LMFDB - Embedded newform 144.3.w.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(5,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.w (of order $12$, degree $4$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	144.5
Dual form			144.3.w.a.29.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.762335 - 1.84901i) q^{2} +(-2.07303 + 2.16854i) q^{3} +(-2.83769 + 2.81913i) q^{4} +(-0.115759 - 0.432017i) q^{5} +(5.58999 + 2.17990i) q^{6} +(7.23679 - 4.17816i) q^{7} +(7.37588 + 3.09780i) q^{8} +(-0.405106 - 8.99088i) q^{9} +O(q^{10})$	\(q+(-0.762335 - 1.84901i) q^{2} +(-2.07303 + 2.16854i) q^{3} +(-2.83769 + 2.81913i) q^{4} +(-0.115759 - 0.432017i) q^{5} +(5.58999 + 2.17990i) q^{6} +(7.23679 - 4.17816i) q^{7} +(7.37588 + 3.09780i) q^{8} +(-0.405106 - 8.99088i) q^{9} +(-0.710557 + 0.543380i) q^{10} +(-20.2288 - 5.42030i) q^{11} +(-0.230778 - 11.9978i) q^{12} +(-1.29383 - 4.82865i) q^{13} +(-13.2423 - 10.1958i) q^{14} +(1.17682 + 0.644556i) q^{15} +(0.104984 - 15.9997i) q^{16} -25.9977i q^{17} +(-16.3154 + 7.60310i) q^{18} +(1.80229 - 1.80229i) q^{19} +(1.54640 + 0.899592i) q^{20} +(-5.94157 + 24.3547i) q^{21} +(5.39895 + 41.5354i) q^{22} +(-1.78994 + 3.10027i) q^{23} +(-22.0081 + 9.57304i) q^{24} +(21.4774 - 12.4000i) q^{25} +(-7.94191 + 6.07337i) q^{26} +(20.3368 + 17.7599i) q^{27} +(-8.75698 + 32.2578i) q^{28} +(13.2056 - 49.2839i) q^{29} +(0.294665 - 2.66731i) q^{30} +(-14.2968 + 24.7628i) q^{31} +(-29.6636 + 12.0030i) q^{32} +(53.6891 - 32.6305i) q^{33} +(-48.0700 + 19.8189i) q^{34} +(-2.64276 - 2.64276i) q^{35} +(26.4960 + 24.3713i) q^{36} +(-22.5902 - 22.5902i) q^{37} +(-4.70639 - 1.95850i) q^{38} +(13.1533 + 7.20421i) q^{39} +(0.484481 - 3.54510i) q^{40} +(-16.3853 + 28.3801i) q^{41} +(49.5616 - 7.58040i) q^{42} +(-4.06313 + 15.1638i) q^{43} +(72.6837 - 41.6466i) q^{44} +(-3.83732 + 1.21578i) q^{45} +(7.09697 + 0.946180i) q^{46} +(33.7785 - 19.5020i) q^{47} +(34.4782 + 33.3954i) q^{48} +(10.4141 - 18.0377i) q^{49} +(-39.3007 - 30.2590i) q^{50} +(56.3769 + 53.8939i) q^{51} +(17.2841 + 10.0547i) q^{52} +(-57.3208 + 57.3208i) q^{53} +(17.3347 - 51.1420i) q^{54} +9.36664i q^{55} +(66.3208 - 8.39948i) q^{56} +(0.172134 + 7.64451i) q^{57} +(-101.194 + 13.1536i) q^{58} +(-11.5988 - 43.2875i) q^{59} +(-5.15653 + 1.48855i) q^{60} +(70.8572 + 18.9861i) q^{61} +(56.6857 + 7.55743i) q^{62} +(-40.4970 - 63.3725i) q^{63} +(44.8072 + 45.6980i) q^{64} +(-1.93629 + 1.11792i) q^{65} +(-101.263 - 74.3964i) q^{66} +(12.2935 + 45.8800i) q^{67} +(73.2909 + 73.7734i) q^{68} +(-3.01245 - 10.3085i) q^{69} +(-2.87182 + 6.90115i) q^{70} -26.4797 q^{71} +(24.8640 - 67.5706i) q^{72} -38.6468i q^{73} +(-24.5483 + 58.9909i) q^{74} +(-17.6334 + 72.2800i) q^{75} +(-0.0334482 + 10.1952i) q^{76} +(-169.039 + 45.2938i) q^{77} +(3.29348 - 29.8126i) q^{78} +(-29.8313 - 51.6693i) q^{79} +(-6.92427 + 1.80674i) q^{80} +(-80.6718 + 7.28451i) q^{81} +(64.9662 + 8.66140i) q^{82} +(-12.5178 + 46.7170i) q^{83} +(-51.7988 - 85.8612i) q^{84} +(-11.2314 + 3.00945i) q^{85} +(31.1356 - 4.04713i) q^{86} +(79.4985 + 130.804i) q^{87} +(-132.414 - 102.644i) q^{88} +79.3499 q^{89} +(5.17332 + 6.16841i) q^{90} +(-29.5381 - 29.5381i) q^{91} +(-3.66077 - 13.8437i) q^{92} +(-24.0614 - 82.3372i) q^{93} +(-61.8100 - 47.5898i) q^{94} +(-0.987248 - 0.569988i) q^{95} +(35.4646 - 89.2091i) q^{96} +(-16.3804 - 28.3718i) q^{97} +(-41.2910 - 5.50499i) q^{98} +(-40.5384 + 184.071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.762335	−	1.84901i	−0.381167	−	0.924506i
$2$	−0.762335	−	1.84901i	−0.381167	−	0.924506i
$3$	−2.07303	+	2.16854i	−0.691009	+	0.722846i
$3$	−2.07303	+	2.16854i	−0.691009	+	0.722846i
$4$	−2.83769	+	2.81913i	−0.709423	+	0.704783i
$5$	−0.115759	−	0.432017i	−0.0231517	−	0.0864034i	0.953383	−	0.301762i	$-0.0975747\pi$
$5$	−0.115759	−	0.432017i	−0.0231517	−	0.0864034i	−0.976535	+	0.215358i	$0.930908\pi$
$6$	5.58999	+	2.17990i	0.931665	+	0.363317i
$7$	7.23679	−	4.17816i	1.03383	−	0.596880i	0.115748	−	0.993279i	$-0.463073\pi$
$7$	7.23679	−	4.17816i	1.03383	−	0.596880i	0.918079	+	0.396398i	$0.129740\pi$
$8$	7.37588	+	3.09780i	0.921985	+	0.387225i
$9$	−0.405106	−	8.99088i	−0.0450117	−	0.998986i
$10$	−0.710557	+	0.543380i	−0.0710557	+	0.0543380i
$11$	−20.2288	−	5.42030i	−1.83899	−	0.492755i	−0.840211	−	0.542259i	$-0.817569\pi$
$11$	−20.2288	−	5.42030i	−1.83899	−	0.492755i	−0.998774	+	0.0495046i	$0.984236\pi$
$12$	−0.230778	−	11.9978i	−0.0192315	−	0.999815i
$13$	−1.29383	−	4.82865i	−0.0995257	−	0.371435i	0.898141	−	0.439708i	$-0.144918\pi$
$13$	−1.29383	−	4.82865i	−0.0995257	−	0.371435i	−0.997667	+	0.0682726i	$0.978251\pi$
$14$	−13.2423	−	10.1958i	−0.945881	−	0.728268i
$15$	1.17682	+	0.644556i	0.0784543	+	0.0429704i
$16$	0.104984	−	15.9997i	0.00656149	−	0.999978i
$17$		−	25.9977i		−	1.52928i	−0.644460	−	0.764638i	$-0.722918\pi$
$17$		−	25.9977i		−	1.52928i	0.644460	−	0.764638i	$-0.277082\pi$
$18$	−16.3154	+	7.60310i	−0.906412	+	0.422395i
$19$	1.80229	−	1.80229i	0.0948571	−	0.0948571i	−0.658086	−	0.752943i	$-0.728634\pi$
$19$	1.80229	−	1.80229i	0.0948571	−	0.0948571i	0.752943	+	0.658086i	$0.228634\pi$
$20$	1.54640	+	0.899592i	0.0773200	+	0.0449796i
$21$	−5.94157	+	24.3547i	−0.282932	+	1.15975i
$22$	5.39895	+	41.5354i	0.245407	+	1.88797i
$23$	−1.78994	+	3.10027i	−0.0778236	+	0.134794i	−0.902311	−	0.431086i	$-0.858130\pi$
$23$	−1.78994	+	3.10027i	−0.0778236	+	0.134794i	0.824487	+	0.565881i	$0.191464\pi$
$24$	−22.0081	+	9.57304i	−0.917005	+	0.398877i
$25$	21.4774	−	12.4000i	0.859096	−	0.495999i
$26$	−7.94191	+	6.07337i	−0.305458	+	0.233591i
$27$	20.3368	+	17.7599i	0.753217	+	0.657773i
$28$	−8.75698	+	32.2578i	−0.312749	+	1.15206i
$29$	13.2056	−	49.2839i	0.455365	−	1.69945i	−0.231647	−	0.972800i	$-0.574411\pi$
$29$	13.2056	−	49.2839i	0.455365	−	1.69945i	0.687012	−	0.726646i	$-0.258922\pi$
$30$	0.294665	−	2.66731i	0.00982218	−	0.0889104i
$31$	−14.2968	+	24.7628i	−0.461188	+	0.798800i	−0.999020	−	0.0442511i	$-0.985910\pi$
$31$	−14.2968	+	24.7628i	−0.461188	+	0.798800i	0.537833	+	0.843052i	$0.319243\pi$
$32$	−29.6636	+	12.0030i	−0.926987	+	0.375093i
$33$	53.6891	−	32.6305i	1.62694	−	0.988804i
$34$	−48.0700	+	19.8189i	−1.41382	+	0.582910i
$35$	−2.64276	−	2.64276i	−0.0755073	−	0.0755073i
$36$	26.4960	+	24.3713i	0.736001	+	0.676980i
$37$	−22.5902	−	22.5902i	−0.610546	−	0.610546i	0.332542	−	0.943088i	$-0.392094\pi$
$37$	−22.5902	−	22.5902i	−0.610546	−	0.610546i	−0.943088	+	0.332542i	$0.892094\pi$
$38$	−4.70639	−	1.95850i	−0.123852	−	0.0515396i
$39$	13.1533	+	7.20421i	0.337263	+	0.184723i
$40$	0.484481	−	3.54510i	0.0121120	−	0.0886275i
$41$	−16.3853	+	28.3801i	−0.399640	+	0.692197i	−0.993681	−	0.112237i	$-0.964198\pi$
$41$	−16.3853	+	28.3801i	−0.399640	+	0.692197i	0.594041	+	0.804435i	$0.297532\pi$
$42$	49.5616	−	7.58040i	1.18004	−	0.180486i
$43$	−4.06313	+	15.1638i	−0.0944915	+	0.352647i	−0.996942	−	0.0781468i	$-0.975100\pi$
$43$	−4.06313	+	15.1638i	−0.0944915	+	0.352647i	0.902450	+	0.430794i	$0.141766\pi$
$44$	72.6837	−	41.6466i	1.65190	−	0.946514i
$45$	−3.83732	+	1.21578i	−0.0852737	+	0.0270174i
$46$	7.09697	+	0.946180i	0.154282	+	0.0205691i
$47$	33.7785	−	19.5020i	0.718691	−	0.414937i	−0.0955796	−	0.995422i	$-0.530470\pi$
$47$	33.7785	−	19.5020i	0.718691	−	0.414937i	0.814271	+	0.580485i	$0.197137\pi$
$48$	34.4782	+	33.3954i	0.718296	+	0.695738i
$49$	10.4141	−	18.0377i	0.212532	−	0.368117i
$50$	−39.3007	−	30.2590i	−0.786014	−	0.605181i
$51$	56.3769	+	53.8939i	1.10543	+	1.05674i
$52$	17.2841	+	10.0547i	0.332387	+	0.193360i
$53$	−57.3208	+	57.3208i	−1.08152	+	1.08152i	−0.0851571	+	0.996368i	$0.527139\pi$
$53$	−57.3208	+	57.3208i	−1.08152	+	1.08152i	−0.996368	+	0.0851571i	$0.972861\pi$
$54$	17.3347	−	51.1420i	0.321013	−	0.947075i
$55$			9.36664i			0.170303i
$56$	66.3208	−	8.39948i	1.18430	−	0.149991i
$57$	0.172134	+	7.64451i	0.00301989	+	0.134114i
$58$	−101.194	+	13.1536i	−1.74472	+	0.226786i
$59$	−11.5988	−	43.2875i	−0.196591	−	0.733686i	−0.991849	−	0.127416i	$-0.959332\pi$
$59$	−11.5988	−	43.2875i	−0.196591	−	0.733686i	0.795259	−	0.606270i	$-0.207335\pi$
$60$	−5.15653	+	1.48855i	−0.0859421	+	0.0248091i
$61$	70.8572	+	18.9861i	1.16159	+	0.311248i	0.787602	−	0.616184i	$-0.211322\pi$
$61$	70.8572	+	18.9861i	1.16159	+	0.311248i	0.373991	+	0.927432i	$0.377989\pi$
$62$	56.6857	+	7.55743i	0.914286	+	0.121894i
$63$	−40.4970	−	63.3725i	−0.642810	−	1.00591i
$64$	44.8072	+	45.6980i	0.700113	+	0.714032i
$65$	−1.93629	+	1.11792i	−0.0297890	+	0.0171987i
$66$	−101.263	−	74.3964i	−1.53429	−	1.12722i
$67$	12.2935	+	45.8800i	0.183485	+	0.684775i	0.994950	+	0.100374i	$0.0320040\pi$
$67$	12.2935	+	45.8800i	0.183485	+	0.684775i	−0.811465	+	0.584401i	$0.801329\pi$
$68$	73.2909	+	73.7734i	1.07781	+	1.08490i
$69$	−3.01245	−	10.3085i	−0.0436587	−	0.149399i
$70$	−2.87182	+	6.90115i	−0.0410261	+	0.0985879i
$71$	−26.4797			−0.372953			−0.186477	−	0.982459i	$-0.559707\pi$
$71$	−26.4797			−0.372953			−0.186477	+	0.982459i	$0.559707\pi$
$72$	24.8640	−	67.5706i	0.345333	−	0.938480i
$73$		−	38.6468i		−	0.529408i	−0.964330	−	0.264704i	$-0.914726\pi$
$73$		−	38.6468i		−	0.529408i	0.964330	−	0.264704i	$-0.0852742\pi$
$74$	−24.5483	+	58.9909i	−0.331733	+	0.797174i
$75$	−17.6334	+	72.2800i	−0.235113	+	0.963734i
