LMFDB - Embedded newform 798.2.bp.d.613.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(289,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 6, 2]))

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

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

chi := DirichletCharacter("798.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bp (of order $9$, degree $6$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			613.3
Character	$\chi$	$=$	798.613
Dual form			798.2.bp.d.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.201991 + 1.14555i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.58268 - 2.12017i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.201991 + 1.14555i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.58268 - 2.12017i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.891079 + 0.747704i) q^{10} +(1.52163 + 2.63554i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.495051 + 2.80757i) q^{13} +(2.57522 - 0.606813i) q^{14} +(-0.891079 + 0.747704i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.655973 - 3.72021i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.780838 + 4.28839i) q^{19} -1.16322 q^{20} +(2.57522 - 0.606813i) q^{21} +(-0.528457 + 2.99703i) q^{22} +(-6.81832 - 2.48167i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(3.42698 + 1.24732i) q^{25} +(-1.42544 + 2.46894i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(2.36279 + 1.19048i) q^{28} +(-0.917183 - 0.333827i) q^{29} -1.16322 q^{30} +5.30811 q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.528457 + 2.99703i) q^{33} +(2.89381 - 2.42819i) q^{34} +(2.10907 + 2.24130i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(0.716851 + 1.24162i) q^{37} +(-2.15837 + 3.78701i) q^{38} +(-1.42544 + 2.46894i) q^{39} +(-0.891079 - 0.747704i) q^{40} +(-1.50894 + 8.55761i) q^{41} +(2.36279 + 1.19048i) q^{42} +(0.494069 + 0.414573i) q^{43} +(-2.33127 + 1.95617i) q^{44} -1.16322 q^{45} +(-3.62795 - 6.28380i) q^{46} +(-1.16848 - 6.62680i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-1.99022 - 6.71111i) q^{49} +(1.82346 + 3.15832i) q^{50} +(2.89381 - 2.42819i) q^{51} +(-2.67896 + 0.975060i) q^{52} +(-2.32528 - 13.1873i) q^{53} +(-0.939693 + 0.342020i) q^{54} +(-3.32650 + 1.21075i) q^{55} +(1.04478 + 2.43073i) q^{56} +(-2.15837 + 3.78701i) q^{57} +(-0.488023 - 0.845280i) q^{58} +(-2.29025 + 12.9887i) q^{59} +(-0.891079 - 0.747704i) q^{60} +(-0.821357 - 0.298949i) q^{61} +(4.06625 + 3.41199i) q^{62} +(2.36279 + 1.19048i) q^{63} +(-0.500000 - 0.866025i) q^{64} -3.31621 q^{65} +(-2.33127 + 1.95617i) q^{66} +(10.4839 - 8.79702i) q^{67} +3.77760 q^{68} +(-3.62795 - 6.28380i) q^{69} +(0.174961 + 3.07262i) q^{70} +(-1.80790 - 1.51700i) q^{71} +(-0.939693 - 0.342020i) q^{72} +(-9.83672 - 8.25399i) q^{73} +(-0.248960 + 1.41192i) q^{74} +(1.82346 + 3.15832i) q^{75} +(-4.08765 + 1.51365i) q^{76} +(7.99605 + 0.945118i) q^{77} +(-2.67896 + 0.975060i) q^{78} +(-13.8690 + 5.04789i) q^{79} +(-0.201991 - 1.14555i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-6.65664 + 5.58558i) q^{82} +(-2.88931 - 5.00443i) q^{83} +(1.04478 + 2.43073i) q^{84} +(4.12918 + 1.50290i) q^{85} +(0.111996 + 0.635163i) q^{86} +(-0.488023 - 0.845280i) q^{87} -3.04326 q^{88} +(10.8024 - 9.06429i) q^{89} +(-0.891079 - 0.747704i) q^{90} +(6.73604 + 3.39391i) q^{91} +(1.25997 - 7.14567i) q^{92} +(4.06625 + 3.41199i) q^{93} +(3.36451 - 5.82751i) q^{94} +(-5.07028 + 0.0282714i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(8.48175 - 3.08711i) q^{97} +(2.78922 - 6.42030i) q^{98} +(-2.33127 + 1.95617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{5} - 18 q^{8}+O(q^{10}) $ 36 * q - 6 * q^5 - 18 * q^8	$ 36 q - 6 q^{5} - 18 q^{8} + 3 q^{10} + 3 q^{11} - 18 q^{12} + 27 q^{13} + 12 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} - 12 q^{19} - 6 q^{20} + 12 q^{21} - 3 q^{22} - 9 q^{23} + 6 q^{25} + 9 q^{26} - 18 q^{27} + 9 q^{29} - 6 q^{30} + 6 q^{31} - 3 q^{33} - 3 q^{34} - 6 q^{35} + 21 q^{37} - 9 q^{38} + 9 q^{39} + 3 q^{40} - 9 q^{41} + 51 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 15 q^{47} + 24 q^{49} - 9 q^{50} - 3 q^{51} - 27 q^{52} + 30 q^{53} + 27 q^{55} - 9 q^{57} + 18 q^{58} + 6 q^{59} + 3 q^{60} + 30 q^{61} - 24 q^{62} - 18 q^{64} - 84 q^{65} + 6 q^{66} + 42 q^{67} - 36 q^{68} + 6 q^{69} - 24 q^{70} + 6 q^{71} + 66 q^{73} - 12 q^{74} - 9 q^{75} - 6 q^{76} + 9 q^{77} - 27 q^{78} + 12 q^{79} - 6 q^{80} - 18 q^{82} + 30 q^{83} + 36 q^{85} - 39 q^{86} + 18 q^{87} - 6 q^{88} + 66 q^{89} + 3 q^{90} - 9 q^{91} - 18 q^{92} - 24 q^{93} + 18 q^{94} - 57 q^{95} - 18 q^{96} + 45 q^{97} + 6 q^{99}+O(q^{100}) $ 36 * q - 6 * q^5 - 18 * q^8 + 3 * q^10 + 3 * q^11 - 18 * q^12 + 27 * q^13 + 12 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 - 12 * q^19 - 6 * q^20 + 12 * q^21 - 3 * q^22 - 9 * q^23 + 6 * q^25 + 9 * q^26 - 18 * q^27 + 9 * q^29 - 6 * q^30 + 6 * q^31 - 3 * q^33 - 3 * q^34 - 6 * q^35 + 21 * q^37 - 9 * q^38 + 9 * q^39 + 3 * q^40 - 9 * q^41 + 51 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 15 * q^47 + 24 * q^49 - 9 * q^50 - 3 * q^51 - 27 * q^52 + 30 * q^53 + 27 * q^55 - 9 * q^57 + 18 * q^58 + 6 * q^59 + 3 * q^60 + 30 * q^61 - 24 * q^62 - 18 * q^64 - 84 * q^65 + 6 * q^66 + 42 * q^67 - 36 * q^68 + 6 * q^69 - 24 * q^70 + 6 * q^71 + 66 * q^73 - 12 * q^74 - 9 * q^75 - 6 * q^76 + 9 * q^77 - 27 * q^78 + 12 * q^79 - 6 * q^80 - 18 * q^82 + 30 * q^83 + 36 * q^85 - 39 * q^86 + 18 * q^87 - 6 * q^88 + 66 * q^89 + 3 * q^90 - 9 * q^91 - 18 * q^92 - 24 * q^93 + 18 * q^94 - 57 * q^95 - 18 * q^96 + 45 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.201991	+	1.14555i	−0.0903332	+	0.512305i	0.905745	+	0.423824i	$0.139312\pi$
$5$	−0.201991	+	1.14555i	−0.0903332	+	0.512305i	−0.996078	+	0.0884812i	$0.971799\pi$
$6$	0.173648	+	0.984808i	0.0708916	+	0.402046i
$7$	1.58268	−	2.12017i	0.598198	−	0.801348i
$7$	1.58268	−	2.12017i	0.598198	−	0.801348i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−0.891079	+	0.747704i	−0.281784	+	0.236445i
$11$	1.52163	+	2.63554i	0.458789	+	0.794645i	0.998897	−	0.0469499i	$-0.0149501\pi$
$11$	1.52163	+	2.63554i	0.458789	+	0.794645i	−0.540108	+	0.841595i	$0.681617\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.495051	+	2.80757i	0.137302	+	0.778681i	0.973229	+	0.229839i	$0.0738200\pi$
$13$	0.495051	+	2.80757i	0.137302	+	0.778681i	−0.835926	+	0.548842i	$0.815069\pi$
$14$	2.57522	−	0.606813i	0.688258	−	0.162177i
$15$	−0.891079	+	0.747704i	−0.230076	+	0.193056i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.655973	−	3.72021i	0.159097	−	0.902283i	−0.795847	−	0.605497i	$-0.792974\pi$
$17$	0.655973	−	3.72021i	0.159097	−	0.902283i	0.954944	−	0.296786i	$-0.0959147\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	0.780838	+	4.28839i	0.179137	+	0.983824i
$19$	0.780838	+	4.28839i	0.179137	+	0.983824i
$20$	−1.16322			−0.260104
$21$	2.57522	−	0.606813i	0.561960	−	0.132417i
$22$	−0.528457	+	2.99703i	−0.112667	+	0.638968i
$23$	−6.81832	−	2.48167i	−1.42172	−	0.517463i	−0.487172	−	0.873306i	$-0.661972\pi$
$23$	−6.81832	−	2.48167i	−1.42172	−	0.517463i	−0.934546	+	0.355843i	$0.884194\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	3.42698	+	1.24732i	0.685396	+	0.249464i
$26$	−1.42544	+	2.46894i	−0.279552	+	0.484199i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	2.36279	+	1.19048i	0.446525	+	0.224979i
$29$	−0.917183	−	0.333827i	−0.170317	−	0.0619902i	0.255455	−	0.966821i	$-0.417775\pi$
$29$	−0.917183	−	0.333827i	−0.170317	−	0.0619902i	−0.425771	+	0.904831i	$0.639997\pi$
$30$	−1.16322			−0.212374
$31$	5.30811			0.953364			0.476682	−	0.879076i	$-0.341839\pi$
$31$	5.30811			0.953364			0.476682	+	0.879076i	$0.341839\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−0.528457	+	2.99703i	−0.0919925	+	0.521715i
$34$	2.89381	−	2.42819i	0.496284	−	0.416432i
$35$	2.10907	+	2.24130i	0.356497	+	0.378848i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	0.716851	+	1.24162i	0.117850	+	0.204121i	0.918915	−	0.394455i	$-0.129067\pi$
$37$	0.716851	+	1.24162i	0.117850	+	0.204121i	−0.801066	+	0.598576i	$0.795733\pi$
$38$	−2.15837	+	3.78701i	−0.350133	+	0.614334i
$39$	−1.42544	+	2.46894i	−0.228253	+	0.395347i
$40$	−0.891079	−	0.747704i	−0.140892	−	0.118222i
$41$	−1.50894	+	8.55761i	−0.235656	+	1.33647i	0.605570	+	0.795792i	$0.292945\pi$
$41$	−1.50894	+	8.55761i	−0.235656	+	1.33647i	−0.841227	+	0.540682i	$0.818166\pi$
$42$	2.36279	+	1.19048i	0.364586	+	0.183695i
$43$	0.494069	+	0.414573i	0.0753448	+	0.0632218i	0.679682	−	0.733507i	$-0.262118\pi$
$43$	0.494069	+	0.414573i	0.0753448	+	0.0632218i	−0.604337	+	0.796728i	$0.706562\pi$
$44$	−2.33127	+	1.95617i	−0.351453	+	0.294904i
$45$	−1.16322			−0.173403
$46$	−3.62795	−	6.28380i	−0.534913	−	0.926496i
$47$	−1.16848	−	6.62680i	−0.170441	−	0.966618i	−0.943276	−	0.332011i	$-0.892273\pi$
$47$	−1.16848	−	6.62680i	−0.170441	−	0.966618i	0.772835	−	0.634607i	$-0.218838\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	−1.99022	−	6.71111i	−0.284317	−	0.958730i
$50$	1.82346	+	3.15832i	0.257876	+	0.446654i
$51$	2.89381	−	2.42819i	0.405214	−	0.340015i
$52$	−2.67896	+	0.975060i	−0.371504	+	0.135216i
$53$	−2.32528	−	13.1873i	−0.319402	−	1.81142i	−0.546400	−	0.837524i	$-0.684002\pi$
$53$	−2.32528	−	13.1873i	−0.319402	−	1.81142i	0.226998	−	0.973895i	$-0.427109\pi$
$54$	−0.939693	+	0.342020i	−0.127876	+	0.0465430i
$55$	−3.32650	+	1.21075i	−0.448545	+	0.163257i
$56$	1.04478	+	2.43073i	0.139614	+	0.324820i
$57$	−2.15837	+	3.78701i	−0.285883	+	0.501602i
$58$	−0.488023	−	0.845280i	−0.0640805	−	0.110991i
