143	+	3.08992i	−0.349306	+	0.199454i
$241$	1.06399	+	0.614295i	0.0685377	+	0.0395702i	0.533877	−	0.845562i	$-0.320734\pi$
$241$	1.06399	+	0.614295i	0.0685377	+	0.0395702i	−0.465340	+	0.885132i	$0.654068\pi$
$242$	12.2444	+	3.85636i	0.787103	+	0.247896i
$243$	8.11438	−	13.3100i	0.520538	−	0.853839i
$244$	2.45779	+	0.798584i	0.157344	+	0.0511241i
$245$	18.2620	−	1.91941i	1.16672	−	0.122627i
$246$	−0.656303	+	0.136228i	−0.0418443	+	0.00868560i
$247$	12.6655	−	14.0665i	0.805887	−	0.895029i
$248$	13.5272	−	15.0234i	0.858975	−	0.953989i
$249$	1.01079	−	3.06107i	0.0640563	−	0.193987i
$250$	−13.6771	+	1.43752i	−0.865014	+	0.0909166i
$251$	−24.9635	−	8.11113i	−1.57568	−	0.511970i	−0.614742	−	0.788728i	$-0.710740\pi$
$251$	−24.9635	−	8.11113i	−1.57568	−	0.511970i	−0.960940	+	0.276759i	$0.910740\pi$
$252$	−8.26727	+	0.789155i	−0.520789	+	0.0497121i
$253$	−6.54463	+	6.60410i	−0.411457	+	0.415196i
$254$	4.53689	+	2.61937i	0.284670	+	0.164354i
$255$	−1.86534	−	1.08887i	−0.116812	−	0.0681876i
$256$	−12.4139	−	5.52701i	−0.775866	−	0.345438i
$257$	−29.8019	−	3.13231i	−1.85899	−	0.195388i	−0.892320	−	0.451403i	$-0.850924\pi$
$257$	−29.8019	−	3.13231i	−1.85899	−	0.195388i	−0.966673	+	0.256015i	$0.917590\pi$
$258$	−2.24755	+	0.225378i	−0.139926	+	0.0140314i
$259$	4.12613	−	19.4119i	0.256385	−	1.20620i
$260$	−4.06113	−	2.95058i	−0.251860	−	0.182987i
$261$	21.5069	−	4.35713i	1.33125	−	0.269700i
$262$	−2.36700	+	7.28489i	−0.146234	+	0.450062i
$263$	−1.05394	+	1.82548i	−0.0649888	+	0.112564i	−0.896689	−	0.442661i	$-0.854034\pi$
$263$	−1.05394	+	1.82548i	−0.0649888	+	0.112564i	0.831700	+	0.555225i	$0.187368\pi$
$264$	12.5025	+	12.5088i	0.769473	+	0.769863i
$265$	4.19015	+	7.25755i	0.257399	+	0.445828i
$266$	18.5035	−	3.93304i	1.13452	−	0.241150i
$267$	9.45494	+	1.03944i	0.578633	+	0.0636125i
$268$	−6.09122	+	2.71199i	−0.372081	+	0.165661i
$269$	26.8186	−	8.71391i	1.63516	−	0.531296i	0.659712	−	0.751519i	$-0.270678\pi$
$269$	26.8186	−	8.71391i	1.63516	−	0.531296i	0.975450	+	0.220222i	$0.0706783\pi$
$270$	8.91317	+	3.03794i	0.542438	+	0.184883i
$271$	−6.37949	+	8.78061i	−0.387526	+	0.533384i	−0.957559	−	0.288238i	$-0.906931\pi$
$271$	−6.37949	+	8.78061i	−0.387526	+	0.533384i	0.570032	+	0.821622i	$0.306931\pi$
$272$	0.194479	+	1.85034i	0.0117920	+	0.112193i
$273$	18.8799	+	33.0646i	1.14266	+	2.00116i
$274$	−8.50144	+	4.90831i	−0.513590	+	0.296522i
$275$	3.11299	+	8.00126i	0.187720	+	0.482494i
$276$	−2.95091	+	0.943249i	−0.177624	+	0.0567769i
$277$	9.54318	−	8.59272i	0.573394	−	0.516287i	−0.330634	−	0.943759i	$-0.607263\pi$
$277$	9.54318	−	8.59272i	0.573394	−	0.516287i	0.904028	+	0.427472i	$0.140596\pi$
$278$	1.40544	+	1.93443i	0.0842929	+	0.116019i
$279$	−19.6985	−	0.188182i	−1.17932	−	0.0112662i
$280$	−6.40982	−	19.7274i	−0.383060	−	1.17894i
$281$	−10.3811	−	2.20656i	−0.619283	−	0.131633i	−0.112422	−	0.993661i	$-0.535861\pi$
$281$	−10.3811	−	2.20656i	−0.619283	−	0.131633i	−0.506861	+	0.862028i	$0.669194\pi$
$282$	8.53658	−	7.61286i	0.508346	−	0.453339i
$283$	−9.05356	+	20.3346i	−0.538179	+	1.20877i	0.415954	+	0.909385i	$0.363448\pi$
$283$	−9.05356	+	20.3346i	−0.538179	+	1.20877i	−0.954133	+	0.299383i	$0.903219\pi$
$284$	−0.586486	−	2.75920i	−0.0348015	−	0.163728i
$285$	9.81859	+	2.13607i	0.581603	+	0.126530i
$286$	6.94497	−	18.3398i	0.410665	−	1.08445i
$287$		−	1.43876i		−	0.0849272i
$288$	3.10730	+	9.88357i	0.183100	+	0.582395i
$289$	13.2316	−	9.61330i	0.778328	−	0.565488i
$290$	5.39163	+	12.1098i	0.316608	+	0.711112i
$291$	2.72081	−	1.95699i	0.159496	−	0.114721i
$292$	1.16580	+	1.04969i	0.0682235	+	0.0614287i
$293$	2.30766	−	21.9559i	0.134815	−	1.28268i	−0.692697	−	0.721229i	$-0.743578\pi$
$293$	2.30766	−	21.9559i	0.134815	−	1.28268i	0.827512	−	0.561448i	$-0.189756\pi$
$294$	−2.61202	+	23.7595i	−0.152336	+	1.38568i
$295$	−7.28305	−	8.08865i	−0.424036	−	0.470939i
$296$	−14.0818			−0.818491
$297$	1.07066	−	17.2004i	0.0621261	−	0.998068i
$298$	−1.84142			−0.106671
$299$	9.50390	+	10.5551i	0.549625	+	0.610420i
$300$	−0.312611	+	2.84357i	−0.0180486	+	0.164174i
$301$	0.506803	−	4.82191i	0.0292117	−	0.277930i
$302$	−8.74434	−	7.87344i	−0.503180	−	0.453066i
$303$	−18.6957	+	13.4473i	−1.07404	+	0.772525i
$304$	−3.52054	−	7.90726i	−0.201917	−	0.453512i
$305$	5.08844	−	3.69697i	0.291363	−	0.211688i
$306$	1.90116	−	2.07131i	0.108682	−	0.118409i
$307$		−	12.8256i		−	0.731997i	−0.930616	−	0.365998i	$-0.880728\pi$
$307$		−	12.8256i		−	0.731997i	0.930616	−	0.365998i	$-0.119272\pi$
$308$	−7.67744	+	5.03530i	−0.437463	+	0.286913i
$309$	−3.68082	−	0.800778i	−0.209395	−	0.0455546i
$310$	−2.47415	−	11.6400i	−0.140522	−	0.661106i
$311$	2.73879	−	6.15143i	0.155303	−	0.348816i	−0.819091	−	0.573663i	$-0.805522\pi$
$311$	2.73879	−	6.15143i	0.155303	−	0.348816i	0.974394	+	0.224848i	$0.0721885\pi$
$312$	20.1637	−	17.9818i	1.14154	−	1.01802i
$313$	8.66114	+	1.84098i	0.489557	+	0.104059i	0.446075	−	0.894996i	$-0.352822\pi$
$313$	8.66114	+	1.84098i	0.489557	+	0.104059i	0.0434821	+	0.999054i	$0.486155\pi$
$314$	8.02095	+	24.6859i	0.452648	+	1.39311i
$315$	−10.2730	+	17.4072i	−0.578820	+	0.980787i
$316$	−0.240214	−	0.330626i	−0.0135131	−	0.0185992i
$317$	12.7373	−	11.4687i	0.715399	−	0.644148i	−0.228819	−	0.973469i	$-0.573486\pi$
$317$	12.7373	−	11.4687i	0.715399	−	0.644148i	0.944218	+	0.329321i	$0.106820\pi$
$318$	−10.3907	+	3.32137i	−0.582683	+	0.186253i
$319$	18.7842	−	15.3523i	1.05171	−	0.859565i
$320$	−11.6516	+	6.72703i	−0.651342	+	0.376052i
$321$	−5.23310	−	9.16480i	−0.292083	−	0.511529i
$322$	1.48376	+	14.1170i	0.0826865	+	0.786710i
$323$	1.76342	−	2.42714i	0.0981194	−	0.135050i
$324$	2.96563	−	4.91721i	0.164757	−	0.273178i
$325$	12.4735	−	4.05290i	0.691908	−	0.224814i
$326$	2.03037	−	0.903981i	0.112452	−	0.0500669i
$327$	−14.1498	−	1.55557i	−0.782485	−	0.0860232i
$328$	−0.998592	+	0.212257i	−0.0551380	+	0.0117199i
$329$	12.2757	+	21.2621i	0.676780	+	1.17222i
$330$	10.2828	−	1.62596i	0.566047	−	0.0895061i
$331$	8.18032	−	14.1687i	0.449631	−	0.778783i	−0.548731	−	0.835999i	$-0.684889\pi$
$331$	8.18032	−	14.1687i	0.449631	−	0.778783i	0.998362	+	0.0572156i	$0.0182222\pi$
$332$	0.366953	−	1.12937i	0.0201392	−	0.0619820i
$333$	9.08398	+	10.2847i	0.497799	+	0.563597i
$334$	14.2478	+	10.3516i	0.779606	+	0.566417i
$335$	−3.37398	+	15.8733i	−0.184340	+	0.867252i
$336$	17.3242	−	1.73723i	0.945113	−	0.0947735i
$337$	−13.4563	−	1.41431i	−0.733012	−	0.0770426i	−0.269334	−	0.963047i	$-0.586804\pi$
$337$	−13.4563	−	1.41431i	−0.733012	−	0.0770426i	−0.463677	+	0.886004i	$0.653470\pi$
$338$	−13.5081	−	6.01419i	−0.734743	−	0.327129i
$339$	8.21424	+	4.79495i	0.446136	+	0.260426i
$340$	−0.689041	−	0.397818i	−0.0373685	−	0.0215747i
$341$	−19.3599	+	9.97491i	−1.04840	+	0.540172i
