LMFDB - Embedded newform 798.2.bp.d.289.4

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			289.4
Character	$\chi$	$=$	798.289
Dual form			798.2.bp.d.613.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.766044 - 0.642788i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0262105 + 0.148647i) q^{5} +(0.173648 - 0.984808i) q^{6} +(2.53143 - 0.769318i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.766044 - 0.642788i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0262105 + 0.148647i) q^{5} +(0.173648 - 0.984808i) q^{6} +(2.53143 - 0.769318i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.115627 + 0.0970226i) q^{10} +(-0.166689 + 0.288713i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.392511 + 2.22604i) q^{13} +(1.44468 - 2.21650i) q^{14} +(0.115627 + 0.0970226i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.929256 - 5.27007i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.07957 - 1.53530i) q^{19} +0.150940 q^{20} +(1.44468 - 2.21650i) q^{21} +(0.0578904 + 0.328313i) q^{22} +(3.88853 - 1.41531i) q^{23} +(-0.939693 - 0.342020i) q^{24} +(4.67705 - 1.70231i) q^{25} +(1.13019 + 1.95755i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.318051 - 2.62656i) q^{28} +(-5.92156 + 2.15527i) q^{29} +0.150940 q^{30} -4.22540 q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.0578904 + 0.328313i) q^{33} +(-4.09939 - 3.43980i) q^{34} +(0.180707 + 0.356126i) q^{35} +(-0.939693 - 0.342020i) q^{36} +(-5.97002 + 10.3404i) q^{37} +(2.13826 - 3.79840i) q^{38} +(1.13019 + 1.95755i) q^{39} +(0.115627 - 0.0970226i) q^{40} +(0.300303 + 1.70311i) q^{41} +(-0.318051 - 2.62656i) q^{42} +(-2.15340 + 1.80692i) q^{43} +(0.255382 + 0.214291i) q^{44} +0.150940 q^{45} +(2.06904 - 3.58369i) q^{46} +(1.10284 - 6.25451i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(5.81630 - 3.89495i) q^{49} +(2.48861 - 4.31040i) q^{50} +(-4.09939 - 3.43980i) q^{51} +(2.12407 + 0.773096i) q^{52} +(1.09737 - 6.22352i) q^{53} +(-0.939693 - 0.342020i) 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} +(1.19854 + 6.79724i) q^{59} +(0.115627 - 0.0970226i) q^{60} +(1.65284 - 0.601585i) q^{61} +(-3.23685 + 2.71604i) q^{62} +(-0.318051 - 2.62656i) q^{63} +(-0.500000 + 0.866025i) q^{64} -0.341183 q^{65} +(0.255382 + 0.214291i) q^{66} +(2.88550 + 2.42122i) q^{67} -5.35137 q^{68} +(2.06904 - 3.58369i) q^{69} +(0.367343 + 0.156652i) q^{70} +(-7.21818 + 6.05678i) q^{71} +(-0.939693 + 0.342020i) q^{72} +(2.09111 - 1.75465i) q^{73} +(2.07337 + 11.7586i) 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} +(9.12369 + 3.32075i) q^{79} +(0.0262105 - 0.148647i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(1.32478 + 1.11162i) q^{82} +(-3.97822 + 6.89048i) q^{83} +(-1.93196 - 1.80763i) q^{84} +(0.759026 - 0.276263i) q^{85} +(-0.488137 + 2.76836i) q^{86} +(-3.15080 + 5.45734i) q^{87} +0.333377 q^{88} +(-3.32127 - 2.78688i) q^{89} +(0.115627 - 0.0970226i) q^{90} +(0.718918 + 5.93704i) q^{91} +(-0.718571 - 4.07522i) q^{92} +(-3.23685 + 2.71604i) q^{93} +(-3.17550 - 5.50012i) q^{94} +(0.335145 + 0.566176i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-3.87650 - 1.41093i) q^{97} +(1.95192 - 6.72235i) q^{98} +(0.255382 + 0.214291i) 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 $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

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

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
$5$	0.0262105	+	0.148647i	0.0117217	+	0.0664771i	0.990108	−	0.140311i	$-0.0448101\pi$
$5$	0.0262105	+	0.148647i	0.0117217	+	0.0664771i	−0.978386	+	0.206788i	$0.933699\pi$
$6$	0.173648	−	0.984808i	0.0708916	−	0.402046i
$7$	2.53143	−	0.769318i	0.956792	−	0.290775i
$7$	2.53143	−	0.769318i	0.956792	−	0.290775i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	0.115627	+	0.0970226i	0.0365645	+	0.0306812i
$11$	−0.166689	+	0.288713i	−0.0502585	+	0.0870504i	−0.890060	−	0.455843i	$-0.849338\pi$
$11$	−0.166689	+	0.288713i	−0.0502585	+	0.0870504i	0.839802	+	0.542893i	$0.182671\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−0.392511	+	2.22604i	−0.108863	+	0.617393i	0.880744	+	0.473593i	$0.157043\pi$
$13$	−0.392511	+	2.22604i	−0.108863	+	0.617393i	−0.989607	+	0.143800i	$0.954068\pi$
$14$	1.44468	−	2.21650i	0.386108	−	0.592386i
$15$	0.115627	+	0.0970226i	0.0298548	+	0.0250511i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.929256	−	5.27007i	−0.225378	−	1.27818i	−0.861962	−	0.506973i	$-0.830764\pi$
$17$	−0.929256	−	5.27007i	−0.225378	−	1.27818i	0.636584	−	0.771207i	$-0.280347\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	4.07957	−	1.53530i	0.935917	−	0.352221i
$19$	4.07957	−	1.53530i	0.935917	−	0.352221i
$20$	0.150940			0.0337513
$21$	1.44468	−	2.21650i	0.315255	−	0.483681i
$22$	0.0578904	+	0.328313i	0.0123423	+	0.0699965i
$23$	3.88853	−	1.41531i	0.810815	−	0.295112i	0.0968543	−	0.995299i	$-0.469122\pi$
$23$	3.88853	−	1.41531i	0.810815	−	0.295112i	0.713960	+	0.700186i	$0.246900\pi$
$24$	−0.939693	−	0.342020i	−0.191814	−	0.0698146i
$25$	4.67705	−	1.70231i	0.935411	−	0.340462i
$26$	1.13019	+	1.95755i	0.221649	+	0.383907i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−0.318051	−	2.62656i	−0.0601060	−	0.496374i
$29$	−5.92156	+	2.15527i	−1.09961	+	0.400224i	−0.827171	−	0.561950i	$-0.810051\pi$
$29$	−5.92156	+	2.15527i	−1.09961	+	0.400224i	−0.272435	+	0.962174i	$0.587829\pi$
$30$	0.150940			0.0275578
$31$	−4.22540			−0.758904			−0.379452	−	0.925211i	$-0.623888\pi$
$31$	−4.22540			−0.758904			−0.379452	+	0.925211i	$0.623888\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.0578904	+	0.328313i	0.0100774	+	0.0571519i
$34$	−4.09939	−	3.43980i	−0.703039	−	0.589920i
$35$	0.180707	+	0.356126i	0.0305451	+	0.0601963i
$36$	−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	$0.728047\pi$
$38$	2.13826	−	3.79840i	0.346872	−	0.616182i
$39$	1.13019	+	1.95755i	0.180975	+	0.313459i
$40$	0.115627	−	0.0970226i	0.0182822	−	0.0153406i
$41$	0.300303	+	1.70311i	0.0468995	+	0.265980i	0.999237	−	0.0390673i	$-0.0124387\pi$
$41$	0.300303	+	1.70311i	0.0468995	+	0.265980i	−0.952337	+	0.305048i	$0.901328\pi$
$42$	−0.318051	−	2.62656i	−0.0490764	−	0.405288i
$43$	−2.15340	+	1.80692i	−0.328391	+	0.275553i	−0.792044	−	0.610464i	$-0.790983\pi$
$43$	−2.15340	+	1.80692i	−0.328391	+	0.275553i	0.463653	+	0.886017i	$0.346538\pi$
$44$	0.255382	+	0.214291i	0.0385003	+	0.0323056i
$45$	0.150940			0.0225009
$46$	2.06904	−	3.58369i	0.305064	−	0.528386i
$47$	1.10284	−	6.25451i	0.160865	−	0.912314i	−0.792360	−	0.610054i	$-0.791148\pi$
$47$	1.10284	−	6.25451i	0.160865	−	0.912314i	0.953226	−	0.302260i	$-0.0977410\pi$
$48$	−0.939693	+	0.342020i	−0.135633	+	0.0493664i
$49$	5.81630	−	3.89495i	0.830900	−	0.556422i
$50$	2.48861	−	4.31040i	0.351942	−	0.609582i
$51$	−4.09939	−	3.43980i	−0.574029	−	0.481668i
$52$	2.12407	+	0.773096i	0.294555	+	0.107209i
$53$	1.09737	−	6.22352i	0.150736	−	0.854866i	−0.811845	−	0.583873i	$-0.801537\pi$
$53$	1.09737	−	6.22352i	0.150736	−	0.854866i	0.962581	−	0.270993i	$-0.0873522\pi$
$54$	−0.939693	−	0.342020i	−0.127876	−	0.0465430i
$55$	−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
$59$	1.19854	+	6.79724i	0.156036	+	0.884926i	0.957832	+	0.287328i	$0.0927669\pi$
$59$	1.19854	+	6.79724i	0.156036	+	0.884926i	−0.801796	+	0.597598i	$0.796122\pi$
$60$	0.115627	−	0.0970226i	0.0149274	−	0.0125256i
$61$	1.65284	−	0.601585i	0.211625	−	0.0770251i	−0.234033	−	0.972229i	$-0.575192\pi$
$61$	1.65284	−	0.601585i	0.211625	−	0.0770251i	0.445657	+	0.895204i	$0.352970\pi$
$62$	−3.23685	+	2.71604i	−0.411080	+	0.344937i
$63$	−0.318051	−	2.62656i	−0.0400707	−	0.330916i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.341183			−0.0423186
$66$	0.255382	+	0.214291i	0.0314353	+	0.0263774i
$67$	2.88550	+	2.42122i	0.352520	+	0.295800i	0.801801	−	0.597591i	$-0.203875\pi$
$67$	2.88550	+	2.42122i	0.352520	+	0.295800i	−0.449281	+	0.893391i	$0.648320\pi$
$68$	−5.35137			−0.648949
$69$	2.06904	−	3.58369i	0.249084	−	0.431425i
$70$	0.367343	+	0.156652i	0.0439059	+	0.0187235i
$71$	−7.21818	+	6.05678i	−0.856641	+	0.718807i	−0.961242	−	0.275707i	$-0.911088\pi$
$71$	−7.21818	+	6.05678i	−0.856641	+	0.718807i	0.104601	+	0.994514i	$0.466644\pi$
$72$	−0.939693	+	0.342020i	−0.110744	+	0.0403075i
$73$	2.09111	−	1.75465i	0.244746	−	0.205366i	−0.512160	−	0.858890i	$-0.671155\pi$
$73$	2.09111	−	1.75465i	0.244746	−	0.205366i	0.756906	+	0.653524i	$0.226710\pi$
$74$	2.07337	+	11.7586i	0.241024	+	1.36692i
$75$	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
$79$	9.12369	+	3.32075i	1.02650	+	0.373614i	0.799745	−	0.600339i	$-0.204968\pi$
$79$	9.12369	+	3.32075i	1.02650	+	0.373614i	0.226750	+	0.973953i	$0.427190\pi$