$76$	−0.0334482	+	10.1952i	−0.000440109	+	0.134148i
$77$	−169.039	+	45.2938i	−2.19531	+	0.588231i
$78$	3.29348	−	29.8126i	0.0422241	−	0.382213i
$79$	−29.8313	−	51.6693i	−0.377611	−	0.654042i	0.613103	−	0.790003i	$-0.289921\pi$
$79$	−29.8313	−	51.6693i	−0.377611	−	0.654042i	−0.990714	+	0.135961i	$0.956588\pi$
$80$	−6.92427	+	1.80674i	−0.0865534	+	0.0225843i
$81$	−80.6718	+	7.28451i	−0.995948	+	0.0899322i
$82$	64.9662	+	8.66140i	0.792271	+	0.105627i
$83$	−12.5178	+	46.7170i	−0.150817	+	0.562855i	0.848611	+	0.529018i	$0.177439\pi$
$83$	−12.5178	+	46.7170i	−0.150817	+	0.562855i	−0.999427	+	0.0338373i	$0.989227\pi$
$84$	−51.7988	−	85.8612i	−0.616652	−	1.02216i
$85$	−11.2314	+	3.00945i	−0.132135	+	0.0354053i
$86$	31.1356	−	4.04713i	0.362041	−	0.0470596i
$87$	79.4985	+	130.804i	0.913776	+	1.50349i
$88$	−132.414	−	102.644i	−1.50471	−	1.16641i
$89$	79.3499			0.891572			0.445786	−	0.895140i	$-0.352924\pi$
$89$	79.3499			0.891572			0.445786	+	0.895140i	$0.352924\pi$
$90$	5.17332	+	6.16841i	0.0574813	+	0.0685379i
$91$	−29.5381	−	29.5381i	−0.324595	−	0.324595i
$92$	−3.66077	−	13.8437i	−0.0397910	−	0.150475i
$93$	−24.0614	−	82.3372i	−0.258724	−	0.885346i
$94$	−61.8100	−	47.5898i	−0.657553	−	0.506274i
$95$	−0.987248	−	0.569988i	−0.0103921	−	0.00599987i
$96$	35.4646	−	89.2091i	0.369423	−	0.929262i
$97$	−16.3804	−	28.3718i	−0.168871	−	0.292492i	0.769152	−	0.639065i	$-0.220679\pi$
$97$	−16.3804	−	28.3718i	−0.168871	−	0.292492i	−0.938023	+	0.346573i	$0.887345\pi$
$98$	−41.2910	−	5.50499i	−0.421337	−	0.0561733i
$99$	−40.5384	+	184.071i	−0.409479	+	1.85930i
$100$	−25.9890	+	95.7349i	−0.259890	+	0.957349i
$101$	−6.84865	−	1.83509i	−0.0678084	−	0.0181692i	0.224755	−	0.974415i	$-0.427842\pi$
$101$	−6.84865	−	1.83509i	−0.0678084	−	0.0181692i	−0.292564	+	0.956246i	$0.594508\pi$
$102$	56.6725	−	145.327i	0.555612	−	1.42477i
$103$	−129.386	−	74.7010i	−1.25617	−	0.725252i	−0.283845	−	0.958870i	$-0.591610\pi$
$103$	−129.386	−	74.7010i	−1.25617	−	0.725252i	−0.972328	+	0.233618i	$0.924943\pi$
$104$	5.41505	−	39.6236i	0.0520678	−	0.380996i
$105$	11.2094	−	0.252406i	0.106756	−	0.00240387i
$106$	149.685	+	62.2892i	1.41212	+	0.587634i
$107$	−35.2400	+	35.2400i	−0.329346	+	0.329346i	−0.852338	−	0.522992i	$-0.824816\pi$
$107$	−35.2400	+	35.2400i	−0.329346	+	0.329346i	0.522992	+	0.852338i	$0.324816\pi$
$108$	−107.777	+	6.93527i	−0.997936	+	0.0642155i
$109$	81.1059	−	81.1059i	0.744091	−	0.744091i	−0.229271	−	0.973363i	$-0.573634\pi$
$109$	81.1059	−	81.1059i	0.744091	−	0.744091i	0.973363	+	0.229271i	$0.0736343\pi$
$110$	17.3190	−	7.14052i	0.157446	−	0.0649138i
$111$	95.8178	−	2.15756i	0.863224	−	0.0194375i
$112$	−66.0894	−	116.225i	−0.590084	−	1.03772i
$113$	53.3280	+	30.7889i	0.471929	+	0.272468i	0.717047	−	0.697025i	$-0.245493\pi$
$113$	53.3280	+	30.7889i	0.471929	+	0.272468i	−0.245118	+	0.969493i	$0.578827\pi$
$114$	14.0036	−	6.14596i	0.122838	−	0.0539119i
$115$	1.54657	+	0.414402i	0.0134484	+	0.00360350i
$116$	101.465	+	177.081i	0.874695	+	1.52656i
$117$	−42.8897	+	13.5888i	−0.366579	+	0.116144i
$118$	−71.1969	+	54.4460i	−0.603363	+	0.461406i
$119$	−108.623	−	188.140i	−0.912795	−	1.58101i
$120$	6.68334	+	8.39971i	0.0556945	+	0.0699976i
$121$	275.037	+	158.793i	2.27303	+	1.31234i
$122$	−18.9113	−	145.490i	−0.155011	−	1.19254i
$123$	−27.5762	−	94.3648i	−0.224197	−	0.767193i
$124$	−29.2397	−	110.574i	−0.235804	−	0.891725i
$125$	−15.7496	−	15.7496i	−0.125997	−	0.125997i
$126$	−86.3042	+	123.191i	−0.684954	+	0.977703i
$127$	−67.0975			−0.528327			−0.264163	−	0.964478i	$-0.585096\pi$
$127$	−67.0975			−0.528327			−0.264163	+	0.964478i	$0.585096\pi$
$128$	50.3381	−	117.686i	0.393267	−	0.919424i
$129$	−24.4603	−	40.2461i	−0.189615	−	0.311985i
$130$	3.54314	+	2.72799i	0.0272549	+	0.0209846i
$131$	125.972	−	33.7541i	0.961619	−	0.257665i	0.256333	−	0.966588i	$-0.417486\pi$
$131$	125.972	−	33.7541i	0.961619	−	0.257665i	0.705285	+	0.708923i	$0.250819\pi$
$132$	−60.3632	+	243.952i	−0.457297	+	1.84812i
$133$	5.51252	−	20.5730i	0.0414475	−	0.154684i
$134$	75.4608	−	57.7067i	0.563141	−	0.430647i
$135$	5.31839	−	10.8417i	0.0393955	−	0.0803090i
$136$	80.5357	−	191.756i	0.592174	−	1.40997i
$137$	−22.0318	−	38.1602i	−0.160816	−	0.278542i	0.774345	−	0.632763i	$-0.218079\pi$
$137$	−22.0318	−	38.1602i	−0.160816	−	0.278542i	−0.935162	+	0.354221i	$0.884746\pi$
$138$	−16.7641	+	13.4286i	−0.121479	+	0.0973086i
$139$	206.983	−	55.4608i	1.48908	−	0.398999i	0.579656	−	0.814861i	$-0.303187\pi$
$139$	206.983	−	55.4608i	1.48908	−	0.398999i	0.909428	+	0.415862i	$0.136520\pi$
$140$	14.9496	+	0.0490464i	0.106783	+	0.000350331i
$141$	−27.7329	+	113.678i	−0.196687	+	0.806228i
$142$	20.1864	+	48.9613i	0.142158	+	0.344798i
$143$			104.691i			0.732105i
$144$	−143.893	+	5.53766i	−0.999260	+	0.0384559i
$145$	−22.8202			−0.157380
$146$	−71.4584	+	29.4618i	−0.489441	+	0.201793i
$147$	17.5268	+	59.9761i	0.119230	+	0.408000i
$148$	127.789	+	0.419247i	0.863438	+	0.00283275i
$149$	66.3271	+	247.536i	0.445148	+	1.66132i	0.715545	+	0.698566i	$0.246178\pi$
$149$	66.3271	+	247.536i	0.445148	+	1.66132i	−0.270397	+	0.962749i	$0.587155\pi$
$150$	147.089	−	22.4972i	0.980595	−	0.149981i
$151$	−110.925	+	64.0428i	−0.734605	+	0.424125i	−0.820105	−	0.572214i	$-0.806085\pi$
$151$	−110.925	+	64.0428i	−0.734605	+	0.424125i	0.0854993	+	0.996338i	$0.472751\pi$
$152$	18.8766	−	7.71032i	0.124188	−	0.0507258i
$153$	−233.742	+	10.5318i	−1.52773	+	0.0688354i
$154$	212.613	+	278.026i	1.38060	+	1.80536i
$155$	12.3529	+	3.30996i	0.0796963	+	0.0213546i
$156$	−57.6345	+	16.6375i	−0.369452	+	0.106651i
$157$	−24.9659	−	93.1741i	−0.159019	−	0.593466i	−0.998728	−	0.0504291i	$-0.983941\pi$
$157$	−24.9659	−	93.1741i	−0.159019	−	0.593466i	0.839709	−	0.543037i	$-0.182726\pi$
$158$	−72.7958	+	94.5477i	−0.460733	+	0.598403i
$159$	−5.47463	−	243.130i	−0.0344316	−	1.52912i
$160$	8.61930	+	11.4257i	0.0538706	+	0.0714108i
$161$			29.9147i			0.185805i
$162$	74.9681	+	143.610i	0.462766	+	0.886481i
$163$	84.5646	−	84.5646i	0.518801	−	0.518801i	−0.398407	−	0.917209i	$-0.630437\pi$
$163$	84.5646	−	84.5646i	0.518801	−	0.518801i	0.917209	+	0.398407i	$0.130437\pi$
$164$	−33.5109	−	126.726i	−0.204335	−	0.772720i
$165$	−20.3119	−	19.4173i	−0.123103	−	0.117681i
$166$	95.9230	−	12.4685i	0.577849	−	0.0751112i
$167$	19.4639	−	33.7125i	0.116551	−	0.201872i	−0.801848	−	0.597528i	$-0.796150\pi$
$167$	19.4639	−	33.7125i	0.116551	−	0.201872i	0.918399	+	0.395657i	$0.129483\pi$
$168$	−119.270	+	161.232i	−0.709943	+	0.959712i
$169$	124.716	−	72.0050i	0.737967	−	0.426065i
$170$	14.1266	+	18.4729i	0.0830978	+	0.108664i
$171$	−16.9342	−	15.4740i	−0.0990307	−	0.0904913i
$172$	−31.2189	−	54.4848i	−0.181505	−	0.316772i
$173$	−55.3918	+	206.725i	−0.320184	+	1.19494i	0.598882	+	0.800838i	$0.295612\pi$
$173$	−55.3918	+	206.725i	−0.320184	+	1.19494i	−0.919065	+	0.394105i	$0.871055\pi$
$174$	181.253	−	246.710i	1.04169	−	1.41787i
$175$	103.618	−	179.472i	0.592104	−	1.02555i
$176$	−88.8466	+	323.085i	−0.504810	+	1.83571i
$177$	117.915	+	64.5837i	0.666188	+	0.364879i
$178$	−60.4912	−	146.719i	−0.339838	−	0.824264i
$179$	29.8384	+	29.8384i	0.166695	+	0.166695i	0.785525	−	0.618830i	$-0.212393\pi$
$179$	29.8384	+	29.8384i	0.166695	+	0.166695i	−0.618830	+	0.785525i	$0.712393\pi$
$180$	7.46166	−	14.2679i	0.0414537	−	0.0792662i
$181$	−165.386	−	165.386i	−0.913733	−	0.913733i	0.0828310	−	0.996564i	$-0.473604\pi$
$181$	−165.386	−	165.386i	−0.913733	−	0.913733i	−0.996564	+	0.0828310i	$0.973604\pi$
$182$	−32.0984	+	77.1342i	−0.176365	+	0.423815i
$183$	−188.061	+	114.298i	−1.02766	+	0.624577i
$184$	−22.8064	+	17.3223i	−0.123948	+	0.0941431i
$185$	−7.14434	+	12.3744i	−0.0386180	+	0.0668884i
$186$	−133.900	+	107.258i	−0.719891	+	0.576657i
$187$	−140.915	+	525.903i	−0.753558	+	2.81232i
$188$	−40.8741	+	150.567i	−0.217416	+	0.800887i
$189$	221.377	+	43.5537i	1.17131	+	0.230443i
$190$	−0.301301	+	2.25995i	−0.00158579	+	0.0118945i
$191$	174.438	−	100.712i	0.913290	−	0.527288i	0.0318019	−	0.999494i	$-0.489875\pi$
$191$	174.438	−	100.712i	0.913290	−	0.527288i	0.881488	+	0.472206i	$0.156542\pi$
$192$	−191.985	+	2.43280i	−0.999920	+	0.0126708i
$193$	−39.0114	+	67.5697i	−0.202132	+	0.350102i	−0.949215	−	0.314628i	$-0.898120\pi$
$193$	−39.0114	+	67.5697i	−0.202132	+	0.350102i	0.747083	+	0.664730i	$0.231454\pi$
$194$	−39.9723	+	51.9164i	−0.206043	+	0.267610i
$195$	1.58974	−	6.51638i	0.00815250	−	0.0334173i
$196$	21.2988	+	80.5442i	0.108667	+	0.410940i
$197$	37.5571	−	37.5571i	0.190645	−	0.190645i	−0.605330	−	0.795975i	$-0.706959\pi$
$197$	37.5571	−	37.5571i	0.190645	−	0.190645i	0.795975	+	0.605330i	$0.206959\pi$
$198$	371.253	−	65.3675i	1.87502	−	0.330139i
$199$		−	31.6063i		−	0.158826i	−0.996842	−	0.0794129i	$-0.974695\pi$
$199$		−	31.6063i		−	0.158826i	0.996842	−	0.0794129i	$-0.0253045\pi$
$200$	196.827	−	24.9280i	0.984137	−	0.124640i
$201$	−124.977	−	68.4516i	−0.621777	−	0.340555i
$202$	1.82786	+	14.0622i	0.00904881	+	0.0696148i
$203$	−110.350	−	411.833i	−0.543597	−	2.02873i
$204$	−311.915	+	5.99970i	−1.52899	+	0.0294103i
$205$	14.1574	+	3.79347i	0.0690605	+	0.0185047i
$206$	−39.4876	+	296.183i	−0.191688	+	1.43778i
$207$	28.5993	+	14.8372i	0.138161	+	0.0716774i
$208$	−77.3926	+	20.1940i	−0.372080	+	0.0970864i
$209$	−46.2271	+	26.6892i	−0.221182	+	0.127700i