$342$	−5.43396	+	11.8977i	−0.293835	+	0.643352i
$343$	−19.9101	−	6.46918i	−1.07504	−	0.349303i
$344$	−3.42149	+	0.359613i	−0.184474	+	0.0193890i
$345$	−2.36420	+	7.15973i	−0.127285	+	0.385467i
$346$	−17.1405	+	19.0365i	−0.921480	+	1.02341i
$347$	12.8446	−	14.2653i	0.689533	−	0.765804i	−0.292140	−	0.956375i	$-0.594367\pi$
$347$	12.8446	−	14.2653i	0.689533	−	0.765804i	0.981673	+	0.190571i	$0.0610341\pi$
$348$	7.91471	−	1.64285i	0.424273	−	0.0880661i
$349$	−9.72281	+	1.02191i	−0.520450	+	0.0547015i	−0.361112	−	0.932522i	$-0.617603\pi$
$349$	−9.72281	+	1.02191i	−0.520450	+	0.0547015i	−0.159338	+	0.987224i	$0.550936\pi$
$350$	12.4660	+	4.05045i	0.666335	+	0.216506i
$351$	−26.1403	−	3.12676i	−1.39527	−	0.166894i
$352$	8.13574	+	8.06247i	0.433636	+	0.429731i
$353$	−14.0240	−	8.09678i	−0.746424	−	0.430948i	0.0779763	−	0.996955i	$-0.475154\pi$
$353$	−14.0240	−	8.09678i	−0.746424	−	0.430948i	−0.824400	+	0.566007i	$0.808487\pi$
$354$	12.3037	−	7.02540i	0.653934	−	0.373396i
$355$	−6.27188	−	2.79242i	−0.332877	−	0.148206i
$356$	3.48469	+	0.366256i	0.184688	+	0.0194115i
$357$	3.52385	+	4.89920i	0.186502	+	0.259293i
$358$	−6.24985	+	29.4032i	−0.330315	+	1.55401i
$359$	−9.80679	−	7.12505i	−0.517583	−	0.376046i	0.298110	−	0.954532i	$-0.403644\pi$
$359$	−9.80679	−	7.12505i	−0.517583	−	0.376046i	−0.815692	+	0.578486i	$0.803644\pi$
$360$	13.5973	+	4.56209i	0.716642	+	0.240443i
$361$	1.55833	−	4.79605i	0.0820175	−	0.252424i
$362$	−7.47820	+	12.9526i	−0.393045	+	0.680775i
$363$	−7.82362	−	17.3721i	−0.410633	−	0.911801i
$364$	7.01285	+	12.1466i	0.367573	+	0.636655i
$365$	3.73461	−	0.793817i	0.195479	−	0.0415503i
$366$	3.29430	+	7.49526i	0.172196	+	0.391784i
$367$	−0.799295	+	0.355869i	−0.0417228	+	0.0185762i	−0.427492	−	0.904019i	$-0.640603\pi$
$367$	−0.799295	+	0.355869i	−0.0417228	+	0.0185762i	0.385769	+	0.922595i	$0.373936\pi$
$368$	6.17705	−	2.00705i	0.322001	−	0.104624i
$369$	0.799198	+	0.592398i	0.0416046	+	0.0308390i
$370$	−4.87226	+	6.70609i	−0.253297	+	0.348633i
$371$	−2.44754	−	23.2868i	−0.127070	−	1.20899i
$372$	−7.25656	−	0.0346606i	−0.376235	−	0.00179707i
$373$	−8.39907	+	4.84920i	−0.434887	+	0.251082i	−0.701427	−	0.712742i	$-0.747453\pi$
$373$	−8.39907	+	4.84920i	−0.434887	+	0.251082i	0.266539	+	0.963824i	$0.414120\pi$
$374$	0.790893	−	3.00597i	0.0408961	−	0.155435i
$375$	15.1026	+	13.7297i	0.779897	+	0.708996i
$376$	12.9463	−	11.6569i	0.667653	−	0.601158i
$377$	−21.7833	−	29.9822i	−1.12190	−	1.54416i
$378$	−19.2984	−	17.8837i	−0.992603	−	0.919837i
$379$	−6.50606	−	20.0236i	−0.334194	−	1.02854i	−0.967118	−	0.254329i	$-0.918145\pi$
$379$	−6.50606	−	20.0236i	−0.334194	−	1.02854i	0.632924	−	0.774214i	$-0.281855\pi$
$380$	3.62057	+	0.769577i	0.185732	+	0.0394785i
$381$	−1.58019	−	7.61281i	−0.0809554	−	0.390016i
$382$	0.460218	−	1.03367i	0.0235468	−	0.0528869i
$383$	5.23594	+	24.6332i	0.267544	+	1.25870i	0.882567	+	0.470187i	$0.155813\pi$
$383$	5.23594	+	24.6332i	0.267544	+	1.25870i	−0.615023	+	0.788509i	$0.710853\pi$
$384$	−1.68978	−	5.28639i	−0.0862313	−	0.269770i
$385$	−1.06855	+	22.3203i	−0.0544582	+	1.13755i
$386$		−	25.5452i		−	1.30021i
$387$	2.46979	+	2.26690i	0.125547	+	0.115233i
$388$	0.998804	−	0.725673i	0.0507066	−	0.0368405i
$389$	−13.7990	−	30.9930i	−0.699636	−	1.57141i	−0.815903	−	0.578189i	$-0.803759\pi$
$389$	−13.7990	−	30.9930i	−0.699636	−	1.57141i	0.116267	−	0.993218i	$-0.462907\pi$
$390$	−1.58679	−	15.8240i	−0.0803504	−	0.801281i
$391$	1.67298	+	1.50636i	0.0846061	+	0.0761797i
$392$	−3.80540	+	36.2059i	−0.192202	+	1.82868i
$393$	10.4074	−	4.57423i	0.524983	−	0.230739i
$394$	−0.304302	−	0.337961i	−0.0153305	−	0.0170262i
$395$	−0.994646			−0.0500461
$396$	0.364130	−	6.33789i	0.0182982	−	0.318491i
$397$	9.40670			0.472109			0.236054	−	0.971740i	$-0.424146\pi$
$397$	9.40670			0.472109			0.236054	+	0.971740i	$0.424146\pi$
$398$	−14.6210	−	16.2383i	−0.732885	−	0.813951i
$399$	−22.6344	−	16.6106i	−1.13314	−	0.831571i
$400$	0.626905	−	5.96460i	0.0313453	−	0.298230i
$401$	15.3093	+	13.7845i	0.764508	+	0.688366i	0.956078	−	0.293113i	$-0.0946912\pi$
$401$	15.3093	+	13.7845i	0.764508	+	0.688366i	−0.191570	+	0.981479i	$0.561358\pi$
$402$	−19.2564	−	8.68396i	−0.960424	−	0.433117i
$403$	13.5319	+	30.3932i	0.674073	+	1.51399i
$404$	−6.86317	+	4.98638i	−0.341455	+	0.248082i
$405$	−5.43949	−	12.8737i	−0.270290	−	0.639701i
$406$		−	37.0376i		−	1.83814i
$407$	14.1871	+	5.37241i	0.703228	+	0.266301i
$408$	2.88050	−	3.16855i	0.142606	−	0.156867i
$409$	−3.90107	−	18.3531i	−0.192896	−	0.907503i	−0.962983	−	0.269564i	$-0.913120\pi$
$409$	−3.90107	−	18.3531i	−0.192896	−	0.907503i	0.770087	−	0.637939i	$-0.220213\pi$
$410$	−0.244427	+	0.548992i	−0.0120714	+	0.0271128i
$411$	13.8346	+	4.56829i	0.682409	+	0.225337i
$412$	−1.35729	−	0.288501i	−0.0668690	−	0.0142134i
$413$	9.39767	+	28.9231i	0.462429	+	1.42321i
$414$	−8.45260	−	4.98838i	−0.415423	−	0.245165i
$415$	−1.69878	−	2.33817i	−0.0833897	−	0.114776i
$416$	13.0031	−	11.7081i	0.637530	−	0.574035i
$417$	0.754392	−	3.46761i	0.0369427	−	0.169810i
$418$	0.822101	+	14.4369i	0.0402103	+	0.706133i
$419$	−32.3807	+	18.6950i	−1.58190	+	0.913310i	−0.587318	+	0.809356i	$0.699816\pi$
$419$	−32.3807	+	18.6950i	−1.58190	+	0.913310i	−0.994582	+	0.103954i	$0.966850\pi$
$420$	−3.75359	+	6.43028i	−0.183156	+	0.313765i
$421$	2.82398	+	26.8684i	0.137633	+	1.30949i	0.817405	+	0.576063i	$0.195412\pi$
$421$	2.82398	+	26.8684i	0.137633	+	1.30949i	−0.679773	+	0.733423i	$0.737922\pi$
$422$	−16.6056	+	22.8557i	−0.808348	+	1.11260i
$423$	−16.8650	−	1.93564i	−0.820006	−	0.0941142i
$424$	−15.8014	+	5.13420i	−0.767386	+	0.249339i
$425$	1.89906	−	0.845517i	0.0921181	−	0.0410136i
$426$	5.28736	−	7.20481i	0.256173	−	0.349074i
$427$	−17.1897	+	3.65377i	−0.831866	+	0.176819i
$428$	−1.94381	−	3.36678i	−0.0939576	−	0.162739i
$429$	−27.1747	+	10.4235i	−1.31201	+	0.503251i
$430$	−1.01256	+	1.75381i	−0.0488302	+	0.0845764i
$431$	−8.97519	+	27.6228i	−0.432320	+	1.33054i	0.463489	+	0.886103i	$0.346597\pi$
$431$	−8.97519	+	27.6228i	−0.432320	+	1.33054i	−0.895808	+	0.444441i	$0.853403\pi$
$432$	−6.16812	+	10.3385i	−0.296764	+	0.497411i
$433$	16.3991	+	11.9146i	0.788089	+	0.572580i	0.907396	−	0.420277i	$-0.138067\pi$
$433$	16.3991	+	11.9146i	0.788089	+	0.572580i	−0.119307	+	0.992857i	$0.538067\pi$
$434$	−6.91293	+	32.5228i	−0.331831	+	1.56114i
$435$	8.08774	−	17.9343i	0.387777	−	0.859885i
$436$	−5.21501	−	0.548120i	−0.249754	−	0.0262502i
$437$	−9.56765	−	4.25979i	−0.457683	−	0.203774i
$438$	−0.0237385	+	4.96991i	−0.00113427	+	0.237471i
$439$	24.6512	+	14.2324i	1.17654	+	0.679273i	0.955211	−	0.295927i	$-0.0956285\pi$
$439$	24.6512	+	14.2324i	1.17654	+	0.679273i	0.221325	+	0.975200i	$0.428962\pi$
$440$	15.6493	−	2.55122i	0.746053	−	0.121625i
$441$	28.8978	−	20.5766i	1.37609	−	0.979838i