$59$	−2.29025	+	12.9887i	−0.298165	+	1.69098i	0.355885	+	0.934530i	$0.384179\pi$
$59$	−2.29025	+	12.9887i	−0.298165	+	1.69098i	−0.654051	+	0.756451i	$0.726932\pi$
$60$	−0.891079	−	0.747704i	−0.115038	−	0.0965282i
$61$	−0.821357	−	0.298949i	−0.105164	−	0.0382765i	0.288902	−	0.957359i	$-0.406710\pi$
$61$	−0.821357	−	0.298949i	−0.105164	−	0.0382765i	−0.394066	+	0.919082i	$0.628932\pi$
$62$	4.06625	+	3.41199i	0.516414	+	0.433323i
$63$	2.36279	+	1.19048i	0.297683	+	0.149986i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−3.31621			−0.411325
$66$	−2.33127	+	1.95617i	−0.286960	+	0.240788i
$67$	10.4839	−	8.79702i	1.28081	−	1.07473i	0.287679	−	0.957727i	$-0.407116\pi$
$67$	10.4839	−	8.79702i	1.28081	−	1.07473i	0.993132	−	0.117001i	$-0.0373280\pi$
$68$	3.77760			0.458101
$69$	−3.62795	−	6.28380i	−0.436754	−	0.756481i
$70$	0.174961	+	3.07262i	0.0209118	+	0.367248i
$71$	−1.80790	−	1.51700i	−0.214558	−	0.180035i	0.529174	−	0.848513i	$-0.322502\pi$
$71$	−1.80790	−	1.51700i	−0.214558	−	0.180035i	−0.743732	+	0.668478i	$0.766946\pi$
$72$	−0.939693	−	0.342020i	−0.110744	−	0.0403075i
$73$	−9.83672	−	8.25399i	−1.15130	−	0.966056i	−0.151552	−	0.988449i	$-0.548427\pi$
$73$	−9.83672	−	8.25399i	−1.15130	−	0.966056i	−0.999749	+	0.0223928i	$0.992872\pi$
$74$	−0.248960	+	1.41192i	−0.0289410	+	0.164132i
$75$	1.82346	+	3.15832i	0.210555	+	0.364692i
$76$	−4.08765	+	1.51365i	−0.468885	+	0.173627i
$77$	7.99605	+	0.945118i	0.911234	+	0.107706i
$78$	−2.67896	+	0.975060i	−0.303332	+	0.110404i
$79$	−13.8690	+	5.04789i	−1.56038	+	0.567932i	−0.970824	−	0.239795i	$-0.922920\pi$
$79$	−13.8690	+	5.04789i	−1.56038	+	0.567932i	−0.589557	+	0.807727i	$0.700698\pi$
$80$	−0.201991	−	1.14555i	−0.0225833	−	0.128076i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−6.65664	+	5.58558i	−0.735103	+	0.616824i
$83$	−2.88931	−	5.00443i	−0.317143	−	0.549307i	0.662748	−	0.748843i	$-0.269390\pi$
$83$	−2.88931	−	5.00443i	−0.317143	−	0.549307i	−0.979891	+	0.199535i	$0.936057\pi$
$84$	1.04478	+	2.43073i	0.113994	+	0.265214i
$85$	4.12918	+	1.50290i	0.447872	+	0.163012i
$86$	0.111996	+	0.635163i	0.0120769	+	0.0684914i
$87$	−0.488023	−	0.845280i	−0.0523215	−	0.0906236i
$88$	−3.04326			−0.324413
$89$	10.8024	−	9.06429i	1.14505	−	0.960813i	0.145460	−	0.989364i	$-0.453534\pi$
$89$	10.8024	−	9.06429i	1.14505	−	0.960813i	0.999592	+	0.0285509i	$0.00908926\pi$
$90$	−0.891079	−	0.747704i	−0.0939280	−	0.0788149i
$91$	6.73604	+	3.39391i	0.706128	+	0.355779i
$92$	1.25997	−	7.14567i	0.131361	−	0.744988i
$93$	4.06625	+	3.41199i	0.421650	+	0.353806i
$94$	3.36451	−	5.82751i	0.347023	−	0.601062i
$95$	−5.07028	+	0.0282714i	−0.520200	+	0.00290059i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	8.48175	−	3.08711i	0.861192	−	0.313448i	0.126597	−	0.991954i	$-0.459595\pi$
$97$	8.48175	−	3.08711i	0.861192	−	0.313448i	0.734595	+	0.678506i	$0.237372\pi$
$98$	2.78922	−	6.42030i	0.281754	−	0.648548i
$99$	−2.33127	+	1.95617i	−0.234302	+	0.196602i
$100$	−0.633280	+	3.59151i	−0.0633280	+	0.359151i
$101$	11.1830	+	4.07028i	1.11275	+	0.405008i	0.832001	−	0.554774i	$-0.187195\pi$
$101$	11.1830	+	4.07028i	1.11275	+	0.405008i	0.280748	+	0.959781i	$0.409417\pi$
$102$	3.77760			0.374038
$103$	13.6429			1.34427			0.672135	−	0.740429i	$-0.265377\pi$
$103$	13.6429			1.34427			0.672135	+	0.740429i	$0.265377\pi$
$104$	−2.67896	−	0.975060i	−0.262693	−	0.0956125i
$105$	0.174961	+	3.07262i	0.0170744	+	0.299857i
$106$	6.69538	−	11.5967i	0.650313	−	1.12638i
$107$	2.98435	−	5.16904i	0.288508	−	0.499710i	−0.684946	−	0.728594i	$-0.740174\pi$
$107$	2.98435	−	5.16904i	0.288508	−	0.499710i	0.973454	+	0.228884i	$0.0735076\pi$
$108$	−0.939693	−	0.342020i	−0.0904220	−	0.0329109i
$109$	14.3855	−	5.23590i	1.37788	−	0.501509i	0.456348	−	0.889802i	$-0.349157\pi$
$109$	14.3855	−	5.23590i	1.37788	−	0.501509i	0.921536	+	0.388293i	$0.126935\pi$
$110$	−3.32650	−	1.21075i	−0.317169	−	0.115440i
$111$	−0.248960	+	1.41192i	−0.0236302	+	0.134014i
$112$	−0.762097	+	2.53362i	−0.0720114	+	0.239404i
$113$	−14.3656			−1.35140			−0.675699	−	0.737177i	$-0.736158\pi$
$113$	−14.3656			−1.35140			−0.675699	+	0.737177i	$0.736158\pi$
$114$	−4.08765	+	1.51365i	−0.382843	+	0.141766i
$115$	4.22011	−	7.30945i	0.393527	−	0.681609i
$116$	0.169489	−	0.961217i	0.0157366	−	0.0892468i
$117$	−2.67896	+	0.975060i	−0.247670	+	0.0901443i
$118$	−10.1034	+	8.47775i	−0.930092	+	0.780440i
$119$	−6.84927	−	7.27869i	−0.627871	−	0.667236i
$120$	−0.201991	−	1.14555i	−0.0184392	−	0.104574i
$121$	0.869283	−	1.50564i	0.0790257	−	0.136877i
$122$	−0.437035	−	0.756966i	−0.0395673	−	0.0685325i
$123$	−6.65664	+	5.58558i	−0.600209	+	0.503635i
$124$	0.921743	+	5.22746i	0.0827750	+	0.469440i
$125$	−5.02914	+	8.71072i	−0.449820	+	0.779111i
$126$	1.04478	+	2.43073i	0.0930761	+	0.216547i
$127$	−3.43447	−	19.4778i	−0.304760	−	1.72838i	−0.624633	−	0.780918i	$-0.714752\pi$
$127$	−3.43447	−	19.4778i	−0.304760	−	1.72838i	0.319874	−	0.947460i	$-0.396360\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	0.111996	+	0.635163i	0.00986073	+	0.0559230i
$130$	−2.54036	−	2.13162i	−0.222805	−	0.186955i
$131$	1.21851	+	1.02245i	0.106462	+	0.0893322i	0.694465	−	0.719527i	$-0.255641\pi$
$131$	1.21851	+	1.02245i	0.106462	+	0.0893322i	−0.588003	+	0.808859i	$0.700086\pi$
$132$	−3.04326			−0.264882
$133$	10.3279	+	5.13166i	0.895545	+	0.444971i
$134$	13.6857			1.18227
$135$	−0.891079	−	0.747704i	−0.0766919	−	0.0643521i
$136$	2.89381	+	2.42819i	0.248142	+	0.208216i
$137$	1.45536	+	8.25375i	0.124340	+	0.705165i	0.981698	+	0.190445i	$0.0609931\pi$
$137$	1.45536	+	8.25375i	0.124340	+	0.705165i	−0.857358	+	0.514720i	$0.827896\pi$
$138$	1.25997	−	7.14567i	0.107256	−	0.608280i
$139$	−0.704802	−	3.99713i	−0.0597805	−	0.339032i	0.940218	−	0.340572i	$-0.110621\pi$
$139$	−0.704802	−	3.99713i	−0.0597805	−	0.339032i	−0.999999	+	0.00154029i	$0.999510\pi$
$140$	−1.84101	+	2.46622i	−0.155594	+	0.208434i
$141$	3.36451	−	5.82751i	0.283343	−	0.490765i
$142$	−0.409817	−	2.32419i	−0.0343910	−	0.195041i
$143$	−6.64619	+	5.57682i	−0.555782	+	0.466357i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.567678	−	0.983248i	0.0471431	−	0.0816543i
$146$	−2.22980	−	12.6458i	−0.184540	−	1.04658i
$147$	2.78922	−	6.42030i	0.230051	−	0.529537i
$148$	−1.09828	+	0.921566i	−0.0902780	+	0.0757522i
$149$	8.44428	−	3.07347i	0.691782	−	0.251788i	0.0278840	−	0.999611i	$-0.491123\pi$
$149$	8.44428	−	3.07347i	0.691782	−	0.251788i	0.663898	+	0.747823i	$0.268901\pi$
$150$	−0.633280	+	3.59151i	−0.0517071	+	0.293246i
$151$	4.68491	−	8.11449i	0.381252	−	0.660348i	−0.609989	−	0.792410i	$-0.708826\pi$
$151$	4.68491	−	8.11449i	0.381252	−	0.660348i	0.991242	+	0.132061i	$0.0421596\pi$
$152$	−4.10427	−	1.46797i	−0.332901	−	0.119068i
$153$	3.77760			0.305401
$154$	5.51782	+	5.86376i	0.444638	+	0.472516i
$155$	−1.07219	+	6.08070i	−0.0861204	+	0.488413i
$156$	−2.67896	−	0.975060i	−0.214488	−	0.0780673i
$157$	−14.4066	+	5.24357i	−1.14977	+	0.418483i	−0.845433	−	0.534081i	$-0.820658\pi$
$157$	−14.4066	+	5.24357i	−1.14977	+	0.418483i	−0.304338	+	0.952564i	$0.598435\pi$
$158$	−13.8690	−	5.04789i	−1.10336	−	0.401589i
$159$	6.69538	−	11.5967i	0.530978	−	0.919682i
$160$	0.581611	−	1.00738i	0.0459803	−	0.0796403i
$161$	−16.0528	+	10.5283i	−1.26514	+	0.829745i
$162$	−0.939693	−	0.342020i	−0.0738292	−	0.0268716i
$163$	−6.44479			−0.504795			−0.252398	−	0.967624i	$-0.581219\pi$
$163$	−6.44479			−0.504795			−0.252398	+	0.967624i	$0.581219\pi$
$164$	−8.68962			−0.678546
$165$	−3.32650	−	1.21075i	−0.258967	−	0.0942564i
$166$	1.00345	−	5.69083i	0.0778825	−	0.441694i
$167$	−9.28585	+	7.79175i	−0.718561	+	0.602944i	−0.926987	−	0.375094i	$-0.877610\pi$
$167$	−9.28585	+	7.79175i	−0.718561	+	0.602944i	0.208426	+	0.978038i	$0.433166\pi$
$168$	−0.762097	+	2.53362i	−0.0587970	+	0.195473i
$169$	4.57861	−	1.66648i	0.352201	−	0.128191i
$170$	2.19709	+	3.80547i	0.168509	+	0.291866i
$171$	−4.08765	+	1.51365i	−0.312590	+	0.115751i
$172$	−0.322481	+	0.558553i	−0.0245889	+	0.0425893i
$173$	10.4859	+	8.79868i	0.797225	+	0.668951i	0.947522	−	0.319690i	$-0.103579\pi$
$173$	10.4859	+	8.79868i	0.797225	+	0.668951i	−0.150297	+	0.988641i	$0.548023\pi$
$174$	0.169489	−	0.961217i	0.0128489	−	0.0728697i
$175$	8.06835	−	5.29166i	0.609910	−	0.400012i
$176$	−2.33127	−	1.95617i	−0.175726	−	0.147452i
$177$	−10.1034	+	8.47775i	−0.759417	+	0.637227i
$178$	14.1015			1.05695
$179$	−10.3548	−	17.9350i	−0.773951	−	1.34052i	−0.935382	−	0.353639i	$-0.884944\pi$
$179$	−10.3548	−	17.9350i	−0.773951	−	1.34052i	0.161431	−	0.986884i	$-0.448389\pi$
$180$	−0.201991	−	1.14555i	−0.0150555	−	0.0853842i
$181$	2.65755	+	0.967271i	0.197534	+	0.0718967i	0.438893	−	0.898539i	$-0.355371\pi$
$181$	2.65755	+	0.967271i	0.197534	+	0.0718967i	−0.241358	+	0.970436i	$0.577593\pi$
$182$	2.97854	+	6.92973i	0.220784	+	0.513666i
$183$	−0.437035	−	0.756966i	−0.0323065	−	0.0559566i
$184$	5.55835	−	4.66401i	0.409767	−	0.343835i
$185$	−1.56714	+	0.570391i	−0.115218	+	0.0419360i
$186$	0.921743	+	5.22746i	0.0675855	+	0.383296i
$187$	10.8029	−	3.93194i	0.789987	−	0.287532i
$188$	6.32322	−	2.30146i	0.461168	−	0.167851i
$189$	1.04478	+	2.43073i	0.0759963	+	0.176809i
$190$	−3.90224	−	3.23746i	−0.283098	−	0.234870i
$191$	−9.08162	−	15.7298i	−0.657123	−	1.13817i	−0.981357	−	0.192194i	$-0.938440\pi$
$191$	−9.08162	−	15.7298i	−0.657123	−	1.13817i	0.324234	−	0.945977i	$-0.394894\pi$
$192$	0.173648	−	0.984808i	0.0125320	−	0.0710724i
$193$	0.689587	+	0.578632i	0.0496376	+	0.0416509i	0.667269	−	0.744817i	$-0.267463\pi$
$193$	0.689587	+	0.578632i	0.0496376	+	0.0416509i	−0.617631	+	0.786468i	$0.711908\pi$
$194$	8.48175	+	3.08711i	0.608955	+	0.221641i
$195$	−2.54036	−	2.13162i	−0.181919	−	0.152648i