$210$	−9.01204	−	20.5339i	−0.0429145	−	0.0977807i
$211$	−78.8088	−	294.118i	−0.373501	−	1.39393i	−0.855522	−	0.517766i	$-0.826764\pi$
$211$	−78.8088	−	294.118i	−0.373501	−	1.39393i	0.482021	−	0.876160i	$-0.339903\pi$
$212$	1.06380	−	324.254i	0.00501795	−	1.52950i
$213$	54.8931	−	57.4222i	0.257714	−	0.269588i
$214$	92.0238	+	38.2945i	0.430018	+	0.178946i
$215$	7.02137			0.0326575
$216$	94.9856	+	193.994i	0.439748	+	0.898121i
$217$			238.938i			1.10110i
$218$	−211.796	−	88.1360i	−0.971540	−	0.404293i
$219$	83.8070	+	80.1159i	0.382680	+	0.365826i
$220$	−26.4058	−	26.5796i	−0.120026	−	0.120817i
$221$	−125.534	+	33.6367i	−0.568026	+	0.152202i
$222$	−77.0346	−	175.524i	−0.347003	−	0.790647i
$223$	−8.67499	−	15.0255i	−0.0389013	−	0.0673790i	0.845919	−	0.533311i	$-0.179052\pi$
$223$	−8.67499	−	15.0255i	−0.0389013	−	0.0673790i	−0.884821	+	0.465932i	$0.845719\pi$
$224$	−164.519	+	210.802i	−0.734459	+	0.941082i
$225$	−120.187	−	188.077i	−0.534166	−	0.835899i
$226$	16.2753	−	122.076i	0.0720147	−	0.540157i
$227$	94.8028	−	353.809i	0.417633	−	1.55863i	−0.361868	−	0.932229i	$-0.617861\pi$
$227$	94.8028	−	353.809i	0.417633	−	1.55863i	0.779502	−	0.626400i	$-0.215472\pi$
$228$	−22.0394	−	21.2075i	−0.0966638	−	0.0930154i
$229$	71.2003	−	19.0781i	0.310918	−	0.0833103i	−0.0999859	−	0.994989i	$-0.531880\pi$
$229$	71.2003	−	19.0781i	0.310918	−	0.0833103i	0.410904	+	0.911679i	$0.365213\pi$
$230$	−0.412770	−	3.17554i	−0.00179465	−	0.0138067i
$231$	252.201	−	460.462i	1.09178	−	1.99334i
$232$	250.075	−	322.604i	1.07791	−	1.39054i
$233$	353.927			1.51900			0.759500	−	0.650507i	$-0.225444\pi$
$233$	353.927			1.51900			0.759500	+	0.650507i	$0.225444\pi$
$234$	57.8222	+	68.9443i	0.247103	+	0.294634i
$235$	−12.3353	−	12.3353i	−0.0524908	−	0.0524908i
$236$	154.947	+	90.1378i	0.656555	+	0.381940i
$237$	173.888	+	42.4217i	0.733704	+	0.178995i
$238$	−265.066	+	344.270i	−1.11372	+	1.44651i
$239$	233.969	+	135.082i	0.978949	+	0.565197i	0.901953	−	0.431835i	$-0.142134\pi$
$239$	233.969	+	135.082i	0.978949	+	0.565197i	0.0769965	+	0.997031i	$0.475467\pi$
$240$	10.4362	−	18.7610i	0.0434843	−	0.0781707i
$241$	132.967	+	230.305i	0.551729	+	0.955622i	0.998150	+	0.0607993i	$0.0193650\pi$
$241$	132.967	+	230.305i	0.551729	+	0.955622i	−0.446421	+	0.894823i	$0.647302\pi$
$242$	83.9394	−	629.600i	0.346857	−	2.60165i
$243$	151.438	−	190.041i	0.623202	−	0.782061i
$244$	−254.595	+	145.879i	−1.04342	+	0.597865i
$245$	−8.99812	−	2.41104i	−0.0367270	−	0.00984098i
$246$	−153.459	+	122.926i	−0.623818	+	0.499700i
$247$	−11.0345	−	6.37076i	−0.0446740	−	0.0257925i
$248$	−182.162	+	138.359i	−0.734524	+	0.557899i
$249$	−75.3578	−	123.991i	−0.302642	−	0.497955i
$250$	−17.1148	+	41.1278i	−0.0684591	+	0.164511i
$251$	174.607	−	174.607i	0.695647	−	0.695647i	−0.267821	−	0.963469i	$-0.586304\pi$
$251$	174.607	−	174.607i	0.695647	−	0.695647i	0.963469	+	0.267821i	$0.0863037\pi$
$252$	293.574	+	65.6651i	1.16497	+	0.260576i
$253$	53.0128	−	53.0128i	0.209537	−	0.209537i
$254$	51.1508	+	124.064i	0.201381	+	0.488441i
$255$	16.7570	−	30.5945i	0.0657136	−	0.119978i
$256$	−255.978	−	3.35941i	−0.999914	−	0.0131227i
$257$	−73.8786	−	42.6539i	−0.287466	−	0.165968i	0.349333	−	0.936999i	$-0.386408\pi$
$257$	−73.8786	−	42.6539i	−0.287466	−	0.165968i	−0.636798	+	0.771030i	$0.719742\pi$
$258$	−55.7686	+	75.9084i	−0.216157	+	0.294219i
$259$	−257.866	−	69.0950i	−0.995622	−	0.266776i
$260$	2.34303	−	8.63095i	0.00901166	−	0.0331960i
$261$	−448.456	−	98.7647i	−1.71822	−	0.378409i
$262$	−158.445	−	207.192i	−0.604751	−	0.790809i
$263$	221.662	+	383.929i	0.842819	+	1.45981i	0.887501	+	0.460805i	$0.152439\pi$
$263$	221.662	+	383.929i	0.842819	+	1.45981i	−0.0446820	+	0.999001i	$0.514227\pi$
$264$	497.087	−	74.3608i	1.88291	−	0.281670i
$265$	31.3989	+	18.1282i	0.118487	+	0.0684082i
$266$	−42.2421	+	5.49080i	−0.158805	+	0.0206421i
$267$	−164.495	+	172.073i	−0.616085	+	0.644469i
$268$	−164.227	−	95.5362i	−0.612787	−	0.356478i
$269$	−131.331	−	131.331i	−0.488220	−	0.488220i	0.419524	−	0.907744i	$-0.362197\pi$
$269$	−131.331	−	131.331i	−0.488220	−	0.488220i	−0.907744	+	0.419524i	$0.862197\pi$
$270$	−24.1009	−	1.56876i	−0.0892624	−	0.00581021i
$271$	−417.793			−1.54167			−0.770835	−	0.637034i	$-0.780161\pi$
$271$	−417.793			−1.54167			−0.770835	+	0.637034i	$0.780161\pi$
$272$	−415.954	−	2.72934i	−1.52924	−	0.0100343i
$273$	125.288	−	2.82114i	0.458930	−	0.0103339i
$274$	−53.7631	+	69.8280i	−0.196216	+	0.254847i
$275$	−501.674	+	134.423i	−1.82427	+	0.488812i
$276$	37.6094	+	20.7599i	0.136266	+	0.0752169i
$277$	−77.3307	+	288.602i	−0.279172	+	1.04189i	0.673821	+	0.738895i	$0.264652\pi$
$277$	−77.3307	+	288.602i	−0.279172	+	1.04189i	−0.952993	+	0.302991i	$0.902015\pi$
$278$	−260.338	−	340.434i	−0.936467	−	1.22458i
$279$	228.431	+	118.509i	0.818750	+	0.424765i
$280$	−11.3059	−	27.6794i	−0.0403783	−	0.0988550i
$281$	52.8235	+	91.4929i	0.187984	+	0.325598i	0.944578	−	0.328287i	$-0.106471\pi$
$281$	52.8235	+	91.4929i	0.187984	+	0.325598i	−0.756594	+	0.653885i	$0.773138\pi$
$282$	231.334	−	35.3823i	0.820333	−	0.125469i
$283$	220.459	−	59.0719i	0.779009	−	0.208735i	0.152661	−	0.988279i	$-0.451216\pi$
$283$	220.459	−	59.0719i	0.779009	−	0.208735i	0.626348	+	0.779544i	$0.284549\pi$
$284$	75.1412	−	74.6498i	0.264582	−	0.262851i
$285$	3.28263	−	0.959282i	0.0115180	−	0.00336590i
$286$	193.575	−	79.8096i	0.676836	−	0.279055i
$287$			273.841i			0.954150i
$288$	119.934	+	261.839i	0.416438	+	0.909164i
$289$	−386.880			−1.33868
$290$	17.3966	+	42.1947i	0.0599883	+	0.145499i
$291$	95.4823	+	23.2939i	0.328118	+	0.0800477i
$292$	108.950	+	109.668i	0.373118	+	0.375574i
$293$	65.6267	+	244.922i	0.223982	+	0.835912i	0.982810	+	0.184621i	$0.0591058\pi$
$293$	65.6267	+	244.922i	0.223982	+	0.835912i	−0.758828	+	0.651291i	$0.774228\pi$
$294$	97.5352	−	78.1291i	0.331752	−	0.265745i
$295$	−17.3583	+	10.0218i	−0.0588415	+	0.0339722i
$296$	−96.6427	−	236.603i	−0.326495	−	0.799333i
$297$	−315.127	−	469.493i	−1.06103	−	1.58078i
$298$	407.134	−	311.345i	1.36622	−	1.04478i
$299$	17.2860	+	4.63178i	0.0578128	+	0.0154909i
$300$	−153.729	−	254.819i	−0.512429	−	0.849398i
$301$	33.9529	+	126.714i	0.112800	+	0.420976i
$302$	202.978	+	156.280i	0.672113	+	0.517485i
$303$	18.1769	−	11.0474i	0.0599898	−	0.0364599i
$304$	−28.6467	−	29.0252i	−0.0942327	−	0.0954775i
$305$		−	32.8093i		−	0.107571i
$306$	197.663	+	424.163i	0.645958	+	1.38615i
$307$	−99.3313	+	99.3313i	−0.323555	+	0.323555i	−0.850129	−	0.526574i	$-0.823476\pi$
$307$	−99.3313	+	99.3313i	−0.323555	+	0.323555i	0.526574	+	0.850129i	$0.323476\pi$
$308$	351.991	−	605.072i	1.14283	−	1.96452i
$309$	430.212	−	125.721i	1.39227	−	0.406863i
$310$	−3.29692	−	25.3640i	−0.0106352	−	0.0818194i
$311$	198.297	−	343.460i	0.637610	−	1.10437i	−0.348346	−	0.937366i	$-0.613256\pi$
$311$	198.297	−	343.460i	0.637610	−	1.10437i	0.985956	−	0.167007i	$-0.0534102\pi$
$312$	74.6997	+	93.8836i	0.239422	+	0.300909i
$313$	−482.430	+	278.531i	−1.54131	+	0.889875i	−0.542552	+	0.840022i	$0.682542\pi$
$313$	−482.430	+	278.531i	−1.54131	+	0.889875i	−0.998757	+	0.0498529i	$0.984125\pi$
$314$	−153.248	+	117.192i	−0.488050	+	0.373223i
$315$	−22.6901	+	24.8313i	−0.0720321	+	0.0788295i
$316$	230.315	+	62.5232i	0.728844	+	0.197858i
$317$	−67.7601	+	252.884i	−0.213754	+	0.797742i	0.772847	+	0.634592i	$0.218832\pi$
$317$	−67.7601	+	252.884i	−0.213754	+	0.797742i	−0.986601	+	0.163150i	$0.947835\pi$
$318$	−445.377	+	195.469i	−1.40056	+	0.614683i
$319$	−534.268	+	925.379i	−1.67482	+	2.90087i
$320$	14.5555	−	24.6474i	0.0454859	−	0.0770232i
$321$	−3.36572	−	149.473i	−0.0104851	−	0.465647i
$322$	55.3126	−	22.8050i	0.171778	−	0.0708230i
$323$	−46.8553	−	46.8553i	−0.145063	−	0.145063i
$324$	208.386	−	248.096i	0.643165	−	0.765727i
$325$	−87.6634	−	87.6634i	−0.269734	−	0.269734i
$326$	−220.827	−	91.8944i	−0.677385	−	0.281885i
$327$	7.74631	+	344.016i	0.0236890	+	1.05204i
$328$	−208.772	+	158.570i	−0.636499	+	0.483445i
$329$	162.965	−	282.264i	0.495335	−	0.857945i
$330$	−20.4184	+	52.3595i	−0.0618739	+	0.158665i
$331$	70.2883	−	262.320i	0.212351	−	0.792506i	−0.774731	−	0.632291i	$-0.782115\pi$
$331$	70.2883	−	262.320i	0.212351	−	0.792506i	0.987082	−	0.160215i	$-0.0512187\pi$
$332$	−96.1797	−	167.858i	−0.289698	−	0.505595i
$333$	−193.954	+	212.257i	−0.582445	+	0.637409i
$334$	−77.1729	−	10.2888i	−0.231057	−	0.0308049i
$335$	18.3978	−	10.6220i	0.0549189	−	0.0317074i
$336$	389.043	+	97.6199i	1.15787	+	0.290536i
$337$	210.750	−	365.030i	0.625372	−	1.08318i	−0.363097	−	0.931751i	$-0.618281\pi$
$337$	210.750	−	365.030i	0.625372	−	1.08318i	0.988469	−	0.151425i	$-0.0483861\pi$
$338$	−228.214	−	175.710i	−0.675189	−	0.519853i
$339$	−177.317	+	51.8174i	−0.523060	+	0.152854i
$340$	23.3873	−	40.2028i	0.0687862	−	0.118244i
$341$	423.430	−	423.430i	1.24173	−	1.24173i
$342$	−15.7021	+	43.1080i	−0.0459125	+	0.126047i
$343$			235.413i			0.686335i
$344$	−76.9437	+	99.2598i	−0.223674	+	0.288546i
$345$	−4.10473	+	2.49473i	−0.0118978	+	0.00723109i
$346$	424.464	−	55.1736i	1.22678	−	0.159461i
$347$	−46.8058	−	174.682i	−0.134887	−	0.503406i	−0.999998	−	0.00182548i	$-0.999419\pi$
$347$	−46.8058	−	174.682i	−0.134887	−	0.503406i	0.865111	−	0.501580i	$-0.167248\pi$
$348$	−594.345	−	147.064i	−1.70789	−	0.422598i