$442$	−4.51589	−	1.46730i	−0.214799	−	0.0697924i
$443$	−0.349328	+	0.0367158i	−0.0165971	+	0.00174442i	−0.112823	−	0.993615i	$-0.535989\pi$
$443$	−0.349328	+	0.0367158i	−0.0165971	+	0.00174442i	0.0962263	+	0.995359i	$0.469323\pi$
$444$	3.36431	+	3.77252i	0.159663	+	0.179036i
$445$	5.70624	−	6.33742i	0.270502	−	0.300423i
$446$	19.7394	−	21.9229i	0.934690	−	1.03808i
$447$	1.81898	+	2.03969i	0.0860346	+	0.0964738i
$448$	37.3855	−	3.92937i	1.76630	−	0.185645i
$449$	−10.7675	−	3.49858i	−0.508151	−	0.165108i	0.0437100	−	0.999044i	$-0.486082\pi$
$449$	−10.7675	−	3.49858i	−0.508151	−	0.165108i	−0.551861	+	0.833936i	$0.686082\pi$
$450$	−7.38271	+	5.25684i	−0.348024	+	0.247810i
$451$	1.08703	+	0.167133i	0.0511864	+	0.00786997i
$452$	3.03427	+	1.75184i	0.142720	+	0.0823994i
$453$	−0.0834125	+	17.4633i	−0.00391906	+	0.820497i
$454$	16.2253	+	7.22398i	0.761493	+	0.339038i
$455$	33.9491	+	3.56819i	1.59156	+	0.167279i
$456$	−8.18964	+	18.1603i	−0.383515	+	0.850434i
$457$	1.73926	−	8.18257i	0.0813591	−	0.382764i	−0.918563	−	0.395275i	$-0.870649\pi$
$457$	1.73926	−	8.18257i	0.0813591	−	0.382764i	0.999922	+	0.0125110i	$0.00398248\pi$
$458$	−7.39471	−	5.37257i	−0.345532	−	0.251044i
$459$	−4.17231	−	0.0597902i	−0.194747	−	0.00279077i
$460$	−0.858291	+	2.64155i	−0.0400180	+	0.123163i
$461$	6.38016	−	11.0508i	0.297153	−	0.514685i	−0.678330	−	0.734757i	$-0.737296\pi$
$461$	6.38016	−	11.0508i	0.297153	−	0.514685i	0.975484	+	0.220072i	$0.0706294\pi$
$462$	−28.0946	−	7.53555i	−1.30708	−	0.350585i
$463$	11.0509	+	19.1407i	0.513579	+	0.889544i	0.999876	+	0.0157509i	$0.00501388\pi$
$463$	11.0509	+	19.1407i	0.513579	+	0.889544i	−0.486297	+	0.873793i	$0.661653\pi$
$464$	−16.5765	+	3.52345i	−0.769546	+	0.163572i
$465$	−10.4492	+	14.2386i	−0.484571	+	0.660300i
$466$	−8.70378	+	3.87517i	−0.403195	+	0.179514i
$467$	7.72240	−	2.50916i	0.357350	−	0.116110i	−0.124840	−	0.992177i	$-0.539842\pi$
$467$	7.72240	−	2.50916i	0.357350	−	0.116110i	0.482190	+	0.876067i	$0.339842\pi$
$468$	−9.63466	−	1.10579i	−0.445362	−	0.0511154i
$469$	26.6513	−	36.6823i	1.23064	−	1.69383i
$470$	−1.07191	−	10.1985i	−0.0494435	−	0.470423i
$471$	19.4207	−	33.2696i	0.894857	−	1.53298i
$472$	18.6881	−	10.7896i	0.860188	−	0.496630i
$473$	3.58426	+	0.943044i	0.164804	+	0.0433612i
$474$	0.275236	−	1.26514i	0.0126420	−	0.0581098i
$475$	−7.18689	+	6.47111i	−0.329757	+	0.296915i
$476$	1.30668	+	1.79849i	0.0598915	+	0.0824336i
$477$	13.9430	+	8.22860i	0.638407	+	0.376762i
$478$	6.73649	+	20.7328i	0.308120	+	0.948295i
$479$	−33.6876	−	7.16053i	−1.53923	−	0.327173i	−0.641290	−	0.767298i	$-0.721601\pi$
$479$	−33.6876	−	7.16053i	−1.53923	−	0.327173i	−0.897936	+	0.440125i	$0.854934\pi$
$480$	8.82022	+	2.91251i	0.402586	+	0.132937i
$481$	9.42591	−	21.1709i	0.429784	−	0.965312i
$482$	0.298105	+	1.40247i	0.0135783	+	0.0638809i
$483$	14.1713	−	15.5884i	0.644816	−	0.709298i
$484$	−2.91251	−	6.38551i	−0.132387	−	0.290250i
$485$		−	3.00477i		−	0.136440i
$486$	17.8800	−	3.35637i	0.811051	−	0.152248i
$487$	−13.5062	+	9.81282i	−0.612024	+	0.444661i	−0.850126	−	0.526579i	$-0.823475\pi$
$487$	−13.5062	+	9.81282i	−0.612024	+	0.444661i	0.238103	+	0.971240i	$0.423475\pi$
$488$	5.07191	+	11.3917i	0.229595	+	0.515678i
$489$	−3.00693	−	1.35602i	−0.135978	−	0.0613213i
$490$	15.9254	+	14.3393i	0.719437	+	0.647784i
$491$	1.79489	−	17.0772i	0.0810023	−	0.770685i	−0.876333	−	0.481706i	$-0.840017\pi$
$491$	1.79489	−	17.0772i	0.0810023	−	0.770685i	0.957335	−	0.288979i	$-0.0933159\pi$
$492$	0.295438	+	0.216812i	0.0133194	+	0.00977463i
$493$	−3.93045	−	4.36520i	−0.177018	−	0.196599i
$494$	22.0900			0.993875
$495$	−11.9584	−	9.78375i	−0.537492	−	0.439747i
$496$	15.2135			0.683107
$497$	12.8355	+	14.2553i	0.575753	+	0.639438i
$498$	3.44411	−	1.51375i	0.154334	−	0.0678327i
$499$	−3.56755	+	33.9430i	−0.159706	+	1.51950i	0.561907	+	0.827201i	$0.310068\pi$
$499$	−3.56755	+	33.9430i	−0.159706	+	1.51950i	−0.721612	+	0.692297i	$0.756599\pi$
$500$	5.58743	+	5.03094i	0.249877	+	0.224990i
$501$	−2.60795	−	26.0073i	−0.116514	−	1.16192i
$502$	−12.4594	−	27.9842i	−0.556088	−	1.24899i
$503$	1.17651	−	0.854786i	0.0524581	−	0.0381130i	−0.561247	−	0.827648i	$-0.689678\pi$
$503$	1.17651	−	0.854786i	0.0524581	−	0.0381130i	0.613705	+	0.789535i	$0.289678\pi$
$504$	−29.5226	−	27.0974i	−1.31504	−	1.20701i
$505$			20.6470i			0.918778i
$506$	−10.8383	−	0.518865i	−0.481820	−	0.0230663i
$507$	6.68170	+	20.9033i	0.296745	+	0.928350i
$508$	−0.595478	−	2.80150i	−0.0264201	−	0.124297i
$509$	−4.77795	+	10.7314i	−0.211779	+	0.475663i	−0.987933	−	0.154880i	$-0.950501\pi$
$509$	−4.77795	+	10.7314i	−0.211779	+	0.475663i	0.776154	+	0.630543i	$0.217168\pi$
$510$	−0.512294	−	2.46806i	−0.0226848	−	0.109288i
$511$	−10.4347	−	2.21797i	−0.461605	−	0.0981172i
$512$	−6.88085	−	21.1771i	−0.304093	−	0.935903i
$513$	18.5464	−	5.73361i	0.818843	−	0.253145i
$514$	−20.5557	−	28.2925i	−0.906672	−	1.24793i
$515$	−2.50976	+	2.25980i	−0.110593	+	0.0995785i
$516$	0.913771	+	0.830701i	0.0402265	+	0.0365696i
$517$	−17.4903	+	6.80481i	−0.769222	+	0.299275i
$518$	20.0575	−	11.5802i	0.881278	−	0.508806i
$519$	38.0176	+	0.181589i	1.66879	+	0.00797089i
$520$	−2.53189	−	24.0893i	−0.111031	−	1.05638i
$521$	6.70232	−	9.22495i	0.293634	−	0.404152i	−0.636556	−	0.771230i	$-0.719642\pi$
$521$	6.70232	−	9.22495i	0.293634	−	0.404152i	0.930190	+	0.367078i	$0.119642\pi$
$522$	20.5735	+	15.2499i	0.900479	+	0.667472i
$523$	−1.48831	+	0.483583i	−0.0650794	+	0.0211456i	−0.341376	−	0.939927i	$-0.610893\pi$
$523$	−1.48831	+	0.483583i	−0.0650794	+	0.0211456i	0.276296	+	0.961072i	$0.410893\pi$
$524$	3.82566	−	1.70329i	0.167125	−	0.0744087i
$525$	−7.82748	−	17.8093i	−0.341619	−	0.777260i
$526$	−2.40621	+	0.511456i	−0.104916	+	0.0223006i
$527$	2.63658	+	4.56670i	0.114851	+	0.198928i
$528$	−0.699922	+	13.2909i	−0.0304602	+	0.578411i
$529$	−7.57062	+	13.1127i	−0.329157	+	0.570117i
$530$	−3.02221	+	9.30141i	−0.131276	+	0.404027i
$531$	−19.9355	−	6.68866i	−0.865128	−	0.290263i
$532$	−8.36693	−	6.07893i	−0.362753	−	0.263555i
$533$	0.349311	−	1.64338i	0.0151304	−	0.0711827i
$534$	6.48187	+	9.01173i	0.280498	+	0.389976i
$535$	−9.40995	−	0.989026i	−0.406828	−	0.0427593i
$536$	−29.3917	−	13.0860i	−1.26953	−	0.565231i
$537$	38.7427	−	22.1220i	1.67187	−	0.954636i
$538$	28.5000	+	16.4545i	1.22872	+	0.709402i
$539$	17.6469	−	35.0247i	0.760105	−	1.50862i
$540$	−2.02636	−	4.73265i	−0.0872008	−	0.203661i
$541$	−4.01286	−	1.30386i	−0.172527	−	0.0560573i	0.221480	−	0.975165i	$-0.428911\pi$
$541$	−4.01286	−	1.30386i	−0.172527	−	0.0560573i	−0.394007	+	0.919108i	$0.628911\pi$
$542$	−12.5969	+	1.32399i	−0.541085	+	0.0568703i
$543$	21.7342	−	4.51136i	0.932706	−	0.193601i
$544$	1.85571	−	2.06098i	0.0795630	−	0.0883636i