$196$	6.26356	−	3.12536i	0.447397	−	0.223240i
$197$	6.25880	+	10.8406i	0.445921	+	0.772357i	0.998116	−	0.0613576i	$-0.0195430\pi$
$197$	6.25880	+	10.8406i	0.445921	+	0.772357i	−0.552195	+	0.833715i	$0.686210\pi$
$198$	−3.04326			−0.216275
$199$	−3.20811	+	2.69192i	−0.227417	+	0.190825i	−0.749375	−	0.662146i	$-0.769646\pi$
$199$	−3.20811	+	2.69192i	−0.227417	+	0.190825i	0.521958	+	0.852971i	$0.325202\pi$
$200$	−2.79370	+	2.34419i	−0.197544	+	0.165759i
$201$	13.6857			0.965318
$202$	5.95035	+	10.3063i	0.418665	+	0.725149i
$203$	−2.15938	+	1.41624i	−0.151559	+	0.0994004i
$204$	2.89381	+	2.42819i	0.202607	+	0.170008i
$205$	−9.49837	−	3.45712i	−0.663395	−	0.241456i
$206$	10.4510	+	8.76946i	0.728158	+	0.610997i
$207$	1.25997	−	7.14567i	0.0875743	−	0.496659i
$208$	−1.42544	−	2.46894i	−0.0988366	−	0.171190i
$209$	−10.1141	+	8.58328i	−0.699606	+	0.593718i
$210$	−1.84101	+	2.46622i	−0.127042	+	0.170186i
$211$	−15.2712	+	5.55825i	−1.05131	+	0.382646i	−0.809157	−	0.587592i	$-0.800076\pi$
$211$	−15.2712	+	5.55825i	−1.05131	+	0.382646i	−0.242154	+	0.970238i	$0.577854\pi$
$212$	12.5832	−	4.57991i	0.864218	−	0.314550i
$213$	−0.409817	−	2.32419i	−0.0280802	−	0.159251i
$214$	5.60874	−	2.04141i	0.383405	−	0.139548i
$215$	−0.574712	+	0.482240i	−0.0391950	+	0.0328885i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	8.40106	−	11.2541i	0.570301	−	0.763976i
$218$	14.3855	+	5.23590i	0.974311	+	0.354620i
$219$	−2.22980	−	12.6458i	−0.150676	−	0.854527i
$220$	−1.76999	−	3.06572i	−0.119333	−	0.206691i
$221$	10.7695			0.724435
$222$	−1.09828	+	0.921566i	−0.0737117	+	0.0618514i
$223$	−5.60730	−	4.70508i	−0.375492	−	0.315076i	0.435437	−	0.900219i	$-0.356594\pi$
$223$	−5.60730	−	4.70508i	−0.375492	−	0.315076i	−0.810930	+	0.585143i	$0.801038\pi$
$224$	−2.21238	+	1.45100i	−0.147821	+	0.0969487i
$225$	−0.633280	+	3.59151i	−0.0422187	+	0.239434i
$226$	−11.0047	−	9.23401i	−0.732019	−	0.614237i
$227$	9.20549	−	15.9444i	0.610990	−	1.05826i	−0.380084	−	0.924952i	$-0.624105\pi$
$227$	9.20549	−	15.9444i	0.610990	−	1.05826i	0.991074	−	0.133313i	$-0.0425616\pi$
$228$	−4.10427	−	1.46797i	−0.271812	−	0.0972186i
$229$	5.20400	+	9.01359i	0.343890	+	0.595635i	0.985151	−	0.171687i	$-0.0549219\pi$
$229$	5.20400	+	9.01359i	0.343890	+	0.595635i	−0.641261	+	0.767322i	$0.721589\pi$
$230$	7.93121	−	2.88673i	0.522969	−	0.190345i
$231$	5.51782	+	5.86376i	0.363046	+	0.385807i
$232$	0.747694	−	0.627390i	0.0490885	−	0.0411902i
$233$	−0.701852	+	3.98040i	−0.0459798	+	0.260765i	−0.999129	−	0.0417373i	$-0.986711\pi$
$233$	−0.701852	+	3.98040i	−0.0459798	+	0.260765i	0.953149	+	0.302502i	$0.0978219\pi$
$234$	−2.67896	−	0.975060i	−0.175129	−	0.0637417i
$235$	7.82735			0.510600
$236$	−13.1890			−0.858533
$237$	−13.8690	−	5.04789i	−0.900886	−	0.327896i
$238$	−0.568192	−	9.97842i	−0.0368304	−	0.646805i
$239$	−0.556442	+	0.963786i	−0.0359933	+	0.0623421i	−0.883461	−	0.468505i	$-0.844793\pi$
$239$	−0.556442	+	0.963786i	−0.0359933	+	0.0623421i	0.847468	+	0.530847i	$0.178126\pi$
$240$	0.581611	−	1.00738i	0.0375428	−	0.0650260i
$241$	16.9889	+	6.18345i	1.09435	+	0.398311i	0.825231	−	0.564795i	$-0.191045\pi$
$241$	16.9889	+	6.18345i	1.09435	+	0.398311i	0.269120	+	0.963107i	$0.413267\pi$
$242$	1.63372	−	0.594625i	0.105019	−	0.0382239i
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$	0.151781	−	0.860790i	0.00971675	−	0.0551065i
$245$	8.08991	−	0.924309i	0.516846	−	0.0590520i
$246$	−8.68962			−0.554030
$247$	−11.6534	+	4.31523i	−0.741489	+	0.274572i
$248$	−2.65405	+	4.59696i	−0.168533	+	0.291907i
$249$	1.00345	−	5.69083i	0.0635908	−	0.360641i
$250$	−9.45169	+	3.44013i	−0.597777	+	0.217573i
$251$	−1.68394	+	1.41299i	−0.106289	+	0.0891875i	−0.694384	−	0.719605i	$-0.744323\pi$
$251$	−1.68394	+	1.41299i	−0.106289	+	0.0891875i	0.588094	+	0.808792i	$0.299878\pi$
$252$	−0.762097	+	2.53362i	−0.0480076	+	0.159603i
$253$	−3.83443	−	21.7461i	−0.241069	−	1.36717i
$254$	9.88916	−	17.1285i	0.620501	−	1.07474i
$255$	2.19709	+	3.80547i	0.137587	+	0.238308i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	0.422243	+	2.39466i	0.0263388	+	0.149375i	0.995141	−	0.0984607i	$-0.0313919\pi$
$257$	0.422243	+	2.39466i	0.0263388	+	0.149375i	−0.968802	+	0.247835i	$0.920281\pi$
$258$	−0.322481	+	0.558553i	−0.0200768	+	0.0347740i
$259$	3.76700	+	0.445252i	0.234070	+	0.0276666i
$260$	−0.575854	−	3.26583i	−0.0357129	−	0.202538i
$261$	0.169489	−	0.961217i	0.0104911	−	0.0594979i
$262$	0.276214	+	1.56649i	0.0170646	+	0.0967780i
$263$	−17.7331	−	14.8799i	−1.09347	−	0.917531i	−0.0965020	−	0.995333i	$-0.530765\pi$
$263$	−17.7331	−	14.8799i	−1.09347	−	0.917531i	−0.996969	+	0.0778018i	$0.975210\pi$
$264$	−2.33127	−	1.95617i	−0.143480	−	0.120394i
$265$	15.5764			0.956852
$266$	4.61308	+	10.5697i	0.282846	+	0.648073i
$267$	14.1015			0.863000
$268$	10.4839	+	8.79702i	0.640405	+	0.537364i
$269$	−11.4987	−	9.64854i	−0.701087	−	0.588282i	0.220996	−	0.975275i	$-0.429069\pi$
$269$	−11.4987	−	9.64854i	−0.701087	−	0.588282i	−0.922083	+	0.386993i	$0.873514\pi$
$270$	−0.201991	−	1.14555i	−0.0122928	−	0.0697159i
$271$	0.160139	−	0.908191i	0.00972772	−	0.0551687i	−0.979557	−	0.201164i	$-0.935527\pi$
$271$	0.160139	−	0.908191i	0.00972772	−	0.0551687i	0.989285	+	0.145996i	$0.0466386\pi$
$272$	0.655973	+	3.72021i	0.0397742	+	0.225571i
$273$	2.97854	+	6.92973i	0.180269	+	0.419406i
$274$	−4.19054	+	7.25822i	−0.253160	+	0.438485i
$275$	1.92724	+	10.9299i	0.116217	+	0.659098i
$276$	5.55835	−	4.66401i	0.334573	−	0.280740i
$277$	−16.3174	−	28.2626i	−0.980420	−	1.69814i	−0.660746	−	0.750609i	$-0.729760\pi$
$277$	−16.3174	−	28.2626i	−0.980420	−	1.69814i	−0.319673	−	0.947528i	$-0.603573\pi$
$278$	2.02940	−	3.51502i	0.121715	−	0.210817i
$279$	0.921743	+	5.22746i	0.0551833	+	0.312960i
$280$	−2.99555	+	0.705857i	−0.179019	+	0.0421830i
$281$	−17.0598	+	14.3148i	−1.01770	+	0.853952i	−0.989337	−	0.145646i	$-0.953474\pi$
$281$	−17.0598	+	14.3148i	−1.01770	+	0.853952i	−0.0283631	+	0.999598i	$0.509029\pi$
$282$	6.32322	−	2.30146i	0.376542	−	0.137050i
$283$	−2.65868	+	15.0781i	−0.158042	+	0.896302i	0.797909	+	0.602778i	$0.205939\pi$
$283$	−2.65868	+	15.0781i	−0.158042	+	0.896302i	−0.955952	+	0.293525i	$0.905172\pi$
$284$	1.18002	−	2.04385i	0.0700213	−	0.121280i
$285$	−3.90224	−	3.23746i	−0.231148	−	0.191770i
$286$	−8.67598			−0.513022
$287$	15.7554	+	16.7432i	0.930011	+	0.988320i
$288$	0.173648	−	0.984808i	0.0102323	−	0.0580304i
$289$	2.56513	+	0.933630i	0.150890	+	0.0549194i
$290$	1.06689	−	0.388315i	0.0626497	−	0.0228026i
$291$	8.48175	+	3.08711i	0.497209	+	0.180969i
$292$	6.42046	−	11.1206i	0.375729	−	0.650782i
$293$	−6.36577	+	11.0258i	−0.371893	+	0.644137i	−0.989857	−	0.142070i	$-0.954624\pi$
$293$	−6.36577	+	11.0258i	−0.371893	+	0.644137i	0.617964	+	0.786206i	$0.287958\pi$
$294$	6.26356	−	3.12536i	0.365298	−	0.182275i
$295$	−14.4165	−	5.24719i	−0.839364	−	0.305503i
$296$	−1.43370			−0.0833322
$297$	−3.04326			−0.176588
$298$	8.44428	+	3.07347i	0.489164	+	0.178041i
$299$	3.59204	−	20.3715i	0.207733	−	1.17811i
$300$	−2.79370	+	2.34419i	−0.161294	+	0.135342i
$301$	1.66092	−	0.391371i	0.0957338	−	0.0225582i
$302$	8.80474	−	3.20466i	0.506656	−	0.184408i
$303$	5.95035	+	10.3063i	0.341839	+	0.592082i
$304$	−2.20046	−	3.76271i	−0.126205	−	0.215806i
$305$	0.508368	−	0.880519i	0.0291091	−	0.0504184i
$306$	2.89381	+	2.42819i	0.165428	+	0.138811i
$307$	−3.03540	+	17.2146i	−0.173240	+	0.982490i	0.766917	+	0.641747i	$0.221790\pi$
$307$	−3.03540	+	17.2146i	−0.173240	+	0.982490i	−0.940156	+	0.340744i	$0.889321\pi$
$308$	0.457739	+	8.03869i	0.0260821	+	0.458047i
$309$	10.4510	+	8.76946i	0.594538	+	0.498877i
$310$	−4.72994	+	3.96889i	−0.268643	+	0.225418i
$311$	−5.26210			−0.298386			−0.149193	−	0.988808i	$-0.547668\pi$
$311$	−5.26210			−0.298386			−0.149193	+	0.988808i	$0.547668\pi$
$312$	−1.42544	−	2.46894i	−0.0806998	−	0.139776i
$313$	4.87641	+	27.6555i	0.275631	+	1.56318i	0.736950	+	0.675947i	$0.236265\pi$
$313$	4.87641	+	27.6555i	0.275631	+	1.56318i	−0.461320	+	0.887234i	$0.652624\pi$
$314$	−14.4066	−	5.24357i	−0.813011	−	0.295912i
$315$	−1.84101	+	2.46622i	−0.103729	+	0.138956i
$316$	−7.37952	−	12.7817i	−0.415130	−	0.719027i
$317$	−5.39651	+	4.52821i	−0.303098	+	0.254330i	−0.781633	−	0.623739i	$-0.785613\pi$
$317$	−5.39651	+	4.52821i	−0.303098	+	0.254330i	0.478534	+	0.878069i	$0.341168\pi$
$318$	12.5832	−	4.57991i	0.705631	−	0.256829i
$319$	−0.515798	−	2.92523i	−0.0288791	−	0.163782i
$320$	1.09307	−	0.397845i	0.0611045	−	0.0222402i
$321$	5.60874	−	2.04141i	0.313049	−	0.113941i
$322$	−19.0646	−	2.25340i	−1.06243	−	0.125577i
$323$	16.4659	−	0.0918123i	0.916188	−	0.00510857i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.80541	+	10.2390i	−0.100146	+	0.567957i
$326$	−4.93700	−	4.14263i	−0.273435	−	0.229439i
$327$	14.3855	+	5.23590i	0.795522	+	0.289546i
$328$	−6.65664	−	5.58558i	−0.367551	−	0.308412i
$329$	−15.8993	−	8.01075i	−0.876555	−	0.441647i
$330$	−1.76999	−	3.06572i	−0.0974349	−	0.168762i
$331$	−24.7430			−1.36000			−0.680000	−	0.733212i	$-0.738020\pi$
$331$	−24.7430			−1.36000			−0.680000	+	0.733212i	$0.738020\pi$
$332$	4.42668	−	3.71442i	0.242945	−	0.203855i
$333$	−1.09828	+	0.921566i	−0.0601853	+	0.0505015i
$334$	−12.1218			−0.663276
$335$	7.95977	+	13.7867i	0.434889	+	0.753249i
$336$	−2.21238	+	1.45100i	−0.120695	+	0.0791583i
$337$	17.7165	+	14.8659i	0.965078	+	0.809796i	0.981772	−	0.190064i	$-0.0608697\pi$
$337$	17.7165	+	14.8659i	0.965078	+	0.809796i	−0.0166940	+	0.999861i	$0.505314\pi$
$338$	4.57861	+	1.66648i	0.249044	+	0.0906445i
$339$	−11.0047	−	9.23401i	−0.597691	−	0.501522i
$340$	−0.763042	+	4.32742i	−0.0413817	+	0.234688i
