LMFDB - Embedded newform 798.2.bq.d.499.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(25,798)]

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, 12, 14]))

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

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

chi := DirichletCharacter("798.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bq (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			499.3
Character	$\chi$	$=$	798.499
Dual form			798.2.bq.d.403.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.141838 + 0.0516247i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-0.599468 + 2.57694i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.141838 + 0.0516247i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-0.599468 + 2.57694i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(0.0262105 + 0.148647i) q^{10} +0.333377 q^{11} +1.00000 q^{12} +(-0.392511 - 2.22604i) q^{13} +(2.43370 + 1.03784i) q^{14} +(0.115627 - 0.0970226i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-4.09939 - 3.43980i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.710179 - 4.30066i) q^{19} +0.150940 q^{20} +(-0.318051 - 2.62656i) q^{21} +(0.0578904 - 0.328313i) q^{22} +(-0.718571 - 4.07522i) q^{23} +(0.173648 - 0.984808i) q^{24} +(-3.81277 + 3.19929i) q^{25} -2.26038 q^{26} +(-0.500000 + 0.866025i) q^{27} +(1.44468 - 2.21650i) q^{28} +(-5.92156 - 2.15527i) q^{29} +(-0.0754702 - 0.130718i) q^{30} +(2.11270 - 3.65930i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.313272 + 0.114022i) q^{33} +(-4.09939 + 3.43980i) q^{34} +(-0.0480068 - 0.396455i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-5.97002 + 10.3404i) q^{37} +(-4.35864 - 0.0474119i) q^{38} +(1.13019 + 1.95755i) q^{39} +(0.0262105 - 0.148647i) q^{40} +(0.300303 - 1.70311i) q^{41} +(-2.64189 - 0.142879i) q^{42} +(-2.15340 - 1.80692i) q^{43} +(-0.313272 - 0.114022i) q^{44} +(-0.0754702 + 0.130718i) q^{45} -4.13809 q^{46} +(4.86514 - 4.08234i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-6.28128 - 3.08959i) q^{49} +(2.48861 + 4.31040i) q^{50} +(5.02864 + 1.83028i) q^{51} +(-0.392511 + 2.22604i) q^{52} +(-5.93841 - 2.16141i) q^{53} +(0.766044 + 0.642788i) q^{54} +(-0.0472855 + 0.0172105i) q^{55} +(-1.93196 - 1.80763i) q^{56} +(2.13826 + 3.79840i) q^{57} +(-3.15080 + 5.45734i) q^{58} +(5.28732 + 4.43658i) q^{59} +(-0.141838 + 0.0516247i) q^{60} +(-0.305433 - 1.73220i) q^{61} +(-3.23685 - 2.71604i) q^{62} +(1.19721 + 2.35938i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.170592 + 0.295473i) q^{65} +(0.0578904 + 0.328313i) q^{66} +(0.654090 + 3.70953i) q^{67} +(2.67569 + 4.63442i) q^{68} +(2.06904 + 3.58369i) q^{69} +(-0.398768 - 0.0215662i) q^{70} +(-7.21818 - 6.05678i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-2.56513 + 0.933629i) q^{73} +(9.14661 + 7.67491i) q^{74} +(2.48861 - 4.31040i) q^{75} +(-0.803562 + 4.28419i) q^{76} +(-0.199849 + 0.859095i) q^{77} +(2.12407 - 0.773096i) q^{78} +(-7.43770 - 6.24097i) q^{79} +(-0.141838 - 0.0516247i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-1.62508 - 0.591482i) q^{82} +(-3.97822 - 6.89048i) q^{83} +(-0.599468 + 2.57694i) q^{84} +(0.759026 + 0.276263i) q^{85} +(-2.15340 + 1.80692i) q^{86} +6.30159 q^{87} +(-0.166689 + 0.288713i) q^{88} +(4.07414 + 1.48287i) q^{89} +(0.115627 + 0.0970226i) q^{90} +(5.97168 + 0.322961i) q^{91} +(-0.718571 + 4.07522i) q^{92} +(-0.733733 + 4.16121i) q^{93} +(-3.17550 - 5.50012i) q^{94} +(0.322750 + 0.573332i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-3.87650 + 1.41093i) q^{97} +(-4.13338 + 5.64935i) q^{98} +(0.255382 - 0.214291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} - 18 q^{8}+O(q^{10}) $ 36 * q + 3 * q^5 - 18 * q^8	$ 36 q + 3 q^{5} - 18 q^{8} - 6 q^{10} - 6 q^{11} + 36 q^{12} + 27 q^{13} + 3 q^{15} - 3 q^{17} - 18 q^{18} + 6 q^{19} - 6 q^{20} - 3 q^{22} - 18 q^{23} - 21 q^{25} - 18 q^{26} - 18 q^{27} + 12 q^{28} + 9 q^{29} + 3 q^{30} - 3 q^{31} - 3 q^{33} - 3 q^{34} + 12 q^{35} + 21 q^{37} + 9 q^{38} + 9 q^{39} - 6 q^{40} - 9 q^{41} - 15 q^{42} + 51 q^{43} - 3 q^{44} + 3 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{49} - 9 q^{50} - 3 q^{51} + 27 q^{52} - 15 q^{53} + 27 q^{55} - 9 q^{57} + 18 q^{58} + 33 q^{59} + 3 q^{60} + 21 q^{61} - 24 q^{62} + 3 q^{63} - 18 q^{64} + 42 q^{65} - 3 q^{66} - 3 q^{67} + 18 q^{68} + 6 q^{69} - 33 q^{70} + 6 q^{71} - 42 q^{73} - 3 q^{74} - 9 q^{75} - 6 q^{76} + 9 q^{77} - 27 q^{78} - 24 q^{79} + 3 q^{80} + 27 q^{82} + 30 q^{83} + 36 q^{85} + 51 q^{86} - 36 q^{87} + 3 q^{88} - 42 q^{89} + 3 q^{90} + 24 q^{91} - 18 q^{92} + 21 q^{93} + 18 q^{94} - 39 q^{95} - 18 q^{96} + 45 q^{97} + 3 q^{98} + 6 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 - 18 * q^8 - 6 * q^10 - 6 * q^11 + 36 * q^12 + 27 * q^13 + 3 * q^15 - 3 * q^17 - 18 * q^18 + 6 * q^19 - 6 * q^20 - 3 * q^22 - 18 * q^23 - 21 * q^25 - 18 * q^26 - 18 * q^27 + 12 * q^28 + 9 * q^29 + 3 * q^30 - 3 * q^31 - 3 * q^33 - 3 * q^34 + 12 * q^35 + 21 * q^37 + 9 * q^38 + 9 * q^39 - 6 * q^40 - 9 * q^41 - 15 * q^42 + 51 * q^43 - 3 * q^44 + 3 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 27 * q^52 - 15 * q^53 + 27 * q^55 - 9 * q^57 + 18 * q^58 + 33 * q^59 + 3 * q^60 + 21 * q^61 - 24 * q^62 + 3 * q^63 - 18 * q^64 + 42 * q^65 - 3 * q^66 - 3 * q^67 + 18 * q^68 + 6 * q^69 - 33 * q^70 + 6 * q^71 - 42 * q^73 - 3 * q^74 - 9 * q^75 - 6 * q^76 + 9 * q^77 - 27 * q^78 - 24 * q^79 + 3 * q^80 + 27 * q^82 + 30 * q^83 + 36 * q^85 + 51 * q^86 - 36 * q^87 + 3 * q^88 - 42 * q^89 + 3 * q^90 + 24 * q^91 - 18 * q^92 + 21 * q^93 + 18 * q^94 - 39 * q^95 - 18 * q^96 + 45 * q^97 + 3 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.141838	+	0.0516247i	−0.0634317	+	0.0230872i	−0.373541	−	0.927614i	$-0.621857\pi$
$5$	−0.141838	+	0.0516247i	−0.0634317	+	0.0230872i	0.310109	+	0.950701i	$0.399634\pi$
$6$	0.173648	+	0.984808i	0.0708916	+	0.402046i
$7$	−0.599468	+	2.57694i	−0.226578	+	0.973993i
$7$	−0.599468	+	2.57694i	−0.226578	+	0.973993i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	0.0262105	+	0.148647i	0.00828850	+	0.0470064i
$11$	0.333377			0.100517			0.0502585	−	0.998736i	$-0.483995\pi$
$11$	0.333377			0.100517			0.0502585	+	0.998736i	$0.483995\pi$
$12$	1.00000			0.288675
$13$	−0.392511	−	2.22604i	−0.108863	−	0.617393i	−0.989607	−	0.143800i	$-0.954068\pi$
$13$	−0.392511	−	2.22604i	−0.108863	−	0.617393i	0.880744	−	0.473593i	$-0.157043\pi$
$14$	2.43370	+	1.03784i	0.650433	+	0.277375i
$15$	0.115627	−	0.0970226i	0.0298548	−	0.0250511i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−4.09939	−	3.43980i	−0.994248	−	0.834273i	−0.00807057	−	0.999967i	$-0.502569\pi$
$17$	−4.09939	−	3.43980i	−0.994248	−	0.834273i	−0.986177	+	0.165695i	$0.947013\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.710179	−	4.30066i	−0.162926	−	0.986638i
$19$	−0.710179	−	4.30066i	−0.162926	−	0.986638i
$20$	0.150940			0.0337513
$21$	−0.318051	−	2.62656i	−0.0694045	−	0.573163i
$22$	0.0578904	−	0.328313i	0.0123423	−	0.0699965i
$23$	−0.718571	−	4.07522i	−0.149832	−	0.849742i	−0.963359	−	0.268215i	$-0.913566\pi$
$23$	−0.718571	−	4.07522i	−0.149832	−	0.849742i	0.813527	−	0.581528i	$-0.197545\pi$
$24$	0.173648	−	0.984808i	0.0354458	−	0.201023i
$25$	−3.81277	+	3.19929i	−0.762554	+	0.639859i
$26$	−2.26038			−0.443298
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	1.44468	−	2.21650i	0.273019	−	0.418880i
$29$	−5.92156	−	2.15527i	−1.09961	−	0.400224i	−0.272435	−	0.962174i	$-0.587829\pi$
$29$	−5.92156	−	2.15527i	−1.09961	−	0.400224i	−0.827171	+	0.561950i	$0.810051\pi$
$30$	−0.0754702	−	0.130718i	−0.0137789	−	0.0238658i
$31$	2.11270	−	3.65930i	0.379452	−	0.657231i	−0.611530	−	0.791221i	$-0.709446\pi$
$31$	2.11270	−	3.65930i	0.379452	−	0.657231i	0.990983	+	0.133990i	$0.0427791\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−0.313272	+	0.114022i	−0.0545337	+	0.0198487i
$34$	−4.09939	+	3.43980i	−0.703039	+	0.589920i
$35$	−0.0480068	−	0.396455i	−0.00811463	−	0.0670131i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	−5.97002	+	10.3404i	−0.981466	+	1.69995i	−0.324770	+	0.945793i	$0.605287\pi$
$37$	−5.97002	+	10.3404i	−0.981466	+	1.69995i	−0.656696	+	0.754155i	$0.728047\pi$
$38$	−4.35864	−	0.0474119i	−0.707065	−	0.00769122i
$39$	1.13019	+	1.95755i	0.180975	+	0.313459i
$40$	0.0262105	−	0.148647i	0.00414425	−	0.0235032i
$41$	0.300303	−	1.70311i	0.0468995	−	0.265980i	−0.952337	−	0.305048i	$-0.901328\pi$
$41$	0.300303	−	1.70311i	0.0468995	−	0.265980i	0.999237	+	0.0390673i	$0.0124387\pi$
$42$	−2.64189	−	0.142879i	−0.407653	−	0.0220467i
$43$	−2.15340	−	1.80692i	−0.328391	−	0.275553i	0.463653	−	0.886017i	$-0.346538\pi$
$43$	−2.15340	−	1.80692i	−0.328391	−	0.275553i	−0.792044	+	0.610464i	$0.790983\pi$
$44$	−0.313272	−	0.114022i	−0.0472276	−	0.0171894i
$45$	−0.0754702	+	0.130718i	−0.0112504	+	0.0194863i
$46$	−4.13809			−0.610128
$47$	4.86514	−	4.08234i	0.709654	−	0.595470i	−0.214848	−	0.976647i	$-0.568926\pi$
$47$	4.86514	−	4.08234i	0.709654	−	0.595470i	0.924502	+	0.381177i	$0.124481\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	−6.28128	−	3.08959i	−0.897325	−	0.441370i
$50$	2.48861	+	4.31040i	0.351942	+	0.609582i
$51$	5.02864	+	1.83028i	0.704151	+	0.256290i
$52$	−0.392511	+	2.22604i	−0.0544315	+	0.308697i
$53$	−5.93841	−	2.16141i	−0.815704	−	0.296892i	−0.0997260	−	0.995015i	$-0.531797\pi$
$53$	−5.93841	−	2.16141i	−0.815704	−	0.296892i	−0.715978	+	0.698123i	$0.754019\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	−0.0472855	+	0.0172105i	−0.00637597	+	0.00232066i
$56$	−1.93196	−	1.80763i	−0.258170	−	0.241554i
$57$	2.13826	+	3.79840i	0.283220	+	0.503110i
$58$	−3.15080	+	5.45734i	−0.413720	+	0.716584i