$545$	−8.53967	+	9.48426i	−0.365799	+	0.406261i
$546$	−13.9329	+	42.1942i	−0.596272	+	1.80574i
$547$	−13.6940	+	1.43930i	−0.585515	+	0.0615401i	−0.392654	−	0.919686i	$-0.628443\pi$
$547$	−13.6940	+	1.43930i	−0.585515	+	0.0615401i	−0.192860	+	0.981226i	$0.561776\pi$
$548$	5.10420	+	1.65845i	0.218041	+	0.0708457i
$549$	5.04812	−	11.0529i	0.215449	−	0.471726i
$550$	−4.50837	+	8.94799i	−0.192237	+	0.381544i
$551$	23.6657	+	13.6634i	1.00819	+	0.582081i
$552$	−12.9100	−	7.53606i	−0.549488	−	0.320756i
$553$	2.53883	+	1.13036i	0.107962	+	0.0480679i
$554$	14.9045	+	1.56653i	0.633232	+	0.0665553i
$555$	12.2410	−	1.22749i	0.519601	−	0.0521042i
$556$	0.271790	−	1.27867i	0.0115265	−	0.0542277i
$557$	−5.50700	−	4.00107i	−0.233339	−	0.169531i	0.464971	−	0.885326i	$-0.346065\pi$
$557$	−5.50700	−	4.00107i	−0.233339	−	0.169531i	−0.698311	+	0.715795i	$0.746065\pi$
$558$	−15.2193	−	17.2310i	−0.644285	−	0.729445i
$559$	1.74958	−	5.38465i	0.0739993	−	0.227746i
$560$	7.80490	−	13.5185i	0.329817	−	0.571261i
$561$	−4.11087	+	2.09328i	−0.173561	+	0.0883783i
$562$	−6.19286	−	10.7263i	−0.261230	−	0.452463i
$563$	−29.9874	+	6.37403i	−1.26382	+	0.268633i	−0.790612	−	0.612317i	$-0.790237\pi$
$563$	−29.9874	+	6.37403i	−1.26382	+	0.268633i	−0.473208	+	0.880951i	$0.656904\pi$
$564$	−6.21588	−	0.683348i	−0.261736	−	0.0287742i
$565$	7.79009	−	3.46837i	0.327732	−	0.145916i
$566$	−24.7056	+	8.02735i	−1.03846	+	0.337415i
$567$	−0.746012	+	39.0419i	−0.0313296	+	1.63961i
$568$	8.00051	−	11.0118i	0.335694	−	0.462043i
$569$	3.94586	+	37.5423i	0.165419	+	1.57386i	0.690836	+	0.723012i	$0.257243\pi$
$569$	3.94586	+	37.5423i	0.165419	+	1.57386i	−0.525417	+	0.850845i	$0.676091\pi$
$570$	5.81475	+	10.1835i	0.243553	+	0.426539i
$571$	−26.9194	+	15.5419i	−1.12654	+	0.650409i	−0.943063	−	0.332615i	$-0.892069\pi$
$571$	−26.9194	+	15.5419i	−1.12654	+	0.650409i	−0.183479	+	0.983024i	$0.558736\pi$
$572$	−9.99185	+	3.88745i	−0.417780	+	0.162543i
$573$	−1.59957	+	0.511297i	−0.0668228	+	0.0213597i
$574$	1.24780	−	1.12352i	0.0520821	−	0.0468949i
$575$	−4.26545	−	5.87089i	−0.177882	−	0.244833i
$576$	−13.2105	+	22.3847i	−0.550438	+	0.932696i
$577$	3.06623	+	9.43689i	0.127649	+	0.392863i	0.994374	−	0.105923i	$-0.0337796\pi$
$577$	3.06623	+	9.43689i	0.127649	+	0.392863i	−0.866726	+	0.498785i	$0.833780\pi$
$578$	18.6699	+	3.96840i	0.776565	+	0.165064i
$579$	−28.2955	+	25.2337i	−1.17592	+	1.04868i
$580$	2.94768	−	6.62059i	0.122396	−	0.274905i
$581$	1.67893	+	7.89874i	0.0696537	+	0.327695i
$582$	3.82192	+	0.831474i	0.158424	+	0.0344657i
$583$	17.8783	+	0.855895i	0.740444	+	0.0354476i
$584$			7.56960i			0.313232i
$585$	−15.9603	+	17.3888i	−0.659878	+	0.718938i
$586$	20.8438	−	15.1439i	0.861051	−	0.625590i
$587$	−0.676425	−	1.51928i	−0.0279191	−	0.0627072i	0.899048	−	0.437851i	$-0.144260\pi$
$587$	−0.676425	−	1.51928i	−0.0279191	−	0.0627072i	−0.926967	+	0.375143i	$0.877593\pi$
$588$	10.6087	−	7.63053i	0.437496	−	0.314678i
$589$	−18.2307	−	16.4150i	−0.751183	−	0.676368i
$590$	1.32776	−	12.6328i	0.0546631	−	0.520085i
$591$	−0.0737567	+	0.670907i	−0.00303395	+	0.0275974i
$592$	−7.09095	−	7.87530i	−0.291436	−	0.323673i
$593$	−16.8012			−0.689945			−0.344972	−	0.938613i	$-0.612112\pi$
$593$	−16.8012			−0.689945			−0.344972	+	0.938613i	$0.612112\pi$
$594$	15.7536	−	12.5032i	0.646376	−	0.513012i
$595$	5.41053			0.221810
$596$	0.673634	+	0.748146i	0.0275931	+	0.0306453i
$597$	−3.54384	+	32.2355i	−0.145040	+	1.31931i
$598$	−1.73264	+	16.4850i	−0.0708530	+	0.674121i
$599$	−31.7328	−	28.5723i	−1.29657	−	1.16743i	−0.975408	−	0.220408i	$-0.929261\pi$
$599$	−31.7328	−	28.5723i	−1.29657	−	1.16743i	−0.321159	−	0.947025i	$-0.604072\pi$
$600$	−11.2060	+	8.06015i	−0.457483	+	0.329054i
$601$	8.37933	+	18.8203i	0.341800	+	0.767696i	0.999891	+	0.0147573i	$0.00469755\pi$
$601$	8.37933	+	18.8203i	0.341800	+	0.767696i	−0.658091	+	0.752938i	$0.728636\pi$
$602$	4.57769	−	3.32588i	0.186573	−	0.135553i
$603$	9.40275	+	29.9078i	0.382909	+	1.21794i
$604$			6.43300i			0.261755i
$605$	−16.7396	−	3.40015i	−0.680563	−	0.138236i
$606$	−26.2619	−	5.71338i	−1.06682	−	0.232090i
$607$	−7.64988	−	35.9899i	−0.310499	−	1.46078i	−0.805865	−	0.592099i	$-0.798299\pi$
$607$	−7.64988	−	35.9899i	−0.310499	−	1.46078i	0.495366	−	0.868684i	$-0.335034\pi$
$608$	−5.24773	+	11.7866i	−0.212824	+	0.478009i
$609$	−41.0253	+	36.5861i	−1.66243	+	1.48254i
$610$	7.17984	+	1.52612i	0.290703	+	0.0617909i
$611$	8.85939	+	27.2664i	0.358413	+	1.10308i
$612$	−1.53704	−	0.0146835i	−0.0621310	−	0.000593545i
$613$	−23.1926	−	31.9219i	−0.936741	−	1.28931i	−0.957171	−	0.289523i	$-0.906503\pi$
$613$	−23.1926	−	31.9219i	−0.936741	−	1.28931i	0.0204297	−	0.999791i	$-0.493497\pi$
$614$	11.1233	−	10.0155i	0.448901	−	0.404193i
$615$	0.849547	−	0.271555i	0.0342571	−	0.0109502i
$616$	−42.8443	−	11.2726i	−1.72625	−	0.454188i
$617$	14.2499	−	8.22721i	0.573681	−	0.331215i	−0.184937	−	0.982750i	$-0.559208\pi$
$617$	14.2499	−	8.22721i	0.573681	−	0.331215i	0.758618	+	0.651535i	$0.225875\pi$
$618$	−2.17985	−	3.81761i	−0.0876866	−	0.153567i
$619$	1.57033	+	14.9407i	0.0631171	+	0.600519i	0.979671	+	0.200609i	$0.0642920\pi$
$619$	1.57033	+	14.9407i	0.0631171	+	0.600519i	−0.916554	+	0.399910i	$0.869041\pi$
$620$	−3.82407	+	5.26338i	−0.153578	+	0.211382i
$621$	2.82410	+	14.2902i	0.113327	+	0.573448i
$622$	7.47370	−	2.42835i	0.299668	−	0.0973681i
$623$	−21.7673	+	9.69143i	−0.872089	+	0.388279i
$624$	20.2099	+	2.22179i	0.809042	+	0.0889428i
$625$	5.23883	−	1.11355i	0.209553	−	0.0445419i
$626$	5.16683	+	8.94921i	0.206508	+	0.357683i
$627$	15.1792	−	15.1715i	0.606200	−	0.605893i
$628$	7.09534	−	12.2895i	0.283135	−	0.490404i
$629$	1.13506	−	3.49335i	0.0452577	−	0.139289i
$630$	−23.1191	+	4.68374i	−0.921085	+	0.186605i
$631$	−4.93444	−	3.58508i	−0.196437	−	0.142720i	0.485219	−	0.874393i	$-0.338740\pi$
$631$	−4.93444	−	3.58508i	−0.196437	−	0.142720i	−0.681656	+	0.731673i	$0.738740\pi$
$632$	0.409995	−	1.92888i	0.0163087	−	0.0767266i
$633$	41.7197	−	4.18354i	1.65821	−	0.166281i
$634$	19.8931	+	2.09085i	0.790056	+	0.0830382i
$635$	−6.36805	−	2.83524i	−0.252708	−	0.112513i
$636$	5.15059	+	3.00659i	0.204234	+	0.119219i
$637$	−51.8855	−	29.9561i	−2.05578	−	1.18690i
$638$	27.9832	+	4.30246i	1.10787	+	0.170336i
$639$	−13.2034	+	1.26034i	−0.522320	+	0.0498582i
$640$	−4.73219	−	1.53758i	−0.187056	−	0.0607783i
$641$	−27.9131	+	2.93378i	−1.10250	+	0.115877i	−0.638252	−	0.769828i	$-0.720342\pi$
$641$	−27.9131	+	2.93378i	−1.10250	+	0.115877i	−0.464248	+	0.885705i	$0.653675\pi$
$642$	3.86189	−	11.6953i	0.152417	−	0.461577i
$643$	3.29636	−	3.66098i	0.129996	−	0.144375i	−0.674633	−	0.738154i	$-0.735698\pi$
$643$	3.29636	−	3.66098i	0.129996	−	0.144375i	0.804628	+	0.593779i	$0.202365\pi$