$341$	8.07698	+	13.9897i	0.437393	+	0.757587i
$342$	−4.10427	−	1.46797i	−0.221934	−	0.0793787i
$343$	−17.3786	−	6.40197i	−0.938355	−	0.345674i
$344$	−0.606066	+	0.220590i	−0.0326769	+	0.0118934i
$345$	7.93121	−	2.88673i	0.427002	−	0.155416i
$346$	2.37695	+	13.4804i	0.127786	+	0.724708i
$347$	−23.3347	+	8.49313i	−1.25267	+	0.455935i	−0.881303	−	0.472551i	$-0.843333\pi$
$347$	−23.3347	+	8.49313i	−1.25267	+	0.455935i	−0.371368	+	0.928486i	$0.621111\pi$
$348$	0.747694	−	0.627390i	0.0400806	−	0.0336316i
$349$	6.79233	+	11.7647i	0.363585	+	0.629748i	0.988548	−	0.150906i	$-0.0482192\pi$
$349$	6.79233	+	11.7647i	0.363585	+	0.629748i	−0.624963	+	0.780655i	$0.714886\pi$
$350$	9.58213	+	1.13259i	0.512187	+	0.0605395i
$351$	−2.67896	−	0.975060i	−0.142992	−	0.0520449i
$352$	−0.528457	−	2.99703i	−0.0281668	−	0.159742i
$353$	8.08995	+	14.0122i	0.430584	+	0.745794i	0.996924	−	0.0783782i	$-0.0249742\pi$
$353$	8.08995	+	14.0122i	0.430584	+	0.745794i	−0.566339	+	0.824172i	$0.691641\pi$
$354$	−13.1890			−0.700989
$355$	2.10298	−	1.76461i	0.111615	−	0.0936558i
$356$	10.8024	+	9.06429i	0.572526	+	0.480407i
$357$	−0.568192	−	9.97842i	−0.0300719	−	0.528114i
$358$	3.59617	−	20.3949i	0.190064	−	1.07790i
$359$	7.13686	+	5.98854i	0.376669	+	0.316063i	0.811393	−	0.584501i	$-0.198710\pi$
$359$	7.13686	+	5.98854i	0.376669	+	0.316063i	−0.434724	+	0.900564i	$0.643154\pi$
$360$	0.581611	−	1.00738i	0.0306536	−	0.0530935i
$361$	−17.7806	+	6.69708i	−0.935820	+	0.352478i
$362$	1.41406	+	2.44922i	0.0743211	+	0.128728i
$363$	1.63372	−	0.594625i	0.0857479	−	0.0312097i
$364$	−2.17265	+	7.22305i	−0.113878	+	0.378590i
$365$	11.4423	−	9.60121i	0.598916	−	0.502551i
$366$	0.151781	−	0.860790i	0.00793370	−	0.0449942i
$367$	−28.7133	−	10.4508i	−1.49882	−	0.545527i	−0.543068	−	0.839689i	$-0.682737\pi$
$367$	−28.7133	−	10.4508i	−1.49882	−	0.545527i	−0.955756	+	0.294162i	$0.904960\pi$
$368$	7.25591			0.378240
$369$	−8.68962			−0.452364
$370$	−1.56714	−	0.570391i	−0.0814715	−	0.0296532i
$371$	−31.6395	−	15.9414i	−1.64264	−	0.827636i
$372$	−2.65405	+	4.59696i	−0.137606	+	0.238341i
$373$	4.66393	−	8.07816i	0.241489	−	0.418271i	−0.719650	−	0.694337i	$-0.755698\pi$
$373$	4.66393	−	8.07816i	0.241489	−	0.418271i	0.961139	+	0.276066i	$0.0890309\pi$
$374$	10.8029	+	3.93194i	0.558605	+	0.203316i
$375$	−9.45169	+	3.44013i	−0.488083	+	0.177648i
$376$	6.32322	+	2.30146i	0.326095	+	0.118689i
$377$	0.483192	−	2.74032i	0.0248857	−	0.141134i
$378$	−0.762097	+	2.53362i	−0.0391980	+	0.130315i
$379$	11.3264			0.581799			0.290899	−	0.956754i	$-0.406045\pi$
$379$	11.3264			0.581799			0.290899	+	0.956754i	$0.406045\pi$
$380$	−0.908287	−	4.98835i	−0.0465942	−	0.255897i
$381$	9.88916	−	17.1285i	0.506637	−	0.877521i
$382$	3.15401	−	17.8873i	0.161373	−	0.915194i
$383$	−16.6039	+	6.04334i	−0.848422	+	0.308800i	−0.729397	−	0.684091i	$-0.760199\pi$
$383$	−16.6039	+	6.04334i	−0.848422	+	0.308800i	−0.119025	+	0.992891i	$0.537977\pi$
$384$	0.766044	−	0.642788i	0.0390920	−	0.0328021i
$385$	−2.69781	+	8.96896i	−0.137493	+	0.457101i
$386$	0.156317	+	0.886516i	0.00795631	+	0.0451225i
$387$	−0.322481	+	0.558553i	−0.0163926	+	0.0283928i
$388$	4.51305	+	7.81683i	0.229115	+	0.396839i
$389$	−11.0490	+	9.27125i	−0.560209	+	0.470071i	−0.878380	−	0.477962i	$-0.841376\pi$
$389$	−11.0490	+	9.27125i	−0.560209	+	0.470071i	0.318172	+	0.948033i	$0.396931\pi$
$390$	−0.575854	−	3.26583i	−0.0291595	−	0.165372i
$391$	−13.7049	+	23.7377i	−0.693089	+	1.20047i
$392$	6.80710	+	1.63197i	0.343811	+	0.0824272i
$393$	0.276214	+	1.56649i	0.0139332	+	0.0790189i
$394$	−2.17366	+	12.3274i	−0.109507	+	0.621046i
$395$	−2.98120	−	16.9072i	−0.150000	−	0.850694i
$396$	−2.33127	−	1.95617i	−0.117151	−	0.0983012i
$397$	2.62349	+	2.20137i	0.131669	+	0.110483i	0.706244	−	0.707969i	$-0.250388\pi$
$397$	2.62349	+	2.20137i	0.131669	+	0.110483i	−0.574575	+	0.818452i	$0.694833\pi$
$398$	−4.18789			−0.209920
$399$	4.61308	+	10.5697i	0.230943	+	0.529149i
$400$	−3.64692			−0.182346
$401$	3.82988	+	3.21365i	0.191255	+	0.160482i	0.733387	−	0.679811i	$-0.237938\pi$
$401$	3.82988	+	3.21365i	0.191255	+	0.160482i	−0.542132	+	0.840293i	$0.682383\pi$
$402$	10.4839	+	8.79702i	0.522889	+	0.438756i
$403$	2.62778	+	14.9029i	0.130899	+	0.742366i
$404$	−2.06653	+	11.7199i	−0.102814	+	0.583087i
$405$	−0.201991	−	1.14555i	−0.0100370	−	0.0569228i
$406$	−2.56452	−	0.303122i	−0.127275	−	0.0150437i
$407$	−2.18156	+	3.77858i	−0.108136	+	0.187297i
$408$	0.655973	+	3.72021i	0.0324755	+	0.184178i
$409$	10.9076	−	9.15256i	0.539346	−	0.452565i	−0.331968	−	0.943291i	$-0.607713\pi$
$409$	10.9076	−	9.15256i	0.539346	−	0.452565i	0.871314	+	0.490726i	$0.163268\pi$
$410$	−5.05398	−	8.75374i	−0.249598	−	0.432317i
$411$	−4.19054	+	7.25822i	−0.206704	+	0.358022i
$412$	2.36906	+	13.4356i	0.116715	+	0.661924i
$413$	23.9134	+	25.4127i	1.17670	+	1.25048i
$414$	5.55835	−	4.66401i	0.273178	−	0.229223i
$415$	6.31643	−	2.29899i	0.310061	−	0.112853i
$416$	0.495051	−	2.80757i	0.0242719	−	0.137653i
$417$	2.02940	−	3.51502i	0.0993799	−	0.172131i
$418$	−13.2651	+	0.0739647i	−0.648815	+	0.00361773i
$419$	14.7788			0.721989			0.360995	−	0.932568i	$-0.382437\pi$
$419$	14.7788			0.721989			0.360995	+	0.932568i	$0.382437\pi$
$420$	−2.99555	+	0.705857i	−0.146168	+	0.0344423i
$421$	−2.11557	+	11.9980i	−0.103107	+	0.584746i	0.888853	+	0.458192i	$0.151503\pi$
$421$	−2.11557	+	11.9980i	−0.103107	+	0.584746i	−0.991960	+	0.126554i	$0.959608\pi$
$422$	−15.2712	−	5.55825i	−0.743389	−	0.270572i
$423$	6.32322	−	2.30146i	0.307445	−	0.111901i
$424$	12.5832	+	4.57991i	0.611094	+	0.222420i
$425$	6.88829	−	11.9309i	0.334131	−	0.578732i
$426$	1.18002	−	2.04385i	0.0571721	−	0.0990251i
$427$	−1.93377	+	1.26827i	−0.0935817	+	0.0613759i
$428$	5.60874	+	2.04141i	0.271109	+	0.0986754i
$429$	−8.67598			−0.418880
$430$	−0.750233			−0.0361794
$431$	7.02733	+	2.55774i	0.338494	+	0.123202i	0.505674	−	0.862725i	$-0.331244\pi$
$431$	7.02733	+	2.55774i	0.338494	+	0.123202i	−0.167180	+	0.985926i	$0.553466\pi$
$432$	0.173648	−	0.984808i	0.00835465	−	0.0473816i
$433$	−19.5422	+	16.3979i	−0.939138	+	0.788030i	−0.977435	−	0.211236i	$-0.932251\pi$
$433$	−19.5422	+	16.3979i	−0.939138	+	0.788030i	0.0382970	+	0.999266i	$0.487807\pi$
$434$	13.6696	−	3.22103i	0.656160	−	0.154614i
$435$	1.06689	−	0.388315i	0.0511533	−	0.0186183i
$436$	7.65438	+	13.2578i	0.366578	+	0.634932i
$437$	5.31835	−	31.1774i	0.254411	−	1.49142i
$438$	6.42046	−	11.1206i	0.306782	−	0.531361i
$439$	9.50997	+	7.97981i	0.453886	+	0.380856i	0.840876	−	0.541229i	$-0.182041\pi$
$439$	9.50997	+	7.97981i	0.453886	+	0.380856i	−0.386990	+	0.922084i	$0.626485\pi$
$440$	0.614712	−	3.48620i	0.0293052	−	0.166198i
$441$	6.26356	−	3.12536i	0.298265	−	0.148827i
$442$	8.24991	+	6.92250i	0.392408	+	0.329270i
$443$	−5.23302	+	4.39103i	−0.248628	+	0.208624i	−0.758581	−	0.651578i	$-0.774107\pi$
$443$	−5.23302	+	4.39103i	−0.248628	+	0.208624i	0.509953	+	0.860202i	$0.329663\pi$
$444$	−1.43370			−0.0680405
$445$	8.20160	+	14.2056i	0.388793	+	0.673410i
$446$	−1.27107	−	7.20860i	−0.0601870	−	0.341337i
$447$	8.44428	+	3.07347i	0.399401	+	0.145370i
$448$	−2.62746	−	0.310561i	−0.124136	−	0.0146726i
$449$	20.3320	+	35.2160i	0.959525	+	1.66195i	0.723656	+	0.690161i	$0.242460\pi$
$449$	20.3320	+	35.2160i	0.959525	+	1.66195i	0.235869	+	0.971785i	$0.424206\pi$
$450$	−2.79370	+	2.34419i	−0.131696	+	0.110506i
$451$	−24.8500	+	9.04465i	−1.17014	+	0.425896i
$452$	−2.49455	−	14.1473i	−0.117334	−	0.665434i
$453$	8.80474	−	3.20466i	0.413683	−	0.150568i
$454$	17.3007	−	6.29692i	0.811960	−	0.295529i
$455$	−5.24851	+	7.03092i	−0.246054	+	0.329615i
$456$	−2.20046	−	3.76271i	−0.103046	−	0.176205i
$457$	−4.91891	−	8.51980i	−0.230097	−	0.398539i	0.727740	−	0.685854i	$-0.240571\pi$
$457$	−4.91891	−	8.51980i	−0.230097	−	0.398539i	−0.957836	+	0.287314i	$0.907238\pi$
$458$	−1.80733	+	10.2499i	−0.0844510	+	0.478945i
$459$	2.89381	+	2.42819i	0.135071	+	0.113338i
$460$	7.93121	+	2.88673i	0.369795	+	0.134594i
$461$	−4.13233	−	3.46743i	−0.192462	−	0.161495i	0.541465	−	0.840723i	$-0.317870\pi$
$461$	−4.13233	−	3.46743i	−0.192462	−	0.161495i	−0.733927	+	0.679229i	$0.762314\pi$
$462$	0.457739	+	8.03869i	0.0212960	+	0.373994i
$463$	−5.78346	−	10.0172i	−0.268780	−	0.465541i	0.699767	−	0.714371i	$-0.253287\pi$
$463$	−5.78346	−	10.0172i	−0.268780	−	0.465541i	−0.968547	+	0.248830i	$0.919954\pi$
$464$	0.976046			0.0453118
$465$	−4.72994	+	3.96889i	−0.219346	+	0.184053i
$466$	−3.09620	+	2.59802i	−0.143429	+	0.120351i
$467$	−18.7392			−0.867146			−0.433573	−	0.901118i	$-0.642747\pi$
$467$	−18.7392			−0.867146			−0.433573	+	0.901118i	$0.642747\pi$
$468$	−1.42544	−	2.46894i	−0.0658911	−	0.114127i
$469$	−2.05848	−	36.1505i	−0.0950519	−	1.66928i
$470$	5.99610	+	5.03132i	0.276579	+	0.232078i
$471$	−14.4066	−	5.24357i	−0.663821	−	0.241611i
$472$	−10.1034	−	8.47775i	−0.465046	−	0.390220i
$473$	−0.340834	+	1.93297i	−0.0156716	+	0.0888779i
$474$	−7.37952	−	12.7817i	−0.338953	−	0.587083i
$475$	−2.67307	+	15.6702i	−0.122649	+	0.718997i
$476$	5.97875	−	8.00914i	0.274035	−	0.367098i
$477$	12.5832	−	4.57991i	0.576145	−	0.209700i
$478$	−1.04577	+	0.380629i	−0.0478324	+	0.0174096i
$479$	−4.66457	−	26.4541i	−0.213130	−	1.20872i	−0.884123	−	0.467255i	$-0.845243\pi$
$479$	−4.66457	−	26.4541i	−0.213130	−	1.20872i	0.670993	−	0.741464i	$-0.265868\pi$
$480$	1.09307	−	0.397845i	0.0498916	−	0.0181591i
$481$	−3.13107	+	2.62728i	−0.142764	+	0.119794i
$482$	9.03960	+	15.6571i	0.411743	+	0.713159i
$483$	−19.0646	−	2.25340i	−0.867470	−	0.102533i
$484$	1.63372	+	0.594625i	0.0742599	+	0.0270284i