$59$	5.28732	+	4.43658i	0.688350	+	0.577594i	0.918433	−	0.395577i	$-0.129455\pi$
$59$	5.28732	+	4.43658i	0.688350	+	0.577594i	−0.230083	+	0.973171i	$0.573900\pi$
$60$	−0.141838	+	0.0516247i	−0.0183112	+	0.00666471i
$61$	−0.305433	−	1.73220i	−0.0391067	−	0.221785i	0.958991	−	0.283436i	$-0.0914744\pi$
$61$	−0.305433	−	1.73220i	−0.0391067	−	0.221785i	−0.998098	+	0.0616513i	$0.980363\pi$
$62$	−3.23685	−	2.71604i	−0.411080	−	0.344937i
$63$	1.19721	+	2.35938i	0.150834	+	0.297254i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.170592	+	0.295473i	0.0211593	+	0.0366489i
$66$	0.0578904	+	0.328313i	0.00712581	+	0.0404125i
$67$	0.654090	+	3.70953i	0.0799098	+	0.453191i	0.998339	+	0.0576066i	$0.0183469\pi$
$67$	0.654090	+	3.70953i	0.0799098	+	0.453191i	−0.918430	+	0.395585i	$0.870542\pi$
$68$	2.67569	+	4.63442i	0.324475	+	0.562006i
$69$	2.06904	+	3.58369i	0.249084	+	0.431425i
$70$	−0.398768	−	0.0215662i	−0.0476619	−	0.00257765i
$71$	−7.21818	−	6.05678i	−0.856641	−	0.718807i	0.104601	−	0.994514i	$-0.466644\pi$
$71$	−7.21818	−	6.05678i	−0.856641	−	0.718807i	−0.961242	+	0.275707i	$0.911088\pi$
$72$	0.173648	+	0.984808i	0.0204646	+	0.116061i
$73$	−2.56513	+	0.933629i	−0.300225	+	0.109273i	−0.487741	−	0.872989i	$-0.662179\pi$
$73$	−2.56513	+	0.933629i	−0.300225	+	0.109273i	0.187515	+	0.982262i	$0.439957\pi$
$74$	9.14661	+	7.67491i	1.06327	+	0.892191i
$75$	2.48861	−	4.31040i	0.287360	−	0.497722i
$76$	−0.803562	+	4.28419i	−0.0921748	+	0.491430i
$77$	−0.199849	+	0.859095i	−0.0227749	+	0.0979030i
$78$	2.12407	−	0.773096i	0.240503	−	0.0875359i
$79$	−7.43770	−	6.24097i	−0.836807	−	0.702164i	0.120036	−	0.992769i	$-0.461699\pi$
$79$	−7.43770	−	6.24097i	−0.836807	−	0.702164i	−0.956843	+	0.290605i	$0.906143\pi$
$80$	−0.141838	−	0.0516247i	−0.0158579	−	0.00577181i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	−1.62508	−	0.591482i	−0.179461	−	0.0653183i
$83$	−3.97822	−	6.89048i	−0.436666	−	0.756328i	0.560764	−	0.827976i	$-0.310508\pi$
$83$	−3.97822	−	6.89048i	−0.436666	−	0.756328i	−0.997430	+	0.0716478i	$0.977174\pi$
$84$	−0.599468	+	2.57694i	−0.0654073	+	0.281168i
$85$	0.759026	+	0.276263i	0.0823279	+	0.0299649i
$86$	−2.15340	+	1.80692i	−0.232207	+	0.194845i
$87$	6.30159			0.675601
$88$	−0.166689	+	0.288713i	−0.0177691	+	0.0307769i
$89$	4.07414	+	1.48287i	0.431858	+	0.157184i	0.548797	−	0.835956i	$-0.315086\pi$
$89$	4.07414	+	1.48287i	0.431858	+	0.157184i	−0.116939	+	0.993139i	$0.537308\pi$
$90$	0.115627	+	0.0970226i	0.0121882	+	0.0102271i
$91$	5.97168	+	0.322961i	0.626003	+	0.0338555i
$92$	−0.718571	+	4.07522i	−0.0749162	+	0.424871i
$93$	−0.733733	+	4.16121i	−0.0760846	+	0.431497i
$94$	−3.17550	−	5.50012i	−0.327527	−	0.567294i
$95$	0.322750	+	0.573332i	0.0331134	+	0.0588226i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−3.87650	+	1.41093i	−0.393598	+	0.143258i	−0.531235	−	0.847225i	$-0.678272\pi$
$97$	−3.87650	+	1.41093i	−0.393598	+	0.143258i	0.137636	+	0.990483i	$0.456050\pi$
$98$	−4.13338	+	5.64935i	−0.417535	+	0.570670i
$99$	0.255382	−	0.214291i	0.0256669	−	0.0215370i
$100$	4.67705	−	1.70231i	0.467705	−	0.170231i
$101$	12.8217	−	10.7586i	1.27580	−	1.07053i	0.281994	−	0.959416i	$-0.409004\pi$
$101$	12.8217	−	10.7586i	1.27580	−	1.07053i	0.993808	−	0.111109i	$-0.0354403\pi$
$102$	2.67569	−	4.63442i	0.264932	−	0.458876i
$103$	3.09556	+	5.36167i	0.305015	+	0.528301i	0.977265	−	0.212023i	$-0.0680052\pi$
$103$	3.09556	+	5.36167i	0.305015	+	0.528301i	−0.672250	+	0.740324i	$0.734672\pi$
$104$	2.12407	+	0.773096i	0.208282	+	0.0758083i
$105$	0.180707	+	0.356126i	0.0176352	+	0.0347544i
$106$	−3.15976	+	5.47287i	−0.306903	+	0.531572i
$107$	−6.60424			−0.638456			−0.319228	−	0.947678i	$-0.603424\pi$
$107$	−6.60424			−0.638456			−0.319228	+	0.947678i	$0.603424\pi$
$108$	0.766044	−	0.642788i	0.0737127	−	0.0618523i
$109$	−1.93559	+	10.9773i	−0.185396	+	1.05143i	0.740049	+	0.672553i	$0.234802\pi$
$109$	−1.93559	+	10.9773i	−0.185396	+	1.05143i	−0.925445	+	0.378881i	$0.876309\pi$
$110$	0.00873800	+	0.0495557i	0.000833135	+	0.00472495i
$111$	2.07337	−	11.7586i	0.196795	−	1.11608i
$112$	−2.11565	+	1.58872i	−0.199910	+	0.150120i
$113$	8.86878			0.834305			0.417152	−	0.908837i	$-0.363028\pi$
$113$	8.86878			0.834305			0.417152	+	0.908837i	$0.363028\pi$
$114$	4.11200	−	1.44619i	0.385124	−	0.135448i
$115$	0.312302	+	0.540923i	0.0291223	+	0.0504414i
$116$	4.82730	+	4.05058i	0.448203	+	0.376087i
$117$	−1.73155	−	1.45295i	−0.160082	−	0.134325i
$118$	5.28732	−	4.43658i	0.486737	−	0.408421i
$119$	11.3216	−	8.50185i	1.03785	−	0.779363i
$120$	0.0262105	+	0.148647i	0.00239268	+	0.0135696i
$121$	−10.8889			−0.989896
$122$	−1.75892			−0.159245
$123$	0.300303	+	1.70311i	0.0270775	+	0.153564i
$124$	−3.23685	+	2.71604i	−0.290677	+	0.243907i
$125$	0.752983	−	1.30420i	0.0673488	−	0.116652i
$126$	2.53143	−	0.769318i	0.225518	−	0.0685363i
$127$	−2.90758	−	16.4897i	−0.258006	−	1.46322i	−0.788237	−	0.615371i	$-0.789006\pi$
$127$	−2.90758	−	16.4897i	−0.258006	−	1.46322i	0.530231	−	0.847853i	$-0.322105\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	2.64154	+	0.961441i	0.232574	+	0.0846502i
$130$	0.320607	−	0.116691i	0.0281191	−	0.0102345i
$131$	1.70115	−	9.64771i	0.148630	−	0.842924i	−0.815750	−	0.578404i	$-0.803676\pi$
$131$	1.70115	−	9.64771i	0.148630	−	0.842924i	0.964380	−	0.264519i	$-0.0852133\pi$
$132$	0.333377			0.0290168
$133$	11.5083	+	0.748015i	0.997894	+	0.0648611i
$134$	3.76676			0.325398
$135$	0.0262105	−	0.148647i	0.00225584	−	0.0127935i
$136$	5.02864	−	1.83028i	0.431203	−	0.156945i
$137$	13.0622	+	4.75426i	1.11598	+	0.406183i	0.833184	−	0.552997i	$-0.186516\pi$
$137$	13.0622	+	4.75426i	1.11598	+	0.406183i	0.282796	+	0.959180i	$0.408738\pi$
$138$	3.88853	−	1.41531i	0.331014	−	0.120479i
$139$	−0.499103	−	2.83055i	−0.0423333	−	0.240084i	0.956298	−	0.292395i	$-0.0944523\pi$
$139$	−0.499103	−	2.83055i	−0.0423333	−	0.240084i	−0.998631	+	0.0523112i	$0.983341\pi$
$140$	−0.0904839	+	0.388965i	−0.00764728	+	0.0328735i
$141$	−3.17550	+	5.50012i	−0.267425	+	0.463194i
$142$	−7.21818	+	6.05678i	−0.605737	+	0.508273i
$143$	−0.130854	−	0.742112i	−0.0109426	−	0.0620586i
$144$	1.00000			0.0833333
$145$	0.951165			0.0789899
$146$	0.474016	+	2.68828i	0.0392298	+	0.222484i
$147$	6.95917	+	0.754941i	0.573983	+	0.0622665i
$148$	9.14661	−	7.67491i	0.751846	−	0.630874i
$149$	6.72281	+	5.64110i	0.550754	+	0.462137i	0.875196	−	0.483768i	$-0.160732\pi$
$149$	6.72281	+	5.64110i	0.550754	+	0.462137i	−0.324442	+	0.945905i	$0.605177\pi$
$150$	−3.81277	−	3.19929i	−0.311311	−	0.261221i
$151$	5.16768	+	8.95069i	0.420540	+	0.728397i	0.995992	−	0.0894386i	$-0.0285073\pi$
$151$	5.16768	+	8.95069i	0.420540	+	0.728397i	−0.575452	+	0.817835i	$0.695174\pi$
$152$	4.07957	+	1.53530i	0.330897	+	0.124529i
$153$	−5.35137			−0.432633
$154$	0.811340	+	0.345993i	0.0653796	+	0.0278809i
$155$	−0.110750	+	0.628094i	−0.00889565	+	0.0504498i
$156$	−0.392511	−	2.22604i	−0.0314261	−	0.178226i
$157$	−3.63758	+	20.6297i	−0.290311	+	1.64643i	0.395364	+	0.918525i	$0.370619\pi$
$157$	−3.63758	+	20.6297i	−0.290311	+	1.64643i	−0.685674	+	0.727908i	$0.740493\pi$
$158$	−7.43770	+	6.24097i	−0.591712	+	0.496505i
$159$	6.31953			0.501171
$160$	−0.0754702	+	0.130718i	−0.00596644	+	0.0103342i
$161$	10.9324	+	0.591245i	0.861592	+	0.0465967i
$162$	−0.939693	−	0.342020i	−0.0738292	−	0.0268716i
$163$	12.0763	+	20.9168i	0.945893	+	1.63833i	0.753954	+	0.656927i	$0.228144\pi$
$163$	12.0763	+	20.9168i	0.945893	+	1.63833i	0.191938	+	0.981407i	$0.438523\pi$
$164$	−0.864689	+	1.49769i	−0.0675209	+	0.116950i
$165$	0.0385475	−	0.0323452i	0.00300092	−	0.00251807i
$166$	−7.47660	+	2.72126i	−0.580297	+	0.211211i
$167$	−13.0200	+	10.9251i	−1.00752	+	0.845409i	−0.988008	−	0.154400i	$-0.950655\pi$
$167$	−13.0200	+	10.9251i	−1.00752	+	0.845409i	−0.0195113	+	0.999810i	$0.506211\pi$
$168$	2.43370	+	1.03784i	0.187764	+	0.0800713i
$169$	7.41480	−	2.69877i	0.570370	−	0.207598i
$170$	0.403869	−	0.699522i	0.0309753	−	0.0536509i
$171$	−3.30844	−	2.83800i	−0.253003	−	0.217027i
$172$	1.40553	+	2.43445i	0.107171	+	0.185625i
$173$	3.00210	−	17.0257i	0.228245	−	1.29444i	−0.628138	−	0.778102i	$-0.716183\pi$
$173$	3.00210	−	17.0257i	0.228245	−	1.29444i	0.856383	−	0.516341i	$-0.172706\pi$
$174$	1.09426	−	6.20586i	0.0829556	−	0.470465i
$175$	−5.95877	−	11.7432i	−0.450440	−	0.887700i
$176$	0.255382	+	0.214291i	0.0192501	+	0.0161528i
$177$	−6.48585	−	2.36066i	−0.487507	−	0.177438i
$178$	2.16781	−	3.75475i	0.162484	−	0.281430i
$179$	12.4860			0.933245			0.466623	−	0.884457i	$-0.345471\pi$
$179$	12.4860			0.933245			0.466623	+	0.884457i	$0.345471\pi$
$180$	0.115627	−	0.0970226i	0.00861833	−	0.00723164i
$181$	−11.6103	−	4.22579i	−0.862985	−	0.314101i	−0.127662	−	0.991818i	$-0.540747\pi$
$181$	−11.6103	−	4.22579i	−0.862985	−	0.314101i	−0.735323	+	0.677717i	$0.762969\pi$
$182$	1.35503	−	5.82488i	0.100441	−	0.431769i
$183$	0.879459	+	1.52327i	0.0650115	+	0.112603i
$184$	3.88853	+	1.41531i	0.286666	+	0.104338i
$185$	0.312955	−	1.77486i	0.0230089	−	0.130490i
$186$	3.97058	+	1.44517i	0.291137	+	0.105965i
$187$	−1.36664	−	1.14675i	−0.0999389	−	0.0838587i
$188$	−5.96798	+	2.17217i	−0.435260	+	0.158422i
$189$	−1.93196	−	1.80763i	−0.140530	−	0.131485i
$190$	0.620667	−	0.218289i	0.0450279	−	0.0158363i
$191$	−0.973162	+	1.68557i	−0.0704155	+	0.121963i	−0.899083	−	0.437777i	$-0.855766\pi$
$191$	−0.973162	+	1.68557i	−0.0704155	+	0.121963i	0.828668	+	0.559741i	$0.189099\pi$
$192$	0.766044	+	0.642788i	0.0552845	+	0.0463892i
$193$	−17.5984	+	6.40528i	−1.26676	+	0.461062i	−0.886031	−	0.463625i	$-0.846548\pi$
$193$	−17.5984	+	6.40528i	−1.26676	+	0.461062i	−0.380727	+	0.924688i	$0.624326\pi$
$194$	0.716347	+	4.06261i	0.0514307	+	0.291678i
$195$	−0.261361	−	0.219308i	−0.0187165	−	0.0157050i