$349$	57.7638	+	15.4778i	0.165512	+	0.0443489i	0.340624	−	0.940200i	$-0.389362\pi$
$349$	57.7638	+	15.4778i	0.165512	+	0.0443489i	−0.175111	+	0.984549i	$0.556029\pi$
$350$	−410.838	−	54.7736i	−1.17382	−	0.156496i
$351$	59.4437	−	121.178i	0.169355	−	0.345236i
$352$	665.120	−	82.0207i	1.88954	−	0.233013i
$353$	−7.41642	+	4.28187i	−0.0210097	+	0.0121299i	−0.510468	−	0.859897i	$-0.670528\pi$
$353$	−7.41642	+	4.28187i	−0.0210097	+	0.0121299i	0.489458	+	0.872027i	$0.337195\pi$
$354$	29.5251	−	267.261i	0.0834041	−	0.754975i
$355$	3.06525	+	11.4397i	0.00863451	+	0.0322244i
$356$	−225.171	+	223.698i	−0.632502	+	0.628365i
$357$	633.166	+	154.467i	1.77357	+	0.432681i
$358$	32.4247	−	77.9185i	0.0905719	−	0.217649i
$359$	−242.593			−0.675746			−0.337873	−	0.941192i	$-0.609707\pi$
$359$	−242.593			−0.675746			−0.337873	+	0.941192i	$0.609707\pi$
$360$	−32.0698	−	2.91977i	−0.0890829	−	0.00811048i
$361$			354.504i			0.982004i
$362$	−179.721	+	431.879i	−0.496466	+	1.19304i
$363$	−914.508	+	267.246i	−2.51931	+	0.736216i
$364$	167.092	+	0.548192i	0.459044	+	0.00150602i
$365$	−16.6961	+	4.47370i	−0.0457426	+	0.0122567i
$366$	354.703	+	260.594i	0.969135	+	0.712006i
$367$	110.239	+	190.940i	0.300379	+	0.520272i	0.976222	−	0.216774i	$-0.0695534\pi$
$367$	110.239	+	190.940i	0.300379	+	0.520272i	−0.675843	+	0.737046i	$0.736220\pi$
$368$	49.4153	+	28.9639i	0.134281	+	0.0787063i
$369$	261.800	+	135.821i	0.709484	+	0.368078i
$370$	28.3267	+	3.77656i	0.0765587	+	0.0102069i
$371$	−175.323	+	654.314i	−0.472569	+	1.76365i
$372$	300.398	+	165.815i	0.807522	+	0.445740i
$373$	202.620	−	54.2918i	0.543217	−	0.145554i	0.0232321	−	0.999730i	$-0.492604\pi$
$373$	202.620	−	54.2918i	0.543217	−	0.145554i	0.519985	+	0.854176i	$0.325938\pi$
$374$	1079.83	−	140.360i	2.88723	−	0.375294i
$375$	66.8032	−	1.50423i	0.178142	−	0.00401127i
$376$	309.559	−	39.2055i	0.823297	−	0.104270i
$377$	−255.061			−0.676554
$378$	−88.2321	−	442.531i	−0.233418	−	1.17072i
$379$	346.957	+	346.957i	0.915453	+	0.915453i	0.996694	−	0.0812412i	$-0.0258884\pi$
$379$	346.957	+	346.957i	0.915453	+	0.915453i	−0.0812412	+	0.996694i	$0.525888\pi$
$380$	4.40837	−	1.16573i	0.0116010	−	0.00306772i
$381$	139.095	−	145.503i	0.365079	−	0.381899i
$382$	−319.198	−	245.762i	−0.835598	−	0.643357i
$383$	−44.9048	−	25.9258i	−0.117245	−	0.0676914i	0.440231	−	0.897885i	$-0.354897\pi$
$383$	−44.9048	−	25.9258i	−0.117245	−	0.0676914i	−0.557476	+	0.830193i	$0.688230\pi$
$384$	150.855	+	353.127i	0.392851	+	0.919602i
$385$	39.1354	+	67.7844i	0.101650	+	0.176063i
$386$	154.677	+	20.6218i	0.400717	+	0.0534243i
$387$	137.982	+	30.3882i	0.356543	+	0.0785225i
$388$	126.466	+	34.3317i	0.325944	+	0.0884837i
$389$	−300.911	−	80.6288i	−0.773549	−	0.207272i	−0.149610	−	0.988745i	$-0.547802\pi$
$389$	−300.911	−	80.6288i	−0.773549	−	0.207272i	−0.623939	+	0.781473i	$0.714469\pi$
$390$	−13.2608	+	2.02822i	−0.0340020	+	0.00520057i
$391$	80.5999	+	46.5344i	0.206138	+	0.119014i
$392$	132.690	−	100.783i	0.338496	−	0.257100i
$393$	−187.947	+	343.148i	−0.478236	+	0.873151i
$394$	−98.0745	−	40.8124i	−0.248920	−	0.103585i
$395$	−18.8688	+	18.8688i	−0.0477691	+	0.0477691i
$396$	−403.884	−	636.619i	−1.01991	−	1.60762i
$397$	470.741	−	470.741i	1.18574	−	1.18574i	0.207512	−	0.978232i	$-0.433463\pi$
$397$	470.741	−	470.741i	1.18574	−	1.18574i	0.978232	−	0.207512i	$-0.0665367\pi$
$398$	−58.4405	+	24.0946i	−0.146835	+	0.0605392i
$399$	33.1857	+	54.6025i	0.0831722	+	0.136848i
$400$	−196.141	−	344.933i	−0.490352	−	0.862332i
$401$	529.827	+	305.896i	1.32126	+	0.762832i	0.983930	−	0.178553i	$-0.0571417\pi$
$401$	529.827	+	305.896i	1.32126	+	0.762832i	0.337333	+	0.941385i	$0.390475\pi$
$402$	−31.2933	+	283.267i	−0.0778441	+	0.704645i
$403$	138.069	+	36.9954i	0.342602	+	0.0918000i
$404$	24.6077	−	14.0998i	0.0609102	−	0.0349006i
$405$	12.4855	+	34.0083i	0.0308283	+	0.0839712i
$406$	−677.360	+	517.993i	−1.66837	+	1.27585i
$407$	334.528	+	579.419i	0.821936	+	1.42363i
$408$	248.877	+	572.160i	0.609992	+	1.40235i
$409$	−310.635	−	179.345i	−0.759499	−	0.438497i	0.0696165	−	0.997574i	$-0.477822\pi$
$409$	−310.635	−	179.345i	−0.759499	−	0.438497i	−0.829116	+	0.559077i	$0.811156\pi$
$410$	−3.77852	−	29.0691i	−0.00921590	−	0.0709003i
$411$	128.425	+	31.3304i	0.312468	+	0.0762298i
$412$	577.749	−	152.778i	1.40230	−	0.370819i
$413$	−264.801	−	264.801i	−0.641164	−	0.641164i
$414$	5.63197	−	64.1913i	0.0136038	−	0.155051i
$415$	21.6315			0.0521242
$416$	96.3380	+	127.705i	0.231582	+	0.306984i
$417$	−308.812	+	563.821i	−0.740556	+	1.35209i
$418$	84.5892	+	65.1283i	0.202366	+	0.155809i
$419$	224.900	−	60.2617i	0.536754	−	0.143823i	0.0197486	−	0.999805i	$-0.493713\pi$
$419$	224.900	−	60.2617i	0.536754	−	0.143823i	0.517005	+	0.855982i	$0.327047\pi$
$420$	−31.0973	+	32.3171i	−0.0740412	+	0.0769455i
$421$	169.109	−	631.122i	0.401683	−	1.49910i	−0.408409	−	0.912799i	$-0.633916\pi$
$421$	169.109	−	631.122i	0.401683	−	1.49910i	0.810092	−	0.586303i	$-0.199417\pi$
$422$	−483.750	+	369.935i	−1.14633	+	0.876623i
$423$	−189.024	−	295.798i	−0.446866	−	0.699286i
$424$	−600.360	+	245.223i	−1.41594	+	0.578356i
$425$	−322.371	−	558.363i	−0.758520	−	1.31379i
$426$	−148.021	−	57.7232i	−0.347468	−	0.135500i
$427$	592.106	−	158.654i	1.38666	−	0.371556i
$428$	0.654012	−	199.346i	0.00152806	−	0.465763i
$429$	−227.026	−	217.027i	−0.529199	−	0.505892i
$430$	−5.35263	−	12.9826i	−0.0124480	−	0.0301921i
$431$			480.071i			1.11385i	0.830562	+	0.556927i	$0.188020\pi$
$431$			480.071i			1.11385i	−0.830562	+	0.556927i	$0.811980\pi$
$432$	286.287	−	323.518i	0.662701	−	0.748884i
$433$	−317.055			−0.732228			−0.366114	−	0.930570i	$-0.619312\pi$
$433$	−317.055			−0.732228			−0.366114	+	0.930570i	$0.619312\pi$
$434$	441.799	−	182.151i	1.01797	−	0.419702i
$435$	47.3068	−	49.4863i	0.108751	−	0.113762i
$436$	−1.50523	+	458.802i	−0.00345236	+	1.05230i
$437$	2.36159	+	8.81356i	0.00540409	+	0.0201683i
$438$	84.2462	−	216.035i	0.192343	−	0.493231i
$439$	157.780	−	91.0945i	0.359409	−	0.207505i	−0.309413	−	0.950928i	$-0.600132\pi$
$439$	157.780	−	91.0945i	0.359409	−	0.207505i	0.668821	+	0.743423i	$0.266799\pi$
$440$	−29.0160	+	69.0872i	−0.0659455	+	0.157016i
$441$	−166.394	−	86.3246i	−0.377310	−	0.195747i
$442$	157.893	+	206.471i	0.357225	+	0.467129i
$443$	183.948	+	49.2888i	0.415233	+	0.111261i	0.460386	−	0.887719i	$-0.347711\pi$
$443$	183.948	+	49.2888i	0.415233	+	0.111261i	−0.0451531	+	0.998980i	$0.514378\pi$
$444$	−265.819	+	276.246i	−0.598691	+	0.622175i
$445$	−9.18543	−	34.2805i	−0.0206414	−	0.0770348i
$446$	−21.1691	+	27.4946i	−0.0474644	+	0.0616471i
$447$	−674.289	−	369.316i	−1.50848	−	0.826211i
$448$	515.194	+	143.495i	1.14999	+	0.320302i
$449$			22.5026i			0.0501172i	0.999686	+	0.0250586i	$0.00797724\pi$
$449$			22.5026i			0.0501172i	−0.999686	+	0.0250586i	$0.992023\pi$
$450$	−256.134	+	365.606i	−0.569187	+	0.812457i
$451$	485.283	−	485.283i	1.07602	−	1.07602i
$452$	−238.126	+	62.9692i	−0.526828	+	0.139312i
$453$	91.0723	−	373.308i	0.201043	−	0.824080i
$454$	−726.468	+	94.4293i	−1.60015	+	0.207994i
$455$	−9.34167	+	16.1802i	−0.0205311	+	0.0355610i
$456$	−22.4116	+	56.9183i	−0.0491481	+	0.124821i
$457$	−8.03399	+	4.63842i	−0.0175798	+	0.0101497i	−0.508764	−	0.860906i	$-0.669897\pi$
$457$	−8.03399	+	4.63842i	−0.0175798	+	0.0101497i	0.491184	+	0.871056i	$0.336564\pi$
$458$	−89.5540	−	117.106i	−0.195533	−	0.255691i
$459$	461.715	−	528.711i	1.00592	−	1.15188i
$460$	−5.55694	+	3.18404i	−0.0120803	+	0.00692183i
$461$	163.564	−	610.429i	0.354803	−	1.32414i	−0.525930	−	0.850528i	$-0.676283\pi$
$461$	163.564	−	610.429i	0.354803	−	1.32414i	0.880733	−	0.473614i	$-0.157051\pi$
$462$	−1043.66	−	115.296i	−2.25901	−	0.249559i
$463$	119.643	−	207.227i	0.258407	−	0.447574i	−0.707408	−	0.706805i	$-0.750136\pi$
$463$	119.643	−	207.227i	0.258407	−	0.447574i	0.965815	+	0.259231i	$0.0834691\pi$
$464$	−787.140	−	216.459i	−1.69642	−	0.466506i
$465$	−32.7857	+	19.9262i	−0.0705070	+	0.0428519i
$466$	−269.811	−	654.415i	−0.578993	−	1.40432i
$467$	−465.534	−	465.534i	−0.996860	−	0.996860i	0.00313466	−	0.999995i	$-0.499002\pi$
$467$	−465.534	−	465.534i	−0.996860	−	0.996860i	−0.999995	+	0.00313466i	$0.999002\pi$
$468$	83.3991	−	159.473i	0.178203	−	0.340753i
$469$	280.659	+	280.659i	0.598421	+	0.598421i
$470$	−13.4045	+	32.2119i	−0.0285203	+	0.0685359i
$471$	253.807	+	139.013i	0.538868	+	0.295144i
$472$	48.5444	−	355.214i	0.102848	−	0.752572i
$473$	164.385	−	284.723i	0.347537	−	0.601952i
$474$	−54.1226	−	353.860i	−0.114183	−	0.746541i
$475$	16.3601	−	61.0567i	0.0344423	−	0.128540i
$476$	838.628	+	227.661i	1.76182	+	0.478280i
$477$	538.585	+	492.143i	1.12911	+	1.03175i
$478$	71.4056	−	535.589i	0.149384	−	1.12048i
$479$	−272.785	+	157.493i	−0.569489	+	0.328794i	−0.756945	−	0.653478i	$-0.773309\pi$
$479$	−272.785	+	157.493i	−0.569489	+	0.328794i	0.187456	+	0.982273i	$0.439976\pi$
$480$	−42.6452	−	4.99457i	−0.0888441	−	0.0104054i
$481$	−79.8523	+	138.308i	−0.166013	+	0.287543i
$482$	324.472	−	421.426i	0.673178	−	0.874329i
$483$	−64.8711	−	62.0140i	−0.134309	−	0.128393i
$484$	−1228.13	+	324.761i	−2.53745	+	0.670994i
$485$	−10.3609	+	10.3609i	−0.0213627	+	0.0213627i
$486$	−466.834	−	135.136i	−0.960564	−	0.278058i