$80$	0.0262105	−	0.148647i	0.00293043	−	0.0166193i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	1.32478	+	1.11162i	0.146298	+	0.122758i
$83$	−3.97822	+	6.89048i	−0.436666	+	0.756328i	−0.997430	−	0.0716478i	$-0.977174\pi$
$83$	−3.97822	+	6.89048i	−0.436666	+	0.756328i	0.560764	+	0.827976i	$0.310508\pi$
$84$	−1.93196	−	1.80763i	−0.210795	−	0.197228i
$85$	0.759026	−	0.276263i	0.0823279	−	0.0299649i
$86$	−0.488137	+	2.76836i	−0.0526371	+	0.298520i
$87$	−3.15080	+	5.45734i	−0.337801	+	0.585088i
$88$	0.333377			0.0355382
$89$	−3.32127	−	2.78688i	−0.352054	−	0.295409i	0.449560	−	0.893250i	$-0.351581\pi$
$89$	−3.32127	−	2.78688i	−0.352054	−	0.295409i	−0.801614	+	0.597842i	$0.796025\pi$
$90$	0.115627	−	0.0970226i	0.0121882	−	0.0102271i
$91$	0.718918	+	5.93704i	0.0753630	+	0.622371i
$92$	−0.718571	−	4.07522i	−0.0749162	−	0.424871i
$93$	−3.23685	+	2.71604i	−0.335645	+	0.281640i
$94$	−3.17550	−	5.50012i	−0.327527	−	0.567294i
$95$	0.335145	+	0.566176i	0.0343852	+	0.0580884i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−3.87650	−	1.41093i	−0.393598	−	0.143258i	0.137636	−	0.990483i	$-0.456050\pi$
$97$	−3.87650	−	1.41093i	−0.393598	−	0.143258i	−0.531235	+	0.847225i	$0.678272\pi$
$98$	1.95192	−	6.72235i	0.197174	−	0.679060i
$99$	0.255382	+	0.214291i	0.0256669	+	0.0215370i
$100$	−0.864285	−	4.90160i	−0.0864285	−	0.490160i
$101$	−15.7281	+	5.72456i	−1.56500	+	0.569615i	−0.971876	−	0.235494i	$-0.924329\pi$
$101$	−15.7281	+	5.72456i	−1.56500	+	0.569615i	−0.593127	+	0.805109i	$0.702107\pi$
$102$	−5.35137			−0.529865
$103$	−6.19112			−0.610030			−0.305015	−	0.952348i	$-0.598661\pi$
$103$	−6.19112			−0.610030			−0.305015	+	0.952348i	$0.598661\pi$
$104$	2.12407	−	0.773096i	0.208282	−	0.0758083i
$105$	0.367343	+	0.156652i	0.0358490	+	0.0152877i
$106$	−3.15976	−	5.47287i	−0.306903	−	0.531572i
$107$	3.30212	+	5.71944i	0.319228	+	0.552919i	0.980327	−	0.197379i	$-0.0632430\pi$
$107$	3.30212	+	5.71944i	0.319228	+	0.552919i	−0.661099	+	0.750299i	$0.729910\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	10.4744	+	3.81237i	1.00327	+	0.365159i	0.790843	−	0.612019i	$-0.209642\pi$
$109$	10.4744	+	3.81237i	1.00327	+	0.365159i	0.212423	+	0.977178i	$0.431864\pi$
$110$	−0.0472855	+	0.0172105i	−0.00450849	+	0.00164096i
$111$	2.07337	+	11.7586i	0.196795	+	1.11608i
$112$	−2.64189	−	0.142879i	−0.249635	−	0.0135008i
$113$	8.86878			0.834305			0.417152	−	0.908837i	$-0.363028\pi$
$113$	8.86878			0.834305			0.417152	+	0.908837i	$0.363028\pi$
$114$	−0.803562	−	4.28419i	−0.0752604	−	0.401251i
$115$	0.312302	+	0.540923i	0.0291223	+	0.0504414i
$116$	1.09426	+	6.20586i	0.101599	+	0.576199i
$117$	2.12407	+	0.773096i	0.196370	+	0.0714728i
$118$	5.28732	+	4.43658i	0.486737	+	0.408421i
$119$	−6.40671	−	12.6259i	−0.587302	−	1.15742i
$120$	0.0262105	−	0.148647i	0.00239268	−	0.0135696i
$121$	5.44443	+	9.43003i	0.494948	+	0.857275i
$122$	0.879459	−	1.52327i	0.0796225	−	0.137910i
$123$	1.32478	+	1.11162i	0.119451	+	0.100232i
$124$	−0.733733	+	4.16121i	−0.0658912	+	0.373688i
$125$	0.752983	+	1.30420i	0.0673488	+	0.116652i
$126$	−1.93196	−	1.80763i	−0.172113	−	0.161036i
$127$	−2.90758	+	16.4897i	−0.258006	+	1.46322i	0.530231	+	0.847853i	$0.322105\pi$
$127$	−2.90758	+	16.4897i	−0.258006	+	1.46322i	−0.788237	+	0.615371i	$0.789006\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−0.488137	+	2.76836i	−0.0429780	+	0.243740i
$130$	−0.261361	+	0.219308i	−0.0229229	+	0.0192346i
$131$	7.50458	−	6.29709i	0.655678	−	0.550180i	−0.253110	−	0.967438i	$-0.581453\pi$
$131$	7.50458	−	6.29709i	0.655678	−	0.550180i	0.908788	+	0.417258i	$0.137009\pi$
$132$	0.333377			0.0290168
$133$	9.14602	−	7.02498i	0.793060	−	0.609143i
$134$	3.76676			0.325398
$135$	0.115627	−	0.0970226i	0.00995159	−	0.00835038i
$136$	−4.09939	+	3.43980i	−0.351520	+	0.294960i
$137$	−2.41380	+	13.6893i	−0.206225	+	1.16956i	0.689276	+	0.724499i	$0.257929\pi$
$137$	−2.41380	+	13.6893i	−0.206225	+	1.16956i	−0.895501	+	0.445060i	$0.853182\pi$
$138$	−0.718571	−	4.07522i	−0.0611689	−	0.346906i
$139$	−0.499103	+	2.83055i	−0.0423333	+	0.240084i	−0.998631	−	0.0523112i	$-0.983341\pi$
$139$	−0.499103	+	2.83055i	−0.0423333	+	0.240084i	0.956298	+	0.292395i	$0.0944523\pi$
$140$	0.382095	−	0.116121i	0.0322930	−	0.00981402i
$141$	−3.17550	−	5.50012i	−0.267425	−	0.463194i
$142$	−1.63623	+	9.27952i	−0.137309	+	0.778720i
$143$	−0.577261	−	0.484380i	−0.0482730	−	0.0405058i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.475582	−	0.823733i	−0.0394950	−	0.0684073i
$146$	0.474016	−	2.68828i	0.0392298	−	0.222484i
$147$	1.95192	−	6.72235i	0.160992	−	0.554450i
$148$	9.14661	+	7.67491i	0.751846	+	0.630874i
$149$	−8.24674	−	3.00157i	−0.675599	−	0.245898i	−0.0186425	−	0.999826i	$-0.505934\pi$
$149$	−8.24674	−	3.00157i	−0.675599	−	0.245898i	−0.656957	+	0.753928i	$0.728157\pi$
$150$	−0.864285	−	4.90160i	−0.0705685	−	0.400214i
$151$	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	$0.695174\pi$
$152$	−3.36939	−	2.76536i	−0.273293	−	0.224300i
$153$	−5.35137			−0.432633
$154$	0.399122	+	0.786565i	0.0321622	+	0.0633832i
$155$	−0.110750	−	0.628094i	−0.00889565	−	0.0504498i
$156$	2.12407	−	0.773096i	0.170061	−	0.0618973i
$157$	19.6847	+	7.16464i	1.57101	+	0.571800i	0.973224	−	0.229857i	$-0.0738259\pi$
$157$	19.6847	+	7.16464i	1.57101	+	0.571800i	0.597784	+	0.801657i	$0.296048\pi$
$158$	9.12369	−	3.32075i	0.725842	−	0.264185i
$159$	−3.15976	−	5.47287i	−0.250586	−	0.434027i
$160$	−0.0754702	−	0.130718i	−0.00596644	−	0.0103342i
$161$	8.75473	−	6.57427i	0.689969	−	0.518125i
$162$	−0.939693	+	0.342020i	−0.0738292	+	0.0268716i
$163$	−24.1527			−1.89179			−0.945893	−	0.324480i	$-0.894811\pi$
$163$	−24.1527			−1.89179			−0.945893	+	0.324480i	$0.894811\pi$
$164$	1.72938			0.135042
$165$	−0.0472855	+	0.0172105i	−0.00368117	+	0.00133984i
$166$	1.38162	+	7.83556i	0.107235	+	0.608157i
$167$	−13.0200	−	10.9251i	−1.00752	−	0.845409i	−0.0195113	−	0.999810i	$-0.506211\pi$
$167$	−13.0200	−	10.9251i	−1.00752	−	0.845409i	−0.988008	+	0.154400i	$0.950655\pi$
$168$	−2.64189	−	0.142879i	−0.203826	−	0.0110233i
$169$	7.41480	+	2.69877i	0.570370	+	0.207598i
$170$	0.403869	−	0.699522i	0.0309753	−	0.0536509i
$171$	−0.803562	−	4.28419i	−0.0614499	−	0.327620i
$172$	1.40553	+	2.43445i	0.107171	+	0.185625i
$173$	13.2437	−	11.1128i	1.00690	−	0.844887i	0.0189724	−	0.999820i	$-0.493961\pi$
$173$	13.2437	−	11.1128i	1.00690	−	0.844887i	0.987925	+	0.154933i	$0.0495161\pi$
$174$	1.09426	+	6.20586i	0.0829556	+	0.470465i
$175$	10.5300	−	7.90742i	0.795996	−	0.597745i
$176$	0.255382	−	0.214291i	0.0192501	−	0.0161528i
$177$	5.28732	+	4.43658i	0.397419	+	0.333474i
$178$	−4.33561			−0.324968
$179$	−6.24298	+	10.8132i	−0.466623	+	0.808214i	−0.999273	−	0.0381212i	$-0.987863\pi$
$179$	−6.24298	+	10.8132i	−0.466623	+	0.808214i	0.532651	+	0.846335i	$0.321196\pi$
$180$	0.0262105	−	0.148647i	0.00195362	−	0.0110795i
$181$	−11.6103	+	4.22579i	−0.862985	+	0.314101i	−0.735323	−	0.677717i	$-0.762969\pi$
$181$	−11.6103	+	4.22579i	−0.862985	+	0.314101i	−0.127662	+	0.991818i	$0.540747\pi$
$182$	4.36698	+	4.08593i	0.323702	+	0.302869i
$183$	0.879459	−	1.52327i	0.0650115	−	0.112603i
$184$	−3.16996	−	2.65991i	−0.233692	−	0.196091i
$185$	−1.69355	−	0.616401i	−0.124512	−	0.0453187i
$186$	−0.733733	+	4.16121i	−0.0537999	+	0.305115i
$187$	1.67644	+	0.610173i	0.122593	+	0.0446203i
$188$	−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	$0.189099\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	14.3463	−	12.0380i	1.03267	−	0.866514i	0.0415045	−	0.999138i	$-0.486785\pi$
$193$	14.3463	−	12.0380i	1.03267	−	0.866514i	0.991166	+	0.132625i	$0.0423405\pi$
$194$	−3.87650	+	1.41093i	−0.278316	+	0.101299i
$195$	−0.261361	+	0.219308i	−0.0187165	+	0.0157050i
$196$	−2.82579	−	6.40429i	−0.201842	−	0.457449i
$197$	−2.34061	+	4.05406i	−0.166762	+	0.288839i	−0.937279	−	0.348579i	$-0.886664\pi$
$197$	−2.34061	+	4.05406i	−0.166762	+	0.288839i	0.770518	+	0.637418i	$0.219998\pi$
$198$	0.333377			0.0236921
$199$	−0.185666	−	0.155792i	−0.0131615	−	0.0110438i	0.636183	−	0.771538i	$-0.280512\pi$
$199$	−0.185666	−	0.155792i	−0.0131615	−	0.0110438i	−0.649345	+	0.760494i	$0.724957\pi$
$200$	−3.81277	−	3.19929i	−0.269604	−	0.226224i
$201$	3.76676			0.265686
$202$	−8.36874	+	14.4951i	−0.588823	+	1.01987i
$203$	−13.3319	+	10.0115i	−0.935719	+	0.702668i
$204$	−4.09939	+	3.43980i	−0.287015	+	0.240834i
$205$	−0.245291	+	0.0892786i	−0.0171319	+	0.00623549i
$206$	−4.74268	+	3.97958i	−0.330438	+	0.277270i
$207$	−0.718571	−	4.07522i	−0.0499442	−	0.283247i
$208$	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	0.858391	−	0.512995i	$-0.171464\pi$
$211$	17.2307	+	6.27146i	1.18621	+	0.431745i	0.327819	+	0.944741i	$0.393686\pi$
$212$	−5.93841	−	2.16141i	−0.407852	−	0.148446i
$213$	−1.63623	+	9.27952i	−0.112113	+	0.635822i