$196$	4.84577	+	5.05159i	0.346126	+	0.360828i
$197$	−2.34061	−	4.05406i	−0.166762	−	0.288839i	0.770518	−	0.637418i	$-0.219998\pi$
$197$	−2.34061	−	4.05406i	−0.166762	−	0.288839i	−0.937279	+	0.348579i	$0.886664\pi$
$198$	−0.166689	−	0.288713i	−0.0118461	−	0.0205180i
$199$	−0.0420870	−	0.238687i	−0.00298347	−	0.0169201i	0.983280	−	0.182102i	$-0.0582900\pi$
$199$	−0.0420870	−	0.238687i	−0.00298347	−	0.0169201i	−0.986263	+	0.165182i	$0.947179\pi$
$200$	−0.864285	−	4.90160i	−0.0611142	−	0.346596i
$201$	−1.88338	−	3.26211i	−0.132843	−	0.230091i
$202$	−8.36874	−	14.4951i	−0.588823	−	1.01987i
$203$	9.10380	−	13.9675i	0.638961	−	0.980327i
$204$	−4.09939	−	3.43980i	−0.287015	−	0.240834i
$205$	0.0453279	+	0.257067i	0.00316584	+	0.0179544i
$206$	5.81775	−	2.11749i	0.405342	−	0.147532i
$207$	−3.16996	−	2.65991i	−0.220327	−	0.184877i
$208$	1.13019	−	1.95755i	0.0783647	−	0.135732i
$209$	−0.236758	−	1.43374i	−0.0163769	−	0.0991740i
$210$	0.382095	−	0.116121i	0.0263671	−	0.00801312i
$211$	17.2307	−	6.27146i	1.18621	−	0.431745i	0.327819	−	0.944741i	$-0.393686\pi$
$211$	17.2307	−	6.27146i	1.18621	−	0.431745i	0.858391	+	0.512995i	$0.171464\pi$
$212$	4.84104	+	4.06211i	0.332484	+	0.278987i
$213$	8.85441	+	3.22274i	0.606694	+	0.220819i
$214$	−1.14682	+	6.50391i	−0.0783947	+	0.444598i
$215$	0.398715	+	0.145120i	0.0271921	+	0.00989712i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	8.16333	+	7.63795i	0.554163	+	0.518498i
$218$	10.4744	+	3.81237i	0.709417	+	0.258207i
$219$	2.09111	−	1.75465i	0.141304	−	0.118568i
$220$	0.0503201			0.00339258
$221$	−6.04807	+	10.4756i	−0.406837	+	0.704663i
$222$	−11.2200	−	4.08374i	−0.753035	−	0.274082i
$223$	−6.39603	−	5.36691i	−0.428310	−	0.359395i	0.403004	−	0.915198i	$-0.367966\pi$
$223$	−6.39603	−	5.36691i	−0.428310	−	0.359395i	−0.831314	+	0.555804i	$0.812411\pi$
$224$	1.19721	+	2.35938i	0.0799919	+	0.157643i
$225$	−0.864285	+	4.90160i	−0.0576190	+	0.326773i
$226$	1.54005	−	8.73405i	0.102442	−	0.580980i
$227$	−2.67656	−	4.63594i	−0.177649	−	0.307698i	0.763426	−	0.645896i	$-0.223516\pi$
$227$	−2.67656	−	4.63594i	−0.177649	−	0.307698i	−0.941075	+	0.338198i	$0.890183\pi$
$228$	−0.710179	−	4.30066i	−0.0470327	−	0.284818i
$229$	−5.28240	+	9.14938i	−0.349071	+	0.604608i	−0.986085	−	0.166244i	$-0.946836\pi$
$229$	−5.28240	+	9.14938i	−0.349071	+	0.604608i	0.637014	+	0.770852i	$0.280169\pi$
$230$	0.586936	−	0.213627i	0.0387014	−	0.0140862i
$231$	−0.106031	−	0.875638i	−0.00697634	−	0.0576127i
$232$	4.82730	−	4.05058i	0.316928	−	0.265934i
$233$	13.1283	−	4.77832i	0.860065	−	0.313038i	0.125928	−	0.992039i	$-0.459809\pi$
$233$	13.1283	−	4.77832i	0.860065	−	0.313038i	0.734137	+	0.679001i	$0.237587\pi$
$234$	−1.73155	+	1.45295i	−0.113195	+	0.0949821i
$235$	−0.479311	+	0.830190i	−0.0312668	+	0.0541557i
$236$	−3.45105	−	5.97739i	−0.224644	−	0.389095i
$237$	9.12369	+	3.32075i	0.592647	+	0.215706i
$238$	−6.40671	−	12.6259i	−0.415285	−	0.818418i
$239$	−3.89702	+	6.74983i	−0.252077	+	0.436610i	−0.964097	−	0.265549i	$-0.914447\pi$
$239$	−3.89702	+	6.74983i	−0.252077	+	0.436610i	0.712021	+	0.702159i	$0.247780\pi$
$240$	0.150940			0.00974316
$241$	16.6715	−	13.9891i	1.07391	−	0.901116i	0.0785071	−	0.996914i	$-0.474985\pi$
$241$	16.6715	−	13.9891i	1.07391	−	0.901116i	0.995401	+	0.0957978i	$0.0305402\pi$
$242$	−1.89083	+	10.7234i	−0.121547	+	0.689328i
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$	−0.305433	+	1.73220i	−0.0195533	+	0.110892i
$245$	1.05042	+	0.113951i	0.0671089	+	0.00728007i
$246$	1.72938			0.110261
$247$	−9.29469	+	3.26894i	−0.591407	+	0.207998i
$248$	2.11270	+	3.65930i	0.134157	+	0.232366i
$249$	6.09498	+	5.11430i	0.386254	+	0.324106i
$250$	−1.15364	−	0.968016i	−0.0729624	−	0.0612227i
$251$	−7.25911	+	6.09112i	−0.458191	+	0.384468i	−0.842465	−	0.538751i	$-0.818896\pi$
$251$	−7.25911	+	6.09112i	−0.458191	+	0.384468i	0.384274	+	0.923219i	$0.374452\pi$
$252$	−0.318051	−	2.62656i	−0.0200353	−	0.165458i
$253$	−0.239556	−	1.35859i	−0.0150607	−	0.0854136i
$254$	−16.7441			−1.05062
$255$	−0.807738			−0.0505825
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	2.51439	−	2.10982i	0.156843	−	0.131607i	−0.560989	−	0.827823i	$-0.689579\pi$
$257$	2.51439	−	2.10982i	0.156843	−	0.131607i	0.717832	+	0.696216i	$0.245135\pi$
$258$	1.40553	−	2.43445i	0.0875047	−	0.151563i
$259$	−23.0677	−	21.5831i	−1.43336	−	1.34111i
$260$	−0.0592458	−	0.336000i	−0.00367427	−	0.0208378i
$261$	−5.92156	+	2.15527i	−0.366535	+	0.133408i
$262$	−9.20573	−	3.35061i	−0.568732	−	0.207002i
$263$	25.5327	−	9.29315i	1.57442	−	0.573040i	0.600435	−	0.799674i	$-0.294994\pi$
$263$	25.5327	−	9.29315i	1.57442	−	0.573040i	0.973980	+	0.226633i	$0.0727719\pi$
$264$	0.0578904	−	0.328313i	0.00356291	−	0.0202063i
$265$	0.953872			0.0585959
$266$	2.73504	−	11.2036i	0.167696	−	0.686934i
$267$	−4.33561			−0.265335
$268$	0.654090	−	3.70953i	0.0399549	−	0.226596i
$269$	−24.6141	+	8.95880i	−1.50075	+	0.546227i	−0.956254	−	0.292538i	$-0.905500\pi$
$269$	−24.6141	+	8.95880i	−1.50075	+	0.546227i	−0.544493	+	0.838765i	$0.683278\pi$
$270$	−0.141838	−	0.0516247i	−0.00863196	−	0.00314178i
$271$	27.4885	−	10.0050i	1.66981	−	0.607760i	0.677949	−	0.735109i	$-0.262869\pi$
$271$	27.4885	−	10.0050i	1.66981	−	0.607760i	0.991858	+	0.127349i	$0.0406469\pi$
$272$	−0.929256	−	5.27007i	−0.0563444	−	0.319545i
$273$	−5.72201	+	1.73895i	−0.346312	+	0.105246i
$274$	6.95026	−	12.0382i	0.419880	−	0.727254i
$275$	−1.27109	+	1.06657i	−0.0766497	+	0.0643167i
$276$	−0.718571	−	4.07522i	−0.0432529	−	0.245299i
$277$	−23.3082			−1.40045			−0.700227	−	0.713920i	$-0.746918\pi$
$277$	−23.3082			−1.40045			−0.700227	+	0.713920i	$0.746918\pi$
$278$	−2.87422			−0.172384
$279$	−0.733733	−	4.16121i	−0.0439275	−	0.249125i
$280$	0.367343	+	0.156652i	0.0219530	+	0.00936176i
$281$	−9.72705	+	8.16196i	−0.580267	+	0.486902i	−0.885035	−	0.465525i	$-0.845866\pi$
$281$	−9.72705	+	8.16196i	−0.580267	+	0.486902i	0.304768	+	0.952427i	$0.401421\pi$
$282$	4.86514	+	4.08234i	0.289715	+	0.243100i
$283$	2.91182	+	2.44331i	0.173090	+	0.145240i	0.725217	−	0.688520i	$-0.241739\pi$
$283$	2.91182	+	2.44331i	0.173090	+	0.145240i	−0.552127	+	0.833760i	$0.686184\pi$
$284$	4.71134	+	8.16027i	0.279566	+	0.484223i
$285$	−0.499377	−	0.428369i	−0.0295805	−	0.0253744i
$286$	−0.753561			−0.0445590
$287$	4.20878	+	1.79482i	0.248437	+	0.105945i
$288$	0.173648	−	0.984808i	0.0102323	−	0.0580304i
$289$	2.02077	+	11.4604i	0.118869	+	0.674140i
$290$	0.165168	−	0.936714i	0.00969900	−	0.0550058i
$291$	3.16015	−	2.65168i	0.185251	−	0.155444i
$292$	2.72975			0.159747
$293$	−10.8603	+	18.8106i	−0.634466	+	1.09893i	0.352162	+	0.935939i	$0.385447\pi$
$293$	−10.8603	+	18.8106i	−0.634466	+	1.09893i	−0.986628	+	0.162988i	$0.947887\pi$
$294$	1.95192	−	6.72235i	0.113838	−	0.392056i
$295$	−0.978977	−	0.356319i	−0.0569983	−	0.0207457i
$296$	−5.97002	−	10.3404i	−0.347001	−	0.601023i
$297$	−0.166689	+	0.288713i	−0.00967226	+	0.0167528i
$298$	6.72281	−	5.64110i	0.389442	−	0.326780i
$299$	−8.78957	+	3.19914i	−0.508314	+	0.185011i
$300$	−3.81277	+	3.19929i	−0.220130	+	0.184711i
$301$	5.94722	−	4.46601i	0.342792	−	0.257416i
$302$	9.71207	−	3.53490i	0.558867	−	0.203411i
$303$	−8.36874	+	14.4951i	−0.480772	+	0.832721i
$304$	2.22038	−	3.75099i	0.127348	−	0.215134i
$305$	0.132746	+	0.229923i	0.00760101	+	0.0131653i
$306$	−0.929256	+	5.27007i	−0.0531220	+	0.301270i
$307$	−4.98944	+	28.2965i	−0.284762	+	1.61497i	0.421370	+	0.906889i	$0.361549\pi$
$307$	−4.98944	+	28.2965i	−0.284762	+	1.61497i	−0.706133	+	0.708079i	$0.749562\pi$
$308$	0.481624	−	0.738933i	0.0274431	−	0.0421046i
$309$	−4.74268	−	3.97958i	−0.269801	−	0.226390i
$310$	0.599321	+	0.218135i	0.0340391	+	0.0123892i
$311$	−0.431791	+	0.747884i	−0.0244846	+	0.0424086i	−0.878008	−	0.478646i	$-0.841128\pi$
$311$	−0.431791	+	0.747884i	−0.0244846	+	0.0424086i	0.853523	+	0.521054i	$0.174461\pi$
$312$	−2.26038			−0.127969
$313$	15.4672	−	12.9785i	0.874256	−	0.733588i	−0.0907337	−	0.995875i	$-0.528921\pi$
$313$	15.4672	−	12.9785i	0.874256	−	0.733588i	0.964990	+	0.262287i	$0.0844768\pi$
$314$	19.6847	+	7.16464i	1.11087	+	0.404324i
$315$	−0.291612	−	0.272844i	−0.0164304	−	0.0153730i
$316$	4.85461	+	8.40844i	0.273093	+	0.473012i
$317$	−31.3450	−	11.4086i	−1.76051	−	0.640773i	−0.760547	−	0.649283i	$-0.775069\pi$
$317$	−31.3450	−	11.4086i	−1.76051	−	0.640773i	−0.999964	+	0.00850986i	$0.997291\pi$
$318$	1.09737	−	6.22352i	0.0615377	−	0.348998i
$319$	−1.97411	−	0.718519i	−0.110529	−	0.0402293i
$320$	0.115627	+	0.0970226i	0.00646375	+	0.00542373i
$321$	6.20596	−	2.25878i	0.346383	−	0.126073i
$322$	2.48065	−	10.6636i	0.138241	−	0.594260i
$323$	−11.8821	+	20.0729i	−0.661137	+	1.11689i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	8.61832	+	7.23163i	0.478058	+	0.401139i
$326$	22.6961	−	8.26071i	1.25702	−	0.457518i
$327$	−1.93559	−	10.9773i	−0.107039	−	0.607046i
$328$	1.32478	+	1.11162i	0.0731488	+	0.0613791i
$329$	7.60346	+	14.9844i	0.419192	+	0.826118i
$330$	−0.0251601	−	0.0435785i	−0.00138502	−	0.00239892i
$331$	3.66229	+	6.34327i	0.201298	+	0.348658i	0.948947	−	0.315436i	$-0.102151\pi$
$331$	3.66229	+	6.34327i	0.201298	+	0.348658i	−0.747649	+	0.664094i	$0.768818\pi$
$332$	1.38162	+	7.83556i	0.0758263	+	0.430032i
$333$	2.07337	+	11.7586i	0.113620	+	0.644370i
$334$	8.49822	+	14.7193i	0.465002	+	0.805407i
$335$	−0.284278	−	0.492384i	−0.0155318	−	0.0269018i
$336$	1.44468	−	2.21650i	0.0788139	−	0.120920i
$337$	5.81514	+	4.87948i	0.316771	+	0.265802i	0.787284	−	0.616591i	$-0.211487\pi$
$337$	5.81514	+	4.87948i	0.316771	+	0.265802i	−0.470513	+	0.882393i	$0.655931\pi$
$338$	−1.37020	−	7.77079i	−0.0745291	−	0.422675i
$339$	−8.33393	+	3.03330i	−0.452637	+	0.164746i