$644$	5.19276	−	5.76715i	0.204624	−	0.227257i
$645$	2.94286	−	0.610848i	0.115875	−	0.0240521i
$646$	3.48205	−	0.365978i	0.137000	−	0.0143992i
$647$	27.9178	+	9.07106i	1.09756	+	0.356620i	0.801165	−	0.598444i	$-0.204214\pi$
$647$	27.9178	+	9.07106i	1.09756	+	0.356620i	0.296399	+	0.955064i	$0.404214\pi$
$648$	27.2077	−	5.24200i	1.06882	−	0.205925i
$649$	−22.9441	+	3.74044i	−0.900634	+	0.146825i
$650$	13.2555	+	7.65309i	0.519925	+	0.300179i
$651$	42.8531	−	24.4691i	1.67954	−	0.959019i
$652$	−1.11003	−	0.494218i	−0.0434722	−	0.0193551i
$653$	21.2908	+	2.23775i	0.833172	+	0.0875700i	0.511502	−	0.859282i	$-0.329089\pi$
$653$	21.2908	+	2.23775i	0.833172	+	0.0875700i	0.321670	+	0.946852i	$0.395756\pi$
$654$	−9.70043	−	13.4865i	−0.379317	−	0.527364i
$655$	2.11907	−	9.96942i	0.0827987	−	0.389537i
$656$	−0.621549	−	0.451582i	−0.0242674	−	0.0176313i
$657$	5.52845	−	4.88303i	0.215686	−	0.190505i
$658$	−8.85404	+	27.2499i	−0.345166	+	1.06231i
$659$	17.1996	−	29.7905i	0.670000	−	1.16047i	−0.307904	−	0.951418i	$-0.599627\pi$
$659$	17.1996	−	29.7905i	0.670000	−	1.16047i	0.977904	−	0.209056i	$-0.0670392\pi$
$660$	−4.42227	−	3.58294i	−0.172137	−	0.139466i
$661$	−3.94192	−	6.82760i	−0.153323	−	0.265563i	0.779124	−	0.626870i	$-0.215664\pi$
$661$	−3.94192	−	6.82760i	−0.153323	−	0.265563i	−0.932447	+	0.361307i	$0.882331\pi$
$662$	18.6762	−	3.96974i	0.725870	−	0.154288i
$663$	2.83556	+	6.45152i	0.110124	+	0.250556i
$664$	5.23455	−	2.33057i	0.203140	−	0.0904437i
$665$	−23.9389	+	7.77822i	−0.928311	+	0.301626i
$666$	−1.82598	+	15.9096i	−0.0707555	+	0.616484i
$667$	−12.0528	+	16.5892i	−0.466686	+	0.642338i
$668$	−1.00643	−	9.57557i	−0.0389401	−	0.370490i
$669$	−43.7821	−	0.209123i	−1.69271	−	0.00808516i
$670$	−16.4013	+	9.46928i	−0.633636	+	0.365830i
$671$	−0.763728	−	13.4118i	−0.0294834	−	0.517759i
$672$	−19.2037	−	17.4579i	−0.740799	−	0.673453i
$673$	−37.7770	+	34.0146i	−1.45620	+	1.31117i	−0.594132	+	0.804367i	$0.702505\pi$
$673$	−37.7770	+	34.0146i	−1.45620	+	1.31117i	−0.862065	+	0.506799i	$0.830829\pi$
$674$	−9.28140	−	12.7748i	−0.357506	−	0.492065i
$675$	13.1155	+	2.98484i	0.504818	+	0.114886i
$676$	2.49808	+	7.68829i	0.0960798	+	0.295703i
$677$	23.0560	+	4.90071i	0.886116	+	0.188350i	0.628418	−	0.777876i	$-0.283703\pi$
$677$	23.0560	+	4.90071i	0.886116	+	0.188350i	0.257698	+	0.966226i	$0.417036\pi$
$678$	2.25594	+	10.8684i	0.0866389	+	0.417397i
$679$	−3.41476	+	7.66968i	−0.131047	+	0.294335i
$680$	−0.798204	−	3.75526i	−0.0306097	−	0.144008i
$681$	−8.02576	−	25.1082i	−0.307548	−	0.962148i
$682$	−23.7691	−	9.00096i	−0.910165	−	0.344665i
$683$		−	14.3587i		−	0.549419i	−0.961527	−	0.274709i	$-0.911418\pi$
$683$		−	14.3587i		−	0.549419i	0.961527	−	0.274709i	$-0.0885816\pi$
$684$	6.82173	−	2.14469i	0.260835	−	0.0820042i
$685$	10.5674	−	7.67766i	0.403760	−	0.293348i
$686$	−9.93718	−	22.3193i	−0.379403	−	0.852154i
$687$	1.35354	+	13.4980i	0.0516408	+	0.514979i
$688$	−1.92402	−	1.73239i	−0.0733524	−	0.0660468i
$689$	2.85809	−	27.1929i	0.108884	−	1.03597i
$690$	−8.05566	+	3.54060i	−0.306674	+	0.134788i
$691$	7.90539	+	8.77983i	0.300735	+	0.334000i	0.874505	−	0.485016i	$-0.161186\pi$
$691$	7.90539	+	8.77983i	0.300735	+	0.334000i	−0.573770	+	0.819017i	$0.694520\pi$
$692$	14.0047			0.532377
$693$	19.4052	+	38.5631i	0.737142	+	1.46489i
$694$	22.4023			0.850379
$695$	−2.12890	−	2.36438i	−0.0807536	−	0.0896860i
$696$	31.4455	+	23.0768i	1.19194	+	0.874723i
$697$	0.0278352	−	0.264834i	0.00105433	−	0.0100313i
$698$	−8.47880	−	7.63435i	−0.320927	−	0.288964i
$699$	12.8901	+	5.81297i	0.487548	+	0.219867i
$700$	−2.91470	−	6.54652i	−0.110165	−	0.247435i
$701$	35.2967	−	25.6445i	1.33314	−	0.968581i	0.333471	−	0.942760i	$-0.391780\pi$
$701$	35.2967	−	25.6445i	1.33314	−	0.968581i	0.999667	−	0.0258206i	$-0.00821985\pi$
$702$	−17.7012	−	25.1125i	−0.668087	−	0.947811i
$703$			17.0881i			0.644490i
$704$	−1.37409	+	28.7025i	−0.0517879	+	1.08177i
$705$	−10.2377	+	11.2615i	−0.385576	+	0.424134i
$706$	−3.92920	−	18.4855i	−0.147878	−	0.695709i
$707$	23.4642	−	52.7014i	0.882460	−	1.98204i
$708$	−7.35530	−	2.42878i	−0.276429	−	0.0912793i
$709$	36.0769	+	7.66839i	1.35490	+	0.287992i	0.827424	−	0.561578i	$-0.189806\pi$
$709$	36.0769	+	7.66839i	1.35490	+	0.287992i	0.527475	+	0.849571i	$0.323139\pi$
$710$	−2.47590	−	7.62004i	−0.0929189	−	0.285975i
$711$	−1.67324	+	0.944847i	−0.0627513	+	0.0354345i
$712$	9.93777	+	13.6782i	0.372434	+	0.512611i
$713$	13.6799	−	12.3174i	0.512316	−	0.461291i
$714$	−1.49719	+	6.88192i	−0.0560309	+	0.257549i
$715$	−6.63958	+	25.2353i	−0.248306	+	0.943745i
$716$	14.2325	−	8.21713i	0.531893	−	0.307088i
$717$	16.3107	−	27.9418i	0.609133	−	1.04351i
$718$	−1.47872	−	14.0691i	−0.0551855	−	0.525055i
$719$	0.103196	−	0.142037i	0.00384856	−	0.00529709i	−0.807088	−	0.590431i	$-0.798958\pi$
$719$	0.103196	−	0.142037i	0.00384856	−	0.00529709i	0.810937	+	0.585134i	$0.198958\pi$
$720$	4.29561	+	9.90159i	0.160088	+	0.369010i
$721$	8.97429	−	2.91592i	0.334220	−	0.108595i
$722$	5.37640	−	2.39373i	0.200089	−	0.0890853i
$723$	1.25900	−	1.71558i	0.0468229	−	0.0638031i
$724$	7.99818	−	1.70006i	0.297250	−	0.0631824i
$725$	9.46741	+	16.3980i	0.351611	+	0.609008i
$726$	8.95697	−	20.3511i	0.332424	−	0.755300i
$727$	10.8837	−	18.8510i	0.403652	−	0.699147i	−0.590511	−	0.807029i	$-0.701074\pi$
$727$	10.8837	−	18.8510i	0.403652	−	0.699147i	0.994164	+	0.107883i	$0.0344072\pi$
$728$	−20.9135	+	64.3652i	−0.775107	+	2.38553i
$729$	−21.3797	−	16.4896i	−0.791842	−	0.610726i
$730$	3.60481	+	2.61905i	0.133420	+	0.0969353i
$731$	0.186576	−	0.877771i	0.00690076	−	0.0324655i
$732$	1.84010	−	4.08037i	0.0680120	−	0.150815i
$733$	21.9705	+	2.30919i	0.811498	+	0.0852919i	0.501183	−	0.865342i	$-0.332899\pi$
$733$	21.9705	+	2.30919i	0.811498	+	0.0852919i	0.310316	+	0.950634i	$0.399565\pi$
$734$	−0.932804	−	0.415311i	−0.0344304	−	0.0153294i
$735$	0.151913	−	31.8046i	0.00560339	−	1.17313i
$736$	−8.38432	−	4.84069i	−0.309050	−	0.178430i
$737$	24.6189	+	24.3972i	0.906848	+	0.898681i
$738$	0.110320	+	1.15573i	0.00406094	+	0.0425429i
$739$	20.5897	+	6.69000i	0.757404	+	0.246096i	0.662164	−	0.749359i	$-0.269638\pi$
$739$	20.5897	+	6.69000i	0.757404	+	0.246096i	0.0952401	+	0.995454i	$0.469638\pi$
$740$	4.50698	−	0.473703i	0.165680	−	0.0174137i
$741$	−21.8207	−	24.4684i	−0.801603	−	0.898868i
$742$	18.2847	−	20.3073i	0.671254	−	0.745503i
$743$	−18.3621	+	20.3932i	−0.673640	+	0.748153i	−0.978950	−	0.204100i	$-0.934573\pi$
$743$	−18.3621	+	20.3932i	−0.673640	+	0.748153i	0.305310	+	0.952253i	$0.401240\pi$
$744$	−23.3052	−	26.1329i	−0.854409	−	0.958080i
$745$	2.43678	−	0.256116i	0.0892768	−	0.00938337i
$746$	−10.7644	−	3.49757i	−0.394113	−	0.128055i
$747$	−5.07886	−	2.31964i	−0.185826	−	0.0848712i
$748$	−1.51061	+	0.778322i	−0.0552335	+	0.0284583i