$214$	6.20596	+	2.25878i	0.424231	+	0.154407i
$215$	−0.325035	−	0.272737i	−0.0221672	−	0.0186005i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−10.6963	+	3.25068i	−0.726113	+	0.220670i
$218$	10.4744	−	3.81237i	0.709417	−	0.258207i
$219$	0.474016	−	2.68828i	0.0320310	−	0.181657i
$220$	−0.0251601	+	0.0435785i	−0.00169629	+	0.00293806i
$221$	12.0961			0.813675
$222$	9.14661	+	7.67491i	0.613880	+	0.515106i
$223$	−6.39603	+	5.36691i	−0.428310	+	0.359395i	−0.831314	−	0.555804i	$-0.812411\pi$
$223$	−6.39603	+	5.36691i	−0.428310	+	0.359395i	0.403004	+	0.915198i	$0.367966\pi$
$224$	−2.11565	+	1.58872i	−0.141358	+	0.106151i
$225$	−0.864285	−	4.90160i	−0.0576190	−	0.326773i
$226$	6.79388	−	5.70074i	0.451922	−	0.379208i
$227$	−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	$0.890183\pi$
$228$	−3.36939	−	2.76536i	−0.223143	−	0.183140i
$229$	−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
$231$	0.399122	+	0.786565i	0.0262603	+	0.0517522i
$232$	4.82730	+	4.05058i	0.316928	+	0.265934i
$233$	−2.42601	−	13.7586i	−0.158934	−	0.901357i	−0.955101	−	0.296280i	$-0.904254\pi$
$233$	−2.42601	−	13.7586i	−0.158934	−	0.901357i	0.796167	−	0.605076i	$-0.206857\pi$
$234$	2.12407	−	0.773096i	0.138854	−	0.0505389i
$235$	0.958621			0.0625336
$236$	6.90210			0.449288
$237$	9.12369	−	3.32075i	0.592647	−	0.215706i
$238$	−13.0236	−	5.55388i	−0.844196	−	0.360004i
$239$	−3.89702	−	6.74983i	−0.252077	−	0.436610i	0.712021	−	0.702159i	$-0.247780\pi$
$239$	−3.89702	−	6.74983i	−0.252077	−	0.436610i	−0.964097	+	0.265549i	$0.914447\pi$
$240$	−0.0754702	−	0.130718i	−0.00487158	−	0.00843782i
$241$	−20.4507	+	7.44343i	−1.31734	+	0.479474i	−0.902606	−	0.430468i	$-0.858349\pi$
$241$	−20.4507	+	7.44343i	−1.31734	+	0.479474i	−0.414737	+	0.909941i	$0.636126\pi$
$242$	10.2322	+	3.72421i	0.657749	+	0.239401i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	−0.305433	−	1.73220i	−0.0195533	−	0.110892i
$245$	0.731422	+	0.762489i	0.0467288	+	0.0487136i
$246$	1.72938			0.110261
$247$	1.81636	+	9.68391i	0.115572	+	0.616172i
$248$	2.11270	+	3.65930i	0.134157	+	0.232366i
$249$	1.38162	+	7.83556i	0.0875567	+	0.496558i
$250$	1.41514	+	0.515070i	0.0895016	+	0.0325759i
$251$	−7.25911	−	6.09112i	−0.458191	−	0.384468i	0.384274	−	0.923219i	$-0.374452\pi$
$251$	−7.25911	−	6.09112i	−0.458191	−	0.384468i	−0.842465	+	0.538751i	$0.818896\pi$
$252$	−2.64189	−	0.142879i	−0.166423	−	0.00900052i
$253$	−0.239556	+	1.35859i	−0.0150607	+	0.0854136i
$254$	8.37204	+	14.5008i	0.525309	+	0.909861i
$255$	0.403869	−	0.699522i	0.0252913	−	0.0438057i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.569965	−	3.23243i	0.0355535	−	0.201634i	−0.961857	−	0.273553i	$-0.911801\pi$
$257$	0.569965	−	3.23243i	0.0355535	−	0.201634i	0.997410	+	0.0719190i	$0.0229123\pi$
$258$	1.40553	+	2.43445i	0.0875047	+	0.151563i
$259$	−7.15767	+	30.7688i	−0.444756	+	1.91188i
$260$	−0.0592458	+	0.336000i	−0.00367427	+	0.0208378i
$261$	1.09426	+	6.20586i	0.0677330	+	0.384133i
$262$	1.70115	−	9.64771i	0.105097	−	0.596037i
$263$	−20.8145	+	17.4654i	−1.28348	+	1.07696i	−0.290720	+	0.956808i	$0.593895\pi$
$263$	−20.8145	+	17.4654i	−1.28348	+	1.07696i	−0.992755	+	0.120155i	$0.961661\pi$
$264$	0.255382	−	0.214291i	0.0157177	−	0.0131887i
$265$	0.953872			0.0585959
$266$	2.49069	−	11.2604i	0.152714	−	0.690419i
$267$	−4.33561			−0.265335
$268$	2.88550	−	2.42122i	0.176260	−	0.147900i
$269$	20.0656	−	16.8370i	1.22342	−	1.02657i	0.224782	−	0.974409i	$-0.427833\pi$
$269$	20.0656	−	16.8370i	1.22342	−	1.02657i	0.998639	−	0.0521626i	$-0.0166114\pi$
$270$	0.0262105	−	0.148647i	0.00159512	−	0.00904638i
$271$	−5.07967	−	28.8082i	−0.308568	−	1.74998i	−0.606217	−	0.795300i	$-0.707314\pi$
$271$	−5.07967	−	28.8082i	−0.308568	−	1.74998i	0.297649	−	0.954675i	$-0.403798\pi$
$272$	−0.929256	+	5.27007i	−0.0563444	+	0.319545i
$273$	4.36698	+	4.08593i	0.264302	+	0.247292i
$274$	6.95026	+	12.0382i	0.419880	+	0.727254i
$275$	−0.288133	+	1.63408i	−0.0173751	+	0.0985390i
$276$	−3.16996	−	2.65991i	−0.190809	−	0.160108i
$277$	11.6541	−	20.1855i	0.700227	−	1.21283i	−0.268159	−	0.963375i	$-0.586415\pi$
$277$	11.6541	−	20.1855i	0.700227	−	1.21283i	0.968387	−	0.249454i	$-0.0802513\pi$
$278$	1.43711	+	2.48915i	0.0861921	+	0.149289i
$279$	−0.733733	+	4.16121i	−0.0439275	+	0.249125i
$280$	0.218061	−	0.334560i	0.0130316	−	0.0199938i
$281$	−9.72705	−	8.16196i	−0.580267	−	0.486902i	0.304768	−	0.952427i	$-0.401421\pi$
$281$	−9.72705	−	8.16196i	−0.580267	−	0.486902i	−0.885035	+	0.465525i	$0.845866\pi$
$282$	−5.96798	−	2.17217i	−0.355388	−	0.129351i
$283$	0.660057	+	3.74337i	0.0392363	+	0.222520i	0.998121	−	0.0612763i	$-0.0195171\pi$
$283$	0.660057	+	3.74337i	0.0392363	+	0.222520i	−0.958885	+	0.283797i	$0.908406\pi$
$284$	4.71134	+	8.16027i	0.279566	+	0.484223i
$285$	0.620667	+	0.218289i	0.0367651	+	0.0129303i
$286$	−0.753561			−0.0445590
$287$	2.07043	+	4.08027i	0.122213	+	0.240851i
$288$	0.173648	+	0.984808i	0.0102323	+	0.0580304i
$289$	−10.9354	+	3.98015i	−0.643257	+	0.234126i
$290$	−0.893802	−	0.325317i	−0.0524859	−	0.0191033i
$291$	−3.87650	+	1.41093i	−0.227244	+	0.0827101i
$292$	−1.36487	−	2.36403i	−0.0798733	−	0.138345i
$293$	−10.8603	−	18.8106i	−0.634466	−	1.09893i	−0.986628	−	0.162988i	$-0.947887\pi$
$293$	−10.8603	−	18.8106i	−0.634466	−	1.09893i	0.352162	−	0.935939i	$-0.385447\pi$
$294$	−2.82579	−	6.40429i	−0.164803	−	0.373506i
$295$	−0.978977	+	0.356319i	−0.0569983	+	0.0207457i
$296$	11.9400			0.694001
$297$	0.333377			0.0193445
$298$	−8.24674	+	3.00157i	−0.477721	+	0.173876i
$299$	1.62425	+	9.21156i	0.0939326	+	0.532718i
$300$	−3.81277	−	3.19929i	−0.220130	−	0.184711i
$301$	−4.06110	+	6.23074i	−0.234078	+	0.359134i
$302$	9.71207	+	3.53490i	0.558867	+	0.203411i
$303$	−8.36874	+	14.4951i	−0.480772	+	0.832721i
$304$	−4.35864	+	0.0474119i	−0.249985	+	0.00271926i
$305$	0.132746	+	0.229923i	0.00760101	+	0.0131653i
$306$	−4.09939	+	3.43980i	−0.234346	+	0.196640i
$307$	−4.98944	−	28.2965i	−0.284762	−	1.61497i	−0.706133	−	0.708079i	$-0.749562\pi$
$307$	−4.98944	−	28.2965i	−0.284762	−	1.61497i	0.421370	−	0.906889i	$-0.361549\pi$
$308$	0.811340	+	0.345993i	0.0462304	+	0.0197148i
$309$	−4.74268	+	3.97958i	−0.269801	+	0.226390i
$310$	−0.488571	−	0.409959i	−0.0277489	−	0.0232841i
$311$	0.863583			0.0489693			0.0244846	−	0.999700i	$-0.492206\pi$
$311$	0.863583			0.0489693			0.0244846	+	0.999700i	$0.492206\pi$
$312$	1.13019	−	1.95755i	0.0639845	−	0.110824i
$313$	3.50612	−	19.8842i	0.198178	−	1.12392i	−0.709642	−	0.704562i	$-0.751143\pi$
$313$	3.50612	−	19.8842i	0.198178	−	1.12392i	0.907820	−	0.419360i	$-0.137745\pi$
$314$	19.6847	−	7.16464i	1.11087	−	0.404324i
$315$	0.382095	−	0.116121i	0.0215286	−	0.00654268i
$316$	4.85461	−	8.40844i	0.273093	−	0.473012i
$317$	25.5527	+	21.4412i	1.43518	+	1.20426i	0.942569	+	0.334011i	$0.108402\pi$
$317$	25.5527	+	21.4412i	1.43518	+	1.20426i	0.492612	+	0.870249i	$0.336042\pi$
$318$	−5.93841	−	2.16141i	−0.333010	−	0.121206i
$319$	0.364802	−	2.06889i	0.0204250	−	0.115836i
$320$	−0.141838	−	0.0516247i	−0.00792896	−	0.00288591i
$321$	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
$325$	1.95361	+	11.0795i	0.108367	+	0.614580i
$326$	−18.5020	+	15.5251i	−1.02473	+	0.859853i
$327$	10.4744	−	3.81237i	0.579236	−	0.210825i
$328$	1.32478	−	1.11162i	0.0731488	−	0.0613791i
$329$	−2.01994	−	16.6813i	−0.111363	−	0.919670i
$330$	−0.0251601	+	0.0435785i	−0.00138502	+	0.00239892i
$331$	−7.32457			−0.402595			−0.201298	−	0.979530i	$-0.564516\pi$
$331$	−7.32457			−0.402595			−0.201298	+	0.979530i	$0.564516\pi$
$332$	6.09498	+	5.11430i	0.334506	+	0.280684i
$333$	9.14661	+	7.67491i	0.501231	+	0.420583i
$334$	−16.9964			−0.930003
$335$	−0.284278	+	0.492384i	−0.0155318	+	0.0269018i
$336$	−2.11565	+	1.58872i	−0.115418	+	0.0866719i
$337$	5.81514	−	4.87948i	0.316771	−	0.265802i	−0.470513	−	0.882393i	$-0.655931\pi$
$337$	5.81514	−	4.87948i	0.316771	−	0.265802i	0.787284	+	0.616591i	$0.211487\pi$
$338$	7.41480	−	2.69877i	0.403312	−	0.146794i
$339$	6.79388	−	5.70074i	0.368993	−	0.309622i
$340$	−0.140262	−	0.795467i	−0.00760679	−	0.0431402i
$341$	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
$345$	0.586936	+	0.213627i	0.0315996	+	0.0115013i
$346$	3.00210	−	17.0257i	0.161394	−	0.915309i
$347$	6.41569	+	2.33512i	0.344412	+	0.125356i	0.508434	−	0.861101i	$-0.330225\pi$
$347$	6.41569	+	2.33512i	0.344412	+	0.125356i	−0.164022	+	0.986457i	$0.552447\pi$
$348$	4.82730	+	4.05058i	0.258770	+	0.217134i
$349$	−7.34213	+	12.7169i	−0.393015	+	0.680722i	−0.992846	−	0.119405i	$-0.961901\pi$
$349$	−7.34213	+	12.7169i	−0.393015	+	0.680722i	0.599831	+	0.800127i	$0.295235\pi$
$350$	2.98368	−	12.8260i	0.159484	−	0.685579i
$351$	2.12407	−	0.773096i	0.113374	−	0.0412648i