$340$	−0.618763	−	0.519204i	−0.0335571	−	0.0281578i
$341$	0.704327	−	1.21993i	0.0381414	−	0.0660629i
$342$	−3.36939	+	2.76536i	−0.182196	+	0.149534i
$343$	11.7271	−	14.3344i	0.633205	−	0.773984i
$344$	2.64154	−	0.961441i	0.142422	−	0.0518374i
$345$	−0.478475	−	0.401488i	−0.0257602	−	0.0216154i
$346$	−16.2458	−	5.91297i	−0.873378	−	0.317883i
$347$	−1.18557	+	6.72371i	−0.0636448	+	0.360948i	0.936307	+	0.351181i	$0.114220\pi$
$347$	−1.18557	+	6.72371i	−0.0636448	+	0.360948i	−0.999952	+	0.00976642i	$0.996891\pi$
$348$	−5.92156	−	2.15527i	−0.317429	−	0.115535i
$349$	−7.34213	−	12.7169i	−0.393015	−	0.680722i	0.599831	−	0.800127i	$-0.295235\pi$
$349$	−7.34213	−	12.7169i	−0.393015	−	0.680722i	−0.992846	+	0.119405i	$0.961901\pi$
$350$	−12.5995	+	3.82906i	−0.673471	+	0.204672i
$351$	2.12407	+	0.773096i	0.113374	+	0.0412648i
$352$	0.255382	−	0.214291i	0.0136119	−	0.0114217i
$353$	−18.9464			−1.00841			−0.504207	−	0.863583i	$-0.668215\pi$
$353$	−18.9464			−1.00841			−0.504207	+	0.863583i	$0.668215\pi$
$354$	−3.45105	+	5.97739i	−0.183421	+	0.317695i
$355$	1.33649	+	0.486442i	0.0709335	+	0.0258177i
$356$	−3.32127	−	2.78688i	−0.176027	−	0.147704i
$357$	−7.73103	+	11.8613i	−0.409169	+	0.627769i
$358$	2.16817	−	12.2963i	0.114591	−	0.649879i
$359$	−5.18165	+	29.3866i	−0.273477	+	1.55097i	0.470280	+	0.882517i	$0.344153\pi$
$359$	−5.18165	+	29.3866i	−0.273477	+	1.55097i	−0.743757	+	0.668450i	$0.766958\pi$
$360$	−0.0754702	−	0.130718i	−0.00397763	−	0.00688945i
$361$	−17.9913	+	6.10847i	−0.946910	+	0.321498i
$362$	−6.17770	+	10.7001i	−0.324692	+	0.562384i
$363$	10.2322	−	3.72421i	0.537050	−	0.195470i
$364$	−5.50109	−	2.34592i	−0.288335	−	0.122960i
$365$	0.315633	−	0.264847i	0.0165210	−	0.0138627i
$366$	1.65284	−	0.601585i	0.0863954	−	0.0314454i
$367$	13.4171	−	11.2583i	0.700369	−	0.587680i	−0.221509	−	0.975158i	$-0.571098\pi$
$367$	13.4171	−	11.2583i	0.700369	−	0.587680i	0.921879	+	0.387479i	$0.126654\pi$
$368$	2.06904	−	3.58369i	0.107856	−	0.186813i
$369$	−0.864689	−	1.49769i	−0.0450139	−	0.0779664i
$370$	−1.69355	−	0.616401i	−0.0880433	−	0.0320451i
$371$	9.12971	−	14.0073i	0.473991	−	0.727221i
$372$	2.11270	−	3.65930i	0.109538	−	0.189726i
$373$	6.30920			0.326678			0.163339	−	0.986570i	$-0.447774\pi$
$373$	6.30920			0.326678			0.163339	+	0.986570i	$0.447774\pi$
$374$	−1.36664	+	1.14675i	−0.0706675	+	0.0592970i
$375$	−0.261508	+	1.48309i	−0.0135042	+	0.0765862i
$376$	1.10284	+	6.25451i	0.0568745	+	0.322552i
$377$	−2.47345	+	14.0276i	−0.127389	+	0.722459i
$378$	−2.11565	+	1.58872i	−0.108817	+	0.0817151i
$379$	−11.0421			−0.567196			−0.283598	−	0.958943i	$-0.591528\pi$
$379$	−11.0421			−0.567196			−0.283598	+	0.958943i	$0.591528\pi$
$380$	−0.107195	−	0.649143i	−0.00549897	−	0.0333003i
$381$	8.37204	+	14.5008i	0.428913	+	0.742898i
$382$	1.49097	+	1.25107i	0.0762847	+	0.0640105i
$383$	5.39132	+	4.52385i	0.275484	+	0.231158i	0.770053	−	0.637980i	$-0.220230\pi$
$383$	5.39132	+	4.52385i	0.275484	+	0.231158i	−0.494569	+	0.869138i	$0.664674\pi$
$384$	0.766044	−	0.642788i	0.0390920	−	0.0328021i
$385$	−0.0160044	−	0.132169i	−0.000815659	−	0.00673596i
$386$	3.25205	+	18.4433i	0.165525	+	0.938738i
$387$	−2.81107			−0.142895
$388$	4.12528			0.209429
$389$	1.21604	+	6.89650i	0.0616556	+	0.349666i	0.999992	+	0.00394333i	$0.00125521\pi$
$389$	1.21604	+	6.89650i	0.0616556	+	0.349666i	−0.938337	+	0.345723i	$0.887634\pi$
$390$	−0.261361	+	0.219308i	−0.0132345	+	0.0111051i
$391$	−11.0722	+	19.1777i	−0.559946	+	0.969855i
$392$	5.81630	−	3.89495i	0.293768	−	0.196725i
$393$	1.70115	+	9.64771i	0.0858117	+	0.486662i
$394$	−4.39891	+	1.60107i	−0.221614	+	0.0806608i
$395$	1.37713	+	0.501236i	0.0692911	+	0.0252199i
$396$	−0.313272	+	0.114022i	−0.0157425	+	0.00572981i
$397$	−1.28283	+	7.27531i	−0.0643836	+	0.365137i	0.935545	+	0.353207i	$0.114909\pi$
$397$	−1.28283	+	7.27531i	−0.0643836	+	0.365137i	−0.999929	+	0.0119305i	$0.996202\pi$
$398$	−0.242369			−0.0121489
$399$	−11.0701	+	3.23316i	−0.554197	+	0.161860i
$400$	−4.97722			−0.248861
$401$	6.51758	−	36.9630i	0.325472	−	1.84585i	−0.180862	−	0.983509i	$-0.557889\pi$
$401$	6.51758	−	36.9630i	0.325472	−	1.84585i	0.506334	−	0.862337i	$-0.331000\pi$
$402$	−3.53959	+	1.28831i	−0.176539	+	0.0642549i
$403$	−8.97503	−	3.26664i	−0.447078	−	0.162723i
$404$	−15.7281	+	5.72456i	−0.782502	+	0.284807i
$405$	0.0262105	+	0.148647i	0.00130241	+	0.00738634i
$406$	−12.1745	−	11.3909i	−0.604208	−	0.565322i
$407$	−1.99027	+	3.44725i	−0.0986541	+	0.170874i
$408$	−4.09939	+	3.43980i	−0.202950	+	0.170295i
$409$	0.178730	+	1.01363i	0.00883764	+	0.0501207i	0.988908	−	0.148532i	$-0.0474547\pi$
$409$	0.178730	+	1.01363i	0.00883764	+	0.0501207i	−0.980070	+	0.198652i	$0.936344\pi$
$410$	0.261033			0.0128915
$411$	−13.9005			−0.685662
$412$	−1.07508	−	6.09707i	−0.0529653	−	0.300381i
$413$	−14.6024	+	10.9655i	−0.718537	+	0.539578i
$414$	−3.16996	+	2.65991i	−0.155795	+	0.130728i
$415$	0.919979	+	0.771954i	0.0451600	+	0.0378937i
$416$	−1.73155	−	1.45295i	−0.0848964	−	0.0712365i
$417$	1.43711	+	2.48915i	0.0703755	+	0.121894i
$418$	−1.45307	−	0.0158061i	−0.0710721	−	0.000773099i
$419$	−36.1220			−1.76467			−0.882337	−	0.470617i	$-0.844031\pi$
$419$	−36.1220			−1.76467			−0.882337	+	0.470617i	$0.844031\pi$
$420$	−0.0480068	−	0.396455i	−0.00234249	−	0.0193450i
$421$	−5.81928	+	33.0028i	−0.283614	+	1.60846i	0.426580	+	0.904450i	$0.359718\pi$
$421$	−5.81928	+	33.0028i	−0.283614	+	1.60846i	−0.710194	+	0.704006i	$0.751393\pi$
$422$	−3.18410	−	18.0580i	−0.155000	−	0.879047i
$423$	1.10284	−	6.25451i	0.0536218	−	0.304105i
$424$	4.84104	−	4.06211i	0.235102	−	0.197274i
$425$	26.6349			1.29198
$426$	4.71134	−	8.16027i	0.228265	−	0.395366i
$427$	4.64687	+	0.251312i	0.224878	+	0.0121619i
$428$	6.20596	+	2.25878i	0.299976	+	0.109182i
$429$	0.376780	+	0.652603i	0.0181911	+	0.0315080i
$430$	0.212152	−	0.367458i	0.0102309	−	0.0177204i
$431$	2.43315	−	2.04165i	0.117201	−	0.0983430i	−0.582304	−	0.812971i	$-0.697849\pi$
$431$	2.43315	−	2.04165i	0.117201	−	0.0983430i	0.699504	+	0.714628i	$0.253404\pi$
$432$	−0.939693	+	0.342020i	−0.0452110	+	0.0164555i
$433$	−9.87076	+	8.28255i	−0.474359	+	0.398034i	−0.848381	−	0.529385i	$-0.822423\pi$
$433$	−9.87076	+	8.28255i	−0.474359	+	0.398034i	0.374023	+	0.927419i	$0.377978\pi$
$434$	8.93945	−	6.71299i	0.429108	−	0.322234i
$435$	−0.893802	+	0.325317i	−0.0428545	+	0.0155978i
$436$	5.57332	−	9.65327i	0.266914	−	0.462308i
$437$	−17.0158	+	5.98446i	−0.813977	+	0.286276i
$438$	−1.36487	−	2.36403i	−0.0652162	−	0.112958i
$439$	4.99292	−	28.3162i	0.238299	−	1.35146i	−0.597255	−	0.802051i	$-0.703742\pi$
$439$	4.99292	−	28.3162i	0.238299	−	1.35146i	0.835554	−	0.549409i	$-0.185147\pi$
$440$	0.00873800	−	0.0495557i	0.000416568	−	0.00236247i
$441$	−6.79769	+	1.67076i	−0.323699	+	0.0795602i
$442$	9.26619	+	7.77525i	0.440748	+	0.369831i
$443$	19.5594	+	7.11906i	0.929297	+	0.338237i	0.761931	−	0.647658i	$-0.224252\pi$
$443$	19.5594	+	7.11906i	0.929297	+	0.338237i	0.167366	+	0.985895i	$0.446474\pi$
$444$	−5.97002	+	10.3404i	−0.283325	+	0.490733i
$445$	−0.654419			−0.0310224
$446$	−6.39603	+	5.36691i	−0.302861	+	0.254130i
$447$	−8.24674	−	3.00157i	−0.390057	−	0.141969i
$448$	2.53143	−	0.769318i	0.119599	−	0.0363468i
$449$	−5.27580	−	9.13796i	−0.248980	−	0.431247i	0.714263	−	0.699878i	$-0.246762\pi$
$449$	−5.27580	−	9.13796i	−0.248980	−	0.431247i	−0.963243	+	0.268631i	$0.913429\pi$
$450$	4.67705	+	1.70231i	0.220478	+	0.0802476i
$451$	0.100114	−	0.567777i	0.00471420	−	0.0267356i
$452$	−8.33393	−	3.03330i	−0.391995	−	0.142675i
$453$	−7.91735	−	6.64345i	−0.371990	−	0.312136i
$454$	−5.03029	+	1.83087i	−0.236083	+	0.0859272i
$455$	−0.863682	+	0.262478i	−0.0404900	+	0.0123052i
$456$	−4.35864	−	0.0474119i	−0.204112	−	0.00222026i
$457$	−7.31283	+	12.6662i	−0.342080	+	0.592499i	−0.984819	−	0.173586i	$-0.944465\pi$
$457$	−7.31283	+	12.6662i	−0.342080	+	0.592499i	0.642739	+	0.766085i	$0.277798\pi$
$458$	8.09310	+	6.79092i	0.378166	+	0.317319i
$459$	5.02864	−	1.83028i	0.234717	−	0.0854300i
$460$	−0.108461	−	0.615115i	−0.00505704	−	0.0286799i
$461$	−25.9439	−	21.7695i	−1.20833	−	1.01391i	−0.999352	−	0.0359884i	$-0.988542\pi$
$461$	−25.9439	−	21.7695i	−1.20833	−	1.01391i	−0.208977	−	0.977920i	$-0.567013\pi$
$462$	−0.880747	−	0.0476326i	−0.0409761	−	0.00221607i
$463$	4.91535	+	8.51364i	0.228436	+	0.395662i	0.957345	−	0.288948i	$-0.0933056\pi$
$463$	4.91535	+	8.51364i	0.228436	+	0.395662i	−0.728909	+	0.684611i	$0.759972\pi$
$464$	−3.15080	−	5.45734i	−0.146272	−	0.253351i
$465$	−0.110750	−	0.628094i	−0.00513591	−	0.0291272i
$466$	−2.42601	−	13.7586i	−0.112383	−	0.637356i
$467$	−16.6549	−	28.8471i	−0.770696	−	1.33489i	−0.937182	−	0.348841i	$-0.886575\pi$
$467$	−16.6549	−	28.8471i	−0.770696	−	1.33489i	0.166485	−	0.986044i	$-0.446758\pi$
$468$	1.13019	+	1.95755i	0.0522431	+	0.0904877i
$469$	−9.95136	−	0.538190i	−0.459511	−	0.0248513i
$470$	0.734347	+	0.616190i	0.0338729	+	0.0284227i
$471$	−3.63758	−	20.6297i	−0.167611	−	0.950569i
$472$	−6.48585	+	2.36066i	−0.298536	+	0.108658i
$473$	−0.717896	−	0.602386i	−0.0330089	−	0.0276977i
$474$	4.85461	−	8.40844i	0.222980	−	0.386212i
$475$	16.4668	+	14.1253i	0.755549	+	0.648115i
$476$	−13.5466	+	4.11690i	−0.620909	+	0.188698i
$477$	−5.93841	+	2.16141i	−0.271901	+	0.0989640i
$478$	5.97057	+	5.00991i	0.273088	+	0.229148i
$479$	26.2782	+	9.56448i	1.20068	+	0.437012i	0.863462	−	0.504414i	$-0.168292\pi$
$479$	26.2782	+	9.56448i	1.20068	+	0.437012i	0.337219	+	0.941426i	$0.390514\pi$
$480$	0.0262105	−	0.148647i	0.00119634	−	0.00678479i
$481$	25.3614	+	9.23081i	1.15638	+	0.420889i
$482$	−10.8816	−	18.8474i	−0.495642	−	0.858477i
$483$	−10.4753	+	3.18350i	−0.476642	+	0.144854i
$484$	10.2322	+	3.72421i	0.465099	+	0.169282i