$749$	22.8949	+	13.2184i	0.836562	+	0.482989i
$750$	−0.113773	+	23.8196i	−0.00415441	+	0.869769i
$751$	21.2166	+	9.44624i	0.774205	+	0.344698i	0.755519	−	0.655127i	$-0.227385\pi$
$751$	21.2166	+	9.44624i	0.774205	+	0.344698i	0.0186861	+	0.999825i	$0.494052\pi$
$752$	13.0383	+	1.37038i	0.475457	+	0.0499725i
$753$	−18.6897	+	41.4439i	−0.681090	+	1.51030i
$754$	8.99223	−	42.3051i	0.327478	−	1.54066i
$755$	12.6666	+	9.20283i	0.460985	+	0.334925i
$756$	−0.206111	+	14.3829i	−0.00749618	+	0.523103i
$757$	−10.8996	+	33.5455i	−0.396152	+	1.21923i	0.531908	+	0.846802i	$0.321475\pi$
$757$	−10.8996	+	33.5455i	−0.396152	+	1.21923i	−0.928060	+	0.372430i	$0.878525\pi$
$758$	12.2854	−	21.2789i	0.446226	−	0.772886i
$759$	10.1314	+	12.5177i	0.367747	+	0.454365i
$760$	8.93025	+	15.4677i	0.323934	+	0.561071i
$761$	−0.834612	+	0.177402i	−0.0302547	+	0.00643083i	−0.223014	−	0.974815i	$-0.571590\pi$
$761$	−0.834612	+	0.177402i	−0.0302547	+	0.00643083i	0.192759	+	0.981246i	$0.438256\pi$
$762$	5.36843	−	7.31528i	0.194478	−	0.265005i
$763$	32.5758	−	14.5037i	1.17932	−	0.525069i
$764$	−0.588323	+	0.191158i	−0.0212848	+	0.00691585i
$765$	−2.22774	+	3.00543i	−0.0805442	+	0.108661i
$766$	−17.2750	+	23.7770i	−0.624171	+	0.859097i
$767$	3.71209	+	35.3182i	0.134036	+	1.27527i
$768$	−11.8653	+	20.3265i	−0.428154	+	0.733471i
$769$	−8.78388	+	5.07138i	−0.316755	+	0.182879i	−0.649945	−	0.759981i	$-0.725208\pi$
$769$	−8.78388	+	5.07138i	−0.316755	+	0.182879i	0.333190	+	0.942860i	$0.391875\pi$
$770$	−20.1922	+	16.5031i	−0.727677	+	0.594731i
$771$	−11.0336	+	50.7165i	−0.397364	+	1.82651i
$772$	−10.3787	+	9.34499i	−0.373536	+	0.336334i
$773$	−11.4055	−	15.6983i	−0.410228	−	0.564630i	0.553046	−	0.833151i	$-0.313465\pi$
$773$	−11.4055	−	15.6983i	−0.410228	−	0.564630i	−0.963274	+	0.268520i	$0.913465\pi$
$774$	−0.0373738	+	3.91221i	−0.00134337	+	0.140621i
$775$	−5.25272	−	16.1662i	−0.188683	−	0.580707i
$776$	5.82703	+	1.23857i	0.209178	+	0.0444622i
$777$	−32.6401	−	10.7780i	−1.17096	−	0.386660i
$778$	16.1039	−	36.1699i	0.577351	−	1.29675i
$779$	0.257571	+	1.21178i	0.00922844	+	0.0434164i
$780$	−5.84862	+	6.43348i	−0.209414	+	0.230356i
$781$	−12.2614	+	8.04175i	−0.438749	+	0.287756i
$782$			2.62724i			0.0939500i
$783$	−3.43087	−	37.8527i	−0.122609	−	1.35274i
$784$	−22.1645	+	16.1034i	−0.791588	+	0.575122i
$785$	−14.0477	−	31.5517i	−0.501384	−	1.12613i
$786$	12.0942	+	5.45406i	0.431387	+	0.194540i
$787$	32.8856	+	29.6104i	1.17225	+	1.05550i	0.997485	+	0.0708847i	$0.0225822\pi$
$787$	32.8856	+	29.6104i	1.17225	+	1.05550i	0.174762	+	0.984611i	$0.444084\pi$
$788$	−0.0259889	+	0.247268i	−0.000925816	+	0.00880855i
$789$	2.94340	+	2.16006i	0.104788	+	0.0769003i
$790$	−0.776717	−	0.862632i	−0.0276343	−	0.0306911i
$791$	−23.8258			−0.847149
$792$	23.9025	−	19.1576i	0.849339	−	0.680736i
$793$	−20.5215			−0.728740
$794$	7.34567	+	8.15819i	0.260688	+	0.289523i
$795$	13.2882	−	5.84042i	0.471285	−	0.207138i
$796$	−1.24871	+	11.8806i	−0.0442592	+	0.421098i
$797$	−10.0748	−	9.07140i	−0.356868	−	0.321325i	0.471122	−	0.882068i	$-0.343849\pi$
$797$	−10.0748	−	9.07140i	−0.356868	−	0.321325i	−0.827990	+	0.560743i	$0.810516\pi$
$798$	−3.26919	−	32.6015i	−0.115728	−	1.15408i
$799$	1.84825	+	4.15124i	0.0653864	+	0.146860i
$800$	−7.23248	+	5.25470i	−0.255707	+	0.185782i
$801$	3.57915	−	16.0816i	0.126463	−	0.568216i
$802$			24.0416i			0.848940i
$803$	2.88790	−	7.62617i	0.101912	−	0.269122i
$804$	3.51626	+	11.0004i	0.124009	+	0.387955i
$805$	−3.92695	−	18.4749i	−0.138407	−	0.651154i
$806$	−15.7922	+	35.4699i	−0.556256	+	1.24937i
$807$	−9.92646	−	47.8224i	−0.349428	−	1.68343i
$808$	−40.0398	−	8.51072i	−1.40859	−	0.299406i
$809$	−7.82320	−	24.0773i	−0.275049	−	0.846514i	−0.989206	−	0.146529i	$-0.953190\pi$
$809$	−7.82320	−	24.0773i	−0.275049	−	0.846514i	0.714157	−	0.699985i	$-0.246810\pi$
$810$	6.91738	−	14.7706i	0.243052	−	0.518986i
$811$	−0.204607	−	0.281618i	−0.00718473	−	0.00988893i	0.805410	−	0.592719i	$-0.201945\pi$
$811$	−0.204607	−	0.281618i	−0.00718473	−	0.00988893i	−0.812594	+	0.582830i	$0.801945\pi$
$812$	−15.0479	+	13.5492i	−0.528077	+	0.475483i
$813$	13.9099	+	12.6454i	0.487842	+	0.443492i
$814$	6.41930	+	16.4994i	0.224996	+	0.578304i
$815$	−2.56109	+	1.47865i	−0.0897111	+	0.0517948i
$816$	3.22250	+	0.0153921i	0.112810	+	0.000538832i
$817$	0.436385	+	4.15193i	0.0152672	+	0.145258i
$818$	12.8709	−	17.7152i	0.450019	−	0.619398i
$819$	60.5001	−	26.2468i	2.11405	−	0.917137i
$820$	0.312465	−	0.101526i	0.0109118	−	0.00354544i
$821$	−49.5773	+	22.0732i	−1.73026	+	0.770361i	−0.734476	+	0.678635i	$0.762572\pi$
$821$	−49.5773	+	22.0732i	−1.73026	+	0.770361i	−0.995784	+	0.0917268i	$0.970761\pi$
$822$	6.84142	+	15.5657i	0.238622	+	0.542918i
$823$	2.21233	−	0.470246i	0.0771170	−	0.0163917i	−0.169192	−	0.985583i	$-0.554116\pi$
$823$	2.21233	−	0.470246i	0.0771170	−	0.0163917i	0.246309	+	0.969191i	$0.420782\pi$
$824$	−3.34780	−	5.79856i	−0.116626	−	0.202002i
$825$	14.3648	−	3.84514i	0.500118	−	0.133870i
$826$	−17.7456	+	30.7363i	−0.617449	+	1.06945i
$827$	10.7309	−	33.0262i	0.373148	−	1.14843i	−0.571571	−	0.820553i	$-0.693666\pi$
$827$	10.7309	−	33.0262i	0.373148	−	1.14843i	0.944719	−	0.327880i	$-0.106334\pi$
$828$	1.06544	+	5.25904i	0.0370266	+	0.182764i
$829$	−21.5813	−	15.6797i	−0.749549	−	0.544579i	0.146138	−	0.989264i	$-0.453316\pi$
$829$	−21.5813	−	15.6797i	−0.749549	−	0.544579i	−0.895687	+	0.444685i	$0.853316\pi$
$830$	0.701262	−	3.29918i	0.0243412	−	0.114516i
$831$	−12.9876	−	18.0567i	−0.450536	−	0.626379i
$832$	43.6565	+	4.58849i	1.51352	+	0.159077i
$833$	−8.67504	−	3.86238i	−0.300572	−	0.133823i
$834$	3.59648	−	2.05358i	0.124536	−	0.0711098i
$835$	−20.2941	−	11.7168i	−0.702307	−	0.405477i
$836$	5.56479	−	5.61536i	0.192462	−	0.194211i
$837$	−4.05241	+	33.8789i	−0.140072	+	1.17103i
$838$	−41.4997	−	13.4841i	−1.43358	−	0.465800i
$839$	14.7365	−	1.54887i	0.508760	−	0.0534729i	0.153329	−	0.988175i	$-0.451001\pi$
$839$	14.7365	−	1.54887i	0.508760	−	0.0534729i	0.355431	+	0.934702i	$0.384334\pi$
$840$	−35.1774	+	7.30176i	−1.21374	+	0.251935i
$841$	16.3961	−	18.2097i	0.565383	−	0.627921i
$842$	−21.0971	+	23.4307i	−0.727052	+	0.807474i
$843$	−5.76386	+	17.4552i	−0.198518	+	0.601189i
$844$	15.3607	−	1.61447i	0.528736	−	0.0555724i
$845$	18.7119	+	6.07988i	0.643710	+	0.209154i
$846$	−11.4911	−	16.1382i	−0.395073	−	0.554842i
$847$	38.8638	+	27.7026i	1.33538	+	0.951871i
$848$	−10.8282	−	6.25165i	−0.371841	−	0.214683i
$849$	33.2961	+	19.4361i	1.14272	+	0.667047i
$850$	2.21627	+	0.986747i	0.0760174	+	0.0338451i
$851$	−12.7523	−	1.34032i	−0.437142	−	0.0459455i
$852$	−4.86146	+	0.487494i	−0.166551	+	0.0167013i
$853$	−6.53175	+	30.7294i	−0.223643	+	1.05216i	0.712809	+	0.701359i	$0.247423\pi$