$485$	1.82319	+	10.3398i	0.0827869	+	0.469508i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	30.4372			1.37924			0.689621	−	0.724171i	$-0.257777\pi$
$487$	30.4372			1.37924			0.689621	+	0.724171i	$0.257777\pi$
$488$	0.669576	−	0.561841i	0.0303103	−	0.0254333i
$489$	−4.93700	−	4.14263i	−0.223259	−	0.187336i
$490$	6.79137	+	4.49204i	0.306803	+	0.202929i
$491$	1.29012	−	7.31664i	0.0582224	−	0.330195i	−0.941759	−	0.336288i	$-0.890828\pi$
$491$	1.29012	−	7.31664i	0.0582224	−	0.330195i	0.999981	+	0.00609289i	$0.00193944\pi$
$492$	−6.65664	−	5.58558i	−0.300104	−	0.251818i
$493$	−1.84355	+	3.19313i	−0.0830295	+	0.143811i
$494$	−11.7008	−	4.18501i	−0.526444	−	0.188293i
$495$	−1.76999	−	3.06572i	−0.0795552	−	0.137794i
$496$	−4.98799	+	1.81548i	−0.223967	+	0.0815174i
$497$	−6.07763	+	1.43210i	−0.272619	+	0.0642385i
$498$	4.42668	−	3.71442i	0.198364	−	0.166447i
$499$	−4.24006	+	24.0466i	−0.189811	+	1.07647i	0.729805	+	0.683655i	$0.239611\pi$
$499$	−4.24006	+	24.0466i	−0.189811	+	1.07647i	−0.919616	+	0.392818i	$0.871500\pi$
$500$	−9.45169	−	3.44013i	−0.422692	−	0.153847i
$501$	−12.1218			−0.541563
$502$	−2.19823			−0.0981118
$503$	14.5516	+	5.29636i	0.648824	+	0.236153i	0.645404	−	0.763841i	$-0.276689\pi$
$503$	14.5516	+	5.29636i	0.648824	+	0.236153i	0.00342044	+	0.999994i	$0.498911\pi$
$504$	−2.21238	+	1.45100i	−0.0985471	+	0.0646325i
$505$	−6.92157	+	11.9885i	−0.308006	+	0.533482i
$506$	11.0408	−	19.1232i	0.490824	−	0.850132i
$507$	4.57861	+	1.66648i	0.203343	+	0.0740109i
$508$	18.5855	−	6.76458i	0.824600	−	0.300130i
$509$	−7.92094	−	2.88299i	−0.351089	−	0.127786i	0.160454	−	0.987043i	$-0.448704\pi$
$509$	−7.92094	−	2.88299i	−0.351089	−	0.127786i	−0.511544	+	0.859257i	$0.670926\pi$
$510$	−0.763042	+	4.32742i	−0.0337880	+	0.191622i
$511$	−33.0683	+	7.79204i	−1.46285	+	0.344699i
$512$	1.00000			0.0441942
$513$	−4.10427	−	1.46797i	−0.181208	−	0.0648124i
$514$	−1.21580	+	2.10583i	−0.0536267	+	0.0928841i
$515$	−2.75574	+	15.6286i	−0.121432	+	0.688677i
$516$	−0.606066	+	0.220590i	−0.0266805	+	0.00971092i
$517$	15.6872	−	13.1631i	0.689922	−	0.578914i
$518$	2.59948	+	2.76246i	0.114215	+	0.121376i
$519$	2.37695	+	13.4804i	0.104337	+	0.591722i
$520$	1.65810	−	2.87192i	0.0727127	−	0.125942i
$521$	3.63942	+	6.30366i	0.159446	+	0.276168i	0.934669	−	0.355519i	$-0.115696\pi$
$521$	3.63942	+	6.30366i	0.159446	+	0.276168i	−0.775223	+	0.631687i	$0.782363\pi$
$522$	0.747694	−	0.627390i	0.0327257	−	0.0274601i
$523$	1.75079	+	9.92924i	0.0765568	+	0.434175i	0.998861	+	0.0477110i	$0.0151927\pi$
$523$	1.75079	+	9.92924i	0.0765568	+	0.434175i	−0.922304	+	0.386464i	$0.873696\pi$
$524$	−0.795328	+	1.37755i	−0.0347440	+	0.0601785i
$525$	9.58213	+	1.13259i	0.418199	+	0.0494303i
$526$	−4.01977	−	22.7973i	−0.175270	−	0.994008i
$527$	3.48197	−	19.7473i	0.151677	−	0.860204i
$528$	−0.528457	−	2.99703i	−0.0229981	−	0.130429i
$529$	22.7118	+	19.0575i	0.987470	+	0.828586i
$530$	11.9322	+	10.0123i	0.518303	+	0.434908i
$531$	−13.1890			−0.572355
$532$	−3.26027	+	11.0621i	−0.141351	+	0.479604i
$533$	−24.7731			−1.07304
$534$	10.8024	+	9.06429i	0.467466	+	0.392250i
$535$	5.31858	+	4.46282i	0.229942	+	0.192944i
$536$	2.37650	+	13.4778i	0.102649	+	0.582153i
$537$	3.59617	−	20.3949i	0.155186	−	0.880105i
$538$	−2.60654	−	14.7824i	−0.112376	−	0.637315i
$539$	14.6590	−	15.4571i	0.631409	−	0.665786i
$540$	0.581611	−	1.00738i	0.0250285	−	0.0433507i
$541$	5.87338	+	33.3096i	0.252516	+	1.43209i	0.802368	+	0.596830i	$0.203573\pi$
$541$	5.87338	+	33.3096i	0.252516	+	1.43209i	−0.549851	+	0.835262i	$0.685316\pi$
$542$	0.706447	−	0.592779i	0.0303445	−	0.0254621i
$543$	1.41406	+	2.44922i	0.0606829	+	0.105106i
$544$	−1.88880	+	3.27150i	−0.0809816	+	0.140264i
$545$	3.09223	+	17.5369i	0.132457	+	0.751200i
$546$	−2.17265	+	7.22305i	−0.0929809	+	0.309118i
$547$	−0.272603	+	0.228741i	−0.0116557	+	0.00978027i	−0.648597	−	0.761132i	$-0.724644\pi$
$547$	−0.272603	+	0.228741i	−0.0116557	+	0.00978027i	0.636941	+	0.770912i	$0.280199\pi$
$548$	−7.87563	+	2.86650i	−0.336430	+	0.122451i
$549$	0.151781	−	0.860790i	0.00647784	−	0.0367376i
$550$	−5.54926	+	9.61160i	−0.236621	+	0.409840i
$551$	0.715410	−	4.19390i	0.0304775	−	0.178666i
$552$	7.25591			0.308832
$553$	−11.2478	+	37.3937i	−0.478306	+	1.59014i
$554$	5.66699	−	32.1391i	0.240767	−	1.36546i
$555$	−1.56714	−	0.570391i	−0.0665212	−	0.0242118i
$556$	3.81402	−	1.38819i	0.161750	−	0.0588723i
$557$	2.22336	+	0.809235i	0.0942066	+	0.0342884i	0.388693	−	0.921367i	$-0.372927\pi$
$557$	2.22336	+	0.809235i	0.0942066	+	0.0342884i	−0.294487	+	0.955656i	$0.595149\pi$
$558$	−2.65405	+	4.59696i	−0.112355	+	0.194605i
$559$	−0.919355	+	1.59237i	−0.0388846	+	0.0673501i
$560$	−2.74844	−	1.38479i	−0.116143	−	0.0585179i
$561$	10.8029	+	3.93194i	0.456099	+	0.166007i
$562$	−22.2699			−0.939400
$563$	22.3010			0.939874			0.469937	−	0.882700i	$-0.344277\pi$
$563$	22.3010			0.939874			0.469937	+	0.882700i	$0.344277\pi$
$564$	6.32322	+	2.30146i	0.266256	+	0.0969091i
$565$	2.90172	−	16.4565i	0.122076	−	0.692328i
$566$	−11.7287	+	9.84155i	−0.492994	+	0.413671i
$567$	−0.762097	+	2.53362i	−0.0320051	+	0.106402i
$568$	2.21771	−	0.807181i	0.0930531	−	0.0338686i
$569$	−15.2474	−	26.4093i	−0.639205	−	1.10714i	−0.985608	−	0.169049i	$-0.945930\pi$
$569$	−15.2474	−	26.4093i	−0.639205	−	1.10714i	0.346403	−	0.938086i	$-0.387403\pi$
$570$	−0.908287	−	4.98835i	−0.0380440	−	0.208939i
$571$	−0.532338	+	0.922036i	−0.0222776	+	0.0385860i	−0.876949	−	0.480583i	$-0.840425\pi$
$571$	−0.532338	+	0.922036i	−0.0222776	+	0.0385860i	0.854672	+	0.519169i	$0.173758\pi$
$572$	−6.64619	−	5.57682i	−0.277891	−	0.233178i
$573$	3.15401	−	17.8873i	0.131761	−	0.747253i
$574$	1.30701	+	22.9534i	0.0545537	+	0.958056i
$575$	−20.2708	−	17.0092i	−0.845352	−	0.709335i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	−41.7481			−1.73800			−0.868998	−	0.494815i	$-0.835236\pi$
$577$	−41.7481			−1.73800			−0.868998	+	0.494815i	$0.835236\pi$
$578$	1.36488	+	2.36404i	0.0567714	+	0.0983309i
$579$	0.156317	+	0.886516i	0.00649630	+	0.0368424i
$580$	1.06689	+	0.388315i	0.0443000	+	0.0161239i
$581$	−15.1831	−	1.79461i	−0.629901	−	0.0744531i
$582$	4.51305	+	7.81683i	0.187072	+	0.324018i
$583$	31.2175	−	26.1946i	1.29290	−	1.08487i
$584$	12.0665	−	4.39186i	0.499316	−	0.181736i
$585$	−0.575854	−	3.26583i	−0.0238086	−	0.135025i
$586$	−11.9637	+	4.35445i	−0.494218	+	0.179881i
$587$	−26.1052	+	9.50153i	−1.07748	+	0.392170i	−0.818969	−	0.573838i	$-0.805454\pi$
$587$	−26.1052	+	9.50153i	−1.07748	+	0.392170i	−0.258510	+	0.966009i	$0.583232\pi$
$588$	6.80710	+	1.63197i	0.280720	+	0.0673015i
$589$	4.14477	+	22.7632i	0.170782	+	0.937943i
$590$	−7.67088	−	13.2864i	−0.315805	−	0.546991i
$591$	−2.17366	+	12.3274i	−0.0894123	+	0.507082i
$592$	−1.09828	−	0.921566i	−0.0451390	−	0.0378761i
$593$	31.0079	+	11.2859i	1.27334	+	0.463458i	0.888224	−	0.459410i	$-0.151939\pi$
$593$	31.0079	+	11.2859i	1.27334	+	0.463458i	0.385116	+	0.922868i	$0.374161\pi$
$594$	−2.33127	−	1.95617i	−0.0956533	−	0.0802626i
$595$	9.72159	−	6.37594i	0.398546	−	0.261388i
$596$	4.49311	+	7.78229i	0.184045	+	0.318775i
$597$	−4.18789			−0.171399
$598$	15.8462	−	13.2965i	0.648000	−	0.543736i
$599$	2.08451	−	1.74911i	0.0851706	−	0.0714666i	−0.599208	−	0.800593i	$-0.704518\pi$
$599$	2.08451	−	1.74911i	0.0851706	−	0.0714666i	0.684379	+	0.729127i	$0.260073\pi$
$600$	−3.64692			−0.148885
$601$	−21.3191	−	36.9258i	−0.869626	−	1.50624i	−0.862380	−	0.506262i	$-0.831027\pi$
$601$	−21.3191	−	36.9258i	−0.869626	−	1.50624i	−0.00724592	−	0.999974i	$-0.502306\pi$
$602$	1.52391	+	0.767812i	0.0621098	+	0.0312937i
$603$	10.4839	+	8.79702i	0.426937	+	0.358243i
$604$	8.80474	+	3.20466i	0.358260	+	0.130396i
$605$	1.54920	+	1.29993i	0.0629839	+	0.0528498i
$606$	−2.06653	+	11.7199i	−0.0839472	+	0.476088i
$607$	20.3474	+	35.2428i	0.825877	+	1.43046i	0.901247	+	0.433305i	$0.142653\pi$
$607$	20.3474	+	35.2428i	0.825877	+	1.43046i	−0.0753708	+	0.997156i	$0.524014\pi$
$608$	0.732968	−	4.29683i	0.0297258	−	0.174260i
$609$	−2.56452	−	0.303122i	−0.103920	−	0.0122831i
$610$	0.955419	−	0.347744i	0.0386838	−	0.0140797i
$611$	18.0268	−	6.56121i	0.729285	−	0.265438i
$612$	0.655973	+	3.72021i	0.0265161	+	0.150380i
$613$	5.69829	−	2.07401i	0.230152	−	0.0837684i	−0.224370	−	0.974504i	$-0.572032\pi$
$613$	5.69829	−	2.07401i	0.230152	−	0.0837684i	0.454522	+	0.890736i	$0.349810\pi$
$614$	−13.3906	+	11.2360i	−0.540401	+	0.453450i
$615$	−5.05398	−	8.75374i	−0.203796	−	0.352985i
$616$	−4.81652	+	6.45222i	−0.194063	+	0.259967i
$617$	16.4193	+	5.97615i	0.661017	+	0.240591i	0.650675	−	0.759356i	$-0.274486\pi$
$617$	16.4193	+	5.97615i	0.661017	+	0.240591i	0.0103417	+	0.999947i	$0.496708\pi$
$618$	2.36906	+	13.4356i	0.0952974	+	0.540459i
$619$	−6.45363	−	11.1780i	−0.259393	−	0.449283i	0.706686	−	0.707527i	$-0.250189\pi$
$619$	−6.45363	−	11.1780i	−0.259393	−	0.449283i	−0.966080	+	0.258245i	$0.916856\pi$
$620$	−6.17450			−0.247974
$621$	5.55835	−	4.66401i	0.223049	−	0.187160i
$622$	−4.03100	−	3.38241i	−0.161628	−	0.135622i
$623$	−2.12102	−	37.2488i	−0.0849770	−	1.49234i
$624$	0.495051	−	2.80757i	0.0198179	−	0.112393i
$625$	5.00578	+	4.20035i	0.200231	+	0.168014i
$626$	−14.0411	+	24.3198i	−0.561194	+	0.972016i
$627$	−13.2651	+	0.0739647i	−0.529755	+	0.00295386i
$628$	−7.66559	−	13.2772i	−0.305890	−	0.529818i
$629$	5.08933	−	1.85236i	0.202925	−	0.0738586i
$630$	−2.99555	+	0.705857i	−0.119346	+	0.0281220i
$631$	−23.7234	+	19.9063i	−0.944414	+	0.792458i	−0.978348	−	0.206966i	$-0.933641\pi$
$631$	−23.7234	+	19.9063i	−0.944414	+	0.792458i	0.0339336	+	0.999424i	$0.489197\pi$
$632$	2.56288	−	14.5348i	0.101946	−	0.578164i
$633$	−15.2712	−	5.55825i	−0.606975	−	0.220921i