$485$	0.476994	−	0.400245i	0.0216592	−	0.0181742i
$486$	1.00000			0.0453609
$487$	8.63054	−	14.9485i	0.391087	−	0.677383i	−0.601506	−	0.798868i	$-0.705432\pi$
$487$	8.63054	−	14.9485i	0.391087	−	0.677383i	0.992593	+	0.121486i	$0.0387658\pi$
$488$	1.65284	+	0.601585i	0.0748206	+	0.0272325i
$489$	−18.5020	−	15.5251i	−0.836691	−	0.702067i
$490$	0.294623	−	1.01467i	0.0133097	−	0.0458383i
$491$	2.01903	−	11.4505i	0.0911176	−	0.516754i	−0.904750	−	0.425942i	$-0.859943\pi$
$491$	2.01903	−	11.4505i	0.0911176	−	0.516754i	0.995868	−	0.0908117i	$-0.0289461\pi$
$492$	0.300303	−	1.70311i	0.0135387	−	0.0767819i
$493$	16.8611	+	29.2042i	0.759385	+	1.31529i
$494$	1.60528	+	9.72113i	0.0722247	+	0.437374i
$495$	−0.0251601	+	0.0435785i	−0.00113086	+	0.00195871i
$496$	3.97058	−	1.44517i	0.178284	−	0.0648902i
$497$	19.9350	−	14.9700i	0.894209	−	0.671497i
$498$	6.09498	−	5.11430i	0.273123	−	0.229177i
$499$	13.9744	−	5.08627i	0.625580	−	0.227693i	−0.00972625	−	0.999953i	$-0.503096\pi$
$499$	13.9744	−	5.08627i	0.625580	−	0.227693i	0.635306	+	0.772260i	$0.280874\pi$
$500$	−1.15364	+	0.968016i	−0.0515922	+	0.0432910i
$501$	8.49822	−	14.7193i	0.379672	−	0.657612i
$502$	4.73805	+	8.20654i	0.211469	+	0.366276i
$503$	−12.4443	−	4.52934i	−0.554862	−	0.201953i	0.0493432	−	0.998782i	$-0.484287\pi$
$503$	−12.4443	−	4.52934i	−0.554862	−	0.201953i	−0.604206	+	0.796829i	$0.706509\pi$
$504$	−2.64189	−	0.142879i	−0.117679	−	0.00636433i
$505$	−1.26318	+	2.18789i	−0.0562108	+	0.0973600i
$506$	−1.37955			−0.0613283
$507$	−6.04460	+	5.07202i	−0.268450	+	0.225257i
$508$	−2.90758	+	16.4897i	−0.129003	+	0.731612i
$509$	−1.80404	−	10.2312i	−0.0799628	−	0.453492i	−0.998330	−	0.0577630i	$-0.981603\pi$
$509$	−1.80404	−	10.2312i	−0.0799628	−	0.453492i	0.918368	−	0.395729i	$-0.129508\pi$
$510$	−0.140262	+	0.795467i	−0.00621092	+	0.0352239i
$511$	−0.868200	−	7.16986i	−0.0384069	−	0.317176i
$512$	1.00000			0.0441942
$513$	4.07957	+	1.53530i	0.180117	+	0.0677850i
$514$	−1.64115	−	2.84256i	−0.0723880	−	0.125380i
$515$	−0.715861	−	0.600679i	−0.0315446	−	0.0264691i
$516$	−2.15340	−	1.80692i	−0.0947982	−	0.0795452i
$517$	1.62193	−	1.36096i	0.0713324	−	0.0598550i
$518$	−25.2609	+	18.9694i	−1.10990	+	0.833469i
$519$	3.00210	+	17.0257i	0.131777	+	0.747347i
$520$	−0.341183			−0.0149619
$521$	−29.3980			−1.28795			−0.643974	−	0.765047i	$-0.722716\pi$
$521$	−29.3980			−1.28795			−0.643974	+	0.765047i	$0.722716\pi$
$522$	1.09426	+	6.20586i	0.0478944	+	0.271623i
$523$	16.1545	−	13.5552i	0.706386	−	0.592728i	−0.217197	−	0.976128i	$-0.569691\pi$
$523$	16.1545	−	13.5552i	0.706386	−	0.592728i	0.923583	+	0.383400i	$0.125247\pi$
$524$	−4.89827	+	8.48405i	−0.213982	+	0.370627i
$525$	9.61581	+	8.99695i	0.419668	+	0.392659i
$526$	−4.71826	−	26.7586i	−0.205726	−	1.16673i
$527$	−21.2480	+	7.73365i	−0.925579	+	0.336883i
$528$	−0.313272	−	0.114022i	−0.0136334	−	0.00496216i
$529$	5.52185	−	2.00979i	0.240080	−	0.0873821i
$530$	0.165638	−	0.939381i	0.00719486	−	0.0408041i
$531$	6.90210			0.299526
$532$	−10.5584	−	4.63897i	−0.457765	−	0.201125i
$533$	−3.90906			−0.169320
$534$	−0.752871	+	4.26975i	−0.0325799	+	0.184770i
$535$	0.936730	−	0.340942i	0.0404984	−	0.0147402i
$536$	−3.53959	−	1.28831i	−0.152887	−	0.0556464i
$537$	−11.7330	+	4.27045i	−0.506315	+	0.184284i
$538$	4.54850	+	25.7958i	0.196100	+	1.11214i
$539$	−2.09404	−	1.03000i	−0.0901965	−	0.0443652i
$540$	−0.0754702	+	0.130718i	−0.00324772	+	0.00562522i
$541$	25.6735	−	21.5426i	1.10379	−	0.926188i	0.106114	−	0.994354i	$-0.466159\pi$
$541$	25.6735	−	21.5426i	1.10379	−	0.926188i	0.997674	+	0.0681658i	$0.0217147\pi$
$542$	−5.07967	−	28.8082i	−0.218190	−	1.23742i
$543$	12.3554			0.530221
$544$	−5.35137			−0.229438
$545$	−0.292159	−	1.65692i	−0.0125147	−	0.0709745i
$546$	0.718918	+	5.93704i	0.0307668	+	0.254082i
$547$	−15.4758	+	12.9857i	−0.661697	+	0.555230i	−0.910595	−	0.413300i	$-0.864376\pi$
$547$	−15.4758	+	12.9857i	−0.661697	+	0.555230i	0.248898	+	0.968530i	$0.419932\pi$
$548$	−10.6484	−	8.93508i	−0.454878	−	0.381688i
$549$	−1.34741	−	1.13061i	−0.0575060	−	0.0482533i
$550$	0.829646	+	1.43699i	0.0353762	+	0.0612734i
$551$	−5.06372	+	26.9972i	−0.215722	+	1.15012i
$552$	−4.13809			−0.176129
$553$	20.5413	−	15.4253i	0.873505	−	0.655949i
$554$	−4.04743	+	22.9541i	−0.171959	+	0.975226i
$555$	0.312955	+	1.77486i	0.0132842	+	0.0753384i
$556$	−0.499103	+	2.83055i	−0.0211667	+	0.120042i
$557$	−24.7337	+	20.7540i	−1.04800	+	0.879375i	−0.992882	−	0.119105i	$-0.961998\pi$
$557$	−24.7337	+	20.7540i	−1.04800	+	0.879375i	−0.0551168	+	0.998480i	$0.517553\pi$
$558$	−4.22540			−0.178875
$559$	−3.17704	+	5.50280i	−0.134375	+	0.232744i
$560$	0.218061	−	0.334560i	0.00921475	−	0.0141377i
$561$	1.67644	+	0.610173i	0.0707792	+	0.0257615i
$562$	6.34888	+	10.9966i	0.267811	+	0.463863i
$563$	−12.3023	+	21.3082i	−0.518480	+	0.898034i	0.481289	+	0.876562i	$0.340169\pi$
$563$	−12.3023	+	21.3082i	−0.518480	+	0.898034i	−0.999769	+	0.0214720i	$0.993165\pi$
$564$	4.86514	−	4.08234i	0.204859	−	0.171897i
$565$	−1.25793	+	0.457848i	−0.0529214	+	0.0192618i
$566$	2.91182	−	2.44331i	0.122393	−	0.102700i
$567$	2.43370	+	1.03784i	0.102206	+	0.0435853i
$568$	8.85441	−	3.22274i	0.371523	−	0.135223i
$569$	10.7325	−	18.5892i	0.449928	−	0.779298i	−0.548453	−	0.836181i	$-0.684783\pi$
$569$	10.7325	−	18.5892i	0.449928	−	0.779298i	0.998381	+	0.0568835i	$0.0181164\pi$
$570$	−0.508577	+	0.417405i	−0.0213019	+	0.0174832i
$571$	−21.0492	−	36.4583i	−0.880883	−	1.52573i	−0.850361	−	0.526200i	$-0.823616\pi$
$571$	−21.0492	−	36.4583i	−0.880883	−	1.52573i	−0.0305217	−	0.999534i	$-0.509717\pi$
$572$	−0.130854	+	0.742112i	−0.00547130	+	0.0310293i
$573$	0.337976	−	1.91676i	0.0141191	−	0.0800736i
$574$	2.49840	−	3.83318i	0.104281	−	0.159994i
$575$	15.7776	+	13.2390i	0.657970	+	0.552103i
$576$	−0.939693	−	0.342020i	−0.0391539	−	0.0142508i
$577$	8.16894	−	14.1490i	0.340078	−	0.589032i	−0.644369	−	0.764714i	$-0.722880\pi$
$577$	8.16894	−	14.1490i	0.340078	−	0.589032i	0.984447	+	0.175683i	$0.0562133\pi$
$578$	11.6372			0.484043
$579$	14.3463	−	12.0380i	0.596213	−	0.500282i
$580$	−0.893802	−	0.325317i	−0.0371131	−	0.0135081i
$581$	20.1412	−	6.12103i	0.835597	−	0.253943i
$582$	−2.06264	−	3.57260i	−0.0854992	−	0.148089i
$583$	−1.97973	−	0.720564i	−0.0819922	−	0.0298427i
$584$	0.474016	−	2.68828i	0.0196149	−	0.111242i
$585$	0.320607	+	0.116691i	0.0132555	+	0.00482460i
$586$	16.6390	+	13.9617i	0.687349	+	0.576754i
$587$	23.1952	−	8.44238i	0.957370	−	0.348454i	0.184368	−	0.982857i	$-0.440976\pi$
$587$	23.1952	−	8.44238i	0.957370	−	0.348454i	0.773002	+	0.634403i	$0.218754\pi$
$588$	−6.28128	−	3.08959i	−0.259035	−	0.127413i
$589$	−17.2378	−	6.48724i	−0.710271	−	0.267302i
$590$	−0.520903	+	0.902230i	−0.0214452	+	0.0371442i
$591$	3.58602	+	3.00903i	0.147509	+	0.123775i
$592$	−11.2200	+	4.08374i	−0.461138	+	0.167841i
$593$	−1.61694	−	9.17011i	−0.0663997	−	0.376571i	−0.999841	−	0.0178408i	$-0.994321\pi$
$593$	−1.61694	−	9.17011i	−0.0663997	−	0.376571i	0.933441	−	0.358731i	$-0.116790\pi$
$594$	0.255382	+	0.214291i	0.0104784	+	0.00879246i
$595$	−1.16692	+	1.79036i	−0.0478392	+	0.0733974i
$596$	−4.38800	−	7.60024i	−0.179739	−	0.311318i
$597$	0.121185	+	0.209898i	0.00495975	+	0.00859055i
$598$	1.62425	+	9.21156i	0.0664204	+	0.376689i
$599$	−2.84926	−	16.1589i	−0.116418	−	0.660237i	−0.986039	−	0.166517i	$-0.946748\pi$
$599$	−2.84926	−	16.1589i	−0.116418	−	0.660237i	0.869621	−	0.493720i	$-0.164363\pi$
$600$	2.48861	+	4.31040i	0.101597	+	0.175971i
$601$	−7.67026	−	13.2853i	−0.312876	−	0.541918i	0.666108	−	0.745856i	$-0.267959\pi$
$601$	−7.67026	−	13.2853i	−0.312876	−	0.541918i	−0.978984	+	0.203938i	$0.934626\pi$
$602$	−3.36543	−	6.63238i	−0.137165	−	0.270316i
$603$	2.88550	+	2.42122i	0.117507	+	0.0985999i
$604$	−1.79472	−	10.1783i	−0.0730260	−	0.414151i
$605$	1.54445	−	0.562134i	0.0627908	−	0.0228540i
$606$	12.8217	+	10.7586i	0.520844	+	0.437040i
$607$	−10.6532	+	18.4519i	−0.432399	+	0.748938i	−0.997079	−	0.0763723i	$-0.975666\pi$
$607$	−10.6532	+	18.4519i	−0.432399	+	0.748938i	0.564680	+	0.825310i	$0.309000\pi$
$608$	−3.30844	−	2.83800i	−0.134175	−	0.115096i
$609$	−3.77760	+	16.2388i	−0.153076	+	0.658031i
$610$	0.249481	−	0.0908035i	0.0101012	−	0.00367653i
$611$	−10.9971	−	9.22765i	−0.444894	−	0.373311i
$612$	5.02864	+	1.83028i	0.203271	+	0.0739846i
$613$	−0.173010	+	0.981188i	−0.00698781	+	0.0396298i	−0.988102	−	0.153798i	$-0.950849\pi$
$613$	−0.173010	+	0.981188i	−0.00698781	+	0.0396298i	0.981114	+	0.193428i	$0.0619606\pi$
$614$	27.0002	+	9.82728i	1.08964	+	0.396597i
$615$	−0.130517	−	0.226061i	−0.00526294	−	0.00911567i
$616$	−0.644074	−	0.602622i	−0.0259505	−	0.0242803i
$617$	−17.5648	−	6.39306i	−0.707132	−	0.257375i	−0.0366789	−	0.999327i	$-0.511678\pi$
$617$	−17.5648	−	6.39306i	−0.707132	−	0.257375i	−0.670453	+	0.741952i	$0.733900\pi$
$618$	−4.74268	+	3.97958i	−0.190778	+	0.160082i
$619$	−20.7534			−0.834150			−0.417075	−	0.908872i	$-0.636945\pi$
$619$	−20.7534			−0.834150			−0.417075	+	0.908872i	$0.636945\pi$
$620$	0.318892	−	0.552337i	0.0128070	−	0.0221824i
$621$	3.88853	+	1.41531i	0.156041	+	0.0567944i
$622$	0.661543	+	0.555100i	0.0265254	+	0.0222575i
$623$	−6.26358	+	9.60991i	−0.250945	+	0.385013i
$624$	−0.392511	+	2.22604i	−0.0157130	+	0.0891130i
$625$	4.28195	−	24.2842i	0.171278	−	0.971366i
$626$	−10.0955	−	17.4859i	−0.403496	−	0.698876i
$627$	0.712848	+	1.26630i	0.0284684	+	0.0505712i
$628$	10.4740	−	18.1415i	0.417958	−	0.723925i
$629$	60.0422	−	21.8536i	2.39404	−	0.871360i
$630$	−0.319336	+	0.239802i	−0.0127227	+	0.00955396i
$631$	32.4828	−	27.2563i	1.29312	−	1.08506i	0.301829	−	0.953362i	$-0.402403\pi$
$631$	32.4828	−	27.2563i	1.29312	−	1.08506i	0.991290	−	0.131694i	$-0.0420417\pi$