$853$	−6.53175	+	30.7294i	−0.223643	+	1.05216i	−0.936451	+	0.350798i	$0.885911\pi$
$854$	−16.5922	−	12.0549i	−0.567773	−	0.412511i
$855$	5.53603	−	16.5001i	0.189328	−	0.564293i
$856$	5.79678	−	17.8407i	0.198130	−	0.609781i
$857$	−13.1784	+	22.8257i	−0.450166	+	0.779710i	−0.998396	−	0.0566174i	$-0.981968\pi$
$857$	−13.1784	+	22.8257i	−0.450166	+	0.779710i	0.548230	+	0.836328i	$0.315302\pi$
$858$	−30.2607	−	15.4283i	−1.03308	−	0.526712i
$859$	−12.2081	−	21.1450i	−0.416535	−	0.721459i	0.579054	−	0.815290i	$-0.303422\pi$
$859$	−12.2081	−	21.1450i	−0.416535	−	0.721459i	−0.995588	+	0.0938303i	$0.970089\pi$
$860$	1.08297	−	0.230193i	0.0369290	−	0.00784950i
$861$	−2.47708	−	0.272320i	−0.0844186	−	0.00928063i
$862$	−30.9653	+	13.7866i	−1.05468	+	0.469574i
$863$	8.44399	−	2.74362i	0.287437	−	0.0933939i	−0.161750	−	0.986832i	$-0.551714\pi$
$863$	8.44399	−	2.74362i	0.287437	−	0.0933939i	0.449187	+	0.893438i	$0.351714\pi$
$864$	17.6045	−	3.47907i	0.598916	−	0.118360i
$865$	20.0346	−	27.5752i	0.681196	−	0.937586i
$866$	2.47275	+	23.5266i	0.0840273	+	0.799467i
$867$	−14.0466	−	24.6001i	−0.477048	−	0.835462i
$868$	15.7425	−	9.08893i	0.534335	−	0.308498i
$869$	−1.14895	+	1.78687i	−0.0389755	+	0.0606155i
$870$	21.8697	−	6.99058i	0.741452	−	0.237003i
$871$	39.3476	−	35.4288i	1.33324	−	1.20046i
$872$	−14.8724	−	20.4701i	−0.503642	−	0.693204i
$873$	−2.85433	−	5.05476i	−0.0966046	−	0.171078i
$874$	−3.77695	−	11.6242i	−0.127757	−	0.393196i
$875$	−50.0112	−	10.6302i	−1.69069	−	0.359367i
$876$	2.02789	−	1.80846i	0.0685161	−	0.0611022i
$877$	−14.0858	+	31.6371i	−0.475642	+	1.06831i	0.503289	+	0.864118i	$0.332123\pi$
$877$	−14.0858	+	31.6371i	−0.475642	+	1.06831i	−0.978931	+	0.204192i	$0.934543\pi$
$878$	6.90667	+	32.4933i	0.233089	+	1.09660i
$879$	−37.3642	−	8.12873i	−1.26026	−	0.274175i
$880$	9.30705	+	7.46726i	0.313741	+	0.251721i
$881$			3.07797i			0.103699i	0.998655	+	0.0518497i	$0.0165117\pi$
$881$			3.07797i			0.103699i	−0.998655	+	0.0518497i	$0.983488\pi$
$882$	40.4118	+	8.99412i	1.36074	+	0.302848i
$883$	44.0733	−	32.0212i	1.48319	−	1.07760i	0.506673	−	0.862138i	$-0.330875\pi$
$883$	44.0733	−	32.0212i	1.48319	−	1.07760i	0.976513	−	0.215460i	$-0.0691250\pi$
$884$	1.05587	+	2.37152i	0.0355127	+	0.0797628i
$885$	−15.3045	+	11.0081i	−0.514456	+	0.370033i
$886$	−0.304632	−	0.274292i	−0.0102343	−	0.00921502i
$887$	−5.47219	+	52.0644i	−0.183738	+	1.74815i	0.382543	+	0.923938i	$0.375049\pi$
$887$	−5.47219	+	52.0644i	−0.183738	+	1.74815i	−0.566281	+	0.824213i	$0.691618\pi$
$888$	−2.66533	+	24.2444i	−0.0894426	+	0.813589i
$889$	13.0323	+	14.4739i	0.437091	+	0.485439i
$890$	9.95228			0.333601
$891$	−29.4109	−	5.09893i	−0.985302	−	0.170820i
$892$	−16.1281			−0.540009
$893$	−14.1455	−	15.7101i	−0.473359	−	0.525719i
$894$	−0.348534	+	3.17034i	−0.0116567	+	0.106032i
$895$	4.18094	−	39.7790i	0.139753	−	1.32966i
$896$	10.3315	+	9.30256i	0.345153	+	0.310777i
$897$	19.9714	−	14.3648i	0.666826	−	0.479628i
$898$	−5.37411	−	12.0704i	−0.179336	−	0.402796i
$899$	−38.8581	+	28.2320i	−1.29599	+	0.941591i
$900$	4.83655	+	1.07643i	0.161218	+	0.0358810i
$901$		−	4.33378i		−	0.144379i
$902$	0.703912	+	1.07327i	0.0234377	+	0.0357360i
$903$	−8.20586	−	1.78522i	−0.273074	−	0.0594083i
$904$	3.51498	+	16.5367i	0.116906	+	0.550002i
$905$	8.09448	−	18.1805i	0.269070	−	0.604341i
$906$	−15.2106	+	13.5647i	−0.505339	+	0.450657i
$907$	−55.0901	−	11.7098i	−1.82924	−	0.388817i	−0.840912	−	0.541172i	$-0.817981\pi$
$907$	−55.0901	−	11.7098i	−1.82924	−	0.388817i	−0.988326	+	0.152355i	$0.951314\pi$
$908$	−3.00058	−	9.23484i	−0.0995778	−	0.306469i
$909$	19.6132	+	34.7332i	0.650530	+	1.15203i
$910$	23.4162	+	32.2296i	0.776238	+	1.06840i
$911$	−18.4676	+	16.6283i	−0.611860	+	0.550921i	−0.915731	−	0.401792i	$-0.868388\pi$
$911$	−18.4676	+	16.6283i	−0.611860	+	0.550921i	0.303871	+	0.952713i	$0.401721\pi$
$912$	−14.2801	+	4.56459i	−0.472861	+	0.151149i
$913$	−6.16281	+	0.350937i	−0.203959	+	0.0116143i
$914$	8.45472	−	4.88134i	0.279657	−	0.161460i
$915$	−5.40188	−	9.46040i	−0.178581	−	0.312751i
$916$	0.522345	+	4.96978i	0.0172588	+	0.164206i
$917$	−16.7386	+	23.0387i	−0.552758	+	0.760806i
$918$	−3.20630	−	3.66523i	−0.105824	−	0.120971i
$919$	−17.1331	+	5.56688i	−0.565168	+	0.183634i	−0.577645	−	0.816288i	$-0.696028\pi$
$919$	−17.1331	+	5.56688i	−0.565168	+	0.183634i	0.0124770	+	0.999922i	$0.496028\pi$
$920$	−12.2434	+	5.45112i	−0.403654	+	0.179718i
$921$	−22.0816	−	2.42756i	−0.727613	−	0.0799908i
$922$	14.5663	−	3.09616i	0.479715	−	0.101967i
$923$	11.2000	+	19.3990i	0.368654	+	0.638527i
$924$	7.21603	+	14.1711i	0.237390	+	0.466196i
$925$	−5.92019	+	10.2541i	−0.194655	+	0.337152i
$926$	−7.97064	+	24.5311i	−0.261931	+	0.806142i
$927$	−2.07537	+	6.18563i	−0.0681640	+	0.203163i
$928$	20.4366	+	14.8481i	0.670865	+	0.487412i
$929$	6.98358	−	32.8552i	0.229124	−	1.07794i	−0.701699	−	0.712473i	$-0.747575\pi$
$929$	6.98358	−	32.8552i	0.229124	−	1.07794i	0.930823	−	0.365470i	$-0.119092\pi$
$930$	−20.5086	+	2.05655i	−0.672503	+	0.0674369i
$931$	43.9354	+	4.61779i	1.43992	+	0.151342i
$932$	4.75847	+	2.11861i	0.155869	+	0.0693973i
$933$	−10.0724	−	5.87963i	−0.329756	−	0.192490i
$934$	8.20654	+	4.73805i	0.268526	+	0.155034i
$935$	−0.628512	+	4.08785i	−0.0205545	+	0.133687i
$936$	−27.1425	−	38.1189i	−0.887179	−	1.24596i
$937$	13.8611	+	4.50374i	0.452822	+	0.147131i	0.526544	−	0.850148i	$-0.323488\pi$
$937$	13.8611	+	4.50374i	0.452822	+	0.147131i	−0.0737215	+	0.997279i	$0.523488\pi$
$938$	52.6256	−	5.53117i	1.71829	−	0.180599i
$939$	4.80891	−	14.5633i	0.156933	−	0.475254i
$940$	−3.75140	+	4.16636i	−0.122357	+	0.135892i
$941$	19.4672	−	21.6205i	0.634613	−	0.704809i	−0.336968	−	0.941516i	$-0.609401\pi$
$941$	19.4672	−	21.6205i	0.634613	−	0.704809i	0.971581	+	0.236707i	$0.0760680\pi$
$942$	44.0194	−	9.13708i	1.43423	−	0.297702i
$943$	−0.924510	+	0.0971699i	−0.0301062	+	0.00316429i
$944$	15.4445	+	5.01823i	0.502676	+	0.163329i
$945$	28.0252	+	20.9816i	0.911661	+	0.682531i
$946$	1.98106	+	3.84496i	0.0644098	+	0.125010i
$947$	−39.8858	−	23.0281i	−1.29611	−	0.748311i	−0.316383	−	0.948632i	$-0.602468\pi$
$947$	−39.8858	−	23.0281i	−1.29611	−	0.748311i	−0.979730	+	0.200320i	$0.935802\pi$
$948$	−0.614698	+	0.350992i	−0.0199645	+	0.0113997i
$949$	−11.3803	−	5.06683i	−0.369420	−	0.164476i
$950$	−11.2245	−	1.17974i	−0.364169	−	0.0382758i
$951$	−17.3346	−	24.1003i	−0.562114	−	0.781506i
$952$	−2.23023	+	10.4924i	−0.0722822	+	0.340061i
$953$	−22.8291	−	16.5863i	−0.739509	−	0.537284i	0.153049	−	0.988219i	$-0.451091\pi$
$953$	−22.8291	−	16.5863i	−0.739509	−	0.537284i	−0.892557	+	0.450934i	$0.851091\pi$
$954$	3.75163	+	18.5181i	0.121463	+	0.599547i
$955$	−0.465244	+	1.43188i	−0.0150550	+	0.0463344i
$956$	5.95910	−	10.3215i	0.192731	−	0.333820i