$487$		−	473.337i		−	0.971945i	−0.873974	−	0.485973i	$-0.838465\pi$
$487$		−	473.337i		−	0.971945i	0.873974	−	0.485973i	$-0.161535\pi$
$488$	463.819	+	359.541i	0.950449	+	0.736764i
$489$	8.07664	+	358.686i	0.0165166	+	0.733510i
$490$	2.40154	+	18.4757i	0.00490110	+	0.0377054i
$491$	−49.4303	−	184.476i	−0.100673	−	0.375716i	0.897146	−	0.441735i	$-0.145637\pi$
$491$	−49.4303	−	184.476i	−0.100673	−	0.375716i	−0.997818	+	0.0660193i	$0.978970\pi$
$492$	344.279	+	190.037i	0.699755	+	0.386254i
$493$	−1281.27	−	343.315i	−2.59892	−	0.696379i
$494$	−3.36764	+	25.2595i	−0.00681709	+	0.0511326i
$495$	84.2143	−	3.79448i	0.170130	−	0.00766562i
$496$	394.696	+	231.344i	0.795757	+	0.466419i
$497$	−191.628	+	110.636i	−0.385569	+	0.222609i
$498$	−171.813	+	233.860i	−0.345005	+	0.469598i
$499$	63.0138	+	235.171i	0.126280	+	0.471284i	0.999882	−	0.0153574i	$-0.00488860\pi$
$499$	63.0138	+	235.171i	0.126280	+	0.471284i	−0.873602	+	0.486641i	$0.838222\pi$
$500$	89.0930	+	0.292294i	0.178186	+	0.000584589i
$501$	32.7576	+	112.095i	0.0653844	+	0.223743i
$502$	−455.961	−	189.742i	−0.908288	−	0.377972i
$503$	−653.388			−1.29898			−0.649491	−	0.760369i	$-0.725018\pi$
$503$	−653.388			−1.29898			−0.649491	+	0.760369i	$0.725018\pi$
$504$	−102.386	−	592.880i	−0.203146	−	1.17635i
$505$			3.17116i			0.00627952i
$506$	−138.435	−	57.6079i	−0.273587	−	0.113850i
$507$	−102.395	+	419.721i	−0.201963	+	0.827851i
$508$	190.402	−	189.157i	0.374807	−	0.372356i
$509$	−8.19536	+	2.19594i	−0.0161009	+	0.00431422i	−0.266861	−	0.963735i	$-0.585986\pi$
$509$	−8.19536	+	2.19594i	−0.0161009	+	0.00431422i	0.250760	+	0.968049i	$0.419320\pi$
$510$	−69.3440	−	7.66062i	−0.135969	−	0.0150208i
$511$	−161.473	−	279.679i	−0.315993	−	0.547316i
$512$	188.929	+	475.867i	0.369003	+	0.929428i
$513$	68.6612	−	4.64447i	0.133842	−	0.00905355i
$514$	−22.5472	+	169.119i	−0.0438662	+	0.329025i
$515$	−17.2945	+	64.5441i	−0.0335816	+	0.125328i
$516$	182.870	+	45.2491i	0.354399	+	0.0876921i
$517$	−789.006	+	211.414i	−1.52612	+	0.408924i
$518$	68.8228	+	529.471i	0.132863	+	1.02214i
$519$	−333.462	−	548.666i	−0.642509	−	1.05716i
$520$	−17.7449	+	2.24738i	−0.0341248	+	0.00432188i
$521$	513.662			0.985916			0.492958	−	0.870053i	$-0.335916\pi$
$521$	513.662			0.985916			0.492958	+	0.870053i	$0.335916\pi$
$522$	159.256	+	904.492i	0.305089	+	1.73274i
$523$	−531.117	−	531.117i	−1.01552	−	1.01552i	−0.999878	−	0.0156428i	$-0.995021\pi$
$523$	−531.117	−	531.117i	−1.01552	−	1.01552i	−0.0156428	−	0.999878i	$-0.504979\pi$
$524$	−262.312	+	450.916i	−0.500596	+	0.860526i
$525$	174.388	+	596.751i	0.332168	+	1.13667i
$526$	540.909	−	702.537i	1.02834	−	1.33562i
$527$	643.776	+	371.684i	1.22159	+	0.705283i
$528$	−516.441	−	862.432i	−0.978108	−	1.63339i
$529$	258.092	+	447.029i	0.487887	+	0.845045i
$530$	9.58273	−	71.8767i	0.0180806	−	0.135616i
$531$	−384.494	+	121.820i	−0.724094	+	0.229416i
$532$	42.3552	+	73.9204i	0.0796150	+	0.138948i
$533$	158.237	+	42.3996i	0.296881	+	0.0795490i
$534$	443.565	+	172.975i	0.830647	+	0.323923i
$535$	19.3036	+	11.1449i	0.0360815	+	0.0208317i
$536$	−51.4517	+	376.488i	−0.0959919	+	0.702403i
$537$	−126.562	+	2.84982i	−0.235683	+	0.00530693i
$538$	−142.715	+	342.952i	−0.265269	+	0.637456i
$539$	−308.435	+	308.435i	−0.572235	+	0.572235i
$540$	15.4723	+	45.7587i	0.0286524	+	0.0847383i
$541$	491.796	−	491.796i	0.909049	−	0.909049i	−0.0871462	−	0.996196i	$-0.527775\pi$
$541$	491.796	−	491.796i	0.909049	−	0.909049i	0.996196	+	0.0871462i	$0.0277747\pi$
$542$	318.498	+	772.504i	0.587635	+	1.42528i
$543$	701.494	−	15.7957i	1.29189	−	0.0290898i
$544$	312.050	+	771.185i	0.573621	+	1.41762i
$545$	−44.4278	−	25.6504i	−0.0815190	−	0.0470650i
$546$	−100.728	−	229.508i	−0.184483	−	0.420344i
$547$	278.723	+	74.6837i	0.509549	+	0.136533i	0.504428	−	0.863454i	$-0.331703\pi$
$547$	278.723	+	74.6837i	0.509549	+	0.136533i	0.00512086	+	0.999987i	$0.498370\pi$
$548$	170.098	+	46.1764i	0.310398	+	0.0842634i
$549$	141.997	−	644.760i	0.258647	−	1.17443i
$550$	630.994	+	825.126i	1.14726	+	1.50023i
$551$	−65.0235	−	112.624i	−0.118010	−	0.204399i
$552$	9.71424	−	85.3663i	0.0175983	−	0.154649i
$553$	−431.766	−	249.280i	−0.780770	−	0.450778i
$554$	592.581	−	77.0261i	1.06964	−	0.139036i
$555$	−12.0238	−	41.1452i	−0.0216646	−	0.0741354i
$556$	−431.001	+	740.892i	−0.775182	+	1.33254i
$557$	560.781	+	560.781i	1.00679	+	1.00679i	0.999977	+	0.00681189i	$0.00216831\pi$
$557$	560.781	+	560.781i	1.00679	+	1.00679i	0.00681189	+	0.999977i	$0.497832\pi$
$558$	44.9843	−	512.716i	0.0806169	−	0.918846i
$559$	78.4779			0.140390
$560$	−42.5606	+	42.0058i	−0.0760012	+	0.0750103i
$561$	−848.319	−	1395.79i	−1.51215	−	2.48804i
$562$	128.902	−	167.419i	0.229364	−	0.297899i
$563$	−62.7879	+	16.8240i	−0.111524	+	0.0298827i	−0.314149	−	0.949374i	$-0.601719\pi$
$563$	−62.7879	+	16.8240i	−0.111524	+	0.0298827i	0.202626	+	0.979256i	$0.435053\pi$
$564$	−241.776	−	400.766i	−0.428681	−	0.710578i
$565$	7.12816	−	26.6027i	0.0126162	−	0.0470844i
$566$	−277.289	−	362.600i	−0.489909	−	0.640635i
$567$	−553.369	+	389.776i	−0.975959	+	0.687436i
$568$	−195.311	−	82.0289i	−0.343857	−	0.144417i
$569$	−376.781	−	652.605i	−0.662182	−	1.14693i	−0.980041	−	0.198795i	$-0.936297\pi$
$569$	−376.781	−	652.605i	−0.662182	−	1.14693i	0.317859	−	0.948138i	$-0.397036\pi$
$570$	−4.27619	−	5.33833i	−0.00750209	−	0.00936549i
$571$	−191.951	+	51.4330i	−0.336166	+	0.0900753i	−0.422953	−	0.906152i	$-0.639007\pi$
$571$	−191.951	+	51.4330i	−0.336166	+	0.0900753i	0.0867876	+	0.996227i	$0.472340\pi$
$572$	−295.138	−	297.081i	−0.515975	−	0.519372i
$573$	−143.218	+	587.055i	−0.249944	+	1.02453i
$574$	506.335	−	208.759i	0.882117	−	0.363691i
$575$			88.7810i			0.154402i
$576$	392.714	−	421.369i	0.681795	−	0.731543i
$577$	321.494			0.557181			0.278591	−	0.960410i	$-0.410133\pi$
$577$	321.494			0.557181			0.278591	+	0.960410i	$0.410133\pi$
$578$	294.932	+	715.345i	0.510263	+	1.23762i
$579$	−65.6557	−	224.672i	−0.113395	−	0.388034i
$580$	64.7565	−	64.3330i	0.111649	−	0.110919i
$581$	104.603	+	390.382i	0.180039	+	0.671914i
$582$	−29.7189	−	194.306i	−0.0510633	−	0.333859i
$583$	1470.23	−	848.837i	2.52183	−	1.45598i
$584$	119.720	−	285.054i	0.205000	−	0.488106i
$585$	10.8354	+	16.9560i	0.0185221	+	0.0289847i
$586$	402.835	−	308.057i	0.687431	−	0.525695i
$587$	519.522	+	139.206i	0.885046	+	0.237147i	0.672583	−	0.740022i	$-0.265185\pi$
$587$	519.522	+	139.206i	0.885046	+	0.237147i	0.212463	+	0.977169i	$0.431851\pi$
$588$	−218.816	−	120.783i	−0.372136	−	0.205414i
$589$	18.8627	+	70.3966i	0.0320250	+	0.119519i
$590$	31.7632	+	24.4557i	0.0538360	+	0.0414503i
$591$	3.58702	+	159.301i	0.00606941	+	0.269544i
$592$	−363.807	+	359.064i	−0.614539	+	0.606527i
$593$		−	150.500i		−	0.253795i	−0.991916	−	0.126897i	$-0.959498\pi$
$593$		−	150.500i		−	0.253795i	0.991916	−	0.126897i	$-0.0405019\pi$
$594$	−627.866	+	940.585i	−1.05701	+	1.58348i
$595$	−68.7056	+	68.7056i	−0.115472	+	0.115472i
$596$	−886.052	−	515.446i	−1.48666	−	0.864842i
$597$	68.5395	+	65.5208i	0.114806	+	0.109750i
$598$	−4.61353	−	35.4930i	−0.00771493	−	0.0593529i
$599$	−447.647	+	775.348i	−0.747325	+	1.29440i	0.201776	+	0.979432i	$0.435329\pi$
$599$	−447.647	+	775.348i	−0.747325	+	1.29440i	−0.949101	+	0.314972i	$0.898005\pi$
$600$	−353.971	+	478.504i	−0.589952	+	0.797507i
$601$	864.629	−	499.194i	1.43865	−	0.830605i	0.440894	−	0.897559i	$-0.354661\pi$
$601$	864.629	−	499.194i	1.43865	−	0.830605i	0.997756	+	0.0669538i	$0.0213280\pi$
$602$	208.412	−	159.378i	0.346199	−	0.264747i
$603$	407.521	−	129.116i	0.675822	−	0.214122i
$604$	134.227	−	494.447i	0.222230	−	0.818621i
$605$	36.7632	−	137.202i	0.0607657	−	0.226781i
$606$	−34.2836	−	25.1875i	−0.0565736	−	0.0415636i
$607$	378.819	−	656.133i	0.624084	−	1.08094i	−0.364634	−	0.931151i	$-0.618806\pi$
$607$	378.819	−	656.133i	0.624084	−	1.08094i	0.988717	−	0.149794i	$-0.0478609\pi$
$608$	−31.8295	+	75.0951i	−0.0523511	+	0.123512i
$609$	1121.83	+	614.442i	1.84209	+	1.00894i
$610$	−60.6648	+	25.0117i	−0.0994505	+	0.0410027i
$611$	−137.872	−	137.872i	−0.225650	−	0.225650i
$612$	633.597	−	688.836i	1.03529	−	1.12555i
$613$	325.410	+	325.410i	0.530849	+	0.530849i	0.920825	−	0.389976i	$-0.127517\pi$
$613$	325.410	+	325.410i	0.530849	+	0.530849i	−0.389976	+	0.920825i	$0.627517\pi$
$614$	259.388	+	107.941i	0.422457	+	0.175800i
$615$	−37.5750	+	22.8369i	−0.0610975	+	0.0371332i
$616$	−1387.12	−	189.567i	−2.25182	−	0.307739i
$617$	−167.571	+	290.242i	−0.271590	+	0.470408i	−0.969269	−	0.246002i	$-0.920883\pi$
$617$	−167.571	+	290.242i	−0.271590	+	0.470408i	0.697679	+	0.716411i	$0.254216\pi$
$618$	−560.425	−	699.627i	−0.906837	−	1.13208i
$619$	−127.580	+	476.135i	−0.206107	+	0.769201i	0.783003	+	0.622018i	$0.213687\pi$
$619$	−127.580	+	476.135i	−0.206107	+	0.769201i	−0.989109	+	0.147183i	$0.952980\pi$
$620$	−44.3850	+	25.4319i	−0.0715887	+	0.0410192i
$621$	−91.4621	+	31.2606i	−0.147282	+	0.0503391i
$622$	−786.230	−	104.822i	−1.26404	−	0.168523i
$623$	574.239	−	331.537i	0.921731	−	0.532162i
$624$	116.646	−	209.691i	0.186932	−	0.336044i
$625$	305.019	−	528.308i	0.488030	−	0.845292i
$626$	882.780	+	679.684i	1.41019	+	1.08576i
$627$	37.9535	−	155.573i	0.0605319	−	0.248122i
$628$	333.516	+	194.017i	0.531076	+	0.308944i
$629$	−587.293	+	587.293i	−0.933693	+	0.933693i