$352$	0.0578904	−	0.328313i	0.00308557	−	0.0174991i
$353$	9.47320	−	16.4081i	0.504207	−	0.873313i	−0.495781	−	0.868448i	$-0.665118\pi$
$353$	9.47320	−	16.4081i	0.504207	−	0.873313i	0.999988	−	0.00486503i	$-0.00154859\pi$
$354$	6.90210			0.366843
$355$	−1.08952	−	0.914212i	−0.0578255	−	0.0485213i
$356$	−3.32127	+	2.78688i	−0.176027	+	0.147704i
$357$	−13.0236	−	5.55388i	−0.689283	−	0.293942i
$358$	2.16817	+	12.2963i	0.114591	+	0.649879i
$359$	−22.8587	+	19.1808i	−1.20644	+	1.01232i	−0.207016	+	0.978338i	$0.566375\pi$
$359$	−22.8587	+	19.1808i	−1.20644	+	1.01232i	−0.999422	+	0.0339840i	$0.989180\pi$
$360$	−0.0754702	−	0.130718i	−0.00397763	−	0.00688945i
$361$	14.2857	−	12.5267i	0.751881	−	0.659299i
$362$	−6.17770	+	10.7001i	−0.324692	+	0.562384i
$363$	10.2322	+	3.72421i	0.537050	+	0.195470i
$364$	5.97168	+	0.322961i	0.313001	+	0.0169278i
$365$	0.315633	+	0.264847i	0.0165210	+	0.0138627i
$366$	−0.305433	−	1.73220i	−0.0159652	−	0.0905433i
$367$	−16.4586	+	5.99043i	−0.859130	+	0.312698i	−0.733757	−	0.679412i	$-0.762235\pi$
$367$	−16.4586	+	5.99043i	−0.859130	+	0.312698i	−0.125373	+	0.992110i	$0.540013\pi$
$368$	−4.13809			−0.215713
$369$	1.72938			0.0900279
$370$	−1.69355	+	0.616401i	−0.0880433	+	0.0320451i
$371$	−2.00993	−	16.5986i	−0.104351	−	0.861759i
$372$	2.11270	+	3.65930i	0.109538	+	0.189726i
$373$	−3.15460	−	5.46393i	−0.163339	−	0.282911i	0.772725	−	0.634741i	$-0.218893\pi$
$373$	−3.15460	−	5.46393i	−0.163339	−	0.282911i	−0.936064	+	0.351829i	$0.885560\pi$
$374$	1.67644	−	0.610173i	0.0866865	−	0.0315513i
$375$	1.41514	+	0.515070i	0.0730777	+	0.0265981i
$376$	−5.96798	+	2.17217i	−0.307775	+	0.112021i
$377$	−2.47345	−	14.0276i	−0.127389	−	0.722459i
$378$	−2.64189	−	0.142879i	−0.135884	−	0.00734890i
$379$	−11.0421			−0.567196			−0.283598	−	0.958943i	$-0.591528\pi$
$379$	−11.0421			−0.567196			−0.283598	+	0.958943i	$0.591528\pi$
$380$	0.615771	−	0.231738i	0.0315884	−	0.0118879i
$381$	8.37204	+	14.5008i	0.428913	+	0.742898i
$382$	0.337976	+	1.91676i	0.0172923	+	0.0980697i
$383$	−6.61343	−	2.40709i	−0.337931	−	0.122997i	0.167480	−	0.985875i	$-0.446437\pi$
$383$	−6.61343	−	2.40709i	−0.337931	−	0.122997i	−0.505411	+	0.862879i	$0.668659\pi$
$384$	0.766044	+	0.642788i	0.0390920	+	0.0328021i
$385$	−0.132940	−	0.00718968i	−0.00677526	−	0.000366420i
$386$	3.25205	−	18.4433i	0.165525	−	0.938738i
$387$	1.40553	+	2.43445i	0.0714473	+	0.123750i
$388$	−2.06264	+	3.57260i	−0.104715	+	0.181371i
$389$	5.36452	+	4.50137i	0.271992	+	0.228228i	0.768573	−	0.639762i	$-0.220967\pi$
$389$	5.36452	+	4.50137i	0.271992	+	0.228228i	−0.496581	+	0.867990i	$0.665411\pi$
$390$	−0.0592458	+	0.336000i	−0.00300003	+	0.0170140i
$391$	−11.0722	−	19.1777i	−0.559946	−	0.969855i
$392$	−6.28128	−	3.08959i	−0.317252	−	0.156048i
$393$	1.70115	−	9.64771i	0.0858117	−	0.486662i
$394$	0.812885	+	4.61010i	0.0409526	+	0.232254i
$395$	−0.254484	+	1.44325i	−0.0128045	+	0.0726178i
$396$	0.255382	−	0.214291i	0.0128334	−	0.0107685i
$397$	−5.65919	+	4.74862i	−0.284026	+	0.238327i	−0.773659	−	0.633603i	$-0.781575\pi$
$397$	−5.65919	+	4.74862i	−0.284026	+	0.238327i	0.489632	+	0.871929i	$0.337131\pi$
$398$	−0.242369			−0.0121489
$399$	2.49069	−	11.2604i	0.124690	−	0.563725i
$400$	−4.97722			−0.248861
$401$	28.7521	−	24.1259i	1.43581	−	1.20479i	0.493639	−	0.869667i	$-0.335666\pi$
$401$	28.7521	−	24.1259i	1.43581	−	1.20479i	0.942174	−	0.335124i	$-0.108778\pi$
$402$	2.88550	−	2.42122i	0.143916	−	0.120760i
$403$	1.65852	−	9.40592i	0.0826167	−	0.468542i
$404$	2.90643	+	16.4832i	0.144600	+	0.820070i
$405$	0.0262105	−	0.148647i	0.00130241	−	0.00738634i
$406$	−3.77760	+	16.2388i	−0.187479	+	0.805920i
$407$	−1.99027	−	3.44725i	−0.0986541	−	0.170874i
$408$	−0.929256	+	5.27007i	−0.0460050	+	0.260907i
$409$	0.788463	+	0.661599i	0.0389870	+	0.0327140i	0.662073	−	0.749439i	$-0.269677\pi$
$409$	0.788463	+	0.661599i	0.0389870	+	0.0327140i	−0.623086	+	0.782153i	$0.714121\pi$
$410$	−0.130517	+	0.226061i	−0.00644575	+	0.0111644i
$411$	6.95026	+	12.0382i	0.342831	+	0.593800i
$412$	−1.07508	+	6.09707i	−0.0529653	+	0.300381i
$413$	8.26325	+	16.2847i	0.406608	+	0.801318i
$414$	−3.16996	−	2.65991i	−0.155795	−	0.130728i
$415$	−1.12852	−	0.410748i	−0.0553969	−	0.0201628i
$416$	−0.392511	−	2.22604i	−0.0192445	−	0.109141i
$417$	1.43711	+	2.48915i	0.0703755	+	0.121894i
$418$	0.740225	+	1.25049i	0.0362056	+	0.0611637i
$419$	−36.1220			−1.76467			−0.882337	−	0.470617i	$-0.844031\pi$
$419$	−36.1220			−1.76467			−0.882337	+	0.470617i	$0.844031\pi$
$420$	0.218061	−	0.334560i	0.0106403	−	0.0163249i
$421$	−5.81928	−	33.0028i	−0.283614	−	1.60846i	−0.710194	−	0.704006i	$-0.751393\pi$
$421$	−5.81928	−	33.0028i	−0.283614	−	1.60846i	0.426580	−	0.904450i	$-0.359718\pi$
$422$	17.2307	−	6.27146i	0.838777	−	0.305290i
$423$	−5.96798	−	2.17217i	−0.290173	−	0.105614i
$424$	−5.93841	+	2.16141i	−0.288395	+	0.104967i
$425$	−13.3175	−	23.0665i	−0.645992	−	1.11889i
$426$	4.71134	+	8.16027i	0.228265	+	0.395366i
$427$	3.72125	−	2.79443i	0.180084	−	0.135232i
$428$	6.20596	−	2.25878i	0.299976	−	0.109182i
$429$	−0.753561			−0.0363823
$430$	−0.424303			−0.0204617
$431$	−2.98470	+	1.08634i	−0.143768	+	0.0523272i	−0.412902	−	0.910776i	$-0.635485\pi$
$431$	−2.98470	+	1.08634i	−0.143768	+	0.0523272i	0.269134	+	0.963103i	$0.413263\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	−9.87076	−	8.28255i	−0.474359	−	0.398034i	0.374023	−	0.927419i	$-0.377978\pi$
$433$	−9.87076	−	8.28255i	−0.474359	−	0.398034i	−0.848381	+	0.529385i	$0.822423\pi$
$434$	−6.10436	+	9.36562i	−0.293019	+	0.449564i
$435$	−0.893802	−	0.325317i	−0.0428545	−	0.0155978i
$436$	5.57332	−	9.65327i	0.266914	−	0.462308i
$437$	13.6906	−	11.7439i	0.654910	−	0.561787i
$438$	−1.36487	−	2.36403i	−0.0652162	−	0.112958i
$439$	22.0261	−	18.4821i	1.05125	−	0.882103i	0.0580250	−	0.998315i	$-0.481520\pi$
$439$	22.0261	−	18.4821i	1.05125	−	0.882103i	0.993224	+	0.116212i	$0.0370753\pi$
$440$	0.00873800	+	0.0495557i	0.000416568	+	0.00236247i
$441$	−2.82579	−	6.40429i	−0.134561	−	0.304966i
$442$	9.26619	−	7.77525i	0.440748	−	0.369831i
$443$	−15.9450	−	13.3794i	−0.757570	−	0.635677i	0.179923	−	0.983681i	$-0.442415\pi$
$443$	−15.9450	−	13.3794i	−0.757570	−	0.635677i	−0.937493	+	0.348004i	$0.886860\pi$
$444$	11.9400			0.566649
$445$	0.327210	−	0.566744i	0.0155112	−	0.0268662i
$446$	−1.44986	+	8.22258i	−0.0686530	+	0.389350i
$447$	−8.24674	+	3.00157i	−0.390057	+	0.141969i
$448$	−0.599468	+	2.57694i	−0.0283222	+	0.121749i
$449$	−5.27580	+	9.13796i	−0.248980	+	0.431247i	−0.963243	−	0.268631i	$-0.913429\pi$
$449$	−5.27580	+	9.13796i	−0.248980	+	0.431247i	0.714263	+	0.699878i	$0.246762\pi$
$450$	−3.81277	−	3.19929i	−0.179736	−	0.150816i
$451$	−0.541767	−	0.197187i	−0.0255108	−	0.00928517i
$452$	1.54005	−	8.73405i	0.0724378	−	0.410815i
$453$	9.71207	+	3.53490i	0.456313	+	0.166084i
$454$	−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	$0.277798\pi$
$458$	1.83456	+	10.4043i	0.0857233	+	0.486161i
$459$	−4.09939	+	3.43980i	−0.191343	+	0.160556i
$460$	0.586936	−	0.213627i	0.0273660	−	0.00996043i
$461$	−25.9439	+	21.7695i	−1.20833	+	1.01391i	−0.208977	+	0.977920i	$0.567013\pi$
$461$	−25.9439	+	21.7695i	−1.20833	+	1.01391i	−0.999352	+	0.0359884i	$0.988542\pi$
$462$	0.811340	+	0.345993i	0.0377470	+	0.0160971i
$463$	4.91535	−	8.51364i	0.228436	−	0.395662i	−0.728909	−	0.684611i	$-0.759972\pi$
$463$	4.91535	−	8.51364i	0.228436	−	0.395662i	0.957345	+	0.288948i	$0.0933056\pi$
$464$	6.30159			0.292544
$465$	−0.488571	−	0.409959i	−0.0226569	−	0.0190114i
$466$	−10.7023	−	8.98030i	−0.495775	−	0.416004i
$467$	33.3098			1.54139			0.770696	−	0.637203i	$-0.219909\pi$
$467$	33.3098			1.54139			0.770696	+	0.637203i	$0.219909\pi$
$468$	1.13019	−	1.95755i	0.0522431	−	0.0904877i
$469$	9.16714	+	3.90930i	0.423299	+	0.180515i
$470$	0.734347	−	0.616190i	0.0338729	−	0.0284227i
$471$	19.6847	−	7.16464i	0.907022	−	0.330129i
$472$	5.28732	−	4.43658i	0.243368	−	0.204210i
$473$	−0.162734	−	0.922909i	−0.00748251	−	0.0424354i
$474$	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
$478$	−7.32399	−	2.66572i	−0.334992	−	0.121927i
$479$	−4.85601	+	27.5398i	−0.221877	+	1.25833i	0.646690	+	0.762753i	$0.276153\pi$
$479$	−4.85601	+	27.5398i	−0.221877	+	1.25833i	−0.868566	+	0.495573i	$0.834958\pi$
$480$	−0.141838	−	0.0516247i	−0.00647397	−	0.00235633i
$481$	−20.6748	−	17.3482i	−0.942691	−	0.791012i
$482$	−10.8816	+	18.8474i	−0.495642	+	0.858477i
$483$	2.48065	−	10.6636i	0.112873	−	0.485211i
$484$	10.2322	−	3.72421i	0.465099	−	0.169282i
$485$	0.108126	−	0.613212i	0.00490974	−	0.0278445i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−17.2611			−0.782174			−0.391087	−	0.920354i	$-0.627901\pi$
$487$	−17.2611			−0.782174			−0.391087	+	0.920354i	$0.627901\pi$