$634$	−7.04465			−0.279779
$635$	23.0065			0.912987
$636$	12.5832	+	4.57991i	0.498957	+	0.181605i
$637$	17.8567	−	8.91003i	0.707507	−	0.353028i
$638$	1.48518	−	2.57241i	0.0587989	−	0.101843i
$639$	1.18002	−	2.04385i	0.0466809	−	0.0808536i
$640$	1.09307	+	0.397845i	0.0432074	+	0.0157262i
$641$	5.61821	−	2.04486i	0.221906	−	0.0807671i	−0.228675	−	0.973503i	$-0.573439\pi$
$641$	5.61821	−	2.04486i	0.221906	−	0.0807671i	0.450581	+	0.892736i	$0.351217\pi$
$642$	5.60874	+	2.04141i	0.221359	+	0.0805681i
$643$	−3.31492	+	18.7999i	−0.130728	+	0.741394i	0.847012	+	0.531574i	$0.178399\pi$
$643$	−3.31492	+	18.7999i	−0.130728	+	0.741394i	−0.977740	+	0.209821i	$0.932712\pi$
$644$	−13.1559	−	13.9807i	−0.518414	−	0.550917i
$645$	−0.750233			−0.0295404
$646$	12.6726	+	10.5138i	0.498598	+	0.413658i
$647$	22.2664	−	38.5665i	0.875381	−	1.51620i	0.0190245	−	0.999819i	$-0.493944\pi$
$647$	22.2664	−	38.5665i	0.875381	−	1.51620i	0.856356	−	0.516385i	$-0.172723\pi$
$648$	0.173648	−	0.984808i	0.00682154	−	0.0386869i
$649$	−37.7171	+	13.7279i	−1.48052	+	0.538867i
$650$	−7.96452	+	6.68302i	−0.312394	+	0.262130i
$651$	13.6696	−	3.22103i	0.535752	−	0.126242i
$652$	−1.11913	−	6.34688i	−0.0438284	−	0.248563i
$653$	8.18709	−	14.1805i	0.320386	−	0.554924i	−0.660182	−	0.751106i	$-0.729521\pi$
$653$	8.18709	−	14.1805i	0.320386	−	0.554924i	0.980568	+	0.196182i	$0.0628542\pi$
$654$	7.65438	+	13.2578i	0.299310	+	0.518420i
$655$	−1.41740	+	1.18934i	−0.0553824	+	0.0464713i
$656$	−1.50894	−	8.55761i	−0.0589141	−	0.334119i
$657$	6.42046	−	11.1206i	0.250486	−	0.433855i
$658$	−7.03033	−	16.3564i	−0.274071	−	0.637641i
$659$	−0.740342	−	4.19869i	−0.0288396	−	0.163558i	0.966987	−	0.254827i	$-0.0820186\pi$
$659$	−0.740342	−	4.19869i	−0.0288396	−	0.163558i	−0.995826	+	0.0912695i	$0.970908\pi$
$660$	0.614712	−	3.48620i	0.0239276	−	0.135700i
$661$	−6.18243	−	35.0623i	−0.240469	−	1.36377i	−0.830785	−	0.556593i	$-0.812108\pi$
$661$	−6.18243	−	35.0623i	−0.240469	−	1.36377i	0.590316	−	0.807172i	$-0.299003\pi$
$662$	−18.9543	−	15.9045i	−0.736679	−	0.618147i
$663$	8.24991	+	6.92250i	0.320400	+	0.268848i
$664$	5.77862			0.224254
$665$	−7.96472	+	10.7946i	−0.308859	+	0.418596i
$666$	−1.43370			−0.0555548
$667$	5.42520	+	4.55228i	0.210065	+	0.176265i
$668$	−9.28585	−	7.79175i	−0.359280	−	0.301472i
$669$	−1.27107	−	7.20860i	−0.0491424	−	0.278701i
$670$	−2.76440	+	15.6777i	−0.106798	+	0.605682i
$671$	−0.461908	−	2.61961i	−0.0178318	−	0.101129i
$672$	−2.62746	−	0.310561i	−0.101357	−	0.0119802i
$673$	9.18884	−	15.9155i	0.354204	−	0.613499i	−0.632778	−	0.774334i	$-0.718085\pi$
$673$	9.18884	−	15.9155i	0.354204	−	0.613499i	0.986981	+	0.160835i	$0.0514186\pi$
$674$	4.01600	+	22.7759i	0.154690	+	0.877293i
$675$	−2.79370	+	2.34419i	−0.107530	+	0.0902280i
$676$	2.43623	+	4.21967i	0.0937011	+	0.162295i
$677$	11.7298	−	20.3167i	0.450814	−	0.780833i	−0.547623	−	0.836725i	$-0.684467\pi$
$677$	11.7298	−	20.3167i	0.450814	−	0.780833i	0.998437	+	0.0558923i	$0.0178004\pi$
$678$	−2.49455	−	14.1473i	−0.0958028	−	0.543325i
$679$	6.87876	−	22.8687i	0.263983	−	0.877618i
$680$	−3.36614	+	2.82453i	−0.129086	+	0.108316i
$681$	17.3007	−	6.29692i	0.662962	−	0.241299i
$682$	−2.80510	+	15.9085i	−0.107413	+	0.609169i
$683$	1.21357	−	2.10196i	0.0464359	−	0.0804294i	−0.841873	−	0.539675i	$-0.818547\pi$
$683$	1.21357	−	2.10196i	0.0464359	−	0.0804294i	0.888309	+	0.459246i	$0.151880\pi$
$684$	−2.20046	−	3.76271i	−0.0841368	−	0.143871i
$685$	−9.74904			−0.372492
$686$	−9.19765	−	16.0749i	−0.351168	−	0.613744i
$687$	−1.80733	+	10.2499i	−0.0689540	+	0.391057i
$688$	−0.606066	−	0.220590i	−0.0231060	−	0.00840991i
$689$	35.8733	−	13.0568i	1.36666	−	0.497425i
$690$	7.93121	+	2.88673i	0.301936	+	0.109896i
$691$	−15.0882	+	26.1335i	−0.573981	+	0.994165i	0.422170	+	0.906517i	$0.361269\pi$
$691$	−15.0882	+	26.1335i	−0.573981	+	0.994165i	−0.996151	+	0.0876483i	$0.972065\pi$
$692$	−6.84416	+	11.8544i	−0.260176	+	0.450638i
$693$	0.457739	+	8.03869i	0.0173881	+	0.305365i
$694$	−23.3347	−	8.49313i	−0.885772	−	0.322395i
$695$	4.72127			0.179088
$696$	0.976046			0.0369969
$697$	30.8463	+	11.2271i	1.16839	+	0.425258i
$698$	−2.35895	+	13.3783i	−0.0892877	+	0.506376i
$699$	−3.09620	+	2.59802i	−0.117109	+	0.0982662i
$700$	6.61232	+	7.02689i	0.249922	+	0.265592i
$701$	11.9552	−	4.35134i	0.451542	−	0.164348i	−0.106231	−	0.994341i	$-0.533878\pi$
$701$	11.9552	−	4.35134i	0.451542	−	0.164348i	0.557773	+	0.829994i	$0.311656\pi$
$702$	−1.42544	−	2.46894i	−0.0537999	−	0.0931841i
$703$	−4.76482	+	4.04364i	−0.179708	+	0.152509i
$704$	1.52163	−	2.63554i	0.0573486	−	0.0993307i
$705$	5.99610	+	5.03132i	0.225826	+	0.189491i
$706$	−2.80961	+	15.9341i	−0.105741	+	0.599687i
$707$	26.3288	−	17.2679i	0.990197	−	0.649425i
$708$	−10.1034	−	8.47775i	−0.379709	−	0.318613i
$709$	10.4911	−	8.80307i	0.394001	−	0.330606i	−0.424168	−	0.905583i	$-0.639434\pi$
$709$	10.4911	−	8.80307i	0.394001	−	0.330606i	0.818169	+	0.574977i	$0.194989\pi$
$710$	2.74525			0.103027
$711$	−7.37952	−	12.7817i	−0.276754	−	0.479351i
$712$	2.44871	+	13.8873i	0.0917691	+	0.520449i
$713$	−36.1924	−	13.1729i	−1.35542	−	0.493331i
$714$	5.97875	−	8.00914i	0.223749	−	0.299735i
$715$	−5.04604	−	8.74000i	−0.188711	−	0.326858i
$716$	15.8644	−	13.3118i	0.592881	−	0.497486i
$717$	−1.04577	+	0.380629i	−0.0390550	+	0.0142148i
$718$	1.61779	+	9.17497i	0.0603756	+	0.342407i
$719$	13.0019	−	4.73231i	0.484890	−	0.176485i	−0.0879957	−	0.996121i	$-0.528046\pi$
$719$	13.0019	−	4.73231i	0.484890	−	0.176485i	0.572885	+	0.819635i	$0.305824\pi$
$720$	1.09307	−	0.397845i	0.0407363	−	0.0148268i
$721$	21.5923	−	28.9251i	0.804140	−	1.07723i
$722$	−17.9255	−	6.29888i	−0.667119	−	0.234420i
$723$	9.03960	+	15.6571i	0.336186	+	0.582292i
$724$	−0.491096	+	2.78515i	−0.0182514	+	0.103509i
$725$	−2.72678	−	2.28804i	−0.101270	−	0.0849757i
$726$	1.63372	+	0.594625i	0.0606329	+	0.0220686i
$727$	10.3199	+	8.65939i	0.382743	+	0.321159i	0.813778	−	0.581176i	$-0.197407\pi$
$727$	10.3199	+	8.65939i	0.382743	+	0.321159i	−0.431035	+	0.902335i	$0.641852\pi$
$728$	−6.30723	+	4.13662i	−0.233762	+	0.153313i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	14.9368			0.552837
$731$	1.86639	−	1.56609i	0.0690311	−	0.0579240i
$732$	0.669576	−	0.561841i	0.0247482	−	0.0207662i
$733$	10.0401			0.370838			0.185419	−	0.982660i	$-0.440636\pi$
$733$	10.0401			0.370838			0.185419	+	0.982660i	$0.440636\pi$
$734$	−15.2780	−	26.4623i	−0.563923	−	0.976743i
$735$	6.79137	+	4.49204i	0.250503	+	0.165691i
$736$	5.55835	+	4.66401i	0.204883	+	0.171918i
$737$	39.1375	+	14.2449i	1.44165	+	0.524717i
$738$	−6.65664	−	5.58558i	−0.245034	−	0.205608i
$739$	−5.93136	+	33.6384i	−0.218189	+	1.23741i	0.657098	+	0.753805i	$0.271784\pi$
$739$	−5.93136	+	33.6384i	−0.218189	+	1.23741i	−0.875287	+	0.483604i	$0.839327\pi$
$740$	−0.833856	−	1.44428i	−0.0306532	−	0.0530928i
$741$	−11.7008	−	4.18501i	−0.429840	−	0.153740i
$742$	−13.9904	−	32.5493i	−0.513602	−	1.19492i
$743$	6.36664	−	2.31727i	0.233569	−	0.0850123i	−0.222584	−	0.974914i	$-0.571449\pi$
$743$	6.36664	−	2.31727i	0.233569	−	0.0850123i	0.456153	+	0.889901i	$0.349227\pi$
$744$	−4.98799	+	1.81548i	−0.182869	+	0.0665587i
$745$	1.81514	+	10.2941i	0.0665014	+	0.377148i
$746$	8.76531	−	3.19031i	0.320921	−	0.116806i
$747$	4.42668	−	3.71442i	0.161964	−	0.135904i
$748$	5.74811	+	9.95601i	0.210172	+	0.364028i
$749$	−6.23595	−	14.5083i	−0.227857	−	0.530121i
$750$	−9.45169	−	3.44013i	−0.345127	−	0.125616i
$751$	0.923741	+	5.23879i	0.0337078	+	0.191166i	0.997012	−	0.0772452i	$-0.0246124\pi$
$751$	0.923741	+	5.23879i	0.0337078	+	0.191166i	−0.963304	+	0.268412i	$0.913501\pi$
$752$	3.36451	+	5.82751i	0.122691	+	0.212507i
$753$	−2.19823			−0.0801080
$754$	2.13159	−	1.78862i	0.0776279	−	0.0651376i
$755$	8.34924	+	7.00585i	0.303860	+	0.254969i
$756$	−2.21238	+	1.45100i	−0.0804634	+	0.0527722i
$757$	4.54880	−	25.7976i	0.165329	−	0.937628i	−0.783395	−	0.621524i	$-0.786514\pi$
$757$	4.54880	−	25.7976i	0.165329	−	0.937628i	0.948724	−	0.316104i	$-0.102375\pi$
$758$	8.67654	+	7.28048i	0.315146	+	0.264439i
$759$	11.0408	−	19.1232i	0.400756	−	0.694130i
$760$	2.51066	−	4.40513i	0.0910711	−	0.159791i
$761$	−4.29353	−	7.43661i	−0.155640	−	0.269577i	0.777652	−	0.628695i	$-0.216411\pi$
$761$	−4.29353	−	7.43661i	−0.155640	−	0.269577i	−0.933292	+	0.359118i	$0.883077\pi$
$762$	18.5855	−	6.76458i	0.673283	−	0.245055i
$763$	11.6668	−	38.7865i	0.422365	−	1.40417i
$764$	13.9139	−	11.6751i	0.503386	−	0.422391i
$765$	−0.763042	+	4.32742i	−0.0275878	+	0.156458i
$766$	−16.6039	−	6.04334i	−0.599925	−	0.218355i
$767$	−37.6004			−1.35767
$768$	1.00000			0.0360844
$769$	−51.7260	−	18.8267i	−1.86529	−	0.678909i	−0.974457	−	0.224575i	$-0.927900\pi$
$769$	−51.7260	−	18.8267i	−1.86529	−	0.678909i	−0.890831	−	0.454334i	$-0.849877\pi$
$770$	−7.83178	+	5.13650i	−0.282238	+	0.185107i
$771$	−1.21580	+	2.10583i	−0.0437860	+	0.0758396i
$772$	−0.450096	+	0.779589i	−0.0161993	+	0.0280580i
$773$	21.3777	+	7.78086i	0.768903	+	0.279858i	0.696538	−	0.717520i	$-0.254723\pi$
$773$	21.3777	+	7.78086i	0.768903	+	0.279858i	0.0723657	+	0.997378i	$0.476945\pi$
$774$	−0.606066	+	0.220590i	−0.0217846	+	0.00792894i
$775$	18.1908	+	6.62090i	0.653432	+	0.237830i
$776$	−1.56736	+	8.88897i	−0.0562651	+	0.319095i
$777$	2.59948	+	2.76246i	0.0932559	+	0.0991027i
$778$	−14.4235			−0.517107
$779$	−37.8766	+	0.211196i	−1.35707	+	0.00756689i
$780$	1.65810	−	2.87192i	0.0593697	−	0.102831i
$781$	1.24718	−	7.07310i	0.0446276	−	0.253095i
$782$	−25.7569	+	9.37474i	−0.921064	+	0.335240i
$783$	0.747694	−	0.627390i	0.0267204	−	0.0224211i
$784$	4.16553	+	5.62569i	0.148769	+	0.200917i