$630$	63.2108	+	23.0245i	0.100335	+	0.0365469i
$631$			298.987i			0.473830i	0.971530	+	0.236915i	$0.0761362\pi$
$631$			298.987i			0.473830i	−0.971530	+	0.236915i	$0.923864\pi$
$632$	−59.9707	−	473.518i	−0.0948904	−	0.749238i
$633$	801.179	+	438.816i	1.26569	+	0.693232i
$634$	519.242	−	67.4932i	0.818994	−	0.106456i
$635$	7.76711	+	28.9872i	0.0122317	+	0.0456492i
$636$	700.951	+	674.494i	1.10212	+	1.06053i
$637$	−100.572	−	26.9482i	−0.157884	−	0.0423049i
$638$	2118.33	+	282.419i	3.32026	+	0.442663i
$639$	10.7271	+	238.076i	0.0167873	+	0.372575i
$640$	−56.6695	−	8.12372i	−0.0885462	−	0.0126933i
$641$	−360.071	+	207.887i	−0.561734	+	0.324317i	−0.753841	−	0.657057i	$-0.771801\pi$
$641$	−360.071	+	207.887i	−0.561734	+	0.324317i	0.192107	+	0.981374i	$0.438468\pi$
$642$	−273.811	+	120.172i	−0.426497	+	0.187183i
$643$	−47.0412	−	175.560i	−0.0731589	−	0.273033i	0.919651	−	0.392738i	$-0.128472\pi$
$643$	−47.0412	−	175.560i	−0.0731589	−	0.273033i	−0.992810	+	0.119705i	$0.961805\pi$
$644$	−84.3334	−	84.8886i	−0.130953	−	0.131815i
$645$	−14.5555	+	15.2261i	−0.0225667	+	0.0236064i
$646$	−50.9165	+	122.355i	−0.0788182	+	0.189405i
$647$	56.1947			0.0868543			0.0434272	−	0.999057i	$-0.486172\pi$
$647$	56.1947			0.0868543			0.0434272	+	0.999057i	$0.486172\pi$
$648$	−617.591	−	196.176i	−0.953073	−	0.302740i
$649$			938.525i			1.44611i
$650$	−95.2618	+	228.920i	−0.146557	+	0.352184i
$651$	−518.145	−	495.325i	−0.795922	−	0.760867i
$652$	−1.56942	+	478.367i	−0.00240708	+	0.733692i
$653$	−93.3761	+	25.0200i	−0.142995	+	0.0383155i	−0.329607	−	0.944118i	$-0.606916\pi$
$653$	−93.3761	+	25.0200i	−0.142995	+	0.0383155i	0.186611	+	0.982434i	$0.440250\pi$
$654$	630.185	−	276.578i	0.963585	−	0.422903i
$655$	−29.1647	−	50.5147i	−0.0445262	−	0.0771217i
$656$	452.352	+	265.138i	0.689560	+	0.404174i
$657$	−347.468	+	15.6560i	−0.528871	+	0.0238296i
$658$	−646.144	−	86.1449i	−0.981981	−	0.130919i
$659$	77.0858	−	287.688i	0.116974	−	0.436552i	−0.882453	−	0.470400i	$-0.844110\pi$
$659$	77.0858	−	287.688i	0.116974	−	0.436552i	0.999427	+	0.0338479i	$0.0107762\pi$
$660$	112.379	−	2.16162i	0.170271	−	0.00327518i
$661$	−435.687	+	116.742i	−0.659133	+	0.176614i	−0.572855	−	0.819657i	$-0.694164\pi$
$661$	−435.687	+	116.742i	−0.659133	+	0.176614i	−0.0862784	+	0.996271i	$0.527497\pi$
$662$	−538.615	+	70.0114i	−0.813618	+	0.105757i
$663$	187.293	−	341.955i	0.282493	−	0.515769i
$664$	−237.050	+	305.801i	−0.357002	+	0.460544i
$665$	−9.52601			−0.0143248
$666$	540.324	+	196.813i	0.811298	+	0.295515i
$667$	129.156	+	129.156i	0.193638	+	0.193638i
$668$	39.8075	+	150.537i	0.0595920	+	0.225355i
$669$	50.5669	+	12.3363i	0.0755858	+	0.0184399i
$670$	−33.6655	−	25.9203i	−0.0502470	−	0.0386870i
$671$	−1330.45	−	768.135i	−1.98278	−	1.14476i
$672$	−116.081	−	793.764i	−0.172739	−	1.18120i
$673$	−64.0278	−	110.899i	−0.0951379	−	0.164784i	0.814528	−	0.580124i	$-0.196996\pi$
$673$	−64.0278	−	110.899i	−0.0951379	−	0.164784i	−0.909666	+	0.415340i	$0.863663\pi$
$674$	−835.608	−	111.405i	−1.23977	−	0.165289i
$675$	657.004	+	129.259i	0.973340	+	0.191495i
$676$	−150.915	+	555.920i	−0.223247	+	0.822367i
$677$	−717.129	−	192.154i	−1.05927	−	0.283832i	−0.313195	−	0.949689i	$-0.601399\pi$
$677$	−717.129	−	192.154i	−1.05927	−	0.283832i	−0.746079	+	0.665857i	$0.768066\pi$
$678$	230.986	+	288.360i	0.340688	+	0.425309i
$679$	−237.084	−	136.880i	−0.349166	−	0.201591i
$680$	−92.1644	−	12.5954i	−0.135536	−	0.0185226i
$681$	570.719	+	939.039i	0.838060	+	1.37891i
$682$	−1105.72	−	460.132i	−1.62129	−	0.674680i
$683$	−413.911	+	413.911i	−0.606019	+	0.606019i	−0.941903	−	0.335885i	$-0.890965\pi$
$683$	−413.911	+	413.911i	−0.606019	+	0.606019i	0.335885	+	0.941903i	$0.390965\pi$
$684$	91.6775	−	3.82941i	0.134031	−	0.00559855i
$685$	−13.9355	+	13.9355i	−0.0203438	+	0.0203438i
$686$	435.281	−	179.463i	0.634521	−	0.261609i
$687$	−106.229	+	193.950i	−0.154627	+	0.282314i
$688$	242.189	+	66.6007i	0.352019	+	0.0968033i
$689$	350.946	+	202.619i	0.509356	+	0.294077i
$690$	7.74196	+	5.68788i	0.0112202	+	0.00824330i
$691$	481.009	+	128.886i	0.696105	+	0.186521i	0.589485	−	0.807779i	$-0.299331\pi$
$691$	481.009	+	128.886i	0.696105	+	0.186521i	0.106620	+	0.994300i	$0.465997\pi$
$692$	−425.600	−	742.779i	−0.615030	−	1.07338i
$693$	475.710	+	1501.46i	0.686450	+	2.16661i
$694$	−287.307	+	219.711i	−0.413987	+	0.316586i
$695$	−47.9200	−	82.9999i	−0.0689497	−	0.119424i
$696$	181.167	+	1211.06i	0.260297	+	1.74003i
$697$	737.817	+	425.979i	1.05856	+	0.611160i
$698$	−15.4168	−	118.605i	−0.0220871	−	0.169921i
$699$	−733.701	+	767.504i	−1.04964	+	1.09800i
$700$	211.919	+	801.400i	0.302741	+	1.14486i
$701$	−270.798	−	270.798i	−0.386303	−	0.386303i	0.487064	−	0.873367i	$-0.338068\pi$
$701$	−270.798	−	270.798i	−0.386303	−	0.386303i	−0.873367	+	0.487064i	$0.838068\pi$
$702$	−269.375	−	17.5340i	−0.383726	−	0.0249772i
$703$	−81.4280			−0.115829
$704$	−658.701	−	1167.29i	−0.935655	−	1.65808i
$705$	52.3212	−	1.17813i	0.0742144	−	0.00167111i
$706$	13.5710	+	10.4488i	0.0192224	+	0.0148000i
$707$	−57.2296	+	15.3346i	−0.0809470	+	0.0216897i
$708$	−516.677	+	149.150i	−0.729770	+	0.210664i
$709$	−110.232	+	411.392i	−0.155475	+	0.580242i	0.843589	+	0.536990i	$0.180439\pi$
$709$	−110.232	+	411.392i	−0.155475	+	0.580242i	−0.999064	+	0.0432524i	$0.986228\pi$
$710$	18.8153	−	14.3885i	0.0265005	−	0.0202656i
$711$	−452.468	+	289.141i	−0.636382	+	0.406668i
$712$	585.275	+	245.810i	0.822016	+	0.345239i
$713$	−51.1810	−	88.6480i	−0.0717825	−	0.124331i
$714$	−197.073	−	1288.49i	−0.276012	−	1.80460i
$715$	45.2283	−	12.1189i	0.0632563	−	0.0169495i
$716$	−168.791	−	0.553765i	−0.235741	−	0.000773415i
$717$	−777.954	+	227.341i	−1.08501	+	0.317073i
$718$	184.937	+	448.557i	0.257572	+	0.624731i
$719$		−	1018.72i		−	1.41685i	−0.705784	−	0.708427i	$-0.749405\pi$
$719$		−	1018.72i		−	1.41685i	0.705784	−	0.708427i	$-0.250595\pi$
$720$	19.0493	+	61.5234i	0.0264573	+	0.0854491i
$721$	−1248.45			−1.73155
$722$	655.481	−	270.250i	0.907869	−	0.374308i
$723$	−775.068	−	189.086i	−1.07202	−	0.261529i
$724$	935.557	+	3.06936i	1.29221	+	0.00423944i
$725$	−327.498	−	1222.24i	−0.451722	−	1.68585i
$726$	1191.30	+	1487.20i	1.64091	+	2.04849i
$727$	−409.462	+	236.403i	−0.563221	+	0.325176i	−0.754437	−	0.656372i	$-0.772090\pi$
$727$	−409.462	+	236.403i	−0.563221	+	0.325176i	0.191216	+	0.981548i	$0.438757\pi$
$728$	−126.366	−	309.373i	−0.173580	−	0.424963i
$729$	98.1748	+	722.359i	0.134670	+	0.990890i
$730$	20.9999	+	27.4608i	0.0287670	+	0.0376175i
$731$	394.224	+	105.632i	0.539295	+	0.144504i
$732$	211.439	−	854.511i	0.288851	−	1.16736i
$733$	227.404	+	848.684i	0.310238	+	1.15782i	0.928342	+	0.371727i	$0.121234\pi$
$733$	227.404	+	848.684i	0.310238	+	1.15782i	−0.618104	+	0.786096i	$0.712099\pi$
$734$	269.011	−	349.394i	0.366500	−	0.476013i
$735$	23.8818	−	14.5146i	0.0324922	−	0.0197478i
$736$	15.8836	−	113.450i	0.0215810	−	0.154144i
$737$		−	994.733i		−	1.34971i
$738$	51.5554	−	587.612i	0.0698583	−	0.796222i
$739$	48.3289	−	48.3289i	0.0653977	−	0.0653977i	−0.673651	−	0.739049i	$-0.735275\pi$
$739$	48.3289	−	48.3289i	0.0653977	−	0.0653977i	0.739049	+	0.673651i	$0.235275\pi$
$740$	−14.6115	−	55.2554i	−0.0197453	−	0.0746695i
$741$	36.6900	−	10.7219i	0.0495142	−	0.0144695i
$742$	1343.49	−	174.632i	1.81063	−	0.235353i
$743$	171.049	−	296.266i	0.230214	−	0.398743i	−0.727657	−	0.685941i	$-0.759391\pi$
$743$	171.049	−	296.266i	0.230214	−	0.398743i	0.957871	+	0.287199i	$0.0927240\pi$
$744$	77.5906	−	681.847i	0.104288	−	0.916461i
$745$	99.2618	−	57.3088i	0.133237	−	0.0769246i
$746$	−254.850	−	333.258i	−0.341622	−	0.446726i
$747$	425.097	+	93.6204i	0.569073	+	0.125329i
$748$	−1082.72	−	1889.61i	−1.44748	−	2.52622i
$749$	−107.786	+	402.263i	−0.143907	+	0.537067i
$750$	−53.7077	−	122.373i	−0.0716103	−	0.163164i
$751$	−583.913	+	1011.37i	−0.777514	+	1.34669i	0.155857	+	0.987780i	$0.450186\pi$
$751$	−583.913	+	1011.37i	−0.777514	+	1.34669i	−0.933371	+	0.358914i	$0.883147\pi$
$752$	−308.479	−	542.492i	−0.410212	−	0.721398i
$753$	16.6765	+	740.609i	0.0221467	+	0.983544i
$754$	194.442	+	471.611i	0.257880	+	0.625479i
$755$	40.5081	+	40.5081i	0.0536532	+	0.0536532i
$756$	−750.984	+	500.499i	−0.993364	+	0.662036i
$757$	−885.032	−	885.032i	−1.16913	−	1.16913i	−0.982414	−	0.186716i	$-0.940215\pi$
$757$	−885.032	−	885.032i	−1.16913	−	1.16913i	−0.186716	−	0.982414i	$-0.559785\pi$
$758$	377.030	−	906.025i	0.497401	−	1.19528i
$759$	5.06318	+	224.857i	0.00667086	+	0.296255i
$760$	−5.51611	−	7.26246i	−0.00725804	−	0.00955587i
$761$	−222.498	+	385.378i	−0.292376	+	0.506410i	−0.974371	−	0.224947i	$-0.927779\pi$
$761$	−222.498	+	385.378i	−0.292376	+	0.506410i	0.681995	+	0.731357i	$0.261113\pi$
$762$	−375.075	−	146.266i	−0.492224	−	0.191950i
$763$	248.073	−	925.820i	0.325128	−	1.21339i
$764$	−211.082	+	777.555i	−0.276285	+	1.01774i
$765$	31.6076	+	99.7613i	0.0413171	+	0.130407i
$766$	−13.7046	+	102.794i	−0.0178912	+	0.134195i
$767$	−194.013	+	112.014i	−0.252951	+	0.146041i
$768$	537.935	−	548.134i	0.700436	−	0.713716i
$769$	27.2858	−	47.2604i	0.0354822	−	0.0614569i	−0.847739	−	0.530414i	$-0.822037\pi$
$769$	27.2858	−	47.2604i	0.0354822	−	0.0614569i	0.883221	+	0.468957i	$0.155370\pi$
$770$	95.5000	−	124.036i	0.124026	−	0.161086i