$488$	−1.34741	−	1.13061i	−0.0609944	−	0.0511803i
$489$	−18.5020	+	15.5251i	−0.836691	+	0.702067i
$490$	1.05042	+	0.113951i	0.0474531	+	0.00514778i
$491$	2.01903	+	11.4505i	0.0911176	+	0.516754i	0.995868	+	0.0908117i	$0.0289461\pi$
$491$	2.01903	+	11.4505i	0.0911176	+	0.516754i	−0.904750	+	0.425942i	$0.859943\pi$
$492$	1.32478	−	1.11162i	0.0597257	−	0.0501158i
$493$	16.8611	+	29.2042i	0.759385	+	1.31529i
$494$	7.61611	+	6.25077i	0.342665	+	0.281236i
$495$	−0.0251601	+	0.0435785i	−0.00113086	+	0.00195871i
$496$	3.97058	+	1.44517i	0.178284	+	0.0648902i
$497$	−13.6128	+	20.8854i	−0.610616	+	0.936838i
$498$	6.09498	+	5.11430i	0.273123	+	0.229177i
$499$	−2.58237	−	14.6453i	−0.115603	−	0.655615i	−0.986450	−	0.164061i	$-0.947540\pi$
$499$	−2.58237	−	14.6453i	−0.115603	−	0.655615i	0.870848	−	0.491553i	$-0.163571\pi$
$500$	1.41514	−	0.515070i	0.0632872	−	0.0230346i
$501$	−16.9964			−0.759345
$502$	−9.47609			−0.422939
$503$	−12.4443	+	4.52934i	−0.554862	+	0.201953i	−0.604206	−	0.796829i	$-0.706509\pi$
$503$	−12.4443	+	4.52934i	−0.554862	+	0.201953i	0.0493432	+	0.998782i	$0.484287\pi$
$504$	−2.11565	+	1.58872i	−0.0942384	+	0.0707673i
$505$	−1.26318	−	2.18789i	−0.0562108	−	0.0973600i
$506$	0.689773	+	1.19472i	0.0306641	+	0.0531118i
$507$	7.41480	−	2.69877i	0.329303	−	0.119856i
$508$	15.7343	+	5.72681i	0.698096	+	0.254086i
$509$	9.76253	−	3.55327i	0.432717	−	0.157496i	−0.116473	−	0.993194i	$-0.537159\pi$
$509$	9.76253	−	3.55327i	0.432717	−	0.157496i	0.549189	+	0.835698i	$0.314937\pi$
$510$	−0.140262	−	0.795467i	−0.00621092	−	0.0352239i
$511$	3.94362	−	6.05050i	0.174455	−	0.267658i
$512$	1.00000			0.0441942
$513$	−3.36939	−	2.76536i	−0.148762	−	0.122094i
$514$	−1.64115	−	2.84256i	−0.0723880	−	0.125380i
$515$	−0.162273	−	0.920294i	−0.00715059	−	0.0405530i
$516$	2.64154	+	0.961441i	0.116287	+	0.0423251i
$517$	1.62193	+	1.36096i	0.0713324	+	0.0598550i
$518$	14.2947	+	28.1711i	0.628074	+	1.23777i
$519$	3.00210	−	17.0257i	0.131777	−	0.747347i
$520$	0.170592	+	0.295473i	0.00748093	+	0.0129574i
$521$	14.6990	−	25.4594i	0.643974	−	1.11540i	−0.340563	−	0.940222i	$-0.610618\pi$
$521$	14.6990	−	25.4594i	0.643974	−	1.11540i	0.984537	−	0.175174i	$-0.0560489\pi$
$522$	4.82730	+	4.05058i	0.211285	+	0.177289i
$523$	3.66192	−	20.7678i	0.160125	−	0.908112i	−0.793825	−	0.608146i	$-0.791913\pi$
$523$	3.66192	−	20.7678i	0.160125	−	0.908112i	0.953950	−	0.299966i	$-0.0969754\pi$
$524$	−4.89827	−	8.48405i	−0.213982	−	0.370627i
$525$	2.98368	−	12.8260i	0.130219	−	0.559773i
$526$	−4.71826	+	26.7586i	−0.205726	+	1.16673i
$527$	3.92648	+	22.2682i	0.171040	+	0.970017i
$528$	0.0578904	−	0.328313i	0.00251936	−	0.0142880i
$529$	−4.50145	+	3.77717i	−0.195715	+	0.164225i
$530$	0.730708	−	0.613137i	0.0317399	−	0.0266330i
$531$	6.90210			0.299526
$532$	−5.33007	−	10.2269i	−0.231088	−	0.443394i
$533$	−3.90906			−0.169320
$534$	−3.32127	+	2.78688i	−0.143726	+	0.120600i
$535$	−0.763629	+	0.640761i	−0.0330146	+	0.0277025i
$536$	0.654090	−	3.70953i	0.0282524	−	0.160227i
$537$	2.16817	+	12.2963i	0.0935633	+	0.530624i
$538$	4.54850	−	25.7958i	0.196100	−	1.11214i
$539$	0.155012	+	2.32849i	0.00667686	+	0.100295i
$540$	−0.0754702	−	0.130718i	−0.00324772	−	0.00562522i
$541$	5.81970	−	33.0052i	0.250208	−	1.41900i	−0.557870	−	0.829928i	$-0.688381\pi$
$541$	5.81970	−	33.0052i	0.250208	−	1.41900i	0.808079	−	0.589074i	$-0.200508\pi$
$542$	−22.4088	−	18.8032i	−0.962541	−	0.807668i
$543$	−6.17770	+	10.7001i	−0.265110	+	0.459185i
$544$	2.67569	+	4.63442i	0.114719	+	0.198699i
$545$	−0.292159	+	1.65692i	−0.0125147	+	0.0709745i
$546$	5.97168	+	0.322961i	0.255564	+	0.0138215i
$547$	−15.4758	−	12.9857i	−0.661697	−	0.555230i	0.248898	−	0.968530i	$-0.419932\pi$
$547$	−15.4758	−	12.9857i	−0.661697	−	0.555230i	−0.910595	+	0.413300i	$0.864376\pi$
$548$	13.0622	+	4.75426i	0.557990	+	0.203092i
$549$	−0.305433	−	1.73220i	−0.0130356	−	0.0739283i
$550$	0.829646	+	1.43699i	0.0353762	+	0.0612734i
$551$	−20.8484	+	17.8839i	−0.888172	+	0.761880i
$552$	−4.13809			−0.176129
$553$	25.6507	+	1.38724i	1.09078	+	0.0589916i
$554$	−4.04743	−	22.9541i	−0.171959	−	0.975226i
$555$	−1.69355	+	0.616401i	−0.0718871	+	0.0261648i
$556$	2.70088	+	0.983040i	0.114543	+	0.0416902i
$557$	30.3403	−	11.0430i	1.28556	−	0.467906i	0.393293	−	0.919413i	$-0.371336\pi$
$557$	30.3403	−	11.0430i	1.28556	−	0.467906i	0.892267	+	0.451507i	$0.149114\pi$
$558$	2.11270	+	3.65930i	0.0894377	+	0.154911i
$559$	−3.17704	−	5.50280i	−0.134375	−	0.232744i
$560$	−0.0480068	−	0.396455i	−0.00202866	−	0.0167533i
$561$	1.67644	−	0.610173i	0.0707792	−	0.0257615i
$562$	−12.6978			−0.535623
$563$	24.6046			1.03696			0.518480	−	0.855090i	$-0.326498\pi$
$563$	24.6046			1.03696			0.518480	+	0.855090i	$0.326498\pi$
$564$	−5.96798	+	2.17217i	−0.251297	+	0.0914647i
$565$	0.232455	+	1.31832i	0.00977947	+	0.0554622i
$566$	2.91182	+	2.44331i	0.122393	+	0.102700i
$567$	−2.64189	−	0.142879i	−0.110949	−	0.00600035i
$568$	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	$0.0181164\pi$
$570$	0.615771	−	0.231738i	0.0257918	−	0.00970644i
$571$	−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	$-0.509717\pi$
$572$	−0.577261	+	0.484380i	−0.0241365	+	0.0202529i
$573$	0.337976	+	1.91676i	0.0141191	+	0.0800736i
$574$	4.20878	+	1.79482i	0.175671	+	0.0749144i
$575$	15.7776	−	13.2390i	0.657970	−	0.552103i
$576$	0.766044	+	0.642788i	0.0319185	+	0.0267828i
$577$	−16.3379			−0.680155			−0.340078	−	0.940397i	$-0.610453\pi$
$577$	−16.3379			−0.680155			−0.340078	+	0.940397i	$0.610453\pi$
$578$	−5.81859	+	10.0781i	−0.242021	+	0.419193i
$579$	3.25205	−	18.4433i	0.135150	−	0.766476i
$580$	−0.893802	+	0.325317i	−0.0371131	+	0.0135081i
$581$	−4.76963	+	20.5033i	−0.197877	+	0.850620i
$582$	−2.06264	+	3.57260i	−0.0854992	+	0.148089i
$583$	1.61389	+	1.35422i	0.0668406	+	0.0560860i
$584$	−2.56513	−	0.933629i	−0.106146	−	0.0386339i
$585$	−0.0592458	+	0.336000i	−0.00244951	+	0.0138919i
$586$	−20.4107	−	7.42889i	−0.843158	−	0.306885i
$587$	23.1952	+	8.44238i	0.957370	+	0.348454i	0.773002	−	0.634403i	$-0.218754\pi$
$587$	23.1952	+	8.44238i	0.957370	+	0.348454i	0.184368	+	0.982857i	$0.440976\pi$
$588$	−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
$591$	0.812885	+	4.61010i	0.0334376	+	0.189634i
$592$	9.14661	−	7.67491i	0.375923	−	0.315437i
$593$	8.75002	−	3.18475i	0.359320	−	0.130782i	−0.156051	−	0.987749i	$-0.549876\pi$
$593$	8.75002	−	3.18475i	0.359320	−	0.130782i	0.515371	+	0.856967i	$0.327654\pi$
$594$	0.255382	−	0.214291i	0.0104784	−	0.00879246i
$595$	1.70889	−	1.28327i	0.0700576	−	0.0526090i
$596$	−4.38800	+	7.60024i	−0.179739	+	0.311318i
$597$	−0.242369			−0.00991951
$598$	7.16532	+	6.01242i	0.293012	+	0.245866i
$599$	−12.5694	−	10.5470i	−0.513573	−	0.430939i	0.348811	−	0.937193i	$-0.386585\pi$
$599$	−12.5694	−	10.5470i	−0.513573	−	0.430939i	−0.862384	+	0.506254i	$0.831030\pi$
$600$	−4.97722			−0.203194
$601$	−7.67026	+	13.2853i	−0.312876	+	0.541918i	−0.978984	−	0.203938i	$-0.934626\pi$
$601$	−7.67026	+	13.2853i	−0.312876	+	0.541918i	0.666108	+	0.745856i	$0.267959\pi$
$602$	0.894063	+	7.38345i	0.0364393	+	0.300927i
$603$	2.88550	−	2.42122i	0.117507	−	0.0985999i
$604$	9.71207	−	3.53490i	0.395178	−	0.143833i
$605$	−1.25905	+	1.05647i	−0.0511875	+	0.0429514i
$606$	2.90643	+	16.4832i	0.118066	+	0.669584i
$607$	−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
$611$	13.4899	+	4.90993i	0.545744	+	0.198635i
$612$	−0.929256	+	5.27007i	−0.0375629	+	0.213030i
$613$	0.936239	+	0.340763i	0.0378143	+	0.0137633i	0.360858	−	0.932621i	$-0.382484\pi$
$613$	0.936239	+	0.340763i	0.0378143	+	0.0137633i	−0.323044	+	0.946384i	$0.604706\pi$
$614$	−22.0108	−	18.4692i	−0.888283	−	0.745358i
$615$	−0.130517	+	0.226061i	−0.00526294	+	0.00911567i
$616$	0.843923	−	0.256473i	0.0340026	−	0.0103336i
$617$	−17.5648	+	6.39306i	−0.707132	+	0.257375i	−0.670453	−	0.741952i	$-0.733900\pi$
$617$	−17.5648	+	6.39306i	−0.707132	+	0.257375i	−0.0366789	+	0.999327i	$0.511678\pi$
$618$	−1.07508	+	6.09707i	−0.0432460	+	0.245260i
$619$	10.3767	−	17.9730i	0.417075	−	0.722395i	−0.578569	−	0.815633i	$-0.696389\pi$
$619$	10.3767	−	17.9730i	0.417075	−	0.722395i	0.995644	+	0.0932387i	$0.0297220\pi$
$620$	−0.637784			−0.0256140
$621$	−3.16996	−	2.65991i	−0.127206	−	0.106739i
$622$	0.661543	−	0.555100i	0.0265254	−	0.0222575i
$623$	−10.5516	−	4.49968i	−0.422740	−	0.180276i
$624$	−0.392511	−	2.22604i	−0.0157130	−	0.0891130i
$625$	18.8897	−	15.8504i	0.755589	−	0.634014i
$626$	−10.0955	−	17.4859i	−0.403496	−	0.698876i
$627$	0.740225	+	1.25049i	0.0295617	+	0.0499400i
$628$	10.4740	−	18.1415i	0.417958	−	0.723925i
$629$	60.0422	+	21.8536i	2.39404	+	0.871360i
$630$	0.218061	−	0.334560i	0.00868775	−	0.0133292i
$631$	32.4828	+	27.2563i	1.29312	+	1.08506i	0.991290	+	0.131694i	$0.0420417\pi$