$785$	−3.09676	−	17.5626i	−0.110528	−	0.626837i
$786$	−0.795328	+	1.37755i	−0.0283684	+	0.0491355i
$787$	−23.6030	−	40.8816i	−0.841356	−	1.45727i	−0.888749	−	0.458394i	$-0.848425\pi$
$787$	−23.6030	−	40.8816i	−0.841356	−	1.45727i	0.0473934	−	0.998876i	$-0.484909\pi$
$788$	−9.58903	+	8.04615i	−0.341595	+	0.286632i
$789$	−4.01977	−	22.7973i	−0.143108	−	0.811604i
$790$	8.58401	−	14.8679i	0.305405	−	0.528978i
$791$	−22.7362	+	30.4574i	−0.808405	+	1.08294i
$792$	−0.528457	−	2.99703i	−0.0187779	−	0.106495i
$793$	0.432709	−	2.45401i	0.0153659	−	0.0871446i
$794$	0.594696	+	3.37269i	0.0211050	+	0.119692i
$795$	11.9322	+	10.0123i	0.423193	+	0.355101i
$796$	−3.20811	−	2.69192i	−0.113708	−	0.0954127i
$797$	42.3518			1.50018			0.750089	−	0.661337i	$-0.230010\pi$
$797$	42.3518			1.50018			0.750089	+	0.661337i	$0.230010\pi$
$798$	−3.26027	+	11.0621i	−0.115412	+	0.391595i
$799$	−25.4196			−0.899280
$800$	−2.79370	−	2.34419i	−0.0987722	−	0.0828797i
$801$	10.8024	+	9.06429i	0.381684	+	0.320271i
$802$	0.868164	+	4.92360i	0.0306559	+	0.173858i
$803$	6.78587	−	38.4846i	0.239468	−	1.35809i
$804$	2.37650	+	13.4778i	0.0838128	+	0.475326i
$805$	−8.81815	−	20.5159i	−0.310799	−	0.723090i
$806$	−7.56640	+	13.1054i	−0.266515	+	0.461618i
$807$	−2.60654	−	14.7824i	−0.0917545	−	0.520366i
$808$	−9.11646	+	7.64962i	−0.320716	+	0.269113i
$809$	17.8596	+	30.9338i	0.627911	+	1.08757i	0.987970	+	0.154644i	$0.0494232\pi$
$809$	17.8596	+	30.9338i	0.627911	+	1.08757i	−0.360059	+	0.932929i	$0.617243\pi$
$810$	0.581611	−	1.00738i	0.0204357	−	0.0353957i
$811$	−0.490901	−	2.78404i	−0.0172379	−	0.0977607i	0.974975	−	0.222315i	$-0.0713612\pi$
$811$	−0.490901	−	2.78404i	−0.0172379	−	0.0977607i	−0.992213	+	0.124554i	$0.960250\pi$
$812$	−1.76969	−	1.88065i	−0.0621041	−	0.0659978i
$813$	0.706447	−	0.592779i	0.0247762	−	0.0207897i
$814$	−4.10000	+	1.49228i	−0.143705	+	0.0523043i
$815$	1.30179	−	7.38283i	0.0455998	−	0.258609i
$816$	−1.88880	+	3.27150i	−0.0661212	+	0.114525i
$817$	−1.39206	+	2.44248i	−0.0487021	+	0.0854514i
$818$	14.2389			0.497850
$819$	−2.17265	+	7.22305i	−0.0759185	+	0.252394i
$820$	1.75523	−	9.95439i	0.0612952	−	0.347622i
$821$	41.9501	+	15.2686i	1.46407	+	0.532878i	0.946483	−	0.322753i	$-0.104608\pi$
$821$	41.9501	+	15.2686i	1.46407	+	0.532878i	0.517586	+	0.855631i	$0.326831\pi$
$822$	−7.87563	+	2.86650i	−0.274694	+	0.0999805i
$823$	10.2267	+	3.72220i	0.356479	+	0.129748i	0.514051	−	0.857760i	$-0.328144\pi$
$823$	10.2267	+	3.72220i	0.356479	+	0.129748i	−0.157572	+	0.987508i	$0.550367\pi$
$824$	−6.82143	+	11.8151i	−0.237636	+	0.411597i
$825$	−5.54926	+	9.61160i	−0.193200	+	0.334633i
$826$	1.98377	+	34.8385i	0.0690243	+	1.21219i
$827$	−8.10974	−	2.95170i	−0.282003	−	0.102641i	0.197146	−	0.980374i	$-0.436833\pi$
$827$	−8.10974	−	2.95170i	−0.282003	−	0.102641i	−0.479150	+	0.877733i	$0.659055\pi$
$828$	7.25591			0.252160
$829$	−2.68657			−0.0933085			−0.0466543	−	0.998911i	$-0.514856\pi$
$829$	−2.68657			−0.0933085			−0.0466543	+	0.998911i	$0.514856\pi$
$830$	6.31643	+	2.29899i	0.219247	+	0.0797992i
$831$	5.66699	−	32.1391i	0.196586	−	1.11489i
$832$	2.18390	−	1.83251i	0.0757133	−	0.0635310i
$833$	−26.2723	+	3.00172i	−0.910280	+	0.104004i
$834$	3.81402	−	1.38819i	0.132069	−	0.0480690i
$835$	−7.05018	−	12.2113i	−0.243981	−	0.422588i
$836$	−10.2092	−	8.46996i	−0.353091	−	0.292940i
$837$	−2.65405	+	4.59696i	−0.0917375	+	0.158894i
$838$	11.3212	+	9.49960i	0.391084	+	0.328158i
$839$	8.93173	−	50.6544i	0.308358	−	1.74878i	−0.298906	−	0.954283i	$-0.596622\pi$
$839$	8.93173	−	50.6544i	0.308358	−	1.74878i	0.607263	−	0.794501i	$-0.292267\pi$
$840$	−2.74844	−	1.38479i	−0.0948303	−	0.0477797i
$841$	−21.4855	−	18.0285i	−0.740879	−	0.621672i
$842$	−9.33278	+	7.83113i	−0.321629	+	0.269879i
$843$	−22.2699			−0.767017
$844$	−8.12562	−	14.0740i	−0.279695	−	0.484447i
$845$	0.984193	+	5.58164i	0.0338573	+	0.192014i
$846$	6.32322	+	2.30146i	0.217397	+	0.0791260i
$847$	−1.81641	−	4.22598i	−0.0624127	−	0.145206i
$848$	6.69538	+	11.5967i	0.229920	+	0.398234i
$849$	−11.7287	+	9.84155i	−0.402528	+	0.337761i
$850$	12.9458	−	4.71187i	0.444036	−	0.161616i
$851$	−1.80643	−	10.2448i	−0.0619236	−	0.351186i
$852$	2.21771	−	0.807181i	0.0759775	−	0.0276536i
$853$	4.97202	−	1.80967i	0.170239	−	0.0619618i	−0.255495	−	0.966810i	$-0.582238\pi$
$853$	4.97202	−	1.80967i	0.170239	−	0.0619618i	0.425733	+	0.904849i	$0.360016\pi$
$854$	−2.29658	−	0.271452i	−0.0785875	−	0.00928890i
$855$	−0.908287	−	4.98835i	−0.0310628	−	0.170598i
$856$	2.98435	+	5.16904i	0.102003	+	0.176674i
$857$	−6.69446	+	37.9661i	−0.228678	+	1.29690i	0.626849	+	0.779141i	$0.284344\pi$
$857$	−6.69446	+	37.9661i	−0.228678	+	1.29690i	−0.855527	+	0.517758i	$0.826767\pi$
$858$	−6.64619	−	5.57682i	−0.226897	−	0.190389i
$859$	−23.5340	−	8.56569i	−0.802971	−	0.292257i	−0.0922538	−	0.995736i	$-0.529407\pi$
$859$	−23.5340	−	8.56569i	−0.802971	−	0.292257i	−0.710717	+	0.703478i	$0.751629\pi$
$860$	−0.574712	−	0.482240i	−0.0195975	−	0.0164443i
$861$	1.30701	+	22.9534i	0.0445429	+	0.782250i
$862$	3.73916	+	6.47642i	0.127356	+	0.220588i
$863$	−39.4753			−1.34376			−0.671878	−	0.740662i	$-0.734512\pi$
$863$	−39.4753			−1.34376			−0.671878	+	0.740662i	$0.734512\pi$
$864$	0.766044	−	0.642788i	0.0260614	−	0.0218681i
$865$	−12.1974	+	10.2348i	−0.414723	+	0.347994i
$866$	−25.5105			−0.866883
$867$	1.36488	+	2.36404i	0.0463536	+	0.0802868i
$868$	12.5419	+	6.31918i	0.425701	+	0.214487i
$869$	−34.4074	−	28.8712i	−1.16719	−	0.979388i
$870$	1.06689	+	0.388315i	0.0361708	+	0.0131651i
$871$	29.8884	+	25.0793i	1.01273	+	0.849780i
$872$	−2.65834	+	15.0762i	−0.0900227	+	0.510544i
$873$	4.51305	+	7.81683i	0.152744	+	0.264560i
$874$	24.1145	−	20.4647i	0.815686	−	0.692229i
$875$	10.5087	+	24.4489i	0.355257	+	0.826525i
$876$	12.0665	−	4.39186i	0.407690	−	0.148387i
$877$	−8.02039	+	2.91918i	−0.270829	+	0.0985739i	−0.473865	−	0.880598i	$-0.657142\pi$
$877$	−8.02039	+	2.91918i	−0.270829	+	0.0985739i	0.203036	+	0.979171i	$0.434919\pi$
$878$	2.15573	+	12.2258i	0.0727525	+	0.412600i
$879$	−11.9637	+	4.35445i	−0.403527	+	0.146872i
$880$	2.71179	−	2.27546i	0.0914143	−	0.0767057i
$881$	−20.8889	−	36.1806i	−0.703765	−	1.21896i	−0.967135	−	0.254262i	$-0.918167\pi$
$881$	−20.8889	−	36.1806i	−0.703765	−	1.21896i	0.263370	−	0.964695i	$-0.415166\pi$
$882$	6.80710	+	1.63197i	0.229207	+	0.0549514i
$883$	−22.2109	−	8.08409i	−0.747455	−	0.272051i	−0.0599204	−	0.998203i	$-0.519085\pi$
$883$	−22.2109	−	8.08409i	−0.747455	−	0.272051i	−0.687534	+	0.726152i	$0.741307\pi$
$884$	1.87010	+	10.6059i	0.0628984	+	0.356714i
$885$	−7.67088	−	13.2864i	−0.257854	−	0.446616i
$886$	−6.83122			−0.229499
$887$	37.3358	−	31.3284i	1.25361	−	1.05191i	0.257280	−	0.966337i	$-0.417174\pi$
$887$	37.3358	−	31.3284i	1.25361	−	1.05191i	0.996332	−	0.0855688i	$-0.0272707\pi$
$888$	−1.09828	−	0.921566i	−0.0368558	−	0.0309257i
$889$	−46.7320	−	23.5456i	−1.56734	−	0.789695i
$890$	−2.84839	+	16.1540i	−0.0954781	+	0.541483i
$891$	−2.33127	−	1.95617i	−0.0781006	−	0.0655342i
$892$	3.65990	−	6.33914i	0.122543	−	0.212250i
$893$	27.5059	−	10.1854i	0.920450	−	0.340841i
$894$	4.49311	+	7.78229i	0.150272	+	0.260279i
$895$	22.6370	−	8.23918i	0.756670	−	0.275405i
$896$	−1.81313	−	1.92680i	−0.0605723	−	0.0643700i
$897$	15.8462	−	13.2965i	0.529089	−	0.443959i
$898$	−7.06122	+	40.0462i	−0.235636	+	1.33636i
$899$	−4.86851	−	1.77199i	−0.162374	−	0.0590992i
$900$	−3.64692			−0.121564
$901$	−50.5849			−1.68523
$902$	−24.8500	−	9.04465i	−0.827414	−	0.301154i
$903$	1.52391	+	0.767812i	0.0507124	+	0.0255512i
$904$	7.18278	−	12.4409i	0.238896	−	0.413780i
$905$	−1.64486	+	2.84898i	−0.0546770	+	0.0947033i
$906$	8.80474	+	3.20466i	0.292518	+	0.106468i
$907$	26.5531	−	9.66453i	0.881681	−	0.320906i	0.138793	−	0.990321i	$-0.455678\pi$
$907$	26.5531	−	9.66453i	0.881681	−	0.320906i	0.742888	+	0.669416i	$0.233456\pi$
$908$	17.3007	+	6.29692i	0.574142	+	0.208971i
$909$	−2.06653	+	11.7199i	−0.0685426	+	0.388725i
$910$	−8.53998	+	2.01232i	−0.283098	+	0.0667077i
$911$	−7.71356			−0.255562			−0.127781	−	0.991802i	$-0.540785\pi$
$911$	−7.71356			−0.255562			−0.127781	+	0.991802i	$0.540785\pi$
$912$	0.732968	−	4.29683i	0.0242710	−	0.142282i
$913$	8.79292	−	15.2298i	0.291003	−	0.504032i
$914$	1.70832	−	9.68836i	0.0565062	−	0.320462i
$915$	0.955419	−	0.347744i	0.0315852	−	0.0114961i
$916$	−7.97299	+	6.69013i	−0.263435	+	0.221048i
$917$	4.09629	−	0.965230i	0.135272	−	0.0318747i
$918$	0.655973	+	3.72021i	0.0216503	+	0.122785i
$919$	13.0681	−	22.6347i	0.431078	−	0.746648i	−0.565889	−	0.824482i	$-0.691467\pi$
$919$	13.0681	−	22.6347i	0.431078	−	0.746648i	0.996966	+	0.0778332i	$0.0248002\pi$
$920$	4.22011	+	7.30945i	0.139133	+	0.240985i
$921$	−13.3906	+	11.2360i	−0.441235	+	0.370240i
$922$	−0.936723	−	5.31242i	−0.0308493	−	0.174955i
$923$	3.36410	−	5.82679i	0.110731	−	0.191791i
$924$	−4.81652	+	6.45222i	−0.158452	+	0.212263i
$925$	0.907935	+	5.14916i	0.0298527	+	0.169303i
$926$	2.00857	−	11.3912i	0.0660058	−	0.374338i
$927$	2.36906	+	13.4356i	0.0778100	+	0.441283i
$928$	0.747694	+	0.627390i	0.0245443	+	0.0205951i
$929$	−15.9797	−	13.4086i	−0.524278	−	0.439922i	0.341842	−	0.939757i	$-0.388949\pi$
$929$	−15.9797	−	13.4086i	−0.524278	−	0.439922i	−0.866120	+	0.499836i	$0.833394\pi$
$930$	−6.17450			−0.202470
$931$	27.2258	−	13.7751i	0.892290	−	0.451462i
$932$	−4.04180			−0.132394
$933$	−4.03100	−	3.38241i	−0.131969	−	0.110735i
$934$	−14.3551	−	12.0453i	−0.469712	−	0.394135i
$935$	2.32213	+	13.1695i	0.0759419	+	0.430688i
$936$	0.495051	−	2.80757i	0.0161812	−	0.0917684i
$937$	−1.70747	−	9.68355i	−0.0557806	−	0.316348i	0.944132	−	0.329568i	$-0.106903\pi$