$771$	245.649	−	71.7859i	0.318611	−	0.0931075i
$772$	−79.7857	−	301.720i	−0.103349	−	0.390829i
$773$	125.828	−	125.828i	0.162779	−	0.162779i	−0.621018	−	0.783796i	$-0.713281\pi$
$773$	125.828	−	125.828i	0.162779	−	0.162779i	0.783796	+	0.621018i	$0.213281\pi$
$774$	−49.0004	−	278.296i	−0.0633080	−	0.359556i
$775$			709.121i			0.914995i
$776$	−32.9301	−	260.010i	−0.0424357	−	0.335065i
$777$	684.399	−	415.956i	0.880822	−	0.535336i
$778$	80.3111	+	617.854i	0.103228	+	0.794156i
$779$	21.6181	+	80.6799i	0.0277511	+	0.103569i
$780$	13.8594	+	22.9732i	0.0177684	+	0.0294528i
$781$	535.653	+	143.528i	0.685856	+	0.183774i
$782$	24.5985	−	184.505i	0.0314559	−	0.235940i
$783$	1143.84	−	767.751i	1.46084	−	0.980524i
$784$	−287.504	−	168.515i	−0.366714	−	0.214943i
$785$	−37.3628	+	21.5714i	−0.0475959	+	0.0274795i
$786$	777.764	+	85.9217i	0.989521	+	0.109315i
$787$	337.696	+	1260.30i	0.429093	+	1.60140i	0.754820	+	0.655932i	$0.227724\pi$
$787$	337.696	+	1260.30i	0.429093	+	1.60140i	−0.325728	+	0.945464i	$0.605609\pi$
$788$	−0.697014	+	212.454i	−0.000884535	+	0.269611i
$789$	−1292.07	−	315.215i	−1.63761	−	0.399511i
$790$	49.2729	+	20.5043i	0.0623708	+	0.0259548i
$791$	514.565			0.650524
$792$	−869.222	+	1232.10i	−1.09750	+	1.55569i
$793$		−	366.710i		−	0.462434i
$794$	−1229.27	−	511.543i	−1.54820	−	0.644261i
$795$	−104.402	+	30.5095i	−0.131324	+	0.0383767i
$796$	89.1024	+	89.6890i	0.111938	+	0.112675i
$797$	353.098	−	94.6123i	0.443034	−	0.118711i	−0.0304042	−	0.999538i	$-0.509679\pi$
$797$	353.098	−	94.6123i	0.443034	−	0.118711i	0.473438	+	0.880827i	$0.343013\pi$
$798$	75.6621	−	102.986i	0.0948147	−	0.129055i
$799$	−507.007	−	878.163i	−0.634552	−	1.09908i
$800$	−488.260	+	625.621i	−0.610325	+	0.782026i
$801$	−32.1451	−	713.425i	−0.0401312	−	0.890668i
$802$	161.699	−	1212.85i	0.201620	−	1.51228i
$803$	−209.477	+	781.779i	−0.260868	+	0.973573i
$804$	547.621	−	158.083i	0.681120	−	0.196620i
$805$	12.9236	−	3.46288i	0.0160542	−	0.00430171i
$806$	−36.8497	−	283.494i	−0.0457192	−	0.351729i
$807$	557.050	−	12.5433i	0.690273	−	0.0155431i
$808$	−44.8301	−	34.7512i	−0.0554828	−	0.0430089i
$809$	857.219			1.05960			0.529802	−	0.848121i	$-0.322266\pi$
$809$	857.219			1.05960			0.529802	+	0.848121i	$0.322266\pi$
$810$	53.3637	−	49.0115i	0.0658811	−	0.0605081i
$811$	−854.936	−	854.936i	−1.05417	−	1.05417i	−0.998446	−	0.0557286i	$-0.982252\pi$
$811$	−854.936	−	854.936i	−1.05417	−	1.05417i	−0.0557286	−	0.998446i	$-0.517748\pi$
$812$	1474.15	+	857.562i	1.81546	+	1.05611i
$813$	866.096	−	905.999i	1.06531	−	1.11439i
$814$	816.331	−	1060.26i	1.00286	−	1.30253i
$815$	−46.3224	−	26.7442i	−0.0568373	−	0.0328150i
$816$	868.203	−	896.354i	1.06397	−	1.09847i
$817$	20.0066	+	34.6525i	0.0244879	+	0.0424143i
$818$	−94.8037	+	711.090i	−0.115897	+	0.869303i
$819$	−253.607	+	277.540i	−0.309655	+	0.338876i
$820$	−50.8686	+	29.1469i	−0.0620349	+	0.0355450i
$821$	−310.441	−	83.1824i	−0.378125	−	0.101318i	0.0647501	−	0.997902i	$-0.479375\pi$
$821$	−310.441	−	83.1824i	−0.378125	−	0.101318i	−0.442876	+	0.896583i	$0.646042\pi$
$822$	−39.9721	−	261.343i	−0.0486279	−	0.317935i
$823$	−822.249	−	474.725i	−0.999087	−	0.576823i	−0.0911090	−	0.995841i	$-0.529041\pi$
$823$	−822.249	−	474.725i	−0.999087	−	0.576823i	−0.907978	+	0.419018i	$0.862374\pi$
$824$	−722.926	−	951.797i	−0.877337	−	1.15509i
$825$	748.483	−	1366.56i	0.907253	−	1.65644i
$826$	−287.753	+	691.486i	−0.348369	+	0.837150i
$827$	−630.068	+	630.068i	−0.761872	+	0.761872i	−0.976661	−	0.214789i	$-0.931094\pi$
$827$	−630.068	+	630.068i	−0.761872	+	0.761872i	0.214789	+	0.976661i	$0.431094\pi$
$828$	−122.984	+	38.5217i	−0.148531	+	0.0465238i
$829$	−1126.08	+	1126.08i	−1.35836	+	1.35836i	−0.482410	+	0.875945i	$0.660239\pi$
$829$	−1126.08	+	1126.08i	−1.35836	+	1.35836i	−0.875945	+	0.482410i	$0.839761\pi$
$830$	−16.4905	−	39.9970i	−0.0198681	−	0.0481892i
$831$	−465.536	−	765.975i	−0.560212	−	0.921751i
$832$	162.687	−	275.484i	0.195537	−	0.331111i
$833$	−468.939	−	270.742i	−0.562952	−	0.325021i
$834$	1277.93	+	141.177i	1.53229	+	0.169276i
$835$	−16.8175	−	4.50624i	−0.0201407	−	0.00539669i
$836$	55.9377	−	206.056i	0.0669112	−	0.246478i
$837$	−730.536	+	249.688i	−0.872803	+	0.298313i
$838$	−282.874	−	369.903i	−0.337558	−	0.441412i
$839$	−811.916	−	1406.28i	−0.967719	−	1.67614i	−0.702126	−	0.712053i	$-0.747766\pi$
$839$	−811.916	−	1406.28i	−0.967719	−	1.67614i	−0.265593	−	0.964085i	$-0.585568\pi$
$840$	83.4613	+	32.8629i	0.0993587	+	0.0391225i
$841$	−1526.19	−	881.147i	−1.81473	−	1.04774i
$842$	−1295.87	+	168.442i	−1.53904	+	0.200050i
$843$	−307.910	−	75.1178i	−0.365255	−	0.0891077i
$844$	1052.79	+	612.445i	1.24739	+	0.725645i
$845$	−45.5444	−	45.5444i	−0.0538987	−	0.0538987i
$846$	−402.834	+	575.005i	−0.476163	+	0.679675i
$847$	2653.85			3.13323
$848$	911.095	+	923.131i	1.07440	+	1.08860i
$849$	−328.919	+	600.532i	−0.387419	+	0.707341i
$850$	−786.665	+	1021.73i	−0.925488	+	1.20203i
$851$	110.471	−	29.6006i	0.129813	−	0.0347833i
$852$	6.11094	+	317.697i	0.00717246	+	0.372884i
$853$	−129.912	+	484.839i	−0.152300	+	0.568393i	0.847021	+	0.531560i	$0.178394\pi$
$853$	−129.912	+	484.839i	−0.152300	+	0.568393i	−0.999321	+	0.0368336i	$0.988273\pi$
$854$	−744.736	−	973.863i	−0.872057	−	1.14035i
$855$	−4.72475	+	9.10713i	−0.00552602	+	0.0106516i
$856$	−369.092	+	150.759i	−0.431183	+	0.176121i
$857$	570.829	+	988.705i	0.666078	+	1.15368i	0.978992	+	0.203899i	$0.0653615\pi$
$857$	570.829	+	988.705i	0.666078	+	1.15368i	−0.312914	+	0.949782i	$0.601305\pi$
$858$	−228.216	+	585.222i	−0.265986	+	0.682077i
$859$	523.261	−	140.207i	0.609151	−	0.163222i	0.0589600	−	0.998260i	$-0.481222\pi$
$859$	523.261	−	140.207i	0.609151	−	0.163222i	0.550191	+	0.835039i	$0.314555\pi$
$860$	−19.9245	+	19.7942i	−0.0231680	+	0.0230165i
$861$	−593.834	−	567.680i	−0.689703	−	0.659327i
$862$	887.657	−	365.975i	1.02976	−	0.424565i
$863$		−	28.7631i		−	0.0333292i	−0.999861	−	0.0166646i	$-0.994695\pi$
$863$		−	28.7631i		−	0.0333292i	0.999861	−	0.0166646i	$-0.00530475\pi$
$864$	−816.435	−	282.718i	−0.944948	−	0.327220i
$865$	95.7208			0.110660
$866$	241.702	+	586.238i	0.279101	+	0.676949i
$867$	802.013	−	838.963i	0.925044	−	0.967662i
$868$	−673.597	−	678.031i	−0.776034	−	0.781142i
$869$	323.389	+	1206.90i	0.372139	+	1.38884i
$870$	−127.564	−	49.7457i	−0.146626	−	0.0571790i
$871$	205.633	−	118.722i	0.236088	−	0.136306i
$872$	849.478	−	346.978i	0.974172	−	0.397910i
$873$	−248.451	+	158.768i	−0.284595	+	0.181865i
$874$	14.4961	−	11.0855i	0.0165859	−	0.0126836i
$875$	−179.781	−	48.1723i	−0.205465	−	0.0550541i
$876$	−463.676	+	8.91884i	−0.529310	+	0.0101813i
$877$	260.939	+	973.836i	0.297535	+	1.11042i	0.939183	+	0.343417i	$0.111585\pi$
$877$	260.939	+	973.836i	0.297535	+	1.11042i	−0.641647	+	0.767000i	$0.721749\pi$
$878$	−288.716	−	222.293i	−0.328834	−	0.253181i
$879$	−667.169	−	365.417i	−0.759009	−	0.415719i
$880$	149.863	+	0.983346i	0.170299	+	0.00111744i
$881$			442.006i			0.501710i	0.968025	+	0.250855i	$0.0807117\pi$
$881$			442.006i			0.501710i	−0.968025	+	0.250855i	$0.919288\pi$
$882$	−32.7674	+	373.472i	−0.0371513	+	0.423438i
$883$	−278.551	+	278.551i	−0.315459	+	0.315459i	−0.847020	−	0.531561i	$-0.821606\pi$
$883$	−278.551	+	278.551i	−0.315459	+	0.315459i	0.531561	+	0.847020i	$0.321606\pi$
$884$	261.400	−	449.347i	0.295701	−	0.508311i
$885$	14.2515	−	58.4175i	0.0161034	−	0.0660084i
$886$	−49.0946	−	377.697i	−0.0554115	−	0.426295i
$887$	−353.953	+	613.064i	−0.399045	+	0.691166i	−0.993608	−	0.112883i	$-0.963992\pi$
$887$	−353.953	+	613.064i	−0.399045	+	0.691166i	0.594563	+	0.804049i	$0.297325\pi$
$888$	713.425	+	280.911i	0.803406	+	0.316341i
$889$	−485.570	+	280.344i	−0.546198	+	0.315348i
$890$	−56.3827	+	43.1172i	−0.0633513	+	0.0484463i
$891$	1671.38	+	289.908i	1.87585	+	0.325374i
$892$	66.9758	+	18.1818i	0.0750850	+	0.0203832i
$893$	25.7303	−	96.0267i	0.0288133	−	0.107533i
$894$	−168.837	+	1528.31i	−0.188855	+	1.70952i
$895$	9.43665	−	16.3447i	0.0105437	−	0.0182623i
$896$	−127.426	−	1061.99i	−0.142217	−	1.18526i
$897$	−45.8786	+	27.8836i	−0.0511467	+	0.0310854i
$898$	41.6076	−	17.1545i	0.0463337	−	0.0191031i
$899$	1031.61	+	1031.61i	1.14751	+	1.14751i
$900$	871.270	+	194.881i	0.968077	+	0.216535i
$901$	1490.21	+	1490.21i	1.65395	+	1.65395i
$902$	−1267.24	−	527.346i	−1.40493	−	0.584641i
$903$	−345.169	−	189.053i	−0.382247	−	0.209361i
$904$	297.963	+	392.295i	0.329605	+	0.433955i
$905$	−52.3046	+	90.5942i	−0.0577951	+	0.100104i
$906$	−759.679	+	116.192i	−0.838498	+	0.128247i
$907$	−269.681	+	1006.46i	−0.297333	+	1.10966i	0.642015	+	0.766692i	$0.278099\pi$
$907$	−269.681	+	1006.46i	−0.297333	+	1.10966i	−0.939347	+	0.342968i	$0.888568\pi$
$908$	728.413	+	1271.26i	0.802217	+	1.40007i
$909$	−13.7246	+	62.3188i	−0.0150986	+	0.0685575i
$910$	37.0390	+	4.93810i	0.0407021	+	0.00542648i
$911$	867.790	−	501.019i	0.952569	−	0.549966i	0.0586910	−	0.998276i	$-0.481307\pi$
$911$	867.790	−	501.019i	0.952569	−	0.549966i	0.893878	+	0.448310i	$0.147974\pi$
$912$	122.328	−	1.95153i	0.134131	−	0.00213983i
$913$	506.440	−	877.180i	0.554699	−	0.960766i
$914$	14.7011	+	11.3189i	0.0160843	+	0.0123839i
$915$	71.1482	+	68.0146i	0.0777576	+	0.0743329i
$916$	−148.261	+	254.861i	−0.161857	+	0.278232i