$632$	9.12369	−	3.32075i	0.362921	−	0.132092i
$633$	−14.0466	+	11.7865i	−0.558302	+	0.468471i
$634$	−16.6783	+	28.8877i	−0.662381	+	1.14728i
$635$	1.26368	+	2.18876i	0.0501476	+	0.0868581i
$636$	−5.93841	−	2.16141i	−0.235473	−	0.0857053i
$637$	−4.41208	+	15.1951i	−0.174813	+	0.602051i
$638$	−1.05040	+	1.81935i	−0.0415859	+	0.0720289i
$639$	−9.42267			−0.372755
$640$	0.115627	−	0.0970226i	0.00457056	−	0.00383516i
$641$	6.84551	−	38.8228i	0.270381	−	1.53341i	−0.482879	−	0.875687i	$-0.660409\pi$
$641$	6.84551	−	38.8228i	0.270381	−	1.53341i	0.753261	−	0.657722i	$-0.228480\pi$
$642$	−1.14682	−	6.50391i	−0.0452612	−	0.256689i
$643$	2.82191	−	16.0038i	0.111285	−	0.631129i	−0.877238	−	0.480056i	$-0.840616\pi$
$643$	2.82191	−	16.0038i	0.111285	−	0.631129i	0.988523	−	0.151073i	$-0.0482727\pi$
$644$	−10.0709	−	4.29468i	−0.396847	−	0.169234i
$645$	−0.424303			−0.0167069
$646$	17.7047	+	15.1872i	0.696581	+	0.597532i
$647$	20.2835	+	35.1321i	0.797428	+	1.38119i	0.921286	+	0.388886i	$0.127140\pi$
$647$	20.2835	+	35.1321i	0.797428	+	1.38119i	−0.123858	+	0.992300i	$0.539527\pi$
$648$	0.766044	+	0.642788i	0.0300931	+	0.0252511i
$649$	1.76267	+	1.47906i	0.0691909	+	0.0580581i
$650$	8.61832	−	7.23163i	0.338038	−	0.283648i
$651$	−10.2833	−	4.38530i	−0.403036	−	0.171873i
$652$	−4.19407	−	23.7858i	−0.164253	−	0.931522i
$653$	−7.83427			−0.306579			−0.153289	−	0.988181i	$-0.548987\pi$
$653$	−7.83427			−0.306579			−0.153289	+	0.988181i	$0.548987\pi$
$654$	−11.1466			−0.435868
$655$	0.256772	+	1.45623i	0.0100329	+	0.0568996i
$656$	1.32478	−	1.11162i	0.0517240	−	0.0434016i
$657$	−1.36487	+	2.36403i	−0.0532488	+	0.0922297i
$658$	16.0771	−	4.88593i	0.626751	−	0.190473i
$659$	−8.13415	−	46.1311i	−0.316862	−	1.79701i	−0.561585	−	0.827419i	$-0.689808\pi$
$659$	−8.13415	−	46.1311i	−0.316862	−	1.79701i	0.244724	−	0.969593i	$-0.421303\pi$
$660$	−0.0472855	+	0.0172105i	−0.00184058	+	0.000669918i
$661$	−0.925895	−	0.336998i	−0.0360131	−	0.0131077i	0.323951	−	0.946074i	$-0.394989\pi$
$661$	−0.925895	−	0.336998i	−0.0360131	−	0.0131077i	−0.359964	+	0.932966i	$0.617211\pi$
$662$	6.88285	−	2.50515i	0.267510	−	0.0973655i
$663$	2.10047	−	11.9124i	0.0815757	−	0.462639i
$664$	7.95644			0.308770
$665$	−1.67092	+	0.488014i	−0.0647956	+	0.0189244i
$666$	11.9400			0.462667
$667$	−4.52814	+	25.6804i	−0.175330	+	0.994348i
$668$	15.9714	−	5.81312i	0.617953	−	0.224916i
$669$	7.84589	+	2.85567i	0.303340	+	0.110407i
$670$	−0.534267	+	0.194457i	−0.0206406	+	0.00751255i
$671$	−0.101824	−	0.577475i	−0.00393089	−	0.0222932i
$672$	−1.93196	−	1.80763i	−0.0745272	−	0.0697307i
$673$	9.75973	−	16.9043i	0.376210	−	0.651615i	−0.614297	−	0.789075i	$-0.710560\pi$
$673$	9.75973	−	16.9043i	0.376210	−	0.651615i	0.990507	+	0.137460i	$0.0438938\pi$
$674$	5.81514	−	4.87948i	0.223991	−	0.187951i
$675$	−0.864285	−	4.90160i	−0.0332663	−	0.188663i
$676$	−7.89067			−0.303487
$677$	−34.3376			−1.31970			−0.659851	−	0.751397i	$-0.729381\pi$
$677$	−34.3376			−1.31970			−0.659851	+	0.751397i	$0.729381\pi$
$678$	1.54005	+	8.73405i	0.0591452	+	0.335429i
$679$	−1.31205	−	10.8353i	−0.0503519	−	0.415821i
$680$	−0.618763	+	0.519204i	−0.0237285	+	0.0199106i
$681$	4.10073	+	3.44092i	0.157140	+	0.131856i
$682$	−1.07909	−	0.905465i	−0.0413205	−	0.0346721i
$683$	7.03539	+	12.1857i	0.269202	+	0.466271i	0.968656	−	0.248406i	$-0.0799068\pi$
$683$	7.03539	+	12.1857i	0.269202	+	0.466271i	−0.699454	+	0.714678i	$0.746573\pi$
$684$	2.13826	+	3.79840i	0.0817584	+	0.145235i
$685$	−2.09815			−0.0801661
$686$	−12.0802	−	14.0381i	−0.461225	−	0.535977i
$687$	1.83456	−	10.4043i	0.0699927	−	0.396949i
$688$	−0.488137	−	2.76836i	−0.0186100	−	0.105543i
$689$	−2.48049	+	14.0675i	−0.0944990	+	0.535930i
$690$	−0.478475	+	0.401488i	−0.0182152	+	0.0152844i
$691$	33.7490			1.28387			0.641935	−	0.766759i	$-0.278132\pi$
$691$	33.7490			1.28387			0.641935	+	0.766759i	$0.278132\pi$
$692$	−8.64419	+	14.9722i	−0.328603	+	0.569157i
$693$	0.399122	+	0.786565i	0.0151614	+	0.0298792i
$694$	6.41569	+	2.33512i	0.243536	+	0.0886399i
$695$	0.216918	+	0.375713i	0.00822816	+	0.0142516i
$696$	−3.15080	+	5.45734i	−0.119431	+	0.206860i
$697$	−7.08939	+	5.94871i	−0.268530	+	0.225323i
$698$	−13.7987	+	5.02231i	−0.522288	+	0.190097i
$699$	−10.7023	+	8.98030i	−0.404798	+	0.339666i
$700$	1.58301	+	13.0730i	0.0598322	+	0.494112i
$701$	13.3889	−	4.87318i	0.505693	−	0.184057i	−0.0765595	−	0.997065i	$-0.524394\pi$
$701$	13.3889	−	4.87318i	0.505693	−	0.184057i	0.582253	+	0.813008i	$0.302171\pi$
$702$	1.13019	−	1.95755i	0.0426563	−	0.0738829i
$703$	48.7102	+	18.3315i	1.83714	+	0.691386i
$704$	−0.166689	−	0.288713i	−0.00628232	−	0.0108813i
$705$	0.166463	−	0.944058i	0.00626935	−	0.0355553i
$706$	−3.29001	+	18.6586i	−0.123821	+	0.702224i
$707$	20.0383	+	39.4901i	0.753616	+	1.48518i
$708$	5.28732	+	4.43658i	0.198709	+	0.166737i
$709$	18.3811	+	6.69018i	0.690317	+	0.251255i	0.663271	−	0.748379i	$-0.269168\pi$
$709$	18.3811	+	6.69018i	0.690317	+	0.251255i	0.0270463	+	0.999634i	$0.491390\pi$
$710$	0.711131	−	1.23171i	0.0266883	−	0.0462254i
$711$	−9.70923			−0.364125
$712$	−3.32127	+	2.78688i	−0.124470	+	0.104443i
$713$	−16.4306	−	5.98025i	−0.615331	−	0.223962i
$714$	10.3387	+	9.67328i	0.386915	+	0.362013i
$715$	0.0568714	+	0.0985041i	0.00212687	+	0.00368384i
$716$	−11.7330	−	4.27045i	−0.438482	−	0.159594i
$717$	1.35342	−	7.67562i	0.0505444	−	0.286651i
$718$	28.0404	+	10.2059i	1.04646	+	0.380880i
$719$	−16.8515	−	14.1401i	−0.628455	−	0.527337i	0.271993	−	0.962299i	$-0.412317\pi$
$719$	−16.8515	−	14.1401i	−0.628455	−	0.527337i	−0.900449	+	0.434963i	$0.856762\pi$
$720$	−0.141838	+	0.0516247i	−0.00528597	+	0.00192394i
$721$	−15.6724	+	4.76294i	−0.583671	+	0.177381i
$722$	2.89151	+	18.7787i	0.107611	+	0.698870i
$723$	−10.8816	+	18.8474i	−0.404690	+	0.700944i
$724$	9.46478	+	7.94189i	0.351756	+	0.295158i
$725$	29.4729	−	10.7273i	1.09460	−	0.398400i
$726$	−1.89083	−	10.7234i	−0.0701753	−	0.397984i
$727$	−5.52758	−	4.63819i	−0.205007	−	0.172021i	0.534504	−	0.845166i	$-0.320498\pi$
$727$	−5.52758	−	4.63819i	−0.205007	−	0.172021i	−0.739510	+	0.673145i	$0.764943\pi$
$728$	−3.26553	+	5.01015i	−0.121029	+	0.185688i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−0.206015	−	0.356828i	−0.00762495	−	0.0132068i
$731$	2.61220	+	14.8145i	0.0966157	+	0.547935i
$732$	−0.305433	−	1.73220i	−0.0112891	−	0.0640238i
$733$	11.1728	+	19.3519i	0.412678	+	0.714779i	0.995182	−	0.0980492i	$-0.0312603\pi$
$733$	11.1728	+	19.3519i	0.412678	+	0.714779i	−0.582504	+	0.812828i	$0.697927\pi$
$734$	−8.75742	−	15.1683i	−0.323242	−	0.559872i
$735$	−1.02605	+	0.252186i	−0.0378463	+	0.00930201i
$736$	−3.16996	−	2.65991i	−0.116846	−	0.0980456i
$737$	0.218059	+	1.23667i	0.00803231	+	0.0455535i
$738$	−1.62508	+	0.591482i	−0.0598202	+	0.0217728i
$739$	−18.4434	−	15.4759i	−0.678452	−	0.569289i	0.237101	−	0.971485i	$-0.423803\pi$
$739$	−18.4434	−	15.4759i	−0.678452	−	0.569289i	−0.915554	+	0.402196i	$0.868247\pi$
$740$	−0.901118	+	1.56078i	−0.0331257	+	0.0573755i
$741$	7.61611	−	6.25077i	0.279785	−	0.229628i
$742$	−12.2091	−	11.4233i	−0.448210	−	0.419364i
$743$	15.6406	−	5.69270i	0.573796	−	0.208845i	−0.0387915	−	0.999247i	$-0.512351\pi$
$743$	15.6406	−	5.69270i	0.573796	−	0.208845i	0.612588	+	0.790403i	$0.290129\pi$
$744$	−3.23685	−	2.71604i	−0.118669	−	0.0995747i
$745$	−1.24477	−	0.453058i	−0.0456047	−	0.0165988i
$746$	1.09558	−	6.21335i	0.0401121	−	0.227487i
$747$	−7.47660	−	2.72126i	−0.273555	−	0.0995658i
$748$	0.892013	+	1.54501i	0.0326152	+	0.0564913i
$749$	3.95903	−	17.0188i	0.144660	−	0.621852i
$750$	1.41514	+	0.515070i	0.0516738	+	0.0188077i
$751$	0.357394	−	0.299889i	0.0130415	−	0.0109431i	−0.636244	−	0.771488i	$-0.719513\pi$
$751$	0.357394	−	0.299889i	0.0130415	−	0.0109431i	0.649285	+	0.760545i	$0.275068\pi$
$752$	6.35099			0.231597
$753$	4.73805	−	8.20654i	0.172664	−	0.299063i
$754$	13.3850	+	4.87174i	0.487453	+	0.177418i
$755$	−1.19505	−	1.00276i	−0.0434922	−	0.0364943i
$756$	1.19721	+	2.35938i	0.0435421	+	0.0858100i
$757$	−0.675242	+	3.82949i	−0.0245421	+	0.139185i	−0.994617	−	0.103621i	$-0.966957\pi$
$757$	−0.675242	+	3.82949i	−0.0245421	+	0.139185i	0.970075	+	0.242807i	$0.0780681\pi$
$758$	−1.91744	+	10.8744i	−0.0696447	+	0.394975i
$759$	0.689773	+	1.19472i	0.0250372	+	0.0433656i
$760$	−0.657895	−	0.00715637i	−0.0238644	−	0.000259589i
$761$	16.8473	−	29.1804i	0.610714	−	1.05779i	−0.380406	−	0.924819i	$-0.624216\pi$
$761$	16.8473	−	29.1804i	0.610714	−	1.05779i	0.991120	−	0.132968i	$-0.0424508\pi$
$762$	15.7343	−	5.72681i	0.569993	−	0.207461i
$763$	−27.1275	−	11.5684i	−0.982083	−	0.418806i
$764$	1.49097	−	1.25107i	0.0539414	−	0.0452622i
$765$	0.759026	−	0.276263i	0.0274426	−	0.00998830i
$766$	5.39132	−	4.52385i	0.194796	−	0.163453i
$767$	7.80069	−	13.5112i	0.281667	−	0.487861i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	40.1478	+	14.6126i	1.44777	+	0.526944i	0.941967	−	0.335707i	$-0.108975\pi$
$769$	40.1478	+	14.6126i	1.44777	+	0.526944i	0.505800	+	0.862651i	$0.331197\pi$
$770$	−0.132940	−	0.00718968i	−0.00479083	−	0.000259098i
$771$	−1.64115	+	2.84256i	−0.0591046	+	0.102372i
$772$	18.7278			0.674028
$773$	−7.10744	+	5.96385i	−0.255637	+	0.214505i	−0.761595	−	0.648053i	$-0.775583\pi$
$773$	−7.10744	+	5.96385i	−0.255637	+	0.214505i	0.505958	+	0.862558i	$0.331139\pi$
$774$	−0.488137	+	2.76836i	−0.0175457	+	0.0995066i
$775$	3.65195	+	20.7112i	0.131182	+	0.743970i
$776$	0.716347	−	4.06261i	0.0257154	−	0.145839i
$777$	29.0585	+	12.3919i	1.04247	+	0.444556i
$778$	7.00289			0.251066
$779$	−7.53774	−	0.0819931i	−0.270068	−	0.00293771i
$780$	0.170592	+	0.295473i	0.00610816	+	0.0105796i
$781$	−2.40638	−	2.01919i	−0.0861071	−	0.0722524i
$782$	16.9636	+	14.2342i	0.606618	+	0.509013i