$631$	32.4828	+	27.2563i	1.29312	+	1.08506i	0.301829	+	0.953362i	$0.402403\pi$
$632$	−1.68599	−	9.56172i	−0.0670651	−	0.380345i
$633$	17.2307	−	6.27146i	0.684859	−	0.249268i
$634$	33.3566			1.32476
$635$	−2.52736			−0.100295
$636$	−5.93841	+	2.16141i	−0.235473	+	0.0857053i
$637$	6.38736	+	14.4761i	0.253076	+	0.573566i
$638$	−1.05040	−	1.81935i	−0.0415859	−	0.0720289i
$639$	4.71134	+	8.16027i	0.186378	+	0.322815i
$640$	−0.141838	+	0.0516247i	−0.00560662	+	0.00204064i
$641$	−37.0443	−	13.4830i	−1.46316	−	0.532547i	−0.516928	−	0.856029i	$-0.672924\pi$
$641$	−37.0443	−	13.4830i	−1.46316	−	0.532547i	−0.946234	+	0.323482i	$0.895147\pi$
$642$	6.20596	−	2.25878i	0.244930	−	0.0891471i
$643$	2.82191	+	16.0038i	0.111285	+	0.631129i	0.988523	+	0.151073i	$0.0482727\pi$
$643$	2.82191	+	16.0038i	0.111285	+	0.631129i	−0.877238	+	0.480056i	$0.840616\pi$
$644$	−4.95415	−	9.76334i	−0.195221	−	0.384729i
$645$	−0.424303			−0.0167069
$646$	−22.0048	−	7.73910i	−0.865769	−	0.304491i
$647$	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	$0.539527\pi$
$648$	0.173648	+	0.984808i	0.00682154	+	0.0386869i
$649$	−2.16224	−	0.786990i	−0.0848752	−	0.0308921i
$650$	8.61832	+	7.23163i	0.338038	+	0.283648i
$651$	−6.10436	+	9.36562i	−0.239249	+	0.367068i
$652$	−4.19407	+	23.7858i	−0.164253	+	0.931522i
$653$	3.91714	+	6.78468i	0.153289	+	0.265505i	0.932435	−	0.361338i	$-0.117680\pi$
$653$	3.91714	+	6.78468i	0.153289	+	0.265505i	−0.779145	+	0.626843i	$0.784347\pi$
$654$	5.57332	−	9.65327i	0.217934	−	0.377473i
$655$	1.13274	+	0.950486i	0.0442600	+	0.0371385i
$656$	0.300303	−	1.70311i	0.0117249	−	0.0664951i
$657$	−1.36487	−	2.36403i	−0.0532488	−	0.0922297i
$658$	−12.2699	−	11.4802i	−0.478330	−	0.447546i
$659$	−8.13415	+	46.1311i	−0.316862	+	1.79701i	0.244724	+	0.969593i	$0.421303\pi$
$659$	−8.13415	+	46.1311i	−0.316862	+	1.79701i	−0.561585	+	0.827419i	$0.689808\pi$
$660$	0.00873800	+	0.0495557i	0.000340126	+	0.00192895i
$661$	0.171098	−	0.970347i	0.00665496	−	0.0377421i	−0.981299	−	0.192487i	$-0.938345\pi$
$661$	0.171098	−	0.970347i	0.00665496	−	0.0377421i	0.987954	+	0.154745i	$0.0494557\pi$
$662$	−5.61095	+	4.70815i	−0.218076	+	0.182987i
$663$	9.26619	−	7.77525i	0.359869	−	0.301966i
$664$	7.95644			0.308770
$665$	1.28397	+	1.17540i	0.0497901	+	0.0455801i
$666$	11.9400			0.462667
$667$	−19.9758	+	16.7617i	−0.773465	+	0.649015i
$668$	−13.0200	+	10.9251i	−0.503760	+	0.422705i
$669$	−1.44986	+	8.22258i	−0.0560549	+	0.317903i
$670$	0.0987286	+	0.559918i	0.00381422	+	0.0216315i
$671$	−0.101824	+	0.577475i	−0.00393089	+	0.0222932i
$672$	−0.599468	+	2.57694i	−0.0231250	+	0.0994078i
$673$	9.75973	+	16.9043i	0.376210	+	0.651615i	0.990507	−	0.137460i	$-0.0438938\pi$
$673$	9.75973	+	16.9043i	0.376210	+	0.651615i	−0.614297	+	0.789075i	$0.710560\pi$
$674$	1.31818	−	7.47580i	0.0507746	−	0.287957i
$675$	−3.81277	−	3.19929i	−0.146754	−	0.123141i
$676$	3.94533	−	6.83352i	0.151744	−	0.262828i
$677$	17.1688	+	29.7372i	0.659851	+	1.14290i	0.980654	+	0.195749i	$0.0627139\pi$
$677$	17.1688	+	29.7372i	0.659851	+	1.14290i	−0.320803	+	0.947146i	$0.603953\pi$
$678$	1.54005	−	8.73405i	0.0591452	−	0.335429i
$679$	−10.8985	−	0.589415i	−0.418248	−	0.0226197i
$680$	−0.618763	−	0.519204i	−0.0237285	−	0.0199106i
$681$	−5.03029	−	1.83087i	−0.192761	−	0.0701592i
$682$	−0.244610	−	1.38725i	−0.00936661	−	0.0531207i
$683$	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	$0.746573\pi$
$684$	−4.35864	+	0.0474119i	−0.166657	+	0.00181284i
$685$	−2.09815			−0.0801661
$686$	−0.230472	−	18.5188i	−0.00879946	−	0.707052i
$687$	1.83456	+	10.4043i	0.0699927	+	0.396949i
$688$	2.64154	−	0.961441i	0.100708	−	0.0366546i
$689$	13.4231	+	4.88560i	0.511379	+	0.186127i
$690$	0.586936	−	0.213627i	0.0223443	−	0.00813265i
$691$	−16.8745	−	29.2275i	−0.641935	−	1.11186i	−0.985000	−	0.172553i	$-0.944798\pi$
$691$	−16.8745	−	29.2275i	−0.641935	−	1.11186i	0.343065	−	0.939312i	$-0.388535\pi$
$692$	−8.64419	−	14.9722i	−0.328603	−	0.569157i
$693$	0.811340	+	0.345993i	0.0308203	+	0.0131432i
$694$	6.41569	−	2.33512i	0.243536	−	0.0886399i
$695$	−0.433835			−0.0164563
$696$	6.30159			0.238861
$697$	8.69643	−	3.16524i	0.329401	−	0.119892i
$698$	2.54989	+	14.4612i	0.0965149	+	0.547363i
$699$	−10.7023	−	8.98030i	−0.404798	−	0.339666i
$700$	−5.95877	−	11.7432i	−0.225220	−	0.443850i
$701$	13.3889	+	4.87318i	0.505693	+	0.184057i	0.582253	−	0.813008i	$-0.302171\pi$
$701$	13.3889	+	4.87318i	0.505693	+	0.184057i	−0.0765595	+	0.997065i	$0.524394\pi$
$702$	1.13019	−	1.95755i	0.0426563	−	0.0738829i
$703$	−8.47956	+	51.3500i	−0.319813	+	1.93670i
$704$	−0.166689	−	0.288713i	−0.00628232	−	0.0108813i
$705$	0.734347	−	0.616190i	0.0276571	−	0.0232071i
$706$	−3.29001	−	18.6586i	−0.123821	−	0.702224i
$707$	−35.4106	+	26.5912i	−1.33175	+	1.00007i
$708$	5.28732	−	4.43658i	0.198709	−	0.166737i
$709$	−14.9844	−	12.5734i	−0.562752	−	0.472205i	0.316480	−	0.948599i	$-0.397499\pi$
$709$	−14.9844	−	12.5734i	−0.562752	−	0.472205i	−0.879232	+	0.476394i	$0.841943\pi$
$710$	−1.42226			−0.0533765
$711$	4.85461	−	8.40844i	0.182062	−	0.315341i
$712$	−0.752871	+	4.26975i	−0.0282150	+	0.160015i
$713$	−16.4306	+	5.98025i	−0.615331	+	0.223962i
$714$	−13.5466	+	4.11690i	−0.506970	+	0.154071i
$715$	0.0568714	−	0.0985041i	0.00212687	−	0.00368384i
$716$	9.56481	+	8.02583i	0.357454	+	0.299939i
$717$	−7.32399	−	2.66572i	−0.273520	−	0.0995530i
$718$	−5.18165	+	29.3866i	−0.193378	+	1.09670i
$719$	20.6714	+	7.52379i	0.770915	+	0.280590i	0.697379	−	0.716703i	$-0.254350\pi$
$719$	20.6714	+	7.52379i	0.770915	+	0.280590i	0.0735356	+	0.997293i	$0.476572\pi$
$720$	−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
$724$	2.14549	+	12.1677i	0.0797366	+	0.452208i
$725$	−24.0265	+	20.1606i	−0.892322	+	0.748747i
$726$	10.2322	−	3.72421i	0.379752	−	0.138218i
$727$	−5.52758	+	4.63819i	−0.205007	+	0.172021i	−0.739510	−	0.673145i	$-0.764943\pi$
$727$	−5.52758	+	4.63819i	−0.205007	+	0.172021i	0.534504	+	0.845166i	$0.320498\pi$
$728$	4.78217	−	3.59112i	0.177239	−	0.133096i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.412029			0.0152499
$731$	11.5237	+	9.66949i	0.426218	+	0.357639i
$732$	−1.34741	−	1.13061i	−0.0498017	−	0.0417886i
$733$	−22.3456			−0.825355			−0.412678	−	0.910877i	$-0.635406\pi$
$733$	−22.3456			−0.825355			−0.412678	+	0.910877i	$0.635406\pi$
$734$	−8.75742	+	15.1683i	−0.323242	+	0.559872i
$735$	1.05042	+	0.113951i	0.0387453	+	0.00420315i
$736$	−3.16996	+	2.65991i	−0.116846	+	0.0980456i
$737$	−1.18002	+	0.429492i	−0.0434666	+	0.0158206i
$738$	1.32478	−	1.11162i	0.0487659	−	0.0409194i
$739$	−4.18079	−	23.7104i	−0.153793	−	0.872202i	−0.959881	−	0.280407i	$-0.909531\pi$
$739$	−4.18079	−	23.7104i	−0.153793	−	0.872202i	0.806089	−	0.591795i	$-0.201580\pi$
$740$	−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	0.612588	−	0.790403i	$-0.290129\pi$
$743$	15.6406	+	5.69270i	0.573796	+	0.208845i	−0.0387915	+	0.999247i	$0.512351\pi$
$744$	3.97058	+	1.44517i	0.145568	+	0.0529826i
$745$	0.230024	−	1.30453i	0.00842741	−	0.0477942i
$746$	−5.92871	−	2.15787i	−0.217065	−	0.0790053i
$747$	6.09498	+	5.11430i	0.223004	+	0.187122i
$748$	0.892013	−	1.54501i	0.0326152	−	0.0564913i
$749$	12.7592	+	11.9380i	0.466210	+	0.436205i
$750$	1.41514	−	0.515070i	0.0516738	−	0.0188077i
$751$	0.0810146	−	0.459456i	0.00295626	−	0.0167658i	−0.983294	−	0.182025i	$-0.941735\pi$
$751$	0.0810146	−	0.459456i	0.00295626	−	0.0167658i	0.986250	+	0.165259i	$0.0528460\pi$
$752$	−3.17550	+	5.50012i	−0.115798	+	0.200569i
$753$	−9.47609			−0.345328
$754$	−10.9115	−	9.15587i	−0.397375	−	0.333437i
$755$	−1.19505	+	1.00276i	−0.0434922	+	0.0364943i
$756$	−2.11565	+	1.58872i	−0.0769453	+	0.0577813i
$757$	−0.675242	−	3.82949i	−0.0245421	−	0.139185i	0.970075	−	0.242807i	$-0.0780681\pi$
$757$	−0.675242	−	3.82949i	−0.0245421	−	0.139185i	−0.994617	+	0.103621i	$0.966957\pi$
$758$	−8.45875	+	7.09774i	−0.307236	+	0.257801i
$759$	0.689773	+	1.19472i	0.0250372	+	0.0433656i
$760$	0.322750	−	0.573332i	0.0117074	−	0.0207969i
$761$	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
$763$	29.4482	+	1.59262i	1.06610	+	0.0576567i
$764$	1.49097	+	1.25107i	0.0539414	+	0.0452622i
$765$	−0.140262	−	0.795467i	−0.00507119	−	0.0287602i
$766$	−6.61343	+	2.40709i	−0.238953	+	0.0869718i
$767$	−15.6014			−0.563334
$768$	1.00000			0.0360844
$769$	40.1478	−	14.6126i	1.44777	−	0.526944i	0.505800	−	0.862651i	$-0.331197\pi$
$769$	40.1478	−	14.6126i	1.44777	−	0.526944i	0.941967	+	0.335707i	$0.108975\pi$
$770$	−0.106460	+	0.0799447i	−0.00383654	+	0.00288101i
$771$	−1.64115	−	2.84256i	−0.0591046	−	0.102372i
$772$	−9.36390	−	16.2187i	−0.337014	−	0.583725i
$773$	8.71856	−	3.17330i	0.313585	−	0.114136i	−0.180433	−	0.983587i	$-0.557750\pi$