$917$	770.603	−	770.603i	0.840352	−	0.840352i
$918$	−1329.57	−	450.662i	−1.44834	−	0.490918i
$919$			1047.84i			1.14020i	0.821576	+	0.570100i	$0.193095\pi$
$919$			1047.84i			1.14020i	−0.821576	+	0.570100i	$0.806905\pi$
$920$	10.1236	+	7.84755i	0.0110039	+	0.00852995i
$921$	−9.48699	−	421.320i	−0.0103007	−	0.457459i
$922$	−1253.38	+	162.920i	−1.35942	+	0.176702i
$923$	34.2603	+	127.861i	0.0371184	+	0.138528i
$924$	582.435	+	2017.64i	0.630341	+	2.18359i
$925$	−765.297	−	205.061i	−0.827348	−	0.221687i
$926$	−474.373	−	63.2442i	−0.512282	−	0.0682982i
$927$	−619.212	+	1193.55i	−0.667974	+	1.28755i
$928$	199.829	+	1620.45i	0.215333	+	1.74617i
$929$	1368.64	−	790.183i	1.47324	−	0.850573i	0.473690	−	0.880692i	$-0.342922\pi$
$929$	1368.64	−	790.183i	1.47324	−	0.850573i	0.999546	+	0.0301183i	$0.00958839\pi$
$930$	61.8374	+	45.4308i	0.0664918	+	0.0488504i
$931$	−13.7400	−	51.2783i	−0.0147583	−	0.0550787i
$932$	−1004.34	+	997.767i	−1.07761	+	1.07057i
$933$	333.731	+	1142.02i	0.357697	+	1.22403i
$934$	−505.885	+	1215.67i	−0.541633	+	1.30157i
$935$	243.511			0.260440
$936$	−358.445	−	32.6343i	−0.382954	−	0.0348657i
$937$		−	810.532i		−	0.865029i	−0.901627	−	0.432514i	$-0.857626\pi$
$937$		−	810.532i		−	0.865029i	0.901627	−	0.432514i	$-0.142374\pi$
$938$	304.986	−	732.899i	0.325145	−	0.781342i
$939$	396.086	−	1623.57i	0.421817	−	1.72904i
$940$	69.7789	+	0.228929i	0.0742329	+	0.000243542i
$941$	818.799	−	219.396i	0.870137	−	0.233152i	0.203990	−	0.978973i	$-0.434609\pi$
$941$	818.799	−	219.396i	0.870137	−	0.233152i	0.666147	+	0.745821i	$0.267942\pi$
$942$	63.5512	−	575.266i	0.0674641	−	0.610686i
$943$	−58.6573	−	101.597i	−0.0622029	−	0.107739i
$944$	−693.802	+	181.033i	−0.734960	+	0.191772i
$945$	−6.81035	−	100.680i	−0.00720672	−	0.106540i
$946$	−651.773	−	86.8954i	−0.688978	−	0.0918556i
$947$	40.3411	−	150.555i	0.0425988	−	0.158981i	−0.941350	−	0.337432i	$-0.890442\pi$
$947$	40.3411	−	150.555i	0.0425988	−	0.158981i	0.983949	+	0.178451i	$0.0571085\pi$
$948$	−613.033	+	369.833i	−0.646659	+	0.390120i
$949$	−186.612	+	50.0025i	−0.196641	+	0.0526897i
$950$	−125.366	+	16.2956i	−0.131965	+	0.0171533i
$951$	−407.920	−	671.177i	−0.428938	−	0.705759i
$952$	−218.367	−	1724.19i	−0.229377	−	1.81112i
$953$	−488.369			−0.512455			−0.256227	−	0.966617i	$-0.582480\pi$
$953$	−488.369			−0.512455			−0.256227	+	0.966617i	$0.582480\pi$
$954$	499.397	−	1371.03i	0.523477	−	1.43714i
$955$	−63.7020	−	63.7020i	−0.0667037	−	0.0667037i
$956$	−1044.75	+	276.268i	−1.09283	+	0.288984i
$957$	−899.166	−	3076.92i	−0.939567	−	3.21517i
$958$	499.159	+	384.321i	0.521043	+	0.401170i
$959$	−318.879	−	184.105i	−0.332512	−	0.191976i
$960$	23.2749	+	82.6589i	0.0242447	+	0.0861031i
$961$	71.7020	+	124.192i	0.0746119	+	0.129232i
$962$	316.608	+	42.2107i	0.329114	+	0.0438781i
$963$	331.114	+	302.563i	0.343836	+	0.314187i
$964$	−1026.58	−	278.684i	−1.06492	−	0.289091i
$965$	33.7071	+	9.03180i	0.0349297	+	0.00935938i
$966$	−65.2111	+	167.223i	−0.0675063	+	0.173109i
$967$	−1242.23	−	717.199i	−1.28462	−	0.741674i	−0.306929	−	0.951732i	$-0.599301\pi$
$967$	−1242.23	−	717.199i	−1.28462	−	0.741674i	−0.977689	+	0.210058i	$0.932635\pi$
$968$	1536.73	+	2023.25i	1.58753	+	2.09013i
$969$	198.740	−	4.47508i	0.205098	−	0.00461824i
$970$	27.0559	+	11.2590i	0.0278927	+	0.0116072i
$971$	889.980	−	889.980i	0.916560	−	0.916560i	−0.0802175	−	0.996777i	$-0.525561\pi$
$971$	889.980	−	889.980i	0.916560	−	0.916560i	0.996777	+	0.0802175i	$0.0255615\pi$
$972$	106.015	+	966.201i	0.109069	+	0.994034i
$973$	1266.17	−	1266.17i	1.30130	−	1.30130i
$974$	−875.207	+	360.842i	−0.898569	+	0.370474i
$975$	371.830	−	8.37260i	0.381364	−	0.00858729i
$976$	311.210	−	1131.70i	0.318863	−	1.15953i
$977$	−608.234	−	351.164i	−0.622553	−	0.359431i	0.155309	−	0.987866i	$-0.450363\pi$
$977$	−608.234	−	351.164i	−0.622553	−	0.359431i	−0.777862	+	0.628435i	$0.783696\pi$
$978$	657.058	−	288.373i	0.671838	−	0.294860i
$979$	−1605.16	−	430.100i	−1.63959	−	0.439326i
$980$	32.3309	−	18.5251i	0.0329907	−	0.0189032i
$981$	−762.070	−	696.357i	−0.776830	−	0.709844i
$982$	−303.417	+	232.030i	−0.308978	+	0.236283i
$983$	902.729	+	1563.57i	0.918341	+	1.59061i	0.801935	+	0.597411i	$0.203804\pi$
$983$	902.729	+	1563.57i	0.918341	+	1.59061i	0.116406	+	0.993202i	$0.462863\pi$
$984$	88.9248	−	781.449i	0.0903707	−	0.794155i
$985$	−20.5728	−	11.8777i	−0.0208861	−	0.0120586i
$986$	341.962	+	2630.80i	0.346818	+	2.66816i
$987$	274.268	+	938.537i	0.277881	+	0.950899i
$988$	49.2724	−	13.0294i	0.0498709	−	0.0131877i
$989$	−39.7392	−	39.7392i	−0.0401812	−	0.0401812i
$990$	−71.2156	−	152.821i	−0.0719349	−	0.154364i
$991$	94.2676			0.0951238			0.0475619	−	0.998868i	$-0.484855\pi$
$991$	94.2676			0.0951238			0.0475619	+	0.998868i	$0.484855\pi$
$992$	126.867	−	906.158i	0.127891	−	0.913466i
$993$	423.140	+	696.219i	0.426123	+	0.701127i
$994$	350.653	+	269.980i	0.352769	+	0.271610i
$995$	−13.6545	+	3.65870i	−0.0137231	+	0.00367709i
$996$	563.389	+	139.404i	0.565651	+	0.139964i
$997$	319.525	−	1192.49i	0.320487	−	1.19607i	−0.598285	−	0.801284i	$-0.704151\pi$
$997$	319.525	−	1192.49i	0.320487	−	1.19607i	0.918772	−	0.394790i	$-0.129183\pi$
$998$	386.796	−	295.792i	0.387571	−	0.296385i
$999$	−58.2147	−	860.612i	−0.0582730	−	0.861474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.5.18	✓	184
3.2	odd	2		432.3.x.a.341.29		184
9.2	odd	6	inner	144.3.w.a.101.33	yes	184
9.7	even	3		432.3.x.a.197.14		184
16.13	even	4	inner	144.3.w.a.77.33	yes	184
48.29	odd	4		432.3.x.a.125.14		184
144.29	odd	12	inner	144.3.w.a.29.18	yes	184
144.61	even	12		432.3.x.a.413.29		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.18	✓	184	1.1	even	1	trivial
144.3.w.a.29.18	yes	184	144.29	odd	12	inner
144.3.w.a.77.33	yes	184	16.13	even	4	inner
144.3.w.a.101.33	yes	184	9.2	odd	6	inner
432.3.x.a.125.14		184	48.29	odd	4
432.3.x.a.197.14		184	9.7	even	3
432.3.x.a.341.29		184	3.2	odd	2
432.3.x.a.413.29		184	144.61	even	12

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.762335 - 1.84901i) q^{2} +(-2.07303 + 2.16854i) q^{3} +(-2.83769 + 2.81913i) q^{4} +(-0.115759 - 0.432017i) q^{5} +(5.58999 + 2.17990i) q^{6} +(7.23679 - 4.17816i) q^{7} +(7.37588 + 3.09780i) q^{8} +(-0.405106 - 8.99088i) q^{9} +O(q^{10})\)	\(q+(-0.762335 - 1.84901i) q^{2} +(-2.07303 + 2.16854i) q^{3} +(-2.83769 + 2.81913i) q^{4} +(-0.115759 - 0.432017i) q^{5} +(5.58999 + 2.17990i) q^{6} +(7.23679 - 4.17816i) q^{7} +(7.37588 + 3.09780i) q^{8} +(-0.405106 - 8.99088i) q^{9} +(-0.710557 + 0.543380i) q^{10} +(-20.2288 - 5.42030i) q^{11} +(-0.230778 - 11.9978i) q^{12} +(-1.29383 - 4.82865i) q^{13} +(-13.2423 - 10.1958i) q^{14} +(1.17682 + 0.644556i) q^{15} +(0.104984 - 15.9997i) q^{16} -25.9977i q^{17} +(-16.3154 + 7.60310i) q^{18} +(1.80229 - 1.80229i) q^{19} +(1.54640 + 0.899592i) q^{20} +(-5.94157 + 24.3547i) q^{21} +(5.39895 + 41.5354i) q^{22} +(-1.78994 + 3.10027i) q^{23} +(-22.0081 + 9.57304i) q^{24} +(21.4774 - 12.4000i) q^{25} +(-7.94191 + 6.07337i) q^{26} +(20.3368 + 17.7599i) q^{27} +(-8.75698 + 32.2578i) q^{28} +(13.2056 - 49.2839i) q^{29} +(0.294665 - 2.66731i) q^{30} +(-14.2968 + 24.7628i) q^{31} +(-29.6636 + 12.0030i) q^{32} +(53.6891 - 32.6305i) q^{33} +(-48.0700 + 19.8189i) q^{34} +(-2.64276 - 2.64276i) q^{35} +(26.4960 + 24.3713i) q^{36} +(-22.5902 - 22.5902i) q^{37} +(-4.70639 - 1.95850i) q^{38} +(13.1533 + 7.20421i) q^{39} +(0.484481 - 3.54510i) q^{40} +(-16.3853 + 28.3801i) q^{41} +(49.5616 - 7.58040i) q^{42} +(-4.06313 + 15.1638i) q^{43} +(72.6837 - 41.6466i) q^{44} +(-3.83732 + 1.21578i) q^{45} +(7.09697 + 0.946180i) q^{46} +(33.7785 - 19.5020i) q^{47} +(34.4782 + 33.3954i) q^{48} +(10.4141 - 18.0377i) q^{49} +(-39.3007 - 30.2590i) q^{50} +(56.3769 + 53.8939i) q^{51} +(17.2841 + 10.0547i) q^{52} +(-57.3208 + 57.3208i) q^{53} +(17.3347 - 51.1420i) q^{54} +9.36664i q^{55} +(66.3208 - 8.39948i) q^{56} +(0.172134 + 7.64451i) q^{57} +(-101.194 + 13.1536i) q^{58} +(-11.5988 - 43.2875i) q^{59} +(-5.15653 + 1.48855i) q^{60} +(70.8572 + 18.9861i) q^{61} +(56.6857 + 7.55743i) q^{62} +(-40.4970 - 63.3725i) q^{63} +(44.8072 + 45.6980i) q^{64} +(-1.93629 + 1.11792i) q^{65} +(-101.263 - 74.3964i) q^{66} +(12.2935 + 45.8800i) q^{67} +(73.2909 + 73.7734i) q^{68} +(-3.01245 - 10.3085i) q^{69} +(-2.87182 + 6.90115i) q^{70} -26.4797 q^{71} +(24.8640 - 67.5706i) q^{72} -38.6468i q^{73} +(-24.5483 + 58.9909i) q^{74} +(-17.6334 + 72.2800i) q^{75} +(-0.0334482 + 10.1952i) q^{76} +(-169.039 + 45.2938i) q^{77} +(3.29348 - 29.8126i) q^{78} +(-29.8313 - 51.6693i) q^{79} +(-6.92427 + 1.80674i) q^{80} +(-80.6718 + 7.28451i) q^{81} +(64.9662 + 8.66140i) q^{82} +(-12.5178 + 46.7170i) q^{83} +(-51.7988 - 85.8612i) q^{84} +(-11.2314 + 3.00945i) q^{85} +(31.1356 - 4.04713i) q^{86} +(79.4985 + 130.804i) q^{87} +(-132.414 - 102.644i) q^{88} +79.3499 q^{89} +(5.17332 + 6.16841i) q^{90} +(-29.5381 - 29.5381i) q^{91} +(-3.66077 - 13.8437i) q^{92} +(-24.0614 - 82.3372i) q^{93} +(-61.8100 - 47.5898i) q^{94} +(-0.987248 - 0.569988i) q^{95} +(35.4646 - 89.2091i) q^{96} +(-16.3804 - 28.3718i) q^{97} +(-41.2910 - 5.50499i) q^{98} +(-40.5384 + 184.071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Introduction

L-functions

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