$783$	4.82730	−	4.05058i	0.172514	−	0.144756i
$784$	−2.82579	−	6.40429i	−0.100921	−	0.228725i
$785$	−0.549058	−	3.11386i	−0.0195967	−	0.111139i
$786$	9.79654			0.349431
$787$	15.2796			0.544658			0.272329	−	0.962204i	$-0.412206\pi$
$787$	15.2796			0.544658			0.272329	+	0.962204i	$0.412206\pi$
$788$	0.812885	+	4.61010i	0.0289578	+	0.164228i
$789$	−20.8145	+	17.4654i	−0.741015	+	0.621785i
$790$	0.732757	−	1.26917i	0.0260703	−	0.0451551i
$791$	−5.31655	+	22.8544i	−0.189035	+	0.812607i
$792$	0.0578904	+	0.328313i	0.00205705	+	0.0116661i
$793$	−3.73606	+	1.35981i	−0.132671	+	0.0482884i
$794$	6.94202	+	2.52669i	0.246363	+	0.0896688i
$795$	−0.896346	+	0.326243i	−0.0317901	+	0.0115707i
$796$	−0.0420870	+	0.238687i	−0.00149173	+	0.00846004i
$797$	−8.10222			−0.286995			−0.143498	−	0.989651i	$-0.545835\pi$
$797$	−8.10222			−0.286995			−0.143498	+	0.989651i	$0.545835\pi$
$798$	1.26174	+	11.4633i	0.0446651	+	0.405798i
$799$	−33.9865			−1.20236
$800$	−0.864285	+	4.90160i	−0.0305571	+	0.173298i
$801$	4.07414	−	1.48287i	0.143953	−	0.0523945i
$802$	−35.2697	−	12.8371i	−1.24542	−	0.453295i
$803$	−0.855155	+	0.311251i	−0.0301778	+	0.0109838i
$804$	0.654090	+	3.70953i	0.0230680	+	0.130825i
$805$	−1.58114	+	0.480519i	−0.0557280	+	0.0169361i
$806$	−4.77551	+	8.27143i	−0.168210	+	0.291349i
$807$	20.0656	−	16.8370i	0.706342	−	0.592691i
$808$	2.90643	+	16.4832i	0.102248	+	0.579877i
$809$	18.8314			0.662076			0.331038	−	0.943617i	$-0.392601\pi$
$809$	18.8314			0.662076			0.331038	+	0.943617i	$0.392601\pi$
$810$	0.150940			0.00530350
$811$	−4.14412	−	23.5025i	−0.145520	−	0.825284i	−0.966948	−	0.254972i	$-0.917934\pi$
$811$	−4.14412	−	23.5025i	−0.145520	−	0.825284i	0.821429	−	0.570311i	$-0.193177\pi$
$812$	−13.3319	+	10.0115i	−0.467859	+	0.351334i
$813$	−22.4088	+	18.8032i	−0.785912	+	0.659458i
$814$	3.04927	+	2.55864i	0.106877	+	0.0896804i
$815$	−2.79270	−	2.34336i	−0.0978242	−	0.0820842i
$816$	2.67569	+	4.63442i	0.0936677	+	0.162237i
$817$	−6.24164	+	10.5443i	−0.218367	+	0.368898i
$818$	1.02927			0.0359874
$819$	4.78217	−	3.59112i	0.167103	−	0.125484i
$820$	0.0453279	−	0.257067i	0.00158292	−	0.00897718i
$821$	6.28322	+	35.6339i	0.219286	+	1.24363i	0.873312	+	0.487161i	$0.161967\pi$
$821$	6.28322	+	35.6339i	0.219286	+	1.24363i	−0.654026	+	0.756472i	$0.726921\pi$
$822$	−2.41380	+	13.6893i	−0.0841909	+	0.477470i
$823$	−5.31927	+	4.46340i	−0.185418	+	0.155584i	−0.730772	−	0.682622i	$-0.760840\pi$
$823$	−5.31927	+	4.46340i	−0.185418	+	0.155584i	0.545354	+	0.838206i	$0.316395\pi$
$824$	−6.19112			−0.215678
$825$	0.829646	−	1.43699i	0.0288846	−	0.0500295i
$826$	8.26325	+	16.2847i	0.287515	+	0.566617i
$827$	29.3361	+	10.6775i	1.02012	+	0.371292i	0.797309	−	0.603571i	$-0.206256\pi$
$827$	29.3361	+	10.6775i	1.02012	+	0.371292i	0.222807	+	0.974863i	$0.428478\pi$
$828$	2.06904	+	3.58369i	0.0719042	+	0.124542i
$829$	16.3663	−	28.3473i	0.568426	−	0.984543i	−0.428296	−	0.903639i	$-0.640886\pi$
$829$	16.3663	−	28.3473i	0.568426	−	0.984543i	0.996722	−	0.0809042i	$-0.0257808\pi$
$830$	0.919979	−	0.771954i	0.0319329	−	0.0267949i
$831$	21.9025	−	7.97187i	0.759791	−	0.276541i
$832$	−1.73155	+	1.45295i	−0.0600308	+	0.0503718i
$833$	15.1218	+	34.2717i	0.523941	+	1.18745i
$834$	2.70088	−	0.983040i	0.0935239	−	0.0340399i
$835$	1.28272	−	2.22174i	0.0443905	−	0.0768866i
$836$	−0.267889	+	1.42825i	−0.00926515	+	0.0493972i
$837$	2.11270	+	3.65930i	0.0730256	+	0.126484i
$838$	−6.27252	+	35.5732i	−0.216681	+	1.22886i
$839$	2.29116	−	12.9938i	0.0790998	−	0.448597i	−0.919375	−	0.393383i	$-0.871305\pi$
$839$	2.29116	−	12.9938i	0.0790998	−	0.448597i	0.998475	−	0.0552143i	$-0.0175842\pi$
$840$	−0.398768	−	0.0215662i	−0.0137588	−	0.000744104i
$841$	8.20437	+	6.88429i	0.282909	+	0.237389i
$842$	31.4909	+	11.4617i	1.08525	+	0.394998i
$843$	6.34888	−	10.9966i	0.218667	−	0.378742i
$844$	−18.3365			−0.631169
$845$	−0.912375	+	0.765573i	−0.0313866	+	0.0263365i
$846$	−5.96798	−	2.17217i	−0.205183	−	0.0746807i
$847$	6.52752	−	28.0600i	0.224288	−	0.964152i
$848$	−3.15976	−	5.47287i	−0.108507	−	0.187939i
$849$	−3.57188	−	1.30006i	−0.122587	−	0.0446179i
$850$	4.62511	−	26.2303i	0.158640	−	0.899692i
$851$	46.4292	+	16.8989i	1.59157	+	0.579285i
$852$	−7.21818	−	6.05678i	−0.247291	−	0.207502i
$853$	14.8689	−	5.41182i	0.509100	−	0.185297i	−0.0746825	−	0.997207i	$-0.523794\pi$
$853$	14.8689	−	5.41182i	0.509100	−	0.185297i	0.583782	+	0.811910i	$0.301572\pi$
$854$	1.05441	−	4.53263i	0.0360813	−	0.155103i
$855$	0.615771	+	0.231738i	0.0210589	+	0.00792528i
$856$	3.30212	−	5.71944i	0.112864	−	0.195487i
$857$	18.1707	+	15.2470i	0.620700	+	0.520829i	0.898024	−	0.439947i	$-0.145003\pi$
$857$	18.1707	+	15.2470i	0.620700	+	0.520829i	−0.277323	+	0.960777i	$0.589447\pi$
$858$	0.708115	−	0.257733i	0.0241747	−	0.00879886i
$859$	−2.13264	−	12.0948i	−0.0727646	−	0.412669i	−0.999332	−	0.0365403i	$-0.988366\pi$
$859$	−2.13264	−	12.0948i	−0.0727646	−	0.412669i	0.926568	−	0.376128i	$-0.122745\pi$
$860$	−0.325035	−	0.272737i	−0.0110836	−	0.00930025i
$861$	−4.56883	−	0.247092i	−0.155705	−	0.00842086i
$862$	−1.58812	−	2.75071i	−0.0540917	−	0.0936897i
$863$	13.3502	+	23.1233i	0.454448	+	0.787127i	0.998656	−	0.0518234i	$-0.0165033\pi$
$863$	13.3502	+	23.1233i	0.454448	+	0.787127i	−0.544209	+	0.838950i	$0.683170\pi$
$864$	0.173648	+	0.984808i	0.00590763	+	0.0335038i
$865$	0.453138	+	2.56987i	0.0154071	+	0.0873782i
$866$	6.44268	+	11.1591i	0.218931	+	0.379200i
$867$	−5.81859	−	10.0781i	−0.197610	−	0.342270i
$868$	−5.05869	−	9.96934i	−0.171703	−	0.338382i
$869$	−2.47956	−	2.08060i	−0.0841134	−	0.0705795i
$870$	0.165168	+	0.936714i	0.00559972	+	0.0317576i
$871$	8.00083	−	2.91207i	0.271098	−	0.0986716i
$872$	−8.53882	−	7.16492i	−0.289161	−	0.242635i
$873$	−2.06264	+	3.57260i	−0.0698098	+	0.120914i
$874$	2.93878	+	17.7965i	0.0994057	+	0.601975i
$875$	2.90947	+	2.72222i	0.0983581	+	0.0920279i
$876$	−2.56513	+	0.933629i	−0.0866676	+	0.0315444i
$877$	−19.1677	−	16.0836i	−0.647248	−	0.543105i	0.258987	−	0.965881i	$-0.416611\pi$
$877$	−19.1677	−	16.0836i	−0.647248	−	0.543105i	−0.906234	+	0.422776i	$0.861056\pi$
$878$	−27.0190	−	9.83413i	−0.911848	−	0.331886i
$879$	3.77174	−	21.3906i	0.127218	−	0.721488i
$880$	−0.0472855	−	0.0172105i	−0.00159399	−	0.000580166i
$881$	22.3494	+	38.7103i	0.752971	+	1.30418i	0.946377	+	0.323065i	$0.104713\pi$
$881$	22.3494	+	38.7103i	0.752971	+	1.30418i	−0.193406	+	0.981119i	$0.561954\pi$
$882$	0.464976	+	6.98454i	0.0156566	+	0.235182i
$883$	18.6424	+	6.78528i	0.627367	+	0.228343i	0.636085	−	0.771619i	$-0.280553\pi$
$883$	18.6424	+	6.78528i	0.627367	+	0.228343i	−0.00871805	+	0.999962i	$0.502775\pi$
$884$	9.26619	−	7.77525i	0.311656	−	0.261510i
$885$	1.04181			0.0350199
$886$	10.4074	−	18.0261i	0.349642	−	0.605598i
$887$	−54.0057	−	19.6565i	−1.81333	−	0.660000i	−0.996544	−	0.0830639i	$-0.973529\pi$
$887$	−54.0057	−	19.6565i	−1.81333	−	0.660000i	−0.816790	−	0.576936i	$-0.804248\pi$
$888$	9.14661	+	7.67491i	0.306940	+	0.257553i
$889$	44.2360	+	2.39238i	1.48363	+	0.0802377i
$890$	−0.113639	+	0.644477i	−0.00380918	+	0.0216029i
$891$	0.0578904	−	0.328313i	0.00193940	−	0.0109989i
$892$	4.17471	+	7.23081i	0.139780	+	0.242106i
$893$	−21.0119	−	18.0241i	−0.703135	−	0.603154i
$894$	−4.38800	+	7.60024i	−0.146757	+	0.254190i
$895$	−1.77098	+	0.644584i	−0.0591973	+	0.0215461i
$896$	−0.318051	−	2.62656i	−0.0106253	−	0.0877474i
$897$	7.16532	−	6.01242i	0.239243	−	0.200749i
$898$	−9.91526	+	3.60886i	−0.330877	+	0.120429i
$899$	−20.3973	+	17.1153i	−0.680287	+	0.570829i
$900$	2.48861	−	4.31040i	0.0829536	−	0.143680i
$901$	16.9091	+	29.2874i	0.563323	+	0.975704i
$902$	−0.541767	−	0.197187i	−0.0180389	−	0.00656561i
$903$	−4.06110	+	6.23074i	−0.135145	+	0.207346i
$904$	−4.43439	+	7.68059i	−0.147486	+	0.255453i
$905$	1.86493			0.0619923
$906$	−7.91735	+	6.64345i	−0.263036	+	0.220714i
$907$	0.555290	−	3.14920i	0.0184381	−	0.104568i	−0.974200	−	0.225687i	$-0.927537\pi$
$907$	0.555290	−	3.14920i	0.0184381	−	0.104568i	0.992638	+	0.121119i	$0.0386484\pi$
$908$	0.929559	+	5.27179i	0.0308485	+	0.174951i
$909$	2.90643	−	16.4832i	0.0964003	−	0.546713i
$910$	0.108514	+	0.896139i	0.00359719	+	0.0297067i
$911$	−42.1891			−1.39779			−0.698894	−	0.715226i	$-0.746324\pi$
$911$	−42.1891			−1.39779			−0.698894	+	0.715226i	$0.746324\pi$
$912$	−0.803562	+	4.28419i	−0.0266086	+	0.141864i
$913$	−1.32625	−	2.29713i	−0.0438924	−	0.0760239i
$914$	11.2039	+	9.40119i	0.370592	+	0.310964i
$915$	−0.203378	−	0.170655i	−0.00672349	−	0.00564167i
$916$	8.09310	−	6.79092i	0.267404	−	0.224378i
$917$	23.8418	+	10.1673i	0.787326	+	0.335752i
$918$	−0.929256	−	5.27007i	−0.0306700	−	0.173938i
$919$	0.996509			0.0328718			0.0164359	−	0.999865i	$-0.494768\pi$
$919$	0.996509			0.0328718			0.0164359	+	0.999865i	$0.494768\pi$
$920$	−0.624605			−0.0205926
$921$	−4.98944	−	28.2965i	−0.164408	−	0.932402i
$922$	−25.9439	+	21.7695i	−0.854418	+	0.716942i
$923$	−10.6494	+	18.4453i	−0.350530	+	0.607136i
$924$	−0.199849	+	0.859095i	−0.00657455	+	0.0282622i
$925$	−10.3196	−	58.5253i	−0.339306	−	1.92430i
$926$	9.23784	−	3.36230i	0.303574	−	0.110492i
$927$	5.81775	+	2.11749i	0.191080	+	0.0695475i
$928$	−5.92156	+	2.15527i	−0.194385	+	0.0707502i
$929$	3.22722	−	18.3024i	0.105882	−	0.600484i	−0.884983	−	0.465623i	$-0.845830\pi$
$929$	3.22722	−	18.3024i	0.105882	−	0.600484i	0.990865	−	0.134861i	$-0.0430587\pi$
$930$	−0.637784			−0.0209138
$931$	−8.82643	+	29.2078i	−0.289275	+	0.957246i
$932$	−13.9709			−0.457631
$933$	0.149960	−	0.850463i	0.00490945	−	0.0278429i
$934$	−31.3010	+	11.3926i	−1.02420	+	0.372778i
$935$	0.253042	+	0.0920998i	0.00827536	+	0.00301198i
$936$	2.12407	−	0.773096i	0.0694272	−	0.0252694i
$937$	−3.46493	−	19.6506i	−0.113194	−	0.641957i	−0.987628	−	0.156813i	$-0.949878\pi$