$773$	8.71856	−	3.17330i	0.313585	−	0.114136i	0.494018	+	0.869452i	$0.335528\pi$
$774$	2.64154	+	0.961441i	0.0949481	+	0.0345583i
$775$	−19.7624	+	7.19294i	−0.709887	+	0.258378i
$776$	0.716347	+	4.06261i	0.0257154	+	0.145839i
$777$	14.2947	+	28.1711i	0.512820	+	1.01063i
$778$	7.00289			0.251066
$779$	3.83988	+	6.48688i	0.137578	+	0.232417i
$780$	0.170592	+	0.295473i	0.00610816	+	0.0105796i
$781$	−0.545482	−	3.09358i	−0.0195189	−	0.110697i
$782$	−20.8090	−	7.57385i	−0.744127	−	0.270840i
$783$	4.82730	+	4.05058i	0.172514	+	0.144756i
$784$	−6.79769	+	1.67076i	−0.242775	+	0.0596702i
$785$	−0.549058	+	3.11386i	−0.0195967	+	0.111139i
$786$	−4.89827	−	8.48405i	−0.174715	−	0.302616i
$787$	−7.63979	+	13.2325i	−0.272329	+	0.471688i	−0.969458	−	0.245258i	$-0.921127\pi$
$787$	−7.63979	+	13.2325i	−0.272329	+	0.471688i	0.697129	+	0.716946i	$0.254461\pi$
$788$	3.58602	+	3.00903i	0.127747	+	0.107192i
$789$	−4.71826	+	26.7586i	−0.167974	+	0.952630i
$790$	0.732757	+	1.26917i	0.0260703	+	0.0451551i
$791$	22.4507	−	6.82291i	0.798256	−	0.242595i
$792$	0.0578904	−	0.328313i	0.00205705	−	0.0116661i
$793$	0.690395	+	3.91543i	0.0245167	+	0.139041i
$794$	−1.28283	+	7.27531i	−0.0455261	+	0.258191i
$795$	0.730708	−	0.613137i	0.0259156	−	0.0217457i
$796$	−0.185666	+	0.155792i	−0.00658074	+	0.00552190i
$797$	−8.10222			−0.286995			−0.143498	−	0.989651i	$-0.545835\pi$
$797$	−8.10222			−0.286995			−0.143498	+	0.989651i	$0.545835\pi$
$798$	−5.33007	−	10.2269i	−0.188682	−	0.362030i
$799$	−33.9865			−1.20236
$800$	−3.81277	+	3.19929i	−0.134802	+	0.113112i
$801$	−3.32127	+	2.78688i	−0.117351	+	0.0984695i
$802$	6.51758	−	36.9630i	0.230144	−	1.30521i
$803$	0.158026	+	0.896212i	0.00557663	+	0.0316266i
$804$	0.654090	−	3.70953i	0.0230680	−	0.130825i
$805$	1.20671	+	1.12905i	0.0425311	+	0.0397938i
$806$	−4.77551	−	8.27143i	−0.168210	−	0.291349i
$807$	4.54850	−	25.7958i	0.160115	−	0.908056i
$808$	12.8217	+	10.7586i	0.451064	+	0.378488i
$809$	−9.41569	+	16.3085i	−0.331038	+	0.573375i	−0.982716	−	0.185121i	$-0.940732\pi$
$809$	−9.41569	+	16.3085i	−0.331038	+	0.573375i	0.651678	+	0.758496i	$0.274066\pi$
$810$	−0.0754702	−	0.130718i	−0.00265175	−	0.00459297i
$811$	−4.14412	+	23.5025i	−0.145520	+	0.825284i	0.821429	+	0.570311i	$0.193177\pi$
$811$	−4.14412	+	23.5025i	−0.145520	+	0.825284i	−0.966948	+	0.254972i	$0.917934\pi$
$812$	7.54432	+	14.8679i	0.264754	+	0.521760i
$813$	−22.4088	−	18.8032i	−0.785912	−	0.659458i
$814$	−3.74049	−	1.36143i	−0.131104	−	0.0477179i
$815$	−0.633055	−	3.59023i	−0.0221749	−	0.125760i
$816$	2.67569	+	4.63442i	0.0936677	+	0.162237i
$817$	−6.01079	+	10.6776i	−0.210291	+	0.373560i
$818$	1.02927			0.0359874
$819$	5.97168	+	0.322961i	0.208668	+	0.0112852i
$820$	0.0453279	+	0.257067i	0.00158292	+	0.00897718i
$821$	−34.0015	+	12.3755i	−1.18666	+	0.431909i	−0.858550	−	0.512730i	$-0.828634\pi$
$821$	−34.0015	+	12.3755i	−1.18666	+	0.431909i	−0.328111	+	0.944639i	$0.606412\pi$
$822$	13.0622	+	4.75426i	0.455597	+	0.165824i
$823$	6.52505	−	2.37493i	0.227449	−	0.0827847i	−0.225782	−	0.974178i	$-0.572494\pi$
$823$	6.52505	−	2.37493i	0.227449	−	0.0827847i	0.453231	+	0.891393i	$0.350271\pi$
$824$	3.09556	+	5.36167i	0.107839	+	0.186783i
$825$	0.829646	+	1.43699i	0.0288846	+	0.0500295i
$826$	16.7976	+	7.16329i	0.584464	+	0.249243i
$827$	29.3361	−	10.6775i	1.02012	−	0.371292i	0.222807	−	0.974863i	$-0.428478\pi$
$827$	29.3361	−	10.6775i	1.02012	−	0.371292i	0.797309	+	0.603571i	$0.206256\pi$
$828$	−4.13809			−0.143808
$829$	−32.7327			−1.13685			−0.568426	−	0.822734i	$-0.692447\pi$
$829$	−32.7327			−1.13685			−0.568426	+	0.822734i	$0.692447\pi$
$830$	−1.12852	+	0.410748i	−0.0391716	+	0.0142573i
$831$	−4.04743	−	22.9541i	−0.140404	−	0.796269i
$832$	−1.73155	−	1.45295i	−0.0600308	−	0.0503718i
$833$	−25.9315	−	27.0329i	−0.898473	−	0.936635i
$834$	2.70088	+	0.983040i	0.0935239	+	0.0340399i
$835$	1.28272	−	2.22174i	0.0443905	−	0.0768866i
$836$	1.37085	+	0.482127i	0.0474118	+	0.0166747i
$837$	2.11270	+	3.65930i	0.0730256	+	0.126484i
$838$	−27.6711	+	23.2188i	−0.955881	+	0.802079i
$839$	2.29116	+	12.9938i	0.0790998	+	0.448597i	0.998475	+	0.0552143i	$0.0175842\pi$
$839$	2.29116	+	12.9938i	0.0790998	+	0.448597i	−0.919375	+	0.393383i	$0.871305\pi$
$840$	−0.0480068	−	0.396455i	−0.00165639	−	0.0136790i
$841$	8.20437	−	6.88429i	0.282909	−	0.237389i
$842$	−25.6716	−	21.5410i	−0.884702	−	0.742353i
$843$	−12.6978			−0.437334
$844$	9.16826	−	15.8799i	0.315585	−	0.546609i
$845$	−0.206819	+	1.17293i	−0.00711478	+	0.0403499i
$846$	−5.96798	+	2.17217i	−0.205183	+	0.0746807i
$847$	21.0369	+	19.6830i	0.722836	+	0.676315i
$848$	−3.15976	+	5.47287i	−0.108507	+	0.187939i
$849$	2.91182	+	2.44331i	0.0999336	+	0.0838542i
$850$	−25.0287	−	9.10968i	−0.858476	−	0.312460i
$851$	−8.57978	+	48.6583i	−0.294111	+	1.66799i
$852$	8.85441	+	3.22274i	0.303347	+	0.110409i
$853$	14.8689	+	5.41182i	0.509100	+	0.185297i	0.583782	−	0.811910i	$-0.301572\pi$
$853$	14.8689	+	5.41182i	0.509100	+	0.185297i	−0.0746825	+	0.997207i	$0.523794\pi$
$854$	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
$857$	4.11897	+	23.3598i	0.140701	+	0.797957i	0.970719	+	0.240219i	$0.0772193\pi$
$857$	4.11897	+	23.3598i	0.140701	+	0.797957i	−0.830017	+	0.557738i	$0.811670\pi$
$858$	−0.577261	+	0.484380i	−0.0197074	+	0.0165364i
$859$	11.5407	−	4.20047i	0.393764	−	0.143318i	−0.137547	−	0.990495i	$-0.543922\pi$
$859$	11.5407	−	4.20047i	0.393764	−	0.143318i	0.531311	+	0.847177i	$0.321700\pi$
$860$	−0.325035	+	0.272737i	−0.0110836	+	0.00930025i
$861$	4.20878	+	1.79482i	0.143435	+	0.0611674i
$862$	−1.58812	+	2.75071i	−0.0540917	+	0.0936897i
$863$	−26.7005			−0.908896			−0.454448	−	0.890773i	$-0.650163\pi$
$863$	−26.7005			−0.908896			−0.454448	+	0.890773i	$0.650163\pi$
$864$	0.766044	+	0.642788i	0.0260614	+	0.0218681i
$865$	1.99900	+	1.67736i	0.0679682	+	0.0570321i
$866$	−12.8854			−0.437863
$867$	−5.81859	+	10.0781i	−0.197610	+	0.342270i
$868$	1.34389	+	11.0983i	0.0456147	+	0.376701i
$869$	−2.47956	+	2.08060i	−0.0841134	+	0.0705795i
$870$	−0.893802	+	0.325317i	−0.0303027	+	0.0110293i
$871$	−6.52234	+	5.47289i	−0.221001	+	0.185442i
$872$	−1.93559	−	10.9773i	−0.0655475	−	0.371738i
$873$	−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
$877$	23.5127	+	8.55792i	0.793967	+	0.288980i	0.706984	−	0.707230i	$-0.250055\pi$
$877$	23.5127	+	8.55792i	0.793967	+	0.288980i	0.0869828	+	0.996210i	$0.472277\pi$
$878$	4.99292	−	28.3162i	0.168503	−	0.955627i
$879$	−20.4107	−	7.42889i	−0.688436	−	0.250570i
$880$	0.0385475	+	0.0323452i	0.00129943	+	0.00109035i
$881$	22.3494	−	38.7103i	0.752971	−	1.30418i	−0.193406	−	0.981119i	$-0.561954\pi$
$881$	22.3494	−	38.7103i	0.752971	−	1.30418i	0.946377	−	0.323065i	$-0.104713\pi$
$882$	−6.28128	−	3.08959i	−0.211502	−	0.104032i
$883$	18.6424	−	6.78528i	0.627367	−	0.228343i	−0.00871805	−	0.999962i	$-0.502775\pi$
$883$	18.6424	−	6.78528i	0.627367	−	0.228343i	0.636085	+	0.771619i	$0.280553\pi$
$884$	2.10047	−	11.9124i	0.0706466	−	0.400657i
$885$	−0.520903	+	0.902230i	−0.0175100	+	0.0303281i
$886$	−20.8147			−0.699284
$887$	44.0258	+	36.9421i	1.47824	+	1.24039i	0.908036	+	0.418893i	$0.137582\pi$
$887$	44.0258	+	36.9421i	1.47824	+	1.24039i	0.570208	+	0.821501i	$0.306863\pi$
$888$	9.14661	−	7.67491i	0.306940	−	0.257553i
$889$	5.32548	+	43.9794i	0.178611	+	1.47502i
$890$	−0.113639	−	0.644477i	−0.00380918	−	0.0216029i
$891$	0.255382	−	0.214291i	0.00855562	−	0.00717902i
$892$	4.17471	+	7.23081i	0.139780	+	0.242106i
$893$	−5.10341	−	27.2089i	−0.170779	−	0.910510i
$894$	−4.38800	+	7.60024i	−0.146757	+	0.254190i
$895$	−1.77098	−	0.644584i	−0.0591973	−	0.0215461i
$896$	1.19721	+	2.35938i	0.0399959	+	0.0788215i
$897$	7.16532	+	6.01242i	0.239243	+	0.200749i
$898$	1.83227	+	10.3913i	0.0611435	+	0.346762i
$899$	25.0210	−	9.10688i	0.834496	−	0.303732i
$900$	−4.97722			−0.165907
$901$	−33.8181			−1.12665
$902$	−0.541767	+	0.197187i	−0.0180389	+	0.00656561i
$903$	0.894063	+	7.38345i	0.0297526	+	0.245706i
$904$	−4.43439	−	7.68059i	−0.147486	−	0.255453i
$905$	−0.932464	−	1.61507i	−0.0309961	−	0.0536869i
$906$	9.71207	−	3.53490i	0.322662	−	0.117439i
$907$	−3.00494	−	1.09371i	−0.0997772	−	0.0363159i	0.291649	−	0.956525i	$-0.405796\pi$
$907$	−3.00494	−	1.09371i	−0.0997772	−	0.0363159i	−0.391426	+	0.920209i	$0.628018\pi$
$908$	−5.03029	+	1.83087i	−0.166936	+	0.0607597i
$909$	2.90643	+	16.4832i	0.0964003	+	0.546713i
$910$	−0.492901	+	0.756234i	−0.0163395	+	0.0250689i
$911$	−42.1891			−1.39779			−0.698894	−	0.715226i	$-0.746324\pi$
$911$	−42.1891			−1.39779			−0.698894	+	0.715226i	$0.746324\pi$
$912$	−3.30844	+	2.83800i	−0.109553	+	0.0939756i
$913$	−1.32625	−	2.29713i	−0.0438924	−	0.0760239i
$914$	2.53972	+	14.4035i	0.0840064	+	0.476424i
$915$	0.249481	+	0.0908035i	0.00824758	+	0.00300187i