$957$	−22.8764	−	35.2461i	−0.739489	−	1.13935i
$958$	−20.0964	−	34.8081i	−0.649287	−	1.12460i
$959$	−35.6985	+	7.58796i	−1.15277	+	0.245028i
$960$	9.37644	+	21.3335i	0.302623	+	0.688535i
$961$	11.0708	−	4.92905i	0.357124	−	0.159002i
$962$	25.7217	−	8.35749i	0.829301	−	0.269456i
$963$	−16.7693	+	7.27504i	−0.540384	+	0.234435i
$964$	0.460754	−	0.634173i	0.0148399	−	0.0204253i
$965$	3.55297	+	33.8043i	0.114374	+	1.08820i
$966$	24.5858	+	0.117433i	0.791034	+	0.00377834i
$967$	36.6176	−	21.1412i	1.17754	−	0.679854i	0.222097	−	0.975025i	$-0.428710\pi$
$967$	36.6176	−	21.1412i	1.17754	−	0.679854i	0.955445	+	0.295170i	$0.0953764\pi$
$968$	13.4939	−	31.0609i	0.433710	−	0.998336i
$969$	−3.84499	−	3.49544i	−0.123519	−	0.112290i
$970$	2.60596	−	2.34642i	0.0836725	−	0.0753391i
$971$	0.665728	+	0.916296i	0.0213642	+	0.0294053i	0.819566	−	0.572986i	$-0.194215\pi$
$971$	0.665728	+	0.916296i	0.0213642	+	0.0294053i	−0.798201	+	0.602391i	$0.794215\pi$
$972$	−7.90454	−	6.03656i	−0.253538	−	0.193623i
$973$	2.74702	+	8.45445i	0.0880654	+	0.271037i
$974$	−19.0574	−	4.05077i	−0.610637	−	0.129795i
$975$	−4.61687	−	22.2425i	−0.147858	−	0.712331i
$976$	−3.81686	+	8.57281i	−0.122175	+	0.274409i
$977$	8.13400	+	38.2675i	0.260230	+	1.22428i	0.893040	+	0.449978i	$0.148568\pi$
$977$	8.13400	+	38.2675i	0.260230	+	1.22428i	−0.632810	+	0.774307i	$0.718099\pi$
$978$	−1.17207	−	3.66675i	−0.0374785	−	0.117250i
$979$	−4.79363	−	17.5718i	−0.153205	−	0.561597i
$980$		−	11.7159i		−	0.374252i
$981$	−5.35638	+	24.0669i	−0.171016	+	0.768398i
$982$	16.2123	−	11.7789i	0.517355	−	0.375880i
$983$	16.5126	+	37.0879i	0.526670	+	1.18292i	0.959568	+	0.281477i	$0.0908243\pi$
$983$	16.5126	+	37.0879i	0.526670	+	1.18292i	−0.432898	+	0.901443i	$0.642509\pi$
$984$	0.176431	+	1.75943i	0.00562441	+	0.0560885i
$985$	0.449693	+	0.404905i	0.0143284	+	0.0129013i
$986$	0.716554	−	6.81756i	0.0228197	−	0.217115i
$987$	38.9300	−	17.1104i	1.23915	−	0.544630i
$988$	−8.08101	−	8.97487i	−0.257091	−	0.285529i
$989$	−3.13267			−0.0996131
$990$	−0.853115	−	18.0114i	−0.0271138	−	0.572439i
$991$	16.7057			0.530675			0.265338	−	0.964156i	$-0.414517\pi$
$991$	16.7057			0.530675			0.265338	+	0.964156i	$0.414517\pi$
$992$	−15.1741	−	16.8525i	−0.481778	−	0.535069i
$993$	−22.8457	−	16.7656i	−0.724985	−	0.532042i
$994$	−2.34003	+	22.2639i	−0.0742212	+	0.706167i
$995$	21.6067	+	19.4548i	0.684978	+	0.616757i
$996$	−1.87495	−	0.845536i	−0.0594101	−	0.0267918i
$997$	−0.873727	−	1.96242i	−0.0276712	−	0.0621505i	0.899181	−	0.437577i	$-0.144163\pi$
$997$	−0.873727	−	1.96242i	−0.0276712	−	0.0621505i	−0.926852	+	0.375426i	$0.877496\pi$
$998$	−32.2238	+	23.4120i	−1.02003	+	0.741093i
$999$	19.4263	−	13.6931i	0.614620	−	0.433229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.p.a.2.8	✓	80
3.2	odd	2		297.2.t.a.35.3		80
9.2	odd	6		891.2.k.a.728.7		80
9.4	even	3		297.2.t.a.233.3		80
9.5	odd	6	inner	99.2.p.a.68.8	yes	80
9.7	even	3		891.2.k.a.728.14		80
11.6	odd	10	inner	99.2.p.a.83.8	yes	80
33.17	even	10		297.2.t.a.116.3		80
99.50	even	30	inner	99.2.p.a.50.8	yes	80
99.61	odd	30		891.2.k.a.809.7		80
99.83	even	30		891.2.k.a.809.14		80
99.94	odd	30		297.2.t.a.17.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.8	✓	80	1.1	even	1	trivial
99.2.p.a.50.8	yes	80	99.50	even	30	inner
99.2.p.a.68.8	yes	80	9.5	odd	6	inner
99.2.p.a.83.8	yes	80	11.6	odd	10	inner
297.2.t.a.17.3		80	99.94	odd	30
297.2.t.a.35.3		80	3.2	odd	2
297.2.t.a.116.3		80	33.17	even	10
297.2.t.a.233.3		80	9.4	even	3
891.2.k.a.728.7		80	9.2	odd	6
891.2.k.a.728.14		80	9.7	even	3
891.2.k.a.809.7		80	99.61	odd	30
891.2.k.a.809.14		80	99.83	even	30

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.780898 + 0.867275i) q^{2} +(0.189274 - 1.72168i) q^{3} +(0.0666926 - 0.634537i) q^{4} +(-1.15400 - 1.03907i) q^{5} +(1.64097 - 1.18030i) q^{6} +(1.76474 + 3.96367i) q^{7} +(2.49070 - 1.80960i) q^{8} +(-2.92835 - 0.651738i) q^{9} -1.81224i q^{10} +(-3.19970 + 0.872887i) q^{11} +(-1.07985 - 0.234925i) q^{12} +(1.05340 + 4.95585i) q^{13} +(-2.05951 + 4.62574i) q^{14} +(-2.00736 + 1.79015i) q^{15} +(2.26622 + 0.481700i) q^{16} +(0.248154 + 0.763741i) q^{17} +(-1.72151 - 3.04863i) q^{18} +(-2.19592 - 3.02243i) q^{19} +(-0.736289 + 0.662958i) q^{20} +(7.15819 - 2.28809i) q^{21} +(-3.25567 - 2.09338i) q^{22} +(2.42777 - 1.40167i) q^{23} +(-2.64412 - 4.63069i) q^{24} +(-0.270585 - 2.57445i) q^{25} +(-3.47549 + 4.78360i) q^{26} +(-1.67634 + 4.91832i) q^{27} +(2.63279 - 0.855447i) q^{28} +(-6.68223 + 2.97512i) q^{29} +(-3.12009 - 0.343010i) q^{30} +(6.42298 - 1.36525i) q^{31} +(-1.72675 - 2.99082i) q^{32} +(0.897210 + 5.67407i) q^{33} +(-0.468590 + 0.811622i) q^{34} +(2.08201 - 6.40776i) q^{35} +(-0.608852 + 1.81468i) q^{36} +(-3.70044 - 2.68853i) q^{37} +(0.906484 - 4.26467i) q^{38} +(8.73176 - 0.875599i) q^{39} +(-4.75456 - 0.499724i) q^{40} +(-0.302935 - 0.134876i) q^{41} +(7.57422 + 4.42135i) q^{42} +(-0.967761 - 0.558737i) q^{43} +(0.340483 + 2.08854i) q^{44} +(2.70212 + 3.79485i) q^{45} +(3.11148 + 1.01098i) q^{46} +(5.62759 - 0.591483i) q^{47} +(1.25827 - 3.81053i) q^{48} +(-7.91248 + 8.78770i) q^{49} +(2.02145 - 2.24505i) q^{50} +(1.36188 - 0.282686i) q^{51} +(3.21493 - 0.337902i) q^{52} +(-5.13255 - 1.66767i) q^{53} +(-5.57459 + 2.38685i) q^{54} +(4.59944 + 2.31739i) q^{55} +(11.5681 + 6.67884i) q^{56} +(-5.61928 + 3.20860i) q^{57} +(-7.79839 - 3.47207i) q^{58} +(6.97083 + 0.732664i) q^{59} +(1.00204 + 1.39313i) q^{60} +(-0.842120 + 3.96186i) q^{61} +(6.19973 + 4.50437i) q^{62} +(-2.58450 - 12.7572i) q^{63} +(2.67734 - 8.24001i) q^{64} +(3.93383 - 6.81360i) q^{65} +(-4.22035 + 5.20899i) q^{66} +(-5.22518 - 9.05028i) q^{67} +(0.501172 - 0.106527i) q^{68} +(-1.95372 - 4.44514i) q^{69} +(7.18312 - 3.19813i) q^{70} +(4.20477 - 1.36621i) q^{71} +(-8.47302 + 3.67585i) q^{72} +(-1.44520 + 1.98915i) q^{73} +(-0.557974 - 5.30877i) q^{74} +(-4.48358 - 0.0214156i) q^{75} +(-2.06429 + 1.19182i) q^{76} +(-9.10648 - 11.1421i) q^{77} +(7.57800 + 6.88908i) q^{78} +(0.476003 - 0.428595i) q^{79} +(-2.11470 - 2.91063i) q^{80} +(8.15047 + 3.81704i) q^{81} +(-0.119587 - 0.368052i) q^{82} +(1.82050 + 0.386959i) q^{83} +(-0.974484 - 4.69474i) q^{84} +(0.507207 - 1.13920i) q^{85} +(-0.271144 - 1.27563i) q^{86} +(3.85743 + 12.0678i) q^{87} +(-6.38991 + 7.96427i) q^{88} +5.49170i q^{89} +(-1.18111 + 5.30687i) q^{90} +(-17.7844 + 12.9211i) q^{91} +(-0.727500 - 1.63399i) q^{92} +(-1.13481 - 11.3167i) q^{93} +(4.90755 + 4.41878i) q^{94} +(-0.606408 + 5.76958i) q^{95} +(-5.47606 + 2.40683i) q^{96} +(1.29476 + 1.43798i) q^{97} -13.8002 q^{98} +(9.93873 - 0.470752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27}+ \cdots + 35 q^{99}+O(q^{100}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more