$937$	−3.46493	−	19.6506i	−0.113194	−	0.641957i	0.874434	−	0.485144i	$-0.161233\pi$
$938$	−2.25805	+	9.70672i	−0.0737279	+	0.316936i
$939$	−10.0955	+	17.4859i	−0.329453	+	0.570630i
$940$	0.734347	−	0.616190i	0.0239517	−	0.0200979i
$941$	−1.06462	−	6.03778i	−0.0347057	−	0.196826i	0.962525	−	0.271192i	$-0.0874178\pi$
$941$	−1.06462	−	6.03778i	−0.0347057	−	0.196826i	−0.997231	+	0.0743659i	$0.976307\pi$
$942$	−20.9480			−0.682523
$943$	−7.15632			−0.233042
$944$	1.19854	+	6.79724i	0.0390091	+	0.221231i
$945$	0.367343	+	0.156652i	0.0119497	+	0.00509590i
$946$	−0.717896	+	0.602386i	−0.0233408	+	0.0195853i
$947$	2.17311	+	1.82345i	0.0706165	+	0.0592543i	0.677413	−	0.735603i	$-0.263101\pi$
$947$	2.17311	+	1.82345i	0.0706165	+	0.0592543i	−0.606796	+	0.794857i	$0.707546\pi$
$948$	−7.43770	−	6.24097i	−0.241565	−	0.202697i
$949$	3.08514	+	5.34362i	0.100148	+	0.173461i
$950$	16.7702	−	13.7638i	0.544096	−	0.446557i
$951$	33.3566			1.08166
$952$	1.70201	+	14.0557i	0.0551625	+	0.455549i
$953$	−4.02186	+	22.8091i	−0.130281	+	0.738860i	0.847749	+	0.530397i	$0.177957\pi$
$953$	−4.02186	+	22.8091i	−0.130281	+	0.738860i	−0.978030	+	0.208463i	$0.933154\pi$
$954$	1.09737	+	6.22352i	0.0355288	+	0.201494i
$955$	0.0510142	−	0.289316i	0.00165078	−	0.00936204i
$956$	5.97057	−	5.00991i	0.193102	−	0.162032i
$957$	2.10081			0.0679095
$958$	13.9823	−	24.2181i	0.451749	−	0.782451i
$959$	−20.0818	+	30.8106i	−0.648476	+	0.994925i
$960$	−0.141838	−	0.0516247i	−0.00457779	−	0.00166618i
$961$	6.57299	+	11.3848i	0.212032	+	0.367250i
$962$	13.4945	−	23.3732i	0.435081	−	0.753583i
$963$	−5.05914	+	4.24513i	−0.163029	+	0.136797i
$964$	−20.4507	+	7.44343i	−0.658672	+	0.239737i
$965$	2.16544	−	1.81702i	0.0697080	−	0.0584919i
$966$	1.31612	+	10.8690i	0.0423456	+	0.349703i
$967$	9.42628	−	3.43088i	0.303129	−	0.110330i	−0.185978	−	0.982554i	$-0.559545\pi$
$967$	9.42628	−	3.43088i	0.303129	−	0.110330i	0.489106	+	0.872224i	$0.337323\pi$
$968$	5.44443	−	9.43003i	0.174991	−	0.303093i
$969$	4.30016	−	22.9263i	0.138141	−	0.736499i
$970$	−0.311336	−	0.539249i	−0.00999639	−	0.0173142i
$971$	1.44562	−	8.19851i	0.0463921	−	0.263103i	−0.952786	−	0.303643i	$-0.901797\pi$
$971$	1.44562	−	8.19851i	0.0463921	−	0.263103i	0.999178	+	0.0405406i	$0.0129080\pi$
$972$	0.173648	−	0.984808i	0.00556977	−	0.0315877i
$973$	7.59337	+	0.410665i	0.243432	+	0.0131653i
$974$	−13.2228	−	11.0952i	−0.423684	−	0.355513i
$975$	−10.5719	−	3.84787i	−0.338573	−	0.123230i
$976$	0.879459	−	1.52327i	0.0281508	−	0.0487586i
$977$	−10.8041			−0.345653			−0.172826	−	0.984952i	$-0.555290\pi$
$977$	−10.8041			−0.345653			−0.172826	+	0.984952i	$0.555290\pi$
$978$	−18.5020	+	15.5251i	−0.591630	+	0.496436i
$979$	1.35823	+	0.494354i	0.0434091	+	0.0157996i
$980$	−0.948098	−	0.466344i	−0.0302859	−	0.0148968i
$981$	5.57332	+	9.65327i	0.177942	+	0.308205i
$982$	−10.9259	−	3.97672i	−0.348661	−	0.126902i
$983$	4.62101	−	26.2070i	0.147387	−	0.835875i	−0.818032	−	0.575173i	$-0.804935\pi$
$983$	4.62101	−	26.2070i	0.147387	−	0.835875i	0.965419	−	0.260702i	$-0.0839540\pi$
$984$	−1.62508	−	0.591482i	−0.0518058	−	0.0188558i
$985$	0.541276	+	0.454184i	0.0172465	+	0.0144715i
$986$	31.6885	−	11.5337i	1.00917	−	0.367306i
$987$	−12.2699	−	11.4802i	−0.390555	−	0.365419i
$988$	9.85220	+	0.107169i	0.313440	+	0.00340950i
$989$	−5.81622	+	10.0740i	−0.184945	+	0.320334i
$990$	0.0385475	+	0.0323452i	0.00122512	+	0.00102800i
$991$	−17.0893	+	6.22001i	−0.542861	+	0.197585i	−0.598872	−	0.800845i	$-0.704384\pi$
$991$	−17.0893	+	6.22001i	−0.542861	+	0.197585i	0.0560110	+	0.998430i	$0.482162\pi$
$992$	−0.733733	−	4.16121i	−0.0232961	−	0.132118i
$993$	−5.61095	−	4.70815i	−0.178058	−	0.149408i
$994$	−11.2809	−	22.2317i	−0.357808	−	0.705147i
$995$	0.0182916	+	0.0316821i	0.000579884	+	0.00100439i
$996$	−3.97822	−	6.89048i	−0.126055	−	0.218333i
$997$	3.94674	+	22.3831i	0.124994	+	0.708879i	0.981311	+	0.192428i	$0.0616361\pi$
$997$	3.94674	+	22.3831i	0.124994	+	0.708879i	−0.856317	+	0.516451i	$0.827253\pi$
$998$	−2.58237	−	14.6453i	−0.0817433	−	0.463590i
$999$	−5.97002	−	10.3404i	−0.188883	−	0.327155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bq.d.499.3	yes	36
7.4	even	3		798.2.bp.d.613.4	yes	36
19.4	even	9		798.2.bp.d.289.4	✓	36
133.4	even	9	inner	798.2.bq.d.403.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.d.289.4	✓	36	19.4	even	9
798.2.bp.d.613.4	yes	36	7.4	even	3
798.2.bq.d.403.3	yes	36	133.4	even	9	inner
798.2.bq.d.499.3	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.141838 + 0.0516247i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-0.599468 + 2.57694i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.141838 + 0.0516247i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-0.599468 + 2.57694i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(0.0262105 + 0.148647i) q^{10} +0.333377 q^{11} +1.00000 q^{12} +(-0.392511 - 2.22604i) q^{13} +(2.43370 + 1.03784i) q^{14} +(0.115627 - 0.0970226i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-4.09939 - 3.43980i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.710179 - 4.30066i) q^{19} +0.150940 q^{20} +(-0.318051 - 2.62656i) q^{21} +(0.0578904 - 0.328313i) q^{22} +(-0.718571 - 4.07522i) q^{23} +(0.173648 - 0.984808i) q^{24} +(-3.81277 + 3.19929i) q^{25} -2.26038 q^{26} +(-0.500000 + 0.866025i) q^{27} +(1.44468 - 2.21650i) q^{28} +(-5.92156 - 2.15527i) q^{29} +(-0.0754702 - 0.130718i) q^{30} +(2.11270 - 3.65930i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.313272 + 0.114022i) q^{33} +(-4.09939 + 3.43980i) q^{34} +(-0.0480068 - 0.396455i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-5.97002 + 10.3404i) q^{37} +(-4.35864 - 0.0474119i) q^{38} +(1.13019 + 1.95755i) q^{39} +(0.0262105 - 0.148647i) q^{40} +(0.300303 - 1.70311i) q^{41} +(-2.64189 - 0.142879i) q^{42} +(-2.15340 - 1.80692i) q^{43} +(-0.313272 - 0.114022i) q^{44} +(-0.0754702 + 0.130718i) q^{45} -4.13809 q^{46} +(4.86514 - 4.08234i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-6.28128 - 3.08959i) q^{49} +(2.48861 + 4.31040i) q^{50} +(5.02864 + 1.83028i) q^{51} +(-0.392511 + 2.22604i) q^{52} +(-5.93841 - 2.16141i) q^{53} +(0.766044 + 0.642788i) q^{54} +(-0.0472855 + 0.0172105i) q^{55} +(-1.93196 - 1.80763i) q^{56} +(2.13826 + 3.79840i) q^{57} +(-3.15080 + 5.45734i) q^{58} +(5.28732 + 4.43658i) q^{59} +(-0.141838 + 0.0516247i) q^{60} +(-0.305433 - 1.73220i) q^{61} +(-3.23685 - 2.71604i) q^{62} +(1.19721 + 2.35938i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.170592 + 0.295473i) q^{65} +(0.0578904 + 0.328313i) q^{66} +(0.654090 + 3.70953i) q^{67} +(2.67569 + 4.63442i) q^{68} +(2.06904 + 3.58369i) q^{69} +(-0.398768 - 0.0215662i) q^{70} +(-7.21818 - 6.05678i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-2.56513 + 0.933629i) q^{73} +(9.14661 + 7.67491i) q^{74} +(2.48861 - 4.31040i) q^{75} +(-0.803562 + 4.28419i) q^{76} +(-0.199849 + 0.859095i) q^{77} +(2.12407 - 0.773096i) q^{78} +(-7.43770 - 6.24097i) q^{79} +(-0.141838 - 0.0516247i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-1.62508 - 0.591482i) q^{82} +(-3.97822 - 6.89048i) q^{83} +(-0.599468 + 2.57694i) q^{84} +(0.759026 + 0.276263i) q^{85} +(-2.15340 + 1.80692i) q^{86} +6.30159 q^{87} +(-0.166689 + 0.288713i) q^{88} +(4.07414 + 1.48287i) q^{89} +(0.115627 + 0.0970226i) q^{90} +(5.97168 + 0.322961i) q^{91} +(-0.718571 + 4.07522i) q^{92} +(-0.733733 + 4.16121i) q^{93} +(-3.17550 - 5.50012i) q^{94} +(0.322750 + 0.573332i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-3.87650 + 1.41093i) q^{97} +(-4.13338 + 5.64935i) q^{98} +(0.255382 - 0.214291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} - 18 q^{8}+O(q^{10}) \) 36 * q + 3 * q^5 - 18 * q^8	\( 36 q + 3 q^{5} - 18 q^{8} - 6 q^{10} - 6 q^{11} + 36 q^{12} + 27 q^{13} + 3 q^{15} - 3 q^{17} - 18 q^{18} + 6 q^{19} - 6 q^{20} - 3 q^{22} - 18 q^{23} - 21 q^{25} - 18 q^{26} - 18 q^{27} + 12 q^{28} + 9 q^{29} + 3 q^{30} - 3 q^{31} - 3 q^{33} - 3 q^{34} + 12 q^{35} + 21 q^{37} + 9 q^{38} + 9 q^{39} - 6 q^{40} - 9 q^{41} - 15 q^{42} + 51 q^{43} - 3 q^{44} + 3 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{49} - 9 q^{50} - 3 q^{51} + 27 q^{52} - 15 q^{53} + 27 q^{55} - 9 q^{57} + 18 q^{58} + 33 q^{59} + 3 q^{60} + 21 q^{61} - 24 q^{62} + 3 q^{63} - 18 q^{64} + 42 q^{65} - 3 q^{66} - 3 q^{67} + 18 q^{68} + 6 q^{69} - 33 q^{70} + 6 q^{71} - 42 q^{73} - 3 q^{74} - 9 q^{75} - 6 q^{76} + 9 q^{77} - 27 q^{78} - 24 q^{79} + 3 q^{80} + 27 q^{82} + 30 q^{83} + 36 q^{85} + 51 q^{86} - 36 q^{87} + 3 q^{88} - 42 q^{89} + 3 q^{90} + 24 q^{91} - 18 q^{92} + 21 q^{93} + 18 q^{94} - 39 q^{95} - 18 q^{96} + 45 q^{97} + 3 q^{98} + 6 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 - 18 * q^8 - 6 * q^10 - 6 * q^11 + 36 * q^12 + 27 * q^13 + 3 * q^15 - 3 * q^17 - 18 * q^18 + 6 * q^19 - 6 * q^20 - 3 * q^22 - 18 * q^23 - 21 * q^25 - 18 * q^26 - 18 * q^27 + 12 * q^28 + 9 * q^29 + 3 * q^30 - 3 * q^31 - 3 * q^33 - 3 * q^34 + 12 * q^35 + 21 * q^37 + 9 * q^38 + 9 * q^39 - 6 * q^40 - 9 * q^41 - 15 * q^42 + 51 * q^43 - 3 * q^44 + 3 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 27 * q^52 - 15 * q^53 + 27 * q^55 - 9 * q^57 + 18 * q^58 + 33 * q^59 + 3 * q^60 + 21 * q^61 - 24 * q^62 + 3 * q^63 - 18 * q^64 + 42 * q^65 - 3 * q^66 - 3 * q^67 + 18 * q^68 + 6 * q^69 - 33 * q^70 + 6 * q^71 - 42 * q^73 - 3 * q^74 - 9 * q^75 - 6 * q^76 + 9 * q^77 - 27 * q^78 - 24 * q^79 + 3 * q^80 + 27 * q^82 + 30 * q^83 + 36 * q^85 + 51 * q^86 - 36 * q^87 + 3 * q^88 - 42 * q^89 + 3 * q^90 + 24 * q^91 - 18 * q^92 + 21 * q^93 + 18 * q^94 - 39 * q^95 - 18 * q^96 + 45 * q^97 + 3 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more