$916$	8.09310	+	6.79092i	0.267404	+	0.224378i
$917$	14.1529	−	21.7141i	0.467369	−	0.717062i
$918$	−0.929256	+	5.27007i	−0.0306700	+	0.173938i
$919$	−0.498255	−	0.863002i	−0.0164359	−	0.0284678i	0.857690	−	0.514166i	$-0.171899\pi$
$919$	−0.498255	−	0.863002i	−0.0164359	−	0.0284678i	−0.874126	+	0.485699i	$0.838565\pi$
$920$	0.312302	−	0.540923i	0.0102963	−	0.0178337i
$921$	−22.0108	−	18.4692i	−0.725280	−	0.608582i
$922$	−5.88101	+	33.3529i	−0.193681	+	1.09842i
$923$	−10.6494	−	18.4453i	−0.350530	−	0.607136i
$924$	0.843923	−	0.256473i	0.0277630	−	0.00843735i
$925$	−10.3196	+	58.5253i	−0.339306	+	1.92430i
$926$	−1.70708	−	9.68135i	−0.0560982	−	0.318149i
$927$	−1.07508	+	6.09707i	−0.0353102	+	0.200254i
$928$	4.82730	−	4.05058i	0.158464	−	0.132967i
$929$	14.2368	−	11.9461i	0.467094	−	0.391938i	−0.378640	−	0.925544i	$-0.623608\pi$
$929$	14.2368	−	11.9461i	0.467094	−	0.391938i	0.845733	+	0.533606i	$0.179164\pi$
$930$	−0.637784			−0.0209138
$931$	17.7481	−	24.8195i	0.581670	−	0.813425i
$932$	−13.9709			−0.457631
$933$	0.661543	−	0.555100i	0.0216579	−	0.0181732i
$934$	25.5168	−	21.4111i	0.834934	−	0.700593i
$935$	−0.0467603	+	0.265191i	−0.00152922	+	0.00867266i
$936$	−0.392511	−	2.22604i	−0.0128296	−	0.0727605i
$937$	−3.46493	+	19.6506i	−0.113194	+	0.641957i	0.874434	+	0.485144i	$0.161233\pi$
$937$	−3.46493	+	19.6506i	−0.113194	+	0.641957i	−0.987628	+	0.156813i	$0.949878\pi$
$938$	9.53529	−	2.89783i	0.311338	−	0.0946175i
$939$	−10.0955	−	17.4859i	−0.329453	−	0.570630i
$940$	0.166463	−	0.944058i	0.00542942	−	0.0307918i
$941$	−4.69656	−	3.94088i	−0.153103	−	0.128469i	0.563018	−	0.826444i	$-0.309640\pi$
$941$	−4.69656	−	3.94088i	−0.153103	−	0.128469i	−0.716122	+	0.697975i	$0.754084\pi$
$942$	10.4740	−	18.1415i	0.341261	−	0.591082i
$943$	3.57816	+	6.19756i	0.116521	+	0.201820i
$944$	1.19854	−	6.79724i	0.0390091	−	0.221231i
$945$	0.218061	−	0.334560i	0.00709352	−	0.0108832i
$946$	−0.717896	−	0.602386i	−0.0233408	−	0.0195853i
$947$	−2.66571	−	0.970240i	−0.0866240	−	0.0315286i	0.298345	−	0.954458i	$-0.403566\pi$
$947$	−2.66571	−	0.970240i	−0.0866240	−	0.0315286i	−0.384969	+	0.922930i	$0.625788\pi$
$948$	−1.68599	−	9.56172i	−0.0547584	−	0.310550i
$949$	3.08514	+	5.34362i	0.100148	+	0.173461i
$950$	3.53471	−	21.4053i	0.114681	−	0.694480i
$951$	33.3566			1.08166
$952$	−7.73103	+	11.8613i	−0.250564	+	0.384428i
$953$	−4.02186	−	22.8091i	−0.130281	−	0.738860i	−0.978030	−	0.208463i	$-0.933154\pi$
$953$	−4.02186	−	22.8091i	−0.130281	−	0.738860i	0.847749	−	0.530397i	$-0.177957\pi$
$954$	−5.93841	+	2.16141i	−0.192263	+	0.0699781i
$955$	−0.276062	−	0.100478i	−0.00893315	−	0.00325140i
$956$	−7.32399	+	2.66572i	−0.236875	+	0.0862154i
$957$	−1.05040	−	1.81935i	−0.0339547	−	0.0588113i
$958$	13.9823	+	24.2181i	0.451749	+	0.782451i
$959$	4.42108	+	36.5106i	0.142764	+	1.17899i
$960$	−0.141838	+	0.0516247i	−0.00457779	+	0.00166618i
$961$	−13.1460			−0.424064
$962$	−26.9891			−0.870163
$963$	6.20596	−	2.25878i	0.199984	−	0.0727883i
$964$	3.77913	+	21.4325i	0.121718	+	0.690295i
$965$	2.16544	+	1.81702i	0.0697080	+	0.0584919i
$966$	−4.95415	−	9.76334i	−0.159397	−	0.314130i
$967$	9.42628	+	3.43088i	0.303129	+	0.110330i	0.489106	−	0.872224i	$-0.337323\pi$
$967$	9.42628	+	3.43088i	0.303129	+	0.110330i	−0.185978	+	0.982554i	$0.559545\pi$
$968$	5.44443	−	9.43003i	0.174991	−	0.303093i
$969$	−22.0048	−	7.73910i	−0.706897	−	0.248616i
$970$	−0.311336	−	0.539249i	−0.00999639	−	0.0173142i
$971$	6.37731	−	5.35120i	0.204658	−	0.171728i	−0.534698	−	0.845043i	$-0.679575\pi$
$971$	6.37731	−	5.35120i	0.204658	−	0.171728i	0.739356	+	0.673315i	$0.235130\pi$
$972$	0.173648	+	0.984808i	0.00556977	+	0.0315877i
$973$	0.914148	+	7.54932i	0.0293063	+	0.242020i
$974$	−13.2228	+	11.0952i	−0.423684	+	0.355513i
$975$	8.61832	+	7.23163i	0.276007	+	0.231597i
$976$	−1.75892			−0.0563016
$977$	5.40203	−	9.35659i	0.172826	−	0.299344i	−0.766581	−	0.642148i	$-0.778043\pi$
$977$	5.40203	−	9.35659i	0.172826	−	0.299344i	0.939407	+	0.342804i	$0.111377\pi$
$978$	−4.19407	+	23.7858i	−0.134112	+	0.760585i
$979$	1.35823	−	0.494354i	0.0434091	−	0.0157996i
$980$	0.877915	−	0.587905i	0.0280440	−	0.0187799i
$981$	5.57332	−	9.65327i	0.177942	−	0.308205i
$982$	8.90691	+	7.47378i	0.284231	+	0.238498i
$983$	−25.0065	−	9.10161i	−0.797582	−	0.290296i	−0.0890981	−	0.996023i	$-0.528398\pi$
$983$	−25.0065	−	9.10161i	−0.797582	−	0.290296i	−0.708484	+	0.705727i	$0.750621\pi$
$984$	0.300303	−	1.70311i	0.00957332	−	0.0542930i
$985$	−0.663973	−	0.241666i	−0.0211559	−	0.00770013i
$986$	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
$990$	0.00873800	+	0.0495557i	0.000277712	+	0.00157498i
$991$	13.9314	−	11.6898i	0.442544	−	0.371338i	−0.394116	−	0.919061i	$-0.628949\pi$
$991$	13.9314	−	11.6898i	0.442544	−	0.371338i	0.836660	+	0.547722i	$0.184505\pi$
$992$	3.97058	−	1.44517i	0.126066	−	0.0458843i
$993$	−5.61095	+	4.70815i	−0.178058	+	0.149408i
$994$	2.99689	+	24.7493i	0.0950556	+	0.784999i
$995$	0.0182916	−	0.0316821i	0.000579884	−	0.00100439i
$996$	7.95644			0.252109
$997$	17.4109	+	14.6095i	0.551410	+	0.462688i	0.875418	−	0.483367i	$-0.160586\pi$
$997$	17.4109	+	14.6095i	0.551410	+	0.462688i	−0.324008	+	0.946054i	$0.605031\pi$
$998$	−11.3920	−	9.55906i	−0.360609	−	0.302587i
$999$	11.9400			0.377766

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.d.289.4	✓	36	1.1	even	1	trivial
798.2.bp.d.613.4	yes	36	133.81	even	9	inner
798.2.bq.d.403.3	yes	36	7.4	even	3
798.2.bq.d.499.3	yes	36	19.5	even	9

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)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.766044 - 0.642788i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0262105 + 0.148647i) q^{5} +(0.173648 - 0.984808i) q^{6} +(2.53143 - 0.769318i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.766044 - 0.642788i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0262105 + 0.148647i) q^{5} +(0.173648 - 0.984808i) q^{6} +(2.53143 - 0.769318i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.115627 + 0.0970226i) q^{10} +(-0.166689 + 0.288713i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.392511 + 2.22604i) q^{13} +(1.44468 - 2.21650i) q^{14} +(0.115627 + 0.0970226i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.929256 - 5.27007i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.07957 - 1.53530i) q^{19} +0.150940 q^{20} +(1.44468 - 2.21650i) q^{21} +(0.0578904 + 0.328313i) q^{22} +(3.88853 - 1.41531i) q^{23} +(-0.939693 - 0.342020i) q^{24} +(4.67705 - 1.70231i) q^{25} +(1.13019 + 1.95755i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.318051 - 2.62656i) q^{28} +(-5.92156 + 2.15527i) q^{29} +0.150940 q^{30} -4.22540 q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.0578904 + 0.328313i) q^{33} +(-4.09939 - 3.43980i) q^{34} +(0.180707 + 0.356126i) q^{35} +(-0.939693 - 0.342020i) q^{36} +(-5.97002 + 10.3404i) q^{37} +(2.13826 - 3.79840i) q^{38} +(1.13019 + 1.95755i) q^{39} +(0.115627 - 0.0970226i) q^{40} +(0.300303 + 1.70311i) q^{41} +(-0.318051 - 2.62656i) q^{42} +(-2.15340 + 1.80692i) q^{43} +(0.255382 + 0.214291i) q^{44} +0.150940 q^{45} +(2.06904 - 3.58369i) q^{46} +(1.10284 - 6.25451i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(5.81630 - 3.89495i) q^{49} +(2.48861 - 4.31040i) q^{50} +(-4.09939 - 3.43980i) q^{51} +(2.12407 + 0.773096i) q^{52} +(1.09737 - 6.22352i) q^{53} +(-0.939693 - 0.342020i) 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} +(1.19854 + 6.79724i) q^{59} +(0.115627 - 0.0970226i) q^{60} +(1.65284 - 0.601585i) q^{61} +(-3.23685 + 2.71604i) q^{62} +(-0.318051 - 2.62656i) q^{63} +(-0.500000 + 0.866025i) q^{64} -0.341183 q^{65} +(0.255382 + 0.214291i) q^{66} +(2.88550 + 2.42122i) q^{67} -5.35137 q^{68} +(2.06904 - 3.58369i) q^{69} +(0.367343 + 0.156652i) q^{70} +(-7.21818 + 6.05678i) q^{71} +(-0.939693 + 0.342020i) q^{72} +(2.09111 - 1.75465i) q^{73} +(2.07337 + 11.7586i) 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} +(9.12369 + 3.32075i) q^{79} +(0.0262105 - 0.148647i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(1.32478 + 1.11162i) q^{82} +(-3.97822 + 6.89048i) q^{83} +(-1.93196 - 1.80763i) q^{84} +(0.759026 - 0.276263i) q^{85} +(-0.488137 + 2.76836i) q^{86} +(-3.15080 + 5.45734i) q^{87} +0.333377 q^{88} +(-3.32127 - 2.78688i) q^{89} +(0.115627 - 0.0970226i) q^{90} +(0.718918 + 5.93704i) q^{91} +(-0.718571 - 4.07522i) q^{92} +(-3.23685 + 2.71604i) q^{93} +(-3.17550 - 5.50012i) q^{94} +(0.335145 + 0.566176i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-3.87650 - 1.41093i) q^{97} +(1.95192 - 6.72235i) q^{98} +(0.255382 + 0.214291i) 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

Modular forms

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