$937$	−1.70747	−	9.68355i	−0.0557806	−	0.316348i	−0.999913	+	0.0132199i	$0.995792\pi$
$938$	21.6602	−	29.0161i	0.707231	−	0.947408i
$939$	−14.0411	+	24.3198i	−0.458213	+	0.793648i
$940$	1.35920	+	7.70843i	0.0443324	+	0.251421i
$941$	14.5264	−	12.1891i	0.473546	−	0.397352i	−0.374540	−	0.927211i	$-0.622199\pi$
$941$	14.5264	−	12.1891i	0.473546	−	0.397352i	0.848086	+	0.529859i	$0.177755\pi$
$942$	−7.66559	−	13.2772i	−0.249758	−	0.432594i
$943$	31.5255	−	54.6039i	1.02661	−	1.77815i
$944$	−2.29025	−	12.9887i	−0.0745414	−	0.422745i
$945$	−2.99555	+	0.705857i	−0.0974454	+	0.0229615i
$946$	−1.50358	+	1.26165i	−0.0488856	+	0.0410199i
$947$	−23.2194	+	8.45117i	−0.754529	+	0.274626i	−0.690510	−	0.723323i	$-0.742614\pi$
$947$	−23.2194	+	8.45117i	−0.754529	+	0.274626i	−0.0640186	+	0.997949i	$0.520392\pi$
$948$	2.56288	−	14.5348i	0.0832385	−	0.472069i
$949$	18.3040	−	31.7035i	0.594173	−	1.02914i
$950$	−12.1203	+	10.2858i	−0.393234	+	0.333717i
$951$	−7.04465			−0.228438
$952$	9.72816	−	2.29229i	0.315292	−	0.0742937i
$953$	−4.68006	+	26.5420i	−0.151602	+	0.859778i	0.810225	+	0.586119i	$0.199345\pi$
$953$	−4.68006	+	26.5420i	−0.151602	+	0.859778i	−0.961827	+	0.273659i	$0.911766\pi$
$954$	12.5832	+	4.57991i	0.407396	+	0.148280i
$955$	19.8537	−	7.22616i	0.642451	−	0.233833i
$956$	−1.04577	−	0.380629i	−0.0338226	−	0.0123104i
$957$	1.48518	−	2.57241i	0.0480091	−	0.0831542i
$958$	13.4311	−	23.2633i	0.433939	−	0.751604i
$959$	19.8027	+	9.97747i	0.639463	+	0.322189i
$960$	1.09307	+	0.397845i	0.0352787	+	0.0128404i
$961$	−2.82400			−0.0910968
$962$	−4.08732			−0.131780
$963$	5.60874	+	2.04141i	0.180739	+	0.0657836i
$964$	−3.13942	+	17.8045i	−0.101114	+	0.573446i
$965$	−0.802142	+	0.673077i	−0.0258219	+	0.0216671i
$966$	−13.1559	−	13.9807i	−0.423284	−	0.449822i
$967$	28.2660	−	10.2880i	0.908973	−	0.330839i	0.155131	−	0.987894i	$-0.450420\pi$
$967$	28.2660	−	10.2880i	0.908973	−	0.330839i	0.753843	+	0.657055i	$0.228198\pi$
$968$	0.869283	+	1.50564i	0.0279398	+	0.0483932i
$969$	12.6726	+	10.5138i	0.407104	+	0.337750i
$970$	−5.24967	+	9.09270i	−0.168557	+	0.291949i
$971$	39.7248	+	33.3330i	1.27483	+	1.06971i	0.993935	+	0.109969i	$0.0350752\pi$
$971$	39.7248	+	33.3330i	1.27483	+	1.06971i	0.280894	+	0.959739i	$0.409369\pi$
$972$	0.173648	−	0.984808i	0.00556977	−	0.0315877i
$973$	−9.59006	−	4.83190i	−0.307443	−	0.154903i
$974$	23.3163	+	19.5647i	0.747101	+	0.626892i
$975$	−7.96452	+	6.68302i	−0.255069	+	0.214028i
$976$	0.874069			0.0279783
$977$	14.7261	+	25.5063i	0.471129	+	0.816020i	0.999455	−	0.0330221i	$-0.0105132\pi$
$977$	14.7261	+	25.5063i	0.471129	+	0.816020i	−0.528325	+	0.849042i	$0.677180\pi$
$978$	−1.11913	−	6.34688i	−0.0357857	−	0.202951i
$979$	40.3266	+	14.6777i	1.28884	+	0.469101i
$980$	2.31507	+	7.80651i	0.0739521	+	0.249370i
$981$	7.65438	+	13.2578i	0.244386	+	0.423288i
$982$	5.69134	−	4.77560i	0.181618	−	0.152395i
$983$	−31.9992	+	11.6468i	−1.02062	+	0.371474i	−0.797501	−	0.603318i	$-0.793845\pi$
$983$	−31.9992	+	11.6468i	−1.02062	+	0.371474i	−0.223116	+	0.974792i	$0.571623\pi$
$984$	−1.50894	−	8.55761i	−0.0481032	−	0.272807i
$985$	−13.6826	+	4.98006i	−0.435964	+	0.158678i
$986$	−3.46475	+	1.26107i	−0.110340	+	0.0401605i
$987$	−7.03033	−	16.3564i	−0.223778	−	0.520631i
$988$	−6.27327	−	10.7270i	−0.199579	−	0.341273i
$989$	−2.33989	−	4.05281i	−0.0744042	−	0.128872i
$990$	0.614712	−	3.48620i	0.0195368	−	0.110799i
$991$	24.1857	+	20.2942i	0.768283	+	0.644666i	0.940269	−	0.340433i	$-0.110574\pi$
$991$	24.1857	+	20.2942i	0.768283	+	0.644666i	−0.171985	+	0.985100i	$0.555018\pi$
$992$	−4.98799	−	1.81548i	−0.158369	−	0.0576415i
$993$	−18.9543	−	15.9045i	−0.601496	−	0.504715i
$994$	−5.57627	−	2.80957i	−0.176869	−	0.0891142i
$995$	−2.43572	−	4.21879i	−0.0772175	−	0.133745i
$996$	5.77862			0.183102
$997$	−29.1021	+	24.4196i	−0.921673	+	0.773375i	−0.974304	−	0.225239i	$-0.927684\pi$
$997$	−29.1021	+	24.4196i	−0.921673	+	0.773375i	0.0526308	+	0.998614i	$0.483239\pi$
$998$	−18.7049	+	15.6953i	−0.592094	+	0.496826i
$999$	−1.43370			−0.0453603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bp.d.613.3	yes	36
7.2	even	3		798.2.bq.d.499.4	yes	36
19.4	even	9		798.2.bq.d.403.4	yes	36
133.23	even	9	inner	798.2.bp.d.289.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.d.289.3	✓	36	133.23	even	9	inner
798.2.bp.d.613.3	yes	36	1.1	even	1	trivial
798.2.bq.d.403.4	yes	36	19.4	even	9
798.2.bq.d.499.4	yes	36	7.2	even	3

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.201991 + 1.14555i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.58268 - 2.12017i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.201991 + 1.14555i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.58268 - 2.12017i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.891079 + 0.747704i) q^{10} +(1.52163 + 2.63554i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.495051 + 2.80757i) q^{13} +(2.57522 - 0.606813i) q^{14} +(-0.891079 + 0.747704i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.655973 - 3.72021i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.780838 + 4.28839i) q^{19} -1.16322 q^{20} +(2.57522 - 0.606813i) q^{21} +(-0.528457 + 2.99703i) q^{22} +(-6.81832 - 2.48167i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(3.42698 + 1.24732i) q^{25} +(-1.42544 + 2.46894i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(2.36279 + 1.19048i) q^{28} +(-0.917183 - 0.333827i) q^{29} -1.16322 q^{30} +5.30811 q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.528457 + 2.99703i) q^{33} +(2.89381 - 2.42819i) q^{34} +(2.10907 + 2.24130i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(0.716851 + 1.24162i) q^{37} +(-2.15837 + 3.78701i) q^{38} +(-1.42544 + 2.46894i) q^{39} +(-0.891079 - 0.747704i) q^{40} +(-1.50894 + 8.55761i) q^{41} +(2.36279 + 1.19048i) q^{42} +(0.494069 + 0.414573i) q^{43} +(-2.33127 + 1.95617i) q^{44} -1.16322 q^{45} +(-3.62795 - 6.28380i) q^{46} +(-1.16848 - 6.62680i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-1.99022 - 6.71111i) q^{49} +(1.82346 + 3.15832i) q^{50} +(2.89381 - 2.42819i) q^{51} +(-2.67896 + 0.975060i) q^{52} +(-2.32528 - 13.1873i) q^{53} +(-0.939693 + 0.342020i) q^{54} +(-3.32650 + 1.21075i) q^{55} +(1.04478 + 2.43073i) q^{56} +(-2.15837 + 3.78701i) q^{57} +(-0.488023 - 0.845280i) q^{58} +(-2.29025 + 12.9887i) q^{59} +(-0.891079 - 0.747704i) q^{60} +(-0.821357 - 0.298949i) q^{61} +(4.06625 + 3.41199i) q^{62} +(2.36279 + 1.19048i) q^{63} +(-0.500000 - 0.866025i) q^{64} -3.31621 q^{65} +(-2.33127 + 1.95617i) q^{66} +(10.4839 - 8.79702i) q^{67} +3.77760 q^{68} +(-3.62795 - 6.28380i) q^{69} +(0.174961 + 3.07262i) q^{70} +(-1.80790 - 1.51700i) q^{71} +(-0.939693 - 0.342020i) q^{72} +(-9.83672 - 8.25399i) q^{73} +(-0.248960 + 1.41192i) q^{74} +(1.82346 + 3.15832i) q^{75} +(-4.08765 + 1.51365i) q^{76} +(7.99605 + 0.945118i) q^{77} +(-2.67896 + 0.975060i) q^{78} +(-13.8690 + 5.04789i) q^{79} +(-0.201991 - 1.14555i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-6.65664 + 5.58558i) q^{82} +(-2.88931 - 5.00443i) q^{83} +(1.04478 + 2.43073i) q^{84} +(4.12918 + 1.50290i) q^{85} +(0.111996 + 0.635163i) q^{86} +(-0.488023 - 0.845280i) q^{87} -3.04326 q^{88} +(10.8024 - 9.06429i) q^{89} +(-0.891079 - 0.747704i) q^{90} +(6.73604 + 3.39391i) q^{91} +(1.25997 - 7.14567i) q^{92} +(4.06625 + 3.41199i) q^{93} +(3.36451 - 5.82751i) q^{94} +(-5.07028 + 0.0282714i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(8.48175 - 3.08711i) q^{97} +(2.78922 - 6.42030i) q^{98} +(-2.33127 + 1.95617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 18 q^{8}+O(q^{10}) \) 36 * q - 6 * q^5 - 18 * q^8	\( 36 q - 6 q^{5} - 18 q^{8} + 3 q^{10} + 3 q^{11} - 18 q^{12} + 27 q^{13} + 12 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} - 12 q^{19} - 6 q^{20} + 12 q^{21} - 3 q^{22} - 9 q^{23} + 6 q^{25} + 9 q^{26} - 18 q^{27} + 9 q^{29} - 6 q^{30} + 6 q^{31} - 3 q^{33} - 3 q^{34} - 6 q^{35} + 21 q^{37} - 9 q^{38} + 9 q^{39} + 3 q^{40} - 9 q^{41} + 51 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 15 q^{47} + 24 q^{49} - 9 q^{50} - 3 q^{51} - 27 q^{52} + 30 q^{53} + 27 q^{55} - 9 q^{57} + 18 q^{58} + 6 q^{59} + 3 q^{60} + 30 q^{61} - 24 q^{62} - 18 q^{64} - 84 q^{65} + 6 q^{66} + 42 q^{67} - 36 q^{68} + 6 q^{69} - 24 q^{70} + 6 q^{71} + 66 q^{73} - 12 q^{74} - 9 q^{75} - 6 q^{76} + 9 q^{77} - 27 q^{78} + 12 q^{79} - 6 q^{80} - 18 q^{82} + 30 q^{83} + 36 q^{85} - 39 q^{86} + 18 q^{87} - 6 q^{88} + 66 q^{89} + 3 q^{90} - 9 q^{91} - 18 q^{92} - 24 q^{93} + 18 q^{94} - 57 q^{95} - 18 q^{96} + 45 q^{97} + 6 q^{99}+O(q^{100}) \) 36 * q - 6 * q^5 - 18 * q^8 + 3 * q^10 + 3 * q^11 - 18 * q^12 + 27 * q^13 + 12 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 - 12 * q^19 - 6 * q^20 + 12 * q^21 - 3 * q^22 - 9 * q^23 + 6 * q^25 + 9 * q^26 - 18 * q^27 + 9 * q^29 - 6 * q^30 + 6 * q^31 - 3 * q^33 - 3 * q^34 - 6 * q^35 + 21 * q^37 - 9 * q^38 + 9 * q^39 + 3 * q^40 - 9 * q^41 + 51 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 15 * q^47 + 24 * q^49 - 9 * q^50 - 3 * q^51 - 27 * q^52 + 30 * q^53 + 27 * q^55 - 9 * q^57 + 18 * q^58 + 6 * q^59 + 3 * q^60 + 30 * q^61 - 24 * q^62 - 18 * q^64 - 84 * q^65 + 6 * q^66 + 42 * q^67 - 36 * q^68 + 6 * q^69 - 24 * q^70 + 6 * q^71 + 66 * q^73 - 12 * q^74 - 9 * q^75 - 6 * q^76 + 9 * q^77 - 27 * q^78 + 12 * q^79 - 6 * q^80 - 18 * q^82 + 30 * q^83 + 36 * q^85 - 39 * q^86 + 18 * q^87 - 6 * q^88 + 66 * q^89 + 3 * q^90 - 9 * q^91 - 18 * q^92 - 24 * q^93 + 18 * q^94 - 57 * q^95 - 18 * q^96 + 45 * q^97 + 6 * q^99

Introduction

L-functions

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